Subgroups — C₂₃×#34497 #19182123

Order 5888.

2268 conjugacy classes of subgroups.

The subgroup lattice has 1516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#553	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2383	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2382	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2377	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2373	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2364	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2364	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2361	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2359	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2349	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2349	C₂	1	1	yes	maximal, characteristic, complemented
14	D₄×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2345	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2343	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2336	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2335	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2334	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2334	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2325	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2325	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2325	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#2322	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂₃×#2318	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂₃×#2318	C₂	1	1	yes	maximal, characteristic, complemented
27	C₂₃×#2318	C₂	1	1	yes	maximal, characteristic, complemented
28	C₂₃×#2314	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×C₂₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂₃×#2290	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×C₂₃×#387	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂₃×#553	C₄	1	16	yes	complemented
33	C₂×C₂₃×#126	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#126	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#123	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#123	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
52	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
54	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
55	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
56	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
57	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
58	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
59	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
60	C₂₃×#390	C₂²	1	1	yes	characteristic
61	C₂₃×#390	C₂²	1	1	yes	characteristic
62	C₂₃×#389	C₂²	1	1	yes	characteristic
63	C₂₃×#389	C₂²	1	1	yes	characteristic
64	C₂₃×#389	C₂²	1	1	yes	characteristic
65	C₂₃×#389	C₂²	1	1	yes	characteristic
66	C₂₃×#389	C₂²	1	1	yes	characteristic
67	C₂₃×#389	C₂²	1	1	yes	characteristic
68	C₂₃×#389	C₂²	1	1	yes	characteristic
69	C₂₃×#389	C₂²	1	1	yes	characteristic
70	C₂₃×#389	C₂²	1	1	yes	characteristic
71	C₂₃×#389	C₂²	1	1	yes	characteristic
72	C₂₃×#388	C₂²	1	1	yes	characteristic
73	C₂₃×#388	C₂²	1	1	yes	characteristic
74	C₂₃×#388	C₂²	1	1	yes	characteristic
75	C₂₃×#388	C₂²	1	1	yes	characteristic
76	C₂₃×#388	C₂²	1	1	yes	characteristic
77	C₂₃×#388	C₂²	1	1	yes	characteristic
78	C₂₃×#388	C₂²	1	1	yes	characteristic
79	C₂₃×#388	C₂²	1	1	yes	characteristic
80	C₂₃×#388	C₂²	1	1	yes	characteristic
81	C₂₃×#388	C₂²	1	1	yes	characteristic
82	C₂₃×#388	C₂²	1	1	yes	characteristic
83	C₂₃×#388	C₂²	1	1	yes	characteristic
84	C₂₃×#388	C₂²	1	1	yes	characteristic
85	C₂₃×#388	C₂²	1	1	yes	characteristic
86	C₂₃×#388	C₂²	1	1	yes	characteristic
87	C₂₃×#388	C₂²	1	1	yes	characteristic
88	C₂₃×#388	C₂²	1	1	yes	characteristic
89	C₂₃×#388	C₂²	1	1	yes	characteristic
90	C₂₃×#387	C₂²	1	1	yes	characteristic
91	C₂₃×#387	C₂²	1	1	yes	characteristic
92	C₂₃×#387	C₂²	1	1	yes	characteristic
93	C₂₃×#387	C₂²	1	1	yes	characteristic
94	C₂₃×#387	C₂²	1	1	yes	characteristic
95	C₂₃×#387	C₂²	1	1	yes	characteristic
96	C₂₃×#387	C₂²	1	1	yes	characteristic
97	C₂₃×#387	C₂²	1	1	yes	characteristic
98	C₂₃×#387	C₂²	1	1	yes	characteristic
99	C₂₃×#387	C₂²	1	1	yes	characteristic
100	C₂₃×#387	C₂²	1	1	yes	characteristic
101	C₂₃×#387	C₂²	1	1	yes	characteristic
102	C₂₃×#387	C₂²	1	1	yes	characteristic
103	C₂₃×#387	C₂²	1	1	yes	characteristic
104	C₂₃×#387	C₂²	1	1	yes	characteristic
105	C₂₃×#387	C₂²	1	1	yes	characteristic
106	C₂₃×#387	C₂²	1	1	yes	characteristic
107	C₂₃×#387	C₂²	1	1	yes	characteristic
108	C₂₃×#387	C₂²	1	1	yes	characteristic
109	C₂₃×#387	C₂²	1	1	yes	characteristic
110	C₂₃×#387	C₂²	1	1	yes	characteristic
111	C₂₃×#387	C₂²	1	1	yes	characteristic
112	C₂₃×#387	C₂²	1	1	yes	characteristic
113	C₂₃×#387	C₂²	1	1	yes	characteristic
114	C₂₃×#387	C₂²	1	1	yes	characteristic
115	C₂₃×#387	C₂²	1	1	yes	characteristic
116	C₂₃×#386	C₂²	1	1	yes	characteristic
117	C₂₃×#386	C₂²	1	1	yes	characteristic
118	C₂₃×#386	C₂²	1	1	yes	characteristic
119	C₂₃×#386	C₂²	1	1	yes	characteristic
120	C₂₃×#386	C₂²	1	1	yes	characteristic
121	C₂₃×#386	C₂²	1	1	yes	characteristic
122	C₂₃×#386	C₂²	1	1	yes	characteristic
123	C₂₃×#386	C₂²	1	1	yes	characteristic
124	C₂₃×#386	C₂²	1	1	yes	characteristic
125	C₂₃×#386	C₂²	1	1	yes	characteristic
126	C₂₃×#386	C₂²	1	1	yes	characteristic
127	C₂₃×#386	C₂²	1	1	yes	characteristic
128	C₂₃×#386	C₂²	1	1	yes	characteristic
129	C₂₃×#386	C₂²	1	1	yes	characteristic
130	C₂₃×#385	C₂²	1	1	yes	characteristic
131	C₂₃×#385	C₂²	1	1	yes	characteristic
132	C₂₃×#385	C₂²	1	1	yes	characteristic
133	C₂₃×#385	C₂²	1	1	yes	characteristic
134	C₂₃×#385	C₂²	1	1	yes	characteristic
135	C₂₃×#385	C₂²	1	1	yes	characteristic
136	C₂₃×#385	C₂²	1	1	yes	characteristic
137	C₂₃×#385	C₂²	1	1	yes	characteristic
138	C₂₃×#385	C₂²	1	1	yes	characteristic
139	C₂₃×#385	C₂²	1	1	yes	characteristic
140	C₂₃×#385	C₂²	1	1	yes	characteristic
141	C₂₃×#385	C₂²	1	1	yes	characteristic
142	C₂₃×#385	C₂²	1	1	yes	characteristic
143	C₂₃×#385	C₂²	1	1	yes	characteristic
144	C₂₃×#385	C₂²	1	1	yes	characteristic
145	C₂₃×#385	C₂²	1	1	yes	characteristic
146	C₂₃×#384	C₂²	1	1	yes	characteristic
147	C₂₃×#383	C₂²	1	1	yes	characteristic
148	C₂₃×#383	C₂²	1	1	yes	characteristic
149	C₂₃×#382	C₂²	1	1	yes	characteristic
150	C₂₃×#382	C₂²	1	1	yes	characteristic
151	C₂₃×#382	C₂²	1	1	yes	characteristic
152	C₂₃×#382	C₂²	1	1	yes	characteristic
153	C₂₃×#381	C₂²	1	1	yes	characteristic
154	C₂₃×#381	C₂²	1	1	yes	characteristic
155	C₂₃×#380	C₂²	1	1	yes	characteristic
156	C₂₃×#380	C₂²	1	1	yes	characteristic
157	C₂₃×#380	C₂²	1	1	yes	characteristic
158	C₂₃×#380	C₂²	1	1	yes	characteristic
159	C₂₃×#380	C₂²	1	1	yes	characteristic
160	C₂₃×#380	C₂²	1	1	yes	characteristic
161	C₂₃×#380	C₂²	1	1	yes	characteristic
162	C₂₃×#380	C₂²	1	1	yes	characteristic
163	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
164	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
165	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
166	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
167	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
168	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
169	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
170	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
171	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
172	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
173	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
174	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
175	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
176	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
177	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
178	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
179	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
180	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
181	C₂₃×#376	C₂²	1	1	yes	characteristic
182	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
183	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
184	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
185	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
186	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
187	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
188	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
189	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
190	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
191	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
192	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
193	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
194	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
195	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
196	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
197	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
198	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
199	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
200	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
201	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
202	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
203	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
204	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
205	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
206	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
207	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
208	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
209	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
210	C₂₃×#126	C₂×C₄	1	8	yes	complemented
211	C₂₃×#126	C₂×C₄	1	8	yes	complemented
212	C₂₃×#125	C₂×C₄	1	8	yes	complemented
213	C₂₃×#123	C₂×C₄	1	8	yes	complemented
214	C₂₃×#123	C₂×C₄	1	8	yes	complemented
215	C₂₃×#121	C₂×C₄	1	8	yes	complemented
216	C₂₃×#121	C₂×C₄	1	8	yes	complemented
217	C₂₃×#121	C₂×C₄	1	8	yes	complemented
218	C₂₃×#121	C₂×C₄	1	8	yes	complemented
219	C₄×D₄×C₂₃	—	4	2	no	—
220	C₄×D₄×C₂₃	—	4	2	no	—
221	C₄×D₄×C₂₃	—	4	2	no	—
222	C₄×D₄×C₂₃	—	4	2	no	—
223	C₄×D₄×C₂₃	—	4	2	no	—
224	C₄×D₄×C₂₃	—	4	2	no	—
225	C₄×D₄×C₂₃	—	4	2	no	—
226	C₄×D₄×C₂₃	—	4	2	no	—
227	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	complemented
228	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	complemented
229	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	complemented
230	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	complemented
231	C₂₃×#117	—	4	2	no	—
232	C₂₃×#117	C₂×C₄	1	8	yes	complemented
233	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
234	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
235	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	8	yes	complemented
236	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
288	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
289	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
290	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
291	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
292	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
294	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
296	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
297	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
298	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
299	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
300	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
301	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₂₃	—	4	2	no	—
303	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
304	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
305	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
306	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
307	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
308	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
309	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
310	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
311	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
312	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
313	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
314	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
315	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
316	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
317	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
318	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
319	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
320	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
321	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
322	C₂₃×#95	C₂³	1	1	yes	characteristic
323	C₂₃×#95	C₂³	1	1	yes	characteristic
324	C₂₃×#95	C₂³	1	1	yes	characteristic
325	C₂₃×#95	C₂³	1	1	yes	characteristic
326	C₂₃×#95	C₂³	1	1	yes	characteristic
327	C₂₃×#95	C₂³	1	1	yes	characteristic
328	C₂₃×#95	C₂³	1	1	yes	characteristic
329	C₂₃×#95	C₂³	1	1	yes	characteristic
330	C₂₃×#95	C₂³	1	1	yes	characteristic
331	C₂₃×#95	C₂³	1	1	yes	characteristic
332	C₂₃×#95	C₂³	1	1	yes	characteristic
333	C₂₃×#95	C₂³	1	1	yes	characteristic
334	C₂₃×#95	C₂³	1	1	yes	characteristic
335	C₂₃×#95	C₂³	1	1	yes	characteristic
336	C₂₃×#95	C₂³	1	1	yes	characteristic
337	C₂₃×#95	C₂³	1	1	yes	characteristic
338	C₂₃×#95	C₂³	1	1	yes	characteristic
339	C₂₃×#95	C₂³	1	1	yes	characteristic
340	C₂₃×#95	C₂³	1	1	yes	characteristic
341	C₂₃×#95	C₂³	1	1	yes	characteristic
342	C₂₃×#95	C₂³	1	1	yes	characteristic
343	C₂₃×#95	C₂³	1	1	yes	characteristic
344	C₂₃×#95	C₂³	1	1	yes	characteristic
345	C₂₃×#95	C₂³	1	1	yes	characteristic
346	C₂₃×#95	C₂³	1	1	yes	characteristic
347	C₂₃×#95	C₂³	1	1	yes	characteristic
348	C₂₃×#95	C₂³	1	1	yes	characteristic
349	C₂₃×#95	C₂³	1	1	yes	characteristic
350	C₂₃×#95	C₂³	1	1	yes	characteristic
351	C₂₃×#95	C₂³	1	1	yes	characteristic
352	C₂₃×#95	C₂³	1	1	yes	characteristic
353	C₂₃×#95	C₂³	1	1	yes	characteristic
354	C₂₃×#95	C₂³	1	1	yes	characteristic
355	C₂₃×#95	C₂³	1	1	yes	characteristic
356	C₂₃×#95	C₂³	1	1	yes	characteristic
357	C₂₃×#95	C₂³	1	1	yes	characteristic
358	C₂₃×#95	C₂³	1	1	yes	characteristic
359	C₂₃×#95	C₂³	1	1	yes	characteristic
360	C₂₃×#95	C₂³	1	1	yes	characteristic
361	C₂₃×#95	C₂³	1	1	yes	characteristic
362	C₂₃×#95	C₂³	1	1	yes	characteristic
363	C₂₃×#95	C₂³	1	1	yes	characteristic
364	C₂₃×#95	C₂³	1	1	yes	characteristic
365	C₂₃×#95	C₂³	1	1	yes	characteristic
366	C₂₃×#95	C₂³	1	1	yes	characteristic
367	C₂₃×#95	C₂³	1	1	yes	characteristic
368	C₂₃×#95	C₂³	1	1	yes	characteristic
369	C₂₃×#95	C₂³	1	1	yes	characteristic
370	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
371	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
372	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
373	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
374	C₂×D₄×C₂₃	—	2	2	no	—
375	C₂×D₄×C₂₃	—	2	2	no	—
376	C₂×D₄×C₂₃	—	2	2	no	—
377	C₂×D₄×C₂₃	—	2	2	no	—
378	C₂×D₄×C₂₃	—	2	2	no	—
379	C₂×D₄×C₂₃	—	2	2	no	—
380	C₂×D₄×C₂₃	—	4	1	no	—
381	C₂×D₄×C₂₃	—	4	1	no	—
382	C₂×D₄×C₂₃	—	4	1	no	—
383	C₂×D₄×C₂₃	—	4	1	no	—
384	C₂×D₄×C₂₃	—	4	1	no	—
385	C₂×D₄×C₂₃	—	4	1	no	—
386	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
387	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
388	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
389	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
390	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
391	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
392	C₂²×C₄×C₂₃	—	2	2	no	—
393	C₂²×C₄×C₂₃	—	2	2	no	—
394	C₂²×C₄×C₂₃	—	2	2	no	—
395	C₂²×C₄×C₂₃	—	2	2	no	—
396	C₂²×C₄×C₂₃	—	2	2	no	—
397	C₂²×C₄×C₂₃	—	2	2	no	—
398	C₂²×C₄×C₂₃	—	2	2	no	—
399	C₂²×C₄×C₂₃	—	4	1	no	—
400	C₂²×C₄×C₂₃	—	4	1	no	—
401	C₂²×C₄×C₂₃	—	4	1	no	—
402	C₂²×C₄×C₂₃	—	4	1	no	—
403	C₂²×C₄×C₂₃	—	4	1	no	—
404	C₂²×C₄×C₂₃	—	4	1	no	—
405	C₂²×C₄×C₂₃	—	4	1	no	—
406	C₂²×C₄×C₂₃	—	4	1	no	—
407	C₂²×C₄×C₂₃	—	4	1	no	—
408	C₂²×C₄×C₂₃	—	4	1	no	—
409	C₂²×C₄×C₂₃	—	4	1	no	—
410	C₂²×C₄×C₂₃	—	4	1	no	—
411	C₂²×C₄×C₂₃	—	4	1	no	—
412	C₂²×C₄×C₂₃	—	4	1	no	—
413	C₂²×C₄×C₂₃	—	4	1	no	—
414	C₂²×C₄×C₂₃	—	4	1	no	—
415	C₂²×C₄×C₂₃	—	4	1	no	—
416	C₂²×C₄×C₂₃	—	4	1	no	—
417	C₂²×C₄×C₂₃	—	4	1	no	—
418	C₂²×C₄×C₂₃	—	4	1	no	—
419	C₂²×C₄×C₂₃	—	4	1	no	—
420	C₂²×C₄×C₂₃	—	4	1	no	—
421	C₂²×C₄×C₂₃	—	4	1	no	—
422	C₂²×C₄×C₂₃	—	4	1	no	—
423	C₂²×C₄×C₂₃	—	4	1	no	—
424	C₂²×C₄×C₂₃	—	4	1	no	—
425	C₂²×C₄×C₂₃	—	4	1	no	—
426	C₂²×C₄×C₂₃	—	4	1	no	—
427	C₂²×C₄×C₂₃	—	4	1	no	—
428	C₂²×C₄×C₂₃	—	4	1	no	—
429	C₂²×C₄×C₂₃	—	4	1	no	—
430	C₂²×C₄×C₂₃	—	4	1	no	—
431	C₂²×C₄×C₂₃	—	4	1	no	—
432	C₂²×C₄×C₂₃	—	4	1	no	—
433	C₂²×C₄×C₂₃	—	4	1	no	—
434	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
435	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
436	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
437	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
438	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
439	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
440	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
441	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
442	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
443	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
444	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
445	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
446	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
447	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
448	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
449	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
450	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
451	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
452	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
453	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
454	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
455	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
456	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
457	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
458	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
459	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
460	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
461	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
462	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
463	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
464	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
465	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
466	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
467	C₄⋊C₄×C₂₃	—	2	2	no	—
468	C₄⋊C₄×C₂₃	—	2	2	no	—
469	C₄⋊C₄×C₂₃	—	2	2	no	—
470	C₄⋊C₄×C₂₃	—	4	1	no	—
471	C₄⋊C₄×C₂₃	—	4	1	no	—
472	C₄⋊C₄×C₂₃	—	4	1	no	—
473	C₄⋊C₄×C₂₃	—	4	1	no	—
474	C₄⋊C₄×C₂₃	—	4	1	no	—
475	C₄⋊C₄×C₂₃	—	4	1	no	—
476	C₄⋊C₄×C₂₃	—	4	1	no	—
477	C₄⋊C₄×C₂₃	—	4	1	no	—
478	C₄⋊C₄×C₂₃	—	4	1	no	—
479	C₄⋊C₄×C₂₃	—	4	1	no	—
480	C₄⋊C₄×C₂₃	—	4	1	no	—
481	C₄⋊C₄×C₂₃	—	4	1	no	—
482	C₄⋊C₄×C₂₃	—	4	1	no	—
483	C₄⋊C₄×C₂₃	—	4	1	no	—
484	C₄⋊C₄×C₂₃	—	4	1	no	—
485	C₄⋊C₄×C₂₃	—	4	1	no	—
486	C₄⋊C₄×C₂₃	—	4	1	no	—
487	C₄⋊C₄×C₂₃	—	4	1	no	—
488	C₄⋊C₄×C₂₃	—	4	1	no	—
489	C₄⋊C₄×C₂₃	—	4	1	no	—
490	C₄⋊C₄×C₂₃	—	4	1	no	—
491	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
492	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
493	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
494	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
495	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
496	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
497	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
498	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
499	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
500	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
501	C₂²⋊C₄×C₂₃	—	2	2	no	—
502	C₂²⋊C₄×C₂₃	—	2	2	no	—
503	C₂²⋊C₄×C₂₃	—	2	2	no	—
504	C₂²⋊C₄×C₂₃	—	2	2	no	—
505	C₂²⋊C₄×C₂₃	—	2	2	no	—
506	C₂²⋊C₄×C₂₃	—	4	1	no	—
507	C₂²⋊C₄×C₂₃	—	4	1	no	—
508	C₂²⋊C₄×C₂₃	—	4	1	no	—
509	C₂²⋊C₄×C₂₃	—	4	1	no	—
510	C₂²⋊C₄×C₂₃	—	4	1	no	—
511	C₂²⋊C₄×C₂₃	—	4	1	no	—
512	C₂²⋊C₄×C₂₃	—	4	1	no	—
513	C₂²⋊C₄×C₂₃	—	4	1	no	—
514	C₂²⋊C₄×C₂₃	—	4	1	no	—
515	C₂²⋊C₄×C₂₃	—	4	1	no	—
516	C₂²⋊C₄×C₂₃	—	4	1	no	—
517	C₂²⋊C₄×C₂₃	—	4	1	no	—
518	C₂²⋊C₄×C₂₃	—	4	1	no	—
519	C₂²⋊C₄×C₂₃	—	4	1	no	—
520	C₂²⋊C₄×C₂₃	—	4	1	no	—
521	C₂²⋊C₄×C₂₃	—	4	1	no	—
522	C₂²⋊C₄×C₂₃	—	4	1	no	—
523	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
524	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
525	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
526	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
527	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
528	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
529	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
530	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
531	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
532	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
533	C₄²×C₂₃	—	2	2	no	—
534	C₄²×C₂₃	—	2	2	no	—
535	C₄²×C₂₃	—	4	1	no	—
536	C₄²×C₂₃	—	4	1	no	—
537	C₄²×C₂₃	—	4	1	no	—
538	C₄²×C₂₃	—	4	1	no	—
539	C₄²×C₂₃	—	4	1	no	—
540	C₄²×C₂₃	—	4	1	no	—
541	C₄²×C₂₃	—	4	1	no	—
542	C₄²×C₂₃	—	4	1	no	—
543	C₄²×C₂₃	—	4	1	no	—
544	C₄²×C₂₃	—	4	1	no	—
545	C₄²×C₂₃	—	4	1	no	—
546	C₄²×C₂₃	—	4	1	no	—
547	C₄²×C₂₃	—	4	1	no	—
548	C₄²×C₂₃	—	4	1	no	—
549	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
550	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
551	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
552	#34497	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
553	C₂³×C₂₃	—	2	1	no	—
554	C₂³×C₂₃	—	2	1	no	—
555	C₂³×C₂₃	—	2	1	no	—
556	C₂³×C₂₃	—	2	1	no	—
557	C₂³×C₂₃	—	2	1	no	—
558	C₂³×C₂₃	—	2	1	no	—
559	C₂³×C₂₃	—	2	1	no	—
560	C₂³×C₂₃	—	2	1	no	—
561	C₂³×C₂₃	—	2	1	no	—
562	C₂³×C₂₃	—	2	1	no	—
563	C₂³×C₂₃	—	2	1	no	—
564	C₂³×C₂₃	—	2	1	no	—
565	C₂³×C₂₃	—	2	1	no	—
566	C₂³×C₂₃	—	2	1	no	—
567	C₂³×C₂₃	—	2	1	no	—
568	C₂³×C₂₃	—	2	1	no	—
569	C₂³×C₂₃	—	2	1	no	—
570	C₂³×C₂₃	—	2	1	no	—
571	C₂³×C₂₃	—	2	1	no	—
572	C₂³×C₂₃	—	2	1	no	—
573	C₂³×C₂₃	—	2	1	no	—
574	C₂³×C₂₃	—	2	1	no	—
575	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
576	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
577	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
578	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
579	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
580	C₂³×C₂₃	2₋¹⁺⁴	1	2	yes	—
581	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
582	D₄×C₂₃	—	2	8	no	—
583	D₄×C₂₃	—	2	8	no	—
584	D₄×C₂₃	—	2	8	no	—
585	D₄×C₂₃	—	4	4	no	—
586	D₄×C₂₃	—	4	4	no	—
587	D₄×C₂₃	—	4	4	no	—
588	C₂×C₄×C₂₃	—	2	1	no	—
589	C₂×C₄×C₂₃	—	2	1	no	—
590	C₂×C₄×C₂₃	—	2	1	no	—
591	C₂×C₄×C₂₃	—	2	1	no	—
592	C₂×C₄×C₂₃	—	2	1	no	—
593	C₂×C₄×C₂₃	—	2	1	no	—
594	C₂×C₄×C₂₃	—	2	1	no	—
595	C₂×C₄×C₂₃	—	2	1	no	—
596	C₂×C₄×C₂₃	—	2	1	no	—
597	C₂×C₄×C₂₃	—	2	1	no	—
598	C₂×C₄×C₂₃	—	2	1	no	—
599	C₂×C₄×C₂₃	—	2	1	no	—
600	C₂×C₄×C₂₃	—	2	1	no	—
601	C₂×C₄×C₂₃	—	2	1	no	—
602	C₂×C₄×C₂₃	—	2	1	no	—
603	C₂×C₄×C₂₃	—	2	1	no	—
604	C₂×C₄×C₂₃	—	2	1	no	—
605	C₂×C₄×C₂₃	—	2	1	no	—
606	C₂×C₄×C₂₃	—	2	1	no	—
607	C₂×C₄×C₂₃	—	2	1	no	—
608	C₂×C₄×C₂₃	—	2	1	no	—
609	C₂×C₄×C₂₃	—	2	1	no	—
610	C₂×C₄×C₂₃	—	2	1	no	—
611	C₂×C₄×C₂₃	—	2	1	no	—
612	C₂×C₄×C₂₃	—	2	1	no	—
613	C₂×C₄×C₂₃	—	2	1	no	—
614	C₂×C₄×C₂₃	—	2	1	no	—
615	C₂×C₄×C₂₃	—	2	1	no	—
616	C₂×C₄×C₂₃	—	2	1	no	—
617	C₂×C₄×C₂₃	—	2	1	no	—
618	C₂×C₄×C₂₃	—	2	1	no	—
619	C₂×C₄×C₂₃	—	2	1	no	—
620	C₂×C₄×C₂₃	—	2	1	no	—
621	C₂×C₄×C₂₃	—	2	1	no	—
622	C₂×C₄×C₂₃	—	2	1	no	—
623	C₂×C₄×C₂₃	—	2	1	no	—
624	C₂×C₄×C₂₃	—	2	1	no	—
625	C₂×C₄×C₂₃	—	2	1	no	—
626	C₂×C₄×C₂₃	—	2	1	no	—
627	C₂×C₄×C₂₃	—	2	1	no	—
628	C₂×C₄×C₂₃	—	2	1	no	—
629	C₂×C₄×C₂₃	—	2	1	no	—
630	C₂×C₄×C₂₃	—	2	1	no	—
631	C₂×C₄×C₂₃	—	2	1	no	—
632	C₂×C₄×C₂₃	—	2	1	no	—
633	C₂×C₄×C₂₃	—	2	1	no	—
634	C₂×C₄×C₂₃	—	2	1	no	—
635	C₂×C₄×C₂₃	—	2	1	no	—
636	C₂×C₄×C₂₃	—	2	1	no	—
637	C₂×C₄×C₂₃	—	2	1	no	—
638	C₂×C₄×C₂₃	—	2	1	no	—
639	C₂×C₄×C₂₃	—	2	1	no	—
640	C₂×C₄×C₂₃	—	2	1	no	—
641	C₂×C₄×C₂₃	—	2	1	no	—
642	C₂×C₄×C₂₃	—	2	1	no	—
643	C₂×C₄×C₂₃	—	2	1	no	—
644	C₂×C₄×C₂₃	—	2	1	no	—
645	C₂×C₄×C₂₃	—	2	1	no	—
646	C₂×C₄×C₂₃	—	2	1	no	—
647	C₂×C₄×C₂₃	—	2	1	no	—
648	C₂×C₄×C₂₃	—	2	1	no	—
649	C₂×C₄×C₂₃	—	2	1	no	—
650	C₂×C₄×C₂₃	—	2	1	no	—
651	C₂×C₄×C₂₃	—	2	1	no	—
652	C₂×C₄×C₂₃	—	2	1	no	—
653	C₂×C₄×C₂₃	—	2	1	no	—
654	C₂×C₄×C₂₃	—	2	1	no	—
655	C₂×C₄×C₂₃	—	2	1	no	—
656	C₂×C₄×C₂₃	—	2	1	no	—
657	C₂×C₄×C₂₃	—	4	4	no	—
658	C₂×C₄×C₂₃	—	4	4	no	—
659	C₂×C₄×C₂₃	—	4	4	no	—
660	C₂×C₄×C₂₃	—	4	4	no	—
661	C₂×C₄×C₂₃	—	4	4	no	—
662	C₂×C₄×C₂₃	—	4	4	no	—
663	C₂×C₄×C₂₃	—	4	4	no	—
664	C₂×C₄×C₂₃	—	4	4	no	—
665	C₂×C₄×C₂₃	—	8	2	no	—
666	C₂×C₄×C₂₃	—	8	2	no	—
667	C₂×C₄×C₂₃	—	8	2	no	—
668	C₂×C₄×C₂₃	—	8	2	no	—
669	C₂×C₄×C₂₃	—	8	2	no	—
670	C₂×C₄×C₂₃	—	8	2	no	—
671	C₂×C₄×C₂₃	—	8	2	no	—
672	C₂×C₄×C₂₃	—	8	2	no	—
673	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
674	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
675	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
676	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
677	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
678	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
679	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
680	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
681	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
682	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
683	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
684	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
685	C₂×#553	C₂×C₂₃	1	1	yes	characteristic
686	#2383	C₂×C₂₃	1	1	yes	characteristic, complemented
687	#2382	C₂×C₂₃	1	1	yes	characteristic, complemented
688	#2377	C₂×C₂₃	1	1	yes	characteristic, complemented
689	#2376	C₂×C₂₃	1	1	yes	characteristic, complemented
690	#2373	C₂×C₂₃	1	1	yes	characteristic, complemented
691	#2364	C₂×C₂₃	1	1	yes	characteristic, complemented
692	#2364	C₂×C₂₃	1	1	yes	characteristic, complemented
693	#2361	C₂×C₂₃	1	1	yes	characteristic, complemented
694	#2359	C₂×C₂₃	1	1	yes	characteristic, complemented
695	#2352	C₂×C₂₃	1	1	yes	characteristic, complemented
696	#2349	C₂×C₂₃	1	1	yes	characteristic, complemented
697	#2349	C₂×C₂₃	1	1	yes	characteristic, complemented
698	D₄×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
699	#2345	C₂×C₂₃	1	1	yes	characteristic, complemented
700	#2343	C₂×C₂₃	1	1	yes	characteristic, complemented
701	#2336	C₂×C₂₃	1	1	yes	characteristic, complemented
702	#2335	C₂×C₂₃	1	1	yes	characteristic, complemented
703	#2334	C₂×C₂₃	1	1	yes	characteristic, complemented
704	#2334	C₂×C₂₃	1	1	yes	characteristic, complemented
705	#2325	C₂×C₂₃	1	1	yes	characteristic, complemented
706	#2325	C₂×C₂₃	1	1	yes	characteristic, complemented
707	#2325	C₂×C₂₃	1	1	yes	characteristic, complemented
708	#2322	C₂×C₂₃	1	1	yes	characteristic, complemented
709	#2318	C₂×C₂₃	1	1	yes	characteristic, complemented
710	#2318	C₂×C₂₃	1	1	yes	characteristic, complemented
711	#2318	C₂×C₂₃	1	1	yes	characteristic, complemented
712	#2314	C₂×C₂₃	1	1	yes	characteristic, complemented
713	C₄×#121	C₂×C₂₃	1	1	yes	characteristic, complemented
714	#2290	C₂×C₂₃	1	1	yes	characteristic, complemented
715	C₂×#387	C₂×C₂₃	1	1	yes	characteristic, complemented
716	C₂²×C₂₃	—	2	2	no	—
717	C₂²×C₂₃	—	2	2	no	—
718	C₂²×C₂₃	—	2	2	no	—
719	C₂²×C₂₃	—	2	2	no	—
720	C₂²×C₂₃	—	2	2	no	—
721	C₂²×C₂₃	—	2	2	no	—
722	C₂²×C₂₃	—	2	2	no	—
723	C₂²×C₂₃	—	2	2	no	—
724	C₂²×C₂₃	—	2	2	no	—
725	C₂²×C₂₃	—	2	2	no	—
726	C₂²×C₂₃	—	2	2	no	—
727	C₂²×C₂₃	—	2	2	no	—
728	C₂²×C₂₃	—	2	2	no	—
729	C₂²×C₂₃	—	2	2	no	—
730	C₂²×C₂₃	—	2	2	no	—
731	C₂²×C₂₃	—	4	1	no	—
732	C₂²×C₂₃	—	4	1	no	—
733	C₂²×C₂₃	—	4	1	no	—
734	C₂²×C₂₃	—	4	1	no	—
735	C₂²×C₂₃	—	4	1	no	—
736	C₂²×C₂₃	—	4	1	no	—
737	C₂²×C₂₃	—	4	1	no	—
738	C₂²×C₂₃	—	4	1	no	—
739	C₂²×C₂₃	—	4	1	no	—
740	C₂²×C₂₃	—	4	1	no	—
741	C₂²×C₂₃	—	4	1	no	—
742	C₂²×C₂₃	—	4	1	no	—
743	C₂²×C₂₃	#520	1	4	yes	—
744	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
745	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
746	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
747	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
748	C₂²×C₂₃	#585	1	1	yes	characteristic
749	C₂²×C₂₃	#585	1	1	yes	characteristic
750	C₂²×C₂₃	#585	1	1	yes	characteristic
751	C₄×C₂₃	—	2	2	no	—
752	C₄×C₂₃	—	2	2	no	—
753	C₄×C₂₃	—	2	2	no	—
754	C₄×C₂₃	—	2	2	no	—
755	C₄×C₂₃	—	2	2	no	—
756	C₄×C₂₃	—	2	2	no	—
757	C₄×C₂₃	—	2	2	no	—
758	C₄×C₂₃	—	2	2	no	—
759	C₄×C₂₃	—	2	2	no	—
760	C₄×C₂₃	—	2	2	no	—
761	C₄×C₂₃	—	2	2	no	—
762	C₄×C₂₃	—	2	2	no	—
763	C₄×C₂₃	—	4	1	no	—
764	C₄×C₂₃	—	4	1	no	—
765	C₄×C₂₃	—	4	1	no	—
766	C₄×C₂₃	—	4	1	no	—
767	C₄×C₂₃	—	4	1	no	—
768	C₄×C₂₃	—	4	1	no	—
769	C₄×C₂₃	—	4	1	no	—
770	C₄×C₂₃	—	4	1	no	—
771	C₄×C₂₃	—	4	1	no	—
772	C₄×C₂₃	—	4	1	no	—
773	C₄×C₂₃	—	4	1	no	—
774	C₄×C₂₃	—	4	1	no	—
775	C₄×C₂₃	—	4	1	no	—
776	C₄×C₂₃	—	4	1	no	—
777	C₄×C₂₃	—	4	1	no	—
778	#553	C₄×C₂₃	1	16	yes	complemented
779	C₂×#126	C₂²×C₂₃	1	1	yes	characteristic
780	C₂×#126	C₂²×C₂₃	1	1	yes	characteristic
781	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
782	C₂×#123	C₂²×C₂₃	1	1	yes	characteristic
783	C₂×#123	C₂²×C₂₃	1	1	yes	characteristic
784	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
785	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
786	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
787	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
788	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
789	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
790	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
791	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
792	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
793	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
794	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
795	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
796	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
797	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
798	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
799	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
800	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
801	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
802	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
803	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
804	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
805	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
806	#390	C₂²×C₂₃	1	1	yes	characteristic
807	#390	C₂²×C₂₃	1	1	yes	characteristic
808	#389	C₂²×C₂₃	1	1	yes	characteristic
809	#389	C₂²×C₂₃	1	1	yes	characteristic
810	#389	C₂²×C₂₃	1	1	yes	characteristic
811	#389	C₂²×C₂₃	1	1	yes	characteristic
812	#389	C₂²×C₂₃	1	1	yes	characteristic
813	#389	C₂²×C₂₃	1	1	yes	characteristic
814	#389	C₂²×C₂₃	1	1	yes	characteristic
815	#389	C₂²×C₂₃	1	1	yes	characteristic
816	#389	C₂²×C₂₃	1	1	yes	characteristic
817	#389	C₂²×C₂₃	1	1	yes	characteristic
818	#388	C₂²×C₂₃	1	1	yes	characteristic
819	#388	C₂²×C₂₃	1	1	yes	characteristic
820	#388	C₂²×C₂₃	1	1	yes	characteristic
821	#388	C₂²×C₂₃	1	1	yes	characteristic
822	#388	C₂²×C₂₃	1	1	yes	characteristic
823	#388	C₂²×C₂₃	1	1	yes	characteristic
824	#388	C₂²×C₂₃	1	1	yes	characteristic
825	#388	C₂²×C₂₃	1	1	yes	characteristic
826	#388	C₂²×C₂₃	1	1	yes	characteristic
827	#388	C₂²×C₂₃	1	1	yes	characteristic
828	#388	C₂²×C₂₃	1	1	yes	characteristic
829	#388	C₂²×C₂₃	1	1	yes	characteristic
830	#388	C₂²×C₂₃	1	1	yes	characteristic
831	#388	C₂²×C₂₃	1	1	yes	characteristic
832	#388	C₂²×C₂₃	1	1	yes	characteristic
833	#388	C₂²×C₂₃	1	1	yes	characteristic
834	#388	C₂²×C₂₃	1	1	yes	characteristic
835	#388	C₂²×C₂₃	1	1	yes	characteristic
836	#387	C₂²×C₂₃	1	1	yes	characteristic
837	#387	C₂²×C₂₃	1	1	yes	characteristic
838	#387	C₂²×C₂₃	1	1	yes	characteristic
839	#387	C₂²×C₂₃	1	1	yes	characteristic
840	#387	C₂²×C₂₃	1	1	yes	characteristic
841	#387	C₂²×C₂₃	1	1	yes	characteristic
842	#387	C₂²×C₂₃	1	1	yes	characteristic
843	#387	C₂²×C₂₃	1	1	yes	characteristic
844	#387	C₂²×C₂₃	1	1	yes	characteristic
845	#387	C₂²×C₂₃	1	1	yes	characteristic
846	#387	C₂²×C₂₃	1	1	yes	characteristic
847	#387	C₂²×C₂₃	1	1	yes	characteristic
848	#387	C₂²×C₂₃	1	1	yes	characteristic
849	#387	C₂²×C₂₃	1	1	yes	characteristic
850	#387	C₂²×C₂₃	1	1	yes	characteristic
851	#387	C₂²×C₂₃	1	1	yes	characteristic
852	#387	C₂²×C₂₃	1	1	yes	characteristic
853	#387	C₂²×C₂₃	1	1	yes	characteristic
854	#387	C₂²×C₂₃	1	1	yes	characteristic
855	#387	C₂²×C₂₃	1	1	yes	characteristic
856	#387	C₂²×C₂₃	1	1	yes	characteristic
857	#387	C₂²×C₂₃	1	1	yes	characteristic
858	#387	C₂²×C₂₃	1	1	yes	characteristic
859	#387	C₂²×C₂₃	1	1	yes	characteristic
860	#387	C₂²×C₂₃	1	1	yes	characteristic
861	#387	C₂²×C₂₃	1	1	yes	characteristic
862	#386	C₂²×C₂₃	1	1	yes	characteristic
863	#386	C₂²×C₂₃	1	1	yes	characteristic
864	#386	C₂²×C₂₃	1	1	yes	characteristic
865	#386	C₂²×C₂₃	1	1	yes	characteristic
866	#386	C₂²×C₂₃	1	1	yes	characteristic
867	#386	C₂²×C₂₃	1	1	yes	characteristic
868	#386	C₂²×C₂₃	1	1	yes	characteristic
869	#386	C₂²×C₂₃	1	1	yes	characteristic
870	#386	C₂²×C₂₃	1	1	yes	characteristic
871	#386	C₂²×C₂₃	1	1	yes	characteristic
872	#386	C₂²×C₂₃	1	1	yes	characteristic
873	#386	C₂²×C₂₃	1	1	yes	characteristic
874	#386	C₂²×C₂₃	1	1	yes	characteristic
875	#386	C₂²×C₂₃	1	1	yes	characteristic
876	#385	C₂²×C₂₃	1	1	yes	characteristic
877	#385	C₂²×C₂₃	1	1	yes	characteristic
878	#385	C₂²×C₂₃	1	1	yes	characteristic
879	#385	C₂²×C₂₃	1	1	yes	characteristic
880	#385	C₂²×C₂₃	1	1	yes	characteristic
881	#385	C₂²×C₂₃	1	1	yes	characteristic
882	#385	C₂²×C₂₃	1	1	yes	characteristic
883	#385	C₂²×C₂₃	1	1	yes	characteristic
884	#385	C₂²×C₂₃	1	1	yes	characteristic
885	#385	C₂²×C₂₃	1	1	yes	characteristic
886	#385	C₂²×C₂₃	1	1	yes	characteristic
887	#385	C₂²×C₂₃	1	1	yes	characteristic
888	#385	C₂²×C₂₃	1	1	yes	characteristic
889	#385	C₂²×C₂₃	1	1	yes	characteristic
890	#385	C₂²×C₂₃	1	1	yes	characteristic
891	#385	C₂²×C₂₃	1	1	yes	characteristic
892	#384	C₂²×C₂₃	1	1	yes	characteristic
893	#383	C₂²×C₂₃	1	1	yes	characteristic
894	#383	C₂²×C₂₃	1	1	yes	characteristic
895	#382	C₂²×C₂₃	1	1	yes	characteristic
896	#382	C₂²×C₂₃	1	1	yes	characteristic
897	#382	C₂²×C₂₃	1	1	yes	characteristic
898	#382	C₂²×C₂₃	1	1	yes	characteristic
899	#381	C₂²×C₂₃	1	1	yes	characteristic
900	#381	C₂²×C₂₃	1	1	yes	characteristic
901	#380	C₂²×C₂₃	1	1	yes	characteristic
902	#380	C₂²×C₂₃	1	1	yes	characteristic
903	#380	C₂²×C₂₃	1	1	yes	characteristic
904	#380	C₂²×C₂₃	1	1	yes	characteristic
905	#380	C₂²×C₂₃	1	1	yes	characteristic
906	#380	C₂²×C₂₃	1	1	yes	characteristic
907	#380	C₂²×C₂₃	1	1	yes	characteristic
908	#380	C₂²×C₂₃	1	1	yes	characteristic
909	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
910	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
911	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
912	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
913	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
914	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
915	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
916	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
917	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
918	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
919	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
920	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
921	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
922	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
923	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
924	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
925	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
926	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
927	#376	C₂²×C₂₃	1	1	yes	characteristic
928	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
929	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
930	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
931	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
932	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
933	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
934	C₂×C₂₃	—	2	4	no	—
935	C₂×C₂₃	—	4	2	no	—
936	C₂×C₂₃	—	4	2	no	—
937	C₂×C₂₃	—	4	2	no	—
938	C₂×C₂₃	C₂×#520	1	1	yes	characteristic
939	C₂×C₂₃	#3428	1	1	yes	characteristic
940	C₂×C₂₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
941	C₂×C₂₃	#3534	1	1	yes	characteristic
942	C₂×C₂₃	#3541	1	1	yes	characteristic
943	C₂×C₂₃	#3553	1	1	yes	characteristic
944	C₂×C₂₃	#3560	1	1	yes	characteristic
945	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
946	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
947	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
948	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
949	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
950	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
951	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
952	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
953	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
954	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
955	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
956	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
957	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
958	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
959	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
960	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
961	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
962	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
963	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
964	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
965	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
966	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
967	#126	C₂×C₄×C₂₃	1	8	yes	complemented
968	#126	C₂×C₄×C₂₃	1	8	yes	complemented
969	#125	C₂×C₄×C₂₃	1	8	yes	complemented
970	#123	C₂×C₄×C₂₃	1	8	yes	complemented
971	#123	C₂×C₄×C₂₃	1	8	yes	complemented
972	#121	C₂×C₄×C₂₃	1	8	yes	complemented
973	#121	C₂×C₄×C₂₃	1	8	yes	complemented
974	#121	C₂×C₄×C₂₃	1	8	yes	complemented
975	#121	C₂×C₄×C₂₃	1	8	yes	complemented
976	C₄×D₄	—	4	2	no	—
977	C₄×D₄	—	4	2	no	—
978	C₄×D₄	—	4	2	no	—
979	C₄×D₄	—	4	2	no	—
980	C₄×D₄	—	4	2	no	—
981	C₄×D₄	—	4	2	no	—
982	C₄×D₄	—	4	2	no	—
983	C₄×D₄	—	4	2	no	—
984	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	complemented
985	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	complemented
986	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	complemented
987	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	complemented
988	#117	—	4	2	no	—
989	#117	C₂×C₄×C₂₃	1	8	yes	complemented
990	C₂×C₄⋊C₄	—	4	2	no	—
991	C₂×C₄⋊C₄	—	4	2	no	—
992	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	8	yes	complemented
993	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
994	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
995	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
996	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
997	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
998	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
999	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1000	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1001	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1002	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1003	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1004	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1005	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1006	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1007	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1008	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1009	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1010	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1011	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1012	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1013	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1014	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1015	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1016	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1017	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1018	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1019	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1020	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1021	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1022	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1023	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1024	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1025	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1026	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1027	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1028	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1029	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1030	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1031	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1032	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1033	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1034	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1035	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1036	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1037	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1038	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1039	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1040	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1041	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1042	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1043	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1044	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1045	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1046	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1047	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1048	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1049	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1050	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1051	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1052	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1053	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1054	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1055	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1056	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1057	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1058	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1059	C₂×C₄²	—	4	2	no	—
1060	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1061	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1062	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1063	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1064	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1065	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1066	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1067	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1068	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1069	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1070	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1071	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1072	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1073	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1074	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1075	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1076	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1077	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1078	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1079	#95	C₂³×C₂₃	1	1	yes	characteristic
1080	#95	C₂³×C₂₃	1	1	yes	characteristic
1081	#95	C₂³×C₂₃	1	1	yes	characteristic
1082	#95	C₂³×C₂₃	1	1	yes	characteristic
1083	#95	C₂³×C₂₃	1	1	yes	characteristic
1084	#95	C₂³×C₂₃	1	1	yes	characteristic
1085	#95	C₂³×C₂₃	1	1	yes	characteristic
1086	#95	C₂³×C₂₃	1	1	yes	characteristic
1087	#95	C₂³×C₂₃	1	1	yes	characteristic
1088	#95	C₂³×C₂₃	1	1	yes	characteristic
1089	#95	C₂³×C₂₃	1	1	yes	characteristic
1090	#95	C₂³×C₂₃	1	1	yes	characteristic
1091	#95	C₂³×C₂₃	1	1	yes	characteristic
1092	#95	C₂³×C₂₃	1	1	yes	characteristic
1093	#95	C₂³×C₂₃	1	1	yes	characteristic
1094	#95	C₂³×C₂₃	1	1	yes	characteristic
1095	#95	C₂³×C₂₃	1	1	yes	characteristic
1096	#95	C₂³×C₂₃	1	1	yes	characteristic
1097	#95	C₂³×C₂₃	1	1	yes	characteristic
1098	#95	C₂³×C₂₃	1	1	yes	characteristic
1099	#95	C₂³×C₂₃	1	1	yes	characteristic
1100	#95	C₂³×C₂₃	1	1	yes	characteristic
1101	#95	C₂³×C₂₃	1	1	yes	characteristic
1102	#95	C₂³×C₂₃	1	1	yes	characteristic
1103	#95	C₂³×C₂₃	1	1	yes	characteristic
1104	#95	C₂³×C₂₃	1	1	yes	characteristic
1105	#95	C₂³×C₂₃	1	1	yes	characteristic
1106	#95	C₂³×C₂₃	1	1	yes	characteristic
1107	#95	C₂³×C₂₃	1	1	yes	characteristic
1108	#95	C₂³×C₂₃	1	1	yes	characteristic
1109	#95	C₂³×C₂₃	1	1	yes	characteristic
1110	#95	C₂³×C₂₃	1	1	yes	characteristic
1111	#95	C₂³×C₂₃	1	1	yes	characteristic
1112	#95	C₂³×C₂₃	1	1	yes	characteristic
1113	#95	C₂³×C₂₃	1	1	yes	characteristic
1114	#95	C₂³×C₂₃	1	1	yes	characteristic
1115	#95	C₂³×C₂₃	1	1	yes	characteristic
1116	#95	C₂³×C₂₃	1	1	yes	characteristic
1117	#95	C₂³×C₂₃	1	1	yes	characteristic
1118	#95	C₂³×C₂₃	1	1	yes	characteristic
1119	#95	C₂³×C₂₃	1	1	yes	characteristic
1120	#95	C₂³×C₂₃	1	1	yes	characteristic
1121	#95	C₂³×C₂₃	1	1	yes	characteristic
1122	#95	C₂³×C₂₃	1	1	yes	characteristic
1123	#95	C₂³×C₂₃	1	1	yes	characteristic
1124	#95	C₂³×C₂₃	1	1	yes	characteristic
1125	#95	C₂³×C₂₃	1	1	yes	characteristic
1126	#95	C₂³×C₂₃	1	1	yes	characteristic
1127	C₂₃	#34497	1	1	yes	characteristic, direct product factor, Sylow
1128	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1129	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1130	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1131	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1132	C₂×D₄	—	2	2	no	—
1133	C₂×D₄	—	2	2	no	—
1134	C₂×D₄	—	2	2	no	—
1135	C₂×D₄	—	2	2	no	—
1136	C₂×D₄	—	2	2	no	—
1137	C₂×D₄	—	2	2	no	—
1138	C₂×D₄	—	4	1	no	—
1139	C₂×D₄	—	4	1	no	—
1140	C₂×D₄	—	4	1	no	—
1141	C₂×D₄	—	4	1	no	—
1142	C₂×D₄	—	4	1	no	—
1143	C₂×D₄	—	4	1	no	—
1144	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
1145	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
1146	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
1147	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
1148	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
1149	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
1150	C₂²×C₄	—	2	2	no	—
1151	C₂²×C₄	—	2	2	no	—
1152	C₂²×C₄	—	2	2	no	—
1153	C₂²×C₄	—	2	2	no	—
1154	C₂²×C₄	—	2	2	no	—
1155	C₂²×C₄	—	2	2	no	—
1156	C₂²×C₄	—	2	2	no	—
1157	C₂²×C₄	—	4	1	no	—
1158	C₂²×C₄	—	4	1	no	—
1159	C₂²×C₄	—	4	1	no	—
1160	C₂²×C₄	—	4	1	no	—
1161	C₂²×C₄	—	4	1	no	—
1162	C₂²×C₄	—	4	1	no	—
1163	C₂²×C₄	—	4	1	no	—
1164	C₂²×C₄	—	4	1	no	—
1165	C₂²×C₄	—	4	1	no	—
1166	C₂²×C₄	—	4	1	no	—
1167	C₂²×C₄	—	4	1	no	—
1168	C₂²×C₄	—	4	1	no	—
1169	C₂²×C₄	—	4	1	no	—
1170	C₂²×C₄	—	4	1	no	—
1171	C₂²×C₄	—	4	1	no	—
1172	C₂²×C₄	—	4	1	no	—
1173	C₂²×C₄	—	4	1	no	—
1174	C₂²×C₄	—	4	1	no	—
1175	C₂²×C₄	—	4	1	no	—
1176	C₂²×C₄	—	4	1	no	—
1177	C₂²×C₄	—	4	1	no	—
1178	C₂²×C₄	—	4	1	no	—
1179	C₂²×C₄	—	4	1	no	—
1180	C₂²×C₄	—	4	1	no	—
1181	C₂²×C₄	—	4	1	no	—
1182	C₂²×C₄	—	4	1	no	—
1183	C₂²×C₄	—	4	1	no	—
1184	C₂²×C₄	—	4	1	no	—
1185	C₂²×C₄	—	4	1	no	—
1186	C₂²×C₄	—	4	1	no	—
1187	C₂²×C₄	—	4	1	no	—
1188	C₂²×C₄	—	4	1	no	—
1189	C₂²×C₄	—	4	1	no	—
1190	C₂²×C₄	—	4	1	no	—
1191	C₂²×C₄	—	4	1	no	—
1192	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
1193	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
1194	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
1195	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
1196	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
1197	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
1198	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1199	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1200	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1201	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1202	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1203	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1204	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1205	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1206	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1207	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1208	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1209	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1210	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1211	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1212	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1213	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1214	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1215	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1216	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1217	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1218	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1219	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1220	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1221	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1222	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1223	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1224	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1225	C₄⋊C₄	—	2	2	no	—
1226	C₄⋊C₄	—	2	2	no	—
1227	C₄⋊C₄	—	2	2	no	—
1228	C₄⋊C₄	—	4	1	no	—
1229	C₄⋊C₄	—	4	1	no	—
1230	C₄⋊C₄	—	4	1	no	—
1231	C₄⋊C₄	—	4	1	no	—
1232	C₄⋊C₄	—	4	1	no	—
1233	C₄⋊C₄	—	4	1	no	—
1234	C₄⋊C₄	—	4	1	no	—
1235	C₄⋊C₄	—	4	1	no	—
1236	C₄⋊C₄	—	4	1	no	—
1237	C₄⋊C₄	—	4	1	no	—
1238	C₄⋊C₄	—	4	1	no	—
1239	C₄⋊C₄	—	4	1	no	—
1240	C₄⋊C₄	—	4	1	no	—
1241	C₄⋊C₄	—	4	1	no	—
1242	C₄⋊C₄	—	4	1	no	—
1243	C₄⋊C₄	—	4	1	no	—
1244	C₄⋊C₄	—	4	1	no	—
1245	C₄⋊C₄	—	4	1	no	—
1246	C₄⋊C₄	—	4	1	no	—
1247	C₄⋊C₄	—	4	1	no	—
1248	C₄⋊C₄	—	4	1	no	—
1249	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1250	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1251	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1252	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1253	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1254	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1255	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1256	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1257	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1258	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1259	C₂²⋊C₄	—	2	2	no	—
1260	C₂²⋊C₄	—	2	2	no	—
1261	C₂²⋊C₄	—	2	2	no	—
1262	C₂²⋊C₄	—	2	2	no	—
1263	C₂²⋊C₄	—	2	2	no	—
1264	C₂²⋊C₄	—	4	1	no	—
1265	C₂²⋊C₄	—	4	1	no	—
1266	C₂²⋊C₄	—	4	1	no	—
1267	C₂²⋊C₄	—	4	1	no	—
1268	C₂²⋊C₄	—	4	1	no	—
1269	C₂²⋊C₄	—	4	1	no	—
1270	C₂²⋊C₄	—	4	1	no	—
1271	C₂²⋊C₄	—	4	1	no	—
1272	C₂²⋊C₄	—	4	1	no	—
1273	C₂²⋊C₄	—	4	1	no	—
1274	C₂²⋊C₄	—	4	1	no	—
1275	C₂²⋊C₄	—	4	1	no	—
1276	C₂²⋊C₄	—	4	1	no	—
1277	C₂²⋊C₄	—	4	1	no	—
1278	C₂²⋊C₄	—	4	1	no	—
1279	C₂²⋊C₄	—	4	1	no	—
1280	C₂²⋊C₄	—	4	1	no	—
1281	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1282	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1283	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1284	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1285	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1286	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1287	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1288	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1289	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1290	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1291	C₄²	—	2	2	no	—
1292	C₄²	—	2	2	no	—
1293	C₄²	—	4	1	no	—
1294	C₄²	—	4	1	no	—
1295	C₄²	—	4	1	no	—
1296	C₄²	—	4	1	no	—
1297	C₄²	—	4	1	no	—
1298	C₄²	—	4	1	no	—
1299	C₄²	—	4	1	no	—
1300	C₄²	—	4	1	no	—
1301	C₄²	—	4	1	no	—
1302	C₄²	—	4	1	no	—
1303	C₄²	—	4	1	no	—
1304	C₄²	—	4	1	no	—
1305	C₄²	—	4	1	no	—
1306	C₄²	—	4	1	no	—
1307	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
1308	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
1309	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
1310	C₂³	—	2	1	no	—
1311	C₂³	—	2	1	no	—
1312	C₂³	—	2	1	no	—
1313	C₂³	—	2	1	no	—
1314	C₂³	—	2	1	no	—
1315	C₂³	—	2	1	no	—
1316	C₂³	—	2	1	no	—
1317	C₂³	—	2	1	no	—
1318	C₂³	—	2	1	no	—
1319	C₂³	—	2	1	no	—
1320	C₂³	—	2	1	no	—
1321	C₂³	—	2	1	no	—
1322	C₂³	—	2	1	no	—
1323	C₂³	—	2	1	no	—
1324	C₂³	—	2	1	no	—
1325	C₂³	—	2	1	no	—
1326	C₂³	—	2	1	no	—
1327	C₂³	—	2	1	no	—
1328	C₂³	—	2	1	no	—
1329	C₂³	—	2	1	no	—
1330	C₂³	—	2	1	no	—
1331	C₂³	—	2	1	no	—
1332	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
1333	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
1334	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
1335	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
1336	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
1337	C₂³	C₂₃×2₋¹⁺⁴	1	2	yes	—
1338	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
1339	D₄	—	2	8	no	—
1340	D₄	—	2	8	no	—
1341	D₄	—	2	8	no	—
1342	D₄	—	4	4	no	—
1343	D₄	—	4	4	no	—
1344	D₄	—	4	4	no	—
1345	C₂×C₄	—	2	1	no	—
1346	C₂×C₄	—	2	1	no	—
1347	C₂×C₄	—	2	1	no	—
1348	C₂×C₄	—	2	1	no	—
1349	C₂×C₄	—	2	1	no	—
1350	C₂×C₄	—	2	1	no	—
1351	C₂×C₄	—	2	1	no	—
1352	C₂×C₄	—	2	1	no	—
1353	C₂×C₄	—	2	1	no	—
1354	C₂×C₄	—	2	1	no	—
1355	C₂×C₄	—	2	1	no	—
1356	C₂×C₄	—	2	1	no	—
1357	C₂×C₄	—	2	1	no	—
1358	C₂×C₄	—	2	1	no	—
1359	C₂×C₄	—	2	1	no	—
1360	C₂×C₄	—	2	1	no	—
1361	C₂×C₄	—	2	1	no	—
1362	C₂×C₄	—	2	1	no	—
1363	C₂×C₄	—	2	1	no	—
1364	C₂×C₄	—	2	1	no	—
1365	C₂×C₄	—	2	1	no	—
1366	C₂×C₄	—	2	1	no	—
1367	C₂×C₄	—	2	1	no	—
1368	C₂×C₄	—	2	1	no	—
1369	C₂×C₄	—	2	1	no	—
1370	C₂×C₄	—	2	1	no	—
1371	C₂×C₄	—	2	1	no	—
1372	C₂×C₄	—	2	1	no	—
1373	C₂×C₄	—	2	1	no	—
1374	C₂×C₄	—	2	1	no	—
1375	C₂×C₄	—	2	1	no	—
1376	C₂×C₄	—	2	1	no	—
1377	C₂×C₄	—	2	1	no	—
1378	C₂×C₄	—	2	1	no	—
1379	C₂×C₄	—	2	1	no	—
1380	C₂×C₄	—	2	1	no	—
1381	C₂×C₄	—	2	1	no	—
1382	C₂×C₄	—	2	1	no	—
1383	C₂×C₄	—	2	1	no	—
1384	C₂×C₄	—	2	1	no	—
1385	C₂×C₄	—	2	1	no	—
1386	C₂×C₄	—	2	1	no	—
1387	C₂×C₄	—	2	1	no	—
1388	C₂×C₄	—	2	1	no	—
1389	C₂×C₄	—	2	1	no	—
1390	C₂×C₄	—	2	1	no	—
1391	C₂×C₄	—	2	1	no	—
1392	C₂×C₄	—	2	1	no	—
1393	C₂×C₄	—	2	1	no	—
1394	C₂×C₄	—	2	1	no	—
1395	C₂×C₄	—	2	1	no	—
1396	C₂×C₄	—	2	1	no	—
1397	C₂×C₄	—	2	1	no	—
1398	C₂×C₄	—	2	1	no	—
1399	C₂×C₄	—	2	1	no	—
1400	C₂×C₄	—	2	1	no	—
1401	C₂×C₄	—	2	1	no	—
1402	C₂×C₄	—	2	1	no	—
1403	C₂×C₄	—	2	1	no	—
1404	C₂×C₄	—	2	1	no	—
1405	C₂×C₄	—	2	1	no	—
1406	C₂×C₄	—	2	1	no	—
1407	C₂×C₄	—	2	1	no	—
1408	C₂×C₄	—	2	1	no	—
1409	C₂×C₄	—	2	1	no	—
1410	C₂×C₄	—	2	1	no	—
1411	C₂×C₄	—	2	1	no	—
1412	C₂×C₄	—	2	1	no	—
1413	C₂×C₄	—	2	1	no	—
1414	C₂×C₄	—	4	4	no	—
1415	C₂×C₄	—	4	4	no	—
1416	C₂×C₄	—	4	4	no	—
1417	C₂×C₄	—	4	4	no	—
1418	C₂×C₄	—	4	4	no	—
1419	C₂×C₄	—	4	4	no	—
1420	C₂×C₄	—	4	4	no	—
1421	C₂×C₄	—	4	4	no	—
1422	C₂×C₄	—	8	2	no	—
1423	C₂×C₄	—	8	2	no	—
1424	C₂×C₄	—	8	2	no	—
1425	C₂×C₄	—	8	2	no	—
1426	C₂×C₄	—	8	2	no	—
1427	C₂×C₄	—	8	2	no	—
1428	C₂×C₄	—	8	2	no	—
1429	C₂×C₄	—	8	2	no	—
1430	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1431	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1432	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1433	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1434	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1435	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1436	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1437	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1438	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1439	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1440	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1441	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1442	C₂²	—	2	2	no	—
1443	C₂²	—	2	2	no	—
1444	C₂²	—	2	2	no	—
1445	C₂²	—	2	2	no	—
1446	C₂²	—	2	2	no	—
1447	C₂²	—	2	2	no	—
1448	C₂²	—	2	2	no	—
1449	C₂²	—	2	2	no	—
1450	C₂²	—	2	2	no	—
1451	C₂²	—	2	2	no	—
1452	C₂²	—	2	2	no	—
1453	C₂²	—	2	2	no	—
1454	C₂²	—	2	2	no	—
1455	C₂²	—	2	2	no	—
1456	C₂²	—	2	2	no	—
1457	C₂²	—	4	1	no	—
1458	C₂²	—	4	1	no	—
1459	C₂²	—	4	1	no	—
1460	C₂²	—	4	1	no	—
1461	C₂²	—	4	1	no	—
1462	C₂²	—	4	1	no	—
1463	C₂²	—	4	1	no	—
1464	C₂²	—	4	1	no	—
1465	C₂²	—	4	1	no	—
1466	C₂²	—	4	1	no	—
1467	C₂²	—	4	1	no	—
1468	C₂²	—	4	1	no	—
1469	C₂²	C₂₃×#520	1	4	yes	—
1470	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
1471	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1472	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1473	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1474	C₂²	C₂₃×#585	1	1	yes	characteristic
1475	C₂²	C₂₃×#585	1	1	yes	characteristic
1476	C₂²	C₂₃×#585	1	1	yes	characteristic
1477	C₄	—	2	2	no	—
1478	C₄	—	2	2	no	—
1479	C₄	—	2	2	no	—
1480	C₄	—	2	2	no	—
1481	C₄	—	2	2	no	—
1482	C₄	—	2	2	no	—
1483	C₄	—	2	2	no	—
1484	C₄	—	2	2	no	—
1485	C₄	—	2	2	no	—
1486	C₄	—	2	2	no	—
1487	C₄	—	2	2	no	—
1488	C₄	—	2	2	no	—
1489	C₄	—	4	1	no	—
1490	C₄	—	4	1	no	—
1491	C₄	—	4	1	no	—
1492	C₄	—	4	1	no	—
1493	C₄	—	4	1	no	—
1494	C₄	—	4	1	no	—
1495	C₄	—	4	1	no	—
1496	C₄	—	4	1	no	—
1497	C₄	—	4	1	no	—
1498	C₄	—	4	1	no	—
1499	C₄	—	4	1	no	—
1500	C₄	—	4	1	no	—
1501	C₄	—	4	1	no	—
1502	C₄	—	4	1	no	—
1503	C₄	—	4	1	no	—
1504	C₂	—	2	4	no	—
1505	C₂	—	4	2	no	—
1506	C₂	—	4	2	no	—
1507	C₂	—	4	2	no	—
1508	C₂	C₂×C₂₃×#520	1	1	yes	characteristic
1509	C₂	C₂₃×#3428	1	1	yes	characteristic
1510	C₂	C₄×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1511	C₂	C₂₃×#3534	1	1	yes	characteristic
1512	C₂	C₂₃×#3541	1	1	yes	characteristic
1513	C₂	C₂₃×#3553	1	1	yes	characteristic
1514	C₂	C₂₃×#3560	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#553	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂₃×#2383	C₂	semidirect
3. C₂₃×#2382	C₂	semidirect
4. C₂₃×#2377	C₂	semidirect
5. C₂₃×#2376	C₂	semidirect
6. C₂₃×#2373	C₂	semidirect
7. C₂₃×#2364	C₂	semidirect
8. C₂₃×#2364	C₂	semidirect
9. C₂₃×#2361	C₂	semidirect
10. C₂₃×#2359	C₂	semidirect
11. C₂₃×#2352	C₂	semidirect
12. C₂₃×#2349	C₂	semidirect
13. C₂₃×#2349	C₂	semidirect
14. D₄×C₄⋊C₄×C₂₃	C₂	semidirect
15. C₂₃×#2345	C₂	semidirect
16. C₂₃×#2343	C₂	semidirect
17. C₂₃×#2336	C₂	semidirect
18. C₂₃×#2335	C₂	semidirect
19. C₂₃×#2334	C₂	semidirect
20. C₂₃×#2334	C₂	semidirect
21. C₂₃×#2325	C₂	semidirect
22. C₂₃×#2325	C₂	semidirect
23. C₂₃×#2325	C₂	semidirect
24. C₂₃×#2322	C₂	semidirect
25. C₂₃×#2318	C₂	semidirect
26. C₂₃×#2318	C₂	semidirect
27. C₂₃×#2318	C₂	semidirect
28. C₂₃×#2314	C₂	semidirect
29. C₄×C₂₃×#121	C₂	semidirect
30. C₂₃×#2290	C₂	semidirect
31. C₂×C₂₃×#387	C₂	semidirect
32. C₂₃×#553	C₄	semidirect
210. C₂₃×#126	C₂×C₄	semidirect
211. C₂₃×#126	C₂×C₄	semidirect
212. C₂₃×#125	C₂×C₄	semidirect
213. C₂₃×#123	C₂×C₄	semidirect
214. C₂₃×#123	C₂×C₄	semidirect
215. C₂₃×#121	C₂×C₄	semidirect
216. C₂₃×#121	C₂×C₄	semidirect
217. C₂₃×#121	C₂×C₄	semidirect
218. C₂₃×#121	C₂×C₄	semidirect
227. C₄×D₄×C₂₃	C₂×C₄	semidirect
228. C₄×D₄×C₂₃	C₂×C₄	semidirect
229. C₄×D₄×C₂₃	C₂×C₄	semidirect
230. C₄×D₄×C₂₃	C₂×C₄	semidirect
232. C₂₃×#117	C₂×C₄	semidirect
235. C₂×C₄⋊C₄×C₂₃	C₂×C₄	semidirect
552. #34497	C₂₃	direct (N × H)
686. #2383	C₂×C₂₃	semidirect
687. #2382	C₂×C₂₃	semidirect
688. #2377	C₂×C₂₃	semidirect
689. #2376	C₂×C₂₃	semidirect
690. #2373	C₂×C₂₃	semidirect
691. #2364	C₂×C₂₃	semidirect
692. #2364	C₂×C₂₃	semidirect
693. #2361	C₂×C₂₃	semidirect
694. #2359	C₂×C₂₃	semidirect
695. #2352	C₂×C₂₃	semidirect
696. #2349	C₂×C₂₃	semidirect
697. #2349	C₂×C₂₃	semidirect
698. D₄×C₄⋊C₄	C₂×C₂₃	semidirect
699. #2345	C₂×C₂₃	semidirect
700. #2343	C₂×C₂₃	semidirect
701. #2336	C₂×C₂₃	semidirect
702. #2335	C₂×C₂₃	semidirect
703. #2334	C₂×C₂₃	semidirect
704. #2334	C₂×C₂₃	semidirect
705. #2325	C₂×C₂₃	semidirect
706. #2325	C₂×C₂₃	semidirect
707. #2325	C₂×C₂₃	semidirect
708. #2322	C₂×C₂₃	semidirect
709. #2318	C₂×C₂₃	semidirect
710. #2318	C₂×C₂₃	semidirect
711. #2318	C₂×C₂₃	semidirect
712. #2314	C₂×C₂₃	semidirect
713. C₄×#121	C₂×C₂₃	semidirect
714. #2290	C₂×C₂₃	semidirect
715. C₂×#387	C₂×C₂₃	semidirect
778. #553	C₄×C₂₃	semidirect
967. #126	C₂×C₄×C₂₃	semidirect
968. #126	C₂×C₄×C₂₃	semidirect
969. #125	C₂×C₄×C₂₃	semidirect
970. #123	C₂×C₄×C₂₃	semidirect
971. #123	C₂×C₄×C₂₃	semidirect
972. #121	C₂×C₄×C₂₃	semidirect
973. #121	C₂×C₄×C₂₃	semidirect
974. #121	C₂×C₄×C₂₃	semidirect
975. #121	C₂×C₄×C₂₃	semidirect
984. C₄×D₄	C₂×C₄×C₂₃	semidirect
985. C₄×D₄	C₂×C₄×C₂₃	semidirect
986. C₄×D₄	C₂×C₄×C₂₃	semidirect
987. C₄×D₄	C₂×C₄×C₂₃	semidirect
989. #117	C₂×C₄×C₂₃	semidirect
992. C₂×C₄⋊C₄	C₂×C₄×C₂₃	semidirect
1127. C₂₃	#34497	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₂₃×#553	2
C₂₃×#2383	2
C₂₃×#2382	2
C₂₃×#2377	2
C₂₃×#2376	2
C₂₃×#2373	2
C₂₃×#2364	2
C₂₃×#2361	2
C₂₃×#2359	2
C₂₃×#2352	2
C₂₃×#2349	2
D₄×C₄⋊C₄×C₂₃	2
C₂₃×#2345	2
C₂₃×#2343	2
C₂₃×#2336	2
C₂₃×#2335	2
C₂₃×#2334	2
C₂₃×#2325	2
C₂₃×#2322	2
C₂₃×#2318	2
C₂₃×#2314	2
C₄×C₂₃×#121	2
C₂₃×#2290	2
C₂×C₂₃×#387	2
#34497	23

Subgroups — C23×#34497 #19182123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34497 #19182123