Subgroups — C₂₃×#34525 #19182151

Order 5888.

2008 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#563	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2383	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2383	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2374	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#2373	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2373	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2368	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2367	C₂	1	1	yes	maximal, characteristic
12	C₂₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2362	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2359	C₂	1	1	yes	maximal, characteristic
17	C₂₃×#2337	C₂	1	1	yes	maximal, characteristic
18	C₂₃×#2336	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2336	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2335	C₂	1	1	yes	maximal, characteristic
21	C₂₃×#2334	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2334	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2332	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#2332	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂₃×#2331	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂₃×#2329	C₂	1	1	yes	maximal, characteristic, complemented
27	C₂₃×#2323	C₂	1	1	yes	maximal, characteristic, complemented
28	C₂₃×#2322	C₂	1	1	yes	maximal, characteristic
29	C₄×C₂₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×C₂₃×#126	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄×C₂₃×#126	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂₃×#563	C₄	1	16	yes	complemented
33	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#126	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#126	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#126	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#126	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×#123	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×#123	C₂²	1	1	yes	characteristic
44	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
48	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
52	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
53	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
54	C₂₃×#391	C₂²	1	1	yes	characteristic
55	C₂₃×#391	C₂²	1	1	yes	characteristic
56	C₂₃×#391	C₂²	1	1	yes	characteristic
57	C₂₃×#391	C₂²	1	1	yes	characteristic
58	C₂₃×#391	C₂²	1	1	yes	characteristic
59	C₂₃×#391	C₂²	1	1	yes	characteristic
60	C₂₃×#391	C₂²	1	1	yes	characteristic
61	C₂₃×#391	C₂²	1	1	yes	characteristic
62	C₂₃×#391	C₂²	1	1	yes	characteristic
63	C₂₃×#390	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×#389	C₂²	1	1	yes	characteristic
73	C₂₃×#389	C₂²	1	1	yes	characteristic
74	C₂₃×#389	C₂²	1	1	yes	characteristic
75	C₂₃×#389	C₂²	1	1	yes	characteristic
76	C₂₃×#389	C₂²	1	1	yes	characteristic
77	C₂₃×#389	C₂²	1	1	yes	characteristic
78	C₂₃×#389	C₂²	1	1	yes	characteristic
79	C₂₃×#389	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×#388	C₂²	1	1	yes	characteristic
91	C₂₃×#388	C₂²	1	1	yes	characteristic
92	C₂₃×#388	C₂²	1	1	yes	characteristic
93	C₂₃×#388	C₂²	1	1	yes	characteristic
94	C₂₃×#388	C₂²	1	1	yes	characteristic
95	C₂₃×#388	C₂²	1	1	yes	characteristic
96	C₂₃×#388	C₂²	1	1	yes	characteristic
97	C₂₃×#388	C₂²	1	1	yes	characteristic
98	C₂₃×#388	C₂²	1	1	yes	characteristic
99	C₂₃×#388	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×#387	C₂²	1	1	yes	characteristic
117	C₂₃×#387	C₂²	1	1	yes	characteristic
118	C₂₃×#387	C₂²	1	1	yes	characteristic
119	C₂₃×#387	C₂²	1	1	yes	characteristic
120	C₂₃×#387	C₂²	1	1	yes	characteristic
121	C₂₃×#387	C₂²	1	1	yes	characteristic
122	C₂₃×#387	C₂²	1	1	yes	characteristic
123	C₂₃×#387	C₂²	1	1	yes	characteristic
124	C₂₃×#387	C₂²	1	1	yes	characteristic
125	C₂₃×#387	C₂²	1	1	yes	characteristic
126	C₂₃×#387	C₂²	1	1	yes	characteristic
127	C₂₃×#387	C₂²	1	1	yes	characteristic
128	C₂₃×#387	C₂²	1	1	yes	characteristic
129	C₂₃×#387	C₂²	1	1	yes	characteristic
130	C₂₃×#387	C₂²	1	1	yes	characteristic
131	C₂₃×#387	C₂²	1	1	yes	characteristic
132	C₂₃×#386	C₂²	1	1	yes	characteristic
133	C₂₃×#386	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×#384	C₂²	1	1	yes	characteristic
145	C₂₃×#383	C₂²	1	1	yes	characteristic
146	C₂₃×#383	C₂²	1	1	yes	characteristic
147	C₂₃×#383	C₂²	1	1	yes	characteristic
148	C₂₃×#382	C₂²	1	1	yes	characteristic
149	C₂₃×#381	C₂²	1	1	yes	characteristic
150	C₂₃×#380	C₂²	1	1	yes	characteristic
151	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
152	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
153	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
154	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
155	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
156	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
157	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
158	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
159	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
160	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
161	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
162	C₄×C₄⋊C₄×C₂₃	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×C₄⋊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	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
182	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
183	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
184	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
185	C₂₃×#376	C₂²	1	1	yes	characteristic
186	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
187	C₄³×C₂₃	C₂²	1	1	yes	characteristic
188	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
189	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
190	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
191	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
192	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
193	C₂³×C₄×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⋊Q₈	C₂×C₄	1	8	yes	complemented
199	C₂₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
200	C₂₃×#126	C₂×C₄	1	8	yes	complemented
201	C₂₃×#126	C₂×C₄	1	8	yes	complemented
202	C₂₃×#126	C₂×C₄	1	8	yes	complemented
203	C₂₃×#126	C₂×C₄	1	8	yes	complemented
204	C₂₃×#125	C₂×C₄	1	8	yes	complemented
205	C₂₃×#125	C₂×C₄	1	8	yes	complemented
206	C₂₃×#124	C₂×C₄	1	8	yes	—
207	C₂₃×#123	C₂×C₄	1	8	yes	—
208	C₂₃×#123	C₂×C₄	1	8	yes	—
209	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
210	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
211	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
212	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
213	C₄×Q₈×C₂₃	—	4	2	no	—
214	C₄×Q₈×C₂₃	—	4	2	no	—
215	C₄×Q₈×C₂₃	—	4	2	no	—
216	C₄×D₄×C₂₃	—	4	2	no	—
217	C₂₃×#117	—	4	2	no	—
218	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
219	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊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×C₄²×C₂₃	C₂³	1	1	yes	characteristic
284	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
285	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
286	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
287	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
288	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
289	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
290	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
291	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
292	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
293	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
294	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
296	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
297	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
298	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
300	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
301	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
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	C₂₃×#95	C₂³	1	1	yes	characteristic
313	C₂₃×#95	C₂³	1	1	yes	characteristic
314	C₂₃×#95	C₂³	1	1	yes	characteristic
315	C₂₃×#95	C₂³	1	1	yes	characteristic
316	C₂₃×#95	C₂³	1	1	yes	characteristic
317	C₂₃×#95	C₂³	1	1	yes	characteristic
318	C₂₃×#95	C₂³	1	1	yes	characteristic
319	C₂₃×#95	C₂³	1	1	yes	characteristic
320	C₂₃×#95	C₂³	1	1	yes	characteristic
321	C₂₃×#95	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	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
365	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
366	C₂×Q₈×C₂₃	—	4	1	no	—
367	C₂×Q₈×C₂₃	—	4	1	no	—
368	C₂×Q₈×C₂₃	—	4	1	no	—
369	C₂×Q₈×C₂₃	—	4	1	no	—
370	C₂×Q₈×C₂₃	—	4	1	no	—
371	C₂×Q₈×C₂₃	—	4	1	no	—
372	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
373	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
374	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
375	C₂×D₄×C₂₃	—	4	1	no	—
376	C₂×D₄×C₂₃	—	4	1	no	—
377	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
378	C₂²×C₄×C₂₃	—	2	2	no	—
379	C₂²×C₄×C₂₃	—	2	2	no	—
380	C₂²×C₄×C₂₃	—	4	1	no	—
381	C₂²×C₄×C₂₃	—	4	1	no	—
382	C₂²×C₄×C₂₃	—	4	1	no	—
383	C₂²×C₄×C₂₃	—	4	1	no	—
384	C₂²×C₄×C₂₃	—	4	1	no	—
385	C₂²×C₄×C₂₃	—	4	1	no	—
386	C₂²×C₄×C₂₃	—	4	1	no	—
387	C₂²×C₄×C₂₃	—	4	1	no	—
388	C₂²×C₄×C₂₃	—	4	1	no	—
389	C₂²×C₄×C₂₃	—	4	1	no	—
390	C₂²×C₄×C₂₃	—	4	1	no	—
391	C₂²×C₄×C₂₃	—	4	1	no	—
392	C₂²×C₄×C₂₃	—	4	1	no	—
393	C₂²×C₄×C₂₃	—	4	1	no	—
394	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
395	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
396	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
401	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
413	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
417	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
418	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
419	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
420	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
421	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
423	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
424	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄×C₂₃	—	2	2	no	—
426	C₄⋊C₄×C₂₃	—	2	2	no	—
427	C₄⋊C₄×C₂₃	—	2	2	no	—
428	C₄⋊C₄×C₂₃	—	2	2	no	—
429	C₄⋊C₄×C₂₃	—	2	2	no	—
430	C₄⋊C₄×C₂₃	—	2	2	no	—
431	C₄⋊C₄×C₂₃	—	2	2	no	—
432	C₄⋊C₄×C₂₃	—	2	2	no	—
433	C₄⋊C₄×C₂₃	—	4	1	no	—
434	C₄⋊C₄×C₂₃	—	4	1	no	—
435	C₄⋊C₄×C₂₃	—	4	1	no	—
436	C₄⋊C₄×C₂₃	—	4	1	no	—
437	C₄⋊C₄×C₂₃	—	4	1	no	—
438	C₄⋊C₄×C₂₃	—	4	1	no	—
439	C₄⋊C₄×C₂₃	—	4	1	no	—
440	C₄⋊C₄×C₂₃	—	4	1	no	—
441	C₄⋊C₄×C₂₃	—	4	1	no	—
442	C₄⋊C₄×C₂₃	—	4	1	no	—
443	C₄⋊C₄×C₂₃	—	4	1	no	—
444	C₄⋊C₄×C₂₃	—	4	1	no	—
445	C₄⋊C₄×C₂₃	—	4	1	no	—
446	C₄⋊C₄×C₂₃	—	4	1	no	—
447	C₄⋊C₄×C₂₃	—	4	1	no	—
448	C₄⋊C₄×C₂₃	—	4	1	no	—
449	C₄⋊C₄×C₂₃	—	4	1	no	—
450	C₄⋊C₄×C₂₃	—	4	1	no	—
451	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
452	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
453	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
454	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
455	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
456	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
457	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
458	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
459	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
460	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
461	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
462	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
463	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
464	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
465	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
466	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
467	C₂²⋊C₄×C₂₃	—	2	2	no	—
468	C₂²⋊C₄×C₂₃	—	2	2	no	—
469	C₂²⋊C₄×C₂₃	—	2	2	no	—
470	C₂²⋊C₄×C₂₃	—	2	2	no	—
471	C₂²⋊C₄×C₂₃	—	4	1	no	—
472	C₂²⋊C₄×C₂₃	—	4	1	no	—
473	C₂²⋊C₄×C₂₃	—	4	1	no	—
474	C₂²⋊C₄×C₂₃	—	4	1	no	—
475	C₂²⋊C₄×C₂₃	—	4	1	no	—
476	C₂²⋊C₄×C₂₃	—	4	1	no	—
477	C₂²⋊C₄×C₂₃	—	4	1	no	—
478	C₂²⋊C₄×C₂₃	—	4	1	no	—
479	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
480	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
481	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
482	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
483	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
484	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
485	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
486	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
487	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
488	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
489	C₄²×C₂₃	—	2	2	no	—
490	C₄²×C₂₃	—	2	2	no	—
491	C₄²×C₂₃	—	2	2	no	—
492	C₄²×C₂₃	—	2	2	no	—
493	C₄²×C₂₃	—	2	2	no	—
494	C₄²×C₂₃	—	4	1	no	—
495	C₄²×C₂₃	—	4	1	no	—
496	C₄²×C₂₃	—	4	1	no	—
497	C₄²×C₂₃	—	4	1	no	—
498	C₄²×C₂₃	—	4	1	no	—
499	C₄²×C₂₃	—	4	1	no	—
500	C₄²×C₂₃	—	4	1	no	—
501	C₄²×C₂₃	—	4	1	no	—
502	C₄²×C₂₃	—	4	1	no	—
503	C₄²×C₂₃	—	4	1	no	—
504	C₄²×C₂₃	—	4	1	no	—
505	C₄²×C₂₃	—	4	1	no	—
506	C₄²×C₂₃	—	4	1	no	—
507	C₄²×C₂₃	—	4	1	no	—
508	C₄²×C₂₃	—	4	1	no	—
509	C₄²×C₂₃	—	4	1	no	—
510	C₄²×C₂₃	—	4	1	no	—
511	C₄²×C₂₃	—	4	1	no	—
512	C₄²×C₂₃	—	4	1	no	—
513	C₄²×C₂₃	—	4	1	no	—
514	C₄²×C₂₃	—	4	1	no	—
515	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
516	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
517	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
518	#34525	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
519	C₂³×C₂₃	—	2	1	no	—
520	C₂³×C₂₃	—	2	1	no	—
521	C₂³×C₂₃	—	2	1	no	—
522	C₂³×C₂₃	—	2	1	no	—
523	C₂³×C₂₃	—	2	1	no	—
524	C₂³×C₂₃	—	2	1	no	—
525	C₂³×C₂₃	—	2	1	no	—
526	C₂³×C₂₃	—	2	1	no	—
527	C₂³×C₂₃	—	2	1	no	—
528	C₂³×C₂₃	—	2	1	no	—
529	C₂³×C₂₃	—	2	1	no	—
530	C₂³×C₂₃	—	2	1	no	—
531	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
532	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
533	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
534	Q₈×C₂₃	—	4	4	no	—
535	Q₈×C₂₃	—	4	4	no	—
536	Q₈×C₂₃	—	4	4	no	—
537	D₄×C₂₃	—	4	4	no	—
538	C₂×C₄×C₂₃	—	2	1	no	—
539	C₂×C₄×C₂₃	—	2	1	no	—
540	C₂×C₄×C₂₃	—	2	1	no	—
541	C₂×C₄×C₂₃	—	2	1	no	—
542	C₂×C₄×C₂₃	—	2	1	no	—
543	C₂×C₄×C₂₃	—	2	1	no	—
544	C₂×C₄×C₂₃	—	2	1	no	—
545	C₂×C₄×C₂₃	—	2	1	no	—
546	C₂×C₄×C₂₃	—	2	1	no	—
547	C₂×C₄×C₂₃	—	2	1	no	—
548	C₂×C₄×C₂₃	—	2	1	no	—
549	C₂×C₄×C₂₃	—	2	1	no	—
550	C₂×C₄×C₂₃	—	2	1	no	—
551	C₂×C₄×C₂₃	—	2	1	no	—
552	C₂×C₄×C₂₃	—	2	1	no	—
553	C₂×C₄×C₂₃	—	2	1	no	—
554	C₂×C₄×C₂₃	—	2	1	no	—
555	C₂×C₄×C₂₃	—	2	1	no	—
556	C₂×C₄×C₂₃	—	2	1	no	—
557	C₂×C₄×C₂₃	—	2	1	no	—
558	C₂×C₄×C₂₃	—	2	1	no	—
559	C₂×C₄×C₂₃	—	2	1	no	—
560	C₂×C₄×C₂₃	—	2	1	no	—
561	C₂×C₄×C₂₃	—	2	1	no	—
562	C₂×C₄×C₂₃	—	2	1	no	—
563	C₂×C₄×C₂₃	—	2	1	no	—
564	C₂×C₄×C₂₃	—	2	1	no	—
565	C₂×C₄×C₂₃	—	2	1	no	—
566	C₂×C₄×C₂₃	—	2	1	no	—
567	C₂×C₄×C₂₃	—	2	1	no	—
568	C₂×C₄×C₂₃	—	2	1	no	—
569	C₂×C₄×C₂₃	—	2	1	no	—
570	C₂×C₄×C₂₃	—	2	1	no	—
571	C₂×C₄×C₂₃	—	2	1	no	—
572	C₂×C₄×C₂₃	—	2	1	no	—
573	C₂×C₄×C₂₃	—	2	1	no	—
574	C₂×C₄×C₂₃	—	2	1	no	—
575	C₂×C₄×C₂₃	—	2	1	no	—
576	C₂×C₄×C₂₃	—	2	1	no	—
577	C₂×C₄×C₂₃	—	2	1	no	—
578	C₂×C₄×C₂₃	—	2	1	no	—
579	C₂×C₄×C₂₃	—	2	1	no	—
580	C₂×C₄×C₂₃	—	2	1	no	—
581	C₂×C₄×C₂₃	—	2	1	no	—
582	C₂×C₄×C₂₃	—	2	1	no	—
583	C₂×C₄×C₂₃	—	2	1	no	—
584	C₂×C₄×C₂₃	—	2	1	no	—
585	C₂×C₄×C₂₃	—	2	1	no	—
586	C₂×C₄×C₂₃	—	2	1	no	—
587	C₂×C₄×C₂₃	—	2	1	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	—	4	4	no	—
610	C₂×C₄×C₂₃	—	4	4	no	—
611	C₂×C₄×C₂₃	—	8	2	no	—
612	C₂×C₄×C₂₃	—	8	2	no	—
613	C₂×C₄×C₂₃	—	8	2	no	—
614	C₂×C₄×C₂₃	—	8	2	no	—
615	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
616	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
617	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
618	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
619	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
620	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
621	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
622	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
623	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
624	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
625	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
626	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
627	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
628	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
629	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
630	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
631	C₂×#563	C₂×C₂₃	1	1	yes	characteristic
632	#2383	C₂×C₂₃	1	1	yes	characteristic, complemented
633	#2383	C₂×C₂₃	1	1	yes	characteristic, complemented
634	#2381	C₂×C₂₃	1	1	yes	characteristic, complemented
635	#2374	C₂×C₂₃	1	1	yes	characteristic
636	#2373	C₂×C₂₃	1	1	yes	characteristic, complemented
637	#2373	C₂×C₂₃	1	1	yes	characteristic, complemented
638	#2370	C₂×C₂₃	1	1	yes	characteristic, complemented
639	#2370	C₂×C₂₃	1	1	yes	characteristic, complemented
640	#2368	C₂×C₂₃	1	1	yes	characteristic, complemented
641	#2367	C₂×C₂₃	1	1	yes	characteristic
642	#2365	C₂×C₂₃	1	1	yes	characteristic, complemented
643	#2362	C₂×C₂₃	1	1	yes	characteristic, complemented
644	#2360	C₂×C₂₃	1	1	yes	characteristic, complemented
645	#2360	C₂×C₂₃	1	1	yes	characteristic, complemented
646	#2359	C₂×C₂₃	1	1	yes	characteristic
647	#2337	C₂×C₂₃	1	1	yes	characteristic
648	#2336	C₂×C₂₃	1	1	yes	characteristic, complemented
649	#2336	C₂×C₂₃	1	1	yes	characteristic, complemented
650	#2335	C₂×C₂₃	1	1	yes	characteristic
651	#2334	C₂×C₂₃	1	1	yes	characteristic, complemented
652	#2334	C₂×C₂₃	1	1	yes	characteristic, complemented
653	#2332	C₂×C₂₃	1	1	yes	characteristic, complemented
654	#2332	C₂×C₂₃	1	1	yes	characteristic, complemented
655	#2331	C₂×C₂₃	1	1	yes	characteristic, complemented
656	#2329	C₂×C₂₃	1	1	yes	characteristic, complemented
657	#2323	C₂×C₂₃	1	1	yes	characteristic, complemented
658	#2322	C₂×C₂₃	1	1	yes	characteristic
659	C₄×C₄⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
660	C₄×#126	C₂×C₂₃	1	1	yes	characteristic, complemented
661	C₄×#126	C₂×C₂₃	1	1	yes	characteristic, complemented
662	C₂²×C₂₃	—	2	2	no	—
663	C₂²×C₂₃	—	2	2	no	—
664	C₂²×C₂₃	—	2	2	no	—
665	C₂²×C₂₃	—	2	2	no	—
666	C₂²×C₂₃	—	2	2	no	—
667	C₂²×C₂₃	—	2	2	no	—
668	C₂²×C₂₃	—	4	1	no	—
669	C₂²×C₂₃	—	4	1	no	—
670	C₂²×C₂₃	—	4	1	no	—
671	C₂²×C₂₃	—	4	1	no	—
672	C₂²×C₂₃	—	4	1	no	—
673	C₂²×C₂₃	—	4	1	no	—
674	C₂²×C₂₃	—	4	1	no	—
675	C₂²×C₂₃	—	4	1	no	—
676	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
677	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
678	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
679	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
680	C₂²×C₂₃	#585	1	1	yes	characteristic
681	C₂²×C₂₃	#585	1	1	yes	characteristic
682	C₂²×C₂₃	#585	1	1	yes	characteristic
683	C₄×C₂₃	—	2	2	no	—
684	C₄×C₂₃	—	2	2	no	—
685	C₄×C₂₃	—	2	2	no	—
686	C₄×C₂₃	—	2	2	no	—
687	C₄×C₂₃	—	2	2	no	—
688	C₄×C₂₃	—	2	2	no	—
689	C₄×C₂₃	—	2	2	no	—
690	C₄×C₂₃	—	2	2	no	—
691	C₄×C₂₃	—	2	2	no	—
692	C₄×C₂₃	—	2	2	no	—
693	C₄×C₂₃	—	2	2	no	—
694	C₄×C₂₃	—	2	2	no	—
695	C₄×C₂₃	—	2	2	no	—
696	C₄×C₂₃	—	2	2	no	—
697	C₄×C₂₃	—	2	2	no	—
698	C₄×C₂₃	—	2	2	no	—
699	C₄×C₂₃	—	4	1	no	—
700	C₄×C₂₃	—	4	1	no	—
701	C₄×C₂₃	—	4	1	no	—
702	C₄×C₂₃	—	4	1	no	—
703	C₄×C₂₃	—	4	1	no	—
704	C₄×C₂₃	—	4	1	no	—
705	C₄×C₂₃	—	4	1	no	—
706	C₄×C₂₃	—	4	1	no	—
707	C₄×C₂₃	—	4	1	no	—
708	C₄×C₂₃	—	4	1	no	—
709	C₄×C₂₃	—	4	1	no	—
710	C₄×C₂₃	—	4	1	no	—
711	C₄×C₂₃	—	4	1	no	—
712	#563	C₄×C₂₃	1	16	yes	complemented
713	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
714	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
715	C₂×#126	C₂²×C₂₃	1	1	yes	characteristic
716	C₂×#126	C₂²×C₂₃	1	1	yes	characteristic
717	C₂×#126	C₂²×C₂₃	1	1	yes	characteristic
718	C₂×#126	C₂²×C₂₃	1	1	yes	characteristic
719	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
720	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
721	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
722	C₂×#123	C₂²×C₂₃	1	1	yes	characteristic
723	C₂×#123	C₂²×C₂₃	1	1	yes	characteristic
724	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
725	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
726	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
727	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
728	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
729	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
730	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
731	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
732	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
733	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
734	#391	C₂²×C₂₃	1	1	yes	characteristic
735	#391	C₂²×C₂₃	1	1	yes	characteristic
736	#391	C₂²×C₂₃	1	1	yes	characteristic
737	#391	C₂²×C₂₃	1	1	yes	characteristic
738	#391	C₂²×C₂₃	1	1	yes	characteristic
739	#391	C₂²×C₂₃	1	1	yes	characteristic
740	#391	C₂²×C₂₃	1	1	yes	characteristic
741	#391	C₂²×C₂₃	1	1	yes	characteristic
742	#391	C₂²×C₂₃	1	1	yes	characteristic
743	#390	C₂²×C₂₃	1	1	yes	characteristic
744	#389	C₂²×C₂₃	1	1	yes	characteristic
745	#389	C₂²×C₂₃	1	1	yes	characteristic
746	#389	C₂²×C₂₃	1	1	yes	characteristic
747	#389	C₂²×C₂₃	1	1	yes	characteristic
748	#389	C₂²×C₂₃	1	1	yes	characteristic
749	#389	C₂²×C₂₃	1	1	yes	characteristic
750	#389	C₂²×C₂₃	1	1	yes	characteristic
751	#389	C₂²×C₂₃	1	1	yes	characteristic
752	#389	C₂²×C₂₃	1	1	yes	characteristic
753	#389	C₂²×C₂₃	1	1	yes	characteristic
754	#389	C₂²×C₂₃	1	1	yes	characteristic
755	#389	C₂²×C₂₃	1	1	yes	characteristic
756	#389	C₂²×C₂₃	1	1	yes	characteristic
757	#389	C₂²×C₂₃	1	1	yes	characteristic
758	#389	C₂²×C₂₃	1	1	yes	characteristic
759	#389	C₂²×C₂₃	1	1	yes	characteristic
760	#388	C₂²×C₂₃	1	1	yes	characteristic
761	#388	C₂²×C₂₃	1	1	yes	characteristic
762	#388	C₂²×C₂₃	1	1	yes	characteristic
763	#388	C₂²×C₂₃	1	1	yes	characteristic
764	#388	C₂²×C₂₃	1	1	yes	characteristic
765	#388	C₂²×C₂₃	1	1	yes	characteristic
766	#388	C₂²×C₂₃	1	1	yes	characteristic
767	#388	C₂²×C₂₃	1	1	yes	characteristic
768	#388	C₂²×C₂₃	1	1	yes	characteristic
769	#388	C₂²×C₂₃	1	1	yes	characteristic
770	#388	C₂²×C₂₃	1	1	yes	characteristic
771	#388	C₂²×C₂₃	1	1	yes	characteristic
772	#388	C₂²×C₂₃	1	1	yes	characteristic
773	#388	C₂²×C₂₃	1	1	yes	characteristic
774	#388	C₂²×C₂₃	1	1	yes	characteristic
775	#388	C₂²×C₂₃	1	1	yes	characteristic
776	#388	C₂²×C₂₃	1	1	yes	characteristic
777	#388	C₂²×C₂₃	1	1	yes	characteristic
778	#388	C₂²×C₂₃	1	1	yes	characteristic
779	#388	C₂²×C₂₃	1	1	yes	characteristic
780	#387	C₂²×C₂₃	1	1	yes	characteristic
781	#387	C₂²×C₂₃	1	1	yes	characteristic
782	#387	C₂²×C₂₃	1	1	yes	characteristic
783	#387	C₂²×C₂₃	1	1	yes	characteristic
784	#387	C₂²×C₂₃	1	1	yes	characteristic
785	#387	C₂²×C₂₃	1	1	yes	characteristic
786	#387	C₂²×C₂₃	1	1	yes	characteristic
787	#387	C₂²×C₂₃	1	1	yes	characteristic
788	#387	C₂²×C₂₃	1	1	yes	characteristic
789	#387	C₂²×C₂₃	1	1	yes	characteristic
790	#387	C₂²×C₂₃	1	1	yes	characteristic
791	#387	C₂²×C₂₃	1	1	yes	characteristic
792	#387	C₂²×C₂₃	1	1	yes	characteristic
793	#387	C₂²×C₂₃	1	1	yes	characteristic
794	#387	C₂²×C₂₃	1	1	yes	characteristic
795	#387	C₂²×C₂₃	1	1	yes	characteristic
796	#387	C₂²×C₂₃	1	1	yes	characteristic
797	#387	C₂²×C₂₃	1	1	yes	characteristic
798	#387	C₂²×C₂₃	1	1	yes	characteristic
799	#387	C₂²×C₂₃	1	1	yes	characteristic
800	#387	C₂²×C₂₃	1	1	yes	characteristic
801	#387	C₂²×C₂₃	1	1	yes	characteristic
802	#387	C₂²×C₂₃	1	1	yes	characteristic
803	#387	C₂²×C₂₃	1	1	yes	characteristic
804	#387	C₂²×C₂₃	1	1	yes	characteristic
805	#387	C₂²×C₂₃	1	1	yes	characteristic
806	#387	C₂²×C₂₃	1	1	yes	characteristic
807	#387	C₂²×C₂₃	1	1	yes	characteristic
808	#387	C₂²×C₂₃	1	1	yes	characteristic
809	#387	C₂²×C₂₃	1	1	yes	characteristic
810	#387	C₂²×C₂₃	1	1	yes	characteristic
811	#387	C₂²×C₂₃	1	1	yes	characteristic
812	#386	C₂²×C₂₃	1	1	yes	characteristic
813	#386	C₂²×C₂₃	1	1	yes	characteristic
814	#385	C₂²×C₂₃	1	1	yes	characteristic
815	#385	C₂²×C₂₃	1	1	yes	characteristic
816	#385	C₂²×C₂₃	1	1	yes	characteristic
817	#385	C₂²×C₂₃	1	1	yes	characteristic
818	#385	C₂²×C₂₃	1	1	yes	characteristic
819	#385	C₂²×C₂₃	1	1	yes	characteristic
820	#385	C₂²×C₂₃	1	1	yes	characteristic
821	#385	C₂²×C₂₃	1	1	yes	characteristic
822	#385	C₂²×C₂₃	1	1	yes	characteristic
823	#385	C₂²×C₂₃	1	1	yes	characteristic
824	#384	C₂²×C₂₃	1	1	yes	characteristic
825	#383	C₂²×C₂₃	1	1	yes	characteristic
826	#383	C₂²×C₂₃	1	1	yes	characteristic
827	#383	C₂²×C₂₃	1	1	yes	characteristic
828	#382	C₂²×C₂₃	1	1	yes	characteristic
829	#381	C₂²×C₂₃	1	1	yes	characteristic
830	#380	C₂²×C₂₃	1	1	yes	characteristic
831	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
832	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
833	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
834	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
835	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
836	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
837	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
838	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
839	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
840	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
841	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
842	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
843	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
844	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
845	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
846	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
847	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
848	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
849	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
850	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
851	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
852	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
853	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
854	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
855	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
856	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
857	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
858	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
859	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
860	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
861	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
862	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
863	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
864	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
865	#376	C₂²×C₂₃	1	1	yes	characteristic
866	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
867	C₄³	C₂²×C₂₃	1	1	yes	characteristic
868	C₂×C₂₃	—	4	2	no	—
869	C₂×C₂₃	—	4	2	no	—
870	C₂×C₂₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
871	C₂×C₂₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
872	C₂×C₂₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
873	C₂×C₂₃	#3552	1	1	yes	characteristic
874	C₂×C₂₃	#3557	1	1	yes	characteristic
875	C₂×C₂₃	#3560	1	1	yes	characteristic
876	C₂×C₂₃	#3564	1	1	yes	characteristic
877	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
878	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
879	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
880	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
881	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
882	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
883	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
884	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
885	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
886	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
887	C₄⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
888	C₄⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
889	#126	C₂×C₄×C₂₃	1	8	yes	complemented
890	#126	C₂×C₄×C₂₃	1	8	yes	complemented
891	#126	C₂×C₄×C₂₃	1	8	yes	complemented
892	#126	C₂×C₄×C₂₃	1	8	yes	complemented
893	#125	C₂×C₄×C₂₃	1	8	yes	complemented
894	#125	C₂×C₄×C₂₃	1	8	yes	complemented
895	#124	C₂×C₄×C₂₃	1	8	yes	—
896	#123	C₂×C₄×C₂₃	1	8	yes	—
897	#123	C₂×C₄×C₂₃	1	8	yes	—
898	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
899	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
900	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
901	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
902	C₄×Q₈	—	4	2	no	—
903	C₄×Q₈	—	4	2	no	—
904	C₄×Q₈	—	4	2	no	—
905	C₄×D₄	—	4	2	no	—
906	#117	—	4	2	no	—
907	C₂×C₄⋊C₄	—	4	2	no	—
908	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
909	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
910	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
911	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
912	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
913	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
914	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
915	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
916	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
917	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
918	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
919	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
920	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
921	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
922	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
923	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
924	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
925	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
926	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
927	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
928	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
929	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
930	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
931	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
932	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
933	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
934	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
935	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
936	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
937	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
938	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
939	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
940	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
941	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
942	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
943	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
944	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
945	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
946	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
947	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
948	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
949	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
950	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
951	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
952	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
953	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
954	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
955	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
956	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
957	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
958	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
959	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
960	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
961	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
962	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
963	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
964	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
965	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
966	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
967	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
968	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
969	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
970	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
971	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
972	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
973	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
974	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
975	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
976	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
977	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
978	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
979	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
980	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
981	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
982	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
983	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
984	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
985	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
986	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
987	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
988	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
989	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
990	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
991	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
992	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
993	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
994	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
995	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
996	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
997	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
998	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
999	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1000	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1001	#95	C₂³×C₂₃	1	1	yes	characteristic
1002	#95	C₂³×C₂₃	1	1	yes	characteristic
1003	#95	C₂³×C₂₃	1	1	yes	characteristic
1004	#95	C₂³×C₂₃	1	1	yes	characteristic
1005	#95	C₂³×C₂₃	1	1	yes	characteristic
1006	#95	C₂³×C₂₃	1	1	yes	characteristic
1007	#95	C₂³×C₂₃	1	1	yes	characteristic
1008	#95	C₂³×C₂₃	1	1	yes	characteristic
1009	#95	C₂³×C₂₃	1	1	yes	characteristic
1010	#95	C₂³×C₂₃	1	1	yes	characteristic
1011	#95	C₂³×C₂₃	1	1	yes	characteristic
1012	#95	C₂³×C₂₃	1	1	yes	characteristic
1013	#95	C₂³×C₂₃	1	1	yes	characteristic
1014	#95	C₂³×C₂₃	1	1	yes	characteristic
1015	#95	C₂³×C₂₃	1	1	yes	characteristic
1016	#95	C₂³×C₂₃	1	1	yes	characteristic
1017	#95	C₂³×C₂₃	1	1	yes	characteristic
1018	#95	C₂³×C₂₃	1	1	yes	characteristic
1019	#95	C₂³×C₂₃	1	1	yes	characteristic
1020	#95	C₂³×C₂₃	1	1	yes	characteristic
1021	#95	C₂³×C₂₃	1	1	yes	characteristic
1022	#95	C₂³×C₂₃	1	1	yes	characteristic
1023	#95	C₂³×C₂₃	1	1	yes	characteristic
1024	#95	C₂³×C₂₃	1	1	yes	characteristic
1025	#95	C₂³×C₂₃	1	1	yes	characteristic
1026	#95	C₂³×C₂₃	1	1	yes	characteristic
1027	#95	C₂³×C₂₃	1	1	yes	characteristic
1028	#95	C₂³×C₂₃	1	1	yes	characteristic
1029	#95	C₂³×C₂₃	1	1	yes	characteristic
1030	#95	C₂³×C₂₃	1	1	yes	characteristic
1031	#95	C₂³×C₂₃	1	1	yes	characteristic
1032	#95	C₂³×C₂₃	1	1	yes	characteristic
1033	#95	C₂³×C₂₃	1	1	yes	characteristic
1034	#95	C₂³×C₂₃	1	1	yes	characteristic
1035	#95	C₂³×C₂₃	1	1	yes	characteristic
1036	#95	C₂³×C₂₃	1	1	yes	characteristic
1037	#95	C₂³×C₂₃	1	1	yes	characteristic
1038	#95	C₂³×C₂₃	1	1	yes	characteristic
1039	#95	C₂³×C₂₃	1	1	yes	characteristic
1040	#95	C₂³×C₂₃	1	1	yes	characteristic
1041	#95	C₂³×C₂₃	1	1	yes	characteristic
1042	#95	C₂³×C₂₃	1	1	yes	characteristic
1043	#95	C₂³×C₂₃	1	1	yes	characteristic
1044	#95	C₂³×C₂₃	1	1	yes	characteristic
1045	#95	C₂³×C₂₃	1	1	yes	characteristic
1046	#95	C₂³×C₂₃	1	1	yes	characteristic
1047	#95	C₂³×C₂₃	1	1	yes	characteristic
1048	#95	C₂³×C₂₃	1	1	yes	characteristic
1049	#95	C₂³×C₂₃	1	1	yes	characteristic
1050	#95	C₂³×C₂₃	1	1	yes	characteristic
1051	#95	C₂³×C₂₃	1	1	yes	characteristic
1052	#95	C₂³×C₂₃	1	1	yes	characteristic
1053	C₂₃	#34525	1	1	yes	characteristic, direct product factor, Sylow
1054	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1055	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1056	C₂×Q₈	—	4	1	no	—
1057	C₂×Q₈	—	4	1	no	—
1058	C₂×Q₈	—	4	1	no	—
1059	C₂×Q₈	—	4	1	no	—
1060	C₂×Q₈	—	4	1	no	—
1061	C₂×Q₈	—	4	1	no	—
1062	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
1063	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
1064	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
1065	C₂×D₄	—	4	1	no	—
1066	C₂×D₄	—	4	1	no	—
1067	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
1068	C₂²×C₄	—	2	2	no	—
1069	C₂²×C₄	—	2	2	no	—
1070	C₂²×C₄	—	4	1	no	—
1071	C₂²×C₄	—	4	1	no	—
1072	C₂²×C₄	—	4	1	no	—
1073	C₂²×C₄	—	4	1	no	—
1074	C₂²×C₄	—	4	1	no	—
1075	C₂²×C₄	—	4	1	no	—
1076	C₂²×C₄	—	4	1	no	—
1077	C₂²×C₄	—	4	1	no	—
1078	C₂²×C₄	—	4	1	no	—
1079	C₂²×C₄	—	4	1	no	—
1080	C₂²×C₄	—	4	1	no	—
1081	C₂²×C₄	—	4	1	no	—
1082	C₂²×C₄	—	4	1	no	—
1083	C₂²×C₄	—	4	1	no	—
1084	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
1085	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
1086	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1087	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1088	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1089	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1090	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1091	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1092	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1093	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1094	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1095	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1096	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1097	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1098	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1099	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1100	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1101	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1102	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1103	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1104	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1105	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1106	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1107	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1108	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1109	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1110	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1111	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1112	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1113	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1114	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1115	C₄⋊C₄	—	2	2	no	—
1116	C₄⋊C₄	—	2	2	no	—
1117	C₄⋊C₄	—	2	2	no	—
1118	C₄⋊C₄	—	2	2	no	—
1119	C₄⋊C₄	—	2	2	no	—
1120	C₄⋊C₄	—	2	2	no	—
1121	C₄⋊C₄	—	2	2	no	—
1122	C₄⋊C₄	—	2	2	no	—
1123	C₄⋊C₄	—	4	1	no	—
1124	C₄⋊C₄	—	4	1	no	—
1125	C₄⋊C₄	—	4	1	no	—
1126	C₄⋊C₄	—	4	1	no	—
1127	C₄⋊C₄	—	4	1	no	—
1128	C₄⋊C₄	—	4	1	no	—
1129	C₄⋊C₄	—	4	1	no	—
1130	C₄⋊C₄	—	4	1	no	—
1131	C₄⋊C₄	—	4	1	no	—
1132	C₄⋊C₄	—	4	1	no	—
1133	C₄⋊C₄	—	4	1	no	—
1134	C₄⋊C₄	—	4	1	no	—
1135	C₄⋊C₄	—	4	1	no	—
1136	C₄⋊C₄	—	4	1	no	—
1137	C₄⋊C₄	—	4	1	no	—
1138	C₄⋊C₄	—	4	1	no	—
1139	C₄⋊C₄	—	4	1	no	—
1140	C₄⋊C₄	—	4	1	no	—
1141	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1142	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1143	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1144	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1145	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1146	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1147	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1148	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1149	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1150	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1151	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1152	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1153	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1154	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1155	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1156	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1157	C₂²⋊C₄	—	2	2	no	—
1158	C₂²⋊C₄	—	2	2	no	—
1159	C₂²⋊C₄	—	2	2	no	—
1160	C₂²⋊C₄	—	2	2	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	C₂²×C₄×C₂₃	1	4	yes	—
1170	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1171	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1172	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1173	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1174	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1175	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1176	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1177	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1178	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1179	C₄²	—	2	2	no	—
1180	C₄²	—	2	2	no	—
1181	C₄²	—	2	2	no	—
1182	C₄²	—	2	2	no	—
1183	C₄²	—	2	2	no	—
1184	C₄²	—	4	1	no	—
1185	C₄²	—	4	1	no	—
1186	C₄²	—	4	1	no	—
1187	C₄²	—	4	1	no	—
1188	C₄²	—	4	1	no	—
1189	C₄²	—	4	1	no	—
1190	C₄²	—	4	1	no	—
1191	C₄²	—	4	1	no	—
1192	C₄²	—	4	1	no	—
1193	C₄²	—	4	1	no	—
1194	C₄²	—	4	1	no	—
1195	C₄²	—	4	1	no	—
1196	C₄²	—	4	1	no	—
1197	C₄²	—	4	1	no	—
1198	C₄²	—	4	1	no	—
1199	C₄²	—	4	1	no	—
1200	C₄²	—	4	1	no	—
1201	C₄²	—	4	1	no	—
1202	C₄²	—	4	1	no	—
1203	C₄²	—	4	1	no	—
1204	C₄²	—	4	1	no	—
1205	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
1206	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
1207	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
1208	C₂³	—	2	1	no	—
1209	C₂³	—	2	1	no	—
1210	C₂³	—	2	1	no	—
1211	C₂³	—	2	1	no	—
1212	C₂³	—	2	1	no	—
1213	C₂³	—	2	1	no	—
1214	C₂³	—	2	1	no	—
1215	C₂³	—	2	1	no	—
1216	C₂³	—	2	1	no	—
1217	C₂³	—	2	1	no	—
1218	C₂³	—	2	1	no	—
1219	C₂³	—	2	1	no	—
1220	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
1221	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
1222	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
1223	Q₈	—	4	4	no	—
1224	Q₈	—	4	4	no	—
1225	Q₈	—	4	4	no	—
1226	D₄	—	4	4	no	—
1227	C₂×C₄	—	2	1	no	—
1228	C₂×C₄	—	2	1	no	—
1229	C₂×C₄	—	2	1	no	—
1230	C₂×C₄	—	2	1	no	—
1231	C₂×C₄	—	2	1	no	—
1232	C₂×C₄	—	2	1	no	—
1233	C₂×C₄	—	2	1	no	—
1234	C₂×C₄	—	2	1	no	—
1235	C₂×C₄	—	2	1	no	—
1236	C₂×C₄	—	2	1	no	—
1237	C₂×C₄	—	2	1	no	—
1238	C₂×C₄	—	2	1	no	—
1239	C₂×C₄	—	2	1	no	—
1240	C₂×C₄	—	2	1	no	—
1241	C₂×C₄	—	2	1	no	—
1242	C₂×C₄	—	2	1	no	—
1243	C₂×C₄	—	2	1	no	—
1244	C₂×C₄	—	2	1	no	—
1245	C₂×C₄	—	2	1	no	—
1246	C₂×C₄	—	2	1	no	—
1247	C₂×C₄	—	2	1	no	—
1248	C₂×C₄	—	2	1	no	—
1249	C₂×C₄	—	2	1	no	—
1250	C₂×C₄	—	2	1	no	—
1251	C₂×C₄	—	2	1	no	—
1252	C₂×C₄	—	2	1	no	—
1253	C₂×C₄	—	2	1	no	—
1254	C₂×C₄	—	2	1	no	—
1255	C₂×C₄	—	2	1	no	—
1256	C₂×C₄	—	2	1	no	—
1257	C₂×C₄	—	2	1	no	—
1258	C₂×C₄	—	2	1	no	—
1259	C₂×C₄	—	2	1	no	—
1260	C₂×C₄	—	2	1	no	—
1261	C₂×C₄	—	2	1	no	—
1262	C₂×C₄	—	2	1	no	—
1263	C₂×C₄	—	2	1	no	—
1264	C₂×C₄	—	2	1	no	—
1265	C₂×C₄	—	2	1	no	—
1266	C₂×C₄	—	2	1	no	—
1267	C₂×C₄	—	2	1	no	—
1268	C₂×C₄	—	2	1	no	—
1269	C₂×C₄	—	2	1	no	—
1270	C₂×C₄	—	2	1	no	—
1271	C₂×C₄	—	2	1	no	—
1272	C₂×C₄	—	2	1	no	—
1273	C₂×C₄	—	2	1	no	—
1274	C₂×C₄	—	2	1	no	—
1275	C₂×C₄	—	2	1	no	—
1276	C₂×C₄	—	2	1	no	—
1277	C₂×C₄	—	2	1	no	—
1278	C₂×C₄	—	2	1	no	—
1279	C₂×C₄	—	2	1	no	—
1280	C₂×C₄	—	2	1	no	—
1281	C₂×C₄	—	2	1	no	—
1282	C₂×C₄	—	2	1	no	—
1283	C₂×C₄	—	2	1	no	—
1284	C₂×C₄	—	2	1	no	—
1285	C₂×C₄	—	2	1	no	—
1286	C₂×C₄	—	2	1	no	—
1287	C₂×C₄	—	2	1	no	—
1288	C₂×C₄	—	2	1	no	—
1289	C₂×C₄	—	2	1	no	—
1290	C₂×C₄	—	2	1	no	—
1291	C₂×C₄	—	2	1	no	—
1292	C₂×C₄	—	2	1	no	—
1293	C₂×C₄	—	2	1	no	—
1294	C₂×C₄	—	2	1	no	—
1295	C₂×C₄	—	2	1	no	—
1296	C₂×C₄	—	2	1	no	—
1297	C₂×C₄	—	2	1	no	—
1298	C₂×C₄	—	4	4	no	—
1299	C₂×C₄	—	4	4	no	—
1300	C₂×C₄	—	8	2	no	—
1301	C₂×C₄	—	8	2	no	—
1302	C₂×C₄	—	8	2	no	—
1303	C₂×C₄	—	8	2	no	—
1304	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1305	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1306	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1307	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1308	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1309	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1310	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1311	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1312	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1313	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1314	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1315	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1316	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1317	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1318	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
1319	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
1320	C₂²	—	2	2	no	—
1321	C₂²	—	2	2	no	—
1322	C₂²	—	2	2	no	—
1323	C₂²	—	2	2	no	—
1324	C₂²	—	2	2	no	—
1325	C₂²	—	2	2	no	—
1326	C₂²	—	4	1	no	—
1327	C₂²	—	4	1	no	—
1328	C₂²	—	4	1	no	—
1329	C₂²	—	4	1	no	—
1330	C₂²	—	4	1	no	—
1331	C₂²	—	4	1	no	—
1332	C₂²	—	4	1	no	—
1333	C₂²	—	4	1	no	—
1334	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
1335	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1336	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1337	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1338	C₂²	C₂₃×#585	1	1	yes	characteristic
1339	C₂²	C₂₃×#585	1	1	yes	characteristic
1340	C₂²	C₂₃×#585	1	1	yes	characteristic
1341	C₄	—	2	2	no	—
1342	C₄	—	2	2	no	—
1343	C₄	—	2	2	no	—
1344	C₄	—	2	2	no	—
1345	C₄	—	2	2	no	—
1346	C₄	—	2	2	no	—
1347	C₄	—	2	2	no	—
1348	C₄	—	2	2	no	—
1349	C₄	—	2	2	no	—
1350	C₄	—	2	2	no	—
1351	C₄	—	2	2	no	—
1352	C₄	—	2	2	no	—
1353	C₄	—	2	2	no	—
1354	C₄	—	2	2	no	—
1355	C₄	—	2	2	no	—
1356	C₄	—	2	2	no	—
1357	C₄	—	4	1	no	—
1358	C₄	—	4	1	no	—
1359	C₄	—	4	1	no	—
1360	C₄	—	4	1	no	—
1361	C₄	—	4	1	no	—
1362	C₄	—	4	1	no	—
1363	C₄	—	4	1	no	—
1364	C₄	—	4	1	no	—
1365	C₄	—	4	1	no	—
1366	C₄	—	4	1	no	—
1367	C₄	—	4	1	no	—
1368	C₄	—	4	1	no	—
1369	C₄	—	4	1	no	—
1370	C₂	—	4	2	no	—
1371	C₂	—	4	2	no	—
1372	C₂	C₄×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1373	C₂	C₄×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1374	C₂	C₄×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1375	C₂	C₂₃×#3552	1	1	yes	characteristic
1376	C₂	C₂₃×#3557	1	1	yes	characteristic
1377	C₂	C₂₃×#3560	1	1	yes	characteristic
1378	C₂	C₂₃×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂²×D₄×C₂₃	C₂³
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×#2383	C₂	semidirect
4. C₂₃×#2381	C₂	semidirect
6. C₂₃×#2373	C₂	semidirect
7. C₂₃×#2373	C₂	semidirect
8. C₂₃×#2370	C₂	semidirect
9. C₂₃×#2370	C₂	semidirect
10. C₂₃×#2368	C₂	semidirect
12. C₂₃×#2365	C₂	semidirect
13. C₂₃×#2362	C₂	semidirect
14. C₂₃×#2360	C₂	semidirect
15. C₂₃×#2360	C₂	semidirect
18. C₂₃×#2336	C₂	semidirect
19. C₂₃×#2336	C₂	semidirect
21. C₂₃×#2334	C₂	semidirect
22. C₂₃×#2334	C₂	semidirect
23. C₂₃×#2332	C₂	semidirect
24. C₂₃×#2332	C₂	semidirect
25. C₂₃×#2331	C₂	semidirect
26. C₂₃×#2329	C₂	semidirect
27. C₂₃×#2323	C₂	semidirect
29. C₄×C₂₃×C₄⋊Q₈	C₂	semidirect
30. C₄×C₂₃×#126	C₂	semidirect
31. C₄×C₂₃×#126	C₂	semidirect
32. C₂₃×#563	C₄	semidirect
198. C₂₃×C₄⋊Q₈	C₂×C₄	semidirect
199. C₂₃×C₄⋊Q₈	C₂×C₄	semidirect
200. C₂₃×#126	C₂×C₄	semidirect
201. C₂₃×#126	C₂×C₄	semidirect
202. C₂₃×#126	C₂×C₄	semidirect
203. C₂₃×#126	C₂×C₄	semidirect
204. C₂₃×#125	C₂×C₄	semidirect
205. C₂₃×#125	C₂×C₄	semidirect
209. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
210. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
211. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
212. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
518. #34525	C₂₃	direct (N × H)
632. #2383	C₂×C₂₃	semidirect
633. #2383	C₂×C₂₃	semidirect
634. #2381	C₂×C₂₃	semidirect
636. #2373	C₂×C₂₃	semidirect
637. #2373	C₂×C₂₃	semidirect
638. #2370	C₂×C₂₃	semidirect
639. #2370	C₂×C₂₃	semidirect
640. #2368	C₂×C₂₃	semidirect
642. #2365	C₂×C₂₃	semidirect
643. #2362	C₂×C₂₃	semidirect
644. #2360	C₂×C₂₃	semidirect
645. #2360	C₂×C₂₃	semidirect
648. #2336	C₂×C₂₃	semidirect
649. #2336	C₂×C₂₃	semidirect
651. #2334	C₂×C₂₃	semidirect
652. #2334	C₂×C₂₃	semidirect
653. #2332	C₂×C₂₃	semidirect
654. #2332	C₂×C₂₃	semidirect
655. #2331	C₂×C₂₃	semidirect
656. #2329	C₂×C₂₃	semidirect
657. #2323	C₂×C₂₃	semidirect
659. C₄×C₄⋊Q₈	C₂×C₂₃	semidirect
660. C₄×#126	C₂×C₂₃	semidirect
661. C₄×#126	C₂×C₂₃	semidirect
712. #563	C₄×C₂₃	semidirect
887. C₄⋊Q₈	C₂×C₄×C₂₃	semidirect
888. C₄⋊Q₈	C₂×C₄×C₂₃	semidirect
889. #126	C₂×C₄×C₂₃	semidirect
890. #126	C₂×C₄×C₂₃	semidirect
891. #126	C₂×C₄×C₂₃	semidirect
892. #126	C₂×C₄×C₂₃	semidirect
893. #125	C₂×C₄×C₂₃	semidirect
894. #125	C₂×C₄×C₂₃	semidirect
898. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
899. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
900. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
901. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
1053. C₂₃	#34525	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×#563	2
C₂₃×#2383	2
C₂₃×#2381	2
C₂₃×#2374	2
C₂₃×#2373	2
C₂₃×#2370	2
C₂₃×#2368	2
C₂₃×#2367	2
C₂₃×#2365	2
C₂₃×#2362	2
C₂₃×#2360	2
C₂₃×#2359	2
C₂₃×#2337	2
C₂₃×#2336	2
C₂₃×#2335	2
C₂₃×#2334	2
C₂₃×#2332	2
C₂₃×#2331	2
C₂₃×#2329	2
C₂₃×#2323	2
C₂₃×#2322	2
C₄×C₂₃×C₄⋊Q₈	2
C₄×C₂₃×#126	2
#34525	23

Subgroups — C23×#34525 #19182151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34525 #19182151