Subgroups — C₂₃×#34414 #19182040

Order 5888.

2494 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#537	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2378	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2377	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2368	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2363	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2362	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2361	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2345	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2344	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2341	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2339	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2333	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2333	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2325	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2324	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2324	C₂	1	2	yes	maximal, complemented
19	C₂₃×#2323	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2311	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₂₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2297	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
26	C₂₃×#537	C₄	1	16	yes	complemented
27	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#121	C₂²	1	2	yes	—
32	C₂×C₂₃×#121	C₂²	1	2	yes	—
33	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#121	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
41	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×#117	C₂²	1	2	yes	—
44	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
47	C₂₃×#391	C₂²	1	1	yes	characteristic
48	C₂₃×#391	C₂²	1	1	yes	characteristic
49	C₂₃×#391	C₂²	1	1	yes	characteristic
50	C₂₃×#391	C₂²	1	2	yes	—
51	C₂₃×#391	C₂²	1	1	yes	characteristic
52	C₂₃×#390	C₂²	1	1	yes	characteristic
53	C₂₃×#390	C₂²	1	1	yes	characteristic
54	C₂₃×#390	C₂²	1	1	yes	characteristic
55	C₂₃×#390	C₂²	1	2	yes	—
56	C₂₃×#390	C₂²	1	2	yes	—
57	C₂₃×#390	C₂²	1	1	yes	characteristic
58	C₂₃×#390	C₂²	1	2	yes	—
59	C₂₃×#390	C₂²	1	2	yes	—
60	C₂₃×#390	C₂²	1	2	yes	—
61	C₂₃×#389	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	2	yes	—
65	C₂₃×#389	C₂²	1	1	yes	characteristic
66	C₂₃×#389	C₂²	1	2	yes	—
67	C₂₃×#388	C₂²	1	2	yes	—
68	C₂₃×#388	C₂²	1	2	yes	—
69	C₂₃×#388	C₂²	1	2	yes	—
70	C₂₃×#388	C₂²	1	2	yes	—
71	C₂₃×#388	C₂²	1	2	yes	—
72	C₂₃×#388	C₂²	1	2	yes	—
73	C₂₃×#388	C₂²	1	2	yes	—
74	C₂₃×#388	C₂²	1	2	yes	—
75	C₂₃×#387	C₂²	1	2	yes	—
76	C₂₃×#387	C₂²	1	2	yes	—
77	C₂₃×#387	C₂²	1	2	yes	—
78	C₂₃×#387	C₂²	1	2	yes	—
79	C₂₃×#387	C₂²	1	2	yes	—
80	C₂₃×#387	C₂²	1	2	yes	—
81	C₂₃×#387	C₂²	1	2	yes	—
82	C₂₃×#387	C₂²	1	2	yes	—
83	C₂₃×#386	C₂²	1	1	yes	characteristic
84	C₂₃×#386	C₂²	1	1	yes	characteristic
85	C₂₃×#386	C₂²	1	1	yes	characteristic
86	C₂₃×#386	C₂²	1	1	yes	characteristic
87	C₂₃×#386	C₂²	1	2	yes	—
88	C₂₃×#386	C₂²	1	2	yes	—
89	C₂₃×#386	C₂²	1	2	yes	—
90	C₂₃×#386	C₂²	1	2	yes	—
91	C₂₃×#386	C₂²	1	2	yes	—
92	C₂₃×#386	C₂²	1	2	yes	—
93	C₂₃×#386	C₂²	1	2	yes	—
94	C₂₃×#386	C₂²	1	2	yes	—
95	C₂₃×#385	C₂²	1	2	yes	—
96	C₂₃×#385	C₂²	1	2	yes	—
97	C₂₃×#385	C₂²	1	2	yes	—
98	C₂₃×#385	C₂²	1	2	yes	—
99	C₂₃×#381	C₂²	1	2	yes	—
100	C₂₃×#381	C₂²	1	2	yes	—
101	C₂₃×#380	C₂²	1	1	yes	characteristic
102	C₂₃×#380	C₂²	1	1	yes	characteristic
103	C₂₃×#380	C₂²	1	1	yes	characteristic
104	C₂₃×#380	C₂²	1	1	yes	characteristic
105	C₂₃×#380	C₂²	1	2	yes	—
106	C₂₃×#380	C₂²	1	2	yes	—
107	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
122	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
123	C₂×C₂₃×#95	C₂²	1	2	yes	—
124	C₂×#41×C₂₃	—	4	2	no	—
125	C₂×#41×C₂₃	—	4	2	no	—
126	C₂×#41×C₂₃	—	4	2	no	—
127	C₂×#41×C₂₃	—	4	2	no	—
128	C₂×#41×C₂₃	C₂×C₄	1	8	yes	complemented
129	C₂×#41×C₂₃	C₂×C₄	1	8	yes	complemented
130	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
137	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
138	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
139	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
143	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
146	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
147	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
148	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
149	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
150	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
151	C₂₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
152	C₂₃×#121	C₂×C₄	1	8	yes	complemented
153	C₂₃×#121	C₂×C₄	1	8	yes	complemented
154	C₂₃×#121	C₂×C₄	1	16	yes	complemented
155	C₂₃×#121	C₂×C₄	1	16	yes	complemented
156	C₂₃×#121	C₂×C₄	1	16	yes	complemented
157	C₄×Q₈×C₂₃	—	4	2	no	—
158	C₄×Q₈×C₂₃	—	4	2	no	—
159	C₄×D₄×C₂₃	—	4	2	no	—
160	C₄×D₄×C₂₃	—	4	2	no	—
161	C₄×D₄×C₂₃	—	4	4	no	—
162	C₄×D₄×C₂₃	—	4	4	no	—
163	C₂₃×#117	—	4	2	no	—
164	C₂₃×#117	—	4	4	no	—
165	C₂₃×#117	—	4	2	no	—
166	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
167	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	8	yes	complemented
168	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
211	C₂×C₄²×C₂₃	—	4	2	no	—
212	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
217	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
218	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
219	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
221	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
222	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
223	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
224	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
225	C₂₃×#95	C₂³	1	1	yes	characteristic
226	C₂₃×#95	C₂³	1	2	yes	—
227	C₂₃×#95	C₂³	1	2	yes	—
228	C₂₃×#95	C₂³	1	2	yes	—
229	C₂₃×#95	C₂³	1	2	yes	—
230	C₂₃×#95	C₂³	1	1	yes	characteristic
231	C₂₃×#95	C₂³	1	1	yes	characteristic
232	C₂₃×#95	C₂³	1	1	yes	characteristic
233	C₂₃×#95	C₂³	1	1	yes	characteristic
234	C₂₃×#95	C₂³	1	2	yes	—
235	C₂₃×#95	C₂³	1	2	yes	—
236	C₂₃×#95	C₂³	1	1	yes	characteristic
237	C₂₃×#95	C₂³	1	2	yes	—
238	C₂₃×#95	C₂³	1	2	yes	—
239	C₂₃×#95	C₂³	1	2	yes	—
240	C₂₃×#95	C₂³	1	2	yes	—
241	C₂₃×#95	C₂³	1	2	yes	—
242	C₂₃×#95	C₂³	1	1	yes	characteristic
243	C₂₃×#95	C₂³	1	1	yes	characteristic
244	C₂₃×#95	C₂³	1	2	yes	—
245	C₂₃×#95	C₂³	1	2	yes	—
246	C₂₃×#95	C₂³	1	2	yes	—
247	C₂₃×#95	C₂³	1	2	yes	—
248	C₂₃×#95	C₂³	1	2	yes	—
249	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
250	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
251	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
252	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
253	#41×C₂₃	—	4	16	no	—
254	#41×C₂₃	—	4	16	no	—
255	C₂×Q₈×C₂₃	—	2	2	no	—
256	C₂×Q₈×C₂₃	—	2	2	no	—
257	C₂×Q₈×C₂₃	—	4	1	no	—
258	C₂×Q₈×C₂₃	—	4	1	no	—
259	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
260	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
261	C₂×D₄×C₂₃	—	2	2	no	—
262	C₂×D₄×C₂₃	—	2	2	no	—
263	C₂×D₄×C₂₃	—	4	2	no	—
264	C₂×D₄×C₂₃	—	4	2	no	—
265	C₂×D₄×C₂₃	—	4	2	no	—
266	C₂×D₄×C₂₃	—	4	2	no	—
267	C₂×D₄×C₂₃	—	4	1	no	—
268	C₂×D₄×C₂₃	—	4	1	no	—
269	C₂×D₄×C₂₃	—	4	2	no	—
270	C₂×D₄×C₂₃	—	4	2	no	—
271	C₂×D₄×C₂₃	—	4	1	no	—
272	C₂×D₄×C₂₃	—	4	1	no	—
273	C₂×D₄×C₂₃	—	4	1	no	—
274	C₂×D₄×C₂₃	—	4	1	no	—
275	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
276	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
277	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
278	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
279	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
280	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
281	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
282	C₂²×C₄×C₂₃	—	2	2	no	—
283	C₂²×C₄×C₂₃	—	2	2	no	—
284	C₂²×C₄×C₂₃	—	2	2	no	—
285	C₂²×C₄×C₂₃	—	2	2	no	—
286	C₂²×C₄×C₂₃	—	2	2	no	—
287	C₂²×C₄×C₂₃	—	2	2	no	—
288	C₂²×C₄×C₂₃	—	2	2	no	—
289	C₂²×C₄×C₂₃	—	2	2	no	—
290	C₂²×C₄×C₂₃	—	2	4	no	—
291	C₂²×C₄×C₂₃	—	4	1	no	—
292	C₂²×C₄×C₂₃	—	4	1	no	—
293	C₂²×C₄×C₂₃	—	4	2	no	—
294	C₂²×C₄×C₂₃	—	4	1	no	—
295	C₂²×C₄×C₂₃	—	4	2	no	—
296	C₂²×C₄×C₂₃	—	4	1	no	—
297	C₂²×C₄×C₂₃	—	4	2	no	—
298	C₂²×C₄×C₂₃	—	4	2	no	—
299	C₂²×C₄×C₂₃	—	4	2	no	—
300	C₂²×C₄×C₂₃	—	4	2	no	—
301	C₂²×C₄×C₂₃	—	4	2	no	—
302	C₂²×C₄×C₂₃	—	4	2	no	—
303	C₂²×C₄×C₂₃	—	4	2	no	—
304	C₂²×C₄×C₂₃	—	4	2	no	—
305	C₂²×C₄×C₂₃	—	4	2	no	—
306	C₂²×C₄×C₂₃	—	4	2	no	—
307	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
308	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
309	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
310	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
311	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
312	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
331	C₄⋊C₄×C₂₃	—	2	2	no	—
332	C₄⋊C₄×C₂₃	—	2	2	no	—
333	C₄⋊C₄×C₂₃	—	2	4	no	—
334	C₄⋊C₄×C₂₃	—	2	2	no	—
335	C₄⋊C₄×C₂₃	—	2	2	no	—
336	C₄⋊C₄×C₂₃	—	4	2	no	—
337	C₄⋊C₄×C₂₃	—	4	2	no	—
338	C₄⋊C₄×C₂₃	—	4	2	no	—
339	C₄⋊C₄×C₂₃	—	4	1	no	—
340	C₄⋊C₄×C₂₃	—	4	1	no	—
341	C₄⋊C₄×C₂₃	—	4	2	no	—
342	C₄⋊C₄×C₂₃	—	4	2	no	—
343	C₄⋊C₄×C₂₃	—	4	2	no	—
344	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
345	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
346	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
347	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
348	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
349	C₂²⋊C₄×C₂₃	—	2	2	no	—
350	C₂²⋊C₄×C₂₃	—	2	2	no	—
351	C₂²⋊C₄×C₂₃	—	2	2	no	—
352	C₂²⋊C₄×C₂₃	—	2	2	no	—
353	C₂²⋊C₄×C₂₃	—	2	4	no	—
354	C₂²⋊C₄×C₂₃	—	4	1	no	—
355	C₂²⋊C₄×C₂₃	—	4	2	no	—
356	C₂²⋊C₄×C₂₃	—	4	2	no	—
357	C₂²⋊C₄×C₂₃	—	4	1	no	—
358	C₂²⋊C₄×C₂₃	—	4	2	no	—
359	C₂²⋊C₄×C₂₃	—	4	1	no	—
360	C₂²⋊C₄×C₂₃	—	4	1	no	—
361	C₂²⋊C₄×C₂₃	—	4	1	no	—
362	C₂²⋊C₄×C₂₃	—	4	2	no	—
363	C₂²⋊C₄×C₂₃	—	4	1	no	—
364	C₂²⋊C₄×C₂₃	—	4	2	no	—
365	C₂²⋊C₄×C₂₃	—	4	2	no	—
366	C₂²⋊C₄×C₂₃	—	4	2	no	—
367	C₂²⋊C₄×C₂₃	—	4	2	no	—
368	C₂²⋊C₄×C₂₃	—	4	2	no	—
369	C₂²⋊C₄×C₂₃	—	4	2	no	—
370	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
371	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
372	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
373	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
374	C₄²×C₂₃	—	2	2	no	—
375	C₄²×C₂₃	—	2	2	no	—
376	C₄²×C₂₃	—	2	4	no	—
377	C₄²×C₂₃	—	2	2	no	—
378	C₄²×C₂₃	—	2	2	no	—
379	C₄²×C₂₃	—	4	1	no	—
380	C₄²×C₂₃	—	4	1	no	—
381	C₄²×C₂₃	—	4	2	no	—
382	C₄²×C₂₃	—	4	2	no	—
383	C₄²×C₂₃	—	4	2	no	—
384	C₄²×C₂₃	—	4	2	no	—
385	C₄²×C₂₃	—	4	2	no	—
386	C₄²×C₂₃	—	4	2	no	—
387	#34414	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
388	C₂³×C₂₃	—	2	1	no	—
389	C₂³×C₂₃	—	2	1	no	—
390	C₂³×C₂₃	—	2	1	no	—
391	C₂³×C₂₃	—	2	1	no	—
392	C₂³×C₂₃	—	2	1	no	—
393	C₂³×C₂₃	—	2	2	no	—
394	C₂³×C₂₃	—	2	2	no	—
395	C₂³×C₂₃	—	2	2	no	—
396	C₂³×C₂₃	—	2	1	no	—
397	C₂³×C₂₃	—	2	1	no	—
398	C₂³×C₂₃	—	2	1	no	—
399	C₂³×C₂₃	—	2	1	no	—
400	C₂³×C₂₃	—	2	1	no	—
401	C₂³×C₂₃	—	2	2	no	—
402	C₂³×C₂₃	—	2	1	no	—
403	C₂³×C₂₃	—	2	1	no	—
404	C₂³×C₂₃	—	2	1	no	—
405	C₂³×C₂₃	—	2	1	no	—
406	C₂³×C₂₃	—	2	1	no	—
407	C₂³×C₂₃	—	2	1	no	—
408	C₂³×C₂₃	—	2	2	no	—
409	C₂³×C₂₃	—	2	1	no	—
410	C₂³×C₂₃	—	2	1	no	—
411	C₂³×C₂₃	—	2	2	no	—
412	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
413	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
414	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
415	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
416	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
417	Q₈×C₂₃	—	2	8	no	—
418	Q₈×C₂₃	—	4	4	no	—
419	D₄×C₂₃	—	2	8	no	—
420	D₄×C₂₃	—	4	8	no	—
421	D₄×C₂₃	—	4	8	no	—
422	D₄×C₂₃	—	4	4	no	—
423	D₄×C₂₃	—	4	4	no	—
424	D₄×C₂₃	—	4	4	no	—
425	D₄×C₂₃	—	4	8	no	—
426	C₂×C₄×C₂₃	—	2	1	no	—
427	C₂×C₄×C₂₃	—	2	2	no	—
428	C₂×C₄×C₂₃	—	2	1	no	—
429	C₂×C₄×C₂₃	—	2	1	no	—
430	C₂×C₄×C₂₃	—	2	1	no	—
431	C₂×C₄×C₂₃	—	2	2	no	—
432	C₂×C₄×C₂₃	—	2	2	no	—
433	C₂×C₄×C₂₃	—	2	2	no	—
434	C₂×C₄×C₂₃	—	2	1	no	—
435	C₂×C₄×C₂₃	—	2	1	no	—
436	C₂×C₄×C₂₃	—	2	1	no	—
437	C₂×C₄×C₂₃	—	2	1	no	—
438	C₂×C₄×C₂₃	—	2	1	no	—
439	C₂×C₄×C₂₃	—	2	2	no	—
440	C₂×C₄×C₂₃	—	2	2	no	—
441	C₂×C₄×C₂₃	—	2	1	no	—
442	C₂×C₄×C₂₃	—	2	8	no	—
443	C₂×C₄×C₂₃	—	2	8	no	—
444	C₂×C₄×C₂₃	—	2	8	no	—
445	C₂×C₄×C₂₃	—	2	1	no	—
446	C₂×C₄×C₂₃	—	2	1	no	—
447	C₂×C₄×C₂₃	—	2	1	no	—
448	C₂×C₄×C₂₃	—	2	1	no	—
449	C₂×C₄×C₂₃	—	2	2	no	—
450	C₂×C₄×C₂₃	—	2	1	no	—
451	C₂×C₄×C₂₃	—	2	1	no	—
452	C₂×C₄×C₂₃	—	2	1	no	—
453	C₂×C₄×C₂₃	—	2	1	no	—
454	C₂×C₄×C₂₃	—	2	2	no	—
455	C₂×C₄×C₂₃	—	2	2	no	—
456	C₂×C₄×C₂₃	—	2	2	no	—
457	C₂×C₄×C₂₃	—	2	2	no	—
458	C₂×C₄×C₂₃	—	2	2	no	—
459	C₂×C₄×C₂₃	—	2	1	no	—
460	C₂×C₄×C₂₃	—	2	2	no	—
461	C₂×C₄×C₂₃	—	2	1	no	—
462	C₂×C₄×C₂₃	—	2	2	no	—
463	C₂×C₄×C₂₃	—	2	1	no	—
464	C₂×C₄×C₂₃	—	2	1	no	—
465	C₂×C₄×C₂₃	—	2	2	no	—
466	C₂×C₄×C₂₃	—	2	1	no	—
467	C₂×C₄×C₂₃	—	2	1	no	—
468	C₂×C₄×C₂₃	—	2	1	no	—
469	C₂×C₄×C₂₃	—	2	2	no	—
470	C₂×C₄×C₂₃	—	2	2	no	—
471	C₂×C₄×C₂₃	—	2	1	no	—
472	C₂×C₄×C₂₃	—	2	2	no	—
473	C₂×C₄×C₂₃	—	2	1	no	—
474	C₂×C₄×C₂₃	—	2	1	no	—
475	C₂×C₄×C₂₃	—	4	8	no	—
476	C₂×C₄×C₂₃	—	4	8	no	—
477	C₂×C₄×C₂₃	—	4	4	no	—
478	C₂×C₄×C₂₃	—	4	4	no	—
479	C₂×C₄×C₂₃	—	8	4	no	—
480	C₂×C₄×C₂₃	—	8	4	no	—
481	C₂×C₄×C₂₃	—	8	4	no	—
482	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
483	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
484	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
485	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
486	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
487	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
488	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
489	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
490	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
491	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
492	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
493	C₂×#537	C₂×C₂₃	1	1	yes	characteristic
494	#2378	C₂×C₂₃	1	2	yes	complemented
495	#2377	C₂×C₂₃	1	2	yes	complemented
496	#2368	C₂×C₂₃	1	2	yes	complemented
497	#2363	C₂×C₂₃	1	1	yes	characteristic, complemented
498	#2363	C₂×C₂₃	1	2	yes	complemented
499	#2362	C₂×C₂₃	1	1	yes	characteristic, complemented
500	#2361	C₂×C₂₃	1	1	yes	characteristic, complemented
501	#2360	C₂×C₂₃	1	1	yes	characteristic, complemented
502	#2345	C₂×C₂₃	1	1	yes	characteristic, complemented
503	#2344	C₂×C₂₃	1	1	yes	characteristic, complemented
504	#2341	C₂×C₂₃	1	1	yes	characteristic, complemented
505	#2339	C₂×C₂₃	1	1	yes	characteristic, complemented
506	#2333	C₂×C₂₃	1	2	yes	complemented
507	#2333	C₂×C₂₃	1	2	yes	complemented
508	#2325	C₂×C₂₃	1	2	yes	complemented
509	#2324	C₂×C₂₃	1	1	yes	characteristic, complemented
510	#2324	C₂×C₂₃	1	2	yes	complemented
511	#2323	C₂×C₂₃	1	1	yes	characteristic, complemented
512	#2311	C₂×C₂₃	1	1	yes	characteristic, complemented
513	C₄×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
514	C₄×#121	C₂×C₂₃	1	1	yes	characteristic, complemented
515	#2297	C₂×C₂₃	1	1	yes	characteristic, complemented
516	C₂²×C₂₃	—	2	2	no	—
517	C₂²×C₂₃	—	2	2	no	—
518	C₂²×C₂₃	—	2	2	no	—
519	C₂²×C₂₃	—	2	4	no	—
520	C₂²×C₂₃	—	2	2	no	—
521	C₂²×C₂₃	—	2	2	no	—
522	C₂²×C₂₃	—	2	2	no	—
523	C₂²×C₂₃	—	2	4	no	—
524	C₂²×C₂₃	—	2	2	no	—
525	C₂²×C₂₃	—	2	2	no	—
526	C₂²×C₂₃	—	2	4	no	—
527	C₂²×C₂₃	—	2	2	no	—
528	C₂²×C₂₃	—	4	1	no	—
529	C₂²×C₂₃	—	4	2	no	—
530	C₂²×C₂₃	—	4	1	no	—
531	C₂²×C₂₃	—	4	1	no	—
532	C₂²×C₂₃	—	4	1	no	—
533	C₂²×C₂₃	—	4	1	no	—
534	C₂²×C₂₃	—	4	2	no	—
535	C₂²×C₂₃	—	4	1	no	—
536	C₂²×C₂₃	—	4	1	no	—
537	C₂²×C₂₃	—	4	1	no	—
538	C₂²×C₂₃	—	4	1	no	—
539	C₂²×C₂₃	—	4	2	no	—
540	C₂²×C₂₃	—	4	2	no	—
541	C₂²×C₂₃	—	4	1	no	—
542	C₂²×C₂₃	—	4	1	no	—
543	C₂²×C₂₃	—	4	1	no	—
544	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
545	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
546	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
547	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
548	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
549	C₂²×C₂₃	#585	1	1	yes	characteristic
550	C₂²×C₂₃	#585	1	1	yes	characteristic
551	C₄×C₂₃	—	2	2	no	—
552	C₄×C₂₃	—	2	2	no	—
553	C₄×C₂₃	—	2	2	no	—
554	C₄×C₂₃	—	2	4	no	—
555	C₄×C₂₃	—	2	4	no	—
556	C₄×C₂₃	—	2	4	no	—
557	C₄×C₂₃	—	2	2	no	—
558	C₄×C₂₃	—	2	2	no	—
559	C₄×C₂₃	—	4	1	no	—
560	C₄×C₂₃	—	4	1	no	—
561	C₄×C₂₃	—	4	2	no	—
562	C₄×C₂₃	—	4	2	no	—
563	C₄×C₂₃	—	4	1	no	—
564	C₄×C₂₃	—	4	2	no	—
565	C₄×C₂₃	—	4	1	no	—
566	C₄×C₂₃	—	4	1	no	—
567	C₄×C₂₃	—	4	2	no	—
568	C₄×C₂₃	—	4	1	no	—
569	C₄×C₂₃	#518	1	4	yes	—
570	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
571	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
572	#537	C₄×C₂₃	1	16	yes	complemented
573	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
574	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
575	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
576	C₂×#121	C₂²×C₂₃	1	2	yes	—
577	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
578	C₂×#121	C₂²×C₂₃	1	2	yes	—
579	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
580	C₂×#121	C₂²×C₂₃	1	2	yes	—
581	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
582	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
583	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
584	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
585	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
586	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
587	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
588	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
589	C₂×#117	C₂²×C₂₃	1	2	yes	—
590	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
591	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
592	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
593	#391	C₂²×C₂₃	1	2	yes	—
594	#391	C₂²×C₂₃	1	1	yes	characteristic
595	#391	C₂²×C₂₃	1	1	yes	characteristic
596	#391	C₂²×C₂₃	1	1	yes	characteristic
597	#391	C₂²×C₂₃	1	1	yes	characteristic
598	#390	C₂²×C₂₃	1	2	yes	—
599	#390	C₂²×C₂₃	1	2	yes	—
600	#390	C₂²×C₂₃	1	1	yes	characteristic
601	#390	C₂²×C₂₃	1	2	yes	—
602	#390	C₂²×C₂₃	1	2	yes	—
603	#390	C₂²×C₂₃	1	2	yes	—
604	#390	C₂²×C₂₃	1	1	yes	characteristic
605	#390	C₂²×C₂₃	1	1	yes	characteristic
606	#390	C₂²×C₂₃	1	1	yes	characteristic
607	#389	C₂²×C₂₃	1	1	yes	characteristic
608	#389	C₂²×C₂₃	1	2	yes	—
609	#389	C₂²×C₂₃	1	1	yes	characteristic
610	#389	C₂²×C₂₃	1	2	yes	—
611	#389	C₂²×C₂₃	1	1	yes	characteristic
612	#389	C₂²×C₂₃	1	1	yes	characteristic
613	#388	C₂²×C₂₃	1	2	yes	—
614	#388	C₂²×C₂₃	1	2	yes	—
615	#388	C₂²×C₂₃	1	2	yes	—
616	#388	C₂²×C₂₃	1	2	yes	—
617	#388	C₂²×C₂₃	1	2	yes	—
618	#388	C₂²×C₂₃	1	2	yes	—
619	#388	C₂²×C₂₃	1	2	yes	—
620	#388	C₂²×C₂₃	1	2	yes	—
621	#387	C₂²×C₂₃	1	2	yes	—
622	#387	C₂²×C₂₃	1	2	yes	—
623	#387	C₂²×C₂₃	1	2	yes	—
624	#387	C₂²×C₂₃	1	2	yes	—
625	#387	C₂²×C₂₃	1	2	yes	—
626	#387	C₂²×C₂₃	1	2	yes	—
627	#387	C₂²×C₂₃	1	2	yes	—
628	#387	C₂²×C₂₃	1	2	yes	—
629	#386	C₂²×C₂₃	1	2	yes	—
630	#386	C₂²×C₂₃	1	2	yes	—
631	#386	C₂²×C₂₃	1	1	yes	characteristic
632	#386	C₂²×C₂₃	1	2	yes	—
633	#386	C₂²×C₂₃	1	2	yes	—
634	#386	C₂²×C₂₃	1	1	yes	characteristic
635	#386	C₂²×C₂₃	1	2	yes	—
636	#386	C₂²×C₂₃	1	1	yes	characteristic
637	#386	C₂²×C₂₃	1	1	yes	characteristic
638	#386	C₂²×C₂₃	1	2	yes	—
639	#386	C₂²×C₂₃	1	2	yes	—
640	#386	C₂²×C₂₃	1	2	yes	—
641	#385	C₂²×C₂₃	1	2	yes	—
642	#385	C₂²×C₂₃	1	2	yes	—
643	#385	C₂²×C₂₃	1	2	yes	—
644	#385	C₂²×C₂₃	1	2	yes	—
645	#381	C₂²×C₂₃	1	2	yes	—
646	#381	C₂²×C₂₃	1	2	yes	—
647	#380	C₂²×C₂₃	1	1	yes	characteristic
648	#380	C₂²×C₂₃	1	1	yes	characteristic
649	#380	C₂²×C₂₃	1	1	yes	characteristic
650	#380	C₂²×C₂₃	1	1	yes	characteristic
651	#380	C₂²×C₂₃	1	2	yes	—
652	#380	C₂²×C₂₃	1	2	yes	—
653	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
654	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
655	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
656	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
657	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
658	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
659	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
660	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
661	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
662	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
663	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
664	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
665	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
666	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
667	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
668	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
669	C₂×#95	C₂²×C₂₃	1	2	yes	—
670	C₂×C₂₃	—	4	2	no	—
671	C₂×C₂₃	—	4	2	no	—
672	C₂×C₂₃	—	4	2	no	—
673	C₂×C₂₃	—	4	4	no	—
674	C₂×C₂₃	C₂×#518	1	1	yes	characteristic
675	C₂×C₂₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
676	C₂×C₂₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
677	C₂×C₂₃	#3541	1	1	yes	characteristic
678	C₂×C₂₃	#3542	1	1	yes	characteristic
679	C₂×C₂₃	#3548	1	1	yes	characteristic
680	C₂×C₂₃	#3551	1	1	yes	characteristic
681	C₂×#41	—	4	2	no	—
682	C₂×#41	—	4	2	no	—
683	C₂×#41	—	4	2	no	—
684	C₂×#41	—	4	2	no	—
685	C₂×#41	C₂×C₄×C₂₃	1	8	yes	complemented
686	C₂×#41	C₂×C₄×C₂₃	1	8	yes	complemented
687	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
688	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
689	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
690	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
691	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
692	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
693	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
694	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
695	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
696	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
697	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
698	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
699	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
700	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
701	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
702	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
703	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
704	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
705	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
706	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
707	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
708	C₂²⋊Q₈	C₂×C₄×C₂₃	1	16	yes	complemented
709	#121	C₂×C₄×C₂₃	1	8	yes	complemented
710	#121	C₂×C₄×C₂₃	1	8	yes	complemented
711	#121	C₂×C₄×C₂₃	1	16	yes	complemented
712	#121	C₂×C₄×C₂₃	1	16	yes	complemented
713	#121	C₂×C₄×C₂₃	1	16	yes	complemented
714	C₄×Q₈	—	4	2	no	—
715	C₄×Q₈	—	4	2	no	—
716	C₄×D₄	—	4	2	no	—
717	C₄×D₄	—	4	2	no	—
718	C₄×D₄	—	4	4	no	—
719	C₄×D₄	—	4	4	no	—
720	#117	—	4	2	no	—
721	#117	—	4	4	no	—
722	#117	—	4	2	no	—
723	C₂×C₄⋊C₄	—	4	2	no	—
724	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	8	yes	complemented
725	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
726	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
727	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
728	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
729	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
730	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
731	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
732	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
733	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
734	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
735	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
736	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
737	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
738	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
739	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
740	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
741	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
742	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
743	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
744	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
745	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
747	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
748	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
750	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
752	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
759	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
760	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
761	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
762	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
764	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
765	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
766	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
767	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
768	C₂×C₄²	—	4	2	no	—
769	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
770	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
771	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
772	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
773	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
774	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
775	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
776	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
777	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
778	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
779	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
780	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
781	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
782	#95	C₂³×C₂₃	1	1	yes	characteristic
783	#95	C₂³×C₂₃	1	2	yes	—
784	#95	C₂³×C₂₃	1	2	yes	—
785	#95	C₂³×C₂₃	1	2	yes	—
786	#95	C₂³×C₂₃	1	2	yes	—
787	#95	C₂³×C₂₃	1	1	yes	characteristic
788	#95	C₂³×C₂₃	1	1	yes	characteristic
789	#95	C₂³×C₂₃	1	1	yes	characteristic
790	#95	C₂³×C₂₃	1	2	yes	—
791	#95	C₂³×C₂₃	1	1	yes	characteristic
792	#95	C₂³×C₂₃	1	2	yes	—
793	#95	C₂³×C₂₃	1	1	yes	characteristic
794	#95	C₂³×C₂₃	1	2	yes	—
795	#95	C₂³×C₂₃	1	2	yes	—
796	#95	C₂³×C₂₃	1	2	yes	—
797	#95	C₂³×C₂₃	1	2	yes	—
798	#95	C₂³×C₂₃	1	2	yes	—
799	#95	C₂³×C₂₃	1	1	yes	characteristic
800	#95	C₂³×C₂₃	1	1	yes	characteristic
801	#95	C₂³×C₂₃	1	2	yes	—
802	#95	C₂³×C₂₃	1	2	yes	—
803	#95	C₂³×C₂₃	1	2	yes	—
804	#95	C₂³×C₂₃	1	2	yes	—
805	#95	C₂³×C₂₃	1	2	yes	—
806	C₂₃	#34414	1	1	yes	characteristic, direct product factor, Sylow
807	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
808	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
809	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
810	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
811	#41	—	4	16	no	—
812	#41	—	4	16	no	—
813	C₂×Q₈	—	2	2	no	—
814	C₂×Q₈	—	2	2	no	—
815	C₂×Q₈	—	4	1	no	—
816	C₂×Q₈	—	4	1	no	—
817	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
818	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	4	2	no	—
822	C₂×D₄	—	4	2	no	—
823	C₂×D₄	—	4	1	no	—
824	C₂×D₄	—	4	1	no	—
825	C₂×D₄	—	4	2	no	—
826	C₂×D₄	—	4	2	no	—
827	C₂×D₄	—	4	1	no	—
828	C₂×D₄	—	4	1	no	—
829	C₂×D₄	—	4	1	no	—
830	C₂×D₄	—	4	1	no	—
831	C₂×D₄	—	4	2	no	—
832	C₂×D₄	—	4	2	no	—
833	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
834	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
835	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
836	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
837	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
838	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
839	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	2	no	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	2	2	no	—
846	C₂²×C₄	—	2	2	no	—
847	C₂²×C₄	—	2	2	no	—
848	C₂²×C₄	—	2	4	no	—
849	C₂²×C₄	—	4	1	no	—
850	C₂²×C₄	—	4	1	no	—
851	C₂²×C₄	—	4	2	no	—
852	C₂²×C₄	—	4	2	no	—
853	C₂²×C₄	—	4	2	no	—
854	C₂²×C₄	—	4	1	no	—
855	C₂²×C₄	—	4	2	no	—
856	C₂²×C₄	—	4	1	no	—
857	C₂²×C₄	—	4	2	no	—
858	C₂²×C₄	—	4	2	no	—
859	C₂²×C₄	—	4	2	no	—
860	C₂²×C₄	—	4	2	no	—
861	C₂²×C₄	—	4	2	no	—
862	C₂²×C₄	—	4	2	no	—
863	C₂²×C₄	—	4	2	no	—
864	C₂²×C₄	—	4	2	no	—
865	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
866	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
867	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
868	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
869	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
870	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
872	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
873	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
874	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
877	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
878	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
880	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
882	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
883	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
884	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
885	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
886	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
888	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	4	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	4	2	no	—
895	C₄⋊C₄	—	4	2	no	—
896	C₄⋊C₄	—	4	1	no	—
897	C₄⋊C₄	—	4	1	no	—
898	C₄⋊C₄	—	4	2	no	—
899	C₄⋊C₄	—	4	2	no	—
900	C₄⋊C₄	—	4	2	no	—
901	C₄⋊C₄	—	4	2	no	—
902	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
903	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
904	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
905	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
906	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	4	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	4	1	no	—
913	C₂²⋊C₄	—	4	2	no	—
914	C₂²⋊C₄	—	4	1	no	—
915	C₂²⋊C₄	—	4	2	no	—
916	C₂²⋊C₄	—	4	2	no	—
917	C₂²⋊C₄	—	4	2	no	—
918	C₂²⋊C₄	—	4	2	no	—
919	C₂²⋊C₄	—	4	2	no	—
920	C₂²⋊C₄	—	4	2	no	—
921	C₂²⋊C₄	—	4	1	no	—
922	C₂²⋊C₄	—	4	2	no	—
923	C₂²⋊C₄	—	4	2	no	—
924	C₂²⋊C₄	—	4	1	no	—
925	C₂²⋊C₄	—	4	2	no	—
926	C₂²⋊C₄	—	4	1	no	—
927	C₂²⋊C₄	—	4	1	no	—
928	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
929	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
930	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
931	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
932	C₄²	—	2	2	no	—
933	C₄²	—	2	2	no	—
934	C₄²	—	2	4	no	—
935	C₄²	—	2	2	no	—
936	C₄²	—	2	2	no	—
937	C₄²	—	4	1	no	—
938	C₄²	—	4	1	no	—
939	C₄²	—	4	2	no	—
940	C₄²	—	4	2	no	—
941	C₄²	—	4	2	no	—
942	C₄²	—	4	2	no	—
943	C₄²	—	4	2	no	—
944	C₄²	—	4	2	no	—
945	C₂³	—	2	1	no	—
946	C₂³	—	2	1	no	—
947	C₂³	—	2	1	no	—
948	C₂³	—	2	1	no	—
949	C₂³	—	2	1	no	—
950	C₂³	—	2	2	no	—
951	C₂³	—	2	2	no	—
952	C₂³	—	2	2	no	—
953	C₂³	—	2	1	no	—
954	C₂³	—	2	1	no	—
955	C₂³	—	2	1	no	—
956	C₂³	—	2	1	no	—
957	C₂³	—	2	1	no	—
958	C₂³	—	2	2	no	—
959	C₂³	—	2	1	no	—
960	C₂³	—	2	1	no	—
961	C₂³	—	2	1	no	—
962	C₂³	—	2	1	no	—
963	C₂³	—	2	1	no	—
964	C₂³	—	2	1	no	—
965	C₂³	—	2	2	no	—
966	C₂³	—	2	1	no	—
967	C₂³	—	2	1	no	—
968	C₂³	—	2	2	no	—
969	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
970	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
971	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
972	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
973	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
974	Q₈	—	2	8	no	—
975	Q₈	—	4	4	no	—
976	D₄	—	2	8	no	—
977	D₄	—	4	4	no	—
978	D₄	—	4	4	no	—
979	D₄	—	4	4	no	—
980	D₄	—	4	8	no	—
981	D₄	—	4	8	no	—
982	D₄	—	4	8	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	8	no	—
1000	C₂×C₄	—	2	8	no	—
1001	C₂×C₄	—	2	8	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	4	8	no	—
1033	C₂×C₄	—	4	8	no	—
1034	C₂×C₄	—	4	4	no	—
1035	C₂×C₄	—	4	4	no	—
1036	C₂×C₄	—	8	4	no	—
1037	C₂×C₄	—	8	4	no	—
1038	C₂×C₄	—	8	4	no	—
1039	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
1040	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
1041	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1042	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1043	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
1044	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1045	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1046	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1047	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1048	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1049	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	2	4	no	—
1054	C₂²	—	2	2	no	—
1055	C₂²	—	2	2	no	—
1056	C₂²	—	2	2	no	—
1057	C₂²	—	2	4	no	—
1058	C₂²	—	2	2	no	—
1059	C₂²	—	2	2	no	—
1060	C₂²	—	2	4	no	—
1061	C₂²	—	2	2	no	—
1062	C₂²	—	4	1	no	—
1063	C₂²	—	4	2	no	—
1064	C₂²	—	4	1	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	1	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	4	1	no	—
1070	C₂²	—	4	1	no	—
1071	C₂²	—	4	1	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	1	no	—
1076	C₂²	—	4	1	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
1079	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1080	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1081	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1082	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1083	C₂²	C₂₃×#585	1	1	yes	characteristic
1084	C₂²	C₂₃×#585	1	1	yes	characteristic
1085	C₄	—	2	2	no	—
1086	C₄	—	2	2	no	—
1087	C₄	—	2	2	no	—
1088	C₄	—	2	4	no	—
1089	C₄	—	2	4	no	—
1090	C₄	—	2	4	no	—
1091	C₄	—	2	2	no	—
1092	C₄	—	2	2	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	1	no	—
1095	C₄	—	4	2	no	—
1096	C₄	—	4	2	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	2	no	—
1099	C₄	—	4	1	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	2	no	—
1102	C₄	—	4	1	no	—
1103	C₄	C₂₃×#518	1	4	yes	—
1104	C₂	—	4	2	no	—
1105	C₂	—	4	2	no	—
1106	C₂	—	4	2	no	—
1107	C₂	—	4	4	no	—
1108	C₂	C₂×C₂₃×#518	1	1	yes	characteristic
1109	C₂	C₄×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1110	C₂	C₄×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1111	C₂	C₂₃×#3541	1	1	yes	characteristic
1112	C₂	C₂₃×#3542	1	1	yes	characteristic
1113	C₂	C₂₃×#3548	1	1	yes	characteristic
1114	C₂	C₂₃×#3551	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×#537	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×#2378	C₂	semidirect
3. C₂₃×#2377	C₂	semidirect
4. C₂₃×#2368	C₂	semidirect
5. C₂₃×#2363	C₂	semidirect
6. C₂₃×#2363	C₂	semidirect
7. C₂₃×#2362	C₂	semidirect
8. C₂₃×#2361	C₂	semidirect
9. C₂₃×#2360	C₂	semidirect
10. C₂₃×#2345	C₂	semidirect
11. C₂₃×#2344	C₂	semidirect
12. C₂₃×#2341	C₂	semidirect
13. C₂₃×#2339	C₂	semidirect
14. C₂₃×#2333	C₂	semidirect
15. C₂₃×#2333	C₂	semidirect
16. C₂₃×#2325	C₂	semidirect
17. C₂₃×#2324	C₂	semidirect
18. C₂₃×#2324	C₂	semidirect
19. C₂₃×#2323	C₂	semidirect
20. C₂₃×#2311	C₂	semidirect
21. C₄×C₂₃×C₂²⋊Q₈	C₂	semidirect
22. C₄×C₂₃×#121	C₂	semidirect
23. C₂₃×#2297	C₂	semidirect
26. C₂₃×#537	C₄	semidirect
128. C₂×#41×C₂₃	C₂×C₄	semidirect
129. C₂×#41×C₂₃	C₂×C₄	semidirect
149. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
150. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
151. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
152. C₂₃×#121	C₂×C₄	semidirect
153. C₂₃×#121	C₂×C₄	semidirect
154. C₂₃×#121	C₂×C₄	semidirect
155. C₂₃×#121	C₂×C₄	semidirect
156. C₂₃×#121	C₂×C₄	semidirect
167. C₂×C₄⋊C₄×C₂₃	C₂×C₄	semidirect
387. #34414	C₂₃	direct (N × H)
494. #2378	C₂×C₂₃	semidirect
495. #2377	C₂×C₂₃	semidirect
496. #2368	C₂×C₂₃	semidirect
497. #2363	C₂×C₂₃	semidirect
498. #2363	C₂×C₂₃	semidirect
499. #2362	C₂×C₂₃	semidirect
500. #2361	C₂×C₂₃	semidirect
501. #2360	C₂×C₂₃	semidirect
502. #2345	C₂×C₂₃	semidirect
503. #2344	C₂×C₂₃	semidirect
504. #2341	C₂×C₂₃	semidirect
505. #2339	C₂×C₂₃	semidirect
506. #2333	C₂×C₂₃	semidirect
507. #2333	C₂×C₂₃	semidirect
508. #2325	C₂×C₂₃	semidirect
509. #2324	C₂×C₂₃	semidirect
510. #2324	C₂×C₂₃	semidirect
511. #2323	C₂×C₂₃	semidirect
512. #2311	C₂×C₂₃	semidirect
513. C₄×C₂²⋊Q₈	C₂×C₂₃	semidirect
514. C₄×#121	C₂×C₂₃	semidirect
515. #2297	C₂×C₂₃	semidirect
572. #537	C₄×C₂₃	semidirect
685. C₂×#41	C₂×C₄×C₂₃	semidirect
686. C₂×#41	C₂×C₄×C₂₃	semidirect
706. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
707. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
708. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
709. #121	C₂×C₄×C₂₃	semidirect
710. #121	C₂×C₄×C₂₃	semidirect
711. #121	C₂×C₄×C₂₃	semidirect
712. #121	C₂×C₄×C₂₃	semidirect
713. #121	C₂×C₄×C₂₃	semidirect
724. C₂×C₄⋊C₄	C₂×C₄×C₂₃	semidirect
806. C₂₃	#34414	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×#537	2
C₂₃×#2378	2
C₂₃×#2377	2
C₂₃×#2368	2
C₂₃×#2363	2
C₂₃×#2362	2
C₂₃×#2361	2
C₂₃×#2360	2
C₂₃×#2345	2
C₂₃×#2344	2
C₂₃×#2341	2
C₂₃×#2339	2
C₂₃×#2333	2
C₂₃×#2325	2
C₂₃×#2324	2
C₂₃×#2323	2
C₂₃×#2311	2
C₄×C₂₃×C₂²⋊Q₈	2
C₄×C₂₃×#121	2
C₂₃×#2297	2
#34414	23

Subgroups — C23×#34414 #19182040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34414 #19182040