Subgroups — C₂₃×#62604 #19210230

Order 5888.

1708 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3561	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3552	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3377	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3367	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3320	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3314	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3313	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3308	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3299	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3297	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3243	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3225	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3211	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3181	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3175	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3137	C₂	1	2	yes	maximal, complemented
18	C₂×C₂₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2968	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#563	—	2	2	no	—
21	C₂₃×#563	—	2	1	no	—
22	C₂₃×#562	—	2	1	no	—
23	C₂₃×#557	C₂²	1	1	yes	characteristic, complemented
24	C₂₃×#556	C₂²	1	2	yes	—
25	C₂₃×#556	C₂²	1	1	yes	characteristic, complemented
26	C₂₃×#554	C₂²	1	2	yes	—
27	C₂₃×#553	C₂²	1	2	yes	—
28	C₂₃×#551	—	2	2	no	—
29	D₄×Q₈×C₂₃	—	2	1	no	—
30	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
31	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
32	C₂₃×#548	—	2	1	no	—
33	C₂₃×#548	C₂²	1	2	yes	—
34	C₂₃×#547	C₂²	1	1	yes	characteristic, complemented
35	C₂₃×#546	C₂²	1	2	yes	—
36	C₂₃×#544	C₂²	1	2	yes	complemented
37	C₂₃×#543	—	2	1	no	—
38	C₂₃×#542	—	2	2	no	—
39	C₂₃×#542	C₂²	1	2	yes	—
40	C₂₃×#542	C₂²	1	2	yes	complemented
41	C₂₃×#541	—	2	1	no	—
42	C₂₃×#539	—	2	2	no	—
43	C₂₃×#538	—	2	1	no	—
44	C₂₃×#536	—	2	1	no	—
45	C₂₃×#536	C₂²	1	2	yes	—
46	C₂₃×#533	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
48	C₂₃×#529	C₂²	1	1	yes	characteristic
49	C₂₃×#529	C₂²	1	1	yes	characteristic
50	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
51	C₂₃×#501	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#500	C₂²	1	2	yes	complemented
53	C₂₃×#497	C₂²	1	1	yes	characteristic, complemented
54	C₂₃×#495	C₂²	1	2	yes	—
55	C₂₃×#491	C₂²	1	1	yes	characteristic, complemented
56	C₂₃×#491	C₂²	1	2	yes	complemented
57	C₂₃×#489	C₂²	1	2	yes	—
58	C₂₃×#489	C₂²	1	2	yes	—
59	C₂₃×#489	C₂²	1	2	yes	—
60	C₂₃×#489	C₂²	1	2	yes	—
61	C₂₃×#489	C₂²	1	2	yes	—
62	C₂₃×#489	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#488	C₂²	1	2	yes	—
64	C₂₃×#488	C₂²	1	2	yes	—
65	C₂₃×#487	C₂²	1	2	yes	complemented
66	C₂₃×#487	C₂²	1	2	yes	complemented
67	C₂₃×#485	C₂²	1	2	yes	complemented
68	C₂₃×#484	C₂²	1	2	yes	—
69	C₂₃×#484	C₂²	1	2	yes	—
70	C₂₃×#484	C₂²	1	2	yes	complemented
71	C₂₃×#482	C₂²	1	2	yes	—
72	C₂₃×#480	C₂²	1	2	yes	—
73	C₂₃×#479	C₂²	1	2	yes	complemented
74	C₂₃×#478	C₂²	1	2	yes	—
75	C₂₃×#477	C₂²	1	2	yes	complemented
76	C₂₃×#477	C₂²	1	2	yes	complemented
77	C₂₃×#477	C₂²	1	2	yes	complemented
78	C₂₃×#474	C₂²	1	2	yes	—
79	C₂₃×#468	C₂²	1	2	yes	—
80	C₂₃×#468	C₂²	1	2	yes	complemented
81	C₂₃×#467	C₂²	1	2	yes	—
82	C₂₃×#467	C₂²	1	2	yes	complemented
83	C₂₃×#466	C₂²	1	2	yes	—
84	C₂₃×#465	C₂²	1	2	yes	—
85	C₂₃×#464	C₂²	1	2	yes	—
86	C₂₃×#464	C₂²	1	2	yes	—
87	C₂₃×#463	C₂²	1	2	yes	—
88	C₂₃×#463	C₂²	1	2	yes	—
89	C₂₃×#462	C₂²	1	2	yes	complemented
90	C₂₃×#461	C₂²	1	2	yes	complemented
91	C₂₃×#452	C₂²	1	2	yes	—
92	C₂₃×#451	C₂²	1	1	yes	characteristic
93	C₂₃×#451	C₂²	1	2	yes	complemented
94	C₂₃×#450	C₂²	1	1	yes	characteristic
95	C₂₃×#449	C₂²	1	2	yes	—
96	C₂₃×#448	C₂²	1	1	yes	characteristic
97	C₂₃×#448	C₂²	1	2	yes	complemented
98	C₂₃×#447	C₂²	1	1	yes	characteristic
99	C₂₃×#446	C₂²	1	2	yes	complemented
100	C₂₃×#441	C₂²	1	2	yes	complemented
101	C₂₃×#440	C₂²	1	2	yes	—
102	C₂₃×#440	C₂²	1	2	yes	complemented
103	C₂₃×#440	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
105	C₄×D₈×C₂₃	C₂²	1	2	yes	—
106	C₂₃×#435	C₂²	1	2	yes	—
107	C₂₃×#435	C₂²	1	2	yes	complemented
108	C₈×D₄×C₂₃	C₂²	1	2	yes	—
109	C₂₃×#433	C₂²	1	2	yes	complemented
110	C₂₃×#431	C₂²	1	1	yes	characteristic
111	C₂₃×#419	C₂²	1	2	yes	complemented
112	C₂₃×#417	C₂²	1	2	yes	—
113	C₂₃×#416	C₂²	1	2	yes	—
114	C₂×C₂₃×#103	C₂²	1	2	yes	—
115	C₂×C₂₃×#103	C₂²	1	2	yes	complemented
116	C₂×C₂₃×#102	C₂²	1	2	yes	—
117	C₂₃×#405	C₂²	1	2	yes	complemented
118	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
119	C₂×#41×C₂₃	—	2	1	no	—
120	C₂×#41×C₂₃	C₂³	1	2	yes	—
121	C₂²×Q₈×C₂₃	—	2	1	no	—
122	C₂²×Q₈×C₂₃	—	2	1	no	—
123	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
124	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
126	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
127	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
131	C₂×D₈×C₂₃	C₂³	1	2	yes	—
132	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
133	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
134	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
135	C₂₃×C₄⋊Q₈	—	2	1	no	—
136	C₂₃×C₄⋊Q₈	—	2	2	no	—
137	C₂₃×C₄⋊Q₈	—	2	2	no	—
138	C₂₃×C₄⋊Q₈	—	2	1	no	—
139	C₂₃×C₄⋊Q₈	—	2	1	no	—
140	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
141	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
142	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
143	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
144	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
145	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
146	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
147	C₂₃×#126	—	2	2	no	—
148	C₂₃×#126	—	2	2	no	—
149	C₂₃×#126	—	2	2	no	—
150	C₂₃×#126	—	2	2	no	—
151	C₂₃×#126	—	2	2	no	—
152	C₂₃×#126	—	2	2	no	—
153	C₂₃×#126	—	2	1	no	—
154	C₂₃×#126	D₄	1	2	yes	—
155	C₂₃×#125	—	2	2	no	—
156	C₂₃×#125	—	2	2	no	—
157	C₂₃×#125	—	2	2	no	—
158	C₂₃×#125	—	2	1	no	—
159	C₂₃×#125	D₄	1	1	yes	characteristic
160	C₂₃×#125	C₂³	1	2	yes	—
161	C₂₃×#125	C₂³	1	1	yes	characteristic
162	C₂₃×#124	—	2	1	no	—
163	C₂₃×#124	—	2	2	no	—
164	C₂₃×#124	—	2	2	no	—
165	C₂₃×#124	—	2	2	no	—
166	C₂₃×#124	—	2	1	no	—
167	C₂₃×#124	—	2	1	no	—
168	C₂₃×#124	D₄	1	1	yes	characteristic
169	C₂₃×#124	C₂³	1	2	yes	—
170	C₂₃×#124	C₂³	1	2	yes	—
171	C₂₃×#124	C₂³	1	2	yes	—
172	C₂₃×#124	C₂³	1	1	yes	characteristic
173	C₂₃×#123	—	2	1	no	—
174	C₂₃×#123	—	2	2	no	—
175	C₂₃×#123	—	2	2	no	—
176	C₂₃×#123	—	2	2	no	—
177	C₂₃×#123	—	2	2	no	—
178	C₂₃×#123	—	2	2	no	—
179	C₂₃×#123	—	2	2	no	—
180	C₂₃×#123	—	2	2	no	—
181	C₂₃×#123	D₄	1	2	yes	—
182	C₂₃×C₂²⋊Q₈	—	2	2	no	—
183	C₂₃×C₂²⋊Q₈	—	2	1	no	—
184	C₂₃×C₂²⋊Q₈	—	2	1	no	—
185	C₂₃×C₂²⋊Q₈	—	2	1	no	—
186	C₂₃×C₂²⋊Q₈	—	2	2	no	—
187	C₂₃×C₂²⋊Q₈	—	2	2	no	—
188	C₂₃×C₂²⋊Q₈	—	2	2	no	—
189	C₂₃×C₂²⋊Q₈	—	2	2	no	—
190	C₂₃×C₂²⋊Q₈	—	2	2	no	—
191	C₂₃×C₂²⋊Q₈	—	2	2	no	—
192	C₂₃×C₂²⋊Q₈	—	2	2	no	—
193	C₂₃×C₂²⋊Q₈	—	2	2	no	—
194	C₂₃×C₂²⋊Q₈	—	2	2	no	—
195	C₂₃×C₂²⋊Q₈	—	2	2	no	—
196	C₂₃×C₂²⋊Q₈	—	2	2	no	—
197	C₂₃×C₂²⋊Q₈	—	2	2	no	—
198	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
199	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
202	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₂₃×#121	—	2	2	no	—
204	C₂₃×#121	—	2	2	no	—
205	C₂₃×#121	—	2	2	no	—
206	C₂₃×#121	D₄	1	1	yes	characteristic
207	C₂₃×#121	C₂³	1	2	yes	—
208	C₂₃×#121	C₂³	1	2	yes	—
209	C₂₃×#121	C₂³	1	1	yes	characteristic
210	C₂₃×#120	—	2	2	no	—
211	C₄×Q₈×C₂₃	—	2	1	no	—
212	C₄×Q₈×C₂₃	—	2	1	no	—
213	C₄×Q₈×C₂₃	—	2	1	no	—
214	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
215	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
216	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
217	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₂₃	—	2	2	no	—
220	C₄×D₄×C₂₃	—	2	2	no	—
221	C₄×D₄×C₂₃	—	2	1	no	—
222	C₄×D₄×C₂₃	—	2	2	no	—
223	C₄×D₄×C₂₃	—	2	2	no	—
224	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₂₃	C₂³	1	2	yes	—
226	C₄×D₄×C₂₃	C₂³	1	2	yes	—
227	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₂₃	C₂³	1	2	yes	—
229	C₂₃×#117	—	2	1	no	—
230	C₂₃×#117	—	2	2	no	—
231	C₂₃×#117	—	2	1	no	—
232	C₂₃×#117	C₂³	1	2	yes	—
233	C₂₃×#117	C₂³	1	2	yes	—
234	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
235	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
236	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
239	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
240	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
241	C₂₃×#107	C₂³	1	2	yes	—
242	C₂₃×#107	C₂³	1	2	yes	—
243	C₂₃×#107	C₂³	1	2	yes	—
244	C₂₃×#107	C₂³	1	2	yes	—
245	C₂₃×#107	C₂³	1	2	yes	—
246	C₂₃×#106	C₂³	1	2	yes	—
247	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
248	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
249	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
250	C₂₃×#103	C₂³	1	2	yes	—
251	C₂₃×#103	C₂³	1	2	yes	—
252	C₂₃×#103	C₂³	1	2	yes	—
253	C₂₃×#103	C₂³	1	2	yes	—
254	C₂₃×#103	C₂³	1	2	yes	—
255	C₂₃×#103	C₂³	1	2	yes	—
256	C₂₃×#103	C₂³	1	2	yes	—
257	C₂₃×#103	C₂³	1	2	yes	—
258	C₂₃×#103	C₂³	1	2	yes	—
259	C₂₃×#103	C₂³	1	2	yes	—
260	C₂₃×#103	C₂³	1	2	yes	—
261	C₂₃×#103	C₂³	1	2	yes	—
262	C₂₃×#103	C₂³	1	2	yes	—
263	C₂₃×#102	C₂³	1	2	yes	—
264	C₂₃×#102	C₂³	1	2	yes	—
265	C₂₃×#102	C₂³	1	2	yes	—
266	C₂₃×#102	C₂³	1	2	yes	—
267	C₂₃×#102	C₂³	1	2	yes	—
268	C₂₃×#102	C₂³	1	2	yes	—
269	C₂₃×#102	C₂³	1	2	yes	—
270	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
274	C₂₃×#97	C₂³	1	1	yes	characteristic
275	C₂₃×#97	C₂³	1	1	yes	characteristic
276	C₂₃×#97	C₂³	1	2	yes	—
277	C₂₃×#97	C₂³	1	2	yes	—
278	C₄×C₈×C₂₃	C₂³	1	2	yes	—
279	C₄×C₈×C₂₃	C₂³	1	2	yes	—
280	C₂⁴×C₂₃	—	2	1	no	—
281	#41×C₂₃	—	4	2	no	—
282	#41×C₂₃	—	4	2	no	—
283	#41×C₂₃	—	8	2	no	—
284	C₂×Q₈×C₂₃	—	2	1	no	—
285	C₂×Q₈×C₂₃	—	2	1	no	—
286	C₂×Q₈×C₂₃	—	2	1	no	—
287	C₂×Q₈×C₂₃	—	2	2	no	—
288	C₂×Q₈×C₂₃	—	2	2	no	—
289	C₂×Q₈×C₂₃	—	2	1	no	—
290	C₂×Q₈×C₂₃	—	2	2	no	—
291	C₂×Q₈×C₂₃	—	4	2	no	—
292	C₂×Q₈×C₂₃	—	4	2	no	—
293	C₂×Q₈×C₂₃	—	4	2	no	—
294	C₂×Q₈×C₂₃	—	8	2	no	—
295	C₂×Q₈×C₂₃	—	8	2	no	—
296	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
297	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
298	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
299	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
300	C₂×D₄×C₂₃	—	2	1	no	—
301	C₂×D₄×C₂₃	—	2	2	no	—
302	C₂×D₄×C₂₃	—	2	2	no	—
303	C₂×D₄×C₂₃	—	2	2	no	—
304	C₂×D₄×C₂₃	—	2	1	no	—
305	C₂×D₄×C₂₃	—	4	2	no	—
306	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
307	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
308	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
309	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₂₃	—	2	1	no	—
311	C₂²×C₄×C₂₃	—	2	2	no	—
312	C₂²×C₄×C₂₃	—	2	2	no	—
313	C₂²×C₄×C₂₃	—	2	2	no	—
314	C₂²×C₄×C₂₃	—	2	1	no	—
315	C₂²×C₄×C₂₃	—	2	2	no	—
316	C₂²×C₄×C₂₃	—	2	2	no	—
317	C₂²×C₄×C₂₃	—	2	2	no	—
318	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
322	Q₁₆×C₂₃	—	4	2	no	—
323	Q₁₆×C₂₃	—	4	2	no	—
324	SD₁₆×C₂₃	—	4	2	no	—
325	SD₁₆×C₂₃	—	4	2	no	—
326	SD₁₆×C₂₃	—	4	2	no	—
327	D₈×C₂₃	—	4	2	no	—
328	M₁₆×C₂₃	—	4	2	no	—
329	C₂×C₈×C₂₃	—	4	2	no	—
330	C₂×C₈×C₂₃	—	4	2	no	—
331	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
332	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
333	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
334	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
335	C₄⋊C₄×C₂₃	—	2	1	no	—
336	C₄⋊C₄×C₂₃	—	2	2	no	—
337	C₄⋊C₄×C₂₃	—	2	1	no	—
338	C₄⋊C₄×C₂₃	—	2	2	no	—
339	C₄⋊C₄×C₂₃	—	2	2	no	—
340	C₄⋊C₄×C₂₃	—	2	2	no	—
341	C₄⋊C₄×C₂₃	—	2	1	no	—
342	C₄⋊C₄×C₂₃	—	2	1	no	—
343	C₄⋊C₄×C₂₃	—	2	1	no	—
344	C₄⋊C₄×C₂₃	—	2	1	no	—
345	C₄⋊C₄×C₂₃	—	2	2	no	—
346	C₄⋊C₄×C₂₃	—	2	2	no	—
347	C₄⋊C₄×C₂₃	—	2	1	no	—
348	C₄⋊C₄×C₂₃	—	2	2	no	—
349	C₄⋊C₄×C₂₃	—	2	2	no	—
350	C₄⋊C₄×C₂₃	—	2	2	no	—
351	C₄⋊C₄×C₂₃	—	2	2	no	—
352	C₄⋊C₄×C₂₃	—	2	1	no	—
353	C₄⋊C₄×C₂₃	—	2	2	no	—
354	C₄⋊C₄×C₂₃	—	2	2	no	—
355	C₄⋊C₄×C₂₃	—	2	2	no	—
356	C₄⋊C₄×C₂₃	—	2	2	no	—
357	C₄⋊C₄×C₂₃	—	2	1	no	—
358	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
359	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
364	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
368	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
369	C₂²⋊C₄×C₂₃	—	2	2	no	—
370	C₂²⋊C₄×C₂₃	—	2	2	no	—
371	C₂²⋊C₄×C₂₃	—	2	1	no	—
372	C₂²⋊C₄×C₂₃	—	2	2	no	—
373	C₂²⋊C₄×C₂₃	—	2	2	no	—
374	C₂²⋊C₄×C₂₃	—	2	2	no	—
375	C₂²⋊C₄×C₂₃	—	2	2	no	—
376	C₂²⋊C₄×C₂₃	—	2	2	no	—
377	C₂²⋊C₄×C₂₃	—	2	2	no	—
378	C₂²⋊C₄×C₂₃	—	2	2	no	—
379	C₂²⋊C₄×C₂₃	—	2	2	no	—
380	C₂²⋊C₄×C₂₃	—	2	2	no	—
381	C₂²⋊C₄×C₂₃	—	2	1	no	—
382	C₂²⋊C₄×C₂₃	—	2	1	no	—
383	C₂²⋊C₄×C₂₃	—	2	2	no	—
384	C₂²⋊C₄×C₂₃	—	2	1	no	—
385	C₂²⋊C₄×C₂₃	—	2	2	no	—
386	C₂²⋊C₄×C₂₃	—	2	2	no	—
387	C₂²⋊C₄×C₂₃	—	2	1	no	—
388	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
389	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
390	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
391	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
392	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
393	C₄²×C₂₃	—	2	2	no	—
394	C₄²×C₂₃	—	2	1	no	—
395	C₄²×C₂₃	—	2	2	no	—
396	C₄²×C₂₃	—	2	2	no	—
397	C₄²×C₂₃	—	2	2	no	—
398	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
401	C₄²×C₂₃	C₂⁴	1	2	yes	—
402	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
403	#62604	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
404	C₂³×C₂₃	—	2	1	no	—
405	C₂³×C₂₃	—	2	2	no	—
406	C₂³×C₂₃	—	4	2	no	—
407	C₂³×C₂₃	—	8	1	no	—
408	C₂³×C₂₃	—	8	1	no	—
409	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
410	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
411	Q₈×C₂₃	—	2	2	no	—
412	Q₈×C₂₃	—	2	2	no	—
413	Q₈×C₂₃	—	2	2	no	—
414	Q₈×C₂₃	—	2	2	no	—
415	Q₈×C₂₃	—	2	2	no	—
416	Q₈×C₂₃	—	4	1	no	—
417	Q₈×C₂₃	—	4	2	no	—
418	Q₈×C₂₃	—	4	2	no	—
419	Q₈×C₂₃	—	8	1	no	—
420	Q₈×C₂₃	—	8	2	no	—
421	Q₈×C₂₃	—	8	1	no	—
422	Q₈×C₂₃	—	8	2	no	—
423	Q₈×C₂₃	—	8	2	no	—
424	D₄×C₂₃	—	2	4	no	—
425	D₄×C₂₃	—	2	2	no	—
426	D₄×C₂₃	—	2	2	no	—
427	D₄×C₂₃	—	2	2	no	—
428	D₄×C₂₃	—	4	1	no	—
429	D₄×C₂₃	—	4	2	no	—
430	D₄×C₂₃	—	8	1	no	—
431	D₄×C₂₃	—	8	2	no	—
432	D₄×C₂₃	—	8	2	no	—
433	D₄×C₂₃	—	8	2	no	—
434	C₂×C₄×C₂₃	—	2	2	no	—
435	C₂×C₄×C₂₃	—	2	2	no	—
436	C₂×C₄×C₂₃	—	2	2	no	—
437	C₂×C₄×C₂₃	—	2	2	no	—
438	C₂×C₄×C₂₃	—	2	1	no	—
439	C₂×C₄×C₂₃	—	2	1	no	—
440	C₂×C₄×C₂₃	—	2	2	no	—
441	C₂×C₄×C₂₃	—	2	2	no	—
442	C₂×C₄×C₂₃	—	2	2	no	—
443	C₂×C₄×C₂₃	—	2	2	no	—
444	C₂×C₄×C₂₃	—	2	2	no	—
445	C₂×C₄×C₂₃	—	2	1	no	—
446	C₂×C₄×C₂₃	—	4	1	no	—
447	C₂×C₄×C₂₃	—	4	2	no	—
448	C₂×C₄×C₂₃	—	8	2	no	—
449	C₂×C₄×C₂₃	—	8	2	no	—
450	C₂×C₄×C₂₃	—	8	2	no	—
451	C₂×C₄×C₂₃	—	8	2	no	—
452	C₂×C₄×C₂₃	—	8	1	no	—
453	C₂×C₄×C₂₃	—	8	2	no	—
454	C₂×C₄×C₂₃	—	8	2	no	—
455	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
457	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
459	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
463	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
464	C₈×C₂₃	—	2	2	no	—
465	C₈×C₂₃	—	2	2	no	—
466	C₈×C₂₃	—	2	2	no	—
467	C₈×C₂₃	—	2	2	no	—
468	#3561	C₂×C₂₃	1	1	yes	characteristic, complemented
469	#3552	C₂×C₂₃	1	1	yes	characteristic, complemented
470	#3377	C₂×C₂₃	1	2	yes	complemented
471	#3367	C₂×C₂₃	1	2	yes	complemented
472	#3320	C₂×C₂₃	1	2	yes	complemented
473	#3314	C₂×C₂₃	1	2	yes	complemented
474	#3313	C₂×C₂₃	1	2	yes	complemented
475	#3308	C₂×C₂₃	1	2	yes	complemented
476	#3299	C₂×C₂₃	1	2	yes	complemented
477	#3297	C₂×C₂₃	1	2	yes	complemented
478	#3243	C₂×C₂₃	1	2	yes	complemented
479	#3230	C₂×C₂₃	1	1	yes	characteristic, complemented
480	#3225	C₂×C₂₃	1	2	yes	complemented
481	#3211	C₂×C₂₃	1	1	yes	characteristic, complemented
482	#3181	C₂×C₂₃	1	1	yes	characteristic, complemented
483	#3175	C₂×C₂₃	1	2	yes	complemented
484	#3137	C₂×C₂₃	1	2	yes	complemented
485	C₂×#489	C₂×C₂₃	1	1	yes	characteristic, complemented
486	#2968	C₂×C₂₃	1	1	yes	characteristic, complemented
487	C₂²×C₂₃	—	2	1	no	—
488	C₂²×C₂₃	—	2	1	no	—
489	C₂²×C₂₃	—	2	2	no	—
490	C₂²×C₂₃	—	2	2	no	—
491	C₂²×C₂₃	—	2	2	no	—
492	C₂²×C₂₃	—	4	1	no	—
493	C₂²×C₂₃	—	4	2	no	—
494	C₂²×C₂₃	—	4	2	no	—
495	C₂²×C₂₃	—	4	1	no	—
496	C₂²×C₂₃	—	4	1	no	—
497	C₂²×C₂₃	—	4	2	no	—
498	C₂²×C₂₃	—	16	2	no	—
499	C₂²×C₂₃	#578	1	2	yes	—
500	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
501	C₄×C₂₃	—	2	1	no	—
502	C₄×C₂₃	—	2	1	no	—
503	C₄×C₂₃	—	2	2	no	—
504	C₄×C₂₃	—	2	2	no	—
505	C₄×C₂₃	—	2	1	no	—
506	C₄×C₂₃	—	2	1	no	—
507	C₄×C₂₃	—	2	1	no	—
508	C₄×C₂₃	—	2	2	no	—
509	C₄×C₂₃	—	4	1	no	—
510	C₄×C₂₃	—	4	2	no	—
511	C₄×C₂₃	—	4	2	no	—
512	C₄×C₂₃	—	4	2	no	—
513	C₄×C₂₃	—	4	2	no	—
514	C₄×C₂₃	—	4	2	no	—
515	C₄×C₂₃	—	4	1	no	—
516	C₄×C₂₃	—	4	1	no	—
517	C₄×C₂₃	#585	1	2	yes	—
518	#563	—	2	2	no	—
519	#563	—	2	1	no	—
520	#562	—	2	1	no	—
521	#557	C₂²×C₂₃	1	1	yes	characteristic, complemented
522	#556	C₂²×C₂₃	1	2	yes	—
523	#556	C₂²×C₂₃	1	1	yes	characteristic, complemented
524	#554	C₂²×C₂₃	1	2	yes	—
525	#553	C₂²×C₂₃	1	2	yes	—
526	#551	—	2	2	no	—
527	D₄×Q₈	—	2	1	no	—
528	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
529	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
530	#548	—	2	1	no	—
531	#548	C₂²×C₂₃	1	2	yes	—
532	#547	C₂²×C₂₃	1	1	yes	characteristic, complemented
533	#546	C₂²×C₂₃	1	2	yes	—
534	#544	C₂²×C₂₃	1	2	yes	complemented
535	#543	—	2	1	no	—
536	#542	—	2	2	no	—
537	#542	C₂²×C₂₃	1	2	yes	—
538	#542	C₂²×C₂₃	1	2	yes	complemented
539	#541	—	2	1	no	—
540	#539	—	2	2	no	—
541	#538	—	2	1	no	—
542	#536	—	2	1	no	—
543	#536	C₂²×C₂₃	1	2	yes	—
544	#533	C₂²×C₂₃	1	1	yes	characteristic
545	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
546	#529	C₂²×C₂₃	1	1	yes	characteristic
547	#529	C₂²×C₂₃	1	1	yes	characteristic
548	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
549	#501	C₂²×C₂₃	1	1	yes	characteristic, complemented
550	#500	C₂²×C₂₃	1	2	yes	complemented
551	#497	C₂²×C₂₃	1	1	yes	characteristic, complemented
552	#495	C₂²×C₂₃	1	2	yes	—
553	#491	C₂²×C₂₃	1	2	yes	complemented
554	#491	C₂²×C₂₃	1	1	yes	characteristic, complemented
555	#489	C₂²×C₂₃	1	2	yes	—
556	#489	C₂²×C₂₃	1	2	yes	—
557	#489	C₂²×C₂₃	1	2	yes	—
558	#489	C₂²×C₂₃	1	2	yes	—
559	#489	C₂²×C₂₃	1	2	yes	—
560	#489	C₂²×C₂₃	1	1	yes	characteristic, complemented
561	#488	C₂²×C₂₃	1	2	yes	—
562	#488	C₂²×C₂₃	1	2	yes	—
563	#487	C₂²×C₂₃	1	2	yes	complemented
564	#487	C₂²×C₂₃	1	2	yes	complemented
565	#485	C₂²×C₂₃	1	2	yes	complemented
566	#484	C₂²×C₂₃	1	2	yes	—
567	#484	C₂²×C₂₃	1	2	yes	—
568	#484	C₂²×C₂₃	1	2	yes	complemented
569	#482	C₂²×C₂₃	1	2	yes	—
570	#480	C₂²×C₂₃	1	2	yes	—
571	#479	C₂²×C₂₃	1	2	yes	complemented
572	#478	C₂²×C₂₃	1	2	yes	—
573	#477	C₂²×C₂₃	1	2	yes	complemented
574	#477	C₂²×C₂₃	1	2	yes	complemented
575	#477	C₂²×C₂₃	1	2	yes	complemented
576	#474	C₂²×C₂₃	1	2	yes	—
577	#468	C₂²×C₂₃	1	2	yes	—
578	#468	C₂²×C₂₃	1	2	yes	complemented
579	#467	C₂²×C₂₃	1	2	yes	—
580	#467	C₂²×C₂₃	1	2	yes	complemented
581	#466	C₂²×C₂₃	1	2	yes	—
582	#465	C₂²×C₂₃	1	2	yes	—
583	#464	C₂²×C₂₃	1	2	yes	—
584	#464	C₂²×C₂₃	1	2	yes	—
585	#463	C₂²×C₂₃	1	2	yes	—
586	#463	C₂²×C₂₃	1	2	yes	—
587	#462	C₂²×C₂₃	1	2	yes	complemented
588	#461	C₂²×C₂₃	1	2	yes	complemented
589	#452	C₂²×C₂₃	1	2	yes	—
590	#451	C₂²×C₂₃	1	1	yes	characteristic
591	#451	C₂²×C₂₃	1	2	yes	complemented
592	#450	C₂²×C₂₃	1	1	yes	characteristic
593	#449	C₂²×C₂₃	1	2	yes	—
594	#448	C₂²×C₂₃	1	1	yes	characteristic
595	#448	C₂²×C₂₃	1	2	yes	complemented
596	#447	C₂²×C₂₃	1	1	yes	characteristic
597	#446	C₂²×C₂₃	1	2	yes	complemented
598	#441	C₂²×C₂₃	1	2	yes	complemented
599	#440	C₂²×C₂₃	1	2	yes	—
600	#440	C₂²×C₂₃	1	2	yes	complemented
601	#440	C₂²×C₂₃	1	2	yes	complemented
602	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
603	C₄×D₈	C₂²×C₂₃	1	2	yes	—
604	#435	C₂²×C₂₃	1	2	yes	—
605	#435	C₂²×C₂₃	1	2	yes	complemented
606	C₈×D₄	C₂²×C₂₃	1	2	yes	—
607	#433	C₂²×C₂₃	1	2	yes	complemented
608	#431	C₂²×C₂₃	1	1	yes	characteristic
609	#419	C₂²×C₂₃	1	2	yes	complemented
610	#417	C₂²×C₂₃	1	2	yes	—
611	#416	C₂²×C₂₃	1	2	yes	—
612	C₂×#103	C₂²×C₂₃	1	2	yes	—
613	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
614	C₂×#102	C₂²×C₂₃	1	2	yes	—
615	#405	C₂²×C₂₃	1	2	yes	complemented
616	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
617	C₂×C₂₃	—	2	2	no	—
618	C₂×C₂₃	—	4	2	no	—
619	C₂×C₂₃	—	8	1	no	—
620	C₂×C₂₃	—	8	2	no	—
621	C₂×C₂₃	#3500	1	1	yes	characteristic
622	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
623	C₂×C₂₃	#3585	1	1	yes	characteristic
624	C₂×#41	—	2	1	no	—
625	C₂×#41	C₂³×C₂₃	1	2	yes	—
626	C₂²×Q₈	—	2	1	no	—
627	C₂²×Q₈	—	2	1	no	—
628	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
629	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
630	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
631	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
632	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
633	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
634	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
635	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
636	C₂×D₈	C₂³×C₂₃	1	2	yes	—
637	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
638	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
639	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
640	C₄⋊Q₈	—	2	1	no	—
641	C₄⋊Q₈	—	2	2	no	—
642	C₄⋊Q₈	—	2	2	no	—
643	C₄⋊Q₈	—	2	1	no	—
644	C₄⋊Q₈	—	2	1	no	—
645	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
646	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
647	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
648	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
649	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
650	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
651	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
652	#126	—	2	2	no	—
653	#126	—	2	2	no	—
654	#126	—	2	2	no	—
655	#126	—	2	2	no	—
656	#126	—	2	2	no	—
657	#126	—	2	2	no	—
658	#126	—	2	1	no	—
659	#126	D₄×C₂₃	1	2	yes	—
660	#125	—	2	2	no	—
661	#125	—	2	2	no	—
662	#125	—	2	2	no	—
663	#125	—	2	1	no	—
664	#125	D₄×C₂₃	1	1	yes	characteristic
665	#125	C₂³×C₂₃	1	1	yes	characteristic
666	#125	C₂³×C₂₃	1	2	yes	—
667	#124	—	2	1	no	—
668	#124	—	2	2	no	—
669	#124	—	2	2	no	—
670	#124	—	2	2	no	—
671	#124	—	2	1	no	—
672	#124	—	2	1	no	—
673	#124	D₄×C₂₃	1	1	yes	characteristic
674	#124	C₂³×C₂₃	1	2	yes	—
675	#124	C₂³×C₂₃	1	2	yes	—
676	#124	C₂³×C₂₃	1	1	yes	characteristic
677	#124	C₂³×C₂₃	1	2	yes	—
678	#123	—	2	1	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	#123	—	2	2	no	—
684	#123	—	2	2	no	—
685	#123	—	2	2	no	—
686	#123	D₄×C₂₃	1	2	yes	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	1	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	—	2	1	no	—
693	C₂²⋊Q₈	—	2	1	no	—
694	C₂²⋊Q₈	—	2	2	no	—
695	C₂²⋊Q₈	—	2	2	no	—
696	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	—	2	2	no	—
698	C₂²⋊Q₈	—	2	2	no	—
699	C₂²⋊Q₈	—	2	2	no	—
700	C₂²⋊Q₈	—	2	2	no	—
701	C₂²⋊Q₈	—	2	2	no	—
702	C₂²⋊Q₈	—	2	2	no	—
703	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
704	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
705	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
706	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
707	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
708	#121	—	2	2	no	—
709	#121	—	2	2	no	—
710	#121	—	2	2	no	—
711	#121	D₄×C₂₃	1	1	yes	characteristic
712	#121	C₂³×C₂₃	1	1	yes	characteristic
713	#121	C₂³×C₂₃	1	2	yes	—
714	#121	C₂³×C₂₃	1	2	yes	—
715	#120	—	2	2	no	—
716	C₄×Q₈	—	2	1	no	—
717	C₄×Q₈	—	2	1	no	—
718	C₄×Q₈	—	2	1	no	—
719	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
720	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
721	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
722	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
723	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
724	C₄×D₄	—	2	2	no	—
725	C₄×D₄	—	2	2	no	—
726	C₄×D₄	—	2	1	no	—
727	C₄×D₄	—	2	2	no	—
728	C₄×D₄	—	2	2	no	—
729	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
730	C₄×D₄	C₂³×C₂₃	1	2	yes	—
731	C₄×D₄	C₂³×C₂₃	1	2	yes	—
732	C₄×D₄	C₂³×C₂₃	1	2	yes	—
733	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
734	#117	—	2	1	no	—
735	#117	—	2	2	no	—
736	#117	—	2	1	no	—
737	#117	C₂³×C₂₃	1	2	yes	—
738	#117	C₂³×C₂₃	1	2	yes	—
739	C₂×C₄⋊C₄	—	2	1	no	—
740	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
741	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
742	C₂×C₂²⋊C₄	—	2	1	no	—
743	C₂×C₂²⋊C₄	—	2	1	no	—
744	C₂×C₂²⋊C₄	—	2	2	no	—
745	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
746	#107	C₂³×C₂₃	1	2	yes	—
747	#107	C₂³×C₂₃	1	2	yes	—
748	#107	C₂³×C₂₃	1	2	yes	—
749	#107	C₂³×C₂₃	1	2	yes	—
750	#107	C₂³×C₂₃	1	2	yes	—
751	#106	C₂³×C₂₃	1	2	yes	—
752	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
753	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
754	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
755	#103	C₂³×C₂₃	1	2	yes	—
756	#103	C₂³×C₂₃	1	2	yes	—
757	#103	C₂³×C₂₃	1	2	yes	—
758	#103	C₂³×C₂₃	1	2	yes	—
759	#103	C₂³×C₂₃	1	2	yes	—
760	#103	C₂³×C₂₃	1	2	yes	—
761	#103	C₂³×C₂₃	1	2	yes	—
762	#103	C₂³×C₂₃	1	2	yes	—
763	#103	C₂³×C₂₃	1	2	yes	—
764	#103	C₂³×C₂₃	1	2	yes	—
765	#103	C₂³×C₂₃	1	2	yes	—
766	#103	C₂³×C₂₃	1	2	yes	—
767	#103	C₂³×C₂₃	1	2	yes	—
768	#102	C₂³×C₂₃	1	2	yes	—
769	#102	C₂³×C₂₃	1	2	yes	—
770	#102	C₂³×C₂₃	1	2	yes	—
771	#102	C₂³×C₂₃	1	2	yes	—
772	#102	C₂³×C₂₃	1	2	yes	—
773	#102	C₂³×C₂₃	1	2	yes	—
774	#102	C₂³×C₂₃	1	2	yes	—
775	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
776	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
777	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
778	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
779	#97	C₂³×C₂₃	1	1	yes	characteristic
780	#97	C₂³×C₂₃	1	1	yes	characteristic
781	#97	C₂³×C₂₃	1	2	yes	—
782	#97	C₂³×C₂₃	1	2	yes	—
783	C₄×C₈	C₂³×C₂₃	1	2	yes	—
784	C₄×C₈	C₂³×C₂₃	1	2	yes	—
785	C₂₃	#62604	1	1	yes	characteristic, direct product factor, Sylow
786	C₂⁴	—	2	1	no	—
787	#41	—	4	2	no	—
788	#41	—	4	2	no	—
789	#41	—	8	2	no	—
790	C₂×Q₈	—	2	1	no	—
791	C₂×Q₈	—	2	1	no	—
792	C₂×Q₈	—	2	1	no	—
793	C₂×Q₈	—	2	2	no	—
794	C₂×Q₈	—	2	2	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	2	2	no	—
797	C₂×Q₈	—	4	2	no	—
798	C₂×Q₈	—	4	2	no	—
799	C₂×Q₈	—	4	2	no	—
800	C₂×Q₈	—	8	2	no	—
801	C₂×Q₈	—	8	2	no	—
802	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
803	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
804	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
805	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
806	C₂×D₄	—	2	1	no	—
807	C₂×D₄	—	2	2	no	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	1	no	—
811	C₂×D₄	—	4	2	no	—
812	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
813	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
814	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
815	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
816	C₂²×C₄	—	2	1	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	2	no	—
820	C₂²×C₄	—	2	1	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	2	2	no	—
824	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
825	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
826	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
828	Q₁₆	—	4	2	no	—
829	Q₁₆	—	4	2	no	—
830	SD₁₆	—	4	2	no	—
831	SD₁₆	—	4	2	no	—
832	SD₁₆	—	4	2	no	—
833	D₈	—	4	2	no	—
834	M₁₆	—	4	2	no	—
835	C₂×C₈	—	4	2	no	—
836	C₂×C₈	—	4	2	no	—
837	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
838	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
839	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
840	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
841	C₄⋊C₄	—	2	1	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	1	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	1	no	—
848	C₄⋊C₄	—	2	1	no	—
849	C₄⋊C₄	—	2	1	no	—
850	C₄⋊C₄	—	2	1	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	1	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	1	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	1	no	—
864	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
865	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
866	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
867	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
868	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
869	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
870	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
871	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
872	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
873	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
874	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	1	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	1	no	—
888	C₂²⋊C₄	—	2	1	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	1	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	1	no	—
894	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
895	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
896	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
897	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
898	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
899	C₄²	—	2	2	no	—
900	C₄²	—	2	1	no	—
901	C₄²	—	2	2	no	—
902	C₄²	—	2	2	no	—
903	C₄²	—	2	2	no	—
904	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
905	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
906	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
907	C₄²	C₂⁴×C₂₃	1	2	yes	—
908	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
909	C₂³	—	2	1	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	4	2	no	—
912	C₂³	—	8	1	no	—
913	C₂³	—	8	1	no	—
914	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
915	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
916	Q₈	—	2	2	no	—
917	Q₈	—	2	2	no	—
918	Q₈	—	2	2	no	—
919	Q₈	—	2	2	no	—
920	Q₈	—	2	2	no	—
921	Q₈	—	4	1	no	—
922	Q₈	—	4	2	no	—
923	Q₈	—	4	2	no	—
924	Q₈	—	8	2	no	—
925	Q₈	—	8	1	no	—
926	Q₈	—	8	2	no	—
927	Q₈	—	8	2	no	—
928	Q₈	—	8	1	no	—
929	D₄	—	2	4	no	—
930	D₄	—	2	2	no	—
931	D₄	—	2	2	no	—
932	D₄	—	2	2	no	—
933	D₄	—	4	1	no	—
934	D₄	—	4	2	no	—
935	D₄	—	8	1	no	—
936	D₄	—	8	2	no	—
937	D₄	—	8	2	no	—
938	D₄	—	8	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	4	1	no	—
952	C₂×C₄	—	4	2	no	—
953	C₂×C₄	—	8	2	no	—
954	C₂×C₄	—	8	2	no	—
955	C₂×C₄	—	8	2	no	—
956	C₂×C₄	—	8	2	no	—
957	C₂×C₄	—	8	1	no	—
958	C₂×C₄	—	8	2	no	—
959	C₂×C₄	—	8	2	no	—
960	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
961	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
962	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
963	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
964	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
965	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
966	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
967	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
968	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
969	C₈	—	2	2	no	—
970	C₈	—	2	2	no	—
971	C₈	—	2	2	no	—
972	C₈	—	2	2	no	—
973	C₂²	—	2	1	no	—
974	C₂²	—	2	1	no	—
975	C₂²	—	2	2	no	—
976	C₂²	—	2	2	no	—
977	C₂²	—	2	2	no	—
978	C₂²	—	4	2	no	—
979	C₂²	—	4	1	no	—
980	C₂²	—	4	1	no	—
981	C₂²	—	4	2	no	—
982	C₂²	—	4	1	no	—
983	C₂²	—	4	2	no	—
984	C₂²	—	16	2	no	—
985	C₂²	C₂₃×#578	1	2	yes	—
986	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
987	C₄	—	2	2	no	—
988	C₄	—	2	1	no	—
989	C₄	—	2	1	no	—
990	C₄	—	2	1	no	—
991	C₄	—	2	2	no	—
992	C₄	—	2	1	no	—
993	C₄	—	2	1	no	—
994	C₄	—	2	2	no	—
995	C₄	—	4	2	no	—
996	C₄	—	4	2	no	—
997	C₄	—	4	1	no	—
998	C₄	—	4	1	no	—
999	C₄	—	4	1	no	—
1000	C₄	—	4	2	no	—
1001	C₄	—	4	2	no	—
1002	C₄	—	4	2	no	—
1003	C₄	C₂₃×#585	1	2	yes	—
1004	C₂	—	2	2	no	—
1005	C₂	—	4	2	no	—
1006	C₂	—	8	2	no	—
1007	C₂	—	8	1	no	—
1008	C₂	C₂₃×#3500	1	1	yes	characteristic
1009	C₂	C₂×C₂₃×#578	1	1	yes	characteristic
1010	C₂	C₂₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3561	C₂	semidirect
2. C₂₃×#3552	C₂	semidirect
3. C₂₃×#3377	C₂	semidirect
4. C₂₃×#3367	C₂	semidirect
5. C₂₃×#3320	C₂	semidirect
6. C₂₃×#3314	C₂	semidirect
7. C₂₃×#3313	C₂	semidirect
8. C₂₃×#3308	C₂	semidirect
9. C₂₃×#3299	C₂	semidirect
10. C₂₃×#3297	C₂	semidirect
11. C₂₃×#3243	C₂	semidirect
12. C₂₃×#3230	C₂	semidirect
13. C₂₃×#3225	C₂	semidirect
14. C₂₃×#3211	C₂	semidirect
15. C₂₃×#3181	C₂	semidirect
16. C₂₃×#3175	C₂	semidirect
17. C₂₃×#3137	C₂	semidirect
18. C₂×C₂₃×#489	C₂	semidirect
19. C₂₃×#2968	C₂	semidirect
23. C₂₃×#557	C₂²	semidirect
25. C₂₃×#556	C₂²	semidirect
31. D₄×Q₈×C₂₃	C₂²	semidirect
34. C₂₃×#547	C₂²	semidirect
36. C₂₃×#544	C₂²	semidirect
40. C₂₃×#542	C₂²	semidirect
51. C₂₃×#501	C₂²	semidirect
52. C₂₃×#500	C₂²	semidirect
53. C₂₃×#497	C₂²	semidirect
55. C₂₃×#491	C₂²	semidirect
56. C₂₃×#491	C₂²	semidirect
62. C₂₃×#489	C₂²	semidirect
65. C₂₃×#487	C₂²	semidirect
66. C₂₃×#487	C₂²	semidirect
67. C₂₃×#485	C₂²	semidirect
70. C₂₃×#484	C₂²	semidirect
73. C₂₃×#479	C₂²	semidirect
75. C₂₃×#477	C₂²	semidirect
76. C₂₃×#477	C₂²	semidirect
77. C₂₃×#477	C₂²	semidirect
80. C₂₃×#468	C₂²	semidirect
82. C₂₃×#467	C₂²	semidirect
89. C₂₃×#462	C₂²	semidirect
90. C₂₃×#461	C₂²	semidirect
93. C₂₃×#451	C₂²	semidirect
97. C₂₃×#448	C₂²	semidirect
99. C₂₃×#446	C₂²	semidirect
100. C₂₃×#441	C₂²	semidirect
102. C₂₃×#440	C₂²	semidirect
103. C₂₃×#440	C₂²	semidirect
104. C₄×Q₁₆×C₂₃	C₂²	semidirect
107. C₂₃×#435	C₂²	semidirect
109. C₂₃×#433	C₂²	semidirect
111. C₂₃×#419	C₂²	semidirect
115. C₂×C₂₃×#103	C₂²	semidirect
117. C₂₃×#405	C₂²	semidirect
403. #62604	C₂₃	direct (N × H)
468. #3561	C₂×C₂₃	semidirect
469. #3552	C₂×C₂₃	semidirect
470. #3377	C₂×C₂₃	semidirect
471. #3367	C₂×C₂₃	semidirect
472. #3320	C₂×C₂₃	semidirect
473. #3314	C₂×C₂₃	semidirect
474. #3313	C₂×C₂₃	semidirect
475. #3308	C₂×C₂₃	semidirect
476. #3299	C₂×C₂₃	semidirect
477. #3297	C₂×C₂₃	semidirect
478. #3243	C₂×C₂₃	semidirect
479. #3230	C₂×C₂₃	semidirect
480. #3225	C₂×C₂₃	semidirect
481. #3211	C₂×C₂₃	semidirect
482. #3181	C₂×C₂₃	semidirect
483. #3175	C₂×C₂₃	semidirect
484. #3137	C₂×C₂₃	semidirect
485. C₂×#489	C₂×C₂₃	semidirect
486. #2968	C₂×C₂₃	semidirect
521. #557	C₂²×C₂₃	semidirect
523. #556	C₂²×C₂₃	semidirect
529. D₄×Q₈	C₂²×C₂₃	semidirect
532. #547	C₂²×C₂₃	semidirect
534. #544	C₂²×C₂₃	semidirect
538. #542	C₂²×C₂₃	semidirect
549. #501	C₂²×C₂₃	semidirect
550. #500	C₂²×C₂₃	semidirect
551. #497	C₂²×C₂₃	semidirect
553. #491	C₂²×C₂₃	semidirect
554. #491	C₂²×C₂₃	semidirect
560. #489	C₂²×C₂₃	semidirect
563. #487	C₂²×C₂₃	semidirect
564. #487	C₂²×C₂₃	semidirect
565. #485	C₂²×C₂₃	semidirect
568. #484	C₂²×C₂₃	semidirect
571. #479	C₂²×C₂₃	semidirect
573. #477	C₂²×C₂₃	semidirect
574. #477	C₂²×C₂₃	semidirect
575. #477	C₂²×C₂₃	semidirect
578. #468	C₂²×C₂₃	semidirect
580. #467	C₂²×C₂₃	semidirect
587. #462	C₂²×C₂₃	semidirect
588. #461	C₂²×C₂₃	semidirect
591. #451	C₂²×C₂₃	semidirect
595. #448	C₂²×C₂₃	semidirect
597. #446	C₂²×C₂₃	semidirect
598. #441	C₂²×C₂₃	semidirect
600. #440	C₂²×C₂₃	semidirect
601. #440	C₂²×C₂₃	semidirect
602. C₄×Q₁₆	C₂²×C₂₃	semidirect
605. #435	C₂²×C₂₃	semidirect
607. #433	C₂²×C₂₃	semidirect
609. #419	C₂²×C₂₃	semidirect
613. C₂×#103	C₂²×C₂₃	semidirect
615. #405	C₂²×C₂₃	semidirect
785. C₂₃	#62604	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3561	2
C₂₃×#3552	2
C₂₃×#3377	2
C₂₃×#3367	2
C₂₃×#3320	2
C₂₃×#3314	2
C₂₃×#3313	2
C₂₃×#3308	2
C₂₃×#3299	2
C₂₃×#3297	2
C₂₃×#3243	2
C₂₃×#3230	2
C₂₃×#3225	2
C₂₃×#3211	2
C₂₃×#3181	2
C₂₃×#3175	2
C₂₃×#3137	2
C₂×C₂₃×#489	2
C₂₃×#2968	2
#62604	23

Subgroups — C23×#62604 #19210230

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62604 #19210230