Subgroups — C₂₃×#61743 #19209369

Order 5888.

1770 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3356	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3353	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3348	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3347	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3342	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3340	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3332	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3315	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3307	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3305	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3197	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3191	C₂	1	2	yes	maximal, complemented
19	C₂₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3093	C₂	1	2	yes	maximal, complemented
22	C₂₃×#3091	C₂	1	2	yes	maximal, complemented
23	C₂₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#559	—	2	1	no	—
25	C₂₃×#559	—	2	1	no	—
26	C₂₃×#556	C₂²	1	1	yes	characteristic
27	C₂₃×#556	C₂²	1	1	yes	characteristic
28	C₂₃×#556	C₂²	1	1	yes	characteristic
29	C₂₃×#555	C₂²	1	1	yes	characteristic
30	C₂₃×#555	C₂²	1	2	yes	—
31	C₂₃×#554	C₂²	1	1	yes	characteristic
32	C₂₃×#553	—	2	2	no	—
33	C₂₃×#553	C₂²	1	2	yes	—
34	C₂₃×#552	—	2	1	no	—
35	C₂₃×#552	C₂²	1	2	yes	—
36	C₂₃×#551	—	2	2	no	—
37	C₂₃×#550	C₂²	1	1	yes	characteristic
38	C₂₃×#550	C₂²	1	1	yes	characteristic
39	C₂₃×#547	C₂²	1	2	yes	—
40	C₂₃×#547	C₂²	1	1	yes	characteristic
41	C₂₃×#546	—	2	1	no	—
42	C₂₃×#538	—	2	2	no	—
43	C₂₃×#535	—	2	1	no	—
44	C₂₃×#533	C₂²	1	1	yes	characteristic
45	C₂₃×#533	C₂²	1	1	yes	characteristic
46	C₂₃×#532	C₂²	1	1	yes	characteristic
47	C₂₃×#529	—	2	2	no	—
48	C₂₃×#529	—	2	1	no	—
49	C₂₃×#525	C₂²	1	2	yes	—
50	C₂₃×#525	C₂²	1	2	yes	—
51	C₂₃×#525	C₂²	1	2	yes	—
52	C₂₃×#520	—	2	1	no	—
53	C₄×#41×C₂₃	—	2	1	no	—
54	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
56	C₂×C₂₃×#117	C₂²	1	2	yes	—
57	C₂₃×#501	C₂²	1	2	yes	complemented
58	C₂₃×#500	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#498	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#491	C₂²	1	2	yes	complemented
61	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#485	C₂²	1	2	yes	—
64	C₂₃×#485	C₂²	1	2	yes	—
65	C₂₃×#485	C₂²	1	1	yes	characteristic
66	C₂₃×#485	C₂²	1	1	yes	characteristic
67	C₂₃×#485	C₂²	1	2	yes	complemented
68	C₂₃×#485	C₂²	1	2	yes	complemented
69	C₂₃×#485	C₂²	1	2	yes	complemented
70	C₂₃×#485	C₂²	1	2	yes	complemented
71	C₂₃×#484	C₂²	1	2	yes	complemented
72	C₂₃×#483	C₂²	1	2	yes	complemented
73	C₂₃×#482	C₂²	1	2	yes	—
74	C₂₃×#482	C₂²	1	2	yes	—
75	C₂₃×#482	C₂²	1	2	yes	—
76	C₂₃×#482	C₂²	1	2	yes	complemented
77	C₂₃×#482	C₂²	1	2	yes	complemented
78	C₂₃×#482	C₂²	1	2	yes	complemented
79	C₂₃×#482	C₂²	1	2	yes	complemented
80	C₂₃×#481	C₂²	1	2	yes	complemented
81	C₂₃×#480	C₂²	1	2	yes	complemented
82	C₂₃×#478	C₂²	1	2	yes	complemented
83	C₂₃×#478	C₂²	1	2	yes	complemented
84	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
85	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
86	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
87	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
88	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
89	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
90	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#470	C₂²	1	2	yes	complemented
93	C₂₃×#469	C₂²	1	2	yes	complemented
94	C₂₃×#468	C₂²	1	2	yes	complemented
95	C₂₃×#468	C₂²	1	2	yes	complemented
96	C₂₃×#467	C₂²	1	2	yes	complemented
97	C₂₃×#466	C₂²	1	2	yes	complemented
98	C₂₃×#465	C₂²	1	2	yes	complemented
99	C₂₃×#465	C₂²	1	2	yes	complemented
100	C₂₃×#462	C₂²	1	1	yes	characteristic, complemented
101	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
102	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
103	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
104	C₂₃×#452	C₂²	1	1	yes	characteristic
105	C₂₃×#452	C₂²	1	1	yes	characteristic
106	C₂₃×#452	C₂²	1	2	yes	complemented
107	C₂₃×#452	C₂²	1	2	yes	complemented
108	C₂₃×#449	C₂²	1	2	yes	—
109	C₂₃×#449	C₂²	1	2	yes	complemented
110	C₂₃×#449	C₂²	1	2	yes	complemented
111	C₂₃×#442	C₂²	1	2	yes	complemented
112	C₂₃×#440	C₂²	1	2	yes	complemented
113	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
114	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
117	C₂₃×#436	C₂²	1	1	yes	characteristic
118	C₂₃×#436	C₂²	1	1	yes	characteristic
119	C₂₃×#435	C₂²	1	2	yes	—
120	C₂₃×#435	C₂²	1	2	yes	—
121	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
122	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
123	C₂₃×#432	C₂²	1	1	yes	characteristic
124	C₂₃×#431	C₂²	1	1	yes	characteristic
125	C₂₃×#428	C₂²	1	2	yes	complemented
126	C₂₃×#428	C₂²	1	2	yes	complemented
127	C₂₃×#427	C₂²	1	2	yes	complemented
128	C₂₃×#427	C₂²	1	2	yes	complemented
129	C₂₃×#417	C₂²	1	2	yes	complemented
130	C₂₃×#417	C₂²	1	2	yes	complemented
131	C₂₃×#416	C₂²	1	2	yes	complemented
132	C₂₃×#416	C₂²	1	2	yes	complemented
133	C₂₃×#407	C₂²	1	2	yes	—
134	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
135	C₂×#41×C₂₃	—	2	1	no	—
136	C₂×#41×C₂₃	—	2	1	no	—
137	C₂×#41×C₂₃	C₂³	1	2	yes	—
138	C₂×#41×C₂₃	C₂³	1	2	yes	—
139	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
141	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
143	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
147	C₂×D₈×C₂₃	C₂³	1	2	yes	—
148	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
149	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
150	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
151	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
152	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₂₃×#127	—	2	1	no	—
158	C₂₃×#127	—	2	1	no	—
159	C₂₃×#127	C₂³	1	1	yes	characteristic
160	C₂₃×#126	—	2	2	no	—
161	C₂₃×#126	—	2	2	no	—
162	C₂₃×#126	—	2	2	no	—
163	C₂₃×#126	—	2	2	no	—
164	C₂₃×#126	—	2	2	no	—
165	C₂₃×#125	—	2	2	no	—
166	C₂₃×#125	—	2	1	no	—
167	C₂₃×#125	—	2	1	no	—
168	C₂₃×#125	C₂³	1	2	yes	—
169	C₂₃×#124	—	2	1	no	—
170	C₂₃×#124	—	2	1	no	—
171	C₂₃×#124	—	2	1	no	—
172	C₂₃×#124	—	2	2	no	—
173	C₂₃×#124	—	2	2	no	—
174	C₂₃×#124	—	2	2	no	—
175	C₂₃×#124	—	2	1	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	—	2	2	no	—
182	C₂₃×#123	—	2	2	no	—
183	C₂₃×#123	—	2	2	no	—
184	C₂₃×C₂²⋊Q₈	—	2	1	no	—
185	C₂₃×C₂²⋊Q₈	—	2	1	no	—
186	C₂₃×C₂²⋊Q₈	—	2	1	no	—
187	C₂₃×C₂²⋊Q₈	—	2	1	no	—
188	C₂₃×C₂²⋊Q₈	—	2	2	no	—
189	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
191	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
192	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
193	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
194	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
195	C₂₃×#121	—	2	2	no	—
196	C₂₃×#121	—	2	2	no	—
197	C₂₃×#121	—	2	2	no	—
198	C₂₃×#121	—	2	1	no	—
199	C₂₃×#121	—	2	1	no	—
200	C₂₃×#121	—	2	2	no	—
201	C₂₃×#121	—	2	2	no	—
202	C₂₃×#121	C₂³	1	2	yes	—
203	C₂₃×#121	C₂³	1	2	yes	—
204	C₂₃×#121	C₂³	1	2	yes	—
205	C₂₃×#121	C₂³	1	2	yes	—
206	C₂₃×#121	C₂³	1	2	yes	—
207	C₂₃×#120	—	2	2	no	—
208	C₂₃×#120	—	2	2	no	—
209	C₂₃×#120	—	2	2	no	—
210	C₄×Q₈×C₂₃	—	2	1	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	—	2	1	no	—
215	C₄×Q₈×C₂₃	—	2	1	no	—
216	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₂₃	—	2	1	no	—
221	C₄×D₄×C₂₃	—	2	1	no	—
222	C₄×D₄×C₂₃	—	2	1	no	—
223	C₄×D₄×C₂₃	—	2	2	no	—
224	C₄×D₄×C₂₃	—	2	2	no	—
225	C₄×D₄×C₂₃	—	2	2	no	—
226	C₄×D₄×C₂₃	—	2	2	no	—
227	C₄×D₄×C₂₃	—	2	2	no	—
228	C₄×D₄×C₂₃	—	2	2	no	—
229	C₄×D₄×C₂₃	—	2	1	no	—
230	C₄×D₄×C₂₃	—	2	1	no	—
231	C₄×D₄×C₂₃	—	2	2	no	—
232	C₄×D₄×C₂₃	—	2	1	no	—
233	C₄×D₄×C₂₃	D₄	1	2	yes	—
234	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
235	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
236	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₂₃	C₂³	1	2	yes	—
238	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₂₃	C₂³	1	2	yes	—
241	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
242	C₂₃×#117	—	2	2	no	—
243	C₂₃×#117	—	2	2	no	—
244	C₂₃×#117	—	2	1	no	—
245	C₂₃×#117	—	2	1	no	—
246	C₂₃×#117	—	2	2	no	—
247	C₂₃×#117	—	2	2	no	—
248	C₂₃×#117	—	2	1	no	—
249	C₂₃×#117	C₂³	1	2	yes	—
250	C₂₃×#117	C₂³	1	2	yes	—
251	C₂₃×#117	C₂³	1	2	yes	—
252	C₂₃×#117	C₂³	1	2	yes	—
253	C₂₃×#117	C₂³	1	1	yes	characteristic
254	C₂₃×#117	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
256	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
259	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
260	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
261	C₂×C₄²×C₂₃	—	2	2	no	—
262	C₂×C₄²×C₂₃	—	2	1	no	—
263	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
264	C₂₃×#107	C₂³	1	1	yes	characteristic
265	C₂₃×#107	C₂³	1	2	yes	—
266	C₂₃×#107	C₂³	1	2	yes	—
267	C₂₃×#107	C₂³	1	2	yes	—
268	C₂₃×#107	C₂³	1	1	yes	characteristic
269	C₂₃×#107	C₂³	1	2	yes	—
270	C₂₃×#107	C₂³	1	2	yes	—
271	C₂₃×#106	C₂³	1	1	yes	characteristic
272	C₂₃×#106	C₂³	1	2	yes	—
273	C₂₃×#106	C₂³	1	2	yes	—
274	C₂₃×#106	C₂³	1	2	yes	—
275	C₂₃×#106	C₂³	1	1	yes	characteristic
276	C₂₃×#106	C₂³	1	2	yes	—
277	C₂₃×#106	C₂³	1	2	yes	—
278	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₂₃×#103	C₂³	1	1	yes	characteristic
283	C₂₃×#103	C₂³	1	1	yes	characteristic
284	C₂₃×#103	C₂³	1	2	yes	—
285	C₂₃×#103	C₂³	1	2	yes	—
286	C₂₃×#103	C₂³	1	1	yes	characteristic
287	C₂₃×#103	C₂³	1	1	yes	characteristic
288	C₂₃×#103	C₂³	1	2	yes	—
289	C₂₃×#103	C₂³	1	2	yes	—
290	C₂₃×#103	C₂³	1	1	yes	characteristic
291	C₂₃×#103	C₂³	1	1	yes	characteristic
292	C₂₃×#103	C₂³	1	2	yes	—
293	C₂₃×#102	C₂³	1	2	yes	—
294	C₂₃×#102	C₂³	1	2	yes	—
295	C₂₃×#102	C₂³	1	2	yes	—
296	C₂₃×#102	C₂³	1	2	yes	—
297	C₂₃×#102	C₂³	1	2	yes	—
298	C₂₃×#102	C₂³	1	2	yes	—
299	C₂₃×#102	C₂³	1	1	yes	characteristic
300	C₂₃×#102	C₂³	1	1	yes	characteristic
301	C₂₃×#102	C₂³	1	2	yes	—
302	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
307	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₂₃×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
312	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
313	#41×C₂₃	—	4	1	no	—
314	#41×C₂₃	—	4	1	no	—
315	#41×C₂₃	—	4	4	no	—
316	#41×C₂₃	—	4	2	no	—
317	#41×C₂₃	—	4	2	no	—
318	#41×C₂₃	—	4	2	no	—
319	#41×C₂₃	—	4	2	no	—
320	#41×C₂₃	—	4	4	no	—
321	C₂×Q₈×C₂₃	—	2	1	no	—
322	C₂×Q₈×C₂₃	—	2	1	no	—
323	C₂×Q₈×C₂₃	—	2	1	no	—
324	C₂×Q₈×C₂₃	—	2	1	no	—
325	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₂₃	—	2	2	no	—
329	C₂×D₄×C₂₃	—	2	1	no	—
330	C₂×D₄×C₂₃	—	2	2	no	—
331	C₂×D₄×C₂₃	—	2	2	no	—
332	C₂×D₄×C₂₃	—	2	2	no	—
333	C₂×D₄×C₂₃	—	2	2	no	—
334	C₂×D₄×C₂₃	—	2	2	no	—
335	C₂×D₄×C₂₃	—	2	2	no	—
336	C₂×D₄×C₂₃	—	2	1	no	—
337	C₂×D₄×C₂₃	—	2	1	no	—
338	C₂×D₄×C₂₃	—	4	2	no	—
339	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
341	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
342	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
343	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₂₃	—	2	2	no	—
345	C₂²×C₄×C₂₃	—	2	2	no	—
346	C₂²×C₄×C₂₃	—	2	1	no	—
347	C₂²×C₄×C₂₃	—	2	1	no	—
348	C₂²×C₄×C₂₃	—	2	2	no	—
349	C₂²×C₄×C₂₃	—	2	1	no	—
350	C₂²×C₄×C₂₃	—	2	2	no	—
351	C₂²×C₄×C₂₃	—	2	2	no	—
352	C₂²×C₄×C₂₃	—	4	2	no	—
353	C₂²×C₄×C₂₃	—	4	2	no	—
354	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
356	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
358	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
359	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
361	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
362	Q₁₆×C₂₃	—	4	1	no	—
363	Q₁₆×C₂₃	—	4	1	no	—
364	SD₁₆×C₂₃	—	4	1	no	—
365	SD₁₆×C₂₃	—	4	2	no	—
366	SD₁₆×C₂₃	—	4	1	no	—
367	D₈×C₂₃	—	4	2	no	—
368	M₁₆×C₂₃	—	4	2	no	—
369	M₁₆×C₂₃	—	4	2	no	—
370	C₂×C₈×C₂₃	—	4	2	no	—
371	C₂×C₈×C₂₃	—	4	2	no	—
372	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
376	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
378	C₄⋊C₄×C₂₃	—	2	1	no	—
379	C₄⋊C₄×C₂₃	—	2	2	no	—
380	C₄⋊C₄×C₂₃	—	2	2	no	—
381	C₄⋊C₄×C₂₃	—	2	2	no	—
382	C₄⋊C₄×C₂₃	—	2	2	no	—
383	C₄⋊C₄×C₂₃	—	2	1	no	—
384	C₄⋊C₄×C₂₃	—	2	1	no	—
385	C₄⋊C₄×C₂₃	—	2	2	no	—
386	C₄⋊C₄×C₂₃	—	2	2	no	—
387	C₄⋊C₄×C₂₃	—	2	1	no	—
388	C₄⋊C₄×C₂₃	—	2	1	no	—
389	C₄⋊C₄×C₂₃	—	2	1	no	—
390	C₄⋊C₄×C₂₃	—	2	1	no	—
391	C₄⋊C₄×C₂₃	—	2	1	no	—
392	C₄⋊C₄×C₂₃	—	2	2	no	—
393	C₄⋊C₄×C₂₃	—	2	2	no	—
394	C₄⋊C₄×C₂₃	—	2	1	no	—
395	C₄⋊C₄×C₂₃	—	2	1	no	—
396	C₄⋊C₄×C₂₃	—	2	1	no	—
397	C₄⋊C₄×C₂₃	—	2	1	no	—
398	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
408	C₂²⋊C₄×C₂₃	—	2	1	no	—
409	C₂²⋊C₄×C₂₃	—	2	2	no	—
410	C₂²⋊C₄×C₂₃	—	2	2	no	—
411	C₂²⋊C₄×C₂₃	—	2	2	no	—
412	C₂²⋊C₄×C₂₃	—	2	1	no	—
413	C₂²⋊C₄×C₂₃	—	2	1	no	—
414	C₂²⋊C₄×C₂₃	—	2	2	no	—
415	C₂²⋊C₄×C₂₃	—	2	2	no	—
416	C₂²⋊C₄×C₂₃	—	2	2	no	—
417	C₂²⋊C₄×C₂₃	—	2	2	no	—
418	C₂²⋊C₄×C₂₃	—	2	2	no	—
419	C₂²⋊C₄×C₂₃	—	2	2	no	—
420	C₂²⋊C₄×C₂₃	—	2	2	no	—
421	C₂²⋊C₄×C₂₃	—	2	2	no	—
422	C₂²⋊C₄×C₂₃	—	2	2	no	—
423	C₂²⋊C₄×C₂₃	—	2	1	no	—
424	C₂²⋊C₄×C₂₃	—	2	1	no	—
425	C₂²⋊C₄×C₂₃	—	2	2	no	—
426	C₂²⋊C₄×C₂₃	—	2	2	no	—
427	C₂²⋊C₄×C₂₃	—	2	2	no	—
428	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
432	C₄²×C₂₃	—	2	1	no	—
433	C₄²×C₂₃	—	2	2	no	—
434	C₄²×C₂₃	—	2	1	no	—
435	C₄²×C₂₃	—	2	2	no	—
436	C₄²×C₂₃	—	2	2	no	—
437	C₄²×C₂₃	—	2	1	no	—
438	C₄²×C₂₃	—	2	2	no	—
439	C₄²×C₂₃	—	2	2	no	—
440	C₄²×C₂₃	—	2	1	no	—
441	C₄²×C₂₃	—	2	1	no	—
442	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
445	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
446	#61743	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
447	C₂³×C₂₃	—	2	1	no	—
448	C₂³×C₂₃	—	2	2	no	—
449	C₂³×C₂₃	—	4	2	no	—
450	C₂³×C₂₃	—	4	2	no	—
451	C₂³×C₂₃	—	4	2	no	—
452	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
453	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
454	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
455	Q₈×C₂₃	—	2	1	no	—
456	Q₈×C₂₃	—	2	1	no	—
457	Q₈×C₂₃	—	2	1	no	—
458	Q₈×C₂₃	—	2	1	no	—
459	Q₈×C₂₃	—	2	1	no	—
460	Q₈×C₂₃	—	2	1	no	—
461	Q₈×C₂₃	—	4	2	no	—
462	Q₈×C₂₃	—	4	2	no	—
463	Q₈×C₂₃	—	8	1	no	—
464	Q₈×C₂₃	—	8	1	no	—
465	D₄×C₂₃	—	2	2	no	—
466	D₄×C₂₃	—	2	2	no	—
467	D₄×C₂₃	—	2	1	no	—
468	D₄×C₂₃	—	2	2	no	—
469	D₄×C₂₃	—	2	1	no	—
470	D₄×C₂₃	—	2	2	no	—
471	D₄×C₂₃	—	4	2	no	—
472	D₄×C₂₃	—	4	2	no	—
473	D₄×C₂₃	—	4	4	no	—
474	D₄×C₂₃	—	4	4	no	—
475	D₄×C₂₃	—	4	2	no	—
476	D₄×C₂₃	—	8	1	no	—
477	D₄×C₂₃	—	8	2	no	—
478	D₄×C₂₃	—	8	2	no	—
479	D₄×C₂₃	—	8	2	no	—
480	D₄×C₂₃	—	8	2	no	—
481	D₄×C₂₃	—	8	2	no	—
482	C₂×C₄×C₂₃	—	2	2	no	—
483	C₂×C₄×C₂₃	—	2	2	no	—
484	C₂×C₄×C₂₃	—	2	2	no	—
485	C₂×C₄×C₂₃	—	2	2	no	—
486	C₂×C₄×C₂₃	—	2	2	no	—
487	C₂×C₄×C₂₃	—	2	1	no	—
488	C₂×C₄×C₂₃	—	2	1	no	—
489	C₂×C₄×C₂₃	—	2	1	no	—
490	C₂×C₄×C₂₃	—	2	1	no	—
491	C₂×C₄×C₂₃	—	2	1	no	—
492	C₂×C₄×C₂₃	—	2	1	no	—
493	C₂×C₄×C₂₃	—	2	2	no	—
494	C₂×C₄×C₂₃	—	2	1	no	—
495	C₂×C₄×C₂₃	—	2	2	no	—
496	C₂×C₄×C₂₃	—	2	2	no	—
497	C₂×C₄×C₂₃	—	2	1	no	—
498	C₂×C₄×C₂₃	—	2	1	no	—
499	C₂×C₄×C₂₃	—	4	2	no	—
500	C₂×C₄×C₂₃	—	4	2	no	—
501	C₂×C₄×C₂₃	—	4	2	no	—
502	C₂×C₄×C₂₃	—	4	1	no	—
503	C₂×C₄×C₂₃	—	4	2	no	—
504	C₂×C₄×C₂₃	—	4	4	no	—
505	C₂×C₄×C₂₃	—	4	4	no	—
506	C₂×C₄×C₂₃	—	4	2	no	—
507	C₂×C₄×C₂₃	—	8	1	no	—
508	C₂×C₄×C₂₃	—	8	2	no	—
509	C₂×C₄×C₂₃	—	8	2	no	—
510	C₂×C₄×C₂₃	—	8	2	no	—
511	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
513	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
515	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
519	C₈×C₂₃	—	2	1	no	—
520	C₈×C₂₃	—	2	1	no	—
521	C₈×C₂₃	—	2	2	no	—
522	C₈×C₂₃	—	2	2	no	—
523	C₈×C₂₃	—	2	1	no	—
524	C₈×C₂₃	—	2	1	no	—
525	#3506	C₂×C₂₃	1	1	yes	characteristic, complemented
526	#3475	C₂×C₂₃	1	1	yes	characteristic, complemented
527	#3356	C₂×C₂₃	1	1	yes	characteristic, complemented
528	#3353	C₂×C₂₃	1	1	yes	characteristic, complemented
529	#3348	C₂×C₂₃	1	2	yes	complemented
530	#3347	C₂×C₂₃	1	2	yes	complemented
531	#3342	C₂×C₂₃	1	1	yes	characteristic, complemented
532	#3340	C₂×C₂₃	1	1	yes	characteristic, complemented
533	#3333	C₂×C₂₃	1	1	yes	characteristic, complemented
534	#3332	C₂×C₂₃	1	1	yes	characteristic, complemented
535	#3315	C₂×C₂₃	1	2	yes	complemented
536	#3307	C₂×C₂₃	1	2	yes	complemented
537	#3305	C₂×C₂₃	1	1	yes	characteristic, complemented
538	#3304	C₂×C₂₃	1	1	yes	characteristic, complemented
539	#3237	C₂×C₂₃	1	1	yes	characteristic, complemented
540	#3228	C₂×C₂₃	1	1	yes	characteristic, complemented
541	#3197	C₂×C₂₃	1	2	yes	complemented
542	#3191	C₂×C₂₃	1	2	yes	complemented
543	#3115	C₂×C₂₃	1	1	yes	characteristic, complemented
544	#3107	C₂×C₂₃	1	1	yes	characteristic, complemented
545	#3093	C₂×C₂₃	1	2	yes	complemented
546	#3091	C₂×C₂₃	1	2	yes	complemented
547	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
548	C₂²×C₂₃	—	2	1	no	—
549	C₂²×C₂₃	—	2	2	no	—
550	C₂²×C₂₃	—	2	2	no	—
551	C₂²×C₂₃	—	2	1	no	—
552	C₂²×C₂₃	—	2	2	no	—
553	C₂²×C₂₃	—	2	2	no	—
554	C₂²×C₂₃	—	2	1	no	—
555	C₂²×C₂₃	—	2	2	no	—
556	C₂²×C₂₃	—	2	2	no	—
557	C₂²×C₂₃	—	4	1	no	—
558	C₂²×C₂₃	—	4	2	no	—
559	C₂²×C₂₃	—	4	1	no	—
560	C₂²×C₂₃	—	4	2	no	—
561	C₂²×C₂₃	—	4	2	no	—
562	C₂²×C₂₃	—	4	1	no	—
563	C₂²×C₂₃	—	8	4	no	—
564	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
565	C₄×C₂₃	—	2	1	no	—
566	C₄×C₂₃	—	2	1	no	—
567	C₄×C₂₃	—	2	1	no	—
568	C₄×C₂₃	—	2	2	no	—
569	C₄×C₂₃	—	2	2	no	—
570	C₄×C₂₃	—	2	1	no	—
571	C₄×C₂₃	—	4	1	no	—
572	C₄×C₂₃	—	4	2	no	—
573	C₄×C₂₃	—	4	1	no	—
574	C₄×C₂₃	—	4	1	no	—
575	C₄×C₂₃	—	4	1	no	—
576	C₄×C₂₃	—	4	1	no	—
577	C₄×C₂₃	—	4	1	no	—
578	C₄×C₂₃	—	4	1	no	—
579	C₄×C₂₃	—	4	2	no	—
580	C₄×C₂₃	—	4	2	no	—
581	C₄×C₂₃	#575	1	2	yes	—
582	C₄×C₂₃	#585	1	1	yes	characteristic
583	C₄×C₂₃	#585	1	1	yes	characteristic
584	#559	—	2	1	no	—
585	#559	—	2	1	no	—
586	#556	C₂²×C₂₃	1	1	yes	characteristic
587	#556	C₂²×C₂₃	1	1	yes	characteristic
588	#556	C₂²×C₂₃	1	1	yes	characteristic
589	#555	C₂²×C₂₃	1	1	yes	characteristic
590	#555	C₂²×C₂₃	1	2	yes	—
591	#554	C₂²×C₂₃	1	1	yes	characteristic
592	#553	—	2	2	no	—
593	#553	C₂²×C₂₃	1	2	yes	—
594	#552	—	2	1	no	—
595	#552	C₂²×C₂₃	1	2	yes	—
596	#551	—	2	2	no	—
597	#550	C₂²×C₂₃	1	1	yes	characteristic
598	#550	C₂²×C₂₃	1	1	yes	characteristic
599	#547	C₂²×C₂₃	1	2	yes	—
600	#547	C₂²×C₂₃	1	1	yes	characteristic
601	#546	—	2	1	no	—
602	#538	—	2	2	no	—
603	#535	—	2	1	no	—
604	#533	C₂²×C₂₃	1	1	yes	characteristic
605	#533	C₂²×C₂₃	1	1	yes	characteristic
606	#532	C₂²×C₂₃	1	1	yes	characteristic
607	#529	—	2	2	no	—
608	#529	—	2	1	no	—
609	#525	C₂²×C₂₃	1	2	yes	—
610	#525	C₂²×C₂₃	1	2	yes	—
611	#525	C₂²×C₂₃	1	2	yes	—
612	#520	—	2	1	no	—
613	C₄×#41	—	2	1	no	—
614	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
615	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
616	C₂×#117	C₂²×C₂₃	1	2	yes	—
617	#501	C₂²×C₂₃	1	2	yes	complemented
618	#500	C₂²×C₂₃	1	1	yes	characteristic, complemented
619	#498	C₂²×C₂₃	1	1	yes	characteristic, complemented
620	#491	C₂²×C₂₃	1	2	yes	complemented
621	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
622	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
623	#485	C₂²×C₂₃	1	1	yes	characteristic
624	#485	C₂²×C₂₃	1	2	yes	—
625	#485	C₂²×C₂₃	1	1	yes	characteristic
626	#485	C₂²×C₂₃	1	2	yes	—
627	#485	C₂²×C₂₃	1	2	yes	complemented
628	#485	C₂²×C₂₃	1	2	yes	complemented
629	#485	C₂²×C₂₃	1	2	yes	complemented
630	#485	C₂²×C₂₃	1	2	yes	complemented
631	#484	C₂²×C₂₃	1	2	yes	complemented
632	#483	C₂²×C₂₃	1	2	yes	complemented
633	#482	C₂²×C₂₃	1	2	yes	—
634	#482	C₂²×C₂₃	1	2	yes	—
635	#482	C₂²×C₂₃	1	2	yes	—
636	#482	C₂²×C₂₃	1	2	yes	complemented
637	#482	C₂²×C₂₃	1	2	yes	complemented
638	#482	C₂²×C₂₃	1	2	yes	complemented
639	#482	C₂²×C₂₃	1	2	yes	complemented
640	#481	C₂²×C₂₃	1	2	yes	complemented
641	#480	C₂²×C₂₃	1	2	yes	complemented
642	#478	C₂²×C₂₃	1	2	yes	complemented
643	#478	C₂²×C₂₃	1	2	yes	complemented
644	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
645	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
646	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
647	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
648	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
649	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
650	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
651	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
652	#470	C₂²×C₂₃	1	2	yes	complemented
653	#469	C₂²×C₂₃	1	2	yes	complemented
654	#468	C₂²×C₂₃	1	2	yes	complemented
655	#468	C₂²×C₂₃	1	2	yes	complemented
656	#467	C₂²×C₂₃	1	2	yes	complemented
657	#466	C₂²×C₂₃	1	2	yes	complemented
658	#465	C₂²×C₂₃	1	2	yes	complemented
659	#465	C₂²×C₂₃	1	2	yes	complemented
660	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
661	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
662	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
663	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
664	#452	C₂²×C₂₃	1	1	yes	characteristic
665	#452	C₂²×C₂₃	1	1	yes	characteristic
666	#452	C₂²×C₂₃	1	2	yes	complemented
667	#452	C₂²×C₂₃	1	2	yes	complemented
668	#449	C₂²×C₂₃	1	2	yes	—
669	#449	C₂²×C₂₃	1	2	yes	complemented
670	#449	C₂²×C₂₃	1	2	yes	complemented
671	#442	C₂²×C₂₃	1	2	yes	complemented
672	#440	C₂²×C₂₃	1	2	yes	complemented
673	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
674	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
675	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
676	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
677	#436	C₂²×C₂₃	1	1	yes	characteristic
678	#436	C₂²×C₂₃	1	1	yes	characteristic
679	#435	C₂²×C₂₃	1	2	yes	—
680	#435	C₂²×C₂₃	1	2	yes	—
681	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
682	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
683	#432	C₂²×C₂₃	1	1	yes	characteristic
684	#431	C₂²×C₂₃	1	1	yes	characteristic
685	#428	C₂²×C₂₃	1	2	yes	complemented
686	#428	C₂²×C₂₃	1	2	yes	complemented
687	#427	C₂²×C₂₃	1	2	yes	complemented
688	#427	C₂²×C₂₃	1	2	yes	complemented
689	#417	C₂²×C₂₃	1	2	yes	complemented
690	#417	C₂²×C₂₃	1	2	yes	complemented
691	#416	C₂²×C₂₃	1	2	yes	complemented
692	#416	C₂²×C₂₃	1	2	yes	complemented
693	#407	C₂²×C₂₃	1	2	yes	—
694	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
695	C₂×C₂₃	—	4	2	no	—
696	C₂×C₂₃	—	4	2	no	—
697	C₂×C₂₃	—	4	1	no	—
698	C₂×C₂₃	—	8	1	no	—
699	C₂×C₂₃	—	8	2	no	—
700	C₂×C₂₃	#3485	1	1	yes	characteristic
701	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
702	C₂×C₂₃	#3584	1	1	yes	characteristic
703	C₂×#41	—	2	1	no	—
704	C₂×#41	—	2	1	no	—
705	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
706	C₂×#41	C₂³×C₂₃	1	2	yes	—
707	C₂×#41	C₂³×C₂₃	1	2	yes	—
708	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
709	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
710	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
711	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
712	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
713	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
714	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
715	C₂×D₈	C₂³×C₂₃	1	2	yes	—
716	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
717	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
718	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
719	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
720	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
721	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
723	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
725	#127	—	2	1	no	—
726	#127	—	2	1	no	—
727	#127	C₂³×C₂₃	1	1	yes	characteristic
728	#126	—	2	2	no	—
729	#126	—	2	2	no	—
730	#126	—	2	2	no	—
731	#126	—	2	2	no	—
732	#126	—	2	2	no	—
733	#125	—	2	2	no	—
734	#125	—	2	1	no	—
735	#125	—	2	1	no	—
736	#125	C₂³×C₂₃	1	2	yes	—
737	#124	—	2	1	no	—
738	#124	—	2	1	no	—
739	#124	—	2	1	no	—
740	#124	—	2	2	no	—
741	#124	—	2	2	no	—
742	#124	—	2	2	no	—
743	#124	—	2	1	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	1	no	—
754	C₂²⋊Q₈	—	2	1	no	—
755	C₂²⋊Q₈	—	2	1	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
758	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
759	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
760	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
762	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
763	#121	—	2	2	no	—
764	#121	—	2	1	no	—
765	#121	—	2	2	no	—
766	#121	—	2	2	no	—
767	#121	—	2	1	no	—
768	#121	—	2	2	no	—
769	#121	—	2	2	no	—
770	#121	C₂³×C₂₃	1	2	yes	—
771	#121	C₂³×C₂₃	1	2	yes	—
772	#121	C₂³×C₂₃	1	2	yes	—
773	#121	C₂³×C₂₃	1	2	yes	—
774	#121	C₂³×C₂₃	1	2	yes	—
775	#120	—	2	2	no	—
776	#120	—	2	2	no	—
777	#120	—	2	2	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	—	2	1	no	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
785	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
786	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
802	C₄×D₄	D₄×C₂₃	1	2	yes	—
803	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
804	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
805	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
806	C₄×D₄	C₂³×C₂₃	1	2	yes	—
807	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
808	C₄×D₄	C₂³×C₂₃	1	2	yes	—
809	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
810	#117	—	2	2	no	—
811	#117	—	2	2	no	—
812	#117	—	2	1	no	—
813	#117	—	2	1	no	—
814	#117	—	2	2	no	—
815	#117	—	2	2	no	—
816	#117	—	2	1	no	—
817	#117	C₂³×C₂₃	1	1	yes	characteristic
818	#117	C₂³×C₂₃	1	2	yes	—
819	#117	C₂³×C₂₃	1	2	yes	—
820	#117	C₂³×C₂₃	1	2	yes	—
821	#117	C₂³×C₂₃	1	2	yes	—
822	#117	C₂³×C₂₃	1	2	yes	—
823	C₂×C₄⋊C₄	—	2	2	no	—
824	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
825	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
826	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
827	C₂×C₂²⋊C₄	—	2	2	no	—
828	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
829	C₂×C₄²	—	2	2	no	—
830	C₂×C₄²	—	2	1	no	—
831	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
832	#107	C₂³×C₂₃	1	1	yes	characteristic
833	#107	C₂³×C₂₃	1	2	yes	—
834	#107	C₂³×C₂₃	1	2	yes	—
835	#107	C₂³×C₂₃	1	2	yes	—
836	#107	C₂³×C₂₃	1	1	yes	characteristic
837	#107	C₂³×C₂₃	1	2	yes	—
838	#107	C₂³×C₂₃	1	2	yes	—
839	#106	C₂³×C₂₃	1	1	yes	characteristic
840	#106	C₂³×C₂₃	1	2	yes	—
841	#106	C₂³×C₂₃	1	2	yes	—
842	#106	C₂³×C₂₃	1	2	yes	—
843	#106	C₂³×C₂₃	1	1	yes	characteristic
844	#106	C₂³×C₂₃	1	2	yes	—
845	#106	C₂³×C₂₃	1	2	yes	—
846	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
847	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
848	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
849	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
850	#103	C₂³×C₂₃	1	1	yes	characteristic
851	#103	C₂³×C₂₃	1	1	yes	characteristic
852	#103	C₂³×C₂₃	1	2	yes	—
853	#103	C₂³×C₂₃	1	2	yes	—
854	#103	C₂³×C₂₃	1	1	yes	characteristic
855	#103	C₂³×C₂₃	1	1	yes	characteristic
856	#103	C₂³×C₂₃	1	2	yes	—
857	#103	C₂³×C₂₃	1	2	yes	—
858	#103	C₂³×C₂₃	1	1	yes	characteristic
859	#103	C₂³×C₂₃	1	1	yes	characteristic
860	#103	C₂³×C₂₃	1	2	yes	—
861	#102	C₂³×C₂₃	1	2	yes	—
862	#102	C₂³×C₂₃	1	2	yes	—
863	#102	C₂³×C₂₃	1	2	yes	—
864	#102	C₂³×C₂₃	1	2	yes	—
865	#102	C₂³×C₂₃	1	2	yes	—
866	#102	C₂³×C₂₃	1	2	yes	—
867	#102	C₂³×C₂₃	1	1	yes	characteristic
868	#102	C₂³×C₂₃	1	1	yes	characteristic
869	#102	C₂³×C₂₃	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
871	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
873	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
874	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
875	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
876	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
877	#97	C₂³×C₂₃	1	2	yes	—
878	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
879	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
880	C₂₃	#61743	1	1	yes	characteristic, direct product factor, Sylow
881	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
882	#41	—	4	1	no	—
883	#41	—	4	1	no	—
884	#41	—	4	4	no	—
885	#41	—	4	2	no	—
886	#41	—	4	2	no	—
887	#41	—	4	2	no	—
888	#41	—	4	2	no	—
889	#41	—	4	4	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	1	no	—
892	C₂×Q₈	—	2	1	no	—
893	C₂×Q₈	—	2	1	no	—
894	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
895	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
896	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	1	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	4	2	no	—
908	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
909	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
910	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
911	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
912	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	4	2	no	—
922	C₂²×C₄	—	4	2	no	—
923	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
924	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
925	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
926	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
927	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
928	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
929	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
930	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
931	Q₁₆	—	4	1	no	—
932	Q₁₆	—	4	1	no	—
933	SD₁₆	—	4	1	no	—
934	SD₁₆	—	4	2	no	—
935	SD₁₆	—	4	1	no	—
936	D₈	—	4	2	no	—
937	M₁₆	—	4	2	no	—
938	M₁₆	—	4	2	no	—
939	C₂×C₈	—	4	2	no	—
940	C₂×C₈	—	4	2	no	—
941	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
942	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
943	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
944	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
945	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
946	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
968	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
969	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
970	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
971	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
973	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
975	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
998	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
999	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1000	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	—	2	2	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1012	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1013	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1014	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1015	C₂³	—	2	1	no	—
1016	C₂³	—	2	2	no	—
1017	C₂³	—	4	2	no	—
1018	C₂³	—	4	2	no	—
1019	C₂³	—	4	2	no	—
1020	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1021	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1022	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1023	Q₈	—	2	1	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	1	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	2	1	no	—
1029	Q₈	—	4	2	no	—
1030	Q₈	—	4	2	no	—
1031	Q₈	—	8	1	no	—
1032	Q₈	—	8	1	no	—
1033	D₄	—	2	2	no	—
1034	D₄	—	2	2	no	—
1035	D₄	—	2	1	no	—
1036	D₄	—	2	2	no	—
1037	D₄	—	2	1	no	—
1038	D₄	—	2	2	no	—
1039	D₄	—	4	2	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	4	4	no	—
1042	D₄	—	4	4	no	—
1043	D₄	—	4	2	no	—
1044	D₄	—	8	1	no	—
1045	D₄	—	8	2	no	—
1046	D₄	—	8	2	no	—
1047	D₄	—	8	2	no	—
1048	D₄	—	8	2	no	—
1049	D₄	—	8	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	4	2	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	4	1	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	4	no	—
1073	C₂×C₄	—	4	4	no	—
1074	C₂×C₄	—	4	2	no	—
1075	C₂×C₄	—	8	2	no	—
1076	C₂×C₄	—	8	2	no	—
1077	C₂×C₄	—	8	1	no	—
1078	C₂×C₄	—	8	2	no	—
1079	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1080	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1081	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1082	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1083	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1084	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1085	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1086	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1087	C₈	—	2	1	no	—
1088	C₈	—	2	1	no	—
1089	C₈	—	2	2	no	—
1090	C₈	—	2	2	no	—
1091	C₈	—	2	1	no	—
1092	C₈	—	2	1	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	2	1	no	—
1097	C₂²	—	2	2	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	2	1	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	4	1	no	—
1103	C₂²	—	4	2	no	—
1104	C₂²	—	4	2	no	—
1105	C₂²	—	4	1	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	2	no	—
1108	C₂²	—	8	4	no	—
1109	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1110	C₄	—	2	1	no	—
1111	C₄	—	2	2	no	—
1112	C₄	—	2	2	no	—
1113	C₄	—	2	1	no	—
1114	C₄	—	2	1	no	—
1115	C₄	—	2	1	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	1	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	2	no	—
1121	C₄	—	4	2	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	2	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	C₂₃×#575	1	2	yes	—
1127	C₄	C₂₃×#585	1	1	yes	characteristic
1128	C₄	C₂₃×#585	1	1	yes	characteristic
1129	C₂	—	4	1	no	—
1130	C₂	—	4	2	no	—
1131	C₂	—	4	2	no	—
1132	C₂	—	8	1	no	—
1133	C₂	—	8	2	no	—
1134	C₂	C₂₃×#3485	1	1	yes	characteristic
1135	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
1136	C₂	C₂₃×#3584	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 ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3506	C₂	semidirect
2. C₂₃×#3475	C₂	semidirect
3. C₂₃×#3356	C₂	semidirect
4. C₂₃×#3353	C₂	semidirect
5. C₂₃×#3348	C₂	semidirect
6. C₂₃×#3347	C₂	semidirect
7. C₂₃×#3342	C₂	semidirect
8. C₂₃×#3340	C₂	semidirect
9. C₂₃×#3333	C₂	semidirect
10. C₂₃×#3332	C₂	semidirect
11. C₂₃×#3315	C₂	semidirect
12. C₂₃×#3307	C₂	semidirect
13. C₂₃×#3305	C₂	semidirect
14. C₂₃×#3304	C₂	semidirect
15. C₂₃×#3237	C₂	semidirect
16. C₂₃×#3228	C₂	semidirect
17. C₂₃×#3197	C₂	semidirect
18. C₂₃×#3191	C₂	semidirect
19. C₂₃×#3115	C₂	semidirect
20. C₂₃×#3107	C₂	semidirect
21. C₂₃×#3093	C₂	semidirect
22. C₂₃×#3091	C₂	semidirect
23. C₂₃×#2974	C₂	semidirect
57. C₂₃×#501	C₂²	semidirect
58. C₂₃×#500	C₂²	semidirect
59. C₂₃×#498	C₂²	semidirect
60. C₂₃×#491	C₂²	semidirect
61. C₂₃×#486	C₂²	semidirect
62. C₂₃×#486	C₂²	semidirect
67. C₂₃×#485	C₂²	semidirect
68. C₂₃×#485	C₂²	semidirect
69. C₂₃×#485	C₂²	semidirect
70. C₂₃×#485	C₂²	semidirect
71. C₂₃×#484	C₂²	semidirect
72. C₂₃×#483	C₂²	semidirect
76. C₂₃×#482	C₂²	semidirect
77. C₂₃×#482	C₂²	semidirect
78. C₂₃×#482	C₂²	semidirect
79. C₂₃×#482	C₂²	semidirect
80. C₂₃×#481	C₂²	semidirect
81. C₂₃×#480	C₂²	semidirect
82. C₂₃×#478	C₂²	semidirect
83. C₂₃×#478	C₂²	semidirect
84. C₂₃×#477	C₂²	semidirect
85. C₂₃×#477	C₂²	semidirect
86. C₂₃×#475	C₂²	semidirect
87. C₂₃×#475	C₂²	semidirect
88. C₂₃×#475	C₂²	semidirect
89. C₂₃×#475	C₂²	semidirect
90. C₂₃×#474	C₂²	semidirect
91. C₂₃×#474	C₂²	semidirect
92. C₂₃×#470	C₂²	semidirect
93. C₂₃×#469	C₂²	semidirect
94. C₂₃×#468	C₂²	semidirect
95. C₂₃×#468	C₂²	semidirect
96. C₂₃×#467	C₂²	semidirect
97. C₂₃×#466	C₂²	semidirect
98. C₂₃×#465	C₂²	semidirect
99. C₂₃×#465	C₂²	semidirect
100. C₂₃×#462	C₂²	semidirect
101. C₂₃×#461	C₂²	semidirect
102. C₂₃×#460	C₂²	semidirect
103. C₂₃×#459	C₂²	semidirect
106. C₂₃×#452	C₂²	semidirect
107. C₂₃×#452	C₂²	semidirect
109. C₂₃×#449	C₂²	semidirect
110. C₂₃×#449	C₂²	semidirect
111. C₂₃×#442	C₂²	semidirect
112. C₂₃×#440	C₂²	semidirect
113. C₄×Q₁₆×C₂₃	C₂²	semidirect
114. C₄×Q₁₆×C₂₃	C₂²	semidirect
115. C₄×SD₁₆×C₂₃	C₂²	semidirect
116. C₄×SD₁₆×C₂₃	C₂²	semidirect
125. C₂₃×#428	C₂²	semidirect
126. C₂₃×#428	C₂²	semidirect
127. C₂₃×#427	C₂²	semidirect
128. C₂₃×#427	C₂²	semidirect
129. C₂₃×#417	C₂²	semidirect
130. C₂₃×#417	C₂²	semidirect
131. C₂₃×#416	C₂²	semidirect
132. C₂₃×#416	C₂²	semidirect
446. #61743	C₂₃	direct (N × H)
525. #3506	C₂×C₂₃	semidirect
526. #3475	C₂×C₂₃	semidirect
527. #3356	C₂×C₂₃	semidirect
528. #3353	C₂×C₂₃	semidirect
529. #3348	C₂×C₂₃	semidirect
530. #3347	C₂×C₂₃	semidirect
531. #3342	C₂×C₂₃	semidirect
532. #3340	C₂×C₂₃	semidirect
533. #3333	C₂×C₂₃	semidirect
534. #3332	C₂×C₂₃	semidirect
535. #3315	C₂×C₂₃	semidirect
536. #3307	C₂×C₂₃	semidirect
537. #3305	C₂×C₂₃	semidirect
538. #3304	C₂×C₂₃	semidirect
539. #3237	C₂×C₂₃	semidirect
540. #3228	C₂×C₂₃	semidirect
541. #3197	C₂×C₂₃	semidirect
542. #3191	C₂×C₂₃	semidirect
543. #3115	C₂×C₂₃	semidirect
544. #3107	C₂×C₂₃	semidirect
545. #3093	C₂×C₂₃	semidirect
546. #3091	C₂×C₂₃	semidirect
547. #2974	C₂×C₂₃	semidirect
617. #501	C₂²×C₂₃	semidirect
618. #500	C₂²×C₂₃	semidirect
619. #498	C₂²×C₂₃	semidirect
620. #491	C₂²×C₂₃	semidirect
621. #486	C₂²×C₂₃	semidirect
622. #486	C₂²×C₂₃	semidirect
627. #485	C₂²×C₂₃	semidirect
628. #485	C₂²×C₂₃	semidirect
629. #485	C₂²×C₂₃	semidirect
630. #485	C₂²×C₂₃	semidirect
631. #484	C₂²×C₂₃	semidirect
632. #483	C₂²×C₂₃	semidirect
636. #482	C₂²×C₂₃	semidirect
637. #482	C₂²×C₂₃	semidirect
638. #482	C₂²×C₂₃	semidirect
639. #482	C₂²×C₂₃	semidirect
640. #481	C₂²×C₂₃	semidirect
641. #480	C₂²×C₂₃	semidirect
642. #478	C₂²×C₂₃	semidirect
643. #478	C₂²×C₂₃	semidirect
644. #477	C₂²×C₂₃	semidirect
645. #477	C₂²×C₂₃	semidirect
646. #475	C₂²×C₂₃	semidirect
647. #475	C₂²×C₂₃	semidirect
648. #475	C₂²×C₂₃	semidirect
649. #475	C₂²×C₂₃	semidirect
650. #474	C₂²×C₂₃	semidirect
651. #474	C₂²×C₂₃	semidirect
652. #470	C₂²×C₂₃	semidirect
653. #469	C₂²×C₂₃	semidirect
654. #468	C₂²×C₂₃	semidirect
655. #468	C₂²×C₂₃	semidirect
656. #467	C₂²×C₂₃	semidirect
657. #466	C₂²×C₂₃	semidirect
658. #465	C₂²×C₂₃	semidirect
659. #465	C₂²×C₂₃	semidirect
660. #462	C₂²×C₂₃	semidirect
661. #461	C₂²×C₂₃	semidirect
662. #460	C₂²×C₂₃	semidirect
663. #459	C₂²×C₂₃	semidirect
666. #452	C₂²×C₂₃	semidirect
667. #452	C₂²×C₂₃	semidirect
669. #449	C₂²×C₂₃	semidirect
670. #449	C₂²×C₂₃	semidirect
671. #442	C₂²×C₂₃	semidirect
672. #440	C₂²×C₂₃	semidirect
673. C₄×Q₁₆	C₂²×C₂₃	semidirect
674. C₄×Q₁₆	C₂²×C₂₃	semidirect
675. C₄×SD₁₆	C₂²×C₂₃	semidirect
676. C₄×SD₁₆	C₂²×C₂₃	semidirect
685. #428	C₂²×C₂₃	semidirect
686. #428	C₂²×C₂₃	semidirect
687. #427	C₂²×C₂₃	semidirect
688. #427	C₂²×C₂₃	semidirect
689. #417	C₂²×C₂₃	semidirect
690. #417	C₂²×C₂₃	semidirect
691. #416	C₂²×C₂₃	semidirect
692. #416	C₂²×C₂₃	semidirect
880. C₂₃	#61743	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×#3506	2
C₂₃×#3475	2
C₂₃×#3356	2
C₂₃×#3353	2
C₂₃×#3348	2
C₂₃×#3347	2
C₂₃×#3342	2
C₂₃×#3340	2
C₂₃×#3333	2
C₂₃×#3332	2
C₂₃×#3315	2
C₂₃×#3307	2
C₂₃×#3305	2
C₂₃×#3304	2
C₂₃×#3237	2
C₂₃×#3228	2
C₂₃×#3197	2
C₂₃×#3191	2
C₂₃×#3115	2
C₂₃×#3107	2
C₂₃×#3093	2
C₂₃×#3091	2
C₂₃×#2974	2
#61743	23

Subgroups — C23×#61743 #19209369

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61743 #19209369