Subgroups — C₂₃×#62548 #19210174

Order 5888.

1748 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3375	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3329	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3328	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3321	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3319	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3313	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3311	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3233	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3233	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3212	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3211	C₂	1	2	yes	maximal, complemented
19	C₂₃×#3183	C₂	1	2	yes	maximal, complemented
20	C₂₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3140	C₂	1	2	yes	maximal, complemented
22	C₂₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#559	C₂²	1	1	yes	characteristic
25	Q₈²×C₂₃	C₂²	1	1	yes	characteristic, complemented
26	C₂₃×#556	—	2	1	no	—
27	C₂₃×#556	—	2	2	no	—
28	C₂₃×#556	C₂²	1	1	yes	characteristic
29	C₂₃×#556	C₂²	1	1	yes	characteristic
30	C₂₃×#556	C₂²	1	2	yes	complemented
31	C₂₃×#555	—	2	1	no	—
32	C₂₃×#555	C₂²	1	1	yes	characteristic
33	C₂₃×#555	C₂²	1	2	yes	complemented
34	C₂₃×#551	—	2	2	no	—
35	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
36	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
37	C₂₃×#548	—	2	1	no	—
38	C₂₃×#548	C₂²	1	2	yes	—
39	C₂₃×#546	—	2	1	no	—
40	C₂₃×#546	C₂²	1	2	yes	—
41	D₄²×C₂₃	C₂²	1	1	yes	characteristic
42	C₂₃×#542	—	2	1	no	—
43	C₂₃×#542	—	2	1	no	—
44	C₂₃×#542	—	2	2	no	—
45	C₂₃×#538	—	2	2	no	—
46	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×#533	C₂²	1	2	yes	complemented
48	C₂₃×#532	C₂²	1	1	yes	characteristic
49	C₂₃×#529	C₂²	1	1	yes	characteristic
50	C₂₃×#529	C₂²	1	2	yes	—
51	C₂₃×#529	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#529	C₂²	1	2	yes	complemented
53	C₂×C₂₃×#124	C₂²	1	2	yes	—
54	C₂₃×#519	—	2	1	no	—
55	C₂₃×#518	—	2	1	no	—
56	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
57	C₂₃×#499	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#499	C₂²	1	2	yes	complemented
59	C₂₃×#495	C₂²	1	1	yes	characteristic
60	C₂₃×#495	C₂²	1	2	yes	complemented
61	C₂₃×#489	C₂²	1	2	yes	—
62	C₂₃×#489	C₂²	1	2	yes	—
63	C₂₃×#489	C₂²	1	2	yes	complemented
64	C₂₃×#489	C₂²	1	2	yes	complemented
65	C₂₃×#488	C₂²	1	1	yes	characteristic
66	C₂₃×#488	C₂²	1	2	yes	—
67	C₂₃×#488	C₂²	1	1	yes	characteristic, complemented
68	C₂₃×#488	C₂²	1	2	yes	complemented
69	C₂₃×#488	C₂²	1	2	yes	complemented
70	C₂₃×#488	C₂²	1	2	yes	complemented
71	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
72	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
73	C₂₃×#486	C₂²	1	1	yes	characteristic
74	C₂₃×#486	C₂²	1	1	yes	characteristic
75	C₂₃×#485	C₂²	1	2	yes	complemented
76	C₂₃×#485	C₂²	1	2	yes	complemented
77	C₂₃×#485	C₂²	1	2	yes	complemented
78	C₂₃×#482	C₂²	1	2	yes	—
79	C₂₃×#482	C₂²	1	2	yes	—
80	C₂₃×#482	C₂²	1	2	yes	—
81	C₂₃×#477	C₂²	1	2	yes	complemented
82	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
83	C₂₃×#476	C₂²	1	1	yes	characteristic
84	C₂₃×#476	C₂²	1	2	yes	complemented
85	C₂₃×#475	C₂²	1	2	yes	complemented
86	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
87	C₂₃×#474	C₂²	1	1	yes	characteristic
88	C₂₃×#474	C₂²	1	2	yes	complemented
89	C₂₃×#470	C₂²	1	2	yes	complemented
90	C₂₃×#469	C₂²	1	2	yes	—
91	C₂₃×#468	C₂²	1	2	yes	—
92	C₂₃×#468	C₂²	1	2	yes	complemented
93	C₂₃×#467	C₂²	1	1	yes	characteristic, complemented
94	C₂₃×#466	C₂²	1	1	yes	characteristic
95	C₂₃×#465	C₂²	1	1	yes	characteristic
96	C₂₃×#465	C₂²	1	1	yes	characteristic, complemented
97	C₂₃×#464	C₂²	1	2	yes	—
98	C₂₃×#464	C₂²	1	2	yes	complemented
99	C₂₃×#463	C₂²	1	2	yes	—
100	C₂₃×#463	C₂²	1	2	yes	complemented
101	C₂₃×#462	C₂²	1	1	yes	characteristic, complemented
102	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
103	C₂₃×#460	C₂²	1	1	yes	characteristic
104	C₂₃×#459	C₂²	1	1	yes	characteristic
105	C₂₃×#452	C₂²	1	2	yes	complemented
106	C₂₃×#451	C₂²	1	2	yes	complemented
107	C₂₃×#450	C₂²	1	2	yes	—
108	C₂₃×#449	C₂²	1	2	yes	complemented
109	C₂₃×#448	C₂²	1	2	yes	complemented
110	C₂₃×#447	C₂²	1	2	yes	—
111	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
112	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
113	C₂₃×#442	C₂²	1	2	yes	complemented
114	C₂₃×#441	C₂²	1	2	yes	complemented
115	C₂₃×#440	C₂²	1	2	yes	complemented
116	C₂₃×#440	C₂²	1	2	yes	complemented
117	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
121	C₂₃×#436	C₂²	1	1	yes	characteristic
122	C₂₃×#436	C₂²	1	1	yes	characteristic
123	C₂₃×#435	C₂²	1	2	yes	complemented
124	C₂₃×#435	C₂²	1	2	yes	complemented
125	C₂₃×#431	C₂²	1	2	yes	complemented
126	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
127	C₂₃×#419	C₂²	1	2	yes	complemented
128	C₂₃×#419	C₂²	1	2	yes	complemented
129	C₂₃×#418	C₂²	1	2	yes	—
130	C₂₃×#418	C₂²	1	2	yes	—
131	C₂₃×#416	C₂²	1	2	yes	complemented
132	C₂₃×#416	C₂²	1	2	yes	complemented
133	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
136	C₂×#41×C₂₃	C₂³	1	2	yes	—
137	C₂²×Q₈×C₂₃	—	2	1	no	—
138	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
139	C₂²×D₄×C₂₃	—	2	1	no	—
140	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
142	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
147	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×D₈×C₂₃	C₂³	1	2	yes	—
149	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
150	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
151	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
153	C₂₃×C₄⋊Q₈	—	2	1	no	—
154	C₂₃×C₄⋊Q₈	—	2	1	no	—
155	C₂₃×C₄⋊Q₈	—	2	2	no	—
156	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
159	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₂₃×#127	C₂³	1	1	yes	characteristic
162	C₂₃×#126	—	2	2	no	—
163	C₂₃×#126	—	2	2	no	—
164	C₂₃×#126	—	2	2	no	—
165	C₂₃×#126	—	2	2	no	—
166	C₂₃×#126	—	2	1	no	—
167	C₂₃×#126	—	2	2	no	—
168	C₂₃×#126	—	2	1	no	—
169	C₂₃×#126	—	2	2	no	—
170	C₂₃×#125	C₂³	1	1	yes	characteristic
171	C₂₃×#125	C₂³	1	2	yes	—
172	C₂₃×#125	C₂³	1	1	yes	characteristic
173	C₂₃×#124	—	2	1	no	—
174	C₂₃×#124	—	2	1	no	—
175	C₂₃×#124	—	2	2	no	—
176	C₂₃×#124	—	2	2	no	—
177	C₂₃×#124	—	2	2	no	—
178	C₂₃×#124	—	2	2	no	—
179	C₂₃×#124	—	2	2	no	—
180	C₂₃×#124	—	2	2	no	—
181	C₂₃×#124	—	2	2	no	—
182	C₂₃×#124	C₂³	1	2	yes	—
183	C₂₃×#124	C₂³	1	2	yes	—
184	C₂₃×#124	C₂³	1	1	yes	characteristic
185	C₂₃×#124	C₂³	1	2	yes	—
186	C₂₃×#124	C₂³	1	1	yes	characteristic
187	C₂₃×#123	—	2	2	no	—
188	C₂₃×#123	—	2	1	no	—
189	C₂₃×#123	—	2	2	no	—
190	C₂₃×#123	—	2	1	no	—
191	C₂₃×#123	—	2	2	no	—
192	C₂₃×#123	—	2	2	no	—
193	C₂₃×C₂²⋊Q₈	—	2	1	no	—
194	C₂₃×C₂²⋊Q₈	—	2	1	no	—
195	C₂₃×C₂²⋊Q₈	—	2	2	no	—
196	C₂₃×C₂²⋊Q₈	—	2	2	no	—
197	C₂₃×C₂²⋊Q₈	—	2	1	no	—
198	C₂₃×C₂²⋊Q₈	—	2	2	no	—
199	C₂₃×C₂²⋊Q₈	—	2	1	no	—
200	C₂₃×C₂²⋊Q₈	—	2	2	no	—
201	C₂₃×C₂²⋊Q₈	—	2	2	no	—
202	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
203	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
205	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
206	C₂₃×#121	—	2	1	no	—
207	C₂₃×#121	—	2	2	no	—
208	C₂₃×#121	—	2	2	no	—
209	C₂₃×#121	—	2	1	no	—
210	C₂₃×#121	—	2	1	no	—
211	C₂₃×#121	—	2	1	no	—
212	C₂₃×#121	—	2	2	no	—
213	C₂₃×#121	C₂³	1	2	yes	—
214	C₂₃×#121	C₂³	1	2	yes	—
215	C₂₃×#121	C₂³	1	1	yes	characteristic
216	C₂₃×#121	C₂³	1	1	yes	characteristic
217	C₂₃×#120	—	2	2	no	—
218	C₂₃×#120	—	2	2	no	—
219	C₄×Q₈×C₂₃	—	2	1	no	—
220	C₄×Q₈×C₂₃	—	2	1	no	—
221	C₄×Q₈×C₂₃	—	2	2	no	—
222	C₄×Q₈×C₂₃	—	2	2	no	—
223	C₄×Q₈×C₂₃	—	2	1	no	—
224	C₄×Q₈×C₂₃	—	2	1	no	—
225	C₄×Q₈×C₂₃	—	2	2	no	—
226	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
227	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
228	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
231	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₂₃	—	2	1	no	—
233	C₄×D₄×C₂₃	—	2	1	no	—
234	C₄×D₄×C₂₃	—	2	2	no	—
235	C₄×D₄×C₂₃	—	2	1	no	—
236	C₄×D₄×C₂₃	—	2	2	no	—
237	C₄×D₄×C₂₃	—	2	1	no	—
238	C₄×D₄×C₂₃	—	2	2	no	—
239	C₄×D₄×C₂₃	—	2	1	no	—
240	C₄×D₄×C₂₃	—	2	1	no	—
241	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
242	C₄×D₄×C₂₃	D₄	1	2	yes	—
243	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₂₃	C₂³	1	2	yes	—
245	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₂₃	C₂³	1	2	yes	—
247	C₄×D₄×C₂₃	C₂³	1	2	yes	—
248	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
249	C₂₃×#117	—	2	1	no	—
250	C₂₃×#117	—	2	1	no	—
251	C₂₃×#117	—	2	2	no	—
252	C₂₃×#117	—	2	2	no	—
253	C₂₃×#117	—	2	1	no	—
254	C₂₃×#117	—	2	1	no	—
255	C₂₃×#117	—	2	2	no	—
256	C₂₃×#117	D₄	1	2	yes	—
257	C₂₃×#117	D₄	1	1	yes	characteristic
258	C₂₃×#117	C₂³	1	2	yes	—
259	C₂₃×#117	C₂³	1	2	yes	—
260	C₂₃×#117	C₂³	1	2	yes	—
261	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
262	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
263	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
264	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
265	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
266	C₂₃×#107	C₂³	1	1	yes	characteristic
267	C₂₃×#107	C₂³	1	1	yes	characteristic
268	C₂₃×#107	C₂³	1	2	yes	—
269	C₂₃×#107	C₂³	1	2	yes	—
270	C₂₃×#106	C₂³	1	1	yes	characteristic
271	C₂₃×#106	C₂³	1	1	yes	characteristic
272	C₂₃×#106	C₂³	1	2	yes	—
273	C₂₃×#106	C₂³	1	2	yes	—
274	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
275	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
276	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₂₃×#103	C₂³	1	2	yes	—
279	C₂₃×#103	C₂³	1	2	yes	—
280	C₂₃×#103	C₂³	1	2	yes	—
281	C₂₃×#103	C₂³	1	2	yes	—
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	2	yes	—
287	C₂₃×#103	C₂³	1	2	yes	—
288	C₂₃×#103	C₂³	1	1	yes	characteristic
289	C₂₃×#103	C₂³	1	1	yes	characteristic
290	C₂₃×#102	C₂³	1	2	yes	—
291	C₂₃×#102	C₂³	1	2	yes	—
292	C₂₃×#102	C₂³	1	2	yes	—
293	C₂₃×#102	C₂³	1	2	yes	—
294	C₂₃×#102	C₂³	1	1	yes	characteristic
295	C₂₃×#102	C₂³	1	1	yes	characteristic
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	2	yes	—
300	C₂₃×#102	C₂³	1	1	yes	characteristic
301	C₂₃×#102	C₂³	1	1	yes	characteristic
302	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
303	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂₃×#97	C₂³	1	2	yes	—
306	C₂₃×#97	C₂³	1	2	yes	—
307	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₂₃	C₂³	1	2	yes	—
312	C₂⁴×C₂₃	—	2	2	no	—
313	#41×C₂₃	—	4	2	no	—
314	#41×C₂₃	—	4	2	no	—
315	#41×C₂₃	—	4	2	no	—
316	C₂×Q₈×C₂₃	—	2	2	no	—
317	C₂×Q₈×C₂₃	—	2	1	no	—
318	C₂×Q₈×C₂₃	—	2	2	no	—
319	C₂×Q₈×C₂₃	—	2	1	no	—
320	C₂×Q₈×C₂₃	—	2	2	no	—
321	C₂×Q₈×C₂₃	—	4	2	no	—
322	C₂×Q₈×C₂₃	—	4	2	no	—
323	C₂×Q₈×C₂₃	—	4	4	no	—
324	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
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	1	no	—
332	C₂×D₄×C₂₃	—	2	2	no	—
333	C₂×D₄×C₂₃	—	2	1	no	—
334	C₂×D₄×C₂₃	—	2	1	no	—
335	C₂×D₄×C₂₃	—	2	2	no	—
336	C₂×D₄×C₂₃	—	4	2	no	—
337	C₂×D₄×C₂₃	—	4	2	no	—
338	C₂×D₄×C₂₃	—	4	4	no	—
339	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
341	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
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	1	no	—
346	C₂²×C₄×C₂₃	—	2	2	no	—
347	C₂²×C₄×C₂₃	—	2	1	no	—
348	C₂²×C₄×C₂₃	—	2	2	no	—
349	C₂²×C₄×C₂₃	—	2	2	no	—
350	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
352	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
353	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
356	Q₁₆×C₂₃	—	4	1	no	—
357	Q₁₆×C₂₃	—	4	2	no	—
358	SD₁₆×C₂₃	—	4	1	no	—
359	SD₁₆×C₂₃	—	4	1	no	—
360	SD₁₆×C₂₃	—	4	2	no	—
361	SD₁₆×C₂₃	—	4	2	no	—
362	D₈×C₂₃	—	4	1	no	—
363	D₈×C₂₃	—	4	2	no	—
364	M₁₆×C₂₃	—	4	2	no	—
365	M₁₆×C₂₃	—	4	2	no	—
366	C₂×C₈×C₂₃	—	4	1	no	—
367	C₂×C₈×C₂₃	—	4	1	no	—
368	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
372	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
374	C₄⋊C₄×C₂₃	—	2	1	no	—
375	C₄⋊C₄×C₂₃	—	2	1	no	—
376	C₄⋊C₄×C₂₃	—	2	1	no	—
377	C₄⋊C₄×C₂₃	—	2	1	no	—
378	C₄⋊C₄×C₂₃	—	2	2	no	—
379	C₄⋊C₄×C₂₃	—	2	1	no	—
380	C₄⋊C₄×C₂₃	—	2	1	no	—
381	C₄⋊C₄×C₂₃	—	2	2	no	—
382	C₄⋊C₄×C₂₃	—	2	1	no	—
383	C₄⋊C₄×C₂₃	—	2	2	no	—
384	C₄⋊C₄×C₂₃	—	2	2	no	—
385	C₄⋊C₄×C₂₃	—	2	1	no	—
386	C₄⋊C₄×C₂₃	—	2	2	no	—
387	C₄⋊C₄×C₂₃	—	2	1	no	—
388	C₄⋊C₄×C₂₃	—	2	2	no	—
389	C₄⋊C₄×C₂₃	—	2	1	no	—
390	C₄⋊C₄×C₂₃	—	2	2	no	—
391	C₄⋊C₄×C₂₃	—	2	1	no	—
392	C₄⋊C₄×C₂₃	—	2	2	no	—
393	C₄⋊C₄×C₂₃	—	2	1	no	—
394	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
399	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
404	C₂²⋊C₄×C₂₃	—	2	2	no	—
405	C₂²⋊C₄×C₂₃	—	2	2	no	—
406	C₂²⋊C₄×C₂₃	—	2	2	no	—
407	C₂²⋊C₄×C₂₃	—	2	2	no	—
408	C₂²⋊C₄×C₂₃	—	2	1	no	—
409	C₂²⋊C₄×C₂₃	—	2	2	no	—
410	C₂²⋊C₄×C₂₃	—	2	1	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	1	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	1	no	—
421	C₂²⋊C₄×C₂₃	—	2	2	no	—
422	C₂²⋊C₄×C₂₃	—	2	1	no	—
423	C₂²⋊C₄×C₂₃	—	2	2	no	—
424	C₂²⋊C₄×C₂₃	—	2	1	no	—
425	C₂²⋊C₄×C₂₃	—	2	1	no	—
426	C₂²⋊C₄×C₂₃	—	2	2	no	—
427	C₂²⋊C₄×C₂₃	—	2	2	no	—
428	C₂²⋊C₄×C₂₃	—	2	1	no	—
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	2	no	—
433	C₄²×C₂₃	—	2	2	no	—
434	C₄²×C₂₃	—	2	2	no	—
435	C₄²×C₂₃	—	2	2	no	—
436	C₄²×C₂₃	—	2	1	no	—
437	C₄²×C₂₃	—	2	2	no	—
438	C₄²×C₂₃	—	2	1	no	—
439	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₂₃	C₂×D₄	1	2	yes	—
441	C₄²×C₂₃	C₂×D₄	1	2	yes	—
442	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₂₃	C₂⁴	1	2	yes	—
444	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
445	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
446	#62548	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
447	C₂³×C₂₃	—	2	1	no	—
448	C₂³×C₂₃	—	2	1	no	—
449	C₂³×C₂₃	—	2	2	no	—
450	C₂³×C₂₃	—	4	4	no	—
451	C₂³×C₂₃	—	8	2	no	—
452	C₂³×C₂₃	—	8	2	no	—
453	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
454	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
455	Q₈×C₂₃	—	2	2	no	—
456	Q₈×C₂₃	—	2	1	no	—
457	Q₈×C₂₃	—	2	1	no	—
458	Q₈×C₂₃	—	2	1	no	—
459	Q₈×C₂₃	—	2	2	no	—
460	Q₈×C₂₃	—	2	1	no	—
461	Q₈×C₂₃	—	2	2	no	—
462	Q₈×C₂₃	—	4	4	no	—
463	Q₈×C₂₃	—	4	2	no	—
464	Q₈×C₂₃	—	8	2	no	—
465	Q₈×C₂₃	—	8	1	no	—
466	Q₈×C₂₃	—	8	2	no	—
467	D₄×C₂₃	—	2	2	no	—
468	D₄×C₂₃	—	2	1	no	—
469	D₄×C₂₃	—	2	1	no	—
470	D₄×C₂₃	—	2	1	no	—
471	D₄×C₂₃	—	2	2	no	—
472	D₄×C₂₃	—	2	1	no	—
473	D₄×C₂₃	—	2	2	no	—
474	D₄×C₂₃	—	4	2	no	—
475	D₄×C₂₃	—	4	4	no	—
476	D₄×C₂₃	—	4	2	no	—
477	D₄×C₂₃	—	8	1	no	—
478	D₄×C₂₃	—	8	2	no	—
479	D₄×C₂₃	—	8	1	no	—
480	D₄×C₂₃	—	8	1	no	—
481	D₄×C₂₃	—	8	2	no	—
482	D₄×C₂₃	—	8	2	no	—
483	C₂×C₄×C₂₃	—	2	2	no	—
484	C₂×C₄×C₂₃	—	2	1	no	—
485	C₂×C₄×C₂₃	—	2	1	no	—
486	C₂×C₄×C₂₃	—	2	2	no	—
487	C₂×C₄×C₂₃	—	2	2	no	—
488	C₂×C₄×C₂₃	—	2	1	no	—
489	C₂×C₄×C₂₃	—	2	2	no	—
490	C₂×C₄×C₂₃	—	2	1	no	—
491	C₂×C₄×C₂₃	—	2	1	no	—
492	C₂×C₄×C₂₃	—	2	2	no	—
493	C₂×C₄×C₂₃	—	2	1	no	—
494	C₂×C₄×C₂₃	—	2	1	no	—
495	C₂×C₄×C₂₃	—	2	1	no	—
496	C₂×C₄×C₂₃	—	2	2	no	—
497	C₂×C₄×C₂₃	—	4	2	no	—
498	C₂×C₄×C₂₃	—	4	1	no	—
499	C₂×C₄×C₂₃	—	4	2	no	—
500	C₂×C₄×C₂₃	—	4	4	no	—
501	C₂×C₄×C₂₃	—	4	2	no	—
502	C₂×C₄×C₂₃	—	4	2	no	—
503	C₂×C₄×C₂₃	—	8	2	no	—
504	C₂×C₄×C₂₃	—	8	2	no	—
505	C₂×C₄×C₂₃	—	8	2	no	—
506	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
515	C₈×C₂₃	—	2	1	no	—
516	C₈×C₂₃	—	2	1	no	—
517	C₈×C₂₃	—	2	1	no	—
518	C₈×C₂₃	—	2	1	no	—
519	C₈×C₂₃	—	2	2	no	—
520	C₈×C₂₃	—	2	2	no	—
521	#3518	C₂×C₂₃	1	1	yes	characteristic, complemented
522	#3514	C₂×C₂₃	1	1	yes	characteristic, complemented
523	#3375	C₂×C₂₃	1	1	yes	characteristic, complemented
524	#3373	C₂×C₂₃	1	1	yes	characteristic, complemented
525	#3369	C₂×C₂₃	1	1	yes	characteristic, complemented
526	#3367	C₂×C₂₃	1	1	yes	characteristic, complemented
527	#3329	C₂×C₂₃	1	1	yes	characteristic, complemented
528	#3328	C₂×C₂₃	1	1	yes	characteristic, complemented
529	#3325	C₂×C₂₃	1	1	yes	characteristic, complemented
530	#3324	C₂×C₂₃	1	1	yes	characteristic, complemented
531	#3321	C₂×C₂₃	1	2	yes	complemented
532	#3319	C₂×C₂₃	1	2	yes	complemented
533	#3313	C₂×C₂₃	1	2	yes	complemented
534	#3311	C₂×C₂₃	1	2	yes	complemented
535	#3233	C₂×C₂₃	1	1	yes	characteristic, complemented
536	#3233	C₂×C₂₃	1	2	yes	complemented
537	#3212	C₂×C₂₃	1	1	yes	characteristic, complemented
538	#3211	C₂×C₂₃	1	2	yes	complemented
539	#3183	C₂×C₂₃	1	2	yes	complemented
540	#3168	C₂×C₂₃	1	1	yes	characteristic, complemented
541	#3140	C₂×C₂₃	1	2	yes	complemented
542	#3131	C₂×C₂₃	1	1	yes	characteristic, complemented
543	#2965	C₂×C₂₃	1	1	yes	characteristic, complemented
544	C₂²×C₂₃	—	2	1	no	—
545	C₂²×C₂₃	—	2	2	no	—
546	C₂²×C₂₃	—	2	2	no	—
547	C₂²×C₂₃	—	2	1	no	—
548	C₂²×C₂₃	—	2	1	no	—
549	C₂²×C₂₃	—	2	2	no	—
550	C₂²×C₂₃	—	4	2	no	—
551	C₂²×C₂₃	—	4	1	no	—
552	C₂²×C₂₃	—	4	1	no	—
553	C₂²×C₂₃	—	4	2	no	—
554	C₂²×C₂₃	—	4	1	no	—
555	C₂²×C₂₃	—	4	1	no	—
556	C₂²×C₂₃	—	4	1	no	—
557	C₂²×C₂₃	—	4	1	no	—
558	C₂²×C₂₃	—	4	2	no	—
559	C₂²×C₂₃	—	16	4	no	—
560	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
561	C₄×C₂₃	—	2	1	no	—
562	C₄×C₂₃	—	2	2	no	—
563	C₄×C₂₃	—	2	1	no	—
564	C₄×C₂₃	—	2	1	no	—
565	C₄×C₂₃	—	2	2	no	—
566	C₄×C₂₃	—	2	1	no	—
567	C₄×C₂₃	—	2	2	no	—
568	C₄×C₂₃	—	4	1	no	—
569	C₄×C₂₃	—	4	1	no	—
570	C₄×C₂₃	—	4	2	no	—
571	C₄×C₂₃	—	4	2	no	—
572	C₄×C₂₃	—	4	1	no	—
573	C₄×C₂₃	—	4	1	no	—
574	C₄×C₂₃	—	4	1	no	—
575	C₄×C₂₃	—	4	2	no	—
576	C₄×C₂₃	—	4	1	no	—
577	C₄×C₂₃	#575	1	2	yes	—
578	C₄×C₂₃	#585	1	1	yes	characteristic
579	C₄×C₂₃	#585	1	1	yes	characteristic
580	#559	C₂²×C₂₃	1	1	yes	characteristic
581	Q₈²	C₂²×C₂₃	1	1	yes	characteristic, complemented
582	#556	—	2	1	no	—
583	#556	—	2	2	no	—
584	#556	C₂²×C₂₃	1	1	yes	characteristic
585	#556	C₂²×C₂₃	1	1	yes	characteristic
586	#556	C₂²×C₂₃	1	2	yes	complemented
587	#555	—	2	1	no	—
588	#555	C₂²×C₂₃	1	1	yes	characteristic
589	#555	C₂²×C₂₃	1	2	yes	complemented
590	#551	—	2	2	no	—
591	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
592	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
593	#548	—	2	1	no	—
594	#548	C₂²×C₂₃	1	2	yes	—
595	#546	—	2	1	no	—
596	#546	C₂²×C₂₃	1	2	yes	—
597	D₄²	C₂²×C₂₃	1	1	yes	characteristic
598	#542	—	2	1	no	—
599	#542	—	2	1	no	—
600	#542	—	2	2	no	—
601	#538	—	2	2	no	—
602	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
603	#533	C₂²×C₂₃	1	2	yes	complemented
604	#532	C₂²×C₂₃	1	1	yes	characteristic
605	#529	C₂²×C₂₃	1	1	yes	characteristic
606	#529	C₂²×C₂₃	1	2	yes	—
607	#529	C₂²×C₂₃	1	1	yes	characteristic, complemented
608	#529	C₂²×C₂₃	1	2	yes	complemented
609	C₂×#124	C₂²×C₂₃	1	2	yes	—
610	#519	—	2	1	no	—
611	#518	—	2	1	no	—
612	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
613	#499	C₂²×C₂₃	1	1	yes	characteristic, complemented
614	#499	C₂²×C₂₃	1	2	yes	complemented
615	#495	C₂²×C₂₃	1	1	yes	characteristic
616	#495	C₂²×C₂₃	1	2	yes	complemented
617	#489	C₂²×C₂₃	1	2	yes	—
618	#489	C₂²×C₂₃	1	2	yes	—
619	#489	C₂²×C₂₃	1	2	yes	complemented
620	#489	C₂²×C₂₃	1	2	yes	complemented
621	#488	C₂²×C₂₃	1	1	yes	characteristic
622	#488	C₂²×C₂₃	1	2	yes	—
623	#488	C₂²×C₂₃	1	2	yes	complemented
624	#488	C₂²×C₂₃	1	2	yes	complemented
625	#488	C₂²×C₂₃	1	2	yes	complemented
626	#488	C₂²×C₂₃	1	1	yes	characteristic, complemented
627	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
628	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
629	#486	C₂²×C₂₃	1	1	yes	characteristic
630	#486	C₂²×C₂₃	1	1	yes	characteristic
631	#485	C₂²×C₂₃	1	2	yes	complemented
632	#485	C₂²×C₂₃	1	2	yes	complemented
633	#485	C₂²×C₂₃	1	2	yes	complemented
634	#482	C₂²×C₂₃	1	2	yes	—
635	#482	C₂²×C₂₃	1	2	yes	—
636	#482	C₂²×C₂₃	1	2	yes	—
637	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
638	#477	C₂²×C₂₃	1	2	yes	complemented
639	#476	C₂²×C₂₃	1	1	yes	characteristic
640	#476	C₂²×C₂₃	1	2	yes	complemented
641	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
642	#475	C₂²×C₂₃	1	2	yes	complemented
643	#474	C₂²×C₂₃	1	1	yes	characteristic
644	#474	C₂²×C₂₃	1	2	yes	complemented
645	#470	C₂²×C₂₃	1	2	yes	complemented
646	#469	C₂²×C₂₃	1	2	yes	—
647	#468	C₂²×C₂₃	1	2	yes	—
648	#468	C₂²×C₂₃	1	2	yes	complemented
649	#467	C₂²×C₂₃	1	1	yes	characteristic, complemented
650	#466	C₂²×C₂₃	1	1	yes	characteristic
651	#465	C₂²×C₂₃	1	1	yes	characteristic
652	#465	C₂²×C₂₃	1	1	yes	characteristic, complemented
653	#464	C₂²×C₂₃	1	2	yes	—
654	#464	C₂²×C₂₃	1	2	yes	complemented
655	#463	C₂²×C₂₃	1	2	yes	—
656	#463	C₂²×C₂₃	1	2	yes	complemented
657	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
658	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
659	#460	C₂²×C₂₃	1	1	yes	characteristic
660	#459	C₂²×C₂₃	1	1	yes	characteristic
661	#452	C₂²×C₂₃	1	2	yes	complemented
662	#451	C₂²×C₂₃	1	2	yes	complemented
663	#450	C₂²×C₂₃	1	2	yes	—
664	#449	C₂²×C₂₃	1	2	yes	complemented
665	#448	C₂²×C₂₃	1	2	yes	complemented
666	#447	C₂²×C₂₃	1	2	yes	—
667	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
668	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
669	#442	C₂²×C₂₃	1	2	yes	complemented
670	#441	C₂²×C₂₃	1	2	yes	complemented
671	#440	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×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
675	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
676	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
677	#436	C₂²×C₂₃	1	1	yes	characteristic
678	#436	C₂²×C₂₃	1	1	yes	characteristic
679	#435	C₂²×C₂₃	1	2	yes	complemented
680	#435	C₂²×C₂₃	1	2	yes	complemented
681	#431	C₂²×C₂₃	1	2	yes	complemented
682	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
683	#419	C₂²×C₂₃	1	2	yes	complemented
684	#419	C₂²×C₂₃	1	2	yes	complemented
685	#418	C₂²×C₂₃	1	2	yes	—
686	#418	C₂²×C₂₃	1	2	yes	—
687	#416	C₂²×C₂₃	1	2	yes	complemented
688	#416	C₂²×C₂₃	1	2	yes	complemented
689	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
690	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
691	C₂×C₂₃	—	4	1	no	—
692	C₂×C₂₃	—	4	2	no	—
693	C₂×C₂₃	—	8	1	no	—
694	C₂×C₂₃	—	8	2	no	—
695	C₂×C₂₃	—	8	1	no	—
696	C₂×C₂₃	#3500	1	1	yes	characteristic
697	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
698	C₂×C₂₃	#3584	1	1	yes	characteristic
699	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
700	C₂×#41	C₂³×C₂₃	1	2	yes	—
701	C₂²×Q₈	—	2	1	no	—
702	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
703	C₂²×D₄	—	2	1	no	—
704	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
705	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
706	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
707	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
708	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
709	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
710	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
711	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
712	C₂×D₈	C₂³×C₂₃	1	2	yes	—
713	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
714	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
715	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
716	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
717	C₄⋊Q₈	—	2	1	no	—
718	C₄⋊Q₈	—	2	1	no	—
719	C₄⋊Q₈	—	2	2	no	—
720	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
721	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
723	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
725	#127	C₂³×C₂₃	1	1	yes	characteristic
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#126	—	2	2	no	—
729	#126	—	2	2	no	—
730	#126	—	2	2	no	—
731	#126	—	2	1	no	—
732	#126	—	2	2	no	—
733	#126	—	2	1	no	—
734	#125	C₂³×C₂₃	1	1	yes	characteristic
735	#125	C₂³×C₂₃	1	1	yes	characteristic
736	#125	C₂³×C₂₃	1	2	yes	—
737	#124	—	2	1	no	—
738	#124	—	2	1	no	—
739	#124	—	2	2	no	—
740	#124	—	2	2	no	—
741	#124	—	2	2	no	—
742	#124	—	2	2	no	—
743	#124	—	2	2	no	—
744	#124	—	2	2	no	—
745	#124	—	2	2	no	—
746	#124	C₂³×C₂₃	1	1	yes	characteristic
747	#124	C₂³×C₂₃	1	2	yes	—
748	#124	C₂³×C₂₃	1	2	yes	—
749	#124	C₂³×C₂₃	1	2	yes	—
750	#124	C₂³×C₂₃	1	1	yes	characteristic
751	#123	—	2	1	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	1	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	C₂²⋊Q₈	—	2	1	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
767	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
768	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
769	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
770	#121	—	2	2	no	—
771	#121	—	2	1	no	—
772	#121	—	2	2	no	—
773	#121	—	2	1	no	—
774	#121	—	2	1	no	—
775	#121	—	2	1	no	—
776	#121	—	2	2	no	—
777	#121	C₂³×C₂₃	1	2	yes	—
778	#121	C₂³×C₂₃	1	1	yes	characteristic
779	#121	C₂³×C₂₃	1	2	yes	—
780	#121	C₂³×C₂₃	1	1	yes	characteristic
781	#120	—	2	2	no	—
782	#120	—	2	2	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	—	2	2	no	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	—	2	2	no	—
788	C₄×Q₈	—	2	2	no	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
791	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
792	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
793	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
794	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
795	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
806	C₄×D₄	D₄×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	C₄×D₄	C₂³×C₂₃	1	2	yes	—
811	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
812	C₄×D₄	C₂³×C₂₃	1	2	yes	—
813	#117	—	2	1	no	—
814	#117	—	2	1	no	—
815	#117	—	2	2	no	—
816	#117	—	2	1	no	—
817	#117	—	2	1	no	—
818	#117	—	2	2	no	—
819	#117	—	2	2	no	—
820	#117	D₄×C₂₃	1	2	yes	—
821	#117	D₄×C₂₃	1	1	yes	characteristic
822	#117	C₂³×C₂₃	1	2	yes	—
823	#117	C₂³×C₂₃	1	2	yes	—
824	#117	C₂³×C₂₃	1	2	yes	—
825	C₂×C₂²⋊C₄	—	2	2	no	—
826	C₂×C₂²⋊C₄	—	2	2	no	—
827	C₂×C₂²⋊C₄	—	2	2	no	—
828	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
829	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
830	#107	C₂³×C₂₃	1	1	yes	characteristic
831	#107	C₂³×C₂₃	1	1	yes	characteristic
832	#107	C₂³×C₂₃	1	2	yes	—
833	#107	C₂³×C₂₃	1	2	yes	—
834	#106	C₂³×C₂₃	1	1	yes	characteristic
835	#106	C₂³×C₂₃	1	1	yes	characteristic
836	#106	C₂³×C₂₃	1	2	yes	—
837	#106	C₂³×C₂₃	1	2	yes	—
838	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
839	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
840	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
841	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
842	#103	C₂³×C₂₃	1	2	yes	—
843	#103	C₂³×C₂₃	1	2	yes	—
844	#103	C₂³×C₂₃	1	2	yes	—
845	#103	C₂³×C₂₃	1	2	yes	—
846	#103	C₂³×C₂₃	1	1	yes	characteristic
847	#103	C₂³×C₂₃	1	1	yes	characteristic
848	#103	C₂³×C₂₃	1	2	yes	—
849	#103	C₂³×C₂₃	1	2	yes	—
850	#103	C₂³×C₂₃	1	2	yes	—
851	#103	C₂³×C₂₃	1	2	yes	—
852	#103	C₂³×C₂₃	1	1	yes	characteristic
853	#103	C₂³×C₂₃	1	1	yes	characteristic
854	#102	C₂³×C₂₃	1	2	yes	—
855	#102	C₂³×C₂₃	1	2	yes	—
856	#102	C₂³×C₂₃	1	2	yes	—
857	#102	C₂³×C₂₃	1	2	yes	—
858	#102	C₂³×C₂₃	1	1	yes	characteristic
859	#102	C₂³×C₂₃	1	1	yes	characteristic
860	#102	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	1	yes	characteristic
865	#102	C₂³×C₂₃	1	1	yes	characteristic
866	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
867	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
869	#97	C₂³×C₂₃	1	2	yes	—
870	#97	C₂³×C₂₃	1	2	yes	—
871	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
872	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
873	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
874	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
875	C₄×C₈	C₂³×C₂₃	1	2	yes	—
876	C₂₃	#62548	1	1	yes	characteristic, direct product factor, Sylow
877	C₂⁴	—	2	2	no	—
878	#41	—	4	2	no	—
879	#41	—	4	2	no	—
880	#41	—	4	2	no	—
881	C₂×Q₈	—	2	2	no	—
882	C₂×Q₈	—	2	1	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	—	2	1	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	—	4	2	no	—
887	C₂×Q₈	—	4	2	no	—
888	C₂×Q₈	—	4	4	no	—
889	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
890	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
891	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
892	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	1	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	1	no	—
899	C₂×D₄	—	2	1	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	4	2	no	—
902	C₂×D₄	—	4	2	no	—
903	C₂×D₄	—	4	4	no	—
904	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
905	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
906	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
907	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
908	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
916	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
917	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
918	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
919	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
920	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
921	Q₁₆	—	4	1	no	—
922	Q₁₆	—	4	2	no	—
923	SD₁₆	—	4	1	no	—
924	SD₁₆	—	4	1	no	—
925	SD₁₆	—	4	2	no	—
926	SD₁₆	—	4	2	no	—
927	D₈	—	4	1	no	—
928	D₈	—	4	2	no	—
929	M₁₆	—	4	2	no	—
930	M₁₆	—	4	2	no	—
931	C₂×C₈	—	4	1	no	—
932	C₂×C₈	—	4	1	no	—
933	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
935	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
936	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
937	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
938	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
960	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
961	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
962	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
963	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
964	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
965	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
966	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
967	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
968	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
995	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
996	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	1	no	—
1004	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1005	C₄²	C₂×D₄×C₂₃	1	2	yes	—
1006	C₄²	C₂×D₄×C₂₃	1	2	yes	—
1007	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1008	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1009	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1010	C₄²	C₂⁴×C₂₃	1	2	yes	—
1011	C₂³	—	2	1	no	—
1012	C₂³	—	2	1	no	—
1013	C₂³	—	2	2	no	—
1014	C₂³	—	4	4	no	—
1015	C₂³	—	8	2	no	—
1016	C₂³	—	8	2	no	—
1017	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1018	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1019	Q₈	—	2	2	no	—
1020	Q₈	—	2	1	no	—
1021	Q₈	—	2	1	no	—
1022	Q₈	—	2	1	no	—
1023	Q₈	—	2	2	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	4	4	no	—
1027	Q₈	—	4	2	no	—
1028	Q₈	—	8	2	no	—
1029	Q₈	—	8	2	no	—
1030	Q₈	—	8	1	no	—
1031	D₄	—	2	2	no	—
1032	D₄	—	2	1	no	—
1033	D₄	—	2	1	no	—
1034	D₄	—	2	1	no	—
1035	D₄	—	2	2	no	—
1036	D₄	—	2	1	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	4	2	no	—
1039	D₄	—	4	4	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	8	2	no	—
1042	D₄	—	8	1	no	—
1043	D₄	—	8	2	no	—
1044	D₄	—	8	1	no	—
1045	D₄	—	8	1	no	—
1046	D₄	—	8	2	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	4	2	no	—
1062	C₂×C₄	—	4	2	no	—
1063	C₂×C₄	—	4	1	no	—
1064	C₂×C₄	—	4	4	no	—
1065	C₂×C₄	—	4	2	no	—
1066	C₂×C₄	—	4	2	no	—
1067	C₂×C₄	—	8	2	no	—
1068	C₂×C₄	—	8	2	no	—
1069	C₂×C₄	—	8	2	no	—
1070	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1071	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1072	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1073	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1074	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1075	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1076	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1077	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1078	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1079	C₈	—	2	1	no	—
1080	C₈	—	2	1	no	—
1081	C₈	—	2	1	no	—
1082	C₈	—	2	1	no	—
1083	C₈	—	2	2	no	—
1084	C₈	—	2	2	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	2	2	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	4	2	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	2	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	16	4	no	—
1101	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1102	C₄	—	2	1	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	2	2	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	1	no	—
1109	C₄	—	4	2	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	2	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	1	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	2	no	—
1118	C₄	C₂₃×#575	1	2	yes	—
1119	C₄	C₂₃×#585	1	1	yes	characteristic
1120	C₄	C₂₃×#585	1	1	yes	characteristic
1121	C₂	—	4	2	no	—
1122	C₂	—	4	1	no	—
1123	C₂	—	8	1	no	—
1124	C₂	—	8	2	no	—
1125	C₂	—	8	1	no	—
1126	C₂	C₂₃×#3500	1	1	yes	characteristic
1127	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
1128	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 ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3518	C₂	semidirect
2. C₂₃×#3514	C₂	semidirect
3. C₂₃×#3375	C₂	semidirect
4. C₂₃×#3373	C₂	semidirect
5. C₂₃×#3369	C₂	semidirect
6. C₂₃×#3367	C₂	semidirect
7. C₂₃×#3329	C₂	semidirect
8. C₂₃×#3328	C₂	semidirect
9. C₂₃×#3325	C₂	semidirect
10. C₂₃×#3324	C₂	semidirect
11. C₂₃×#3321	C₂	semidirect
12. C₂₃×#3319	C₂	semidirect
13. C₂₃×#3313	C₂	semidirect
14. C₂₃×#3311	C₂	semidirect
15. C₂₃×#3233	C₂	semidirect
16. C₂₃×#3233	C₂	semidirect
17. C₂₃×#3212	C₂	semidirect
18. C₂₃×#3211	C₂	semidirect
19. C₂₃×#3183	C₂	semidirect
20. C₂₃×#3168	C₂	semidirect
21. C₂₃×#3140	C₂	semidirect
22. C₂₃×#3131	C₂	semidirect
23. C₂₃×#2965	C₂	semidirect
25. Q₈²×C₂₃	C₂²	semidirect
30. C₂₃×#556	C₂²	semidirect
33. C₂₃×#555	C₂²	semidirect
36. D₄×Q₈×C₂₃	C₂²	semidirect
46. C₂₃×#533	C₂²	semidirect
47. C₂₃×#533	C₂²	semidirect
51. C₂₃×#529	C₂²	semidirect
52. C₂₃×#529	C₂²	semidirect
57. C₂₃×#499	C₂²	semidirect
58. C₂₃×#499	C₂²	semidirect
60. C₂₃×#495	C₂²	semidirect
63. C₂₃×#489	C₂²	semidirect
64. C₂₃×#489	C₂²	semidirect
67. C₂₃×#488	C₂²	semidirect
68. C₂₃×#488	C₂²	semidirect
69. C₂₃×#488	C₂²	semidirect
70. C₂₃×#488	C₂²	semidirect
71. C₂₃×#487	C₂²	semidirect
72. C₂₃×#487	C₂²	semidirect
75. C₂₃×#485	C₂²	semidirect
76. C₂₃×#485	C₂²	semidirect
77. C₂₃×#485	C₂²	semidirect
81. C₂₃×#477	C₂²	semidirect
82. C₂₃×#477	C₂²	semidirect
84. C₂₃×#476	C₂²	semidirect
85. C₂₃×#475	C₂²	semidirect
86. C₂₃×#475	C₂²	semidirect
88. C₂₃×#474	C₂²	semidirect
89. C₂₃×#470	C₂²	semidirect
92. C₂₃×#468	C₂²	semidirect
93. C₂₃×#467	C₂²	semidirect
96. C₂₃×#465	C₂²	semidirect
98. C₂₃×#464	C₂²	semidirect
100. C₂₃×#463	C₂²	semidirect
101. C₂₃×#462	C₂²	semidirect
102. C₂₃×#461	C₂²	semidirect
105. C₂₃×#452	C₂²	semidirect
106. C₂₃×#451	C₂²	semidirect
108. C₂₃×#449	C₂²	semidirect
109. C₂₃×#448	C₂²	semidirect
111. C₂₃×#446	C₂²	semidirect
112. C₂₃×#446	C₂²	semidirect
113. C₂₃×#442	C₂²	semidirect
114. C₂₃×#441	C₂²	semidirect
115. C₂₃×#440	C₂²	semidirect
116. C₂₃×#440	C₂²	semidirect
117. C₄×Q₁₆×C₂₃	C₂²	semidirect
119. C₄×SD₁₆×C₂₃	C₂²	semidirect
123. C₂₃×#435	C₂²	semidirect
124. C₂₃×#435	C₂²	semidirect
125. C₂₃×#431	C₂²	semidirect
126. C₂₃×#431	C₂²	semidirect
127. C₂₃×#419	C₂²	semidirect
128. C₂₃×#419	C₂²	semidirect
131. C₂₃×#416	C₂²	semidirect
132. C₂₃×#416	C₂²	semidirect
133. C₄×M₁₆×C₂₃	C₂²	semidirect
134. C₂×C₄×C₈×C₂₃	C₂²	semidirect
446. #62548	C₂₃	direct (N × H)
521. #3518	C₂×C₂₃	semidirect
522. #3514	C₂×C₂₃	semidirect
523. #3375	C₂×C₂₃	semidirect
524. #3373	C₂×C₂₃	semidirect
525. #3369	C₂×C₂₃	semidirect
526. #3367	C₂×C₂₃	semidirect
527. #3329	C₂×C₂₃	semidirect
528. #3328	C₂×C₂₃	semidirect
529. #3325	C₂×C₂₃	semidirect
530. #3324	C₂×C₂₃	semidirect
531. #3321	C₂×C₂₃	semidirect
532. #3319	C₂×C₂₃	semidirect
533. #3313	C₂×C₂₃	semidirect
534. #3311	C₂×C₂₃	semidirect
535. #3233	C₂×C₂₃	semidirect
536. #3233	C₂×C₂₃	semidirect
537. #3212	C₂×C₂₃	semidirect
538. #3211	C₂×C₂₃	semidirect
539. #3183	C₂×C₂₃	semidirect
540. #3168	C₂×C₂₃	semidirect
541. #3140	C₂×C₂₃	semidirect
542. #3131	C₂×C₂₃	semidirect
543. #2965	C₂×C₂₃	semidirect
581. Q₈²	C₂²×C₂₃	semidirect
586. #556	C₂²×C₂₃	semidirect
589. #555	C₂²×C₂₃	semidirect
592. D₄×Q₈	C₂²×C₂₃	semidirect
602. #533	C₂²×C₂₃	semidirect
603. #533	C₂²×C₂₃	semidirect
607. #529	C₂²×C₂₃	semidirect
608. #529	C₂²×C₂₃	semidirect
613. #499	C₂²×C₂₃	semidirect
614. #499	C₂²×C₂₃	semidirect
616. #495	C₂²×C₂₃	semidirect
619. #489	C₂²×C₂₃	semidirect
620. #489	C₂²×C₂₃	semidirect
623. #488	C₂²×C₂₃	semidirect
624. #488	C₂²×C₂₃	semidirect
625. #488	C₂²×C₂₃	semidirect
626. #488	C₂²×C₂₃	semidirect
627. #487	C₂²×C₂₃	semidirect
628. #487	C₂²×C₂₃	semidirect
631. #485	C₂²×C₂₃	semidirect
632. #485	C₂²×C₂₃	semidirect
633. #485	C₂²×C₂₃	semidirect
637. #477	C₂²×C₂₃	semidirect
638. #477	C₂²×C₂₃	semidirect
640. #476	C₂²×C₂₃	semidirect
641. #475	C₂²×C₂₃	semidirect
642. #475	C₂²×C₂₃	semidirect
644. #474	C₂²×C₂₃	semidirect
645. #470	C₂²×C₂₃	semidirect
648. #468	C₂²×C₂₃	semidirect
649. #467	C₂²×C₂₃	semidirect
652. #465	C₂²×C₂₃	semidirect
654. #464	C₂²×C₂₃	semidirect
656. #463	C₂²×C₂₃	semidirect
657. #462	C₂²×C₂₃	semidirect
658. #461	C₂²×C₂₃	semidirect
661. #452	C₂²×C₂₃	semidirect
662. #451	C₂²×C₂₃	semidirect
664. #449	C₂²×C₂₃	semidirect
665. #448	C₂²×C₂₃	semidirect
667. #446	C₂²×C₂₃	semidirect
668. #446	C₂²×C₂₃	semidirect
669. #442	C₂²×C₂₃	semidirect
670. #441	C₂²×C₂₃	semidirect
671. #440	C₂²×C₂₃	semidirect
672. #440	C₂²×C₂₃	semidirect
673. C₄×Q₁₆	C₂²×C₂₃	semidirect
675. C₄×SD₁₆	C₂²×C₂₃	semidirect
679. #435	C₂²×C₂₃	semidirect
680. #435	C₂²×C₂₃	semidirect
681. #431	C₂²×C₂₃	semidirect
682. #431	C₂²×C₂₃	semidirect
683. #419	C₂²×C₂₃	semidirect
684. #419	C₂²×C₂₃	semidirect
687. #416	C₂²×C₂₃	semidirect
688. #416	C₂²×C₂₃	semidirect
689. C₄×M₁₆	C₂²×C₂₃	semidirect
690. C₂×C₄×C₈	C₂²×C₂₃	semidirect
876. C₂₃	#62548	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×#3518	2
C₂₃×#3514	2
C₂₃×#3375	2
C₂₃×#3373	2
C₂₃×#3369	2
C₂₃×#3367	2
C₂₃×#3329	2
C₂₃×#3328	2
C₂₃×#3325	2
C₂₃×#3324	2
C₂₃×#3321	2
C₂₃×#3319	2
C₂₃×#3313	2
C₂₃×#3311	2
C₂₃×#3233	2
C₂₃×#3212	2
C₂₃×#3211	2
C₂₃×#3183	2
C₂₃×#3168	2
C₂₃×#3140	2
C₂₃×#3131	2
C₂₃×#2965	2
#62548	23

Subgroups — C23×#62548 #19210174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62548 #19210174