Subgroups — C₂₃×#62608 #19210234

Order 5888.

1774 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3543	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3375	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3368	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3324	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3323	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3311	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3310	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3295	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3241	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3233	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3222	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3174	C₂	1	2	yes	maximal, complemented
20	C₂₃×#3172	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#3136	C₂	1	2	yes	maximal, complemented
23	C₂₃×#2969	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#563	—	2	2	no	—
25	C₂₃×#560	—	2	2	no	—
26	C₂₃×#559	C₂²	1	1	yes	characteristic
27	Q₈²×C₂₃	C₂²	1	1	yes	characteristic, complemented
28	C₂₃×#557	—	2	1	no	—
29	C₂₃×#557	C₂²	1	1	yes	characteristic, complemented
30	C₂₃×#556	—	2	1	no	—
31	C₂₃×#556	C₂²	1	1	yes	characteristic, complemented
32	C₂₃×#556	C₂²	1	2	yes	complemented
33	C₂₃×#554	C₂²	1	1	yes	characteristic, complemented
34	C₂₃×#552	C₂²	1	2	yes	complemented
35	C₂₃×#550	C₂²	1	1	yes	characteristic
36	C₂₃×#550	C₂²	1	1	yes	characteristic
37	C₂₃×#546	—	2	1	no	—
38	C₂₃×#546	C₂²	1	2	yes	—
39	D₄²×C₂₃	—	2	1	no	—
40	D₄²×C₂₃	C₂²	1	1	yes	characteristic
41	D₄²×C₂₃	C₂²	1	2	yes	—
42	C₂₃×#544	C₂²	1	2	yes	complemented
43	C₂₃×#542	—	2	1	no	—
44	C₂₃×#541	—	2	2	no	—
45	C₂₃×#541	—	2	1	no	—
46	C₂₃×#541	C₂²	1	2	yes	complemented
47	C₂₃×#540	—	2	1	no	—
48	C₂₃×#540	C₂²	1	2	yes	—
49	C₂₃×#535	—	2	1	no	—
50	C₂₃×#535	C₂²	1	2	yes	—
51	C₂₃×#534	—	2	2	no	—
52	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
55	C₂₃×#529	C₂²	1	1	yes	characteristic
56	C₂₃×#529	C₂²	1	1	yes	characteristic
57	C₂₃×#501	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#499	C₂²	1	2	yes	complemented
59	C₂₃×#497	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#492	C₂²	1	2	yes	complemented
61	C₂₃×#491	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#490	C₂²	1	2	yes	complemented
63	C₂₃×#490	C₂²	1	2	yes	complemented
64	C₂₃×#490	C₂²	1	2	yes	complemented
65	C₂₃×#489	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#489	C₂²	1	2	yes	complemented
67	C₂₃×#488	C₂²	1	2	yes	complemented
68	C₂₃×#488	C₂²	1	2	yes	complemented
69	C₂₃×#486	C₂²	1	1	yes	characteristic
70	C₂₃×#486	C₂²	1	1	yes	characteristic
71	C₂₃×#486	C₂²	1	2	yes	complemented
72	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
73	C₂₃×#486	C₂²	1	2	yes	complemented
74	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
75	C₂₃×#485	C₂²	1	2	yes	complemented
76	C₂₃×#482	C₂²	1	2	yes	—
77	C₂₃×#482	C₂²	1	2	yes	complemented
78	C₂₃×#482	C₂²	1	2	yes	complemented
79	C₂₃×#481	C₂²	1	2	yes	complemented
80	C₂₃×#480	C₂²	1	2	yes	complemented
81	C₂₃×#478	C₂²	1	2	yes	complemented
82	C₂₃×#478	C₂²	1	2	yes	complemented
83	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
84	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
85	C₂₃×#476	C₂²	1	2	yes	complemented
86	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
87	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
88	C₂₃×#474	C₂²	1	2	yes	complemented
89	C₂₃×#470	C₂²	1	1	yes	characteristic, complemented
90	C₂₃×#470	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#468	C₂²	1	1	yes	characteristic
92	C₂₃×#468	C₂²	1	1	yes	characteristic
93	C₂₃×#468	C₂²	1	2	yes	complemented
94	C₂₃×#468	C₂²	1	2	yes	complemented
95	C₂₃×#465	C₂²	1	2	yes	complemented
96	C₂₃×#465	C₂²	1	2	yes	complemented
97	C₂₃×#464	C₂²	1	2	yes	complemented
98	C₂₃×#464	C₂²	1	2	yes	complemented
99	C₂₃×#460	C₂²	1	1	yes	characteristic
100	C₂₃×#460	C₂²	1	1	yes	characteristic
101	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
102	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
103	C₂₃×#460	C₂²	1	2	yes	complemented
104	C₂₃×#460	C₂²	1	2	yes	complemented
105	C₂₃×#452	C₂²	1	2	yes	complemented
106	C₂₃×#452	C₂²	1	2	yes	complemented
107	C₂₃×#450	C₂²	1	2	yes	complemented
108	C₂₃×#450	C₂²	1	2	yes	complemented
109	C₂₃×#450	C₂²	1	2	yes	complemented
110	C₂₃×#450	C₂²	1	2	yes	complemented
111	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
113	C₂₃×#440	C₂²	1	2	yes	complemented
114	C₂₃×#440	C₂²	1	2	yes	complemented
115	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
121	C₂₃×#436	C₂²	1	2	yes	complemented
122	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
123	C₂₃×#435	C₂²	1	2	yes	complemented
124	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
125	C₂₃×#433	C₂²	1	2	yes	complemented
126	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
127	C₂₃×#418	C₂²	1	2	yes	complemented
128	C₂₃×#418	C₂²	1	2	yes	complemented
129	C₂₃×#418	C₂²	1	2	yes	complemented
130	C₂₃×#417	C₂²	1	2	yes	complemented
131	C₂₃×#416	C₂²	1	2	yes	complemented
132	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
133	C₂₃×#405	C₂²	1	2	yes	complemented
134	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₂₃	—	2	1	no	—
136	C₂×#41×C₂₃	C₂³	1	2	yes	—
137	C₂²×D₄×C₂₃	—	2	2	no	—
138	C₂²×D₄×C₂₃	—	2	1	no	—
139	C₂²×D₄×C₂₃	—	2	1	no	—
140	C₂²×D₄×C₂₃	—	2	1	no	—
141	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
142	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
143	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
151	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
152	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
153	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
154	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
155	C₂₃×C₄⋊Q₈	—	2	1	no	—
156	C₂₃×C₄⋊Q₈	—	2	1	no	—
157	C₂₃×C₄⋊Q₈	—	2	2	no	—
158	C₂₃×C₄⋊Q₈	—	2	2	no	—
159	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₂₃×#127	—	2	1	no	—
165	C₂₃×#127	—	2	1	no	—
166	C₂₃×#127	—	2	1	no	—
167	C₂₃×#127	C₂³	1	1	yes	characteristic
168	C₂₃×#127	C₂³	1	2	yes	—
169	C₂₃×#127	C₂³	1	1	yes	characteristic
170	C₂₃×#127	C₂³	1	2	yes	—
171	C₂₃×#126	—	2	2	no	—
172	C₂₃×#126	—	2	2	no	—
173	C₂₃×#126	—	2	2	no	—
174	C₂₃×#126	—	2	2	no	—
175	C₂₃×#126	—	2	2	no	—
176	C₂₃×#126	—	2	2	no	—
177	C₂₃×#126	—	2	1	no	—
178	C₂₃×#126	D₄	1	2	yes	—
179	C₂₃×#125	—	2	2	no	—
180	C₂₃×#125	—	2	1	no	—
181	C₂₃×#125	—	2	2	no	—
182	C₂₃×#125	—	2	2	no	—
183	C₂₃×#125	—	2	2	no	—
184	C₂₃×#125	—	2	2	no	—
185	C₂₃×#125	—	2	1	no	—
186	C₂₃×#125	D₄	1	1	yes	characteristic
187	C₂₃×#125	C₂³	1	2	yes	—
188	C₂₃×#125	C₂³	1	2	yes	—
189	C₂₃×#125	C₂³	1	1	yes	characteristic
190	C₂₃×#124	—	2	1	no	—
191	C₂₃×#124	—	2	1	no	—
192	C₂₃×#124	—	2	2	no	—
193	C₂₃×#124	D₄	1	1	yes	characteristic
194	C₂₃×#124	C₂³	1	2	yes	—
195	C₂₃×#124	C₂³	1	1	yes	characteristic
196	C₂₃×#123	—	2	2	no	—
197	C₂₃×#123	—	2	1	no	—
198	C₂₃×#123	—	2	2	no	—
199	C₂₃×#123	—	2	2	no	—
200	C₂₃×#123	—	2	2	no	—
201	C₂₃×#123	—	2	2	no	—
202	C₂₃×#123	D₄	1	2	yes	—
203	C₂₃×C₂²⋊Q₈	—	2	1	no	—
204	C₂₃×C₂²⋊Q₈	—	2	1	no	—
205	C₂₃×C₂²⋊Q₈	—	2	1	no	—
206	C₂₃×C₂²⋊Q₈	—	2	2	no	—
207	C₂₃×C₂²⋊Q₈	—	2	2	no	—
208	C₂₃×C₂²⋊Q₈	—	2	2	no	—
209	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
210	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₂₃×#121	—	2	2	no	—
216	C₂₃×#121	—	2	1	no	—
217	C₂₃×#121	—	2	2	no	—
218	C₂₃×#121	—	2	2	no	—
219	C₂₃×#121	—	2	2	no	—
220	C₂₃×#121	—	2	1	no	—
221	C₂₃×#121	—	2	2	no	—
222	C₂₃×#121	—	2	2	no	—
223	C₂₃×#121	—	2	2	no	—
224	C₂₃×#121	—	2	2	no	—
225	C₂₃×#121	D₄	1	1	yes	characteristic
226	C₂₃×#121	C₂³	1	2	yes	—
227	C₂₃×#121	C₂³	1	2	yes	—
228	C₂₃×#121	C₂³	1	1	yes	characteristic
229	C₂₃×#120	—	2	2	no	—
230	C₂₃×#120	—	2	2	no	—
231	C₂₃×#120	—	2	2	no	—
232	C₂₃×#120	—	2	2	no	—
233	C₂₃×#120	—	2	2	no	—
234	C₂₃×#120	—	2	2	no	—
235	C₄×Q₈×C₂₃	—	2	1	no	—
236	C₄×Q₈×C₂₃	—	2	2	no	—
237	C₄×Q₈×C₂₃	—	2	1	no	—
238	C₄×Q₈×C₂₃	—	2	1	no	—
239	C₄×Q₈×C₂₃	—	2	1	no	—
240	C₄×Q₈×C₂₃	—	2	1	no	—
241	C₄×Q₈×C₂₃	—	2	1	no	—
242	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
243	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
244	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
245	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
246	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
247	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₂₃	—	2	1	no	—
249	C₄×D₄×C₂₃	—	2	1	no	—
250	C₄×D₄×C₂₃	—	2	1	no	—
251	C₄×D₄×C₂₃	—	2	1	no	—
252	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₂₃	C₂³	1	2	yes	—
254	C₄×D₄×C₂₃	C₂³	1	2	yes	—
255	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₂₃	C₂³	1	2	yes	—
257	C₂₃×#117	—	2	1	no	—
258	C₂₃×#117	—	2	2	no	—
259	C₂₃×#117	—	2	1	no	—
260	C₂₃×#117	C₂³	1	2	yes	—
261	C₂₃×#117	C₂³	1	2	yes	—
262	C₂₃×#117	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
265	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
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	2	yes	—
271	C₂₃×#106	C₂³	1	2	yes	—
272	C₂₃×#106	C₂³	1	1	yes	characteristic
273	C₂₃×#106	C₂³	1	1	yes	characteristic
274	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
277	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
278	C₂₃×#103	C₂³	1	1	yes	characteristic
279	C₂₃×#103	C₂³	1	2	yes	—
280	C₂₃×#103	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
285	C₂₃×#103	C₂³	1	1	yes	characteristic
286	C₂₃×#102	C₂³	1	1	yes	characteristic
287	C₂₃×#102	C₂³	1	2	yes	—
288	C₂₃×#102	C₂³	1	2	yes	—
289	C₂₃×#102	C₂³	1	2	yes	—
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	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	2	yes	—
300	C₂₃×#102	C₂³	1	2	yes	—
301	C₂₃×#102	C₂³	1	2	yes	—
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	1	yes	characteristic
306	C₂₃×#97	C₂³	1	1	yes	characteristic
307	C₂₃×#97	C₂³	1	2	yes	—
308	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₂₃	C₂³	1	2	yes	—
311	C₄×C₈×C₂₃	C₂³	1	2	yes	—
312	C₂⁴×C₂₃	—	2	2	no	—
313	C₂⁴×C₂₃	—	2	2	no	—
314	#41×C₂₃	—	4	2	no	—
315	#41×C₂₃	—	4	2	no	—
316	#41×C₂₃	—	8	2	no	—
317	C₂×Q₈×C₂₃	—	2	1	no	—
318	C₂×Q₈×C₂₃	—	2	1	no	—
319	C₂×Q₈×C₂₃	—	2	1	no	—
320	C₂×Q₈×C₂₃	—	2	2	no	—
321	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
323	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
324	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₂₃	—	2	1	no	—
326	C₂×D₄×C₂₃	—	2	2	no	—
327	C₂×D₄×C₂₃	—	2	2	no	—
328	C₂×D₄×C₂₃	—	2	2	no	—
329	C₂×D₄×C₂₃	—	2	1	no	—
330	C₂×D₄×C₂₃	—	2	1	no	—
331	C₂×D₄×C₂₃	—	2	2	no	—
332	C₂×D₄×C₂₃	—	2	2	no	—
333	C₂×D₄×C₂₃	—	2	1	no	—
334	C₂×D₄×C₂₃	—	2	2	no	—
335	C₂×D₄×C₂₃	—	2	2	no	—
336	C₂×D₄×C₂₃	—	2	2	no	—
337	C₂×D₄×C₂₃	—	2	2	no	—
338	C₂×D₄×C₂₃	—	2	1	no	—
339	C₂×D₄×C₂₃	—	4	2	no	—
340	C₂×D₄×C₂₃	—	4	2	no	—
341	C₂×D₄×C₂₃	—	4	2	no	—
342	C₂×D₄×C₂₃	—	4	2	no	—
343	C₂×D₄×C₂₃	—	8	2	no	—
344	C₂×D₄×C₂₃	—	8	2	no	—
345	C₂×D₄×C₂₃	—	8	2	no	—
346	C₂×D₄×C₂₃	—	8	4	no	—
347	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
348	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
350	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
351	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
352	C₂²×C₄×C₂₃	—	2	2	no	—
353	C₂²×C₄×C₂₃	—	2	1	no	—
354	C₂²×C₄×C₂₃	—	2	2	no	—
355	C₂²×C₄×C₂₃	—	2	2	no	—
356	C₂²×C₄×C₂₃	—	2	2	no	—
357	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
361	Q₁₆×C₂₃	—	4	1	no	—
362	Q₁₆×C₂₃	—	4	1	no	—
363	SD₁₆×C₂₃	—	4	2	no	—
364	SD₁₆×C₂₃	—	4	2	no	—
365	SD₁₆×C₂₃	—	4	2	no	—
366	SD₁₆×C₂₃	—	4	2	no	—
367	SD₁₆×C₂₃	—	4	1	no	—
368	SD₁₆×C₂₃	—	4	1	no	—
369	M₁₆×C₂₃	—	4	1	no	—
370	M₁₆×C₂₃	—	4	2	no	—
371	M₁₆×C₂₃	—	4	1	no	—
372	C₂×C₈×C₂₃	—	4	2	no	—
373	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
378	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
379	C₄⋊C₄×C₂₃	—	2	2	no	—
380	C₄⋊C₄×C₂₃	—	2	1	no	—
381	C₄⋊C₄×C₂₃	—	2	1	no	—
382	C₄⋊C₄×C₂₃	—	2	1	no	—
383	C₄⋊C₄×C₂₃	—	2	1	no	—
384	C₄⋊C₄×C₂₃	—	2	2	no	—
385	C₄⋊C₄×C₂₃	—	2	1	no	—
386	C₄⋊C₄×C₂₃	—	2	1	no	—
387	C₄⋊C₄×C₂₃	—	2	1	no	—
388	C₄⋊C₄×C₂₃	—	2	1	no	—
389	C₄⋊C₄×C₂₃	—	2	2	no	—
390	C₄⋊C₄×C₂₃	—	2	2	no	—
391	C₄⋊C₄×C₂₃	—	2	2	no	—
392	C₄⋊C₄×C₂₃	—	2	2	no	—
393	C₄⋊C₄×C₂₃	—	2	1	no	—
394	C₄⋊C₄×C₂₃	—	2	1	no	—
395	C₄⋊C₄×C₂₃	—	2	2	no	—
396	C₄⋊C₄×C₂₃	—	2	2	no	—
397	C₄⋊C₄×C₂₃	—	2	1	no	—
398	C₄⋊C₄×C₂₃	—	2	1	no	—
399	C₄⋊C₄×C₂₃	—	2	1	no	—
400	C₄⋊C₄×C₂₃	—	2	2	no	—
401	C₄⋊C₄×C₂₃	—	2	2	no	—
402	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
414	C₂²⋊C₄×C₂₃	—	2	1	no	—
415	C₂²⋊C₄×C₂₃	—	2	1	no	—
416	C₂²⋊C₄×C₂₃	—	2	1	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	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	—	2	2	no	—
430	C₂²⋊C₄×C₂₃	—	2	2	no	—
431	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
436	C₄²×C₂₃	—	2	2	no	—
437	C₄²×C₂₃	—	2	1	no	—
438	C₄²×C₂₃	—	2	1	no	—
439	C₄²×C₂₃	—	2	1	no	—
440	C₄²×C₂₃	—	2	2	no	—
441	C₄²×C₂₃	—	2	2	no	—
442	C₄²×C₂₃	—	2	2	no	—
443	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
445	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
446	C₄²×C₂₃	C₂⁴	1	2	yes	—
447	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
448	#62608	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
449	C₂³×C₂₃	—	2	2	no	—
450	C₂³×C₂₃	—	2	1	no	—
451	C₂³×C₂₃	—	2	2	no	—
452	C₂³×C₂₃	—	4	4	no	—
453	C₂³×C₂₃	—	8	2	no	—
454	C₂³×C₂₃	—	8	2	no	—
455	C₂³×C₂₃	—	8	2	no	—
456	C₂³×C₂₃	—	8	2	no	—
457	C₂³×C₂₃	—	8	2	no	—
458	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
459	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
460	Q₈×C₂₃	—	2	2	no	—
461	Q₈×C₂₃	—	2	1	no	—
462	Q₈×C₂₃	—	2	1	no	—
463	Q₈×C₂₃	—	2	1	no	—
464	Q₈×C₂₃	—	2	1	no	—
465	Q₈×C₂₃	—	2	1	no	—
466	Q₈×C₂₃	—	2	1	no	—
467	Q₈×C₂₃	—	4	2	no	—
468	Q₈×C₂₃	—	8	1	no	—
469	Q₈×C₂₃	—	8	1	no	—
470	Q₈×C₂₃	—	8	2	no	—
471	D₄×C₂₃	—	2	2	no	—
472	D₄×C₂₃	—	2	2	no	—
473	D₄×C₂₃	—	2	1	no	—
474	D₄×C₂₃	—	2	2	no	—
475	D₄×C₂₃	—	2	1	no	—
476	D₄×C₂₃	—	2	2	no	—
477	D₄×C₂₃	—	2	2	no	—
478	D₄×C₂₃	—	4	2	no	—
479	D₄×C₂₃	—	4	2	no	—
480	D₄×C₂₃	—	4	2	no	—
481	D₄×C₂₃	—	4	2	no	—
482	D₄×C₂₃	—	8	2	no	—
483	D₄×C₂₃	—	8	2	no	—
484	D₄×C₂₃	—	8	1	no	—
485	D₄×C₂₃	—	8	2	no	—
486	D₄×C₂₃	—	8	1	no	—
487	D₄×C₂₃	—	8	2	no	—
488	D₄×C₂₃	—	8	2	no	—
489	D₄×C₂₃	—	8	2	no	—
490	D₄×C₂₃	—	8	2	no	—
491	D₄×C₂₃	—	8	2	no	—
492	D₄×C₂₃	—	8	2	no	—
493	C₂×C₄×C₂₃	—	2	2	no	—
494	C₂×C₄×C₂₃	—	2	2	no	—
495	C₂×C₄×C₂₃	—	2	1	no	—
496	C₂×C₄×C₂₃	—	2	1	no	—
497	C₂×C₄×C₂₃	—	2	2	no	—
498	C₂×C₄×C₂₃	—	2	1	no	—
499	C₂×C₄×C₂₃	—	2	1	no	—
500	C₂×C₄×C₂₃	—	2	2	no	—
501	C₂×C₄×C₂₃	—	2	1	no	—
502	C₂×C₄×C₂₃	—	2	2	no	—
503	C₂×C₄×C₂₃	—	2	1	no	—
504	C₂×C₄×C₂₃	—	2	1	no	—
505	C₂×C₄×C₂₃	—	2	1	no	—
506	C₂×C₄×C₂₃	—	2	1	no	—
507	C₂×C₄×C₂₃	—	4	1	no	—
508	C₂×C₄×C₂₃	—	4	2	no	—
509	C₂×C₄×C₂₃	—	8	2	no	—
510	C₂×C₄×C₂₃	—	8	2	no	—
511	C₂×C₄×C₂₃	—	8	2	no	—
512	C₂×C₄×C₂₃	—	8	2	no	—
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	2	yes	—
516	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
522	C₈×C₂₃	—	2	1	no	—
523	C₈×C₂₃	—	2	2	no	—
524	C₈×C₂₃	—	2	1	no	—
525	C₈×C₂₃	—	2	2	no	—
526	C₈×C₂₃	—	2	1	no	—
527	C₈×C₂₃	—	2	1	no	—
528	#3555	C₂×C₂₃	1	1	yes	characteristic, complemented
529	#3543	C₂×C₂₃	1	1	yes	characteristic
530	#3375	C₂×C₂₃	1	1	yes	characteristic, complemented
531	#3368	C₂×C₂₃	1	1	yes	characteristic, complemented
532	#3365	C₂×C₂₃	1	1	yes	characteristic, complemented
533	#3362	C₂×C₂₃	1	1	yes	characteristic, complemented
534	#3333	C₂×C₂₃	1	1	yes	characteristic, complemented
535	#3324	C₂×C₂₃	1	1	yes	characteristic, complemented
536	#3324	C₂×C₂₃	1	2	yes	complemented
537	#3323	C₂×C₂₃	1	2	yes	complemented
538	#3311	C₂×C₂₃	1	2	yes	complemented
539	#3310	C₂×C₂₃	1	2	yes	complemented
540	#3304	C₂×C₂₃	1	1	yes	characteristic, complemented
541	#3295	C₂×C₂₃	1	1	yes	characteristic, complemented
542	#3241	C₂×C₂₃	1	2	yes	complemented
543	#3233	C₂×C₂₃	1	1	yes	characteristic, complemented
544	#3222	C₂×C₂₃	1	2	yes	complemented
545	#3208	C₂×C₂₃	1	1	yes	characteristic, complemented
546	#3174	C₂×C₂₃	1	2	yes	complemented
547	#3172	C₂×C₂₃	1	1	yes	characteristic, complemented
548	#3138	C₂×C₂₃	1	1	yes	characteristic, complemented
549	#3136	C₂×C₂₃	1	2	yes	complemented
550	#2969	C₂×C₂₃	1	1	yes	characteristic, complemented
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	1	no	—
556	C₂²×C₂₃	—	2	2	no	—
557	C₂²×C₂₃	—	4	2	no	—
558	C₂²×C₂₃	—	4	1	no	—
559	C₂²×C₂₃	—	4	2	no	—
560	C₂²×C₂₃	—	4	2	no	—
561	C₂²×C₂₃	—	4	2	no	—
562	C₂²×C₂₃	—	4	1	no	—
563	C₂²×C₂₃	—	4	1	no	—
564	C₂²×C₂₃	—	4	2	no	—
565	C₂²×C₂₃	—	4	2	no	—
566	C₂²×C₂₃	—	16	4	no	—
567	C₂²×C₂₃	—	16	4	no	—
568	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
569	C₄×C₂₃	—	2	1	no	—
570	C₄×C₂₃	—	2	1	no	—
571	C₄×C₂₃	—	2	2	no	—
572	C₄×C₂₃	—	2	2	no	—
573	C₄×C₂₃	—	2	1	no	—
574	C₄×C₂₃	—	2	1	no	—
575	C₄×C₂₃	—	2	2	no	—
576	C₄×C₂₃	—	4	1	no	—
577	C₄×C₂₃	—	4	1	no	—
578	C₄×C₂₃	—	4	2	no	—
579	C₄×C₂₃	—	4	1	no	—
580	C₄×C₂₃	—	4	1	no	—
581	C₄×C₂₃	—	4	1	no	—
582	C₄×C₂₃	—	4	1	no	—
583	C₄×C₂₃	—	4	1	no	—
584	C₄×C₂₃	—	4	2	no	—
585	C₄×C₂₃	#577	1	2	yes	—
586	C₄×C₂₃	#585	1	1	yes	characteristic
587	C₄×C₂₃	#585	1	1	yes	characteristic
588	#563	—	2	2	no	—
589	#560	—	2	2	no	—
590	#559	C₂²×C₂₃	1	1	yes	characteristic
591	Q₈²	C₂²×C₂₃	1	1	yes	characteristic, complemented
592	#557	—	2	1	no	—
593	#557	C₂²×C₂₃	1	1	yes	characteristic, complemented
594	#556	—	2	1	no	—
595	#556	C₂²×C₂₃	1	1	yes	characteristic, complemented
596	#556	C₂²×C₂₃	1	2	yes	complemented
597	#554	C₂²×C₂₃	1	1	yes	characteristic, complemented
598	#552	C₂²×C₂₃	1	2	yes	complemented
599	#550	C₂²×C₂₃	1	1	yes	characteristic
600	#550	C₂²×C₂₃	1	1	yes	characteristic
601	#546	—	2	1	no	—
602	#546	C₂²×C₂₃	1	2	yes	—
603	D₄²	—	2	1	no	—
604	D₄²	C₂²×C₂₃	1	1	yes	characteristic
605	D₄²	C₂²×C₂₃	1	2	yes	—
606	#544	C₂²×C₂₃	1	2	yes	complemented
607	#542	—	2	1	no	—
608	#541	—	2	2	no	—
609	#541	—	2	1	no	—
610	#541	C₂²×C₂₃	1	2	yes	complemented
611	#540	—	2	1	no	—
612	#540	C₂²×C₂₃	1	2	yes	—
613	#535	—	2	1	no	—
614	#535	C₂²×C₂₃	1	2	yes	—
615	#534	—	2	2	no	—
616	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
617	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
618	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
619	#529	C₂²×C₂₃	1	1	yes	characteristic
620	#529	C₂²×C₂₃	1	1	yes	characteristic
621	#501	C₂²×C₂₃	1	1	yes	characteristic, complemented
622	#499	C₂²×C₂₃	1	2	yes	complemented
623	#497	C₂²×C₂₃	1	1	yes	characteristic, complemented
624	#492	C₂²×C₂₃	1	2	yes	complemented
625	#491	C₂²×C₂₃	1	1	yes	characteristic, complemented
626	#490	C₂²×C₂₃	1	2	yes	complemented
627	#490	C₂²×C₂₃	1	2	yes	complemented
628	#490	C₂²×C₂₃	1	2	yes	complemented
629	#489	C₂²×C₂₃	1	2	yes	complemented
630	#489	C₂²×C₂₃	1	1	yes	characteristic, complemented
631	#488	C₂²×C₂₃	1	2	yes	complemented
632	#488	C₂²×C₂₃	1	2	yes	complemented
633	#486	C₂²×C₂₃	1	1	yes	characteristic
634	#486	C₂²×C₂₃	1	1	yes	characteristic
635	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
636	#486	C₂²×C₂₃	1	2	yes	complemented
637	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
638	#486	C₂²×C₂₃	1	2	yes	complemented
639	#485	C₂²×C₂₃	1	2	yes	complemented
640	#482	C₂²×C₂₃	1	2	yes	—
641	#482	C₂²×C₂₃	1	2	yes	complemented
642	#482	C₂²×C₂₃	1	2	yes	complemented
643	#481	C₂²×C₂₃	1	2	yes	complemented
644	#480	C₂²×C₂₃	1	2	yes	complemented
645	#478	C₂²×C₂₃	1	2	yes	complemented
646	#478	C₂²×C₂₃	1	2	yes	complemented
647	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
648	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
649	#476	C₂²×C₂₃	1	2	yes	complemented
650	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
651	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
652	#474	C₂²×C₂₃	1	2	yes	complemented
653	#470	C₂²×C₂₃	1	1	yes	characteristic, complemented
654	#470	C₂²×C₂₃	1	1	yes	characteristic, complemented
655	#468	C₂²×C₂₃	1	1	yes	characteristic
656	#468	C₂²×C₂₃	1	1	yes	characteristic
657	#468	C₂²×C₂₃	1	2	yes	complemented
658	#468	C₂²×C₂₃	1	2	yes	complemented
659	#465	C₂²×C₂₃	1	2	yes	complemented
660	#465	C₂²×C₂₃	1	2	yes	complemented
661	#464	C₂²×C₂₃	1	2	yes	complemented
662	#464	C₂²×C₂₃	1	2	yes	complemented
663	#460	C₂²×C₂₃	1	1	yes	characteristic
664	#460	C₂²×C₂₃	1	1	yes	characteristic
665	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
666	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
667	#460	C₂²×C₂₃	1	2	yes	complemented
668	#460	C₂²×C₂₃	1	2	yes	complemented
669	#452	C₂²×C₂₃	1	2	yes	complemented
670	#452	C₂²×C₂₃	1	2	yes	complemented
671	#450	C₂²×C₂₃	1	2	yes	complemented
672	#450	C₂²×C₂₃	1	2	yes	complemented
673	#450	C₂²×C₂₃	1	2	yes	complemented
674	#450	C₂²×C₂₃	1	2	yes	complemented
675	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
676	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
677	#440	C₂²×C₂₃	1	2	yes	complemented
678	#440	C₂²×C₂₃	1	2	yes	complemented
679	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
680	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
681	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
682	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
683	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
684	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
685	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
686	#436	C₂²×C₂₃	1	2	yes	complemented
687	#435	C₂²×C₂₃	1	2	yes	complemented
688	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
689	#433	C₂²×C₂₃	1	2	yes	complemented
690	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
691	#418	C₂²×C₂₃	1	2	yes	complemented
692	#418	C₂²×C₂₃	1	2	yes	complemented
693	#418	C₂²×C₂₃	1	2	yes	complemented
694	#417	C₂²×C₂₃	1	2	yes	complemented
695	#416	C₂²×C₂₃	1	2	yes	complemented
696	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
697	#405	C₂²×C₂₃	1	2	yes	complemented
698	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
699	C₂×C₂₃	—	4	2	no	—
700	C₂×C₂₃	—	4	1	no	—
701	C₂×C₂₃	—	8	2	no	—
702	C₂×C₂₃	—	8	2	no	—
703	C₂×C₂₃	—	8	1	no	—
704	C₂×C₂₃	#3500	1	1	yes	characteristic
705	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
706	C₂×C₂₃	#3585	1	1	yes	characteristic
707	C₂×#41	—	2	1	no	—
708	C₂×#41	C₂³×C₂₃	1	2	yes	—
709	C₂²×D₄	—	2	2	no	—
710	C₂²×D₄	—	2	1	no	—
711	C₂²×D₄	—	2	1	no	—
712	C₂²×D₄	—	2	1	no	—
713	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
714	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
715	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
716	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
717	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
719	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
720	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
721	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
723	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
724	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
725	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
726	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
727	C₄⋊Q₈	—	2	1	no	—
728	C₄⋊Q₈	—	2	2	no	—
729	C₄⋊Q₈	—	2	1	no	—
730	C₄⋊Q₈	—	2	2	no	—
731	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
732	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
733	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
734	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
735	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
736	#127	—	2	1	no	—
737	#127	—	2	1	no	—
738	#127	—	2	1	no	—
739	#127	C₂³×C₂₃	1	2	yes	—
740	#127	C₂³×C₂₃	1	1	yes	characteristic
741	#127	C₂³×C₂₃	1	1	yes	characteristic
742	#127	C₂³×C₂₃	1	2	yes	—
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#126	—	2	2	no	—
747	#126	—	2	2	no	—
748	#126	—	2	2	no	—
749	#126	—	2	1	no	—
750	#126	D₄×C₂₃	1	2	yes	—
751	#125	—	2	2	no	—
752	#125	—	2	2	no	—
753	#125	—	2	2	no	—
754	#125	—	2	1	no	—
755	#125	—	2	2	no	—
756	#125	—	2	2	no	—
757	#125	—	2	1	no	—
758	#125	D₄×C₂₃	1	1	yes	characteristic
759	#125	C₂³×C₂₃	1	1	yes	characteristic
760	#125	C₂³×C₂₃	1	2	yes	—
761	#125	C₂³×C₂₃	1	2	yes	—
762	#124	—	2	1	no	—
763	#124	—	2	1	no	—
764	#124	—	2	2	no	—
765	#124	D₄×C₂₃	1	1	yes	characteristic
766	#124	C₂³×C₂₃	1	1	yes	characteristic
767	#124	C₂³×C₂₃	1	2	yes	—
768	#123	—	2	2	no	—
769	#123	—	2	1	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	D₄×C₂₃	1	2	yes	—
775	C₂²⋊Q₈	—	2	1	no	—
776	C₂²⋊Q₈	—	2	1	no	—
777	C₂²⋊Q₈	—	2	1	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
782	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
783	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
784	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
785	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
786	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	—	2	2	no	—
790	#121	—	2	1	no	—
791	#121	—	2	1	no	—
792	#121	—	2	2	no	—
793	#121	—	2	2	no	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	D₄×C₂₃	1	1	yes	characteristic
798	#121	C₂³×C₂₃	1	1	yes	characteristic
799	#121	C₂³×C₂₃	1	2	yes	—
800	#121	C₂³×C₂₃	1	2	yes	—
801	#120	—	2	2	no	—
802	#120	—	2	2	no	—
803	#120	—	2	2	no	—
804	#120	—	2	2	no	—
805	#120	—	2	2	no	—
806	#120	—	2	2	no	—
807	C₄×Q₈	—	2	1	no	—
808	C₄×Q₈	—	2	2	no	—
809	C₄×Q₈	—	2	1	no	—
810	C₄×Q₈	—	2	1	no	—
811	C₄×Q₈	—	2	1	no	—
812	C₄×Q₈	—	2	1	no	—
813	C₄×Q₈	—	2	1	no	—
814	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
815	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
816	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
817	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
818	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
819	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₂₃	1	2	yes	—
826	C₄×D₄	C₂³×C₂₃	1	2	yes	—
827	C₄×D₄	C₂³×C₂₃	1	2	yes	—
828	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
829	#117	—	2	1	no	—
830	#117	—	2	2	no	—
831	#117	—	2	1	no	—
832	#117	C₂³×C₂₃	1	2	yes	—
833	#117	C₂³×C₂₃	1	2	yes	—
834	#117	C₂³×C₂₃	1	2	yes	—
835	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
836	C₂×C₂²⋊C₄	—	2	2	no	—
837	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
838	#107	C₂³×C₂₃	1	1	yes	characteristic
839	#107	C₂³×C₂₃	1	1	yes	characteristic
840	#107	C₂³×C₂₃	1	2	yes	—
841	#107	C₂³×C₂₃	1	2	yes	—
842	#106	C₂³×C₂₃	1	2	yes	—
843	#106	C₂³×C₂₃	1	2	yes	—
844	#106	C₂³×C₂₃	1	1	yes	characteristic
845	#106	C₂³×C₂₃	1	1	yes	characteristic
846	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
847	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
848	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
849	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
850	#103	C₂³×C₂₃	1	1	yes	characteristic
851	#103	C₂³×C₂₃	1	2	yes	—
852	#103	C₂³×C₂₃	1	1	yes	characteristic
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	1	yes	characteristic
857	#103	C₂³×C₂₃	1	1	yes	characteristic
858	#102	C₂³×C₂₃	1	1	yes	characteristic
859	#102	C₂³×C₂₃	1	2	yes	—
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	2	yes	—
865	#102	C₂³×C₂₃	1	2	yes	—
866	#102	C₂³×C₂₃	1	1	yes	characteristic
867	#102	C₂³×C₂₃	1	2	yes	—
868	#102	C₂³×C₂₃	1	2	yes	—
869	#102	C₂³×C₂₃	1	2	yes	—
870	#102	C₂³×C₂₃	1	2	yes	—
871	#102	C₂³×C₂₃	1	2	yes	—
872	#102	C₂³×C₂₃	1	2	yes	—
873	#102	C₂³×C₂₃	1	2	yes	—
874	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
875	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
876	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
877	#97	C₂³×C₂₃	1	1	yes	characteristic
878	#97	C₂³×C₂₃	1	1	yes	characteristic
879	#97	C₂³×C₂₃	1	2	yes	—
880	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
881	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
882	C₄×C₈	C₂³×C₂₃	1	2	yes	—
883	C₄×C₈	C₂³×C₂₃	1	2	yes	—
884	C₂₃	#62608	1	1	yes	characteristic, direct product factor, Sylow
885	C₂⁴	—	2	2	no	—
886	C₂⁴	—	2	2	no	—
887	#41	—	4	2	no	—
888	#41	—	4	2	no	—
889	#41	—	8	2	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	1	no	—
892	C₂×Q₈	—	2	1	no	—
893	C₂×Q₈	—	2	2	no	—
894	C₂×Q₈	C₂×D₄×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×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
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	1	no	—
903	C₂×D₄	—	2	1	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	4	2	no	—
913	C₂×D₄	—	4	2	no	—
914	C₂×D₄	—	4	2	no	—
915	C₂×D₄	—	4	2	no	—
916	C₂×D₄	—	8	2	no	—
917	C₂×D₄	—	8	2	no	—
918	C₂×D₄	—	8	2	no	—
919	C₂×D₄	—	8	4	no	—
920	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
921	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
922	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
923	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
924	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
931	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
932	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
933	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
934	Q₁₆	—	4	1	no	—
935	Q₁₆	—	4	1	no	—
936	SD₁₆	—	4	2	no	—
937	SD₁₆	—	4	2	no	—
938	SD₁₆	—	4	2	no	—
939	SD₁₆	—	4	2	no	—
940	SD₁₆	—	4	1	no	—
941	SD₁₆	—	4	1	no	—
942	M₁₆	—	4	1	no	—
943	M₁₆	—	4	2	no	—
944	M₁₆	—	4	1	no	—
945	C₂×C₈	—	4	2	no	—
946	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
947	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
948	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
949	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
950	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
951	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
976	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
977	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
978	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
979	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
980	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
981	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
982	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
983	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
984	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
985	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
986	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1005	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1006	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1007	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1008	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1009	C₄²	—	2	2	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	2	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1017	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1018	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1019	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1020	C₄²	C₂⁴×C₂₃	1	2	yes	—
1021	C₂³	—	2	1	no	—
1022	C₂³	—	2	2	no	—
1023	C₂³	—	2	2	no	—
1024	C₂³	—	4	4	no	—
1025	C₂³	—	8	2	no	—
1026	C₂³	—	8	2	no	—
1027	C₂³	—	8	2	no	—
1028	C₂³	—	8	2	no	—
1029	C₂³	—	8	2	no	—
1030	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1031	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	2	1	no	—
1034	Q₈	—	2	1	no	—
1035	Q₈	—	2	1	no	—
1036	Q₈	—	2	1	no	—
1037	Q₈	—	2	1	no	—
1038	Q₈	—	2	1	no	—
1039	Q₈	—	4	2	no	—
1040	Q₈	—	8	1	no	—
1041	Q₈	—	8	1	no	—
1042	Q₈	—	8	2	no	—
1043	D₄	—	2	2	no	—
1044	D₄	—	2	2	no	—
1045	D₄	—	2	1	no	—
1046	D₄	—	2	2	no	—
1047	D₄	—	2	1	no	—
1048	D₄	—	2	2	no	—
1049	D₄	—	2	2	no	—
1050	D₄	—	4	2	no	—
1051	D₄	—	4	2	no	—
1052	D₄	—	4	2	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	8	2	no	—
1055	D₄	—	8	2	no	—
1056	D₄	—	8	2	no	—
1057	D₄	—	8	1	no	—
1058	D₄	—	8	2	no	—
1059	D₄	—	8	1	no	—
1060	D₄	—	8	2	no	—
1061	D₄	—	8	2	no	—
1062	D₄	—	8	2	no	—
1063	D₄	—	8	2	no	—
1064	D₄	—	8	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	4	1	no	—
1080	C₂×C₄	—	4	2	no	—
1081	C₂×C₄	—	8	2	no	—
1082	C₂×C₄	—	8	2	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	—	8	2	no	—
1085	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1086	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1087	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1088	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1089	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1090	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1091	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1092	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1093	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1094	C₈	—	2	1	no	—
1095	C₈	—	2	2	no	—
1096	C₈	—	2	1	no	—
1097	C₈	—	2	2	no	—
1098	C₈	—	2	1	no	—
1099	C₈	—	2	1	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	2	1	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	4	2	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	2	no	—
1111	C₂²	—	4	2	no	—
1112	C₂²	—	4	2	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	2	no	—
1115	C₂²	—	16	4	no	—
1116	C₂²	—	16	4	no	—
1117	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1118	C₄	—	2	2	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	2	1	no	—
1121	C₄	—	2	2	no	—
1122	C₄	—	2	1	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	2	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	2	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	1	no	—
1132	C₄	—	4	2	no	—
1133	C₄	—	4	1	no	—
1134	C₄	C₂₃×#577	1	2	yes	—
1135	C₄	C₂₃×#585	1	1	yes	characteristic
1136	C₄	C₂₃×#585	1	1	yes	characteristic
1137	C₂	—	4	1	no	—
1138	C₂	—	4	2	no	—
1139	C₂	—	8	1	no	—
1140	C₂	—	8	2	no	—
1141	C₂	—	8	2	no	—
1142	C₂	C₂₃×#3500	1	1	yes	characteristic
1143	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
1144	C₂	C₂₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3543	C₂
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×#3555	C₂	semidirect
3. C₂₃×#3375	C₂	semidirect
4. C₂₃×#3368	C₂	semidirect
5. C₂₃×#3365	C₂	semidirect
6. C₂₃×#3362	C₂	semidirect
7. C₂₃×#3333	C₂	semidirect
8. C₂₃×#3324	C₂	semidirect
9. C₂₃×#3324	C₂	semidirect
10. C₂₃×#3323	C₂	semidirect
11. C₂₃×#3311	C₂	semidirect
12. C₂₃×#3310	C₂	semidirect
13. C₂₃×#3304	C₂	semidirect
14. C₂₃×#3295	C₂	semidirect
15. C₂₃×#3241	C₂	semidirect
16. C₂₃×#3233	C₂	semidirect
17. C₂₃×#3222	C₂	semidirect
18. C₂₃×#3208	C₂	semidirect
19. C₂₃×#3174	C₂	semidirect
20. C₂₃×#3172	C₂	semidirect
21. C₂₃×#3138	C₂	semidirect
22. C₂₃×#3136	C₂	semidirect
23. C₂₃×#2969	C₂	semidirect
27. Q₈²×C₂₃	C₂²	semidirect
29. C₂₃×#557	C₂²	semidirect
31. C₂₃×#556	C₂²	semidirect
32. C₂₃×#556	C₂²	semidirect
33. C₂₃×#554	C₂²	semidirect
34. C₂₃×#552	C₂²	semidirect
42. C₂₃×#544	C₂²	semidirect
46. C₂₃×#541	C₂²	semidirect
52. C₂₃×#533	C₂²	semidirect
53. C₂₃×#533	C₂²	semidirect
57. C₂₃×#501	C₂²	semidirect
58. C₂₃×#499	C₂²	semidirect
59. C₂₃×#497	C₂²	semidirect
60. C₂₃×#492	C₂²	semidirect
61. C₂₃×#491	C₂²	semidirect
62. C₂₃×#490	C₂²	semidirect
63. C₂₃×#490	C₂²	semidirect
64. C₂₃×#490	C₂²	semidirect
65. C₂₃×#489	C₂²	semidirect
66. C₂₃×#489	C₂²	semidirect
67. C₂₃×#488	C₂²	semidirect
68. C₂₃×#488	C₂²	semidirect
71. C₂₃×#486	C₂²	semidirect
72. C₂₃×#486	C₂²	semidirect
73. C₂₃×#486	C₂²	semidirect
74. C₂₃×#486	C₂²	semidirect
75. C₂₃×#485	C₂²	semidirect
77. C₂₃×#482	C₂²	semidirect
78. C₂₃×#482	C₂²	semidirect
79. C₂₃×#481	C₂²	semidirect
80. C₂₃×#480	C₂²	semidirect
81. C₂₃×#478	C₂²	semidirect
82. C₂₃×#478	C₂²	semidirect
83. C₂₃×#477	C₂²	semidirect
84. C₂₃×#476	C₂²	semidirect
85. C₂₃×#476	C₂²	semidirect
86. C₂₃×#475	C₂²	semidirect
87. C₂₃×#474	C₂²	semidirect
88. C₂₃×#474	C₂²	semidirect
89. C₂₃×#470	C₂²	semidirect
90. C₂₃×#470	C₂²	semidirect
93. C₂₃×#468	C₂²	semidirect
94. C₂₃×#468	C₂²	semidirect
95. C₂₃×#465	C₂²	semidirect
96. C₂₃×#465	C₂²	semidirect
97. C₂₃×#464	C₂²	semidirect
98. C₂₃×#464	C₂²	semidirect
101. C₂₃×#460	C₂²	semidirect
102. C₂₃×#460	C₂²	semidirect
103. C₂₃×#460	C₂²	semidirect
104. C₂₃×#460	C₂²	semidirect
105. C₂₃×#452	C₂²	semidirect
106. C₂₃×#452	C₂²	semidirect
107. C₂₃×#450	C₂²	semidirect
108. C₂₃×#450	C₂²	semidirect
109. C₂₃×#450	C₂²	semidirect
110. C₂₃×#450	C₂²	semidirect
111. C₂₃×#446	C₂²	semidirect
112. C₈×Q₈×C₂₃	C₂²	semidirect
113. C₂₃×#440	C₂²	semidirect
114. C₂₃×#440	C₂²	semidirect
115. C₄×Q₁₆×C₂₃	C₂²	semidirect
116. C₄×Q₁₆×C₂₃	C₂²	semidirect
117. C₄×SD₁₆×C₂₃	C₂²	semidirect
118. C₄×SD₁₆×C₂₃	C₂²	semidirect
119. C₄×SD₁₆×C₂₃	C₂²	semidirect
120. C₄×SD₁₆×C₂₃	C₂²	semidirect
121. C₂₃×#436	C₂²	semidirect
122. C₂₃×#436	C₂²	semidirect
123. C₂₃×#435	C₂²	semidirect
124. C₈×D₄×C₂₃	C₂²	semidirect
125. C₂₃×#433	C₂²	semidirect
126. C₂₃×#431	C₂²	semidirect
127. C₂₃×#418	C₂²	semidirect
128. C₂₃×#418	C₂²	semidirect
129. C₂₃×#418	C₂²	semidirect
130. C₂₃×#417	C₂²	semidirect
131. C₂₃×#416	C₂²	semidirect
132. C₂×C₂₃×#102	C₂²	semidirect
133. C₂₃×#405	C₂²	semidirect
134. C₄×M₁₆×C₂₃	C₂²	semidirect
448. #62608	C₂₃	direct (N × H)
528. #3555	C₂×C₂₃	semidirect
530. #3375	C₂×C₂₃	semidirect
531. #3368	C₂×C₂₃	semidirect
532. #3365	C₂×C₂₃	semidirect
533. #3362	C₂×C₂₃	semidirect
534. #3333	C₂×C₂₃	semidirect
535. #3324	C₂×C₂₃	semidirect
536. #3324	C₂×C₂₃	semidirect
537. #3323	C₂×C₂₃	semidirect
538. #3311	C₂×C₂₃	semidirect
539. #3310	C₂×C₂₃	semidirect
540. #3304	C₂×C₂₃	semidirect
541. #3295	C₂×C₂₃	semidirect
542. #3241	C₂×C₂₃	semidirect
543. #3233	C₂×C₂₃	semidirect
544. #3222	C₂×C₂₃	semidirect
545. #3208	C₂×C₂₃	semidirect
546. #3174	C₂×C₂₃	semidirect
547. #3172	C₂×C₂₃	semidirect
548. #3138	C₂×C₂₃	semidirect
549. #3136	C₂×C₂₃	semidirect
550. #2969	C₂×C₂₃	semidirect
591. Q₈²	C₂²×C₂₃	semidirect
593. #557	C₂²×C₂₃	semidirect
595. #556	C₂²×C₂₃	semidirect
596. #556	C₂²×C₂₃	semidirect
597. #554	C₂²×C₂₃	semidirect
598. #552	C₂²×C₂₃	semidirect
606. #544	C₂²×C₂₃	semidirect
610. #541	C₂²×C₂₃	semidirect
616. #533	C₂²×C₂₃	semidirect
617. #533	C₂²×C₂₃	semidirect
621. #501	C₂²×C₂₃	semidirect
622. #499	C₂²×C₂₃	semidirect
623. #497	C₂²×C₂₃	semidirect
624. #492	C₂²×C₂₃	semidirect
625. #491	C₂²×C₂₃	semidirect
626. #490	C₂²×C₂₃	semidirect
627. #490	C₂²×C₂₃	semidirect
628. #490	C₂²×C₂₃	semidirect
629. #489	C₂²×C₂₃	semidirect
630. #489	C₂²×C₂₃	semidirect
631. #488	C₂²×C₂₃	semidirect
632. #488	C₂²×C₂₃	semidirect
635. #486	C₂²×C₂₃	semidirect
636. #486	C₂²×C₂₃	semidirect
637. #486	C₂²×C₂₃	semidirect
638. #486	C₂²×C₂₃	semidirect
639. #485	C₂²×C₂₃	semidirect
641. #482	C₂²×C₂₃	semidirect
642. #482	C₂²×C₂₃	semidirect
643. #481	C₂²×C₂₃	semidirect
644. #480	C₂²×C₂₃	semidirect
645. #478	C₂²×C₂₃	semidirect
646. #478	C₂²×C₂₃	semidirect
647. #477	C₂²×C₂₃	semidirect
648. #476	C₂²×C₂₃	semidirect
649. #476	C₂²×C₂₃	semidirect
650. #475	C₂²×C₂₃	semidirect
651. #474	C₂²×C₂₃	semidirect
652. #474	C₂²×C₂₃	semidirect
653. #470	C₂²×C₂₃	semidirect
654. #470	C₂²×C₂₃	semidirect
657. #468	C₂²×C₂₃	semidirect
658. #468	C₂²×C₂₃	semidirect
659. #465	C₂²×C₂₃	semidirect
660. #465	C₂²×C₂₃	semidirect
661. #464	C₂²×C₂₃	semidirect
662. #464	C₂²×C₂₃	semidirect
665. #460	C₂²×C₂₃	semidirect
666. #460	C₂²×C₂₃	semidirect
667. #460	C₂²×C₂₃	semidirect
668. #460	C₂²×C₂₃	semidirect
669. #452	C₂²×C₂₃	semidirect
670. #452	C₂²×C₂₃	semidirect
671. #450	C₂²×C₂₃	semidirect
672. #450	C₂²×C₂₃	semidirect
673. #450	C₂²×C₂₃	semidirect
674. #450	C₂²×C₂₃	semidirect
675. #446	C₂²×C₂₃	semidirect
676. C₈×Q₈	C₂²×C₂₃	semidirect
677. #440	C₂²×C₂₃	semidirect
678. #440	C₂²×C₂₃	semidirect
679. C₄×Q₁₆	C₂²×C₂₃	semidirect
680. C₄×Q₁₆	C₂²×C₂₃	semidirect
681. C₄×SD₁₆	C₂²×C₂₃	semidirect
682. C₄×SD₁₆	C₂²×C₂₃	semidirect
683. C₄×SD₁₆	C₂²×C₂₃	semidirect
684. C₄×SD₁₆	C₂²×C₂₃	semidirect
685. #436	C₂²×C₂₃	semidirect
686. #436	C₂²×C₂₃	semidirect
687. #435	C₂²×C₂₃	semidirect
688. C₈×D₄	C₂²×C₂₃	semidirect
689. #433	C₂²×C₂₃	semidirect
690. #431	C₂²×C₂₃	semidirect
691. #418	C₂²×C₂₃	semidirect
692. #418	C₂²×C₂₃	semidirect
693. #418	C₂²×C₂₃	semidirect
694. #417	C₂²×C₂₃	semidirect
695. #416	C₂²×C₂₃	semidirect
696. C₂×#102	C₂²×C₂₃	semidirect
697. #405	C₂²×C₂₃	semidirect
698. C₄×M₁₆	C₂²×C₂₃	semidirect
884. C₂₃	#62608	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×#3555	2
C₂₃×#3543	2
C₂₃×#3375	2
C₂₃×#3368	2
C₂₃×#3365	2
C₂₃×#3362	2
C₂₃×#3333	2
C₂₃×#3324	2
C₂₃×#3323	2
C₂₃×#3311	2
C₂₃×#3310	2
C₂₃×#3304	2
C₂₃×#3295	2
C₂₃×#3241	2
C₂₃×#3233	2
C₂₃×#3222	2
C₂₃×#3208	2
C₂₃×#3174	2
C₂₃×#3172	2
C₂₃×#3138	2
C₂₃×#3136	2
C₂₃×#2969	2
#62608	23

Subgroups — C23×#62608 #19210234

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62608 #19210234