Subgroups — C₂₃×#61274 #19208900

Order 5888.

1824 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3493	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3355	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3353	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3350	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3348	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3347	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3345	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3341	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3337	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3096	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3091	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3084	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3062	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3055	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2946	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2912	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2911	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
27	C₂₃×#556	—	2	1	no	—
28	C₂₃×#556	C₂²	1	2	yes	complemented
29	C₂₃×#555	—	2	1	no	—
30	C₂₃×#555	C₂²	1	2	yes	—
31	C₂₃×#555	C₂²	1	2	yes	complemented
32	C₂₃×#553	—	2	1	no	—
33	C₂₃×#553	C₂²	1	2	yes	—
34	C₂₃×#553	C₂²	1	2	yes	—
35	C₂₃×#553	C₂²	1	2	yes	complemented
36	C₂₃×#552	—	2	1	no	—
37	C₂₃×#552	C₂²	1	2	yes	complemented
38	C₂₃×#551	—	2	2	no	—
39	C₂₃×#547	C₂²	1	2	yes	—
40	C₂₃×#546	—	2	2	no	—
41	C₂₃×#544	C₂²	1	1	yes	characteristic
42	C₂₃×#544	C₂²	1	1	yes	characteristic
43	C₂₃×#542	—	2	1	no	—
44	C₂₃×#540	—	2	1	no	—
45	C₂₃×#538	—	2	2	no	—
46	C₂₃×#537	C₂²	1	1	yes	characteristic
47	C₂₃×#535	C₂²	1	1	yes	characteristic
48	C₂₃×#532	—	2	1	no	—
49	C₂₃×#529	—	2	2	no	—
50	C₂₃×#529	—	2	1	no	—
51	C₂₃×#525	C₂²	1	1	yes	characteristic
52	C₂₃×#525	C₂²	1	1	yes	characteristic
53	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
54	C₂₃×#520	C₂²	1	1	yes	characteristic
55	C₂₃×#520	C₂²	1	1	yes	characteristic
56	C₂₃×#520	C₂²	1	1	yes	characteristic
57	C₂₃×#518	C₂²	1	1	yes	characteristic
58	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
59	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
60	C₂₃×#501	C₂²	1	2	yes	complemented
61	C₂₃×#501	C₂²	1	2	yes	complemented
62	C₂₃×#500	C₂²	1	2	yes	complemented
63	C₂₃×#499	C₂²	1	2	yes	complemented
64	C₂₃×#485	C₂²	1	1	yes	characteristic, complemented
65	C₂₃×#485	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#485	C₂²	1	2	yes	complemented
67	C₂₃×#484	C₂²	1	2	yes	complemented
68	C₂₃×#484	C₂²	1	1	yes	characteristic, complemented
69	C₂₃×#483	C₂²	1	1	yes	characteristic, complemented
70	C₂₃×#482	C₂²	1	2	yes	—
71	C₂₃×#482	C₂²	1	2	yes	—
72	C₂₃×#482	C₂²	1	2	yes	—
73	C₂₃×#482	C₂²	1	2	yes	—
74	C₂₃×#482	C₂²	1	1	yes	characteristic, complemented
75	C₂₃×#482	C₂²	1	2	yes	complemented
76	C₂₃×#482	C₂²	1	2	yes	complemented
77	C₂₃×#482	C₂²	1	1	yes	characteristic, complemented
78	C₂₃×#482	C₂²	1	2	yes	complemented
79	C₂₃×#481	C₂²	1	1	yes	characteristic, complemented
80	C₂₃×#481	C₂²	1	2	yes	complemented
81	C₂₃×#480	C₂²	1	2	yes	complemented
82	C₂₃×#480	C₂²	1	2	yes	complemented
83	C₂₃×#480	C₂²	1	1	yes	characteristic, complemented
84	C₂₃×#479	C₂²	1	2	yes	complemented
85	C₂₃×#478	C₂²	1	2	yes	complemented
86	C₂₃×#478	C₂²	1	2	yes	complemented
87	C₂₃×#478	C₂²	1	2	yes	complemented
88	C₂₃×#476	C₂²	1	2	yes	complemented
89	C₂₃×#476	C₂²	1	2	yes	complemented
90	C₂₃×#475	C₂²	1	2	yes	complemented
91	C₂₃×#474	C₂²	1	2	yes	complemented
92	C₂₃×#469	C₂²	1	2	yes	—
93	C₂₃×#469	C₂²	1	2	yes	complemented
94	C₂₃×#468	C₂²	1	2	yes	—
95	C₂₃×#468	C₂²	1	2	yes	complemented
96	C₂₃×#466	C₂²	1	2	yes	—
97	C₂₃×#466	C₂²	1	2	yes	complemented
98	C₂₃×#465	C₂²	1	2	yes	—
99	C₂₃×#465	C₂²	1	2	yes	complemented
100	C₂₃×#442	C₂²	1	2	yes	complemented
101	C₂₃×#440	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
103	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
104	C₂₃×#436	C₂²	1	2	yes	complemented
105	C₂₃×#435	C₂²	1	2	yes	complemented
106	C₂₃×#435	C₂²	1	2	yes	complemented
107	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
108	C₂₃×#428	C₂²	1	1	yes	characteristic
109	C₂₃×#428	C₂²	1	1	yes	characteristic
110	C₂₃×#428	C₂²	1	1	yes	characteristic
111	C₂₃×#428	C₂²	1	1	yes	characteristic
112	C₂₃×#428	C₂²	1	1	yes	characteristic
113	C₂₃×#428	C₂²	1	2	yes	complemented
114	C₂₃×#428	C₂²	1	2	yes	complemented
115	C₂₃×#428	C₂²	1	2	yes	complemented
116	C₂₃×#428	C₂²	1	2	yes	complemented
117	C₂₃×#427	C₂²	1	1	yes	characteristic
118	C₂₃×#427	C₂²	1	1	yes	characteristic
119	C₂₃×#427	C₂²	1	2	yes	complemented
120	C₂₃×#427	C₂²	1	2	yes	complemented
121	C₂₃×#427	C₂²	1	2	yes	complemented
122	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
123	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
124	C₂×C₂₃×#106	C₂²	1	2	yes	complemented
125	C₂₃×#424	C₂²	1	1	yes	characteristic
126	C₂₃×#418	C₂²	1	1	yes	characteristic
127	C₂₃×#417	C₂²	1	1	yes	characteristic
128	C₂₃×#416	C₂²	1	1	yes	characteristic
129	C₂₃×#416	C₂²	1	1	yes	characteristic
130	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
131	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
132	C₂₃×#408	C₂²	1	1	yes	characteristic
133	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
134	C₂₃×#405	C₂²	1	1	yes	characteristic
135	C₂×#41×C₂₃	—	2	2	no	—
136	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
137	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₂₃	—	2	1	no	—
139	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
141	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
142	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
143	C₂×D₈×C₂₃	C₂³	1	2	yes	—
144	C₂₃×#131	—	2	4	no	—
145	C₂×M₁₆×C₂₃	—	2	4	no	—
146	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
148	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
149	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
151	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
153	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
154	C₂₃×C₄⋊Q₈	—	2	1	no	—
155	C₂₃×C₄⋊Q₈	—	2	1	no	—
156	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
157	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
158	C₂₃×#127	—	2	1	no	—
159	C₂₃×#126	—	2	2	no	—
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×#125	C₂³	1	2	yes	—
170	C₂₃×#124	—	2	1	no	—
171	C₂₃×#124	—	2	2	no	—
172	C₂₃×#124	—	2	2	no	—
173	C₂₃×#124	—	2	2	no	—
174	C₂₃×#124	—	2	2	no	—
175	C₂₃×#124	—	2	2	no	—
176	C₂₃×#123	—	2	2	no	—
177	C₂₃×#123	—	2	1	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	D₄	1	2	yes	—
184	C₂₃×C₂²⋊Q₈	—	2	1	no	—
185	C₂₃×C₂²⋊Q₈	—	2	2	no	—
186	C₂₃×C₂²⋊Q₈	—	2	2	no	—
187	C₂₃×C₂²⋊Q₈	—	2	2	no	—
188	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
189	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
190	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
191	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
192	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
193	C₂₃×#121	—	2	1	no	—
194	C₂₃×#121	—	2	2	no	—
195	C₂₃×#121	—	2	2	no	—
196	C₂₃×#121	—	2	2	no	—
197	C₂₃×#121	—	2	2	no	—
198	C₂₃×#121	—	2	2	no	—
199	C₂₃×#121	—	2	2	no	—
200	C₂₃×#121	—	2	1	no	—
201	C₂₃×#121	—	2	1	no	—
202	C₂₃×#121	D₄	1	1	yes	characteristic
203	C₂₃×#121	D₄	1	1	yes	characteristic
204	C₂₃×#121	C₂³	1	2	yes	—
205	C₂₃×#121	C₂³	1	2	yes	—
206	C₂₃×#121	C₂³	1	2	yes	—
207	C₂₃×#121	C₂³	1	2	yes	—
208	C₂₃×#121	C₂³	1	1	yes	characteristic
209	C₂₃×#121	C₂³	1	2	yes	—
210	C₂₃×#121	C₂³	1	1	yes	characteristic
211	C₂₃×#120	—	2	1	no	—
212	C₂₃×#120	—	2	2	no	—
213	C₂₃×#120	D₄	1	2	yes	—
214	C₄×Q₈×C₂₃	—	2	1	no	—
215	C₄×Q₈×C₂₃	—	2	1	no	—
216	C₄×Q₈×C₂₃	—	2	2	no	—
217	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
218	C₄×D₄×C₂₃	—	2	2	no	—
219	C₄×D₄×C₂₃	—	2	1	no	—
220	C₄×D₄×C₂₃	—	2	2	no	—
221	C₄×D₄×C₂₃	—	2	1	no	—
222	C₄×D₄×C₂₃	—	2	1	no	—
223	C₄×D₄×C₂₃	—	2	1	no	—
224	C₄×D₄×C₂₃	—	2	1	no	—
225	C₄×D₄×C₂₃	—	2	1	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	2	no	—
230	C₄×D₄×C₂₃	C₂³	1	2	yes	—
231	C₄×D₄×C₂₃	C₂³	1	2	yes	—
232	C₄×D₄×C₂₃	C₂³	1	2	yes	—
233	C₄×D₄×C₂₃	C₂³	1	2	yes	—
234	C₄×D₄×C₂₃	C₂³	1	2	yes	—
235	C₂₃×#117	—	2	1	no	—
236	C₂₃×#117	—	2	1	no	—
237	C₂₃×#117	—	2	1	no	—
238	C₂₃×#117	—	2	1	no	—
239	C₂₃×#117	—	2	2	no	—
240	C₂₃×#117	—	2	2	no	—
241	C₂₃×#117	—	2	1	no	—
242	C₂₃×#117	—	2	2	no	—
243	C₂₃×#117	C₂³	1	2	yes	—
244	C₂₃×#117	C₂³	1	1	yes	characteristic
245	C₂₃×#117	C₂³	1	2	yes	—
246	C₂₃×#117	C₂³	1	2	yes	—
247	C₂₃×#117	C₂³	1	1	yes	characteristic
248	C₂₃×#117	C₂³	1	2	yes	—
249	C₂₃×#117	C₂³	1	1	yes	characteristic
250	C₂₃×#117	C₂³	1	1	yes	characteristic
251	C₂₃×#117	C₂³	1	1	yes	characteristic
252	C₂₃×#117	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
254	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
262	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
263	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
265	C₂×C₄²×C₂₃	—	2	1	no	—
266	C₂×C₄²×C₂₃	—	2	1	no	—
267	C₂₃×#107	C₂³	1	2	yes	—
268	C₂₃×#107	C₂³	1	2	yes	—
269	C₂₃×#107	C₂³	1	1	yes	characteristic
270	C₂₃×#107	C₂³	1	1	yes	characteristic
271	C₂₃×#107	C₂³	1	1	yes	characteristic
272	C₂₃×#107	C₂³	1	1	yes	characteristic
273	C₂₃×#107	C₂³	1	2	yes	—
274	C₂₃×#107	C₂³	1	2	yes	—
275	C₂₃×#107	C₂³	1	2	yes	—
276	C₂₃×#107	C₂³	1	2	yes	—
277	C₂₃×#107	C₂³	1	2	yes	—
278	C₂₃×#106	C₂³	1	2	yes	—
279	C₂₃×#106	C₂³	1	2	yes	—
280	C₂₃×#106	C₂³	1	1	yes	characteristic
281	C₂₃×#106	C₂³	1	2	yes	—
282	C₂₃×#106	C₂³	1	2	yes	—
283	C₂₃×#106	C₂³	1	1	yes	characteristic
284	C₂₃×#106	C₂³	1	1	yes	characteristic
285	C₂₃×#106	C₂³	1	1	yes	characteristic
286	C₂₃×#106	C₂³	1	2	yes	—
287	C₂₃×#106	C₂³	1	2	yes	—
288	C₂₃×#106	C₂³	1	2	yes	—
289	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
290	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
291	C₂₃×#103	C₂³	1	1	yes	characteristic
292	C₂₃×#103	C₂³	1	1	yes	characteristic
293	C₂₃×#103	C₂³	1	1	yes	characteristic
294	C₂₃×#103	C₂³	1	1	yes	characteristic
295	C₂₃×#103	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	1	yes	characteristic
301	C₂₃×#102	C₂³	1	1	yes	characteristic
302	C₂₃×#102	C₂³	1	1	yes	characteristic
303	C₂₃×#102	C₂³	1	1	yes	characteristic
304	C₂₃×#102	C₂³	1	2	yes	—
305	C₂₃×#102	C₂³	1	2	yes	—
306	C₂₃×#102	C₂³	1	2	yes	—
307	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
311	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₂₃×#97	C₂³	1	2	yes	—
314	C₄×C₈×C₂₃	C₂³	1	2	yes	—
315	C₂⁴×C₂₃	—	2	1	no	—
316	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
317	#41×C₂₃	—	2	2	no	—
318	#41×C₂₃	—	2	2	no	—
319	#41×C₂₃	—	2	2	no	—
320	#41×C₂₃	—	2	2	no	—
321	#41×C₂₃	—	8	4	no	—
322	C₂×Q₈×C₂₃	—	2	2	no	—
323	C₂×Q₈×C₂₃	—	2	2	no	—
324	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
326	C₂×D₄×C₂₃	—	2	1	no	—
327	C₂×D₄×C₂₃	—	2	2	no	—
328	C₂×D₄×C₂₃	—	2	1	no	—
329	C₂×D₄×C₂₃	—	2	2	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	2	no	—
334	C₂×D₄×C₂₃	—	2	1	no	—
335	C₂×D₄×C₂₃	—	2	2	no	—
336	C₂×D₄×C₂₃	—	2	2	no	—
337	C₂×D₄×C₂₃	—	8	2	no	—
338	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
339	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
341	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
342	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
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	1	no	—
349	C₂²×C₄×C₂₃	—	2	1	no	—
350	C₂²×C₄×C₂₃	—	2	1	no	—
351	C₂²×C₄×C₂₃	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
361	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
364	SD₁₆×C₂₃	—	2	4	no	—
365	D₈×C₂₃	—	2	4	no	—
366	M₁₆×C₂₃	—	2	2	no	—
367	M₁₆×C₂₃	—	2	4	no	—
368	M₁₆×C₂₃	—	2	4	no	—
369	M₁₆×C₂₃	#41	1	4	yes	complemented
370	C₂×C₈×C₂₃	—	2	2	no	—
371	C₂×C₈×C₂₃	—	2	2	no	—
372	C₂×C₈×C₂₃	—	2	4	no	—
373	C₂×C₈×C₂₃	—	2	4	no	—
374	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
377	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
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	1	no	—
384	C₄⋊C₄×C₂₃	—	2	1	no	—
385	C₄⋊C₄×C₂₃	—	2	1	no	—
386	C₄⋊C₄×C₂₃	—	2	2	no	—
387	C₄⋊C₄×C₂₃	—	2	2	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	1	no	—
393	C₄⋊C₄×C₂₃	—	2	2	no	—
394	C₄⋊C₄×C₂₃	—	2	2	no	—
395	C₄⋊C₄×C₂₃	—	2	2	no	—
396	C₄⋊C₄×C₂₃	—	2	2	no	—
397	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
401	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
410	C₂²⋊C₄×C₂₃	—	2	1	no	—
411	C₂²⋊C₄×C₂₃	—	2	1	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	1	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	1	no	—
422	C₂²⋊C₄×C₂₃	—	2	2	no	—
423	C₂²⋊C₄×C₂₃	—	2	2	no	—
424	C₂²⋊C₄×C₂₃	—	2	2	no	—
425	C₂²⋊C₄×C₂₃	—	2	2	no	—
426	C₂²⋊C₄×C₂₃	—	2	1	no	—
427	C₂²⋊C₄×C₂₃	—	2	2	no	—
428	C₂²⋊C₄×C₂₃	—	2	2	no	—
429	C₂²⋊C₄×C₂₃	—	2	2	no	—
430	C₂²⋊C₄×C₂₃	—	2	1	no	—
431	C₂²⋊C₄×C₂₃	—	2	2	no	—
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	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
437	C₄²×C₂₃	—	2	1	no	—
438	C₄²×C₂₃	—	2	2	no	—
439	C₄²×C₂₃	—	2	1	no	—
440	C₄²×C₂₃	—	2	1	no	—
441	C₄²×C₂₃	—	2	2	no	—
442	C₄²×C₂₃	—	2	1	no	—
443	C₄²×C₂₃	—	2	2	no	—
444	C₄²×C₂₃	—	2	2	no	—
445	C₄²×C₂₃	—	2	2	no	—
446	C₄²×C₂₃	—	2	1	no	—
447	C₄²×C₂₃	C₂⁴	1	2	yes	—
448	#61274	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	1	no	—
453	C₂³×C₂₃	—	4	1	no	—
454	C₂³×C₂₃	—	4	2	no	—
455	C₂³×C₂₃	—	8	1	no	—
456	C₂³×C₂₃	—	8	1	no	—
457	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
458	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
459	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
460	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
461	Q₈×C₂₃	—	2	2	no	—
462	Q₈×C₂₃	—	2	1	no	—
463	Q₈×C₂₃	—	2	1	no	—
464	Q₈×C₂₃	—	8	2	no	—
465	Q₈×C₂₃	—	8	2	no	—
466	D₄×C₂₃	—	2	4	no	—
467	D₄×C₂₃	—	2	2	no	—
468	D₄×C₂₃	—	2	1	no	—
469	D₄×C₂₃	—	2	2	no	—
470	D₄×C₂₃	—	2	2	no	—
471	D₄×C₂₃	—	2	1	no	—
472	D₄×C₂₃	—	4	2	no	—
473	D₄×C₂₃	—	4	2	no	—
474	D₄×C₂₃	—	4	4	no	—
475	D₄×C₂₃	—	4	2	no	—
476	D₄×C₂₃	—	4	2	no	—
477	D₄×C₂₃	—	8	1	no	—
478	D₄×C₂₃	—	8	2	no	—
479	D₄×C₂₃	—	8	2	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	2	no	—
485	C₂×C₄×C₂₃	—	2	2	no	—
486	C₂×C₄×C₂₃	—	2	1	no	—
487	C₂×C₄×C₂₃	—	2	2	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	2	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	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	1	no	—
501	C₂×C₄×C₂₃	—	2	2	no	—
502	C₂×C₄×C₂₃	—	4	2	no	—
503	C₂×C₄×C₂₃	—	4	2	no	—
504	C₂×C₄×C₂₃	—	8	2	no	—
505	C₂×C₄×C₂₃	—	8	2	no	—
506	C₂×C₄×C₂₃	—	8	2	no	—
507	C₂×C₄×C₂₃	—	8	1	no	—
508	C₂×C₄×C₂₃	—	8	2	no	—
509	C₂×C₄×C₂₃	—	8	1	no	—
510	C₂×C₄×C₂₃	—	8	1	no	—
511	C₂×C₄×C₂₃	—	8	1	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	1	yes	characteristic
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	2	yes	—
518	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
520	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
521	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
522	C₈×C₂₃	—	2	1	no	—
523	C₈×C₂₃	—	2	1	no	—
524	C₈×C₂₃	—	2	2	no	—
525	C₈×C₂₃	—	2	1	no	—
526	C₈×C₂₃	—	2	1	no	—
527	C₈×C₂₃	C₂×#41	1	4	yes	—
528	#3494	C₂×C₂₃	1	1	yes	characteristic, complemented
529	#3493	C₂×C₂₃	1	1	yes	characteristic, complemented
530	#3355	C₂×C₂₃	1	2	yes	complemented
531	#3353	C₂×C₂₃	1	2	yes	complemented
532	#3350	C₂×C₂₃	1	2	yes	complemented
533	#3348	C₂×C₂₃	1	2	yes	complemented
534	#3347	C₂×C₂₃	1	2	yes	complemented
535	#3345	C₂×C₂₃	1	2	yes	complemented
536	#3341	C₂×C₂₃	1	2	yes	complemented
537	#3337	C₂×C₂₃	1	2	yes	complemented
538	#3164	C₂×C₂₃	1	1	yes	characteristic, complemented
539	#3098	C₂×C₂₃	1	1	yes	characteristic, complemented
540	#3096	C₂×C₂₃	1	1	yes	characteristic, complemented
541	#3091	C₂×C₂₃	1	1	yes	characteristic, complemented
542	C₂×#482	C₂×C₂₃	1	1	yes	characteristic, complemented
543	#3084	C₂×C₂₃	1	1	yes	characteristic, complemented
544	#3081	C₂×C₂₃	1	1	yes	characteristic, complemented
545	#3062	C₂×C₂₃	1	1	yes	characteristic, complemented
546	#3055	C₂×C₂₃	1	1	yes	characteristic, complemented
547	#2946	C₂×C₂₃	1	1	yes	characteristic, complemented
548	#2933	C₂×C₂₃	1	1	yes	characteristic, complemented
549	#2912	C₂×C₂₃	1	1	yes	characteristic, complemented
550	#2911	C₂×C₂₃	1	1	yes	characteristic, complemented
551	C₂²×C₂₃	—	2	1	no	—
552	C₂²×C₂₃	—	2	1	no	—
553	C₂²×C₂₃	—	2	2	no	—
554	C₂²×C₂₃	—	2	1	no	—
555	C₂²×C₂₃	—	2	1	no	—
556	C₂²×C₂₃	—	2	1	no	—
557	C₂²×C₂₃	—	2	2	no	—
558	C₂²×C₂₃	—	2	1	no	—
559	C₂²×C₂₃	—	2	1	no	—
560	C₂²×C₂₃	—	2	1	no	—
561	C₂²×C₂₃	—	2	2	no	—
562	C₂²×C₂₃	—	4	1	no	—
563	C₂²×C₂₃	—	4	2	no	—
564	C₂²×C₂₃	—	4	2	no	—
565	C₂²×C₂₃	—	4	1	no	—
566	C₂²×C₂₃	—	4	1	no	—
567	C₂²×C₂₃	—	4	2	no	—
568	C₂²×C₂₃	—	8	2	no	—
569	C₂²×C₂₃	—	16	2	no	—
570	C₂²×C₂₃	#547	1	2	yes	—
571	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
572	C₄×C₂₃	—	2	2	no	—
573	C₄×C₂₃	—	2	2	no	—
574	C₄×C₂₃	—	2	1	no	—
575	C₄×C₂₃	—	2	1	no	—
576	C₄×C₂₃	—	2	2	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	2	no	—
584	C₄×C₂₃	—	4	2	no	—
585	C₄×C₂₃	—	4	1	no	—
586	C₄×C₂₃	—	4	1	no	—
587	C₄×C₂₃	#547	1	2	yes	—
588	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
589	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
590	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
591	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
592	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
593	#556	—	2	1	no	—
594	#556	C₂²×C₂₃	1	2	yes	complemented
595	#555	—	2	1	no	—
596	#555	C₂²×C₂₃	1	2	yes	—
597	#555	C₂²×C₂₃	1	2	yes	complemented
598	#553	—	2	1	no	—
599	#553	C₂²×C₂₃	1	2	yes	—
600	#553	C₂²×C₂₃	1	2	yes	—
601	#553	C₂²×C₂₃	1	2	yes	complemented
602	#552	—	2	1	no	—
603	#552	C₂²×C₂₃	1	2	yes	complemented
604	#551	—	2	2	no	—
605	#547	C₂²×C₂₃	1	2	yes	—
606	#546	—	2	2	no	—
607	#544	C₂²×C₂₃	1	1	yes	characteristic
608	#544	C₂²×C₂₃	1	1	yes	characteristic
609	#542	—	2	1	no	—
610	#540	—	2	1	no	—
611	#538	—	2	2	no	—
612	#537	C₂²×C₂₃	1	1	yes	characteristic
613	#535	C₂²×C₂₃	1	1	yes	characteristic
614	#532	—	2	1	no	—
615	#529	—	2	2	no	—
616	#529	—	2	1	no	—
617	#525	C₂²×C₂₃	1	1	yes	characteristic
618	#525	C₂²×C₂₃	1	1	yes	characteristic
619	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
620	#520	C₂²×C₂₃	1	1	yes	characteristic
621	#520	C₂²×C₂₃	1	1	yes	characteristic
622	#520	C₂²×C₂₃	1	1	yes	characteristic
623	#518	C₂²×C₂₃	1	1	yes	characteristic
624	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
625	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
626	#501	C₂²×C₂₃	1	2	yes	complemented
627	#501	C₂²×C₂₃	1	2	yes	complemented
628	#500	C₂²×C₂₃	1	2	yes	complemented
629	#499	C₂²×C₂₃	1	2	yes	complemented
630	#485	C₂²×C₂₃	1	1	yes	characteristic, complemented
631	#485	C₂²×C₂₃	1	1	yes	characteristic, complemented
632	#485	C₂²×C₂₃	1	2	yes	complemented
633	#484	C₂²×C₂₃	1	2	yes	complemented
634	#484	C₂²×C₂₃	1	1	yes	characteristic, complemented
635	#483	C₂²×C₂₃	1	1	yes	characteristic, complemented
636	#482	C₂²×C₂₃	1	2	yes	—
637	#482	C₂²×C₂₃	1	2	yes	—
638	#482	C₂²×C₂₃	1	2	yes	—
639	#482	C₂²×C₂₃	1	2	yes	—
640	#482	C₂²×C₂₃	1	1	yes	characteristic, complemented
641	#482	C₂²×C₂₃	1	2	yes	complemented
642	#482	C₂²×C₂₃	1	2	yes	complemented
643	#482	C₂²×C₂₃	1	1	yes	characteristic, complemented
644	#482	C₂²×C₂₃	1	2	yes	complemented
645	#481	C₂²×C₂₃	1	1	yes	characteristic, complemented
646	#481	C₂²×C₂₃	1	2	yes	complemented
647	#480	C₂²×C₂₃	1	2	yes	complemented
648	#480	C₂²×C₂₃	1	2	yes	complemented
649	#480	C₂²×C₂₃	1	1	yes	characteristic, complemented
650	#479	C₂²×C₂₃	1	2	yes	complemented
651	#478	C₂²×C₂₃	1	2	yes	complemented
652	#478	C₂²×C₂₃	1	2	yes	complemented
653	#478	C₂²×C₂₃	1	2	yes	complemented
654	#476	C₂²×C₂₃	1	2	yes	complemented
655	#476	C₂²×C₂₃	1	2	yes	complemented
656	#475	C₂²×C₂₃	1	2	yes	complemented
657	#474	C₂²×C₂₃	1	2	yes	complemented
658	#469	C₂²×C₂₃	1	2	yes	—
659	#469	C₂²×C₂₃	1	2	yes	complemented
660	#468	C₂²×C₂₃	1	2	yes	—
661	#468	C₂²×C₂₃	1	2	yes	complemented
662	#466	C₂²×C₂₃	1	2	yes	—
663	#466	C₂²×C₂₃	1	2	yes	complemented
664	#465	C₂²×C₂₃	1	2	yes	—
665	#465	C₂²×C₂₃	1	2	yes	complemented
666	#442	C₂²×C₂₃	1	2	yes	complemented
667	#440	C₂²×C₂₃	1	2	yes	complemented
668	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
669	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
670	#436	C₂²×C₂₃	1	2	yes	complemented
671	#435	C₂²×C₂₃	1	2	yes	complemented
672	#435	C₂²×C₂₃	1	2	yes	complemented
673	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
674	#428	C₂²×C₂₃	1	1	yes	characteristic
675	#428	C₂²×C₂₃	1	1	yes	characteristic
676	#428	C₂²×C₂₃	1	1	yes	characteristic
677	#428	C₂²×C₂₃	1	1	yes	characteristic
678	#428	C₂²×C₂₃	1	1	yes	characteristic
679	#428	C₂²×C₂₃	1	2	yes	complemented
680	#428	C₂²×C₂₃	1	2	yes	complemented
681	#428	C₂²×C₂₃	1	2	yes	complemented
682	#428	C₂²×C₂₃	1	2	yes	complemented
683	#427	C₂²×C₂₃	1	1	yes	characteristic
684	#427	C₂²×C₂₃	1	1	yes	characteristic
685	#427	C₂²×C₂₃	1	2	yes	complemented
686	#427	C₂²×C₂₃	1	2	yes	complemented
687	#427	C₂²×C₂₃	1	2	yes	complemented
688	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
689	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
690	C₂×#106	C₂²×C₂₃	1	2	yes	complemented
691	#424	C₂²×C₂₃	1	1	yes	characteristic
692	#418	C₂²×C₂₃	1	1	yes	characteristic
693	#417	C₂²×C₂₃	1	1	yes	characteristic
694	#416	C₂²×C₂₃	1	1	yes	characteristic
695	#416	C₂²×C₂₃	1	1	yes	characteristic
696	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
697	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
698	#408	C₂²×C₂₃	1	1	yes	characteristic
699	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
700	#405	C₂²×C₂₃	1	1	yes	characteristic
701	C₂×C₂₃	—	2	2	no	—
702	C₂×C₂₃	—	4	2	no	—
703	C₂×C₂₃	—	4	1	no	—
704	C₂×C₂₃	—	4	1	no	—
705	C₂×C₂₃	—	8	1	no	—
706	C₂×C₂₃	—	8	2	no	—
707	C₂×C₂₃	C₂×#547	1	1	yes	characteristic
708	C₂×C₂₃	#3584	1	1	yes	characteristic
709	C₂×C₂₃	#3585	1	1	yes	characteristic
710	C₂×#41	—	2	2	no	—
711	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
712	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
713	C₂²×D₄	—	2	1	no	—
714	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
715	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
716	AGL(1,ℤ/8)	—	2	4	no	—
717	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
718	C₂×D₈	C₂³×C₂₃	1	2	yes	—
719	#131	—	2	4	no	—
720	C₂×M₁₆	—	2	4	no	—
721	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
722	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
723	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
724	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
725	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
726	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
727	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
728	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
729	C₄⋊Q₈	—	2	1	no	—
730	C₄⋊Q₈	—	2	1	no	—
731	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
732	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
733	#127	—	2	1	no	—
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	—	2	2	no	—
739	#126	—	2	2	no	—
740	#125	—	2	1	no	—
741	#125	—	2	2	no	—
742	#125	—	2	1	no	—
743	#125	C₂³×C₂₃	1	2	yes	—
744	#125	C₂³×C₂₃	1	2	yes	—
745	#124	—	2	1	no	—
746	#124	—	2	2	no	—
747	#124	—	2	2	no	—
748	#124	—	2	2	no	—
749	#124	—	2	2	no	—
750	#124	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	1	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	D₄×C₂₃	1	2	yes	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
764	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
765	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
766	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
767	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
768	#121	—	2	2	no	—
769	#121	—	2	2	no	—
770	#121	—	2	1	no	—
771	#121	—	2	2	no	—
772	#121	—	2	2	no	—
773	#121	—	2	2	no	—
774	#121	—	2	2	no	—
775	#121	—	2	1	no	—
776	#121	—	2	1	no	—
777	#121	D₄×C₂₃	1	1	yes	characteristic
778	#121	D₄×C₂₃	1	1	yes	characteristic
779	#121	C₂³×C₂₃	1	2	yes	—
780	#121	C₂³×C₂₃	1	2	yes	—
781	#121	C₂³×C₂₃	1	1	yes	characteristic
782	#121	C₂³×C₂₃	1	1	yes	characteristic
783	#121	C₂³×C₂₃	1	2	yes	—
784	#121	C₂³×C₂₃	1	2	yes	—
785	#121	C₂³×C₂₃	1	2	yes	—
786	#120	—	2	1	no	—
787	#120	—	2	2	no	—
788	#120	D₄×C₂₃	1	2	yes	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	2	no	—
792	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	C₂³×C₂₃	1	2	yes	—
806	C₄×D₄	C₂³×C₂₃	1	2	yes	—
807	C₄×D₄	C₂³×C₂₃	1	2	yes	—
808	C₄×D₄	C₂³×C₂₃	1	2	yes	—
809	C₄×D₄	C₂³×C₂₃	1	2	yes	—
810	#117	—	2	1	no	—
811	#117	—	2	1	no	—
812	#117	—	2	1	no	—
813	#117	—	2	1	no	—
814	#117	—	2	1	no	—
815	#117	—	2	2	no	—
816	#117	—	2	2	no	—
817	#117	—	2	2	no	—
818	#117	C₂³×C₂₃	1	1	yes	characteristic
819	#117	C₂³×C₂₃	1	1	yes	characteristic
820	#117	C₂³×C₂₃	1	2	yes	—
821	#117	C₂³×C₂₃	1	1	yes	characteristic
822	#117	C₂³×C₂₃	1	2	yes	—
823	#117	C₂³×C₂₃	1	1	yes	characteristic
824	#117	C₂³×C₂₃	1	1	yes	characteristic
825	#117	C₂³×C₂₃	1	2	yes	—
826	#117	C₂³×C₂₃	1	2	yes	—
827	#117	C₂³×C₂₃	1	1	yes	characteristic
828	C₂×C₄⋊C₄	—	2	1	no	—
829	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
830	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
831	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
832	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
833	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
834	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
835	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
836	C₂×C₂²⋊C₄	—	2	1	no	—
837	C₂×C₂²⋊C₄	—	2	1	no	—
838	C₂×C₂²⋊C₄	—	2	1	no	—
839	C₂×C₂²⋊C₄	—	2	2	no	—
840	C₂×C₄²	—	2	1	no	—
841	C₂×C₄²	—	2	1	no	—
842	#107	C₂³×C₂₃	1	2	yes	—
843	#107	C₂³×C₂₃	1	2	yes	—
844	#107	C₂³×C₂₃	1	1	yes	characteristic
845	#107	C₂³×C₂₃	1	1	yes	characteristic
846	#107	C₂³×C₂₃	1	1	yes	characteristic
847	#107	C₂³×C₂₃	1	1	yes	characteristic
848	#107	C₂³×C₂₃	1	2	yes	—
849	#107	C₂³×C₂₃	1	2	yes	—
850	#107	C₂³×C₂₃	1	2	yes	—
851	#107	C₂³×C₂₃	1	2	yes	—
852	#107	C₂³×C₂₃	1	2	yes	—
853	#106	C₂³×C₂₃	1	2	yes	—
854	#106	C₂³×C₂₃	1	2	yes	—
855	#106	C₂³×C₂₃	1	1	yes	characteristic
856	#106	C₂³×C₂₃	1	2	yes	—
857	#106	C₂³×C₂₃	1	2	yes	—
858	#106	C₂³×C₂₃	1	1	yes	characteristic
859	#106	C₂³×C₂₃	1	1	yes	characteristic
860	#106	C₂³×C₂₃	1	1	yes	characteristic
861	#106	C₂³×C₂₃	1	2	yes	—
862	#106	C₂³×C₂₃	1	2	yes	—
863	#106	C₂³×C₂₃	1	2	yes	—
864	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
865	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
866	#103	C₂³×C₂₃	1	1	yes	characteristic
867	#103	C₂³×C₂₃	1	1	yes	characteristic
868	#103	C₂³×C₂₃	1	1	yes	characteristic
869	#103	C₂³×C₂₃	1	1	yes	characteristic
870	#103	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	#102	C₂³×C₂₃	1	2	yes	—
875	#102	C₂³×C₂₃	1	1	yes	characteristic
876	#102	C₂³×C₂₃	1	1	yes	characteristic
877	#102	C₂³×C₂₃	1	1	yes	characteristic
878	#102	C₂³×C₂₃	1	1	yes	characteristic
879	#102	C₂³×C₂₃	1	2	yes	—
880	#102	C₂³×C₂₃	1	2	yes	—
881	#102	C₂³×C₂₃	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
883	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
884	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
885	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
886	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
887	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
888	#97	C₂³×C₂₃	1	2	yes	—
889	C₄×C₈	C₂³×C₂₃	1	2	yes	—
890	C₂₃	#61274	1	1	yes	characteristic, direct product factor, Sylow
891	C₂⁴	—	2	1	no	—
892	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
893	#41	—	2	2	no	—
894	#41	—	2	2	no	—
895	#41	—	2	2	no	—
896	#41	—	2	2	no	—
897	#41	—	8	4	no	—
898	C₂×Q₈	—	2	2	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
901	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
902	C₂×D₄	—	2	1	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	1	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	1	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	8	2	no	—
914	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
915	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
916	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
917	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
918	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
919	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
934	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
935	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
936	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
937	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
938	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
939	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
940	SD₁₆	—	2	4	no	—
941	D₈	—	2	4	no	—
942	M₁₆	—	2	2	no	—
943	M₁₆	—	2	4	no	—
944	M₁₆	—	2	4	no	—
945	M₁₆	#41×C₂₃	1	4	yes	complemented
946	C₂×C₈	—	2	2	no	—
947	C₂×C₈	—	2	2	no	—
948	C₂×C₈	—	2	4	no	—
949	C₂×C₈	—	2	4	no	—
950	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
951	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
952	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
953	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
954	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
955	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
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	1	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
974	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
975	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
976	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
977	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
978	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
979	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
980	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
981	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
982	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
983	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
984	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
985	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
986	C₂²⋊C₄	—	2	1	no	—
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	1	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	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1009	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1010	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1011	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1012	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	—	2	2	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	C₂⁴×C₂₃	1	2	yes	—
1024	C₂³	—	2	2	no	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	2	no	—
1027	C₂³	—	4	1	no	—
1028	C₂³	—	4	1	no	—
1029	C₂³	—	4	2	no	—
1030	C₂³	—	8	1	no	—
1031	C₂³	—	8	1	no	—
1032	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1033	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1034	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1035	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1036	Q₈	—	2	2	no	—
1037	Q₈	—	2	1	no	—
1038	Q₈	—	2	1	no	—
1039	Q₈	—	8	2	no	—
1040	Q₈	—	8	2	no	—
1041	D₄	—	2	4	no	—
1042	D₄	—	2	2	no	—
1043	D₄	—	2	1	no	—
1044	D₄	—	2	2	no	—
1045	D₄	—	2	2	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	4	2	no	—
1048	D₄	—	4	2	no	—
1049	D₄	—	4	4	no	—
1050	D₄	—	4	2	no	—
1051	D₄	—	4	2	no	—
1052	D₄	—	8	2	no	—
1053	D₄	—	8	2	no	—
1054	D₄	—	8	1	no	—
1055	D₄	—	8	2	no	—
1056	D₄	—	8	2	no	—
1057	D₄	—	8	1	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	1	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	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	4	2	no	—
1079	C₂×C₄	—	8	2	no	—
1080	C₂×C₄	—	8	2	no	—
1081	C₂×C₄	—	8	2	no	—
1082	C₂×C₄	—	8	1	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	—	8	1	no	—
1085	C₂×C₄	—	8	2	no	—
1086	C₂×C₄	—	8	1	no	—
1087	C₂×C₄	—	8	1	no	—
1088	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1089	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1090	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1091	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1092	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1093	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1094	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1095	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
1096	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1097	C₈	—	2	1	no	—
1098	C₈	—	2	1	no	—
1099	C₈	—	2	2	no	—
1100	C₈	—	2	1	no	—
1101	C₈	—	2	1	no	—
1102	C₈	C₂×#41×C₂₃	1	4	yes	—
1103	C₂²	—	2	1	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	2	no	—
1109	C₂²	—	2	1	no	—
1110	C₂²	—	2	1	no	—
1111	C₂²	—	2	1	no	—
1112	C₂²	—	2	2	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	2	no	—
1116	C₂²	—	4	1	no	—
1117	C₂²	—	4	2	no	—
1118	C₂²	—	4	2	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	8	2	no	—
1121	C₂²	—	16	2	no	—
1122	C₂²	C₂₃×#547	1	2	yes	—
1123	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1124	C₄	—	2	1	no	—
1125	C₄	—	2	1	no	—
1126	C₄	—	2	2	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	2	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	2	no	—
1132	C₄	—	4	1	no	—
1133	C₄	—	4	1	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	2	no	—
1137	C₄	—	4	2	no	—
1138	C₄	—	4	1	no	—
1139	C₄	C₂₃×#547	1	2	yes	—
1140	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1141	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1142	C₂	—	2	2	no	—
1143	C₂	—	4	1	no	—
1144	C₂	—	4	1	no	—
1145	C₂	—	4	2	no	—
1146	C₂	—	8	2	no	—
1147	C₂	—	8	1	no	—
1148	C₂	C₂×C₂₃×#547	1	1	yes	characteristic
1149	C₂	C₂₃×#3584	1	1	yes	characteristic
1150	C₂	C₂₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3494	C₂	semidirect
2. C₂₃×#3493	C₂	semidirect
3. C₂₃×#3355	C₂	semidirect
4. C₂₃×#3353	C₂	semidirect
5. C₂₃×#3350	C₂	semidirect
6. C₂₃×#3348	C₂	semidirect
7. C₂₃×#3347	C₂	semidirect
8. C₂₃×#3345	C₂	semidirect
9. C₂₃×#3341	C₂	semidirect
10. C₂₃×#3337	C₂	semidirect
11. C₂₃×#3164	C₂	semidirect
12. C₂₃×#3098	C₂	semidirect
13. C₂₃×#3096	C₂	semidirect
14. C₂₃×#3091	C₂	semidirect
15. C₂×C₂₃×#482	C₂	semidirect
16. C₂₃×#3084	C₂	semidirect
17. C₂₃×#3081	C₂	semidirect
18. C₂₃×#3062	C₂	semidirect
19. C₂₃×#3055	C₂	semidirect
20. C₂₃×#2946	C₂	semidirect
21. C₂₃×#2933	C₂	semidirect
22. C₂₃×#2912	C₂	semidirect
23. C₂₃×#2911	C₂	semidirect
28. C₂₃×#556	C₂²	semidirect
31. C₂₃×#555	C₂²	semidirect
35. C₂₃×#553	C₂²	semidirect
37. C₂₃×#552	C₂²	semidirect
60. C₂₃×#501	C₂²	semidirect
61. C₂₃×#501	C₂²	semidirect
62. C₂₃×#500	C₂²	semidirect
63. C₂₃×#499	C₂²	semidirect
64. C₂₃×#485	C₂²	semidirect
65. C₂₃×#485	C₂²	semidirect
66. C₂₃×#485	C₂²	semidirect
67. C₂₃×#484	C₂²	semidirect
68. C₂₃×#484	C₂²	semidirect
69. C₂₃×#483	C₂²	semidirect
74. C₂₃×#482	C₂²	semidirect
75. C₂₃×#482	C₂²	semidirect
76. C₂₃×#482	C₂²	semidirect
77. C₂₃×#482	C₂²	semidirect
78. C₂₃×#482	C₂²	semidirect
79. C₂₃×#481	C₂²	semidirect
80. C₂₃×#481	C₂²	semidirect
81. C₂₃×#480	C₂²	semidirect
82. C₂₃×#480	C₂²	semidirect
83. C₂₃×#480	C₂²	semidirect
84. C₂₃×#479	C₂²	semidirect
85. C₂₃×#478	C₂²	semidirect
86. C₂₃×#478	C₂²	semidirect
87. C₂₃×#478	C₂²	semidirect
88. C₂₃×#476	C₂²	semidirect
89. C₂₃×#476	C₂²	semidirect
90. C₂₃×#475	C₂²	semidirect
91. C₂₃×#474	C₂²	semidirect
93. C₂₃×#469	C₂²	semidirect
95. C₂₃×#468	C₂²	semidirect
97. C₂₃×#466	C₂²	semidirect
99. C₂₃×#465	C₂²	semidirect
100. C₂₃×#442	C₂²	semidirect
101. C₂₃×#440	C₂²	semidirect
102. C₄×SD₁₆×C₂₃	C₂²	semidirect
103. C₄×D₈×C₂₃	C₂²	semidirect
104. C₂₃×#436	C₂²	semidirect
105. C₂₃×#435	C₂²	semidirect
106. C₂₃×#435	C₂²	semidirect
107. C₈×D₄×C₂₃	C₂²	semidirect
113. C₂₃×#428	C₂²	semidirect
114. C₂₃×#428	C₂²	semidirect
115. C₂₃×#428	C₂²	semidirect
116. C₂₃×#428	C₂²	semidirect
119. C₂₃×#427	C₂²	semidirect
120. C₂₃×#427	C₂²	semidirect
121. C₂₃×#427	C₂²	semidirect
124. C₂×C₂₃×#106	C₂²	semidirect
369. M₁₆×C₂₃	#41	semidirect
448. #61274	C₂₃	direct (N × H)
528. #3494	C₂×C₂₃	semidirect
529. #3493	C₂×C₂₃	semidirect
530. #3355	C₂×C₂₃	semidirect
531. #3353	C₂×C₂₃	semidirect
532. #3350	C₂×C₂₃	semidirect
533. #3348	C₂×C₂₃	semidirect
534. #3347	C₂×C₂₃	semidirect
535. #3345	C₂×C₂₃	semidirect
536. #3341	C₂×C₂₃	semidirect
537. #3337	C₂×C₂₃	semidirect
538. #3164	C₂×C₂₃	semidirect
539. #3098	C₂×C₂₃	semidirect
540. #3096	C₂×C₂₃	semidirect
541. #3091	C₂×C₂₃	semidirect
542. C₂×#482	C₂×C₂₃	semidirect
543. #3084	C₂×C₂₃	semidirect
544. #3081	C₂×C₂₃	semidirect
545. #3062	C₂×C₂₃	semidirect
546. #3055	C₂×C₂₃	semidirect
547. #2946	C₂×C₂₃	semidirect
548. #2933	C₂×C₂₃	semidirect
549. #2912	C₂×C₂₃	semidirect
550. #2911	C₂×C₂₃	semidirect
594. #556	C₂²×C₂₃	semidirect
597. #555	C₂²×C₂₃	semidirect
601. #553	C₂²×C₂₃	semidirect
603. #552	C₂²×C₂₃	semidirect
626. #501	C₂²×C₂₃	semidirect
627. #501	C₂²×C₂₃	semidirect
628. #500	C₂²×C₂₃	semidirect
629. #499	C₂²×C₂₃	semidirect
630. #485	C₂²×C₂₃	semidirect
631. #485	C₂²×C₂₃	semidirect
632. #485	C₂²×C₂₃	semidirect
633. #484	C₂²×C₂₃	semidirect
634. #484	C₂²×C₂₃	semidirect
635. #483	C₂²×C₂₃	semidirect
640. #482	C₂²×C₂₃	semidirect
641. #482	C₂²×C₂₃	semidirect
642. #482	C₂²×C₂₃	semidirect
643. #482	C₂²×C₂₃	semidirect
644. #482	C₂²×C₂₃	semidirect
645. #481	C₂²×C₂₃	semidirect
646. #481	C₂²×C₂₃	semidirect
647. #480	C₂²×C₂₃	semidirect
648. #480	C₂²×C₂₃	semidirect
649. #480	C₂²×C₂₃	semidirect
650. #479	C₂²×C₂₃	semidirect
651. #478	C₂²×C₂₃	semidirect
652. #478	C₂²×C₂₃	semidirect
653. #478	C₂²×C₂₃	semidirect
654. #476	C₂²×C₂₃	semidirect
655. #476	C₂²×C₂₃	semidirect
656. #475	C₂²×C₂₃	semidirect
657. #474	C₂²×C₂₃	semidirect
659. #469	C₂²×C₂₃	semidirect
661. #468	C₂²×C₂₃	semidirect
663. #466	C₂²×C₂₃	semidirect
665. #465	C₂²×C₂₃	semidirect
666. #442	C₂²×C₂₃	semidirect
667. #440	C₂²×C₂₃	semidirect
668. C₄×SD₁₆	C₂²×C₂₃	semidirect
669. C₄×D₈	C₂²×C₂₃	semidirect
670. #436	C₂²×C₂₃	semidirect
671. #435	C₂²×C₂₃	semidirect
672. #435	C₂²×C₂₃	semidirect
673. C₈×D₄	C₂²×C₂₃	semidirect
679. #428	C₂²×C₂₃	semidirect
680. #428	C₂²×C₂₃	semidirect
681. #428	C₂²×C₂₃	semidirect
682. #428	C₂²×C₂₃	semidirect
685. #427	C₂²×C₂₃	semidirect
686. #427	C₂²×C₂₃	semidirect
687. #427	C₂²×C₂₃	semidirect
690. C₂×#106	C₂²×C₂₃	semidirect
890. C₂₃	#61274	direct (N × H)
945. M₁₆	#41×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3494	2
C₂₃×#3493	2
C₂₃×#3355	2
C₂₃×#3353	2
C₂₃×#3350	2
C₂₃×#3348	2
C₂₃×#3347	2
C₂₃×#3345	2
C₂₃×#3341	2
C₂₃×#3337	2
C₂₃×#3164	2
C₂₃×#3098	2
C₂₃×#3096	2
C₂₃×#3091	2
C₂×C₂₃×#482	2
C₂₃×#3084	2
C₂₃×#3081	2
C₂₃×#3062	2
C₂₃×#3055	2
C₂₃×#2946	2
C₂₃×#2933	2
C₂₃×#2912	2
C₂₃×#2911	2
#61274	23

Subgroups — C23×#61274 #19208900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61274 #19208900