Subgroups — C₂₃×#61725 #19209351

Order 5888.

1820 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3357	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3357	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3356	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3355	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3354	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3351	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3332	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3323	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3322	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3233	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3197	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3194	C₂	1	2	yes	maximal, complemented
19	C₂₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3094	C₂	1	2	yes	maximal, complemented
22	C₂₃×#3093	C₂	1	2	yes	maximal, complemented
23	C₂₃×#2975	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#556	C₂²	1	1	yes	characteristic
25	C₂₃×#555	C₂²	1	1	yes	characteristic
26	C₂₃×#555	C₂²	1	1	yes	characteristic
27	C₂₃×#554	C₂²	1	1	yes	characteristic
28	C₂₃×#554	C₂²	1	1	yes	characteristic, complemented
29	C₂₃×#553	—	2	1	no	—
30	C₂₃×#553	C₂²	1	2	yes	—
31	C₂₃×#553	C₂²	1	2	yes	complemented
32	C₂₃×#552	—	2	1	no	—
33	C₂₃×#552	C₂²	1	2	yes	complemented
34	C₂₃×#551	—	2	2	no	—
35	C₂₃×#550	C₂²	1	1	yes	characteristic
36	C₂₃×#547	C₂²	1	1	yes	characteristic, complemented
37	C₂₃×#546	—	2	1	no	—
38	C₂₃×#546	—	2	2	no	—
39	C₂₃×#546	C₂²	1	2	yes	—
40	D₄²×C₂₃	—	2	1	no	—
41	D₄²×C₂₃	C₂²	1	1	yes	characteristic
42	C₂₃×#540	—	2	1	no	—
43	C₂₃×#538	—	2	2	no	—
44	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
45	C₂₃×#532	C₂²	1	1	yes	characteristic
46	C₂₃×#529	—	2	2	no	—
47	C₂₃×#529	—	2	1	no	—
48	C₂₃×#529	C₂²	1	1	yes	characteristic
49	C₂₃×#525	C₂²	1	2	yes	—
50	C₂₃×#525	C₂²	1	2	yes	complemented
51	C₂×C₂₃×#121	C₂²	1	2	yes	—
52	C₂₃×#518	—	2	1	no	—
53	C₄×#41×C₂₃	—	2	1	no	—
54	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
56	C₂×C₂₃×#117	C₂²	1	2	yes	complemented
57	C₂₃×#500	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#499	C₂²	1	2	yes	complemented
59	C₂₃×#498	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#488	C₂²	1	2	yes	complemented
61	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#485	C₂²	1	2	yes	complemented
64	C₂₃×#485	C₂²	1	2	yes	complemented
65	C₂₃×#485	C₂²	1	2	yes	complemented
66	C₂₃×#485	C₂²	1	2	yes	complemented
67	C₂₃×#485	C₂²	1	1	yes	characteristic, complemented
68	C₂₃×#483	C₂²	1	2	yes	complemented
69	C₂₃×#482	C₂²	1	2	yes	—
70	C₂₃×#482	C₂²	1	1	yes	characteristic
71	C₂₃×#482	C₂²	1	2	yes	complemented
72	C₂₃×#482	C₂²	1	2	yes	complemented
73	C₂₃×#482	C₂²	1	2	yes	complemented
74	C₂₃×#482	C₂²	1	2	yes	complemented
75	C₂₃×#482	C₂²	1	2	yes	complemented
76	C₂₃×#482	C₂²	1	2	yes	complemented
77	C₂₃×#481	C₂²	1	2	yes	complemented
78	C₂₃×#481	C₂²	1	2	yes	complemented
79	C₂₃×#480	C₂²	1	2	yes	complemented
80	C₂₃×#480	C₂²	1	2	yes	complemented
81	C₂₃×#480	C₂²	1	2	yes	complemented
82	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
83	C₂₃×#478	C₂²	1	2	yes	complemented
84	C₂₃×#478	C₂²	1	2	yes	complemented
85	C₂₃×#478	C₂²	1	1	yes	characteristic, complemented
86	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
87	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
88	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
89	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
90	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#470	C₂²	1	2	yes	complemented
93	C₂₃×#469	C₂²	1	2	yes	complemented
94	C₂₃×#469	C₂²	1	2	yes	complemented
95	C₂₃×#469	C₂²	1	2	yes	complemented
96	C₂₃×#468	C₂²	1	2	yes	complemented
97	C₂₃×#468	C₂²	1	2	yes	complemented
98	C₂₃×#468	C₂²	1	2	yes	complemented
99	C₂₃×#468	C₂²	1	2	yes	complemented
100	C₂₃×#464	C₂²	1	1	yes	characteristic, complemented
101	C₂₃×#463	C₂²	1	1	yes	characteristic, complemented
102	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
103	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
104	C₂₃×#452	C₂²	1	1	yes	characteristic, complemented
105	C₂₃×#452	C₂²	1	2	yes	complemented
106	C₂₃×#450	C₂²	1	2	yes	complemented
107	C₂₃×#449	C₂²	1	1	yes	characteristic
108	C₂₃×#449	C₂²	1	2	yes	complemented
109	C₂₃×#449	C₂²	1	2	yes	complemented
110	C₂₃×#447	C₂²	1	2	yes	complemented
111	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
112	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
113	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
116	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
117	C₂₃×#436	C₂²	1	1	yes	characteristic
118	C₂₃×#436	C₂²	1	1	yes	characteristic
119	C₂₃×#436	C₂²	1	2	yes	complemented
120	C₂₃×#436	C₂²	1	2	yes	complemented
121	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
122	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
123	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
124	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
125	C₂₃×#428	C₂²	1	2	yes	complemented
126	C₂₃×#428	C₂²	1	2	yes	complemented
127	C₂₃×#428	C₂²	1	2	yes	complemented
128	C₂₃×#428	C₂²	1	2	yes	complemented
129	C₂₃×#418	C₂²	1	2	yes	complemented
130	C₂₃×#418	C₂²	1	2	yes	complemented
131	C₂₃×#417	C₂²	1	2	yes	complemented
132	C₂₃×#417	C₂²	1	2	yes	complemented
133	C₂₃×#407	C₂²	1	2	yes	complemented
134	C₂₃×#407	C₂²	1	2	yes	complemented
135	C₂×#41×C₂₃	—	2	1	no	—
136	C₂×#41×C₂₃	—	2	1	no	—
137	C₂×#41×C₂₃	C₂³	1	2	yes	—
138	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₂₃	—	2	2	no	—
140	C₂²×D₄×C₂₃	—	2	1	no	—
141	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
142	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
143	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
144	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
148	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×D₈×C₂₃	C₂³	1	2	yes	—
150	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
151	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
152	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
153	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
154	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₂₃×#127	—	2	1	no	—
158	C₂₃×#127	C₂³	1	1	yes	characteristic
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	1	no	—
164	C₂₃×#125	—	2	2	no	—
165	C₂₃×#125	—	2	1	no	—
166	C₂₃×#125	—	2	1	no	—
167	C₂₃×#125	C₂³	1	2	yes	—
168	C₂₃×#125	C₂³	1	1	yes	characteristic
169	C₂₃×#124	—	2	1	no	—
170	C₂₃×#124	—	2	2	no	—
171	C₂₃×#124	—	2	2	no	—
172	C₂₃×#124	—	2	1	no	—
173	C₂₃×#124	C₂³	1	1	yes	characteristic
174	C₂₃×#123	—	2	2	no	—
175	C₂₃×#123	—	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×C₂²⋊Q₈	—	2	1	no	—
183	C₂₃×C₂²⋊Q₈	—	2	1	no	—
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	C₂³	1	2	yes	—
188	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
189	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
191	C₂₃×#121	—	2	2	no	—
192	C₂₃×#121	—	2	2	no	—
193	C₂₃×#121	—	2	1	no	—
194	C₂₃×#121	—	2	1	no	—
195	C₂₃×#121	—	2	2	no	—
196	C₂₃×#121	—	2	1	no	—
197	C₂₃×#121	—	2	2	no	—
198	C₂₃×#121	—	2	1	no	—
199	C₂₃×#121	—	2	2	no	—
200	C₂₃×#121	—	2	2	no	—
201	C₂₃×#121	C₂³	1	2	yes	—
202	C₂₃×#121	C₂³	1	2	yes	—
203	C₂₃×#121	C₂³	1	2	yes	—
204	C₂₃×#121	C₂³	1	2	yes	—
205	C₂₃×#121	C₂³	1	2	yes	—
206	C₂₃×#121	C₂³	1	1	yes	characteristic
207	C₂₃×#121	C₂³	1	2	yes	—
208	C₂₃×#120	—	2	2	no	—
209	C₂₃×#120	—	2	2	no	—
210	C₂₃×#120	—	2	2	no	—
211	C₂₃×#120	—	2	2	no	—
212	C₄×Q₈×C₂₃	—	2	1	no	—
213	C₄×Q₈×C₂₃	—	2	1	no	—
214	C₄×Q₈×C₂₃	—	2	1	no	—
215	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
218	C₄×D₄×C₂₃	—	2	1	no	—
219	C₄×D₄×C₂₃	—	2	1	no	—
220	C₄×D₄×C₂₃	—	2	1	no	—
221	C₄×D₄×C₂₃	—	2	1	no	—
222	C₄×D₄×C₂₃	—	2	2	no	—
223	C₄×D₄×C₂₃	—	2	1	no	—
224	C₄×D₄×C₂₃	—	2	2	no	—
225	C₄×D₄×C₂₃	—	2	2	no	—
226	C₄×D₄×C₂₃	—	2	2	no	—
227	C₄×D₄×C₂₃	—	2	1	no	—
228	C₄×D₄×C₂₃	—	2	2	no	—
229	C₄×D₄×C₂₃	—	2	2	no	—
230	C₄×D₄×C₂₃	—	2	1	no	—
231	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
232	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
233	C₄×D₄×C₂₃	D₄	1	2	yes	—
234	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₂₃	C₂³	1	2	yes	—
236	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₂₃	C₂³	1	2	yes	—
240	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
241	C₂₃×#117	—	2	2	no	—
242	C₂₃×#117	—	2	2	no	—
243	C₂₃×#117	—	2	1	no	—
244	C₂₃×#117	—	2	1	no	—
245	C₂₃×#117	—	2	2	no	—
246	C₂₃×#117	—	2	1	no	—
247	C₂₃×#117	—	2	1	no	—
248	C₂₃×#117	C₂³	1	2	yes	—
249	C₂₃×#117	C₂³	1	2	yes	—
250	C₂₃×#117	C₂³	1	2	yes	—
251	C₂₃×#117	C₂³	1	1	yes	characteristic
252	C₂₃×#117	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
257	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
258	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
259	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
260	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
261	C₂×C₄²×C₂₃	—	2	2	no	—
262	C₂×C₄²×C₂₃	—	2	1	no	—
263	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
264	C₂₃×#107	C₂³	1	2	yes	—
265	C₂₃×#107	C₂³	1	1	yes	characteristic
266	C₂₃×#107	C₂³	1	1	yes	characteristic
267	C₂₃×#107	C₂³	1	2	yes	—
268	C₂₃×#107	C₂³	1	2	yes	—
269	C₂₃×#107	C₂³	1	2	yes	—
270	C₂₃×#107	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×#106	C₂³	1	2	yes	—
275	C₂₃×#106	C₂³	1	2	yes	—
276	C₂₃×#106	C₂³	1	2	yes	—
277	C₂₃×#106	C₂³	1	2	yes	—
278	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₂₃×#103	C₂³	1	1	yes	characteristic
283	C₂₃×#103	C₂³	1	1	yes	characteristic
284	C₂₃×#103	C₂³	1	2	yes	—
285	C₂₃×#103	C₂³	1	2	yes	—
286	C₂₃×#103	C₂³	1	2	yes	—
287	C₂₃×#103	C₂³	1	1	yes	characteristic
288	C₂₃×#103	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
301	C₂₃×#102	C₂³	1	1	yes	characteristic
302	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
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	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
314	#41×C₂₃	—	4	1	no	—
315	#41×C₂₃	—	4	1	no	—
316	#41×C₂₃	—	4	2	no	—
317	#41×C₂₃	—	4	2	no	—
318	#41×C₂₃	—	4	4	no	—
319	#41×C₂₃	—	8	2	no	—
320	C₂×Q₈×C₂₃	—	2	1	no	—
321	C₂×Q₈×C₂₃	—	2	1	no	—
322	C₂×Q₈×C₂₃	—	2	1	no	—
323	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
324	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₂₃	—	2	2	no	—
326	C₂×D₄×C₂₃	—	2	1	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	2	no	—
331	C₂×D₄×C₂₃	—	2	2	no	—
332	C₂×D₄×C₂₃	—	2	2	no	—
333	C₂×D₄×C₂₃	—	2	2	no	—
334	C₂×D₄×C₂₃	—	2	1	no	—
335	C₂×D₄×C₂₃	—	2	1	no	—
336	C₂×D₄×C₂₃	—	2	2	no	—
337	C₂×D₄×C₂₃	—	4	2	no	—
338	C₂×D₄×C₂₃	—	4	2	no	—
339	C₂×D₄×C₂₃	—	4	2	no	—
340	C₂×D₄×C₂₃	—	4	4	no	—
341	C₂×D₄×C₂₃	—	8	4	no	—
342	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
343	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
344	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
345	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
347	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₂₃	—	2	2	no	—
349	C₂²×C₄×C₂₃	—	2	2	no	—
350	C₂²×C₄×C₂₃	—	2	2	no	—
351	C₂²×C₄×C₂₃	—	2	1	no	—
352	C₂²×C₄×C₂₃	—	2	1	no	—
353	C₂²×C₄×C₂₃	—	2	1	no	—
354	C₂²×C₄×C₂₃	—	2	1	no	—
355	C₂²×C₄×C₂₃	—	2	2	no	—
356	C₂²×C₄×C₂₃	—	2	2	no	—
357	C₂²×C₄×C₂₃	—	4	2	no	—
358	C₂²×C₄×C₂₃	—	4	2	no	—
359	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
361	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
363	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
364	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
366	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
367	Q₁₆×C₂₃	—	4	1	no	—
368	SD₁₆×C₂₃	—	4	1	no	—
369	SD₁₆×C₂₃	—	4	1	no	—
370	SD₁₆×C₂₃	—	4	2	no	—
371	D₈×C₂₃	—	4	2	no	—
372	D₈×C₂₃	—	4	1	no	—
373	M₁₆×C₂₃	—	4	2	no	—
374	M₁₆×C₂₃	—	4	2	no	—
375	M₁₆×C₂₃	—	4	2	no	—
376	M₁₆×C₂₃	—	4	2	no	—
377	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
379	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
382	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
383	C₄⋊C₄×C₂₃	—	2	2	no	—
384	C₄⋊C₄×C₂₃	—	2	2	no	—
385	C₄⋊C₄×C₂₃	—	2	2	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	1	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	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	2	no	—
398	C₄⋊C₄×C₂₃	—	2	1	no	—
399	C₄⋊C₄×C₂₃	—	2	1	no	—
400	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
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	2	yes	—
409	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
410	C₂²⋊C₄×C₂₃	—	2	1	no	—
411	C₂²⋊C₄×C₂₃	—	2	2	no	—
412	C₂²⋊C₄×C₂₃	—	2	2	no	—
413	C₂²⋊C₄×C₂₃	—	2	2	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	1	no	—
420	C₂²⋊C₄×C₂₃	—	2	1	no	—
421	C₂²⋊C₄×C₂₃	—	2	2	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	1	no	—
426	C₂²⋊C₄×C₂₃	—	2	1	no	—
427	C₂²⋊C₄×C₂₃	—	2	1	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	C₄²×C₂₃	—	2	1	no	—
437	C₄²×C₂₃	—	2	2	no	—
438	C₄²×C₂₃	—	2	1	no	—
439	C₄²×C₂₃	—	2	2	no	—
440	C₄²×C₂₃	—	2	2	no	—
441	C₄²×C₂₃	—	2	1	no	—
442	C₄²×C₂₃	—	2	2	no	—
443	C₄²×C₂₃	—	2	1	no	—
444	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
445	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
447	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
448	#61725	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
449	C₂³×C₂₃	—	2	1	no	—
450	C₂³×C₂₃	—	2	1	no	—
451	C₂³×C₂₃	—	2	2	no	—
452	C₂³×C₂₃	—	4	2	no	—
453	C₂³×C₂₃	—	4	2	no	—
454	C₂³×C₂₃	—	4	2	no	—
455	C₂³×C₂₃	—	4	4	no	—
456	C₂³×C₂₃	—	8	2	no	—
457	C₂³×C₂₃	—	8	2	no	—
458	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
459	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
460	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
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	—	4	2	no	—
466	Q₈×C₂₃	—	8	1	no	—
467	Q₈×C₂₃	—	8	1	no	—
468	D₄×C₂₃	—	2	2	no	—
469	D₄×C₂₃	—	2	2	no	—
470	D₄×C₂₃	—	2	1	no	—
471	D₄×C₂₃	—	2	1	no	—
472	D₄×C₂₃	—	2	1	no	—
473	D₄×C₂₃	—	2	2	no	—
474	D₄×C₂₃	—	2	1	no	—
475	D₄×C₂₃	—	2	2	no	—
476	D₄×C₂₃	—	4	2	no	—
477	D₄×C₂₃	—	4	4	no	—
478	D₄×C₂₃	—	4	2	no	—
479	D₄×C₂₃	—	4	4	no	—
480	D₄×C₂₃	—	4	2	no	—
481	D₄×C₂₃	—	4	4	no	—
482	D₄×C₂₃	—	4	2	no	—
483	D₄×C₂₃	—	8	2	no	—
484	D₄×C₂₃	—	8	1	no	—
485	D₄×C₂₃	—	8	2	no	—
486	D₄×C₂₃	—	8	2	no	—
487	D₄×C₂₃	—	8	2	no	—
488	D₄×C₂₃	—	8	2	no	—
489	C₂×C₄×C₂₃	—	2	2	no	—
490	C₂×C₄×C₂₃	—	2	2	no	—
491	C₂×C₄×C₂₃	—	2	2	no	—
492	C₂×C₄×C₂₃	—	2	2	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	1	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	2	no	—
502	C₂×C₄×C₂₃	—	2	1	no	—
503	C₂×C₄×C₂₃	—	2	2	no	—
504	C₂×C₄×C₂₃	—	2	1	no	—
505	C₂×C₄×C₂₃	—	4	2	no	—
506	C₂×C₄×C₂₃	—	4	2	no	—
507	C₂×C₄×C₂₃	—	4	2	no	—
508	C₂×C₄×C₂₃	—	4	1	no	—
509	C₂×C₄×C₂₃	—	4	2	no	—
510	C₂×C₄×C₂₃	—	4	4	no	—
511	C₂×C₄×C₂₃	—	4	2	no	—
512	C₂×C₄×C₂₃	—	4	2	no	—
513	C₂×C₄×C₂₃	—	8	1	no	—
514	C₂×C₄×C₂₃	—	8	2	no	—
515	C₂×C₄×C₂₃	—	8	2	no	—
516	C₂×C₄×C₂₃	—	8	2	no	—
517	C₂×C₄×C₂₃	—	8	2	no	—
518	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
520	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
526	C₈×C₂₃	—	2	2	no	—
527	C₈×C₂₃	—	2	1	no	—
528	C₈×C₂₃	—	2	1	no	—
529	C₈×C₂₃	—	2	2	no	—
530	C₈×C₂₃	—	2	1	no	—
531	C₈×C₂₃	—	2	1	no	—
532	#3519	C₂×C₂₃	1	1	yes	characteristic, complemented
533	#3475	C₂×C₂₃	1	1	yes	characteristic, complemented
534	#3357	C₂×C₂₃	1	1	yes	characteristic, complemented
535	#3357	C₂×C₂₃	1	1	yes	characteristic, complemented
536	#3356	C₂×C₂₃	1	1	yes	characteristic, complemented
537	#3355	C₂×C₂₃	1	2	yes	complemented
538	#3354	C₂×C₂₃	1	1	yes	characteristic, complemented
539	#3351	C₂×C₂₃	1	2	yes	complemented
540	#3333	C₂×C₂₃	1	1	yes	characteristic, complemented
541	#3332	C₂×C₂₃	1	1	yes	characteristic, complemented
542	#3325	C₂×C₂₃	1	1	yes	characteristic, complemented
543	#3324	C₂×C₂₃	1	1	yes	characteristic, complemented
544	#3323	C₂×C₂₃	1	2	yes	complemented
545	#3322	C₂×C₂₃	1	2	yes	complemented
546	#3233	C₂×C₂₃	1	1	yes	characteristic, complemented
547	#3228	C₂×C₂₃	1	1	yes	characteristic, complemented
548	#3197	C₂×C₂₃	1	2	yes	complemented
549	#3194	C₂×C₂₃	1	2	yes	complemented
550	#3106	C₂×C₂₃	1	1	yes	characteristic, complemented
551	#3102	C₂×C₂₃	1	1	yes	characteristic, complemented
552	#3094	C₂×C₂₃	1	2	yes	complemented
553	#3093	C₂×C₂₃	1	2	yes	complemented
554	#2975	C₂×C₂₃	1	1	yes	characteristic, complemented
555	C₂²×C₂₃	—	2	1	no	—
556	C₂²×C₂₃	—	2	2	no	—
557	C₂²×C₂₃	—	2	2	no	—
558	C₂²×C₂₃	—	2	1	no	—
559	C₂²×C₂₃	—	2	2	no	—
560	C₂²×C₂₃	—	2	2	no	—
561	C₂²×C₂₃	—	2	1	no	—
562	C₂²×C₂₃	—	2	2	no	—
563	C₂²×C₂₃	—	2	2	no	—
564	C₂²×C₂₃	—	4	2	no	—
565	C₂²×C₂₃	—	4	1	no	—
566	C₂²×C₂₃	—	4	1	no	—
567	C₂²×C₂₃	—	4	1	no	—
568	C₂²×C₂₃	—	4	2	no	—
569	C₂²×C₂₃	—	4	1	no	—
570	C₂²×C₂₃	—	4	1	no	—
571	C₂²×C₂₃	—	4	1	no	—
572	C₂²×C₂₃	—	4	2	no	—
573	C₂²×C₂₃	—	8	4	no	—
574	C₂²×C₂₃	—	16	4	no	—
575	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
576	C₄×C₂₃	—	2	1	no	—
577	C₄×C₂₃	—	2	1	no	—
578	C₄×C₂₃	—	2	1	no	—
579	C₄×C₂₃	—	2	2	no	—
580	C₄×C₂₃	—	2	2	no	—
581	C₄×C₂₃	—	2	1	no	—
582	C₄×C₂₃	—	4	1	no	—
583	C₄×C₂₃	—	4	1	no	—
584	C₄×C₂₃	—	4	2	no	—
585	C₄×C₂₃	—	4	2	no	—
586	C₄×C₂₃	—	4	1	no	—
587	C₄×C₂₃	—	4	1	no	—
588	C₄×C₂₃	—	4	1	no	—
589	C₄×C₂₃	—	4	1	no	—
590	C₄×C₂₃	—	4	2	no	—
591	C₄×C₂₃	#575	1	2	yes	—
592	C₄×C₂₃	#585	1	1	yes	characteristic
593	C₄×C₂₃	#585	1	1	yes	characteristic
594	#556	C₂²×C₂₃	1	1	yes	characteristic
595	#555	C₂²×C₂₃	1	1	yes	characteristic
596	#555	C₂²×C₂₃	1	1	yes	characteristic
597	#554	C₂²×C₂₃	1	1	yes	characteristic
598	#554	C₂²×C₂₃	1	1	yes	characteristic, complemented
599	#553	—	2	1	no	—
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	#550	C₂²×C₂₃	1	1	yes	characteristic
606	#547	C₂²×C₂₃	1	1	yes	characteristic, complemented
607	#546	—	2	1	no	—
608	#546	—	2	2	no	—
609	#546	C₂²×C₂₃	1	2	yes	—
610	D₄²	—	2	1	no	—
611	D₄²	C₂²×C₂₃	1	1	yes	characteristic
612	#540	—	2	1	no	—
613	#538	—	2	2	no	—
614	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
615	#532	C₂²×C₂₃	1	1	yes	characteristic
616	#529	—	2	2	no	—
617	#529	—	2	1	no	—
618	#529	C₂²×C₂₃	1	1	yes	characteristic
619	#525	C₂²×C₂₃	1	2	yes	—
620	#525	C₂²×C₂₃	1	2	yes	complemented
621	C₂×#121	C₂²×C₂₃	1	2	yes	—
622	#518	—	2	1	no	—
623	C₄×#41	—	2	1	no	—
624	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic, complemented
625	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
626	C₂×#117	C₂²×C₂₃	1	2	yes	complemented
627	#500	C₂²×C₂₃	1	1	yes	characteristic, complemented
628	#499	C₂²×C₂₃	1	2	yes	complemented
629	#498	C₂²×C₂₃	1	1	yes	characteristic, complemented
630	#488	C₂²×C₂₃	1	2	yes	complemented
631	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
632	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
633	#485	C₂²×C₂₃	1	1	yes	characteristic, complemented
634	#485	C₂²×C₂₃	1	2	yes	complemented
635	#485	C₂²×C₂₃	1	2	yes	complemented
636	#485	C₂²×C₂₃	1	2	yes	complemented
637	#485	C₂²×C₂₃	1	2	yes	complemented
638	#483	C₂²×C₂₃	1	2	yes	complemented
639	#482	C₂²×C₂₃	1	1	yes	characteristic
640	#482	C₂²×C₂₃	1	2	yes	—
641	#482	C₂²×C₂₃	1	2	yes	complemented
642	#482	C₂²×C₂₃	1	2	yes	complemented
643	#482	C₂²×C₂₃	1	2	yes	complemented
644	#482	C₂²×C₂₃	1	2	yes	complemented
645	#482	C₂²×C₂₃	1	2	yes	complemented
646	#482	C₂²×C₂₃	1	2	yes	complemented
647	#481	C₂²×C₂₃	1	2	yes	complemented
648	#481	C₂²×C₂₃	1	2	yes	complemented
649	#480	C₂²×C₂₃	1	2	yes	complemented
650	#480	C₂²×C₂₃	1	2	yes	complemented
651	#480	C₂²×C₂₃	1	2	yes	complemented
652	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
653	#478	C₂²×C₂₃	1	2	yes	complemented
654	#478	C₂²×C₂₃	1	1	yes	characteristic, complemented
655	#478	C₂²×C₂₃	1	2	yes	complemented
656	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
657	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
658	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
659	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
660	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
661	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
662	#470	C₂²×C₂₃	1	2	yes	complemented
663	#469	C₂²×C₂₃	1	2	yes	complemented
664	#469	C₂²×C₂₃	1	2	yes	complemented
665	#469	C₂²×C₂₃	1	2	yes	complemented
666	#468	C₂²×C₂₃	1	2	yes	complemented
667	#468	C₂²×C₂₃	1	2	yes	complemented
668	#468	C₂²×C₂₃	1	2	yes	complemented
669	#468	C₂²×C₂₃	1	2	yes	complemented
670	#464	C₂²×C₂₃	1	1	yes	characteristic, complemented
671	#463	C₂²×C₂₃	1	1	yes	characteristic, complemented
672	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
673	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
674	#452	C₂²×C₂₃	1	2	yes	complemented
675	#452	C₂²×C₂₃	1	1	yes	characteristic, complemented
676	#450	C₂²×C₂₃	1	2	yes	complemented
677	#449	C₂²×C₂₃	1	1	yes	characteristic
678	#449	C₂²×C₂₃	1	2	yes	complemented
679	#449	C₂²×C₂₃	1	2	yes	complemented
680	#447	C₂²×C₂₃	1	2	yes	complemented
681	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
682	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
683	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
684	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
685	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
686	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
687	#436	C₂²×C₂₃	1	1	yes	characteristic
688	#436	C₂²×C₂₃	1	1	yes	characteristic
689	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
690	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
691	#436	C₂²×C₂₃	1	2	yes	complemented
692	#436	C₂²×C₂₃	1	2	yes	complemented
693	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
694	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
695	#428	C₂²×C₂₃	1	2	yes	complemented
696	#428	C₂²×C₂₃	1	2	yes	complemented
697	#428	C₂²×C₂₃	1	2	yes	complemented
698	#428	C₂²×C₂₃	1	2	yes	complemented
699	#418	C₂²×C₂₃	1	2	yes	complemented
700	#418	C₂²×C₂₃	1	2	yes	complemented
701	#417	C₂²×C₂₃	1	2	yes	complemented
702	#417	C₂²×C₂₃	1	2	yes	complemented
703	#407	C₂²×C₂₃	1	2	yes	complemented
704	#407	C₂²×C₂₃	1	2	yes	complemented
705	C₂×C₂₃	—	4	2	no	—
706	C₂×C₂₃	—	4	1	no	—
707	C₂×C₂₃	—	4	2	no	—
708	C₂×C₂₃	—	8	1	no	—
709	C₂×C₂₃	—	8	2	no	—
710	C₂×C₂₃	—	8	1	no	—
711	C₂×C₂₃	#3485	1	1	yes	characteristic
712	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
713	C₂×C₂₃	#3585	1	1	yes	characteristic
714	C₂×#41	—	2	1	no	—
715	C₂×#41	—	2	1	no	—
716	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
717	C₂×#41	C₂³×C₂₃	1	2	yes	—
718	C₂²×D₄	—	2	2	no	—
719	C₂²×D₄	—	2	1	no	—
720	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
721	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
722	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
723	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
724	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
725	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
726	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
727	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
728	C₂×D₈	C₂³×C₂₃	1	2	yes	—
729	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
730	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
731	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
732	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
733	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
734	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
735	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
736	#127	—	2	1	no	—
737	#127	C₂³×C₂₃	1	1	yes	characteristic
738	#126	—	2	2	no	—
739	#126	—	2	2	no	—
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#126	—	2	1	no	—
743	#125	—	2	2	no	—
744	#125	—	2	1	no	—
745	#125	—	2	1	no	—
746	#125	C₂³×C₂₃	1	1	yes	characteristic
747	#125	C₂³×C₂₃	1	2	yes	—
748	#124	—	2	1	no	—
749	#124	—	2	2	no	—
750	#124	—	2	2	no	—
751	#124	—	2	1	no	—
752	#124	C₂³×C₂₃	1	1	yes	characteristic
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	1	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	1	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	1	yes	characteristic
767	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
768	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
769	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
770	#121	—	2	2	no	—
771	#121	—	2	1	no	—
772	#121	—	2	2	no	—
773	#121	—	2	1	no	—
774	#121	—	2	2	no	—
775	#121	—	2	2	no	—
776	#121	—	2	1	no	—
777	#121	—	2	1	no	—
778	#121	—	2	2	no	—
779	#121	—	2	2	no	—
780	#121	C₂³×C₂₃	1	1	yes	characteristic
781	#121	C₂³×C₂₃	1	2	yes	—
782	#121	C₂³×C₂₃	1	2	yes	—
783	#121	C₂³×C₂₃	1	2	yes	—
784	#121	C₂³×C₂₃	1	2	yes	—
785	#121	C₂³×C₂₃	1	2	yes	—
786	#121	C₂³×C₂₃	1	2	yes	—
787	#120	—	2	2	no	—
788	#120	—	2	2	no	—
789	#120	—	2	2	no	—
790	#120	—	2	2	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	—	2	1	no	—
794	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
795	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
796	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
811	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
812	C₄×D₄	D₄×C₂₃	1	2	yes	—
813	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
816	C₄×D₄	C₂³×C₂₃	1	2	yes	—
817	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₂₃	1	2	yes	—
819	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
820	#117	—	2	2	no	—
821	#117	—	2	2	no	—
822	#117	—	2	1	no	—
823	#117	—	2	1	no	—
824	#117	—	2	2	no	—
825	#117	—	2	1	no	—
826	#117	—	2	1	no	—
827	#117	C₂³×C₂₃	1	1	yes	characteristic
828	#117	C₂³×C₂₃	1	2	yes	—
829	#117	C₂³×C₂₃	1	2	yes	—
830	#117	C₂³×C₂₃	1	2	yes	—
831	#117	C₂³×C₂₃	1	2	yes	—
832	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
833	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
834	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
835	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
836	C₂×C₂²⋊C₄	—	2	2	no	—
837	C₂×C₂²⋊C₄	—	2	2	no	—
838	C₂×C₂²⋊C₄	—	2	2	no	—
839	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
840	C₂×C₄²	—	2	2	no	—
841	C₂×C₄²	—	2	1	no	—
842	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
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	2	yes	—
847	#107	C₂³×C₂₃	1	2	yes	—
848	#107	C₂³×C₂₃	1	2	yes	—
849	#107	C₂³×C₂₃	1	2	yes	—
850	#106	C₂³×C₂₃	1	2	yes	—
851	#106	C₂³×C₂₃	1	1	yes	characteristic
852	#106	C₂³×C₂₃	1	1	yes	characteristic
853	#106	C₂³×C₂₃	1	2	yes	—
854	#106	C₂³×C₂₃	1	2	yes	—
855	#106	C₂³×C₂₃	1	2	yes	—
856	#106	C₂³×C₂₃	1	2	yes	—
857	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
858	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
861	#103	C₂³×C₂₃	1	1	yes	characteristic
862	#103	C₂³×C₂₃	1	1	yes	characteristic
863	#103	C₂³×C₂₃	1	2	yes	—
864	#103	C₂³×C₂₃	1	2	yes	—
865	#103	C₂³×C₂₃	1	2	yes	—
866	#103	C₂³×C₂₃	1	1	yes	characteristic
867	#103	C₂³×C₂₃	1	1	yes	characteristic
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	1	yes	characteristic
873	#102	C₂³×C₂₃	1	1	yes	characteristic
874	#102	C₂³×C₂₃	1	2	yes	—
875	#102	C₂³×C₂₃	1	2	yes	—
876	#102	C₂³×C₂₃	1	2	yes	—
877	#102	C₂³×C₂₃	1	2	yes	—
878	#102	C₂³×C₂₃	1	2	yes	—
879	#102	C₂³×C₂₃	1	1	yes	characteristic
880	#102	C₂³×C₂₃	1	1	yes	characteristic
881	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
882	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
884	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
885	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
886	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
887	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
888	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
889	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
890	C₄×C₈	C₂³×C₂₃	1	2	yes	—
891	C₂₃	#61725	1	1	yes	characteristic, direct product factor, Sylow
892	C₂⁴	—	2	2	no	—
893	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
894	#41	—	4	1	no	—
895	#41	—	4	1	no	—
896	#41	—	4	2	no	—
897	#41	—	4	2	no	—
898	#41	—	4	4	no	—
899	#41	—	8	2	no	—
900	C₂×Q₈	—	2	1	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	—	2	1	no	—
903	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
904	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
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	1	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	1	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	4	2	no	—
918	C₂×D₄	—	4	2	no	—
919	C₂×D₄	—	4	2	no	—
920	C₂×D₄	—	4	4	no	—
921	C₂×D₄	—	8	4	no	—
922	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
923	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
924	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
925	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
926	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
927	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	4	2	no	—
938	C₂²×C₄	—	4	2	no	—
939	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
940	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
941	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
942	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
943	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
944	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
945	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
946	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
947	Q₁₆	—	4	1	no	—
948	SD₁₆	—	4	1	no	—
949	SD₁₆	—	4	1	no	—
950	SD₁₆	—	4	2	no	—
951	D₈	—	4	2	no	—
952	D₈	—	4	1	no	—
953	M₁₆	—	4	2	no	—
954	M₁₆	—	4	2	no	—
955	M₁₆	—	4	2	no	—
956	M₁₆	—	4	2	no	—
957	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
958	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
959	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
960	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
961	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
962	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
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	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
981	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
982	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
983	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
984	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
985	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
986	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
987	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
988	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
989	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
990	C₂²⋊C₄	—	2	1	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	2	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1013	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1014	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1015	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
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	1	no	—
1022	C₄²	—	2	2	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1025	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1026	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1027	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	1	no	—
1030	C₂³	—	2	2	no	—
1031	C₂³	—	4	2	no	—
1032	C₂³	—	4	2	no	—
1033	C₂³	—	4	2	no	—
1034	C₂³	—	4	4	no	—
1035	C₂³	—	8	2	no	—
1036	C₂³	—	8	2	no	—
1037	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1038	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1039	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1040	Q₈	—	2	1	no	—
1041	Q₈	—	2	1	no	—
1042	Q₈	—	2	1	no	—
1043	Q₈	—	2	1	no	—
1044	Q₈	—	4	2	no	—
1045	Q₈	—	8	1	no	—
1046	Q₈	—	8	1	no	—
1047	D₄	—	2	2	no	—
1048	D₄	—	2	2	no	—
1049	D₄	—	2	1	no	—
1050	D₄	—	2	1	no	—
1051	D₄	—	2	1	no	—
1052	D₄	—	2	2	no	—
1053	D₄	—	2	1	no	—
1054	D₄	—	2	2	no	—
1055	D₄	—	4	2	no	—
1056	D₄	—	4	4	no	—
1057	D₄	—	4	2	no	—
1058	D₄	—	4	4	no	—
1059	D₄	—	4	2	no	—
1060	D₄	—	4	4	no	—
1061	D₄	—	4	2	no	—
1062	D₄	—	8	2	no	—
1063	D₄	—	8	1	no	—
1064	D₄	—	8	2	no	—
1065	D₄	—	8	2	no	—
1066	D₄	—	8	2	no	—
1067	D₄	—	8	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	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	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	4	1	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	4	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	8	2	no	—
1093	C₂×C₄	—	8	2	no	—
1094	C₂×C₄	—	8	1	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1098	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1099	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1100	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1101	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1102	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1103	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1104	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1105	C₈	—	2	2	no	—
1106	C₈	—	2	1	no	—
1107	C₈	—	2	1	no	—
1108	C₈	—	2	1	no	—
1109	C₈	—	2	2	no	—
1110	C₈	—	2	1	no	—
1111	C₂²	—	2	1	no	—
1112	C₂²	—	2	2	no	—
1113	C₂²	—	2	2	no	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	1	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	2	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	8	4	no	—
1130	C₂²	—	16	4	no	—
1131	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	2	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	2	no	—
1146	C₄	—	4	2	no	—
1147	C₄	C₂₃×#575	1	2	yes	—
1148	C₄	C₂₃×#585	1	1	yes	characteristic
1149	C₄	C₂₃×#585	1	1	yes	characteristic
1150	C₂	—	4	1	no	—
1151	C₂	—	4	2	no	—
1152	C₂	—	4	2	no	—
1153	C₂	—	8	1	no	—
1154	C₂	—	8	2	no	—
1155	C₂	—	8	1	no	—
1156	C₂	C₂₃×#3485	1	1	yes	characteristic
1157	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
1158	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 ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3519	C₂	semidirect
2. C₂₃×#3475	C₂	semidirect
3. C₂₃×#3357	C₂	semidirect
4. C₂₃×#3357	C₂	semidirect
5. C₂₃×#3356	C₂	semidirect
6. C₂₃×#3355	C₂	semidirect
7. C₂₃×#3354	C₂	semidirect
8. C₂₃×#3351	C₂	semidirect
9. C₂₃×#3333	C₂	semidirect
10. C₂₃×#3332	C₂	semidirect
11. C₂₃×#3325	C₂	semidirect
12. C₂₃×#3324	C₂	semidirect
13. C₂₃×#3323	C₂	semidirect
14. C₂₃×#3322	C₂	semidirect
15. C₂₃×#3233	C₂	semidirect
16. C₂₃×#3228	C₂	semidirect
17. C₂₃×#3197	C₂	semidirect
18. C₂₃×#3194	C₂	semidirect
19. C₂₃×#3106	C₂	semidirect
20. C₂₃×#3102	C₂	semidirect
21. C₂₃×#3094	C₂	semidirect
22. C₂₃×#3093	C₂	semidirect
23. C₂₃×#2975	C₂	semidirect
28. C₂₃×#554	C₂²	semidirect
31. C₂₃×#553	C₂²	semidirect
33. C₂₃×#552	C₂²	semidirect
36. C₂₃×#547	C₂²	semidirect
44. C₂₃×#533	C₂²	semidirect
50. C₂₃×#525	C₂²	semidirect
54. C₄×#41×C₂₃	C₂²	semidirect
56. C₂×C₂₃×#117	C₂²	semidirect
57. C₂₃×#500	C₂²	semidirect
58. C₂₃×#499	C₂²	semidirect
59. C₂₃×#498	C₂²	semidirect
60. C₂₃×#488	C₂²	semidirect
61. C₂₃×#486	C₂²	semidirect
62. C₂₃×#486	C₂²	semidirect
63. C₂₃×#485	C₂²	semidirect
64. C₂₃×#485	C₂²	semidirect
65. C₂₃×#485	C₂²	semidirect
66. C₂₃×#485	C₂²	semidirect
67. C₂₃×#485	C₂²	semidirect
68. C₂₃×#483	C₂²	semidirect
71. C₂₃×#482	C₂²	semidirect
72. C₂₃×#482	C₂²	semidirect
73. C₂₃×#482	C₂²	semidirect
74. C₂₃×#482	C₂²	semidirect
75. C₂₃×#482	C₂²	semidirect
76. C₂₃×#482	C₂²	semidirect
77. C₂₃×#481	C₂²	semidirect
78. C₂₃×#481	C₂²	semidirect
79. C₂₃×#480	C₂²	semidirect
80. C₂₃×#480	C₂²	semidirect
81. C₂₃×#480	C₂²	semidirect
82. C₂₃×#479	C₂²	semidirect
83. C₂₃×#478	C₂²	semidirect
84. C₂₃×#478	C₂²	semidirect
85. C₂₃×#478	C₂²	semidirect
86. C₂₃×#477	C₂²	semidirect
87. C₂₃×#477	C₂²	semidirect
88. C₂₃×#476	C₂²	semidirect
89. C₂₃×#476	C₂²	semidirect
90. C₂₃×#475	C₂²	semidirect
91. C₂₃×#474	C₂²	semidirect
92. C₂₃×#470	C₂²	semidirect
93. C₂₃×#469	C₂²	semidirect
94. C₂₃×#469	C₂²	semidirect
95. C₂₃×#469	C₂²	semidirect
96. C₂₃×#468	C₂²	semidirect
97. C₂₃×#468	C₂²	semidirect
98. C₂₃×#468	C₂²	semidirect
99. C₂₃×#468	C₂²	semidirect
100. C₂₃×#464	C₂²	semidirect
101. C₂₃×#463	C₂²	semidirect
102. C₂₃×#460	C₂²	semidirect
103. C₂₃×#459	C₂²	semidirect
104. C₂₃×#452	C₂²	semidirect
105. C₂₃×#452	C₂²	semidirect
106. C₂₃×#450	C₂²	semidirect
108. C₂₃×#449	C₂²	semidirect
109. C₂₃×#449	C₂²	semidirect
110. C₂₃×#447	C₂²	semidirect
111. C₄×Q₁₆×C₂₃	C₂²	semidirect
112. C₄×SD₁₆×C₂₃	C₂²	semidirect
113. C₄×SD₁₆×C₂₃	C₂²	semidirect
114. C₄×SD₁₆×C₂₃	C₂²	semidirect
115. C₄×D₈×C₂₃	C₂²	semidirect
116. C₄×D₈×C₂₃	C₂²	semidirect
119. C₂₃×#436	C₂²	semidirect
120. C₂₃×#436	C₂²	semidirect
121. C₂₃×#436	C₂²	semidirect
122. C₂₃×#436	C₂²	semidirect
123. C₂₃×#431	C₂²	semidirect
124. C₂₃×#431	C₂²	semidirect
125. C₂₃×#428	C₂²	semidirect
126. C₂₃×#428	C₂²	semidirect
127. C₂₃×#428	C₂²	semidirect
128. C₂₃×#428	C₂²	semidirect
129. C₂₃×#418	C₂²	semidirect
130. C₂₃×#418	C₂²	semidirect
131. C₂₃×#417	C₂²	semidirect
132. C₂₃×#417	C₂²	semidirect
133. C₂₃×#407	C₂²	semidirect
134. C₂₃×#407	C₂²	semidirect
448. #61725	C₂₃	direct (N × H)
532. #3519	C₂×C₂₃	semidirect
533. #3475	C₂×C₂₃	semidirect
534. #3357	C₂×C₂₃	semidirect
535. #3357	C₂×C₂₃	semidirect
536. #3356	C₂×C₂₃	semidirect
537. #3355	C₂×C₂₃	semidirect
538. #3354	C₂×C₂₃	semidirect
539. #3351	C₂×C₂₃	semidirect
540. #3333	C₂×C₂₃	semidirect
541. #3332	C₂×C₂₃	semidirect
542. #3325	C₂×C₂₃	semidirect
543. #3324	C₂×C₂₃	semidirect
544. #3323	C₂×C₂₃	semidirect
545. #3322	C₂×C₂₃	semidirect
546. #3233	C₂×C₂₃	semidirect
547. #3228	C₂×C₂₃	semidirect
548. #3197	C₂×C₂₃	semidirect
549. #3194	C₂×C₂₃	semidirect
550. #3106	C₂×C₂₃	semidirect
551. #3102	C₂×C₂₃	semidirect
552. #3094	C₂×C₂₃	semidirect
553. #3093	C₂×C₂₃	semidirect
554. #2975	C₂×C₂₃	semidirect
598. #554	C₂²×C₂₃	semidirect
601. #553	C₂²×C₂₃	semidirect
603. #552	C₂²×C₂₃	semidirect
606. #547	C₂²×C₂₃	semidirect
614. #533	C₂²×C₂₃	semidirect
620. #525	C₂²×C₂₃	semidirect
624. C₄×#41	C₂²×C₂₃	semidirect
626. C₂×#117	C₂²×C₂₃	semidirect
627. #500	C₂²×C₂₃	semidirect
628. #499	C₂²×C₂₃	semidirect
629. #498	C₂²×C₂₃	semidirect
630. #488	C₂²×C₂₃	semidirect
631. #486	C₂²×C₂₃	semidirect
632. #486	C₂²×C₂₃	semidirect
633. #485	C₂²×C₂₃	semidirect
634. #485	C₂²×C₂₃	semidirect
635. #485	C₂²×C₂₃	semidirect
636. #485	C₂²×C₂₃	semidirect
637. #485	C₂²×C₂₃	semidirect
638. #483	C₂²×C₂₃	semidirect
641. #482	C₂²×C₂₃	semidirect
642. #482	C₂²×C₂₃	semidirect
643. #482	C₂²×C₂₃	semidirect
644. #482	C₂²×C₂₃	semidirect
645. #482	C₂²×C₂₃	semidirect
646. #482	C₂²×C₂₃	semidirect
647. #481	C₂²×C₂₃	semidirect
648. #481	C₂²×C₂₃	semidirect
649. #480	C₂²×C₂₃	semidirect
650. #480	C₂²×C₂₃	semidirect
651. #480	C₂²×C₂₃	semidirect
652. #479	C₂²×C₂₃	semidirect
653. #478	C₂²×C₂₃	semidirect
654. #478	C₂²×C₂₃	semidirect
655. #478	C₂²×C₂₃	semidirect
656. #477	C₂²×C₂₃	semidirect
657. #477	C₂²×C₂₃	semidirect
658. #476	C₂²×C₂₃	semidirect
659. #476	C₂²×C₂₃	semidirect
660. #475	C₂²×C₂₃	semidirect
661. #474	C₂²×C₂₃	semidirect
662. #470	C₂²×C₂₃	semidirect
663. #469	C₂²×C₂₃	semidirect
664. #469	C₂²×C₂₃	semidirect
665. #469	C₂²×C₂₃	semidirect
666. #468	C₂²×C₂₃	semidirect
667. #468	C₂²×C₂₃	semidirect
668. #468	C₂²×C₂₃	semidirect
669. #468	C₂²×C₂₃	semidirect
670. #464	C₂²×C₂₃	semidirect
671. #463	C₂²×C₂₃	semidirect
672. #460	C₂²×C₂₃	semidirect
673. #459	C₂²×C₂₃	semidirect
674. #452	C₂²×C₂₃	semidirect
675. #452	C₂²×C₂₃	semidirect
676. #450	C₂²×C₂₃	semidirect
678. #449	C₂²×C₂₃	semidirect
679. #449	C₂²×C₂₃	semidirect
680. #447	C₂²×C₂₃	semidirect
681. C₄×Q₁₆	C₂²×C₂₃	semidirect
682. C₄×SD₁₆	C₂²×C₂₃	semidirect
683. C₄×SD₁₆	C₂²×C₂₃	semidirect
684. C₄×SD₁₆	C₂²×C₂₃	semidirect
685. C₄×D₈	C₂²×C₂₃	semidirect
686. C₄×D₈	C₂²×C₂₃	semidirect
689. #436	C₂²×C₂₃	semidirect
690. #436	C₂²×C₂₃	semidirect
691. #436	C₂²×C₂₃	semidirect
692. #436	C₂²×C₂₃	semidirect
693. #431	C₂²×C₂₃	semidirect
694. #431	C₂²×C₂₃	semidirect
695. #428	C₂²×C₂₃	semidirect
696. #428	C₂²×C₂₃	semidirect
697. #428	C₂²×C₂₃	semidirect
698. #428	C₂²×C₂₃	semidirect
699. #418	C₂²×C₂₃	semidirect
700. #418	C₂²×C₂₃	semidirect
701. #417	C₂²×C₂₃	semidirect
702. #417	C₂²×C₂₃	semidirect
703. #407	C₂²×C₂₃	semidirect
704. #407	C₂²×C₂₃	semidirect
891. C₂₃	#61725	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×#3519	2
C₂₃×#3475	2
C₂₃×#3357	2
C₂₃×#3356	2
C₂₃×#3355	2
C₂₃×#3354	2
C₂₃×#3351	2
C₂₃×#3333	2
C₂₃×#3332	2
C₂₃×#3325	2
C₂₃×#3324	2
C₂₃×#3323	2
C₂₃×#3322	2
C₂₃×#3233	2
C₂₃×#3228	2
C₂₃×#3197	2
C₂₃×#3194	2
C₂₃×#3106	2
C₂₃×#3102	2
C₂₃×#3094	2
C₂₃×#3093	2
C₂₃×#2975	2
#61725	23

Subgroups — C23×#61725 #19209351

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61725 #19209351