Subgroups — C₂₃×#18739 #19166365

Order 5888.

938 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3546	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#3246	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3233	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3182	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1650	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1647	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1642	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1639	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1638	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1635	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1631	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1629	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1540	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1484	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1483	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#560	—	2	2	no	—
17	C₂₃×#556	C₂²	1	1	yes	characteristic
18	C₂₃×#553	—	2	1	no	—
19	C₂₃×#550	—	2	1	no	—
20	C₂₃×#550	C₂²	1	1	yes	characteristic
21	C₂₃×#547	C₂²	1	1	yes	characteristic
22	C₂₃×#546	—	2	1	no	—
23	C₂₃×#546	—	2	1	no	—
24	D₄²×C₂₃	C₂²	1	1	yes	characteristic
25	C₂₃×#542	—	2	1	no	—
26	C₂₃×#538	—	2	2	no	—
27	C₂₃×#537	—	2	1	no	—
28	C₂₃×#535	—	2	1	no	—
29	C₂₃×#535	—	2	1	no	—
30	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#532	C₂²	1	1	yes	characteristic
32	C₂₃×#532	C₂²	1	1	yes	characteristic
33	C₂₃×#529	C₂²	1	1	yes	characteristic
34	C₂₃×#500	C₂²	1	1	yes	characteristic, complemented
35	C₂₃×#499	—	2	1	no	—
36	C₂₃×#492	C₂²	1	1	yes	characteristic
37	C₂₃×#488	—	2	1	no	—
38	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
39	C₂₃×#486	C₂²	1	1	yes	characteristic
40	C₂₃×#485	—	2	1	no	—
41	C₂₃×#482	—	2	1	no	—
42	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
43	C₂₃×#476	C₂²	1	1	yes	characteristic
44	C₂₃×#476	C₂²	1	1	yes	characteristic
45	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#475	—	2	1	no	—
47	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
48	C₂₃×#474	C₂²	1	1	yes	characteristic
49	C₂₃×#468	—	2	2	no	—
50	C₂₃×#465	—	2	1	no	—
51	C₂₃×#465	—	2	1	no	—
52	C₂₃×#461	C₂²	1	1	yes	characteristic
53	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
54	C₂₃×#460	—	2	1	no	—
55	C₂₃×#440	—	2	2	no	—
56	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
58	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#332	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#332	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#331	C₂²	1	1	yes	characteristic
62	C₂₃×#331	C₂²	1	1	yes	characteristic
63	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
64	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
65	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
67	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
69	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
70	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
71	C₂×#41×C₂₃	—	2	1	no	—
72	C₂×#41×C₂₃	—	2	1	no	—
73	C₂×#41×C₂₃	—	2	1	no	—
74	C₂×#41×C₂₃	—	2	1	no	—
75	C₂²×D₄×C₂₃	—	2	1	no	—
76	C₂²×D₄×C₂₃	—	2	1	no	—
77	C₂×SD₁₆×C₂₃	—	2	2	no	—
78	C₂×SD₁₆×C₂₃	—	2	1	no	—
79	C₂×SD₁₆×C₂₃	—	2	1	no	—
80	C₂×M₁₆×C₂₃	—	2	1	no	—
81	C₂²×C₈×C₂₃	—	2	1	no	—
82	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
83	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₂₃×#127	—	2	2	no	—
87	C₂₃×#127	—	2	1	no	—
88	C₂₃×#127	D₄	1	1	yes	characteristic
89	C₂₃×#127	C₂³	1	1	yes	characteristic
90	C₂₃×#126	—	2	2	no	—
91	C₂₃×#126	—	2	2	no	—
92	C₂₃×#126	—	2	1	no	—
93	C₂₃×#125	—	2	1	no	—
94	C₂₃×#125	D₄	1	1	yes	characteristic
95	C₂₃×#124	—	2	2	no	—
96	C₂₃×#124	—	2	1	no	—
97	C₂₃×#124	—	2	1	no	—
98	C₂₃×#124	—	2	1	no	—
99	C₂₃×#124	D₄	1	1	yes	characteristic
100	C₂₃×#123	—	2	2	no	—
101	C₂₃×#123	—	2	2	no	—
102	C₂₃×#123	—	2	1	no	—
103	C₂₃×#123	—	2	2	no	—
104	C₂₃×C₂²⋊Q₈	—	2	2	no	—
105	C₂₃×C₂²⋊Q₈	—	2	1	no	—
106	C₂₃×C₂²⋊Q₈	—	2	1	no	—
107	C₂₃×C₂²⋊Q₈	—	2	1	no	—
108	C₂₃×C₂²⋊Q₈	—	2	1	no	—
109	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
110	C₂₃×#121	—	2	2	no	—
111	C₂₃×#121	—	2	2	no	—
112	C₂₃×#121	—	2	2	no	—
113	C₂₃×#121	—	2	2	no	—
114	C₂₃×#121	—	2	2	no	—
115	C₂₃×#121	—	2	1	no	—
116	C₂₃×#121	—	2	2	no	—
117	C₂₃×#121	—	2	1	no	—
118	C₂₃×#121	—	2	1	no	—
119	C₂₃×#121	—	2	1	no	—
120	C₂₃×#121	—	2	1	no	—
121	C₂₃×#121	—	2	1	no	—
122	C₂₃×#121	D₄	1	1	yes	characteristic
123	C₂₃×#121	D₄	1	2	yes	—
124	C₂₃×#121	D₄	1	1	yes	characteristic
125	C₂₃×#121	D₄	1	1	yes	characteristic
126	C₂₃×#120	—	2	2	no	—
127	C₂₃×#120	—	2	2	no	—
128	C₂₃×#120	—	2	2	no	—
129	C₂₃×#120	—	2	2	no	—
130	C₄×Q₈×C₂₃	—	2	1	no	—
131	C₄×Q₈×C₂₃	—	2	1	no	—
132	C₄×Q₈×C₂₃	—	2	1	no	—
133	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
134	C₄×D₄×C₂₃	—	2	2	no	—
135	C₄×D₄×C₂₃	—	2	1	no	—
136	C₄×D₄×C₂₃	—	2	1	no	—
137	C₄×D₄×C₂₃	—	2	1	no	—
138	C₄×D₄×C₂₃	—	2	1	no	—
139	C₄×D₄×C₂₃	D₄	1	2	yes	—
140	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
141	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
142	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
143	C₂₃×#117	—	2	1	no	—
144	C₂₃×#117	—	2	1	no	—
145	C₂₃×#117	—	2	1	no	—
146	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
147	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
148	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
149	C₂₃×#107	—	2	2	no	—
150	C₂₃×#107	—	2	1	no	—
151	C₂₃×#107	—	2	1	no	—
152	C₂₃×#106	—	2	1	no	—
153	C₂₃×#106	—	2	1	no	—
154	C₂₃×#106	—	2	1	no	—
155	C₂₃×#106	—	2	1	no	—
156	C₂₃×C₄⋊C₈	—	2	1	no	—
157	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₂₃×#103	—	2	1	no	—
162	C₂₃×#103	—	2	1	no	—
163	C₂₃×#103	—	2	2	no	—
164	C₂₃×#103	—	2	1	no	—
165	C₂₃×#103	—	2	1	no	—
166	C₂₃×#102	—	2	2	no	—
167	C₂₃×#102	—	2	1	no	—
168	C₂₃×#102	—	2	1	no	—
169	C₂₃×#102	—	2	1	no	—
170	C₂₃×#102	—	2	1	no	—
171	C₂₃×C₂²⋊C₈	—	2	1	no	—
172	C₂₃×#97	—	2	1	no	—
173	C₄×C₈×C₂₃	—	2	1	no	—
174	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
175	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
176	C₂⁴×C₂₃	—	2	2	no	—
177	#41×C₂₃	—	8	1	no	—
178	#41×C₂₃	—	8	1	no	—
179	#41×C₂₃	—	8	1	no	—
180	#41×C₂₃	—	8	1	no	—
181	#41×C₂₃	—	8	1	no	—
182	#41×C₂₃	—	8	1	no	—
183	#41×C₂₃	—	8	1	no	—
184	#41×C₂₃	—	8	1	no	—
185	C₂×Q₈×C₂₃	—	2	1	no	—
186	C₂×Q₈×C₂₃	—	2	1	no	—
187	C₂×Q₈×C₂₃	—	2	1	no	—
188	C₂×Q₈×C₂₃	—	2	1	no	—
189	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
190	C₂×D₄×C₂₃	—	2	2	no	—
191	C₂×D₄×C₂₃	—	2	2	no	—
192	C₂×D₄×C₂₃	—	2	2	no	—
193	C₂×D₄×C₂₃	—	2	2	no	—
194	C₂×D₄×C₂₃	—	2	2	no	—
195	C₂×D₄×C₂₃	—	2	1	no	—
196	C₂×D₄×C₂₃	—	2	1	no	—
197	C₂×D₄×C₂₃	—	2	2	no	—
198	C₂×D₄×C₂₃	—	2	1	no	—
199	C₂×D₄×C₂₃	—	2	1	no	—
200	C₂×D₄×C₂₃	—	2	1	no	—
201	C₂×D₄×C₂₃	—	2	1	no	—
202	C₂×D₄×C₂₃	—	2	1	no	—
203	C₂×D₄×C₂₃	—	8	1	no	—
204	C₂×D₄×C₂₃	—	8	1	no	—
205	C₂×D₄×C₂₃	—	8	1	no	—
206	C₂×D₄×C₂₃	—	8	1	no	—
207	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
208	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
209	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
210	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
211	C₂²×C₄×C₂₃	—	2	2	no	—
212	C₂²×C₄×C₂₃	—	2	2	no	—
213	C₂²×C₄×C₂₃	—	2	1	no	—
214	C₂²×C₄×C₂₃	—	2	1	no	—
215	C₂²×C₄×C₂₃	—	2	1	no	—
216	C₂²×C₄×C₂₃	—	2	2	no	—
217	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
220	SD₁₆×C₂₃	—	4	4	no	—
221	SD₁₆×C₂₃	—	8	1	no	—
222	SD₁₆×C₂₃	—	8	1	no	—
223	M₁₆×C₂₃	—	4	2	no	—
224	C₂×C₈×C₂₃	—	2	1	no	—
225	C₂×C₈×C₂₃	—	2	1	no	—
226	C₂×C₈×C₂₃	—	2	1	no	—
227	C₂×C₈×C₂₃	—	2	1	no	—
228	C₂×C₈×C₂₃	—	2	1	no	—
229	C₂×C₈×C₂₃	—	2	1	no	—
230	C₂×C₈×C₂₃	—	8	1	no	—
231	C₄⋊C₄×C₂₃	—	2	2	no	—
232	C₄⋊C₄×C₂₃	—	2	2	no	—
233	C₄⋊C₄×C₂₃	—	2	1	no	—
234	C₄⋊C₄×C₂₃	—	2	1	no	—
235	C₄⋊C₄×C₂₃	—	2	1	no	—
236	C₄⋊C₄×C₂₃	—	2	1	no	—
237	C₄⋊C₄×C₂₃	—	2	1	no	—
238	C₄⋊C₄×C₂₃	—	2	1	no	—
239	C₄⋊C₄×C₂₃	—	2	1	no	—
240	C₄⋊C₄×C₂₃	—	2	1	no	—
241	C₄⋊C₄×C₂₃	—	2	1	no	—
242	C₄⋊C₄×C₂₃	—	2	1	no	—
243	C₄⋊C₄×C₂₃	—	4	1	no	—
244	C₄⋊C₄×C₂₃	—	4	1	no	—
245	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
246	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
247	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
248	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
249	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
250	C₂²⋊C₄×C₂₃	—	2	2	no	—
251	C₂²⋊C₄×C₂₃	—	2	2	no	—
252	C₂²⋊C₄×C₂₃	—	2	2	no	—
253	C₂²⋊C₄×C₂₃	—	2	2	no	—
254	C₂²⋊C₄×C₂₃	—	2	2	no	—
255	C₂²⋊C₄×C₂₃	—	2	1	no	—
256	C₂²⋊C₄×C₂₃	—	2	1	no	—
257	C₂²⋊C₄×C₂₃	—	2	1	no	—
258	C₂²⋊C₄×C₂₃	—	2	1	no	—
259	C₂²⋊C₄×C₂₃	—	2	1	no	—
260	C₂²⋊C₄×C₂₃	—	2	1	no	—
261	C₂²⋊C₄×C₂₃	—	2	2	no	—
262	C₂²⋊C₄×C₂₃	—	2	2	no	—
263	C₂²⋊C₄×C₂₃	—	2	1	no	—
264	C₂²⋊C₄×C₂₃	—	2	1	no	—
265	C₂²⋊C₄×C₂₃	—	2	1	no	—
266	C₂²⋊C₄×C₂₃	—	4	1	no	—
267	C₄²×C₂₃	—	2	2	no	—
268	C₄²×C₂₃	—	2	1	no	—
269	C₄²×C₂₃	—	4	1	no	—
270	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
271	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
272	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
273	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
274	#18739	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
275	C₂³×C₂₃	—	2	1	no	—
276	C₂³×C₂₃	—	2	1	no	—
277	C₂³×C₂₃	—	2	2	no	—
278	C₂³×C₂₃	—	2	1	no	—
279	C₂³×C₂₃	—	8	2	no	—
280	C₂³×C₂₃	—	8	2	no	—
281	C₂³×C₂₃	—	8	2	no	—
282	C₂³×C₂₃	#120	1	1	yes	characteristic
283	Q₈×C₂₃	—	2	1	no	—
284	Q₈×C₂₃	—	2	1	no	—
285	Q₈×C₂₃	—	4	2	no	—
286	Q₈×C₂₃	—	4	1	no	—
287	Q₈×C₂₃	—	4	1	no	—
288	Q₈×C₂₃	—	4	1	no	—
289	Q₈×C₂₃	—	4	1	no	—
290	Q₈×C₂₃	—	8	1	no	—
291	D₄×C₂₃	—	2	1	no	—
292	D₄×C₂₃	—	2	1	no	—
293	D₄×C₂₃	—	2	1	no	—
294	D₄×C₂₃	—	2	1	no	—
295	D₄×C₂₃	—	2	1	no	—
296	D₄×C₂₃	—	2	1	no	—
297	D₄×C₂₃	—	4	2	no	—
298	D₄×C₂₃	—	4	1	no	—
299	D₄×C₂₃	—	4	1	no	—
300	D₄×C₂₃	—	4	1	no	—
301	D₄×C₂₃	—	4	1	no	—
302	D₄×C₂₃	—	8	1	no	—
303	D₄×C₂₃	—	8	1	no	—
304	D₄×C₂₃	—	8	1	no	—
305	D₄×C₂₃	—	8	1	no	—
306	D₄×C₂₃	—	8	1	no	—
307	D₄×C₂₃	—	8	2	no	—
308	D₄×C₂₃	—	8	2	no	—
309	D₄×C₂₃	—	8	2	no	—
310	D₄×C₂₃	—	8	2	no	—
311	D₄×C₂₃	—	8	2	no	—
312	D₄×C₂₃	—	8	2	no	—
313	C₂×C₄×C₂₃	—	2	1	no	—
314	C₂×C₄×C₂₃	—	2	1	no	—
315	C₂×C₄×C₂₃	—	2	1	no	—
316	C₂×C₄×C₂₃	—	2	1	no	—
317	C₂×C₄×C₂₃	—	2	1	no	—
318	C₂×C₄×C₂₃	—	2	1	no	—
319	C₂×C₄×C₂₃	—	2	1	no	—
320	C₂×C₄×C₂₃	—	2	2	no	—
321	C₂×C₄×C₂₃	—	2	1	no	—
322	C₂×C₄×C₂₃	—	2	1	no	—
323	C₂×C₄×C₂₃	—	4	1	no	—
324	C₂×C₄×C₂₃	—	4	1	no	—
325	C₂×C₄×C₂₃	—	4	1	no	—
326	C₂×C₄×C₂₃	—	4	1	no	—
327	C₂×C₄×C₂₃	—	4	1	no	—
328	C₂×C₄×C₂₃	—	4	1	no	—
329	C₂×C₄×C₂₃	—	4	1	no	—
330	C₂×C₄×C₂₃	—	4	1	no	—
331	C₂×C₄×C₂₃	—	4	1	no	—
332	C₂×C₄×C₂₃	—	8	2	no	—
333	C₂×C₄×C₂₃	—	8	2	no	—
334	C₂×C₄×C₂₃	—	8	2	no	—
335	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
336	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
337	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
338	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
341	C₈×C₂₃	—	2	2	no	—
342	C₈×C₂₃	—	4	1	no	—
343	C₈×C₂₃	—	4	1	no	—
344	C₈×C₂₃	—	4	1	no	—
345	C₈×C₂₃	—	4	1	no	—
346	C₈×C₂₃	—	4	1	no	—
347	#3546	C₂×C₂₃	1	1	yes	characteristic
348	#3246	C₂×C₂₃	1	1	yes	characteristic, complemented
349	#3233	C₂×C₂₃	1	1	yes	characteristic, complemented
350	#3182	C₂×C₂₃	1	1	yes	characteristic, complemented
351	#1650	C₂×C₂₃	1	1	yes	characteristic, complemented
352	#1647	C₂×C₂₃	1	1	yes	characteristic, complemented
353	#1642	C₂×C₂₃	1	1	yes	characteristic, complemented
354	#1639	C₂×C₂₃	1	1	yes	characteristic, complemented
355	#1638	C₂×C₂₃	1	1	yes	characteristic, complemented
356	#1635	C₂×C₂₃	1	1	yes	characteristic, complemented
357	#1631	C₂×C₂₃	1	1	yes	characteristic, complemented
358	#1629	C₂×C₂₃	1	1	yes	characteristic, complemented
359	#1540	C₂×C₂₃	1	1	yes	characteristic, complemented
360	#1484	C₂×C₂₃	1	1	yes	characteristic, complemented
361	#1483	C₂×C₂₃	1	1	yes	characteristic, complemented
362	C₂²×C₂₃	—	2	1	no	—
363	C₂²×C₂₃	—	2	1	no	—
364	C₂²×C₂₃	—	2	1	no	—
365	C₂²×C₂₃	—	4	1	no	—
366	C₂²×C₂₃	—	4	1	no	—
367	C₂²×C₂₃	—	4	2	no	—
368	C₂²×C₂₃	—	4	1	no	—
369	C₂²×C₂₃	—	4	1	no	—
370	C₂²×C₂₃	—	4	1	no	—
371	C₂²×C₂₃	—	4	2	no	—
372	C₂²×C₂₃	—	4	1	no	—
373	C₂²×C₂₃	—	4	2	no	—
374	C₂²×C₂₃	—	4	1	no	—
375	C₂²×C₂₃	—	4	1	no	—
376	C₂²×C₂₃	—	4	1	no	—
377	C₂²×C₂₃	—	16	4	no	—
378	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
379	C₄×C₂₃	—	2	1	no	—
380	C₄×C₂₃	—	2	1	no	—
381	C₄×C₂₃	—	2	1	no	—
382	C₄×C₂₃	—	2	1	no	—
383	C₄×C₂₃	—	4	1	no	—
384	C₄×C₂₃	—	4	1	no	—
385	C₄×C₂₃	—	4	1	no	—
386	C₄×C₂₃	—	4	1	no	—
387	C₄×C₂₃	—	4	2	no	—
388	C₄×C₂₃	—	4	1	no	—
389	C₄×C₂₃	—	8	1	no	—
390	C₄×C₂₃	—	8	1	no	—
391	C₄×C₂₃	#576	1	1	yes	characteristic
392	C₄×C₂₃	#577	1	1	yes	characteristic
393	C₄×C₂₃	#577	1	1	yes	characteristic
394	C₄×C₂₃	#577	1	1	yes	characteristic
395	#560	—	2	2	no	—
396	#556	C₂²×C₂₃	1	1	yes	characteristic
397	#553	—	2	1	no	—
398	#550	—	2	1	no	—
399	#550	C₂²×C₂₃	1	1	yes	characteristic
400	#547	C₂²×C₂₃	1	1	yes	characteristic
401	#546	—	2	1	no	—
402	#546	—	2	1	no	—
403	D₄²	C₂²×C₂₃	1	1	yes	characteristic
404	#542	—	2	1	no	—
405	#538	—	2	2	no	—
406	#537	—	2	1	no	—
407	#535	—	2	1	no	—
408	#535	—	2	1	no	—
409	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
410	#532	C₂²×C₂₃	1	1	yes	characteristic
411	#532	C₂²×C₂₃	1	1	yes	characteristic
412	#529	C₂²×C₂₃	1	1	yes	characteristic
413	#500	C₂²×C₂₃	1	1	yes	characteristic, complemented
414	#499	—	2	1	no	—
415	#492	C₂²×C₂₃	1	1	yes	characteristic
416	#488	—	2	1	no	—
417	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
418	#486	C₂²×C₂₃	1	1	yes	characteristic
419	#485	—	2	1	no	—
420	#482	—	2	1	no	—
421	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
422	#476	C₂²×C₂₃	1	1	yes	characteristic
423	#476	C₂²×C₂₃	1	1	yes	characteristic
424	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
425	#475	—	2	1	no	—
426	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
427	#474	C₂²×C₂₃	1	1	yes	characteristic
428	#468	—	2	2	no	—
429	#465	—	2	1	no	—
430	#465	—	2	1	no	—
431	#461	C₂²×C₂₃	1	1	yes	characteristic
432	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
433	#460	—	2	1	no	—
434	#440	—	2	2	no	—
435	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
436	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
437	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
438	#332	C₂²×C₂₃	1	1	yes	characteristic, complemented
439	#332	C₂²×C₂₃	1	1	yes	characteristic, complemented
440	#331	C₂²×C₂₃	1	1	yes	characteristic
441	#331	C₂²×C₂₃	1	1	yes	characteristic
442	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
443	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
444	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
445	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
446	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
447	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
448	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
449	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
450	C₂×C₂₃	—	4	1	no	—
451	C₂×C₂₃	—	8	1	no	—
452	C₂×C₂₃	—	8	2	no	—
453	C₂×C₂₃	—	8	1	no	—
454	C₂×C₂₃	—	8	1	no	—
455	C₂×C₂₃	#3009	1	1	yes	characteristic
456	C₂×C₂₃	#3012	1	1	yes	characteristic
457	C₂×C₂₃	#3018	1	1	yes	characteristic
458	C₂×#41	—	2	1	no	—
459	C₂×#41	—	2	1	no	—
460	C₂×#41	—	2	1	no	—
461	C₂×#41	—	2	1	no	—
462	C₂²×D₄	—	2	1	no	—
463	C₂²×D₄	—	2	1	no	—
464	C₂×SD₁₆	—	2	2	no	—
465	C₂×SD₁₆	—	2	1	no	—
466	C₂×SD₁₆	—	2	1	no	—
467	C₂×M₁₆	—	2	1	no	—
468	C₂²×C₈	—	2	1	no	—
469	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
470	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
471	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
472	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
473	#127	—	2	2	no	—
474	#127	—	2	1	no	—
475	#127	D₄×C₂₃	1	1	yes	characteristic
476	#127	C₂³×C₂₃	1	1	yes	characteristic
477	#126	—	2	2	no	—
478	#126	—	2	2	no	—
479	#126	—	2	1	no	—
480	#125	—	2	1	no	—
481	#125	D₄×C₂₃	1	1	yes	characteristic
482	#124	—	2	2	no	—
483	#124	—	2	1	no	—
484	#124	—	2	1	no	—
485	#124	—	2	1	no	—
486	#124	D₄×C₂₃	1	1	yes	characteristic
487	#123	—	2	2	no	—
488	#123	—	2	2	no	—
489	#123	—	2	1	no	—
490	#123	—	2	2	no	—
491	C₂²⋊Q₈	—	2	2	no	—
492	C₂²⋊Q₈	—	2	1	no	—
493	C₂²⋊Q₈	—	2	1	no	—
494	C₂²⋊Q₈	—	2	1	no	—
495	C₂²⋊Q₈	—	2	1	no	—
496	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
497	#121	—	2	2	no	—
498	#121	—	2	2	no	—
499	#121	—	2	2	no	—
500	#121	—	2	2	no	—
501	#121	—	2	2	no	—
502	#121	—	2	1	no	—
503	#121	—	2	2	no	—
504	#121	—	2	1	no	—
505	#121	—	2	1	no	—
506	#121	—	2	1	no	—
507	#121	—	2	1	no	—
508	#121	—	2	1	no	—
509	#121	D₄×C₂₃	1	1	yes	characteristic
510	#121	D₄×C₂₃	1	1	yes	characteristic
511	#121	D₄×C₂₃	1	1	yes	characteristic
512	#121	D₄×C₂₃	1	2	yes	—
513	#120	—	2	2	no	—
514	#120	—	2	2	no	—
515	#120	—	2	2	no	—
516	#120	—	2	2	no	—
517	C₄×Q₈	—	2	1	no	—
518	C₄×Q₈	—	2	1	no	—
519	C₄×Q₈	—	2	1	no	—
520	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
521	C₄×D₄	—	2	2	no	—
522	C₄×D₄	—	2	1	no	—
523	C₄×D₄	—	2	1	no	—
524	C₄×D₄	—	2	1	no	—
525	C₄×D₄	—	2	1	no	—
526	C₄×D₄	D₄×C₂₃	1	2	yes	—
527	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
528	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
529	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
530	#117	—	2	1	no	—
531	#117	—	2	1	no	—
532	#117	—	2	1	no	—
533	C₂×C₄⋊C₄	—	2	1	no	—
534	C₂×C₂²⋊C₄	—	2	2	no	—
535	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
536	#107	—	2	2	no	—
537	#107	—	2	1	no	—
538	#107	—	2	1	no	—
539	#106	—	2	1	no	—
540	#106	—	2	1	no	—
541	#106	—	2	1	no	—
542	#106	—	2	1	no	—
543	C₄⋊C₈	—	2	1	no	—
544	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
545	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
546	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
547	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
548	#103	—	2	1	no	—
549	#103	—	2	1	no	—
550	#103	—	2	2	no	—
551	#103	—	2	1	no	—
552	#103	—	2	1	no	—
553	#102	—	2	2	no	—
554	#102	—	2	1	no	—
555	#102	—	2	1	no	—
556	#102	—	2	1	no	—
557	#102	—	2	1	no	—
558	C₂²⋊C₈	—	2	1	no	—
559	#97	—	2	1	no	—
560	C₄×C₈	—	2	1	no	—
561	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
562	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
563	C₂₃	#18739	1	1	yes	characteristic, direct product factor, Sylow
564	C₂⁴	—	2	2	no	—
565	#41	—	8	1	no	—
566	#41	—	8	1	no	—
567	#41	—	8	1	no	—
568	#41	—	8	1	no	—
569	#41	—	8	1	no	—
570	#41	—	8	1	no	—
571	#41	—	8	1	no	—
572	#41	—	8	1	no	—
573	C₂×Q₈	—	2	1	no	—
574	C₂×Q₈	—	2	1	no	—
575	C₂×Q₈	—	2	1	no	—
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	1	no	—
584	C₂×D₄	—	2	1	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	8	1	no	—
592	C₂×D₄	—	8	1	no	—
593	C₂×D₄	—	8	1	no	—
594	C₂×D₄	—	8	1	no	—
595	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
596	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
597	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
598	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
606	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
607	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
608	SD₁₆	—	4	4	no	—
609	SD₁₆	—	8	1	no	—
610	SD₁₆	—	8	1	no	—
611	M₁₆	—	4	2	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	—	2	1	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	8	1	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	4	1	no	—
632	C₄⋊C₄	—	4	1	no	—
633	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
634	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
635	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
636	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
637	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	1	no	—
644	C₂²⋊C₄	—	2	1	no	—
645	C₂²⋊C₄	—	2	1	no	—
646	C₂²⋊C₄	—	2	1	no	—
647	C₂²⋊C₄	—	2	1	no	—
648	C₂²⋊C₄	—	2	1	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	1	no	—
652	C₂²⋊C₄	—	2	1	no	—
653	C₂²⋊C₄	—	2	1	no	—
654	C₂²⋊C₄	—	4	1	no	—
655	C₄²	—	2	2	no	—
656	C₄²	—	2	1	no	—
657	C₄²	—	4	1	no	—
658	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
659	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
660	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
661	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
662	C₂³	—	2	1	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	8	2	no	—
667	C₂³	—	8	2	no	—
668	C₂³	—	8	2	no	—
669	C₂³	C₂₃×#120	1	1	yes	characteristic
670	Q₈	—	2	1	no	—
671	Q₈	—	2	1	no	—
672	Q₈	—	4	2	no	—
673	Q₈	—	4	1	no	—
674	Q₈	—	4	1	no	—
675	Q₈	—	4	1	no	—
676	Q₈	—	4	1	no	—
677	Q₈	—	8	1	no	—
678	D₄	—	2	1	no	—
679	D₄	—	2	1	no	—
680	D₄	—	2	1	no	—
681	D₄	—	2	1	no	—
682	D₄	—	2	1	no	—
683	D₄	—	2	1	no	—
684	D₄	—	4	2	no	—
685	D₄	—	4	1	no	—
686	D₄	—	4	1	no	—
687	D₄	—	4	1	no	—
688	D₄	—	4	1	no	—
689	D₄	—	8	1	no	—
690	D₄	—	8	1	no	—
691	D₄	—	8	1	no	—
692	D₄	—	8	1	no	—
693	D₄	—	8	2	no	—
694	D₄	—	8	1	no	—
695	D₄	—	8	2	no	—
696	D₄	—	8	2	no	—
697	D₄	—	8	2	no	—
698	D₄	—	8	2	no	—
699	D₄	—	8	2	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	8	2	no	—
720	C₂×C₄	—	8	2	no	—
721	C₂×C₄	—	8	2	no	—
722	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
723	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
724	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
725	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
726	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
727	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
728	C₈	—	2	2	no	—
729	C₈	—	4	1	no	—
730	C₈	—	4	1	no	—
731	C₈	—	4	1	no	—
732	C₈	—	4	1	no	—
733	C₈	—	4	1	no	—
734	C₂²	—	2	1	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	1	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	1	no	—
741	C₂²	—	4	1	no	—
742	C₂²	—	4	1	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	4	1	no	—
748	C₂²	—	4	1	no	—
749	C₂²	—	16	4	no	—
750	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
751	C₄	—	2	1	no	—
752	C₄	—	2	1	no	—
753	C₄	—	2	1	no	—
754	C₄	—	2	1	no	—
755	C₄	—	4	1	no	—
756	C₄	—	4	1	no	—
757	C₄	—	4	1	no	—
758	C₄	—	4	1	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	1	no	—
761	C₄	—	8	1	no	—
762	C₄	—	8	1	no	—
763	C₄	C₂₃×#576	1	1	yes	characteristic
764	C₄	C₂₃×#577	1	1	yes	characteristic
765	C₄	C₂₃×#577	1	1	yes	characteristic
766	C₄	C₂₃×#577	1	1	yes	characteristic
767	C₂	—	4	1	no	—
768	C₂	—	8	1	no	—
769	C₂	—	8	1	no	—
770	C₂	—	8	2	no	—
771	C₂	—	8	1	no	—
772	C₂	C₂₃×#3009	1	1	yes	characteristic
773	C₂	C₂₃×#3012	1	1	yes	characteristic
774	C₂	C₂₃×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
prime radical	C₂₃×#3546	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#3246	C₂	semidirect
3. C₂₃×#3233	C₂	semidirect
4. C₂₃×#3182	C₂	semidirect
5. C₂₃×#1650	C₂	semidirect
6. C₂₃×#1647	C₂	semidirect
7. C₂₃×#1642	C₂	semidirect
8. C₂₃×#1639	C₂	semidirect
9. C₂₃×#1638	C₂	semidirect
10. C₂₃×#1635	C₂	semidirect
11. C₂₃×#1631	C₂	semidirect
12. C₂₃×#1629	C₂	semidirect
13. C₂₃×#1540	C₂	semidirect
14. C₂₃×#1484	C₂	semidirect
15. C₂₃×#1483	C₂	semidirect
30. C₂₃×#533	C₂²	semidirect
34. C₂₃×#500	C₂²	semidirect
38. C₂₃×#487	C₂²	semidirect
42. C₂₃×#477	C₂²	semidirect
45. C₂₃×#476	C₂²	semidirect
47. C₂₃×#475	C₂²	semidirect
53. C₂₃×#461	C₂²	semidirect
56. C₂₃×#431	C₂²	semidirect
57. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
58. C₄×M₁₆×C₂₃	C₂²	semidirect
59. C₂₃×#332	C₂²	semidirect
60. C₂₃×#332	C₂²	semidirect
63. C₂₃×Q₈⋊C₈	C₂²	semidirect
64. C₂₃×Q₈⋊C₈	C₂²	semidirect
69. C₂₃×D₄⋊C₈	C₂²	semidirect
70. C₂₃×D₄⋊C₈	C₂²	semidirect
274. #18739	C₂₃	direct (N × H)
348. #3246	C₂×C₂₃	semidirect
349. #3233	C₂×C₂₃	semidirect
350. #3182	C₂×C₂₃	semidirect
351. #1650	C₂×C₂₃	semidirect
352. #1647	C₂×C₂₃	semidirect
353. #1642	C₂×C₂₃	semidirect
354. #1639	C₂×C₂₃	semidirect
355. #1638	C₂×C₂₃	semidirect
356. #1635	C₂×C₂₃	semidirect
357. #1631	C₂×C₂₃	semidirect
358. #1629	C₂×C₂₃	semidirect
359. #1540	C₂×C₂₃	semidirect
360. #1484	C₂×C₂₃	semidirect
361. #1483	C₂×C₂₃	semidirect
409. #533	C₂²×C₂₃	semidirect
413. #500	C₂²×C₂₃	semidirect
417. #487	C₂²×C₂₃	semidirect
421. #477	C₂²×C₂₃	semidirect
424. #476	C₂²×C₂₃	semidirect
426. #475	C₂²×C₂₃	semidirect
432. #461	C₂²×C₂₃	semidirect
435. #431	C₂²×C₂₃	semidirect
436. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
437. C₄×M₁₆	C₂²×C₂₃	semidirect
438. #332	C₂²×C₂₃	semidirect
439. #332	C₂²×C₂₃	semidirect
442. Q₈⋊C₈	C₂²×C₂₃	semidirect
443. Q₈⋊C₈	C₂²×C₂₃	semidirect
448. D₄⋊C₈	C₂²×C₂₃	semidirect
449. D₄⋊C₈	C₂²×C₂₃	semidirect
563. C₂₃	#18739	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×#3546	2
C₂₃×#3246	2
C₂₃×#3233	2
C₂₃×#3182	2
C₂₃×#1650	2
C₂₃×#1647	2
C₂₃×#1642	2
C₂₃×#1639	2
C₂₃×#1638	2
C₂₃×#1635	2
C₂₃×#1631	2
C₂₃×#1629	2
C₂₃×#1540	2
C₂₃×#1484	2
C₂₃×#1483	2
#18739	23

Subgroups — C23×#18739 #19166365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#18739 #19166365