Subgroups — C₂₃×#8953 #19156579

Order 5888.

514 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2988	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₃×#137	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1479	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1476	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#1283	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1278	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#137	C₄	1	1	yes	characteristic
9	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
11	C₈×Q₈×C₂₃	—	2	1	no	—
12	C₂₃×#441	—	2	1	no	—
13	C₂₃×#440	—	2	1	no	—
14	C₄×Q₁₆×C₂₃	—	2	1	no	—
15	C₄×SD₁₆×C₂₃	—	2	1	no	—
16	C₈×D₄×C₂₃	—	2	2	no	—
17	C₈×D₄×C₂₃	—	2	1	no	—
18	C₂₃×#431	—	2	1	no	—
19	C₂₃×#431	C₂²	1	1	yes	characteristic
20	C₂₃×#431	C₂²	1	1	yes	characteristic
21	C₂₃×#428	C₄	1	1	yes	characteristic
22	C₂×C₂₃×C₄⋊C₈	—	2	1	no	—
23	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂₃×#419	C₄	1	1	yes	characteristic
25	C₂₃×#417	C₄	1	1	yes	characteristic
26	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
28	C₂₃×#336	—	2	2	no	—
29	C₂₃×Q₈⋊C₈	—	2	1	no	—
30	C₂₃×Q₈⋊C₈	—	2	1	no	—
31	C₂₃×Q₈⋊C₈	—	2	1	no	—
32	C₂₃×D₄⋊C₈	—	2	1	no	—
33	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
35	C₂₃×#137	—	2	2	no	—
36	C₂₃×#137	C₈	1	4	yes	complemented
37	C₂×Q₁₆×C₂₃	—	2	1	no	—
38	C₂×SD₁₆×C₂₃	—	2	1	no	—
39	C₂×M₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
40	C₂×M₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₂₃	—	2	1	no	—
42	C₂²×C₈×C₂₃	—	2	2	no	—
43	C₂²×C₈×C₂₃	D₄	1	2	yes	—
44	C₄×Q₈×C₂₃	—	2	1	no	—
45	C₄×Q₈×C₂₃	—	2	1	no	—
46	C₄×Q₈×C₂₃	—	2	1	no	—
47	C₄×Q₈×C₂₃	—	2	1	no	—
48	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
49	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
50	C₄×D₄×C₂₃	—	2	1	no	—
51	C₄×D₄×C₂₃	—	2	1	no	—
52	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
53	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
54	C₂₃×#117	—	2	1	no	—
55	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
57	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₂₃	—	2	1	no	—
59	C₂×C₄²×C₂₃	—	2	1	no	—
60	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
61	C₂₃×#107	—	2	1	no	—
62	C₂₃×#106	—	2	1	no	—
63	C₂₃×C₄⋊C₈	—	2	2	no	—
64	C₂₃×C₄⋊C₈	—	2	1	no	—
65	C₂₃×C₄⋊C₈	—	2	1	no	—
66	C₂₃×C₄⋊C₈	—	2	1	no	—
67	C₂₃×C₄⋊C₈	D₄	1	1	yes	characteristic
68	C₂₃×C₄⋊C₈	D₄	1	1	yes	characteristic
69	C₂₃×#103	—	2	1	no	—
70	C₂₃×#103	—	2	1	no	—
71	C₂₃×#103	—	2	1	no	—
72	C₂₃×#102	—	2	1	no	—
73	C₂₃×C₂²⋊C₈	—	2	2	no	—
74	C₂₃×C₂²⋊C₈	—	2	1	no	—
75	C₂₃×C₂²⋊C₈	—	2	1	no	—
76	C₂₃×#97	—	2	1	no	—
77	C₄×C₈×C₂₃	—	2	2	no	—
78	C₄×C₈×C₂₃	—	2	1	no	—
79	C₄×C₈×C₂₃	—	2	1	no	—
80	C₄×C₈×C₂₃	—	2	1	no	—
81	C₄×C₈×C₂₃	—	2	1	no	—
82	C₄×C₈×C₂₃	—	2	1	no	—
83	#41×C₂₃	—	2	1	no	—
84	#41×C₂₃	—	2	1	no	—
85	#41×C₂₃	C₂×C₈	1	2	yes	—
86	#41×C₂₃	M₁₆	1	2	yes	—
87	C₂×Q₈×C₂₃	—	2	1	no	—
88	C₂×Q₈×C₂₃	—	2	1	no	—
89	C₂×Q₈×C₂₃	—	2	1	no	—
90	C₂×Q₈×C₂₃	—	2	1	no	—
91	C₂×Q₈×C₂₃	—	2	1	no	—
92	C₂×Q₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×Q₈×C₂₃	C₂×C₈	1	2	yes	complemented
94	C₂×D₄×C₂₃	—	2	1	no	—
95	C₂×D₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₂₃	—	2	1	no	—
97	C₂²×C₄×C₂₃	—	2	1	no	—
98	C₂²×C₄×C₂₃	—	2	1	no	—
99	C₂²×C₄×C₂₃	—	2	1	no	—
100	C₂²×C₄×C₂₃	—	2	1	no	—
101	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
104	Q₁₆×C₂₃	—	2	4	no	—
105	SD₁₆×C₂₃	—	2	4	no	—
106	M₁₆×C₂₃	—	2	1	no	—
107	M₁₆×C₂₃	—	2	1	no	—
108	M₁₆×C₂₃	—	2	1	no	—
109	M₁₆×C₂₃	C₂×C₈	1	2	yes	complemented
110	C₂×C₈×C₂₃	—	2	1	no	—
111	C₂×C₈×C₂₃	—	2	2	no	—
112	C₂×C₈×C₂₃	—	2	1	no	—
113	C₂×C₈×C₂₃	—	2	2	no	—
114	C₂×C₈×C₂₃	—	2	1	no	—
115	C₂×C₈×C₂₃	—	2	1	no	—
116	C₂×C₈×C₂₃	—	4	1	no	—
117	C₂×C₈×C₂₃	—	4	1	no	—
118	C₂×C₈×C₂₃	—	4	2	no	—
119	C₂×C₈×C₂₃	—	4	1	no	—
120	C₂×C₈×C₂₃	—	8	2	no	—
121	C₄⋊C₄×C₂₃	—	2	1	no	—
122	C₄⋊C₄×C₂₃	—	2	1	no	—
123	C₄⋊C₄×C₂₃	—	2	1	no	—
124	C₄⋊C₄×C₂₃	—	2	1	no	—
125	C₄⋊C₄×C₂₃	—	4	1	no	—
126	C₄⋊C₄×C₂₃	—	4	1	no	—
127	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
128	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²⋊C₄×C₂₃	—	2	1	no	—
130	C₂²⋊C₄×C₂₃	—	2	1	no	—
131	C₂²⋊C₄×C₂₃	—	2	1	no	—
132	C₄²×C₂₃	—	2	1	no	—
133	C₄²×C₂₃	—	2	1	no	—
134	C₄²×C₂₃	—	2	1	no	—
135	C₄²×C₂₃	—	4	1	no	—
136	C₄²×C₂₃	—	4	1	no	—
137	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₂₃	#41	1	1	yes	characteristic
141	#8953	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂³×C₂₃	—	2	1	no	—
143	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
144	Q₈×C₂₃	—	2	1	no	—
145	Q₈×C₂₃	—	2	2	no	—
146	Q₈×C₂₃	—	2	2	no	—
147	Q₈×C₂₃	—	4	1	no	—
148	Q₈×C₂₃	—	4	1	no	—
149	Q₈×C₂₃	C₂²⋊C₈	1	2	yes	—
150	D₄×C₂₃	—	2	2	no	—
151	D₄×C₂₃	—	2	2	no	—
152	D₄×C₂₃	—	2	1	no	—
153	D₄×C₂₃	C₂²⋊C₈	1	2	yes	—
154	C₂×C₄×C₂₃	—	2	1	no	—
155	C₂×C₄×C₂₃	—	2	2	no	—
156	C₂×C₄×C₂₃	—	2	2	no	—
157	C₂×C₄×C₂₃	—	2	1	no	—
158	C₂×C₄×C₂₃	—	2	1	no	—
159	C₂×C₄×C₂₃	—	2	1	no	—
160	C₂×C₄×C₂₃	—	2	1	no	—
161	C₂×C₄×C₂₃	—	2	2	no	—
162	C₂×C₄×C₂₃	—	4	1	no	—
163	C₂×C₄×C₂₃	—	4	1	no	—
164	C₂×C₄×C₂₃	—	4	1	no	—
165	C₂×C₄×C₂₃	—	4	1	no	—
166	C₂×C₄×C₂₃	—	4	1	no	—
167	C₂×C₄×C₂₃	—	4	2	no	—
168	C₂×C₄×C₂₃	—	4	1	no	—
169	C₂×C₄×C₂₃	—	8	1	no	—
170	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
173	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
174	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
175	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
176	C₂×C₄×C₂₃	C₂²×C₈	1	1	yes	characteristic
177	C₂×C₄×C₂₃	C₂×M₁₆	1	1	yes	characteristic
178	C₂×C₄×C₂₃	#131	1	1	yes	characteristic
179	C₂×C₄×C₂₃	#131	1	1	yes	characteristic
180	C₈×C₂₃	—	2	2	no	—
181	C₈×C₂₃	—	4	2	no	—
182	C₈×C₂₃	—	4	1	no	—
183	C₈×C₂₃	—	4	2	no	—
184	C₈×C₂₃	—	4	1	no	—
185	C₈×C₂₃	—	4	1	no	—
186	C₈×C₂₃	—	8	1	no	—
187	#2988	C₂×C₂₃	1	1	yes	characteristic
188	C₄×#137	C₂×C₂₃	1	1	yes	characteristic
189	#1984	C₂×C₂₃	1	1	yes	characteristic, complemented
190	#1479	C₂×C₂₃	1	1	yes	characteristic, complemented
191	#1476	C₂×C₂₃	1	1	yes	characteristic
192	#1283	C₂×C₂₃	1	1	yes	characteristic, complemented
193	#1278	C₂×C₂₃	1	1	yes	characteristic, complemented
194	C₂²×C₂₃	—	2	1	no	—
195	C₂²×C₂₃	—	2	1	no	—
196	C₂²×C₂₃	—	2	2	no	—
197	C₂²×C₂₃	—	4	1	no	—
198	C₂²×C₂₃	—	4	1	no	—
199	C₂²×C₂₃	#386	1	1	yes	characteristic
200	C₂²×C₂₃	C₈×D₄	1	1	yes	characteristic
201	C₂²×C₂₃	#435	1	1	yes	characteristic
202	C₄×C₂₃	—	2	2	no	—
203	C₄×C₂₃	—	2	1	no	—
204	C₄×C₂₃	—	2	1	no	—
205	C₄×C₂₃	—	2	1	no	—
206	C₄×C₂₃	—	4	2	no	—
207	C₄×C₂₃	—	4	1	no	—
208	C₄×C₂₃	—	4	1	no	—
209	C₄×C₂₃	—	8	1	no	—
210	C₄×C₂₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
211	C₄×C₂₃	#408	1	1	yes	characteristic
212	C₄×C₂₃	C₈×D₄	1	1	yes	characteristic
213	C₄×C₂₃	#435	1	1	yes	characteristic
214	C₄×C₂₃	#455	1	1	yes	characteristic
215	C₄×C₂₃	#456	1	1	yes	characteristic
216	C₂×#137	C₄×C₂₃	1	1	yes	characteristic
217	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
218	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
219	C₈×Q₈	—	2	1	no	—
220	#441	—	2	1	no	—
221	#440	—	2	1	no	—
222	C₄×Q₁₆	—	2	1	no	—
223	C₄×SD₁₆	—	2	1	no	—
224	C₈×D₄	—	2	2	no	—
225	C₈×D₄	—	2	1	no	—
226	#431	—	2	1	no	—
227	#431	C₂²×C₂₃	1	1	yes	characteristic
228	#431	C₂²×C₂₃	1	1	yes	characteristic
229	#428	C₄×C₂₃	1	1	yes	characteristic
230	C₂×C₄⋊C₈	—	2	1	no	—
231	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
232	#419	C₄×C₂₃	1	1	yes	characteristic
233	#417	C₄×C₂₃	1	1	yes	characteristic
234	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
235	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
236	#336	—	2	2	no	—
237	Q₈⋊C₈	—	2	1	no	—
238	Q₈⋊C₈	—	2	1	no	—
239	Q₈⋊C₈	—	2	1	no	—
240	D₄⋊C₈	—	2	1	no	—
241	C₂×C₂₃	—	2	1	no	—
242	C₂×C₂₃	—	2	1	no	—
243	C₂×C₂₃	—	4	2	no	—
244	C₂×C₂₃	#1869	1	1	yes	characteristic
245	C₂×C₂₃	#1881	1	1	yes	characteristic
246	C₂×C₂₃	#1882	1	1	yes	characteristic
247	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
248	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
249	#137	—	2	2	no	—
250	#137	C₈×C₂₃	1	4	yes	complemented
251	C₂×Q₁₆	—	2	1	no	—
252	C₂×SD₁₆	—	2	1	no	—
253	C₂×M₁₆	C₂×C₄×C₂₃	1	1	yes	characteristic
254	C₂×M₁₆	C₂×C₄×C₂₃	1	1	yes	characteristic
255	C₂²×C₈	—	2	1	no	—
256	C₂²×C₈	—	2	2	no	—
257	C₂²×C₈	D₄×C₂₃	1	2	yes	—
258	C₄×Q₈	—	2	1	no	—
259	C₄×Q₈	—	2	1	no	—
260	C₄×Q₈	—	2	1	no	—
261	C₄×Q₈	—	2	1	no	—
262	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
263	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
267	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
268	#117	—	2	1	no	—
269	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
275	#107	—	2	1	no	—
276	#106	—	2	1	no	—
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	—	2	1	no	—
281	C₄⋊C₈	D₄×C₂₃	1	1	yes	characteristic
282	C₄⋊C₈	D₄×C₂₃	1	1	yes	characteristic
283	#103	—	2	1	no	—
284	#103	—	2	1	no	—
285	#103	—	2	1	no	—
286	#102	—	2	1	no	—
287	C₂²⋊C₈	—	2	2	no	—
288	C₂²⋊C₈	—	2	1	no	—
289	C₂²⋊C₈	—	2	1	no	—
290	#97	—	2	1	no	—
291	C₄×C₈	—	2	2	no	—
292	C₄×C₈	—	2	1	no	—
293	C₄×C₈	—	2	1	no	—
294	C₄×C₈	—	2	1	no	—
295	C₄×C₈	—	2	1	no	—
296	C₄×C₈	—	2	1	no	—
297	C₂₃	#8953	1	1	yes	characteristic, direct product factor, Sylow
298	#41	—	2	1	no	—
299	#41	—	2	1	no	—
300	#41	C₂×C₈×C₂₃	1	2	yes	—
301	#41	M₁₆×C₂₃	1	2	yes	—
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	2	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
308	C₂×Q₈	C₂×C₈×C₂₃	1	2	yes	complemented
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
318	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
319	Q₁₆	—	2	4	no	—
320	SD₁₆	—	2	4	no	—
321	M₁₆	—	2	1	no	—
322	M₁₆	—	2	1	no	—
323	M₁₆	—	2	1	no	—
324	M₁₆	C₂×C₈×C₂₃	1	2	yes	complemented
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	2	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	8	2	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	—	4	1	no	—
342	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
343	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
344	C₂²⋊C₄	—	2	1	no	—
345	C₂²⋊C₄	—	2	1	no	—
346	C₂²⋊C₄	—	2	1	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	2	1	no	—
350	C₄²	—	4	1	no	—
351	C₄²	—	4	1	no	—
352	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
353	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
354	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
355	C₄²	#41×C₂₃	1	1	yes	characteristic
356	C₂³	—	2	1	no	—
357	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
358	Q₈	—	2	1	no	—
359	Q₈	—	2	2	no	—
360	Q₈	—	2	2	no	—
361	Q₈	—	4	1	no	—
362	Q₈	—	4	1	no	—
363	Q₈	C₂₃×C₂²⋊C₈	1	2	yes	—
364	D₄	—	2	2	no	—
365	D₄	—	2	2	no	—
366	D₄	—	2	1	no	—
367	D₄	C₂₃×C₂²⋊C₈	1	2	yes	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	8	1	no	—
384	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
385	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
386	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
387	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
388	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
389	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
390	C₂×C₄	C₂²×C₈×C₂₃	1	1	yes	characteristic
391	C₂×C₄	C₂×M₁₆×C₂₃	1	1	yes	characteristic
392	C₂×C₄	C₂₃×#131	1	1	yes	characteristic
393	C₂×C₄	C₂₃×#131	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	—	4	2	no	—
396	C₈	—	4	1	no	—
397	C₈	—	4	2	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	1	no	—
400	C₈	—	8	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	C₂₃×#386	1	1	yes	characteristic
407	C₂²	C₈×D₄×C₂₃	1	1	yes	characteristic
408	C₂²	C₂₃×#435	1	1	yes	characteristic
409	C₄	—	2	2	no	—
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	1	no	—
415	C₄	—	4	1	no	—
416	C₄	—	8	1	no	—
417	C₄	C₂×C₂₃×C₂²⋊C₈	1	1	yes	characteristic
418	C₄	C₂₃×#408	1	1	yes	characteristic
419	C₄	C₈×D₄×C₂₃	1	1	yes	characteristic
420	C₄	C₂₃×#435	1	1	yes	characteristic
421	C₄	C₂₃×#455	1	1	yes	characteristic
422	C₄	C₂₃×#456	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	2	1	no	—
425	C₂	—	4	2	no	—
426	C₂	C₂₃×#1869	1	1	yes	characteristic
427	C₂	C₂₃×#1881	1	1	yes	characteristic
428	C₂	C₂₃×#1882	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	#120
commutator	C₂×C₄	C₂²×C₈×C₂₃
Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
socle	C₂²×C₂₃	#386
prime radical	C₂×#41×C₂₃	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₃×#1984	C₂	semidirect
4. C₂₃×#1479	C₂	semidirect
6. C₂₃×#1283	C₂	semidirect
7. C₂₃×#1278	C₂	semidirect
36. C₂₃×#137	C₈	semidirect
93. C₂×Q₈×C₂₃	C₂×C₈	semidirect
109. M₁₆×C₂₃	C₂×C₈	semidirect
141. #8953	C₂₃	direct (N × H)
189. #1984	C₂×C₂₃	semidirect
190. #1479	C₂×C₂₃	semidirect
192. #1283	C₂×C₂₃	semidirect
193. #1278	C₂×C₂₃	semidirect
250. #137	C₈×C₂₃	semidirect
297. C₂₃	#8953	direct (N × H)
308. C₂×Q₈	C₂×C₈×C₂₃	semidirect
324. M₁₆	C₂×C₈×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#2988	2
C₄×C₂₃×#137	2
C₂₃×#1984	2
C₂₃×#1479	2
C₂₃×#1476	2
C₂₃×#1283	2
C₂₃×#1278	2
#8953	23

Subgroups — C23×#8953 #19156579

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#8953 #19156579