Subgroups — C₂₃×#21041 #19168667

Order 5888.

798 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2911	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#424	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#405	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1922	C₂	1	8	yes	maximal, complemented
5	C₂₃×#1738	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#1733	C₂	1	1	yes	maximal, characteristic
7	C₂₃×#1733	C₂	1	1	yes	maximal, characteristic
8	C₂₃×#1729	C₂	1	1	yes	maximal, characteristic
9	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
13	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
16	C₂₃×#428	C₄	1	4	yes	complemented
17	C₂₃×#428	C₄	1	4	yes	complemented
18	C₂₃×#427	C₂²	1	4	yes	—
19	C₂₃×#424	—	2	1	no	—
20	C₂₃×#424	—	2	1	no	—
21	C₂₃×#424	C₂²	1	4	yes	—
22	C₂×C₂₃×C₄⋊C₈	—	2	2	no	—
23	C₂₃×#405	—	2	2	no	—
24	C₂₃×#405	C₂²	1	4	yes	—
25	C₂×C₂₃×#97	—	2	1	no	—
26	C₂×C₄×C₈×C₂₃	—	2	1	no	—
27	C₂₃×#341	C₂²	1	4	yes	—
28	C₂₃×#339	C₂²	1	4	yes	—
29	C₂₃×#339	C₂²	1	4	yes	—
30	C₂₃×#336	C₂²	1	4	yes	—
31	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
32	C₂×M₁₆×C₂₃	—	2	1	no	—
33	C₂×M₁₆×C₂₃	—	2	2	no	—
34	C₂×M₁₆×C₂₃	—	2	2	no	—
35	C₂×M₁₆×C₂₃	—	2	2	no	—
36	C₂×M₁₆×C₂₃	—	2	1	no	—
37	C₂×M₁₆×C₂₃	—	2	2	no	—
38	C₂×M₁₆×C₂₃	—	2	2	no	—
39	C₂×M₁₆×C₂₃	C₂×C₄	1	2	yes	—
40	C₂×M₁₆×C₂₃	C₂×C₄	1	2	yes	—
41	C₂×M₁₆×C₂₃	Q₈	1	4	yes	—
42	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
43	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
44	C₂²×C₈×C₂₃	—	2	1	no	—
45	C₂²×C₈×C₂₃	—	2	2	no	—
46	C₂²×C₈×C₂₃	—	2	2	no	—
47	C₂²×C₈×C₂₃	—	2	1	no	—
48	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
49	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₂₃	D₄	1	2	yes	—
51	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
53	C₂₃×#117	—	2	1	no	—
54	C₂₃×#117	—	2	1	no	—
55	C₂₃×#117	—	2	1	no	—
56	C₂₃×#117	—	2	1	no	—
57	C₂₃×#117	—	2	2	no	—
58	C₂₃×#117	—	2	2	no	—
59	C₂₃×#117	C₂×C₄	1	2	yes	—
60	C₂₃×#117	C₂×C₄	1	2	yes	—
61	C₂₃×#117	C₂³	1	2	yes	—
62	C₂₃×#117	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
66	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
69	C₂×C₄²×C₂₃	—	2	1	no	—
70	C₂×C₄²×C₂₃	—	2	1	no	—
71	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
72	C₂₃×#107	C₂×C₄	1	8	yes	—
73	C₂₃×#106	C₂×C₄	1	8	yes	—
74	C₂₃×C₄⋊C₈	—	2	4	no	—
75	C₂₃×C₄⋊C₈	—	2	4	no	—
76	C₂₃×#97	—	2	4	no	—
77	C₄×C₈×C₂₃	—	2	4	no	—
78	C₂⁴×C₂₃	#41	1	1	yes	characteristic
79	C₂²×C₄×C₂₃	—	2	2	no	—
80	C₂²×C₄×C₂₃	—	2	2	no	—
81	C₂²×C₄×C₂₃	—	2	2	no	—
82	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₂₃	C₂×Q₈	1	2	yes	—
87	C₂²×C₄×C₂₃	#41	1	2	yes	—
88	C₂²×C₄×C₂₃	#41	1	2	yes	—
89	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
90	C₂²×C₄×C₂₃	#41	1	2	yes	—
91	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
92	M₁₆×C₂₃	—	2	4	no	—
93	M₁₆×C₂₃	—	2	4	no	—
94	M₁₆×C₂₃	—	2	4	no	—
95	M₁₆×C₂₃	—	2	2	no	—
96	M₁₆×C₂₃	—	2	2	no	—
97	M₁₆×C₂₃	—	2	2	no	—
98	M₁₆×C₂₃	—	4	2	no	—
99	M₁₆×C₂₃	C₂×Q₈	1	4	yes	—
100	C₂×C₈×C₂₃	—	2	4	no	—
101	C₂×C₈×C₂₃	—	2	4	no	—
102	C₂×C₈×C₂₃	—	2	2	no	—
103	C₂×C₈×C₂₃	—	2	2	no	—
104	C₂×C₈×C₂₃	—	2	2	no	—
105	C₂×C₈×C₂₃	—	2	2	no	—
106	C₂×C₈×C₂₃	—	2	2	no	—
107	C₂×C₈×C₂₃	—	2	2	no	—
108	C₂×C₈×C₂₃	—	2	2	no	—
109	C₂×C₈×C₂₃	—	2	2	no	—
110	C₂×C₈×C₂₃	—	4	2	no	—
111	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
112	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
114	C₄⋊C₄×C₂₃	—	2	2	no	—
115	C₄⋊C₄×C₂₃	—	2	2	no	—
116	C₄⋊C₄×C₂₃	—	4	2	no	—
117	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
118	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
119	C₂²⋊C₄×C₂₃	—	2	2	no	—
120	C₂²⋊C₄×C₂₃	—	2	2	no	—
121	C₂²⋊C₄×C₂₃	—	2	2	no	—
122	C₂²⋊C₄×C₂₃	—	2	2	no	—
123	C₂²⋊C₄×C₂₃	—	4	2	no	—
124	C₄²×C₂₃	—	2	2	no	—
125	C₄²×C₂₃	—	2	2	no	—
126	C₄²×C₂₃	—	2	2	no	—
127	C₄²×C₂₃	—	2	2	no	—
128	C₄²×C₂₃	—	2	2	no	—
129	C₄²×C₂₃	—	2	2	no	—
130	#21041	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂³×C₂₃	—	4	2	no	—
132	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
133	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
134	C₂³×C₂₃	#125	1	2	yes	—
135	C₂³×C₂₃	#126	1	2	yes	—
136	C₂³×C₂₃	C₂×#41	1	1	yes	characteristic
137	C₂×C₄×C₂₃	—	2	4	no	—
138	C₂×C₄×C₂₃	—	2	4	no	—
139	C₂×C₄×C₂₃	—	4	4	no	—
140	C₂×C₄×C₂₃	—	4	4	no	—
141	C₂×C₄×C₂₃	—	4	4	no	—
142	C₂×C₄×C₂₃	—	4	2	no	—
143	C₂×C₄×C₂₃	#117	1	2	yes	—
144	C₂×C₄×C₂₃	#117	1	2	yes	—
145	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₂₃	C₄×Q₈	1	2	yes	—
148	C₂×C₄×C₂₃	C₄×Q₈	1	2	yes	—
149	C₂×C₄×C₂₃	C₂²⋊Q₈	1	2	yes	—
150	C₂×C₄×C₂₃	C₂²⋊Q₈	1	2	yes	—
151	C₂×C₄×C₂₃	#123	1	2	yes	—
152	C₂×C₄×C₂₃	#123	1	2	yes	—
153	C₂×C₄×C₂₃	#125	1	2	yes	—
154	C₂×C₄×C₂₃	#126	1	2	yes	—
155	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₂₃	C₂²×Q₈	1	1	yes	characteristic
158	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
161	C₈×C₂₃	—	2	4	no	—
162	C₈×C₂₃	—	2	4	no	—
163	C₈×C₂₃	—	2	2	no	—
164	C₈×C₂₃	—	2	2	no	—
165	C₈×C₂₃	—	4	2	no	—
166	#2911	C₂×C₂₃	1	1	yes	characteristic
167	C₂×#424	C₂×C₂₃	1	1	yes	characteristic
168	C₂×#405	C₂×C₂₃	1	1	yes	characteristic
169	#1922	C₂×C₂₃	1	8	yes	complemented
170	#1738	C₂×C₂₃	1	1	yes	characteristic
171	#1733	C₂×C₂₃	1	1	yes	characteristic
172	#1733	C₂×C₂₃	1	1	yes	characteristic
173	#1729	C₂×C₂₃	1	1	yes	characteristic
174	C₂²×C₂₃	—	2	2	no	—
175	C₂²×C₂₃	—	2	2	no	—
176	C₂²×C₂₃	—	2	2	no	—
177	C₂²×C₂₃	—	4	2	no	—
178	C₂²×C₂₃	—	4	2	no	—
179	C₂²×C₂₃	#387	1	2	yes	—
180	C₂²×C₂₃	#387	1	2	yes	—
181	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
182	C₂²×C₂₃	C₂×#125	1	1	yes	characteristic
183	C₂²×C₂₃	C₂×#126	1	1	yes	characteristic
184	C₄×C₂₃	—	4	4	no	—
185	C₄×C₂₃	—	4	4	no	—
186	C₄×C₂₃	—	8	2	no	—
187	C₄×C₂₃	#387	1	2	yes	—
188	C₄×C₂₃	#387	1	2	yes	—
189	C₄×C₂₃	C₂×#117	1	1	yes	characteristic
190	C₄×C₂₃	C₂×C₄×Q₈	1	1	yes	characteristic
191	C₄×C₂₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
192	C₄×C₂₃	C₂×#123	1	1	yes	characteristic
193	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
194	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
195	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
196	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
197	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
198	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
199	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
200	#428	C₄×C₂₃	1	4	yes	complemented
201	#428	C₄×C₂₃	1	4	yes	complemented
202	#427	C₂²×C₂₃	1	4	yes	—
203	#424	—	2	1	no	—
204	#424	—	2	1	no	—
205	#424	C₂²×C₂₃	1	4	yes	—
206	C₂×C₄⋊C₈	—	2	2	no	—
207	#405	—	2	2	no	—
208	#405	C₂²×C₂₃	1	4	yes	—
209	C₂×#97	—	2	1	no	—
210	C₂×C₄×C₈	—	2	1	no	—
211	#341	C₂²×C₂₃	1	4	yes	—
212	#339	C₂²×C₂₃	1	4	yes	—
213	#339	C₂²×C₂₃	1	4	yes	—
214	#336	C₂²×C₂₃	1	4	yes	—
215	C₂×C₂₃	—	2	1	no	—
216	C₂×C₂₃	—	2	1	no	—
217	C₂×C₂₃	—	2	2	no	—
218	C₂×C₂₃	—	2	2	no	—
219	C₂×C₂₃	C₂×#387	1	1	yes	characteristic
220	C₂×C₂₃	#2955	1	2	yes	—
221	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
222	C₂×M₁₆	—	2	1	no	—
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	—	2	2	no	—
225	C₂×M₁₆	—	2	2	no	—
226	C₂×M₁₆	—	2	1	no	—
227	C₂×M₁₆	—	2	2	no	—
228	C₂×M₁₆	—	2	2	no	—
229	C₂×M₁₆	C₂×C₄×C₂₃	1	2	yes	—
230	C₂×M₁₆	C₂×C₄×C₂₃	1	2	yes	—
231	C₂×M₁₆	Q₈×C₂₃	1	4	yes	—
232	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
233	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
234	C₂²×C₈	—	2	1	no	—
235	C₂²×C₈	—	2	2	no	—
236	C₂²×C₈	—	2	2	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
239	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
240	C₂²×C₈	D₄×C₂₃	1	2	yes	—
241	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
242	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
243	#117	—	2	1	no	—
244	#117	—	2	1	no	—
245	#117	—	2	1	no	—
246	#117	—	2	1	no	—
247	#117	—	2	2	no	—
248	#117	—	2	2	no	—
249	#117	C₂×C₄×C₂₃	1	2	yes	—
250	#117	C₂×C₄×C₂₃	1	2	yes	—
251	#117	C₂³×C₂₃	1	2	yes	—
252	#117	C₂³×C₂₃	1	2	yes	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
255	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
256	C₂×C₂²⋊C₄	—	2	1	no	—
257	C₂×C₂²⋊C₄	—	2	1	no	—
258	C₂×C₂²⋊C₄	—	2	1	no	—
259	C₂×C₄²	—	2	1	no	—
260	C₂×C₄²	—	2	1	no	—
261	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
262	#107	C₂×C₄×C₂₃	1	8	yes	—
263	#106	C₂×C₄×C₂₃	1	8	yes	—
264	C₄⋊C₈	—	2	4	no	—
265	C₄⋊C₈	—	2	4	no	—
266	#97	—	2	4	no	—
267	C₄×C₈	—	2	4	no	—
268	C₂₃	#21041	1	1	yes	characteristic, direct product factor, Sylow
269	C₂⁴	#41×C₂₃	1	1	yes	characteristic
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
274	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
277	C₂²×C₄	C₂×Q₈×C₂₃	1	2	yes	—
278	C₂²×C₄	#41×C₂₃	1	2	yes	—
279	C₂²×C₄	#41×C₂₃	1	2	yes	—
280	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
281	C₂²×C₄	#41×C₂₃	1	2	yes	—
282	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
283	M₁₆	—	2	4	no	—
284	M₁₆	—	2	4	no	—
285	M₁₆	—	2	4	no	—
286	M₁₆	—	2	2	no	—
287	M₁₆	—	2	2	no	—
288	M₁₆	—	2	2	no	—
289	M₁₆	—	4	2	no	—
290	M₁₆	C₂×Q₈×C₂₃	1	4	yes	—
291	C₂×C₈	—	2	4	no	—
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
303	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
304	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	4	2	no	—
308	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
309	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
310	C₂²⋊C₄	—	2	2	no	—
311	C₂²⋊C₄	—	2	2	no	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₂³	—	4	2	no	—
322	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
323	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
324	C₂³	C₂₃×#125	1	2	yes	—
325	C₂³	C₂₃×#126	1	2	yes	—
326	C₂³	C₂×#41×C₂₃	1	1	yes	characteristic
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	C₂₃×#117	1	2	yes	—
334	C₂×C₄	C₂₃×#117	1	2	yes	—
335	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
336	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
337	C₂×C₄	C₄×Q₈×C₂₃	1	2	yes	—
338	C₂×C₄	C₄×Q₈×C₂₃	1	2	yes	—
339	C₂×C₄	C₂₃×C₂²⋊Q₈	1	2	yes	—
340	C₂×C₄	C₂₃×C₂²⋊Q₈	1	2	yes	—
341	C₂×C₄	C₂₃×#123	1	2	yes	—
342	C₂×C₄	C₂₃×#123	1	2	yes	—
343	C₂×C₄	C₂₃×#125	1	2	yes	—
344	C₂×C₄	C₂₃×#126	1	2	yes	—
345	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
346	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
347	C₂×C₄	C₂²×Q₈×C₂₃	1	1	yes	characteristic
348	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
349	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
350	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
351	C₈	—	2	4	no	—
352	C₈	—	2	4	no	—
353	C₈	—	2	2	no	—
354	C₈	—	2	2	no	—
355	C₈	—	4	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	4	2	no	—
360	C₂²	—	4	2	no	—
361	C₂²	C₂₃×#387	1	2	yes	—
362	C₂²	C₂₃×#387	1	2	yes	—
363	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
364	C₂²	C₂×C₂₃×#125	1	1	yes	characteristic
365	C₂²	C₂×C₂₃×#126	1	1	yes	characteristic
366	C₄	—	4	4	no	—
367	C₄	—	4	4	no	—
368	C₄	—	8	2	no	—
369	C₄	C₂₃×#387	1	2	yes	—
370	C₄	C₂₃×#387	1	2	yes	—
371	C₄	C₂×C₂₃×#117	1	1	yes	characteristic
372	C₄	C₂×C₄×Q₈×C₂₃	1	1	yes	characteristic
373	C₄	C₂×C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
374	C₄	C₂×C₂₃×#123	1	1	yes	characteristic
375	C₂	—	2	1	no	—
376	C₂	—	2	2	no	—
377	C₂	—	2	2	no	—
378	C₂	—	2	1	no	—
379	C₂	C₂×C₂₃×#387	1	1	yes	characteristic
380	C₂	C₂₃×#2955	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂×C₄×D₄
prime radical	C₂⁴×C₂₃	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂³×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₃×#1922	C₂	semidirect
16. C₂₃×#428	C₄	semidirect
17. C₂₃×#428	C₄	semidirect
130. #21041	C₂₃	direct (N × H)
169. #1922	C₂×C₂₃	semidirect
200. #428	C₄×C₂₃	semidirect
201. #428	C₄×C₂₃	semidirect
268. C₂₃	#21041	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×#2911	2
C₂×C₂₃×#424	2
C₂×C₂₃×#405	2
C₂₃×#1922	2
C₂₃×#1738	2
C₂₃×#1733	2
C₂₃×#1729	2
#21041	23

Subgroups — C23×#21041 #19168667

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21041 #19168667