Subgroups — C₂₃×#21925 #19169551

Order 5888.

648 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2298	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#1924	C₂	1	2	yes	maximal
3	C₂₃×#1923	C₂	1	2	yes	maximal
4	C₂₃×#1917	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1916	C₂	1	2	yes	maximal, complemented
6	C₂₃×#1843	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1832	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1798	C₂	1	1	yes	maximal, characteristic
9	C₂₃×#1798	C₂	1	1	yes	maximal, characteristic
10	C₂₃×#1767	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₂₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
13	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₂₃×#97	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
23	C₂₃×#388	C₄	1	2	yes	—
24	C₂₃×#388	C₄	1	2	yes	—
25	C₂₃×#387	C₄	1	2	yes	—
26	C₂₃×#387	C₄	1	2	yes	—
27	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
29	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
30	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂₃×#376	C₂²	1	1	yes	characteristic
32	C₄³×C₂₃	C₂²	1	1	yes	characteristic
33	C₂₃×#336	C₂²	1	2	yes	—
34	C₂₃×#336	C₂²	1	2	yes	—
35	C₂₃×#336	C₂²	1	2	yes	—
36	C₂₃×#336	C₂²	1	2	yes	—
37	C₂₃×#336	C₂²	1	2	yes	—
38	C₂₃×#336	C₂²	1	2	yes	—
39	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
41	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
42	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
44	C₂₃×#117	—	2	2	no	—
45	C₂₃×#117	—	2	2	no	—
46	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
50	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
51	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
62	C₂₃×C₄⋊C₈	—	2	2	no	—
63	C₂₃×C₄⋊C₈	—	2	2	no	—
64	C₂₃×C₄⋊C₈	—	2	2	no	—
65	C₂₃×C₄⋊C₈	—	2	2	no	—
66	C₂₃×C₄⋊C₈	—	4	2	no	—
67	C₂₃×C₄⋊C₈	—	4	2	no	—
68	C₂₃×C₂²⋊C₈	—	4	2	no	—
69	C₂₃×C₂²⋊C₈	—	4	2	no	—
70	C₂₃×#97	—	4	2	no	—
71	C₄×C₈×C₂₃	—	4	2	no	—
72	C₂₃×#95	C₂×C₄	1	2	yes	—
73	C₂₃×#95	C₂×C₄	1	2	yes	—
74	C₂₃×#95	C₂×C₄	1	2	yes	—
75	C₂₃×#95	C₂×C₄	1	2	yes	—
76	C₂₃×#95	C₂×C₄	1	2	yes	—
77	C₂₃×#95	C₂×C₄	1	2	yes	—
78	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₂₃	—	2	1	no	—
80	C₂²×C₄×C₂₃	—	2	1	no	—
81	C₂²×C₄×C₂₃	—	2	1	no	—
82	C₂²×C₄×C₂₃	—	2	1	no	—
83	C₂²×C₄×C₂₃	—	2	1	no	—
84	C₂²×C₄×C₂₃	—	2	1	no	—
85	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
95	C₂×C₈×C₂₃	—	2	2	no	—
96	C₂×C₈×C₂₃	—	2	2	no	—
97	C₂×C₈×C₂₃	—	2	2	no	—
98	C₂×C₈×C₂₃	—	2	2	no	—
99	C₂×C₈×C₂₃	—	2	2	no	—
100	C₂×C₈×C₂₃	—	2	2	no	—
101	C₂×C₈×C₂₃	—	2	2	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	C₄⋊C₄×C₂₃	—	2	2	no	—
108	C₄⋊C₄×C₂₃	—	2	2	no	—
109	C₄⋊C₄×C₂₃	—	2	4	no	—
110	C₄⋊C₄×C₂₃	—	4	2	no	—
111	C₂²⋊C₄×C₂₃	—	2	2	no	—
112	C₂²⋊C₄×C₂₃	—	2	2	no	—
113	C₂²⋊C₄×C₂₃	—	2	4	no	—
114	C₂²⋊C₄×C₂₃	—	4	2	no	—
115	C₄²×C₂₃	—	2	4	no	—
116	C₄²×C₂₃	—	2	1	no	—
117	C₄²×C₂₃	—	2	1	no	—
118	C₄²×C₂₃	—	2	1	no	—
119	C₄²×C₂₃	—	2	1	no	—
120	C₄²×C₂₃	—	2	1	no	—
121	C₄²×C₂₃	—	2	1	no	—
122	C₄²×C₂₃	—	2	1	no	—
123	C₄²×C₂₃	—	2	1	no	—
124	C₄²×C₂₃	—	2	1	no	—
125	C₄²×C₂₃	—	2	1	no	—
126	C₄²×C₂₃	—	4	2	no	—
127	C₄²×C₂₃	#41	1	2	yes	—
128	C₄²×C₂₃	#41	1	2	yes	—
129	#21925	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₂₃	—	2	1	no	—
131	C₂³×C₂₃	—	2	1	no	—
132	C₂³×C₂₃	—	2	1	no	—
133	C₂³×C₂₃	—	2	2	no	—
134	C₂³×C₂₃	—	2	2	no	—
135	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
136	C₂×C₄×C₂₃	—	2	2	no	—
137	C₂×C₄×C₂₃	—	2	2	no	—
138	C₂×C₄×C₂₃	—	2	2	no	—
139	C₂×C₄×C₂₃	—	2	2	no	—
140	C₂×C₄×C₂₃	—	2	1	no	—
141	C₂×C₄×C₂₃	—	2	1	no	—
142	C₂×C₄×C₂₃	—	2	1	no	—
143	C₂×C₄×C₂₃	—	2	2	no	—
144	C₂×C₄×C₂₃	—	2	2	no	—
145	C₂×C₄×C₂₃	—	2	2	no	—
146	C₂×C₄×C₂₃	—	2	1	no	—
147	C₂×C₄×C₂₃	—	2	1	no	—
148	C₂×C₄×C₂₃	—	2	2	no	—
149	C₂×C₄×C₂₃	—	2	2	no	—
150	C₂×C₄×C₂₃	—	2	2	no	—
151	C₂×C₄×C₂₃	—	2	2	no	—
152	C₂×C₄×C₂₃	—	2	2	no	—
153	C₂×C₄×C₂₃	—	2	2	no	—
154	C₂×C₄×C₂₃	—	2	2	no	—
155	C₂×C₄×C₂₃	—	2	2	no	—
156	C₂×C₄×C₂₃	—	4	1	no	—
157	C₂×C₄×C₂₃	—	4	1	no	—
158	C₂×C₄×C₂₃	—	4	1	no	—
159	C₂×C₄×C₂₃	—	4	1	no	—
160	C₂×C₄×C₂₃	#117	1	2	yes	—
161	C₂×C₄×C₂₃	#117	1	2	yes	—
162	C₂×C₄×C₂₃	#131	1	4	yes	—
163	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
166	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
167	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
168	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
169	C₈×C₂₃	—	4	2	no	—
170	C₈×C₂₃	—	4	2	no	—
171	C₈×C₂₃	—	4	2	no	—
172	C₈×C₂₃	—	4	2	no	—
173	#2298	C₂×C₂₃	1	1	yes	characteristic
174	#1924	C₂×C₂₃	1	2	yes	—
175	#1923	C₂×C₂₃	1	2	yes	—
176	#1917	C₂×C₂₃	1	2	yes	complemented
177	#1916	C₂×C₂₃	1	2	yes	complemented
178	#1843	C₂×C₂₃	1	1	yes	characteristic, complemented
179	#1832	C₂×C₂₃	1	1	yes	characteristic, complemented
180	#1798	C₂×C₂₃	1	1	yes	characteristic
181	#1798	C₂×C₂₃	1	1	yes	characteristic
182	#1767	C₂×C₂₃	1	1	yes	characteristic, complemented
183	C₄×C₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
184	C₂²×C₂₃	—	4	1	no	—
185	C₂²×C₂₃	—	4	1	no	—
186	C₂²×C₂₃	—	4	1	no	—
187	C₂²×C₂₃	—	4	2	no	—
188	C₂²×C₂₃	—	4	2	no	—
189	C₂²×C₂₃	C₂×#117	1	1	yes	characteristic
190	C₂²×C₂₃	#520	1	1	yes	characteristic
191	C₂²×C₂₃	#520	1	1	yes	characteristic
192	C₂²×C₂₃	C₂×#131	1	2	yes	—
193	C₂²×C₂₃	#568	1	2	yes	—
194	C₄×C₂₃	—	2	2	no	—
195	C₄×C₂₃	—	2	2	no	—
196	C₄×C₂₃	—	2	4	no	—
197	C₄×C₂₃	—	4	1	no	—
198	C₄×C₂₃	—	4	1	no	—
199	C₄×C₂₃	—	4	1	no	—
200	C₄×C₂₃	—	4	2	no	—
201	C₄×C₂₃	—	4	2	no	—
202	C₄×C₂₃	—	4	2	no	—
203	C₄×C₂₃	#540	1	1	yes	characteristic
204	C₄×C₂₃	#541	1	1	yes	characteristic
205	C₄×C₂₃	#542	1	1	yes	characteristic
206	C₄×C₂₃	#542	1	1	yes	characteristic
207	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
208	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
209	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
210	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
211	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
212	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
213	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
214	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
215	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
216	C₂×#97	C₂²×C₂₃	1	2	yes	—
217	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
218	#388	C₄×C₂₃	1	2	yes	—
219	#388	C₄×C₂₃	1	2	yes	—
220	#387	C₄×C₂₃	1	2	yes	—
221	#387	C₄×C₂₃	1	2	yes	—
222	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
223	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
224	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
225	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
226	#376	C₂²×C₂₃	1	1	yes	characteristic
227	C₄³	C₂²×C₂₃	1	1	yes	characteristic
228	#336	C₂²×C₂₃	1	2	yes	—
229	#336	C₂²×C₂₃	1	2	yes	—
230	#336	C₂²×C₂₃	1	2	yes	—
231	#336	C₂²×C₂₃	1	2	yes	—
232	#336	C₂²×C₂₃	1	2	yes	—
233	#336	C₂²×C₂₃	1	2	yes	—
234	C₂×C₂₃	—	8	1	no	—
235	C₂×C₂₃	#2314	1	1	yes	characteristic
236	C₂×C₂₃	#2922	1	1	yes	characteristic
237	C₂×C₂₃	#2923	1	1	yes	characteristic
238	C₂×C₂₃	#2992	1	2	yes	—
239	C₂×C₂₃	#2993	1	2	yes	—
240	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
241	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
242	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
243	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
244	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
245	#117	—	2	2	no	—
246	#117	—	2	2	no	—
247	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
250	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
251	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
254	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
255	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
256	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
257	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
258	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	—	2	2	no	—
265	C₄⋊C₈	—	2	2	no	—
266	C₄⋊C₈	—	2	2	no	—
267	C₄⋊C₈	—	4	2	no	—
268	C₄⋊C₈	—	4	2	no	—
269	C₂²⋊C₈	—	4	2	no	—
270	C₂²⋊C₈	—	4	2	no	—
271	#97	—	4	2	no	—
272	C₄×C₈	—	4	2	no	—
273	#95	C₂×C₄×C₂₃	1	2	yes	—
274	#95	C₂×C₄×C₂₃	1	2	yes	—
275	#95	C₂×C₄×C₂₃	1	2	yes	—
276	#95	C₂×C₄×C₂₃	1	2	yes	—
277	#95	C₂×C₄×C₂₃	1	2	yes	—
278	#95	C₂×C₄×C₂₃	1	2	yes	—
279	C₂₃	#21925	1	1	yes	characteristic, direct product factor, Sylow
280	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
288	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
289	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
290	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
291	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
292	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
293	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
294	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
295	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
296	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
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	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	4	no	—
316	C₂²⋊C₄	—	4	2	no	—
317	C₄²	—	2	4	no	—
318	C₄²	—	2	1	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	2	1	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	2	1	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	2	1	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	4	2	no	—
329	C₄²	#41×C₂₃	1	2	yes	—
330	C₄²	#41×C₂₃	1	2	yes	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	C₂₃×#117	1	2	yes	—
362	C₂×C₄	C₂₃×#117	1	2	yes	—
363	C₂×C₄	C₂₃×#131	1	4	yes	—
364	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
365	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
366	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
367	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
368	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
369	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
370	C₈	—	4	2	no	—
371	C₈	—	4	2	no	—
372	C₈	—	4	2	no	—
373	C₈	—	4	2	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	1	no	—
379	C₂²	C₂×C₂₃×#117	1	1	yes	characteristic
380	C₂²	C₂₃×#520	1	1	yes	characteristic
381	C₂²	C₂₃×#520	1	1	yes	characteristic
382	C₂²	C₂×C₂₃×#131	1	2	yes	—
383	C₂²	C₂₃×#568	1	2	yes	—
384	C₄	—	2	2	no	—
385	C₄	—	2	2	no	—
386	C₄	—	2	4	no	—
387	C₄	—	4	1	no	—
388	C₄	—	4	1	no	—
389	C₄	—	4	2	no	—
390	C₄	—	4	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	1	no	—
393	C₄	C₂₃×#540	1	1	yes	characteristic
394	C₄	C₂₃×#541	1	1	yes	characteristic
395	C₄	C₂₃×#542	1	1	yes	characteristic
396	C₄	C₂₃×#542	1	1	yes	characteristic
397	C₂	—	8	1	no	—
398	C₂	C₂₃×#2314	1	1	yes	characteristic
399	C₂	C₂₃×#2922	1	1	yes	characteristic
400	C₂	C₂₃×#2923	1	1	yes	characteristic
401	C₂	C₂₃×#2992	1	2	yes	—
402	C₂	C₂₃×#2993	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₂₃×#1917	C₂	semidirect
5. C₂₃×#1916	C₂	semidirect
6. C₂₃×#1843	C₂	semidirect
7. C₂₃×#1832	C₂	semidirect
10. C₂₃×#1767	C₂	semidirect
11. C₄×C₂₃×C₄⋊C₈	C₂	semidirect
129. #21925	C₂₃	direct (N × H)
176. #1917	C₂×C₂₃	semidirect
177. #1916	C₂×C₂₃	semidirect
178. #1843	C₂×C₂₃	semidirect
179. #1832	C₂×C₂₃	semidirect
182. #1767	C₂×C₂₃	semidirect
183. C₄×C₄⋊C₈	C₂×C₂₃	semidirect
279. C₂₃	#21925	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×#2298	2
C₂₃×#1924	2
C₂₃×#1923	2
C₂₃×#1917	2
C₂₃×#1916	2
C₂₃×#1843	2
C₂₃×#1832	2
C₂₃×#1798	2
C₂₃×#1767	2
C₄×C₂₃×C₄⋊C₈	2
#21925	23

Subgroups — C23×#21925 #19169551

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21925 #19169551