Subgroups — C₂₃×#3539 #15671158

Order 2944.

1050 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#560	C₂	1	4	yes	maximal, complemented
2	C₂₃×#553	C₂	1	2	yes	maximal, complemented
3	C₂₃×#553	C₂	1	4	yes	maximal, complemented
4	C₂₃×#552	C₂	1	2	yes	maximal, complemented
5	C₂₃×#550	C₂	1	2	yes	maximal, complemented
6	C₂₃×#547	C₂	1	2	yes	maximal, complemented
7	C₂₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#540	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#540	C₂	1	4	yes	maximal, complemented
10	C₂₃×#539	C₂	1	4	yes	maximal, complemented
11	C₂₃×#537	C₂	1	2	yes	maximal, complemented
12	C₂₃×#525	C₂	1	2	yes	maximal, complemented
13	C₂₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#41×C₂₃	C₂²	1	2	yes	—
15	C₂×#41×C₂₃	C₂²	1	1	yes	characteristic
16	C₂×#41×C₂₃	C₂²	1	2	yes	complemented
17	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂₃×#127	C₂²	1	4	yes	—
20	C₂₃×#127	C₂²	1	1	yes	characteristic, complemented
21	C₂₃×#126	C₂²	1	4	yes	—
22	C₂₃×#126	C₂²	1	4	yes	—
23	C₂₃×#126	C₂²	1	4	yes	complemented
24	C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
25	C₂₃×#125	C₂²	1	4	yes	complemented
26	C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
27	C₂₃×#125	C₂²	1	4	yes	complemented
28	C₂₃×#123	C₂²	1	4	yes	—
29	C₂₃×#123	C₂²	1	4	yes	—
30	C₂₃×#123	C₂²	1	2	yes	—
31	C₂₃×#123	C₂²	1	4	yes	—
32	C₂₃×#123	C₂²	1	4	yes	—
33	C₂₃×#123	C₂²	1	4	yes	complemented
34	C₂₃×#123	C₂²	1	4	yes	complemented
35	C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
36	C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
37	C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
38	C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
39	C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
40	C₂₃×#121	C₂²	1	4	yes	—
41	C₂₃×#121	C₂²	1	2	yes	—
42	C₂₃×#121	C₂²	1	4	yes	—
43	C₂₃×#121	C₂²	1	4	yes	—
44	C₂₃×#121	C₂²	1	4	yes	—
45	C₂₃×#121	C₂²	1	4	yes	—
46	C₂₃×#121	C₂²	1	4	yes	—
47	C₂₃×#121	C₂²	1	2	yes	—
48	C₂₃×#121	C₂²	1	2	yes	—
49	C₂₃×#121	C₂²	1	2	yes	complemented
50	C₂₃×#121	C₂²	1	4	yes	complemented
51	C₂₃×#121	C₂²	1	4	yes	complemented
52	C₂₃×#120	C₂²	1	2	yes	—
53	C₂₃×#120	C₂²	1	4	yes	—
54	C₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
55	C₄×D₄×C₂₃	C₂²	1	2	yes	—
56	C₄×D₄×C₂₃	C₂²	1	2	yes	—
57	C₄×D₄×C₂₃	C₂²	1	4	yes	—
58	C₄×D₄×C₂₃	C₂²	1	4	yes	—
59	C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
60	C₄×D₄×C₂₃	C₂²	1	4	yes	complemented
61	C₄×D₄×C₂₃	C₂²	1	4	yes	complemented
62	C₂₃×#117	C₂²	1	2	yes	—
63	C₂₃×#117	C₂²	1	1	yes	characteristic
64	C₂₃×#117	C₂²	1	4	yes	complemented
65	C₂×C₄⋊C₄×C₂₃	C₂²	1	4	yes	complemented
66	C₂×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
67	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
68	#41×C₂₃	—	4	2	no	—
69	#41×C₂₃	—	4	4	no	—
70	#41×C₂₃	—	4	4	no	—
71	C₂×Q₈×C₂₃	C₂³	1	2	yes	—
72	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
73	C₂×D₄×C₂₃	C₂³	1	2	yes	—
74	C₂×D₄×C₂₃	C₂³	1	2	yes	—
75	C₂×D₄×C₂₃	C₂³	1	4	yes	—
76	C₂×D₄×C₂₃	C₂³	1	4	yes	—
77	C₂×D₄×C₂₃	C₂³	1	2	yes	—
78	C₂×D₄×C₂₃	C₂³	1	4	yes	—
79	C₂×D₄×C₂₃	C₂³	1	4	yes	—
80	C₂×D₄×C₂₃	C₂³	1	2	yes	—
81	C₂×D₄×C₂₃	C₂³	1	4	yes	—
82	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
83	C₂×D₄×C₂₃	C₂³	1	4	yes	—
84	C₂²×C₄×C₂₃	—	4	2	no	—
85	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
86	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
87	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₂₃	C₂³	1	4	yes	—
89	C₂²×C₄×C₂₃	C₂³	1	4	yes	—
90	C₂²×C₄×C₂₃	C₂³	1	4	yes	—
91	C₂²×C₄×C₂₃	C₂³	1	4	yes	—
92	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
94	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
95	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
96	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
97	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
98	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
99	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
100	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
101	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
102	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
103	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
104	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
105	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
106	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
107	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
108	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
109	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
110	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
111	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
112	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
113	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
114	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
115	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
116	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
117	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
118	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
119	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
120	C₄²×C₂₃	C₂³	1	4	yes	—
121	C₄²×C₂₃	C₂³	1	1	yes	characteristic
122	C₄²×C₂₃	C₂³	1	1	yes	characteristic
123	C₄²×C₂₃	C₂³	1	4	yes	—
124	C₂³×C₂₃	—	4	1	no	—
125	C₂³×C₂₃	—	4	2	no	—
126	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
127	C₂³×C₂₃	C₂⁴	1	2	yes	—
128	C₂³×C₂₃	C₂⁴	1	2	yes	—
129	C₂³×C₂₃	C₂⁴	1	4	yes	—
130	Q₈×C₂₃	—	2	4	no	—
131	Q₈×C₂₃	—	4	1	no	—
132	D₄×C₂₃	—	2	4	no	—
133	D₄×C₂₃	—	4	2	no	—
134	D₄×C₂₃	—	4	4	no	—
135	D₄×C₂₃	—	4	4	no	—
136	D₄×C₂₃	—	4	4	no	—
137	D₄×C₂₃	—	4	2	no	—
138	D₄×C₂₃	—	4	4	no	—
139	D₄×C₂₃	—	4	2	no	—
140	D₄×C₂₃	—	4	1	no	—
141	D₄×C₂₃	—	4	4	no	—
142	D₄×C₂₃	—	4	4	no	—
143	C₂×C₄×C₂₃	—	2	4	no	—
144	C₂×C₄×C₂₃	—	2	2	no	—
145	C₂×C₄×C₂₃	—	2	4	no	—
146	C₂×C₄×C₂₃	—	4	1	no	—
147	C₂×C₄×C₂₃	—	4	2	no	—
148	C₂×C₄×C₂₃	—	4	4	no	—
149	C₂×C₄×C₂₃	—	4	4	no	—
150	C₂×C₄×C₂₃	—	4	4	no	—
151	C₂×C₄×C₂₃	—	4	4	no	—
152	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
153	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
154	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
155	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
156	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
157	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
158	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
159	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
160	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
161	#3539	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂²×C₂₃	—	2	2	no	—
163	C₂²×C₂₃	—	2	1	no	—
164	C₂²×C₂₃	—	2	2	no	—
165	C₂²×C₂₃	—	2	4	no	—
166	C₂²×C₂₃	—	2	2	no	—
167	C₂²×C₂₃	—	2	4	no	—
168	C₂²×C₂₃	—	2	2	no	—
169	C₂²×C₂₃	—	2	4	no	—
170	C₂²×C₂₃	—	2	2	no	—
171	C₂²×C₂₃	—	2	2	no	—
172	C₂²×C₂₃	—	2	2	no	—
173	C₂²×C₂₃	—	4	4	no	—
174	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
175	C₄×C₂₃	—	2	2	no	—
176	C₄×C₂₃	—	2	1	no	—
177	C₄×C₂₃	—	2	2	no	—
178	C₄×C₂₃	—	2	4	no	—
179	C₄×C₂₃	—	2	2	no	—
180	C₄×C₂₃	—	2	4	no	—
181	C₄×C₂₃	—	2	4	no	—
182	C₄×C₂₃	—	2	2	no	—
183	C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
184	#560	C₂×C₂₃	1	4	yes	complemented
185	#553	C₂×C₂₃	1	2	yes	complemented
186	#553	C₂×C₂₃	1	4	yes	complemented
187	#552	C₂×C₂₃	1	2	yes	complemented
188	#550	C₂×C₂₃	1	2	yes	complemented
189	#547	C₂×C₂₃	1	2	yes	complemented
190	#541	C₂×C₂₃	1	1	yes	characteristic, complemented
191	#540	C₂×C₂₃	1	1	yes	characteristic, complemented
192	#540	C₂×C₂₃	1	4	yes	complemented
193	#539	C₂×C₂₃	1	4	yes	complemented
194	#537	C₂×C₂₃	1	2	yes	complemented
195	#525	C₂×C₂₃	1	1	yes	characteristic, complemented
196	#525	C₂×C₂₃	1	2	yes	complemented
197	C₂×C₂₃	—	4	2	no	—
198	C₂×C₂₃	—	4	4	no	—
199	C₂×C₂₃	—	4	2	no	—
200	C₂×C₂₃	—	4	1	no	—
201	C₂×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₂₃	#585	1	2	yes	—
203	C₂×#41	C₂²×C₂₃	1	1	yes	characteristic
204	C₂×#41	C₂²×C₂₃	1	2	yes	—
205	C₂×#41	C₂²×C₂₃	1	2	yes	complemented
206	C₂³×C₄	C₂²×C₂₃	1	1	yes	characteristic
207	C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
208	#127	C₂²×C₂₃	1	4	yes	—
209	#127	C₂²×C₂₃	1	1	yes	characteristic, complemented
210	#126	C₂²×C₂₃	1	4	yes	—
211	#126	C₂²×C₂₃	1	4	yes	—
212	#126	C₂²×C₂₃	1	4	yes	complemented
213	#125	C₂²×C₂₃	1	4	yes	complemented
214	#125	C₂²×C₂₃	1	4	yes	complemented
215	#125	C₂²×C₂₃	1	1	yes	characteristic, complemented
216	#125	C₂²×C₂₃	1	1	yes	characteristic, complemented
217	#123	C₂²×C₂₃	1	4	yes	—
218	#123	C₂²×C₂₃	1	2	yes	—
219	#123	C₂²×C₂₃	1	4	yes	—
220	#123	C₂²×C₂₃	1	4	yes	—
221	#123	C₂²×C₂₃	1	4	yes	—
222	#123	C₂²×C₂₃	1	4	yes	complemented
223	#123	C₂²×C₂₃	1	4	yes	complemented
224	C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
225	C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
226	C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
227	C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	complemented
228	C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
229	#121	C₂²×C₂₃	1	2	yes	—
230	#121	C₂²×C₂₃	1	2	yes	—
231	#121	C₂²×C₂₃	1	2	yes	—
232	#121	C₂²×C₂₃	1	4	yes	—
233	#121	C₂²×C₂₃	1	4	yes	—
234	#121	C₂²×C₂₃	1	4	yes	—
235	#121	C₂²×C₂₃	1	4	yes	—
236	#121	C₂²×C₂₃	1	4	yes	—
237	#121	C₂²×C₂₃	1	4	yes	—
238	#121	C₂²×C₂₃	1	4	yes	complemented
239	#121	C₂²×C₂₃	1	2	yes	complemented
240	#121	C₂²×C₂₃	1	4	yes	complemented
241	#120	C₂²×C₂₃	1	2	yes	—
242	#120	C₂²×C₂₃	1	4	yes	—
243	C₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
244	C₄×D₄	C₂²×C₂₃	1	4	yes	—
245	C₄×D₄	C₂²×C₂₃	1	2	yes	—
246	C₄×D₄	C₂²×C₂₃	1	2	yes	—
247	C₄×D₄	C₂²×C₂₃	1	4	yes	—
248	C₄×D₄	C₂²×C₂₃	1	4	yes	complemented
249	C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
250	C₄×D₄	C₂²×C₂₃	1	4	yes	complemented
251	#117	C₂²×C₂₃	1	1	yes	characteristic
252	#117	C₂²×C₂₃	1	2	yes	—
253	#117	C₂²×C₂₃	1	4	yes	complemented
254	C₂×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
255	C₂×C₄⋊C₄	C₂²×C₂₃	1	4	yes	complemented
256	C₂₃	#3539	1	1	yes	characteristic, direct product factor, Sylow
257	C₂⁴	C₂³×C₂₃	1	1	yes	characteristic
258	#41	—	4	2	no	—
259	#41	—	4	4	no	—
260	#41	—	4	4	no	—
261	C₂×Q₈	C₂³×C₂₃	1	2	yes	—
262	C₂×Q₈	C₂³×C₂₃	1	1	yes	characteristic
263	C₂×D₄	C₂³×C₂₃	1	2	yes	—
264	C₂×D₄	C₂³×C₂₃	1	2	yes	—
265	C₂×D₄	C₂³×C₂₃	1	4	yes	—
266	C₂×D₄	C₂³×C₂₃	1	4	yes	—
267	C₂×D₄	C₂³×C₂₃	1	2	yes	—
268	C₂×D₄	C₂³×C₂₃	1	4	yes	—
269	C₂×D₄	C₂³×C₂₃	1	4	yes	—
270	C₂×D₄	C₂³×C₂₃	1	2	yes	—
271	C₂×D₄	C₂³×C₂₃	1	4	yes	—
272	C₂×D₄	C₂³×C₂₃	1	1	yes	characteristic
273	C₂×D₄	C₂³×C₂₃	1	4	yes	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	C₂³×C₂₃	1	2	yes	—
276	C₂²×C₄	C₂³×C₂₃	1	2	yes	—
277	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
278	C₂²×C₄	C₂³×C₂₃	1	4	yes	—
279	C₂²×C₄	C₂³×C₂₃	1	4	yes	—
280	C₂²×C₄	C₂³×C₂₃	1	4	yes	—
281	C₂²×C₄	C₂³×C₂₃	1	4	yes	—
282	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
283	C₂²×C₄	C₂³×C₂₃	1	2	yes	—
284	C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
285	C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
286	C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
287	C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
288	C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
289	C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
290	C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
291	C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
292	C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
293	C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
294	C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
295	C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
296	C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
297	C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
298	C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
299	C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
300	C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
301	C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
302	C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
303	C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
304	C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
305	C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
306	C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
307	C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
308	C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
309	C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
310	C₄²	C₂³×C₂₃	1	4	yes	—
311	C₄²	C₂³×C₂₃	1	1	yes	characteristic
312	C₄²	C₂³×C₂₃	1	1	yes	characteristic
313	C₄²	C₂³×C₂₃	1	4	yes	—
314	C₂³	—	4	1	no	—
315	C₂³	—	4	2	no	—
316	C₂³	C₂⁴×C₂₃	1	1	yes	characteristic
317	C₂³	C₂⁴×C₂₃	1	2	yes	—
318	C₂³	C₂⁴×C₂₃	1	2	yes	—
319	C₂³	C₂⁴×C₂₃	1	4	yes	—
320	Q₈	—	2	4	no	—
321	Q₈	—	4	1	no	—
322	D₄	—	2	4	no	—
323	D₄	—	4	2	no	—
324	D₄	—	4	1	no	—
325	D₄	—	4	4	no	—
326	D₄	—	4	4	no	—
327	D₄	—	4	2	no	—
328	D₄	—	4	4	no	—
329	D₄	—	4	4	no	—
330	D₄	—	4	4	no	—
331	D₄	—	4	2	no	—
332	D₄	—	4	4	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	C₂⁴×C₂₃	1	2	yes	—
343	C₂×C₄	C₂⁴×C₂₃	1	4	yes	—
344	C₂×C₄	C₂⁴×C₂₃	1	2	yes	—
345	C₂×C₄	C₂⁴×C₂₃	1	4	yes	—
346	C₂×C₄	C₂⁴×C₂₃	1	2	yes	—
347	C₂×C₄	C₂⁴×C₂₃	1	4	yes	—
348	C₂×C₄	C₂⁴×C₂₃	1	2	yes	—
349	C₂×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
350	C₂×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
351	C₂²	—	2	2	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	4	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	4	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	4	4	no	—
363	C₂²	C₂⁵×C₂₃	1	1	yes	characteristic
364	C₄	—	2	2	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	2	no	—
367	C₄	—	2	4	no	—
368	C₄	—	2	2	no	—
369	C₄	—	2	4	no	—
370	C₄	—	2	4	no	—
371	C₄	—	2	2	no	—
372	C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
373	C₂	—	4	2	no	—
374	C₂	—	4	1	no	—
375	C₂	—	4	2	no	—
376	C₂	—	4	4	no	—
377	C₂	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂	C₂₃×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#560	C₂	semidirect
2. C₂₃×#553	C₂	semidirect
3. C₂₃×#553	C₂	semidirect
4. C₂₃×#552	C₂	semidirect
5. C₂₃×#550	C₂	semidirect
6. C₂₃×#547	C₂	semidirect
7. C₂₃×#541	C₂	semidirect
8. C₂₃×#540	C₂	semidirect
9. C₂₃×#540	C₂	semidirect
10. C₂₃×#539	C₂	semidirect
11. C₂₃×#537	C₂	semidirect
12. C₂₃×#525	C₂	semidirect
13. C₂₃×#525	C₂	semidirect
16. C₂×#41×C₂₃	C₂²	semidirect
18. C₂₃×C₄⋊Q₈	C₂²	semidirect
20. C₂₃×#127	C₂²	semidirect
23. C₂₃×#126	C₂²	semidirect
24. C₂₃×#125	C₂²	semidirect
25. C₂₃×#125	C₂²	semidirect
26. C₂₃×#125	C₂²	semidirect
27. C₂₃×#125	C₂²	semidirect
33. C₂₃×#123	C₂²	semidirect
34. C₂₃×#123	C₂²	semidirect
38. C₂₃×C₂²⋊Q₈	C₂²	semidirect
39. C₂₃×C₂²⋊Q₈	C₂²	semidirect
49. C₂₃×#121	C₂²	semidirect
50. C₂₃×#121	C₂²	semidirect
51. C₂₃×#121	C₂²	semidirect
54. C₄×Q₈×C₂₃	C₂²	semidirect
59. C₄×D₄×C₂₃	C₂²	semidirect
60. C₄×D₄×C₂₃	C₂²	semidirect
61. C₄×D₄×C₂₃	C₂²	semidirect
64. C₂₃×#117	C₂²	semidirect
65. C₂×C₄⋊C₄×C₂₃	C₂²	semidirect
66. C₂×C₄⋊C₄×C₂₃	C₂²	semidirect
161. #3539	C₂₃	direct (N × H)
184. #560	C₂×C₂₃	semidirect
185. #553	C₂×C₂₃	semidirect
186. #553	C₂×C₂₃	semidirect
187. #552	C₂×C₂₃	semidirect
188. #550	C₂×C₂₃	semidirect
189. #547	C₂×C₂₃	semidirect
190. #541	C₂×C₂₃	semidirect
191. #540	C₂×C₂₃	semidirect
192. #540	C₂×C₂₃	semidirect
193. #539	C₂×C₂₃	semidirect
194. #537	C₂×C₂₃	semidirect
195. #525	C₂×C₂₃	semidirect
196. #525	C₂×C₂₃	semidirect
205. C₂×#41	C₂²×C₂₃	semidirect
207. C₄⋊Q₈	C₂²×C₂₃	semidirect
209. #127	C₂²×C₂₃	semidirect
212. #126	C₂²×C₂₃	semidirect
213. #125	C₂²×C₂₃	semidirect
214. #125	C₂²×C₂₃	semidirect
215. #125	C₂²×C₂₃	semidirect
216. #125	C₂²×C₂₃	semidirect
222. #123	C₂²×C₂₃	semidirect
223. #123	C₂²×C₂₃	semidirect
227. C₂²⋊Q₈	C₂²×C₂₃	semidirect
228. C₂²⋊Q₈	C₂²×C₂₃	semidirect
238. #121	C₂²×C₂₃	semidirect
239. #121	C₂²×C₂₃	semidirect
240. #121	C₂²×C₂₃	semidirect
243. C₄×Q₈	C₂²×C₂₃	semidirect
248. C₄×D₄	C₂²×C₂₃	semidirect
249. C₄×D₄	C₂²×C₂₃	semidirect
250. C₄×D₄	C₂²×C₂₃	semidirect
253. #117	C₂²×C₂₃	semidirect
254. C₂×C₄⋊C₄	C₂²×C₂₃	semidirect
255. C₂×C₄⋊C₄	C₂²×C₂₃	semidirect
256. C₂₃	#3539	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×#560	2
C₂₃×#553	2
C₂₃×#552	2
C₂₃×#550	2
C₂₃×#547	2
C₂₃×#541	2
C₂₃×#540	2
C₂₃×#539	2
C₂₃×#537	2
C₂₃×#525	2
#3539	23

Subgroups — C23×#3539 #15671158

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#3539 #15671158