Subgroups — C₂×C₂₃×#2851 #19184242

Order 5888.

3182 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄²×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2851	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#389	C₂	1	2	yes	maximal, complemented
5	C₂×C₂₃×#387	C₂	1	4	yes	maximal, complemented
6	C₂×C₂₃×#385	C₂	1	4	yes	maximal
7	C₂×C₂₃×#382	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#380	C₂	1	2	yes	maximal
9	C₂⁴×C₄×C₂₃	C₂²	1	2	yes	—
10	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
11	C₂×C₂₃×#125	—	2	8	no	—
12	C₂×C₂₃×#125	C₂²	1	8	yes	complemented
13	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
15	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
17	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
18	C₂²×C₄²×C₂₃	—	2	8	no	—
19	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
20	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₂₃	C₂²	1	8	yes	—
22	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
23	C₂₃×#389	C₂²	1	16	yes	complemented
24	C₂₃×#387	C₂²	1	32	yes	complemented
25	C₂₃×#385	C₂²	1	32	yes	—
26	C₂₃×#382	C₂²	1	8	yes	complemented
27	C₂₃×#380	C₂²	1	16	yes	—
28	C₂×C₂₃×#95	C₂²	1	4	yes	—
29	C₂×C₂₃×#95	C₂²	1	4	yes	—
30	C₂×C₂₃×#95	C₂²	1	4	yes	—
31	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
32	C₂³×C₄×C₂₃	—	2	8	no	—
33	C₂³×C₄×C₂₃	—	2	8	no	—
34	C₂³×C₄×C₂₃	—	2	4	no	—
35	C₂³×C₄×C₂₃	—	2	8	no	—
36	C₂³×C₄×C₂₃	—	2	4	no	—
37	C₂³×C₄×C₂₃	Q₈	1	8	yes	—
38	C₂³×C₄×C₂₃	C₂³	1	8	yes	—
39	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
40	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
41	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
42	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
43	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
46	C₂₃×#125	—	2	32	no	—
47	C₂×C₄⋊C₄×C₂₃	—	2	16	no	—
48	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
49	C₂×C₄⋊C₄×C₂₃	—	2	16	no	—
50	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
51	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
52	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
53	C₂×C₄⋊C₄×C₂₃	C₂³	1	16	yes	—
54	C₂×C₄⋊C₄×C₂₃	C₂³	1	16	yes	—
55	C₂×C₂²⋊C₄×C₂₃	—	2	16	no	—
56	C₂×C₂²⋊C₄×C₂₃	C₂³	1	16	yes	—
57	C₂×C₄²×C₂₃	—	2	8	no	—
58	C₂×C₄²×C₂₃	—	2	4	no	—
59	C₂×C₄²×C₂₃	—	2	32	no	—
60	C₂×C₄²×C₂₃	D₄	1	8	yes	—
61	C₂×C₄²×C₂₃	C₂³	1	8	yes	—
62	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
63	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
64	C₂₃×#95	C₂³	1	16	yes	—
65	C₂₃×#95	C₂³	1	16	yes	—
66	C₂₃×#95	C₂³	1	16	yes	—
67	C₂⁴×C₂₃	—	2	2	no	—
68	C₂⁴×C₂₃	—	2	2	no	—
69	C₂⁴×C₂₃	—	2	4	no	—
70	C₂⁴×C₂₃	C₂×Q₈	1	4	yes	—
71	C₂⁴×C₂₃	#41	1	8	yes	—
72	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
73	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
74	C₂²×C₄×C₂₃	—	2	64	no	—
75	C₂²×C₄×C₂₃	—	2	2	no	—
76	C₂²×C₄×C₂₃	—	2	4	no	—
77	C₂²×C₄×C₂₃	—	2	16	no	—
78	C₂²×C₄×C₂₃	—	2	2	no	—
79	C₂²×C₄×C₂₃	—	2	4	no	—
80	C₂²×C₄×C₂₃	—	2	4	no	—
81	C₂²×C₄×C₂₃	—	2	4	no	—
82	C₂²×C₄×C₂₃	—	2	32	no	—
83	C₂²×C₄×C₂₃	—	2	16	no	—
84	C₂²×C₄×C₂₃	—	2	8	no	—
85	C₂²×C₄×C₂₃	—	2	16	no	—
86	C₂²×C₄×C₂₃	—	2	8	no	—
87	C₂²×C₄×C₂₃	—	2	8	no	—
88	C₂²×C₄×C₂₃	—	2	8	no	—
89	C₂²×C₄×C₂₃	—	2	8	no	—
90	C₂²×C₄×C₂₃	—	2	8	no	—
91	C₂²×C₄×C₂₃	—	2	8	no	—
92	C₂²×C₄×C₂₃	—	2	8	no	—
93	C₂²×C₄×C₂₃	C₂×D₄	1	8	yes	—
94	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
95	C₂²×C₄×C₂₃	C₂×Q₈	1	4	yes	—
96	C₂²×C₄×C₂₃	C₂×Q₈	1	16	yes	—
97	C₂²×C₄×C₂₃	C₂×Q₈	1	4	yes	—
98	C₂²×C₄×C₂₃	#41	1	8	yes	—
99	C₂²×C₄×C₂₃	#41	1	4	yes	—
100	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
101	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
102	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
103	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
104	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
105	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
106	C₄⋊C₄×C₂₃	—	2	32	no	—
107	C₄⋊C₄×C₂₃	—	2	16	no	—
108	C₄⋊C₄×C₂₃	—	2	32	no	—
109	C₄⋊C₄×C₂₃	—	2	16	no	—
110	C₂²⋊C₄×C₂₃	—	2	32	no	—
111	C₄²×C₂₃	—	2	16	no	—
112	C₄²×C₂₃	—	2	8	no	—
113	C₄²×C₂₃	C₂×D₄	1	16	yes	—
114	C₂×#2851	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂³×C₂₃	—	2	8	no	—
116	C₂³×C₂₃	—	2	16	no	—
117	C₂³×C₂₃	—	2	16	no	—
118	C₂³×C₂₃	—	2	8	no	—
119	C₂³×C₂₃	—	2	2	no	—
120	C₂³×C₂₃	—	2	2	no	—
121	C₂³×C₂₃	—	2	4	no	—
122	C₂³×C₂₃	#125	1	16	yes	complemented
123	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
124	C₂³×C₂₃	C₂²×Q₈	1	4	yes	—
125	C₂³×C₂₃	C₂²×Q₈	1	2	yes	—
126	C₂³×C₂₃	C₂×#41	1	8	yes	—
127	C₂³×C₂₃	C₂×#41	1	2	yes	—
128	C₂³×C₂₃	C₂×#41	1	4	yes	—
129	C₂³×C₂₃	C₂×#41	1	4	yes	—
130	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
131	C₂×C₄×C₂₃	—	2	64	no	—
132	C₂×C₄×C₂₃	—	2	8	no	—
133	C₂×C₄×C₂₃	—	2	16	no	—
134	C₂×C₄×C₂₃	—	2	16	no	—
135	C₂×C₄×C₂₃	—	2	2	no	—
136	C₂×C₄×C₂₃	—	2	4	no	—
137	C₂×C₄×C₂₃	—	2	2	no	—
138	C₂×C₄×C₂₃	—	2	4	no	—
139	C₂×C₄×C₂₃	—	2	4	no	—
140	C₂×C₄×C₂₃	—	2	4	no	—
141	C₂×C₄×C₂₃	—	2	32	no	—
142	C₂×C₄×C₂₃	—	2	8	no	—
143	C₂×C₄×C₂₃	—	2	8	no	—
144	C₂×C₄×C₂₃	—	2	8	no	—
145	C₂×C₄×C₂₃	—	2	8	no	—
146	C₂×C₄×C₂₃	—	2	8	no	—
147	C₂×C₄×C₂₃	—	2	8	no	—
148	C₂×C₄×C₂₃	—	4	16	no	—
149	C₂×C₄×C₂₃	—	4	16	no	—
150	C₂×C₄×C₂₃	C₂²⋊Q₈	1	16	yes	—
151	C₂×C₄×C₂₃	C₂²×D₄	1	8	yes	—
152	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
153	C₂×C₄×C₂₃	C₂²×Q₈	1	4	yes	—
154	C₂×C₄×C₂₃	C₂²×Q₈	1	4	yes	—
155	C₂×C₄×C₂₃	C₂×#41	1	8	yes	—
156	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
157	C₂²×#125	C₂×C₂₃	1	1	yes	characteristic, complemented
158	C₂³×C₄²	C₂×C₂₃	1	1	yes	characteristic
159	#2851	C₂×C₂₃	1	16	yes	direct product factor
160	C₂×#389	C₂×C₂₃	1	2	yes	complemented
161	C₂×#387	C₂×C₂₃	1	4	yes	complemented
162	C₂×#385	C₂×C₂₃	1	4	yes	—
163	C₂×#382	C₂×C₂₃	1	1	yes	characteristic, complemented
164	C₂×#380	C₂×C₂₃	1	2	yes	—
165	C₂²×C₂₃	—	2	32	no	—
166	C₂²×C₂₃	—	2	4	no	—
167	C₂²×C₂₃	—	2	8	no	—
168	C₂²×C₂₃	—	2	8	no	—
169	C₂²×C₂₃	—	2	4	no	—
170	C₂²×C₂₃	C₂×C₂²⋊Q₈	1	4	yes	—
171	C₂²×C₂₃	#525	1	8	yes	—
172	C₂²×C₂₃	C₂×#125	1	4	yes	—
173	C₂²×C₂₃	C₂×#125	1	8	yes	complemented
174	C₂²×C₂₃	#529	1	8	yes	—
175	C₂²×C₂₃	#533	1	4	yes	—
176	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
177	C₂²×C₂₃	C₂³×Q₈	1	1	yes	characteristic
178	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
179	C₂²×C₂₃	C₂²×#41	1	2	yes	—
180	C₂²×C₂₃	C₂²×#41	1	2	yes	—
181	C₄×C₂₃	—	2	4	no	—
182	C₄×C₂₃	—	2	8	no	—
183	C₄×C₂₃	—	2	8	no	—
184	C₄×C₂₃	—	4	8	no	—
185	C₄×C₂₃	—	4	8	no	—
186	C₄×C₂₃	C₂×C₂²⋊Q₈	1	8	yes	—
187	C₂⁴×C₄	C₂²×C₂₃	1	2	yes	—
188	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
189	C₂×#125	—	2	8	no	—
190	C₂×#125	C₂²×C₂₃	1	8	yes	complemented
191	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
192	C₂²×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
193	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
194	C₂²×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
195	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
196	C₂²×C₄²	—	2	8	no	—
197	C₂²×C₄²	C₂²×C₂₃	1	8	yes	—
198	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
199	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
200	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
201	#389	C₂²×C₂₃	1	16	yes	complemented
202	#387	C₂²×C₂₃	1	32	yes	complemented
203	#385	C₂²×C₂₃	1	32	yes	—
204	#382	C₂²×C₂₃	1	8	yes	complemented
205	#380	C₂²×C₂₃	1	16	yes	—
206	C₂×#95	C₂²×C₂₃	1	4	yes	—
207	C₂×#95	C₂²×C₂₃	1	4	yes	—
208	C₂×#95	C₂²×C₂₃	1	4	yes	—
209	C₂×C₂₃	—	2	8	no	—
210	C₂×C₂₃	#2851	1	8	yes	direct product factor
211	C₂×C₂₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
212	C₂×C₂₃	C₂×#525	1	2	yes	—
213	C₂×C₂₃	C₂²×#125	1	1	yes	characteristic
214	C₂×C₂₃	C₂×#529	1	2	yes	—
215	C₂×C₂₃	C₂×#533	1	1	yes	characteristic
216	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
217	C₂³×C₄	—	2	8	no	—
218	C₂³×C₄	—	2	8	no	—
219	C₂³×C₄	—	2	4	no	—
220	C₂³×C₄	—	2	8	no	—
221	C₂³×C₄	—	2	4	no	—
222	C₂³×C₄	Q₈×C₂₃	1	8	yes	—
223	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
224	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
225	C₂³×C₄	C₂³×C₂₃	1	8	yes	—
226	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
227	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
228	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
229	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
230	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
231	#125	—	2	32	no	—
232	C₂×C₄⋊C₄	—	2	16	no	—
233	C₂×C₄⋊C₄	—	2	8	no	—
234	C₂×C₄⋊C₄	—	2	16	no	—
235	C₂×C₄⋊C₄	—	2	8	no	—
236	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
237	C₂×C₄⋊C₄	C₂³×C₂₃	1	16	yes	—
238	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
239	C₂×C₄⋊C₄	C₂³×C₂₃	1	16	yes	—
240	C₂×C₂²⋊C₄	—	2	16	no	—
241	C₂×C₂²⋊C₄	C₂³×C₂₃	1	16	yes	—
242	C₂×C₄²	—	2	8	no	—
243	C₂×C₄²	—	2	4	no	—
244	C₂×C₄²	—	2	32	no	—
245	C₂×C₄²	D₄×C₂₃	1	8	yes	—
246	C₂×C₄²	C₂³×C₂₃	1	8	yes	—
247	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
248	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
249	#95	C₂³×C₂₃	1	16	yes	—
250	#95	C₂³×C₂₃	1	16	yes	—
251	#95	C₂³×C₂₃	1	16	yes	—
252	C₂₃	C₂×#2851	1	1	yes	characteristic, direct product factor, Sylow
253	C₂⁴	—	2	2	no	—
254	C₂⁴	—	2	2	no	—
255	C₂⁴	—	2	4	no	—
256	C₂⁴	C₂×Q₈×C₂₃	1	4	yes	—
257	C₂⁴	#41×C₂₃	1	8	yes	—
258	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
259	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
260	C₂²×C₄	—	2	64	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	16	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	32	no	—
269	C₂²×C₄	—	2	16	no	—
270	C₂²×C₄	—	2	8	no	—
271	C₂²×C₄	—	2	16	no	—
272	C₂²×C₄	—	2	8	no	—
273	C₂²×C₄	—	2	8	no	—
274	C₂²×C₄	—	2	8	no	—
275	C₂²×C₄	—	2	8	no	—
276	C₂²×C₄	—	2	8	no	—
277	C₂²×C₄	—	2	8	no	—
278	C₂²×C₄	—	2	8	no	—
279	C₂²×C₄	C₂×D₄×C₂₃	1	8	yes	—
280	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
281	C₂²×C₄	C₂×Q₈×C₂₃	1	4	yes	—
282	C₂²×C₄	C₂×Q₈×C₂₃	1	16	yes	—
283	C₂²×C₄	C₂×Q₈×C₂₃	1	4	yes	—
284	C₂²×C₄	#41×C₂₃	1	8	yes	—
285	C₂²×C₄	#41×C₂₃	1	4	yes	—
286	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
287	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
288	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
289	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
290	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
291	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
292	C₄⋊C₄	—	2	32	no	—
293	C₄⋊C₄	—	2	16	no	—
294	C₄⋊C₄	—	2	32	no	—
295	C₄⋊C₄	—	2	16	no	—
296	C₂²⋊C₄	—	2	32	no	—
297	C₄²	—	2	16	no	—
298	C₄²	—	2	8	no	—
299	C₄²	C₂×D₄×C₂₃	1	16	yes	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	2	no	—
302	C₂³	—	2	4	no	—
303	C₂³	—	2	8	no	—
304	C₂³	—	2	16	no	—
305	C₂³	—	2	16	no	—
306	C₂³	—	2	8	no	—
307	C₂³	C₂₃×#125	1	16	yes	complemented
308	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
309	C₂³	C₂²×Q₈×C₂₃	1	4	yes	—
310	C₂³	C₂²×Q₈×C₂₃	1	2	yes	—
311	C₂³	C₂×#41×C₂₃	1	8	yes	—
312	C₂³	C₂×#41×C₂₃	1	2	yes	—
313	C₂³	C₂×#41×C₂₃	1	4	yes	—
314	C₂³	C₂×#41×C₂₃	1	4	yes	—
315	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
316	C₂×C₄	—	2	64	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	8	no	—
324	C₂×C₄	—	2	16	no	—
325	C₂×C₄	—	2	16	no	—
326	C₂×C₄	—	2	32	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	4	16	no	—
334	C₂×C₄	—	4	16	no	—
335	C₂×C₄	C₂₃×C₂²⋊Q₈	1	16	yes	—
336	C₂×C₄	C₂²×D₄×C₂₃	1	8	yes	—
337	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
338	C₂×C₄	C₂²×Q₈×C₂₃	1	4	yes	—
339	C₂×C₄	C₂²×Q₈×C₂₃	1	4	yes	—
340	C₂×C₄	C₂×#41×C₂₃	1	8	yes	—
341	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	8	no	—
344	C₂²	—	2	8	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	2	32	no	—
347	C₂²	C₂×C₂₃×C₂²⋊Q₈	1	4	yes	—
348	C₂²	C₂₃×#525	1	8	yes	—
349	C₂²	C₂×C₂₃×#125	1	4	yes	—
350	C₂²	C₂×C₂₃×#125	1	8	yes	complemented
351	C₂²	C₂₃×#529	1	8	yes	—
352	C₂²	C₂₃×#533	1	4	yes	—
353	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
354	C₂²	C₂³×Q₈×C₂₃	1	1	yes	characteristic
355	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
356	C₂²	C₂²×#41×C₂₃	1	2	yes	—
357	C₂²	C₂²×#41×C₂₃	1	2	yes	—
358	C₄	—	2	4	no	—
359	C₄	—	2	8	no	—
360	C₄	—	2	8	no	—
361	C₄	—	4	8	no	—
362	C₄	—	4	8	no	—
363	C₄	C₂×C₂₃×C₂²⋊Q₈	1	8	yes	—
364	C₂	—	2	8	no	—
365	C₂	C₂₃×#2851	1	8	yes	direct product factor
366	C₂	C₂²×C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
367	C₂	C₂×C₂₃×#525	1	2	yes	—
368	C₂	C₂²×C₂₃×#125	1	1	yes	characteristic
369	C₂	C₂×C₂₃×#529	1	2	yes	—
370	C₂	C₂×C₂₃×#533	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂⁵×C₂₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂₃×#125	C₂	semidirect
3. C₂₃×#2851	C₂	direct (N × H)
4. C₂×C₂₃×#389	C₂	semidirect
5. C₂×C₂₃×#387	C₂	semidirect
7. C₂×C₂₃×#382	C₂	semidirect
12. C₂×C₂₃×#125	C₂²	semidirect
23. C₂₃×#389	C₂²	semidirect
24. C₂₃×#387	C₂²	semidirect
26. C₂₃×#382	C₂²	semidirect
114. C₂×#2851	C₂₃	direct (N × H)
122. C₂³×C₂₃	#125	semidirect
157. C₂²×#125	C₂×C₂₃	semidirect
159. #2851	C₂×C₂₃	direct (N × H)
160. C₂×#389	C₂×C₂₃	semidirect
161. C₂×#387	C₂×C₂₃	semidirect
163. C₂×#382	C₂×C₂₃	semidirect
173. C₂²×C₂₃	C₂×#125	semidirect
190. C₂×#125	C₂²×C₂₃	semidirect
201. #389	C₂²×C₂₃	semidirect
202. #387	C₂²×C₂₃	semidirect
204. #382	C₂²×C₂₃	semidirect
210. C₂×C₂₃	#2851	direct (N × H)
252. C₂₃	C₂×#2851	direct (N × H)
307. C₂³	C₂₃×#125	semidirect
350. C₂²	C₂×C₂₃×#125	semidirect
365. C₂	C₂₃×#2851	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂₃×#125	2
C₂³×C₄²×C₂₃	2
C₂₃×#2851	2
C₂×C₂₃×#389	2
C₂×C₂₃×#387	2
C₂×C₂₃×#385	2
C₂×C₂₃×#382	2
C₂×C₂₃×#380	2
C₂×#2851	23

Subgroups — C2×C23×#2851 #19184242

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2851 #19184242