Subgroups — C₂×C₂₃×#2501 #19182382

Order 5888.

4222 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	C₂²×C₂₃×#123	C₂	1	4	yes	maximal, complemented
2	C₂²×C₂₃×#121	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2501	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₂₃×#399	C₂	1	4	yes	maximal, complemented
6	C₂×C₂₃×#390	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₃×#384	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₂₃	C₂²	1	2	yes	—
10	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₂₃	C₂²	1	2	yes	—
12	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
13	C₂×C₂₃×#123	—	2	32	no	—
14	C₂×C₂₃×#123	C₂²	1	32	yes	complemented
15	C₂×C₂₃×#121	—	2	8	no	—
16	C₂×C₂₃×#121	C₂²	1	8	yes	—
17	C₂²×C₄⋊C₄×C₂₃	—	2	8	no	—
18	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₂₃	C₂²	1	8	yes	—
20	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
22	C₂²×C₄⋊C₄×C₂₃	C₂²	1	8	yes	complemented
23	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	8	yes	—
25	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
26	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
27	C₂₃×#399	C₂²	1	32	yes	complemented
28	C₂₃×#390	C₂²	1	16	yes	complemented
29	C₂₃×#384	C₂²	1	16	yes	complemented
30	C₄×C₂²⋊C₄×C₂₃	C₂²	1	8	yes	complemented
31	C₂×C₂₃×#95	C₂²	1	2	yes	—
32	C₂⁵×C₂₃	C₂³	1	2	yes	—
33	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
34	C₂²×D₄×C₂₃	—	2	8	no	—
35	C₂²×D₄×C₂₃	—	2	16	no	—
36	C₂²×D₄×C₂₃	—	2	4	no	—
37	C₂²×D₄×C₂₃	—	2	8	no	—
38	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
39	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
40	C₂³×C₄×C₂₃	—	2	8	no	—
41	C₂³×C₄×C₂₃	—	2	8	no	—
42	C₂³×C₄×C₂₃	—	2	16	no	—
43	C₂³×C₄×C₂₃	D₄	1	8	yes	—
44	C₂³×C₄×C₂₃	C₂³	1	8	yes	—
45	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
46	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
48	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
50	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
51	C₂₃×#123	—	2	128	no	—
52	C₂₃×#121	—	2	32	no	—
53	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
54	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
55	C₂×C₄⋊C₄×C₂₃	—	2	32	no	—
56	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
57	C₂×C₄⋊C₄×C₂₃	—	2	32	no	—
58	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
59	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
60	C₂×C₄⋊C₄×C₂₃	C₂³	1	32	yes	—
61	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
62	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
63	C₂×C₂²⋊C₄×C₂₃	—	2	32	no	—
64	C₂×C₂²⋊C₄×C₂₃	D₄	1	16	yes	complemented
65	C₂×C₂²⋊C₄×C₂₃	C₂³	1	32	yes	—
66	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
67	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
68	C₂×C₄²×C₂₃	—	2	8	no	—
69	C₂×C₄²×C₂₃	C₂³	1	8	yes	—
70	C₂₃×#95	C₂³	1	8	yes	—
71	C₂⁴×C₂₃	—	2	4	no	—
72	C₂⁴×C₂₃	—	2	4	no	—
73	C₂⁴×C₂₃	—	2	8	no	—
74	C₂⁴×C₂₃	—	2	4	no	—
75	C₂⁴×C₂₃	—	2	8	no	—
76	C₂⁴×C₂₃	—	2	8	no	—
77	C₂⁴×C₂₃	C₂×D₄	1	8	yes	—
78	C₂⁴×C₂₃	C₂×D₄	1	4	yes	—
79	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
80	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
81	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
82	C₂×D₄×C₂₃	—	2	16	no	—
83	C₂×D₄×C₂₃	—	2	32	no	—
84	C₂×D₄×C₂₃	—	2	8	no	—
85	C₂×D₄×C₂₃	—	2	16	no	—
86	C₂×D₄×C₂₃	—	4	32	no	—
87	C₂×D₄×C₂₃	—	4	16	no	—
88	C₂²×C₄×C₂₃	—	2	8	no	—
89	C₂²×C₄×C₂₃	—	2	4	no	—
90	C₂²×C₄×C₂₃	—	2	8	no	—
91	C₂²×C₄×C₂₃	—	2	32	no	—
92	C₂²×C₄×C₂₃	—	2	16	no	—
93	C₂²×C₄×C₂₃	—	2	16	no	—
94	C₂²×C₄×C₂₃	—	2	4	no	—
95	C₂²×C₄×C₂₃	—	2	16	no	—
96	C₂²×C₄×C₂₃	—	2	8	no	—
97	C₂²×C₄×C₂₃	—	2	8	no	—
98	C₂²×C₄×C₂₃	—	2	32	no	—
99	C₂²×C₄×C₂₃	—	4	32	no	—
100	C₂²×C₄×C₂₃	C₂×D₄	1	16	yes	—
101	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₂₃	C₂×D₄	1	16	yes	—
103	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₂₃	#41	1	8	yes	—
105	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
106	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
107	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
108	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
109	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
110	C₄⋊C₄×C₂₃	—	2	16	no	—
111	C₄⋊C₄×C₂₃	—	2	16	no	—
112	C₄⋊C₄×C₂₃	—	2	8	no	—
113	C₄⋊C₄×C₂₃	—	2	64	no	—
114	C₂²⋊C₄×C₂₃	—	2	16	no	—
115	C₂²⋊C₄×C₂₃	—	2	64	no	—
116	C₂²⋊C₄×C₂₃	C₂×D₄	1	32	yes	complemented
117	C₄²×C₂₃	—	2	16	no	—
118	C₂×#2501	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂³×C₂₃	—	2	8	no	—
120	C₂³×C₂₃	—	2	8	no	—
121	C₂³×C₂₃	—	2	32	no	—
122	C₂³×C₂₃	—	2	4	no	—
123	C₂³×C₂₃	—	2	4	no	—
124	C₂³×C₂₃	—	2	8	no	—
125	C₂³×C₂₃	—	2	4	no	—
126	C₂³×C₂₃	—	2	8	no	—
127	C₂³×C₂₃	—	2	8	no	—
128	C₂³×C₂₃	—	4	8	no	—
129	C₂³×C₂₃	—	4	8	no	—
130	C₂³×C₂₃	—	4	8	no	—
131	C₂³×C₂₃	—	4	32	no	—
132	C₂³×C₂₃	#127	1	16	yes	—
133	C₂³×C₂₃	C₂²×D₄	1	8	yes	—
134	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
135	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
136	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
137	C₂³×C₂₃	C₂×#41	1	4	yes	—
138	C₂³×C₂₃	2₋¹⁺⁴	1	4	yes	—
139	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
140	D₄×C₂₃	—	4	32	no	—
141	D₄×C₂₃	—	4	16	no	—
142	C₂×C₄×C₂₃	—	2	8	no	—
143	C₂×C₄×C₂₃	—	2	32	no	—
144	C₂×C₄×C₂₃	—	2	8	no	—
145	C₂×C₄×C₂₃	—	2	4	no	—
146	C₂×C₄×C₂₃	—	2	8	no	—
147	C₂×C₄×C₂₃	—	2	32	no	—
148	C₂×C₄×C₂₃	—	2	16	no	—
149	C₂×C₄×C₂₃	—	2	4	no	—
150	C₂×C₄×C₂₃	—	2	8	no	—
151	C₂×C₄×C₂₃	—	2	8	no	—
152	C₂×C₄×C₂₃	—	4	32	no	—
153	C₂×C₄×C₂₃	—	4	16	no	—
154	C₂×C₄×C₂₃	—	4	8	no	—
155	C₂×C₄×C₂₃	#123	1	16	yes	complemented
156	C₂×C₄×C₂₃	C₂²×D₄	1	16	yes	—
157	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
158	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
159	C₂×C₄×C₂₃	C₂×#41	1	8	yes	—
160	C₂²×#123	C₂×C₂₃	1	4	yes	complemented
161	C₂²×#121	C₂×C₂₃	1	1	yes	characteristic
162	C₂³×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
163	#2501	C₂×C₂₃	1	16	yes	direct product factor
164	C₂×#399	C₂×C₂₃	1	4	yes	complemented
165	C₂×#390	C₂×C₂₃	1	2	yes	complemented
166	C₂×#384	C₂×C₂₃	1	2	yes	complemented
167	C₂×C₄×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
168	C₂²×C₂₃	—	2	4	no	—
169	C₂²×C₂₃	—	2	4	no	—
170	C₂²×C₂₃	—	2	16	no	—
171	C₂²×C₂₃	—	2	32	no	—
172	C₂²×C₂₃	—	4	4	no	—
173	C₂²×C₂₃	—	4	4	no	—
174	C₂²×C₂₃	—	4	4	no	—
175	C₂²×C₂₃	—	4	16	no	—
176	C₂²×C₂₃	—	8	16	no	—
177	C₂²×C₂₃	C₂×#123	1	4	yes	—
178	C₂²×C₂₃	C₂×#127	1	8	yes	—
179	C₂²×C₂₃	C₂×#127	1	4	yes	—
180	C₂²×C₂₃	#536	1	4	yes	—
181	C₂²×C₂₃	#547	1	16	yes	—
182	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
183	C₂²×C₂₃	C₂³×D₄	1	2	yes	—
184	C₂²×C₂₃	C₂²×#41	1	2	yes	—
185	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
186	C₄×C₂₃	—	2	4	no	—
187	C₄×C₂₃	—	2	16	no	—
188	C₄×C₂₃	—	4	8	no	—
189	C₄×C₂₃	—	4	4	no	—
190	C₄×C₂₃	C₂×#123	1	8	yes	complemented
191	C₂³×D₄	C₂²×C₂₃	1	2	yes	—
192	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
193	C₂⁴×C₄	C₂²×C₂₃	1	2	yes	—
194	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
195	C₂×#123	—	2	32	no	—
196	C₂×#123	C₂²×C₂₃	1	32	yes	complemented
197	C₂×#121	—	2	8	no	—
198	C₂×#121	C₂²×C₂₃	1	8	yes	—
199	C₂²×C₄⋊C₄	—	2	8	no	—
200	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
201	C₂²×C₄⋊C₄	C₂²×C₂₃	1	8	yes	—
202	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
203	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
204	C₂²×C₄⋊C₄	C₂²×C₂₃	1	8	yes	complemented
205	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
206	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	8	yes	—
207	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
208	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
209	#399	C₂²×C₂₃	1	32	yes	complemented
210	#390	C₂²×C₂₃	1	16	yes	complemented
211	#384	C₂²×C₂₃	1	16	yes	complemented
212	C₄×C₂²⋊C₄	C₂²×C₂₃	1	8	yes	complemented
213	C₂×#95	C₂²×C₂₃	1	2	yes	—
214	C₂×C₂₃	—	2	8	no	—
215	C₂×C₂₃	—	8	4	no	—
216	C₂×C₂₃	#2501	1	8	yes	direct product factor
217	C₂×C₂₃	C₂²×#123	1	1	yes	characteristic
218	C₂×C₂₃	C₂²×#127	1	1	yes	characteristic
219	C₂×C₂₃	C₂×#536	1	1	yes	characteristic
220	C₂×C₂₃	C₂×#547	1	4	yes	—
221	C₂⁵	C₂³×C₂₃	1	2	yes	—
222	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
223	C₂²×D₄	—	2	8	no	—
224	C₂²×D₄	—	2	16	no	—
225	C₂²×D₄	—	2	4	no	—
226	C₂²×D₄	—	2	8	no	—
227	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
228	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
229	C₂³×C₄	—	2	8	no	—
230	C₂³×C₄	—	2	8	no	—
231	C₂³×C₄	—	2	16	no	—
232	C₂³×C₄	D₄×C₂₃	1	8	yes	—
233	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
234	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
235	C₂³×C₄	C₂³×C₂₃	1	8	yes	—
236	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
237	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
238	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
239	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
240	#123	—	2	128	no	—
241	#121	—	2	32	no	—
242	C₂×C₄⋊C₄	—	2	8	no	—
243	C₂×C₄⋊C₄	—	2	8	no	—
244	C₂×C₄⋊C₄	—	2	32	no	—
245	C₂×C₄⋊C₄	—	2	4	no	—
246	C₂×C₄⋊C₄	—	2	32	no	—
247	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
248	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
249	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
250	C₂×C₄⋊C₄	C₂³×C₂₃	1	32	yes	—
251	C₂×C₂²⋊C₄	—	2	8	no	—
252	C₂×C₂²⋊C₄	—	2	32	no	—
253	C₂×C₂²⋊C₄	D₄×C₂₃	1	16	yes	complemented
254	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
255	C₂×C₂²⋊C₄	C₂³×C₂₃	1	32	yes	—
256	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
257	C₂×C₄²	—	2	8	no	—
258	C₂×C₄²	C₂³×C₂₃	1	8	yes	—
259	#95	C₂³×C₂₃	1	8	yes	—
260	C₂₃	C₂×#2501	1	1	yes	characteristic, direct product factor, Sylow
261	C₂⁴	—	2	4	no	—
262	C₂⁴	—	2	4	no	—
263	C₂⁴	—	2	8	no	—
264	C₂⁴	—	2	4	no	—
265	C₂⁴	—	2	8	no	—
266	C₂⁴	—	2	8	no	—
267	C₂⁴	C₂×D₄×C₂₃	1	8	yes	—
268	C₂⁴	C₂×D₄×C₂₃	1	4	yes	—
269	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
270	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
271	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
272	C₂×D₄	—	2	16	no	—
273	C₂×D₄	—	2	32	no	—
274	C₂×D₄	—	2	8	no	—
275	C₂×D₄	—	2	16	no	—
276	C₂×D₄	—	4	32	no	—
277	C₂×D₄	—	4	16	no	—
278	C₂²×C₄	—	2	8	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	8	no	—
281	C₂²×C₄	—	2	32	no	—
282	C₂²×C₄	—	2	16	no	—
283	C₂²×C₄	—	2	16	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	16	no	—
286	C₂²×C₄	—	2	8	no	—
287	C₂²×C₄	—	2	8	no	—
288	C₂²×C₄	—	2	32	no	—
289	C₂²×C₄	—	4	32	no	—
290	C₂²×C₄	C₂×D₄×C₂₃	1	16	yes	—
291	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
292	C₂²×C₄	C₂×D₄×C₂₃	1	16	yes	—
293	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
294	C₂²×C₄	#41×C₂₃	1	8	yes	—
295	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
296	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
297	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
298	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
299	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
300	C₄⋊C₄	—	2	16	no	—
301	C₄⋊C₄	—	2	16	no	—
302	C₄⋊C₄	—	2	8	no	—
303	C₄⋊C₄	—	2	64	no	—
304	C₂²⋊C₄	—	2	16	no	—
305	C₂²⋊C₄	—	2	64	no	—
306	C₂²⋊C₄	C₂×D₄×C₂₃	1	32	yes	complemented
307	C₄²	—	2	16	no	—
308	C₂³	—	2	32	no	—
309	C₂³	—	2	4	no	—
310	C₂³	—	2	4	no	—
311	C₂³	—	2	8	no	—
312	C₂³	—	2	8	no	—
313	C₂³	—	2	8	no	—
314	C₂³	—	2	4	no	—
315	C₂³	—	2	8	no	—
316	C₂³	—	2	8	no	—
317	C₂³	—	4	32	no	—
318	C₂³	—	4	8	no	—
319	C₂³	—	4	8	no	—
320	C₂³	—	4	8	no	—
321	C₂³	C₂₃×#127	1	16	yes	—
322	C₂³	C₂²×D₄×C₂₃	1	8	yes	—
323	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
324	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
325	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
326	C₂³	C₂×#41×C₂₃	1	4	yes	—
327	C₂³	C₂₃×2₋¹⁺⁴	1	4	yes	—
328	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
329	D₄	—	4	32	no	—
330	D₄	—	4	16	no	—
331	C₂×C₄	—	2	32	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	8	no	—
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	2	32	no	—
337	C₂×C₄	—	2	16	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	8	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	4	32	no	—
342	C₂×C₄	—	4	16	no	—
343	C₂×C₄	—	4	8	no	—
344	C₂×C₄	C₂₃×#123	1	16	yes	complemented
345	C₂×C₄	C₂²×D₄×C₂₃	1	16	yes	—
346	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
347	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
348	C₂×C₄	C₂×#41×C₂₃	1	8	yes	—
349	C₂²	—	2	4	no	—
350	C₂²	—	2	4	no	—
351	C₂²	—	2	16	no	—
352	C₂²	—	2	32	no	—
353	C₂²	—	4	4	no	—
354	C₂²	—	4	4	no	—
355	C₂²	—	4	4	no	—
356	C₂²	—	4	16	no	—
357	C₂²	—	8	16	no	—
358	C₂²	C₂×C₂₃×#123	1	4	yes	—
359	C₂²	C₂×C₂₃×#127	1	8	yes	—
360	C₂²	C₂×C₂₃×#127	1	4	yes	—
361	C₂²	C₂₃×#536	1	4	yes	—
362	C₂²	C₂₃×#547	1	16	yes	—
363	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
364	C₂²	C₂³×D₄×C₂₃	1	2	yes	—
365	C₂²	C₂²×#41×C₂₃	1	2	yes	—
366	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
367	C₄	—	2	4	no	—
368	C₄	—	2	16	no	—
369	C₄	—	4	8	no	—
370	C₄	—	4	4	no	—
371	C₄	C₂×C₂₃×#123	1	8	yes	complemented
372	C₂	—	2	8	no	—
373	C₂	—	8	4	no	—
374	C₂	C₂₃×#2501	1	8	yes	direct product factor
375	C₂	C₂²×C₂₃×#123	1	1	yes	characteristic
376	C₂	C₂²×C₂₃×#127	1	1	yes	characteristic
377	C₂	C₂×C₂₃×#536	1	1	yes	characteristic
378	C₂	C₂×C₂₃×#547	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂²×C₂₃×#121	C₂
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×#123	C₂	semidirect
3. C₂³×C₄⋊C₄×C₂₃	C₂	semidirect
4. C₂₃×#2501	C₂	direct (N × H)
5. C₂×C₂₃×#399	C₂	semidirect
6. C₂×C₂₃×#390	C₂	semidirect
7. C₂×C₂₃×#384	C₂	semidirect
8. C₂×C₄×C₂²⋊C₄×C₂₃	C₂	semidirect
14. C₂×C₂₃×#123	C₂²	semidirect
22. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
27. C₂₃×#399	C₂²	semidirect
28. C₂₃×#390	C₂²	semidirect
29. C₂₃×#384	C₂²	semidirect
30. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
64. C₂×C₂²⋊C₄×C₂₃	D₄	semidirect
116. C₂²⋊C₄×C₂₃	C₂×D₄	semidirect
118. C₂×#2501	C₂₃	direct (N × H)
155. C₂×C₄×C₂₃	#123	semidirect
160. C₂²×#123	C₂×C₂₃	semidirect
162. C₂³×C₄⋊C₄	C₂×C₂₃	semidirect
163. #2501	C₂×C₂₃	direct (N × H)
164. C₂×#399	C₂×C₂₃	semidirect
165. C₂×#390	C₂×C₂₃	semidirect
166. C₂×#384	C₂×C₂₃	semidirect
167. C₂×C₄×C₂²⋊C₄	C₂×C₂₃	semidirect
190. C₄×C₂₃	C₂×#123	semidirect
196. C₂×#123	C₂²×C₂₃	semidirect
204. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
209. #399	C₂²×C₂₃	semidirect
210. #390	C₂²×C₂₃	semidirect
211. #384	C₂²×C₂₃	semidirect
212. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
216. C₂×C₂₃	#2501	direct (N × H)
253. C₂×C₂²⋊C₄	D₄×C₂₃	semidirect
260. C₂₃	C₂×#2501	direct (N × H)
306. C₂²⋊C₄	C₂×D₄×C₂₃	semidirect
344. C₂×C₄	C₂₃×#123	semidirect
371. C₄	C₂×C₂₃×#123	semidirect
374. C₂	C₂₃×#2501	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×#123	2
C₂²×C₂₃×#121	2
C₂³×C₄⋊C₄×C₂₃	2
C₂₃×#2501	2
C₂×C₂₃×#399	2
C₂×C₂₃×#390	2
C₂×C₂₃×#384	2
C₂×C₄×C₂²⋊C₄×C₂₃	2
C₂×#2501	23

Subgroups — C2×C23×#2501 #19182382

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2501 #19182382