Subgroups — C₂×C₂₃×#2324 #19181690

Order 5888.

3934 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×#121	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2324	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₂₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#390	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#388	C₂	1	2	yes	maximal, complemented
9	C₂×C₂₃×#386	C₂	1	2	yes	maximal, complemented
10	C₂×C₂₃×#385	C₂	1	2	yes	maximal, complemented
11	C₂×C₂₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₂₃	C₂²	1	2	yes	—
15	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₂₃	C₂²	1	2	yes	—
17	C₂×C₂₃×#121	C₄	1	16	yes	complemented
18	C₂×C₂₃×#121	C₂²	1	8	yes	—
19	C₂×C₄×D₄×C₂₃	—	2	8	no	—
20	C₂×C₄×D₄×C₂₃	C₂²	1	8	yes	complemented
21	C₂×C₂₃×#117	—	2	8	no	—
22	C₂×C₂₃×#117	C₂²	1	8	yes	complemented
23	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
28	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
32	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
33	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
34	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
35	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
36	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
38	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
39	C₂₃×#390	C₂²	1	8	yes	complemented
40	C₂₃×#390	C₂²	1	16	yes	complemented
41	C₂₃×#389	C₂²	1	8	yes	complemented
42	C₂₃×#388	C₂²	1	16	yes	complemented
43	C₂₃×#386	C₂²	1	16	yes	complemented
44	C₂₃×#385	C₂²	1	16	yes	complemented
45	C₂₃×#380	C₂²	1	8	yes	complemented
46	C₄×C₄⋊C₄×C₂₃	C₂²	1	8	yes	complemented
47	C₂×C₂₃×#95	C₂²	1	2	yes	—
48	C₂×C₂₃×#95	C₂²	1	2	yes	—
49	C₂×C₂₃×#95	C₂²	1	2	yes	—
50	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
51	C₂⁵×C₂₃	C₂³	1	2	yes	—
52	C₂²×D₄×C₂₃	—	2	4	no	—
53	C₂²×D₄×C₂₃	—	2	4	no	—
54	C₂²×D₄×C₂₃	—	4	4	no	—
55	C₂²×D₄×C₂₃	—	4	4	no	—
56	C₂²×D₄×C₂₃	C₂×C₄	1	8	yes	—
57	C₂²×D₄×C₂₃	C₂×C₄	1	16	yes	complemented
58	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
59	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
60	C₂³×C₄×C₂₃	—	2	4	no	—
61	C₂³×C₄×C₂₃	—	2	4	no	—
62	C₂³×C₄×C₂₃	—	2	8	no	—
63	C₂³×C₄×C₂₃	—	4	4	no	—
64	C₂³×C₄×C₂₃	—	4	4	no	—
65	C₂³×C₄×C₂₃	C₂×C₄	1	8	yes	complemented
66	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
67	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
69	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
72	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
73	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₂₃	C₂³	1	8	yes	—
76	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
77	C₂₃×#121	C₂×C₄	1	64	yes	complemented
78	C₄×D₄×C₂₃	—	2	32	no	—
79	C₂₃×#117	—	2	32	no	—
80	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
81	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
82	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
83	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
84	C₂×C₄⋊C₄×C₂₃	—	4	4	no	—
85	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	8	yes	complemented
86	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
91	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
92	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
93	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
94	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
95	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
96	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
97	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
98	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	16	yes	complemented
99	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
101	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
102	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
103	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
104	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
105	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
106	C₂×C₄²×C₂₃	—	2	4	no	—
107	C₂×C₄²×C₂₃	—	4	4	no	—
108	C₂×C₄²×C₂₃	D₄	1	8	yes	complemented
109	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
110	C₂×C₄²×C₂₃	C₂³	1	8	yes	—
111	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
112	C₂₃×#95	C₂³	1	8	yes	—
113	C₂₃×#95	C₂³	1	8	yes	—
114	C₂₃×#95	C₂³	1	8	yes	—
115	C₂⁴×C₂₃	—	2	2	no	—
116	C₂⁴×C₂₃	—	2	4	no	—
117	C₂⁴×C₂₃	—	2	2	no	—
118	C₂⁴×C₂₃	—	2	4	no	—
119	C₂⁴×C₂₃	—	2	2	no	—
120	C₂⁴×C₂₃	—	2	4	no	—
121	C₂⁴×C₂₃	—	2	4	no	—
122	C₂⁴×C₂₃	—	2	4	no	—
123	C₂⁴×C₂₃	—	2	2	no	—
124	C₂⁴×C₂₃	—	2	2	no	—
125	C₂⁴×C₂₃	—	2	2	no	—
126	C₂⁴×C₂₃	—	2	4	no	—
127	C₂⁴×C₂₃	C₂²×C₄	1	8	yes	—
128	C₂⁴×C₂₃	C₂²×C₄	1	4	yes	—
129	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
130	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
131	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
132	C₂×D₄×C₂₃	—	2	32	no	—
133	C₂×D₄×C₂₃	—	2	8	no	—
134	C₂×D₄×C₂₃	—	2	8	no	—
135	C₂×D₄×C₂₃	—	4	32	no	—
136	C₂×D₄×C₂₃	—	4	8	no	—
137	C₂×D₄×C₂₃	—	4	8	no	—
138	C₂×D₄×C₂₃	C₂²×C₄	1	16	yes	—
139	C₂×D₄×C₂₃	C₂²×C₄	1	32	yes	complemented
140	C₂²×C₄×C₂₃	—	2	2	no	—
141	C₂²×C₄×C₂₃	—	2	2	no	—
142	C₂²×C₄×C₂₃	—	2	2	no	—
143	C₂²×C₄×C₂₃	—	2	4	no	—
144	C₂²×C₄×C₂₃	—	2	4	no	—
145	C₂²×C₄×C₂₃	—	2	2	no	—
146	C₂²×C₄×C₂₃	—	2	2	no	—
147	C₂²×C₄×C₂₃	—	2	2	no	—
148	C₂²×C₄×C₂₃	—	2	32	no	—
149	C₂²×C₄×C₂₃	—	2	8	no	—
150	C₂²×C₄×C₂₃	—	2	8	no	—
151	C₂²×C₄×C₂₃	—	2	2	no	—
152	C₂²×C₄×C₂₃	—	2	2	no	—
153	C₂²×C₄×C₂₃	—	2	4	no	—
154	C₂²×C₄×C₂₃	—	2	4	no	—
155	C₂²×C₄×C₂₃	—	2	4	no	—
156	C₂²×C₄×C₂₃	—	2	2	no	—
157	C₂²×C₄×C₂₃	—	2	2	no	—
158	C₂²×C₄×C₂₃	—	2	4	no	—
159	C₂²×C₄×C₂₃	—	2	4	no	—
160	C₂²×C₄×C₂₃	—	2	2	no	—
161	C₂²×C₄×C₂₃	—	2	4	no	—
162	C₂²×C₄×C₂₃	—	2	2	no	—
163	C₂²×C₄×C₂₃	—	2	16	no	—
164	C₂²×C₄×C₂₃	—	4	8	no	—
165	C₂²×C₄×C₂₃	—	4	8	no	—
166	C₂²×C₄×C₂₃	—	4	32	no	—
167	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
168	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
169	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
170	C₂²×C₄×C₂₃	C₂²×C₄	1	16	yes	complemented
171	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
172	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
173	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
174	C₂²×C₄×C₂₃	#41	1	4	yes	—
175	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
184	C₄⋊C₄×C₂₃	—	2	8	no	—
185	C₄⋊C₄×C₂₃	—	2	8	no	—
186	C₄⋊C₄×C₂₃	—	2	8	no	—
187	C₄⋊C₄×C₂₃	—	2	8	no	—
188	C₄⋊C₄×C₂₃	—	4	8	no	—
189	C₄⋊C₄×C₂₃	C₂²×C₄	1	16	yes	complemented
190	C₂²⋊C₄×C₂₃	—	2	8	no	—
191	C₂²⋊C₄×C₂₃	—	2	8	no	—
192	C₂²⋊C₄×C₂₃	—	2	16	no	—
193	C₂²⋊C₄×C₂₃	—	4	8	no	—
194	C₂²⋊C₄×C₂₃	—	4	8	no	—
195	C₂²⋊C₄×C₂₃	—	4	8	no	—
196	C₂²⋊C₄×C₂₃	C₂²×C₄	1	32	yes	complemented
197	C₄²×C₂₃	—	2	8	no	—
198	C₄²×C₂₃	—	4	8	no	—
199	C₄²×C₂₃	C₂×D₄	1	16	yes	complemented
200	C₂×#2324	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂³×C₂₃	—	2	8	no	—
202	C₂³×C₂₃	—	2	16	no	—
203	C₂³×C₂₃	—	2	8	no	—
204	C₂³×C₂₃	—	2	16	no	—
205	C₂³×C₂₃	—	2	8	no	—
206	C₂³×C₂₃	—	2	16	no	—
207	C₂³×C₂₃	—	2	2	no	—
208	C₂³×C₂₃	—	2	4	no	—
209	C₂³×C₂₃	—	2	2	no	—
210	C₂³×C₂₃	—	2	4	no	—
211	C₂³×C₂₃	—	2	2	no	—
212	C₂³×C₂₃	—	2	4	no	—
213	C₂³×C₂₃	—	2	4	no	—
214	C₂³×C₂₃	—	2	4	no	—
215	C₂³×C₂₃	—	2	2	no	—
216	C₂³×C₂₃	—	2	2	no	—
217	C₂³×C₂₃	—	2	2	no	—
218	C₂³×C₂₃	—	2	4	no	—
219	C₂³×C₂₃	—	4	8	no	—
220	C₂³×C₂₃	—	4	4	no	—
221	C₂³×C₂₃	—	4	4	no	—
222	C₂³×C₂₃	—	4	8	no	—
223	C₂³×C₂₃	—	4	4	no	—
224	C₂³×C₂₃	—	4	8	no	—
225	C₂³×C₂₃	—	4	4	no	—
226	C₂³×C₂₃	—	4	8	no	—
227	C₂³×C₂₃	C₂³×C₄	1	8	yes	—
228	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
229	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
230	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
231	C₂³×C₂₃	C₂×#41	1	2	yes	—
232	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
233	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
234	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
235	C₂³×C₂₃	2₋¹⁺⁴	1	2	yes	—
236	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
237	D₄×C₂₃	—	2	32	no	—
238	D₄×C₂₃	—	4	32	no	—
239	C₂×C₄×C₂₃	—	2	8	no	—
240	C₂×C₄×C₂₃	—	2	16	no	—
241	C₂×C₄×C₂₃	—	2	8	no	—
242	C₂×C₄×C₂₃	—	2	8	no	—
243	C₂×C₄×C₂₃	—	2	2	no	—
244	C₂×C₄×C₂₃	—	2	2	no	—
245	C₂×C₄×C₂₃	—	2	2	no	—
246	C₂×C₄×C₂₃	—	2	4	no	—
247	C₂×C₄×C₂₃	—	2	4	no	—
248	C₂×C₄×C₂₃	—	2	2	no	—
249	C₂×C₄×C₂₃	—	2	2	no	—
250	C₂×C₄×C₂₃	—	2	2	no	—
251	C₂×C₄×C₂₃	—	2	32	no	—
252	C₂×C₄×C₂₃	—	2	2	no	—
253	C₂×C₄×C₂₃	—	2	2	no	—
254	C₂×C₄×C₂₃	—	2	4	no	—
255	C₂×C₄×C₂₃	—	2	4	no	—
256	C₂×C₄×C₂₃	—	2	4	no	—
257	C₂×C₄×C₂₃	—	2	2	no	—
258	C₂×C₄×C₂₃	—	2	2	no	—
259	C₂×C₄×C₂₃	—	2	4	no	—
260	C₂×C₄×C₂₃	—	2	4	no	—
261	C₂×C₄×C₂₃	—	2	2	no	—
262	C₂×C₄×C₂₃	—	2	4	no	—
263	C₂×C₄×C₂₃	—	2	2	no	—
264	C₂×C₄×C₂₃	—	4	32	no	—
265	C₂×C₄×C₂₃	—	4	4	no	—
266	C₂×C₄×C₂₃	—	4	8	no	—
267	C₂×C₄×C₂₃	—	4	4	no	—
268	C₂×C₄×C₂₃	—	4	8	no	—
269	C₂×C₄×C₂₃	C₄×D₄	1	16	yes	—
270	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
271	C₂×C₄×C₂₃	C₂³×C₄	1	8	yes	—
272	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
273	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
274	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
275	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
276	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
277	C₂²×#121	C₂×C₂₃	1	1	yes	characteristic
278	C₂²×C₄×D₄	C₂×C₂₃	1	1	yes	characteristic, complemented
279	C₂²×#117	C₂×C₂₃	1	1	yes	characteristic, complemented
280	#2324	C₂×C₂₃	1	16	yes	direct product factor
281	C₂×#390	C₂×C₂₃	1	2	yes	complemented
282	C₂×#390	C₂×C₂₃	1	1	yes	characteristic, complemented
283	C₂×#389	C₂×C₂₃	1	1	yes	characteristic, complemented
284	C₂×#388	C₂×C₂₃	1	2	yes	complemented
285	C₂×#386	C₂×C₂₃	1	2	yes	complemented
286	C₂×#385	C₂×C₂₃	1	2	yes	complemented
287	C₂×#380	C₂×C₂₃	1	1	yes	characteristic, complemented
288	C₂×C₄×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
289	C₂²×C₂₃	—	2	4	no	—
290	C₂²×C₂₃	—	2	8	no	—
291	C₂²×C₂₃	—	2	4	no	—
292	C₂²×C₂₃	—	2	8	no	—
293	C₂²×C₂₃	—	2	4	no	—
294	C₂²×C₂₃	—	2	8	no	—
295	C₂²×C₂₃	—	4	16	no	—
296	C₂²×C₂₃	—	4	32	no	—
297	C₂²×C₂₃	—	4	4	no	—
298	C₂²×C₂₃	—	4	2	no	—
299	C₂²×C₂₃	—	4	2	no	—
300	C₂²×C₂₃	—	4	4	no	—
301	C₂²×C₂₃	—	4	2	no	—
302	C₂²×C₂₃	—	4	4	no	—
303	C₂²×C₂₃	—	4	2	no	—
304	C₂²×C₂₃	—	4	4	no	—
305	C₂²×C₂₃	C₂×C₄×D₄	1	4	yes	—
306	C₂²×C₂₃	#518	1	4	yes	—
307	C₂²×C₂₃	#520	1	4	yes	—
308	C₂²×C₂₃	#535	1	4	yes	—
309	C₂²×C₂₃	#537	1	4	yes	—
310	C₂²×C₂₃	#540	1	4	yes	—
311	C₂²×C₂₃	#542	1	4	yes	—
312	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
313	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
314	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
315	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
316	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
317	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
318	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
319	C₄×C₂₃	—	2	4	no	—
320	C₄×C₂₃	—	2	8	no	—
321	C₄×C₂₃	—	2	4	no	—
322	C₄×C₂₃	—	2	4	no	—
323	C₄×C₂₃	—	4	2	no	—
324	C₄×C₂₃	—	4	4	no	—
325	C₄×C₂₃	—	4	2	no	—
326	C₄×C₂₃	—	4	4	no	—
327	C₄×C₂₃	C₂×C₄×D₄	1	8	yes	—
328	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
329	C₂³×D₄	C₂²×C₂₃	1	2	yes	—
330	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
331	C₂⁴×C₄	C₂²×C₂₃	1	2	yes	—
332	C₂×#121	C₄×C₂₃	1	16	yes	complemented
333	C₂×#121	C₂²×C₂₃	1	8	yes	—
334	C₂×C₄×D₄	—	2	8	no	—
335	C₂×C₄×D₄	C₂²×C₂₃	1	8	yes	complemented
336	C₂×#117	—	2	8	no	—
337	C₂×#117	C₂²×C₂₃	1	8	yes	complemented
338	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
339	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
340	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
341	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
342	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
343	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
344	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
345	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
346	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
347	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
348	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
349	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
350	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
351	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
352	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
353	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
354	#390	C₂²×C₂₃	1	8	yes	complemented
355	#390	C₂²×C₂₃	1	16	yes	complemented
356	#389	C₂²×C₂₃	1	8	yes	complemented
357	#388	C₂²×C₂₃	1	16	yes	complemented
358	#386	C₂²×C₂₃	1	16	yes	complemented
359	#385	C₂²×C₂₃	1	16	yes	complemented
360	#380	C₂²×C₂₃	1	8	yes	complemented
361	C₄×C₄⋊C₄	C₂²×C₂₃	1	8	yes	complemented
362	C₂×#95	C₂²×C₂₃	1	2	yes	—
363	C₂×#95	C₂²×C₂₃	1	2	yes	—
364	C₂×#95	C₂²×C₂₃	1	2	yes	—
365	C₂×C₂₃	—	4	4	no	—
366	C₂×C₂₃	—	4	8	no	—
367	C₂×C₂₃	#2324	1	8	yes	direct product factor
368	C₂×C₂₃	C₂²×C₄×D₄	1	1	yes	characteristic
369	C₂×C₂₃	C₂×#518	1	1	yes	characteristic
370	C₂×C₂₃	C₂×#520	1	1	yes	characteristic
371	C₂×C₂₃	C₂×#535	1	1	yes	characteristic
372	C₂×C₂₃	C₂×#537	1	1	yes	characteristic
373	C₂×C₂₃	C₂×#540	1	1	yes	characteristic
374	C₂×C₂₃	C₂×#542	1	1	yes	characteristic
375	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
376	C₂⁵	C₂³×C₂₃	1	2	yes	—
377	C₂²×D₄	—	2	4	no	—
378	C₂²×D₄	—	2	4	no	—
379	C₂²×D₄	—	4	4	no	—
380	C₂²×D₄	—	4	4	no	—
381	C₂²×D₄	C₂×C₄×C₂₃	1	8	yes	—
382	C₂²×D₄	C₂×C₄×C₂₃	1	16	yes	complemented
383	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
384	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
385	C₂³×C₄	—	2	4	no	—
386	C₂³×C₄	—	2	4	no	—
387	C₂³×C₄	—	2	8	no	—
388	C₂³×C₄	—	4	4	no	—
389	C₂³×C₄	—	4	4	no	—
390	C₂³×C₄	C₂×C₄×C₂₃	1	8	yes	complemented
391	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
393	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
394	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
395	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
396	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
397	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
398	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
399	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
400	C₂³×C₄	C₂³×C₂₃	1	8	yes	—
401	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
402	#121	C₂×C₄×C₂₃	1	64	yes	complemented
403	C₄×D₄	—	2	32	no	—
404	#117	—	2	32	no	—
405	C₂×C₄⋊C₄	—	2	4	no	—
406	C₂×C₄⋊C₄	—	2	4	no	—
407	C₂×C₄⋊C₄	—	2	4	no	—
408	C₂×C₄⋊C₄	—	2	4	no	—
409	C₂×C₄⋊C₄	—	4	4	no	—
410	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	8	yes	complemented
411	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
412	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
413	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
414	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
415	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
416	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
417	C₂×C₂²⋊C₄	—	2	4	no	—
418	C₂×C₂²⋊C₄	—	2	4	no	—
419	C₂×C₂²⋊C₄	—	2	8	no	—
420	C₂×C₂²⋊C₄	—	4	4	no	—
421	C₂×C₂²⋊C₄	—	4	4	no	—
422	C₂×C₂²⋊C₄	—	4	4	no	—
423	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	16	yes	complemented
424	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
431	C₂×C₄²	—	2	4	no	—
432	C₂×C₄²	—	4	4	no	—
433	C₂×C₄²	D₄×C₂₃	1	8	yes	complemented
434	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
435	C₂×C₄²	C₂³×C₂₃	1	8	yes	—
436	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
437	#95	C₂³×C₂₃	1	8	yes	—
438	#95	C₂³×C₂₃	1	8	yes	—
439	#95	C₂³×C₂₃	1	8	yes	—
440	C₂₃	C₂×#2324	1	1	yes	characteristic, direct product factor, Sylow
441	C₂⁴	—	2	2	no	—
442	C₂⁴	—	2	4	no	—
443	C₂⁴	—	2	2	no	—
444	C₂⁴	—	2	4	no	—
445	C₂⁴	—	2	2	no	—
446	C₂⁴	—	2	4	no	—
447	C₂⁴	—	2	4	no	—
448	C₂⁴	—	2	4	no	—
449	C₂⁴	—	2	2	no	—
450	C₂⁴	—	2	2	no	—
451	C₂⁴	—	2	2	no	—
452	C₂⁴	—	2	4	no	—
453	C₂⁴	C₂²×C₄×C₂₃	1	8	yes	—
454	C₂⁴	C₂²×C₄×C₂₃	1	4	yes	—
455	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
456	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
457	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
458	C₂×D₄	—	2	32	no	—
459	C₂×D₄	—	2	8	no	—
460	C₂×D₄	—	2	8	no	—
461	C₂×D₄	—	4	32	no	—
462	C₂×D₄	—	4	8	no	—
463	C₂×D₄	—	4	8	no	—
464	C₂×D₄	C₂²×C₄×C₂₃	1	16	yes	—
465	C₂×D₄	C₂²×C₄×C₂₃	1	32	yes	complemented
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	32	no	—
475	C₂²×C₄	—	2	8	no	—
476	C₂²×C₄	—	2	8	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	4	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	16	no	—
490	C₂²×C₄	—	4	8	no	—
491	C₂²×C₄	—	4	8	no	—
492	C₂²×C₄	—	4	32	no	—
493	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
494	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
495	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
496	C₂²×C₄	C₂²×C₄×C₂₃	1	16	yes	complemented
497	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
498	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
499	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
500	C₂²×C₄	#41×C₂₃	1	4	yes	—
501	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
502	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
503	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
504	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
505	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
506	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
507	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
508	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
509	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
510	C₄⋊C₄	—	2	8	no	—
511	C₄⋊C₄	—	2	8	no	—
512	C₄⋊C₄	—	2	8	no	—
513	C₄⋊C₄	—	2	8	no	—
514	C₄⋊C₄	—	4	8	no	—
515	C₄⋊C₄	C₂²×C₄×C₂₃	1	16	yes	complemented
516	C₂²⋊C₄	—	2	8	no	—
517	C₂²⋊C₄	—	2	8	no	—
518	C₂²⋊C₄	—	2	16	no	—
519	C₂²⋊C₄	—	4	8	no	—
520	C₂²⋊C₄	—	4	8	no	—
521	C₂²⋊C₄	—	4	8	no	—
522	C₂²⋊C₄	C₂²×C₄×C₂₃	1	32	yes	complemented
523	C₄²	—	2	8	no	—
524	C₄²	—	4	8	no	—
525	C₄²	C₂×D₄×C₂₃	1	16	yes	complemented
526	C₂³	—	2	2	no	—
527	C₂³	—	2	4	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	4	no	—
530	C₂³	—	2	2	no	—
531	C₂³	—	2	4	no	—
532	C₂³	—	2	4	no	—
533	C₂³	—	2	4	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	8	no	—
539	C₂³	—	2	16	no	—
540	C₂³	—	2	8	no	—
541	C₂³	—	2	16	no	—
542	C₂³	—	2	8	no	—
543	C₂³	—	2	16	no	—
544	C₂³	—	4	8	no	—
545	C₂³	—	4	4	no	—
546	C₂³	—	4	4	no	—
547	C₂³	—	4	8	no	—
548	C₂³	—	4	4	no	—
549	C₂³	—	4	8	no	—
550	C₂³	—	4	4	no	—
551	C₂³	—	4	8	no	—
552	C₂³	C₂³×C₄×C₂₃	1	8	yes	—
553	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
554	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
555	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
556	C₂³	C₂×#41×C₂₃	1	2	yes	—
557	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
558	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
559	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
560	C₂³	C₂₃×2₋¹⁺⁴	1	2	yes	—
561	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
562	D₄	—	2	32	no	—
563	D₄	—	4	32	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	8	no	—
573	C₂×C₄	—	2	16	no	—
574	C₂×C₄	—	2	8	no	—
575	C₂×C₄	—	2	8	no	—
576	C₂×C₄	—	2	32	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	4	32	no	—
590	C₂×C₄	—	4	8	no	—
591	C₂×C₄	—	4	4	no	—
592	C₂×C₄	—	4	4	no	—
593	C₂×C₄	—	4	8	no	—
594	C₂×C₄	C₄×D₄×C₂₃	1	16	yes	—
595	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
596	C₂×C₄	C₂³×C₄×C₂₃	1	8	yes	—
597	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
598	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
599	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
600	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
601	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
602	C₂²	—	2	4	no	—
603	C₂²	—	2	8	no	—
604	C₂²	—	2	4	no	—
605	C₂²	—	2	8	no	—
606	C₂²	—	2	4	no	—
607	C₂²	—	2	8	no	—
608	C₂²	—	4	4	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	4	no	—
612	C₂²	—	4	2	no	—
613	C₂²	—	4	4	no	—
614	C₂²	—	4	2	no	—
615	C₂²	—	4	4	no	—
616	C₂²	—	4	16	no	—
617	C₂²	—	4	32	no	—
618	C₂²	C₂×C₄×D₄×C₂₃	1	4	yes	—
619	C₂²	C₂₃×#518	1	4	yes	—
620	C₂²	C₂₃×#520	1	4	yes	—
621	C₂²	C₂₃×#535	1	4	yes	—
622	C₂²	C₂₃×#537	1	4	yes	—
623	C₂²	C₂₃×#540	1	4	yes	—
624	C₂²	C₂₃×#542	1	4	yes	—
625	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
626	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
627	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
628	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
629	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
630	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
631	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
632	C₄	—	2	4	no	—
633	C₄	—	2	8	no	—
634	C₄	—	2	4	no	—
635	C₄	—	2	4	no	—
636	C₄	—	4	4	no	—
637	C₄	—	4	2	no	—
638	C₄	—	4	2	no	—
639	C₄	—	4	4	no	—
640	C₄	C₂×C₄×D₄×C₂₃	1	8	yes	—
641	C₂	—	4	4	no	—
642	C₂	—	4	8	no	—
643	C₂	C₂₃×#2324	1	8	yes	direct product factor
644	C₂	C₂²×C₄×D₄×C₂₃	1	1	yes	characteristic
645	C₂	C₂×C₂₃×#518	1	1	yes	characteristic
646	C₂	C₂×C₂₃×#520	1	1	yes	characteristic
647	C₂	C₂×C₂₃×#535	1	1	yes	characteristic
648	C₂	C₂×C₂₃×#537	1	1	yes	characteristic
649	C₂	C₂×C₂₃×#540	1	1	yes	characteristic
650	C₂	C₂×C₂₃×#542	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₂₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂²×C₂₃×#121	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×D₄×C₂₃	C₂	semidirect
3. C₂²×C₂₃×#117	C₂	semidirect
4. C₂₃×#2324	C₂	direct (N × H)
5. C₂×C₂₃×#390	C₂	semidirect
6. C₂×C₂₃×#390	C₂	semidirect
7. C₂×C₂₃×#389	C₂	semidirect
8. C₂×C₂₃×#388	C₂	semidirect
9. C₂×C₂₃×#386	C₂	semidirect
10. C₂×C₂₃×#385	C₂	semidirect
11. C₂×C₂₃×#380	C₂	semidirect
12. C₂×C₄×C₄⋊C₄×C₂₃	C₂	semidirect
17. C₂×C₂₃×#121	C₄	semidirect
20. C₂×C₄×D₄×C₂₃	C₂²	semidirect
22. C₂×C₂₃×#117	C₂²	semidirect
39. C₂₃×#390	C₂²	semidirect
40. C₂₃×#390	C₂²	semidirect
41. C₂₃×#389	C₂²	semidirect
42. C₂₃×#388	C₂²	semidirect
43. C₂₃×#386	C₂²	semidirect
44. C₂₃×#385	C₂²	semidirect
45. C₂₃×#380	C₂²	semidirect
46. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
57. C₂²×D₄×C₂₃	C₂×C₄	semidirect
65. C₂³×C₄×C₂₃	C₂×C₄	semidirect
77. C₂₃×#121	C₂×C₄	semidirect
85. C₂×C₄⋊C₄×C₂₃	C₂×C₄	semidirect
98. C₂×C₂²⋊C₄×C₂₃	C₂×C₄	semidirect
108. C₂×C₄²×C₂₃	D₄	semidirect
139. C₂×D₄×C₂₃	C₂²×C₄	semidirect
170. C₂²×C₄×C₂₃	C₂²×C₄	semidirect
189. C₄⋊C₄×C₂₃	C₂²×C₄	semidirect
196. C₂²⋊C₄×C₂₃	C₂²×C₄	semidirect
199. C₄²×C₂₃	C₂×D₄	semidirect
200. C₂×#2324	C₂₃	direct (N × H)
278. C₂²×C₄×D₄	C₂×C₂₃	semidirect
279. C₂²×#117	C₂×C₂₃	semidirect
280. #2324	C₂×C₂₃	direct (N × H)
281. C₂×#390	C₂×C₂₃	semidirect
282. C₂×#390	C₂×C₂₃	semidirect
283. C₂×#389	C₂×C₂₃	semidirect
284. C₂×#388	C₂×C₂₃	semidirect
285. C₂×#386	C₂×C₂₃	semidirect
286. C₂×#385	C₂×C₂₃	semidirect
287. C₂×#380	C₂×C₂₃	semidirect
288. C₂×C₄×C₄⋊C₄	C₂×C₂₃	semidirect
332. C₂×#121	C₄×C₂₃	semidirect
335. C₂×C₄×D₄	C₂²×C₂₃	semidirect
337. C₂×#117	C₂²×C₂₃	semidirect
354. #390	C₂²×C₂₃	semidirect
355. #390	C₂²×C₂₃	semidirect
356. #389	C₂²×C₂₃	semidirect
357. #388	C₂²×C₂₃	semidirect
358. #386	C₂²×C₂₃	semidirect
359. #385	C₂²×C₂₃	semidirect
360. #380	C₂²×C₂₃	semidirect
361. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
367. C₂×C₂₃	#2324	direct (N × H)
382. C₂²×D₄	C₂×C₄×C₂₃	semidirect
390. C₂³×C₄	C₂×C₄×C₂₃	semidirect
402. #121	C₂×C₄×C₂₃	semidirect
410. C₂×C₄⋊C₄	C₂×C₄×C₂₃	semidirect
423. C₂×C₂²⋊C₄	C₂×C₄×C₂₃	semidirect
433. C₂×C₄²	D₄×C₂₃	semidirect
440. C₂₃	C₂×#2324	direct (N × H)
465. C₂×D₄	C₂²×C₄×C₂₃	semidirect
496. C₂²×C₄	C₂²×C₄×C₂₃	semidirect
515. C₄⋊C₄	C₂²×C₄×C₂₃	semidirect
522. C₂²⋊C₄	C₂²×C₄×C₂₃	semidirect
525. C₄²	C₂×D₄×C₂₃	semidirect
643. C₂	C₂₃×#2324	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×#121	2
C₂²×C₄×D₄×C₂₃	2
C₂²×C₂₃×#117	2
C₂₃×#2324	2
C₂×C₂₃×#390	2
C₂×C₂₃×#389	2
C₂×C₂₃×#388	2
C₂×C₂₃×#386	2
C₂×C₂₃×#385	2
C₂×C₂₃×#380	2
C₂×C₄×C₄⋊C₄×C₂₃	2
C₂×#2324	23

Subgroups — C2×C23×#2324 #19181690

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2324 #19181690