Subgroups — C₂×#13093054 #15686839

Order 2944.

1900 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#67290	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₂²⋊D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093054	C₂	1	16	yes	maximal, direct product factor
4	C₂×#10625056	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10625057	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625054	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#10625049	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10625110	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#10625110	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#10625109	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#10625108	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₄×Dic₂₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×(C₂²⋊D₂₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×C₂²⋊Dic₂₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂²⋊C₄×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#120	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁵×C₂₃	C₂²	1	1	yes	characteristic
18	C₂⁴×D₂₃	C₂²	1	1	yes	characteristic
19	C₂²×D₄×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
21	C₂²×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₂²⋊D₂₃	—	2	8	no	—
23	C₂²×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊D₂₃	C₂²	1	8	yes	complemented
28	C₂²×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic, complemented
30	C₂³×Dic₂₃	C₂²	1	1	yes	characteristic
31	C₂³×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
32	C₂³×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
33	C₂³×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×#67290	—	2	8	no	—
35	C₂×#67290	C₂²	1	8	yes	complemented
36	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
38	C₂²×Dic₄₆	C₂²	1	1	yes	characteristic, complemented
39	C₂₃×#120	C₂²	1	8	yes	complemented
40	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊Dic₂₃	C₂²	1	8	yes	complemented
46	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
49	#10625110	C₂²	1	8	yes	complemented
50	#10625110	C₂²	1	8	yes	complemented
51	#10625109	C₂²	1	8	yes	complemented
52	#10625108	C₂²	1	8	yes	complemented
53	D₄×Dic₂₃	C₂²	1	8	yes	complemented
54	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
55	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
56	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
57	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
60	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
61	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
63	#10625057	C₂²	1	8	yes	complemented
64	#10625056	C₂²	1	8	yes	complemented
65	#10625054	C₂²	1	8	yes	complemented
66	(C₂²⋊D₂₃)⋊C₄	C₂²	1	8	yes	complemented
67	C₂²⋊C₄×D₂₃	C₂²	1	8	yes	complemented
68	#10625049	C₂²	1	8	yes	complemented
69	C₂⁴×C₂₃	—	2	4	no	—
70	C₂⁴×C₂₃	—	2	4	no	—
71	C₂⁴×C₂₃	—	4	2	no	—
72	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
73	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
74	C₂⁴×C₂₃	C₂³	1	4	yes	—
75	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
76	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
77	C₂³×D₂₃	—	2	4	no	—
78	C₂³×D₂₃	—	2	4	no	—
79	C₂³×D₂₃	—	4	2	no	—
80	C₂³×D₂₃	C₂³	1	1	yes	characteristic
81	C₂³×D₂₃	C₂³	1	4	yes	—
82	C₂³×D₂₃	C₂³	1	1	yes	characteristic
83	C₂×D₄×C₂₃	—	2	4	no	—
84	C₂×D₄×C₂₃	—	2	4	no	—
85	C₂×D₄×C₂₃	—	4	2	no	—
86	C₂×D₄×C₂₃	C₂³	1	4	yes	—
87	C₂×D₄×C₂₃	C₂³	1	4	yes	complemented
88	C₂×D₄×C₂₃	C₂³	1	4	yes	complemented
89	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
92	C₂×C₂²⋊D₂₃	—	2	4	no	—
93	C₂×C₂²⋊D₂₃	—	2	4	no	—
94	C₂×C₂²⋊D₂₃	—	2	4	no	—
95	C₂×C₂²⋊D₂₃	—	2	32	no	—
96	C₂×C₂²⋊D₂₃	—	2	4	no	—
97	C₂×C₂²⋊D₂₃	—	4	2	no	—
98	C₂×C₂²⋊D₂₃	D₄	1	8	yes	complemented
99	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
101	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
102	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
103	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	complemented
104	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	complemented
105	C₂²×Dic₂₃	—	2	4	no	—
106	C₂²×Dic₂₃	—	2	4	no	—
107	C₂²×Dic₂₃	—	2	4	no	—
108	C₂²×Dic₂₃	—	4	2	no	—
109	C₂²×Dic₂₃	C₂³	1	4	yes	—
110	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
111	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
112	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
113	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
114	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
115	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
116	C₂²×Dic₂₃	C₂³	1	4	yes	complemented
117	C₂²×Dic₂₃	C₂³	1	4	yes	complemented
118	C₂²×Dic₂₃	C₂³	1	4	yes	complemented
119	#67290	—	2	32	no	—
120	C₂×C₄×D₂₃	—	2	4	no	—
121	C₂×C₄×D₂₃	—	4	2	no	—
122	C₂×C₄×D₂₃	C₂³	1	4	yes	complemented
123	C₂×C₄×D₂₃	C₂³	1	4	yes	complemented
124	C₂×Dic₄₆	—	2	4	no	—
125	C₂×Dic₄₆	C₂³	1	4	yes	complemented
126	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
127	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	complemented
128	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	complemented
129	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
130	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
131	C₂²⋊Dic₂₃	C₂³	1	4	yes	complemented
132	C₂²⋊Dic₂₃	C₂³	1	4	yes	complemented
133	C₂²⋊Dic₂₃	C₂³	1	4	yes	complemented
134	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	complemented
135	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	complemented
136	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	complemented
137	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	complemented
138	C₄⋊Dic₂₃	C₂³	1	4	yes	complemented
139	C₄⋊Dic₂₃	C₂³	1	4	yes	complemented
140	Dic₂₃⋊C₄	C₂³	1	4	yes	complemented
141	Dic₂₃⋊C₄	C₂³	1	4	yes	complemented
142	C₄×Dic₂₃	C₂³	1	4	yes	complemented
143	C₂³×C₂₃	—	2	2	no	—
144	C₂³×C₂₃	—	2	2	no	—
145	C₂³×C₂₃	—	2	2	no	—
146	C₂³×C₂₃	—	2	2	no	—
147	C₂³×C₂₃	—	2	2	no	—
148	C₂³×C₂₃	—	2	8	no	—
149	C₂³×C₂₃	—	2	2	no	—
150	C₂³×C₂₃	—	2	2	no	—
151	C₂³×C₂₃	—	2	2	no	—
152	C₂³×C₂₃	—	2	8	no	—
153	C₂³×C₂₃	—	2	2	no	—
154	C₂³×C₂₃	—	2	2	no	—
155	C₂³×C₂₃	—	4	4	no	—
156	C₂³×C₂₃	—	4	16	no	—
157	C₂³×C₂₃	C₂×D₄	1	4	yes	—
158	C₂³×C₂₃	#41	1	4	yes	complemented
159	C₂³×C₂₃	C₂⁴	1	2	yes	—
160	C₂³×C₂₃	C₂⁴	1	2	yes	—
161	C₂³×C₂₃	C₂⁴	1	2	yes	—
162	C₂³×C₂₃	C₂⁴	1	2	yes	—
163	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
164	C₂²×D₂₃	—	2	2	no	—
165	C₂²×D₂₃	—	2	2	no	—
166	C₂²×D₂₃	—	2	2	no	—
167	C₂²×D₂₃	—	2	2	no	—
168	C₂²×D₂₃	—	2	8	no	—
169	C₂²×D₂₃	—	2	2	no	—
170	C₂²×D₂₃	—	2	8	no	—
171	C₂²×D₂₃	—	4	4	no	—
172	C₂²×D₂₃	—	4	16	no	—
173	C₂²×D₂₃	C₂×D₄	1	4	yes	—
174	C₂²×D₂₃	C₂⁴	1	2	yes	—
175	C₂²×D₂₃	C₂⁴	1	2	yes	—
176	D₄×C₂₃	—	2	8	no	—
177	D₄×C₂₃	—	2	8	no	—
178	D₄×C₂₃	—	4	4	no	—
179	C₂×C₄×C₂₃	—	2	2	no	—
180	C₂×C₄×C₂₃	—	2	2	no	—
181	C₂×C₄×C₂₃	—	2	2	no	—
182	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
183	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
184	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
185	C₂²⋊D₂₃	—	2	8	no	—
186	C₂²⋊D₂₃	—	2	8	no	—
187	C₂²⋊D₂₃	—	2	8	no	—
188	C₂²⋊D₂₃	—	2	8	no	—
189	C₂²⋊D₂₃	—	4	4	no	—
190	C₂²⋊D₂₃	C₂×D₄	1	16	yes	complemented
191	C₂×Dic₂₃	—	2	2	no	—
192	C₂×Dic₂₃	—	2	2	no	—
193	C₂×Dic₂₃	—	2	8	no	—
194	C₂×Dic₂₃	—	2	2	no	—
195	C₂×Dic₂₃	—	2	2	no	—
196	C₂×Dic₂₃	—	2	2	no	—
197	C₂×Dic₂₃	—	2	8	no	—
198	C₂×Dic₂₃	—	2	8	no	—
199	C₂×Dic₂₃	—	4	4	no	—
200	C₂×Dic₂₃	C₂×D₄	1	4	yes	—
201	C₂×Dic₂₃	C₂⁴	1	2	yes	—
202	C₂×Dic₂₃	C₂⁴	1	2	yes	—
203	C₂×Dic₂₃	C₂⁴	1	2	yes	—
204	C₂×Dic₂₃	C₂⁴	1	2	yes	—
205	C₂×Dic₂₃	C₂⁴	1	2	yes	—
206	C₂×Dic₂₃	C₂⁴	1	2	yes	—
207	C₄×D₂₃	—	2	8	no	—
208	C₄×D₂₃	—	4	4	no	—
209	Dic₄₆	—	2	8	no	—
210	C₂×#546	—	23	1	no	maximal, Sylow
211	C₂²×C₂₃	—	2	8	no	—
212	C₂²×C₂₃	—	2	8	no	—
213	C₂²×C₂₃	—	2	2	no	—
214	C₂²×C₂₃	—	2	2	no	—
215	C₂²×C₂₃	—	2	2	no	—
216	C₂²×C₂₃	—	2	2	no	—
217	C₂²×C₂₃	—	2	2	no	—
218	C₂²×C₂₃	—	2	2	no	—
219	C₂²×C₂₃	—	2	2	no	—
220	C₂²×C₂₃	—	2	2	no	—
221	C₂²×C₂₃	—	2	2	no	—
222	C₂²×C₂₃	—	2	2	no	—
223	C₂²×C₂₃	—	4	16	no	—
224	C₂²×C₂₃	—	4	4	no	—
225	C₂²×C₂₃	—	4	4	no	—
226	C₂²×C₂₃	C₂²×D₄	1	4	yes	—
227	C₂²×C₂₃	C₂²×D₄	1	2	yes	—
228	C₂²×C₂₃	C₂×#41	1	2	yes	—
229	C₂²×C₂₃	C₂×#41	1	4	yes	complemented
230	C₂²×C₂₃	H(5,𝔽₂)	1	2	yes	—
231	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
232	C₂×D₂₃	—	2	8	no	—
233	C₂×D₂₃	—	2	2	no	—
234	C₂×D₂₃	—	2	2	no	—
235	C₂×D₂₃	—	2	2	no	—
236	C₂×D₂₃	—	2	2	no	—
237	C₂×D₂₃	—	2	2	no	—
238	C₂×D₂₃	—	4	16	no	—
239	C₂×D₂₃	—	4	4	no	—
240	C₂×D₂₃	C₂²×D₄	1	4	yes	—
241	C₄×C₂₃	—	2	2	no	—
242	C₄×C₂₃	—	2	2	no	—
243	C₄×C₂₃	—	2	2	no	—
244	Dic₂₃	—	2	2	no	—
245	Dic₂₃	—	2	2	no	—
246	Dic₂₃	—	2	2	no	—
247	Dic₂₃	—	2	2	no	—
248	Dic₂₃	—	2	2	no	—
249	Dic₂₃	C₂²×D₄	1	4	yes	—
250	C₂²×#41	—	23	1	no	—
251	C₂³×D₄	—	23	1	no	—
252	#546	—	23	16	no	—
253	C₂×#124	—	23	1	no	—
254	C₂×#123	—	23	1	no	—
255	C₂×#123	—	23	1	no	—
256	C₂×C₂²⋊Q₈	—	23	1	no	—
257	C₂×#121	—	23	1	no	—
258	C₂×#121	—	23	1	no	—
259	C₂×#121	—	23	1	no	—
260	C₂×#120	—	23	1	no	—
261	C₂×#120	D₂₃	1	1	yes	characteristic, complemented
262	C₂×C₄×D₄	—	23	1	no	—
263	C₂×C₄×D₄	—	23	1	no	—
264	C₂²×C₂²⋊C₄	—	23	1	no	—
265	C₂²×C₂²⋊C₄	—	23	1	no	—
266	C₂×C₂₃	—	2	4	no	—
267	C₂×C₂₃	—	2	4	no	—
268	C₂×C₂₃	—	4	2	no	—
269	C₂×C₂₃	—	4	2	no	—
270	C₂×C₂₃	#546	1	4	yes	complemented
271	C₂×C₂₃	C₂³×D₄	1	1	yes	characteristic
272	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
273	C₂×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
274	D₂₃	—	2	4	no	—
275	D₂₃	—	4	2	no	—
276	C₂⁵	—	23	1	no	—
277	C₂⁵	C₂×D₂₃	1	1	yes	characteristic
278	C₂×#41	—	23	8	no	—
279	C₂×#41	—	46	8	no	—
280	C₂²×Q₈	—	23	1	no	—
281	C₂²×D₄	—	23	1	no	—
282	C₂²×D₄	—	23	1	no	—
283	C₂²×D₄	—	23	1	no	—
284	C₂²×D₄	—	23	1	no	—
285	C₂²×D₄	—	23	1	no	—
286	C₂²×D₄	—	23	8	no	—
287	C₂²×D₄	—	23	1	no	—
288	C₂²×D₄	—	46	8	no	—
289	C₂²×D₄	C₂×D₂₃	1	1	yes	characteristic
290	C₂²×D₄	C₂×D₂₃	1	1	yes	characteristic, complemented
291	C₂²×D₄	C₂×D₂₃	1	1	yes	characteristic, complemented
292	C₂³×C₄	—	23	1	no	—
293	C₂³×C₄	—	23	1	no	—
294	C₂³×C₄	—	23	1	no	—
295	C₂³×C₄	—	23	1	no	—
296	C₂³×C₄	—	23	1	no	—
297	C₂³×C₄	—	23	1	no	—
298	#124	—	23	8	no	—
299	#123	—	23	8	no	—
300	#123	—	23	8	no	—
301	C₂²⋊Q₈	—	23	8	no	—
302	#121	—	23	8	no	—
303	#121	—	23	8	no	—
304	#121	—	23	8	no	—
305	#120	—	23	8	no	—
306	#120	C₂×D₂₃	1	8	yes	complemented
307	C₄×D₄	—	23	8	no	—
308	C₄×D₄	—	23	8	no	—
309	C₂×C₄⋊C₄	—	23	1	no	—
310	C₂×C₄⋊C₄	—	23	1	no	—
311	C₂×C₄⋊C₄	—	23	1	no	—
312	C₂×C₄⋊C₄	—	23	1	no	—
313	C₂×C₂²⋊C₄	—	23	1	no	—
314	C₂×C₂²⋊C₄	—	23	1	no	—
315	C₂×C₂²⋊C₄	—	23	1	no	—
316	C₂×C₂²⋊C₄	—	23	1	no	—
317	C₂×C₂²⋊C₄	—	23	8	no	—
318	C₂×C₂²⋊C₄	—	23	1	no	—
319	C₂×C₂²⋊C₄	—	23	1	no	—
320	C₂×C₂²⋊C₄	—	23	1	no	—
321	C₂×C₂²⋊C₄	—	23	1	no	—
322	C₂×C₂²⋊C₄	—	23	1	no	—
323	C₂×C₂²⋊C₄	—	23	8	no	—
324	C₂×C₂²⋊C₄	C₂×D₂₃	1	1	yes	characteristic
325	C₂×C₂²⋊C₄	C₂×D₂₃	1	1	yes	characteristic, complemented
326	C₂×C₂²⋊C₄	C₂×D₂₃	1	1	yes	characteristic, complemented
327	C₂×C₄²	—	23	1	no	—
328	C₂₃	C₂×#546	1	1	yes	characteristic, complemented, Sylow
329	C₂⁴	—	2	4	no	—
330	C₂⁴	—	2	4	no	—
331	C₂⁴	—	4	2	no	—
332	C₂⁴	—	23	1	no	—
333	C₂⁴	—	23	1	no	—
334	C₂⁴	—	23	4	no	—
335	C₂⁴	—	46	4	no	—
336	C₂⁴	—	46	4	no	—
337	C₂⁴	—	92	2	no	—
338	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
339	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
340	C₂⁴	C₂²×D₂₃	1	4	yes	—
341	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
342	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
343	#41	—	46	32	no	—
344	C₂×Q₈	—	23	4	no	—
345	C₂×Q₈	—	46	4	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	4	2	no	—
349	C₂×D₄	—	23	8	no	—
350	C₂×D₄	—	23	4	no	—
351	C₂×D₄	—	23	4	no	—
352	C₂×D₄	—	23	4	no	—
353	C₂×D₄	—	23	4	no	—
354	C₂×D₄	—	23	4	no	—
355	C₂×D₄	—	23	4	no	—
356	C₂×D₄	—	46	4	no	—
357	C₂×D₄	—	46	32	no	—
358	C₂×D₄	—	46	4	no	—
359	C₂×D₄	—	46	4	no	—
360	C₂×D₄	—	46	4	no	—
361	C₂×D₄	—	92	2	no	—
362	C₂×D₄	C₂²×D₂₃	1	4	yes	—
363	C₂×D₄	C₂²×D₂₃	1	4	yes	complemented
364	C₂×D₄	C₂²×D₂₃	1	4	yes	complemented
365	C₂²×C₄	—	23	1	no	—
366	C₂²×C₄	—	23	4	no	—
367	C₂²×C₄	—	23	4	no	—
368	C₂²×C₄	—	23	4	no	—
369	C₂²×C₄	—	23	1	no	—
370	C₂²×C₄	—	23	1	no	—
371	C₂²×C₄	—	23	1	no	—
372	C₂²×C₄	—	23	1	no	—
373	C₂²×C₄	—	23	1	no	—
374	C₂²×C₄	—	23	4	no	—
375	C₂²×C₄	—	23	4	no	—
376	C₂²×C₄	—	23	4	no	—
377	C₂²×C₄	—	46	4	no	—
378	C₂²×C₄	—	46	4	no	—
379	C₂²×C₄	—	46	4	no	—
380	C₂²×C₄	—	46	4	no	—
381	C₂²×C₄	—	92	2	no	—
382	C₂²×C₄	—	92	2	no	—
383	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
384	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
385	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
386	C₄⋊C₄	—	23	4	no	—
387	C₄⋊C₄	—	23	4	no	—
388	C₄⋊C₄	—	23	4	no	—
389	C₄⋊C₄	—	23	4	no	—
390	C₂²⋊C₄	—	23	4	no	—
391	C₂²⋊C₄	—	23	4	no	—
392	C₂²⋊C₄	—	23	4	no	—
393	C₂²⋊C₄	—	23	4	no	—
394	C₂²⋊C₄	—	23	4	no	—
395	C₂²⋊C₄	—	23	4	no	—
396	C₂²⋊C₄	—	23	4	no	—
397	C₂²⋊C₄	—	23	4	no	—
398	C₂²⋊C₄	—	23	4	no	—
399	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	—
400	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	complemented
401	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	complemented
402	C₄²	—	23	4	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	8	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	8	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	4	4	no	—
416	C₂³	—	4	16	no	—
417	C₂³	—	23	4	no	—
418	C₂³	—	23	2	no	—
419	C₂³	—	23	2	no	—
420	C₂³	—	46	8	no	—
421	C₂³	—	46	2	no	—
422	C₂³	—	46	2	no	—
423	C₂³	—	46	2	no	—
424	C₂³	—	46	2	no	—
425	C₂³	—	46	8	no	—
426	C₂³	—	46	2	no	—
427	C₂³	—	92	4	no	—
428	C₂³	—	92	16	no	—
429	C₂³	D₄×D₂₃	1	4	yes	—
430	C₂³	#67290	1	4	yes	complemented
431	C₂³	C₂³×D₂₃	1	2	yes	—
432	C₂³	C₂³×D₂₃	1	2	yes	—
433	C₂³	C₂³×D₂₃	1	2	yes	—
434	C₂³	C₂³×D₂₃	1	2	yes	—
435	C₂³	C₂³×D₂₃	1	1	yes	characteristic
436	Q₈	—	46	8	no	—
437	D₄	—	2	8	no	—
438	D₄	—	2	8	no	—
439	D₄	—	4	4	no	—
440	D₄	—	23	16	no	—
441	D₄	—	46	8	no	—
442	D₄	—	46	8	no	—
443	D₄	—	46	8	no	—
444	D₄	—	46	8	no	—
445	D₄	—	92	4	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	23	4	no	—
450	C₂×C₄	—	23	2	no	—
451	C₂×C₄	—	23	2	no	—
452	C₂×C₄	—	23	2	no	—
453	C₂×C₄	—	23	2	no	—
454	C₂×C₄	—	23	2	no	—
455	C₂×C₄	—	23	2	no	—
456	C₂×C₄	—	46	8	no	—
457	C₂×C₄	—	46	8	no	—
458	C₂×C₄	—	46	8	no	—
459	C₂×C₄	—	46	2	no	—
460	C₂×C₄	—	46	2	no	—
461	C₂×C₄	—	46	2	no	—
462	C₂×C₄	—	46	8	no	—
463	C₂×C₄	—	46	2	no	—
464	C₂×C₄	—	46	2	no	—
465	C₂×C₄	—	92	4	no	—
466	C₂×C₄	—	92	4	no	—
467	C₂×C₄	C₂³×D₂₃	1	2	yes	—
468	C₂×C₄	C₂³×D₂₃	1	2	yes	—
469	C₂×C₄	C₂³×D₂₃	1	2	yes	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	8	no	—
475	C₂²	—	2	8	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	4	16	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	23	4	no	—
486	C₂²	—	46	2	no	—
487	C₂²	—	46	2	no	—
488	C₂²	—	46	8	no	—
489	C₂²	—	46	2	no	—
490	C₂²	—	46	2	no	—
491	C₂²	—	46	2	no	—
492	C₂²	—	92	16	no	—
493	C₂²	—	92	4	no	—
494	C₂²	C₂×D₄×D₂₃	1	4	yes	—
495	C₂²	C₂×D₄×D₂₃	1	2	yes	—
496	C₂²	C₂×#67290	1	2	yes	—
497	C₂²	C₂×#67290	1	4	yes	complemented
498	C₂²	#10625155	1	2	yes	—
499	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	2	2	no	—
502	C₄	—	2	2	no	—
503	C₄	—	23	4	no	—
504	C₄	—	46	2	no	—
505	C₄	—	46	2	no	—
506	C₄	—	46	2	no	—
507	C₄	—	46	2	no	—
508	C₄	—	46	2	no	—
509	C₂	—	2	4	no	—
510	C₂	—	2	4	no	—
511	C₂	—	4	2	no	—
512	C₂	—	4	2	no	—
513	C₂	—	46	4	no	—
514	C₂	—	92	2	no	—
515	C₂	#13093054	1	4	yes	direct product factor
516	C₂	C₂²×D₄×D₂₃	1	1	yes	characteristic
517	C₂	C₂²×#67290	1	1	yes	characteristic
518	C₂	C₂×#10625155	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₂₃
commutator, cosocle	C₂²×C₂₃	C₂⁵
Frattini	C₂²	C₂⁴×D₂₃
Fitting	C₂×C₂₃×#120	C₂
socle	C₂³×C₂₃	C₂⁴
hypercenter	C₂×#120	D₂₃
hypocenter	C₂₃	C₂×#546
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂×#120

Complements

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

N	H ≅ G/N	type
1. C₂²×#67290	C₂	semidirect
2. C₂³×C₂²⋊D₂₃	C₂	semidirect
3. #13093054	C₂	direct (N × H)
4. C₂×#10625056	C₂	semidirect
5. C₂×#10625057	C₂	semidirect
6. C₂×#10625054	C₂	semidirect
7. C₂×#10625049	C₂	semidirect
8. C₂×#10625110	C₂	semidirect
9. C₂×#10625110	C₂	semidirect
10. C₂×#10625109	C₂	semidirect
11. C₂×#10625108	C₂	semidirect
12. C₂×D₄×Dic₂₃	C₂	semidirect
13. C₂×(C₂²⋊D₂₃)⋊C₄	C₂	semidirect
14. C₂²×C₂²⋊Dic₂₃	C₂	semidirect
15. C₂×C₂²⋊C₄×D₂₃	C₂	semidirect
16. C₂×C₂₃×#120	C₂	semidirect
20. C₂²×D₄×C₂₃	C₂²	semidirect
21. C₂²×D₄×C₂₃	C₂²	semidirect
27. C₂²×C₂²⋊D₂₃	C₂²	semidirect
28. C₂²×C₂²⋊D₂₃	C₂²	semidirect
29. C₂²×C₂²⋊D₂₃	C₂²	semidirect
31. C₂³×Dic₂₃	C₂²	semidirect
32. C₂³×Dic₂₃	C₂²	semidirect
33. C₂³×Dic₂₃	C₂²	semidirect
35. C₂×#67290	C₂²	semidirect
36. C₂²×C₄×D₂₃	C₂²	semidirect
37. C₂²×C₄×D₂₃	C₂²	semidirect
38. C₂²×Dic₄₆	C₂²	semidirect
39. C₂₃×#120	C₂²	semidirect
41. C₂×C₂²⋊C₄×C₂₃	C₂²	semidirect
42. C₂×C₂²⋊C₄×C₂₃	C₂²	semidirect
45. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
46. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
47. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
48. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
49. #10625110	C₂²	semidirect
50. #10625110	C₂²	semidirect
51. #10625109	C₂²	semidirect
52. #10625108	C₂²	semidirect
53. D₄×Dic₂₃	C₂²	semidirect
54. C₂×(C₂×D₂₃)⋊C₄	C₂²	semidirect
55. C₂×(C₂×D₂₃)⋊C₄	C₂²	semidirect
56. C₂×(C₂×D₂₃)⋊C₄	C₂²	semidirect
57. C₂×(C₂×D₂₃)⋊C₄	C₂²	semidirect
58. C₂×C₄⋊Dic₂₃	C₂²	semidirect
59. C₂×C₄⋊Dic₂₃	C₂²	semidirect
60. C₂×Dic₂₃⋊C₄	C₂²	semidirect
61. C₂×Dic₂₃⋊C₄	C₂²	semidirect
62. C₂×C₄×Dic₂₃	C₂²	semidirect
63. #10625057	C₂²	semidirect
64. #10625056	C₂²	semidirect
65. #10625054	C₂²	semidirect
66. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
67. C₂²⋊C₄×D₂₃	C₂²	semidirect
68. #10625049	C₂²	semidirect
87. C₂×D₄×C₂₃	C₂³	semidirect
88. C₂×D₄×C₂₃	C₂³	semidirect
98. C₂×C₂²⋊D₂₃	D₄	semidirect
103. C₂×C₂²⋊D₂₃	C₂³	semidirect
104. C₂×C₂²⋊D₂₃	C₂³	semidirect
116. C₂²×Dic₂₃	C₂³	semidirect
117. C₂²×Dic₂₃	C₂³	semidirect
118. C₂²×Dic₂₃	C₂³	semidirect
122. C₂×C₄×D₂₃	C₂³	semidirect
123. C₂×C₄×D₂₃	C₂³	semidirect
125. C₂×Dic₄₆	C₂³	semidirect
127. C₂²⋊C₄×C₂₃	C₂³	semidirect
128. C₂²⋊C₄×C₂₃	C₂³	semidirect
131. C₂²⋊Dic₂₃	C₂³	semidirect
132. C₂²⋊Dic₂₃	C₂³	semidirect
133. C₂²⋊Dic₂₃	C₂³	semidirect
134. (C₂×D₂₃)⋊C₄	C₂³	semidirect
135. (C₂×D₂₃)⋊C₄	C₂³	semidirect
136. (C₂×D₂₃)⋊C₄	C₂³	semidirect
137. (C₂×D₂₃)⋊C₄	C₂³	semidirect
138. C₄⋊Dic₂₃	C₂³	semidirect
139. C₄⋊Dic₂₃	C₂³	semidirect
140. Dic₂₃⋊C₄	C₂³	semidirect
141. Dic₂₃⋊C₄	C₂³	semidirect
142. C₄×Dic₂₃	C₂³	semidirect
158. C₂³×C₂₃	#41	semidirect
190. C₂²⋊D₂₃	C₂×D₄	semidirect
229. C₂²×C₂₃	C₂×#41	semidirect
261. C₂×#120	D₂₃	semidirect
270. C₂×C₂₃	#546	semidirect
290. C₂²×D₄	C₂×D₂₃	semidirect
291. C₂²×D₄	C₂×D₂₃	semidirect
306. #120	C₂×D₂₃	semidirect
325. C₂×C₂²⋊C₄	C₂×D₂₃	semidirect
326. C₂×C₂²⋊C₄	C₂×D₂₃	semidirect
328. C₂₃	C₂×#546	semidirect
363. C₂×D₄	C₂²×D₂₃	semidirect
364. C₂×D₄	C₂²×D₂₃	semidirect
400. C₂²⋊C₄	C₂²×D₂₃	semidirect
401. C₂²⋊C₄	C₂²×D₂₃	semidirect
430. C₂³	#67290	semidirect
497. C₂²	C₂×#67290	semidirect
515. C₂	#13093054	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×#67290	2
C₂³×C₂²⋊D₂₃	2
#13093054	2
C₂×#10625056	2
C₂×#10625057	2
C₂×#10625054	2
C₂×#10625049	2
C₂×#10625110	2
C₂×#10625109	2
C₂×#10625108	2
C₂×D₄×Dic₂₃	2
C₂×(C₂²⋊D₂₃)⋊C₄	2
C₂²×C₂²⋊Dic₂₃	2
C₂×C₂²⋊C₄×D₂₃	2
C₂×C₂₃×#120	2
C₂×#546	23

Subgroups — C2×#13093054 #15686839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13093054 #15686839