Subgroups — C₂×#13092999 #15686732

Order 2944.

1336 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092999	C₂	1	16	yes	maximal, direct product factor
2	C₂×#10625069	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10625050	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10625107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10625056	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625100	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#10625106	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10625067	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×#10625108	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄×C₂²⋊D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×(C₂²⋊D₂₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂²⋊C₄×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁴×D₂₃	C₂²	1	1	yes	characteristic
18	C₂²×D₄×C₂₃	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	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
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	C₂³×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
29	C₂²×Dic₄₆	C₂²	1	1	yes	characteristic, complemented
30	C₂₃×#121	C₂²	1	8	yes	complemented
31	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
40	#10625110	C₂²	1	8	yes	complemented
41	#10625109	C₂²	1	8	yes	complemented
42	#10625108	C₂²	1	8	yes	complemented
43	#10625108	C₂²	1	8	yes	complemented
44	#10625107	C₂²	1	8	yes	complemented
45	#10625106	C₂²	1	8	yes	complemented
46	#10625100	C₂²	1	8	yes	complemented
47	C₄×C₂²⋊D₂₃	C₂²	1	8	yes	complemented
48	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
49	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
50	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
51	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
52	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
53	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
54	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
56	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
57	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
58	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
61	#10625069	C₂²	1	8	yes	complemented
62	#10625067	C₂²	1	8	yes	complemented
63	#10625056	C₂²	1	8	yes	complemented
64	(C₂²⋊D₂₃)⋊C₄	C₂²	1	8	yes	complemented
65	C₂²⋊C₄×D₂₃	C₂²	1	8	yes	complemented
66	#10625050	C₂²	1	8	yes	complemented
67	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
68	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
69	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
70	C₂³×D₂₃	—	2	4	no	—
71	C₂³×D₂₃	—	4	2	no	—
72	C₂³×D₂₃	—	4	2	no	—
73	C₂³×D₂₃	C₂³	1	1	yes	characteristic
74	C₂³×D₂₃	C₂³	1	1	yes	characteristic
75	C₂³×D₂₃	C₂³	1	4	yes	—
76	C₂×D₄×C₂₃	—	4	2	no	—
77	C₂×D₄×C₂₃	—	4	2	no	—
78	C₂×D₄×C₂₃	—	4	2	no	—
79	C₂×D₄×C₂₃	C₂³	1	4	yes	—
80	C₂×D₄×C₂₃	C₂³	1	4	yes	—
81	C₂×D₄×C₂₃	C₂³	1	4	yes	complemented
82	C₂²×C₄×C₂₃	—	4	2	no	—
83	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₂₃	C₂³	1	4	yes	complemented
88	C₂×C₂²⋊D₂₃	—	2	4	no	—
89	C₂×C₂²⋊D₂₃	—	2	4	no	—
90	C₂×C₂²⋊D₂₃	—	4	2	no	—
91	C₂×C₂²⋊D₂₃	—	4	2	no	—
92	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
93	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
96	C₂²×Dic₂₃	—	4	2	no	—
97	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
98	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
99	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
100	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
101	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
102	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
103	C₂²×Dic₂₃	C₂³	1	4	yes	complemented
104	C₂×C₄×D₂₃	—	4	2	no	—
105	C₂×C₄×D₂₃	—	4	2	no	—
106	C₂×C₄×D₂₃	C₂³	1	4	yes	—
107	C₂×C₄×D₂₃	C₂³	1	4	yes	—
108	C₂×Dic₄₆	—	4	2	no	—
109	C₂×Dic₄₆	C₂³	1	4	yes	complemented
110	C₄⋊C₄×C₂₃	C₂³	1	4	yes	complemented
111	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
112	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	complemented
113	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
114	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
115	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
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	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
120	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
121	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
122	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
123	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
124	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
125	C₄⋊Dic₂₃	C₂³	1	4	yes	complemented
126	Dic₂₃⋊C₄	C₂³	1	4	yes	complemented
127	Dic₂₃⋊C₄	C₂³	1	4	yes	complemented
128	Dic₂₃⋊C₄	C₂³	1	4	yes	complemented
129	Dic₂₃⋊C₄	C₂³	1	4	yes	complemented
130	C₄×Dic₂₃	C₂³	1	4	yes	complemented
131	C₄×Dic₂₃	C₂³	1	4	yes	complemented
132	C₂³×C₂₃	—	2	2	no	—
133	C₂³×C₂₃	—	2	2	no	—
134	C₂³×C₂₃	—	2	2	no	—
135	C₂³×C₂₃	—	2	2	no	—
136	C₂³×C₂₃	—	2	2	no	—
137	C₂³×C₂₃	—	2	2	no	—
138	C₂³×C₂₃	—	2	2	no	—
139	C₂³×C₂₃	—	2	2	no	—
140	C₂³×C₂₃	—	2	2	no	—
141	C₂³×C₂₃	C₂⁴	1	2	yes	—
142	C₂³×C₂₃	C₂⁴	1	2	yes	—
143	C₂³×C₂₃	C₂⁴	1	2	yes	—
144	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
145	C₂²×D₂₃	—	2	2	no	—
146	C₂²×D₂₃	—	2	2	no	—
147	C₂²×D₂₃	—	2	2	no	—
148	C₂²×D₂₃	—	2	2	no	—
149	C₂²×D₂₃	—	2	2	no	—
150	C₂²×D₂₃	—	2	8	no	—
151	C₂²×D₂₃	—	4	4	no	—
152	C₂²×D₂₃	—	4	4	no	—
153	C₂²×D₂₃	—	4	16	no	—
154	C₂²×D₂₃	#41	1	4	yes	—
155	C₂²×D₂₃	C₂⁴	1	2	yes	—
156	C₂²×D₂₃	C₂⁴	1	2	yes	—
157	D₄×C₂₃	—	4	4	no	—
158	D₄×C₂₃	—	4	4	no	—
159	D₄×C₂₃	—	4	4	no	—
160	C₂×C₄×C₂₃	—	2	2	no	—
161	C₂×C₄×C₂₃	—	2	2	no	—
162	C₂×C₄×C₂₃	—	2	2	no	—
163	C₂×C₄×C₂₃	—	2	2	no	—
164	C₂×C₄×C₂₃	—	4	4	no	—
165	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
166	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
167	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
168	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
169	C₂²⋊D₂₃	—	2	8	no	—
170	C₂²⋊D₂₃	—	2	8	no	—
171	C₂²⋊D₂₃	—	4	4	no	—
172	C₂²⋊D₂₃	—	4	4	no	—
173	C₂×Dic₂₃	—	2	2	no	—
174	C₂×Dic₂₃	—	2	2	no	—
175	C₂×Dic₂₃	—	2	2	no	—
176	C₂×Dic₂₃	—	2	2	no	—
177	C₂×Dic₂₃	—	2	2	no	—
178	C₂×Dic₂₃	—	2	2	no	—
179	C₂×Dic₂₃	—	4	4	no	—
180	C₂×Dic₂₃	C₂⁴	1	2	yes	—
181	C₂×Dic₂₃	C₂⁴	1	2	yes	—
182	C₂×Dic₂₃	C₂⁴	1	2	yes	—
183	C₂×Dic₂₃	C₂⁴	1	2	yes	—
184	C₂×Dic₂₃	C₂⁴	1	2	yes	—
185	C₂×Dic₂₃	C₂⁴	1	2	yes	—
186	C₄×D₂₃	—	4	4	no	—
187	C₄×D₂₃	—	4	4	no	—
188	Dic₄₆	—	4	4	no	—
189	C₂×#538	—	23	1	no	maximal, Sylow
190	C₂²×C₂₃	—	2	2	no	—
191	C₂²×C₂₃	—	2	2	no	—
192	C₂²×C₂₃	—	2	2	no	—
193	C₂²×C₂₃	—	2	2	no	—
194	C₂²×C₂₃	—	2	2	no	—
195	C₂²×C₂₃	—	2	2	no	—
196	C₂²×C₂₃	—	2	2	no	—
197	C₂²×C₂₃	—	2	2	no	—
198	C₂²×C₂₃	—	2	2	no	—
199	C₂²×C₂₃	—	4	4	no	—
200	C₂²×C₂₃	—	4	4	no	—
201	C₂²×C₂₃	—	4	4	no	—
202	C₂²×C₂₃	C₂×#41	1	2	yes	—
203	C₂²×C₂₃	H(5,𝔽₂)	1	2	yes	—
204	C₂²×C₂₃	H(5,𝔽₂)	1	2	yes	—
205	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
206	C₂×D₂₃	—	2	8	no	—
207	C₂×D₂₃	—	2	2	no	—
208	C₂×D₂₃	—	2	2	no	—
209	C₂×D₂₃	—	2	2	no	—
210	C₂×D₂₃	—	2	2	no	—
211	C₂×D₂₃	—	2	2	no	—
212	C₂×D₂₃	—	4	16	no	—
213	C₂×D₂₃	—	4	4	no	—
214	C₂×D₂₃	C₂×#41	1	4	yes	—
215	C₄×C₂₃	—	2	2	no	—
216	C₄×C₂₃	—	2	2	no	—
217	C₄×C₂₃	—	2	2	no	—
218	C₄×C₂₃	—	2	2	no	—
219	Dic₂₃	—	2	2	no	—
220	Dic₂₃	—	2	2	no	—
221	Dic₂₃	—	2	2	no	—
222	Dic₂₃	—	2	2	no	—
223	Dic₂₃	—	2	2	no	—
224	Dic₂₃	—	2	2	no	—
225	#538	—	23	16	no	—
226	C₂×#126	—	23	1	no	—
227	C₂×#126	—	23	1	no	—
228	C₂×#124	—	23	1	no	—
229	C₂×#124	—	23	1	no	—
230	C₂×#123	—	23	1	no	—
231	C₂×#123	—	23	1	no	—
232	C₂×C₂²⋊Q₈	—	23	1	no	—
233	C₂×#121	—	23	1	no	—
234	C₂×#121	—	23	1	no	—
235	C₂×#121	D₂₃	1	1	yes	characteristic, complemented
236	C₂×#120	—	23	1	no	—
237	C₂×#120	—	23	1	no	—
238	C₂×C₄×D₄	—	23	1	no	—
239	C₂×C₄×D₄	—	23	1	no	—
240	C₂²×C₂²⋊C₄	—	23	1	no	—
241	C₂×C₂₃	—	4	2	no	—
242	C₂×C₂₃	—	4	2	no	—
243	C₂×C₂₃	—	4	2	no	—
244	C₂×C₂₃	#538	1	4	yes	complemented
245	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
246	C₂×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
247	C₂×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
248	D₂₃	—	2	4	no	—
249	D₂₃	—	4	2	no	—
250	C₂⁵	—	23	1	no	—
251	C₂²×Q₈	—	23	1	no	—
252	C₂²×D₄	—	23	1	no	—
253	C₂²×D₄	—	23	1	no	—
254	C₂²×D₄	—	23	1	no	—
255	C₂²×D₄	—	23	1	no	—
256	C₂²×D₄	C₂×D₂₃	1	1	yes	characteristic
257	C₂²×D₄	C₂×D₂₃	1	1	yes	characteristic
258	C₂²×D₄	C₂×D₂₃	1	1	yes	characteristic, complemented
259	C₂³×C₄	—	23	1	no	—
260	C₂³×C₄	—	23	1	no	—
261	C₂³×C₄	—	23	1	no	—
262	C₂³×C₄	C₂×D₂₃	1	1	yes	characteristic, complemented
263	#126	—	23	8	no	—
264	#126	—	23	8	no	—
265	#124	—	23	8	no	—
266	#124	—	23	8	no	—
267	#123	—	23	8	no	—
268	#123	—	23	8	no	—
269	C₂²⋊Q₈	—	23	8	no	—
270	#121	—	23	8	no	—
271	#121	—	23	8	no	—
272	#121	C₂×D₂₃	1	8	yes	complemented
273	#120	—	23	8	no	—
274	#120	—	23	8	no	—
275	C₄×D₄	—	23	8	no	—
276	C₄×D₄	—	23	8	no	—
277	C₂×C₄⋊C₄	—	23	1	no	—
278	C₂×C₄⋊C₄	—	23	1	no	—
279	C₂×C₄⋊C₄	—	23	1	no	—
280	C₂×C₄⋊C₄	—	23	1	no	—
281	C₂×C₄⋊C₄	—	23	1	no	—
282	C₂×C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic, complemented
283	C₂×C₂²⋊C₄	—	23	1	no	—
284	C₂×C₂²⋊C₄	—	23	1	no	—
285	C₂×C₂²⋊C₄	—	23	1	no	—
286	C₂×C₂²⋊C₄	—	23	1	no	—
287	C₂×C₂²⋊C₄	—	23	1	no	—
288	C₂×C₂²⋊C₄	—	23	1	no	—
289	C₂×C₂²⋊C₄	—	23	1	no	—
290	C₂×C₂²⋊C₄	—	23	1	no	—
291	C₂×C₂²⋊C₄	—	23	1	no	—
292	C₂×C₂²⋊C₄	—	23	1	no	—
293	C₂×C₂²⋊C₄	—	23	1	no	—
294	C₂×C₂²⋊C₄	—	23	1	no	—
295	C₂×C₂²⋊C₄	—	23	8	no	—
296	C₂×C₂²⋊C₄	C₂×D₂₃	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	C₂×D₂₃	1	1	yes	characteristic, complemented
298	C₂×C₄²	—	23	1	no	—
299	C₂×C₄²	—	23	1	no	—
300	C₂₃	C₂×#538	1	1	yes	characteristic, complemented, Sylow
301	C₂⁴	—	23	1	no	—
302	C₂⁴	—	23	1	no	—
303	C₂⁴	—	23	4	no	—
304	C₂⁴	—	46	4	no	—
305	C₂⁴	—	92	2	no	—
306	C₂⁴	—	92	2	no	—
307	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
308	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
309	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
310	C₂×Q₈	—	23	4	no	—
311	C₂×Q₈	—	92	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	23	4	no	—
316	C₂×D₄	—	23	4	no	—
317	C₂×D₄	—	23	4	no	—
318	C₂×D₄	—	23	4	no	—
319	C₂×D₄	—	46	4	no	—
320	C₂×D₄	—	46	4	no	—
321	C₂×D₄	—	92	2	no	—
322	C₂×D₄	—	92	2	no	—
323	C₂×D₄	C₂²×D₂₃	1	4	yes	—
324	C₂×D₄	C₂²×D₂₃	1	4	yes	—
325	C₂×D₄	C₂²×D₂₃	1	4	yes	complemented
326	C₂²×C₄	—	4	2	no	—
327	C₂²×C₄	—	23	1	no	—
328	C₂²×C₄	—	23	1	no	—
329	C₂²×C₄	—	23	1	no	—
330	C₂²×C₄	—	23	1	no	—
331	C₂²×C₄	—	23	1	no	—
332	C₂²×C₄	—	23	1	no	—
333	C₂²×C₄	—	23	4	no	—
334	C₂²×C₄	—	23	4	no	—
335	C₂²×C₄	—	23	4	no	—
336	C₂²×C₄	—	92	2	no	—
337	C₂²×C₄	—	92	2	no	—
338	C₂²×C₄	—	92	2	no	—
339	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
340	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
341	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
342	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
343	C₂²×C₄	C₂²×D₂₃	1	4	yes	complemented
344	C₄⋊C₄	—	23	4	no	—
345	C₄⋊C₄	—	23	4	no	—
346	C₄⋊C₄	—	23	4	no	—
347	C₄⋊C₄	—	23	4	no	—
348	C₄⋊C₄	—	23	4	no	—
349	C₄⋊C₄	C₂²×D₂₃	1	4	yes	complemented
350	C₂²⋊C₄	—	23	4	no	—
351	C₂²⋊C₄	—	23	4	no	—
352	C₂²⋊C₄	—	23	4	no	—
353	C₂²⋊C₄	—	23	4	no	—
354	C₂²⋊C₄	—	23	4	no	—
355	C₂²⋊C₄	—	23	4	no	—
356	C₂²⋊C₄	—	23	4	no	—
357	C₂²⋊C₄	—	23	4	no	—
358	C₂²⋊C₄	—	23	4	no	—
359	C₂²⋊C₄	—	23	4	no	—
360	C₂²⋊C₄	—	23	4	no	—
361	C₂²⋊C₄	—	23	4	no	—
362	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	—
363	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	complemented
364	C₄²	—	23	4	no	—
365	C₄²	—	23	4	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	2	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	23	4	no	—
376	C₂³	—	23	2	no	—
377	C₂³	—	23	2	no	—
378	C₂³	—	46	8	no	—
379	C₂³	—	46	2	no	—
380	C₂³	—	46	2	no	—
381	C₂³	—	46	2	no	—
382	C₂³	—	46	2	no	—
383	C₂³	—	46	2	no	—
384	C₂³	—	92	4	no	—
385	C₂³	—	92	4	no	—
386	C₂³	—	92	16	no	—
387	C₂³	C₂³×D₂₃	1	2	yes	—
388	C₂³	C₂³×D₂₃	1	2	yes	—
389	C₂³	C₂³×D₂₃	1	2	yes	—
390	C₂³	C₂³×D₂₃	1	1	yes	characteristic
391	Q₈	—	92	4	no	—
392	D₄	—	4	4	no	—
393	D₄	—	4	4	no	—
394	D₄	—	4	4	no	—
395	D₄	—	46	8	no	—
396	D₄	—	46	8	no	—
397	D₄	—	92	4	no	—
398	D₄	—	92	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	23	2	no	—
405	C₂×C₄	—	23	2	no	—
406	C₂×C₄	—	23	2	no	—
407	C₂×C₄	—	23	2	no	—
408	C₂×C₄	—	23	2	no	—
409	C₂×C₄	—	23	2	no	—
410	C₂×C₄	—	46	2	no	—
411	C₂×C₄	—	46	2	no	—
412	C₂×C₄	—	46	2	no	—
413	C₂×C₄	—	46	2	no	—
414	C₂×C₄	—	46	2	no	—
415	C₂×C₄	—	46	2	no	—
416	C₂×C₄	—	92	4	no	—
417	C₂×C₄	—	92	4	no	—
418	C₂×C₄	—	92	4	no	—
419	C₂×C₄	C₂³×D₂₃	1	2	yes	—
420	C₂×C₄	C₂³×D₂₃	1	2	yes	—
421	C₂×C₄	C₂³×D₂₃	1	2	yes	—
422	C₂×C₄	C₂³×D₂₃	1	2	yes	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	23	4	no	—
436	C₂²	—	46	2	no	—
437	C₂²	—	46	2	no	—
438	C₂²	—	46	8	no	—
439	C₂²	—	46	2	no	—
440	C₂²	—	46	2	no	—
441	C₂²	—	46	2	no	—
442	C₂²	—	92	16	no	—
443	C₂²	—	92	4	no	—
444	C₂²	#10625155	1	2	yes	—
445	C₂²	#10625155	1	2	yes	—
446	C₂²	#41×D₂₃	1	2	yes	—
447	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	46	2	no	—
453	C₄	—	46	2	no	—
454	C₄	—	46	2	no	—
455	C₄	—	46	2	no	—
456	C₄	—	46	2	no	—
457	C₄	—	46	2	no	—
458	C₂	—	4	2	no	—
459	C₂	—	4	2	no	—
460	C₂	—	4	2	no	—
461	C₂	—	46	4	no	—
462	C₂	—	92	2	no	—
463	C₂	#13092999	1	4	yes	direct product factor
464	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
465	C₂	C₂×#10625155	1	1	yes	characteristic
466	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×#121	C₂
socle	C₂³×C₂₃	C₂⁴
hypercenter	C₂×#121	D₂₃
hypocenter	C₂₃	C₂×#538
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. #13092999	C₂	direct (N × H)
2. C₂×#10625069	C₂	semidirect
3. C₂×#10625050	C₂	semidirect
4. C₂×#10625107	C₂	semidirect
5. C₂×#10625056	C₂	semidirect
6. C₂×#10625100	C₂	semidirect
7. C₂×#10625106	C₂	semidirect
8. C₂×#10625067	C₂	semidirect
9. C₂×#10625110	C₂	semidirect
10. C₂×#10625109	C₂	semidirect
11. C₂×#10625108	C₂	semidirect
12. C₂×#10625108	C₂	semidirect
13. C₂×C₄×C₂²⋊D₂₃	C₂	semidirect
14. C₂×(C₂²⋊D₂₃)⋊C₄	C₂	semidirect
15. C₂×C₂²⋊C₄×D₂₃	C₂	semidirect
16. C₂×C₂₃×#121	C₂	semidirect
20. C₂²×D₄×C₂₃	C₂²	semidirect
21. C₂³×C₄×C₂₃	C₂²	semidirect
26. C₂³×Dic₂₃	C₂²	semidirect
29. C₂²×Dic₄₆	C₂²	semidirect
30. C₂₃×#121	C₂²	semidirect
31. C₂×C₄⋊C₄×C₂₃	C₂²	semidirect
33. C₂×C₂²⋊C₄×C₂₃	C₂²	semidirect
37. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
38. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
39. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
40. #10625110	C₂²	semidirect
41. #10625109	C₂²	semidirect
42. #10625108	C₂²	semidirect
43. #10625108	C₂²	semidirect
44. #10625107	C₂²	semidirect
45. #10625106	C₂²	semidirect
46. #10625100	C₂²	semidirect
47. C₄×C₂²⋊D₂₃	C₂²	semidirect
54. C₂×C₄⋊Dic₂₃	C₂²	semidirect
55. C₂×Dic₂₃⋊C₄	C₂²	semidirect
56. C₂×Dic₂₃⋊C₄	C₂²	semidirect
57. C₂×Dic₂₃⋊C₄	C₂²	semidirect
58. C₂×Dic₂₃⋊C₄	C₂²	semidirect
59. C₂×C₄×Dic₂₃	C₂²	semidirect
60. C₂×C₄×Dic₂₃	C₂²	semidirect
61. #10625069	C₂²	semidirect
62. #10625067	C₂²	semidirect
63. #10625056	C₂²	semidirect
64. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
65. C₂²⋊C₄×D₂₃	C₂²	semidirect
66. #10625050	C₂²	semidirect
81. C₂×D₄×C₂₃	C₂³	semidirect
87. C₂²×C₄×C₂₃	C₂³	semidirect
103. C₂²×Dic₂₃	C₂³	semidirect
109. C₂×Dic₄₆	C₂³	semidirect
110. C₄⋊C₄×C₂₃	C₂³	semidirect
112. C₂²⋊C₄×C₂₃	C₂³	semidirect
116. C₂²⋊Dic₂₃	C₂³	semidirect
117. C₂²⋊Dic₂₃	C₂³	semidirect
118. C₂²⋊Dic₂₃	C₂³	semidirect
125. C₄⋊Dic₂₃	C₂³	semidirect
126. Dic₂₃⋊C₄	C₂³	semidirect
127. Dic₂₃⋊C₄	C₂³	semidirect
128. Dic₂₃⋊C₄	C₂³	semidirect
129. Dic₂₃⋊C₄	C₂³	semidirect
130. C₄×Dic₂₃	C₂³	semidirect
131. C₄×Dic₂₃	C₂³	semidirect
235. C₂×#121	D₂₃	semidirect
244. C₂×C₂₃	#538	semidirect
258. C₂²×D₄	C₂×D₂₃	semidirect
262. C₂³×C₄	C₂×D₂₃	semidirect
272. #121	C₂×D₂₃	semidirect
282. C₂×C₄⋊C₄	C₂×D₂₃	semidirect
297. C₂×C₂²⋊C₄	C₂×D₂₃	semidirect
300. C₂₃	C₂×#538	semidirect
325. C₂×D₄	C₂²×D₂₃	semidirect
343. C₂²×C₄	C₂²×D₂₃	semidirect
349. C₄⋊C₄	C₂²×D₂₃	semidirect
363. C₂²⋊C₄	C₂²×D₂₃	semidirect
463. C₂	#13092999	direct (N × H)

Maximal subgroups

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

subgroup	index
#13092999	2
C₂×#10625069	2
C₂×#10625050	2
C₂×#10625107	2
C₂×#10625056	2
C₂×#10625100	2
C₂×#10625106	2
C₂×#10625067	2
C₂×#10625110	2
C₂×#10625109	2
C₂×#10625108	2
C₂×C₄×C₂²⋊D₂₃	2
C₂×(C₂²⋊D₂₃)⋊C₄	2
C₂×C₂²⋊C₄×D₂₃	2
C₂×C₂₃×#121	2
C₂×#538	23

Subgroups — C2×#13092999 #15686732

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13092999 #15686732