Subgroups — C₂×#13093155 #15687512

Order 2944.

1344 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093155	C₂	1	16	yes	maximal, direct product factor
2	C₂×#10625111	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10625069	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10625050	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10625065	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625057	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#10625100	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10625101	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#10625055	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#10625110	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#10625110	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10625109	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#10625053	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#10625108	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#10625108	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	C₂²×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic, complemented
29	C₂³×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
30	C₂²×D₉₂	C₂²	1	1	yes	characteristic
31	C₂²×D₉₂	C₂²	1	1	yes	characteristic
32	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#121	C₂²	1	8	yes	complemented
34	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
40	#10625111	C₂²	1	8	yes	complemented
41	#10625110	C₂²	1	8	yes	complemented
42	#10625110	C₂²	1	8	yes	complemented
43	#10625109	C₂²	1	8	yes	complemented
44	#10625108	C₂²	1	8	yes	complemented
45	#10625108	C₂²	1	8	yes	complemented
46	#10625101	C₂²	1	8	yes	complemented
47	#10625100	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×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄⋊Dic₂₃	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×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
61	#10625069	C₂²	1	8	yes	complemented
62	#10625065	C₂²	1	8	yes	complemented
63	#10625057	C₂²	1	8	yes	complemented
64	#10625055	C₂²	1	8	yes	complemented
65	#10625053	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	—	4	2	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	1	yes	characteristic
76	C₂³×D₂₃	C₂³	1	4	yes	—
77	C₂×D₄×C₂₃	—	4	2	no	—
78	C₂×D₄×C₂₃	—	4	2	no	—
79	C₂×D₄×C₂₃	—	4	2	no	—
80	C₂×D₄×C₂₃	C₂³	1	4	yes	—
81	C₂×D₄×C₂₃	C₂³	1	4	yes	—
82	C₂×D₄×C₂₃	C₂³	1	4	yes	complemented
83	C₂²×C₄×C₂₃	—	4	2	no	—
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	1	yes	characteristic
88	C₂²×C₄×C₂₃	C₂³	1	4	yes	complemented
89	C₂×C₂²⋊D₂₃	—	4	2	no	—
90	C₂×C₂²⋊D₂₃	—	4	2	no	—
91	C₂×C₂²⋊D₂₃	—	4	2	no	—
92	C₂×C₂²⋊D₂₃	—	4	2	no	—
93	C₂×C₂²⋊D₂₃	—	4	2	no	—
94	C₂×C₂²⋊D₂₃	—	4	2	no	—
95	C₂×C₂²⋊D₂₃	—	4	2	no	—
96	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
98	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
99	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
101	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	complemented
102	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	complemented
103	C₂²×Dic₂₃	—	4	2	no	—
104	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
105	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
106	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
107	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
108	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
109	C₂²×Dic₂₃	C₂³	1	4	yes	complemented
110	C₂×D₉₂	—	4	2	no	—
111	C₂×D₉₂	—	4	2	no	—
112	C₂×D₉₂	C₂³	1	4	yes	—
113	C₂×D₉₂	C₂³	1	4	yes	—
114	C₂×C₄×D₂₃	—	4	2	no	—
115	C₂×C₄×D₂₃	C₂³	1	4	yes	complemented
116	C₄⋊C₄×C₂₃	C₂³	1	4	yes	complemented
117	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
118	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	complemented
119	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
120	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
121	C₂²⋊Dic₂₃	C₂³	1	4	yes	complemented
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	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
126	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
127	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
128	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	complemented
129	C₄⋊Dic₂₃	C₂³	1	4	yes	complemented
130	C₄⋊Dic₂₃	C₂³	1	4	yes	complemented
131	Dic₂₃⋊C₄	C₂³	1	4	yes	complemented
132	Dic₂₃⋊C₄	C₂³	1	4	yes	complemented
133	Dic₂₃⋊C₄	C₂³	1	4	yes	complemented
134	C₄×Dic₂₃	C₂³	1	4	yes	complemented
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	—	2	2	no	—
142	C₂³×C₂₃	—	2	2	no	—
143	C₂³×C₂₃	—	2	2	no	—
144	C₂³×C₂₃	C₂⁴	1	2	yes	—
145	C₂³×C₂₃	C₂⁴	1	2	yes	—
146	C₂³×C₂₃	C₂⁴	1	2	yes	—
147	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
148	C₂²×D₂₃	—	2	2	no	—
149	C₂²×D₂₃	—	2	2	no	—
150	C₂²×D₂₃	—	2	2	no	—
151	C₂²×D₂₃	—	2	2	no	—
152	C₂²×D₂₃	—	2	2	no	—
153	C₂²×D₂₃	—	2	2	no	—
154	C₂²×D₂₃	—	2	2	no	—
155	C₂²×D₂₃	—	2	2	no	—
156	C₂²×D₂₃	—	2	2	no	—
157	C₂²×D₂₃	—	4	4	no	—
158	C₂²×D₂₃	—	4	4	no	—
159	C₂²×D₂₃	—	4	4	no	—
160	C₂²×D₂₃	—	4	16	no	—
161	C₂²×D₂₃	C₂⁴	1	2	yes	—
162	C₂²×D₂₃	C₂⁴	1	2	yes	—
163	C₂²×D₂₃	C₂⁴	1	2	yes	—
164	D₄×C₂₃	—	4	4	no	—
165	D₄×C₂₃	—	4	4	no	—
166	D₄×C₂₃	—	4	4	no	—
167	C₂×C₄×C₂₃	—	2	2	no	—
168	C₂×C₄×C₂₃	—	2	2	no	—
169	C₂×C₄×C₂₃	—	2	2	no	—
170	C₂×C₄×C₂₃	—	2	2	no	—
171	C₂×C₄×C₂₃	—	4	4	no	—
172	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
173	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
174	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
175	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
176	C₂²⋊D₂₃	—	4	4	no	—
177	C₂²⋊D₂₃	—	4	4	no	—
178	C₂²⋊D₂₃	—	4	4	no	—
179	C₂²⋊D₂₃	—	4	4	no	—
180	C₂²⋊D₂₃	—	4	4	no	—
181	C₂²⋊D₂₃	—	4	4	no	—
182	C₂²⋊D₂₃	—	4	4	no	—
183	C₂×Dic₂₃	—	2	2	no	—
184	C₂×Dic₂₃	—	2	2	no	—
185	C₂×Dic₂₃	—	2	2	no	—
186	C₂×Dic₂₃	—	2	2	no	—
187	C₂×Dic₂₃	—	2	2	no	—
188	C₂×Dic₂₃	—	4	4	no	—
189	C₂×Dic₂₃	C₂⁴	1	2	yes	—
190	C₂×Dic₂₃	C₂⁴	1	2	yes	—
191	C₂×Dic₂₃	C₂⁴	1	2	yes	—
192	C₂×Dic₂₃	C₂⁴	1	2	yes	—
193	C₂×Dic₂₃	C₂⁴	1	2	yes	—
194	D₉₂	—	4	4	no	—
195	D₉₂	—	4	4	no	—
196	C₄×D₂₃	—	4	4	no	—
197	C₂×#560	—	23	1	no	maximal, Sylow
198	C₂²×C₂₃	—	2	2	no	—
199	C₂²×C₂₃	—	2	2	no	—
200	C₂²×C₂₃	—	2	2	no	—
201	C₂²×C₂₃	—	2	2	no	—
202	C₂²×C₂₃	—	2	2	no	—
203	C₂²×C₂₃	—	2	2	no	—
204	C₂²×C₂₃	—	2	2	no	—
205	C₂²×C₂₃	—	2	2	no	—
206	C₂²×C₂₃	—	2	2	no	—
207	C₂²×C₂₃	—	4	4	no	—
208	C₂²×C₂₃	—	4	4	no	—
209	C₂²×C₂₃	—	4	4	no	—
210	C₂²×C₂₃	H(5,𝔽₂)	1	2	yes	—
211	C₂²×C₂₃	H(5,𝔽₂)	1	2	yes	—
212	C₂²×C₂₃	H(5,𝔽₂)	1	2	yes	—
213	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
214	C₂×D₂₃	—	2	2	no	—
215	C₂×D₂₃	—	2	2	no	—
216	C₂×D₂₃	—	2	2	no	—
217	C₂×D₂₃	—	2	2	no	—
218	C₂×D₂₃	—	2	2	no	—
219	C₂×D₂₃	—	2	2	no	—
220	C₂×D₂₃	—	2	2	no	—
221	C₂×D₂₃	—	2	2	no	—
222	C₂×D₂₃	—	2	2	no	—
223	C₂×D₂₃	—	4	16	no	—
224	C₂×D₂₃	—	4	4	no	—
225	C₂×D₂₃	—	4	4	no	—
226	C₂×D₂₃	—	4	4	no	—
227	C₄×C₂₃	—	2	2	no	—
228	C₄×C₂₃	—	2	2	no	—
229	C₄×C₂₃	—	2	2	no	—
230	C₄×C₂₃	—	2	2	no	—
231	Dic₂₃	—	2	2	no	—
232	Dic₂₃	—	2	2	no	—
233	Dic₂₃	—	2	2	no	—
234	Dic₂₃	—	2	2	no	—
235	Dic₂₃	—	2	2	no	—
236	#560	—	23	16	no	—
237	C₂×#127	—	23	1	no	—
238	C₂×#126	—	23	1	no	—
239	C₂×#126	—	23	1	no	—
240	C₂×#123	—	23	1	no	—
241	C₂×#123	—	23	1	no	—
242	C₂×#123	—	23	1	no	—
243	C₂×#121	—	23	1	no	—
244	C₂×#121	—	23	1	no	—
245	C₂×#121	—	23	1	no	—
246	C₂×#121	—	23	1	no	—
247	C₂×#121	—	23	1	no	—
248	C₂×#121	D₂₃	1	1	yes	characteristic, complemented
249	C₂×#120	—	23	1	no	—
250	C₂×#120	—	23	1	no	—
251	C₂×#120	—	23	1	no	—
252	C₂×C₂₃	—	4	2	no	—
253	C₂×C₂₃	—	4	2	no	—
254	C₂×C₂₃	—	4	2	no	—
255	C₂×C₂₃	#560	1	4	yes	complemented
256	C₂×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
257	C₂×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
258	C₂×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
259	D₂₃	—	4	2	no	—
260	D₂₃	—	4	2	no	—
261	D₂₃	—	4	2	no	—
262	C₂⁵	—	23	1	no	—
263	C₂²×D₄	—	23	1	no	—
264	C₂²×D₄	—	23	1	no	—
265	C₂²×D₄	—	23	1	no	—
266	C₂²×D₄	—	23	1	no	—
267	C₂²×D₄	—	23	1	no	—
268	C₂²×D₄	—	23	1	no	—
269	C₂²×D₄	—	23	1	no	—
270	C₂²×D₄	—	23	1	no	—
271	C₂²×D₄	—	23	1	no	—
272	C₂²×D₄	C₂×D₂₃	1	1	yes	characteristic
273	C₂²×D₄	C₂×D₂₃	1	1	yes	characteristic
274	C₂²×D₄	C₂×D₂₃	1	1	yes	characteristic, complemented
275	C₂³×C₄	—	23	1	no	—
276	C₂³×C₄	—	23	1	no	—
277	C₂³×C₄	C₂×D₂₃	1	1	yes	characteristic, complemented
278	#127	—	23	8	no	—
279	#126	—	23	8	no	—
280	#126	—	23	8	no	—
281	#123	—	23	8	no	—
282	#123	—	23	8	no	—
283	#123	—	23	8	no	—
284	#121	—	23	8	no	—
285	#121	—	23	8	no	—
286	#121	—	23	8	no	—
287	#121	—	23	8	no	—
288	#121	—	23	8	no	—
289	#121	C₂×D₂₃	1	8	yes	complemented
290	#120	—	23	8	no	—
291	#120	—	23	8	no	—
292	#120	—	23	8	no	—
293	C₂×C₄⋊C₄	—	23	1	no	—
294	C₂×C₄⋊C₄	—	23	1	no	—
295	C₂×C₄⋊C₄	—	23	1	no	—
296	C₂×C₄⋊C₄	—	23	1	no	—
297	C₂×C₄⋊C₄	—	23	1	no	—
298	C₂×C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic, complemented
299	C₂×C₂²⋊C₄	—	23	1	no	—
300	C₂×C₂²⋊C₄	—	23	1	no	—
301	C₂×C₂²⋊C₄	—	23	1	no	—
302	C₂×C₂²⋊C₄	—	23	1	no	—
303	C₂×C₂²⋊C₄	—	23	1	no	—
304	C₂×C₂²⋊C₄	—	23	1	no	—
305	C₂×C₂²⋊C₄	—	23	1	no	—
306	C₂×C₂²⋊C₄	—	23	1	no	—
307	C₂×C₂²⋊C₄	—	23	1	no	—
308	C₂×C₂²⋊C₄	—	23	1	no	—
309	C₂×C₂²⋊C₄	C₂×D₂₃	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	C₂×D₂₃	1	1	yes	characteristic, complemented
311	C₂×C₄²	—	23	1	no	—
312	C₂₃	C₂×#560	1	1	yes	characteristic, complemented, Sylow
313	C₂⁴	—	23	1	no	—
314	C₂⁴	—	23	1	no	—
315	C₂⁴	—	23	1	no	—
316	C₂⁴	—	23	4	no	—
317	C₂⁴	—	92	2	no	—
318	C₂⁴	—	92	2	no	—
319	C₂⁴	—	92	2	no	—
320	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
321	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
322	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
323	C₂×D₄	—	4	2	no	—
324	C₂×D₄	—	4	2	no	—
325	C₂×D₄	—	4	2	no	—
326	C₂×D₄	—	23	4	no	—
327	C₂×D₄	—	23	4	no	—
328	C₂×D₄	—	23	4	no	—
329	C₂×D₄	—	23	4	no	—
330	C₂×D₄	—	23	4	no	—
331	C₂×D₄	—	23	4	no	—
332	C₂×D₄	—	23	4	no	—
333	C₂×D₄	—	23	4	no	—
334	C₂×D₄	—	23	4	no	—
335	C₂×D₄	—	92	2	no	—
336	C₂×D₄	—	92	2	no	—
337	C₂×D₄	—	92	2	no	—
338	C₂×D₄	—	92	2	no	—
339	C₂×D₄	—	92	2	no	—
340	C₂×D₄	—	92	2	no	—
341	C₂×D₄	—	92	2	no	—
342	C₂×D₄	—	92	2	no	—
343	C₂×D₄	—	92	2	no	—
344	C₂×D₄	C₂²×D₂₃	1	4	yes	—
345	C₂×D₄	C₂²×D₂₃	1	4	yes	—
346	C₂×D₄	C₂²×D₂₃	1	4	yes	complemented
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	23	1	no	—
349	C₂²×C₄	—	23	1	no	—
350	C₂²×C₄	—	23	1	no	—
351	C₂²×C₄	—	23	1	no	—
352	C₂²×C₄	—	23	1	no	—
353	C₂²×C₄	—	23	4	no	—
354	C₂²×C₄	—	23	4	no	—
355	C₂²×C₄	—	92	2	no	—
356	C₂²×C₄	—	92	2	no	—
357	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
358	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
359	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
360	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
361	C₂²×C₄	C₂²×D₂₃	1	4	yes	complemented
362	C₄⋊C₄	—	23	4	no	—
363	C₄⋊C₄	—	23	4	no	—
364	C₄⋊C₄	—	23	4	no	—
365	C₄⋊C₄	—	23	4	no	—
366	C₄⋊C₄	—	23	4	no	—
367	C₄⋊C₄	C₂²×D₂₃	1	4	yes	complemented
368	C₂²⋊C₄	—	23	4	no	—
369	C₂²⋊C₄	—	23	4	no	—
370	C₂²⋊C₄	—	23	4	no	—
371	C₂²⋊C₄	—	23	4	no	—
372	C₂²⋊C₄	—	23	4	no	—
373	C₂²⋊C₄	—	23	4	no	—
374	C₂²⋊C₄	—	23	4	no	—
375	C₂²⋊C₄	—	23	4	no	—
376	C₂²⋊C₄	—	23	4	no	—
377	C₂²⋊C₄	—	23	4	no	—
378	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	—
379	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	complemented
380	C₄²	—	23	4	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	23	2	no	—
391	C₂³	—	23	2	no	—
392	C₂³	—	23	2	no	—
393	C₂³	—	46	2	no	—
394	C₂³	—	46	2	no	—
395	C₂³	—	46	2	no	—
396	C₂³	—	46	2	no	—
397	C₂³	—	46	2	no	—
398	C₂³	—	46	2	no	—
399	C₂³	—	46	2	no	—
400	C₂³	—	46	2	no	—
401	C₂³	—	46	2	no	—
402	C₂³	—	92	4	no	—
403	C₂³	—	92	4	no	—
404	C₂³	—	92	4	no	—
405	C₂³	—	92	16	no	—
406	C₂³	C₂³×D₂₃	1	2	yes	—
407	C₂³	C₂³×D₂₃	1	2	yes	—
408	C₂³	C₂³×D₂₃	1	2	yes	—
409	C₂³	C₂³×D₂₃	1	1	yes	characteristic
410	D₄	—	4	4	no	—
411	D₄	—	4	4	no	—
412	D₄	—	4	4	no	—
413	D₄	—	92	4	no	—
414	D₄	—	92	4	no	—
415	D₄	—	92	4	no	—
416	D₄	—	92	4	no	—
417	D₄	—	92	4	no	—
418	D₄	—	92	4	no	—
419	D₄	—	92	4	no	—
420	D₄	—	92	4	no	—
421	D₄	—	92	4	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	23	2	no	—
428	C₂×C₄	—	23	2	no	—
429	C₂×C₄	—	23	2	no	—
430	C₂×C₄	—	23	2	no	—
431	C₂×C₄	—	23	2	no	—
432	C₂×C₄	—	46	2	no	—
433	C₂×C₄	—	46	2	no	—
434	C₂×C₄	—	46	2	no	—
435	C₂×C₄	—	46	2	no	—
436	C₂×C₄	—	46	2	no	—
437	C₂×C₄	—	92	4	no	—
438	C₂×C₄	—	92	4	no	—
439	C₂×C₄	C₂³×D₂₃	1	2	yes	—
440	C₂×C₄	C₂³×D₂₃	1	2	yes	—
441	C₂×C₄	C₂³×D₂₃	1	2	yes	—
442	C₂×C₄	C₂³×D₂₃	1	2	yes	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	4	4	no	—
453	C₂²	—	4	4	no	—
454	C₂²	—	4	4	no	—
455	C₂²	—	46	2	no	—
456	C₂²	—	46	2	no	—
457	C₂²	—	46	2	no	—
458	C₂²	—	46	2	no	—
459	C₂²	—	46	2	no	—
460	C₂²	—	46	2	no	—
461	C₂²	—	46	2	no	—
462	C₂²	—	46	2	no	—
463	C₂²	—	46	2	no	—
464	C₂²	—	92	16	no	—
465	C₂²	—	92	4	no	—
466	C₂²	—	92	4	no	—
467	C₂²	—	92	4	no	—
468	C₂²	#10625155	1	2	yes	—
469	C₂²	#10625155	1	2	yes	—
470	C₂²	#10625160	1	2	yes	—
471	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	46	2	no	—
477	C₄	—	46	2	no	—
478	C₄	—	46	2	no	—
479	C₄	—	46	2	no	—
480	C₄	—	46	2	no	—
481	C₂	—	4	2	no	—
482	C₂	—	4	2	no	—
483	C₂	—	4	2	no	—
484	C₂	—	92	2	no	—
485	C₂	—	92	2	no	—
486	C₂	—	92	2	no	—
487	C₂	#13093155	1	4	yes	direct product factor
488	C₂	C₂×#10625155	1	1	yes	characteristic
489	C₂	C₂×#10625155	1	1	yes	characteristic
490	C₂	C₂×#10625160	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×#560
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. #13093155	C₂	direct (N × H)
2. C₂×#10625111	C₂	semidirect
3. C₂×#10625069	C₂	semidirect
4. C₂×#10625050	C₂	semidirect
5. C₂×#10625065	C₂	semidirect
6. C₂×#10625057	C₂	semidirect
7. C₂×#10625100	C₂	semidirect
8. C₂×#10625101	C₂	semidirect
9. C₂×#10625055	C₂	semidirect
10. C₂×#10625110	C₂	semidirect
11. C₂×#10625110	C₂	semidirect
12. C₂×#10625109	C₂	semidirect
13. C₂×#10625053	C₂	semidirect
14. C₂×#10625108	C₂	semidirect
15. C₂×#10625108	C₂	semidirect
16. C₂×C₂₃×#121	C₂	semidirect
20. C₂²×D₄×C₂₃	C₂²	semidirect
21. C₂³×C₄×C₂₃	C₂²	semidirect
27. C₂²×C₂²⋊D₂₃	C₂²	semidirect
28. C₂²×C₂²⋊D₂₃	C₂²	semidirect
29. C₂³×Dic₂₃	C₂²	semidirect
32. C₂²×C₄×D₂₃	C₂²	semidirect
33. C₂₃×#121	C₂²	semidirect
34. C₂×C₄⋊C₄×C₂₃	C₂²	semidirect
36. C₂×C₂²⋊C₄×C₂₃	C₂²	semidirect
39. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
40. #10625111	C₂²	semidirect
41. #10625110	C₂²	semidirect
42. #10625110	C₂²	semidirect
43. #10625109	C₂²	semidirect
44. #10625108	C₂²	semidirect
45. #10625108	C₂²	semidirect
46. #10625101	C₂²	semidirect
47. #10625100	C₂²	semidirect
54. C₂×(C₂×D₂₃)⋊C₄	C₂²	semidirect
55. C₂×C₄⋊Dic₂₃	C₂²	semidirect
56. C₂×C₄⋊Dic₂₃	C₂²	semidirect
57. C₂×Dic₂₃⋊C₄	C₂²	semidirect
58. C₂×Dic₂₃⋊C₄	C₂²	semidirect
59. C₂×Dic₂₃⋊C₄	C₂²	semidirect
60. C₂×C₄×Dic₂₃	C₂²	semidirect
61. #10625069	C₂²	semidirect
62. #10625065	C₂²	semidirect
63. #10625057	C₂²	semidirect
64. #10625055	C₂²	semidirect
65. #10625053	C₂²	semidirect
66. #10625050	C₂²	semidirect
82. C₂×D₄×C₂₃	C₂³	semidirect
88. C₂²×C₄×C₂₃	C₂³	semidirect
101. C₂×C₂²⋊D₂₃	C₂³	semidirect
102. C₂×C₂²⋊D₂₃	C₂³	semidirect
109. C₂²×Dic₂₃	C₂³	semidirect
115. C₂×C₄×D₂₃	C₂³	semidirect
116. C₄⋊C₄×C₂₃	C₂³	semidirect
118. C₂²⋊C₄×C₂₃	C₂³	semidirect
121. C₂²⋊Dic₂₃	C₂³	semidirect
128. (C₂×D₂₃)⋊C₄	C₂³	semidirect
129. C₄⋊Dic₂₃	C₂³	semidirect
130. C₄⋊Dic₂₃	C₂³	semidirect
131. Dic₂₃⋊C₄	C₂³	semidirect
132. Dic₂₃⋊C₄	C₂³	semidirect
133. Dic₂₃⋊C₄	C₂³	semidirect
134. C₄×Dic₂₃	C₂³	semidirect
248. C₂×#121	D₂₃	semidirect
255. C₂×C₂₃	#560	semidirect
274. C₂²×D₄	C₂×D₂₃	semidirect
277. C₂³×C₄	C₂×D₂₃	semidirect
289. #121	C₂×D₂₃	semidirect
298. C₂×C₄⋊C₄	C₂×D₂₃	semidirect
310. C₂×C₂²⋊C₄	C₂×D₂₃	semidirect
312. C₂₃	C₂×#560	semidirect
346. C₂×D₄	C₂²×D₂₃	semidirect
361. C₂²×C₄	C₂²×D₂₃	semidirect
367. C₄⋊C₄	C₂²×D₂₃	semidirect
379. C₂²⋊C₄	C₂²×D₂₃	semidirect
487. C₂	#13093155	direct (N × H)

Maximal subgroups

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

subgroup	index
#13093155	2
C₂×#10625111	2
C₂×#10625069	2
C₂×#10625050	2
C₂×#10625065	2
C₂×#10625057	2
C₂×#10625100	2
C₂×#10625101	2
C₂×#10625055	2
C₂×#10625110	2
C₂×#10625109	2
C₂×#10625053	2
C₂×#10625108	2
C₂×C₂₃×#121	2
C₂×#560	23

Subgroups — C2×#13093155 #15687512

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13093155 #15687512