Subgroups — C₂×#11725035 #13183448

Order 1760.

328 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#11725035	C₂	1	8	yes	maximal, direct product factor
3	C₂×D₂₂₀	C₂	1	3	yes	maximal, complemented
4	C₂×C₄×D₅₅	C₂	1	3	yes	maximal, complemented
5	C₂²×D₅₅	C₂²	1	3	yes	—
6	C₅×Q₈×C₁₁	C₂²	1	4	yes	complemented
7	C₂×C₄×C₅×C₁₁	C₂²	1	3	yes	—
8	C₂×Dic₅₅	C₂²	1	1	yes	characteristic
9	D₂₂₀	C₂²	1	12	yes	complemented
10	C₄×D₅₅	C₂²	1	12	yes	complemented
11	C₂×#4343	—	5	1	no	maximal, Hall
12	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
13	C₂×D₅₅	—	2	6	no	—
14	C₂×D₅₅	C₂³	1	6	yes	—
15	C₄×C₅×C₁₁	C₂³	1	6	yes	—
16	Dic₅₅	C₂³	1	2	yes	—
17	C₂×Q₈×C₁₁	D₅	1	1	yes	characteristic, complemented
18	#4343	—	5	8	no	—
19	C₂×D₄₄	—	5	3	no	—
20	C₂×C₄×D₁₁	—	5	3	no	—
21	C₂×#713	—	11	1	no	maximal, Hall
22	C₂×C₅×C₁₁	#41	1	2	yes	complemented
23	C₂×C₅×C₁₁	C₂⁴	1	1	yes	characteristic
24	D₅₅	—	2	6	no	—
25	C₂²×D₁₁	—	5	3	no	—
26	Q₈×C₁₁	C₂×D₅	1	4	yes	complemented
27	C₂×C₄×C₁₁	C₂×D₅	1	3	yes	—
28	C₂×Dic₁₁	—	5	1	no	—
29	D₄₄	—	5	12	no	—
30	C₄×D₁₁	—	5	12	no	—
31	C₂×C₅×Q₈	D₁₁	1	1	yes	characteristic, complemented
32	#713	—	11	8	no	—
33	C₂×D₂₀	—	11	3	no	—
34	C₂×C₄×D₅	—	11	3	no	—
35	C₅×C₁₁	C₂×#41	1	1	yes	characteristic, complemented, Hall
36	C₂²×C₁₁	C₂²×D₅	1	1	yes	characteristic
37	C₂×D₁₁	—	5	6	no	—
38	C₂×D₁₁	—	10	6	no	—
39	C₄×C₁₁	C₂²×D₅	1	6	yes	—
40	Dic₁₁	—	5	2	no	—
41	C₂²×D₅	—	11	3	no	—
42	C₅×Q₈	C₂×D₁₁	1	4	yes	complemented
43	C₂×C₄×C₅	C₂×D₁₁	1	3	yes	—
44	C₂×Dic₅	—	11	1	no	—
45	D₂₀	—	11	12	no	—
46	C₄×D₅	—	11	12	no	—
47	C₂×#41	—	55	1	no	Sylow
48	C₂×C₁₁	#713	1	2	yes	complemented
49	C₂×C₁₁	C₂³×D₅	1	1	yes	characteristic
50	D₁₁	—	10	6	no	—
51	C₂²×C₅	C₂²×D₁₁	1	1	yes	characteristic
52	C₂×D₅	—	11	6	no	—
53	C₂×D₅	—	22	6	no	—
54	C₄×C₅	C₂²×D₁₁	1	6	yes	—
55	Dic₅	—	11	2	no	—
56	#41	—	55	8	no	—
57	C₂×Q₈	D₅₅	1	1	yes	characteristic, complemented
58	C₂×D₄	—	55	3	no	—
59	C₂²×C₄	—	55	3	no	—
60	C₁₁	C₂×#713	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₅	#4343	1	2	yes	complemented
62	C₂×C₅	C₂³×D₁₁	1	1	yes	characteristic
63	D₅	—	22	6	no	—
64	C₂³	—	55	3	no	—
65	Q₈	C₂×D₅₅	1	4	yes	complemented
66	D₄	—	55	12	no	—
67	C₂×C₄	—	55	1	no	—
68	C₂×C₄	—	55	12	no	—
69	C₂×C₄	C₂×D₅₅	1	3	yes	—
70	C₅	C₂×#4343	1	1	yes	characteristic, complemented, Sylow
71	C₂²	—	55	6	no	—
72	C₂²	—	110	6	no	—
73	C₂²	C₂²×D₅₅	1	1	yes	characteristic
74	C₄	—	55	2	no	—
75	C₄	C₂²×D₅₅	1	6	yes	—
76	C₂	—	110	6	no	—
77	C₂	#11725035	1	2	yes	direct product factor
78	C₂	C₂³×D₅₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₅₅
commutator, cosocle	C₂×C₅×C₁₁	C₂⁴
Frattini	C₂	C₂³×D₅₅
Fitting	C₂×C₅×Q₈×C₁₁	C₂
socle	C₂²×C₅×C₁₁	C₂³
hypercenter	C₂×Q₈	D₅₅
hypocenter	C₅×C₁₁	C₂×#41
LCS	G ▷ C₂×C₅×C₁₁ ▷ C₅×C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×Q₈×C₁₁	C₂	semidirect
2. #11725035	C₂	direct (N × H)
3. C₂×D₂₂₀	C₂	semidirect
4. C₂×C₄×D₅₅	C₂	semidirect
6. C₅×Q₈×C₁₁	C₂²	semidirect
9. D₂₂₀	C₂²	semidirect
10. C₄×D₅₅	C₂²	semidirect
17. C₂×Q₈×C₁₁	D₅	semidirect
22. C₂×C₅×C₁₁	#41	semidirect
26. Q₈×C₁₁	C₂×D₅	semidirect
31. C₂×C₅×Q₈	D₁₁	semidirect
35. C₅×C₁₁	C₂×#41	semidirect
42. C₅×Q₈	C₂×D₁₁	semidirect
48. C₂×C₁₁	#713	semidirect
57. C₂×Q₈	D₅₅	semidirect
60. C₁₁	C₂×#713	semidirect
61. C₂×C₅	#4343	semidirect
65. Q₈	C₂×D₅₅	semidirect
70. C₅	C₂×#4343	semidirect
77. C₂	#11725035	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×Q₈×C₁₁	2
#11725035	2
C₂×D₂₂₀	2
C₂×C₄×D₅₅	2
C₂×#4343	5
C₂×#713	11

Subgroups — C2×#11725035 #13183448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11725035 #13183448