Subgroups — C₂×#11724935 #13183242

Order 1760.

136 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	C₂×D₂₂₀	C₂	1	1	yes	maximal, characteristic
3	#11724935	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₁⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₅₅	—	2	1	no	—
6	C₅×Q₈×C₁₁	—	2	1	no	—
7	C₅×Q₈×C₁₁	C₂²	1	2	yes	complemented
8	C₂×C₄×C₅×C₁₁	—	2	1	no	—
9	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
10	D₂₂₀	—	2	1	no	—
11	D₂₂₀	C₂²	1	2	yes	—
12	C₁₁⋊#168	C₂²	1	2	yes	complemented
13	C₂×#4325	—	5	1	no	maximal, Hall
14	C₂²×C₅×C₁₁	D₄	1	1	yes	characteristic
15	C₂×D₅₅	—	2	2	no	—
16	C₂×D₅₅	—	4	2	no	—
17	C₄×C₅×C₁₁	—	2	2	no	—
18	C₄×C₅×C₁₁	D₄	1	1	yes	characteristic
19	C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
20	C₂×Q₈×C₁₁	D₅	1	1	yes	characteristic, complemented
21	C₂×D₄₄	—	5	1	no	—
22	#4325	—	5	4	no	—
23	C₂×C₁₁⋊C₈	—	5	1	no	—
24	C₂×#688	—	11	1	no	maximal, Hall
25	C₂×C₅×C₁₁	SD₁₆	1	2	yes	complemented
26	C₂×C₅×C₁₁	C₂×D₄	1	1	yes	characteristic
27	D₅₅	—	4	2	no	—
28	C₂²×D₁₁	—	10	1	no	—
29	Q₈×C₁₁	—	2	1	no	—
30	Q₈×C₁₁	C₂×D₅	1	2	yes	complemented
31	C₂×C₄×C₁₁	—	2	1	no	—
32	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
33	D₄₄	—	5	2	no	—
34	D₄₄	—	10	1	no	—
35	C₁₁⋊C₈	—	5	2	no	—
36	C₂×C₅×Q₈	D₁₁	1	1	yes	characteristic, complemented
37	C₂×D₂₀	—	11	1	no	—
38	#688	—	11	4	no	—
39	C₂×#168	—	11	1	no	—
40	C₅×C₁₁	C₂×SD₁₆	1	1	yes	characteristic, complemented, Hall
41	C₂²×C₁₁	C₂²⋊D₅	1	1	yes	characteristic
42	C₂×D₁₁	—	10	2	no	—
43	C₂×D₁₁	—	20	2	no	—
44	C₄×C₁₁	—	2	2	no	—
45	C₄×C₁₁	C₂²⋊D₅	1	1	yes	characteristic
46	C₄×C₁₁	C₂²×D₅	1	1	yes	characteristic
47	C₂²×D₅	—	22	1	no	—
48	C₅×Q₈	—	2	1	no	—
49	C₅×Q₈	C₂×D₁₁	1	2	yes	complemented
50	C₂×C₄×C₅	—	2	1	no	—
51	C₂×C₄×C₅	C₂×D₁₁	1	1	yes	characteristic
52	D₂₀	—	11	2	no	—
53	D₂₀	—	22	1	no	—
54	#168	—	11	2	no	—
55	C₂×SD₁₆	—	55	1	no	Sylow
56	C₂×C₁₁	#688	1	2	yes	complemented
57	C₂×C₁₁	C₂×C₂²⋊D₅	1	1	yes	characteristic
58	D₁₁	—	20	2	no	—
59	C₂²×C₅	C₂²⋊D₁₁	1	1	yes	characteristic
60	C₂×D₅	—	22	2	no	—
61	C₂×D₅	—	44	2	no	—
62	C₄×C₅	—	2	2	no	—
63	C₄×C₅	C₂²⋊D₁₁	1	1	yes	characteristic
64	C₄×C₅	C₂²×D₁₁	1	1	yes	characteristic
65	C₂×Q₈	D₅₅	1	1	yes	characteristic, complemented
66	C₂×D₄	—	55	1	no	—
67	SD₁₆	—	55	4	no	—
68	C₂×C₈	—	55	1	no	—
69	C₁₁	C₂×#688	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₅	#4325	1	2	yes	complemented
71	C₂×C₅	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
72	D₅	—	44	2	no	—
73	C₂³	—	110	1	no	—
74	Q₈	—	2	1	no	—
75	Q₈	C₂×D₅₅	1	2	yes	complemented
76	D₄	—	55	2	no	—
77	D₄	—	110	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	C₂×D₅₅	1	1	yes	characteristic
80	C₈	—	55	2	no	—
81	C₅	C₂×#4325	1	1	yes	characteristic, complemented, Sylow
82	C₂²	—	110	2	no	—
83	C₂²	—	220	2	no	—
84	C₂²	C₂²⋊D₅₅	1	1	yes	characteristic
85	C₄	—	2	2	no	—
86	C₄	C₂²⋊D₅₅	1	1	yes	characteristic
87	C₄	C₂²×D₅₅	1	1	yes	characteristic
88	C₂	—	220	2	no	—
89	C₂	#11724935	1	2	yes	direct product factor
90	C₂	C₂×C₂²⋊D₅₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊D₅₅
commutator, cosocle	C₄×C₅×C₁₁	C₂³
Frattini	C₄	C₂²×D₅₅
Fitting	C₂×C₅×Q₈×C₁₁	C₂
socle	C₂²×C₅×C₁₁	D₄
prime radical	C₂×D₂₂₀	C₂
hypercenter	C₂×Q₈	D₅₅
hypocenter	C₅×C₁₁	C₂×SD₁₆
LCS	G ▷ C₄×C₅×C₁₁ ▷ C₂×C₅×C₁₁ ▷ C₅×C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ 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
3. #11724935	C₂	direct (N × H)
4. C₂×C₁₁⋊#168	C₂	semidirect
7. C₅×Q₈×C₁₁	C₂²	semidirect
12. C₁₁⋊#168	C₂²	semidirect
20. C₂×Q₈×C₁₁	D₅	semidirect
25. C₂×C₅×C₁₁	SD₁₆	semidirect
30. Q₈×C₁₁	C₂×D₅	semidirect
36. C₂×C₅×Q₈	D₁₁	semidirect
40. C₅×C₁₁	C₂×SD₁₆	semidirect
49. C₅×Q₈	C₂×D₁₁	semidirect
56. C₂×C₁₁	#688	semidirect
65. C₂×Q₈	D₅₅	semidirect
69. C₁₁	C₂×#688	semidirect
70. C₂×C₅	#4325	semidirect
75. Q₈	C₂×D₅₅	semidirect
81. C₅	C₂×#4325	semidirect
89. C₂	#11724935	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
C₂×D₂₂₀	2
#11724935	2
C₂×C₁₁⋊#168	2
C₂×#4325	5
C₂×#688	11

Subgroups — C2×#11724935 #13183242

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11724935 #13183242