Subgroups — C₂×#11724936 #13183244

Order 1760.

120 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
2	C₂×Dic₁₁₀	C₂	1	1	yes	maximal, characteristic
3	#11724936	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₁⋊#168	C₂	1	1	yes	maximal, characteristic
5	C₅×Q₈×C₁₁	—	2	1	no	—
6	C₅×Q₈×C₁₁	C₂²	1	2	yes	—
7	C₂×C₄×C₅×C₁₁	—	2	1	no	—
8	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×Dic₅₅	—	2	1	no	—
10	Dic₁₁₀	—	2	1	no	—
11	Dic₁₁₀	C₂²	1	2	yes	—
12	C₁₁⋊#168	C₂²	1	2	yes	—
13	C₂×#4326	—	5	1	no	maximal, Hall
14	C₂²×C₅×C₁₁	D₄	1	1	yes	characteristic
15	C₄×C₅×C₁₁	—	2	2	no	—
16	C₄×C₅×C₁₁	D₄	1	1	yes	characteristic
17	C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
18	Dic₅₅	—	2	2	no	—
19	C₂×Q₈×C₁₁	D₅	1	1	yes	characteristic
20	C₂×Dic₂₂	—	5	1	no	—
21	#4326	—	5	4	no	—
22	C₂×C₁₁⋊C₈	—	5	1	no	—
23	C₂×#689	—	11	1	no	maximal, Hall
24	C₂×C₅×C₁₁	Q₁₆	1	2	yes	complemented
25	C₂×C₅×C₁₁	C₂×D₄	1	1	yes	characteristic
26	Q₈×C₁₁	—	2	1	no	—
27	Q₈×C₁₁	C₂×D₅	1	2	yes	—
28	C₂×C₄×C₁₁	—	2	1	no	—
29	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
30	C₂×Dic₁₁	—	10	1	no	—
31	Dic₂₂	—	5	2	no	—
32	Dic₂₂	—	10	1	no	—
33	C₁₁⋊C₈	—	5	2	no	—
34	C₂×C₅×Q₈	D₁₁	1	1	yes	characteristic
35	C₂×Dic₁₀	—	11	1	no	—
36	#689	—	11	4	no	—
37	C₂×#168	—	11	1	no	—
38	C₅×C₁₁	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
39	C₂²×C₁₁	C₂²⋊D₅	1	1	yes	characteristic
40	C₄×C₁₁	—	2	2	no	—
41	C₄×C₁₁	C₂²⋊D₅	1	1	yes	characteristic
42	C₄×C₁₁	C₂²×D₅	1	1	yes	characteristic
43	Dic₁₁	—	10	2	no	—
44	C₅×Q₈	—	2	1	no	—
45	C₅×Q₈	C₂×D₁₁	1	2	yes	—
46	C₂×C₄×C₅	—	2	1	no	—
47	C₂×C₄×C₅	C₂×D₁₁	1	1	yes	characteristic
48	C₂×Dic₅	—	22	1	no	—
49	Dic₁₀	—	11	2	no	—
50	Dic₁₀	—	22	1	no	—
51	#168	—	11	2	no	—
52	C₂×Q₁₆	—	55	1	no	Sylow
53	C₂×C₁₁	#689	1	2	yes	complemented
54	C₂×C₁₁	C₂×C₂²⋊D₅	1	1	yes	characteristic
55	C₂²×C₅	C₂²⋊D₁₁	1	1	yes	characteristic
56	C₄×C₅	—	2	2	no	—
57	C₄×C₅	C₂²⋊D₁₁	1	1	yes	characteristic
58	C₄×C₅	C₂²×D₁₁	1	1	yes	characteristic
59	Dic₅	—	22	2	no	—
60	C₂×Q₈	—	55	1	no	—
61	C₂×Q₈	D₅₅	1	1	yes	characteristic
62	Q₁₆	—	55	4	no	—
63	C₂×C₈	—	55	1	no	—
64	C₁₁	C₂×#689	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₅	#4326	1	2	yes	complemented
66	C₂×C₅	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
67	Q₈	—	2	1	no	—
68	Q₈	—	55	2	no	—
69	Q₈	—	110	1	no	—
70	Q₈	C₂×D₅₅	1	2	yes	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	110	1	no	—
73	C₂×C₄	C₂×D₅₅	1	1	yes	characteristic
74	C₈	—	55	2	no	—
75	C₅	C₂×#4326	1	1	yes	characteristic, complemented, Sylow
76	C₂²	C₂²⋊D₅₅	1	1	yes	characteristic
77	C₄	—	2	2	no	—
78	C₄	—	110	2	no	—
79	C₄	C₂²⋊D₅₅	1	1	yes	characteristic
80	C₄	C₂²×D₅₅	1	1	yes	characteristic
81	C₂	#11724936	1	2	yes	direct product factor
82	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, prime radical	C₂²×C₅×C₁₁	D₄
hypercenter	C₂×Q₈	D₅₅
hypocenter	C₅×C₁₁	C₂×Q₁₆
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
3. #11724936	C₂	direct (N × H)
24. C₂×C₅×C₁₁	Q₁₆	semidirect
38. C₅×C₁₁	C₂×Q₁₆	semidirect
53. C₂×C₁₁	#689	semidirect
64. C₁₁	C₂×#689	semidirect
65. C₂×C₅	#4326	semidirect
75. C₅	C₂×#4326	semidirect
81. C₂	#11724936	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×Dic₁₁₀	2
#11724936	2
C₂×C₁₁⋊#168	2
C₂×#4326	5
C₂×#689	11

Subgroups — C2×#11724936 #13183244

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11724936 #13183244