Subgroups — #11764441

Order 1120.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Dic₁₄	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₃₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×#168	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₅×C₇	C₂²	1	1	yes	characteristic
5	C₂×Dic₃₅	—	2	1	no	—
6	C₂×C₅×Dic₇	—	2	1	no	—
7	C₅×Dic₁₄	—	2	1	no	—
8	C₅×Dic₁₄	C₄	1	2	yes	complemented
9	C₇×#168	—	2	1	no	—
10	#6390	—	5	1	no	maximal, Hall
11	#3967	—	7	1	no	maximal, Hall
12	C₂²×C₅×C₇	D₄	1	1	yes	characteristic
13	C₄×C₅×C₇	C₂×C₄	1	1	yes	characteristic
14	C₄×C₅×C₇	D₄	1	1	yes	characteristic
15	Dic₃₅	—	4	1	no	—
16	C₅×Dic₇	—	2	2	no	—
17	C₂×Dic₁₄	D₅	1	1	yes	characteristic
18	C₂×C₇×C₈	—	5	1	no	—
19	C₄⋊Dic₇	—	5	1	no	—
20	C₂×C₅×Q₈	—	7	1	no	—
21	C₄⋊Dic₅	—	7	1	no	—
22	C₂×#168	D₇	1	1	yes	characteristic
23	C₂×C₅×C₇	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₅×C₇	SD₁₆	1	1	yes	characteristic
25	C₂×C₅×C₇	Q₁₆	1	1	yes	characteristic
26	C₂×C₄×C₇	C₂×D₅	1	1	yes	characteristic
27	C₂×Dic₇	—	2	1	no	—
28	C₂×Dic₇	—	10	1	no	—
29	Dic₁₄	—	2	1	no	—
30	Dic₁₄	Dic₅	1	2	yes	complemented
31	C₇×C₈	—	10	1	no	—
32	C₅×Q₈	—	7	2	no	—
33	C₅×Q₈	—	14	1	no	—
34	C₂×C₄×C₅	—	14	1	no	—
35	C₂×C₄×C₅	C₂×D₇	1	1	yes	characteristic
36	C₂×Dic₅	—	14	1	no	—
37	#168	—	2	1	no	—
38	C₅×C₇	#103	1	1	yes	characteristic, complemented, Hall
39	#103	—	35	1	no	Sylow
40	C₂²×C₇	C₂²⋊D₅	1	1	yes	characteristic
41	C₄×C₇	C₂×Dic₅	1	1	yes	characteristic
42	C₄×C₇	C₂²⋊D₅	1	1	yes	characteristic
43	Dic₇	—	2	2	no	—
44	Dic₇	—	20	1	no	—
45	C₂²×C₅	D₂₈	1	1	yes	characteristic
46	C₄×C₅	—	14	2	no	—
47	C₄×C₅	C₄×D₇	1	1	yes	characteristic
48	C₄×C₅	C₂²⋊D₇	1	1	yes	characteristic
49	Dic₅	—	28	1	no	—
50	C₂×Q₈	—	7	1	no	—
51	C₂×C₈	—	5	1	no	—
52	C₄⋊C₄	—	35	1	no	—
53	C₂×C₇	#688	1	1	yes	characteristic
54	C₂×C₇	#689	1	1	yes	characteristic
55	C₂×C₇	C₂²⋊Dic₅	1	1	yes	characteristic
56	C₂×C₅	#1132	1	1	yes	characteristic
57	C₂×C₅	Dic₂₈	1	1	yes	characteristic
58	C₂×C₅	(C₂×D₇)⋊C₄	1	1	yes	characteristic
59	Q₈	—	7	2	no	—
60	Q₈	—	14	1	no	—
61	C₂×C₄	—	14	1	no	—
62	C₂×C₄	—	70	1	no	—
63	C₂×C₄	D₅×D₇	1	1	yes	characteristic
64	C₈	—	10	1	no	—
65	C₇	#3967	1	1	yes	characteristic, complemented, Sylow
66	C₅	#6390	1	1	yes	characteristic, complemented, Sylow
67	C₂²	#63306	1	1	yes	characteristic
68	C₄	—	14	2	no	—
69	C₄	—	140	1	no	—
70	C₄	D₇×Dic₅	1	1	yes	characteristic
71	C₄	#63305	1	1	yes	characteristic
72	C₂	#10587847	1	1	yes	characteristic
73	C₂	#10587851	1	1	yes	characteristic
74	C₂	(C₂×D₇)⋊Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#63306
commutator	C₄×C₅×C₇	C₂×C₄
Frattini, hypercenter	C₂×C₄	D₅×D₇
Fitting, cosocle	C₂×C₄×C₅×C₇	C₂²
socle, prime radical	C₂²×C₅×C₇	D₄
hypocenter	C₅×C₇	#103
LCS	G ▷ C₄×C₅×C₇ ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
8. C₅×Dic₁₄	C₄	semidirect
30. Dic₁₄	Dic₅	semidirect
38. C₅×C₇	#103	semidirect
65. C₇	#3967	semidirect
66. C₅	#6390	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×Dic₁₄	2
C₄⋊Dic₃₅	2
C₂×C₇×#168	2
#6390	5
#3967	7