Subgroups — #11764690

Order 1120.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic
2	#10587935	C₂	1	2	yes	maximal, complemented
3	C₂³×C₅×C₇	C₄	1	1	yes	characteristic
4	C₂²×C₇×D₅	C₄	1	1	yes	characteristic
5	C₇×C₂²⋊D₅	—	2	2	no	—
6	C₂×C₇×Dic₅	C₂²	1	1	yes	characteristic
7	C₇⋊#170	—	2	2	no	—
8	#6407	—	5	1	no	maximal, Hall
9	#4013	—	7	1	no	maximal, Hall
10	C₂²×C₅×C₇	—	2	1	no	—
11	C₂²×C₅×C₇	—	4	1	no	—
12	C₂²×C₅×C₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₇×D₅	—	2	1	no	—
14	C₂×C₇×D₅	—	4	1	no	—
15	C₇×Dic₅	D₄	1	2	yes	—
16	C₂×C₇×D₄	—	5	1	no	—
17	#1136	—	5	2	no	—
18	C₂×C₂²⋊D₅	D₇	1	1	yes	characteristic
19	#704	—	7	2	no	—
20	C₂×C₅×C₇	—	2	1	no	—
21	C₂×C₅×C₇	—	4	1	no	—
22	C₂×C₅×C₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₇×D₅	—	4	1	no	—
24	C₂³×C₇	—	5	1	no	—
25	C₂³×C₇	AGL(1,𝔽₅)	1	1	yes	characteristic
26	C₇×D₄	—	10	2	no	—
27	C₂×C₄×C₇	—	5	1	no	—
28	C₇⋊C₈	—	10	2	no	—
29	C₂³×C₅	Dic₇	1	1	yes	characteristic
30	C₂²×D₅	Dic₇	1	1	yes	characteristic
31	C₂²⋊D₅	—	2	2	no	—
32	C₂×Dic₅	C₂×D₇	1	1	yes	characteristic
33	#170	—	14	2	no	—
34	C₅×C₇	#100	1	1	yes	characteristic, complemented, Hall
35	#100	—	35	1	no	Sylow
36	C₂²×C₇	—	2	1	no	—
37	C₂²×C₇	—	4	1	no	—
38	C₂²×C₇	—	10	1	no	—
39	C₂²×C₇	—	20	1	no	—
40	C₂²×C₇	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
41	C₄×C₇	—	5	2	no	—
42	C₂²×C₅	—	2	1	no	—
43	C₂²×C₅	—	4	1	no	—
44	C₂²×C₅	C₂×Dic₇	1	1	yes	characteristic
45	C₂×D₅	—	2	1	no	—
46	C₂×D₅	—	4	1	no	—
47	Dic₅	C₂²⋊D₇	1	2	yes	—
48	C₂×D₄	—	5	1	no	—
49	M₁₆	—	35	2	no	—
50	C₂×C₇	—	2	1	no	—
51	C₂×C₇	—	4	1	no	—
52	C₂×C₇	—	20	1	no	—
53	C₂×C₇	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
54	C₂×C₅	—	2	1	no	—
55	C₂×C₅	—	4	1	no	—
56	C₂×C₅	C₂²⋊Dic₇	1	1	yes	characteristic
57	D₅	—	4	1	no	—
58	C₂³	—	5	1	no	—
59	C₂³	C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic
60	D₄	—	10	2	no	—
61	C₂×C₄	—	5	1	no	—
62	C₈	—	70	2	no	—
63	C₇	#4013	1	1	yes	characteristic, complemented, Sylow
64	C₅	#6407	1	1	yes	characteristic, complemented, Sylow
65	C₂²	—	2	1	no	—
66	C₂²	—	4	1	no	—
67	C₂²	—	10	1	no	—
68	C₂²	—	20	1	no	—
69	C₂²	C₂×C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic
70	C₄	—	5	2	no	—
71	C₂	—	2	1	no	—
72	C₂	—	4	1	no	—
73	C₂	—	20	1	no	—
74	C₂	C₂²⋊(C₇⋊AGL(1,𝔽₅))	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊(C₇⋊AGL(1,𝔽₅))
commutator	C₂²×C₅×C₇	C₂×C₄
Frattini	C₂²	C₂×C₇⋊AGL(1,𝔽₅)
Fitting	C₂³×C₅×C₇	C₄
socle	C₂×C₅×C₇	C₂²⋊C₄
prime radical	C₂×C₇×C₂²⋊D₅	C₂
cosocle	C₂×C₇×Dic₅	C₂²
hypercenter	C₂³	C₇⋊AGL(1,𝔽₅)
hypocenter	C₅×C₇	#100
LCS	G ▷ C₂²×C₅×C₇ ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂³

Complements

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

N	H ≅ G/N	type
2. #10587935	C₂	semidirect
34. C₅×C₇	#100	semidirect
63. C₇	#4013	semidirect
64. C₅	#6407	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×C₂²⋊D₅	2
#10587935	2
#6407	5
#4013	7