Subgroups — #11765200

Order 1120.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₅×C₇	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₃₅	C₂	1	2	yes	maximal
3	#10587900	C₂	1	4	yes	maximal
4	C₂×C₄×C₅×C₇	C₂²	1	2	yes	—
5	C₂×C₄×C₅×C₇	C₂²	1	1	yes	characteristic
6	C₂×Dic₃₅	C₂²	1	4	yes	—
7	#6433	—	5	1	no	maximal, Hall
8	#4016	—	7	1	no	maximal, Hall
9	C₂²×C₅×C₇	C₂³	1	1	yes	characteristic
10	C₄×C₅×C₇	—	2	2	no	—
11	C₄×C₅×C₇	Q₈	1	2	yes	—
12	Dic₃₅	—	2	4	no	—
13	C₄²×C₇	D₅	1	1	yes	characteristic
14	C₄⋊Dic₇	—	5	2	no	—
15	Dic₇⋊C₄	—	5	4	no	—
16	C₄²×C₅	D₇	1	1	yes	characteristic
17	C₄⋊Dic₅	—	7	2	no	—
18	#683	—	7	4	no	—
19	C₂×C₅×C₇	C₂×Q₈	1	1	yes	characteristic
20	C₂×C₅×C₇	#41	1	2	yes	—
21	C₂×C₄×C₇	C₂×D₅	1	2	yes	—
22	C₂×C₄×C₇	C₂×D₅	1	1	yes	characteristic
23	C₂×Dic₇	—	5	4	no	—
24	C₂×C₄×C₅	C₂×D₇	1	2	yes	—
25	C₂×C₄×C₅	C₂×D₇	1	1	yes	characteristic
26	C₂×Dic₅	—	7	4	no	—
27	C₅×C₇	#125	1	1	yes	characteristic, complemented, Hall
28	#125	—	35	1	no	Sylow
29	C₂²×C₇	C₂²×D₅	1	1	yes	characteristic
30	C₄×C₇	—	2	2	no	—
31	C₄×C₇	Dic₁₀	1	2	yes	—
32	Dic₇	—	10	4	no	—
33	C₂²×C₅	C₂²×D₇	1	1	yes	characteristic
34	C₄×C₅	—	2	2	no	—
35	C₄×C₅	Dic₁₄	1	2	yes	—
36	Dic₅	—	14	4	no	—
37	C₄⋊C₄	—	35	4	no	—
38	C₄⋊C₄	—	35	2	no	—
39	C₄²	D₃₅	1	1	yes	characteristic
40	C₂×C₇	C₂×Dic₁₀	1	1	yes	characteristic
41	C₂×C₇	#709	1	2	yes	—
42	C₂×C₅	C₂×Dic₁₄	1	1	yes	characteristic
43	C₂×C₅	#1157	1	2	yes	—
44	C₂×C₄	—	35	4	no	—
45	C₂×C₄	C₂×D₃₅	1	2	yes	—
46	C₂×C₄	C₂×D₃₅	1	1	yes	characteristic
47	C₇	#4016	1	1	yes	characteristic, complemented, Sylow
48	C₅	#6433	1	1	yes	characteristic, complemented, Sylow
49	C₂²	C₂²×D₃₅	1	1	yes	characteristic
50	C₄	—	2	2	no	—
51	C₄	—	70	4	no	—
52	C₄	Dic₇₀	1	2	yes	—
53	C₂	C₂×Dic₇₀	1	1	yes	characteristic
54	C₂	#10587987	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃₅
commutator, socle, prime radical, cosocle	C₂²×C₅×C₇	C₂³
Fitting	C₄²×C₅×C₇	C₂
hypercenter	C₄²	D₃₅
hypocenter	C₅×C₇	#125
LCS	G ▷ C₂²×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂² ◁ C₄²

Complements

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

N	H ≅ G/N	type
27. C₅×C₇	#125	semidirect
47. C₇	#4016	semidirect
48. C₅	#6433	semidirect

Maximal subgroups

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

subgroup	index
C₄²×C₅×C₇	2
C₄⋊Dic₃₅	2
#10587900	2
#6433	5
#4016	7