Subgroups — C₅×#6439 #11765034

Order 1120.

120 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, complemented
2	C₅×(C₂×D₇)⋊C₄	C₂	1	3	yes	maximal
3	C₅×Dic₇⋊C₄	C₂	1	3	yes	maximal, complemented
4	C₂²×C₅×D₇	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₅×C₇	C₂²	1	3	yes	—
6	C₂×C₅×Dic₇	C₂²	1	3	yes	—
7	#6439	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×#126	—	7	1	no	maximal, Hall
9	C₂²×C₅×C₇	C₂³	1	1	yes	characteristic
10	C₂×C₅×D₇	—	2	3	no	—
11	C₄×C₅×C₇	—	2	3	no	—
12	C₅×Dic₇	—	2	3	no	—
13	C₄²×C₇	C₂×C₅	1	1	yes	characteristic, complemented
14	(C₂×D₇)⋊C₄	C₂×C₅	1	3	yes	—
15	Dic₇⋊C₄	C₂×C₅	1	3	yes	complemented
16	C₅×C₄⋊C₄	—	7	3	no	—
17	C₅×C₂²⋊C₄	—	7	3	no	—
18	C₄²×C₅	D₇	1	1	yes	characteristic, complemented
19	C₂×C₅×C₇	#41	1	3	yes	—
20	C₅×D₇	—	4	1	no	—
21	C₂²×D₇	C₂²×C₅	1	1	yes	characteristic
22	C₂×C₄×C₇	C₂²×C₅	1	3	yes	—
23	C₂×Dic₇	C₂²×C₅	1	3	yes	—
24	C₂³×C₅	—	7	1	no	—
25	C₂×C₄×C₅	—	7	3	no	—
26	C₂×C₄×C₅	C₂×D₇	1	3	yes	—
27	C₅×C₇	#126	1	1	yes	characteristic, complemented, Hall
28	#126	—	7	1	no	Sylow
29	C₂²×C₇	C₂³×C₅	1	1	yes	characteristic
30	C₂×D₇	—	2	3	no	—
31	C₄×C₇	—	2	3	no	—
32	Dic₇	—	2	3	no	—
33	C₂²×C₅	—	14	3	no	—
34	C₂²×C₅	C₂²×D₇	1	1	yes	characteristic
35	C₄×C₅	—	2	3	no	—
36	C₄×C₅	—	14	3	no	—
37	C₄⋊C₄	—	7	3	no	—
38	C₂²⋊C₄	—	7	3	no	—
39	C₄²	C₅×D₇	1	1	yes	characteristic, complemented
40	C₂×C₇	C₅×#41	1	3	yes	—
41	D₇	—	4	1	no	—
42	C₂×C₅	—	28	1	no	—
43	C₂×C₅	#1157	1	3	yes	—
44	C₂³	—	7	1	no	—
45	C₂×C₄	—	7	3	no	—
46	C₂×C₄	C₂×C₅×D₇	1	3	yes	—
47	C₇	C₅×#126	1	1	yes	characteristic, complemented, Sylow
48	C₅	#6439	1	1	yes	characteristic, direct product factor, Sylow
49	C₂²	—	14	3	no	—
50	C₂²	C₂²×C₅×D₇	1	1	yes	characteristic
51	C₄	—	2	3	no	—
52	C₄	—	14	3	no	—
53	C₂	—	28	1	no	—
54	C₂	C₅×#1157	1	3	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂²×D₇
commutator, cosocle	C₂²×C₇	C₂³×C₅
Frattini	C₂²	C₂²×C₅×D₇
Fitting	C₄²×C₅×C₇	C₂
socle	C₂²×C₅×C₇	C₂³
prime radical	C₂²×C₅×D₇	C₂²
hypercenter	C₄²×C₅	D₇
hypocenter	C₇	C₅×#126
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅

Complements

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

N	H ≅ G/N	type
1. C₄²×C₅×C₇	C₂	semidirect
3. C₅×Dic₇⋊C₄	C₂	semidirect
7. #6439	C₅	direct (N × H)
13. C₄²×C₇	C₂×C₅	semidirect
15. Dic₇⋊C₄	C₂×C₅	semidirect
18. C₄²×C₅	D₇	semidirect
27. C₅×C₇	#126	semidirect
39. C₄²	C₅×D₇	semidirect
47. C₇	C₅×#126	semidirect
48. C₅	#6439	direct (N × H)

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
C₅×(C₂×D₇)⋊C₄	2
C₅×Dic₇⋊C₄	2
#6439	5
C₅×#126	7

Subgroups — C5×#6439 #11765034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#6439 #11765034