Subgroups — C₅×#6433 #11765028

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	C₅×C₄⋊Dic₇	C₂	1	2	yes	maximal
3	C₅×Dic₇⋊C₄	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×C₅×Dic₇	C₂²	1	4	yes	—
7	#6433	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×#125	—	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	C₅×Dic₇	—	2	4	no	—
13	C₄²×C₇	C₂×C₅	1	1	yes	characteristic
14	C₄⋊Dic₇	C₂×C₅	1	2	yes	—
15	Dic₇⋊C₄	C₂×C₅	1	4	yes	—
16	C₅×C₄⋊C₄	—	7	4	no	—
17	C₅×C₄⋊C₄	—	7	2	no	—
18	C₄²×C₅	D₇	1	1	yes	characteristic
19	C₂×C₅×C₇	C₂×Q₈	1	1	yes	characteristic
20	C₂×C₅×C₇	#41	1	2	yes	—
21	C₂×C₄×C₇	C₂²×C₅	1	2	yes	—
22	C₂×C₄×C₇	C₂²×C₅	1	1	yes	characteristic
23	C₂×Dic₇	C₂²×C₅	1	4	yes	—
24	C₂×C₄×C₅	—	7	4	no	—
25	C₂×C₄×C₅	C₂×D₇	1	2	yes	—
26	C₂×C₄×C₅	C₂×D₇	1	1	yes	characteristic
27	C₅×C₇	#125	1	1	yes	characteristic, complemented, Hall
28	#125	—	7	1	no	Sylow
29	C₂²×C₇	C₂³×C₅	1	1	yes	characteristic
30	C₄×C₇	—	2	2	no	—
31	C₄×C₇	C₅×Q₈	1	2	yes	—
32	Dic₇	—	2	4	no	—
33	C₂²×C₅	C₂²×D₇	1	1	yes	characteristic
34	C₄×C₅	—	2	2	no	—
35	C₄×C₅	—	14	4	no	—
36	C₄×C₅	Dic₁₄	1	2	yes	—
37	C₄⋊C₄	—	7	4	no	—
38	C₄⋊C₄	—	7	2	no	—
39	C₄²	C₅×D₇	1	1	yes	characteristic
40	C₂×C₇	C₂×C₅×Q₈	1	1	yes	characteristic
41	C₂×C₇	C₅×#41	1	2	yes	—
42	C₂×C₅	C₂×Dic₁₄	1	1	yes	characteristic
43	C₂×C₅	#1157	1	2	yes	—
44	C₂×C₄	—	7	4	no	—
45	C₂×C₄	C₂×C₅×D₇	1	2	yes	—
46	C₂×C₄	C₂×C₅×D₇	1	1	yes	characteristic
47	C₇	C₅×#125	1	1	yes	characteristic, complemented, Sylow
48	C₅	#6433	1	1	yes	characteristic, direct product factor, Sylow
49	C₂²	C₂²×C₅×D₇	1	1	yes	characteristic
50	C₄	—	2	2	no	—
51	C₄	—	14	4	no	—
52	C₄	C₅×Dic₁₄	1	2	yes	—
53	C₂	C₂×C₅×Dic₁₄	1	1	yes	characteristic
54	C₂	C₅×#1157	1	2	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, prime radical	C₂²×C₅×C₇	C₂³
hypercenter	C₄²×C₅	D₇
hypocenter	C₇	C₅×#125
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
7. #6433	C₅	direct (N × H)
27. C₅×C₇	#125	semidirect
47. C₇	C₅×#125	semidirect
48. C₅	#6433	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×C₄⋊Dic₇	2
C₅×Dic₇⋊C₄	2
#6433	5
C₅×#125	7

Subgroups — C5×#6433 #11765028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#6433 #11765028