Subgroups — C₃₁×C₇⋊Dic₃₅ #44477136

Order 30380.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇²×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇²×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₃₁×C₇⋊Dic₇	—	5	1	no	maximal, Hall
4	C₃₁×Dic₃₅	—	7	8	no	maximal
5	C₂×C₇²×C₃₁	D₅	1	1	yes	characteristic
6	C₂×C₅×C₇×C₃₁	D₇	1	8	yes	—
7	C₇²×C₃₁	Dic₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₇×C₃₁	Dic₇	1	8	yes	complemented
9	C₇⋊Dic₃₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	Dic₇×C₃₁	—	35	8	no	—
11	Dic₅×C₃₁	—	49	1	no	Hall
12	C₂×C₅×C₇²	C₂×C₃₁	1	1	yes	characteristic
13	C₂×C₇×C₃₁	D₃₅	1	8	yes	—
14	C₂×C₅×C₃₁	C₇⋊D₇	1	1	yes	characteristic
15	C₅×C₇²	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
16	C₇×C₃₁	Dic₃₅	1	8	yes	complemented
17	C₇⋊Dic₇	—	5	1	no	Hall
18	C₅×C₃₁	C₇⋊Dic₇	1	1	yes	characteristic, complemented, Hall
19	Dic₃₅	—	7	8	no	—
20	C₄×C₃₁	—	245	1	no	Hall
21	C₂×C₇²	D₅×C₃₁	1	1	yes	characteristic
22	C₂×C₅×C₇	D₇×C₃₁	1	8	yes	—
23	C₂×C₃₁	C₅⋊(C₇⋊D₇)	1	1	yes	characteristic
24	C₇²	Dic₅×C₃₁	1	1	yes	characteristic, complemented, Sylow
25	C₅×C₇	Dic₇×C₃₁	1	8	yes	complemented
26	C₃₁	C₇⋊Dic₃₅	1	1	yes	characteristic, direct product factor, Sylow
27	Dic₇	—	35	8	no	—
28	Dic₅	—	49	1	no	Hall
29	C₂×C₇	C₃₁×D₃₅	1	8	yes	—
30	C₂×C₅	C₃₁×C₇⋊D₇	1	1	yes	characteristic
31	C₇	C₃₁×Dic₃₅	1	8	yes	complemented
32	C₅	C₃₁×C₇⋊Dic₇	1	1	yes	characteristic, complemented, Sylow
33	C₄	—	245	1	no	Sylow
34	C₂	C₃₁×C₅⋊(C₇⋊D₇)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃₁	C₅⋊(C₇⋊D₇)
commutator, hypocenter	C₅×C₇²	C₄×C₃₁
Frattini	C₂	C₃₁×C₅⋊(C₇⋊D₇)
Fitting, socle, prime radical	C₂×C₅×C₇²×C₃₁	C₂
cosocle	C₂×C₅×C₇²	C₂×C₃₁
LCS	G ▷ C₅×C₇²
UCS	C₁ ◁ C₂×C₃₁

Complements

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

N	H ≅ G/N	type
2. C₅×C₇²×C₃₁	C₄	semidirect
7. C₇²×C₃₁	Dic₅	semidirect
8. C₅×C₇×C₃₁	Dic₇	semidirect
9. C₇⋊Dic₃₅	C₃₁	direct (N × H)
15. C₅×C₇²	C₄×C₃₁	semidirect
16. C₇×C₃₁	Dic₃₅	semidirect
18. C₅×C₃₁	C₇⋊Dic₇	semidirect
24. C₇²	Dic₅×C₃₁	semidirect
25. C₅×C₇	Dic₇×C₃₁	semidirect
26. C₃₁	C₇⋊Dic₃₅	direct (N × H)
31. C₇	C₃₁×Dic₃₅	semidirect
32. C₅	C₃₁×C₇⋊Dic₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₇²×C₃₁	2
C₃₁×C₇⋊Dic₇	5
C₃₁×Dic₃₅	7
C₇⋊Dic₃₅	31

Subgroups — C31×C7⋊Dic35 #44477136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×C₇⋊Dic₃₅ #44477136