Subgroups — C₇²×Dic₃₁⋊C₅ #44477129

Order 30380.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇²×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic
2	C₇²×ΓL(1,𝔽₃₂)	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇²×Dic₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇×Dic₃₁⋊C₅	C₇	1	8	yes	maximal, direct product factor
5	C₂×C₇²×C₃₁	C₂×C₅	1	1	yes	characteristic
6	C₂×C₇×ΓL(1,𝔽₃₂)	C₂×C₇	1	8	yes	—
7	C₇²×C₃₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
8	C₇×ΓL(1,𝔽₃₂)	C₄×C₇	1	8	yes	complemented
9	C₄×C₅×C₇²	—	31	1	no	maximal, Hall
10	C₇×Dic₃₁	C₅×C₇	1	8	yes	complemented
11	Dic₃₁⋊C₅	C₇²	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₅×C₇²	—	31	1	no	—
13	C₂×C₇×C₃₁	C₂×C₅×C₇	1	8	yes	—
14	C₂×ΓL(1,𝔽₃₂)	C₂×C₇²	1	1	yes	characteristic
15	C₅×C₇²	—	31	1	no	Hall
16	C₇×C₃₁	C₄×C₅×C₇	1	8	yes	complemented
17	C₄×C₇²	—	31	1	no	Hall
18	ΓL(1,𝔽₃₂)	C₄×C₇²	1	1	yes	characteristic, complemented, Hall
19	C₄×C₅×C₇	—	31	8	no	—
20	Dic₃₁	C₅×C₇²	1	1	yes	characteristic, complemented, Hall
21	C₂×C₇²	D₃₁⋊C₅	1	1	yes	characteristic
22	C₂×C₅×C₇	—	31	8	no	—
23	C₂×C₃₁	C₂×C₅×C₇²	1	1	yes	characteristic
24	C₇²	Dic₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
25	C₅×C₇	—	31	8	no	—
26	C₃₁	C₄×C₅×C₇²	1	1	yes	characteristic, complemented, Sylow
27	C₄×C₇	—	31	8	no	—
28	C₄×C₅	—	31	1	no	Hall
29	C₂×C₇	C₇×D₃₁⋊C₅	1	8	yes	—
30	C₂×C₅	—	31	1	no	—
31	C₇	C₇×Dic₃₁⋊C₅	1	8	yes	direct product factor
32	C₅	—	31	1	no	Sylow
33	C₄	—	31	1	no	Sylow
34	C₂	C₇²×D₃₁⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇²	D₃₁⋊C₅
commutator, hypocenter	C₃₁	C₄×C₅×C₇²
Frattini	C₂	C₇²×D₃₁⋊C₅
Fitting, socle	C₂×C₇²×C₃₁	C₂×C₅
prime radical	C₂×C₇²×ΓL(1,𝔽₃₂)	C₂
cosocle	C₂×C₃₁	C₂×C₅×C₇²
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₇²

Complements

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

N	H ≅ G/N	type
2. C₇²×ΓL(1,𝔽₃₂)	C₄	semidirect
3. C₇²×Dic₃₁	C₅	semidirect
4. C₇×Dic₃₁⋊C₅	C₇	direct (N × H)
7. C₇²×C₃₁	C₄×C₅	semidirect
8. C₇×ΓL(1,𝔽₃₂)	C₄×C₇	semidirect
10. C₇×Dic₃₁	C₅×C₇	semidirect
11. Dic₃₁⋊C₅	C₇²	direct (N × H)
16. C₇×C₃₁	C₄×C₅×C₇	semidirect
18. ΓL(1,𝔽₃₂)	C₄×C₇²	semidirect
20. Dic₃₁	C₅×C₇²	semidirect
24. C₇²	Dic₃₁⋊C₅	direct (N × H)
26. C₃₁	C₄×C₅×C₇²	semidirect
31. C₇	C₇×Dic₃₁⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇²×ΓL(1,𝔽₃₂)	2
C₇²×Dic₃₁	5
C₇×Dic₃₁⋊C₅	7
C₄×C₅×C₇²	31

Subgroups — C72×Dic31⋊C5 #44477129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇²×Dic₃₁⋊C₅ #44477129