Subgroups — C₂×C₇²×D₃₁⋊C₅ #44477154

Order 30380.

200 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, complemented
2	C₇²×D₃₁⋊C₅	C₂	1	2	yes	maximal, direct product factor
3	C₇²×ΓL(1,𝔽₃₂)	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇²×D₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₇×D₃₁⋊C₅	C₇	1	8	yes	maximal, direct product factor
6	C₇²×D₃₁	C₂×C₅	1	2	yes	complemented
7	C₂×C₇²×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
8	C₇×D₃₁⋊C₅	C₂×C₇	1	16	yes	direct product factor
9	C₂×C₇×ΓL(1,𝔽₃₂)	C₂×C₇	1	8	yes	complemented
10	C₇²×C₃₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
11	C₇×ΓL(1,𝔽₃₂)	C₂²×C₇	1	8	yes	complemented
12	C₂²×C₅×C₇²	—	31	1	no	maximal, Hall
13	C₂×C₇×D₃₁	C₅×C₇	1	8	yes	complemented
14	C₂×D₃₁⋊C₅	C₇²	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₅×C₇²	—	31	2	no	—
16	C₂×C₅×C₇²	—	31	1	no	—
17	C₂×C₇×C₃₁	C₂×C₅×C₇	1	8	yes	complemented
18	C₇×D₃₁	C₂×C₅×C₇	1	16	yes	complemented
19	C₂×ΓL(1,𝔽₃₂)	C₂×C₇²	1	1	yes	characteristic, complemented
20	D₃₁⋊C₅	C₂×C₇²	1	2	yes	direct product factor
21	C₅×C₇²	—	31	1	no	Hall
22	C₇×C₃₁	C₂²×C₅×C₇	1	8	yes	complemented
23	C₂²×C₇²	—	31	1	no	Hall
24	ΓL(1,𝔽₃₂)	C₂²×C₇²	1	1	yes	characteristic, complemented, Hall
25	C₂²×C₅×C₇	—	31	8	no	—
26	C₂×D₃₁	C₅×C₇²	1	1	yes	characteristic, complemented, Hall
27	C₂×C₇²	—	31	2	no	—
28	C₂×C₇²	D₃₁⋊C₅	1	1	yes	characteristic, direct product factor
29	C₂×C₅×C₇	—	31	16	no	—
30	C₂×C₅×C₇	—	31	8	no	—
31	C₂×C₃₁	C₂×C₅×C₇²	1	1	yes	characteristic, complemented
32	D₃₁	C₂×C₅×C₇²	1	2	yes	complemented
33	C₇²	C₂×D₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
34	C₅×C₇	—	31	8	no	—
35	C₃₁	C₂²×C₅×C₇²	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₇	—	31	8	no	—
37	C₂²×C₅	—	31	1	no	Hall
38	C₂×C₇	—	31	16	no	—
39	C₂×C₇	C₇×D₃₁⋊C₅	1	8	yes	direct product factor
40	C₂×C₅	—	31	2	no	—
41	C₂×C₅	—	31	1	no	—
42	C₇	C₂×C₇×D₃₁⋊C₅	1	8	yes	direct product factor
43	C₅	—	31	1	no	Sylow
44	C₂²	—	31	1	no	Sylow
45	C₂	—	31	2	no	—
46	C₂	C₇²×D₃₁⋊C₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇²	D₃₁⋊C₅
commutator, cosocle, hypocenter	C₃₁	C₂²×C₅×C₇²
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₃₁	C₂×C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₇²

Complements

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

N	H ≅ G/N	type
1. C₂×C₇²×ΓL(1,𝔽₃₂)	C₂	semidirect
2. C₇²×D₃₁⋊C₅	C₂	direct (N × H)
3. C₇²×ΓL(1,𝔽₃₂)	C₂²	semidirect
4. C₂×C₇²×D₃₁	C₅	semidirect
5. C₂×C₇×D₃₁⋊C₅	C₇	direct (N × H)
6. C₇²×D₃₁	C₂×C₅	semidirect
7. C₂×C₇²×C₃₁	C₂×C₅	semidirect
8. C₇×D₃₁⋊C₅	C₂×C₇	direct (N × H)
9. C₂×C₇×ΓL(1,𝔽₃₂)	C₂×C₇	semidirect
10. C₇²×C₃₁	C₂²×C₅	semidirect
11. C₇×ΓL(1,𝔽₃₂)	C₂²×C₇	semidirect
13. C₂×C₇×D₃₁	C₅×C₇	semidirect
14. C₂×D₃₁⋊C₅	C₇²	direct (N × H)
17. C₂×C₇×C₃₁	C₂×C₅×C₇	semidirect
18. C₇×D₃₁	C₂×C₅×C₇	semidirect
19. C₂×ΓL(1,𝔽₃₂)	C₂×C₇²	semidirect
20. D₃₁⋊C₅	C₂×C₇²	direct (N × H)
22. C₇×C₃₁	C₂²×C₅×C₇	semidirect
24. ΓL(1,𝔽₃₂)	C₂²×C₇²	semidirect
26. C₂×D₃₁	C₅×C₇²	semidirect
28. C₂×C₇²	D₃₁⋊C₅	direct (N × H)
31. C₂×C₃₁	C₂×C₅×C₇²	semidirect
32. D₃₁	C₂×C₅×C₇²	semidirect
33. C₇²	C₂×D₃₁⋊C₅	direct (N × H)
35. C₃₁	C₂²×C₅×C₇²	semidirect
39. C₂×C₇	C₇×D₃₁⋊C₅	direct (N × H)
42. C₇	C₂×C₇×D₃₁⋊C₅	direct (N × H)
46. C₂	C₇²×D₃₁⋊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×D₃₁⋊C₅	2
C₂×C₇²×D₃₁	5
C₂×C₇×D₃₁⋊C₅	7
C₂²×C₅×C₇²	31

Subgroups — C2×C72×D31⋊C5 #44477154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇²×D₃₁⋊C₅ #44477154