Subgroups — C₂×C₃₁×D₂₉⋊C₇ #38737752

Order 25172.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×D₂₉⋊C₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃₁×C₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×C₂₉⋊C₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃₁×D₂₉	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₂₉×C₃₁	C₂×C₇	1	1	yes	characteristic, complemented
6	C₃₁×D₂₉	C₂×C₇	1	2	yes	complemented
7	C₂₉×C₃₁	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₇×C₃₁	—	29	1	no	maximal, Hall
9	C₂×D₂₉⋊C₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₇×C₃₁	—	29	2	no	—
11	C₂×C₇×C₃₁	—	29	1	no	—
12	C₂×C₂₉⋊C₇	C₂×C₃₁	1	1	yes	characteristic, complemented
13	D₂₉⋊C₇	C₂×C₃₁	1	2	yes	direct product factor
14	C₇×C₃₁	—	29	1	no	Hall
15	C₂₉⋊C₇	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₃₁	—	29	1	no	Hall
17	C₂×D₂₉	C₇×C₃₁	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃₁	—	29	2	no	—
19	C₂×C₃₁	D₂₉⋊C₇	1	1	yes	characteristic, direct product factor
20	C₂×C₂₉	C₂×C₇×C₃₁	1	1	yes	characteristic, complemented
21	D₂₉	C₂×C₇×C₃₁	1	2	yes	complemented
22	C₃₁	C₂×D₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
23	C₂₉	C₂²×C₇×C₃₁	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₇	—	29	1	no	Hall
25	C₂×C₇	—	29	2	no	—
26	C₂×C₇	—	29	1	no	—
27	C₇	—	29	1	no	Sylow
28	C₂²	—	29	1	no	Sylow
29	C₂	—	29	2	no	—
30	C₂	C₃₁×D₂₉⋊C₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃₁	D₂₉⋊C₇
commutator, cosocle, hypocenter	C₂₉	C₂²×C₇×C₃₁
Frattini	C₁	G
Fitting, socle	C₂×C₂₉×C₃₁	C₂×C₇
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃₁×D₂₉⋊C₇	C₂	direct (N × H)
2. C₂×C₃₁×C₂₉⋊C₇	C₂	semidirect
3. C₃₁×C₂₉⋊C₇	C₂²	semidirect
4. C₂×C₃₁×D₂₉	C₇	semidirect
5. C₂×C₂₉×C₃₁	C₂×C₇	semidirect
6. C₃₁×D₂₉	C₂×C₇	semidirect
7. C₂₉×C₃₁	C₂²×C₇	semidirect
9. C₂×D₂₉⋊C₇	C₃₁	direct (N × H)
12. C₂×C₂₉⋊C₇	C₂×C₃₁	semidirect
13. D₂₉⋊C₇	C₂×C₃₁	direct (N × H)
15. C₂₉⋊C₇	C₂²×C₃₁	semidirect
17. C₂×D₂₉	C₇×C₃₁	semidirect
19. C₂×C₃₁	D₂₉⋊C₇	direct (N × H)
20. C₂×C₂₉	C₂×C₇×C₃₁	semidirect
21. D₂₉	C₂×C₇×C₃₁	semidirect
22. C₃₁	C₂×D₂₉⋊C₇	direct (N × H)
23. C₂₉	C₂²×C₇×C₃₁	semidirect
30. C₂	C₃₁×D₂₉⋊C₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×D₂₉⋊C₇	2
C₂×C₃₁×C₂₉⋊C₇	2
C₂×C₃₁×D₂₉	7
C₂²×C₇×C₃₁	29
C₂×D₂₉⋊C₇	31

Subgroups — C2×C31×D29⋊C7 #38737752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×D₂₉⋊C₇ #38737752