Subgroups — D₃₁×D₂₉⋊C₇ #38737751

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	1	yes	maximal, characteristic, complemented
2	C₃₁×D₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₁×C₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×C₂₉⋊C₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₂₉×D₃₁	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	D₈₉₉	C₂×C₇	1	1	yes	characteristic, complemented
7	C₂₉×D₃₁	C₂×C₇	1	1	yes	characteristic, complemented
8	C₃₁×D₂₉	C₂×C₇	1	1	yes	characteristic, complemented
9	C₂₉×C₃₁	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇×D₃₁	—	29	1	no	maximal, Hall
11	C₂×D₂₉⋊C₇	—	31	1	no	maximal, Hall
12	C₂×C₇×C₃₁	—	29	1	no	—
13	C₇×D₃₁	—	29	1	no	—
14	C₇×D₃₁	—	29	1	no	—
15	C₂×C₂₉⋊C₇	—	31	1	no	—
16	D₂₉⋊C₇	—	31	1	no	—
17	D₂₉⋊C₇	D₃₁	1	1	yes	characteristic, direct product factor
18	C₇×C₃₁	—	29	1	no	Hall
19	C₂₉⋊C₇	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
20	C₂×D₃₁	—	203	1	no	Hall
21	C₂×D₂₉	—	31	1	no	Hall
22	C₂×C₃₁	—	203	1	no	—
23	D₃₁	—	203	1	no	—
24	D₃₁	D₂₉⋊C₇	1	1	yes	characteristic, direct product factor
25	C₂×C₂₉	—	31	1	no	—
26	D₂₉	—	31	1	no	—
27	D₂₉	C₇×D₃₁	1	1	yes	characteristic, complemented
28	C₃₁	C₂×D₂₉⋊C₇	1	1	yes	characteristic, complemented, Sylow
29	C₂₉	C₂×C₇×D₃₁	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₇	—	899	1	no	Hall
31	C₂×C₇	—	29	1	no	—
32	C₂×C₇	—	899	1	no	—
33	C₂×C₇	—	899	1	no	—
34	C₇	—	29	1	no	Sylow
35	C₂²	—	6293	1	no	Sylow
36	C₂	—	31	1	no	—
37	C₂	—	6293	1	no	—
38	C₂	—	203	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃₁⋊(D₂₉⋊C₇)	C₂	semidirect
2. C₃₁×D₂₉⋊C₇	C₂	semidirect
3. D₃₁×C₂₉⋊C₇	C₂	semidirect
4. C₃₁×C₂₉⋊C₇	C₂²	semidirect
5. D₂₉×D₃₁	C₇	semidirect
6. D₈₉₉	C₂×C₇	semidirect
7. C₂₉×D₃₁	C₂×C₇	semidirect
8. C₃₁×D₂₉	C₂×C₇	semidirect
9. C₂₉×C₃₁	C₂²×C₇	semidirect
17. D₂₉⋊C₇	D₃₁	direct (N × H)
19. C₂₉⋊C₇	C₂×D₃₁	semidirect
24. D₃₁	D₂₉⋊C₇	direct (N × H)
27. D₂₉	C₇×D₃₁	semidirect
28. C₃₁	C₂×D₂₉⋊C₇	semidirect
29. C₂₉	C₂×C₇×D₃₁	semidirect

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
C₃₁×D₂₉⋊C₇	2
D₃₁×C₂₉⋊C₇	2
D₂₉×D₃₁	7
C₂×C₇×D₃₁	29
C₂×D₂₉⋊C₇	31

Subgroups — D31×D29⋊C7 #38737751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₁×D₂₉⋊C₇ #38737751