Subgroups — C₃₁⋊C₃×D₂₉⋊C₇ #49180010

Order 37758.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁⋊C₃×C₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₁×D₂₉⋊C₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃₁×C₂₉⋊C₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	D₂₉×C₃₁⋊C₃	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂₉×C₃₁⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₃₁×D₂₉	C₃×C₇	1	1	yes	characteristic, complemented, Hall
7	C₂×C₇×C₃₁⋊C₃	—	29	1	no	maximal, Hall
8	C₃×D₂₉⋊C₇	—	31	1	no	maximal, Hall
9	C₂₉×C₃₁	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
10	C₇×C₃₁⋊C₃	—	29	1	no	Hall
11	C₃×C₂₉⋊C₇	—	31	1	no	Hall
12	C₂×C₇×C₃₁	—	29	1	no	Hall
13	D₂₉⋊C₇	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
14	C₇×C₃₁	—	29	1	no	Hall
15	C₂₉⋊C₇	C₂×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃₁⋊C₃	—	29	1	no	Hall
17	C₃×D₂₉	—	31	1	no	Hall
18	C₃₁⋊C₃	D₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₂₉	—	31	1	no	Hall
20	C₂×C₃₁	—	29	1	no	Hall
21	D₂₉	C₇×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇	—	899	1	no	Hall
23	C₃₁	C₃×D₂₉⋊C₇	1	1	yes	characteristic, complemented, Sylow
24	C₂₉	C₂×C₇×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₇	—	899	1	no	Hall
26	C₂×C₇	—	29	1	no	Hall
27	C₇	—	29	1	no	Sylow
28	C₂×C₃	—	899	1	no	Hall
29	C₃	—	31	1	no	Sylow
30	C₂	—	29	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂₉×C₃₁	C₂×C₃×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⋊C₃×C₂₉⋊C₇	C₂	semidirect
2. C₃₁×D₂₉⋊C₇	C₃	semidirect
3. C₃₁×C₂₉⋊C₇	C₂×C₃	semidirect
4. D₂₉×C₃₁⋊C₃	C₇	semidirect
5. C₂₉×C₃₁⋊C₃	C₂×C₇	semidirect
6. C₃₁×D₂₉	C₃×C₇	semidirect
9. C₂₉×C₃₁	C₂×C₃×C₇	semidirect
13. D₂₉⋊C₇	C₃₁⋊C₃	direct (N × H)
15. C₂₉⋊C₇	C₂×C₃₁⋊C₃	semidirect
18. C₃₁⋊C₃	D₂₉⋊C₇	direct (N × H)
21. D₂₉	C₇×C₃₁⋊C₃	semidirect
23. C₃₁	C₃×D₂₉⋊C₇	semidirect
24. C₂₉	C₂×C₇×C₃₁⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃₁⋊C₃×C₂₉⋊C₇	2
C₃₁×D₂₉⋊C₇	3
D₂₉×C₃₁⋊C₃	7
C₂×C₇×C₃₁⋊C₃	29
C₃×D₂₉⋊C₇	31

Subgroups — C31⋊C3×D29⋊C7 #49180010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁⋊C₃×D₂₉⋊C₇ #49180010