Subgroups — C₂₉×C₃⋊(D₃₁⋊C₃) #30633652

Order 16182.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₉×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₉×D₃₁⋊C₃	—	3	1	no	maximal
3	C₂₉×D₉₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₂₉×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
5	C₂₉×C₃₁⋊C₃	—	2	1	no	—
6	C₂₉×C₃₁⋊C₃	D₃	1	1	yes	characteristic, complemented
7	C₂₉×D₃₁	—	3	1	no	Hall
8	C₂₉×C₃₁	C₃×D₃	1	1	yes	characteristic, complemented, Hall
9	C₃⋊(D₃₁⋊C₃)	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×D₃×C₂₉	—	31	1	no	maximal, Hall
11	C₃×C₃₁⋊C₃	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
12	C₃²×C₂₉	—	31	1	no	Hall
13	D₉₃	C₃×C₂₉	1	1	yes	characteristic, complemented
14	D₃₁⋊C₃	—	3	1	no	—
15	C₂×C₃×C₂₉	—	93	1	no	—
16	D₃×C₂₉	—	31	1	no	—
17	C₃×C₃₁	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented
18	C₃₁⋊C₃	—	2	1	no	—
19	C₃₁⋊C₃	D₃×C₂₉	1	1	yes	characteristic, complemented
20	C₃×C₂₉	—	31	1	no	—
21	C₃×C₂₉	—	62	1	no	—
22	C₃×C₂₉	D₃₁⋊C₃	1	1	yes	characteristic, complemented
23	D₃₁	—	3	1	no	Hall
24	C₂×C₂₉	—	93	1	no	Hall
25	C₃₁	C₃×D₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
26	C₂₉	C₃⋊(D₃₁⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
27	C₃×D₃	—	31	1	no	Hall
28	C₃²	—	31	1	no	Sylow
29	C₂×C₃	—	93	1	no	—
30	D₃	—	31	1	no	—
31	C₃	—	31	1	no	—
32	C₃	—	62	1	no	—
33	C₃	C₂₉×D₃₁⋊C₃	1	1	yes	characteristic, complemented
34	C₂	—	93	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₉	C₃⋊(D₃₁⋊C₃)
commutator, cosocle, hypocenter	C₃×C₃₁	C₂×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₂₉×C₃₁	C₂×C₃
LCS	G ▷ C₃×C₃₁
UCS	C₁ ◁ C₂₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₂₉×C₃₁⋊C₃	C₂	semidirect
3. C₂₉×D₉₃	C₃	semidirect
4. C₃×C₂₉×C₃₁	C₂×C₃	semidirect
6. C₂₉×C₃₁⋊C₃	D₃	semidirect
8. C₂₉×C₃₁	C₃×D₃	semidirect
9. C₃⋊(D₃₁⋊C₃)	C₂₉	direct (N × H)
11. C₃×C₃₁⋊C₃	C₂×C₂₉	semidirect
13. D₉₃	C₃×C₂₉	semidirect
17. C₃×C₃₁	C₂×C₃×C₂₉	semidirect
19. C₃₁⋊C₃	D₃×C₂₉	semidirect
22. C₃×C₂₉	D₃₁⋊C₃	semidirect
25. C₃₁	C₃×D₃×C₂₉	semidirect
26. C₂₉	C₃⋊(D₃₁⋊C₃)	direct (N × H)
33. C₃	C₂₉×D₃₁⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₂₉×C₃₁⋊C₃	2
C₂₉×D₃₁⋊C₃	3
C₂₉×D₉₃	3
C₃⋊(D₃₁⋊C₃)	29
C₃×D₃×C₂₉	31

Subgroups — C29×C3⋊(D31⋊C3) #30633652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×C₃⋊(D₃₁⋊C₃) #30633652