Subgroups — C₇×C₉×D₃₁⋊C₅ #34086121

Order 19530.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₃₁⋊C₅	C₃	1	1	yes	maximal, characteristic
3	C₇×C₉×D₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃×C₇×ΓL(1,𝔽₃₂)	C₂×C₃	1	1	yes	characteristic
5	C₉×D₃₁⋊C₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×D₃₁⋊C₅	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₇×C₉×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
8	C₉×ΓL(1,𝔽₃₂)	C₂×C₇	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×D₃₁	C₃×C₅	1	1	yes	characteristic
10	C₇×ΓL(1,𝔽₃₂)	C₂×C₉	1	1	yes	characteristic, complemented, Hall
11	C₃×D₃₁⋊C₅	C₃×C₇	1	1	yes	characteristic
12	C₃×C₇×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic
13	C₂×C₅×C₇×C₉	—	31	1	no	maximal, Hall
14	C₉×D₃₁	C₅×C₇	1	1	yes	characteristic, complemented, Hall
15	C₃×ΓL(1,𝔽₃₂)	C₂×C₃×C₇	1	1	yes	characteristic
16	C₇×D₃₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
17	C₅×C₇×C₉	—	31	1	no	Hall
18	D₃₁⋊C₅	C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
19	C₉×C₃₁	C₂×C₅×C₇	1	1	yes	characteristic, complemented, Hall
20	C₇×C₃₁	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₅×C₇	—	31	1	no	—
22	C₃×D₃₁	C₃×C₅×C₇	1	1	yes	characteristic
23	ΓL(1,𝔽₃₂)	C₂×C₇×C₉	1	1	yes	characteristic, complemented, Hall
24	C₂×C₇×C₉	—	31	1	no	Hall
25	C₃×C₅×C₇	—	31	1	no	—
26	C₃×C₃₁	C₂×C₃×C₅×C₇	1	1	yes	characteristic
27	C₂×C₅×C₉	—	31	1	no	Hall
28	C₂×C₅×C₇	—	31	1	no	Hall
29	C₇×C₉	D₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
30	D₃₁	C₅×C₇×C₉	1	1	yes	characteristic, complemented, Hall
31	C₅×C₉	—	31	1	no	Hall
32	C₂×C₃×C₇	—	31	1	no	—
33	C₅×C₇	—	31	1	no	Hall
34	C₃₁	C₂×C₅×C₇×C₉	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃×C₅	—	31	1	no	—
36	C₃×C₇	C₃×D₃₁⋊C₅	1	1	yes	characteristic
37	C₂×C₉	—	31	1	no	Hall
38	C₃×C₅	—	31	1	no	—
39	C₂×C₇	—	31	1	no	Hall
40	C₂×C₅	—	31	1	no	Hall
41	C₉	C₇×D₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₉×D₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	—	31	1	no	—
44	C₅	—	31	1	no	Sylow
45	C₃	C₃×C₇×D₃₁⋊C₅	1	1	yes	characteristic
46	C₂	—	31	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₉	D₃₁⋊C₅
commutator, hypocenter	C₃₁	C₂×C₅×C₇×C₉
Frattini	C₃	C₃×C₇×D₃₁⋊C₅
Fitting	C₇×C₉×C₃₁	C₂×C₅
socle	C₃×C₇×C₃₁	C₂×C₃×C₅
prime radical	C₃×C₇×D₃₁⋊C₅	C₃
cosocle	C₃×C₃₁	C₂×C₃×C₅×C₇
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₇×C₉

Complements

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

N	H ≅ G/N	type
1. C₇×C₉×ΓL(1,𝔽₃₂)	C₂	semidirect
3. C₇×C₉×D₃₁	C₅	semidirect
5. C₉×D₃₁⋊C₅	C₇	direct (N × H)
6. C₇×D₃₁⋊C₅	C₉	direct (N × H)
7. C₇×C₉×C₃₁	C₂×C₅	semidirect
8. C₉×ΓL(1,𝔽₃₂)	C₂×C₇	semidirect
10. C₇×ΓL(1,𝔽₃₂)	C₂×C₉	semidirect
14. C₉×D₃₁	C₅×C₇	semidirect
16. C₇×D₃₁	C₅×C₉	semidirect
18. D₃₁⋊C₅	C₇×C₉	direct (N × H)
19. C₉×C₃₁	C₂×C₅×C₇	semidirect
20. C₇×C₃₁	C₂×C₅×C₉	semidirect
23. ΓL(1,𝔽₃₂)	C₂×C₇×C₉	semidirect
29. C₇×C₉	D₃₁⋊C₅	direct (N × H)
30. D₃₁	C₅×C₇×C₉	semidirect
34. C₃₁	C₂×C₅×C₇×C₉	semidirect
41. C₉	C₇×D₃₁⋊C₅	direct (N × H)
42. C₇	C₉×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
C₇×C₉×ΓL(1,𝔽₃₂)	2
C₃×C₇×D₃₁⋊C₅	3
C₇×C₉×D₃₁	5
C₉×D₃₁⋊C₅	7
C₂×C₅×C₇×C₉	31

Subgroups — C7×C9×D31⋊C5 #34086121

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₉×D₃₁⋊C₅ #34086121