Subgroups — C₃×C₁₇×D₃₁⋊C₅ #30629039

Order 15810.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×D₃₁⋊C₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₇×D₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₇×ΓL(1,𝔽₃₂)	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₇×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₁₇×D₃₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×D₃₁⋊C₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₅×C₁₇	—	31	1	no	maximal, Hall
10	C₃×ΓL(1,𝔽₃₂)	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
11	D₃₁⋊C₅	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₅×C₁₇	—	31	1	no	Hall
13	C₃×D₃₁	C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅×C₁₇	—	31	1	no	Hall
15	ΓL(1,𝔽₃₂)	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₁₇	—	31	1	no	Hall
17	C₃×C₃₁	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
18	C₅×C₁₇	—	31	1	no	Hall
19	D₃₁	C₃×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
20	C₃×C₁₇	D₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₁₇	—	31	1	no	Hall
22	C₃₁	C₂×C₃×C₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₃×C₅	—	31	1	no	Hall
24	C₁₇	C₃×D₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₅	—	31	1	no	Hall
26	C₂×C₅	—	31	1	no	Hall
27	C₂×C₃	—	31	1	no	Hall
28	C₅	—	31	1	no	Sylow
29	C₃	C₁₇×D₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	31	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₇	D₃₁⋊C₅
commutator, cosocle, hypocenter	C₃₁	C₂×C₃×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₇×C₃₁	C₂×C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₃×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₇×ΓL(1,𝔽₃₂)	C₂	semidirect
2. C₁₇×D₃₁⋊C₅	C₃	direct (N × H)
3. C₃×C₁₇×D₃₁	C₅	semidirect
4. C₁₇×ΓL(1,𝔽₃₂)	C₂×C₃	semidirect
5. C₃×C₁₇×C₃₁	C₂×C₅	semidirect
6. C₁₇×D₃₁	C₃×C₅	semidirect
7. C₃×D₃₁⋊C₅	C₁₇	direct (N × H)
8. C₁₇×C₃₁	C₂×C₃×C₅	semidirect
10. C₃×ΓL(1,𝔽₃₂)	C₂×C₁₇	semidirect
11. D₃₁⋊C₅	C₃×C₁₇	direct (N × H)
13. C₃×D₃₁	C₅×C₁₇	semidirect
15. ΓL(1,𝔽₃₂)	C₂×C₃×C₁₇	semidirect
17. C₃×C₃₁	C₂×C₅×C₁₇	semidirect
19. D₃₁	C₃×C₅×C₁₇	semidirect
20. C₃×C₁₇	D₃₁⋊C₅	direct (N × H)
22. C₃₁	C₂×C₃×C₅×C₁₇	semidirect
24. C₁₇	C₃×D₃₁⋊C₅	direct (N × H)
29. C₃	C₁₇×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
C₃×C₁₇×ΓL(1,𝔽₃₂)	2
C₁₇×D₃₁⋊C₅	3
C₃×C₁₇×D₃₁	5
C₃×D₃₁⋊C₅	17
C₂×C₃×C₅×C₁₇	31

Subgroups — C3×C17×D31⋊C5 #30629039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₇×D₃₁⋊C₅ #30629039