Subgroups — C₂×C₃×C₇×C₁₅₁⋊C₅ #44540233

Order 31710.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₅₁⋊C₅	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇×C₁₅₁⋊C₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₇×C₁₅₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇×C₁₅₁⋊C₅	C₂×C₃	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₃×C₁₅₁⋊C₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₇×C₁₅₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₅₁⋊C₅	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₇×C₁₅₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₅₁⋊C₅	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
10	C₇×C₁₅₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₁₅₁	C₅×C₇	1	1	yes	characteristic, complemented, Hall
12	C₁₅₁⋊C₅	C₂×C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₁₅₁	C₂×C₅×C₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₅₁	C₃×C₅×C₇	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₅×C₇	—	151	1	no	maximal, Hall
16	C₁₅₁	C₂×C₃×C₅×C₇	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₅×C₇	—	151	1	no	Hall
18	C₂×C₅×C₇	—	151	1	no	Hall
19	C₂×C₃×C₇	C₁₅₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
20	C₅×C₇	—	151	1	no	Hall
21	C₂×C₃×C₅	—	151	1	no	Hall
22	C₃×C₇	C₂×C₁₅₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₅	—	151	1	no	Hall
24	C₂×C₇	C₃×C₁₅₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₅	—	151	1	no	Hall
26	C₇	C₂×C₃×C₁₅₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	C₇×C₁₅₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
28	C₅	—	151	1	no	Sylow
29	C₃	C₂×C₇×C₁₅₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	C₃×C₇×C₁₅₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇	C₁₅₁⋊C₅
commutator, cosocle, hypocenter	C₁₅₁	C₂×C₃×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₅₁	C₅
LCS	G ▷ C₁₅₁
UCS	C₁ ◁ C₂×C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₅₁⋊C₅	C₂	direct (N × H)
2. C₂×C₇×C₁₅₁⋊C₅	C₃	direct (N × H)
3. C₂×C₃×C₇×C₁₅₁	C₅	semidirect
4. C₇×C₁₅₁⋊C₅	C₂×C₃	direct (N × H)
5. C₂×C₃×C₁₅₁⋊C₅	C₇	direct (N × H)
6. C₃×C₇×C₁₅₁	C₂×C₅	semidirect
7. C₃×C₁₅₁⋊C₅	C₂×C₇	direct (N × H)
8. C₂×C₇×C₁₅₁	C₃×C₅	semidirect
9. C₂×C₁₅₁⋊C₅	C₃×C₇	direct (N × H)
10. C₇×C₁₅₁	C₂×C₃×C₅	semidirect
11. C₂×C₃×C₁₅₁	C₅×C₇	semidirect
12. C₁₅₁⋊C₅	C₂×C₃×C₇	direct (N × H)
13. C₃×C₁₅₁	C₂×C₅×C₇	semidirect
14. C₂×C₁₅₁	C₃×C₅×C₇	semidirect
16. C₁₅₁	C₂×C₃×C₅×C₇	semidirect
19. C₂×C₃×C₇	C₁₅₁⋊C₅	direct (N × H)
22. C₃×C₇	C₂×C₁₅₁⋊C₅	direct (N × H)
24. C₂×C₇	C₃×C₁₅₁⋊C₅	direct (N × H)
26. C₇	C₂×C₃×C₁₅₁⋊C₅	direct (N × H)
27. C₂×C₃	C₇×C₁₅₁⋊C₅	direct (N × H)
29. C₃	C₂×C₇×C₁₅₁⋊C₅	direct (N × H)
30. C₂	C₃×C₇×C₁₅₁⋊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×C₇×C₁₅₁⋊C₅	2
C₂×C₇×C₁₅₁⋊C₅	3
C₂×C₃×C₇×C₁₅₁	5
C₂×C₃×C₁₅₁⋊C₅	7
C₂×C₃×C₅×C₇	151

Subgroups — C2×C3×C7×C151⋊C5 #44540233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₇×C₁₅₁⋊C₅ #44540233