Subgroups — C₅×C₇×D₁₅₅ #24925765

Order 10850.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₁₅₅	C₅	1	1	yes	maximal, characteristic, direct product factor
3	C₅×C₇×D₃₁	—	5	1	no	maximal
4	C₅×D₁₅₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₇×C₃₁	—	2	2	no	—
6	C₅×C₇×C₃₁	D₅	1	1	yes	characteristic, complemented
7	C₅×C₇×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
8	C₅²×C₃₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
9	C₇×D₃₁	—	5	1	no	Hall
10	C₅×C₇×D₅	—	31	1	no	maximal, Hall
11	D₁₅₅	C₅×C₇	1	1	yes	characteristic, direct product factor
12	C₅×D₃₁	—	5	1	no	—
13	C₇×C₃₁	C₅×D₅	1	1	yes	characteristic, complemented, Hall
14	C₅²×C₇	D₃₁	1	1	yes	characteristic, complemented, Hall
15	C₅×C₃₁	—	2	2	no	—
16	C₅×C₃₁	C₇×D₅	1	1	yes	characteristic, complemented
17	C₅×C₃₁	C₂×C₅×C₇	1	1	yes	characteristic, complemented
18	C₂×C₅×C₇	—	155	1	no	—
19	C₇×D₅	—	31	1	no	—
20	D₃₁	—	5	1	no	Hall
21	C₅×D₅	—	31	1	no	Hall
22	C₅×C₇	—	2	2	no	—
23	C₅×C₇	C₅×D₃₁	1	1	yes	characteristic, complemented
24	C₅×C₇	D₁₅₅	1	1	yes	characteristic, direct product factor
25	C₃₁	C₅×C₇×D₅	1	1	yes	characteristic, complemented, Sylow
26	C₅²	C₇×D₃₁	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₇	—	155	1	no	Hall
28	C₂×C₅	—	155	1	no	—
29	D₅	—	31	1	no	—
30	C₇	C₅×D₁₅₅	1	1	yes	characteristic, direct product factor, Sylow
31	C₅	—	2	2	no	—
32	C₅	C₅×C₇×D₃₁	1	1	yes	characteristic, complemented
33	C₅	C₇×D₁₅₅	1	1	yes	characteristic, direct product factor
34	C₂	—	155	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₇	D₁₅₅
commutator, cosocle, hypocenter	C₅×C₃₁	C₂×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₃₁	C₂
LCS	G ▷ C₅×C₃₁
UCS	C₁ ◁ C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₅²×C₇×C₃₁	C₂	semidirect
2. C₇×D₁₅₅	C₅	direct (N × H)
4. C₅×D₁₅₅	C₇	direct (N × H)
6. C₅×C₇×C₃₁	D₅	semidirect
7. C₅×C₇×C₃₁	C₂×C₅	semidirect
8. C₅²×C₃₁	C₂×C₇	semidirect
11. D₁₅₅	C₅×C₇	direct (N × H)
13. C₇×C₃₁	C₅×D₅	semidirect
14. C₅²×C₇	D₃₁	semidirect
16. C₅×C₃₁	C₇×D₅	semidirect
17. C₅×C₃₁	C₂×C₅×C₇	semidirect
23. C₅×C₇	C₅×D₃₁	semidirect
24. C₅×C₇	D₁₅₅	direct (N × H)
25. C₃₁	C₅×C₇×D₅	semidirect
26. C₅²	C₇×D₃₁	semidirect
30. C₇	C₅×D₁₅₅	direct (N × H)
32. C₅	C₅×C₇×D₃₁	semidirect
33. C₅	C₇×D₁₅₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₇×C₃₁	2
C₇×D₁₅₅	5
C₅×C₇×D₃₁	5
C₅×D₁₅₅	7
C₅×C₇×D₅	31

Subgroups — C5×C7×D155 #24925765

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×D₁₅₅ #24925765