Subgroups — C₂×C₅⋊(C₅⋊(D₃₁⋊C₃)) #22604878

Order 9300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅⋊(C₅⋊(D₃₁⋊C₃))	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅⋊D₁₅₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅²×C₃₁⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅⋊(D₃₁⋊C₃)	—	5	6	no	maximal
6	C₂×C₅²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅⋊D₁₅₅	C₂×C₃	1	2	yes	complemented
8	C₂×C₅×C₃₁⋊C₃	D₅	1	6	yes	complemented
9	C₅⋊(D₃₁⋊C₃)	—	5	12	no	—
10	C₅²×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₁₅₅	—	5	6	no	—
12	C₅×C₃₁⋊C₃	C₂×D₅	1	6	yes	complemented
13	C₂×D₃₁⋊C₃	—	25	1	no	Hall
14	C₂×C₅×C₃₁	C₃×D₅	1	6	yes	complemented
15	D₁₅₅	—	5	12	no	—
16	C₂×C₃×C₅⋊D₅	—	31	1	no	maximal, Hall
17	C₂×C₃₁⋊C₃	C₅⋊D₅	1	1	yes	characteristic, complemented
18	D₃₁⋊C₃	—	25	2	no	—
19	C₅×C₃₁	C₂×C₃×D₅	1	6	yes	complemented
20	C₂×C₃×C₅²	—	31	1	no	—
21	C₃×C₅⋊D₅	—	31	2	no	—
22	C₂×D₃₁	—	25	1	no	Hall
23	C₂×C₅⋊D₅	—	31	1	no	Hall
24	C₃₁⋊C₃	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
25	C₃×C₅²	—	31	1	no	Hall
26	C₂×C₃₁	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented
27	D₃₁	—	25	2	no	—
28	C₂×C₃×D₅	—	155	6	no	—
29	C₂×C₅²	D₃₁⋊C₃	1	1	yes	characteristic, complemented
30	C₅⋊D₅	—	31	2	no	—
31	C₃₁	C₂×C₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₃×C₅	—	31	6	no	—
33	C₃×D₅	—	155	12	no	—
34	C₅²	C₂×D₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
35	C₂×D₅	—	155	6	no	—
36	C₃×C₅	—	31	6	no	—
37	C₂²×C₃	—	775	1	no	Hall
38	C₂×C₅	C₅⋊(D₃₁⋊C₃)	1	6	yes	complemented
39	D₅	—	155	12	no	—
40	C₂×C₃	—	775	2	no	—
41	C₂×C₃	—	31	1	no	—
42	C₅	C₂×C₅⋊(D₃₁⋊C₃)	1	6	yes	complemented
43	C₂²	—	775	1	no	Sylow
44	C₃	—	31	1	no	Sylow
45	C₂	—	775	2	no	—
46	C₂	C₅⋊(C₅⋊(D₃₁⋊C₃))	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊(C₅⋊(D₃₁⋊C₃))
commutator, hypocenter	C₅²×C₃₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₃₁	C₂×C₃
LCS	G ▷ C₅²×C₃₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₅²×C₃₁⋊C₃	C₂	semidirect
2. C₅⋊(C₅⋊(D₃₁⋊C₃))	C₂	direct (N × H)
3. C₂×C₅⋊D₁₅₅	C₃	semidirect
4. C₅²×C₃₁⋊C₃	C₂²	semidirect
6. C₂×C₅²×C₃₁	C₂×C₃	semidirect
7. C₅⋊D₁₅₅	C₂×C₃	semidirect
8. C₂×C₅×C₃₁⋊C₃	D₅	semidirect
10. C₅²×C₃₁	C₂²×C₃	semidirect
12. C₅×C₃₁⋊C₃	C₂×D₅	semidirect
14. C₂×C₅×C₃₁	C₃×D₅	semidirect
17. C₂×C₃₁⋊C₃	C₅⋊D₅	semidirect
19. C₅×C₃₁	C₂×C₃×D₅	semidirect
24. C₃₁⋊C₃	C₂×C₅⋊D₅	semidirect
26. C₂×C₃₁	C₃×C₅⋊D₅	semidirect
29. C₂×C₅²	D₃₁⋊C₃	semidirect
31. C₃₁	C₂×C₃×C₅⋊D₅	semidirect
34. C₅²	C₂×D₃₁⋊C₃	semidirect
38. C₂×C₅	C₅⋊(D₃₁⋊C₃)	semidirect
42. C₅	C₂×C₅⋊(D₃₁⋊C₃)	semidirect
46. C₂	C₅⋊(C₅⋊(D₃₁⋊C₃))	direct (N × H)

Subgroups — C2×C5⋊(C5⋊(D31⋊C3)) #22604878

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅⋊(C₅⋊(D₃₁⋊C₃)) #22604878