Subgroups — C₂×C₅⋊D₅×C₃₁⋊C₃ #22604879

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⋊D₅×C₃₁⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃₁×C₅⋊D₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅²×C₃₁⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₅×C₃₁⋊C₃	—	5	6	no	maximal
6	C₂×C₅²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃₁×C₅⋊D₅	C₂×C₃	1	2	yes	complemented
8	C₂×C₅×C₃₁⋊C₃	D₅	1	6	yes	complemented
9	D₅×C₃₁⋊C₃	—	5	12	no	—
10	C₅²×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₅×C₃₁	—	5	6	no	—
12	C₅×C₃₁⋊C₃	C₂×D₅	1	6	yes	complemented
13	C₂²×C₃₁⋊C₃	—	25	1	no	Hall
14	C₂×C₅×C₃₁	C₃×D₅	1	6	yes	complemented
15	D₅×C₃₁	—	5	12	no	—
16	C₂×C₃×C₅⋊D₅	—	31	1	no	maximal, Hall
17	C₂×C₃₁⋊C₃	—	25	2	no	—
18	C₂×C₃₁⋊C₃	C₅⋊D₅	1	1	yes	characteristic, direct product factor
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	C₂²×C₃₁	—	25	1	no	Hall
23	C₂×C₅⋊D₅	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
24	C₃₁⋊C₃	C₂×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₅²	—	31	1	no	Hall
26	C₂×C₃₁	—	25	2	no	—
27	C₂×C₃₁	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented
28	C₂×C₃×D₅	—	155	6	no	—
29	C₂×C₅²	C₂×C₃₁⋊C₃	1	1	yes	characteristic, complemented
30	C₅⋊D₅	C₂×C₃₁⋊C₃	1	2	yes	direct product factor
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	C₂²×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
35	C₂×D₅	—	5	6	no	—
36	C₃×C₅	—	31	6	no	—
37	C₂²×C₃	—	775	1	no	Hall
38	C₂×C₅	D₅×C₃₁⋊C₃	1	6	yes	complemented
39	D₅	—	5	12	no	—
40	C₂×C₃	—	775	2	no	—
41	C₂×C₃	—	31	1	no	—
42	C₅	C₂×D₅×C₃₁⋊C₃	1	6	yes	complemented
43	C₂²	—	25	1	no	Sylow
44	C₃	—	31	1	no	Sylow
45	C₂	—	25	2	no	—
46	C₂	C₅⋊D₅×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊D₅×C₃₁⋊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⋊D₅×C₃₁⋊C₃	C₂	direct (N × H)
3. C₂×C₃₁×C₅⋊D₅	C₃	semidirect
4. C₅²×C₃₁⋊C₃	C₂²	semidirect
6. C₂×C₅²×C₃₁	C₂×C₃	semidirect
7. C₃₁×C₅⋊D₅	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
18. C₂×C₃₁⋊C₃	C₅⋊D₅	direct (N × H)
19. C₅×C₃₁	C₂×C₃×D₅	semidirect
23. C₂×C₅⋊D₅	C₃₁⋊C₃	direct (N × H)
24. C₃₁⋊C₃	C₂×C₅⋊D₅	direct (N × H)
27. C₂×C₃₁	C₃×C₅⋊D₅	semidirect
29. C₂×C₅²	C₂×C₃₁⋊C₃	semidirect
30. C₅⋊D₅	C₂×C₃₁⋊C₃	direct (N × H)
31. C₃₁	C₂×C₃×C₅⋊D₅	semidirect
34. C₅²	C₂²×C₃₁⋊C₃	semidirect
38. C₂×C₅	D₅×C₃₁⋊C₃	semidirect
42. C₅	C₂×D₅×C₃₁⋊C₃	semidirect
46. C₂	C₅⋊D₅×C₃₁⋊C₃	direct (N × H)

Subgroups — C2×C5⋊D5×C31⋊C3 #22604879

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅⋊D₅×C₃₁⋊C₃ #22604879