Subgroups — C₂×C₅×D₅×C₃₁⋊C₃ #22604877

Order 9300.

96 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×C₅×D₅×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅²×C₃₁⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂²×C₅×C₃₁⋊C₃	—	5	1	no	maximal
6	C₂×D₅×C₃₁⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₂×C₅²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅×D₅×C₃₁	C₂×C₃	1	2	yes	complemented
9	C₂×C₅×C₃₁⋊C₃	—	2	2	no	—
10	C₂×C₅×C₃₁⋊C₃	—	5	2	no	—
11	C₂×C₅×C₃₁⋊C₃	D₅	1	1	yes	characteristic, direct product factor
12	C₂×C₅×C₃₁⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented
13	D₅×C₃₁⋊C₃	C₂×C₅	1	2	yes	direct product factor
14	C₅²×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
15	C₂²×C₅×C₃₁	—	5	1	no	—
16	C₂×D₅×C₃₁	C₃×C₅	1	1	yes	characteristic, complemented
17	C₅×C₃₁⋊C₃	—	2	2	no	—
18	C₅×C₃₁⋊C₃	C₂×D₅	1	1	yes	characteristic, direct product factor
19	C₅×C₃₁⋊C₃	C₂²×C₅	1	1	yes	characteristic, complemented
20	C₂²×C₃₁⋊C₃	—	5	1	no	Hall
21	C₂×C₅×C₃₁	—	2	2	no	—
22	C₂×C₅×C₃₁	—	5	2	no	—
23	C₂×C₅×C₃₁	C₃×D₅	1	1	yes	characteristic, complemented
24	C₂×C₅×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented
25	D₅×C₃₁	C₂×C₃×C₅	1	2	yes	complemented
26	C₂×C₃×C₅×D₅	—	31	1	no	maximal, Hall
27	C₂×C₃₁⋊C₃	—	5	2	no	—
28	C₂×C₃₁⋊C₃	C₅×D₅	1	1	yes	characteristic, direct product factor
29	C₅×C₃₁	—	2	2	no	—
30	C₅×C₃₁	C₂×C₃×D₅	1	1	yes	characteristic, complemented
31	C₅×C₃₁	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
32	C₂×C₃×C₅²	—	31	1	no	—
33	C₃×C₅×D₅	—	31	2	no	—
34	C₂²×C₃₁	—	5	1	no	Hall
35	C₂×C₅×D₅	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
36	C₃₁⋊C₃	C₂×C₅×D₅	1	1	yes	characteristic, direct product factor, Hall
37	C₃×C₅²	—	31	1	no	Hall
38	C₂×C₃₁	—	5	2	no	—
39	C₂×C₃₁	C₃×C₅×D₅	1	1	yes	characteristic, complemented
40	C₂²×C₃×C₅	—	155	1	no	—
41	C₂×C₃×D₅	—	31	1	no	—
42	C₂×C₅²	C₂×C₃₁⋊C₃	1	1	yes	characteristic, complemented
43	C₅×D₅	C₂×C₃₁⋊C₃	1	2	yes	direct product factor
44	C₃₁	C₂×C₃×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₃×C₅	—	31	1	no	—
46	C₂×C₃×C₅	—	31	1	no	—
47	C₂×C₃×C₅	—	62	2	no	—
48	C₂×C₃×C₅	—	155	2	no	—
49	C₃×D₅	—	31	2	no	—
50	C₅²	C₂²×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₅	—	5	1	no	—
52	C₂×D₅	C₅×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
53	C₃×C₅	—	31	1	no	—
54	C₃×C₅	—	31	1	no	—
55	C₃×C₅	—	62	2	no	—
56	C₂²×C₃	—	155	1	no	Hall
57	C₂×C₅	—	2	2	no	—
58	C₂×C₅	—	5	2	no	—
59	C₂×C₅	D₅×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
60	C₂×C₅	C₂×C₅×C₃₁⋊C₃	1	1	yes	characteristic, complemented
61	D₅	C₂×C₅×C₃₁⋊C₃	1	2	yes	direct product factor
62	C₂×C₃	—	31	1	no	—
63	C₂×C₃	—	155	2	no	—
64	C₅	—	2	2	no	—
65	C₅	C₂×D₅×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
66	C₅	C₂²×C₅×C₃₁⋊C₃	1	1	yes	characteristic, complemented
67	C₂²	—	5	1	no	Sylow
68	C₃	—	31	1	no	Sylow
69	C₂	—	5	2	no	—
70	C₂	C₅×D₅×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₅×C₃₁⋊C₃
commutator, hypocenter	C₅×C₃₁	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₃₁	C₂×C₃
LCS	G ▷ C₅×C₃₁
UCS	C₁ ◁ C₂×C₅

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×C₅×D₅×C₃₁	C₃	semidirect
4. C₅²×C₃₁⋊C₃	C₂²	semidirect
6. C₂×D₅×C₃₁⋊C₃	C₅	direct (N × H)
7. C₂×C₅²×C₃₁	C₂×C₃	semidirect
8. C₅×D₅×C₃₁	C₂×C₃	semidirect
11. C₂×C₅×C₃₁⋊C₃	D₅	direct (N × H)
12. C₂×C₅×C₃₁⋊C₃	C₂×C₅	semidirect
13. D₅×C₃₁⋊C₃	C₂×C₅	direct (N × H)
14. C₅²×C₃₁	C₂²×C₃	semidirect
16. C₂×D₅×C₃₁	C₃×C₅	semidirect
18. C₅×C₃₁⋊C₃	C₂×D₅	direct (N × H)
19. C₅×C₃₁⋊C₃	C₂²×C₅	semidirect
23. C₂×C₅×C₃₁	C₃×D₅	semidirect
24. C₂×C₅×C₃₁	C₂×C₃×C₅	semidirect
25. D₅×C₃₁	C₂×C₃×C₅	semidirect
28. C₂×C₃₁⋊C₃	C₅×D₅	direct (N × H)
30. C₅×C₃₁	C₂×C₃×D₅	semidirect
31. C₅×C₃₁	C₂²×C₃×C₅	semidirect
35. C₂×C₅×D₅	C₃₁⋊C₃	direct (N × H)
36. C₃₁⋊C₃	C₂×C₅×D₅	direct (N × H)
39. C₂×C₃₁	C₃×C₅×D₅	semidirect
42. C₂×C₅²	C₂×C₃₁⋊C₃	semidirect
43. C₅×D₅	C₂×C₃₁⋊C₃	direct (N × H)
44. C₃₁	C₂×C₃×C₅×D₅	semidirect
50. C₅²	C₂²×C₃₁⋊C₃	semidirect
52. C₂×D₅	C₅×C₃₁⋊C₃	direct (N × H)
59. C₂×C₅	D₅×C₃₁⋊C₃	direct (N × H)
60. C₂×C₅	C₂×C₅×C₃₁⋊C₃	semidirect
61. D₅	C₂×C₅×C₃₁⋊C₃	direct (N × H)
65. C₅	C₂×D₅×C₃₁⋊C₃	direct (N × H)
66. C₅	C₂²×C₅×C₃₁⋊C₃	semidirect
70. C₂	C₅×D₅×C₃₁⋊C₃	direct (N × H)

Subgroups — C2×C5×D5×C31⋊C3 #22604877

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×D₅×C₃₁⋊C₃ #22604877