Subgroups — C₂×C₅×C₅⋊(D₃₁⋊C₃) #22604876

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×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)	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₅×D₃₁⋊C₃	—	5	1	no	maximal
7	C₂×C₅²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅×D₁₅₅	C₂×C₃	1	2	yes	complemented
9	C₂×C₅×C₃₁⋊C₃	—	2	2	no	—
10	C₂×C₅×C₃₁⋊C₃	D₅	1	1	yes	characteristic, complemented
11	C₂×C₅×C₃₁⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented
12	C₅⋊(D₃₁⋊C₃)	C₂×C₅	1	2	yes	direct product factor
13	C₅×D₃₁⋊C₃	—	5	2	no	—
14	C₅²×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
15	C₂×D₁₅₅	C₃×C₅	1	1	yes	characteristic, complemented
16	C₂×C₅×D₃₁	—	5	1	no	—
17	C₅×C₃₁⋊C₃	—	2	2	no	—
18	C₅×C₃₁⋊C₃	C₂×D₅	1	1	yes	characteristic, complemented
19	C₅×C₃₁⋊C₃	C₂²×C₅	1	1	yes	characteristic, complemented
20	C₂×D₃₁⋊C₃	—	5	1	no	Hall
21	C₂×C₅×C₃₁	—	2	2	no	—
22	C₂×C₅×C₃₁	C₃×D₅	1	1	yes	characteristic, complemented
23	C₂×C₅×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented
24	D₁₅₅	C₂×C₃×C₅	1	2	yes	complemented
25	C₅×D₃₁	—	5	2	no	—
26	C₂×C₃×C₅×D₅	—	31	1	no	maximal, Hall
27	C₂×C₃₁⋊C₃	C₅×D₅	1	1	yes	characteristic, complemented
28	D₃₁⋊C₃	—	5	2	no	—
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	C₂×D₃₁	—	5	1	no	Hall
35	C₂×C₅×D₅	—	31	1	no	Hall
36	C₃₁⋊C₃	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
37	C₃×C₅²	—	31	1	no	Hall
38	C₂×C₃₁	C₃×C₅×D₅	1	1	yes	characteristic, complemented
39	D₃₁	—	5	2	no	—
40	C₂²×C₃×C₅	—	155	1	no	—
41	C₂×C₃×D₅	—	31	1	no	—
42	C₂×C₅²	D₃₁⋊C₃	1	1	yes	characteristic, complemented
43	C₅×D₅	—	31	2	no	—
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	C₂×D₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₅	—	155	1	no	—
52	C₂×D₅	—	31	1	no	—
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	—	155	2	no	—
59	C₂×C₅	C₅×D₃₁⋊C₃	1	1	yes	characteristic, complemented
60	C₂×C₅	C₅⋊(D₃₁⋊C₃)	1	1	yes	characteristic, direct product factor
61	D₅	—	31	2	no	—
62	C₂×C₃	—	31	1	no	—
63	C₂×C₃	—	155	2	no	—
64	C₅	—	2	2	no	—
65	C₅	C₂×C₅×D₃₁⋊C₃	1	1	yes	characteristic, complemented
66	C₅	C₂×C₅⋊(D₃₁⋊C₃)	1	1	yes	characteristic, direct product factor
67	C₂²	—	155	1	no	Sylow
68	C₃	—	31	1	no	Sylow
69	C₂	—	155	2	no	—
70	C₂	C₅×C₅⋊(D₃₁⋊C₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	C₅⋊(D₃₁⋊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×C₅⋊(D₃₁⋊C₃)	C₂	direct (N × H)
3. C₂×C₅×D₁₅₅	C₃	semidirect
4. C₅²×C₃₁⋊C₃	C₂²	semidirect
5. C₂×C₅⋊(D₃₁⋊C₃)	C₅	direct (N × H)
7. C₂×C₅²×C₃₁	C₂×C₃	semidirect
8. C₅×D₁₅₅	C₂×C₃	semidirect
10. C₂×C₅×C₃₁⋊C₃	D₅	semidirect
11. C₂×C₅×C₃₁⋊C₃	C₂×C₅	semidirect
12. C₅⋊(D₃₁⋊C₃)	C₂×C₅	direct (N × H)
14. C₅²×C₃₁	C₂²×C₃	semidirect
15. C₂×D₁₅₅	C₃×C₅	semidirect
18. C₅×C₃₁⋊C₃	C₂×D₅	semidirect
19. C₅×C₃₁⋊C₃	C₂²×C₅	semidirect
22. C₂×C₅×C₃₁	C₃×D₅	semidirect
23. C₂×C₅×C₃₁	C₂×C₃×C₅	semidirect
24. D₁₅₅	C₂×C₃×C₅	semidirect
27. C₂×C₃₁⋊C₃	C₅×D₅	semidirect
30. C₅×C₃₁	C₂×C₃×D₅	semidirect
31. C₅×C₃₁	C₂²×C₃×C₅	semidirect
36. C₃₁⋊C₃	C₂×C₅×D₅	semidirect
38. C₂×C₃₁	C₃×C₅×D₅	semidirect
42. C₂×C₅²	D₃₁⋊C₃	semidirect
44. C₃₁	C₂×C₃×C₅×D₅	semidirect
50. C₅²	C₂×D₃₁⋊C₃	semidirect
59. C₂×C₅	C₅×D₃₁⋊C₃	semidirect
60. C₂×C₅	C₅⋊(D₃₁⋊C₃)	direct (N × H)
65. C₅	C₂×C₅×D₃₁⋊C₃	semidirect
66. C₅	C₂×C₅⋊(D₃₁⋊C₃)	direct (N × H)
70. C₂	C₅×C₅⋊(D₃₁⋊C₃)	direct (N × H)

Subgroups — C2×C5×C5⋊(D31⋊C3) #22604876

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×C₅⋊(D₃₁⋊C₃) #22604876