Subgroups — C₂×C₅×D₄₆₅ #22604937

Order 9300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₄₆₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₁₅₅	—	3	1	no	maximal, Hall
4	C₃×C₅²×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₄₆₅	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₅×D₉₃	—	5	1	no	maximal
7	C₂×C₅²×C₃₁	D₃	1	1	yes	characteristic, complemented
8	C₅×D₁₅₅	—	3	2	no	—
9	C₂×C₃×C₅×C₃₁	—	2	2	no	—
10	C₂×C₃×C₅×C₃₁	D₅	1	1	yes	characteristic, complemented
11	C₂×C₃×C₅×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
12	D₄₆₅	C₂×C₅	1	2	yes	direct product factor
13	C₅×D₉₃	—	5	2	no	—
14	C₅²×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	C₂×D₁₅₅	—	3	1	no	—
16	C₂×C₅×D₃₁	—	15	1	no	—
17	C₃×C₅×C₃₁	—	2	2	no	—
18	C₃×C₅×C₃₁	C₂×D₅	1	1	yes	characteristic, complemented
19	C₃×C₅×C₃₁	C₂²×C₅	1	1	yes	characteristic, complemented
20	C₂×D₉₃	—	5	1	no	Hall
21	C₂×C₅×C₃₁	—	2	2	no	—
22	C₂×C₅×C₃₁	C₅×D₃	1	1	yes	characteristic, complemented
23	C₂×C₅×C₃₁	D₁₅	1	1	yes	characteristic, complemented
24	D₁₅₅	—	3	2	no	—
25	C₅×D₃₁	—	15	2	no	—
26	C₂×C₅×D₁₅	—	31	1	no	maximal, Hall
27	C₂×C₃×C₃₁	C₅×D₅	1	1	yes	characteristic, complemented
28	D₉₃	—	5	2	no	—
29	C₅×C₃₁	—	2	2	no	—
30	C₅×C₃₁	C₂×C₅×D₃	1	1	yes	characteristic, complemented
31	C₅×C₃₁	C₂×D₁₅	1	1	yes	characteristic, complemented
32	C₂×C₃×C₅²	D₃₁	1	1	yes	characteristic, complemented
33	C₅×D₁₅	—	31	2	no	—
34	C₂×D₃₁	—	15	1	no	Hall
35	C₂×C₅×D₅	—	93	1	no	Hall
36	C₃×C₃₁	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
37	C₃×C₅²	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
38	C₂×C₃₁	C₅×D₁₅	1	1	yes	characteristic, complemented
39	D₃₁	—	15	2	no	—
40	C₂×D₁₅	—	31	1	no	—
41	C₂×C₅×D₃	—	155	1	no	—
42	C₂×C₅²	D₉₃	1	1	yes	characteristic, complemented
43	C₅×D₅	—	93	2	no	—
44	C₃₁	C₂×C₅×D₁₅	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₃×C₅	—	2	2	no	—
46	C₂×C₃×C₅	C₅×D₃₁	1	1	yes	characteristic, complemented
47	C₂×C₃×C₅	D₁₅₅	1	1	yes	characteristic, complemented
48	D₁₅	—	31	2	no	—
49	C₅×D₃	—	155	2	no	—
50	C₅²	C₂×D₉₃	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₅	—	465	1	no	—
52	C₂×D₅	—	93	1	no	—
53	C₃×C₅	—	2	2	no	—
54	C₃×C₅	C₂×C₅×D₃₁	1	1	yes	characteristic, complemented
55	C₃×C₅	C₂×D₁₅₅	1	1	yes	characteristic, complemented
56	C₂×D₃	—	155	1	no	Hall
57	C₂×C₅	—	2	2	no	—
58	C₂×C₅	—	465	2	no	—
59	C₂×C₅	C₅×D₉₃	1	1	yes	characteristic, complemented
60	C₂×C₅	D₄₆₅	1	1	yes	characteristic, direct product factor
61	D₅	—	93	2	no	—
62	C₂×C₃	C₅×D₁₅₅	1	1	yes	characteristic, complemented
63	D₃	—	155	2	no	—
64	C₅	—	2	2	no	—
65	C₅	C₂×C₅×D₉₃	1	1	yes	characteristic, complemented
66	C₅	C₂×D₄₆₅	1	1	yes	characteristic, direct product factor
67	C₂²	—	465	1	no	Sylow
68	C₃	C₂×C₅×D₁₅₅	1	1	yes	characteristic, complemented, Sylow
69	C₂	—	465	2	no	—
70	C₂	C₅×D₄₆₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₄₆₅
commutator, hypocenter	C₃×C₅×C₃₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₃₁	C₂
LCS	G ▷ C₃×C₅×C₃₁
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₄₆₅	C₂	direct (N × H)
2. C₂×C₃×C₅²×C₃₁	C₂	semidirect
4. C₃×C₅²×C₃₁	C₂²	semidirect
5. C₂×D₄₆₅	C₅	direct (N × H)
7. C₂×C₅²×C₃₁	D₃	semidirect
10. C₂×C₃×C₅×C₃₁	D₅	semidirect
11. C₂×C₃×C₅×C₃₁	C₂×C₅	semidirect
12. D₄₆₅	C₂×C₅	direct (N × H)
14. C₅²×C₃₁	C₂×D₃	semidirect
18. C₃×C₅×C₃₁	C₂×D₅	semidirect
19. C₃×C₅×C₃₁	C₂²×C₅	semidirect
22. C₂×C₅×C₃₁	C₅×D₃	semidirect
23. C₂×C₅×C₃₁	D₁₅	semidirect
27. C₂×C₃×C₃₁	C₅×D₅	semidirect
30. C₅×C₃₁	C₂×C₅×D₃	semidirect
31. C₅×C₃₁	C₂×D₁₅	semidirect
32. C₂×C₃×C₅²	D₃₁	semidirect
36. C₃×C₃₁	C₂×C₅×D₅	semidirect
37. C₃×C₅²	C₂×D₃₁	semidirect
38. C₂×C₃₁	C₅×D₁₅	semidirect
42. C₂×C₅²	D₉₃	semidirect
44. C₃₁	C₂×C₅×D₁₅	semidirect
46. C₂×C₃×C₅	C₅×D₃₁	semidirect
47. C₂×C₃×C₅	D₁₅₅	semidirect
50. C₅²	C₂×D₉₃	semidirect
54. C₃×C₅	C₂×C₅×D₃₁	semidirect
55. C₃×C₅	C₂×D₁₅₅	semidirect
59. C₂×C₅	C₅×D₉₃	semidirect
60. C₂×C₅	D₄₆₅	direct (N × H)
62. C₂×C₃	C₅×D₁₅₅	semidirect
65. C₅	C₂×C₅×D₉₃	semidirect
66. C₅	C₂×D₄₆₅	direct (N × H)
68. C₃	C₂×C₅×D₁₅₅	semidirect
70. C₂	C₅×D₄₆₅	direct (N × H)

Subgroups — C2×C5×D465 #22604937

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×D₄₆₅ #22604937