Subgroups — C₅×D₃×D₁₅₅ #22604908

Order 9300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₅	D₃×D₁₅₅
commutator, hypocenter	C₃×C₅×C₃₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₃₁	C₂²
LCS	G ▷ C₃×C₅×C₃₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₄₆₅	C₂	semidirect
2. C₅²×D₃×C₃₁	C₂	semidirect
3. C₃×C₅×D₁₅₅	C₂	semidirect
5. C₃×C₅²×C₃₁	C₂²	semidirect
6. D₃×D₁₅₅	C₅	direct (N × H)
10. C₅×D₁₅₅	D₃	direct (N × H)
11. D₄₆₅	C₂×C₅	semidirect
14. C₅×D₃×C₃₁	D₅	semidirect
15. C₅×D₃×C₃₁	C₂×C₅	semidirect
16. C₃×D₁₅₅	C₂×C₅	semidirect
18. C₅²×C₃₁	C₂×D₃	semidirect
22. C₃×C₅×C₃₁	C₂×D₅	semidirect
23. C₃×C₅×C₃₁	C₂²×C₅	semidirect
29. D₁₅₅	C₅×D₃	direct (N × H)
35. D₃×C₃₁	C₅×D₅	semidirect
37. C₅×C₃₁	D₃×D₅	semidirect
38. C₅×C₃₁	C₂×C₅×D₃	semidirect
40. C₅²×D₃	D₃₁	semidirect
44. C₃×C₃₁	C₂×C₅×D₅	semidirect
45. C₃×C₅²	C₂×D₃₁	semidirect
54. C₃₁	C₅×D₃×D₅	semidirect
60. C₅×D₃	C₅×D₃₁	semidirect
61. C₅×D₃	D₁₅₅	direct (N × H)
62. C₅²	D₃×D₃₁	semidirect
66. C₃×C₅	C₂×C₅×D₃₁	semidirect
67. C₃×C₅	C₂×D₁₅₅	semidirect
78. D₃	C₅×D₁₅₅	direct (N × H)
80. C₅	C₅×D₃×D₃₁	semidirect
81. C₅	D₃×D₁₅₅	direct (N × H)
83. C₃	C₂×C₅×D₁₅₅	semidirect

Subgroups — C5×D3×D155 #22604908

Conjugacy classes of subgroups

Complements

Subgroups — C₅×D₃×D₁₅₅ #22604908