Subgroups — C₅×D₃₁₃₅ #44535539

Order 31350.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₁₁×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₀₄₅	—	3	1	no	maximal, Hall
3	D₃₁₃₅	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×D₆₂₇	—	5	1	no	maximal
5	C₅²×C₁₁×C₁₉	D₃	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×C₁₁×C₁₉	—	2	2	no	—
7	C₃×C₅×C₁₁×C₁₉	D₅	1	1	yes	characteristic, complemented
8	C₃×C₅×C₁₁×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented
9	C₅×D₂₈₅	—	11	1	no	maximal, Hall
10	D₁₀₄₅	—	3	1	no	—
11	C₅×D₂₀₉	—	15	1	no	—
12	C₅×D₁₆₅	—	19	1	no	maximal, Hall
13	C₃×C₅²×C₁₉	D₁₁	1	1	yes	characteristic, complemented, Hall
14	D₆₂₇	—	5	1	no	Hall
15	C₅×C₁₁×C₁₉	—	2	2	no	—
16	C₅×C₁₁×C₁₉	C₅×D₃	1	1	yes	characteristic, complemented
17	C₅×C₁₁×C₁₉	D₁₅	1	1	yes	characteristic, complemented
18	C₅×D₉₅	—	33	1	no	Hall
19	C₃×C₅²×C₁₁	D₁₉	1	1	yes	characteristic, complemented, Hall
20	C₃×C₁₁×C₁₉	C₅×D₅	1	1	yes	characteristic, complemented, Hall
21	D₂₈₅	—	11	1	no	—
22	C₅×D₅₇	—	55	1	no	—
23	C₅×D₅₅	—	57	1	no	Hall
24	C₅²×C₁₉	D₃₃	1	1	yes	characteristic, complemented, Hall
25	D₂₀₉	—	15	1	no	Hall
26	D₁₆₅	—	19	1	no	—
27	C₅×D₃₃	—	95	1	no	—
28	C₃×C₅×C₁₉	—	2	2	no	—
29	C₃×C₅×C₁₉	C₅×D₁₁	1	1	yes	characteristic, complemented
30	C₃×C₅×C₁₉	D₅₅	1	1	yes	characteristic, complemented
31	C₅²×C₁₁	D₅₇	1	1	yes	characteristic, complemented, Hall
32	C₁₁×C₁₉	C₅×D₁₅	1	1	yes	characteristic, complemented, Hall
33	D₉₅	—	33	1	no	—
34	C₅×D₁₉	—	165	1	no	—
35	C₃×C₅×C₁₁	—	2	2	no	—
36	C₃×C₅×C₁₁	C₅×D₁₉	1	1	yes	characteristic, complemented
37	C₃×C₅×C₁₁	D₉₅	1	1	yes	characteristic, complemented
38	C₅×D₁₅	—	209	1	no	Hall
39	D₅₇	—	55	1	no	Hall
40	D₅₅	—	57	1	no	—
41	C₅×D₁₁	—	285	1	no	—
42	C₅×C₁₉	—	2	2	no	—
43	C₅×C₁₉	C₅×D₃₃	1	1	yes	characteristic, complemented
44	C₅×C₁₉	D₁₆₅	1	1	yes	characteristic, complemented
45	C₃×C₅²	D₂₀₉	1	1	yes	characteristic, complemented, Hall
46	D₃₃	—	95	1	no	Hall
47	C₃×C₁₉	C₅×D₅₅	1	1	yes	characteristic, complemented, Hall
48	C₅×C₁₁	—	2	2	no	—
49	C₅×C₁₁	C₅×D₅₇	1	1	yes	characteristic, complemented
50	C₅×C₁₁	D₂₈₅	1	1	yes	characteristic, complemented
51	C₅×D₅	—	627	1	no	Hall
52	D₁₉	—	165	1	no	Hall
53	C₃×C₁₁	C₅×D₉₅	1	1	yes	characteristic, complemented, Hall
54	D₁₅	—	209	1	no	—
55	C₅×D₃	—	1045	1	no	—
56	C₅²	D₆₂₇	1	1	yes	characteristic, complemented, Sylow
57	D₁₁	—	285	1	no	Hall
58	C₁₉	C₅×D₁₆₅	1	1	yes	characteristic, complemented, Sylow
59	C₃×C₅	—	2	2	no	—
60	C₃×C₅	C₅×D₂₀₉	1	1	yes	characteristic, complemented
61	C₃×C₅	D₁₀₄₅	1	1	yes	characteristic, complemented
62	C₁₁	C₅×D₂₈₅	1	1	yes	characteristic, complemented, Sylow
63	C₂×C₅	—	3135	1	no	—
64	D₅	—	627	1	no	—
65	D₃	—	1045	1	no	Hall
66	C₅	—	2	2	no	—
67	C₅	C₅×D₆₂₇	1	1	yes	characteristic, complemented
68	C₅	D₃₁₃₅	1	1	yes	characteristic, direct product factor
69	C₃	C₅×D₁₀₄₅	1	1	yes	characteristic, complemented, Sylow
70	C₂	—	3135	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₃₁₃₅
commutator, cosocle, hypocenter	C₃×C₅×C₁₁×C₁₉	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₁×C₁₉	C₂
LCS	G ▷ C₃×C₅×C₁₁×C₁₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₁₁×C₁₉	C₂	semidirect
3. D₃₁₃₅	C₅	direct (N × H)
5. C₅²×C₁₁×C₁₉	D₃	semidirect
7. C₃×C₅×C₁₁×C₁₉	D₅	semidirect
8. C₃×C₅×C₁₁×C₁₉	C₂×C₅	semidirect
13. C₃×C₅²×C₁₉	D₁₁	semidirect
16. C₅×C₁₁×C₁₉	C₅×D₃	semidirect
17. C₅×C₁₁×C₁₉	D₁₅	semidirect
19. C₃×C₅²×C₁₁	D₁₉	semidirect
20. C₃×C₁₁×C₁₉	C₅×D₅	semidirect
24. C₅²×C₁₉	D₃₃	semidirect
29. C₃×C₅×C₁₉	C₅×D₁₁	semidirect
30. C₃×C₅×C₁₉	D₅₅	semidirect
31. C₅²×C₁₁	D₅₇	semidirect
32. C₁₁×C₁₉	C₅×D₁₅	semidirect
36. C₃×C₅×C₁₁	C₅×D₁₉	semidirect
37. C₃×C₅×C₁₁	D₉₅	semidirect
43. C₅×C₁₉	C₅×D₃₃	semidirect
44. C₅×C₁₉	D₁₆₅	semidirect
45. C₃×C₅²	D₂₀₉	semidirect
47. C₃×C₁₉	C₅×D₅₅	semidirect
49. C₅×C₁₁	C₅×D₅₇	semidirect
50. C₅×C₁₁	D₂₈₅	semidirect
53. C₃×C₁₁	C₅×D₉₅	semidirect
56. C₅²	D₆₂₇	semidirect
58. C₁₉	C₅×D₁₆₅	semidirect
60. C₃×C₅	C₅×D₂₀₉	semidirect
61. C₃×C₅	D₁₀₄₅	semidirect
62. C₁₁	C₅×D₂₈₅	semidirect
67. C₅	C₅×D₆₂₇	semidirect
68. C₅	D₃₁₃₅	direct (N × H)
69. C₃	C₅×D₁₀₄₅	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅²×C₁₁×C₁₉	2
C₅×D₁₀₄₅	3
D₃₁₃₅	5
C₅×D₆₂₇	5
C₅×D₂₈₅	11
C₅×D₁₆₅	19

Subgroups — C5×D3135 #44535539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃₁₃₅ #44535539