Subgroups — C₅×D₃×D₅₅ #15693199

Order 3300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₆₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×D₃×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₅₅	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₅₅	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₅×D₃×D₁₁	—	5	1	no	maximal
8	C₂×C₅²×C₁₁	—	3	1	no	—
9	C₅×D₅₅	—	3	1	no	—
10	C₅×D₅₅	D₃	1	1	yes	characteristic, direct product factor
11	D₁₆₅	C₂×C₅	1	1	yes	characteristic, complemented
12	C₅×D₃₃	—	5	1	no	—
13	C₅×D₃×C₁₁	—	2	2	no	—
14	C₅×D₃×C₁₁	D₅	1	1	yes	characteristic, complemented
15	C₅×D₃×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
16	C₃×D₅₅	C₂×C₅	1	1	yes	characteristic, complemented
17	C₃×C₅×D₁₁	—	5	1	no	—
18	C₅×D₃×D₅	—	11	1	no	maximal, Hall
19	C₅²×C₁₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
20	C₂×D₅₅	—	3	1	no	—
21	C₂×C₅×D₁₁	—	15	1	no	—
22	C₃×C₅×C₁₁	—	2	2	no	—
23	C₃×C₅×C₁₁	C₂×D₅	1	1	yes	characteristic, complemented
24	C₃×C₅×C₁₁	C₂²×C₅	1	1	yes	characteristic, complemented
25	C₅×D₁₅	—	11	1	no	—
26	C₅²×D₃	D₁₁	1	1	yes	characteristic, complemented
27	C₃×C₅×D₅	—	11	1	no	—
28	D₃×D₁₁	—	5	1	no	Hall
29	C₂×C₅×C₁₁	—	3	1	no	—
30	C₂×C₅×C₁₁	—	3	1	no	—
31	C₂×C₅×C₁₁	—	6	2	no	—
32	D₅₅	—	3	1	no	—
33	D₅₅	C₅×D₃	1	1	yes	characteristic, direct product factor
34	C₅×D₁₁	—	5	1	no	—
35	C₅×D₁₁	—	15	1	no	—
36	C₂×C₅×D₅	—	33	1	no	Hall
37	C₃×C₅²	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
38	D₃₃	—	5	1	no	—
39	C₃×D₁₁	—	5	1	no	—
40	D₃×C₁₁	C₅×D₅	1	1	yes	characteristic, complemented
41	C₂×C₅×D₃	—	55	1	no	—
42	D₃×D₅	—	11	1	no	—
43	C₅×C₁₁	—	2	2	no	—
44	C₅×C₁₁	D₃×D₅	1	1	yes	characteristic, complemented
45	C₅×C₁₁	C₂×C₅×D₃	1	1	yes	characteristic, complemented
46	C₂×C₅²	—	3	1	no	—
47	C₅×D₅	—	11	1	no	—
48	C₅×D₅	—	33	1	no	—
49	C₂×D₁₁	—	15	1	no	Hall
50	C₃×C₁₁	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
51	C₂×C₃×C₅	—	55	1	no	—
52	D₁₅	—	11	1	no	—
53	C₃×D₅	—	11	1	no	—
54	C₅×D₃	—	2	2	no	—
55	C₅×D₃	—	55	1	no	—
56	C₅×D₃	C₅×D₁₁	1	1	yes	characteristic, complemented
57	C₅×D₃	D₅₅	1	1	yes	characteristic, direct product factor
58	C₅²	D₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₁₁	—	3	1	no	—
60	D₁₁	—	5	1	no	—
61	D₁₁	—	15	1	no	—
62	C₂²×C₅	—	165	1	no	—
63	C₂×D₅	—	33	1	no	—
64	C₃×C₅	—	2	2	no	—
65	C₃×C₅	C₂×C₅×D₁₁	1	1	yes	characteristic, complemented
66	C₃×C₅	C₂×D₅₅	1	1	yes	characteristic, complemented
67	C₂×D₃	—	55	1	no	Hall
68	C₁₁	C₅×D₃×D₅	1	1	yes	characteristic, complemented, Sylow
69	C₂×C₅	—	3	1	no	—
70	C₂×C₅	—	3	1	no	—
71	C₂×C₅	—	6	2	no	—
72	C₂×C₅	—	55	1	no	—
73	C₂×C₅	—	165	1	no	—
74	D₅	—	11	1	no	—
75	D₅	—	33	1	no	—
76	C₂×C₃	—	55	1	no	—
77	D₃	—	55	1	no	—
78	D₃	C₅×D₅₅	1	1	yes	characteristic, direct product factor
79	C₅	—	2	2	no	—
80	C₅	C₅×D₃×D₁₁	1	1	yes	characteristic, complemented
81	C₅	D₃×D₅₅	1	1	yes	characteristic, direct product factor
82	C₂²	—	165	1	no	Sylow
83	C₃	C₂×C₅×D₅₅	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	3	1	no	—
85	C₂	—	55	1	no	—
86	C₂	—	165	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₃×D₅₅
commutator, cosocle, hypocenter	C₃×C₅×C₁₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₁	C₂²
LCS	G ▷ C₃×C₅×C₁₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₆₅	C₂	semidirect
2. C₅²×D₃×C₁₁	C₂	semidirect
3. C₃×C₅×D₅₅	C₂	semidirect
5. C₃×C₅²×C₁₁	C₂²	semidirect
6. D₃×D₅₅	C₅	direct (N × H)
10. C₅×D₅₅	D₃	direct (N × H)
11. D₁₆₅	C₂×C₅	semidirect
14. C₅×D₃×C₁₁	D₅	semidirect
15. C₅×D₃×C₁₁	C₂×C₅	semidirect
16. C₃×D₅₅	C₂×C₅	semidirect
19. C₅²×C₁₁	C₂×D₃	semidirect
23. C₃×C₅×C₁₁	C₂×D₅	semidirect
24. C₃×C₅×C₁₁	C₂²×C₅	semidirect
26. C₅²×D₃	D₁₁	semidirect
33. D₅₅	C₅×D₃	direct (N × H)
37. C₃×C₅²	C₂×D₁₁	semidirect
40. D₃×C₁₁	C₅×D₅	semidirect
44. C₅×C₁₁	D₃×D₅	semidirect
45. C₅×C₁₁	C₂×C₅×D₃	semidirect
50. C₃×C₁₁	C₂×C₅×D₅	semidirect
56. C₅×D₃	C₅×D₁₁	semidirect
57. C₅×D₃	D₅₅	direct (N × H)
58. C₅²	D₃×D₁₁	semidirect
65. C₃×C₅	C₂×C₅×D₁₁	semidirect
66. C₃×C₅	C₂×D₅₅	semidirect
68. C₁₁	C₅×D₃×D₅	semidirect
78. D₃	C₅×D₅₅	direct (N × H)
80. C₅	C₅×D₃×D₁₁	semidirect
81. C₅	D₃×D₅₅	direct (N × H)
83. C₃	C₂×C₅×D₅₅	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₁₆₅	2
C₅²×D₃×C₁₁	2
C₃×C₅×D₅₅	2
C₂×C₅×D₅₅	3
D₃×D₅₅	5
C₅×D₃×D₁₁	5
C₅×D₃×D₅	11

Subgroups — C5×D3×D55 #15693199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×D₅₅ #15693199