Subgroups — C₃×C₅×C₁₁×D₅₅ #31827717

Order 18150.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₁₁²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₁×D₅₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₁×D₅₅	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₃×C₅×C₁₁×D₁₁	—	5	1	no	maximal
5	C₅²×C₁₁²	C₂×C₃	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×C₁₁²	—	2	2	no	—
7	C₃×C₅×C₁₁²	D₅	1	1	yes	characteristic, complemented
8	C₃×C₅×C₁₁²	C₂×C₅	1	1	yes	characteristic, complemented
9	C₃×C₅×D₅₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor
10	C₃×C₅×D₅×C₁₁	—	11	1	no	maximal
11	C₁₁×D₅₅	C₃×C₅	1	1	yes	characteristic, direct product factor
12	C₅×C₁₁×D₁₁	—	5	1	no	—
13	C₃×C₅²×C₁₁	—	2	5	no	—
14	C₃×C₅²×C₁₁	D₁₁	1	1	yes	characteristic, complemented
15	C₃×C₅²×C₁₁	C₂×C₁₁	1	1	yes	characteristic, complemented
16	C₃×C₁₁×D₁₁	—	5	1	no	Hall
17	C₅×C₁₁²	—	2	2	no	—
18	C₅×C₁₁²	C₃×D₅	1	1	yes	characteristic, complemented
19	C₅×C₁₁²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
20	C₅×D₅₅	C₃×C₁₁	1	1	yes	characteristic, direct product factor
21	C₅×D₅×C₁₁	—	11	1	no	—
22	C₃×C₁₁²	C₅×D₅	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₅×C₁₁	—	55	1	no	—
24	C₃×D₅₅	C₅×C₁₁	1	1	yes	characteristic, direct product factor
25	C₃×D₅×C₁₁	—	11	1	no	—
26	C₃×C₅×D₁₁	—	5	1	no	—
27	C₅²×C₁₁	—	2	5	no	—
28	C₅²×C₁₁	C₃×D₁₁	1	1	yes	characteristic, complemented
29	C₅²×C₁₁	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
30	C₁₁×D₁₁	—	5	1	no	Hall
31	C₃×C₅×C₁₁	—	2	20	no	—
32	C₃×C₅×C₁₁	—	2	2	no	—
33	C₃×C₅×C₁₁	—	2	2	no	—
34	C₃×C₅×C₁₁	—	2	5	no	—
35	C₃×C₅×C₁₁	—	2	5	no	—
36	C₃×C₅×C₁₁	D₅×C₁₁	1	1	yes	characteristic, complemented
37	C₃×C₅×C₁₁	C₅×D₁₁	1	1	yes	characteristic, complemented
38	C₃×C₅×C₁₁	D₅₅	1	1	yes	characteristic, direct product factor
39	C₃×C₅×C₁₁	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
40	C₃×C₅×D₅	—	11	1	no	Hall
41	C₁₁²	C₃×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₅×C₁₁	—	55	1	no	—
43	D₅₅	C₃×C₅×C₁₁	1	1	yes	characteristic, direct product factor
44	C₅×D₁₁	—	5	1	no	—
45	D₅×C₁₁	—	11	1	no	—
46	C₃×C₅²	C₁₁×D₁₁	1	1	yes	characteristic, complemented, Hall
47	C₂×C₃×C₁₁	—	55	1	no	—
48	C₃×D₁₁	—	5	1	no	—
49	C₅×C₁₁	—	2	20	no	—
50	C₅×C₁₁	—	2	2	no	—
51	C₅×C₁₁	—	2	2	no	—
52	C₅×C₁₁	—	2	5	no	—
53	C₅×C₁₁	—	2	5	no	—
54	C₅×C₁₁	C₃×C₅×D₁₁	1	1	yes	characteristic, complemented
55	C₅×C₁₁	C₃×D₅×C₁₁	1	1	yes	characteristic, complemented
56	C₅×C₁₁	C₃×D₅₅	1	1	yes	characteristic, direct product factor
57	C₅×C₁₁	C₂×C₃×C₅×C₁₁	1	1	yes	characteristic, complemented
58	C₅×D₅	—	11	1	no	Hall
59	C₃×C₁₁	—	2	5	no	—
60	C₃×C₁₁	C₅×D₅×C₁₁	1	1	yes	characteristic, complemented
61	C₃×C₁₁	C₅×D₅₅	1	1	yes	characteristic, direct product factor
62	C₂×C₃×C₅	—	55	1	no	—
63	C₃×D₅	—	11	1	no	—
64	C₅²	C₃×C₁₁×D₁₁	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₁₁	—	55	1	no	—
66	D₁₁	—	5	1	no	—
67	C₃×C₅	—	2	2	no	—
68	C₃×C₅	C₅×C₁₁×D₁₁	1	1	yes	characteristic, complemented
69	C₃×C₅	C₁₁×D₅₅	1	1	yes	characteristic, direct product factor
70	C₁₁	—	2	5	no	—
71	C₁₁	C₃×C₅×D₅×C₁₁	1	1	yes	characteristic, complemented
72	C₁₁	C₃×C₅×D₅₅	1	1	yes	characteristic, direct product factor
73	C₂×C₅	—	55	1	no	—
74	D₅	—	11	1	no	—
75	C₂×C₃	—	55	1	no	Hall
76	C₅	—	2	2	no	—
77	C₅	C₃×C₅×C₁₁×D₁₁	1	1	yes	characteristic, complemented
78	C₅	C₃×C₁₁×D₅₅	1	1	yes	characteristic, direct product factor
79	C₃	C₅×C₁₁×D₅₅	1	1	yes	characteristic, direct product factor, Sylow
80	C₂	—	55	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₁	D₅₅
commutator, cosocle, hypocenter	C₅×C₁₁	C₂×C₃×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₁²	C₂
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₃×C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₁₁²	C₂	semidirect
2. C₅×C₁₁×D₅₅	C₃	direct (N × H)
3. C₃×C₁₁×D₅₅	C₅	direct (N × H)
5. C₅²×C₁₁²	C₂×C₃	semidirect
7. C₃×C₅×C₁₁²	D₅	semidirect
8. C₃×C₅×C₁₁²	C₂×C₅	semidirect
9. C₃×C₅×D₅₅	C₁₁	direct (N × H)
11. C₁₁×D₅₅	C₃×C₅	direct (N × H)
14. C₃×C₅²×C₁₁	D₁₁	semidirect
15. C₃×C₅²×C₁₁	C₂×C₁₁	semidirect
18. C₅×C₁₁²	C₃×D₅	semidirect
19. C₅×C₁₁²	C₂×C₃×C₅	semidirect
20. C₅×D₅₅	C₃×C₁₁	direct (N × H)
22. C₃×C₁₁²	C₅×D₅	semidirect
24. C₃×D₅₅	C₅×C₁₁	direct (N × H)
28. C₅²×C₁₁	C₃×D₁₁	semidirect
29. C₅²×C₁₁	C₂×C₃×C₁₁	semidirect
36. C₃×C₅×C₁₁	D₅×C₁₁	semidirect
37. C₃×C₅×C₁₁	C₅×D₁₁	semidirect
38. C₃×C₅×C₁₁	D₅₅	direct (N × H)
39. C₃×C₅×C₁₁	C₂×C₅×C₁₁	semidirect
41. C₁₁²	C₃×C₅×D₅	semidirect
43. D₅₅	C₃×C₅×C₁₁	direct (N × H)
46. C₃×C₅²	C₁₁×D₁₁	semidirect
54. C₅×C₁₁	C₃×C₅×D₁₁	semidirect
55. C₅×C₁₁	C₃×D₅×C₁₁	semidirect
56. C₅×C₁₁	C₃×D₅₅	direct (N × H)
57. C₅×C₁₁	C₂×C₃×C₅×C₁₁	semidirect
60. C₃×C₁₁	C₅×D₅×C₁₁	semidirect
61. C₃×C₁₁	C₅×D₅₅	direct (N × H)
64. C₅²	C₃×C₁₁×D₁₁	semidirect
68. C₃×C₅	C₅×C₁₁×D₁₁	semidirect
69. C₃×C₅	C₁₁×D₅₅	direct (N × H)
71. C₁₁	C₃×C₅×D₅×C₁₁	semidirect
72. C₁₁	C₃×C₅×D₅₅	direct (N × H)
77. C₅	C₃×C₅×C₁₁×D₁₁	semidirect
78. C₅	C₃×C₁₁×D₅₅	direct (N × H)
79. C₃	C₅×C₁₁×D₅₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅²×C₁₁²	2
C₅×C₁₁×D₅₅	3
C₃×C₁₁×D₅₅	5
C₃×C₅×C₁₁×D₁₁	5
C₃×C₅×D₅₅	11
C₃×C₅×D₅×C₁₁	11

Subgroups — C3×C5×C11×D55 #31827717

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₁₁×D₅₅ #31827717