Subgroups — C₅×D₃²×C₁₁² #36345323

Order 21780.

616 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₃×C₁₁²	C₂	1	2	yes	maximal, complemented
2	C₅×C₁₁²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₃×C₁₁²	—	3	2	no	maximal
4	C₃²×C₅×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃²×C₁₁²	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×D₃×C₁₁²	—	3	2	no	—
7	C₅×D₃×C₁₁²	—	6	1	no	—
8	C₅×D₃×C₁₁²	D₃	1	2	yes	direct product factor
9	C₂×C₃×C₅×C₁₁²	—	3	2	no	—
10	C₂²×C₅×C₁₁²	—	9	1	no	Hall
11	C₁₁²×C₃⋊D₃	C₂×C₅	1	1	yes	characteristic, complemented
12	C₃×D₃×C₁₁²	C₂×C₅	1	2	yes	complemented
13	C₅×D₃²×C₁₁	C₁₁	1	12	yes	maximal, direct product factor
14	C₃×C₅×C₁₁²	—	2	1	no	—
15	C₃×C₅×C₁₁²	C₂×D₃	1	2	yes	complemented
16	C₂×D₃×C₁₁²	—	3	2	no	—
17	C₂×C₅×C₁₁²	—	3	2	no	—
18	C₂×C₅×C₁₁²	—	9	1	no	—
19	C₃²×C₁₁²	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
20	C₅×C₁₁×C₃⋊D₃	C₂×C₁₁	1	12	yes	complemented
21	C₃×C₅×D₃×C₁₁	C₂×C₁₁	1	24	yes	complemented
22	C₂×C₃×C₁₁²	—	3	2	no	—
23	D₃×C₁₁²	—	3	2	no	—
24	D₃×C₁₁²	—	6	1	no	—
25	D₃×C₁₁²	C₅×D₃	1	2	yes	direct product factor
26	C₂×C₅×D₃×C₁₁	—	3	24	no	—
27	C₅×C₁₁²	D₃²	1	1	yes	characteristic, direct product factor, Hall
28	C₃²×C₅×C₁₁	C₂²×C₁₁	1	12	yes	complemented
29	C₂²×C₁₁²	—	9	1	no	Hall
30	D₃²×C₁₁	C₅×C₁₁	1	12	yes	direct product factor
31	C₃×C₁₁²	—	2	1	no	—
32	C₃×C₁₁²	C₂×C₅×D₃	1	2	yes	complemented
33	C₂×C₃×C₅×C₁₁	—	3	24	no	—
34	C₅×D₃×C₁₁	—	3	24	no	—
35	C₅×D₃×C₁₁	—	6	12	no	—
36	C₅×D₃×C₁₁	D₃×C₁₁	1	24	yes	direct product factor
37	C₂×C₁₁²	—	3	2	no	—
38	C₂×C₁₁²	—	9	1	no	—
39	C₂²×C₅×C₁₁	—	9	12	no	—
40	C₁₁×C₃⋊D₃	C₂×C₅×C₁₁	1	12	yes	complemented
41	C₃×D₃×C₁₁	C₂×C₅×C₁₁	1	24	yes	complemented
42	C₅×D₃²	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
43	C₃×C₅×C₁₁	—	2	12	no	—
44	C₃×C₅×C₁₁	C₂×D₃×C₁₁	1	24	yes	complemented
45	C₂×D₃×C₁₁	—	3	24	no	—
46	C₁₁²	C₅×D₃²	1	1	yes	characteristic, direct product factor, Sylow
47	C₂×C₅×C₁₁	—	3	24	no	—
48	C₂×C₅×C₁₁	—	9	12	no	—
49	C₃²×C₁₁	C₂²×C₅×C₁₁	1	12	yes	complemented
50	C₅×C₃⋊D₃	C₂×C₁₁²	1	1	yes	characteristic, complemented
51	C₃×C₅×D₃	C₂×C₁₁²	1	2	yes	complemented
52	C₂×C₃×C₁₁	—	3	24	no	—
53	D₃×C₁₁	—	3	24	no	—
54	D₃×C₁₁	—	6	12	no	—
55	D₃×C₁₁	C₅×D₃×C₁₁	1	24	yes	direct product factor
56	C₂×C₅×D₃	—	3	2	no	—
57	C₅×C₁₁	D₃²×C₁₁	1	12	yes	direct product factor
58	C₃²×C₅	C₂²×C₁₁²	1	1	yes	characteristic, complemented, Hall
59	C₂²×C₁₁	—	9	12	no	—
60	D₃²	C₅×C₁₁²	1	1	yes	characteristic, direct product factor, Hall
61	C₃×C₁₁	—	2	12	no	—
62	C₃×C₁₁	C₂×C₅×D₃×C₁₁	1	24	yes	complemented
63	C₂×C₃×C₅	—	3	2	no	—
64	C₅×D₃	—	3	2	no	—
65	C₅×D₃	—	6	1	no	—
66	C₅×D₃	D₃×C₁₁²	1	2	yes	direct product factor
67	C₂×C₁₁	—	3	24	no	—
68	C₂×C₁₁	—	9	12	no	—
69	C₂²×C₅	—	9	1	no	Hall
70	C₃⋊D₃	C₂×C₅×C₁₁²	1	1	yes	characteristic, complemented
71	C₃×D₃	C₂×C₅×C₁₁²	1	2	yes	complemented
72	C₃×C₅	—	2	1	no	—
73	C₃×C₅	C₂×D₃×C₁₁²	1	2	yes	complemented
74	C₂×D₃	—	3	2	no	—
75	C₁₁	C₅×D₃²×C₁₁	1	12	yes	direct product factor
76	C₂×C₅	—	3	2	no	—
77	C₂×C₅	—	9	1	no	—
78	C₃²	C₂²×C₅×C₁₁²	1	1	yes	characteristic, complemented, Sylow
79	C₂×C₃	—	3	2	no	—
80	D₃	—	3	2	no	—
81	D₃	—	6	1	no	—
82	D₃	C₅×D₃×C₁₁²	1	2	yes	direct product factor
83	C₅	D₃²×C₁₁²	1	1	yes	characteristic, direct product factor, Sylow
84	C₂²	—	9	1	no	Sylow
85	C₃	—	2	1	no	—
86	C₃	C₂×C₅×D₃×C₁₁²	1	2	yes	complemented
87	C₂	—	3	2	no	—
88	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₁₁²	D₃²
commutator, cosocle, hypocenter	C₃²	C₂²×C₅×C₁₁²
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₁²	C₂²
LCS	G ▷ C₃²
UCS	C₁ ◁ C₅×C₁₁²

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×D₃×C₁₁²	C₂	semidirect
2. C₅×C₁₁²×C₃⋊D₃	C₂	semidirect
4. C₃²×C₅×C₁₁²	C₂²	semidirect
5. D₃²×C₁₁²	C₅	direct (N × H)
8. C₅×D₃×C₁₁²	D₃	direct (N × H)
11. C₁₁²×C₃⋊D₃	C₂×C₅	semidirect
12. C₃×D₃×C₁₁²	C₂×C₅	semidirect
13. C₅×D₃²×C₁₁	C₁₁	direct (N × H)
15. C₃×C₅×C₁₁²	C₂×D₃	semidirect
19. C₃²×C₁₁²	C₂²×C₅	semidirect
20. C₅×C₁₁×C₃⋊D₃	C₂×C₁₁	semidirect
21. C₃×C₅×D₃×C₁₁	C₂×C₁₁	semidirect
25. D₃×C₁₁²	C₅×D₃	direct (N × H)
27. C₅×C₁₁²	D₃²	direct (N × H)
28. C₃²×C₅×C₁₁	C₂²×C₁₁	semidirect
30. D₃²×C₁₁	C₅×C₁₁	direct (N × H)
32. C₃×C₁₁²	C₂×C₅×D₃	semidirect
36. C₅×D₃×C₁₁	D₃×C₁₁	direct (N × H)
40. C₁₁×C₃⋊D₃	C₂×C₅×C₁₁	semidirect
41. C₃×D₃×C₁₁	C₂×C₅×C₁₁	semidirect
42. C₅×D₃²	C₁₁²	direct (N × H)
44. C₃×C₅×C₁₁	C₂×D₃×C₁₁	semidirect
46. C₁₁²	C₅×D₃²	direct (N × H)
49. C₃²×C₁₁	C₂²×C₅×C₁₁	semidirect
50. C₅×C₃⋊D₃	C₂×C₁₁²	semidirect
51. C₃×C₅×D₃	C₂×C₁₁²	semidirect
55. D₃×C₁₁	C₅×D₃×C₁₁	direct (N × H)
57. C₅×C₁₁	D₃²×C₁₁	direct (N × H)
58. C₃²×C₅	C₂²×C₁₁²	semidirect
60. D₃²	C₅×C₁₁²	direct (N × H)
62. C₃×C₁₁	C₂×C₅×D₃×C₁₁	semidirect
66. C₅×D₃	D₃×C₁₁²	direct (N × H)
70. C₃⋊D₃	C₂×C₅×C₁₁²	semidirect
71. C₃×D₃	C₂×C₅×C₁₁²	semidirect
73. C₃×C₅	C₂×D₃×C₁₁²	semidirect
75. C₁₁	C₅×D₃²×C₁₁	direct (N × H)
78. C₃²	C₂²×C₅×C₁₁²	semidirect
82. D₃	C₅×D₃×C₁₁²	direct (N × H)
83. C₅	D₃²×C₁₁²	direct (N × H)
86. C₃	C₂×C₅×D₃×C₁₁²	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×D₃×C₁₁²	2
C₅×C₁₁²×C₃⋊D₃	2
C₂×C₅×D₃×C₁₁²	3
D₃²×C₁₁²	5
C₅×D₃²×C₁₁	11

Subgroups — C5×D32×C112 #36345323

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃²×C₁₁² #36345323