Subgroups — D₃×C₇×D₅×C₁₁ #17987708

Order 4620.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₁×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃×C₇×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×D₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×D₅×C₁₁	—	3	1	no	maximal, Hall
5	C₃×C₅×C₇×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×D₃×C₇×C₁₁	—	5	1	no	maximal, Hall
7	C₂×C₅×C₇×C₁₁	—	3	1	no	—
8	C₇×D₅×C₁₁	—	3	1	no	—
9	C₇×D₅×C₁₁	D₃	1	1	yes	characteristic, direct product factor
10	D₃×D₅×C₁₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₇×C₁₁	—	5	1	no	—
12	D₃×C₇×C₁₁	—	5	1	no	—
13	D₃×C₇×C₁₁	D₅	1	1	yes	characteristic, direct product factor
14	D₃×C₇×D₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₅×C₇×C₁₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
16	C₁₁×D₁₅	C₂×C₇	1	1	yes	characteristic, complemented
17	C₅×D₃×C₁₁	C₂×C₇	1	1	yes	characteristic, complemented
18	C₃×D₅×C₁₁	C₂×C₇	1	1	yes	characteristic, complemented
19	C₂²×C₇×C₁₁	—	15	1	no	Hall
20	C₃×C₇×C₁₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
21	C₂×D₅×C₁₁	—	3	1	no	Hall
22	C₇×D₁₅	C₂×C₁₁	1	1	yes	characteristic, complemented
23	C₅×D₃×C₇	C₂×C₁₁	1	1	yes	characteristic, complemented
24	C₃×C₇×D₅	C₂×C₁₁	1	1	yes	characteristic, complemented
25	C₃×C₅×C₁₁	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇×C₁₁	—	3	1	no	—
27	C₂×C₇×C₁₁	—	5	1	no	—
28	C₂×C₇×C₁₁	—	15	1	no	—
29	C₂×C₇×D₅	—	3	1	no	Hall
30	C₂×D₃×C₁₁	—	5	1	no	Hall
31	C₂×C₅×C₁₁	—	3	1	no	—
32	D₅×C₁₁	—	3	1	no	—
33	D₅×C₁₁	D₃×C₇	1	1	yes	characteristic, direct product factor
34	C₃×C₅×C₇	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
35	C₂×D₃×C₇	—	5	1	no	Hall
36	C₇×C₁₁	D₃×D₅	1	1	yes	characteristic, direct product factor, Hall
37	C₂×C₅×C₇	—	3	1	no	—
38	C₇×D₅	—	3	1	no	—
39	C₇×D₅	D₃×C₁₁	1	1	yes	characteristic, direct product factor
40	C₂×C₃×C₁₁	—	5	1	no	—
41	D₃×C₁₁	—	5	1	no	—
42	D₃×C₁₁	C₇×D₅	1	1	yes	characteristic, direct product factor
43	D₃×D₅	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
44	C₅×C₁₁	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Hall
45	C₂²×C₁₁	—	15	1	no	Hall
46	C₂×C₃×C₇	—	5	1	no	—
47	D₃×C₇	—	5	1	no	—
48	D₃×C₇	D₅×C₁₁	1	1	yes	characteristic, direct product factor
49	C₅×C₇	C₂×D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
50	C₃×C₁₁	C₂×C₇×D₅	1	1	yes	characteristic, complemented, Hall
51	D₁₅	C₂×C₇×C₁₁	1	1	yes	characteristic, complemented
52	C₃×D₅	C₂×C₇×C₁₁	1	1	yes	characteristic, complemented
53	C₅×D₃	C₂×C₇×C₁₁	1	1	yes	characteristic, complemented
54	C₂²×C₇	—	15	1	no	Hall
55	C₂×C₁₁	—	3	1	no	—
56	C₂×C₁₁	—	5	1	no	—
57	C₂×C₁₁	—	15	1	no	—
58	C₃×C₇	C₂×D₅×C₁₁	1	1	yes	characteristic, complemented, Hall
59	C₂×D₅	—	3	1	no	Hall
60	C₃×C₅	C₂²×C₇×C₁₁	1	1	yes	characteristic, complemented, Hall
61	C₂×C₇	—	3	1	no	—
62	C₂×C₇	—	5	1	no	—
63	C₂×C₇	—	15	1	no	—
64	C₂×D₃	—	5	1	no	Hall
65	C₁₁	D₃×C₇×D₅	1	1	yes	characteristic, direct product factor, Sylow
66	C₂×C₅	—	3	1	no	—
67	D₅	—	3	1	no	—
68	D₅	D₃×C₇×C₁₁	1	1	yes	characteristic, direct product factor
69	C₇	D₃×D₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
70	C₂×C₃	—	5	1	no	—
71	D₃	—	5	1	no	—
72	D₃	C₇×D₅×C₁₁	1	1	yes	characteristic, direct product factor
73	C₅	C₂×D₃×C₇×C₁₁	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	15	1	no	Sylow
75	C₃	C₂×C₇×D₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	3	1	no	—
77	C₂	—	5	1	no	—
78	C₂	—	15	1	no	—

	subgroup	G/H
center, hypercenter	C₇×C₁₁	D₃×D₅
commutator, cosocle, hypocenter	C₃×C₅	C₂²×C₇×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₁	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₇×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₁×D₁₅	C₂	semidirect
2. C₅×D₃×C₇×C₁₁	C₂	semidirect
3. C₃×C₇×D₅×C₁₁	C₂	semidirect
5. C₃×C₅×C₇×C₁₁	C₂²	semidirect
9. C₇×D₅×C₁₁	D₃	direct (N × H)
10. D₃×D₅×C₁₁	C₇	direct (N × H)
13. D₃×C₇×C₁₁	D₅	direct (N × H)
14. D₃×C₇×D₅	C₁₁	direct (N × H)
15. C₅×C₇×C₁₁	C₂×D₃	semidirect
16. C₁₁×D₁₅	C₂×C₇	semidirect
17. C₅×D₃×C₁₁	C₂×C₇	semidirect
18. C₃×D₅×C₁₁	C₂×C₇	semidirect
20. C₃×C₇×C₁₁	C₂×D₅	semidirect
22. C₇×D₁₅	C₂×C₁₁	semidirect
23. C₅×D₃×C₇	C₂×C₁₁	semidirect
24. C₃×C₇×D₅	C₂×C₁₁	semidirect
25. C₃×C₅×C₁₁	C₂²×C₇	semidirect
33. D₅×C₁₁	D₃×C₇	direct (N × H)
34. C₃×C₅×C₇	C₂²×C₁₁	semidirect
36. C₇×C₁₁	D₃×D₅	direct (N × H)
39. C₇×D₅	D₃×C₁₁	direct (N × H)
42. D₃×C₁₁	C₇×D₅	direct (N × H)
43. D₃×D₅	C₇×C₁₁	direct (N × H)
44. C₅×C₁₁	C₂×D₃×C₇	semidirect
48. D₃×C₇	D₅×C₁₁	direct (N × H)
49. C₅×C₇	C₂×D₃×C₁₁	semidirect
50. C₃×C₁₁	C₂×C₇×D₅	semidirect
51. D₁₅	C₂×C₇×C₁₁	semidirect
52. C₃×D₅	C₂×C₇×C₁₁	semidirect
53. C₅×D₃	C₂×C₇×C₁₁	semidirect
58. C₃×C₇	C₂×D₅×C₁₁	semidirect
60. C₃×C₅	C₂²×C₇×C₁₁	semidirect
65. C₁₁	D₃×C₇×D₅	direct (N × H)
68. D₅	D₃×C₇×C₁₁	direct (N × H)
69. C₇	D₃×D₅×C₁₁	direct (N × H)
72. D₃	C₇×D₅×C₁₁	direct (N × H)
73. C₅	C₂×D₃×C₇×C₁₁	semidirect
75. C₃	C₂×C₇×D₅×C₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₁₁×D₁₅	2
C₅×D₃×C₇×C₁₁	2
C₃×C₇×D₅×C₁₁	2
C₂×C₇×D₅×C₁₁	3
C₂×D₃×C₇×C₁₁	5
D₃×D₅×C₁₁	7
D₃×C₇×D₅	11

Subgroups — D3×C7×D5×C11 #17987708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₇×D₅×C₁₁ #17987708