Subgroups — C₃×D₅×C₁₃×C₁₁⋊C₅ #36339727

Order 21450.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₃×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅×C₁₃×C₁₁⋊C₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₅×C₁₁×C₁₃	C₅	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₁₃×C₁₁⋊C₅	—	5	1	no	maximal
5	C₅×C₁₃×C₁₁⋊C₅	C₂×C₃	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₃×C₁₁⋊C₅	—	2	2	no	—
7	C₃×C₁₃×C₁₁⋊C₅	D₅	1	1	yes	characteristic, direct product factor
8	C₃×C₅×C₁₁×C₁₃	C₂×C₅	1	1	yes	characteristic, complemented
9	C₃×C₅×D₅×C₁₃	—	11	1	no	maximal, Hall
10	C₃×D₅×C₁₁⋊C₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	D₅×C₁₁×C₁₃	C₃×C₅	1	1	yes	characteristic, complemented
12	C₂×C₁₃×C₁₁⋊C₅	—	5	1	no	—
13	C₃×C₅²×C₁₃	—	11	1	no	Hall
14	C₂×C₃×C₁₁×C₁₃	—	5	1	no	Hall
15	C₃×C₅×C₁₁⋊C₅	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
16	C₅×C₁₁×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
17	C₁₃×C₁₁⋊C₅	—	2	2	no	—
18	C₁₃×C₁₁⋊C₅	C₃×D₅	1	1	yes	characteristic, direct product factor
19	C₅×D₅×C₁₃	—	11	1	no	Hall
20	D₅×C₁₁⋊C₅	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₁₁×C₁₃	C₅×D₅	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₅×C₁₃	—	55	1	no	—
23	C₃×D₅×C₁₃	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
24	C₃×D₅×C₁₁	C₅×C₁₃	1	1	yes	characteristic, complemented
25	C₂×C₃×C₁₁⋊C₅	—	5	1	no	—
26	C₅²×C₁₃	—	11	1	no	Hall
27	C₂×C₁₁×C₁₃	—	5	1	no	Hall
28	C₅×C₁₁⋊C₅	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
29	C₃×C₅×C₁₃	—	11	1	no	—
30	C₃×C₅×C₁₃	—	22	2	no	—
31	C₃×C₅×C₁₃	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented
32	C₃×C₅×C₁₁	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented
33	C₃×C₁₁⋊C₅	—	2	2	no	—
34	C₃×C₁₁⋊C₅	D₅×C₁₃	1	1	yes	characteristic, direct product factor
35	C₃×C₅×D₅	—	11	1	no	Hall
36	C₁₁×C₁₃	C₃×C₅×D₅	1	1	yes	characteristic, complemented, Hall
37	C₂×C₅×C₁₃	—	55	1	no	—
38	D₅×C₁₃	C₃×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
39	D₅×C₁₁	C₃×C₅×C₁₃	1	1	yes	characteristic, complemented
40	C₂×C₁₁⋊C₅	—	5	1	no	—
41	C₂×C₃×C₁₃	—	5	1	no	Hall
42	C₃×C₅²	—	11	1	no	Hall
43	C₂×C₃×C₁₁	—	5	1	no	Hall
44	C₅×C₁₃	—	11	1	no	—
45	C₅×C₁₃	—	22	2	no	—
46	C₅×C₁₃	C₂×C₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
47	C₅×C₁₁	C₂×C₃×C₅×C₁₃	1	1	yes	characteristic, complemented
48	C₁₁⋊C₅	—	2	2	no	—
49	C₁₁⋊C₅	C₃×D₅×C₁₃	1	1	yes	characteristic, direct product factor
50	C₅×D₅	—	11	1	no	Hall
51	C₃×C₁₃	D₅×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
52	C₃×C₁₁	C₅×D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
53	C₂×C₃×C₅	—	55	1	no	—
54	C₃×D₅	C₁₃×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
55	C₂×C₁₃	—	5	1	no	Hall
56	C₅²	—	11	1	no	Sylow
57	C₂×C₁₁	—	5	1	no	Hall
58	C₃×C₅	—	11	1	no	—
59	C₃×C₅	—	22	2	no	—
60	C₃×C₅	C₂×C₁₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
61	C₁₃	C₃×D₅×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
62	C₁₁	C₃×C₅×D₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
63	C₂×C₅	—	55	1	no	—
64	D₅	C₃×C₁₃×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
65	C₂×C₃	—	5	1	no	Hall
66	C₅	—	11	1	no	—
67	C₅	—	22	2	no	—
68	C₅	C₂×C₃×C₁₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
69	C₃	D₅×C₁₃×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
70	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₃	D₅×C₁₁⋊C₅
commutator, cosocle, hypocenter	C₅×C₁₁	C₂×C₃×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₁₃	C₂×C₅
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₃×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₃×C₁₁⋊C₅	C₂	semidirect
2. D₅×C₁₃×C₁₁⋊C₅	C₃	direct (N × H)
3. C₃×D₅×C₁₁×C₁₃	C₅	semidirect
5. C₅×C₁₃×C₁₁⋊C₅	C₂×C₃	semidirect
7. C₃×C₁₃×C₁₁⋊C₅	D₅	direct (N × H)
8. C₃×C₅×C₁₁×C₁₃	C₂×C₅	semidirect
10. C₃×D₅×C₁₁⋊C₅	C₁₃	direct (N × H)
11. D₅×C₁₁×C₁₃	C₃×C₅	semidirect
15. C₃×C₅×C₁₁⋊C₅	C₂×C₁₃	semidirect
16. C₅×C₁₁×C₁₃	C₂×C₃×C₅	semidirect
18. C₁₃×C₁₁⋊C₅	C₃×D₅	direct (N × H)
20. D₅×C₁₁⋊C₅	C₃×C₁₃	direct (N × H)
21. C₃×C₁₁×C₁₃	C₅×D₅	semidirect
23. C₃×D₅×C₁₃	C₁₁⋊C₅	direct (N × H)
24. C₃×D₅×C₁₁	C₅×C₁₃	semidirect
28. C₅×C₁₁⋊C₅	C₂×C₃×C₁₃	semidirect
31. C₃×C₅×C₁₃	C₂×C₁₁⋊C₅	semidirect
32. C₃×C₅×C₁₁	C₂×C₅×C₁₃	semidirect
34. C₃×C₁₁⋊C₅	D₅×C₁₃	direct (N × H)
36. C₁₁×C₁₃	C₃×C₅×D₅	semidirect
38. D₅×C₁₃	C₃×C₁₁⋊C₅	direct (N × H)
39. D₅×C₁₁	C₃×C₅×C₁₃	semidirect
46. C₅×C₁₃	C₂×C₃×C₁₁⋊C₅	semidirect
47. C₅×C₁₁	C₂×C₃×C₅×C₁₃	semidirect
49. C₁₁⋊C₅	C₃×D₅×C₁₃	direct (N × H)
51. C₃×C₁₃	D₅×C₁₁⋊C₅	direct (N × H)
52. C₃×C₁₁	C₅×D₅×C₁₃	semidirect
54. C₃×D₅	C₁₃×C₁₁⋊C₅	direct (N × H)
60. C₃×C₅	C₂×C₁₃×C₁₁⋊C₅	semidirect
61. C₁₃	C₃×D₅×C₁₁⋊C₅	direct (N × H)
62. C₁₁	C₃×C₅×D₅×C₁₃	semidirect
64. D₅	C₃×C₁₃×C₁₁⋊C₅	direct (N × H)
68. C₅	C₂×C₃×C₁₃×C₁₁⋊C₅	semidirect
69. C₃	D₅×C₁₃×C₁₁⋊C₅	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×C₅×C₁₃×C₁₁⋊C₅	2
D₅×C₁₃×C₁₁⋊C₅	3
C₃×D₅×C₁₁×C₁₃	5
C₂×C₃×C₁₃×C₁₁⋊C₅	5
C₃×C₅×D₅×C₁₃	11
C₃×D₅×C₁₁⋊C₅	13

Subgroups — C3×D5×C13×C11⋊C5 #36339727

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×C₁₃×C₁₁⋊C₅ #36339727