Subgroups — C₃×C₁₃×D₃₈₅ #44473239

Order 30030.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₃₈₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₃×D₇₇	—	5	1	no	maximal, Hall
4	C₅×C₇×C₁₁×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₃×D₅₅	—	7	1	no	maximal, Hall
6	C₃×C₇×C₁₁×C₁₃	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₃×D₃₅	—	11	1	no	maximal, Hall
8	C₃×D₃₈₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₅×C₁₁×C₁₃	D₇	1	1	yes	characteristic, complemented, Hall
10	C₁₃×D₇₇	—	5	1	no	Hall
11	C₁₃×D₅₅	—	7	1	no	Hall
12	C₃×C₅×C₇×C₁₃	D₁₁	1	1	yes	characteristic, complemented, Hall
13	C₃×C₅×C₇×C₁₁	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
14	C₇×C₁₁×C₁₃	C₃×D₅	1	1	yes	characteristic, complemented, Hall
15	C₁₃×D₃₅	—	11	1	no	Hall
16	C₃×C₁₃×D₁₁	—	35	1	no	Hall
17	D₃₈₅	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
18	C₅×C₁₁×C₁₃	C₃×D₇	1	1	yes	characteristic, complemented, Hall
19	C₃×C₁₃×D₇	—	55	1	no	Hall
20	C₃×D₇₇	—	5	1	no	Hall
21	C₅×C₇×C₁₃	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
22	C₃×C₁₁×C₁₃	D₃₅	1	1	yes	characteristic, complemented, Hall
23	C₃×D₅×C₁₃	—	77	1	no	Hall
24	C₅×C₇×C₁₁	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₃×D₅₅	—	7	1	no	Hall
26	C₁₃×D₁₁	—	35	1	no	Hall
27	C₃×C₇×C₁₃	D₅₅	1	1	yes	characteristic, complemented, Hall
28	C₃×C₇×C₁₁	D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
29	C₃×D₃₅	—	11	1	no	Hall
30	C₃×C₅×C₁₃	D₇₇	1	1	yes	characteristic, complemented, Hall
31	C₁₃×D₇	—	55	1	no	Hall
32	C₃×C₅×C₁₁	C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
33	D₇₇	—	5	1	no	Hall
34	C₁₁×C₁₃	C₃×D₃₅	1	1	yes	characteristic, complemented, Hall
35	D₅×C₁₃	—	77	1	no	Hall
36	D₅₅	—	7	1	no	Hall
37	C₃×C₅×C₇	C₁₃×D₁₁	1	1	yes	characteristic, complemented, Hall
38	C₇×C₁₃	C₃×D₅₅	1	1	yes	characteristic, complemented, Hall
39	C₂×C₃×C₁₃	—	385	1	no	Hall
40	C₇×C₁₁	C₃×D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
41	D₃₅	—	11	1	no	Hall
42	C₃×D₁₁	—	35	1	no	Hall
43	C₅×C₁₃	C₃×D₇₇	1	1	yes	characteristic, complemented, Hall
44	C₅×C₁₁	C₃×C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
45	C₃×D₇	—	55	1	no	Hall
46	C₃×C₁₃	D₃₈₅	1	1	yes	characteristic, direct product factor, Hall
47	C₅×C₇	C₃×C₁₃×D₁₁	1	1	yes	characteristic, complemented, Hall
48	C₃×C₁₁	C₁₃×D₃₅	1	1	yes	characteristic, complemented, Hall
49	C₃×D₅	—	77	1	no	Hall
50	C₂×C₁₃	—	385	1	no	Hall
51	D₁₁	—	35	1	no	Hall
52	C₃×C₇	C₁₃×D₅₅	1	1	yes	characteristic, complemented, Hall
53	C₃×C₅	C₁₃×D₇₇	1	1	yes	characteristic, complemented, Hall
54	D₇	—	55	1	no	Hall
55	C₁₃	C₃×D₃₈₅	1	1	yes	characteristic, direct product factor, Sylow
56	C₁₁	C₃×C₁₃×D₃₅	1	1	yes	characteristic, complemented, Sylow
57	D₅	—	77	1	no	Hall
58	C₇	C₃×C₁₃×D₅₅	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₃	—	385	1	no	Hall
60	C₅	C₃×C₁₃×D₇₇	1	1	yes	characteristic, complemented, Sylow
61	C₃	C₁₃×D₃₈₅	1	1	yes	characteristic, direct product factor, Sylow
62	C₂	—	385	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₃	D₃₈₅
commutator, cosocle, hypocenter	C₅×C₇×C₁₁	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₁×C₁₃	C₂
LCS	G ▷ C₅×C₇×C₁₁
UCS	C₁ ◁ C₃×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇×C₁₁×C₁₃	C₂	semidirect
2. C₁₃×D₃₈₅	C₃	direct (N × H)
4. C₅×C₇×C₁₁×C₁₃	C₂×C₃	semidirect
6. C₃×C₇×C₁₁×C₁₃	D₅	semidirect
8. C₃×D₃₈₅	C₁₃	direct (N × H)
9. C₃×C₅×C₁₁×C₁₃	D₇	semidirect
12. C₃×C₅×C₇×C₁₃	D₁₁	semidirect
13. C₃×C₅×C₇×C₁₁	C₂×C₁₃	semidirect
14. C₇×C₁₁×C₁₃	C₃×D₅	semidirect
17. D₃₈₅	C₃×C₁₃	direct (N × H)
18. C₅×C₁₁×C₁₃	C₃×D₇	semidirect
21. C₅×C₇×C₁₃	C₃×D₁₁	semidirect
22. C₃×C₁₁×C₁₃	D₃₅	semidirect
24. C₅×C₇×C₁₁	C₂×C₃×C₁₃	semidirect
27. C₃×C₇×C₁₃	D₅₅	semidirect
28. C₃×C₇×C₁₁	D₅×C₁₃	semidirect
30. C₃×C₅×C₁₃	D₇₇	semidirect
32. C₃×C₅×C₁₁	C₁₃×D₇	semidirect
34. C₁₁×C₁₃	C₃×D₃₅	semidirect
37. C₃×C₅×C₇	C₁₃×D₁₁	semidirect
38. C₇×C₁₃	C₃×D₅₅	semidirect
40. C₇×C₁₁	C₃×D₅×C₁₃	semidirect
43. C₅×C₁₃	C₃×D₇₇	semidirect
44. C₅×C₁₁	C₃×C₁₃×D₇	semidirect
46. C₃×C₁₃	D₃₈₅	direct (N × H)
47. C₅×C₇	C₃×C₁₃×D₁₁	semidirect
48. C₃×C₁₁	C₁₃×D₃₅	semidirect
52. C₃×C₇	C₁₃×D₅₅	semidirect
53. C₃×C₅	C₁₃×D₇₇	semidirect
55. C₁₃	C₃×D₃₈₅	direct (N × H)
56. C₁₁	C₃×C₁₃×D₃₅	semidirect
58. C₇	C₃×C₁₃×D₅₅	semidirect
60. C₅	C₃×C₁₃×D₇₇	semidirect
61. C₃	C₁₃×D₃₈₅	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×C₇×C₁₁×C₁₃	2
C₁₃×D₃₈₅	3
C₃×C₁₃×D₇₇	5
C₃×C₁₃×D₅₅	7
C₃×C₁₃×D₃₅	11
C₃×D₃₈₅	13

Subgroups — C3×C13×D385 #44473239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₃×D₃₈₅ #44473239