Subgroups — C₁₃×C₃⋊(C₅⋊D₈₅) #45684196

Order 33150.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₁₃×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×C₅⋊D₈₅	—	3	1	no	maximal, Hall
3	C₁₃×D₂₅₅	—	5	6	no	maximal
4	C₅²×C₁₃×C₁₇	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₁₃×C₁₇	D₅	1	6	yes	complemented
6	C₃⋊(C₅⋊D₈₅)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₃×D₈₅	—	15	6	no	—
8	C₁₃×C₃⋊(C₅⋊D₅)	—	17	1	no	maximal, Hall
9	C₁₃×D₅₁	—	25	1	no	Hall
10	C₃×C₅²×C₁₇	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
11	C₅×C₁₃×C₁₇	D₁₅	1	6	yes	complemented
12	C₃×C₅²×C₁₃	D₁₇	1	1	yes	characteristic, complemented, Hall
13	C₅⋊D₈₅	—	3	1	no	Hall
14	C₃×C₁₃×C₁₇	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
15	C₁₃×C₅⋊D₅	—	51	1	no	Hall
16	D₂₅₅	—	5	6	no	—
17	C₁₃×D₁₇	—	75	1	no	Hall
18	C₅²×C₁₇	D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
19	C₁₃×D₁₅	—	85	6	no	—
20	C₅²×C₁₃	D₅₁	1	1	yes	characteristic, complemented, Hall
21	C₃×C₅×C₁₇	D₅×C₁₃	1	6	yes	complemented
22	C₁₃×C₁₇	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₁₃	D₈₅	1	6	yes	complemented
24	D₈₅	—	15	6	no	—
25	C₃⋊(C₅⋊D₅)	—	17	1	no	Hall
26	D₅×C₁₃	—	255	6	no	—
27	D₅₁	—	25	1	no	Hall
28	C₅×C₁₇	C₁₃×D₁₅	1	6	yes	complemented
29	D₃×C₁₃	—	425	1	no	Hall
30	C₃×C₅²	C₁₃×D₁₇	1	1	yes	characteristic, complemented, Hall
31	C₅×C₁₃	D₂₅₅	1	6	yes	complemented
32	C₃×C₁₇	C₁₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
33	C₅⋊D₅	—	51	1	no	Hall
34	C₃×C₁₃	C₅⋊D₈₅	1	1	yes	characteristic, complemented, Hall
35	D₁₇	—	75	1	no	Hall
36	D₁₅	—	85	6	no	—
37	C₂×C₁₃	—	1275	1	no	Hall
38	C₅²	C₁₃×D₅₁	1	1	yes	characteristic, complemented, Sylow
39	C₁₇	C₁₃×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₅	C₁₃×D₈₅	1	6	yes	complemented
41	C₁₃	C₃⋊(C₅⋊D₈₅)	1	1	yes	characteristic, direct product factor, Sylow
42	D₅	—	255	6	no	—
43	D₃	—	425	1	no	Hall
44	C₅	C₁₃×D₂₅₅	1	6	yes	complemented
45	C₃	C₁₃×C₅⋊D₈₅	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	1275	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	C₃⋊(C₅⋊D₈₅)
commutator, cosocle, hypocenter	C₃×C₅²×C₁₇	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₃×C₁₇	C₂
LCS	G ▷ C₃×C₅²×C₁₇
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₁₃×C₁₇	C₂	semidirect
4. C₅²×C₁₃×C₁₇	D₃	semidirect
5. C₃×C₅×C₁₃×C₁₇	D₅	semidirect
6. C₃⋊(C₅⋊D₈₅)	C₁₃	direct (N × H)
10. C₃×C₅²×C₁₇	C₂×C₁₃	semidirect
11. C₅×C₁₃×C₁₇	D₁₅	semidirect
12. C₃×C₅²×C₁₃	D₁₇	semidirect
14. C₃×C₁₃×C₁₇	C₅⋊D₅	semidirect
18. C₅²×C₁₇	D₃×C₁₃	semidirect
20. C₅²×C₁₃	D₅₁	semidirect
21. C₃×C₅×C₁₇	D₅×C₁₃	semidirect
22. C₁₃×C₁₇	C₃⋊(C₅⋊D₅)	semidirect
23. C₃×C₅×C₁₃	D₈₅	semidirect
28. C₅×C₁₇	C₁₃×D₁₅	semidirect
30. C₃×C₅²	C₁₃×D₁₇	semidirect
31. C₅×C₁₃	D₂₅₅	semidirect
32. C₃×C₁₇	C₁₃×C₅⋊D₅	semidirect
34. C₃×C₁₃	C₅⋊D₈₅	semidirect
38. C₅²	C₁₃×D₅₁	semidirect
39. C₁₇	C₁₃×C₃⋊(C₅⋊D₅)	semidirect
40. C₃×C₅	C₁₃×D₈₅	semidirect
41. C₁₃	C₃⋊(C₅⋊D₈₅)	direct (N × H)
44. C₅	C₁₃×D₂₅₅	semidirect
45. C₃	C₁₃×C₅⋊D₈₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅²×C₁₃×C₁₇	2
C₁₃×C₅⋊D₈₅	3
C₁₃×D₂₅₅	5
C₃⋊(C₅⋊D₈₅)	13
C₁₃×C₃⋊(C₅⋊D₅)	17

Subgroups — C13×C3⋊(C5⋊D85) #45684196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₃⋊(C₅⋊D₈₅) #45684196