Subgroups — C₃²×C₁₃×D₈₅ #34091075

Order 19890.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₃×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₃×D₈₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₁₃×D₁₇	—	5	1	no	maximal, Hall
4	C₃×C₅×C₁₃×C₁₇	C₂×C₃	1	4	yes	complemented
5	C₁₃×D₈₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₁₃×C₁₇	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃²×D₈₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×C₁₃×D₁₇	—	5	4	no	—
9	C₃²×D₅×C₁₃	—	17	1	no	maximal, Hall
10	C₅×C₁₃×C₁₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃²×C₅×C₁₇	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₃×C₁₇	C₃×D₅	1	4	yes	complemented
13	C₃²×C₅×C₁₃	D₁₇	1	1	yes	characteristic, complemented, Hall
14	C₃×D₈₅	C₃×C₁₃	1	4	yes	direct product factor
15	C₁₃×D₁₇	—	5	1	no	Hall
16	C₃×D₅×C₁₃	—	17	4	no	—
17	C₃²×D₁₇	—	5	1	no	Hall
18	C₃×C₅×C₁₇	C₂×C₃×C₁₃	1	4	yes	complemented
19	C₂×C₃²×C₁₃	—	85	1	no	Hall
20	C₁₃×C₁₇	C₃²×D₅	1	1	yes	characteristic, complemented, Hall
21	C₃×C₅×C₁₃	C₃×D₁₇	1	4	yes	complemented
22	D₈₅	C₃²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
23	C₃²×C₁₇	D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
24	D₅×C₁₃	—	17	1	no	Hall
25	C₃²×C₁₃	D₈₅	1	1	yes	characteristic, direct product factor, Hall
26	C₃×D₁₇	—	5	4	no	—
27	C₃²×D₅	—	17	1	no	Hall
28	C₅×C₁₇	C₂×C₃²×C₁₃	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₁₃	—	85	4	no	—
30	C₅×C₁₃	C₃²×D₁₇	1	1	yes	characteristic, complemented, Hall
31	C₃×C₁₇	C₃×D₅×C₁₃	1	4	yes	complemented
32	C₃²×C₅	C₁₃×D₁₇	1	1	yes	characteristic, complemented, Hall
33	C₃×C₁₃	C₃×D₈₅	1	4	yes	direct product factor
34	D₁₇	—	5	1	no	Hall
35	C₃×D₅	—	17	4	no	—
36	C₂×C₁₃	—	85	1	no	Hall
37	C₂×C₃²	—	85	1	no	Hall
38	C₁₇	C₃²×D₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	C₃×C₁₃×D₁₇	1	4	yes	complemented
40	C₁₃	C₃²×D₈₅	1	1	yes	characteristic, direct product factor, Sylow
41	D₅	—	17	1	no	Hall
42	C₃²	C₁₃×D₈₅	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	—	85	4	no	—
44	C₅	C₃²×C₁₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₃×C₁₃×D₈₅	1	4	yes	direct product factor
46	C₂	—	85	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₁₃	D₈₅
commutator, cosocle, hypocenter	C₅×C₁₇	C₂×C₃²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₃×C₁₇	C₂
LCS	G ▷ C₅×C₁₇
UCS	C₁ ◁ C₃²×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₃×C₁₇	C₂	semidirect
2. C₃×C₁₃×D₈₅	C₃	direct (N × H)
4. C₃×C₅×C₁₃×C₁₇	C₂×C₃	semidirect
5. C₁₃×D₈₅	C₃²	direct (N × H)
6. C₃²×C₁₃×C₁₇	D₅	semidirect
7. C₃²×D₈₅	C₁₃	direct (N × H)
10. C₅×C₁₃×C₁₇	C₂×C₃²	semidirect
11. C₃²×C₅×C₁₇	C₂×C₁₃	semidirect
12. C₃×C₁₃×C₁₇	C₃×D₅	semidirect
13. C₃²×C₅×C₁₃	D₁₇	semidirect
14. C₃×D₈₅	C₃×C₁₃	direct (N × H)
18. C₃×C₅×C₁₇	C₂×C₃×C₁₃	semidirect
20. C₁₃×C₁₇	C₃²×D₅	semidirect
21. C₃×C₅×C₁₃	C₃×D₁₇	semidirect
22. D₈₅	C₃²×C₁₃	direct (N × H)
23. C₃²×C₁₇	D₅×C₁₃	semidirect
25. C₃²×C₁₃	D₈₅	direct (N × H)
28. C₅×C₁₇	C₂×C₃²×C₁₃	semidirect
30. C₅×C₁₃	C₃²×D₁₇	semidirect
31. C₃×C₁₇	C₃×D₅×C₁₃	semidirect
32. C₃²×C₅	C₁₃×D₁₇	semidirect
33. C₃×C₁₃	C₃×D₈₅	direct (N × H)
38. C₁₇	C₃²×D₅×C₁₃	semidirect
39. C₃×C₅	C₃×C₁₃×D₁₇	semidirect
40. C₁₃	C₃²×D₈₅	direct (N × H)
42. C₃²	C₁₃×D₈₅	direct (N × H)
44. C₅	C₃²×C₁₃×D₁₇	semidirect
45. C₃	C₃×C₁₃×D₈₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₁₃×C₁₇	2
C₃×C₁₃×D₈₅	3
C₃²×C₁₃×D₁₇	5
C₃²×D₈₅	13
C₃²×D₅×C₁₃	17

Subgroups — C32×C13×D85 #34091075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₁₃×D₈₅ #34091075