Subgroups — C₂×C₁₃⋊C₃×D₈₅ #27210517

Order 13260.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃⋊C₃×D₈₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₁₇×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×D₈₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×C₁₇×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₇×C₁₃⋊C₃	—	5	1	no	maximal, Hall
6	C₁₃×D₈₅	C₂×C₃	1	2	yes	complemented
7	C₂×C₅×C₁₃×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₁₇×C₁₃⋊C₃	D₅	1	1	yes	characteristic, complemented
9	D₁₇×C₁₃⋊C₃	—	5	2	no	—
10	C₅×C₁₃×C₁₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×D₈₅	—	13	1	no	maximal, Hall
12	C₂×C₁₃×D₁₇	—	5	1	no	Hall
13	C₂×D₅×C₁₃⋊C₃	—	17	1	no	maximal, Hall
14	C₁₇×C₁₃⋊C₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₅×C₁₇	—	13	1	no	—
16	C₃×D₈₅	—	13	2	no	—
17	C₂×C₁₃×C₁₇	C₃×D₅	1	1	yes	characteristic, complemented
18	C₁₃×D₁₇	—	5	2	no	—
19	C₂×C₅×C₁₃⋊C₃	D₁₇	1	1	yes	characteristic, complemented
20	D₅×C₁₃⋊C₃	—	17	2	no	—
21	C₂×D₈₅	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
22	C₂×D₅×C₁₃	—	17	1	no	Hall
23	C₃×C₅×C₁₇	—	13	1	no	Hall
24	C₁₃×C₁₇	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×D₁₇	—	65	1	no	Hall
26	C₅×C₁₃⋊C₃	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
27	C₂×C₅×C₁₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
28	D₈₅	C₂×C₁₃⋊C₃	1	2	yes	direct product factor
29	C₂²×C₁₃⋊C₃	—	85	1	no	Hall
30	C₂×C₅×C₁₃	C₃×D₁₇	1	1	yes	characteristic, complemented
31	D₅×C₁₃	—	17	2	no	—
32	C₂×C₃×C₁₇	—	13	1	no	—
33	C₃×D₁₇	—	65	2	no	—
34	C₅×C₁₇	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
35	C₂×C₁₃⋊C₃	—	85	2	no	—
36	C₂×C₁₃⋊C₃	D₈₅	1	1	yes	characteristic, direct product factor
37	C₂×D₁₇	—	5	1	no	Hall
38	C₅×C₁₃	C₂×C₃×D₁₇	1	1	yes	characteristic, complemented, Hall
39	C₂×C₃×D₅	—	221	1	no	Hall
40	C₂²×C₁₃	—	85	1	no	Hall
41	C₃×C₁₇	—	13	1	no	Hall
42	C₁₃⋊C₃	C₂×D₈₅	1	1	yes	characteristic, direct product factor, Hall
43	C₂×C₁₇	D₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented
44	D₁₇	—	5	2	no	—
45	C₂×C₃×C₅	—	13	1	no	—
46	C₃×D₅	—	221	2	no	—
47	C₂×C₁₃	—	85	2	no	—
48	C₂×C₁₃	C₃×D₈₅	1	1	yes	characteristic, complemented
49	C₂×D₅	—	17	1	no	Hall
50	C₁₇	C₂×D₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
51	C₃×C₅	—	13	1	no	Hall
52	C₁₃	C₂×C₃×D₈₅	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₃	—	1105	1	no	Hall
54	C₂×C₅	D₁₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented
55	D₅	—	17	2	no	—
56	C₂×C₃	—	13	1	no	—
57	C₂×C₃	—	1105	2	no	—
58	C₅	C₂×D₁₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	85	1	no	Sylow
60	C₃	—	13	1	no	Sylow
61	C₂	—	85	2	no	—
62	C₂	C₁₃⋊C₃×D₈₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₁₃⋊C₃×D₈₅
commutator, cosocle, hypocenter	C₅×C₁₃×C₁₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₃×C₁₇	C₂×C₃
LCS	G ▷ C₅×C₁₃×C₁₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₁₃⋊C₃×D₈₅	C₂	direct (N × H)
2. C₂×C₅×C₁₇×C₁₃⋊C₃	C₂	semidirect
3. C₂×C₁₃×D₈₅	C₃	semidirect
4. C₅×C₁₇×C₁₃⋊C₃	C₂²	semidirect
6. C₁₃×D₈₅	C₂×C₃	semidirect
7. C₂×C₅×C₁₃×C₁₇	C₂×C₃	semidirect
8. C₂×C₁₇×C₁₃⋊C₃	D₅	semidirect
10. C₅×C₁₃×C₁₇	C₂²×C₃	semidirect
14. C₁₇×C₁₃⋊C₃	C₂×D₅	semidirect
17. C₂×C₁₃×C₁₇	C₃×D₅	semidirect
19. C₂×C₅×C₁₃⋊C₃	D₁₇	semidirect
21. C₂×D₈₅	C₁₃⋊C₃	direct (N × H)
24. C₁₃×C₁₇	C₂×C₃×D₅	semidirect
26. C₅×C₁₃⋊C₃	C₂×D₁₇	semidirect
27. C₂×C₅×C₁₇	C₂×C₁₃⋊C₃	semidirect
28. D₈₅	C₂×C₁₃⋊C₃	direct (N × H)
30. C₂×C₅×C₁₃	C₃×D₁₇	semidirect
34. C₅×C₁₇	C₂²×C₁₃⋊C₃	semidirect
36. C₂×C₁₃⋊C₃	D₈₅	direct (N × H)
38. C₅×C₁₃	C₂×C₃×D₁₇	semidirect
42. C₁₃⋊C₃	C₂×D₈₅	direct (N × H)
43. C₂×C₁₇	D₅×C₁₃⋊C₃	semidirect
48. C₂×C₁₃	C₃×D₈₅	semidirect
50. C₁₇	C₂×D₅×C₁₃⋊C₃	semidirect
52. C₁₃	C₂×C₃×D₈₅	semidirect
54. C₂×C₅	D₁₇×C₁₃⋊C₃	semidirect
58. C₅	C₂×D₁₇×C₁₃⋊C₃	semidirect
62. C₂	C₁₃⋊C₃×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
C₁₃⋊C₃×D₈₅	2
C₂×C₅×C₁₇×C₁₃⋊C₃	2
C₂×C₁₃×D₈₅	3
C₂×D₁₇×C₁₃⋊C₃	5
C₂×C₃×D₈₅	13
C₂×D₅×C₁₃⋊C₃	17

Subgroups — C2×C13⋊C3×D85 #27210517

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃⋊C₃×D₈₅ #27210517