Subgroups — #13062804

Order 1360.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅×D₁₇	C₂	1	2	yes	maximal, complemented
2	C₄×D₈₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₆₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#10621754	C₂	1	2	yes	maximal, complemented
6	C₂×D₈₅	C₂²	1	1	yes	characteristic
7	C₂×D₅×C₁₇	C₂²	1	2	yes	complemented
8	C₂×C₅×D₁₇	C₂²	1	2	yes	complemented
9	D₅×D₁₇	—	2	4	no	—
10	C₄×C₅×C₁₇	C₂²	1	1	yes	characteristic, complemented
11	Dic₈₅	C₂²	1	1	yes	characteristic, complemented
12	D₄×D₁₇	—	5	1	no	maximal, Hall
13	C₂×C₅×C₁₇	C₂³	1	1	yes	characteristic
14	D₈₅	D₄	1	2	yes	complemented
15	C₅×D₁₇	—	2	2	no	—
16	D₅×C₁₇	—	2	2	no	—
17	C₂²×D₁₇	—	5	2	no	—
18	D₄×C₁₇	—	5	1	no	—
19	C₂²⋊D₁₇	—	5	2	no	—
20	D₆₈	D₅	1	1	yes	characteristic, complemented
21	C₄×D₁₇	—	5	1	no	—
22	C₅×C₁₇	C₂×D₄	1	1	yes	characteristic, complemented, Hall
23	D₄×D₅	—	17	1	no	maximal, Hall
24	C₂²×C₁₇	—	5	2	no	—
25	C₂×D₁₇	—	5	1	no	—
26	C₂×D₁₇	—	10	4	no	—
27	C₂×D₁₇	C₂×D₅	1	2	yes	complemented
28	C₄×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented
29	Dic₁₇	—	5	1	no	—
30	C₂²×D₅	—	17	2	no	—
31	C₅×D₄	—	17	1	no	—
32	C₂²⋊D₅	—	17	2	no	—
33	D₂₀	D₁₇	1	1	yes	characteristic, complemented
34	C₄×D₅	—	17	1	no	—
35	C₂×C₁₇	—	10	2	no	—
36	C₂×C₁₇	C₂²×D₅	1	1	yes	characteristic
37	D₁₇	—	2	2	no	—
38	D₁₇	—	5	2	no	—
39	C₂²×C₅	—	17	2	no	—
40	C₂×D₅	—	17	1	no	—
41	C₂×D₅	—	34	4	no	—
42	C₂×D₅	C₂×D₁₇	1	2	yes	complemented
43	C₄×C₅	C₂×D₁₇	1	1	yes	characteristic, complemented
44	Dic₅	—	17	1	no	—
45	C₁₇	D₄×D₅	1	1	yes	characteristic, complemented, Sylow
46	C₂×D₄	—	85	1	no	Sylow
47	C₂×C₅	—	34	2	no	—
48	C₂×C₅	C₂²×D₁₇	1	1	yes	characteristic
49	D₅	—	2	2	no	—
50	D₅	—	17	2	no	—
51	C₂³	—	85	2	no	—
52	D₄	—	5	1	no	—
53	D₄	—	17	1	no	—
54	D₄	—	85	2	no	—
55	C₂×C₄	—	85	1	no	—
56	C₅	D₄×D₁₇	1	1	yes	characteristic, complemented, Sylow
57	C₂²	—	5	2	no	—
58	C₂²	—	17	2	no	—
59	C₂²	—	85	1	no	—
60	C₂²	—	170	4	no	—
61	C₄	—	85	1	no	—
62	C₄	D₅×D₁₇	1	1	yes	characteristic, complemented
63	C₂	—	10	2	no	—
64	C₂	—	34	2	no	—
65	C₂	—	85	2	no	—
66	C₂	C₂×D₅×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×D₅×D₁₇
commutator, socle, cosocle	C₂×C₅×C₁₇	C₂³
Fitting	C₄×C₅×C₁₇	C₂²
hypercenter	C₄	D₅×D₁₇
hypocenter	C₅×C₁₇	C₂×D₄
LCS	G ▷ C₂×C₅×C₁₇ ▷ C₅×C₁₇
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
1. C₂×D₅×D₁₇	C₂	semidirect
2. C₄×D₈₅	C₂	semidirect
3. C₁₇×D₂₀	C₂	semidirect
4. C₅×D₆₈	C₂	semidirect
5. #10621754	C₂	semidirect
7. C₂×D₅×C₁₇	C₂²	semidirect
8. C₂×C₅×D₁₇	C₂²	semidirect
10. C₄×C₅×C₁₇	C₂²	semidirect
11. Dic₈₅	C₂²	semidirect
14. D₈₅	D₄	semidirect
20. D₆₈	D₅	semidirect
22. C₅×C₁₇	C₂×D₄	semidirect
27. C₂×D₁₇	C₂×D₅	semidirect
28. C₄×C₁₇	C₂×D₅	semidirect
33. D₂₀	D₁₇	semidirect
42. C₂×D₅	C₂×D₁₇	semidirect
43. C₄×C₅	C₂×D₁₇	semidirect
45. C₁₇	D₄×D₅	semidirect
56. C₅	D₄×D₁₇	semidirect
62. C₄	D₅×D₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅×D₁₇	2
C₄×D₈₅	2
C₁₇×D₂₀	2
C₅×D₆₈	2
#10621754	2
D₄×D₁₇	5
D₄×D₅	17