Subgroups — C₂×#10621755 #13062812

Order 1360.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₈₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	#10621755	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₅×C₁₇	C₂²	1	1	yes	characteristic
6	C₂×D₈₅	—	2	2	no	—
7	C₂×D₈₅	C₂²	1	2	yes	complemented
8	C₂×C₅×D₁₇	—	2	2	no	—
9	C₂×C₅×D₁₇	C₂²	1	2	yes	complemented
10	C₁₇×Dic₅	C₂²	1	2	yes	complemented
11	C₂×D₆₈	—	5	1	no	maximal, Hall
12	C₂×C₅×C₁₇	D₄	1	2	yes	complemented
13	C₂×C₅×C₁₇	C₂³	1	1	yes	characteristic
14	D₈₅	—	2	2	no	—
15	C₅×D₁₇	—	2	2	no	—
16	C₂²×D₁₇	—	5	1	no	—
17	C₂²×D₁₇	D₅	1	1	yes	characteristic, complemented
18	C₂×C₄×C₁₇	—	5	1	no	—
19	D₆₈	—	5	4	no	—
20	C₅×C₁₇	C₂×D₄	1	1	yes	characteristic, complemented, Hall
21	C₂×C₂²⋊D₅	—	17	1	no	maximal, Hall
22	C₂²×C₁₇	C₂×D₅	1	1	yes	characteristic
23	C₂×D₁₇	—	2	2	no	—
24	C₂×D₁₇	—	5	2	no	—
25	C₂×D₁₇	—	10	2	no	—
26	C₂×D₁₇	C₂×D₅	1	2	yes	complemented
27	C₄×C₁₇	—	5	2	no	—
28	C₂³×C₅	—	17	1	no	—
29	C₂²×D₅	—	17	1	no	—
30	C₂²⋊D₅	—	17	4	no	—
31	C₂×Dic₅	D₁₇	1	1	yes	characteristic, complemented
32	C₂×C₁₇	C₂²⋊D₅	1	2	yes	complemented
33	C₂×C₁₇	C₂²×D₅	1	1	yes	characteristic
34	D₁₇	—	2	2	no	—
35	D₁₇	—	10	2	no	—
36	C₂²×C₅	—	17	2	no	—
37	C₂²×C₅	—	34	2	no	—
38	C₂²×C₅	C₂×D₁₇	1	1	yes	characteristic
39	C₂×D₅	—	17	2	no	—
40	C₂×D₅	—	34	2	no	—
41	Dic₅	C₂×D₁₇	1	2	yes	complemented
42	C₁₇	C₂×C₂²⋊D₅	1	1	yes	characteristic, complemented, Sylow
43	C₂×D₄	—	85	1	no	Sylow
44	C₂×C₅	—	34	2	no	—
45	C₂×C₅	D₆₈	1	2	yes	complemented
46	C₂×C₅	C₂²×D₁₇	1	1	yes	characteristic
47	D₅	—	34	2	no	—
48	C₂³	—	17	1	no	—
49	C₂³	—	85	1	no	—
50	D₄	—	85	4	no	—
51	C₂×C₄	—	5	1	no	—
52	C₅	C₂×D₆₈	1	1	yes	characteristic, complemented, Sylow
53	C₂²	—	17	2	no	—
54	C₂²	—	34	2	no	—
55	C₂²	—	85	2	no	—
56	C₂²	—	170	2	no	—
57	C₂²	D₅×D₁₇	1	1	yes	characteristic
58	C₄	—	5	2	no	—
59	C₂	—	34	2	no	—
60	C₂	—	170	2	no	—
61	C₂	#10621755	1	2	yes	direct product factor
62	C₂	C₂×D₅×D₁₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×D₈₅	C₂	semidirect
2. C₂²×C₅×D₁₇	C₂	semidirect
3. C₂×C₁₇×Dic₅	C₂	semidirect
4. #10621755	C₂	direct (N × H)
7. C₂×D₈₅	C₂²	semidirect
9. C₂×C₅×D₁₇	C₂²	semidirect
10. C₁₇×Dic₅	C₂²	semidirect
12. C₂×C₅×C₁₇	D₄	semidirect
17. C₂²×D₁₇	D₅	semidirect
20. C₅×C₁₇	C₂×D₄	semidirect
26. C₂×D₁₇	C₂×D₅	semidirect
31. C₂×Dic₅	D₁₇	semidirect
32. C₂×C₁₇	C₂²⋊D₅	semidirect
41. Dic₅	C₂×D₁₇	semidirect
42. C₁₇	C₂×C₂²⋊D₅	semidirect
45. C₂×C₅	D₆₈	semidirect
52. C₅	C₂×D₆₈	semidirect
61. C₂	#10621755	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₈₅	2
C₂²×C₅×D₁₇	2
C₂×C₁₇×Dic₅	2
#10621755	2
C₂×D₆₈	5
C₂×C₂²⋊D₅	17

Subgroups — C2×#10621755 #13062812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10621755 #13062812