Subgroups — C₂×#10621757 #13062814

Order 1360.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₈₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₇×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×Dic₁₇	C₂	1	1	yes	maximal, characteristic
4	#10621757	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₅×C₁₇	C₂²	1	1	yes	characteristic
6	Dic₈₅	C₂²	1	2	yes	—
7	C₅×Dic₁₇	C₂²	1	2	yes	—
8	C₁₇×Dic₅	C₂²	1	2	yes	—
9	C₂×Dic₃₄	—	5	1	no	maximal, Hall
10	C₂×C₅×C₁₇	Q₈	1	2	yes	complemented
11	C₂×C₅×C₁₇	C₂³	1	1	yes	characteristic
12	C₂×C₄×C₁₇	—	5	1	no	—
13	C₂×Dic₁₇	—	5	1	no	—
14	C₂×Dic₁₇	D₅	1	1	yes	characteristic
15	Dic₃₄	—	5	4	no	—
16	C₅×C₁₇	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
17	C₂×Dic₁₀	—	17	1	no	maximal, Hall
18	C₂²×C₁₇	C₂×D₅	1	1	yes	characteristic
19	C₄×C₁₇	—	5	2	no	—
20	Dic₁₇	—	5	2	no	—
21	Dic₁₇	C₂×D₅	1	2	yes	—
22	C₂×C₄×C₅	—	17	1	no	—
23	C₂×Dic₅	—	17	1	no	—
24	C₂×Dic₅	D₁₇	1	1	yes	characteristic
25	Dic₁₀	—	17	4	no	—
26	C₂×C₁₇	Dic₁₀	1	2	yes	complemented
27	C₂×C₁₇	C₂²×D₅	1	1	yes	characteristic
28	C₂²×C₅	C₂×D₁₇	1	1	yes	characteristic
29	C₄×C₅	—	17	2	no	—
30	Dic₅	—	17	2	no	—
31	Dic₅	C₂×D₁₇	1	2	yes	—
32	C₁₇	C₂×Dic₁₀	1	1	yes	characteristic, complemented, Sylow
33	C₂×Q₈	—	85	1	no	Sylow
34	C₂×C₅	Dic₃₄	1	2	yes	complemented
35	C₂×C₅	C₂²×D₁₇	1	1	yes	characteristic
36	Q₈	—	85	4	no	—
37	C₂×C₄	—	5	1	no	—
38	C₂×C₄	—	17	1	no	—
39	C₂×C₄	—	85	1	no	—
40	C₅	C₂×Dic₃₄	1	1	yes	characteristic, complemented, Sylow
41	C₂²	D₅×D₁₇	1	1	yes	characteristic
42	C₄	—	5	2	no	—
43	C₄	—	17	2	no	—
44	C₄	—	85	2	no	—
45	C₂	#10621757	1	2	yes	direct product factor
46	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, prime radical	C₂²×C₅×C₁₇	C₂²
hypocenter	C₅×C₁₇	C₂×Q₈
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
4. #10621757	C₂	direct (N × H)
10. C₂×C₅×C₁₇	Q₈	semidirect
16. C₅×C₁₇	C₂×Q₈	semidirect
26. C₂×C₁₇	Dic₁₀	semidirect
32. C₁₇	C₂×Dic₁₀	semidirect
34. C₂×C₅	Dic₃₄	semidirect
40. C₅	C₂×Dic₃₄	semidirect
45. C₂	#10621757	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Dic₈₅	2
C₂×C₁₇×Dic₅	2
C₂×C₅×Dic₁₇	2
#10621757	2
C₂×Dic₃₄	5
C₂×Dic₁₀	17

Subgroups — C2×#10621757 #13062814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10621757 #13062814