Subgroups — C₂×Dic₁₇₀ #13062838

Order 1360.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₈₅	C₂	1	2	yes	maximal
3	Dic₁₇₀	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₅×C₁₇	C₂²	1	1	yes	characteristic
5	C₄×C₅×C₁₇	C₂²	1	2	yes	—
6	Dic₈₅	C₂²	1	4	yes	—
7	C₂×Dic₃₄	—	5	1	no	maximal, Hall
8	C₂×C₅×C₁₇	Q₈	1	2	yes	complemented
9	C₂×C₅×C₁₇	C₂³	1	1	yes	characteristic
10	C₂×C₄×C₁₇	D₅	1	1	yes	characteristic
11	C₂×Dic₁₇	—	5	2	no	—
12	Dic₃₄	—	5	4	no	—
13	C₅×C₁₇	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
14	C₂×Dic₁₀	—	17	1	no	maximal, Hall
15	C₂²×C₁₇	C₂×D₅	1	1	yes	characteristic
16	C₄×C₁₇	C₂×D₅	1	2	yes	—
17	Dic₁₇	—	5	4	no	—
18	C₂×C₄×C₅	D₁₇	1	1	yes	characteristic
19	C₂×Dic₅	—	17	2	no	—
20	Dic₁₀	—	17	4	no	—
21	C₂×C₁₇	Dic₁₀	1	2	yes	complemented
22	C₂×C₁₇	C₂²×D₅	1	1	yes	characteristic
23	C₂²×C₅	C₂×D₁₇	1	1	yes	characteristic
24	C₄×C₅	C₂×D₁₇	1	2	yes	—
25	Dic₅	—	17	4	no	—
26	C₁₇	C₂×Dic₁₀	1	1	yes	characteristic, complemented, Sylow
27	C₂×Q₈	—	85	1	no	Sylow
28	C₂×C₅	Dic₃₄	1	2	yes	complemented
29	C₂×C₅	C₂²×D₁₇	1	1	yes	characteristic
30	Q₈	—	85	4	no	—
31	C₂×C₄	—	85	2	no	—
32	C₂×C₄	D₈₅	1	1	yes	characteristic
33	C₅	C₂×Dic₃₄	1	1	yes	characteristic, complemented, Sylow
34	C₂²	C₂×D₈₅	1	1	yes	characteristic
35	C₄	—	85	4	no	—
36	C₄	C₂×D₈₅	1	2	yes	—
37	C₂	Dic₁₇₀	1	2	yes	direct product factor
38	C₂	C₂²×D₈₅	1	1	yes	characteristic

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

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