Subgroups — Q₈×D₃₅ #10587990

Order 560.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₃₅	C₂	1	3	yes	maximal
3	Dic₇₀	C₂	1	3	yes	maximal, complemented
4	C₂×D₃₅	C₂²	1	1	yes	characteristic
5	C₄×C₅×C₇	C₂²	1	3	yes	—
6	Dic₃₅	C₂²	1	3	yes	—
7	Q₈×D₇	—	5	1	no	maximal, Hall
8	Q₈×D₅	—	7	1	no	maximal, Hall
9	C₂×C₅×C₇	C₂³	1	1	yes	characteristic
10	D₃₅	Q₈	1	2	yes	direct product factor
11	C₇×Q₈	D₅	1	1	yes	characteristic, complemented
12	C₄×D₇	—	5	3	no	—
13	Dic₁₄	—	5	3	no	—
14	C₅×Q₈	D₇	1	1	yes	characteristic, complemented
15	C₄×D₅	—	7	3	no	—
16	Dic₁₀	—	7	3	no	—
17	C₅×C₇	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
18	C₂×D₇	—	5	1	no	—
19	C₄×C₇	C₂×D₅	1	3	yes	—
20	Dic₇	—	5	3	no	—
21	C₂×D₅	—	7	1	no	—
22	C₄×C₅	C₂×D₇	1	3	yes	—
23	Dic₅	—	7	3	no	—
24	C₂×Q₈	—	35	1	no	Sylow
25	C₂×C₇	C₂²×D₅	1	1	yes	characteristic
26	D₇	—	5	2	no	—
27	C₂×C₅	C₂²×D₇	1	1	yes	characteristic
28	D₅	—	7	2	no	—
29	Q₈	—	35	3	no	—
30	Q₈	D₃₅	1	1	yes	characteristic, direct product factor
31	C₂×C₄	—	35	3	no	—
32	C₇	Q₈×D₅	1	1	yes	characteristic, complemented, Sylow
33	C₅	Q₈×D₇	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	35	1	no	—
35	C₄	—	35	3	no	—
36	C₄	C₂×D₃₅	1	3	yes	—
37	C₂	—	35	2	no	—
38	C₂	C₂²×D₃₅	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.