Subgroups — C₂×Dic₃₅ #63322

Order 280.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₇	C₂	1	1	yes	maximal, characteristic
2	Dic₃₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×C₇	C₄	1	2	yes	complemented
4	C₂×C₅×C₇	C₂²	1	1	yes	characteristic
5	C₂×Dic₇	—	5	1	no	maximal, Hall
6	C₂×Dic₅	—	7	1	no	maximal, Hall
7	C₅×C₇	C₂×C₄	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₇	D₅	1	1	yes	characteristic
9	Dic₇	—	5	2	no	—
10	C₂²×C₅	D₇	1	1	yes	characteristic
11	Dic₅	—	7	2	no	—
12	C₂×C₇	Dic₅	1	2	yes	complemented
13	C₂×C₇	C₂×D₅	1	1	yes	characteristic
14	C₂×C₅	Dic₇	1	2	yes	complemented
15	C₂×C₅	C₂×D₇	1	1	yes	characteristic
16	C₂×C₄	—	35	1	no	Sylow
17	C₇	C₂×Dic₅	1	1	yes	characteristic, complemented, Sylow
18	C₅	C₂×Dic₇	1	1	yes	characteristic, complemented, Sylow
19	C₂²	D₃₅	1	1	yes	characteristic
20	C₄	—	35	2	no	—
21	C₂	Dic₃₅	1	2	yes	direct product factor
22	C₂	C₂×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.