Subgroups — C₅×C₂²⋊D₇ #63313

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, complemented
2	C₂×C₅×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₇	—	2	1	no	—
5	C₂×C₅×C₇	C₂²	1	1	yes	characteristic
6	C₅×D₇	—	2	1	no	—
7	C₂²⋊D₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×D₄	—	7	1	no	maximal, Hall
9	C₅×C₇	D₄	1	1	yes	characteristic, complemented, Hall
10	C₂²×C₇	C₂×C₅	1	1	yes	characteristic, complemented
11	C₂×D₇	C₂×C₅	1	1	yes	characteristic, complemented
12	Dic₇	C₂×C₅	1	1	yes	characteristic, complemented
13	C₂²×C₅	—	7	1	no	—
14	C₂²×C₅	D₇	1	1	yes	characteristic, complemented
15	C₄×C₅	—	7	1	no	—
16	C₂×C₇	—	2	1	no	—
17	C₂×C₇	C₂²×C₅	1	1	yes	characteristic
18	D₇	—	2	1	no	—
19	C₂×C₅	—	2	1	no	—
20	C₂×C₅	—	14	1	no	—
21	C₂×C₅	C₂×D₇	1	1	yes	characteristic
22	D₄	—	7	1	no	Sylow
23	C₇	C₅×D₄	1	1	yes	characteristic, complemented, Sylow
24	C₅	C₂²⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₂²	—	7	1	no	—
26	C₂²	C₅×D₇	1	1	yes	characteristic, complemented
27	C₄	—	7	1	no	—
28	C₂	—	2	1	no	—
29	C₂	—	14	1	no	—
30	C₂	C₂×C₅×D₇	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.