Subgroups — C₅×C₇²×C₈ #14519949

Order 1960.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×C₇²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₇²	C₄	1	1	yes	characteristic
3	C₇²×C₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₈	C₇	1	8	yes	maximal, direct product factor
5	C₅×C₇²	C₈	1	1	yes	characteristic, direct product factor, Hall
6	C₄×C₇²	C₂×C₅	1	1	yes	characteristic
7	C₄×C₅×C₇	C₂×C₇	1	8	yes	—
8	C₂×C₇²	C₄×C₅	1	1	yes	characteristic
9	C₂×C₅×C₇	C₄×C₇	1	8	yes	—
10	C₇×C₈	C₅×C₇	1	8	yes	direct product factor
11	C₇²	C₅×C₈	1	1	yes	characteristic, direct product factor, Sylow
12	C₅×C₈	C₇²	1	1	yes	characteristic, direct product factor, Hall
13	C₅×C₇	C₇×C₈	1	8	yes	direct product factor
14	C₄×C₇	C₂×C₅×C₇	1	8	yes	—
15	C₄×C₅	C₂×C₇²	1	1	yes	characteristic
16	C₂×C₇	C₄×C₅×C₇	1	8	yes	—
17	C₂×C₅	C₄×C₇²	1	1	yes	characteristic
18	C₈	C₅×C₇²	1	1	yes	characteristic, direct product factor, Sylow
19	C₇	C₅×C₇×C₈	1	8	yes	direct product factor
20	C₅	C₇²×C₈	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	C₂×C₅×C₇²	1	1	yes	characteristic
22	C₂	C₄×C₅×C₇²	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.