Subgroups — C₅×C₇×Dic₃ #88283

Order 420.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₇	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×C₇	—	3	1	no	maximal, Hall
3	C₃×C₅×C₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×Dic₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₇	D₃	1	1	yes	characteristic
6	C₅×Dic₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₇	C₂×C₅	1	1	yes	characteristic
8	C₅×C₇	Dic₃	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃×C₅	C₂×C₇	1	1	yes	characteristic
10	C₄×C₇	—	3	1	no	Hall
11	C₃×C₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₄×C₅	—	3	1	no	Hall
13	C₃×C₅	C₄×C₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇	C₅×D₃	1	1	yes	characteristic
15	Dic₃	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₅	D₃×C₇	1	1	yes	characteristic
17	C₇	C₅×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₃	C₂×C₅×C₇	1	1	yes	characteristic
19	C₅	C₇×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₄	—	3	1	no	Sylow
21	C₃	C₄×C₅×C₇	1	1	yes	characteristic, complemented, Sylow
22	C₂	C₅×D₃×C₇	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.