Subgroups — C₃×C₇×Dic₃₁ #14579607

Order 2604.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₃₁	C₂×C₃	1	1	yes	characteristic
5	C₃×Dic₃₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₃₁	C₂×C₇	1	1	yes	characteristic
8	Dic₃₁	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₃₁	C₄×C₇	1	1	yes	characteristic, complemented, Hall
10	C₃×C₄×C₇	—	31	1	no	maximal, Hall
11	C₂×C₃₁	C₂×C₃×C₇	1	1	yes	characteristic
12	C₂×C₃×C₇	D₃₁	1	1	yes	characteristic
13	C₃₁	C₃×C₄×C₇	1	1	yes	characteristic, complemented, Sylow
14	C₄×C₇	—	31	1	no	Hall
15	C₃×C₇	Dic₃₁	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₇	C₃×D₃₁	1	1	yes	characteristic
17	C₃×C₄	—	31	1	no	Hall
18	C₇	C₃×Dic₃₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃	C₇×D₃₁	1	1	yes	characteristic
20	C₄	—	31	1	no	Sylow
21	C₃	C₇×Dic₃₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×C₇×D₃₁	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.