Subgroups — C₅×C₄₇×Dic₁₃ #27132007

Order 12220.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₃×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₃×C₄₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄₇×Dic₁₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₁₃×C₄₇	C₂×C₅	1	1	yes	characteristic
5	C₄×C₅×C₄₇	—	13	1	no	maximal, Hall
6	C₁₃×C₄₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×C₄₇	D₁₃	1	1	yes	characteristic
8	C₅×Dic₁₃	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₄₇	Dic₁₃	1	1	yes	characteristic, direct product factor, Hall
10	C₄×C₄₇	—	13	1	no	Hall
11	C₂×C₅×C₁₃	C₂×C₄₇	1	1	yes	characteristic
12	C₂×C₄₇	C₅×D₁₃	1	1	yes	characteristic
13	C₅×C₁₃	C₄×C₄₇	1	1	yes	characteristic, complemented, Hall
14	Dic₁₃	C₅×C₄₇	1	1	yes	characteristic, direct product factor, Hall
15	C₄₇	C₅×Dic₁₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₁₃	C₂×C₅×C₄₇	1	1	yes	characteristic
17	C₄×C₅	—	13	1	no	Hall
18	C₁₃	C₄×C₅×C₄₇	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	D₁₃×C₄₇	1	1	yes	characteristic
20	C₅	C₄₇×Dic₁₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	13	1	no	Sylow
22	C₂	C₅×D₁₃×C₄₇	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.