Subgroups — Dic₅×C₂₃×C₅₃ #37567167

Order 24380.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₂₃×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₂₃×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄×C₂₃×C₅₃	—	5	1	no	maximal, Hall
4	C₂×C₂₃×C₅₃	D₅	1	1	yes	characteristic
5	C₂₃×C₅₃	Dic₅	1	1	yes	characteristic, direct product factor, Hall
6	Dic₅×C₅₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅×C₅₃	C₂×C₂₃	1	1	yes	characteristic
8	Dic₅×C₂₃	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₅₃	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₂₃	C₂×C₅₃	1	1	yes	characteristic
11	C₄×C₅₃	—	5	1	no	Hall
12	C₅×C₂₃	C₄×C₅₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅₃	D₅×C₂₃	1	1	yes	characteristic
14	C₄×C₂₃	—	5	1	no	Hall
15	C₅₃	Dic₅×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₂₃	D₅×C₅₃	1	1	yes	characteristic
17	C₂₃	Dic₅×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
18	Dic₅	C₂₃×C₅₃	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₅	C₂×C₂₃×C₅₃	1	1	yes	characteristic
20	C₅	C₄×C₂₃×C₅₃	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	5	1	no	Sylow
22	C₂	D₅×C₂₃×C₅₃	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.