Subgroups — D₃×C₂₅×C₁₅₇ #37555482

Order 23550.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₅×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₂₅×C₁₅₇	—	3	1	no	maximal, Hall
3	C₅×D₃×C₁₅₇	C₅	1	1	yes	maximal, characteristic
4	C₂₅×C₁₅₇	D₃	1	1	yes	characteristic, direct product factor, Hall
5	C₃×C₅×C₁₅₇	C₂×C₅	1	1	yes	characteristic
6	C₂×C₅×C₁₅₇	—	3	1	no	—
7	D₃×C₁₅₇	C₂₅	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₁₅₇	C₅×D₃	1	1	yes	characteristic
9	C₃×C₁₅₇	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₅₇	—	3	1	no	Hall
11	C₁₅₇	D₃×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
12	D₃×C₂₅	C₁₅₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₂₅	C₂×C₁₅₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₂₅	—	3	1	no	Hall
15	C₅×D₃	C₅×C₁₅₇	1	1	yes	characteristic
16	C₂₅	D₃×C₁₅₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₅	C₂×C₅×C₁₅₇	1	1	yes	characteristic
18	C₂×C₅	—	3	1	no	—
19	D₃	C₂₅×C₁₅₇	1	1	yes	characteristic, direct product factor, Hall
20	C₅	C₅×D₃×C₁₅₇	1	1	yes	characteristic
21	C₃	C₂×C₂₅×C₁₅₇	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	3	1	no	Sylow

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.