Subgroups — C₃×C₅×C₂₅×C₃₇ #72192094

Order 13875.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₅×C₃₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₅²×C₃₇	C₅	1	1	yes	maximal, characteristic
3	C₃×C₂₅×C₃₇	C₅	1	5	yes	maximal, direct product factor
4	C₅²×C₃₇	C₃×C₅	1	1	yes	characteristic
5	C₂₅×C₃₇	C₃×C₅	1	5	yes	direct product factor
6	C₃×C₅×C₃₇	C₂₅	1	5	yes	direct product factor
7	C₃×C₅×C₃₇	C₅²	1	1	yes	characteristic
8	C₃×C₅×C₂₅	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₃₇	C₃×C₂₅	1	5	yes	direct product factor
10	C₅×C₃₇	C₃×C₅²	1	1	yes	characteristic
11	C₅×C₂₅	C₃×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×C₃₇	C₅×C₂₅	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅²	C₅×C₃₇	1	1	yes	characteristic
14	C₃×C₂₅	C₅×C₃₇	1	5	yes	direct product factor
15	C₃₇	C₃×C₅×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
16	C₅²	C₃×C₅×C₃₇	1	1	yes	characteristic
17	C₂₅	C₃×C₅×C₃₇	1	5	yes	direct product factor
18	C₃×C₅	C₂₅×C₃₇	1	5	yes	direct product factor
19	C₃×C₅	C₅²×C₃₇	1	1	yes	characteristic
20	C₅	C₃×C₂₅×C₃₇	1	5	yes	direct product factor
21	C₅	C₃×C₅²×C₃₇	1	1	yes	characteristic
22	C₃	C₅×C₂₅×C₃₇	1	1	yes	characteristic, direct product factor, 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.