Subgroups — C₅²×C₂₇×C₃₇ #72202196

Order 24975.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₇×C₃₇	C₅	1	6	yes	maximal, direct product factor
2	C₅²×C₉×C₃₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₅²×C₃₇	C₉	1	1	yes	characteristic
4	C₅×C₉×C₃₇	C₃×C₅	1	6	yes	—
5	C₂₇×C₃₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
6	C₅²×C₃₇	C₂₇	1	1	yes	characteristic, direct product factor, Hall
7	C₅²×C₂₇	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×C₅×C₃₇	C₅×C₉	1	6	yes	—
9	C₉×C₃₇	C₃×C₅²	1	1	yes	characteristic
10	C₅²×C₉	C₃×C₃₇	1	1	yes	characteristic
11	C₅×C₃₇	C₅×C₂₇	1	6	yes	direct product factor
12	C₅×C₂₇	C₅×C₃₇	1	6	yes	direct product factor
13	C₃×C₃₇	C₅²×C₉	1	1	yes	characteristic
14	C₃×C₅²	C₉×C₃₇	1	1	yes	characteristic
15	C₅×C₉	C₃×C₅×C₃₇	1	6	yes	—
16	C₃₇	C₅²×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₂₇	C₅²×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
18	C₅²	C₂₇×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×C₅	C₅×C₉×C₃₇	1	6	yes	—
20	C₉	C₃×C₅²×C₃₇	1	1	yes	characteristic
21	C₅	C₅×C₂₇×C₃₇	1	6	yes	direct product factor
22	C₃	C₅²×C₉×C₃₇	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.