Subgroups — C₅³×C₂₄₃ #72207152

Order 30375.

384 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅³×C₈₁	C₃	1	1	yes	maximal, characteristic
2	C₅²×C₂₄₃	C₅	1	31	yes	maximal, direct product factor
3	C₅³×C₂₇	C₉	1	1	yes	characteristic
4	C₅²×C₈₁	C₃×C₅	1	31	yes	—
5	C₅×C₂₄₃	C₅²	1	31	yes	direct product factor
6	C₅³×C₉	C₂₇	1	1	yes	characteristic
7	C₅²×C₂₇	C₅×C₉	1	31	yes	—
8	C₅×C₈₁	C₃×C₅²	1	31	yes	—
9	C₃×C₅³	C₈₁	1	1	yes	characteristic
10	C₂₄₃	C₅³	1	1	yes	characteristic, direct product factor, Sylow
11	C₅²×C₉	C₅×C₂₇	1	31	yes	—
12	C₅×C₂₇	C₅²×C₉	1	31	yes	—
13	C₅³	C₂₄₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₈₁	C₃×C₅³	1	1	yes	characteristic
15	C₃×C₅²	C₅×C₈₁	1	31	yes	—
16	C₅×C₉	C₅²×C₂₇	1	31	yes	—
17	C₂₇	C₅³×C₉	1	1	yes	characteristic
18	C₅²	C₅×C₂₄₃	1	31	yes	direct product factor
19	C₃×C₅	C₅²×C₈₁	1	31	yes	—
20	C₉	C₅³×C₂₇	1	1	yes	characteristic
21	C₅	C₅²×C₂₄₃	1	31	yes	direct product factor
22	C₃	C₅³×C₈₁	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.

subgroup	index
C₅³×C₈₁	3
C₅²×C₂₄₃	5