Subgroups — C₄₇×C₅²⋊C₂₅ #44440367

Order 29375.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅³×C₄₇	C₅	1	1	yes	maximal, characteristic
2	C₅×C₂₅×C₄₇	C₅	1	5	yes	maximal, complemented
3	C₅²×C₄₇	—	5	1	no	—
4	C₅²×C₄₇	—	5	4	no	—
5	C₅²×C₄₇	C₂₅	1	5	yes	complemented
6	C₅²×C₄₇	C₅²	1	1	yes	characteristic
7	C₂₅×C₄₇	—	5	5	no	—
8	C₅²⋊C₂₅	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₅×C₄₇	—	5	5	no	—
10	C₅×C₄₇	C₅×C₂₅	1	1	yes	characteristic
11	C₅×C₄₇	H(3,𝔽₅)	1	1	yes	characteristic
12	C₅×C₄₇	5₋¹⁺²	1	4	yes	—
13	C₅³	C₅×C₄₇	1	1	yes	characteristic
14	C₅×C₂₅	C₅×C₄₇	1	5	yes	complemented
15	C₄₇	C₅²⋊C₂₅	1	1	yes	characteristic, direct product factor, Sylow
16	C₅²	—	5	1	no	—
17	C₅²	—	5	4	no	—
18	C₅²	C₂₅×C₄₇	1	5	yes	complemented
19	C₅²	C₅²×C₄₇	1	1	yes	characteristic
20	C₂₅	—	5	5	no	—
21	C₅	—	5	5	no	—
22	C₅	C₅×C₂₅×C₄₇	1	1	yes	characteristic
23	C₅	C₄₇×H(3,𝔽₅)	1	1	yes	characteristic
24	C₅	C₄₇×5₋¹⁺²	1	4	yes	—

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.