Subgroups — #30627030

Order 15625.

572 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×5₋¹⁺²	C₅	1	1	yes	maximal, characteristic
2	C₅×C₅²⋊C₂₅	C₅	1	5	yes	maximal
3	#15691077	C₅	1	25	yes	maximal, complemented
4	C₅⁴	C₅²	1	1	yes	characteristic
5	C₅×5₋¹⁺²	—	5	5	no	—
6	C₅×5₋¹⁺²	—	5	20	no	—
7	C₅×5₋¹⁺²	C₂₅	1	25	yes	complemented
8	C₅²×C₂₅	—	5	5	no	—
9	C₅²×C₂₅	C₅²	1	5	yes	—
10	C₅²⋊C₂₅	—	5	20	no	—
11	C₅²⋊C₂₅	C₅²	1	25	yes	—
12	C₅³	—	25	5	no	—
13	C₅³	C₅×C₂₅	1	5	yes	—
14	C₅³	H(3,𝔽₅)	1	5	yes	—
15	C₅³	5₋¹⁺²	1	20	yes	—
16	C₅³	C₅³	1	1	yes	characteristic
17	5₋¹⁺²	—	5	125	no	—
18	C₅×C₂₅	—	5	5	no	—
19	C₅×C₂₅	—	5	20	no	—
20	C₅×C₂₅	—	5	25	no	—
21	C₅×C₂₅	—	25	25	no	—
22	C₅×C₂₅	C₅×C₂₅	1	25	yes	complemented
23	C₅²	—	5	5	no	—
24	C₅²	—	5	20	no	—
25	C₅²	—	5	5	no	—
26	C₅²	—	25	5	no	—
27	C₅²	—	25	20	no	—
28	C₅²	C₅²⋊C₂₅	1	25	yes	—
29	C₅²	C₅²×C₂₅	1	1	yes	characteristic
30	C₅²	C₅×H(3,𝔽₅)	1	1	yes	characteristic
31	C₅²	C₅×5₋¹⁺²	1	4	yes	—
32	C₂₅	—	5	25	no	—
33	C₂₅	—	25	25	no	—
34	C₅	—	5	25	no	—
35	C₅	—	5	1	no	—
36	C₅	—	5	4	no	—
37	C₅	C₅×C₅²⋊C₂₅	1	1	yes	characteristic
38	C₅	#15691126	1	5	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.