Subgroups — C₅×#15691084 #30627044

Order 15625.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₂₅⋊C₅	C₅	1	4	yes	maximal
2	C₅×C₁₂₅⋊C₅	C₅	1	1	yes	maximal, characteristic
3	C₅×C₂₅⋊C₂₅	C₅	1	1	yes	maximal, characteristic
4	#15691084	C₅	1	25	yes	maximal, direct product factor
5	C₅²×C₂₅	—	5	1	no	—
6	C₅²×C₂₅	C₅²	1	1	yes	characteristic
7	C₁₂₅⋊C₅	—	5	16	no	—
8	C₁₂₅⋊C₅	C₂₅	1	20	yes	complemented
9	C₁₂₅⋊C₅	C₅²	1	20	yes	—
10	C₁₂₅⋊C₅	C₅²	1	5	yes	—
11	C₅×C₁₂₅	—	5	4	no	—
12	C₅×C₁₂₅	C₂₅	1	5	yes	complemented
13	C₂₅⋊C₂₅	—	5	4	no	—
14	C₂₅⋊C₂₅	C₅²	1	5	yes	—
15	C₅³	5₋¹⁺²	1	1	yes	characteristic
16	C₅×C₂₅	—	5	5	no	—
17	C₅×C₂₅	—	25	5	no	—
18	C₅×C₂₅	C₅×C₂₅	1	4	yes	—
19	C₅×C₂₅	C₅×C₂₅	1	1	yes	characteristic
20	C₅×C₂₅	5₋¹⁺²	1	4	yes	—
21	C₅×C₂₅	5₋¹⁺²	1	16	yes	—
22	C₅×C₂₅	5₋¹⁺²	1	4	yes	—
23	C₅×C₂₅	C₅³	1	1	yes	characteristic
24	C₁₂₅	—	5	20	no	—
25	C₁₂₅	C₅×C₂₅	1	25	yes	complemented
26	C₅²	—	5	5	no	—
27	C₅²	C₂₅⋊C₂₅	1	4	yes	—
28	C₅²	C₂₅⋊C₂₅	1	1	yes	characteristic
29	C₅²	C₅×5₋¹⁺²	1	1	yes	characteristic
30	C₂₅	—	25	5	no	—
31	C₂₅	C₂₅⋊C₂₅	1	16	yes	—
32	C₂₅	C₂₅⋊C₂₅	1	4	yes	—
33	C₂₅	C₅²×C₂₅	1	1	yes	characteristic
34	C₂₅	C₅×5₋¹⁺²	1	4	yes	—
35	C₅	—	5	1	no	—
36	C₅	—	5	4	no	—
37	C₅	#15691084	1	5	yes	direct product factor
38	C₅	C₅×C₂₅⋊C₂₅	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.