Subgroups — #30627042

Order 15625.

174 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₂₅⋊C₅	C₅	1	5	yes	maximal
2	#15691099	C₅	1	1	yes	maximal, characteristic
3	C₅²×C₂₅	C₅²	1	1	yes	characteristic
4	C₁₂₅⋊C₅	—	5	5	no	—
5	C₁₂₅⋊C₅	—	5	15	no	—
6	C₁₂₅⋊C₅	C₂₅	1	25	yes	complemented
7	C₅×C₁₂₅	—	5	5	no	—
8	C₂₅⋊C₂₅	—	5	1	no	—
9	C₂₅⋊C₂₅	—	5	3	no	—
10	C₅²⋊C₂₅	—	5	1	no	—
11	C₂₅²	C₂₅	1	5	yes	—
12	C₅³	5₋¹⁺²	1	1	yes	characteristic
13	C₅×C₂₅	—	5	5	no	—
14	C₅×C₂₅	C₅×C₂₅	1	5	yes	—
15	C₅×C₂₅	C₅×C₂₅	1	1	yes	characteristic
16	C₅×C₂₅	H(3,𝔽₅)	1	1	yes	characteristic
17	C₅×C₂₅	5₋¹⁺²	1	15	yes	—
18	C₅×C₂₅	5₋¹⁺²	1	5	yes	—
19	C₅×C₂₅	5₋¹⁺²	1	3	yes	—
20	C₁₂₅	—	5	25	no	—
21	C₅²	—	25	1	no	—
22	C₅²	C₅²⋊C₂₅	1	1	yes	characteristic
23	C₅²	C₂₅⋊C₂₅	1	5	yes	—
24	C₂₅	—	25	5	no	—
25	C₂₅	C₂₅²	1	1	yes	characteristic
26	C₂₅	C₅²⋊C₂₅	1	5	yes	—
27	C₂₅	C₂₅⋊C₂₅	1	15	yes	—
28	C₂₅	C₂₅⋊C₂₅	1	3	yes	—
29	C₂₅	C₂₅⋊C₂₅	1	1	yes	characteristic
30	C₅	—	5	1	no	—
31	C₅	—	5	5	no	—
32	C₅	#15691059	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
6. C₁₂₅⋊C₅	C₂₅	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×C₁₂₅⋊C₅	5
#15691099	5