Subgroups — #30627032

Order 15625.

507 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	#15691099	C₅	1	5	yes	maximal, complemented
3	#15691077	C₅	1	10	yes	maximal, complemented
4	#15691076	C₅	1	10	yes	maximal, complemented
5	#15691075	C₅	1	5	yes	maximal
6	C₅⁴	C₅²	1	1	yes	characteristic
7	C₅×5₋¹⁺²	—	5	5	no	—
8	C₅×5₋¹⁺²	—	5	20	no	—
9	C₅×5₋¹⁺²	C₂₅	1	25	yes	complemented
10	C₅²×C₂₅	C₅²	1	2	yes	—
11	C₅²×C₂₅	C₅²	1	2	yes	—
12	C₅²×C₂₅	C₅²	1	1	yes	characteristic
13	C₂₅⋊C₂₅	—	5	20	no	—
14	C₅²⋊C₂₅	C₅²	1	25	yes	—
15	C₂₅²	—	5	5	no	—
16	C₅³	—	5	1	no	—
17	C₅³	—	5	4	no	—
18	C₅³	—	25	5	no	—
19	C₅³	C₅×C₂₅	1	5	yes	—
20	C₅³	C₅³	1	1	yes	characteristic
21	5₋¹⁺²	—	5	125	no	—
22	C₅×C₂₅	—	5	2	no	—
23	C₅×C₂₅	—	5	2	no	—
24	C₅×C₂₅	—	5	8	no	—
25	C₅×C₂₅	—	5	8	no	—
26	C₅×C₂₅	—	5	25	no	—
27	C₅×C₂₅	C₅×C₂₅	1	10	yes	—
28	C₅×C₂₅	C₅×C₂₅	1	10	yes	—
29	C₅×C₂₅	C₅×C₂₅	1	5	yes	—
30	C₅×C₂₅	H(3,𝔽₅)	1	5	yes	—
31	C₅×C₂₅	5₋¹⁺²	1	20	yes	—
32	C₅²	—	5	5	no	—
33	C₅²	—	5	5	no	—
34	C₅²	—	25	5	no	—
35	C₅²	—	25	20	no	—
36	C₅²	—	25	5	no	—
37	C₅²	C₅²×C₂₅	1	1	yes	characteristic
38	C₅²	C₅×H(3,𝔽₅)	1	1	yes	characteristic
39	C₅²	C₅×5₋¹⁺²	1	4	yes	—
40	C₂₅	—	5	10	no	—
41	C₂₅	—	5	10	no	—
42	C₂₅	—	25	25	no	—
43	C₂₅	C₅²⋊C₂₅	1	25	yes	—
44	C₅	—	5	1	no	—
45	C₅	—	5	4	no	—
46	C₅	—	25	5	no	—
47	C₅	C₅×C₅²⋊C₂₅	1	1	yes	characteristic
48	C₅	#15691127	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.