Subgroups — #30627033

Order 15625.

335 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#10597831	C₅	1	1	yes	maximal, characteristic
2	C₂₅×5₋¹⁺²	C₅	1	5	yes	maximal, complemented
3	C₅×C₅²⋊C₂₅	C₅	1	1	yes	maximal, characteristic
4	5₋¹⁺²⋊C₂₅	C₅	1	20	yes	maximal, complemented
5	#15691075	C₅	1	4	yes	maximal
6	C₅⁴	C₅²	1	1	yes	characteristic
7	C₅×5₋¹⁺²	C₅²	1	5	yes	—
8	C₅²×C₂₅	C₅²	1	4	yes	—
9	C₅²×C₂₅	C₅²	1	1	yes	characteristic
10	#10597831	C₂₅	1	25	yes	complemented
11	C₂₅⋊C₂₅	—	5	20	no	—
12	C₅²⋊C₂₅	—	5	5	no	—
13	C₅²⋊C₂₅	C₅²	1	20	yes	—
14	C₂₅²	—	5	5	no	—
15	C₅³	—	5	1	no	—
16	C₅³	—	5	4	no	—
17	C₅³	—	25	1	no	—
18	C₅³	—	25	4	no	—
19	C₅³	C₅×C₂₅	1	5	yes	—
20	C₅³	C₅³	1	1	yes	characteristic
21	5₋¹⁺²	—	5	20	no	—
22	5₋¹⁺²	C₅×C₂₅	1	25	yes	—
23	C₅×C₂₅	—	5	5	no	—
24	C₅×C₂₅	—	5	20	no	—
25	C₅×C₂₅	—	5	4	no	—
26	C₅×C₂₅	—	25	1	no	—
27	C₅×C₂₅	—	25	4	no	—
28	C₅×C₂₅	H(3,𝔽₅)	1	5	yes	—
29	C₅²	—	5	1	no	—
30	C₅²	—	5	4	no	—
31	C₅²	—	5	5	no	—
32	C₅²	—	25	5	no	—
33	C₅²	—	25	20	no	—
34	C₅²	—	25	1	no	—
35	C₅²	—	25	4	no	—
36	C₅²	C₅²×C₂₅	1	1	yes	characteristic
37	C₅²	C₅×H(3,𝔽₅)	1	1	yes	characteristic
38	C₅²	#10597837	1	4	yes	—
39	C₂₅	—	5	25	no	—
40	C₂₅	—	5	5	no	—
41	C₂₅	—	25	4	no	—
42	C₂₅	—	25	20	no	—
43	C₅	—	5	1	no	—
44	C₅	—	5	4	no	—
45	C₅	—	25	5	no	—
46	C₅	C₂₅×H(3,𝔽₅)	1	1	yes	characteristic
47	C₅	#15691124	1	1	yes	characteristic
48	C₅	#15691127	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.