Subgroups — H(3,𝔽₅)⋊C₁₂₅ #30626913

Order 15625.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₂₅	C₅	1	1	yes	maximal, characteristic, complemented
2	C₂₅×H(3,𝔽₅)	C₅	1	1	yes	maximal, characteristic
3	C₅²⋊C₁₂₅	C₅	1	4	yes	maximal, complemented
4	C₅×H(3,𝔽₅)	C₂₅	1	1	yes	characteristic
5	C₅²×C₂₅	—	5	1	no	—
6	C₅²×C₂₅	C₅²	1	1	yes	characteristic
7	C₅×C₁₂₅	—	5	1	no	—
8	C₅×C₁₂₅	—	5	5	no	—
9	C₅×C₁₂₅	—	5	4	no	—
10	C₅²⋊C₂₅	—	5	4	no	—
11	C₅²⋊C₂₅	C₂₅	1	4	yes	—
12	C₅³	—	5	1	no	—
13	C₅³	C₅×C₂₅	1	1	yes	characteristic
14	H(3,𝔽₅)	—	5	4	no	—
15	H(3,𝔽₅)	C₁₂₅	1	5	yes	complemented
16	C₅×C₂₅	—	5	1	no	—
17	C₅×C₂₅	—	5	2	no	—
18	C₅×C₂₅	—	5	2	no	—
19	C₅×C₂₅	—	5	4	no	—
20	C₅×C₂₅	—	25	1	no	—
21	C₅×C₂₅	—	25	2	no	—
22	C₅×C₂₅	—	25	2	no	—
23	C₅×C₂₅	H(3,𝔽₅)	1	1	yes	characteristic
24	C₅×C₂₅	5₋¹⁺²	1	4	yes	—
25	C₁₂₅	—	5	5	no	—
26	C₁₂₅	—	25	4	no	—
27	C₅²	—	5	1	no	—
28	C₅²	—	5	2	no	—
29	C₅²	—	5	2	no	—
30	C₅²	—	5	5	no	—
31	C₅²	—	25	1	no	—
32	C₅²	—	25	2	no	—
33	C₅²	—	25	2	no	—
34	C₅²	C₅²⋊C₂₅	1	1	yes	characteristic
35	C₅²	C₅×C₁₂₅	1	1	yes	characteristic
36	C₅²	C₁₂₅⋊C₅	1	4	yes	—
37	C₂₅	—	5	4	no	—
38	C₂₅	—	25	4	no	—
39	C₂₅	H(3,𝔽₅)⋊C₅	1	1	yes	characteristic
40	C₂₅	#10597832	1	2	yes	—
41	C₂₅	#10597833	1	2	yes	—
42	C₅	—	5	1	no	—
43	C₅	—	5	4	no	—
44	C₅	—	25	5	no	—
45	C₅	C₅²⋊C₁₂₅	1	1	yes	characteristic
46	C₅	H(3,𝔽₅)⋊C₂₅	1	1	yes	characteristic
47	C₅	#15691081	1	2	yes	—
48	C₅	#15691082	1	2	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.