Subgroups — C₂×#15691092 #20262113

Order 6250.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15691092	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₅×H(3,𝔽₅)	C₅	1	1	yes	maximal, characteristic
3	C₂×#10597831	C₅	1	5	yes	maximal, complemented
4	C₅×H(3,𝔽₅)	C₂×C₅	1	1	yes	characteristic
5	#10597831	C₂×C₅	1	5	yes	complemented
6	C₂×C₅³	—	5	1	no	—
7	C₂×C₅³	C₅²	1	1	yes	characteristic
8	C₂×5₋¹⁺²	—	5	5	no	—
9	C₂×H(3,𝔽₅)	—	5	5	no	—
10	C₅³	—	5	1	no	—
11	C₅³	C₂×C₅²	1	1	yes	characteristic
12	5₋¹⁺²	—	5	5	no	—
13	H(3,𝔽₅)	—	5	5	no	—
14	C₂×C₅²	—	5	1	no	—
15	C₂×C₅²	—	5	5	no	—
16	C₂×C₅²	—	25	5	no	—
17	C₂×C₅²	—	25	1	no	—
18	C₂×C₅²	H(3,𝔽₅)	1	1	yes	characteristic
19	C₂×C₂₅	—	25	5	no	—
20	C₅²	—	5	1	no	—
21	C₅²	—	5	5	no	—
22	C₅²	—	25	1	no	—
23	C₅²	—	25	5	no	—
24	C₅²	C₂×H(3,𝔽₅)	1	1	yes	characteristic
25	C₂₅	—	25	5	no	—
26	C₂×C₅	—	5	1	no	—
27	C₂×C₅	—	25	1	no	—
28	C₂×C₅	—	25	5	no	—
29	C₂×C₅	H(3,𝔽₅)⋊C₅	1	1	yes	characteristic
30	C₅	—	5	1	no	—
31	C₅	—	25	1	no	—
32	C₅	—	25	5	no	—
33	C₅	C₂×H(3,𝔽₅)⋊C₅	1	1	yes	characteristic
34	C₂	#15691092	1	1	yes	characteristic, direct product factor, Sylow

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