Subgroups — Dic₂₆₅₀ #72212866

Order 10600.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₅₃₀	—	5	1	no	maximal
2	Dic₁₃₂₅	C₂	1	2	yes	maximal
3	C₄×C₂₅×C₅₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₅×C₅₃	C₂²	1	1	yes	characteristic
5	C₂₅×C₅₃	Q₈	1	1	yes	characteristic, complemented, Hall
6	C₄×C₅×C₅₃	D₅	1	1	yes	characteristic
7	Dic₂₆₅	—	5	2	no	—
8	C₂×C₅×C₅₃	C₂×D₅	1	1	yes	characteristic
9	Dic₁₀₆	—	25	1	no	Hall
10	C₅×C₅₃	Dic₁₀	1	1	yes	characteristic
11	C₄×C₅₃	D₂₅	1	1	yes	characteristic
12	Dic₅₃	—	25	2	no	—
13	Dic₅₀	—	53	1	no	maximal, Hall
14	C₂×C₅₃	C₂×D₂₅	1	1	yes	characteristic
15	C₄×C₂₅	D₅₃	1	1	yes	characteristic
16	Dic₂₅	—	53	2	no	—
17	C₅₃	Dic₅₀	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₂₅	C₂×D₅₃	1	1	yes	characteristic
19	Dic₁₀	—	265	1	no	—
20	C₂₅	Dic₁₀₆	1	1	yes	characteristic, complemented, Sylow
21	C₄×C₅	D₂₆₅	1	1	yes	characteristic
22	Dic₅	—	265	2	no	—
23	C₂×C₅	C₂×D₂₆₅	1	1	yes	characteristic
24	Q₈	—	1325	1	no	Sylow
25	C₅	Dic₅₃₀	1	1	yes	characteristic
26	C₄	—	1325	2	no	—
27	C₄	D₁₃₂₅	1	1	yes	characteristic
28	C₂	C₂×D₁₃₂₅	1	1	yes	characteristic

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.