Subgroups — Dic₆₈₇₅ #72236321

Order 27500.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₃₇₅	—	5	1	no	maximal
2	Dic₆₂₅	—	11	1	no	maximal, Hall
3	C₂×C₁₁×C₆₂₅	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×C₁₂₅	D₅	1	1	yes	characteristic
5	C₁₁×C₆₂₅	C₄	1	1	yes	characteristic, complemented, Hall
6	C₁₁×C₁₂₅	Dic₅	1	1	yes	characteristic
7	C₂×C₆₂₅	D₁₁	1	1	yes	characteristic
8	Dic₂₇₅	—	25	1	no	—
9	C₆₂₅	Dic₁₁	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₁₁×C₂₅	D₂₅	1	1	yes	characteristic
11	Dic₁₂₅	—	55	1	no	—
12	C₁₁×C₂₅	Dic₂₅	1	1	yes	characteristic
13	C₂×C₁₂₅	D₅₅	1	1	yes	characteristic
14	Dic₅₅	—	125	1	no	—
15	C₁₂₅	Dic₅₅	1	1	yes	characteristic
16	C₂×C₅×C₁₁	D₁₂₅	1	1	yes	characteristic
17	Dic₂₅	—	275	1	no	—
18	C₅×C₁₁	Dic₁₂₅	1	1	yes	characteristic
19	C₂×C₂₅	D₂₇₅	1	1	yes	characteristic
20	Dic₁₁	—	625	1	no	Hall
21	C₂₅	Dic₂₇₅	1	1	yes	characteristic
22	C₂×C₁₁	D₆₂₅	1	1	yes	characteristic
23	Dic₅	—	1375	1	no	—
24	C₁₁	Dic₆₂₅	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₅	D₁₃₇₅	1	1	yes	characteristic
26	C₅	Dic₁₃₇₅	1	1	yes	characteristic
27	C₄	—	6875	1	no	Sylow
28	C₂	D₆₈₇₅	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.