Subgroups — Dic₄₃₇₅ #72215821

Order 17500.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₈₇₅	—	5	1	no	maximal
2	Dic₆₂₅	—	7	1	no	maximal, Hall
3	C₂×C₇×C₆₂₅	C₂	1	1	yes	maximal, characteristic
4	C₇×C₆₂₅	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×C₁₂₅	D₅	1	1	yes	characteristic
6	C₂×C₆₂₅	D₇	1	1	yes	characteristic
7	C₇×C₁₂₅	Dic₅	1	1	yes	characteristic
8	Dic₁₇₅	—	25	1	no	—
9	C₆₂₅	Dic₇	1	1	yes	characteristic, complemented, Sylow
10	Dic₁₂₅	—	35	1	no	—
11	C₂×C₇×C₂₅	D₂₅	1	1	yes	characteristic
12	C₂×C₁₂₅	D₃₅	1	1	yes	characteristic
13	C₇×C₂₅	Dic₂₅	1	1	yes	characteristic
14	Dic₃₅	—	125	1	no	—
15	C₁₂₅	Dic₃₅	1	1	yes	characteristic
16	Dic₂₅	—	175	1	no	—
17	C₂×C₅×C₇	D₁₂₅	1	1	yes	characteristic
18	C₂×C₂₅	D₁₇₅	1	1	yes	characteristic
19	C₅×C₇	Dic₁₂₅	1	1	yes	characteristic
20	Dic₇	—	625	1	no	Hall
21	C₂₅	Dic₁₇₅	1	1	yes	characteristic
22	Dic₅	—	875	1	no	—
23	C₂×C₇	D₆₂₅	1	1	yes	characteristic
24	C₂×C₅	D₈₇₅	1	1	yes	characteristic
25	C₇	Dic₆₂₅	1	1	yes	characteristic, complemented, Sylow
26	C₅	Dic₈₇₅	1	1	yes	characteristic
27	C₄	—	4375	1	no	Sylow
28	C₂	D₄₃₇₅	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.