Subgroups — C₂₅×D₃₂₃ #30633366

Order 16150.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₁₉×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₃₂₃	C₅	1	1	yes	maximal, characteristic
3	C₅×C₁₇×C₁₉	C₂×C₅	1	1	yes	characteristic
4	C₂₅×D₁₉	—	17	1	no	maximal, Hall
5	C₂₅×D₁₇	—	19	1	no	maximal, Hall
6	D₃₂₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
7	C₁₉×C₂₅	D₁₇	1	1	yes	characteristic, complemented, Hall
8	C₁₇×C₂₅	D₁₉	1	1	yes	characteristic, complemented, Hall
9	C₁₇×C₁₉	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
10	C₅×D₁₉	—	17	1	no	—
11	C₅×D₁₇	—	19	1	no	—
12	C₅×C₁₉	C₅×D₁₇	1	1	yes	characteristic
13	C₅×C₁₇	C₅×D₁₉	1	1	yes	characteristic
14	C₂×C₂₅	—	323	1	no	Hall
15	D₁₉	—	17	1	no	Hall
16	D₁₇	—	19	1	no	Hall
17	C₂₅	D₃₂₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₁₉	C₂₅×D₁₇	1	1	yes	characteristic, complemented, Sylow
19	C₁₇	C₂₅×D₁₉	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₅	—	323	1	no	—
21	C₅	C₅×D₃₂₃	1	1	yes	characteristic
22	C₂	—	323	1	no	Sylow

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.