Subgroups — D₂₅×#66524 #30659201

Order 16650.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×#66524	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₃₇×D₂₅	C₃	1	1	yes	maximal, characteristic
3	D₅×#66524	—	5	1	no	maximal
4	C₃×C₂₅×C₃₇	C₂×C₃	1	1	yes	characteristic
5	C₃₇×D₂₅	C₉	1	1	yes	characteristic, complemented, Hall
6	C₅×#66524	D₅	1	1	yes	characteristic
7	C₃×D₅×C₃₇	—	5	1	no	—
8	C₂₅×C₃₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₂×#66524	—	25	1	no	Hall
10	C₃×C₅×C₃₇	C₃×D₅	1	1	yes	characteristic
11	C₉×D₂₅	—	37	1	no	maximal, Hall
12	D₅×C₃₇	—	5	1	no	—
13	#66524	D₂₅	1	1	yes	characteristic, direct product factor, Hall
14	C₉×C₂₅	—	37	1	no	Hall
15	C₂×C₃×C₃₇	—	25	1	no	—
16	C₅×C₃₇	C₉×D₅	1	1	yes	characteristic
17	C₃×D₂₅	C₃₇⋊C₃	1	1	yes	characteristic
18	C₃×C₃₇	C₃×D₂₅	1	1	yes	characteristic
19	C₉×D₅	—	185	1	no	—
20	C₃×C₂₅	C₂×C₃₇⋊C₃	1	1	yes	characteristic
21	C₂×C₃₇	—	25	1	no	Hall
22	D₂₅	#66524	1	1	yes	characteristic, direct product factor, Hall
23	C₅×C₉	—	37	1	no	—
24	C₃₇	C₉×D₂₅	1	1	yes	characteristic, complemented, Sylow
25	C₃×D₅	—	5	1	no	—
26	C₂₅	C₂×#66524	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₉	—	925	1	no	Hall
28	C₃×C₅	D₅×C₃₇⋊C₃	1	1	yes	characteristic
29	D₅	—	5	1	no	—
30	C₉	—	37	1	no	Sylow
31	C₂×C₃	—	25	1	no	—
32	C₅	D₅×#66524	1	1	yes	characteristic
33	C₃	D₂₅×C₃₇⋊C₃	1	1	yes	characteristic
34	C₂	—	25	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.