Subgroups — C₂₅⋊(D₃₁⋊C₉) #28358366

Order 13950.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×C₃₁⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₇₇₅	C₃	1	1	yes	maximal, characteristic
3	C₅⋊(D₃₁⋊C₉)	—	5	1	no	maximal
4	C₃×C₂₅×C₃₁	C₂×C₃	1	1	yes	characteristic
5	D₇₇₅	C₉	1	1	yes	characteristic, complemented, Hall
6	C₅×C₃₁⋊C₉	D₅	1	1	yes	characteristic
7	C₃×D₁₅₅	—	5	1	no	—
8	C₂₅×C₃₁	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	D₃₁⋊C₉	—	25	1	no	Hall
10	C₃×C₅×C₃₁	C₃×D₅	1	1	yes	characteristic
11	C₉×D₂₅	—	31	1	no	maximal, Hall
12	D₁₅₅	—	5	1	no	—
13	C₃₁⋊C₉	D₂₅	1	1	yes	characteristic, complemented, Hall
14	C₉×C₂₅	—	31	1	no	Hall
15	C₃×D₃₁	—	25	1	no	—
16	C₅×C₃₁	C₉×D₅	1	1	yes	characteristic
17	C₃×D₂₅	—	31	1	no	—
18	C₃×C₃₁	C₃×D₂₅	1	1	yes	characteristic
19	C₉×D₅	—	155	1	no	—
20	C₃×C₂₅	D₃₁⋊C₃	1	1	yes	characteristic
21	D₃₁	—	25	1	no	Hall
22	D₂₅	—	31	1	no	Hall
23	C₅×C₉	—	31	1	no	—
24	C₃₁	C₉×D₂₅	1	1	yes	characteristic, complemented, Sylow
25	C₃×D₅	—	155	1	no	—
26	C₂₅	D₃₁⋊C₉	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₉	—	775	1	no	Hall
28	C₃×C₅	C₅⋊(D₃₁⋊C₃)	1	1	yes	characteristic
29	D₅	—	155	1	no	—
30	C₉	—	31	1	no	Sylow
31	C₂×C₃	—	775	1	no	—
32	C₅	C₅⋊(D₃₁⋊C₉)	1	1	yes	characteristic
33	C₃	C₂₅⋊(D₃₁⋊C₃)	1	1	yes	characteristic
34	C₂	—	775	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.