Subgroups — C₉×D₇₂₅ #27189372

Order 13050.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₅×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₇₂₅	C₃	1	1	yes	maximal, characteristic
3	C₉×D₁₄₅	—	5	1	no	maximal
4	C₃×C₂₅×C₂₉	C₂×C₃	1	1	yes	characteristic
5	D₇₂₅	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₅×C₉×C₂₉	D₅	1	1	yes	characteristic
7	C₃×D₁₄₅	—	5	1	no	—
8	C₂₅×C₂₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₉×D₂₉	—	25	1	no	Hall
10	C₉×D₂₅	—	29	1	no	maximal, Hall
11	C₃×C₅×C₂₉	C₃×D₅	1	1	yes	characteristic
12	D₁₄₅	—	5	1	no	—
13	C₉×C₂₉	D₂₅	1	1	yes	characteristic, complemented, Hall
14	C₉×C₂₅	D₂₉	1	1	yes	characteristic, complemented, Hall
15	C₃×D₂₉	—	25	1	no	—
16	C₃×D₂₅	—	29	1	no	—
17	C₅×C₂₉	C₉×D₅	1	1	yes	characteristic
18	C₉×D₅	—	145	1	no	—
19	C₃×C₂₉	C₃×D₂₅	1	1	yes	characteristic
20	C₃×C₂₅	C₃×D₂₉	1	1	yes	characteristic
21	D₂₉	—	25	1	no	Hall
22	D₂₅	—	29	1	no	Hall
23	C₅×C₉	D₁₄₅	1	1	yes	characteristic
24	C₃×D₅	—	145	1	no	—
25	C₂₉	C₉×D₂₅	1	1	yes	characteristic, complemented, Sylow
26	C₂₅	C₉×D₂₉	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₉	—	725	1	no	Hall
28	C₃×C₅	C₃×D₁₄₅	1	1	yes	characteristic
29	D₅	—	145	1	no	—
30	C₉	D₇₂₅	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	725	1	no	—
32	C₅	C₉×D₁₄₅	1	1	yes	characteristic
33	C₃	C₃×D₇₂₅	1	1	yes	characteristic
34	C₂	—	725	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.