Subgroups — C₇₁×(C₅⋊D₅)⋊C₉ #44544038

Order 31950.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×C₅²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅⋊D₅×C₇₁	C₃	1	1	yes	maximal, characteristic
3	C₃×C₅²×C₇₁	C₂×C₃	1	1	yes	characteristic
4	C₅⋊D₅×C₇₁	C₉	1	1	yes	characteristic, complemented, Hall
5	C₃×D₅×C₇₁	—	15	2	no	—
6	C₅²×C₇₁	C₂×C₉	1	1	yes	characteristic, complemented, Hall
7	C₂×C₉×C₇₁	—	25	1	no	maximal, Hall
8	C₃×C₅×C₇₁	—	3	2	no	—
9	D₅×C₇₁	—	15	2	no	—
10	C₉×C₇₁	—	25	1	no	Hall
11	(C₅⋊D₅)⋊C₉	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₃×C₇₁	—	25	1	no	—
13	C₅×C₇₁	—	3	2	no	—
14	C₅²⋊C₉	C₂×C₇₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₇₁	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
16	C₃×C₅⋊D₅	C₃×C₇₁	1	1	yes	characteristic
17	C₂×C₇₁	—	25	1	no	Hall
18	C₃×C₅²	C₂×C₃×C₇₁	1	1	yes	characteristic
19	C₇₁	(C₅⋊D₅)⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₅⋊D₅	C₉×C₇₁	1	1	yes	characteristic, complemented, Hall
21	C₃×D₅	—	15	2	no	—
22	C₅²	C₂×C₉×C₇₁	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₉	—	25	1	no	Hall
24	C₃×C₅	—	3	2	no	—
25	D₅	—	15	2	no	—
26	C₉	—	25	1	no	Sylow
27	C₂×C₃	—	25	1	no	—
28	C₅	—	3	2	no	—
29	C₃	C₇₁×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
30	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.