Subgroups — C₉×C₅⋊D₃₅₅ #44544049

Order 31950.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₉×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅⋊D₃₅₅	C₃	1	1	yes	maximal, characteristic
3	C₉×D₃₅₅	—	5	6	no	maximal
4	C₃×C₅²×C₇₁	C₂×C₃	1	1	yes	characteristic
5	C₅⋊D₃₅₅	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₅×C₉×C₇₁	D₅	1	6	yes	complemented
7	C₃×D₃₅₅	—	5	6	no	—
8	C₅²×C₇₁	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₉×D₇₁	—	25	1	no	Hall
10	C₃×C₅×C₇₁	C₃×D₅	1	6	yes	—
11	D₃₅₅	—	5	6	no	—
12	C₉×C₇₁	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
13	C₉×C₅⋊D₅	—	71	1	no	maximal, Hall
14	C₃×D₇₁	—	25	1	no	—
15	C₅×C₇₁	C₉×D₅	1	6	yes	complemented
16	C₅²×C₉	D₇₁	1	1	yes	characteristic, complemented, Hall
17	C₃×C₇₁	C₃×C₅⋊D₅	1	1	yes	characteristic
18	C₃×C₅⋊D₅	—	71	1	no	—
19	D₇₁	—	25	1	no	Hall
20	C₉×D₅	—	355	6	no	—
21	C₃×C₅²	C₃×D₇₁	1	1	yes	characteristic
22	C₇₁	C₉×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
23	C₅⋊D₅	—	71	1	no	Hall
24	C₅×C₉	D₃₅₅	1	6	yes	complemented
25	C₃×D₅	—	355	6	no	—
26	C₅²	C₉×D₇₁	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₉	—	1775	1	no	Hall
28	C₃×C₅	C₃×D₃₅₅	1	6	yes	—
29	D₅	—	355	6	no	—
30	C₉	C₅⋊D₃₅₅	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	1775	1	no	—
32	C₅	C₉×D₃₅₅	1	6	yes	complemented
33	C₃	C₃×C₅⋊D₃₅₅	1	1	yes	characteristic
34	C₂	—	1775	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.