Subgroups — C₂₅×D₆₃₉ #44544004

Order 31950.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₅×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₅×D₂₁₃	—	3	1	no	maximal
3	C₅×D₆₃₉	C₅	1	1	yes	maximal, characteristic
4	C₃×C₂₅×C₇₁	D₃	1	1	yes	characteristic
5	C₂₅×D₇₁	—	9	1	no	Hall
6	C₅×C₉×C₇₁	C₂×C₅	1	1	yes	characteristic
7	C₅×D₂₁₃	—	3	1	no	—
8	C₂₅×C₇₁	D₉	1	1	yes	characteristic, complemented, Hall
9	D₆₃₉	C₂₅	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₅×C₇₁	C₅×D₃	1	1	yes	characteristic
11	C₅×D₇₁	—	9	1	no	—
12	C₉×C₇₁	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
13	D₉×C₂₅	—	71	1	no	maximal, Hall
14	D₂₁₃	—	3	1	no	—
15	C₅×C₇₁	C₅×D₉	1	1	yes	characteristic
16	C₉×C₂₅	D₇₁	1	1	yes	characteristic, complemented, Hall
17	C₃×C₇₁	D₃×C₂₅	1	1	yes	characteristic
18	D₃×C₂₅	—	213	1	no	—
19	D₇₁	—	9	1	no	Hall
20	C₅×D₉	—	71	1	no	—
21	C₃×C₂₅	D₂₁₃	1	1	yes	characteristic
22	C₇₁	D₉×C₂₅	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₂₅	—	639	1	no	Hall
24	C₅×C₉	C₅×D₇₁	1	1	yes	characteristic
25	C₅×D₃	—	213	1	no	—
26	C₂₅	D₆₃₉	1	1	yes	characteristic, direct product factor, Sylow
27	D₉	—	71	1	no	Hall
28	C₃×C₅	C₅×D₂₁₃	1	1	yes	characteristic
29	C₂×C₅	—	639	1	no	—
30	C₉	C₂₅×D₇₁	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	213	1	no	—
32	C₅	C₅×D₆₃₉	1	1	yes	characteristic
33	C₃	C₂₅×D₂₁₃	1	1	yes	characteristic
34	C₂	—	639	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.