Subgroups — C₇₁×D₂₂₅ #44544005

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	C₇₁×D₇₅	—	3	1	no	maximal
3	C₇₁×D₄₅	—	5	1	no	maximal
4	C₃×C₂₅×C₇₁	D₃	1	1	yes	characteristic
5	D₂₅×C₇₁	—	9	1	no	Hall
6	C₅×C₉×C₇₁	D₅	1	1	yes	characteristic
7	D₁₅×C₇₁	—	15	1	no	—
8	C₂₅×C₇₁	D₉	1	1	yes	characteristic, complemented, Hall
9	D₉×C₇₁	—	25	1	no	Hall
10	C₃×C₅×C₇₁	D₁₅	1	1	yes	characteristic
11	D₅×C₇₁	—	45	1	no	—
12	C₉×C₇₁	D₂₅	1	1	yes	characteristic, complemented, Hall
13	D₂₂₅	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	D₃×C₇₁	—	75	1	no	—
15	C₅×C₇₁	D₄₅	1	1	yes	characteristic
16	C₉×C₂₅	C₂×C₇₁	1	1	yes	characteristic, complemented, Hall
17	C₃×C₇₁	D₇₅	1	1	yes	characteristic
18	D₇₅	—	3	1	no	—
19	C₂×C₇₁	—	225	1	no	Hall
20	D₄₅	—	5	1	no	—
21	C₃×C₂₅	D₃×C₇₁	1	1	yes	characteristic
22	C₇₁	D₂₂₅	1	1	yes	characteristic, direct product factor, Sylow
23	D₂₅	—	9	1	no	Hall
24	C₅×C₉	D₅×C₇₁	1	1	yes	characteristic
25	D₁₅	—	15	1	no	—
26	C₂₅	D₉×C₇₁	1	1	yes	characteristic, complemented, Sylow
27	D₉	—	25	1	no	Hall
28	C₃×C₅	D₁₅×C₇₁	1	1	yes	characteristic
29	D₅	—	45	1	no	—
30	C₉	D₂₅×C₇₁	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	75	1	no	—
32	C₅	C₇₁×D₄₅	1	1	yes	characteristic
33	C₃	C₇₁×D₇₅	1	1	yes	characteristic
34	C₂	—	225	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇₁	D₂₂₅
commutator, cosocle, hypocenter	C₉×C₂₅	C₂×C₇₁
Frattini	C₃×C₅	D₁₅×C₇₁
Fitting	C₉×C₂₅×C₇₁	C₂
socle	C₃×C₅×C₇₁	D₁₅
LCS	G ▷ C₉×C₂₅
UCS	C₁ ◁ C₇₁

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.