Subgroups — D₁₅₉₇₅ #44544006

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	D₅₃₂₅	—	3	1	no	maximal
3	D₃₁₉₅	—	5	1	no	maximal
4	C₃×C₂₅×C₇₁	D₃	1	1	yes	characteristic
5	D₁₇₇₅	—	9	1	no	Hall
6	C₅×C₉×C₇₁	D₅	1	1	yes	characteristic
7	D₁₀₆₅	—	15	1	no	—
8	C₂₅×C₇₁	D₉	1	1	yes	characteristic, complemented, Hall
9	D₆₃₉	—	25	1	no	Hall
10	C₃×C₅×C₇₁	D₁₅	1	1	yes	characteristic
11	D₃₅₅	—	45	1	no	—
12	C₉×C₇₁	D₂₅	1	1	yes	characteristic, complemented, Hall
13	D₂₂₅	—	71	1	no	maximal, Hall
14	D₂₁₃	—	75	1	no	—
15	C₅×C₇₁	D₄₅	1	1	yes	characteristic
16	C₉×C₂₅	D₇₁	1	1	yes	characteristic, complemented, Hall
17	C₃×C₇₁	D₇₅	1	1	yes	characteristic
18	D₇₅	—	213	1	no	—
19	D₇₁	—	225	1	no	Hall
20	D₄₅	—	355	1	no	—
21	C₃×C₂₅	D₂₁₃	1	1	yes	characteristic
22	C₇₁	D₂₂₅	1	1	yes	characteristic, complemented, Sylow
23	D₂₅	—	639	1	no	Hall
24	C₅×C₉	D₃₅₅	1	1	yes	characteristic
25	D₁₅	—	1065	1	no	—
26	C₂₅	D₆₃₉	1	1	yes	characteristic, complemented, Sylow
27	D₉	—	1775	1	no	Hall
28	C₃×C₅	D₁₀₆₅	1	1	yes	characteristic
29	D₅	—	3195	1	no	—
30	C₉	D₁₇₇₅	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	5325	1	no	—
32	C₅	D₃₁₉₅	1	1	yes	characteristic
33	C₃	D₅₃₂₅	1	1	yes	characteristic
34	C₂	—	15975	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₂₅×C₇₁	C₂
Frattini	C₃×C₅	D₁₀₆₅
socle	C₃×C₅×C₇₁	D₁₅
LCS	G ▷ C₉×C₂₅×C₇₁
UCS	C₁

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.