Subgroups — D₁₂₆₃₅ #38760134

Order 25270.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₃₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₅₂₇	—	5	1	no	maximal, Hall
3	D₁₈₀₅	—	7	1	no	maximal, Hall
4	C₇×C₃₆₁	D₅	1	1	yes	characteristic, complemented, Hall
5	C₅×C₃₆₁	D₇	1	1	yes	characteristic, complemented, Hall
6	D₆₆₅	—	19	1	no	maximal
7	D₃₆₁	—	35	1	no	Hall
8	C₅×C₇×C₁₉	D₁₉	1	1	yes	characteristic
9	C₃₆₁	D₃₅	1	1	yes	characteristic, complemented, Sylow
10	D₁₃₃	—	95	1	no	—
11	D₉₅	—	133	1	no	—
12	C₇×C₁₉	D₉₅	1	1	yes	characteristic
13	C₅×C₁₉	D₁₃₃	1	1	yes	characteristic
14	D₃₅	—	361	1	no	Hall
15	D₁₉	—	665	1	no	—
16	C₅×C₇	D₃₆₁	1	1	yes	characteristic, complemented, Hall
17	C₁₉	D₆₆₅	1	1	yes	characteristic
18	D₇	—	1805	1	no	Hall
19	D₅	—	2527	1	no	Hall
20	C₇	D₁₈₀₅	1	1	yes	characteristic, complemented, Sylow
21	C₅	D₂₅₂₇	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	12635	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₇×C₃₆₁	C₂
Frattini	C₁₉	D₆₆₅
socle	C₅×C₇×C₁₉	D₁₉
LCS	G ▷ C₅×C₇×C₃₆₁
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.