Subgroups — D₂₈₄₃₅ #72291997

Order 56870.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄₇×C₁₂₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₆₈₇	—	5	1	no	maximal, Hall
3	C₄₇×C₁₂₁	D₅	1	1	yes	characteristic, complemented, Hall
4	D₂₅₈₅	—	11	1	no	maximal
5	C₅×C₁₁×C₄₇	D₁₁	1	1	yes	characteristic
6	D₆₀₅	—	47	1	no	maximal, Hall
7	D₅₁₇	—	55	1	no	—
8	C₅×C₁₂₁	D₄₇	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₄₇	D₅₅	1	1	yes	characteristic
10	D₂₃₅	—	121	1	no	Hall
11	D₁₂₁	—	235	1	no	Hall
12	C₅×C₄₇	D₁₂₁	1	1	yes	characteristic, complemented, Hall
13	C₁₂₁	D₂₃₅	1	1	yes	characteristic, complemented, Sylow
14	D₅₅	—	517	1	no	—
15	D₄₇	—	605	1	no	Hall
16	C₅×C₁₁	D₅₁₇	1	1	yes	characteristic
17	C₄₇	D₆₀₅	1	1	yes	characteristic, complemented, Sylow
18	D₁₁	—	2585	1	no	—
19	C₁₁	D₂₅₈₅	1	1	yes	characteristic
20	D₅	—	5687	1	no	Hall
21	C₅	D₅₆₈₇	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	28435	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₄₇×C₁₂₁	C₂
Frattini	C₁₁	D₂₅₈₅
socle	C₅×C₁₁×C₄₇	D₁₁
LCS	G ▷ C₅×C₄₇×C₁₂₁
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.