Subgroups — #30626798

Order 15620.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16840846	C₂	1	1	yes	maximal, characteristic
2	#16840846	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₇₈₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₁₁×C₇₁	C₂×C₅	1	1	yes	characteristic
5	Dic₇₁⋊C₅	—	11	1	no	maximal, Hall
6	C₁₁×C₇₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₇₁⋊C₅	—	11	1	no	—
8	C₇₁⋊C₅	—	11	1	no	Hall
9	Dic₇₁	—	55	1	no	Hall
10	Dic₁₁⋊C₅	—	71	1	no	maximal, Hall
11	C₂×C₇₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic
12	C₂×C₁₁⋊C₅	—	71	1	no	—
13	C₇₁	Dic₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
14	C₁₁⋊C₅	—	71	1	no	Hall
15	Dic₁₁	—	355	1	no	Hall
16	C₂×C₁₁	D₇₁⋊C₅	1	1	yes	characteristic
17	C₄×C₅	—	781	1	no	Hall
18	C₁₁	Dic₇₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	—	781	1	no	—
20	C₅	—	781	1	no	Sylow
21	C₄	—	3905	1	no	Sylow
22	C₂	#21462849	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#21462849
commutator, hypocenter	C₁₁×C₇₁	C₄×C₅
Fitting, socle, cosocle	C₂×C₁₁×C₇₁	C₂×C₅
prime radical	C₂×#16840846	C₂
LCS	G ▷ C₁₁×C₇₁
UCS	C₁ ◁ C₂

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.