Subgroups — C₅⋊((C₁₁⋊C₅)⋊D₅₉) #44570095

Order 32450.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁⋊C₅×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	(C₁₁⋊C₅)⋊D₅₉	—	5	1	no	maximal
3	D₃₂₄₅	C₅	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₁×C₅₉	C₂×C₅	1	1	yes	characteristic, complemented
5	C₁₁⋊C₅×C₅₉	—	2	2	no	—
6	C₁₁⋊C₅×C₅₉	D₅	1	1	yes	characteristic, complemented
7	C₅×D₂₉₅	—	11	1	no	maximal, Hall
8	C₅²×C₅₉	—	11	1	no	Hall
9	D₆₄₉	—	5	1	no	Hall
10	C₁₁×C₅₉	C₅×D₅	1	1	yes	characteristic, complemented, Hall
11	D₂₉₅	—	11	1	no	—
12	C₅×D₅₉	—	55	1	no	—
13	C₅⋊AGL(1,𝔽₁₁)	—	59	1	no	maximal, Hall
14	C₅×C₅₉	—	11	1	no	—
15	C₅×C₅₉	—	22	2	no	—
16	C₅×C₅₉	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
17	C₅×C₁₁⋊C₅	D₅₉	1	1	yes	characteristic, complemented, Hall
18	D₅₉	—	55	1	no	Hall
19	D₅₅	—	59	1	no	—
20	AGL(1,𝔽₁₁)	—	295	1	no	—
21	C₅₉	C₅⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
22	C₅×C₁₁	C₅×D₅₉	1	1	yes	characteristic, complemented
23	C₁₁⋊C₅	—	2	2	no	—
24	C₁₁⋊C₅	D₂₉₅	1	1	yes	characteristic, complemented
25	C₅×D₅	—	649	1	no	Hall
26	C₅²	—	11	1	no	Sylow
27	D₁₁	—	295	1	no	Hall
28	C₁₁	C₅×D₂₉₅	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₅	—	3245	1	no	—
30	D₅	—	649	1	no	—
31	C₅	—	11	1	no	—
32	C₅	—	22	2	no	—
33	C₅	(C₁₁⋊C₅)⋊D₅₉	1	1	yes	characteristic, complemented
34	C₂	—	3245	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₁×C₅₉	C₂×C₅
LCS	G ▷ C₅×C₁₁×C₅₉
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.