Subgroups — D₅×#16809824 #46776713

Order 33550.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#16809824	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅×C₁₁×C₆₁	C₅	1	1	yes	maximal, characteristic, complemented
3	C₂×#16809824	—	5	1	no	maximal
4	C₅×C₁₁×C₆₁	C₂×C₅	1	1	yes	characteristic, complemented
5	#16809824	—	2	2	no	—
6	#16809824	D₅	1	1	yes	characteristic, direct product factor
7	D₅×C₆₁⋊C₅	—	11	1	no	maximal, Hall
8	C₅×C₆₁⋊C₅	—	11	1	no	Hall
9	C₂×C₁₁×C₆₁	—	5	1	no	Hall
10	C₁₁×C₆₁	C₅×D₅	1	1	yes	characteristic, complemented, Hall
11	D₅×C₆₁	C₁₁⋊C₅	1	1	yes	characteristic, complemented
12	C₂×C₆₁⋊C₅	—	55	1	no	—
13	D₅×C₁₁⋊C₅	—	61	1	no	maximal, Hall
14	C₅×C₆₁	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented
15	C₆₁⋊C₅	—	11	1	no	—
16	C₆₁⋊C₅	—	22	2	no	—
17	C₅×C₁₁⋊C₅	—	61	1	no	Hall
18	C₂×C₆₁	—	5	1	no	Hall
19	D₅×C₁₁	C₆₁⋊C₅	1	1	yes	characteristic, complemented
20	C₂×C₁₁⋊C₅	—	305	1	no	—
21	C₆₁	D₅×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
22	C₅×C₁₁	C₂×C₆₁⋊C₅	1	1	yes	characteristic, complemented
23	C₁₁⋊C₅	—	61	1	no	—
24	C₁₁⋊C₅	—	122	2	no	—
25	C₅×D₅	—	671	1	no	Hall
26	C₅²	—	671	1	no	Sylow
27	C₂×C₁₁	—	5	1	no	Hall
28	C₁₁	D₅×C₆₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₅	—	3355	1	no	—
30	D₅	#16809824	1	1	yes	characteristic, direct product factor
31	C₅	—	1342	2	no	—
32	C₅	—	671	1	no	—
33	C₅	C₂×#16809824	1	1	yes	characteristic, complemented
34	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₁×C₆₁	C₂×C₅
LCS	G ▷ C₅×C₁₁×C₆₁
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.