Subgroups — #13183169

Order 1760.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₅₅	C₂	1	2	yes	maximal
3	#11724930	C₂	1	4	yes	maximal
4	C₂×C₄×C₅×C₁₁	C₂²	1	2	yes	—
5	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×Dic₅₅	C₂²	1	4	yes	—
7	#66923	—	5	1	no	maximal, Hall
8	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
9	C₄×C₅×C₁₁	—	2	2	no	—
10	C₄×C₅×C₁₁	Q₈	1	2	yes	—
11	Dic₅₅	—	2	4	no	—
12	C₄²×C₁₁	D₅	1	1	yes	characteristic
13	C₄⋊Dic₁₁	—	5	2	no	—
14	Dic₁₁⋊C₄	—	5	4	no	—
15	#4016	—	11	1	no	maximal, Hall
16	C₂×C₅×C₁₁	C₂×Q₈	1	1	yes	characteristic
17	C₂×C₅×C₁₁	#41	1	2	yes	—
18	C₂×C₄×C₁₁	C₂×D₅	1	2	yes	—
19	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
20	C₂×Dic₁₁	—	5	4	no	—
21	C₄²×C₅	D₁₁	1	1	yes	characteristic
22	C₄⋊Dic₅	—	11	2	no	—
23	#683	—	11	4	no	—
24	C₅×C₁₁	#125	1	1	yes	characteristic, complemented, Hall
25	C₂²×C₁₁	C₂²×D₅	1	1	yes	characteristic
26	C₄×C₁₁	—	2	2	no	—
27	C₄×C₁₁	Dic₁₀	1	2	yes	—
28	Dic₁₁	—	10	4	no	—
29	C₂×C₄×C₅	C₂×D₁₁	1	2	yes	—
30	C₂×C₄×C₅	C₂×D₁₁	1	1	yes	characteristic
31	C₂×Dic₅	—	11	4	no	—
32	#125	—	55	1	no	Sylow
33	C₂×C₁₁	C₂×Dic₁₀	1	1	yes	characteristic
34	C₂×C₁₁	#709	1	2	yes	—
35	C₂²×C₅	C₂²×D₁₁	1	1	yes	characteristic
36	C₄×C₅	—	2	2	no	—
37	C₄×C₅	Dic₂₂	1	2	yes	—
38	Dic₅	—	22	4	no	—
39	C₄⋊C₄	—	55	4	no	—
40	C₄⋊C₄	—	55	2	no	—
41	C₄²	D₅₅	1	1	yes	characteristic
42	C₁₁	#4016	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₅	C₂×Dic₂₂	1	1	yes	characteristic
44	C₂×C₅	#4339	1	2	yes	—
45	C₂×C₄	—	55	4	no	—
46	C₂×C₄	C₂×D₅₅	1	2	yes	—
47	C₂×C₄	C₂×D₅₅	1	1	yes	characteristic
48	C₅	#66923	1	1	yes	characteristic, complemented, Sylow
49	C₂²	C₂²×D₅₅	1	1	yes	characteristic
50	C₄	—	2	2	no	—
51	C₄	—	110	4	no	—
52	C₄	Dic₁₁₀	1	2	yes	—
53	C₂	C₂×Dic₁₁₀	1	1	yes	characteristic
54	C₂	#11725031	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₅₅
commutator, socle, prime radical, cosocle	C₂²×C₅×C₁₁	C₂³
Fitting	C₄²×C₅×C₁₁	C₂
hypercenter	C₄²	D₅₅
hypocenter	C₅×C₁₁	#125
LCS	G ▷ C₂²×C₅×C₁₁ ▷ C₅×C₁₁
UCS	C₁ ◁ C₂² ◁ C₄²

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
24. C₅×C₁₁	#125	semidirect
42. C₁₁	#4016	semidirect
48. C₅	#66923	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄²×C₅×C₁₁	2
C₄⋊Dic₅₅	2
#11724930	2
#66923	5
#4016	11