Subgroups — #11725033

Order 880.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²⋊D₅₅	C₂	1	2	yes	maximal, complemented
3	C₂×Dic₅₅	C₂	1	2	yes	maximal, complemented
4	C₄×D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₁₁₀	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₅×C₁₁	C₂²	1	2	yes	—
7	C₂×D₅₅	C₂²	1	1	yes	characteristic
8	C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
9	Dic₅₅	C₂²	1	2	yes	—
10	Dic₅₅	C₂²	1	1	yes	characteristic
11	#4341	—	5	1	no	maximal, Hall
12	C₂×C₅×C₁₁	—	2	2	no	—
13	C₂×C₅×C₁₁	C₂³	1	1	yes	characteristic
14	D₅₅	—	2	1	no	—
15	D₄×C₁₁	D₅	1	1	yes	characteristic, complemented
16	C₂²⋊D₁₁	—	5	2	no	—
17	C₂×Dic₁₁	—	5	2	no	—
18	C₄×D₁₁	—	5	1	no	—
19	Dic₂₂	—	5	1	no	—
20	#711	—	11	1	no	maximal, Hall
21	C₅×C₁₁	#41	1	1	yes	characteristic, complemented, Hall
22	C₂²×C₁₁	C₂×D₅	1	2	yes	—
23	C₂×D₁₁	—	5	1	no	—
24	C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
25	Dic₁₁	—	5	2	no	—
26	Dic₁₁	—	5	1	no	—
27	C₅×D₄	D₁₁	1	1	yes	characteristic, complemented
28	C₂²⋊D₅	—	11	2	no	—
29	C₂×Dic₅	—	11	2	no	—
30	C₄×D₅	—	11	1	no	—
31	Dic₁₀	—	11	1	no	—
32	C₂×C₁₁	—	2	2	no	—
33	C₂×C₁₁	C₂²×D₅	1	1	yes	characteristic
34	D₁₁	—	10	1	no	—
35	C₂²×C₅	C₂×D₁₁	1	2	yes	—
36	C₂×D₅	—	11	1	no	—
37	C₄×C₅	C₂×D₁₁	1	1	yes	characteristic
38	Dic₅	—	11	2	no	—
39	Dic₅	—	11	1	no	—
40	#41	—	55	1	no	Sylow
41	C₁₁	#711	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₅	—	2	2	no	—
43	C₂×C₅	C₂²×D₁₁	1	1	yes	characteristic
44	D₅	—	22	1	no	—
45	Q₈	—	55	1	no	—
46	D₄	—	55	2	no	—
47	D₄	D₅₅	1	1	yes	characteristic, complemented
48	C₂×C₄	—	55	2	no	—
49	C₂×C₄	—	55	1	no	—
50	C₅	#4341	1	1	yes	characteristic, complemented, Sylow
51	C₂²	—	55	1	no	—
52	C₂²	C₂×D₅₅	1	2	yes	—
53	C₄	—	55	1	no	—
54	C₄	—	55	2	no	—
55	C₄	C₂×D₅₅	1	1	yes	characteristic
56	C₂	—	2	2	no	—
57	C₂	—	110	1	no	—
58	C₂	C₂²×D₅₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×D₅₅
commutator, socle, cosocle	C₂×C₅×C₁₁	C₂³
Fitting	C₅×D₄×C₁₁	C₂
hypercenter	D₄	D₅₅
hypocenter	C₅×C₁₁	#41
LCS	G ▷ C₂×C₅×C₁₁ ▷ C₅×C₁₁
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. C₅×D₄×C₁₁	C₂	semidirect
2. C₂²⋊D₅₅	C₂	semidirect
3. C₂×Dic₅₅	C₂	semidirect
4. C₄×D₅₅	C₂	semidirect
5. Dic₁₁₀	C₂	semidirect
15. D₄×C₁₁	D₅	semidirect
21. C₅×C₁₁	#41	semidirect
27. C₅×D₄	D₁₁	semidirect
41. C₁₁	#711	semidirect
47. D₄	D₅₅	semidirect
50. C₅	#4341	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₄×C₁₁	2
C₂²⋊D₅₅	2
C₂×Dic₅₅	2
C₄×D₅₅	2
Dic₁₁₀	2
#4341	5
#711	11