Subgroups — C₂²×Dic₁₁₀ #13183440

Order 1760.

312 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₅₅	C₂	1	2	yes	maximal
3	C₂×Dic₁₁₀	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₅×C₁₁	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₅×C₁₁	C₂²	1	6	yes	—
6	C₂×Dic₅₅	C₂²	1	12	yes	—
7	Dic₁₁₀	C₂²	1	16	yes	direct product factor
8	C₂²×Dic₂₂	—	5	1	no	maximal, Hall
9	C₂²×C₅×C₁₁	Q₈	1	4	yes	complemented
10	C₂²×C₅×C₁₁	C₂³	1	3	yes	—
11	C₄×C₅×C₁₁	C₂³	1	4	yes	—
12	Dic₅₅	C₂³	1	8	yes	—
13	C₂²×C₄×C₁₁	D₅	1	1	yes	characteristic
14	C₂²×Dic₁₁	—	5	2	no	—
15	C₂×Dic₂₂	—	5	12	no	—
16	C₂²×Dic₁₀	—	11	1	no	maximal, Hall
17	C₂×C₅×C₁₁	C₂×Q₈	1	6	yes	complemented
18	C₂×C₅×C₁₁	C₂⁴	1	1	yes	characteristic
19	C₂³×C₁₁	C₂×D₅	1	1	yes	characteristic
20	C₂×C₄×C₁₁	C₂×D₅	1	6	yes	—
21	C₂×Dic₁₁	—	5	12	no	—
22	Dic₂₂	—	5	16	no	—
23	C₂²×C₄×C₅	D₁₁	1	1	yes	characteristic
24	C₂²×Dic₅	—	11	2	no	—
25	C₂×Dic₁₀	—	11	12	no	—
26	C₅×C₁₁	C₂²×Q₈	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₁₁	Dic₁₀	1	4	yes	complemented
28	C₂²×C₁₁	C₂²×D₅	1	3	yes	—
29	C₄×C₁₁	C₂²×D₅	1	4	yes	—
30	Dic₁₁	—	5	8	no	—
31	C₂³×C₅	C₂×D₁₁	1	1	yes	characteristic
32	C₂×C₄×C₅	C₂×D₁₁	1	6	yes	—
33	C₂×Dic₅	—	11	12	no	—
34	Dic₁₀	—	11	16	no	—
35	C₂²×Q₈	—	55	1	no	Sylow
36	C₂×C₁₁	C₂×Dic₁₀	1	6	yes	complemented
37	C₂×C₁₁	C₂³×D₅	1	1	yes	characteristic
38	C₂²×C₅	Dic₂₂	1	4	yes	complemented
39	C₂²×C₅	C₂²×D₁₁	1	3	yes	—
40	C₄×C₅	C₂²×D₁₁	1	4	yes	—
41	Dic₅	—	11	8	no	—
42	C₂×Q₈	—	55	12	no	—
43	C₂²×C₄	—	55	2	no	—
44	C₂²×C₄	D₅₅	1	1	yes	characteristic
45	C₁₁	C₂²×Dic₁₀	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₅	C₂×Dic₂₂	1	6	yes	complemented
47	C₂×C₅	C₂³×D₁₁	1	1	yes	characteristic
48	C₂³	C₂×D₅₅	1	1	yes	characteristic
49	Q₈	—	55	16	no	—
50	C₂×C₄	—	55	12	no	—
51	C₂×C₄	C₂×D₅₅	1	6	yes	—
52	C₅	C₂²×Dic₂₂	1	1	yes	characteristic, complemented, Sylow
53	C₂²	Dic₁₁₀	1	4	yes	direct product factor
54	C₂²	C₂²×D₅₅	1	3	yes	—
55	C₄	—	55	8	no	—
56	C₄	C₂²×D₅₅	1	4	yes	—
57	C₂	C₂×Dic₁₁₀	1	6	yes	direct product factor
58	C₂	C₂³×D₅₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₅₅
commutator, cosocle	C₂×C₅×C₁₁	C₂⁴
Frattini	C₂	C₂³×D₅₅
Fitting	C₂²×C₄×C₅×C₁₁	C₂
socle, prime radical	C₂³×C₅×C₁₁	C₂²
hypercenter	C₂²×C₄	D₅₅
hypocenter	C₅×C₁₁	C₂²×Q₈
LCS	G ▷ C₂×C₅×C₁₁ ▷ C₅×C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
3. C₂×Dic₁₁₀	C₂	direct (N × H)
7. Dic₁₁₀	C₂²	direct (N × H)
9. C₂²×C₅×C₁₁	Q₈	semidirect
17. C₂×C₅×C₁₁	C₂×Q₈	semidirect
26. C₅×C₁₁	C₂²×Q₈	semidirect
27. C₂²×C₁₁	Dic₁₀	semidirect
36. C₂×C₁₁	C₂×Dic₁₀	semidirect
38. C₂²×C₅	Dic₂₂	semidirect
45. C₁₁	C₂²×Dic₁₀	semidirect
46. C₂×C₅	C₂×Dic₂₂	semidirect
52. C₅	C₂²×Dic₂₂	semidirect
53. C₂²	Dic₁₁₀	direct (N × H)
57. C₂	C₂×Dic₁₁₀	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₅×C₁₁	2
C₂²×Dic₅₅	2
C₂×Dic₁₁₀	2
C₂²×Dic₂₂	5
C₂²×Dic₁₀	11

Subgroups — C22×Dic110 #13183440

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×Dic₁₁₀ #13183440