Subgroups — C₂×D₅×Dic₁₁ #11724998

Order 880.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂²	D₅×D₁₁
commutator, hypocenter	C₅×C₁₁	C₂²×C₄
Frattini	C₂	C₂×D₅×D₁₁
Fitting, socle	C₂²×C₅×C₁₁	C₂²
prime radical	C₂²×D₅×C₁₁	C₂
cosocle	C₂×C₅×C₁₁	C₂³
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₅₅	C₂	semidirect
3. C₂×C₅×Dic₁₁	C₂	semidirect
4. D₅×Dic₁₁	C₂	direct (N × H)
6. C₂×D₅×C₁₁	C₄	semidirect
8. Dic₅₅	C₂²	semidirect
9. C₅×Dic₁₁	C₂²	semidirect
11. C₂×C₅×C₁₁	C₂×C₄	semidirect
13. D₅×C₁₁	C₂×C₄	semidirect
17. C₂×Dic₁₁	D₅	direct (N × H)
19. C₅×C₁₁	C₂²×C₄	semidirect
24. Dic₁₁	C₂×D₅	direct (N × H)
30. C₂×C₁₁	C₄×D₅	semidirect
33. C₂×D₅	Dic₁₁	direct (N × H)
38. C₁₁	C₂×C₄×D₅	semidirect
39. C₂×C₅	C₂×Dic₁₁	semidirect
41. D₅	C₂×Dic₁₁	direct (N × H)
46. C₅	C₂²×Dic₁₁	semidirect
53. C₂	D₅×Dic₁₁	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×D₅×C₁₁	2
C₂×Dic₅₅	2
C₂×C₅×Dic₁₁	2
D₅×Dic₁₁	2
C₂²×Dic₁₁	5
C₂×C₄×D₅	11

Subgroups — C2×D5×Dic11 #11724998

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×Dic₁₁ #11724998