Subgroups — D₃×C₁₁×Dic₅ #13050362

Order 1320.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₁×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₁×Dic₅	—	3	1	no	maximal, Hall
5	C₂×C₃×C₅×C₁₁	C₂²	1	1	yes	characteristic
6	C₅×D₃×C₁₁	C₄	1	2	yes	complemented
7	C₄×D₃×C₁₁	—	5	1	no	maximal, Hall
8	C₂²×C₅×C₁₁	—	3	1	no	—
9	C₁₁×Dic₅	—	3	1	no	—
10	C₁₁×Dic₅	D₃	1	1	yes	characteristic, direct product factor
11	C₃×C₅×C₁₁	C₂×C₄	1	1	yes	characteristic, complemented, Hall
12	C₂×D₃×C₁₁	D₅	1	1	yes	characteristic
13	C₃×C₄×C₁₁	—	5	1	no	—
14	C₁₁×Dic₃	—	5	1	no	—
15	D₃×Dic₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₅×C₁₁	—	3	2	no	—
17	C₂×C₅×C₁₁	C₂×D₃	1	1	yes	characteristic
18	C₂×C₄×C₁₁	—	15	1	no	Hall
19	C₂×C₃×C₁₁	C₂×D₅	1	1	yes	characteristic
20	D₃×C₁₁	Dic₅	1	2	yes	direct product factor
21	C₂×C₅×D₃	C₂×C₁₁	1	1	yes	characteristic
22	Dic₁₅	C₂×C₁₁	1	1	yes	characteristic, complemented
23	C₃×Dic₅	C₂×C₁₁	1	1	yes	characteristic, complemented
24	C₅×C₁₁	C₄×D₃	1	1	yes	characteristic, complemented, Hall
25	C₂²×C₁₁	—	3	1	no	—
26	C₄×C₁₁	—	5	1	no	—
27	C₄×C₁₁	—	15	1	no	—
28	C₂×Dic₅	—	3	1	no	Hall
29	C₃×C₁₁	C₂×Dic₅	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₅	C₂²×C₁₁	1	1	yes	characteristic
31	C₅×D₃	C₄×C₁₁	1	2	yes	complemented
32	C₄×D₃	—	5	1	no	Hall
33	C₂×C₁₁	—	3	2	no	—
34	C₂×C₁₁	D₃×D₅	1	1	yes	characteristic
35	C₂²×C₅	—	3	1	no	—
36	Dic₅	—	3	1	no	—
37	Dic₅	D₃×C₁₁	1	1	yes	characteristic, direct product factor
38	C₃×C₅	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
39	C₂×D₃	D₅×C₁₁	1	1	yes	characteristic
40	C₃×C₄	—	5	1	no	—
41	Dic₃	—	5	1	no	—
42	C₁₁	D₃×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₅	—	3	2	no	—
44	C₂×C₅	C₂×D₃×C₁₁	1	1	yes	characteristic
45	C₂×C₄	—	15	1	no	Sylow
46	C₂×C₃	C₂×D₅×C₁₁	1	1	yes	characteristic
47	D₃	C₁₁×Dic₅	1	2	yes	direct product factor
48	C₅	C₄×D₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
49	C₂²	—	3	1	no	—
50	C₄	—	5	1	no	—
51	C₄	—	15	1	no	—
52	C₃	C₂×C₁₁×Dic₅	1	1	yes	characteristic, complemented, Sylow
53	C₂	—	3	2	no	—
54	C₂	D₃×D₅×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₃×D₅
commutator, hypocenter	C₃×C₅	C₂×C₄×C₁₁
Frattini	C₂	D₃×D₅×C₁₁
Fitting, socle	C₂×C₃×C₅×C₁₁	C₂²
prime radical	C₂×C₅×D₃×C₁₁	C₂
cosocle	C₂×C₃×C₅	C₂²×C₁₁
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₁₁×Dic₁₅	C₂	semidirect
3. C₃×C₁₁×Dic₅	C₂	semidirect
6. C₅×D₃×C₁₁	C₄	semidirect
10. C₁₁×Dic₅	D₃	direct (N × H)
11. C₃×C₅×C₁₁	C₂×C₄	semidirect
15. D₃×Dic₅	C₁₁	direct (N × H)
20. D₃×C₁₁	Dic₅	direct (N × H)
22. Dic₁₅	C₂×C₁₁	semidirect
23. C₃×Dic₅	C₂×C₁₁	semidirect
24. C₅×C₁₁	C₄×D₃	semidirect
29. C₃×C₁₁	C₂×Dic₅	semidirect
31. C₅×D₃	C₄×C₁₁	semidirect
37. Dic₅	D₃×C₁₁	direct (N × H)
38. C₃×C₅	C₂×C₄×C₁₁	semidirect
42. C₁₁	D₃×Dic₅	direct (N × H)
47. D₃	C₁₁×Dic₅	direct (N × H)
48. C₅	C₄×D₃×C₁₁	semidirect
52. C₃	C₂×C₁₁×Dic₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×C₁₁	2
C₁₁×Dic₁₅	2
C₃×C₁₁×Dic₅	2
C₂×C₁₁×Dic₅	3
C₄×D₃×C₁₁	5
D₃×Dic₅	11

Subgroups — D3×C11×Dic5 #13050362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₁×Dic₅ #13050362