Subgroups — C₂³×C₁₁×Dic₅ #13183438

Order 1760.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₁×Dic₅	C₂	1	14	yes	maximal, direct product factor
3	C₂³×C₅×C₁₁	C₄	1	8	yes	complemented
4	C₂³×C₅×C₁₁	C₂²	1	7	yes	—
5	C₂×C₁₁×Dic₅	C₂²	1	28	yes	direct product factor
6	C₂³×C₄×C₁₁	—	5	1	no	maximal, Hall
7	C₂²×C₅×C₁₁	C₂×C₄	1	28	yes	complemented
8	C₂²×C₅×C₁₁	C₂³	1	7	yes	—
9	C₁₁×Dic₅	C₂³	1	8	yes	direct product factor
10	C₂⁴×C₁₁	D₅	1	1	yes	characteristic
11	C₂²×C₄×C₁₁	—	5	14	no	—
12	C₂³×Dic₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₅×C₁₁	C₂²×C₄	1	14	yes	complemented
14	C₂×C₅×C₁₁	C₂⁴	1	1	yes	characteristic
15	C₂³×C₁₁	Dic₅	1	8	yes	direct product factor
16	C₂³×C₁₁	C₂×D₅	1	7	yes	—
17	C₂×C₄×C₁₁	—	5	28	no	—
18	C₂⁴×C₅	C₂×C₁₁	1	1	yes	characteristic
19	C₂²×Dic₅	C₂×C₁₁	1	14	yes	direct product factor
20	C₅×C₁₁	C₂³×C₄	1	1	yes	characteristic, complemented, Hall
21	C₂²×C₁₁	C₂×Dic₅	1	28	yes	direct product factor
22	C₂²×C₁₁	C₂²×D₅	1	7	yes	—
23	C₄×C₁₁	—	5	8	no	—
24	C₂³×C₅	C₄×C₁₁	1	8	yes	complemented
25	C₂³×C₅	C₂²×C₁₁	1	7	yes	—
26	C₂×Dic₅	C₂²×C₁₁	1	28	yes	direct product factor
27	C₂³×C₄	—	5	1	no	Sylow
28	C₂×C₁₁	C₂²×Dic₅	1	14	yes	direct product factor
29	C₂×C₁₁	C₂³×D₅	1	1	yes	characteristic
30	C₂²×C₅	C₂×C₄×C₁₁	1	28	yes	complemented
31	C₂²×C₅	C₂³×C₁₁	1	7	yes	—
32	Dic₅	C₂³×C₁₁	1	8	yes	direct product factor
33	C₂⁴	D₅×C₁₁	1	1	yes	characteristic
34	C₂²×C₄	—	5	14	no	—
35	C₁₁	C₂³×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₅	C₂²×C₄×C₁₁	1	14	yes	complemented
37	C₂×C₅	C₂⁴×C₁₁	1	1	yes	characteristic
38	C₂³	C₁₁×Dic₅	1	8	yes	direct product factor
39	C₂³	C₂×D₅×C₁₁	1	7	yes	—
40	C₂×C₄	—	5	28	no	—
41	C₅	C₂³×C₄×C₁₁	1	1	yes	characteristic, complemented, Sylow
42	C₂²	C₂×C₁₁×Dic₅	1	28	yes	direct product factor
43	C₂²	C₂²×D₅×C₁₁	1	7	yes	—
44	C₄	—	5	8	no	—
45	C₂	C₂²×C₁₁×Dic₅	1	14	yes	direct product factor
46	C₂	C₂³×D₅×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁴×C₁₁	D₅
commutator, hypocenter	C₅	C₂³×C₄×C₁₁
Frattini	C₂	C₂³×D₅×C₁₁
Fitting, socle, prime radical	C₂⁴×C₅×C₁₁	C₂
cosocle	C₂×C₅	C₂⁴×C₁₁
LCS	G ▷ C₅
UCS	C₁ ◁ C₂⁴×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₁×Dic₅	C₂	direct (N × H)
3. C₂³×C₅×C₁₁	C₄	semidirect
5. C₂×C₁₁×Dic₅	C₂²	direct (N × H)
7. C₂²×C₅×C₁₁	C₂×C₄	semidirect
9. C₁₁×Dic₅	C₂³	direct (N × H)
12. C₂³×Dic₅	C₁₁	direct (N × H)
13. C₂×C₅×C₁₁	C₂²×C₄	semidirect
15. C₂³×C₁₁	Dic₅	direct (N × H)
19. C₂²×Dic₅	C₂×C₁₁	direct (N × H)
20. C₅×C₁₁	C₂³×C₄	semidirect
21. C₂²×C₁₁	C₂×Dic₅	direct (N × H)
24. C₂³×C₅	C₄×C₁₁	semidirect
26. C₂×Dic₅	C₂²×C₁₁	direct (N × H)
28. C₂×C₁₁	C₂²×Dic₅	direct (N × H)
30. C₂²×C₅	C₂×C₄×C₁₁	semidirect
32. Dic₅	C₂³×C₁₁	direct (N × H)
35. C₁₁	C₂³×Dic₅	direct (N × H)
36. C₂×C₅	C₂²×C₄×C₁₁	semidirect
38. C₂³	C₁₁×Dic₅	direct (N × H)
41. C₅	C₂³×C₄×C₁₁	semidirect
42. C₂²	C₂×C₁₁×Dic₅	direct (N × H)
45. C₂	C₂²×C₁₁×Dic₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₅×C₁₁	2
C₂²×C₁₁×Dic₅	2
C₂³×C₄×C₁₁	5
C₂³×Dic₅	11

Subgroups — C23×C11×Dic5 #13183438

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₁₁×Dic₅ #13183438