Subgroups — C₂³×C₅×Dic₁₁ #13183423

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×C₅×Dic₁₁	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×C₅×Dic₁₁	C₂²	1	28	yes	direct product factor
6	C₂³×Dic₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₅×C₁₁	C₂×C₄	1	28	yes	complemented
8	C₂²×C₅×C₁₁	C₂³	1	7	yes	—
9	C₅×Dic₁₁	C₂³	1	8	yes	direct product factor
10	C₂⁴×C₁₁	C₂×C₅	1	1	yes	characteristic
11	C₂²×Dic₁₁	C₂×C₅	1	14	yes	direct product factor
12	C₂³×C₄×C₅	—	11	1	no	maximal, Hall
13	C₂×C₅×C₁₁	C₂²×C₄	1	14	yes	complemented
14	C₂×C₅×C₁₁	C₂⁴	1	1	yes	characteristic
15	C₂³×C₁₁	C₄×C₅	1	8	yes	complemented
16	C₂³×C₁₁	C₂²×C₅	1	7	yes	—
17	C₂×Dic₁₁	C₂²×C₅	1	28	yes	direct product factor
18	C₂⁴×C₅	D₁₁	1	1	yes	characteristic
19	C₂²×C₄×C₅	—	11	14	no	—
20	C₅×C₁₁	C₂³×C₄	1	1	yes	characteristic, complemented, Hall
21	C₂²×C₁₁	C₂×C₄×C₅	1	28	yes	complemented
22	C₂²×C₁₁	C₂³×C₅	1	7	yes	—
23	Dic₁₁	C₂³×C₅	1	8	yes	direct product factor
24	C₂³×C₅	Dic₁₁	1	8	yes	direct product factor
25	C₂³×C₅	C₂×D₁₁	1	7	yes	—
26	C₂×C₄×C₅	—	11	28	no	—
27	C₂³×C₄	—	11	1	no	Sylow
28	C₂×C₁₁	C₂²×C₄×C₅	1	14	yes	complemented
29	C₂×C₁₁	C₂⁴×C₅	1	1	yes	characteristic
30	C₂²×C₅	C₂×Dic₁₁	1	28	yes	direct product factor
31	C₂²×C₅	C₂²×D₁₁	1	7	yes	—
32	C₄×C₅	—	11	8	no	—
33	C₂⁴	C₅×D₁₁	1	1	yes	characteristic
34	C₂²×C₄	—	11	14	no	—
35	C₁₁	C₂³×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₅	C₂²×Dic₁₁	1	14	yes	direct product factor
37	C₂×C₅	C₂³×D₁₁	1	1	yes	characteristic
38	C₂³	C₅×Dic₁₁	1	8	yes	direct product factor
39	C₂³	C₂×C₅×D₁₁	1	7	yes	—
40	C₂×C₄	—	11	28	no	—
41	C₅	C₂³×Dic₁₁	1	1	yes	characteristic, direct product factor, Sylow
42	C₂²	C₂×C₅×Dic₁₁	1	28	yes	direct product factor
43	C₂²	C₂²×C₅×D₁₁	1	7	yes	—
44	C₄	—	11	8	no	—
45	C₂	C₂²×C₅×Dic₁₁	1	14	yes	direct product factor
46	C₂	C₂³×C₅×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁴×C₅	D₁₁
commutator, hypocenter	C₁₁	C₂³×C₄×C₅
Frattini	C₂	C₂³×C₅×D₁₁
Fitting, socle, prime radical	C₂⁴×C₅×C₁₁	C₂
cosocle	C₂×C₁₁	C₂⁴×C₅
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂⁴×C₅

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×Dic₁₁	C₂	direct (N × H)
3. C₂³×C₅×C₁₁	C₄	semidirect
5. C₂×C₅×Dic₁₁	C₂²	direct (N × H)
6. C₂³×Dic₁₁	C₅	direct (N × H)
7. C₂²×C₅×C₁₁	C₂×C₄	semidirect
9. C₅×Dic₁₁	C₂³	direct (N × H)
11. C₂²×Dic₁₁	C₂×C₅	direct (N × H)
13. C₂×C₅×C₁₁	C₂²×C₄	semidirect
15. C₂³×C₁₁	C₄×C₅	semidirect
17. C₂×Dic₁₁	C₂²×C₅	direct (N × H)
20. C₅×C₁₁	C₂³×C₄	semidirect
21. C₂²×C₁₁	C₂×C₄×C₅	semidirect
23. Dic₁₁	C₂³×C₅	direct (N × H)
24. C₂³×C₅	Dic₁₁	direct (N × H)
28. C₂×C₁₁	C₂²×C₄×C₅	semidirect
30. C₂²×C₅	C₂×Dic₁₁	direct (N × H)
35. C₁₁	C₂³×C₄×C₅	semidirect
36. C₂×C₅	C₂²×Dic₁₁	direct (N × H)
38. C₂³	C₅×Dic₁₁	direct (N × H)
41. C₅	C₂³×Dic₁₁	direct (N × H)
42. C₂²	C₂×C₅×Dic₁₁	direct (N × H)
45. C₂	C₂²×C₅×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
C₂⁴×C₅×C₁₁	2
C₂²×C₅×Dic₁₁	2
C₂³×Dic₁₁	5
C₂³×C₄×C₅	11

Subgroups — C23×C5×Dic11 #13183423

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₅×Dic₁₁ #13183423