Subgroups — C₂×C₃×C₄×C₁₁⋊C₅ #13050334

Order 1320.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₁₁⋊C₅	C₂	direct (N × H)
3. C₂×C₄×C₁₁⋊C₅	C₃	direct (N × H)
4. C₂×C₃×C₁₁⋊C₅	C₄	direct (N × H)
6. C₂×C₃×C₄×C₁₁	C₅	semidirect
8. C₄×C₁₁⋊C₅	C₂×C₃	direct (N × H)
9. C₃×C₁₁⋊C₅	C₂×C₄	direct (N × H)
11. C₃×C₄×C₁₁	C₂×C₅	semidirect
13. C₂×C₁₁⋊C₅	C₃×C₄	direct (N × H)
15. C₂×C₄×C₁₁	C₃×C₅	semidirect
16. C₂×C₃×C₁₁	C₄×C₅	semidirect
20. C₁₁⋊C₅	C₂×C₃×C₄	direct (N × H)
22. C₄×C₁₁	C₂×C₃×C₅	semidirect
24. C₃×C₁₁	C₂×C₄×C₅	semidirect
27. C₂×C₃×C₄	C₁₁⋊C₅	direct (N × H)
28. C₂×C₁₁	C₃×C₄×C₅	semidirect
34. C₃×C₄	C₂×C₁₁⋊C₅	direct (N × H)
35. C₁₁	C₂×C₃×C₄×C₅	semidirect
38. C₂×C₄	C₃×C₁₁⋊C₅	direct (N × H)
39. C₂×C₃	C₄×C₁₁⋊C₅	direct (N × H)
43. C₄	C₂×C₃×C₁₁⋊C₅	direct (N × H)
44. C₃	C₂×C₄×C₁₁⋊C₅	direct (N × H)
45. C₂	C₃×C₄×C₁₁⋊C₅	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×C₃×C₁₁⋊C₅	2
C₃×C₄×C₁₁⋊C₅	2
C₂×C₄×C₁₁⋊C₅	3
C₂×C₃×C₄×C₁₁	5
C₂×C₃×C₄×C₅	11

Subgroups — C2×C3×C4×C11⋊C5 #13050334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄×C₁₁⋊C₅ #13050334