Subgroups — C₃×Dic₅×C₁₁⋊C₅ #15693121

Order 3300.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	Dic₅×C₁₁⋊C₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₁×Dic₅	C₅	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×C₁₁⋊C₅	—	5	1	no	maximal
6	C₂×C₅×C₁₁⋊C₅	C₂×C₃	1	1	yes	characteristic
7	C₂×C₃×C₅×C₁₁	C₂×C₅	1	1	yes	characteristic
8	C₂×C₃×C₁₁⋊C₅	—	2	2	no	—
9	C₂×C₃×C₁₁⋊C₅	D₅	1	1	yes	characteristic
10	C₃×C₅×Dic₅	—	11	1	no	maximal, Hall
11	C₅×C₁₁⋊C₅	C₃×C₄	1	1	yes	characteristic, complemented, Hall
12	C₁₁×Dic₅	C₃×C₅	1	1	yes	characteristic, complemented
13	C₄×C₁₁⋊C₅	—	5	1	no	—
14	C₃×C₅×C₁₁	C₄×C₅	1	1	yes	characteristic, complemented
15	C₃×C₁₁⋊C₅	—	2	2	no	—
16	C₃×C₁₁⋊C₅	Dic₅	1	1	yes	characteristic, direct product factor
17	C₂×C₃×C₅²	—	11	1	no	—
18	C₃×C₄×C₁₁	—	5	1	no	Hall
19	C₂×C₅×C₁₁	C₂×C₃×C₅	1	1	yes	characteristic
20	C₂×C₁₁⋊C₅	—	2	2	no	—
21	C₂×C₁₁⋊C₅	C₃×D₅	1	1	yes	characteristic
22	C₅×Dic₅	—	11	1	no	Hall
23	C₃×C₅²	—	11	1	no	Hall
24	C₂×C₃×C₁₁	C₅×D₅	1	1	yes	characteristic
25	C₃×C₄×C₅	—	55	1	no	—
26	C₃×Dic₅	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
27	C₅×C₁₁	C₃×C₄×C₅	1	1	yes	characteristic, complemented
28	C₁₁⋊C₅	—	2	2	no	—
29	C₁₁⋊C₅	C₃×Dic₅	1	1	yes	characteristic, direct product factor
30	C₂×C₅²	—	11	1	no	—
31	C₄×C₁₁	—	5	1	no	Hall
32	C₃×C₁₁	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₅	—	11	1	no	—
34	C₂×C₃×C₅	—	22	2	no	—
35	C₂×C₃×C₅	C₂×C₁₁⋊C₅	1	1	yes	characteristic
36	C₅²	—	11	1	no	Sylow
37	C₂×C₁₁	C₃×C₅×D₅	1	1	yes	characteristic
38	C₄×C₅	—	55	1	no	—
39	Dic₅	C₃×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
40	C₃×C₅	—	11	1	no	—
41	C₃×C₅	—	22	2	no	—
42	C₃×C₅	C₄×C₁₁⋊C₅	1	1	yes	characteristic, complemented
43	C₃×C₄	—	5	1	no	Hall
44	C₁₁	C₃×C₅×Dic₅	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₅	—	11	1	no	—
46	C₂×C₅	—	22	2	no	—
47	C₂×C₅	C₂×C₃×C₁₁⋊C₅	1	1	yes	characteristic
48	C₂×C₃	D₅×C₁₁⋊C₅	1	1	yes	characteristic
49	C₅	—	11	1	no	—
50	C₅	—	22	2	no	—
51	C₅	C₃×C₄×C₁₁⋊C₅	1	1	yes	characteristic, complemented
52	C₄	—	5	1	no	Sylow
53	C₃	Dic₅×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
54	C₂	C₃×D₅×C₁₁⋊C₅	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. Dic₅×C₁₁⋊C₅	C₃	direct (N × H)
3. C₃×C₅×C₁₁⋊C₅	C₄	semidirect
4. C₃×C₁₁×Dic₅	C₅	semidirect
11. C₅×C₁₁⋊C₅	C₃×C₄	semidirect
12. C₁₁×Dic₅	C₃×C₅	semidirect
14. C₃×C₅×C₁₁	C₄×C₅	semidirect
16. C₃×C₁₁⋊C₅	Dic₅	direct (N × H)
26. C₃×Dic₅	C₁₁⋊C₅	direct (N × H)
27. C₅×C₁₁	C₃×C₄×C₅	semidirect
29. C₁₁⋊C₅	C₃×Dic₅	direct (N × H)
32. C₃×C₁₁	C₅×Dic₅	semidirect
39. Dic₅	C₃×C₁₁⋊C₅	direct (N × H)
42. C₃×C₅	C₄×C₁₁⋊C₅	semidirect
44. C₁₁	C₃×C₅×Dic₅	semidirect
51. C₅	C₃×C₄×C₁₁⋊C₅	semidirect
53. C₃	Dic₅×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
C₂×C₃×C₅×C₁₁⋊C₅	2
Dic₅×C₁₁⋊C₅	3
C₃×C₁₁×Dic₅	5
C₃×C₄×C₁₁⋊C₅	5
C₃×C₅×Dic₅	11

Subgroups — C3×Dic5×C11⋊C5 #15693121

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Dic₅×C₁₁⋊C₅ #15693121