Subgroups — C₅×C₃⋊#11925896 #31827653

Order 18150.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#10597245	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×#11925896	—	3	1	no	maximal, Hall
3	C₅×C₁₁×D₃₃	C₅	1	1	yes	maximal, characteristic, complemented
4	C₃⋊#11925896	C₅	1	5	yes	maximal, direct product factor
5	C₅×#10597245	D₃	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×C₁₁²	C₂×C₅	1	1	yes	characteristic, complemented
7	C₃×#10597245	C₂×C₅	1	5	yes	complemented
8	C₅×C₃⋊AGL(1,𝔽₁₁)	—	11	1	no	maximal
9	C₅×D₃×C₁₁⋊C₅	—	11	1	no	maximal
10	C₅×C₁₁×D₁₁	—	3	1	no	—
11	#11925896	—	3	5	no	—
12	C₃×C₅×C₁₁⋊C₅	—	11	1	no	—
13	C₃×C₅×C₁₁⋊C₅	—	11	1	no	—
14	C₁₁×D₃₃	C₅²	1	1	yes	characteristic, complemented, Hall
15	C₅×C₁₁²	C₅×D₃	1	1	yes	characteristic, complemented
16	#10597245	C₅×D₃	1	5	yes	complemented
17	C₂×C₅×C₁₁⋊C₅	—	33	1	no	—
18	C₅×AGL(1,𝔽₁₁)	—	33	1	no	—
19	C₃×C₁₁²	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
20	C₅×D₃₃	C₁₁⋊C₅	1	1	yes	characteristic, complemented
21	C₅×D₃×C₁₁	—	55	1	no	—
22	C₃⋊AGL(1,𝔽₁₁)	—	11	5	no	—
23	D₃×C₁₁⋊C₅	—	11	5	no	—
24	C₅×C₁₁⋊C₅	—	11	1	no	—
25	C₅×C₁₁⋊C₅	—	11	1	no	—
26	C₁₁×D₁₁	—	3	1	no	Hall
27	C₃×C₅×C₁₁	—	10	1	no	—
28	C₃×C₅×C₁₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
29	C₃×C₅×C₁₁	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented
30	C₃×C₁₁⋊C₅	—	11	5	no	—
31	C₃×C₁₁⋊C₅	—	11	5	no	—
32	C₅²×D₃	—	121	1	no	Hall
33	C₁₁²	C₅²×D₃	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₅×C₁₁	—	165	1	no	—
35	C₅×D₁₁	—	3	1	no	—
36	C₂×C₁₁⋊C₅	—	33	5	no	—
37	AGL(1,𝔽₁₁)	—	33	5	no	—
38	C₃×C₅²	—	121	1	no	Hall
39	D₃₃	C₅×C₁₁⋊C₅	1	1	yes	characteristic, complemented
40	D₃×C₁₁	—	55	1	no	—
41	C₅×C₁₁	—	10	1	no	—
42	C₅×C₁₁	D₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
43	C₅×C₁₁	C₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
44	C₁₁⋊C₅	—	11	5	no	—
45	C₁₁⋊C₅	—	11	5	no	—
46	C₂×C₅²	—	363	1	no	Hall
47	C₃×C₁₁	—	10	1	no	—
48	C₃×C₁₁	C₅×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
49	C₃×C₁₁	C₂×C₅×C₁₁⋊C₅	1	1	yes	characteristic, complemented
50	C₅×D₃	—	55	1	no	—
51	C₅×D₃	—	121	5	no	—
52	C₅²	—	121	1	no	Sylow
53	C₂×C₁₁	—	165	1	no	—
54	D₁₁	—	3	1	no	—
55	C₃×C₅	—	121	5	no	—
56	C₃×C₅	#11925896	1	1	yes	characteristic, complemented
57	C₁₁	—	10	1	no	—
58	C₁₁	C₅×D₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
59	C₁₁	C₅×C₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
60	C₂×C₅	—	363	5	no	—
61	C₂×C₅	—	165	1	no	—
62	D₃	—	55	1	no	Hall
63	C₅	—	121	5	no	—
64	C₅	C₃⋊#11925896	1	1	yes	characteristic, direct product factor
65	C₃	C₅×#11925896	1	1	yes	characteristic, complemented, Sylow
66	C₂	—	165	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₃⋊#11925896
commutator, cosocle, hypocenter	C₃×C₁₁²	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁²	C₂×C₅
LCS	G ▷ C₃×C₁₁²
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#10597245	C₂	semidirect
3. C₅×C₁₁×D₃₃	C₅	semidirect
4. C₃⋊#11925896	C₅	direct (N × H)
5. C₅×#10597245	D₃	semidirect
6. C₃×C₅×C₁₁²	C₂×C₅	semidirect
7. C₃×#10597245	C₂×C₅	semidirect
14. C₁₁×D₃₃	C₅²	semidirect
15. C₅×C₁₁²	C₅×D₃	semidirect
16. #10597245	C₅×D₃	semidirect
19. C₃×C₁₁²	C₂×C₅²	semidirect
20. C₅×D₃₃	C₁₁⋊C₅	semidirect
28. C₃×C₅×C₁₁	AGL(1,𝔽₁₁)	semidirect
29. C₃×C₅×C₁₁	C₂×C₁₁⋊C₅	semidirect
33. C₁₁²	C₅²×D₃	semidirect
39. D₃₃	C₅×C₁₁⋊C₅	semidirect
42. C₅×C₁₁	D₃×C₁₁⋊C₅	semidirect
43. C₅×C₁₁	C₃⋊AGL(1,𝔽₁₁)	semidirect
48. C₃×C₁₁	C₅×AGL(1,𝔽₁₁)	semidirect
49. C₃×C₁₁	C₂×C₅×C₁₁⋊C₅	semidirect
56. C₃×C₅	#11925896	semidirect
58. C₁₁	C₅×D₃×C₁₁⋊C₅	semidirect
59. C₁₁	C₅×C₃⋊AGL(1,𝔽₁₁)	semidirect
64. C₅	C₃⋊#11925896	direct (N × H)
65. C₃	C₅×#11925896	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#10597245	2
C₅×#11925896	3
C₅×C₁₁×D₃₃	5
C₃⋊#11925896	5
C₅×C₃⋊AGL(1,𝔽₁₁)	11
C₅×D₃×C₁₁⋊C₅	11

Subgroups — C5×C3⋊#11925896 #31827653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊#11925896 #31827653