Subgroups — C₃×C₅×#11925892 #31827622

Order 18150.

448 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#10597243	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×#11925892	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₁⋊D₁₁	C₅	1	1	yes	maximal, characteristic, complemented
4	C₃×#11925892	C₅	1	5	yes	maximal, direct product factor
5	C₅×#10597243	C₂×C₃	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×C₁₁²	C₂×C₅	1	1	yes	characteristic, complemented
7	C₃×#10597243	C₂×C₅	1	5	yes	complemented
8	C₃×C₅×AGL(1,𝔽₁₁)	—	11	2	no	maximal
9	C₃×C₅×AGL(1,𝔽₁₁)	—	11	1	no	maximal
10	C₃×C₅×AGL(1,𝔽₁₁)	—	11	9	no	maximal
11	C₅×C₁₁⋊D₁₁	C₃×C₅	1	1	yes	characteristic, complemented
12	#11925892	C₃×C₅	1	5	yes	direct product factor
13	C₃×C₅×C₁₁⋊C₅	—	11	2	no	—
14	C₃×C₅×C₁₁⋊C₅	—	11	1	no	—
15	C₃×C₅×C₁₁⋊C₅	—	11	9	no	—
16	C₃×C₁₁⋊D₁₁	C₅²	1	1	yes	characteristic, complemented, Hall
17	C₅×C₁₁²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
18	#10597243	C₂×C₃×C₅	1	5	yes	complemented
19	C₅×AGL(1,𝔽₁₁)	—	11	1	no	—
20	C₅×AGL(1,𝔽₁₁)	—	11	2	no	—
21	C₅×AGL(1,𝔽₁₁)	—	11	9	no	—
22	C₃×C₁₁²	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×D₁₁	—	11	2	no	—
24	C₃×C₅×D₁₁	—	55	1	no	—
25	C₃×C₅×D₁₁	—	55	9	no	—
26	C₃×AGL(1,𝔽₁₁)	—	11	10	no	—
27	C₃×AGL(1,𝔽₁₁)	—	11	5	no	—
28	C₃×AGL(1,𝔽₁₁)	—	11	45	no	—
29	C₅×C₁₁⋊C₅	—	11	1	no	—
30	C₅×C₁₁⋊C₅	—	11	2	no	—
31	C₅×C₁₁⋊C₅	—	11	9	no	—
32	C₁₁⋊D₁₁	C₃×C₅²	1	1	yes	characteristic, complemented, Hall
33	C₃×C₅×C₁₁	AGL(1,𝔽₁₁)	1	2	yes	complemented
34	C₃×C₅×C₁₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
35	C₃×C₅×C₁₁	AGL(1,𝔽₁₁)	1	9	yes	complemented
36	C₃×C₁₁⋊C₅	—	11	10	no	—
37	C₃×C₁₁⋊C₅	—	11	5	no	—
38	C₃×C₁₁⋊C₅	—	11	45	no	—
39	C₂×C₃×C₅²	—	121	1	no	Hall
40	C₁₁²	C₂×C₃×C₅²	1	1	yes	characteristic, complemented, Sylow
41	C₅×D₁₁	—	11	1	no	—
42	C₅×D₁₁	—	55	2	no	—
43	C₅×D₁₁	—	55	9	no	—
44	AGL(1,𝔽₁₁)	—	11	5	no	—
45	AGL(1,𝔽₁₁)	—	11	10	no	—
46	AGL(1,𝔽₁₁)	—	11	45	no	—
47	C₃×C₅²	—	121	1	no	Hall
48	C₃×D₁₁	—	11	2	no	—
49	C₃×D₁₁	—	55	1	no	—
50	C₃×D₁₁	—	55	9	no	—
51	C₅×C₁₁	C₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
52	C₅×C₁₁	C₃×AGL(1,𝔽₁₁)	1	2	yes	complemented
53	C₅×C₁₁	C₃×AGL(1,𝔽₁₁)	1	9	yes	complemented
54	C₁₁⋊C₅	—	11	5	no	—
55	C₁₁⋊C₅	—	11	10	no	—
56	C₁₁⋊C₅	—	11	45	no	—
57	C₂×C₅²	—	121	1	no	Hall
58	C₃×C₁₁	C₅×AGL(1,𝔽₁₁)	1	2	yes	complemented
59	C₃×C₁₁	C₅×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
60	C₃×C₁₁	C₅×AGL(1,𝔽₁₁)	1	9	yes	complemented
61	C₂×C₃×C₅	—	605	1	no	—
62	C₂×C₃×C₅	—	121	5	no	—
63	C₅²	—	121	1	no	Sylow
64	D₁₁	—	11	1	no	—
65	D₁₁	—	55	2	no	—
66	D₁₁	—	55	9	no	—
67	C₃×C₅	—	121	5	no	—
68	C₃×C₅	#11925892	1	1	yes	characteristic, direct product factor
69	C₁₁	C₃×C₅×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
70	C₁₁	C₃×C₅×AGL(1,𝔽₁₁)	1	2	yes	complemented
71	C₁₁	C₃×C₅×AGL(1,𝔽₁₁)	1	9	yes	complemented
72	C₂×C₅	—	605	1	no	—
73	C₂×C₅	—	121	5	no	—
74	C₂×C₃	—	605	1	no	Hall
75	C₅	—	121	5	no	—
76	C₅	C₃×#11925892	1	1	yes	characteristic, direct product factor
77	C₃	C₅×#11925892	1	1	yes	characteristic, direct product factor, Sylow
78	C₂	—	605	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅	#11925892
commutator, cosocle, hypocenter	C₁₁²	C₂×C₃×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁²	C₂×C₅
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#10597243	C₂	semidirect
2. C₅×#11925892	C₃	direct (N × H)
3. C₃×C₅×C₁₁⋊D₁₁	C₅	semidirect
4. C₃×#11925892	C₅	direct (N × H)
5. C₅×#10597243	C₂×C₃	semidirect
6. C₃×C₅×C₁₁²	C₂×C₅	semidirect
7. C₃×#10597243	C₂×C₅	semidirect
11. C₅×C₁₁⋊D₁₁	C₃×C₅	semidirect
12. #11925892	C₃×C₅	direct (N × H)
16. C₃×C₁₁⋊D₁₁	C₅²	semidirect
17. C₅×C₁₁²	C₂×C₃×C₅	semidirect
18. #10597243	C₂×C₃×C₅	semidirect
22. C₃×C₁₁²	C₂×C₅²	semidirect
32. C₁₁⋊D₁₁	C₃×C₅²	semidirect
33. C₃×C₅×C₁₁	AGL(1,𝔽₁₁)	semidirect
34. C₃×C₅×C₁₁	AGL(1,𝔽₁₁)	semidirect
35. C₃×C₅×C₁₁	AGL(1,𝔽₁₁)	semidirect
40. C₁₁²	C₂×C₃×C₅²	semidirect
51. C₅×C₁₁	C₃×AGL(1,𝔽₁₁)	semidirect
52. C₅×C₁₁	C₃×AGL(1,𝔽₁₁)	semidirect
53. C₅×C₁₁	C₃×AGL(1,𝔽₁₁)	semidirect
58. C₃×C₁₁	C₅×AGL(1,𝔽₁₁)	semidirect
59. C₃×C₁₁	C₅×AGL(1,𝔽₁₁)	semidirect
60. C₃×C₁₁	C₅×AGL(1,𝔽₁₁)	semidirect
68. C₃×C₅	#11925892	direct (N × H)
69. C₁₁	C₃×C₅×AGL(1,𝔽₁₁)	semidirect
70. C₁₁	C₃×C₅×AGL(1,𝔽₁₁)	semidirect
71. C₁₁	C₃×C₅×AGL(1,𝔽₁₁)	semidirect
76. C₅	C₃×#11925892	direct (N × H)
77. C₃	C₅×#11925892	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#10597243	2
C₅×#11925892	3
C₃×C₅×C₁₁⋊D₁₁	5
C₃×#11925892	5
C₃×C₅×AGL(1,𝔽₁₁)	11

Subgroups — C3×C5×#11925892 #31827622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#11925892 #31827622