Subgroups — C₃×C₅×#14559097 #49137713

Order 36300.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₅⋊(C₁₁⋊D₁₁)	C₂	1	1	yes	maximal, characteristic
2	C₅×#14559097	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₁₁²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×#14559097	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₃×C₅×#92150	—	5	1	no	maximal
6	C₅×C₅⋊(C₁₁⋊D₁₁)	C₂×C₃	1	1	yes	characteristic
7	C₃×C₅⋊(C₁₁⋊D₁₁)	C₂×C₅	1	1	yes	characteristic
8	C₃×C₅×C₁₁⋊D₁₁	—	5	1	no	—
9	C₅²×C₁₁²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
10	#14559097	C₃×C₅	1	1	yes	characteristic, direct product factor
11	C₅×#92150	—	5	1	no	—
12	C₃×C₅×C₁₁²	—	4	1	no	—
13	C₃×C₅×C₁₁²	C₄×C₅	1	1	yes	characteristic, complemented
14	C₃×C₅×C₁₁²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
15	C₃×C₅×D₅₅	—	22	6	no	—
16	C₃×#92150	—	5	1	no	Hall
17	C₅⋊(C₁₁⋊D₁₁)	C₂×C₃×C₅	1	1	yes	characteristic
18	C₅×C₁₁⋊D₁₁	—	5	1	no	—
19	C₃×C₅²×C₁₁	—	2	6	no	—
20	C₃×C₁₁⋊D₁₁	—	5	1	no	—
21	C₅×C₁₁²	—	4	1	no	—
22	C₅×C₁₁²	C₃×C₄×C₅	1	1	yes	characteristic, complemented
23	C₅×C₁₁²	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
24	C₅×D₅₅	—	22	6	no	—
25	#92150	—	5	1	no	Hall
26	C₃×C₁₁²	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
27	C₃×D₅₅	—	22	6	no	—
28	C₃×C₅×D₁₁	—	110	6	no	—
29	C₃×C₅×AGL(1,𝔽₅)	—	121	1	no	maximal, Hall
30	C₅²×C₁₁	—	2	6	no	—
31	C₁₁⋊D₁₁	—	5	1	no	—
32	C₃×C₅×C₁₁	—	2	6	no	—
33	C₃×C₅×C₁₁	—	2	6	no	—
34	C₃×C₅×C₁₁	—	4	12	no	—
35	C₃×C₅×D₅	—	121	1	no	—
36	C₁₁²	C₃×C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
37	D₅₅	—	22	6	no	—
38	C₅×D₁₁	—	110	6	no	—
39	C₅×AGL(1,𝔽₅)	—	121	1	no	Hall
40	C₃×C₅²	#92150	1	1	yes	characteristic, complemented, Hall
41	C₃×D₁₁	—	110	6	no	—
42	C₃×AGL(1,𝔽₅)	—	121	1	no	—
43	C₃×C₄×C₅	—	605	1	no	—
44	C₅×C₁₁	—	2	6	no	—
45	C₅×C₁₁	—	2	6	no	—
46	C₅×C₁₁	—	4	12	no	—
47	C₅×D₅	—	121	1	no	—
48	C₃×C₁₁	—	2	6	no	—
49	C₂×C₃×C₅	—	605	1	no	—
50	C₃×D₅	—	121	1	no	—
51	C₅²	C₃×#92150	1	1	yes	characteristic, complemented, Sylow
52	D₁₁	—	110	6	no	—
53	AGL(1,𝔽₅)	—	121	1	no	—
54	C₄×C₅	—	605	1	no	—
55	C₃×C₅	—	4	1	no	—
56	C₃×C₅	C₅×#92150	1	1	yes	characteristic, complemented
57	C₃×C₅	#14559097	1	1	yes	characteristic, direct product factor
58	C₃×C₄	—	605	1	no	Hall
59	C₁₁	—	2	6	no	—
60	C₂×C₅	—	605	1	no	—
61	D₅	—	121	1	no	—
62	C₂×C₃	—	605	1	no	—
63	C₅	—	4	1	no	—
64	C₅	C₃×C₅×#92150	1	1	yes	characteristic, complemented
65	C₅	C₃×#14559097	1	1	yes	characteristic, direct product factor
66	C₄	—	605	1	no	Sylow
67	C₃	C₅×#14559097	1	1	yes	characteristic, direct product factor, Sylow
68	C₂	—	605	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₅	#14559097
commutator, hypocenter	C₅×C₁₁²	C₃×C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₁²	C₄
prime radical	C₃×C₅×C₅⋊(C₁₁⋊D₁₁)	C₂
cosocle	C₅⋊(C₁₁⋊D₁₁)	C₂×C₃×C₅
LCS	G ▷ C₅×C₁₁²
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×#14559097	C₃	direct (N × H)
3. C₃×C₅²×C₁₁²	C₄	semidirect
4. C₃×#14559097	C₅	direct (N × H)
9. C₅²×C₁₁²	C₃×C₄	semidirect
10. #14559097	C₃×C₅	direct (N × H)
13. C₃×C₅×C₁₁²	C₄×C₅	semidirect
14. C₃×C₅×C₁₁²	AGL(1,𝔽₅)	semidirect
22. C₅×C₁₁²	C₃×C₄×C₅	semidirect
23. C₅×C₁₁²	C₃×AGL(1,𝔽₅)	semidirect
26. C₃×C₁₁²	C₅×AGL(1,𝔽₅)	semidirect
36. C₁₁²	C₃×C₅×AGL(1,𝔽₅)	semidirect
40. C₃×C₅²	#92150	semidirect
51. C₅²	C₃×#92150	semidirect
56. C₃×C₅	C₅×#92150	semidirect
57. C₃×C₅	#14559097	direct (N × H)
64. C₅	C₃×C₅×#92150	semidirect
65. C₅	C₃×#14559097	direct (N × H)
67. C₃	C₅×#14559097	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×C₅⋊(C₁₁⋊D₁₁)	2
C₅×#14559097	3
C₃×#14559097	5
C₃×C₅×#92150	5
C₃×C₅×AGL(1,𝔽₅)	121

Subgroups — C3×C5×#14559097 #49137713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#14559097 #49137713