Subgroups — C₅×C₃⋊#14523144 #44478012

Order 30420.

448 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#11759815	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃⋊#10621728	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅×#14523144	—	3	1	no	maximal
4	C₃×C₅×#92788	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃⋊#14523144	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×C₁₃⋊D₁₃	C₂×C₃	1	1	yes	characteristic
7	C₅×#11759815	—	2	1	no	—
8	C₅×#11759815	D₃	1	1	yes	characteristic
9	C₅×#10621728	—	3	1	no	Hall
10	C₃×#11759815	C₂×C₅	1	1	yes	characteristic
11	C₅×#92788	—	2	1	no	—
12	C₅×#92788	Dic₃	1	1	yes	characteristic, complemented
13	C₃×C₅×C₁₃²	C₃×C₄	1	1	yes	characteristic, complemented
14	C₅×C₃⋊AGL(1,𝔽₁₃)	—	13	14	no	maximal
15	C₃⋊#10621728	C₃×C₅	1	1	yes	characteristic, complemented
16	#14523144	—	3	1	no	—
17	C₅×C₁₃⋊D₁₃	C₃×D₃	1	1	yes	characteristic
18	C₃×#92788	C₄×C₅	1	1	yes	characteristic, complemented, Hall
19	C₃×C₅×D₁₃⋊C₃	—	13	14	no	—
20	C₃×C₁₃⋊D₁₃	C₂×C₃×C₅	1	1	yes	characteristic
21	#11759815	—	2	1	no	—
22	#11759815	C₅×D₃	1	1	yes	characteristic
23	C₅×C₁₃²	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
24	C₅×C₃⋊#261	—	13	14	no	—
25	C₅×AGL(1,𝔽₁₃)	—	39	14	no	—
26	#10621728	—	3	1	no	Hall
27	C₃×C₅×C₁₃⋊C₃	—	13	14	no	—
28	C₃×C₁₃²	C₃×C₄×C₅	1	1	yes	characteristic, complemented
29	#92788	—	2	1	no	—
30	#92788	C₅×Dic₃	1	1	yes	characteristic, complemented
31	C₃⋊AGL(1,𝔽₁₃)	—	13	14	no	—
32	C₃×C₅×D₁₃	—	13	14	no	—
33	C₅×D₁₃⋊C₃	—	13	14	no	—
34	C₅×D₁₃⋊C₃	—	26	14	no	—
35	C₁₃⋊D₁₃	C₃×C₅×D₃	1	1	yes	characteristic
36	C₅×#261	—	39	14	no	—
37	C₃×D₁₃⋊C₃	—	13	14	no	—
38	C₃×C₅×C₁₃	AGL(1,𝔽₁₃)	1	14	yes	complemented
39	C₅×C₁₃⋊C₃	—	13	14	no	—
40	C₅×C₁₃⋊C₃	—	26	14	no	—
41	C₃×C₅×Dic₃	—	169	1	no	Hall
42	C₁₃²	C₃×C₅×Dic₃	1	1	yes	characteristic, complemented, Sylow
43	C₃⋊#261	—	13	14	no	—
44	AGL(1,𝔽₁₃)	—	39	14	no	—
45	C₅×D₁₃	—	13	14	no	—
46	C₃×C₁₃⋊C₃	—	13	14	no	—
47	C₂×C₃²×C₅	—	169	1	no	—
48	C₃×D₁₃	—	13	14	no	—
49	D₁₃⋊C₃	—	13	14	no	—
50	D₁₃⋊C₃	—	26	14	no	—
51	C₅×C₁₃	C₃⋊AGL(1,𝔽₁₃)	1	14	yes	complemented
52	C₃×C₄×C₅	—	507	1	no	—
53	C₅×Dic₃	—	169	1	no	—
54	#261	—	39	14	no	—
55	C₃²×C₅	—	169	1	no	Hall
56	C₃×C₁₃	C₅×AGL(1,𝔽₁₃)	1	14	yes	complemented
57	C₁₃⋊C₃	—	13	14	no	—
58	C₁₃⋊C₃	—	26	14	no	—
59	C₃×Dic₃	—	169	1	no	Hall
60	C₂×C₃×C₅	—	338	1	no	—
61	C₂×C₃×C₅	—	169	1	no	—
62	C₂×C₃×C₅	—	169	1	no	—
63	D₁₃	—	13	14	no	—
64	C₄×C₅	—	507	1	no	Hall
65	C₂×C₃²	—	169	1	no	—
66	C₃×C₅	—	338	1	no	—
67	C₃×C₅	—	169	1	no	—
68	C₃×C₅	#14523144	1	1	yes	characteristic, complemented
69	C₁₃	C₅×C₃⋊AGL(1,𝔽₁₃)	1	14	yes	complemented
70	C₃×C₄	—	507	1	no	—
71	Dic₃	—	169	1	no	—
72	C₂×C₅	—	169	1	no	—
73	C₃²	—	169	1	no	Sylow
74	C₂×C₃	—	338	1	no	—
75	C₂×C₃	—	169	1	no	—
76	C₂×C₃	—	169	1	no	—
77	C₅	C₃⋊#14523144	1	1	yes	characteristic, direct product factor, Sylow
78	C₄	—	507	1	no	Sylow
79	C₃	—	338	1	no	—
80	C₃	—	169	1	no	—
81	C₃	C₅×#14523144	1	1	yes	characteristic, complemented
82	C₂	—	169	1	no	—

	subgroup	G/H
center, hypercenter	C₅	C₃⋊#14523144
commutator, hypocenter	C₃×C₁₃²	C₃×C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃²	C₃×C₄
prime radical	C₃×C₅×#11759815	C₂
cosocle	C₃×C₁₃⋊D₁₃	C₂×C₃×C₅
LCS	G ▷ C₃×C₁₃²
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
2. C₅×C₃⋊#10621728	C₃	semidirect
4. C₃×C₅×#92788	C₄	semidirect
5. C₃⋊#14523144	C₅	direct (N × H)
12. C₅×#92788	Dic₃	semidirect
13. C₃×C₅×C₁₃²	C₃×C₄	semidirect
15. C₃⋊#10621728	C₃×C₅	semidirect
18. C₃×#92788	C₄×C₅	semidirect
23. C₅×C₁₃²	C₃×Dic₃	semidirect
28. C₃×C₁₃²	C₃×C₄×C₅	semidirect
30. #92788	C₅×Dic₃	semidirect
38. C₃×C₅×C₁₃	AGL(1,𝔽₁₃)	semidirect
42. C₁₃²	C₃×C₅×Dic₃	semidirect
51. C₅×C₁₃	C₃⋊AGL(1,𝔽₁₃)	semidirect
56. C₃×C₁₃	C₅×AGL(1,𝔽₁₃)	semidirect
68. C₃×C₅	#14523144	semidirect
69. C₁₃	C₅×C₃⋊AGL(1,𝔽₁₃)	semidirect
77. C₅	C₃⋊#14523144	direct (N × H)
81. C₃	C₅×#14523144	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#11759815	2
C₅×C₃⋊#10621728	3
C₅×#14523144	3
C₃⋊#14523144	5
C₅×C₃⋊AGL(1,𝔽₁₃)	13

Subgroups — C5×C3⋊#14523144 #44478012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊#14523144 #44478012