Subgroups — C₅×C₃⋊(#131⋊C₃) #13086232

Order 1440.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#41⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₅×#948	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅×#131⋊C₃	—	3	1	no	maximal
4	C₃×C₅×SL(2,𝔽₃)	C₄	1	1	yes	characteristic
5	C₃×C₅×C₃⋊C₈	—	4	1	no	maximal
6	C₃⋊(#131⋊C₃)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₅×#41	C₂×C₃	1	1	yes	characteristic
8	C₅×#41⋊C₃	—	2	1	no	—
9	C₅×#41⋊C₃	D₃	1	1	yes	characteristic
10	C₅×#208	—	3	1	no	—
11	C₂×C₅×C₃⋊C₈	—	3	1	no	—
12	C₃²×C₄×C₅	—	4	1	no	—
13	C₅×#131	—	3	1	no	Hall
14	C₃×#41⋊C₃	C₂×C₅	1	1	yes	characteristic
15	C₃×C₅×Q₈	C₃×C₄	1	1	yes	characteristic
16	C₃×C₅×D₄	—	3	1	no	—
17	C₂×C₃×C₄×C₅	—	3	1	no	—
18	C₅×SL(2,𝔽₃)	—	2	1	no	—
19	C₅×SL(2,𝔽₃)	Dic₃	1	1	yes	characteristic
20	C₃×C₅×C₈	—	12	1	no	—
21	C₅×C₃⋊C₈	—	3	1	no	—
22	C₅×C₃⋊C₈	A₄	1	1	yes	characteristic
23	#948	C₃×C₅	1	1	yes	characteristic, complemented
24	#131⋊C₃	—	3	1	no	—
25	C₂×C₃²×C₅	—	4	1	no	—
26	C₅×#41	C₃×D₃	1	1	yes	characteristic
27	C₅×M₁₆	—	9	1	no	—
28	C₂×C₅×C₈	—	9	1	no	—
29	C₃×SL(2,𝔽₃)	C₄×C₅	1	1	yes	characteristic
30	C₃×C₃⋊C₈	—	4	1	no	—
31	C₂²×C₃×C₅	—	3	1	no	—
32	C₃×C₄×C₅	—	3	1	no	—
33	C₃×C₄×C₅	—	4	1	no	—
34	C₃×C₄×C₅	—	8	1	no	—
35	C₃×C₄×C₅	C₂×A₄	1	1	yes	characteristic
36	C₃×#41	C₂×C₃×C₅	1	1	yes	characteristic
37	#41⋊C₃	—	2	1	no	—
38	#41⋊C₃	C₅×D₃	1	1	yes	characteristic
39	#208	—	3	1	no	—
40	C₂×C₃⋊C₈	—	3	1	no	—
41	C₃²×C₅	—	4	1	no	Hall
42	C₅×Q₈	C₃×Dic₃	1	1	yes	characteristic
43	C₅×D₄	—	3	1	no	—
44	C₂×C₄×C₅	—	3	1	no	—
45	C₅×C₈	—	3	1	no	—
46	C₅×C₈	—	9	1	no	—
47	C₃²×C₄	—	4	1	no	—
48	#131	—	3	1	no	Sylow
49	C₂×C₃×C₅	—	4	1	no	—
50	C₂×C₃×C₅	—	6	1	no	—
51	C₂×C₃×C₅	—	8	1	no	—
52	C₂×C₃×C₅	C₄×A₄	1	1	yes	characteristic
53	C₃×Q₈	C₃×C₄×C₅	1	1	yes	characteristic
54	C₃×D₄	—	3	1	no	—
55	C₂×C₃×C₄	—	3	1	no	—
56	SL(2,𝔽₃)	—	2	1	no	—
57	SL(2,𝔽₃)	C₅×Dic₃	1	1	yes	characteristic
58	C₃×C₈	—	12	1	no	—
59	C₃⋊C₈	—	3	1	no	—
60	C₃⋊C₈	C₅×A₄	1	1	yes	characteristic
61	C₂²×C₅	—	3	1	no	—
62	C₄×C₅	—	3	1	no	—
63	C₄×C₅	D₃×A₄	1	1	yes	characteristic
64	C₂×C₃²	—	4	1	no	—
65	#41	C₃×C₅×D₃	1	1	yes	characteristic
66	M₁₆	—	9	1	no	—
67	C₂×C₈	—	9	1	no	—
68	C₃×C₅	—	4	1	no	—
69	C₃×C₅	—	8	1	no	—
70	C₃×C₅	#131⋊C₃	1	1	yes	characteristic, complemented
71	C₂²×C₃	—	3	1	no	—
72	C₃×C₄	—	3	1	no	—
73	C₃×C₄	—	4	1	no	—
74	C₃×C₄	—	8	1	no	—
75	C₃×C₄	C₂×C₅×A₄	1	1	yes	characteristic
76	C₂×C₅	—	6	1	no	—
77	C₂×C₅	Dic₃×A₄	1	1	yes	characteristic
78	C₃²	—	4	1	no	Sylow
79	Q₈	C₃×C₅×Dic₃	1	1	yes	characteristic
80	D₄	—	3	1	no	—
81	C₂×C₄	—	3	1	no	—
82	C₈	—	3	1	no	—
83	C₈	—	9	1	no	—
84	C₂×C₃	—	4	1	no	—
85	C₂×C₃	—	6	1	no	—
86	C₂×C₃	—	8	1	no	—
87	C₂×C₃	C₄×C₅×A₄	1	1	yes	characteristic
88	C₅	C₃⋊(#131⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
89	C₂²	—	3	1	no	—
90	C₄	—	3	1	no	—
91	C₄	C₅×D₃×A₄	1	1	yes	characteristic
92	C₃	—	4	1	no	—
93	C₃	—	8	1	no	—
94	C₃	C₅×#131⋊C₃	1	1	yes	characteristic, complemented
95	C₂	—	6	1	no	—
96	C₂	C₅×Dic₃×A₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₅	D₃×A₄
commutator, hypocenter	C₃×Q₈	C₃×C₄×C₅
Frattini	C₄	C₅×D₃×A₄
Fitting	C₃×C₅×#41	C₂×C₃
socle	C₂×C₃×C₅	C₄×A₄
prime radical	C₃×C₅×#41⋊C₃	C₂
cosocle	C₃×#41	C₂×C₃×C₅
LCS	G ▷ C₃×Q₈
UCS	C₁ ◁ C₄×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×#948	C₃	semidirect
6. C₃⋊(#131⋊C₃)	C₅	direct (N × H)
23. #948	C₃×C₅	semidirect
70. C₃×C₅	#131⋊C₃	semidirect
88. C₅	C₃⋊(#131⋊C₃)	direct (N × H)
94. C₃	C₅×#131⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#41⋊C₃	2
C₅×#948	3
C₅×#131⋊C₃	3
C₃×C₅×C₃⋊C₈	4
C₃⋊(#131⋊C₃)	5

Subgroups — C5×C3⋊(#131⋊C3) #13086232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊(#131⋊C₃) #13086232