Subgroups — #10604774⋊C₃ #14511602

Order 1920.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#65429⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#10604774	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×#131⋊C₃	C₄	1	1	yes	characteristic
4	C₃×#3928	—	4	1	no	maximal
5	#2258⋊C₃	—	5	1	no	maximal, Hall
6	#65429	C₂×C₃	1	1	yes	characteristic
7	#64877	—	3	1	no	—
8	C₂×#3928	—	3	1	no	—
9	C₅×#41⋊C₃	C₈	1	1	yes	characteristic
10	C₃×#672	—	4	1	no	—
11	#504⋊C₃	—	5	1	no	—
12	C₅×#131	C₃×C₄	1	1	yes	characteristic
13	#3944	—	3	1	no	—
14	C₂×#672	—	3	1	no	—
15	#3928	—	3	1	no	—
16	#3928	A₄	1	1	yes	characteristic
17	#2258	—	5	1	no	Sylow
18	C₅×SL(2,𝔽₃)	C₁₆	1	1	yes	characteristic
19	C₃×C₅×C₈	—	4	1	no	—
20	#131⋊C₃	AGL(1,𝔽₅)	1	1	yes	characteristic
21	C₃×C₃₂	—	20	1	no	—
22	C₅×#41	C₃×C₈	1	1	yes	characteristic
23	C₅×M₁₆	—	3	1	no	—
24	C₂×C₅×C₈	—	3	1	no	—
25	#672	—	3	1	no	—
26	#672	C₂×A₄	1	1	yes	characteristic
27	#504	—	5	1	no	—
28	M₆₄	—	15	1	no	—
29	C₂×C₃₂	—	15	1	no	—
30	C₃×C₄×C₅	—	4	1	no	—
31	#41⋊C₃	#170	1	1	yes	characteristic
32	C₃×C₁₆	—	20	1	no	—
33	C₅×Q₈	C₃×C₁₆	1	1	yes	characteristic
34	C₅×D₄	—	3	1	no	—
35	C₂×C₄×C₅	—	3	1	no	—
36	C₅×C₈	—	3	1	no	—
37	C₅×C₈	C₄×A₄	1	1	yes	characteristic
38	#131	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
39	M₃₂	—	15	1	no	—
40	C₂×C₁₆	—	15	1	no	—
41	C₃₂	—	5	1	no	—
42	C₃₂	—	15	1	no	—
43	C₂×C₃×C₅	—	4	1	no	—
44	SL(2,𝔽₃)	#674	1	1	yes	characteristic
45	C₃×C₈	—	4	1	no	—
46	C₂²×C₅	—	3	1	no	—
47	C₄×C₅	—	3	1	no	—
48	C₄×C₅	C₈×A₄	1	1	yes	characteristic
49	#41	C₃×#170	1	1	yes	characteristic
50	M₁₆	—	3	1	no	—
51	C₂×C₈	—	3	1	no	—
52	C₁₆	—	5	1	no	—
53	C₁₆	—	15	1	no	—
54	C₃×C₅	—	4	1	no	Hall
55	C₃×C₄	—	4	1	no	—
56	C₂×C₅	—	6	1	no	—
57	C₂×C₅	A₄×C₁₆	1	1	yes	characteristic
58	Q₈	C₃×#674	1	1	yes	characteristic
59	D₄	—	3	1	no	—
60	C₂×C₄	—	3	1	no	—
61	C₈	—	3	1	no	—
62	C₈	A₄×AGL(1,𝔽₅)	1	1	yes	characteristic
63	C₂×C₃	—	4	1	no	—
64	C₅	#2258⋊C₃	1	1	yes	characteristic, complemented, Sylow
65	C₂²	—	3	1	no	—
66	C₄	—	3	1	no	—
67	C₄	A₄×#170	1	1	yes	characteristic
68	C₃	—	4	1	no	Sylow
69	C₂	—	6	1	no	—
70	C₂	A₄×#674	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₈	A₄×AGL(1,𝔽₅)
commutator, hypocenter	C₅×Q₈	C₃×C₁₆
Fitting	C₅×#131	C₃×C₄
socle	C₂×C₅	A₄×C₁₆
prime radical	C₅×#41⋊C₃	C₈
cosocle	#65429	C₂×C₃
LCS	G ▷ C₅×Q₈
UCS	C₁ ◁ C₈

Complements

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

N	H ≅ G/N	type
2. #10604774	C₃	semidirect
64. C₅	#2258⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#65429⋊C₃	2
#10604774	3
C₃×#3928	4
#2258⋊C₃	5

Subgroups — #10604774⋊C3 #14511602

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10604774⋊C₃ #14511602