Subgroups — ΓL(1,𝔽₁₆)⋊D₃ #67199

Order 360.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃×ΓL(1,𝔽₁₆)	C₂	1	2	yes	maximal, complemented
3	D₃×AGL(1,𝔽₅)	—	3	2	no	maximal
4	C₃⋊D₁₅	C₄	1	1	yes	characteristic, complemented
5	C₅×C₃⋊D₃	C₄	1	1	yes	characteristic, complemented
6	C₃²×D₅	C₂²	1	1	yes	characteristic
7	#624	—	5	1	no	maximal, Hall
8	D₃×D₅	—	3	2	no	—
9	D₃×D₅	—	6	1	no	—
10	ΓL(1,𝔽₁₆)	D₃	1	2	yes	complemented
11	C₃×AGL(1,𝔽₅)	—	3	2	no	—
12	C₃²×C₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
13	C₂×AGL(1,𝔽₅)	—	9	1	no	Hall
14	C₂×C₃⋊D₃	—	5	1	no	—
15	C₃×Dic₃	—	5	2	no	—
16	D₁₅	—	3	2	no	—
17	D₁₅	—	6	1	no	—
18	C₃×D₅	—	2	1	no	—
19	C₃×D₅	C₂×D₃	1	2	yes	—
20	C₅×D₃	—	3	2	no	—
21	C₅×D₃	—	6	1	no	—
22	C₄×D₃	—	15	2	no	—
23	C₂×D₅	—	9	1	no	—
24	AGL(1,𝔽₅)	—	3	2	no	—
25	C₂×C₃²	—	5	1	no	—
26	C₃⋊D₃	—	5	1	no	—
27	C₃⋊D₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
28	C₃×C₅	—	2	1	no	—
29	C₃×C₅	C₄×D₃	1	2	yes	complemented
30	C₂×D₃	—	15	2	no	—
31	C₂×D₃	—	30	1	no	—
32	C₃×C₄	—	15	2	no	—
33	Dic₃	—	5	2	no	—
34	C₂×C₅	—	9	1	no	—
35	D₅	—	9	1	no	—
36	D₅	D₃²	1	1	yes	characteristic
37	C₃²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₄	—	45	1	no	Sylow
39	C₂×C₃	—	5	2	no	—
40	C₂×C₃	—	10	1	no	—
41	D₃	—	3	2	no	—
42	D₃	—	6	1	no	—
43	D₃	—	15	2	no	—
44	D₃	—	30	1	no	—
45	C₅	#624	1	1	yes	characteristic, complemented, Sylow
46	C₂²	—	45	1	no	—
47	C₄	—	15	2	no	—
48	C₃	—	2	1	no	—
49	C₃	D₃×AGL(1,𝔽₅)	1	2	yes	complemented
50	C₂	—	5	1	no	—
51	C₂	—	9	1	no	—
52	C₂	—	45	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅	C₂×C₄
prime radical	D₅×C₃⋊D₃	C₂
cosocle	C₃²×D₅	C₂²
LCS	G ▷ C₃²×C₅
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃×ΓL(1,𝔽₁₆)	C₂	semidirect
4. C₃⋊D₁₅	C₄	semidirect
5. C₅×C₃⋊D₃	C₄	semidirect
10. ΓL(1,𝔽₁₆)	D₃	semidirect
12. C₃²×C₅	C₂×C₄	semidirect
27. C₃⋊D₃	AGL(1,𝔽₅)	semidirect
29. C₃×C₅	C₄×D₃	semidirect
37. C₃²	C₂×AGL(1,𝔽₅)	semidirect
45. C₅	#624	semidirect
49. C₃	D₃×AGL(1,𝔽₅)	semidirect

Maximal subgroups

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

subgroup	index
D₅×C₃⋊D₃	2
C₃×ΓL(1,𝔽₁₆)	2
D₃×AGL(1,𝔽₅)	3
#624	5

Subgroups — ΓL(1,𝔽16)⋊D3 #67199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — ΓL(1,𝔽₁₆)⋊D₃ #67199