Subgroups — #14514269

Order 1920.

69 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#66245⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#10619374	—	3	1	no	maximal, Hall
3	C₂×AGL(1,𝔽₁₆)	C₄	1	1	yes	characteristic
4	#67998	—	5	1	no	maximal, Hall
5	#66245	D₃	1	1	yes	characteristic
6	AGL(1,𝔽₁₆)	C₈	1	1	yes	characteristic, complemented
7	#379⋊C₃	—	5	1	no	—
8	C₂×C₂⁴⋊C₅	Dic₃	1	1	yes	characteristic
9	#1316	—	15	1	no	Sylow
10	C₃⋊#170	—	16	1	no	maximal
11	C₂×C₂²⋊A₄	AGL(1,𝔽₅)	1	1	yes	characteristic
12	A₄⋊C₈	—	20	1	no	—
13	C₂⁴⋊C₅	C₃⋊C₈	1	1	yes	characteristic, complemented
14	#379	—	5	1	no	—
15	#323	—	15	1	no	—
16	#323	—	15	1	no	—
17	C₃×Dic₅	—	16	1	no	—
18	C₂²⋊A₄	#170	1	1	yes	characteristic, complemented
19	C₄×A₄	—	20	1	no	—
20	#170	—	48	1	no	—
21	C₂⁵	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
22	C₂×C₂²⋊C₄	—	15	1	no	—
23	C₂×C₂²⋊C₄	—	15	1	no	—
24	C₂²⋊C₈	—	30	1	no	—
25	C₂²⋊C₈	—	30	1	no	—
26	C₂×C₃×C₅	—	16	1	no	—
27	C₂×A₄	—	20	1	no	—
28	C₃⋊C₈	—	80	1	no	—
29	Dic₅	—	16	1	no	—
30	C₂⁴	—	15	1	no	—
31	C₂⁴	—	15	1	no	—
32	C₂⁴	C₃⋊#170	1	1	yes	characteristic, complemented
33	C₂²×C₄	—	5	1	no	—
34	C₂²×C₄	—	15	1	no	—
35	C₂×C₈	—	60	1	no	—
36	C₂×C₈	—	60	1	no	—
37	C₂²⋊C₄	—	60	1	no	—
38	C₂²⋊C₄	—	60	1	no	—
39	C₃×C₅	—	16	1	no	Hall
40	A₄	—	20	1	no	—
41	C₃×C₄	—	80	1	no	—
42	C₂×C₅	—	16	1	no	—
43	C₂³	—	5	1	no	—
44	C₂³	—	15	1	no	—
45	C₂³	—	15	1	no	—
46	C₂³	—	30	1	no	—
47	C₂³	—	30	1	no	—
48	C₂³	—	60	1	no	—
49	C₂×C₄	—	30	1	no	—
50	C₂×C₄	—	30	1	no	—
51	C₂×C₄	—	60	1	no	—
52	C₈	—	120	1	no	—
53	C₈	—	120	1	no	—
54	C₂×C₃	—	16	1	no	—
55	C₅	—	16	1	no	Sylow
56	C₂²	—	5	1	no	—
57	C₂²	—	15	1	no	—
58	C₂²	—	15	1	no	—
59	C₂²	—	30	1	no	—
60	C₂²	—	30	1	no	—
61	C₂²	—	60	1	no	—
62	C₄	—	20	1	no	—
63	C₄	—	60	1	no	—
64	C₃	—	16	1	no	Sylow
65	C₂	—	15	1	no	—
66	C₂	—	15	1	no	—
67	C₂	AΓL(1,𝔽₁₆)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	AΓL(1,𝔽₁₆)
commutator, hypocenter	AGL(1,𝔽₁₆)	C₈
Fitting, socle	C₂⁵	ΓL(1,𝔽₁₆)
prime radical	C₂×AGL(1,𝔽₁₆)	C₄
cosocle	#66245⋊C₃	C₂
LCS	G ▷ AGL(1,𝔽₁₆)
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
6. AGL(1,𝔽₁₆)	C₈	semidirect
13. C₂⁴⋊C₅	C₃⋊C₈	semidirect
18. C₂²⋊A₄	#170	semidirect
32. C₂⁴	C₃⋊#170	semidirect

Maximal subgroups

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

subgroup	index
#66245⋊C₃	2
#10619374	3
#67998	5
C₃⋊#170	16