Subgroups — #66245⋊C₃ #11756698

Order 960.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×AGL(1,𝔽₁₆)	C₂	1	1	yes	maximal, characteristic
2	#66245	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	AGL(1,𝔽₁₆)	C₄	1	1	yes	characteristic, complemented
4	#379⋊C₃	—	5	1	no	maximal, Hall
5	C₂×C₂⁴⋊C₅	C₂×C₃	1	1	yes	characteristic
6	C₂×C₂²⋊A₄	D₅	1	1	yes	characteristic
7	C₂⁴⋊C₅	C₃×C₄	1	1	yes	characteristic, complemented
8	#379	—	5	1	no	Sylow
9	C₃×Dic₅	—	16	1	no	maximal
10	C₂²⋊A₄	Dic₅	1	1	yes	characteristic, complemented
11	C₄×A₄	—	20	1	no	—
12	C₂⁵	C₃×D₅	1	1	yes	characteristic
13	C₂×C₂²⋊C₄	—	15	1	no	—
14	C₂×C₂²⋊C₄	—	15	1	no	—
15	C₂×C₃×C₅	—	16	1	no	—
16	C₂×A₄	—	20	1	no	—
17	Dic₅	—	16	1	no	—
18	C₂⁴	—	15	1	no	—
19	C₂⁴	—	15	1	no	—
20	C₂⁴	C₃×Dic₅	1	1	yes	characteristic, complemented
21	C₂²×C₄	—	5	1	no	—
22	C₂²×C₄	—	15	1	no	—
23	C₂²⋊C₄	—	30	2	no	—
24	C₂²⋊C₄	—	30	2	no	—
25	C₃×C₅	—	16	1	no	Hall
26	A₄	—	20	1	no	—
27	C₃×C₄	—	80	1	no	—
28	C₂×C₅	—	16	1	no	—
29	C₂³	—	5	1	no	—
30	C₂³	—	15	1	no	—
31	C₂³	—	15	1	no	—
32	C₂³	—	15	2	no	—
33	C₂³	—	15	2	no	—
34	C₂³	—	30	2	no	—
35	C₂×C₄	—	30	1	no	—
36	C₂×C₄	—	30	2	no	—
37	C₂×C₄	—	30	1	no	—
38	C₂×C₃	—	16	1	no	—
39	C₅	—	16	1	no	Sylow
40	C₂²	—	5	1	no	—
41	C₂²	—	15	2	no	—
42	C₂²	—	15	1	no	—
43	C₂²	—	15	2	no	—
44	C₂²	—	15	1	no	—
45	C₂²	—	30	2	no	—
46	C₄	—	20	1	no	—
47	C₄	—	60	1	no	—
48	C₃	—	16	1	no	Sylow
49	C₂	—	15	1	no	—
50	C₂	—	15	1	no	—
51	C₂	((C₂⁴⋊C₅)⋊C₂)⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	((C₂⁴⋊C₅)⋊C₂)⋊C₃
commutator, hypocenter	C₂⁴⋊C₅	C₃×C₄
Fitting, socle	C₂⁵	C₃×D₅
prime radical	C₂×AGL(1,𝔽₁₆)	C₂
cosocle	C₂×C₂⁴⋊C₅	C₂×C₃
LCS	G ▷ C₂⁴⋊C₅
UCS	C₁ ◁ C₂

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

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