Subgroups — #14279229

Order 1920.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11746748	C₂	1	2	yes	maximal
2	C₃×#64681	C₂	1	1	yes	maximal, characteristic
3	#10598537	—	3	1	no	maximal, Hall
4	C₃×C₄×C₅×C₈	C₄	1	1	yes	characteristic
5	C₂×C₃×#672	C₄	1	1	yes	characteristic
6	C₂×C₃×#672	C₂²	1	1	yes	characteristic
7	C₃⋊#3928	C₄	1	4	yes	complemented
8	#67519	—	5	1	no	maximal, Hall
9	#64877	—	3	2	no	—
10	#64681	D₃	1	1	yes	characteristic
11	C₂×C₃×C₅×C₈	C₈	1	1	yes	characteristic
12	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
13	C₃×C₄²×C₅	C₈	1	1	yes	characteristic
14	C₃×#672	C₈	1	2	yes	—
15	C₃×#672	C₂×C₄	1	2	yes	—
16	C₃×#346	—	5	1	no	—
17	#4499	—	5	2	no	—
18	C₄×C₅×C₈	Dic₃	1	1	yes	characteristic
19	C₂×#672	Dic₃	1	1	yes	characteristic
20	C₂×#672	C₂×D₃	1	1	yes	characteristic
21	#3928	—	3	4	no	—
22	#1398	—	15	1	no	Sylow
23	C₂×C₃×C₄×C₅	—	2	1	no	—
24	C₂×C₃×C₄×C₅	C₂×C₈	1	1	yes	characteristic
25	C₃×C₅×C₈	—	2	1	no	—
26	C₃×C₅×C₈	C₄²	1	1	yes	characteristic
27	C₃×C₅×C₈	C₂×C₈	1	1	yes	characteristic
28	C₂×C₃×C₁₆	—	5	1	no	—
29	C₂×C₃×C₁₆	—	5	1	no	—
30	C₃×C₄×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
31	C₃⋊C₃₂	—	5	4	no	—
32	C₂×C₅×C₈	C₃⋊C₈	1	1	yes	characteristic
33	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
34	C₄²×C₅	C₃⋊C₈	1	1	yes	characteristic
35	#672	C₃⋊C₈	1	2	yes	—
36	#672	C₄×D₃	1	2	yes	—
37	M₆₄	—	15	2	no	—
38	#346	—	5	1	no	—
39	C₂²×C₃×C₅	M₃₂	1	1	yes	characteristic
40	C₃×C₄×C₅	—	4	1	no	—
41	C₃×C₄×C₅	C₄×C₈	1	1	yes	characteristic
42	C₃×C₄×C₅	M₃₂	1	1	yes	characteristic
43	C₂×C₃×C₈	#170	1	1	yes	characteristic
44	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
45	C₃×C₄²	#170	1	1	yes	characteristic
46	C₃×C₁₆	—	5	2	no	—
47	C₃×C₁₆	—	5	2	no	—
48	C₂×C₄×C₅	—	2	1	no	—
49	C₂×C₄×C₅	C₂×C₃⋊C₈	1	1	yes	characteristic
50	C₅×C₈	—	2	1	no	—
51	C₅×C₈	C₂×C₃⋊C₈	1	1	yes	characteristic
52	C₅×C₈	C₄×Dic₃	1	1	yes	characteristic
53	C₂×C₁₆	—	5	1	no	—
54	C₂×C₁₆	—	5	1	no	—
55	C₄×C₈	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
56	C₃₂	—	15	4	no	—
57	C₂×C₃×C₅	—	2	1	no	—
58	C₂×C₃×C₅	#346	1	1	yes	characteristic
59	C₂×C₃×C₄	—	2	1	no	—
60	C₂×C₃×C₄	C₂×#170	1	1	yes	characteristic
61	C₃×C₈	—	2	1	no	—
62	C₃×C₈	D₅⋊C₈	1	1	yes	characteristic
63	C₃×C₈	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
64	C₂²×C₅	#812	1	1	yes	characteristic
65	C₄×C₅	—	4	1	no	—
66	C₄×C₅	C₄×C₃⋊C₈	1	1	yes	characteristic
67	C₄×C₅	#812	1	1	yes	characteristic
68	C₂×C₈	C₃⋊#170	1	1	yes	characteristic
69	C₂×C₈	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
70	C₄²	C₃⋊#170	1	1	yes	characteristic
71	C₁₆	—	5	2	no	—
72	C₁₆	—	5	2	no	—
73	C₃×C₅	#1398	1	1	yes	characteristic, complemented, Hall
74	C₂²×C₃	#3998	1	1	yes	characteristic
75	C₃×C₄	—	4	1	no	—
76	C₃×C₄	#3998	1	1	yes	characteristic
77	C₃×C₄	C₄×#170	1	1	yes	characteristic
78	C₂×C₅	—	2	1	no	—
79	C₂×C₅	#4461	1	1	yes	characteristic
80	C₂×C₄	—	2	1	no	—
81	C₂×C₄	C₂×C₃⋊#170	1	1	yes	characteristic
82	C₈	—	2	1	no	—
83	C₈	D₅⋊(C₃⋊C₈)	1	1	yes	characteristic
84	C₈	C₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
85	C₂×C₃	—	2	1	no	—
86	C₂×C₃	#64859	1	1	yes	characteristic
87	C₅	#67519	1	1	yes	characteristic, complemented, Sylow
88	C₂²	#91227	1	1	yes	characteristic
89	C₄	—	4	1	no	—
90	C₄	#91227	1	1	yes	characteristic
91	C₄	C₄×C₃⋊#170	1	1	yes	characteristic
92	C₃	#10598537	1	1	yes	characteristic, complemented, Sylow
93	C₂	—	2	1	no	—
94	C₂	#11746730	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄×ΓL(1,𝔽₁₆)
commutator	C₃×C₄×C₅	C₄×C₈
Frattini	C₂×C₈	C₂×ΓL(1,𝔽₁₆)
Fitting	C₃×C₄×C₅×C₈	C₄
socle	C₂×C₃×C₅	#346
prime radical	C₂²×C₃×C₅	M₃₂
cosocle	C₂×C₃×#672	C₂²
hypercenter	C₄×C₈	ΓL(1,𝔽₁₆)
hypocenter	C₃×C₅	#1398
LCS	G ▷ C₃×C₄×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
7. C₃⋊#3928	C₄	semidirect
73. C₃×C₅	#1398	semidirect
87. C₅	#67519	semidirect
92. C₃	#10598537	semidirect

Maximal subgroups

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

subgroup	index
#11746748	2
C₃×#64681	2
#10598537	3
#67519	5