Subgroups — #14279210

Order 1920.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊#3928	C₂	1	2	yes	maximal
2	C₃×C₁₆×Dic₅	C₂	1	1	yes	maximal, characteristic
3	#10598653	—	3	1	no	maximal, Hall
4	C₂×C₃×C₅×C₁₆	C₄	1	1	yes	characteristic
5	C₃×C₈×Dic₅	C₄	1	1	yes	characteristic
6	C₂×C₃×#672	C₂²	1	1	yes	characteristic
7	C₃⋊#3928	C₄	1	4	yes	complemented
8	#67508	—	5	1	no	maximal, Hall
9	C₂×#3928	—	3	2	no	—
10	C₁₆×Dic₅	D₃	1	1	yes	characteristic
11	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
12	C₃×C₄×Dic₅	C₈	1	1	yes	characteristic
13	C₂×C₃×#168	C₈	1	1	yes	characteristic
14	C₃×C₅×C₁₆	C₈	1	2	yes	—
15	C₃×#672	C₂×C₄	1	2	yes	—
16	C₃×C₄×C₁₆	—	5	1	no	—
17	C₂×C₃⋊C₃₂	—	5	2	no	—
18	C₂×C₅×C₁₆	Dic₃	1	1	yes	characteristic
19	C₈×Dic₅	Dic₃	1	1	yes	characteristic
20	C₂×#672	C₂×D₃	1	1	yes	characteristic
21	#3928	—	3	4	no	—
22	#1397	—	15	1	no	Sylow
23	C₂×C₃×C₄×C₅	C₂×C₈	1	1	yes	characteristic
24	C₂×C₃×Dic₅	C₁₆	1	2	yes	—
25	C₃×C₅×C₈	C₄²	1	1	yes	characteristic
26	C₃×C₅×C₈	C₂×C₈	1	1	yes	characteristic
27	C₃×#168	C₁₆	1	2	yes	—
28	C₂×C₃×C₁₆	—	5	1	no	—
29	C₂×C₃×C₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic
30	C₃×C₄×C₈	—	5	1	no	—
31	C₃⋊C₃₂	—	5	4	no	—
32	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
33	C₄×Dic₅	C₃⋊C₈	1	1	yes	characteristic
34	C₂×#168	C₃⋊C₈	1	1	yes	characteristic
35	C₅×C₁₆	C₃⋊C₈	1	2	yes	—
36	#672	C₄×D₃	1	2	yes	—
37	C₂×C₃₂	—	15	2	no	—
38	C₄×C₁₆	—	5	1	no	—
39	C₂²×C₃×C₅	C₂×C₁₆	1	1	yes	characteristic
40	C₃×C₄×C₅	C₄×C₈	1	1	yes	characteristic
41	C₃×C₄×C₅	C₂×C₁₆	1	1	yes	characteristic
42	C₃×Dic₅	—	2	2	no	—
43	C₂×C₃×C₈	—	5	1	no	—
44	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
45	C₃×C₄²	—	5	1	no	—
46	C₃×C₁₆	—	5	2	no	—
47	C₃×C₁₆	#170	1	2	yes	—
48	C₂×C₄×C₅	C₂×C₃⋊C₈	1	1	yes	characteristic
49	C₂×Dic₅	C₃⋊C₁₆	1	2	yes	—
50	C₅×C₈	C₂×C₃⋊C₈	1	1	yes	characteristic
51	C₅×C₈	C₄×Dic₃	1	1	yes	characteristic
52	#168	C₃⋊C₁₆	1	2	yes	—
53	C₂×C₁₆	—	5	1	no	—
54	C₂×C₁₆	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
55	C₄×C₈	—	5	1	no	—
56	C₃₂	—	15	4	no	—
57	C₂×C₃×C₅	C₄×C₁₆	1	1	yes	characteristic
58	C₂×C₃×C₅	M₆₄	1	2	yes	—
59	C₂×C₃×C₄	—	5	2	no	—
60	C₂×C₃×C₄	D₅⋊C₈	1	1	yes	characteristic
61	C₃×C₈	—	5	2	no	—
62	C₃×C₈	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
63	C₃×C₈	C₂×#170	1	1	yes	characteristic
64	C₂²×C₅	C₂×C₃⋊C₁₆	1	1	yes	characteristic
65	C₄×C₅	C₄×C₃⋊C₈	1	1	yes	characteristic
66	C₄×C₅	C₂×C₃⋊C₁₆	1	1	yes	characteristic
67	Dic₅	—	2	2	no	—
68	C₂×C₈	—	5	1	no	—
69	C₂×C₈	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
70	C₄²	—	5	1	no	—
71	C₁₆	—	5	2	no	—
72	C₁₆	C₃⋊#170	1	2	yes	—
73	C₃×C₅	#1397	1	1	yes	characteristic, complemented, Hall
74	C₂²×C₃	D₅⋊C₁₆	1	1	yes	characteristic
75	C₃×C₄	—	10	2	no	—
76	C₃×C₄	D₅⋊C₁₆	1	1	yes	characteristic
77	C₃×C₄	C₄×#170	1	1	yes	characteristic
78	C₂×C₅	C₄×C₃⋊C₁₆	1	1	yes	characteristic
79	C₂×C₅	#4499	1	2	yes	—
80	C₂×C₄	—	5	2	no	—
81	C₂×C₄	D₅⋊(C₃⋊C₈)	1	1	yes	characteristic
82	C₈	—	5	2	no	—
83	C₈	C₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
84	C₈	C₂×C₃⋊#170	1	1	yes	characteristic
85	C₂×C₃	#64842	1	2	yes	—
86	C₂×C₃	#64885	1	1	yes	characteristic
87	C₅	#67508	1	1	yes	characteristic, complemented, Sylow
88	C₂²	D₅⋊(C₃⋊C₁₆)	1	1	yes	characteristic
89	C₄	—	10	2	no	—
90	C₄	D₅⋊(C₃⋊C₁₆)	1	1	yes	characteristic
91	C₄	C₄×C₃⋊#170	1	1	yes	characteristic
92	C₃	#10598653	1	1	yes	characteristic, complemented, Sylow
93	C₂	#11746713	1	2	yes	—
94	C₂	#11746756	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×ΓL(1,𝔽₁₆)
commutator	C₂×C₃×C₅	C₄×C₁₆
Fitting	C₂×C₃×C₅×C₁₆	C₄
socle, prime radical	C₂²×C₃×C₅	C₂×C₁₆
cosocle	C₂×C₃×#672	C₂²
hypercenter	C₂×C₁₆	ΓL(1,𝔽₁₆)
hypocenter	C₃×C₅	#1397
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
7. C₃⋊#3928	C₄	semidirect
73. C₃×C₅	#1397	semidirect
87. C₅	#67508	semidirect
92. C₃	#10598653	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃⋊#3928	2
C₃×C₁₆×Dic₅	2
#10598653	3
#67508	5