Subgroups — #11746475

Order 960.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#91222	C₂	1	1	yes	maximal, characteristic
2	C₃×#3995	C₂	1	1	yes	maximal, characteristic
3	#90934	C₂	1	1	yes	maximal, characteristic
4	ΓL(1,𝔽₈₁)	—	3	1	no	maximal, Hall
5	C₄⋊ΓL(1,𝔽₁₆)	—	2	1	no	—
6	C₃×#700	—	2	1	no	—
7	C₃×C₈×D₅	C₂²	1	1	yes	characteristic
8	C₃⋊#672	C₄	1	1	yes	characteristic, complemented
9	C₅×C₃⋊C₁₆	C₄	1	1	yes	characteristic, complemented
10	#4494	—	5	1	no	maximal, Hall
11	#3995	D₃	1	1	yes	characteristic
12	#3993	—	3	1	no	—
13	#3930	—	3	1	no	—
14	C₂×ΓL(1,𝔽₁₆)	—	4	1	no	—
15	C₃×C₄×D₅	D₄	1	1	yes	characteristic
16	C₃×#170	—	4	1	no	—
17	C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
18	C₃×#168	Q₈	1	1	yes	characteristic
19	C₃×#108	—	5	1	no	—
20	#817	—	5	1	no	—
21	#812	—	5	1	no	—
22	C₄⋊AGL(1,𝔽₅)	—	6	1	no	—
23	#700	—	2	1	no	—
24	C₈×D₅	C₂×D₃	1	1	yes	characteristic
25	C₅×C₁₆	—	3	1	no	—
26	#672	—	3	1	no	—
27	#365	—	15	1	no	Sylow
28	C₂×C₃×D₅	SD₁₆	1	1	yes	characteristic
29	ΓL(1,𝔽₁₆)	—	8	1	no	—
30	C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
31	C₃×Dic₅	SD₁₆	1	1	yes	characteristic
32	C₃×M₁₆	—	10	1	no	—
33	C₂×C₃×C₈	—	5	1	no	—
34	C₄⋊Dic₃	—	10	1	no	—
35	C₃⋊C₁₆	—	5	1	no	—
36	C₃⋊C₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
37	C₂×AGL(1,𝔽₅)	—	12	1	no	—
38	C₄×D₅	#67	1	1	yes	characteristic
39	#170	—	4	1	no	—
40	C₅×C₈	C₄×D₃	1	1	yes	characteristic
41	#168	Dic₆	1	1	yes	characteristic
42	M₃₂	—	15	1	no	—
43	#108	—	5	1	no	—
44	#106	—	15	1	no	—
45	C₂×C₃×C₅	#106	1	1	yes	characteristic
46	C₃×D₅	—	2	1	no	—
47	C₂×C₃×C₄	—	5	1	no	—
48	C₂×Dic₃	—	20	1	no	—
49	C₃×C₈	—	5	1	no	—
50	C₃×C₈	—	20	1	no	—
51	C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
52	C₂×D₅	#215	1	1	yes	characteristic
53	AGL(1,𝔽₅)	—	24	1	no	—
54	C₄×C₅	Dic₃⋊C₄	1	1	yes	characteristic
55	Dic₅	#214	1	1	yes	characteristic
56	M₁₆	—	10	1	no	—
57	C₂×C₈	—	5	1	no	—
58	C₄⋊C₄	—	30	1	no	—
59	C₁₆	—	3	1	no	—
60	C₁₆	—	15	1	no	—
61	C₃×C₅	#365	1	1	yes	characteristic, complemented, Hall
62	C₂²×C₃	—	5	1	no	—
63	C₃×C₄	—	5	1	no	—
64	C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
65	Dic₃	—	40	1	no	—
66	C₂×C₅	#808	1	1	yes	characteristic
67	D₅	—	2	1	no	—
68	C₂×C₄	—	5	1	no	—
69	C₂×C₄	—	60	1	no	—
70	C₈	—	5	1	no	—
71	C₈	—	20	1	no	—
72	C₈	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
73	C₂×C₃	—	10	1	no	—
74	C₂×C₃	#3993	1	1	yes	characteristic
75	C₅	#4494	1	1	yes	characteristic, complemented, Sylow
76	C₂²	—	5	1	no	—
77	C₄	—	5	1	no	—
78	C₄	—	120	1	no	—
79	C₄	Dic₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic
80	C₃	ΓL(1,𝔽₈₁)	1	1	yes	characteristic, complemented, Sylow
81	C₂	—	10	1	no	—
82	C₂	#91159	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#91159
commutator, Fitting	C₃×C₅×C₈	C₂×C₄
Frattini, hypercenter	C₈	D₃×AGL(1,𝔽₅)
socle	C₂×C₃×C₅	#106
prime radical	C₂×C₃×D₅	SD₁₆
cosocle	C₃×C₈×D₅	C₂²
hypocenter	C₃×C₅	#365
LCS	G ▷ C₃×C₅×C₈ ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
8. C₃⋊#672	C₄	semidirect
9. C₅×C₃⋊C₁₆	C₄	semidirect
36. C₃⋊C₁₆	AGL(1,𝔽₅)	semidirect
61. C₃×C₅	#365	semidirect
75. C₅	#4494	semidirect
80. C₃	ΓL(1,𝔽₈₁)	semidirect

Maximal subgroups

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

subgroup	index
#91222	2
C₃×#3995	2
#90934	2
ΓL(1,𝔽₈₁)	3
#4494	5