Subgroups — #11746565

Order 960.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#91227	C₂	1	1	yes	maximal, characteristic
2	C₃×#3998	C₂	1	1	yes	maximal, characteristic
3	Dic₃×#168	C₂	1	1	yes	maximal, characteristic
4	#64861	—	3	1	no	maximal, Hall
5	C₂×C₃⋊#168	C₄	1	1	yes	characteristic
6	C₄×C₅×Dic₃	C₄	1	1	yes	characteristic
7	C₂×C₃×#168	C₂²	1	1	yes	characteristic
8	C₃⋊#674	—	2	1	no	—
9	C₃×#674	—	2	1	no	—
10	#4511	—	5	1	no	maximal, Hall
11	#3998	—	3	1	no	—
12	#3998	D₃	1	1	yes	characteristic
13	C₄×#168	—	3	1	no	—
14	C₂×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
15	C₂×C₅×Dic₃	—	2	1	no	—
16	C₃⋊#168	C₈	1	2	yes	—
17	C₃×#168	D₄	1	1	yes	characteristic
18	C₃×#168	Q₈	1	1	yes	characteristic
19	C₃×M₃₂	—	5	1	no	—
20	C₈×Dic₃	—	5	1	no	—
21	#812	—	5	1	no	—
22	C₄²×C₅	—	3	1	no	—
23	C₂×#168	—	3	1	no	—
24	C₂×#168	C₂×D₃	1	1	yes	characteristic
25	#674	—	2	1	no	—
26	#674	—	6	1	no	—
27	#364	—	15	1	no	Sylow
28	C₂²×C₃×C₅	M₁₆	1	1	yes	characteristic
29	C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
30	C₃×C₄×C₅	C₂×C₈	1	1	yes	characteristic
31	C₅×Dic₃	—	2	2	no	—
32	C₂×C₃×C₈	—	5	1	no	—
33	C₄×Dic₃	AGL(1,𝔽₅)	1	1	yes	characteristic
34	C₂×C₃⋊C₈	—	5	1	no	—
35	C₃×C₁₆	—	10	1	no	—
36	C₃⋊C₁₆	—	10	1	no	—
37	C₂×C₄×C₅	—	6	1	no	—
38	C₂×C₄×C₅	C₄×D₃	1	1	yes	characteristic
39	#168	—	3	2	no	—
40	#168	Dic₆	1	1	yes	characteristic
41	#168	#67	1	1	yes	characteristic
42	M₃₂	—	5	1	no	—
43	M₃₂	—	15	1	no	—
44	C₄×C₈	—	15	1	no	—
45	C₂×C₃×C₅	—	2	1	no	—
46	C₂×C₃×C₅	C₄⋊C₈	1	1	yes	characteristic
47	C₂×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
48	C₂×Dic₃	—	2	1	no	—
49	C₃×C₈	—	5	1	no	—
50	C₃×C₈	—	5	1	no	—
51	C₃⋊C₈	—	5	2	no	—
52	C₂²×C₅	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
53	C₄×C₅	—	6	2	no	—
54	C₄×C₅	D₃×C₈	1	1	yes	characteristic
55	C₄×C₅	Dic₃⋊C₄	1	1	yes	characteristic
56	C₂×C₈	—	5	1	no	—
57	C₂×C₈	—	15	1	no	—
58	C₄²	—	3	1	no	—
59	C₁₆	—	10	1	no	—
60	C₁₆	—	30	1	no	—
61	C₃×C₅	#364	1	1	yes	characteristic, complemented, Hall
62	C₂²×C₃	#704	1	1	yes	characteristic
63	C₃×C₄	D₅⋊C₈	1	1	yes	characteristic
64	C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
65	Dic₃	—	2	2	no	—
66	C₂×C₅	—	2	1	no	—
67	C₂×C₅	Dic₃⋊C₈	1	1	yes	characteristic
68	C₂×C₄	—	6	1	no	—
69	C₂×C₄	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
70	C₈	—	5	1	no	—
71	C₈	—	5	1	no	—
72	C₈	—	15	2	no	—
73	C₂×C₃	—	2	1	no	—
74	C₂×C₃	#4004	1	1	yes	characteristic
75	C₅	#4511	1	1	yes	characteristic, complemented, Sylow
76	C₂²	#6739	1	1	yes	characteristic
77	C₄	—	6	2	no	—
78	C₄	Dic₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic
79	C₄	#6738	1	1	yes	characteristic
80	C₃	#64861	1	1	yes	characteristic, complemented, Sylow
81	C₂	—	2	1	no	—
82	C₂	#91177	1	1	yes	characteristic

	subgroup	G/H
center	C₄	Dic₃⋊AGL(1,𝔽₅)
commutator	C₃×C₄×C₅	C₂×C₈
Frattini, hypercenter	C₂×C₄	D₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₄×C₅	C₂×C₄
socle	C₂×C₃×C₅	C₄⋊C₈
prime radical	C₂²×C₃×C₅	M₁₆
cosocle	C₂×C₃×#168	C₂²
hypocenter	C₃×C₅	#364
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
61. C₃×C₅	#364	semidirect
75. C₅	#4511	semidirect
80. C₃	#64861	semidirect

Maximal subgroups

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

subgroup	index
#91227	2
C₃×#3998	2
Dic₃×#168	2
#64861	3
#4511	5