Subgroups — #11746800

Order 960.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#4090	C₂	1	1	yes	maximal, characteristic
2	#91234	C₂	1	2	yes	maximal
3	#64929	—	3	1	no	maximal, Hall
4	C₂×C₃×C₅×Q₈	C₄	1	1	yes	characteristic
5	C₂×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
6	#6762	—	2	2	no	—
7	C₃×#683	—	2	2	no	—
8	C₃×C₄×Dic₅	C₄	1	1	yes	characteristic
9	#4548	—	5	1	no	maximal, Hall
10	#4090	D₃	1	1	yes	characteristic
11	#4005	—	3	2	no	—
12	C₃×C₅×Q₈	—	4	1	no	—
13	C₂×C₃×C₄×C₅	—	2	1	no	—
14	C₂×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
15	C₂×C₃×Dic₅	—	2	1	no	—
16	C₂×C₃×Dic₅	D₄	1	2	yes	—
17	C₃×Dic₁₀	—	4	1	no	—
18	C₃⋊#170	—	4	2	no	—
19	C₃×C₄⋊Q₈	—	5	1	no	—
20	#836	—	5	2	no	—
21	C₂×C₅×Q₈	Dic₃	1	1	yes	characteristic
22	C₂×Dic₁₀	C₂×D₃	1	1	yes	characteristic
23	#704	—	6	2	no	—
24	#683	—	2	2	no	—
25	C₄×Dic₅	Dic₃	1	1	yes	characteristic
26	#356	—	15	1	no	Sylow
27	C₂²×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
28	C₃×C₄×C₅	—	2	1	no	—
29	C₃×C₄×C₅	—	4	1	no	—
30	C₃×Dic₅	—	2	2	no	—
31	C₃×Dic₅	—	2	2	no	—
32	C₂×C₃×Q₈	—	5	1	no	—
33	C₂×C₃×Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic
34	C₃×C₄⋊C₄	—	10	2	no	—
35	C₃×C₄²	—	5	1	no	—
36	#208	—	10	2	no	—
37	C₅×Q₈	—	4	1	no	—
38	C₂×C₄×C₅	—	2	1	no	—
39	C₂×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
40	C₂×Dic₅	—	2	1	no	—
41	C₂×Dic₅	#67	1	2	yes	—
42	Dic₁₀	—	4	1	no	—
43	#170	—	12	2	no	—
44	C₄⋊Q₈	—	5	1	no	—
45	#101	—	15	2	no	—
46	C₂×C₃×C₅	—	2	1	no	—
47	C₂×C₃×C₅	#99	1	1	yes	characteristic
48	C₃×Q₈	—	4	1	no	—
49	C₃×Q₈	—	20	1	no	—
50	C₂×C₃×C₄	—	2	1	no	—
51	C₂×C₃×C₄	—	5	2	no	—
52	C₂×C₃×C₄	—	10	1	no	—
53	C₂×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
54	C₃⋊C₈	—	20	2	no	—
55	C₂²×C₅	#217	1	1	yes	characteristic
56	C₄×C₅	—	2	1	no	—
57	C₄×C₅	—	4	1	no	—
58	Dic₅	—	2	2	no	—
59	Dic₅	—	2	2	no	—
60	C₂×Q₈	—	5	1	no	—
61	C₂×Q₈	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
62	M₁₆	—	30	2	no	—
63	C₄⋊C₄	—	10	2	no	—
64	C₄²	—	5	1	no	—
65	C₃×C₅	#356	1	1	yes	characteristic, complemented, Hall
66	C₂²×C₃	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
67	C₃×C₄	—	2	1	no	—
68	C₃×C₄	—	4	1	no	—
69	C₃×C₄	—	10	2	no	—
70	C₃×C₄	—	10	2	no	—
71	C₂×C₅	—	2	1	no	—
72	C₂×C₅	#834	1	1	yes	characteristic
73	Q₈	—	4	1	no	—
74	Q₈	—	20	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	5	2	no	—
77	C₂×C₄	—	10	1	no	—
78	C₂×C₄	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
79	C₈	—	60	2	no	—
80	C₂×C₃	—	2	1	no	—
81	C₂×C₃	#4011	1	1	yes	characteristic
82	C₅	#4548	1	1	yes	characteristic, complemented, Sylow
83	C₂²	#6763	1	1	yes	characteristic
84	C₄	—	2	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	10	2	no	—
87	C₄	—	10	2	no	—
88	C₃	#64929	1	1	yes	characteristic, complemented, Sylow
89	C₂	—	2	1	no	—
90	C₂	#91240	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#91240
commutator	C₂×C₃×C₄×C₅	C₂×C₄
Frattini	C₂×C₄	C₂×ΓL(1,𝔽₁₆)
Fitting	C₂×C₃×C₅×Q₈	C₄
socle	C₂×C₃×C₅	#99
prime radical	C₂²×C₃×C₅	C₂²⋊C₄
cosocle	C₂×C₃×Dic₁₀	C₂²
hypercenter	C₂×Q₈	ΓL(1,𝔽₁₆)
hypocenter	C₃×C₅	#356
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂²×C₃×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
65. C₃×C₅	#356	semidirect
82. C₅	#4548	semidirect
88. C₃	#64929	semidirect

Maximal subgroups

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

subgroup	index
C₃×#4090	2
#91234	2
#64929	3
#4548	5