Subgroups — #11746802

Order 960.

128 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	#91233	C₂	1	2	yes	maximal
3	#64931	—	3	1	no	maximal, Hall
4	C₂×C₃×C₅×Q₈	C₄	1	1	yes	characteristic
5	C₂×C₃×Dic₁₀	C₄	1	1	yes	characteristic
6	C₂×C₃⋊#170	—	2	2	no	—
7	C₃×#683	—	2	2	no	—
8	C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
9	#4546	—	5	1	no	maximal, Hall
10	#4090	D₃	1	1	yes	characteristic
11	#4004	—	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	C₄⋊(C₃⋊C₈)	—	5	2	no	—
21	C₂×C₅×Q₈	Dic₃	1	1	yes	characteristic
22	C₂×Dic₁₀	Dic₃	1	1	yes	characteristic
23	C₂×#170	—	6	2	no	—
24	#683	—	2	2	no	—
25	C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
26	#333	—	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	—	4	1	no	—
31	C₃×Dic₅	SD₁₆	1	2	yes	—
32	C₃×Dic₅	Q₁₆	1	2	yes	—
33	C₂×C₃×Q₈	—	5	1	no	—
34	C₂×C₃×Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic
35	C₃×C₄⋊C₄	—	10	2	no	—
36	C₃×C₄²	—	5	1	no	—
37	C₂×C₃⋊C₈	—	10	2	no	—
38	C₅×Q₈	—	4	1	no	—
39	C₂×C₄×C₅	—	2	1	no	—
40	C₂×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
41	C₂×Dic₅	—	2	1	no	—
42	C₂×Dic₅	#67	1	2	yes	—
43	Dic₁₀	—	4	1	no	—
44	#170	—	12	2	no	—
45	C₄⋊Q₈	—	5	1	no	—
46	C₄⋊C₈	—	15	2	no	—
47	C₂×C₃×C₅	#100	1	1	yes	characteristic
48	C₂×C₃×C₅	#103	1	2	yes	—
49	C₃×Q₈	—	4	1	no	—
50	C₃×Q₈	—	20	1	no	—
51	C₂×C₃×C₄	—	2	1	no	—
52	C₂×C₃×C₄	—	5	2	no	—
53	C₂×C₃×C₄	—	10	1	no	—
54	C₂×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
55	C₃⋊C₈	—	20	2	no	—
56	C₂²×C₅	#217	1	1	yes	characteristic
57	C₄×C₅	—	2	1	no	—
58	C₄×C₅	—	4	1	no	—
59	Dic₅	—	4	1	no	—
60	Dic₅	#215	1	2	yes	—
61	Dic₅	#216	1	2	yes	—
62	C₂×Q₈	—	5	1	no	—
63	C₂×Q₈	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
64	C₂×C₈	—	30	2	no	—
65	C₄⋊C₄	—	10	2	no	—
66	C₄²	—	5	1	no	—
67	C₃×C₅	#333	1	1	yes	characteristic, complemented, Hall
68	C₂²×C₃	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
69	C₃×C₄	—	2	1	no	—
70	C₃×C₄	—	4	1	no	—
71	C₃×C₄	—	5	2	no	—
72	C₃×C₄	—	5	2	no	—
73	C₃×C₄	—	20	1	no	—
74	C₂×C₅	#833	1	1	yes	characteristic
75	C₂×C₅	#835	1	2	yes	—
76	Q₈	—	4	1	no	—
77	Q₈	—	20	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	5	2	no	—
80	C₂×C₄	—	10	1	no	—
81	C₂×C₄	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
82	C₈	—	60	2	no	—
83	C₂×C₃	#4009	1	2	yes	—
84	C₂×C₃	#4013	1	1	yes	characteristic
85	C₅	#4546	1	1	yes	characteristic, complemented, Sylow
86	C₂²	#6763	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	4	1	no	—
89	C₄	—	5	2	no	—
90	C₄	—	5	2	no	—
91	C₄	—	20	1	no	—
92	C₃	#64931	1	1	yes	characteristic, complemented, Sylow
93	C₂	#91238	1	2	yes	—
94	C₂	#91242	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#6763
commutator	C₂×C₃×C₄×C₅	C₂×C₄
Frattini	C₂×C₄	C₂×ΓL(1,𝔽₁₆)
Fitting	C₂×C₃×C₅×Q₈	C₄
socle, prime radical	C₂²×C₃×C₅	C₂²⋊C₄
cosocle	C₃×C₄×Dic₅	C₂²
hypercenter	C₂×Q₈	ΓL(1,𝔽₁₆)
hypocenter	C₃×C₅	#333
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
67. C₃×C₅	#333	semidirect
85. C₅	#4546	semidirect
92. C₃	#64931	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
#91233	2
#64931	3
#4546	5