Subgroups — C₃×#65688 #11752221

Order 960.

372 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂	1	6	yes	maximal
2	C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic
3	#65688	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₃×AGL(1,𝔽₅)	C₂²	1	4	yes	—
5	C₂×C₃×C₄×D₅	C₂²	1	3	yes	—
6	C₃×C₄⋊AGL(1,𝔽₅)	—	2	12	no	—
7	C₃×C₄²×C₅	C₄	1	1	yes	characteristic, complemented
8	C₃×C₄×Dic₅	C₄	1	3	yes	complemented
9	C₃×#384	—	5	1	no	maximal, Hall
10	C₂×C₄⋊AGL(1,𝔽₅)	C₂×C₃	1	6	yes	—
11	C₄²×D₅	C₂×C₃	1	1	yes	characteristic
12	C₂²×C₃×D₅	C₂³	1	1	yes	characteristic
13	C₂×C₃×AGL(1,𝔽₅)	—	2	12	no	—
14	C₂×C₃×C₄×C₅	C₂×C₄	1	3	yes	—
15	C₂×C₃×Dic₅	C₂×C₄	1	3	yes	—
16	C₃×C₄×D₅	D₄	1	6	yes	—
17	C₃×C₄×D₅	Q₈	1	6	yes	—
18	C₂×C₃×C₄⋊C₄	—	5	6	no	—
19	C₂×C₃×C₄²	—	5	1	no	—
20	C₂²×AGL(1,𝔽₅)	C₂²×C₃	1	4	yes	—
21	C₂×C₄×D₅	C₂²×C₃	1	3	yes	—
22	C₄⋊AGL(1,𝔽₅)	—	2	12	no	—
23	C₄²×C₅	C₃×C₄	1	1	yes	characteristic, complemented
24	C₄×Dic₅	C₃×C₄	1	3	yes	complemented
25	#384	—	5	1	no	Sylow
26	C₂²×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₃×D₅	C₂×D₄	1	3	yes	—
28	C₂×C₃×D₅	C₂×Q₈	1	3	yes	—
29	C₃×AGL(1,𝔽₅)	—	4	4	no	—
30	C₃×C₄×C₅	C₄⋊C₄	1	6	yes	complemented
31	C₃×Dic₅	C₄⋊C₄	1	6	yes	complemented
32	C₂²×C₃×C₄	—	5	3	no	—
33	C₂²×C₃×C₄	—	5	4	no	—
34	C₃×C₄⋊C₄	—	10	12	no	—
35	C₃×C₄²	—	5	3	no	—
36	C₃×C₄²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
37	C₂²×D₅	C₂³×C₃	1	1	yes	characteristic
38	C₂×AGL(1,𝔽₅)	—	2	12	no	—
39	C₂×C₄×C₅	C₂×C₃×C₄	1	3	yes	—
40	C₂×Dic₅	C₂×C₃×C₄	1	3	yes	—
41	C₄×D₅	C₃×D₄	1	6	yes	—
42	C₄×D₅	C₃×Q₈	1	6	yes	—
43	C₂×C₄⋊C₄	—	5	6	no	—
44	C₂×C₄²	—	5	1	no	—
45	C₂×C₃×C₅	C₂×C₄⋊C₄	1	3	yes	—
46	C₃×D₅	#127	1	1	yes	characteristic
47	C₃×D₅	C₄⋊Q₈	1	3	yes	—
48	C₂³×C₃	—	5	1	no	—
49	C₂×C₃×C₄	—	5	3	no	—
50	C₂×C₃×C₄	—	5	6	no	—
51	C₂×C₃×C₄	—	5	6	no	—
52	C₂×C₃×C₄	—	10	12	no	—
53	C₂×C₃×C₄	C₂×AGL(1,𝔽₅)	1	3	yes	—
54	C₂²×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
55	C₂×D₅	C₂×C₃×D₄	1	3	yes	—
56	C₂×D₅	C₂×C₃×Q₈	1	3	yes	—
57	AGL(1,𝔽₅)	—	4	4	no	—
58	C₄×C₅	C₃×C₄⋊C₄	1	6	yes	complemented
59	Dic₅	C₃×C₄⋊C₄	1	6	yes	complemented
60	C₂²×C₄	—	5	3	no	—
61	C₂²×C₄	—	5	4	no	—
62	C₄⋊C₄	—	10	12	no	—
63	C₄²	—	5	3	no	—
64	C₄²	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
65	C₃×C₅	#384	1	1	yes	characteristic, complemented, Hall
66	C₂²×C₃	—	5	3	no	—
67	C₂²×C₃	—	5	3	no	—
68	C₂²×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
69	C₃×C₄	—	5	6	no	—
70	C₃×C₄	—	20	4	no	—
71	C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	6	yes	complemented
72	C₂×C₅	C₂×C₃×C₄⋊C₄	1	3	yes	—
73	D₅	C₃×#127	1	1	yes	characteristic
74	D₅	C₃×C₄⋊Q₈	1	3	yes	—
75	C₂³	—	5	1	no	—
76	C₂×C₄	—	5	3	no	—
77	C₂×C₄	—	5	6	no	—
78	C₂×C₄	—	5	6	no	—
79	C₂×C₄	—	10	12	no	—
80	C₂×C₄	C₂×C₃×AGL(1,𝔽₅)	1	3	yes	—
81	C₂×C₃	—	5	1	no	—
82	C₂×C₃	—	5	3	no	—
83	C₂×C₃	C₂×C₄⋊AGL(1,𝔽₅)	1	3	yes	—
84	C₅	C₃×#384	1	1	yes	characteristic, complemented, Sylow
85	C₂²	—	5	3	no	—
86	C₂²	—	5	3	no	—
87	C₂²	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
88	C₄	—	5	6	no	—
89	C₄	—	20	4	no	—
90	C₄	C₃×C₄⋊AGL(1,𝔽₅)	1	6	yes	complemented
91	C₃	#65688	1	1	yes	characteristic, direct product factor, Sylow
92	C₂	—	5	1	no	—
93	C₂	—	5	3	no	—
94	C₂	C₂×C₃×C₄⋊AGL(1,𝔽₅)	1	3	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂²×AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂²×C₃×C₄
Frattini	C₂²	C₂²×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₄²×C₅	C₄
socle	C₂²×C₃×C₅	C₂²×C₄
prime radical	C₂²×C₃×D₅	C₂³
cosocle	C₂²×D₅	C₂³×C₃
hypercenter	C₃×C₄²	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#384
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄²

Complements

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

N	H ≅ G/N	type
3. #65688	C₃	direct (N × H)
7. C₃×C₄²×C₅	C₄	semidirect
8. C₃×C₄×Dic₅	C₄	semidirect
23. C₄²×C₅	C₃×C₄	semidirect
24. C₄×Dic₅	C₃×C₄	semidirect
30. C₃×C₄×C₅	C₄⋊C₄	semidirect
31. C₃×Dic₅	C₄⋊C₄	semidirect
36. C₃×C₄²	AGL(1,𝔽₅)	semidirect
58. C₄×C₅	C₃×C₄⋊C₄	semidirect
59. Dic₅	C₃×C₄⋊C₄	semidirect
64. C₄²	C₃×AGL(1,𝔽₅)	semidirect
65. C₃×C₅	#384	semidirect
71. C₃×C₄	C₄⋊AGL(1,𝔽₅)	semidirect
84. C₅	C₃×#384	semidirect
90. C₄	C₃×C₄⋊AGL(1,𝔽₅)	semidirect
91. C₃	#65688	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄⋊AGL(1,𝔽₅)	2
C₃×C₄²×D₅	2
#65688	3
C₃×#384	5

Subgroups — C3×#65688 #11752221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#65688 #11752221