Subgroups — C₅×PSU(3,𝔽₂)⋊C₄ #13088391

Order 1440.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×PSU(3,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×AGL(1,𝔽₉)	C₂	1	1	yes	maximal, characteristic
3	C₅×#3773	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#157	—	2	1	no	—
5	C₂×C₅×#157	C₂²	1	1	yes	characteristic
6	C₅×PSU(3,𝔽₂)	—	2	1	no	—
7	C₅×PSU(3,𝔽₂)	C₄	1	2	yes	complemented
8	C₅×AGL(1,𝔽₉)	—	2	1	no	—
9	C₅×#624	—	2	1	no	—
10	PSU(3,𝔽₂)⋊C₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₅×C₃⋊D₃	D₄	1	1	yes	characteristic
12	C₅×#157	—	2	2	no	—
13	C₅×#157	C₂×C₄	1	1	yes	characteristic
14	C₅×#157	D₄	1	1	yes	characteristic
15	C₃×C₅×Dic₃	—	4	1	no	—
16	C₅×#103	—	9	1	no	maximal, Hall
17	C₂×PSU(3,𝔽₂)	C₂×C₅	1	1	yes	characteristic
18	C₂×AGL(1,𝔽₉)	C₂×C₅	1	1	yes	characteristic
19	#3773	C₂×C₅	1	1	yes	characteristic
20	C₄×C₅×D₃	—	12	1	no	—
21	C₂×C₃²×C₅	SD₁₆	1	1	yes	characteristic
22	C₅×C₃⋊D₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₅×C₃⋊D₃	Q₁₆	1	1	yes	characteristic
24	C₂×C₅×Q₈	—	9	1	no	—
25	C₂×C₅×C₈	—	9	1	no	—
26	C₅×C₄⋊C₄	—	9	1	no	—
27	C₂×#157	—	2	1	no	—
28	C₂×#157	C₂²×C₅	1	1	yes	characteristic
29	PSU(3,𝔽₂)	—	2	1	no	—
30	PSU(3,𝔽₂)	C₄×C₅	1	2	yes	complemented
31	AGL(1,𝔽₉)	—	2	1	no	—
32	#624	—	2	1	no	—
33	C₂×C₅×D₃	—	12	1	no	—
34	C₃×C₄×C₅	—	12	1	no	—
35	C₅×Dic₃	—	4	1	no	—
36	C₃²×C₅	#103	1	1	yes	characteristic, complemented, Hall
37	C₅×Q₈	—	9	2	no	—
38	C₅×Q₈	—	18	1	no	—
39	C₂×C₄×C₅	—	9	1	no	—
40	C₂×C₄×C₅	—	18	1	no	—
41	C₂×C₄×C₅	—	18	1	no	—
42	C₅×C₈	—	18	1	no	—
43	C₂×C₃⋊D₃	C₅×D₄	1	1	yes	characteristic
44	#157	—	2	2	no	—
45	#157	C₂×C₄×C₅	1	1	yes	characteristic
46	#157	C₅×D₄	1	1	yes	characteristic
47	C₃×Dic₃	—	4	1	no	—
48	#103	—	9	1	no	Sylow
49	C₂×C₃×C₅	—	4	1	no	—
50	C₅×D₃	—	12	1	no	—
51	C₅×D₃	—	12	1	no	—
52	C₄×D₃	—	12	1	no	—
53	C₂²×C₅	—	9	1	no	—
54	C₄×C₅	—	9	1	no	—
55	C₄×C₅	—	9	1	no	—
56	C₄×C₅	—	12	1	no	—
57	C₄×C₅	—	18	2	no	—
58	C₂×C₃²	C₅×SD₁₆	1	1	yes	characteristic
59	C₃⋊D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
60	C₃⋊D₃	C₅×Q₁₆	1	1	yes	characteristic
61	C₂×Q₈	—	9	1	no	—
62	C₂×C₈	—	9	1	no	—
63	C₄⋊C₄	—	9	1	no	—
64	C₃×C₅	—	4	1	no	—
65	C₂×D₃	—	12	1	no	—
66	C₃×C₄	—	12	1	no	—
67	Dic₃	—	4	1	no	—
68	C₂×C₅	—	9	1	no	—
69	C₂×C₅	—	9	1	no	—
70	C₂×C₅	AΓL(1,𝔽₉)	1	1	yes	characteristic
71	C₃²	C₅×#103	1	1	yes	characteristic, complemented, Sylow
72	Q₈	—	9	2	no	—
73	Q₈	—	18	1	no	—
74	C₂×C₄	—	9	1	no	—
75	C₂×C₄	—	18	1	no	—
76	C₂×C₄	—	18	1	no	—
77	C₈	—	18	1	no	—
78	C₂×C₃	—	4	1	no	—
79	D₃	—	12	1	no	—
80	D₃	—	12	1	no	—
81	C₅	PSU(3,𝔽₂)⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
82	C₂²	—	9	1	no	—
83	C₄	—	9	1	no	—
84	C₄	—	9	1	no	—
85	C₄	—	12	1	no	—
86	C₄	—	18	2	no	—
87	C₃	—	4	1	no	—
88	C₂	—	9	1	no	—
89	C₂	—	9	1	no	—
90	C₂	C₅×AΓL(1,𝔽₉)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	AΓL(1,𝔽₉)
commutator	#157	C₂×C₄×C₅
Frattini	C₂	C₅×AΓL(1,𝔽₉)
Fitting, socle	C₂×C₃²×C₅	SD₁₆
prime radical	C₂×C₅×C₃⋊D₃	D₄
cosocle	C₂×#157	C₂²×C₅
hypocenter	C₃²	C₅×#103
LCS	G ▷ #157 ▷ C₃⋊D₃ ▷ C₃²
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
7. C₅×PSU(3,𝔽₂)	C₄	semidirect
10. PSU(3,𝔽₂)⋊C₄	C₅	direct (N × H)
30. PSU(3,𝔽₂)	C₄×C₅	semidirect
36. C₃²×C₅	#103	semidirect
71. C₃²	C₅×#103	semidirect
81. C₅	PSU(3,𝔽₂)⋊C₄	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×C₅×PSU(3,𝔽₂)	2
C₂×C₅×AGL(1,𝔽₉)	2
C₅×#3773	2
PSU(3,𝔽₂)⋊C₄	5
C₅×#103	9

Subgroups — C5×PSU(3,𝔽2)⋊C4 #13088391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×PSU(3,𝔽₂)⋊C₄ #13088391