Subgroups — C₃×#19129738 #30655340

Order 16380.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊#10587716	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇×#63121	C₃	1	1	yes	maximal, characteristic, complemented
3	#19129738	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₅×#63270	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×#11763982	—	5	1	no	maximal, Hall
6	C₅⋊#10587716	C₂×C₃	1	3	yes	—
7	C₃×C₇×D₆₅	C₂×C₃	1	1	yes	characteristic
8	C₃×#63121⋊C₃	—	7	1	no	maximal, Hall
9	C₇×#63121	C₃²	1	1	yes	characteristic, complemented, Hall
10	C₃×#10587716	—	5	1	no	—
11	C₃×C₅×C₇×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented
12	C₅×#63270	C₃×C₄	1	3	yes	complemented
13	C₃×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	—	13	1	no	maximal, Hall
14	C₃×C₅⋊(D₁₃⋊C₃)	—	7	1	no	—
15	C₃×C₇×#261	—	5	1	no	—
16	#11763982	—	5	3	no	—
17	C₇×D₆₅	C₂×C₃²	1	1	yes	characteristic
18	C₃×#63270	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
19	C₃×#63121	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
20	#63121⋊C₃	—	7	3	no	—
21	C₃×D₅×ΓL(1,𝔽₈)	—	13	1	no	—
22	C₃×C₅×C₁₃⋊C₃	—	7	1	no	Hall
23	C₃×C₇×D₁₃	—	5	1	no	—
24	#10587716	—	5	3	no	—
25	C₃×AGL(1,𝔽₁₃)	—	35	1	no	Hall
26	C₅×C₇×C₁₃	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
27	C₃×C₇×AGL(1,𝔽₅)	—	39	1	no	—
28	AGL(1,𝔽₅)×ΓL(1,𝔽₈)	—	13	3	no	—
29	C₃×D₆₅	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
30	C₅⋊(D₁₃⋊C₃)	—	7	3	no	—
31	C₇×#261	—	5	1	no	Hall
32	C₃×C₅×ΓL(1,𝔽₈)	—	13	1	no	Hall
33	C₃×C₇×C₁₃	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
34	#63270	C₃×AGL(1,𝔽₅)	1	3	yes	complemented
35	#63121	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
36	C₃×C₄×ΓL(1,𝔽₈)	—	65	1	no	Hall
37	C₃×D₁₃⋊C₃	—	35	1	no	—
38	C₃×C₇×D₅	—	39	1	no	—
39	D₅×ΓL(1,𝔽₈)	—	13	3	no	—
40	C₃×C₅×C₁₃	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
41	C₅×C₁₃⋊C₃	—	7	3	no	—
42	C₇×D₁₃	—	5	1	no	—
43	C₃²×AGL(1,𝔽₅)	—	91	1	no	Hall
44	C₃×#261	—	5	1	no	—
45	AGL(1,𝔽₁₃)	—	35	3	no	—
46	C₇×AGL(1,𝔽₅)	—	39	1	no	Hall
47	D₆₅	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
48	C₂×C₃×ΓL(1,𝔽₈)	—	65	1	no	—
49	C₃×C₁₃⋊C₃	—	7	1	no	Hall
50	C₃×C₅×C₇	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented
51	C₅×ΓL(1,𝔽₈)	—	13	3	no	—
52	C₇×C₁₃	C₃²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
53	C₃²×D₅	—	91	1	no	—
54	C₃×C₄×C₇	—	195	1	no	—
55	C₄×ΓL(1,𝔽₈)	—	65	3	no	—
56	C₃×D₁₃	—	5	1	no	—
57	D₁₃⋊C₃	—	35	3	no	—
58	C₇×D₅	—	39	1	no	—
59	C₅×C₁₃	C₃×C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
60	C₃×ΓL(1,𝔽₈)	—	13	1	no	Hall
61	C₃×AGL(1,𝔽₅)	—	39	1	no	—
62	C₃×AGL(1,𝔽₅)	—	91	3	no	—
63	#261	—	5	1	no	Hall
64	C₃²×C₅	—	91	1	no	Hall
65	C₂×C₃×C₇	—	195	1	no	—
66	C₂×ΓL(1,𝔽₈)	—	65	3	no	—
67	C₃×C₁₃	AGL(1,𝔽₅)×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
68	C₁₃⋊C₃	—	7	3	no	—
69	C₃²×C₄	—	455	1	no	Hall
70	C₅×C₇	C₃×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Hall
71	C₃×D₅	—	39	1	no	—
72	C₃×D₅	—	91	3	no	—
73	C₄×C₇	—	195	1	no	Hall
74	D₁₃	—	5	1	no	—
75	C₃×C₇	#63121⋊C₃	1	1	yes	characteristic, complemented
76	ΓL(1,𝔽₈)	—	13	3	no	—
77	AGL(1,𝔽₅)	—	39	1	no	Hall
78	C₂×C₃²	—	455	1	no	—
79	C₃×C₅	—	91	3	no	—
80	C₃×C₅	#11763982	1	1	yes	characteristic, complemented
81	C₂×C₇	—	195	1	no	—
82	C₁₃	C₃×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
83	C₃×C₄	—	195	1	no	—
84	C₃×C₄	—	455	3	no	—
85	D₅	—	39	1	no	—
86	C₃²	—	91	1	no	Sylow
87	C₇	C₃×#63121⋊C₃	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	—	195	1	no	—
89	C₂×C₃	—	455	3	no	—
90	C₅	C₃×#11763982	1	1	yes	characteristic, complemented, Sylow
91	C₄	—	195	1	no	Sylow
92	C₃	—	91	3	no	—
93	C₃	#19129738	1	1	yes	characteristic, direct product factor
94	C₂	—	195	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#19129738
commutator, hypocenter	C₅×C₇×C₁₃	C₃²×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₃	C₃×C₄
prime radical	C₃×C₅⋊#10587716	C₂
cosocle	C₇×D₆₅	C₂×C₃²
LCS	G ▷ C₅×C₇×C₁₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃×C₇×#63121	C₃	semidirect
3. #19129738	C₃	direct (N × H)
4. C₃×C₅×#63270	C₄	semidirect
9. C₇×#63121	C₃²	semidirect
11. C₃×C₅×C₇×C₁₃	C₃×C₄	semidirect
12. C₅×#63270	C₃×C₄	semidirect
18. C₃×#63270	AGL(1,𝔽₅)	semidirect
19. C₃×#63121	ΓL(1,𝔽₈)	semidirect
26. C₅×C₇×C₁₃	C₃²×C₄	semidirect
33. C₃×C₇×C₁₃	C₃×AGL(1,𝔽₅)	semidirect
34. #63270	C₃×AGL(1,𝔽₅)	semidirect
35. #63121	C₃×ΓL(1,𝔽₈)	semidirect
40. C₃×C₅×C₁₃	C₄×ΓL(1,𝔽₈)	semidirect
50. C₃×C₅×C₇	AGL(1,𝔽₁₃)	semidirect
52. C₇×C₁₃	C₃²×AGL(1,𝔽₅)	semidirect
59. C₅×C₁₃	C₃×C₄×ΓL(1,𝔽₈)	semidirect
67. C₃×C₁₃	AGL(1,𝔽₅)×ΓL(1,𝔽₈)	semidirect
70. C₅×C₇	C₃×AGL(1,𝔽₁₃)	semidirect
75. C₃×C₇	#63121⋊C₃	semidirect
80. C₃×C₅	#11763982	semidirect
82. C₁₃	C₃×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	semidirect
87. C₇	C₃×#63121⋊C₃	semidirect
90. C₅	C₃×#11763982	semidirect
93. C₃	#19129738	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅⋊#10587716	2
C₃×C₇×#63121	3
#19129738	3
C₃×#11763982	5
C₃×#63121⋊C₃	7
C₃×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	13

Subgroups — C3×#19129738 #30655340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#19129738 #30655340