Subgroups — C₃×#19129750 #30655352

Order 16380.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₅×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇⋊#63120	C₃	1	1	yes	maximal, characteristic, complemented
3	#19129750	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₅×C₇×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×#11763955	—	5	1	no	maximal, Hall
6	C₇×D₅×C₁₃⋊C₃	C₂×C₃	1	3	yes	—
7	C₃×C₇×D₅×C₁₃	C₂×C₃	1	1	yes	characteristic
8	C₃×#63120⋊C₃	—	7	1	no	maximal, Hall
9	C₇⋊#63120	C₃²	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₇×C₁₃⋊C₃	—	5	1	no	—
11	C₃×C₅×C₇×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented
12	C₅×C₇×C₁₃⋊C₃	C₃×C₄	1	3	yes	complemented
13	C₃²×C₇⋊AGL(1,𝔽₅)	—	13	1	no	maximal, Hall
14	C₃×D₅×C₁₃⋊C₃	D₇	1	1	yes	characteristic
15	C₃×Dic₉₁	—	5	1	no	—
16	#11763955	—	5	3	no	—
17	C₇×D₅×C₁₃	C₂×C₃²	1	1	yes	characteristic
18	C₃×C₇×C₁₃⋊C₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
19	C₃×#63120	—	7	1	no	—
20	#63120⋊C₃	—	7	3	no	—
21	C₃²×C₇×D₅	—	13	1	no	—
22	C₃×C₅×C₁₃⋊C₃	Dic₇	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₇×C₁₃	—	5	1	no	—
24	C₂×C₇×C₁₃⋊C₃	—	5	3	no	—
25	C₃×Dic₁₃⋊C₃	—	35	1	no	Hall
26	C₅×C₇×C₁₃	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
27	C₃×C₇⋊AGL(1,𝔽₅)	—	13	3	no	—
28	C₃×C₇⋊AGL(1,𝔽₅)	—	39	1	no	—
29	C₃×D₅×C₁₃	C₃×D₇	1	1	yes	characteristic
30	D₅×C₁₃⋊C₃	C₃×D₇	1	3	yes	—
31	Dic₉₁	—	5	1	no	Hall
32	C₃²×C₅×C₇	—	13	1	no	Hall
33	C₃×C₇×C₁₃	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
34	C₇×C₁₃⋊C₃	C₃×AGL(1,𝔽₅)	1	3	yes	complemented
35	#63120	—	7	1	no	Hall
36	C₃²×Dic₇	—	65	1	no	Hall
37	C₂×C₃×C₁₃⋊C₃	—	5	1	no	—
38	C₃×C₇×D₅	—	13	3	no	—
39	C₃×C₇×D₅	D₁₃⋊C₃	1	1	yes	characteristic
40	C₃×C₅×C₁₃	C₃×Dic₇	1	1	yes	characteristic, complemented
41	C₅×C₁₃⋊C₃	C₃×Dic₇	1	3	yes	complemented
42	C₂×C₇×C₁₃	—	5	1	no	—
43	C₃²×AGL(1,𝔽₅)	—	91	1	no	Hall
44	C₃×Dic₁₃	—	35	1	no	—
45	Dic₁₃⋊C₃	—	35	3	no	—
46	C₇⋊AGL(1,𝔽₅)	—	39	1	no	Hall
47	D₅×C₁₃	C₃²×D₇	1	1	yes	characteristic
48	C₂×C₃²×C₇	—	65	1	no	—
49	C₃×C₁₃⋊C₃	C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
50	C₃×C₅×C₇	—	13	3	no	—
51	C₃×C₅×C₇	Dic₁₃⋊C₃	1	1	yes	characteristic, complemented
52	C₇×C₁₃	C₃²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
53	C₃²×D₅	—	13	1	no	—
54	C₃×Dic₇	—	65	3	no	—
55	C₃×Dic₇	—	195	1	no	—
56	C₂×C₃×C₁₃	—	5	1	no	—
57	C₂×C₁₃⋊C₃	—	5	3	no	—
58	C₇×D₅	C₃×D₁₃⋊C₃	1	1	yes	characteristic
59	C₅×C₁₃	C₃²×Dic₇	1	1	yes	characteristic, complemented, Hall
60	C₃²×C₇	—	13	1	no	Hall
61	C₃×AGL(1,𝔽₅)	—	273	1	no	—
62	C₃×AGL(1,𝔽₅)	—	91	3	no	—
63	Dic₁₃	—	35	1	no	Hall
64	C₃²×C₅	—	13	1	no	Hall
65	C₂×C₃×C₇	—	5	1	no	—
66	C₂×C₃×C₇	—	65	3	no	—
67	C₃×C₁₃	C₃×C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
68	C₁₃⋊C₃	C₃×C₇⋊AGL(1,𝔽₅)	1	3	yes	complemented
69	C₃²×C₄	—	455	1	no	Hall
70	C₅×C₇	C₃×Dic₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
71	C₃×D₅	—	13	3	no	—
72	C₃×D₅	(C₁₃⋊C₃)⋊D₇	1	1	yes	characteristic
73	Dic₇	—	195	1	no	Hall
74	C₂×C₁₃	—	5	1	no	—
75	C₃×C₇	—	13	3	no	—
76	C₃×C₇	#63120⋊C₃	1	1	yes	characteristic, complemented
77	AGL(1,𝔽₅)	—	273	1	no	Hall
78	C₂×C₃²	—	65	1	no	—
79	C₃×C₅	—	13	3	no	—
80	C₃×C₅	#11763955	1	1	yes	characteristic, complemented
81	C₂×C₇	—	5	1	no	—
82	C₁₃	C₃²×C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
83	C₃×C₄	—	1365	1	no	—
84	C₃×C₄	—	455	3	no	—
85	D₅	C₃×(C₁₃⋊C₃)⋊D₇	1	1	yes	characteristic
86	C₃²	—	13	1	no	Sylow
87	C₇	C₃×#63120⋊C₃	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	—	5	1	no	—
89	C₂×C₃	—	65	3	no	—
90	C₅	C₃×#11763955	1	1	yes	characteristic, complemented, Sylow
91	C₄	—	1365	1	no	Sylow
92	C₃	—	13	3	no	—
93	C₃	#19129750	1	1	yes	characteristic, direct product factor
94	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#19129750
commutator, hypocenter	C₅×C₇×C₁₃	C₃²×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₃	C₃×C₄
prime radical	C₃×C₇×D₅×C₁₃⋊C₃	C₂
cosocle	C₇×D₅×C₁₃	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⋊#63120	C₃	semidirect
3. #19129750	C₃	direct (N × H)
4. C₃×C₅×C₇×C₁₃⋊C₃	C₄	semidirect
9. C₇⋊#63120	C₃²	semidirect
11. C₃×C₅×C₇×C₁₃	C₃×C₄	semidirect
12. C₅×C₇×C₁₃⋊C₃	C₃×C₄	semidirect
18. C₃×C₇×C₁₃⋊C₃	AGL(1,𝔽₅)	semidirect
22. C₃×C₅×C₁₃⋊C₃	Dic₇	semidirect
26. C₅×C₇×C₁₃	C₃²×C₄	semidirect
33. C₃×C₇×C₁₃	C₃×AGL(1,𝔽₅)	semidirect
34. C₇×C₁₃⋊C₃	C₃×AGL(1,𝔽₅)	semidirect
40. C₃×C₅×C₁₃	C₃×Dic₇	semidirect
41. C₅×C₁₃⋊C₃	C₃×Dic₇	semidirect
49. C₃×C₁₃⋊C₃	C₇⋊AGL(1,𝔽₅)	semidirect
51. C₃×C₅×C₇	Dic₁₃⋊C₃	semidirect
52. C₇×C₁₃	C₃²×AGL(1,𝔽₅)	semidirect
59. C₅×C₁₃	C₃²×Dic₇	semidirect
67. C₃×C₁₃	C₃×C₇⋊AGL(1,𝔽₅)	semidirect
68. C₁₃⋊C₃	C₃×C₇⋊AGL(1,𝔽₅)	semidirect
70. C₅×C₇	C₃×Dic₁₃⋊C₃	semidirect
76. C₃×C₇	#63120⋊C₃	semidirect
80. C₃×C₅	#11763955	semidirect
82. C₁₃	C₃²×C₇⋊AGL(1,𝔽₅)	semidirect
87. C₇	C₃×#63120⋊C₃	semidirect
90. C₅	C₃×#11763955	semidirect
93. C₃	#19129750	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×C₇×D₅×C₁₃⋊C₃	2
C₃×C₇⋊#63120	3
#19129750	3
C₃×#11763955	5
C₃×#63120⋊C₃	7
C₃²×C₇⋊AGL(1,𝔽₅)	13

Subgroups — C3×#19129750 #30655352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#19129750 #30655352