Subgroups — C₃×#23778490 #44477993

Order 30420.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#11759816	C₂	1	1	yes	maximal, characteristic
2	C₃×#16810010	C₃	1	1	yes	maximal, characteristic, complemented
3	#23778490	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₅×#92789	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×#14523145	—	5	1	no	maximal, Hall
6	C₃×C₅×C₁₃⋊D₁₃	C₂×C₃	1	1	yes	characteristic
7	C₅×#11759816	C₂×C₃	1	3	yes	—
8	#16810010	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×#11759816	D₅	1	1	yes	characteristic
10	C₅×#92789	C₃×C₄	1	3	yes	complemented
11	C₃×C₅×C₁₃²	C₃×C₄	1	1	yes	characteristic, complemented
12	C₃×#63118⋊C₃	—	13	2	no	maximal
13	C₃×#10621728	—	5	1	no	—
14	#14523145	—	5	3	no	—
15	C₅×C₁₃⋊D₁₃	C₂×C₃²	1	1	yes	characteristic
16	C₃×#92789	Dic₅	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅×D₁₃⋊C₃	—	13	2	no	—
18	C₃×C₁₃⋊D₁₃	C₃×D₅	1	1	yes	characteristic
19	#11759816	C₃×D₅	1	3	yes	—
20	C₅×C₁₃²	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
21	C₃×#63118	—	39	2	no	—
22	C₃×#63118	—	39	4	no	—
23	#63118⋊C₃	—	13	6	no	—
24	#10621728	—	5	1	no	Hall
25	C₃×C₅×C₁₃⋊C₃	—	13	2	no	—
26	C₃×C₁₃²	C₃×Dic₅	1	1	yes	characteristic, complemented
27	#92789	C₃×Dic₅	1	3	yes	complemented
28	C₃×AGL(1,𝔽₁₃)	—	65	2	no	—
29	C₃×C₅×D₁₃	—	39	4	no	—
30	C₃×C₅×D₁₃	—	39	2	no	—
31	C₅×D₁₃⋊C₃	—	13	6	no	—
32	C₁₃⋊D₁₃	C₃²×D₅	1	1	yes	characteristic
33	#63118	—	39	2	no	—
34	#63118	—	39	4	no	—
35	C₃×D₁₃⋊C₃	—	13	2	no	—
36	C₃×C₅×C₁₃	—	3	4	no	—
37	C₃×C₅×C₁₃	AGL(1,𝔽₁₃)	1	2	yes	complemented
38	C₅×C₁₃⋊C₃	—	13	6	no	—
39	C₃²×Dic₅	—	169	1	no	Hall
40	C₁₃²	C₃²×Dic₅	1	1	yes	characteristic, complemented, Sylow
41	C₃×#261	—	195	4	no	—
42	C₃×#261	—	195	2	no	—
43	AGL(1,𝔽₁₃)	—	65	6	no	—
44	C₅×D₁₃	—	39	4	no	—
45	C₅×D₁₃	—	39	2	no	—
46	C₃×C₁₃⋊C₃	—	13	2	no	—
47	C₂×C₃²×C₅	—	169	1	no	—
48	C₃×D₁₃	—	39	4	no	—
49	C₃×D₁₃	—	39	2	no	—
50	D₁₃⋊C₃	—	13	6	no	—
51	C₅×C₁₃	—	3	4	no	—
52	C₅×C₁₃	C₃×AGL(1,𝔽₁₃)	1	2	yes	complemented
53	C₃×Dic₅	—	169	3	no	—
54	C₃×Dic₅	—	507	1	no	—
55	#261	—	195	2	no	—
56	#261	—	195	4	no	—
57	C₃²×C₅	—	169	1	no	Hall
58	C₃×C₁₃	—	3	4	no	—
59	C₃×C₁₃	#63118⋊C₃	1	2	yes	complemented
60	C₁₃⋊C₃	—	13	6	no	—
61	C₃²×C₄	—	845	1	no	Hall
62	C₂×C₃×C₅	—	169	3	no	—
63	C₂×C₃×C₅	—	507	1	no	—
64	D₁₃	—	39	4	no	—
65	D₁₃	—	39	2	no	—
66	Dic₅	—	507	1	no	Hall
67	C₂×C₃²	—	169	1	no	—
68	C₃×C₅	—	169	3	no	—
69	C₃×C₅	#14523145	1	1	yes	characteristic, complemented
70	C₁₃	—	3	4	no	—
71	C₁₃	C₃×#63118⋊C₃	1	2	yes	complemented
72	C₃×C₄	—	845	3	no	—
73	C₃×C₄	—	2535	1	no	—
74	C₂×C₅	—	507	1	no	—
75	C₃²	—	169	1	no	Sylow
76	C₂×C₃	—	169	3	no	—
77	C₂×C₃	—	507	1	no	—
78	C₅	C₃×#14523145	1	1	yes	characteristic, complemented, Sylow
79	C₄	—	2535	1	no	Sylow
80	C₃	—	169	3	no	—
81	C₃	#23778490	1	1	yes	characteristic, direct product factor
82	C₂	—	507	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#23778490
commutator, hypocenter	C₅×C₁₃²	C₃²×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃²	C₃×C₄
prime radical	C₃×C₅×#11759816	C₂
cosocle	C₅×C₁₃⋊D₁₃	C₂×C₃²
LCS	G ▷ C₅×C₁₃²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃×#16810010	C₃	semidirect
3. #23778490	C₃	direct (N × H)
4. C₃×C₅×#92789	C₄	semidirect
8. #16810010	C₃²	semidirect
10. C₅×#92789	C₃×C₄	semidirect
11. C₃×C₅×C₁₃²	C₃×C₄	semidirect
16. C₃×#92789	Dic₅	semidirect
20. C₅×C₁₃²	C₃²×C₄	semidirect
26. C₃×C₁₃²	C₃×Dic₅	semidirect
27. #92789	C₃×Dic₅	semidirect
37. C₃×C₅×C₁₃	AGL(1,𝔽₁₃)	semidirect
40. C₁₃²	C₃²×Dic₅	semidirect
52. C₅×C₁₃	C₃×AGL(1,𝔽₁₃)	semidirect
59. C₃×C₁₃	#63118⋊C₃	semidirect
69. C₃×C₅	#14523145	semidirect
71. C₁₃	C₃×#63118⋊C₃	semidirect
78. C₅	C₃×#14523145	semidirect
81. C₃	#23778490	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×#11759816	2
C₃×#16810010	3
#23778490	3
C₃×#14523145	5
C₃×#63118⋊C₃	13

Subgroups — C3×#23778490 #44477993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#23778490 #44477993