Subgroups — #44477643

Order 30420.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊#15690151	C₂	1	1	yes	maximal, characteristic
2	C₃×#16810005	C₃	1	1	yes	maximal, characteristic
3	C₅×#13095201	C₄	1	1	yes	characteristic, complemented, Hall
4	#20258773	—	5	1	no	maximal, Hall
5	C₃×C₁₃×D₆₅	C₂×C₃	1	1	yes	characteristic
6	#16810005	C₉	1	1	yes	characteristic, complemented, Hall
7	#15690151	—	5	1	no	—
8	C₃×C₅×C₁₃²	C₃×C₄	1	1	yes	characteristic
9	#63120⋊C₉	—	13	1	no	maximal
10	#63122⋊C₉	—	13	1	no	maximal
11	C₃×#10621730	—	5	1	no	—
12	C₁₃×D₆₅	C₂×C₉	1	1	yes	characteristic
13	#13095201	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
14	C₅⋊(D₁₃⋊C₉)	—	13	1	no	—
15	D₅×C₁₃⋊C₉	—	13	1	no	—
16	C₃×C₁₃×D₁₃	—	5	1	no	—
17	C₅×C₁₃²	C₄×C₉	1	1	yes	characteristic, complemented, Hall
18	C₃×#63120	—	39	1	no	—
19	C₃×#63122	—	39	1	no	—
20	#10621730	—	5	1	no	Hall
21	C₅×C₁₃⋊C₉	—	13	1	no	—
22	C₅×C₁₃⋊C₉	—	13	1	no	—
23	C₃×C₁₃²	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
24	#261⋊C₉	—	65	1	no	—
25	Dic₁₃⋊C₉	—	65	1	no	—
26	C₃×D₆₅	D₁₃⋊C₃	1	1	yes	characteristic
27	C₃×D₅×C₁₃	—	13	1	no	—
28	C₁₃×D₁₃	—	5	1	no	—
29	#63122	—	39	1	no	—
30	#63120	—	39	1	no	—
31	C₂×C₁₃⋊C₉	—	65	1	no	—
32	D₁₃⋊C₉	—	65	1	no	—
33	C₃×C₅×C₁₃	—	12	1	no	—
34	C₃×C₅×C₁₃	Dic₁₃⋊C₃	1	1	yes	characteristic
35	C₃×C₅×C₁₃	AGL(1,𝔽₁₃)	1	1	yes	characteristic
36	C₉×AGL(1,𝔽₅)	—	169	1	no	Hall
37	C₁₃²	C₉×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
38	C₃×#261	—	195	1	no	—
39	C₃×Dic₁₃	—	195	1	no	—
40	D₆₅	D₁₃⋊C₉	1	1	yes	characteristic
41	D₅×C₁₃	—	13	1	no	—
42	C₁₃⋊C₉	—	13	1	no	—
43	C₁₃⋊C₉	—	13	1	no	—
44	C₉×D₅	—	169	1	no	—
45	C₂×C₃×C₁₃	—	195	1	no	—
46	C₃×D₁₃	—	5	1	no	—
47	C₅×C₁₃	—	12	1	no	—
48	C₅×C₁₃	Dic₁₃⋊C₉	1	1	yes	characteristic, complemented
49	C₅×C₁₃	#261⋊C₉	1	1	yes	characteristic, complemented
50	C₃×AGL(1,𝔽₅)	—	507	1	no	—
51	#261	—	195	1	no	—
52	Dic₁₃	—	195	1	no	—
53	C₅×C₉	—	169	1	no	Hall
54	C₃×C₁₃	—	12	1	no	—
55	C₃×C₁₃	#63122⋊C₃	1	1	yes	characteristic
56	C₃×C₁₃	#63120⋊C₃	1	1	yes	characteristic
57	C₄×C₉	—	845	1	no	Hall
58	C₃×D₅	—	39	1	no	—
59	C₂×C₁₃	—	195	1	no	—
60	D₁₃	—	5	1	no	—
61	AGL(1,𝔽₅)	—	507	1	no	Hall
62	C₂×C₉	—	845	1	no	—
63	C₃×C₅	#14523149	1	1	yes	characteristic
64	C₁₃	—	12	1	no	—
65	C₁₃	#63122⋊C₉	1	1	yes	characteristic, complemented
66	C₁₃	#63120⋊C₉	1	1	yes	characteristic, complemented
67	C₃×C₄	—	2535	1	no	—
68	D₅	—	39	1	no	—
69	C₉	—	169	1	no	Sylow
70	C₂×C₃	—	195	1	no	—
71	C₅	#20258773	1	1	yes	characteristic, complemented, Sylow
72	C₄	—	2535	1	no	Sylow
73	C₃	#23778461	1	1	yes	characteristic
74	C₂	—	195	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	#23778461
commutator, hypocenter	C₅×C₁₃²	C₄×C₉
Fitting, socle	C₃×C₅×C₁₃²	C₃×C₄
prime radical, cosocle	C₃×C₁₃×D₆₅	C₂×C₃
LCS	G ▷ C₅×C₁₃²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
3. C₅×#13095201	C₄	semidirect
6. #16810005	C₉	semidirect
13. #13095201	AGL(1,𝔽₅)	semidirect
17. C₅×C₁₃²	C₄×C₉	semidirect
37. C₁₃²	C₉×AGL(1,𝔽₅)	semidirect
48. C₅×C₁₃	Dic₁₃⋊C₉	semidirect
49. C₅×C₁₃	#261⋊C₉	semidirect
65. C₁₃	#63122⋊C₉	semidirect
66. C₁₃	#63120⋊C₉	semidirect
71. C₅	#20258773	semidirect

Maximal subgroups

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

subgroup	index
C₅⋊#15690151	2
C₃×#16810005	3
#20258773	5
#63120⋊C₉	13
#63122⋊C₉	13