Subgroups — #44477646

Order 30420.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊((C₁₃⋊C₉)⋊D₁₃)	C₂	1	1	yes	maximal, characteristic
2	C₃×#16810003	C₃	1	1	yes	maximal, characteristic
3	C₅×C₁₃×C₁₃⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	#20258774	—	5	1	no	maximal, Hall
5	C₃×C₅⋊(C₁₃⋊D₁₃)	C₂×C₃	1	1	yes	characteristic
6	#16810003	C₉	1	1	yes	characteristic, complemented, Hall
7	(C₁₃⋊C₉)⋊D₁₃	—	5	1	no	—
8	C₃×C₅×C₁₃²	C₃×C₄	1	1	yes	characteristic
9	C₉×#63121	—	13	1	no	maximal
10	#63121⋊C₉	—	13	1	no	maximal
11	C₃×#10621728	—	5	1	no	—
12	C₅⋊(C₁₃⋊D₁₃)	C₂×C₉	1	1	yes	characteristic
13	C₁₃×C₁₃⋊C₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
14	C₉×D₆₅	—	13	1	no	—
15	C₅⋊(D₁₃⋊C₉)	—	13	1	no	—
16	C₃×C₁₃⋊D₁₃	—	5	1	no	—
17	C₅×C₁₃²	C₄×C₉	1	1	yes	characteristic, complemented, Hall
18	C₃×#63121	—	13	1	no	—
19	C₃×#63121	—	13	1	no	—
20	C₃×#63121	—	39	4	no	—
21	#10621728	—	5	1	no	Hall
22	C₅×C₉×C₁₃	—	13	1	no	—
23	C₅×C₁₃⋊C₉	#261	1	1	yes	characteristic, complemented
24	C₃×C₁₃²	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
25	C₉×#261	—	65	1	no	—
26	#261⋊C₉	—	65	1	no	—
27	C₃×D₆₅	—	13	1	no	—
28	C₃×D₆₅	—	13	1	no	—
29	C₃×D₆₅	—	39	4	no	—
30	C₁₃⋊D₁₃	—	5	1	no	—
31	#63121	—	13	1	no	—
32	#63121	—	13	1	no	—
33	#63121	—	39	4	no	—
34	C₉×D₁₃	—	65	1	no	—
35	D₁₃⋊C₉	—	65	1	no	—
36	C₃×C₅×C₁₃	—	3	4	no	—
37	C₃×C₅×C₁₃	AGL(1,𝔽₁₃)	1	1	yes	characteristic
38	C₃×C₅×C₁₃	C₃×#261	1	1	yes	characteristic
39	C₉×AGL(1,𝔽₅)	—	169	1	no	Hall
40	C₁₃²	C₉×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
41	C₃×#261	—	65	1	no	—
42	C₃×#261	—	65	1	no	—
43	C₃×#261	—	195	4	no	—
44	D₆₅	—	13	1	no	—
45	D₆₅	—	13	1	no	—
46	D₆₅	—	39	4	no	—
47	C₉×C₁₃	—	13	1	no	—
48	C₁₃⋊C₉	#63121	1	1	yes	characteristic, complemented
49	C₉×D₅	—	169	1	no	—
50	C₃×D₁₃	—	65	1	no	—
51	C₃×D₁₃	—	65	1	no	—
52	C₃×D₁₃	—	195	4	no	—
53	C₅×C₁₃	—	3	4	no	—
54	C₅×C₁₃	#261⋊C₉	1	1	yes	characteristic, complemented
55	C₅×C₁₃	C₉×#261	1	1	yes	characteristic, complemented
56	C₃×AGL(1,𝔽₅)	—	169	1	no	—
57	#261	—	65	1	no	—
58	#261	—	65	1	no	—
59	#261	—	195	4	no	—
60	C₅×C₉	—	13	1	no	Hall
61	C₃×C₁₃	—	3	4	no	—
62	C₃×C₁₃	#63121⋊C₃	1	1	yes	characteristic
63	C₃×C₁₃	C₃×#63121	1	1	yes	characteristic
64	C₄×C₉	—	845	1	no	Hall
65	C₃×D₅	—	169	1	no	—
66	D₁₃	—	65	1	no	—
67	D₁₃	—	65	1	no	—
68	D₁₃	—	195	4	no	—
69	AGL(1,𝔽₅)	—	169	1	no	Hall
70	C₂×C₉	—	845	1	no	—
71	C₃×C₅	#14523150	1	1	yes	characteristic
72	C₁₃	—	3	4	no	—
73	C₁₃	#63121⋊C₉	1	1	yes	characteristic, complemented
74	C₁₃	C₉×#63121	1	1	yes	characteristic, complemented
75	C₃×C₄	—	845	1	no	—
76	D₅	—	169	1	no	—
77	C₉	—	13	1	no	Sylow
78	C₂×C₃	—	845	1	no	—
79	C₅	#20258774	1	1	yes	characteristic, complemented, Sylow
80	C₄	—	845	1	no	Sylow
81	C₃	#23778464	1	1	yes	characteristic
82	C₂	—	845	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	#23778464
commutator, hypocenter	C₅×C₁₃²	C₄×C₉
Fitting, socle	C₃×C₅×C₁₃²	C₃×C₄
prime radical, cosocle	C₃×C₅⋊(C₁₃⋊D₁₃)	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×C₁₃×C₁₃⋊C₉	C₄	semidirect
6. #16810003	C₉	semidirect
13. C₁₃×C₁₃⋊C₉	AGL(1,𝔽₅)	semidirect
17. C₅×C₁₃²	C₄×C₉	semidirect
23. C₅×C₁₃⋊C₉	#261	semidirect
40. C₁₃²	C₉×AGL(1,𝔽₅)	semidirect
48. C₁₃⋊C₉	#63121	semidirect
54. C₅×C₁₃	#261⋊C₉	semidirect
55. C₅×C₁₃	C₉×#261	semidirect
73. C₁₃	#63121⋊C₉	semidirect
74. C₁₃	C₉×#63121	semidirect
79. C₅	#20258774	semidirect

Maximal subgroups

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

subgroup	index
C₅⋊((C₁₃⋊C₉)⋊D₁₃)	2
C₃×#16810003	3
#20258774	5
C₉×#63121	13
#63121⋊C₉	13