Subgroups — #44477667

Order 30420.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×#13095201	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₃⋊#63120	—	3	1	no	maximal
3	C₅×#13095201	C₄	1	1	yes	characteristic, complemented, Hall
4	#20258750	—	5	1	no	maximal, Hall
5	C₃×D₅×C₁₃²	D₃	1	1	yes	characteristic
6	C₁₃×#63120	—	9	1	no	Hall
7	C₂×#13095201	—	5	1	no	—
8	C₃×C₅×C₁₃²	Dic₃	1	1	yes	characteristic
9	C₁₃×Dic₃₉	—	15	1	no	—
10	D₅×C₁₃²	D₉	1	1	yes	characteristic
11	#13095201	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	D₅×C₁₃⋊C₉	—	26	1	no	—
13	C₂×C₃×C₁₃²	—	5	1	no	—
14	C₅×C₁₃²	Dic₉	1	1	yes	characteristic, complemented, Hall
15	C₃⋊#63120	—	3	1	no	—
16	C₁₃×ΓL(1,𝔽₁₆)	—	39	1	no	—
17	C₁₃×Dic₁₃	—	45	1	no	Hall
18	C₅×C₁₃⋊C₉	—	26	1	no	—
19	C₃×C₁₃²	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
20	C₃×D₅×C₁₃	—	2	1	no	—
21	C₃×D₅×C₁₃	—	3	1	no	—
22	C₃×D₅×C₁₃	—	6	1	no	—
23	C₃×D₅×C₁₃	—	6	1	no	—
24	C₂×C₁₃²	—	5	1	no	—
25	#63120	—	9	1	no	—
26	C₁₃×AGL(1,𝔽₅)	—	117	1	no	—
27	C₂×C₁₃⋊C₉	—	130	1	no	—
28	C₃×C₅×C₁₃	—	2	1	no	—
29	C₃×C₅×C₁₃	—	3	1	no	—
30	C₃×C₅×C₁₃	—	6	1	no	—
31	C₃×C₅×C₁₃	—	6	1	no	—
32	C₉⋊AGL(1,𝔽₅)	—	169	1	no	maximal, Hall
33	C₁₃²	C₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
34	Dic₃₉	—	15	1	no	—
35	Dic₃×C₁₃	—	195	1	no	—
36	D₅×C₁₃	—	2	1	no	—
37	D₅×C₁₃	—	3	1	no	—
38	D₅×C₁₃	—	3	1	no	—
39	D₅×C₁₃	—	6	1	no	—
40	C₁₃⋊C₉	—	26	1	no	—
41	C₉×D₅	—	338	1	no	—
42	C₂×C₃×C₁₃	—	10	1	no	—
43	C₂×C₃×C₁₃	—	30	1	no	—
44	C₂×C₃×C₁₃	—	30	1	no	—
45	C₂×C₃×C₁₃	—	30	1	no	—
46	C₅×C₁₃	—	2	1	no	—
47	C₅×C₁₃	—	3	1	no	—
48	C₅×C₁₃	—	3	1	no	—
49	C₅×C₁₃	—	6	1	no	—
50	ΓL(1,𝔽₁₆)	—	39	1	no	—
51	C₄×C₁₃	—	585	1	no	—
52	Dic₁₃	—	45	1	no	—
53	C₅×C₉	—	338	1	no	Hall
54	C₃×C₁₃	—	2	1	no	—
55	C₃×C₁₃	—	6	1	no	—
56	C₃×C₁₃	—	6	1	no	—
57	C₃×C₁₃	—	6	1	no	—
58	Dic₉	—	845	1	no	Hall
59	C₃×D₅	#11759813	1	1	yes	characteristic
60	C₂×C₁₃	—	10	1	no	—
61	C₂×C₁₃	—	15	1	no	—
62	C₂×C₁₃	—	30	1	no	—
63	C₂×C₁₃	—	30	1	no	—
64	AGL(1,𝔽₅)	—	117	1	no	Hall
65	C₂×C₉	—	1690	1	no	—
66	C₃×C₅	#14523126	1	1	yes	characteristic
67	C₁₃	—	2	1	no	—
68	C₁₃	—	3	1	no	—
69	C₁₃	—	6	1	no	—
70	C₁₃	—	6	1	no	—
71	Dic₃	—	195	1	no	—
72	D₅	#15690146	1	1	yes	characteristic
73	C₉	—	338	1	no	Sylow
74	C₂×C₃	—	5	1	no	—
75	C₅	#20258750	1	1	yes	characteristic, complemented, Sylow
76	C₄	—	585	1	no	Sylow
77	C₃	#23778485	1	1	yes	characteristic
78	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, hypocenter	C₅×#13095201	C₄
Frattini	C₃	#23778485
Fitting, socle	C₃×C₅×C₁₃²	Dic₃
prime radical	C₃×D₅×C₁₃²	D₃
cosocle	D₅×#13095201	C₂
LCS	G ▷ C₅×#13095201
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₅×#13095201	C₄	semidirect
11. #13095201	AGL(1,𝔽₅)	semidirect
14. C₅×C₁₃²	Dic₉	semidirect
33. C₁₃²	C₉⋊AGL(1,𝔽₅)	semidirect
75. C₅	#20258750	semidirect

Maximal subgroups

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

subgroup	index
D₅×#13095201	2
C₁₃×C₃⋊#63120	3
#20258750	5
C₉⋊AGL(1,𝔽₅)	169