Subgroups — C₁₃×#15668773 #50303812

Order 38220.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₃×#3862	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₃×C₇⋊AGL(1,𝔽₅)	—	3	1	no	maximal, Hall
3	C₅×C₁₃×#3862	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₃×#10596868	—	5	1	no	maximal, Hall
5	C₇²×D₅×C₁₃	D₃	1	1	yes	characteristic
6	C₂×C₁₃×#3862	—	5	1	no	—
7	C₅×C₇²×C₁₃	Dic₃	1	1	yes	characteristic, complemented, Hall
8	#15668773	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	D₅×C₁₃×ΓL(1,𝔽₈)	—	14	1	no	—
10	C₇×C₁₃×Dic₇	—	15	1	no	Hall
11	C₁₃×#3862	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₁₃×C₇⋊AGL(1,𝔽₅)	—	3	1	no	—
13	C₇×C₁₃×AGL(1,𝔽₅)	—	21	1	no	—
14	D₅×#3862	C₂×C₁₃	1	1	yes	characteristic
15	C₅×C₁₃×ΓL(1,𝔽₈)	—	14	1	no	—
16	C₂×C₇²×C₁₃	—	5	1	no	—
17	C₇×C₇⋊AGL(1,𝔽₅)	—	3	1	no	Hall
18	C₇×D₅×C₁₃	—	2	1	no	—
19	C₇×D₅×C₁₃	—	3	1	no	—
20	C₇×D₅×C₁₃	—	3	1	no	—
21	C₁₃×ΓL(1,𝔽₁₆)	—	49	1	no	maximal, Hall
22	C₅×#3862	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
23	C₇²×C₁₃	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Hall
24	#10596868	—	5	1	no	Hall
25	C₂×C₁₃×ΓL(1,𝔽₈)	—	70	1	no	—
26	C₇²×D₅	D₃×C₁₃	1	1	yes	characteristic
27	C₅×C₇×C₁₃	—	2	1	no	—
28	C₅×C₇×C₁₃	—	3	1	no	—
29	C₅×C₇×C₁₃	—	3	1	no	—
30	C₃×D₅×C₁₃	—	49	1	no	—
31	C₄×C₇×C₁₃	—	105	1	no	—
32	C₁₃×Dic₇	—	15	1	no	—
33	C₂×#3862	—	5	1	no	—
34	C₁₃×ΓL(1,𝔽₈)	—	14	1	no	—
35	C₁₃×AGL(1,𝔽₅)	—	21	1	no	Hall
36	C₅×C₇²	Dic₃×C₁₃	1	1	yes	characteristic, complemented, Hall
37	D₅×ΓL(1,𝔽₈)	—	14	1	no	—
38	C₇×Dic₇	—	15	1	no	Hall
39	C₃×C₅×C₁₃	—	49	1	no	Hall
40	C₂×C₇×C₁₃	—	10	1	no	—
41	C₂×C₇×C₁₃	—	15	1	no	—
42	C₂×C₇×C₁₃	—	15	1	no	—
43	Dic₃×C₁₃	—	245	1	no	Hall
44	#3862	C₁₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
45	C₇⋊AGL(1,𝔽₅)	—	3	1	no	—
46	C₇×AGL(1,𝔽₅)	—	21	1	no	—
47	D₅×C₁₃	#64418	1	1	yes	characteristic
48	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
49	C₂×C₇²	—	5	1	no	—
50	C₇×C₁₃	—	2	1	no	—
51	C₇×C₁₃	—	3	1	no	—
52	C₇×C₁₃	—	3	1	no	—
53	C₂×C₃×C₁₃	—	245	1	no	—
54	C₇×D₅	—	2	1	no	—
55	C₇×D₅	—	3	1	no	—
56	C₇×D₅	—	3	1	no	—
57	C₅×C₁₃	#10596868	1	1	yes	characteristic, complemented, Hall
58	ΓL(1,𝔽₁₆)	—	49	1	no	Hall
59	C₄×C₁₃	—	105	1	no	Hall
60	C₇²	C₁₃×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
61	C₂×ΓL(1,𝔽₈)	—	70	1	no	—
62	C₃×C₁₃	—	49	1	no	Hall
63	C₅×C₇	—	2	1	no	—
64	C₅×C₇	—	3	1	no	—
65	C₅×C₇	—	3	1	no	—
66	C₃×D₅	—	49	1	no	—
67	C₄×C₇	—	105	1	no	—
68	Dic₇	—	15	1	no	—
69	C₂×C₁₃	—	5	1	no	—
70	ΓL(1,𝔽₈)	—	14	1	no	—
71	AGL(1,𝔽₅)	—	21	1	no	Hall
72	C₃×C₅	—	49	1	no	Hall
73	C₂×C₇	—	10	1	no	—
74	C₂×C₇	—	15	1	no	—
75	C₂×C₇	—	15	1	no	—
76	C₁₃	#15668773	1	1	yes	characteristic, direct product factor, Sylow
77	Dic₃	—	245	1	no	Hall
78	D₅	C₁₃×#64418	1	1	yes	characteristic
79	C₇	—	2	1	no	—
80	C₇	—	3	1	no	—
81	C₇	—	3	1	no	—
82	C₂×C₃	—	245	1	no	—
83	C₅	C₁₃×#10596868	1	1	yes	characteristic, complemented, Sylow
84	C₄	—	105	1	no	Sylow
85	C₃	—	49	1	no	Sylow
86	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	#15668773
commutator, hypocenter	C₅×#3862	C₄×C₁₃
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₃	Dic₃
prime radical	D₅×C₁₃×#3862	C₂
cosocle	D₅×#3862	C₂×C₁₃
LCS	G ▷ C₅×#3862
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
3. C₅×C₁₃×#3862	C₄	semidirect
7. C₅×C₇²×C₁₃	Dic₃	semidirect
8. #15668773	C₁₃	direct (N × H)
11. C₁₃×#3862	AGL(1,𝔽₅)	semidirect
22. C₅×#3862	C₄×C₁₃	semidirect
23. C₇²×C₁₃	ΓL(1,𝔽₁₆)	semidirect
36. C₅×C₇²	Dic₃×C₁₃	semidirect
44. #3862	C₁₃×AGL(1,𝔽₅)	semidirect
57. C₅×C₁₃	#10596868	semidirect
60. C₇²	C₁₃×ΓL(1,𝔽₁₆)	semidirect
76. C₁₃	#15668773	direct (N × H)
83. C₅	C₁₃×#10596868	semidirect

Maximal subgroups

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

subgroup	index
D₅×C₁₃×#3862	2
C₇×C₁₃×C₇⋊AGL(1,𝔽₅)	3
C₁₃×#10596868	5
#15668773	13
C₁₃×ΓL(1,𝔽₁₆)	49

Subgroups — C13×#15668773 #50303812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#15668773 #50303812