Subgroups — D₁₃×#1044 #72246830

Order 2600.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	#13049932	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#1044	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅⋊D₆₅	C₄	1	1	yes	characteristic, complemented
5	C₁₃×C₅⋊D₅	C₂²	1	1	yes	characteristic
6	C₅²×D₁₃	C₄	1	1	yes	characteristic, complemented
7	AGL(1,𝔽₅)×D₁₃	—	5	2	no	maximal
8	C₅²×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented, Hall
9	D₅×D₁₃	—	5	2	no	—
10	D₅×D₁₃	—	10	2	no	—
11	#63120	—	5	2	no	—
12	C₁₃×AGL(1,𝔽₅)	—	5	2	no	—
13	C₂×#1044	—	13	1	no	maximal, Hall
14	D₆₅	—	5	2	no	—
15	D₆₅	—	10	2	no	—
16	C₅×D₁₃	—	2	2	no	—
17	C₅×D₁₃	AGL(1,𝔽₅)	1	2	yes	complemented
18	D₅×C₁₃	—	5	2	no	—
19	D₅×C₁₃	—	10	2	no	—
20	C₄×D₁₃	—	25	1	no	Hall
21	C₂×C₅⋊D₅	—	13	1	no	—
22	#1044	—	13	1	no	—
23	#1044	D₁₃	1	1	yes	characteristic, direct product factor
24	C₅×C₁₃	—	2	2	no	—
25	C₅×C₁₃	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
26	C₂×D₁₃	—	25	1	no	—
27	C₄×C₁₃	—	25	1	no	—
28	Dic₁₃	—	25	1	no	—
29	C₂×C₅²	—	13	1	no	—
30	C₅⋊D₅	—	13	1	no	—
31	C₅⋊D₅	C₂×D₁₃	1	1	yes	characteristic
32	C₂×AGL(1,𝔽₅)	—	65	2	no	—
33	C₂×C₁₃	—	25	1	no	—
34	D₁₃	—	25	1	no	—
35	D₁₃	#1044	1	1	yes	characteristic, direct product factor
36	C₅²	C₄×D₁₃	1	1	yes	characteristic, complemented, Sylow
37	C₂×D₅	—	65	2	no	—
38	C₂×D₅	—	130	2	no	—
39	AGL(1,𝔽₅)	—	5	2	no	—
40	AGL(1,𝔽₅)	—	65	2	no	—
41	C₁₃	C₂×#1044	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₅	—	13	2	no	—
43	C₂×C₅	—	26	2	no	—
44	D₅	—	5	2	no	—
45	D₅	—	10	2	no	—
46	D₅	—	65	2	no	—
47	D₅	—	130	2	no	—
48	C₂×C₄	—	325	1	no	Sylow
49	C₅	—	2	2	no	—
50	C₅	AGL(1,𝔽₅)×D₁₃	1	2	yes	complemented
51	C₂²	—	325	1	no	—
52	C₄	—	25	1	no	—
53	C₄	—	325	1	no	—
54	C₂	—	13	1	no	—
55	C₂	—	25	1	no	—
56	C₂	—	325	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₁₃	C₂×C₄
prime radical	D₁₃×C₅⋊D₅	C₂
cosocle	C₁₃×C₅⋊D₅	C₂²
LCS	G ▷ C₅²×C₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. #13049932	C₂	semidirect
3. C₁₃×#1044	C₂	semidirect
4. C₅⋊D₆₅	C₄	semidirect
6. C₅²×D₁₃	C₄	semidirect
8. C₅²×C₁₃	C₂×C₄	semidirect
17. C₅×D₁₃	AGL(1,𝔽₅)	semidirect
23. #1044	D₁₃	direct (N × H)
25. C₅×C₁₃	C₂×AGL(1,𝔽₅)	semidirect
35. D₁₃	#1044	direct (N × H)
36. C₅²	C₄×D₁₃	semidirect
41. C₁₃	C₂×#1044	semidirect
50. C₅	AGL(1,𝔽₅)×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
D₁₃×C₅⋊D₅	2
#13049932	2
C₁₃×#1044	2
AGL(1,𝔽₅)×D₁₃	5
C₂×#1044	13

Subgroups — D13×#1044 #72246830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#1044 #72246830