Subgroups — #13129548

Order 1664.

1424 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#585	C₂	1	1	yes	maximal, characteristic
2	#11719524	C₂	1	15	yes	maximal, complemented
3	C₂×#88202	C₂	1	15	yes	maximal, complemented
4	C₁₃×2₋¹⁺⁴	C₄	1	6	yes	—
5	C₁₃×H(5,𝔽₂)	C₄	1	10	yes	—
6	C₂×C₁₃×#41	C₂²	1	15	yes	—
7	#88202	C₂²	1	20	yes	complemented
8	#88202	C₂²	1	60	yes	complemented
9	C₂×#6099	C₂²	1	45	yes	complemented
10	C₂²×#1055	C₂²	1	15	yes	complemented
11	C₁₃×#41	C₂×C₄	1	60	yes	—
12	C₁₃×#41	C₂³	1	20	yes	—
13	C₂×Q₈×C₁₃	C₂×C₄	1	15	yes	—
14	C₂×D₄×C₁₃	C₂×C₄	1	45	yes	—
15	C₂²×C₄×C₁₃	C₂³	1	15	yes	—
16	#6099	C₂³	1	60	yes	—
17	C₂×#1055	C₂³	1	15	yes	—
18	C₂×#1055	C₂³	1	45	yes	—
19	#3573	—	13	1	no	maximal, Sylow
20	C₂³×C₁₃	C₂²×C₄	1	15	yes	—
21	Q₈×C₁₃	C₂²×C₄	1	20	yes	—
22	D₄×C₁₃	C₂²×C₄	1	60	yes	—
23	C₂×C₄×C₁₃	C₂²×C₄	1	45	yes	—
24	C₂×C₄×C₁₃	C₂⁴	1	15	yes	—
25	#1055	C₂⁴	1	1	yes	characteristic
26	#1055	C₂⁴	1	15	yes	—
27	#585	D₁₃	1	1	yes	characteristic
28	#568	—	13	15	no	—
29	C₂×#131	—	13	15	no	—
30	C₂²×C₁₃	—	4	15	no	—
31	C₂²×C₁₃	C₂³×C₄	1	15	yes	—
32	C₄×C₁₃	C₂³×C₄	1	15	yes	—
33	C₄×C₁₃	C₂⁵	1	1	yes	characteristic
34	2₋¹⁺⁴	Dic₁₃	1	6	yes	—
35	H(5,𝔽₂)	Dic₁₃	1	10	yes	—
36	C₂×#41	C₂×D₁₃	1	15	yes	—
37	#131	—	13	20	no	—
38	#131	—	13	60	no	—
39	C₂×M₁₆	—	13	45	no	—
40	C₂²×C₈	—	13	15	no	—
41	C₂×C₁₃	—	2	15	no	—
42	C₂×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
43	#41	C₂×Dic₁₃	1	60	yes	—
44	#41	C₂²×D₁₃	1	20	yes	—
45	C₂×Q₈	C₂×Dic₁₃	1	15	yes	—
46	C₂×D₄	C₂×Dic₁₃	1	45	yes	—
47	C₂²×C₄	C₂²×D₁₃	1	15	yes	—
48	M₁₆	—	13	60	no	—
49	C₂×C₈	—	13	15	no	—
50	C₂×C₈	—	13	45	no	—
51	C₁₃	#3573	1	1	yes	characteristic, complemented, Sylow
52	C₂³	C₂²×Dic₁₃	1	15	yes	—
53	Q₈	C₂²×Dic₁₃	1	20	yes	—
54	D₄	C₂²×Dic₁₃	1	60	yes	—
55	C₂×C₄	C₂²×Dic₁₃	1	45	yes	—
56	C₂×C₄	C₂³×D₁₃	1	15	yes	—
57	C₈	—	13	1	no	—
58	C₈	—	13	15	no	—
59	C₂²	—	4	15	no	—
60	C₂²	C₂³×Dic₁₃	1	15	yes	—
61	C₄	C₂³×Dic₁₃	1	15	yes	—
62	C₄	C₂⁴×D₁₃	1	1	yes	characteristic
63	C₂	—	2	15	no	—
64	C₂	C₂⁴×Dic₁₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂⁴×D₁₃
commutator, socle	C₂×C₁₃	C₂⁴×C₄
Fitting, prime radical	C₁₃×#585	C₂
cosocle	C₄×C₁₃	C₂⁵
hypercenter	#585	D₁₃
hypocenter	C₁₃	#3573
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ #585

Complements

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

N	H ≅ G/N	type
2. #11719524	C₂	semidirect
3. C₂×#88202	C₂	semidirect
7. #88202	C₂²	semidirect
8. #88202	C₂²	semidirect
9. C₂×#6099	C₂²	semidirect
10. C₂²×#1055	C₂²	semidirect
51. C₁₃	#3573	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#585	2
#11719524	2
C₂×#88202	2
#3573	13