Subgroups — #13114523

Order 1664.

328 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#376	C₂	1	1	yes	maximal, characteristic
2	C₂×#88043	C₂	1	3	yes	maximal
3	C₂×C₄×#1055	C₂	1	3	yes	maximal
4	C₂×C₄²×C₁₃	C₂²	1	3	yes	—
5	C₂²×#1055	C₂²	1	1	yes	characteristic
6	C₂²×#1055	C₂²	1	3	yes	—
7	C₁₃×#95	C₄	1	4	yes	—
8	#88043	C₄	1	12	yes	complemented
9	C₄×#1055	C₄	1	12	yes	complemented
10	C₂²×C₄×C₁₃	C₂×C₄	1	6	yes	—
11	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
12	C₄²×C₁₃	C₂×C₄	1	6	yes	—
13	C₄²×C₁₃	C₂×C₄	1	6	yes	—
14	C₂×#1055	C₂×C₄	1	6	yes	—
15	C₂×#1055	C₂×C₄	1	6	yes	—
16	C₂×#1055	C₂×C₄	1	12	yes	—
17	#1726	—	13	1	no	maximal, Sylow
18	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
19	C₂×C₄×C₁₃	—	2	12	no	—
20	C₂×C₄×C₁₃	C₄²	1	12	yes	—
21	C₂×C₄×C₁₃	C₂²×C₄	1	3	yes	—
22	C₂×C₄×C₁₃	C₂²×C₄	1	3	yes	—
23	#1055	C₄²	1	4	yes	—
24	#1055	C₄²	1	12	yes	—
25	C₂×#97	—	13	3	no	—
26	C₂×C₄×C₈	—	13	3	no	—
27	#376	D₁₃	1	1	yes	characteristic
28	C₂²×C₁₃	C₂×C₄²	1	3	yes	—
29	C₂²×C₁₃	#131	1	4	yes	—
30	C₄×C₁₃	—	2	12	no	—
31	C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
32	C₄×C₁₃	C₂×C₄²	1	3	yes	—
33	C₂²×C₈	—	13	1	no	—
34	C₂²×C₈	—	13	3	no	—
35	C₂×C₄²	C₂×D₁₃	1	3	yes	—
36	#97	—	13	12	no	—
37	C₄×C₈	—	13	12	no	—
38	#95	Dic₁₃	1	4	yes	—
39	C₂×C₁₃	C₄³	1	1	yes	characteristic
40	C₂×C₁₃	#405	1	6	yes	—
41	C₂²×C₄	C₂×Dic₁₃	1	6	yes	—
42	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
43	C₂×C₈	—	13	6	no	—
44	C₂×C₈	—	13	6	no	—
45	C₂×C₈	—	13	12	no	—
46	C₄²	C₄×D₁₃	1	6	yes	—
47	C₄²	C₄×D₁₃	1	6	yes	—
48	C₁₃	#1726	1	1	yes	characteristic, complemented, Sylow
49	C₂³	C₂²×Dic₁₃	1	1	yes	characteristic
50	C₂×C₄	—	2	12	no	—
51	C₂×C₄	C₄×Dic₁₃	1	12	yes	—
52	C₂×C₄	C₂×C₄×D₁₃	1	3	yes	—
53	C₂×C₄	C₂×C₄×D₁₃	1	3	yes	—
54	C₈	—	13	4	no	—
55	C₈	—	13	12	no	—
56	C₂²	C₂×C₄×Dic₁₃	1	3	yes	—
57	C₂²	#88202	1	4	yes	—
58	C₄	—	2	12	no	—
59	C₄	C₄²×D₁₃	1	1	yes	characteristic
60	C₄	C₄²×D₁₃	1	3	yes	—
61	C₂	C₄²×Dic₁₃	1	1	yes	characteristic
62	C₂	#11718658	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₃
commutator	C₂×C₁₃	C₄³
Fitting	C₁₃×#376	C₂
socle, prime radical	C₂³×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	#376	D₁₃
hypocenter	C₁₃	#1726
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
8. #88043	C₄	semidirect
9. C₄×#1055	C₄	semidirect
48. C₁₃	#1726	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#376	2
C₂×#88043	2
C₂×C₄×#1055	2
#1726	13