Subgroups — C₁₃×#1726 #13110784

Order 1664.

328 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂²×C₈×C₁₃	C₂²
commutator	C₂	C₄³×C₁₃
Frattini, cosocle	C₂²×C₄	C₂³×C₁₃
socle, prime radical	C₂³×C₁₃	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₁₃×#97	C₄	semidirect
8. C₄×C₈×C₁₃	C₄	semidirect
17. #1726	C₁₃	direct (N × H)
36. #97	C₄×C₁₃	semidirect
37. C₄×C₈	C₄×C₁₃	semidirect
48. C₁₃	#1726	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#97	2
C₂×C₄×C₈×C₁₃	2
C₁₃×#376	2
#1726	13

Subgroups — C13×#1726 #13110784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#1726 #13110784