Subgroups — C₁₃×#1710 #13110768

Order 1664.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#500	C₂	1	2	yes	maximal
2	C₁₃×#487	C₂	1	4	yes	maximal
3	C₈²×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₁₃×C₄⋊Q₈	C₂²	1	4	yes	—
5	C₁₃×#107	—	2	4	no	—
6	C₁₃×#103	—	2	8	no	—
7	C₄×C₈×C₁₃	C₂²	1	2	yes	—
8	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×Q₈×C₁₃	—	2	4	no	—
10	C₂×C₈×C₁₃	D₄	1	4	yes	—
11	C₂×C₈×C₁₃	D₄	1	2	yes	—
12	C₁₃×C₄⋊C₄	—	2	4	no	—
13	C₁₃×C₄⋊C₄	—	2	4	no	—
14	C₄²×C₁₃	C₂³	1	1	yes	characteristic
15	#1710	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	Q₈×C₁₃	—	4	8	no	—
17	C₂×C₄×C₁₃	—	4	4	no	—
18	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
19	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
20	C₈×C₁₃	—	2	4	no	—
21	C₈×C₁₃	Q₁₆	1	4	yes	—
22	#500	C₂×C₁₃	1	2	yes	—
23	#487	C₂×C₁₃	1	4	yes	—
24	C₈²	C₂×C₁₃	1	1	yes	characteristic
25	C₂²×C₁₃	#127	1	1	yes	characteristic
26	C₄×C₁₃	—	8	4	no	—
27	C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
28	C₄×C₁₃	#135	1	4	yes	—
29	C₄⋊Q₈	C₂²×C₁₃	1	4	yes	—
30	#107	—	2	4	no	—
31	#103	—	2	8	no	—
32	C₄×C₈	C₂²×C₁₃	1	2	yes	—
33	C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
34	C₂×C₁₃	#494	1	1	yes	characteristic
35	C₂×C₁₃	#495	1	2	yes	—
36	C₂×Q₈	—	2	4	no	—
37	C₂×C₈	D₄×C₁₃	1	4	yes	—
38	C₂×C₈	D₄×C₁₃	1	2	yes	—
39	C₄⋊C₄	—	2	4	no	—
40	C₄⋊C₄	—	2	4	no	—
41	C₄²	C₂³×C₁₃	1	1	yes	characteristic
42	C₁₃	#1710	1	1	yes	characteristic, direct product factor, Sylow
43	Q₈	—	4	8	no	—
44	C₂×C₄	—	4	4	no	—
45	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
46	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
47	C₈	—	2	4	no	—
48	C₈	C₁₃×Q₁₆	1	4	yes	—
49	C₂²	C₁₃×#127	1	1	yes	characteristic
50	C₄	—	8	4	no	—
51	C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
52	C₄	C₁₃×#135	1	4	yes	—
53	C₂	C₁₃×#494	1	1	yes	characteristic
54	C₂	C₁₃×#495	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₃	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₁₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
15. #1710	C₁₃	direct (N × H)
42. C₁₃	#1710	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#500	2
C₁₃×#487	2
C₈²×C₁₃	2
#1710	13

Subgroups — C13×#1710 #13110768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#1710 #13110768