Subgroups — C₁₃×#2253 #13111311

Order 1664.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#499	C₂	1	2	yes	maximal
2	C₁₃×#367	C₂	1	2	yes	maximal
3	C₁₃×#366	C₂	1	2	yes	maximal
4	C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#125	—	2	2	no	—
6	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₁₃×#107	C₂²	1	4	yes	—
9	C₁₃×#106	—	2	2	no	—
10	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
12	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
13	C₁₃×C₄⋊C₄	—	2	4	no	—
14	C₁₃×C₄⋊C₄	—	4	4	no	—
15	C₄²×C₁₃	D₄	1	1	yes	characteristic
16	C₁₃×C₁₆	Q₈	1	2	yes	—
17	C₁₃×C₁₆	Q₈	1	2	yes	—
18	#2253	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₄×C₁₃	—	4	4	no	—
20	C₂×C₄×C₁₃	D₈	1	2	yes	—
21	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
22	C₈×C₁₃	Q₁₆	1	2	yes	—
23	C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
24	C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
25	#499	C₂×C₁₃	1	2	yes	—
26	#367	C₂×C₁₃	1	2	yes	—
27	#366	C₂×C₁₃	1	2	yes	—
28	C₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic
29	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
30	C₄×C₁₃	—	2	2	no	—
31	C₄×C₁₃	—	8	4	no	—
32	C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
33	C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
34	#125	—	2	2	no	—
35	C₂×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
36	C₂×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
37	#107	C₂²×C₁₃	1	4	yes	—
38	#106	—	2	2	no	—
39	C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
40	C₂×C₁₃	#500	1	1	yes	characteristic
41	C₂×C₁₃	#508	1	2	yes	—
42	C₂×C₈	D₄×C₁₃	1	1	yes	characteristic
43	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
44	C₄⋊C₄	—	2	4	no	—
45	C₄⋊C₄	—	4	4	no	—
46	C₄²	D₄×C₁₃	1	1	yes	characteristic
47	C₁₆	Q₈×C₁₃	1	2	yes	—
48	C₁₆	Q₈×C₁₃	1	2	yes	—
49	C₁₃	#2253	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₄	—	4	4	no	—
51	C₂×C₄	C₁₃×D₈	1	2	yes	—
52	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
53	C₈	C₁₃×Q₁₆	1	2	yes	—
54	C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
55	C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
56	C₂²	C₂×C₁₃×D₈	1	1	yes	characteristic
57	C₄	—	2	2	no	—
58	C₄	—	8	4	no	—
59	C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
60	C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
61	C₂	C₁₃×#500	1	1	yes	characteristic
62	C₂	C₁₃×#508	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
18. #2253	C₁₃	direct (N × H)
49. C₁₃	#2253	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×#499	2
C₁₃×#367	2
C₁₃×#366	2
C₄×C₁₃×C₁₆	2
#2253	13

Subgroups — C13×#2253 #13111311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2253 #13111311