Subgroups — C₁₃×#2252 #13111310

Order 1664.

128 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×#366	C₂	1	4	yes	maximal
3	C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₁₃×C₄⋊Q₈	—	2	2	no	—
5	C₂×C₁₃×C₁₆	C₂²	1	2	yes	—
6	C₁₃×#107	—	2	2	no	—
7	C₁₃×#107	C₂²	1	4	yes	—
8	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×Q₈×C₁₃	—	4	2	no	—
10	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
11	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
12	C₁₃×C₄⋊C₄	—	2	4	no	—
13	C₁₃×C₄⋊C₄	—	4	2	no	—
14	C₄²×C₁₃	D₄	1	1	yes	characteristic
15	C₁₃×C₁₆	Q₈	1	4	yes	complemented
16	#2252	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	Q₈×C₁₃	—	8	4	no	—
18	C₂×C₄×C₁₃	—	4	4	no	—
19	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
20	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
21	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
22	C₈×C₁₃	Q₁₆	1	2	yes	—
23	C₈×C₁₃	C₂×Q₈	1	2	yes	—
24	#500	C₂×C₁₃	1	2	yes	—
25	#366	C₂×C₁₃	1	4	yes	—
26	C₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic
27	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
28	C₄×C₁₃	—	8	4	no	—
29	C₄×C₁₃	D₁₆	1	2	yes	—
30	C₄×C₁₃	Q₃₂	1	2	yes	—
31	C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
32	C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
33	C₄⋊Q₈	—	2	2	no	—
34	C₂×C₁₆	C₂²×C₁₃	1	2	yes	—
35	#107	—	2	2	no	—
36	#107	C₂²×C₁₃	1	4	yes	—
37	C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
38	C₂×C₁₃	#500	1	1	yes	characteristic
39	C₂×C₁₃	C₂×D₁₆	1	1	yes	characteristic
40	C₂×C₁₃	C₂×Q₃₂	1	1	yes	characteristic
41	C₂×Q₈	—	4	2	no	—
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	2	no	—
46	C₄²	D₄×C₁₃	1	1	yes	characteristic
47	C₁₆	Q₈×C₁₃	1	4	yes	complemented
48	C₁₃	#2252	1	1	yes	characteristic, direct product factor, Sylow
49	Q₈	—	8	4	no	—
50	C₂×C₄	—	4	4	no	—
51	C₂×C₄	C₁₃×D₈	1	1	yes	characteristic
52	C₂×C₄	C₁₃×D₈	1	1	yes	characteristic
53	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
54	C₈	C₁₃×Q₁₆	1	2	yes	—
55	C₈	C₂×Q₈×C₁₃	1	2	yes	—
56	C₂²	C₂×C₁₃×D₈	1	1	yes	characteristic
57	C₄	—	8	4	no	—
58	C₄	C₁₃×D₁₆	1	2	yes	—
59	C₄	C₁₃×Q₃₂	1	2	yes	—
60	C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
61	C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
62	C₂	C₁₃×#500	1	1	yes	characteristic
63	C₂	C₂×C₁₃×D₁₆	1	1	yes	characteristic
64	C₂	C₂×C₁₃×Q₃₂	1	1	yes	characteristic

	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
15. C₁₃×C₁₆	Q₈	semidirect
16. #2252	C₁₃	direct (N × H)
47. C₁₆	Q₈×C₁₃	semidirect
48. C₁₃	#2252	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×#366	2
C₄×C₁₃×C₁₆	2
#2252	13

Subgroups — C13×#2252 #13111310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2252 #13111310