Subgroups — C₁₃×#2254 #13111312

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×#367	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	#2254	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	2	yes	—
20	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
21	C₈×C₁₃	Q₁₆	1	2	yes	—
22	C₈×C₁₃	C₂×Q₈	1	2	yes	—
23	#500	C₂×C₁₃	1	2	yes	—
24	#367	C₂×C₁₃	1	4	yes	—
25	C₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic
26	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
27	C₄×C₁₃	—	8	4	no	—
28	C₄×C₁₃	SD₃₂	1	4	yes	—
29	C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
30	C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
31	C₄⋊Q₈	—	2	2	no	—
32	C₂×C₁₆	C₂²×C₁₃	1	2	yes	—
33	#107	—	2	2	no	—
34	#107	C₂²×C₁₃	1	4	yes	—
35	C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
36	C₂×C₁₃	#500	1	1	yes	characteristic
37	C₂×C₁₃	C₂×SD₃₂	1	2	yes	—
38	C₂×Q₈	—	4	2	no	—
39	C₂×C₈	D₄×C₁₃	1	1	yes	characteristic
40	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
41	C₄⋊C₄	—	2	4	no	—
42	C₄⋊C₄	—	4	2	no	—
43	C₄²	D₄×C₁₃	1	1	yes	characteristic
44	C₁₆	Q₈×C₁₃	1	4	yes	complemented
45	C₁₃	#2254	1	1	yes	characteristic, direct product factor, Sylow
46	Q₈	—	8	4	no	—
47	C₂×C₄	—	4	4	no	—
48	C₂×C₄	C₁₃×D₈	1	2	yes	—
49	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
50	C₈	C₁₃×Q₁₆	1	2	yes	—
51	C₈	C₂×Q₈×C₁₃	1	2	yes	—
52	C₂²	C₂×C₁₃×D₈	1	1	yes	characteristic
53	C₄	—	8	4	no	—
54	C₄	C₁₃×SD₃₂	1	4	yes	—
55	C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
56	C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
57	C₂	C₁₃×#500	1	1	yes	characteristic
58	C₂	C₂×C₁₃×SD₃₂	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
15. C₁₃×C₁₆	Q₈	semidirect
16. #2254	C₁₃	direct (N × H)
44. C₁₆	Q₈×C₁₃	semidirect
45. C₁₃	#2254	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×#367	2
C₄×C₁₃×C₁₆	2
#2254	13

Subgroups — C13×#2254 #13111312

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2254 #13111312