Subgroups — C₁₃×#1424 #13110482

Order 1664.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#366	C₂	1	2	yes	maximal
3	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
4	C₁₃×#107	—	2	2	no	—
5	C₁₃×C₃₂	C₄	1	2	yes	complemented
6	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
7	C₁₃×C₄⋊C₄	—	4	2	no	—
8	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
9	C₁₃×C₁₆	Q₈	1	1	yes	characteristic
10	#1424	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂×C₄×C₁₃	—	8	2	no	—
12	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
13	C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
14	C₈×C₁₃	Q₁₆	1	1	yes	characteristic
15	C₂×C₃₂	C₂×C₁₃	1	1	yes	characteristic
16	#366	C₂×C₁₃	1	2	yes	—
17	C₂²×C₁₃	D₁₆	1	1	yes	characteristic
18	C₄×C₁₃	—	16	2	no	—
19	C₄×C₁₃	#107	1	1	yes	characteristic
20	C₄×C₁₃	Q₃₂	1	1	yes	characteristic
21	C₂×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
22	#107	—	2	2	no	—
23	C₃₂	C₄×C₁₃	1	2	yes	complemented
24	C₂×C₁₃	#366	1	1	yes	characteristic
25	C₂×C₁₃	SD₆₄	1	2	yes	—
26	C₂×C₈	D₄×C₁₃	1	1	yes	characteristic
27	C₄⋊C₄	—	4	2	no	—
28	C₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
29	C₁₆	Q₈×C₁₃	1	1	yes	characteristic
30	C₁₃	#1424	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₄	—	8	2	no	—
32	C₂×C₄	C₁₃×D₈	1	1	yes	characteristic
33	C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
34	C₈	C₁₃×Q₁₆	1	1	yes	characteristic
35	C₂²	C₁₃×D₁₆	1	1	yes	characteristic
36	C₄	—	16	2	no	—
37	C₄	C₁₃×#107	1	1	yes	characteristic
38	C₄	C₁₃×Q₃₂	1	1	yes	characteristic
39	C₂	C₁₃×#366	1	1	yes	characteristic
40	C₂	C₁₃×SD₆₄	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₃	D₁₆
commutator	C₁₆	C₂×C₄×C₁₃
Frattini, cosocle	C₂×C₁₆	C₂²×C₁₃
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₈×C₁₃ ◁ C₂×C₁₃×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₁₃×C₃₂	C₄	semidirect
10. #1424	C₁₃	direct (N × H)
23. C₃₂	C₄×C₁₃	semidirect
30. C₁₃	#1424	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×C₃₂	2
C₁₃×#366	2
#1424	13

Subgroups — C13×#1424 #13110482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#1424 #13110482