Subgroups — C₁₃×#1416 #13110474

Order 1664.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#366	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×Q₁₆	—	2	1	no	—
5	C₁₃×Q₃₂	—	2	1	no	—
6	C₁₃×Q₃₂	C₄	1	2	yes	complemented
7	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₁₃×#107	—	2	1	no	—
9	C₁₃×C₃₂	—	2	1	no	—
10	C₂×Q₈×C₁₃	—	4	1	no	—
11	C₁₃×Q₁₆	—	2	2	no	—
12	C₁₃×Q₁₆	—	4	1	no	—
13	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
14	C₁₃×C₄⋊C₄	—	4	1	no	—
15	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
16	C₁₃×C₁₆	D₄	1	1	yes	characteristic
17	#1416	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	Q₈×C₁₃	—	4	2	no	—
19	Q₈×C₁₃	—	8	1	no	—
20	C₂×C₄×C₁₃	—	8	1	no	—
21	C₂×C₄×C₁₃	—	8	1	no	—
22	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
23	C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
24	C₈×C₁₃	SD₁₆	1	1	yes	characteristic
25	C₂×Q₃₂	C₂×C₁₃	1	1	yes	characteristic
26	C₂×C₃₂	C₂×C₁₃	1	1	yes	characteristic
27	#366	C₂×C₁₃	1	1	yes	characteristic
28	C₂²×C₁₃	D₁₆	1	1	yes	characteristic
29	C₄×C₁₃	—	8	2	no	—
30	C₄×C₁₃	—	16	1	no	—
31	C₄×C₁₃	#102	1	1	yes	characteristic
32	C₄×C₁₃	SD₃₂	1	1	yes	characteristic
33	C₂×Q₁₆	—	2	1	no	—
34	Q₃₂	—	2	1	no	—
35	Q₃₂	C₄×C₁₃	1	2	yes	complemented
36	C₂×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
37	#107	—	2	1	no	—
38	C₃₂	—	2	1	no	—
39	C₂×C₁₃	#357	1	1	yes	characteristic
40	C₂×C₁₃	SD₆₄	1	1	yes	characteristic
41	C₂×C₁₃	Q₆₄	1	1	yes	characteristic
42	C₂×Q₈	—	4	1	no	—
43	Q₁₆	—	2	2	no	—
44	Q₁₆	—	4	1	no	—
45	C₂×C₈	D₄×C₁₃	1	1	yes	characteristic
46	C₄⋊C₄	—	4	1	no	—
47	C₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
48	C₁₆	D₄×C₁₃	1	1	yes	characteristic
49	C₁₃	#1416	1	1	yes	characteristic, direct product factor, Sylow
50	Q₈	—	4	2	no	—
51	Q₈	—	8	1	no	—
52	C₂×C₄	—	8	1	no	—
53	C₂×C₄	—	8	1	no	—
54	C₂×C₄	C₁₃×D₈	1	1	yes	characteristic
55	C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
56	C₈	C₁₃×SD₁₆	1	1	yes	characteristic
57	C₂²	C₁₃×D₁₆	1	1	yes	characteristic
58	C₄	—	8	2	no	—
59	C₄	—	16	1	no	—
60	C₄	C₁₃×#102	1	1	yes	characteristic
61	C₄	C₁₃×SD₃₂	1	1	yes	characteristic
62	C₂	C₁₃×#357	1	1	yes	characteristic
63	C₂	C₁₃×SD₆₄	1	1	yes	characteristic
64	C₂	C₁₃×Q₆₄	1	1	yes	characteristic

	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
6. C₁₃×Q₃₂	C₄	semidirect
17. #1416	C₁₃	direct (N × H)
35. Q₃₂	C₄×C₁₃	semidirect
49. C₁₃	#1416	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×Q₃₂	2
C₂×C₁₃×C₃₂	2
C₁₃×#366	2
#1416	13

Subgroups — C13×#1416 #13110474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#1416 #13110474