Subgroups — C₁₃×#1273 #13110331

Order 1664.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈×C₁₃	C₂	1	3	yes	maximal
2	C₂²×C₈×C₁₃	C₄	1	6	yes	—
3	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
4	C₄×C₈×C₁₃	—	2	6	no	—
5	C₂²×C₄×C₁₃	C₂×C₄	1	3	yes	—
6	C₂×C₈×C₁₃	—	2	6	no	—
7	C₂×C₈×C₁₃	—	2	6	no	—
8	C₂×C₈×C₁₃	C₈	1	12	yes	complemented
9	C₄²×C₁₃	D₄	1	3	yes	—
10	C₄²×C₁₃	Q₈	1	1	yes	characteristic
11	#1273	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂³×C₁₃	C₄²	1	1	yes	characteristic
13	C₂×C₄×C₁₃	C₂²⋊C₄	1	3	yes	—
14	C₂×C₄×C₁₃	C₄⋊C₄	1	3	yes	—
15	C₂×C₄×C₁₃	C₂×C₈	1	6	yes	—
16	C₂×C₄×C₁₃	M₁₆	1	6	yes	—
17	C₈×C₁₃	—	2	12	no	—
18	C₂×C₄×C₈	C₂×C₁₃	1	3	yes	—
19	C₂²×C₁₃	#95	1	1	yes	characteristic
20	C₂²×C₁₃	C₄×C₈	1	3	yes	—
21	C₂²×C₁₃	#97	1	3	yes	—
22	C₄×C₁₃	C₂²⋊C₈	1	6	yes	—
23	C₄×C₁₃	C₄⋊C₈	1	6	yes	—
24	C₂²×C₈	C₄×C₁₃	1	6	yes	—
25	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
26	C₄×C₈	—	2	6	no	—
27	C₂×C₁₃	C₈²	1	1	yes	characteristic
28	C₂×C₁₃	#322	1	3	yes	—
29	C₂×C₁₃	#336	1	3	yes	—
30	C₂²×C₄	C₂×C₄×C₁₃	1	3	yes	—
31	C₂×C₈	—	2	6	no	—
32	C₂×C₈	—	2	6	no	—
33	C₂×C₈	C₈×C₁₃	1	12	yes	complemented
34	C₄²	D₄×C₁₃	1	3	yes	—
35	C₄²	Q₈×C₁₃	1	1	yes	characteristic
36	C₁₃	#1273	1	1	yes	characteristic, direct product factor, Sylow
37	C₂³	C₄²×C₁₃	1	1	yes	characteristic
38	C₂×C₄	C₁₃×C₂²⋊C₄	1	3	yes	—
39	C₂×C₄	C₁₃×C₄⋊C₄	1	3	yes	—
40	C₂×C₄	C₂×C₈×C₁₃	1	6	yes	—
41	C₂×C₄	C₁₃×M₁₆	1	6	yes	—
42	C₈	—	2	12	no	—
43	C₂²	C₁₃×#95	1	1	yes	characteristic
44	C₂²	C₄×C₈×C₁₃	1	3	yes	—
45	C₂²	C₁₃×#97	1	3	yes	—
46	C₄	C₁₃×C₂²⋊C₈	1	6	yes	—
47	C₄	C₁₃×C₄⋊C₈	1	6	yes	—
48	C₂	C₈²×C₁₃	1	1	yes	characteristic
49	C₂	C₁₃×#322	1	3	yes	—
50	C₂	C₁₃×#336	1	3	yes	—

	subgroup	G/H
center	C₂×C₄²×C₁₃	C₂²
commutator	C₂	C₈²×C₁₃
Frattini, cosocle	C₂×C₄²	C₂²×C₁₃
socle, prime radical	C₂³×C₁₃	C₄²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₂×C₈×C₁₃	C₈	semidirect
11. #1273	C₁₃	direct (N × H)
33. C₂×C₈	C₈×C₁₃	semidirect
36. C₁₃	#1273	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×C₄×C₈×C₁₃	2
#1273	13

Subgroups — C13×#1273 #13110331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#1273 #13110331