Subgroups — C₁₃×#2811 #13111869

Order 1664.

432 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#395	C₂	1	6	yes	maximal
2	C₁₃×#391	C₂	1	9	yes	maximal
3	C₂²×Q₈×C₁₃	C₂²	1	2	yes	—
4	C₂²×Q₈×C₁₃	C₂²	1	3	yes	—
5	C₂×C₁₃×C₄⋊C₄	C₂²	1	9	yes	—
6	C₂×C₄²×C₁₃	C₂²	1	3	yes	—
7	C₁₃×#95	C₂²	1	18	yes	—
8	C₂×Q₈×C₁₃	—	4	3	no	—
9	C₂×Q₈×C₁₃	—	4	3	no	—
10	C₂×Q₈×C₁₃	—	4	6	no	—
11	C₂×Q₈×C₁₃	Q₈	1	12	yes	complemented
12	C₂²×C₄×C₁₃	C₂³	1	6	yes	—
13	C₂²×C₄×C₁₃	C₂³	1	9	yes	—
14	C₁₃×C₄⋊C₄	—	4	9	no	—
15	C₄²×C₁₃	—	4	3	no	—
16	#2811	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
18	Q₈×C₁₃	—	4	12	no	—
19	Q₈×C₁₃	—	4	8	no	—
20	C₂×C₄×C₁₃	—	2	9	no	—
21	C₂×C₄×C₁₃	—	2	9	no	—
22	C₂×C₄×C₁₃	—	2	18	no	—
23	C₂×C₄×C₁₃	C₂×Q₈	1	18	yes	—
24	#395	C₂×C₁₃	1	6	yes	—
25	#391	C₂×C₁₃	1	9	yes	—
26	C₂²×C₁₃	C₂²×Q₈	1	3	yes	—
27	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
28	C₂²×C₁₃	H(5,𝔽₂)	1	3	yes	—
29	C₄×C₁₃	—	2	18	no	—
30	C₄×C₁₃	—	4	6	no	—
31	C₂²×Q₈	C₂²×C₁₃	1	2	yes	—
32	C₂²×Q₈	C₂²×C₁₃	1	3	yes	—
33	C₂×C₄⋊C₄	C₂²×C₁₃	1	9	yes	—
34	C₂×C₄²	C₂²×C₁₃	1	3	yes	—
35	#95	C₂²×C₁₃	1	18	yes	—
36	C₂×C₁₃	#543	1	3	yes	—
37	C₂×C₁₃	Q₈²	1	3	yes	—
38	C₂×C₁₃	H(3,𝔽₄)	1	1	yes	characteristic
39	C₂×Q₈	—	4	3	no	—
40	C₂×Q₈	—	4	3	no	—
41	C₂×Q₈	—	4	6	no	—
42	C₂×Q₈	Q₈×C₁₃	1	12	yes	complemented
43	C₂²×C₄	C₂³×C₁₃	1	6	yes	—
44	C₂²×C₄	C₂³×C₁₃	1	9	yes	—
45	C₄⋊C₄	—	4	9	no	—
46	C₄²	—	4	3	no	—
47	C₁₃	#2811	1	1	yes	characteristic, direct product factor, Sylow
48	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
49	Q₈	—	4	12	no	—
50	Q₈	—	4	8	no	—
51	C₂×C₄	—	2	9	no	—
52	C₂×C₄	—	2	9	no	—
53	C₂×C₄	—	2	18	no	—
54	C₂×C₄	C₂×Q₈×C₁₃	1	18	yes	—
55	C₂²	C₂²×Q₈×C₁₃	1	3	yes	—
56	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
57	C₂²	C₁₃×H(5,𝔽₂)	1	3	yes	—
58	C₄	—	2	18	no	—
59	C₄	—	4	6	no	—
60	C₂	C₁₃×#543	1	3	yes	—
61	C₂	Q₈²×C₁₃	1	3	yes	—
62	C₂	C₁₃×H(3,𝔽₄)	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
11. C₂×Q₈×C₁₃	Q₈	semidirect
16. #2811	C₁₃	direct (N × H)
42. C₂×Q₈	Q₈×C₁₃	semidirect
47. C₁₃	#2811	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×#395	2
C₁₃×#391	2
#2811	13

Subgroups — C13×#2811 #13111869

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2811 #13111869