Subgroups — C₁₃×#2865 #13111923

Order 1664.

418 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#388	C₂	1	7	yes	maximal
2	C₁₃×#387	C₂	1	7	yes	maximal, complemented
3	C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×C₄⋊C₄	C₂²	1	7	yes	—
5	C₂×C₁₃×C₂²⋊C₄	C₂²	1	7	yes	—
6	C₂×C₄²×C₁₃	C₂²	1	7	yes	—
7	C₁₃×#95	C₂²	1	14	yes	—
8	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
9	C₂²×C₄×C₁₃	C₂³	1	7	yes	—
10	C₂²×C₄×C₁₃	C₂³	1	7	yes	—
11	C₁₃×C₄⋊C₄	—	2	14	no	—
12	C₁₃×C₂²⋊C₄	—	2	14	no	—
13	C₄²×C₁₃	—	2	14	no	—
14	#2865	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂³×C₁₃	—	2	7	no	—
16	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
17	C₂×C₄×C₁₃	—	2	14	no	—
18	C₂×C₄×C₁₃	—	2	7	no	—
19	C₂×C₄×C₁₃	—	2	14	no	—
20	C₂×C₄×C₁₃	#41	1	14	yes	—
21	#388	C₂×C₁₃	1	7	yes	—
22	#387	C₂×C₁₃	1	7	yes	complemented
23	C₄³	C₂×C₁₃	1	1	yes	characteristic, complemented
24	C₂²×C₁₃	—	4	7	no	—
25	C₂²×C₁₃	C₂×#41	1	7	yes	—
26	C₄×C₁₃	—	2	14	no	—
27	C₄×C₁₃	—	4	7	no	—
28	C₂×C₄⋊C₄	C₂²×C₁₃	1	7	yes	—
29	C₂×C₂²⋊C₄	C₂²×C₁₃	1	7	yes	—
30	C₂×C₄²	C₂²×C₁₃	1	7	yes	—
31	#95	C₂²×C₁₃	1	14	yes	—
32	C₂×C₁₃	—	8	1	no	—
33	C₂×C₁₃	#529	1	7	yes	—
34	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
35	C₂²×C₄	C₂³×C₁₃	1	7	yes	—
36	C₂²×C₄	C₂³×C₁₃	1	7	yes	—
37	C₄⋊C₄	—	2	14	no	—
38	C₂²⋊C₄	—	2	14	no	—
39	C₄²	—	2	14	no	—
40	C₁₃	#2865	1	1	yes	characteristic, direct product factor, Sylow
41	C₂³	—	2	7	no	—
42	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
43	C₂×C₄	—	2	14	no	—
44	C₂×C₄	—	2	7	no	—
45	C₂×C₄	—	2	14	no	—
46	C₂×C₄	C₁₃×#41	1	14	yes	—
47	C₂²	—	4	7	no	—
48	C₂²	C₂×C₁₃×#41	1	7	yes	—
49	C₄	—	2	14	no	—
50	C₄	—	4	7	no	—
51	C₂	—	8	1	no	—
52	C₂	C₁₃×#529	1	7	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂³
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
2. C₁₃×#387	C₂	semidirect
3. C₄³×C₁₃	C₂	semidirect
14. #2865	C₁₃	direct (N × H)
22. #387	C₂×C₁₃	semidirect
23. C₄³	C₂×C₁₃	semidirect
40. C₁₃	#2865	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×#388	2
C₁₃×#387	2
C₄³×C₁₃	2
#2865	13

Subgroups — C13×#2865 #13111923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2865 #13111923