Subgroups — C₁₃×#23847 #15710186

Order 3328.

604 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2104	C₂	1	8	yes	maximal
2	C₁₃×#1740	C₂	1	7	yes	maximal
3	C₂×C₁₃×#117	C₂²	1	7	yes	—
4	C₁₃×#342	C₂²	1	28	yes	—
5	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
6	C₁₃×#117	—	2	14	no	—
7	C₁₃×#117	—	2	14	no	—
8	C₂×C₁₃×C₄⋊C₄	—	2	7	no	—
9	C₂×C₁₃×C₂²⋊C₄	C₂³	1	14	yes	—
10	C₂×C₄²×C₁₃	—	2	7	no	—
11	#23847	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
13	C₂²×C₄×C₁₃	—	2	14	no	—
14	C₂²×C₄×C₁₃	#41	1	7	yes	—
15	C₂²×C₄×C₁₃	#41	1	7	yes	—
16	C₁₃×C₄⋊C₄	—	4	14	no	—
17	C₁₃×C₂²⋊C₄	—	2	28	no	—
18	C₄²×C₁₃	—	4	7	no	—
19	C₄²×C₁₃	—	4	7	no	—
20	#2104	C₂×C₁₃	1	8	yes	—
21	#1740	C₂×C₁₃	1	7	yes	—
22	C₂³×C₁₃	—	8	1	no	—
23	C₂³×C₁₃	C₂×#41	1	7	yes	—
24	C₂×C₄×C₁₃	—	4	14	no	—
25	C₂×C₄×C₁₃	—	8	14	no	—
26	C₂×C₄×C₁₃	#126	1	7	yes	—
27	C₂×C₄×C₁₃	#126	1	14	yes	—
28	C₂×C₄×C₁₃	#126	1	7	yes	—
29	C₂×#117	C₂²×C₁₃	1	7	yes	—
30	#342	C₂²×C₁₃	1	28	yes	—
31	C₂²×C₁₃	—	4	7	no	—
32	C₂²×C₁₃	C₂×#126	1	7	yes	—
33	C₄×C₁₃	—	8	14	no	—
34	C₄×C₁₃	#401	1	7	yes	—
35	C₄×C₁₃	#401	1	1	yes	characteristic
36	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
37	#117	—	2	14	no	—
38	#117	—	2	14	no	—
39	C₂×C₄⋊C₄	—	2	7	no	—
40	C₂×C₂²⋊C₄	C₂³×C₁₃	1	14	yes	—
41	C₂×C₄²	—	2	7	no	—
42	C₂×C₁₃	—	2	7	no	—
43	C₂×C₁₃	C₂×#401	1	1	yes	characteristic
44	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
45	C₂²×C₄	—	2	14	no	—
46	C₂²×C₄	C₁₃×#41	1	7	yes	—
47	C₂²×C₄	C₁₃×#41	1	7	yes	—
48	C₄⋊C₄	—	4	14	no	—
49	C₂²⋊C₄	—	2	28	no	—
50	C₄²	—	4	7	no	—
51	C₄²	—	4	7	no	—
52	C₁₃	#23847	1	1	yes	characteristic, direct product factor, Sylow
53	C₂³	—	8	1	no	—
54	C₂³	C₂×C₁₃×#41	1	7	yes	—
55	C₂×C₄	—	4	14	no	—
56	C₂×C₄	—	8	14	no	—
57	C₂×C₄	C₁₃×#126	1	7	yes	—
58	C₂×C₄	C₁₃×#126	1	7	yes	—
59	C₂×C₄	C₁₃×#126	1	14	yes	—
60	C₂²	—	4	7	no	—
61	C₂²	C₂×C₁₃×#126	1	7	yes	—
62	C₄	—	8	14	no	—
63	C₄	C₁₃×#401	1	7	yes	—
64	C₄	C₁₃×#401	1	1	yes	characteristic
65	C₂	—	2	7	no	—
66	C₂	C₂×C₁₃×#401	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	#401
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
socle	C₂×C₁₃	C₂×#401
prime radical	C₂⁴×C₁₃	C₂⁴
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
11. #23847	C₁₃	direct (N × H)
52. C₁₃	#23847	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×#2104	2
C₁₃×#1740	2
#23847	13

Subgroups — C13×#23847 #15710186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23847 #15710186