Subgroups — C₁₃×#14690 #15701029

Order 3328.

1278 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1434	C₂	1	14	yes	maximal
3	C₂²×C₄²×C₁₃	C₂²	1	7	yes	—
4	C₂×C₁₃×#95	C₂²	1	28	yes	—
5	C₄³×C₁₃	C₄	1	8	yes	complemented
6	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
7	C₂³×C₄×C₁₃	C₂³	1	7	yes	—
8	C₂×C₄²×C₁₃	—	2	28	no	—
9	C₂×C₄²×C₁₃	C₂×C₄	1	28	yes	—
10	C₁₃×#95	—	2	56	no	—
11	#14690	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
13	C₂²×C₄×C₁₃	—	2	28	no	—
14	C₂²×C₄×C₁₃	—	2	56	no	—
15	C₂²×C₄×C₁₃	C₂²×C₄	1	14	yes	—
16	C₂²×C₄×C₁₃	#41	1	28	yes	—
17	C₄²×C₁₃	—	2	56	no	—
18	C₂×C₄³	C₂×C₁₃	1	1	yes	characteristic
19	#1434	C₂×C₁₃	1	14	yes	—
20	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
21	C₂³×C₁₃	C₂×#41	1	14	yes	—
22	C₂×C₄×C₁₃	—	2	28	no	—
23	C₂×C₄×C₁₃	—	2	56	no	—
24	C₂×C₄×C₁₃	—	4	56	no	—
25	C₂×C₄×C₁₃	#117	1	28	yes	—
26	C₂²×C₄²	C₂²×C₁₃	1	7	yes	—
27	C₂×#95	C₂²×C₁₃	1	28	yes	—
28	C₄³	C₄×C₁₃	1	8	yes	complemented
29	C₂²×C₁₃	C₂×#117	1	7	yes	—
30	C₂²×C₁₃	#529	1	28	yes	—
31	C₄×C₁₃	—	2	28	no	—
32	C₄×C₁₃	—	8	8	no	—
33	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
34	C₂³×C₄	C₂³×C₁₃	1	7	yes	—
35	C₂×C₄²	—	2	28	no	—
36	C₂×C₄²	C₂×C₄×C₁₃	1	28	yes	—
37	#95	—	2	56	no	—
38	C₂×C₁₃	#2283	1	7	yes	—
39	C₂×C₁₃	#2865	1	8	yes	—
40	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
41	C₂²×C₄	—	2	28	no	—
42	C₂²×C₄	—	2	56	no	—
43	C₂²×C₄	C₂²×C₄×C₁₃	1	14	yes	—
44	C₂²×C₄	C₁₃×#41	1	28	yes	—
45	C₄²	—	2	56	no	—
46	C₁₃	#14690	1	1	yes	characteristic, direct product factor, Sylow
47	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
48	C₂³	C₂×C₁₃×#41	1	14	yes	—
49	C₂×C₄	—	2	28	no	—
50	C₂×C₄	—	2	56	no	—
51	C₂×C₄	—	4	56	no	—
52	C₂×C₄	C₁₃×#117	1	28	yes	—
53	C₂²	C₂×C₁₃×#117	1	7	yes	—
54	C₂²	C₁₃×#529	1	28	yes	—
55	C₄	—	2	28	no	—
56	C₄	—	8	8	no	—
57	C₂	C₁₃×#2283	1	7	yes	—
58	C₂	C₁₃×#2865	1	8	yes	—

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

Complements

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

N	H ≅ G/N	type
5. C₄³×C₁₃	C₄	semidirect
11. #14690	C₁₃	direct (N × H)
28. C₄³	C₄×C₁₃	semidirect
46. C₁₃	#14690	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×C₄³×C₁₃	2
C₁₃×#1434	2
#14690	13

Subgroups — C13×#14690 #15701029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#14690 #15701029