Subgroups — C₁₃×#2864 #13111922

Order 1664.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#389	C₂	1	4	yes	maximal
2	C₁₃×#387	C₂	1	8	yes	maximal
3	C₁₃×#382	C₂	1	2	yes	maximal
4	C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
6	C₂×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
7	C₂×C₄²×C₁₃	C₂²	1	4	yes	—
8	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
9	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
10	C₁₃×#95	C₂²	1	8	yes	—
11	C₁₃×#95	C₂²	1	8	yes	—
12	C₂²×C₄×C₁₃	C₂³	1	8	yes	—
13	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
14	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
15	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
16	C₁₃×C₄⋊C₄	—	2	16	no	—
17	C₁₃×C₄⋊C₄	—	2	8	no	—
18	C₄²×C₁₃	—	2	8	no	—
19	C₄²×C₁₃	—	2	4	no	—
20	C₄²×C₁₃	Q₈	1	4	yes	—
21	#2864	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
23	C₂×C₄×C₁₃	—	2	4	no	—
24	C₂×C₄×C₁₃	—	2	4	no	—
25	C₂×C₄×C₁₃	—	2	4	no	—
26	C₂×C₄×C₁₃	—	2	8	no	—
27	C₂×C₄×C₁₃	—	2	16	no	—
28	C₂×C₄×C₁₃	C₂×Q₈	1	4	yes	—
29	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
30	C₂×C₄×C₁₃	#41	1	8	yes	—
31	C₂×C₄×C₁₃	#41	1	4	yes	—
32	#389	C₂×C₁₃	1	4	yes	—
33	#387	C₂×C₁₃	1	8	yes	—
34	#382	C₂×C₁₃	1	2	yes	—
35	C₄³	C₂×C₁₃	1	1	yes	characteristic
36	C₂²×C₁₃	C₂²×Q₈	1	1	yes	characteristic
37	C₂²×C₁₃	C₂×#41	1	2	yes	—
38	C₂²×C₁₃	C₂×#41	1	4	yes	—
39	C₄×C₁₃	—	2	8	no	—
40	C₄×C₁₃	—	2	4	no	—
41	C₄×C₁₃	—	4	8	no	—
42	C₄×C₁₃	#125	1	4	yes	—
43	C₂×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
44	C₂×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
45	C₂×C₄²	C₂²×C₁₃	1	4	yes	—
46	C₂×C₄²	C₂²×C₁₃	1	2	yes	—
47	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
48	#95	C₂²×C₁₃	1	8	yes	—
49	#95	C₂²×C₁₃	1	8	yes	—
50	C₂×C₁₃	C₂×#125	1	1	yes	characteristic
51	C₂×C₁₃	#529	1	4	yes	—
52	C₂×C₁₃	#533	1	2	yes	—
53	C₂²×C₄	C₂³×C₁₃	1	8	yes	—
54	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
55	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
56	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
57	C₄⋊C₄	—	2	16	no	—
58	C₄⋊C₄	—	2	8	no	—
59	C₄²	—	2	8	no	—
60	C₄²	—	2	4	no	—
61	C₄²	Q₈×C₁₃	1	4	yes	—
62	C₁₃	#2864	1	1	yes	characteristic, direct product factor, Sylow
63	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	2	4	no	—
66	C₂×C₄	—	2	4	no	—
67	C₂×C₄	—	2	8	no	—
68	C₂×C₄	—	2	16	no	—
69	C₂×C₄	C₂×Q₈×C₁₃	1	4	yes	—
70	C₂×C₄	C₂×Q₈×C₁₃	1	2	yes	—
71	C₂×C₄	C₁₃×#41	1	8	yes	—
72	C₂×C₄	C₁₃×#41	1	4	yes	—
73	C₂²	C₂²×Q₈×C₁₃	1	1	yes	characteristic
74	C₂²	C₂×C₁₃×#41	1	2	yes	—
75	C₂²	C₂×C₁₃×#41	1	4	yes	—
76	C₄	—	2	8	no	—
77	C₄	—	2	4	no	—
78	C₄	—	4	8	no	—
79	C₄	C₁₃×#125	1	4	yes	—
80	C₂	C₂×C₁₃×#125	1	1	yes	characteristic
81	C₂	C₁₃×#529	1	4	yes	—
82	C₂	C₁₃×#533	1	2	yes	—

	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
21. #2864	C₁₃	direct (N × H)
62. C₁₃	#2864	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×#389	2
C₁₃×#387	2
C₁₃×#382	2
C₄³×C₁₃	2
#2864	13

Subgroups — C13×#2864 #13111922

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2864 #13111922