Subgroups — C₁₃×#2245 #13111303

Order 1664.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#499	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#494	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#358	C₂	1	4	yes	maximal
4	C₁₃×#346	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×Q₁₆	—	2	1	no	—
6	C₂×C₁₃×Q₁₆	C₂²	1	2	yes	—
7	C₁₃×C₄⋊Q₈	—	2	1	no	—
8	C₁₃×#125	—	2	1	no	—
9	C₂×C₁₃×C₁₆	C₂²	1	2	yes	—
10	C₁₃×#107	C₂²	1	2	yes	—
11	C₁₃×#106	—	2	1	no	—
12	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×Q₈×C₁₃	—	2	2	no	—
14	C₁₃×Q₁₆	—	2	4	no	—
15	C₁₃×Q₁₆	—	4	2	no	—
16	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
17	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
18	C₁₃×C₄⋊C₄	—	2	2	no	—
19	C₁₃×C₄⋊C₄	—	4	2	no	—
20	C₁₃×C₄⋊C₄	—	4	2	no	—
21	C₄²×C₁₃	D₄	1	1	yes	characteristic
22	C₁₃×C₁₆	—	2	2	no	—
23	#2245	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	Q₈×C₁₃	—	4	2	no	—
25	Q₈×C₁₃	—	4	2	no	—
26	C₂×C₄×C₁₃	—	4	2	no	—
27	C₂×C₄×C₁₃	—	4	2	no	—
28	C₂×C₄×C₁₃	D₈	1	2	yes	—
29	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
30	C₈×C₁₃	SD₁₆	1	2	yes	—
31	C₈×C₁₃	#41	1	2	yes	—
32	#499	C₂×C₁₃	1	1	yes	characteristic
33	#494	C₂×C₁₃	1	1	yes	characteristic
34	#358	C₂×C₁₃	1	4	yes	—
35	#346	C₂×C₁₃	1	1	yes	characteristic
36	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
37	C₄×C₁₃	—	2	2	no	—
38	C₄×C₁₃	—	8	2	no	—
39	C₄×C₁₃	—	8	2	no	—
40	C₄×C₁₃	#124	1	1	yes	characteristic
41	C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
42	C₂×Q₁₆	—	2	1	no	—
43	C₂×Q₁₆	C₂²×C₁₃	1	2	yes	—
44	C₄⋊Q₈	—	2	1	no	—
45	#125	—	2	1	no	—
46	C₂×C₁₆	C₂²×C₁₃	1	2	yes	—
47	#107	C₂²×C₁₃	1	2	yes	—
48	#106	—	2	1	no	—
49	C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
50	C₂×C₁₃	#486	1	1	yes	characteristic
51	C₂×C₁₃	#510	1	2	yes	—
52	C₂×Q₈	—	2	2	no	—
53	Q₁₆	—	2	4	no	—
54	Q₁₆	—	4	2	no	—
55	C₂×C₈	D₄×C₁₃	1	1	yes	characteristic
56	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
57	C₄⋊C₄	—	2	2	no	—
58	C₄⋊C₄	—	4	2	no	—
59	C₄⋊C₄	—	4	2	no	—
60	C₄²	D₄×C₁₃	1	1	yes	characteristic
61	C₁₆	—	2	2	no	—
62	C₁₃	#2245	1	1	yes	characteristic, direct product factor, Sylow
63	Q₈	—	4	2	no	—
64	Q₈	—	4	2	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	—	4	2	no	—
67	C₂×C₄	C₁₃×D₈	1	2	yes	—
68	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
69	C₈	C₁₃×SD₁₆	1	2	yes	—
70	C₈	C₁₃×#41	1	2	yes	—
71	C₂²	C₂×C₁₃×D₈	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	—	8	2	no	—
74	C₄	—	8	2	no	—
75	C₄	C₁₃×#124	1	1	yes	characteristic
76	C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
77	C₂	C₁₃×#486	1	1	yes	characteristic
78	C₂	C₁₃×#510	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
23. #2245	C₁₃	direct (N × H)
62. C₁₃	#2245	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×#499	2
C₁₃×#494	2
C₁₃×#358	2
C₁₃×#346	2
#2245	13

Subgroups — C13×#2245 #13111303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2245 #13111303