Subgroups — C₁₃×#2244 #13111302

Order 1664.

152 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, complemented
2	C₁₃×#493	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#357	C₂	1	4	yes	maximal, complemented
4	C₁₃×#346	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×D₈	—	2	1	no	—
6	C₂×C₁₃×D₈	C₂²	1	2	yes	—
7	C₁₃×#127	—	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×D₄×C₁₃	—	2	2	no	—
14	C₂×D₄×C₁₃	—	4	2	no	—
15	C₁₃×D₈	—	2	4	no	—
16	C₁₃×D₈	—	4	2	no	—
17	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
18	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
19	C₁₃×C₄⋊C₄	—	2	2	no	—
20	C₁₃×C₄⋊C₄	—	4	2	no	—
21	C₄²×C₁₃	D₄	1	1	yes	characteristic
22	C₁₃×C₁₆	—	2	2	no	—
23	#2244	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂³×C₁₃	—	4	2	no	—
25	D₄×C₁₃	—	4	2	no	—
26	D₄×C₁₃	—	4	2	no	—
27	D₄×C₁₃	—	8	4	no	—
28	C₂×C₄×C₁₃	—	4	2	no	—
29	C₂×C₄×C₁₃	D₈	1	2	yes	—
30	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
31	C₈×C₁₃	SD₁₆	1	2	yes	—
32	C₈×C₁₃	#41	1	2	yes	—
33	#499	C₂×C₁₃	1	1	yes	characteristic, complemented
34	#493	C₂×C₁₃	1	1	yes	characteristic
35	#357	C₂×C₁₃	1	4	yes	complemented
36	#346	C₂×C₁₃	1	1	yes	characteristic, complemented
37	C₂²×C₁₃	—	8	2	no	—
38	C₂²×C₁₃	—	8	4	no	—
39	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
40	C₄×C₁₃	—	2	2	no	—
41	C₄×C₁₃	—	8	2	no	—
42	C₄×C₁₃	#124	1	1	yes	characteristic
43	C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
44	C₂×D₈	—	2	1	no	—
45	C₂×D₈	C₂²×C₁₃	1	2	yes	—
46	#127	—	2	1	no	—
47	#125	—	2	1	no	—
48	C₂×C₁₆	C₂²×C₁₃	1	2	yes	—
49	#107	C₂²×C₁₃	1	2	yes	—
50	#106	—	2	1	no	—
51	C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
52	C₂×C₁₃	—	16	2	no	—
53	C₂×C₁₃	#486	1	1	yes	characteristic
54	C₂×C₁₃	#509	1	2	yes	—
55	C₂×D₄	—	2	2	no	—
56	C₂×D₄	—	4	2	no	—
57	D₈	—	2	4	no	—
58	D₈	—	4	2	no	—
59	C₂×C₈	D₄×C₁₃	1	1	yes	characteristic
60	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
61	C₄⋊C₄	—	2	2	no	—
62	C₄⋊C₄	—	4	2	no	—
63	C₄²	D₄×C₁₃	1	1	yes	characteristic
64	C₁₆	—	2	2	no	—
65	C₁₃	#2244	1	1	yes	characteristic, direct product factor, Sylow
66	C₂³	—	4	2	no	—
67	D₄	—	4	2	no	—
68	D₄	—	4	2	no	—
69	D₄	—	8	4	no	—
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	C₁₃×D₈	1	2	yes	—
72	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
73	C₈	C₁₃×SD₁₆	1	2	yes	—
74	C₈	C₁₃×#41	1	2	yes	—
75	C₂²	—	8	2	no	—
76	C₂²	—	8	4	no	—
77	C₂²	C₂×C₁₃×D₈	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	8	2	no	—
80	C₄	C₁₃×#124	1	1	yes	characteristic
81	C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
82	C₂	—	16	2	no	—
83	C₂	C₁₃×#486	1	1	yes	characteristic
84	C₂	C₁₃×#509	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₃
prime radical	C₁₃×#493	C₂
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
1. C₁₃×#499	C₂	semidirect
3. C₁₃×#357	C₂	semidirect
4. C₁₃×#346	C₂	semidirect
23. #2244	C₁₃	direct (N × H)
33. #499	C₂×C₁₃	semidirect
35. #357	C₂×C₁₃	semidirect
36. #346	C₂×C₁₃	semidirect
65. C₁₃	#2244	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×#493	2
C₁₃×#357	2
C₁₃×#346	2
#2244	13

Subgroups — C13×#2244 #13111302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2244 #13111302