Subgroups — C₁₃×#2255 #13111313

Order 1664.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#500	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#499	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#367	C₂	1	2	yes	maximal
4	C₁₃×#366	C₂	1	2	yes	maximal
5	C₁₃×#346	C₂	1	1	yes	maximal, characteristic
6	C₁₃×C₄⋊Q₈	—	2	1	no	—
7	C₁₃×#125	—	2	1	no	—
8	C₂×C₁₃×C₁₆	C₂²	1	2	yes	—
9	C₁₃×#107	—	2	1	no	—
10	C₁₃×#107	C₂²	1	1	yes	characteristic
11	C₁₃×#107	C₂²	1	2	yes	—
12	C₁₃×#107	C₂²	1	1	yes	characteristic
13	C₁₃×#106	—	2	1	no	—
14	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₁₃	—	4	1	no	—
16	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
17	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
18	C₁₃×C₄⋊C₄	—	2	1	no	—
19	C₁₃×C₄⋊C₄	—	2	1	no	—
20	C₁₃×C₄⋊C₄	—	2	2	no	—
21	C₁₃×C₄⋊C₄	—	4	1	no	—
22	C₁₃×C₄⋊C₄	—	4	1	no	—
23	C₁₃×C₄⋊C₄	—	4	1	no	—
24	C₄²×C₁₃	D₄	1	1	yes	characteristic
25	C₁₃×C₁₆	Q₈	1	4	yes	complemented
26	#2255	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	Q₈×C₁₃	—	8	2	no	—
28	C₂×C₄×C₁₃	—	4	1	no	—
29	C₂×C₄×C₁₃	—	4	1	no	—
30	C₂×C₄×C₁₃	—	4	2	no	—
31	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
32	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
33	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
34	C₈×C₁₃	Q₁₆	1	2	yes	—
35	C₈×C₁₃	C₂×Q₈	1	2	yes	—
36	#500	C₂×C₁₃	1	1	yes	characteristic
37	#499	C₂×C₁₃	1	1	yes	characteristic
38	#367	C₂×C₁₃	1	2	yes	—
39	#366	C₂×C₁₃	1	2	yes	—
40	#346	C₂×C₁₃	1	1	yes	characteristic
41	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
42	C₄×C₁₃	—	2	1	no	—
43	C₄×C₁₃	—	2	1	no	—
44	C₄×C₁₃	—	8	1	no	—
45	C₄×C₁₃	—	8	2	no	—
46	C₄×C₁₃	—	8	1	no	—
47	C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
48	C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
49	C₄⋊Q₈	—	2	1	no	—
50	#125	—	2	1	no	—
51	C₂×C₁₆	C₂²×C₁₃	1	2	yes	—
52	#107	—	2	1	no	—
53	#107	C₂²×C₁₃	1	1	yes	characteristic
54	#107	C₂²×C₁₃	1	2	yes	—
55	#107	C₂²×C₁₃	1	1	yes	characteristic
56	#106	—	2	1	no	—
57	C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
58	C₂×C₁₃	#500	1	1	yes	characteristic
59	C₂×C₁₃	#509	1	1	yes	characteristic
60	C₂×C₁₃	#510	1	1	yes	characteristic
61	C₂×Q₈	—	4	1	no	—
62	C₂×C₈	D₄×C₁₃	1	1	yes	characteristic
63	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
64	C₄⋊C₄	—	2	1	no	—
65	C₄⋊C₄	—	2	1	no	—
66	C₄⋊C₄	—	2	2	no	—
67	C₄⋊C₄	—	4	1	no	—
68	C₄⋊C₄	—	4	1	no	—
69	C₄⋊C₄	—	4	1	no	—
70	C₄²	D₄×C₁₃	1	1	yes	characteristic
71	C₁₆	Q₈×C₁₃	1	4	yes	complemented
72	C₁₃	#2255	1	1	yes	characteristic, direct product factor, Sylow
73	Q₈	—	8	2	no	—
74	C₂×C₄	—	4	1	no	—
75	C₂×C₄	—	4	1	no	—
76	C₂×C₄	—	4	2	no	—
77	C₂×C₄	C₁₃×D₈	1	1	yes	characteristic
78	C₂×C₄	C₁₃×D₈	1	1	yes	characteristic
79	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
80	C₈	C₁₃×Q₁₆	1	2	yes	—
81	C₈	C₂×Q₈×C₁₃	1	2	yes	—
82	C₂²	C₂×C₁₃×D₈	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	2	1	no	—
85	C₄	—	8	1	no	—
86	C₄	—	8	2	no	—
87	C₄	—	8	1	no	—
88	C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
89	C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
90	C₂	C₁₃×#500	1	1	yes	characteristic
91	C₂	C₁₃×#509	1	1	yes	characteristic
92	C₂	C₁₃×#510	1	1	yes	characteristic

	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
25. C₁₃×C₁₆	Q₈	semidirect
26. #2255	C₁₃	direct (N × H)
71. C₁₆	Q₈×C₁₃	semidirect
72. C₁₃	#2255	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×#500	2
C₁₃×#499	2
C₁₃×#367	2
C₁₃×#366	2
C₁₃×#346	2
#2255	13

Subgroups — C13×#2255 #13111313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2255 #13111313