Subgroups — C₁₃×#2103 #13111161

Order 1664.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#430	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#424	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#344	C₂	1	2	yes	maximal
4	C₁₃×#341	C₂	1	2	yes	maximal
5	C₁₃×#338	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
7	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
8	C₂×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₁₃×#117	C₂²	1	1	yes	characteristic
11	C₁₃×#108	—	2	2	no	—
12	C₁₃×C₄⋊C₈	—	2	2	no	—
13	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
14	C₁₃×M₁₆	—	2	2	no	—
15	C₁₃×M₁₆	—	2	2	no	—
16	C₁₃×M₁₆	—	2	2	no	—
17	C₁₃×M₁₆	—	2	2	no	—
18	C₁₃×M₁₆	—	2	2	no	—
19	C₂×C₈×C₁₃	—	2	1	no	—
20	C₂×C₈×C₁₃	—	2	2	no	—
21	C₂×C₈×C₁₃	—	2	2	no	—
22	C₂×C₈×C₁₃	—	2	2	no	—
23	C₂×C₈×C₁₃	D₄	1	2	yes	—
24	C₁₃×C₄⋊C₄	—	2	1	no	—
25	C₁₃×C₂²⋊C₄	Q₈	1	2	yes	—
26	C₄²×C₁₃	—	2	1	no	—
27	#2103	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂³×C₁₃	C₂×Q₈	1	1	yes	characteristic
29	C₂×C₄×C₁₃	—	2	2	no	—
30	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₁₃	#41	1	2	yes	—
32	C₂×C₄×C₁₃	#41	1	2	yes	—
33	C₂×C₄×C₁₃	#41	1	1	yes	characteristic
34	C₈×C₁₃	—	2	2	no	—
35	C₈×C₁₃	—	4	1	no	—
36	C₈×C₁₃	—	4	2	no	—
37	C₈×C₁₃	—	4	2	no	—
38	#430	C₂×C₁₃	1	1	yes	characteristic
39	#424	C₂×C₁₃	1	1	yes	characteristic
40	#344	C₂×C₁₃	1	2	yes	—
41	#341	C₂×C₁₃	1	2	yes	—
42	#338	C₂×C₁₃	1	1	yes	characteristic
43	C₂²×C₁₃	—	4	1	no	—
44	C₂²×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
45	C₂²×C₁₃	#125	1	2	yes	—
46	C₄×C₁₃	—	4	2	no	—
47	C₄×C₁₃	#123	1	1	yes	characteristic
48	C₄×C₁₃	#124	1	1	yes	characteristic
49	C₄×C₁₃	#126	1	2	yes	—
50	C₂×M₁₆	C₂²×C₁₃	1	2	yes	—
51	C₂×M₁₆	C₂²×C₁₃	1	2	yes	—
52	C₂×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
53	C₂²×C₈	C₂²×C₁₃	1	1	yes	characteristic
54	#117	C₂²×C₁₃	1	1	yes	characteristic
55	#108	—	2	2	no	—
56	C₄⋊C₈	—	2	2	no	—
57	C₂×C₁₃	—	2	1	no	—
58	C₂×C₁₃	—	2	2	no	—
59	C₂×C₁₃	#400	1	1	yes	characteristic
60	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
61	M₁₆	—	2	2	no	—
62	M₁₆	—	2	2	no	—
63	M₁₆	—	2	2	no	—
64	M₁₆	—	2	2	no	—
65	M₁₆	—	2	2	no	—
66	C₂×C₈	—	2	1	no	—
67	C₂×C₈	—	2	2	no	—
68	C₂×C₈	—	2	2	no	—
69	C₂×C₈	—	2	2	no	—
70	C₂×C₈	D₄×C₁₃	1	2	yes	—
71	C₄⋊C₄	—	2	1	no	—
72	C₂²⋊C₄	Q₈×C₁₃	1	2	yes	—
73	C₄²	—	2	1	no	—
74	C₁₃	#2103	1	1	yes	characteristic, direct product factor, Sylow
75	C₂³	C₂×Q₈×C₁₃	1	1	yes	characteristic
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
78	C₂×C₄	C₁₃×#41	1	2	yes	—
79	C₂×C₄	C₁₃×#41	1	2	yes	—
80	C₂×C₄	C₁₃×#41	1	1	yes	characteristic
81	C₈	—	2	2	no	—
82	C₈	—	4	1	no	—
83	C₈	—	4	2	no	—
84	C₈	—	4	2	no	—
85	C₂²	—	4	1	no	—
86	C₂²	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
87	C₂²	C₁₃×#125	1	2	yes	—
88	C₄	—	4	2	no	—
89	C₄	C₁₃×#123	1	1	yes	characteristic
90	C₄	C₁₃×#124	1	1	yes	characteristic
91	C₄	C₁₃×#126	1	2	yes	—
92	C₂	—	2	1	no	—
93	C₂	—	2	2	no	—
94	C₂	C₁₃×#400	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₃
socle	C₂×C₁₃	#400
prime radical	C₂³×C₁₃	C₂×Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
27. #2103	C₁₃	direct (N × H)
74. C₁₃	#2103	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×#430	2
C₁₃×#424	2
C₁₃×#344	2
C₁₃×#341	2
C₁₃×#338	2
#2103	13

Subgroups — C13×#2103 #13111161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2103 #13111161