Subgroups — C₁₃×#1829 #13110887

Order 1664.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#518	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#100	C₂	1	2	yes	maximal
3	C₁₃×#344	C₂	1	4	yes	maximal, complemented
4	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
5	C₂×C₁₃×M₁₆	C₂²	1	4	yes	—
6	C₄×D₄×C₁₃	—	2	4	no	—
7	C₁₃×#117	C₂²	1	2	yes	—
8	C₂×C₁₃×C₂²⋊C₄	C₄	1	4	yes	—
9	C₁₃×#100	—	2	4	no	—
10	C₂⁴×C₁₃	C₂×C₄	1	2	yes	—
11	C₂×D₄×C₁₃	—	2	4	no	—
12	C₂×D₄×C₁₃	D₄	1	4	yes	—
13	C₂²×C₄×C₁₃	—	2	4	no	—
14	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
15	C₁₃×M₁₆	—	2	4	no	—
16	C₁₃×M₁₆	—	2	4	no	—
17	C₂×C₈×C₁₃	—	2	4	no	—
18	C₁₃×C₄⋊C₄	—	2	2	no	—
19	C₁₃×C₂²⋊C₄	—	2	4	no	—
20	C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
21	C₄²×C₁₃	—	2	2	no	—
22	#1829	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₂³×C₁₃	—	2	4	no	—
24	C₂³×C₁₃	—	8	2	no	—
25	C₂³×C₁₃	C₂²⋊C₄	1	4	yes	—
26	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
27	D₄×C₁₃	—	2	8	no	—
28	C₂×C₄×C₁₃	—	2	4	no	—
29	C₂×C₄×C₁₃	—	8	4	no	—
30	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
31	C₂×C₄×C₁₃	#41	1	4	yes	—
32	C₈×C₁₃	—	4	4	no	—
33	#518	C₂×C₁₃	1	1	yes	characteristic
34	C₂×#100	C₂×C₁₃	1	2	yes	—
35	#344	C₂×C₁₃	1	4	yes	complemented
36	C₂²×C₁₃	—	2	4	no	—
37	C₂²×C₁₃	—	4	1	no	—
38	C₂²×C₁₃	—	4	4	no	—
39	C₂²×C₁₃	—	8	4	no	—
40	C₂²×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
41	C₂²×C₁₃	#117	1	2	yes	—
42	C₄×C₁₃	—	4	4	no	—
43	C₄×C₁₃	#123	1	4	yes	—
44	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
45	C₂×M₁₆	C₂²×C₁₃	1	4	yes	—
46	C₄×D₄	—	2	4	no	—
47	#117	C₂²×C₁₃	1	2	yes	—
48	C₂×C₂²⋊C₄	C₄×C₁₃	1	4	yes	—
49	#100	—	2	4	no	—
50	C₂×C₁₃	—	2	1	no	—
51	C₂×C₁₃	—	2	2	no	—
52	C₂×C₁₃	—	4	4	no	—
53	C₂×C₁₃	#381	1	1	yes	characteristic
54	C₂⁴	C₂×C₄×C₁₃	1	2	yes	—
55	C₂×D₄	—	2	4	no	—
56	C₂×D₄	D₄×C₁₃	1	4	yes	—
57	C₂²×C₄	—	2	4	no	—
58	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
59	M₁₆	—	2	4	no	—
60	M₁₆	—	2	4	no	—
61	C₂×C₈	—	2	4	no	—
62	C₄⋊C₄	—	2	2	no	—
63	C₂²⋊C₄	—	2	4	no	—
64	C₂²⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
65	C₄²	—	2	2	no	—
66	C₁₃	#1829	1	1	yes	characteristic, direct product factor, Sylow
67	C₂³	—	2	4	no	—
68	C₂³	—	8	2	no	—
69	C₂³	C₁₃×C₂²⋊C₄	1	4	yes	—
70	C₂³	C₂²×C₄×C₁₃	1	1	yes	characteristic
71	D₄	—	2	8	no	—
72	C₂×C₄	—	2	4	no	—
73	C₂×C₄	—	8	4	no	—
74	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
75	C₂×C₄	C₁₃×#41	1	4	yes	—
76	C₈	—	4	4	no	—
77	C₂²	—	2	4	no	—
78	C₂²	—	4	1	no	—
79	C₂²	—	4	4	no	—
80	C₂²	—	8	4	no	—
81	C₂²	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
82	C₂²	C₁₃×#117	1	2	yes	—
83	C₄	—	4	4	no	—
84	C₄	C₁₃×#123	1	4	yes	—
85	C₂	—	2	1	no	—
86	C₂	—	2	2	no	—
87	C₂	—	4	4	no	—
88	C₂	C₁₃×#381	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	#381
commutator	C₂³	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂³×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#344	C₂	semidirect
22. #1829	C₁₃	direct (N × H)
35. #344	C₂×C₁₃	semidirect
66. C₁₃	#1829	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×#518	2
C₂×C₁₃×#100	2
C₁₃×#344	2
#1829	13

Subgroups — C13×#1829 #13110887

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#1829 #13110887