Subgroups — C₁₃×#1327 #13110385

Order 1664.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#423	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#349	C₂	1	2	yes	maximal
3	C₂×C₁₃×M₁₆	C₄	1	1	yes	characteristic
4	C₂×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
5	C₂×C₄²×C₁₃	C₄	1	1	yes	characteristic
6	C₁₃×M₃₂	—	2	2	no	—
7	C₁₃×C₄⋊C₈	—	2	2	no	—
8	C₂²×C₄×C₁₃	—	2	1	no	—
9	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
10	C₁₃×M₁₆	—	4	1	no	—
11	C₁₃×M₁₆	—	4	1	no	—
12	C₂×C₈×C₁₃	—	2	1	no	—
13	C₂×C₈×C₁₃	D₄	1	2	yes	—
14	C₄²×C₁₃	—	2	1	no	—
15	C₄²×C₁₃	C₈	1	1	yes	characteristic
16	C₄²×C₁₃	C₈	1	1	yes	characteristic
17	C₁₃×C₁₆	—	4	2	no	—
18	#1327	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂³×C₁₃	M₁₆	1	1	yes	characteristic
20	C₂×C₄×C₁₃	—	2	1	no	—
21	C₂×C₄×C₁₃	—	2	1	no	—
22	C₂×C₄×C₁₃	—	2	1	no	—
23	C₂×C₄×C₁₃	—	2	1	no	—
24	C₂×C₄×C₁₃	—	4	2	no	—
25	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
27	C₈×C₁₃	—	2	2	no	—
28	C₈×C₁₃	—	4	1	no	—
29	#423	C₂×C₁₃	1	1	yes	characteristic
30	#349	C₂×C₁₃	1	2	yes	—
31	C₂²×C₁₃	—	2	1	no	—
32	C₂²×C₁₃	—	4	1	no	—
33	C₂²×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
34	C₄×C₁₃	—	2	2	no	—
35	C₄×C₁₃	—	2	1	no	—
36	C₄×C₁₃	—	4	1	no	—
37	C₄×C₁₃	#99	1	1	yes	characteristic
38	C₄×C₁₃	#101	1	1	yes	characteristic
39	C₂×M₁₆	C₄×C₁₃	1	1	yes	characteristic
40	C₂×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
41	C₂×C₄²	C₄×C₁₃	1	1	yes	characteristic
42	M₃₂	—	2	2	no	—
43	C₄⋊C₈	—	2	2	no	—
44	C₂×C₁₃	—	2	1	no	—
45	C₂×C₁₃	—	4	1	no	—
46	C₂×C₁₃	#324	1	1	yes	characteristic
47	C₂²×C₄	—	2	1	no	—
48	C₂²×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
49	M₁₆	—	4	1	no	—
50	M₁₆	—	4	1	no	—
51	C₂×C₈	—	2	1	no	—
52	C₂×C₈	D₄×C₁₃	1	2	yes	—
53	C₄²	—	2	1	no	—
54	C₄²	C₈×C₁₃	1	1	yes	characteristic
55	C₄²	C₈×C₁₃	1	1	yes	characteristic
56	C₁₆	—	4	2	no	—
57	C₁₃	#1327	1	1	yes	characteristic, direct product factor, Sylow
58	C₂³	C₁₃×M₁₆	1	1	yes	characteristic
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	4	2	no	—
64	C₂×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
66	C₈	—	2	2	no	—
67	C₈	—	4	1	no	—
68	C₂²	—	2	1	no	—
69	C₂²	—	4	1	no	—
70	C₂²	C₁₃×C₂²⋊C₈	1	1	yes	characteristic
71	C₄	—	2	2	no	—
72	C₄	—	2	1	no	—
73	C₄	—	4	1	no	—
74	C₄	C₁₃×#99	1	1	yes	characteristic
75	C₄	C₁₃×#101	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	4	1	no	—
78	C₂	C₁₃×#324	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	#99
commutator	C₂×C₄	C₂×C₈×C₁₃
Frattini, cosocle	C₂×M₁₆	C₂²×C₁₃
socle	C₂×C₁₃	#324
prime radical	C₂³×C₁₃	M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
18. #1327	C₁₃	direct (N × H)
57. C₁₃	#1327	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×#423	2
C₁₃×#349	2
#1327	13

Subgroups — C13×#1327 #13110385

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#1327 #13110385