Subgroups — C₁₃×#1453 #13110511

Order 1664.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#431	C₂	1	2	yes	maximal
2	C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#322	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#322	C₂	1	2	yes	maximal, complemented
5	C₈²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×M₁₆	C₄	1	2	yes	—
7	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
8	C₁₃×C₄⋊C₈	C₄	1	4	yes	—
9	C₁₃×C₂²⋊C₈	C₄	1	4	yes	—
10	C₁₃×#97	C₄	1	2	yes	—
11	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₁₃	C₂²	1	2	yes	—
13	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₁₃	C₂²	1	2	yes	—
15	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
16	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₁₃×M₁₆	—	2	4	no	—
18	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₁₃	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₁₃	C₂×C₄	1	4	yes	—
21	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
22	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₁₃	C₂×C₄	1	2	yes	—
24	C₄²×C₁₃	C₂³	1	1	yes	characteristic
25	#1453	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
26	C₂³×C₁₃	C₄²	1	1	yes	characteristic
27	C₂×C₄×C₁₃	—	2	2	no	—
28	C₂×C₄×C₁₃	—	2	4	no	—
29	C₂×C₄×C₁₃	C₄²	1	1	yes	characteristic
30	C₂×C₄×C₁₃	C₄²	1	2	yes	—
31	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
33	C₈×C₁₃	—	2	2	no	—
34	C₈×C₁₃	—	2	4	no	—
35	C₈×C₁₃	—	2	4	no	—
36	C₈×C₁₃	M₁₆	1	4	yes	—
37	#431	C₂×C₁₃	1	2	yes	—
38	C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic
39	#322	C₂×C₁₃	1	1	yes	characteristic, complemented
40	#322	C₂×C₁₃	1	2	yes	complemented
41	C₈²	C₂×C₁₃	1	1	yes	characteristic, complemented
42	C₂²×C₁₃	—	2	1	no	—
43	C₂²×C₁₃	—	2	2	no	—
44	C₂²×C₁₃	C₂×C₄²	1	1	yes	characteristic
45	C₄×C₁₃	—	2	1	no	—
46	C₄×C₁₃	—	2	2	no	—
47	C₄×C₁₃	C₂×M₁₆	1	2	yes	—
48	C₄×C₁₃	#131	1	4	yes	—
49	C₂×M₁₆	C₄×C₁₃	1	2	yes	—
50	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
51	C₄⋊C₈	C₄×C₁₃	1	4	yes	—
52	C₂²⋊C₈	C₄×C₁₃	1	4	yes	—
53	#97	C₄×C₁₃	1	2	yes	—
54	C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
55	C₄×C₈	C₂²×C₁₃	1	2	yes	—
56	C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
57	C₄×C₈	C₂²×C₁₃	1	2	yes	—
58	C₂×C₁₃	—	4	1	no	—
59	C₂×C₁₃	C₄×M₁₆	1	1	yes	characteristic
60	C₂×C₁₃	#405	1	2	yes	—
61	C₂²×C₄	C₂×C₄×C₁₃	1	2	yes	—
62	C₂²×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
63	M₁₆	—	2	4	no	—
64	C₂×C₈	C₂×C₄×C₁₃	1	2	yes	—
65	C₂×C₈	C₂×C₄×C₁₃	1	4	yes	—
66	C₂×C₈	C₂×C₄×C₁₃	1	4	yes	—
67	C₂×C₈	C₂×C₄×C₁₃	1	2	yes	—
68	C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
69	C₄²	C₂×C₄×C₁₃	1	2	yes	—
70	C₄²	C₂³×C₁₃	1	1	yes	characteristic
71	C₁₃	#1453	1	1	yes	characteristic, direct product factor, Sylow
72	C₂³	C₄²×C₁₃	1	1	yes	characteristic
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	C₄²×C₁₃	1	1	yes	characteristic
76	C₂×C₄	C₄²×C₁₃	1	2	yes	—
77	C₂×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
78	C₂×C₄	C₂²×C₄×C₁₃	1	2	yes	—
79	C₈	—	2	2	no	—
80	C₈	—	2	4	no	—
81	C₈	—	2	4	no	—
82	C₈	C₁₃×M₁₆	1	4	yes	—
83	C₂²	—	2	1	no	—
84	C₂²	—	2	2	no	—
85	C₂²	C₂×C₄²×C₁₃	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	2	2	no	—
88	C₄	C₂×C₁₃×M₁₆	1	2	yes	—
89	C₄	C₁₃×#131	1	4	yes	—
90	C₂	—	4	1	no	—
91	C₂	C₄×C₁₃×M₁₆	1	1	yes	characteristic
92	C₂	C₁₃×#405	1	2	yes	—

	subgroup	G/H
center	C₄²×C₁₃	C₂³
commutator	C₂²	C₂×C₄²×C₁₃
Frattini, cosocle	C₄²	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×C₄²
prime radical	C₂³×C₁₃	C₄²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#322	C₂	semidirect
4. C₁₃×#322	C₂	semidirect
5. C₈²×C₁₃	C₂	semidirect
25. #1453	C₁₃	direct (N × H)
39. #322	C₂×C₁₃	semidirect
40. #322	C₂×C₁₃	semidirect
41. C₈²	C₂×C₁₃	semidirect
71. C₁₃	#1453	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×#431	2
C₄×C₁₃×M₁₆	2
C₁₃×#322	2
C₈²×C₁₃	2
#1453	13

Subgroups — C13×#1453 #13110511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#1453 #13110511