Subgroups — C₁₃×#2179 #13111237

Order 1664.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#508	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#443	C₂	1	2	yes	maximal, complemented
3	C₁₃×#368	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#359	C₂	1	2	yes	maximal, complemented
5	C₁₃×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#135	C₂²	1	2	yes	—
7	C₁₃×#131	—	2	2	no	—
8	C₁₃×Q₃₂	C₄	1	1	yes	characteristic, complemented
9	C₁₃×SD₃₂	C₄	1	2	yes	complemented
10	C₁₃×D₁₆	C₄	1	1	yes	characteristic, complemented
11	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
13	C₁₃×#108	C₂²	1	2	yes	—
14	C₁₃×#104	—	2	2	no	—
15	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#41	—	2	2	no	—
17	C₁₃×Q₁₆	C₂×C₄	1	2	yes	—
18	C₁₃×SD₁₆	—	2	2	no	—
19	C₁₃×D₈	C₂×C₄	1	2	yes	—
20	C₁₃×M₁₆	—	2	2	no	—
21	C₁₃×M₁₆	—	4	2	no	—
22	C₂×C₈×C₁₃	—	4	2	no	—
23	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
24	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
25	C₄²×C₁₃	D₄	1	1	yes	characteristic
26	C₁₃×C₁₆	—	2	1	no	—
27	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
28	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
29	#2179	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	Q₈×C₁₃	—	2	2	no	—
31	D₄×C₁₃	—	2	2	no	—
32	D₄×C₁₃	—	4	2	no	—
33	C₂×C₄×C₁₃	—	2	1	no	—
34	C₂×C₄×C₁₃	—	4	2	no	—
35	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
36	C₈×C₁₃	—	4	2	no	—
37	C₈×C₁₃	D₈	1	2	yes	—
38	C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
39	C₈×C₁₃	#41	1	1	yes	characteristic
40	#508	C₂×C₁₃	1	1	yes	characteristic
41	#443	C₂×C₁₃	1	2	yes	complemented
42	#368	C₂×C₁₃	1	1	yes	characteristic, complemented
43	#359	C₂×C₁₃	1	2	yes	complemented
44	#346	C₂×C₁₃	1	1	yes	characteristic, complemented
45	C₂²×C₁₃	—	4	2	no	—
46	C₂²×C₁₃	#135	1	1	yes	characteristic
47	C₄×C₁₃	—	4	1	no	—
48	C₄×C₁₃	—	4	2	no	—
49	C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
50	C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
51	#135	C₂²×C₁₃	1	2	yes	—
52	#131	—	2	2	no	—
53	Q₃₂	C₄×C₁₃	1	1	yes	characteristic, complemented
54	SD₃₂	C₄×C₁₃	1	2	yes	complemented
55	D₁₆	C₄×C₁₃	1	1	yes	characteristic, complemented
56	C₂×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
57	C₂×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
58	#108	C₂²×C₁₃	1	2	yes	—
59	#104	—	2	2	no	—
60	C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
61	C₂×C₁₃	—	2	1	no	—
62	C₂×C₁₃	—	8	2	no	—
63	C₂×C₁₃	C₄×D₈	1	1	yes	characteristic
64	#41	—	2	2	no	—
65	Q₁₆	C₂×C₄×C₁₃	1	2	yes	—
66	SD₁₆	—	2	2	no	—
67	D₈	C₂×C₄×C₁₃	1	2	yes	—
68	M₁₆	—	2	2	no	—
69	M₁₆	—	4	2	no	—
70	C₂×C₈	—	4	2	no	—
71	C₂×C₈	D₄×C₁₃	1	1	yes	characteristic
72	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
73	C₄²	D₄×C₁₃	1	1	yes	characteristic
74	C₁₆	—	2	1	no	—
75	C₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
76	C₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
77	C₁₃	#2179	1	1	yes	characteristic, direct product factor, Sylow
78	Q₈	—	2	2	no	—
79	D₄	—	2	2	no	—
80	D₄	—	4	2	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
84	C₈	—	4	2	no	—
85	C₈	C₁₃×D₈	1	2	yes	—
86	C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
87	C₈	C₁₃×#41	1	1	yes	characteristic
88	C₂²	—	4	2	no	—
89	C₂²	C₁₃×#135	1	1	yes	characteristic
90	C₄	—	4	1	no	—
91	C₄	—	4	2	no	—
92	C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
93	C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	8	2	no	—
96	C₂	C₄×C₁₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	C₂×D₈
commutator	C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₈	C₂³×C₁₃
socle	C₂×C₁₃	C₄×D₈
prime radical	C₁₃×#508	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂×C₈×C₁₃ ◁ C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#443	C₂	semidirect
3. C₁₃×#368	C₂	semidirect
4. C₁₃×#359	C₂	semidirect
5. C₁₃×#346	C₂	semidirect
8. C₁₃×Q₃₂	C₄	semidirect
9. C₁₃×SD₃₂	C₄	semidirect
10. C₁₃×D₁₆	C₄	semidirect
29. #2179	C₁₃	direct (N × H)
41. #443	C₂×C₁₃	semidirect
42. #368	C₂×C₁₃	semidirect
43. #359	C₂×C₁₃	semidirect
44. #346	C₂×C₁₃	semidirect
53. Q₃₂	C₄×C₁₃	semidirect
54. SD₃₂	C₄×C₁₃	semidirect
55. D₁₆	C₄×C₁₃	semidirect
77. C₁₃	#2179	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×#508	2
C₁₃×#443	2
C₁₃×#368	2
C₁₃×#359	2
C₁₃×#346	2
#2179	13

Subgroups — C13×#2179 #13111237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2179 #13111237