Subgroups — C₁₃×#1849 #13110907

Order 1664.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#108	C₂	1	4	yes	maximal
2	C₁₃×#423	C₂	1	2	yes	maximal
3	C₂×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×M₁₆	C₂²	1	4	yes	—
5	C₂²×C₈×C₁₃	C₂²	1	2	yes	—
6	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₁₃×#108	—	2	8	no	—
8	C₁₃×C₄⋊C₈	—	2	4	no	—
9	C₁₃×#97	C₄	1	4	yes	—
10	C₂²×C₄×C₁₃	Q₈	1	2	yes	—
11	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
12	C₁₃×M₁₆	—	2	8	no	—
13	C₂×C₈×C₁₃	—	2	4	no	—
14	C₂×C₈×C₁₃	C₂×C₄	1	4	yes	—
15	C₂×C₈×C₁₃	D₄	1	4	yes	—
16	C₂×C₈×C₁₃	Q₈	1	4	yes	—
17	C₄²×C₁₃	C₂×C₄	1	2	yes	—
18	C₄²×C₁₃	D₄	1	2	yes	—
19	#1849	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂³×C₁₃	C₂×Q₈	1	1	yes	characteristic
21	C₂×C₄×C₁₃	—	4	2	no	—
22	C₂×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
23	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
25	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
26	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
27	C₈×C₁₃	—	4	4	no	—
28	C₈×C₁₃	C₄⋊C₄	1	8	yes	—
29	C₂×#108	C₂×C₁₃	1	4	yes	—
30	#423	C₂×C₁₃	1	2	yes	—
31	C₂×#97	C₂×C₁₃	1	1	yes	characteristic
32	C₂²×C₁₃	—	2	2	no	—
33	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
34	C₂²×C₁₃	C₄⋊Q₈	1	2	yes	—
35	C₄×C₁₃	—	2	4	no	—
36	C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
37	C₄×C₁₃	#127	1	1	yes	characteristic
38	C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
39	C₂×M₁₆	C₂²×C₁₃	1	4	yes	—
40	C₂²×C₈	C₂²×C₁₃	1	2	yes	—
41	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
42	#108	—	2	8	no	—
43	C₄⋊C₈	—	2	4	no	—
44	#97	C₄×C₁₃	1	4	yes	—
45	C₂×C₁₃	—	2	2	no	—
46	C₂×C₁₃	#384	1	1	yes	characteristic
47	C₂×C₁₃	#430	1	2	yes	—
48	C₂²×C₄	Q₈×C₁₃	1	2	yes	—
49	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
50	M₁₆	—	2	8	no	—
51	C₂×C₈	—	2	4	no	—
52	C₂×C₈	C₂×C₄×C₁₃	1	4	yes	—
53	C₂×C₈	D₄×C₁₃	1	4	yes	—
54	C₂×C₈	Q₈×C₁₃	1	4	yes	—
55	C₄²	C₂×C₄×C₁₃	1	2	yes	—
56	C₄²	D₄×C₁₃	1	2	yes	—
57	C₁₃	#1849	1	1	yes	characteristic, direct product factor, Sylow
58	C₂³	C₂×Q₈×C₁₃	1	1	yes	characteristic
59	C₂×C₄	—	4	2	no	—
60	C₂×C₄	C₁₃×C₄⋊C₄	1	4	yes	—
61	C₂×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
62	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
63	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
64	C₂×C₄	C₂×Q₈×C₁₃	1	2	yes	—
65	C₈	—	4	4	no	—
66	C₈	C₁₃×C₄⋊C₄	1	8	yes	—
67	C₂²	—	2	2	no	—
68	C₂²	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
69	C₂²	C₁₃×C₄⋊Q₈	1	2	yes	—
70	C₄	—	2	4	no	—
71	C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
72	C₄	C₁₃×#127	1	1	yes	characteristic
73	C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
74	C₂	—	2	2	no	—
75	C₂	C₁₃×#384	1	1	yes	characteristic
76	C₂	C₁₃×#430	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×C₄⋊C₄
prime radical	C₂³×C₁₃	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
19. #1849	C₁₃	direct (N × H)
57. C₁₃	#1849	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#108	2
C₁₃×#423	2
C₂×C₁₃×#97	2
#1849	13

Subgroups — C13×#1849 #13110907

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#1849 #13110907