Subgroups — C₁₃×#2844 #13111902

Order 1664.

356 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#400	C₂	1	6	yes	maximal
2	C₁₃×#395	C₂	1	6	yes	maximal
3	C₁₃×#382	C₂	1	3	yes	maximal
4	C₂²×Q₈×C₁₃	C₂²	1	2	yes	—
5	C₂×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
6	C₂×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
7	C₂×C₁₃×C₄⋊C₄	C₂²	1	6	yes	—
8	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#95	C₂²	1	12	yes	—
10	C₁₃×#95	C₂²	1	6	yes	—
11	C₁₃×#95	C₂²	1	2	yes	—
12	C₂×Q₈×C₁₃	—	4	6	no	—
13	C₂²×C₄×C₁₃	C₂³	1	6	yes	—
14	C₂²×C₄×C₁₃	C₂³	1	6	yes	—
15	C₂²×C₄×C₁₃	C₂³	1	3	yes	—
16	C₁₃×C₄⋊C₄	—	4	3	no	—
17	C₁₃×C₄⋊C₄	—	4	3	no	—
18	C₁₃×C₄⋊C₄	—	4	6	no	—
19	C₄²×C₁₃	Q₈	1	4	yes	complemented
20	#2844	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
22	Q₈×C₁₃	—	4	8	no	—
23	C₂×C₄×C₁₃	—	2	3	no	—
24	C₂×C₄×C₁₃	—	2	3	no	—
25	C₂×C₄×C₁₃	—	2	6	no	—
26	C₂×C₄×C₁₃	—	2	6	no	—
27	C₂×C₄×C₁₃	—	2	12	no	—
28	C₂×C₄×C₁₃	—	2	12	no	—
29	C₂×C₄×C₁₃	C₂×Q₈	1	6	yes	—
30	#400	C₂×C₁₃	1	6	yes	—
31	#395	C₂×C₁₃	1	6	yes	—
32	#382	C₂×C₁₃	1	3	yes	—
33	C₂²×C₁₃	C₂²×Q₈	1	1	yes	characteristic
34	C₂²×C₁₃	H(5,𝔽₂)	1	3	yes	—
35	C₂²×C₁₃	2₋¹⁺⁴	1	3	yes	—
36	C₄×C₁₃	—	2	6	no	—
37	C₄×C₁₃	—	4	6	no	—
38	C₄×C₁₃	—	4	6	no	—
39	C₂²×Q₈	C₂²×C₁₃	1	2	yes	—
40	C₂×C₄⋊C₄	C₂²×C₁₃	1	3	yes	—
41	C₂×C₄⋊C₄	C₂²×C₁₃	1	3	yes	—
42	C₂×C₄⋊C₄	C₂²×C₁₃	1	6	yes	—
43	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
44	#95	C₂²×C₁₃	1	12	yes	—
45	#95	C₂²×C₁₃	1	6	yes	—
46	#95	C₂²×C₁₃	1	2	yes	—
47	C₂×C₁₃	#544	1	3	yes	—
48	C₂×C₁₃	H(3,𝔽₄)	1	1	yes	characteristic
49	C₂×C₁₃	#563	1	3	yes	—
50	C₂×Q₈	—	4	6	no	—
51	C₂²×C₄	C₂³×C₁₃	1	6	yes	—
52	C₂²×C₄	C₂³×C₁₃	1	6	yes	—
53	C₂²×C₄	C₂³×C₁₃	1	3	yes	—
54	C₄⋊C₄	—	4	3	no	—
55	C₄⋊C₄	—	4	3	no	—
56	C₄⋊C₄	—	4	6	no	—
57	C₄²	Q₈×C₁₃	1	4	yes	complemented
58	C₁₃	#2844	1	1	yes	characteristic, direct product factor, Sylow
59	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
60	Q₈	—	4	8	no	—
61	C₂×C₄	—	2	3	no	—
62	C₂×C₄	—	2	3	no	—
63	C₂×C₄	—	2	6	no	—
64	C₂×C₄	—	2	6	no	—
65	C₂×C₄	—	2	12	no	—
66	C₂×C₄	—	2	12	no	—
67	C₂×C₄	C₂×Q₈×C₁₃	1	6	yes	—
68	C₂²	C₂²×Q₈×C₁₃	1	1	yes	characteristic
69	C₂²	C₁₃×H(5,𝔽₂)	1	3	yes	—
70	C₂²	C₁₃×2₋¹⁺⁴	1	3	yes	—
71	C₄	—	2	6	no	—
72	C₄	—	4	6	no	—
73	C₄	—	4	6	no	—
74	C₂	C₁₃×#544	1	3	yes	—
75	C₂	C₁₃×H(3,𝔽₄)	1	1	yes	characteristic
76	C₂	C₁₃×#563	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
19. C₄²×C₁₃	Q₈	semidirect
20. #2844	C₁₃	direct (N × H)
57. C₄²	Q₈×C₁₃	semidirect
58. C₁₃	#2844	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×#400	2
C₁₃×#395	2
C₁₃×#382	2
#2844	13

Subgroups — C13×#2844 #13111902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2844 #13111902