Subgroups — C₁₃×#2658 #13111716

Order 1664.

612 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₄⋊Q₈	C₂	1	3	yes	maximal, complemented
2	C₂×C₁₃×#124	C₂	1	3	yes	maximal
3	C₁₃×#399	C₂	1	8	yes	maximal, complemented
4	C₁₃×#376	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×Q₈×C₁₃	C₂²	1	3	yes	—
6	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
7	C₁₃×C₄⋊Q₈	—	2	12	no	—
8	C₁₃×#124	—	2	12	no	—
9	C₂×C₁₃×C₄⋊C₄	C₂²	1	12	yes	—
10	C₂×C₁₃×C₂²⋊C₄	C₂²	1	12	yes	—
11	C₂×C₄²×C₁₃	C₂²	1	3	yes	—
12	C₁₃×#95	C₂²	1	4	yes	—
13	C₂⁴×C₁₃	C₂³	1	2	yes	—
14	C₂×Q₈×C₁₃	—	2	6	no	—
15	C₂×Q₈×C₁₃	—	2	12	no	—
16	C₂×D₄×C₁₃	—	2	6	no	—
17	C₂²×C₄×C₁₃	C₂³	1	6	yes	—
18	C₂²×C₄×C₁₃	C₂³	1	6	yes	—
19	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
20	C₁₃×C₄⋊C₄	—	2	24	no	—
21	C₁₃×C₂²⋊C₄	—	2	24	no	—
22	C₄²×C₁₃	D₄	1	12	yes	—
23	#2658	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂³×C₁₃	—	2	6	no	—
25	C₂³×C₁₃	—	2	8	no	—
26	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
27	Q₈×C₁₃	—	4	12	no	—
28	D₄×C₁₃	—	4	4	no	—
29	C₂×C₄×C₁₃	—	2	12	no	—
30	C₂×C₄×C₁₃	—	2	6	no	—
31	C₂×C₄×C₁₃	—	2	12	no	—
32	C₂×C₄×C₁₃	C₂×D₄	1	12	yes	—
33	C₂×C₄×C₁₃	C₂×D₄	1	6	yes	—
34	C₂×C₄⋊Q₈	C₂×C₁₃	1	3	yes	complemented
35	C₂×#124	C₂×C₁₃	1	3	yes	—
36	#399	C₂×C₁₃	1	8	yes	complemented
37	#376	C₂×C₁₃	1	1	yes	characteristic, complemented
38	C₂²×C₁₃	—	4	2	no	—
39	C₂²×C₁₃	—	4	12	no	—
40	C₂²×C₁₃	C₂²×D₄	1	3	yes	—
41	C₂²×C₁₃	2₋¹⁺⁴	1	4	yes	—
42	C₄×C₁₃	—	2	12	no	—
43	C₄×C₁₃	—	4	6	no	—
44	C₄×C₁₃	#127	1	4	yes	—
45	C₂²×Q₈	C₂²×C₁₃	1	3	yes	—
46	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
47	C₄⋊Q₈	—	2	12	no	—
48	#124	—	2	12	no	—
49	C₂×C₄⋊C₄	C₂²×C₁₃	1	12	yes	—
50	C₂×C₂²⋊C₄	C₂²×C₁₃	1	12	yes	—
51	C₂×C₄²	C₂²×C₁₃	1	3	yes	—
52	#95	C₂²×C₁₃	1	4	yes	—
53	C₂×C₁₃	—	8	2	no	—
54	C₂×C₁₃	C₂×#127	1	1	yes	characteristic
55	C₂×C₁₃	#536	1	6	yes	—
56	C₂⁴	C₂³×C₁₃	1	2	yes	—
57	C₂×Q₈	—	2	6	no	—
58	C₂×Q₈	—	2	12	no	—
59	C₂×D₄	—	2	6	no	—
60	C₂²×C₄	C₂³×C₁₃	1	6	yes	—
61	C₂²×C₄	C₂³×C₁₃	1	6	yes	—
62	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
63	C₄⋊C₄	—	2	24	no	—
64	C₂²⋊C₄	—	2	24	no	—
65	C₄²	D₄×C₁₃	1	12	yes	—
66	C₁₃	#2658	1	1	yes	characteristic, direct product factor, Sylow
67	C₂³	—	2	6	no	—
68	C₂³	—	2	8	no	—
69	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
70	Q₈	—	4	12	no	—
71	D₄	—	4	4	no	—
72	C₂×C₄	—	2	12	no	—
73	C₂×C₄	—	2	6	no	—
74	C₂×C₄	—	2	12	no	—
75	C₂×C₄	C₂×D₄×C₁₃	1	12	yes	—
76	C₂×C₄	C₂×D₄×C₁₃	1	6	yes	—
77	C₂²	—	4	2	no	—
78	C₂²	—	4	12	no	—
79	C₂²	C₂²×D₄×C₁₃	1	3	yes	—
80	C₂²	C₁₃×2₋¹⁺⁴	1	4	yes	—
81	C₄	—	2	12	no	—
82	C₄	—	4	6	no	—
83	C₄	C₁₃×#127	1	4	yes	—
84	C₂	—	8	2	no	—
85	C₂	C₂×C₁₃×#127	1	1	yes	characteristic
86	C₂	C₁₃×#536	1	6	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂²
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
1. C₂×C₁₃×C₄⋊Q₈	C₂	semidirect
3. C₁₃×#399	C₂	semidirect
4. C₁₃×#376	C₂	semidirect
23. #2658	C₁₃	direct (N × H)
34. C₂×C₄⋊Q₈	C₂×C₁₃	semidirect
36. #399	C₂×C₁₃	semidirect
37. #376	C₂×C₁₃	semidirect
66. C₁₃	#2658	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×C₄⋊Q₈	2
C₂×C₁₃×#124	2
C₁₃×#399	2
C₁₃×#376	2
#2658	13

Subgroups — C13×#2658 #13111716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2658 #13111716