Subgroups — C₁₃×#3556 #13112614

Order 1664.

890 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#564	C₂	1	4	yes	maximal, complemented
2	C₁₃×#557	C₂	1	12	yes	maximal, complemented
3	C₁₃×#541	C₂	1	12	yes	maximal
4	C₁₃×#533	C₂	1	3	yes	maximal
5	C₁₃×C₄⋊Q₈	C₂²	1	6	yes	—
6	C₁₃×C₄⋊Q₈	C₂²	1	12	yes	—
7	C₁₃×#126	C₂²	1	16	yes	—
8	C₁₃×#125	C₂²	1	6	yes	—
9	C₁₃×#125	C₂²	1	12	yes	—
10	C₁₃×#125	C₂²	1	48	yes	—
11	C₁₃×C₂²⋊Q₈	C₂²	1	12	yes	—
12	C₄×Q₈×C₁₃	C₂²	1	12	yes	—
13	C₄×Q₈×C₁₃	C₂²	1	24	yes	—
14	C₁₃×#117	C₂²	1	6	yes	—
15	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₁₃	C₂³	1	12	yes	—
17	C₂²×C₄×C₁₃	C₂³	1	3	yes	—
18	C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
19	C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
20	C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
21	C₁₃×C₄⋊C₄	C₂³	1	48	yes	—
22	C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
23	C₄²×C₁₃	C₂³	1	3	yes	—
24	C₄²×C₁₃	C₂³	1	1	yes	characteristic
25	C₄²×C₁₃	C₂³	1	12	yes	—
26	C₄²×C₁₃	C₂³	1	16	yes	—
27	#3556	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
29	Q₈×C₁₃	—	2	24	no	—
30	C₂×C₄×C₁₃	—	2	6	no	—
31	C₂×C₄×C₁₃	C₂⁴	1	24	yes	—
32	C₂×C₄×C₁₃	C₂⁴	1	3	yes	—
33	C₂×C₄×C₁₃	C₂⁴	1	3	yes	—
34	#564	C₂×C₁₃	1	4	yes	complemented
35	#557	C₂×C₁₃	1	12	yes	complemented
36	#541	C₂×C₁₃	1	12	yes	—
37	#533	C₂×C₁₃	1	3	yes	—
38	C₂²×C₁₃	—	2	3	no	—
39	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
40	C₄×C₁₃	—	2	3	no	—
41	C₄×C₁₃	—	2	24	no	—
42	C₄×C₁₃	2₋¹⁺⁴	1	6	yes	—
43	C₄⋊Q₈	C₂²×C₁₃	1	6	yes	—
44	C₄⋊Q₈	C₂²×C₁₃	1	12	yes	—
45	#126	C₂²×C₁₃	1	16	yes	—
46	#125	C₂²×C₁₃	1	6	yes	—
47	#125	C₂²×C₁₃	1	12	yes	—
48	#125	C₂²×C₁₃	1	48	yes	—
49	C₂²⋊Q₈	C₂²×C₁₃	1	12	yes	—
50	C₄×Q₈	C₂²×C₁₃	1	12	yes	—
51	C₄×Q₈	C₂²×C₁₃	1	24	yes	—
52	#117	C₂²×C₁₃	1	6	yes	—
53	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
54	C₂×C₁₃	—	4	1	no	—
55	C₂×C₁₃	C₂×2₋¹⁺⁴	1	3	yes	—
56	C₂×Q₈	C₂³×C₁₃	1	12	yes	—
57	C₂²×C₄	C₂³×C₁₃	1	3	yes	—
58	C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
59	C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
60	C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
61	C₄⋊C₄	C₂³×C₁₃	1	48	yes	—
62	C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
63	C₄²	C₂³×C₁₃	1	3	yes	—
64	C₄²	C₂³×C₁₃	1	1	yes	characteristic
65	C₄²	C₂³×C₁₃	1	12	yes	—
66	C₄²	C₂³×C₁₃	1	16	yes	—
67	C₁₃	#3556	1	1	yes	characteristic, direct product factor, Sylow
68	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
69	Q₈	—	2	24	no	—
70	C₂×C₄	—	2	6	no	—
71	C₂×C₄	C₂⁴×C₁₃	1	24	yes	—
72	C₂×C₄	C₂⁴×C₁₃	1	3	yes	—
73	C₂×C₄	C₂⁴×C₁₃	1	3	yes	—
74	C₂²	—	2	3	no	—
75	C₂²	C₂⁵×C₁₃	1	1	yes	characteristic
76	C₄	—	2	3	no	—
77	C₄	—	2	24	no	—
78	C₄	C₁₃×2₋¹⁺⁴	1	6	yes	—
79	C₂	—	4	1	no	—
80	C₂	C₂×C₁₃×2₋¹⁺⁴	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₃
prime radical	C₂³×C₁₃	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#564	C₂	semidirect
2. C₁₃×#557	C₂	semidirect
27. #3556	C₁₃	direct (N × H)
34. #564	C₂×C₁₃	semidirect
35. #557	C₂×C₁₃	semidirect
67. C₁₃	#3556	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×#564	2
C₁₃×#557	2
C₁₃×#541	2
C₁₃×#533	2
#3556	13

Subgroups — C13×#3556 #13112614

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3556 #13112614