Subgroups — Dic₁₃×#564 #16025641

Order 3328.

1800 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13118022	C₂	1	15	yes	maximal
2	#125×Dic₁₃	C₂	1	15	yes	maximal
3	C₂×C₁₃×#564	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#564	C₄	1	16	yes	complemented
5	C₂×C₁₃×#125	C₂²	1	15	yes	—
6	#11718646	C₂²	1	30	yes	—
7	#11718642	C₂²	1	60	yes	—
8	C₄⋊C₄×Dic₁₃	C₂²	1	30	yes	—
9	#11718597	C₂²	1	15	yes	—
10	C₄²×Dic₁₃	C₂²	1	5	yes	—
11	C₁₃×#125	C₂×C₄	1	120	yes	—
12	C₂×C₁₃×C₄⋊C₄	C₂³	1	30	yes	—
13	C₂×C₄²×C₁₃	C₂³	1	5	yes	—
14	C₂×C₄⋊Dic₁₃	C₂³	1	30	yes	—
15	C₂×C₄×Dic₁₃	C₂³	1	15	yes	—
16	C₂×C₄×Dic₁₃	C₂³	1	15	yes	—
17	#88071	C₂³	1	60	yes	—
18	C₄×#564	—	13	1	no	maximal, Sylow
19	C₂²×C₄×C₁₃	C₂⁴	1	15	yes	—
20	C₂²×Dic₁₃	C₂⁴	1	15	yes	—
21	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
22	C₁₃×C₄⋊C₄	C₂²×C₄	1	120	yes	—
23	C₄²×C₁₃	C₂²×C₄	1	20	yes	—
24	C₄⋊Dic₁₃	—	4	30	no	—
25	C₄×Dic₁₃	—	2	30	no	—
26	C₄×Dic₁₃	—	4	15	no	—
27	C₂×#564	D₁₃	1	1	yes	characteristic
28	#2382	—	13	15	no	—
29	C₄×#125	—	13	15	no	—
30	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
31	C₂×C₄×C₁₃	—	2	15	no	—
32	C₂×C₄×C₁₃	—	2	15	no	—
33	C₂×C₄×C₁₃	C₂³×C₄	1	30	yes	—
34	C₂×Dic₁₃	—	2	15	no	—
35	C₂×Dic₁₃	—	2	30	no	—
36	C₂×Dic₁₃	2₋¹⁺⁴	1	6	yes	—
37	#564	Dic₁₃	1	16	yes	direct product factor
38	C₂×#125	C₂×D₁₃	1	15	yes	—
39	#389	—	13	30	no	—
40	#387	—	13	60	no	—
41	#382	—	13	15	no	—
42	C₄×C₄⋊C₄	—	13	30	no	—
43	C₄³	—	13	5	no	—
44	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
45	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	3	yes	—
46	C₂²×C₁₃	#585	1	3	yes	—
47	C₄×C₁₃	—	2	30	no	—
48	Dic₁₃	—	4	15	no	—
49	Dic₁₃	#564	1	4	yes	direct product factor
50	#125	C₂×Dic₁₃	1	120	yes	—
51	C₂×C₄⋊C₄	—	13	30	no	—
52	C₂×C₄⋊C₄	C₂²×D₁₃	1	30	yes	—
53	C₂×C₄²	—	13	15	no	—
54	C₂×C₄²	—	13	15	no	—
55	C₂×C₄²	C₂²×D₁₃	1	5	yes	—
56	#95	—	13	60	no	—
57	C₂×C₁₃	C₄×2₋¹⁺⁴	1	3	yes	—
58	C₂×C₁₃	C₂×#564	1	1	yes	characteristic
59	C₂×C₁₃	#3531	1	3	yes	—
60	C₂²×C₄	—	13	1	no	—
61	C₂²×C₄	—	13	15	no	—
62	C₂²×C₄	C₂³×D₁₃	1	15	yes	—
63	C₄⋊C₄	—	52	30	no	—
64	C₄⋊C₄	C₂²×Dic₁₃	1	120	yes	—
65	C₄²	—	26	30	no	—
66	C₄²	—	52	15	no	—
67	C₄²	C₂²×Dic₁₃	1	20	yes	—
68	C₁₃	C₄×#564	1	1	yes	characteristic, complemented, Sylow
69	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
70	C₂×C₄	—	2	15	no	—
71	C₂×C₄	—	2	15	no	—
72	C₂×C₄	—	13	6	no	—
73	C₂×C₄	—	26	15	no	—
74	C₂×C₄	—	26	30	no	—
75	C₂×C₄	C₂³×Dic₁₃	1	30	yes	—
76	C₂²	D₁₃×2₋¹⁺⁴	1	3	yes	—
77	C₂²	#11719652	1	3	yes	—
78	C₂²	C₂⁴×Dic₁₃	1	1	yes	characteristic
79	C₄	—	2	30	no	—
80	C₄	—	13	4	no	—
81	C₄	—	52	15	no	—
82	C₂	2₋¹⁺⁴×Dic₁₃	1	3	yes	—
83	C₂	D₁₃×#564	1	1	yes	characteristic
84	C₂	#13128984	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₁₃
commutator	C₂²×C₁₃	C₂⁴×C₄
Fitting	C₂×C₁₃×#564	C₂
socle, prime radical, cosocle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×#564	D₁₃
hypocenter	C₁₃	C₄×#564
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#564

Complements

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

N	H ≅ G/N	type
4. C₁₃×#564	C₄	semidirect
37. #564	Dic₁₃	direct (N × H)
49. Dic₁₃	#564	direct (N × H)
68. C₁₃	C₄×#564	semidirect

Maximal subgroups

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

subgroup	index
#13118022	2
#125×Dic₁₃	2
C₂×C₁₃×#564	2
C₄×#564	13

Subgroups — Dic13×#564 #16025641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₃×#564 #16025641