Subgroups — D₁₃×#383 #13117224

Order 1664.

624 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#383	C₂	1	1	yes	maximal, characteristic, complemented
3	#11718598	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×#95	C₂	1	6	yes	maximal
5	#11718312	C₂	1	6	yes	maximal, complemented
6	C₂²×C₄×D₁₃	C₂²	1	4	yes	—
7	C₂²×C₄×D₁₃	C₂²	1	3	yes	—
8	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×Dic₁₃	C₂²	1	3	yes	—
10	C₄²×D₁₃	C₄	1	8	yes	complemented
11	C₁₃×#95	C₂²	1	6	yes	—
12	#88071	C₂²	1	12	yes	—
13	#88071	C₂²	1	6	yes	—
14	C₂³×D₁₃	C₂³	1	1	yes	characteristic
15	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
16	C₂²×C₄×C₁₃	C₂³	1	3	yes	—
17	C₂²×Dic₁₃	C₂³	1	4	yes	—
18	C₂²×Dic₁₃	C₂³	1	3	yes	—
19	C₂×C₄×D₁₃	—	2	12	no	—
20	C₂×C₄×D₁₃	—	2	24	no	—
21	C₂×C₄×D₁₃	C₂×C₄	1	12	yes	—
22	C₄²×C₁₃	C₂×C₄	1	4	yes	complemented
23	C₄×Dic₁₃	C₂×C₄	1	12	yes	complemented
24	C₂×#383	—	13	1	no	maximal, Sylow
25	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
26	C₂²×D₁₃	C₂²×C₄	1	2	yes	—
27	C₂²×D₁₃	#41	1	12	yes	—
28	C₂×C₄×C₁₃	—	2	6	no	—
29	C₂×C₄×C₁₃	—	2	12	no	—
30	C₂×C₄×C₁₃	C₂²×C₄	1	6	yes	—
31	C₂×Dic₁₃	—	2	6	no	—
32	C₂×Dic₁₃	—	2	12	no	—
33	C₂×Dic₁₃	C₂²×C₄	1	6	yes	—
34	C₄×D₁₃	—	2	24	no	—
35	C₄×D₁₃	—	4	16	no	—
36	C₂²×C₄²	—	13	1	no	—
37	#383	—	13	1	no	—
38	#383	—	13	6	no	—
39	#383	D₁₃	1	1	yes	characteristic, direct product factor
40	C₂×#95	—	13	6	no	—
41	C₂²×C₁₃	C₂³×C₄	1	1	yes	characteristic
42	C₂²×C₁₃	C₂×#41	1	6	yes	—
43	C₂×D₁₃	#117	1	12	yes	—
44	C₂×D₁₃	#126	1	16	yes	—
45	C₄×C₁₃	—	2	6	no	—
46	C₄×C₁₃	—	4	4	no	—
47	Dic₁₃	—	2	6	no	—
48	Dic₁₃	—	4	4	no	—
49	C₂³×C₄	—	13	3	no	—
50	C₂³×C₄	—	13	4	no	—
51	C₂×C₄²	—	13	3	no	—
52	C₂×C₄²	—	13	8	no	—
53	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
54	#95	—	13	12	no	—
55	#95	—	13	6	no	—
56	#95	C₂×D₁₃	1	6	yes	—
57	C₂×C₁₃	C₂×#117	1	3	yes	—
58	C₂×C₁₃	C₂×#126	1	4	yes	—
59	D₁₃	#383	1	8	yes	direct product factor
60	C₂⁴	—	13	1	no	—
61	C₂²×C₄	—	13	3	no	—
62	C₂²×C₄	—	13	12	no	—
63	C₂²×C₄	—	13	4	no	—
64	C₂²×C₄	—	26	12	no	—
65	C₂²×C₄	—	26	24	no	—
66	C₂²×C₄	C₂²×D₁₃	1	4	yes	—
67	C₂²×C₄	C₂²×D₁₃	1	3	yes	—
68	C₄²	—	13	12	no	—
69	C₄²	C₄×D₁₃	1	4	yes	complemented
70	C₁₃	C₂×#383	1	1	yes	characteristic, complemented, Sylow
71	C₂³	—	13	2	no	—
72	C₂³	—	13	12	no	—
73	C₂³	C₂³×D₁₃	1	1	yes	characteristic
74	C₂×C₄	—	2	6	no	—
75	C₂×C₄	—	2	12	no	—
76	C₂×C₄	—	13	6	no	—
77	C₂×C₄	—	26	24	no	—
78	C₂×C₄	—	26	6	no	—
79	C₂×C₄	—	26	12	no	—
80	C₂×C₄	—	52	16	no	—
81	C₂×C₄	C₂×C₄×D₁₃	1	6	yes	—
82	C₂²	—	13	12	no	—
83	C₂²	—	13	16	no	—
84	C₂²	C₂²×C₄×D₁₃	1	1	yes	characteristic
85	C₂²	#41×D₁₃	1	6	yes	—
86	C₄	—	2	6	no	—
87	C₄	—	4	4	no	—
88	C₄	—	26	6	no	—
89	C₄	—	52	4	no	—
90	C₂	—	13	8	no	—
91	C₂	D₁₃×#117	1	3	yes	—
92	C₂	D₁₃×#126	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃
commutator	C₂²×C₁₃	C₂³×C₄
Fitting	C₁₃×#383	C₂
socle, cosocle	C₂³×C₁₃	C₂⁴
prime radical	C₂³×D₁₃	C₂³
hypercenter	#383	D₁₃
hypocenter	C₁₃	C₂×#383
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ #383

Complements

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

N	H ≅ G/N	type
2. C₁₃×#383	C₂	semidirect
3. #11718598	C₂	semidirect
5. #11718312	C₂	semidirect
10. C₄²×D₁₃	C₄	semidirect
22. C₄²×C₁₃	C₂×C₄	semidirect
23. C₄×Dic₁₃	C₂×C₄	semidirect
39. #383	D₁₃	direct (N × H)
59. D₁₃	#383	direct (N × H)
69. C₄²	C₄×D₁₃	semidirect
70. C₁₃	C₂×#383	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄²×D₁₃	2
C₁₃×#383	2
#11718598	2
D₁₃×#95	2
#11718312	2
C₂×#383	13

Subgroups — D13×#383 #13117224

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#383 #13117224