Subgroups — D₁₃×#1367 #15774459

Order 3328.

286 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×C₄⋊C₁₆	C₂	1	2	yes	maximal
2	C₈²×D₁₃	C₂	1	1	yes	maximal, characteristic
3	#13112900	C₂	1	1	yes	maximal, characteristic, complemented
4	#13112899	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₆×D₁₃	—	2	2	no	—
7	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
8	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
9	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
10	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
11	C₈²×C₁₃	C₂²	1	1	yes	characteristic
12	#11718093	—	2	2	no	—
13	C₄⋊#6090	C₂²	1	2	yes	—
14	C₈×#1055	C₄	1	1	yes	characteristic
15	C₈×#1055	C₄	1	1	yes	characteristic
16	C₈×#1055	C₂²	1	1	yes	characteristic
17	C₂×C₈×D₁₃	—	2	1	no	—
18	C₂×C₈×D₁₃	C₈	1	1	yes	characteristic
19	C₂×C₈×D₁₃	C₈	1	1	yes	characteristic
20	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
21	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
22	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₁₃×C₁₆	—	2	2	no	—
24	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
27	C₈×Dic₁₃	—	2	1	no	—
28	C₈×Dic₁₃	C₈	1	1	yes	characteristic
29	C₈×Dic₁₃	C₈	1	1	yes	characteristic
30	C₈×Dic₁₃	D₄	1	1	yes	characteristic
31	C₈×Dic₁₃	Q₈	1	1	yes	characteristic
32	C₂×#6090	—	2	2	no	—
33	C₄×#1055	C₂×C₄	1	1	yes	characteristic
34	C₄×#1055	C₂×C₄	1	1	yes	characteristic
35	C₄×#1055	C₂×C₄	1	1	yes	characteristic
36	C₁₆×D₁₃	—	4	4	no	—
37	C₂×#1367	—	13	1	no	maximal, Sylow
38	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
40	C₂×C₄×D₁₃	M₁₆	1	1	yes	characteristic
41	C₂×C₈×C₁₃	—	2	1	no	—
42	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
43	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
44	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
45	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
46	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
47	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
48	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
49	C₄×Dic₁₃	M₁₆	1	1	yes	characteristic
50	C₂×#1055	—	2	1	no	—
51	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
52	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
53	C₂×#1055	C₂×C₈	1	1	yes	characteristic
54	C₂×#1055	C₂×C₈	1	1	yes	characteristic
55	C₈×D₁₃	—	2	4	no	—
56	C₈×D₁₃	—	2	2	no	—
57	C₈×D₁₃	—	2	2	no	—
58	C₈×D₁₃	C₁₆	1	4	yes	complemented
59	C₈×D₁₃	SD₁₆	1	4	yes	—
60	C₁₃×C₁₆	—	4	2	no	—
61	#6090	—	4	2	no	—
62	C₂×C₄⋊C₁₆	—	13	2	no	—
63	C₂×C₈²	—	13	1	no	—
64	#1367	—	13	2	no	—
65	#1367	—	13	1	no	—
66	#1367	D₁₃	1	1	yes	characteristic, direct product factor
67	C₂²×D₁₃	C₄⋊C₈	1	1	yes	characteristic
68	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
69	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
70	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
71	C₂×Dic₁₃	C₄⋊C₈	1	1	yes	characteristic
72	C₂×Dic₁₃	C₄⋊C₈	1	1	yes	characteristic
73	C₂×Dic₁₃	C₄⋊C₈	1	1	yes	characteristic
74	C₄×D₁₃	—	2	2	no	—
75	C₄×D₁₃	#106	1	2	yes	—
76	C₄×D₁₃	#108	1	2	yes	—
77	C₄×D₁₃	C₂×C₁₆	1	2	yes	—
78	C₄×D₁₃	M₃₂	1	2	yes	—
79	C₈×C₁₃	—	2	2	no	—
80	C₈×C₁₃	—	2	1	no	—
81	C₈×C₁₃	—	2	1	no	—
82	C₈×C₁₃	C₂×C₁₆	1	2	yes	complemented
83	C₈×C₁₃	C₂×SD₁₆	1	2	yes	—
84	#1055	—	2	2	no	—
85	#1055	—	2	1	no	—
86	#1055	—	2	1	no	—
87	#1055	#106	1	2	yes	—
88	#1055	C₂×C₁₆	1	2	yes	complemented
89	C₂²×C₁₆	—	26	2	no	—
90	C₂×C₄×C₈	—	13	1	no	—
91	C₂×C₄×C₈	—	13	1	no	—
92	C₂×C₄×C₈	—	13	1	no	—
93	C₄⋊C₁₆	—	13	2	no	—
94	C₄⋊C₁₆	—	26	2	no	—
95	C₄⋊C₁₆	C₂×D₁₃	1	2	yes	—
96	C₈²	—	13	1	no	—
97	C₈²	—	13	1	no	—
98	C₈²	—	13	1	no	—
99	C₈²	C₂×D₁₃	1	1	yes	characteristic
100	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
101	C₂×D₁₃	#334	1	2	yes	—
102	C₂×D₁₃	C₄⋊C₁₆	1	2	yes	—
103	C₂×D₁₃	#364	1	2	yes	—
104	C₄×C₁₃	—	2	1	no	—
105	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
106	C₄×C₁₃	C₂×#108	1	1	yes	characteristic
107	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
108	C₄×C₁₃	C₂×M₃₂	1	1	yes	characteristic
109	Dic₁₃	—	2	1	no	—
110	Dic₁₃	#334	1	2	yes	—
111	Dic₁₃	C₄⋊C₁₆	1	2	yes	—
112	C₂²×C₈	—	13	1	no	—
113	C₂²×C₈	—	13	1	no	—
114	C₂²×C₈	—	13	1	no	—
115	C₂²×C₈	—	13	1	no	—
116	C₂²×C₈	—	26	1	no	—
117	C₂×C₄²	—	13	1	no	—
118	C₂×C₁₆	—	2	2	no	—
119	C₂×C₁₆	—	26	2	no	—
120	C₂×C₁₆	—	52	4	no	—
121	C₄×C₈	—	13	1	no	—
122	C₄×C₈	—	13	1	no	—
123	C₄×C₈	—	13	1	no	—
124	C₄×C₈	—	13	1	no	—
125	C₄×C₈	—	13	1	no	—
126	C₄×C₈	—	13	1	no	—
127	C₄×C₈	—	13	1	no	—
128	C₄×C₈	—	26	1	no	—
129	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
130	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
131	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
132	C₂×C₁₃	C₂×#334	1	1	yes	characteristic
133	C₂×C₁₃	C₂×C₄⋊C₁₆	1	1	yes	characteristic
134	C₂×C₁₃	C₂×#364	1	1	yes	characteristic
135	D₁₃	#1367	1	4	yes	direct product factor
136	C₂²×C₄	—	13	1	no	—
137	C₂²×C₄	—	13	1	no	—
138	C₂²×C₄	—	13	1	no	—
139	C₂×C₈	—	2	1	no	—
140	C₂×C₈	—	13	1	no	—
141	C₂×C₈	—	13	1	no	—
142	C₂×C₈	—	13	4	no	—
143	C₂×C₈	—	13	4	no	—
144	C₂×C₈	—	13	1	no	—
145	C₂×C₈	—	13	1	no	—
146	C₂×C₈	—	26	2	no	—
147	C₂×C₈	—	26	2	no	—
148	C₂×C₈	—	26	4	no	—
149	C₂×C₈	—	26	1	no	—
150	C₂×C₈	C₈×D₁₃	1	1	yes	characteristic
151	C₂×C₈	C₈×D₁₃	1	1	yes	characteristic
152	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
153	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
154	C₄²	—	13	1	no	—
155	C₄²	—	13	1	no	—
156	C₄²	—	13	1	no	—
157	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
158	C₁₆	—	4	2	no	—
159	C₁₆	—	52	2	no	—
160	C₁₃	C₂×#1367	1	1	yes	characteristic, complemented, Sylow
161	C₂³	—	13	1	no	—
162	C₂×C₄	—	13	1	no	—
163	C₂×C₄	—	13	1	no	—
164	C₂×C₄	—	13	2	no	—
165	C₂×C₄	—	13	2	no	—
166	C₂×C₄	—	13	2	no	—
167	C₂×C₄	—	13	2	no	—
168	C₂×C₄	—	13	1	no	—
169	C₂×C₄	—	26	2	no	—
170	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
171	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
172	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
173	C₈	—	2	2	no	—
174	C₈	—	2	1	no	—
175	C₈	—	2	1	no	—
176	C₈	—	13	2	no	—
177	C₈	—	13	2	no	—
178	C₈	—	26	2	no	—
179	C₈	—	26	1	no	—
180	C₈	—	26	1	no	—
181	C₈	C₁₆×D₁₃	1	2	yes	complemented
182	C₈	SD₁₆×D₁₃	1	2	yes	—
183	C₂²	—	13	2	no	—
184	C₂²	—	13	2	no	—
185	C₂²	—	13	2	no	—
186	C₂²	D₁₃×C₄⋊C₈	1	1	yes	characteristic
187	C₄	—	2	1	no	—
188	C₄	—	13	2	no	—
189	C₄	—	13	2	no	—
190	C₄	—	26	1	no	—
191	C₄	D₁₃×#106	1	1	yes	characteristic
192	C₄	D₁₃×#108	1	1	yes	characteristic
193	C₄	C₂×C₁₆×D₁₃	1	1	yes	characteristic
194	C₄	D₁₃×M₃₂	1	1	yes	characteristic
195	C₂	—	13	4	no	—
196	C₂	D₁₃×#334	1	1	yes	characteristic
197	C₂	D₁₃×C₄⋊C₁₆	1	1	yes	characteristic
198	C₂	D₁₃×#364	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₁₃
commutator	C₄×C₁₃	C₂²×C₁₆
Frattini	C₄×C₈	C₂²×D₁₃
Fitting	C₁₃×#1367	C₂
socle	C₂²×C₁₃	C₂×C₄⋊C₈
prime radical	C₂²×D₁₃	C₄⋊C₈
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	#1367	D₁₃
hypocenter	C₁₃	C₂×#1367
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1367

Complements

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

N	H ≅ G/N	type
3. #13112900	C₂	semidirect
4. #13112899	C₂	semidirect
5. C₁₃×#1367	C₂	semidirect
58. C₈×D₁₃	C₁₆	semidirect
66. #1367	D₁₃	direct (N × H)
82. C₈×C₁₃	C₂×C₁₆	semidirect
88. #1055	C₂×C₁₆	semidirect
135. D₁₃	#1367	direct (N × H)
160. C₁₃	C₂×#1367	semidirect
181. C₈	C₁₆×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
D₁₃×C₄⋊C₁₆	2
C₈²×D₁₃	2
#13112900	2
#13112899	2
C₁₃×#1367	2
C₂×#1367	13

Subgroups — D13×#1367 #15774459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#1367 #15774459