Subgroups — D₁₃×#2150 #16015895

Order 3328.

798 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃×M₃₂	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
3	#13116592	C₂	1	1	yes	maximal, characteristic, complemented
4	#13116591	C₂	1	2	yes	maximal, complemented
5	#13116590	C₂	1	4	yes	maximal, complemented
6	D₁₃×C₄⋊C₁₆	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2150	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₁₃	C₄	1	1	yes	characteristic
9	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄²×D₁₃	C₄	1	1	yes	characteristic
11	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
12	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
14	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
15	C₂×#88052	C₂²	1	2	yes	—
16	C₂×C₄×#1055	C₄	1	1	yes	characteristic
17	D₁₃×M₃₂	—	2	8	no	—
18	C₂×#88038	C₂²	1	4	yes	—
19	C₂×C₁₆×D₁₃	C₂²	1	4	yes	—
20	C₄×C₈×D₁₃	C₄	1	2	yes	—
21	C₄×C₈×D₁₃	C₄	1	2	yes	—
22	C₄×C₈×D₁₃	C₂²	1	2	yes	—
23	C₄×C₈×D₁₃	C₂²	1	2	yes	—
24	C₁₃×C₄⋊C₁₆	C₂²	1	4	yes	complemented
25	#11718093	C₂²	1	8	yes	complemented
26	C₄⋊#6090	C₂²	1	4	yes	complemented
27	C₂²×C₄×D₁₃	C₈	1	2	yes	—
28	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
31	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄×Dic₁₃	C₈	1	2	yes	—
33	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
35	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
36	C₂×C₈×D₁₃	—	2	4	no	—
37	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
38	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
39	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₈×D₁₃	D₄	1	4	yes	—
42	C₂×C₈×D₁₃	Q₈	1	4	yes	—
43	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
44	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
45	C₄²×D₁₃	C₈	1	1	yes	characteristic
46	C₄²×D₁₃	C₈	1	1	yes	characteristic
47	C₄²×D₁₃	C₈	1	1	yes	characteristic
48	C₄²×D₁₃	C₈	1	1	yes	characteristic
49	C₄²×D₁₃	C₂×C₄	1	2	yes	—
50	C₄²×D₁₃	C₂×C₄	1	2	yes	—
51	C₁₃×M₃₂	—	2	4	no	—
52	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
53	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
54	C₄×C₈×C₁₃	C₂³	1	2	yes	—
55	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
56	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
57	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
58	C₈×Dic₁₃	C₂³	1	2	yes	—
59	#88052	—	2	4	no	—
60	C₂×#6090	C₂³	1	4	yes	—
61	C₄×#1055	C₂×C₄	1	2	yes	—
62	C₄×#1055	C₂×C₄	1	2	yes	—
63	#88038	—	2	8	no	—
64	C₁₆×D₁₃	—	2	8	no	—
65	C₂×#2150	—	13	1	no	maximal, Sylow
66	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
67	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
68	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
69	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
70	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
71	C₂×C₄×D₁₃	—	2	8	no	—
72	C₂×C₄×D₁₃	C₄⋊C₄	1	4	yes	—
73	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
74	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
75	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
76	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
77	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
78	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
79	C₂×C₄×D₁₃	M₁₆	1	4	yes	—
80	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₂×C₈×C₁₃	—	2	2	no	—
83	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
84	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
86	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
87	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
88	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
89	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
90	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
91	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
92	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
93	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
94	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
95	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
96	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
97	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
98	C₂×#1055	—	2	2	no	—
99	C₂×#1055	C₄⋊C₄	1	4	yes	—
100	C₂×#1055	C₂²×C₄	1	2	yes	—
101	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
102	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
103	C₈×D₁₃	—	2	4	no	—
104	C₈×D₁₃	—	2	4	no	—
105	C₈×D₁₃	C₄⋊C₄	1	4	yes	—
106	C₈×D₁₃	C₄⋊C₄	1	4	yes	—
107	C₈×D₁₃	C₂×D₄	1	2	yes	—
108	C₈×D₁₃	C₂×D₄	1	2	yes	—
109	C₈×D₁₃	C₂×Q₈	1	2	yes	—
110	C₈×D₁₃	C₂×Q₈	1	2	yes	—
111	C₁₃×C₁₆	—	2	4	no	—
112	#6090	—	2	4	no	—
113	C₂²×M₃₂	—	13	2	no	—
114	C₂²×C₄×C₈	—	13	1	no	—
115	#2150	—	13	2	no	—
116	#2150	—	13	1	no	—
117	#2150	—	13	4	no	—
118	#2150	D₁₃	1	1	yes	characteristic, direct product factor
119	C₂×C₄⋊C₁₆	—	13	4	no	—
120	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
121	C₂²×D₁₃	—	2	4	no	—
122	C₂²×D₁₃	C₄⋊C₈	1	4	yes	—
123	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
124	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
125	C₂×C₄×C₁₃	—	2	4	no	—
126	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
127	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
128	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
129	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
130	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
131	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
132	C₂×Dic₁₃	—	2	4	no	—
133	C₂×Dic₁₃	C₄⋊C₈	1	4	yes	—
134	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
135	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
136	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
137	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
138	C₄×D₁₃	—	2	4	no	—
139	C₄×D₁₃	—	2	4	no	—
140	C₄×D₁₃	—	2	4	no	—
141	C₄×D₁₃	C₄⋊C₈	1	4	yes	—
142	C₄×D₁₃	C₄⋊C₈	1	4	yes	—
143	C₄×D₁₃	M₃₂	1	8	yes	complemented
144	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
145	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
146	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
147	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
148	C₈×C₁₃	—	2	2	no	—
149	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
150	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
151	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
152	#1055	—	2	2	no	—
153	#1055	C₂×C₄⋊C₄	1	2	yes	—
154	#1055	C₂×C₄⋊C₄	1	2	yes	—
155	C₂³×C₈	—	13	1	no	—
156	C₂³×C₈	—	13	1	no	—
157	C₂²×C₄²	—	13	1	no	—
158	C₂×M₃₂	—	13	2	no	—
159	C₂×M₃₂	—	13	4	no	—
160	C₂×M₃₂	—	26	8	no	—
161	C₂×M₃₂	C₂×D₁₃	1	2	yes	—
162	C₂²×C₁₆	—	13	4	no	—
163	C₂×C₄×C₈	—	13	1	no	—
164	C₂×C₄×C₈	—	13	1	no	—
165	C₂×C₄×C₈	—	13	1	no	—
166	C₂×C₄×C₈	—	13	2	no	—
167	C₂×C₄×C₈	—	13	2	no	—
168	C₂×C₄×C₈	—	13	2	no	—
169	C₂×C₄×C₈	—	13	2	no	—
170	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
171	C₄⋊C₁₆	—	13	8	no	—
172	C₄⋊C₁₆	—	13	4	no	—
173	C₄⋊C₁₆	C₂×D₁₃	1	4	yes	complemented
174	C₂²×C₁₃	—	2	2	no	—
175	C₂²×C₁₃	C₂×C₄⋊C₈	1	2	yes	—
176	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
177	C₂×D₁₃	—	2	2	no	—
178	C₂×D₁₃	—	2	8	no	—
179	C₂×D₁₃	C₂×C₄⋊C₈	1	2	yes	—
180	C₂×D₁₃	C₂×C₄⋊C₈	1	2	yes	—
181	C₂×D₁₃	C₂×M₃₂	1	4	yes	—
182	C₄×C₁₃	—	2	2	no	—
183	C₄×C₁₃	C₂×C₄⋊C₈	1	2	yes	—
184	C₄×C₁₃	C₂×M₃₂	1	4	yes	complemented
185	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
186	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
187	Dic₁₃	—	2	2	no	—
188	Dic₁₃	C₂×C₄⋊C₈	1	2	yes	—
189	Dic₁₃	C₂×C₄⋊C₈	1	2	yes	—
190	Dic₁₃	C₂×M₃₂	1	4	yes	complemented
191	C₂³×C₄	—	13	1	no	—
192	C₂³×C₄	—	13	2	no	—
193	C₂²×C₈	—	13	1	no	—
194	C₂²×C₈	—	13	1	no	—
195	C₂²×C₈	—	13	1	no	—
196	C₂²×C₈	—	13	4	no	—
197	C₂²×C₈	—	13	4	no	—
198	C₂²×C₈	—	13	1	no	—
199	C₂²×C₈	—	13	1	no	—
200	C₂²×C₈	—	13	1	no	—
201	C₂²×C₈	—	13	2	no	—
202	C₂²×C₈	—	13	2	no	—
203	C₂²×C₈	—	26	4	no	—
204	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
205	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
206	C₂×C₄²	—	13	2	no	—
207	C₂×C₄²	—	13	1	no	—
208	C₂×C₄²	—	13	1	no	—
209	C₂×C₄²	—	13	1	no	—
210	C₂×C₄²	—	13	1	no	—
211	C₂×C₄²	—	13	1	no	—
212	C₂×C₄²	—	13	2	no	—
213	C₂×C₄²	—	13	2	no	—
214	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
215	M₃₂	—	2	4	no	—
216	M₃₂	—	26	8	no	—
217	M₃₂	—	26	4	no	—
218	C₂×C₁₆	—	13	4	no	—
219	C₂×C₁₆	—	26	8	no	—
220	C₂×C₁₆	C₂²×D₁₃	1	4	yes	—
221	C₄×C₈	—	13	2	no	—
222	C₄×C₈	—	13	2	no	—
223	C₄×C₈	—	13	2	no	—
224	C₄×C₈	—	13	2	no	—
225	C₄×C₈	—	13	2	no	—
226	C₄×C₈	—	13	2	no	—
227	C₄×C₈	C₄×D₁₃	1	2	yes	—
228	C₄×C₈	C₂²×D₁₃	1	2	yes	—
229	C₂×C₁₃	—	2	2	no	—
230	C₂×C₁₃	C₂²×C₄⋊C₈	1	1	yes	characteristic
231	C₂×C₁₃	C₂²×M₃₂	1	2	yes	—
232	D₁₃	—	2	2	no	—
233	D₁₃	#2150	1	4	yes	direct product factor
234	C₂⁴	—	13	1	no	—
235	C₂²×C₄	—	13	1	no	—
236	C₂²×C₄	—	13	4	no	—
237	C₂²×C₄	—	13	1	no	—
238	C₂²×C₄	—	13	1	no	—
239	C₂²×C₄	—	13	2	no	—
240	C₂²×C₄	—	13	4	no	—
241	C₂²×C₄	—	13	1	no	—
242	C₂²×C₄	—	13	1	no	—
243	C₂²×C₄	—	13	2	no	—
244	C₂²×C₄	—	13	2	no	—
245	C₂²×C₄	—	13	2	no	—
246	C₂²×C₄	—	13	2	no	—
247	C₂²×C₄	—	26	8	no	—
248	C₂²×C₄	C₈×D₁₃	1	2	yes	—
249	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
250	C₂×C₈	—	2	2	no	—
251	C₂×C₈	—	13	4	no	—
252	C₂×C₈	—	13	1	no	—
253	C₂×C₈	—	13	1	no	—
254	C₂×C₈	—	13	4	no	—
255	C₂×C₈	—	13	4	no	—
256	C₂×C₈	—	13	2	no	—
257	C₂×C₈	—	13	2	no	—
258	C₂×C₈	—	13	2	no	—
259	C₂×C₈	—	13	2	no	—
260	C₂×C₈	—	13	2	no	—
261	C₂×C₈	—	26	4	no	—
262	C₂×C₈	—	26	4	no	—
263	C₂×C₈	—	26	2	no	—
264	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
265	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
266	C₂×C₈	D₄×D₁₃	1	2	yes	—
267	C₂×C₈	Q₈×D₁₃	1	2	yes	—
268	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
269	C₄²	—	13	2	no	—
270	C₄²	—	13	1	no	—
271	C₄²	—	13	2	no	—
272	C₄²	—	13	2	no	—
273	C₄²	—	13	2	no	—
274	C₄²	—	13	1	no	—
275	C₄²	—	13	2	no	—
276	C₄²	C₈×D₁₃	1	1	yes	characteristic
277	C₄²	C₈×D₁₃	1	1	yes	characteristic
278	C₄²	C₂×C₄×D₁₃	1	2	yes	—
279	C₁₆	—	2	4	no	—
280	C₁₆	—	26	4	no	—
281	C₁₃	C₂×#2150	1	1	yes	characteristic, complemented, Sylow
282	C₂³	—	13	1	no	—
283	C₂³	—	13	1	no	—
284	C₂³	—	13	4	no	—
285	C₂³	—	26	4	no	—
286	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	13	1	no	—
289	C₂×C₄	—	13	1	no	—
290	C₂×C₄	—	13	2	no	—
291	C₂×C₄	—	13	4	no	—
292	C₂×C₄	—	13	2	no	—
293	C₂×C₄	—	13	2	no	—
294	C₂×C₄	—	13	2	no	—
295	C₂×C₄	—	13	2	no	—
296	C₂×C₄	—	13	4	no	—
297	C₂×C₄	—	13	4	no	—
298	C₂×C₄	—	13	8	no	—
299	C₂×C₄	—	13	2	no	—
300	C₂×C₄	—	26	4	no	—
301	C₂×C₄	—	26	4	no	—
302	C₂×C₄	—	26	4	no	—
303	C₂×C₄	—	26	4	no	—
304	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
305	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
306	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
307	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
308	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
309	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
310	C₈	—	2	2	no	—
311	C₈	—	13	2	no	—
312	C₈	—	13	2	no	—
313	C₈	—	26	2	no	—
314	C₈	C₄⋊C₄×D₁₃	1	2	yes	—
315	C₈	C₂×D₄×D₁₃	1	1	yes	characteristic
316	C₈	C₂×Q₈×D₁₃	1	1	yes	characteristic
317	C₂²	—	2	2	no	—
318	C₂²	—	13	2	no	—
319	C₂²	—	13	4	no	—
320	C₂²	—	13	2	no	—
321	C₂²	—	26	8	no	—
322	C₂²	—	26	2	no	—
323	C₂²	D₁₃×C₄⋊C₈	1	2	yes	—
324	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
325	C₄	—	2	2	no	—
326	C₄	—	13	2	no	—
327	C₄	—	13	2	no	—
328	C₄	—	13	4	no	—
329	C₄	—	26	2	no	—
330	C₄	D₁₃×C₄⋊C₈	1	2	yes	—
331	C₄	D₁₃×M₃₂	1	4	yes	complemented
332	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
333	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
334	C₂	—	2	2	no	—
335	C₂	—	13	4	no	—
336	C₂	—	26	2	no	—
337	C₂	C₂×D₁₃×C₄⋊C₈	1	1	yes	characteristic
338	C₂	C₂×D₁₃×M₃₂	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂³×C₈
Fitting	C₁₃×#2150	C₂
prime radical	C₂³×D₁₃	C₂×C₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	#2150	D₁₃
hypocenter	C₁₃	C₂×#2150
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ #2150

Complements

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

N	H ≅ G/N	type
3. #13116592	C₂	semidirect
4. #13116591	C₂	semidirect
5. #13116590	C₂	semidirect
6. D₁₃×C₄⋊C₁₆	C₂	semidirect
7. C₁₃×#2150	C₂	semidirect
24. C₁₃×C₄⋊C₁₆	C₂²	semidirect
25. #11718093	C₂²	semidirect
26. C₄⋊#6090	C₂²	semidirect
118. #2150	D₁₃	direct (N × H)
143. C₄×D₁₃	M₃₂	semidirect
173. C₄⋊C₁₆	C₂×D₁₃	semidirect
184. C₄×C₁₃	C₂×M₃₂	semidirect
190. Dic₁₃	C₂×M₃₂	semidirect
233. D₁₃	#2150	direct (N × H)
281. C₁₃	C₂×#2150	semidirect
331. C₄	D₁₃×M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₃×M₃₂	2
C₂×C₄×C₈×D₁₃	2
#13116592	2
#13116591	2
#13116590	2
D₁₃×C₄⋊C₁₆	2
C₁₃×#2150	2
C₂×#2150	13

Subgroups — D13×#2150 #16015895

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#2150 #16015895