Subgroups — D₁₃⋊#2150 #16806992

Order 3328.

798 conjugacy classes of subgroups.

The subgroup lattice has 328 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	#13131170	C₂	1	2	yes	maximal, complemented
3	#13131169	C₂	1	4	yes	maximal, complemented
4	#13131168	C₂	1	2	yes	maximal, complemented
5	D₁₃⋊(C₄⋊C₁₆)	C₂	1	4	yes	maximal, complemented
6	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₈×D₁₃	C₄	1	1	yes	characteristic
8	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₄²×D₁₃	C₄	1	1	yes	characteristic
10	C₂×#88106	C₂²	1	4	yes	—
11	D₁₃⋊M₃₂	—	2	8	no	—
12	C₂×#88098	C₂²	1	4	yes	—
13	C₂×D₁₃⋊C₁₆	C₂²	1	4	yes	—
14	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
15	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
16	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
18	C₄×C₈×D₁₃	C₄	1	2	yes	—
19	C₄×C₈×D₁₃	C₄	1	2	yes	—
20	C₄×C₈×D₁₃	C₂²	1	2	yes	—
21	C₄×C₈×D₁₃	C₂²	1	2	yes	—
22	#11718260	C₂²	1	8	yes	complemented
23	C₄⋊#6092	C₂²	1	8	yes	complemented
24	C₂²×C₄×D₁₃	C₈	1	2	yes	—
25	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×Dic₁₃	C₈	1	2	yes	—
30	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
32	C₂²×#1055	C₂³	1	1	yes	characteristic
33	C₂×C₈×D₁₃	—	2	4	no	—
34	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
35	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
36	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₈×D₁₃	D₄	1	4	yes	—
39	C₂×C₈×D₁₃	Q₈	1	4	yes	—
40	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
41	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
42	C₄²×D₁₃	C₈	1	1	yes	characteristic
43	C₄²×D₁₃	C₈	1	1	yes	characteristic
44	C₄²×D₁₃	C₈	1	1	yes	characteristic
45	C₄²×D₁₃	C₈	1	1	yes	characteristic
46	C₄²×D₁₃	C₂×C₄	1	2	yes	—
47	C₄²×D₁₃	C₂×C₄	1	2	yes	—
48	#88106	—	2	8	no	—
49	C₂×#6092	C₂³	1	8	yes	—
50	#88098	—	2	8	no	—
51	D₁₃⋊C₁₆	—	2	8	no	—
52	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
53	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
54	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
55	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
56	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
57	C₈×Dic₁₃	C₂³	1	2	yes	—
58	C₄×#1055	C₂×C₄	1	2	yes	—
59	C₄×#1055	C₂³	1	2	yes	—
60	C₂×#2150	—	13	1	no	maximal, Sylow
61	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
62	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
63	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
64	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
65	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
66	C₂×C₄×D₁₃	—	2	8	no	—
67	C₂×C₄×D₁₃	C₄⋊C₄	1	4	yes	—
68	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
69	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
70	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
71	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
72	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
73	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
74	C₂×C₄×D₁₃	M₁₆	1	4	yes	—
75	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
76	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₈×C₁₃	—	2	2	no	—
78	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
79	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
80	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
83	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
84	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
85	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
86	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
87	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
88	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
89	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
90	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
91	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
92	C₂×#1055	—	2	2	no	—
93	C₂×#1055	C₂²×C₄	1	2	yes	—
94	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
95	C₂×#1055	C₂×D₄	1	2	yes	—
96	C₂×#1055	C₂×Q₈	1	2	yes	—
97	C₂×#1055	C₂⁴	1	1	yes	characteristic
98	C₈×D₁₃	—	2	4	no	—
99	C₈×D₁₃	—	2	4	no	—
100	C₈×D₁₃	C₄⋊C₄	1	4	yes	—
101	C₈×D₁₃	C₄⋊C₄	1	4	yes	—
102	C₈×D₁₃	C₂×D₄	1	2	yes	—
103	C₈×D₁₃	C₂×D₄	1	2	yes	—
104	C₈×D₁₃	C₂×Q₈	1	2	yes	—
105	C₈×D₁₃	C₂×Q₈	1	2	yes	—
106	#6092	—	2	8	no	—
107	C₂²×M₃₂	—	13	2	no	—
108	C₂²×C₄×C₈	—	13	1	no	—
109	#2150	—	13	2	no	—
110	#2150	—	13	4	no	—
111	#2150	—	13	2	no	—
112	C₂×C₄⋊C₁₆	—	13	4	no	—
113	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
114	C₂²×D₁₃	—	2	4	no	—
115	C₂²×D₁₃	C₄⋊C₈	1	4	yes	—
116	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
117	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
118	C₂×C₄×C₁₃	—	2	4	no	—
119	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
120	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
121	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
122	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
123	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
124	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
125	C₂×Dic₁₃	—	2	4	no	—
126	C₂×Dic₁₃	C₄⋊C₈	1	4	yes	—
127	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
128	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
129	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
130	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
131	C₄×D₁₃	—	2	4	no	—
132	C₄×D₁₃	—	2	4	no	—
133	C₄×D₁₃	—	2	4	no	—
134	C₄×D₁₃	C₄⋊C₈	1	4	yes	—
135	C₄×D₁₃	C₄⋊C₈	1	4	yes	—
136	C₄×D₁₃	M₃₂	1	8	yes	complemented
137	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
138	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
139	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
140	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
141	C₈×C₁₃	—	2	2	no	—
142	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
143	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
144	#1055	—	2	2	no	—
145	#1055	C₂×C₄⋊C₄	1	2	yes	—
146	#1055	C₂²×D₄	1	1	yes	characteristic
147	#1055	C₂²×Q₈	1	1	yes	characteristic
148	C₂³×C₈	—	13	1	no	—
149	C₂³×C₈	—	13	1	no	—
150	C₂²×C₄²	—	13	1	no	—
151	C₂×M₃₂	—	13	4	no	—
152	C₂×M₃₂	—	13	4	no	—
153	C₂×M₃₂	—	26	8	no	—
154	C₂²×C₁₆	—	13	4	no	—
155	C₂×C₄×C₈	—	13	1	no	—
156	C₂×C₄×C₈	—	13	1	no	—
157	C₂×C₄×C₈	—	13	1	no	—
158	C₂×C₄×C₈	—	13	2	no	—
159	C₂×C₄×C₈	—	13	2	no	—
160	C₂×C₄×C₈	—	13	2	no	—
161	C₂×C₄×C₈	—	13	2	no	—
162	C₂×C₄×C₈	#261	1	1	yes	characteristic
163	C₄⋊C₁₆	—	13	8	no	—
164	C₄⋊C₁₆	—	13	8	no	—
165	C₂²×C₁₃	—	2	2	no	—
166	C₂²×C₁₃	C₂×C₄⋊C₈	1	2	yes	—
167	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
168	C₂×D₁₃	—	2	2	no	—
169	C₂×D₁₃	—	2	8	no	—
170	C₂×D₁₃	C₂×C₄⋊C₈	1	2	yes	—
171	C₂×D₁₃	C₂×C₄⋊C₈	1	2	yes	—
172	C₂×D₁₃	C₂×M₃₂	1	4	yes	—
173	C₄×C₁₃	—	2	2	no	—
174	C₄×C₁₃	C₂×C₄⋊C₈	1	2	yes	—
175	C₄×C₁₃	C₂×M₃₂	1	4	yes	complemented
176	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
177	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
178	Dic₁₃	—	2	2	no	—
179	Dic₁₃	C₂×C₄⋊C₈	1	2	yes	—
180	Dic₁₃	C₂×C₄⋊C₈	1	2	yes	—
181	Dic₁₃	C₂×M₃₂	1	4	yes	complemented
182	C₂³×C₄	—	13	1	no	—
183	C₂³×C₄	—	13	2	no	—
184	C₂²×C₈	—	13	1	no	—
185	C₂²×C₈	—	13	4	no	—
186	C₂²×C₈	—	13	4	no	—
187	C₂²×C₈	—	13	1	no	—
188	C₂²×C₈	—	13	1	no	—
189	C₂²×C₈	—	13	1	no	—
190	C₂²×C₈	—	13	1	no	—
191	C₂²×C₈	—	13	1	no	—
192	C₂²×C₈	—	13	2	no	—
193	C₂²×C₈	—	13	2	no	—
194	C₂²×C₈	—	26	4	no	—
195	C₂²×C₈	C₂×#261	1	1	yes	characteristic
196	C₂²×C₈	C₂×#261	1	1	yes	characteristic
197	C₂×C₄²	—	13	2	no	—
198	C₂×C₄²	—	13	1	no	—
199	C₂×C₄²	—	13	1	no	—
200	C₂×C₄²	—	13	1	no	—
201	C₂×C₄²	—	13	1	no	—
202	C₂×C₄²	—	13	1	no	—
203	C₂×C₄²	—	13	2	no	—
204	C₂×C₄²	—	13	2	no	—
205	C₂×C₄²	C₂×#261	1	1	yes	characteristic
206	M₃₂	—	26	8	no	—
207	M₃₂	—	26	8	no	—
208	C₂×C₁₆	—	13	8	no	—
209	C₂×C₁₆	—	26	8	no	—
210	C₄×C₈	—	13	2	no	—
211	C₄×C₈	—	13	2	no	—
212	C₄×C₈	—	13	2	no	—
213	C₄×C₈	—	13	2	no	—
214	C₄×C₈	—	13	2	no	—
215	C₄×C₈	—	13	2	no	—
216	C₄×C₈	C₂×#261	1	2	yes	—
217	C₄×C₈	C₂×#261	1	2	yes	—
218	C₂×C₁₃	—	2	2	no	—
219	C₂×C₁₃	C₂²×C₄⋊C₈	1	1	yes	characteristic
220	C₂×C₁₃	C₂²×M₃₂	1	2	yes	—
221	D₁₃	—	2	2	no	—
222	D₁₃	#2150	1	4	yes	complemented
223	C₂⁴	—	13	1	no	—
224	C₂²×C₄	—	13	1	no	—
225	C₂²×C₄	—	13	1	no	—
226	C₂²×C₄	—	13	1	no	—
227	C₂²×C₄	—	13	2	no	—
228	C₂²×C₄	—	13	4	no	—
229	C₂²×C₄	—	13	4	no	—
230	C₂²×C₄	—	13	1	no	—
231	C₂²×C₄	—	13	1	no	—
232	C₂²×C₄	—	13	2	no	—
233	C₂²×C₄	—	13	2	no	—
234	C₂²×C₄	—	13	2	no	—
235	C₂²×C₄	—	13	2	no	—
236	C₂²×C₄	—	26	8	no	—
237	C₂²×C₄	D₁₃⋊C₈	1	2	yes	—
238	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
239	C₂×C₈	—	2	2	no	—
240	C₂×C₈	—	13	2	no	—
241	C₂×C₈	—	13	2	no	—
242	C₂×C₈	—	13	1	no	—
243	C₂×C₈	—	13	1	no	—
244	C₂×C₈	—	13	2	no	—
245	C₂×C₈	—	13	2	no	—
246	C₂×C₈	—	13	4	no	—
247	C₂×C₈	—	13	4	no	—
248	C₂×C₈	—	13	2	no	—
249	C₂×C₈	—	13	2	no	—
250	C₂×C₈	—	13	2	no	—
251	C₂×C₈	—	26	4	no	—
252	C₂×C₈	—	26	4	no	—
253	C₂×C₈	—	26	2	no	—
254	C₂×C₈	C₄⋊#261	1	4	yes	—
255	C₂×C₈	C₂²×#261	1	2	yes	—
256	C₂×C₈	C₂²×#261	1	1	yes	characteristic
257	C₂×C₈	C₂²×#261	1	1	yes	characteristic
258	C₄²	—	13	2	no	—
259	C₄²	—	13	1	no	—
260	C₄²	—	13	2	no	—
261	C₄²	—	13	2	no	—
262	C₄²	—	13	2	no	—
263	C₄²	—	13	1	no	—
264	C₄²	—	13	2	no	—
265	C₄²	D₁₃⋊C₈	1	1	yes	characteristic
266	C₄²	D₁₃⋊C₈	1	1	yes	characteristic
267	C₄²	C₂²×#261	1	2	yes	—
268	C₁₆	—	26	8	no	—
269	C₁₃	C₂×#2150	1	1	yes	characteristic, complemented, Sylow
270	C₂³	—	13	1	no	—
271	C₂³	—	13	4	no	—
272	C₂³	—	13	1	no	—
273	C₂³	—	26	4	no	—
274	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
275	C₂×C₄	—	2	4	no	—
276	C₂×C₄	—	13	4	no	—
277	C₂×C₄	—	13	2	no	—
278	C₂×C₄	—	13	1	no	—
279	C₂×C₄	—	13	1	no	—
280	C₂×C₄	—	13	4	no	—
281	C₂×C₄	—	13	4	no	—
282	C₂×C₄	—	13	8	no	—
283	C₂×C₄	—	13	2	no	—
284	C₂×C₄	—	13	2	no	—
285	C₂×C₄	—	13	2	no	—
286	C₂×C₄	—	13	2	no	—
287	C₂×C₄	—	13	2	no	—
288	C₂×C₄	—	26	4	no	—
289	C₂×C₄	—	26	4	no	—
290	C₂×C₄	—	26	4	no	—
291	C₂×C₄	—	26	4	no	—
292	C₂×C₄	C₂×D₁₃⋊C₈	1	2	yes	—
293	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
294	C₂×C₄	C₂×D₁₃⋊C₈	1	2	yes	—
295	C₂×C₄	D₁₃⋊M₁₆	1	2	yes	—
296	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
297	C₂×C₄	C₂³×#261	1	1	yes	characteristic
298	C₈	—	2	2	no	—
299	C₈	—	13	1	no	—
300	C₈	—	13	2	no	—
301	C₈	—	13	1	no	—
302	C₈	—	26	2	no	—
303	C₈	C₂×C₄⋊#261	1	2	yes	—
304	C₈	C₂×C₄⋊#261	1	2	yes	—
305	C₂²	—	2	2	no	—
306	C₂²	—	13	4	no	—
307	C₂²	—	13	2	no	—
308	C₂²	—	13	2	no	—
309	C₂²	—	26	8	no	—
310	C₂²	—	26	2	no	—
311	C₂²	D₁₃⋊(C₄⋊C₈)	1	2	yes	—
312	C₂²	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
313	C₄	—	2	2	no	—
314	C₄	—	13	4	no	—
315	C₄	—	13	2	no	—
316	C₄	—	13	2	no	—
317	C₄	—	26	2	no	—
318	C₄	D₁₃⋊(C₄⋊C₈)	1	2	yes	—
319	C₄	D₁₃⋊M₃₂	1	4	yes	complemented
320	C₄	C₂×D₁₃⋊M₁₆	1	1	yes	characteristic
321	C₄	C₂²×C₄⋊#261	1	1	yes	characteristic
322	C₂	—	2	2	no	—
323	C₂	—	13	4	no	—
324	C₂	—	26	2	no	—
325	C₂	C₂×D₁₃⋊(C₄⋊C₈)	1	1	yes	characteristic
326	C₂	C₂×D₁₃⋊M₃₂	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂³×C₈
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
prime radical	C₂³×D₁₃	C₂×C₈
cosocle	C₂×#1055	C₂⁴
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	C₂×#2150
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #13131170	C₂	semidirect
3. #13131169	C₂	semidirect
4. #13131168	C₂	semidirect
5. D₁₃⋊(C₄⋊C₁₆)	C₂	semidirect
22. #11718260	C₂²	semidirect
23. C₄⋊#6092	C₂²	semidirect
136. C₄×D₁₃	M₃₂	semidirect
175. C₄×C₁₃	C₂×M₃₂	semidirect
181. Dic₁₃	C₂×M₃₂	semidirect
222. D₁₃	#2150	semidirect
269. C₁₃	C₂×#2150	semidirect
319. 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
#13131170	2
#13131169	2
#13131168	2
D₁₃⋊(C₄⋊C₁₆)	2
C₂×C₄×C₈×D₁₃	2
C₂×#2150	13

Subgroups — D13⋊#2150 #16806992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃⋊#2150 #16806992