Subgroups — D₁₃×#2161 #16015972

Order 3328.

642 conjugacy classes of subgroups.

The subgroup lattice has 308 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	1	yes	maximal, characteristic
2	C₂×D₁₃×#108	C₂	1	2	yes	maximal
3	#13116631	C₂	1	1	yes	maximal, characteristic, complemented
4	#13116630	C₂	1	2	yes	maximal, complemented
5	#13116629	C₂	1	4	yes	maximal, complemented
6	D₁₃×#368	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2161	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₁₃	—	2	2	no	—
9	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#108	C₂²	1	2	yes	—
12	C₂×#88062	—	2	2	no	—
13	C₂×#88059	C₂²	1	2	yes	—
14	C₂×#88052	C₂²	1	1	yes	characteristic
15	D₁₃×M₃₂	C₄	1	4	yes	—
16	D₁₃×M₃₂	C₄	1	4	yes	—
17	C₂×#88038	C₂²	1	2	yes	—
18	C₂×C₁₆×D₁₃	C₂²	1	2	yes	—
19	D₁₃×#108	—	2	2	no	—
20	D₁₃×#108	—	2	2	no	—
21	D₁₃×#108	C₂²	1	4	yes	—
22	D₁₃×#108	C₂²	1	4	yes	—
23	C₁₃×#368	C₂²	1	4	yes	complemented
24	#11718098	C₂²	1	4	yes	complemented
25	#11718085	C₂²	1	8	yes	complemented
26	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
27	C₂×C₁₃×M₁₆	—	2	2	no	—
28	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
29	C₂×#6099	—	2	2	no	—
30	C₂²×#1055	D₄	1	1	yes	characteristic
31	M₁₆×D₁₃	—	2	4	no	—
32	M₁₆×D₁₃	—	2	4	no	—
33	M₁₆×D₁₃	—	4	2	no	—
34	M₁₆×D₁₃	—	4	2	no	—
35	C₂×#6094	—	4	2	no	—
36	C₂×C₈×D₁₃	—	4	2	no	—
37	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
38	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
39	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
40	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
41	C₂×C₈×D₁₃	Q₈	1	2	yes	—
42	C₂×C₈×D₁₃	Q₈	1	2	yes	—
43	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
44	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
45	C₁₃×M₃₂	C₂×C₄	1	4	yes	—
46	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
47	C₁₃×#108	—	2	2	no	—
48	C₁₃×#108	C₂³	1	4	yes	—
49	#88062	—	2	4	no	—
50	#88062	—	2	4	no	—
51	#88059	—	2	2	no	—
52	#88059	C₂³	1	4	yes	—
53	#88052	C₂×C₄	1	4	yes	—
54	C₂×#6090	C₂³	1	2	yes	—
55	#88038	C₂×C₄	1	8	yes	—
56	C₁₆×D₁₃	C₂×C₄	1	4	yes	—
57	C₁₆×D₁₃	C₂×C₄	1	4	yes	—
58	C₂×#2161	—	13	1	no	maximal, Sylow
59	C₂³×D₁₃	Q₁₆	1	1	yes	characteristic
60	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
61	C₂²×Dic₁₃	Q₁₆	1	1	yes	characteristic
62	C₂×C₄×D₁₃	C₄⋊C₄	1	2	yes	—
63	C₂×C₄×D₁₃	C₄⋊C₄	1	2	yes	—
64	C₂×C₄×D₁₃	D₈	1	2	yes	—
65	C₂×C₄×D₁₃	D₈	1	2	yes	—
66	C₂×C₄×D₁₃	Q₁₆	1	1	yes	characteristic
67	C₂×C₄×D₁₃	Q₁₆	1	1	yes	characteristic
68	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
69	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
70	C₁₃×M₁₆	—	2	4	no	—
71	C₁₃×M₁₆	—	4	2	no	—
72	C₂×C₈×C₁₃	—	4	2	no	—
73	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
74	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
75	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
76	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
77	#6099	—	2	4	no	—
78	#6099	—	4	2	no	—
79	C₂×#1055	—	4	2	no	—
80	C₂×#1055	C₄⋊C₄	1	2	yes	—
81	C₂×#1055	C₄⋊C₄	1	2	yes	—
82	C₂×#1055	C₂×D₄	1	1	yes	characteristic
83	C₂×#1055	C₂×D₄	1	1	yes	characteristic
84	#6094	—	4	4	no	—
85	#6094	—	4	4	no	—
86	C₈×D₁₃	—	4	4	no	—
87	C₈×D₁₃	—	4	4	no	—
88	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
89	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
90	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
91	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
92	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₈×D₁₃	C₂²×C₄	1	2	yes	—
95	C₈×D₁₃	C₂×Q₈	1	1	yes	characteristic
96	C₈×D₁₃	C₂×Q₈	1	1	yes	characteristic
97	C₈×D₁₃	C₂×Q₈	1	2	yes	—
98	C₁₃×C₁₆	C₂²×C₄	1	4	yes	—
99	#6090	C₂²×C₄	1	4	yes	—
100	C₂²×M₃₂	—	13	1	no	—
101	C₂²×#108	—	13	2	no	—
102	#2161	—	13	1	no	—
103	#2161	—	13	2	no	—
104	#2161	—	13	4	no	—
105	#2161	D₁₃	1	1	yes	characteristic, direct product factor
106	C₂×#368	—	13	4	no	—
107	C₂³×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
108	C₂²×D₁₃	—	4	2	no	—
109	C₂²×D₁₃	#107	1	2	yes	—
110	C₂²×D₁₃	#107	1	2	yes	—
111	C₂²×D₁₃	C₂×Q₁₆	1	1	yes	characteristic
112	C₂²×D₁₃	C₂×Q₁₆	1	1	yes	characteristic
113	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
114	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
115	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
116	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
117	C₂×Dic₁₃	#107	1	2	yes	—
118	C₂×Dic₁₃	#107	1	2	yes	—
119	C₂×Dic₁₃	C₂×Q₁₆	1	1	yes	characteristic
120	C₂×Dic₁₃	C₂×Q₁₆	1	1	yes	characteristic
121	C₄×D₁₃	#107	1	2	yes	—
122	C₄×D₁₃	#107	1	2	yes	—
123	C₄×D₁₃	#107	1	2	yes	—
124	C₄×D₁₃	#107	1	2	yes	—
125	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
127	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₄×D₁₃	C₂×D₈	1	1	yes	characteristic
129	C₄×D₁₃	C₂×D₈	1	2	yes	—
130	C₄×D₁₃	C₂×D₈	1	1	yes	characteristic
131	C₈×C₁₃	—	4	4	no	—
132	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
133	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
134	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
135	#1055	—	4	4	no	—
136	#1055	C₂×C₄⋊C₄	1	1	yes	characteristic
137	#1055	C₂×C₄⋊C₄	1	1	yes	characteristic
138	#1055	C₂×C₄⋊C₄	1	2	yes	—
139	C₂²×M₁₆	—	26	2	no	—
140	C₂³×C₈	—	13	1	no	—
141	C₂×M₃₂	—	13	1	no	—
142	C₂×M₃₂	—	13	4	no	—
143	C₂×M₃₂	—	13	4	no	—
144	C₂×M₃₂	—	13	2	no	—
145	C₂×M₃₂	C₂×D₁₃	1	1	yes	characteristic
146	C₂²×C₁₆	—	13	2	no	—
147	C₂×#108	—	13	2	no	—
148	C₂×#108	—	13	4	no	—
149	C₂×#108	—	13	4	no	—
150	C₂×#108	—	26	2	no	—
151	C₂×#108	—	26	2	no	—
152	C₂×#108	—	26	2	no	—
153	C₂×#108	C₂×D₁₃	1	2	yes	—
154	#368	—	13	4	no	—
155	#368	—	13	8	no	—
156	#368	C₂×D₁₃	1	4	yes	complemented
157	C₂²×C₁₃	—	4	1	no	—
158	C₂²×C₁₃	C₂×#107	1	2	yes	—
159	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
160	C₂×D₁₃	—	2	4	no	—
161	C₂×D₁₃	—	2	2	no	—
162	C₂×D₁₃	—	4	2	no	—
163	C₂×D₁₃	—	4	1	no	—
164	C₂×D₁₃	C₂×#107	1	2	yes	—
165	C₂×D₁₃	C₂×#107	1	1	yes	characteristic
166	C₂×D₁₃	C₂×#107	1	1	yes	characteristic
167	C₄×C₁₃	C₂×#107	1	2	yes	—
168	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
169	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
170	Dic₁₃	C₂×#107	1	1	yes	characteristic
171	Dic₁₃	C₂×#107	1	2	yes	—
172	Dic₁₃	C₂×#107	1	1	yes	characteristic
173	C₂³×C₄	—	13	1	no	—
174	C₂×M₁₆	—	2	2	no	—
175	C₂×M₁₆	—	26	4	no	—
176	C₂×M₁₆	—	26	4	no	—
177	C₂×M₁₆	—	26	2	no	—
178	C₂×M₁₆	—	52	2	no	—
179	C₂×M₁₆	—	52	2	no	—
180	C₂×M₁₆	—	52	2	no	—
181	C₂²×C₈	—	13	1	no	—
182	C₂²×C₈	—	13	2	no	—
183	C₂²×C₈	—	13	2	no	—
184	C₂²×C₈	—	13	1	no	—
185	C₂²×C₈	—	13	1	no	—
186	C₂²×C₈	—	13	2	no	—
187	C₂²×C₈	—	13	2	no	—
188	C₂²×C₈	—	13	1	no	—
189	C₂²×C₈	—	13	1	no	—
190	C₂²×C₈	—	52	2	no	—
191	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
192	M₃₂	—	13	4	no	—
193	M₃₂	—	13	8	no	—
194	M₃₂	C₄×D₁₃	1	4	yes	—
195	C₂×C₁₆	—	13	2	no	—
196	C₂×C₁₆	—	13	4	no	—
197	C₂×C₁₆	—	13	4	no	—
198	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
199	#108	—	2	2	no	—
200	#108	—	13	4	no	—
201	#108	—	26	4	no	—
202	#108	—	26	4	no	—
203	#108	—	26	2	no	—
204	#108	C₂²×D₁₃	1	4	yes	—
205	C₂×C₁₃	—	2	1	no	—
206	C₂×C₁₃	—	2	2	no	—
207	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
208	D₁₃	—	2	2	no	—
209	D₁₃	—	2	1	no	—
210	D₁₃	#2161	1	2	yes	direct product factor
211	C₂⁴	—	13	1	no	—
212	C₂²×C₄	—	13	1	no	—
213	C₂²×C₄	—	13	2	no	—
214	C₂²×C₄	—	13	2	no	—
215	C₂²×C₄	—	13	2	no	—
216	C₂²×C₄	—	13	2	no	—
217	C₂²×C₄	—	13	1	no	—
218	C₂²×C₄	—	13	1	no	—
219	C₂²×C₄	—	13	1	no	—
220	C₂²×C₄	—	13	1	no	—
221	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
222	M₁₆	—	2	4	no	—
223	M₁₆	—	4	2	no	—
224	M₁₆	—	26	4	no	—
225	M₁₆	—	52	4	no	—
226	M₁₆	—	52	4	no	—
227	M₁₆	—	52	2	no	—
228	C₂×C₈	—	4	2	no	—
229	C₂×C₈	—	13	2	no	—
230	C₂×C₈	—	13	2	no	—
231	C₂×C₈	—	13	1	no	—
232	C₂×C₈	—	13	1	no	—
233	C₂×C₈	—	13	2	no	—
234	C₂×C₈	—	13	2	no	—
235	C₂×C₈	—	13	2	no	—
236	C₂×C₈	—	13	2	no	—
237	C₂×C₈	—	13	1	no	—
238	C₂×C₈	—	13	1	no	—
239	C₂×C₈	—	13	2	no	—
240	C₂×C₈	—	13	1	no	—
241	C₂×C₈	—	13	1	no	—
242	C₂×C₈	—	13	2	no	—
243	C₂×C₈	—	52	4	no	—
244	C₂×C₈	—	52	4	no	—
245	C₂×C₈	—	52	2	no	—
246	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
247	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
248	C₂×C₈	Q₈×D₁₃	1	2	yes	—
249	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
250	C₁₆	—	13	4	no	—
251	C₁₆	C₂×C₄×D₁₃	1	4	yes	—
252	C₁₃	C₂×#2161	1	1	yes	characteristic, complemented, Sylow
253	C₂³	—	13	1	no	—
254	C₂³	—	13	2	no	—
255	C₂³	—	13	1	no	—
256	C₂³	—	13	2	no	—
257	C₂³	—	52	2	no	—
258	C₂³	Q₁₆×D₁₃	1	1	yes	characteristic
259	C₂×C₄	—	13	1	no	—
260	C₂×C₄	—	13	1	no	—
261	C₂×C₄	—	13	2	no	—
262	C₂×C₄	—	13	2	no	—
263	C₂×C₄	—	13	1	no	—
264	C₂×C₄	—	13	2	no	—
265	C₂×C₄	—	13	1	no	—
266	C₂×C₄	—	13	1	no	—
267	C₂×C₄	—	13	1	no	—
268	C₂×C₄	—	13	2	no	—
269	C₂×C₄	—	13	2	no	—
270	C₂×C₄	—	13	2	no	—
271	C₂×C₄	—	13	2	no	—
272	C₂×C₄	—	13	2	no	—
273	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
274	C₂×C₄	D₈×D₁₃	1	2	yes	—
275	C₂×C₄	Q₁₆×D₁₃	1	1	yes	characteristic
276	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
277	C₈	—	4	4	no	—
278	C₈	—	13	1	no	—
279	C₈	—	13	1	no	—
280	C₈	—	13	2	no	—
281	C₈	—	52	4	no	—
282	C₈	C₄⋊C₄×D₁₃	1	2	yes	—
283	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
284	C₈	C₂×Q₈×D₁₃	1	1	yes	characteristic
285	C₂²	—	4	1	no	—
286	C₂²	—	13	1	no	—
287	C₂²	—	13	2	no	—
288	C₂²	—	13	1	no	—
289	C₂²	—	26	2	no	—
290	C₂²	—	26	4	no	—
291	C₂²	—	52	1	no	—
292	C₂²	—	52	2	no	—
293	C₂²	D₁₃×#107	1	2	yes	—
294	C₂²	C₂×Q₁₆×D₁₃	1	1	yes	characteristic
295	C₄	—	13	1	no	—
296	C₄	—	13	2	no	—
297	C₄	—	13	1	no	—
298	C₄	D₁₃×#107	1	2	yes	—
299	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
300	C₄	C₂×D₈×D₁₃	1	1	yes	characteristic
301	C₂	—	2	1	no	—
302	C₂	—	2	2	no	—
303	C₂	—	13	2	no	—
304	C₂	—	26	2	no	—
305	C₂	—	26	1	no	—
306	C₂	C₂×D₁₃×#107	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₈×D₁₃
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₁₃×#2161	C₂
socle	C₂×C₁₃	C₂²×#107
prime radical	C₂³×D₁₃	Q₁₆
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	#2161	D₁₃
hypocenter	C₁₃	C₂×#2161
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2161

Complements

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

N	H ≅ G/N	type
3. #13116631	C₂	semidirect
4. #13116630	C₂	semidirect
5. #13116629	C₂	semidirect
6. D₁₃×#368	C₂	semidirect
7. C₁₃×#2161	C₂	semidirect
23. C₁₃×#368	C₂²	semidirect
24. #11718098	C₂²	semidirect
25. #11718085	C₂²	semidirect
105. #2161	D₁₃	direct (N × H)
156. #368	C₂×D₁₃	semidirect
210. D₁₃	#2161	direct (N × H)
252. C₁₃	C₂×#2161	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×D₁₃×#108	2
#13116631	2
#13116630	2
#13116629	2
D₁₃×#368	2
C₁₃×#2161	2
C₂×#2161	13

Subgroups — D13×#2161 #16015972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#2161 #16015972