Subgroups — D₁₃×#2168 #16016071

Order 3328.

754 conjugacy classes of subgroups.

The subgroup lattice has 582 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, complemented
2	C₂²×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic
4	#13116664	C₂	1	1	yes	maximal, characteristic, complemented
5	#13116663	C₂	1	1	yes	maximal, characteristic, complemented
6	#13116662	C₂	1	1	yes	maximal, characteristic, complemented
7	#13116661	C₂	1	1	yes	maximal, characteristic, complemented
8	#13116660	C₂	1	1	yes	maximal, characteristic, complemented
9	#13116659	C₂	1	1	yes	maximal, characteristic, complemented
10	#13116658	C₂	1	1	yes	maximal, characteristic, complemented
11	D₁₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	D₁₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	D₁₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
14	D₁₃×#346	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2168	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
18	C₄×D₄×D₁₃	C₄	1	1	yes	characteristic
19	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₈×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
23	C₈×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
24	C₂×#88052	C₂²	1	1	yes	characteristic, complemented
25	C₂²×#6090	C₂²	1	1	yes	characteristic, complemented
26	D₄×#1055	C₄	1	1	yes	characteristic
27	D₁₃×M₃₂	—	2	4	no	—
28	C₂×#88038	C₂²	1	1	yes	characteristic, complemented
29	C₂×#88038	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₆×D₁₃	—	2	4	no	—
31	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic, complemented
37	#11718495	C₄	1	1	yes	characteristic
38	D₁₃×C₄⋊C₈	C₄	1	1	yes	characteristic
39	#11718386	C₄	1	1	yes	characteristic
40	#11718386	C₄	1	1	yes	characteristic
41	D₁₃×C₂²⋊C₈	C₄	1	1	yes	characteristic
42	D₁₃×C₂²⋊C₈	C₄	1	1	yes	characteristic
43	C₈×D₅₂	C₂²	1	1	yes	characteristic
44	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#346	C₂²	1	1	yes	characteristic, complemented
49	C₂²⋊#6090	C₂²	1	1	yes	characteristic, complemented
50	C₂²⋊#6090	C₂²	1	1	yes	characteristic, complemented
51	#11718099	C₂²	1	1	yes	characteristic, complemented
52	#11718099	C₂²	1	1	yes	characteristic, complemented
53	#11718099	C₂²	1	1	yes	characteristic, complemented
54	#11718099	C₂²	1	1	yes	characteristic, complemented
55	#11718094	C₂²	1	1	yes	characteristic, complemented
56	#11718094	C₂²	1	1	yes	characteristic, complemented
57	#11718093	C₂²	1	1	yes	characteristic, complemented
58	#11718093	C₂²	1	1	yes	characteristic, complemented
59	C₄⋊#6090	C₂²	1	1	yes	characteristic, complemented
60	#11718053	C₂²	1	1	yes	characteristic, complemented
61	C₂×D₄×D₁₃	C₈	1	1	yes	characteristic
62	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
67	D₄×Dic₁₃	C₈	1	1	yes	characteristic
68	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
69	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
70	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
71	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₁₃	—	2	2	no	—
73	C₂×C₈×D₁₃	—	2	2	no	—
74	C₂×C₈×D₁₃	—	2	2	no	—
75	C₂×C₈×D₁₃	—	2	2	no	—
76	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
81	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
82	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
83	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
84	#88147	C₈	1	1	yes	characteristic
85	C₄⋊C₄×D₁₃	C₈	1	1	yes	characteristic
86	#88135	C₈	1	1	yes	characteristic
87	#88135	C₈	1	1	yes	characteristic
88	C₂²⋊C₄×D₁₃	C₈	1	1	yes	characteristic
89	C₂²⋊C₄×D₁₃	C₈	1	1	yes	characteristic
90	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
91	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
92	C₁₃×M₃₂	—	2	2	no	—
93	C₂×C₁₃×C₁₆	—	2	2	no	—
94	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
95	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
96	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
98	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
100	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
101	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
102	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
103	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
104	#88060	C₂×C₄	1	1	yes	characteristic
105	#88060	C₂×C₄	1	1	yes	characteristic
106	#88060	C₂×C₄	1	1	yes	characteristic
107	#88060	C₂×C₄	1	1	yes	characteristic
108	#88054	C₂×C₄	1	1	yes	characteristic
109	#88054	C₂×C₄	1	1	yes	characteristic
110	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
111	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
112	#88052	—	2	2	no	—
113	C₂×#6090	—	2	2	no	—
114	C₂×#6090	C₂³	1	1	yes	characteristic
115	C₂×#6090	C₂³	1	1	yes	characteristic
116	C₂×#6090	C₂³	1	1	yes	characteristic
117	C₂×#6090	C₂³	1	1	yes	characteristic
118	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
119	C₄×#1055	C₂×C₄	1	1	yes	characteristic
120	#88038	—	2	2	no	—
121	#88038	—	2	2	no	—
122	C₁₆×D₁₃	—	2	2	no	—
123	C₁₆×D₁₃	—	2	2	no	—
124	C₁₆×D₁₃	—	2	2	no	—
125	C₁₆×D₁₃	—	2	2	no	—
126	C₁₆×D₁₃	—	2	2	no	—
127	C₁₆×D₁₃	D₄	1	4	yes	complemented
128	C₂×#2168	—	13	1	no	maximal, Sylow
129	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
130	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
131	C₂×D₄×C₁₃	C₂×C₈	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
136	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
137	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
138	D₄×D₁₃	—	2	4	no	—
139	C₂×D₅₂	C₂×C₈	1	1	yes	characteristic
140	C₂×C₄×D₁₃	—	2	2	no	—
141	C₂×C₄×D₁₃	—	2	2	no	—
142	C₂×C₄×D₁₃	—	2	2	no	—
143	C₂×C₄×D₁₃	—	2	2	no	—
144	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
145	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
146	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
147	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
148	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
149	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
150	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₈×C₁₃	—	2	1	no	—
154	C₂×C₈×C₁₃	—	2	1	no	—
155	C₂×C₈×C₁₃	—	2	1	no	—
156	C₂×C₈×C₁₃	—	2	1	no	—
157	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
162	C₁₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
163	C₁₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
164	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
165	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
166	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
167	#6103	C₂×C₈	1	1	yes	characteristic
168	#6103	C₂×C₈	1	1	yes	characteristic
169	#6103	C₂×C₈	1	1	yes	characteristic
170	#6103	C₂×C₈	1	1	yes	characteristic
171	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
172	#6101	C₂×C₈	1	1	yes	characteristic
173	#6101	C₂×C₈	1	1	yes	characteristic
174	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
175	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
176	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
177	C₂×#1055	—	2	2	no	—
178	C₂×#1055	—	2	2	no	—
179	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
180	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
181	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
182	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
183	C₈×D₁₃	—	2	2	no	—
184	C₈×D₁₃	—	2	2	no	—
185	C₈×D₁₃	—	2	2	no	—
186	C₈×D₁₃	—	2	1	no	—
187	C₈×D₁₃	—	2	1	no	—
188	C₈×D₁₃	—	2	1	no	—
189	C₈×D₁₃	—	2	1	no	—
190	C₈×D₁₃	—	2	2	no	—
191	C₈×D₁₃	—	2	2	no	—
192	C₈×D₁₃	C₂×D₄	1	2	yes	—
193	C₈×D₁₃	#41	1	2	yes	—
194	C₁₃×C₁₆	—	2	1	no	—
195	C₁₃×C₁₆	—	2	1	no	—
196	C₁₃×C₁₆	—	2	1	no	—
197	C₁₃×C₁₆	C₂×D₄	1	2	yes	complemented
198	#6090	—	2	1	no	—
199	#6090	—	2	1	no	—
200	#6090	—	2	1	no	—
201	#6090	C₂×D₄	1	2	yes	complemented
202	C₂²×M₃₂	—	13	1	no	—
203	C₂³×C₁₆	—	13	1	no	—
204	C₂×C₈×D₄	—	13	1	no	—
205	#2168	—	13	1	no	—
206	#2168	—	13	1	no	—
207	#2168	—	13	1	no	—
208	#2168	—	13	1	no	—
209	#2168	—	13	1	no	—
210	#2168	—	13	1	no	—
211	#2168	—	13	1	no	—
212	#2168	D₁₃	1	1	yes	characteristic, direct product factor
213	C₂×C₄⋊C₁₆	—	13	1	no	—
214	C₂×C₂²⋊C₁₆	—	13	1	no	—
215	C₂×C₂²⋊C₁₆	—	13	1	no	—
216	C₂×#346	—	13	1	no	—
217	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
218	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
219	C₂²×D₁₃	—	2	2	no	—
220	C₂²×D₁₃	—	2	2	no	—
221	C₂²×D₁₃	—	2	2	no	—
222	C₂²×D₁₃	—	2	2	no	—
223	C₂²×D₁₃	—	2	2	no	—
224	C₂²×D₁₃	M₃₂	1	4	yes	complemented
225	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
226	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
227	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
228	D₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	2	1	no	—
230	C₂×C₄×C₁₃	—	2	1	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
238	C₂²⋊D₁₃	—	2	2	no	—
239	C₂²⋊D₁₃	—	2	2	no	—
240	C₂×Dic₁₃	—	2	2	no	—
241	C₂×Dic₁₃	—	2	2	no	—
242	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
243	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
244	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
245	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
246	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
247	D₅₂	—	2	2	no	—
248	C₄×D₁₃	—	2	2	no	—
249	C₄×D₁₃	—	2	2	no	—
250	C₄×D₁₃	—	2	2	no	—
251	C₄×D₁₃	—	2	2	no	—
252	C₄×D₁₃	—	2	1	no	—
253	C₄×D₁₃	—	2	1	no	—
254	C₄×D₁₃	—	2	1	no	—
255	C₄×D₁₃	—	2	1	no	—
256	C₄×D₁₃	—	2	2	no	—
257	C₄×D₁₃	—	2	2	no	—
258	C₄×D₁₃	C₄×D₄	1	2	yes	—
259	C₄×D₁₃	#131	1	2	yes	—
260	C₈×C₁₃	—	2	1	no	—
261	C₈×C₁₃	—	2	1	no	—
262	C₈×C₁₃	—	2	1	no	—
263	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
264	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
265	#1055	—	2	1	no	—
266	#1055	—	2	1	no	—
267	#1055	—	2	1	no	—
268	#1055	C₄×D₄	1	2	yes	—
269	C₂³×C₈	—	13	1	no	—
270	C₂³×C₈	—	13	1	no	—
271	C₂×C₄×D₄	—	13	1	no	—
272	C₂×M₃₂	—	13	1	no	—
273	C₂×M₃₂	—	13	1	no	—
274	C₂×M₃₂	—	13	1	no	—
275	C₂×M₃₂	—	26	4	no	—
276	C₂×M₃₂	C₂×D₁₃	1	1	yes	characteristic, complemented
277	C₂²×C₁₆	—	13	1	no	—
278	C₂²×C₁₆	—	13	1	no	—
279	C₂²×C₁₆	—	13	1	no	—
280	C₂²×C₁₆	—	13	1	no	—
281	C₂²×C₁₆	—	13	1	no	—
282	C₂²×C₁₆	—	13	1	no	—
283	C₂²×C₁₆	—	13	1	no	—
284	C₂²×C₁₆	—	26	4	no	—
285	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
286	C₈×D₄	—	13	1	no	—
287	C₈×D₄	—	13	1	no	—
288	C₈×D₄	—	13	1	no	—
289	C₈×D₄	—	13	1	no	—
290	C₈×D₄	—	13	1	no	—
291	C₈×D₄	—	13	1	no	—
292	C₈×D₄	—	13	1	no	—
293	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
294	C₂×C₄⋊C₈	—	13	1	no	—
295	C₂×C₂²⋊C₈	—	13	1	no	—
296	C₂×C₂²⋊C₈	—	13	1	no	—
297	C₂×C₄×C₈	—	13	1	no	—
298	C₄⋊C₁₆	—	13	1	no	—
299	C₄⋊C₁₆	—	13	1	no	—
300	C₄⋊C₁₆	—	13	1	no	—
301	C₄⋊C₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
302	C₂²⋊C₁₆	—	13	1	no	—
303	C₂²⋊C₁₆	—	13	1	no	—
304	C₂²⋊C₁₆	—	13	1	no	—
305	C₂²⋊C₁₆	—	13	1	no	—
306	C₂²⋊C₁₆	—	13	1	no	—
307	C₂²⋊C₁₆	—	13	1	no	—
308	C₂²⋊C₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
309	C₂²⋊C₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
310	#346	—	13	1	no	—
311	#346	—	13	1	no	—
312	#346	—	13	1	no	—
313	#346	C₂×D₁₃	1	1	yes	characteristic, complemented
314	C₂²×C₁₃	—	2	1	no	—
315	C₂²×C₁₃	—	2	1	no	—
316	C₂²×C₁₃	—	2	1	no	—
317	C₂²×C₁₃	—	2	1	no	—
318	C₂²×C₁₃	—	2	1	no	—
319	C₂²×C₁₃	C₂×M₃₂	1	2	yes	complemented
320	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
321	C₂×D₁₃	—	2	1	no	—
322	C₂×D₁₃	—	2	1	no	—
323	C₂×D₁₃	—	2	8	no	—
324	C₂×D₁₃	—	2	1	no	—
325	C₂×D₁₃	—	2	1	no	—
326	C₂×D₁₃	—	2	1	no	—
327	C₂×D₁₃	—	4	4	no	—
328	C₂×D₁₃	C₈×D₄	1	2	yes	—
329	C₂×D₁₃	C₂×M₃₂	1	2	yes	—
330	C₂×D₁₃	C₂×M₃₂	1	2	yes	complemented
331	C₂×D₁₃	#504	1	2	yes	—
332	C₄×C₁₃	—	2	1	no	—
333	C₄×C₁₃	—	2	1	no	—
334	C₄×C₁₃	—	2	1	no	—
335	C₄×C₁₃	—	2	1	no	—
336	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
337	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
338	Dic₁₃	—	2	1	no	—
339	Dic₁₃	—	2	1	no	—
340	Dic₁₃	—	2	1	no	—
341	Dic₁₃	—	2	1	no	—
342	Dic₁₃	C₈×D₄	1	2	yes	—
343	C₂²×D₄	—	13	1	no	—
344	C₂³×C₄	—	13	1	no	—
345	C₂³×C₄	—	13	1	no	—
346	C₂²×C₈	—	13	1	no	—
347	C₂²×C₈	—	13	1	no	—
348	C₂²×C₈	—	13	1	no	—
349	C₂²×C₈	—	13	1	no	—
350	C₂²×C₈	—	13	1	no	—
351	C₂²×C₈	—	13	1	no	—
352	C₂²×C₈	—	13	1	no	—
353	C₂²×C₈	—	13	1	no	—
354	C₂²×C₈	—	13	1	no	—
355	C₂²×C₈	—	13	1	no	—
356	C₂²×C₈	—	26	2	no	—
357	C₂²×C₈	—	26	2	no	—
358	C₂²×C₈	—	26	2	no	—
359	C₂²×C₈	—	26	2	no	—
360	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
361	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
362	C₄×D₄	—	13	1	no	—
363	C₄×D₄	—	13	1	no	—
364	C₄×D₄	—	13	1	no	—
365	C₄×D₄	—	13	1	no	—
366	C₄×D₄	—	13	1	no	—
367	C₄×D₄	—	13	1	no	—
368	C₄×D₄	—	13	1	no	—
369	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
370	C₂×C₄⋊C₄	—	13	1	no	—
371	C₂×C₂²⋊C₄	—	13	1	no	—
372	C₂×C₂²⋊C₄	—	13	1	no	—
373	C₂×C₄²	—	13	1	no	—
374	M₃₂	—	2	2	no	—
375	M₃₂	—	26	2	no	—
376	M₃₂	—	26	2	no	—
377	M₃₂	—	26	2	no	—
378	C₂×C₁₆	—	2	2	no	—
379	C₂×C₁₆	—	13	1	no	—
380	C₂×C₁₆	—	13	4	no	—
381	C₂×C₁₆	—	13	1	no	—
382	C₂×C₁₆	—	13	1	no	—
383	C₂×C₁₆	—	13	1	no	—
384	C₂×C₁₆	—	26	2	no	—
385	C₂×C₁₆	—	26	2	no	—
386	C₂×C₁₆	—	26	2	no	—
387	C₂×C₁₆	—	26	2	no	—
388	C₂×C₁₆	—	26	2	no	—
389	C₂×C₁₆	—	26	2	no	—
390	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
391	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
392	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
393	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
394	C₄⋊C₈	—	13	1	no	—
395	C₄⋊C₈	—	13	1	no	—
396	C₄⋊C₈	—	13	1	no	—
397	C₄⋊C₈	C₄×D₁₃	1	1	yes	characteristic
398	C₂²⋊C₈	—	13	1	no	—
399	C₂²⋊C₈	—	13	1	no	—
400	C₂²⋊C₈	—	13	1	no	—
401	C₂²⋊C₈	—	13	1	no	—
402	C₂²⋊C₈	—	13	1	no	—
403	C₂²⋊C₈	—	13	1	no	—
404	C₂²⋊C₈	C₄×D₁₃	1	1	yes	characteristic
405	C₂²⋊C₈	C₄×D₁₃	1	1	yes	characteristic
406	C₄×C₈	—	13	1	no	—
407	C₄×C₈	—	13	1	no	—
408	C₄×C₈	—	13	1	no	—
409	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
410	C₂×C₁₃	—	2	2	no	—
411	C₂×C₁₃	—	4	1	no	—
412	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
413	C₂×C₁₃	C₂²×M₃₂	1	1	yes	characteristic
414	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
415	D₁₃	—	2	2	no	—
416	D₁₃	—	4	1	no	—
417	D₁₃	#2168	1	4	yes	direct product factor
418	C₂⁴	—	13	1	no	—
419	C₂⁴	—	13	1	no	—
420	C₂×D₄	—	13	1	no	—
421	C₂×D₄	—	13	1	no	—
422	C₂×D₄	—	13	1	no	—
423	C₂×D₄	—	26	4	no	—
424	C₂×D₄	C₈×D₁₃	1	1	yes	characteristic
425	C₂²×C₄	—	13	1	no	—
426	C₂²×C₄	—	13	1	no	—
427	C₂²×C₄	—	13	1	no	—
428	C₂²×C₄	—	13	1	no	—
429	C₂²×C₄	—	13	1	no	—
430	C₂²×C₄	—	13	1	no	—
431	C₂²×C₄	—	13	1	no	—
432	C₂²×C₄	—	13	1	no	—
433	C₂²×C₄	—	13	1	no	—
434	C₂²×C₄	—	13	1	no	—
435	C₂²×C₄	—	13	1	no	—
436	C₂²×C₄	—	26	2	no	—
437	C₂²×C₄	—	26	2	no	—
438	C₂²×C₄	—	26	2	no	—
439	C₂²×C₄	—	26	2	no	—
440	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
441	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	13	1	no	—
447	C₂×C₈	—	13	2	no	—
448	C₂×C₈	—	13	2	no	—
449	C₂×C₈	—	13	1	no	—
450	C₂×C₈	—	13	1	no	—
451	C₂×C₈	—	13	1	no	—
452	C₂×C₈	—	26	2	no	—
453	C₂×C₈	—	26	2	no	—
454	C₂×C₈	—	26	2	no	—
455	C₂×C₈	—	26	2	no	—
456	C₂×C₈	—	26	2	no	—
457	C₂×C₈	—	26	2	no	—
458	C₂×C₈	—	26	2	no	—
459	C₂×C₈	—	26	1	no	—
460	C₂×C₈	—	26	1	no	—
461	C₂×C₈	—	26	1	no	—
462	C₂×C₈	—	26	1	no	—
463	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
464	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
465	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
466	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
467	C₄⋊C₄	—	13	1	no	—
468	C₄⋊C₄	—	13	1	no	—
469	C₄⋊C₄	—	13	1	no	—
470	C₄⋊C₄	C₈×D₁₃	1	1	yes	characteristic
471	C₂²⋊C₄	—	13	1	no	—
472	C₂²⋊C₄	—	13	1	no	—
473	C₂²⋊C₄	—	13	1	no	—
474	C₂²⋊C₄	—	13	1	no	—
475	C₂²⋊C₄	—	13	1	no	—
476	C₂²⋊C₄	—	13	1	no	—
477	C₂²⋊C₄	C₈×D₁₃	1	1	yes	characteristic
478	C₂²⋊C₄	C₈×D₁₃	1	1	yes	characteristic
479	C₄²	—	13	1	no	—
480	C₄²	—	13	1	no	—
481	C₄²	—	13	1	no	—
482	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
483	C₁₆	—	2	1	no	—
484	C₁₆	—	2	1	no	—
485	C₁₆	—	2	1	no	—
486	C₁₆	—	13	2	no	—
487	C₁₆	—	26	1	no	—
488	C₁₆	—	26	1	no	—
489	C₁₆	—	26	1	no	—
490	C₁₆	D₄×D₁₃	1	2	yes	complemented
491	C₁₃	C₂×#2168	1	1	yes	characteristic, complemented, Sylow
492	C₂³	—	13	1	no	—
493	C₂³	—	13	1	no	—
494	C₂³	—	13	4	no	—
495	C₂³	—	13	1	no	—
496	C₂³	—	26	2	no	—
497	C₂³	—	26	2	no	—
498	C₂³	—	26	2	no	—
499	C₂³	—	26	2	no	—
500	C₂³	—	26	2	no	—
501	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
502	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
503	D₄	—	2	2	no	—
504	D₄	—	26	2	no	—
505	D₄	—	26	2	no	—
506	D₄	—	26	2	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	13	1	no	—
512	C₂×C₄	—	13	2	no	—
513	C₂×C₄	—	13	2	no	—
514	C₂×C₄	—	13	1	no	—
515	C₂×C₄	—	13	1	no	—
516	C₂×C₄	—	13	1	no	—
517	C₂×C₄	—	13	1	no	—
518	C₂×C₄	—	26	2	no	—
519	C₂×C₄	—	26	2	no	—
520	C₂×C₄	—	26	2	no	—
521	C₂×C₄	—	26	2	no	—
522	C₂×C₄	—	26	2	no	—
523	C₂×C₄	—	26	2	no	—
524	C₂×C₄	—	26	2	no	—
525	C₂×C₄	—	26	2	no	—
526	C₂×C₄	—	26	1	no	—
527	C₂×C₄	—	26	1	no	—
528	C₂×C₄	—	26	1	no	—
529	C₂×C₄	—	26	1	no	—
530	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
531	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
532	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
533	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
534	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	13	2	no	—
539	C₈	—	26	1	no	—
540	C₈	—	26	1	no	—
541	C₈	—	26	1	no	—
542	C₈	C₂×D₄×D₁₃	1	1	yes	characteristic
543	C₈	#41×D₁₃	1	1	yes	characteristic
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	13	2	no	—
550	C₂²	—	13	2	no	—
551	C₂²	—	13	2	no	—
552	C₂²	—	13	2	no	—
553	C₂²	—	26	8	no	—
554	C₂²	—	26	1	no	—
555	C₂²	—	26	1	no	—
556	C₂²	—	26	1	no	—
557	C₂²	—	26	1	no	—
558	C₂²	—	26	1	no	—
559	C₂²	—	52	4	no	—
560	C₂²	D₁₃×M₃₂	1	2	yes	complemented
561	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	13	2	no	—
567	C₄	—	26	1	no	—
568	C₄	—	26	1	no	—
569	C₄	—	26	1	no	—
570	C₄	—	26	1	no	—
571	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
572	C₄	D₁₃×#131	1	1	yes	characteristic
573	C₂	—	2	2	no	—
574	C₂	—	4	1	no	—
575	C₂	—	13	4	no	—
576	C₂	—	26	2	no	—
577	C₂	—	52	1	no	—
578	C₂	C₈×D₄×D₁₃	1	1	yes	characteristic
579	C₂	C₂×D₁₃×M₃₂	1	1	yes	characteristic
580	C₂	D₁₃×#504	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂³×C₈
Fitting	C₁₃×#2168	C₂
prime radical	C₂×D₄×D₁₃	C₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	#2168	D₁₃
hypocenter	C₁₃	C₂×#2168
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ #2168

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₃×M₃₂	C₂	semidirect
2. C₂²×C₁₆×D₁₃	C₂	semidirect
4. #13116664	C₂	semidirect
5. #13116663	C₂	semidirect
6. #13116662	C₂	semidirect
7. #13116661	C₂	semidirect
8. #13116660	C₂	semidirect
9. #13116659	C₂	semidirect
10. #13116658	C₂	semidirect
11. D₁₃×C₄⋊C₁₆	C₂	semidirect
12. D₁₃×C₂²⋊C₁₆	C₂	semidirect
13. D₁₃×C₂²⋊C₁₆	C₂	semidirect
14. D₁₃×#346	C₂	semidirect
15. C₁₃×#2168	C₂	semidirect
19. C₂×C₁₃×M₃₂	C₂²	semidirect
20. C₂²×C₁₃×C₁₆	C₂²	semidirect
24. C₂×#88052	C₂²	semidirect
25. C₂²×#6090	C₂²	semidirect
28. C₂×#88038	C₂²	semidirect
29. C₂×#88038	C₂²	semidirect
35. C₂×C₁₆×D₁₃	C₂²	semidirect
36. C₂×C₁₆×D₁₃	C₂²	semidirect
45. C₁₃×C₄⋊C₁₆	C₂²	semidirect
46. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
47. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
48. C₁₃×#346	C₂²	semidirect
49. C₂²⋊#6090	C₂²	semidirect
50. C₂²⋊#6090	C₂²	semidirect
51. #11718099	C₂²	semidirect
52. #11718099	C₂²	semidirect
53. #11718099	C₂²	semidirect
54. #11718099	C₂²	semidirect
55. #11718094	C₂²	semidirect
56. #11718094	C₂²	semidirect
57. #11718093	C₂²	semidirect
58. #11718093	C₂²	semidirect
59. C₄⋊#6090	C₂²	semidirect
60. #11718053	C₂²	semidirect
127. C₁₆×D₁₃	D₄	semidirect
197. C₁₃×C₁₆	C₂×D₄	semidirect
201. #6090	C₂×D₄	semidirect
212. #2168	D₁₃	direct (N × H)
224. C₂²×D₁₃	M₃₂	semidirect
276. C₂×M₃₂	C₂×D₁₃	semidirect
285. C₂²×C₁₆	C₂×D₁₃	semidirect
301. C₄⋊C₁₆	C₂×D₁₃	semidirect
308. C₂²⋊C₁₆	C₂×D₁₃	semidirect
309. C₂²⋊C₁₆	C₂×D₁₃	semidirect
313. #346	C₂×D₁₃	semidirect
319. C₂²×C₁₃	C₂×M₃₂	semidirect
330. C₂×D₁₃	C₂×M₃₂	semidirect
417. D₁₃	#2168	direct (N × H)
490. C₁₆	D₄×D₁₃	semidirect
491. C₁₃	C₂×#2168	semidirect
560. C₂²	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
C₂²×C₁₆×D₁₃	2
C₈×D₄×D₁₃	2
#13116664	2
#13116663	2
#13116662	2
#13116661	2
#13116660	2
#13116659	2
#13116658	2
D₁₃×C₄⋊C₁₆	2
D₁₃×C₂²⋊C₁₆	2
D₁₃×#346	2
C₁₃×#2168	2
C₂×#2168	13

Subgroups — D13×#2168 #16016071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#2168 #16016071