Subgroups — #16016024

Order 3328.

600 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×#405	C₂	1	1	yes	maximal, characteristic
2	#13116643	C₂	1	1	yes	maximal, characteristic, complemented
3	#13116640	C₂	1	1	yes	maximal, characteristic, complemented
4	#13116640	C₂	1	1	yes	maximal, characteristic, complemented
5	#13116638	C₂	1	1	yes	maximal, characteristic, complemented
6	#13116637	C₂	1	1	yes	maximal, characteristic, complemented
7	#13116634	C₂	1	1	yes	maximal, characteristic, complemented
8	#13116633	C₂	1	1	yes	maximal, characteristic, complemented
9	#13116593	C₂	1	1	yes	maximal, characteristic, complemented
10	#13116593	C₂	1	1	yes	maximal, characteristic, complemented
11	#13116445	C₂	1	1	yes	maximal, characteristic
12	D₁₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
13	#13116434	C₂	1	1	yes	maximal, characteristic, complemented
14	#13116431	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2164	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×M₁₆×D₁₃	C₄	1	1	yes	characteristic
17	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
18	D₁₃×#117	C₄	1	1	yes	characteristic
19	C₁₃×#405	C₂²	1	1	yes	characteristic
20	#11718783	C₄	1	1	yes	characteristic
21	#11718762	C₂²	1	1	yes	characteristic
22	#11718658	C₄	1	1	yes	characteristic
23	C₂×#88038	C₂²	1	1	yes	characteristic
24	C₂×#88038	C₂²	1	1	yes	characteristic
25	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
27	#11718369	C₄	1	1	yes	characteristic
28	#11718369	C₄	1	1	yes	characteristic
29	D₁₃×#97	C₄	1	1	yes	characteristic
30	D₁₃×#97	C₄	1	1	yes	characteristic
31	#11718350	C₂²	1	1	yes	characteristic
32	#11718350	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
38	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₁₃×#346	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
41	C₂²⋊#6090	C₂²	1	1	yes	characteristic
42	C₂²⋊#6090	C₂²	1	1	yes	characteristic
43	#11718099	C₂²	1	1	yes	characteristic
44	#11718099	C₂²	1	1	yes	characteristic
45	#11718099	C₂²	1	1	yes	characteristic
46	#11718099	C₂²	1	1	yes	characteristic
47	#11718094	C₂²	1	1	yes	characteristic, complemented
48	#11718094	C₂²	1	1	yes	characteristic, complemented
49	#11718093	C₂²	1	1	yes	characteristic, complemented
50	#11718093	C₂²	1	1	yes	characteristic, complemented
51	#11718093	C₂²	1	1	yes	characteristic, complemented
52	#11718093	C₂²	1	1	yes	characteristic, complemented
53	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
54	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
55	C₄⋊#6090	C₂²	1	1	yes	characteristic, complemented
56	C₄⋊#6090	C₂²	1	1	yes	characteristic, complemented
57	#11718053	C₂²	1	1	yes	characteristic, complemented
58	C₄×#6090	C₂²	1	1	yes	characteristic, complemented
59	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
63	#88180	C₂×C₄	1	1	yes	characteristic
64	C₂×#6099	C₂×C₄	1	1	yes	characteristic
65	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
66	M₁₆×D₁₃	—	2	4	no	—
67	C₂×#6094	C₂×C₄	1	1	yes	characteristic
68	C₂×#6094	C₂×C₄	1	1	yes	characteristic
69	C₂×C₈×D₁₃	—	2	2	no	—
70	C₂×C₈×D₁₃	—	2	2	no	—
71	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
77	#88146	C₈	1	1	yes	characteristic
78	#88146	C₈	1	1	yes	characteristic
79	C₄⋊C₄×D₁₃	C₈	1	1	yes	characteristic
80	C₄⋊C₄×D₁₃	C₈	1	1	yes	characteristic
81	C₂²⋊C₄×D₁₃	C₈	1	1	yes	characteristic
82	C₂²⋊C₄×D₁₃	C₈	1	1	yes	characteristic
83	#88131	C₈	1	1	yes	characteristic
84	#88131	C₈	1	1	yes	characteristic
85	#88126	C₂×C₄	1	1	yes	characteristic
86	#88126	C₂×C₄	1	1	yes	characteristic
87	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
88	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
89	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
93	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
94	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
95	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	#88055	C₂×C₄	1	1	yes	characteristic
98	#88055	C₂×C₄	1	1	yes	characteristic
99	#88055	C₂×C₄	1	1	yes	characteristic
100	#88055	C₂×C₄	1	1	yes	characteristic
101	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
102	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
103	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
104	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
105	C₂×#6090	C₂³	1	1	yes	characteristic
106	C₂×#6090	C₂³	1	1	yes	characteristic
107	C₂×#6090	C₂³	1	1	yes	characteristic
108	C₂×#6090	C₂³	1	1	yes	characteristic
109	#88043	C₂×C₄	1	1	yes	characteristic
110	#88043	C₂×C₄	1	1	yes	characteristic
111	C₄×#1055	C₂×C₄	1	1	yes	characteristic
112	C₄×#1055	C₂×C₄	1	1	yes	characteristic
113	#88038	—	2	2	no	—
114	#88038	—	2	2	no	—
115	C₁₆×D₁₃	—	2	2	no	—
116	C₁₆×D₁₃	—	2	2	no	—
117	#33422	—	13	1	no	maximal, Sylow
118	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
121	C₂×C₄×D₁₃	—	2	2	no	—
122	C₂×C₄×D₁₃	—	2	2	no	—
123	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
124	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
125	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
126	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
127	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
128	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
129	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₁₃×M₁₆	—	2	2	no	—
132	C₂×C₈×C₁₃	—	2	1	no	—
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
139	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
140	C₁₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
141	C₁₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
142	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
145	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
146	#6103	C₂×C₈	1	1	yes	characteristic
147	#6103	C₂×C₈	1	1	yes	characteristic
148	#6103	C₂×C₈	1	1	yes	characteristic
149	#6103	C₂×C₈	1	1	yes	characteristic
150	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
151	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
152	#6101	C₂×C₈	1	1	yes	characteristic
153	#6101	C₂×C₈	1	1	yes	characteristic
154	#6101	C₂×C₈	1	1	yes	characteristic
155	#6101	C₂×C₈	1	1	yes	characteristic
156	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
157	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
158	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
159	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
160	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
162	#6099	—	2	2	no	—
163	C₂×#1055	—	2	2	no	—
164	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
165	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
166	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
167	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
168	#6094	—	2	2	no	—
169	#6094	M₁₆	1	4	yes	—
170	C₈×D₁₃	—	2	2	no	—
171	C₈×D₁₃	—	2	2	no	—
172	C₈×D₁₃	—	2	1	no	—
173	C₈×D₁₃	—	2	1	no	—
174	C₈×D₁₃	—	2	2	no	—
175	C₈×D₁₃	—	2	2	no	—
176	C₈×D₁₃	#41	1	2	yes	—
177	C₈×D₁₃	#41	1	2	yes	—
178	C₁₃×C₁₆	—	2	1	no	—
179	C₁₃×C₁₆	—	2	1	no	—
180	C₁₃×C₁₆	—	2	1	no	—
181	C₁₃×C₁₆	—	2	1	no	—
182	#6090	—	2	1	no	—
183	#6090	—	2	1	no	—
184	#6090	—	2	1	no	—
185	#6090	—	2	1	no	—
186	C₂×#405	—	13	1	no	—
187	#2164	—	13	1	no	—
188	#2164	—	13	1	no	—
189	#2164	—	13	1	no	—
190	#2164	D₁₃	1	1	yes	characteristic, complemented
191	#2163	—	13	1	no	—
192	#2163	—	13	1	no	—
193	#2162	—	13	1	no	—
194	#2162	—	13	1	no	—
195	#2151	—	13	1	no	—
196	#2151	—	13	1	no	—
197	#2112	—	13	1	no	—
198	C₂×C₂²⋊C₁₆	—	13	1	no	—
199	#2108	—	13	1	no	—
200	#2108	—	13	1	no	—
201	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
202	C₂²×D₁₃	—	2	2	no	—
203	C₂²×D₁₃	—	2	2	no	—
204	C₂²×D₁₃	—	4	1	no	—
205	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
206	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
215	C₂×Dic₁₃	—	2	2	no	—
216	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
217	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
218	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
219	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
220	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
221	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
222	C₄×D₁₃	—	2	2	no	—
223	C₄×D₁₃	—	2	2	no	—
224	C₄×D₁₃	—	2	2	no	—
225	C₄×D₁₃	—	2	1	no	—
226	C₄×D₁₃	—	2	1	no	—
227	C₄×D₁₃	—	2	2	no	—
228	C₄×D₁₃	—	4	1	no	—
229	C₄×D₁₃	—	4	1	no	—
230	C₄×D₁₃	#117	1	2	yes	—
231	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
232	C₈×C₁₃	—	2	1	no	—
233	C₈×C₁₃	—	2	1	no	—
234	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
235	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
236	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
237	#1055	—	2	1	no	—
238	#1055	—	2	1	no	—
239	#1055	#117	1	2	yes	—
240	#1055	C₂×M₁₆	1	2	yes	—
241	C₂²×M₁₆	—	13	1	no	—
242	C₂³×C₈	—	13	1	no	—
243	C₂×#117	—	13	1	no	—
244	C₂×M₃₂	—	13	1	no	—
245	C₂×M₃₂	—	13	1	no	—
246	C₂²×C₁₆	—	13	1	no	—
247	C₂²×C₁₆	—	13	1	no	—
248	#405	—	13	1	no	—
249	#405	—	13	1	no	—
250	#405	—	13	1	no	—
251	#405	—	13	1	no	—
252	#405	—	13	1	no	—
253	#405	—	13	1	no	—
254	#405	—	13	1	no	—
255	#405	C₂×D₁₃	1	1	yes	characteristic
256	C₂×#97	—	13	1	no	—
257	C₂×#97	—	13	1	no	—
258	C₂×C₄×C₈	—	13	1	no	—
259	C₂×C₄×C₈	—	13	1	no	—
260	C₄⋊C₁₆	—	13	1	no	—
261	C₄⋊C₁₆	—	13	1	no	—
262	C₄⋊C₁₆	—	13	1	no	—
263	C₄⋊C₁₆	—	13	1	no	—
264	C₄⋊C₁₆	—	13	1	no	—
265	C₄⋊C₁₆	—	13	1	no	—
266	C₄⋊C₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
267	C₄⋊C₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
268	C₂²⋊C₁₆	—	13	1	no	—
269	C₂²⋊C₁₆	—	13	1	no	—
270	C₂²⋊C₁₆	—	13	1	no	—
271	C₂²⋊C₁₆	—	13	1	no	—
272	C₂²⋊C₁₆	—	13	1	no	—
273	C₂²⋊C₁₆	—	13	1	no	—
274	C₂²⋊C₁₆	C₂×D₁₃	1	1	yes	characteristic
275	C₂²⋊C₁₆	C₂×D₁₃	1	1	yes	characteristic
276	#346	—	13	1	no	—
277	#346	—	13	1	no	—
278	#346	—	13	1	no	—
279	#346	C₂×D₁₃	1	1	yes	characteristic, complemented
280	C₄×C₁₆	—	13	1	no	—
281	C₄×C₁₆	—	13	1	no	—
282	C₄×C₁₆	—	13	1	no	—
283	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
284	C₂²×C₁₃	—	2	1	no	—
285	C₂²×C₁₃	—	2	1	no	—
286	C₂²×C₁₃	—	2	1	no	—
287	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
288	C₂×D₁₃	—	2	1	no	—
289	C₂×D₁₃	—	2	1	no	—
290	C₂×D₁₃	—	2	1	no	—
291	C₂×D₁₃	—	2	1	no	—
292	C₂×D₁₃	—	4	4	no	—
293	C₂×D₁₃	#431	1	2	yes	—
294	C₂×D₁₃	#504	1	2	yes	—
295	C₄×C₁₃	—	2	1	no	—
296	C₄×C₁₃	—	2	1	no	—
297	C₄×C₁₃	—	2	1	no	—
298	C₄×C₁₃	—	2	1	no	—
299	C₄×C₁₃	—	2	1	no	—
300	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
301	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
302	Dic₁₃	—	2	1	no	—
303	Dic₁₃	—	2	1	no	—
304	Dic₁₃	—	2	1	no	—
305	Dic₁₃	—	2	1	no	—
306	Dic₁₃	—	2	1	no	—
307	Dic₁₃	#431	1	2	yes	—
308	C₂³×C₄	—	13	1	no	—
309	C₂×M₁₆	—	13	1	no	—
310	C₂×M₁₆	—	13	1	no	—
311	C₂×M₁₆	—	13	1	no	—
312	C₂×M₁₆	—	26	4	no	—
313	C₂×M₁₆	C₄×D₁₃	1	1	yes	characteristic
314	C₂²×C₈	—	13	1	no	—
315	C₂²×C₈	—	13	1	no	—
316	C₂²×C₈	—	13	1	no	—
317	C₂²×C₈	—	13	1	no	—
318	C₂²×C₈	—	13	1	no	—
319	C₂²×C₈	—	13	1	no	—
320	C₂²×C₈	—	13	1	no	—
321	C₂²×C₈	—	26	2	no	—
322	C₂²×C₈	—	26	2	no	—
323	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
324	#117	—	13	1	no	—
325	#117	—	13	1	no	—
326	#117	—	13	1	no	—
327	#117	—	13	1	no	—
328	#117	—	13	1	no	—
329	#117	—	13	1	no	—
330	#117	—	13	1	no	—
331	#117	C₄×D₁₃	1	1	yes	characteristic
332	C₂×C₄⋊C₄	—	13	1	no	—
333	C₂×C₄⋊C₄	—	13	1	no	—
334	C₂×C₂²⋊C₄	—	13	1	no	—
335	C₂×C₂²⋊C₄	—	13	1	no	—
336	C₂×C₄²	—	13	1	no	—
337	C₂×C₄²	—	13	1	no	—
338	M₃₂	—	26	2	no	—
339	M₃₂	—	26	2	no	—
340	C₂×C₁₆	—	13	1	no	—
341	C₂×C₁₆	—	13	1	no	—
342	C₂×C₁₆	—	13	1	no	—
343	C₂×C₁₆	—	13	1	no	—
344	C₂×C₁₆	—	26	2	no	—
345	C₂×C₁₆	—	26	2	no	—
346	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
347	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
348	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
349	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
350	#97	—	13	1	no	—
351	#97	—	13	1	no	—
352	#97	—	13	1	no	—
353	#97	—	13	1	no	—
354	#97	—	13	1	no	—
355	#97	—	13	1	no	—
356	#97	C₄×D₁₃	1	1	yes	characteristic
357	#97	C₄×D₁₃	1	1	yes	characteristic
358	C₄×C₈	—	13	1	no	—
359	C₄×C₈	—	13	1	no	—
360	C₄×C₈	—	13	1	no	—
361	C₄×C₈	—	13	1	no	—
362	C₄×C₈	—	13	1	no	—
363	C₄×C₈	—	13	1	no	—
364	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
365	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
366	C₂×C₁₃	—	4	1	no	—
367	C₂×C₁₃	C₂×#431	1	1	yes	characteristic
368	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
369	C₂×C₁₃	#3407	1	1	yes	characteristic
370	D₁₃	—	2	2	no	—
371	D₁₃	—	2	2	no	—
372	C₂⁴	—	13	1	no	—
373	C₂²×C₄	—	13	1	no	—
374	C₂²×C₄	—	13	1	no	—
375	C₂²×C₄	—	13	1	no	—
376	C₂²×C₄	—	13	1	no	—
377	C₂²×C₄	—	13	1	no	—
378	C₂²×C₄	—	13	1	no	—
379	C₂²×C₄	—	13	1	no	—
380	C₂²×C₄	—	13	1	no	—
381	C₂²×C₄	—	13	1	no	—
382	C₂²×C₄	—	26	2	no	—
383	C₂²×C₄	—	26	2	no	—
384	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
385	M₁₆	—	2	2	no	—
386	M₁₆	—	13	4	no	—
387	M₁₆	—	26	2	no	—
388	M₁₆	—	26	2	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	13	1	no	—
392	C₂×C₈	—	13	1	no	—
393	C₂×C₈	—	13	2	no	—
394	C₂×C₈	—	13	2	no	—
395	C₂×C₈	—	13	1	no	—
396	C₂×C₈	—	13	1	no	—
397	C₂×C₈	—	26	2	no	—
398	C₂×C₈	—	26	2	no	—
399	C₂×C₈	—	26	2	no	—
400	C₂×C₈	—	26	2	no	—
401	C₂×C₈	—	26	2	no	—
402	C₂×C₈	—	26	1	no	—
403	C₂×C₈	—	26	1	no	—
404	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
405	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
406	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
407	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
408	C₄⋊C₄	—	13	1	no	—
409	C₄⋊C₄	—	13	1	no	—
410	C₄⋊C₄	—	13	1	no	—
411	C₄⋊C₄	—	13	1	no	—
412	C₄⋊C₄	—	13	1	no	—
413	C₄⋊C₄	—	13	1	no	—
414	C₄⋊C₄	C₈×D₁₃	1	1	yes	characteristic
415	C₄⋊C₄	C₈×D₁₃	1	1	yes	characteristic
416	C₂²⋊C₄	—	13	1	no	—
417	C₂²⋊C₄	—	13	1	no	—
418	C₂²⋊C₄	—	13	1	no	—
419	C₂²⋊C₄	—	13	1	no	—
420	C₂²⋊C₄	—	13	1	no	—
421	C₂²⋊C₄	—	13	1	no	—
422	C₂²⋊C₄	C₈×D₁₃	1	1	yes	characteristic
423	C₂²⋊C₄	C₈×D₁₃	1	1	yes	characteristic
424	C₄²	—	13	1	no	—
425	C₄²	—	13	1	no	—
426	C₄²	—	13	1	no	—
427	C₄²	—	13	1	no	—
428	C₄²	—	13	1	no	—
429	C₄²	—	13	1	no	—
430	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
431	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
432	C₁₆	—	2	1	no	—
433	C₁₆	—	2	1	no	—
434	C₁₆	—	2	1	no	—
435	C₁₆	—	2	1	no	—
436	C₁₆	—	26	1	no	—
437	C₁₆	—	26	1	no	—
438	C₁₆	—	26	1	no	—
439	C₁₆	—	26	1	no	—
440	C₁₃	#33422	1	1	yes	characteristic, complemented, Sylow
441	C₂³	—	13	1	no	—
442	C₂³	—	13	1	no	—
443	C₂³	—	26	2	no	—
444	C₂³	—	26	2	no	—
445	C₂³	—	52	1	no	—
446	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	13	1	no	—
450	C₂×C₄	—	13	2	no	—
451	C₂×C₄	—	13	2	no	—
452	C₂×C₄	—	13	1	no	—
453	C₂×C₄	—	13	1	no	—
454	C₂×C₄	—	13	1	no	—
455	C₂×C₄	—	13	1	no	—
456	C₂×C₄	—	13	1	no	—
457	C₂×C₄	—	26	2	no	—
458	C₂×C₄	—	26	2	no	—
459	C₂×C₄	—	26	2	no	—
460	C₂×C₄	—	26	2	no	—
461	C₂×C₄	—	26	2	no	—
462	C₂×C₄	—	26	1	no	—
463	C₂×C₄	—	26	1	no	—
464	C₂×C₄	—	52	1	no	—
465	C₂×C₄	—	52	1	no	—
466	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
467	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
468	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
469	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
470	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
471	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
472	C₈	—	2	1	no	—
473	C₈	—	2	1	no	—
474	C₈	—	13	2	no	—
475	C₈	—	13	2	no	—
476	C₈	—	26	1	no	—
477	C₈	—	26	1	no	—
478	C₈	M₁₆×D₁₃	1	2	yes	—
479	C₈	#41×D₁₃	1	1	yes	characteristic
480	C₈	#41×D₁₃	1	1	yes	characteristic
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	13	2	no	—
485	C₂²	—	13	2	no	—
486	C₂²	—	26	1	no	—
487	C₂²	—	26	1	no	—
488	C₂²	—	26	1	no	—
489	C₂²	—	26	1	no	—
490	C₂²	—	52	4	no	—
491	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	13	2	no	—
498	C₄	—	26	1	no	—
499	C₄	—	26	1	no	—
500	C₄	—	26	1	no	—
501	C₄	—	26	1	no	—
502	C₄	—	26	1	no	—
503	C₄	D₁₃×#117	1	1	yes	characteristic
504	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
505	C₂	—	4	1	no	—
506	C₂	—	26	2	no	—
507	C₂	—	26	2	no	—
508	C₂	D₁₃×#431	1	1	yes	characteristic
509	C₂	D₁₃×#504	1	1	yes	characteristic
510	C₂	#13127937	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂³×C₈
Fitting	C₁₃×#2164	C₂
prime radical	C₂³×D₁₃	C₂×C₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	#2164	D₁₃
hypocenter	C₁₃	#33422
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ #2164

Complements

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

N	H ≅ G/N	type
2. #13116643	C₂	semidirect
3. #13116640	C₂	semidirect
4. #13116640	C₂	semidirect
5. #13116638	C₂	semidirect
6. #13116637	C₂	semidirect
7. #13116634	C₂	semidirect
8. #13116633	C₂	semidirect
9. #13116593	C₂	semidirect
10. #13116593	C₂	semidirect
13. #13116434	C₂	semidirect
14. #13116431	C₂	semidirect
15. C₁₃×#2164	C₂	semidirect
35. C₁₃×C₄⋊C₁₆	C₂²	semidirect
36. C₁₃×C₄⋊C₁₆	C₂²	semidirect
39. C₁₃×#346	C₂²	semidirect
40. C₄×C₁₃×C₁₆	C₂²	semidirect
47. #11718094	C₂²	semidirect
48. #11718094	C₂²	semidirect
49. #11718093	C₂²	semidirect
50. #11718093	C₂²	semidirect
51. #11718093	C₂²	semidirect
52. #11718093	C₂²	semidirect
53. C₁₆×Dic₁₃	C₂²	semidirect
54. C₁₆×Dic₁₃	C₂²	semidirect
55. C₄⋊#6090	C₂²	semidirect
56. C₄⋊#6090	C₂²	semidirect
57. #11718053	C₂²	semidirect
58. C₄×#6090	C₂²	semidirect
190. #2164	D₁₃	semidirect
266. C₄⋊C₁₆	C₂×D₁₃	semidirect
267. C₄⋊C₁₆	C₂×D₁₃	semidirect
279. #346	C₂×D₁₃	semidirect
283. C₄×C₁₆	C₂×D₁₃	semidirect
440. C₁₃	#33422	semidirect

Maximal subgroups

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

subgroup	index
D₁₃×#405	2
#13116643	2
#13116640	2
#13116638	2
#13116637	2
#13116634	2
#13116633	2
#13116593	2
#13116445	2
D₁₃×C₂²⋊C₁₆	2
#13116434	2
#13116431	2
C₁₃×#2164	2
#33422	13