Subgroups — #15828638

Order 3328.

814 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	#13123800	C₂	1	1	yes	maximal, characteristic
2	#13123798	C₂	1	1	yes	maximal, characteristic
3	C₄×#88155	C₂	1	1	yes	maximal, characteristic
4	#13113140	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113139	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113132	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113131	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113124	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113122	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113118	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#6099	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈×#6094	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈×#6094	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈²×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#88155	C₄	1	2	yes	—
17	C₄×#6127	C₂²	1	1	yes	characteristic
18	C₁₃×#431	C₂²	1	1	yes	characteristic
19	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	#11718789	C₄	1	2	yes	—
22	#11718788	C₄	1	2	yes	—
23	#11718762	C₄	1	2	yes	—
24	#11718586	C₂²	1	1	yes	characteristic
25	C₄×#6099	C₂²	1	1	yes	characteristic
26	C₄×#6099	C₂²	1	1	yes	characteristic
27	#11718497	C₄	1	2	yes	—
28	#11718489	C₄	1	2	yes	—
29	#11718390	C₄	1	2	yes	—
30	#11718389	C₄	1	2	yes	—
31	#11718367	C₄	1	2	yes	—
32	#11718362	C₄	1	2	yes	—
33	#11718350	C₄	1	2	yes	—
34	#11718350	C₄	1	2	yes	—
35	C₄×#6094	C₂²	1	1	yes	characteristic
36	C₄×#6094	C₂²	1	1	yes	characteristic
37	C₄×#6094	C₂²	1	1	yes	characteristic
38	C₄×#6094	C₂²	1	1	yes	characteristic
39	#11718346	C₂²	1	1	yes	characteristic
40	#11718346	C₂²	1	1	yes	characteristic
41	#11718346	C₂²	1	1	yes	characteristic
42	#11718346	C₂²	1	1	yes	characteristic
43	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
44	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
45	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
47	C₁₃×#322	C₂²	1	1	yes	characteristic
48	C₁₃×#322	C₂²	1	1	yes	characteristic
49	C₈²×C₁₃	C₂²	1	1	yes	characteristic
50	C₈²×C₁₃	C₂²	1	1	yes	characteristic
51	#11718047	C₂²	1	1	yes	characteristic
52	#11718047	C₂²	1	1	yes	characteristic
53	#11718046	C₂²	1	1	yes	characteristic
54	#11718046	C₂²	1	1	yes	characteristic
55	#11718046	C₂²	1	1	yes	characteristic
56	#11718046	C₂²	1	1	yes	characteristic
57	#11718046	C₂²	1	1	yes	characteristic
58	#11718046	C₂²	1	1	yes	characteristic
59	C₈×#1055	C₂²	1	1	yes	characteristic
60	C₈×#1055	C₂²	1	1	yes	characteristic
61	C₈×#1055	C₂²	1	1	yes	characteristic
62	C₈×#1055	C₂²	1	1	yes	characteristic
63	C₂×#6127	C₂×C₄	1	1	yes	characteristic
64	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
65	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₄×C₂²⋊D₁₃	C₂×C₄	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	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
71	#88180	C₂×C₄	1	1	yes	characteristic
72	C₂×#6099	C₂×C₄	1	2	yes	—
73	C₂×#6099	C₂×C₄	1	2	yes	—
74	#88155	—	2	8	no	—
75	C₂×#6094	C₂×C₄	1	2	yes	—
76	C₂×#6094	C₂×C₄	1	2	yes	—
77	C₂×#6094	C₂×C₄	1	2	yes	—
78	C₂×#6094	C₂×C₄	1	2	yes	—
79	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
80	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
81	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
82	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
83	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
84	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
85	#88126	C₂×C₄	1	1	yes	characteristic
86	#88126	C₂×C₄	1	1	yes	characteristic
87	C₄²×D₁₃	C₂³	1	1	yes	characteristic
88	C₄²×D₁₃	C₂³	1	1	yes	characteristic
89	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
90	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
91	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
92	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
93	C₁₃×#97	C₂×C₄	1	2	yes	—
94	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
95	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
101	C₂²⋊#1055	C₂×C₄	1	2	yes	—
102	#88060	C₂×C₄	1	2	yes	—
103	#88060	C₂×C₄	1	2	yes	—
104	#88060	C₂×C₄	1	2	yes	—
105	#88060	C₂×C₄	1	2	yes	—
106	#88055	C₂×C₄	1	2	yes	—
107	#88055	C₂×C₄	1	2	yes	—
108	#88055	C₂×C₄	1	2	yes	—
109	#88055	C₂×C₄	1	2	yes	—
110	#88054	C₂×C₄	1	2	yes	—
111	#88054	C₂×C₄	1	2	yes	—
112	#88054	C₂×C₄	1	2	yes	—
113	#88054	C₂×C₄	1	2	yes	—
114	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
115	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
116	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
117	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
118	C₄⋊#1055	C₂×C₄	1	2	yes	—
119	#88043	C₂×C₄	1	2	yes	—
120	#88043	C₂×C₄	1	2	yes	—
121	C₄×#1055	C₂³	1	1	yes	characteristic
122	C₄×#1055	C₂³	1	1	yes	characteristic
123	C₄×#1055	C₂³	1	1	yes	characteristic
124	C₄×#1055	C₂³	1	1	yes	characteristic
125	C₄×#1055	C₂³	1	1	yes	characteristic
126	C₄×#1055	C₂³	1	1	yes	characteristic
127	#17335	—	13	1	no	maximal, Sylow
128	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₂²⋊D₁₃	C₄²	1	1	yes	characteristic
132	C₂×C₂²⋊D₁₃	C₄²	1	1	yes	characteristic
133	#6127	—	2	4	no	—
134	C₂×D₅₂	C₄²	1	1	yes	characteristic
135	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₂×Dic₂₆	C₄²	1	1	yes	characteristic
142	C₁₃×M₁₆	—	2	4	no	—
143	C₂×C₈×C₁₃	—	2	4	no	—
144	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
146	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
147	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
148	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
149	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
150	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
154	C₂²⋊Dic₁₃	C₄²	1	1	yes	characteristic
155	C₂²⋊Dic₁₃	C₄²	1	1	yes	characteristic
156	#6103	C₄²	1	1	yes	characteristic
157	#6103	C₄²	1	1	yes	characteristic
158	#6103	C₄²	1	1	yes	characteristic
159	#6103	C₄²	1	1	yes	characteristic
160	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
161	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
162	#6101	C₄²	1	1	yes	characteristic
163	#6101	C₄²	1	1	yes	characteristic
164	#6101	C₄²	1	1	yes	characteristic
165	#6101	C₄²	1	1	yes	characteristic
166	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
167	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
168	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
169	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
170	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
171	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
172	#6099	—	2	4	no	—
173	#6099	—	2	4	no	—
174	C₂×#1055	C₂²×C₄	1	2	yes	—
175	C₂×#1055	C₂²×C₄	1	2	yes	—
176	C₂×#1055	C₂²×C₄	1	2	yes	—
177	C₂×#1055	C₂²×C₄	1	2	yes	—
178	C₂×#1055	C₂²×C₄	1	2	yes	—
179	C₂×#1055	C₂²×C₄	1	2	yes	—
180	#6094	—	2	4	no	—
181	#6094	—	2	4	no	—
182	#6094	—	2	4	no	—
183	#6094	—	2	4	no	—
184	C₈×D₁₃	—	2	4	no	—
185	C₈×D₁₃	—	2	4	no	—
186	C₈×D₁₃	—	2	4	no	—
187	C₈×D₁₃	M₁₆	1	8	yes	complemented
188	#2965	—	13	1	no	—
189	#2965	—	13	1	no	—
190	C₄×#131	—	13	1	no	—
191	#1455	—	13	1	no	—
192	#1455	—	13	1	no	—
193	#1453	—	13	1	no	—
194	#1453	—	13	1	no	—
195	#1451	—	13	1	no	—
196	#1451	—	13	1	no	—
197	#1450	—	13	1	no	—
198	C₈×M₁₆	—	13	1	no	—
199	C₈×M₁₆	—	13	1	no	—
200	C₈×M₁₆	—	13	1	no	—
201	C₈×M₁₆	D₁₃	1	1	yes	characteristic, complemented
202	C₂×C₈²	—	13	1	no	—
203	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
204	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
205	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
215	C₂²⋊D₁₃	—	2	2	no	—
216	C₂²⋊D₁₃	—	2	2	no	—
217	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
218	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
219	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
220	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
221	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
222	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
223	D₅₂	—	2	2	no	—
224	C₄×D₁₃	—	2	2	no	—
225	C₄×D₁₃	—	2	2	no	—
226	C₄×D₁₃	—	2	2	no	—
227	C₄×D₁₃	—	2	2	no	—
228	C₄×D₁₃	—	2	2	no	—
229	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
230	Dic₂₆	—	2	2	no	—
231	C₈×C₁₃	—	2	2	no	—
232	C₈×C₁₃	—	2	2	no	—
233	C₈×C₁₃	—	2	2	no	—
234	C₈×C₁₃	—	2	2	no	—
235	C₈×C₁₃	C₂×M₁₆	1	4	yes	—
236	C₈×C₁₃	#131	1	4	yes	complemented
237	#1055	—	2	2	no	—
238	#1055	—	2	2	no	—
239	#1055	—	2	2	no	—
240	#1055	—	2	2	no	—
241	#1055	C₂×M₁₆	1	4	yes	—
242	#1055	#131	1	4	yes	complemented
243	C₂×#131	—	13	2	no	—
244	C₄×#41	—	13	1	no	—
245	#446	—	13	2	no	—
246	#446	—	13	2	no	—
247	#436	—	13	2	no	—
248	#436	—	13	2	no	—
249	#435	—	13	2	no	—
250	#435	—	13	2	no	—
251	#435	—	13	2	no	—
252	#435	—	13	2	no	—
253	#431	—	13	1	no	—
254	#431	—	13	1	no	—
255	#431	—	13	1	no	—
256	#431	—	13	1	no	—
257	#431	—	13	1	no	—
258	#431	C₂×D₁₃	1	1	yes	characteristic
259	#405	—	13	2	no	—
260	#405	—	13	2	no	—
261	#405	—	13	2	no	—
262	C₄×M₁₆	—	13	1	no	—
263	C₄×M₁₆	—	13	1	no	—
264	C₄×M₁₆	—	13	1	no	—
265	C₄×M₁₆	—	13	1	no	—
266	C₄×M₁₆	—	13	1	no	—
267	C₄×M₁₆	—	13	1	no	—
268	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
269	C₂×C₄×C₈	—	13	1	no	—
270	C₂×C₄×C₈	—	13	1	no	—
271	C₂×C₄×C₈	—	13	1	no	—
272	C₂×C₄×C₈	—	13	1	no	—
273	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
274	#322	—	13	1	no	—
275	#322	—	13	1	no	—
276	#322	—	13	1	no	—
277	#322	—	13	1	no	—
278	#322	—	13	1	no	—
279	#322	—	13	1	no	—
280	#322	—	13	1	no	—
281	#322	—	13	1	no	—
282	#322	C₂×D₁₃	1	1	yes	characteristic
283	#322	C₂×D₁₃	1	1	yes	characteristic
284	C₈²	—	13	1	no	—
285	C₈²	—	13	1	no	—
286	C₈²	—	13	1	no	—
287	C₈²	—	13	1	no	—
288	C₈²	C₂×D₁₃	1	1	yes	characteristic
289	C₈²	C₂×D₁₃	1	1	yes	characteristic
290	C₂²×C₁₃	—	2	1	no	—
291	C₂²×C₁₃	—	2	1	no	—
292	C₂²×C₁₃	—	2	1	no	—
293	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
294	C₂×D₁₃	—	2	1	no	—
295	C₂×D₁₃	—	2	1	no	—
296	C₂×D₁₃	—	2	1	no	—
297	C₂×D₁₃	—	2	1	no	—
298	C₂×D₁₃	—	2	1	no	—
299	C₂×D₁₃	C₄×M₁₆	1	2	yes	—
300	C₄×C₁₃	—	2	1	no	—
301	C₄×C₁₃	—	2	1	no	—
302	C₄×C₁₃	—	2	1	no	—
303	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
304	C₄×C₁₃	C₂×#131	1	2	yes	—
305	C₄×C₁₃	C₂×#131	1	2	yes	—
306	Dic₁₃	—	2	1	no	—
307	Dic₁₃	—	2	1	no	—
308	Dic₁₃	—	2	1	no	—
309	Dic₁₃	—	2	1	no	—
310	Dic₁₃	—	2	1	no	—
311	Dic₁₃	C₄×M₁₆	1	2	yes	—
312	C₂×#41	—	13	1	no	—
313	#131	—	26	8	no	—
314	C₂×M₁₆	—	13	2	no	—
315	C₂×M₁₆	—	13	2	no	—
316	C₂×M₁₆	—	13	2	no	—
317	C₂×M₁₆	—	13	2	no	—
318	C₂×M₁₆	—	13	2	no	—
319	C₂×M₁₆	—	13	2	no	—
320	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
321	C₂²×C₈	—	13	2	no	—
322	C₂²×C₈	—	13	2	no	—
323	C₂²×C₈	—	13	2	no	—
324	C₂²×C₈	—	13	2	no	—
325	C₂²×C₈	C₄×D₁₃	1	2	yes	—
326	C₄×Q₈	—	13	1	no	—
327	C₄×Q₈	—	13	1	no	—
328	C₄×D₄	—	13	1	no	—
329	C₄×D₄	—	13	1	no	—
330	C₄×D₄	—	13	1	no	—
331	C₄×D₄	—	13	1	no	—
332	C₄×D₄	—	13	1	no	—
333	C₄×D₄	—	13	1	no	—
334	#117	—	13	1	no	—
335	#117	—	13	1	no	—
336	#117	—	13	1	no	—
337	C₂×C₄²	—	13	1	no	—
338	C₂×C₄²	—	13	1	no	—
339	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
340	C₄⋊C₈	—	13	2	no	—
341	C₄⋊C₈	—	13	2	no	—
342	C₄⋊C₈	—	13	2	no	—
343	C₄⋊C₈	—	13	2	no	—
344	C₄⋊C₈	—	13	2	no	—
345	C₄⋊C₈	C₄×D₁₃	1	2	yes	—
346	C₂²⋊C₈	—	13	2	no	—
347	C₂²⋊C₈	—	13	2	no	—
348	C₂²⋊C₈	—	13	2	no	—
349	C₂²⋊C₈	—	13	2	no	—
350	C₂²⋊C₈	—	13	2	no	—
351	C₂²⋊C₈	C₄×D₁₃	1	2	yes	—
352	#97	—	13	2	no	—
353	#97	—	13	2	no	—
354	#97	—	13	2	no	—
355	#97	—	13	2	no	—
356	#97	—	13	2	no	—
357	#97	—	13	2	no	—
358	#97	C₄×D₁₃	1	2	yes	—
359	C₄×C₈	—	13	2	no	—
360	C₄×C₈	—	13	2	no	—
361	C₄×C₈	—	13	2	no	—
362	C₄×C₈	—	13	2	no	—
363	C₄×C₈	—	13	1	no	—
364	C₄×C₈	—	13	1	no	—
365	C₄×C₈	—	13	1	no	—
366	C₄×C₈	—	13	1	no	—
367	C₄×C₈	—	13	1	no	—
368	C₄×C₈	—	13	1	no	—
369	C₄×C₈	C₄×D₁₃	1	2	yes	—
370	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
371	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
372	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
373	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
374	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
375	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
376	C₂×C₁₃	—	4	1	no	—
377	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
378	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
379	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
380	D₁₃	—	2	2	no	—
381	D₁₃	—	4	1	no	—
382	#41	—	26	4	no	—
383	C₂×Q₈	—	13	1	no	—
384	C₂×D₄	—	13	1	no	—
385	C₂×D₄	—	13	1	no	—
386	C₂×D₄	—	13	1	no	—
387	C₂²×C₄	—	13	1	no	—
388	C₂²×C₄	—	13	1	no	—
389	C₂²×C₄	—	13	1	no	—
390	C₂²×C₄	—	13	1	no	—
391	C₂²×C₄	—	13	1	no	—
392	C₂²×C₄	—	13	1	no	—
393	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
396	M₁₆	—	2	4	no	—
397	M₁₆	—	26	4	no	—
398	M₁₆	—	26	4	no	—
399	M₁₆	—	26	4	no	—
400	M₁₆	—	26	4	no	—
401	M₁₆	—	26	4	no	—
402	M₁₆	—	26	4	no	—
403	C₂×C₈	—	2	4	no	—
404	C₂×C₈	—	13	2	no	—
405	C₂×C₈	—	13	2	no	—
406	C₂×C₈	—	13	8	no	—
407	C₂×C₈	—	13	2	no	—
408	C₂×C₈	—	13	2	no	—
409	C₂×C₈	—	13	2	no	—
410	C₂×C₈	—	13	2	no	—
411	C₂×C₈	—	26	4	no	—
412	C₂×C₈	—	26	4	no	—
413	C₂×C₈	—	26	4	no	—
414	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
415	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
416	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
417	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
418	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
419	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
420	C₄⋊C₄	—	13	1	no	—
421	C₄⋊C₄	—	13	1	no	—
422	C₄⋊C₄	—	13	1	no	—
423	C₄⋊C₄	—	13	1	no	—
424	C₄⋊C₄	—	13	1	no	—
425	C₄⋊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	C₄²	—	13	1	no	—
433	C₄²	—	13	1	no	—
434	C₄²	—	13	1	no	—
435	C₄²	—	13	1	no	—
436	C₄²	—	13	1	no	—
437	C₄²	—	13	1	no	—
438	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
439	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
440	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
441	C₄²	C₂³×D₁₃	1	1	yes	characteristic
442	C₁₃	#17335	1	1	yes	characteristic, complemented, Sylow
443	C₂³	—	13	1	no	—
444	C₂³	—	13	1	no	—
445	C₂³	C₄²×D₁₃	1	1	yes	characteristic
446	Q₈	—	26	2	no	—
447	D₄	—	26	2	no	—
448	D₄	—	26	2	no	—
449	D₄	—	26	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	13	1	no	—
454	C₂×C₄	—	13	4	no	—
455	C₂×C₄	—	13	1	no	—
456	C₂×C₄	—	13	1	no	—
457	C₂×C₄	—	13	1	no	—
458	C₂×C₄	—	13	1	no	—
459	C₂×C₄	—	13	1	no	—
460	C₂×C₄	—	26	2	no	—
461	C₂×C₄	—	26	2	no	—
462	C₂×C₄	—	26	2	no	—
463	C₂×C₄	—	26	2	no	—
464	C₂×C₄	—	26	2	no	—
465	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
466	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
467	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
468	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
469	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
470	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
471	C₈	—	2	2	no	—
472	C₈	—	2	2	no	—
473	C₈	—	2	2	no	—
474	C₈	—	2	2	no	—
475	C₈	—	13	4	no	—
476	C₈	—	13	4	no	—
477	C₈	—	26	2	no	—
478	C₈	—	26	2	no	—
479	C₈	—	26	2	no	—
480	C₈	—	26	2	no	—
481	C₈	#88155	1	4	yes	complemented
482	C₈	M₁₆×D₁₃	1	4	yes	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	13	2	no	—
487	C₂²	—	26	1	no	—
488	C₂²	—	26	1	no	—
489	C₂²	—	26	1	no	—
490	C₂²	—	26	1	no	—
491	C₂²	—	26	1	no	—
492	C₂²	C₂×C₄²×D₁₃	1	1	yes	characteristic
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	13	2	no	—
497	C₄	—	26	1	no	—
498	C₄	—	26	1	no	—
499	C₄	—	26	1	no	—
500	C₄	—	26	1	no	—
501	C₄	—	26	1	no	—
502	C₄	C₂×#88155	1	2	yes	—
503	C₄	C₂×M₁₆×D₁₃	1	2	yes	—
504	C₄	D₁₃×#131	1	2	yes	—
505	C₂	—	4	1	no	—
506	C₂	—	26	2	no	—
507	C₂	—	52	1	no	—
508	C₂	C₄×M₁₆×D₁₃	1	1	yes	characteristic
509	C₂	C₄×#88155	1	1	yes	characteristic
510	C₂	#13123258	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈	C₂²×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Frattini	C₄²	C₂³×D₁₃
Fitting	C₈×C₁₃×M₁₆	C₂
prime radical	C₂×#6127	C₂×C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₈×M₁₆	D₁₃
hypocenter	C₁₃	#17335
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄×C₈ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
4. #13113140	C₂	semidirect
5. #13113139	C₂	semidirect
6. #13113132	C₂	semidirect
7. #13113131	C₂	semidirect
8. #13113124	C₂	semidirect
9. #13113122	C₂	semidirect
10. #13113118	C₂	semidirect
11. C₈×#6099	C₂	semidirect
12. C₈×#6094	C₂	semidirect
13. C₈×#6094	C₂	semidirect
14. C₈²×D₁₃	C₂	semidirect
15. C₈×C₁₃×M₁₆	C₂	semidirect
187. C₈×D₁₃	M₁₆	semidirect
201. C₈×M₁₆	D₁₃	semidirect
236. C₈×C₁₃	#131	semidirect
242. #1055	#131	semidirect
442. C₁₃	#17335	semidirect
481. C₈	#88155	semidirect

Maximal subgroups

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

subgroup	index
#13123800	2
#13123798	2
C₄×#88155	2
#13113140	2
#13113139	2
#13113132	2
#13113131	2
#13113124	2
#13113122	2
#13113118	2
C₈×#6099	2
C₈×#6094	2
C₈²×D₁₃	2
C₈×C₁₃×M₁₆	2
#17335	13