Subgroups — #15828596

Order 3328.

718 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123798	C₂	1	1	yes	maximal, characteristic
2	C₈×#6127	C₂	1	1	yes	maximal, characteristic
3	#13123475	C₂	1	1	yes	maximal, characteristic
4	#13113137	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113136	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113133	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113132	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113128	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113127	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113127	C₂	1	1	yes	maximal, characteristic, complemented
11	#13113124	C₂	1	1	yes	maximal, characteristic, complemented
12	#13113124	C₂	1	1	yes	maximal, characteristic, complemented
13	#13113115	C₂	1	1	yes	maximal, characteristic, complemented
14	D₁₃×#322	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1451	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#6127	C₂²	1	1	yes	characteristic
17	C₁₃×#431	C₂²	1	1	yes	characteristic
18	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	#11718789	C₄	1	2	yes	—
21	#11718788	C₄	1	2	yes	—
22	C₈×C₂²⋊D₁₃	C₄	1	2	yes	—
23	C₈×C₂²⋊D₁₃	C₄	1	2	yes	—
24	#11718586	C₂²	1	1	yes	characteristic
25	#11718586	C₂²	1	1	yes	characteristic
26	#11718586	C₂²	1	1	yes	characteristic
27	#11718501	C₄	1	2	yes	—
28	#11718500	C₄	1	2	yes	—
29	#11718388	C₄	1	2	yes	—
30	#11718381	C₄	1	2	yes	—
31	#11718367	C₄	1	2	yes	—
32	#11718362	C₄	1	2	yes	—
33	C₄×#6094	C₂²	1	1	yes	characteristic
34	C₄×#6094	C₂²	1	1	yes	characteristic
35	C₈×D₅₂	C₄	1	2	yes	—
36	#11718346	C₂²	1	1	yes	characteristic
37	#11718346	C₂²	1	1	yes	characteristic
38	#11718346	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	C₄×C₈×D₁₃	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	C₈×Dic₂₆	C₄	1	2	yes	—
47	C₁₃×#322	C₂²	1	1	yes	characteristic
48	C₁₃×#322	C₂²	1	1	yes	characteristic
49	C₁₃×#322	C₂²	1	1	yes	characteristic
50	C₁₃×#322	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	#11718046	C₂²	1	1	yes	characteristic
60	#11718046	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×#6094	C₂×C₄	1	2	yes	—
73	C₂×#6094	C₂×C₄	1	2	yes	—
74	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
75	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
76	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
77	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
78	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
79	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
80	#88126	C₂×C₄	1	1	yes	characteristic
81	#88126	C₂×C₄	1	1	yes	characteristic
82	C₄²×D₁₃	C₂³	1	1	yes	characteristic
83	C₄²×D₁₃	C₂³	1	1	yes	characteristic
84	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
85	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
86	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
87	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
88	C₁₃×#97	C₂×C₄	1	2	yes	—
89	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
90	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²⋊#1055	C₂×C₄	1	2	yes	—
97	C₂²⋊#1055	C₂×C₄	1	2	yes	—
98	C₂²⋊#1055	C₂×C₄	1	2	yes	—
99	#88060	C₂×C₄	1	2	yes	—
100	#88060	C₂×C₄	1	2	yes	—
101	#88060	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	#88055	C₂×C₄	1	2	yes	—
106	#88055	C₂×C₄	1	2	yes	—
107	#88054	C₂×C₄	1	2	yes	—
108	#88054	C₂×C₄	1	2	yes	—
109	#88054	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	C₈×Dic₁₃	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	C₄⋊#1055	C₂×C₄	1	2	yes	—
118	C₄⋊#1055	C₂×C₄	1	2	yes	—
119	C₄⋊#1055	C₂×C₄	1	2	yes	—
120	C₄×#1055	C₂³	1	1	yes	characteristic
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	#17329	—	13	1	no	maximal, Sylow
127	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₂²⋊D₁₃	C₄²	1	1	yes	characteristic
131	C₂×C₂²⋊D₁₃	C₄²	1	1	yes	characteristic
132	#6127	—	2	4	no	—
133	C₂×D₅₂	C₄²	1	1	yes	characteristic
134	C₂×C₄×D₁₃	C₂²×C₄	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×Dic₂₆	C₄²	1	1	yes	characteristic
141	C₁₃×M₁₆	—	4	2	no	—
142	C₂×C₈×C₁₃	—	4	2	no	—
143	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
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	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
153	C₂²⋊Dic₁₃	C₄²	1	1	yes	characteristic
154	C₂²⋊Dic₁₃	C₄²	1	1	yes	characteristic
155	#6103	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	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
160	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
161	#6101	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	C₄×Dic₁₃	C₂²×C₄	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	C₂×#1055	C₂²×C₄	1	2	yes	—
172	C₂×#1055	C₂²×C₄	1	2	yes	—
173	C₂×#1055	C₂²×C₄	1	2	yes	—
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	#6094	—	2	4	no	—
178	#6094	—	4	2	no	—
179	C₈×D₁₃	—	2	4	no	—
180	C₈×D₁₃	—	4	2	no	—
181	C₈×D₁₃	—	4	2	no	—
182	C₈×D₁₃	—	4	2	no	—
183	#2965	—	13	1	no	—
184	C₈×#41	—	13	1	no	—
185	#2922	—	13	1	no	—
186	#1454	—	13	1	no	—
187	#1454	—	13	1	no	—
188	#1453	—	13	1	no	—
189	#1453	—	13	1	no	—
190	#1452	—	13	1	no	—
191	#1452	—	13	1	no	—
192	#1452	—	13	1	no	—
193	#1451	—	13	1	no	—
194	#1451	—	13	1	no	—
195	#1451	D₁₃	1	1	yes	characteristic, complemented
196	C₈×M₁₆	—	13	1	no	—
197	C₂×#322	—	13	1	no	—
198	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
199	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
200	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
210	C₂²⋊D₁₃	—	2	2	no	—
211	C₂²⋊D₁₃	—	2	2	no	—
212	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
213	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
214	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
215	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
216	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
217	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
218	D₅₂	—	2	2	no	—
219	C₄×D₁₃	—	2	2	no	—
220	C₄×D₁₃	—	2	2	no	—
221	C₄×D₁₃	—	2	2	no	—
222	C₄×D₁₃	—	2	2	no	—
223	C₄×D₁₃	—	2	2	no	—
224	C₄×D₁₃	#131	1	4	yes	—
225	Dic₂₆	—	2	2	no	—
226	C₈×C₁₃	—	2	2	no	—
227	C₈×C₁₃	—	2	2	no	—
228	C₈×C₁₃	—	2	2	no	—
229	C₈×C₁₃	—	2	2	no	—
230	C₈×C₁₃	—	2	2	no	—
231	C₈×C₁₃	—	2	2	no	—
232	#1055	—	2	2	no	—
233	#1055	—	2	2	no	—
234	#1055	—	2	2	no	—
235	#1055	—	2	2	no	—
236	#1055	—	2	2	no	—
237	#1055	—	2	2	no	—
238	C₄×#41	—	13	1	no	—
239	#446	—	13	2	no	—
240	C₈×Q₈	—	13	2	no	—
241	#436	—	13	2	no	—
242	#435	—	13	2	no	—
243	#435	—	13	2	no	—
244	C₈×D₄	—	13	2	no	—
245	C₈×D₄	—	13	2	no	—
246	C₈×D₄	—	13	2	no	—
247	#433	—	13	2	no	—
248	#433	—	13	2	no	—
249	#431	—	13	1	no	—
250	#431	—	13	1	no	—
251	#431	—	13	1	no	—
252	#431	—	13	1	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	#424	—	13	2	no	—
260	#408	—	13	2	no	—
261	C₄×M₁₆	—	13	1	no	—
262	C₄×M₁₆	—	13	1	no	—
263	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
264	C₂×C₄×C₈	—	13	1	no	—
265	C₂×C₄×C₈	—	13	1	no	—
266	C₂×C₄×C₈	—	13	1	no	—
267	C₂×C₄×C₈	—	13	1	no	—
268	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
269	#322	—	13	1	no	—
270	#322	—	13	1	no	—
271	#322	—	13	1	no	—
272	#322	—	13	1	no	—
273	#322	—	13	1	no	—
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	C₂×D₁₃	1	1	yes	characteristic
280	#322	C₂×D₁₃	1	1	yes	characteristic
281	#322	C₂×D₁₃	1	1	yes	characteristic
282	#322	C₂×D₁₃	1	1	yes	characteristic
283	C₈²	—	13	1	no	—
284	C₈²	—	13	1	no	—
285	C₂²×C₁₃	—	2	1	no	—
286	C₂²×C₁₃	—	2	1	no	—
287	C₂²×C₁₃	—	2	1	no	—
288	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
289	C₂×D₁₃	—	2	1	no	—
290	C₂×D₁₃	—	2	1	no	—
291	C₂×D₁₃	—	2	1	no	—
292	C₂×D₁₃	—	2	1	no	—
293	C₂×D₁₃	—	2	1	no	—
294	C₂×D₁₃	#405	1	2	yes	—
295	C₄×C₁₃	—	2	1	no	—
296	C₄×C₁₃	—	2	1	no	—
297	C₄×C₁₃	—	2	1	no	—
298	C₄×C₁₃	C₂×#131	1	2	yes	—
299	C₄×C₁₃	#568	1	2	yes	—
300	C₄×C₁₃	#568	1	2	yes	—
301	Dic₁₃	—	2	1	no	—
302	Dic₁₃	—	2	1	no	—
303	Dic₁₃	—	2	1	no	—
304	Dic₁₃	—	2	1	no	—
305	Dic₁₃	—	2	1	no	—
306	Dic₁₃	#405	1	2	yes	—
307	C₂×#41	—	13	1	no	—
308	C₂×M₁₆	—	13	2	no	—
309	C₂×M₁₆	—	13	2	no	—
310	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
311	C₂²×C₈	—	13	2	no	—
312	C₂²×C₈	—	13	2	no	—
313	C₂²×C₈	—	13	2	no	—
314	C₂²×C₈	—	13	2	no	—
315	C₂²×C₈	C₄×D₁₃	1	2	yes	—
316	C₄×Q₈	—	13	1	no	—
317	C₄×Q₈	—	13	1	no	—
318	C₄×D₄	—	13	1	no	—
319	C₄×D₄	—	13	1	no	—
320	C₄×D₄	—	13	1	no	—
321	C₄×D₄	—	13	1	no	—
322	C₄×D₄	—	13	1	no	—
323	C₄×D₄	—	13	1	no	—
324	#117	—	13	1	no	—
325	#117	—	13	1	no	—
326	#117	—	13	1	no	—
327	C₂×C₄²	—	13	1	no	—
328	C₂×C₄²	—	13	1	no	—
329	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
330	C₄⋊C₈	—	13	2	no	—
331	C₄⋊C₈	—	13	2	no	—
332	C₄⋊C₈	—	13	2	no	—
333	C₄⋊C₈	—	13	2	no	—
334	C₄⋊C₈	—	13	2	no	—
335	C₄⋊C₈	—	13	2	no	—
336	C₄⋊C₈	—	13	2	no	—
337	C₄⋊C₈	—	13	2	no	—
338	C₄⋊C₈	—	13	2	no	—
339	C₄⋊C₈	C₄×D₁₃	1	2	yes	—
340	C₂²⋊C₈	—	13	2	no	—
341	C₂²⋊C₈	—	13	2	no	—
342	C₂²⋊C₈	—	13	2	no	—
343	C₂²⋊C₈	—	13	2	no	—
344	C₂²⋊C₈	—	13	2	no	—
345	C₂²⋊C₈	—	13	2	no	—
346	C₂²⋊C₈	—	13	2	no	—
347	C₂²⋊C₈	—	13	2	no	—
348	C₂²⋊C₈	—	13	2	no	—
349	C₂²⋊C₈	C₄×D₁₃	1	2	yes	—
350	#97	—	13	2	no	—
351	#97	—	13	2	no	—
352	#97	C₄×D₁₃	1	2	yes	—
353	C₄×C₈	—	13	2	no	—
354	C₄×C₈	—	13	2	no	—
355	C₄×C₈	—	13	2	no	—
356	C₄×C₈	—	13	2	no	—
357	C₄×C₈	—	13	1	no	—
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	C₄×D₁₃	1	2	yes	—
364	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
365	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
366	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
367	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
368	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
369	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
370	C₂×C₁₃	—	4	1	no	—
371	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
372	C₂×C₁₃	#2875	1	1	yes	characteristic
373	C₂×C₁₃	#2875	1	1	yes	characteristic
374	D₁₃	—	2	2	no	—
375	D₁₃	—	4	1	no	—
376	#41	—	26	4	no	—
377	C₂×Q₈	—	13	1	no	—
378	C₂×D₄	—	13	1	no	—
379	C₂×D₄	—	13	1	no	—
380	C₂×D₄	—	13	1	no	—
381	C₂²×C₄	—	13	1	no	—
382	C₂²×C₄	—	13	1	no	—
383	C₂²×C₄	—	13	1	no	—
384	C₂²×C₄	—	13	1	no	—
385	C₂²×C₄	—	13	1	no	—
386	C₂²×C₄	—	13	1	no	—
387	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
388	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
390	M₁₆	—	4	2	no	—
391	M₁₆	—	26	4	no	—
392	M₁₆	—	52	2	no	—
393	C₂×C₈	—	4	2	no	—
394	C₂×C₈	—	13	2	no	—
395	C₂×C₈	—	13	2	no	—
396	C₂×C₈	—	13	2	no	—
397	C₂×C₈	—	13	2	no	—
398	C₂×C₈	—	13	2	no	—
399	C₂×C₈	—	13	2	no	—
400	C₂×C₈	—	26	4	no	—
401	C₂×C₈	—	52	2	no	—
402	C₂×C₈	—	52	2	no	—
403	C₂×C₈	—	52	2	no	—
404	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
405	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
406	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
407	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
408	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
409	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
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	—	13	1	no	—
415	C₄⋊C₄	—	13	1	no	—
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	C₄²	—	13	1	no	—
423	C₄²	—	13	1	no	—
424	C₄²	—	13	1	no	—
425	C₄²	—	13	1	no	—
426	C₄²	—	13	1	no	—
427	C₄²	—	13	1	no	—
428	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
429	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
430	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
431	C₄²	C₂³×D₁₃	1	1	yes	characteristic
432	C₁₃	#17329	1	1	yes	characteristic, complemented, Sylow
433	C₂³	—	13	1	no	—
434	C₂³	—	13	1	no	—
435	C₂³	C₄²×D₁₃	1	1	yes	characteristic
436	Q₈	—	26	2	no	—
437	D₄	—	26	2	no	—
438	D₄	—	26	2	no	—
439	D₄	—	26	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	13	1	no	—
444	C₂×C₄	—	13	4	no	—
445	C₂×C₄	—	13	1	no	—
446	C₂×C₄	—	13	1	no	—
447	C₂×C₄	—	13	1	no	—
448	C₂×C₄	—	13	1	no	—
449	C₂×C₄	—	13	1	no	—
450	C₂×C₄	—	26	2	no	—
451	C₂×C₄	—	26	2	no	—
452	C₂×C₄	—	26	2	no	—
453	C₂×C₄	—	26	2	no	—
454	C₂×C₄	—	26	2	no	—
455	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
456	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
457	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
458	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
459	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
460	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	—	2	2	no	—
463	C₈	—	2	2	no	—
464	C₈	—	2	2	no	—
465	C₈	—	2	2	no	—
466	C₈	—	2	2	no	—
467	C₈	—	26	2	no	—
468	C₈	—	26	2	no	—
469	C₈	—	26	2	no	—
470	C₈	—	26	2	no	—
471	C₈	—	26	2	no	—
472	C₈	—	26	2	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	13	2	no	—
477	C₂²	—	26	1	no	—
478	C₂²	—	26	1	no	—
479	C₂²	—	26	1	no	—
480	C₂²	—	26	1	no	—
481	C₂²	—	26	1	no	—
482	C₂²	C₂×C₄²×D₁₃	1	1	yes	characteristic
483	C₄	—	2	1	no	—
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	13	2	no	—
487	C₄	—	26	1	no	—
488	C₄	—	26	1	no	—
489	C₄	—	26	1	no	—
490	C₄	—	26	1	no	—
491	C₄	—	26	1	no	—
492	C₄	#11719450	1	2	yes	—
493	C₄	#11719450	1	2	yes	—
494	C₄	D₁₃×#131	1	2	yes	—
495	C₂	—	4	1	no	—
496	C₂	—	26	2	no	—
497	C₂	—	52	1	no	—
498	C₂	D₁₃×#405	1	1	yes	characteristic
499	C₂	#13123261	1	1	yes	characteristic
500	C₂	#13123265	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#1451	C₂
prime radical	C₂×#6127	C₂×C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1451	D₁₃
hypocenter	C₁₃	#17329
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ #1451

Complements

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

N	H ≅ G/N	type
4. #13113137	C₂	semidirect
5. #13113136	C₂	semidirect
6. #13113133	C₂	semidirect
7. #13113132	C₂	semidirect
8. #13113128	C₂	semidirect
9. #13113127	C₂	semidirect
10. #13113127	C₂	semidirect
11. #13113124	C₂	semidirect
12. #13113124	C₂	semidirect
13. #13113115	C₂	semidirect
14. D₁₃×#322	C₂	semidirect
15. C₁₃×#1451	C₂	semidirect
195. #1451	D₁₃	semidirect
432. C₁₃	#17329	semidirect

Maximal subgroups

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

subgroup	index
#13123798	2
C₈×#6127	2
#13123475	2
#13113137	2
#13113136	2
#13113133	2
#13113132	2
#13113128	2
#13113127	2
#13113124	2
#13113115	2
D₁₃×#322	2
C₁₃×#1451	2
#17329	13