Subgroups — #15860415

Order 3328.

1042 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718369	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718350	C₂	1	1	yes	maximal, characteristic
3	#13117175	C₂	1	1	yes	maximal, characteristic
4	#13114588	C₂	1	1	yes	maximal, characteristic, complemented
5	#13114586	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114586	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114584	C₂	1	1	yes	maximal, characteristic, complemented
8	#13114583	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114581	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114580	C₂	1	1	yes	maximal, characteristic, complemented
11	#13114531	C₂	1	1	yes	maximal, characteristic
12	#13114531	C₂	1	1	yes	maximal, characteristic
13	#13114528	C₂	1	1	yes	maximal, characteristic
14	D₁₃×#336	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1746	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#6094	C₂²	1	1	yes	characteristic
17	C₂²×#6094	C₂²	1	1	yes	characteristic
18	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
20	C₂×#88126	C₂²	1	1	yes	characteristic
21	C₂×#88126	C₂²	1	1	yes	characteristic
22	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#376	C₂²	1	1	yes	characteristic
26	C₂×#88055	C₂²	1	1	yes	characteristic
27	C₂×#88055	C₂²	1	1	yes	characteristic
28	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
30	#11718593	C₂²	1	1	yes	characteristic
31	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
32	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
33	C₂×#88043	C₂²	1	1	yes	characteristic
34	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
35	#11718369	C₄	1	8	yes	complemented
36	#11718350	C₄	1	8	yes	complemented
37	#11718327	C₄	1	2	yes	—
38	#11718327	C₄	1	2	yes	—
39	#11718310	C₄	1	2	yes	—
40	#11718310	C₄	1	2	yes	—
41	C₁₃×#336	C₂²	1	1	yes	characteristic
42	C₁₃×#336	C₂²	1	1	yes	characteristic
43	C₁₃×#336	C₂²	1	1	yes	characteristic
44	C₁₃×#336	C₂²	1	1	yes	characteristic
45	#11718142	C₂²	1	1	yes	characteristic
46	#11718142	C₂²	1	1	yes	characteristic
47	#11718142	C₂²	1	1	yes	characteristic
48	#11718142	C₂²	1	1	yes	characteristic
49	#11718142	C₂²	1	1	yes	characteristic
50	#11718142	C₂²	1	1	yes	characteristic
51	#11718142	C₂²	1	1	yes	characteristic
52	#11718142	C₂²	1	1	yes	characteristic
53	#11718116	C₂²	1	1	yes	characteristic
54	#11718116	C₂²	1	1	yes	characteristic
55	#11718116	C₂²	1	1	yes	characteristic
56	#11718116	C₂²	1	1	yes	characteristic
57	C₂²×C₄×D₁₃	C₂×C₄	1	2	yes	—
58	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×#6103	C₂×C₄	1	2	yes	—
67	C₂×#6103	C₂×C₄	1	1	yes	characteristic
68	C₂×#6103	C₂×C₄	1	1	yes	characteristic
69	C₂×#6101	C₂×C₄	1	2	yes	—
70	C₂×#6101	C₂×C₄	1	1	yes	characteristic
71	C₂×#6101	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
73	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
74	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
75	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
76	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
77	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
78	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
79	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
80	C₂²×#1055	C₂³	1	1	yes	characteristic
81	C₂²×#1055	C₂³	1	1	yes	characteristic
82	C₂²×#1055	C₂³	1	1	yes	characteristic
83	C₂²×#1055	C₂³	1	1	yes	characteristic
84	C₂×#6094	—	2	2	no	—
85	C₂×#6094	—	2	2	no	—
86	C₂×#6094	—	2	2	no	—
87	C₂×#6094	—	2	2	no	—
88	C₂×#6094	C₂×C₄	1	4	yes	—
89	C₂×#6094	C₂×C₄	1	4	yes	—
90	C₂×C₈×D₁₃	—	2	2	no	—
91	C₂×C₈×D₁₃	—	2	2	no	—
92	C₂×C₈×D₁₃	—	2	2	no	—
93	C₂×C₈×D₁₃	—	2	2	no	—
94	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
95	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
96	#88126	—	2	2	no	—
97	#88126	—	2	2	no	—
98	#88126	C₂×C₄	1	4	yes	—
99	#88126	C₂×C₄	1	4	yes	—
100	C₄²×D₁₃	—	2	2	no	—
101	C₄²×D₁₃	—	2	2	no	—
102	C₁₃×#97	C₂×C₄	1	4	yes	complemented
103	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
104	C₁₃×#95	C₂×C₄	1	2	yes	—
105	C₁₃×#95	C₂×C₄	1	2	yes	—
106	#88071	C₂×C₄	1	2	yes	—
107	#88071	C₂×C₄	1	2	yes	—
108	#88055	C₂×C₄	1	4	yes	complemented
109	#88055	C₂×C₄	1	4	yes	complemented
110	C₈×Dic₁₃	C₂×C₄	1	4	yes	complemented
111	C₈×Dic₁₃	C₂×C₄	1	4	yes	complemented
112	#88043	C₂×C₄	1	4	yes	complemented
113	C₄×#1055	C₂×C₄	1	4	yes	complemented
114	#20368	—	13	1	no	maximal, Sylow
115	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
122	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
125	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₄×D₁₃	—	2	4	no	—
127	C₂×C₄×D₁₃	—	2	4	no	—
128	C₂×C₄×D₁₃	—	4	2	no	—
129	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
130	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
131	C₂×C₄×D₁₃	#41	1	2	yes	—
132	C₂×C₄×D₁₃	#41	1	2	yes	—
133	C₂×C₄×D₁₃	#41	1	2	yes	—
134	C₂×C₄×D₁₃	#41	1	2	yes	—
135	C₂×C₈×C₁₃	—	2	1	no	—
136	C₂×C₈×C₁₃	—	2	1	no	—
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	—	2	1	no	—
140	C₂×C₈×C₁₃	—	2	1	no	—
141	C₂×C₈×C₁₃	—	2	1	no	—
142	C₂×C₈×C₁₃	—	2	1	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	C₄²×C₁₃	—	2	1	no	—
148	C₄²×C₁₃	—	2	1	no	—
149	C₄²×C₁₃	—	2	1	no	—
150	C₄²×C₁₃	—	2	1	no	—
151	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
152	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
153	#6103	—	2	4	no	—
154	#6103	C₄²	1	4	yes	—
155	#6103	C₄²	1	4	yes	—
156	#6101	—	2	4	no	—
157	#6101	C₄²	1	4	yes	—
158	#6101	C₄²	1	4	yes	—
159	C₄×Dic₁₃	—	2	1	no	—
160	C₄×Dic₁₃	—	2	1	no	—
161	C₄×Dic₁₃	—	2	1	no	—
162	C₄×Dic₁₃	—	2	1	no	—
163	C₄×Dic₁₃	—	2	4	no	—
164	C₄×Dic₁₃	—	2	4	no	—
165	C₄×Dic₁₃	—	2	4	no	—
166	C₄×Dic₁₃	—	4	2	no	—
167	C₄×Dic₁₃	—	4	2	no	—
168	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
169	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
170	C₂×#1055	—	2	1	no	—
171	C₂×#1055	—	2	1	no	—
172	C₂×#1055	—	2	1	no	—
173	C₂×#1055	—	2	1	no	—
174	C₂×#1055	—	2	1	no	—
175	C₂×#1055	—	2	1	no	—
176	C₂×#1055	—	2	1	no	—
177	C₂×#1055	—	2	1	no	—
178	C₂×#1055	C₂²×C₄	1	2	yes	—
179	C₂×#1055	C₂²×C₄	1	2	yes	—
180	C₂×#1055	C₂²×C₄	1	2	yes	—
181	C₂×#1055	C₂²×C₄	1	2	yes	—
182	#6094	—	2	8	no	—
183	#6094	—	2	8	no	—
184	C₈×D₁₃	—	2	8	no	—
185	C₈×D₁₃	—	2	8	no	—
186	C₂×#405	—	13	1	no	—
187	C₂×#405	—	13	1	no	—
188	C₄×#117	—	13	1	no	—
189	#1746	—	13	1	no	—
190	#1746	—	13	1	no	—
191	#1746	—	13	1	no	—
192	#1746	D₁₃	1	1	yes	characteristic, complemented
193	#1745	—	13	1	no	—
194	#1745	—	13	1	no	—
195	#1744	—	13	1	no	—
196	#1744	—	13	1	no	—
197	#1729	—	13	1	no	—
198	#1729	—	13	1	no	—
199	#1728	—	13	1	no	—
200	C₂×#336	—	13	1	no	—
201	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
202	C₂²×D₁₃	—	2	2	no	—
203	C₂²×D₁₃	—	2	2	no	—
204	C₂²×D₁₃	C₂×C₄²	1	2	yes	—
205	C₂²×D₁₃	#117	1	2	yes	—
206	C₂²×D₁₃	#117	1	2	yes	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
216	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
217	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
223	C₂×Dic₁₃	—	2	2	no	—
224	C₂×Dic₁₃	—	2	2	no	—
225	C₂×Dic₁₃	—	2	2	no	—
226	C₂×Dic₁₃	—	2	2	no	—
227	C₂×Dic₁₃	—	2	2	no	—
228	C₂×Dic₁₃	—	2	2	no	—
229	C₂×Dic₁₃	—	2	2	no	—
230	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
231	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
232	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
233	C₂×Dic₁₃	#117	1	2	yes	—
234	C₂×Dic₁₃	#117	1	2	yes	—
235	C₂×Dic₁₃	#131	1	4	yes	—
236	C₄×D₁₃	—	4	8	no	—
237	C₄×D₁₃	#117	1	4	yes	—
238	C₄×D₁₃	#117	1	4	yes	—
239	C₄×D₁₃	#117	1	4	yes	—
240	C₄×D₁₃	#117	1	4	yes	—
241	C₈×C₁₃	—	2	2	no	—
242	C₈×C₁₃	—	2	2	no	—
243	C₈×C₁₃	—	2	2	no	—
244	C₈×C₁₃	—	2	2	no	—
245	#1055	—	2	2	no	—
246	#1055	—	2	2	no	—
247	#1055	—	2	2	no	—
248	#1055	—	2	2	no	—
249	C₂²×M₁₆	—	13	1	no	—
250	C₂²×M₁₆	—	13	1	no	—
251	C₂³×C₈	—	13	1	no	—
252	C₂³×C₈	—	13	1	no	—
253	C₂×#117	—	13	1	no	—
254	C₂×#117	—	13	1	no	—
255	C₂²×C₄²	—	13	1	no	—
256	#405	—	13	8	no	—
257	#405	—	13	8	no	—
258	C₂×#97	—	13	1	no	—
259	C₂×#97	—	13	1	no	—
260	C₂×#97	—	13	1	no	—
261	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
262	C₂×C₄×C₈	—	13	1	no	—
263	C₂×C₄×C₈	—	13	1	no	—
264	C₂×C₄×C₈	—	13	1	no	—
265	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
266	C₄×C₄⋊C₄	—	13	2	no	—
267	C₄×C₄⋊C₄	—	13	2	no	—
268	C₄×C₂²⋊C₄	—	13	2	no	—
269	C₄×C₂²⋊C₄	—	13	2	no	—
270	#376	—	13	1	no	—
271	#376	C₂×D₁₃	1	1	yes	characteristic
272	C₄³	—	13	1	no	—
273	C₄³	—	13	1	no	—
274	#336	—	13	1	no	—
275	#336	—	13	1	no	—
276	#336	—	13	1	no	—
277	#336	—	13	1	no	—
278	#336	—	13	1	no	—
279	#336	—	13	1	no	—
280	#336	—	13	1	no	—
281	#336	—	13	1	no	—
282	#336	—	13	1	no	—
283	#336	—	13	1	no	—
284	#336	—	13	1	no	—
285	#336	—	13	1	no	—
286	#336	C₂×D₁₃	1	1	yes	characteristic
287	#336	C₂×D₁₃	1	1	yes	characteristic
288	#336	C₂×D₁₃	1	1	yes	characteristic
289	#336	C₂×D₁₃	1	1	yes	characteristic
290	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
291	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
292	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
293	C₂²×C₁₃	C₂×#131	1	2	yes	—
294	C₂²×C₁₃	#568	1	2	yes	—
295	C₂×D₁₃	—	2	2	no	—
296	C₂×D₁₃	—	2	2	no	—
297	C₂×D₁₃	—	2	4	no	—
298	C₂×D₁₃	—	2	4	no	—
299	C₂×D₁₃	#376	1	4	yes	—
300	C₄×C₁₃	—	2	2	no	—
301	C₄×C₁₃	—	2	2	no	—
302	C₄×C₁₃	—	4	2	no	—
303	C₄×C₁₃	—	4	2	no	—
304	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
305	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
306	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
307	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
308	Dic₁₃	—	2	2	no	—
309	Dic₁₃	—	2	2	no	—
310	Dic₁₃	—	2	4	no	—
311	Dic₁₃	—	4	2	no	—
312	Dic₁₃	#376	1	4	yes	—
313	C₂³×C₄	—	13	1	no	—
314	C₂³×C₄	—	13	2	no	—
315	C₂×M₁₆	—	13	4	no	—
316	C₂×M₁₆	—	13	4	no	—
317	C₂×M₁₆	—	26	2	no	—
318	C₂×M₁₆	—	26	2	no	—
319	C₂×M₁₆	—	26	2	no	—
320	C₂×M₁₆	—	26	2	no	—
321	C₂²×C₈	—	13	1	no	—
322	C₂²×C₈	—	13	1	no	—
323	C₂²×C₈	—	13	1	no	—
324	C₂²×C₈	—	13	1	no	—
325	C₂²×C₈	—	13	4	no	—
326	C₂²×C₈	—	13	4	no	—
327	C₂²×C₈	—	26	2	no	—
328	C₂²×C₈	—	26	2	no	—
329	C₂²×C₈	—	26	2	no	—
330	C₂²×C₈	—	26	2	no	—
331	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
332	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
333	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
334	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
335	#117	—	13	4	no	—
336	#117	—	13	4	no	—
337	#117	—	26	2	no	—
338	#117	—	26	2	no	—
339	C₂×C₄⋊C₄	—	13	1	no	—
340	C₂×C₄⋊C₄	—	13	1	no	—
341	C₂×C₄⋊C₄	—	13	2	no	—
342	C₂×C₂²⋊C₄	—	13	1	no	—
343	C₂×C₂²⋊C₄	—	13	1	no	—
344	C₂×C₂²⋊C₄	—	13	2	no	—
345	C₂×C₄²	—	13	1	no	—
346	C₂×C₄²	—	13	2	no	—
347	C₂×C₄²	—	13	2	no	—
348	C₂×C₄²	—	13	2	no	—
349	C₂×C₄²	—	13	1	no	—
350	C₂×C₄²	—	13	1	no	—
351	C₂×C₄²	—	13	2	no	—
352	C₂×C₄²	—	13	2	no	—
353	C₂×C₄²	—	26	2	no	—
354	C₂×C₄²	—	26	2	no	—
355	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
356	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
357	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
358	#97	—	13	4	no	—
359	#97	—	13	4	no	—
360	#97	—	13	4	no	—
361	#97	C₄×D₁₃	1	4	yes	complemented
362	C₄×C₈	—	13	4	no	—
363	C₄×C₈	—	13	4	no	—
364	C₄×C₈	—	13	4	no	—
365	C₄×C₈	C₄×D₁₃	1	4	yes	complemented
366	#95	—	13	2	no	—
367	#95	—	13	2	no	—
368	#95	C₄×D₁₃	1	2	yes	—
369	#95	C₄×D₁₃	1	2	yes	—
370	C₂×C₁₃	C₂×#376	1	1	yes	characteristic
371	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
372	C₂×C₁₃	#2875	1	1	yes	characteristic
373	C₂×C₁₃	#2924	1	2	yes	—
374	C₂×C₁₃	#2925	1	2	yes	—
375	D₁₃	—	2	4	no	—
376	C₂⁴	—	13	1	no	—
377	C₂²×C₄	—	13	1	no	—
378	C₂²×C₄	—	13	2	no	—
379	C₂²×C₄	—	13	2	no	—
380	C₂²×C₄	—	13	2	no	—
381	C₂²×C₄	—	13	2	no	—
382	C₂²×C₄	—	13	2	no	—
383	C₂²×C₄	—	13	2	no	—
384	C₂²×C₄	—	13	1	no	—
385	C₂²×C₄	—	13	1	no	—
386	C₂²×C₄	—	13	2	no	—
387	C₂²×C₄	—	13	2	no	—
388	C₂²×C₄	—	26	4	no	—
389	C₂²×C₄	—	26	4	no	—
390	C₂²×C₄	—	52	2	no	—
391	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
392	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
393	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
396	M₁₆	—	26	8	no	—
397	M₁₆	—	26	8	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	13	2	no	—
407	C₂×C₈	—	13	2	no	—
408	C₂×C₈	—	13	2	no	—
409	C₂×C₈	—	13	2	no	—
410	C₂×C₈	—	26	8	no	—
411	C₂×C₈	—	26	8	no	—
412	C₂×C₈	—	26	1	no	—
413	C₂×C₈	—	26	1	no	—
414	C₂×C₈	—	26	1	no	—
415	C₂×C₈	—	26	1	no	—
416	C₂×C₈	—	26	1	no	—
417	C₂×C₈	—	26	1	no	—
418	C₂×C₈	—	26	1	no	—
419	C₂×C₈	—	26	1	no	—
420	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
421	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
422	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
423	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
424	C₄⋊C₄	—	13	4	no	—
425	C₄⋊C₄	—	13	4	no	—
426	C₄⋊C₄	—	26	4	no	—
427	C₂²⋊C₄	—	13	4	no	—
428	C₂²⋊C₄	—	13	4	no	—
429	C₂²⋊C₄	—	26	4	no	—
430	C₄²	—	2	1	no	—
431	C₄²	—	2	1	no	—
432	C₄²	—	2	1	no	—
433	C₄²	—	2	1	no	—
434	C₄²	—	13	2	no	—
435	C₄²	—	13	2	no	—
436	C₄²	—	26	4	no	—
437	C₄²	—	26	4	no	—
438	C₄²	—	26	4	no	—
439	C₄²	—	26	1	no	—
440	C₄²	—	26	1	no	—
441	C₄²	—	26	1	no	—
442	C₄²	—	26	1	no	—
443	C₄²	—	52	2	no	—
444	C₄²	—	52	2	no	—
445	C₄²	C₂×C₄×D₁₃	1	2	yes	—
446	C₄²	C₂×C₄×D₁₃	1	2	yes	—
447	C₁₃	#20368	1	1	yes	characteristic, complemented, Sylow
448	C₂³	—	13	2	no	—
449	C₂³	—	13	2	no	—
450	C₂³	—	13	2	no	—
451	C₂³	—	26	2	no	—
452	C₂³	—	26	2	no	—
453	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	13	2	no	—
463	C₂×C₄	—	13	2	no	—
464	C₂×C₄	—	13	2	no	—
465	C₂×C₄	—	13	4	no	—
466	C₂×C₄	—	13	4	no	—
467	C₂×C₄	—	13	4	no	—
468	C₂×C₄	—	13	4	no	—
469	C₂×C₄	—	13	2	no	—
470	C₂×C₄	—	13	2	no	—
471	C₂×C₄	—	13	4	no	—
472	C₂×C₄	—	26	2	no	—
473	C₂×C₄	—	26	2	no	—
474	C₂×C₄	—	26	2	no	—
475	C₂×C₄	—	26	2	no	—
476	C₂×C₄	—	26	2	no	—
477	C₂×C₄	—	26	2	no	—
478	C₂×C₄	—	26	2	no	—
479	C₂×C₄	—	52	8	no	—
480	C₂×C₄	C₄²×D₁₃	1	2	yes	—
481	C₂×C₄	C₄²×D₁₃	1	2	yes	—
482	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
483	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
484	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
485	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
486	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
487	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
488	C₈	—	2	2	no	—
489	C₈	—	2	2	no	—
490	C₈	—	2	2	no	—
491	C₈	—	2	2	no	—
492	C₈	—	26	2	no	—
493	C₈	—	26	2	no	—
494	C₈	—	26	2	no	—
495	C₈	—	26	2	no	—
496	C₂²	—	13	4	no	—
497	C₂²	—	26	4	no	—
498	C₂²	—	26	4	no	—
499	C₂²	—	26	2	no	—
500	C₂²	—	26	2	no	—
501	C₂²	C₂×C₄²×D₁₃	1	1	yes	characteristic
502	C₂²	D₁₃×#117	1	1	yes	characteristic
503	C₂²	D₁₃×#117	1	1	yes	characteristic
504	C₂²	D₁₃×#131	1	2	yes	—
505	C₂²	#11719455	1	2	yes	—
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	4	2	no	—
509	C₄	—	4	2	no	—
510	C₄	—	13	4	no	—
511	C₄	—	26	4	no	—
512	C₄	—	26	2	no	—
513	C₄	—	26	2	no	—
514	C₄	—	52	2	no	—
515	C₄	D₁₃×#117	1	1	yes	characteristic
516	C₄	D₁₃×#117	1	1	yes	characteristic
517	C₄	D₁₃×#117	1	1	yes	characteristic
518	C₄	D₁₃×#117	1	1	yes	characteristic
519	C₂	—	26	4	no	—
520	C₂	D₁₃×#376	1	1	yes	characteristic
521	C₂	#13123258	1	1	yes	characteristic
522	C₂	#13123263	1	1	yes	characteristic
523	C₂	#13123492	1	2	yes	—
524	C₂	#13123499	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#1746	C₂
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1746	D₁₃
hypocenter	C₁₃	#20368
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1746

Complements

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

N	H ≅ G/N	type
4. #13114588	C₂	semidirect
5. #13114586	C₂	semidirect
6. #13114586	C₂	semidirect
7. #13114584	C₂	semidirect
8. #13114583	C₂	semidirect
9. #13114581	C₂	semidirect
10. #13114580	C₂	semidirect
15. C₁₃×#1746	C₂	semidirect
35. #11718369	C₄	semidirect
36. #11718350	C₄	semidirect
102. C₁₃×#97	C₂×C₄	semidirect
103. C₄×C₈×C₁₃	C₂×C₄	semidirect
108. #88055	C₂×C₄	semidirect
109. #88055	C₂×C₄	semidirect
110. C₈×Dic₁₃	C₂×C₄	semidirect
111. C₈×Dic₁₃	C₂×C₄	semidirect
112. #88043	C₂×C₄	semidirect
113. C₄×#1055	C₂×C₄	semidirect
192. #1746	D₁₃	semidirect
361. #97	C₄×D₁₃	semidirect
365. C₄×C₈	C₄×D₁₃	semidirect
447. C₁₃	#20368	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718369	2
C₂×#11718350	2
#13117175	2
#13114588	2
#13114586	2
#13114584	2
#13114583	2
#13114581	2
#13114580	2
#13114531	2
#13114528	2
D₁₃×#336	2
C₁₃×#1746	2
#20368	13