Subgroups — #13128682

Order 1664.

1140 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719409	C₂	1	2	yes	maximal, complemented
3	#11719407	C₂	1	2	yes	maximal, complemented
4	#11719400	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719393	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719369	C₂	1	2	yes	maximal, complemented
7	#11719361	C₂	1	2	yes	maximal, complemented
8	#11719321	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719318	C₂	1	2	yes	maximal, complemented
10	#11719316	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719312	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719312	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719304	C₂	1	2	yes	maximal, complemented
14	#11719270	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719264	C₂	1	2	yes	maximal, complemented
16	#11719263	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719253	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719252	C₂	1	2	yes	maximal, complemented
19	C₄×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719237	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719228	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719212	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719209	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#6129	C₂²	1	2	yes	complemented
25	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
26	C₂×#6127	C₂²	1	1	yes	characteristic
27	C₂×#6127	C₂²	1	1	yes	characteristic
28	C₂×#6127	C₂²	1	2	yes	complemented
29	C₂²×C₄×D₁₃	C₂²	1	2	yes	—
30	C₁₃×#126	C₂²	1	2	yes	complemented
31	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#123	C₂²	1	2	yes	complemented
33	C₁₃×#121	C₂²	1	1	yes	characteristic
34	C₁₃×#121	C₂²	1	1	yes	characteristic
35	C₁₃×#121	C₂²	1	2	yes	complemented
36	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
38	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	#88194	C₂²	1	2	yes	—
42	#88194	C₂²	1	2	yes	—
43	#88194	C₂²	1	1	yes	characteristic, complemented
44	#88193	C₂²	1	2	yes	complemented
45	#88193	C₂²	1	2	yes	complemented
46	#88192	C₂²	1	1	yes	characteristic
47	#88192	C₂²	1	1	yes	characteristic
48	#88192	C₂²	1	1	yes	characteristic
49	#88191	C₂²	1	2	yes	—
50	#88191	C₂²	1	2	yes	—
51	#88190	C₂²	1	2	yes	complemented
52	#88189	C₂²	1	2	yes	complemented
53	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
54	#88184	C₂²	1	1	yes	characteristic
55	#88184	C₂²	1	1	yes	characteristic
56	#88183	C₂²	1	2	yes	complemented
57	#88183	C₂²	1	2	yes	complemented
58	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
59	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
60	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
62	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
63	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
64	#88180	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
66	#88152	C₂²	1	2	yes	complemented
67	#88152	C₂²	1	2	yes	complemented
68	#88150	C₂²	1	2	yes	—
69	#88150	C₂²	1	2	yes	—
70	#88150	C₂²	1	2	yes	complemented
71	#88149	C₂²	1	1	yes	characteristic
72	#88149	C₂²	1	1	yes	characteristic
73	#88149	C₂²	1	1	yes	characteristic
74	#88149	C₂²	1	2	yes	complemented
75	#88148	C₂²	1	2	yes	complemented
76	#88148	C₂²	1	2	yes	complemented
77	#88147	C₂²	1	2	yes	—
78	#88147	C₂²	1	1	yes	characteristic
79	#88147	C₂²	1	2	yes	complemented
80	#88146	C₂²	1	1	yes	characteristic
81	#88146	C₂²	1	1	yes	characteristic
82	#88146	C₂²	1	1	yes	characteristic, complemented
83	#88146	C₂²	1	1	yes	characteristic, complemented
84	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
85	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
86	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
87	#88142	C₂²	1	1	yes	characteristic, complemented
88	#88142	C₂²	1	1	yes	characteristic, complemented
89	#88142	C₂²	1	1	yes	characteristic, complemented
90	#88141	C₂²	1	2	yes	complemented
91	#88141	C₂²	1	2	yes	complemented
92	#88141	C₂²	1	2	yes	complemented
93	#88139	C₂²	1	2	yes	—
94	#88139	C₂²	1	2	yes	—
95	#88139	C₂²	1	2	yes	complemented
96	#88139	C₂²	1	1	yes	characteristic, complemented
97	#88139	C₂²	1	1	yes	characteristic, complemented
98	#88139	C₂²	1	2	yes	complemented
99	#88138	C₂²	1	1	yes	characteristic
100	#88138	C₂²	1	1	yes	characteristic
101	#88138	C₂²	1	2	yes	complemented
102	#88138	C₂²	1	2	yes	complemented
103	#88137	C₂²	1	2	yes	complemented
104	#88137	C₂²	1	2	yes	complemented
105	#88136	C₂²	1	2	yes	—
106	#88136	C₂²	1	2	yes	—
107	#88135	C₂²	1	2	yes	—
108	#88135	C₂²	1	2	yes	—
109	#88135	C₂²	1	2	yes	complemented
110	#88135	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
112	#88133	C₂²	1	2	yes	complemented
113	#88132	C₂²	1	2	yes	complemented
114	#88131	C₂²	1	2	yes	complemented
115	#88129	C₂²	1	2	yes	complemented
116	C₄×D₅₂	C₂²	1	2	yes	—
117	C₄×D₅₂	C₂²	1	1	yes	characteristic
118	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
119	#88126	C₂²	1	2	yes	complemented
120	C₄²×D₁₃	C₂²	1	1	yes	characteristic
121	#88124	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₆	C₂²	1	2	yes	complemented
123	C₂³×D₁₃	C₂³	1	2	yes	—
124	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₁₃	C₂³	1	2	yes	—
126	C₂×D₄×C₁₃	C₂³	1	2	yes	—
127	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
143	C₂²×Dic₁₃	C₂³	1	2	yes	—
144	C₂²×Dic₁₃	C₂³	1	2	yes	—
145	#6129	—	4	4	no	—
146	D₄×D₁₃	—	2	4	no	—
147	#6127	—	2	4	no	—
148	#6127	—	2	4	no	—
149	#6127	—	4	4	no	—
150	C₂×D₅₂	C₂³	1	1	yes	characteristic
151	C₂×D₅₂	C₂³	1	1	yes	characteristic
152	C₂×D₅₂	C₂³	1	1	yes	characteristic
153	C₂×D₅₂	C₂³	1	1	yes	characteristic
154	C₂×D₅₂	C₂³	1	2	yes	—
155	C₂×D₅₂	C₂³	1	2	yes	—
156	C₂×C₄×D₁₃	—	4	4	no	—
157	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₃	C₂³	1	2	yes	—
159	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₁₃	C₂³	1	2	yes	—
163	C₂×C₄×D₁₃	C₂³	1	2	yes	—
164	C₂×C₄×D₁₃	C₂³	1	2	yes	—
165	C₂×C₄×D₁₃	C₂³	1	2	yes	—
166	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
167	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
168	C₂×Dic₂₆	C₂³	1	2	yes	—
169	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
170	C₂×Dic₂₆	C₂³	1	2	yes	—
171	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
183	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
184	C₄²×C₁₃	C₂³	1	2	yes	—
185	C₄²×C₁₃	C₂³	1	1	yes	characteristic
186	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
188	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
189	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
190	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
191	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
192	#6103	C₂³	1	2	yes	—
193	#6103	C₂³	1	2	yes	—
194	#6103	C₂³	1	2	yes	—
195	#6103	C₂³	1	2	yes	—
196	#6103	C₂³	1	2	yes	—
197	#6103	C₂³	1	1	yes	characteristic
198	#6103	C₂³	1	1	yes	characteristic
199	#6103	C₂³	1	1	yes	characteristic
200	#6103	C₂³	1	2	yes	—
201	#6103	C₂³	1	2	yes	—
202	#6103	C₂³	1	2	yes	—
203	#6103	C₂³	1	2	yes	—
204	#6103	C₂³	1	2	yes	—
205	#6103	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₁₃	C₂³	1	2	yes	—
207	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
211	#6101	C₂³	1	2	yes	—
212	#6101	C₂³	1	2	yes	—
213	#6101	C₂³	1	2	yes	—
214	#6101	C₂³	1	2	yes	—
215	#6101	C₂³	1	1	yes	characteristic
216	#6101	C₂³	1	2	yes	—
217	#6101	C₂³	1	1	yes	characteristic
218	#6101	C₂³	1	2	yes	—
219	#6101	C₂³	1	2	yes	—
220	C₄×Dic₁₃	C₂³	1	2	yes	—
221	C₄×Dic₁₃	C₂³	1	2	yes	—
222	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
225	C₄×Dic₁₃	C₂³	1	2	yes	—
226	C₄×Dic₁₃	C₂³	1	2	yes	—
227	C₄×Dic₁₃	C₂³	1	2	yes	—
228	#3506	—	13	1	no	maximal, Sylow
229	C₂³×C₁₃	C₂⁴	1	2	yes	—
230	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₃	—	2	4	no	—
233	C₂²×D₁₃	—	4	2	no	—
234	C₂²×D₁₃	—	4	2	no	—
235	C₂²×D₁₃	C₂⁴	1	2	yes	—
236	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
237	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
238	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
239	D₄×C₁₃	—	2	2	no	—
240	D₄×C₁₃	—	4	2	no	—
241	D₄×C₁₃	—	4	2	no	—
242	D₄×C₁₃	—	4	1	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	4	2	no	—
246	C₂×C₄×C₁₃	—	4	2	no	—
247	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
248	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
252	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂²⋊D₁₃	—	2	2	no	—
256	C₂²⋊D₁₃	—	2	2	no	—
257	C₂²⋊D₁₃	—	2	2	no	—
258	C₂²⋊D₁₃	—	2	2	no	—
259	C₂²⋊D₁₃	—	2	4	no	—
260	C₂²⋊D₁₃	—	2	2	no	—
261	C₂²⋊D₁₃	—	2	2	no	—
262	C₂²⋊D₁₃	—	4	2	no	—
263	C₂²⋊D₁₃	—	4	2	no	—
264	C₂²⋊D₁₃	—	4	2	no	—
265	C₂²⋊D₁₃	—	4	2	no	—
266	C₂×Dic₁₃	—	2	4	no	—
267	C₂×Dic₁₃	—	4	2	no	—
268	C₂×Dic₁₃	C₂⁴	1	2	yes	—
269	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₁₃	C₂⁴	1	2	yes	—
272	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₁₃	C₂⁴	1	2	yes	—
274	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
276	D₅₂	—	2	2	no	—
277	D₅₂	—	2	2	no	—
278	D₅₂	—	2	2	no	—
279	D₅₂	—	4	2	no	—
280	D₅₂	—	4	1	no	—
281	D₅₂	—	4	2	no	—
282	C₄×D₁₃	—	2	2	no	—
283	C₄×D₁₃	—	2	2	no	—
284	C₄×D₁₃	—	2	2	no	—
285	C₄×D₁₃	—	2	4	no	—
286	C₄×D₁₃	—	4	2	no	—
287	C₄×D₁₃	—	4	2	no	—
288	C₄×D₁₃	—	4	1	no	—
289	C₄×D₁₃	—	4	2	no	—
290	C₄×D₁₃	—	4	2	no	—
291	C₄×D₁₃	#41	1	4	yes	complemented
292	Dic₂₆	—	2	2	no	—
293	Dic₂₆	—	2	2	no	—
294	Dic₂₆	—	2	4	no	—
295	Dic₂₆	—	4	2	no	—
296	#559	—	13	2	no	—
297	#559	—	13	2	no	—
298	#556	—	13	2	no	—
299	#555	—	13	1	no	—
300	#555	—	13	1	no	—
301	#553	—	13	1	no	—
302	#553	—	13	1	no	—
303	#553	—	13	1	no	—
304	#553	D₁₃	1	1	yes	characteristic, complemented
305	#550	—	13	2	no	—
306	#547	—	13	1	no	—
307	#547	—	13	1	no	—
308	#538	—	13	2	no	—
309	#538	—	13	2	no	—
310	#535	—	13	1	no	—
311	#535	—	13	1	no	—
312	#533	—	13	1	no	—
313	#532	—	13	1	no	—
314	#525	—	13	2	no	—
315	#525	—	13	2	no	—
316	#520	—	13	1	no	—
317	#520	—	13	1	no	—
318	C₂×C₄×D₄	—	13	1	no	—
319	C₂²×C₁₃	—	2	1	no	—
320	C₂²×C₁₃	—	2	1	no	—
321	C₂²×C₁₃	—	2	2	no	—
322	C₂²×C₁₃	—	2	2	no	—
323	C₂²×C₁₃	—	2	1	no	—
324	C₂²×C₁₃	—	2	1	no	—
325	C₂²×C₁₃	—	2	1	no	—
326	C₂²×C₁₃	—	2	2	no	—
327	C₂²×C₁₃	—	2	1	no	—
328	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
329	C₂×D₁₃	—	2	1	no	—
330	C₂×D₁₃	—	2	1	no	—
331	C₂×D₁₃	—	2	1	no	—
332	C₂×D₁₃	—	2	1	no	—
333	C₂×D₁₃	—	2	2	no	—
334	C₂×D₁₃	—	2	2	no	—
335	C₂×D₁₃	—	2	1	no	—
336	C₂×D₁₃	—	2	1	no	—
337	C₂×D₁₃	—	2	1	no	—
338	C₂×D₁₃	—	2	1	no	—
339	C₂×D₁₃	—	2	2	no	—
340	C₂×D₁₃	—	4	8	no	—
341	C₂×D₁₃	C₂×#41	1	2	yes	—
342	C₄×C₁₃	—	2	1	no	—
343	C₄×C₁₃	—	2	1	no	—
344	C₄×C₁₃	—	2	2	no	—
345	C₄×C₁₃	—	2	1	no	—
346	C₄×C₁₃	—	2	2	no	—
347	C₄×C₁₃	—	2	2	no	—
348	C₄×C₁₃	—	2	1	no	—
349	C₄×C₁₃	C₂×#41	1	2	yes	—
350	Dic₁₃	—	2	1	no	—
351	Dic₁₃	—	2	1	no	—
352	Dic₁₃	—	2	2	no	—
353	Dic₁₃	—	2	2	no	—
354	Dic₁₃	—	2	1	no	—
355	Dic₁₃	—	2	2	no	—
356	Dic₁₃	C₂×#41	1	2	yes	—
357	Dic₁₃	H(5,𝔽₂)	1	2	yes	—
358	C₂×#41	—	13	2	no	—
359	C₂×#41	—	13	1	no	—
360	C₂×#41	—	13	1	no	—
361	C₂×#41	—	13	2	no	—
362	C₂²×D₄	—	13	1	no	—
363	C₂³×C₄	—	13	2	no	—
364	C₄⋊Q₈	—	13	1	no	—
365	C₄⋊Q₈	—	13	1	no	—
366	C₄⋊Q₈	—	13	1	no	—
367	#127	—	13	1	no	—
368	#127	—	13	2	no	—
369	#127	—	13	2	no	—
370	#126	—	13	2	no	—
371	#126	—	13	2	no	—
372	#126	—	13	2	no	—
373	#126	C₂×D₁₃	1	2	yes	complemented
374	#125	—	13	1	no	—
375	#125	C₂×D₁₃	1	1	yes	characteristic, complemented
376	#124	—	13	2	no	—
377	#124	—	13	1	no	—
378	#124	—	13	1	no	—
379	#124	—	13	2	no	—
380	#124	—	13	2	no	—
381	#124	—	13	2	no	—
382	#124	—	13	2	no	—
383	#124	—	13	2	no	—
384	#123	—	13	2	no	—
385	#123	—	13	2	no	—
386	#123	—	13	2	no	—
387	#123	—	13	2	no	—
388	#123	—	13	2	no	—
389	#123	—	13	2	no	—
390	#123	—	13	2	no	—
391	#123	C₂×D₁₃	1	2	yes	complemented
392	C₂²⋊Q₈	—	13	2	no	—
393	C₂²⋊Q₈	—	13	2	no	—
394	C₂²⋊Q₈	—	13	2	no	—
395	C₂²⋊Q₈	—	13	2	no	—
396	#121	—	13	2	no	—
397	#121	—	13	1	no	—
398	#121	—	13	1	no	—
399	#121	—	13	1	no	—
400	#121	—	13	2	no	—
401	#121	—	13	1	no	—
402	#121	—	13	1	no	—
403	#121	—	13	1	no	—
404	#121	—	13	1	no	—
405	#121	—	13	1	no	—
406	#121	—	13	2	no	—
407	#121	—	13	1	no	—
408	#121	—	13	1	no	—
409	#121	—	13	2	no	—
410	#121	—	13	2	no	—
411	#121	C₂×D₁₃	1	1	yes	characteristic
412	#121	C₂×D₁₃	1	1	yes	characteristic
413	#121	C₂×D₁₃	1	2	yes	complemented
414	#120	—	13	2	no	—
415	#120	—	13	2	no	—
416	#120	—	13	2	no	—
417	#120	—	13	2	no	—
418	C₄×Q₈	—	13	2	no	—
419	C₄×Q₈	—	13	2	no	—
420	C₄×Q₈	—	13	2	no	—
421	C₄×Q₈	—	13	2	no	—
422	C₄×D₄	—	13	1	no	—
423	C₄×D₄	—	13	2	no	—
424	C₄×D₄	—	13	2	no	—
425	C₄×D₄	—	13	2	no	—
426	C₄×D₄	—	13	2	no	—
427	C₄×D₄	—	13	1	no	—
428	C₄×D₄	—	13	1	no	—
429	C₄×D₄	—	13	1	no	—
430	C₄×D₄	—	13	2	no	—
431	C₄×D₄	—	13	2	no	—
432	C₄×D₄	—	13	2	no	—
433	C₄×D₄	—	13	2	no	—
434	C₄×D₄	—	13	2	no	—
435	C₄×D₄	—	13	2	no	—
436	C₄×D₄	—	13	1	no	—
437	C₄×D₄	—	13	2	no	—
438	C₄×D₄	—	13	1	no	—
439	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
440	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
441	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
442	#117	—	13	1	no	—
443	#117	—	13	1	no	—
444	#117	—	13	1	no	—
445	#117	—	13	1	no	—
446	#117	—	13	1	no	—
447	#117	—	13	2	no	—
448	#117	—	13	2	no	—
449	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
450	C₂×C₄⋊C₄	—	13	1	no	—
451	C₂×C₄⋊C₄	—	13	1	no	—
452	C₂×C₄⋊C₄	—	13	1	no	—
453	C₂×C₄⋊C₄	—	13	1	no	—
454	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
455	C₂×C₂²⋊C₄	—	13	2	no	—
456	C₂×C₄²	—	13	1	no	—
457	C₂×C₁₃	—	4	2	no	—
458	C₂×C₁₃	—	4	1	no	—
459	C₂×C₁₃	—	4	1	no	—
460	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
461	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
462	C₂×C₁₃	#585	1	1	yes	characteristic
463	D₁₃	—	2	2	no	—
464	D₁₃	—	4	1	no	—
465	D₁₃	—	4	1	no	—
466	D₁₃	—	4	2	no	—
467	C₂⁴	—	13	2	no	—
468	#41	—	26	4	no	—
469	#41	—	26	4	no	—
470	#41	—	52	4	no	—
471	#41	—	52	4	no	—
472	C₂×Q₈	—	13	1	no	—
473	C₂×Q₈	—	13	1	no	—
474	C₂×Q₈	—	13	2	no	—
475	C₂×Q₈	—	13	2	no	—
476	C₂×D₄	—	13	1	no	—
477	C₂×D₄	—	13	1	no	—
478	C₂×D₄	—	13	2	no	—
479	C₂×D₄	—	13	1	no	—
480	C₂×D₄	—	13	1	no	—
481	C₂×D₄	—	13	1	no	—
482	C₂×D₄	—	13	1	no	—
483	C₂×D₄	—	13	2	no	—
484	C₂×D₄	—	13	2	no	—
485	C₂×D₄	—	13	2	no	—
486	C₂×D₄	—	13	2	no	—
487	C₂×D₄	—	13	1	no	—
488	C₂×D₄	—	13	1	no	—
489	C₂×D₄	—	13	1	no	—
490	C₂×D₄	—	13	2	no	—
491	C₂×D₄	—	13	1	no	—
492	C₂×D₄	—	13	2	no	—
493	C₂×D₄	—	26	4	no	—
494	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
495	C₂×D₄	C₂²×D₁₃	1	2	yes	—
496	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
497	C₂×D₄	C₂²×D₁₃	1	2	yes	—
498	C₂²×C₄	—	13	1	no	—
499	C₂²×C₄	—	13	2	no	—
500	C₂²×C₄	—	13	2	no	—
501	C₂²×C₄	—	13	1	no	—
502	C₂²×C₄	—	13	1	no	—
503	C₂²×C₄	—	13	1	no	—
504	C₂²×C₄	—	13	2	no	—
505	C₂²×C₄	—	13	1	no	—
506	C₂²×C₄	—	13	2	no	—
507	C₂²×C₄	—	13	2	no	—
508	C₂²×C₄	—	13	2	no	—
509	C₂²×C₄	—	13	2	no	—
510	C₂²×C₄	—	52	4	no	—
511	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
512	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
513	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
514	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
515	C₄⋊C₄	—	13	1	no	—
516	C₄⋊C₄	—	13	1	no	—
517	C₄⋊C₄	—	13	2	no	—
518	C₄⋊C₄	—	13	2	no	—
519	C₄⋊C₄	—	13	2	no	—
520	C₄⋊C₄	—	13	2	no	—
521	C₄⋊C₄	—	13	1	no	—
522	C₄⋊C₄	—	13	1	no	—
523	C₄⋊C₄	—	13	1	no	—
524	C₄⋊C₄	—	13	2	no	—
525	C₄⋊C₄	—	13	2	no	—
526	C₄⋊C₄	—	13	1	no	—
527	C₄⋊C₄	—	13	2	no	—
528	C₄⋊C₄	—	13	2	no	—
529	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
530	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
531	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
532	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
533	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
534	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
535	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
536	C₂²⋊C₄	—	13	2	no	—
537	C₂²⋊C₄	—	13	2	no	—
538	C₂²⋊C₄	—	13	2	no	—
539	C₂²⋊C₄	—	13	2	no	—
540	C₂²⋊C₄	—	13	1	no	—
541	C₂²⋊C₄	—	13	1	no	—
542	C₂²⋊C₄	—	13	2	no	—
543	C₂²⋊C₄	—	13	2	no	—
544	C₂²⋊C₄	—	13	2	no	—
545	C₂²⋊C₄	—	13	2	no	—
546	C₂²⋊C₄	—	13	2	no	—
547	C₂²⋊C₄	—	13	2	no	—
548	C₂²⋊C₄	—	13	2	no	—
549	C₂²⋊C₄	—	13	2	no	—
550	C₂²⋊C₄	—	13	1	no	—
551	C₂²⋊C₄	—	13	1	no	—
552	C₂²⋊C₄	—	13	2	no	—
553	C₂²⋊C₄	—	13	2	no	—
554	C₂²⋊C₄	—	13	1	no	—
555	C₂²⋊C₄	—	13	1	no	—
556	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
557	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
558	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
559	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
560	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
561	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
562	C₄²	—	13	1	no	—
563	C₄²	—	13	1	no	—
564	C₄²	—	13	1	no	—
565	C₄²	—	13	2	no	—
566	C₄²	—	13	2	no	—
567	C₄²	—	13	2	no	—
568	C₄²	—	13	2	no	—
569	C₄²	—	13	2	no	—
570	C₄²	C₂²×D₁₃	1	1	yes	characteristic
571	C₄²	C₂²×D₁₃	1	2	yes	—
572	C₁₃	#3506	1	1	yes	characteristic, complemented, Sylow
573	C₂³	—	13	1	no	—
574	C₂³	—	13	2	no	—
575	C₂³	—	13	1	no	—
576	C₂³	—	13	1	no	—
577	C₂³	—	26	4	no	—
578	C₂³	—	52	2	no	—
579	C₂³	—	52	2	no	—
580	C₂³	C₂³×D₁₃	1	2	yes	—
581	C₂³	C₂³×D₁₃	1	1	yes	characteristic
582	C₂³	C₂³×D₁₃	1	1	yes	characteristic
583	Q₈	—	26	2	no	—
584	Q₈	—	26	2	no	—
585	Q₈	—	26	4	no	—
586	Q₈	—	52	2	no	—
587	D₄	—	2	2	no	—
588	D₄	—	4	1	no	—
589	D₄	—	4	2	no	—
590	D₄	—	4	2	no	—
591	D₄	—	26	2	no	—
592	D₄	—	26	2	no	—
593	D₄	—	26	4	no	—
594	D₄	—	26	2	no	—
595	D₄	—	26	2	no	—
596	D₄	—	26	2	no	—
597	D₄	—	26	2	no	—
598	D₄	—	26	2	no	—
599	D₄	—	26	2	no	—
600	D₄	—	26	2	no	—
601	D₄	—	52	1	no	—
602	D₄	—	52	2	no	—
603	D₄	—	52	2	no	—
604	D₄	—	52	2	no	—
605	D₄	—	52	2	no	—
606	D₄	—	52	2	no	—
607	D₄	—	52	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	13	1	no	—
613	C₂×C₄	—	13	1	no	—
614	C₂×C₄	—	13	4	no	—
615	C₂×C₄	—	13	2	no	—
616	C₂×C₄	—	13	1	no	—
617	C₂×C₄	—	13	1	no	—
618	C₂×C₄	—	13	1	no	—
619	C₂×C₄	—	13	2	no	—
620	C₂×C₄	—	13	2	no	—
621	C₂×C₄	—	26	2	no	—
622	C₂×C₄	—	26	4	no	—
623	C₂×C₄	—	26	4	no	—
624	C₂×C₄	—	26	2	no	—
625	C₂×C₄	—	26	2	no	—
626	C₂×C₄	—	52	1	no	—
627	C₂×C₄	—	52	2	no	—
628	C₂×C₄	—	52	2	no	—
629	C₂×C₄	—	52	2	no	—
630	C₂×C₄	—	52	2	no	—
631	C₂×C₄	—	52	2	no	—
632	C₂×C₄	C₂³×D₁₃	1	2	yes	—
633	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
634	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
635	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₁₃	1	2	yes	—
637	C₂×C₄	C₂³×D₁₃	1	2	yes	—
638	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
639	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	13	2	no	—
650	C₂²	—	26	1	no	—
651	C₂²	—	26	1	no	—
652	C₂²	—	26	1	no	—
653	C₂²	—	26	1	no	—
654	C₂²	—	26	2	no	—
655	C₂²	—	26	1	no	—
656	C₂²	—	26	1	no	—
657	C₂²	—	26	2	no	—
658	C₂²	—	26	2	no	—
659	C₂²	—	26	1	no	—
660	C₂²	—	26	1	no	—
661	C₂²	—	52	8	no	—
662	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	2	no	—
670	C₄	—	13	2	no	—
671	C₄	—	13	2	no	—
672	C₄	—	26	1	no	—
673	C₄	—	26	1	no	—
674	C₄	—	26	1	no	—
675	C₄	—	26	2	no	—
676	C₄	—	26	2	no	—
677	C₄	—	26	2	no	—
678	C₄	#41×D₁₃	1	2	yes	—
679	C₂	—	4	2	no	—
680	C₂	—	4	1	no	—
681	C₂	—	4	1	no	—
682	C₂	—	26	2	no	—
683	C₂	—	52	2	no	—
684	C₂	—	52	1	no	—
685	C₂	—	52	1	no	—
686	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
687	C₂	#11719648	1	1	yes	characteristic
688	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#553	C₂
hypercenter	#553	D₁₃
hypocenter	C₁₃	#3506
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. C₁₃×#553	C₂	semidirect
2. #11719409	C₂	semidirect
3. #11719407	C₂	semidirect
4. #11719400	C₂	semidirect
5. #11719393	C₂	semidirect
6. #11719369	C₂	semidirect
7. #11719361	C₂	semidirect
8. #11719321	C₂	semidirect
9. #11719318	C₂	semidirect
10. #11719316	C₂	semidirect
11. #11719312	C₂	semidirect
12. #11719312	C₂	semidirect
13. #11719304	C₂	semidirect
14. #11719270	C₂	semidirect
15. #11719264	C₂	semidirect
16. #11719263	C₂	semidirect
17. #11719253	C₂	semidirect
18. #11719252	C₂	semidirect
19. C₄×D₄×D₁₃	C₂	semidirect
20. #11719237	C₂	semidirect
21. #11719228	C₂	semidirect
22. #11719212	C₂	semidirect
23. #11719209	C₂	semidirect
24. C₂×#6129	C₂²	semidirect
28. C₂×#6127	C₂²	semidirect
30. C₁₃×#126	C₂²	semidirect
31. C₁₃×#125	C₂²	semidirect
32. C₁₃×#123	C₂²	semidirect
35. C₁₃×#121	C₂²	semidirect
37. C₄×D₄×C₁₃	C₂²	semidirect
38. C₄×D₄×C₁₃	C₂²	semidirect
39. C₁₃×#117	C₂²	semidirect
40. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
43. #88194	C₂²	semidirect
44. #88193	C₂²	semidirect
45. #88193	C₂²	semidirect
51. #88190	C₂²	semidirect
52. #88189	C₂²	semidirect
56. #88183	C₂²	semidirect
57. #88183	C₂²	semidirect
60. C₄×C₂²⋊D₁₃	C₂²	semidirect
61. C₄×C₂²⋊D₁₃	C₂²	semidirect
62. C₄×C₂²⋊D₁₃	C₂²	semidirect
63. C₄×C₂²⋊D₁₃	C₂²	semidirect
64. #88180	C₂²	semidirect
65. C₂×C₄⋊Dic₁₃	C₂²	semidirect
66. #88152	C₂²	semidirect
67. #88152	C₂²	semidirect
70. #88150	C₂²	semidirect
74. #88149	C₂²	semidirect
75. #88148	C₂²	semidirect
76. #88148	C₂²	semidirect
79. #88147	C₂²	semidirect
82. #88146	C₂²	semidirect
83. #88146	C₂²	semidirect
85. C₄⋊C₄×D₁₃	C₂²	semidirect
86. C₄⋊C₄×D₁₃	C₂²	semidirect
87. #88142	C₂²	semidirect
88. #88142	C₂²	semidirect
89. #88142	C₂²	semidirect
90. #88141	C₂²	semidirect
91. #88141	C₂²	semidirect
92. #88141	C₂²	semidirect
95. #88139	C₂²	semidirect
96. #88139	C₂²	semidirect
97. #88139	C₂²	semidirect
98. #88139	C₂²	semidirect
101. #88138	C₂²	semidirect
102. #88138	C₂²	semidirect
103. #88137	C₂²	semidirect
104. #88137	C₂²	semidirect
109. #88135	C₂²	semidirect
110. #88135	C₂²	semidirect
112. #88133	C₂²	semidirect
113. #88132	C₂²	semidirect
114. #88131	C₂²	semidirect
115. #88129	C₂²	semidirect
118. C₄×D₅₂	C₂²	semidirect
119. #88126	C₂²	semidirect
121. #88124	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
291. C₄×D₁₃	#41	semidirect
304. #553	D₁₃	semidirect
373. #126	C₂×D₁₃	semidirect
375. #125	C₂×D₁₃	semidirect
391. #123	C₂×D₁₃	semidirect
413. #121	C₂×D₁₃	semidirect
440. C₄×D₄	C₂×D₁₃	semidirect
441. C₄×D₄	C₂×D₁₃	semidirect
449. #117	C₂×D₁₃	semidirect
454. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
572. C₁₃	#3506	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#553	2
#11719409	2
#11719407	2
#11719400	2
#11719393	2
#11719369	2
#11719361	2
#11719321	2
#11719318	2
#11719316	2
#11719312	2
#11719304	2
#11719270	2
#11719264	2
#11719263	2
#11719253	2
#11719252	2
C₄×D₄×D₁₃	2
#11719237	2
#11719228	2
#11719212	2
#11719209	2
#3506	13