Subgroups — #13128785

Order 1664.

1142 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719415	C₂	1	2	yes	maximal, complemented
3	#11719409	C₂	1	2	yes	maximal, complemented
4	#11719396	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719396	C₂	1	1	yes	maximal, characteristic, complemented
6	D₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719373	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719363	C₂	1	2	yes	maximal, complemented
9	#11719359	C₂	1	2	yes	maximal, complemented
10	#11719337	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719335	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719314	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719303	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719281	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719273	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719265	C₂	1	2	yes	maximal, complemented
17	#11719264	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719259	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719250	C₂	1	2	yes	maximal, complemented
20	#11719237	C₂	1	2	yes	maximal, complemented
21	#11719232	C₂	1	2	yes	maximal, complemented
22	C₂×#88129	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#6127	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#6131	C₂²	1	1	yes	characteristic, complemented
25	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×#6129	C₂²	1	1	yes	characteristic, complemented
27	C₂×D₄×D₁₃	C₂²	1	2	yes	—
28	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
29	C₂×#6127	C₂²	1	1	yes	characteristic
30	C₂²×D₅₂	C₂²	1	1	yes	characteristic
31	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#126	C₂²	1	2	yes	complemented
33	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#123	C₂²	1	2	yes	complemented
36	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#121	C₂²	1	1	yes	characteristic
38	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
40	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#117	C₂²	1	2	yes	complemented
42	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
43	#88201	C₂²	1	1	yes	characteristic
44	#88198	C₂²	1	1	yes	characteristic, complemented
45	#88194	C₂²	1	1	yes	characteristic
46	#88193	C₂²	1	2	yes	complemented
47	#88191	C₂²	1	2	yes	—
48	#88190	C₂²	1	1	yes	characteristic, complemented
49	D₄×Dic₁₃	C₂²	1	2	yes	complemented
50	#88184	C₂²	1	2	yes	complemented
51	#88183	C₂²	1	2	yes	complemented
52	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
55	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
56	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
57	C₂×#6103	C₂²	1	2	yes	complemented
58	C₂×#6103	C₂²	1	2	yes	complemented
59	C₂×#6103	C₂²	1	2	yes	complemented
60	#88180	C₂²	1	1	yes	characteristic, complemented
61	#88152	C₂²	1	2	yes	complemented
62	#88152	C₂²	1	2	yes	complemented
63	#88152	C₂²	1	2	yes	complemented
64	#88151	C₂²	1	1	yes	characteristic, complemented
65	#88151	C₂²	1	1	yes	characteristic, complemented
66	#88151	C₂²	1	2	yes	complemented
67	#88150	C₂²	1	2	yes	complemented
68	#88150	C₂²	1	2	yes	complemented
69	#88149	C₂²	1	1	yes	characteristic
70	#88149	C₂²	1	1	yes	characteristic
71	#88149	C₂²	1	2	yes	complemented
72	#88149	C₂²	1	2	yes	complemented
73	#88148	C₂²	1	2	yes	complemented
74	#88148	C₂²	1	2	yes	complemented
75	#88148	C₂²	1	2	yes	complemented
76	#88147	C₂²	1	1	yes	characteristic
77	#88147	C₂²	1	2	yes	complemented
78	#88147	C₂²	1	2	yes	complemented
79	#88147	C₂²	1	1	yes	characteristic, complemented
80	#88146	C₂²	1	2	yes	complemented
81	#88146	C₂²	1	2	yes	complemented
82	#88142	C₂²	1	2	yes	complemented
83	#88141	C₂²	1	1	yes	characteristic, complemented
84	#88141	C₂²	1	1	yes	characteristic, complemented
85	#88140	C₂²	1	2	yes	complemented
86	#88139	C₂²	1	2	yes	complemented
87	#88139	C₂²	1	2	yes	complemented
88	#88139	C₂²	1	2	yes	complemented
89	#88139	C₂²	1	2	yes	complemented
90	#88138	C₂²	1	2	yes	—
91	#88138	C₂²	1	2	yes	complemented
92	#88138	C₂²	1	2	yes	complemented
93	#88137	C₂²	1	2	yes	complemented
94	#88136	C₂²	1	2	yes	—
95	#88136	C₂²	1	2	yes	complemented
96	#88136	C₂²	1	2	yes	complemented
97	#88135	C₂²	1	2	yes	—
98	#88135	C₂²	1	2	yes	complemented
99	#88135	C₂²	1	2	yes	complemented
100	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
101	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
102	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
103	#88132	C₂²	1	2	yes	complemented
104	#88132	C₂²	1	2	yes	complemented
105	#88130	C₂²	1	2	yes	complemented
106	#88129	C₂²	1	1	yes	characteristic
107	#88129	C₂²	1	1	yes	characteristic
108	#88129	C₂²	1	2	yes	complemented
109	#88129	C₂²	1	1	yes	characteristic, complemented
110	#88129	C₂²	1	1	yes	characteristic, complemented
111	#88129	C₂²	1	2	yes	complemented
112	#88129	C₂²	1	2	yes	complemented
113	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
114	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₅₂	C₂²	1	2	yes	complemented
116	#88126	C₂²	1	1	yes	characteristic, complemented
117	#88126	C₂²	1	1	yes	characteristic, complemented
118	#88126	C₂²	1	2	yes	complemented
119	C₄²×D₁₃	C₂²	1	1	yes	characteristic, complemented
120	C₄²×D₁₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₃	C₂³	1	2	yes	—
124	C₂³×D₁₃	C₂³	1	2	yes	—
125	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
138	C₂²×Dic₁₃	C₂³	1	2	yes	—
139	C₂²×Dic₁₃	C₂³	1	2	yes	—
140	#6131	—	4	2	no	—
141	Q₈×D₁₃	—	4	2	no	—
142	#6129	—	4	2	no	—
143	D₄×D₁₃	—	2	8	no	—
144	D₄×D₁₃	—	4	2	no	—
145	#6127	—	2	4	no	—
146	C₂×D₅₂	—	4	2	no	—
147	C₂×D₅₂	C₂³	1	1	yes	characteristic
148	C₂×D₅₂	C₂³	1	2	yes	—
149	C₂×D₅₂	C₂³	1	1	yes	characteristic
150	C₂×D₅₂	C₂³	1	1	yes	characteristic
151	C₂×D₅₂	C₂³	1	2	yes	—
152	C₂×D₅₂	C₂³	1	2	yes	—
153	C₂×D₅₂	C₂³	1	2	yes	—
154	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
162	C₂×C₄×D₁₃	C₂³	1	2	yes	—
163	C₂×C₄×D₁₃	C₂³	1	2	yes	—
164	C₂×Dic₂₆	—	4	2	no	—
165	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
166	C₂×Dic₂₆	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	2	yes	—
170	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
175	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
176	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	C₄²×C₁₃	C₂³	1	1	yes	characteristic
182	C₄²×C₁₃	C₂³	1	1	yes	characteristic
183	C₄²×C₁₃	C₂³	1	1	yes	characteristic
184	C₄²×C₁₃	C₂³	1	1	yes	characteristic
185	C₄²×C₁₃	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
187	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
188	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
189	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
190	#6103	C₂³	1	1	yes	characteristic
191	#6103	C₂³	1	1	yes	characteristic
192	#6103	C₂³	1	1	yes	characteristic
193	#6103	C₂³	1	1	yes	characteristic
194	#6103	C₂³	1	2	yes	—
195	#6103	C₂³	1	2	yes	—
196	#6103	C₂³	1	2	yes	—
197	#6103	C₂³	1	2	yes	—
198	#6103	C₂³	1	2	yes	—
199	#6103	C₂³	1	2	yes	—
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	2	yes	—
206	#6103	C₂³	1	2	yes	—
207	#6103	C₂³	1	2	yes	—
208	#6103	C₂³	1	2	yes	—
209	#6103	C₂³	1	2	yes	—
210	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₁₃	C₂³	1	2	yes	—
213	C₄⋊Dic₁₃	C₂³	1	2	yes	—
214	#6101	C₂³	1	1	yes	characteristic
215	#6101	C₂³	1	1	yes	characteristic
216	#6101	C₂³	1	1	yes	characteristic
217	#6101	C₂³	1	1	yes	characteristic
218	#6101	C₂³	1	2	yes	—
219	#6101	C₂³	1	2	yes	—
220	#6101	C₂³	1	2	yes	—
221	#6101	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	1	yes	characteristic
226	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
228	C₄×Dic₁₃	C₂³	1	2	yes	—
229	C₄×Dic₁₃	C₂³	1	2	yes	—
230	#3514	—	13	1	no	maximal, Sylow
231	C₂³×C₁₃	C₂⁴	1	2	yes	—
232	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂²×D₁₃	—	2	4	no	—
234	C₂²×D₁₃	—	2	4	no	—
235	C₂²×D₁₃	—	4	2	no	—
236	C₂²×D₁₃	—	4	2	no	—
237	C₂²×D₁₃	—	4	2	no	—
238	C₂²×D₁₃	—	4	2	no	—
239	C₂²×D₁₃	C₂⁴	1	2	yes	—
240	C₂²×D₁₃	C₂⁴	1	2	yes	—
241	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
242	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
243	Q₈×C₁₃	—	2	2	no	—
244	D₄×C₁₃	—	2	4	no	—
245	D₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	2	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	—	4	2	no	—
250	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
257	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂²⋊D₁₃	—	2	2	no	—
260	C₂²⋊D₁₃	—	2	4	no	—
261	C₂²⋊D₁₃	—	4	2	no	—
262	C₂²⋊D₁₃	—	4	2	no	—
263	C₂²⋊D₁₃	—	4	2	no	—
264	C₂²⋊D₁₃	#41	1	4	yes	complemented
265	C₂×Dic₁₃	—	4	2	no	—
266	C₂×Dic₁₃	—	4	2	no	—
267	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₃	C₂⁴	1	2	yes	—
273	C₂×Dic₁₃	C₂⁴	1	2	yes	—
274	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
275	D₅₂	—	2	2	no	—
276	D₅₂	—	2	4	no	—
277	D₅₂	—	2	2	no	—
278	D₅₂	—	2	2	no	—
279	D₅₂	—	4	2	no	—
280	D₅₂	—	4	2	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	2	no	—
286	C₄×D₁₃	—	2	4	no	—
287	C₄×D₁₃	—	4	1	no	—
288	C₄×D₁₃	—	4	2	no	—
289	C₄×D₁₃	—	4	1	no	—
290	C₄×D₁₃	—	4	2	no	—
291	C₄×D₁₃	—	4	2	no	—
292	Dic₂₆	—	2	2	no	—
293	Dic₂₆	—	2	2	no	—
294	Dic₂₆	—	2	2	no	—
295	Dic₂₆	—	4	2	no	—
296	Dic₂₆	—	4	2	no	—
297	#559	—	13	1	no	—
298	#556	—	13	1	no	—
299	#555	—	13	2	no	—
300	#551	—	13	2	no	—
301	#551	—	13	2	no	—
302	D₄×Q₈	—	13	1	no	—
303	#548	—	13	1	no	—
304	#548	—	13	1	no	—
305	#546	—	13	2	no	—
306	#546	—	13	1	no	—
307	#546	—	13	1	no	—
308	D₄²	—	13	1	no	—
309	#542	—	13	2	no	—
310	#538	—	13	2	no	—
311	#538	—	13	2	no	—
312	#532	—	13	1	no	—
313	#529	—	13	1	no	—
314	#529	—	13	1	no	—
315	#529	D₁₃	1	1	yes	characteristic, complemented
316	C₂×#124	—	13	1	no	—
317	C₂×#124	—	13	1	no	—
318	#518	—	13	2	no	—
319	C₄×#41	—	13	1	no	—
320	C₂²×C₁₃	—	2	1	no	—
321	C₂²×C₁₃	—	2	1	no	—
322	C₂²×C₁₃	—	2	2	no	—
323	C₂²×C₁₃	—	2	2	no	—
324	C₂²×C₁₃	—	2	2	no	—
325	C₂²×C₁₃	C₂×#41	1	2	yes	—
326	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
327	C₂×D₁₃	—	2	1	no	—
328	C₂×D₁₃	—	2	1	no	—
329	C₂×D₁₃	—	2	1	no	—
330	C₂×D₁₃	—	2	2	no	—
331	C₂×D₁₃	—	2	2	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	2	no	—
337	C₂×D₁₃	—	2	2	no	—
338	C₂×D₁₃	—	8	4	no	—
339	C₂×D₁₃	—	8	4	no	—
340	C₂×D₁₃	C₂×#41	1	2	yes	—
341	C₄×C₁₃	—	2	1	no	—
342	C₄×C₁₃	—	2	1	no	—
343	C₄×C₁₃	—	2	2	no	—
344	C₄×C₁₃	—	2	1	no	—
345	C₄×C₁₃	—	2	2	no	—
346	C₄×C₁₃	—	2	1	no	—
347	C₄×C₁₃	—	2	2	no	—
348	C₄×C₁₃	—	2	1	no	—
349	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
350	Dic₁₃	—	2	1	no	—
351	Dic₁₃	—	2	2	no	—
352	Dic₁₃	—	2	2	no	—
353	Dic₁₃	—	2	1	no	—
354	Dic₁₃	—	2	1	no	—
355	Dic₁₃	—	2	1	no	—
356	Dic₁₃	—	2	1	no	—
357	Dic₁₃	C₂×#41	1	2	yes	—
358	C₂×#41	—	13	1	no	—
359	C₂×#41	—	13	1	no	—
360	C₂×#41	—	13	1	no	—
361	C₂²×Q₈	—	13	1	no	—
362	C₂²×Q₈	—	13	1	no	—
363	C₂²×D₄	—	13	2	no	—
364	C₂²×D₄	—	13	1	no	—
365	C₂²×D₄	—	13	1	no	—
366	C₄⋊Q₈	—	13	1	no	—
367	C₄⋊Q₈	—	13	2	no	—
368	#127	—	13	1	no	—
369	#126	—	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	C₂×D₁₃	1	1	yes	characteristic, complemented
375	#124	—	13	1	no	—
376	#124	—	13	1	no	—
377	#124	—	13	2	no	—
378	#124	—	13	2	no	—
379	#124	—	13	2	no	—
380	#124	—	13	2	no	—
381	#124	—	13	1	no	—
382	#124	—	13	1	no	—
383	#124	—	13	2	no	—
384	#124	—	13	1	no	—
385	#124	—	13	1	no	—
386	#124	—	13	2	no	—
387	#124	—	13	2	no	—
388	#124	C₂×D₁₃	1	1	yes	characteristic, complemented
389	#123	—	13	2	no	—
390	#123	—	13	2	no	—
391	#123	—	13	2	no	—
392	#123	—	13	2	no	—
393	#123	—	13	2	no	—
394	#123	—	13	2	no	—
395	#123	C₂×D₁₃	1	2	yes	complemented
396	C₂²⋊Q₈	—	13	1	no	—
397	C₂²⋊Q₈	—	13	1	no	—
398	C₂²⋊Q₈	—	13	2	no	—
399	C₂²⋊Q₈	—	13	2	no	—
400	C₂²⋊Q₈	—	13	2	no	—
401	C₂²⋊Q₈	—	13	2	no	—
402	C₂²⋊Q₈	—	13	2	no	—
403	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
404	#121	—	13	2	no	—
405	#121	—	13	2	no	—
406	#121	—	13	1	no	—
407	#121	—	13	1	no	—
408	#121	—	13	2	no	—
409	#121	—	13	2	no	—
410	#121	—	13	2	no	—
411	#121	—	13	2	no	—
412	#121	—	13	2	no	—
413	#121	C₂×D₁₃	1	1	yes	characteristic
414	#120	—	13	2	no	—
415	#120	—	13	2	no	—
416	#120	—	13	2	no	—
417	#120	—	13	2	no	—
418	C₄×Q₈	—	13	1	no	—
419	C₄×Q₈	—	13	1	no	—
420	C₄×Q₈	—	13	1	no	—
421	C₄×Q₈	—	13	1	no	—
422	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
423	C₄×D₄	—	13	2	no	—
424	C₄×D₄	—	13	1	no	—
425	C₄×D₄	—	13	1	no	—
426	C₄×D₄	—	13	1	no	—
427	C₄×D₄	—	13	1	no	—
428	C₄×D₄	—	13	2	no	—
429	C₄×D₄	—	13	2	no	—
430	C₄×D₄	—	13	1	no	—
431	C₄×D₄	—	13	2	no	—
432	C₄×D₄	—	13	1	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	1	no	—
438	C₄×D₄	—	13	2	no	—
439	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
440	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
441	#117	—	13	1	no	—
442	#117	—	13	2	no	—
443	#117	—	13	2	no	—
444	#117	—	13	1	no	—
445	#117	—	13	1	no	—
446	#117	—	13	2	no	—
447	#117	C₂×D₁₃	1	2	yes	complemented
448	C₂×C₂²⋊C₄	—	13	2	no	—
449	C₂×C₂²⋊C₄	—	13	2	no	—
450	C₂×C₂²⋊C₄	—	13	2	no	—
451	C₂×C₂²⋊C₄	—	13	2	no	—
452	C₂×C₂²⋊C₄	—	13	2	no	—
453	C₂×C₂²⋊C₄	—	13	2	no	—
454	C₂×C₄²	—	13	1	no	—
455	C₂×C₄²	—	13	1	no	—
456	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
457	C₂×C₁₃	—	2	2	no	—
458	C₂×C₁₃	—	4	2	no	—
459	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
460	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
461	C₂×C₁₃	#585	1	1	yes	characteristic
462	D₁₃	—	2	2	no	—
463	D₁₃	—	4	1	no	—
464	D₁₃	—	4	2	no	—
465	D₁₃	—	4	2	no	—
466	C₂⁴	—	13	2	no	—
467	C₂⁴	—	13	2	no	—
468	#41	—	26	4	no	—
469	#41	—	52	2	no	—
470	#41	—	52	2	no	—
471	C₂×Q₈	—	13	1	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×Q₈	—	52	2	no	—
477	C₂×Q₈	—	52	2	no	—
478	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
479	C₂×D₄	—	13	1	no	—
480	C₂×D₄	—	13	1	no	—
481	C₂×D₄	—	13	2	no	—
482	C₂×D₄	—	13	2	no	—
483	C₂×D₄	—	13	2	no	—
484	C₂×D₄	—	13	2	no	—
485	C₂×D₄	—	13	1	no	—
486	C₂×D₄	—	13	2	no	—
487	C₂×D₄	—	13	1	no	—
488	C₂×D₄	—	13	1	no	—
489	C₂×D₄	—	13	2	no	—
490	C₂×D₄	—	13	2	no	—
491	C₂×D₄	—	13	2	no	—
492	C₂×D₄	—	26	8	no	—
493	C₂×D₄	—	52	2	no	—
494	C₂×D₄	—	52	2	no	—
495	C₂×D₄	C₂²×D₁₃	1	2	yes	—
496	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
497	C₂²×C₄	—	13	2	no	—
498	C₂²×C₄	—	13	2	no	—
499	C₂²×C₄	—	13	1	no	—
500	C₂²×C₄	—	13	1	no	—
501	C₂²×C₄	—	13	1	no	—
502	C₂²×C₄	—	13	1	no	—
503	C₂²×C₄	—	13	2	no	—
504	C₂²×C₄	—	13	1	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	C₂²×D₁₃	1	1	yes	characteristic
510	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
511	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
512	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
513	C₄⋊C₄	—	13	1	no	—
514	C₄⋊C₄	—	13	2	no	—
515	C₄⋊C₄	—	13	2	no	—
516	C₄⋊C₄	—	13	1	no	—
517	C₄⋊C₄	—	13	1	no	—
518	C₄⋊C₄	—	13	1	no	—
519	C₄⋊C₄	—	13	1	no	—
520	C₄⋊C₄	—	13	1	no	—
521	C₄⋊C₄	—	13	2	no	—
522	C₄⋊C₄	—	13	2	no	—
523	C₄⋊C₄	—	13	2	no	—
524	C₄⋊C₄	—	13	2	no	—
525	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
526	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
527	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
528	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
529	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
530	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
531	C₂²⋊C₄	—	13	1	no	—
532	C₂²⋊C₄	—	13	2	no	—
533	C₂²⋊C₄	—	13	2	no	—
534	C₂²⋊C₄	—	13	1	no	—
535	C₂²⋊C₄	—	13	1	no	—
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	2	no	—
541	C₂²⋊C₄	—	13	2	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	1	no	—
549	C₂²⋊C₄	—	13	1	no	—
550	C₂²⋊C₄	—	13	1	no	—
551	C₂²⋊C₄	—	13	2	no	—
552	C₂²⋊C₄	—	13	2	no	—
553	C₂²⋊C₄	—	13	2	no	—
554	C₂²⋊C₄	—	13	2	no	—
555	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
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	2	yes	—
560	C₄²	—	13	1	no	—
561	C₄²	—	13	1	no	—
562	C₄²	—	13	1	no	—
563	C₄²	—	13	1	no	—
564	C₄²	—	13	1	no	—
565	C₄²	—	13	1	no	—
566	C₄²	—	13	2	no	—
567	C₄²	—	13	2	no	—
568	C₄²	C₂²×D₁₃	1	1	yes	characteristic
569	C₄²	C₂²×D₁₃	1	1	yes	characteristic
570	C₄²	C₂²×D₁₃	1	1	yes	characteristic
571	C₄²	C₂²×D₁₃	1	1	yes	characteristic
572	C₄²	C₂²×D₁₃	1	2	yes	—
573	C₁₃	#3514	1	1	yes	characteristic, complemented, Sylow
574	C₂³	—	13	1	no	—
575	C₂³	—	13	2	no	—
576	C₂³	—	13	2	no	—
577	C₂³	—	13	1	no	—
578	C₂³	—	26	4	no	—
579	C₂³	—	26	4	no	—
580	C₂³	—	52	2	no	—
581	C₂³	—	52	2	no	—
582	C₂³	—	52	2	no	—
583	C₂³	—	52	2	no	—
584	C₂³	C₂³×D₁₃	1	2	yes	—
585	C₂³	C₂³×D₁₃	1	1	yes	characteristic
586	Q₈	—	2	2	no	—
587	Q₈	—	26	2	no	—
588	Q₈	—	26	2	no	—
589	Q₈	—	26	2	no	—
590	Q₈	—	52	2	no	—
591	Q₈	—	52	2	no	—
592	D₄	—	2	4	no	—
593	D₄	—	2	2	no	—
594	D₄	—	13	4	no	—
595	D₄	—	26	4	no	—
596	D₄	—	26	2	no	—
597	D₄	—	26	4	no	—
598	D₄	—	26	2	no	—
599	D₄	—	26	2	no	—
600	D₄	—	26	2	no	—
601	D₄	—	52	2	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	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	13	1	no	—
612	C₂×C₄	—	13	1	no	—
613	C₂×C₄	—	13	1	no	—
614	C₂×C₄	—	13	1	no	—
615	C₂×C₄	—	13	1	no	—
616	C₂×C₄	—	13	1	no	—
617	C₂×C₄	—	13	2	no	—
618	C₂×C₄	—	13	2	no	—
619	C₂×C₄	—	26	4	no	—
620	C₂×C₄	—	26	2	no	—
621	C₂×C₄	—	26	2	no	—
622	C₂×C₄	—	26	2	no	—
623	C₂×C₄	—	26	2	no	—
624	C₂×C₄	—	52	1	no	—
625	C₂×C₄	—	52	1	no	—
626	C₂×C₄	—	52	2	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	C₂³×D₁₃	1	1	yes	characteristic
632	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₁₃	1	2	yes	—
634	C₂×C₄	C₂³×D₁₃	1	2	yes	—
635	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
638	C₂×C₄	C₂³×D₁₃	1	2	yes	—
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	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	13	2	no	—
646	C₂²	—	26	1	no	—
647	C₂²	—	26	1	no	—
648	C₂²	—	26	1	no	—
649	C₂²	—	26	2	no	—
650	C₂²	—	26	2	no	—
651	C₂²	—	26	1	no	—
652	C₂²	—	26	2	no	—
653	C₂²	—	26	2	no	—
654	C₂²	—	26	1	no	—
655	C₂²	—	26	2	no	—
656	C₂²	—	26	2	no	—
657	C₂²	—	104	4	no	—
658	C₂²	—	104	4	no	—
659	C₂²	#41×D₁₃	1	2	yes	—
660	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	2	no	—
669	C₄	—	13	2	no	—
670	C₄	—	26	1	no	—
671	C₄	—	26	1	no	—
672	C₄	—	26	1	no	—
673	C₄	—	26	2	no	—
674	C₄	—	26	2	no	—
675	C₄	—	26	1	no	—
676	C₄	—	26	1	no	—
677	C₄	#88256	1	2	yes	—
678	C₂	—	2	2	no	—
679	C₂	—	4	2	no	—
680	C₂	—	26	2	no	—
681	C₂	—	52	2	no	—
682	C₂	—	52	2	no	—
683	C₂	—	52	1	no	—
684	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
685	C₂	C₂×#88256	1	1	yes	characteristic
686	C₂	#11719648	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#529	C₂
hypercenter	#529	D₁₃
hypocenter	C₁₃	#3514
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. C₁₃×#529	C₂	semidirect
2. #11719415	C₂	semidirect
3. #11719409	C₂	semidirect
4. #11719396	C₂	semidirect
5. #11719396	C₂	semidirect
6. D₁₃×#124	C₂	semidirect
7. #11719373	C₂	semidirect
8. #11719363	C₂	semidirect
9. #11719359	C₂	semidirect
10. #11719337	C₂	semidirect
11. #11719335	C₂	semidirect
12. #11719314	C₂	semidirect
13. #11719303	C₂	semidirect
14. #11719281	C₂	semidirect
15. #11719273	C₂	semidirect
16. #11719265	C₂	semidirect
17. #11719264	C₂	semidirect
18. #11719259	C₂	semidirect
19. #11719250	C₂	semidirect
20. #11719237	C₂	semidirect
21. #11719232	C₂	semidirect
22. C₂×#88129	C₂	semidirect
23. C₄×#6127	C₂	semidirect
24. C₂×#6131	C₂²	semidirect
25. C₂×Q₈×D₁₃	C₂²	semidirect
26. C₂×#6129	C₂²	semidirect
31. C₂²×Dic₂₆	C₂²	semidirect
32. C₁₃×#126	C₂²	semidirect
33. C₁₃×#125	C₂²	semidirect
34. C₁₃×#124	C₂²	semidirect
35. C₁₃×#123	C₂²	semidirect
36. C₁₃×C₂²⋊Q₈	C₂²	semidirect
38. C₄×Q₈×C₁₃	C₂²	semidirect
39. C₄×D₄×C₁₃	C₂²	semidirect
40. C₄×D₄×C₁₃	C₂²	semidirect
41. C₁₃×#117	C₂²	semidirect
42. C₂×C₄²×C₁₃	C₂²	semidirect
44. #88198	C₂²	semidirect
46. #88193	C₂²	semidirect
48. #88190	C₂²	semidirect
49. D₄×Dic₁₃	C₂²	semidirect
50. #88184	C₂²	semidirect
51. #88183	C₂²	semidirect
54. C₄×C₂²⋊D₁₃	C₂²	semidirect
55. C₄×C₂²⋊D₁₃	C₂²	semidirect
56. C₄×C₂²⋊D₁₃	C₂²	semidirect
57. C₂×#6103	C₂²	semidirect
58. C₂×#6103	C₂²	semidirect
59. C₂×#6103	C₂²	semidirect
60. #88180	C₂²	semidirect
61. #88152	C₂²	semidirect
62. #88152	C₂²	semidirect
63. #88152	C₂²	semidirect
64. #88151	C₂²	semidirect
65. #88151	C₂²	semidirect
66. #88151	C₂²	semidirect
67. #88150	C₂²	semidirect
68. #88150	C₂²	semidirect
71. #88149	C₂²	semidirect
72. #88149	C₂²	semidirect
73. #88148	C₂²	semidirect
74. #88148	C₂²	semidirect
75. #88148	C₂²	semidirect
77. #88147	C₂²	semidirect
78. #88147	C₂²	semidirect
79. #88147	C₂²	semidirect
80. #88146	C₂²	semidirect
81. #88146	C₂²	semidirect
82. #88142	C₂²	semidirect
83. #88141	C₂²	semidirect
84. #88141	C₂²	semidirect
85. #88140	C₂²	semidirect
86. #88139	C₂²	semidirect
87. #88139	C₂²	semidirect
88. #88139	C₂²	semidirect
89. #88139	C₂²	semidirect
91. #88138	C₂²	semidirect
92. #88138	C₂²	semidirect
93. #88137	C₂²	semidirect
95. #88136	C₂²	semidirect
96. #88136	C₂²	semidirect
98. #88135	C₂²	semidirect
99. #88135	C₂²	semidirect
100. C₂²⋊C₄×D₁₃	C₂²	semidirect
101. C₂²⋊C₄×D₁₃	C₂²	semidirect
102. C₂²⋊C₄×D₁₃	C₂²	semidirect
103. #88132	C₂²	semidirect
104. #88132	C₂²	semidirect
105. #88130	C₂²	semidirect
108. #88129	C₂²	semidirect
109. #88129	C₂²	semidirect
110. #88129	C₂²	semidirect
111. #88129	C₂²	semidirect
112. #88129	C₂²	semidirect
113. C₄×D₅₂	C₂²	semidirect
114. C₄×D₅₂	C₂²	semidirect
115. C₄×D₅₂	C₂²	semidirect
116. #88126	C₂²	semidirect
117. #88126	C₂²	semidirect
118. #88126	C₂²	semidirect
119. C₄²×D₁₃	C₂²	semidirect
120. C₄²×D₁₃	C₂²	semidirect
121. C₄×Dic₂₆	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
264. C₂²⋊D₁₃	#41	semidirect
315. #529	D₁₃	semidirect
373. #126	C₂×D₁₃	semidirect
374. #125	C₂×D₁₃	semidirect
388. #124	C₂×D₁₃	semidirect
395. #123	C₂×D₁₃	semidirect
403. C₂²⋊Q₈	C₂×D₁₃	semidirect
422. C₄×Q₈	C₂×D₁₃	semidirect
439. C₄×D₄	C₂×D₁₃	semidirect
440. C₄×D₄	C₂×D₁₃	semidirect
447. #117	C₂×D₁₃	semidirect
456. C₂×C₄²	C₂×D₁₃	semidirect
573. C₁₃	#3514	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#529	2
#11719415	2
#11719409	2
#11719396	2
D₁₃×#124	2
#11719373	2
#11719363	2
#11719359	2
#11719337	2
#11719335	2
#11719314	2
#11719303	2
#11719281	2
#11719273	2
#11719265	2
#11719264	2
#11719259	2
#11719250	2
#11719237	2
#11719232	2
C₂×#88129	2
C₄×#6127	2
#3514	13