Subgroups — #13129205

Order 1664.

1150 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719438	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719430	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719416	C₂	1	2	yes	maximal, complemented
5	#11719414	C₂	1	2	yes	maximal, complemented
6	#11719383	C₂	1	2	yes	maximal, complemented
7	#11719379	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719379	C₂	1	2	yes	maximal, complemented
9	#11719373	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719371	C₂	1	2	yes	maximal, complemented
11	#11719359	C₂	1	2	yes	maximal, complemented
12	#11719349	C₂	1	2	yes	maximal, complemented
13	#11719336	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719335	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719334	C₂	1	2	yes	maximal, complemented
16	#11719314	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719304	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719282	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719273	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719259	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719258	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719233	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719230	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#6131	C₂²	1	2	yes	complemented
25	C₂×#6131	C₂²	1	1	yes	characteristic, complemented
26	C₂×#6131	C₂²	1	1	yes	characteristic, complemented
27	C₂×#6129	C₂²	1	1	yes	characteristic, complemented
28	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
29	C₂×D₄×D₁₃	C₂²	1	2	yes	—
30	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
31	C₂×#6127	C₂²	1	2	yes	complemented
32	C₂²×D₅₂	C₂²	1	1	yes	characteristic
33	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#126	C₂²	1	2	yes	complemented
35	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#124	C₂²	1	2	yes	complemented
37	C₁₃×#123	C₂²	1	2	yes	complemented
38	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
39	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#121	C₂²	1	1	yes	characteristic
41	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
42	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
44	#88201	C₂²	1	1	yes	characteristic
45	#88201	C₂²	1	2	yes	complemented
46	#88201	C₂²	1	2	yes	complemented
47	#88200	C₂²	1	2	yes	complemented
48	#88198	C₂²	1	1	yes	characteristic, complemented
49	#88194	C₂²	1	1	yes	characteristic
50	#88194	C₂²	1	1	yes	characteristic, complemented
51	#88194	C₂²	1	2	yes	complemented
52	#88193	C₂²	1	2	yes	complemented
53	#88191	C₂²	1	2	yes	—
54	#88184	C₂²	1	2	yes	complemented
55	#88184	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
58	C₂×#6103	C₂²	1	2	yes	complemented
59	#88152	C₂²	1	2	yes	complemented
60	#88152	C₂²	1	1	yes	characteristic, complemented
61	#88152	C₂²	1	2	yes	complemented
62	#88151	C₂²	1	1	yes	characteristic, complemented
63	#88150	C₂²	1	1	yes	characteristic, complemented
64	#88150	C₂²	1	2	yes	complemented
65	#88149	C₂²	1	1	yes	characteristic
66	#88149	C₂²	1	1	yes	characteristic
67	#88149	C₂²	1	1	yes	characteristic, complemented
68	#88149	C₂²	1	2	yes	complemented
69	#88149	C₂²	1	2	yes	complemented
70	#88149	C₂²	1	2	yes	complemented
71	#88149	C₂²	1	2	yes	complemented
72	#88149	C₂²	1	2	yes	complemented
73	#88149	C₂²	1	2	yes	complemented
74	#88148	C₂²	1	2	yes	complemented
75	#88148	C₂²	1	1	yes	characteristic, complemented
76	#88148	C₂²	1	2	yes	complemented
77	#88148	C₂²	1	2	yes	complemented
78	#88147	C₂²	1	1	yes	characteristic
79	#88147	C₂²	1	1	yes	characteristic, complemented
80	#88147	C₂²	1	2	yes	complemented
81	#88147	C₂²	1	1	yes	characteristic, complemented
82	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
83	#88143	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	1	yes	characteristic
87	#88138	C₂²	1	1	yes	characteristic
88	#88138	C₂²	1	2	yes	—
89	#88138	C₂²	1	2	yes	—
90	#88138	C₂²	1	2	yes	complemented
91	#88138	C₂²	1	2	yes	complemented
92	#88138	C₂²	1	2	yes	complemented
93	#88138	C₂²	1	2	yes	complemented
94	#88138	C₂²	1	2	yes	complemented
95	#88138	C₂²	1	2	yes	complemented
96	#88138	C₂²	1	2	yes	complemented
97	#88137	C₂²	1	1	yes	characteristic, complemented
98	#88137	C₂²	1	2	yes	complemented
99	#88136	C₂²	1	2	yes	—
100	#88136	C₂²	1	2	yes	complemented
101	#88136	C₂²	1	2	yes	complemented
102	#88136	C₂²	1	2	yes	complemented
103	#88136	C₂²	1	2	yes	complemented
104	#88136	C₂²	1	2	yes	complemented
105	#88136	C₂²	1	2	yes	complemented
106	#88135	C₂²	1	2	yes	complemented
107	#88135	C₂²	1	2	yes	complemented
108	#88135	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
110	#88133	C₂²	1	1	yes	characteristic, complemented
111	#88130	C₂²	1	2	yes	complemented
112	#88129	C₂²	1	1	yes	characteristic
113	#88129	C₂²	1	1	yes	characteristic, complemented
114	#88128	C₂²	1	1	yes	characteristic
115	#88128	C₂²	1	1	yes	characteristic, complemented
116	#88128	C₂²	1	2	yes	complemented
117	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₅₂	C₂²	1	2	yes	complemented
119	#88126	C₂²	1	1	yes	characteristic, complemented
120	#88126	C₂²	1	2	yes	complemented
121	C₄²×D₁₃	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×Q₈×C₁₃	C₂³	1	2	yes	—
127	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₃	C₂³	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₃	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	2	yes	—
135	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
140	C₂²×Dic₁₃	C₂³	1	2	yes	—
141	#6131	—	4	4	no	—
142	#6131	—	4	2	no	—
143	#6131	—	4	2	no	—
144	#6129	—	4	2	no	—
145	D₄×D₁₃	—	4	2	no	—
146	D₄×D₁₃	—	4	4	no	—
147	#6127	—	4	4	no	—
148	#6127	—	4	2	no	—
149	C₂×D₅₂	—	4	2	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×D₅₂	C₂³	1	2	yes	—
157	C₂×D₅₂	C₂³	1	2	yes	—
158	C₂×D₅₂	C₂³	1	2	yes	—
159	C₂×D₅₂	C₂³	1	2	yes	—
160	C₂×D₅₂	C₂³	1	2	yes	—
161	C₂×D₅₂	C₂³	1	2	yes	—
162	C₂×D₅₂	C₂³	1	2	yes	—
163	C₂×D₅₂	C₂³	1	2	yes	—
164	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
166	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
167	C₂×C₄×D₁₃	C₂³	1	2	yes	—
168	C₂×C₄×D₁₃	C₂³	1	2	yes	—
169	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
170	C₂×C₄×D₁₃	C₂³	1	2	yes	—
171	C₂×C₄×D₁₃	C₂³	1	2	yes	—
172	C₂×C₄×D₁₃	C₂³	1	2	yes	—
173	C₂×C₄×D₁₃	C₂³	1	2	yes	—
174	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
175	C₂×Dic₂₆	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×C₄⋊C₄	C₂³	1	2	yes	—
179	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
183	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
184	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
189	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₄²×C₁₃	C₂³	1	1	yes	characteristic
191	C₄²×C₁₃	C₂³	1	1	yes	characteristic
192	C₄²×C₁₃	C₂³	1	2	yes	—
193	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
194	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
195	#6103	C₂³	1	2	yes	—
196	#6103	C₂³	1	1	yes	characteristic
197	#6103	C₂³	1	2	yes	—
198	#6103	C₂³	1	1	yes	characteristic
199	#6103	C₂³	1	2	yes	—
200	#6103	C₂³	1	1	yes	characteristic
201	#6103	C₂³	1	2	yes	—
202	#6103	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
210	#6103	C₂³	1	2	yes	—
211	#6103	C₂³	1	2	yes	—
212	#6103	C₂³	1	2	yes	—
213	#6103	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
215	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
216	C₄⋊Dic₁₃	C₂³	1	2	yes	—
217	#6101	C₂³	1	1	yes	characteristic
218	#6101	C₂³	1	1	yes	characteristic
219	#6101	C₂³	1	1	yes	characteristic
220	#6101	C₂³	1	2	yes	—
221	#6101	C₂³	1	1	yes	characteristic
222	#6101	C₂³	1	2	yes	—
223	#6101	C₂³	1	2	yes	—
224	#6101	C₂³	1	1	yes	characteristic
225	#6101	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	1	yes	characteristic
229	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
230	C₄×Dic₁₃	C₂³	1	2	yes	—
231	#3546	—	13	1	no	maximal, Sylow
232	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂³×C₁₃	C₂⁴	1	2	yes	—
234	C₂²×D₁₃	—	4	2	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	—	4	2	no	—
240	C₂²×D₁₃	C₂⁴	1	2	yes	—
241	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
242	C₂²×D₁₃	C₂⁴	1	2	yes	—
243	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
244	C₂²×D₁₃	C₂⁴	1	2	yes	—
245	Q₈×C₁₃	—	2	2	no	—
246	Q₈×C₁₃	—	4	2	no	—
247	D₄×C₁₃	—	2	2	no	—
248	D₄×C₁₃	—	4	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	4	2	no	—
251	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₂²⋊D₁₃	—	2	4	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	C₂²⋊D₁₃	—	4	2	no	—
267	C₂²⋊D₁₃	—	4	1	no	—
268	C₂²⋊D₁₃	—	4	2	no	—
269	C₂×Dic₁₃	—	4	2	no	—
270	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₃	C₂⁴	1	2	yes	—
275	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
277	D₅₂	—	2	2	no	—
278	D₅₂	—	2	2	no	—
279	D₅₂	—	2	2	no	—
280	D₅₂	—	4	2	no	—
281	D₅₂	—	4	2	no	—
282	D₅₂	—	4	1	no	—
283	D₅₂	—	4	2	no	—
284	D₅₂	—	4	2	no	—
285	D₅₂	—	4	2	no	—
286	D₅₂	—	4	2	no	—
287	D₅₂	—	4	2	no	—
288	D₅₂	—	4	2	no	—
289	D₅₂	—	4	2	no	—
290	D₅₂	—	4	2	no	—
291	C₄×D₁₃	—	2	2	no	—
292	C₄×D₁₃	—	2	2	no	—
293	C₄×D₁₃	—	2	4	no	—
294	C₄×D₁₃	—	2	4	no	—
295	C₄×D₁₃	—	2	2	no	—
296	C₄×D₁₃	—	4	1	no	—
297	C₄×D₁₃	—	4	2	no	—
298	C₄×D₁₃	—	4	2	no	—
299	C₄×D₁₃	—	4	2	no	—
300	C₄×D₁₃	—	4	2	no	—
301	Dic₂₆	—	2	2	no	—
302	Dic₂₆	—	2	2	no	—
303	#560	—	13	2	no	—
304	#560	—	13	2	no	—
305	#556	—	13	1	no	—
306	#553	—	13	2	no	—
307	#550	—	13	1	no	—
308	#550	—	13	1	no	—
309	#550	—	13	1	no	—
310	#547	—	13	1	no	—
311	#546	—	13	2	no	—
312	#546	—	13	1	no	—
313	#546	—	13	1	no	—
314	D₄²	—	13	1	no	—
315	#542	—	13	1	no	—
316	#542	D₁₃	1	1	yes	characteristic, complemented
317	#538	—	13	2	no	—
318	#538	—	13	2	no	—
319	#537	—	13	2	no	—
320	#535	—	13	1	no	—
321	#535	—	13	2	no	—
322	#535	—	13	1	no	—
323	#532	—	13	1	no	—
324	#532	—	13	1	no	—
325	#529	—	13	1	no	—
326	C₂²×C₁₃	—	2	2	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	1	no	—
329	C₂²×C₁₃	—	2	1	no	—
330	C₂²×C₁₃	—	2	2	no	—
331	C₂²×C₁₃	—	2	1	no	—
332	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
333	C₂×D₁₃	—	2	1	no	—
334	C₂×D₁₃	—	2	2	no	—
335	C₂×D₁₃	—	2	1	no	—
336	C₂×D₁₃	—	2	1	no	—
337	C₂×D₁₃	—	2	2	no	—
338	C₂×D₁₃	—	2	2	no	—
339	C₂×D₁₃	—	2	2	no	—
340	C₂×D₁₃	—	2	2	no	—
341	C₂×D₁₃	—	2	2	no	—
342	C₂×D₁₃	—	2	1	no	—
343	C₂×D₁₃	—	2	1	no	—
344	C₂×D₁₃	—	2	2	no	—
345	C₂×D₁₃	—	2	2	no	—
346	C₂×D₁₃	—	2	2	no	—
347	C₂×D₁₃	—	2	1	no	—
348	C₂×D₁₃	—	8	4	no	—
349	C₂×D₁₃	—	8	4	no	—
350	C₄×C₁₃	—	2	1	no	—
351	C₄×C₁₃	—	2	2	no	—
352	C₄×C₁₃	—	2	2	no	—
353	C₄×C₁₃	—	2	1	no	—
354	C₄×C₁₃	—	2	1	no	—
355	C₄×C₁₃	—	2	2	no	—
356	C₄×C₁₃	—	2	1	no	—
357	C₄×C₁₃	—	2	1	no	—
358	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
359	Dic₁₃	—	2	1	no	—
360	Dic₁₃	—	2	2	no	—
361	Dic₁₃	—	2	1	no	—
362	Dic₁₃	—	2	1	no	—
363	Dic₁₃	—	2	1	no	—
364	Dic₁₃	—	2	1	no	—
365	Dic₁₃	H(5,𝔽₂)	1	2	yes	—
366	C₂×#41	—	13	2	no	—
367	C₂×#41	—	13	1	no	—
368	C₂×#41	—	13	1	no	—
369	C₂×#41	—	13	1	no	—
370	C₂×#41	—	13	1	no	—
371	C₂×#41	—	13	2	no	—
372	C₂²×D₄	—	13	2	no	—
373	C₂²×D₄	—	13	1	no	—
374	C₂²×D₄	—	13	1	no	—
375	C₄⋊Q₈	—	13	1	no	—
376	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
377	#127	—	13	1	no	—
378	#127	—	13	1	no	—
379	#127	—	13	2	no	—
380	#127	—	13	1	no	—
381	#127	—	13	1	no	—
382	#127	—	13	2	no	—
383	#126	—	13	1	no	—
384	#126	—	13	2	no	—
385	#126	—	13	2	no	—
386	#126	—	13	1	no	—
387	#126	—	13	2	no	—
388	#126	C₂×D₁₃	1	2	yes	complemented
389	#125	—	13	1	no	—
390	#124	—	13	2	no	—
391	#124	—	13	2	no	—
392	#124	—	13	1	no	—
393	#124	—	13	1	no	—
394	#124	—	13	1	no	—
395	#124	—	13	1	no	—
396	#124	C₂×D₁₃	1	1	yes	characteristic, complemented
397	#124	C₂×D₁₃	1	2	yes	complemented
398	#123	—	13	1	no	—
399	#123	—	13	2	no	—
400	#123	—	13	2	no	—
401	#123	—	13	2	no	—
402	#123	—	13	1	no	—
403	#123	—	13	2	no	—
404	#123	—	13	2	no	—
405	#123	C₂×D₁₃	1	2	yes	complemented
406	C₂²⋊Q₈	—	13	2	no	—
407	C₂²⋊Q₈	—	13	1	no	—
408	C₂²⋊Q₈	—	13	2	no	—
409	C₂²⋊Q₈	—	13	1	no	—
410	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
411	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
412	#121	—	13	2	no	—
413	#121	—	13	2	no	—
414	#121	—	13	2	no	—
415	#121	—	13	1	no	—
416	#121	—	13	1	no	—
417	#121	—	13	2	no	—
418	#121	—	13	2	no	—
419	#121	—	13	2	no	—
420	#121	—	13	2	no	—
421	#121	—	13	2	no	—
422	#121	—	13	2	no	—
423	#121	—	13	1	no	—
424	#121	—	13	1	no	—
425	#121	—	13	2	no	—
426	#121	—	13	2	no	—
427	#121	—	13	2	no	—
428	#121	—	13	2	no	—
429	#121	—	13	2	no	—
430	#121	—	13	2	no	—
431	#121	—	13	2	no	—
432	#121	—	13	2	no	—
433	#121	—	13	2	no	—
434	#121	C₂×D₁₃	1	1	yes	characteristic
435	#120	—	13	2	no	—
436	#120	—	13	2	no	—
437	#120	—	13	2	no	—
438	#120	—	13	2	no	—
439	#120	—	13	2	no	—
440	#120	—	13	2	no	—
441	#120	—	13	2	no	—
442	#120	—	13	2	no	—
443	C₄×Q₈	—	13	1	no	—
444	C₄×Q₈	—	13	1	no	—
445	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
446	C₄×D₄	—	13	1	no	—
447	C₄×D₄	—	13	1	no	—
448	C₄×D₄	—	13	1	no	—
449	C₄×D₄	—	13	2	no	—
450	C₄×D₄	—	13	1	no	—
451	C₄×D₄	—	13	1	no	—
452	C₄×D₄	—	13	2	no	—
453	C₄×D₄	—	13	2	no	—
454	C₄×D₄	—	13	2	no	—
455	C₄×D₄	—	13	1	no	—
456	C₄×D₄	—	13	2	no	—
457	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
458	#117	—	13	1	no	—
459	#117	—	13	2	no	—
460	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
461	C₂×C₄⋊C₄	—	13	2	no	—
462	C₂×C₂²⋊C₄	—	13	2	no	—
463	C₂×C₂²⋊C₄	—	13	2	no	—
464	C₂×C₄²	—	13	1	no	—
465	C₂×C₁₃	—	4	1	no	—
466	C₂×C₁₃	—	4	2	no	—
467	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
468	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
469	C₂×C₁₃	#585	1	1	yes	characteristic
470	D₁₃	—	4	1	no	—
471	D₁₃	—	4	2	no	—
472	D₁₃	—	4	2	no	—
473	D₁₃	—	4	2	no	—
474	D₁₃	—	4	1	no	—
475	C₂⁴	—	13	2	no	—
476	C₂⁴	—	13	2	no	—
477	#41	—	52	2	no	—
478	#41	—	52	4	no	—
479	#41	—	52	4	no	—
480	#41	—	52	2	no	—
481	#41	—	52	2	no	—
482	#41	—	52	2	no	—
483	C₂×Q₈	—	13	1	no	—
484	C₂×Q₈	—	13	1	no	—
485	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
486	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
487	C₂×D₄	—	13	1	no	—
488	C₂×D₄	—	13	2	no	—
489	C₂×D₄	—	13	2	no	—
490	C₂×D₄	—	13	1	no	—
491	C₂×D₄	—	13	2	no	—
492	C₂×D₄	—	13	2	no	—
493	C₂×D₄	—	13	2	no	—
494	C₂×D₄	—	13	2	no	—
495	C₂×D₄	—	13	2	no	—
496	C₂×D₄	—	13	1	no	—
497	C₂×D₄	—	13	1	no	—
498	C₂×D₄	—	13	1	no	—
499	C₂×D₄	—	13	2	no	—
500	C₂×D₄	—	13	1	no	—
501	C₂×D₄	—	13	2	no	—
502	C₂×D₄	—	13	2	no	—
503	C₂×D₄	—	13	2	no	—
504	C₂×D₄	—	13	2	no	—
505	C₂×D₄	—	13	2	no	—
506	C₂×D₄	—	13	2	no	—
507	C₂×D₄	—	13	2	no	—
508	C₂×D₄	—	13	2	no	—
509	C₂×D₄	—	13	2	no	—
510	C₂×D₄	—	52	2	no	—
511	C₂×D₄	—	52	2	no	—
512	C₂×D₄	—	52	4	no	—
513	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
514	C₂×D₄	C₂²×D₁₃	1	2	yes	—
515	C₂²×C₄	—	13	2	no	—
516	C₂²×C₄	—	13	1	no	—
517	C₂²×C₄	—	13	1	no	—
518	C₂²×C₄	—	13	2	no	—
519	C₂²×C₄	—	13	2	no	—
520	C₂²×C₄	—	13	1	no	—
521	C₂²×C₄	—	13	1	no	—
522	C₂²×C₄	—	13	2	no	—
523	C₂²×C₄	—	13	2	no	—
524	C₂²×C₄	—	13	2	no	—
525	C₂²×C₄	—	13	2	no	—
526	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
527	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
528	C₄⋊C₄	—	13	1	no	—
529	C₄⋊C₄	—	13	2	no	—
530	C₄⋊C₄	—	13	2	no	—
531	C₄⋊C₄	—	13	1	no	—
532	C₄⋊C₄	—	13	1	no	—
533	C₄⋊C₄	—	13	1	no	—
534	C₄⋊C₄	—	13	1	no	—
535	C₄⋊C₄	—	13	1	no	—
536	C₄⋊C₄	—	13	2	no	—
537	C₄⋊C₄	—	13	2	no	—
538	C₄⋊C₄	—	13	1	no	—
539	C₄⋊C₄	—	13	1	no	—
540	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
541	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
542	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
543	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
544	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
545	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
546	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
547	C₂²⋊C₄	—	13	1	no	—
548	C₂²⋊C₄	—	13	1	no	—
549	C₂²⋊C₄	—	13	1	no	—
550	C₂²⋊C₄	—	13	2	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	—	13	2	no	—
556	C₂²⋊C₄	—	13	1	no	—
557	C₂²⋊C₄	—	13	1	no	—
558	C₂²⋊C₄	—	13	2	no	—
559	C₂²⋊C₄	—	13	2	no	—
560	C₂²⋊C₄	—	13	1	no	—
561	C₂²⋊C₄	—	13	2	no	—
562	C₂²⋊C₄	—	13	2	no	—
563	C₂²⋊C₄	—	13	2	no	—
564	C₂²⋊C₄	—	13	2	no	—
565	C₂²⋊C₄	—	13	1	no	—
566	C₂²⋊C₄	—	13	1	no	—
567	C₂²⋊C₄	—	13	2	no	—
568	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
569	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
570	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
571	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
572	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
573	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
574	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
575	C₄²	—	13	1	no	—
576	C₄²	—	13	1	no	—
577	C₄²	—	13	1	no	—
578	C₄²	—	13	1	no	—
579	C₄²	—	13	2	no	—
580	C₄²	C₂²×D₁₃	1	1	yes	characteristic
581	C₄²	C₂²×D₁₃	1	2	yes	—
582	C₄²	C₂²×D₁₃	1	1	yes	characteristic
583	C₁₃	#3546	1	1	yes	characteristic, complemented, Sylow
584	C₂³	—	13	1	no	—
585	C₂³	—	13	2	no	—
586	C₂³	—	13	2	no	—
587	C₂³	—	13	1	no	—
588	C₂³	—	13	2	no	—
589	C₂³	—	52	2	no	—
590	C₂³	—	52	2	no	—
591	C₂³	—	52	2	no	—
592	C₂³	—	52	2	no	—
593	C₂³	—	52	2	no	—
594	C₂³	—	52	2	no	—
595	C₂³	C₂³×D₁₃	1	1	yes	characteristic
596	C₂³	C₂³×D₁₃	1	2	yes	—
597	Q₈	—	2	2	no	—
598	Q₈	—	4	2	no	—
599	Q₈	—	26	2	no	—
600	Q₈	—	26	2	no	—
601	D₄	—	2	2	no	—
602	D₄	—	4	2	no	—
603	D₄	—	26	2	no	—
604	D₄	—	26	4	no	—
605	D₄	—	26	2	no	—
606	D₄	—	26	2	no	—
607	D₄	—	26	2	no	—
608	D₄	—	52	2	no	—
609	D₄	—	52	1	no	—
610	D₄	—	52	2	no	—
611	D₄	—	52	2	no	—
612	D₄	—	52	2	no	—
613	D₄	—	52	2	no	—
614	D₄	—	52	2	no	—
615	D₄	—	52	2	no	—
616	D₄	—	52	2	no	—
617	D₄	—	52	2	no	—
618	D₄	—	52	2	no	—
619	D₄	—	52	2	no	—
620	D₄	—	52	2	no	—
621	D₄	—	52	1	no	—
622	D₄	—	52	2	no	—
623	D₄	—	52	2	no	—
624	D₄	—	52	2	no	—
625	D₄	—	52	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	13	1	no	—
629	C₂×C₄	—	13	1	no	—
630	C₂×C₄	—	13	1	no	—
631	C₂×C₄	—	13	1	no	—
632	C₂×C₄	—	13	2	no	—
633	C₂×C₄	—	13	1	no	—
634	C₂×C₄	—	13	1	no	—
635	C₂×C₄	—	26	4	no	—
636	C₂×C₄	—	26	4	no	—
637	C₂×C₄	—	26	2	no	—
638	C₂×C₄	—	26	2	no	—
639	C₂×C₄	—	26	2	no	—
640	C₂×C₄	—	52	1	no	—
641	C₂×C₄	—	52	2	no	—
642	C₂×C₄	—	52	2	no	—
643	C₂×C₄	—	52	2	no	—
644	C₂×C₄	—	52	2	no	—
645	C₂×C₄	—	52	2	no	—
646	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
647	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
648	C₂×C₄	C₂³×D₁₃	1	2	yes	—
649	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
650	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₁₃	1	2	yes	—
652	C₂×C₄	C₂³×D₁₃	1	2	yes	—
653	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
654	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
655	C₂²	—	2	1	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	26	1	no	—
662	C₂²	—	26	1	no	—
663	C₂²	—	26	2	no	—
664	C₂²	—	26	2	no	—
665	C₂²	—	26	2	no	—
666	C₂²	—	26	1	no	—
667	C₂²	—	26	2	no	—
668	C₂²	—	26	2	no	—
669	C₂²	—	26	2	no	—
670	C₂²	—	26	1	no	—
671	C₂²	—	26	1	no	—
672	C₂²	—	26	2	no	—
673	C₂²	—	26	2	no	—
674	C₂²	—	26	1	no	—
675	C₂²	—	26	2	no	—
676	C₂²	—	104	4	no	—
677	C₂²	—	104	4	no	—
678	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
679	C₄	—	2	1	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	1	no	—
687	C₄	—	13	2	no	—
688	C₄	—	26	1	no	—
689	C₄	—	26	1	no	—
690	C₄	—	26	2	no	—
691	C₄	—	26	1	no	—
692	C₄	—	26	1	no	—
693	C₄	—	26	1	no	—
694	C₄	#88256	1	2	yes	—
695	C₂	—	4	1	no	—
696	C₂	—	4	2	no	—
697	C₂	—	52	1	no	—
698	C₂	—	52	2	no	—
699	C₂	—	52	2	no	—
700	C₂	—	52	1	no	—
701	C₂	—	52	2	no	—
702	C₂	C₂×#88256	1	1	yes	characteristic
703	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic
704	C₂	#11719652	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#542	C₂
hypercenter	#542	D₁₃
hypocenter	C₁₃	#3546
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. C₁₃×#542	C₂	semidirect
2. #11719438	C₂	semidirect
3. #11719430	C₂	semidirect
4. #11719416	C₂	semidirect
5. #11719414	C₂	semidirect
6. #11719383	C₂	semidirect
7. #11719379	C₂	semidirect
8. #11719379	C₂	semidirect
9. #11719373	C₂	semidirect
10. #11719371	C₂	semidirect
11. #11719359	C₂	semidirect
12. #11719349	C₂	semidirect
13. #11719336	C₂	semidirect
14. #11719335	C₂	semidirect
15. #11719334	C₂	semidirect
16. #11719314	C₂	semidirect
17. #11719304	C₂	semidirect
18. #11719282	C₂	semidirect
19. #11719273	C₂	semidirect
20. #11719259	C₂	semidirect
21. #11719258	C₂	semidirect
22. #11719233	C₂	semidirect
23. #11719230	C₂	semidirect
24. C₂×#6131	C₂²	semidirect
25. C₂×#6131	C₂²	semidirect
26. C₂×#6131	C₂²	semidirect
27. C₂×#6129	C₂²	semidirect
30. C₂×#6127	C₂²	semidirect
31. C₂×#6127	C₂²	semidirect
33. C₁₃×C₄⋊Q₈	C₂²	semidirect
34. C₁₃×#126	C₂²	semidirect
35. C₁₃×#124	C₂²	semidirect
36. C₁₃×#124	C₂²	semidirect
37. C₁₃×#123	C₂²	semidirect
38. C₁₃×C₂²⋊Q₈	C₂²	semidirect
39. C₁₃×C₂²⋊Q₈	C₂²	semidirect
41. C₄×Q₈×C₁₃	C₂²	semidirect
42. C₄×D₄×C₁₃	C₂²	semidirect
43. C₁₃×#117	C₂²	semidirect
45. #88201	C₂²	semidirect
46. #88201	C₂²	semidirect
47. #88200	C₂²	semidirect
48. #88198	C₂²	semidirect
50. #88194	C₂²	semidirect
51. #88194	C₂²	semidirect
52. #88193	C₂²	semidirect
54. #88184	C₂²	semidirect
55. #88184	C₂²	semidirect
57. C₄×C₂²⋊D₁₃	C₂²	semidirect
58. C₂×#6103	C₂²	semidirect
59. #88152	C₂²	semidirect
60. #88152	C₂²	semidirect
61. #88152	C₂²	semidirect
62. #88151	C₂²	semidirect
63. #88150	C₂²	semidirect
64. #88150	C₂²	semidirect
67. #88149	C₂²	semidirect
68. #88149	C₂²	semidirect
69. #88149	C₂²	semidirect
70. #88149	C₂²	semidirect
71. #88149	C₂²	semidirect
72. #88149	C₂²	semidirect
73. #88149	C₂²	semidirect
74. #88148	C₂²	semidirect
75. #88148	C₂²	semidirect
76. #88148	C₂²	semidirect
77. #88148	C₂²	semidirect
79. #88147	C₂²	semidirect
80. #88147	C₂²	semidirect
81. #88147	C₂²	semidirect
82. C₄⋊C₄×D₁₃	C₂²	semidirect
83. #88143	C₂²	semidirect
84. #88141	C₂²	semidirect
85. #88140	C₂²	semidirect
90. #88138	C₂²	semidirect
91. #88138	C₂²	semidirect
92. #88138	C₂²	semidirect
93. #88138	C₂²	semidirect
94. #88138	C₂²	semidirect
95. #88138	C₂²	semidirect
96. #88138	C₂²	semidirect
97. #88137	C₂²	semidirect
98. #88137	C₂²	semidirect
100. #88136	C₂²	semidirect
101. #88136	C₂²	semidirect
102. #88136	C₂²	semidirect
103. #88136	C₂²	semidirect
104. #88136	C₂²	semidirect
105. #88136	C₂²	semidirect
106. #88135	C₂²	semidirect
107. #88135	C₂²	semidirect
108. #88135	C₂²	semidirect
109. C₂²⋊C₄×D₁₃	C₂²	semidirect
110. #88133	C₂²	semidirect
111. #88130	C₂²	semidirect
113. #88129	C₂²	semidirect
115. #88128	C₂²	semidirect
116. #88128	C₂²	semidirect
117. C₄×D₅₂	C₂²	semidirect
118. C₄×D₅₂	C₂²	semidirect
119. #88126	C₂²	semidirect
120. #88126	C₂²	semidirect
121. C₄²×D₁₃	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
316. #542	D₁₃	semidirect
376. C₄⋊Q₈	C₂×D₁₃	semidirect
388. #126	C₂×D₁₃	semidirect
396. #124	C₂×D₁₃	semidirect
397. #124	C₂×D₁₃	semidirect
405. #123	C₂×D₁₃	semidirect
410. C₂²⋊Q₈	C₂×D₁₃	semidirect
411. C₂²⋊Q₈	C₂×D₁₃	semidirect
445. C₄×Q₈	C₂×D₁₃	semidirect
457. C₄×D₄	C₂×D₁₃	semidirect
460. #117	C₂×D₁₃	semidirect
583. C₁₃	#3546	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#542	2
#11719438	2
#11719430	2
#11719416	2
#11719414	2
#11719383	2
#11719379	2
#11719373	2
#11719371	2
#11719359	2
#11719349	2
#11719336	2
#11719335	2
#11719334	2
#11719314	2
#11719304	2
#11719282	2
#11719273	2
#11719259	2
#11719258	2
#11719233	2
#11719230	2
#3546	13