Subgroups — #13129206

Order 1664.

1150 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719538	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719537	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719511	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719425	C₂	1	2	yes	maximal, complemented
7	#11719423	C₂	1	2	yes	maximal, complemented
8	#11719383	C₂	1	2	yes	maximal, complemented
9	#11719374	C₂	1	2	yes	maximal, complemented
10	#11719323	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719317	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719316	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719313	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719312	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719305	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719304	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719301	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719300	C₂	1	2	yes	maximal, complemented
19	#11719298	C₂	1	2	yes	maximal, complemented
20	#11719297	C₂	1	2	yes	maximal, complemented
21	#11719296	C₂	1	2	yes	maximal, complemented
22	#11719238	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719235	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
25	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊D₁₃	C₂²	1	2	yes	—
27	C₂×#6129	C₂²	1	1	yes	characteristic, complemented
28	C₂×#6129	C₂²	1	2	yes	complemented
29	C₂×#6129	C₂²	1	2	yes	complemented
30	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
31	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
32	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#127	C₂²	1	2	yes	complemented
34	C₁₃×#124	C₂²	1	2	yes	complemented
35	C₁₃×#121	C₂²	1	1	yes	characteristic
36	C₁₃×#121	C₂²	1	1	yes	characteristic
37	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#120	C₂²	1	2	yes	complemented
40	C₁₃×#120	C₂²	1	2	yes	complemented
41	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
42	#88207	C₂²	1	2	yes	—
43	#88207	C₂²	1	2	yes	complemented
44	C₂×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
45	#88201	C₂²	1	1	yes	characteristic, complemented
46	#88200	C₂²	1	2	yes	complemented
47	#88198	C₂²	1	1	yes	characteristic, complemented
48	#88194	C₂²	1	1	yes	characteristic
49	#88194	C₂²	1	1	yes	characteristic
50	#88194	C₂²	1	2	yes	complemented
51	#88194	C₂²	1	2	yes	complemented
52	#88193	C₂²	1	2	yes	—
53	#88193	C₂²	1	1	yes	characteristic
54	#88193	C₂²	1	1	yes	characteristic, complemented
55	#88193	C₂²	1	2	yes	complemented
56	#88193	C₂²	1	2	yes	complemented
57	#88193	C₂²	1	2	yes	complemented
58	#88193	C₂²	1	2	yes	complemented
59	#88193	C₂²	1	2	yes	complemented
60	#88193	C₂²	1	2	yes	complemented
61	#88193	C₂²	1	1	yes	characteristic, complemented
62	#88193	C₂²	1	1	yes	characteristic, complemented
63	#88193	C₂²	1	2	yes	complemented
64	#88192	C₂²	1	1	yes	characteristic
65	#88192	C₂²	1	1	yes	characteristic
66	#88192	C₂²	1	2	yes	complemented
67	#88192	C₂²	1	2	yes	complemented
68	#88192	C₂²	1	2	yes	complemented
69	#88191	C₂²	1	2	yes	—
70	#88191	C₂²	1	2	yes	complemented
71	#88191	C₂²	1	2	yes	complemented
72	#88190	C₂²	1	1	yes	characteristic
73	#88190	C₂²	1	1	yes	characteristic, complemented
74	#88189	C₂²	1	2	yes	complemented
75	#88189	C₂²	1	2	yes	complemented
76	#88189	C₂²	1	2	yes	complemented
77	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
78	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
79	D₄×Dic₁₃	C₂²	1	2	yes	complemented
80	D₄×Dic₁₃	C₂²	1	2	yes	complemented
81	#88184	C₂²	1	1	yes	characteristic
82	#88184	C₂²	1	1	yes	characteristic, complemented
83	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
84	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
85	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
86	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
88	#88178	C₂²	1	1	yes	characteristic, complemented
89	#88178	C₂²	1	1	yes	characteristic, complemented
90	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
91	#88151	C₂²	1	1	yes	characteristic, complemented
92	#88149	C₂²	1	1	yes	characteristic, complemented
93	#88147	C₂²	1	1	yes	characteristic, complemented
94	#88146	C₂²	1	1	yes	characteristic, complemented
95	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
96	#88144	C₂²	1	1	yes	characteristic, complemented
97	#88142	C₂²	1	1	yes	characteristic, complemented
98	#88141	C₂²	1	1	yes	characteristic, complemented
99	#88140	C₂²	1	2	yes	complemented
100	#88139	C₂²	1	2	yes	—
101	#88139	C₂²	1	2	yes	complemented
102	#88139	C₂²	1	2	yes	complemented
103	#88138	C₂²	1	2	yes	complemented
104	#88138	C₂²	1	2	yes	complemented
105	#88138	C₂²	1	2	yes	complemented
106	#88137	C₂²	1	2	yes	complemented
107	#88137	C₂²	1	2	yes	complemented
108	#88137	C₂²	1	2	yes	complemented
109	#88136	C₂²	1	2	yes	complemented
110	#88135	C₂²	1	2	yes	complemented
111	#88135	C₂²	1	2	yes	complemented
112	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
113	#88133	C₂²	1	2	yes	complemented
114	#88133	C₂²	1	2	yes	complemented
115	#88133	C₂²	1	2	yes	complemented
116	#88132	C₂²	1	2	yes	complemented
117	#88132	C₂²	1	2	yes	complemented
118	#88131	C₂²	1	2	yes	complemented
119	#88130	C₂²	1	2	yes	complemented
120	#88130	C₂²	1	2	yes	complemented
121	C₄×D₅₂	C₂²	1	2	yes	complemented
122	C₄×Dic₂₆	C₂²	1	2	yes	complemented
123	C₂⁴×C₁₃	C₂³	1	2	yes	—
124	C₂³×D₁₃	C₂³	1	2	yes	—
125	C₁₃×#41	—	4	2	no	—
126	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₃	—	4	2	no	—
128	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₁₃	C₂³	1	2	yes	—
131	C₂×D₄×C₁₃	C₂³	1	2	yes	—
132	C₂×D₄×C₁₃	C₂³	1	2	yes	—
133	C₂×D₄×C₁₃	C₂³	1	2	yes	—
134	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
135	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
136	C₂×D₄×C₁₃	C₂³	1	2	yes	—
137	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₁₃	—	4	4	no	—
142	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
153	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
155	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
157	C₂²×Dic₁₃	C₂³	1	2	yes	—
158	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
159	C₂²×Dic₁₃	C₂³	1	2	yes	—
160	C₂²×Dic₁₃	C₂³	1	2	yes	—
161	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
162	C₂²×Dic₁₃	C₂³	1	2	yes	—
163	#6129	—	4	2	no	—
164	#6129	—	4	4	no	—
165	#6129	—	4	4	no	—
166	D₄×D₁₃	—	4	2	no	—
167	#6127	—	4	2	no	—
168	#6127	—	4	2	no	—
169	C₂×D₅₂	C₂³	1	1	yes	characteristic
170	C₂×D₅₂	C₂³	1	2	yes	—
171	C₂×D₅₂	C₂³	1	1	yes	characteristic
172	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
173	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
174	C₂×C₄×D₁₃	C₂³	1	2	yes	—
175	C₂×C₄×D₁₃	C₂³	1	2	yes	—
176	C₂×C₄×D₁₃	C₂³	1	2	yes	—
177	C₂×Dic₂₆	C₂³	1	2	yes	—
178	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
179	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
180	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	C₄²×C₁₃	C₂³	1	2	yes	—
188	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
189	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
190	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
191	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
192	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
193	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
194	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
195	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
196	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
197	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
198	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
199	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
208	#6103	C₂³	1	2	yes	—
209	#6103	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₁₃	C₂³	1	2	yes	—
211	C₄⋊Dic₁₃	C₂³	1	2	yes	—
212	C₄⋊Dic₁₃	C₂³	1	2	yes	—
213	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
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	#6101	C₂³	1	2	yes	—
221	#6101	C₂³	1	2	yes	—
222	#6101	C₂³	1	2	yes	—
223	#6101	C₂³	1	1	yes	characteristic
224	#6101	C₂³	1	1	yes	characteristic
225	C₄×Dic₁₃	C₂³	1	2	yes	—
226	C₄×Dic₁₃	C₂³	1	2	yes	—
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	1	yes	characteristic
231	#3546	—	13	1	no	maximal, Sylow
232	C₂³×C₁₃	—	4	2	no	—
233	C₂³×C₁₃	—	4	2	no	—
234	C₂³×C₁₃	—	4	2	no	—
235	C₂³×C₁₃	C₂⁴	1	2	yes	—
236	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₂³×C₁₃	C₂⁴	1	2	yes	—
238	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂²×D₁₃	—	4	2	no	—
241	C₂²×D₁₃	—	4	2	no	—
242	C₂²×D₁₃	—	4	2	no	—
243	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
244	C₂²×D₁₃	C₂⁴	1	2	yes	—
245	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
246	Q₈×C₁₃	—	4	1	no	—
247	D₄×C₁₃	—	2	2	no	—
248	D₄×C₁₃	—	2	2	no	—
249	D₄×C₁₃	—	4	2	no	—
250	D₄×C₁₃	—	4	2	no	—
251	D₄×C₁₃	—	4	2	no	—
252	D₄×C₁₃	—	4	2	no	—
253	D₄×C₁₃	—	4	2	no	—
254	D₄×C₁₃	—	4	1	no	—
255	D₄×C₁₃	—	4	1	no	—
256	D₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
261	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
265	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
266	C₂²⋊D₁₃	—	2	2	no	—
267	C₂²⋊D₁₃	—	2	4	no	—
268	C₂²⋊D₁₃	—	2	2	no	—
269	C₂²⋊D₁₃	—	4	2	no	—
270	C₂²⋊D₁₃	—	4	1	no	—
271	C₂²⋊D₁₃	—	4	1	no	—
272	C₂²⋊D₁₃	—	4	2	no	—
273	C₂²⋊D₁₃	—	4	2	no	—
274	C₂²⋊D₁₃	—	4	2	no	—
275	C₂²⋊D₁₃	—	4	2	no	—
276	C₂²⋊D₁₃	—	4	2	no	—
277	C₂²⋊D₁₃	—	4	2	no	—
278	C₂²⋊D₁₃	—	4	1	no	—
279	C₂²⋊D₁₃	—	4	2	no	—
280	C₂²⋊D₁₃	—	4	1	no	—
281	C₂×Dic₁₃	—	2	2	no	—
282	C₂×Dic₁₃	—	2	4	no	—
283	C₂×Dic₁₃	—	4	2	no	—
284	C₂×Dic₁₃	—	4	2	no	—
285	C₂×Dic₁₃	—	4	2	no	—
286	C₂×Dic₁₃	—	4	1	no	—
287	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
288	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
289	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
290	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
291	C₂×Dic₁₃	C₂⁴	1	2	yes	—
292	C₂×Dic₁₃	C₂⁴	1	2	yes	—
293	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
294	C₂×Dic₁₃	C₂⁴	1	2	yes	—
295	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
296	D₅₂	—	2	2	no	—
297	D₅₂	—	4	2	no	—
298	D₅₂	—	4	1	no	—
299	C₄×D₁₃	—	2	2	no	—
300	C₄×D₁₃	—	2	2	no	—
301	C₄×D₁₃	—	4	2	no	—
302	C₄×D₁₃	—	4	2	no	—
303	C₄×D₁₃	—	4	2	no	—
304	Dic₂₆	—	2	2	no	—
305	Dic₂₆	—	2	4	no	—
306	Dic₂₆	—	4	1	no	—
307	#560	—	13	2	no	—
308	#560	—	13	2	no	—
309	#556	—	13	1	no	—
310	#553	—	13	1	no	—
311	#553	—	13	1	no	—
312	#550	—	13	2	no	—
313	#550	—	13	1	no	—
314	#547	—	13	1	no	—
315	#546	—	13	1	no	—
316	#546	—	13	1	no	—
317	#546	—	13	2	no	—
318	D₄²	—	13	1	no	—
319	#542	—	13	2	no	—
320	#538	—	13	2	no	—
321	#538	—	13	2	no	—
322	#537	—	13	1	no	—
323	#537	—	13	1	no	—
324	#535	—	13	1	no	—
325	#535	—	13	2	no	—
326	#535	D₁₃	1	1	yes	characteristic, complemented
327	#532	—	13	1	no	—
328	#532	—	13	1	no	—
329	#529	—	13	1	no	—
330	C₂²×C₁₃	—	2	1	no	—
331	C₂²×C₁₃	—	2	2	no	—
332	C₂²×C₁₃	—	2	1	no	—
333	C₂²×C₁₃	—	2	2	no	—
334	C₂²×C₁₃	—	2	2	no	—
335	C₂²×C₁₃	—	2	1	no	—
336	C₂²×C₁₃	—	2	1	no	—
337	C₂²×C₁₃	—	2	1	no	—
338	C₂²×C₁₃	—	2	2	no	—
339	C₂²×C₁₃	—	2	1	no	—
340	C₂²×C₁₃	—	2	1	no	—
341	C₂²×C₁₃	—	2	1	no	—
342	C₂²×C₁₃	—	2	2	no	—
343	C₂²×C₁₃	—	2	1	no	—
344	C₂²×C₁₃	—	2	2	no	—
345	C₂²×C₁₃	—	8	4	no	—
346	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
347	C₂×D₁₃	—	2	1	no	—
348	C₂×D₁₃	—	2	1	no	—
349	C₂×D₁₃	—	2	1	no	—
350	C₂×D₁₃	—	2	2	no	—
351	C₂×D₁₃	—	2	2	no	—
352	C₂×D₁₃	—	2	1	no	—
353	C₂×D₁₃	—	2	1	no	—
354	C₂×D₁₃	—	2	2	no	—
355	C₂×D₁₃	—	2	1	no	—
356	C₂×D₁₃	—	8	4	no	—
357	C₄×C₁₃	—	2	2	no	—
358	C₄×C₁₃	—	2	1	no	—
359	C₄×C₁₃	—	2	1	no	—
360	C₄×C₁₃	—	2	1	no	—
361	C₄×C₁₃	—	2	2	no	—
362	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
363	Dic₁₃	—	2	2	no	—
364	Dic₁₃	—	2	2	no	—
365	Dic₁₃	—	2	1	no	—
366	Dic₁₃	—	2	1	no	—
367	Dic₁₃	—	2	1	no	—
368	Dic₁₃	—	2	2	no	—
369	Dic₁₃	—	2	1	no	—
370	Dic₁₃	—	2	1	no	—
371	Dic₁₃	H(5,𝔽₂)	1	2	yes	—
372	C₂×#41	—	13	2	no	—
373	C₂×#41	—	13	2	no	—
374	C₂×#41	—	13	1	no	—
375	C₂×#41	—	13	1	no	—
376	C₂×#41	—	13	1	no	—
377	C₂×#41	C₂×D₁₃	1	1	yes	characteristic, complemented
378	C₂²×D₄	—	13	2	no	—
379	C₂²×D₄	—	13	1	no	—
380	C₂²×D₄	C₂×D₁₃	1	1	yes	characteristic
381	C₄⋊Q₈	—	13	1	no	—
382	C₄⋊Q₈	—	13	1	no	—
383	#127	—	13	1	no	—
384	#127	—	13	1	no	—
385	#127	—	13	2	no	—
386	#127	—	13	2	no	—
387	#127	C₂×D₁₃	1	2	yes	complemented
388	#126	—	13	2	no	—
389	#126	—	13	2	no	—
390	#126	—	13	2	no	—
391	#126	—	13	2	no	—
392	#126	—	13	2	no	—
393	#125	—	13	1	no	—
394	#124	—	13	1	no	—
395	#124	—	13	1	no	—
396	#124	—	13	1	no	—
397	#124	—	13	2	no	—
398	#124	—	13	2	no	—
399	#124	—	13	2	no	—
400	#124	C₂×D₁₃	1	2	yes	complemented
401	#123	—	13	2	no	—
402	#123	—	13	2	no	—
403	#123	—	13	2	no	—
404	#123	—	13	2	no	—
405	#123	—	13	2	no	—
406	#123	—	13	2	no	—
407	#123	—	13	2	no	—
408	C₂²⋊Q₈	—	13	2	no	—
409	C₂²⋊Q₈	—	13	1	no	—
410	C₂²⋊Q₈	—	13	1	no	—
411	C₂²⋊Q₈	—	13	1	no	—
412	C₂²⋊Q₈	—	13	2	no	—
413	C₂²⋊Q₈	—	13	2	no	—
414	#121	—	13	1	no	—
415	#121	—	13	1	no	—
416	#121	—	13	1	no	—
417	#121	—	13	2	no	—
418	#121	—	13	1	no	—
419	#121	—	13	2	no	—
420	#121	—	13	1	no	—
421	#121	—	13	2	no	—
422	#121	—	13	1	no	—
423	#121	—	13	2	no	—
424	#121	—	13	2	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	1	no	—
432	#121	—	13	1	no	—
433	#121	—	13	1	no	—
434	#121	—	13	2	no	—
435	#121	—	13	2	no	—
436	#121	—	13	2	no	—
437	#121	C₂×D₁₃	1	1	yes	characteristic
438	#121	C₂×D₁₃	1	1	yes	characteristic
439	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
440	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
441	#120	—	13	2	no	—
442	#120	—	13	2	no	—
443	#120	—	13	2	no	—
444	#120	—	13	2	no	—
445	#120	—	13	2	no	—
446	#120	—	13	2	no	—
447	#120	C₂×D₁₃	1	2	yes	complemented
448	#120	C₂×D₁₃	1	2	yes	complemented
449	C₄×Q₈	—	13	1	no	—
450	C₄×Q₈	—	13	2	no	—
451	C₄×D₄	—	13	1	no	—
452	C₄×D₄	—	13	2	no	—
453	C₄×D₄	—	13	1	no	—
454	C₄×D₄	—	13	2	no	—
455	C₄×D₄	—	13	1	no	—
456	C₄×D₄	—	13	1	no	—
457	C₄×D₄	—	13	1	no	—
458	C₄×D₄	—	13	1	no	—
459	C₄×D₄	—	13	1	no	—
460	C₄×D₄	—	13	2	no	—
461	C₄×D₄	—	13	2	no	—
462	C₄×D₄	—	13	2	no	—
463	#117	—	13	1	no	—
464	#117	—	13	2	no	—
465	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
466	C₂×C₄⋊C₄	—	13	1	no	—
467	C₂×C₄⋊C₄	—	13	1	no	—
468	C₂×C₂²⋊C₄	—	13	2	no	—
469	C₂×C₂²⋊C₄	—	13	2	no	—
470	C₂×C₄²	—	13	1	no	—
471	C₂×C₁₃	—	4	2	no	—
472	C₂×C₁₃	—	4	1	no	—
473	C₂×C₁₃	—	4	1	no	—
474	C₂×C₁₃	—	4	2	no	—
475	C₂×C₁₃	—	4	1	no	—
476	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
477	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
478	C₂×C₁₃	#585	1	1	yes	characteristic
479	D₁₃	—	4	1	no	—
480	D₁₃	—	4	2	no	—
481	D₁₃	—	4	1	no	—
482	C₂⁴	—	13	2	no	—
483	C₂⁴	C₂²×D₁₃	1	2	yes	—
484	#41	—	4	2	no	—
485	#41	—	52	2	no	—
486	#41	—	52	2	no	—
487	#41	—	52	2	no	—
488	#41	—	52	4	no	—
489	#41	—	52	4	no	—
490	C₂×Q₈	—	13	1	no	—
491	C₂×Q₈	—	13	2	no	—
492	C₂×Q₈	—	13	1	no	—
493	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
494	C₂×D₄	—	4	2	no	—
495	C₂×D₄	—	13	1	no	—
496	C₂×D₄	—	13	2	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	1	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	1	no	—
510	C₂×D₄	—	13	1	no	—
511	C₂×D₄	—	13	2	no	—
512	C₂×D₄	—	13	1	no	—
513	C₂×D₄	—	52	2	no	—
514	C₂×D₄	—	52	4	no	—
515	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
516	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
517	C₂×D₄	C₂²×D₁₃	1	2	yes	—
518	C₂×D₄	C₂²×D₁₃	1	2	yes	—
519	C₂×D₄	C₂²×D₁₃	1	2	yes	—
520	C₂×D₄	C₂²×D₁₃	1	2	yes	—
521	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
522	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
523	C₂×D₄	C₂²×D₁₃	1	2	yes	—
524	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
525	C₂²×C₄	—	13	1	no	—
526	C₂²×C₄	—	13	2	no	—
527	C₂²×C₄	—	13	1	no	—
528	C₂²×C₄	—	13	2	no	—
529	C₂²×C₄	—	13	2	no	—
530	C₂²×C₄	—	13	2	no	—
531	C₂²×C₄	—	13	1	no	—
532	C₂²×C₄	—	13	1	no	—
533	C₂²×C₄	—	13	2	no	—
534	C₂²×C₄	—	13	2	no	—
535	C₂²×C₄	—	13	2	no	—
536	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
537	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
538	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
539	C₄⋊C₄	—	13	1	no	—
540	C₄⋊C₄	—	13	1	no	—
541	C₄⋊C₄	—	13	2	no	—
542	C₄⋊C₄	—	13	2	no	—
543	C₄⋊C₄	—	13	2	no	—
544	C₄⋊C₄	—	13	2	no	—
545	C₄⋊C₄	—	13	1	no	—
546	C₄⋊C₄	—	13	2	no	—
547	C₄⋊C₄	—	13	1	no	—
548	C₄⋊C₄	—	13	1	no	—
549	C₄⋊C₄	—	13	2	no	—
550	C₄⋊C₄	—	13	1	no	—
551	C₄⋊C₄	—	13	2	no	—
552	C₄⋊C₄	—	13	2	no	—
553	C₄⋊C₄	—	13	2	no	—
554	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
555	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
556	C₂²⋊C₄	—	13	2	no	—
557	C₂²⋊C₄	—	13	1	no	—
558	C₂²⋊C₄	—	13	2	no	—
559	C₂²⋊C₄	—	13	2	no	—
560	C₂²⋊C₄	—	13	2	no	—
561	C₂²⋊C₄	—	13	1	no	—
562	C₂²⋊C₄	—	13	1	no	—
563	C₂²⋊C₄	—	13	2	no	—
564	C₂²⋊C₄	—	13	2	no	—
565	C₂²⋊C₄	—	13	2	no	—
566	C₂²⋊C₄	—	13	2	no	—
567	C₂²⋊C₄	—	13	1	no	—
568	C₂²⋊C₄	—	13	1	no	—
569	C₂²⋊C₄	—	13	2	no	—
570	C₂²⋊C₄	—	13	2	no	—
571	C₂²⋊C₄	—	13	1	no	—
572	C₂²⋊C₄	—	13	1	no	—
573	C₂²⋊C₄	—	13	2	no	—
574	C₂²⋊C₄	—	13	2	no	—
575	C₂²⋊C₄	—	13	2	no	—
576	C₂²⋊C₄	—	13	2	no	—
577	C₂²⋊C₄	—	13	1	no	—
578	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
579	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
580	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
581	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
582	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
583	C₄²	—	13	1	no	—
584	C₄²	—	13	1	no	—
585	C₄²	—	13	1	no	—
586	C₄²	—	13	1	no	—
587	C₄²	—	13	2	no	—
588	C₄²	—	13	2	no	—
589	C₄²	C₂²×D₁₃	1	2	yes	—
590	C₁₃	#3546	1	1	yes	characteristic, complemented, Sylow
591	C₂³	—	4	2	no	—
592	C₂³	—	4	2	no	—
593	C₂³	—	4	2	no	—
594	C₂³	—	13	1	no	—
595	C₂³	—	13	2	no	—
596	C₂³	—	13	1	no	—
597	C₂³	—	52	2	no	—
598	C₂³	—	52	2	no	—
599	C₂³	—	52	2	no	—
600	C₂³	C₂³×D₁₃	1	2	yes	—
601	C₂³	C₂³×D₁₃	1	1	yes	characteristic
602	C₂³	C₂³×D₁₃	1	2	yes	—
603	C₂³	C₂³×D₁₃	1	1	yes	characteristic
604	C₂³	C₂³×D₁₃	1	1	yes	characteristic
605	Q₈	—	4	1	no	—
606	Q₈	—	26	4	no	—
607	Q₈	—	26	2	no	—
608	Q₈	—	52	1	no	—
609	D₄	—	2	2	no	—
610	D₄	—	2	2	no	—
611	D₄	—	4	2	no	—
612	D₄	—	4	2	no	—
613	D₄	—	4	2	no	—
614	D₄	—	4	1	no	—
615	D₄	—	4	1	no	—
616	D₄	—	4	1	no	—
617	D₄	—	4	2	no	—
618	D₄	—	4	2	no	—
619	D₄	—	26	2	no	—
620	D₄	—	26	4	no	—
621	D₄	—	26	2	no	—
622	D₄	—	26	2	no	—
623	D₄	—	52	2	no	—
624	D₄	—	52	1	no	—
625	D₄	—	52	1	no	—
626	D₄	—	52	2	no	—
627	D₄	—	52	1	no	—
628	D₄	—	52	2	no	—
629	D₄	—	52	2	no	—
630	D₄	—	52	2	no	—
631	D₄	—	52	1	no	—
632	D₄	—	52	1	no	—
633	D₄	—	52	2	no	—
634	D₄	—	52	2	no	—
635	D₄	—	52	2	no	—
636	D₄	—	52	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	13	1	no	—
641	C₂×C₄	—	13	1	no	—
642	C₂×C₄	—	13	1	no	—
643	C₂×C₄	—	13	1	no	—
644	C₂×C₄	—	13	1	no	—
645	C₂×C₄	—	13	2	no	—
646	C₂×C₄	—	13	2	no	—
647	C₂×C₄	—	13	1	no	—
648	C₂×C₄	—	13	2	no	—
649	C₂×C₄	—	26	4	no	—
650	C₂×C₄	—	26	2	no	—
651	C₂×C₄	—	26	2	no	—
652	C₂×C₄	—	26	2	no	—
653	C₂×C₄	—	52	2	no	—
654	C₂×C₄	—	52	2	no	—
655	C₂×C₄	—	52	2	no	—
656	C₂×C₄	—	52	1	no	—
657	C₂×C₄	—	52	2	no	—
658	C₂×C₄	—	52	2	no	—
659	C₂×C₄	—	52	2	no	—
660	C₂×C₄	C₂³×D₁₃	1	2	yes	—
661	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
662	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
663	C₂×C₄	C₂³×D₁₃	1	2	yes	—
664	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
665	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
666	C₂²	—	2	1	no	—
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	2	1	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	2	1	no	—
681	C₂²	—	8	4	no	—
682	C₂²	—	26	1	no	—
683	C₂²	—	26	1	no	—
684	C₂²	—	26	2	no	—
685	C₂²	—	26	1	no	—
686	C₂²	—	26	2	no	—
687	C₂²	—	26	1	no	—
688	C₂²	—	26	1	no	—
689	C₂²	—	26	2	no	—
690	C₂²	—	26	1	no	—
691	C₂²	—	104	4	no	—
692	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
693	C₄	—	2	1	no	—
694	C₄	—	2	1	no	—
695	C₄	—	2	1	no	—
696	C₄	—	2	2	no	—
697	C₄	—	2	2	no	—
698	C₄	—	13	2	no	—
699	C₄	—	26	1	no	—
700	C₄	—	26	1	no	—
701	C₄	—	26	2	no	—
702	C₄	—	26	1	no	—
703	C₄	—	26	2	no	—
704	C₄	—	26	2	no	—
705	C₄	—	26	1	no	—
706	C₄	—	26	1	no	—
707	C₄	#88251	1	2	yes	—
708	C₂	—	4	1	no	—
709	C₂	—	4	2	no	—
710	C₂	—	4	2	no	—
711	C₂	—	4	1	no	—
712	C₂	—	4	1	no	—
713	C₂	—	52	1	no	—
714	C₂	—	52	2	no	—
715	C₂	—	52	1	no	—
716	C₂	C₂×#88251	1	1	yes	characteristic
717	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic
718	C₂	#11719650	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#535	C₂
hypercenter	#535	D₁₃
hypocenter	C₁₃	#3546
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #535

Complements

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

N	H ≅ G/N	type
1. C₁₃×#535	C₂	semidirect
2. #11719538	C₂	semidirect
3. #11719537	C₂	semidirect
4. #11719511	C₂	semidirect
5. D₄×C₂²⋊D₁₃	C₂	semidirect
6. #11719425	C₂	semidirect
7. #11719423	C₂	semidirect
8. #11719383	C₂	semidirect
9. #11719374	C₂	semidirect
10. #11719323	C₂	semidirect
11. #11719317	C₂	semidirect
12. #11719316	C₂	semidirect
13. #11719313	C₂	semidirect
14. #11719312	C₂	semidirect
15. #11719305	C₂	semidirect
16. #11719304	C₂	semidirect
17. #11719301	C₂	semidirect
18. #11719300	C₂	semidirect
19. #11719298	C₂	semidirect
20. #11719297	C₂	semidirect
21. #11719296	C₂	semidirect
22. #11719238	C₂	semidirect
23. #11719235	C₂	semidirect
24. C₂×C₁₃×#41	C₂²	semidirect
27. C₂×#6129	C₂²	semidirect
28. C₂×#6129	C₂²	semidirect
29. C₂×#6129	C₂²	semidirect
31. C₂×#6127	C₂²	semidirect
32. C₂×#6127	C₂²	semidirect
33. C₁₃×#127	C₂²	semidirect
34. C₁₃×#124	C₂²	semidirect
37. C₁₃×#121	C₂²	semidirect
38. C₁₃×#121	C₂²	semidirect
39. C₁₃×#120	C₂²	semidirect
40. C₁₃×#120	C₂²	semidirect
41. C₁₃×#117	C₂²	semidirect
43. #88207	C₂²	semidirect
44. C₂×C₂²⋊Dic₁₃	C₂²	semidirect
45. #88201	C₂²	semidirect
46. #88200	C₂²	semidirect
47. #88198	C₂²	semidirect
50. #88194	C₂²	semidirect
51. #88194	C₂²	semidirect
54. #88193	C₂²	semidirect
55. #88193	C₂²	semidirect
56. #88193	C₂²	semidirect
57. #88193	C₂²	semidirect
58. #88193	C₂²	semidirect
59. #88193	C₂²	semidirect
60. #88193	C₂²	semidirect
61. #88193	C₂²	semidirect
62. #88193	C₂²	semidirect
63. #88193	C₂²	semidirect
66. #88192	C₂²	semidirect
67. #88192	C₂²	semidirect
68. #88192	C₂²	semidirect
70. #88191	C₂²	semidirect
71. #88191	C₂²	semidirect
73. #88190	C₂²	semidirect
74. #88189	C₂²	semidirect
75. #88189	C₂²	semidirect
76. #88189	C₂²	semidirect
78. D₄×Dic₁₃	C₂²	semidirect
79. D₄×Dic₁₃	C₂²	semidirect
80. D₄×Dic₁₃	C₂²	semidirect
82. #88184	C₂²	semidirect
84. C₄×C₂²⋊D₁₃	C₂²	semidirect
85. C₄×C₂²⋊D₁₃	C₂²	semidirect
86. C₄×C₂²⋊D₁₃	C₂²	semidirect
87. C₂×C₄⋊Dic₁₃	C₂²	semidirect
88. #88178	C₂²	semidirect
89. #88178	C₂²	semidirect
90. C₂×C₄×Dic₁₃	C₂²	semidirect
91. #88151	C₂²	semidirect
92. #88149	C₂²	semidirect
93. #88147	C₂²	semidirect
94. #88146	C₂²	semidirect
95. C₄⋊C₄×D₁₃	C₂²	semidirect
96. #88144	C₂²	semidirect
97. #88142	C₂²	semidirect
98. #88141	C₂²	semidirect
99. #88140	C₂²	semidirect
101. #88139	C₂²	semidirect
102. #88139	C₂²	semidirect
103. #88138	C₂²	semidirect
104. #88138	C₂²	semidirect
105. #88138	C₂²	semidirect
106. #88137	C₂²	semidirect
107. #88137	C₂²	semidirect
108. #88137	C₂²	semidirect
109. #88136	C₂²	semidirect
110. #88135	C₂²	semidirect
111. #88135	C₂²	semidirect
112. C₂²⋊C₄×D₁₃	C₂²	semidirect
113. #88133	C₂²	semidirect
114. #88133	C₂²	semidirect
115. #88133	C₂²	semidirect
116. #88132	C₂²	semidirect
117. #88132	C₂²	semidirect
118. #88131	C₂²	semidirect
119. #88130	C₂²	semidirect
120. #88130	C₂²	semidirect
121. C₄×D₅₂	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
326. #535	D₁₃	semidirect
377. C₂×#41	C₂×D₁₃	semidirect
387. #127	C₂×D₁₃	semidirect
400. #124	C₂×D₁₃	semidirect
439. #121	C₂×D₁₃	semidirect
440. #121	C₂×D₁₃	semidirect
447. #120	C₂×D₁₃	semidirect
448. #120	C₂×D₁₃	semidirect
465. #117	C₂×D₁₃	semidirect
590. 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×#535	2
#11719538	2
#11719537	2
#11719511	2
D₄×C₂²⋊D₁₃	2
#11719425	2
#11719423	2
#11719383	2
#11719374	2
#11719323	2
#11719317	2
#11719316	2
#11719313	2
#11719312	2
#11719305	2
#11719304	2
#11719301	2
#11719300	2
#11719298	2
#11719297	2
#11719296	2
#11719238	2
#11719235	2
#3546	13