Subgroups — #13129100

Order 1664.

1058 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×#546	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719536	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719533	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719511	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719510	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719387	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719382	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719369	C₂	1	2	yes	maximal, complemented
9	#11719367	C₂	1	2	yes	maximal, complemented
10	#11719346	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719333	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719325	C₂	1	2	yes	maximal, complemented
13	#11719321	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719311	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719308	C₂	1	2	yes	maximal, complemented
16	#11719299	C₂	1	2	yes	maximal, complemented
17	#11719298	C₂	1	2	yes	maximal, complemented
18	#11719268	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719266	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719252	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719247	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719200	C₂	1	2	yes	maximal, complemented
23	#11719199	C₂	1	2	yes	maximal, complemented
24	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×#6129	C₂²	1	1	yes	characteristic
28	C₂×#6127	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#123	C₂²	1	2	yes	complemented
32	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#121	C₂²	1	2	yes	—
34	C₁₃×#121	C₂²	1	1	yes	characteristic
35	C₁₃×#120	C₂²	1	2	yes	—
36	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
39	#88207	C₂²	1	2	yes	—
40	#88207	C₂²	1	2	yes	—
41	#88207	C₂²	1	2	yes	complemented
42	C₂×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
43	#88200	C₂²	1	1	yes	characteristic, complemented
44	#88200	C₂²	1	1	yes	characteristic, complemented
45	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
46	#88194	C₂²	1	2	yes	—
47	#88193	C₂²	1	1	yes	characteristic
48	#88193	C₂²	1	2	yes	—
49	#88193	C₂²	1	2	yes	complemented
50	#88192	C₂²	1	1	yes	characteristic
51	#88192	C₂²	1	1	yes	characteristic
52	#88192	C₂²	1	1	yes	characteristic
53	#88192	C₂²	1	1	yes	characteristic, complemented
54	#88192	C₂²	1	1	yes	characteristic, complemented
55	#88192	C₂²	1	2	yes	complemented
56	#88191	C₂²	1	1	yes	characteristic
57	#88191	C₂²	1	2	yes	complemented
58	#88191	C₂²	1	2	yes	complemented
59	#88190	C₂²	1	2	yes	—
60	#88190	C₂²	1	2	yes	complemented
61	#88190	C₂²	1	1	yes	characteristic, complemented
62	#88190	C₂²	1	2	yes	complemented
63	#88190	C₂²	1	2	yes	complemented
64	#88189	C₂²	1	2	yes	complemented
65	#88189	C₂²	1	2	yes	complemented
66	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
67	D₄×Dic₁₃	C₂²	1	2	yes	complemented
68	#88184	C₂²	1	2	yes	complemented
69	#88183	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
71	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
72	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
73	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
74	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
75	#88180	C₂²	1	2	yes	complemented
76	#88180	C₂²	1	1	yes	characteristic, complemented
77	#88180	C₂²	1	1	yes	characteristic, complemented
78	#88178	C₂²	1	2	yes	complemented
79	#88178	C₂²	1	2	yes	complemented
80	#88178	C₂²	1	1	yes	characteristic, complemented
81	#88178	C₂²	1	1	yes	characteristic, complemented
82	#88152	C₂²	1	2	yes	complemented
83	#88151	C₂²	1	1	yes	characteristic, complemented
84	#88150	C₂²	1	1	yes	characteristic, complemented
85	#88148	C₂²	1	1	yes	characteristic, complemented
86	#88148	C₂²	1	2	yes	complemented
87	#88146	C₂²	1	1	yes	characteristic, complemented
88	#88146	C₂²	1	1	yes	characteristic, complemented
89	#88142	C₂²	1	1	yes	characteristic, complemented
90	#88142	C₂²	1	2	yes	complemented
91	#88141	C₂²	1	2	yes	complemented
92	#88141	C₂²	1	2	yes	complemented
93	#88140	C₂²	1	2	yes	complemented
94	#88139	C₂²	1	2	yes	—
95	#88139	C₂²	1	2	yes	—
96	#88139	C₂²	1	2	yes	complemented
97	#88139	C₂²	1	2	yes	complemented
98	#88139	C₂²	1	2	yes	complemented
99	#88139	C₂²	1	2	yes	complemented
100	#88139	C₂²	1	2	yes	complemented
101	#88139	C₂²	1	2	yes	complemented
102	#88138	C₂²	1	1	yes	characteristic
103	#88138	C₂²	1	2	yes	complemented
104	#88137	C₂²	1	1	yes	characteristic
105	#88137	C₂²	1	2	yes	complemented
106	#88137	C₂²	1	2	yes	complemented
107	#88136	C₂²	1	1	yes	characteristic, complemented
108	#88135	C₂²	1	2	yes	complemented
109	#88135	C₂²	1	2	yes	complemented
110	#88133	C₂²	1	2	yes	complemented
111	#88133	C₂²	1	2	yes	complemented
112	#88133	C₂²	1	2	yes	complemented
113	#88133	C₂²	1	2	yes	complemented
114	#88133	C₂²	1	2	yes	complemented
115	#88132	C₂²	1	2	yes	complemented
116	#88132	C₂²	1	1	yes	characteristic, complemented
117	#88132	C₂²	1	2	yes	complemented
118	#88131	C₂²	1	2	yes	complemented
119	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
120	#88126	C₂²	1	1	yes	characteristic, complemented
121	#88123	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
123	C₂⁴×C₁₃	C₂³	1	2	yes	—
124	C₂³×D₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
137	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
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	C₂²×Dic₁₃	C₂³	1	2	yes	—
149	C₂²×Dic₁₃	C₂³	1	2	yes	—
150	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
151	Q₈×D₁₃	—	4	2	no	—
152	#6129	—	4	2	no	—
153	#6127	—	4	2	no	—
154	C₂×D₅₂	C₂³	1	1	yes	characteristic
155	C₂×D₅₂	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₃	—	4	2	no	—
157	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
163	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
164	C₂×Dic₂₆	C₂³	1	2	yes	—
165	C₂×Dic₂₆	C₂³	1	2	yes	—
166	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
167	C₂×Dic₂₆	C₂³	1	2	yes	—
168	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₄²×C₁₃	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
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	2	yes	—
191	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
192	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
193	#6103	C₂³	1	1	yes	characteristic
194	#6103	C₂³	1	1	yes	characteristic
195	#6103	C₂³	1	1	yes	characteristic
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	2	yes	—
201	#6103	C₂³	1	1	yes	characteristic
202	#6103	C₂³	1	2	yes	—
203	#6103	C₂³	1	2	yes	—
204	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₁₃	C₂³	1	2	yes	—
206	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₁₃	C₂³	1	2	yes	—
210	C₄⋊Dic₁₃	C₂³	1	2	yes	—
211	#6101	C₂³	1	2	yes	—
212	#6101	C₂³	1	1	yes	characteristic
213	#6101	C₂³	1	1	yes	characteristic
214	#6101	C₂³	1	1	yes	characteristic
215	#6101	C₂³	1	2	yes	—
216	#6101	C₂³	1	2	yes	—
217	#6101	C₂³	1	2	yes	—
218	#6101	C₂³	1	1	yes	characteristic
219	#6101	C₂³	1	2	yes	—
220	#6101	C₂³	1	2	yes	—
221	C₄×Dic₁₃	C₂³	1	2	yes	—
222	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₃	C₂³	1	2	yes	—
224	C₄×Dic₁₃	C₂³	1	2	yes	—
225	C₄×Dic₁₃	C₂³	1	2	yes	—
226	C₄×Dic₁₃	C₂³	1	2	yes	—
227	C₄×Dic₁₃	C₂³	1	2	yes	—
228	#3540	—	13	1	no	maximal, Sylow
229	C₂³×C₁₃	—	4	2	no	—
230	C₂³×C₁₃	—	4	2	no	—
231	C₂³×C₁₃	—	4	2	no	—
232	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
234	C₂³×C₁₃	C₂⁴	1	2	yes	—
235	C₂³×C₁₃	C₂⁴	1	2	yes	—
236	C₂²×D₁₃	—	4	1	no	—
237	C₂²×D₁₃	—	4	1	no	—
238	C₂²×D₁₃	—	4	1	no	—
239	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
240	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
241	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
242	Q₈×C₁₃	—	2	2	no	—
243	D₄×C₁₃	—	2	2	no	—
244	D₄×C₁₃	—	2	2	no	—
245	D₄×C₁₃	—	4	2	no	—
246	D₄×C₁₃	—	4	1	no	—
247	D₄×C₁₃	—	4	2	no	—
248	D₄×C₁₃	—	4	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	4	2	no	—
252	C₂×C₄×C₁₃	—	4	2	no	—
253	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
258	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₂²⋊D₁₃	—	4	1	no	—
261	C₂²⋊D₁₃	—	4	1	no	—
262	C₂²⋊D₁₃	—	4	2	no	—
263	C₂²⋊D₁₃	—	4	1	no	—
264	C₂²⋊D₁₃	—	4	2	no	—
265	C₂²⋊D₁₃	—	4	2	no	—
266	C₂²⋊D₁₃	—	4	2	no	—
267	C₂²⋊D₁₃	—	4	2	no	—
268	C₂²⋊D₁₃	—	4	2	no	—
269	C₂²⋊D₁₃	—	4	1	no	—
270	C₂×Dic₁₃	—	4	1	no	—
271	C₂×Dic₁₃	—	4	2	no	—
272	C₂×Dic₁₃	—	4	2	no	—
273	C₂×Dic₁₃	C₂⁴	1	2	yes	—
274	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₁₃	C₂⁴	1	2	yes	—
276	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₁₃	C₂⁴	1	2	yes	—
278	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₁₃	C₂⁴	1	2	yes	—
281	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
282	D₅₂	—	4	1	no	—
283	D₅₂	—	4	1	no	—
284	C₄×D₁₃	—	2	2	no	—
285	C₄×D₁₃	—	2	2	no	—
286	C₄×D₁₃	—	2	2	no	—
287	C₄×D₁₃	—	4	1	no	—
288	C₄×D₁₃	—	4	1	no	—
289	C₄×D₁₃	—	4	2	no	—
290	Dic₂₆	—	2	2	no	—
291	Dic₂₆	—	4	2	no	—
292	Dic₂₆	—	4	2	no	—
293	Dic₂₆	—	4	1	no	—
294	Dic₂₆	—	4	2	no	—
295	H(3,𝔽₄)	—	13	2	no	—
296	#560	—	13	2	no	—
297	#559	—	13	2	no	—
298	#556	—	13	1	no	—
299	#556	—	13	1	no	—
300	#555	—	13	1	no	—
301	#555	—	13	1	no	—
302	#551	—	13	2	no	—
303	#548	—	13	1	no	—
304	#548	—	13	1	no	—
305	#546	—	13	1	no	—
306	#546	D₁₃	1	1	yes	characteristic, complemented
307	#542	—	13	1	no	—
308	#542	—	13	2	no	—
309	#542	—	13	2	no	—
310	#542	—	13	1	no	—
311	#538	—	13	2	no	—
312	#538	—	13	2	no	—
313	#536	—	13	1	no	—
314	#535	—	13	1	no	—
315	#525	—	13	1	no	—
316	#525	—	13	1	no	—
317	#525	—	13	1	no	—
318	C₂²×C₁₃	—	2	2	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	2	no	—
324	C₂²×C₁₃	—	2	2	no	—
325	C₂²×C₁₃	—	2	1	no	—
326	C₂²×C₁₃	—	2	2	no	—
327	C₂²×C₁₃	—	2	1	no	—
328	C₂²×C₁₃	—	2	1	no	—
329	C₂²×C₁₃	—	2	1	no	—
330	C₂²×C₁₃	—	8	4	no	—
331	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
332	C₂×D₁₃	—	2	1	no	—
333	C₂×D₁₃	—	2	1	no	—
334	C₂×D₁₃	—	2	1	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	1	no	—
340	C₂×D₁₃	—	2	1	no	—
341	C₂×D₁₃	—	4	4	no	—
342	C₄×C₁₃	—	2	2	no	—
343	C₄×C₁₃	—	2	1	no	—
344	C₄×C₁₃	—	2	1	no	—
345	C₄×C₁₃	—	2	1	no	—
346	C₄×C₁₃	—	2	2	no	—
347	C₄×C₁₃	—	2	1	no	—
348	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
349	Dic₁₃	—	2	2	no	—
350	Dic₁₃	—	2	1	no	—
351	Dic₁₃	—	2	1	no	—
352	Dic₁₃	—	2	1	no	—
353	Dic₁₃	—	2	1	no	—
354	Dic₁₃	—	2	2	no	—
355	Dic₁₃	—	2	2	no	—
356	Dic₁₃	—	2	2	no	—
357	Dic₁₃	—	2	1	no	—
358	C₂×#41	—	13	1	no	—
359	C₂×#41	—	13	1	no	—
360	C₂×#41	C₂×D₁₃	1	1	yes	characteristic
361	C₂²×Q₈	—	13	1	no	—
362	C₂²×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
363	C₂³×C₄	—	13	1	no	—
364	C₄⋊Q₈	—	13	2	no	—
365	C₄⋊Q₈	—	13	1	no	—
366	C₄⋊Q₈	—	13	1	no	—
367	#127	—	13	2	no	—
368	#126	—	13	2	no	—
369	#126	—	13	2	no	—
370	#126	—	13	2	no	—
371	#126	—	13	2	no	—
372	#126	—	13	2	no	—
373	#126	—	13	2	no	—
374	#124	—	13	2	no	—
375	#124	—	13	2	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	2	no	—
382	#124	—	13	2	no	—
383	#124	—	13	2	no	—
384	#124	—	13	2	no	—
385	#124	—	13	2	no	—
386	#124	—	13	2	no	—
387	#124	C₂×D₁₃	1	1	yes	characteristic, complemented
388	#123	—	13	2	no	—
389	#123	—	13	2	no	—
390	#123	—	13	2	no	—
391	#123	—	13	1	no	—
392	#123	—	13	2	no	—
393	#123	—	13	2	no	—
394	#123	—	13	1	no	—
395	#123	—	13	2	no	—
396	#123	—	13	2	no	—
397	#123	C₂×D₁₃	1	2	yes	complemented
398	C₂²⋊Q₈	—	13	1	no	—
399	C₂²⋊Q₈	—	13	1	no	—
400	C₂²⋊Q₈	—	13	1	no	—
401	C₂²⋊Q₈	—	13	1	no	—
402	C₂²⋊Q₈	—	13	2	no	—
403	C₂²⋊Q₈	—	13	2	no	—
404	C₂²⋊Q₈	—	13	1	no	—
405	C₂²⋊Q₈	—	13	1	no	—
406	C₂²⋊Q₈	—	13	1	no	—
407	C₂²⋊Q₈	—	13	2	no	—
408	C₂²⋊Q₈	—	13	2	no	—
409	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
410	#121	—	13	1	no	—
411	#121	—	13	1	no	—
412	#121	—	13	1	no	—
413	#121	—	13	1	no	—
414	#121	—	13	1	no	—
415	#121	—	13	1	no	—
416	#121	—	13	2	no	—
417	#121	—	13	2	no	—
418	#121	—	13	2	no	—
419	#121	—	13	2	no	—
420	#121	—	13	1	no	—
421	#121	—	13	2	no	—
422	#121	C₂×D₁₃	1	1	yes	characteristic
423	#121	C₂×D₁₃	1	2	yes	—
424	#120	—	13	2	no	—
425	#120	—	13	2	no	—
426	#120	—	13	2	no	—
427	#120	—	13	2	no	—
428	#120	—	13	2	no	—
429	#120	—	13	1	no	—
430	#120	—	13	1	no	—
431	#120	C₂×D₁₃	1	2	yes	—
432	C₄×Q₈	—	13	1	no	—
433	C₄×Q₈	—	13	2	no	—
434	C₄×Q₈	—	13	2	no	—
435	C₄×Q₈	—	13	1	no	—
436	C₄×D₄	—	13	2	no	—
437	C₄×D₄	—	13	1	no	—
438	C₄×D₄	—	13	2	no	—
439	C₄×D₄	—	13	1	no	—
440	C₄×D₄	—	13	1	no	—
441	C₄×D₄	—	13	2	no	—
442	C₄×D₄	—	13	2	no	—
443	C₄×D₄	—	13	2	no	—
444	C₄×D₄	—	13	2	no	—
445	C₄×D₄	—	13	1	no	—
446	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
447	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
448	#117	—	13	1	no	—
449	#117	—	13	1	no	—
450	#117	—	13	2	no	—
451	#117	—	13	1	no	—
452	#117	—	13	1	no	—
453	#117	—	13	2	no	—
454	#117	—	13	1	no	—
455	C₂×C₂²⋊C₄	—	13	2	no	—
456	C₂×C₂²⋊C₄	C₂×D₁₃	1	2	yes	complemented
457	C₂×C₁₃	—	4	1	no	—
458	C₂×C₁₃	—	4	2	no	—
459	C₂×C₁₃	—	4	2	no	—
460	C₂×C₁₃	—	4	1	no	—
461	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
462	C₂×C₁₃	#585	1	1	yes	characteristic
463	C₂×C₁₃	#585	1	1	yes	characteristic
464	D₁₃	—	4	1	no	—
465	D₁₃	—	4	1	no	—
466	D₁₃	—	4	1	no	—
467	C₂⁴	—	13	1	no	—
468	C₂⁴	C₂²×D₁₃	1	2	yes	—
469	#41	—	4	2	no	—
470	#41	—	52	2	no	—
471	#41	—	52	2	no	—
472	C₂×Q₈	—	13	1	no	—
473	C₂×Q₈	—	13	2	no	—
474	C₂×Q₈	—	13	2	no	—
475	C₂×Q₈	—	13	2	no	—
476	C₂×Q₈	—	13	1	no	—
477	C₂×Q₈	—	52	2	no	—
478	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
479	C₂×D₄	—	4	2	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	1	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	2	no	—
490	C₂×D₄	—	13	1	no	—
491	C₂×D₄	—	13	1	no	—
492	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
493	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
494	C₂×D₄	C₂²×D₁₃	1	2	yes	—
495	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
496	C₂×D₄	C₂²×D₁₃	1	2	yes	—
497	C₂×D₄	C₂²×D₁₃	1	2	yes	—
498	C₂²×C₄	—	13	2	no	—
499	C₂²×C₄	—	13	2	no	—
500	C₂²×C₄	—	13	1	no	—
501	C₂²×C₄	—	13	1	no	—
502	C₂²×C₄	—	13	1	no	—
503	C₂²×C₄	—	13	1	no	—
504	C₂²×C₄	—	13	1	no	—
505	C₂²×C₄	—	13	2	no	—
506	C₂²×C₄	—	13	1	no	—
507	C₂²×C₄	—	52	2	no	—
508	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
509	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
510	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
511	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
512	C₄⋊C₄	—	13	1	no	—
513	C₄⋊C₄	—	13	1	no	—
514	C₄⋊C₄	—	13	1	no	—
515	C₄⋊C₄	—	13	1	no	—
516	C₄⋊C₄	—	13	1	no	—
517	C₄⋊C₄	—	13	1	no	—
518	C₄⋊C₄	—	13	1	no	—
519	C₄⋊C₄	—	13	2	no	—
520	C₄⋊C₄	—	13	2	no	—
521	C₄⋊C₄	—	13	2	no	—
522	C₄⋊C₄	—	13	2	no	—
523	C₄⋊C₄	—	13	1	no	—
524	C₄⋊C₄	—	13	2	no	—
525	C₄⋊C₄	—	13	2	no	—
526	C₄⋊C₄	—	13	2	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	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	—	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	1	no	—
545	C₂²⋊C₄	—	13	2	no	—
546	C₂²⋊C₄	—	13	2	no	—
547	C₂²⋊C₄	—	13	1	no	—
548	C₂²⋊C₄	—	13	1	no	—
549	C₂²⋊C₄	—	13	2	no	—
550	C₂²⋊C₄	—	13	1	no	—
551	C₂²⋊C₄	—	13	1	no	—
552	C₂²⋊C₄	—	13	1	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	C₂²×D₁₃	1	1	yes	characteristic
558	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
559	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
560	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
563	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
564	C₄²	—	13	2	no	—
565	C₄²	—	13	2	no	—
566	C₄²	—	13	2	no	—
567	C₄²	—	13	1	no	—
568	C₄²	—	13	2	no	—
569	C₄²	—	13	2	no	—
570	C₄²	—	13	2	no	—
571	C₄²	C₂²×D₁₃	1	1	yes	characteristic
572	C₁₃	#3540	1	1	yes	characteristic, complemented, Sylow
573	C₂³	—	4	2	no	—
574	C₂³	—	4	2	no	—
575	C₂³	—	4	2	no	—
576	C₂³	—	13	1	no	—
577	C₂³	—	13	1	no	—
578	C₂³	—	13	1	no	—
579	C₂³	—	52	1	no	—
580	C₂³	—	52	1	no	—
581	C₂³	—	52	1	no	—
582	C₂³	C₂³×D₁₃	1	1	yes	characteristic
583	C₂³	C₂³×D₁₃	1	1	yes	characteristic
584	C₂³	C₂³×D₁₃	1	2	yes	—
585	C₂³	C₂³×D₁₃	1	2	yes	—
586	Q₈	—	2	2	no	—
587	Q₈	—	26	2	no	—
588	Q₈	—	52	2	no	—
589	Q₈	—	52	2	no	—
590	Q₈	—	52	2	no	—
591	Q₈	—	52	1	no	—
592	D₄	—	2	2	no	—
593	D₄	—	2	2	no	—
594	D₄	—	4	2	no	—
595	D₄	—	4	1	no	—
596	D₄	—	4	2	no	—
597	D₄	—	4	2	no	—
598	D₄	—	52	1	no	—
599	D₄	—	52	1	no	—
600	D₄	—	52	1	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	1	no	—
607	D₄	—	52	1	no	—
608	D₄	—	52	1	no	—
609	D₄	—	52	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	4	2	no	—
614	C₂×C₄	—	13	1	no	—
615	C₂×C₄	—	13	2	no	—
616	C₂×C₄	—	13	2	no	—
617	C₂×C₄	—	13	2	no	—
618	C₂×C₄	—	13	1	no	—
619	C₂×C₄	—	13	1	no	—
620	C₂×C₄	—	13	1	no	—
621	C₂×C₄	—	13	2	no	—
622	C₂×C₄	—	13	1	no	—
623	C₂×C₄	—	26	2	no	—
624	C₂×C₄	—	26	2	no	—
625	C₂×C₄	—	26	2	no	—
626	C₂×C₄	—	52	1	no	—
627	C₂×C₄	—	52	1	no	—
628	C₂×C₄	—	52	2	no	—
629	C₂×C₄	—	52	2	no	—
630	C₂×C₄	—	52	1	no	—
631	C₂×C₄	—	52	2	no	—
632	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₁₃	1	2	yes	—
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	1	yes	characteristic
638	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	1	no	—
651	C₂²	—	8	4	no	—
652	C₂²	—	26	1	no	—
653	C₂²	—	26	1	no	—
654	C₂²	—	26	1	no	—
655	C₂²	—	26	1	no	—
656	C₂²	—	26	1	no	—
657	C₂²	—	26	1	no	—
658	C₂²	—	26	1	no	—
659	C₂²	—	26	1	no	—
660	C₂²	—	26	1	no	—
661	C₂²	—	52	4	no	—
662	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
663	C₄	—	2	1	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	—	26	1	no	—
670	C₄	—	26	1	no	—
671	C₄	—	26	1	no	—
672	C₄	—	26	2	no	—
673	C₄	—	26	1	no	—
674	C₄	—	26	2	no	—
675	C₄	—	26	2	no	—
676	C₄	—	26	2	no	—
677	C₄	—	26	1	no	—
678	C₄	#88251	1	2	yes	—
679	C₂	—	4	1	no	—
680	C₂	—	4	2	no	—
681	C₂	—	4	2	no	—
682	C₂	—	4	1	no	—
683	C₂	—	52	1	no	—
684	C₂	—	52	1	no	—
685	C₂	—	52	1	no	—
686	C₂	C₂×#88251	1	1	yes	characteristic
687	C₂	#11719648	1	1	yes	characteristic
688	C₂	#11719650	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#546	C₂
hypercenter	#546	D₁₃
hypocenter	C₁₃	#3540
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₁₃×#546	C₂	semidirect
2. #11719536	C₂	semidirect
3. #11719533	C₂	semidirect
4. #11719511	C₂	semidirect
5. #11719510	C₂	semidirect
6. #11719387	C₂	semidirect
7. #11719382	C₂	semidirect
8. #11719369	C₂	semidirect
9. #11719367	C₂	semidirect
10. #11719346	C₂	semidirect
11. #11719333	C₂	semidirect
12. #11719325	C₂	semidirect
13. #11719321	C₂	semidirect
14. #11719311	C₂	semidirect
15. #11719308	C₂	semidirect
16. #11719299	C₂	semidirect
17. #11719298	C₂	semidirect
18. #11719268	C₂	semidirect
19. #11719266	C₂	semidirect
20. #11719252	C₂	semidirect
21. #11719247	C₂	semidirect
22. #11719200	C₂	semidirect
23. #11719199	C₂	semidirect
25. C₂²×D₄×C₁₃	C₂²	semidirect
26. C₂×Q₈×D₁₃	C₂²	semidirect
29. C₂²×C₄×D₁₃	C₂²	semidirect
30. C₁₃×#124	C₂²	semidirect
31. C₁₃×#123	C₂²	semidirect
32. C₁₃×C₂²⋊Q₈	C₂²	semidirect
37. C₄×D₄×C₁₃	C₂²	semidirect
38. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
41. #88207	C₂²	semidirect
42. C₂×C₂²⋊Dic₁₃	C₂²	semidirect
43. #88200	C₂²	semidirect
44. #88200	C₂²	semidirect
45. Q₈×Dic₁₃	C₂²	semidirect
49. #88193	C₂²	semidirect
53. #88192	C₂²	semidirect
54. #88192	C₂²	semidirect
55. #88192	C₂²	semidirect
57. #88191	C₂²	semidirect
58. #88191	C₂²	semidirect
60. #88190	C₂²	semidirect
61. #88190	C₂²	semidirect
62. #88190	C₂²	semidirect
63. #88190	C₂²	semidirect
64. #88189	C₂²	semidirect
65. #88189	C₂²	semidirect
66. D₄×Dic₁₃	C₂²	semidirect
67. D₄×Dic₁₃	C₂²	semidirect
68. #88184	C₂²	semidirect
69. #88183	C₂²	semidirect
71. C₄×C₂²⋊D₁₃	C₂²	semidirect
72. C₄×C₂²⋊D₁₃	C₂²	semidirect
73. C₄×C₂²⋊D₁₃	C₂²	semidirect
74. C₄×C₂²⋊D₁₃	C₂²	semidirect
75. #88180	C₂²	semidirect
76. #88180	C₂²	semidirect
77. #88180	C₂²	semidirect
78. #88178	C₂²	semidirect
79. #88178	C₂²	semidirect
80. #88178	C₂²	semidirect
81. #88178	C₂²	semidirect
82. #88152	C₂²	semidirect
83. #88151	C₂²	semidirect
84. #88150	C₂²	semidirect
85. #88148	C₂²	semidirect
86. #88148	C₂²	semidirect
87. #88146	C₂²	semidirect
88. #88146	C₂²	semidirect
89. #88142	C₂²	semidirect
90. #88142	C₂²	semidirect
91. #88141	C₂²	semidirect
92. #88141	C₂²	semidirect
93. #88140	C₂²	semidirect
96. #88139	C₂²	semidirect
97. #88139	C₂²	semidirect
98. #88139	C₂²	semidirect
99. #88139	C₂²	semidirect
100. #88139	C₂²	semidirect
101. #88139	C₂²	semidirect
103. #88138	C₂²	semidirect
105. #88137	C₂²	semidirect
106. #88137	C₂²	semidirect
107. #88136	C₂²	semidirect
108. #88135	C₂²	semidirect
109. #88135	C₂²	semidirect
110. #88133	C₂²	semidirect
111. #88133	C₂²	semidirect
112. #88133	C₂²	semidirect
113. #88133	C₂²	semidirect
114. #88133	C₂²	semidirect
115. #88132	C₂²	semidirect
116. #88132	C₂²	semidirect
117. #88132	C₂²	semidirect
118. #88131	C₂²	semidirect
119. C₄×D₅₂	C₂²	semidirect
120. #88126	C₂²	semidirect
121. #88123	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
306. #546	D₁₃	semidirect
362. C₂²×D₄	C₂×D₁₃	semidirect
387. #124	C₂×D₁₃	semidirect
397. #123	C₂×D₁₃	semidirect
409. C₂²⋊Q₈	C₂×D₁₃	semidirect
447. C₄×D₄	C₂×D₁₃	semidirect
456. C₂×C₂²⋊C₄	C₂×D₁₃	semidirect
572. C₁₃	#3540	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#546	2
#11719536	2
#11719533	2
#11719511	2
#11719510	2
#11719387	2
#11719382	2
#11719369	2
#11719367	2
#11719346	2
#11719333	2
#11719325	2
#11719321	2
#11719311	2
#11719308	2
#11719299	2
#11719298	2
#11719268	2
#11719266	2
#11719252	2
#11719247	2
#11719200	2
#11719199	2
#3540	13