Subgroups — #13129072

Order 1664.

1270 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719416	C₂	1	2	yes	maximal, complemented
3	#11719409	C₂	1	2	yes	maximal, complemented
4	#11719403	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719400	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719371	C₂	1	2	yes	maximal, complemented
7	#11719358	C₂	1	2	yes	maximal, complemented
8	#11719314	C₂	1	2	yes	maximal, complemented
9	#11719314	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719314	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719312	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719310	C₂	1	2	yes	maximal, complemented
13	D₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719267	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719265	C₂	1	2	yes	maximal, complemented
16	D₄×D₅₂	C₂	1	2	yes	maximal, complemented
17	D₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
18	D₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719252	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719235	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719230	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719219	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#88149	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×D₄×D₁₃	C₂²	1	2	yes	complemented
26	C₂×D₄×D₁₃	C₂²	1	2	yes	complemented
27	C₂×D₄×D₁₃	C₂²	1	2	yes	complemented
28	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×D₁₃	C₂²	1	2	yes	complemented
30	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
31	C₂²×D₅₂	C₂²	1	1	yes	characteristic, complemented
32	C₂²×D₅₂	C₂²	1	2	yes	complemented
33	C₂²×D₅₂	C₂²	1	1	yes	characteristic, complemented
34	C₂²×D₅₂	C₂²	1	2	yes	complemented
35	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#126	C₂²	1	2	yes	complemented
37	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#123	C₂²	1	2	yes	complemented
39	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#121	C₂²	1	2	yes	complemented
41	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
42	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
43	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
44	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	#88194	C₂²	1	1	yes	characteristic, complemented
48	#88194	C₂²	1	2	yes	complemented
49	#88193	C₂²	1	1	yes	characteristic, complemented
50	#88193	C₂²	1	2	yes	complemented
51	#88192	C₂²	1	1	yes	characteristic, complemented
52	#88191	C₂²	1	1	yes	characteristic, complemented
53	#88191	C₂²	1	2	yes	complemented
54	#88191	C₂²	1	2	yes	complemented
55	#88191	C₂²	1	2	yes	complemented
56	#88184	C₂²	1	1	yes	characteristic, complemented
57	#88184	C₂²	1	2	yes	complemented
58	#88184	C₂²	1	1	yes	characteristic, complemented
59	#88184	C₂²	1	2	yes	complemented
60	#88184	C₂²	1	2	yes	complemented
61	#88183	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
63	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
64	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
65	C₂×#6103	C₂²	1	2	yes	complemented
66	#88152	C₂²	1	2	yes	complemented
67	#88152	C₂²	1	2	yes	complemented
68	#88150	C₂²	1	1	yes	characteristic, complemented
69	#88149	C₂²	1	1	yes	characteristic, complemented
70	#88149	C₂²	1	1	yes	characteristic, complemented
71	#88149	C₂²	1	1	yes	characteristic, complemented
72	#88149	C₂²	1	1	yes	characteristic, complemented
73	#88149	C₂²	1	2	yes	complemented
74	#88149	C₂²	1	2	yes	complemented
75	#88149	C₂²	1	1	yes	characteristic, complemented
76	#88149	C₂²	1	1	yes	characteristic, complemented
77	#88149	C₂²	1	1	yes	characteristic, complemented
78	#88149	C₂²	1	2	yes	complemented
79	#88149	C₂²	1	2	yes	complemented
80	#88149	C₂²	1	2	yes	complemented
81	#88149	C₂²	1	2	yes	complemented
82	#88148	C₂²	1	2	yes	complemented
83	#88148	C₂²	1	1	yes	characteristic, complemented
84	#88148	C₂²	1	2	yes	complemented
85	#88148	C₂²	1	2	yes	complemented
86	#88148	C₂²	1	2	yes	complemented
87	#88147	C₂²	1	1	yes	characteristic, complemented
88	#88147	C₂²	1	1	yes	characteristic, complemented
89	#88147	C₂²	1	2	yes	complemented
90	#88146	C₂²	1	1	yes	characteristic, complemented
91	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
92	#88144	C₂²	1	1	yes	characteristic, complemented
93	#88139	C₂²	1	2	yes	complemented
94	#88138	C₂²	1	2	yes	complemented
95	#88138	C₂²	1	1	yes	characteristic, complemented
96	#88138	C₂²	1	2	yes	complemented
97	#88138	C₂²	1	2	yes	complemented
98	#88138	C₂²	1	2	yes	complemented
99	#88138	C₂²	1	2	yes	complemented
100	#88137	C₂²	1	2	yes	complemented
101	#88137	C₂²	1	1	yes	characteristic, complemented
102	#88137	C₂²	1	2	yes	complemented
103	#88136	C₂²	1	2	yes	complemented
104	#88136	C₂²	1	2	yes	complemented
105	#88136	C₂²	1	1	yes	characteristic, complemented
106	#88136	C₂²	1	2	yes	complemented
107	#88136	C₂²	1	2	yes	complemented
108	#88136	C₂²	1	2	yes	complemented
109	#88136	C₂²	1	2	yes	complemented
110	#88136	C₂²	1	2	yes	complemented
111	#88136	C₂²	1	2	yes	complemented
112	#88136	C₂²	1	2	yes	complemented
113	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
114	#88132	C₂²	1	1	yes	characteristic, complemented
115	#88130	C₂²	1	2	yes	complemented
116	#88129	C₂²	1	2	yes	complemented
117	#88128	C₂²	1	2	yes	complemented
118	#88128	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₅₂	C₂²	1	2	yes	complemented
120	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
122	#88126	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₃	C₂³	1	1	yes	characteristic
124	C₂³×D₁₃	C₂³	1	2	yes	—
125	C₂³×D₁₃	C₂³	1	2	yes	—
126	C₂³×D₁₃	C₂³	1	2	yes	—
127	C₂³×D₁₃	C₂³	1	2	yes	—
128	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₃	C₂³	1	2	yes	—
130	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₁₃	C₂³	1	2	yes	—
132	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
135	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
147	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
148	D₄×D₁₃	—	4	2	no	—
149	D₄×D₁₃	—	4	2	no	—
150	D₄×D₁₃	—	4	4	no	—
151	D₄×D₁₃	—	4	4	no	—
152	D₄×D₁₃	—	4	4	no	—
153	D₄×D₁₃	—	4	4	no	—
154	#6127	—	4	2	no	—
155	C₂×D₅₂	—	4	2	no	—
156	C₂×D₅₂	—	4	2	no	—
157	C₂×D₅₂	—	4	4	no	—
158	C₂×D₅₂	—	4	4	no	—
159	C₂×D₅₂	C₂³	1	2	yes	—
160	C₂×D₅₂	C₂³	1	1	yes	characteristic
161	C₂×D₅₂	C₂³	1	1	yes	characteristic
162	C₂×D₅₂	C₂³	1	1	yes	characteristic
163	C₂×D₅₂	C₂³	1	1	yes	characteristic
164	C₂×D₅₂	C₂³	1	2	yes	—
165	C₂×D₅₂	C₂³	1	1	yes	characteristic
166	C₂×D₅₂	C₂³	1	2	yes	—
167	C₂×D₅₂	C₂³	1	2	yes	—
168	C₂×D₅₂	C₂³	1	2	yes	—
169	C₂×D₅₂	C₂³	1	2	yes	—
170	C₂×D₅₂	C₂³	1	2	yes	—
171	C₂×D₅₂	C₂³	1	2	yes	—
172	C₂×D₅₂	C₂³	1	2	yes	—
173	C₂×D₅₂	C₂³	1	2	yes	—
174	C₂×D₅₂	C₂³	1	2	yes	—
175	C₂×C₄×D₁₃	—	4	2	no	—
176	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
177	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
178	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
179	C₂×C₄×D₁₃	C₂³	1	2	yes	—
180	C₂×C₄×D₁₃	C₂³	1	2	yes	—
181	C₂×C₄×D₁₃	C₂³	1	2	yes	—
182	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
183	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
184	C₂×C₄×D₁₃	C₂³	1	2	yes	—
185	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
186	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
192	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
194	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
198	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₄²×C₁₃	C₂³	1	1	yes	characteristic
200	C₄²×C₁₃	C₂³	1	2	yes	—
201	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
202	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
203	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
204	#6103	C₂³	1	1	yes	characteristic
205	#6103	C₂³	1	1	yes	characteristic
206	#6103	C₂³	1	1	yes	characteristic
207	#6103	C₂³	1	2	yes	—
208	#6103	C₂³	1	1	yes	characteristic
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	2	yes	—
214	#6103	C₂³	1	2	yes	—
215	#6103	C₂³	1	2	yes	—
216	#6103	C₂³	1	2	yes	—
217	#6103	C₂³	1	2	yes	—
218	#6103	C₂³	1	1	yes	characteristic
219	#6103	C₂³	1	2	yes	—
220	#6103	C₂³	1	2	yes	—
221	#6103	C₂³	1	2	yes	—
222	#6103	C₂³	1	2	yes	—
223	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
224	C₄⋊Dic₁₃	C₂³	1	2	yes	—
225	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
226	#6101	C₂³	1	1	yes	characteristic
227	#6101	C₂³	1	1	yes	characteristic
228	#6101	C₂³	1	1	yes	characteristic
229	#6101	C₂³	1	2	yes	—
230	#6101	C₂³	1	2	yes	—
231	#6101	C₂³	1	1	yes	characteristic
232	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
233	C₄×Dic₁₃	C₂³	1	2	yes	—
234	#3537	—	13	1	no	maximal, Sylow
235	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₂³×C₁₃	C₂⁴	1	2	yes	—
237	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
238	C₂²×D₁₃	—	2	2	no	—
239	C₂²×D₁₃	—	2	4	no	—
240	C₂²×D₁₃	—	2	2	no	—
241	C₂²×D₁₃	—	2	4	no	—
242	C₂²×D₁₃	—	4	1	no	—
243	C₂²×D₁₃	—	4	2	no	—
244	C₂²×D₁₃	—	4	2	no	—
245	C₂²×D₁₃	—	4	2	no	—
246	C₂²×D₁₃	—	4	2	no	—
247	C₂²×D₁₃	—	4	2	no	—
248	C₂²×D₁₃	—	4	2	no	—
249	C₂²×D₁₃	—	4	2	no	—
250	C₂²×D₁₃	—	4	2	no	—
251	C₂²×D₁₃	—	4	2	no	—
252	C₂²×D₁₃	—	4	2	no	—
253	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
254	C₂²×D₁₃	C₂⁴	1	2	yes	—
255	C₂²×D₁₃	C₂⁴	1	2	yes	—
256	C₂²×D₁₃	C₂⁴	1	2	yes	—
257	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
258	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
259	D₄×C₁₃	—	2	4	no	—
260	D₄×C₁₃	—	2	2	no	—
261	D₄×C₁₃	—	2	2	no	—
262	D₄×C₁₃	—	4	2	no	—
263	C₂×C₄×C₁₃	—	2	2	no	—
264	C₂×C₄×C₁₃	—	2	2	no	—
265	C₂×C₄×C₁₃	—	4	2	no	—
266	C₂×C₄×C₁₃	—	4	2	no	—
267	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
268	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
269	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
270	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
273	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
275	C₂²⋊D₁₃	—	2	4	no	—
276	C₂²⋊D₁₃	—	2	2	no	—
277	C₂²⋊D₁₃	—	2	2	no	—
278	C₂²⋊D₁₃	—	4	1	no	—
279	C₂²⋊D₁₃	—	4	1	no	—
280	C₂²⋊D₁₃	—	4	2	no	—
281	C₂²⋊D₁₃	—	4	2	no	—
282	C₂²⋊D₁₃	—	4	2	no	—
283	C₂²⋊D₁₃	—	4	2	no	—
284	C₂²⋊D₁₃	—	4	2	no	—
285	C₂²⋊D₁₃	—	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	2	yes	—
291	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
292	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
293	D₅₂	—	2	2	no	—
294	D₅₂	—	2	4	no	—
295	D₅₂	—	2	4	no	—
296	D₅₂	—	2	2	no	—
297	D₅₂	—	2	2	no	—
298	D₅₂	—	2	2	no	—
299	D₅₂	—	4	2	no	—
300	D₅₂	—	4	2	no	—
301	D₅₂	—	4	2	no	—
302	D₅₂	—	4	2	no	—
303	D₅₂	—	4	2	no	—
304	D₅₂	—	4	2	no	—
305	D₅₂	—	4	1	no	—
306	D₅₂	—	4	2	no	—
307	D₅₂	—	4	2	no	—
308	D₅₂	—	4	2	no	—
309	C₄×D₁₃	—	2	2	no	—
310	C₄×D₁₃	—	2	2	no	—
311	C₄×D₁₃	—	2	2	no	—
312	C₄×D₁₃	—	4	1	no	—
313	C₄×D₁₃	—	4	1	no	—
314	C₄×D₁₃	—	4	2	no	—
315	C₄×D₁₃	—	4	2	no	—
316	C₄×D₁₃	—	4	2	no	—
317	C₄×D₁₃	—	4	2	no	—
318	Dic₂₆	—	4	1	no	—
319	#560	—	13	2	no	—
320	#560	—	13	2	no	—
321	#553	—	13	1	no	—
322	#553	—	13	1	no	—
323	#553	—	13	1	no	—
324	#553	D₁₃	1	1	yes	characteristic, complemented
325	D₄²	—	13	1	no	—
326	D₄²	—	13	1	no	—
327	D₄²	—	13	2	no	—
328	D₄²	—	13	1	no	—
329	D₄²	—	13	2	no	—
330	D₄²	—	13	1	no	—
331	#540	—	13	1	no	—
332	#540	—	13	1	no	—
333	#538	—	13	2	no	—
334	#538	—	13	2	no	—
335	#535	—	13	1	no	—
336	#535	—	13	1	no	—
337	#534	—	13	2	no	—
338	#534	—	13	2	no	—
339	#525	—	13	1	no	—
340	C₂×#121	—	13	1	no	—
341	C₂×#121	—	13	1	no	—
342	C₂²×C₁₃	—	2	1	no	—
343	C₂²×C₁₃	—	2	1	no	—
344	C₂²×C₁₃	—	2	1	no	—
345	C₂²×C₁₃	—	2	1	no	—
346	C₂²×C₁₃	—	2	2	no	—
347	C₂²×C₁₃	—	2	1	no	—
348	C₂²×C₁₃	—	2	2	no	—
349	C₂²×C₁₃	—	2	2	no	—
350	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
351	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
352	C₂×D₁₃	—	2	1	no	—
353	C₂×D₁₃	—	2	1	no	—
354	C₂×D₁₃	—	2	1	no	—
355	C₂×D₁₃	—	2	1	no	—
356	C₂×D₁₃	—	2	2	no	—
357	C₂×D₁₃	—	2	2	no	—
358	C₂×D₁₃	—	2	2	no	—
359	C₂×D₁₃	—	2	2	no	—
360	C₂×D₁₃	—	2	1	no	—
361	C₂×D₁₃	—	2	2	no	—
362	C₂×D₁₃	—	2	2	no	—
363	C₂×D₁₃	—	2	2	no	—
364	C₂×D₁₃	—	2	2	no	—
365	C₂×D₁₃	—	2	1	no	—
366	C₂×D₁₃	—	2	1	no	—
367	C₂×D₁₃	—	2	2	no	—
368	C₂×D₁₃	—	2	1	no	—
369	C₂×D₁₃	—	4	4	no	—
370	C₂×D₁₃	—	8	4	no	—
371	C₂×D₁₃	—	8	4	no	—
372	C₂×D₁₃	—	8	4	no	—
373	C₂×D₁₃	—	8	4	no	—
374	C₂×D₁₃	H(5,𝔽₂)	1	2	yes	—
375	C₄×C₁₃	—	2	1	no	—
376	C₄×C₁₃	—	2	1	no	—
377	C₄×C₁₃	—	2	2	no	—
378	C₄×C₁₃	—	2	1	no	—
379	C₄×C₁₃	—	2	2	no	—
380	C₄×C₁₃	—	2	1	no	—
381	C₄×C₁₃	—	2	2	no	—
382	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
383	Dic₁₃	—	2	1	no	—
384	Dic₁₃	—	2	1	no	—
385	Dic₁₃	—	2	1	no	—
386	Dic₁₃	—	2	2	no	—
387	Dic₁₃	—	2	1	no	—
388	Dic₁₃	—	2	1	no	—
389	C₂×#41	—	13	1	no	—
390	C₂²×D₄	—	13	1	no	—
391	C₂²×D₄	—	13	2	no	—
392	C₂²×D₄	—	13	2	no	—
393	C₂²×D₄	—	13	2	no	—
394	C₂²×D₄	—	13	2	no	—
395	C₂²×D₄	—	13	1	no	—
396	C₂²×D₄	—	13	1	no	—
397	C₂²×D₄	—	13	2	no	—
398	C₂²×D₄	—	13	2	no	—
399	C₂²×D₄	—	13	1	no	—
400	C₂³×C₄	—	13	1	no	—
401	#127	—	13	2	no	—
402	#127	—	13	1	no	—
403	#127	—	13	2	no	—
404	#127	—	13	1	no	—
405	#126	—	13	2	no	—
406	#126	—	13	2	no	—
407	#126	—	13	2	no	—
408	#126	C₂×D₁₃	1	2	yes	complemented
409	#125	—	13	1	no	—
410	#125	C₂×D₁₃	1	1	yes	characteristic, complemented
411	#124	—	13	2	no	—
412	#124	—	13	2	no	—
413	#123	—	13	2	no	—
414	#123	—	13	1	no	—
415	#123	—	13	2	no	—
416	#123	—	13	2	no	—
417	#123	—	13	2	no	—
418	#123	—	13	2	no	—
419	#123	—	13	1	no	—
420	#123	—	13	2	no	—
421	#123	—	13	2	no	—
422	#123	C₂×D₁₃	1	2	yes	complemented
423	C₂²⋊Q₈	—	13	1	no	—
424	C₂²⋊Q₈	—	13	1	no	—
425	#121	—	13	2	no	—
426	#121	—	13	1	no	—
427	#121	—	13	1	no	—
428	#121	—	13	1	no	—
429	#121	—	13	2	no	—
430	#121	—	13	1	no	—
431	#121	—	13	2	no	—
432	#121	—	13	2	no	—
433	#121	—	13	2	no	—
434	#121	—	13	1	no	—
435	#121	—	13	1	no	—
436	#121	—	13	1	no	—
437	#121	—	13	1	no	—
438	#121	—	13	1	no	—
439	#121	—	13	2	no	—
440	#121	—	13	2	no	—
441	#121	—	13	1	no	—
442	#121	—	13	1	no	—
443	#121	—	13	2	no	—
444	#121	—	13	2	no	—
445	#121	—	13	2	no	—
446	#121	—	13	2	no	—
447	#121	—	13	1	no	—
448	#121	—	13	2	no	—
449	#121	—	13	2	no	—
450	#121	—	13	2	no	—
451	#121	—	13	2	no	—
452	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
453	#121	C₂×D₁₃	1	2	yes	complemented
454	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
455	#120	—	13	1	no	—
456	#120	—	13	2	no	—
457	#120	—	13	2	no	—
458	#120	—	13	2	no	—
459	#120	—	13	1	no	—
460	#120	—	13	2	no	—
461	#120	—	13	2	no	—
462	#120	—	13	2	no	—
463	#120	—	13	2	no	—
464	#120	—	13	2	no	—
465	#120	—	13	2	no	—
466	#120	—	13	2	no	—
467	#120	—	13	2	no	—
468	#120	—	13	2	no	—
469	C₄×D₄	—	13	1	no	—
470	C₄×D₄	—	13	1	no	—
471	C₄×D₄	—	13	2	no	—
472	C₄×D₄	—	13	2	no	—
473	C₄×D₄	—	13	1	no	—
474	C₄×D₄	—	13	1	no	—
475	C₄×D₄	—	13	1	no	—
476	C₄×D₄	—	13	2	no	—
477	C₄×D₄	—	13	1	no	—
478	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
479	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
480	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
481	#117	—	13	1	no	—
482	#117	—	13	1	no	—
483	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
484	C₂×C₄⋊C₄	—	13	1	no	—
485	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
486	C₂×C₂²⋊C₄	—	13	2	no	—
487	C₂×C₂²⋊C₄	—	13	2	no	—
488	C₂×C₁₃	—	2	2	no	—
489	C₂×C₁₃	—	4	2	no	—
490	C₂×C₁₃	—	4	1	no	—
491	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
492	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
493	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
494	D₁₃	—	2	2	no	—
495	D₁₃	—	4	1	no	—
496	D₁₃	—	4	1	no	—
497	D₁₃	—	4	2	no	—
498	D₁₃	—	4	2	no	—
499	D₁₃	—	4	2	no	—
500	C₂⁴	—	13	1	no	—
501	C₂⁴	—	13	2	no	—
502	C₂⁴	—	13	2	no	—
503	C₂⁴	—	13	2	no	—
504	C₂⁴	—	13	2	no	—
505	#41	—	52	2	no	—
506	C₂×Q₈	—	13	1	no	—
507	C₂×D₄	—	13	1	no	—
508	C₂×D₄	—	13	1	no	—
509	C₂×D₄	—	13	2	no	—
510	C₂×D₄	—	13	1	no	—
511	C₂×D₄	—	13	1	no	—
512	C₂×D₄	—	13	2	no	—
513	C₂×D₄	—	13	2	no	—
514	C₂×D₄	—	13	2	no	—
515	C₂×D₄	—	13	2	no	—
516	C₂×D₄	—	13	2	no	—
517	C₂×D₄	—	13	2	no	—
518	C₂×D₄	—	13	2	no	—
519	C₂×D₄	—	13	1	no	—
520	C₂×D₄	—	13	2	no	—
521	C₂×D₄	—	13	1	no	—
522	C₂×D₄	—	13	1	no	—
523	C₂×D₄	—	13	1	no	—
524	C₂×D₄	—	13	1	no	—
525	C₂×D₄	—	13	2	no	—
526	C₂×D₄	—	13	2	no	—
527	C₂×D₄	—	13	2	no	—
528	C₂×D₄	—	13	2	no	—
529	C₂×D₄	—	13	2	no	—
530	C₂×D₄	—	13	2	no	—
531	C₂×D₄	—	13	2	no	—
532	C₂×D₄	—	13	2	no	—
533	C₂×D₄	—	13	2	no	—
534	C₂×D₄	—	52	2	no	—
535	C₂×D₄	—	52	2	no	—
536	C₂×D₄	—	52	4	no	—
537	C₂×D₄	—	52	4	no	—
538	C₂×D₄	—	52	2	no	—
539	C₂×D₄	—	52	2	no	—
540	C₂×D₄	—	52	4	no	—
541	C₂×D₄	—	52	4	no	—
542	C₂×D₄	—	52	4	no	—
543	C₂×D₄	—	52	4	no	—
544	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
545	C₂×D₄	C₂²×D₁₃	1	2	yes	—
546	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
547	C₂×D₄	C₂²×D₁₃	1	2	yes	—
548	C₂²×C₄	—	13	1	no	—
549	C₂²×C₄	—	13	1	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	2	no	—
557	C₂²×C₄	—	13	1	no	—
558	C₂²×C₄	—	52	2	no	—
559	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
560	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
561	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
562	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
563	C₄⋊C₄	—	13	1	no	—
564	C₄⋊C₄	—	13	2	no	—
565	C₄⋊C₄	—	13	1	no	—
566	C₄⋊C₄	—	13	1	no	—
567	C₄⋊C₄	—	13	1	no	—
568	C₄⋊C₄	—	13	1	no	—
569	C₄⋊C₄	—	13	1	no	—
570	C₄⋊C₄	—	13	2	no	—
571	C₄⋊C₄	—	13	2	no	—
572	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
573	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
574	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
575	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
576	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
577	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
578	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
579	C₂²⋊C₄	—	13	2	no	—
580	C₂²⋊C₄	—	13	1	no	—
581	C₂²⋊C₄	—	13	1	no	—
582	C₂²⋊C₄	—	13	2	no	—
583	C₂²⋊C₄	—	13	2	no	—
584	C₂²⋊C₄	—	13	2	no	—
585	C₂²⋊C₄	—	13	2	no	—
586	C₂²⋊C₄	—	13	2	no	—
587	C₂²⋊C₄	—	13	2	no	—
588	C₂²⋊C₄	—	13	2	no	—
589	C₂²⋊C₄	—	13	1	no	—
590	C₂²⋊C₄	—	13	1	no	—
591	C₂²⋊C₄	—	13	1	no	—
592	C₂²⋊C₄	—	13	1	no	—
593	C₂²⋊C₄	—	13	2	no	—
594	C₂²⋊C₄	—	13	2	no	—
595	C₂²⋊C₄	—	13	2	no	—
596	C₂²⋊C₄	—	13	2	no	—
597	C₂²⋊C₄	—	13	2	no	—
598	C₂²⋊C₄	—	13	2	no	—
599	C₂²⋊C₄	—	13	1	no	—
600	C₂²⋊C₄	—	13	1	no	—
601	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
602	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
603	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
604	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
605	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
606	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
607	C₄²	—	13	1	no	—
608	C₄²	—	13	2	no	—
609	C₄²	C₂²×D₁₃	1	1	yes	characteristic
610	C₄²	C₂²×D₁₃	1	2	yes	—
611	C₁₃	#3537	1	1	yes	characteristic, complemented, Sylow
612	C₂³	—	13	1	no	—
613	C₂³	—	13	1	no	—
614	C₂³	—	13	2	no	—
615	C₂³	—	13	2	no	—
616	C₂³	—	13	2	no	—
617	C₂³	—	13	1	no	—
618	C₂³	—	26	2	no	—
619	C₂³	—	26	4	no	—
620	C₂³	—	26	2	no	—
621	C₂³	—	26	4	no	—
622	C₂³	—	52	1	no	—
623	C₂³	—	52	2	no	—
624	C₂³	—	52	2	no	—
625	C₂³	—	52	2	no	—
626	C₂³	—	52	2	no	—
627	C₂³	—	52	2	no	—
628	C₂³	—	52	2	no	—
629	C₂³	—	52	2	no	—
630	C₂³	—	52	2	no	—
631	C₂³	—	52	2	no	—
632	C₂³	—	52	2	no	—
633	C₂³	C₂³×D₁₃	1	1	yes	characteristic
634	C₂³	C₂³×D₁₃	1	2	yes	—
635	C₂³	C₂³×D₁₃	1	1	yes	characteristic
636	Q₈	—	52	1	no	—
637	D₄	—	2	4	no	—
638	D₄	—	2	2	no	—
639	D₄	—	2	2	no	—
640	D₄	—	4	2	no	—
641	D₄	—	26	2	no	—
642	D₄	—	26	4	no	—
643	D₄	—	26	4	no	—
644	D₄	—	26	2	no	—
645	D₄	—	26	2	no	—
646	D₄	—	26	4	no	—
647	D₄	—	26	2	no	—
648	D₄	—	26	2	no	—
649	D₄	—	26	2	no	—
650	D₄	—	52	2	no	—
651	D₄	—	52	2	no	—
652	D₄	—	52	2	no	—
653	D₄	—	52	2	no	—
654	D₄	—	52	2	no	—
655	D₄	—	52	2	no	—
656	D₄	—	52	2	no	—
657	D₄	—	52	2	no	—
658	D₄	—	52	2	no	—
659	D₄	—	52	1	no	—
660	D₄	—	52	2	no	—
661	D₄	—	52	2	no	—
662	D₄	—	52	2	no	—
663	D₄	—	52	2	no	—
664	D₄	—	52	2	no	—
665	D₄	—	52	2	no	—
666	D₄	—	52	1	no	—
667	D₄	—	52	1	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	4	2	no	—
671	C₂×C₄	—	4	2	no	—
672	C₂×C₄	—	13	1	no	—
673	C₂×C₄	—	13	1	no	—
674	C₂×C₄	—	13	2	no	—
675	C₂×C₄	—	13	1	no	—
676	C₂×C₄	—	13	1	no	—
677	C₂×C₄	—	13	1	no	—
678	C₂×C₄	—	26	2	no	—
679	C₂×C₄	—	26	2	no	—
680	C₂×C₄	—	26	2	no	—
681	C₂×C₄	—	52	1	no	—
682	C₂×C₄	—	52	1	no	—
683	C₂×C₄	—	52	2	no	—
684	C₂×C₄	—	52	2	no	—
685	C₂×C₄	—	52	2	no	—
686	C₂×C₄	—	52	2	no	—
687	C₂×C₄	—	52	1	no	—
688	C₂×C₄	C₂³×D₁₃	1	2	yes	—
689	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
690	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
691	C₂×C₄	C₂³×D₁₃	1	2	yes	—
692	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
693	C₂×C₄	C₂³×D₁₃	1	2	yes	—
694	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
695	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
696	C₂²	—	2	1	no	—
697	C₂²	—	2	1	no	—
698	C₂²	—	2	1	no	—
699	C₂²	—	2	1	no	—
700	C₂²	—	2	2	no	—
701	C₂²	—	2	2	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	2	1	no	—
704	C₂²	—	13	2	no	—
705	C₂²	—	26	1	no	—
706	C₂²	—	26	1	no	—
707	C₂²	—	26	1	no	—
708	C₂²	—	26	1	no	—
709	C₂²	—	26	2	no	—
710	C₂²	—	26	2	no	—
711	C₂²	—	26	1	no	—
712	C₂²	—	26	2	no	—
713	C₂²	—	26	2	no	—
714	C₂²	—	26	2	no	—
715	C₂²	—	26	2	no	—
716	C₂²	—	26	1	no	—
717	C₂²	—	26	2	no	—
718	C₂²	—	26	1	no	—
719	C₂²	—	26	2	no	—
720	C₂²	—	26	2	no	—
721	C₂²	—	26	1	no	—
722	C₂²	—	52	4	no	—
723	C₂²	—	104	4	no	—
724	C₂²	—	104	4	no	—
725	C₂²	—	104	4	no	—
726	C₂²	—	104	4	no	—
727	C₂²	#88256	1	2	yes	—
728	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
729	C₄	—	2	1	no	—
730	C₄	—	2	1	no	—
731	C₄	—	2	2	no	—
732	C₄	—	2	1	no	—
733	C₄	—	2	1	no	—
734	C₄	—	2	2	no	—
735	C₄	—	2	2	no	—
736	C₄	—	26	1	no	—
737	C₄	—	26	1	no	—
738	C₄	—	26	1	no	—
739	C₄	—	26	1	no	—
740	C₄	—	26	2	no	—
741	C₄	—	26	1	no	—
742	C₄	#88256	1	2	yes	—
743	C₂	—	2	2	no	—
744	C₂	—	4	1	no	—
745	C₂	—	4	2	no	—
746	C₂	—	26	2	no	—
747	C₂	—	52	1	no	—
748	C₂	—	52	1	no	—
749	C₂	—	52	2	no	—
750	C₂	—	52	2	no	—
751	C₂	—	52	2	no	—
752	C₂	C₂×#88256	1	1	yes	characteristic
753	C₂	C₂×#88256	1	1	yes	characteristic
754	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#553	C₂
hypercenter	#553	D₁₃
hypocenter	C₁₃	#3537
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. C₁₃×#553	C₂	semidirect
2. #11719416	C₂	semidirect
3. #11719409	C₂	semidirect
4. #11719403	C₂	semidirect
5. #11719400	C₂	semidirect
6. #11719371	C₂	semidirect
7. #11719358	C₂	semidirect
8. #11719314	C₂	semidirect
9. #11719314	C₂	semidirect
10. #11719314	C₂	semidirect
11. #11719312	C₂	semidirect
12. #11719310	C₂	semidirect
13. D₁₃×#121	C₂	semidirect
14. #11719267	C₂	semidirect
15. #11719265	C₂	semidirect
16. D₄×D₅₂	C₂	semidirect
17. D₄×D₅₂	C₂	semidirect
18. D₄×D₅₂	C₂	semidirect
19. #11719252	C₂	semidirect
20. #11719235	C₂	semidirect
21. #11719230	C₂	semidirect
22. #11719219	C₂	semidirect
23. C₂×#88149	C₂	semidirect
24. C₂×D₄×D₁₃	C₂²	semidirect
25. C₂×D₄×D₁₃	C₂²	semidirect
26. C₂×D₄×D₁₃	C₂²	semidirect
27. C₂×D₄×D₁₃	C₂²	semidirect
28. C₂×D₄×D₁₃	C₂²	semidirect
29. C₂×D₄×D₁₃	C₂²	semidirect
30. C₂×#6127	C₂²	semidirect
31. C₂²×D₅₂	C₂²	semidirect
32. C₂²×D₅₂	C₂²	semidirect
33. C₂²×D₅₂	C₂²	semidirect
34. C₂²×D₅₂	C₂²	semidirect
35. C₂²×C₄×D₁₃	C₂²	semidirect
36. C₁₃×#126	C₂²	semidirect
37. C₁₃×#125	C₂²	semidirect
38. C₁₃×#123	C₂²	semidirect
39. C₁₃×#121	C₂²	semidirect
40. C₁₃×#121	C₂²	semidirect
41. C₁₃×#121	C₂²	semidirect
42. C₄×D₄×C₁₃	C₂²	semidirect
43. C₄×D₄×C₁₃	C₂²	semidirect
44. C₄×D₄×C₁₃	C₂²	semidirect
45. C₁₃×#117	C₂²	semidirect
46. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
47. #88194	C₂²	semidirect
48. #88194	C₂²	semidirect
49. #88193	C₂²	semidirect
50. #88193	C₂²	semidirect
51. #88192	C₂²	semidirect
52. #88191	C₂²	semidirect
53. #88191	C₂²	semidirect
54. #88191	C₂²	semidirect
55. #88191	C₂²	semidirect
56. #88184	C₂²	semidirect
57. #88184	C₂²	semidirect
58. #88184	C₂²	semidirect
59. #88184	C₂²	semidirect
60. #88184	C₂²	semidirect
61. #88183	C₂²	semidirect
62. C₄×C₂²⋊D₁₃	C₂²	semidirect
63. C₄×C₂²⋊D₁₃	C₂²	semidirect
64. C₄×C₂²⋊D₁₃	C₂²	semidirect
65. C₂×#6103	C₂²	semidirect
66. #88152	C₂²	semidirect
67. #88152	C₂²	semidirect
68. #88150	C₂²	semidirect
69. #88149	C₂²	semidirect
70. #88149	C₂²	semidirect
71. #88149	C₂²	semidirect
72. #88149	C₂²	semidirect
73. #88149	C₂²	semidirect
74. #88149	C₂²	semidirect
75. #88149	C₂²	semidirect
76. #88149	C₂²	semidirect
77. #88149	C₂²	semidirect
78. #88149	C₂²	semidirect
79. #88149	C₂²	semidirect
80. #88149	C₂²	semidirect
81. #88149	C₂²	semidirect
82. #88148	C₂²	semidirect
83. #88148	C₂²	semidirect
84. #88148	C₂²	semidirect
85. #88148	C₂²	semidirect
86. #88148	C₂²	semidirect
87. #88147	C₂²	semidirect
88. #88147	C₂²	semidirect
89. #88147	C₂²	semidirect
90. #88146	C₂²	semidirect
91. C₄⋊C₄×D₁₃	C₂²	semidirect
92. #88144	C₂²	semidirect
93. #88139	C₂²	semidirect
94. #88138	C₂²	semidirect
95. #88138	C₂²	semidirect
96. #88138	C₂²	semidirect
97. #88138	C₂²	semidirect
98. #88138	C₂²	semidirect
99. #88138	C₂²	semidirect
100. #88137	C₂²	semidirect
101. #88137	C₂²	semidirect
102. #88137	C₂²	semidirect
103. #88136	C₂²	semidirect
104. #88136	C₂²	semidirect
105. #88136	C₂²	semidirect
106. #88136	C₂²	semidirect
107. #88136	C₂²	semidirect
108. #88136	C₂²	semidirect
109. #88136	C₂²	semidirect
110. #88136	C₂²	semidirect
111. #88136	C₂²	semidirect
112. #88136	C₂²	semidirect
113. C₂²⋊C₄×D₁₃	C₂²	semidirect
114. #88132	C₂²	semidirect
115. #88130	C₂²	semidirect
116. #88129	C₂²	semidirect
117. #88128	C₂²	semidirect
118. #88128	C₂²	semidirect
119. C₄×D₅₂	C₂²	semidirect
120. C₄×D₅₂	C₂²	semidirect
121. C₄×D₅₂	C₂²	semidirect
122. #88126	C₂²	semidirect
324. #553	D₁₃	semidirect
408. #126	C₂×D₁₃	semidirect
410. #125	C₂×D₁₃	semidirect
422. #123	C₂×D₁₃	semidirect
452. #121	C₂×D₁₃	semidirect
453. #121	C₂×D₁₃	semidirect
454. #121	C₂×D₁₃	semidirect
478. C₄×D₄	C₂×D₁₃	semidirect
479. C₄×D₄	C₂×D₁₃	semidirect
480. C₄×D₄	C₂×D₁₃	semidirect
483. #117	C₂×D₁₃	semidirect
485. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
611. C₁₃	#3537	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#553	2
#11719416	2
#11719409	2
#11719403	2
#11719400	2
#11719371	2
#11719358	2
#11719314	2
#11719312	2
#11719310	2
D₁₃×#121	2
#11719267	2
#11719265	2
D₄×D₅₂	2
#11719252	2
#11719235	2
#11719230	2
#11719219	2
C₂×#88149	2
#3537	13