Subgroups — #13128665

Order 1664.

1152 conjugacy classes of subgroups.

The subgroup lattice has 704 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	#11719412	C₂	1	2	yes	maximal, complemented
3	#11719410	C₂	1	2	yes	maximal, complemented
4	#11719399	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719396	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719363	C₂	1	2	yes	maximal, complemented
7	#11719362	C₂	1	2	yes	maximal, complemented
8	#11719323	C₂	1	2	yes	maximal, complemented
9	#11719317	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719311	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719310	C₂	1	2	yes	maximal, complemented
12	D₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719303	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719270	C₂	1	2	yes	maximal, complemented
15	#11719262	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719259	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719257	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719250	C₂	1	2	yes	maximal, complemented
19	C₄×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719234	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719229	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719219	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#88151	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#6129	C₂²	1	1	yes	characteristic, complemented
25	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₁₃	C₂²	1	2	yes	—
27	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
31	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#126	C₂²	1	2	yes	complemented
33	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#123	C₂²	1	2	yes	complemented
35	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#121	C₂²	1	2	yes	complemented
37	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
38	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
40	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
43	#88193	C₂²	1	2	yes	complemented
44	#88193	C₂²	1	2	yes	complemented
45	#88193	C₂²	1	2	yes	complemented
46	#88192	C₂²	1	1	yes	characteristic
47	#88192	C₂²	1	2	yes	complemented
48	#88191	C₂²	1	2	yes	—
49	#88191	C₂²	1	2	yes	complemented
50	#88190	C₂²	1	1	yes	characteristic, complemented
51	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
52	D₄×Dic₁₃	C₂²	1	2	yes	complemented
53	D₄×Dic₁₃	C₂²	1	2	yes	complemented
54	#88184	C₂²	1	1	yes	characteristic, complemented
55	#88184	C₂²	1	2	yes	complemented
56	#88184	C₂²	1	2	yes	complemented
57	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
58	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
61	C₂×#6103	C₂²	1	2	yes	—
62	C₂×#6103	C₂²	1	2	yes	complemented
63	#88180	C₂²	1	2	yes	complemented
64	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	complemented
65	#88178	C₂²	1	1	yes	characteristic, complemented
66	#88152	C₂²	1	2	yes	complemented
67	#88152	C₂²	1	2	yes	complemented
68	#88152	C₂²	1	2	yes	complemented
69	#88151	C₂²	1	1	yes	characteristic, complemented
70	#88151	C₂²	1	1	yes	characteristic, complemented
71	#88151	C₂²	1	1	yes	characteristic, complemented
72	#88151	C₂²	1	1	yes	characteristic, complemented
73	#88151	C₂²	1	2	yes	complemented
74	#88151	C₂²	1	2	yes	complemented
75	#88151	C₂²	1	1	yes	characteristic, complemented
76	#88150	C₂²	1	2	yes	complemented
77	#88149	C₂²	1	1	yes	characteristic
78	#88149	C₂²	1	1	yes	characteristic, complemented
79	#88148	C₂²	1	2	yes	—
80	#88148	C₂²	1	2	yes	complemented
81	#88148	C₂²	1	2	yes	complemented
82	#88147	C₂²	1	1	yes	characteristic
83	#88147	C₂²	1	1	yes	characteristic, complemented
84	#88147	C₂²	1	2	yes	complemented
85	#88146	C₂²	1	1	yes	characteristic, complemented
86	#88146	C₂²	1	2	yes	complemented
87	#88146	C₂²	1	2	yes	complemented
88	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
89	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
90	#88144	C₂²	1	1	yes	characteristic, complemented
91	#88144	C₂²	1	2	yes	complemented
92	#88141	C₂²	1	1	yes	characteristic, complemented
93	#88140	C₂²	1	2	yes	complemented
94	#88140	C₂²	1	2	yes	complemented
95	#88139	C₂²	1	2	yes	complemented
96	#88139	C₂²	1	2	yes	complemented
97	#88138	C₂²	1	2	yes	—
98	#88137	C₂²	1	2	yes	—
99	#88137	C₂²	1	2	yes	complemented
100	#88137	C₂²	1	2	yes	complemented
101	#88137	C₂²	1	2	yes	complemented
102	#88136	C₂²	1	2	yes	—
103	#88136	C₂²	1	2	yes	complemented
104	#88135	C₂²	1	1	yes	characteristic
105	#88135	C₂²	1	1	yes	characteristic, complemented
106	#88135	C₂²	1	2	yes	complemented
107	#88135	C₂²	1	2	yes	complemented
108	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
109	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
110	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
112	#88133	C₂²	1	2	yes	complemented
113	#88133	C₂²	1	2	yes	complemented
114	#88132	C₂²	1	2	yes	complemented
115	#88129	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₅₂	C₂²	1	1	yes	characteristic
117	C₄×D₅₂	C₂²	1	2	yes	complemented
118	C₄×D₅₂	C₂²	1	2	yes	complemented
119	#88126	C₂²	1	2	yes	complemented
120	C₄²×D₁₃	C₂²	1	1	yes	characteristic, complemented
121	#88124	C₂²	1	2	yes	complemented
122	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₃	C₂³	1	2	yes	—
124	C₂³×D₁₃	C₂³	1	1	yes	characteristic
125	C₂³×D₁₃	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₃	C₂³	1	2	yes	—
128	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₃	C₂³	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₃	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	2	yes	—
139	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
141	C₂²×Dic₁₃	C₂³	1	2	yes	—
142	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
143	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
144	C₂²×Dic₁₃	C₂³	1	2	yes	—
145	#6129	—	4	2	no	—
146	D₄×D₁₃	—	2	4	no	—
147	D₄×D₁₃	—	2	8	no	—
148	D₄×D₁₃	—	4	2	no	—
149	#6127	—	4	2	no	—
150	C₂×D₅₂	C₂³	1	1	yes	characteristic
151	C₂×D₅₂	C₂³	1	2	yes	—
152	C₂×D₅₂	C₂³	1	1	yes	characteristic
153	C₂×D₅₂	C₂³	1	2	yes	—
154	C₂×C₄×D₁₃	—	4	2	no	—
155	C₂×C₄×D₁₃	—	4	2	no	—
156	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₃	C₂³	1	2	yes	—
159	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₁₃	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×Dic₂₆	—	4	2	no	—
169	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
170	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
171	C₂×Dic₂₆	C₂³	1	2	yes	—
172	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
178	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
183	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
184	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₄²×C₁₃	C₂³	1	1	yes	characteristic
186	C₄²×C₁₃	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
188	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
193	#6103	C₂³	1	1	yes	characteristic
194	#6103	C₂³	1	2	yes	—
195	#6103	C₂³	1	1	yes	characteristic
196	#6103	C₂³	1	1	yes	characteristic
197	#6103	C₂³	1	2	yes	—
198	#6103	C₂³	1	2	yes	—
199	#6103	C₂³	1	2	yes	—
200	#6103	C₂³	1	2	yes	—
201	#6103	C₂³	1	2	yes	—
202	#6103	C₂³	1	2	yes	—
203	#6103	C₂³	1	2	yes	—
204	#6103	C₂³	1	1	yes	characteristic
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	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₁₃	C₂³	1	2	yes	—
211	C₄⋊Dic₁₃	C₂³	1	2	yes	—
212	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₁₃	C₂³	1	2	yes	—
214	C₄⋊Dic₁₃	C₂³	1	2	yes	—
215	C₄⋊Dic₁₃	C₂³	1	2	yes	—
216	C₄⋊Dic₁₃	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	#6101	C₂³	1	2	yes	—
222	#6101	C₂³	1	2	yes	—
223	#6101	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₃	C₂³	1	2	yes	—
225	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
226	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
228	C₄×Dic₁₃	C₂³	1	2	yes	—
229	C₄×Dic₁₃	C₂³	1	2	yes	—
230	#3505	—	13	1	no	maximal, Sylow
231	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₂³×C₁₃	C₂⁴	1	2	yes	—
233	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
234	C₂²×D₁₃	—	2	2	no	—
235	C₂²×D₁₃	—	2	4	no	—
236	C₂²×D₁₃	—	4	1	no	—
237	C₂²×D₁₃	—	4	1	no	—
238	C₂²×D₁₃	—	4	1	no	—
239	C₂²×D₁₃	—	4	1	no	—
240	C₂²×D₁₃	—	4	2	no	—
241	C₂²×D₁₃	—	4	2	no	—
242	C₂²×D₁₃	#41	1	4	yes	complemented
243	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
244	C₂²×D₁₃	C₂⁴	1	2	yes	—
245	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
246	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
247	D₄×C₁₃	—	2	2	no	—
248	D₄×C₁₃	—	2	4	no	—
249	D₄×C₁₃	—	2	2	no	—
250	D₄×C₁₃	—	4	2	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	4	2	no	—
254	C₂×C₄×C₁₃	—	4	2	no	—
255	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
258	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	C₂²⋊D₁₃	—	2	2	no	—
264	C₂²⋊D₁₃	—	2	4	no	—
265	C₂²⋊D₁₃	—	2	2	no	—
266	C₂²⋊D₁₃	—	2	4	no	—
267	C₂²⋊D₁₃	—	4	2	no	—
268	C₂²⋊D₁₃	—	4	2	no	—
269	C₂²⋊D₁₃	—	4	2	no	—
270	C₂×Dic₁₃	—	4	2	no	—
271	C₂×Dic₁₃	—	4	1	no	—
272	C₂×Dic₁₃	—	4	1	no	—
273	C₂×Dic₁₃	—	4	2	no	—
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	1	yes	characteristic
278	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₁₃	C₂⁴	1	2	yes	—
280	C₂×Dic₁₃	C₂⁴	1	2	yes	—
281	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
282	D₅₂	—	2	2	no	—
283	D₅₂	—	2	4	no	—
284	D₅₂	—	2	2	no	—
285	D₅₂	—	4	2	no	—
286	C₄×D₁₃	—	2	4	no	—
287	C₄×D₁₃	—	2	2	no	—
288	C₄×D₁₃	—	2	2	no	—
289	C₄×D₁₃	—	2	2	no	—
290	C₄×D₁₃	—	2	2	no	—
291	C₄×D₁₃	—	4	1	no	—
292	C₄×D₁₃	—	4	1	no	—
293	C₄×D₁₃	—	4	1	no	—
294	C₄×D₁₃	—	4	1	no	—
295	C₄×D₁₃	—	4	1	no	—
296	C₄×D₁₃	—	4	2	no	—
297	C₄×D₁₃	—	4	2	no	—
298	Dic₂₆	—	2	2	no	—
299	Dic₂₆	—	2	2	no	—
300	Dic₂₆	—	4	2	no	—
301	#553	—	13	2	no	—
302	#553	—	13	2	no	—
303	#553	—	13	1	no	—
304	#553	D₁₃	1	1	yes	characteristic, complemented
305	#552	—	13	1	no	—
306	#552	—	13	1	no	—
307	#551	—	13	2	no	—
308	#551	—	13	2	no	—
309	#548	—	13	1	no	—
310	#548	—	13	1	no	—
311	#546	—	13	1	no	—
312	#546	—	13	1	no	—
313	#539	—	13	2	no	—
314	#538	—	13	2	no	—
315	#534	—	13	2	no	—
316	#529	—	13	1	no	—
317	#529	—	13	1	no	—
318	#525	—	13	1	no	—
319	#525	—	13	1	no	—
320	C₂×C₂²⋊Q₈	—	13	1	no	—
321	C₂×#121	—	13	1	no	—
322	#518	—	13	2	no	—
323	C₂×C₄×D₄	—	13	1	no	—
324	C₂²×C₁₃	—	2	1	no	—
325	C₂²×C₁₃	—	2	1	no	—
326	C₂²×C₁₃	—	2	1	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	1	no	—
329	C₂²×C₁₃	—	2	2	no	—
330	C₂²×C₁₃	—	2	2	no	—
331	C₂²×C₁₃	—	2	1	no	—
332	C₂²×C₁₃	C₂×#41	1	2	yes	—
333	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
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	2	no	—
340	C₂×D₁₃	—	2	1	no	—
341	C₂×D₁₃	—	2	2	no	—
342	C₂×D₁₃	—	2	2	no	—
343	C₂×D₁₃	—	2	1	no	—
344	C₂×D₁₃	—	4	4	no	—
345	C₂×D₁₃	—	4	4	no	—
346	C₂×D₁₃	—	8	4	no	—
347	C₂×D₁₃	C₂×#41	1	2	yes	—
348	C₂×D₁₃	C₂×#41	1	2	yes	—
349	C₄×C₁₃	—	2	2	no	—
350	C₄×C₁₃	—	2	1	no	—
351	C₄×C₁₃	—	2	1	no	—
352	C₄×C₁₃	—	2	1	no	—
353	C₄×C₁₃	—	2	1	no	—
354	C₄×C₁₃	—	2	2	no	—
355	C₄×C₁₃	—	2	2	no	—
356	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
357	Dic₁₃	—	2	2	no	—
358	Dic₁₃	—	2	1	no	—
359	Dic₁₃	—	2	2	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	C₂×#41	—	13	1	no	—
366	C₂×#41	—	13	1	no	—
367	C₂²×Q₈	—	13	1	no	—
368	C₂²×D₄	—	13	1	no	—
369	C₂²×D₄	—	13	2	no	—
370	C₂²×D₄	—	13	1	no	—
371	C₂³×C₄	—	13	1	no	—
372	C₂³×C₄	—	13	1	no	—
373	#126	—	13	2	no	—
374	#126	—	13	2	no	—
375	#126	—	13	2	no	—
376	#126	—	13	2	no	—
377	#126	—	13	2	no	—
378	#126	C₂×D₁₃	1	2	yes	complemented
379	#125	—	13	1	no	—
380	#125	—	13	2	no	—
381	#125	—	13	2	no	—
382	#125	C₂×D₁₃	1	1	yes	characteristic, complemented
383	#124	—	13	1	no	—
384	#124	—	13	2	no	—
385	#124	—	13	2	no	—
386	#124	—	13	1	no	—
387	#123	—	13	2	no	—
388	#123	—	13	2	no	—
389	#123	—	13	2	no	—
390	#123	—	13	2	no	—
391	#123	—	13	2	no	—
392	#123	—	13	2	no	—
393	#123	—	13	2	no	—
394	#123	—	13	2	no	—
395	#123	—	13	2	no	—
396	#123	C₂×D₁₃	1	2	yes	complemented
397	C₂²⋊Q₈	—	13	1	no	—
398	C₂²⋊Q₈	—	13	1	no	—
399	C₂²⋊Q₈	—	13	1	no	—
400	C₂²⋊Q₈	—	13	2	no	—
401	C₂²⋊Q₈	—	13	1	no	—
402	C₂²⋊Q₈	—	13	1	no	—
403	C₂²⋊Q₈	—	13	2	no	—
404	C₂²⋊Q₈	—	13	1	no	—
405	C₂²⋊Q₈	—	13	2	no	—
406	C₂²⋊Q₈	—	13	2	no	—
407	#121	—	13	1	no	—
408	#121	—	13	2	no	—
409	#121	—	13	2	no	—
410	#121	—	13	2	no	—
411	#121	—	13	2	no	—
412	#121	—	13	1	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	C₂×D₁₃	1	1	yes	characteristic, complemented
419	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
420	#121	C₂×D₁₃	1	2	yes	complemented
421	#120	—	13	2	no	—
422	#120	—	13	2	no	—
423	#120	—	13	2	no	—
424	#120	—	13	2	no	—
425	C₄×Q₈	—	13	1	no	—
426	C₄×Q₈	—	13	1	no	—
427	C₄×D₄	—	13	1	no	—
428	C₄×D₄	—	13	2	no	—
429	C₄×D₄	—	13	2	no	—
430	C₄×D₄	—	13	1	no	—
431	C₄×D₄	—	13	1	no	—
432	C₄×D₄	—	13	2	no	—
433	C₄×D₄	—	13	2	no	—
434	C₄×D₄	—	13	1	no	—
435	C₄×D₄	—	13	2	no	—
436	C₄×D₄	—	13	1	no	—
437	C₄×D₄	—	13	1	no	—
438	C₄×D₄	—	13	1	no	—
439	C₄×D₄	—	13	2	no	—
440	C₄×D₄	—	13	2	no	—
441	C₄×D₄	—	13	1	no	—
442	C₄×D₄	—	13	2	no	—
443	C₄×D₄	—	13	2	no	—
444	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
445	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
446	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
447	#117	—	13	2	no	—
448	#117	—	13	2	no	—
449	#117	—	13	1	no	—
450	#117	—	13	2	no	—
451	#117	—	13	2	no	—
452	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
453	C₂×C₄⋊C₄	—	13	2	no	—
454	C₂×C₄⋊C₄	—	13	1	no	—
455	C₂×C₄⋊C₄	—	13	1	no	—
456	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
457	C₂×C₂²⋊C₄	—	13	2	no	—
458	C₂×C₂²⋊C₄	—	13	2	no	—
459	C₂×C₂²⋊C₄	—	13	1	no	—
460	C₂×C₂²⋊C₄	—	13	1	no	—
461	C₂×C₂²⋊C₄	—	13	2	no	—
462	C₂×C₂²⋊C₄	—	13	2	no	—
463	C₂×C₄²	—	13	1	no	—
464	C₂×C₁₃	—	2	2	no	—
465	C₂×C₁₃	—	4	1	no	—
466	C₂×C₁₃	—	4	2	no	—
467	C₂×C₁₃	C₂²×#41	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	—	2	2	no	—
471	D₁₃	—	2	2	no	—
472	D₁₃	—	4	1	no	—
473	D₁₃	—	4	2	no	—
474	C₂⁴	—	13	1	no	—
475	C₂⁴	—	13	2	no	—
476	C₂⁴	—	13	1	no	—
477	#41	—	52	2	no	—
478	#41	—	52	2	no	—
479	C₂×Q₈	—	13	1	no	—
480	C₂×Q₈	—	13	1	no	—
481	C₂×Q₈	—	13	2	no	—
482	C₂×Q₈	—	52	2	no	—
483	C₂×D₄	—	13	1	no	—
484	C₂×D₄	—	13	2	no	—
485	C₂×D₄	—	13	1	no	—
486	C₂×D₄	—	13	2	no	—
487	C₂×D₄	—	13	2	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	1	no	—
493	C₂×D₄	—	13	2	no	—
494	C₂×D₄	—	26	4	no	—
495	C₂×D₄	—	26	8	no	—
496	C₂×D₄	—	52	2	no	—
497	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
498	C₂×D₄	C₂²×D₁₃	1	2	yes	—
499	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
500	C₂×D₄	C₂²×D₁₃	1	2	yes	—
501	C₂²×C₄	—	13	2	no	—
502	C₂²×C₄	—	13	2	no	—
503	C₂²×C₄	—	13	1	no	—
504	C₂²×C₄	—	13	1	no	—
505	C₂²×C₄	—	13	1	no	—
506	C₂²×C₄	—	13	1	no	—
507	C₂²×C₄	—	13	2	no	—
508	C₂²×C₄	—	13	1	no	—
509	C₂²×C₄	—	13	1	no	—
510	C₂²×C₄	—	13	1	no	—
511	C₂²×C₄	—	13	1	no	—
512	C₂²×C₄	—	13	1	no	—
513	C₂²×C₄	—	13	1	no	—
514	C₂²×C₄	—	13	2	no	—
515	C₂²×C₄	—	13	2	no	—
516	C₂²×C₄	—	13	1	no	—
517	C₂²×C₄	—	52	2	no	—
518	C₂²×C₄	—	52	2	no	—
519	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
520	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
521	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
522	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
523	C₄⋊C₄	—	13	2	no	—
524	C₄⋊C₄	—	13	2	no	—
525	C₄⋊C₄	—	13	1	no	—
526	C₄⋊C₄	—	13	1	no	—
527	C₄⋊C₄	—	13	1	no	—
528	C₄⋊C₄	—	13	1	no	—
529	C₄⋊C₄	—	13	2	no	—
530	C₄⋊C₄	—	13	2	no	—
531	C₄⋊C₄	—	13	2	no	—
532	C₄⋊C₄	—	13	2	no	—
533	C₄⋊C₄	—	13	2	no	—
534	C₄⋊C₄	—	13	2	no	—
535	C₄⋊C₄	—	13	2	no	—
536	C₄⋊C₄	—	13	2	no	—
537	C₄⋊C₄	—	13	2	no	—
538	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
539	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
540	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
541	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
542	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
543	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
544	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
545	C₂²⋊C₄	—	13	2	no	—
546	C₂²⋊C₄	—	13	1	no	—
547	C₂²⋊C₄	—	13	1	no	—
548	C₂²⋊C₄	—	13	2	no	—
549	C₂²⋊C₄	—	13	2	no	—
550	C₂²⋊C₄	—	13	2	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	2	no	—
558	C₂²⋊C₄	—	13	1	no	—
559	C₂²⋊C₄	—	13	2	no	—
560	C₂²⋊C₄	—	13	2	no	—
561	C₂²⋊C₄	—	13	1	no	—
562	C₂²⋊C₄	—	13	2	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	C₂²×D₁₃	1	1	yes	characteristic
568	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
569	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
570	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
571	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
572	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
573	C₄²	—	13	1	no	—
574	C₄²	—	13	1	no	—
575	C₄²	—	13	1	no	—
576	C₄²	—	13	2	no	—
577	C₄²	—	13	2	no	—
578	C₄²	—	13	2	no	—
579	C₄²	C₂²×D₁₃	1	1	yes	characteristic
580	C₄²	C₂²×D₁₃	1	2	yes	—
581	C₁₃	#3505	1	1	yes	characteristic, complemented, Sylow
582	C₂³	—	13	1	no	—
583	C₂³	—	13	1	no	—
584	C₂³	—	13	4	no	—
585	C₂³	—	13	1	no	—
586	C₂³	—	13	2	no	—
587	C₂³	—	26	2	no	—
588	C₂³	—	26	4	no	—
589	C₂³	—	52	1	no	—
590	C₂³	—	52	1	no	—
591	C₂³	—	52	1	no	—
592	C₂³	—	52	1	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	C₂³	C₂³×D₁₃	1	1	yes	characteristic
598	Q₈	—	26	2	no	—
599	Q₈	—	26	2	no	—
600	Q₈	—	52	2	no	—
601	D₄	—	2	2	no	—
602	D₄	—	2	4	no	—
603	D₄	—	2	2	no	—
604	D₄	—	4	2	no	—
605	D₄	—	26	2	no	—
606	D₄	—	26	4	no	—
607	D₄	—	26	2	no	—
608	D₄	—	26	4	no	—
609	D₄	—	26	2	no	—
610	D₄	—	26	4	no	—
611	D₄	—	26	2	no	—
612	D₄	—	52	2	no	—
613	D₄	—	52	2	no	—
614	D₄	—	52	2	no	—
615	D₄	—	52	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	4	2	no	—
619	C₂×C₄	—	4	2	no	—
620	C₂×C₄	—	13	1	no	—
621	C₂×C₄	—	13	1	no	—
622	C₂×C₄	—	13	2	no	—
623	C₂×C₄	—	13	1	no	—
624	C₂×C₄	—	13	1	no	—
625	C₂×C₄	—	13	2	no	—
626	C₂×C₄	—	13	2	no	—
627	C₂×C₄	—	13	1	no	—
628	C₂×C₄	—	26	4	no	—
629	C₂×C₄	—	26	2	no	—
630	C₂×C₄	—	26	2	no	—
631	C₂×C₄	—	26	2	no	—
632	C₂×C₄	—	26	2	no	—
633	C₂×C₄	—	52	1	no	—
634	C₂×C₄	—	52	2	no	—
635	C₂×C₄	—	52	1	no	—
636	C₂×C₄	—	52	1	no	—
637	C₂×C₄	—	52	1	no	—
638	C₂×C₄	—	52	1	no	—
639	C₂×C₄	—	52	2	no	—
640	C₂×C₄	—	52	1	no	—
641	C₂×C₄	—	52	1	no	—
642	C₂×C₄	—	52	2	no	—
643	C₂×C₄	—	52	2	no	—
644	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
645	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
646	C₂×C₄	C₂³×D₁₃	1	2	yes	—
647	C₂×C₄	C₂³×D₁₃	1	2	yes	—
648	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
649	C₂×C₄	C₂³×D₁₃	1	2	yes	—
650	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
652	C₂²	—	2	1	no	—
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	13	2	no	—
661	C₂²	—	13	2	no	—
662	C₂²	—	26	1	no	—
663	C₂²	—	26	1	no	—
664	C₂²	—	26	1	no	—
665	C₂²	—	26	1	no	—
666	C₂²	—	26	1	no	—
667	C₂²	—	26	2	no	—
668	C₂²	—	26	1	no	—
669	C₂²	—	26	2	no	—
670	C₂²	—	26	2	no	—
671	C₂²	—	26	1	no	—
672	C₂²	—	52	4	no	—
673	C₂²	—	52	4	no	—
674	C₂²	—	104	4	no	—
675	C₂²	#41×D₁₃	1	2	yes	—
676	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
677	C₄	—	2	2	no	—
678	C₄	—	2	1	no	—
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	26	1	no	—
685	C₄	—	26	2	no	—
686	C₄	—	26	1	no	—
687	C₄	—	26	1	no	—
688	C₄	—	26	1	no	—
689	C₄	—	26	2	no	—
690	C₄	—	26	2	no	—
691	C₄	—	26	1	no	—
692	C₄	#88256	1	2	yes	—
693	C₂	—	2	2	no	—
694	C₂	—	4	1	no	—
695	C₂	—	4	2	no	—
696	C₂	—	26	2	no	—
697	C₂	—	26	2	no	—
698	C₂	—	52	1	no	—
699	C₂	—	52	2	no	—
700	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
701	C₂	C₂×#88256	1	1	yes	characteristic
702	C₂	#11719650	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	#3505
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. #11719412	C₂	semidirect
3. #11719410	C₂	semidirect
4. #11719399	C₂	semidirect
5. #11719396	C₂	semidirect
6. #11719363	C₂	semidirect
7. #11719362	C₂	semidirect
8. #11719323	C₂	semidirect
9. #11719317	C₂	semidirect
10. #11719311	C₂	semidirect
11. #11719310	C₂	semidirect
12. D₁₃×#121	C₂	semidirect
13. #11719303	C₂	semidirect
14. #11719270	C₂	semidirect
15. #11719262	C₂	semidirect
16. #11719259	C₂	semidirect
17. #11719257	C₂	semidirect
18. #11719250	C₂	semidirect
19. C₄×D₄×D₁₃	C₂	semidirect
20. #11719234	C₂	semidirect
21. #11719229	C₂	semidirect
22. #11719219	C₂	semidirect
23. C₂×#88151	C₂	semidirect
24. C₂×#6129	C₂²	semidirect
27. C₂×D₄×D₁₃	C₂²	semidirect
28. C₂×#6127	C₂²	semidirect
30. C₂²×C₄×D₁₃	C₂²	semidirect
31. C₂²×Dic₂₆	C₂²	semidirect
32. C₁₃×#126	C₂²	semidirect
33. C₁₃×#125	C₂²	semidirect
34. C₁₃×#123	C₂²	semidirect
35. C₁₃×#121	C₂²	semidirect
36. C₁₃×#121	C₂²	semidirect
37. C₁₃×#121	C₂²	semidirect
38. C₄×D₄×C₁₃	C₂²	semidirect
39. C₄×D₄×C₁₃	C₂²	semidirect
40. C₄×D₄×C₁₃	C₂²	semidirect
41. C₁₃×#117	C₂²	semidirect
42. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
43. #88193	C₂²	semidirect
44. #88193	C₂²	semidirect
45. #88193	C₂²	semidirect
47. #88192	C₂²	semidirect
49. #88191	C₂²	semidirect
50. #88190	C₂²	semidirect
51. D₄×Dic₁₃	C₂²	semidirect
52. D₄×Dic₁₃	C₂²	semidirect
53. D₄×Dic₁₃	C₂²	semidirect
54. #88184	C₂²	semidirect
55. #88184	C₂²	semidirect
56. #88184	C₂²	semidirect
58. C₄×C₂²⋊D₁₃	C₂²	semidirect
59. C₄×C₂²⋊D₁₃	C₂²	semidirect
60. C₄×C₂²⋊D₁₃	C₂²	semidirect
62. C₂×#6103	C₂²	semidirect
63. #88180	C₂²	semidirect
64. C₂×C₄⋊Dic₁₃	C₂²	semidirect
65. #88178	C₂²	semidirect
66. #88152	C₂²	semidirect
67. #88152	C₂²	semidirect
68. #88152	C₂²	semidirect
69. #88151	C₂²	semidirect
70. #88151	C₂²	semidirect
71. #88151	C₂²	semidirect
72. #88151	C₂²	semidirect
73. #88151	C₂²	semidirect
74. #88151	C₂²	semidirect
75. #88151	C₂²	semidirect
76. #88150	C₂²	semidirect
78. #88149	C₂²	semidirect
80. #88148	C₂²	semidirect
81. #88148	C₂²	semidirect
83. #88147	C₂²	semidirect
84. #88147	C₂²	semidirect
85. #88146	C₂²	semidirect
86. #88146	C₂²	semidirect
87. #88146	C₂²	semidirect
88. C₄⋊C₄×D₁₃	C₂²	semidirect
89. C₄⋊C₄×D₁₃	C₂²	semidirect
90. #88144	C₂²	semidirect
91. #88144	C₂²	semidirect
92. #88141	C₂²	semidirect
93. #88140	C₂²	semidirect
94. #88140	C₂²	semidirect
95. #88139	C₂²	semidirect
96. #88139	C₂²	semidirect
99. #88137	C₂²	semidirect
100. #88137	C₂²	semidirect
101. #88137	C₂²	semidirect
103. #88136	C₂²	semidirect
105. #88135	C₂²	semidirect
106. #88135	C₂²	semidirect
107. #88135	C₂²	semidirect
109. C₂²⋊C₄×D₁₃	C₂²	semidirect
110. C₂²⋊C₄×D₁₃	C₂²	semidirect
111. C₂²⋊C₄×D₁₃	C₂²	semidirect
112. #88133	C₂²	semidirect
113. #88133	C₂²	semidirect
114. #88132	C₂²	semidirect
115. #88129	C₂²	semidirect
117. C₄×D₅₂	C₂²	semidirect
118. C₄×D₅₂	C₂²	semidirect
119. #88126	C₂²	semidirect
120. C₄²×D₁₃	C₂²	semidirect
121. #88124	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
242. C₂²×D₁₃	#41	semidirect
304. #553	D₁₃	semidirect
378. #126	C₂×D₁₃	semidirect
382. #125	C₂×D₁₃	semidirect
396. #123	C₂×D₁₃	semidirect
418. #121	C₂×D₁₃	semidirect
419. #121	C₂×D₁₃	semidirect
420. #121	C₂×D₁₃	semidirect
444. C₄×D₄	C₂×D₁₃	semidirect
445. C₄×D₄	C₂×D₁₃	semidirect
446. C₄×D₄	C₂×D₁₃	semidirect
452. #117	C₂×D₁₃	semidirect
456. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
581. C₁₃	#3505	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
#11719412	2
#11719410	2
#11719399	2
#11719396	2
#11719363	2
#11719362	2
#11719323	2
#11719317	2
#11719311	2
#11719310	2
D₁₃×#121	2
#11719303	2
#11719270	2
#11719262	2
#11719259	2
#11719257	2
#11719250	2
C₄×D₄×D₁₃	2
#11719234	2
#11719229	2
#11719219	2
C₂×#88151	2
#3505	13