Subgroups — #13128676

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×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719414	C₂	1	2	yes	maximal, complemented
3	#11719409	C₂	1	2	yes	maximal, complemented
4	#11719400	C₂	1	2	yes	maximal, complemented
5	#11719400	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719397	C₂	1	2	yes	maximal, complemented
7	#11719396	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719363	C₂	1	2	yes	maximal, complemented
9	#11719358	C₂	1	2	yes	maximal, complemented
10	#11719338	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719335	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719332	C₂	1	1	yes	maximal, characteristic, complemented
13	D₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719285	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719281	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719255	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719235	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719232	C₂	1	2	yes	maximal, complemented
20	#11719229	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719226	C₂	1	2	yes	maximal, complemented
22	#11719218	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#88149	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#6131	C₂²	1	1	yes	characteristic, complemented
25	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
27	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
28	C₂²×D₅₂	C₂²	1	2	yes	—
29	C₂²×D₅₂	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₁₃	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×#125	C₂²	1	2	yes	complemented
35	C₁₃×#123	C₂²	1	2	yes	—
36	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
40	C₁₃×#117	C₂²	1	2	yes	complemented
41	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
43	#88201	C₂²	1	1	yes	characteristic, complemented
44	#88200	C₂²	1	1	yes	characteristic, complemented
45	#88191	C₂²	1	2	yes	—
46	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
47	#88184	C₂²	1	1	yes	characteristic, complemented
48	#88183	C₂²	1	2	yes	—
49	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
50	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
51	C₂×#6103	C₂²	1	2	yes	complemented
52	#88180	C₂²	1	2	yes	complemented
53	#88178	C₂²	1	1	yes	characteristic, complemented
54	#88152	C₂²	1	2	yes	complemented
55	#88152	C₂²	1	2	yes	complemented
56	#88152	C₂²	1	2	yes	complemented
57	#88152	C₂²	1	2	yes	complemented
58	#88151	C₂²	1	1	yes	characteristic, complemented
59	#88151	C₂²	1	1	yes	characteristic, complemented
60	#88151	C₂²	1	2	yes	complemented
61	#88150	C₂²	1	2	yes	complemented
62	#88150	C₂²	1	2	yes	complemented
63	#88149	C₂²	1	1	yes	characteristic
64	#88149	C₂²	1	1	yes	characteristic
65	#88149	C₂²	1	2	yes	—
66	#88149	C₂²	1	1	yes	characteristic, complemented
67	#88149	C₂²	1	1	yes	characteristic, complemented
68	#88149	C₂²	1	2	yes	complemented
69	#88149	C₂²	1	1	yes	characteristic, complemented
70	#88149	C₂²	1	2	yes	complemented
71	#88149	C₂²	1	2	yes	complemented
72	#88149	C₂²	1	2	yes	complemented
73	#88148	C₂²	1	2	yes	complemented
74	#88148	C₂²	1	2	yes	complemented
75	#88148	C₂²	1	2	yes	complemented
76	#88148	C₂²	1	2	yes	complemented
77	#88148	C₂²	1	2	yes	complemented
78	#88148	C₂²	1	2	yes	complemented
79	#88147	C₂²	1	2	yes	complemented
80	#88147	C₂²	1	2	yes	complemented
81	#88147	C₂²	1	2	yes	complemented
82	#88147	C₂²	1	2	yes	complemented
83	#88147	C₂²	1	1	yes	characteristic, complemented
84	#88147	C₂²	1	1	yes	characteristic, complemented
85	#88146	C₂²	1	1	yes	characteristic, complemented
86	#88146	C₂²	1	2	yes	complemented
87	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
88	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
89	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
90	#88144	C₂²	1	1	yes	characteristic, complemented
91	#88143	C₂²	1	2	yes	complemented
92	#88141	C₂²	1	1	yes	characteristic, complemented
93	#88140	C₂²	1	2	yes	complemented
94	#88139	C₂²	1	2	yes	complemented
95	#88138	C₂²	1	2	yes	complemented
96	#88138	C₂²	1	2	yes	complemented
97	#88138	C₂²	1	2	yes	complemented
98	#88137	C₂²	1	2	yes	complemented
99	#88136	C₂²	1	2	yes	—
100	#88136	C₂²	1	2	yes	complemented
101	#88136	C₂²	1	2	yes	complemented
102	#88135	C₂²	1	1	yes	characteristic
103	#88135	C₂²	1	1	yes	characteristic, complemented
104	#88135	C₂²	1	2	yes	complemented
105	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
106	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
108	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
110	#88132	C₂²	1	2	yes	complemented
111	#88130	C₂²	1	2	yes	complemented
112	#88129	C₂²	1	2	yes	complemented
113	#88129	C₂²	1	1	yes	characteristic, complemented
114	C₄×D₅₂	C₂²	1	2	yes	complemented
115	C₄×D₅₂	C₂²	1	2	yes	complemented
116	C₄×D₅₂	C₂²	1	2	yes	complemented
117	C₄×D₅₂	C₂²	1	2	yes	complemented
118	C₄×D₅₂	C₂²	1	2	yes	complemented
119	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
121	#88126	C₂²	1	2	yes	complemented
122	C₄²×D₁₃	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×Q₈×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
135	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
136	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
137	#6131	—	4	2	no	—
138	Q₈×D₁₃	—	4	2	no	—
139	D₄×D₁₃	—	2	4	no	—
140	#6127	—	4	2	no	—
141	C₂×D₅₂	—	2	8	no	—
142	C₂×D₅₂	—	4	2	no	—
143	C₂×D₅₂	C₂³	1	2	yes	—
144	C₂×D₅₂	C₂³	1	2	yes	—
145	C₂×D₅₂	C₂³	1	1	yes	characteristic
146	C₂×D₅₂	C₂³	1	1	yes	characteristic
147	C₂×D₅₂	C₂³	1	1	yes	characteristic
148	C₂×D₅₂	C₂³	1	2	yes	—
149	C₂×D₅₂	C₂³	1	2	yes	—
150	C₂×D₅₂	C₂³	1	2	yes	—
151	C₂×D₅₂	C₂³	1	2	yes	—
152	C₂×D₅₂	C₂³	1	2	yes	—
153	C₂×C₄×D₁₃	—	4	2	no	—
154	C₂×C₄×D₁₃	—	4	2	no	—
155	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
161	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₁₃	C₂³	1	2	yes	—
163	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₁₃	C₂³	1	2	yes	—
165	C₂×C₄×D₁₃	C₂³	1	2	yes	—
166	C₂×C₄×D₁₃	C₂³	1	2	yes	—
167	C₂×C₄×D₁₃	C₂³	1	2	yes	—
168	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
169	C₂×C₄×D₁₃	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×C₄⋊C₄	C₂³	1	2	yes	—
180	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
182	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
184	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
185	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₄²×C₁₃	C₂³	1	1	yes	characteristic
188	C₄²×C₁₃	C₂³	1	2	yes	—
189	C₄²×C₁₃	C₂³	1	2	yes	—
190	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
191	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
192	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
193	#6103	C₂³	1	2	yes	—
194	#6103	C₂³	1	2	yes	—
195	#6103	C₂³	1	1	yes	characteristic
196	#6103	C₂³	1	1	yes	characteristic
197	#6103	C₂³	1	1	yes	characteristic
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	2	yes	—
205	#6103	C₂³	1	2	yes	—
206	#6103	C₂³	1	2	yes	—
207	#6103	C₂³	1	2	yes	—
208	#6103	C₂³	1	2	yes	—
209	#6103	C₂³	1	1	yes	characteristic
210	#6103	C₂³	1	2	yes	—
211	#6103	C₂³	1	2	yes	—
212	#6103	C₂³	1	2	yes	—
213	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	1	yes	characteristic
217	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
218	#6101	C₂³	1	2	yes	—
219	#6101	C₂³	1	2	yes	—
220	#6101	C₂³	1	1	yes	characteristic
221	#6101	C₂³	1	2	yes	—
222	#6101	C₂³	1	1	yes	characteristic
223	#6101	C₂³	1	2	yes	—
224	#6101	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	1	yes	characteristic
233	C₂²×D₁₃	—	2	4	no	—
234	C₂²×D₁₃	—	2	2	no	—
235	C₂²×D₁₃	—	4	1	no	—
236	C₂²×D₁₃	—	4	1	no	—
237	C₂²×D₁₃	—	4	1	no	—
238	C₂²×D₁₃	—	4	1	no	—
239	C₂²×D₁₃	—	4	2	no	—
240	C₂²×D₁₃	—	4	2	no	—
241	C₂²×D₁₃	#41	1	4	yes	complemented
242	C₂²×D₁₃	C₂⁴	1	2	yes	—
243	C₂²×D₁₃	C₂⁴	1	2	yes	—
244	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
245	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
246	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
247	Q₈×C₁₃	—	2	2	no	—
248	D₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	4	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
257	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
258	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
260	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₂²⋊D₁₃	—	2	2	no	—
262	C₂²⋊D₁₃	—	2	2	no	—
263	C₂²⋊D₁₃	—	4	2	no	—
264	C₂²⋊D₁₃	—	4	2	no	—
265	C₂×Dic₁₃	—	4	1	no	—
266	C₂×Dic₁₃	—	4	1	no	—
267	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₁₃	C₂⁴	1	2	yes	—
272	C₂×Dic₁₃	C₂⁴	1	2	yes	—
273	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
274	D₅₂	—	2	4	no	—
275	D₅₂	—	2	4	no	—
276	D₅₂	—	2	4	no	—
277	D₅₂	—	2	4	no	—
278	D₅₂	—	2	2	no	—
279	D₅₂	—	2	2	no	—
280	D₅₂	—	2	2	no	—
281	D₅₂	—	4	2	no	—
282	D₅₂	—	4	2	no	—
283	D₅₂	—	4	2	no	—
284	C₄×D₁₃	—	2	2	no	—
285	C₄×D₁₃	—	2	2	no	—
286	C₄×D₁₃	—	2	2	no	—
287	C₄×D₁₃	—	2	2	no	—
288	C₄×D₁₃	—	4	1	no	—
289	C₄×D₁₃	—	4	1	no	—
290	C₄×D₁₃	—	4	1	no	—
291	C₄×D₁₃	—	4	1	no	—
292	C₄×D₁₃	—	4	1	no	—
293	C₄×D₁₃	—	4	2	no	—
294	C₄×D₁₃	—	4	2	no	—
295	C₄×D₁₃	—	4	2	no	—
296	C₄×D₁₃	—	4	2	no	—
297	C₄×D₁₃	—	4	2	no	—
298	C₄×D₁₃	—	4	2	no	—
299	Dic₂₆	—	2	2	no	—
300	Dic₂₆	—	4	2	no	—
301	#553	—	13	2	no	—
302	#553	—	13	1	no	—
303	#553	—	13	2	no	—
304	#553	—	13	1	no	—
305	#552	—	13	1	no	—
306	#552	D₁₃	1	1	yes	characteristic, complemented
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	1	no	—
328	C₂²×C₁₃	—	2	1	no	—
329	C₂²×C₁₃	C₂×#41	1	2	yes	—
330	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
331	C₂×D₁₃	—	2	1	no	—
332	C₂×D₁₃	—	2	1	no	—
333	C₂×D₁₃	—	2	1	no	—
334	C₂×D₁₃	—	2	1	no	—
335	C₂×D₁₃	—	2	2	no	—
336	C₂×D₁₃	—	2	2	no	—
337	C₂×D₁₃	—	2	1	no	—
338	C₂×D₁₃	—	2	1	no	—
339	C₂×D₁₃	—	2	2	no	—
340	C₂×D₁₃	—	2	2	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	1	no	—
350	C₄×C₁₃	—	2	2	no	—
351	C₄×C₁₃	—	2	2	no	—
352	C₄×C₁₃	—	2	2	no	—
353	C₄×C₁₃	—	2	1	no	—
354	C₄×C₁₃	—	2	1	no	—
355	C₄×C₁₃	—	2	1	no	—
356	C₄×C₁₃	—	2	2	no	—
357	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
358	Dic₁₃	—	2	1	no	—
359	Dic₁₃	—	2	2	no	—
360	Dic₁₃	—	2	1	no	—
361	Dic₁₃	—	2	1	no	—
362	Dic₁₃	—	2	1	no	—
363	Dic₁₃	—	2	1	no	—
364	Dic₁₃	—	2	2	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	C₂×D₁₃	1	1	yes	characteristic, complemented
382	#125	C₂×D₁₃	1	2	yes	complemented
383	#124	—	13	1	no	—
384	#124	—	13	2	no	—
385	#124	—	13	1	no	—
386	#124	—	13	2	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	—
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	2	no	—
403	C₂²⋊Q₈	—	13	2	no	—
404	C₂²⋊Q₈	—	13	2	no	—
405	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
406	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
407	#121	—	13	1	no	—
408	#121	—	13	1	no	—
409	#121	—	13	1	no	—
410	#121	—	13	2	no	—
411	#121	—	13	1	no	—
412	#121	—	13	1	no	—
413	#121	—	13	2	no	—
414	#121	—	13	1	no	—
415	#121	—	13	2	no	—
416	#121	—	13	2	no	—
417	#121	—	13	2	no	—
418	#121	—	13	2	no	—
419	#121	—	13	2	no	—
420	#121	—	13	2	no	—
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	C₂×D₁₃	1	1	yes	characteristic, complemented
427	C₄×D₄	—	13	1	no	—
428	C₄×D₄	—	13	1	no	—
429	C₄×D₄	—	13	1	no	—
430	C₄×D₄	—	13	1	no	—
431	C₄×D₄	—	13	2	no	—
432	C₄×D₄	—	13	2	no	—
433	C₄×D₄	—	13	2	no	—
434	C₄×D₄	—	13	2	no	—
435	C₄×D₄	—	13	1	no	—
436	C₄×D₄	—	13	1	no	—
437	C₄×D₄	—	13	1	no	—
438	C₄×D₄	—	13	2	no	—
439	C₄×D₄	—	13	1	no	—
440	C₄×D₄	—	13	2	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	#117	—	13	2	no	—
448	#117	—	13	1	no	—
449	#117	—	13	2	no	—
450	#117	—	13	2	no	—
451	#117	C₂×D₁₃	1	2	yes	complemented
452	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
453	C₂×C₄⋊C₄	—	13	1	no	—
454	C₂×C₄⋊C₄	—	13	1	no	—
455	C₂×C₄⋊C₄	—	13	2	no	—
456	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
457	C₂×C₂²⋊C₄	—	13	2	no	—
458	C₂×C₂²⋊C₄	—	13	1	no	—
459	C₂×C₂²⋊C₄	—	13	1	no	—
460	C₂×C₂²⋊C₄	—	13	2	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	C₂²×#41	1	1	yes	characteristic
467	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
468	C₂×C₁₃	#585	1	1	yes	characteristic
469	D₁₃	—	2	2	no	—
470	D₁₃	—	2	2	no	—
471	D₁₃	—	4	1	no	—
472	D₁₃	—	4	2	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	2	no	—
481	C₂×Q₈	—	52	2	no	—
482	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
483	C₂×D₄	—	13	1	no	—
484	C₂×D₄	—	13	1	no	—
485	C₂×D₄	—	13	2	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	1	no	—
494	C₂×D₄	—	13	2	no	—
495	C₂×D₄	—	13	2	no	—
496	C₂×D₄	—	13	2	no	—
497	C₂×D₄	—	26	8	no	—
498	C₂×D₄	—	26	4	no	—
499	C₂×D₄	—	52	2	no	—
500	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
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	1	no	—
506	C₂²×C₄	—	13	1	no	—
507	C₂²×C₄	—	13	1	no	—
508	C₂²×C₄	—	13	2	no	—
509	C₂²×C₄	—	13	1	no	—
510	C₂²×C₄	—	13	2	no	—
511	C₂²×C₄	—	13	1	no	—
512	C₂²×C₄	—	13	2	no	—
513	C₂²×C₄	—	13	2	no	—
514	C₂²×C₄	—	13	2	no	—
515	C₂²×C₄	—	13	2	no	—
516	C₂²×C₄	—	13	1	no	—
517	C₂²×C₄	—	13	1	no	—
518	C₂²×C₄	—	52	2	no	—
519	C₂²×C₄	—	52	2	no	—
520	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
521	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
522	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
523	C₄⋊C₄	—	13	1	no	—
524	C₄⋊C₄	—	13	2	no	—
525	C₄⋊C₄	—	13	2	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	C₂²×D₁₃	1	1	yes	characteristic
536	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
537	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
538	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
539	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
540	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
541	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
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	1	no	—
546	C₂²⋊C₄	—	13	2	no	—
547	C₂²⋊C₄	—	13	1	no	—
548	C₂²⋊C₄	—	13	2	no	—
549	C₂²⋊C₄	—	13	2	no	—
550	C₂²⋊C₄	—	13	1	no	—
551	C₂²⋊C₄	—	13	1	no	—
552	C₂²⋊C₄	—	13	2	no	—
553	C₂²⋊C₄	—	13	2	no	—
554	C₂²⋊C₄	—	13	1	no	—
555	C₂²⋊C₄	—	13	2	no	—
556	C₂²⋊C₄	—	13	2	no	—
557	C₂²⋊C₄	—	13	2	no	—
558	C₂²⋊C₄	—	13	2	no	—
559	C₂²⋊C₄	—	13	1	no	—
560	C₂²⋊C₄	—	13	2	no	—
561	C₂²⋊C₄	—	13	2	no	—
562	C₂²⋊C₄	—	13	2	no	—
563	C₂²⋊C₄	—	13	2	no	—
564	C₂²⋊C₄	—	13	2	no	—
565	C₂²⋊C₄	—	13	2	no	—
566	C₂²⋊C₄	—	13	2	no	—
567	C₂²⋊C₄	—	13	2	no	—
568	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
569	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
570	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
571	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
572	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
573	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	C₂²×D₁₃	1	1	yes	characteristic
579	C₄²	C₂²×D₁₃	1	2	yes	—
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	—	13	2	no	—
588	C₂³	—	26	2	no	—
589	C₂³	—	26	4	no	—
590	C₂³	—	52	1	no	—
591	C₂³	—	52	1	no	—
592	C₂³	—	52	1	no	—
593	C₂³	—	52	1	no	—
594	C₂³	—	52	2	no	—
595	C₂³	—	52	2	no	—
596	C₂³	C₂³×D₁₃	1	1	yes	characteristic
597	C₂³	C₂³×D₁₃	1	1	yes	characteristic
598	Q₈	—	2	2	no	—
599	Q₈	—	26	2	no	—
600	Q₈	—	52	2	no	—
601	D₄	—	2	2	no	—
602	D₄	—	26	4	no	—
603	D₄	—	26	4	no	—
604	D₄	—	26	4	no	—
605	D₄	—	26	4	no	—
606	D₄	—	26	2	no	—
607	D₄	—	26	2	no	—
608	D₄	—	26	2	no	—
609	D₄	—	26	2	no	—
610	D₄	—	26	2	no	—
611	D₄	—	52	2	no	—
612	D₄	—	52	2	no	—
613	D₄	—	52	2	no	—
614	D₄	—	52	2	no	—
615	D₄	—	52	2	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	13	1	no	—
620	C₂×C₄	—	13	1	no	—
621	C₂×C₄	—	13	1	no	—
622	C₂×C₄	—	13	1	no	—
623	C₂×C₄	—	13	2	no	—
624	C₂×C₄	—	13	2	no	—
625	C₂×C₄	—	13	1	no	—
626	C₂×C₄	—	26	2	no	—
627	C₂×C₄	—	26	2	no	—
628	C₂×C₄	—	26	2	no	—
629	C₂×C₄	—	26	2	no	—
630	C₂×C₄	—	52	1	no	—
631	C₂×C₄	—	52	2	no	—
632	C₂×C₄	—	52	2	no	—
633	C₂×C₄	—	52	2	no	—
634	C₂×C₄	—	52	1	no	—
635	C₂×C₄	—	52	1	no	—
636	C₂×C₄	—	52	1	no	—
637	C₂×C₄	—	52	1	no	—
638	C₂×C₄	—	52	2	no	—
639	C₂×C₄	—	52	2	no	—
640	C₂×C₄	—	52	2	no	—
641	C₂×C₄	—	52	1	no	—
642	C₂×C₄	—	52	1	no	—
643	C₂×C₄	C₂³×D₁₃	1	2	yes	—
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	1	yes	characteristic
648	C₂×C₄	C₂³×D₁₃	1	2	yes	—
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	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	13	2	no	—
658	C₂²	—	13	2	no	—
659	C₂²	—	26	1	no	—
660	C₂²	—	26	1	no	—
661	C₂²	—	26	1	no	—
662	C₂²	—	26	1	no	—
663	C₂²	—	26	1	no	—
664	C₂²	—	26	2	no	—
665	C₂²	—	26	2	no	—
666	C₂²	—	26	1	no	—
667	C₂²	—	26	2	no	—
668	C₂²	—	26	2	no	—
669	C₂²	—	26	2	no	—
670	C₂²	—	26	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	2	no	—
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	2	no	—
685	C₄	—	26	1	no	—
686	C₄	—	26	1	no	—
687	C₄	—	26	1	no	—
688	C₄	—	26	1	no	—
689	C₄	—	26	2	no	—
690	C₄	—	26	1	no	—
691	C₄	—	26	2	no	—
692	C₄	#88256	1	2	yes	—
693	C₂	—	2	2	no	—
694	C₂	—	4	1	no	—
695	C₂	—	26	2	no	—
696	C₂	—	26	2	no	—
697	C₂	—	52	1	no	—
698	C₂	—	52	2	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	#11719652	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#552	C₂
hypercenter	#552	D₁₃
hypocenter	C₁₃	#3505
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. C₁₃×#552	C₂	semidirect
2. #11719414	C₂	semidirect
3. #11719409	C₂	semidirect
4. #11719400	C₂	semidirect
5. #11719400	C₂	semidirect
6. #11719397	C₂	semidirect
7. #11719396	C₂	semidirect
8. #11719363	C₂	semidirect
9. #11719358	C₂	semidirect
10. #11719338	C₂	semidirect
11. #11719335	C₂	semidirect
12. #11719332	C₂	semidirect
13. D₁₃×C₂²⋊Q₈	C₂	semidirect
14. #11719285	C₂	semidirect
15. #11719281	C₂	semidirect
16. #11719255	C₂	semidirect
17. C₄×D₄×D₁₃	C₂	semidirect
18. #11719235	C₂	semidirect
19. #11719232	C₂	semidirect
20. #11719229	C₂	semidirect
21. #11719226	C₂	semidirect
22. #11719218	C₂	semidirect
23. C₂×#88149	C₂	semidirect
24. C₂×#6131	C₂²	semidirect
25. C₂×Q₈×D₁₃	C₂²	semidirect
27. C₂×#6127	C₂²	semidirect
29. C₂²×D₅₂	C₂²	semidirect
31. C₂²×C₄×D₁₃	C₂²	semidirect
32. C₁₃×#126	C₂²	semidirect
33. C₁₃×#125	C₂²	semidirect
34. C₁₃×#125	C₂²	semidirect
36. C₁₃×C₂²⋊Q₈	C₂²	semidirect
37. C₁₃×C₂²⋊Q₈	C₂²	semidirect
38. C₄×Q₈×C₁₃	C₂²	semidirect
40. C₁₃×#117	C₂²	semidirect
41. C₁₃×#117	C₂²	semidirect
42. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
43. #88201	C₂²	semidirect
44. #88200	C₂²	semidirect
47. #88184	C₂²	semidirect
50. C₄×C₂²⋊D₁₃	C₂²	semidirect
51. C₂×#6103	C₂²	semidirect
52. #88180	C₂²	semidirect
53. #88178	C₂²	semidirect
54. #88152	C₂²	semidirect
55. #88152	C₂²	semidirect
56. #88152	C₂²	semidirect
57. #88152	C₂²	semidirect
58. #88151	C₂²	semidirect
59. #88151	C₂²	semidirect
60. #88151	C₂²	semidirect
61. #88150	C₂²	semidirect
62. #88150	C₂²	semidirect
66. #88149	C₂²	semidirect
67. #88149	C₂²	semidirect
68. #88149	C₂²	semidirect
69. #88149	C₂²	semidirect
70. #88149	C₂²	semidirect
71. #88149	C₂²	semidirect
72. #88149	C₂²	semidirect
73. #88148	C₂²	semidirect
74. #88148	C₂²	semidirect
75. #88148	C₂²	semidirect
76. #88148	C₂²	semidirect
77. #88148	C₂²	semidirect
78. #88148	C₂²	semidirect
79. #88147	C₂²	semidirect
80. #88147	C₂²	semidirect
81. #88147	C₂²	semidirect
82. #88147	C₂²	semidirect
83. #88147	C₂²	semidirect
84. #88147	C₂²	semidirect
85. #88146	C₂²	semidirect
86. #88146	C₂²	semidirect
87. C₄⋊C₄×D₁₃	C₂²	semidirect
88. C₄⋊C₄×D₁₃	C₂²	semidirect
89. C₄⋊C₄×D₁₃	C₂²	semidirect
90. #88144	C₂²	semidirect
91. #88143	C₂²	semidirect
92. #88141	C₂²	semidirect
93. #88140	C₂²	semidirect
94. #88139	C₂²	semidirect
95. #88138	C₂²	semidirect
96. #88138	C₂²	semidirect
97. #88138	C₂²	semidirect
98. #88137	C₂²	semidirect
100. #88136	C₂²	semidirect
101. #88136	C₂²	semidirect
103. #88135	C₂²	semidirect
104. #88135	C₂²	semidirect
107. C₂²⋊C₄×D₁₃	C₂²	semidirect
108. C₂²⋊C₄×D₁₃	C₂²	semidirect
109. C₂²⋊C₄×D₁₃	C₂²	semidirect
110. #88132	C₂²	semidirect
111. #88130	C₂²	semidirect
112. #88129	C₂²	semidirect
113. #88129	C₂²	semidirect
114. C₄×D₅₂	C₂²	semidirect
115. C₄×D₅₂	C₂²	semidirect
116. C₄×D₅₂	C₂²	semidirect
117. C₄×D₅₂	C₂²	semidirect
118. C₄×D₅₂	C₂²	semidirect
119. C₄×D₅₂	C₂²	semidirect
120. C₄×D₅₂	C₂²	semidirect
121. #88126	C₂²	semidirect
122. C₄²×D₁₃	C₂²	semidirect
241. C₂²×D₁₃	#41	semidirect
306. #552	D₁₃	semidirect
378. #126	C₂×D₁₃	semidirect
381. #125	C₂×D₁₃	semidirect
382. #125	C₂×D₁₃	semidirect
405. C₂²⋊Q₈	C₂×D₁₃	semidirect
406. C₂²⋊Q₈	C₂×D₁₃	semidirect
426. C₄×Q₈	C₂×D₁₃	semidirect
451. #117	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×#552	2
#11719414	2
#11719409	2
#11719400	2
#11719397	2
#11719396	2
#11719363	2
#11719358	2
#11719338	2
#11719335	2
#11719332	2
D₁₃×C₂²⋊Q₈	2
#11719285	2
#11719281	2
#11719255	2
C₄×D₄×D₁₃	2
#11719235	2
#11719232	2
#11719229	2
#11719226	2
#11719218	2
C₂×#88149	2
#3505	13