Subgroups — #13128679

Order 1664.

1140 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719539	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719529	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719496	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719369	C₂	1	2	yes	maximal, complemented
7	#11719366	C₂	1	2	yes	maximal, complemented
8	#11719346	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719336	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719332	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719327	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719321	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719311	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719304	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719301	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719298	C₂	1	2	yes	maximal, complemented
17	#11719297	C₂	1	2	yes	maximal, complemented
18	#11719265	C₂	1	2	yes	maximal, complemented
19	#11719264	C₂	1	2	yes	maximal, complemented
20	#11719251	C₂	1	2	yes	maximal, complemented
21	#11719245	C₂	1	2	yes	maximal, complemented
22	#11719238	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719237	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
25	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
27	C₂×#6131	C₂²	1	1	yes	characteristic, complemented
28	C₂×#6129	C₂²	1	2	yes	—
29	C₂×#6129	C₂²	1	1	yes	characteristic, complemented
30	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#123	C₂²	1	2	yes	complemented
33	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#121	C₂²	1	1	yes	characteristic
36	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#120	C₂²	1	2	yes	—
38	C₄×D₄×C₁₃	C₂²	1	2	yes	—
39	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
40	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
41	#88207	C₂²	1	2	yes	—
42	C₂×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
43	#88200	C₂²	1	1	yes	characteristic, complemented
44	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
45	#88198	C₂²	1	1	yes	characteristic, complemented
46	#88194	C₂²	1	2	yes	—
47	#88194	C₂²	1	2	yes	—
48	#88194	C₂²	1	1	yes	characteristic, complemented
49	#88193	C₂²	1	2	yes	—
50	#88193	C₂²	1	2	yes	—
51	#88193	C₂²	1	2	yes	—
52	#88193	C₂²	1	2	yes	complemented
53	#88192	C₂²	1	2	yes	complemented
54	#88192	C₂²	1	1	yes	characteristic, complemented
55	#88191	C₂²	1	2	yes	—
56	#88190	C₂²	1	2	yes	complemented
57	#88189	C₂²	1	2	yes	complemented
58	D₄×Dic₁₃	C₂²	1	2	yes	—
59	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
60	#88184	C₂²	1	1	yes	characteristic
61	#88184	C₂²	1	1	yes	characteristic, complemented
62	#88184	C₂²	1	2	yes	complemented
63	#88183	C₂²	1	2	yes	complemented
64	#88183	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
68	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
70	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
71	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
72	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
73	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
74	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
75	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
76	C₂×#6103	C₂²	1	1	yes	characteristic
77	#88180	C₂²	1	1	yes	characteristic, complemented
78	#88178	C₂²	1	1	yes	characteristic
79	#88178	C₂²	1	1	yes	characteristic, complemented
80	C₂×#6101	C₂²	1	1	yes	characteristic
81	C₂×#6101	C₂²	1	2	yes	complemented
82	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
83	#88152	C₂²	1	2	yes	complemented
84	#88151	C₂²	1	1	yes	characteristic, complemented
85	#88149	C₂²	1	1	yes	characteristic, complemented
86	#88148	C₂²	1	2	yes	complemented
87	#88148	C₂²	1	2	yes	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	#88146	C₂²	1	1	yes	characteristic, complemented
92	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
93	#88143	C₂²	1	2	yes	complemented
94	#88142	C₂²	1	1	yes	characteristic, complemented
95	#88142	C₂²	1	1	yes	characteristic, complemented
96	#88141	C₂²	1	1	yes	characteristic, complemented
97	#88141	C₂²	1	2	yes	complemented
98	#88141	C₂²	1	2	yes	complemented
99	#88139	C₂²	1	2	yes	—
100	#88139	C₂²	1	2	yes	—
101	#88139	C₂²	1	2	yes	complemented
102	#88139	C₂²	1	2	yes	complemented
103	#88139	C₂²	1	2	yes	complemented
104	#88138	C₂²	1	2	yes	—
105	#88138	C₂²	1	2	yes	—
106	#88138	C₂²	1	2	yes	complemented
107	#88137	C₂²	1	2	yes	complemented
108	#88137	C₂²	1	2	yes	complemented
109	#88136	C₂²	1	2	yes	—
110	#88135	C₂²	1	2	yes	—
111	#88135	C₂²	1	2	yes	complemented
112	#88135	C₂²	1	2	yes	complemented
113	#88135	C₂²	1	2	yes	complemented
114	#88133	C₂²	1	2	yes	complemented
115	#88133	C₂²	1	2	yes	complemented
116	#88132	C₂²	1	2	yes	—
117	#88131	C₂²	1	2	yes	—
118	#88131	C₂²	1	2	yes	complemented
119	#88130	C₂²	1	2	yes	complemented
120	#88129	C₂²	1	2	yes	complemented
121	#88126	C₂²	1	2	yes	complemented
122	C₄×Dic₂₆	C₂²	1	2	yes	complemented
123	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
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	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	2	yes	—
131	C₂²×C₄×C₁₃	—	4	2	no	—
132	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
133	C₂²×C₄×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	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₃	—	2	4	no	—
140	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
151	C₂²×Dic₁₃	C₂³	1	2	yes	—
152	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
153	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
154	C₂²×Dic₁₃	C₂³	1	2	yes	—
155	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
156	#6131	—	4	2	no	—
157	#6129	—	2	8	no	—
158	#6129	—	4	2	no	—
159	#6127	—	4	2	no	—
160	C₂×D₅₂	C₂³	1	1	yes	characteristic
161	C₂×D₅₂	C₂³	1	2	yes	—
162	C₂×D₅₂	C₂³	1	2	yes	—
163	C₂×C₄×D₁₃	—	4	2	no	—
164	C₂×C₄×D₁₃	C₂³	1	2	yes	—
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×C₄×D₁₃	C₂³	1	1	yes	characteristic
169	C₂×C₄×D₁₃	C₂³	1	2	yes	—
170	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
171	C₂×Dic₂₆	C₂³	1	2	yes	—
172	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
173	C₂×Dic₂₆	C₂³	1	2	yes	—
174	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
176	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
177	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₁₃×C₂²⋊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	2	yes	—
183	C₄²×C₁₃	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
187	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
189	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
190	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
191	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
192	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
193	#6103	C₂³	1	2	yes	—
194	#6103	C₂³	1	2	yes	—
195	#6103	C₂³	1	1	yes	characteristic
196	#6103	C₂³	1	2	yes	—
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	2	yes	—
202	#6103	C₂³	1	2	yes	—
203	#6103	C₂³	1	1	yes	characteristic
204	#6103	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₁₃	C₂³	1	2	yes	—
206	C₄⋊Dic₁₃	C₂³	1	2	yes	—
207	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
209	#6101	C₂³	1	1	yes	characteristic
210	#6101	C₂³	1	2	yes	—
211	#6101	C₂³	1	1	yes	characteristic
212	#6101	C₂³	1	2	yes	—
213	#6101	C₂³	1	2	yes	—
214	#6101	C₂³	1	2	yes	—
215	#6101	C₂³	1	2	yes	—
216	#6101	C₂³	1	1	yes	characteristic
217	#6101	C₂³	1	2	yes	—
218	#6101	C₂³	1	2	yes	—
219	#6101	C₂³	1	1	yes	characteristic
220	#6101	C₂³	1	2	yes	—
221	C₄×Dic₁₃	C₂³	1	2	yes	—
222	C₄×Dic₁₃	C₂³	1	2	yes	—
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	1	yes	characteristic
227	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
228	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
229	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
230	#3506	—	13	1	no	maximal, Sylow
231	C₂³×C₁₃	—	2	2	no	—
232	C₂³×C₁₃	—	4	1	no	—
233	C₂³×C₁₃	—	4	1	no	—
234	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
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	—	4	1	no	—
240	C₂²×D₁₃	—	4	1	no	—
241	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
242	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
243	C₂²×D₁₃	C₂⁴	1	2	yes	—
244	Q₈×C₁₃	—	2	2	no	—
245	D₄×C₁₃	—	2	4	no	—
246	D₄×C₁₃	—	2	2	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	—	2	2	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	2	no	—
256	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
257	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
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	4	no	—
264	C₂²⋊D₁₃	—	2	4	no	—
265	C₂²⋊D₁₃	—	2	2	no	—
266	C₂²⋊D₁₃	—	2	2	no	—
267	C₂²⋊D₁₃	—	2	2	no	—
268	C₂²⋊D₁₃	—	2	2	no	—
269	C₂²⋊D₁₃	—	4	2	no	—
270	C₂²⋊D₁₃	—	4	2	no	—
271	C₂²⋊D₁₃	—	4	2	no	—
272	C₂²⋊D₁₃	—	4	2	no	—
273	C₂²⋊D₁₃	—	4	2	no	—
274	C₂×Dic₁₃	—	2	4	no	—
275	C₂×Dic₁₃	—	4	1	no	—
276	C₂×Dic₁₃	—	4	2	no	—
277	C₂×Dic₁₃	—	4	1	no	—
278	C₂×Dic₁₃	#41	1	4	yes	complemented
279	C₂×Dic₁₃	C₂⁴	1	2	yes	—
280	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
282	C₂×Dic₁₃	C₂⁴	1	2	yes	—
283	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₁₃	C₂⁴	1	2	yes	—
286	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
287	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
288	D₅₂	—	2	2	no	—
289	D₅₂	—	4	2	no	—
290	D₅₂	—	4	2	no	—
291	C₄×D₁₃	—	2	2	no	—
292	C₄×D₁₃	—	2	2	no	—
293	C₄×D₁₃	—	2	4	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	4	no	—
300	Dic₂₆	—	4	2	no	—
301	#559	—	13	2	no	—
302	#559	—	13	2	no	—
303	#556	—	13	1	no	—
304	#556	—	13	1	no	—
305	#555	—	13	1	no	—
306	#555	—	13	1	no	—
307	#553	—	13	2	no	—
308	#553	—	13	2	no	—
309	#550	—	13	1	no	—
310	#550	—	13	1	no	—
311	#547	—	13	1	no	—
312	#547	—	13	1	no	—
313	#538	—	13	2	no	—
314	#538	—	13	2	no	—
315	#535	—	13	2	no	—
316	#533	—	13	1	no	—
317	#532	—	13	1	no	—
318	#525	—	13	1	no	—
319	#525	—	13	1	no	—
320	#525	—	13	1	no	—
321	#525	D₁₃	1	1	yes	characteristic, complemented
322	#520	—	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	2	no	—
327	C₂²×C₁₃	—	2	1	no	—
328	C₂²×C₁₃	—	2	1	no	—
329	C₂²×C₁₃	—	2	2	no	—
330	C₂²×C₁₃	—	2	1	no	—
331	C₂²×C₁₃	—	2	1	no	—
332	C₂²×C₁₃	—	2	2	no	—
333	C₂²×C₁₃	—	2	1	no	—
334	C₂²×C₁₃	—	2	1	no	—
335	C₂²×C₁₃	—	4	4	no	—
336	C₂²×C₁₃	C₂×#41	1	2	yes	—
337	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
338	C₂×D₁₃	—	2	2	no	—
339	C₂×D₁₃	—	2	1	no	—
340	C₂×D₁₃	—	2	1	no	—
341	C₂×D₁₃	—	2	1	no	—
342	C₂×D₁₃	—	2	1	no	—
343	C₂×D₁₃	—	2	2	no	—
344	C₂×D₁₃	—	2	1	no	—
345	C₂×D₁₃	—	2	2	no	—
346	C₂×D₁₃	—	2	1	no	—
347	C₂×D₁₃	—	4	4	no	—
348	C₄×C₁₃	—	2	2	no	—
349	C₄×C₁₃	—	2	1	no	—
350	C₄×C₁₃	—	2	1	no	—
351	C₄×C₁₃	—	2	2	no	—
352	C₄×C₁₃	—	2	1	no	—
353	C₄×C₁₃	—	2	2	no	—
354	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
355	Dic₁₃	—	2	2	no	—
356	Dic₁₃	—	2	2	no	—
357	Dic₁₃	—	2	1	no	—
358	Dic₁₃	—	2	1	no	—
359	Dic₁₃	—	2	1	no	—
360	Dic₁₃	—	2	2	no	—
361	Dic₁₃	—	2	1	no	—
362	Dic₁₃	C₂×#41	1	2	yes	—
363	Dic₁₃	C₂×#41	1	2	yes	—
364	C₂×#41	—	13	1	no	—
365	C₂×#41	—	13	2	no	—
366	C₂×#41	—	13	1	no	—
367	C₂×#41	—	13	1	no	—
368	C₂×#41	C₂×D₁₃	1	1	yes	characteristic, complemented
369	C₂²×D₄	—	13	1	no	—
370	C₂³×C₄	—	13	1	no	—
371	C₂³×C₄	C₂×D₁₃	1	1	yes	characteristic
372	C₄⋊Q₈	—	13	1	no	—
373	C₄⋊Q₈	—	13	1	no	—
374	C₄⋊Q₈	—	13	1	no	—
375	#127	—	13	1	no	—
376	#127	—	13	2	no	—
377	#127	—	13	2	no	—
378	#126	—	13	2	no	—
379	#126	—	13	2	no	—
380	#126	—	13	2	no	—
381	#126	—	13	2	no	—
382	#125	—	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	—	13	2	no	—
388	#124	—	13	2	no	—
389	#124	—	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	—	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	C₂×D₁₃	1	1	yes	characteristic
404	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
405	#121	—	13	1	no	—
406	#121	—	13	2	no	—
407	#121	—	13	2	no	—
408	#121	—	13	2	no	—
409	#121	—	13	2	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	C₂×D₁₃	1	1	yes	characteristic
419	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
420	#120	—	13	2	no	—
421	#120	—	13	2	no	—
422	#120	—	13	2	no	—
423	#120	C₂×D₁₃	1	2	yes	—
424	C₄×Q₈	—	13	1	no	—
425	C₄×Q₈	—	13	2	no	—
426	C₄×Q₈	—	13	1	no	—
427	C₄×Q₈	—	13	2	no	—
428	C₄×Q₈	—	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	1	no	—
433	C₄×D₄	—	13	1	no	—
434	C₄×D₄	—	13	1	no	—
435	C₄×D₄	—	13	1	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	2	no	—
442	C₄×D₄	—	13	2	no	—
443	C₄×D₄	—	13	1	no	—
444	C₄×D₄	—	13	2	no	—
445	C₄×D₄	—	13	2	no	—
446	C₄×D₄	—	13	2	no	—
447	C₄×D₄	—	13	2	no	—
448	C₄×D₄	C₂×D₁₃	1	2	yes	—
449	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
450	#117	—	13	1	no	—
451	#117	—	13	1	no	—
452	#117	—	13	1	no	—
453	#117	—	13	2	no	—
454	#117	—	13	2	no	—
455	#117	—	13	2	no	—
456	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
457	C₂×C₄⋊C₄	—	13	1	no	—
458	C₂×C₄⋊C₄	—	13	2	no	—
459	C₂×C₄⋊C₄	—	13	2	no	—
460	C₂×C₂²⋊C₄	—	13	1	no	—
461	C₂×C₂²⋊C₄	—	13	1	no	—
462	C₂×C₄²	—	13	1	no	—
463	C₂×C₁₃	—	2	2	no	—
464	C₂×C₁₃	—	4	2	no	—
465	C₂×C₁₃	—	4	1	no	—
466	C₂×C₁₃	—	4	1	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	—	4	2	no	—
471	D₁₃	—	4	1	no	—
472	D₁₃	—	4	1	no	—
473	C₂⁴	—	13	1	no	—
474	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
475	#41	—	4	2	no	—
476	#41	—	26	8	no	—
477	#41	—	52	2	no	—
478	#41	—	52	2	no	—
479	#41	—	52	2	no	—
480	C₂×Q₈	—	13	2	no	—
481	C₂×Q₈	—	13	1	no	—
482	C₂×Q₈	—	13	2	no	—
483	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
484	C₂×D₄	—	13	2	no	—
485	C₂×D₄	—	13	1	no	—
486	C₂×D₄	—	13	1	no	—
487	C₂×D₄	—	13	1	no	—
488	C₂×D₄	—	13	1	no	—
489	C₂×D₄	—	13	2	no	—
490	C₂×D₄	—	13	2	no	—
491	C₂×D₄	—	13	2	no	—
492	C₂×D₄	—	13	2	no	—
493	C₂×D₄	—	13	2	no	—
494	C₂×D₄	—	13	2	no	—
495	C₂×D₄	—	13	1	no	—
496	C₂×D₄	—	13	2	no	—
497	C₂×D₄	—	13	2	no	—
498	C₂×D₄	—	26	4	no	—
499	C₂×D₄	C₂²×D₁₃	1	2	yes	—
500	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
501	C₂×D₄	C₂²×D₁₃	1	2	yes	—
502	C₂×D₄	C₂²×D₁₃	1	2	yes	—
503	C₂²×C₄	—	4	2	no	—
504	C₂²×C₄	—	13	1	no	—
505	C₂²×C₄	—	13	2	no	—
506	C₂²×C₄	—	13	1	no	—
507	C₂²×C₄	—	13	1	no	—
508	C₂²×C₄	—	13	2	no	—
509	C₂²×C₄	—	13	2	no	—
510	C₂²×C₄	—	13	1	no	—
511	C₂²×C₄	—	13	1	no	—
512	C₂²×C₄	—	13	2	no	—
513	C₂²×C₄	—	13	2	no	—
514	C₂²×C₄	—	13	1	no	—
515	C₂²×C₄	—	13	1	no	—
516	C₂²×C₄	—	52	2	no	—
517	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
518	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
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	1	yes	characteristic
523	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
524	C₄⋊C₄	—	13	1	no	—
525	C₄⋊C₄	—	13	1	no	—
526	C₄⋊C₄	—	13	2	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	1	no	—
534	C₄⋊C₄	—	13	1	no	—
535	C₄⋊C₄	—	13	2	no	—
536	C₄⋊C₄	—	13	2	no	—
537	C₄⋊C₄	—	13	2	no	—
538	C₄⋊C₄	—	13	2	no	—
539	C₄⋊C₄	—	13	2	no	—
540	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
541	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
542	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
543	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
544	C₂²⋊C₄	—	13	1	no	—
545	C₂²⋊C₄	—	13	1	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	2	no	—
552	C₂²⋊C₄	—	13	2	no	—
553	C₂²⋊C₄	—	13	1	no	—
554	C₂²⋊C₄	—	13	1	no	—
555	C₂²⋊C₄	—	13	1	no	—
556	C₂²⋊C₄	—	13	1	no	—
557	C₂²⋊C₄	—	13	2	no	—
558	C₂²⋊C₄	—	13	2	no	—
559	C₂²⋊C₄	—	13	2	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	C₂²×D₁₃	1	2	yes	—
566	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
567	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
568	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
569	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
570	C₄²	—	13	1	no	—
571	C₄²	—	13	1	no	—
572	C₄²	—	13	1	no	—
573	C₄²	—	13	1	no	—
574	C₄²	—	13	2	no	—
575	C₄²	—	13	2	no	—
576	C₄²	—	13	2	no	—
577	C₄²	—	13	2	no	—
578	C₄²	—	13	2	no	—
579	C₄²	C₂²×D₁₃	1	2	yes	—
580	C₁₃	#3506	1	1	yes	characteristic, complemented, Sylow
581	C₂³	—	2	2	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	4	1	no	—
584	C₂³	—	13	1	no	—
585	C₂³	—	13	1	no	—
586	C₂³	—	13	2	no	—
587	C₂³	—	26	2	no	—
588	C₂³	—	52	1	no	—
589	C₂³	—	52	1	no	—
590	C₂³	C₂³×D₁₃	1	1	yes	characteristic
591	C₂³	C₂³×D₁₃	1	1	yes	characteristic
592	C₂³	C₂³×D₁₃	1	2	yes	—
593	C₂³	C₂³×D₁₃	1	1	yes	characteristic
594	Q₈	—	2	2	no	—
595	Q₈	—	26	4	no	—
596	Q₈	—	26	2	no	—
597	Q₈	—	52	2	no	—
598	D₄	—	2	4	no	—
599	D₄	—	2	2	no	—
600	D₄	—	4	2	no	—
601	D₄	—	4	2	no	—
602	D₄	—	26	2	no	—
603	D₄	—	26	2	no	—
604	D₄	—	26	2	no	—
605	D₄	—	26	2	no	—
606	D₄	—	26	4	no	—
607	D₄	—	26	4	no	—
608	D₄	—	26	2	no	—
609	D₄	—	52	2	no	—
610	D₄	—	52	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	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	2	no	—
623	C₂×C₄	—	13	4	no	—
624	C₂×C₄	—	13	1	no	—
625	C₂×C₄	—	13	1	no	—
626	C₂×C₄	—	13	2	no	—
627	C₂×C₄	—	13	1	no	—
628	C₂×C₄	—	13	2	no	—
629	C₂×C₄	—	13	1	no	—
630	C₂×C₄	—	13	1	no	—
631	C₂×C₄	—	13	1	no	—
632	C₂×C₄	—	13	2	no	—
633	C₂×C₄	—	26	4	no	—
634	C₂×C₄	—	26	4	no	—
635	C₂×C₄	—	26	2	no	—
636	C₂×C₄	—	26	2	no	—
637	C₂×C₄	—	52	1	no	—
638	C₂×C₄	—	52	1	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	—	52	2	no	—
644	C₂×C₄	C₂³×D₁₃	1	2	yes	—
645	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
646	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
647	C₂×C₄	C₂³×D₁₃	1	2	yes	—
648	C₂×C₄	C₂³×D₁₃	1	2	yes	—
649	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
650	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
651	C₂²	—	2	1	no	—
652	C₂²	—	2	1	no	—
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	4	4	no	—
663	C₂²	—	26	1	no	—
664	C₂²	—	26	1	no	—
665	C₂²	—	26	2	no	—
666	C₂²	—	26	2	no	—
667	C₂²	—	26	1	no	—
668	C₂²	—	26	1	no	—
669	C₂²	—	26	2	no	—
670	C₂²	—	26	1	no	—
671	C₂²	—	26	1	no	—
672	C₂²	—	52	4	no	—
673	C₂²	#41×D₁₃	1	2	yes	—
674	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
675	C₄	—	2	1	no	—
676	C₄	—	2	1	no	—
677	C₄	—	2	1	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	2	no	—
681	C₄	—	13	2	no	—
682	C₄	—	13	2	no	—
683	C₄	—	26	1	no	—
684	C₄	—	26	1	no	—
685	C₄	—	26	2	no	—
686	C₄	—	26	2	no	—
687	C₄	—	26	1	no	—
688	C₄	—	26	1	no	—
689	C₄	—	26	2	no	—
690	C₄	#88251	1	2	yes	—
691	C₂	—	2	2	no	—
692	C₂	—	4	1	no	—
693	C₂	—	4	1	no	—
694	C₂	—	4	2	no	—
695	C₂	—	52	1	no	—
696	C₂	—	52	1	no	—
697	C₂	—	52	2	no	—
698	C₂	C₂×#88251	1	1	yes	characteristic
699	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
700	C₂	#11719648	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#525	C₂
hypercenter	#525	D₁₃
hypocenter	C₁₃	#3506
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. C₁₃×#525	C₂	semidirect
2. #11719539	C₂	semidirect
3. #11719529	C₂	semidirect
4. #11719496	C₂	semidirect
5. C₂×C₄×C₂²⋊D₁₃	C₂	semidirect
6. #11719369	C₂	semidirect
7. #11719366	C₂	semidirect
8. #11719346	C₂	semidirect
9. #11719336	C₂	semidirect
10. #11719332	C₂	semidirect
11. #11719327	C₂	semidirect
12. #11719321	C₂	semidirect
13. #11719311	C₂	semidirect
14. #11719304	C₂	semidirect
15. #11719301	C₂	semidirect
16. #11719298	C₂	semidirect
17. #11719297	C₂	semidirect
18. #11719265	C₂	semidirect
19. #11719264	C₂	semidirect
20. #11719251	C₂	semidirect
21. #11719245	C₂	semidirect
22. #11719238	C₂	semidirect
23. #11719237	C₂	semidirect
24. C₂×C₁₃×#41	C₂²	semidirect
27. C₂×#6131	C₂²	semidirect
29. C₂×#6129	C₂²	semidirect
30. C₂×#6127	C₂²	semidirect
32. C₁₃×#123	C₂²	semidirect
34. C₁₃×C₂²⋊Q₈	C₂²	semidirect
36. C₁₃×#121	C₂²	semidirect
39. C₄×D₄×C₁₃	C₂²	semidirect
40. C₁₃×#117	C₂²	semidirect
43. #88200	C₂²	semidirect
44. Q₈×Dic₁₃	C₂²	semidirect
45. #88198	C₂²	semidirect
48. #88194	C₂²	semidirect
52. #88193	C₂²	semidirect
53. #88192	C₂²	semidirect
54. #88192	C₂²	semidirect
56. #88190	C₂²	semidirect
57. #88189	C₂²	semidirect
59. D₄×Dic₁₃	C₂²	semidirect
61. #88184	C₂²	semidirect
62. #88184	C₂²	semidirect
63. #88183	C₂²	semidirect
64. #88183	C₂²	semidirect
74. C₄×C₂²⋊D₁₃	C₂²	semidirect
75. C₄×C₂²⋊D₁₃	C₂²	semidirect
77. #88180	C₂²	semidirect
79. #88178	C₂²	semidirect
81. C₂×#6101	C₂²	semidirect
83. #88152	C₂²	semidirect
84. #88151	C₂²	semidirect
85. #88149	C₂²	semidirect
86. #88148	C₂²	semidirect
87. #88148	C₂²	semidirect
88. #88147	C₂²	semidirect
89. #88147	C₂²	semidirect
90. #88146	C₂²	semidirect
91. #88146	C₂²	semidirect
92. C₄⋊C₄×D₁₃	C₂²	semidirect
93. #88143	C₂²	semidirect
94. #88142	C₂²	semidirect
95. #88142	C₂²	semidirect
96. #88141	C₂²	semidirect
97. #88141	C₂²	semidirect
98. #88141	C₂²	semidirect
101. #88139	C₂²	semidirect
102. #88139	C₂²	semidirect
103. #88139	C₂²	semidirect
106. #88138	C₂²	semidirect
107. #88137	C₂²	semidirect
108. #88137	C₂²	semidirect
111. #88135	C₂²	semidirect
112. #88135	C₂²	semidirect
113. #88135	C₂²	semidirect
114. #88133	C₂²	semidirect
115. #88133	C₂²	semidirect
118. #88131	C₂²	semidirect
119. #88130	C₂²	semidirect
120. #88129	C₂²	semidirect
121. #88126	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
278. C₂×Dic₁₃	#41	semidirect
321. #525	D₁₃	semidirect
368. C₂×#41	C₂×D₁₃	semidirect
397. #123	C₂×D₁₃	semidirect
404. C₂²⋊Q₈	C₂×D₁₃	semidirect
419. #121	C₂×D₁₃	semidirect
449. C₄×D₄	C₂×D₁₃	semidirect
456. #117	C₂×D₁₃	semidirect
580. C₁₃	#3506	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#525	2
#11719539	2
#11719529	2
#11719496	2
C₂×C₄×C₂²⋊D₁₃	2
#11719369	2
#11719366	2
#11719346	2
#11719336	2
#11719332	2
#11719327	2
#11719321	2
#11719311	2
#11719304	2
#11719301	2
#11719298	2
#11719297	2
#11719265	2
#11719264	2
#11719251	2
#11719245	2
#11719238	2
#11719237	2
#3506	13