Subgroups — #13128858

Order 1664.

1252 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719267	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719265	C₂	1	2	yes	maximal, complemented
6	#11719263	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719258	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719255	C₂	1	2	yes	maximal, complemented
9	D₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719253	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719252	C₂	1	2	yes	maximal, complemented
12	#11719250	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719245	C₂	1	2	yes	maximal, complemented
15	#11719244	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719240	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719237	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719235	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719233	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719199	C₂	1	2	yes	maximal, complemented
21	#11719195	C₂	1	2	yes	maximal, complemented
22	#11719195	C₂	1	2	yes	maximal, complemented
23	C₂×#88138	C₂	1	2	yes	maximal, complemented
24	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
26	C₂²×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
27	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
29	C₂×#6127	C₂²	1	2	yes	complemented
30	C₂×#6127	C₂²	1	2	yes	complemented
31	C₂²×D₅₂	C₂²	1	2	yes	complemented
32	C₂²×C₄×D₁₃	C₂²	1	2	yes	complemented
33	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
36	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
37	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
38	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
42	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
43	#88207	C₂²	1	2	yes	complemented
44	#88207	C₂²	1	2	yes	complemented
45	#88194	C₂²	1	1	yes	characteristic, complemented
46	#88194	C₂²	1	1	yes	characteristic, complemented
47	#88193	C₂²	1	2	yes	complemented
48	#88193	C₂²	1	2	yes	complemented
49	#88192	C₂²	1	1	yes	characteristic, complemented
50	#88192	C₂²	1	1	yes	characteristic, complemented
51	#88191	C₂²	1	2	yes	complemented
52	#88191	C₂²	1	2	yes	complemented
53	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
54	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
55	#88184	C₂²	1	2	yes	complemented
56	#88184	C₂²	1	2	yes	complemented
57	#88184	C₂²	1	2	yes	complemented
58	#88184	C₂²	1	1	yes	characteristic, complemented
59	#88184	C₂²	1	1	yes	characteristic, complemented
60	#88183	C₂²	1	2	yes	complemented
61	#88183	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
64	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
66	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
67	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
68	C₂×#6103	C₂²	1	2	yes	complemented
69	#88178	C₂²	1	2	yes	complemented
70	C₂×#6101	C₂²	1	2	yes	complemented
71	#88152	C₂²	1	1	yes	characteristic, complemented
72	#88150	C₂²	1	1	yes	characteristic, complemented
73	#88149	C₂²	1	1	yes	characteristic, complemented
74	#88149	C₂²	1	1	yes	characteristic, complemented
75	#88148	C₂²	1	1	yes	characteristic, complemented
76	#88148	C₂²	1	2	yes	complemented
77	#88148	C₂²	1	2	yes	complemented
78	#88147	C₂²	1	1	yes	characteristic, complemented
79	#88147	C₂²	1	1	yes	characteristic, complemented
80	#88146	C₂²	1	1	yes	characteristic, complemented
81	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
82	#88144	C₂²	1	1	yes	characteristic, complemented
83	#88143	C₂²	1	1	yes	characteristic, complemented
84	#88142	C₂²	1	1	yes	characteristic, complemented
85	#88139	C₂²	1	1	yes	characteristic, complemented
86	#88139	C₂²	1	2	yes	complemented
87	#88139	C₂²	1	2	yes	complemented
88	#88138	C₂²	1	1	yes	characteristic
89	#88138	C₂²	1	2	yes	complemented
90	#88138	C₂²	1	2	yes	complemented
91	#88138	C₂²	1	2	yes	complemented
92	#88138	C₂²	1	2	yes	complemented
93	#88138	C₂²	1	2	yes	complemented
94	#88138	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	1	yes	characteristic, complemented
99	#88137	C₂²	1	2	yes	complemented
100	#88137	C₂²	1	2	yes	complemented
101	#88136	C₂²	1	2	yes	complemented
102	#88136	C₂²	1	2	yes	complemented
103	#88135	C₂²	1	2	yes	complemented
104	#88135	C₂²	1	2	yes	complemented
105	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
106	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
107	#88133	C₂²	1	1	yes	characteristic, complemented
108	#88133	C₂²	1	2	yes	complemented
109	#88132	C₂²	1	2	yes	complemented
110	#88132	C₂²	1	2	yes	complemented
111	#88130	C₂²	1	2	yes	complemented
112	#88129	C₂²	1	2	yes	complemented
113	#88128	C₂²	1	1	yes	characteristic, complemented
114	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₅₂	C₂²	1	2	yes	complemented
116	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
118	#88126	C₂²	1	1	yes	characteristic, complemented
119	#88126	C₂²	1	2	yes	complemented
120	C₄²×D₁₃	C₂²	1	1	yes	characteristic, complemented
121	#88124	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
123	C₂⁴×C₁₃	C₂³	1	2	yes	—
124	C₂³×D₁₃	C₂³	1	2	yes	—
125	C₂³×D₁₃	C₂³	1	2	yes	—
126	C₂×D₄×C₁₃	—	2	4	no	—
127	C₂×D₄×C₁₃	C₂³	1	2	yes	—
128	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
132	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₃	—	4	4	no	—
136	C₂×C₂²⋊D₁₃	—	4	4	no	—
137	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
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	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
149	C₂²×Dic₁₃	C₂³	1	2	yes	—
150	C₂²×Dic₁₃	C₂³	1	2	yes	—
151	D₄×D₁₃	—	2	4	no	—
152	D₄×D₁₃	—	2	4	no	—
153	#6127	—	4	4	no	—
154	#6127	—	4	4	no	—
155	C₂×D₅₂	—	4	4	no	—
156	C₂×D₅₂	C₂³	1	1	yes	characteristic
157	C₂×D₅₂	C₂³	1	1	yes	characteristic
158	C₂×D₅₂	C₂³	1	2	yes	—
159	C₂×D₅₂	C₂³	1	1	yes	characteristic
160	C₂×D₅₂	C₂³	1	2	yes	—
161	C₂×D₅₂	C₂³	1	2	yes	—
162	C₂×D₅₂	C₂³	1	2	yes	—
163	C₂×C₄×D₁₃	—	4	4	no	—
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	1	yes	characteristic
168	C₂×C₄×D₁₃	C₂³	1	2	yes	—
169	C₂×C₄×D₁₃	C₂³	1	2	yes	—
170	C₂×C₄×D₁₃	C₂³	1	2	yes	—
171	C₂×C₄×D₁₃	C₂³	1	2	yes	—
172	C₂×C₄×D₁₃	C₂³	1	2	yes	—
173	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
174	C₂×Dic₂₆	C₂³	1	2	yes	—
175	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
181	C₁₃×C₂²⋊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	2	yes	—
185	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₄²×C₁₃	C₂³	1	1	yes	characteristic
187	C₄²×C₁₃	C₂³	1	1	yes	characteristic
188	C₄²×C₁₃	C₂³	1	2	yes	—
189	C₂²⋊Dic₁₃	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	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
194	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
195	#6103	C₂³	1	2	yes	—
196	#6103	C₂³	1	1	yes	characteristic
197	#6103	C₂³	1	2	yes	—
198	#6103	C₂³	1	1	yes	characteristic
199	#6103	C₂³	1	1	yes	characteristic
200	#6103	C₂³	1	2	yes	—
201	#6103	C₂³	1	2	yes	—
202	#6103	C₂³	1	1	yes	characteristic
203	#6103	C₂³	1	1	yes	characteristic
204	#6103	C₂³	1	2	yes	—
205	#6103	C₂³	1	1	yes	characteristic
206	#6103	C₂³	1	2	yes	—
207	#6103	C₂³	1	2	yes	—
208	#6103	C₂³	1	2	yes	—
209	#6103	C₂³	1	2	yes	—
210	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₁₃	C₂³	1	2	yes	—
214	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
215	#6101	C₂³	1	1	yes	characteristic
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	#6101	C₂³	1	1	yes	characteristic
222	#6101	C₂³	1	1	yes	characteristic
223	#6101	C₂³	1	1	yes	characteristic
224	#6101	C₂³	1	2	yes	—
225	#6101	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	C₄×Dic₁₃	C₂³	1	2	yes	—
231	#3519	—	13	1	no	maximal, Sylow
232	C₂³×C₁₃	—	2	4	no	—
233	C₂³×C₁₃	—	4	2	no	—
234	C₂³×C₁₃	—	4	2	no	—
235	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₂³×C₁₃	C₂⁴	1	2	yes	—
237	C₂³×C₁₃	C₂⁴	1	2	yes	—
238	C₂²×D₁₃	—	2	4	no	—
239	C₂²×D₁₃	—	2	4	no	—
240	C₂²×D₁₃	—	2	4	no	—
241	C₂²×D₁₃	—	4	2	no	—
242	C₂²×D₁₃	—	4	2	no	—
243	C₂²×D₁₃	—	4	2	no	—
244	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
245	C₂²×D₁₃	C₂⁴	1	2	yes	—
246	C₂²×D₁₃	C₂⁴	1	2	yes	—
247	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
248	D₄×C₁₃	—	2	4	no	—
249	D₄×C₁₃	—	2	2	no	—
250	D₄×C₁₃	#41	1	4	yes	complemented
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	4	2	no	—
253	C₂×C₄×C₁₃	—	4	2	no	—
254	C₂×C₄×C₁₃	—	4	2	no	—
255	C₂×C₄×C₁₃	—	4	2	no	—
256	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
262	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂²⋊D₁₃	—	2	4	no	—
265	C₂²⋊D₁₃	—	2	4	no	—
266	C₂²⋊D₁₃	—	2	4	no	—
267	C₂²⋊D₁₃	—	2	2	no	—
268	C₂²⋊D₁₃	—	2	4	no	—
269	C₂²⋊D₁₃	—	2	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	C₂²⋊D₁₃	—	4	2	no	—
275	C₂²⋊D₁₃	—	4	2	no	—
276	C₂×Dic₁₃	—	2	4	no	—
277	C₂×Dic₁₃	—	4	2	no	—
278	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
285	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
286	D₅₂	—	2	2	no	—
287	D₅₂	—	2	4	no	—
288	D₅₂	—	2	2	no	—
289	D₅₂	—	2	2	no	—
290	D₅₂	—	4	2	no	—
291	D₅₂	—	4	2	no	—
292	D₅₂	—	4	2	no	—
293	C₄×D₁₃	—	2	2	no	—
294	C₄×D₁₃	—	2	2	no	—
295	C₄×D₁₃	—	2	2	no	—
296	C₄×D₁₃	—	2	2	no	—
297	C₄×D₁₃	—	2	4	no	—
298	C₄×D₁₃	—	4	2	no	—
299	C₄×D₁₃	—	4	2	no	—
300	C₄×D₁₃	—	4	2	no	—
301	C₄×D₁₃	—	4	2	no	—
302	Dic₂₆	—	2	2	no	—
303	Dic₂₆	—	4	2	no	—
304	#555	—	13	1	no	—
305	#554	—	13	1	no	—
306	#553	—	13	2	no	—
307	#553	—	13	1	no	—
308	#553	—	13	1	no	—
309	#550	—	13	1	no	—
310	#546	—	13	2	no	—
311	#546	—	13	2	no	—
312	#546	—	13	2	no	—
313	D₄²	—	13	1	no	—
314	D₄²	—	13	1	no	—
315	D₄²	—	13	1	no	—
316	#540	—	13	1	no	—
317	#540	—	13	1	no	—
318	#538	—	13	2	no	—
319	#538	—	13	2	no	—
320	#532	—	13	1	no	—
321	#529	—	13	1	no	—
322	#525	—	13	2	no	—
323	C₂×#121	—	13	2	no	—
324	#518	—	13	1	no	—
325	#518	D₁₃	1	1	yes	characteristic, complemented
326	C₂×C₄×D₄	—	13	1	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	2	no	—
329	C₂²×C₁₃	—	2	1	no	—
330	C₂²×C₁₃	—	2	2	no	—
331	C₂²×C₁₃	—	2	2	no	—
332	C₂²×C₁₃	—	2	2	no	—
333	C₂²×C₁₃	—	2	1	no	—
334	C₂²×C₁₃	—	2	1	no	—
335	C₂²×C₁₃	—	8	4	no	—
336	C₂²×C₁₃	C₂×#41	1	4	yes	—
337	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
338	C₂×D₁₃	—	2	1	no	—
339	C₂×D₁₃	—	2	1	no	—
340	C₂×D₁₃	—	2	1	no	—
341	C₂×D₁₃	—	2	2	no	—
342	C₂×D₁₃	—	2	2	no	—
343	C₂×D₁₃	—	2	2	no	—
344	C₂×D₁₃	—	2	2	no	—
345	C₂×D₁₃	—	2	2	no	—
346	C₂×D₁₃	—	2	1	no	—
347	C₂×D₁₃	—	2	2	no	—
348	C₂×D₁₃	—	2	1	no	—
349	C₂×D₁₃	—	4	8	no	—
350	C₂×D₁₃	—	8	4	no	—
351	C₂×D₁₃	H(5,𝔽₂)	1	2	yes	—
352	C₄×C₁₃	—	2	1	no	—
353	C₄×C₁₃	—	2	1	no	—
354	C₄×C₁₃	—	2	2	no	—
355	C₄×C₁₃	—	2	1	no	—
356	C₄×C₁₃	—	2	1	no	—
357	C₄×C₁₃	—	2	2	no	—
358	C₄×C₁₃	—	2	1	no	—
359	C₄×C₁₃	C₂×#41	1	2	yes	—
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	Dic₁₃	—	2	2	no	—
366	Dic₁₃	—	2	1	no	—
367	Dic₁₃	H(5,𝔽₂)	1	2	yes	—
368	C₂×#41	—	13	2	no	—
369	C₂×#41	—	13	2	no	—
370	C₂²×D₄	—	13	2	no	—
371	C₂²×D₄	—	13	2	no	—
372	C₂²×D₄	—	13	1	no	—
373	C₂²×D₄	—	13	1	no	—
374	C₂²×D₄	—	13	2	no	—
375	C₂²×D₄	C₂×D₁₃	1	1	yes	characteristic
376	C₂³×C₄	—	13	2	no	—
377	C₄⋊Q₈	—	13	1	no	—
378	#127	—	13	1	no	—
379	#127	—	13	1	no	—
380	#127	—	13	1	no	—
381	#126	—	13	1	no	—
382	#126	—	13	1	no	—
383	#126	—	13	2	no	—
384	#126	—	13	2	no	—
385	#125	—	13	1	no	—
386	#125	—	13	1	no	—
387	#125	—	13	1	no	—
388	#124	—	13	1	no	—
389	#124	—	13	2	no	—
390	#124	—	13	2	no	—
391	#124	—	13	2	no	—
392	#123	—	13	2	no	—
393	#123	—	13	2	no	—
394	#123	—	13	2	no	—
395	#123	—	13	1	no	—
396	#123	—	13	2	no	—
397	#123	—	13	2	no	—
398	#123	—	13	1	no	—
399	#123	—	13	2	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	#121	—	13	2	no	—
405	#121	—	13	1	no	—
406	#121	—	13	2	no	—
407	#121	—	13	1	no	—
408	#121	—	13	2	no	—
409	#121	—	13	2	no	—
410	#121	—	13	1	no	—
411	#121	—	13	1	no	—
412	#121	—	13	2	no	—
413	#121	—	13	1	no	—
414	#121	—	13	1	no	—
415	#121	—	13	1	no	—
416	#121	—	13	2	no	—
417	#121	—	13	2	no	—
418	#121	—	13	2	no	—
419	#121	—	13	2	no	—
420	#121	—	13	2	no	—
421	#121	—	13	2	no	—
422	#121	—	13	2	no	—
423	#121	—	13	2	no	—
424	#121	—	13	2	no	—
425	#120	—	13	2	no	—
426	#120	—	13	2	no	—
427	#120	—	13	2	no	—
428	#120	—	13	2	no	—
429	#120	—	13	2	no	—
430	#120	—	13	2	no	—
431	C₄×Q₈	—	13	1	no	—
432	C₄×D₄	—	13	1	no	—
433	C₄×D₄	—	13	1	no	—
434	C₄×D₄	—	13	2	no	—
435	C₄×D₄	—	13	2	no	—
436	C₄×D₄	—	13	2	no	—
437	C₄×D₄	—	13	1	no	—
438	C₄×D₄	—	13	1	no	—
439	C₄×D₄	—	13	2	no	—
440	C₄×D₄	—	13	1	no	—
441	C₄×D₄	—	13	1	no	—
442	C₄×D₄	—	13	2	no	—
443	C₄×D₄	—	13	2	no	—
444	C₄×D₄	—	13	1	no	—
445	C₄×D₄	—	13	1	no	—
446	C₄×D₄	—	13	2	no	—
447	C₄×D₄	—	13	1	no	—
448	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
449	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
450	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
451	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
452	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
453	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
454	#117	—	13	1	no	—
455	#117	—	13	1	no	—
456	#117	—	13	2	no	—
457	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
458	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
459	C₂×C₄⋊C₄	—	13	2	no	—
460	C₂×C₄⋊C₄	—	13	1	no	—
461	C₂×C₂²⋊C₄	—	13	2	no	—
462	C₂×C₂²⋊C₄	—	13	2	no	—
463	C₂×C₂²⋊C₄	—	13	2	no	—
464	C₂×C₂²⋊C₄	C₂×D₁₃	1	2	yes	complemented
465	C₂×C₂²⋊C₄	C₂×D₁₃	1	2	yes	complemented
466	C₂×C₄²	—	13	1	no	—
467	C₂×C₁₃	—	2	4	no	—
468	C₂×C₁₃	—	4	2	no	—
469	C₂×C₁₃	—	4	1	no	—
470	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
471	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
472	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
473	D₁₃	—	2	2	no	—
474	D₁₃	—	4	2	no	—
475	D₁₃	—	4	2	no	—
476	D₁₃	—	4	1	no	—
477	C₂⁴	—	13	2	no	—
478	C₂⁴	—	13	2	no	—
479	C₂⁴	C₂²×D₁₃	1	2	yes	—
480	#41	—	52	4	no	—
481	#41	—	52	4	no	—
482	C₂×Q₈	—	13	1	no	—
483	C₂×Q₈	—	13	2	no	—
484	C₂×D₄	—	2	4	no	—
485	C₂×D₄	—	13	2	no	—
486	C₂×D₄	—	13	2	no	—
487	C₂×D₄	—	13	2	no	—
488	C₂×D₄	—	13	1	no	—
489	C₂×D₄	—	13	1	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	2	no	—
496	C₂×D₄	—	13	2	no	—
497	C₂×D₄	—	13	1	no	—
498	C₂×D₄	—	13	1	no	—
499	C₂×D₄	—	13	2	no	—
500	C₂×D₄	—	13	1	no	—
501	C₂×D₄	—	13	2	no	—
502	C₂×D₄	—	13	2	no	—
503	C₂×D₄	—	13	2	no	—
504	C₂×D₄	—	26	4	no	—
505	C₂×D₄	—	26	4	no	—
506	C₂×D₄	—	52	4	no	—
507	C₂×D₄	—	52	4	no	—
508	C₂×D₄	—	52	4	no	—
509	C₂×D₄	C₂²×D₁₃	1	2	yes	—
510	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
511	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
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	—	13	1	no	—
517	C₂²×C₄	—	13	1	no	—
518	C₂²×C₄	—	13	2	no	—
519	C₂²×C₄	—	13	2	no	—
520	C₂²×C₄	—	13	2	no	—
521	C₂²×C₄	—	13	2	no	—
522	C₂²×C₄	—	13	2	no	—
523	C₂²×C₄	—	52	4	no	—
524	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
525	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
526	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
527	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
528	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
529	C₄⋊C₄	—	13	1	no	—
530	C₄⋊C₄	—	13	2	no	—
531	C₄⋊C₄	—	13	1	no	—
532	C₄⋊C₄	—	13	2	no	—
533	C₄⋊C₄	—	13	2	no	—
534	C₄⋊C₄	—	13	2	no	—
535	C₄⋊C₄	—	13	1	no	—
536	C₄⋊C₄	—	13	1	no	—
537	C₄⋊C₄	—	13	1	no	—
538	C₄⋊C₄	—	13	1	no	—
539	C₄⋊C₄	—	13	1	no	—
540	C₄⋊C₄	—	13	1	no	—
541	C₄⋊C₄	—	13	2	no	—
542	C₄⋊C₄	—	13	2	no	—
543	C₄⋊C₄	—	13	1	no	—
544	C₄⋊C₄	—	13	1	no	—
545	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
546	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
547	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
548	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
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	1	no	—
556	C₂²⋊C₄	—	13	2	no	—
557	C₂²⋊C₄	—	13	1	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	1	no	—
565	C₂²⋊C₄	—	13	1	no	—
566	C₂²⋊C₄	—	13	1	no	—
567	C₂²⋊C₄	—	13	1	no	—
568	C₂²⋊C₄	—	13	2	no	—
569	C₂²⋊C₄	—	13	2	no	—
570	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
571	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
572	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
573	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
574	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
575	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
576	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
577	C₄²	—	13	1	no	—
578	C₄²	—	13	1	no	—
579	C₄²	—	13	1	no	—
580	C₄²	—	13	2	no	—
581	C₄²	—	13	1	no	—
582	C₄²	C₂²×D₁₃	1	1	yes	characteristic
583	C₄²	C₂²×D₁₃	1	2	yes	—
584	C₄²	C₂²×D₁₃	1	1	yes	characteristic
585	C₁₃	#3519	1	1	yes	characteristic, complemented, Sylow
586	C₂³	—	2	4	no	—
587	C₂³	—	4	2	no	—
588	C₂³	—	4	2	no	—
589	C₂³	—	13	1	no	—
590	C₂³	—	13	1	no	—
591	C₂³	—	13	2	no	—
592	C₂³	—	13	2	no	—
593	C₂³	—	26	4	no	—
594	C₂³	—	26	4	no	—
595	C₂³	—	26	4	no	—
596	C₂³	—	52	2	no	—
597	C₂³	—	52	2	no	—
598	C₂³	—	52	2	no	—
599	C₂³	C₂³×D₁₃	1	1	yes	characteristic
600	C₂³	C₂³×D₁₃	1	2	yes	—
601	C₂³	C₂³×D₁₃	1	2	yes	—
602	Q₈	—	26	2	no	—
603	Q₈	—	52	2	no	—
604	D₄	—	2	4	no	—
605	D₄	—	2	2	no	—
606	D₄	—	26	2	no	—
607	D₄	—	26	4	no	—
608	D₄	—	26	2	no	—
609	D₄	—	26	4	no	—
610	D₄	—	26	2	no	—
611	D₄	—	26	4	no	—
612	D₄	—	26	4	no	—
613	D₄	—	26	4	no	—
614	D₄	—	26	2	no	—
615	D₄	—	26	2	no	—
616	D₄	—	52	2	no	—
617	D₄	—	52	2	no	—
618	D₄	—	52	2	no	—
619	D₄	—	52	2	no	—
620	D₄	—	52	2	no	—
621	D₄	—	52	2	no	—
622	D₄	—	52	2	no	—
623	D₄	—	52	2	no	—
624	D₄	—	52	2	no	—
625	D₄	#6127	1	4	yes	complemented
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	4	2	no	—
631	C₂×C₄	—	13	1	no	—
632	C₂×C₄	—	13	1	no	—
633	C₂×C₄	—	13	1	no	—
634	C₂×C₄	—	13	1	no	—
635	C₂×C₄	—	13	2	no	—
636	C₂×C₄	—	13	1	no	—
637	C₂×C₄	—	13	1	no	—
638	C₂×C₄	—	13	2	no	—
639	C₂×C₄	—	26	2	no	—
640	C₂×C₄	—	26	4	no	—
641	C₂×C₄	—	26	2	no	—
642	C₂×C₄	—	26	4	no	—
643	C₂×C₄	—	26	2	no	—
644	C₂×C₄	—	26	2	no	—
645	C₂×C₄	—	52	2	no	—
646	C₂×C₄	—	52	2	no	—
647	C₂×C₄	—	52	2	no	—
648	C₂×C₄	—	52	2	no	—
649	C₂×C₄	—	52	2	no	—
650	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
652	C₂×C₄	C₂³×D₁₃	1	2	yes	—
653	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
654	C₂×C₄	C₂³×D₁₃	1	2	yes	—
655	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
656	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
657	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	8	4	no	—
667	C₂²	—	13	2	no	—
668	C₂²	—	26	1	no	—
669	C₂²	—	26	1	no	—
670	C₂²	—	26	1	no	—
671	C₂²	—	26	2	no	—
672	C₂²	—	26	2	no	—
673	C₂²	—	26	2	no	—
674	C₂²	—	26	2	no	—
675	C₂²	—	26	2	no	—
676	C₂²	—	26	1	no	—
677	C₂²	—	26	1	no	—
678	C₂²	—	26	2	no	—
679	C₂²	—	52	8	no	—
680	C₂²	—	104	4	no	—
681	C₂²	C₂×#6127	1	4	yes	—
682	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	2	no	—
689	C₄	—	2	1	no	—
690	C₄	—	13	2	no	—
691	C₄	—	26	1	no	—
692	C₄	—	26	1	no	—
693	C₄	—	26	2	no	—
694	C₄	—	26	1	no	—
695	C₄	—	26	1	no	—
696	C₄	—	26	2	no	—
697	C₄	—	26	1	no	—
698	C₄	C₂×#6127	1	2	yes	—
699	C₂	—	2	4	no	—
700	C₂	—	4	1	no	—
701	C₂	—	4	2	no	—
702	C₂	—	26	2	no	—
703	C₂	—	52	2	no	—
704	C₂	—	52	1	no	—
705	C₂	—	52	2	no	—
706	C₂	C₂²×#6127	1	1	yes	characteristic
707	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic
708	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×#518	C₂
hypercenter	#518	D₁₃
hypocenter	C₁₃	#3519
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #518

Complements

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

N	H ≅ G/N	type
1. C₁₃×#518	C₂	semidirect
2. D₄×C₂²⋊D₁₃	C₂	semidirect
3. D₄×C₂²⋊D₁₃	C₂	semidirect
4. #11719267	C₂	semidirect
5. #11719265	C₂	semidirect
6. #11719263	C₂	semidirect
7. #11719258	C₂	semidirect
8. #11719255	C₂	semidirect
9. D₄×D₅₂	C₂	semidirect
10. #11719253	C₂	semidirect
11. #11719252	C₂	semidirect
12. #11719250	C₂	semidirect
13. C₄×D₄×D₁₃	C₂	semidirect
14. #11719245	C₂	semidirect
15. #11719244	C₂	semidirect
16. #11719240	C₂	semidirect
17. #11719237	C₂	semidirect
18. #11719235	C₂	semidirect
19. #11719233	C₂	semidirect
20. #11719199	C₂	semidirect
21. #11719195	C₂	semidirect
22. #11719195	C₂	semidirect
23. C₂×#88138	C₂	semidirect
25. C₂²×C₂²⋊D₁₃	C₂²	semidirect
26. C₂²×C₂²⋊D₁₃	C₂²	semidirect
29. C₂×#6127	C₂²	semidirect
30. C₂×#6127	C₂²	semidirect
31. C₂²×D₅₂	C₂²	semidirect
32. C₂²×C₄×D₁₃	C₂²	semidirect
35. C₄×D₄×C₁₃	C₂²	semidirect
36. C₄×D₄×C₁₃	C₂²	semidirect
37. C₄×D₄×C₁₃	C₂²	semidirect
38. C₄×D₄×C₁₃	C₂²	semidirect
39. C₁₃×#117	C₂²	semidirect
40. C₁₃×#117	C₂²	semidirect
41. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
42. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
43. #88207	C₂²	semidirect
44. #88207	C₂²	semidirect
45. #88194	C₂²	semidirect
46. #88194	C₂²	semidirect
47. #88193	C₂²	semidirect
48. #88193	C₂²	semidirect
49. #88192	C₂²	semidirect
50. #88192	C₂²	semidirect
51. #88191	C₂²	semidirect
52. #88191	C₂²	semidirect
55. #88184	C₂²	semidirect
56. #88184	C₂²	semidirect
57. #88184	C₂²	semidirect
58. #88184	C₂²	semidirect
59. #88184	C₂²	semidirect
60. #88183	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. C₄×C₂²⋊D₁₃	C₂²	semidirect
66. C₄×C₂²⋊D₁₃	C₂²	semidirect
67. C₄×C₂²⋊D₁₃	C₂²	semidirect
68. C₂×#6103	C₂²	semidirect
69. #88178	C₂²	semidirect
70. C₂×#6101	C₂²	semidirect
71. #88152	C₂²	semidirect
72. #88150	C₂²	semidirect
73. #88149	C₂²	semidirect
74. #88149	C₂²	semidirect
75. #88148	C₂²	semidirect
76. #88148	C₂²	semidirect
77. #88148	C₂²	semidirect
78. #88147	C₂²	semidirect
79. #88147	C₂²	semidirect
80. #88146	C₂²	semidirect
81. C₄⋊C₄×D₁₃	C₂²	semidirect
82. #88144	C₂²	semidirect
83. #88143	C₂²	semidirect
84. #88142	C₂²	semidirect
85. #88139	C₂²	semidirect
86. #88139	C₂²	semidirect
87. #88139	C₂²	semidirect
89. #88138	C₂²	semidirect
90. #88138	C₂²	semidirect
91. #88138	C₂²	semidirect
92. #88138	C₂²	semidirect
93. #88138	C₂²	semidirect
94. #88138	C₂²	semidirect
95. #88138	C₂²	semidirect
96. #88138	C₂²	semidirect
97. #88138	C₂²	semidirect
98. #88137	C₂²	semidirect
99. #88137	C₂²	semidirect
100. #88137	C₂²	semidirect
101. #88136	C₂²	semidirect
102. #88136	C₂²	semidirect
103. #88135	C₂²	semidirect
104. #88135	C₂²	semidirect
105. C₂²⋊C₄×D₁₃	C₂²	semidirect
106. C₂²⋊C₄×D₁₃	C₂²	semidirect
107. #88133	C₂²	semidirect
108. #88133	C₂²	semidirect
109. #88132	C₂²	semidirect
110. #88132	C₂²	semidirect
111. #88130	C₂²	semidirect
112. #88129	C₂²	semidirect
113. #88128	C₂²	semidirect
114. C₄×D₅₂	C₂²	semidirect
115. C₄×D₅₂	C₂²	semidirect
116. C₄×D₅₂	C₂²	semidirect
117. C₄×D₅₂	C₂²	semidirect
118. #88126	C₂²	semidirect
119. #88126	C₂²	semidirect
120. C₄²×D₁₃	C₂²	semidirect
121. #88124	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
250. D₄×C₁₃	#41	semidirect
325. #518	D₁₃	semidirect
450. C₄×D₄	C₂×D₁₃	semidirect
451. C₄×D₄	C₂×D₁₃	semidirect
452. C₄×D₄	C₂×D₁₃	semidirect
453. C₄×D₄	C₂×D₁₃	semidirect
457. #117	C₂×D₁₃	semidirect
458. #117	C₂×D₁₃	semidirect
464. C₂×C₂²⋊C₄	C₂×D₁₃	semidirect
465. C₂×C₂²⋊C₄	C₂×D₁₃	semidirect
585. C₁₃	#3519	semidirect
625. D₄	#6127	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#518	2
D₄×C₂²⋊D₁₃	2
#11719267	2
#11719265	2
#11719263	2
#11719258	2
#11719255	2
D₄×D₅₂	2
#11719253	2
#11719252	2
#11719250	2
C₄×D₄×D₁₃	2
#11719245	2
#11719244	2
#11719240	2
#11719237	2
#11719235	2
#11719233	2
#11719199	2
#11719195	2
C₂×#88138	2
#3519	13