Subgroups — #13128519

Order 1664.

1328 conjugacy classes of subgroups.

The subgroup lattice has 658 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	#11719534	C₂	1	2	yes	maximal, complemented
3	#11719496	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#6103	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719363	C₂	1	2	yes	maximal, complemented
6	#11719359	C₂	1	2	yes	maximal, complemented
7	#11719349	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719342	C₂	1	2	yes	maximal, complemented
9	#11719339	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719322	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719315	C₂	1	2	yes	maximal, complemented
12	#11719310	C₂	1	1	yes	maximal, characteristic, complemented
13	D₁₃×#120	C₂	1	2	yes	maximal, complemented
14	#11719291	C₂	1	2	yes	maximal, complemented
15	#11719265	C₂	1	2	yes	maximal, complemented
16	#11719261	C₂	1	2	yes	maximal, complemented
17	#11719259	C₂	1	2	yes	maximal, complemented
18	#11719250	C₂	1	2	yes	maximal, complemented
19	#11719232	C₂	1	2	yes	maximal, complemented
20	C₂⁴×D₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
22	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
23	C₂³×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
24	C₂×#6129	C₂²	1	2	yes	complemented
25	C₂×D₄×D₁₃	C₂²	1	2	yes	—
26	C₂×D₄×D₁₃	C₂²	1	2	yes	complemented
27	C₂×D₄×D₁₃	C₂²	1	2	yes	complemented
28	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#123	C₂²	1	2	yes	complemented
30	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#120	C₂²	1	2	yes	complemented
35	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
36	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
37	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
38	#88207	C₂²	1	2	yes	complemented
39	#88201	C₂²	1	2	yes	complemented
40	#88200	C₂²	1	2	yes	complemented
41	#88193	C₂²	1	2	yes	complemented
42	#88193	C₂²	1	2	yes	complemented
43	#88193	C₂²	1	2	yes	complemented
44	#88191	C₂²	1	2	yes	—
45	#88191	C₂²	1	2	yes	—
46	#88191	C₂²	1	2	yes	complemented
47	#88191	C₂²	1	2	yes	complemented
48	#88189	C₂²	1	2	yes	complemented
49	D₄×Dic₁₃	C₂²	1	2	yes	complemented
50	D₄×Dic₁₃	C₂²	1	2	yes	complemented
51	#88184	C₂²	1	2	yes	complemented
52	#88184	C₂²	1	1	yes	characteristic, complemented
53	#88184	C₂²	1	1	yes	characteristic, complemented
54	#88183	C₂²	1	2	yes	complemented
55	#88183	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
57	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
58	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
59	C₂×#6103	C₂²	1	1	yes	characteristic
60	C₂×#6103	C₂²	1	1	yes	characteristic
61	C₂×#6103	C₂²	1	2	yes	complemented
62	C₂×#6103	C₂²	1	2	yes	complemented
63	C₂×#6103	C₂²	1	1	yes	characteristic, complemented
64	C₂×#6103	C₂²	1	2	yes	complemented
65	C₂×#6103	C₂²	1	1	yes	characteristic, complemented
66	C₂×#6103	C₂²	1	2	yes	complemented
67	C₂×#6103	C₂²	1	2	yes	complemented
68	#88180	C₂²	1	1	yes	characteristic, complemented
69	#88178	C₂²	1	1	yes	characteristic, complemented
70	#88178	C₂²	1	1	yes	characteristic, complemented
71	#88152	C₂²	1	2	yes	complemented
72	#88152	C₂²	1	2	yes	complemented
73	#88152	C₂²	1	2	yes	complemented
74	#88151	C₂²	1	2	yes	complemented
75	#88150	C₂²	1	2	yes	complemented
76	#88150	C₂²	1	2	yes	complemented
77	#88149	C₂²	1	2	yes	complemented
78	#88148	C₂²	1	2	yes	complemented
79	#88148	C₂²	1	2	yes	complemented
80	#88148	C₂²	1	2	yes	complemented
81	#88147	C₂²	1	2	yes	complemented
82	#88146	C₂²	1	2	yes	complemented
83	#88140	C₂²	1	2	yes	complemented
84	#88140	C₂²	1	2	yes	complemented
85	#88139	C₂²	1	2	yes	complemented
86	#88139	C₂²	1	2	yes	complemented
87	#88138	C₂²	1	2	yes	complemented
88	#88137	C₂²	1	2	yes	complemented
89	#88136	C₂²	1	2	yes	—
90	#88136	C₂²	1	2	yes	—
91	#88136	C₂²	1	2	yes	complemented
92	#88136	C₂²	1	2	yes	complemented
93	#88135	C₂²	1	2	yes	complemented
94	#88135	C₂²	1	2	yes	complemented
95	#88135	C₂²	1	2	yes	complemented
96	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
97	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
98	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
99	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
100	#88132	C₂²	1	2	yes	complemented
101	#88132	C₂²	1	2	yes	complemented
102	#88131	C₂²	1	2	yes	complemented
103	#88130	C₂²	1	2	yes	complemented
104	#88129	C₂²	1	2	yes	complemented
105	C₄×D₅₂	C₂²	1	2	yes	complemented
106	#88126	C₂²	1	2	yes	complemented
107	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
108	C₂³×D₁₃	—	2	4	no	—
109	C₂³×D₁₃	—	4	2	no	—
110	C₂³×D₁₃	—	4	2	no	—
111	C₂³×D₁₃	C₂³	1	2	yes	—
112	C₂³×D₁₃	C₂³	1	2	yes	—
113	C₂³×D₁₃	C₂³	1	2	yes	—
114	C₂³×D₁₃	C₂³	1	1	yes	characteristic
115	C₂³×D₁₃	C₂³	1	1	yes	characteristic
116	C₁₃×#41	—	4	2	no	—
117	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic, complemented
118	C₂×D₄×C₁₃	C₂³	1	2	yes	—
119	C₂×D₄×C₁₃	C₂³	1	2	yes	—
120	C₂×D₄×C₁₃	C₂³	1	2	yes	—
121	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic, complemented
122	C₂²×C₄×C₁₃	—	4	2	no	—
123	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂³	1	2	yes	complemented
130	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	complemented
137	C₂²×Dic₁₃	—	4	2	no	—
138	C₂²×Dic₁₃	C₂³	1	2	yes	—
139	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
140	C₂²×Dic₁₃	C₂³	1	2	yes	—
141	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
142	C₂²×Dic₁₃	C₂³	1	2	yes	complemented
143	#6129	—	4	4	no	—
144	D₄×D₁₃	—	2	8	no	—
145	D₄×D₁₃	—	4	4	no	—
146	D₄×D₁₃	—	4	4	no	—
147	#6127	—	4	2	no	—
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	1	yes	characteristic, complemented
152	C₂×C₄×D₁₃	C₂³	1	2	yes	—
153	C₂×C₄×D₁₃	C₂³	1	2	yes	—
154	C₂×C₄×D₁₃	C₂³	1	2	yes	—
155	C₂×C₄×D₁₃	C₂³	1	2	yes	complemented
156	C₂×C₄×D₁₃	C₂³	1	2	yes	complemented
157	C₂×Dic₂₆	C₂³	1	2	yes	complemented
158	C₂×Dic₂₆	C₂³	1	1	yes	characteristic, complemented
159	C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
160	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
161	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
162	C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
163	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	complemented
167	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	complemented
168	C₄²×C₁₃	C₂³	1	2	yes	complemented
169	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
170	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
171	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
172	C₂²⋊Dic₁₃	C₂³	1	2	yes	complemented
173	C₂²⋊Dic₁₃	C₂³	1	2	yes	complemented
174	#6103	C₂³	1	2	yes	—
175	#6103	C₂³	1	2	yes	—
176	#6103	C₂³	1	2	yes	—
177	#6103	C₂³	1	2	yes	—
178	#6103	C₂³	1	2	yes	—
179	#6103	C₂³	1	2	yes	—
180	#6103	C₂³	1	2	yes	—
181	#6103	C₂³	1	2	yes	—
182	#6103	C₂³	1	2	yes	—
183	#6103	C₂³	1	2	yes	—
184	#6103	C₂³	1	2	yes	—
185	#6103	C₂³	1	2	yes	—
186	#6103	C₂³	1	2	yes	—
187	#6103	C₂³	1	2	yes	—
188	#6103	C₂³	1	2	yes	complemented
189	#6103	C₂³	1	2	yes	complemented
190	#6103	C₂³	1	2	yes	complemented
191	#6103	C₂³	1	2	yes	complemented
192	C₄⋊Dic₁₃	C₂³	1	2	yes	complemented
193	C₄⋊Dic₁₃	C₂³	1	2	yes	complemented
194	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic, complemented
195	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic, complemented
196	#6101	C₂³	1	2	yes	complemented
197	#6101	C₂³	1	2	yes	complemented
198	#6101	C₂³	1	2	yes	complemented
199	#6101	C₂³	1	2	yes	complemented
200	#6101	C₂³	1	2	yes	complemented
201	#6101	C₂³	1	2	yes	complemented
202	C₄×Dic₁₃	C₂³	1	2	yes	complemented
203	C₄×Dic₁₃	C₂³	1	2	yes	complemented
204	C₄×Dic₁₃	C₂³	1	2	yes	complemented
205	#3490	—	13	1	no	maximal, Sylow
206	C₂³×C₁₃	—	2	2	no	—
207	C₂³×C₁₃	—	2	2	no	—
208	C₂³×C₁₃	—	2	2	no	—
209	C₂³×C₁₃	C₂⁴	1	2	yes	—
210	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
211	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
212	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
213	C₂²×D₁₃	—	2	2	no	—
214	C₂²×D₁₃	—	2	4	no	—
215	C₂²×D₁₃	—	2	4	no	—
216	C₂²×D₁₃	—	2	4	no	—
217	C₂²×D₁₃	—	2	4	no	—
218	C₂²×D₁₃	—	2	4	no	—
219	C₂²×D₁₃	—	4	1	no	—
220	C₂²×D₁₃	—	4	1	no	—
221	C₂²×D₁₃	—	4	2	no	—
222	C₂²×D₁₃	—	4	2	no	—
223	C₂²×D₁₃	—	4	1	no	—
224	C₂²×D₁₃	—	4	1	no	—
225	C₂²×D₁₃	—	4	2	no	—
226	C₂²×D₁₃	—	4	2	no	—
227	C₂²×D₁₃	—	4	16	no	—
228	C₂²×D₁₃	#41	1	4	yes	complemented
229	C₂²×D₁₃	C₂⁴	1	2	yes	—
230	C₂²×D₁₃	C₂⁴	1	2	yes	—
231	C₂²×D₁₃	C₂⁴	1	2	yes	—
232	Q₈×C₁₃	—	4	1	no	—
233	D₄×C₁₃	—	2	4	no	—
234	D₄×C₁₃	—	2	4	no	—
235	D₄×C₁₃	—	2	4	no	—
236	D₄×C₁₃	—	4	1	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	4	1	no	—
240	C₂×C₄×C₁₃	—	4	1	no	—
241	C₂×C₄×C₁₃	—	4	1	no	—
242	C₂×C₄×C₁₃	—	4	1	no	—
243	C₂×C₄×C₁₃	—	4	2	no	—
244	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
246	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂²⋊D₁₃	—	2	4	no	—
252	C₂²⋊D₁₃	—	2	4	no	—
253	C₂²⋊D₁₃	—	2	4	no	—
254	C₂²⋊D₁₃	—	2	4	no	—
255	C₂²⋊D₁₃	—	4	2	no	—
256	C₂²⋊D₁₃	—	4	2	no	—
257	C₂²⋊D₁₃	—	4	2	no	—
258	C₂×Dic₁₃	—	2	4	no	—
259	C₂×Dic₁₃	—	4	2	no	—
260	C₂×Dic₁₃	—	4	1	no	—
261	C₂×Dic₁₃	—	4	2	no	—
262	C₂×Dic₁₃	—	4	1	no	—
263	C₂×Dic₁₃	C₂⁴	1	2	yes	—
264	C₂×Dic₁₃	C₂⁴	1	2	yes	—
265	C₂×Dic₁₃	C₂⁴	1	2	yes	—
266	C₂×Dic₁₃	C₂⁴	1	2	yes	—
267	C₂×Dic₁₃	C₂⁴	1	2	yes	—
268	D₅₂	—	2	4	no	—
269	D₅₂	—	4	2	no	—
270	D₅₂	—	4	2	no	—
271	D₅₂	—	4	1	no	—
272	C₄×D₁₃	—	2	4	no	—
273	C₄×D₁₃	—	4	2	no	—
274	C₄×D₁₃	—	4	2	no	—
275	C₄×D₁₃	—	4	2	no	—
276	C₄×D₁₃	—	4	2	no	—
277	Dic₂₆	—	4	1	no	—
278	Dic₂₆	—	4	2	no	—
279	#551	—	13	2	no	—
280	#551	—	13	2	no	—
281	#551	—	13	2	no	—
282	#551	—	13	2	no	—
283	#546	—	13	2	no	—
284	#546	—	13	2	no	—
285	#546	—	13	2	no	—
286	#546	—	13	2	no	—
287	#543	—	13	1	no	—
288	#538	—	13	1	no	—
289	#538	—	13	1	no	—
290	#538	—	13	2	no	—
291	#534	—	13	1	no	—
292	#525	—	13	1	no	—
293	#525	—	13	2	no	—
294	#525	D₁₃	1	1	yes	characteristic, complemented
295	C₂×#120	—	13	2	no	—
296	#518	—	13	2	no	—
297	C₂²×C₂²⋊C₄	—	13	1	no	—
298	C₂²×C₁₃	—	2	8	no	—
299	C₂²×C₁₃	—	2	1	no	—
300	C₂²×C₁₃	—	2	1	no	—
301	C₂²×C₁₃	—	2	1	no	—
302	C₂²×C₁₃	—	2	1	no	—
303	C₂²×C₁₃	—	2	1	no	—
304	C₂²×C₁₃	—	2	1	no	—
305	C₂²×C₁₃	—	2	2	no	—
306	C₂²×C₁₃	—	2	2	no	—
307	C₂²×C₁₃	—	2	2	no	—
308	C₂²×C₁₃	C₂×#41	1	2	yes	—
309	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
310	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
311	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
312	C₂×D₁₃	—	2	2	no	—
313	C₂×D₁₃	—	2	2	no	—
314	C₂×D₁₃	—	2	2	no	—
315	C₂×D₁₃	—	2	2	no	—
316	C₂×D₁₃	—	2	2	no	—
317	C₂×D₁₃	—	2	2	no	—
318	C₂×D₁₃	—	2	2	no	—
319	C₂×D₁₃	—	2	2	no	—
320	C₂×D₁₃	—	4	4	no	—
321	C₂×D₁₃	—	4	8	no	—
322	C₂×D₁₃	—	4	8	no	—
323	C₂×D₁₃	—	4	4	no	—
324	C₂×D₁₃	—	8	4	no	—
325	C₂×D₁₃	C₂×#41	1	4	yes	—
326	C₄×C₁₃	—	2	2	no	—
327	C₄×C₁₃	—	2	2	no	—
328	C₄×C₁₃	—	2	1	no	—
329	C₄×C₁₃	—	2	1	no	—
330	C₄×C₁₃	—	2	2	no	—
331	C₄×C₁₃	—	2	1	no	—
332	C₄×C₁₃	—	2	1	no	—
333	Dic₁₃	—	2	2	no	—
334	Dic₁₃	—	2	2	no	—
335	Dic₁₃	—	2	2	no	—
336	Dic₁₃	—	2	2	no	—
337	Dic₁₃	—	2	2	no	—
338	C₂⁵	—	13	1	no	—
339	C₂×#41	—	13	2	no	—
340	C₂×#41	—	13	1	no	—
341	C₂×#41	C₂×D₁₃	1	1	yes	characteristic, complemented
342	C₂²×D₄	—	13	2	no	—
343	C₂²×D₄	—	13	2	no	—
344	C₂²×D₄	—	13	2	no	—
345	C₂³×C₄	—	13	1	no	—
346	C₂³×C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
347	#126	—	13	2	no	—
348	#126	—	13	2	no	—
349	#126	—	13	2	no	—
350	#126	—	13	2	no	—
351	#124	—	13	2	no	—
352	#124	—	13	2	no	—
353	#124	—	13	2	no	—
354	#124	—	13	2	no	—
355	#123	—	13	2	no	—
356	#123	—	13	2	no	—
357	#123	—	13	2	no	—
358	#123	—	13	2	no	—
359	#123	—	13	2	no	—
360	#123	—	13	2	no	—
361	#123	—	13	2	no	—
362	#123	—	13	2	no	—
363	#123	—	13	2	no	—
364	#123	C₂×D₁₃	1	2	yes	complemented
365	C₂²⋊Q₈	—	13	2	no	—
366	C₂²⋊Q₈	—	13	1	no	—
367	C₂²⋊Q₈	—	13	1	no	—
368	C₂²⋊Q₈	—	13	2	no	—
369	C₂²⋊Q₈	—	13	2	no	—
370	C₂²⋊Q₈	—	13	2	no	—
371	C₂²⋊Q₈	—	13	2	no	—
372	C₂²⋊Q₈	—	13	2	no	—
373	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
374	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
375	#121	—	13	2	no	—
376	#121	—	13	2	no	—
377	#121	—	13	2	no	—
378	#121	—	13	1	no	—
379	#121	—	13	1	no	—
380	#121	—	13	2	no	—
381	#121	—	13	2	no	—
382	#121	—	13	2	no	—
383	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
384	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
385	#120	—	13	2	no	—
386	#120	—	13	2	no	—
387	#120	—	13	2	no	—
388	#120	—	13	2	no	—
389	#120	—	13	2	no	—
390	#120	—	13	2	no	—
391	#120	—	13	2	no	—
392	#120	—	13	2	no	—
393	#120	—	13	2	no	—
394	#120	C₂×D₁₃	1	2	yes	complemented
395	C₄×D₄	—	13	2	no	—
396	C₄×D₄	—	13	2	no	—
397	C₄×D₄	—	13	2	no	—
398	C₄×D₄	—	13	2	no	—
399	C₄×D₄	—	13	2	no	—
400	C₄×D₄	—	13	2	no	—
401	C₄×D₄	—	13	2	no	—
402	C₄×D₄	—	13	2	no	—
403	C₄×D₄	—	13	2	no	—
404	C₄×D₄	—	13	2	no	—
405	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
406	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
407	#117	—	13	1	no	—
408	#117	—	13	2	no	—
409	#117	—	13	2	no	—
410	#117	—	13	2	no	—
411	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
412	C₂×C₂²⋊C₄	—	13	1	no	—
413	C₂×C₂²⋊C₄	—	13	1	no	—
414	C₂×C₂²⋊C₄	—	13	1	no	—
415	C₂×C₂²⋊C₄	—	13	1	no	—
416	C₂×C₂²⋊C₄	—	13	2	no	—
417	C₂×C₂²⋊C₄	—	13	2	no	—
418	C₂×C₂²⋊C₄	—	13	2	no	—
419	C₂×C₂²⋊C₄	—	13	2	no	—
420	C₂×C₂²⋊C₄	—	13	2	no	—
421	C₂×C₂²⋊C₄	—	13	2	no	—
422	C₂×C₂²⋊C₄	—	13	2	no	—
423	C₂×C₂²⋊C₄	—	13	2	no	—
424	C₂×C₂²⋊C₄	—	13	2	no	—
425	C₂×C₁₃	—	2	2	no	—
426	C₂×C₁₃	—	2	2	no	—
427	C₂×C₁₃	—	2	2	no	—
428	C₂×C₁₃	—	4	2	no	—
429	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
430	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
431	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
432	D₁₃	—	2	4	no	—
433	D₁₃	—	4	2	no	—
434	D₁₃	—	4	2	no	—
435	C₂⁴	—	13	1	no	—
436	C₂⁴	—	13	2	no	—
437	C₂⁴	—	13	2	no	—
438	C₂⁴	—	13	1	no	—
439	C₂⁴	—	13	2	no	—
440	C₂⁴	—	26	4	no	—
441	C₂⁴	—	52	2	no	—
442	C₂⁴	—	52	2	no	—
443	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
444	#41	—	4	2	no	—
445	#41	—	52	2	no	—
446	#41	—	52	4	no	—
447	C₂×Q₈	—	13	1	no	—
448	C₂×Q₈	—	13	2	no	—
449	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic, complemented
450	C₂×D₄	—	13	2	no	—
451	C₂×D₄	—	13	2	no	—
452	C₂×D₄	—	13	2	no	—
453	C₂×D₄	—	13	2	no	—
454	C₂×D₄	—	13	2	no	—
455	C₂×D₄	—	13	2	no	—
456	C₂×D₄	—	13	2	no	—
457	C₂×D₄	—	13	2	no	—
458	C₂×D₄	—	13	1	no	—
459	C₂×D₄	—	13	2	no	—
460	C₂×D₄	—	13	2	no	—
461	C₂×D₄	—	26	8	no	—
462	C₂×D₄	—	52	4	no	—
463	C₂×D₄	—	52	4	no	—
464	C₂×D₄	C₂²×D₁₃	1	2	yes	—
465	C₂×D₄	C₂²×D₁₃	1	2	yes	—
466	C₂×D₄	C₂²×D₁₃	1	2	yes	—
467	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic, complemented
468	C₂²×C₄	—	4	2	no	—
469	C₂²×C₄	—	13	2	no	—
470	C₂²×C₄	—	13	1	no	—
471	C₂²×C₄	—	13	2	no	—
472	C₂²×C₄	—	13	1	no	—
473	C₂²×C₄	—	13	2	no	—
474	C₂²×C₄	—	13	2	no	—
475	C₂²×C₄	—	13	2	no	—
476	C₂²×C₄	—	13	2	no	—
477	C₂²×C₄	—	13	2	no	—
478	C₂²×C₄	—	13	2	no	—
479	C₂²×C₄	—	52	2	no	—
480	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
481	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
482	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
483	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
484	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
485	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
486	C₂²×C₄	C₂²×D₁₃	1	2	yes	complemented
487	C₄⋊C₄	—	13	2	no	—
488	C₄⋊C₄	—	13	2	no	—
489	C₄⋊C₄	—	13	2	no	—
490	C₄⋊C₄	—	13	2	no	—
491	C₄⋊C₄	—	13	1	no	—
492	C₄⋊C₄	—	13	2	no	—
493	C₄⋊C₄	—	13	1	no	—
494	C₄⋊C₄	—	13	2	no	—
495	C₄⋊C₄	—	13	2	no	—
496	C₄⋊C₄	—	13	2	no	—
497	C₄⋊C₄	C₂²×D₁₃	1	2	yes	complemented
498	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic, complemented
499	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic, complemented
500	C₄⋊C₄	C₂²×D₁₃	1	2	yes	complemented
501	C₂²⋊C₄	—	13	2	no	—
502	C₂²⋊C₄	—	13	2	no	—
503	C₂²⋊C₄	—	13	2	no	—
504	C₂²⋊C₄	—	13	2	no	—
505	C₂²⋊C₄	—	13	2	no	—
506	C₂²⋊C₄	—	13	2	no	—
507	C₂²⋊C₄	—	13	2	no	—
508	C₂²⋊C₄	—	13	2	no	—
509	C₂²⋊C₄	—	13	2	no	—
510	C₂²⋊C₄	—	13	2	no	—
511	C₂²⋊C₄	—	13	2	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	2	no	—
517	C₂²⋊C₄	—	13	2	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	—	13	2	no	—
524	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
525	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
526	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
527	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	complemented
528	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	complemented
529	C₄²	—	13	2	no	—
530	C₄²	—	13	2	no	—
531	C₄²	—	13	2	no	—
532	C₄²	C₂²×D₁₃	1	2	yes	complemented
533	C₁₃	#3490	1	1	yes	characteristic, complemented, Sylow
534	C₂³	—	2	2	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	13	2	no	—
538	C₂³	—	13	4	no	—
539	C₂³	—	13	2	no	—
540	C₂³	—	13	2	no	—
541	C₂³	—	26	4	no	—
542	C₂³	—	26	4	no	—
543	C₂³	—	26	4	no	—
544	C₂³	—	26	4	no	—
545	C₂³	—	26	2	no	—
546	C₂³	—	26	4	no	—
547	C₂³	—	52	1	no	—
548	C₂³	—	52	2	no	—
549	C₂³	—	52	1	no	—
550	C₂³	—	52	1	no	—
551	C₂³	—	52	2	no	—
552	C₂³	—	52	1	no	—
553	C₂³	—	52	2	no	—
554	C₂³	—	52	2	no	—
555	C₂³	—	52	16	no	—
556	C₂³	C₂³×D₁₃	1	2	yes	—
557	C₂³	C₂³×D₁₃	1	1	yes	characteristic
558	C₂³	C₂³×D₁₃	1	1	yes	characteristic
559	C₂³	C₂³×D₁₃	1	1	yes	characteristic
560	Q₈	—	4	1	no	—
561	Q₈	—	52	1	no	—
562	Q₈	—	52	2	no	—
563	D₄	—	2	4	no	—
564	D₄	—	2	4	no	—
565	D₄	—	2	4	no	—
566	D₄	—	4	1	no	—
567	D₄	—	26	4	no	—
568	D₄	—	26	4	no	—
569	D₄	—	26	4	no	—
570	D₄	—	26	4	no	—
571	D₄	—	26	4	no	—
572	D₄	—	52	2	no	—
573	D₄	—	52	2	no	—
574	D₄	—	52	1	no	—
575	D₄	—	52	2	no	—
576	D₄	—	52	2	no	—
577	D₄	—	52	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	13	2	no	—
586	C₂×C₄	—	13	2	no	—
587	C₂×C₄	—	13	2	no	—
588	C₂×C₄	—	13	2	no	—
589	C₂×C₄	—	13	2	no	—
590	C₂×C₄	—	26	4	no	—
591	C₂×C₄	—	26	4	no	—
592	C₂×C₄	—	52	2	no	—
593	C₂×C₄	—	52	2	no	—
594	C₂×C₄	—	52	2	no	—
595	C₂×C₄	—	52	2	no	—
596	C₂×C₄	—	52	1	no	—
597	C₂×C₄	—	52	2	no	—
598	C₂×C₄	—	52	1	no	—
599	C₂×C₄	—	52	2	no	—
600	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₁₃	1	2	yes	—
602	C₂×C₄	C₂³×D₁₃	1	2	yes	—
603	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
604	C₂×C₄	C₂³×D₁₃	1	2	yes	—
605	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
607	C₂²	—	2	8	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	1	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	13	4	no	—
618	C₂²	—	26	2	no	—
619	C₂²	—	26	2	no	—
620	C₂²	—	26	2	no	—
621	C₂²	—	26	2	no	—
622	C₂²	—	26	2	no	—
623	C₂²	—	26	2	no	—
624	C₂²	—	26	2	no	—
625	C₂²	—	26	2	no	—
626	C₂²	—	52	4	no	—
627	C₂²	—	52	8	no	—
628	C₂²	—	52	8	no	—
629	C₂²	—	52	4	no	—
630	C₂²	—	104	4	no	—
631	C₂²	#88251	1	2	yes	—
632	C₂²	#41×D₁₃	1	2	yes	—
633	C₂²	#88256	1	2	yes	—
634	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	2	no	—
640	C₄	—	2	2	no	—
641	C₄	—	2	2	no	—
642	C₄	—	26	2	no	—
643	C₄	—	26	2	no	—
644	C₄	—	26	2	no	—
645	C₄	—	26	2	no	—
646	C₄	—	26	2	no	—
647	C₂	—	2	2	no	—
648	C₂	—	2	2	no	—
649	C₂	—	2	2	no	—
650	C₂	—	4	2	no	—
651	C₂	—	26	4	no	—
652	C₂	—	52	2	no	—
653	C₂	—	52	2	no	—
654	C₂	C₂×#88251	1	1	yes	characteristic
655	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
656	C₂	C₂×#88256	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	#3490
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. #11719534	C₂	semidirect
3. #11719496	C₂	semidirect
4. C₂²×#6103	C₂	semidirect
5. #11719363	C₂	semidirect
6. #11719359	C₂	semidirect
7. #11719349	C₂	semidirect
8. #11719342	C₂	semidirect
9. #11719339	C₂	semidirect
10. #11719322	C₂	semidirect
11. #11719315	C₂	semidirect
12. #11719310	C₂	semidirect
13. D₁₃×#120	C₂	semidirect
14. #11719291	C₂	semidirect
15. #11719265	C₂	semidirect
16. #11719261	C₂	semidirect
17. #11719259	C₂	semidirect
18. #11719250	C₂	semidirect
19. #11719232	C₂	semidirect
21. C₂×C₁₃×#41	C₂²	semidirect
22. C₂³×C₄×C₁₃	C₂²	semidirect
23. C₂³×Dic₁₃	C₂²	semidirect
24. C₂×#6129	C₂²	semidirect
26. C₂×D₄×D₁₃	C₂²	semidirect
27. C₂×D₄×D₁₃	C₂²	semidirect
28. C₂×#6127	C₂²	semidirect
29. C₁₃×#123	C₂²	semidirect
30. C₁₃×C₂²⋊Q₈	C₂²	semidirect
31. C₁₃×C₂²⋊Q₈	C₂²	semidirect
32. C₁₃×#121	C₂²	semidirect
33. C₁₃×#121	C₂²	semidirect
34. C₁₃×#120	C₂²	semidirect
35. C₄×D₄×C₁₃	C₂²	semidirect
36. C₄×D₄×C₁₃	C₂²	semidirect
37. C₁₃×#117	C₂²	semidirect
38. #88207	C₂²	semidirect
39. #88201	C₂²	semidirect
40. #88200	C₂²	semidirect
41. #88193	C₂²	semidirect
42. #88193	C₂²	semidirect
43. #88193	C₂²	semidirect
46. #88191	C₂²	semidirect
47. #88191	C₂²	semidirect
48. #88189	C₂²	semidirect
49. D₄×Dic₁₃	C₂²	semidirect
50. D₄×Dic₁₃	C₂²	semidirect
51. #88184	C₂²	semidirect
52. #88184	C₂²	semidirect
53. #88184	C₂²	semidirect
54. #88183	C₂²	semidirect
55. #88183	C₂²	semidirect
56. C₄×C₂²⋊D₁₃	C₂²	semidirect
57. C₄×C₂²⋊D₁₃	C₂²	semidirect
58. C₄×C₂²⋊D₁₃	C₂²	semidirect
61. C₂×#6103	C₂²	semidirect
62. C₂×#6103	C₂²	semidirect
63. C₂×#6103	C₂²	semidirect
64. C₂×#6103	C₂²	semidirect
65. C₂×#6103	C₂²	semidirect
66. C₂×#6103	C₂²	semidirect
67. C₂×#6103	C₂²	semidirect
68. #88180	C₂²	semidirect
69. #88178	C₂²	semidirect
70. #88178	C₂²	semidirect
71. #88152	C₂²	semidirect
72. #88152	C₂²	semidirect
73. #88152	C₂²	semidirect
74. #88151	C₂²	semidirect
75. #88150	C₂²	semidirect
76. #88150	C₂²	semidirect
77. #88149	C₂²	semidirect
78. #88148	C₂²	semidirect
79. #88148	C₂²	semidirect
80. #88148	C₂²	semidirect
81. #88147	C₂²	semidirect
82. #88146	C₂²	semidirect
83. #88140	C₂²	semidirect
84. #88140	C₂²	semidirect
85. #88139	C₂²	semidirect
86. #88139	C₂²	semidirect
87. #88138	C₂²	semidirect
88. #88137	C₂²	semidirect
91. #88136	C₂²	semidirect
92. #88136	C₂²	semidirect
93. #88135	C₂²	semidirect
94. #88135	C₂²	semidirect
95. #88135	C₂²	semidirect
97. C₂²⋊C₄×D₁₃	C₂²	semidirect
98. C₂²⋊C₄×D₁₃	C₂²	semidirect
99. C₂²⋊C₄×D₁₃	C₂²	semidirect
100. #88132	C₂²	semidirect
101. #88132	C₂²	semidirect
102. #88131	C₂²	semidirect
103. #88130	C₂²	semidirect
104. #88129	C₂²	semidirect
105. C₄×D₅₂	C₂²	semidirect
106. #88126	C₂²	semidirect
117. C₂×Q₈×C₁₃	C₂³	semidirect
121. C₂×D₄×C₁₃	C₂³	semidirect
129. C₂²×C₄×C₁₃	C₂³	semidirect
136. C₂×C₂²⋊D₁₃	C₂³	semidirect
142. C₂²×Dic₁₃	C₂³	semidirect
151. C₂×D₅₂	C₂³	semidirect
155. C₂×C₄×D₁₃	C₂³	semidirect
156. C₂×C₄×D₁₃	C₂³	semidirect
157. C₂×Dic₂₆	C₂³	semidirect
158. C₂×Dic₂₆	C₂³	semidirect
159. C₁₃×C₄⋊C₄	C₂³	semidirect
160. C₁₃×C₄⋊C₄	C₂³	semidirect
161. C₁₃×C₄⋊C₄	C₂³	semidirect
162. C₁₃×C₄⋊C₄	C₂³	semidirect
166. C₁₃×C₂²⋊C₄	C₂³	semidirect
167. C₁₃×C₂²⋊C₄	C₂³	semidirect
168. C₄²×C₁₃	C₂³	semidirect
172. C₂²⋊Dic₁₃	C₂³	semidirect
173. C₂²⋊Dic₁₃	C₂³	semidirect
188. #6103	C₂³	semidirect
189. #6103	C₂³	semidirect
190. #6103	C₂³	semidirect
191. #6103	C₂³	semidirect
192. C₄⋊Dic₁₃	C₂³	semidirect
193. C₄⋊Dic₁₃	C₂³	semidirect
194. C₄⋊Dic₁₃	C₂³	semidirect
195. C₄⋊Dic₁₃	C₂³	semidirect
196. #6101	C₂³	semidirect
197. #6101	C₂³	semidirect
198. #6101	C₂³	semidirect
199. #6101	C₂³	semidirect
200. #6101	C₂³	semidirect
201. #6101	C₂³	semidirect
202. C₄×Dic₁₃	C₂³	semidirect
203. C₄×Dic₁₃	C₂³	semidirect
204. C₄×Dic₁₃	C₂³	semidirect
228. C₂²×D₁₃	#41	semidirect
294. #525	D₁₃	semidirect
341. C₂×#41	C₂×D₁₃	semidirect
346. C₂³×C₄	C₂×D₁₃	semidirect
364. #123	C₂×D₁₃	semidirect
373. C₂²⋊Q₈	C₂×D₁₃	semidirect
374. C₂²⋊Q₈	C₂×D₁₃	semidirect
383. #121	C₂×D₁₃	semidirect
384. #121	C₂×D₁₃	semidirect
394. #120	C₂×D₁₃	semidirect
405. C₄×D₄	C₂×D₁₃	semidirect
406. C₄×D₄	C₂×D₁₃	semidirect
411. #117	C₂×D₁₃	semidirect
449. C₂×Q₈	C₂²×D₁₃	semidirect
467. C₂×D₄	C₂²×D₁₃	semidirect
486. C₂²×C₄	C₂²×D₁₃	semidirect
497. C₄⋊C₄	C₂²×D₁₃	semidirect
498. C₄⋊C₄	C₂²×D₁₃	semidirect
499. C₄⋊C₄	C₂²×D₁₃	semidirect
500. C₄⋊C₄	C₂²×D₁₃	semidirect
527. C₂²⋊C₄	C₂²×D₁₃	semidirect
528. C₂²⋊C₄	C₂²×D₁₃	semidirect
532. C₄²	C₂²×D₁₃	semidirect
533. C₁₃	#3490	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
#11719534	2
#11719496	2
C₂²×#6103	2
#11719363	2
#11719359	2
#11719349	2
#11719342	2
#11719339	2
#11719322	2
#11719315	2
#11719310	2
D₁₃×#120	2
#11719291	2
#11719265	2
#11719261	2
#11719259	2
#11719250	2
#11719232	2
#3490	13