Subgroups — #13129339

Order 1664.

930 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719437	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719436	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719417	C₂	1	2	yes	maximal, complemented
5	#11719415	C₂	1	2	yes	maximal, complemented
6	#11719413	C₂	1	2	yes	maximal, complemented
7	#11719412	C₂	1	2	yes	maximal, complemented
8	#11719387	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719386	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719386	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719385	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719351	C₂	1	2	yes	maximal, complemented
13	#11719350	C₂	1	2	yes	maximal, complemented
14	#11719287	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719285	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719284	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719283	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719275	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719274	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719267	C₂	1	1	yes	maximal, characteristic
21	#11719244	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719239	C₂	1	2	yes	maximal, complemented
23	#11719236	C₂	1	2	yes	maximal, complemented
24	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₁₃×#126	C₂²	1	2	yes	—
26	C₁₃×#126	C₂²	1	2	yes	—
27	C₁₃×#124	C₂²	1	1	yes	characteristic
28	C₁₃×#124	C₂²	1	1	yes	characteristic
29	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#117	C₂²	1	2	yes	—
35	#88201	C₂²	1	1	yes	characteristic
36	#88201	C₂²	1	1	yes	characteristic
37	#88200	C₂²	1	1	yes	characteristic
38	#88200	C₂²	1	1	yes	characteristic
39	#88200	C₂²	1	1	yes	characteristic
40	#88200	C₂²	1	2	yes	—
41	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic
42	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic
43	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic
44	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic
45	#88198	C₂²	1	1	yes	characteristic
46	#88194	C₂²	1	1	yes	characteristic
47	#88192	C₂²	1	1	yes	characteristic
48	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
49	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
50	#88184	C₂²	1	2	yes	—
51	#88183	C₂²	1	2	yes	—
52	#88178	C₂²	1	2	yes	—
53	C₂×#6101	C₂²	1	2	yes	—
54	#88152	C₂²	1	2	yes	—
55	#88152	C₂²	1	2	yes	—
56	#88152	C₂²	1	2	yes	—
57	#88152	C₂²	1	2	yes	—
58	#88152	C₂²	1	2	yes	—
59	#88151	C₂²	1	2	yes	—
60	#88151	C₂²	1	1	yes	characteristic
61	#88150	C₂²	1	2	yes	—
62	#88150	C₂²	1	1	yes	characteristic
63	#88150	C₂²	1	1	yes	characteristic
64	#88150	C₂²	1	2	yes	—
65	#88150	C₂²	1	2	yes	—
66	#88149	C₂²	1	1	yes	characteristic
67	#88148	C₂²	1	2	yes	—
68	#88148	C₂²	1	2	yes	—
69	#88146	C₂²	1	2	yes	—
70	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
71	#88144	C₂²	1	1	yes	characteristic
72	#88144	C₂²	1	1	yes	characteristic
73	#88144	C₂²	1	2	yes	—
74	#88144	C₂²	1	2	yes	—
75	#88144	C₂²	1	2	yes	—
76	#88143	C₂²	1	2	yes	—
77	#88143	C₂²	1	2	yes	—
78	#88143	C₂²	1	1	yes	characteristic
79	#88143	C₂²	1	1	yes	characteristic
80	#88142	C₂²	1	1	yes	characteristic
81	#88142	C₂²	1	2	yes	—
82	#88142	C₂²	1	1	yes	characteristic
83	#88140	C₂²	1	2	yes	—
84	#88140	C₂²	1	2	yes	—
85	#88140	C₂²	1	2	yes	—
86	#88139	C₂²	1	2	yes	—
87	#88139	C₂²	1	2	yes	—
88	#88139	C₂²	1	2	yes	—
89	#88138	C₂²	1	2	yes	—
90	#88137	C₂²	1	2	yes	—
91	#88137	C₂²	1	2	yes	—
92	#88137	C₂²	1	2	yes	—
93	#88137	C₂²	1	2	yes	—
94	#88135	C₂²	1	2	yes	—
95	#88135	C₂²	1	2	yes	—
96	#88135	C₂²	1	2	yes	—
97	#88133	C₂²	1	2	yes	—
98	#88133	C₂²	1	2	yes	—
99	#88132	C₂²	1	2	yes	—
100	#88132	C₂²	1	2	yes	—
101	#88132	C₂²	1	2	yes	—
102	#88131	C₂²	1	2	yes	—
103	#88130	C₂²	1	2	yes	—
104	#88129	C₂²	1	2	yes	—
105	C₄×D₅₂	C₂²	1	1	yes	characteristic
106	C₄×D₅₂	C₂²	1	2	yes	—
107	C₄×D₅₂	C₂²	1	1	yes	characteristic
108	C₄×D₅₂	C₂²	1	1	yes	characteristic
109	#88126	C₂²	1	1	yes	characteristic
110	#88126	C₂²	1	2	yes	—
111	#88126	C₂²	1	1	yes	characteristic
112	C₄²×D₁₃	C₂²	1	1	yes	characteristic
113	#88124	C₂²	1	1	yes	characteristic
114	#88124	C₂²	1	2	yes	—
115	#88124	C₂²	1	1	yes	characteristic
116	#88123	C₂²	1	2	yes	—
117	#88123	C₂²	1	1	yes	characteristic
118	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
119	C₄×Dic₂₆	C₂²	1	2	yes	—
120	C₄×Dic₂₆	C₂²	1	2	yes	—
121	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
122	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
123	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
131	C₂²×Dic₁₃	C₂³	1	2	yes	—
132	C₂²×Dic₁₃	C₂³	1	2	yes	—
133	C₂×D₅₂	C₂³	1	1	yes	characteristic
134	C₂×D₅₂	C₂³	1	2	yes	—
135	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₁₃	C₂³	1	2	yes	—
139	C₂×C₄×D₁₃	C₂³	1	2	yes	—
140	C₂×C₄×D₁₃	C₂³	1	2	yes	—
141	C₂×Dic₂₆	C₂³	1	2	yes	—
142	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
143	C₂×Dic₂₆	C₂³	1	2	yes	—
144	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
145	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
146	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₄²×C₁₃	C₂³	1	1	yes	characteristic
160	C₄²×C₁₃	C₂³	1	2	yes	—
161	C₄²×C₁₃	C₂³	1	1	yes	characteristic
162	C₄²×C₁₃	C₂³	1	2	yes	—
163	C₄²×C₁₃	C₂³	1	1	yes	characteristic
164	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
165	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
166	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
167	#6103	C₂³	1	1	yes	characteristic
168	#6103	C₂³	1	2	yes	—
169	#6103	C₂³	1	2	yes	—
170	#6103	C₂³	1	1	yes	characteristic
171	#6103	C₂³	1	1	yes	characteristic
172	#6103	C₂³	1	1	yes	characteristic
173	#6103	C₂³	1	2	yes	—
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	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
182	C₄⋊Dic₁₃	C₂³	1	2	yes	—
183	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
184	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
185	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
186	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
187	C₄⋊Dic₁₃	C₂³	1	2	yes	—
188	C₄⋊Dic₁₃	C₂³	1	2	yes	—
189	C₄⋊Dic₁₃	C₂³	1	2	yes	—
190	C₄⋊Dic₁₃	C₂³	1	2	yes	—
191	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₁₃	C₂³	1	2	yes	—
193	C₄⋊Dic₁₃	C₂³	1	2	yes	—
194	#6101	C₂³	1	1	yes	characteristic
195	#6101	C₂³	1	2	yes	—
196	#6101	C₂³	1	1	yes	characteristic
197	#6101	C₂³	1	2	yes	—
198	#6101	C₂³	1	2	yes	—
199	#6101	C₂³	1	1	yes	characteristic
200	#6101	C₂³	1	1	yes	characteristic
201	#6101	C₂³	1	1	yes	characteristic
202	#6101	C₂³	1	1	yes	characteristic
203	#6101	C₂³	1	2	yes	—
204	#6101	C₂³	1	2	yes	—
205	#6101	C₂³	1	2	yes	—
206	#6101	C₂³	1	2	yes	—
207	#6101	C₂³	1	1	yes	characteristic
208	#6101	C₂³	1	2	yes	—
209	#6101	C₂³	1	1	yes	characteristic
210	#6101	C₂³	1	1	yes	characteristic
211	#6101	C₂³	1	1	yes	characteristic
212	#6101	C₂³	1	2	yes	—
213	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
214	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
215	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
216	C₄×Dic₁₃	C₂³	1	2	yes	—
217	C₄×Dic₁₃	C₂³	1	2	yes	—
218	C₄×Dic₁₃	C₂³	1	2	yes	—
219	C₄×Dic₁₃	C₂³	1	2	yes	—
220	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
222	#3557	—	13	1	no	maximal, Sylow
223	C₂³×C₁₃	C₂⁴	1	2	yes	—
224	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
225	C₂²×D₁₃	C₂⁴	1	2	yes	—
226	Q₈×C₁₃	—	2	2	no	—
227	Q₈×C₁₃	—	2	2	no	—
228	Q₈×C₁₃	—	4	1	no	—
229	D₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	4	2	no	—
231	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
232	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
233	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
237	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂²⋊D₁₃	—	4	2	no	—
242	C₂²⋊D₁₃	—	4	2	no	—
243	C₂²⋊D₁₃	—	4	2	no	—
244	C₂×Dic₁₃	—	4	2	no	—
245	C₂×Dic₁₃	—	4	2	no	—
246	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₃	C₂⁴	1	2	yes	—
252	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₃	C₂⁴	1	2	yes	—
254	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₃	C₂⁴	1	2	yes	—
256	D₅₂	—	2	2	no	—
257	D₅₂	—	4	2	no	—
258	C₄×D₁₃	—	2	2	no	—
259	C₄×D₁₃	—	4	1	no	—
260	C₄×D₁₃	—	4	2	no	—
261	C₄×D₁₃	—	4	2	no	—
262	C₄×D₁₃	—	4	2	no	—
263	C₄×D₁₃	—	4	1	no	—
264	Dic₂₆	—	4	2	no	—
265	Dic₂₆	—	4	1	no	—
266	Dic₂₆	—	4	1	no	—
267	Dic₂₆	—	4	1	no	—
268	Dic₂₆	—	4	2	no	—
269	#563	—	13	2	no	—
270	#563	—	13	2	no	—
271	#559	—	13	1	no	—
272	#559	—	13	1	no	—
273	#557	—	13	1	no	—
274	#557	—	13	1	no	—
275	#556	—	13	1	no	—
276	#556	D₁₃	1	1	yes	characteristic, complemented
277	#554	—	13	1	no	—
278	#554	—	13	1	no	—
279	#552	—	13	2	no	—
280	#552	—	13	2	no	—
281	#542	—	13	2	no	—
282	#542	—	13	1	no	—
283	#542	—	13	1	no	—
284	#542	—	13	2	no	—
285	#541	—	13	1	no	—
286	#540	—	13	1	no	—
287	#539	—	13	2	no	—
288	#539	—	13	2	no	—
289	#533	—	13	1	no	—
290	#529	—	13	1	no	—
291	#529	—	13	1	no	—
292	C₂²×C₁₃	—	2	2	no	—
293	C₂²×C₁₃	—	2	2	no	—
294	C₂²×C₁₃	—	2	2	no	—
295	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
296	C₂×D₁₃	—	2	1	no	—
297	C₂×D₁₃	—	2	2	no	—
298	C₂×D₁₃	—	2	2	no	—
299	C₂×D₁₃	—	2	1	no	—
300	C₂×D₁₃	—	2	2	no	—
301	C₂×D₁₃	—	2	1	no	—
302	C₄×C₁₃	—	2	2	no	—
303	C₄×C₁₃	—	2	2	no	—
304	C₄×C₁₃	—	2	1	no	—
305	C₄×C₁₃	—	2	1	no	—
306	C₄×C₁₃	—	2	1	no	—
307	C₄×C₁₃	—	2	2	no	—
308	C₄×C₁₃	—	2	1	no	—
309	C₄×C₁₃	—	2	1	no	—
310	C₄×C₁₃	—	2	1	no	—
311	C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
312	Dic₁₃	—	2	1	no	—
313	Dic₁₃	—	2	1	no	—
314	Dic₁₃	—	2	1	no	—
315	Dic₁₃	—	2	2	no	—
316	Dic₁₃	—	2	2	no	—
317	Dic₁₃	—	2	2	no	—
318	Dic₁₃	—	2	1	no	—
319	Dic₁₃	—	2	1	no	—
320	Dic₁₃	—	2	1	no	—
321	Dic₁₃	—	2	1	no	—
322	C₄⋊Q₈	—	13	1	no	—
323	C₄⋊Q₈	—	13	1	no	—
324	C₄⋊Q₈	—	13	1	no	—
325	C₄⋊Q₈	—	13	2	no	—
326	C₄⋊Q₈	—	13	1	no	—
327	C₄⋊Q₈	—	13	2	no	—
328	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
329	#127	—	13	1	no	—
330	#126	—	13	2	no	—
331	#126	—	13	2	no	—
332	#126	—	13	2	no	—
333	#126	—	13	2	no	—
334	#126	—	13	2	no	—
335	#126	—	13	2	no	—
336	#126	—	13	2	no	—
337	#126	—	13	2	no	—
338	#126	C₂×D₁₃	1	2	yes	—
339	#126	C₂×D₁₃	1	2	yes	—
340	#125	—	13	1	no	—
341	#125	—	13	1	no	—
342	#125	—	13	1	no	—
343	#125	—	13	2	no	—
344	#125	—	13	2	no	—
345	#125	—	13	2	no	—
346	#125	—	13	1	no	—
347	#125	—	13	2	no	—
348	#125	—	13	2	no	—
349	#125	—	13	1	no	—
350	#125	—	13	2	no	—
351	#125	—	13	1	no	—
352	#124	—	13	1	no	—
353	#124	—	13	1	no	—
354	#124	—	13	2	no	—
355	#124	—	13	2	no	—
356	#124	—	13	2	no	—
357	#124	—	13	2	no	—
358	#124	C₂×D₁₃	1	1	yes	characteristic
359	#124	C₂×D₁₃	1	1	yes	characteristic
360	#123	—	13	2	no	—
361	#123	—	13	2	no	—
362	#123	—	13	2	no	—
363	#123	—	13	2	no	—
364	#123	—	13	2	no	—
365	#123	—	13	2	no	—
366	#123	—	13	2	no	—
367	#123	—	13	2	no	—
368	#123	—	13	2	no	—
369	#123	—	13	2	no	—
370	C₂²⋊Q₈	—	13	1	no	—
371	C₂²⋊Q₈	—	13	1	no	—
372	C₂²⋊Q₈	—	13	1	no	—
373	C₂²⋊Q₈	—	13	2	no	—
374	C₂²⋊Q₈	—	13	2	no	—
375	C₂²⋊Q₈	—	13	1	no	—
376	C₂²⋊Q₈	—	13	1	no	—
377	C₂²⋊Q₈	—	13	1	no	—
378	C₂²⋊Q₈	—	13	2	no	—
379	C₂²⋊Q₈	—	13	2	no	—
380	C₂²⋊Q₈	—	13	2	no	—
381	C₂²⋊Q₈	—	13	2	no	—
382	C₂²⋊Q₈	—	13	2	no	—
383	C₂²⋊Q₈	—	13	2	no	—
384	C₂²⋊Q₈	—	13	2	no	—
385	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
386	#121	—	13	1	no	—
387	#121	—	13	2	no	—
388	#121	—	13	1	no	—
389	#121	—	13	2	no	—
390	C₄×Q₈	—	13	1	no	—
391	C₄×Q₈	—	13	1	no	—
392	C₄×Q₈	—	13	1	no	—
393	C₄×Q₈	—	13	1	no	—
394	C₄×Q₈	—	13	1	no	—
395	C₄×Q₈	—	13	1	no	—
396	C₄×Q₈	—	13	1	no	—
397	C₄×Q₈	—	13	2	no	—
398	C₄×Q₈	—	13	2	no	—
399	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
400	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
401	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
402	C₄×D₄	—	13	1	no	—
403	C₄×D₄	—	13	1	no	—
404	C₄×D₄	—	13	2	no	—
405	C₄×D₄	—	13	2	no	—
406	C₄×D₄	—	13	2	no	—
407	C₄×D₄	—	13	2	no	—
408	C₄×D₄	—	13	1	no	—
409	C₄×D₄	—	13	1	no	—
410	C₄×D₄	—	13	1	no	—
411	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
412	#117	—	13	2	no	—
413	#117	—	13	2	no	—
414	#117	—	13	2	no	—
415	#117	—	13	1	no	—
416	#117	—	13	1	no	—
417	#117	C₂×D₁₃	1	2	yes	—
418	C₂×C₄⋊C₄	—	13	2	no	—
419	C₂×C₄⋊C₄	—	13	2	no	—
420	C₂×C₄²	—	13	1	no	—
421	C₂×C₁₃	—	4	2	no	—
422	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
423	C₂×C₁₃	#585	1	1	yes	characteristic
424	C₂×C₁₃	#585	1	1	yes	characteristic
425	D₁₃	—	4	1	no	—
426	D₁₃	—	4	2	no	—
427	C₂×Q₈	—	13	1	no	—
428	C₂×Q₈	—	13	2	no	—
429	C₂×Q₈	—	13	2	no	—
430	C₂×Q₈	—	13	1	no	—
431	C₂×Q₈	—	13	1	no	—
432	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
433	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
434	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
435	C₂×D₄	—	13	2	no	—
436	C₂×D₄	—	13	2	no	—
437	C₂×D₄	—	13	2	no	—
438	C₂×D₄	—	13	1	no	—
439	C₂×D₄	—	13	2	no	—
440	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
441	C₂²×C₄	—	13	2	no	—
442	C₂²×C₄	—	13	2	no	—
443	C₂²×C₄	—	13	1	no	—
444	C₂²×C₄	—	13	1	no	—
445	C₂²×C₄	—	13	1	no	—
446	C₂²×C₄	—	13	2	no	—
447	C₂²×C₄	—	13	2	no	—
448	C₂²×C₄	—	13	2	no	—
449	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
450	C₄⋊C₄	—	13	1	no	—
451	C₄⋊C₄	—	13	2	no	—
452	C₄⋊C₄	—	13	2	no	—
453	C₄⋊C₄	—	13	2	no	—
454	C₄⋊C₄	—	13	2	no	—
455	C₄⋊C₄	—	13	2	no	—
456	C₄⋊C₄	—	13	2	no	—
457	C₄⋊C₄	—	13	1	no	—
458	C₄⋊C₄	—	13	2	no	—
459	C₄⋊C₄	—	13	2	no	—
460	C₄⋊C₄	—	13	1	no	—
461	C₄⋊C₄	—	13	1	no	—
462	C₄⋊C₄	—	13	1	no	—
463	C₄⋊C₄	—	13	1	no	—
464	C₄⋊C₄	—	13	1	no	—
465	C₄⋊C₄	—	13	1	no	—
466	C₄⋊C₄	—	13	1	no	—
467	C₄⋊C₄	—	13	1	no	—
468	C₄⋊C₄	—	13	1	no	—
469	C₄⋊C₄	—	13	2	no	—
470	C₄⋊C₄	—	13	2	no	—
471	C₄⋊C₄	—	13	1	no	—
472	C₄⋊C₄	—	13	1	no	—
473	C₄⋊C₄	—	13	2	no	—
474	C₄⋊C₄	—	13	2	no	—
475	C₄⋊C₄	—	13	1	no	—
476	C₄⋊C₄	—	13	2	no	—
477	C₄⋊C₄	—	13	1	no	—
478	C₄⋊C₄	—	13	1	no	—
479	C₄⋊C₄	—	13	2	no	—
480	C₄⋊C₄	—	13	2	no	—
481	C₄⋊C₄	—	13	2	no	—
482	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
483	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
484	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
485	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
486	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
487	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
488	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
489	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
490	C₂²⋊C₄	—	13	2	no	—
491	C₂²⋊C₄	—	13	2	no	—
492	C₂²⋊C₄	—	13	2	no	—
493	C₂²⋊C₄	—	13	2	no	—
494	C₂²⋊C₄	—	13	1	no	—
495	C₂²⋊C₄	—	13	1	no	—
496	C₂²⋊C₄	—	13	2	no	—
497	C₂²⋊C₄	—	13	1	no	—
498	C₂²⋊C₄	—	13	1	no	—
499	C₂²⋊C₄	—	13	2	no	—
500	C₂²⋊C₄	—	13	2	no	—
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	C₂²×D₁₃	1	2	yes	—
508	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
509	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
510	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
511	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
512	C₄²	—	13	1	no	—
513	C₄²	—	13	1	no	—
514	C₄²	—	13	1	no	—
515	C₄²	—	13	2	no	—
516	C₄²	—	13	1	no	—
517	C₄²	—	13	1	no	—
518	C₄²	—	13	2	no	—
519	C₄²	—	13	2	no	—
520	C₄²	—	13	2	no	—
521	C₄²	C₂²×D₁₃	1	1	yes	characteristic
522	C₄²	C₂²×D₁₃	1	2	yes	—
523	C₄²	C₂²×D₁₃	1	1	yes	characteristic
524	C₄²	C₂²×D₁₃	1	1	yes	characteristic
525	C₄²	C₂²×D₁₃	1	2	yes	—
526	C₁₃	#3557	1	1	yes	characteristic, complemented, Sylow
527	C₂³	—	13	1	no	—
528	C₂³	—	13	2	no	—
529	C₂³	C₂³×D₁₃	1	2	yes	—
530	Q₈	—	2	2	no	—
531	Q₈	—	2	2	no	—
532	Q₈	—	4	1	no	—
533	Q₈	—	52	2	no	—
534	Q₈	—	52	1	no	—
535	Q₈	—	52	1	no	—
536	Q₈	—	52	2	no	—
537	Q₈	—	52	1	no	—
538	D₄	—	2	2	no	—
539	D₄	—	26	2	no	—
540	D₄	—	52	2	no	—
541	D₄	—	52	2	no	—
542	D₄	—	52	2	no	—
543	D₄	—	52	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	13	1	no	—
546	C₂×C₄	—	13	1	no	—
547	C₂×C₄	—	13	1	no	—
548	C₂×C₄	—	13	1	no	—
549	C₂×C₄	—	13	1	no	—
550	C₂×C₄	—	13	1	no	—
551	C₂×C₄	—	13	2	no	—
552	C₂×C₄	—	13	2	no	—
553	C₂×C₄	—	13	1	no	—
554	C₂×C₄	—	13	2	no	—
555	C₂×C₄	—	26	2	no	—
556	C₂×C₄	—	52	2	no	—
557	C₂×C₄	—	52	1	no	—
558	C₂×C₄	—	52	2	no	—
559	C₂×C₄	—	52	1	no	—
560	C₂×C₄	—	52	2	no	—
561	C₂×C₄	—	52	2	no	—
562	C₂×C₄	—	52	2	no	—
563	C₂×C₄	C₂³×D₁₃	1	2	yes	—
564	C₂×C₄	C₂³×D₁₃	1	2	yes	—
565	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
566	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
567	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
568	C₂×C₄	C₂³×D₁₃	1	2	yes	—
569	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
572	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	26	1	no	—
577	C₂²	—	26	2	no	—
578	C₂²	—	26	1	no	—
579	C₂²	—	26	2	no	—
580	C₂²	—	26	2	no	—
581	C₂²	—	26	1	no	—
582	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
583	C₄	—	2	2	no	—
584	C₄	—	2	2	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	26	1	no	—
593	C₄	—	26	1	no	—
594	C₄	—	26	2	no	—
595	C₄	—	26	1	no	—
596	C₄	—	26	1	no	—
597	C₄	—	26	2	no	—
598	C₄	—	26	1	no	—
599	C₄	—	26	2	no	—
600	C₄	—	26	1	no	—
601	C₄	—	26	1	no	—
602	C₄	#88257	1	2	yes	—
603	C₂	—	4	2	no	—
604	C₂	—	52	1	no	—
605	C₂	—	52	2	no	—
606	C₂	C₂×#88257	1	1	yes	characteristic
607	C₂	#11719648	1	1	yes	characteristic
608	C₂	#11719652	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#556	C₂
prime radical	#11719267	C₂
hypercenter	#556	D₁₃
hypocenter	C₁₃	#3557
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. C₁₃×#556	C₂	semidirect
2. #11719437	C₂	semidirect
3. #11719436	C₂	semidirect
4. #11719417	C₂	semidirect
5. #11719415	C₂	semidirect
6. #11719413	C₂	semidirect
7. #11719412	C₂	semidirect
8. #11719387	C₂	semidirect
9. #11719386	C₂	semidirect
10. #11719386	C₂	semidirect
11. #11719385	C₂	semidirect
12. #11719351	C₂	semidirect
13. #11719350	C₂	semidirect
14. #11719287	C₂	semidirect
15. #11719285	C₂	semidirect
16. #11719284	C₂	semidirect
17. #11719283	C₂	semidirect
18. #11719275	C₂	semidirect
19. #11719274	C₂	semidirect
21. #11719244	C₂	semidirect
22. #11719239	C₂	semidirect
23. #11719236	C₂	semidirect
276. #556	D₁₃	semidirect
526. C₁₃	#3557	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#556	2
#11719437	2
#11719436	2
#11719417	2
#11719415	2
#11719413	2
#11719412	2
#11719387	2
#11719386	2
#11719385	2
#11719351	2
#11719350	2
#11719287	2
#11719285	2
#11719284	2
#11719283	2
#11719275	2
#11719274	2
#11719267	2
#11719244	2
#11719239	2
#11719236	2
#3557	13