Subgroups — #13129343

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×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719440	C₂	1	2	yes	maximal, complemented
3	#11719438	C₂	1	2	yes	maximal, complemented
4	#11719438	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719435	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719404	C₂	1	2	yes	maximal, complemented
7	#11719403	C₂	1	1	yes	maximal, characteristic
8	#11719398	C₂	1	2	yes	maximal, complemented
9	#11719397	C₂	1	2	yes	maximal, complemented
10	#11719397	C₂	1	2	yes	maximal, complemented
11	#11719396	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719395	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719390	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719290	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719290	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719288	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719287	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719287	C₂	1	2	yes	maximal, complemented
19	#11719286	C₂	1	2	yes	maximal, complemented
20	#11719285	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719283	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719273	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719273	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
26	C₁₃×#125	C₂²	1	1	yes	characteristic
27	C₁₃×#125	C₂²	1	1	yes	characteristic
28	C₁₃×#125	C₂²	1	2	yes	—
29	C₁₃×#125	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×Q₈×C₁₃	C₂²	1	2	yes	—
34	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
35	#88201	C₂²	1	2	yes	—
36	#88201	C₂²	1	2	yes	—
37	#88201	C₂²	1	1	yes	characteristic
38	#88201	C₂²	1	1	yes	characteristic
39	#88200	C₂²	1	2	yes	—
40	#88200	C₂²	1	2	yes	—
41	#88200	C₂²	1	1	yes	characteristic
42	#88200	C₂²	1	2	yes	—
43	#88200	C₂²	1	1	yes	characteristic
44	#88198	C₂²	1	1	yes	characteristic
45	#88198	C₂²	1	1	yes	characteristic
46	#88152	C₂²	1	2	yes	—
47	#88152	C₂²	1	2	yes	—
48	#88152	C₂²	1	2	yes	—
49	#88152	C₂²	1	2	yes	—
50	#88152	C₂²	1	2	yes	—
51	#88152	C₂²	1	2	yes	—
52	#88151	C₂²	1	2	yes	—
53	#88151	C₂²	1	1	yes	characteristic
54	#88151	C₂²	1	2	yes	—
55	#88151	C₂²	1	1	yes	characteristic
56	#88150	C₂²	1	2	yes	—
57	#88150	C₂²	1	2	yes	—
58	#88150	C₂²	1	2	yes	—
59	#88150	C₂²	1	1	yes	characteristic
60	#88150	C₂²	1	1	yes	characteristic
61	#88150	C₂²	1	2	yes	—
62	#88150	C₂²	1	2	yes	—
63	#88149	C₂²	1	1	yes	characteristic
64	#88149	C₂²	1	2	yes	—
65	#88149	C₂²	1	1	yes	characteristic
66	#88149	C₂²	1	2	yes	—
67	#88148	C₂²	1	2	yes	—
68	#88148	C₂²	1	2	yes	—
69	#88148	C₂²	1	2	yes	—
70	#88148	C₂²	1	2	yes	—
71	#88148	C₂²	1	2	yes	—
72	#88148	C₂²	1	2	yes	—
73	#88148	C₂²	1	2	yes	—
74	#88148	C₂²	1	2	yes	—
75	#88148	C₂²	1	2	yes	—
76	#88148	C₂²	1	2	yes	—
77	#88147	C₂²	1	1	yes	characteristic
78	#88147	C₂²	1	1	yes	characteristic
79	#88147	C₂²	1	1	yes	characteristic
80	#88147	C₂²	1	2	yes	—
81	#88147	C₂²	1	1	yes	characteristic
82	#88147	C₂²	1	2	yes	—
83	#88146	C₂²	1	2	yes	—
84	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
85	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
86	#88144	C₂²	1	1	yes	characteristic
87	#88144	C₂²	1	1	yes	characteristic
88	#88143	C₂²	1	2	yes	—
89	#88143	C₂²	1	2	yes	—
90	#88143	C₂²	1	1	yes	characteristic
91	#88143	C₂²	1	1	yes	characteristic
92	#88143	C₂²	1	2	yes	—
93	#88142	C₂²	1	1	yes	characteristic
94	#88142	C₂²	1	1	yes	characteristic
95	#88142	C₂²	1	2	yes	—
96	#88141	C₂²	1	1	yes	characteristic
97	#88141	C₂²	1	2	yes	—
98	#88141	C₂²	1	1	yes	characteristic
99	#88130	C₂²	1	2	yes	—
100	#88130	C₂²	1	2	yes	—
101	#88130	C₂²	1	2	yes	—
102	#88130	C₂²	1	2	yes	—
103	#88129	C₂²	1	1	yes	characteristic
104	#88129	C₂²	1	2	yes	—
105	#88129	C₂²	1	1	yes	characteristic
106	#88129	C₂²	1	2	yes	—
107	#88128	C₂²	1	1	yes	characteristic
108	C₄×D₅₂	C₂²	1	1	yes	characteristic
109	C₄×D₅₂	C₂²	1	2	yes	—
110	C₄×D₅₂	C₂²	1	1	yes	characteristic
111	C₄×D₅₂	C₂²	1	2	yes	—
112	#88126	C₂²	1	2	yes	—
113	#88126	C₂²	1	1	yes	characteristic
114	#88126	C₂²	1	2	yes	—
115	#88126	C₂²	1	1	yes	characteristic
116	#88126	C₂²	1	2	yes	—
117	C₄²×D₁₃	C₂²	1	1	yes	characteristic
118	#88124	C₂²	1	2	yes	—
119	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
120	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
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	2	yes	—
126	C₂×D₅₂	C₂³	1	1	yes	characteristic
127	C₂×D₅₂	C₂³	1	1	yes	characteristic
128	C₂×D₅₂	C₂³	1	2	yes	—
129	C₂×D₅₂	C₂³	1	2	yes	—
130	C₂×D₅₂	C₂³	1	2	yes	—
131	C₂×D₅₂	C₂³	1	2	yes	—
132	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
133	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
134	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
135	C₂×C₄×D₁₃	C₂³	1	2	yes	—
136	C₂×C₄×D₁₃	C₂³	1	2	yes	—
137	C₂×C₄×D₁₃	C₂³	1	2	yes	—
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	1	yes	characteristic
142	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
143	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
144	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
145	C₂×Dic₂₆	C₂³	1	2	yes	—
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	2	yes	—
150	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₄²×C₁₃	C₂³	1	1	yes	characteristic
161	C₄²×C₁₃	C₂³	1	1	yes	characteristic
162	C₄²×C₁₃	C₂³	1	1	yes	characteristic
163	C₄²×C₁₃	C₂³	1	2	yes	—
164	C₄²×C₁₃	C₂³	1	2	yes	—
165	C₄²×C₁₃	C₂³	1	2	yes	—
166	#6103	C₂³	1	2	yes	—
167	#6103	C₂³	1	2	yes	—
168	#6103	C₂³	1	1	yes	characteristic
169	#6103	C₂³	1	2	yes	—
170	#6103	C₂³	1	2	yes	—
171	#6103	C₂³	1	1	yes	characteristic
172	#6103	C₂³	1	1	yes	characteristic
173	#6103	C₂³	1	2	yes	—
174	#6103	C₂³	1	1	yes	characteristic
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	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
189	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
190	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
191	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₁₃	C₂³	1	2	yes	—
193	C₄⋊Dic₁₃	C₂³	1	2	yes	—
194	C₄⋊Dic₁₃	C₂³	1	2	yes	—
195	#6101	C₂³	1	2	yes	—
196	#6101	C₂³	1	1	yes	characteristic
197	#6101	C₂³	1	1	yes	characteristic
198	#6101	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
207	#6101	C₂³	1	2	yes	—
208	#6101	C₂³	1	1	yes	characteristic
209	#6101	C₂³	1	1	yes	characteristic
210	#6101	C₂³	1	2	yes	—
211	#6101	C₂³	1	2	yes	—
212	#6101	C₂³	1	2	yes	—
213	#6101	C₂³	1	2	yes	—
214	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
215	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
216	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
217	C₄×Dic₁₃	C₂³	1	2	yes	—
218	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
219	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
220	C₄×Dic₁₃	C₂³	1	2	yes	—
221	C₄×Dic₁₃	C₂³	1	2	yes	—
222	#3557	—	13	1	no	maximal, Sylow
223	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
224	C₂²×D₁₃	C₂⁴	1	2	yes	—
225	C₂²×D₁₃	C₂⁴	1	2	yes	—
226	Q₈×C₁₃	—	2	2	no	—
227	Q₈×C₁₃	—	4	1	no	—
228	Q₈×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
231	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
236	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
238	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
241	C₂×Dic₁₃	C₂⁴	1	2	yes	—
242	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
243	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
244	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
245	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×Dic₁₃	C₂⁴	1	2	yes	—
249	D₅₂	—	2	2	no	—
250	D₅₂	—	2	2	no	—
251	D₅₂	—	4	2	no	—
252	D₅₂	—	4	2	no	—
253	D₅₂	—	4	2	no	—
254	D₅₂	—	4	2	no	—
255	C₄×D₁₃	—	2	2	no	—
256	C₄×D₁₃	—	4	1	no	—
257	C₄×D₁₃	—	4	2	no	—
258	C₄×D₁₃	—	4	2	no	—
259	C₄×D₁₃	—	4	2	no	—
260	C₄×D₁₃	—	4	2	no	—
261	C₄×D₁₃	—	4	2	no	—
262	C₄×D₁₃	—	4	1	no	—
263	C₄×D₁₃	—	4	2	no	—
264	Dic₂₆	—	2	2	no	—
265	Dic₂₆	—	4	1	no	—
266	Dic₂₆	—	4	2	no	—
267	Dic₂₆	—	4	1	no	—
268	Dic₂₆	—	4	1	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	D₁₃	1	1	yes	characteristic, complemented
275	#556	—	13	1	no	—
276	#556	—	13	1	no	—
277	#554	—	13	1	no	—
278	#554	—	13	1	no	—
279	#552	—	13	2	no	—
280	#552	—	13	2	no	—
281	#542	—	13	1	no	—
282	#542	—	13	2	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	C₂⁵	1	1	yes	characteristic
293	C₂×D₁₃	—	2	1	no	—
294	C₂×D₁₃	—	2	2	no	—
295	C₂×D₁₃	—	2	2	no	—
296	C₂×D₁₃	—	2	2	no	—
297	C₂×D₁₃	—	2	2	no	—
298	C₂×D₁₃	—	2	1	no	—
299	C₂×D₁₃	—	2	2	no	—
300	C₂×D₁₃	—	2	1	no	—
301	C₂×D₁₃	—	2	2	no	—
302	C₄×C₁₃	—	2	2	no	—
303	C₄×C₁₃	—	2	1	no	—
304	C₄×C₁₃	—	2	2	no	—
305	C₄×C₁₃	—	2	1	no	—
306	C₄×C₁₃	—	2	1	no	—
307	C₄×C₁₃	—	2	1	no	—
308	C₄×C₁₃	—	2	2	no	—
309	C₄×C₁₃	—	2	2	no	—
310	C₄×C₁₃	—	2	1	no	—
311	C₄×C₁₃	—	2	1	no	—
312	C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
313	Dic₁₃	—	2	2	no	—
314	Dic₁₃	—	2	1	no	—
315	Dic₁₃	—	2	1	no	—
316	Dic₁₃	—	2	1	no	—
317	Dic₁₃	—	2	1	no	—
318	Dic₁₃	—	2	1	no	—
319	Dic₁₃	—	2	2	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	1	no	—
326	C₄⋊Q₈	—	13	2	no	—
327	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
328	C₄⋊Q₈	C₂×D₁₃	1	2	yes	—
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	—	13	2	no	—
339	#126	—	13	2	no	—
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	C₂×D₁₃	1	1	yes	characteristic
349	#125	C₂×D₁₃	1	2	yes	—
350	#125	C₂×D₁₃	1	2	yes	—
351	#125	C₂×D₁₃	1	1	yes	characteristic
352	#124	—	13	1	no	—
353	#124	—	13	2	no	—
354	#124	—	13	1	no	—
355	#124	—	13	2	no	—
356	#124	—	13	1	no	—
357	#124	—	13	2	no	—
358	#124	—	13	1	no	—
359	#124	—	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	—	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	2	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	1	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	—	13	2	no	—
386	#121	—	13	1	no	—
387	#121	—	13	1	no	—
388	#121	—	13	2	no	—
389	#121	—	13	2	no	—
390	C₄×Q₈	—	13	1	no	—
391	C₄×Q₈	—	13	2	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	C₂×D₁₃	1	1	yes	characteristic
398	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
399	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
400	C₄×Q₈	C₂×D₁₃	1	2	yes	—
401	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
402	C₄×D₄	—	13	2	no	—
403	C₄×D₄	—	13	1	no	—
404	C₄×D₄	—	13	2	no	—
405	C₄×D₄	—	13	1	no	—
406	C₄×D₄	—	13	1	no	—
407	C₄×D₄	—	13	1	no	—
408	C₄×D₄	—	13	2	no	—
409	C₄×D₄	—	13	1	no	—
410	C₄×D₄	—	13	2	no	—
411	C₄×D₄	—	13	1	no	—
412	#117	—	13	2	no	—
413	#117	—	13	2	no	—
414	#117	—	13	1	no	—
415	#117	—	13	1	no	—
416	#117	—	13	2	no	—
417	#117	—	13	2	no	—
418	C₂×C₄⋊C₄	—	13	2	no	—
419	C₂×C₄⋊C₄	—	13	2	no	—
420	C₂×C₄²	—	13	1	no	—
421	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
422	C₂×C₁₃	#585	1	1	yes	characteristic
423	C₂×C₁₃	#585	1	1	yes	characteristic
424	D₁₃	—	4	1	no	—
425	D₁₃	—	4	2	no	—
426	D₁₃	—	4	2	no	—
427	C₂×Q₈	—	13	1	no	—
428	C₂×Q₈	—	13	1	no	—
429	C₂×Q₈	—	13	1	no	—
430	C₂×Q₈	—	13	2	no	—
431	C₂×Q₈	—	13	1	no	—
432	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
433	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
434	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
435	C₂×D₄	—	13	1	no	—
436	C₂×D₄	—	13	1	no	—
437	C₂×D₄	—	13	2	no	—
438	C₂×D₄	—	13	2	no	—
439	C₂×D₄	—	13	2	no	—
440	C₂×D₄	—	13	2	no	—
441	C₂²×C₄	—	13	1	no	—
442	C₂²×C₄	—	13	1	no	—
443	C₂²×C₄	—	13	1	no	—
444	C₂²×C₄	—	13	2	no	—
445	C₂²×C₄	—	13	2	no	—
446	C₂²×C₄	—	13	2	no	—
447	C₂²×C₄	—	13	2	no	—
448	C₂²×C₄	—	13	2	no	—
449	C₂²×C₄	—	13	2	no	—
450	C₄⋊C₄	—	13	1	no	—
451	C₄⋊C₄	—	13	1	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	1	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	2	no	—
463	C₄⋊C₄	—	13	2	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	2	no	—
469	C₄⋊C₄	—	13	1	no	—
470	C₄⋊C₄	—	13	1	no	—
471	C₄⋊C₄	—	13	1	no	—
472	C₄⋊C₄	—	13	2	no	—
473	C₄⋊C₄	—	13	1	no	—
474	C₄⋊C₄	—	13	2	no	—
475	C₄⋊C₄	—	13	2	no	—
476	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
477	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
478	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
479	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
481	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
482	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
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	2	yes	—
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	1	no	—
493	C₂²⋊C₄	—	13	1	no	—
494	C₂²⋊C₄	—	13	2	no	—
495	C₂²⋊C₄	—	13	2	no	—
496	C₂²⋊C₄	—	13	1	no	—
497	C₂²⋊C₄	—	13	1	no	—
498	C₂²⋊C₄	—	13	2	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	—	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	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	C₂²×D₁₃	1	1	yes	characteristic
521	C₄²	C₂²×D₁₃	1	2	yes	—
522	C₄²	C₂²×D₁₃	1	1	yes	characteristic
523	C₄²	C₂²×D₁₃	1	1	yes	characteristic
524	C₄²	C₂²×D₁₃	1	2	yes	—
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	—	13	2	no	—
530	Q₈	—	2	2	no	—
531	Q₈	—	4	2	no	—
532	Q₈	—	4	1	no	—
533	Q₈	—	26	2	no	—
534	Q₈	—	52	1	no	—
535	Q₈	—	52	1	no	—
536	Q₈	—	52	2	no	—
537	Q₈	—	52	1	no	—
538	D₄	—	26	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	—	13	1	no	—
545	C₂×C₄	—	13	2	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	1	no	—
552	C₂×C₄	—	13	2	no	—
553	C₂×C₄	—	26	2	no	—
554	C₂×C₄	—	52	2	no	—
555	C₂×C₄	—	52	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	C₂³×D₁₃	1	1	yes	characteristic
563	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
564	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
565	C₂×C₄	C₂³×D₁₃	1	2	yes	—
566	C₂×C₄	C₂³×D₁₃	1	2	yes	—
567	C₂×C₄	C₂³×D₁₃	1	2	yes	—
568	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
569	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₁₃	1	2	yes	—
571	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
572	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
573	C₂²	—	26	1	no	—
574	C₂²	—	26	2	no	—
575	C₂²	—	26	2	no	—
576	C₂²	—	26	2	no	—
577	C₂²	—	26	1	no	—
578	C₂²	—	26	2	no	—
579	C₂²	—	26	2	no	—
580	C₂²	—	26	1	no	—
581	C₂²	—	26	2	no	—
582	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
583	C₄	—	2	2	no	—
584	C₄	—	2	2	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	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	1	no	—
598	C₄	—	26	1	no	—
599	C₄	—	26	2	no	—
600	C₄	—	26	1	no	—
601	C₄	—	26	1	no	—
602	C₄	#88254	1	2	yes	—
603	C₂	—	52	1	no	—
604	C₂	—	52	2	no	—
605	C₂	—	52	2	no	—
606	C₂	C₂×#88254	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×#557	C₂
prime radical	#11719403	C₂
hypercenter	#557	D₁₃
hypocenter	C₁₃	#3557
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #557

Complements

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

N	H ≅ G/N	type
1. C₁₃×#557	C₂	semidirect
2. #11719440	C₂	semidirect
3. #11719438	C₂	semidirect
4. #11719438	C₂	semidirect
5. #11719435	C₂	semidirect
6. #11719404	C₂	semidirect
8. #11719398	C₂	semidirect
9. #11719397	C₂	semidirect
10. #11719397	C₂	semidirect
11. #11719396	C₂	semidirect
12. #11719395	C₂	semidirect
13. #11719390	C₂	semidirect
14. #11719290	C₂	semidirect
15. #11719290	C₂	semidirect
16. #11719288	C₂	semidirect
17. #11719287	C₂	semidirect
18. #11719287	C₂	semidirect
19. #11719286	C₂	semidirect
20. #11719285	C₂	semidirect
21. #11719283	C₂	semidirect
22. #11719273	C₂	semidirect
23. #11719273	C₂	semidirect
274. #557	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×#557	2
#11719440	2
#11719438	2
#11719435	2
#11719404	2
#11719403	2
#11719398	2
#11719397	2
#11719396	2
#11719395	2
#11719390	2
#11719290	2
#11719288	2
#11719287	2
#11719286	2
#11719285	2
#11719283	2
#11719273	2
#3557	13