Subgroups — #13129482

Order 1664.

930 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719407	C₂	1	2	yes	maximal, complemented
3	#11719406	C₂	1	2	yes	maximal, complemented
4	#11719394	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719390	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719370	C₂	1	2	yes	maximal, complemented
7	#11719356	C₂	1	2	yes	maximal, complemented
8	#11719326	C₂	1	2	yes	maximal, complemented
9	#11719321	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719319	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719308	C₂	1	2	yes	maximal, complemented
12	#11719308	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719305	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719266	C₂	1	2	yes	maximal, complemented
15	#11719266	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719248	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719247	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719246	C₂	1	2	yes	maximal, complemented
19	#11719243	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719234	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719222	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719218	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719205	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#126	C₂²	1	2	yes	—
25	C₁₃×#125	C₂²	1	1	yes	characteristic
26	C₁₃×#123	C₂²	1	2	yes	—
27	C₁₃×#121	C₂²	1	1	yes	characteristic
28	C₁₃×#121	C₂²	1	1	yes	characteristic
29	C₁₃×#121	C₂²	1	2	yes	—
30	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₄×D₄×C₁₃	C₂²	1	2	yes	—
32	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#117	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	#88193	C₂²	1	1	yes	characteristic
36	#88193	C₂²	1	2	yes	—
37	#88192	C₂²	1	1	yes	characteristic
38	#88192	C₂²	1	2	yes	—
39	#88190	C₂²	1	2	yes	—
40	#88190	C₂²	1	1	yes	characteristic
41	#88190	C₂²	1	2	yes	—
42	#88190	C₂²	1	2	yes	—
43	#88189	C₂²	1	1	yes	characteristic
44	#88189	C₂²	1	2	yes	—
45	#88189	C₂²	1	2	yes	—
46	#88189	C₂²	1	2	yes	—
47	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
48	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
49	D₄×Dic₁₃	C₂²	1	2	yes	—
50	#88183	C₂²	1	2	yes	—
51	#88183	C₂²	1	2	yes	—
52	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
54	#88180	C₂²	1	1	yes	characteristic
55	#88180	C₂²	1	1	yes	characteristic
56	#88180	C₂²	1	2	yes	—
57	#88180	C₂²	1	1	yes	characteristic
58	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
59	#88178	C₂²	1	2	yes	—
60	#88178	C₂²	1	2	yes	—
61	#88178	C₂²	1	1	yes	characteristic
62	#88178	C₂²	1	1	yes	characteristic
63	#88178	C₂²	1	2	yes	—
64	#88178	C₂²	1	2	yes	—
65	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
66	#88152	C₂²	1	2	yes	—
67	#88152	C₂²	1	1	yes	characteristic
68	#88151	C₂²	1	1	yes	characteristic
69	#88151	C₂²	1	2	yes	—
70	#88150	C₂²	1	2	yes	—
71	#88146	C₂²	1	1	yes	characteristic
72	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
73	#88144	C₂²	1	1	yes	characteristic
74	#88144	C₂²	1	1	yes	characteristic
75	#88144	C₂²	1	2	yes	—
76	#88144	C₂²	1	1	yes	characteristic
77	#88144	C₂²	1	1	yes	characteristic
78	#88143	C₂²	1	2	yes	—
79	#88143	C₂²	1	1	yes	characteristic
80	#88143	C₂²	1	2	yes	—
81	#88143	C₂²	1	2	yes	—
82	#88143	C₂²	1	2	yes	—
83	#88142	C₂²	1	1	yes	characteristic
84	#88142	C₂²	1	1	yes	characteristic
85	#88142	C₂²	1	2	yes	—
86	#88142	C₂²	1	1	yes	characteristic
87	#88142	C₂²	1	2	yes	—
88	#88142	C₂²	1	2	yes	—
89	#88141	C₂²	1	1	yes	characteristic
90	#88141	C₂²	1	1	yes	characteristic
91	#88141	C₂²	1	2	yes	—
92	#88141	C₂²	1	2	yes	—
93	#88140	C₂²	1	1	yes	characteristic
94	#88139	C₂²	1	1	yes	characteristic
95	#88139	C₂²	1	2	yes	—
96	#88139	C₂²	1	2	yes	—
97	#88137	C₂²	1	2	yes	—
98	#88135	C₂²	1	2	yes	—
99	#88133	C₂²	1	2	yes	—
100	#88133	C₂²	1	1	yes	characteristic
101	#88133	C₂²	1	2	yes	—
102	#88133	C₂²	1	2	yes	—
103	#88133	C₂²	1	2	yes	—
104	#88133	C₂²	1	2	yes	—
105	#88133	C₂²	1	2	yes	—
106	#88133	C₂²	1	2	yes	—
107	#88132	C₂²	1	2	yes	—
108	#88132	C₂²	1	2	yes	—
109	#88132	C₂²	1	1	yes	characteristic
110	#88132	C₂²	1	2	yes	—
111	#88132	C₂²	1	2	yes	—
112	#88132	C₂²	1	2	yes	—
113	#88131	C₂²	1	2	yes	—
114	#88131	C₂²	1	2	yes	—
115	#88126	C₂²	1	2	yes	—
116	#88126	C₂²	1	1	yes	characteristic
117	#88124	C₂²	1	2	yes	—
118	#88123	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×D₄×C₁₃	C₂³	1	1	yes	characteristic
124	C₂×D₄×C₁₃	C₂³	1	2	yes	—
125	C₂×D₄×C₁₃	C₂³	1	2	yes	—
126	C₂×D₄×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	—
130	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
134	C₂²×Dic₁₃	C₂³	1	2	yes	—
135	C₂²×Dic₁₃	C₂³	1	2	yes	—
136	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
137	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₁₃	C₂³	1	2	yes	—
140	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
141	C₂×Dic₂₆	C₂³	1	2	yes	—
142	C₂×Dic₂₆	C₂³	1	2	yes	—
143	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
144	C₂×Dic₂₆	C₂³	1	2	yes	—
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	1	yes	characteristic
150	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₁₃×C₂²⋊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	1	yes	characteristic
158	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
159	C₄²×C₁₃	C₂³	1	1	yes	characteristic
160	C₄²×C₁₃	C₂³	1	2	yes	—
161	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
162	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
163	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
164	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
165	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
166	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
167	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
168	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
169	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
170	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
171	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
172	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
174	#6103	C₂³	1	1	yes	characteristic
175	#6103	C₂³	1	2	yes	—
176	#6103	C₂³	1	1	yes	characteristic
177	#6103	C₂³	1	1	yes	characteristic
178	#6103	C₂³	1	1	yes	characteristic
179	#6103	C₂³	1	2	yes	—
180	C₄⋊Dic₁₃	C₂³	1	2	yes	—
181	C₄⋊Dic₁₃	C₂³	1	2	yes	—
182	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
183	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
184	C₄⋊Dic₁₃	C₂³	1	2	yes	—
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	1	yes	characteristic
190	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
191	C₄⋊Dic₁₃	C₂³	1	2	yes	—
192	#6101	C₂³	1	1	yes	characteristic
193	#6101	C₂³	1	1	yes	characteristic
194	#6101	C₂³	1	2	yes	—
195	#6101	C₂³	1	2	yes	—
196	#6101	C₂³	1	2	yes	—
197	#6101	C₂³	1	2	yes	—
198	#6101	C₂³	1	2	yes	—
199	#6101	C₂³	1	1	yes	characteristic
200	#6101	C₂³	1	2	yes	—
201	#6101	C₂³	1	2	yes	—
202	#6101	C₂³	1	2	yes	—
203	#6101	C₂³	1	2	yes	—
204	#6101	C₂³	1	1	yes	characteristic
205	#6101	C₂³	1	1	yes	characteristic
206	#6101	C₂³	1	2	yes	—
207	#6101	C₂³	1	2	yes	—
208	#6101	C₂³	1	2	yes	—
209	#6101	C₂³	1	1	yes	characteristic
210	#6101	C₂³	1	2	yes	—
211	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
212	C₄×Dic₁₃	C₂³	1	2	yes	—
213	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
214	C₄×Dic₁₃	C₂³	1	2	yes	—
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	2	yes	—
220	C₄×Dic₁₃	C₂³	1	2	yes	—
221	C₄×Dic₁₃	C₂³	1	2	yes	—
222	#3565	—	13	1	no	maximal, Sylow
223	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
224	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
225	C₂³×C₁₃	C₂⁴	1	2	yes	—
226	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
227	D₄×C₁₃	—	2	2	no	—
228	D₄×C₁₃	—	4	1	no	—
229	D₄×C₁₃	—	4	2	no	—
230	D₄×C₁₃	—	4	2	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	4	2	no	—
234	C₂×C₄×C₁₃	—	4	2	no	—
235	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
240	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
241	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂²⋊D₁₃	—	4	2	no	—
244	C₂²⋊D₁₃	—	4	1	no	—
245	C₂²⋊D₁₃	—	4	1	no	—
246	C₂×Dic₁₃	—	4	1	no	—
247	C₂×Dic₁₃	—	4	1	no	—
248	C₂×Dic₁₃	—	4	2	no	—
249	C₂×Dic₁₃	—	4	2	no	—
250	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₃	C₂⁴	1	2	yes	—
252	C₂×Dic₁₃	C₂⁴	1	2	yes	—
253	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₃	C₂⁴	1	2	yes	—
258	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₃	C₂⁴	1	2	yes	—
261	C₄×D₁₃	—	2	2	no	—
262	C₄×D₁₃	—	4	2	no	—
263	Dic₂₆	—	2	2	no	—
264	Dic₂₆	—	4	2	no	—
265	Dic₂₆	—	4	1	no	—
266	Dic₂₆	—	4	2	no	—
267	Dic₂₆	—	4	2	no	—
268	Dic₂₆	—	4	2	no	—
269	#563	—	13	2	no	—
270	#562	—	13	2	no	—
271	#557	—	13	1	no	—
272	#556	—	13	2	no	—
273	#556	—	13	1	no	—
274	#555	—	13	1	no	—
275	#554	—	13	1	no	—
276	#553	—	13	1	no	—
277	#553	D₁₃	1	1	yes	characteristic, complemented
278	#552	—	13	2	no	—
279	#552	—	13	1	no	—
280	#552	—	13	1	no	—
281	#544	—	13	1	no	—
282	#544	—	13	1	no	—
283	#542	—	13	1	no	—
284	#542	—	13	2	no	—
285	#542	—	13	1	no	—
286	#542	—	13	2	no	—
287	#541	—	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	1	no	—
293	C₂²×C₁₃	—	2	1	no	—
294	C₂²×C₁₃	—	2	2	no	—
295	C₂²×C₁₃	—	2	2	no	—
296	C₂²×C₁₃	—	2	1	no	—
297	C₂²×C₁₃	—	2	1	no	—
298	C₂²×C₁₃	—	2	1	no	—
299	C₂²×C₁₃	—	2	2	no	—
300	C₂²×C₁₃	—	2	1	no	—
301	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
302	C₂×D₁₃	—	2	1	no	—
303	C₂×D₁₃	—	2	1	no	—
304	C₂×D₁₃	—	2	1	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	1	no	—
310	C₄×C₁₃	—	2	2	no	—
311	C₄×C₁₃	—	2	2	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	2	no	—
318	Dic₁₃	—	2	1	no	—
319	Dic₁₃	—	2	2	no	—
320	Dic₁₃	—	2	2	no	—
321	Dic₁₃	—	2	1	no	—
322	Dic₁₃	—	2	1	no	—
323	Dic₁₃	—	2	1	no	—
324	C₄⋊Q₈	—	13	1	no	—
325	C₄⋊Q₈	—	13	1	no	—
326	C₄⋊Q₈	—	13	2	no	—
327	C₄⋊Q₈	—	13	2	no	—
328	C₄⋊Q₈	—	13	1	no	—
329	C₄⋊Q₈	—	13	2	no	—
330	C₄⋊Q₈	—	13	1	no	—
331	#126	—	13	1	no	—
332	#126	—	13	2	no	—
333	#126	—	13	2	no	—
334	#126	—	13	1	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	#126	—	13	2	no	—
341	#126	C₂×D₁₃	1	2	yes	—
342	#125	—	13	1	no	—
343	#125	—	13	1	no	—
344	#125	—	13	1	no	—
345	#125	—	13	1	no	—
346	#125	—	13	2	no	—
347	#125	—	13	2	no	—
348	#125	—	13	2	no	—
349	#125	—	13	2	no	—
350	#125	—	13	1	no	—
351	#125	—	13	2	no	—
352	#125	—	13	2	no	—
353	#125	C₂×D₁₃	1	1	yes	characteristic
354	#124	—	13	1	no	—
355	#124	—	13	2	no	—
356	#124	—	13	2	no	—
357	#124	—	13	2	no	—
358	#124	—	13	1	no	—
359	#124	—	13	2	no	—
360	#124	—	13	2	no	—
361	#123	—	13	1	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	1	no	—
368	#123	—	13	2	no	—
369	#123	C₂×D₁₃	1	2	yes	—
370	C₂²⋊Q₈	—	13	1	no	—
371	C₂²⋊Q₈	—	13	2	no	—
372	C₂²⋊Q₈	—	13	1	no	—
373	C₂²⋊Q₈	—	13	2	no	—
374	C₂²⋊Q₈	—	13	2	no	—
375	C₂²⋊Q₈	—	13	2	no	—
376	C₂²⋊Q₈	—	13	2	no	—
377	C₂²⋊Q₈	—	13	1	no	—
378	C₂²⋊Q₈	—	13	2	no	—
379	C₂²⋊Q₈	—	13	1	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	#121	—	13	1	no	—
386	#121	—	13	2	no	—
387	#121	—	13	1	no	—
388	#121	—	13	2	no	—
389	#121	C₂×D₁₃	1	1	yes	characteristic
390	#121	C₂×D₁₃	1	1	yes	characteristic
391	#121	C₂×D₁₃	1	2	yes	—
392	C₄×Q₈	—	13	1	no	—
393	C₄×Q₈	—	13	2	no	—
394	C₄×Q₈	—	13	1	no	—
395	C₄×Q₈	—	13	2	no	—
396	C₄×Q₈	—	13	1	no	—
397	C₄×Q₈	—	13	2	no	—
398	C₄×Q₈	—	13	2	no	—
399	C₄×Q₈	—	13	1	no	—
400	C₄×D₄	—	13	2	no	—
401	C₄×D₄	—	13	1	no	—
402	C₄×D₄	—	13	1	no	—
403	C₄×D₄	—	13	1	no	—
404	C₄×D₄	—	13	1	no	—
405	C₄×D₄	—	13	2	no	—
406	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
407	C₄×D₄	C₂×D₁₃	1	2	yes	—
408	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
409	#117	—	13	1	no	—
410	#117	—	13	1	no	—
411	#117	—	13	2	no	—
412	#117	—	13	1	no	—
413	#117	—	13	1	no	—
414	#117	—	13	2	no	—
415	#117	—	13	2	no	—
416	#117	—	13	1	no	—
417	#117	—	13	2	no	—
418	#117	C₂×D₁₃	1	1	yes	characteristic
419	C₂×C₄⋊C₄	—	13	2	no	—
420	C₂×C₄⋊C₄	—	13	1	no	—
421	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
422	C₂×C₄²	—	13	1	no	—
423	C₂×C₁₃	—	4	1	no	—
424	C₂×C₁₃	—	4	1	no	—
425	C₂×C₁₃	—	4	2	no	—
426	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
427	C₂×C₁₃	#585	1	1	yes	characteristic
428	C₂×C₁₃	#585	1	1	yes	characteristic
429	D₁₃	—	4	1	no	—
430	C₂×Q₈	—	13	1	no	—
431	C₂×Q₈	—	13	1	no	—
432	C₂×Q₈	—	13	2	no	—
433	C₂×Q₈	—	13	2	no	—
434	C₂×Q₈	—	13	2	no	—
435	C₂×Q₈	—	13	2	no	—
436	C₂×D₄	—	13	1	no	—
437	C₂×D₄	—	13	1	no	—
438	C₂×D₄	—	13	2	no	—
439	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
440	C₂×D₄	C₂²×D₁₃	1	2	yes	—
441	C₂×D₄	C₂²×D₁₃	1	2	yes	—
442	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
443	C₂²×C₄	—	13	1	no	—
444	C₂²×C₄	—	13	1	no	—
445	C₂²×C₄	—	13	2	no	—
446	C₂²×C₄	—	13	2	no	—
447	C₂²×C₄	—	13	1	no	—
448	C₂²×C₄	—	13	2	no	—
449	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
450	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
451	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
452	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
453	C₄⋊C₄	—	13	1	no	—
454	C₄⋊C₄	—	13	1	no	—
455	C₄⋊C₄	—	13	2	no	—
456	C₄⋊C₄	—	13	2	no	—
457	C₄⋊C₄	—	13	2	no	—
458	C₄⋊C₄	—	13	2	no	—
459	C₄⋊C₄	—	13	1	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	2	no	—
466	C₄⋊C₄	—	13	1	no	—
467	C₄⋊C₄	—	13	2	no	—
468	C₄⋊C₄	—	13	2	no	—
469	C₄⋊C₄	—	13	1	no	—
470	C₄⋊C₄	—	13	1	no	—
471	C₄⋊C₄	—	13	2	no	—
472	C₄⋊C₄	—	13	2	no	—
473	C₄⋊C₄	—	13	1	no	—
474	C₄⋊C₄	—	13	1	no	—
475	C₄⋊C₄	—	13	1	no	—
476	C₄⋊C₄	—	13	2	no	—
477	C₄⋊C₄	—	13	2	no	—
478	C₄⋊C₄	—	13	2	no	—
479	C₄⋊C₄	—	13	2	no	—
480	C₄⋊C₄	—	13	2	no	—
481	C₄⋊C₄	—	13	2	no	—
482	C₄⋊C₄	—	13	2	no	—
483	C₄⋊C₄	—	13	2	no	—
484	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
485	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
486	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
487	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
488	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
490	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
491	C₂²⋊C₄	—	13	1	no	—
492	C₂²⋊C₄	—	13	1	no	—
493	C₂²⋊C₄	—	13	2	no	—
494	C₂²⋊C₄	—	13	2	no	—
495	C₂²⋊C₄	—	13	2	no	—
496	C₂²⋊C₄	—	13	1	no	—
497	C₂²⋊C₄	—	13	2	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	1	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	1	no	—
510	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
511	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
512	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
513	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
514	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
515	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
516	C₄²	—	13	1	no	—
517	C₄²	—	13	1	no	—
518	C₄²	—	13	1	no	—
519	C₄²	—	13	1	no	—
520	C₄²	—	13	2	no	—
521	C₄²	—	13	2	no	—
522	C₄²	—	13	2	no	—
523	C₄²	—	13	1	no	—
524	C₄²	—	13	2	no	—
525	C₄²	—	13	2	no	—
526	C₄²	—	13	2	no	—
527	C₄²	C₂²×D₁₃	1	2	yes	—
528	C₄²	C₂²×D₁₃	1	1	yes	characteristic
529	C₁₃	#3565	1	1	yes	characteristic, complemented, Sylow
530	C₂³	—	13	1	no	—
531	C₂³	C₂³×D₁₃	1	1	yes	characteristic
532	C₂³	C₂³×D₁₃	1	1	yes	characteristic
533	C₂³	C₂³×D₁₃	1	2	yes	—
534	Q₈	—	26	2	no	—
535	Q₈	—	52	2	no	—
536	Q₈	—	52	2	no	—
537	Q₈	—	52	1	no	—
538	Q₈	—	52	2	no	—
539	Q₈	—	52	2	no	—
540	D₄	—	2	2	no	—
541	D₄	—	4	2	no	—
542	D₄	—	4	1	no	—
543	D₄	—	4	2	no	—
544	D₄	—	52	1	no	—
545	D₄	—	52	1	no	—
546	D₄	—	52	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	13	1	no	—
552	C₂×C₄	—	13	2	no	—
553	C₂×C₄	—	13	1	no	—
554	C₂×C₄	—	13	2	no	—
555	C₂×C₄	—	13	1	no	—
556	C₂×C₄	—	13	1	no	—
557	C₂×C₄	—	13	2	no	—
558	C₂×C₄	—	13	1	no	—
559	C₂×C₄	—	13	1	no	—
560	C₂×C₄	—	13	2	no	—
561	C₂×C₄	—	13	1	no	—
562	C₂×C₄	—	26	2	no	—
563	C₂×C₄	—	52	2	no	—
564	C₂×C₄	—	52	2	no	—
565	C₂×C₄	—	52	1	no	—
566	C₂×C₄	—	52	2	no	—
567	C₂×C₄	—	52	1	no	—
568	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
569	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₁₃	1	2	yes	—
572	C₂×C₄	C₂³×D₁₃	1	2	yes	—
573	C₂×C₄	C₂³×D₁₃	1	2	yes	—
574	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
575	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	2	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	26	1	no	—
586	C₂²	—	26	1	no	—
587	C₂²	—	26	1	no	—
588	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	2	no	—
595	C₄	—	2	2	no	—
596	C₄	—	26	1	no	—
597	C₄	—	26	2	no	—
598	C₄	—	26	1	no	—
599	C₄	—	26	1	no	—
600	C₄	—	26	2	no	—
601	C₄	—	26	1	no	—
602	C₄	—	26	2	no	—
603	C₄	—	26	1	no	—
604	C₄	—	26	1	no	—
605	C₄	—	26	2	no	—
606	C₄	—	26	1	no	—
607	C₄	#88257	1	2	yes	—
608	C₂	—	4	1	no	—
609	C₂	—	4	1	no	—
610	C₂	—	4	2	no	—
611	C₂	—	52	1	no	—
612	C₂	C₂×#88257	1	1	yes	characteristic
613	C₂	#11719648	1	1	yes	characteristic
614	C₂	#11719650	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#553	C₂
hypercenter	#553	D₁₃
hypocenter	C₁₃	#3565
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. C₁₃×#553	C₂	semidirect
2. #11719407	C₂	semidirect
3. #11719406	C₂	semidirect
4. #11719394	C₂	semidirect
5. #11719390	C₂	semidirect
6. #11719370	C₂	semidirect
7. #11719356	C₂	semidirect
8. #11719326	C₂	semidirect
9. #11719321	C₂	semidirect
10. #11719319	C₂	semidirect
11. #11719308	C₂	semidirect
12. #11719308	C₂	semidirect
13. #11719305	C₂	semidirect
14. #11719266	C₂	semidirect
15. #11719266	C₂	semidirect
16. #11719248	C₂	semidirect
17. #11719247	C₂	semidirect
18. #11719246	C₂	semidirect
19. #11719243	C₂	semidirect
20. #11719234	C₂	semidirect
21. #11719222	C₂	semidirect
22. #11719218	C₂	semidirect
23. #11719205	C₂	semidirect
277. #553	D₁₃	semidirect
529. C₁₃	#3565	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#553	2
#11719407	2
#11719406	2
#11719394	2
#11719390	2
#11719370	2
#11719356	2
#11719326	2
#11719321	2
#11719319	2
#11719308	2
#11719305	2
#11719266	2
#11719248	2
#11719247	2
#11719246	2
#11719243	2
#11719234	2
#11719222	2
#11719218	2
#11719205	2
#3565	13