Subgroups — #13128530

Order 1664.

1052 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#539	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719413	C₂	1	2	yes	maximal, complemented
3	#11719410	C₂	1	2	yes	maximal, complemented
4	#11719399	C₂	1	2	yes	maximal, complemented
5	#11719398	C₂	1	2	yes	maximal, complemented
6	#11719370	C₂	1	2	yes	maximal, complemented
7	#11719364	C₂	1	2	yes	maximal, complemented
8	#11719363	C₂	1	2	yes	maximal, complemented
9	D₁₃×#123	C₂	1	2	yes	maximal, complemented
10	#11719344	C₂	1	2	yes	maximal, complemented
11	#11719342	C₂	1	2	yes	maximal, complemented
12	#11719339	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719329	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719310	C₂	1	1	yes	maximal, characteristic
15	#11719305	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719250	C₂	1	2	yes	maximal, complemented
17	#11719243	C₂	1	2	yes	maximal, complemented
18	#11719220	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#88146	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×D₄×D₁₃	C₂²	1	2	yes	—
21	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#126	C₂²	1	2	yes	complemented
23	C₁₃×#125	C₂²	1	2	yes	complemented
24	C₁₃×#123	C₂²	1	2	yes	complemented
25	C₁₃×#123	C₂²	1	2	yes	complemented
26	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₁₃×#121	C₂²	1	1	yes	characteristic
29	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
30	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	#88201	C₂²	1	1	yes	characteristic, complemented
32	#88200	C₂²	1	2	yes	complemented
33	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
34	#88193	C₂²	1	2	yes	—
35	#88191	C₂²	1	2	yes	—
36	#88190	C₂²	1	1	yes	characteristic, complemented
37	#88189	C₂²	1	2	yes	complemented
38	D₄×Dic₁₃	C₂²	1	2	yes	complemented
39	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
40	#88184	C₂²	1	1	yes	characteristic
41	#88183	C₂²	1	2	yes	complemented
42	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
43	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
44	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
45	C₂×#6103	C₂²	1	1	yes	characteristic
46	C₂×#6103	C₂²	1	1	yes	characteristic
47	C₂×#6103	C₂²	1	2	yes	complemented
48	#88180	C₂²	1	2	yes	complemented
49	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
50	#88178	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
53	#88152	C₂²	1	2	yes	complemented
54	#88152	C₂²	1	2	yes	complemented
55	#88152	C₂²	1	2	yes	complemented
56	#88152	C₂²	1	2	yes	complemented
57	#88151	C₂²	1	2	yes	complemented
58	#88151	C₂²	1	2	yes	complemented
59	#88150	C₂²	1	2	yes	complemented
60	#88150	C₂²	1	2	yes	complemented
61	#88150	C₂²	1	2	yes	complemented
62	#88148	C₂²	1	2	yes	—
63	#88148	C₂²	1	2	yes	—
64	#88148	C₂²	1	2	yes	—
65	#88148	C₂²	1	2	yes	complemented
66	#88147	C₂²	1	2	yes	—
67	#88147	C₂²	1	1	yes	characteristic, complemented
68	#88146	C₂²	1	2	yes	complemented
69	#88146	C₂²	1	2	yes	complemented
70	#88146	C₂²	1	2	yes	complemented
71	#88146	C₂²	1	2	yes	complemented
72	#88146	C₂²	1	2	yes	complemented
73	#88146	C₂²	1	2	yes	complemented
74	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
75	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
76	#88144	C₂²	1	1	yes	characteristic, complemented
77	#88144	C₂²	1	1	yes	characteristic, complemented
78	#88144	C₂²	1	2	yes	complemented
79	#88143	C₂²	1	2	yes	complemented
80	#88143	C₂²	1	2	yes	complemented
81	#88143	C₂²	1	2	yes	complemented
82	#88141	C₂²	1	1	yes	characteristic, complemented
83	#88140	C₂²	1	2	yes	complemented
84	#88140	C₂²	1	2	yes	complemented
85	#88139	C₂²	1	2	yes	complemented
86	#88137	C₂²	1	2	yes	—
87	#88137	C₂²	1	2	yes	—
88	#88137	C₂²	1	2	yes	—
89	#88137	C₂²	1	2	yes	complemented
90	#88136	C₂²	1	2	yes	—
91	#88135	C₂²	1	2	yes	—
92	#88135	C₂²	1	2	yes	complemented
93	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
94	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
96	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
97	#88133	C₂²	1	2	yes	complemented
98	#88133	C₂²	1	2	yes	complemented
99	#88133	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	C₄×D₅₂	C₂²	1	2	yes	—
104	#88126	C₂²	1	2	yes	complemented
105	#88126	C₂²	1	2	yes	complemented
106	C₄×Dic₂₆	C₂²	1	2	yes	complemented
107	C₂³×D₁₃	C₂³	1	2	yes	—
108	C₂³×D₁₃	C₂³	1	1	yes	characteristic
109	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₂×D₄×C₁₃	C₂³	1	2	yes	—
111	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
116	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
119	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
120	C₂²×Dic₁₃	C₂³	1	2	yes	—
121	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
122	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
123	D₄×D₁₃	—	2	8	no	—
124	C₂×D₅₂	C₂³	1	2	yes	—
125	C₂×D₅₂	C₂³	1	1	yes	characteristic
126	C₂×C₄×D₁₃	—	2	4	no	—
127	C₂×C₄×D₁₃	C₂³	1	2	yes	—
128	C₂×C₄×D₁₃	C₂³	1	2	yes	—
129	C₂×C₄×D₁₃	C₂³	1	2	yes	—
130	C₂×C₄×D₁₃	C₂³	1	2	yes	—
131	C₂×C₄×D₁₃	C₂³	1	2	yes	—
132	C₂×C₄×D₁₃	C₂³	1	2	yes	—
133	C₂×C₄×D₁₃	C₂³	1	2	yes	—
134	C₂×Dic₂₆	C₂³	1	2	yes	—
135	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
136	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
137	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₄²×C₁₃	C₂³	1	2	yes	—
150	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
151	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
152	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
153	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
154	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
155	#6103	C₂³	1	2	yes	—
156	#6103	C₂³	1	2	yes	—
157	#6103	C₂³	1	2	yes	—
158	#6103	C₂³	1	2	yes	—
159	#6103	C₂³	1	2	yes	—
160	#6103	C₂³	1	2	yes	—
161	#6103	C₂³	1	2	yes	—
162	#6103	C₂³	1	2	yes	—
163	#6103	C₂³	1	2	yes	—
164	#6103	C₂³	1	2	yes	—
165	#6103	C₂³	1	2	yes	—
166	#6103	C₂³	1	2	yes	—
167	#6103	C₂³	1	2	yes	—
168	#6103	C₂³	1	2	yes	—
169	C₄⋊Dic₁₃	C₂³	1	2	yes	—
170	C₄⋊Dic₁₃	C₂³	1	2	yes	—
171	C₄⋊Dic₁₃	C₂³	1	2	yes	—
172	C₄⋊Dic₁₃	C₂³	1	2	yes	—
173	C₄⋊Dic₁₃	C₂³	1	2	yes	—
174	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
175	C₄⋊Dic₁₃	C₂³	1	2	yes	—
176	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
177	#6101	C₂³	1	2	yes	—
178	#6101	C₂³	1	2	yes	—
179	#6101	C₂³	1	2	yes	—
180	#6101	C₂³	1	2	yes	—
181	#6101	C₂³	1	2	yes	—
182	#6101	C₂³	1	2	yes	—
183	#6101	C₂³	1	2	yes	—
184	#6101	C₂³	1	2	yes	—
185	#6101	C₂³	1	2	yes	—
186	#6101	C₂³	1	2	yes	—
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	1	yes	characteristic
193	C₄×Dic₁₃	C₂³	1	2	yes	—
194	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
195	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
196	#3491	—	13	1	no	maximal, Sylow
197	C₂³×C₁₃	C₂⁴	1	2	yes	—
198	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
199	C₂²×D₁₃	—	2	4	no	—
200	C₂²×D₁₃	—	4	1	no	—
201	C₂²×D₁₃	—	4	1	no	—
202	C₂²×D₁₃	—	4	2	no	—
203	C₂²×D₁₃	—	4	2	no	—
204	C₂²×D₁₃	#41	1	4	yes	—
205	C₂²×D₁₃	C₂⁴	1	2	yes	—
206	C₂²×D₁₃	C₂⁴	1	2	yes	—
207	Q₈×C₁₃	—	4	1	no	—
208	D₄×C₁₃	—	2	4	no	—
209	D₄×C₁₃	—	4	1	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	4	1	no	—
212	C₂×C₄×C₁₃	—	4	1	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
215	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
218	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
219	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
220	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
221	C₂²⋊D₁₃	—	2	4	no	—
222	C₂²⋊D₁₃	—	2	4	no	—
223	C₂²⋊D₁₃	—	4	2	no	—
224	C₂×Dic₁₃	—	2	2	no	—
225	C₂×Dic₁₃	—	4	2	no	—
226	C₂×Dic₁₃	—	4	1	no	—
227	C₂×Dic₁₃	—	4	1	no	—
228	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
229	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
230	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
231	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
232	C₂×Dic₁₃	C₂⁴	1	2	yes	—
233	C₂×Dic₁₃	C₂⁴	1	2	yes	—
234	C₂×Dic₁₃	C₂⁴	1	2	yes	—
235	C₂×Dic₁₃	C₂⁴	1	2	yes	—
236	D₅₂	—	2	4	no	—
237	D₅₂	—	4	1	no	—
238	C₄×D₁₃	—	2	4	no	—
239	C₄×D₁₃	—	2	4	no	—
240	C₄×D₁₃	—	2	4	no	—
241	C₄×D₁₃	—	4	2	no	—
242	C₄×D₁₃	—	4	2	no	—
243	C₄×D₁₃	—	4	2	no	—
244	C₄×D₁₃	—	4	2	no	—
245	Dic₂₆	—	4	1	no	—
246	Dic₂₆	—	4	2	no	—
247	#552	—	13	2	no	—
248	#552	—	13	2	no	—
249	#552	—	13	2	no	—
250	#552	—	13	2	no	—
251	#551	—	13	2	no	—
252	#551	—	13	2	no	—
253	#551	—	13	2	no	—
254	#551	—	13	2	no	—
255	#543	—	13	1	no	—
256	#539	—	13	2	no	—
257	#539	—	13	1	no	—
258	#539	D₁₃	1	1	yes	characteristic, complemented
259	#534	—	13	1	no	—
260	#529	—	13	1	no	—
261	#529	—	13	1	no	—
262	#529	—	13	2	no	—
263	C₂×#123	—	13	2	no	—
264	#518	—	13	2	no	—
265	C₂×#117	—	13	1	no	—
266	C₂²×C₁₃	—	2	1	no	—
267	C₂²×C₁₃	—	2	1	no	—
268	C₂²×C₁₃	—	2	2	no	—
269	C₂²×C₁₃	—	2	2	no	—
270	C₂²×C₁₃	—	2	2	no	—
271	C₂²×C₁₃	C₂×#41	1	2	yes	—
272	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
273	C₂×D₁₃	—	2	2	no	—
274	C₂×D₁₃	—	2	2	no	—
275	C₂×D₁₃	—	2	2	no	—
276	C₂×D₁₃	—	2	2	no	—
277	C₂×D₁₃	—	2	2	no	—
278	C₂×D₁₃	—	4	4	no	—
279	C₂×D₁₃	—	8	4	no	—
280	C₂×D₁₃	C₂×#41	1	4	yes	—
281	C₄×C₁₃	—	2	2	no	—
282	C₄×C₁₃	—	2	2	no	—
283	C₄×C₁₃	—	2	2	no	—
284	C₄×C₁₃	—	2	1	no	—
285	C₄×C₁₃	—	2	2	no	—
286	C₄×C₁₃	—	2	2	no	—
287	C₄×C₁₃	—	2	1	no	—
288	Dic₁₃	—	2	1	no	—
289	Dic₁₃	—	2	1	no	—
290	Dic₁₃	—	2	2	no	—
291	Dic₁₃	—	2	2	no	—
292	Dic₁₃	—	2	2	no	—
293	Dic₁₃	—	2	2	no	—
294	Dic₁₃	—	2	1	no	—
295	Dic₁₃	—	2	1	no	—
296	C₂²×D₄	—	13	2	no	—
297	C₂³×C₄	—	13	1	no	—
298	#126	—	13	2	no	—
299	#126	—	13	2	no	—
300	#126	—	13	2	no	—
301	#126	—	13	2	no	—
302	#126	—	13	2	no	—
303	#126	—	13	2	no	—
304	#126	—	13	2	no	—
305	#126	C₂×D₁₃	1	2	yes	complemented
306	#125	—	13	2	no	—
307	#125	—	13	1	no	—
308	#125	—	13	1	no	—
309	#125	—	13	2	no	—
310	#125	—	13	2	no	—
311	#125	—	13	2	no	—
312	#125	C₂×D₁₃	1	2	yes	complemented
313	#124	—	13	1	no	—
314	#124	—	13	1	no	—
315	#124	—	13	2	no	—
316	#123	—	13	2	no	—
317	#123	—	13	2	no	—
318	#123	—	13	2	no	—
319	#123	—	13	2	no	—
320	#123	—	13	2	no	—
321	#123	—	13	2	no	—
322	#123	—	13	2	no	—
323	#123	—	13	2	no	—
324	#123	—	13	2	no	—
325	#123	—	13	2	no	—
326	#123	—	13	2	no	—
327	#123	—	13	2	no	—
328	#123	C₂×D₁₃	1	2	yes	complemented
329	#123	C₂×D₁₃	1	2	yes	complemented
330	C₂²⋊Q₈	—	13	2	no	—
331	C₂²⋊Q₈	—	13	1	no	—
332	C₂²⋊Q₈	—	13	2	no	—
333	C₂²⋊Q₈	—	13	2	no	—
334	C₂²⋊Q₈	—	13	2	no	—
335	C₂²⋊Q₈	—	13	2	no	—
336	C₂²⋊Q₈	—	13	2	no	—
337	C₂²⋊Q₈	—	13	2	no	—
338	C₂²⋊Q₈	—	13	2	no	—
339	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
340	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
341	#121	—	13	2	no	—
342	#121	—	13	1	no	—
343	#121	C₂×D₁₃	1	1	yes	characteristic
344	#120	—	13	2	no	—
345	#120	—	13	2	no	—
346	C₄×Q₈	—	13	1	no	—
347	C₄×Q₈	—	13	1	no	—
348	C₄×Q₈	—	13	2	no	—
349	C₄×D₄	—	13	2	no	—
350	C₄×D₄	—	13	1	no	—
351	C₄×D₄	—	13	2	no	—
352	C₄×D₄	—	13	2	no	—
353	C₄×D₄	—	13	2	no	—
354	C₄×D₄	—	13	2	no	—
355	C₄×D₄	—	13	1	no	—
356	C₄×D₄	—	13	2	no	—
357	C₄×D₄	—	13	2	no	—
358	C₄×D₄	—	13	2	no	—
359	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
360	#117	—	13	2	no	—
361	#117	—	13	2	no	—
362	#117	—	13	2	no	—
363	#117	—	13	2	no	—
364	#117	—	13	2	no	—
365	#117	—	13	2	no	—
366	#117	—	13	2	no	—
367	#117	—	13	2	no	—
368	#117	—	13	2	no	—
369	#117	—	13	2	no	—
370	C₂×C₄⋊C₄	—	13	1	no	—
371	C₂×C₄⋊C₄	—	13	2	no	—
372	C₂×C₄⋊C₄	—	13	2	no	—
373	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
374	C₂×C₂²⋊C₄	—	13	1	no	—
375	C₂×C₂²⋊C₄	—	13	1	no	—
376	C₂×C₂²⋊C₄	—	13	2	no	—
377	C₂×C₂²⋊C₄	—	13	2	no	—
378	C₂×C₂²⋊C₄	—	13	2	no	—
379	C₂×C₂²⋊C₄	—	13	2	no	—
380	C₂×C₂²⋊C₄	—	13	2	no	—
381	C₂×C₄²	—	13	1	no	—
382	C₂×C₄²	—	13	1	no	—
383	C₂×C₁₃	—	2	2	no	—
384	C₂×C₁₃	—	4	2	no	—
385	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
386	C₂×C₁₃	#585	1	1	yes	characteristic
387	C₂×C₁₃	#585	1	1	yes	characteristic
388	D₁₃	—	2	4	no	—
389	D₁₃	—	4	2	no	—
390	C₂⁴	—	13	1	no	—
391	C₂⁴	—	13	2	no	—
392	C₂×Q₈	—	13	2	no	—
393	C₂×Q₈	—	13	1	no	—
394	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
395	C₂×D₄	—	13	2	no	—
396	C₂×D₄	—	13	2	no	—
397	C₂×D₄	—	13	2	no	—
398	C₂×D₄	—	13	2	no	—
399	C₂×D₄	—	13	1	no	—
400	C₂×D₄	—	26	8	no	—
401	C₂×D₄	C₂²×D₁₃	1	2	yes	—
402	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
403	C₂²×C₄	—	13	1	no	—
404	C₂²×C₄	—	13	1	no	—
405	C₂²×C₄	—	13	1	no	—
406	C₂²×C₄	—	13	2	no	—
407	C₂²×C₄	—	13	2	no	—
408	C₂²×C₄	—	13	2	no	—
409	C₂²×C₄	—	13	2	no	—
410	C₂²×C₄	—	13	2	no	—
411	C₂²×C₄	—	13	2	no	—
412	C₂²×C₄	—	13	2	no	—
413	C₂²×C₄	—	13	2	no	—
414	C₂²×C₄	—	26	4	no	—
415	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
416	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
417	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
418	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
419	C₄⋊C₄	—	13	2	no	—
420	C₄⋊C₄	—	13	2	no	—
421	C₄⋊C₄	—	13	2	no	—
422	C₄⋊C₄	—	13	2	no	—
423	C₄⋊C₄	—	13	2	no	—
424	C₄⋊C₄	—	13	2	no	—
425	C₄⋊C₄	—	13	2	no	—
426	C₄⋊C₄	—	13	2	no	—
427	C₄⋊C₄	—	13	2	no	—
428	C₄⋊C₄	—	13	2	no	—
429	C₄⋊C₄	—	13	2	no	—
430	C₄⋊C₄	—	13	2	no	—
431	C₄⋊C₄	—	13	2	no	—
432	C₄⋊C₄	—	13	2	no	—
433	C₄⋊C₄	—	13	2	no	—
434	C₄⋊C₄	—	13	1	no	—
435	C₄⋊C₄	—	13	2	no	—
436	C₄⋊C₄	—	13	1	no	—
437	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
438	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
439	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
440	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
441	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
442	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
443	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
444	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
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	C₂²⋊C₄	—	13	2	no	—
451	C₂²⋊C₄	—	13	2	no	—
452	C₂²⋊C₄	—	13	2	no	—
453	C₂²⋊C₄	—	13	2	no	—
454	C₂²⋊C₄	—	13	2	no	—
455	C₂²⋊C₄	—	13	2	no	—
456	C₂²⋊C₄	—	13	2	no	—
457	C₂²⋊C₄	—	13	2	no	—
458	C₂²⋊C₄	—	13	2	no	—
459	C₂²⋊C₄	—	13	2	no	—
460	C₂²⋊C₄	—	13	2	no	—
461	C₂²⋊C₄	—	13	2	no	—
462	C₂²⋊C₄	—	13	2	no	—
463	C₂²⋊C₄	—	13	2	no	—
464	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
465	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
466	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
467	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
468	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
469	C₄²	—	13	1	no	—
470	C₄²	—	13	1	no	—
471	C₄²	—	13	2	no	—
472	C₄²	—	13	1	no	—
473	C₄²	—	13	1	no	—
474	C₄²	—	13	2	no	—
475	C₄²	—	13	2	no	—
476	C₄²	—	13	2	no	—
477	C₄²	—	13	2	no	—
478	C₄²	C₂²×D₁₃	1	2	yes	—
479	C₁₃	#3491	1	1	yes	characteristic, complemented, Sylow
480	C₂³	—	13	2	no	—
481	C₂³	—	13	4	no	—
482	C₂³	—	13	2	no	—
483	C₂³	—	26	4	no	—
484	C₂³	—	52	1	no	—
485	C₂³	—	52	1	no	—
486	C₂³	—	52	2	no	—
487	C₂³	—	52	2	no	—
488	C₂³	C₂³×D₁₃	1	2	yes	—
489	C₂³	C₂³×D₁₃	1	1	yes	characteristic
490	Q₈	—	4	1	no	—
491	Q₈	—	52	1	no	—
492	Q₈	—	52	2	no	—
493	D₄	—	2	4	no	—
494	D₄	—	4	1	no	—
495	D₄	—	26	4	no	—
496	D₄	—	26	4	no	—
497	D₄	—	26	4	no	—
498	D₄	—	52	1	no	—
499	D₄	—	52	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	13	1	no	—
505	C₂×C₄	—	13	1	no	—
506	C₂×C₄	—	13	1	no	—
507	C₂×C₄	—	13	1	no	—
508	C₂×C₄	—	13	2	no	—
509	C₂×C₄	—	13	2	no	—
510	C₂×C₄	—	13	2	no	—
511	C₂×C₄	—	13	2	no	—
512	C₂×C₄	—	26	4	no	—
513	C₂×C₄	—	26	4	no	—
514	C₂×C₄	—	26	4	no	—
515	C₂×C₄	—	26	2	no	—
516	C₂×C₄	—	52	2	no	—
517	C₂×C₄	—	52	2	no	—
518	C₂×C₄	—	52	2	no	—
519	C₂×C₄	—	52	2	no	—
520	C₂×C₄	—	52	1	no	—
521	C₂×C₄	—	52	2	no	—
522	C₂×C₄	—	52	1	no	—
523	C₂×C₄	C₂³×D₁₃	1	2	yes	—
524	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
525	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
526	C₂×C₄	C₂³×D₁₃	1	2	yes	—
527	C₂×C₄	C₂³×D₁₃	1	2	yes	—
528	C₂×C₄	C₂³×D₁₃	1	2	yes	—
529	C₂×C₄	C₂³×D₁₃	1	2	yes	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	13	4	no	—
536	C₂²	—	26	2	no	—
537	C₂²	—	26	2	no	—
538	C₂²	—	26	2	no	—
539	C₂²	—	26	2	no	—
540	C₂²	—	26	2	no	—
541	C₂²	—	52	4	no	—
542	C₂²	—	104	4	no	—
543	C₂²	#41×D₁₃	1	2	yes	—
544	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
545	C₄	—	2	2	no	—
546	C₄	—	2	2	no	—
547	C₄	—	2	2	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	2	no	—
552	C₄	—	26	1	no	—
553	C₄	—	26	1	no	—
554	C₄	—	26	2	no	—
555	C₄	—	26	2	no	—
556	C₄	—	26	1	no	—
557	C₄	—	26	1	no	—
558	C₄	—	26	2	no	—
559	C₄	—	26	2	no	—
560	C₂	—	2	2	no	—
561	C₂	—	4	2	no	—
562	C₂	—	26	4	no	—
563	C₂	—	52	2	no	—
564	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
565	C₂	#11719650	1	1	yes	characteristic
566	C₂	#11719652	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#539	C₂
prime radical	#11719310	C₂
hypercenter	#539	D₁₃
hypocenter	C₁₃	#3491
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #539

Complements

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

N	H ≅ G/N	type
1. C₁₃×#539	C₂	semidirect
2. #11719413	C₂	semidirect
3. #11719410	C₂	semidirect
4. #11719399	C₂	semidirect
5. #11719398	C₂	semidirect
6. #11719370	C₂	semidirect
7. #11719364	C₂	semidirect
8. #11719363	C₂	semidirect
9. D₁₃×#123	C₂	semidirect
10. #11719344	C₂	semidirect
11. #11719342	C₂	semidirect
12. #11719339	C₂	semidirect
13. #11719329	C₂	semidirect
15. #11719305	C₂	semidirect
16. #11719250	C₂	semidirect
17. #11719243	C₂	semidirect
18. #11719220	C₂	semidirect
19. C₂×#88146	C₂	semidirect
22. C₁₃×#126	C₂²	semidirect
23. C₁₃×#125	C₂²	semidirect
24. C₁₃×#123	C₂²	semidirect
25. C₁₃×#123	C₂²	semidirect
26. C₁₃×C₂²⋊Q₈	C₂²	semidirect
27. C₁₃×C₂²⋊Q₈	C₂²	semidirect
29. C₄×D₄×C₁₃	C₂²	semidirect
30. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
31. #88201	C₂²	semidirect
32. #88200	C₂²	semidirect
33. Q₈×Dic₁₃	C₂²	semidirect
36. #88190	C₂²	semidirect
37. #88189	C₂²	semidirect
38. D₄×Dic₁₃	C₂²	semidirect
39. D₄×Dic₁₃	C₂²	semidirect
41. #88183	C₂²	semidirect
43. C₄×C₂²⋊D₁₃	C₂²	semidirect
44. C₄×C₂²⋊D₁₃	C₂²	semidirect
47. C₂×#6103	C₂²	semidirect
48. #88180	C₂²	semidirect
49. C₂×C₄⋊Dic₁₃	C₂²	semidirect
50. #88178	C₂²	semidirect
51. C₂×C₄×Dic₁₃	C₂²	semidirect
52. C₂×C₄×Dic₁₃	C₂²	semidirect
53. #88152	C₂²	semidirect
54. #88152	C₂²	semidirect
55. #88152	C₂²	semidirect
56. #88152	C₂²	semidirect
57. #88151	C₂²	semidirect
58. #88151	C₂²	semidirect
59. #88150	C₂²	semidirect
60. #88150	C₂²	semidirect
61. #88150	C₂²	semidirect
65. #88148	C₂²	semidirect
67. #88147	C₂²	semidirect
68. #88146	C₂²	semidirect
69. #88146	C₂²	semidirect
70. #88146	C₂²	semidirect
71. #88146	C₂²	semidirect
72. #88146	C₂²	semidirect
73. #88146	C₂²	semidirect
74. C₄⋊C₄×D₁₃	C₂²	semidirect
75. C₄⋊C₄×D₁₃	C₂²	semidirect
76. #88144	C₂²	semidirect
77. #88144	C₂²	semidirect
78. #88144	C₂²	semidirect
79. #88143	C₂²	semidirect
80. #88143	C₂²	semidirect
81. #88143	C₂²	semidirect
82. #88141	C₂²	semidirect
83. #88140	C₂²	semidirect
84. #88140	C₂²	semidirect
85. #88139	C₂²	semidirect
89. #88137	C₂²	semidirect
92. #88135	C₂²	semidirect
94. C₂²⋊C₄×D₁₃	C₂²	semidirect
95. C₂²⋊C₄×D₁₃	C₂²	semidirect
96. C₂²⋊C₄×D₁₃	C₂²	semidirect
97. #88133	C₂²	semidirect
98. #88133	C₂²	semidirect
99. #88133	C₂²	semidirect
100. #88132	C₂²	semidirect
101. #88132	C₂²	semidirect
102. #88131	C₂²	semidirect
104. #88126	C₂²	semidirect
105. #88126	C₂²	semidirect
106. C₄×Dic₂₆	C₂²	semidirect
258. #539	D₁₃	semidirect
305. #126	C₂×D₁₃	semidirect
312. #125	C₂×D₁₃	semidirect
328. #123	C₂×D₁₃	semidirect
329. #123	C₂×D₁₃	semidirect
339. C₂²⋊Q₈	C₂×D₁₃	semidirect
340. C₂²⋊Q₈	C₂×D₁₃	semidirect
359. C₄×D₄	C₂×D₁₃	semidirect
373. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
479. C₁₃	#3491	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#539	2
#11719413	2
#11719410	2
#11719399	2
#11719398	2
#11719370	2
#11719364	2
#11719363	2
D₁₃×#123	2
#11719344	2
#11719342	2
#11719339	2
#11719329	2
#11719310	2
#11719305	2
#11719250	2
#11719243	2
#11719220	2
C₂×#88146	2
#3491	13