Subgroups — #13129420

Order 1664.

1050 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719536	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719529	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719511	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719511	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719424	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719423	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719421	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719418	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719385	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719382	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719380	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719376	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719326	C₂	1	2	yes	maximal, complemented
15	#11719320	C₂	1	2	yes	maximal, complemented
16	#11719307	C₂	1	2	yes	maximal, complemented
17	#11719306	C₂	1	2	yes	maximal, complemented
18	#11719300	C₂	1	2	yes	maximal, complemented
19	#11719298	C₂	1	2	yes	maximal, complemented
20	#11719298	C₂	1	2	yes	maximal, complemented
21	#11719292	C₂	1	2	yes	maximal, complemented
22	#11719233	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719223	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×#6129	C₂²	1	1	yes	characteristic
28	C₂×#6129	C₂²	1	1	yes	characteristic
29	C₂×#6129	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#127	C₂²	1	1	yes	characteristic
31	C₁₃×#127	C₂²	1	1	yes	characteristic
32	C₁₃×#124	C₂²	1	1	yes	characteristic
33	C₁₃×#124	C₂²	1	1	yes	characteristic
34	C₁₃×#121	C₂²	1	2	yes	—
35	C₁₃×#121	C₂²	1	2	yes	—
36	C₁₃×#120	C₂²	1	2	yes	—
37	C₁₃×#120	C₂²	1	2	yes	—
38	C₁₃×#117	C₂²	1	1	yes	characteristic
39	#88207	C₂²	1	2	yes	—
40	#88207	C₂²	1	2	yes	—
41	C₂×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
42	C₂×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
43	#88200	C₂²	1	1	yes	characteristic, complemented
44	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
45	#88198	C₂²	1	1	yes	characteristic, complemented
46	#88194	C₂²	1	2	yes	complemented
47	#88193	C₂²	1	2	yes	—
48	#88193	C₂²	1	2	yes	—
49	#88193	C₂²	1	2	yes	—
50	#88193	C₂²	1	2	yes	complemented
51	#88193	C₂²	1	2	yes	complemented
52	#88193	C₂²	1	2	yes	complemented
53	#88193	C₂²	1	2	yes	complemented
54	#88192	C₂²	1	1	yes	characteristic
55	#88192	C₂²	1	1	yes	characteristic
56	#88192	C₂²	1	2	yes	—
57	#88192	C₂²	1	1	yes	characteristic, complemented
58	#88192	C₂²	1	2	yes	complemented
59	#88192	C₂²	1	2	yes	complemented
60	#88190	C₂²	1	1	yes	characteristic
61	#88190	C₂²	1	1	yes	characteristic
62	#88190	C₂²	1	2	yes	—
63	#88190	C₂²	1	1	yes	characteristic, complemented
64	#88190	C₂²	1	2	yes	complemented
65	#88189	C₂²	1	2	yes	—
66	#88189	C₂²	1	2	yes	—
67	#88189	C₂²	1	2	yes	—
68	#88189	C₂²	1	2	yes	complemented
69	#88189	C₂²	1	2	yes	complemented
70	#88189	C₂²	1	2	yes	complemented
71	#88189	C₂²	1	2	yes	complemented
72	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
73	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
74	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
75	D₄×Dic₁₃	C₂²	1	2	yes	complemented
76	D₄×Dic₁₃	C₂²	1	2	yes	complemented
77	D₄×Dic₁₃	C₂²	1	2	yes	complemented
78	D₄×Dic₁₃	C₂²	1	2	yes	complemented
79	#88183	C₂²	1	2	yes	complemented
80	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
81	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
82	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
83	#88178	C₂²	1	1	yes	characteristic
84	#88178	C₂²	1	1	yes	characteristic
85	#88178	C₂²	1	2	yes	complemented
86	C₂×#6101	C₂²	1	2	yes	complemented
87	#88152	C₂²	1	1	yes	characteristic, complemented
88	#88150	C₂²	1	1	yes	characteristic, complemented
89	#88148	C₂²	1	1	yes	characteristic, complemented
90	#88143	C₂²	1	2	yes	complemented
91	#88143	C₂²	1	2	yes	complemented
92	#88143	C₂²	1	1	yes	characteristic, complemented
93	#88139	C₂²	1	1	yes	characteristic
94	#88139	C₂²	1	2	yes	complemented
95	#88138	C₂²	1	1	yes	characteristic
96	#88138	C₂²	1	2	yes	complemented
97	#88137	C₂²	1	1	yes	characteristic
98	#88137	C₂²	1	2	yes	complemented
99	#88137	C₂²	1	2	yes	complemented
100	#88137	C₂²	1	2	yes	complemented
101	#88135	C₂²	1	2	yes	complemented
102	#88135	C₂²	1	2	yes	complemented
103	#88133	C₂²	1	2	yes	—
104	#88133	C₂²	1	2	yes	—
105	#88133	C₂²	1	1	yes	characteristic
106	#88133	C₂²	1	2	yes	complemented
107	#88133	C₂²	1	2	yes	complemented
108	#88133	C₂²	1	2	yes	complemented
109	#88132	C₂²	1	2	yes	complemented
110	#88132	C₂²	1	2	yes	complemented
111	#88132	C₂²	1	2	yes	complemented
112	#88132	C₂²	1	2	yes	complemented
113	#88131	C₂²	1	2	yes	complemented
114	#88131	C₂²	1	2	yes	complemented
115	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
116	#88126	C₂²	1	1	yes	characteristic, complemented
117	C₄²×D₁₃	C₂²	1	1	yes	characteristic, complemented
118	#88124	C₂²	1	1	yes	characteristic, complemented
119	#88123	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
123	C₂⁴×C₁₃	C₂³	1	2	yes	—
124	C₁₃×#41	—	4	2	no	—
125	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₃	—	4	2	no	—
127	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₁₃	C₂³	1	2	yes	—
131	C₂×D₄×C₁₃	C₂³	1	2	yes	—
132	C₂×D₄×C₁₃	C₂³	1	2	yes	—
133	C₂×D₄×C₁₃	C₂³	1	2	yes	—
134	C₂×D₄×C₁₃	C₂³	1	2	yes	—
135	C₂×D₄×C₁₃	C₂³	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
146	C₂²×Dic₁₃	C₂³	1	2	yes	—
147	C₂²×Dic₁₃	C₂³	1	2	yes	—
148	C₂²×Dic₁₃	C₂³	1	2	yes	—
149	C₂²×Dic₁₃	C₂³	1	2	yes	—
150	C₂²×Dic₁₃	C₂³	1	2	yes	—
151	C₂²×Dic₁₃	C₂³	1	2	yes	—
152	Q₈×D₁₃	—	4	2	no	—
153	#6129	—	4	2	no	—
154	#6129	—	4	2	no	—
155	#6129	—	4	2	no	—
156	C₂×D₅₂	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₁₃	C₂³	1	2	yes	—
162	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
163	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
164	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
165	C₂×Dic₂₆	C₂³	1	2	yes	—
166	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
174	C₄²×C₁₃	C₂³	1	1	yes	characteristic
175	C₄²×C₁₃	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
186	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
188	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
189	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
190	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
191	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
192	#6103	C₂³	1	1	yes	characteristic
193	#6103	C₂³	1	1	yes	characteristic
194	#6103	C₂³	1	1	yes	characteristic
195	#6103	C₂³	1	1	yes	characteristic
196	#6103	C₂³	1	2	yes	—
197	#6103	C₂³	1	1	yes	characteristic
198	#6103	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₁₃	C₂³	1	2	yes	—
203	C₄⋊Dic₁₃	C₂³	1	2	yes	—
204	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₁₃	C₂³	1	2	yes	—
206	#6101	C₂³	1	1	yes	characteristic
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	#6101	C₂³	1	2	yes	—
212	#6101	C₂³	1	1	yes	characteristic
213	#6101	C₂³	1	1	yes	characteristic
214	#6101	C₂³	1	2	yes	—
215	#6101	C₂³	1	2	yes	—
216	#6101	C₂³	1	2	yes	—
217	#6101	C₂³	1	2	yes	—
218	#6101	C₂³	1	2	yes	—
219	#6101	C₂³	1	1	yes	characteristic
220	#6101	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
222	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₃	C₂³	1	2	yes	—
224	C₄×Dic₁₃	C₂³	1	2	yes	—
225	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
226	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₃	C₂³	1	2	yes	—
228	#3562	—	13	1	no	maximal, Sylow
229	C₂³×C₁₃	—	4	2	no	—
230	C₂³×C₁₃	—	4	2	no	—
231	C₂³×C₁₃	—	4	2	no	—
232	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂³×C₁₃	C₂⁴	1	2	yes	—
234	C₂³×C₁₃	C₂⁴	1	2	yes	—
235	C₂³×C₁₃	C₂⁴	1	2	yes	—
236	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
237	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
238	Q₈×C₁₃	—	2	2	no	—
239	D₄×C₁₃	—	2	2	no	—
240	D₄×C₁₃	—	2	2	no	—
241	D₄×C₁₃	—	2	2	no	—
242	D₄×C₁₃	—	4	2	no	—
243	D₄×C₁₃	—	4	2	no	—
244	D₄×C₁₃	—	4	2	no	—
245	D₄×C₁₃	—	4	2	no	—
246	D₄×C₁₃	—	4	2	no	—
247	D₄×C₁₃	—	4	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	4	2	no	—
250	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂²⋊D₁₃	—	4	2	no	—
258	C₂²⋊D₁₃	—	4	2	no	—
259	C₂²⋊D₁₃	—	4	2	no	—
260	C₂²⋊D₁₃	—	4	1	no	—
261	C₂²⋊D₁₃	—	4	1	no	—
262	C₂²⋊D₁₃	—	4	2	no	—
263	C₂²⋊D₁₃	—	4	2	no	—
264	C₂²⋊D₁₃	—	4	2	no	—
265	C₂×Dic₁₃	—	4	2	no	—
266	C₂×Dic₁₃	—	4	2	no	—
267	C₂×Dic₁₃	—	4	2	no	—
268	C₂×Dic₁₃	—	4	2	no	—
269	C₂×Dic₁₃	—	4	2	no	—
270	C₂×Dic₁₃	—	4	2	no	—
271	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₃	C₂⁴	1	2	yes	—
273	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₁₃	C₂⁴	1	2	yes	—
277	C₂×Dic₁₃	C₂⁴	1	2	yes	—
278	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₁₃	C₂⁴	1	2	yes	—
280	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
281	D₅₂	—	4	1	no	—
282	C₄×D₁₃	—	2	2	no	—
283	C₄×D₁₃	—	2	2	no	—
284	C₄×D₁₃	—	4	1	no	—
285	C₄×D₁₃	—	4	1	no	—
286	C₄×D₁₃	—	4	2	no	—
287	Dic₂₆	—	2	2	no	—
288	Dic₂₆	—	2	2	no	—
289	Dic₂₆	—	4	1	no	—
290	Dic₂₆	—	4	2	no	—
291	#562	—	13	2	no	—
292	#560	—	13	2	no	—
293	#559	—	13	1	no	—
294	#556	—	13	1	no	—
295	#553	—	13	2	no	—
296	#551	—	13	2	no	—
297	#550	—	13	1	no	—
298	#548	—	13	1	no	—
299	#548	—	13	1	no	—
300	#547	—	13	1	no	—
301	#546	—	13	1	no	—
302	#546	—	13	1	no	—
303	#541	—	13	1	no	—
304	#540	—	13	1	no	—
305	#540	—	13	2	no	—
306	#539	—	13	2	no	—
307	#538	—	13	2	no	—
308	#538	—	13	2	no	—
309	#536	—	13	1	no	—
310	#535	D₁₃	1	1	yes	characteristic, complemented
311	#532	—	13	1	no	—
312	#529	—	13	1	no	—
313	#529	—	13	1	no	—
314	C₂²×C₁₃	—	2	2	no	—
315	C₂²×C₁₃	—	2	2	no	—
316	C₂²×C₁₃	—	2	2	no	—
317	C₂²×C₁₃	—	2	1	no	—
318	C₂²×C₁₃	—	2	2	no	—
319	C₂²×C₁₃	—	2	2	no	—
320	C₂²×C₁₃	—	2	2	no	—
321	C₂²×C₁₃	—	2	2	no	—
322	C₂²×C₁₃	—	2	2	no	—
323	C₂²×C₁₃	—	2	2	no	—
324	C₂²×C₁₃	—	2	1	no	—
325	C₂²×C₁₃	—	2	1	no	—
326	C₂²×C₁₃	—	8	4	no	—
327	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
328	C₂×D₁₃	—	2	1	no	—
329	C₂×D₁₃	—	2	1	no	—
330	C₂×D₁₃	—	2	1	no	—
331	C₂×D₁₃	—	2	1	no	—
332	C₂×D₁₃	—	2	1	no	—
333	C₂×D₁₃	—	2	1	no	—
334	C₄×C₁₃	—	2	2	no	—
335	C₄×C₁₃	—	2	1	no	—
336	C₄×C₁₃	—	2	1	no	—
337	C₄×C₁₃	—	2	1	no	—
338	C₄×C₁₃	—	2	1	no	—
339	C₄×C₁₃	—	2	1	no	—
340	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
341	Dic₁₃	—	2	2	no	—
342	Dic₁₃	—	2	2	no	—
343	Dic₁₃	—	2	1	no	—
344	Dic₁₃	—	2	1	no	—
345	Dic₁₃	—	2	1	no	—
346	Dic₁₃	—	2	1	no	—
347	Dic₁₃	—	2	1	no	—
348	Dic₁₃	—	2	2	no	—
349	Dic₁₃	—	2	1	no	—
350	Dic₁₃	—	2	2	no	—
351	C₂×#41	—	13	1	no	—
352	C₂×#41	—	13	1	no	—
353	C₂×#41	—	13	1	no	—
354	C₂×#41	C₂×D₁₃	1	1	yes	characteristic
355	C₂²×Q₈	—	13	1	no	—
356	C₂²×D₄	C₂×D₁₃	1	1	yes	characteristic
357	C₄⋊Q₈	—	13	1	no	—
358	C₄⋊Q₈	—	13	1	no	—
359	#127	—	13	2	no	—
360	#127	C₂×D₁₃	1	1	yes	characteristic
361	#127	C₂×D₁₃	1	1	yes	characteristic
362	#126	—	13	1	no	—
363	#126	—	13	2	no	—
364	#126	—	13	1	no	—
365	#126	—	13	2	no	—
366	#126	—	13	2	no	—
367	#126	—	13	2	no	—
368	#126	—	13	2	no	—
369	#125	—	13	1	no	—
370	#125	—	13	2	no	—
371	#125	—	13	2	no	—
372	#125	—	13	1	no	—
373	#124	—	13	1	no	—
374	#124	—	13	1	no	—
375	#124	—	13	1	no	—
376	#124	—	13	2	no	—
377	#124	—	13	2	no	—
378	#124	—	13	1	no	—
379	#124	—	13	2	no	—
380	#124	C₂×D₁₃	1	1	yes	characteristic
381	#124	C₂×D₁₃	1	1	yes	characteristic
382	#123	—	13	2	no	—
383	#123	—	13	2	no	—
384	#123	—	13	2	no	—
385	#123	—	13	2	no	—
386	#123	—	13	2	no	—
387	#123	—	13	2	no	—
388	#123	—	13	2	no	—
389	#123	—	13	2	no	—
390	#123	—	13	1	no	—
391	#123	—	13	1	no	—
392	#123	—	13	2	no	—
393	#123	—	13	2	no	—
394	#123	—	13	2	no	—
395	C₂²⋊Q₈	—	13	1	no	—
396	C₂²⋊Q₈	—	13	2	no	—
397	C₂²⋊Q₈	—	13	1	no	—
398	C₂²⋊Q₈	—	13	1	no	—
399	C₂²⋊Q₈	—	13	1	no	—
400	C₂²⋊Q₈	—	13	2	no	—
401	C₂²⋊Q₈	—	13	2	no	—
402	C₂²⋊Q₈	—	13	2	no	—
403	C₂²⋊Q₈	—	13	2	no	—
404	#121	—	13	1	no	—
405	#121	—	13	2	no	—
406	#121	—	13	2	no	—
407	#121	—	13	2	no	—
408	#121	—	13	2	no	—
409	#121	—	13	2	no	—
410	#121	—	13	2	no	—
411	#121	—	13	2	no	—
412	#121	—	13	1	no	—
413	#121	—	13	2	no	—
414	#121	—	13	2	no	—
415	#121	—	13	1	no	—
416	#121	—	13	2	no	—
417	#121	—	13	1	no	—
418	#121	—	13	2	no	—
419	#121	C₂×D₁₃	1	2	yes	—
420	#121	C₂×D₁₃	1	2	yes	—
421	#120	—	13	2	no	—
422	#120	—	13	2	no	—
423	#120	C₂×D₁₃	1	2	yes	—
424	#120	C₂×D₁₃	1	2	yes	—
425	C₄×Q₈	—	13	1	no	—
426	C₄×Q₈	—	13	1	no	—
427	C₄×Q₈	—	13	1	no	—
428	C₄×Q₈	—	13	1	no	—
429	C₄×D₄	—	13	1	no	—
430	C₄×D₄	—	13	2	no	—
431	C₄×D₄	—	13	2	no	—
432	C₄×D₄	—	13	2	no	—
433	C₄×D₄	—	13	2	no	—
434	C₄×D₄	—	13	1	no	—
435	C₄×D₄	—	13	1	no	—
436	C₄×D₄	—	13	1	no	—
437	C₄×D₄	—	13	1	no	—
438	C₄×D₄	—	13	2	no	—
439	C₄×D₄	—	13	2	no	—
440	C₄×D₄	—	13	2	no	—
441	C₄×D₄	—	13	1	no	—
442	#117	—	13	2	no	—
443	#117	—	13	2	no	—
444	#117	—	13	1	no	—
445	#117	C₂×D₁₃	1	1	yes	characteristic
446	C₂×C₄⋊C₄	—	13	2	no	—
447	C₂×C₂²⋊C₄	—	13	2	no	—
448	C₂×C₂²⋊C₄	—	13	2	no	—
449	C₂×C₄²	—	13	1	no	—
450	C₂×C₁₃	—	4	2	no	—
451	C₂×C₁₃	—	4	2	no	—
452	C₂×C₁₃	—	4	2	no	—
453	C₂×C₁₃	—	4	1	no	—
454	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
455	C₂×C₁₃	#585	1	1	yes	characteristic
456	C₂×C₁₃	#585	1	1	yes	characteristic
457	D₁₃	—	4	1	no	—
458	D₁₃	—	4	1	no	—
459	C₂⁴	C₂²×D₁₃	1	2	yes	—
460	#41	—	4	2	no	—
461	#41	—	52	2	no	—
462	#41	—	52	2	no	—
463	#41	—	52	2	no	—
464	C₂×Q₈	—	13	1	no	—
465	C₂×Q₈	—	13	1	no	—
466	C₂×Q₈	—	13	1	no	—
467	C₂×Q₈	—	13	2	no	—
468	C₂×Q₈	—	52	2	no	—
469	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
470	C₂×D₄	—	4	2	no	—
471	C₂×D₄	—	13	1	no	—
472	C₂×D₄	—	13	1	no	—
473	C₂×D₄	—	13	2	no	—
474	C₂×D₄	—	13	2	no	—
475	C₂×D₄	—	13	2	no	—
476	C₂×D₄	—	13	2	no	—
477	C₂×D₄	—	13	2	no	—
478	C₂×D₄	—	13	2	no	—
479	C₂×D₄	—	13	1	no	—
480	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
481	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
482	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
483	C₂×D₄	C₂²×D₁₃	1	2	yes	—
484	C₂×D₄	C₂²×D₁₃	1	2	yes	—
485	C₂×D₄	C₂²×D₁₃	1	2	yes	—
486	C₂×D₄	C₂²×D₁₃	1	2	yes	—
487	C₂×D₄	C₂²×D₁₃	1	2	yes	—
488	C₂×D₄	C₂²×D₁₃	1	2	yes	—
489	C₂²×C₄	—	13	2	no	—
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	2	no	—
495	C₂²×C₄	—	13	1	no	—
496	C₂²×C₄	—	13	1	no	—
497	C₂²×C₄	—	13	1	no	—
498	C₂²×C₄	—	13	1	no	—
499	C₂²×C₄	—	13	2	no	—
500	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
501	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
502	C₄⋊C₄	—	13	1	no	—
503	C₄⋊C₄	—	13	2	no	—
504	C₄⋊C₄	—	13	2	no	—
505	C₄⋊C₄	—	13	2	no	—
506	C₄⋊C₄	—	13	1	no	—
507	C₄⋊C₄	—	13	2	no	—
508	C₄⋊C₄	—	13	1	no	—
509	C₄⋊C₄	—	13	1	no	—
510	C₄⋊C₄	—	13	2	no	—
511	C₄⋊C₄	—	13	1	no	—
512	C₄⋊C₄	—	13	1	no	—
513	C₄⋊C₄	—	13	1	no	—
514	C₄⋊C₄	—	13	1	no	—
515	C₄⋊C₄	—	13	2	no	—
516	C₄⋊C₄	—	13	2	no	—
517	C₄⋊C₄	—	13	2	no	—
518	C₄⋊C₄	—	13	2	no	—
519	C₄⋊C₄	—	13	1	no	—
520	C₄⋊C₄	—	13	2	no	—
521	C₄⋊C₄	—	13	2	no	—
522	C₄⋊C₄	—	13	2	no	—
523	C₄⋊C₄	—	13	1	no	—
524	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
526	C₂²⋊C₄	—	13	1	no	—
527	C₂²⋊C₄	—	13	1	no	—
528	C₂²⋊C₄	—	13	2	no	—
529	C₂²⋊C₄	—	13	2	no	—
530	C₂²⋊C₄	—	13	2	no	—
531	C₂²⋊C₄	—	13	2	no	—
532	C₂²⋊C₄	—	13	2	no	—
533	C₂²⋊C₄	—	13	2	no	—
534	C₂²⋊C₄	—	13	2	no	—
535	C₂²⋊C₄	—	13	2	no	—
536	C₂²⋊C₄	—	13	2	no	—
537	C₂²⋊C₄	—	13	2	no	—
538	C₂²⋊C₄	—	13	2	no	—
539	C₂²⋊C₄	—	13	2	no	—
540	C₂²⋊C₄	—	13	2	no	—
541	C₂²⋊C₄	—	13	2	no	—
542	C₂²⋊C₄	—	13	1	no	—
543	C₂²⋊C₄	—	13	1	no	—
544	C₂²⋊C₄	—	13	1	no	—
545	C₂²⋊C₄	—	13	1	no	—
546	C₂²⋊C₄	—	13	1	no	—
547	C₂²⋊C₄	—	13	2	no	—
548	C₂²⋊C₄	—	13	1	no	—
549	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
551	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
552	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
553	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
555	C₄²	—	13	1	no	—
556	C₄²	—	13	1	no	—
557	C₄²	—	13	1	no	—
558	C₄²	—	13	2	no	—
559	C₄²	—	13	1	no	—
560	C₄²	—	13	2	no	—
561	C₄²	—	13	2	no	—
562	C₄²	C₂²×D₁₃	1	1	yes	characteristic
563	C₄²	C₂²×D₁₃	1	1	yes	characteristic
564	C₁₃	#3562	1	1	yes	characteristic, complemented, Sylow
565	C₂³	—	4	2	no	—
566	C₂³	—	4	2	no	—
567	C₂³	—	4	2	no	—
568	C₂³	—	13	1	no	—
569	C₂³	—	13	1	no	—
570	C₂³	C₂³×D₁₃	1	1	yes	characteristic
571	C₂³	C₂³×D₁₃	1	2	yes	—
572	C₂³	C₂³×D₁₃	1	2	yes	—
573	C₂³	C₂³×D₁₃	1	2	yes	—
574	Q₈	—	2	2	no	—
575	Q₈	—	26	2	no	—
576	Q₈	—	26	2	no	—
577	Q₈	—	52	1	no	—
578	Q₈	—	52	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	2	2	no	—
581	D₄	—	2	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	4	2	no	—
584	D₄	—	4	2	no	—
585	D₄	—	4	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	4	2	no	—
588	D₄	—	52	1	no	—
589	D₄	—	52	2	no	—
590	D₄	—	52	1	no	—
591	D₄	—	52	2	no	—
592	D₄	—	52	2	no	—
593	D₄	—	52	1	no	—
594	D₄	—	52	2	no	—
595	D₄	—	52	2	no	—
596	D₄	—	52	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	13	1	no	—
600	C₂×C₄	—	13	1	no	—
601	C₂×C₄	—	13	2	no	—
602	C₂×C₄	—	13	1	no	—
603	C₂×C₄	—	13	1	no	—
604	C₂×C₄	—	13	1	no	—
605	C₂×C₄	—	13	2	no	—
606	C₂×C₄	—	13	2	no	—
607	C₂×C₄	—	13	2	no	—
608	C₂×C₄	—	13	1	no	—
609	C₂×C₄	—	26	2	no	—
610	C₂×C₄	—	26	2	no	—
611	C₂×C₄	—	52	1	no	—
612	C₂×C₄	—	52	1	no	—
613	C₂×C₄	—	52	2	no	—
614	C₂×C₄	—	52	2	no	—
615	C₂×C₄	—	52	2	no	—
616	C₂×C₄	—	52	2	no	—
617	C₂×C₄	—	52	2	no	—
618	C₂×C₄	—	52	2	no	—
619	C₂×C₄	—	52	2	no	—
620	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₃	1	2	yes	—
625	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
627	C₂²	—	2	1	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	8	4	no	—
640	C₂²	—	26	1	no	—
641	C₂²	—	26	1	no	—
642	C₂²	—	26	1	no	—
643	C₂²	—	26	1	no	—
644	C₂²	—	26	1	no	—
645	C₂²	—	26	1	no	—
646	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	26	1	no	—
654	C₄	—	26	1	no	—
655	C₄	—	26	2	no	—
656	C₄	—	26	2	no	—
657	C₄	—	26	1	no	—
658	C₄	—	26	1	no	—
659	C₄	—	26	2	no	—
660	C₄	—	26	1	no	—
661	C₄	—	26	2	no	—
662	C₄	—	26	1	no	—
663	C₄	#88251	1	2	yes	—
664	C₂	—	4	1	no	—
665	C₂	—	4	2	no	—
666	C₂	—	4	2	no	—
667	C₂	—	4	2	no	—
668	C₂	—	52	1	no	—
669	C₂	—	52	1	no	—
670	C₂	C₂×#88251	1	1	yes	characteristic
671	C₂	#11719650	1	1	yes	characteristic
672	C₂	#11719650	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#535	C₂
hypercenter	#535	D₁₃
hypocenter	C₁₃	#3562
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #535

Complements

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

N	H ≅ G/N	type
1. C₁₃×#535	C₂	semidirect
2. #11719536	C₂	semidirect
3. #11719529	C₂	semidirect
4. #11719511	C₂	semidirect
5. #11719511	C₂	semidirect
6. #11719424	C₂	semidirect
7. #11719423	C₂	semidirect
8. #11719421	C₂	semidirect
9. #11719418	C₂	semidirect
10. #11719385	C₂	semidirect
11. #11719382	C₂	semidirect
12. #11719380	C₂	semidirect
13. #11719376	C₂	semidirect
14. #11719326	C₂	semidirect
15. #11719320	C₂	semidirect
16. #11719307	C₂	semidirect
17. #11719306	C₂	semidirect
18. #11719300	C₂	semidirect
19. #11719298	C₂	semidirect
20. #11719298	C₂	semidirect
21. #11719292	C₂	semidirect
22. #11719233	C₂	semidirect
23. #11719223	C₂	semidirect
26. C₂×Q₈×D₁₃	C₂²	semidirect
29. C₂×#6129	C₂²	semidirect
43. #88200	C₂²	semidirect
44. Q₈×Dic₁₃	C₂²	semidirect
45. #88198	C₂²	semidirect
46. #88194	C₂²	semidirect
50. #88193	C₂²	semidirect
51. #88193	C₂²	semidirect
52. #88193	C₂²	semidirect
53. #88193	C₂²	semidirect
57. #88192	C₂²	semidirect
58. #88192	C₂²	semidirect
59. #88192	C₂²	semidirect
63. #88190	C₂²	semidirect
64. #88190	C₂²	semidirect
68. #88189	C₂²	semidirect
69. #88189	C₂²	semidirect
70. #88189	C₂²	semidirect
71. #88189	C₂²	semidirect
74. D₄×Dic₁₃	C₂²	semidirect
75. D₄×Dic₁₃	C₂²	semidirect
76. D₄×Dic₁₃	C₂²	semidirect
77. D₄×Dic₁₃	C₂²	semidirect
78. D₄×Dic₁₃	C₂²	semidirect
79. #88183	C₂²	semidirect
82. C₄×C₂²⋊D₁₃	C₂²	semidirect
85. #88178	C₂²	semidirect
86. C₂×#6101	C₂²	semidirect
87. #88152	C₂²	semidirect
88. #88150	C₂²	semidirect
89. #88148	C₂²	semidirect
90. #88143	C₂²	semidirect
91. #88143	C₂²	semidirect
92. #88143	C₂²	semidirect
94. #88139	C₂²	semidirect
96. #88138	C₂²	semidirect
98. #88137	C₂²	semidirect
99. #88137	C₂²	semidirect
100. #88137	C₂²	semidirect
101. #88135	C₂²	semidirect
102. #88135	C₂²	semidirect
106. #88133	C₂²	semidirect
107. #88133	C₂²	semidirect
108. #88133	C₂²	semidirect
109. #88132	C₂²	semidirect
110. #88132	C₂²	semidirect
111. #88132	C₂²	semidirect
112. #88132	C₂²	semidirect
113. #88131	C₂²	semidirect
114. #88131	C₂²	semidirect
115. C₄×D₅₂	C₂²	semidirect
116. #88126	C₂²	semidirect
117. C₄²×D₁₃	C₂²	semidirect
118. #88124	C₂²	semidirect
119. #88123	C₂²	semidirect
120. C₄×Dic₂₆	C₂²	semidirect
121. C₄×Dic₂₆	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
310. #535	D₁₃	semidirect
564. C₁₃	#3562	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#535	2
#11719536	2
#11719529	2
#11719511	2
#11719424	2
#11719423	2
#11719421	2
#11719418	2
#11719385	2
#11719382	2
#11719380	2
#11719376	2
#11719326	2
#11719320	2
#11719307	2
#11719306	2
#11719300	2
#11719298	2
#11719292	2
#11719233	2
#11719223	2
#3562	13