Subgroups — #13129427

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×#548	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719535	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719529	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719522	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719521	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719386	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719384	C₂	1	2	yes	maximal, complemented
8	#11719383	C₂	1	2	yes	maximal, complemented
9	#11719373	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719352	C₂	1	2	yes	maximal, complemented
11	#11719350	C₂	1	2	yes	maximal, complemented
12	#11719335	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719330	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719325	C₂	1	2	yes	maximal, complemented
15	#11719324	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719318	C₂	1	2	yes	maximal, complemented
17	#11719304	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719285	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719273	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719267	C₂	1	2	yes	maximal, complemented
21	#11719262	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719255	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719245	C₂	1	2	yes	maximal, complemented
24	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×#6131	C₂²	1	1	yes	characteristic
27	C₂×#6129	C₂²	1	1	yes	characteristic, complemented
28	C₂×#6127	C₂²	1	1	yes	characteristic
29	C₂²×D₅₂	C₂²	1	1	yes	characteristic
30	C₁₃×#124	C₂²	1	2	yes	—
31	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
34	C₁₃×#121	C₂²	1	2	yes	—
35	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
36	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
37	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
39	#88201	C₂²	1	1	yes	characteristic
40	#88201	C₂²	1	1	yes	characteristic
41	#88201	C₂²	1	1	yes	characteristic
42	#88201	C₂²	1	2	yes	complemented
43	#88200	C₂²	1	2	yes	complemented
44	#88200	C₂²	1	2	yes	complemented
45	#88200	C₂²	1	1	yes	characteristic, complemented
46	#88200	C₂²	1	2	yes	complemented
47	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
48	#88198	C₂²	1	1	yes	characteristic, complemented
49	#88198	C₂²	1	1	yes	characteristic, complemented
50	#88194	C₂²	1	1	yes	characteristic
51	#88194	C₂²	1	1	yes	characteristic
52	#88194	C₂²	1	2	yes	complemented
53	#88193	C₂²	1	2	yes	—
54	#88193	C₂²	1	2	yes	complemented
55	#88193	C₂²	1	2	yes	complemented
56	#88192	C₂²	1	1	yes	characteristic
57	#88192	C₂²	1	2	yes	complemented
58	#88191	C₂²	1	2	yes	—
59	#88191	C₂²	1	2	yes	—
60	#88191	C₂²	1	2	yes	—
61	#88190	C₂²	1	1	yes	characteristic
62	#88189	C₂²	1	2	yes	—
63	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
64	#88184	C₂²	1	2	yes	—
65	#88184	C₂²	1	1	yes	characteristic
66	#88184	C₂²	1	2	yes	—
67	#88184	C₂²	1	2	yes	complemented
68	#88183	C₂²	1	2	yes	complemented
69	#88183	C₂²	1	2	yes	complemented
70	#88183	C₂²	1	2	yes	complemented
71	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
72	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
73	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
74	#88180	C₂²	1	1	yes	characteristic
75	#88180	C₂²	1	1	yes	characteristic, complemented
76	#88178	C₂²	1	1	yes	characteristic
77	C₂×#6101	C₂²	1	2	yes	complemented
78	#88152	C₂²	1	2	yes	complemented
79	#88152	C₂²	1	2	yes	complemented
80	#88151	C₂²	1	1	yes	characteristic, complemented
81	#88150	C₂²	1	2	yes	complemented
82	#88149	C₂²	1	2	yes	—
83	#88149	C₂²	1	1	yes	characteristic
84	#88148	C₂²	1	2	yes	—
85	#88148	C₂²	1	2	yes	—
86	#88148	C₂²	1	2	yes	complemented
87	#88147	C₂²	1	1	yes	characteristic
88	#88144	C₂²	1	1	yes	characteristic, complemented
89	#88144	C₂²	1	2	yes	complemented
90	#88144	C₂²	1	1	yes	characteristic, complemented
91	#88143	C₂²	1	2	yes	complemented
92	#88141	C₂²	1	1	yes	characteristic, complemented
93	#88140	C₂²	1	2	yes	complemented
94	#88140	C₂²	1	2	yes	complemented
95	#88139	C₂²	1	2	yes	complemented
96	#88138	C₂²	1	2	yes	—
97	#88138	C₂²	1	2	yes	complemented
98	#88138	C₂²	1	2	yes	complemented
99	#88138	C₂²	1	2	yes	complemented
100	#88137	C₂²	1	1	yes	characteristic
101	#88137	C₂²	1	1	yes	characteristic, complemented
102	#88137	C₂²	1	2	yes	complemented
103	#88137	C₂²	1	2	yes	complemented
104	#88136	C₂²	1	2	yes	—
105	#88135	C₂²	1	2	yes	complemented
106	#88135	C₂²	1	2	yes	complemented
107	#88135	C₂²	1	2	yes	complemented
108	#88135	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
111	#88133	C₂²	1	1	yes	characteristic
112	#88133	C₂²	1	2	yes	—
113	#88133	C₂²	1	2	yes	—
114	#88133	C₂²	1	1	yes	characteristic, complemented
115	#88130	C₂²	1	2	yes	complemented
116	#88129	C₂²	1	1	yes	characteristic
117	C₄×D₅₂	C₂²	1	1	yes	characteristic
118	C₄×D₅₂	C₂²	1	2	yes	complemented
119	#88126	C₂²	1	2	yes	complemented
120	#88126	C₂²	1	2	yes	complemented
121	C₄²×D₁₃	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₃	C₂³	1	2	yes	—
124	C₁₃×#41	—	4	2	no	—
125	C₂×Q₈×C₁₃	—	4	2	no	—
126	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
129	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₁₃	C₂³	1	2	yes	—
131	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
132	C₂×D₄×C₁₃	C₂³	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₃	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	2	yes	—
141	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
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	#6131	—	4	2	no	—
149	#6129	—	4	2	no	—
150	#6127	—	4	2	no	—
151	C₂×D₅₂	—	4	2	no	—
152	C₂×D₅₂	C₂³	1	1	yes	characteristic
153	C₂×D₅₂	C₂³	1	1	yes	characteristic
154	C₂×D₅₂	C₂³	1	2	yes	—
155	C₂×D₅₂	C₂³	1	2	yes	—
156	C₂×D₅₂	C₂³	1	2	yes	—
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	2	yes	—
161	C₂×C₄×D₁₃	C₂³	1	2	yes	—
162	C₂×C₄×D₁₃	C₂³	1	2	yes	—
163	C₂×C₄×D₁₃	C₂³	1	2	yes	—
164	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
165	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
166	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
172	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₄²×C₁₃	C₂³	1	1	yes	characteristic
177	C₄²×C₁₃	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
186	#6103	C₂³	1	2	yes	—
187	#6103	C₂³	1	2	yes	—
188	#6103	C₂³	1	2	yes	—
189	#6103	C₂³	1	2	yes	—
190	#6103	C₂³	1	2	yes	—
191	#6103	C₂³	1	2	yes	—
192	#6103	C₂³	1	2	yes	—
193	#6103	C₂³	1	2	yes	—
194	#6103	C₂³	1	2	yes	—
195	#6103	C₂³	1	2	yes	—
196	#6103	C₂³	1	2	yes	—
197	#6103	C₂³	1	2	yes	—
198	#6103	C₂³	1	2	yes	—
199	#6103	C₂³	1	1	yes	characteristic
200	#6103	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₁₃	C₂³	1	2	yes	—
204	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₁₃	C₂³	1	2	yes	—
206	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
209	#6101	C₂³	1	1	yes	characteristic
210	#6101	C₂³	1	1	yes	characteristic
211	#6101	C₂³	1	2	yes	—
212	#6101	C₂³	1	2	yes	—
213	#6101	C₂³	1	2	yes	—
214	#6101	C₂³	1	2	yes	—
215	#6101	C₂³	1	2	yes	—
216	#6101	C₂³	1	1	yes	characteristic
217	#6101	C₂³	1	2	yes	—
218	#6101	C₂³	1	2	yes	—
219	#6101	C₂³	1	1	yes	characteristic
220	#6101	C₂³	1	2	yes	—
221	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
222	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
225	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
226	C₄×Dic₁₃	C₂³	1	2	yes	—
227	C₄×Dic₁₃	C₂³	1	2	yes	—
228	#3562	—	13	1	no	maximal, Sylow
229	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₂³×C₁₃	C₂⁴	1	2	yes	—
232	C₂²×D₁₃	—	4	2	no	—
233	C₂²×D₁₃	—	4	2	no	—
234	C₂²×D₁₃	—	4	2	no	—
235	C₂²×D₁₃	C₂⁴	1	2	yes	—
236	C₂²×D₁₃	C₂⁴	1	2	yes	—
237	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
238	Q₈×C₁₃	—	2	2	no	—
239	Q₈×C₁₃	—	2	2	no	—
240	Q₈×C₁₃	—	4	2	no	—
241	D₄×C₁₃	—	2	2	no	—
242	D₄×C₁₃	—	4	1	no	—
243	D₄×C₁₃	—	4	2	no	—
244	D₄×C₁₃	—	4	2	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	2	no	—
247	C₂×C₄×C₁₃	—	4	2	no	—
248	C₂×C₄×C₁₃	—	4	2	no	—
249	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
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	2	no	—
261	C₂²⋊D₁₃	—	4	2	no	—
262	C₂²⋊D₁₃	—	4	2	no	—
263	C₂²⋊D₁₃	—	4	1	no	—
264	C₂²⋊D₁₃	—	4	1	no	—
265	C₂²⋊D₁₃	—	4	2	no	—
266	C₂×Dic₁₃	—	4	2	no	—
267	C₂×Dic₁₃	—	4	2	no	—
268	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₁₃	C₂⁴	1	2	yes	—
274	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₁₃	C₂⁴	1	2	yes	—
276	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
277	D₅₂	—	2	2	no	—
278	D₅₂	—	2	2	no	—
279	D₅₂	—	4	2	no	—
280	D₅₂	—	4	2	no	—
281	D₅₂	—	4	2	no	—
282	C₄×D₁₃	—	2	2	no	—
283	C₄×D₁₃	—	4	2	no	—
284	C₄×D₁₃	—	4	2	no	—
285	C₄×D₁₃	—	4	1	no	—
286	C₄×D₁₃	—	4	1	no	—
287	C₄×D₁₃	—	4	2	no	—
288	C₄×D₁₃	—	4	2	no	—
289	Dic₂₆	—	2	2	no	—
290	Dic₂₆	—	4	1	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	D₁₃	1	1	yes	characteristic, complemented
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	—	13	1	no	—
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	1	no	—
316	C₂²×C₁₃	—	2	1	no	—
317	C₂²×C₁₃	—	2	2	no	—
318	C₂²×C₁₃	—	2	1	no	—
319	C₂²×C₁₃	—	2	2	no	—
320	C₂²×C₁₃	—	2	1	no	—
321	C₂²×C₁₃	—	2	1	no	—
322	C₂²×C₁₃	—	2	1	no	—
323	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
324	C₂×D₁₃	—	2	1	no	—
325	C₂×D₁₃	—	2	2	no	—
326	C₂×D₁₃	—	2	2	no	—
327	C₂×D₁₃	—	2	1	no	—
328	C₂×D₁₃	—	2	1	no	—
329	C₂×D₁₃	—	2	2	no	—
330	C₂×D₁₃	—	2	2	no	—
331	C₂×D₁₃	—	2	2	no	—
332	C₂×D₁₃	—	2	2	no	—
333	C₂×D₁₃	—	8	4	no	—
334	C₄×C₁₃	—	2	1	no	—
335	C₄×C₁₃	—	2	2	no	—
336	C₄×C₁₃	—	2	1	no	—
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	2	1	no	—
339	C₄×C₁₃	—	2	1	no	—
340	C₄×C₁₃	—	2	2	no	—
341	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
342	Dic₁₃	—	2	2	no	—
343	Dic₁₃	—	2	1	no	—
344	Dic₁₃	—	2	1	no	—
345	Dic₁₃	—	2	1	no	—
346	Dic₁₃	—	2	2	no	—
347	Dic₁₃	—	2	1	no	—
348	Dic₁₃	—	2	1	no	—
349	Dic₁₃	—	2	1	no	—
350	Dic₁₃	—	2	1	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	C₂×D₁₃	1	1	yes	characteristic, complemented
356	C₂²×D₄	—	13	1	no	—
357	C₄⋊Q₈	—	13	1	no	—
358	C₄⋊Q₈	—	13	1	no	—
359	#127	—	13	1	no	—
360	#127	—	13	1	no	—
361	#127	—	13	2	no	—
362	#126	—	13	2	no	—
363	#126	—	13	2	no	—
364	#126	—	13	1	no	—
365	#126	—	13	1	no	—
366	#126	—	13	2	no	—
367	#126	—	13	2	no	—
368	#126	—	13	2	no	—
369	#125	—	13	1	no	—
370	#125	—	13	1	no	—
371	#125	—	13	2	no	—
372	#125	—	13	2	no	—
373	#124	—	13	1	no	—
374	#124	—	13	1	no	—
375	#124	—	13	1	no	—
376	#124	—	13	2	no	—
377	#124	—	13	1	no	—
378	#124	—	13	2	no	—
379	#124	—	13	1	no	—
380	#124	C₂×D₁₃	1	2	yes	—
381	#124	C₂×D₁₃	1	1	yes	characteristic, complemented
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	1	no	—
390	#123	—	13	1	no	—
391	#123	—	13	2	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	2	no	—
398	C₂²⋊Q₈	—	13	2	no	—
399	C₂²⋊Q₈	—	13	1	no	—
400	C₂²⋊Q₈	—	13	1	no	—
401	C₂²⋊Q₈	—	13	2	no	—
402	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
403	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
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	1	no	—
412	#121	—	13	2	no	—
413	#121	—	13	1	no	—
414	#121	—	13	2	no	—
415	#121	—	13	2	no	—
416	#121	—	13	2	no	—
417	#121	—	13	2	no	—
418	#121	—	13	2	no	—
419	#121	C₂×D₁₃	1	2	yes	—
420	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
421	#120	—	13	2	no	—
422	#120	—	13	2	no	—
423	#120	—	13	2	no	—
424	#120	—	13	2	no	—
425	C₄×Q₈	—	13	1	no	—
426	C₄×Q₈	—	13	1	no	—
427	C₄×Q₈	—	13	1	no	—
428	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
429	C₄×D₄	—	13	1	no	—
430	C₄×D₄	—	13	1	no	—
431	C₄×D₄	—	13	1	no	—
432	C₄×D₄	—	13	2	no	—
433	C₄×D₄	—	13	1	no	—
434	C₄×D₄	—	13	2	no	—
435	C₄×D₄	—	13	2	no	—
436	C₄×D₄	—	13	2	no	—
437	C₄×D₄	—	13	2	no	—
438	C₄×D₄	—	13	2	no	—
439	C₄×D₄	—	13	1	no	—
440	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
441	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
442	#117	—	13	1	no	—
443	#117	—	13	1	no	—
444	#117	—	13	2	no	—
445	#117	—	13	2	no	—
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	1	no	—
451	C₂×C₁₃	—	4	2	no	—
452	C₂×C₁₃	—	4	1	no	—
453	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
454	C₂×C₁₃	#585	1	1	yes	characteristic
455	C₂×C₁₃	#585	1	1	yes	characteristic
456	D₁₃	—	4	1	no	—
457	D₁₃	—	4	2	no	—
458	D₁₃	—	4	2	no	—
459	C₂⁴	—	13	2	no	—
460	#41	—	4	2	no	—
461	#41	—	52	2	no	—
462	#41	—	52	2	no	—
463	#41	—	52	2	no	—
464	C₂×Q₈	—	4	2	no	—
465	C₂×Q₈	—	13	1	no	—
466	C₂×Q₈	—	13	1	no	—
467	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
468	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
469	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
470	C₂×D₄	—	13	1	no	—
471	C₂×D₄	—	13	2	no	—
472	C₂×D₄	—	13	2	no	—
473	C₂×D₄	—	13	2	no	—
474	C₂×D₄	—	13	2	no	—
475	C₂×D₄	—	13	2	no	—
476	C₂×D₄	—	13	1	no	—
477	C₂×D₄	—	13	2	no	—
478	C₂×D₄	—	13	2	no	—
479	C₂×D₄	—	13	1	no	—
480	C₂×D₄	—	13	1	no	—
481	C₂×D₄	—	13	2	no	—
482	C₂×D₄	—	13	2	no	—
483	C₂×D₄	—	13	2	no	—
484	C₂×D₄	—	52	2	no	—
485	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
486	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
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	1	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	2	no	—
497	C₂²×C₄	—	13	2	no	—
498	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
499	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
500	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
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	1	no	—
508	C₄⋊C₄	—	13	1	no	—
509	C₄⋊C₄	—	13	2	no	—
510	C₄⋊C₄	—	13	1	no	—
511	C₄⋊C₄	—	13	1	no	—
512	C₄⋊C₄	—	13	2	no	—
513	C₄⋊C₄	—	13	1	no	—
514	C₄⋊C₄	—	13	1	no	—
515	C₄⋊C₄	—	13	1	no	—
516	C₄⋊C₄	—	13	2	no	—
517	C₄⋊C₄	—	13	2	no	—
518	C₄⋊C₄	—	13	2	no	—
519	C₄⋊C₄	—	13	2	no	—
520	C₄⋊C₄	—	13	2	no	—
521	C₄⋊C₄	—	13	1	no	—
522	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
525	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
526	C₂²⋊C₄	—	13	1	no	—
527	C₂²⋊C₄	—	13	2	no	—
528	C₂²⋊C₄	—	13	1	no	—
529	C₂²⋊C₄	—	13	1	no	—
530	C₂²⋊C₄	—	13	1	no	—
531	C₂²⋊C₄	—	13	1	no	—
532	C₂²⋊C₄	—	13	1	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	2	no	—
543	C₂²⋊C₄	—	13	2	no	—
544	C₂²⋊C₄	—	13	2	no	—
545	C₂²⋊C₄	—	13	2	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	1	yes	characteristic
550	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
551	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
555	C₄²	—	13	1	no	—
556	C₄²	—	13	1	no	—
557	C₄²	—	13	1	no	—
558	C₄²	—	13	1	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	2	yes	—
564	C₁₃	#3562	1	1	yes	characteristic, complemented, Sylow
565	C₂³	—	13	2	no	—
566	C₂³	—	13	2	no	—
567	C₂³	—	13	1	no	—
568	C₂³	—	52	2	no	—
569	C₂³	—	52	2	no	—
570	C₂³	—	52	2	no	—
571	C₂³	C₂³×D₁₃	1	1	yes	characteristic
572	C₂³	C₂³×D₁₃	1	1	yes	characteristic
573	C₂³	C₂³×D₁₃	1	2	yes	—
574	Q₈	—	2	2	no	—
575	Q₈	—	2	2	no	—
576	Q₈	—	4	2	no	—
577	Q₈	—	26	2	no	—
578	Q₈	—	52	1	no	—
579	D₄	—	2	2	no	—
580	D₄	—	4	2	no	—
581	D₄	—	4	1	no	—
582	D₄	—	4	2	no	—
583	D₄	—	26	2	no	—
584	D₄	—	26	2	no	—
585	D₄	—	52	2	no	—
586	D₄	—	52	2	no	—
587	D₄	—	52	2	no	—
588	D₄	—	52	2	no	—
589	D₄	—	52	2	no	—
590	D₄	—	52	2	no	—
591	D₄	—	52	1	no	—
592	D₄	—	52	2	no	—
593	D₄	—	52	2	no	—
594	D₄	—	52	1	no	—
595	D₄	—	52	2	no	—
596	D₄	—	52	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	13	1	no	—
602	C₂×C₄	—	13	1	no	—
603	C₂×C₄	—	13	1	no	—
604	C₂×C₄	—	13	1	no	—
605	C₂×C₄	—	13	1	no	—
606	C₂×C₄	—	13	1	no	—
607	C₂×C₄	—	13	1	no	—
608	C₂×C₄	—	13	2	no	—
609	C₂×C₄	—	13	2	no	—
610	C₂×C₄	—	26	2	no	—
611	C₂×C₄	—	52	2	no	—
612	C₂×C₄	—	52	1	no	—
613	C₂×C₄	—	52	2	no	—
614	C₂×C₄	—	52	1	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	C₂³×D₁₃	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₁₃	1	2	yes	—
622	C₂×C₄	C₂³×D₁₃	1	2	yes	—
623	C₂×C₄	C₂³×D₁₃	1	2	yes	—
624	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
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	1	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	26	1	no	—
637	C₂²	—	26	2	no	—
638	C₂²	—	26	2	no	—
639	C₂²	—	26	1	no	—
640	C₂²	—	26	2	no	—
641	C₂²	—	26	2	no	—
642	C₂²	—	26	1	no	—
643	C₂²	—	26	2	no	—
644	C₂²	—	26	2	no	—
645	C₂²	—	104	4	no	—
646	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	26	1	no	—
655	C₄	—	26	2	no	—
656	C₄	—	26	1	no	—
657	C₄	—	26	1	no	—
658	C₄	—	26	1	no	—
659	C₄	—	26	2	no	—
660	C₄	—	26	1	no	—
661	C₄	—	26	1	no	—
662	C₄	—	26	1	no	—
663	C₄	#88251	1	2	yes	—
664	C₂	—	4	1	no	—
665	C₂	—	4	1	no	—
666	C₂	—	4	2	no	—
667	C₂	—	52	2	no	—
668	C₂	—	52	2	no	—
669	C₂	—	52	1	no	—
670	C₂	C₂×#88251	1	1	yes	characteristic
671	C₂	#11719648	1	1	yes	characteristic
672	C₂	#11719652	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#548	C₂
hypercenter	#548	D₁₃
hypocenter	C₁₃	#3562
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #548

Complements

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

N	H ≅ G/N	type
1. C₁₃×#548	C₂	semidirect
2. #11719535	C₂	semidirect
3. #11719529	C₂	semidirect
4. #11719522	C₂	semidirect
5. #11719521	C₂	semidirect
6. #11719386	C₂	semidirect
7. #11719384	C₂	semidirect
8. #11719383	C₂	semidirect
9. #11719373	C₂	semidirect
10. #11719352	C₂	semidirect
11. #11719350	C₂	semidirect
12. #11719335	C₂	semidirect
13. #11719330	C₂	semidirect
14. #11719325	C₂	semidirect
15. #11719324	C₂	semidirect
16. #11719318	C₂	semidirect
17. #11719304	C₂	semidirect
18. #11719285	C₂	semidirect
19. #11719273	C₂	semidirect
20. #11719267	C₂	semidirect
21. #11719262	C₂	semidirect
22. #11719255	C₂	semidirect
23. #11719245	C₂	semidirect
25. C₂²×Q₈×C₁₃	C₂²	semidirect
27. C₂×#6129	C₂²	semidirect
31. C₁₃×#124	C₂²	semidirect
33. C₁₃×C₂²⋊Q₈	C₂²	semidirect
35. C₁₃×#121	C₂²	semidirect
36. C₄×Q₈×C₁₃	C₂²	semidirect
38. C₄×D₄×C₁₃	C₂²	semidirect
42. #88201	C₂²	semidirect
43. #88200	C₂²	semidirect
44. #88200	C₂²	semidirect
45. #88200	C₂²	semidirect
46. #88200	C₂²	semidirect
47. Q₈×Dic₁₃	C₂²	semidirect
48. #88198	C₂²	semidirect
49. #88198	C₂²	semidirect
52. #88194	C₂²	semidirect
54. #88193	C₂²	semidirect
55. #88193	C₂²	semidirect
57. #88192	C₂²	semidirect
63. D₄×Dic₁₃	C₂²	semidirect
67. #88184	C₂²	semidirect
68. #88183	C₂²	semidirect
69. #88183	C₂²	semidirect
70. #88183	C₂²	semidirect
72. C₄×C₂²⋊D₁₃	C₂²	semidirect
73. C₄×C₂²⋊D₁₃	C₂²	semidirect
75. #88180	C₂²	semidirect
77. C₂×#6101	C₂²	semidirect
78. #88152	C₂²	semidirect
79. #88152	C₂²	semidirect
80. #88151	C₂²	semidirect
81. #88150	C₂²	semidirect
86. #88148	C₂²	semidirect
88. #88144	C₂²	semidirect
89. #88144	C₂²	semidirect
90. #88144	C₂²	semidirect
91. #88143	C₂²	semidirect
92. #88141	C₂²	semidirect
93. #88140	C₂²	semidirect
94. #88140	C₂²	semidirect
95. #88139	C₂²	semidirect
97. #88138	C₂²	semidirect
98. #88138	C₂²	semidirect
99. #88138	C₂²	semidirect
101. #88137	C₂²	semidirect
102. #88137	C₂²	semidirect
103. #88137	C₂²	semidirect
105. #88135	C₂²	semidirect
106. #88135	C₂²	semidirect
107. #88135	C₂²	semidirect
108. #88135	C₂²	semidirect
114. #88133	C₂²	semidirect
115. #88130	C₂²	semidirect
118. C₄×D₅₂	C₂²	semidirect
119. #88126	C₂²	semidirect
120. #88126	C₂²	semidirect
121. C₄²×D₁₃	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
299. #548	D₁₃	semidirect
355. C₂²×Q₈	C₂×D₁₃	semidirect
381. #124	C₂×D₁₃	semidirect
403. C₂²⋊Q₈	C₂×D₁₃	semidirect
420. #121	C₂×D₁₃	semidirect
428. C₄×Q₈	C₂×D₁₃	semidirect
441. C₄×D₄	C₂×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×#548	2
#11719535	2
#11719529	2
#11719522	2
#11719521	2
#11719386	2
#11719384	2
#11719383	2
#11719373	2
#11719352	2
#11719350	2
#11719335	2
#11719330	2
#11719325	2
#11719324	2
#11719318	2
#11719304	2
#11719285	2
#11719273	2
#11719267	2
#11719262	2
#11719255	2
#11719245	2
#3562	13