Subgroups — #13128729

Order 1664.

1040 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719420	C₂	1	1	yes	maximal, characteristic
3	#11719418	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719386	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719384	C₂	1	2	yes	maximal, complemented
6	#11719380	C₂	1	1	yes	maximal, characteristic, complemented
7	D₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719376	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719374	C₂	1	2	yes	maximal, complemented
10	#11719367	C₂	1	2	yes	maximal, complemented
11	#11719364	C₂	1	2	yes	maximal, complemented
12	#11719363	C₂	1	2	yes	maximal, complemented
13	#11719354	C₂	1	2	yes	maximal, complemented
14	#11719289	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719283	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719277	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719273	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719264	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719261	C₂	1	2	yes	maximal, complemented
20	#11719250	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719247	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719243	C₂	1	2	yes	maximal, complemented
23	C₄×#6129	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic
25	C₂×#6129	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#127	C₂²	1	1	yes	characteristic
28	C₁₃×#124	C₂²	1	1	yes	characteristic
29	C₁₃×#124	C₂²	1	2	yes	complemented
30	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#123	C₂²	1	2	yes	complemented
32	C₁₃×#123	C₂²	1	2	yes	complemented
33	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
34	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
35	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
36	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
37	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
38	#88201	C₂²	1	1	yes	characteristic
39	#88200	C₂²	1	1	yes	characteristic
40	#88200	C₂²	1	2	yes	complemented
41	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
42	#88198	C₂²	1	1	yes	characteristic, complemented
43	#88198	C₂²	1	1	yes	characteristic, complemented
44	#88194	C₂²	1	1	yes	characteristic
45	#88193	C₂²	1	2	yes	—
46	#88193	C₂²	1	2	yes	—
47	#88191	C₂²	1	2	yes	—
48	#88191	C₂²	1	2	yes	—
49	#88190	C₂²	1	1	yes	characteristic
50	#88190	C₂²	1	1	yes	characteristic
51	#88190	C₂²	1	1	yes	characteristic, complemented
52	#88190	C₂²	1	2	yes	complemented
53	#88189	C₂²	1	2	yes	complemented
54	#88189	C₂²	1	2	yes	complemented
55	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
56	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
57	D₄×Dic₁₃	C₂²	1	2	yes	complemented
58	#88183	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
60	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
61	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
62	C₂×#6103	C₂²	1	2	yes	—
63	#88180	C₂²	1	2	yes	complemented
64	#88178	C₂²	1	2	yes	complemented
65	C₂×C₄×Dic₁₃	C₂²	1	2	yes	complemented
66	#88152	C₂²	1	2	yes	complemented
67	#88152	C₂²	1	2	yes	complemented
68	#88152	C₂²	1	2	yes	complemented
69	#88151	C₂²	1	1	yes	characteristic
70	#88150	C₂²	1	1	yes	characteristic
71	#88150	C₂²	1	1	yes	characteristic
72	#88150	C₂²	1	2	yes	complemented
73	#88147	C₂²	1	1	yes	characteristic
74	#88146	C₂²	1	1	yes	characteristic
75	#88146	C₂²	1	2	yes	—
76	#88146	C₂²	1	2	yes	complemented
77	#88143	C₂²	1	1	yes	characteristic, complemented
78	#88143	C₂²	1	1	yes	characteristic, complemented
79	#88142	C₂²	1	1	yes	characteristic, complemented
80	#88141	C₂²	1	1	yes	characteristic, complemented
81	#88141	C₂²	1	1	yes	characteristic, complemented
82	#88141	C₂²	1	2	yes	complemented
83	#88140	C₂²	1	2	yes	complemented
84	#88139	C₂²	1	2	yes	—
85	#88139	C₂²	1	2	yes	—
86	#88139	C₂²	1	2	yes	complemented
87	#88139	C₂²	1	2	yes	complemented
88	#88137	C₂²	1	2	yes	—
89	#88137	C₂²	1	2	yes	—
90	#88137	C₂²	1	2	yes	complemented
91	#88137	C₂²	1	2	yes	complemented
92	#88135	C₂²	1	2	yes	—
93	#88135	C₂²	1	2	yes	—
94	#88135	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
96	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
97	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
98	#88133	C₂²	1	2	yes	complemented
99	#88133	C₂²	1	2	yes	complemented
100	#88133	C₂²	1	2	yes	complemented
101	#88133	C₂²	1	2	yes	complemented
102	#88132	C₂²	1	2	yes	complemented
103	#88132	C₂²	1	2	yes	complemented
104	#88132	C₂²	1	2	yes	complemented
105	#88131	C₂²	1	2	yes	complemented
106	#88131	C₂²	1	2	yes	complemented
107	#88130	C₂²	1	2	yes	complemented
108	#88129	C₂²	1	1	yes	characteristic
109	#88129	C₂²	1	1	yes	characteristic
110	C₄×D₅₂	C₂²	1	1	yes	characteristic
111	#88126	C₂²	1	1	yes	characteristic
112	#88126	C₂²	1	2	yes	—
113	#88126	C₂²	1	1	yes	characteristic
114	#88126	C₂²	1	2	yes	complemented
115	C₄²×D₁₃	C₂²	1	1	yes	characteristic
116	#88123	C₂²	1	1	yes	characteristic, complemented
117	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
118	C₄×Dic₂₆	C₂²	1	2	yes	complemented
119	C₄×Dic₂₆	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	C₂³×D₁₃	C₂³	1	2	yes	—
124	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₃	C₂³	1	2	yes	—
129	C₂×D₄×C₁₃	C₂³	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
136	C₂²×Dic₁₃	C₂³	1	2	yes	—
137	C₂²×Dic₁₃	C₂³	1	2	yes	—
138	C₂²×Dic₁₃	C₂³	1	2	yes	—
139	Q₈×D₁₃	—	2	4	no	—
140	#6129	—	2	4	no	—
141	D₄×D₁₃	—	2	4	no	—
142	C₂×D₅₂	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₁₃	C₂³	1	2	yes	—
144	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₁₃	C₂³	1	2	yes	—
147	C₂×C₄×D₁₃	C₂³	1	2	yes	—
148	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
149	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
150	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
151	C₂×Dic₂₆	C₂³	1	2	yes	—
152	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
153	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
154	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
155	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₄²×C₁₃	C₂³	1	1	yes	characteristic
167	C₄²×C₁₃	C₂³	1	1	yes	characteristic
168	C₄²×C₁₃	C₂³	1	1	yes	characteristic
169	C₄²×C₁₃	C₂³	1	2	yes	—
170	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
171	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
172	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
178	#6103	C₂³	1	1	yes	characteristic
179	#6103	C₂³	1	1	yes	characteristic
180	#6103	C₂³	1	2	yes	—
181	#6103	C₂³	1	1	yes	characteristic
182	#6103	C₂³	1	1	yes	characteristic
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	#6103	C₂³	1	2	yes	—
189	#6103	C₂³	1	2	yes	—
190	#6103	C₂³	1	2	yes	—
191	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₁₃	C₂³	1	2	yes	—
193	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
194	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
195	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
196	C₄⋊Dic₁₃	C₂³	1	2	yes	—
197	C₄⋊Dic₁₃	C₂³	1	2	yes	—
198	#6101	C₂³	1	1	yes	characteristic
199	#6101	C₂³	1	2	yes	—
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	1	yes	characteristic
205	#6101	C₂³	1	1	yes	characteristic
206	#6101	C₂³	1	1	yes	characteristic
207	#6101	C₂³	1	1	yes	characteristic
208	#6101	C₂³	1	1	yes	characteristic
209	#6101	C₂³	1	2	yes	—
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	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	2	yes	—
219	C₄×Dic₁₃	C₂³	1	2	yes	—
220	C₄×Dic₁₃	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	2	yes	—
224	C₄×Dic₁₃	C₂³	1	2	yes	—
225	#3510	—	13	1	no	maximal, Sylow
226	C₂³×C₁₃	C₂⁴	1	2	yes	—
227	C₂³×C₁₃	C₂⁴	1	2	yes	—
228	C₂²×D₁₃	—	2	4	no	—
229	C₂²×D₁₃	—	4	2	no	—
230	C₂²×D₁₃	—	4	2	no	—
231	C₂²×D₁₃	C₂⁴	1	2	yes	—
232	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
233	Q₈×C₁₃	—	2	2	no	—
234	Q₈×C₁₃	—	4	1	no	—
235	D₄×C₁₃	—	2	2	no	—
236	D₄×C₁₃	—	2	2	no	—
237	D₄×C₁₃	—	4	2	no	—
238	D₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	—	4	2	no	—
240	C₂×C₄×C₁₃	—	4	2	no	—
241	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
243	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
245	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₂²⋊D₁₃	—	2	4	no	—
251	C₂²⋊D₁₃	—	2	4	no	—
252	C₂²⋊D₁₃	—	4	2	no	—
253	C₂²⋊D₁₃	—	4	2	no	—
254	C₂×Dic₁₃	—	2	4	no	—
255	C₂×Dic₁₃	—	4	2	no	—
256	C₂×Dic₁₃	—	4	2	no	—
257	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₃	C₂⁴	1	2	yes	—
259	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₃	C₂⁴	1	2	yes	—
262	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₃	C₂⁴	1	2	yes	—
264	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
267	D₅₂	—	2	2	no	—
268	C₄×D₁₃	—	2	4	no	—
269	C₄×D₁₃	—	4	1	no	—
270	C₄×D₁₃	—	4	2	no	—
271	C₄×D₁₃	—	4	1	no	—
272	C₄×D₁₃	—	4	2	no	—
273	C₄×D₁₃	#41	1	4	yes	—
274	Dic₂₆	—	2	2	no	—
275	Dic₂₆	—	2	2	no	—
276	Dic₂₆	—	2	4	no	—
277	Dic₂₆	—	4	1	no	—
278	Dic₂₆	—	4	1	no	—
279	Dic₂₆	—	4	1	no	—
280	#559	—	13	1	no	—
281	#559	—	13	1	no	—
282	#559	—	13	1	no	—
283	#559	D₁₃	1	1	yes	characteristic, complemented
284	#556	—	13	1	no	—
285	#556	—	13	1	no	—
286	#556	—	13	1	no	—
287	#556	—	13	1	no	—
288	#551	—	13	2	no	—
289	#551	—	13	2	no	—
290	#551	—	13	2	no	—
291	#551	—	13	2	no	—
292	#542	—	13	2	no	—
293	#542	—	13	2	no	—
294	#536	—	13	1	no	—
295	#535	—	13	1	no	—
296	#533	—	13	1	no	—
297	#529	—	13	2	no	—
298	#529	—	13	2	no	—
299	C₂×#124	—	13	1	no	—
300	#519	—	13	1	no	—
301	#518	—	13	1	no	—
302	C₄×#41	—	13	1	no	—
303	C₂²×C₁₃	—	2	2	no	—
304	C₂²×C₁₃	—	2	2	no	—
305	C₂²×C₁₃	—	2	2	no	—
306	C₂²×C₁₃	—	2	2	no	—
307	C₂²×C₁₃	—	2	2	no	—
308	C₂²×C₁₃	—	2	2	no	—
309	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
310	C₂×D₁₃	—	2	1	no	—
311	C₂×D₁₃	—	2	1	no	—
312	C₂×D₁₃	—	2	2	no	—
313	C₂×D₁₃	—	2	2	no	—
314	C₂×D₁₃	—	2	2	no	—
315	C₂×D₁₃	—	8	4	no	—
316	C₂×D₁₃	C₂×#41	1	2	yes	—
317	C₄×C₁₃	—	2	2	no	—
318	C₄×C₁₃	—	2	1	no	—
319	C₄×C₁₃	—	2	1	no	—
320	C₄×C₁₃	—	2	1	no	—
321	C₄×C₁₃	—	2	1	no	—
322	C₄×C₁₃	—	2	1	no	—
323	C₄×C₁₃	—	2	2	no	—
324	C₄×C₁₃	—	2	1	no	—
325	C₄×C₁₃	C₂×#41	1	2	yes	—
326	Dic₁₃	—	2	2	no	—
327	Dic₁₃	—	2	2	no	—
328	Dic₁₃	—	2	1	no	—
329	Dic₁₃	—	2	1	no	—
330	Dic₁₃	—	2	1	no	—
331	Dic₁₃	—	2	1	no	—
332	Dic₁₃	—	2	1	no	—
333	Dic₁₃	—	2	1	no	—
334	Dic₁₃	—	2	2	no	—
335	Dic₁₃	C₂×#41	1	2	yes	—
336	C₂×#41	—	13	1	no	—
337	C₂²×Q₈	—	13	1	no	—
338	C₂²×D₄	—	13	1	no	—
339	C₄⋊Q₈	—	13	1	no	—
340	C₄⋊Q₈	—	13	1	no	—
341	C₄⋊Q₈	—	13	1	no	—
342	C₄⋊Q₈	—	13	1	no	—
343	#127	—	13	1	no	—
344	#127	C₂×D₁₃	1	1	yes	characteristic
345	#126	—	13	2	no	—
346	#126	—	13	2	no	—
347	#126	—	13	2	no	—
348	#126	—	13	2	no	—
349	#126	—	13	2	no	—
350	#126	—	13	2	no	—
351	#126	—	13	2	no	—
352	#126	—	13	2	no	—
353	#125	—	13	1	no	—
354	#125	—	13	1	no	—
355	#124	—	13	1	no	—
356	#124	—	13	1	no	—
357	#124	—	13	1	no	—
358	#124	—	13	1	no	—
359	#124	—	13	2	no	—
360	#124	—	13	2	no	—
361	#124	—	13	2	no	—
362	#124	—	13	2	no	—
363	#124	—	13	2	no	—
364	#124	—	13	1	no	—
365	#124	—	13	1	no	—
366	#124	C₂×D₁₃	1	1	yes	characteristic
367	#124	C₂×D₁₃	1	1	yes	characteristic, complemented
368	#124	C₂×D₁₃	1	2	yes	complemented
369	#123	—	13	2	no	—
370	#123	—	13	2	no	—
371	#123	—	13	2	no	—
372	#123	—	13	2	no	—
373	#123	—	13	2	no	—
374	#123	—	13	2	no	—
375	#123	—	13	2	no	—
376	#123	—	13	2	no	—
377	#123	C₂×D₁₃	1	2	yes	complemented
378	#123	C₂×D₁₃	1	2	yes	complemented
379	C₂²⋊Q₈	—	13	1	no	—
380	C₂²⋊Q₈	—	13	2	no	—
381	C₂²⋊Q₈	—	13	2	no	—
382	C₂²⋊Q₈	—	13	1	no	—
383	C₂²⋊Q₈	—	13	1	no	—
384	C₂²⋊Q₈	—	13	1	no	—
385	C₂²⋊Q₈	—	13	2	no	—
386	C₂²⋊Q₈	—	13	2	no	—
387	C₂²⋊Q₈	—	13	2	no	—
388	C₂²⋊Q₈	—	13	2	no	—
389	#121	—	13	2	no	—
390	#121	—	13	2	no	—
391	#120	—	13	2	no	—
392	#120	—	13	2	no	—
393	C₄×Q₈	—	13	1	no	—
394	C₄×Q₈	—	13	1	no	—
395	C₄×Q₈	—	13	2	no	—
396	C₄×Q₈	—	13	1	no	—
397	C₄×Q₈	—	13	1	no	—
398	C₄×Q₈	—	13	2	no	—
399	C₄×Q₈	—	13	1	no	—
400	C₄×Q₈	—	13	1	no	—
401	C₄×Q₈	—	13	1	no	—
402	C₄×Q₈	—	13	1	no	—
403	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
404	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
405	C₄×D₄	—	13	1	no	—
406	C₄×D₄	—	13	1	no	—
407	C₄×D₄	—	13	2	no	—
408	C₄×D₄	—	13	2	no	—
409	C₄×D₄	—	13	2	no	—
410	C₄×D₄	—	13	2	no	—
411	C₄×D₄	—	13	1	no	—
412	C₄×D₄	—	13	2	no	—
413	C₄×D₄	—	13	2	no	—
414	C₄×D₄	—	13	2	no	—
415	C₄×D₄	—	13	1	no	—
416	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
417	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
418	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
419	#117	—	13	2	no	—
420	#117	—	13	1	no	—
421	#117	—	13	2	no	—
422	#117	—	13	2	no	—
423	#117	—	13	2	no	—
424	#117	—	13	2	no	—
425	#117	—	13	1	no	—
426	#117	—	13	1	no	—
427	#117	—	13	2	no	—
428	#117	—	13	2	no	—
429	C₂×C₂²⋊C₄	—	13	2	no	—
430	C₂×C₂²⋊C₄	—	13	2	no	—
431	C₂×C₂²⋊C₄	—	13	2	no	—
432	C₂×C₂²⋊C₄	—	13	2	no	—
433	C₂×C₄²	—	13	2	no	—
434	C₂×C₄²	—	13	1	no	—
435	C₂×C₁₃	—	4	2	no	—
436	C₂×C₁₃	—	4	2	no	—
437	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
438	C₂×C₁₃	#585	1	1	yes	characteristic
439	C₂×C₁₃	#585	1	1	yes	characteristic
440	D₁₃	—	2	2	no	—
441	D₁₃	—	4	2	no	—
442	C₂⁴	—	13	2	no	—
443	#41	—	26	4	no	—
444	C₂×Q₈	—	13	2	no	—
445	C₂×Q₈	—	13	1	no	—
446	C₂×Q₈	—	13	1	no	—
447	C₂×Q₈	—	13	1	no	—
448	C₂×Q₈	—	13	1	no	—
449	C₂×Q₈	—	13	1	no	—
450	C₂×Q₈	—	26	4	no	—
451	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
452	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
453	C₂×D₄	—	13	2	no	—
454	C₂×D₄	—	13	2	no	—
455	C₂×D₄	—	13	2	no	—
456	C₂×D₄	—	13	2	no	—
457	C₂×D₄	—	13	1	no	—
458	C₂×D₄	—	26	4	no	—
459	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
460	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
461	C₂×D₄	C₂²×D₁₃	1	2	yes	—
462	C₂×D₄	C₂²×D₁₃	1	2	yes	—
463	C₂²×C₄	—	13	1	no	—
464	C₂²×C₄	—	13	2	no	—
465	C₂²×C₄	—	13	2	no	—
466	C₂²×C₄	—	13	2	no	—
467	C₂²×C₄	—	13	2	no	—
468	C₂²×C₄	—	13	1	no	—
469	C₂²×C₄	—	13	1	no	—
470	C₂²×C₄	—	13	2	no	—
471	C₂²×C₄	—	13	2	no	—
472	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
473	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
474	C₄⋊C₄	—	13	1	no	—
475	C₄⋊C₄	—	13	1	no	—
476	C₄⋊C₄	—	13	1	no	—
477	C₄⋊C₄	—	13	1	no	—
478	C₄⋊C₄	—	13	1	no	—
479	C₄⋊C₄	—	13	1	no	—
480	C₄⋊C₄	—	13	2	no	—
481	C₄⋊C₄	—	13	2	no	—
482	C₄⋊C₄	—	13	1	no	—
483	C₄⋊C₄	—	13	1	no	—
484	C₄⋊C₄	—	13	2	no	—
485	C₄⋊C₄	—	13	2	no	—
486	C₄⋊C₄	—	13	2	no	—
487	C₄⋊C₄	—	13	2	no	—
488	C₄⋊C₄	—	13	2	no	—
489	C₄⋊C₄	—	13	2	no	—
490	C₄⋊C₄	—	13	2	no	—
491	C₄⋊C₄	—	13	1	no	—
492	C₄⋊C₄	—	13	1	no	—
493	C₄⋊C₄	—	13	1	no	—
494	C₄⋊C₄	—	13	1	no	—
495	C₄⋊C₄	—	13	1	no	—
496	C₄⋊C₄	—	13	1	no	—
497	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
499	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
500	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
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	1	no	—
512	C₂²⋊C₄	—	13	1	no	—
513	C₂²⋊C₄	—	13	2	no	—
514	C₂²⋊C₄	—	13	2	no	—
515	C₂²⋊C₄	—	13	2	no	—
516	C₂²⋊C₄	—	13	2	no	—
517	C₂²⋊C₄	—	13	2	no	—
518	C₂²⋊C₄	—	13	2	no	—
519	C₂²⋊C₄	—	13	1	no	—
520	C₂²⋊C₄	—	13	1	no	—
521	C₂²⋊C₄	—	13	2	no	—
522	C₂²⋊C₄	—	13	2	no	—
523	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
524	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
525	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
526	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
527	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
528	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
529	C₄²	—	13	1	no	—
530	C₄²	—	13	2	no	—
531	C₄²	—	13	2	no	—
532	C₄²	—	13	2	no	—
533	C₄²	—	13	1	no	—
534	C₄²	—	13	1	no	—
535	C₄²	—	13	2	no	—
536	C₄²	—	13	2	no	—
537	C₄²	—	13	2	no	—
538	C₄²	—	13	1	no	—
539	C₄²	—	13	1	no	—
540	C₄²	C₂²×D₁₃	1	1	yes	characteristic
541	C₄²	C₂²×D₁₃	1	2	yes	—
542	C₄²	C₂²×D₁₃	1	1	yes	characteristic
543	C₄²	C₂²×D₁₃	1	1	yes	characteristic
544	C₁₃	#3510	1	1	yes	characteristic, complemented, Sylow
545	C₂³	—	13	1	no	—
546	C₂³	—	13	2	no	—
547	C₂³	—	26	4	no	—
548	C₂³	—	52	2	no	—
549	C₂³	—	52	2	no	—
550	C₂³	C₂³×D₁₃	1	2	yes	—
551	C₂³	C₂³×D₁₃	1	2	yes	—
552	Q₈	—	2	2	no	—
553	Q₈	—	4	1	no	—
554	Q₈	—	26	4	no	—
555	Q₈	—	26	2	no	—
556	Q₈	—	26	2	no	—
557	Q₈	—	52	1	no	—
558	Q₈	—	52	1	no	—
559	Q₈	—	52	1	no	—
560	D₄	—	2	2	no	—
561	D₄	—	2	2	no	—
562	D₄	—	4	2	no	—
563	D₄	—	4	2	no	—
564	D₄	—	26	4	no	—
565	D₄	—	26	4	no	—
566	D₄	—	26	2	no	—
567	D₄	—	52	2	no	—
568	D₄	—	52	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	13	1	no	—
572	C₂×C₄	—	13	4	no	—
573	C₂×C₄	—	13	1	no	—
574	C₂×C₄	—	13	2	no	—
575	C₂×C₄	—	13	1	no	—
576	C₂×C₄	—	13	1	no	—
577	C₂×C₄	—	13	2	no	—
578	C₂×C₄	—	13	1	no	—
579	C₂×C₄	—	13	2	no	—
580	C₂×C₄	—	13	1	no	—
581	C₂×C₄	—	13	1	no	—
582	C₂×C₄	—	26	4	no	—
583	C₂×C₄	—	26	4	no	—
584	C₂×C₄	—	52	2	no	—
585	C₂×C₄	—	52	1	no	—
586	C₂×C₄	—	52	2	no	—
587	C₂×C₄	—	52	1	no	—
588	C₂×C₄	—	52	2	no	—
589	C₂×C₄	—	52	2	no	—
590	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₁₃	1	2	yes	—
592	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₁₃	1	2	yes	—
594	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	13	2	no	—
606	C₂²	—	26	1	no	—
607	C₂²	—	26	1	no	—
608	C₂²	—	26	2	no	—
609	C₂²	—	26	2	no	—
610	C₂²	—	26	2	no	—
611	C₂²	—	104	4	no	—
612	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
613	C₄	—	2	2	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	2	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	13	2	no	—
622	C₄	—	26	2	no	—
623	C₄	—	26	2	no	—
624	C₄	—	26	1	no	—
625	C₄	—	26	2	no	—
626	C₄	—	26	1	no	—
627	C₄	—	26	1	no	—
628	C₄	—	26	1	no	—
629	C₄	—	26	1	no	—
630	C₄	—	26	1	no	—
631	C₄	#41×D₁₃	1	2	yes	—
632	C₂	—	4	2	no	—
633	C₂	—	4	2	no	—
634	C₂	—	26	2	no	—
635	C₂	—	52	2	no	—
636	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
637	C₂	#11719648	1	1	yes	characteristic
638	C₂	#11719650	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#559	C₂
prime radical	#11719420	C₂
hypercenter	#559	D₁₃
hypocenter	C₁₃	#3510
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #559

Complements

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

N	H ≅ G/N	type
1. C₁₃×#559	C₂	semidirect
3. #11719418	C₂	semidirect
4. #11719386	C₂	semidirect
5. #11719384	C₂	semidirect
6. #11719380	C₂	semidirect
7. D₁₃×#124	C₂	semidirect
8. #11719376	C₂	semidirect
9. #11719374	C₂	semidirect
10. #11719367	C₂	semidirect
11. #11719364	C₂	semidirect
12. #11719363	C₂	semidirect
13. #11719354	C₂	semidirect
14. #11719289	C₂	semidirect
15. #11719283	C₂	semidirect
16. #11719277	C₂	semidirect
17. #11719273	C₂	semidirect
18. #11719264	C₂	semidirect
19. #11719261	C₂	semidirect
20. #11719250	C₂	semidirect
21. #11719247	C₂	semidirect
22. #11719243	C₂	semidirect
23. C₄×#6129	C₂	semidirect
29. C₁₃×#124	C₂²	semidirect
30. C₁₃×#124	C₂²	semidirect
31. C₁₃×#123	C₂²	semidirect
32. C₁₃×#123	C₂²	semidirect
33. C₄×Q₈×C₁₃	C₂²	semidirect
34. C₄×Q₈×C₁₃	C₂²	semidirect
36. C₄×D₄×C₁₃	C₂²	semidirect
37. C₄×D₄×C₁₃	C₂²	semidirect
40. #88200	C₂²	semidirect
41. Q₈×Dic₁₃	C₂²	semidirect
42. #88198	C₂²	semidirect
43. #88198	C₂²	semidirect
51. #88190	C₂²	semidirect
52. #88190	C₂²	semidirect
53. #88189	C₂²	semidirect
54. #88189	C₂²	semidirect
56. D₄×Dic₁₃	C₂²	semidirect
57. D₄×Dic₁₃	C₂²	semidirect
58. #88183	C₂²	semidirect
61. C₄×C₂²⋊D₁₃	C₂²	semidirect
63. #88180	C₂²	semidirect
64. #88178	C₂²	semidirect
65. C₂×C₄×Dic₁₃	C₂²	semidirect
66. #88152	C₂²	semidirect
67. #88152	C₂²	semidirect
68. #88152	C₂²	semidirect
72. #88150	C₂²	semidirect
76. #88146	C₂²	semidirect
77. #88143	C₂²	semidirect
78. #88143	C₂²	semidirect
79. #88142	C₂²	semidirect
80. #88141	C₂²	semidirect
81. #88141	C₂²	semidirect
82. #88141	C₂²	semidirect
83. #88140	C₂²	semidirect
86. #88139	C₂²	semidirect
87. #88139	C₂²	semidirect
90. #88137	C₂²	semidirect
91. #88137	C₂²	semidirect
94. #88135	C₂²	semidirect
98. #88133	C₂²	semidirect
99. #88133	C₂²	semidirect
100. #88133	C₂²	semidirect
101. #88133	C₂²	semidirect
102. #88132	C₂²	semidirect
103. #88132	C₂²	semidirect
104. #88132	C₂²	semidirect
105. #88131	C₂²	semidirect
106. #88131	C₂²	semidirect
107. #88130	C₂²	semidirect
114. #88126	C₂²	semidirect
116. #88123	C₂²	semidirect
117. C₄×Dic₂₆	C₂²	semidirect
118. C₄×Dic₂₆	C₂²	semidirect
119. C₄×Dic₂₆	C₂²	semidirect
120. C₄×Dic₂₆	C₂²	semidirect
121. C₄×Dic₂₆	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
283. #559	D₁₃	semidirect
367. #124	C₂×D₁₃	semidirect
368. #124	C₂×D₁₃	semidirect
377. #123	C₂×D₁₃	semidirect
378. #123	C₂×D₁₃	semidirect
403. C₄×Q₈	C₂×D₁₃	semidirect
404. C₄×Q₈	C₂×D₁₃	semidirect
417. C₄×D₄	C₂×D₁₃	semidirect
418. C₄×D₄	C₂×D₁₃	semidirect
544. C₁₃	#3510	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#559	2
#11719420	2
#11719418	2
#11719386	2
#11719384	2
#11719380	2
D₁₃×#124	2
#11719376	2
#11719374	2
#11719367	2
#11719364	2
#11719363	2
#11719354	2
#11719289	2
#11719283	2
#11719277	2
#11719273	2
#11719264	2
#11719261	2
#11719250	2
#11719247	2
#11719243	2
C₄×#6129	2
#3510	13