Subgroups — #13128684

Order 1664.

1140 conjugacy classes of subgroups.

The subgroup lattice has 670 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	#11719423	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719420	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719386	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719383	C₂	1	2	yes	maximal, complemented
6	#11719379	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719376	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719375	C₂	1	2	yes	maximal, complemented
9	#11719373	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719366	C₂	1	2	yes	maximal, complemented
11	#11719362	C₂	1	2	yes	maximal, complemented
12	#11719361	C₂	1	2	yes	maximal, complemented
13	#11719360	C₂	1	2	yes	maximal, complemented
14	#11719290	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719283	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719279	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	#11719258	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719252	C₂	1	2	yes	maximal, complemented
21	#11719251	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719245	C₂	1	2	yes	maximal, complemented
24	C₂×#6131	C₂²	1	1	yes	characteristic
25	C₂×#6129	C₂²	1	1	yes	characteristic
26	C₂×#6129	C₂²	1	2	yes	complemented
27	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
28	C₂×#6127	C₂²	1	2	yes	complemented
29	C₂²×C₄×D₁₃	C₂²	1	2	yes	—
30	C₁₃×#127	C₂²	1	1	yes	characteristic
31	C₁₃×#124	C₂²	1	1	yes	characteristic
32	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#124	C₂²	1	2	yes	complemented
34	C₁₃×#123	C₂²	1	2	yes	complemented
35	C₁₃×#123	C₂²	1	2	yes	complemented
36	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
37	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
38	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
40	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
41	#88201	C₂²	1	1	yes	characteristic
42	#88201	C₂²	1	2	yes	complemented
43	#88200	C₂²	1	1	yes	characteristic
44	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
45	#88198	C₂²	1	1	yes	characteristic, complemented
46	#88198	C₂²	1	1	yes	characteristic, complemented
47	#88194	C₂²	1	1	yes	characteristic
48	#88194	C₂²	1	1	yes	characteristic
49	#88194	C₂²	1	1	yes	characteristic, complemented
50	#88193	C₂²	1	2	yes	—
51	#88193	C₂²	1	2	yes	—
52	#88193	C₂²	1	2	yes	complemented
53	#88193	C₂²	1	2	yes	complemented
54	#88192	C₂²	1	2	yes	complemented
55	#88191	C₂²	1	2	yes	—
56	#88191	C₂²	1	2	yes	—
57	#88190	C₂²	1	1	yes	characteristic
58	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
59	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
60	#88184	C₂²	1	2	yes	complemented
61	#88183	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
63	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
64	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
65	C₂×#6101	C₂²	1	2	yes	complemented
66	#88152	C₂²	1	2	yes	complemented
67	#88151	C₂²	1	1	yes	characteristic
68	#88150	C₂²	1	1	yes	characteristic
69	#88150	C₂²	1	1	yes	characteristic
70	#88150	C₂²	1	2	yes	complemented
71	#88148	C₂²	1	2	yes	complemented
72	#88148	C₂²	1	2	yes	complemented
73	#88147	C₂²	1	1	yes	characteristic
74	#88147	C₂²	1	2	yes	—
75	#88147	C₂²	1	1	yes	characteristic, complemented
76	#88147	C₂²	1	2	yes	complemented
77	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
78	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
79	#88143	C₂²	1	1	yes	characteristic, complemented
80	#88143	C₂²	1	1	yes	characteristic, complemented
81	#88142	C₂²	1	1	yes	characteristic, complemented
82	#88141	C₂²	1	1	yes	characteristic, complemented
83	#88140	C₂²	1	2	yes	complemented
84	#88139	C₂²	1	2	yes	complemented
85	#88139	C₂²	1	2	yes	complemented
86	#88138	C₂²	1	2	yes	—
87	#88138	C₂²	1	2	yes	—
88	#88138	C₂²	1	2	yes	—
89	#88138	C₂²	1	2	yes	—
90	#88138	C₂²	1	2	yes	complemented
91	#88138	C₂²	1	2	yes	complemented
92	#88137	C₂²	1	2	yes	complemented
93	#88137	C₂²	1	2	yes	complemented
94	#88136	C₂²	1	2	yes	—
95	#88136	C₂²	1	2	yes	—
96	#88135	C₂²	1	2	yes	—
97	#88135	C₂²	1	2	yes	—
98	#88135	C₂²	1	2	yes	complemented
99	#88135	C₂²	1	2	yes	complemented
100	#88135	C₂²	1	2	yes	complemented
101	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
102	#88133	C₂²	1	2	yes	complemented
103	#88133	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, complemented
110	#88128	C₂²	1	1	yes	characteristic
111	C₄×D₅₂	C₂²	1	1	yes	characteristic
112	C₄×D₅₂	C₂²	1	2	yes	—
113	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
114	#88126	C₂²	1	1	yes	characteristic
115	#88126	C₂²	1	1	yes	characteristic
116	#88126	C₂²	1	2	yes	complemented
117	#88126	C₂²	1	2	yes	complemented
118	C₄²×D₁₃	C₂²	1	1	yes	characteristic
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	C₂×C₂²⋊D₁₃	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	C₂²×Dic₁₃	C₂³	1	2	yes	—
141	C₂²×Dic₁₃	C₂³	1	2	yes	—
142	C₂²×Dic₁₃	C₂³	1	2	yes	—
143	#6131	—	2	4	no	—
144	#6129	—	2	4	no	—
145	#6129	—	4	4	no	—
146	D₄×D₁₃	—	2	4	no	—
147	#6127	—	4	4	no	—
148	C₂×D₅₂	C₂³	1	1	yes	characteristic
149	C₂×D₅₂	C₂³	1	2	yes	—
150	C₂×D₅₂	C₂³	1	1	yes	characteristic
151	C₂×D₅₂	C₂³	1	2	yes	—
152	C₂×D₅₂	C₂³	1	2	yes	—
153	C₂×C₄×D₁₃	—	4	4	no	—
154	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₃	C₂³	1	2	yes	—
156	C₂×C₄×D₁₃	C₂³	1	2	yes	—
157	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₃	C₂³	1	2	yes	—
159	C₂×C₄×D₁₃	C₂³	1	2	yes	—
160	C₂×C₄×D₁₃	C₂³	1	2	yes	—
161	C₂×C₄×D₁₃	C₂³	1	2	yes	—
162	C₂×C₄×D₁₃	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	1	yes	characteristic
166	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
167	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₄²×C₁₃	C₂³	1	1	yes	characteristic
179	C₄²×C₁₃	C₂³	1	1	yes	characteristic
180	C₄²×C₁₃	C₂³	1	1	yes	characteristic
181	C₄²×C₁₃	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
186	#6103	C₂³	1	1	yes	characteristic
187	#6103	C₂³	1	1	yes	characteristic
188	#6103	C₂³	1	1	yes	characteristic
189	#6103	C₂³	1	1	yes	characteristic
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	2	yes	—
200	C₄⋊Dic₁₃	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	1	yes	characteristic
204	C₄⋊Dic₁₃	C₂³	1	2	yes	—
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	2	yes	—
209	#6101	C₂³	1	1	yes	characteristic
210	#6101	C₂³	1	1	yes	characteristic
211	#6101	C₂³	1	1	yes	characteristic
212	#6101	C₂³	1	1	yes	characteristic
213	#6101	C₂³	1	1	yes	characteristic
214	#6101	C₂³	1	1	yes	characteristic
215	#6101	C₂³	1	1	yes	characteristic
216	#6101	C₂³	1	2	yes	—
217	#6101	C₂³	1	2	yes	—
218	#6101	C₂³	1	2	yes	—
219	#6101	C₂³	1	2	yes	—
220	C₄×Dic₁₃	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	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	#3506	—	13	1	no	maximal, Sylow
229	C₂³×C₁₃	C₂⁴	1	2	yes	—
230	C₂³×C₁₃	C₂⁴	1	2	yes	—
231	C₂²×D₁₃	—	2	4	no	—
232	C₂²×D₁₃	—	4	2	no	—
233	C₂²×D₁₃	—	4	2	no	—
234	C₂²×D₁₃	C₂⁴	1	2	yes	—
235	C₂²×D₁₃	C₂⁴	1	2	yes	—
236	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
237	Q₈×C₁₃	—	2	2	no	—
238	Q₈×C₁₃	—	4	1	no	—
239	D₄×C₁₃	—	2	2	no	—
240	D₄×C₁₃	—	2	2	no	—
241	D₄×C₁₃	—	4	2	no	—
242	D₄×C₁₃	—	4	2	no	—
243	C₂×C₄×C₁₃	—	4	2	no	—
244	C₂×C₄×C₁₃	—	4	2	no	—
245	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
249	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	C₂²⋊D₁₃	—	2	4	no	—
255	C₂²⋊D₁₃	—	2	4	no	—
256	C₂²⋊D₁₃	—	2	4	no	—
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	C₂×Dic₁₃	—	2	4	no	—
263	C₂×Dic₁₃	—	2	4	no	—
264	C₂×Dic₁₃	—	4	2	no	—
265	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₁₃	C₂⁴	1	2	yes	—
269	C₂×Dic₁₃	C₂⁴	1	2	yes	—
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	1	yes	characteristic
274	D₅₂	—	2	4	no	—
275	D₅₂	—	2	2	no	—
276	D₅₂	—	2	2	no	—
277	D₅₂	—	4	2	no	—
278	D₅₂	—	4	2	no	—
279	C₄×D₁₃	—	2	4	no	—
280	C₄×D₁₃	—	2	2	no	—
281	C₄×D₁₃	—	2	4	no	—
282	C₄×D₁₃	—	4	2	no	—
283	C₄×D₁₃	—	4	2	no	—
284	C₄×D₁₃	—	4	1	no	—
285	C₄×D₁₃	—	4	2	no	—
286	C₄×D₁₃	—	4	2	no	—
287	C₄×D₁₃	#41	1	4	yes	complemented
288	Dic₂₆	—	2	2	no	—
289	Dic₂₆	—	2	2	no	—
290	Dic₂₆	—	2	2	no	—
291	Dic₂₆	—	4	1	no	—
292	#559	—	13	1	no	—
293	#559	—	13	1	no	—
294	#559	—	13	1	no	—
295	#559	D₁₃	1	1	yes	characteristic, complemented
296	#556	—	13	1	no	—
297	#556	—	13	1	no	—
298	#555	—	13	2	no	—
299	#553	—	13	2	no	—
300	#553	—	13	2	no	—
301	#550	—	13	1	no	—
302	#550	—	13	1	no	—
303	#547	—	13	2	no	—
304	#538	—	13	2	no	—
305	#538	—	13	2	no	—
306	#535	—	13	1	no	—
307	#535	—	13	1	no	—
308	#533	—	13	1	no	—
309	#532	—	13	1	no	—
310	#525	—	13	2	no	—
311	#525	—	13	2	no	—
312	#520	—	13	1	no	—
313	#520	—	13	1	no	—
314	C₂×C₄×D₄	—	13	1	no	—
315	C₂²×C₁₃	—	2	2	no	—
316	C₂²×C₁₃	—	2	2	no	—
317	C₂²×C₁₃	—	2	2	no	—
318	C₂²×C₁₃	—	2	2	no	—
319	C₂²×C₁₃	—	2	2	no	—
320	C₂²×C₁₃	—	2	2	no	—
321	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
322	C₂×D₁₃	—	2	1	no	—
323	C₂×D₁₃	—	2	1	no	—
324	C₂×D₁₃	—	2	2	no	—
325	C₂×D₁₃	—	2	2	no	—
326	C₂×D₁₃	—	2	2	no	—
327	C₂×D₁₃	—	2	2	no	—
328	C₂×D₁₃	—	2	2	no	—
329	C₂×D₁₃	—	2	2	no	—
330	C₂×D₁₃	—	4	8	no	—
331	C₂×D₁₃	C₂×#41	1	2	yes	—
332	C₄×C₁₃	—	2	2	no	—
333	C₄×C₁₃	—	2	1	no	—
334	C₄×C₁₃	—	2	1	no	—
335	C₄×C₁₃	—	2	1	no	—
336	C₄×C₁₃	—	2	2	no	—
337	C₄×C₁₃	—	2	1	no	—
338	C₄×C₁₃	—	2	1	no	—
339	C₄×C₁₃	—	2	1	no	—
340	C₄×C₁₃	C₂×#41	1	2	yes	—
341	Dic₁₃	—	2	2	no	—
342	Dic₁₃	—	2	1	no	—
343	Dic₁₃	—	2	1	no	—
344	Dic₁₃	—	2	2	no	—
345	Dic₁₃	—	2	1	no	—
346	Dic₁₃	—	2	1	no	—
347	Dic₁₃	—	2	1	no	—
348	Dic₁₃	C₂×#41	1	2	yes	—
349	Dic₁₃	H(5,𝔽₂)	1	2	yes	—
350	C₂×#41	—	13	1	no	—
351	C₂×#41	—	13	1	no	—
352	C₂×#41	—	13	2	no	—
353	C₂×#41	—	13	2	no	—
354	C₂²×D₄	—	13	1	no	—
355	C₂³×C₄	—	13	2	no	—
356	C₄⋊Q₈	—	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	1	no	—
362	#127	—	13	1	no	—
363	#127	C₂×D₁₃	1	1	yes	characteristic
364	#126	—	13	2	no	—
365	#126	—	13	2	no	—
366	#126	—	13	2	no	—
367	#126	—	13	2	no	—
368	#125	—	13	1	no	—
369	#125	—	13	1	no	—
370	#124	—	13	1	no	—
371	#124	—	13	2	no	—
372	#124	—	13	1	no	—
373	#124	—	13	2	no	—
374	#124	—	13	2	no	—
375	#124	—	13	1	no	—
376	#124	—	13	1	no	—
377	#124	C₂×D₁₃	1	1	yes	characteristic
378	#124	C₂×D₁₃	1	1	yes	characteristic, complemented
379	#124	C₂×D₁₃	1	2	yes	complemented
380	#123	—	13	2	no	—
381	#123	—	13	2	no	—
382	#123	—	13	2	no	—
383	#123	—	13	2	no	—
384	#123	—	13	2	no	—
385	#123	—	13	2	no	—
386	#123	C₂×D₁₃	1	2	yes	complemented
387	#123	C₂×D₁₃	1	2	yes	complemented
388	C₂²⋊Q₈	—	13	1	no	—
389	C₂²⋊Q₈	—	13	1	no	—
390	C₂²⋊Q₈	—	13	1	no	—
391	C₂²⋊Q₈	—	13	2	no	—
392	C₂²⋊Q₈	—	13	1	no	—
393	C₂²⋊Q₈	—	13	2	no	—
394	#121	—	13	2	no	—
395	#121	—	13	2	no	—
396	#121	—	13	2	no	—
397	#121	—	13	2	no	—
398	#121	—	13	2	no	—
399	#121	—	13	2	no	—
400	#121	—	13	2	no	—
401	#121	—	13	2	no	—
402	#121	—	13	2	no	—
403	#121	—	13	2	no	—
404	#121	—	13	2	no	—
405	#121	—	13	2	no	—
406	#120	—	13	2	no	—
407	#120	—	13	2	no	—
408	#120	—	13	2	no	—
409	#120	—	13	2	no	—
410	C₄×Q₈	—	13	1	no	—
411	C₄×Q₈	—	13	1	no	—
412	C₄×Q₈	—	13	1	no	—
413	C₄×Q₈	—	13	1	no	—
414	C₄×Q₈	—	13	1	no	—
415	C₄×Q₈	—	13	1	no	—
416	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
417	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
418	C₄×D₄	—	13	1	no	—
419	C₄×D₄	—	13	1	no	—
420	C₄×D₄	—	13	2	no	—
421	C₄×D₄	—	13	2	no	—
422	C₄×D₄	—	13	2	no	—
423	C₄×D₄	—	13	1	no	—
424	C₄×D₄	—	13	2	no	—
425	C₄×D₄	—	13	1	no	—
426	C₄×D₄	—	13	2	no	—
427	C₄×D₄	—	13	2	no	—
428	C₄×D₄	—	13	2	no	—
429	C₄×D₄	—	13	2	no	—
430	C₄×D₄	—	13	2	no	—
431	C₄×D₄	—	13	2	no	—
432	C₄×D₄	—	13	1	no	—
433	C₄×D₄	—	13	2	no	—
434	C₄×D₄	—	13	1	no	—
435	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
436	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
437	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
438	#117	—	13	2	no	—
439	#117	—	13	2	no	—
440	#117	—	13	1	no	—
441	#117	—	13	1	no	—
442	#117	—	13	2	no	—
443	#117	—	13	2	no	—
444	C₂×C₄⋊C₄	—	13	2	no	—
445	C₂×C₄⋊C₄	—	13	1	no	—
446	C₂×C₄⋊C₄	—	13	2	no	—
447	C₂×C₂²⋊C₄	—	13	2	no	—
448	C₂×C₄²	—	13	1	no	—
449	C₂×C₁₃	—	4	2	no	—
450	C₂×C₁₃	—	4	2	no	—
451	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
452	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
453	C₂×C₁₃	#585	1	1	yes	characteristic
454	D₁₃	—	2	2	no	—
455	D₁₃	—	4	2	no	—
456	D₁₃	—	4	2	no	—
457	C₂⁴	—	13	2	no	—
458	#41	—	26	4	no	—
459	#41	—	26	4	no	—
460	#41	—	52	4	no	—
461	#41	—	52	4	no	—
462	C₂×Q₈	—	13	1	no	—
463	C₂×Q₈	—	13	1	no	—
464	C₂×Q₈	—	13	1	no	—
465	C₂×Q₈	—	13	1	no	—
466	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
467	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
468	C₂×D₄	—	13	2	no	—
469	C₂×D₄	—	13	2	no	—
470	C₂×D₄	—	13	2	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	2	no	—
477	C₂×D₄	—	13	1	no	—
478	C₂×D₄	—	13	1	no	—
479	C₂×D₄	—	13	2	no	—
480	C₂×D₄	—	13	2	no	—
481	C₂×D₄	—	26	4	no	—
482	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
483	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
484	C₂×D₄	C₂²×D₁₃	1	2	yes	—
485	C₂×D₄	C₂²×D₁₃	1	2	yes	—
486	C₂²×C₄	—	13	1	no	—
487	C₂²×C₄	—	13	2	no	—
488	C₂²×C₄	—	13	2	no	—
489	C₂²×C₄	—	13	2	no	—
490	C₂²×C₄	—	13	1	no	—
491	C₂²×C₄	—	13	2	no	—
492	C₂²×C₄	—	13	2	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	—	52	4	no	—
499	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
500	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
501	C₄⋊C₄	—	13	2	no	—
502	C₄⋊C₄	—	13	1	no	—
503	C₄⋊C₄	—	13	1	no	—
504	C₄⋊C₄	—	13	1	no	—
505	C₄⋊C₄	—	13	2	no	—
506	C₄⋊C₄	—	13	2	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	1	no	—
517	C₄⋊C₄	—	13	1	no	—
518	C₄⋊C₄	—	13	1	no	—
519	C₄⋊C₄	—	13	1	no	—
520	C₄⋊C₄	—	13	1	no	—
521	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
523	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
526	C₂²⋊C₄	—	13	2	no	—
527	C₂²⋊C₄	—	13	2	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	1	no	—
533	C₂²⋊C₄	—	13	1	no	—
534	C₂²⋊C₄	—	13	1	no	—
535	C₂²⋊C₄	—	13	1	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	C₂²×D₁₃	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
548	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
549	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
550	C₄²	—	13	1	no	—
551	C₄²	—	13	1	no	—
552	C₄²	—	13	1	no	—
553	C₄²	—	13	2	no	—
554	C₄²	—	13	2	no	—
555	C₄²	—	13	2	no	—
556	C₄²	—	13	1	no	—
557	C₄²	—	13	1	no	—
558	C₄²	C₂²×D₁₃	1	1	yes	characteristic
559	C₄²	C₂²×D₁₃	1	2	yes	—
560	C₄²	C₂²×D₁₃	1	1	yes	characteristic
561	C₄²	C₂²×D₁₃	1	1	yes	characteristic
562	C₁₃	#3506	1	1	yes	characteristic, complemented, Sylow
563	C₂³	—	13	1	no	—
564	C₂³	—	13	2	no	—
565	C₂³	—	13	2	no	—
566	C₂³	—	26	4	no	—
567	C₂³	—	52	2	no	—
568	C₂³	—	52	2	no	—
569	C₂³	C₂³×D₁₃	1	2	yes	—
570	C₂³	C₂³×D₁₃	1	2	yes	—
571	Q₈	—	2	2	no	—
572	Q₈	—	4	1	no	—
573	Q₈	—	26	2	no	—
574	Q₈	—	26	2	no	—
575	Q₈	—	26	2	no	—
576	Q₈	—	52	1	no	—
577	D₄	—	2	2	no	—
578	D₄	—	2	2	no	—
579	D₄	—	4	2	no	—
580	D₄	—	4	2	no	—
581	D₄	—	26	4	no	—
582	D₄	—	26	4	no	—
583	D₄	—	26	4	no	—
584	D₄	—	26	4	no	—
585	D₄	—	26	2	no	—
586	D₄	—	26	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	2	no	—
592	D₄	—	52	2	no	—
593	D₄	—	52	2	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	13	1	no	—
597	C₂×C₄	—	13	1	no	—
598	C₂×C₄	—	13	4	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	2	no	—
604	C₂×C₄	—	13	1	no	—
605	C₂×C₄	—	13	1	no	—
606	C₂×C₄	—	26	2	no	—
607	C₂×C₄	—	26	4	no	—
608	C₂×C₄	—	26	4	no	—
609	C₂×C₄	—	26	4	no	—
610	C₂×C₄	—	26	4	no	—
611	C₂×C₄	—	52	1	no	—
612	C₂×C₄	—	52	2	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	C₂³×D₁₃	1	1	yes	characteristic
618	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₁₃	1	2	yes	—
620	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₁₃	1	2	yes	—
622	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
626	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	13	2	no	—
633	C₂²	—	26	1	no	—
634	C₂²	—	26	1	no	—
635	C₂²	—	26	2	no	—
636	C₂²	—	26	2	no	—
637	C₂²	—	26	2	no	—
638	C₂²	—	26	2	no	—
639	C₂²	—	26	2	no	—
640	C₂²	—	26	2	no	—
641	C₂²	—	52	8	no	—
642	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
643	C₄	—	2	2	no	—
644	C₄	—	2	1	no	—
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	13	2	no	—
652	C₄	—	13	2	no	—
653	C₄	—	26	2	no	—
654	C₄	—	26	1	no	—
655	C₄	—	26	1	no	—
656	C₄	—	26	1	no	—
657	C₄	—	26	2	no	—
658	C₄	—	26	1	no	—
659	C₄	—	26	1	no	—
660	C₄	#41×D₁₃	1	2	yes	—
661	C₂	—	4	2	no	—
662	C₂	—	4	2	no	—
663	C₂	—	26	2	no	—
664	C₂	—	52	2	no	—
665	C₂	—	52	2	no	—
666	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
667	C₂	#11719648	1	1	yes	characteristic
668	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#559	C₂
hypercenter	#559	D₁₃
hypocenter	C₁₃	#3506
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
2. #11719423	C₂	semidirect
3. #11719420	C₂	semidirect
4. #11719386	C₂	semidirect
5. #11719383	C₂	semidirect
6. #11719379	C₂	semidirect
7. #11719376	C₂	semidirect
8. #11719375	C₂	semidirect
9. #11719373	C₂	semidirect
10. #11719366	C₂	semidirect
11. #11719362	C₂	semidirect
12. #11719361	C₂	semidirect
13. #11719360	C₂	semidirect
14. #11719290	C₂	semidirect
15. #11719283	C₂	semidirect
16. #11719279	C₂	semidirect
17. #11719273	C₂	semidirect
18. #11719264	C₂	semidirect
19. #11719258	C₂	semidirect
20. #11719252	C₂	semidirect
21. #11719251	C₂	semidirect
22. C₄×D₄×D₁₃	C₂	semidirect
23. #11719245	C₂	semidirect
26. C₂×#6129	C₂²	semidirect
28. C₂×#6127	C₂²	semidirect
32. C₁₃×#124	C₂²	semidirect
33. C₁₃×#124	C₂²	semidirect
34. C₁₃×#123	C₂²	semidirect
35. C₁₃×#123	C₂²	semidirect
36. C₄×Q₈×C₁₃	C₂²	semidirect
37. C₄×Q₈×C₁₃	C₂²	semidirect
39. C₄×D₄×C₁₃	C₂²	semidirect
40. C₄×D₄×C₁₃	C₂²	semidirect
42. #88201	C₂²	semidirect
44. Q₈×Dic₁₃	C₂²	semidirect
45. #88198	C₂²	semidirect
46. #88198	C₂²	semidirect
49. #88194	C₂²	semidirect
52. #88193	C₂²	semidirect
53. #88193	C₂²	semidirect
54. #88192	C₂²	semidirect
59. D₄×Dic₁₃	C₂²	semidirect
60. #88184	C₂²	semidirect
61. #88183	C₂²	semidirect
64. C₄×C₂²⋊D₁₃	C₂²	semidirect
65. C₂×#6101	C₂²	semidirect
66. #88152	C₂²	semidirect
70. #88150	C₂²	semidirect
71. #88148	C₂²	semidirect
72. #88148	C₂²	semidirect
75. #88147	C₂²	semidirect
76. #88147	C₂²	semidirect
78. C₄⋊C₄×D₁₃	C₂²	semidirect
79. #88143	C₂²	semidirect
80. #88143	C₂²	semidirect
81. #88142	C₂²	semidirect
82. #88141	C₂²	semidirect
83. #88140	C₂²	semidirect
84. #88139	C₂²	semidirect
85. #88139	C₂²	semidirect
90. #88138	C₂²	semidirect
91. #88138	C₂²	semidirect
92. #88137	C₂²	semidirect
93. #88137	C₂²	semidirect
98. #88135	C₂²	semidirect
99. #88135	C₂²	semidirect
100. #88135	C₂²	semidirect
102. #88133	C₂²	semidirect
103. #88133	C₂²	semidirect
104. #88132	C₂²	semidirect
105. #88131	C₂²	semidirect
106. #88131	C₂²	semidirect
107. #88130	C₂²	semidirect
109. #88129	C₂²	semidirect
113. C₄×D₅₂	C₂²	semidirect
116. #88126	C₂²	semidirect
117. #88126	C₂²	semidirect
119. C₄×Dic₂₆	C₂²	semidirect
120. C₄×Dic₂₆	C₂²	semidirect
121. C₄×Dic₂₆	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
287. C₄×D₁₃	#41	semidirect
295. #559	D₁₃	semidirect
378. #124	C₂×D₁₃	semidirect
379. #124	C₂×D₁₃	semidirect
386. #123	C₂×D₁₃	semidirect
387. #123	C₂×D₁₃	semidirect
416. C₄×Q₈	C₂×D₁₃	semidirect
417. C₄×Q₈	C₂×D₁₃	semidirect
436. C₄×D₄	C₂×D₁₃	semidirect
437. C₄×D₄	C₂×D₁₃	semidirect
562. C₁₃	#3506	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
#11719423	2
#11719420	2
#11719386	2
#11719383	2
#11719379	2
#11719376	2
#11719375	2
#11719373	2
#11719366	2
#11719362	2
#11719361	2
#11719360	2
#11719290	2
#11719283	2
#11719279	2
#11719273	2
#11719264	2
#11719258	2
#11719252	2
#11719251	2
C₄×D₄×D₁₃	2
#11719245	2
#3506	13