Subgroups — #13129148

Order 1664.

1160 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719439	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719431	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719416	C₂	1	2	yes	maximal, complemented
5	#11719410	C₂	1	2	yes	maximal, complemented
6	#11719383	C₂	1	2	yes	maximal, complemented
7	#11719381	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719381	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719379	C₂	1	2	yes	maximal, complemented
10	#11719368	C₂	1	2	yes	maximal, complemented
11	#11719358	C₂	1	2	yes	maximal, complemented
12	#11719352	C₂	1	2	yes	maximal, complemented
13	#11719335	C₂	1	2	yes	maximal, complemented
14	#11719334	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719332	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719312	C₂	1	1	yes	maximal, characteristic, complemented
17	D₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719286	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719282	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719263	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719240	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719229	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#6131	C₂²	1	2	yes	complemented
25	C₂×#6131	C₂²	1	1	yes	characteristic, complemented
26	C₂×#6131	C₂²	1	1	yes	characteristic, complemented
27	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×D₁₃	C₂²	1	2	yes	complemented
30	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
31	C₂²×D₅₂	C₂²	1	2	yes	—
32	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#126	C₂²	1	2	yes	complemented
35	C₁₃×#124	C₂²	1	2	yes	complemented
36	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#123	C₂²	1	2	yes	complemented
38	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
40	C₁₃×#121	C₂²	1	1	yes	characteristic
41	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
42	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
44	#88201	C₂²	1	2	yes	complemented
45	#88201	C₂²	1	2	yes	complemented
46	#88200	C₂²	1	2	yes	complemented
47	#88200	C₂²	1	1	yes	characteristic, complemented
48	#88200	C₂²	1	1	yes	characteristic, complemented
49	#88194	C₂²	1	2	yes	complemented
50	#88193	C₂²	1	2	yes	complemented
51	#88192	C₂²	1	1	yes	characteristic
52	#88192	C₂²	1	1	yes	characteristic, complemented
53	#88191	C₂²	1	2	yes	complemented
54	#88184	C₂²	1	1	yes	characteristic, complemented
55	#88184	C₂²	1	1	yes	characteristic, complemented
56	#88184	C₂²	1	2	yes	complemented
57	#88183	C₂²	1	2	yes	complemented
58	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
59	#88151	C₂²	1	1	yes	characteristic, complemented
60	#88151	C₂²	1	1	yes	characteristic, complemented
61	#88150	C₂²	1	2	yes	complemented
62	#88149	C₂²	1	1	yes	characteristic
63	#88149	C₂²	1	1	yes	characteristic
64	#88149	C₂²	1	1	yes	characteristic, complemented
65	#88149	C₂²	1	1	yes	characteristic, complemented
66	#88149	C₂²	1	1	yes	characteristic, complemented
67	#88149	C₂²	1	2	yes	complemented
68	#88149	C₂²	1	1	yes	characteristic, complemented
69	#88149	C₂²	1	2	yes	complemented
70	#88149	C₂²	1	2	yes	complemented
71	#88149	C₂²	1	2	yes	complemented
72	#88148	C₂²	1	2	yes	—
73	#88148	C₂²	1	2	yes	complemented
74	#88148	C₂²	1	2	yes	complemented
75	#88148	C₂²	1	2	yes	complemented
76	#88148	C₂²	1	2	yes	complemented
77	#88148	C₂²	1	2	yes	complemented
78	#88147	C₂²	1	2	yes	complemented
79	#88146	C₂²	1	1	yes	characteristic, complemented
80	#88146	C₂²	1	1	yes	characteristic, complemented
81	#88146	C₂²	1	2	yes	complemented
82	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
83	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
84	#88143	C₂²	1	2	yes	complemented
85	#88140	C₂²	1	1	yes	characteristic, complemented
86	#88140	C₂²	1	1	yes	characteristic, complemented
87	#88139	C₂²	1	2	yes	complemented
88	#88138	C₂²	1	2	yes	complemented
89	#88138	C₂²	1	2	yes	complemented
90	#88138	C₂²	1	2	yes	complemented
91	#88138	C₂²	1	2	yes	complemented
92	#88138	C₂²	1	2	yes	complemented
93	#88138	C₂²	1	2	yes	complemented
94	#88138	C₂²	1	2	yes	complemented
95	#88138	C₂²	1	2	yes	complemented
96	#88137	C₂²	1	2	yes	complemented
97	#88137	C₂²	1	2	yes	complemented
98	#88136	C₂²	1	1	yes	characteristic
99	#88136	C₂²	1	2	yes	—
100	#88136	C₂²	1	1	yes	characteristic, complemented
101	#88136	C₂²	1	2	yes	complemented
102	#88136	C₂²	1	2	yes	complemented
103	#88136	C₂²	1	2	yes	complemented
104	#88136	C₂²	1	2	yes	complemented
105	#88136	C₂²	1	2	yes	complemented
106	#88135	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
108	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
110	#88133	C₂²	1	2	yes	complemented
111	#88130	C₂²	1	2	yes	complemented
112	#88128	C₂²	1	1	yes	characteristic, complemented
113	#88128	C₂²	1	2	yes	complemented
114	C₄×D₅₂	C₂²	1	1	yes	characteristic
115	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₅₂	C₂²	1	2	yes	complemented
121	#88126	C₂²	1	2	yes	complemented
122	#88124	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₃	C₂³	1	2	yes	—
124	C₂³×D₁₃	C₂³	1	1	yes	characteristic
125	C₂³×D₁₃	C₂³	1	2	yes	—
126	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
128	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₃	C₂³	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
139	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
140	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
141	#6131	—	4	4	no	—
142	#6131	—	4	2	no	—
143	#6131	—	4	2	no	—
144	D₄×D₁₃	—	4	2	no	—
145	D₄×D₁₃	—	4	2	no	—
146	D₄×D₁₃	—	4	4	no	—
147	#6127	—	4	2	no	—
148	C₂×D₅₂	—	4	4	no	—
149	C₂×D₅₂	C₂³	1	1	yes	characteristic
150	C₂×D₅₂	C₂³	1	1	yes	characteristic
151	C₂×D₅₂	C₂³	1	1	yes	characteristic
152	C₂×D₅₂	C₂³	1	1	yes	characteristic
153	C₂×D₅₂	C₂³	1	2	yes	—
154	C₂×D₅₂	C₂³	1	2	yes	—
155	C₂×D₅₂	C₂³	1	1	yes	characteristic
156	C₂×D₅₂	C₂³	1	1	yes	characteristic
157	C₂×D₅₂	C₂³	1	2	yes	—
158	C₂×D₅₂	C₂³	1	2	yes	—
159	C₂×D₅₂	C₂³	1	2	yes	—
160	C₂×D₅₂	C₂³	1	2	yes	—
161	C₂×D₅₂	C₂³	1	2	yes	—
162	C₂×D₅₂	C₂³	1	1	yes	characteristic
163	C₂×D₅₂	C₂³	1	2	yes	—
164	C₂×C₄×D₁₃	—	4	2	no	—
165	C₂×C₄×D₁₃	C₂³	1	2	yes	—
166	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
167	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
168	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
169	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
170	C₂×C₄×D₁₃	C₂³	1	2	yes	—
171	C₂×C₄×D₁₃	C₂³	1	2	yes	—
172	C₂×C₄×D₁₃	C₂³	1	2	yes	—
173	C₂×C₄×D₁₃	C₂³	1	2	yes	—
174	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
175	C₂×C₄×D₁₃	C₂³	1	2	yes	—
176	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
177	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
178	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
182	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
183	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
191	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
192	C₄²×C₁₃	C₂³	1	1	yes	characteristic
193	C₄²×C₁₃	C₂³	1	2	yes	—
194	C₄²×C₁₃	C₂³	1	1	yes	characteristic
195	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
196	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
197	#6103	C₂³	1	1	yes	characteristic
198	#6103	C₂³	1	2	yes	—
199	#6103	C₂³	1	1	yes	characteristic
200	#6103	C₂³	1	1	yes	characteristic
201	#6103	C₂³	1	1	yes	characteristic
202	#6103	C₂³	1	2	yes	—
203	#6103	C₂³	1	1	yes	characteristic
204	#6103	C₂³	1	2	yes	—
205	#6103	C₂³	1	2	yes	—
206	#6103	C₂³	1	1	yes	characteristic
207	#6103	C₂³	1	1	yes	characteristic
208	#6103	C₂³	1	2	yes	—
209	#6103	C₂³	1	1	yes	characteristic
210	#6103	C₂³	1	2	yes	—
211	#6103	C₂³	1	2	yes	—
212	#6103	C₂³	1	2	yes	—
213	#6103	C₂³	1	2	yes	—
214	#6103	C₂³	1	2	yes	—
215	#6103	C₂³	1	2	yes	—
216	#6103	C₂³	1	2	yes	—
217	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
218	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
219	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
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	#6101	C₂³	1	2	yes	—
224	#6101	C₂³	1	2	yes	—
225	#6101	C₂³	1	2	yes	—
226	#6101	C₂³	1	2	yes	—
227	#6101	C₂³	1	2	yes	—
228	#6101	C₂³	1	2	yes	—
229	C₄×Dic₁₃	C₂³	1	2	yes	—
230	C₄×Dic₁₃	C₂³	1	2	yes	—
231	#3542	—	13	1	no	maximal, Sylow
232	C₂³×C₁₃	C₂⁴	1	2	yes	—
233	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
234	C₂²×D₁₃	—	2	2	no	—
235	C₂²×D₁₃	—	2	4	no	—
236	C₂²×D₁₃	—	4	1	no	—
237	C₂²×D₁₃	—	4	1	no	—
238	C₂²×D₁₃	—	4	2	no	—
239	C₂²×D₁₃	—	4	2	no	—
240	C₂²×D₁₃	—	4	2	no	—
241	C₂²×D₁₃	—	4	2	no	—
242	C₂²×D₁₃	—	4	2	no	—
243	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
244	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
245	C₂²×D₁₃	C₂⁴	1	2	yes	—
246	C₂²×D₁₃	C₂⁴	1	2	yes	—
247	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
248	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
249	Q₈×C₁₃	—	2	2	no	—
250	Q₈×C₁₃	—	4	2	no	—
251	D₄×C₁₃	—	2	2	no	—
252	D₄×C₁₃	—	4	2	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	4	2	no	—
255	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
257	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
260	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂²⋊D₁₃	—	4	1	no	—
265	C₂²⋊D₁₃	—	4	1	no	—
266	C₂²⋊D₁₃	—	4	2	no	—
267	C₂²⋊D₁₃	—	4	2	no	—
268	C₂²⋊D₁₃	—	4	2	no	—
269	C₂²⋊D₁₃	—	4	2	no	—
270	C₂²⋊D₁₃	—	4	2	no	—
271	C₂²⋊D₁₃	—	4	2	no	—
272	C₂×Dic₁₃	—	4	1	no	—
273	C₂×Dic₁₃	C₂⁴	1	2	yes	—
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	1	yes	characteristic
278	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
279	D₅₂	—	2	2	no	—
280	D₅₂	—	2	4	no	—
281	D₅₂	—	2	2	no	—
282	D₅₂	—	2	2	no	—
283	D₅₂	—	2	2	no	—
284	D₅₂	—	4	2	no	—
285	D₅₂	—	4	2	no	—
286	D₅₂	—	4	1	no	—
287	D₅₂	—	4	2	no	—
288	D₅₂	—	4	1	no	—
289	D₅₂	—	4	1	no	—
290	D₅₂	—	4	2	no	—
291	D₅₂	—	4	2	no	—
292	D₅₂	—	4	2	no	—
293	D₅₂	—	4	2	no	—
294	C₄×D₁₃	—	2	4	no	—
295	C₄×D₁₃	—	2	2	no	—
296	C₄×D₁₃	—	2	2	no	—
297	C₄×D₁₃	—	2	2	no	—
298	C₄×D₁₃	—	2	2	no	—
299	C₄×D₁₃	—	4	1	no	—
300	C₄×D₁₃	—	4	1	no	—
301	C₄×D₁₃	—	4	2	no	—
302	C₄×D₁₃	—	4	2	no	—
303	C₄×D₁₃	—	4	2	no	—
304	C₄×D₁₃	—	4	2	no	—
305	C₄×D₁₃	—	4	2	no	—
306	Dic₂₆	—	4	1	no	—
307	#562	—	13	2	no	—
308	#560	—	13	2	no	—
309	#555	—	13	1	no	—
310	#553	—	13	1	no	—
311	#552	—	13	1	no	—
312	#551	—	13	2	no	—
313	#550	—	13	1	no	—
314	#547	—	13	1	no	—
315	#546	—	13	1	no	—
316	#546	—	13	1	no	—
317	#546	—	13	2	no	—
318	D₄²	—	13	1	no	—
319	#542	D₁₃	1	1	yes	characteristic, complemented
320	#540	—	13	2	no	—
321	#540	—	13	1	no	—
322	#538	—	13	2	no	—
323	#537	—	13	1	no	—
324	#535	—	13	2	no	—
325	#535	—	13	1	no	—
326	#534	—	13	2	no	—
327	#525	—	13	1	no	—
328	#525	—	13	1	no	—
329	C₂×#121	—	13	1	no	—
330	C₂²×C₁₃	—	2	1	no	—
331	C₂²×C₁₃	—	2	2	no	—
332	C₂²×C₁₃	—	2	1	no	—
333	C₂²×C₁₃	—	2	2	no	—
334	C₂²×C₁₃	—	2	1	no	—
335	C₂²×C₁₃	—	2	2	no	—
336	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
337	C₂×D₁₃	—	2	1	no	—
338	C₂×D₁₃	—	2	1	no	—
339	C₂×D₁₃	—	2	1	no	—
340	C₂×D₁₃	—	2	1	no	—
341	C₂×D₁₃	—	2	1	no	—
342	C₂×D₁₃	—	2	1	no	—
343	C₂×D₁₃	—	2	2	no	—
344	C₂×D₁₃	—	2	2	no	—
345	C₂×D₁₃	—	2	2	no	—
346	C₂×D₁₃	—	2	1	no	—
347	C₂×D₁₃	—	2	2	no	—
348	C₂×D₁₃	—	2	1	no	—
349	C₂×D₁₃	—	2	2	no	—
350	C₂×D₁₃	—	2	1	no	—
351	C₂×D₁₃	—	2	1	no	—
352	C₂×D₁₃	—	2	2	no	—
353	C₂×D₁₃	—	2	1	no	—
354	C₂×D₁₃	—	4	4	no	—
355	C₂×D₁₃	—	8	4	no	—
356	C₂×D₁₃	—	8	4	no	—
357	C₂×D₁₃	H(5,𝔽₂)	1	2	yes	—
358	C₄×C₁₃	—	2	1	no	—
359	C₄×C₁₃	—	2	2	no	—
360	C₄×C₁₃	—	2	1	no	—
361	C₄×C₁₃	—	2	2	no	—
362	C₄×C₁₃	—	2	2	no	—
363	C₄×C₁₃	—	2	1	no	—
364	C₄×C₁₃	—	2	1	no	—
365	C₄×C₁₃	—	2	1	no	—
366	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
367	Dic₁₃	—	2	1	no	—
368	Dic₁₃	—	2	1	no	—
369	Dic₁₃	—	2	1	no	—
370	Dic₁₃	—	2	2	no	—
371	Dic₁₃	—	2	1	no	—
372	Dic₁₃	—	2	2	no	—
373	C₂×#41	—	13	1	no	—
374	C₂×#41	—	13	2	no	—
375	C₂×#41	—	13	1	no	—
376	C₂×#41	—	13	1	no	—
377	C₂²×D₄	—	13	2	no	—
378	C₂²×D₄	—	13	1	no	—
379	C₂²×D₄	—	13	1	no	—
380	C₂²×D₄	—	13	2	no	—
381	C₂³×C₄	—	13	1	no	—
382	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
383	#127	—	13	2	no	—
384	#127	—	13	2	no	—
385	#127	—	13	1	no	—
386	#126	—	13	2	no	—
387	#126	—	13	2	no	—
388	#126	C₂×D₁₃	1	2	yes	complemented
389	#125	—	13	2	no	—
390	#125	—	13	1	no	—
391	#124	—	13	2	no	—
392	#124	—	13	2	no	—
393	#124	—	13	2	no	—
394	#124	C₂×D₁₃	1	2	yes	complemented
395	#124	C₂×D₁₃	1	1	yes	characteristic, complemented
396	#123	—	13	2	no	—
397	#123	—	13	2	no	—
398	#123	—	13	2	no	—
399	#123	—	13	2	no	—
400	#123	—	13	2	no	—
401	#123	—	13	2	no	—
402	#123	—	13	2	no	—
403	#123	—	13	1	no	—
404	#123	—	13	1	no	—
405	#123	—	13	2	no	—
406	#123	—	13	2	no	—
407	#123	C₂×D₁₃	1	2	yes	complemented
408	C₂²⋊Q₈	—	13	1	no	—
409	C₂²⋊Q₈	—	13	1	no	—
410	C₂²⋊Q₈	—	13	2	no	—
411	C₂²⋊Q₈	—	13	1	no	—
412	C₂²⋊Q₈	—	13	1	no	—
413	C₂²⋊Q₈	—	13	2	no	—
414	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
415	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
416	#121	—	13	2	no	—
417	#121	—	13	1	no	—
418	#121	—	13	1	no	—
419	#121	—	13	1	no	—
420	#121	—	13	1	no	—
421	#121	—	13	2	no	—
422	#121	—	13	1	no	—
423	#121	—	13	1	no	—
424	#121	—	13	1	no	—
425	#121	—	13	1	no	—
426	#121	—	13	2	no	—
427	#121	—	13	2	no	—
428	#121	—	13	1	no	—
429	#121	—	13	1	no	—
430	#121	—	13	2	no	—
431	#121	—	13	2	no	—
432	#121	—	13	2	no	—
433	#121	—	13	2	no	—
434	#121	—	13	2	no	—
435	#121	—	13	2	no	—
436	#121	—	13	2	no	—
437	#121	—	13	2	no	—
438	#121	—	13	2	no	—
439	#121	—	13	2	no	—
440	#121	C₂×D₁₃	1	1	yes	characteristic
441	#120	—	13	2	no	—
442	#120	—	13	1	no	—
443	#120	—	13	2	no	—
444	#120	—	13	1	no	—
445	#120	—	13	2	no	—
446	#120	—	13	2	no	—
447	#120	—	13	2	no	—
448	#120	—	13	2	no	—
449	#120	—	13	2	no	—
450	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
451	C₄×D₄	—	13	2	no	—
452	C₄×D₄	—	13	2	no	—
453	C₄×D₄	—	13	2	no	—
454	C₄×D₄	—	13	1	no	—
455	C₄×D₄	—	13	1	no	—
456	C₄×D₄	—	13	1	no	—
457	C₄×D₄	—	13	1	no	—
458	C₄×D₄	—	13	2	no	—
459	C₄×D₄	—	13	1	no	—
460	C₄×D₄	—	13	1	no	—
461	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
462	#117	—	13	1	no	—
463	#117	—	13	1	no	—
464	#117	—	13	2	no	—
465	#117	—	13	2	no	—
466	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
467	C₂×C₄⋊C₄	—	13	1	no	—
468	C₂×C₄⋊C₄	—	13	1	no	—
469	C₂×C₂²⋊C₄	—	13	2	no	—
470	C₂×C₂²⋊C₄	—	13	2	no	—
471	C₂×C₂²⋊C₄	—	13	2	no	—
472	C₂×C₁₃	—	4	1	no	—
473	C₂×C₁₃	—	4	2	no	—
474	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
475	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
476	C₂×C₁₃	#585	1	1	yes	characteristic
477	D₁₃	—	2	2	no	—
478	D₁₃	—	4	1	no	—
479	D₁₃	—	4	1	no	—
480	D₁₃	—	4	2	no	—
481	D₁₃	—	4	2	no	—
482	D₁₃	—	4	1	no	—
483	C₂⁴	—	13	2	no	—
484	C₂⁴	—	13	1	no	—
485	C₂⁴	—	13	2	no	—
486	#41	—	52	2	no	—
487	#41	—	52	4	no	—
488	#41	—	52	2	no	—
489	#41	—	52	2	no	—
490	C₂×Q₈	—	13	1	no	—
491	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
492	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
493	C₂×D₄	—	13	2	no	—
494	C₂×D₄	—	13	2	no	—
495	C₂×D₄	—	13	1	no	—
496	C₂×D₄	—	13	2	no	—
497	C₂×D₄	—	13	2	no	—
498	C₂×D₄	—	13	2	no	—
499	C₂×D₄	—	13	1	no	—
500	C₂×D₄	—	13	2	no	—
501	C₂×D₄	—	13	1	no	—
502	C₂×D₄	—	13	2	no	—
503	C₂×D₄	—	13	1	no	—
504	C₂×D₄	—	13	1	no	—
505	C₂×D₄	—	13	1	no	—
506	C₂×D₄	—	13	1	no	—
507	C₂×D₄	—	13	2	no	—
508	C₂×D₄	—	13	1	no	—
509	C₂×D₄	—	13	1	no	—
510	C₂×D₄	—	13	2	no	—
511	C₂×D₄	—	13	2	no	—
512	C₂×D₄	—	13	2	no	—
513	C₂×D₄	—	13	2	no	—
514	C₂×D₄	—	13	2	no	—
515	C₂×D₄	—	13	2	no	—
516	C₂×D₄	—	52	4	no	—
517	C₂×D₄	—	52	2	no	—
518	C₂×D₄	—	52	2	no	—
519	C₂×D₄	—	52	4	no	—
520	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
521	C₂×D₄	C₂²×D₁₃	1	2	yes	—
522	C₂²×C₄	—	13	1	no	—
523	C₂²×C₄	—	13	2	no	—
524	C₂²×C₄	—	13	1	no	—
525	C₂²×C₄	—	13	1	no	—
526	C₂²×C₄	—	13	1	no	—
527	C₂²×C₄	—	13	1	no	—
528	C₂²×C₄	—	13	1	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	1	no	—
535	C₂²×C₄	—	52	2	no	—
536	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
537	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
538	C₄⋊C₄	—	13	1	no	—
539	C₄⋊C₄	—	13	2	no	—
540	C₄⋊C₄	—	13	2	no	—
541	C₄⋊C₄	—	13	1	no	—
542	C₄⋊C₄	—	13	1	no	—
543	C₄⋊C₄	—	13	2	no	—
544	C₄⋊C₄	—	13	2	no	—
545	C₄⋊C₄	—	13	1	no	—
546	C₄⋊C₄	—	13	1	no	—
547	C₄⋊C₄	—	13	2	no	—
548	C₄⋊C₄	—	13	2	no	—
549	C₄⋊C₄	—	13	1	no	—
550	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
551	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
552	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
553	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
554	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
555	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
556	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
557	C₂²⋊C₄	—	13	2	no	—
558	C₂²⋊C₄	—	13	2	no	—
559	C₂²⋊C₄	—	13	1	no	—
560	C₂²⋊C₄	—	13	1	no	—
561	C₂²⋊C₄	—	13	2	no	—
562	C₂²⋊C₄	—	13	2	no	—
563	C₂²⋊C₄	—	13	2	no	—
564	C₂²⋊C₄	—	13	2	no	—
565	C₂²⋊C₄	—	13	1	no	—
566	C₂²⋊C₄	—	13	2	no	—
567	C₂²⋊C₄	—	13	2	no	—
568	C₂²⋊C₄	—	13	2	no	—
569	C₂²⋊C₄	—	13	1	no	—
570	C₂²⋊C₄	—	13	1	no	—
571	C₂²⋊C₄	—	13	1	no	—
572	C₂²⋊C₄	—	13	2	no	—
573	C₂²⋊C₄	—	13	2	no	—
574	C₂²⋊C₄	—	13	1	no	—
575	C₂²⋊C₄	—	13	2	no	—
576	C₂²⋊C₄	—	13	2	no	—
577	C₂²⋊C₄	—	13	2	no	—
578	C₂²⋊C₄	—	13	1	no	—
579	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
580	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
581	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
582	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
583	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
584	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
585	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
586	C₄²	—	13	2	no	—
587	C₄²	—	13	2	no	—
588	C₄²	C₂²×D₁₃	1	2	yes	—
589	C₄²	C₂²×D₁₃	1	1	yes	characteristic
590	C₄²	C₂²×D₁₃	1	1	yes	characteristic
591	C₁₃	#3542	1	1	yes	characteristic, complemented, Sylow
592	C₂³	—	13	1	no	—
593	C₂³	—	13	1	no	—
594	C₂³	—	13	1	no	—
595	C₂³	—	13	2	no	—
596	C₂³	—	13	2	no	—
597	C₂³	—	13	1	no	—
598	C₂³	—	26	2	no	—
599	C₂³	—	26	4	no	—
600	C₂³	—	52	1	no	—
601	C₂³	—	52	1	no	—
602	C₂³	—	52	2	no	—
603	C₂³	—	52	2	no	—
604	C₂³	—	52	2	no	—
605	C₂³	—	52	2	no	—
606	C₂³	—	52	2	no	—
607	C₂³	C₂³×D₁₃	1	2	yes	—
608	C₂³	C₂³×D₁₃	1	1	yes	characteristic
609	Q₈	—	2	2	no	—
610	Q₈	—	4	2	no	—
611	Q₈	—	52	1	no	—
612	D₄	—	2	2	no	—
613	D₄	—	4	2	no	—
614	D₄	—	26	2	no	—
615	D₄	—	26	4	no	—
616	D₄	—	26	2	no	—
617	D₄	—	26	2	no	—
618	D₄	—	26	2	no	—
619	D₄	—	52	1	no	—
620	D₄	—	52	2	no	—
621	D₄	—	52	1	no	—
622	D₄	—	52	2	no	—
623	D₄	—	52	2	no	—
624	D₄	—	52	2	no	—
625	D₄	—	52	1	no	—
626	D₄	—	52	2	no	—
627	D₄	—	52	2	no	—
628	D₄	—	52	2	no	—
629	D₄	—	52	2	no	—
630	D₄	—	52	2	no	—
631	D₄	—	52	2	no	—
632	D₄	—	52	2	no	—
633	D₄	—	52	2	no	—
634	D₄	—	52	2	no	—
635	D₄	—	52	1	no	—
636	D₄	—	52	1	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	4	2	no	—
639	C₂×C₄	—	13	2	no	—
640	C₂×C₄	—	13	1	no	—
641	C₂×C₄	—	13	1	no	—
642	C₂×C₄	—	13	1	no	—
643	C₂×C₄	—	13	1	no	—
644	C₂×C₄	—	13	2	no	—
645	C₂×C₄	—	26	4	no	—
646	C₂×C₄	—	26	2	no	—
647	C₂×C₄	—	26	2	no	—
648	C₂×C₄	—	26	2	no	—
649	C₂×C₄	—	26	2	no	—
650	C₂×C₄	—	52	2	no	—
651	C₂×C₄	—	52	1	no	—
652	C₂×C₄	—	52	1	no	—
653	C₂×C₄	—	52	2	no	—
654	C₂×C₄	—	52	2	no	—
655	C₂×C₄	—	52	2	no	—
656	C₂×C₄	—	52	2	no	—
657	C₂×C₄	—	52	1	no	—
658	C₂×C₄	C₂³×D₁₃	1	2	yes	—
659	C₂×C₄	C₂³×D₁₃	1	2	yes	—
660	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
661	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
662	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
663	C₂×C₄	C₂³×D₁₃	1	2	yes	—
664	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
665	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
666	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
667	C₂²	—	2	1	no	—
668	C₂²	—	2	2	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	13	2	no	—
674	C₂²	—	26	1	no	—
675	C₂²	—	26	1	no	—
676	C₂²	—	26	1	no	—
677	C₂²	—	26	1	no	—
678	C₂²	—	26	1	no	—
679	C₂²	—	26	2	no	—
680	C₂²	—	26	2	no	—
681	C₂²	—	26	1	no	—
682	C₂²	—	26	2	no	—
683	C₂²	—	26	1	no	—
684	C₂²	—	26	1	no	—
685	C₂²	—	26	2	no	—
686	C₂²	—	26	2	no	—
687	C₂²	—	26	1	no	—
688	C₂²	—	26	1	no	—
689	C₂²	—	26	2	no	—
690	C₂²	—	26	1	no	—
691	C₂²	—	52	4	no	—
692	C₂²	—	104	4	no	—
693	C₂²	—	104	4	no	—
694	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
695	C₄	—	2	1	no	—
696	C₄	—	2	2	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	2	no	—
699	C₄	—	2	2	no	—
700	C₄	—	2	1	no	—
701	C₄	—	2	1	no	—
702	C₄	—	2	1	no	—
703	C₄	—	26	1	no	—
704	C₄	—	26	1	no	—
705	C₄	—	26	1	no	—
706	C₄	—	26	1	no	—
707	C₄	—	26	2	no	—
708	C₄	—	26	2	no	—
709	C₄	#88256	1	2	yes	—
710	C₂	—	4	1	no	—
711	C₂	—	4	2	no	—
712	C₂	—	26	2	no	—
713	C₂	—	52	1	no	—
714	C₂	—	52	1	no	—
715	C₂	—	52	2	no	—
716	C₂	—	52	2	no	—
717	C₂	—	52	1	no	—
718	C₂	C₂×#88256	1	1	yes	characteristic
719	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic
720	C₂	#11719652	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#542	C₂
hypercenter	#542	D₁₃
hypocenter	C₁₃	#3542
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. C₁₃×#542	C₂	semidirect
2. #11719439	C₂	semidirect
3. #11719431	C₂	semidirect
4. #11719416	C₂	semidirect
5. #11719410	C₂	semidirect
6. #11719383	C₂	semidirect
7. #11719381	C₂	semidirect
8. #11719381	C₂	semidirect
9. #11719379	C₂	semidirect
10. #11719368	C₂	semidirect
11. #11719358	C₂	semidirect
12. #11719352	C₂	semidirect
13. #11719335	C₂	semidirect
14. #11719334	C₂	semidirect
15. #11719332	C₂	semidirect
16. #11719312	C₂	semidirect
17. D₁₃×#121	C₂	semidirect
18. #11719286	C₂	semidirect
19. #11719282	C₂	semidirect
20. #11719263	C₂	semidirect
21. D₄×D₅₂	C₂	semidirect
22. #11719240	C₂	semidirect
23. #11719229	C₂	semidirect
24. C₂×#6131	C₂²	semidirect
25. C₂×#6131	C₂²	semidirect
26. C₂×#6131	C₂²	semidirect
28. C₂×D₄×D₁₃	C₂²	semidirect
29. C₂×D₄×D₁₃	C₂²	semidirect
30. C₂×#6127	C₂²	semidirect
32. C₂²×C₄×D₁₃	C₂²	semidirect
33. C₁₃×C₄⋊Q₈	C₂²	semidirect
34. C₁₃×#126	C₂²	semidirect
35. C₁₃×#124	C₂²	semidirect
36. C₁₃×#124	C₂²	semidirect
37. C₁₃×#123	C₂²	semidirect
38. C₁₃×C₂²⋊Q₈	C₂²	semidirect
39. C₁₃×C₂²⋊Q₈	C₂²	semidirect
41. C₄×Q₈×C₁₃	C₂²	semidirect
42. C₄×D₄×C₁₃	C₂²	semidirect
43. C₁₃×#117	C₂²	semidirect
44. #88201	C₂²	semidirect
45. #88201	C₂²	semidirect
46. #88200	C₂²	semidirect
47. #88200	C₂²	semidirect
48. #88200	C₂²	semidirect
49. #88194	C₂²	semidirect
50. #88193	C₂²	semidirect
52. #88192	C₂²	semidirect
53. #88191	C₂²	semidirect
54. #88184	C₂²	semidirect
55. #88184	C₂²	semidirect
56. #88184	C₂²	semidirect
57. #88183	C₂²	semidirect
58. C₄×C₂²⋊D₁₃	C₂²	semidirect
59. #88151	C₂²	semidirect
60. #88151	C₂²	semidirect
61. #88150	C₂²	semidirect
64. #88149	C₂²	semidirect
65. #88149	C₂²	semidirect
66. #88149	C₂²	semidirect
67. #88149	C₂²	semidirect
68. #88149	C₂²	semidirect
69. #88149	C₂²	semidirect
70. #88149	C₂²	semidirect
71. #88149	C₂²	semidirect
73. #88148	C₂²	semidirect
74. #88148	C₂²	semidirect
75. #88148	C₂²	semidirect
76. #88148	C₂²	semidirect
77. #88148	C₂²	semidirect
78. #88147	C₂²	semidirect
79. #88146	C₂²	semidirect
80. #88146	C₂²	semidirect
81. #88146	C₂²	semidirect
82. C₄⋊C₄×D₁₃	C₂²	semidirect
83. C₄⋊C₄×D₁₃	C₂²	semidirect
84. #88143	C₂²	semidirect
85. #88140	C₂²	semidirect
86. #88140	C₂²	semidirect
87. #88139	C₂²	semidirect
88. #88138	C₂²	semidirect
89. #88138	C₂²	semidirect
90. #88138	C₂²	semidirect
91. #88138	C₂²	semidirect
92. #88138	C₂²	semidirect
93. #88138	C₂²	semidirect
94. #88138	C₂²	semidirect
95. #88138	C₂²	semidirect
96. #88137	C₂²	semidirect
97. #88137	C₂²	semidirect
100. #88136	C₂²	semidirect
101. #88136	C₂²	semidirect
102. #88136	C₂²	semidirect
103. #88136	C₂²	semidirect
104. #88136	C₂²	semidirect
105. #88136	C₂²	semidirect
106. #88135	C₂²	semidirect
107. C₂²⋊C₄×D₁₃	C₂²	semidirect
108. C₂²⋊C₄×D₁₃	C₂²	semidirect
109. C₂²⋊C₄×D₁₃	C₂²	semidirect
110. #88133	C₂²	semidirect
111. #88130	C₂²	semidirect
112. #88128	C₂²	semidirect
113. #88128	C₂²	semidirect
115. C₄×D₅₂	C₂²	semidirect
116. C₄×D₅₂	C₂²	semidirect
117. C₄×D₅₂	C₂²	semidirect
118. C₄×D₅₂	C₂²	semidirect
119. C₄×D₅₂	C₂²	semidirect
120. C₄×D₅₂	C₂²	semidirect
121. #88126	C₂²	semidirect
122. #88124	C₂²	semidirect
319. #542	D₁₃	semidirect
382. C₄⋊Q₈	C₂×D₁₃	semidirect
388. #126	C₂×D₁₃	semidirect
394. #124	C₂×D₁₃	semidirect
395. #124	C₂×D₁₃	semidirect
407. #123	C₂×D₁₃	semidirect
414. C₂²⋊Q₈	C₂×D₁₃	semidirect
415. C₂²⋊Q₈	C₂×D₁₃	semidirect
450. C₄×Q₈	C₂×D₁₃	semidirect
461. C₄×D₄	C₂×D₁₃	semidirect
466. #117	C₂×D₁₃	semidirect
591. C₁₃	#3542	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#542	2
#11719439	2
#11719431	2
#11719416	2
#11719410	2
#11719383	2
#11719381	2
#11719379	2
#11719368	2
#11719358	2
#11719352	2
#11719335	2
#11719334	2
#11719332	2
#11719312	2
D₁₃×#121	2
#11719286	2
#11719282	2
#11719263	2
D₄×D₅₂	2
#11719240	2
#11719229	2
#3542	13