Subgroups — #13129064

Order 1664.

1134 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719438	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719431	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719405	C₂	1	2	yes	maximal, complemented
5	#11719397	C₂	1	2	yes	maximal, complemented
6	#11719352	C₂	1	2	yes	maximal, complemented
7	#11719339	C₂	1	2	yes	maximal, complemented
8	#11719338	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719335	C₂	1	2	yes	maximal, complemented
10	#11719335	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719334	C₂	1	2	yes	maximal, complemented
12	#11719334	C₂	1	1	yes	maximal, characteristic, complemented
13	D₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719287	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719281	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719265	C₂	1	2	yes	maximal, complemented
17	#11719255	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719255	C₂	1	2	yes	maximal, complemented
19	#11719252	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719216	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719215	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719212	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#88149	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×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×#6127	C₂²	1	2	yes	complemented
28	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
29	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
30	C₂²×D₅₂	C₂²	1	1	yes	characteristic
31	C₂²×D₅₂	C₂²	1	2	yes	—
32	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#125	C₂²	1	2	yes	complemented
35	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
37	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
39	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
40	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
41	C₄×D₄×C₁₃	C₂²	1	2	yes	—
42	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
44	#88201	C₂²	1	2	yes	complemented
45	#88201	C₂²	1	1	yes	characteristic, complemented
46	#88200	C₂²	1	2	yes	complemented
47	#88200	C₂²	1	2	yes	complemented
48	#88200	C₂²	1	1	yes	characteristic, complemented
49	#88193	C₂²	1	1	yes	characteristic
50	#88191	C₂²	1	1	yes	characteristic
51	#88191	C₂²	1	2	yes	—
52	#88184	C₂²	1	1	yes	characteristic, complemented
53	#88184	C₂²	1	2	yes	complemented
54	#88184	C₂²	1	2	yes	complemented
55	#88183	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
58	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
59	C₂×#6103	C₂²	1	2	yes	—
60	#88178	C₂²	1	1	yes	characteristic
61	#88178	C₂²	1	2	yes	—
62	#88152	C₂²	1	2	yes	complemented
63	#88151	C₂²	1	1	yes	characteristic, complemented
64	#88151	C₂²	1	1	yes	characteristic, complemented
65	#88151	C₂²	1	2	yes	complemented
66	#88151	C₂²	1	2	yes	complemented
67	#88150	C₂²	1	2	yes	complemented
68	#88150	C₂²	1	2	yes	complemented
69	#88150	C₂²	1	1	yes	characteristic, complemented
70	#88150	C₂²	1	2	yes	complemented
71	#88150	C₂²	1	2	yes	complemented
72	#88150	C₂²	1	2	yes	complemented
73	#88150	C₂²	1	2	yes	complemented
74	#88149	C₂²	1	1	yes	characteristic
75	#88149	C₂²	1	1	yes	characteristic
76	#88149	C₂²	1	1	yes	characteristic
77	#88149	C₂²	1	1	yes	characteristic
78	#88149	C₂²	1	2	yes	—
79	#88149	C₂²	1	2	yes	—
80	#88149	C₂²	1	1	yes	characteristic, complemented
81	#88149	C₂²	1	2	yes	complemented
82	#88149	C₂²	1	2	yes	complemented
83	#88149	C₂²	1	2	yes	complemented
84	#88149	C₂²	1	2	yes	complemented
85	#88148	C₂²	1	2	yes	complemented
86	#88148	C₂²	1	2	yes	complemented
87	#88148	C₂²	1	2	yes	complemented
88	#88148	C₂²	1	2	yes	complemented
89	#88148	C₂²	1	1	yes	characteristic, complemented
90	#88148	C₂²	1	2	yes	complemented
91	#88148	C₂²	1	2	yes	complemented
92	#88148	C₂²	1	2	yes	complemented
93	#88147	C₂²	1	1	yes	characteristic, complemented
94	#88147	C₂²	1	2	yes	complemented
95	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
96	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
97	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
98	#88143	C₂²	1	2	yes	complemented
99	#88142	C₂²	1	1	yes	characteristic, complemented
100	#88141	C₂²	1	1	yes	characteristic, complemented
101	#88139	C₂²	1	2	yes	complemented
102	#88138	C₂²	1	1	yes	characteristic, complemented
103	#88138	C₂²	1	2	yes	complemented
104	#88138	C₂²	1	2	yes	complemented
105	#88138	C₂²	1	2	yes	complemented
106	#88138	C₂²	1	2	yes	complemented
107	#88137	C₂²	1	1	yes	characteristic, complemented
108	#88136	C₂²	1	1	yes	characteristic
109	#88136	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
111	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
112	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
113	#88132	C₂²	1	1	yes	characteristic
114	#88132	C₂²	1	2	yes	—
115	#88130	C₂²	1	2	yes	complemented
116	#88129	C₂²	1	1	yes	characteristic, complemented
117	#88129	C₂²	1	2	yes	complemented
118	#88129	C₂²	1	2	yes	complemented
119	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₅₂	C₂²	1	2	yes	complemented
122	#88126	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₃	C₂³	1	1	yes	characteristic
124	C₂³×D₁₃	C₂³	1	2	yes	—
125	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
126	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
127	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
138	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
139	#6131	—	4	4	no	—
140	#6131	—	4	2	no	—
141	Q₈×D₁₃	—	4	2	no	—
142	#6127	—	4	2	no	—
143	#6127	—	4	2	no	—
144	#6127	—	4	4	no	—
145	C₂×D₅₂	—	4	2	no	—
146	C₂×D₅₂	—	4	4	no	—
147	C₂×D₅₂	C₂³	1	1	yes	characteristic
148	C₂×D₅₂	C₂³	1	2	yes	—
149	C₂×D₅₂	C₂³	1	1	yes	characteristic
150	C₂×D₅₂	C₂³	1	1	yes	characteristic
151	C₂×D₅₂	C₂³	1	2	yes	—
152	C₂×D₅₂	C₂³	1	2	yes	—
153	C₂×D₅₂	C₂³	1	2	yes	—
154	C₂×D₅₂	C₂³	1	1	yes	characteristic
155	C₂×D₅₂	C₂³	1	2	yes	—
156	C₂×D₅₂	C₂³	1	2	yes	—
157	C₂×D₅₂	C₂³	1	2	yes	—
158	C₂×C₄×D₁₃	—	4	2	no	—
159	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₁₃	C₂³	1	2	yes	—
163	C₂×C₄×D₁₃	C₂³	1	2	yes	—
164	C₂×C₄×D₁₃	C₂³	1	2	yes	—
165	C₂×C₄×D₁₃	C₂³	1	2	yes	—
166	C₂×C₄×D₁₃	C₂³	1	2	yes	—
167	C₂×C₄×D₁₃	C₂³	1	2	yes	—
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×Dic₂₆	C₂³	1	1	yes	characteristic
172	C₂×Dic₂₆	C₂³	1	2	yes	—
173	C₂×Dic₂₆	C₂³	1	2	yes	—
174	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
175	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
178	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
180	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
183	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
184	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
185	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
186	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
188	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₄²×C₁₃	C₂³	1	1	yes	characteristic
190	C₄²×C₁₃	C₂³	1	2	yes	—
191	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
192	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
193	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
194	#6103	C₂³	1	1	yes	characteristic
195	#6103	C₂³	1	1	yes	characteristic
196	#6103	C₂³	1	1	yes	characteristic
197	#6103	C₂³	1	1	yes	characteristic
198	#6103	C₂³	1	2	yes	—
199	#6103	C₂³	1	2	yes	—
200	#6103	C₂³	1	2	yes	—
201	#6103	C₂³	1	2	yes	—
202	#6103	C₂³	1	2	yes	—
203	#6103	C₂³	1	2	yes	—
204	#6103	C₂³	1	2	yes	—
205	#6103	C₂³	1	2	yes	—
206	#6103	C₂³	1	2	yes	—
207	#6103	C₂³	1	2	yes	—
208	#6103	C₂³	1	2	yes	—
209	#6103	C₂³	1	2	yes	—
210	#6103	C₂³	1	1	yes	characteristic
211	#6103	C₂³	1	2	yes	—
212	#6103	C₂³	1	1	yes	characteristic
213	#6103	C₂³	1	2	yes	—
214	#6103	C₂³	1	2	yes	—
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	#6101	C₂³	1	1	yes	characteristic
220	#6101	C₂³	1	1	yes	characteristic
221	#6101	C₂³	1	2	yes	—
222	#6101	C₂³	1	2	yes	—
223	#6101	C₂³	1	2	yes	—
224	#6101	C₂³	1	1	yes	characteristic
225	#6101	C₂³	1	1	yes	characteristic
226	#6101	C₂³	1	2	yes	—
227	#6101	C₂³	1	2	yes	—
228	#6101	C₂³	1	2	yes	—
229	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
230	C₄×Dic₁₃	C₂³	1	2	yes	—
231	#3536	—	13	1	no	maximal, Sylow
232	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
234	C₂²×D₁₃	—	2	2	no	—
235	C₂²×D₁₃	—	2	4	no	—
236	C₂²×D₁₃	—	2	2	no	—
237	C₂²×D₁₃	—	4	1	no	—
238	C₂²×D₁₃	—	4	2	no	—
239	C₂²×D₁₃	—	4	2	no	—
240	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
241	C₂²×D₁₃	C₂⁴	1	2	yes	—
242	C₂²×D₁₃	C₂⁴	1	2	yes	—
243	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
244	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
245	Q₈×C₁₃	—	2	2	no	—
246	Q₈×C₁₃	—	4	2	no	—
247	D₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	4	2	no	—
251	C₂×C₄×C₁₃	—	4	2	no	—
252	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
259	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₂²⋊D₁₃	—	2	2	no	—
262	C₂²⋊D₁₃	—	2	2	no	—
263	C₂²⋊D₁₃	—	4	2	no	—
264	C₂²⋊D₁₃	—	4	1	no	—
265	C₂²⋊D₁₃	—	4	2	no	—
266	C₂²⋊D₁₃	—	4	1	no	—
267	C₂×Dic₁₃	—	4	1	no	—
268	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₃	C₂⁴	1	2	yes	—
271	C₂×Dic₁₃	C₂⁴	1	2	yes	—
272	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
275	D₅₂	—	2	4	no	—
276	D₅₂	—	2	4	no	—
277	D₅₂	—	2	2	no	—
278	D₅₂	—	2	2	no	—
279	D₅₂	—	2	2	no	—
280	D₅₂	—	4	2	no	—
281	D₅₂	—	4	2	no	—
282	D₅₂	—	4	2	no	—
283	D₅₂	—	4	1	no	—
284	D₅₂	—	4	2	no	—
285	D₅₂	—	4	2	no	—
286	C₄×D₁₃	—	2	4	no	—
287	C₄×D₁₃	—	2	2	no	—
288	C₄×D₁₃	—	2	2	no	—
289	C₄×D₁₃	—	2	2	no	—
290	C₄×D₁₃	—	4	1	no	—
291	C₄×D₁₃	—	4	1	no	—
292	C₄×D₁₃	—	4	2	no	—
293	C₄×D₁₃	—	4	2	no	—
294	C₄×D₁₃	—	4	2	no	—
295	C₄×D₁₃	—	4	2	no	—
296	C₄×D₁₃	—	4	2	no	—
297	C₄×D₁₃	—	4	2	no	—
298	Dic₂₆	—	2	2	no	—
299	Dic₂₆	—	4	2	no	—
300	Dic₂₆	—	4	1	no	—
301	Dic₂₆	—	4	2	no	—
302	#562	—	13	2	no	—
303	#562	—	13	2	no	—
304	#554	—	13	1	no	—
305	#554	D₁₃	1	1	yes	characteristic, complemented
306	#548	—	13	1	no	—
307	#548	—	13	1	no	—
308	#547	—	13	1	no	—
309	#547	—	13	1	no	—
310	#546	—	13	2	no	—
311	#546	—	13	1	no	—
312	#546	—	13	2	no	—
313	#546	—	13	1	no	—
314	#543	—	13	2	no	—
315	#542	—	13	1	no	—
316	#542	—	13	1	no	—
317	#539	—	13	2	no	—
318	#538	—	13	2	no	—
319	#537	—	13	2	no	—
320	#537	—	13	1	no	—
321	#537	—	13	1	no	—
322	#525	—	13	1	no	—
323	C₂×C₂²⋊Q₈	—	13	1	no	—
324	C₂×#121	—	13	1	no	—
325	C₂²×C₁₃	—	2	1	no	—
326	C₂²×C₁₃	—	2	1	no	—
327	C₂²×C₁₃	—	2	1	no	—
328	C₂²×C₁₃	—	2	1	no	—
329	C₂²×C₁₃	—	2	1	no	—
330	C₂²×C₁₃	2₋¹⁺⁴	1	2	yes	—
331	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
332	C₂×D₁₃	—	2	1	no	—
333	C₂×D₁₃	—	2	1	no	—
334	C₂×D₁₃	—	2	1	no	—
335	C₂×D₁₃	—	2	1	no	—
336	C₂×D₁₃	—	2	1	no	—
337	C₂×D₁₃	—	2	2	no	—
338	C₂×D₁₃	—	2	2	no	—
339	C₂×D₁₃	—	2	2	no	—
340	C₂×D₁₃	—	2	2	no	—
341	C₂×D₁₃	—	2	1	no	—
342	C₂×D₁₃	—	2	1	no	—
343	C₂×D₁₃	—	2	1	no	—
344	C₂×D₁₃	—	2	2	no	—
345	C₂×D₁₃	—	2	2	no	—
346	C₂×D₁₃	—	4	4	no	—
347	C₂×D₁₃	—	8	4	no	—
348	C₂×D₁₃	H(5,𝔽₂)	1	2	yes	—
349	C₄×C₁₃	—	2	1	no	—
350	C₄×C₁₃	—	2	2	no	—
351	C₄×C₁₃	—	2	2	no	—
352	C₄×C₁₃	—	2	2	no	—
353	C₄×C₁₃	—	2	1	no	—
354	C₄×C₁₃	—	2	1	no	—
355	C₄×C₁₃	—	2	2	no	—
356	C₄×C₁₃	—	2	1	no	—
357	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
358	Dic₁₃	—	2	2	no	—
359	Dic₁₃	—	2	1	no	—
360	Dic₁₃	—	2	1	no	—
361	Dic₁₃	—	2	1	no	—
362	Dic₁₃	—	2	2	no	—
363	Dic₁₃	—	2	1	no	—
364	Dic₁₃	—	2	1	no	—
365	C₂×#41	—	13	2	no	—
366	C₂×#41	—	13	1	no	—
367	C₂×#41	—	13	1	no	—
368	C₂×#41	—	13	2	no	—
369	C₂×#41	—	13	1	no	—
370	C₂²×Q₈	—	13	1	no	—
371	C₂²×D₄	—	13	1	no	—
372	C₂²×D₄	—	13	2	no	—
373	C₂³×C₄	—	13	1	no	—
374	C₄⋊Q₈	—	13	1	no	—
375	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
376	#126	—	13	2	no	—
377	#126	—	13	2	no	—
378	#125	—	13	2	no	—
379	#125	C₂×D₁₃	1	2	yes	complemented
380	#124	—	13	1	no	—
381	#124	—	13	2	no	—
382	#124	—	13	2	no	—
383	#124	—	13	2	no	—
384	#124	—	13	1	no	—
385	#124	—	13	2	no	—
386	#123	—	13	2	no	—
387	#123	—	13	1	no	—
388	#123	—	13	2	no	—
389	#123	—	13	2	no	—
390	#123	—	13	2	no	—
391	#123	—	13	2	no	—
392	#123	—	13	2	no	—
393	#123	—	13	2	no	—
394	#123	—	13	2	no	—
395	#123	—	13	1	no	—
396	C₂²⋊Q₈	—	13	1	no	—
397	C₂²⋊Q₈	—	13	2	no	—
398	C₂²⋊Q₈	—	13	2	no	—
399	C₂²⋊Q₈	—	13	1	no	—
400	C₂²⋊Q₈	—	13	2	no	—
401	C₂²⋊Q₈	—	13	1	no	—
402	C₂²⋊Q₈	—	13	2	no	—
403	C₂²⋊Q₈	—	13	1	no	—
404	C₂²⋊Q₈	—	13	2	no	—
405	C₂²⋊Q₈	—	13	2	no	—
406	C₂²⋊Q₈	—	13	2	no	—
407	C₂²⋊Q₈	—	13	1	no	—
408	C₂²⋊Q₈	—	13	2	no	—
409	C₂²⋊Q₈	—	13	2	no	—
410	C₂²⋊Q₈	—	13	2	no	—
411	C₂²⋊Q₈	—	13	2	no	—
412	C₂²⋊Q₈	—	13	2	no	—
413	C₂²⋊Q₈	—	13	1	no	—
414	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
415	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
416	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
417	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
418	#121	—	13	1	no	—
419	#121	—	13	2	no	—
420	#121	—	13	1	no	—
421	#121	—	13	2	no	—
422	#121	—	13	2	no	—
423	#121	—	13	1	no	—
424	#121	—	13	1	no	—
425	#121	—	13	1	no	—
426	#121	—	13	1	no	—
427	#121	—	13	2	no	—
428	#121	—	13	1	no	—
429	#121	—	13	2	no	—
430	#121	—	13	2	no	—
431	#121	—	13	2	no	—
432	#121	—	13	2	no	—
433	#121	—	13	1	no	—
434	#121	—	13	2	no	—
435	#121	—	13	2	no	—
436	#121	—	13	2	no	—
437	#121	—	13	2	no	—
438	#120	—	13	1	no	—
439	#120	—	13	2	no	—
440	#120	—	13	1	no	—
441	#120	—	13	2	no	—
442	C₄×Q₈	—	13	1	no	—
443	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
444	C₄×D₄	—	13	1	no	—
445	C₄×D₄	—	13	1	no	—
446	C₄×D₄	—	13	2	no	—
447	C₄×D₄	—	13	2	no	—
448	C₄×D₄	—	13	1	no	—
449	C₄×D₄	—	13	1	no	—
450	C₄×D₄	—	13	2	no	—
451	C₄×D₄	—	13	1	no	—
452	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
453	C₄×D₄	C₂×D₁₃	1	2	yes	—
454	#117	—	13	1	no	—
455	C₂×C₄⋊C₄	—	13	2	no	—
456	C₂×C₄⋊C₄	—	13	1	no	—
457	C₂×C₄⋊C₄	—	13	1	no	—
458	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
460	C₂×C₂²⋊C₄	—	13	2	no	—
461	C₂×C₂²⋊C₄	—	13	2	no	—
462	C₂×C₂²⋊C₄	—	13	2	no	—
463	C₂×C₂²⋊C₄	—	13	2	no	—
464	C₂×C₁₃	—	2	2	no	—
465	C₂×C₁₃	—	4	1	no	—
466	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
467	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
468	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
469	D₁₃	—	2	2	no	—
470	D₁₃	—	4	1	no	—
471	D₁₃	—	4	1	no	—
472	D₁₃	—	4	2	no	—
473	D₁₃	—	4	2	no	—
474	C₂⁴	—	13	1	no	—
475	C₂⁴	—	13	2	no	—
476	#41	—	52	2	no	—
477	#41	—	52	2	no	—
478	#41	—	52	4	no	—
479	#41	—	52	4	no	—
480	#41	—	52	2	no	—
481	C₂×Q₈	—	13	1	no	—
482	C₂×Q₈	—	13	1	no	—
483	C₂×Q₈	—	13	2	no	—
484	C₂×Q₈	—	13	2	no	—
485	C₂×Q₈	—	52	2	no	—
486	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
487	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
488	C₂×D₄	—	13	1	no	—
489	C₂×D₄	—	13	1	no	—
490	C₂×D₄	—	13	1	no	—
491	C₂×D₄	—	13	2	no	—
492	C₂×D₄	—	13	2	no	—
493	C₂×D₄	—	13	1	no	—
494	C₂×D₄	—	13	1	no	—
495	C₂×D₄	—	13	2	no	—
496	C₂×D₄	—	13	2	no	—
497	C₂×D₄	—	13	1	no	—
498	C₂×D₄	—	13	1	no	—
499	C₂×D₄	—	13	2	no	—
500	C₂×D₄	—	13	1	no	—
501	C₂×D₄	—	13	2	no	—
502	C₂×D₄	—	13	2	no	—
503	C₂×D₄	—	13	2	no	—
504	C₂×D₄	—	13	2	no	—
505	C₂×D₄	—	52	2	no	—
506	C₂×D₄	—	52	4	no	—
507	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
508	C₂²×C₄	—	13	1	no	—
509	C₂²×C₄	—	13	2	no	—
510	C₂²×C₄	—	13	1	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	1	no	—
519	C₂²×C₄	—	13	2	no	—
520	C₂²×C₄	—	13	1	no	—
521	C₂²×C₄	—	52	2	no	—
522	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
523	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
524	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
525	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
526	C₄⋊C₄	—	13	1	no	—
527	C₄⋊C₄	—	13	2	no	—
528	C₄⋊C₄	—	13	2	no	—
529	C₄⋊C₄	—	13	2	no	—
530	C₄⋊C₄	—	13	2	no	—
531	C₄⋊C₄	—	13	2	no	—
532	C₄⋊C₄	—	13	1	no	—
533	C₄⋊C₄	—	13	1	no	—
534	C₄⋊C₄	—	13	2	no	—
535	C₄⋊C₄	—	13	1	no	—
536	C₄⋊C₄	—	13	1	no	—
537	C₄⋊C₄	—	13	1	no	—
538	C₄⋊C₄	—	13	2	no	—
539	C₄⋊C₄	—	13	2	no	—
540	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
541	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
542	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
543	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
544	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
545	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
546	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
547	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
548	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
549	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
550	C₂²⋊C₄	—	13	2	no	—
551	C₂²⋊C₄	—	13	1	no	—
552	C₂²⋊C₄	—	13	1	no	—
553	C₂²⋊C₄	—	13	2	no	—
554	C₂²⋊C₄	—	13	2	no	—
555	C₂²⋊C₄	—	13	2	no	—
556	C₂²⋊C₄	—	13	2	no	—
557	C₂²⋊C₄	—	13	2	no	—
558	C₂²⋊C₄	—	13	2	no	—
559	C₂²⋊C₄	—	13	2	no	—
560	C₂²⋊C₄	—	13	2	no	—
561	C₂²⋊C₄	—	13	2	no	—
562	C₂²⋊C₄	—	13	2	no	—
563	C₂²⋊C₄	—	13	1	no	—
564	C₂²⋊C₄	—	13	1	no	—
565	C₂²⋊C₄	—	13	1	no	—
566	C₂²⋊C₄	—	13	1	no	—
567	C₂²⋊C₄	—	13	2	no	—
568	C₂²⋊C₄	—	13	2	no	—
569	C₂²⋊C₄	—	13	2	no	—
570	C₂²⋊C₄	—	13	2	no	—
571	C₂²⋊C₄	—	13	1	no	—
572	C₂²⋊C₄	—	13	2	no	—
573	C₂²⋊C₄	—	13	1	no	—
574	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
575	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
576	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
577	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
578	C₄²	—	13	1	no	—
579	C₄²	—	13	2	no	—
580	C₄²	C₂²×D₁₃	1	1	yes	characteristic
581	C₄²	C₂²×D₁₃	1	2	yes	—
582	C₁₃	#3536	1	1	yes	characteristic, complemented, Sylow
583	C₂³	—	13	1	no	—
584	C₂³	—	13	1	no	—
585	C₂³	—	13	2	no	—
586	C₂³	—	13	2	no	—
587	C₂³	—	13	1	no	—
588	C₂³	—	26	2	no	—
589	C₂³	—	26	2	no	—
590	C₂³	—	26	4	no	—
591	C₂³	—	52	1	no	—
592	C₂³	—	52	2	no	—
593	C₂³	—	52	2	no	—
594	C₂³	C₂³×D₁₃	1	1	yes	characteristic
595	C₂³	C₂³×D₁₃	1	1	yes	characteristic
596	Q₈	—	2	2	no	—
597	Q₈	—	4	2	no	—
598	Q₈	—	26	2	no	—
599	Q₈	—	52	2	no	—
600	Q₈	—	52	1	no	—
601	Q₈	—	52	2	no	—
602	D₄	—	2	2	no	—
603	D₄	—	26	4	no	—
604	D₄	—	26	4	no	—
605	D₄	—	26	2	no	—
606	D₄	—	26	2	no	—
607	D₄	—	26	2	no	—
608	D₄	—	26	2	no	—
609	D₄	—	26	2	no	—
610	D₄	—	52	2	no	—
611	D₄	—	52	2	no	—
612	D₄	—	52	2	no	—
613	D₄	—	52	1	no	—
614	D₄	—	52	2	no	—
615	D₄	—	52	2	no	—
616	D₄	—	52	1	no	—
617	D₄	—	52	1	no	—
618	D₄	—	52	2	no	—
619	D₄	—	52	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	4	2	no	—
623	C₂×C₄	—	4	2	no	—
624	C₂×C₄	—	13	1	no	—
625	C₂×C₄	—	13	2	no	—
626	C₂×C₄	—	13	1	no	—
627	C₂×C₄	—	13	1	no	—
628	C₂×C₄	—	13	1	no	—
629	C₂×C₄	—	13	1	no	—
630	C₂×C₄	—	13	2	no	—
631	C₂×C₄	—	26	4	no	—
632	C₂×C₄	—	26	2	no	—
633	C₂×C₄	—	26	2	no	—
634	C₂×C₄	—	26	2	no	—
635	C₂×C₄	—	52	1	no	—
636	C₂×C₄	—	52	1	no	—
637	C₂×C₄	—	52	2	no	—
638	C₂×C₄	—	52	2	no	—
639	C₂×C₄	—	52	2	no	—
640	C₂×C₄	—	52	2	no	—
641	C₂×C₄	—	52	2	no	—
642	C₂×C₄	—	52	2	no	—
643	C₂×C₄	—	52	1	no	—
644	C₂×C₄	C₂³×D₁₃	1	2	yes	—
645	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
646	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
647	C₂×C₄	C₂³×D₁₃	1	2	yes	—
648	C₂×C₄	C₂³×D₁₃	1	2	yes	—
649	C₂×C₄	C₂³×D₁₃	1	2	yes	—
650	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
652	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	13	2	no	—
659	C₂²	—	26	1	no	—
660	C₂²	—	26	1	no	—
661	C₂²	—	26	1	no	—
662	C₂²	—	26	1	no	—
663	C₂²	—	26	2	no	—
664	C₂²	—	26	2	no	—
665	C₂²	—	26	1	no	—
666	C₂²	—	26	1	no	—
667	C₂²	—	26	2	no	—
668	C₂²	—	26	2	no	—
669	C₂²	—	26	1	no	—
670	C₂²	—	26	2	no	—
671	C₂²	—	26	2	no	—
672	C₂²	—	26	1	no	—
673	C₂²	—	52	4	no	—
674	C₂²	—	104	4	no	—
675	C₂²	#88254	1	2	yes	—
676	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
677	C₄	—	2	1	no	—
678	C₄	—	2	1	no	—
679	C₄	—	2	1	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	1	no	—
685	C₄	—	26	1	no	—
686	C₄	—	26	1	no	—
687	C₄	—	26	1	no	—
688	C₄	—	26	1	no	—
689	C₄	—	26	2	no	—
690	C₄	—	26	2	no	—
691	C₄	—	26	1	no	—
692	C₄	#88256	1	2	yes	—
693	C₂	—	2	2	no	—
694	C₂	—	4	1	no	—
695	C₂	—	26	2	no	—
696	C₂	—	52	1	no	—
697	C₂	—	52	2	no	—
698	C₂	—	52	2	no	—
699	C₂	—	52	1	no	—
700	C₂	C₂×#88254	1	1	yes	characteristic
701	C₂	C₂×#88256	1	1	yes	characteristic
702	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×#554	C₂
hypercenter	#554	D₁₃
hypocenter	C₁₃	#3536
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. C₁₃×#554	C₂	semidirect
2. #11719438	C₂	semidirect
3. #11719431	C₂	semidirect
4. #11719405	C₂	semidirect
5. #11719397	C₂	semidirect
6. #11719352	C₂	semidirect
7. #11719339	C₂	semidirect
8. #11719338	C₂	semidirect
9. #11719335	C₂	semidirect
10. #11719335	C₂	semidirect
11. #11719334	C₂	semidirect
12. #11719334	C₂	semidirect
13. D₁₃×C₂²⋊Q₈	C₂	semidirect
14. #11719287	C₂	semidirect
15. #11719281	C₂	semidirect
16. #11719265	C₂	semidirect
17. #11719255	C₂	semidirect
18. #11719255	C₂	semidirect
19. #11719252	C₂	semidirect
20. #11719216	C₂	semidirect
21. #11719215	C₂	semidirect
22. #11719212	C₂	semidirect
23. C₂×#88149	C₂	semidirect
24. C₂×#6131	C₂²	semidirect
25. C₂×#6131	C₂²	semidirect
26. C₂×Q₈×D₁₃	C₂²	semidirect
27. C₂×#6127	C₂²	semidirect
28. C₂×#6127	C₂²	semidirect
29. C₂×#6127	C₂²	semidirect
33. C₁₃×C₄⋊Q₈	C₂²	semidirect
34. C₁₃×#125	C₂²	semidirect
37. C₁₃×C₂²⋊Q₈	C₂²	semidirect
38. C₁₃×C₂²⋊Q₈	C₂²	semidirect
39. C₄×Q₈×C₁₃	C₂²	semidirect
43. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
44. #88201	C₂²	semidirect
45. #88201	C₂²	semidirect
46. #88200	C₂²	semidirect
47. #88200	C₂²	semidirect
48. #88200	C₂²	semidirect
52. #88184	C₂²	semidirect
53. #88184	C₂²	semidirect
54. #88184	C₂²	semidirect
55. #88183	C₂²	semidirect
58. C₄×C₂²⋊D₁₃	C₂²	semidirect
62. #88152	C₂²	semidirect
63. #88151	C₂²	semidirect
64. #88151	C₂²	semidirect
65. #88151	C₂²	semidirect
66. #88151	C₂²	semidirect
67. #88150	C₂²	semidirect
68. #88150	C₂²	semidirect
69. #88150	C₂²	semidirect
70. #88150	C₂²	semidirect
71. #88150	C₂²	semidirect
72. #88150	C₂²	semidirect
73. #88150	C₂²	semidirect
80. #88149	C₂²	semidirect
81. #88149	C₂²	semidirect
82. #88149	C₂²	semidirect
83. #88149	C₂²	semidirect
84. #88149	C₂²	semidirect
85. #88148	C₂²	semidirect
86. #88148	C₂²	semidirect
87. #88148	C₂²	semidirect
88. #88148	C₂²	semidirect
89. #88148	C₂²	semidirect
90. #88148	C₂²	semidirect
91. #88148	C₂²	semidirect
92. #88148	C₂²	semidirect
93. #88147	C₂²	semidirect
94. #88147	C₂²	semidirect
95. C₄⋊C₄×D₁₃	C₂²	semidirect
96. C₄⋊C₄×D₁₃	C₂²	semidirect
97. C₄⋊C₄×D₁₃	C₂²	semidirect
98. #88143	C₂²	semidirect
99. #88142	C₂²	semidirect
100. #88141	C₂²	semidirect
101. #88139	C₂²	semidirect
102. #88138	C₂²	semidirect
103. #88138	C₂²	semidirect
104. #88138	C₂²	semidirect
105. #88138	C₂²	semidirect
106. #88138	C₂²	semidirect
107. #88137	C₂²	semidirect
115. #88130	C₂²	semidirect
116. #88129	C₂²	semidirect
117. #88129	C₂²	semidirect
118. #88129	C₂²	semidirect
119. C₄×D₅₂	C₂²	semidirect
120. C₄×D₅₂	C₂²	semidirect
121. C₄×D₅₂	C₂²	semidirect
122. #88126	C₂²	semidirect
305. #554	D₁₃	semidirect
375. C₄⋊Q₈	C₂×D₁₃	semidirect
379. #125	C₂×D₁₃	semidirect
416. C₂²⋊Q₈	C₂×D₁₃	semidirect
417. C₂²⋊Q₈	C₂×D₁₃	semidirect
443. C₄×Q₈	C₂×D₁₃	semidirect
459. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
582. C₁₃	#3536	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#554	2
#11719438	2
#11719431	2
#11719405	2
#11719397	2
#11719352	2
#11719339	2
#11719338	2
#11719335	2
#11719334	2
D₁₃×C₂²⋊Q₈	2
#11719287	2
#11719281	2
#11719265	2
#11719255	2
#11719252	2
#11719216	2
#11719215	2
#11719212	2
C₂×#88149	2
#3536	13