Subgroups — #13129354

Order 1664.

1160 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719536	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719534	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719511	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719422	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719421	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719420	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719418	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719387	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719386	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719382	C₂	1	1	yes	maximal, characteristic, complemented
13	D₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719326	C₂	1	2	yes	maximal, complemented
15	#11719322	C₂	1	2	yes	maximal, complemented
16	#11719318	C₂	1	2	yes	maximal, complemented
17	#11719315	C₂	1	2	yes	maximal, complemented
18	#11719299	C₂	1	2	yes	maximal, complemented
19	#11719298	C₂	1	2	yes	maximal, complemented
20	#11719296	C₂	1	2	yes	maximal, complemented
21	#11719294	C₂	1	2	yes	maximal, complemented
22	#11719239	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719233	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
25	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
27	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×#6129	C₂²	1	1	yes	characteristic, complemented
29	C₂×#6129	C₂²	1	2	yes	complemented
30	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
31	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×D₄×D₁₃	C₂²	1	2	yes	complemented
33	C₁₃×#127	C₂²	1	1	yes	characteristic
34	C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#121	C₂²	1	2	yes	complemented
38	C₁₃×#121	C₂²	1	2	yes	complemented
39	C₁₃×#120	C₂²	1	2	yes	complemented
40	C₁₃×#120	C₂²	1	2	yes	complemented
41	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
42	#88207	C₂²	1	2	yes	complemented
43	#88207	C₂²	1	2	yes	complemented
44	C₂×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
45	#88201	C₂²	1	1	yes	characteristic, complemented
46	#88200	C₂²	1	1	yes	characteristic, complemented
47	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
48	#88194	C₂²	1	1	yes	characteristic
49	#88193	C₂²	1	2	yes	complemented
50	#88193	C₂²	1	2	yes	complemented
51	#88193	C₂²	1	2	yes	complemented
52	#88193	C₂²	1	2	yes	complemented
53	#88193	C₂²	1	2	yes	complemented
54	#88192	C₂²	1	1	yes	characteristic
55	#88192	C₂²	1	1	yes	characteristic, complemented
56	#88192	C₂²	1	2	yes	complemented
57	#88192	C₂²	1	1	yes	characteristic, complemented
58	#88192	C₂²	1	2	yes	complemented
59	#88192	C₂²	1	2	yes	complemented
60	#88191	C₂²	1	2	yes	complemented
61	#88191	C₂²	1	2	yes	complemented
62	#88191	C₂²	1	2	yes	complemented
63	#88191	C₂²	1	2	yes	complemented
64	#88191	C₂²	1	2	yes	complemented
65	#88191	C₂²	1	2	yes	complemented
66	#88190	C₂²	1	1	yes	characteristic, complemented
67	#88190	C₂²	1	2	yes	complemented
68	#88190	C₂²	1	1	yes	characteristic, complemented
69	#88190	C₂²	1	2	yes	complemented
70	#88190	C₂²	1	2	yes	complemented
71	#88189	C₂²	1	2	yes	complemented
72	#88189	C₂²	1	2	yes	complemented
73	#88189	C₂²	1	2	yes	complemented
74	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
75	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
76	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
77	D₄×Dic₁₃	C₂²	1	2	yes	complemented
78	D₄×Dic₁₃	C₂²	1	2	yes	complemented
79	#88184	C₂²	1	1	yes	characteristic
80	#88183	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
82	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
83	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
84	C₂×#6103	C₂²	1	2	yes	complemented
85	#88178	C₂²	1	1	yes	characteristic, complemented
86	#88178	C₂²	1	2	yes	complemented
87	#88152	C₂²	1	1	yes	characteristic, complemented
88	#88152	C₂²	1	2	yes	complemented
89	#88150	C₂²	1	1	yes	characteristic, complemented
90	#88150	C₂²	1	2	yes	complemented
91	#88148	C₂²	1	1	yes	characteristic, complemented
92	#88143	C₂²	1	1	yes	characteristic, complemented
93	#88140	C₂²	1	2	yes	complemented
94	#88140	C₂²	1	2	yes	complemented
95	#88139	C₂²	1	1	yes	characteristic, complemented
96	#88139	C₂²	1	2	yes	complemented
97	#88139	C₂²	1	2	yes	complemented
98	#88139	C₂²	1	2	yes	complemented
99	#88139	C₂²	1	2	yes	complemented
100	#88139	C₂²	1	2	yes	complemented
101	#88139	C₂²	1	2	yes	complemented
102	#88138	C₂²	1	1	yes	characteristic
103	#88138	C₂²	1	2	yes	complemented
104	#88137	C₂²	1	1	yes	characteristic, complemented
105	#88137	C₂²	1	2	yes	complemented
106	#88137	C₂²	1	2	yes	complemented
107	#88135	C₂²	1	2	yes	complemented
108	#88135	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
111	#88133	C₂²	1	1	yes	characteristic, complemented
112	#88133	C₂²	1	2	yes	complemented
113	#88132	C₂²	1	2	yes	complemented
114	#88132	C₂²	1	2	yes	complemented
115	#88129	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	#88126	C₂²	1	1	yes	characteristic, complemented
119	C₄²×D₁₃	C₂²	1	1	yes	characteristic, complemented
120	#88123	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	C₂⁴×C₁₃	C₂³	1	2	yes	—
124	C₂³×D₁₃	C₂³	1	2	yes	—
125	C₂³×D₁₃	C₂³	1	2	yes	—
126	C₁₃×#41	—	4	2	no	—
127	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₃	—	4	2	no	—
129	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
132	C₂×D₄×C₁₃	C₂³	1	2	yes	—
133	C₂×D₄×C₁₃	C₂³	1	2	yes	—
134	C₂×D₄×C₁₃	C₂³	1	2	yes	—
135	C₂×D₄×C₁₃	C₂³	1	2	yes	—
136	C₂×D₄×C₁₃	C₂³	1	2	yes	—
137	C₂×D₄×C₁₃	C₂³	1	2	yes	—
138	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₃	—	4	4	no	—
141	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
152	C₂²×Dic₁₃	C₂³	1	2	yes	—
153	C₂²×Dic₁₃	C₂³	1	2	yes	—
154	C₂²×Dic₁₃	C₂³	1	2	yes	—
155	C₂²×Dic₁₃	C₂³	1	2	yes	—
156	Q₈×D₁₃	—	4	2	no	—
157	#6129	—	4	2	no	—
158	#6129	—	4	4	no	—
159	D₄×D₁₃	—	4	2	no	—
160	D₄×D₁₃	—	4	2	no	—
161	D₄×D₁₃	—	4	4	no	—
162	C₂×D₅₂	C₂³	1	1	yes	characteristic
163	C₂×D₅₂	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
166	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
167	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
168	C₂×C₄×D₁₃	C₂³	1	2	yes	—
169	C₂×C₄×D₁₃	C₂³	1	2	yes	—
170	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
171	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
172	C₂×Dic₂₆	C₂³	1	2	yes	—
173	C₂×Dic₂₆	C₂³	1	2	yes	—
174	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
182	C₄²×C₁₃	C₂³	1	1	yes	characteristic
183	C₄²×C₁₃	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
187	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
189	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
190	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
191	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
192	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
193	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
194	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
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	1	yes	characteristic
199	#6103	C₂³	1	1	yes	characteristic
200	#6103	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
208	#6103	C₂³	1	1	yes	characteristic
209	#6103	C₂³	1	2	yes	—
210	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₁₃	C₂³	1	2	yes	—
214	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
215	C₄⋊Dic₁₃	C₂³	1	2	yes	—
216	#6101	C₂³	1	2	yes	—
217	#6101	C₂³	1	1	yes	characteristic
218	#6101	C₂³	1	1	yes	characteristic
219	#6101	C₂³	1	1	yes	characteristic
220	#6101	C₂³	1	1	yes	characteristic
221	#6101	C₂³	1	2	yes	—
222	#6101	C₂³	1	1	yes	characteristic
223	#6101	C₂³	1	1	yes	characteristic
224	#6101	C₂³	1	2	yes	—
225	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
226	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₃	C₂³	1	2	yes	—
228	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
229	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
230	C₄×Dic₁₃	C₂³	1	2	yes	—
231	#3558	—	13	1	no	maximal, Sylow
232	C₂³×C₁₃	—	4	2	no	—
233	C₂³×C₁₃	—	4	2	no	—
234	C₂³×C₁₃	—	4	2	no	—
235	C₂³×C₁₃	C₂⁴	1	2	yes	—
236	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₂³×C₁₃	C₂⁴	1	2	yes	—
238	C₂³×C₁₃	C₂⁴	1	2	yes	—
239	C₂²×D₁₃	—	2	4	no	—
240	C₂²×D₁₃	—	4	2	no	—
241	C₂²×D₁₃	—	4	2	no	—
242	C₂²×D₁₃	—	4	2	no	—
243	C₂²×D₁₃	—	4	2	no	—
244	C₂²×D₁₃	—	4	2	no	—
245	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
246	C₂²×D₁₃	C₂⁴	1	2	yes	—
247	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
248	Q₈×C₁₃	—	2	2	no	—
249	D₄×C₁₃	—	2	2	no	—
250	D₄×C₁₃	—	2	2	no	—
251	D₄×C₁₃	—	2	2	no	—
252	D₄×C₁₃	—	4	2	no	—
253	D₄×C₁₃	—	4	2	no	—
254	D₄×C₁₃	—	4	2	no	—
255	D₄×C₁₃	—	4	2	no	—
256	D₄×C₁₃	—	4	2	no	—
257	D₄×C₁₃	—	4	2	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	4	2	no	—
260	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
263	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
267	C₂²⋊D₁₃	—	2	4	no	—
268	C₂²⋊D₁₃	—	2	4	no	—
269	C₂²⋊D₁₃	—	2	2	no	—
270	C₂²⋊D₁₃	—	4	2	no	—
271	C₂²⋊D₁₃	—	4	2	no	—
272	C₂²⋊D₁₃	—	4	2	no	—
273	C₂²⋊D₁₃	—	4	2	no	—
274	C₂²⋊D₁₃	—	4	2	no	—
275	C₂²⋊D₁₃	—	4	2	no	—
276	C₂²⋊D₁₃	—	4	1	no	—
277	C₂²⋊D₁₃	—	4	2	no	—
278	C₂×Dic₁₃	—	4	2	no	—
279	C₂×Dic₁₃	—	4	2	no	—
280	C₂×Dic₁₃	—	4	2	no	—
281	C₂×Dic₁₃	—	4	2	no	—
282	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
287	C₂×Dic₁₃	C₂⁴	1	2	yes	—
288	C₂×Dic₁₃	C₂⁴	1	2	yes	—
289	C₂×Dic₁₃	C₂⁴	1	2	yes	—
290	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
291	D₅₂	—	2	2	no	—
292	D₅₂	—	2	2	no	—
293	C₄×D₁₃	—	2	2	no	—
294	C₄×D₁₃	—	2	2	no	—
295	C₄×D₁₃	—	2	2	no	—
296	C₄×D₁₃	—	4	1	no	—
297	C₄×D₁₃	—	4	2	no	—
298	C₄×D₁₃	—	4	2	no	—
299	Dic₂₆	—	2	2	no	—
300	Dic₂₆	—	4	1	no	—
301	Dic₂₆	—	4	2	no	—
302	Dic₂₆	—	4	2	no	—
303	#562	—	13	2	no	—
304	H(3,𝔽₄)	—	13	2	no	—
305	#559	—	13	1	no	—
306	#559	—	13	1	no	—
307	#548	—	13	1	no	—
308	#548	—	13	1	no	—
309	#546	—	13	1	no	—
310	#546	—	13	1	no	—
311	#546	—	13	2	no	—
312	#546	—	13	2	no	—
313	D₄²	—	13	1	no	—
314	D₄²	—	13	1	no	—
315	#542	—	13	1	no	—
316	#542	—	13	1	no	—
317	#538	—	13	2	no	—
318	#538	—	13	2	no	—
319	#538	—	13	2	no	—
320	#535	—	13	1	no	—
321	#535	D₁₃	1	1	yes	characteristic, complemented
322	#534	—	13	2	no	—
323	#532	—	13	1	no	—
324	#529	—	13	1	no	—
325	C₂×#124	—	13	1	no	—
326	C₂²×C₁₃	—	2	2	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	2	no	—
329	C₂²×C₁₃	—	2	2	no	—
330	C₂²×C₁₃	—	2	1	no	—
331	C₂²×C₁₃	—	2	2	no	—
332	C₂²×C₁₃	—	2	2	no	—
333	C₂²×C₁₃	—	2	1	no	—
334	C₂²×C₁₃	—	2	2	no	—
335	C₂²×C₁₃	—	2	1	no	—
336	C₂²×C₁₃	—	2	2	no	—
337	C₂²×C₁₃	—	2	2	no	—
338	C₂²×C₁₃	—	8	4	no	—
339	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
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	1	no	—
346	C₂×D₁₃	—	2	1	no	—
347	C₂×D₁₃	—	2	2	no	—
348	C₂×D₁₃	—	8	4	no	—
349	C₂×D₁₃	—	8	4	no	—
350	C₂×D₁₃	H(5,𝔽₂)	1	2	yes	—
351	C₄×C₁₃	—	2	1	no	—
352	C₄×C₁₃	—	2	2	no	—
353	C₄×C₁₃	—	2	1	no	—
354	C₄×C₁₃	—	2	1	no	—
355	C₄×C₁₃	—	2	1	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	2	no	—
361	Dic₁₃	—	2	2	no	—
362	Dic₁₃	—	2	1	no	—
363	Dic₁₃	—	2	1	no	—
364	Dic₁₃	—	2	1	no	—
365	Dic₁₃	—	2	1	no	—
366	Dic₁₃	—	2	1	no	—
367	C₂×#41	—	13	2	no	—
368	C₂×#41	—	13	1	no	—
369	C₂×#41	C₂×D₁₃	1	1	yes	characteristic, complemented
370	C₂²×Q₈	—	13	1	no	—
371	C₂²×D₄	—	13	2	no	—
372	C₂²×D₄	—	13	1	no	—
373	C₂²×D₄	—	13	2	no	—
374	C₂²×D₄	—	13	1	no	—
375	C₂²×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
376	C₄⋊Q₈	—	13	1	no	—
377	#127	—	13	1	no	—
378	#127	C₂×D₁₃	1	1	yes	characteristic
379	#127	C₂×D₁₃	1	1	yes	characteristic, complemented
380	#126	—	13	1	no	—
381	#126	—	13	2	no	—
382	#126	—	13	1	no	—
383	#126	—	13	2	no	—
384	#125	—	13	1	no	—
385	#124	—	13	1	no	—
386	#124	—	13	1	no	—
387	#124	—	13	2	no	—
388	#124	—	13	1	no	—
389	#124	—	13	2	no	—
390	#124	—	13	2	no	—
391	#124	—	13	2	no	—
392	#124	—	13	2	no	—
393	#124	—	13	1	no	—
394	#124	—	13	2	no	—
395	#124	—	13	2	no	—
396	#124	—	13	2	no	—
397	#124	—	13	2	no	—
398	#124	—	13	1	no	—
399	#124	C₂×D₁₃	1	1	yes	characteristic, complemented
400	#124	C₂×D₁₃	1	1	yes	characteristic, complemented
401	#123	—	13	2	no	—
402	#123	—	13	2	no	—
403	#123	—	13	2	no	—
404	#123	—	13	2	no	—
405	#123	—	13	1	no	—
406	#123	—	13	1	no	—
407	#123	—	13	2	no	—
408	#123	—	13	2	no	—
409	#123	—	13	2	no	—
410	#123	—	13	2	no	—
411	C₂²⋊Q₈	—	13	1	no	—
412	C₂²⋊Q₈	—	13	2	no	—
413	C₂²⋊Q₈	—	13	1	no	—
414	C₂²⋊Q₈	—	13	1	no	—
415	C₂²⋊Q₈	—	13	2	no	—
416	C₂²⋊Q₈	—	13	2	no	—
417	C₂²⋊Q₈	—	13	2	no	—
418	#121	—	13	2	no	—
419	#121	—	13	1	no	—
420	#121	—	13	1	no	—
421	#121	—	13	2	no	—
422	#121	—	13	2	no	—
423	#121	—	13	2	no	—
424	#121	—	13	2	no	—
425	#121	—	13	2	no	—
426	#121	—	13	2	no	—
427	#121	—	13	2	no	—
428	#121	—	13	1	no	—
429	#121	—	13	1	no	—
430	#121	—	13	1	no	—
431	#121	—	13	2	no	—
432	#121	C₂×D₁₃	1	2	yes	complemented
433	#121	C₂×D₁₃	1	2	yes	complemented
434	#120	—	13	2	no	—
435	#120	—	13	2	no	—
436	#120	—	13	2	no	—
437	#120	—	13	2	no	—
438	#120	—	13	2	no	—
439	#120	—	13	2	no	—
440	#120	—	13	2	no	—
441	#120	—	13	2	no	—
442	#120	C₂×D₁₃	1	2	yes	complemented
443	#120	C₂×D₁₃	1	2	yes	complemented
444	C₄×Q₈	—	13	1	no	—
445	C₄×Q₈	—	13	1	no	—
446	C₄×Q₈	—	13	1	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	—	13	1	no	—
453	C₄×D₄	—	13	1	no	—
454	C₄×D₄	—	13	2	no	—
455	C₄×D₄	—	13	2	no	—
456	C₄×D₄	—	13	2	no	—
457	C₄×D₄	—	13	1	no	—
458	C₄×D₄	—	13	1	no	—
459	#117	—	13	1	no	—
460	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
461	C₂×C₂²⋊C₄	—	13	2	no	—
462	C₂×C₂²⋊C₄	—	13	2	no	—
463	C₂×C₂²⋊C₄	—	13	2	no	—
464	C₂×C₂²⋊C₄	—	13	2	no	—
465	C₂×C₄²	—	13	1	no	—
466	C₂×C₁₃	—	4	2	no	—
467	C₂×C₁₃	—	4	2	no	—
468	C₂×C₁₃	—	4	2	no	—
469	C₂×C₁₃	—	4	1	no	—
470	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
471	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
472	C₂×C₁₃	#585	1	1	yes	characteristic
473	D₁₃	—	2	2	no	—
474	D₁₃	—	4	1	no	—
475	D₁₃	—	4	2	no	—
476	C₂⁴	—	13	2	no	—
477	C₂⁴	—	13	2	no	—
478	C₂⁴	C₂²×D₁₃	1	2	yes	—
479	#41	—	4	2	no	—
480	#41	—	52	2	no	—
481	#41	—	52	4	no	—
482	C₂×Q₈	—	13	1	no	—
483	C₂×Q₈	—	13	1	no	—
484	C₂×Q₈	—	13	2	no	—
485	C₂×Q₈	—	13	2	no	—
486	C₂×Q₈	—	52	2	no	—
487	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
488	C₂×D₄	—	4	2	no	—
489	C₂×D₄	—	13	2	no	—
490	C₂×D₄	—	13	2	no	—
491	C₂×D₄	—	13	1	no	—
492	C₂×D₄	—	13	1	no	—
493	C₂×D₄	—	13	2	no	—
494	C₂×D₄	—	13	2	no	—
495	C₂×D₄	—	13	2	no	—
496	C₂×D₄	—	13	2	no	—
497	C₂×D₄	—	13	2	no	—
498	C₂×D₄	—	13	2	no	—
499	C₂×D₄	—	13	2	no	—
500	C₂×D₄	—	13	1	no	—
501	C₂×D₄	—	13	1	no	—
502	C₂×D₄	—	52	2	no	—
503	C₂×D₄	—	52	2	no	—
504	C₂×D₄	—	52	4	no	—
505	C₂×D₄	—	52	4	no	—
506	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
507	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
508	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
509	C₂×D₄	C₂²×D₁₃	1	2	yes	—
510	C₂×D₄	C₂²×D₁₃	1	2	yes	—
511	C₂×D₄	C₂²×D₁₃	1	2	yes	—
512	C₂×D₄	C₂²×D₁₃	1	2	yes	—
513	C₂×D₄	C₂²×D₁₃	1	2	yes	—
514	C₂×D₄	C₂²×D₁₃	1	2	yes	—
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	1	no	—
522	C₂²×C₄	—	13	1	no	—
523	C₂²×C₄	—	13	2	no	—
524	C₂²×C₄	—	13	2	no	—
525	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
526	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
527	C₄⋊C₄	—	13	1	no	—
528	C₄⋊C₄	—	13	1	no	—
529	C₄⋊C₄	—	13	1	no	—
530	C₄⋊C₄	—	13	1	no	—
531	C₄⋊C₄	—	13	1	no	—
532	C₄⋊C₄	—	13	1	no	—
533	C₄⋊C₄	—	13	1	no	—
534	C₄⋊C₄	—	13	1	no	—
535	C₄⋊C₄	—	13	2	no	—
536	C₄⋊C₄	—	13	2	no	—
537	C₄⋊C₄	—	13	2	no	—
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	C₂²×D₁₃	1	1	yes	characteristic
543	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
544	C₂²⋊C₄	—	13	1	no	—
545	C₂²⋊C₄	—	13	2	no	—
546	C₂²⋊C₄	—	13	2	no	—
547	C₂²⋊C₄	—	13	2	no	—
548	C₂²⋊C₄	—	13	2	no	—
549	C₂²⋊C₄	—	13	2	no	—
550	C₂²⋊C₄	—	13	1	no	—
551	C₂²⋊C₄	—	13	2	no	—
552	C₂²⋊C₄	—	13	2	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	1	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	2	no	—
564	C₂²⋊C₄	—	13	1	no	—
565	C₂²⋊C₄	—	13	1	no	—
566	C₂²⋊C₄	—	13	1	no	—
567	C₂²⋊C₄	—	13	1	no	—
568	C₂²⋊C₄	—	13	2	no	—
569	C₂²⋊C₄	—	13	1	no	—
570	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
571	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
572	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
573	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
574	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
575	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
576	C₄²	—	13	1	no	—
577	C₄²	—	13	1	no	—
578	C₄²	—	13	1	no	—
579	C₄²	—	13	1	no	—
580	C₄²	—	13	2	no	—
581	C₄²	—	13	2	no	—
582	C₄²	C₂²×D₁₃	1	1	yes	characteristic
583	C₄²	C₂²×D₁₃	1	1	yes	characteristic
584	C₁₃	#3558	1	1	yes	characteristic, complemented, Sylow
585	C₂³	—	4	2	no	—
586	C₂³	—	4	2	no	—
587	C₂³	—	4	2	no	—
588	C₂³	—	13	1	no	—
589	C₂³	—	13	1	no	—
590	C₂³	—	13	2	no	—
591	C₂³	—	26	4	no	—
592	C₂³	—	52	2	no	—
593	C₂³	—	52	2	no	—
594	C₂³	—	52	2	no	—
595	C₂³	—	52	2	no	—
596	C₂³	—	52	2	no	—
597	C₂³	C₂³×D₁₃	1	2	yes	—
598	C₂³	C₂³×D₁₃	1	1	yes	characteristic
599	C₂³	C₂³×D₁₃	1	2	yes	—
600	C₂³	C₂³×D₁₃	1	2	yes	—
601	Q₈	—	2	2	no	—
602	Q₈	—	26	2	no	—
603	Q₈	—	52	1	no	—
604	Q₈	—	52	2	no	—
605	Q₈	—	52	2	no	—
606	D₄	—	2	2	no	—
607	D₄	—	2	2	no	—
608	D₄	—	2	2	no	—
609	D₄	—	4	2	no	—
610	D₄	—	4	2	no	—
611	D₄	—	4	2	no	—
612	D₄	—	4	2	no	—
613	D₄	—	4	2	no	—
614	D₄	—	4	2	no	—
615	D₄	—	26	2	no	—
616	D₄	—	26	2	no	—
617	D₄	—	26	4	no	—
618	D₄	—	26	4	no	—
619	D₄	—	26	2	no	—
620	D₄	—	52	1	no	—
621	D₄	—	52	2	no	—
622	D₄	—	52	2	no	—
623	D₄	—	52	2	no	—
624	D₄	—	52	2	no	—
625	D₄	—	52	2	no	—
626	D₄	—	52	2	no	—
627	D₄	—	52	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	13	1	no	—
631	C₂×C₄	—	13	1	no	—
632	C₂×C₄	—	13	1	no	—
633	C₂×C₄	—	13	1	no	—
634	C₂×C₄	—	13	2	no	—
635	C₂×C₄	—	13	2	no	—
636	C₂×C₄	—	13	2	no	—
637	C₂×C₄	—	13	1	no	—
638	C₂×C₄	—	13	1	no	—
639	C₂×C₄	—	26	2	no	—
640	C₂×C₄	—	26	2	no	—
641	C₂×C₄	—	26	2	no	—
642	C₂×C₄	—	52	1	no	—
643	C₂×C₄	—	52	2	no	—
644	C₂×C₄	—	52	2	no	—
645	C₂×C₄	—	52	2	no	—
646	C₂×C₄	—	52	2	no	—
647	C₂×C₄	—	52	2	no	—
648	C₂×C₄	—	52	2	no	—
649	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
650	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
652	C₂×C₄	C₂³×D₁₃	1	2	yes	—
653	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
654	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
655	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
656	C₂²	—	2	1	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	2	1	no	—
668	C₂²	—	8	4	no	—
669	C₂²	—	13	2	no	—
670	C₂²	—	26	1	no	—
671	C₂²	—	26	1	no	—
672	C₂²	—	26	1	no	—
673	C₂²	—	26	2	no	—
674	C₂²	—	26	2	no	—
675	C₂²	—	26	1	no	—
676	C₂²	—	26	1	no	—
677	C₂²	—	26	2	no	—
678	C₂²	—	104	4	no	—
679	C₂²	—	104	4	no	—
680	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
681	C₄	—	2	1	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	1	no	—
687	C₄	—	26	1	no	—
688	C₄	—	26	1	no	—
689	C₄	—	26	2	no	—
690	C₄	—	26	1	no	—
691	C₄	—	26	1	no	—
692	C₄	—	26	2	no	—
693	C₄	—	26	2	no	—
694	C₄	—	26	1	no	—
695	C₄	—	26	1	no	—
696	C₄	#88251	1	2	yes	—
697	C₂	—	4	1	no	—
698	C₂	—	4	2	no	—
699	C₂	—	4	2	no	—
700	C₂	—	4	2	no	—
701	C₂	—	26	2	no	—
702	C₂	—	52	1	no	—
703	C₂	—	52	2	no	—
704	C₂	C₂×#88251	1	1	yes	characteristic
705	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic
706	C₂	#11719650	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#535	C₂
hypercenter	#535	D₁₃
hypocenter	C₁₃	#3558
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #535

Complements

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

N	H ≅ G/N	type
1. C₁₃×#535	C₂	semidirect
2. #11719536	C₂	semidirect
3. #11719534	C₂	semidirect
4. #11719511	C₂	semidirect
5. D₄×C₂²⋊D₁₃	C₂	semidirect
6. #11719422	C₂	semidirect
7. #11719421	C₂	semidirect
8. #11719420	C₂	semidirect
9. #11719418	C₂	semidirect
10. #11719387	C₂	semidirect
11. #11719386	C₂	semidirect
12. #11719382	C₂	semidirect
13. D₁₃×#124	C₂	semidirect
14. #11719326	C₂	semidirect
15. #11719322	C₂	semidirect
16. #11719318	C₂	semidirect
17. #11719315	C₂	semidirect
18. #11719299	C₂	semidirect
19. #11719298	C₂	semidirect
20. #11719296	C₂	semidirect
21. #11719294	C₂	semidirect
22. #11719239	C₂	semidirect
23. #11719233	C₂	semidirect
24. C₂×C₁₃×#41	C₂²	semidirect
25. C₂²×D₄×C₁₃	C₂²	semidirect
26. C₂²×C₂²⋊D₁₃	C₂²	semidirect
27. C₂×Q₈×D₁₃	C₂²	semidirect
28. C₂×#6129	C₂²	semidirect
29. C₂×#6129	C₂²	semidirect
31. C₂×D₄×D₁₃	C₂²	semidirect
32. C₂×D₄×D₁₃	C₂²	semidirect
34. C₁₃×#127	C₂²	semidirect
35. C₁₃×#124	C₂²	semidirect
36. C₁₃×#124	C₂²	semidirect
37. C₁₃×#121	C₂²	semidirect
38. C₁₃×#121	C₂²	semidirect
39. C₁₃×#120	C₂²	semidirect
40. C₁₃×#120	C₂²	semidirect
41. C₁₃×#117	C₂²	semidirect
42. #88207	C₂²	semidirect
43. #88207	C₂²	semidirect
44. C₂×C₂²⋊Dic₁₃	C₂²	semidirect
45. #88201	C₂²	semidirect
46. #88200	C₂²	semidirect
47. Q₈×Dic₁₃	C₂²	semidirect
49. #88193	C₂²	semidirect
50. #88193	C₂²	semidirect
51. #88193	C₂²	semidirect
52. #88193	C₂²	semidirect
53. #88193	C₂²	semidirect
55. #88192	C₂²	semidirect
56. #88192	C₂²	semidirect
57. #88192	C₂²	semidirect
58. #88192	C₂²	semidirect
59. #88192	C₂²	semidirect
60. #88191	C₂²	semidirect
61. #88191	C₂²	semidirect
62. #88191	C₂²	semidirect
63. #88191	C₂²	semidirect
64. #88191	C₂²	semidirect
65. #88191	C₂²	semidirect
66. #88190	C₂²	semidirect
67. #88190	C₂²	semidirect
68. #88190	C₂²	semidirect
69. #88190	C₂²	semidirect
70. #88190	C₂²	semidirect
71. #88189	C₂²	semidirect
72. #88189	C₂²	semidirect
73. #88189	C₂²	semidirect
74. D₄×Dic₁₃	C₂²	semidirect
75. D₄×Dic₁₃	C₂²	semidirect
76. D₄×Dic₁₃	C₂²	semidirect
77. D₄×Dic₁₃	C₂²	semidirect
78. D₄×Dic₁₃	C₂²	semidirect
80. #88183	C₂²	semidirect
81. C₄×C₂²⋊D₁₃	C₂²	semidirect
82. C₄×C₂²⋊D₁₃	C₂²	semidirect
83. C₄×C₂²⋊D₁₃	C₂²	semidirect
84. C₂×#6103	C₂²	semidirect
85. #88178	C₂²	semidirect
86. #88178	C₂²	semidirect
87. #88152	C₂²	semidirect
88. #88152	C₂²	semidirect
89. #88150	C₂²	semidirect
90. #88150	C₂²	semidirect
91. #88148	C₂²	semidirect
92. #88143	C₂²	semidirect
93. #88140	C₂²	semidirect
94. #88140	C₂²	semidirect
95. #88139	C₂²	semidirect
96. #88139	C₂²	semidirect
97. #88139	C₂²	semidirect
98. #88139	C₂²	semidirect
99. #88139	C₂²	semidirect
100. #88139	C₂²	semidirect
101. #88139	C₂²	semidirect
103. #88138	C₂²	semidirect
104. #88137	C₂²	semidirect
105. #88137	C₂²	semidirect
106. #88137	C₂²	semidirect
107. #88135	C₂²	semidirect
108. #88135	C₂²	semidirect
109. C₂²⋊C₄×D₁₃	C₂²	semidirect
110. C₂²⋊C₄×D₁₃	C₂²	semidirect
111. #88133	C₂²	semidirect
112. #88133	C₂²	semidirect
113. #88132	C₂²	semidirect
114. #88132	C₂²	semidirect
115. #88129	C₂²	semidirect
116. C₄×D₅₂	C₂²	semidirect
117. C₄×D₅₂	C₂²	semidirect
118. #88126	C₂²	semidirect
119. C₄²×D₁₃	C₂²	semidirect
120. #88123	C₂²	semidirect
121. C₄×Dic₂₆	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
321. #535	D₁₃	semidirect
369. C₂×#41	C₂×D₁₃	semidirect
375. C₂²×D₄	C₂×D₁₃	semidirect
379. #127	C₂×D₁₃	semidirect
399. #124	C₂×D₁₃	semidirect
400. #124	C₂×D₁₃	semidirect
432. #121	C₂×D₁₃	semidirect
433. #121	C₂×D₁₃	semidirect
442. #120	C₂×D₁₃	semidirect
443. #120	C₂×D₁₃	semidirect
460. #117	C₂×D₁₃	semidirect
584. C₁₃	#3558	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#535	2
#11719536	2
#11719534	2
#11719511	2
D₄×C₂²⋊D₁₃	2
#11719422	2
#11719421	2
#11719420	2
#11719418	2
#11719387	2
#11719386	2
#11719382	2
D₁₃×#124	2
#11719326	2
#11719322	2
#11719318	2
#11719315	2
#11719299	2
#11719298	2
#11719296	2
#11719294	2
#11719239	2
#11719233	2
#3558	13