Subgroups — #13129089

Order 1664.

1050 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#537	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719539	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719538	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719533	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719529	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719350	C₂	1	2	yes	maximal, complemented
7	#11719347	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719343	C₂	1	2	yes	maximal, complemented
9	#11719336	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719332	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719330	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719325	C₂	1	2	yes	maximal, complemented
13	#11719325	C₂	1	2	yes	maximal, complemented
14	#11719324	C₂	1	2	yes	maximal, complemented
15	#11719324	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719323	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719320	C₂	1	2	yes	maximal, complemented
18	#11719319	C₂	1	2	yes	maximal, complemented
19	#11719311	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719306	C₂	1	2	yes	maximal, complemented
21	#11719304	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719219	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719218	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
26	C₂×#6131	C₂²	1	1	yes	characteristic
27	C₂×#6129	C₂²	1	1	yes	characteristic
28	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
33	C₁₃×#121	C₂²	1	2	yes	—
34	C₁₃×#121	C₂²	1	1	yes	characteristic
35	C₁₃×#121	C₂²	1	2	yes	—
36	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#121	C₂²	1	2	yes	complemented
38	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	#88200	C₂²	1	1	yes	characteristic
40	#88200	C₂²	1	1	yes	characteristic
41	#88200	C₂²	1	1	yes	characteristic
42	#88200	C₂²	1	2	yes	complemented
43	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
44	#88198	C₂²	1	1	yes	characteristic, complemented
45	#88194	C₂²	1	2	yes	—
46	#88194	C₂²	1	2	yes	—
47	#88194	C₂²	1	1	yes	characteristic, complemented
48	#88193	C₂²	1	2	yes	—
49	#88193	C₂²	1	2	yes	—
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	1	yes	characteristic
55	#88192	C₂²	1	1	yes	characteristic
56	#88192	C₂²	1	2	yes	—
57	#88192	C₂²	1	1	yes	characteristic
58	#88192	C₂²	1	2	yes	—
59	#88192	C₂²	1	2	yes	complemented
60	#88191	C₂²	1	1	yes	characteristic
61	#88191	C₂²	1	1	yes	characteristic
62	#88191	C₂²	1	2	yes	—
63	#88189	C₂²	1	1	yes	characteristic
64	#88189	C₂²	1	1	yes	characteristic
65	#88189	C₂²	1	2	yes	complemented
66	D₄×Dic₁₃	C₂²	1	2	yes	—
67	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
68	D₄×Dic₁₃	C₂²	1	2	yes	complemented
69	#88184	C₂²	1	2	yes	—
70	#88184	C₂²	1	1	yes	characteristic
71	#88184	C₂²	1	2	yes	—
72	#88184	C₂²	1	1	yes	characteristic, complemented
73	#88183	C₂²	1	2	yes	—
74	#88183	C₂²	1	2	yes	—
75	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
77	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
78	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
79	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
80	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
81	#88180	C₂²	1	1	yes	characteristic
82	#88180	C₂²	1	2	yes	complemented
83	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
84	#88178	C₂²	1	1	yes	characteristic
85	#88178	C₂²	1	1	yes	characteristic, complemented
86	C₂×#6101	C₂²	1	2	yes	complemented
87	#88152	C₂²	1	2	yes	—
88	#88152	C₂²	1	2	yes	—
89	#88152	C₂²	1	2	yes	complemented
90	#88151	C₂²	1	1	yes	characteristic
91	#88149	C₂²	1	1	yes	characteristic
92	#88148	C₂²	1	2	yes	—
93	#88148	C₂²	1	2	yes	—
94	#88148	C₂²	1	2	yes	—
95	#88147	C₂²	1	2	yes	—
96	#88147	C₂²	1	1	yes	characteristic, complemented
97	#88146	C₂²	1	1	yes	characteristic
98	#88146	C₂²	1	1	yes	characteristic
99	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
100	#88144	C₂²	1	1	yes	characteristic, complemented
101	#88144	C₂²	1	1	yes	characteristic, complemented
102	#88144	C₂²	1	2	yes	complemented
103	#88144	C₂²	1	2	yes	complemented
104	#88143	C₂²	1	2	yes	complemented
105	#88143	C₂²	1	2	yes	complemented
106	#88141	C₂²	1	1	yes	characteristic, complemented
107	#88140	C₂²	1	2	yes	—
108	#88140	C₂²	1	2	yes	—
109	#88140	C₂²	1	2	yes	complemented
110	#88138	C₂²	1	2	yes	—
111	#88138	C₂²	1	2	yes	—
112	#88137	C₂²	1	2	yes	—
113	#88137	C₂²	1	2	yes	complemented
114	#88137	C₂²	1	2	yes	complemented
115	#88136	C₂²	1	2	yes	—
116	#88135	C₂²	1	2	yes	—
117	#88135	C₂²	1	2	yes	—
118	#88135	C₂²	1	2	yes	complemented
119	#88133	C₂²	1	2	yes	—
120	#88133	C₂²	1	2	yes	—
121	#88133	C₂²	1	2	yes	complemented
122	#88131	C₂²	1	2	yes	complemented
123	C₂³×D₁₃	C₂³	1	1	yes	characteristic
124	C₁₃×#41	—	4	2	no	—
125	C₁₃×#41	—	4	2	no	—
126	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₃	C₂³	1	2	yes	—
130	C₂×D₄×C₁₃	C₂³	1	2	yes	—
131	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
132	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
133	C₂×D₄×C₁₃	C₂³	1	2	yes	—
134	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
139	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
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	1	yes	characteristic
147	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
151	C₂²×Dic₁₃	C₂³	1	2	yes	—
152	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
153	C₂²×Dic₁₃	C₂³	1	2	yes	—
154	C₂²×Dic₁₃	C₂³	1	2	yes	—
155	#6131	—	4	2	no	—
156	#6129	—	4	2	no	—
157	#6127	—	4	2	no	—
158	C₂×D₅₂	C₂³	1	1	yes	characteristic
159	C₂×D₅₂	C₂³	1	2	yes	—
160	C₂×D₅₂	C₂³	1	2	yes	—
161	C₂×C₄×D₁₃	—	4	2	no	—
162	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₁₃	C₂³	1	2	yes	—
166	C₂×C₄×D₁₃	C₂³	1	2	yes	—
167	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
168	C₂×C₄×D₁₃	C₂³	1	2	yes	—
169	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
170	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
186	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
189	#6103	C₂³	1	2	yes	—
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	1	yes	characteristic
197	#6103	C₂³	1	1	yes	characteristic
198	#6103	C₂³	1	1	yes	characteristic
199	#6103	C₂³	1	2	yes	—
200	#6103	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₁₃	C₂³	1	2	yes	—
202	C₄⋊Dic₁₃	C₂³	1	2	yes	—
203	C₄⋊Dic₁₃	C₂³	1	2	yes	—
204	C₄⋊Dic₁₃	C₂³	1	2	yes	—
205	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₁₃	C₂³	1	2	yes	—
207	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
210	#6101	C₂³	1	2	yes	—
211	#6101	C₂³	1	2	yes	—
212	#6101	C₂³	1	2	yes	—
213	#6101	C₂³	1	2	yes	—
214	#6101	C₂³	1	2	yes	—
215	#6101	C₂³	1	2	yes	—
216	#6101	C₂³	1	1	yes	characteristic
217	#6101	C₂³	1	2	yes	—
218	#6101	C₂³	1	1	yes	characteristic
219	#6101	C₂³	1	1	yes	characteristic
220	#6101	C₂³	1	2	yes	—
221	#6101	C₂³	1	1	yes	characteristic
222	C₄×Dic₁₃	C₂³	1	2	yes	—
223	C₄×Dic₁₃	C₂³	1	2	yes	—
224	C₄×Dic₁₃	C₂³	1	2	yes	—
225	C₄×Dic₁₃	C₂³	1	2	yes	—
226	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
228	#3539	—	13	1	no	maximal, Sylow
229	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₂³×C₁₃	C₂⁴	1	2	yes	—
232	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂²×D₁₃	—	4	1	no	—
234	C₂²×D₁₃	—	4	1	no	—
235	C₂²×D₁₃	—	4	1	no	—
236	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
237	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
238	C₂²×D₁₃	C₂⁴	1	2	yes	—
239	Q₈×C₁₃	—	2	2	no	—
240	Q₈×C₁₃	—	4	1	no	—
241	D₄×C₁₃	—	2	2	no	—
242	D₄×C₁₃	—	4	2	no	—
243	D₄×C₁₃	—	4	2	no	—
244	D₄×C₁₃	—	4	1	no	—
245	D₄×C₁₃	—	4	1	no	—
246	D₄×C₁₃	—	4	2	no	—
247	D₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	4	2	no	—
252	C₂×C₄×C₁₃	—	4	2	no	—
253	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₂²⋊D₁₃	—	4	2	no	—
261	C₂²⋊D₁₃	—	4	2	no	—
262	C₂²⋊D₁₃	—	4	1	no	—
263	C₂²⋊D₁₃	—	4	2	no	—
264	C₂²⋊D₁₃	—	4	1	no	—
265	C₂²⋊D₁₃	—	4	2	no	—
266	C₂²⋊D₁₃	—	4	2	no	—
267	C₂²⋊D₁₃	—	4	2	no	—
268	C₂²⋊D₁₃	—	4	2	no	—
269	C₂²⋊D₁₃	—	4	1	no	—
270	C₂²⋊D₁₃	—	4	1	no	—
271	C₂×Dic₁₃	—	4	1	no	—
272	C₂×Dic₁₃	—	4	2	no	—
273	C₂×Dic₁₃	—	4	2	no	—
274	C₂×Dic₁₃	—	4	2	no	—
275	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₁₃	C₂⁴	1	2	yes	—
279	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₁₃	C₂⁴	1	2	yes	—
282	C₂×Dic₁₃	C₂⁴	1	2	yes	—
283	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
284	D₅₂	—	2	2	no	—
285	D₅₂	—	4	2	no	—
286	D₅₂	—	4	2	no	—
287	C₄×D₁₃	—	2	2	no	—
288	C₄×D₁₃	—	2	2	no	—
289	C₄×D₁₃	—	4	1	no	—
290	C₄×D₁₃	—	4	1	no	—
291	C₄×D₁₃	—	4	2	no	—
292	C₄×D₁₃	—	4	2	no	—
293	C₄×D₁₃	—	4	2	no	—
294	Dic₂₆	—	2	2	no	—
295	#560	—	13	2	no	—
296	#560	—	13	2	no	—
297	#553	—	13	2	no	—
298	#553	—	13	2	no	—
299	#553	—	13	1	no	—
300	#553	—	13	1	no	—
301	#552	—	13	1	no	—
302	#552	—	13	1	no	—
303	#550	—	13	1	no	—
304	#550	—	13	1	no	—
305	#547	—	13	1	no	—
306	#547	—	13	1	no	—
307	#541	—	13	1	no	—
308	#540	—	13	1	no	—
309	#540	—	13	2	no	—
310	#540	—	13	2	no	—
311	#539	—	13	2	no	—
312	#539	—	13	2	no	—
313	#537	—	13	1	no	—
314	#537	D₁₃	1	1	yes	characteristic, complemented
315	#525	—	13	1	no	—
316	#525	—	13	1	no	—
317	#525	—	13	1	no	—
318	C₂²×C₁₃	—	2	2	no	—
319	C₂²×C₁₃	—	2	1	no	—
320	C₂²×C₁₃	—	2	1	no	—
321	C₂²×C₁₃	—	2	1	no	—
322	C₂²×C₁₃	—	2	1	no	—
323	C₂²×C₁₃	—	2	2	no	—
324	C₂²×C₁₃	—	2	1	no	—
325	C₂²×C₁₃	—	2	1	no	—
326	C₂²×C₁₃	—	2	1	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	1	no	—
329	C₂²×C₁₃	—	2	1	no	—
330	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
331	C₂×D₁₃	—	2	1	no	—
332	C₂×D₁₃	—	2	1	no	—
333	C₂×D₁₃	—	2	2	no	—
334	C₂×D₁₃	—	2	2	no	—
335	C₂×D₁₃	—	2	1	no	—
336	C₂×D₁₃	—	2	2	no	—
337	C₂×D₁₃	—	2	1	no	—
338	C₂×D₁₃	—	2	1	no	—
339	C₂×D₁₃	—	2	1	no	—
340	C₂×D₁₃	—	4	4	no	—
341	C₄×C₁₃	—	2	1	no	—
342	C₄×C₁₃	—	2	1	no	—
343	C₄×C₁₃	—	2	2	no	—
344	C₄×C₁₃	—	2	1	no	—
345	C₄×C₁₃	—	2	2	no	—
346	C₄×C₁₃	—	2	2	no	—
347	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
348	Dic₁₃	—	2	2	no	—
349	Dic₁₃	—	2	1	no	—
350	Dic₁₃	—	2	1	no	—
351	Dic₁₃	—	2	1	no	—
352	Dic₁₃	—	2	1	no	—
353	Dic₁₃	—	2	2	no	—
354	Dic₁₃	—	2	2	no	—
355	Dic₁₃	—	2	1	no	—
356	Dic₁₃	—	2	1	no	—
357	C₂×#41	—	13	1	no	—
358	C₂×#41	—	13	1	no	—
359	C₂×#41	—	13	1	no	—
360	C₂×#41	C₂×D₁₃	1	1	yes	characteristic
361	C₂×#41	C₂×D₁₃	1	1	yes	characteristic, complemented
362	C₂³×C₄	—	13	1	no	—
363	C₄⋊Q₈	—	13	1	no	—
364	#127	—	13	1	no	—
365	#127	—	13	2	no	—
366	#127	—	13	2	no	—
367	#126	—	13	2	no	—
368	#126	—	13	2	no	—
369	#126	—	13	2	no	—
370	#126	—	13	2	no	—
371	#126	—	13	2	no	—
372	#126	—	13	2	no	—
373	#125	—	13	2	no	—
374	#125	—	13	2	no	—
375	#125	—	13	2	no	—
376	#125	—	13	2	no	—
377	#125	—	13	1	no	—
378	#125	—	13	1	no	—
379	#123	—	13	1	no	—
380	#123	—	13	1	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	—	13	2	no	—
387	#123	—	13	2	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	C₂²⋊Q₈	—	13	1	no	—
394	C₂²⋊Q₈	—	13	1	no	—
395	C₂²⋊Q₈	—	13	1	no	—
396	C₂²⋊Q₈	—	13	2	no	—
397	C₂²⋊Q₈	—	13	1	no	—
398	C₂²⋊Q₈	—	13	1	no	—
399	C₂²⋊Q₈	—	13	1	no	—
400	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
401	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
402	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
403	#121	—	13	1	no	—
404	#121	—	13	1	no	—
405	#121	—	13	1	no	—
406	#121	—	13	2	no	—
407	#121	—	13	2	no	—
408	#121	—	13	2	no	—
409	#121	—	13	2	no	—
410	#121	—	13	2	no	—
411	#121	—	13	2	no	—
412	#121	—	13	2	no	—
413	#121	—	13	2	no	—
414	#121	—	13	2	no	—
415	#121	—	13	1	no	—
416	#121	—	13	1	no	—
417	#121	—	13	2	no	—
418	#121	—	13	2	no	—
419	#121	—	13	1	no	—
420	#121	—	13	2	no	—
421	#121	—	13	2	no	—
422	#121	C₂×D₁₃	1	1	yes	characteristic
423	#121	C₂×D₁₃	1	2	yes	—
424	#121	C₂×D₁₃	1	2	yes	—
425	#121	C₂×D₁₃	1	2	yes	complemented
426	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
427	#120	—	13	1	no	—
428	#120	—	13	1	no	—
429	#120	—	13	2	no	—
430	#120	—	13	2	no	—
431	C₄×Q₈	—	13	1	no	—
432	C₄×Q₈	—	13	1	no	—
433	C₄×D₄	—	13	2	no	—
434	C₄×D₄	—	13	1	no	—
435	C₄×D₄	—	13	2	no	—
436	C₄×D₄	—	13	1	no	—
437	C₄×D₄	—	13	1	no	—
438	C₄×D₄	—	13	1	no	—
439	C₄×D₄	—	13	1	no	—
440	C₄×D₄	—	13	2	no	—
441	C₄×D₄	—	13	2	no	—
442	C₄×D₄	—	13	2	no	—
443	C₄×D₄	—	13	1	no	—
444	C₄×D₄	—	13	2	no	—
445	C₄×D₄	—	13	2	no	—
446	C₄×D₄	—	13	2	no	—
447	#117	—	13	1	no	—
448	#117	—	13	2	no	—
449	#117	—	13	1	no	—
450	#117	—	13	1	no	—
451	#117	—	13	2	no	—
452	C₂×C₄⋊C₄	—	13	1	no	—
453	C₂×C₄⋊C₄	—	13	2	no	—
454	C₂×C₄⋊C₄	—	13	2	no	—
455	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
456	C₂×C₁₃	—	4	1	no	—
457	C₂×C₁₃	—	4	2	no	—
458	C₂×C₁₃	—	4	1	no	—
459	C₂×C₁₃	—	4	1	no	—
460	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
461	C₂×C₁₃	#585	1	1	yes	characteristic
462	C₂×C₁₃	#585	1	1	yes	characteristic
463	D₁₃	—	4	2	no	—
464	D₁₃	—	4	1	no	—
465	D₁₃	—	4	1	no	—
466	C₂⁴	—	13	1	no	—
467	#41	—	4	2	no	—
468	#41	—	4	2	no	—
469	#41	—	52	2	no	—
470	#41	—	52	2	no	—
471	#41	—	52	2	no	—
472	C₂×Q₈	—	13	1	no	—
473	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
474	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
475	C₂×D₄	—	13	1	no	—
476	C₂×D₄	—	13	1	no	—
477	C₂×D₄	—	13	2	no	—
478	C₂×D₄	—	13	2	no	—
479	C₂×D₄	—	13	1	no	—
480	C₂×D₄	—	13	1	no	—
481	C₂×D₄	—	13	2	no	—
482	C₂×D₄	—	13	2	no	—
483	C₂×D₄	—	13	2	no	—
484	C₂×D₄	—	13	2	no	—
485	C₂×D₄	—	13	2	no	—
486	C₂×D₄	—	13	1	no	—
487	C₂×D₄	—	13	2	no	—
488	C₂×D₄	—	13	2	no	—
489	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
490	C₂×D₄	C₂²×D₁₃	1	2	yes	—
491	C₂×D₄	C₂²×D₁₃	1	2	yes	—
492	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
493	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
494	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
495	C₂×D₄	C₂²×D₁₃	1	2	yes	—
496	C₂²×C₄	—	13	2	no	—
497	C₂²×C₄	—	13	2	no	—
498	C₂²×C₄	—	13	2	no	—
499	C₂²×C₄	—	13	1	no	—
500	C₂²×C₄	—	13	1	no	—
501	C₂²×C₄	—	13	1	no	—
502	C₂²×C₄	—	13	2	no	—
503	C₂²×C₄	—	13	2	no	—
504	C₂²×C₄	—	13	2	no	—
505	C₂²×C₄	—	13	1	no	—
506	C₂²×C₄	—	13	1	no	—
507	C₂²×C₄	—	52	2	no	—
508	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
509	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
510	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
511	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
512	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
513	C₄⋊C₄	—	13	1	no	—
514	C₄⋊C₄	—	13	1	no	—
515	C₄⋊C₄	—	13	1	no	—
516	C₄⋊C₄	—	13	2	no	—
517	C₄⋊C₄	—	13	2	no	—
518	C₄⋊C₄	—	13	1	no	—
519	C₄⋊C₄	—	13	2	no	—
520	C₄⋊C₄	—	13	2	no	—
521	C₄⋊C₄	—	13	2	no	—
522	C₄⋊C₄	—	13	2	no	—
523	C₄⋊C₄	—	13	1	no	—
524	C₄⋊C₄	—	13	1	no	—
525	C₄⋊C₄	—	13	2	no	—
526	C₄⋊C₄	—	13	2	no	—
527	C₄⋊C₄	—	13	1	no	—
528	C₄⋊C₄	—	13	1	no	—
529	C₄⋊C₄	—	13	2	no	—
530	C₄⋊C₄	—	13	2	no	—
531	C₄⋊C₄	—	13	2	no	—
532	C₄⋊C₄	—	13	2	no	—
533	C₄⋊C₄	—	13	2	no	—
534	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
535	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
536	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
537	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
538	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
539	C₂²⋊C₄	—	13	1	no	—
540	C₂²⋊C₄	—	13	1	no	—
541	C₂²⋊C₄	—	13	1	no	—
542	C₂²⋊C₄	—	13	1	no	—
543	C₂²⋊C₄	—	13	2	no	—
544	C₂²⋊C₄	—	13	2	no	—
545	C₂²⋊C₄	—	13	1	no	—
546	C₂²⋊C₄	—	13	1	no	—
547	C₂²⋊C₄	—	13	2	no	—
548	C₂²⋊C₄	—	13	2	no	—
549	C₂²⋊C₄	—	13	2	no	—
550	C₂²⋊C₄	—	13	2	no	—
551	C₂²⋊C₄	—	13	2	no	—
552	C₂²⋊C₄	—	13	1	no	—
553	C₂²⋊C₄	—	13	1	no	—
554	C₂²⋊C₄	—	13	2	no	—
555	C₂²⋊C₄	—	13	2	no	—
556	C₂²⋊C₄	—	13	1	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	C₂²×D₁₃	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
563	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
564	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
565	C₄²	—	13	2	no	—
566	C₄²	—	13	2	no	—
567	C₄²	—	13	1	no	—
568	C₄²	—	13	1	no	—
569	C₄²	—	13	2	no	—
570	C₄²	—	13	2	no	—
571	C₁₃	#3539	1	1	yes	characteristic, complemented, Sylow
572	C₂³	—	13	1	no	—
573	C₂³	—	13	1	no	—
574	C₂³	—	13	2	no	—
575	C₂³	—	52	1	no	—
576	C₂³	—	52	1	no	—
577	C₂³	—	52	1	no	—
578	C₂³	C₂³×D₁₃	1	1	yes	characteristic
579	C₂³	C₂³×D₁₃	1	1	yes	characteristic
580	C₂³	C₂³×D₁₃	1	1	yes	characteristic
581	C₂³	C₂³×D₁₃	1	2	yes	—
582	Q₈	—	2	2	no	—
583	Q₈	—	4	1	no	—
584	Q₈	—	26	2	no	—
585	D₄	—	2	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	4	2	no	—
588	D₄	—	4	1	no	—
589	D₄	—	4	1	no	—
590	D₄	—	4	1	no	—
591	D₄	—	4	2	no	—
592	D₄	—	26	2	no	—
593	D₄	—	52	2	no	—
594	D₄	—	52	2	no	—
595	D₄	—	52	1	no	—
596	D₄	—	52	1	no	—
597	D₄	—	52	2	no	—
598	D₄	—	52	1	no	—
599	D₄	—	52	2	no	—
600	D₄	—	52	2	no	—
601	D₄	—	52	2	no	—
602	D₄	—	52	1	no	—
603	D₄	—	52	2	no	—
604	D₄	—	52	2	no	—
605	D₄	—	52	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	13	1	no	—
612	C₂×C₄	—	13	1	no	—
613	C₂×C₄	—	13	2	no	—
614	C₂×C₄	—	13	1	no	—
615	C₂×C₄	—	13	1	no	—
616	C₂×C₄	—	13	1	no	—
617	C₂×C₄	—	13	2	no	—
618	C₂×C₄	—	13	1	no	—
619	C₂×C₄	—	13	2	no	—
620	C₂×C₄	—	26	2	no	—
621	C₂×C₄	—	26	2	no	—
622	C₂×C₄	—	52	2	no	—
623	C₂×C₄	—	52	1	no	—
624	C₂×C₄	—	52	1	no	—
625	C₂×C₄	—	52	2	no	—
626	C₂×C₄	—	52	2	no	—
627	C₂×C₄	—	52	2	no	—
628	C₂×C₄	—	52	2	no	—
629	C₂×C₄	—	52	1	no	—
630	C₂×C₄	—	52	2	no	—
631	C₂×C₄	C₂³×D₁₃	1	2	yes	—
632	C₂×C₄	C₂³×D₁₃	1	2	yes	—
633	C₂×C₄	C₂³×D₁₃	1	2	yes	—
634	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
635	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
638	C₂²	—	2	1	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	26	1	no	—
651	C₂²	—	26	1	no	—
652	C₂²	—	26	2	no	—
653	C₂²	—	26	2	no	—
654	C₂²	—	26	1	no	—
655	C₂²	—	26	1	no	—
656	C₂²	—	26	2	no	—
657	C₂²	—	26	1	no	—
658	C₂²	—	26	1	no	—
659	C₂²	—	52	4	no	—
660	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	26	1	no	—
668	C₄	—	26	1	no	—
669	C₄	—	26	2	no	—
670	C₄	—	26	1	no	—
671	C₄	—	26	1	no	—
672	C₄	—	26	2	no	—
673	C₄	—	26	1	no	—
674	C₄	—	26	2	no	—
675	C₄	—	26	1	no	—
676	C₄	#88251	1	2	yes	—
677	C₂	—	4	1	no	—
678	C₂	—	4	1	no	—
679	C₂	—	4	1	no	—
680	C₂	—	4	2	no	—
681	C₂	—	52	1	no	—
682	C₂	—	52	1	no	—
683	C₂	—	52	2	no	—
684	C₂	C₂×#88251	1	1	yes	characteristic
685	C₂	#11719650	1	1	yes	characteristic
686	C₂	#11719652	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#537	C₂
hypercenter	#537	D₁₃
hypocenter	C₁₃	#3539
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #537

Complements

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

N	H ≅ G/N	type
1. C₁₃×#537	C₂	semidirect
2. #11719539	C₂	semidirect
3. #11719538	C₂	semidirect
4. #11719533	C₂	semidirect
5. #11719529	C₂	semidirect
6. #11719350	C₂	semidirect
7. #11719347	C₂	semidirect
8. #11719343	C₂	semidirect
9. #11719336	C₂	semidirect
10. #11719332	C₂	semidirect
11. #11719330	C₂	semidirect
12. #11719325	C₂	semidirect
13. #11719325	C₂	semidirect
14. #11719324	C₂	semidirect
15. #11719324	C₂	semidirect
16. #11719323	C₂	semidirect
17. #11719320	C₂	semidirect
18. #11719319	C₂	semidirect
19. #11719311	C₂	semidirect
20. #11719306	C₂	semidirect
21. #11719304	C₂	semidirect
22. #11719219	C₂	semidirect
23. #11719218	C₂	semidirect
25. C₂×C₁₃×#41	C₂²	semidirect
28. C₂×#6127	C₂²	semidirect
31. C₁₃×C₂²⋊Q₈	C₂²	semidirect
32. C₁₃×C₂²⋊Q₈	C₂²	semidirect
36. C₁₃×#121	C₂²	semidirect
37. C₁₃×#121	C₂²	semidirect
38. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
42. #88200	C₂²	semidirect
43. Q₈×Dic₁₃	C₂²	semidirect
44. #88198	C₂²	semidirect
47. #88194	C₂²	semidirect
52. #88193	C₂²	semidirect
53. #88193	C₂²	semidirect
59. #88192	C₂²	semidirect
65. #88189	C₂²	semidirect
67. D₄×Dic₁₃	C₂²	semidirect
68. D₄×Dic₁₃	C₂²	semidirect
72. #88184	C₂²	semidirect
79. C₄×C₂²⋊D₁₃	C₂²	semidirect
80. C₄×C₂²⋊D₁₃	C₂²	semidirect
82. #88180	C₂²	semidirect
83. C₂×C₄⋊Dic₁₃	C₂²	semidirect
85. #88178	C₂²	semidirect
86. C₂×#6101	C₂²	semidirect
89. #88152	C₂²	semidirect
96. #88147	C₂²	semidirect
99. C₄⋊C₄×D₁₃	C₂²	semidirect
100. #88144	C₂²	semidirect
101. #88144	C₂²	semidirect
102. #88144	C₂²	semidirect
103. #88144	C₂²	semidirect
104. #88143	C₂²	semidirect
105. #88143	C₂²	semidirect
106. #88141	C₂²	semidirect
109. #88140	C₂²	semidirect
113. #88137	C₂²	semidirect
114. #88137	C₂²	semidirect
118. #88135	C₂²	semidirect
121. #88133	C₂²	semidirect
122. #88131	C₂²	semidirect
314. #537	D₁₃	semidirect
361. C₂×#41	C₂×D₁₃	semidirect
401. C₂²⋊Q₈	C₂×D₁₃	semidirect
402. C₂²⋊Q₈	C₂×D₁₃	semidirect
425. #121	C₂×D₁₃	semidirect
426. #121	C₂×D₁₃	semidirect
455. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
571. C₁₃	#3539	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#537	2
#11719539	2
#11719538	2
#11719533	2
#11719529	2
#11719350	2
#11719347	2
#11719343	2
#11719336	2
#11719332	2
#11719330	2
#11719325	2
#11719324	2
#11719323	2
#11719320	2
#11719319	2
#11719311	2
#11719306	2
#11719304	2
#11719219	2
#11719218	2
#3539	13