Subgroups — #13128873

Order 1664.

1124 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719536	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719529	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#88178	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719367	C₂	1	2	yes	maximal, complemented
7	#11719365	C₂	1	2	yes	maximal, complemented
8	#11719347	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719337	C₂	1	1	yes	maximal, characteristic, complemented
10	D₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719327	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719316	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719311	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719305	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719303	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719296	C₂	1	2	yes	maximal, complemented
17	#11719292	C₂	1	2	yes	maximal, complemented
18	#11719269	C₂	1	2	yes	maximal, complemented
19	#11719261	C₂	1	2	yes	maximal, complemented
20	#11719251	C₂	1	2	yes	maximal, complemented
21	#11719244	C₂	1	2	yes	maximal, complemented
22	#11719238	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719234	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
25	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
27	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×#6129	C₂²	1	2	yes	—
29	C₂×#6129	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
31	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#123	C₂²	1	2	yes	complemented
33	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#121	C₂²	1	1	yes	characteristic
36	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#120	C₂²	1	2	yes	—
38	C₄×D₄×C₁₃	C₂²	1	2	yes	—
39	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
40	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
42	C₂×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
43	#88200	C₂²	1	1	yes	characteristic, complemented
44	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
45	#88198	C₂²	1	1	yes	characteristic, complemented
46	#88193	C₂²	1	2	yes	—
47	#88193	C₂²	1	2	yes	—
48	#88192	C₂²	1	2	yes	—
49	#88192	C₂²	1	1	yes	characteristic, complemented
50	#88191	C₂²	1	2	yes	—
51	#88190	C₂²	1	2	yes	complemented
52	#88190	C₂²	1	1	yes	characteristic, complemented
53	#88189	C₂²	1	2	yes	—
54	#88189	C₂²	1	2	yes	complemented
55	#88189	C₂²	1	2	yes	complemented
56	D₄×Dic₁₃	C₂²	1	2	yes	—
57	D₄×Dic₁₃	C₂²	1	2	yes	—
58	D₄×Dic₁₃	C₂²	1	2	yes	complemented
59	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
60	#88183	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
63	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
64	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
65	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
68	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
70	C₂×#6103	C₂²	1	1	yes	characteristic
71	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
72	#88178	C₂²	1	2	yes	—
73	#88178	C₂²	1	1	yes	characteristic
74	#88178	C₂²	1	1	yes	characteristic
75	#88178	C₂²	1	1	yes	characteristic, complemented
76	#88178	C₂²	1	1	yes	characteristic, complemented
77	#88178	C₂²	1	2	yes	complemented
78	#88178	C₂²	1	2	yes	complemented
79	C₂×#6101	C₂²	1	1	yes	characteristic
80	C₂×#6101	C₂²	1	2	yes	complemented
81	C₂×#6101	C₂²	1	2	yes	complemented
82	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
83	#88152	C₂²	1	2	yes	complemented
84	#88151	C₂²	1	1	yes	characteristic, complemented
85	#88151	C₂²	1	1	yes	characteristic, complemented
86	#88150	C₂²	1	2	yes	complemented
87	#88150	C₂²	1	2	yes	complemented
88	#88146	C₂²	1	1	yes	characteristic, complemented
89	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
90	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
91	#88144	C₂²	1	1	yes	characteristic, complemented
92	#88144	C₂²	1	2	yes	complemented
93	#88143	C₂²	1	2	yes	complemented
94	#88142	C₂²	1	1	yes	characteristic, complemented
95	#88142	C₂²	1	2	yes	complemented
96	#88141	C₂²	1	1	yes	characteristic, complemented
97	#88141	C₂²	1	1	yes	characteristic, complemented
98	#88141	C₂²	1	2	yes	complemented
99	#88140	C₂²	1	2	yes	—
100	#88139	C₂²	1	2	yes	—
101	#88139	C₂²	1	2	yes	complemented
102	#88137	C₂²	1	2	yes	—
103	#88137	C₂²	1	2	yes	complemented
104	#88137	C₂²	1	2	yes	complemented
105	#88135	C₂²	1	2	yes	—
106	#88135	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
108	#88133	C₂²	1	2	yes	complemented
109	#88133	C₂²	1	2	yes	complemented
110	#88133	C₂²	1	2	yes	complemented
111	#88132	C₂²	1	2	yes	—
112	#88132	C₂²	1	2	yes	—
113	#88132	C₂²	1	2	yes	complemented
114	#88132	C₂²	1	2	yes	complemented
115	#88132	C₂²	1	2	yes	complemented
116	#88131	C₂²	1	2	yes	—
117	#88131	C₂²	1	2	yes	complemented
118	#88131	C₂²	1	2	yes	complemented
119	#88130	C₂²	1	2	yes	complemented
120	#88126	C₂²	1	2	yes	complemented
121	#88124	C₂²	1	2	yes	complemented
122	C₄×Dic₂₆	C₂²	1	2	yes	complemented
123	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
124	C₂³×D₁₃	C₂³	1	1	yes	characteristic
125	C₁₃×#41	—	4	2	no	—
126	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₃	C₂³	1	2	yes	—
128	C₂×D₄×C₁₃	C₂³	1	2	yes	—
129	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₁₃	C₂³	1	2	yes	—
131	C₂²×C₄×C₁₃	—	4	2	no	—
132	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
134	C₂²×C₄×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	2	yes	—
138	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₃	—	2	4	no	—
140	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
146	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
147	C₂²×Dic₁₃	C₂³	1	2	yes	—
148	C₂²×Dic₁₃	C₂³	1	2	yes	—
149	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
150	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
151	C₂²×Dic₁₃	C₂³	1	2	yes	—
152	C₂²×Dic₁₃	C₂³	1	2	yes	—
153	Q₈×D₁₃	—	4	2	no	—
154	#6129	—	2	8	no	—
155	#6129	—	4	2	no	—
156	C₂×C₄×D₁₃	—	4	2	no	—
157	C₂×C₄×D₁₃	C₂³	1	2	yes	—
158	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₁₃	C₂³	1	2	yes	—
161	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
163	C₂×Dic₂₆	—	4	2	no	—
164	C₂×Dic₂₆	C₂³	1	2	yes	—
165	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
166	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
167	C₂×Dic₂₆	C₂³	1	2	yes	—
168	C₂×Dic₂₆	C₂³	1	2	yes	—
169	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
171	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₄²×C₁₃	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₃	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	#6103	C₂³	1	1	yes	characteristic
192	#6103	C₂³	1	2	yes	—
193	#6103	C₂³	1	1	yes	characteristic
194	#6103	C₂³	1	2	yes	—
195	#6103	C₂³	1	2	yes	—
196	#6103	C₂³	1	2	yes	—
197	#6103	C₂³	1	1	yes	characteristic
198	#6103	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₁₃	C₂³	1	2	yes	—
200	C₄⋊Dic₁₃	C₂³	1	2	yes	—
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	1	yes	characteristic
205	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
206	#6101	C₂³	1	1	yes	characteristic
207	#6101	C₂³	1	2	yes	—
208	#6101	C₂³	1	1	yes	characteristic
209	#6101	C₂³	1	2	yes	—
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	2	yes	—
217	#6101	C₂³	1	2	yes	—
218	#6101	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	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	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
229	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
230	#3520	—	13	1	no	maximal, Sylow
231	C₂³×C₁₃	—	2	2	no	—
232	C₂³×C₁₃	—	2	2	no	—
233	C₂³×C₁₃	—	4	1	no	—
234	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₂³×C₁₃	C₂⁴	1	2	yes	—
236	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
238	C₂²×D₁₃	—	2	2	no	—
239	C₂²×D₁₃	—	2	2	no	—
240	C₂²×D₁₃	—	4	1	no	—
241	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
242	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
243	Q₈×C₁₃	—	2	2	no	—
244	D₄×C₁₃	—	2	4	no	—
245	D₄×C₁₃	—	2	4	no	—
246	D₄×C₁₃	—	2	2	no	—
247	D₄×C₁₃	—	4	2	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	1	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	2	no	—
255	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
257	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
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	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
262	C₂²⋊D₁₃	—	2	2	no	—
263	C₂²⋊D₁₃	—	2	4	no	—
264	C₂²⋊D₁₃	—	2	2	no	—
265	C₂²⋊D₁₃	—	2	2	no	—
266	C₂²⋊D₁₃	—	4	2	no	—
267	C₂²⋊D₁₃	#41	1	4	yes	complemented
268	C₂×Dic₁₃	—	2	4	no	—
269	C₂×Dic₁₃	—	2	2	no	—
270	C₂×Dic₁₃	—	2	4	no	—
271	C₂×Dic₁₃	—	2	2	no	—
272	C₂×Dic₁₃	—	4	2	no	—
273	C₂×Dic₁₃	—	4	1	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	1	yes	characteristic
279	C₂×Dic₁₃	C₂⁴	1	2	yes	—
280	C₂×Dic₁₃	C₂⁴	1	2	yes	—
281	C₂×Dic₁₃	C₂⁴	1	2	yes	—
282	C₂×Dic₁₃	C₂⁴	1	2	yes	—
283	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
285	C₄×D₁₃	—	2	4	no	—
286	C₄×D₁₃	—	2	2	no	—
287	C₄×D₁₃	—	2	2	no	—
288	C₄×D₁₃	—	4	1	no	—
289	C₄×D₁₃	—	4	1	no	—
290	C₄×D₁₃	—	4	2	no	—
291	Dic₂₆	—	2	2	no	—
292	Dic₂₆	—	2	2	no	—
293	Dic₂₆	—	2	4	no	—
294	Dic₂₆	—	4	2	no	—
295	Dic₂₆	—	4	2	no	—
296	#556	—	13	1	no	—
297	#554	—	13	2	no	—
298	#552	—	13	1	no	—
299	#552	—	13	1	no	—
300	#551	—	13	2	no	—
301	#551	—	13	2	no	—
302	D₄×Q₈	—	13	1	no	—
303	#548	—	13	1	no	—
304	#548	—	13	1	no	—
305	#547	—	13	1	no	—
306	#547	—	13	1	no	—
307	#546	—	13	2	no	—
308	#542	—	13	2	no	—
309	#539	—	13	2	no	—
310	#539	—	13	2	no	—
311	#533	—	13	1	no	—
312	#529	—	13	1	no	—
313	#525	—	13	1	no	—
314	#525	D₁₃	1	1	yes	characteristic, complemented
315	C₂×C₂²⋊Q₈	—	13	1	no	—
316	C₂×C₂²⋊Q₈	—	13	1	no	—
317	#520	—	13	2	no	—
318	C₂×C₄×D₄	—	13	1	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	2	no	—
326	C₂²×C₁₃	—	2	1	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	1	no	—
329	C₂²×C₁₃	—	4	4	no	—
330	C₂²×C₁₃	C₂×#41	1	2	yes	—
331	C₂²×C₁₃	2₋¹⁺⁴	1	2	yes	—
332	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
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	1	no	—
338	C₂×D₁₃	—	4	4	no	—
339	C₂×D₁₃	C₂×#41	1	2	yes	—
340	C₄×C₁₃	—	2	2	no	—
341	C₄×C₁₃	—	2	1	no	—
342	C₄×C₁₃	—	2	2	no	—
343	C₄×C₁₃	—	2	1	no	—
344	C₄×C₁₃	—	2	1	no	—
345	C₄×C₁₃	—	2	2	no	—
346	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
347	Dic₁₃	—	2	2	no	—
348	Dic₁₃	—	2	2	no	—
349	Dic₁₃	—	2	1	no	—
350	Dic₁₃	—	2	2	no	—
351	Dic₁₃	—	2	2	no	—
352	Dic₁₃	—	2	1	no	—
353	Dic₁₃	—	2	1	no	—
354	Dic₁₃	—	2	1	no	—
355	Dic₁₃	—	2	1	no	—
356	Dic₁₃	C₂×#41	1	2	yes	—
357	C₂×#41	—	13	2	no	—
358	C₂×#41	—	13	1	no	—
359	C₂×#41	C₂×D₁₃	1	1	yes	characteristic, complemented
360	C₂²×Q₈	—	13	1	no	—
361	C₂²×Q₈	—	13	1	no	—
362	C₂²×D₄	—	13	1	no	—
363	C₂³×C₄	—	13	1	no	—
364	C₂³×C₄	C₂×D₁₃	1	1	yes	characteristic
365	C₄⋊Q₈	—	13	1	no	—
366	C₄⋊Q₈	—	13	1	no	—
367	C₄⋊Q₈	—	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	1	no	—
374	#125	—	13	2	no	—
375	#125	—	13	2	no	—
376	#125	—	13	2	no	—
377	#124	—	13	1	no	—
378	#124	—	13	2	no	—
379	#124	—	13	2	no	—
380	#124	—	13	2	no	—
381	#123	—	13	2	no	—
382	#123	—	13	2	no	—
383	#123	—	13	2	no	—
384	#123	—	13	2	no	—
385	#123	—	13	2	no	—
386	#123	—	13	2	no	—
387	#123	—	13	2	no	—
388	#123	—	13	2	no	—
389	#123	C₂×D₁₃	1	2	yes	complemented
390	C₂²⋊Q₈	—	13	1	no	—
391	C₂²⋊Q₈	—	13	1	no	—
392	C₂²⋊Q₈	—	13	1	no	—
393	C₂²⋊Q₈	—	13	2	no	—
394	C₂²⋊Q₈	—	13	1	no	—
395	C₂²⋊Q₈	—	13	1	no	—
396	C₂²⋊Q₈	—	13	2	no	—
397	C₂²⋊Q₈	—	13	2	no	—
398	C₂²⋊Q₈	—	13	2	no	—
399	C₂²⋊Q₈	—	13	1	no	—
400	C₂²⋊Q₈	—	13	1	no	—
401	C₂²⋊Q₈	—	13	2	no	—
402	C₂²⋊Q₈	—	13	2	no	—
403	C₂²⋊Q₈	—	13	2	no	—
404	C₂²⋊Q₈	—	13	2	no	—
405	C₂²⋊Q₈	—	13	2	no	—
406	C₂²⋊Q₈	—	13	2	no	—
407	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
408	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
409	#121	—	13	1	no	—
410	#121	—	13	2	no	—
411	#121	—	13	2	no	—
412	#121	—	13	2	no	—
413	#121	C₂×D₁₃	1	1	yes	characteristic
414	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
415	#120	—	13	2	no	—
416	#120	C₂×D₁₃	1	2	yes	—
417	C₄×Q₈	—	13	1	no	—
418	C₄×Q₈	—	13	2	no	—
419	C₄×Q₈	—	13	1	no	—
420	C₄×Q₈	—	13	1	no	—
421	C₄×Q₈	—	13	2	no	—
422	C₄×D₄	—	13	2	no	—
423	C₄×D₄	—	13	2	no	—
424	C₄×D₄	—	13	2	no	—
425	C₄×D₄	—	13	1	no	—
426	C₄×D₄	—	13	1	no	—
427	C₄×D₄	—	13	1	no	—
428	C₄×D₄	—	13	1	no	—
429	C₄×D₄	—	13	1	no	—
430	C₄×D₄	—	13	1	no	—
431	C₄×D₄	—	13	1	no	—
432	C₄×D₄	—	13	1	no	—
433	C₄×D₄	—	13	1	no	—
434	C₄×D₄	—	13	2	no	—
435	C₄×D₄	—	13	2	no	—
436	C₄×D₄	—	13	2	no	—
437	C₄×D₄	C₂×D₁₃	1	2	yes	—
438	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
439	#117	—	13	1	no	—
440	#117	—	13	2	no	—
441	#117	—	13	2	no	—
442	#117	—	13	2	no	—
443	#117	—	13	2	no	—
444	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
445	C₂×C₄⋊C₄	—	13	1	no	—
446	C₂×C₄⋊C₄	—	13	2	no	—
447	C₂×C₄⋊C₄	—	13	2	no	—
448	C₂×C₄⋊C₄	—	13	1	no	—
449	C₂×C₄⋊C₄	—	13	2	no	—
450	C₂×C₄⋊C₄	—	13	1	no	—
451	C₂×C₂²⋊C₄	—	13	1	no	—
452	C₂×C₂²⋊C₄	—	13	2	no	—
453	C₂×C₂²⋊C₄	—	13	1	no	—
454	C₂×C₂²⋊C₄	—	13	2	no	—
455	C₂×C₄²	—	13	1	no	—
456	C₂×C₁₃	—	2	2	no	—
457	C₂×C₁₃	—	2	2	no	—
458	C₂×C₁₃	—	4	2	no	—
459	C₂×C₁₃	—	4	1	no	—
460	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
461	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
462	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
463	D₁₃	—	2	2	no	—
464	D₁₃	—	4	1	no	—
465	C₂⁴	—	13	1	no	—
466	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
467	#41	—	4	2	no	—
468	#41	—	26	8	no	—
469	#41	—	52	2	no	—
470	C₂×Q₈	—	13	2	no	—
471	C₂×Q₈	—	13	1	no	—
472	C₂×Q₈	—	13	1	no	—
473	C₂×Q₈	—	13	2	no	—
474	C₂×Q₈	—	13	2	no	—
475	C₂×Q₈	—	52	2	no	—
476	C₂×Q₈	—	52	2	no	—
477	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
478	C₂×D₄	—	13	1	no	—
479	C₂×D₄	—	13	2	no	—
480	C₂×D₄	—	13	1	no	—
481	C₂×D₄	—	13	1	no	—
482	C₂×D₄	—	13	1	no	—
483	C₂×D₄	—	13	2	no	—
484	C₂×D₄	—	26	4	no	—
485	C₂×D₄	C₂²×D₁₃	1	2	yes	—
486	C₂×D₄	C₂²×D₁₃	1	2	yes	—
487	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
488	C₂×D₄	C₂²×D₁₃	1	2	yes	—
489	C₂²×C₄	—	4	2	no	—
490	C₂²×C₄	—	13	1	no	—
491	C₂²×C₄	—	13	1	no	—
492	C₂²×C₄	—	13	2	no	—
493	C₂²×C₄	—	13	2	no	—
494	C₂²×C₄	—	13	2	no	—
495	C₂²×C₄	—	13	1	no	—
496	C₂²×C₄	—	13	2	no	—
497	C₂²×C₄	—	13	2	no	—
498	C₂²×C₄	—	13	1	no	—
499	C₂²×C₄	—	13	1	no	—
500	C₂²×C₄	—	13	2	no	—
501	C₂²×C₄	—	13	1	no	—
502	C₂²×C₄	—	13	1	no	—
503	C₂²×C₄	—	52	2	no	—
504	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
505	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
506	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
507	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
508	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
509	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
510	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
511	C₄⋊C₄	—	13	1	no	—
512	C₄⋊C₄	—	13	2	no	—
513	C₄⋊C₄	—	13	2	no	—
514	C₄⋊C₄	—	13	2	no	—
515	C₄⋊C₄	—	13	1	no	—
516	C₄⋊C₄	—	13	1	no	—
517	C₄⋊C₄	—	13	1	no	—
518	C₄⋊C₄	—	13	1	no	—
519	C₄⋊C₄	—	13	1	no	—
520	C₄⋊C₄	—	13	2	no	—
521	C₄⋊C₄	—	13	2	no	—
522	C₄⋊C₄	—	13	2	no	—
523	C₄⋊C₄	—	13	2	no	—
524	C₄⋊C₄	—	13	2	no	—
525	C₄⋊C₄	—	13	2	no	—
526	C₄⋊C₄	—	13	2	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	2	no	—
533	C₄⋊C₄	—	13	2	no	—
534	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
535	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
536	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
537	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
538	C₂²⋊C₄	—	13	2	no	—
539	C₂²⋊C₄	—	13	1	no	—
540	C₂²⋊C₄	—	13	2	no	—
541	C₂²⋊C₄	—	13	1	no	—
542	C₂²⋊C₄	—	13	1	no	—
543	C₂²⋊C₄	—	13	1	no	—
544	C₂²⋊C₄	—	13	2	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	1	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	2	no	—
557	C₂²⋊C₄	—	13	2	no	—
558	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
559	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
560	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
563	C₄²	—	13	1	no	—
564	C₄²	—	13	1	no	—
565	C₄²	—	13	1	no	—
566	C₄²	—	13	1	no	—
567	C₄²	—	13	2	no	—
568	C₄²	—	13	2	no	—
569	C₄²	—	13	2	no	—
570	C₄²	—	13	2	no	—
571	C₄²	C₂²×D₁₃	1	2	yes	—
572	C₁₃	#3520	1	1	yes	characteristic, complemented, Sylow
573	C₂³	—	2	2	no	—
574	C₂³	—	2	2	no	—
575	C₂³	—	4	1	no	—
576	C₂³	—	13	1	no	—
577	C₂³	—	13	1	no	—
578	C₂³	—	26	2	no	—
579	C₂³	—	26	2	no	—
580	C₂³	—	52	1	no	—
581	C₂³	C₂³×D₁₃	1	1	yes	characteristic
582	C₂³	C₂³×D₁₃	1	2	yes	—
583	C₂³	C₂³×D₁₃	1	1	yes	characteristic
584	C₂³	C₂³×D₁₃	1	1	yes	characteristic
585	Q₈	—	2	2	no	—
586	Q₈	—	26	4	no	—
587	Q₈	—	26	2	no	—
588	Q₈	—	26	2	no	—
589	Q₈	—	52	2	no	—
590	Q₈	—	52	2	no	—
591	D₄	—	2	4	no	—
592	D₄	—	2	4	no	—
593	D₄	—	2	2	no	—
594	D₄	—	4	2	no	—
595	D₄	—	13	4	no	—
596	D₄	—	26	2	no	—
597	D₄	—	26	2	no	—
598	D₄	—	26	4	no	—
599	D₄	—	26	2	no	—
600	D₄	—	52	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	13	1	no	—
609	C₂×C₄	—	13	1	no	—
610	C₂×C₄	—	13	1	no	—
611	C₂×C₄	—	13	2	no	—
612	C₂×C₄	—	13	1	no	—
613	C₂×C₄	—	13	1	no	—
614	C₂×C₄	—	13	2	no	—
615	C₂×C₄	—	13	2	no	—
616	C₂×C₄	—	13	2	no	—
617	C₂×C₄	—	13	1	no	—
618	C₂×C₄	—	26	4	no	—
619	C₂×C₄	—	26	2	no	—
620	C₂×C₄	—	26	4	no	—
621	C₂×C₄	—	26	4	no	—
622	C₂×C₄	—	26	2	no	—
623	C₂×C₄	—	26	2	no	—
624	C₂×C₄	—	26	2	no	—
625	C₂×C₄	—	52	1	no	—
626	C₂×C₄	—	52	1	no	—
627	C₂×C₄	—	52	2	no	—
628	C₂×C₄	—	52	1	no	—
629	C₂×C₄	—	52	2	no	—
630	C₂×C₄	—	52	2	no	—
631	C₂×C₄	C₂³×D₁₃	1	2	yes	—
632	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₁₃	1	2	yes	—
634	C₂×C₄	C₂³×D₁₃	1	2	yes	—
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	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	4	4	no	—
649	C₂²	—	13	2	no	—
650	C₂²	—	26	1	no	—
651	C₂²	—	26	1	no	—
652	C₂²	—	26	1	no	—
653	C₂²	—	26	1	no	—
654	C₂²	—	26	1	no	—
655	C₂²	—	52	4	no	—
656	C₂²	#41×D₁₃	1	2	yes	—
657	C₂²	#88257	1	2	yes	—
658	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	2	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	13	2	no	—
666	C₄	—	26	1	no	—
667	C₄	—	26	1	no	—
668	C₄	—	26	2	no	—
669	C₄	—	26	2	no	—
670	C₄	—	26	2	no	—
671	C₄	—	26	1	no	—
672	C₄	—	26	2	no	—
673	C₄	—	26	1	no	—
674	C₄	—	26	1	no	—
675	C₄	#88251	1	2	yes	—
676	C₂	—	2	2	no	—
677	C₂	—	2	2	no	—
678	C₂	—	4	1	no	—
679	C₂	—	4	2	no	—
680	C₂	—	26	2	no	—
681	C₂	—	52	1	no	—
682	C₂	C₂×#88251	1	1	yes	characteristic
683	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
684	C₂	C₂×#88257	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#525	C₂
hypercenter	#525	D₁₃
hypocenter	C₁₃	#3520
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. C₁₃×#525	C₂	semidirect
2. #11719536	C₂	semidirect
3. #11719529	C₂	semidirect
4. C₂×C₄×C₂²⋊D₁₃	C₂	semidirect
5. C₂×#88178	C₂	semidirect
6. #11719367	C₂	semidirect
7. #11719365	C₂	semidirect
8. #11719347	C₂	semidirect
9. #11719337	C₂	semidirect
10. D₁₃×C₂²⋊Q₈	C₂	semidirect
11. #11719327	C₂	semidirect
12. #11719316	C₂	semidirect
13. #11719311	C₂	semidirect
14. #11719305	C₂	semidirect
15. #11719303	C₂	semidirect
16. #11719296	C₂	semidirect
17. #11719292	C₂	semidirect
18. #11719269	C₂	semidirect
19. #11719261	C₂	semidirect
20. #11719251	C₂	semidirect
21. #11719244	C₂	semidirect
22. #11719238	C₂	semidirect
23. #11719234	C₂	semidirect
24. C₂×C₁₃×#41	C₂²	semidirect
27. C₂×Q₈×D₁₃	C₂²	semidirect
29. C₂×#6129	C₂²	semidirect
31. C₂²×Dic₂₆	C₂²	semidirect
32. C₁₃×#123	C₂²	semidirect
34. C₁₃×C₂²⋊Q₈	C₂²	semidirect
36. C₁₃×#121	C₂²	semidirect
39. C₄×D₄×C₁₃	C₂²	semidirect
40. C₁₃×#117	C₂²	semidirect
43. #88200	C₂²	semidirect
44. Q₈×Dic₁₃	C₂²	semidirect
45. #88198	C₂²	semidirect
49. #88192	C₂²	semidirect
51. #88190	C₂²	semidirect
52. #88190	C₂²	semidirect
54. #88189	C₂²	semidirect
55. #88189	C₂²	semidirect
58. D₄×Dic₁₃	C₂²	semidirect
59. D₄×Dic₁₃	C₂²	semidirect
60. #88183	C₂²	semidirect
69. C₄×C₂²⋊D₁₃	C₂²	semidirect
71. C₂×C₄⋊Dic₁₃	C₂²	semidirect
75. #88178	C₂²	semidirect
76. #88178	C₂²	semidirect
77. #88178	C₂²	semidirect
78. #88178	C₂²	semidirect
80. C₂×#6101	C₂²	semidirect
81. C₂×#6101	C₂²	semidirect
83. #88152	C₂²	semidirect
84. #88151	C₂²	semidirect
85. #88151	C₂²	semidirect
86. #88150	C₂²	semidirect
87. #88150	C₂²	semidirect
88. #88146	C₂²	semidirect
89. C₄⋊C₄×D₁₃	C₂²	semidirect
90. C₄⋊C₄×D₁₃	C₂²	semidirect
91. #88144	C₂²	semidirect
92. #88144	C₂²	semidirect
93. #88143	C₂²	semidirect
94. #88142	C₂²	semidirect
95. #88142	C₂²	semidirect
96. #88141	C₂²	semidirect
97. #88141	C₂²	semidirect
98. #88141	C₂²	semidirect
101. #88139	C₂²	semidirect
103. #88137	C₂²	semidirect
104. #88137	C₂²	semidirect
106. #88135	C₂²	semidirect
108. #88133	C₂²	semidirect
109. #88133	C₂²	semidirect
110. #88133	C₂²	semidirect
113. #88132	C₂²	semidirect
114. #88132	C₂²	semidirect
115. #88132	C₂²	semidirect
117. #88131	C₂²	semidirect
118. #88131	C₂²	semidirect
119. #88130	C₂²	semidirect
120. #88126	C₂²	semidirect
121. #88124	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
267. C₂²⋊D₁₃	#41	semidirect
314. #525	D₁₃	semidirect
359. C₂×#41	C₂×D₁₃	semidirect
389. #123	C₂×D₁₃	semidirect
408. C₂²⋊Q₈	C₂×D₁₃	semidirect
414. #121	C₂×D₁₃	semidirect
438. C₄×D₄	C₂×D₁₃	semidirect
444. #117	C₂×D₁₃	semidirect
572. C₁₃	#3520	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#525	2
#11719536	2
#11719529	2
C₂×C₄×C₂²⋊D₁₃	2
C₂×#88178	2
#11719367	2
#11719365	2
#11719347	2
#11719337	2
D₁₃×C₂²⋊Q₈	2
#11719327	2
#11719316	2
#11719311	2
#11719305	2
#11719303	2
#11719296	2
#11719292	2
#11719269	2
#11719261	2
#11719251	2
#11719244	2
#11719238	2
#11719234	2
#3520	13