Subgroups — #13129161

Order 1664.

1260 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719511	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719510	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719509	C₂	1	2	yes	maximal, complemented
5	C₂×#88194	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×C₂²⋊D₁₃	C₂	1	2	yes	maximal, complemented
7	D₄×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719423	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719420	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719325	C₂	1	2	yes	maximal, complemented
11	#11719324	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719320	C₂	1	2	yes	maximal, complemented
13	#11719314	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719305	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719304	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719300	C₂	1	2	yes	maximal, complemented
17	#11719297	C₂	1	2	yes	maximal, complemented
18	#11719296	C₂	1	2	yes	maximal, complemented
19	#11719294	C₂	1	2	yes	maximal, complemented
20	#11719267	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719264	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719255	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719243	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×D₄×C₁₃	C₂²	1	2	yes	complemented
25	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
28	C₂²×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
29	C₂²×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
30	C₂×#6129	C₂²	1	1	yes	characteristic, complemented
31	C₂×#6129	C₂²	1	2	yes	complemented
32	C₂×D₄×D₁₃	C₂²	1	2	yes	complemented
33	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
35	C₂²×D₅₂	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#121	C₂²	1	1	yes	characteristic
38	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#121	C₂²	1	2	yes	complemented
40	C₁₃×#120	C₂²	1	2	yes	complemented
41	C₁₃×#120	C₂²	1	2	yes	complemented
42	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
43	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
44	#88207	C₂²	1	2	yes	complemented
45	#88207	C₂²	1	2	yes	complemented
46	#88207	C₂²	1	2	yes	complemented
47	#88207	C₂²	1	2	yes	complemented
48	C₂×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
49	#88194	C₂²	1	1	yes	characteristic
50	#88194	C₂²	1	2	yes	complemented
51	#88194	C₂²	1	1	yes	characteristic, complemented
52	#88194	C₂²	1	2	yes	complemented
53	#88194	C₂²	1	2	yes	complemented
54	#88194	C₂²	1	1	yes	characteristic, complemented
55	#88194	C₂²	1	1	yes	characteristic, complemented
56	#88194	C₂²	1	1	yes	characteristic, complemented
57	#88193	C₂²	1	1	yes	characteristic
58	#88193	C₂²	1	2	yes	complemented
59	#88193	C₂²	1	2	yes	complemented
60	#88193	C₂²	1	2	yes	complemented
61	#88193	C₂²	1	2	yes	complemented
62	#88193	C₂²	1	2	yes	complemented
63	#88193	C₂²	1	2	yes	complemented
64	#88193	C₂²	1	2	yes	complemented
65	#88193	C₂²	1	2	yes	complemented
66	#88192	C₂²	1	1	yes	characteristic, complemented
67	#88192	C₂²	1	2	yes	complemented
68	#88192	C₂²	1	2	yes	complemented
69	#88192	C₂²	1	2	yes	complemented
70	#88192	C₂²	1	2	yes	complemented
71	#88191	C₂²	1	2	yes	complemented
72	#88191	C₂²	1	2	yes	complemented
73	#88191	C₂²	1	2	yes	complemented
74	#88191	C₂²	1	2	yes	complemented
75	#88191	C₂²	1	2	yes	complemented
76	#88190	C₂²	1	1	yes	characteristic, complemented
77	#88190	C₂²	1	1	yes	characteristic, complemented
78	#88189	C₂²	1	1	yes	characteristic, complemented
79	#88189	C₂²	1	2	yes	complemented
80	#88189	C₂²	1	2	yes	complemented
81	D₄×Dic₁₃	C₂²	1	2	yes	complemented
82	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
83	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
84	#88184	C₂²	1	1	yes	characteristic, complemented
85	#88184	C₂²	1	2	yes	complemented
86	#88183	C₂²	1	2	yes	complemented
87	#88183	C₂²	1	2	yes	complemented
88	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
89	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
90	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
91	#88180	C₂²	1	1	yes	characteristic, complemented
92	#88178	C₂²	1	1	yes	characteristic, complemented
93	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
94	#88152	C₂²	1	1	yes	characteristic, complemented
95	#88149	C₂²	1	1	yes	characteristic, complemented
96	#88148	C₂²	1	2	yes	complemented
97	#88147	C₂²	1	1	yes	characteristic, complemented
98	#88144	C₂²	1	1	yes	characteristic, complemented
99	#88143	C₂²	1	1	yes	characteristic, complemented
100	#88141	C₂²	1	1	yes	characteristic, complemented
101	#88140	C₂²	1	1	yes	characteristic, complemented
102	#88140	C₂²	1	2	yes	complemented
103	#88139	C₂²	1	1	yes	characteristic, complemented
104	#88139	C₂²	1	2	yes	complemented
105	#88138	C₂²	1	2	yes	complemented
106	#88138	C₂²	1	2	yes	complemented
107	#88138	C₂²	1	2	yes	complemented
108	#88138	C₂²	1	2	yes	complemented
109	#88137	C₂²	1	2	yes	complemented
110	#88137	C₂²	1	2	yes	complemented
111	#88137	C₂²	1	2	yes	complemented
112	#88136	C₂²	1	2	yes	complemented
113	#88135	C₂²	1	2	yes	complemented
114	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
115	#88133	C₂²	1	1	yes	characteristic, complemented
116	#88133	C₂²	1	2	yes	complemented
117	#88132	C₂²	1	1	yes	characteristic, complemented
118	#88131	C₂²	1	2	yes	complemented
119	#88129	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
121	#88126	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
123	C₂⁴×C₁₃	C₂³	1	2	yes	—
124	C₂⁴×C₁₃	C₂³	1	2	yes	—
125	C₂³×D₁₃	C₂³	1	2	yes	—
126	C₂³×D₁₃	C₂³	1	2	yes	—
127	C₂×D₄×C₁₃	—	4	2	no	—
128	C₂×D₄×C₁₃	—	4	2	no	—
129	C₂×D₄×C₁₃	—	4	4	no	—
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	1	yes	characteristic
134	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
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	C₂×D₄×C₁₃	C₂³	1	2	yes	—
139	C₂×D₄×C₁₃	C₂³	1	2	yes	—
140	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₃	—	4	4	no	—
144	C₂×C₂²⋊D₁₃	—	4	4	no	—
145	C₂×C₂²⋊D₁₃	—	4	4	no	—
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	1	yes	characteristic
150	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
155	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
157	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
158	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
159	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
160	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
161	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
162	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
163	C₂²×Dic₁₃	C₂³	1	2	yes	—
164	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
165	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
166	C₂²×Dic₁₃	C₂³	1	2	yes	—
167	C₂²×Dic₁₃	C₂³	1	2	yes	—
168	#6129	—	4	2	no	—
169	#6129	—	4	4	no	—
170	D₄×D₁₃	—	4	2	no	—
171	D₄×D₁₃	—	4	4	no	—
172	#6127	—	4	2	no	—
173	C₂×D₅₂	—	4	2	no	—
174	C₂×D₅₂	C₂³	1	1	yes	characteristic
175	C₂×D₅₂	C₂³	1	1	yes	characteristic
176	C₂×D₅₂	C₂³	1	2	yes	—
177	C₂×D₅₂	C₂³	1	2	yes	—
178	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
179	C₂×C₄×D₁₃	C₂³	1	2	yes	—
180	C₂×C₄×D₁₃	C₂³	1	2	yes	—
181	C₂×C₄×D₁₃	C₂³	1	2	yes	—
182	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
183	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
184	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₁₃×C₄⋊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	1	yes	characteristic
189	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₄²×C₁₃	C₂³	1	1	yes	characteristic
192	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
193	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
194	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
195	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
196	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
197	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
198	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
199	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
200	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
201	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
202	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
203	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
204	#6103	C₂³	1	1	yes	characteristic
205	#6103	C₂³	1	1	yes	characteristic
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	2	yes	—
211	#6103	C₂³	1	1	yes	characteristic
212	#6103	C₂³	1	2	yes	—
213	#6103	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
219	#6101	C₂³	1	1	yes	characteristic
220	#6101	C₂³	1	1	yes	characteristic
221	#6101	C₂³	1	1	yes	characteristic
222	#6101	C₂³	1	1	yes	characteristic
223	#6101	C₂³	1	2	yes	—
224	#6101	C₂³	1	2	yes	—
225	#6101	C₂³	1	1	yes	characteristic
226	#6101	C₂³	1	2	yes	—
227	#6101	C₂³	1	1	yes	characteristic
228	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
229	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
230	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
231	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
232	C₄×Dic₁₃	C₂³	1	2	yes	—
233	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
234	#3543	—	13	1	no	maximal, Sylow
235	C₂³×C₁₃	—	2	4	no	—
236	C₂³×C₁₃	—	4	2	no	—
237	C₂³×C₁₃	—	4	2	no	—
238	C₂³×C₁₃	—	4	2	no	—
239	C₂³×C₁₃	—	4	2	no	—
240	C₂³×C₁₃	—	4	2	no	—
241	C₂³×C₁₃	C₂⁴	1	2	yes	—
242	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂³×C₁₃	C₂⁴	1	2	yes	—
244	C₂³×C₁₃	C₂⁴	1	2	yes	—
245	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂²×D₁₃	—	2	4	no	—
247	C₂²×D₁₃	—	4	2	no	—
248	C₂²×D₁₃	—	4	2	no	—
249	C₂²×D₁₃	—	4	2	no	—
250	C₂²×D₁₃	—	4	2	no	—
251	C₂²×D₁₃	—	4	2	no	—
252	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
253	C₂²×D₁₃	C₂⁴	1	2	yes	—
254	C₂²×D₁₃	C₂⁴	1	2	yes	—
255	D₄×C₁₃	—	2	4	no	—
256	D₄×C₁₃	—	2	2	no	—
257	D₄×C₁₃	—	2	2	no	—
258	D₄×C₁₃	—	2	2	no	—
259	D₄×C₁₃	—	2	2	no	—
260	D₄×C₁₃	—	4	2	no	—
261	D₄×C₁₃	—	4	2	no	—
262	D₄×C₁₃	—	4	2	no	—
263	D₄×C₁₃	—	4	2	no	—
264	D₄×C₁₃	—	4	2	no	—
265	C₂×C₄×C₁₃	—	2	2	no	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	4	2	no	—
268	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
269	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
270	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
274	C₂²⋊D₁₃	—	2	2	no	—
275	C₂²⋊D₁₃	—	2	4	no	—
276	C₂²⋊D₁₃	—	2	2	no	—
277	C₂²⋊D₁₃	—	2	4	no	—
278	C₂²⋊D₁₃	—	4	2	no	—
279	C₂²⋊D₁₃	—	4	2	no	—
280	C₂²⋊D₁₃	—	4	2	no	—
281	C₂²⋊D₁₃	—	4	2	no	—
282	C₂²⋊D₁₃	—	4	2	no	—
283	C₂²⋊D₁₃	—	4	2	no	—
284	C₂²⋊D₁₃	—	4	2	no	—
285	C₂²⋊D₁₃	—	4	2	no	—
286	C₂²⋊D₁₃	—	4	2	no	—
287	C₂²⋊D₁₃	—	4	2	no	—
288	C₂²⋊D₁₃	—	4	2	no	—
289	C₂²⋊D₁₃	—	4	2	no	—
290	C₂²⋊D₁₃	—	4	2	no	—
291	C₂×Dic₁₃	—	2	2	no	—
292	C₂×Dic₁₃	—	2	4	no	—
293	C₂×Dic₁₃	—	2	2	no	—
294	C₂×Dic₁₃	—	4	2	no	—
295	C₂×Dic₁₃	—	4	2	no	—
296	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
297	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
298	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
299	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
300	C₂×Dic₁₃	C₂⁴	1	2	yes	—
301	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
302	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
303	C₂×Dic₁₃	C₂⁴	1	2	yes	—
304	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
305	D₅₂	—	2	2	no	—
306	D₅₂	—	2	2	no	—
307	D₅₂	—	4	2	no	—
308	D₅₂	—	4	2	no	—
309	C₄×D₁₃	—	2	2	no	—
310	C₄×D₁₃	—	4	2	no	—
311	C₄×D₁₃	—	4	2	no	—
312	C₄×D₁₃	—	4	2	no	—
313	Dic₂₆	—	2	2	no	—
314	Dic₂₆	—	2	2	no	—
315	#560	—	13	2	no	—
316	#560	—	13	2	no	—
317	#559	—	13	1	no	—
318	#550	—	13	1	no	—
319	#550	—	13	1	no	—
320	#546	—	13	1	no	—
321	#546	—	13	2	no	—
322	#546	—	13	1	no	—
323	D₄²	—	13	2	no	—
324	D₄²	—	13	1	no	—
325	D₄²	—	13	1	no	—
326	D₄²	D₁₃	1	1	yes	characteristic, complemented
327	#540	—	13	2	no	—
328	#540	—	13	1	no	—
329	#540	—	13	1	no	—
330	#535	—	13	1	no	—
331	#535	—	13	1	no	—
332	#535	—	13	2	no	—
333	#534	—	13	2	no	—
334	#534	—	13	2	no	—
335	C₂×#127	—	13	1	no	—
336	#529	—	13	1	no	—
337	#529	—	13	1	no	—
338	C₂²×C₁₃	—	2	1	no	—
339	C₂²×C₁₃	—	2	1	no	—
340	C₂²×C₁₃	—	2	2	no	—
341	C₂²×C₁₃	—	2	2	no	—
342	C₂²×C₁₃	—	2	2	no	—
343	C₂²×C₁₃	—	2	1	no	—
344	C₂²×C₁₃	—	2	2	no	—
345	C₂²×C₁₃	—	2	1	no	—
346	C₂²×C₁₃	—	2	2	no	—
347	C₂²×C₁₃	—	2	2	no	—
348	C₂²×C₁₃	—	2	2	no	—
349	C₂²×C₁₃	—	2	2	no	—
350	C₂²×C₁₃	—	2	1	no	—
351	C₂²×C₁₃	—	2	2	no	—
352	C₂²×C₁₃	—	8	4	no	—
353	C₂²×C₁₃	—	8	4	no	—
354	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
355	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
356	C₂×D₁₃	—	2	1	no	—
357	C₂×D₁₃	—	2	2	no	—
358	C₂×D₁₃	—	2	2	no	—
359	C₂×D₁₃	—	2	2	no	—
360	C₂×D₁₃	—	2	2	no	—
361	C₂×D₁₃	—	2	1	no	—
362	C₂×D₁₃	—	2	2	no	—
363	C₂×D₁₃	—	2	1	no	—
364	C₂×D₁₃	—	2	2	no	—
365	C₂×D₁₃	—	8	4	no	—
366	C₂×D₁₃	—	8	4	no	—
367	C₄×C₁₃	—	2	1	no	—
368	C₄×C₁₃	—	2	1	no	—
369	C₄×C₁₃	—	2	2	no	—
370	C₄×C₁₃	—	2	1	no	—
371	C₄×C₁₃	—	2	1	no	—
372	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
373	Dic₁₃	—	2	2	no	—
374	Dic₁₃	—	2	1	no	—
375	Dic₁₃	—	2	1	no	—
376	Dic₁₃	—	2	1	no	—
377	Dic₁₃	—	2	2	no	—
378	Dic₁₃	—	2	1	no	—
379	Dic₁₃	—	2	1	no	—
380	Dic₁₃	—	2	1	no	—
381	Dic₁₃	H(5,𝔽₂)	1	2	yes	—
382	C₂×#41	—	13	2	no	—
383	C₂×#41	—	13	1	no	—
384	C₂×#41	—	13	1	no	—
385	C₂²×D₄	—	13	2	no	—
386	C₂²×D₄	—	13	2	no	—
387	C₂²×D₄	—	13	2	no	—
388	C₂²×D₄	—	13	2	no	—
389	C₂²×D₄	—	13	1	no	—
390	C₂²×D₄	—	13	1	no	—
391	C₂²×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
392	C₂²×D₄	C₂×D₁₃	1	2	yes	complemented
393	C₂²×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
394	#127	—	13	2	no	—
395	#127	—	13	1	no	—
396	#127	—	13	1	no	—
397	#127	—	13	1	no	—
398	#127	—	13	1	no	—
399	#127	—	13	2	no	—
400	#127	—	13	2	no	—
401	#127	—	13	1	no	—
402	#127	C₂×D₁₃	1	1	yes	characteristic, complemented
403	#126	—	13	1	no	—
404	#126	—	13	1	no	—
405	#126	—	13	2	no	—
406	#125	—	13	1	no	—
407	#125	—	13	1	no	—
408	#124	—	13	1	no	—
409	#124	—	13	1	no	—
410	#124	—	13	1	no	—
411	#124	—	13	2	no	—
412	#124	—	13	1	no	—
413	#123	—	13	2	no	—
414	#123	—	13	1	no	—
415	#123	—	13	2	no	—
416	#123	—	13	2	no	—
417	#123	—	13	2	no	—
418	#123	—	13	2	no	—
419	#123	—	13	1	no	—
420	#123	—	13	2	no	—
421	#123	—	13	2	no	—
422	#123	—	13	2	no	—
423	#123	—	13	2	no	—
424	C₂²⋊Q₈	—	13	1	no	—
425	C₂²⋊Q₈	—	13	1	no	—
426	#121	—	13	1	no	—
427	#121	—	13	2	no	—
428	#121	—	13	2	no	—
429	#121	—	13	2	no	—
430	#121	—	13	2	no	—
431	#121	—	13	2	no	—
432	#121	—	13	2	no	—
433	#121	—	13	2	no	—
434	#121	—	13	2	no	—
435	#121	—	13	2	no	—
436	#121	—	13	1	no	—
437	#121	—	13	2	no	—
438	#121	—	13	2	no	—
439	#121	—	13	2	no	—
440	#121	—	13	1	no	—
441	#121	—	13	2	no	—
442	#121	—	13	1	no	—
443	#121	—	13	2	no	—
444	#121	—	13	2	no	—
445	#121	—	13	2	no	—
446	#121	—	13	2	no	—
447	#121	C₂×D₁₃	1	1	yes	characteristic
448	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
449	#121	C₂×D₁₃	1	2	yes	complemented
450	#120	—	13	2	no	—
451	#120	—	13	2	no	—
452	#120	—	13	2	no	—
453	#120	—	13	2	no	—
454	#120	—	13	2	no	—
455	#120	—	13	2	no	—
456	#120	—	13	2	no	—
457	#120	—	13	2	no	—
458	#120	—	13	2	no	—
459	#120	—	13	2	no	—
460	#120	C₂×D₁₃	1	2	yes	complemented
461	#120	C₂×D₁₃	1	2	yes	complemented
462	C₄×Q₈	—	13	1	no	—
463	C₄×Q₈	—	13	1	no	—
464	C₄×D₄	—	13	2	no	—
465	C₄×D₄	—	13	1	no	—
466	C₄×D₄	—	13	1	no	—
467	C₄×D₄	—	13	1	no	—
468	C₄×D₄	—	13	1	no	—
469	C₄×D₄	—	13	2	no	—
470	C₄×D₄	—	13	1	no	—
471	C₄×D₄	—	13	2	no	—
472	C₄×D₄	—	13	1	no	—
473	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
474	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
475	#117	—	13	1	no	—
476	#117	—	13	2	no	—
477	#117	—	13	1	no	—
478	C₂×C₂²⋊C₄	—	13	2	no	—
479	C₂×C₂²⋊C₄	—	13	2	no	—
480	C₂×C₄²	—	13	1	no	—
481	C₂×C₁₃	—	2	2	no	—
482	C₂×C₁₃	—	4	2	no	—
483	C₂×C₁₃	—	4	2	no	—
484	C₂×C₁₃	—	4	1	no	—
485	C₂×C₁₃	—	4	2	no	—
486	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
487	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
488	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
489	D₁₃	—	4	2	no	—
490	D₁₃	—	4	1	no	—
491	D₁₃	—	4	2	no	—
492	C₂⁴	—	13	2	no	—
493	C₂⁴	—	13	2	no	—
494	C₂⁴	C₂²×D₁₃	1	2	yes	—
495	C₂⁴	C₂²×D₁₃	1	2	yes	—
496	#41	—	52	2	no	—
497	#41	—	52	2	no	—
498	#41	—	52	4	no	—
499	C₂×Q₈	—	13	1	no	—
500	C₂×Q₈	—	13	1	no	—
501	C₂×D₄	—	4	2	no	—
502	C₂×D₄	—	4	2	no	—
503	C₂×D₄	—	4	4	no	—
504	C₂×D₄	—	13	1	no	—
505	C₂×D₄	—	13	1	no	—
506	C₂×D₄	—	13	2	no	—
507	C₂×D₄	—	13	2	no	—
508	C₂×D₄	—	13	2	no	—
509	C₂×D₄	—	13	2	no	—
510	C₂×D₄	—	13	2	no	—
511	C₂×D₄	—	13	2	no	—
512	C₂×D₄	—	13	2	no	—
513	C₂×D₄	—	13	2	no	—
514	C₂×D₄	—	13	2	no	—
515	C₂×D₄	—	13	2	no	—
516	C₂×D₄	—	13	2	no	—
517	C₂×D₄	—	13	2	no	—
518	C₂×D₄	—	13	2	no	—
519	C₂×D₄	—	13	2	no	—
520	C₂×D₄	—	13	2	no	—
521	C₂×D₄	—	13	1	no	—
522	C₂×D₄	—	13	1	no	—
523	C₂×D₄	—	13	2	no	—
524	C₂×D₄	—	13	2	no	—
525	C₂×D₄	—	52	2	no	—
526	C₂×D₄	—	52	2	no	—
527	C₂×D₄	—	52	4	no	—
528	C₂×D₄	—	52	4	no	—
529	C₂×D₄	—	52	4	no	—
530	C₂×D₄	—	52	4	no	—
531	C₂×D₄	C₂²×D₁₃	1	2	yes	—
532	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
533	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
534	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
535	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
536	C₂×D₄	C₂²×D₁₃	1	2	yes	—
537	C₂×D₄	C₂²×D₁₃	1	2	yes	—
538	C₂×D₄	C₂²×D₁₃	1	2	yes	—
539	C₂×D₄	C₂²×D₁₃	1	2	yes	—
540	C₂×D₄	C₂²×D₁₃	1	2	yes	—
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	2	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	C₂²×D₁₃	1	1	yes	characteristic
551	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
552	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
553	C₄⋊C₄	—	13	1	no	—
554	C₄⋊C₄	—	13	2	no	—
555	C₄⋊C₄	—	13	1	no	—
556	C₄⋊C₄	—	13	2	no	—
557	C₄⋊C₄	—	13	1	no	—
558	C₄⋊C₄	—	13	1	no	—
559	C₄⋊C₄	—	13	1	no	—
560	C₄⋊C₄	—	13	1	no	—
561	C₄⋊C₄	—	13	1	no	—
562	C₄⋊C₄	—	13	1	no	—
563	C₄⋊C₄	—	13	2	no	—
564	C₄⋊C₄	—	13	2	no	—
565	C₄⋊C₄	—	13	1	no	—
566	C₄⋊C₄	—	13	1	no	—
567	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
568	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
569	C₂²⋊C₄	—	13	1	no	—
570	C₂²⋊C₄	—	13	2	no	—
571	C₂²⋊C₄	—	13	2	no	—
572	C₂²⋊C₄	—	13	2	no	—
573	C₂²⋊C₄	—	13	1	no	—
574	C₂²⋊C₄	—	13	2	no	—
575	C₂²⋊C₄	—	13	1	no	—
576	C₂²⋊C₄	—	13	2	no	—
577	C₂²⋊C₄	—	13	1	no	—
578	C₂²⋊C₄	—	13	2	no	—
579	C₂²⋊C₄	—	13	2	no	—
580	C₂²⋊C₄	—	13	2	no	—
581	C₂²⋊C₄	—	13	2	no	—
582	C₂²⋊C₄	—	13	2	no	—
583	C₂²⋊C₄	—	13	1	no	—
584	C₂²⋊C₄	—	13	1	no	—
585	C₂²⋊C₄	—	13	1	no	—
586	C₂²⋊C₄	—	13	1	no	—
587	C₂²⋊C₄	—	13	2	no	—
588	C₂²⋊C₄	—	13	2	no	—
589	C₂²⋊C₄	—	13	2	no	—
590	C₂²⋊C₄	—	13	2	no	—
591	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
592	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
593	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
594	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
595	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
596	C₄²	—	13	1	no	—
597	C₄²	—	13	1	no	—
598	C₄²	—	13	1	no	—
599	C₄²	—	13	1	no	—
600	C₄²	—	13	2	no	—
601	C₄²	—	13	1	no	—
602	C₄²	C₂²×D₁₃	1	1	yes	characteristic
603	C₁₃	#3543	1	1	yes	characteristic, complemented, Sylow
604	C₂³	—	2	4	no	—
605	C₂³	—	4	2	no	—
606	C₂³	—	4	2	no	—
607	C₂³	—	4	2	no	—
608	C₂³	—	4	2	no	—
609	C₂³	—	4	2	no	—
610	C₂³	—	13	1	no	—
611	C₂³	—	13	2	no	—
612	C₂³	—	13	2	no	—
613	C₂³	—	26	4	no	—
614	C₂³	—	52	2	no	—
615	C₂³	—	52	2	no	—
616	C₂³	—	52	2	no	—
617	C₂³	—	52	2	no	—
618	C₂³	—	52	2	no	—
619	C₂³	C₂³×D₁₃	1	2	yes	—
620	C₂³	C₂³×D₁₃	1	1	yes	characteristic
621	C₂³	C₂³×D₁₃	1	2	yes	—
622	C₂³	C₂³×D₁₃	1	2	yes	—
623	C₂³	C₂³×D₁₃	1	1	yes	characteristic
624	Q₈	—	26	2	no	—
625	Q₈	—	26	2	no	—
626	D₄	—	2	2	no	—
627	D₄	—	2	4	no	—
628	D₄	—	2	2	no	—
629	D₄	—	2	2	no	—
630	D₄	—	2	2	no	—
631	D₄	—	4	2	no	—
632	D₄	—	4	2	no	—
633	D₄	—	4	2	no	—
634	D₄	—	4	2	no	—
635	D₄	—	4	2	no	—
636	D₄	—	26	2	no	—
637	D₄	—	26	4	no	—
638	D₄	—	26	4	no	—
639	D₄	—	26	2	no	—
640	D₄	—	26	2	no	—
641	D₄	—	26	2	no	—
642	D₄	—	52	2	no	—
643	D₄	—	52	2	no	—
644	D₄	—	52	2	no	—
645	D₄	—	52	2	no	—
646	D₄	—	52	2	no	—
647	D₄	—	52	2	no	—
648	D₄	—	52	2	no	—
649	D₄	—	52	2	no	—
650	D₄	—	52	2	no	—
651	D₄	—	52	2	no	—
652	D₄	—	52	2	no	—
653	D₄	—	52	2	no	—
654	D₄	—	52	2	no	—
655	D₄	—	52	2	no	—
656	D₄	—	52	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	4	2	no	—
660	C₂×C₄	—	13	1	no	—
661	C₂×C₄	—	13	1	no	—
662	C₂×C₄	—	13	1	no	—
663	C₂×C₄	—	13	1	no	—
664	C₂×C₄	—	13	2	no	—
665	C₂×C₄	—	13	1	no	—
666	C₂×C₄	—	13	1	no	—
667	C₂×C₄	—	13	1	no	—
668	C₂×C₄	—	13	2	no	—
669	C₂×C₄	—	26	2	no	—
670	C₂×C₄	—	26	4	no	—
671	C₂×C₄	—	26	2	no	—
672	C₂×C₄	—	26	2	no	—
673	C₂×C₄	—	52	2	no	—
674	C₂×C₄	—	52	2	no	—
675	C₂×C₄	—	52	2	no	—
676	C₂×C₄	—	52	2	no	—
677	C₂×C₄	—	52	2	no	—
678	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
679	C₂×C₄	C₂³×D₁₃	1	2	yes	—
680	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
681	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
682	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
683	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
684	C₂²	—	2	1	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	1	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	2	2	no	—
689	C₂²	—	2	1	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	8	4	no	—
699	C₂²	—	8	4	no	—
700	C₂²	—	26	1	no	—
701	C₂²	—	26	2	no	—
702	C₂²	—	26	2	no	—
703	C₂²	—	26	1	no	—
704	C₂²	—	26	2	no	—
705	C₂²	—	26	2	no	—
706	C₂²	—	26	2	no	—
707	C₂²	—	26	1	no	—
708	C₂²	—	26	2	no	—
709	C₂²	—	104	4	no	—
710	C₂²	—	104	4	no	—
711	C₂²	#88251	1	2	yes	—
712	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
713	C₄	—	2	1	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	1	no	—
716	C₄	—	2	2	no	—
717	C₄	—	2	1	no	—
718	C₄	—	13	2	no	—
719	C₄	—	26	1	no	—
720	C₄	—	26	1	no	—
721	C₄	—	26	1	no	—
722	C₄	—	26	1	no	—
723	C₄	—	26	2	no	—
724	C₄	—	26	2	no	—
725	C₄	—	26	1	no	—
726	C₄	—	26	1	no	—
727	C₄	#88251	1	2	yes	—
728	C₂	—	2	2	no	—
729	C₂	—	4	1	no	—
730	C₂	—	4	2	no	—
731	C₂	—	4	2	no	—
732	C₂	—	4	2	no	—
733	C₂	—	52	1	no	—
734	C₂	—	52	2	no	—
735	C₂	—	52	2	no	—
736	C₂	C₂×#88251	1	1	yes	characteristic
737	C₂	C₂×#88251	1	1	yes	characteristic
738	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	D₄²×C₁₃	C₂
hypercenter	D₄²	D₁₃
hypocenter	C₁₃	#3543
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. D₄²×C₁₃	C₂	semidirect
2. #11719511	C₂	semidirect
3. #11719510	C₂	semidirect
4. #11719509	C₂	semidirect
5. C₂×#88194	C₂	semidirect
6. D₄×C₂²⋊D₁₃	C₂	semidirect
7. D₄×C₂²⋊D₁₃	C₂	semidirect
8. #11719423	C₂	semidirect
9. #11719420	C₂	semidirect
10. #11719325	C₂	semidirect
11. #11719324	C₂	semidirect
12. #11719320	C₂	semidirect
13. #11719314	C₂	semidirect
14. #11719305	C₂	semidirect
15. #11719304	C₂	semidirect
16. #11719300	C₂	semidirect
17. #11719297	C₂	semidirect
18. #11719296	C₂	semidirect
19. #11719294	C₂	semidirect
20. #11719267	C₂	semidirect
21. #11719264	C₂	semidirect
22. #11719255	C₂	semidirect
23. #11719243	C₂	semidirect
24. C₂²×D₄×C₁₃	C₂²	semidirect
25. C₂²×D₄×C₁₃	C₂²	semidirect
26. C₂²×D₄×C₁₃	C₂²	semidirect
27. C₂²×C₂²⋊D₁₃	C₂²	semidirect
28. C₂²×C₂²⋊D₁₃	C₂²	semidirect
29. C₂²×C₂²⋊D₁₃	C₂²	semidirect
30. C₂×#6129	C₂²	semidirect
31. C₂×#6129	C₂²	semidirect
32. C₂×D₄×D₁₃	C₂²	semidirect
33. C₂×D₄×D₁₃	C₂²	semidirect
34. C₂×#6127	C₂²	semidirect
35. C₂²×D₅₂	C₂²	semidirect
36. C₁₃×#127	C₂²	semidirect
38. C₁₃×#121	C₂²	semidirect
39. C₁₃×#121	C₂²	semidirect
40. C₁₃×#120	C₂²	semidirect
41. C₁₃×#120	C₂²	semidirect
42. C₄×D₄×C₁₃	C₂²	semidirect
43. C₄×D₄×C₁₃	C₂²	semidirect
44. #88207	C₂²	semidirect
45. #88207	C₂²	semidirect
46. #88207	C₂²	semidirect
47. #88207	C₂²	semidirect
48. C₂×C₂²⋊Dic₁₃	C₂²	semidirect
50. #88194	C₂²	semidirect
51. #88194	C₂²	semidirect
52. #88194	C₂²	semidirect
53. #88194	C₂²	semidirect
54. #88194	C₂²	semidirect
55. #88194	C₂²	semidirect
56. #88194	C₂²	semidirect
58. #88193	C₂²	semidirect
59. #88193	C₂²	semidirect
60. #88193	C₂²	semidirect
61. #88193	C₂²	semidirect
62. #88193	C₂²	semidirect
63. #88193	C₂²	semidirect
64. #88193	C₂²	semidirect
65. #88193	C₂²	semidirect
66. #88192	C₂²	semidirect
67. #88192	C₂²	semidirect
68. #88192	C₂²	semidirect
69. #88192	C₂²	semidirect
70. #88192	C₂²	semidirect
71. #88191	C₂²	semidirect
72. #88191	C₂²	semidirect
73. #88191	C₂²	semidirect
74. #88191	C₂²	semidirect
75. #88191	C₂²	semidirect
76. #88190	C₂²	semidirect
77. #88190	C₂²	semidirect
78. #88189	C₂²	semidirect
79. #88189	C₂²	semidirect
80. #88189	C₂²	semidirect
81. D₄×Dic₁₃	C₂²	semidirect
82. D₄×Dic₁₃	C₂²	semidirect
83. D₄×Dic₁₃	C₂²	semidirect
84. #88184	C₂²	semidirect
85. #88184	C₂²	semidirect
86. #88183	C₂²	semidirect
87. #88183	C₂²	semidirect
88. C₄×C₂²⋊D₁₃	C₂²	semidirect
89. C₄×C₂²⋊D₁₃	C₂²	semidirect
90. C₄×C₂²⋊D₁₃	C₂²	semidirect
91. #88180	C₂²	semidirect
92. #88178	C₂²	semidirect
93. C₂×C₄×Dic₁₃	C₂²	semidirect
94. #88152	C₂²	semidirect
95. #88149	C₂²	semidirect
96. #88148	C₂²	semidirect
97. #88147	C₂²	semidirect
98. #88144	C₂²	semidirect
99. #88143	C₂²	semidirect
100. #88141	C₂²	semidirect
101. #88140	C₂²	semidirect
102. #88140	C₂²	semidirect
103. #88139	C₂²	semidirect
104. #88139	C₂²	semidirect
105. #88138	C₂²	semidirect
106. #88138	C₂²	semidirect
107. #88138	C₂²	semidirect
108. #88138	C₂²	semidirect
109. #88137	C₂²	semidirect
110. #88137	C₂²	semidirect
111. #88137	C₂²	semidirect
112. #88136	C₂²	semidirect
113. #88135	C₂²	semidirect
114. C₂²⋊C₄×D₁₃	C₂²	semidirect
115. #88133	C₂²	semidirect
116. #88133	C₂²	semidirect
117. #88132	C₂²	semidirect
118. #88131	C₂²	semidirect
119. #88129	C₂²	semidirect
120. C₄×D₅₂	C₂²	semidirect
121. #88126	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
326. D₄²	D₁₃	semidirect
391. C₂²×D₄	C₂×D₁₃	semidirect
392. C₂²×D₄	C₂×D₁₃	semidirect
393. C₂²×D₄	C₂×D₁₃	semidirect
402. #127	C₂×D₁₃	semidirect
448. #121	C₂×D₁₃	semidirect
449. #121	C₂×D₁₃	semidirect
460. #120	C₂×D₁₃	semidirect
461. #120	C₂×D₁₃	semidirect
473. C₄×D₄	C₂×D₁₃	semidirect
474. C₄×D₄	C₂×D₁₃	semidirect
603. C₁₃	#3543	semidirect

Maximal subgroups

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

subgroup	index
D₄²×C₁₃	2
#11719511	2
#11719510	2
#11719509	2
C₂×#88194	2
D₄×C₂²⋊D₁₃	2
#11719423	2
#11719420	2
#11719325	2
#11719324	2
#11719320	2
#11719314	2
#11719305	2
#11719304	2
#11719300	2
#11719297	2
#11719296	2
#11719294	2
#11719267	2
#11719264	2
#11719255	2
#11719243	2
#3543	13