Subgroups — #13128781

Order 1664.

1152 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719410	C₂	1	2	yes	maximal, complemented
3	#11719409	C₂	1	2	yes	maximal, complemented
4	#11719403	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719400	C₂	1	2	yes	maximal, complemented
6	#11719397	C₂	1	2	yes	maximal, complemented
7	#11719395	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719359	C₂	1	2	yes	maximal, complemented
9	D₁₃×#123	C₂	1	2	yes	maximal, complemented
10	#11719348	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719335	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719335	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719329	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719290	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719279	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719243	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719235	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719232	C₂	1	2	yes	maximal, complemented
20	#11719229	C₂	1	2	yes	maximal, complemented
21	#11719226	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719212	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#88147	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#6131	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₁₃	C₂²	1	2	yes	—
26	C₂×#6127	C₂²	1	2	yes	complemented
27	C₂²×D₅₂	C₂²	1	1	yes	characteristic
28	C₂²×D₅₂	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₃	C₂²	1	2	yes	complemented
30	C₁₃×#126	C₂²	1	2	yes	complemented
31	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#125	C₂²	1	2	yes	complemented
33	C₁₃×#123	C₂²	1	2	yes	—
34	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
37	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#117	C₂²	1	2	yes	complemented
40	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	#88201	C₂²	1	1	yes	characteristic, complemented
42	#88201	C₂²	1	1	yes	characteristic, complemented
43	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
44	#88193	C₂²	1	1	yes	characteristic
45	#88189	C₂²	1	1	yes	characteristic
46	#88184	C₂²	1	1	yes	characteristic
47	#88184	C₂²	1	1	yes	characteristic
48	#88183	C₂²	1	2	yes	complemented
49	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
50	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
51	C₂×#6103	C₂²	1	2	yes	complemented
52	#88180	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
54	#88152	C₂²	1	2	yes	complemented
55	#88152	C₂²	1	1	yes	characteristic, complemented
56	#88152	C₂²	1	2	yes	complemented
57	#88151	C₂²	1	2	yes	complemented
58	#88151	C₂²	1	2	yes	complemented
59	#88150	C₂²	1	2	yes	complemented
60	#88150	C₂²	1	2	yes	complemented
61	#88150	C₂²	1	2	yes	complemented
62	#88149	C₂²	1	2	yes	—
63	#88149	C₂²	1	1	yes	characteristic, complemented
64	#88149	C₂²	1	2	yes	complemented
65	#88149	C₂²	1	2	yes	complemented
66	#88149	C₂²	1	1	yes	characteristic, complemented
67	#88149	C₂²	1	2	yes	complemented
68	#88149	C₂²	1	2	yes	complemented
69	#88148	C₂²	1	2	yes	complemented
70	#88148	C₂²	1	2	yes	complemented
71	#88148	C₂²	1	2	yes	complemented
72	#88148	C₂²	1	2	yes	complemented
73	#88148	C₂²	1	2	yes	complemented
74	#88148	C₂²	1	2	yes	complemented
75	#88148	C₂²	1	2	yes	complemented
76	#88147	C₂²	1	1	yes	characteristic
77	#88147	C₂²	1	1	yes	characteristic
78	#88147	C₂²	1	1	yes	characteristic
79	#88147	C₂²	1	1	yes	characteristic, complemented
80	#88147	C₂²	1	1	yes	characteristic, complemented
81	#88147	C₂²	1	2	yes	complemented
82	#88147	C₂²	1	2	yes	complemented
83	#88147	C₂²	1	1	yes	characteristic, complemented
84	#88147	C₂²	1	1	yes	characteristic, complemented
85	#88147	C₂²	1	2	yes	complemented
86	#88146	C₂²	1	2	yes	complemented
87	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
88	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
89	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
90	#88144	C₂²	1	1	yes	characteristic, complemented
91	#88143	C₂²	1	1	yes	characteristic, complemented
92	#88142	C₂²	1	1	yes	characteristic, complemented
93	#88140	C₂²	1	1	yes	characteristic, complemented
94	#88140	C₂²	1	2	yes	complemented
95	#88139	C₂²	1	1	yes	characteristic, complemented
96	#88139	C₂²	1	2	yes	complemented
97	#88138	C₂²	1	2	yes	complemented
98	#88137	C₂²	1	2	yes	complemented
99	#88137	C₂²	1	2	yes	complemented
100	#88136	C₂²	1	2	yes	—
101	#88136	C₂²	1	2	yes	—
102	#88136	C₂²	1	2	yes	complemented
103	#88136	C₂²	1	2	yes	complemented
104	#88135	C₂²	1	2	yes	complemented
105	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
106	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
108	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
109	#88133	C₂²	1	1	yes	characteristic, complemented
110	#88132	C₂²	1	1	yes	characteristic, complemented
111	#88130	C₂²	1	2	yes	complemented
112	#88129	C₂²	1	2	yes	complemented
113	#88128	C₂²	1	1	yes	characteristic
114	C₄×D₅₂	C₂²	1	1	yes	characteristic
115	C₄×D₅₂	C₂²	1	2	yes	complemented
116	C₄×D₅₂	C₂²	1	2	yes	complemented
117	C₄×D₅₂	C₂²	1	2	yes	complemented
118	C₄×D₅₂	C₂²	1	2	yes	complemented
119	C₄×D₅₂	C₂²	1	2	yes	complemented
120	#88126	C₂²	1	2	yes	complemented
121	#88126	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₃	C₂³	1	2	yes	—
124	C₂³×D₁₃	C₂³	1	2	yes	—
125	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
134	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
135	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
136	#6131	—	2	4	no	—
137	D₄×D₁₃	—	4	4	no	—
138	#6127	—	4	4	no	—
139	C₂×D₅₂	—	2	4	no	—
140	C₂×D₅₂	—	2	4	no	—
141	C₂×D₅₂	C₂³	1	2	yes	—
142	C₂×D₅₂	C₂³	1	2	yes	—
143	C₂×D₅₂	C₂³	1	1	yes	characteristic
144	C₂×D₅₂	C₂³	1	1	yes	characteristic
145	C₂×D₅₂	C₂³	1	2	yes	—
146	C₂×D₅₂	C₂³	1	2	yes	—
147	C₂×D₅₂	C₂³	1	2	yes	—
148	C₂×D₅₂	C₂³	1	2	yes	—
149	C₂×D₅₂	C₂³	1	2	yes	—
150	C₂×D₅₂	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₃	—	4	4	no	—
152	C₂×C₄×D₁₃	C₂³	1	2	yes	—
153	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₃	C₂³	1	2	yes	—
155	C₂×C₄×D₁₃	C₂³	1	2	yes	—
156	C₂×C₄×D₁₃	C₂³	1	2	yes	—
157	C₂×C₄×D₁₃	C₂³	1	2	yes	—
158	C₂×C₄×D₁₃	C₂³	1	2	yes	—
159	C₂×C₄×D₁₃	C₂³	1	2	yes	—
160	C₂×C₄×D₁₃	C₂³	1	2	yes	—
161	C₂×C₄×D₁₃	C₂³	1	2	yes	—
162	C₂×C₄×D₁₃	C₂³	1	2	yes	—
163	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
164	C₂×Dic₂₆	C₂³	1	2	yes	—
165	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
175	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
177	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₄²×C₁₃	C₂³	1	1	yes	characteristic
181	C₄²×C₁₃	C₂³	1	2	yes	—
182	C₄²×C₁₃	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
186	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
187	#6103	C₂³	1	2	yes	—
188	#6103	C₂³	1	1	yes	characteristic
189	#6103	C₂³	1	2	yes	—
190	#6103	C₂³	1	1	yes	characteristic
191	#6103	C₂³	1	1	yes	characteristic
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	2	yes	—
197	#6103	C₂³	1	2	yes	—
198	#6103	C₂³	1	2	yes	—
199	#6103	C₂³	1	2	yes	—
200	#6103	C₂³	1	2	yes	—
201	#6103	C₂³	1	2	yes	—
202	#6103	C₂³	1	2	yes	—
203	#6103	C₂³	1	2	yes	—
204	#6103	C₂³	1	2	yes	—
205	#6103	C₂³	1	2	yes	—
206	#6103	C₂³	1	1	yes	characteristic
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	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₁₃	C₂³	1	2	yes	—
212	C₄⋊Dic₁₃	C₂³	1	2	yes	—
213	#6101	C₂³	1	1	yes	characteristic
214	#6101	C₂³	1	1	yes	characteristic
215	#6101	C₂³	1	1	yes	characteristic
216	#6101	C₂³	1	2	yes	—
217	#6101	C₂³	1	1	yes	characteristic
218	#6101	C₂³	1	1	yes	characteristic
219	#6101	C₂³	1	2	yes	—
220	#6101	C₂³	1	1	yes	characteristic
221	#6101	C₂³	1	2	yes	—
222	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₃	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	1	yes	characteristic
228	#3513	—	13	1	no	maximal, Sylow
229	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₃	—	2	4	no	—
232	C₂²×D₁₃	—	2	4	no	—
233	C₂²×D₁₃	—	2	4	no	—
234	C₂²×D₁₃	—	4	2	no	—
235	C₂²×D₁₃	—	4	2	no	—
236	C₂²×D₁₃	—	4	2	no	—
237	C₂²×D₁₃	C₂⁴	1	2	yes	—
238	C₂²×D₁₃	C₂⁴	1	2	yes	—
239	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
240	C₂²×D₁₃	C₂⁴	1	2	yes	—
241	Q₈×C₁₃	—	2	2	no	—
242	D₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	4	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
248	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
252	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂²⋊D₁₃	—	2	2	no	—
256	C₂²⋊D₁₃	—	2	4	no	—
257	C₂²⋊D₁₃	—	4	2	no	—
258	C₂²⋊D₁₃	—	4	1	no	—
259	C₂×Dic₁₃	—	2	2	no	—
260	C₂×Dic₁₃	—	4	1	no	—
261	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₃	C₂⁴	1	2	yes	—
266	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
269	D₅₂	—	2	4	no	—
270	D₅₂	—	2	4	no	—
271	D₅₂	—	2	4	no	—
272	D₅₂	—	2	2	no	—
273	D₅₂	—	2	2	no	—
274	D₅₂	—	4	2	no	—
275	D₅₂	—	4	2	no	—
276	D₅₂	—	4	2	no	—
277	D₅₂	—	4	2	no	—
278	D₅₂	#41	1	4	yes	complemented
279	C₄×D₁₃	—	2	4	no	—
280	C₄×D₁₃	—	2	2	no	—
281	C₄×D₁₃	—	4	2	no	—
282	C₄×D₁₃	—	4	2	no	—
283	C₄×D₁₃	—	4	2	no	—
284	C₄×D₁₃	—	4	2	no	—
285	C₄×D₁₃	—	4	2	no	—
286	C₄×D₁₃	—	4	2	no	—
287	C₄×D₁₃	—	4	2	no	—
288	C₄×D₁₃	—	4	2	no	—
289	C₄×D₁₃	—	4	2	no	—
290	Dic₂₆	—	4	1	no	—
291	Dic₂₆	—	4	2	no	—
292	#559	—	13	1	no	—
293	#554	—	13	1	no	—
294	#553	—	13	2	no	—
295	#553	—	13	1	no	—
296	#552	D₁₃	1	1	yes	characteristic, complemented
297	#551	—	13	2	no	—
298	#551	—	13	2	no	—
299	#547	—	13	1	no	—
300	#546	—	13	2	no	—
301	#546	—	13	1	no	—
302	#546	—	13	1	no	—
303	D₄²	—	13	1	no	—
304	#542	—	13	1	no	—
305	#540	—	13	1	no	—
306	#539	—	13	2	no	—
307	#538	—	13	2	no	—
308	#529	—	13	1	no	—
309	#529	—	13	1	no	—
310	#525	—	13	2	no	—
311	C₂×#123	—	13	2	no	—
312	#520	—	13	1	no	—
313	#518	—	13	1	no	—
314	C₂×C₄×D₄	—	13	1	no	—
315	C₂²×C₁₃	—	2	1	no	—
316	C₂²×C₁₃	—	2	1	no	—
317	C₂²×C₁₃	—	2	1	no	—
318	C₂²×C₁₃	—	2	1	no	—
319	C₂²×C₁₃	—	2	1	no	—
320	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
321	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
322	C₂×D₁₃	—	2	2	no	—
323	C₂×D₁₃	—	2	2	no	—
324	C₂×D₁₃	—	2	1	no	—
325	C₂×D₁₃	—	2	2	no	—
326	C₂×D₁₃	—	2	2	no	—
327	C₂×D₁₃	—	2	1	no	—
328	C₂×D₁₃	—	2	2	no	—
329	C₂×D₁₃	—	2	2	no	—
330	C₂×D₁₃	—	2	2	no	—
331	C₂×D₁₃	—	2	1	no	—
332	C₂×D₁₃	—	2	2	no	—
333	C₂×D₁₃	—	4	8	no	—
334	C₂×D₁₃	—	8	4	no	—
335	C₂×D₁₃	C₂×#41	1	4	yes	—
336	C₄×C₁₃	—	2	2	no	—
337	C₄×C₁₃	—	2	1	no	—
338	C₄×C₁₃	—	2	1	no	—
339	C₄×C₁₃	—	2	2	no	—
340	C₄×C₁₃	—	2	2	no	—
341	C₄×C₁₃	—	2	1	no	—
342	C₄×C₁₃	—	2	1	no	—
343	C₄×C₁₃	—	2	2	no	—
344	C₄×C₁₃	C₂×#41	1	2	yes	—
345	Dic₁₃	—	2	1	no	—
346	Dic₁₃	—	2	1	no	—
347	Dic₁₃	—	2	2	no	—
348	Dic₁₃	—	2	1	no	—
349	Dic₁₃	—	2	1	no	—
350	Dic₁₃	—	2	1	no	—
351	Dic₁₃	—	2	1	no	—
352	Dic₁₃	—	2	1	no	—
353	C₂×#41	—	13	1	no	—
354	C₂×#41	—	13	2	no	—
355	C₂²×D₄	—	13	2	no	—
356	C₂²×D₄	—	13	1	no	—
357	C₂²×D₄	—	13	1	no	—
358	C₂³×C₄	—	13	2	no	—
359	C₄⋊Q₈	—	13	1	no	—
360	#127	—	13	1	no	—
361	#126	—	13	2	no	—
362	#126	—	13	1	no	—
363	#126	—	13	2	no	—
364	#126	—	13	1	no	—
365	#126	—	13	2	no	—
366	#126	C₂×D₁₃	1	2	yes	complemented
367	#125	—	13	1	no	—
368	#125	—	13	1	no	—
369	#125	C₂×D₁₃	1	2	yes	complemented
370	#125	C₂×D₁₃	1	1	yes	characteristic, complemented
371	#124	—	13	1	no	—
372	#124	—	13	1	no	—
373	#124	—	13	1	no	—
374	#124	—	13	2	no	—
375	#124	—	13	2	no	—
376	#123	—	13	1	no	—
377	#123	—	13	2	no	—
378	#123	—	13	2	no	—
379	#123	—	13	2	no	—
380	#123	—	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	1	no	—
389	#123	C₂×D₁₃	1	2	yes	—
390	C₂²⋊Q₈	—	13	2	no	—
391	C₂²⋊Q₈	—	13	2	no	—
392	C₂²⋊Q₈	—	13	2	no	—
393	C₂²⋊Q₈	—	13	2	no	—
394	C₂²⋊Q₈	—	13	2	no	—
395	C₂²⋊Q₈	—	13	1	no	—
396	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
397	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
398	#121	—	13	1	no	—
399	#121	—	13	1	no	—
400	#121	—	13	1	no	—
401	#121	—	13	2	no	—
402	#121	—	13	2	no	—
403	#121	—	13	2	no	—
404	#121	—	13	2	no	—
405	#121	—	13	1	no	—
406	#121	—	13	2	no	—
407	#121	—	13	1	no	—
408	#121	—	13	2	no	—
409	#120	—	13	2	no	—
410	#120	—	13	2	no	—
411	#120	—	13	2	no	—
412	#120	—	13	2	no	—
413	C₄×Q₈	—	13	1	no	—
414	C₄×Q₈	—	13	1	no	—
415	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
416	C₄×D₄	—	13	1	no	—
417	C₄×D₄	—	13	1	no	—
418	C₄×D₄	—	13	1	no	—
419	C₄×D₄	—	13	2	no	—
420	C₄×D₄	—	13	1	no	—
421	C₄×D₄	—	13	1	no	—
422	C₄×D₄	—	13	2	no	—
423	C₄×D₄	—	13	1	no	—
424	C₄×D₄	—	13	1	no	—
425	C₄×D₄	—	13	1	no	—
426	C₄×D₄	—	13	1	no	—
427	C₄×D₄	—	13	2	no	—
428	C₄×D₄	—	13	2	no	—
429	C₄×D₄	—	13	2	no	—
430	C₄×D₄	—	13	2	no	—
431	C₄×D₄	—	13	2	no	—
432	C₄×D₄	—	13	1	no	—
433	C₄×D₄	—	13	2	no	—
434	C₄×D₄	—	13	2	no	—
435	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
436	#117	—	13	1	no	—
437	#117	—	13	2	no	—
438	#117	—	13	1	no	—
439	#117	—	13	2	no	—
440	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
441	#117	C₂×D₁₃	1	2	yes	complemented
442	C₂×C₄⋊C₄	—	13	2	no	—
443	C₂×C₄⋊C₄	—	13	1	no	—
444	C₂×C₄⋊C₄	—	13	2	no	—
445	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
446	C₂×C₂²⋊C₄	—	13	2	no	—
447	C₂×C₂²⋊C₄	—	13	2	no	—
448	C₂×C₂²⋊C₄	—	13	2	no	—
449	C₂×C₂²⋊C₄	—	13	2	no	—
450	C₂×C₂²⋊C₄	—	13	2	no	—
451	C₂×C₄²	—	13	1	no	—
452	C₂×C₁₃	—	2	2	no	—
453	C₂×C₁₃	—	4	1	no	—
454	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
455	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
456	C₂×C₁₃	#585	1	1	yes	characteristic
457	D₁₃	—	2	4	no	—
458	D₁₃	—	4	1	no	—
459	D₁₃	—	4	2	no	—
460	D₁₃	—	4	2	no	—
461	C₂⁴	—	13	2	no	—
462	C₂⁴	—	13	2	no	—
463	#41	—	26	4	no	—
464	#41	—	52	4	no	—
465	C₂×Q₈	—	13	1	no	—
466	C₂×Q₈	—	13	2	no	—
467	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
468	C₂×D₄	—	13	1	no	—
469	C₂×D₄	—	13	2	no	—
470	C₂×D₄	—	13	1	no	—
471	C₂×D₄	—	13	2	no	—
472	C₂×D₄	—	13	1	no	—
473	C₂×D₄	—	13	2	no	—
474	C₂×D₄	—	13	2	no	—
475	C₂×D₄	—	13	2	no	—
476	C₂×D₄	—	13	1	no	—
477	C₂×D₄	—	13	1	no	—
478	C₂×D₄	—	13	2	no	—
479	C₂×D₄	—	13	2	no	—
480	C₂×D₄	—	13	2	no	—
481	C₂×D₄	—	13	2	no	—
482	C₂×D₄	—	26	4	no	—
483	C₂×D₄	—	26	4	no	—
484	C₂×D₄	—	52	4	no	—
485	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
486	C₂²×C₄	—	13	1	no	—
487	C₂²×C₄	—	13	1	no	—
488	C₂²×C₄	—	13	2	no	—
489	C₂²×C₄	—	13	1	no	—
490	C₂²×C₄	—	13	2	no	—
491	C₂²×C₄	—	13	2	no	—
492	C₂²×C₄	—	13	2	no	—
493	C₂²×C₄	—	13	2	no	—
494	C₂²×C₄	—	13	2	no	—
495	C₂²×C₄	—	13	2	no	—
496	C₂²×C₄	—	13	2	no	—
497	C₂²×C₄	—	13	2	no	—
498	C₂²×C₄	—	13	2	no	—
499	C₂²×C₄	—	52	4	no	—
500	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
501	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
502	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
503	C₄⋊C₄	—	13	2	no	—
504	C₄⋊C₄	—	13	1	no	—
505	C₄⋊C₄	—	13	1	no	—
506	C₄⋊C₄	—	13	2	no	—
507	C₄⋊C₄	—	13	1	no	—
508	C₄⋊C₄	—	13	2	no	—
509	C₄⋊C₄	—	13	2	no	—
510	C₄⋊C₄	—	13	1	no	—
511	C₄⋊C₄	—	13	1	no	—
512	C₄⋊C₄	—	13	1	no	—
513	C₄⋊C₄	—	13	1	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	C₂²×D₁₃	1	1	yes	characteristic
519	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
520	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
521	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
523	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
524	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
526	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
527	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
528	C₂²⋊C₄	—	13	1	no	—
529	C₂²⋊C₄	—	13	1	no	—
530	C₂²⋊C₄	—	13	1	no	—
531	C₂²⋊C₄	—	13	1	no	—
532	C₂²⋊C₄	—	13	2	no	—
533	C₂²⋊C₄	—	13	2	no	—
534	C₂²⋊C₄	—	13	2	no	—
535	C₂²⋊C₄	—	13	2	no	—
536	C₂²⋊C₄	—	13	2	no	—
537	C₂²⋊C₄	—	13	2	no	—
538	C₂²⋊C₄	—	13	2	no	—
539	C₂²⋊C₄	—	13	2	no	—
540	C₂²⋊C₄	—	13	2	no	—
541	C₂²⋊C₄	—	13	2	no	—
542	C₂²⋊C₄	—	13	2	no	—
543	C₂²⋊C₄	—	13	2	no	—
544	C₂²⋊C₄	—	13	1	no	—
545	C₂²⋊C₄	—	13	1	no	—
546	C₂²⋊C₄	—	13	2	no	—
547	C₂²⋊C₄	—	13	1	no	—
548	C₂²⋊C₄	—	13	2	no	—
549	C₂²⋊C₄	—	13	2	no	—
550	C₂²⋊C₄	—	13	2	no	—
551	C₂²⋊C₄	—	13	1	no	—
552	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
556	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
557	C₄²	—	13	1	no	—
558	C₄²	—	13	1	no	—
559	C₄²	—	13	1	no	—
560	C₄²	—	13	1	no	—
561	C₄²	—	13	2	no	—
562	C₄²	—	13	1	no	—
563	C₄²	C₂²×D₁₃	1	2	yes	—
564	C₄²	C₂²×D₁₃	1	1	yes	characteristic
565	C₄²	C₂²×D₁₃	1	2	yes	—
566	C₁₃	#3513	1	1	yes	characteristic, complemented, Sylow
567	C₂³	—	13	2	no	—
568	C₂³	—	13	2	no	—
569	C₂³	—	13	2	no	—
570	C₂³	—	13	1	no	—
571	C₂³	—	26	4	no	—
572	C₂³	—	26	4	no	—
573	C₂³	—	26	4	no	—
574	C₂³	—	52	2	no	—
575	C₂³	—	52	2	no	—
576	C₂³	—	52	2	no	—
577	C₂³	C₂³×D₁₃	1	1	yes	characteristic
578	C₂³	C₂³×D₁₃	1	1	yes	characteristic
579	Q₈	—	2	2	no	—
580	Q₈	—	52	1	no	—
581	Q₈	—	52	2	no	—
582	D₄	—	2	2	no	—
583	D₄	—	13	4	no	—
584	D₄	—	26	4	no	—
585	D₄	—	26	4	no	—
586	D₄	—	26	4	no	—
587	D₄	—	26	4	no	—
588	D₄	—	26	2	no	—
589	D₄	—	26	2	no	—
590	D₄	—	26	2	no	—
591	D₄	—	52	2	no	—
592	D₄	—	52	2	no	—
593	D₄	—	52	2	no	—
594	D₄	—	52	2	no	—
595	D₄	—	52	1	no	—
596	D₄	—	52	2	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	13	1	no	—
601	C₂×C₄	—	13	1	no	—
602	C₂×C₄	—	13	1	no	—
603	C₂×C₄	—	13	1	no	—
604	C₂×C₄	—	13	1	no	—
605	C₂×C₄	—	13	1	no	—
606	C₂×C₄	—	13	2	no	—
607	C₂×C₄	—	13	1	no	—
608	C₂×C₄	—	26	4	no	—
609	C₂×C₄	—	26	2	no	—
610	C₂×C₄	—	26	2	no	—
611	C₂×C₄	—	52	2	no	—
612	C₂×C₄	—	52	2	no	—
613	C₂×C₄	—	52	2	no	—
614	C₂×C₄	—	52	2	no	—
615	C₂×C₄	—	52	2	no	—
616	C₂×C₄	—	52	2	no	—
617	C₂×C₄	—	52	2	no	—
618	C₂×C₄	—	52	2	no	—
619	C₂×C₄	—	52	2	no	—
620	C₂×C₄	—	52	1	no	—
621	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₁₃	1	2	yes	—
623	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₃	1	2	yes	—
626	C₂×C₄	C₂³×D₁₃	1	2	yes	—
627	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₁₃	1	2	yes	—
629	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	13	4	no	—
636	C₂²	—	26	2	no	—
637	C₂²	—	26	2	no	—
638	C₂²	—	26	1	no	—
639	C₂²	—	26	2	no	—
640	C₂²	—	26	2	no	—
641	C₂²	—	26	1	no	—
642	C₂²	—	26	2	no	—
643	C₂²	—	26	2	no	—
644	C₂²	—	26	2	no	—
645	C₂²	—	26	1	no	—
646	C₂²	—	26	2	no	—
647	C₂²	—	52	8	no	—
648	C₂²	—	104	4	no	—
649	C₂²	#88256	1	2	yes	—
650	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	1	no	—
659	C₄	—	26	1	no	—
660	C₄	—	26	1	no	—
661	C₄	—	26	1	no	—
662	C₄	—	26	2	no	—
663	C₄	—	26	1	no	—
664	C₄	—	26	1	no	—
665	C₄	—	26	1	no	—
666	C₄	—	26	1	no	—
667	C₄	#41×D₁₃	1	2	yes	—
668	C₂	—	2	2	no	—
669	C₂	—	4	1	no	—
670	C₂	—	26	4	no	—
671	C₂	—	52	2	no	—
672	C₂	—	52	2	no	—
673	C₂	—	52	1	no	—
674	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
675	C₂	C₂×#88256	1	1	yes	characteristic
676	C₂	#11719652	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#552	C₂
hypercenter	#552	D₁₃
hypocenter	C₁₃	#3513
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. C₁₃×#552	C₂	semidirect
2. #11719410	C₂	semidirect
3. #11719409	C₂	semidirect
4. #11719403	C₂	semidirect
5. #11719400	C₂	semidirect
6. #11719397	C₂	semidirect
7. #11719395	C₂	semidirect
8. #11719359	C₂	semidirect
9. D₁₃×#123	C₂	semidirect
10. #11719348	C₂	semidirect
11. #11719335	C₂	semidirect
12. #11719335	C₂	semidirect
13. #11719329	C₂	semidirect
14. #11719290	C₂	semidirect
15. #11719279	C₂	semidirect
16. D₄×D₅₂	C₂	semidirect
17. #11719243	C₂	semidirect
18. #11719235	C₂	semidirect
19. #11719232	C₂	semidirect
20. #11719229	C₂	semidirect
21. #11719226	C₂	semidirect
22. #11719212	C₂	semidirect
23. C₂×#88147	C₂	semidirect
26. C₂×#6127	C₂²	semidirect
29. C₂²×C₄×D₁₃	C₂²	semidirect
30. C₁₃×#126	C₂²	semidirect
31. C₁₃×#125	C₂²	semidirect
32. C₁₃×#125	C₂²	semidirect
34. C₁₃×C₂²⋊Q₈	C₂²	semidirect
35. C₁₃×C₂²⋊Q₈	C₂²	semidirect
36. C₄×Q₈×C₁₃	C₂²	semidirect
38. C₁₃×#117	C₂²	semidirect
39. C₁₃×#117	C₂²	semidirect
40. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
41. #88201	C₂²	semidirect
42. #88201	C₂²	semidirect
43. Q₈×Dic₁₃	C₂²	semidirect
48. #88183	C₂²	semidirect
49. C₄×C₂²⋊D₁₃	C₂²	semidirect
50. C₄×C₂²⋊D₁₃	C₂²	semidirect
51. C₂×#6103	C₂²	semidirect
52. #88180	C₂²	semidirect
53. C₂×C₄×Dic₁₃	C₂²	semidirect
54. #88152	C₂²	semidirect
55. #88152	C₂²	semidirect
56. #88152	C₂²	semidirect
57. #88151	C₂²	semidirect
58. #88151	C₂²	semidirect
59. #88150	C₂²	semidirect
60. #88150	C₂²	semidirect
61. #88150	C₂²	semidirect
63. #88149	C₂²	semidirect
64. #88149	C₂²	semidirect
65. #88149	C₂²	semidirect
66. #88149	C₂²	semidirect
67. #88149	C₂²	semidirect
68. #88149	C₂²	semidirect
69. #88148	C₂²	semidirect
70. #88148	C₂²	semidirect
71. #88148	C₂²	semidirect
72. #88148	C₂²	semidirect
73. #88148	C₂²	semidirect
74. #88148	C₂²	semidirect
75. #88148	C₂²	semidirect
79. #88147	C₂²	semidirect
80. #88147	C₂²	semidirect
81. #88147	C₂²	semidirect
82. #88147	C₂²	semidirect
83. #88147	C₂²	semidirect
84. #88147	C₂²	semidirect
85. #88147	C₂²	semidirect
86. #88146	C₂²	semidirect
87. C₄⋊C₄×D₁₃	C₂²	semidirect
88. C₄⋊C₄×D₁₃	C₂²	semidirect
89. C₄⋊C₄×D₁₃	C₂²	semidirect
90. #88144	C₂²	semidirect
91. #88143	C₂²	semidirect
92. #88142	C₂²	semidirect
93. #88140	C₂²	semidirect
94. #88140	C₂²	semidirect
95. #88139	C₂²	semidirect
96. #88139	C₂²	semidirect
97. #88138	C₂²	semidirect
98. #88137	C₂²	semidirect
99. #88137	C₂²	semidirect
102. #88136	C₂²	semidirect
103. #88136	C₂²	semidirect
104. #88135	C₂²	semidirect
105. C₂²⋊C₄×D₁₃	C₂²	semidirect
106. C₂²⋊C₄×D₁₃	C₂²	semidirect
107. C₂²⋊C₄×D₁₃	C₂²	semidirect
108. C₂²⋊C₄×D₁₃	C₂²	semidirect
109. #88133	C₂²	semidirect
110. #88132	C₂²	semidirect
111. #88130	C₂²	semidirect
112. #88129	C₂²	semidirect
115. C₄×D₅₂	C₂²	semidirect
116. C₄×D₅₂	C₂²	semidirect
117. C₄×D₅₂	C₂²	semidirect
118. C₄×D₅₂	C₂²	semidirect
119. C₄×D₅₂	C₂²	semidirect
120. #88126	C₂²	semidirect
121. #88126	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
278. D₅₂	#41	semidirect
296. #552	D₁₃	semidirect
366. #126	C₂×D₁₃	semidirect
369. #125	C₂×D₁₃	semidirect
370. #125	C₂×D₁₃	semidirect
396. C₂²⋊Q₈	C₂×D₁₃	semidirect
397. C₂²⋊Q₈	C₂×D₁₃	semidirect
415. C₄×Q₈	C₂×D₁₃	semidirect
440. #117	C₂×D₁₃	semidirect
441. #117	C₂×D₁₃	semidirect
445. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
566. C₁₃	#3513	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#552	2
#11719410	2
#11719409	2
#11719403	2
#11719400	2
#11719397	2
#11719395	2
#11719359	2
D₁₃×#123	2
#11719348	2
#11719335	2
#11719329	2
#11719290	2
#11719279	2
D₄×D₅₂	2
#11719243	2
#11719235	2
#11719232	2
#11719229	2
#11719226	2
#11719212	2
C₂×#88147	2
#3513	13