Subgroups — #13129166

Order 1664.

1260 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719416	C₂	1	4	yes	maximal, complemented
3	#11719403	C₂	1	2	yes	maximal, complemented
4	#11719379	C₂	1	2	yes	maximal, complemented
5	#11719358	C₂	1	4	yes	maximal, complemented
6	#11719335	C₂	1	2	yes	maximal, complemented
7	#11719314	C₂	1	2	yes	maximal, complemented
8	#11719290	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719282	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719258	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719255	C₂	1	2	yes	maximal, complemented
12	D₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×D₅₂	C₂	1	2	yes	maximal, complemented
14	#11719240	C₂	1	2	yes	maximal, complemented
15	#11719230	C₂	1	2	yes	maximal, complemented
16	#11719184	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#88128	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#6131	C₂²	1	2	yes	complemented
19	C₂×D₄×D₁₃	C₂²	1	4	yes	complemented
20	C₂×D₄×D₁₃	C₂²	1	2	yes	complemented
21	C₂×#6127	C₂²	1	2	yes	complemented
22	C₂²×D₅₂	C₂²	1	2	yes	complemented
23	C₂²×D₅₂	C₂²	1	2	yes	complemented
24	C₂²×D₅₂	C₂²	1	2	yes	complemented
25	C₂²×D₅₂	C₂²	1	2	yes	complemented
26	C₁₃×#126	C₂²	1	2	yes	complemented
27	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#123	C₂²	1	2	yes	complemented
30	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#121	C₂²	1	1	yes	characteristic
32	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
33	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
34	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#117	C₂²	1	2	yes	complemented
36	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
37	#88201	C₂²	1	2	yes	complemented
38	#88194	C₂²	1	2	yes	complemented
39	#88191	C₂²	1	4	yes	complemented
40	#88184	C₂²	1	1	yes	characteristic
41	#88184	C₂²	1	2	yes	complemented
42	#88184	C₂²	1	2	yes	complemented
43	#88183	C₂²	1	2	yes	complemented
44	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
45	#88178	C₂²	1	1	yes	characteristic, complemented
46	#88149	C₂²	1	4	yes	complemented
47	#88149	C₂²	1	4	yes	complemented
48	#88149	C₂²	1	2	yes	complemented
49	#88149	C₂²	1	4	yes	complemented
50	#88149	C₂²	1	2	yes	complemented
51	#88149	C₂²	1	4	yes	complemented
52	#88148	C₂²	1	4	yes	complemented
53	#88148	C₂²	1	4	yes	complemented
54	#88148	C₂²	1	4	yes	complemented
55	#88148	C₂²	1	4	yes	complemented
56	#88147	C₂²	1	2	yes	complemented
57	#88147	C₂²	1	2	yes	complemented
58	#88138	C₂²	1	4	yes	complemented
59	#88138	C₂²	1	4	yes	complemented
60	#88138	C₂²	1	4	yes	complemented
61	#88138	C₂²	1	4	yes	complemented
62	#88136	C₂²	1	4	yes	complemented
63	#88136	C₂²	1	4	yes	complemented
64	#88136	C₂²	1	4	yes	complemented
65	#88136	C₂²	1	4	yes	complemented
66	#88136	C₂²	1	4	yes	complemented
67	C₂²⋊C₄×D₁₃	C₂²	1	4	yes	complemented
68	#88130	C₂²	1	2	yes	complemented
69	#88129	C₂²	1	1	yes	characteristic, complemented
70	#88129	C₂²	1	2	yes	complemented
71	#88128	C₂²	1	1	yes	characteristic
72	#88128	C₂²	1	2	yes	complemented
73	#88128	C₂²	1	1	yes	characteristic, complemented
74	#88128	C₂²	1	2	yes	complemented
75	#88128	C₂²	1	2	yes	complemented
76	#88128	C₂²	1	2	yes	complemented
77	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
78	C₄×D₅₂	C₂²	1	2	yes	complemented
79	C₄×D₅₂	C₂²	1	2	yes	complemented
80	#88126	C₂²	1	2	yes	complemented
81	#88124	C₂²	1	1	yes	characteristic, complemented
82	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₁₃	C₂³	1	4	yes	—
84	C₂³×D₁₃	C₂³	1	4	yes	—
85	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₁₃	C₂³	1	2	yes	—
87	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
93	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
96	#6131	—	4	4	no	—
97	D₄×D₁₃	—	4	4	no	—
98	D₄×D₁₃	—	4	8	no	—
99	#6127	—	4	4	no	—
100	C₂×D₅₂	—	4	4	no	—
101	C₂×D₅₂	—	4	4	no	—
102	C₂×D₅₂	—	4	4	no	—
103	C₂×D₅₂	—	4	4	no	—
104	C₂×D₅₂	C₂³	1	2	yes	—
105	C₂×D₅₂	C₂³	1	2	yes	—
106	C₂×D₅₂	C₂³	1	1	yes	characteristic
107	C₂×D₅₂	C₂³	1	2	yes	—
108	C₂×D₅₂	C₂³	1	2	yes	—
109	C₂×D₅₂	C₂³	1	2	yes	—
110	C₂×D₅₂	C₂³	1	4	yes	—
111	C₂×D₅₂	C₂³	1	4	yes	—
112	C₂×D₅₂	C₂³	1	4	yes	—
113	C₂×D₅₂	C₂³	1	2	yes	—
114	C₂×D₅₂	C₂³	1	4	yes	—
115	C₂×D₅₂	C₂³	1	4	yes	—
116	C₂×D₅₂	C₂³	1	4	yes	—
117	C₂×C₄×D₁₃	C₂³	1	2	yes	—
118	C₂×C₄×D₁₃	C₂³	1	4	yes	—
119	C₂×C₄×D₁₃	C₂³	1	4	yes	—
120	C₂×C₄×D₁₃	C₂³	1	4	yes	—
121	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
122	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
123	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
124	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
126	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
127	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
130	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
131	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
132	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
133	C₄²×C₁₃	C₂³	1	1	yes	characteristic
134	C₄²×C₁₃	C₂³	1	1	yes	characteristic
135	C₄²×C₁₃	C₂³	1	1	yes	characteristic
136	C₄²×C₁₃	C₂³	1	2	yes	—
137	C₄²×C₁₃	C₂³	1	1	yes	characteristic
138	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
139	#6103	C₂³	1	2	yes	—
140	#6103	C₂³	1	2	yes	—
141	#6103	C₂³	1	2	yes	—
142	#6103	C₂³	1	4	yes	—
143	#6103	C₂³	1	4	yes	—
144	#6103	C₂³	1	2	yes	—
145	#6103	C₂³	1	4	yes	—
146	#6103	C₂³	1	4	yes	—
147	#6103	C₂³	1	4	yes	—
148	#6103	C₂³	1	4	yes	—
149	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
150	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
151	#6101	C₂³	1	2	yes	—
152	#6101	C₂³	1	2	yes	—
153	#6101	C₂³	1	2	yes	—
154	#6101	C₂³	1	2	yes	—
155	C₄×Dic₁₃	C₂³	1	2	yes	—
156	#3543	—	13	1	no	maximal, Sylow
157	C₂³×C₁₃	C₂⁴	1	2	yes	—
158	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
159	C₂²×D₁₃	—	2	8	no	—
160	C₂²×D₁₃	—	4	4	no	—
161	C₂²×D₁₃	—	4	4	no	—
162	C₂²×D₁₃	—	4	4	no	—
163	C₂²×D₁₃	—	4	4	no	—
164	C₂²×D₁₃	—	4	4	no	—
165	C₂²×D₁₃	C₂⁴	1	2	yes	—
166	C₂²×D₁₃	C₂⁴	1	4	yes	—
167	C₂²×D₁₃	C₂⁴	1	4	yes	—
168	Q₈×C₁₃	—	2	2	no	—
169	D₄×C₁₃	—	2	4	no	—
170	D₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	4	no	—
175	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
180	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
181	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
182	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
184	C₂²⋊D₁₃	—	2	4	no	—
185	C₂²⋊D₁₃	—	4	4	no	—
186	C₂²⋊D₁₃	—	4	4	no	—
187	C₂²⋊D₁₃	—	4	4	no	—
188	C₂×Dic₁₃	C₂⁴	1	2	yes	—
189	C₂×Dic₁₃	C₂⁴	1	2	yes	—
190	C₂×Dic₁₃	C₂⁴	1	2	yes	—
191	D₅₂	—	2	4	no	—
192	D₅₂	—	2	2	no	—
193	D₅₂	—	2	4	no	—
194	D₅₂	—	2	4	no	—
195	D₅₂	—	2	4	no	—
196	D₅₂	—	4	4	no	—
197	D₅₂	—	4	4	no	—
198	D₅₂	—	4	4	no	—
199	D₅₂	—	4	2	no	—
200	D₅₂	—	4	4	no	—
201	D₅₂	—	4	2	no	—
202	D₅₂	—	4	4	no	—
203	D₅₂	—	4	4	no	—
204	C₄×D₁₃	—	2	4	no	—
205	C₄×D₁₃	—	4	4	no	—
206	C₄×D₁₃	—	4	4	no	—
207	C₄×D₁₃	—	4	4	no	—
208	Dic₂₆	—	2	2	no	—
209	#560	—	13	4	no	—
210	#559	—	13	1	no	—
211	#550	—	13	1	no	—
212	#550	—	13	1	no	—
213	#546	—	13	2	no	—
214	#546	—	13	2	no	—
215	D₄²	—	13	2	no	—
216	D₄²	—	13	1	no	—
217	D₄²	—	13	2	no	—
218	#540	—	13	2	no	—
219	#540	—	13	2	no	—
220	#535	—	13	2	no	—
221	#535	—	13	2	no	—
222	#534	—	13	4	no	—
223	C₂×#127	—	13	1	no	—
224	#529	—	13	1	no	—
225	#529	D₁₃	1	1	yes	characteristic, complemented
226	C₂²×C₁₃	—	2	1	no	—
227	C₂²×C₁₃	—	2	1	no	—
228	C₂²×C₁₃	—	2	2	no	—
229	C₂²×C₁₃	—	2	2	no	—
230	C₂²×C₁₃	—	2	2	no	—
231	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
232	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
233	C₂×D₁₃	—	2	2	no	—
234	C₂×D₁₃	—	2	4	no	—
235	C₂×D₁₃	—	2	4	no	—
236	C₂×D₁₃	—	2	4	no	—
237	C₂×D₁₃	—	2	2	no	—
238	C₂×D₁₃	—	2	4	no	—
239	C₂×D₁₃	—	2	4	no	—
240	C₂×D₁₃	—	2	4	no	—
241	C₂×D₁₃	—	2	2	no	—
242	C₂×D₁₃	—	8	8	no	—
243	C₂×D₁₃	—	8	8	no	—
244	C₄×C₁₃	—	2	2	no	—
245	C₄×C₁₃	—	2	2	no	—
246	C₄×C₁₃	—	2	2	no	—
247	C₄×C₁₃	—	2	1	no	—
248	C₄×C₁₃	—	2	1	no	—
249	C₄×C₁₃	—	2	1	no	—
250	C₄×C₁₃	—	2	1	no	—
251	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
252	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
253	Dic₁₃	—	2	2	no	—
254	Dic₁₃	—	2	2	no	—
255	Dic₁₃	—	2	2	no	—
256	C₂×#41	—	13	2	no	—
257	C₂×#41	—	13	2	no	—
258	C₂²×D₄	—	13	4	no	—
259	C₂²×D₄	—	13	2	no	—
260	C₂²×D₄	—	13	2	no	—
261	C₂²×D₄	—	13	2	no	—
262	C₂²×D₄	—	13	2	no	—
263	C₂²×D₄	—	13	2	no	—
264	#127	—	13	2	no	—
265	#127	—	13	2	no	—
266	#127	—	13	2	no	—
267	#127	—	13	1	no	—
268	#127	—	13	1	no	—
269	#127	—	13	2	no	—
270	#127	—	13	2	no	—
271	#126	—	13	2	no	—
272	#126	C₂×D₁₃	1	2	yes	complemented
273	#125	—	13	1	no	—
274	#125	C₂×D₁₃	1	1	yes	characteristic, complemented
275	#124	—	13	2	no	—
276	#124	—	13	1	no	—
277	#124	—	13	2	no	—
278	#124	C₂×D₁₃	1	1	yes	characteristic, complemented
279	#123	—	13	2	no	—
280	#123	—	13	4	no	—
281	#123	—	13	4	no	—
282	#123	—	13	4	no	—
283	#123	—	13	4	no	—
284	#123	C₂×D₁₃	1	2	yes	complemented
285	C₂²⋊Q₈	—	13	1	no	—
286	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
287	#121	—	13	1	no	—
288	#121	—	13	2	no	—
289	#121	—	13	2	no	—
290	#121	—	13	4	no	—
291	#121	—	13	4	no	—
292	#121	—	13	4	no	—
293	#121	—	13	2	no	—
294	#121	—	13	2	no	—
295	#121	—	13	4	no	—
296	#121	—	13	4	no	—
297	#121	—	13	4	no	—
298	#121	—	13	4	no	—
299	#121	—	13	4	no	—
300	#121	C₂×D₁₃	1	1	yes	characteristic
301	#120	—	13	4	no	—
302	#120	—	13	4	no	—
303	#120	—	13	4	no	—
304	#120	—	13	4	no	—
305	#120	—	13	4	no	—
306	#120	—	13	4	no	—
307	C₄×Q₈	—	13	1	no	—
308	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
309	C₄×D₄	—	13	2	no	—
310	C₄×D₄	—	13	2	no	—
311	C₄×D₄	—	13	2	no	—
312	C₄×D₄	—	13	1	no	—
313	C₄×D₄	—	13	2	no	—
314	C₄×D₄	—	13	2	no	—
315	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
316	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
317	#117	—	13	2	no	—
318	#117	C₂×D₁₃	1	2	yes	complemented
319	C₂×C₂²⋊C₄	—	13	4	no	—
320	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
321	C₂×C₁₃	—	2	2	no	—
322	C₂×C₁₃	—	4	2	no	—
323	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
324	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
325	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
326	D₁₃	—	4	4	no	—
327	D₁₃	—	4	2	no	—
328	D₁₃	—	4	4	no	—
329	C₂⁴	—	13	4	no	—
330	C₂⁴	—	13	4	no	—
331	#41	—	52	4	no	—
332	#41	—	52	4	no	—
333	C₂×Q₈	—	13	1	no	—
334	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
335	C₂×D₄	—	13	2	no	—
336	C₂×D₄	—	13	4	no	—
337	C₂×D₄	—	13	4	no	—
338	C₂×D₄	—	13	4	no	—
339	C₂×D₄	—	13	2	no	—
340	C₂×D₄	—	13	1	no	—
341	C₂×D₄	—	13	2	no	—
342	C₂×D₄	—	13	2	no	—
343	C₂×D₄	—	13	2	no	—
344	C₂×D₄	—	13	4	no	—
345	C₂×D₄	—	13	4	no	—
346	C₂×D₄	—	13	2	no	—
347	C₂×D₄	—	13	4	no	—
348	C₂×D₄	—	13	4	no	—
349	C₂×D₄	—	13	4	no	—
350	C₂×D₄	—	13	4	no	—
351	C₂×D₄	—	13	2	no	—
352	C₂×D₄	—	52	4	no	—
353	C₂×D₄	—	52	4	no	—
354	C₂×D₄	—	52	4	no	—
355	C₂×D₄	—	52	4	no	—
356	C₂×D₄	—	52	4	no	—
357	C₂×D₄	—	52	8	no	—
358	C₂×D₄	C₂²×D₁₃	1	2	yes	—
359	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
360	C₂²×C₄	—	13	2	no	—
361	C₂²×C₄	—	13	4	no	—
362	C₂²×C₄	—	13	4	no	—
363	C₂²×C₄	—	13	4	no	—
364	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
365	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
366	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
367	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
368	C₄⋊C₄	—	13	2	no	—
369	C₄⋊C₄	—	13	2	no	—
370	C₄⋊C₄	—	13	1	no	—
371	C₄⋊C₄	—	13	1	no	—
372	C₄⋊C₄	—	13	2	no	—
373	C₄⋊C₄	—	13	2	no	—
374	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
375	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
376	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
377	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
378	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
379	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
380	C₂²⋊C₄	—	13	2	no	—
381	C₂²⋊C₄	—	13	4	no	—
382	C₂²⋊C₄	—	13	4	no	—
383	C₂²⋊C₄	—	13	2	no	—
384	C₂²⋊C₄	—	13	2	no	—
385	C₂²⋊C₄	—	13	2	no	—
386	C₂²⋊C₄	—	13	2	no	—
387	C₂²⋊C₄	—	13	4	no	—
388	C₂²⋊C₄	—	13	4	no	—
389	C₂²⋊C₄	—	13	4	no	—
390	C₂²⋊C₄	—	13	4	no	—
391	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
392	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
393	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
394	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
395	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
396	C₄²	—	13	2	no	—
397	C₄²	C₂²×D₁₃	1	1	yes	characteristic
398	C₄²	C₂²×D₁₃	1	1	yes	characteristic
399	C₄²	C₂²×D₁₃	1	1	yes	characteristic
400	C₄²	C₂²×D₁₃	1	1	yes	characteristic
401	C₄²	C₂²×D₁₃	1	2	yes	—
402	C₁₃	#3543	1	1	yes	characteristic, complemented, Sylow
403	C₂³	—	13	2	no	—
404	C₂³	—	13	4	no	—
405	C₂³	—	13	4	no	—
406	C₂³	—	26	8	no	—
407	C₂³	—	52	4	no	—
408	C₂³	—	52	4	no	—
409	C₂³	—	52	4	no	—
410	C₂³	—	52	4	no	—
411	C₂³	—	52	4	no	—
412	C₂³	C₂³×D₁₃	1	2	yes	—
413	C₂³	C₂³×D₁₃	1	1	yes	characteristic
414	Q₈	—	2	2	no	—
415	Q₈	—	26	2	no	—
416	D₄	—	2	4	no	—
417	D₄	—	2	2	no	—
418	D₄	—	26	4	no	—
419	D₄	—	26	4	no	—
420	D₄	—	26	2	no	—
421	D₄	—	26	4	no	—
422	D₄	—	26	4	no	—
423	D₄	—	26	4	no	—
424	D₄	—	52	4	no	—
425	D₄	—	52	4	no	—
426	D₄	—	52	4	no	—
427	D₄	—	52	2	no	—
428	D₄	—	52	4	no	—
429	D₄	—	52	2	no	—
430	D₄	—	52	4	no	—
431	D₄	—	52	4	no	—
432	D₄	—	52	4	no	—
433	D₄	—	52	4	no	—
434	D₄	—	52	4	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	13	2	no	—
440	C₂×C₄	—	13	2	no	—
441	C₂×C₄	—	13	2	no	—
442	C₂×C₄	—	26	4	no	—
443	C₂×C₄	—	52	4	no	—
444	C₂×C₄	—	52	4	no	—
445	C₂×C₄	—	52	4	no	—
446	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
447	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
448	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
449	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
450	C₂×C₄	C₂³×D₁₃	1	2	yes	—
451	C₂×C₄	C₂³×D₁₃	1	2	yes	—
452	C₂×C₄	C₂³×D₁₃	1	2	yes	—
453	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
454	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	26	2	no	—
461	C₂²	—	26	4	no	—
462	C₂²	—	26	4	no	—
463	C₂²	—	26	4	no	—
464	C₂²	—	26	2	no	—
465	C₂²	—	26	2	no	—
466	C₂²	—	26	4	no	—
467	C₂²	—	26	4	no	—
468	C₂²	—	26	4	no	—
469	C₂²	—	104	8	no	—
470	C₂²	—	104	8	no	—
471	C₂²	#88256	1	2	yes	—
472	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
473	C₄	—	2	2	no	—
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	2	no	—
479	C₄	—	2	2	no	—
480	C₄	—	26	2	no	—
481	C₄	—	26	2	no	—
482	C₄	—	26	2	no	—
483	C₄	#88256	1	2	yes	—
484	C₄	#88256	1	2	yes	—
485	C₂	—	2	2	no	—
486	C₂	—	4	2	no	—
487	C₂	—	52	2	no	—
488	C₂	—	52	4	no	—
489	C₂	—	52	4	no	—
490	C₂	C₂×#88256	1	1	yes	characteristic
491	C₂	C₂×#88256	1	1	yes	characteristic
492	C₂	C₂×#88256	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#529	C₂
hypercenter	#529	D₁₃
hypocenter	C₁₃	#3543
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. C₁₃×#529	C₂	semidirect
2. #11719416	C₂	semidirect
3. #11719403	C₂	semidirect
4. #11719379	C₂	semidirect
5. #11719358	C₂	semidirect
6. #11719335	C₂	semidirect
7. #11719314	C₂	semidirect
8. #11719290	C₂	semidirect
9. #11719282	C₂	semidirect
10. #11719258	C₂	semidirect
11. #11719255	C₂	semidirect
12. D₄×D₅₂	C₂	semidirect
13. D₄×D₅₂	C₂	semidirect
14. #11719240	C₂	semidirect
15. #11719230	C₂	semidirect
16. #11719184	C₂	semidirect
17. C₂×#88128	C₂	semidirect
18. C₂×#6131	C₂²	semidirect
19. C₂×D₄×D₁₃	C₂²	semidirect
20. C₂×D₄×D₁₃	C₂²	semidirect
21. C₂×#6127	C₂²	semidirect
22. C₂²×D₅₂	C₂²	semidirect
23. C₂²×D₅₂	C₂²	semidirect
24. C₂²×D₅₂	C₂²	semidirect
25. C₂²×D₅₂	C₂²	semidirect
26. C₁₃×#126	C₂²	semidirect
27. C₁₃×#125	C₂²	semidirect
28. C₁₃×#124	C₂²	semidirect
29. C₁₃×#123	C₂²	semidirect
30. C₁₃×C₂²⋊Q₈	C₂²	semidirect
32. C₄×Q₈×C₁₃	C₂²	semidirect
33. C₄×D₄×C₁₃	C₂²	semidirect
34. C₄×D₄×C₁₃	C₂²	semidirect
35. C₁₃×#117	C₂²	semidirect
36. C₂×C₄²×C₁₃	C₂²	semidirect
37. #88201	C₂²	semidirect
38. #88194	C₂²	semidirect
39. #88191	C₂²	semidirect
41. #88184	C₂²	semidirect
42. #88184	C₂²	semidirect
43. #88183	C₂²	semidirect
44. C₄×C₂²⋊D₁₃	C₂²	semidirect
45. #88178	C₂²	semidirect
46. #88149	C₂²	semidirect
47. #88149	C₂²	semidirect
48. #88149	C₂²	semidirect
49. #88149	C₂²	semidirect
50. #88149	C₂²	semidirect
51. #88149	C₂²	semidirect
52. #88148	C₂²	semidirect
53. #88148	C₂²	semidirect
54. #88148	C₂²	semidirect
55. #88148	C₂²	semidirect
56. #88147	C₂²	semidirect
57. #88147	C₂²	semidirect
58. #88138	C₂²	semidirect
59. #88138	C₂²	semidirect
60. #88138	C₂²	semidirect
61. #88138	C₂²	semidirect
62. #88136	C₂²	semidirect
63. #88136	C₂²	semidirect
64. #88136	C₂²	semidirect
65. #88136	C₂²	semidirect
66. #88136	C₂²	semidirect
67. C₂²⋊C₄×D₁₃	C₂²	semidirect
68. #88130	C₂²	semidirect
69. #88129	C₂²	semidirect
70. #88129	C₂²	semidirect
72. #88128	C₂²	semidirect
73. #88128	C₂²	semidirect
74. #88128	C₂²	semidirect
75. #88128	C₂²	semidirect
76. #88128	C₂²	semidirect
77. C₄×D₅₂	C₂²	semidirect
78. C₄×D₅₂	C₂²	semidirect
79. C₄×D₅₂	C₂²	semidirect
80. #88126	C₂²	semidirect
81. #88124	C₂²	semidirect
82. C₄×Dic₂₆	C₂²	semidirect
225. #529	D₁₃	semidirect
272. #126	C₂×D₁₃	semidirect
274. #125	C₂×D₁₃	semidirect
278. #124	C₂×D₁₃	semidirect
284. #123	C₂×D₁₃	semidirect
286. C₂²⋊Q₈	C₂×D₁₃	semidirect
308. C₄×Q₈	C₂×D₁₃	semidirect
315. C₄×D₄	C₂×D₁₃	semidirect
316. C₄×D₄	C₂×D₁₃	semidirect
318. #117	C₂×D₁₃	semidirect
320. C₂×C₄²	C₂×D₁₃	semidirect
402. C₁₃	#3543	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#529	2
#11719416	2
#11719403	2
#11719379	2
#11719358	2
#11719335	2
#11719314	2
#11719290	2
#11719282	2
#11719258	2
#11719255	2
D₄×D₅₂	2
#11719240	2
#11719230	2
#11719184	2
C₂×#88128	2
#3543	13