Subgroups — #13128899

Order 1664.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719413	C₂	1	2	yes	maximal, complemented
3	D₁₃×#126	C₂	1	2	yes	maximal, complemented
4	#11719402	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719395	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719365	C₂	1	2	yes	maximal, complemented
7	#11719363	C₂	1	2	yes	maximal, complemented
8	#11719319	C₂	1	2	yes	maximal, complemented
9	#11719318	C₂	1	2	yes	maximal, complemented
10	#11719317	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719317	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719308	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719305	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719262	C₂	1	2	yes	maximal, complemented
15	#11719261	C₂	1	2	yes	maximal, complemented
16	#11719256	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719250	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719247	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719243	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719238	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719227	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719218	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719209	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
25	C₂×#6127	C₂²	1	1	yes	characteristic
26	C₂×#6127	C₂²	1	1	yes	characteristic
27	C₁₃×#126	C₂²	1	2	yes	complemented
28	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#123	C₂²	1	2	yes	complemented
30	C₁₃×#121	C₂²	1	1	yes	characteristic
31	C₁₃×#121	C₂²	1	1	yes	characteristic
32	C₁₃×#121	C₂²	1	2	yes	complemented
33	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
35	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
36	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	#88193	C₂²	1	1	yes	characteristic
39	#88192	C₂²	1	2	yes	—
40	#88192	C₂²	1	2	yes	—
41	#88192	C₂²	1	2	yes	complemented
42	#88191	C₂²	1	2	yes	—
43	#88191	C₂²	1	2	yes	—
44	#88190	C₂²	1	1	yes	characteristic
45	#88190	C₂²	1	1	yes	characteristic
46	#88190	C₂²	1	2	yes	complemented
47	#88189	C₂²	1	1	yes	characteristic, complemented
48	#88189	C₂²	1	2	yes	complemented
49	#88189	C₂²	1	2	yes	complemented
50	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
51	D₄×Dic₁₃	C₂²	1	2	yes	complemented
52	#88183	C₂²	1	2	yes	—
53	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
55	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
56	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
57	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
58	C₂×#6103	C₂²	1	2	yes	—
59	#88180	C₂²	1	1	yes	characteristic, complemented
60	#88180	C₂²	1	2	yes	complemented
61	#88180	C₂²	1	2	yes	complemented
62	#88178	C₂²	1	1	yes	characteristic, complemented
63	#88178	C₂²	1	1	yes	characteristic, complemented
64	#88178	C₂²	1	2	yes	complemented
65	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
66	#88152	C₂²	1	2	yes	—
67	#88152	C₂²	1	1	yes	characteristic
68	#88152	C₂²	1	2	yes	—
69	#88152	C₂²	1	2	yes	—
70	#88151	C₂²	1	1	yes	characteristic
71	#88151	C₂²	1	1	yes	characteristic
72	#88151	C₂²	1	2	yes	complemented
73	#88150	C₂²	1	2	yes	complemented
74	#88150	C₂²	1	2	yes	complemented
75	#88147	C₂²	1	1	yes	characteristic
76	#88147	C₂²	1	1	yes	characteristic
77	#88147	C₂²	1	1	yes	characteristic
78	#88146	C₂²	1	1	yes	characteristic
79	#88146	C₂²	1	2	yes	complemented
80	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
81	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
82	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
83	#88144	C₂²	1	1	yes	characteristic, complemented
84	#88144	C₂²	1	2	yes	complemented
85	#88144	C₂²	1	2	yes	complemented
86	#88143	C₂²	1	2	yes	complemented
87	#88143	C₂²	1	1	yes	characteristic, complemented
88	#88142	C₂²	1	1	yes	characteristic, complemented
89	#88141	C₂²	1	1	yes	characteristic, complemented
90	#88141	C₂²	1	1	yes	characteristic, complemented
91	#88141	C₂²	1	1	yes	characteristic, complemented
92	#88141	C₂²	1	1	yes	characteristic, complemented
93	#88140	C₂²	1	1	yes	characteristic
94	#88139	C₂²	1	2	yes	—
95	#88139	C₂²	1	1	yes	characteristic
96	#88137	C₂²	1	2	yes	—
97	#88137	C₂²	1	2	yes	—
98	#88137	C₂²	1	2	yes	complemented
99	#88137	C₂²	1	2	yes	complemented
100	#88135	C₂²	1	2	yes	—
101	#88135	C₂²	1	2	yes	complemented
102	#88135	C₂²	1	2	yes	complemented
103	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
104	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
105	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
106	#88133	C₂²	1	2	yes	complemented
107	#88133	C₂²	1	1	yes	characteristic, complemented
108	#88133	C₂²	1	2	yes	complemented
109	#88133	C₂²	1	2	yes	complemented
110	#88133	C₂²	1	2	yes	complemented
111	#88133	C₂²	1	2	yes	complemented
112	#88132	C₂²	1	1	yes	characteristic, complemented
113	#88132	C₂²	1	2	yes	complemented
114	#88131	C₂²	1	2	yes	complemented
115	#88130	C₂²	1	2	yes	—
116	C₄×D₅₂	C₂²	1	1	yes	characteristic
117	#88126	C₂²	1	1	yes	characteristic
118	#88126	C₂²	1	2	yes	complemented
119	C₄²×D₁₃	C₂²	1	2	yes	complemented
120	#88123	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₂₆	C₂²	1	2	yes	complemented
122	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₃	C₂³	1	2	yes	—
124	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₁₃	C₂³	1	2	yes	—
126	C₂×D₄×C₁₃	C₂³	1	2	yes	—
127	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
137	C₂²×Dic₁₃	C₂³	1	2	yes	—
138	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
139	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
140	D₄×D₁₃	—	2	4	no	—
141	#6127	—	2	4	no	—
142	#6127	—	2	4	no	—
143	C₂×D₅₂	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₃	C₂³	1	2	yes	—
145	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₁₃	C₂³	1	2	yes	—
147	C₂×C₄×D₁₃	C₂³	1	2	yes	—
148	C₂×C₄×D₁₃	C₂³	1	2	yes	—
149	C₂×C₄×D₁₃	C₂³	1	2	yes	—
150	C₂×C₄×D₁₃	C₂³	1	2	yes	—
151	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
152	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
153	C₂×Dic₂₆	C₂³	1	2	yes	—
154	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
155	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
165	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
168	C₄²×C₁₃	C₂³	1	1	yes	characteristic
169	C₄²×C₁₃	C₂³	1	2	yes	—
170	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
171	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
181	#6103	C₂³	1	1	yes	characteristic
182	#6103	C₂³	1	1	yes	characteristic
183	#6103	C₂³	1	2	yes	—
184	#6103	C₂³	1	2	yes	—
185	#6103	C₂³	1	2	yes	—
186	#6103	C₂³	1	1	yes	characteristic
187	#6103	C₂³	1	2	yes	—
188	#6103	C₂³	1	2	yes	—
189	#6103	C₂³	1	1	yes	characteristic
190	#6103	C₂³	1	2	yes	—
191	#6103	C₂³	1	2	yes	—
192	C₄⋊Dic₁₃	C₂³	1	2	yes	—
193	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
194	C₄⋊Dic₁₃	C₂³	1	2	yes	—
195	C₄⋊Dic₁₃	C₂³	1	2	yes	—
196	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₁₃	C₂³	1	2	yes	—
200	C₄⋊Dic₁₃	C₂³	1	2	yes	—
201	#6101	C₂³	1	1	yes	characteristic
202	#6101	C₂³	1	2	yes	—
203	#6101	C₂³	1	1	yes	characteristic
204	#6101	C₂³	1	1	yes	characteristic
205	#6101	C₂³	1	1	yes	characteristic
206	#6101	C₂³	1	1	yes	characteristic
207	#6101	C₂³	1	2	yes	—
208	#6101	C₂³	1	2	yes	—
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	1	yes	characteristic
214	#6101	C₂³	1	2	yes	—
215	C₄×Dic₁₃	C₂³	1	2	yes	—
216	C₄×Dic₁₃	C₂³	1	2	yes	—
217	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
218	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
219	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
220	C₄×Dic₁₃	C₂³	1	2	yes	—
221	C₄×Dic₁₃	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	#3521	—	13	1	no	maximal, Sylow
226	C₂³×C₁₃	C₂⁴	1	2	yes	—
227	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
229	C₂²×D₁₃	—	2	4	no	—
230	C₂²×D₁₃	—	4	2	no	—
231	C₂²×D₁₃	—	4	2	no	—
232	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
233	C₂²×D₁₃	C₂⁴	1	2	yes	—
234	D₄×C₁₃	—	2	2	no	—
235	D₄×C₁₃	—	4	2	no	—
236	D₄×C₁₃	—	4	1	no	—
237	D₄×C₁₃	—	4	2	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	4	2	no	—
241	C₂×C₄×C₁₃	—	4	2	no	—
242	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
243	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
245	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
246	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₂²⋊D₁₃	—	2	4	no	—
251	C₂²⋊D₁₃	—	2	4	no	—
252	C₂²⋊D₁₃	—	2	4	no	—
253	C₂²⋊D₁₃	—	4	1	no	—
254	C₂²⋊D₁₃	—	4	1	no	—
255	C₂×Dic₁₃	—	4	2	no	—
256	C₂×Dic₁₃	—	4	1	no	—
257	C₂×Dic₁₃	—	4	1	no	—
258	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
265	C₂×Dic₁₃	C₂⁴	1	2	yes	—
266	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₁₃	C₂⁴	1	2	yes	—
268	D₅₂	#41	1	4	yes	—
269	C₄×D₁₃	—	2	4	no	—
270	C₄×D₁₃	—	2	4	no	—
271	C₄×D₁₃	—	2	2	no	—
272	C₄×D₁₃	—	4	2	no	—
273	C₄×D₁₃	—	4	2	no	—
274	C₄×D₁₃	—	4	2	no	—
275	C₄×D₁₃	—	4	2	no	—
276	Dic₂₆	—	2	2	no	—
277	Dic₂₆	—	2	2	no	—
278	Dic₂₆	—	4	2	no	—
279	Dic₂₆	—	4	1	no	—
280	#556	—	13	1	no	—
281	#556	—	13	1	no	—
282	#554	—	13	1	no	—
283	#553	—	13	2	no	—
284	#553	D₁₃	1	1	yes	characteristic, complemented
285	#552	—	13	2	no	—
286	#552	—	13	1	no	—
287	#551	—	13	2	no	—
288	#551	—	13	2	no	—
289	#547	—	13	1	no	—
290	#546	—	13	1	no	—
291	#546	—	13	1	no	—
292	#542	—	13	1	no	—
293	#541	—	13	1	no	—
294	#539	—	13	2	no	—
295	#538	—	13	2	no	—
296	#529	—	13	1	no	—
297	#529	—	13	1	no	—
298	#529	—	13	2	no	—
299	C₂×#126	—	13	2	no	—
300	#520	—	13	1	no	—
301	#518	—	13	1	no	—
302	C₄×#41	—	13	1	no	—
303	C₂²×C₁₃	—	2	1	no	—
304	C₂²×C₁₃	—	2	1	no	—
305	C₂²×C₁₃	—	2	2	no	—
306	C₂²×C₁₃	—	2	1	no	—
307	C₂²×C₁₃	—	2	1	no	—
308	C₂²×C₁₃	—	2	2	no	—
309	C₂²×C₁₃	—	2	1	no	—
310	C₂²×C₁₃	—	2	2	no	—
311	C₂²×C₁₃	—	2	1	no	—
312	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
313	C₂×D₁₃	—	2	2	no	—
314	C₂×D₁₃	—	2	2	no	—
315	C₂×D₁₃	—	2	1	no	—
316	C₂×D₁₃	—	2	1	no	—
317	C₂×D₁₃	—	2	1	no	—
318	C₂×D₁₃	—	8	4	no	—
319	C₂×D₁₃	C₂×#41	1	4	yes	—
320	C₄×C₁₃	—	2	1	no	—
321	C₄×C₁₃	—	2	1	no	—
322	C₄×C₁₃	—	2	2	no	—
323	C₄×C₁₃	—	2	1	no	—
324	C₄×C₁₃	—	2	1	no	—
325	C₄×C₁₃	—	2	2	no	—
326	C₄×C₁₃	—	2	2	no	—
327	C₄×C₁₃	C₂×#41	1	2	yes	—
328	Dic₁₃	—	2	2	no	—
329	Dic₁₃	—	2	2	no	—
330	Dic₁₃	—	2	1	no	—
331	Dic₁₃	—	2	1	no	—
332	Dic₁₃	—	2	1	no	—
333	Dic₁₃	—	2	2	no	—
334	Dic₁₃	—	2	1	no	—
335	Dic₁₃	—	2	1	no	—
336	Dic₁₃	—	2	1	no	—
337	Dic₁₃	—	2	1	no	—
338	C₂×#41	—	13	1	no	—
339	C₂×#41	—	13	1	no	—
340	C₂²×D₄	—	13	1	no	—
341	C₄⋊Q₈	—	13	1	no	—
342	C₄⋊Q₈	—	13	1	no	—
343	#126	—	13	1	no	—
344	#126	—	13	2	no	—
345	#126	—	13	2	no	—
346	#126	—	13	2	no	—
347	#126	—	13	2	no	—
348	#126	—	13	2	no	—
349	#126	—	13	2	no	—
350	#126	—	13	1	no	—
351	#126	—	13	2	no	—
352	#126	—	13	2	no	—
353	#126	—	13	2	no	—
354	#126	C₂×D₁₃	1	2	yes	complemented
355	#125	—	13	2	no	—
356	#125	—	13	1	no	—
357	#125	—	13	1	no	—
358	#125	—	13	2	no	—
359	#125	—	13	2	no	—
360	#125	C₂×D₁₃	1	1	yes	characteristic, complemented
361	#124	—	13	2	no	—
362	#124	—	13	1	no	—
363	#124	—	13	1	no	—
364	#124	—	13	1	no	—
365	#124	—	13	2	no	—
366	#123	—	13	2	no	—
367	#123	—	13	1	no	—
368	#123	—	13	2	no	—
369	#123	—	13	2	no	—
370	#123	—	13	2	no	—
371	#123	—	13	2	no	—
372	#123	—	13	1	no	—
373	#123	—	13	2	no	—
374	#123	—	13	2	no	—
375	#123	C₂×D₁₃	1	2	yes	complemented
376	C₂²⋊Q₈	—	13	1	no	—
377	C₂²⋊Q₈	—	13	2	no	—
378	C₂²⋊Q₈	—	13	1	no	—
379	C₂²⋊Q₈	—	13	2	no	—
380	C₂²⋊Q₈	—	13	2	no	—
381	C₂²⋊Q₈	—	13	2	no	—
382	C₂²⋊Q₈	—	13	1	no	—
383	C₂²⋊Q₈	—	13	1	no	—
384	C₂²⋊Q₈	—	13	1	no	—
385	C₂²⋊Q₈	—	13	2	no	—
386	#121	—	13	1	no	—
387	#121	—	13	2	no	—
388	#121	—	13	2	no	—
389	#121	—	13	2	no	—
390	#121	C₂×D₁₃	1	1	yes	characteristic
391	#121	C₂×D₁₃	1	1	yes	characteristic
392	#121	C₂×D₁₃	1	2	yes	complemented
393	#120	—	13	2	no	—
394	#120	—	13	2	no	—
395	C₄×Q₈	—	13	1	no	—
396	C₄×Q₈	—	13	1	no	—
397	C₄×Q₈	—	13	1	no	—
398	C₄×Q₈	—	13	1	no	—
399	C₄×Q₈	—	13	2	no	—
400	C₄×Q₈	—	13	1	no	—
401	C₄×D₄	—	13	1	no	—
402	C₄×D₄	—	13	2	no	—
403	C₄×D₄	—	13	2	no	—
404	C₄×D₄	—	13	2	no	—
405	C₄×D₄	—	13	2	no	—
406	C₄×D₄	—	13	1	no	—
407	C₄×D₄	—	13	1	no	—
408	C₄×D₄	—	13	1	no	—
409	C₄×D₄	—	13	1	no	—
410	C₄×D₄	—	13	1	no	—
411	C₄×D₄	—	13	2	no	—
412	C₄×D₄	—	13	2	no	—
413	C₄×D₄	—	13	2	no	—
414	C₄×D₄	—	13	1	no	—
415	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
416	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
417	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
418	#117	—	13	1	no	—
419	#117	—	13	2	no	—
420	#117	—	13	2	no	—
421	#117	—	13	1	no	—
422	#117	—	13	2	no	—
423	#117	—	13	2	no	—
424	#117	—	13	2	no	—
425	#117	—	13	1	no	—
426	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
427	C₂×C₄⋊C₄	—	13	2	no	—
428	C₂×C₄⋊C₄	—	13	2	no	—
429	C₂×C₄⋊C₄	—	13	2	no	—
430	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
431	C₂×C₂²⋊C₄	—	13	2	no	—
432	C₂×C₂²⋊C₄	—	13	2	no	—
433	C₂×C₂²⋊C₄	—	13	2	no	—
434	C₂×C₂²⋊C₄	—	13	2	no	—
435	C₂×C₄²	—	13	1	no	—
436	C₂×C₄²	—	13	2	no	—
437	C₂×C₁₃	—	4	2	no	—
438	C₂×C₁₃	—	4	1	no	—
439	C₂×C₁₃	—	4	1	no	—
440	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
441	C₂×C₁₃	#585	1	1	yes	characteristic
442	C₂×C₁₃	#585	1	1	yes	characteristic
443	D₁₃	—	2	4	no	—
444	D₁₃	—	4	1	no	—
445	C₂⁴	—	13	2	no	—
446	#41	—	26	4	no	—
447	#41	—	26	4	no	—
448	C₂×Q₈	—	13	1	no	—
449	C₂×Q₈	—	13	1	no	—
450	C₂×Q₈	—	13	1	no	—
451	C₂×Q₈	—	13	2	no	—
452	C₂×D₄	—	13	2	no	—
453	C₂×D₄	—	13	2	no	—
454	C₂×D₄	—	13	2	no	—
455	C₂×D₄	—	13	1	no	—
456	C₂×D₄	—	13	1	no	—
457	C₂×D₄	—	13	1	no	—
458	C₂×D₄	—	26	4	no	—
459	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
460	C₂×D₄	C₂²×D₁₃	1	2	yes	—
461	C₂×D₄	C₂²×D₁₃	1	2	yes	—
462	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
463	C₂²×C₄	—	13	1	no	—
464	C₂²×C₄	—	13	1	no	—
465	C₂²×C₄	—	13	2	no	—
466	C₂²×C₄	—	13	2	no	—
467	C₂²×C₄	—	13	2	no	—
468	C₂²×C₄	—	13	1	no	—
469	C₂²×C₄	—	13	2	no	—
470	C₂²×C₄	—	13	2	no	—
471	C₂²×C₄	—	13	2	no	—
472	C₂²×C₄	—	13	2	no	—
473	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
474	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
475	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
476	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
477	C₄⋊C₄	—	13	1	no	—
478	C₄⋊C₄	—	13	1	no	—
479	C₄⋊C₄	—	13	2	no	—
480	C₄⋊C₄	—	13	2	no	—
481	C₄⋊C₄	—	13	2	no	—
482	C₄⋊C₄	—	13	2	no	—
483	C₄⋊C₄	—	13	2	no	—
484	C₄⋊C₄	—	13	2	no	—
485	C₄⋊C₄	—	13	2	no	—
486	C₄⋊C₄	—	13	1	no	—
487	C₄⋊C₄	—	13	1	no	—
488	C₄⋊C₄	—	13	1	no	—
489	C₄⋊C₄	—	13	1	no	—
490	C₄⋊C₄	—	13	1	no	—
491	C₄⋊C₄	—	13	2	no	—
492	C₄⋊C₄	—	13	2	no	—
493	C₄⋊C₄	—	13	2	no	—
494	C₄⋊C₄	—	13	2	no	—
495	C₄⋊C₄	—	13	2	no	—
496	C₄⋊C₄	—	13	1	no	—
497	C₄⋊C₄	—	13	1	no	—
498	C₄⋊C₄	—	13	1	no	—
499	C₄⋊C₄	—	13	2	no	—
500	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
502	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
503	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
507	C₂²⋊C₄	—	13	2	no	—
508	C₂²⋊C₄	—	13	2	no	—
509	C₂²⋊C₄	—	13	2	no	—
510	C₂²⋊C₄	—	13	1	no	—
511	C₂²⋊C₄	—	13	1	no	—
512	C₂²⋊C₄	—	13	1	no	—
513	C₂²⋊C₄	—	13	2	no	—
514	C₂²⋊C₄	—	13	2	no	—
515	C₂²⋊C₄	—	13	2	no	—
516	C₂²⋊C₄	—	13	1	no	—
517	C₂²⋊C₄	—	13	2	no	—
518	C₂²⋊C₄	—	13	1	no	—
519	C₂²⋊C₄	—	13	1	no	—
520	C₂²⋊C₄	—	13	2	no	—
521	C₂²⋊C₄	—	13	1	no	—
522	C₂²⋊C₄	—	13	1	no	—
523	C₂²⋊C₄	—	13	2	no	—
524	C₂²⋊C₄	—	13	2	no	—
525	C₂²⋊C₄	—	13	2	no	—
526	C₂²⋊C₄	—	13	2	no	—
527	C₂²⋊C₄	—	13	2	no	—
528	C₂²⋊C₄	—	13	2	no	—
529	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
530	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
531	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
534	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
535	C₄²	—	13	1	no	—
536	C₄²	—	13	1	no	—
537	C₄²	—	13	1	no	—
538	C₄²	—	13	2	no	—
539	C₄²	—	13	1	no	—
540	C₄²	—	13	2	no	—
541	C₄²	—	13	2	no	—
542	C₄²	—	13	2	no	—
543	C₄²	—	13	2	no	—
544	C₄²	—	13	1	no	—
545	C₄²	C₂²×D₁₃	1	2	yes	—
546	C₄²	C₂²×D₁₃	1	1	yes	characteristic
547	C₁₃	#3521	1	1	yes	characteristic, complemented, Sylow
548	C₂³	—	13	2	no	—
549	C₂³	—	13	1	no	—
550	C₂³	—	26	4	no	—
551	C₂³	—	52	2	no	—
552	C₂³	—	52	2	no	—
553	C₂³	C₂³×D₁₃	1	2	yes	—
554	C₂³	C₂³×D₁₃	1	1	yes	characteristic
555	C₂³	C₂³×D₁₃	1	1	yes	characteristic
556	Q₈	—	26	2	no	—
557	Q₈	—	26	2	no	—
558	Q₈	—	52	2	no	—
559	Q₈	—	52	1	no	—
560	D₄	—	2	2	no	—
561	D₄	—	4	1	no	—
562	D₄	—	4	2	no	—
563	D₄	—	4	2	no	—
564	D₄	—	13	4	no	—
565	D₄	—	26	4	no	—
566	D₄	—	26	4	no	—
567	D₄	—	26	4	no	—
568	D₄	—	52	1	no	—
569	D₄	—	52	1	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	13	1	no	—
575	C₂×C₄	—	13	1	no	—
576	C₂×C₄	—	13	1	no	—
577	C₂×C₄	—	13	1	no	—
578	C₂×C₄	—	13	2	no	—
579	C₂×C₄	—	13	2	no	—
580	C₂×C₄	—	13	1	no	—
581	C₂×C₄	—	13	1	no	—
582	C₂×C₄	—	13	2	no	—
583	C₂×C₄	—	13	1	no	—
584	C₂×C₄	—	26	4	no	—
585	C₂×C₄	—	26	4	no	—
586	C₂×C₄	—	26	2	no	—
587	C₂×C₄	—	52	2	no	—
588	C₂×C₄	—	52	2	no	—
589	C₂×C₄	—	52	2	no	—
590	C₂×C₄	—	52	2	no	—
591	C₂×C₄	—	52	1	no	—
592	C₂×C₄	—	52	2	no	—
593	C₂×C₄	—	52	1	no	—
594	C₂×C₄	C₂³×D₁₃	1	2	yes	—
595	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₁₃	1	2	yes	—
597	C₂×C₄	C₂³×D₁₃	1	2	yes	—
598	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	1	no	—
611	C₂²	—	13	4	no	—
612	C₂²	—	26	2	no	—
613	C₂²	—	26	2	no	—
614	C₂²	—	26	1	no	—
615	C₂²	—	26	1	no	—
616	C₂²	—	26	1	no	—
617	C₂²	—	104	4	no	—
618	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	2	no	—
626	C₄	—	26	1	no	—
627	C₄	—	26	2	no	—
628	C₄	—	26	2	no	—
629	C₄	—	26	1	no	—
630	C₄	—	26	1	no	—
631	C₄	—	26	2	no	—
632	C₄	—	26	1	no	—
633	C₄	—	26	1	no	—
634	C₄	—	26	1	no	—
635	C₄	—	26	1	no	—
636	C₄	#41×D₁₃	1	2	yes	—
637	C₂	—	4	2	no	—
638	C₂	—	4	1	no	—
639	C₂	—	4	1	no	—
640	C₂	—	26	4	no	—
641	C₂	—	52	1	no	—
642	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
643	C₂	#11719648	1	1	yes	characteristic
644	C₂	#11719650	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#553	C₂
hypercenter	#553	D₁₃
hypocenter	C₁₃	#3521
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. C₁₃×#553	C₂	semidirect
2. #11719413	C₂	semidirect
3. D₁₃×#126	C₂	semidirect
4. #11719402	C₂	semidirect
5. #11719395	C₂	semidirect
6. #11719365	C₂	semidirect
7. #11719363	C₂	semidirect
8. #11719319	C₂	semidirect
9. #11719318	C₂	semidirect
10. #11719317	C₂	semidirect
11. #11719317	C₂	semidirect
12. #11719308	C₂	semidirect
13. #11719305	C₂	semidirect
14. #11719262	C₂	semidirect
15. #11719261	C₂	semidirect
16. #11719256	C₂	semidirect
17. #11719250	C₂	semidirect
18. #11719247	C₂	semidirect
19. #11719243	C₂	semidirect
20. #11719238	C₂	semidirect
21. #11719227	C₂	semidirect
22. #11719218	C₂	semidirect
23. #11719209	C₂	semidirect
27. C₁₃×#126	C₂²	semidirect
28. C₁₃×#125	C₂²	semidirect
29. C₁₃×#123	C₂²	semidirect
32. C₁₃×#121	C₂²	semidirect
34. C₄×D₄×C₁₃	C₂²	semidirect
35. C₄×D₄×C₁₃	C₂²	semidirect
36. C₁₃×#117	C₂²	semidirect
37. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
41. #88192	C₂²	semidirect
46. #88190	C₂²	semidirect
47. #88189	C₂²	semidirect
48. #88189	C₂²	semidirect
49. #88189	C₂²	semidirect
51. D₄×Dic₁₃	C₂²	semidirect
56. C₄×C₂²⋊D₁₃	C₂²	semidirect
57. C₄×C₂²⋊D₁₃	C₂²	semidirect
59. #88180	C₂²	semidirect
60. #88180	C₂²	semidirect
61. #88180	C₂²	semidirect
62. #88178	C₂²	semidirect
63. #88178	C₂²	semidirect
64. #88178	C₂²	semidirect
65. C₂×C₄×Dic₁₃	C₂²	semidirect
72. #88151	C₂²	semidirect
73. #88150	C₂²	semidirect
74. #88150	C₂²	semidirect
79. #88146	C₂²	semidirect
80. C₄⋊C₄×D₁₃	C₂²	semidirect
81. C₄⋊C₄×D₁₃	C₂²	semidirect
82. C₄⋊C₄×D₁₃	C₂²	semidirect
83. #88144	C₂²	semidirect
84. #88144	C₂²	semidirect
85. #88144	C₂²	semidirect
86. #88143	C₂²	semidirect
87. #88143	C₂²	semidirect
88. #88142	C₂²	semidirect
89. #88141	C₂²	semidirect
90. #88141	C₂²	semidirect
91. #88141	C₂²	semidirect
92. #88141	C₂²	semidirect
98. #88137	C₂²	semidirect
99. #88137	C₂²	semidirect
101. #88135	C₂²	semidirect
102. #88135	C₂²	semidirect
106. #88133	C₂²	semidirect
107. #88133	C₂²	semidirect
108. #88133	C₂²	semidirect
109. #88133	C₂²	semidirect
110. #88133	C₂²	semidirect
111. #88133	C₂²	semidirect
112. #88132	C₂²	semidirect
113. #88132	C₂²	semidirect
114. #88131	C₂²	semidirect
118. #88126	C₂²	semidirect
119. C₄²×D₁₃	C₂²	semidirect
120. #88123	C₂²	semidirect
121. C₄×Dic₂₆	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
284. #553	D₁₃	semidirect
354. #126	C₂×D₁₃	semidirect
360. #125	C₂×D₁₃	semidirect
375. #123	C₂×D₁₃	semidirect
392. #121	C₂×D₁₃	semidirect
416. C₄×D₄	C₂×D₁₃	semidirect
417. C₄×D₄	C₂×D₁₃	semidirect
426. #117	C₂×D₁₃	semidirect
430. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
547. C₁₃	#3521	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#553	2
#11719413	2
D₁₃×#126	2
#11719402	2
#11719395	2
#11719365	2
#11719363	2
#11719319	2
#11719318	2
#11719317	2
#11719308	2
#11719305	2
#11719262	2
#11719261	2
#11719256	2
#11719250	2
#11719247	2
#11719243	2
#11719238	2
#11719227	2
#11719218	2
#11719209	2
#3521	13