Subgroups — #13128552

Order 1664.

1040 conjugacy classes of subgroups.

The subgroup lattice has 660 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	#11719411	C₂	1	2	yes	maximal, complemented
3	#11719407	C₂	1	2	yes	maximal, complemented
4	#11719399	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719394	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719362	C₂	1	2	yes	maximal, complemented
7	#11719355	C₂	1	2	yes	maximal, complemented
8	#11719321	C₂	1	2	yes	maximal, complemented
9	#11719321	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719319	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719318	C₂	1	2	yes	maximal, complemented
12	#11719313	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719311	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719268	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719262	C₂	1	2	yes	maximal, complemented
16	#11719252	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719251	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719247	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719245	C₂	1	2	yes	maximal, complemented
20	#11719238	C₂	1	1	yes	maximal, characteristic, complemented
21	D₁₃×#117	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×#6129	C₂²	1	1	yes	characteristic
25	C₂×#6127	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₃	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	—
30	C₁₃×#121	C₂²	1	1	yes	characteristic
31	C₁₃×#121	C₂²	1	2	yes	—
32	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
33	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
35	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#117	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	#88193	C₂²	1	2	yes	—
39	#88193	C₂²	1	1	yes	characteristic
40	#88193	C₂²	1	2	yes	complemented
41	#88192	C₂²	1	2	yes	—
42	#88192	C₂²	1	1	yes	characteristic
43	#88192	C₂²	1	2	yes	—
44	#88192	C₂²	1	1	yes	characteristic, complemented
45	#88191	C₂²	1	1	yes	characteristic
46	#88191	C₂²	1	2	yes	—
47	#88190	C₂²	1	2	yes	—
48	#88190	C₂²	1	2	yes	complemented
49	#88189	C₂²	1	2	yes	—
50	D₄×Dic₁₃	C₂²	1	2	yes	—
51	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
52	#88184	C₂²	1	2	yes	—
53	#88183	C₂²	1	2	yes	—
54	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
55	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
58	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
59	#88180	C₂²	1	1	yes	characteristic
60	#88180	C₂²	1	1	yes	characteristic, complemented
61	#88180	C₂²	1	2	yes	complemented
62	#88180	C₂²	1	2	yes	complemented
63	#88178	C₂²	1	1	yes	characteristic
64	#88178	C₂²	1	1	yes	characteristic, complemented
65	C₂×#6101	C₂²	1	2	yes	complemented
66	#88152	C₂²	1	2	yes	—
67	#88152	C₂²	1	2	yes	—
68	#88151	C₂²	1	1	yes	characteristic
69	#88151	C₂²	1	2	yes	—
70	#88151	C₂²	1	1	yes	characteristic, complemented
71	#88150	C₂²	1	1	yes	characteristic
72	#88150	C₂²	1	2	yes	—
73	#88148	C₂²	1	2	yes	—
74	#88148	C₂²	1	1	yes	characteristic
75	#88147	C₂²	1	2	yes	—
76	#88146	C₂²	1	1	yes	characteristic
77	#88146	C₂²	1	1	yes	characteristic
78	#88146	C₂²	1	1	yes	characteristic
79	#88146	C₂²	1	1	yes	characteristic, complemented
80	#88146	C₂²	1	2	yes	complemented
81	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
82	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
83	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
84	#88144	C₂²	1	1	yes	characteristic, complemented
85	#88144	C₂²	1	2	yes	complemented
86	#88143	C₂²	1	2	yes	complemented
87	#88143	C₂²	1	2	yes	complemented
88	#88142	C₂²	1	1	yes	characteristic, complemented
89	#88142	C₂²	1	2	yes	complemented
90	#88141	C₂²	1	2	yes	complemented
91	#88141	C₂²	1	1	yes	characteristic, complemented
92	#88141	C₂²	1	2	yes	complemented
93	#88139	C₂²	1	2	yes	—
94	#88139	C₂²	1	2	yes	—
95	#88139	C₂²	1	2	yes	—
96	#88139	C₂²	1	2	yes	complemented
97	#88138	C₂²	1	1	yes	characteristic
98	#88138	C₂²	1	2	yes	—
99	#88137	C₂²	1	1	yes	characteristic
100	#88137	C₂²	1	2	yes	—
101	#88136	C₂²	1	1	yes	characteristic
102	#88135	C₂²	1	2	yes	—
103	#88135	C₂²	1	2	yes	—
104	#88135	C₂²	1	2	yes	complemented
105	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
106	#88133	C₂²	1	2	yes	—
107	#88133	C₂²	1	2	yes	—
108	#88133	C₂²	1	2	yes	complemented
109	#88133	C₂²	1	2	yes	complemented
110	#88132	C₂²	1	1	yes	characteristic
111	#88132	C₂²	1	2	yes	complemented
112	#88131	C₂²	1	2	yes	—
113	#88131	C₂²	1	2	yes	complemented
114	#88131	C₂²	1	2	yes	complemented
115	#88130	C₂²	1	2	yes	complemented
116	C₄×D₅₂	C₂²	1	1	yes	characteristic
117	#88126	C₂²	1	2	yes	—
118	#88126	C₂²	1	1	yes	characteristic
119	C₄²×D₁₃	C₂²	1	2	yes	—
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	1	yes	characteristic
124	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₁₃	C₂³	1	2	yes	—
126	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₃	C₂³	1	2	yes	—
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	1	yes	characteristic
134	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
139	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
140	C₂²×Dic₁₃	C₂³	1	2	yes	—
141	C₂²×Dic₁₃	C₂³	1	2	yes	—
142	#6129	—	2	4	no	—
143	#6127	—	2	4	no	—
144	C₂×D₅₂	C₂³	1	1	yes	characteristic
145	C₂×D₅₂	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₁₃	—	2	4	no	—
147	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₃	C₂³	1	2	yes	—
152	C₂×C₄×D₁₃	C₂³	1	2	yes	—
153	C₂×C₄×D₁₃	C₂³	1	2	yes	—
154	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
155	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
156	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
157	C₂×Dic₂₆	C₂³	1	2	yes	—
158	C₂×Dic₂₆	C₂³	1	2	yes	—
159	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₄²×C₁₃	C₂³	1	1	yes	characteristic
173	C₄²×C₁₃	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	2	yes	—
179	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
183	#6103	C₂³	1	2	yes	—
184	#6103	C₂³	1	2	yes	—
185	#6103	C₂³	1	1	yes	characteristic
186	#6103	C₂³	1	1	yes	characteristic
187	#6103	C₂³	1	1	yes	characteristic
188	#6103	C₂³	1	1	yes	characteristic
189	#6103	C₂³	1	1	yes	characteristic
190	#6103	C₂³	1	2	yes	—
191	#6103	C₂³	1	2	yes	—
192	#6103	C₂³	1	2	yes	—
193	#6103	C₂³	1	1	yes	characteristic
194	#6103	C₂³	1	2	yes	—
195	C₄⋊Dic₁₃	C₂³	1	2	yes	—
196	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₁₃	C₂³	1	2	yes	—
198	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₁₃	C₂³	1	2	yes	—
202	C₄⋊Dic₁₃	C₂³	1	2	yes	—
203	#6101	C₂³	1	1	yes	characteristic
204	#6101	C₂³	1	2	yes	—
205	#6101	C₂³	1	2	yes	—
206	#6101	C₂³	1	2	yes	—
207	#6101	C₂³	1	2	yes	—
208	#6101	C₂³	1	1	yes	characteristic
209	#6101	C₂³	1	1	yes	characteristic
210	#6101	C₂³	1	2	yes	—
211	#6101	C₂³	1	2	yes	—
212	#6101	C₂³	1	1	yes	characteristic
213	#6101	C₂³	1	2	yes	—
214	#6101	C₂³	1	2	yes	—
215	#6101	C₂³	1	2	yes	—
216	C₄×Dic₁₃	C₂³	1	2	yes	—
217	C₄×Dic₁₃	C₂³	1	2	yes	—
218	C₄×Dic₁₃	C₂³	1	2	yes	—
219	C₄×Dic₁₃	C₂³	1	2	yes	—
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	2	yes	—
224	C₄×Dic₁₃	C₂³	1	2	yes	—
225	#3493	—	13	1	no	maximal, Sylow
226	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₂³×C₁₃	C₂⁴	1	2	yes	—
229	C₂²×D₁₃	—	2	2	no	—
230	C₂²×D₁₃	—	4	1	no	—
231	C₂²×D₁₃	—	4	1	no	—
232	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
233	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
234	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
235	D₄×C₁₃	—	2	2	no	—
236	D₄×C₁₃	—	4	1	no	—
237	D₄×C₁₃	—	4	2	no	—
238	D₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	4	2	no	—
242	C₂×C₄×C₁₃	—	4	2	no	—
243	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
244	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
248	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
249	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂²⋊D₁₃	—	2	2	no	—
252	C₂²⋊D₁₃	—	2	4	no	—
253	C₂²⋊D₁₃	—	2	2	no	—
254	C₂²⋊D₁₃	—	4	1	no	—
255	C₂²⋊D₁₃	—	4	2	no	—
256	C₂²⋊D₁₃	—	4	2	no	—
257	C₂²⋊D₁₃	—	4	1	no	—
258	C₂×Dic₁₃	—	2	2	no	—
259	C₂×Dic₁₃	—	2	4	no	—
260	C₂×Dic₁₃	—	4	2	no	—
261	C₂×Dic₁₃	C₂⁴	1	2	yes	—
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	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
270	D₅₂	—	2	2	no	—
271	D₅₂	—	4	1	no	—
272	C₄×D₁₃	—	2	2	no	—
273	C₄×D₁₃	—	2	2	no	—
274	C₄×D₁₃	—	2	2	no	—
275	C₄×D₁₃	—	2	2	no	—
276	C₄×D₁₃	—	4	2	no	—
277	C₄×D₁₃	—	4	2	no	—
278	C₄×D₁₃	—	4	2	no	—
279	C₄×D₁₃	#41	1	4	yes	—
280	Dic₂₆	—	2	2	no	—
281	Dic₂₆	—	2	2	no	—
282	Dic₂₆	—	4	2	no	—
283	Dic₂₆	—	4	2	no	—
284	#556	—	13	2	no	—
285	#556	—	13	1	no	—
286	#556	—	13	1	no	—
287	#555	—	13	2	no	—
288	#555	—	13	1	no	—
289	#555	—	13	1	no	—
290	#553	—	13	1	no	—
291	#553	—	13	2	no	—
292	#553	D₁₃	1	1	yes	characteristic, complemented
293	#552	—	13	1	no	—
294	#552	—	13	2	no	—
295	#552	—	13	1	no	—
296	#544	—	13	1	no	—
297	#538	—	13	2	no	—
298	#538	—	13	2	no	—
299	#537	—	13	1	no	—
300	#529	—	13	2	no	—
301	#529	—	13	2	no	—
302	#525	—	13	1	no	—
303	#525	—	13	1	no	—
304	#520	—	13	1	no	—
305	#520	—	13	1	no	—
306	C₂×#117	—	13	1	no	—
307	C₂²×C₁₃	—	2	2	no	—
308	C₂²×C₁₃	—	2	1	no	—
309	C₂²×C₁₃	—	2	1	no	—
310	C₂²×C₁₃	—	2	2	no	—
311	C₂²×C₁₃	—	2	2	no	—
312	C₂²×C₁₃	—	2	1	no	—
313	C₂²×C₁₃	—	2	1	no	—
314	C₂²×C₁₃	—	2	1	no	—
315	C₂²×C₁₃	—	2	1	no	—
316	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
317	C₂×D₁₃	—	2	1	no	—
318	C₂×D₁₃	—	2	1	no	—
319	C₂×D₁₃	—	2	1	no	—
320	C₂×D₁₃	—	2	1	no	—
321	C₂×D₁₃	—	2	1	no	—
322	C₂×D₁₃	—	2	1	no	—
323	C₂×D₁₃	—	2	1	no	—
324	C₂×D₁₃	—	2	1	no	—
325	C₂×D₁₃	—	4	4	no	—
326	C₂×D₁₃	C₂×#41	1	2	yes	—
327	C₄×C₁₃	—	2	1	no	—
328	C₄×C₁₃	—	2	1	no	—
329	C₄×C₁₃	—	2	1	no	—
330	C₄×C₁₃	—	2	2	no	—
331	C₄×C₁₃	—	2	2	no	—
332	C₄×C₁₃	—	2	2	no	—
333	C₄×C₁₃	—	2	1	no	—
334	C₄×C₁₃	C₂×#41	1	2	yes	—
335	Dic₁₃	—	2	1	no	—
336	Dic₁₃	—	2	2	no	—
337	Dic₁₃	—	2	1	no	—
338	Dic₁₃	—	2	1	no	—
339	Dic₁₃	—	2	2	no	—
340	Dic₁₃	—	2	2	no	—
341	Dic₁₃	—	2	2	no	—
342	Dic₁₃	—	2	1	no	—
343	Dic₁₃	C₂×#41	1	2	yes	—
344	C₂×#41	—	13	1	no	—
345	C₂×#41	—	13	1	no	—
346	C₂³×C₄	—	13	1	no	—
347	C₄⋊Q₈	—	13	2	no	—
348	C₄⋊Q₈	—	13	1	no	—
349	C₄⋊Q₈	—	13	1	no	—
350	#126	—	13	2	no	—
351	#126	—	13	2	no	—
352	#126	—	13	2	no	—
353	#126	—	13	2	no	—
354	#126	—	13	2	no	—
355	#126	—	13	2	no	—
356	#126	—	13	2	no	—
357	#126	C₂×D₁₃	1	2	yes	complemented
358	#125	—	13	2	no	—
359	#125	—	13	2	no	—
360	#125	—	13	2	no	—
361	#125	—	13	1	no	—
362	#125	C₂×D₁₃	1	1	yes	characteristic, complemented
363	#124	—	13	2	no	—
364	#124	—	13	2	no	—
365	#124	—	13	2	no	—
366	#124	—	13	2	no	—
367	#124	—	13	2	no	—
368	#124	—	13	2	no	—
369	#123	—	13	2	no	—
370	#123	—	13	2	no	—
371	#123	—	13	1	no	—
372	#123	—	13	2	no	—
373	#123	—	13	2	no	—
374	#123	—	13	1	no	—
375	#123	C₂×D₁₃	1	2	yes	—
376	C₂²⋊Q₈	—	13	1	no	—
377	C₂²⋊Q₈	—	13	1	no	—
378	C₂²⋊Q₈	—	13	1	no	—
379	C₂²⋊Q₈	—	13	1	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	2	no	—
385	#121	—	13	1	no	—
386	#121	—	13	1	no	—
387	#121	—	13	2	no	—
388	#121	—	13	1	no	—
389	#121	—	13	2	no	—
390	#121	—	13	2	no	—
391	#121	—	13	2	no	—
392	#121	—	13	2	no	—
393	#121	—	13	1	no	—
394	#121	—	13	2	no	—
395	#121	C₂×D₁₃	1	1	yes	characteristic
396	#121	C₂×D₁₃	1	2	yes	—
397	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
398	#120	—	13	1	no	—
399	#120	—	13	2	no	—
400	#120	—	13	1	no	—
401	C₄×Q₈	—	13	2	no	—
402	C₄×Q₈	—	13	1	no	—
403	C₄×Q₈	—	13	2	no	—
404	C₄×Q₈	—	13	1	no	—
405	C₄×Q₈	—	13	2	no	—
406	C₄×D₄	—	13	1	no	—
407	C₄×D₄	—	13	2	no	—
408	C₄×D₄	—	13	2	no	—
409	C₄×D₄	—	13	2	no	—
410	C₄×D₄	—	13	2	no	—
411	C₄×D₄	—	13	1	no	—
412	C₄×D₄	—	13	1	no	—
413	C₄×D₄	—	13	2	no	—
414	C₄×D₄	—	13	2	no	—
415	C₄×D₄	—	13	2	no	—
416	C₄×D₄	—	13	2	no	—
417	C₄×D₄	—	13	1	no	—
418	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
419	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
420	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
421	#117	—	13	1	no	—
422	#117	—	13	1	no	—
423	#117	—	13	2	no	—
424	#117	—	13	2	no	—
425	#117	—	13	1	no	—
426	#117	—	13	1	no	—
427	#117	—	13	1	no	—
428	#117	—	13	1	no	—
429	#117	—	13	2	no	—
430	#117	—	13	2	no	—
431	#117	—	13	2	no	—
432	#117	—	13	2	no	—
433	#117	—	13	2	no	—
434	#117	—	13	1	no	—
435	#117	C₂×D₁₃	1	1	yes	characteristic
436	C₂×C₄⋊C₄	—	13	2	no	—
437	C₂×C₄⋊C₄	—	13	1	no	—
438	C₂×C₄⋊C₄	—	13	1	no	—
439	C₂×C₄⋊C₄	—	13	1	no	—
440	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
441	C₂×C₂²⋊C₄	—	13	2	no	—
442	C₂×C₄²	—	13	2	no	—
443	C₂×C₁₃	—	4	1	no	—
444	C₂×C₁₃	—	4	2	no	—
445	C₂×C₁₃	—	4	1	no	—
446	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
447	C₂×C₁₃	#585	1	1	yes	characteristic
448	C₂×C₁₃	#585	1	1	yes	characteristic
449	D₁₃	—	2	2	no	—
450	D₁₃	—	4	1	no	—
451	D₁₃	—	4	1	no	—
452	C₂⁴	—	13	1	no	—
453	#41	—	26	4	no	—
454	#41	—	26	4	no	—
455	C₂×Q₈	—	13	1	no	—
456	C₂×Q₈	—	13	1	no	—
457	C₂×Q₈	—	13	2	no	—
458	C₂×Q₈	—	13	2	no	—
459	C₂×D₄	—	13	1	no	—
460	C₂×D₄	—	13	2	no	—
461	C₂×D₄	—	13	1	no	—
462	C₂×D₄	—	13	1	no	—
463	C₂×D₄	—	13	2	no	—
464	C₂×D₄	—	13	1	no	—
465	C₂×D₄	—	13	2	no	—
466	C₂×D₄	—	13	1	no	—
467	C₂×D₄	—	13	1	no	—
468	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
469	C₂×D₄	C₂²×D₁₃	1	2	yes	—
470	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
471	C₂×D₄	C₂²×D₁₃	1	2	yes	—
472	C₂²×C₄	—	13	1	no	—
473	C₂²×C₄	—	13	2	no	—
474	C₂²×C₄	—	13	1	no	—
475	C₂²×C₄	—	13	2	no	—
476	C₂²×C₄	—	13	1	no	—
477	C₂²×C₄	—	13	1	no	—
478	C₂²×C₄	—	13	1	no	—
479	C₂²×C₄	—	13	1	no	—
480	C₂²×C₄	—	13	2	no	—
481	C₂²×C₄	—	13	2	no	—
482	C₂²×C₄	—	13	2	no	—
483	C₂²×C₄	—	26	4	no	—
484	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
485	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
486	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
487	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
488	C₄⋊C₄	—	13	2	no	—
489	C₄⋊C₄	—	13	1	no	—
490	C₄⋊C₄	—	13	1	no	—
491	C₄⋊C₄	—	13	2	no	—
492	C₄⋊C₄	—	13	1	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	—	13	1	no	—
501	C₄⋊C₄	—	13	2	no	—
502	C₄⋊C₄	—	13	2	no	—
503	C₄⋊C₄	—	13	2	no	—
504	C₄⋊C₄	—	13	1	no	—
505	C₄⋊C₄	—	13	2	no	—
506	C₄⋊C₄	—	13	2	no	—
507	C₄⋊C₄	—	13	2	no	—
508	C₄⋊C₄	—	13	2	no	—
509	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
510	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
511	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
512	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
513	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
514	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
516	C₂²⋊C₄	—	13	2	no	—
517	C₂²⋊C₄	—	13	1	no	—
518	C₂²⋊C₄	—	13	2	no	—
519	C₂²⋊C₄	—	13	2	no	—
520	C₂²⋊C₄	—	13	2	no	—
521	C₂²⋊C₄	—	13	2	no	—
522	C₂²⋊C₄	—	13	2	no	—
523	C₂²⋊C₄	—	13	1	no	—
524	C₂²⋊C₄	—	13	2	no	—
525	C₂²⋊C₄	—	13	2	no	—
526	C₂²⋊C₄	—	13	2	no	—
527	C₂²⋊C₄	—	13	1	no	—
528	C₂²⋊C₄	—	13	2	no	—
529	C₂²⋊C₄	—	13	1	no	—
530	C₂²⋊C₄	—	13	1	no	—
531	C₂²⋊C₄	—	13	2	no	—
532	C₂²⋊C₄	—	13	2	no	—
533	C₂²⋊C₄	—	13	1	no	—
534	C₂²⋊C₄	—	13	2	no	—
535	C₂²⋊C₄	—	13	1	no	—
536	C₂²⋊C₄	—	13	1	no	—
537	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
538	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
539	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
540	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
541	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
542	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
543	C₄²	—	13	2	no	—
544	C₄²	—	13	2	no	—
545	C₄²	—	13	2	no	—
546	C₄²	—	13	2	no	—
547	C₄²	—	13	2	no	—
548	C₄²	—	13	2	no	—
549	C₄²	—	13	2	no	—
550	C₄²	—	13	2	no	—
551	C₄²	—	13	1	no	—
552	C₄²	C₂²×D₁₃	1	2	yes	—
553	C₄²	C₂²×D₁₃	1	1	yes	characteristic
554	C₁₃	#3493	1	1	yes	characteristic, complemented, Sylow
555	C₂³	—	13	1	no	—
556	C₂³	—	13	1	no	—
557	C₂³	—	13	1	no	—
558	C₂³	—	26	2	no	—
559	C₂³	—	52	1	no	—
560	C₂³	—	52	1	no	—
561	C₂³	C₂³×D₁₃	1	1	yes	characteristic
562	C₂³	C₂³×D₁₃	1	1	yes	characteristic
563	C₂³	C₂³×D₁₃	1	2	yes	—
564	Q₈	—	26	2	no	—
565	Q₈	—	26	2	no	—
566	Q₈	—	52	2	no	—
567	Q₈	—	52	2	no	—
568	D₄	—	2	2	no	—
569	D₄	—	4	2	no	—
570	D₄	—	4	1	no	—
571	D₄	—	4	2	no	—
572	D₄	—	26	2	no	—
573	D₄	—	26	2	no	—
574	D₄	—	26	2	no	—
575	D₄	—	26	4	no	—
576	D₄	—	52	1	no	—
577	D₄	—	52	2	no	—
578	D₄	—	52	2	no	—
579	D₄	—	52	1	no	—
580	D₄	—	52	1	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	13	1	no	—
586	C₂×C₄	—	13	4	no	—
587	C₂×C₄	—	13	1	no	—
588	C₂×C₄	—	13	2	no	—
589	C₂×C₄	—	13	1	no	—
590	C₂×C₄	—	13	2	no	—
591	C₂×C₄	—	13	1	no	—
592	C₂×C₄	—	13	2	no	—
593	C₂×C₄	—	13	2	no	—
594	C₂×C₄	—	13	1	no	—
595	C₂×C₄	—	26	2	no	—
596	C₂×C₄	—	26	2	no	—
597	C₂×C₄	—	26	2	no	—
598	C₂×C₄	—	26	4	no	—
599	C₂×C₄	—	26	2	no	—
600	C₂×C₄	—	26	2	no	—
601	C₂×C₄	—	52	2	no	—
602	C₂×C₄	—	52	2	no	—
603	C₂×C₄	—	52	2	no	—
604	C₂×C₄	—	52	2	no	—
605	C₂×C₄	C₂³×D₁₃	1	2	yes	—
606	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₁₃	1	2	yes	—
610	C₂×C₄	C₂³×D₁₃	1	2	yes	—
611	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	1	no	—
622	C₂²	—	13	2	no	—
623	C₂²	—	26	1	no	—
624	C₂²	—	26	1	no	—
625	C₂²	—	26	1	no	—
626	C₂²	—	26	1	no	—
627	C₂²	—	26	1	no	—
628	C₂²	—	26	1	no	—
629	C₂²	—	26	1	no	—
630	C₂²	—	26	1	no	—
631	C₂²	—	52	4	no	—
632	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	2	no	—
640	C₄	—	13	2	no	—
641	C₄	—	26	1	no	—
642	C₄	—	26	1	no	—
643	C₄	—	26	2	no	—
644	C₄	—	26	2	no	—
645	C₄	—	26	1	no	—
646	C₄	—	26	2	no	—
647	C₄	—	26	2	no	—
648	C₄	—	26	1	no	—
649	C₄	#41×D₁₃	1	2	yes	—
650	C₂	—	4	1	no	—
651	C₂	—	4	1	no	—
652	C₂	—	4	2	no	—
653	C₂	—	26	2	no	—
654	C₂	—	52	1	no	—
655	C₂	—	52	1	no	—
656	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
657	C₂	#11719648	1	1	yes	characteristic
658	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	#3493
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. #11719411	C₂	semidirect
3. #11719407	C₂	semidirect
4. #11719399	C₂	semidirect
5. #11719394	C₂	semidirect
6. #11719362	C₂	semidirect
7. #11719355	C₂	semidirect
8. #11719321	C₂	semidirect
9. #11719321	C₂	semidirect
10. #11719319	C₂	semidirect
11. #11719318	C₂	semidirect
12. #11719313	C₂	semidirect
13. #11719311	C₂	semidirect
14. #11719268	C₂	semidirect
15. #11719262	C₂	semidirect
16. #11719252	C₂	semidirect
17. #11719251	C₂	semidirect
18. #11719247	C₂	semidirect
19. #11719245	C₂	semidirect
20. #11719238	C₂	semidirect
21. D₁₃×#117	C₂	semidirect
22. #11719218	C₂	semidirect
23. #11719209	C₂	semidirect
27. C₁₃×#126	C₂²	semidirect
28. C₁₃×#125	C₂²	semidirect
32. C₁₃×#121	C₂²	semidirect
34. C₄×D₄×C₁₃	C₂²	semidirect
35. C₄×D₄×C₁₃	C₂²	semidirect
37. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
40. #88193	C₂²	semidirect
44. #88192	C₂²	semidirect
48. #88190	C₂²	semidirect
51. D₄×Dic₁₃	C₂²	semidirect
58. C₄×C₂²⋊D₁₃	C₂²	semidirect
60. #88180	C₂²	semidirect
61. #88180	C₂²	semidirect
62. #88180	C₂²	semidirect
64. #88178	C₂²	semidirect
65. C₂×#6101	C₂²	semidirect
70. #88151	C₂²	semidirect
79. #88146	C₂²	semidirect
80. #88146	C₂²	semidirect
83. C₄⋊C₄×D₁₃	C₂²	semidirect
84. #88144	C₂²	semidirect
85. #88144	C₂²	semidirect
86. #88143	C₂²	semidirect
87. #88143	C₂²	semidirect
88. #88142	C₂²	semidirect
89. #88142	C₂²	semidirect
90. #88141	C₂²	semidirect
91. #88141	C₂²	semidirect
92. #88141	C₂²	semidirect
96. #88139	C₂²	semidirect
104. #88135	C₂²	semidirect
108. #88133	C₂²	semidirect
109. #88133	C₂²	semidirect
111. #88132	C₂²	semidirect
113. #88131	C₂²	semidirect
114. #88131	C₂²	semidirect
115. #88130	C₂²	semidirect
120. #88123	C₂²	semidirect
121. C₄×Dic₂₆	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
292. #553	D₁₃	semidirect
357. #126	C₂×D₁₃	semidirect
362. #125	C₂×D₁₃	semidirect
397. #121	C₂×D₁₃	semidirect
419. C₄×D₄	C₂×D₁₃	semidirect
420. C₄×D₄	C₂×D₁₃	semidirect
440. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
554. C₁₃	#3493	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
#11719411	2
#11719407	2
#11719399	2
#11719394	2
#11719362	2
#11719355	2
#11719321	2
#11719319	2
#11719318	2
#11719313	2
#11719311	2
#11719268	2
#11719262	2
#11719252	2
#11719251	2
#11719247	2
#11719245	2
#11719238	2
D₁₃×#117	2
#11719218	2
#11719209	2
#3493	13