Subgroups — #13128559

Order 1664.

1142 conjugacy classes of subgroups.

The subgroup lattice has 682 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	#11719414	C₂	1	2	yes	maximal, complemented
3	#11719410	C₂	1	2	yes	maximal, complemented
4	#11719403	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719394	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719387	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719379	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719360	C₂	1	2	yes	maximal, complemented
9	#11719359	C₂	1	2	yes	maximal, complemented
10	#11719332	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719329	C₂	1	1	yes	maximal, characteristic, complemented
12	D₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719301	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719287	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719279	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719267	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719259	C₂	1	2	yes	maximal, complemented
18	#11719250	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719245	C₂	1	2	yes	maximal, complemented
20	#11719237	C₂	1	2	yes	maximal, complemented
21	#11719232	C₂	1	2	yes	maximal, complemented
22	#11719182	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#88126	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#6131	C₂²	1	1	yes	characteristic
25	C₂×#6129	C₂²	1	2	yes	complemented
26	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₁₃	C₂²	1	2	yes	—
28	C₂×#6127	C₂²	1	2	yes	complemented
29	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#126	C₂²	1	2	yes	complemented
31	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#123	C₂²	1	2	yes	complemented
34	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#121	C₂²	1	1	yes	characteristic
36	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
37	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
38	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#117	C₂²	1	2	yes	complemented
40	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
41	#88201	C₂²	1	1	yes	characteristic, complemented
42	#88200	C₂²	1	1	yes	characteristic, complemented
43	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
44	#88194	C₂²	1	1	yes	characteristic, complemented
45	#88193	C₂²	1	2	yes	—
46	#88193	C₂²	1	2	yes	complemented
47	#88192	C₂²	1	1	yes	characteristic
48	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
49	#88184	C₂²	1	1	yes	characteristic
50	#88184	C₂²	1	2	yes	complemented
51	#88184	C₂²	1	1	yes	characteristic, complemented
52	#88184	C₂²	1	2	yes	complemented
53	#88183	C₂²	1	2	yes	complemented
54	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
55	C₂×#6103	C₂²	1	1	yes	characteristic
56	C₂×#6103	C₂²	1	1	yes	characteristic
57	C₂×#6103	C₂²	1	2	yes	—
58	C₂×#6101	C₂²	1	1	yes	characteristic, complemented
59	C₂×#6101	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
61	#88152	C₂²	1	2	yes	complemented
62	#88151	C₂²	1	2	yes	—
63	#88150	C₂²	1	2	yes	—
64	#88150	C₂²	1	2	yes	complemented
65	#88149	C₂²	1	1	yes	characteristic
66	#88149	C₂²	1	2	yes	complemented
67	#88149	C₂²	1	2	yes	complemented
68	#88149	C₂²	1	1	yes	characteristic, complemented
69	#88148	C₂²	1	2	yes	—
70	#88148	C₂²	1	2	yes	complemented
71	#88148	C₂²	1	2	yes	complemented
72	#88148	C₂²	1	2	yes	complemented
73	#88147	C₂²	1	2	yes	—
74	#88147	C₂²	1	2	yes	complemented
75	#88147	C₂²	1	1	yes	characteristic, complemented
76	#88147	C₂²	1	1	yes	characteristic, complemented
77	#88146	C₂²	1	1	yes	characteristic
78	#88146	C₂²	1	2	yes	complemented
79	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
80	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
81	#88144	C₂²	1	1	yes	characteristic, complemented
82	#88143	C₂²	1	2	yes	complemented
83	#88142	C₂²	1	2	yes	complemented
84	#88142	C₂²	1	1	yes	characteristic, complemented
85	#88140	C₂²	1	2	yes	complemented
86	#88140	C₂²	1	2	yes	complemented
87	#88139	C₂²	1	2	yes	complemented
88	#88139	C₂²	1	2	yes	complemented
89	#88138	C₂²	1	2	yes	—
90	#88138	C₂²	1	2	yes	complemented
91	#88138	C₂²	1	2	yes	complemented
92	#88138	C₂²	1	2	yes	complemented
93	#88137	C₂²	1	2	yes	complemented
94	#88136	C₂²	1	2	yes	—
95	#88136	C₂²	1	2	yes	—
96	#88136	C₂²	1	2	yes	—
97	#88135	C₂²	1	2	yes	complemented
98	#88135	C₂²	1	2	yes	complemented
99	#88135	C₂²	1	2	yes	complemented
100	#88135	C₂²	1	2	yes	complemented
101	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
102	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
103	#88133	C₂²	1	2	yes	complemented
104	#88132	C₂²	1	2	yes	complemented
105	#88130	C₂²	1	2	yes	complemented
106	#88129	C₂²	1	2	yes	complemented
107	#88129	C₂²	1	2	yes	complemented
108	#88128	C₂²	1	1	yes	characteristic, complemented
109	C₄×D₅₂	C₂²	1	2	yes	—
110	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
111	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
112	C₄×D₅₂	C₂²	1	2	yes	complemented
113	#88126	C₂²	1	1	yes	characteristic
114	#88126	C₂²	1	1	yes	characteristic
115	#88126	C₂²	1	1	yes	characteristic
116	#88126	C₂²	1	1	yes	characteristic
117	#88126	C₂²	1	1	yes	characteristic, complemented
118	#88126	C₂²	1	1	yes	characteristic, complemented
119	#88126	C₂²	1	1	yes	characteristic, complemented
120	#88126	C₂²	1	1	yes	characteristic, complemented
121	#88126	C₂²	1	2	yes	complemented
122	#88123	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₃	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
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	2	yes	—
136	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
138	C₂²×Dic₁₃	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	1	yes	characteristic
142	#6131	—	2	4	no	—
143	#6129	—	4	4	no	—
144	D₄×D₁₃	—	2	4	no	—
145	D₄×D₁₃	—	4	4	no	—
146	#6127	—	4	4	no	—
147	C₂×D₅₂	C₂³	1	2	yes	—
148	C₂×D₅₂	C₂³	1	1	yes	characteristic
149	C₂×D₅₂	C₂³	1	1	yes	characteristic
150	C₂×D₅₂	C₂³	1	2	yes	—
151	C₂×D₅₂	C₂³	1	2	yes	—
152	C₂×D₅₂	C₂³	1	2	yes	—
153	C₂×D₅₂	C₂³	1	2	yes	—
154	C₂×C₄×D₁₃	—	2	4	no	—
155	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
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×C₄×D₁₃	C₂³	1	2	yes	—
164	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
165	C₂×Dic₂₆	C₂³	1	2	yes	—
166	C₂×Dic₂₆	C₂³	1	2	yes	—
167	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₄²×C₁₃	C₂³	1	1	yes	characteristic
179	C₄²×C₁₃	C₂³	1	1	yes	characteristic
180	C₄²×C₁₃	C₂³	1	1	yes	characteristic
181	C₄²×C₁₃	C₂³	1	1	yes	characteristic
182	C₄²×C₁₃	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₃	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	1	yes	characteristic
191	#6103	C₂³	1	1	yes	characteristic
192	#6103	C₂³	1	1	yes	characteristic
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	C₄⋊Dic₁₃	C₂³	1	2	yes	—
206	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₁₃	C₂³	1	2	yes	—
209	C₄⋊Dic₁₃	C₂³	1	2	yes	—
210	#6101	C₂³	1	1	yes	characteristic
211	#6101	C₂³	1	1	yes	characteristic
212	#6101	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
217	#6101	C₂³	1	1	yes	characteristic
218	#6101	C₂³	1	2	yes	—
219	#6101	C₂³	1	2	yes	—
220	#6101	C₂³	1	2	yes	—
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	1	yes	characteristic
225	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
226	C₄×Dic₁₃	C₂³	1	2	yes	—
227	C₄×Dic₁₃	C₂³	1	2	yes	—
228	#3494	—	13	1	no	maximal, Sylow
229	C₂³×C₁₃	C₂⁴	1	2	yes	—
230	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₃	—	2	2	no	—
232	C₂²×D₁₃	—	2	2	no	—
233	C₂²×D₁₃	—	2	4	no	—
234	C₂²×D₁₃	—	4	1	no	—
235	C₂²×D₁₃	—	4	2	no	—
236	C₂²×D₁₃	—	4	2	no	—
237	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
238	C₂²×D₁₃	C₂⁴	1	2	yes	—
239	C₂²×D₁₃	C₂⁴	1	2	yes	—
240	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
241	Q₈×C₁₃	—	2	2	no	—
242	D₄×C₁₃	—	2	4	no	—
243	D₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	4	2	no	—
247	C₂×C₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂²⋊D₁₃	—	2	4	no	—
258	C₂²⋊D₁₃	—	2	4	no	—
259	C₂²⋊D₁₃	—	2	4	no	—
260	C₂²⋊D₁₃	—	4	2	no	—
261	C₂²⋊D₁₃	—	4	2	no	—
262	C₂²⋊D₁₃	—	4	2	no	—
263	C₂×Dic₁₃	—	2	2	no	—
264	C₂×Dic₁₃	—	2	2	no	—
265	C₂×Dic₁₃	—	4	2	no	—
266	C₂×Dic₁₃	—	4	1	no	—
267	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₁₃	C₂⁴	1	2	yes	—
272	C₂×Dic₁₃	C₂⁴	1	2	yes	—
273	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
275	D₅₂	—	2	4	no	—
276	D₅₂	—	2	2	no	—
277	D₅₂	—	2	2	no	—
278	D₅₂	—	4	2	no	—
279	D₅₂	—	4	2	no	—
280	D₅₂	—	4	2	no	—
281	D₅₂	—	4	2	no	—
282	C₄×D₁₃	—	2	2	no	—
283	C₄×D₁₃	—	2	2	no	—
284	C₄×D₁₃	—	2	2	no	—
285	C₄×D₁₃	—	2	4	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	C₄×D₁₃	—	4	2	no	—
291	C₄×D₁₃	#41	1	4	yes	complemented
292	Dic₂₆	—	4	2	no	—
293	Dic₂₆	—	4	2	no	—
294	#555	—	13	2	no	—
295	#553	—	13	2	no	—
296	#553	—	13	2	no	—
297	#551	—	13	2	no	—
298	#551	—	13	2	no	—
299	#547	—	13	2	no	—
300	#546	—	13	2	no	—
301	#546	—	13	2	no	—
302	#544	—	13	1	no	—
303	#542	—	13	1	no	—
304	#542	—	13	1	no	—
305	#540	—	13	1	no	—
306	#540	—	13	1	no	—
307	#535	—	13	1	no	—
308	#532	—	13	1	no	—
309	#532	—	13	1	no	—
310	#529	—	13	1	no	—
311	#529	D₁₃	1	1	yes	characteristic, complemented
312	#525	—	13	1	no	—
313	C₂×#121	—	13	1	no	—
314	#520	—	13	1	no	—
315	#518	—	13	1	no	—
316	C₂×#117	—	13	1	no	—
317	C₂²×C₁₃	—	2	1	no	—
318	C₂²×C₁₃	—	2	1	no	—
319	C₂²×C₁₃	—	2	2	no	—
320	C₂²×C₁₃	—	2	2	no	—
321	C₂²×C₁₃	—	2	2	no	—
322	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
323	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
324	C₂×D₁₃	—	2	1	no	—
325	C₂×D₁₃	—	2	1	no	—
326	C₂×D₁₃	—	2	1	no	—
327	C₂×D₁₃	—	2	2	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	—	2	2	no	—
334	C₂×D₁₃	—	2	1	no	—
335	C₂×D₁₃	—	4	4	no	—
336	C₂×D₁₃	—	8	4	no	—
337	C₂×D₁₃	C₂×#41	1	2	yes	—
338	C₄×C₁₃	—	2	1	no	—
339	C₄×C₁₃	—	2	2	no	—
340	C₄×C₁₃	—	2	1	no	—
341	C₄×C₁₃	—	2	2	no	—
342	C₄×C₁₃	—	2	1	no	—
343	C₄×C₁₃	—	2	2	no	—
344	C₄×C₁₃	—	2	1	no	—
345	C₄×C₁₃	—	2	1	no	—
346	C₄×C₁₃	C₂×#41	1	2	yes	—
347	Dic₁₃	—	2	1	no	—
348	Dic₁₃	—	2	2	no	—
349	Dic₁₃	—	2	1	no	—
350	Dic₁₃	—	2	2	no	—
351	Dic₁₃	—	2	1	no	—
352	Dic₁₃	—	2	1	no	—
353	Dic₁₃	—	2	1	no	—
354	Dic₁₃	C₂×#41	1	2	yes	—
355	C₂×#41	—	13	1	no	—
356	C₂×#41	—	13	2	no	—
357	C₂×#41	—	13	2	no	—
358	C₂²×D₄	—	13	1	no	—
359	C₂²×D₄	—	13	2	no	—
360	C₂³×C₄	—	13	1	no	—
361	C₄⋊Q₈	—	13	1	no	—
362	C₄⋊Q₈	—	13	2	no	—
363	C₄⋊Q₈	—	13	1	no	—
364	#127	—	13	1	no	—
365	#127	—	13	1	no	—
366	#126	—	13	2	no	—
367	#126	—	13	2	no	—
368	#126	—	13	2	no	—
369	#126	C₂×D₁₃	1	2	yes	complemented
370	#125	—	13	1	no	—
371	#125	—	13	2	no	—
372	#125	C₂×D₁₃	1	1	yes	characteristic, complemented
373	#124	—	13	1	no	—
374	#124	—	13	2	no	—
375	#124	—	13	2	no	—
376	#124	—	13	2	no	—
377	#124	—	13	2	no	—
378	#124	C₂×D₁₃	1	1	yes	characteristic, complemented
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	C₂×D₁₃	1	2	yes	complemented
388	C₂²⋊Q₈	—	13	1	no	—
389	C₂²⋊Q₈	—	13	2	no	—
390	C₂²⋊Q₈	—	13	2	no	—
391	C₂²⋊Q₈	—	13	2	no	—
392	C₂²⋊Q₈	—	13	2	no	—
393	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
394	#121	—	13	1	no	—
395	#121	—	13	2	no	—
396	#121	—	13	2	no	—
397	#121	—	13	1	no	—
398	#121	—	13	1	no	—
399	#121	—	13	2	no	—
400	#121	—	13	2	no	—
401	#121	—	13	1	no	—
402	#121	—	13	1	no	—
403	#121	—	13	2	no	—
404	#121	—	13	2	no	—
405	#121	—	13	2	no	—
406	#121	—	13	2	no	—
407	#121	—	13	2	no	—
408	#121	—	13	2	no	—
409	#121	C₂×D₁₃	1	1	yes	characteristic
410	#120	—	13	2	no	—
411	#120	—	13	2	no	—
412	#120	—	13	2	no	—
413	C₄×Q₈	—	13	1	no	—
414	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
415	C₄×D₄	—	13	1	no	—
416	C₄×D₄	—	13	2	no	—
417	C₄×D₄	—	13	1	no	—
418	C₄×D₄	—	13	1	no	—
419	C₄×D₄	—	13	2	no	—
420	C₄×D₄	—	13	2	no	—
421	C₄×D₄	—	13	2	no	—
422	C₄×D₄	—	13	2	no	—
423	C₄×D₄	—	13	2	no	—
424	C₄×D₄	—	13	2	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	C₂×D₁₃	1	1	yes	characteristic, complemented
430	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
431	#117	—	13	1	no	—
432	#117	—	13	2	no	—
433	#117	—	13	1	no	—
434	#117	—	13	1	no	—
435	#117	—	13	1	no	—
436	#117	—	13	1	no	—
437	#117	—	13	1	no	—
438	#117	—	13	1	no	—
439	#117	—	13	1	no	—
440	#117	—	13	1	no	—
441	#117	—	13	2	no	—
442	#117	C₂×D₁₃	1	2	yes	complemented
443	C₂×C₄⋊C₄	—	13	1	no	—
444	C₂×C₄⋊C₄	—	13	1	no	—
445	C₂×C₄⋊C₄	—	13	1	no	—
446	C₂×C₄⋊C₄	—	13	2	no	—
447	C₂×C₂²⋊C₄	—	13	1	no	—
448	C₂×C₂²⋊C₄	—	13	1	no	—
449	C₂×C₂²⋊C₄	—	13	2	no	—
450	C₂×C₂²⋊C₄	—	13	2	no	—
451	C₂×C₂²⋊C₄	—	13	2	no	—
452	C₂×C₄²	—	13	1	no	—
453	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
454	C₂×C₁₃	—	2	2	no	—
455	C₂×C₁₃	—	4	2	no	—
456	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
457	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
458	C₂×C₁₃	#585	1	1	yes	characteristic
459	D₁₃	—	2	2	no	—
460	D₁₃	—	4	2	no	—
461	D₁₃	—	4	1	no	—
462	D₁₃	—	4	2	no	—
463	C₂⁴	—	13	1	no	—
464	C₂⁴	—	13	2	no	—
465	#41	—	26	4	no	—
466	#41	—	52	4	no	—
467	#41	—	52	4	no	—
468	C₂×Q₈	—	13	2	no	—
469	C₂×Q₈	—	13	2	no	—
470	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
471	C₂×D₄	—	13	2	no	—
472	C₂×D₄	—	13	2	no	—
473	C₂×D₄	—	13	2	no	—
474	C₂×D₄	—	13	2	no	—
475	C₂×D₄	—	13	2	no	—
476	C₂×D₄	—	13	2	no	—
477	C₂×D₄	—	13	2	no	—
478	C₂×D₄	—	13	1	no	—
479	C₂×D₄	—	13	1	no	—
480	C₂×D₄	—	13	2	no	—
481	C₂×D₄	—	13	2	no	—
482	C₂×D₄	—	13	2	no	—
483	C₂×D₄	—	13	2	no	—
484	C₂×D₄	—	26	4	no	—
485	C₂×D₄	—	52	4	no	—
486	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
487	C₂×D₄	C₂²×D₁₃	1	2	yes	—
488	C₂²×C₄	—	13	1	no	—
489	C₂²×C₄	—	13	1	no	—
490	C₂²×C₄	—	13	1	no	—
491	C₂²×C₄	—	13	1	no	—
492	C₂²×C₄	—	13	2	no	—
493	C₂²×C₄	—	13	1	no	—
494	C₂²×C₄	—	13	2	no	—
495	C₂²×C₄	—	13	1	no	—
496	C₂²×C₄	—	13	1	no	—
497	C₂²×C₄	—	13	2	no	—
498	C₂²×C₄	—	13	2	no	—
499	C₂²×C₄	—	13	2	no	—
500	C₂²×C₄	—	13	2	no	—
501	C₂²×C₄	—	13	2	no	—
502	C₂²×C₄	—	26	4	no	—
503	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
504	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
505	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
506	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
507	C₄⋊C₄	—	13	1	no	—
508	C₄⋊C₄	—	13	2	no	—
509	C₄⋊C₄	—	13	1	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	1	no	—
515	C₄⋊C₄	—	13	1	no	—
516	C₄⋊C₄	—	13	1	no	—
517	C₄⋊C₄	—	13	2	no	—
518	C₄⋊C₄	—	13	1	no	—
519	C₄⋊C₄	—	13	2	no	—
520	C₄⋊C₄	—	13	2	no	—
521	C₄⋊C₄	—	13	2	no	—
522	C₄⋊C₄	—	13	2	no	—
523	C₄⋊C₄	—	13	2	no	—
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	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
529	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
530	C₂²⋊C₄	—	13	2	no	—
531	C₂²⋊C₄	—	13	2	no	—
532	C₂²⋊C₄	—	13	1	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	—	13	1	no	—
538	C₂²⋊C₄	—	13	1	no	—
539	C₂²⋊C₄	—	13	1	no	—
540	C₂²⋊C₄	—	13	1	no	—
541	C₂²⋊C₄	—	13	2	no	—
542	C₂²⋊C₄	—	13	2	no	—
543	C₂²⋊C₄	—	13	2	no	—
544	C₂²⋊C₄	—	13	2	no	—
545	C₂²⋊C₄	—	13	2	no	—
546	C₂²⋊C₄	—	13	2	no	—
547	C₂²⋊C₄	—	13	2	no	—
548	C₂²⋊C₄	—	13	2	no	—
549	C₂²⋊C₄	—	13	2	no	—
550	C₂²⋊C₄	—	13	2	no	—
551	C₂²⋊C₄	—	13	2	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	2	yes	—
556	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
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	2	no	—
563	C₄²	C₂²×D₁₃	1	1	yes	characteristic
564	C₄²	C₂²×D₁₃	1	1	yes	characteristic
565	C₄²	C₂²×D₁₃	1	1	yes	characteristic
566	C₄²	C₂²×D₁₃	1	1	yes	characteristic
567	C₄²	C₂²×D₁₃	1	2	yes	—
568	C₁₃	#3494	1	1	yes	characteristic, complemented, Sylow
569	C₂³	—	13	1	no	—
570	C₂³	—	13	1	no	—
571	C₂³	—	13	2	no	—
572	C₂³	—	13	2	no	—
573	C₂³	—	26	2	no	—
574	C₂³	—	26	4	no	—
575	C₂³	—	26	2	no	—
576	C₂³	—	52	1	no	—
577	C₂³	—	52	2	no	—
578	C₂³	—	52	2	no	—
579	C₂³	C₂³×D₁₃	1	2	yes	—
580	C₂³	C₂³×D₁₃	1	1	yes	characteristic
581	Q₈	—	2	2	no	—
582	Q₈	—	52	2	no	—
583	Q₈	—	52	2	no	—
584	D₄	—	2	4	no	—
585	D₄	—	2	2	no	—
586	D₄	—	26	4	no	—
587	D₄	—	26	4	no	—
588	D₄	—	26	4	no	—
589	D₄	—	26	4	no	—
590	D₄	—	26	2	no	—
591	D₄	—	26	2	no	—
592	D₄	—	52	2	no	—
593	D₄	—	52	2	no	—
594	D₄	—	52	2	no	—
595	D₄	—	52	2	no	—
596	D₄	—	52	2	no	—
597	D₄	—	52	2	no	—
598	D₄	—	52	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	13	1	no	—
604	C₂×C₄	—	13	4	no	—
605	C₂×C₄	—	13	1	no	—
606	C₂×C₄	—	13	1	no	—
607	C₂×C₄	—	13	1	no	—
608	C₂×C₄	—	13	1	no	—
609	C₂×C₄	—	13	2	no	—
610	C₂×C₄	—	13	2	no	—
611	C₂×C₄	—	13	1	no	—
612	C₂×C₄	—	26	2	no	—
613	C₂×C₄	—	26	4	no	—
614	C₂×C₄	—	26	2	no	—
615	C₂×C₄	—	26	2	no	—
616	C₂×C₄	—	26	2	no	—
617	C₂×C₄	—	26	2	no	—
618	C₂×C₄	—	52	2	no	—
619	C₂×C₄	—	52	2	no	—
620	C₂×C₄	—	52	2	no	—
621	C₂×C₄	—	52	2	no	—
622	C₂×C₄	—	52	2	no	—
623	C₂×C₄	—	52	1	no	—
624	C₂×C₄	—	52	2	no	—
625	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₁₃	1	2	yes	—
627	C₂×C₄	C₂³×D₁₃	1	2	yes	—
628	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
630	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
631	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
632	C₂×C₄	C₂³×D₁₃	1	2	yes	—
633	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
634	C₂²	—	2	1	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	13	2	no	—
640	C₂²	—	26	1	no	—
641	C₂²	—	26	1	no	—
642	C₂²	—	26	1	no	—
643	C₂²	—	26	2	no	—
644	C₂²	—	26	2	no	—
645	C₂²	—	26	2	no	—
646	C₂²	—	26	2	no	—
647	C₂²	—	26	1	no	—
648	C₂²	—	26	2	no	—
649	C₂²	—	26	2	no	—
650	C₂²	—	26	1	no	—
651	C₂²	—	52	4	no	—
652	C₂²	—	104	4	no	—
653	C₂²	#88256	1	2	yes	—
654	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
655	C₄	—	2	1	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	2	no	—
660	C₄	—	2	1	no	—
661	C₄	—	2	2	no	—
662	C₄	—	2	1	no	—
663	C₄	—	13	2	no	—
664	C₄	—	26	1	no	—
665	C₄	—	26	1	no	—
666	C₄	—	26	1	no	—
667	C₄	—	26	2	no	—
668	C₄	—	26	2	no	—
669	C₄	—	26	1	no	—
670	C₄	—	26	1	no	—
671	C₄	#41×D₁₃	1	2	yes	—
672	C₂	—	2	2	no	—
673	C₂	—	4	2	no	—
674	C₂	—	26	2	no	—
675	C₂	—	52	1	no	—
676	C₂	—	52	2	no	—
677	C₂	—	52	2	no	—
678	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
679	C₂	C₂×#88256	1	1	yes	characteristic
680	C₂	#11719648	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	#3494
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. #11719414	C₂	semidirect
3. #11719410	C₂	semidirect
4. #11719403	C₂	semidirect
5. #11719394	C₂	semidirect
6. #11719387	C₂	semidirect
7. #11719379	C₂	semidirect
8. #11719360	C₂	semidirect
9. #11719359	C₂	semidirect
10. #11719332	C₂	semidirect
11. #11719329	C₂	semidirect
12. D₁₃×#121	C₂	semidirect
13. #11719301	C₂	semidirect
14. #11719287	C₂	semidirect
15. #11719279	C₂	semidirect
16. #11719267	C₂	semidirect
17. #11719259	C₂	semidirect
18. #11719250	C₂	semidirect
19. #11719245	C₂	semidirect
20. #11719237	C₂	semidirect
21. #11719232	C₂	semidirect
22. #11719182	C₂	semidirect
23. C₂×#88126	C₂	semidirect
25. C₂×#6129	C₂²	semidirect
28. C₂×#6127	C₂²	semidirect
30. C₁₃×#126	C₂²	semidirect
31. C₁₃×#125	C₂²	semidirect
32. C₁₃×#124	C₂²	semidirect
33. C₁₃×#123	C₂²	semidirect
34. C₁₃×C₂²⋊Q₈	C₂²	semidirect
36. C₄×Q₈×C₁₃	C₂²	semidirect
37. C₄×D₄×C₁₃	C₂²	semidirect
38. C₄×D₄×C₁₃	C₂²	semidirect
39. C₁₃×#117	C₂²	semidirect
40. C₂×C₄²×C₁₃	C₂²	semidirect
41. #88201	C₂²	semidirect
42. #88200	C₂²	semidirect
43. Q₈×Dic₁₃	C₂²	semidirect
44. #88194	C₂²	semidirect
46. #88193	C₂²	semidirect
48. D₄×Dic₁₃	C₂²	semidirect
50. #88184	C₂²	semidirect
51. #88184	C₂²	semidirect
52. #88184	C₂²	semidirect
53. #88183	C₂²	semidirect
54. C₄×C₂²⋊D₁₃	C₂²	semidirect
58. C₂×#6101	C₂²	semidirect
59. C₂×#6101	C₂²	semidirect
60. C₂×C₄×Dic₁₃	C₂²	semidirect
61. #88152	C₂²	semidirect
64. #88150	C₂²	semidirect
66. #88149	C₂²	semidirect
67. #88149	C₂²	semidirect
68. #88149	C₂²	semidirect
70. #88148	C₂²	semidirect
71. #88148	C₂²	semidirect
72. #88148	C₂²	semidirect
74. #88147	C₂²	semidirect
75. #88147	C₂²	semidirect
76. #88147	C₂²	semidirect
78. #88146	C₂²	semidirect
80. C₄⋊C₄×D₁₃	C₂²	semidirect
81. #88144	C₂²	semidirect
82. #88143	C₂²	semidirect
83. #88142	C₂²	semidirect
84. #88142	C₂²	semidirect
85. #88140	C₂²	semidirect
86. #88140	C₂²	semidirect
87. #88139	C₂²	semidirect
88. #88139	C₂²	semidirect
90. #88138	C₂²	semidirect
91. #88138	C₂²	semidirect
92. #88138	C₂²	semidirect
93. #88137	C₂²	semidirect
97. #88135	C₂²	semidirect
98. #88135	C₂²	semidirect
99. #88135	C₂²	semidirect
100. #88135	C₂²	semidirect
103. #88133	C₂²	semidirect
104. #88132	C₂²	semidirect
105. #88130	C₂²	semidirect
106. #88129	C₂²	semidirect
107. #88129	C₂²	semidirect
108. #88128	C₂²	semidirect
110. C₄×D₅₂	C₂²	semidirect
111. C₄×D₅₂	C₂²	semidirect
112. C₄×D₅₂	C₂²	semidirect
117. #88126	C₂²	semidirect
118. #88126	C₂²	semidirect
119. #88126	C₂²	semidirect
120. #88126	C₂²	semidirect
121. #88126	C₂²	semidirect
122. #88123	C₂²	semidirect
291. C₄×D₁₃	#41	semidirect
311. #529	D₁₃	semidirect
369. #126	C₂×D₁₃	semidirect
372. #125	C₂×D₁₃	semidirect
378. #124	C₂×D₁₃	semidirect
387. #123	C₂×D₁₃	semidirect
393. C₂²⋊Q₈	C₂×D₁₃	semidirect
414. C₄×Q₈	C₂×D₁₃	semidirect
429. C₄×D₄	C₂×D₁₃	semidirect
430. C₄×D₄	C₂×D₁₃	semidirect
442. #117	C₂×D₁₃	semidirect
453. C₂×C₄²	C₂×D₁₃	semidirect
568. C₁₃	#3494	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
#11719414	2
#11719410	2
#11719403	2
#11719394	2
#11719387	2
#11719379	2
#11719360	2
#11719359	2
#11719332	2
#11719329	2
D₁₃×#121	2
#11719301	2
#11719287	2
#11719279	2
#11719267	2
#11719259	2
#11719250	2
#11719245	2
#11719237	2
#11719232	2
#11719182	2
C₂×#88126	2
#3494	13