Subgroups — #13128563

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×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719421	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719420	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719396	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719394	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719366	C₂	1	2	yes	maximal, complemented
7	#11719364	C₂	1	2	yes	maximal, complemented
8	#11719363	C₂	1	2	yes	maximal, complemented
9	#11719360	C₂	1	2	yes	maximal, complemented
10	#11719324	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719321	C₂	1	2	yes	maximal, complemented
12	#11719317	C₂	1	2	yes	maximal, complemented
13	#11719315	C₂	1	2	yes	maximal, complemented
14	#11719311	C₂	1	1	yes	maximal, characteristic, complemented
15	D₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719308	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719306	C₂	1	2	yes	maximal, complemented
18	#11719262	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719253	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719251	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719250	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719239	C₂	1	1	yes	maximal, characteristic, complemented
23	D₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#6129	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×#127	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#123	C₂²	1	2	yes	complemented
33	C₁₃×#123	C₂²	1	2	yes	complemented
34	C₁₃×#121	C₂²	1	1	yes	characteristic
35	C₁₃×#121	C₂²	1	2	yes	complemented
36	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#121	C₂²	1	2	yes	complemented
38	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
41	#88194	C₂²	1	1	yes	characteristic, complemented
42	#88193	C₂²	1	2	yes	—
43	#88193	C₂²	1	2	yes	complemented
44	#88193	C₂²	1	2	yes	complemented
45	#88193	C₂²	1	2	yes	complemented
46	#88192	C₂²	1	1	yes	characteristic
47	#88192	C₂²	1	1	yes	characteristic, complemented
48	#88192	C₂²	1	2	yes	complemented
49	#88192	C₂²	1	2	yes	complemented
50	#88191	C₂²	1	2	yes	—
51	#88191	C₂²	1	2	yes	—
52	#88191	C₂²	1	2	yes	—
53	#88190	C₂²	1	1	yes	characteristic, complemented
54	#88190	C₂²	1	2	yes	complemented
55	#88190	C₂²	1	2	yes	complemented
56	#88189	C₂²	1	2	yes	complemented
57	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
58	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
59	D₄×Dic₁₃	C₂²	1	2	yes	complemented
60	D₄×Dic₁₃	C₂²	1	2	yes	complemented
61	#88184	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
63	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
64	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
66	C₂×#6103	C₂²	1	2	yes	—
67	#88180	C₂²	1	1	yes	characteristic, complemented
68	#88180	C₂²	1	2	yes	complemented
69	#88178	C₂²	1	1	yes	characteristic, complemented
70	C₂×#6101	C₂²	1	2	yes	complemented
71	#88152	C₂²	1	2	yes	complemented
72	#88152	C₂²	1	2	yes	complemented
73	#88151	C₂²	1	2	yes	—
74	#88151	C₂²	1	1	yes	characteristic, complemented
75	#88150	C₂²	1	2	yes	—
76	#88150	C₂²	1	2	yes	complemented
77	#88149	C₂²	1	1	yes	characteristic
78	#88148	C₂²	1	2	yes	complemented
79	#88147	C₂²	1	1	yes	characteristic, complemented
80	#88147	C₂²	1	2	yes	complemented
81	#88146	C₂²	1	1	yes	characteristic
82	#88146	C₂²	1	1	yes	characteristic
83	#88146	C₂²	1	1	yes	characteristic
84	#88146	C₂²	1	2	yes	complemented
85	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
86	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
87	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
88	#88144	C₂²	1	1	yes	characteristic, complemented
89	#88143	C₂²	1	2	yes	complemented
90	#88142	C₂²	1	1	yes	characteristic, complemented
91	#88142	C₂²	1	2	yes	complemented
92	#88141	C₂²	1	1	yes	characteristic, complemented
93	#88140	C₂²	1	2	yes	complemented
94	#88139	C₂²	1	2	yes	complemented
95	#88139	C₂²	1	2	yes	complemented
96	#88138	C₂²	1	2	yes	—
97	#88138	C₂²	1	2	yes	complemented
98	#88137	C₂²	1	2	yes	—
99	#88137	C₂²	1	2	yes	complemented
100	#88137	C₂²	1	2	yes	complemented
101	#88137	C₂²	1	2	yes	complemented
102	#88135	C₂²	1	2	yes	—
103	#88135	C₂²	1	2	yes	complemented
104	#88135	C₂²	1	2	yes	complemented
105	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
106	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
107	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
109	#88133	C₂²	1	2	yes	complemented
110	#88133	C₂²	1	2	yes	complemented
111	#88132	C₂²	1	2	yes	complemented
112	#88131	C₂²	1	1	yes	characteristic, complemented
113	#88131	C₂²	1	1	yes	characteristic, complemented
114	#88131	C₂²	1	2	yes	complemented
115	#88129	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
117	#88126	C₂²	1	1	yes	characteristic
118	#88126	C₂²	1	1	yes	characteristic
119	C₄²×D₁₃	C₂²	1	1	yes	characteristic, complemented
120	C₄²×D₁₃	C₂²	1	1	yes	characteristic, complemented
121	#88123	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₃	C₂³	1	1	yes	characteristic
124	C₂³×D₁₃	C₂³	1	2	yes	—
125	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₃	C₂³	1	2	yes	—
128	C₂×D₄×C₁₃	C₂³	1	2	yes	—
129	C₂×D₄×C₁₃	C₂³	1	2	yes	—
130	C₂×D₄×C₁₃	C₂³	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
133	C₂²×C₄×C₁₃	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	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
141	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
142	C₂²×Dic₁₃	C₂³	1	2	yes	—
143	C₂²×Dic₁₃	C₂³	1	2	yes	—
144	C₂²×Dic₁₃	C₂³	1	2	yes	—
145	#6129	—	2	4	no	—
146	#6129	—	4	4	no	—
147	D₄×D₁₃	—	2	4	no	—
148	D₄×D₁₃	—	4	4	no	—
149	#6127	—	4	4	no	—
150	C₂×D₅₂	C₂³	1	1	yes	characteristic
151	C₂×D₅₂	C₂³	1	2	yes	—
152	C₂×C₄×D₁₃	—	2	4	no	—
153	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
159	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
164	C₂×Dic₂₆	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	1	yes	characteristic
172	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
174	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₄²×C₁₃	C₂³	1	1	yes	characteristic
180	C₄²×C₁₃	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
188	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
189	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
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	1	yes	characteristic
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	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₁₃	C₂³	1	2	yes	—
205	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₁₃	C₂³	1	2	yes	—
208	C₄⋊Dic₁₃	C₂³	1	2	yes	—
209	#6101	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	2	yes	—
215	#6101	C₂³	1	2	yes	—
216	#6101	C₂³	1	2	yes	—
217	#6101	C₂³	1	2	yes	—
218	#6101	C₂³	1	2	yes	—
219	C₄×Dic₁₃	C₂³	1	2	yes	—
220	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
230	C₂³×C₁₃	C₂⁴	1	2	yes	—
231	C₂³×C₁₃	C₂⁴	1	2	yes	—
232	C₂²×D₁₃	—	2	2	no	—
233	C₂²×D₁₃	—	2	2	no	—
234	C₂²×D₁₃	—	2	4	no	—
235	C₂²×D₁₃	—	4	1	no	—
236	C₂²×D₁₃	—	4	2	no	—
237	C₂²×D₁₃	—	4	2	no	—
238	C₂²×D₁₃	C₂⁴	1	2	yes	—
239	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
240	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
241	D₄×C₁₃	—	2	2	no	—
242	D₄×C₁₃	—	2	2	no	—
243	D₄×C₁₃	—	4	2	no	—
244	D₄×C₁₃	—	4	2	no	—
245	D₄×C₁₃	—	4	2	no	—
246	D₄×C₁₃	—	4	2	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	4	2	no	—
249	C₂×C₄×C₁₃	—	4	2	no	—
250	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂²⋊D₁₃	—	2	4	no	—
259	C₂²⋊D₁₃	—	2	4	no	—
260	C₂²⋊D₁₃	—	2	4	no	—
261	C₂²⋊D₁₃	—	2	4	no	—
262	C₂²⋊D₁₃	—	4	2	no	—
263	C₂²⋊D₁₃	—	4	2	no	—
264	C₂²⋊D₁₃	—	4	2	no	—
265	C₂×Dic₁₃	—	2	2	no	—
266	C₂×Dic₁₃	—	2	4	no	—
267	C₂×Dic₁₃	—	4	2	no	—
268	C₂×Dic₁₃	—	4	2	no	—
269	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₃	C₂⁴	1	2	yes	—
273	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₁₃	C₂⁴	1	2	yes	—
276	C₂×Dic₁₃	C₂⁴	1	2	yes	—
277	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
278	D₅₂	—	2	4	no	—
279	D₅₂	—	2	2	no	—
280	C₄×D₁₃	—	2	2	no	—
281	C₄×D₁₃	—	2	2	no	—
282	C₄×D₁₃	—	2	2	no	—
283	C₄×D₁₃	—	2	2	no	—
284	C₄×D₁₃	—	2	2	no	—
285	C₄×D₁₃	—	4	2	no	—
286	C₄×D₁₃	—	4	1	no	—
287	C₄×D₁₃	—	4	1	no	—
288	C₄×D₁₃	—	4	2	no	—
289	C₄×D₁₃	—	4	2	no	—
290	C₄×D₁₃	#41	1	4	yes	complemented
291	Dic₂₆	—	2	2	no	—
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	D₁₃	1	1	yes	characteristic, complemented
307	#535	—	13	1	no	—
308	#532	—	13	1	no	—
309	#532	—	13	1	no	—
310	#529	—	13	1	no	—
311	#529	—	13	1	no	—
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	2	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	—	2	1	no	—
323	C₂²×C₁₃	—	2	2	no	—
324	C₂²×C₁₃	—	2	2	no	—
325	C₂²×C₁₃	—	2	1	no	—
326	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
327	C₂×D₁₃	—	2	1	no	—
328	C₂×D₁₃	—	2	1	no	—
329	C₂×D₁₃	—	2	1	no	—
330	C₂×D₁₃	—	2	1	no	—
331	C₂×D₁₃	—	2	2	no	—
332	C₂×D₁₃	—	2	2	no	—
333	C₂×D₁₃	—	2	2	no	—
334	C₂×D₁₃	—	4	4	no	—
335	C₂×D₁₃	—	8	4	no	—
336	C₂×D₁₃	C₂×#41	1	2	yes	—
337	C₂×D₁₃	H(5,𝔽₂)	1	2	yes	—
338	C₄×C₁₃	—	2	1	no	—
339	C₄×C₁₃	—	2	1	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	—	2	1	no	—
345	C₄×C₁₃	C₂×#41	1	2	yes	—
346	Dic₁₃	—	2	2	no	—
347	Dic₁₃	—	2	1	no	—
348	Dic₁₃	—	2	1	no	—
349	Dic₁₃	—	2	2	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	C₂×D₁₃	1	1	yes	characteristic, complemented
366	#126	—	13	2	no	—
367	#126	—	13	2	no	—
368	#126	—	13	2	no	—
369	#126	—	13	2	no	—
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	—	13	1	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	C₂×D₁₃	1	2	yes	complemented
387	#123	C₂×D₁₃	1	2	yes	complemented
388	C₂²⋊Q₈	—	13	1	no	—
389	C₂²⋊Q₈	—	13	1	no	—
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	#121	—	13	1	no	—
395	#121	—	13	2	no	—
396	#121	—	13	1	no	—
397	#121	—	13	2	no	—
398	#121	—	13	2	no	—
399	#121	—	13	2	no	—
400	#121	—	13	2	no	—
401	#121	—	13	2	no	—
402	#121	—	13	1	no	—
403	#121	—	13	1	no	—
404	#121	—	13	2	no	—
405	#121	—	13	2	no	—
406	#121	C₂×D₁₃	1	1	yes	characteristic
407	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
408	#121	C₂×D₁₃	1	2	yes	complemented
409	#121	C₂×D₁₃	1	2	yes	complemented
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×D₄	—	13	1	no	—
416	C₄×D₄	—	13	1	no	—
417	C₄×D₄	—	13	2	no	—
418	C₄×D₄	—	13	2	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	1	no	—
424	C₄×D₄	—	13	2	no	—
425	C₄×D₄	—	13	2	no	—
426	C₄×D₄	—	13	2	no	—
427	C₄×D₄	—	13	2	no	—
428	C₄×D₄	—	13	1	no	—
429	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
430	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, 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	2	no	—
437	#117	—	13	1	no	—
438	#117	—	13	1	no	—
439	#117	—	13	2	no	—
440	#117	—	13	1	no	—
441	#117	—	13	1	no	—
442	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
443	C₂×C₄⋊C₄	—	13	2	no	—
444	C₂×C₄⋊C₄	—	13	1	no	—
445	C₂×C₄⋊C₄	—	13	1	no	—
446	C₂×C₄⋊C₄	—	13	1	no	—
447	C₂×C₂²⋊C₄	—	13	2	no	—
448	C₂×C₂²⋊C₄	—	13	1	no	—
449	C₂×C₂²⋊C₄	—	13	1	no	—
450	C₂×C₂²⋊C₄	—	13	2	no	—
451	C₂×C₂²⋊C₄	—	13	2	no	—
452	C₂×C₄²	—	13	1	no	—
453	C₂×C₄²	—	13	1	no	—
454	C₂×C₁₃	—	4	1	no	—
455	C₂×C₁₃	—	4	2	no	—
456	C₂×C₁₃	—	4	2	no	—
457	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
458	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂×C₁₃	#585	1	1	yes	characteristic
460	D₁₃	—	2	2	no	—
461	D₁₃	—	2	2	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	1	no	—
469	C₂×Q₈	—	13	2	no	—
470	C₂×Q₈	—	13	2	no	—
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	2	no	—
480	C₂×D₄	—	26	4	no	—
481	C₂×D₄	—	52	4	no	—
482	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
483	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
484	C₂×D₄	C₂²×D₁₃	1	2	yes	—
485	C₂×D₄	C₂²×D₁₃	1	2	yes	—
486	C₂×D₄	C₂²×D₁₃	1	2	yes	—
487	C₂×D₄	C₂²×D₁₃	1	2	yes	—
488	C₂²×C₄	—	13	1	no	—
489	C₂²×C₄	—	13	2	no	—
490	C₂²×C₄	—	13	1	no	—
491	C₂²×C₄	—	13	2	no	—
492	C₂²×C₄	—	13	2	no	—
493	C₂²×C₄	—	13	1	no	—
494	C₂²×C₄	—	13	1	no	—
495	C₂²×C₄	—	13	1	no	—
496	C₂²×C₄	—	13	1	no	—
497	C₂²×C₄	—	13	1	no	—
498	C₂²×C₄	—	13	1	no	—
499	C₂²×C₄	—	13	1	no	—
500	C₂²×C₄	—	13	2	no	—
501	C₂²×C₄	—	13	2	no	—
502	C₂²×C₄	—	13	2	no	—
503	C₂²×C₄	—	26	4	no	—
504	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
505	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
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	2	no	—
516	C₄⋊C₄	—	13	2	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	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
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	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	1	no	—
540	C₂²⋊C₄	—	13	1	no	—
541	C₂²⋊C₄	—	13	2	no	—
542	C₂²⋊C₄	—	13	1	no	—
543	C₂²⋊C₄	—	13	1	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	C₂²×D₁₃	1	1	yes	characteristic
552	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
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	1	no	—
562	C₄²	—	13	1	no	—
563	C₄²	—	13	2	no	—
564	C₄²	—	13	2	no	—
565	C₄²	—	13	2	no	—
566	C₄²	C₂²×D₁₃	1	1	yes	characteristic
567	C₄²	C₂²×D₁₃	1	1	yes	characteristic
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	—	26	2	no	—
573	C₂³	—	26	2	no	—
574	C₂³	—	26	4	no	—
575	C₂³	—	52	1	no	—
576	C₂³	—	52	2	no	—
577	C₂³	—	52	2	no	—
578	C₂³	C₂³×D₁₃	1	1	yes	characteristic
579	C₂³	C₂³×D₁₃	1	2	yes	—
580	C₂³	C₂³×D₁₃	1	2	yes	—
581	Q₈	—	26	2	no	—
582	Q₈	—	52	2	no	—
583	Q₈	—	52	2	no	—
584	D₄	—	2	2	no	—
585	D₄	—	2	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	4	2	no	—
588	D₄	—	4	2	no	—
589	D₄	—	4	2	no	—
590	D₄	—	26	4	no	—
591	D₄	—	26	4	no	—
592	D₄	—	26	4	no	—
593	D₄	—	26	4	no	—
594	D₄	—	26	4	no	—
595	D₄	—	26	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	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	13	1	no	—
603	C₂×C₄	—	13	4	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	—	13	1	no	—
609	C₂×C₄	—	13	1	no	—
610	C₂×C₄	—	13	2	no	—
611	C₂×C₄	—	13	2	no	—
612	C₂×C₄	—	26	2	no	—
613	C₂×C₄	—	26	2	no	—
614	C₂×C₄	—	26	2	no	—
615	C₂×C₄	—	26	2	no	—
616	C₂×C₄	—	26	2	no	—
617	C₂×C₄	—	26	4	no	—
618	C₂×C₄	—	26	2	no	—
619	C₂×C₄	—	52	1	no	—
620	C₂×C₄	—	52	2	no	—
621	C₂×C₄	—	52	1	no	—
622	C₂×C₄	—	52	2	no	—
623	C₂×C₄	—	52	2	no	—
624	C₂×C₄	—	52	2	no	—
625	C₂×C₄	—	52	2	no	—
626	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
630	C₂×C₄	C₂³×D₁₃	1	2	yes	—
631	C₂×C₄	C₂³×D₁₃	1	2	yes	—
632	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
634	C₂²	—	2	1	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	13	2	no	—
644	C₂²	—	13	2	no	—
645	C₂²	—	26	1	no	—
646	C₂²	—	26	1	no	—
647	C₂²	—	26	1	no	—
648	C₂²	—	26	1	no	—
649	C₂²	—	26	2	no	—
650	C₂²	—	26	2	no	—
651	C₂²	—	26	2	no	—
652	C₂²	—	52	4	no	—
653	C₂²	—	104	4	no	—
654	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	1	no	—
662	C₄	—	13	2	no	—
663	C₄	—	26	1	no	—
664	C₄	—	26	2	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	—	4	1	no	—
673	C₂	—	4	2	no	—
674	C₂	—	4	2	no	—
675	C₂	—	26	2	no	—
676	C₂	—	26	2	no	—
677	C₂	—	52	2	no	—
678	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
679	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic
680	C₂	#11719650	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#540	C₂
hypercenter	#540	D₁₃
hypocenter	C₁₃	#3494
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #540

Complements

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

N	H ≅ G/N	type
1. C₁₃×#540	C₂	semidirect
2. #11719421	C₂	semidirect
3. #11719420	C₂	semidirect
4. #11719396	C₂	semidirect
5. #11719394	C₂	semidirect
6. #11719366	C₂	semidirect
7. #11719364	C₂	semidirect
8. #11719363	C₂	semidirect
9. #11719360	C₂	semidirect
10. #11719324	C₂	semidirect
11. #11719321	C₂	semidirect
12. #11719317	C₂	semidirect
13. #11719315	C₂	semidirect
14. #11719311	C₂	semidirect
15. D₁₃×#121	C₂	semidirect
16. #11719308	C₂	semidirect
17. #11719306	C₂	semidirect
18. #11719262	C₂	semidirect
19. #11719253	C₂	semidirect
20. #11719251	C₂	semidirect
21. #11719250	C₂	semidirect
22. #11719239	C₂	semidirect
23. D₁₃×#117	C₂	semidirect
25. C₂×#6129	C₂²	semidirect
28. C₂×#6127	C₂²	semidirect
30. C₁₃×#127	C₂²	semidirect
31. C₁₃×#125	C₂²	semidirect
32. C₁₃×#123	C₂²	semidirect
33. C₁₃×#123	C₂²	semidirect
35. C₁₃×#121	C₂²	semidirect
36. C₁₃×#121	C₂²	semidirect
37. C₁₃×#121	C₂²	semidirect
38. C₄×D₄×C₁₃	C₂²	semidirect
39. C₄×D₄×C₁₃	C₂²	semidirect
40. C₁₃×#117	C₂²	semidirect
41. #88194	C₂²	semidirect
43. #88193	C₂²	semidirect
44. #88193	C₂²	semidirect
45. #88193	C₂²	semidirect
47. #88192	C₂²	semidirect
48. #88192	C₂²	semidirect
49. #88192	C₂²	semidirect
53. #88190	C₂²	semidirect
54. #88190	C₂²	semidirect
55. #88190	C₂²	semidirect
56. #88189	C₂²	semidirect
57. D₄×Dic₁₃	C₂²	semidirect
58. D₄×Dic₁₃	C₂²	semidirect
59. D₄×Dic₁₃	C₂²	semidirect
60. D₄×Dic₁₃	C₂²	semidirect
63. C₄×C₂²⋊D₁₃	C₂²	semidirect
64. C₄×C₂²⋊D₁₃	C₂²	semidirect
65. C₄×C₂²⋊D₁₃	C₂²	semidirect
67. #88180	C₂²	semidirect
68. #88180	C₂²	semidirect
69. #88178	C₂²	semidirect
70. C₂×#6101	C₂²	semidirect
71. #88152	C₂²	semidirect
72. #88152	C₂²	semidirect
74. #88151	C₂²	semidirect
76. #88150	C₂²	semidirect
78. #88148	C₂²	semidirect
79. #88147	C₂²	semidirect
80. #88147	C₂²	semidirect
84. #88146	C₂²	semidirect
86. C₄⋊C₄×D₁₃	C₂²	semidirect
87. C₄⋊C₄×D₁₃	C₂²	semidirect
88. #88144	C₂²	semidirect
89. #88143	C₂²	semidirect
90. #88142	C₂²	semidirect
91. #88142	C₂²	semidirect
92. #88141	C₂²	semidirect
93. #88140	C₂²	semidirect
94. #88139	C₂²	semidirect
95. #88139	C₂²	semidirect
97. #88138	C₂²	semidirect
99. #88137	C₂²	semidirect
100. #88137	C₂²	semidirect
101. #88137	C₂²	semidirect
103. #88135	C₂²	semidirect
104. #88135	C₂²	semidirect
109. #88133	C₂²	semidirect
110. #88133	C₂²	semidirect
111. #88132	C₂²	semidirect
112. #88131	C₂²	semidirect
113. #88131	C₂²	semidirect
114. #88131	C₂²	semidirect
115. #88129	C₂²	semidirect
116. C₄×D₅₂	C₂²	semidirect
119. C₄²×D₁₃	C₂²	semidirect
120. C₄²×D₁₃	C₂²	semidirect
121. #88123	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
290. C₄×D₁₃	#41	semidirect
306. #540	D₁₃	semidirect
365. #127	C₂×D₁₃	semidirect
372. #125	C₂×D₁₃	semidirect
386. #123	C₂×D₁₃	semidirect
387. #123	C₂×D₁₃	semidirect
407. #121	C₂×D₁₃	semidirect
408. #121	C₂×D₁₃	semidirect
409. #121	C₂×D₁₃	semidirect
429. C₄×D₄	C₂×D₁₃	semidirect
430. C₄×D₄	C₂×D₁₃	semidirect
442. #117	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×#540	2
#11719421	2
#11719420	2
#11719396	2
#11719394	2
#11719366	2
#11719364	2
#11719363	2
#11719360	2
#11719324	2
#11719321	2
#11719317	2
#11719315	2
#11719311	2
D₁₃×#121	2
#11719308	2
#11719306	2
#11719262	2
#11719253	2
#11719251	2
#11719250	2
#11719239	2
D₁₃×#117	2
#3494	13