Subgroups — #13128875

Order 1664.

1124 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×#520	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719534	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719529	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719287	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719284	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719283	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719273	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719269	C₂	1	2	yes	maximal, complemented
9	#11719261	C₂	1	2	yes	maximal, complemented
10	#11719259	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719257	C₂	1	2	yes	maximal, complemented
12	#11719252	C₂	1	2	yes	maximal, complemented
13	#11719251	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719239	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719236	C₂	1	2	yes	maximal, complemented
18	#11719233	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719232	C₂	1	2	yes	maximal, complemented
20	#11719220	C₂	1	2	yes	maximal, complemented
21	#11719216	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#88150	C₂	1	2	yes	maximal, complemented
23	#11719212	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₂×#6129	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
27	C₂×#6127	C₂²	1	2	yes	complemented
28	C₂²×C₄×D₁₃	C₂²	1	2	yes	—
29	C₂²×Dic₂₆	C₂²	1	2	yes	complemented
30	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
31	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
32	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
35	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
36	C₁₃×#117	C₂²	1	2	yes	complemented
37	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
40	#88201	C₂²	1	1	yes	characteristic
41	#88200	C₂²	1	1	yes	characteristic
42	#88200	C₂²	1	1	yes	characteristic, complemented
43	#88198	C₂²	1	1	yes	characteristic, complemented
44	#88193	C₂²	1	2	yes	—
45	#88193	C₂²	1	2	yes	complemented
46	#88191	C₂²	1	2	yes	—
47	#88189	C₂²	1	2	yes	complemented
48	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
49	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
50	#88184	C₂²	1	1	yes	characteristic
51	#88184	C₂²	1	2	yes	—
52	#88183	C₂²	1	2	yes	—
53	#88183	C₂²	1	2	yes	complemented
54	#88183	C₂²	1	2	yes	complemented
55	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
57	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
58	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
60	C₂×#6103	C₂²	1	2	yes	—
61	C₂×#6103	C₂²	1	2	yes	—
62	#88178	C₂²	1	1	yes	characteristic, complemented
63	#88178	C₂²	1	2	yes	complemented
64	#88178	C₂²	1	2	yes	complemented
65	C₂×#6101	C₂²	1	2	yes	complemented
66	C₂×#6101	C₂²	1	2	yes	complemented
67	#88152	C₂²	1	1	yes	characteristic, complemented
68	#88152	C₂²	1	2	yes	complemented
69	#88152	C₂²	1	2	yes	complemented
70	#88151	C₂²	1	1	yes	characteristic
71	#88150	C₂²	1	1	yes	characteristic
72	#88150	C₂²	1	2	yes	—
73	#88150	C₂²	1	2	yes	—
74	#88150	C₂²	1	2	yes	—
75	#88150	C₂²	1	2	yes	complemented
76	#88150	C₂²	1	2	yes	complemented
77	#88150	C₂²	1	2	yes	complemented
78	#88150	C₂²	1	2	yes	complemented
79	#88150	C₂²	1	2	yes	complemented
80	#88149	C₂²	1	1	yes	characteristic
81	#88148	C₂²	1	1	yes	characteristic
82	#88148	C₂²	1	2	yes	complemented
83	#88148	C₂²	1	2	yes	complemented
84	#88147	C₂²	1	1	yes	characteristic
85	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
86	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
87	#88143	C₂²	1	2	yes	complemented
88	#88143	C₂²	1	2	yes	complemented
89	#88143	C₂²	1	1	yes	characteristic, complemented
90	#88142	C₂²	1	1	yes	characteristic, complemented
91	#88142	C₂²	1	1	yes	characteristic, complemented
92	#88141	C₂²	1	1	yes	characteristic, complemented
93	#88140	C₂²	1	2	yes	—
94	#88139	C₂²	1	1	yes	characteristic, complemented
95	#88139	C₂²	1	2	yes	complemented
96	#88138	C₂²	1	1	yes	characteristic
97	#88137	C₂²	1	1	yes	characteristic
98	#88137	C₂²	1	2	yes	complemented
99	#88136	C₂²	1	2	yes	—
100	#88135	C₂²	1	2	yes	—
101	#88135	C₂²	1	2	yes	complemented
102	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
103	#88133	C₂²	1	1	yes	characteristic, complemented
104	#88132	C₂²	1	2	yes	complemented
105	#88132	C₂²	1	2	yes	complemented
106	#88131	C₂²	1	2	yes	complemented
107	#88130	C₂²	1	2	yes	complemented
108	#88130	C₂²	1	2	yes	complemented
109	#88129	C₂²	1	1	yes	characteristic
110	#88129	C₂²	1	2	yes	complemented
111	C₄×D₅₂	C₂²	1	2	yes	—
112	C₄×D₅₂	C₂²	1	1	yes	characteristic
113	C₄×D₅₂	C₂²	1	1	yes	characteristic
114	#88126	C₂²	1	2	yes	—
115	#88126	C₂²	1	1	yes	characteristic, complemented
116	#88126	C₂²	1	2	yes	complemented
117	C₄²×D₁₃	C₂²	1	1	yes	characteristic
118	#88124	C₂²	1	2	yes	complemented
119	#88123	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₂₆	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	C₁₃×#41	—	2	4	no	—
125	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₃	C₂³	1	2	yes	—
127	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
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	C₂²×C₄×C₁₃	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	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
138	C₂²×Dic₁₃	C₂³	1	2	yes	—
139	C₂²×Dic₁₃	C₂³	1	2	yes	—
140	C₂²×Dic₁₃	C₂³	1	2	yes	—
141	#6129	—	2	4	no	—
142	D₄×D₁₃	—	2	4	no	—
143	#6127	—	4	4	no	—
144	C₂×D₅₂	C₂³	1	1	yes	characteristic
145	C₂×D₅₂	C₂³	1	1	yes	characteristic
146	C₂×D₅₂	C₂³	1	2	yes	—
147	C₂×C₄×D₁₃	—	4	4	no	—
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	1	yes	characteristic
152	C₂×C₄×D₁₃	C₂³	1	2	yes	—
153	C₂×C₄×D₁₃	C₂³	1	2	yes	—
154	C₂×C₄×D₁₃	C₂³	1	2	yes	—
155	C₂×C₄×D₁₃	C₂³	1	2	yes	—
156	C₂×Dic₂₆	—	4	4	no	—
157	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
158	C₂×Dic₂₆	C₂³	1	2	yes	—
159	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
160	C₂×Dic₂₆	C₂³	1	2	yes	—
161	C₂×Dic₂₆	C₂³	1	2	yes	—
162	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
172	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₄²×C₁₃	C₂³	1	1	yes	characteristic
174	C₄²×C₁₃	C₂³	1	1	yes	characteristic
175	C₄²×C₁₃	C₂³	1	2	yes	—
176	C₄²×C₁₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
182	#6103	C₂³	1	2	yes	—
183	#6103	C₂³	1	2	yes	—
184	#6103	C₂³	1	2	yes	—
185	#6103	C₂³	1	1	yes	characteristic
186	#6103	C₂³	1	2	yes	—
187	#6103	C₂³	1	1	yes	characteristic
188	#6103	C₂³	1	2	yes	—
189	#6103	C₂³	1	2	yes	—
190	#6103	C₂³	1	1	yes	characteristic
191	#6103	C₂³	1	1	yes	characteristic
192	#6103	C₂³	1	2	yes	—
193	#6103	C₂³	1	2	yes	—
194	#6103	C₂³	1	2	yes	—
195	#6103	C₂³	1	2	yes	—
196	#6103	C₂³	1	1	yes	characteristic
197	#6103	C₂³	1	1	yes	characteristic
198	#6103	C₂³	1	2	yes	—
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	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
205	#6101	C₂³	1	2	yes	—
206	#6101	C₂³	1	1	yes	characteristic
207	#6101	C₂³	1	2	yes	—
208	#6101	C₂³	1	1	yes	characteristic
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	2	yes	—
214	#6101	C₂³	1	2	yes	—
215	#6101	C₂³	1	1	yes	characteristic
216	#6101	C₂³	1	1	yes	characteristic
217	#6101	C₂³	1	2	yes	—
218	#6101	C₂³	1	2	yes	—
219	#6101	C₂³	1	1	yes	characteristic
220	#6101	C₂³	1	1	yes	characteristic
221	#6101	C₂³	1	2	yes	—
222	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₃	C₂³	1	2	yes	—
224	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
225	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
226	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₃	C₂³	1	2	yes	—
228	#3520	—	13	1	no	maximal, Sylow
229	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂³×C₁₃	C₂⁴	1	2	yes	—
231	C₂²×D₁₃	—	2	4	no	—
232	C₂²×D₁₃	—	2	4	no	—
233	C₂²×D₁₃	—	4	2	no	—
234	C₂²×D₁₃	C₂⁴	1	2	yes	—
235	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
236	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
237	Q₈×C₁₃	—	2	2	no	—
238	D₄×C₁₃	—	2	4	no	—
239	D₄×C₁₃	#41	1	4	yes	complemented
240	C₂×C₄×C₁₃	—	2	4	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	4	2	no	—
243	C₂×C₄×C₁₃	—	4	2	no	—
244	C₂×C₄×C₁₃	—	4	2	no	—
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	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
252	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂²⋊D₁₃	—	2	4	no	—
255	C₂²⋊D₁₃	—	2	4	no	—
256	C₂²⋊D₁₃	—	2	2	no	—
257	C₂²⋊D₁₃	—	2	2	no	—
258	C₂²⋊D₁₃	—	4	2	no	—
259	C₂×Dic₁₃	—	2	4	no	—
260	C₂×Dic₁₃	—	2	4	no	—
261	C₂×Dic₁₃	—	4	2	no	—
262	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₃	C₂⁴	1	2	yes	—
266	C₂×Dic₁₃	C₂⁴	1	2	yes	—
267	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₁₃	C₂⁴	1	2	yes	—
270	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
271	D₅₂	—	2	2	no	—
272	D₅₂	—	2	2	no	—
273	D₅₂	—	4	2	no	—
274	C₄×D₁₃	—	2	2	no	—
275	C₄×D₁₃	—	2	2	no	—
276	C₄×D₁₃	—	2	2	no	—
277	C₄×D₁₃	—	2	2	no	—
278	C₄×D₁₃	—	2	4	no	—
279	C₄×D₁₃	—	4	2	no	—
280	C₄×D₁₃	—	4	2	no	—
281	C₄×D₁₃	—	4	2	no	—
282	Dic₂₆	—	2	2	no	—
283	Dic₂₆	—	2	2	no	—
284	Dic₂₆	—	2	4	no	—
285	Dic₂₆	—	4	2	no	—
286	Dic₂₆	—	4	2	no	—
287	#556	—	13	1	no	—
288	#554	—	13	1	no	—
289	#554	—	13	1	no	—
290	#552	—	13	2	no	—
291	#551	—	13	2	no	—
292	#551	—	13	2	no	—
293	D₄×Q₈	—	13	1	no	—
294	#548	—	13	2	no	—
295	#547	—	13	1	no	—
296	#547	—	13	1	no	—
297	#546	—	13	1	no	—
298	#546	—	13	1	no	—
299	#542	—	13	1	no	—
300	#542	—	13	1	no	—
301	#539	—	13	2	no	—
302	#539	—	13	2	no	—
303	#533	—	13	1	no	—
304	#529	—	13	1	no	—
305	#525	—	13	2	no	—
306	C₂×C₂²⋊Q₈	—	13	2	no	—
307	#520	—	13	1	no	—
308	#520	D₁₃	1	1	yes	characteristic, complemented
309	C₂×C₄×D₄	—	13	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	C₂×#41	1	4	yes	—
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	2	no	—
321	C₂×D₁₃	—	2	2	no	—
322	C₂×D₁₃	—	2	1	no	—
323	C₂×D₁₃	—	2	1	no	—
324	C₂×D₁₃	—	2	2	no	—
325	C₂×D₁₃	—	4	8	no	—
326	C₂×D₁₃	2₋¹⁺⁴	1	2	yes	—
327	C₄×C₁₃	—	2	1	no	—
328	C₄×C₁₃	—	2	2	no	—
329	C₄×C₁₃	—	2	1	no	—
330	C₄×C₁₃	—	2	2	no	—
331	C₄×C₁₃	—	2	1	no	—
332	C₄×C₁₃	—	2	2	no	—
333	C₄×C₁₃	—	2	1	no	—
334	C₄×C₁₃	—	2	1	no	—
335	C₄×C₁₃	C₂×#41	1	2	yes	—
336	Dic₁₃	—	2	2	no	—
337	Dic₁₃	—	2	1	no	—
338	Dic₁₃	—	2	1	no	—
339	Dic₁₃	—	2	1	no	—
340	Dic₁₃	—	2	2	no	—
341	Dic₁₃	—	2	2	no	—
342	Dic₁₃	—	2	1	no	—
343	Dic₁₃	—	2	1	no	—
344	Dic₁₃	H(5,𝔽₂)	1	2	yes	—
345	C₂×#41	—	13	1	no	—
346	C₂×#41	—	13	2	no	—
347	C₂×#41	C₂×D₁₃	1	1	yes	characteristic
348	C₂²×Q₈	—	13	2	no	—
349	C₂²×D₄	—	13	1	no	—
350	C₂³×C₄	—	13	2	no	—
351	C₄⋊Q₈	—	13	1	no	—
352	C₄⋊Q₈	—	13	1	no	—
353	C₄⋊Q₈	—	13	1	no	—
354	C₄⋊Q₈	—	13	1	no	—
355	#126	—	13	1	no	—
356	#126	—	13	2	no	—
357	#126	—	13	2	no	—
358	#126	—	13	1	no	—
359	#126	—	13	2	no	—
360	#126	—	13	2	no	—
361	#125	—	13	1	no	—
362	#125	—	13	2	no	—
363	#125	—	13	2	no	—
364	#125	—	13	2	no	—
365	#124	—	13	1	no	—
366	#124	—	13	1	no	—
367	#124	—	13	2	no	—
368	#124	—	13	1	no	—
369	#124	—	13	2	no	—
370	#123	—	13	2	no	—
371	#123	—	13	2	no	—
372	#123	—	13	2	no	—
373	#123	—	13	2	no	—
374	#123	—	13	2	no	—
375	#123	—	13	1	no	—
376	#123	—	13	2	no	—
377	#123	—	13	2	no	—
378	#123	—	13	1	no	—
379	#123	—	13	2	no	—
380	C₂²⋊Q₈	—	13	1	no	—
381	C₂²⋊Q₈	—	13	1	no	—
382	C₂²⋊Q₈	—	13	2	no	—
383	C₂²⋊Q₈	—	13	2	no	—
384	C₂²⋊Q₈	—	13	1	no	—
385	C₂²⋊Q₈	—	13	1	no	—
386	C₂²⋊Q₈	—	13	2	no	—
387	C₂²⋊Q₈	—	13	2	no	—
388	C₂²⋊Q₈	—	13	2	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	—	13	1	no	—
394	C₂²⋊Q₈	—	13	2	no	—
395	C₂²⋊Q₈	—	13	2	no	—
396	C₂²⋊Q₈	—	13	2	no	—
397	#121	—	13	2	no	—
398	#121	—	13	2	no	—
399	#121	—	13	2	no	—
400	#121	—	13	1	no	—
401	#121	—	13	1	no	—
402	#121	—	13	1	no	—
403	#120	—	13	2	no	—
404	#120	—	13	2	no	—
405	C₄×Q₈	—	13	1	no	—
406	C₄×Q₈	—	13	1	no	—
407	C₄×Q₈	—	13	1	no	—
408	C₄×Q₈	—	13	2	no	—
409	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
410	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
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	1	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	1	no	—
422	C₄×D₄	—	13	2	no	—
423	C₄×D₄	—	13	1	no	—
424	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
425	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
426	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
427	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
428	#117	—	13	2	no	—
429	#117	—	13	1	no	—
430	#117	—	13	2	no	—
431	#117	—	13	2	no	—
432	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
433	#117	C₂×D₁₃	1	2	yes	complemented
434	C₂×C₄⋊C₄	—	13	2	no	—
435	C₂×C₄⋊C₄	—	13	2	no	—
436	C₂×C₄⋊C₄	—	13	1	no	—
437	C₂×C₄⋊C₄	—	13	1	no	—
438	C₂×C₄⋊C₄	C₂×D₁₃	1	2	yes	complemented
439	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
440	C₂×C₂²⋊C₄	—	13	2	no	—
441	C₂×C₂²⋊C₄	—	13	2	no	—
442	C₂×C₂²⋊C₄	—	13	2	no	—
443	C₂×C₄²	—	13	1	no	—
444	C₂×C₁₃	—	2	4	no	—
445	C₂×C₁₃	—	4	1	no	—
446	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
447	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
448	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
449	D₁₃	—	2	2	no	—
450	D₁₃	—	4	1	no	—
451	D₁₃	—	4	2	no	—
452	C₂⁴	—	13	2	no	—
453	#41	—	2	4	no	—
454	#41	—	26	4	no	—
455	#41	—	52	4	no	—
456	C₂×Q₈	—	13	1	no	—
457	C₂×Q₈	—	13	1	no	—
458	C₂×Q₈	—	13	2	no	—
459	C₂×Q₈	—	13	2	no	—
460	C₂×Q₈	—	13	2	no	—
461	C₂×Q₈	—	52	4	no	—
462	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
463	C₂×D₄	—	13	1	no	—
464	C₂×D₄	—	13	2	no	—
465	C₂×D₄	—	13	2	no	—
466	C₂×D₄	—	13	1	no	—
467	C₂×D₄	—	13	2	no	—
468	C₂×D₄	—	13	1	no	—
469	C₂×D₄	—	13	1	no	—
470	C₂×D₄	—	13	2	no	—
471	C₂×D₄	—	26	4	no	—
472	C₂×D₄	C₂²×D₁₃	1	2	yes	—
473	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
474	C₂²×C₄	—	13	2	no	—
475	C₂²×C₄	—	13	2	no	—
476	C₂²×C₄	—	13	2	no	—
477	C₂²×C₄	—	13	1	no	—
478	C₂²×C₄	—	13	1	no	—
479	C₂²×C₄	—	13	1	no	—
480	C₂²×C₄	—	13	1	no	—
481	C₂²×C₄	—	13	2	no	—
482	C₂²×C₄	—	13	2	no	—
483	C₂²×C₄	—	13	2	no	—
484	C₂²×C₄	—	13	2	no	—
485	C₂²×C₄	—	52	4	no	—
486	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
487	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
488	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
489	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
490	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
491	C₄⋊C₄	—	13	1	no	—
492	C₄⋊C₄	—	13	2	no	—
493	C₄⋊C₄	—	13	1	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	2	no	—
499	C₄⋊C₄	—	13	2	no	—
500	C₄⋊C₄	—	13	2	no	—
501	C₄⋊C₄	—	13	2	no	—
502	C₄⋊C₄	—	13	1	no	—
503	C₄⋊C₄	—	13	1	no	—
504	C₄⋊C₄	—	13	2	no	—
505	C₄⋊C₄	—	13	2	no	—
506	C₄⋊C₄	—	13	2	no	—
507	C₄⋊C₄	—	13	2	no	—
508	C₄⋊C₄	—	13	1	no	—
509	C₄⋊C₄	—	13	1	no	—
510	C₄⋊C₄	—	13	2	no	—
511	C₄⋊C₄	—	13	2	no	—
512	C₄⋊C₄	—	13	1	no	—
513	C₄⋊C₄	—	13	1	no	—
514	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
517	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
519	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
520	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
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	1	no	—
526	C₂²⋊C₄	—	13	1	no	—
527	C₂²⋊C₄	—	13	1	no	—
528	C₂²⋊C₄	—	13	2	no	—
529	C₂²⋊C₄	—	13	2	no	—
530	C₂²⋊C₄	—	13	2	no	—
531	C₂²⋊C₄	—	13	2	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	1	no	—
537	C₂²⋊C₄	—	13	1	no	—
538	C₂²⋊C₄	—	13	2	no	—
539	C₂²⋊C₄	—	13	2	no	—
540	C₂²⋊C₄	—	13	1	no	—
541	C₂²⋊C₄	—	13	2	no	—
542	C₂²⋊C₄	—	13	1	no	—
543	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
546	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
547	C₄²	—	13	1	no	—
548	C₄²	—	13	1	no	—
549	C₄²	—	13	1	no	—
550	C₄²	—	13	2	no	—
551	C₄²	—	13	2	no	—
552	C₄²	—	13	1	no	—
553	C₄²	C₂²×D₁₃	1	1	yes	characteristic
554	C₄²	C₂²×D₁₃	1	2	yes	—
555	C₄²	C₂²×D₁₃	1	2	yes	—
556	C₄²	C₂²×D₁₃	1	1	yes	characteristic
557	C₁₃	#3520	1	1	yes	characteristic, complemented, Sylow
558	C₂³	—	13	1	no	—
559	C₂³	—	13	2	no	—
560	C₂³	—	13	1	no	—
561	C₂³	—	26	4	no	—
562	C₂³	—	26	4	no	—
563	C₂³	—	52	2	no	—
564	C₂³	C₂³×D₁₃	1	1	yes	characteristic
565	C₂³	C₂³×D₁₃	1	2	yes	—
566	Q₈	—	2	2	no	—
567	Q₈	—	26	2	no	—
568	Q₈	—	26	4	no	—
569	Q₈	—	26	2	no	—
570	Q₈	—	52	2	no	—
571	Q₈	—	52	2	no	—
572	D₄	—	2	4	no	—
573	D₄	—	26	2	no	—
574	D₄	—	26	2	no	—
575	D₄	—	26	2	no	—
576	D₄	—	26	4	no	—
577	D₄	—	26	4	no	—
578	D₄	—	26	2	no	—
579	D₄	—	52	2	no	—
580	D₄	—	52	2	no	—
581	D₄	#6127	1	4	yes	complemented
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	13	1	no	—
588	C₂×C₄	—	13	1	no	—
589	C₂×C₄	—	13	1	no	—
590	C₂×C₄	—	13	2	no	—
591	C₂×C₄	—	13	1	no	—
592	C₂×C₄	—	13	1	no	—
593	C₂×C₄	—	13	2	no	—
594	C₂×C₄	—	13	1	no	—
595	C₂×C₄	—	13	2	no	—
596	C₂×C₄	—	26	2	no	—
597	C₂×C₄	—	26	4	no	—
598	C₂×C₄	—	26	2	no	—
599	C₂×C₄	—	26	4	no	—
600	C₂×C₄	—	26	4	no	—
601	C₂×C₄	—	26	2	no	—
602	C₂×C₄	—	26	2	no	—
603	C₂×C₄	—	52	2	no	—
604	C₂×C₄	—	52	2	no	—
605	C₂×C₄	—	52	2	no	—
606	C₂×C₄	—	52	2	no	—
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	1	yes	characteristic
611	C₂×C₄	C₂³×D₁₃	1	2	yes	—
612	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₁₃	1	2	yes	—
614	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
615	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	13	2	no	—
622	C₂²	—	26	1	no	—
623	C₂²	—	26	1	no	—
624	C₂²	—	26	1	no	—
625	C₂²	—	26	2	no	—
626	C₂²	—	26	2	no	—
627	C₂²	—	26	1	no	—
628	C₂²	—	26	1	no	—
629	C₂²	—	26	2	no	—
630	C₂²	—	52	8	no	—
631	C₂²	C₂×#6127	1	4	yes	—
632	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	1	no	—
640	C₄	—	2	1	no	—
641	C₄	—	13	2	no	—
642	C₄	—	26	1	no	—
643	C₄	—	26	1	no	—
644	C₄	—	26	2	no	—
645	C₄	—	26	2	no	—
646	C₄	—	26	2	no	—
647	C₄	—	26	1	no	—
648	C₄	—	26	1	no	—
649	C₄	—	26	1	no	—
650	C₄	C₂×#6127	1	2	yes	—
651	C₂	—	2	4	no	—
652	C₂	—	4	1	no	—
653	C₂	—	26	2	no	—
654	C₂	—	52	2	no	—
655	C₂	—	52	1	no	—
656	C₂	C₂²×#6127	1	1	yes	characteristic
657	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic
658	C₂	D₁₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#520	C₂
hypercenter	#520	D₁₃
hypocenter	C₁₃	#3520
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #520

Complements

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

N	H ≅ G/N	type
1. C₁₃×#520	C₂	semidirect
2. #11719534	C₂	semidirect
3. #11719529	C₂	semidirect
4. #11719287	C₂	semidirect
5. #11719284	C₂	semidirect
6. #11719283	C₂	semidirect
7. #11719273	C₂	semidirect
8. #11719269	C₂	semidirect
9. #11719261	C₂	semidirect
10. #11719259	C₂	semidirect
11. #11719257	C₂	semidirect
12. #11719252	C₂	semidirect
13. #11719251	C₂	semidirect
14. C₄×D₄×D₁₃	C₂	semidirect
15. D₄×Dic₂₆	C₂	semidirect
16. #11719239	C₂	semidirect
17. #11719236	C₂	semidirect
18. #11719233	C₂	semidirect
19. #11719232	C₂	semidirect
20. #11719220	C₂	semidirect
21. #11719216	C₂	semidirect
22. C₂×#88150	C₂	semidirect
23. #11719212	C₂	semidirect
27. C₂×#6127	C₂²	semidirect
29. C₂²×Dic₂₆	C₂²	semidirect
30. C₄×Q₈×C₁₃	C₂²	semidirect
31. C₄×Q₈×C₁₃	C₂²	semidirect
34. C₄×D₄×C₁₃	C₂²	semidirect
35. C₄×D₄×C₁₃	C₂²	semidirect
36. C₁₃×#117	C₂²	semidirect
37. C₁₃×#117	C₂²	semidirect
38. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
39. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
42. #88200	C₂²	semidirect
43. #88198	C₂²	semidirect
45. #88193	C₂²	semidirect
47. #88189	C₂²	semidirect
53. #88183	C₂²	semidirect
54. #88183	C₂²	semidirect
58. C₄×C₂²⋊D₁₃	C₂²	semidirect
59. C₄×C₂²⋊D₁₃	C₂²	semidirect
62. #88178	C₂²	semidirect
63. #88178	C₂²	semidirect
64. #88178	C₂²	semidirect
65. C₂×#6101	C₂²	semidirect
66. C₂×#6101	C₂²	semidirect
67. #88152	C₂²	semidirect
68. #88152	C₂²	semidirect
69. #88152	C₂²	semidirect
75. #88150	C₂²	semidirect
76. #88150	C₂²	semidirect
77. #88150	C₂²	semidirect
78. #88150	C₂²	semidirect
79. #88150	C₂²	semidirect
82. #88148	C₂²	semidirect
83. #88148	C₂²	semidirect
86. C₄⋊C₄×D₁₃	C₂²	semidirect
87. #88143	C₂²	semidirect
88. #88143	C₂²	semidirect
89. #88143	C₂²	semidirect
90. #88142	C₂²	semidirect
91. #88142	C₂²	semidirect
92. #88141	C₂²	semidirect
94. #88139	C₂²	semidirect
95. #88139	C₂²	semidirect
98. #88137	C₂²	semidirect
101. #88135	C₂²	semidirect
103. #88133	C₂²	semidirect
104. #88132	C₂²	semidirect
105. #88132	C₂²	semidirect
106. #88131	C₂²	semidirect
107. #88130	C₂²	semidirect
108. #88130	C₂²	semidirect
110. #88129	C₂²	semidirect
115. #88126	C₂²	semidirect
116. #88126	C₂²	semidirect
118. #88124	C₂²	semidirect
119. #88123	C₂²	semidirect
120. C₄×Dic₂₆	C₂²	semidirect
121. C₄×Dic₂₆	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
239. D₄×C₁₃	#41	semidirect
308. #520	D₁₃	semidirect
409. C₄×Q₈	C₂×D₁₃	semidirect
410. C₄×Q₈	C₂×D₁₃	semidirect
426. C₄×D₄	C₂×D₁₃	semidirect
427. C₄×D₄	C₂×D₁₃	semidirect
432. #117	C₂×D₁₃	semidirect
433. #117	C₂×D₁₃	semidirect
438. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
439. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
557. C₁₃	#3520	semidirect
581. D₄	#6127	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#520	2
#11719534	2
#11719529	2
#11719287	2
#11719284	2
#11719283	2
#11719273	2
#11719269	2
#11719261	2
#11719259	2
#11719257	2
#11719252	2
#11719251	2
C₄×D₄×D₁₃	2
D₄×Dic₂₆	2
#11719239	2
#11719236	2
#11719233	2
#11719232	2
#11719220	2
#11719216	2
C₂×#88150	2
#11719212	2
#3520	13