Subgroups — #15768418

Order 3328.

1164 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719450	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718800	C₂	1	1	yes	maximal, characteristic
3	#13123356	C₂	1	1	yes	maximal, characteristic
4	C₂×#11718151	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11718151	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114547	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1738	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#6127	C₂²	1	1	yes	characteristic
9	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₂×#88180	C₂²	1	1	yes	characteristic
13	C₂×#88180	C₂²	1	1	yes	characteristic
14	C₂²×#6099	C₂²	1	1	yes	characteristic
15	#11719450	—	2	2	no	—
16	#11719450	—	2	2	no	—
17	#11719450	—	2	2	no	—
18	#11719450	—	2	2	no	—
19	C₂×#88161	C₄	1	4	yes	complemented
20	C₂×M₁₆×D₁₃	—	2	2	no	—
21	C₂×#88155	—	2	2	no	—
22	#11718800	—	2	2	no	—
23	#11718800	C₄	1	4	yes	complemented
24	C₂×#88065	—	2	2	no	—
25	#11718794	—	2	2	no	—
26	#11718792	C₄	1	2	yes	complemented
27	#11718781	C₄	1	2	yes	complemented
28	#11718774	—	2	2	no	—
29	C₁₃×#341	—	2	2	no	—
30	#11718151	—	2	2	no	—
31	#11718151	—	2	2	no	—
32	#11718147	—	2	2	no	—
33	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
34	C₂²×C₂²⋊D₁₃	—	2	1	no	—
35	C₂×#6127	—	2	1	no	—
36	C₂×#6127	—	2	1	no	—
37	C₂×#6127	—	2	1	no	—
38	C₂×#6127	—	2	1	no	—
39	C₂×#6127	—	2	1	no	—
40	C₂×#6127	—	2	1	no	—
41	C₂×#6127	C₂×C₄	1	2	yes	—
42	C₂×#6127	C₂×C₄	1	2	yes	—
43	C₂×#6127	D₄	1	2	yes	—
44	C₂×#6127	D₄	1	2	yes	—
45	C₂×#6127	D₄	1	2	yes	—
46	C₂×#6127	Q₈	1	2	yes	—
47	C₂²×D₅₂	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₁₃	—	2	1	no	—
49	C₂²×Dic₂₆	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₃×M₁₆	—	2	1	no	—
51	C₂×C₁₃×M₁₆	—	2	1	no	—
52	C₂×C₁₃×M₁₆	—	2	1	no	—
53	C₂×C₁₃×M₁₆	—	2	1	no	—
54	C₂×C₁₃×M₁₆	—	2	1	no	—
55	C₂×C₁₃×M₁₆	—	2	1	no	—
56	C₂×C₁₃×M₁₆	—	2	1	no	—
57	C₂×C₁₃×M₁₆	—	2	1	no	—
58	C₂×C₁₃×M₁₆	—	2	1	no	—
59	C₂×C₁₃×M₁₆	—	2	1	no	—
60	C₂×C₁₃×M₁₆	—	2	1	no	—
61	C₂×C₁₃×M₁₆	—	2	1	no	—
62	C₂×C₁₃×M₁₆	—	2	1	no	—
63	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
64	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
65	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
66	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
67	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
68	C₂²×C₈×C₁₃	—	2	1	no	—
69	C₂²×C₈×C₁₃	—	2	1	no	—
70	C₂²×C₈×C₁₃	—	2	1	no	—
71	C₂×C₂²⋊Dic₁₃	—	2	1	no	—
72	C₂×C₂²⋊Dic₁₃	—	2	1	no	—
73	#88180	—	2	1	no	—
74	#88180	—	2	1	no	—
75	#88180	—	2	1	no	—
76	#88180	—	2	1	no	—
77	#88180	—	2	1	no	—
78	#88180	—	2	1	no	—
79	#88180	C₂×C₄	1	2	yes	—
80	#88180	C₂×C₄	1	2	yes	—
81	C₂×C₄⋊Dic₁₃	—	2	1	no	—
82	C₂×C₄⋊Dic₁₃	—	2	1	no	—
83	C₂×C₄×Dic₁₃	—	2	1	no	—
84	C₂×C₄×Dic₁₃	—	2	1	no	—
85	C₂×#6099	—	2	1	no	—
86	C₂×#6099	—	2	1	no	—
87	C₂×#6099	—	2	1	no	—
88	C₂×#6099	—	2	1	no	—
89	C₂×#6099	D₄	1	2	yes	—
90	C₂×#6099	D₄	1	2	yes	—
91	C₂²×#1055	C₂×C₄	1	2	yes	—
92	#88161	—	2	8	no	—
93	#88161	—	2	8	no	—
94	M₁₆×D₁₃	—	2	8	no	—
95	M₁₆×D₁₃	—	2	8	no	—
96	#88155	—	2	8	no	—
97	#88155	—	2	8	no	—
98	C₂×#6094	—	2	4	no	—
99	C₂×C₈×D₁₃	—	2	4	no	—
100	#88065	—	2	8	no	—
101	#88061	—	2	4	no	—
102	#88056	—	2	4	no	—
103	#10778	—	13	1	no	maximal, Sylow
104	C₂⁴×C₁₃	#41	1	1	yes	characteristic
105	C₂³×D₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
120	C₂×C₂²⋊D₁₃	—	2	2	no	—
121	C₂×C₂²⋊D₁₃	—	2	2	no	—
122	C₂×C₂²⋊D₁₃	—	2	2	no	—
123	C₂×C₂²⋊D₁₃	—	2	2	no	—
124	C₂×C₂²⋊D₁₃	—	2	2	no	—
125	C₂×C₂²⋊D₁₃	—	2	2	no	—
126	C₂²×Dic₁₃	—	2	1	no	—
127	C₂²×Dic₁₃	—	4	1	no	—
128	C₂²×Dic₁₃	—	4	1	no	—
129	#6127	—	2	2	no	—
130	#6127	—	2	2	no	—
131	#6127	—	2	2	no	—
132	#6127	—	2	2	no	—
133	#6127	—	2	2	no	—
134	#6127	—	2	2	no	—
135	#6127	—	2	2	no	—
136	#6127	—	2	2	no	—
137	#6127	—	2	2	no	—
138	#6127	—	2	2	no	—
139	#6127	—	2	2	no	—
140	#6127	—	2	2	no	—
141	#6127	C₂²⋊C₄	1	4	yes	—
142	#6127	C₂²⋊C₄	1	4	yes	—
143	#6127	C₄⋊C₄	1	4	yes	—
144	#6127	C₄⋊C₄	1	4	yes	—
145	C₂×D₅₂	—	2	1	no	—
146	C₂×D₅₂	—	2	1	no	—
147	C₂×D₅₂	—	2	1	no	—
148	C₂×D₅₂	C₄²	1	2	yes	—
149	C₂×D₅₂	C₂²⋊C₄	1	2	yes	—
150	C₂×D₅₂	C₄⋊C₄	1	2	yes	—
151	C₂×C₄×D₁₃	—	2	2	no	—
152	C₂×C₄×D₁₃	—	2	2	no	—
153	C₂×C₄×D₁₃	—	2	2	no	—
154	C₂×C₄×D₁₃	—	2	2	no	—
155	C₂×C₄×D₁₃	—	2	2	no	—
156	C₂×C₄×D₁₃	—	2	2	no	—
157	C₂×Dic₂₆	—	2	1	no	—
158	C₂×Dic₂₆	—	2	1	no	—
159	C₂×Dic₂₆	—	2	1	no	—
160	C₂×Dic₂₆	C₄²	1	2	yes	—
161	C₂×Dic₂₆	C₂²⋊C₄	1	2	yes	—
162	C₂×Dic₂₆	C₄⋊C₄	1	2	yes	—
163	C₁₃×M₁₆	—	2	2	no	—
164	C₁₃×M₁₆	—	2	2	no	—
165	C₁₃×M₁₆	—	2	2	no	—
166	C₁₃×M₁₆	—	2	2	no	—
167	C₁₃×M₁₆	—	2	2	no	—
168	C₁₃×M₁₆	—	2	2	no	—
169	C₁₃×M₁₆	—	2	2	no	—
170	C₁₃×M₁₆	—	4	1	no	—
171	C₁₃×M₁₆	—	4	1	no	—
172	C₁₃×M₁₆	—	4	1	no	—
173	C₁₃×M₁₆	—	4	1	no	—
174	C₁₃×M₁₆	C₂²⋊C₄	1	4	yes	—
175	C₂×C₈×C₁₃	—	2	2	no	—
176	C₂×C₈×C₁₃	—	2	2	no	—
177	C₂×C₈×C₁₃	—	2	2	no	—
178	C₂×C₈×C₁₃	—	2	2	no	—
179	C₂×C₈×C₁₃	—	2	2	no	—
180	C₂×C₈×C₁₃	—	4	1	no	—
181	C₂×C₈×C₁₃	—	4	1	no	—
182	C₂×C₈×C₁₃	—	4	1	no	—
183	C₂×C₈×C₁₃	—	4	1	no	—
184	C₂²⋊Dic₁₃	—	2	2	no	—
185	C₂²⋊Dic₁₃	—	2	2	no	—
186	C₂²⋊Dic₁₃	—	4	1	no	—
187	C₂²⋊Dic₁₃	—	4	1	no	—
188	C₄⋊Dic₁₃	—	2	2	no	—
189	C₄⋊Dic₁₃	—	2	2	no	—
190	C₄⋊Dic₁₃	—	4	1	no	—
191	C₄⋊Dic₁₃	—	4	1	no	—
192	C₄×Dic₁₃	—	2	2	no	—
193	C₄×Dic₁₃	—	2	2	no	—
194	C₄×Dic₁₃	—	4	1	no	—
195	C₄×Dic₁₃	—	4	1	no	—
196	#6099	—	2	2	no	—
197	#6099	—	2	2	no	—
198	#6099	—	2	2	no	—
199	#6099	—	2	2	no	—
200	C₂×#1055	—	2	2	no	—
201	C₂×#1055	—	2	2	no	—
202	C₂×#1055	C₂²⋊C₄	1	4	yes	—
203	#6094	—	2	16	no	—
204	C₈×D₁₃	—	2	16	no	—
205	C₂×#568	—	13	1	no	—
206	C₂×#421	—	13	1	no	—
207	#2896	—	13	1	no	—
208	C₂×#344	—	13	1	no	—
209	C₂×#344	—	13	1	no	—
210	#1738	D₁₃	1	1	yes	characteristic, complemented
211	#1733	—	13	1	no	—
212	C₂³×C₁₃	—	8	1	no	—
213	C₂³×C₁₃	#117	1	1	yes	characteristic
214	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
215	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
216	C₂³×C₁₃	#121	1	1	yes	characteristic
217	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
218	C₂³×C₁₃	#123	1	1	yes	characteristic
219	C₂³×C₁₃	#123	1	1	yes	characteristic
220	C₂²×D₁₃	—	2	2	no	—
221	C₂²×D₁₃	—	2	2	no	—
222	C₂²×D₁₃	—	2	2	no	—
223	C₂²×D₁₃	—	8	2	no	—
224	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
241	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
242	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
243	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
244	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
245	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
246	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
250	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
251	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
252	C₂²⋊D₁₃	—	2	4	no	—
253	C₂²⋊D₁₃	—	2	4	no	—
254	C₂²⋊D₁₃	—	2	4	no	—
255	C₂²⋊D₁₃	—	2	4	no	—
256	C₂×Dic₁₃	—	2	2	no	—
257	C₂×Dic₁₃	—	2	2	no	—
258	C₂×Dic₁₃	—	2	2	no	—
259	C₂×Dic₁₃	—	4	2	no	—
260	C₂×Dic₁₃	—	4	2	no	—
261	C₂×Dic₁₃	—	8	2	no	—
262	C₂×Dic₁₃	—	8	2	no	—
263	D₅₂	—	2	2	no	—
264	D₅₂	—	2	2	no	—
265	D₅₂	—	2	2	no	—
266	D₅₂	#95	1	4	yes	—
267	C₄×D₁₃	—	2	4	no	—
268	C₄×D₁₃	—	2	4	no	—
269	C₄×D₁₃	—	2	4	no	—
270	C₄×D₁₃	—	2	4	no	—
271	Dic₂₆	—	2	2	no	—
272	Dic₂₆	—	2	2	no	—
273	Dic₂₆	—	2	2	no	—
274	Dic₂₆	#95	1	4	yes	—
275	C₈×C₁₃	—	2	4	no	—
276	C₈×C₁₃	—	4	2	no	—
277	C₈×C₁₃	—	4	2	no	—
278	#1055	—	2	4	no	—
279	C₂²×#41	—	13	1	no	—
280	#568	—	26	2	no	—
281	#568	—	26	2	no	—
282	#568	—	26	2	no	—
283	#568	—	26	2	no	—
284	C₂×#131	—	13	4	no	—
285	C₂×#131	—	26	2	no	—
286	C₂²×M₁₆	—	13	1	no	—
287	C₂²×M₁₆	—	26	2	no	—
288	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
289	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
290	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
291	C₂×#117	—	13	1	no	—
292	C₂×#117	—	13	1	no	—
293	#421	—	13	4	no	—
294	#421	—	26	2	no	—
295	C₂×#104	—	26	2	no	—
296	#419	—	13	2	no	—
297	#418	—	13	2	no	—
298	#417	—	26	2	no	—
299	#416	—	26	2	no	—
300	#344	—	26	2	no	—
301	#344	—	26	2	no	—
302	#341	—	2	2	no	—
303	#339	—	26	2	no	—
304	C₂²×C₁₃	—	4	1	no	—
305	C₂²×C₁₃	—	4	1	no	—
306	C₂²×C₁₃	—	4	1	no	—
307	C₂²×C₁₃	—	4	1	no	—
308	C₂²×C₁₃	—	4	1	no	—
309	C₂²×C₁₃	—	4	1	no	—
310	C₂²×C₁₃	—	4	1	no	—
311	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
312	C₂²×C₁₃	#380	1	1	yes	characteristic
313	C₂²×C₁₃	#381	1	1	yes	characteristic
314	C₂²×C₁₃	#385	1	1	yes	characteristic
315	C₂²×C₁₃	#385	1	1	yes	characteristic
316	C₂²×C₁₃	#386	1	1	yes	characteristic
317	C₂²×C₁₃	#386	1	1	yes	characteristic
318	C₂×D₁₃	—	2	4	no	—
319	C₂×D₁₃	—	4	4	no	—
320	C₂×D₁₃	—	8	2	no	—
321	C₂×D₁₃	—	8	2	no	—
322	C₄×C₁₃	C₂×#95	1	1	yes	characteristic
323	C₄×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
324	C₄×C₁₃	#379	1	1	yes	characteristic
325	C₄×C₁₃	#380	1	1	yes	characteristic
326	C₄×C₁₃	#385	1	1	yes	characteristic
327	C₄×C₁₃	#385	1	1	yes	characteristic
328	C₄×C₁₃	#386	1	1	yes	characteristic
329	C₄×C₁₃	#386	1	1	yes	characteristic
330	Dic₁₃	—	2	4	no	—
331	Dic₁₃	—	8	2	no	—
332	Dic₁₃	—	8	2	no	—
333	C₂×#41	—	13	2	no	—
334	C₂×#41	—	13	2	no	—
335	C₂×#41	—	13	2	no	—
336	C₂×#41	—	13	2	no	—
337	C₂×#41	—	13	2	no	—
338	C₂×#41	—	13	2	no	—
339	C₂×#41	—	26	1	no	—
340	C₂×#41	—	26	1	no	—
341	C₂×#41	—	26	1	no	—
342	C₂×#41	—	26	1	no	—
343	C₂×#41	—	26	1	no	—
344	C₂×#41	—	26	1	no	—
345	C₂²×Q₈	—	13	1	no	—
346	C₂²×D₄	—	13	1	no	—
347	C₂²×D₄	—	26	1	no	—
348	C₂³×C₄	—	26	1	no	—
349	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
350	#131	—	26	8	no	—
351	#131	—	26	8	no	—
352	#131	—	26	8	no	—
353	#131	—	26	8	no	—
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	13	2	no	—
368	C₂×M₁₆	—	13	2	no	—
369	C₂×M₁₆	—	26	4	no	—
370	C₂×M₁₆	—	26	8	no	—
371	C₂×M₁₆	—	26	8	no	—
372	C₂×M₁₆	—	26	1	no	—
373	C₂×M₁₆	—	26	1	no	—
374	C₂×M₁₆	—	26	1	no	—
375	C₂×M₁₆	—	26	1	no	—
376	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
377	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
378	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
379	C₂×M₁₆	D₅₂	1	2	yes	—
380	C₂×M₁₆	C₂²⋊D₁₃	1	2	yes	—
381	C₂²×C₈	—	2	1	no	—
382	C₂²×C₈	—	2	1	no	—
383	C₂²×C₈	—	2	1	no	—
384	C₂²×C₈	—	13	2	no	—
385	C₂²×C₈	—	26	4	no	—
386	#117	—	13	2	no	—
387	#117	—	13	2	no	—
388	#117	—	26	1	no	—
389	#117	—	26	1	no	—
390	#117	—	26	1	no	—
391	#117	—	26	1	no	—
392	#117	—	26	1	no	—
393	#117	—	26	1	no	—
394	C₂×C₄⋊C₄	—	26	1	no	—
395	C₂×C₄⋊C₄	—	26	1	no	—
396	C₂×C₂²⋊C₄	—	26	1	no	—
397	C₂×C₂²⋊C₄	—	26	1	no	—
398	C₂×C₄²	—	26	1	no	—
399	C₂×C₄²	—	26	1	no	—
400	#104	—	26	8	no	—
401	#103	—	26	4	no	—
402	#102	—	26	4	no	—
403	C₂×C₁₃	—	2	1	no	—
404	C₂×C₁₃	—	2	1	no	—
405	C₂×C₁₃	—	2	1	no	—
406	C₂×C₁₃	—	2	1	no	—
407	C₂×C₁₃	—	2	1	no	—
408	C₂×C₁₃	—	2	1	no	—
409	C₂×C₁₃	—	2	1	no	—
410	C₂×C₁₃	C₂²⋊#95	1	1	yes	characteristic
411	D₁₃	—	4	4	no	—
412	C₂⁴	—	26	1	no	—
413	C₂⁴	#6131	1	1	yes	characteristic
414	#41	—	13	4	no	—
415	#41	—	13	4	no	—
416	#41	—	13	4	no	—
417	#41	—	13	4	no	—
418	#41	—	26	2	no	—
419	#41	—	26	2	no	—
420	#41	—	26	2	no	—
421	#41	—	26	2	no	—
422	#41	—	26	2	no	—
423	#41	—	26	2	no	—
424	#41	—	26	2	no	—
425	#41	—	26	2	no	—
426	#41	—	26	2	no	—
427	#41	—	26	2	no	—
428	#41	—	26	2	no	—
429	#41	—	26	2	no	—
430	C₂×Q₈	—	13	2	no	—
431	C₂×Q₈	—	13	2	no	—
432	C₂×Q₈	—	13	2	no	—
433	C₂×Q₈	—	26	1	no	—
434	C₂×Q₈	—	26	1	no	—
435	C₂×Q₈	—	26	1	no	—
436	C₂×D₄	—	13	2	no	—
437	C₂×D₄	—	13	2	no	—
438	C₂×D₄	—	13	2	no	—
439	C₂×D₄	—	26	2	no	—
440	C₂×D₄	—	26	2	no	—
441	C₂×D₄	—	26	2	no	—
442	C₂×D₄	—	26	2	no	—
443	C₂×D₄	—	26	2	no	—
444	C₂×D₄	—	26	2	no	—
445	C₂×D₄	—	26	1	no	—
446	C₂×D₄	—	26	1	no	—
447	C₂×D₄	—	26	1	no	—
448	C₂²×C₄	—	26	1	no	—
449	C₂²×C₄	—	26	2	no	—
450	C₂²×C₄	—	26	2	no	—
451	C₂²×C₄	—	26	2	no	—
452	C₂²×C₄	—	26	2	no	—
453	C₂²×C₄	—	26	2	no	—
454	C₂²×C₄	—	26	2	no	—
455	C₂²×C₄	—	52	1	no	—
456	C₂²×C₄	—	52	1	no	—
457	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
458	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
459	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
461	C₂²×C₄	#6127	1	1	yes	characteristic
462	C₂²×C₄	#6127	1	1	yes	characteristic
463	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
464	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
465	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
466	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
467	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
468	C₂²×C₄	#6129	1	1	yes	characteristic
469	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
470	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
471	M₁₆	—	2	2	no	—
472	M₁₆	—	2	2	no	—
473	M₁₆	—	2	2	no	—
474	M₁₆	—	2	2	no	—
475	M₁₆	—	2	2	no	—
476	M₁₆	—	2	2	no	—
477	M₁₆	—	2	2	no	—
478	M₁₆	—	4	1	no	—
479	M₁₆	—	4	1	no	—
480	M₁₆	—	4	1	no	—
481	M₁₆	—	4	1	no	—
482	M₁₆	—	26	16	no	—
483	M₁₆	—	26	2	no	—
484	M₁₆	—	26	2	no	—
485	M₁₆	—	26	2	no	—
486	M₁₆	—	26	2	no	—
487	M₁₆	#6103	1	4	yes	—
488	C₂×C₈	—	2	2	no	—
489	C₂×C₈	—	2	2	no	—
490	C₂×C₈	—	2	2	no	—
491	C₂×C₈	—	2	2	no	—
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	—	4	1	no	—
494	C₂×C₈	—	4	1	no	—
495	C₂×C₈	—	4	1	no	—
496	C₂×C₈	—	4	1	no	—
497	C₂×C₈	—	13	4	no	—
498	C₂×C₈	—	26	16	no	—
499	C₂×C₈	—	26	2	no	—
500	C₂×C₈	—	26	2	no	—
501	C₄⋊C₄	—	26	2	no	—
502	C₄⋊C₄	—	26	2	no	—
503	C₄⋊C₄	—	52	1	no	—
504	C₄⋊C₄	—	52	1	no	—
505	C₂²⋊C₄	—	26	2	no	—
506	C₂²⋊C₄	—	26	2	no	—
507	C₂²⋊C₄	—	52	1	no	—
508	C₂²⋊C₄	—	52	1	no	—
509	C₄²	—	26	2	no	—
510	C₄²	—	26	2	no	—
511	C₄²	—	52	1	no	—
512	C₄²	—	52	1	no	—
513	C₁₃	#10778	1	1	yes	characteristic, complemented, Sylow
514	C₂³	—	8	1	no	—
515	C₂³	—	26	2	no	—
516	C₂³	—	26	2	no	—
517	C₂³	—	26	2	no	—
518	C₂³	—	104	2	no	—
519	C₂³	#88146	1	1	yes	characteristic
520	C₂³	#88147	1	1	yes	characteristic
521	C₂³	#88147	1	1	yes	characteristic
522	C₂³	#88148	1	1	yes	characteristic
523	C₂³	#88148	1	1	yes	characteristic
524	C₂³	#88149	1	1	yes	characteristic
525	C₂³	#88200	1	1	yes	characteristic
526	Q₈	—	13	4	no	—
527	Q₈	—	26	2	no	—
528	Q₈	—	26	2	no	—
529	Q₈	—	26	2	no	—
530	D₄	—	13	4	no	—
531	D₄	—	26	4	no	—
532	D₄	—	26	4	no	—
533	D₄	—	26	4	no	—
534	D₄	—	26	4	no	—
535	D₄	—	26	2	no	—
536	D₄	—	26	2	no	—
537	D₄	—	26	2	no	—
538	C₂×C₄	—	26	2	no	—
539	C₂×C₄	—	26	2	no	—
540	C₂×C₄	—	26	2	no	—
541	C₂×C₄	—	26	4	no	—
542	C₂×C₄	—	26	4	no	—
543	C₂×C₄	—	26	4	no	—
544	C₂×C₄	—	26	4	no	—
545	C₂×C₄	—	52	2	no	—
546	C₂×C₄	—	52	2	no	—
547	C₂×C₄	—	104	2	no	—
548	C₂×C₄	—	104	2	no	—
549	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
550	C₂×C₄	#88126	1	1	yes	characteristic
551	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
552	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
553	C₂×C₄	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
554	C₂×C₄	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
555	C₂×C₄	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
556	C₂×C₄	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
557	C₂×C₄	#88135	1	1	yes	characteristic
558	C₂×C₄	#88135	1	1	yes	characteristic
559	C₂×C₄	#88136	1	1	yes	characteristic
560	C₂×C₄	#88136	1	1	yes	characteristic
561	C₂×C₄	#88137	1	1	yes	characteristic
562	C₂×C₄	#88137	1	1	yes	characteristic
563	C₂×C₄	#88138	1	1	yes	characteristic
564	C₂×C₄	#88138	1	1	yes	characteristic
565	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
566	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
567	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
568	C₂×C₄	#88150	1	1	yes	characteristic
569	C₂×C₄	#88150	1	1	yes	characteristic
570	C₂×C₄	#88151	1	1	yes	characteristic
571	C₂×C₄	C₂×#6103	1	1	yes	characteristic
572	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
573	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
574	C₂×C₄	#88191	1	1	yes	characteristic
575	C₂×C₄	#88191	1	1	yes	characteristic
576	C₂×C₄	#88192	1	1	yes	characteristic
577	C₈	—	2	4	no	—
578	C₈	—	4	2	no	—
579	C₈	—	4	2	no	—
580	C₈	—	26	4	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	26	4	no	—
589	C₂²	—	52	4	no	—
590	C₂²	—	104	2	no	—
591	C₂²	—	104	2	no	—
592	C₂²	#11718325	1	1	yes	characteristic
593	C₂²	#11718326	1	1	yes	characteristic
594	C₂²	#11718326	1	1	yes	characteristic
595	C₂²	#11718327	1	1	yes	characteristic
596	C₂²	#11718648	1	1	yes	characteristic
597	C₂²	#11718650	1	1	yes	characteristic
598	C₂²	#11718650	1	1	yes	characteristic
599	C₄	—	26	4	no	—
600	C₄	—	104	2	no	—
601	C₄	—	104	2	no	—
602	C₄	D₁₃×#95	1	1	yes	characteristic
603	C₄	#11718328	1	1	yes	characteristic
604	C₄	#11718329	1	1	yes	characteristic
605	C₄	#11718329	1	1	yes	characteristic
606	C₄	C₄×#6103	1	1	yes	characteristic
607	C₄	#11718616	1	1	yes	characteristic
608	C₄	#11718617	1	1	yes	characteristic
609	C₄	#11718617	1	1	yes	characteristic
610	C₂	—	2	1	no	—
611	C₂	—	2	1	no	—
612	C₂	—	2	1	no	—
613	C₂	—	2	1	no	—
614	C₂	—	2	1	no	—
615	C₂	—	2	1	no	—
616	C₂	—	2	1	no	—
617	C₂	—	52	4	no	—
618	C₂	#13113057	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11718616
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₁₃×#1738	C₂
socle	C₂×C₁₃	C₂²⋊#95
prime radical	C₂²×#6127	C₂²
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	#1738	D₁₃
hypocenter	C₁₃	#10778
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ #1738

Complements

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

N	H ≅ G/N	type
4. C₂×#11718151	C₂	semidirect
5. C₂×#11718151	C₂	semidirect
6. #13114547	C₂	semidirect
7. C₁₃×#1738	C₂	semidirect
19. C₂×#88161	C₄	semidirect
23. #11718800	C₄	semidirect
26. #11718792	C₄	semidirect
27. #11718781	C₄	semidirect
210. #1738	D₁₃	semidirect
513. C₁₃	#10778	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11719450	2
C₂×#11718800	2
#13123356	2
C₂×#11718151	2
#13114547	2
C₁₃×#1738	2
#10778	13