Subgroups — #15863821

Order 3328.

1312 conjugacy classes of subgroups.

The subgroup lattice has 630 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	#13123399	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11718800	C₂	1	1	yes	maximal, characteristic
4	C₂×#11718800	C₂	1	1	yes	maximal, characteristic
5	#13115073	C₂	1	8	yes	maximal, complemented
6	C₂×#11718151	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114547	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#430	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#6127	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
13	C₂×#88180	C₂²	1	1	yes	characteristic
14	C₂×#88180	C₂²	1	1	yes	characteristic
15	C₂²×#6099	C₂²	1	1	yes	characteristic
16	#11719450	—	2	2	no	—
17	#11719450	—	2	2	no	—
18	#11719450	—	2	2	no	—
19	#11719450	C₂²	1	4	yes	—
20	C₂×#88161	—	2	2	no	—
21	C₂×M₁₆×D₁₃	—	2	2	no	—
22	C₂×#88155	—	2	2	no	—
23	C₁₃×#430	—	2	2	no	—
24	C₁₃×#430	C₂²	1	4	yes	complemented
25	C₂×C₁₃×#108	—	2	2	no	—
26	#11718800	—	2	2	no	—
27	#11718800	C₄	1	4	yes	complemented
28	#11718800	C₄	1	4	yes	complemented
29	#11718800	C₂²	1	4	yes	—
30	C₂×#88065	—	2	2	no	—
31	C₂×#88065	C₂²	1	4	yes	—
32	#11718780	—	2	2	no	—
33	#11718779	C₂²	1	4	yes	complemented
34	#11718763	—	2	2	no	—
35	#11718151	C₂²	1	4	yes	complemented
36	#11718147	C₂²	1	4	yes	complemented
37	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
38	C₂²×C₂²⋊D₁₃	—	2	1	no	—
39	C₂×#6127	—	2	1	no	—
40	C₂×#6127	—	2	1	no	—
41	C₂×#6127	—	2	1	no	—
42	C₂×#6127	—	2	1	no	—
43	C₂×#6127	—	2	1	no	—
44	C₂×#6127	—	2	1	no	—
45	C₂×#6127	C₂×C₄	1	2	yes	—
46	C₂×#6127	C₂×C₄	1	2	yes	—
47	C₂×#6127	D₄	1	2	yes	—
48	C₂×#6127	D₄	1	2	yes	—
49	C₂×#6127	Q₈	1	2	yes	—
50	C₂×#6127	C₂³	1	2	yes	—
51	C₂²×D₅₂	Q₈	1	1	yes	characteristic
52	C₂²×C₄×D₁₃	—	2	1	no	—
53	C₂²×Dic₂₆	Q₈	1	1	yes	characteristic
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	—	2	1	no	—
64	C₂×C₁₃×M₁₆	—	2	1	no	—
65	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
66	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
67	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
68	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
69	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
70	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
71	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
72	C₂²×C₈×C₁₃	—	2	1	no	—
73	C₂²×C₈×C₁₃	—	2	1	no	—
74	C₂²×C₈×C₁₃	—	2	1	no	—
75	C₂×C₂²⋊Dic₁₃	—	2	1	no	—
76	C₂×C₂²⋊Dic₁₃	—	2	1	no	—
77	#88180	—	2	1	no	—
78	#88180	—	2	1	no	—
79	#88180	—	2	1	no	—
80	#88180	—	2	1	no	—
81	#88180	—	2	1	no	—
82	#88180	C₂×C₄	1	2	yes	—
83	#88180	C₂×C₄	1	2	yes	—
84	#88180	C₂³	1	2	yes	—
85	C₂×C₄⋊Dic₁₃	—	2	1	no	—
86	C₂×C₄⋊Dic₁₃	—	2	1	no	—
87	C₂×C₄×Dic₁₃	—	2	1	no	—
88	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
89	C₂×#6099	—	2	1	no	—
90	C₂×#6099	—	2	1	no	—
91	C₂×#6099	—	2	1	no	—
92	C₂×#6099	—	2	1	no	—
93	C₂×#6099	D₄	1	2	yes	—
94	C₂×#6099	C₂³	1	2	yes	—
95	C₂²×#1055	D₄	1	2	yes	—
96	#88161	—	2	8	no	—
97	#88161	—	2	8	no	—
98	M₁₆×D₁₃	—	2	8	no	—
99	M₁₆×D₁₃	—	2	8	no	—
100	#88155	—	2	8	no	—
101	#88155	—	2	8	no	—
102	C₂×#6094	—	2	4	no	—
103	C₂×C₈×D₁₃	—	2	4	no	—
104	C₁₃×#108	—	2	8	no	—
105	#88065	—	2	8	no	—
106	#88065	C₂×C₄	1	16	yes	complemented
107	#88054	—	2	8	no	—
108	#20867	—	13	1	no	maximal, Sylow
109	C₂⁴×C₁₃	#41	1	1	yes	characteristic
110	C₂³×D₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂²×C₄	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×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₂×C₂²⋊D₁₃	—	2	2	no	—
126	C₂×C₂²⋊D₁₃	—	2	2	no	—
127	C₂×C₂²⋊D₁₃	—	2	2	no	—
128	C₂×C₂²⋊D₁₃	—	2	2	no	—
129	C₂×C₂²⋊D₁₃	—	2	2	no	—
130	C₂×C₂²⋊D₁₃	—	2	2	no	—
131	C₂²×Dic₁₃	—	2	1	no	—
132	C₂²×Dic₁₃	—	2	2	no	—
133	C₂²×Dic₁₃	—	4	1	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	—	2	2	no	—
142	#6127	—	2	2	no	—
143	#6127	—	2	2	no	—
144	#6127	—	2	2	no	—
145	#6127	—	2	2	no	—
146	#6127	C₄⋊C₄	1	4	yes	—
147	#6127	C₄⋊C₄	1	4	yes	—
148	#6127	C₂²×C₄	1	4	yes	—
149	#6127	C₂×D₄	1	4	yes	—
150	C₂×D₅₂	—	2	1	no	—
151	C₂×D₅₂	—	2	1	no	—
152	C₂×D₅₂	—	2	1	no	—
153	C₂×D₅₂	C₄⋊C₄	1	2	yes	—
154	C₂×D₅₂	C₄⋊C₄	1	2	yes	—
155	C₂×D₅₂	C₂×Q₈	1	2	yes	—
156	C₂×C₄×D₁₃	—	2	2	no	—
157	C₂×C₄×D₁₃	—	2	2	no	—
158	C₂×C₄×D₁₃	—	2	2	no	—
159	C₂×C₄×D₁₃	—	2	2	no	—
160	C₂×C₄×D₁₃	—	2	2	no	—
161	C₂×C₄×D₁₃	—	2	2	no	—
162	C₂×Dic₂₆	—	2	1	no	—
163	C₂×Dic₂₆	—	2	1	no	—
164	C₂×Dic₂₆	—	2	1	no	—
165	C₂×Dic₂₆	C₄⋊C₄	1	2	yes	—
166	C₂×Dic₂₆	C₄⋊C₄	1	2	yes	—
167	C₂×Dic₂₆	C₂×Q₈	1	2	yes	—
168	C₁₃×M₁₆	—	2	2	no	—
169	C₁₃×M₁₆	—	2	2	no	—
170	C₁₃×M₁₆	—	2	2	no	—
171	C₁₃×M₁₆	—	2	2	no	—
172	C₁₃×M₁₆	—	2	2	no	—
173	C₁₃×M₁₆	—	2	2	no	—
174	C₁₃×M₁₆	—	2	2	no	—
175	C₁₃×M₁₆	—	2	2	no	—
176	C₁₃×M₁₆	—	4	1	no	—
177	C₁₃×M₁₆	—	4	1	no	—
178	C₁₃×M₁₆	C₂²×C₄	1	4	yes	—
179	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
180	C₂×C₈×C₁₃	—	2	2	no	—
181	C₂×C₈×C₁₃	—	2	2	no	—
182	C₂×C₈×C₁₃	—	2	2	no	—
183	C₂×C₈×C₁₃	—	2	2	no	—
184	C₂×C₈×C₁₃	—	2	2	no	—
185	C₂×C₈×C₁₃	—	2	2	no	—
186	C₂×C₈×C₁₃	—	2	2	no	—
187	C₂×C₈×C₁₃	—	4	1	no	—
188	C₂×C₈×C₁₃	—	4	1	no	—
189	C₂²⋊Dic₁₃	—	2	2	no	—
190	C₂²⋊Dic₁₃	—	2	2	no	—
191	C₂²⋊Dic₁₃	—	2	2	no	—
192	C₂²⋊Dic₁₃	—	4	1	no	—
193	C₄⋊Dic₁₃	—	2	2	no	—
194	C₄⋊Dic₁₃	—	2	2	no	—
195	C₄⋊Dic₁₃	—	2	2	no	—
196	C₄⋊Dic₁₃	—	4	1	no	—
197	C₄×Dic₁₃	—	2	2	no	—
198	C₄×Dic₁₃	—	2	2	no	—
199	C₄×Dic₁₃	—	4	1	no	—
200	C₄×Dic₁₃	C₂²×C₄	1	4	yes	—
201	#6099	—	2	2	no	—
202	#6099	—	2	2	no	—
203	#6099	—	2	2	no	—
204	#6099	—	2	2	no	—
205	C₂×#1055	—	2	2	no	—
206	C₂×#1055	—	2	2	no	—
207	C₂×#1055	C₂×D₄	1	4	yes	—
208	#6094	—	2	16	no	—
209	C₈×D₁₃	—	2	16	no	—
210	C₂×#568	—	13	1	no	—
211	C₂×#430	D₁₃	1	1	yes	characteristic, complemented
212	#2905	—	13	1	no	—
213	C₂×#421	—	13	1	no	—
214	C₂×#421	—	13	1	no	—
215	#1861	—	13	8	no	—
216	C₂×#344	—	13	1	no	—
217	#1733	—	13	1	no	—
218	C₂³×C₁₃	—	8	1	no	—
219	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
220	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
221	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
222	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
223	C₂³×C₁₃	#123	1	1	yes	characteristic
224	C₂³×C₁₃	#123	1	1	yes	characteristic
225	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
226	C₂²×D₁₃	—	2	2	no	—
227	C₂²×D₁₃	—	2	2	no	—
228	C₂²×D₁₃	—	2	2	no	—
229	C₂²×D₁₃	—	8	2	no	—
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	C₂×C₄⋊C₄	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	C₂²⋊Q₈	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂²⋊Q₈	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	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂×#41	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	C₂×Dic₁₃	—	2	2	no	—
263	C₂×Dic₁₃	—	2	2	no	—
264	C₂×Dic₁₃	—	2	2	no	—
265	C₂×Dic₁₃	—	2	4	no	—
266	C₂×Dic₁₃	—	4	2	no	—
267	C₂×Dic₁₃	—	8	2	no	—
268	C₂×Dic₁₃	—	8	2	no	—
269	D₅₂	—	2	2	no	—
270	D₅₂	—	2	2	no	—
271	D₅₂	—	2	2	no	—
272	D₅₂	C₂×C₄⋊C₄	1	4	yes	—
273	C₄×D₁₃	—	2	4	no	—
274	C₄×D₁₃	—	2	4	no	—
275	C₄×D₁₃	—	2	4	no	—
276	C₄×D₁₃	—	2	4	no	—
277	Dic₂₆	—	2	2	no	—
278	Dic₂₆	—	2	2	no	—
279	Dic₂₆	—	2	2	no	—
280	Dic₂₆	C₂×C₄⋊C₄	1	4	yes	—
281	C₈×C₁₃	—	2	4	no	—
282	C₈×C₁₃	—	2	4	no	—
283	C₈×C₁₃	—	4	2	no	—
284	#1055	—	2	4	no	—
285	C₂²×#41	—	13	1	no	—
286	#568	—	13	4	no	—
287	#568	—	26	2	no	—
288	#568	—	26	2	no	—
289	#568	—	26	2	no	—
290	C₂×#131	—	26	2	no	—
291	C₂×#131	—	26	2	no	—
292	C₂²×M₁₆	—	13	1	no	—
293	C₂²×M₁₆	—	26	2	no	—
294	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
295	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
296	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
297	C₂×#117	—	13	1	no	—
298	C₂×#117	—	13	1	no	—
299	#430	—	2	2	no	—
300	#430	C₂×D₁₃	1	4	yes	complemented
301	C₂×#108	—	2	2	no	—
302	#424	—	26	2	no	—
303	#424	—	26	2	no	—
304	#423	—	13	4	no	—
305	#421	—	13	4	no	—
306	#421	—	13	4	no	—
307	#421	—	13	4	no	—
308	#421	—	26	2	no	—
309	C₂×#104	—	13	4	no	—
310	C₂×#104	—	26	2	no	—
311	#344	—	13	4	no	—
312	#339	—	13	4	no	—
313	C₂²×C₁₃	—	4	1	no	—
314	C₂²×C₁₃	—	4	1	no	—
315	C₂²×C₁₃	—	4	1	no	—
316	C₂²×C₁₃	—	4	1	no	—
317	C₂²×C₁₃	—	4	1	no	—
318	C₂²×C₁₃	—	4	1	no	—
319	C₂²×C₁₃	—	4	1	no	—
320	C₂²×C₁₃	#385	1	1	yes	characteristic
321	C₂²×C₁₃	#385	1	1	yes	characteristic
322	C₂²×C₁₃	#385	1	1	yes	characteristic
323	C₂²×C₁₃	#385	1	1	yes	characteristic
324	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
325	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
326	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
327	C₂×D₁₃	—	2	4	no	—
328	C₂×D₁₃	—	4	4	no	—
329	C₂×D₁₃	—	8	2	no	—
330	C₂×D₁₃	—	8	2	no	—
331	C₄×C₁₃	#385	1	1	yes	characteristic
332	C₄×C₁₃	#385	1	1	yes	characteristic
333	C₄×C₁₃	#385	1	1	yes	characteristic
334	C₄×C₁₃	#385	1	1	yes	characteristic
335	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
336	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
337	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
338	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
339	Dic₁₃	—	2	4	no	—
340	Dic₁₃	—	4	4	no	—
341	Dic₁₃	—	8	2	no	—
342	C₂×#41	—	13	2	no	—
343	C₂×#41	—	13	2	no	—
344	C₂×#41	—	13	2	no	—
345	C₂×#41	—	13	2	no	—
346	C₂×#41	—	13	2	no	—
347	C₂×#41	—	13	2	no	—
348	C₂×#41	—	26	1	no	—
349	C₂×#41	—	26	1	no	—
350	C₂×#41	—	26	1	no	—
351	C₂×#41	—	26	1	no	—
352	C₂×#41	—	26	1	no	—
353	C₂×#41	—	26	1	no	—
354	C₂²×Q₈	—	13	1	no	—
355	C₂²×D₄	—	13	1	no	—
356	C₂²×D₄	—	26	1	no	—
357	C₂³×C₄	—	26	1	no	—
358	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
359	#131	—	26	8	no	—
360	#131	—	26	8	no	—
361	#131	—	26	8	no	—
362	#131	—	26	8	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	—	2	1	no	—
368	C₂×M₁₆	—	2	1	no	—
369	C₂×M₁₆	—	2	1	no	—
370	C₂×M₁₆	—	2	1	no	—
371	C₂×M₁₆	—	2	1	no	—
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	13	2	no	—
375	C₂×M₁₆	—	13	2	no	—
376	C₂×M₁₆	—	26	4	no	—
377	C₂×M₁₆	—	26	8	no	—
378	C₂×M₁₆	—	26	1	no	—
379	C₂×M₁₆	—	26	1	no	—
380	C₂×M₁₆	—	26	1	no	—
381	C₂×M₁₆	—	26	1	no	—
382	C₂×M₁₆	—	26	8	no	—
383	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
384	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
385	C₂×M₁₆	C₂²⋊D₁₃	1	2	yes	—
386	C₂×M₁₆	C₂²⋊D₁₃	1	2	yes	—
387	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
388	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
389	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
390	C₂²×C₈	—	2	1	no	—
391	C₂²×C₈	—	2	1	no	—
392	C₂²×C₈	—	2	1	no	—
393	C₂²×C₈	—	13	2	no	—
394	C₂²×C₈	—	26	4	no	—
395	#117	—	13	2	no	—
396	#117	—	13	2	no	—
397	#117	—	13	2	no	—
398	#117	—	26	1	no	—
399	#117	—	26	1	no	—
400	#117	—	26	1	no	—
401	#117	—	26	1	no	—
402	#117	—	26	1	no	—
403	C₂×C₄⋊C₄	—	26	1	no	—
404	C₂×C₄⋊C₄	—	26	1	no	—
405	C₂×C₂²⋊C₄	—	26	1	no	—
406	C₂×C₂²⋊C₄	—	26	1	no	—
407	C₂×C₄²	—	13	2	no	—
408	C₂×C₄²	—	26	1	no	—
409	#108	—	2	8	no	—
410	C₄⋊C₈	—	26	8	no	—
411	#104	—	13	16	no	—
412	#104	—	26	8	no	—
413	C₂×C₁₃	—	2	1	no	—
414	C₂×C₁₃	—	2	1	no	—
415	C₂×C₁₃	—	2	1	no	—
416	C₂×C₁₃	—	2	1	no	—
417	C₂×C₁₃	—	2	1	no	—
418	C₂×C₁₃	—	2	1	no	—
419	C₂×C₁₃	—	2	1	no	—
420	C₂×C₁₃	C₂×#385	1	1	yes	characteristic
421	D₁₃	—	4	4	no	—
422	C₂⁴	—	26	1	no	—
423	C₂⁴	#6131	1	1	yes	characteristic
424	#41	—	13	4	no	—
425	#41	—	13	4	no	—
426	#41	—	13	4	no	—
427	#41	—	13	4	no	—
428	#41	—	26	2	no	—
429	#41	—	26	2	no	—
430	#41	—	26	2	no	—
431	#41	—	26	2	no	—
432	#41	—	26	2	no	—
433	#41	—	26	2	no	—
434	#41	—	26	2	no	—
435	#41	—	26	2	no	—
436	#41	—	26	2	no	—
437	#41	—	26	2	no	—
438	#41	—	26	2	no	—
439	#41	—	26	2	no	—
440	C₂×Q₈	—	13	2	no	—
441	C₂×Q₈	—	13	2	no	—
442	C₂×Q₈	—	13	2	no	—
443	C₂×Q₈	—	26	1	no	—
444	C₂×Q₈	—	26	1	no	—
445	C₂×Q₈	—	26	1	no	—
446	C₂×D₄	—	13	2	no	—
447	C₂×D₄	—	13	2	no	—
448	C₂×D₄	—	13	2	no	—
449	C₂×D₄	—	26	2	no	—
450	C₂×D₄	—	26	2	no	—
451	C₂×D₄	—	26	2	no	—
452	C₂×D₄	—	26	2	no	—
453	C₂×D₄	—	26	2	no	—
454	C₂×D₄	—	26	2	no	—
455	C₂×D₄	—	26	1	no	—
456	C₂×D₄	—	26	1	no	—
457	C₂×D₄	—	26	1	no	—
458	C₂²×C₄	—	26	1	no	—
459	C₂²×C₄	—	26	2	no	—
460	C₂²×C₄	—	26	2	no	—
461	C₂²×C₄	—	26	2	no	—
462	C₂²×C₄	—	26	2	no	—
463	C₂²×C₄	—	26	2	no	—
464	C₂²×C₄	—	26	2	no	—
465	C₂²×C₄	—	26	2	no	—
466	C₂²×C₄	—	52	1	no	—
467	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
468	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
469	C₂²×C₄	#6127	1	1	yes	characteristic
470	C₂²×C₄	#6127	1	1	yes	characteristic
471	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
472	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
473	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
474	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
475	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
476	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
477	C₂²×C₄	#6131	1	1	yes	characteristic
478	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
479	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
480	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
481	M₁₆	—	2	2	no	—
482	M₁₆	—	2	2	no	—
483	M₁₆	—	2	2	no	—
484	M₁₆	—	2	2	no	—
485	M₁₆	—	2	2	no	—
486	M₁₆	—	2	2	no	—
487	M₁₆	—	2	2	no	—
488	M₁₆	—	2	2	no	—
489	M₁₆	—	4	1	no	—
490	M₁₆	—	4	1	no	—
491	M₁₆	—	26	16	no	—
492	M₁₆	—	26	2	no	—
493	M₁₆	—	26	2	no	—
494	M₁₆	—	26	2	no	—
495	M₁₆	—	26	2	no	—
496	M₁₆	C₂×C₄×D₁₃	1	4	yes	—
497	M₁₆	C₂×C₂²⋊D₁₃	1	4	yes	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	2	2	no	—
503	C₂×C₈	—	2	2	no	—
504	C₂×C₈	—	2	2	no	—
505	C₂×C₈	—	4	1	no	—
506	C₂×C₈	—	4	1	no	—
507	C₂×C₈	—	13	4	no	—
508	C₂×C₈	—	26	16	no	—
509	C₂×C₈	—	26	2	no	—
510	C₂×C₈	—	26	2	no	—
511	C₄⋊C₄	—	26	2	no	—
512	C₄⋊C₄	—	26	2	no	—
513	C₄⋊C₄	—	26	2	no	—
514	C₄⋊C₄	—	52	1	no	—
515	C₂²⋊C₄	—	26	2	no	—
516	C₂²⋊C₄	—	26	2	no	—
517	C₂²⋊C₄	—	26	2	no	—
518	C₂²⋊C₄	—	52	1	no	—
519	C₄²	—	13	4	no	—
520	C₄²	—	26	2	no	—
521	C₄²	—	26	2	no	—
522	C₄²	—	52	1	no	—
523	C₁₃	#20867	1	1	yes	characteristic, complemented, Sylow
524	C₂³	—	8	1	no	—
525	C₂³	—	26	2	no	—
526	C₂³	—	26	2	no	—
527	C₂³	—	26	2	no	—
528	C₂³	—	104	2	no	—
529	C₂³	#88147	1	1	yes	characteristic
530	C₂³	#88147	1	1	yes	characteristic
531	C₂³	#88148	1	1	yes	characteristic
532	C₂³	#88148	1	1	yes	characteristic
533	C₂³	#88200	1	1	yes	characteristic
534	C₂³	#88200	1	1	yes	characteristic
535	C₂³	C₂×#6131	1	1	yes	characteristic
536	Q₈	—	13	4	no	—
537	Q₈	—	26	2	no	—
538	Q₈	—	26	2	no	—
539	Q₈	—	26	2	no	—
540	D₄	—	13	4	no	—
541	D₄	—	26	4	no	—
542	D₄	—	26	4	no	—
543	D₄	—	26	4	no	—
544	D₄	—	26	4	no	—
545	D₄	—	26	2	no	—
546	D₄	—	26	2	no	—
547	D₄	—	26	2	no	—
548	C₂×C₄	—	26	2	no	—
549	C₂×C₄	—	26	2	no	—
550	C₂×C₄	—	26	2	no	—
551	C₂×C₄	—	26	4	no	—
552	C₂×C₄	—	26	4	no	—
553	C₂×C₄	—	26	4	no	—
554	C₂×C₄	—	26	4	no	—
555	C₂×C₄	—	26	4	no	—
556	C₂×C₄	—	52	2	no	—
557	C₂×C₄	—	104	2	no	—
558	C₂×C₄	—	104	2	no	—
559	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
560	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
561	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
562	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
563	C₂×C₄	#88147	1	1	yes	characteristic
564	C₂×C₄	#88147	1	1	yes	characteristic
565	C₂×C₄	#88148	1	1	yes	characteristic
566	C₂×C₄	#88148	1	1	yes	characteristic
567	C₂×C₄	#88150	1	1	yes	characteristic
568	C₂×C₄	#88150	1	1	yes	characteristic
569	C₂×C₄	#88150	1	1	yes	characteristic
570	C₂×C₄	#88150	1	1	yes	characteristic
571	C₂×C₄	C₄×C₂²⋊D₁₃	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	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
575	C₂×C₄	#88191	1	1	yes	characteristic
576	C₂×C₄	#88191	1	1	yes	characteristic
577	C₂×C₄	#88191	1	1	yes	characteristic
578	C₂×C₄	#88191	1	1	yes	characteristic
579	C₂×C₄	#88200	1	1	yes	characteristic
580	C₂×C₄	#88200	1	1	yes	characteristic
581	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
582	C₂×C₄	C₂×#6127	1	1	yes	characteristic
583	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
584	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
585	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
586	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
587	C₈	—	2	4	no	—
588	C₈	—	2	4	no	—
589	C₈	—	4	2	no	—
590	C₈	—	26	4	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	26	4	no	—
599	C₂²	—	52	4	no	—
600	C₂²	—	104	2	no	—
601	C₂²	—	104	2	no	—
602	C₂²	#11718650	1	1	yes	characteristic
603	C₂²	#11718650	1	1	yes	characteristic
604	C₂²	#11718650	1	1	yes	characteristic
605	C₂²	#11718650	1	1	yes	characteristic
606	C₂²	C₂×#88147	1	1	yes	characteristic
607	C₂²	C₂×#88148	1	1	yes	characteristic
608	C₂²	C₂×#88200	1	1	yes	characteristic
609	C₄	—	26	4	no	—
610	C₄	—	52	4	no	—
611	C₄	—	104	2	no	—
612	C₄	#11718650	1	1	yes	characteristic
613	C₄	#11718650	1	1	yes	characteristic
614	C₄	#11718650	1	1	yes	characteristic
615	C₄	#11718650	1	1	yes	characteristic
616	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
617	C₄	C₂×#88150	1	1	yes	characteristic
618	C₄	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
619	C₄	C₂×#88191	1	1	yes	characteristic
620	C₂	—	2	1	no	—
621	C₂	—	2	1	no	—
622	C₂	—	2	1	no	—
623	C₂	—	2	1	no	—
624	C₂	—	2	1	no	—
625	C₂	—	2	1	no	—
626	C₂	—	2	1	no	—
627	C₂	—	52	4	no	—
628	C₂	C₂×#11718650	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#88191
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×#430	C₂
socle	C₂×C₁₃	C₂×#385
prime radical	C₂²×#6127	C₂²
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×#430	D₁₃
hypocenter	C₁₃	#20867
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ C₂×#430

Complements

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

N	H ≅ G/N	type
2. #13123399	C₂	semidirect
5. #13115073	C₂	semidirect
6. C₂×#11718151	C₂	semidirect
7. #13114547	C₂	semidirect
8. C₂×C₁₃×#430	C₂	semidirect
24. C₁₃×#430	C₂²	semidirect
27. #11718800	C₄	semidirect
28. #11718800	C₄	semidirect
33. #11718779	C₂²	semidirect
35. #11718151	C₂²	semidirect
36. #11718147	C₂²	semidirect
106. #88065	C₂×C₄	semidirect
211. C₂×#430	D₁₃	semidirect
300. #430	C₂×D₁₃	semidirect
523. C₁₃	#20867	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
#13123399	2
C₂×#11718800	2
#13115073	2
C₂×#11718151	2
#13114547	2
C₂×C₁₃×#430	2
#20867	13