Subgroups — #15868780

Order 3328.

1320 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124054	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718806	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11718805	C₂	1	1	yes	maximal, characteristic, complemented
4	#13123539	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115163	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115163	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115138	C₂	1	1	yes	maximal, characteristic, complemented
8	#13115111	C₂	1	1	yes	maximal, characteristic, complemented
9	#13115111	C₂	1	1	yes	maximal, characteristic, complemented
10	#13115041	C₂	1	1	yes	maximal, characteristic, complemented
11	#13114780	C₂	1	1	yes	maximal, characteristic, complemented
12	#13114678	C₂	1	1	yes	maximal, characteristic, complemented
13	#13114671	C₂	1	1	yes	maximal, characteristic, complemented
14	#13114617	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#568	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₁₃×#568	—	2	4	no	—
18	C₁₃×#568	—	2	4	no	—
19	C₂×C₁₃×#131	—	2	1	no	—
20	C₂×C₁₃×#131	—	2	1	no	—
21	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×M₁₆	—	2	1	no	—
26	C₂²×C₁₃×M₁₆	—	2	1	no	—
27	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
29	C₂×#88204	C₂²	1	1	yes	characteristic
30	C₂×#88204	C₂²	1	1	yes	characteristic
31	#11719496	C₂²	1	1	yes	characteristic
32	C₂×#88155	C₂²	1	1	yes	characteristic, complemented
33	#11718900	C₄	1	1	yes	characteristic, complemented
34	#11718900	C₄	1	1	yes	characteristic, complemented
35	#11718899	C₄	1	1	yes	characteristic, complemented
36	#11718899	C₄	1	1	yes	characteristic, complemented
37	C₂×#88077	C₂²	1	1	yes	characteristic
38	C₂×#88077	C₂²	1	1	yes	characteristic
39	C₂×#88077	C₂²	1	1	yes	characteristic
40	C₂×#88077	C₂²	1	1	yes	characteristic
41	#11718894	C₂²	1	1	yes	characteristic
42	#11718894	C₂²	1	1	yes	characteristic
43	#11718889	C₄	1	1	yes	characteristic, complemented
44	#11718888	C₄	1	1	yes	characteristic, complemented
45	#11718879	C₄	1	1	yes	characteristic, complemented
46	#11718878	C₄	1	1	yes	characteristic, complemented
47	C₄×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
48	#11718868	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
50	#11718806	—	2	4	no	—
51	#11718805	—	2	4	no	—
52	C₂×#88065	C₂²	1	1	yes	characteristic, complemented
53	C₂×#88065	C₂²	1	1	yes	characteristic, complemented
54	#11718789	—	2	1	no	—
55	#11718789	—	2	1	no	—
56	#11718788	—	2	1	no	—
57	#11718788	—	2	1	no	—
58	C₂×#88062	C₂²	1	1	yes	characteristic, complemented
59	C₂×#88062	C₂²	1	1	yes	characteristic, complemented
60	#11718771	C₂²	1	1	yes	characteristic, complemented
61	#11718763	C₂²	1	1	yes	characteristic, complemented
62	#11718762	C₂²	1	1	yes	characteristic, complemented
63	C₂×#88055	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
65	#11718150	C₂²	1	1	yes	characteristic, complemented
66	#11718150	C₂²	1	1	yes	characteristic, complemented
67	#11718147	C₂²	1	1	yes	characteristic, complemented
68	#11718147	C₂²	1	1	yes	characteristic, complemented
69	#11718142	C₂²	1	1	yes	characteristic, complemented
70	#11718142	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₁₃×#41	—	2	2	no	—
72	C₂×C₁₃×#41	—	2	2	no	—
73	C₂×C₁₃×#41	—	2	2	no	—
74	C₂×C₁₃×#41	—	2	2	no	—
75	C₂×C₁₃×#41	—	2	1	no	—
76	C₂×C₁₃×#41	—	2	1	no	—
77	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
78	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
79	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
81	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
82	C₂²×D₄×C₁₃	—	2	1	no	—
83	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
84	C₂³×C₄×C₁₃	—	2	1	no	—
85	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×#6127	C₂³	1	1	yes	characteristic
87	C₁₃×#131	—	2	8	no	—
88	C₁₃×#131	—	2	8	no	—
89	C₁₃×#131	—	2	2	no	—
90	C₁₃×#131	—	2	2	no	—
91	C₁₃×#131	—	2	2	no	—
92	C₁₃×#131	—	2	2	no	—
93	C₁₃×#131	—	2	2	no	—
94	C₁₃×#131	—	2	2	no	—
95	C₁₃×#131	D₄	1	4	yes	complemented
96	C₁₃×#131	D₄	1	4	yes	complemented
97	C₂×C₁₃×M₁₆	—	2	8	no	—
98	C₂×C₁₃×M₁₆	—	2	8	no	—
99	C₂×C₁₃×M₁₆	—	2	1	no	—
100	C₂×C₁₃×M₁₆	—	2	2	no	—
101	C₂×C₁₃×M₁₆	—	2	2	no	—
102	C₂×C₁₃×M₁₆	—	2	1	no	—
103	C₂×C₁₃×M₁₆	—	2	1	no	—
104	C₂×C₁₃×M₁₆	—	2	1	no	—
105	C₂×C₁₃×M₁₆	—	2	1	no	—
106	C₂×C₁₃×M₁₆	—	2	2	no	—
107	C₂×C₁₃×M₁₆	—	2	2	no	—
108	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
109	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
110	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
111	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
112	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₁₃	—	2	1	no	—
115	C₂²×C₈×C₁₃	—	2	1	no	—
116	C₂²×C₈×C₁₃	—	2	1	no	—
117	C₂²×C₈×C₁₃	—	2	1	no	—
118	C₂²×C₈×C₁₃	—	2	1	no	—
119	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
121	#88207	—	2	1	no	—
122	C₂×C₂²⋊Dic₁₃	—	2	1	no	—
123	#88204	—	2	2	no	—
124	#88204	—	2	2	no	—
125	#88204	—	2	2	no	—
126	#88204	—	2	2	no	—
127	C₂×#6107	C₂×C₄	1	1	yes	characteristic
128	C₂×#6107	C₂×C₄	1	1	yes	characteristic
129	C₂×#6106	C₂×C₄	1	1	yes	characteristic
130	C₂×#6106	C₂×C₄	1	1	yes	characteristic
131	C₂×#6105	C₂×C₄	1	1	yes	characteristic
132	C₂×#6105	C₂×C₄	1	1	yes	characteristic
133	C₂×#6104	C₂×C₄	1	1	yes	characteristic
134	C₂×#6104	C₂×C₄	1	1	yes	characteristic
135	#88184	C₂×C₄	1	1	yes	characteristic
136	#88184	C₂×C₄	1	1	yes	characteristic
137	#88183	—	2	1	no	—
138	C₄×C₂²⋊D₁₃	—	2	1	no	—
139	C₄×C₂²⋊D₁₃	—	2	1	no	—
140	#88180	C₂³	1	1	yes	characteristic
141	#88178	C₂×C₄	1	1	yes	characteristic
142	#88178	C₂×C₄	1	1	yes	characteristic
143	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
145	C₂×#6099	C₂³	1	1	yes	characteristic
146	C₂×#6099	C₂³	1	1	yes	characteristic
147	C₂²×#1055	C₂³	1	1	yes	characteristic
148	C₂²×#1055	C₂³	1	1	yes	characteristic
149	#88155	—	2	2	no	—
150	#88155	—	2	2	no	—
151	C₂×#6094	—	2	1	no	—
152	C₂×C₈×D₁₃	—	2	1	no	—
153	#88077	—	2	2	no	—
154	#88077	—	2	2	no	—
155	#88077	—	2	2	no	—
156	#88077	—	2	2	no	—
157	#88075	C₂×C₄	1	1	yes	characteristic
158	#88075	C₂×C₄	1	1	yes	characteristic
159	#88075	C₂×C₄	1	1	yes	characteristic
160	#88075	C₂×C₄	1	1	yes	characteristic
161	#88072	C₂×C₄	1	1	yes	characteristic
162	#88072	C₂×C₄	1	1	yes	characteristic
163	#88072	C₂×C₄	1	1	yes	characteristic
164	#88072	C₂×C₄	1	1	yes	characteristic
165	#88071	—	2	1	no	—
166	C₂²⋊#1055	—	2	1	no	—
167	C₂²⋊#1055	—	2	1	no	—
168	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
169	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
170	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
171	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
172	#88065	—	2	2	no	—
173	#88065	—	2	2	no	—
174	#88062	—	2	2	no	—
175	#88062	—	2	2	no	—
176	#88060	—	2	1	no	—
177	#88060	—	2	1	no	—
178	#88055	—	2	2	no	—
179	#88055	—	2	1	no	—
180	#88054	—	2	1	no	—
181	#88054	—	2	1	no	—
182	C₈×Dic₁₃	—	2	2	no	—
183	C₈×Dic₁₃	—	2	1	no	—
184	#21468	—	13	1	no	maximal, Sylow
185	C₂⁴×C₁₃	—	2	1	no	—
186	C₂⁴×C₁₃	#41	1	1	yes	characteristic
187	C₁₃×#41	—	2	4	no	—
188	C₁₃×#41	—	2	4	no	—
189	C₁₃×#41	—	2	4	no	—
190	C₁₃×#41	—	2	4	no	—
191	C₁₃×#41	—	2	2	no	—
192	C₁₃×#41	—	2	2	no	—
193	C₁₃×#41	—	2	2	no	—
194	C₁₃×#41	—	2	2	no	—
195	C₁₃×#41	—	2	1	no	—
196	C₁₃×#41	—	2	1	no	—
197	C₁₃×#41	—	2	1	no	—
198	C₁₃×#41	—	2	1	no	—
199	C₁₃×#41	C₂×D₄	1	2	yes	—
200	C₁₃×#41	C₂×D₄	1	2	yes	—
201	C₁₃×#41	#41	1	2	yes	—
202	C₁₃×#41	#41	1	2	yes	—
203	C₂×Q₈×C₁₃	—	2	2	no	—
204	C₂×Q₈×C₁₃	—	2	2	no	—
205	C₂×Q₈×C₁₃	—	2	1	no	—
206	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
207	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
208	C₂×D₄×C₁₃	—	2	4	no	—
209	C₂×D₄×C₁₃	—	2	4	no	—
210	C₂×D₄×C₁₃	—	2	1	no	—
211	C₂×D₄×C₁₃	—	2	1	no	—
212	C₂×D₄×C₁₃	—	2	1	no	—
213	C₂×D₄×C₁₃	—	2	1	no	—
214	C₂×D₄×C₁₃	—	2	2	no	—
215	C₂×D₄×C₁₃	—	2	2	no	—
216	C₂×D₄×C₁₃	—	2	1	no	—
217	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
218	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
219	C₂²×C₄×C₁₃	—	2	4	no	—
220	C₂²×C₄×C₁₃	—	2	4	no	—
221	C₂²×C₄×C₁₃	—	2	1	no	—
222	C₂²×C₄×C₁₃	—	2	1	no	—
223	C₂²×C₄×C₁₃	—	2	1	no	—
224	C₂²×C₄×C₁₃	—	2	1	no	—
225	C₂²×C₄×C₁₃	—	2	1	no	—
226	C₂²×C₄×C₁₃	—	2	1	no	—
227	C₂²×C₄×C₁₃	—	2	1	no	—
228	C₂²×C₄×C₁₃	—	2	1	no	—
229	C₂²×C₄×C₁₃	—	2	1	no	—
230	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
231	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
235	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₂×C₂²⋊D₁₃	—	2	1	no	—
237	C₂×C₂²⋊D₁₃	—	2	1	no	—
238	C₂×C₂²⋊D₁₃	—	2	1	no	—
239	C₂²×Dic₁₃	—	2	1	no	—
240	C₂²×Dic₁₃	—	2	1	no	—
241	#6127	—	2	1	no	—
242	#6127	—	2	1	no	—
243	#6127	—	2	1	no	—
244	#6127	—	2	1	no	—
245	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
246	C₂×C₄×D₁₃	—	2	1	no	—
247	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
248	C₁₃×M₁₆	—	2	4	no	—
249	C₁₃×M₁₆	—	2	4	no	—
250	C₁₃×M₁₆	—	2	4	no	—
251	C₁₃×M₁₆	—	2	1	no	—
252	C₁₃×M₁₆	—	2	1	no	—
253	C₁₃×M₁₆	—	2	2	no	—
254	C₁₃×M₁₆	—	2	2	no	—
255	C₁₃×M₁₆	—	2	4	no	—
256	C₁₃×M₁₆	—	2	4	no	—
257	C₁₃×M₁₆	—	2	2	no	—
258	C₁₃×M₁₆	—	2	2	no	—
259	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
260	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
261	C₂×C₈×C₁₃	—	2	4	no	—
262	C₂×C₈×C₁₃	—	2	4	no	—
263	C₂×C₈×C₁₃	—	2	4	no	—
264	C₂×C₈×C₁₃	—	2	1	no	—
265	C₂×C₈×C₁₃	—	2	1	no	—
266	C₂×C₈×C₁₃	—	2	1	no	—
267	C₂×C₈×C₁₃	—	2	1	no	—
268	C₂×C₈×C₁₃	—	2	4	no	—
269	C₂×C₈×C₁₃	—	2	4	no	—
270	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
271	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
272	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
273	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
274	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
275	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
276	C₂²⋊Dic₁₃	—	2	1	no	—
277	C₂²⋊Dic₁₃	—	2	1	no	—
278	C₂²⋊Dic₁₃	—	2	1	no	—
279	C₂²⋊Dic₁₃	—	4	2	no	—
280	#6107	—	2	2	no	—
281	#6107	—	2	2	no	—
282	#6106	—	2	2	no	—
283	#6106	—	2	2	no	—
284	#6105	—	2	2	no	—
285	#6105	—	2	2	no	—
286	#6104	—	2	2	no	—
287	#6104	—	2	2	no	—
288	#6103	—	2	1	no	—
289	#6103	—	2	1	no	—
290	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
291	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
292	#6101	—	2	1	no	—
293	#6101	—	2	1	no	—
294	C₄×Dic₁₃	—	2	1	no	—
295	C₄×Dic₁₃	—	2	1	no	—
296	C₄×Dic₁₃	—	2	1	no	—
297	C₄×Dic₁₃	—	2	1	no	—
298	C₄×Dic₁₃	—	2	1	no	—
299	#6099	—	2	1	no	—
300	#6099	—	2	1	no	—
301	#6099	—	2	1	no	—
302	#6099	—	2	1	no	—
303	C₂×#1055	—	2	1	no	—
304	C₂×#1055	—	2	1	no	—
305	C₂×#1055	—	2	1	no	—
306	C₂×#1055	—	2	1	no	—
307	C₂×#1055	—	2	1	no	—
308	C₂×#1055	—	2	1	no	—
309	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
310	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
311	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
312	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
313	#6094	—	4	2	no	—
314	C₈×D₁₃	—	4	2	no	—
315	C₂×#568	D₁₃	1	1	yes	characteristic, complemented
316	#3002	—	13	1	no	—
317	C₂×#444	—	13	1	no	—
318	C₂×#443	—	13	1	no	—
319	#2930	—	13	1	no	—
320	#1876	—	13	1	no	—
321	#1876	—	13	1	no	—
322	#1871	—	13	1	no	—
323	#1866	—	13	1	no	—
324	#1866	—	13	1	no	—
325	#1855	—	13	1	no	—
326	#1789	—	13	1	no	—
327	#1765	—	13	1	no	—
328	#1764	—	13	1	no	—
329	#1753	—	13	1	no	—
330	C₂³×C₁₃	—	2	4	no	—
331	C₂³×C₁₃	—	2	1	no	—
332	C₂³×C₁₃	—	2	1	no	—
333	C₂³×C₁₃	—	2	1	no	—
334	C₂³×C₁₃	—	2	1	no	—
335	C₂³×C₁₃	—	4	1	no	—
336	C₂³×C₁₃	—	4	1	no	—
337	C₂³×C₁₃	—	8	1	no	—
338	C₂³×C₁₃	—	8	1	no	—
339	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
340	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
341	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
342	C₂²×D₁₃	—	2	1	no	—
343	Q₈×C₁₃	—	2	4	no	—
344	Q₈×C₁₃	—	2	1	no	—
345	Q₈×C₁₃	—	2	1	no	—
346	Q₈×C₁₃	C₄×D₄	1	2	yes	—
347	Q₈×C₁₃	C₄×D₄	1	2	yes	—
348	D₄×C₁₃	—	2	4	no	—
349	D₄×C₁₃	—	2	4	no	—
350	D₄×C₁₃	—	2	4	no	—
351	D₄×C₁₃	—	2	2	no	—
352	D₄×C₁₃	—	2	2	no	—
353	D₄×C₁₃	—	2	2	no	—
354	D₄×C₁₃	—	2	2	no	—
355	D₄×C₁₃	—	2	1	no	—
356	D₄×C₁₃	—	2	1	no	—
357	D₄×C₁₃	C₄×D₄	1	2	yes	—
358	D₄×C₁₃	C₄×D₄	1	2	yes	—
359	C₂×C₄×C₁₃	—	2	4	no	—
360	C₂×C₄×C₁₃	—	2	4	no	—
361	C₂×C₄×C₁₃	—	2	4	no	—
362	C₂×C₄×C₁₃	—	2	1	no	—
363	C₂×C₄×C₁₃	—	2	1	no	—
364	C₂×C₄×C₁₃	—	2	1	no	—
365	C₂×C₄×C₁₃	—	2	1	no	—
366	C₂×C₄×C₁₃	—	2	1	no	—
367	C₂×C₄×C₁₃	—	2	1	no	—
368	C₂×C₄×C₁₃	—	2	1	no	—
369	C₂×C₄×C₁₃	—	2	1	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	2	1	no	—
373	C₂×C₄×C₁₃	—	2	1	no	—
374	C₂×C₄×C₁₃	—	2	1	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	1	no	—
378	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
379	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
380	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
381	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
385	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
386	C₂²⋊D₁₃	—	4	1	no	—
387	C₂²⋊D₁₃	—	4	1	no	—
388	C₂²⋊D₁₃	—	8	1	no	—
389	C₂²⋊D₁₃	—	8	1	no	—
390	C₂×Dic₁₃	—	2	2	no	—
391	C₂×Dic₁₃	—	2	1	no	—
392	C₂×Dic₁₃	—	2	1	no	—
393	C₂×Dic₁₃	—	2	1	no	—
394	C₂×Dic₁₃	—	4	1	no	—
395	C₂×Dic₁₃	—	4	1	no	—
396	C₂×Dic₁₃	—	4	1	no	—
397	C₂×Dic₁₃	—	4	1	no	—
398	C₂×Dic₁₃	—	4	1	no	—
399	D₅₂	—	2	1	no	—
400	D₅₂	—	2	1	no	—
401	C₄×D₁₃	—	4	1	no	—
402	C₄×D₁₃	—	4	1	no	—
403	Dic₂₆	—	2	1	no	—
404	Dic₂₆	—	2	1	no	—
405	C₈×C₁₃	—	2	2	no	—
406	C₈×C₁₃	—	2	2	no	—
407	C₈×C₁₃	—	2	1	no	—
408	C₈×C₁₃	—	2	1	no	—
409	C₈×C₁₃	#120	1	2	yes	—
410	C₈×C₁₃	#120	1	2	yes	—
411	#1055	—	2	1	no	—
412	#1055	—	2	1	no	—
413	#1055	—	2	1	no	—
414	#1055	—	2	1	no	—
415	#1055	—	4	1	no	—
416	#1055	—	4	1	no	—
417	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic
418	C₂×#135	—	13	1	no	—
419	C₂×#135	—	13	1	no	—
420	#568	—	2	4	no	—
421	#568	—	2	4	no	—
422	C₂×#131	—	2	1	no	—
423	C₂×#131	—	2	1	no	—
424	C₂×#131	—	13	1	no	—
425	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
426	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
427	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
428	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
429	C₂²×M₁₆	—	2	1	no	—
430	C₂²×M₁₆	—	2	1	no	—
431	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
432	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
433	#525	—	13	1	no	—
434	#452	—	13	1	no	—
435	#452	—	13	1	no	—
436	#451	—	13	1	no	—
437	#450	—	13	1	no	—
438	#449	—	13	1	no	—
439	#449	—	13	1	no	—
440	#448	—	13	1	no	—
441	#447	—	13	1	no	—
442	#444	—	26	4	no	—
443	#443	—	26	4	no	—
444	#436	—	26	1	no	—
445	#436	—	26	1	no	—
446	#435	—	26	1	no	—
447	#435	—	26	1	no	—
448	C₂×#108	—	13	1	no	—
449	C₂×#108	—	13	1	no	—
450	#424	—	13	1	no	—
451	C₂×#104	—	13	1	no	—
452	C₂×#104	—	13	1	no	—
453	C₂×#104	—	13	1	no	—
454	C₂×#104	—	13	1	no	—
455	C₂×#104	—	13	1	no	—
456	C₂×#104	—	13	1	no	—
457	#416	—	13	1	no	—
458	#416	—	13	1	no	—
459	#408	—	13	1	no	—
460	#407	—	13	1	no	—
461	C₂×C₂²⋊C₈	—	13	1	no	—
462	#405	—	13	1	no	—
463	C₂×#97	—	13	1	no	—
464	C₂×C₄×C₈	—	13	1	no	—
465	C₄×C₂²⋊C₄	—	13	1	no	—
466	#341	—	13	1	no	—
467	#341	—	13	1	no	—
468	#339	—	13	1	no	—
469	#339	—	13	1	no	—
470	#336	—	13	1	no	—
471	#336	—	13	1	no	—
472	C₂²×C₁₃	—	2	1	no	—
473	C₂²×C₁₃	—	2	1	no	—
474	C₂²×C₁₃	—	2	1	no	—
475	C₂²×C₁₃	—	2	1	no	—
476	C₂²×C₁₃	—	2	1	no	—
477	C₂²×C₁₃	—	2	1	no	—
478	C₂²×C₁₃	—	2	1	no	—
479	C₂²×C₁₃	—	2	1	no	—
480	C₂²×C₁₃	—	2	2	no	—
481	C₂²×C₁₃	—	2	2	no	—
482	C₂²×C₁₃	—	4	1	no	—
483	C₂²×C₁₃	—	4	1	no	—
484	C₂²×C₁₃	—	4	1	no	—
485	C₂²×C₁₃	—	4	1	no	—
486	C₂²×C₁₃	—	8	1	no	—
487	C₂²×C₁₃	—	8	1	no	—
488	C₂²×C₁₃	—	8	4	no	—
489	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
490	C₂²×C₁₃	#525	1	1	yes	characteristic
491	C₂²×C₁₃	#525	1	1	yes	characteristic
492	C₂×D₁₃	—	4	1	no	—
493	C₂×D₁₃	—	4	1	no	—
494	C₂×D₁₃	—	4	1	no	—
495	C₄×C₁₃	—	2	1	no	—
496	C₄×C₁₃	—	2	2	no	—
497	C₄×C₁₃	—	2	2	no	—
498	C₄×C₁₃	—	2	1	no	—
499	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
500	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
501	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
502	C₄×C₁₃	#525	1	1	yes	characteristic
503	Dic₁₃	—	4	2	no	—
504	Dic₁₃	—	4	1	no	—
505	Dic₁₃	—	4	1	no	—
506	Dic₁₃	—	4	1	no	—
507	Dic₁₃	—	8	1	no	—
508	C₂×#41	—	2	2	no	—
509	C₂×#41	—	2	2	no	—
510	C₂×#41	—	2	2	no	—
511	C₂×#41	—	2	2	no	—
512	C₂×#41	—	2	1	no	—
513	C₂×#41	—	2	1	no	—
514	C₂×#41	—	13	1	no	—
515	C₂×#41	C₄×D₁₃	1	1	yes	characteristic
516	C₂×#41	C₄×D₁₃	1	1	yes	characteristic
517	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
518	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
519	C₂²×Q₈	C₄×D₁₃	1	1	yes	characteristic
520	C₂²×D₄	—	2	1	no	—
521	C₂²×D₄	C₄×D₁₃	1	1	yes	characteristic
522	C₂³×C₄	—	2	1	no	—
523	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
524	#135	—	26	2	no	—
525	#135	—	26	2	no	—
526	#135	—	26	2	no	—
527	#135	—	26	2	no	—
528	C₂×Q₁₆	—	13	1	no	—
529	C₂×Q₁₆	—	13	1	no	—
530	C₂×SD₁₆	—	13	1	no	—
531	C₂×SD₁₆	—	13	1	no	—
532	C₂×SD₁₆	—	13	1	no	—
533	C₂×SD₁₆	—	13	1	no	—
534	C₂×D₈	—	13	1	no	—
535	C₂×D₈	—	13	1	no	—
536	#131	—	2	8	no	—
537	#131	—	2	8	no	—
538	#131	—	2	2	no	—
539	#131	—	2	2	no	—
540	#131	—	2	2	no	—
541	#131	—	2	2	no	—
542	#131	—	2	2	no	—
543	#131	—	2	2	no	—
544	#131	—	26	2	no	—
545	#131	—	26	2	no	—
546	#131	C₂²⋊D₁₃	1	4	yes	complemented
547	#131	C₂²⋊D₁₃	1	4	yes	complemented
548	C₂×M₁₆	—	2	8	no	—
549	C₂×M₁₆	—	2	8	no	—
550	C₂×M₁₆	—	2	1	no	—
551	C₂×M₁₆	—	2	2	no	—
552	C₂×M₁₆	—	2	2	no	—
553	C₂×M₁₆	—	2	1	no	—
554	C₂×M₁₆	—	2	1	no	—
555	C₂×M₁₆	—	2	1	no	—
556	C₂×M₁₆	—	2	1	no	—
557	C₂×M₁₆	—	2	2	no	—
558	C₂×M₁₆	—	2	2	no	—
559	C₂×M₁₆	—	13	1	no	—
560	C₂×M₁₆	—	13	1	no	—
561	C₂×M₁₆	—	26	1	no	—
562	C₂×M₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
563	C₂×M₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
564	C₂×M₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
565	C₂×M₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
566	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
567	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
568	C₂²×C₈	—	2	1	no	—
569	C₂²×C₈	—	2	1	no	—
570	C₂²×C₈	—	2	1	no	—
571	C₂²×C₈	—	2	1	no	—
572	C₂²×C₈	—	2	1	no	—
573	C₂²×C₈	—	13	1	no	—
574	C₂²×C₈	—	13	1	no	—
575	C₂²×C₈	—	26	1	no	—
576	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
577	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
578	#123	—	26	1	no	—
579	C₂²⋊Q₈	—	13	1	no	—
580	C₂²⋊Q₈	—	13	1	no	—
581	#121	—	13	1	no	—
582	#121	—	13	1	no	—
583	#120	—	26	1	no	—
584	C₄×D₄	—	26	1	no	—
585	C₄×D₄	—	26	1	no	—
586	#117	—	13	1	no	—
587	C₂×C₂²⋊C₄	—	26	1	no	—
588	C₂×C₄²	—	13	1	no	—
589	C₂×C₄²	—	13	1	no	—
590	#108	—	26	2	no	—
591	#108	—	26	2	no	—
592	C₄⋊C₈	—	26	1	no	—
593	C₄⋊C₈	—	26	1	no	—
594	#104	—	26	2	no	—
595	#104	—	26	2	no	—
596	#104	—	26	2	no	—
597	#104	—	26	2	no	—
598	#104	—	26	2	no	—
599	#104	—	26	2	no	—
600	#103	—	13	1	no	—
601	#103	—	13	1	no	—
602	#103	—	13	1	no	—
603	#103	—	13	1	no	—
604	#102	—	13	1	no	—
605	#102	—	13	1	no	—
606	#102	—	13	1	no	—
607	#102	—	13	1	no	—
608	C₂²⋊C₈	—	13	1	no	—
609	C₂²⋊C₈	—	13	1	no	—
610	C₂²⋊C₈	—	13	1	no	—
611	C₂²⋊C₈	—	13	1	no	—
612	C₂²⋊C₈	—	26	1	no	—
613	C₂²⋊C₈	—	26	1	no	—
614	C₂²⋊C₈	—	26	1	no	—
615	C₂²⋊C₈	—	26	1	no	—
616	#97	—	26	2	no	—
617	#97	—	26	1	no	—
618	C₄×C₈	—	26	2	no	—
619	C₄×C₈	—	26	1	no	—
620	#95	—	26	1	no	—
621	C₂×C₁₃	—	2	1	no	—
622	C₂×C₁₃	—	2	1	no	—
623	C₂×C₁₃	—	4	1	no	—
624	C₂×C₁₃	—	4	1	no	—
625	C₂×C₁₃	—	4	2	no	—
626	C₂×C₁₃	—	4	2	no	—
627	C₂×C₁₃	C₄×#120	1	1	yes	characteristic
628	C₂×C₁₃	#2956	1	1	yes	characteristic
629	C₂×C₁₃	#2957	1	1	yes	characteristic
630	D₁₃	—	8	1	no	—
631	C₂⁴	—	2	1	no	—
632	C₂⁴	#6127	1	1	yes	characteristic
633	#41	—	2	4	no	—
634	#41	—	2	4	no	—
635	#41	—	2	4	no	—
636	#41	—	2	4	no	—
637	#41	—	2	2	no	—
638	#41	—	2	2	no	—
639	#41	—	2	2	no	—
640	#41	—	2	2	no	—
641	#41	—	2	1	no	—
642	#41	—	2	1	no	—
643	#41	—	2	1	no	—
644	#41	—	2	1	no	—
645	#41	—	26	1	no	—
646	#41	—	26	1	no	—
647	#41	—	26	1	no	—
648	#41	—	26	1	no	—
649	#41	#6127	1	2	yes	—
650	#41	#6127	1	2	yes	—
651	#41	C₂×C₂²⋊D₁₃	1	2	yes	—
652	#41	C₂×C₂²⋊D₁₃	1	2	yes	—
653	C₂×Q₈	—	2	2	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	13	1	no	—
657	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
658	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
659	C₂×D₄	—	2	4	no	—
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	2	no	—
666	C₂×D₄	—	2	2	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	13	1	no	—
669	C₂×D₄	—	26	1	no	—
670	C₂×D₄	—	26	1	no	—
671	C₂×D₄	—	26	1	no	—
672	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
673	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
674	C₂²×C₄	—	2	4	no	—
675	C₂²×C₄	—	2	4	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	26	1	no	—
686	C₂²×C₄	—	26	1	no	—
687	C₂²×C₄	—	26	1	no	—
688	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
689	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
690	C₂²×C₄	#6127	1	1	yes	characteristic
691	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
692	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
693	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
694	Q₁₆	—	26	2	no	—
695	Q₁₆	—	26	2	no	—
696	SD₁₆	—	26	2	no	—
697	SD₁₆	—	26	2	no	—
698	SD₁₆	—	26	2	no	—
699	SD₁₆	—	26	2	no	—
700	D₈	—	26	2	no	—
701	D₈	—	26	2	no	—
702	M₁₆	—	2	4	no	—
703	M₁₆	—	2	4	no	—
704	M₁₆	—	2	4	no	—
705	M₁₆	—	2	1	no	—
706	M₁₆	—	2	1	no	—
707	M₁₆	—	2	2	no	—
708	M₁₆	—	2	2	no	—
709	M₁₆	—	2	4	no	—
710	M₁₆	—	2	4	no	—
711	M₁₆	—	2	2	no	—
712	M₁₆	—	2	2	no	—
713	M₁₆	—	26	1	no	—
714	M₁₆	—	26	1	no	—
715	M₁₆	—	26	1	no	—
716	M₁₆	—	26	1	no	—
717	M₁₆	—	52	2	no	—
718	M₁₆	C₂×C₂²⋊D₁₃	1	2	yes	—
719	M₁₆	C₂×C₂²⋊D₁₃	1	2	yes	—
720	C₂×C₈	—	2	4	no	—
721	C₂×C₈	—	2	4	no	—
722	C₂×C₈	—	2	4	no	—
723	C₂×C₈	—	2	1	no	—
724	C₂×C₈	—	2	1	no	—
725	C₂×C₈	—	2	1	no	—
726	C₂×C₈	—	2	1	no	—
727	C₂×C₈	—	2	4	no	—
728	C₂×C₈	—	2	4	no	—
729	C₂×C₈	—	13	1	no	—
730	C₂×C₈	—	13	1	no	—
731	C₂×C₈	—	13	1	no	—
732	C₂×C₈	—	13	1	no	—
733	C₂×C₈	—	26	1	no	—
734	C₂×C₈	—	26	1	no	—
735	C₂×C₈	—	26	1	no	—
736	C₂×C₈	—	26	1	no	—
737	C₂×C₈	—	26	1	no	—
738	C₂×C₈	—	26	1	no	—
739	C₂×C₈	—	52	2	no	—
740	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
741	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
742	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
743	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
744	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
745	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
746	C₄⋊C₄	—	13	1	no	—
747	C₄⋊C₄	—	13	1	no	—
748	C₄⋊C₄	—	26	1	no	—
749	C₄⋊C₄	—	26	1	no	—
750	C₂²⋊C₄	—	26	1	no	—
751	C₂²⋊C₄	—	26	1	no	—
752	C₂²⋊C₄	—	26	1	no	—
753	C₂²⋊C₄	—	26	1	no	—
754	C₂²⋊C₄	—	26	1	no	—
755	C₂²⋊C₄	—	52	2	no	—
756	C₄²	—	26	1	no	—
757	C₄²	—	26	1	no	—
758	C₄²	—	26	1	no	—
759	C₄²	—	26	1	no	—
760	C₄²	—	26	1	no	—
761	C₁₃	#21468	1	1	yes	characteristic, complemented, Sylow
762	C₂³	—	2	4	no	—
763	C₂³	—	2	1	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	4	1	no	—
768	C₂³	—	4	1	no	—
769	C₂³	—	8	1	no	—
770	C₂³	—	8	1	no	—
771	C₂³	—	26	1	no	—
772	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
773	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
774	C₂³	C₂×#6127	1	1	yes	characteristic
775	Q₈	—	2	4	no	—
776	Q₈	—	2	1	no	—
777	Q₈	—	2	1	no	—
778	Q₈	—	26	1	no	—
779	Q₈	—	26	1	no	—
780	Q₈	C₄×C₂²⋊D₁₃	1	2	yes	—
781	Q₈	C₄×C₂²⋊D₁₃	1	2	yes	—
782	D₄	—	2	4	no	—
783	D₄	—	2	4	no	—
784	D₄	—	2	4	no	—
785	D₄	—	2	2	no	—
786	D₄	—	2	2	no	—
787	D₄	—	2	2	no	—
788	D₄	—	2	2	no	—
789	D₄	—	2	1	no	—
790	D₄	—	2	1	no	—
791	D₄	—	26	1	no	—
792	D₄	—	26	1	no	—
793	D₄	—	52	1	no	—
794	D₄	—	52	1	no	—
795	D₄	—	104	1	no	—
796	D₄	—	104	1	no	—
797	D₄	C₄×C₂²⋊D₁₃	1	2	yes	—
798	D₄	C₄×C₂²⋊D₁₃	1	2	yes	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	26	2	no	—
819	C₂×C₄	—	26	1	no	—
820	C₂×C₄	—	26	1	no	—
821	C₂×C₄	—	26	1	no	—
822	C₂×C₄	—	52	1	no	—
823	C₂×C₄	—	52	1	no	—
824	C₂×C₄	—	52	1	no	—
825	C₂×C₄	—	52	1	no	—
826	C₂×C₄	—	52	1	no	—
827	C₂×C₄	—	52	1	no	—
828	C₂×C₄	—	52	1	no	—
829	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
830	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
831	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
832	C₂×C₄	C₂×#6127	1	1	yes	characteristic
833	C₂×C₄	C₂×#6127	1	1	yes	characteristic
834	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
835	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
836	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
837	C₈	—	2	2	no	—
838	C₈	—	2	2	no	—
839	C₈	—	2	1	no	—
840	C₈	—	2	1	no	—
841	C₈	—	26	1	no	—
842	C₈	—	26	1	no	—
843	C₈	—	26	1	no	—
844	C₈	—	26	1	no	—
845	C₈	—	52	1	no	—
846	C₈	—	52	1	no	—
847	C₈	#88207	1	2	yes	—
848	C₈	#88207	1	2	yes	—
849	C₂²	—	2	1	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	2	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	8	1	no	—
864	C₂²	—	8	1	no	—
865	C₂²	—	8	4	no	—
866	C₂²	—	52	1	no	—
867	C₂²	—	52	1	no	—
868	C₂²	—	52	1	no	—
869	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
870	C₂²	#11719496	1	1	yes	characteristic
871	C₂²	#11719496	1	1	yes	characteristic
872	C₄	—	2	1	no	—
873	C₄	—	2	2	no	—
874	C₄	—	2	2	no	—
875	C₄	—	2	1	no	—
876	C₄	—	52	2	no	—
877	C₄	—	52	1	no	—
878	C₄	—	52	1	no	—
879	C₄	—	52	1	no	—
880	C₄	—	104	1	no	—
881	C₄	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
882	C₄	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
883	C₄	#11719496	1	1	yes	characteristic
884	C₄	C₂×#88207	1	1	yes	characteristic
885	C₂	—	2	1	no	—
886	C₂	—	2	1	no	—
887	C₂	—	4	1	no	—
888	C₂	—	4	1	no	—
889	C₂	—	4	2	no	—
890	C₂	—	4	2	no	—
891	C₂	—	104	1	no	—
892	C₂	C₄×#88207	1	1	yes	characteristic
893	C₂	#13123743	1	1	yes	characteristic
894	C₂	#13123751	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×#568	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#13124054	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×#568	D₁₃
hypocenter	C₁₃	#21468
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×M₁₆ ◁ C₂×#568

Complements

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

N	H ≅ G/N	type
2. C₂×#11718806	C₂	semidirect
3. C₂×#11718805	C₂	semidirect
4. #13123539	C₂	semidirect
5. #13115163	C₂	semidirect
6. #13115163	C₂	semidirect
7. #13115138	C₂	semidirect
8. #13115111	C₂	semidirect
9. #13115111	C₂	semidirect
10. #13115041	C₂	semidirect
11. #13114780	C₂	semidirect
12. #13114678	C₂	semidirect
13. #13114671	C₂	semidirect
14. #13114617	C₂	semidirect
15. C₂×C₁₃×#568	C₂	semidirect
32. C₂×#88155	C₂²	semidirect
33. #11718900	C₄	semidirect
34. #11718900	C₄	semidirect
35. #11718899	C₄	semidirect
36. #11718899	C₄	semidirect
43. #11718889	C₄	semidirect
44. #11718888	C₄	semidirect
45. #11718879	C₄	semidirect
46. #11718878	C₄	semidirect
52. C₂×#88065	C₂²	semidirect
53. C₂×#88065	C₂²	semidirect
58. C₂×#88062	C₂²	semidirect
59. C₂×#88062	C₂²	semidirect
60. #11718771	C₂²	semidirect
61. #11718763	C₂²	semidirect
62. #11718762	C₂²	semidirect
63. C₂×#88055	C₂²	semidirect
64. C₂×C₈×Dic₁₃	C₂²	semidirect
65. #11718150	C₂²	semidirect
66. #11718150	C₂²	semidirect
67. #11718147	C₂²	semidirect
68. #11718147	C₂²	semidirect
69. #11718142	C₂²	semidirect
70. #11718142	C₂²	semidirect
95. C₁₃×#131	D₄	semidirect
96. C₁₃×#131	D₄	semidirect
315. C₂×#568	D₁₃	semidirect
546. #131	C₂²⋊D₁₃	semidirect
547. #131	C₂²⋊D₁₃	semidirect
761. C₁₃	#21468	semidirect

Maximal subgroups

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

subgroup	index
#13124054	2
C₂×#11718806	2
C₂×#11718805	2
#13123539	2
#13115163	2
#13115138	2
#13115111	2
#13115041	2
#13114780	2
#13114678	2
#13114671	2
#13114617	2
C₂×C₁₃×#568	2
#21468	13