Subgroups — #36719891

Order 22784.

2268 conjugacy classes of subgroups.

The subgroup lattice has 1516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26023444	C₂	1	1	yes	maximal, characteristic, complemented
2	#26023438	C₂	1	1	yes	maximal, characteristic, complemented
3	#26023409	C₂	1	1	yes	maximal, characteristic, complemented
4	#26023400	C₂	1	1	yes	maximal, characteristic, complemented
5	#26023376	C₂	1	1	yes	maximal, characteristic, complemented
6	#26023304	C₂	1	1	yes	maximal, characteristic, complemented
7	#26023304	C₂	1	1	yes	maximal, characteristic, complemented
8	#26023272	C₂	1	1	yes	maximal, characteristic, complemented
9	#26023248	C₂	1	1	yes	maximal, characteristic, complemented
10	#26023181	C₂	1	1	yes	maximal, characteristic, complemented
11	#26023162	C₂	1	1	yes	maximal, characteristic, complemented
12	#26023162	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×C₄⋊Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#26023129	C₂	1	1	yes	maximal, characteristic, complemented
15	#26023112	C₂	1	1	yes	maximal, characteristic, complemented
16	#26023058	C₂	1	1	yes	maximal, characteristic, complemented
17	#26023046	C₂	1	1	yes	maximal, characteristic, complemented
18	#26023031	C₂	1	1	yes	maximal, characteristic, complemented
19	#26023031	C₂	1	1	yes	maximal, characteristic, complemented
20	#26022957	C₂	1	1	yes	maximal, characteristic, complemented
21	#26022957	C₂	1	1	yes	maximal, characteristic, complemented
22	#26022957	C₂	1	1	yes	maximal, characteristic, complemented
23	#26022924	C₂	1	1	yes	maximal, characteristic, complemented
24	#26022885	C₂	1	1	yes	maximal, characteristic, complemented
25	#26022885	C₂	1	1	yes	maximal, characteristic, complemented
26	#26022885	C₂	1	1	yes	maximal, characteristic, complemented
27	#26022861	C₂	1	1	yes	maximal, characteristic, complemented
28	#121×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
29	#26022697	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#19151484	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#553×C₈₉	C₂	1	1	yes	maximal, characteristic
32	C₂×D₄×Dic₈₉	C₂²	1	1	yes	characteristic
33	C₂×D₄×Dic₈₉	C₂²	1	1	yes	characteristic
34	C₂×D₄×Dic₈₉	C₂²	1	1	yes	characteristic
35	C₂×D₄×Dic₈₉	C₂²	1	1	yes	characteristic
36	C₂×D₄×Dic₈₉	C₂²	1	1	yes	characteristic
37	C₂×D₄×Dic₈₉	C₂²	1	1	yes	characteristic
38	C₂×D₄×Dic₈₉	C₂²	1	1	yes	characteristic
39	C₂×D₄×Dic₈₉	C₂²	1	1	yes	characteristic
40	C₂×#15667971	C₂²	1	1	yes	characteristic
41	C₂²×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
43	C₂²×C₄×Dic₈₉	C₂²	1	1	yes	characteristic
44	#19151501	C₂²	1	1	yes	characteristic
45	#19151501	C₂²	1	1	yes	characteristic
46	#19151497	C₂²	1	1	yes	characteristic
47	#19151497	C₂²	1	1	yes	characteristic
48	#19151497	C₂²	1	1	yes	characteristic
49	#19151497	C₂²	1	1	yes	characteristic
50	#19151497	C₂²	1	1	yes	characteristic
51	#19151497	C₂²	1	1	yes	characteristic
52	#19151497	C₂²	1	1	yes	characteristic
53	#19151497	C₂²	1	1	yes	characteristic
54	#19151497	C₂²	1	1	yes	characteristic
55	#19151497	C₂²	1	1	yes	characteristic
56	#19151491	C₂²	1	1	yes	characteristic
57	#19151491	C₂²	1	1	yes	characteristic
58	#19151491	C₂²	1	1	yes	characteristic
59	#19151491	C₂²	1	1	yes	characteristic
60	#19151491	C₂²	1	1	yes	characteristic
61	#19151491	C₂²	1	1	yes	characteristic
62	#19151491	C₂²	1	1	yes	characteristic
63	#19151491	C₂²	1	1	yes	characteristic
64	#19151491	C₂²	1	1	yes	characteristic
65	#19151491	C₂²	1	1	yes	characteristic
66	#19151491	C₂²	1	1	yes	characteristic
67	#19151491	C₂²	1	1	yes	characteristic
68	#19151491	C₂²	1	1	yes	characteristic
69	#19151491	C₂²	1	1	yes	characteristic
70	#19151491	C₂²	1	1	yes	characteristic
71	#19151491	C₂²	1	1	yes	characteristic
72	#19151491	C₂²	1	1	yes	characteristic
73	#19151491	C₂²	1	1	yes	characteristic
74	#19151484	C₂²	1	1	yes	characteristic
75	#19151484	C₂²	1	1	yes	characteristic
76	#19151484	C₂²	1	1	yes	characteristic
77	#19151484	C₂²	1	1	yes	characteristic
78	#19151484	C₂²	1	1	yes	characteristic
79	#19151484	C₂²	1	1	yes	characteristic
80	#19151484	C₂²	1	1	yes	characteristic
81	#19151484	C₂²	1	1	yes	characteristic
82	#19151484	C₂²	1	1	yes	characteristic
83	#19151484	C₂²	1	1	yes	characteristic
84	#19151484	C₂²	1	1	yes	characteristic
85	#19151484	C₂²	1	1	yes	characteristic
86	#19151484	C₂²	1	1	yes	characteristic
87	#19151484	C₂²	1	1	yes	characteristic
88	#19151484	C₂²	1	1	yes	characteristic
89	#19151484	C₂²	1	1	yes	characteristic
90	#19151484	C₂²	1	1	yes	characteristic
91	#19151484	C₂²	1	1	yes	characteristic
92	#19151484	C₂²	1	1	yes	characteristic
93	#19151484	C₂²	1	1	yes	characteristic
94	#19151484	C₂²	1	1	yes	characteristic
95	#19151484	C₂²	1	1	yes	characteristic
96	#19151484	C₂²	1	1	yes	characteristic
97	#19151484	C₂²	1	1	yes	characteristic
98	#19151484	C₂²	1	1	yes	characteristic
99	#19151484	C₂²	1	1	yes	characteristic
100	#19151478	C₂²	1	1	yes	characteristic
101	#19151478	C₂²	1	1	yes	characteristic
102	#19151478	C₂²	1	1	yes	characteristic
103	#19151478	C₂²	1	1	yes	characteristic
104	#19151478	C₂²	1	1	yes	characteristic
105	#19151478	C₂²	1	1	yes	characteristic
106	#19151478	C₂²	1	1	yes	characteristic
107	#19151478	C₂²	1	1	yes	characteristic
108	#19151478	C₂²	1	1	yes	characteristic
109	#19151478	C₂²	1	1	yes	characteristic
110	#19151478	C₂²	1	1	yes	characteristic
111	#19151478	C₂²	1	1	yes	characteristic
112	#19151478	C₂²	1	1	yes	characteristic
113	#19151478	C₂²	1	1	yes	characteristic
114	#19151473	C₂²	1	1	yes	characteristic
115	#19151473	C₂²	1	1	yes	characteristic
116	#19151473	C₂²	1	1	yes	characteristic
117	#19151473	C₂²	1	1	yes	characteristic
118	#19151473	C₂²	1	1	yes	characteristic
119	#19151473	C₂²	1	1	yes	characteristic
120	#19151473	C₂²	1	1	yes	characteristic
121	#19151473	C₂²	1	1	yes	characteristic
122	#19151473	C₂²	1	1	yes	characteristic
123	#19151473	C₂²	1	1	yes	characteristic
124	#19151473	C₂²	1	1	yes	characteristic
125	#19151473	C₂²	1	1	yes	characteristic
126	#19151473	C₂²	1	1	yes	characteristic
127	#19151473	C₂²	1	1	yes	characteristic
128	#19151473	C₂²	1	1	yes	characteristic
129	#19151473	C₂²	1	1	yes	characteristic
130	#19151468	C₂²	1	1	yes	characteristic
131	#19151466	C₂²	1	1	yes	characteristic
132	#19151466	C₂²	1	1	yes	characteristic
133	#19151464	C₂²	1	1	yes	characteristic
134	#19151464	C₂²	1	1	yes	characteristic
135	#19151464	C₂²	1	1	yes	characteristic
136	#19151464	C₂²	1	1	yes	characteristic
137	#19151461	C₂²	1	1	yes	characteristic
138	#19151461	C₂²	1	1	yes	characteristic
139	#19151458	C₂²	1	1	yes	characteristic
140	#19151458	C₂²	1	1	yes	characteristic
141	#19151458	C₂²	1	1	yes	characteristic
142	#19151458	C₂²	1	1	yes	characteristic
143	#19151458	C₂²	1	1	yes	characteristic
144	#19151458	C₂²	1	1	yes	characteristic
145	#19151458	C₂²	1	1	yes	characteristic
146	#19151458	C₂²	1	1	yes	characteristic
147	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
148	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
149	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
150	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
151	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
152	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
153	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
154	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
155	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
156	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
157	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
158	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
159	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
160	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
161	C₄×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
162	C₄×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
163	C₄×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
164	C₄×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
165	#19151444	C₂²	1	1	yes	characteristic
166	C₂×#15667919	C₂²	1	1	yes	characteristic
167	C₂×#15667919	C₂²	1	1	yes	characteristic
168	C₂×#15667919	C₂²	1	1	yes	characteristic
169	C₂×#15667919	C₂²	1	1	yes	characteristic
170	C₂×#15667919	C₂²	1	1	yes	characteristic
171	C₂×#15667919	C₂²	1	1	yes	characteristic
172	#553×C₈₉	C₄	1	16	yes	complemented
173	C₂×#126×C₈₉	C₂²	1	1	yes	characteristic
174	C₂×#126×C₈₉	C₂²	1	1	yes	characteristic
175	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
176	C₂×#123×C₈₉	C₂²	1	1	yes	characteristic
177	C₂×#123×C₈₉	C₂²	1	1	yes	characteristic
178	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
179	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
180	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
181	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
182	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
183	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
184	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
185	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
186	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
187	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
188	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
189	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
190	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
191	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
192	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
193	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
194	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
195	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
196	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
197	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
198	D₄×Dic₈₉	—	4	2	no	—
199	D₄×Dic₈₉	—	4	2	no	—
200	D₄×Dic₈₉	—	4	2	no	—
201	D₄×Dic₈₉	—	4	2	no	—
202	D₄×Dic₈₉	—	4	2	no	—
203	D₄×Dic₈₉	—	4	2	no	—
204	D₄×Dic₈₉	—	4	2	no	—
205	D₄×Dic₈₉	—	4	2	no	—
206	#15667971	—	4	2	no	—
207	C₂×C₄⋊Dic₈₉	—	4	2	no	—
208	C₂×C₄⋊Dic₈₉	—	4	2	no	—
209	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
210	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
213	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
233	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
234	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
235	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
236	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
237	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
238	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
239	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
240	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
241	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
242	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
243	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
244	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
245	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
246	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
247	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
248	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
249	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
252	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
253	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
254	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
255	C₂×C₄×Dic₈₉	—	4	2	no	—
256	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
257	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
258	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
259	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
260	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
261	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
262	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
263	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
264	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
265	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
266	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
267	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
268	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
269	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
270	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
271	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
272	#15667919	C₂³	1	1	yes	characteristic
273	#15667919	C₂³	1	1	yes	characteristic
274	#15667919	C₂³	1	1	yes	characteristic
275	#15667919	C₂³	1	1	yes	characteristic
276	#15667919	C₂³	1	1	yes	characteristic
277	#15667919	C₂³	1	1	yes	characteristic
278	#15667919	C₂³	1	1	yes	characteristic
279	#15667919	C₂³	1	1	yes	characteristic
280	#15667919	C₂³	1	1	yes	characteristic
281	#15667919	C₂³	1	1	yes	characteristic
282	#15667919	C₂³	1	1	yes	characteristic
283	#15667919	C₂³	1	1	yes	characteristic
284	#15667919	C₂³	1	1	yes	characteristic
285	#15667919	C₂³	1	1	yes	characteristic
286	#15667919	C₂³	1	1	yes	characteristic
287	#15667919	C₂³	1	1	yes	characteristic
288	#15667919	C₂³	1	1	yes	characteristic
289	#15667919	C₂³	1	1	yes	characteristic
290	#15667919	C₂³	1	1	yes	characteristic
291	#15667919	C₂³	1	1	yes	characteristic
292	#15667919	C₂³	1	1	yes	characteristic
293	#15667919	C₂³	1	1	yes	characteristic
294	#15667919	C₂³	1	1	yes	characteristic
295	#15667919	C₂³	1	1	yes	characteristic
296	#15667919	C₂³	1	1	yes	characteristic
297	#15667919	C₂³	1	1	yes	characteristic
298	#15667919	C₂³	1	1	yes	characteristic
299	#15667919	C₂³	1	1	yes	characteristic
300	#15667919	C₂³	1	1	yes	characteristic
301	#15667919	C₂³	1	1	yes	characteristic
302	#15667919	C₂³	1	1	yes	characteristic
303	#15667919	C₂³	1	1	yes	characteristic
304	#15667919	C₂³	1	1	yes	characteristic
305	#15667919	C₂³	1	1	yes	characteristic
306	#15667919	C₂³	1	1	yes	characteristic
307	#15667919	C₂³	1	1	yes	characteristic
308	#15667919	C₂³	1	1	yes	characteristic
309	#15667919	C₂³	1	1	yes	characteristic
310	#15667919	C₂³	1	1	yes	characteristic
311	#15667919	C₂³	1	1	yes	characteristic
312	#15667919	C₂³	1	1	yes	characteristic
313	#15667919	C₂³	1	1	yes	characteristic
314	#15667919	C₂³	1	1	yes	characteristic
315	#15667919	C₂³	1	1	yes	characteristic
316	#15667919	C₂³	1	1	yes	characteristic
317	#15667919	C₂³	1	1	yes	characteristic
318	#15667919	C₂³	1	1	yes	characteristic
319	#15667919	C₂³	1	1	yes	characteristic
320	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
321	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
322	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
323	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
324	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
325	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
326	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
327	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
328	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
329	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
330	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
331	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
332	#126×C₈₉	C₂×C₄	1	8	yes	complemented
333	#126×C₈₉	C₂×C₄	1	8	yes	complemented
334	#125×C₈₉	C₂×C₄	1	8	yes	complemented
335	#123×C₈₉	C₂×C₄	1	8	yes	complemented
336	#123×C₈₉	C₂×C₄	1	8	yes	complemented
337	#121×C₈₉	C₂×C₄	1	8	yes	complemented
338	#121×C₈₉	C₂×C₄	1	8	yes	complemented
339	#121×C₈₉	C₂×C₄	1	8	yes	complemented
340	#121×C₈₉	C₂×C₄	1	8	yes	complemented
341	C₄×D₄×C₈₉	C₂×C₄	1	8	yes	complemented
342	C₄×D₄×C₈₉	C₂×C₄	1	8	yes	complemented
343	C₄×D₄×C₈₉	C₂×C₄	1	8	yes	complemented
344	C₄×D₄×C₈₉	C₂×C₄	1	8	yes	complemented
345	#117×C₈₉	C₂×C₄	1	8	yes	complemented
346	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	8	yes	complemented
347	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
348	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
349	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
350	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
351	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
352	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
353	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
354	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
355	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
356	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
357	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
358	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
359	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
360	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
361	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
362	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
363	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
364	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
365	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
366	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
367	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
368	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
369	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
370	C₂²×Dic₈₉	—	2	2	no	—
371	C₂²×Dic₈₉	—	2	2	no	—
372	C₂²×Dic₈₉	—	2	2	no	—
373	C₂²×Dic₈₉	—	2	2	no	—
374	C₂²×Dic₈₉	—	2	2	no	—
375	C₂²×Dic₈₉	—	2	2	no	—
376	C₂²×Dic₈₉	—	2	2	no	—
377	C₂²×Dic₈₉	—	4	1	no	—
378	C₂²×Dic₈₉	—	4	1	no	—
379	C₂²×Dic₈₉	—	4	1	no	—
380	C₂²×Dic₈₉	—	4	1	no	—
381	C₂²×Dic₈₉	—	4	1	no	—
382	C₂²×Dic₈₉	—	4	1	no	—
383	C₂²×Dic₈₉	—	4	1	no	—
384	C₂²×Dic₈₉	—	4	1	no	—
385	C₂²×Dic₈₉	—	4	1	no	—
386	C₂²×Dic₈₉	—	4	1	no	—
387	C₂²×Dic₈₉	—	4	1	no	—
388	C₂²×Dic₈₉	—	4	1	no	—
389	C₂²×Dic₈₉	—	4	1	no	—
390	C₂²×Dic₈₉	—	4	1	no	—
391	C₂²×Dic₈₉	—	4	1	no	—
392	C₂²×Dic₈₉	—	4	1	no	—
393	C₂²×Dic₈₉	—	4	1	no	—
394	C₂²×Dic₈₉	—	4	1	no	—
395	C₂²×Dic₈₉	—	4	1	no	—
396	C₂²×Dic₈₉	—	4	1	no	—
397	C₂²×Dic₈₉	—	4	1	no	—
398	C₂²×Dic₈₉	—	4	1	no	—
399	C₂²×Dic₈₉	—	4	1	no	—
400	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
401	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
402	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
403	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
404	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
405	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
406	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
407	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
408	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
409	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
410	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
411	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
412	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
413	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
414	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
415	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
416	C₄⋊Dic₈₉	—	2	2	no	—
417	C₄⋊Dic₈₉	—	2	2	no	—
418	C₄⋊Dic₈₉	—	2	2	no	—
419	C₄⋊Dic₈₉	—	4	1	no	—
420	C₄⋊Dic₈₉	—	4	1	no	—
421	C₄⋊Dic₈₉	—	4	1	no	—
422	C₄⋊Dic₈₉	—	4	1	no	—
423	C₄⋊Dic₈₉	—	4	1	no	—
424	C₄⋊Dic₈₉	—	4	1	no	—
425	C₄⋊Dic₈₉	—	4	1	no	—
426	C₄⋊Dic₈₉	—	4	1	no	—
427	C₄⋊Dic₈₉	—	4	1	no	—
428	C₄⋊Dic₈₉	—	4	1	no	—
429	C₄⋊Dic₈₉	—	4	1	no	—
430	C₄⋊Dic₈₉	—	4	1	no	—
431	C₄⋊Dic₈₉	—	4	1	no	—
432	C₄⋊Dic₈₉	—	4	1	no	—
433	C₄⋊Dic₈₉	—	4	1	no	—
434	C₄⋊Dic₈₉	—	4	1	no	—
435	C₄⋊Dic₈₉	—	4	1	no	—
436	C₄⋊Dic₈₉	—	4	1	no	—
437	C₄⋊Dic₈₉	—	4	1	no	—
438	C₄⋊Dic₈₉	—	4	1	no	—
439	C₄⋊Dic₈₉	—	4	1	no	—
440	C₂²⋊Dic₈₉	—	2	2	no	—
441	C₂²⋊Dic₈₉	—	2	2	no	—
442	C₂²⋊Dic₈₉	—	2	2	no	—
443	C₂²⋊Dic₈₉	—	2	2	no	—
444	C₂²⋊Dic₈₉	—	2	2	no	—
445	C₂²⋊Dic₈₉	—	4	1	no	—
446	C₂²⋊Dic₈₉	—	4	1	no	—
447	C₂²⋊Dic₈₉	—	4	1	no	—
448	C₂²⋊Dic₈₉	—	4	1	no	—
449	C₂²⋊Dic₈₉	—	4	1	no	—
450	C₂²⋊Dic₈₉	—	4	1	no	—
451	C₂²⋊Dic₈₉	—	4	1	no	—
452	C₂²⋊Dic₈₉	—	4	1	no	—
453	C₂²⋊Dic₈₉	—	4	1	no	—
454	C₂²⋊Dic₈₉	—	4	1	no	—
455	C₂²⋊Dic₈₉	—	4	1	no	—
456	C₂²⋊Dic₈₉	—	4	1	no	—
457	C₂²⋊Dic₈₉	—	4	1	no	—
458	C₂²⋊Dic₈₉	—	4	1	no	—
459	C₂²⋊Dic₈₉	—	4	1	no	—
460	C₂²⋊Dic₈₉	—	4	1	no	—
461	C₂²⋊Dic₈₉	—	4	1	no	—
462	C₄×Dic₈₉	—	2	2	no	—
463	C₄×Dic₈₉	—	2	2	no	—
464	C₄×Dic₈₉	—	4	1	no	—
465	C₄×Dic₈₉	—	4	1	no	—
466	C₄×Dic₈₉	—	4	1	no	—
467	C₄×Dic₈₉	—	4	1	no	—
468	C₄×Dic₈₉	—	4	1	no	—
469	C₄×Dic₈₉	—	4	1	no	—
470	C₄×Dic₈₉	—	4	1	no	—
471	C₄×Dic₈₉	—	4	1	no	—
472	C₄×Dic₈₉	—	4	1	no	—
473	C₄×Dic₈₉	—	4	1	no	—
474	C₄×Dic₈₉	—	4	1	no	—
475	C₄×Dic₈₉	—	4	1	no	—
476	C₄×Dic₈₉	—	4	1	no	—
477	C₄×Dic₈₉	—	4	1	no	—
478	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
479	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
480	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
481	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
482	C₂×D₄×C₈₉	—	2	2	no	—
483	C₂×D₄×C₈₉	—	2	2	no	—
484	C₂×D₄×C₈₉	—	2	2	no	—
485	C₂×D₄×C₈₉	—	2	2	no	—
486	C₂×D₄×C₈₉	—	2	2	no	—
487	C₂×D₄×C₈₉	—	2	2	no	—
488	C₂×D₄×C₈₉	—	4	1	no	—
489	C₂×D₄×C₈₉	—	4	1	no	—
490	C₂×D₄×C₈₉	—	4	1	no	—
491	C₂×D₄×C₈₉	—	4	1	no	—
492	C₂×D₄×C₈₉	—	4	1	no	—
493	C₂×D₄×C₈₉	—	4	1	no	—
494	C₂×D₄×C₈₉	C₂²×C₄	1	4	yes	—
495	C₂×D₄×C₈₉	C₂²×C₄	1	4	yes	—
496	C₂×D₄×C₈₉	C₂²×C₄	1	4	yes	—
497	C₂×D₄×C₈₉	C₂²×C₄	1	4	yes	—
498	C₂×D₄×C₈₉	C₂²×C₄	1	4	yes	—
499	C₂×D₄×C₈₉	C₂²×C₄	1	4	yes	—
500	C₂²×C₄×C₈₉	—	4	1	no	—
501	C₂²×C₄×C₈₉	—	4	1	no	—
502	C₂²×C₄×C₈₉	—	4	1	no	—
503	C₂²×C₄×C₈₉	—	4	1	no	—
504	C₂²×C₄×C₈₉	—	4	1	no	—
505	C₂²×C₄×C₈₉	—	4	1	no	—
506	C₂²×C₄×C₈₉	—	4	1	no	—
507	C₂²×C₄×C₈₉	—	4	1	no	—
508	C₂²×C₄×C₈₉	—	4	1	no	—
509	C₂²×C₄×C₈₉	—	4	1	no	—
510	C₂²×C₄×C₈₉	—	4	1	no	—
511	C₂²×C₄×C₈₉	—	4	1	no	—
512	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
513	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
514	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
515	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
516	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
517	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
518	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
519	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
520	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
521	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
522	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
523	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
524	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
525	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
526	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
527	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
528	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
529	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
530	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
531	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
532	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
533	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
534	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
535	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
536	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
537	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
538	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
539	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
540	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
541	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
542	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
543	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
544	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
545	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
546	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
547	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
548	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
549	C₄²×C₈₉	C₂²×C₄	1	4	yes	—
550	C₄²×C₈₉	C₂²×C₄	1	4	yes	—
551	C₄²×C₈₉	C₂²×C₄	1	4	yes	—
552	C₂³×C₈₉	—	2	1	no	—
553	C₂³×C₈₉	—	2	1	no	—
554	C₂³×C₈₉	—	2	1	no	—
555	C₂³×C₈₉	—	2	1	no	—
556	C₂³×C₈₉	—	2	1	no	—
557	C₂³×C₈₉	—	2	1	no	—
558	C₂³×C₈₉	—	2	1	no	—
559	C₂³×C₈₉	—	2	1	no	—
560	C₂³×C₈₉	—	2	1	no	—
561	C₂³×C₈₉	—	2	1	no	—
562	C₂³×C₈₉	—	2	1	no	—
563	C₂³×C₈₉	—	2	1	no	—
564	C₂³×C₈₉	—	2	1	no	—
565	C₂³×C₈₉	—	2	1	no	—
566	C₂³×C₈₉	—	2	1	no	—
567	C₂³×C₈₉	—	2	1	no	—
568	C₂³×C₈₉	—	2	1	no	—
569	C₂³×C₈₉	—	2	1	no	—
570	C₂³×C₈₉	—	2	1	no	—
571	C₂³×C₈₉	—	2	1	no	—
572	C₂³×C₈₉	—	2	1	no	—
573	C₂³×C₈₉	—	2	1	no	—
574	C₂³×C₈₉	C₂³×C₄	1	2	yes	—
575	C₂³×C₈₉	C₂³×C₄	1	2	yes	—
576	C₂³×C₈₉	C₂³×C₄	1	2	yes	—
577	C₂³×C₈₉	C₂³×C₄	1	2	yes	—
578	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
579	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
580	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
581	D₄×C₈₉	—	2	8	no	—
582	D₄×C₈₉	—	2	8	no	—
583	D₄×C₈₉	—	2	8	no	—
584	D₄×C₈₉	—	4	4	no	—
585	D₄×C₈₉	—	4	4	no	—
586	D₄×C₈₉	—	4	4	no	—
587	C₂×C₄×C₈₉	—	2	1	no	—
588	C₂×C₄×C₈₉	—	2	1	no	—
589	C₂×C₄×C₈₉	—	2	1	no	—
590	C₂×C₄×C₈₉	—	2	1	no	—
591	C₂×C₄×C₈₉	—	2	1	no	—
592	C₂×C₄×C₈₉	—	2	1	no	—
593	C₂×C₄×C₈₉	—	2	1	no	—
594	C₂×C₄×C₈₉	—	2	1	no	—
595	C₂×C₄×C₈₉	—	2	1	no	—
596	C₂×C₄×C₈₉	—	2	1	no	—
597	C₂×C₄×C₈₉	—	2	1	no	—
598	C₂×C₄×C₈₉	—	2	1	no	—
599	C₂×C₄×C₈₉	—	2	1	no	—
600	C₂×C₄×C₈₉	—	2	1	no	—
601	C₂×C₄×C₈₉	—	2	1	no	—
602	C₂×C₄×C₈₉	—	2	1	no	—
603	C₂×C₄×C₈₉	—	2	1	no	—
604	C₂×C₄×C₈₉	—	2	1	no	—
605	C₂×C₄×C₈₉	—	2	1	no	—
606	C₂×C₄×C₈₉	—	2	1	no	—
607	C₂×C₄×C₈₉	—	2	1	no	—
608	C₂×C₄×C₈₉	—	2	1	no	—
609	C₂×C₄×C₈₉	—	4	4	no	—
610	C₂×C₄×C₈₉	—	4	4	no	—
611	C₂×C₄×C₈₉	—	4	4	no	—
612	C₂×C₄×C₈₉	—	4	4	no	—
613	C₂×C₄×C₈₉	—	4	4	no	—
614	C₂×C₄×C₈₉	—	4	4	no	—
615	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
616	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
617	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
618	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
619	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
620	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
621	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
622	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
623	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
624	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
625	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
626	C₂×Dic₈₉	—	2	1	no	—
627	C₂×Dic₈₉	—	2	1	no	—
628	C₂×Dic₈₉	—	2	1	no	—
629	C₂×Dic₈₉	—	2	1	no	—
630	C₂×Dic₈₉	—	2	1	no	—
631	C₂×Dic₈₉	—	2	1	no	—
632	C₂×Dic₈₉	—	2	1	no	—
633	C₂×Dic₈₉	—	2	1	no	—
634	C₂×Dic₈₉	—	2	1	no	—
635	C₂×Dic₈₉	—	2	1	no	—
636	C₂×Dic₈₉	—	2	1	no	—
637	C₂×Dic₈₉	—	2	1	no	—
638	C₂×Dic₈₉	—	2	1	no	—
639	C₂×Dic₈₉	—	2	1	no	—
640	C₂×Dic₈₉	—	2	1	no	—
641	C₂×Dic₈₉	—	2	1	no	—
642	C₂×Dic₈₉	—	2	1	no	—
643	C₂×Dic₈₉	—	2	1	no	—
644	C₂×Dic₈₉	—	2	1	no	—
645	C₂×Dic₈₉	—	2	1	no	—
646	C₂×Dic₈₉	—	2	1	no	—
647	C₂×Dic₈₉	—	2	1	no	—
648	C₂×Dic₈₉	—	2	1	no	—
649	C₂×Dic₈₉	—	2	1	no	—
650	C₂×Dic₈₉	—	2	1	no	—
651	C₂×Dic₈₉	—	2	1	no	—
652	C₂×Dic₈₉	—	2	1	no	—
653	C₂×Dic₈₉	—	2	1	no	—
654	C₂×Dic₈₉	—	2	1	no	—
655	C₂×Dic₈₉	—	2	1	no	—
656	C₂×Dic₈₉	—	2	1	no	—
657	C₂×Dic₈₉	—	2	1	no	—
658	C₂×Dic₈₉	—	2	1	no	—
659	C₂×Dic₈₉	—	2	1	no	—
660	C₂×Dic₈₉	—	2	1	no	—
661	C₂×Dic₈₉	—	2	1	no	—
662	C₂×Dic₈₉	—	2	1	no	—
663	C₂×Dic₈₉	—	2	1	no	—
664	C₂×Dic₈₉	—	2	1	no	—
665	C₂×Dic₈₉	—	2	1	no	—
666	C₂×Dic₈₉	—	2	1	no	—
667	C₂×Dic₈₉	—	2	1	no	—
668	C₂×Dic₈₉	—	2	1	no	—
669	C₂×Dic₈₉	—	2	1	no	—
670	C₂×Dic₈₉	—	2	1	no	—
671	C₂×Dic₈₉	—	2	1	no	—
672	C₂×Dic₈₉	—	2	1	no	—
673	C₂×Dic₈₉	—	4	4	no	—
674	C₂×Dic₈₉	—	4	4	no	—
675	C₂×Dic₈₉	—	8	2	no	—
676	C₂×Dic₈₉	—	8	2	no	—
677	C₂×Dic₈₉	—	8	2	no	—
678	C₂×Dic₈₉	—	8	2	no	—
679	C₂×Dic₈₉	—	8	2	no	—
680	C₂×Dic₈₉	—	8	2	no	—
681	C₂×Dic₈₉	—	8	2	no	—
682	C₂×Dic₈₉	—	8	2	no	—
683	C₂×Dic₈₉	H(5,𝔽₂)	1	2	yes	—
684	C₂²×C₈₉	—	2	2	no	—
685	C₂²×C₈₉	—	2	2	no	—
686	C₂²×C₈₉	—	2	2	no	—
687	C₂²×C₈₉	—	2	2	no	—
688	C₂²×C₈₉	—	2	2	no	—
689	C₂²×C₈₉	—	2	2	no	—
690	C₂²×C₈₉	—	2	2	no	—
691	C₂²×C₈₉	—	2	2	no	—
692	C₂²×C₈₉	—	2	2	no	—
693	C₂²×C₈₉	—	2	2	no	—
694	C₂²×C₈₉	—	2	2	no	—
695	C₂²×C₈₉	—	2	2	no	—
696	C₂²×C₈₉	—	2	2	no	—
697	C₂²×C₈₉	—	2	2	no	—
698	C₂²×C₈₉	—	2	2	no	—
699	C₂²×C₈₉	—	4	1	no	—
700	C₂²×C₈₉	—	4	1	no	—
701	C₂²×C₈₉	—	4	1	no	—
702	C₂²×C₈₉	—	4	1	no	—
703	C₂²×C₈₉	—	4	1	no	—
704	C₂²×C₈₉	—	4	1	no	—
705	C₂²×C₈₉	—	4	1	no	—
706	C₂²×C₈₉	—	4	1	no	—
707	C₂²×C₈₉	—	4	1	no	—
708	C₂²×C₈₉	—	4	1	no	—
709	C₂²×C₈₉	—	4	1	no	—
710	C₂²×C₈₉	—	4	1	no	—
711	C₂²×C₈₉	#520	1	4	yes	—
712	C₂²×C₈₉	C₂⁴×C₄	1	1	yes	characteristic
713	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
714	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
715	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
716	C₂²×C₈₉	#585	1	1	yes	characteristic
717	C₂²×C₈₉	#585	1	1	yes	characteristic
718	C₂²×C₈₉	#585	1	1	yes	characteristic
719	C₄×C₈₉	—	2	2	no	—
720	C₄×C₈₉	—	2	2	no	—
721	C₄×C₈₉	—	2	2	no	—
722	C₄×C₈₉	—	2	2	no	—
723	C₄×C₈₉	—	2	2	no	—
724	C₄×C₈₉	—	2	2	no	—
725	C₄×C₈₉	—	2	2	no	—
726	C₄×C₈₉	—	2	2	no	—
727	C₄×C₈₉	—	2	2	no	—
728	C₄×C₈₉	—	2	2	no	—
729	C₄×C₈₉	—	2	2	no	—
730	Dic₈₉	—	2	2	no	—
731	Dic₈₉	—	4	1	no	—
732	Dic₈₉	—	4	1	no	—
733	Dic₈₉	—	4	1	no	—
734	Dic₈₉	—	4	1	no	—
735	Dic₈₉	—	4	1	no	—
736	Dic₈₉	—	4	1	no	—
737	Dic₈₉	—	4	1	no	—
738	Dic₈₉	—	4	1	no	—
739	Dic₈₉	—	4	1	no	—
740	Dic₈₉	—	4	1	no	—
741	Dic₈₉	—	4	1	no	—
742	Dic₈₉	—	4	1	no	—
743	Dic₈₉	—	4	1	no	—
744	Dic₈₉	—	4	1	no	—
745	Dic₈₉	—	4	1	no	—
746	#34497	—	89	1	no	maximal, Sylow
747	C₂×C₈₉	—	2	4	no	—
748	C₂×C₈₉	—	4	2	no	—
749	C₂×C₈₉	—	4	2	no	—
750	C₂×C₈₉	—	4	2	no	—
751	C₂×C₈₉	C₂×#520	1	1	yes	characteristic
752	C₂×C₈₉	#3428	1	1	yes	characteristic
753	C₂×C₈₉	C₄×H(5,𝔽₂)	1	1	yes	characteristic
754	C₂×C₈₉	#3534	1	1	yes	characteristic
755	C₂×C₈₉	#3541	1	1	yes	characteristic
756	C₂×C₈₉	#3553	1	1	yes	characteristic
757	C₂×C₈₉	#3560	1	1	yes	characteristic
758	C₂×#553	D₈₉	1	1	yes	characteristic
759	#2383	—	89	1	no	—
760	#2382	—	89	1	no	—
761	#2377	—	89	1	no	—
762	#2376	—	89	1	no	—
763	#2373	—	89	1	no	—
764	#2364	—	89	1	no	—
765	#2364	—	89	1	no	—
766	#2361	—	89	1	no	—
767	#2359	—	89	1	no	—
768	#2352	—	89	1	no	—
769	#2349	—	89	1	no	—
770	#2349	—	89	1	no	—
771	D₄×C₄⋊C₄	—	89	1	no	—
772	#2345	—	89	1	no	—
773	#2343	—	89	1	no	—
774	#2336	—	89	1	no	—
775	#2335	—	89	1	no	—
776	#2334	—	89	1	no	—
777	#2334	—	89	1	no	—
778	#2325	—	89	1	no	—
779	#2325	—	89	1	no	—
780	#2325	—	89	1	no	—
781	#2322	—	89	1	no	—
782	#2318	—	89	1	no	—
783	#2318	—	89	1	no	—
784	#2318	—	89	1	no	—
785	#2314	—	89	1	no	—
786	C₄×#121	—	89	1	no	—
787	#2290	—	89	1	no	—
788	C₂×#387	—	89	1	no	—
789	C₈₉	#34497	1	1	yes	characteristic, complemented, Sylow
790	#553	Dic₈₉	1	16	yes	complemented
791	C₂×#126	C₂×D₈₉	1	1	yes	characteristic
792	C₂×#126	C₂×D₈₉	1	1	yes	characteristic
793	C₂×#125	C₂×D₈₉	1	1	yes	characteristic
794	C₂×#123	C₂×D₈₉	1	1	yes	characteristic
795	C₂×#123	C₂×D₈₉	1	1	yes	characteristic
796	C₂×#121	C₂×D₈₉	1	1	yes	characteristic
797	C₂×#121	C₂×D₈₉	1	1	yes	characteristic
798	C₂×#121	C₂×D₈₉	1	1	yes	characteristic
799	C₂×#121	C₂×D₈₉	1	1	yes	characteristic
800	C₂×C₄×D₄	—	89	1	no	—
801	C₂×C₄×D₄	—	89	1	no	—
802	C₂×C₄×D₄	—	89	1	no	—
803	C₂×C₄×D₄	—	89	1	no	—
804	C₂×C₄×D₄	—	89	1	no	—
805	C₂×C₄×D₄	—	89	1	no	—
806	C₂×C₄×D₄	—	89	1	no	—
807	C₂×C₄×D₄	—	89	1	no	—
808	C₂×C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
809	C₂×C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
810	C₂×C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
811	C₂×C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
812	C₂×#117	—	89	1	no	—
813	C₂×#117	C₂×D₈₉	1	1	yes	characteristic
814	C₂²×C₄⋊C₄	—	89	1	no	—
815	C₂²×C₄⋊C₄	—	89	1	no	—
816	C₂²×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
817	C₂²×C₄²	—	89	1	no	—
818	#390	—	89	1	no	—
819	#390	—	89	1	no	—
820	#389	—	89	1	no	—
821	#389	—	89	1	no	—
822	#389	—	89	1	no	—
823	#389	—	89	1	no	—
824	#389	—	89	1	no	—
825	#389	—	89	1	no	—
826	#389	—	89	1	no	—
827	#389	—	89	1	no	—
828	#389	—	89	1	no	—
829	#389	—	89	1	no	—
830	#388	—	89	1	no	—
831	#388	—	89	1	no	—
832	#388	—	89	1	no	—
833	#388	—	89	1	no	—
834	#388	—	89	1	no	—
835	#388	—	89	1	no	—
836	#388	—	89	1	no	—
837	#388	—	89	1	no	—
838	#388	—	89	1	no	—
839	#388	—	89	1	no	—
840	#388	—	89	1	no	—
841	#388	—	89	1	no	—
842	#388	—	89	1	no	—
843	#388	—	89	1	no	—
844	#388	—	89	1	no	—
845	#388	—	89	1	no	—
846	#388	—	89	1	no	—
847	#388	—	89	1	no	—
848	#387	—	89	1	no	—
849	#387	—	89	1	no	—
850	#387	—	89	1	no	—
851	#387	—	89	1	no	—
852	#387	—	89	1	no	—
853	#387	—	89	1	no	—
854	#387	—	89	1	no	—
855	#387	—	89	1	no	—
856	#387	—	89	1	no	—
857	#387	—	89	1	no	—
858	#387	—	89	1	no	—
859	#387	—	89	1	no	—
860	#387	—	89	1	no	—
861	#387	—	89	1	no	—
862	#387	—	89	1	no	—
863	#387	—	89	1	no	—
864	#387	—	89	1	no	—
865	#387	—	89	1	no	—
866	#387	—	89	1	no	—
867	#387	—	89	1	no	—
868	#387	—	89	1	no	—
869	#387	—	89	1	no	—
870	#387	—	89	1	no	—
871	#387	—	89	1	no	—
872	#387	—	89	1	no	—
873	#387	—	89	1	no	—
874	#386	—	89	1	no	—
875	#386	—	89	1	no	—
876	#386	—	89	1	no	—
877	#386	—	89	1	no	—
878	#386	—	89	1	no	—
879	#386	—	89	1	no	—
880	#386	—	89	1	no	—
881	#386	—	89	1	no	—
882	#386	—	89	1	no	—
883	#386	—	89	1	no	—
884	#386	—	89	1	no	—
885	#386	—	89	1	no	—
886	#386	—	89	1	no	—
887	#386	—	89	1	no	—
888	#385	—	89	1	no	—
889	#385	—	89	1	no	—
890	#385	—	89	1	no	—
891	#385	—	89	1	no	—
892	#385	—	89	1	no	—
893	#385	—	89	1	no	—
894	#385	—	89	1	no	—
895	#385	—	89	1	no	—
896	#385	—	89	1	no	—
897	#385	—	89	1	no	—
898	#385	—	89	1	no	—
899	#385	—	89	1	no	—
900	#385	—	89	1	no	—
901	#385	—	89	1	no	—
902	#385	—	89	1	no	—
903	#385	—	89	1	no	—
904	#384	—	89	1	no	—
905	#383	—	89	1	no	—
906	#383	—	89	1	no	—
907	#382	—	89	1	no	—
908	#382	—	89	1	no	—
909	#382	—	89	1	no	—
910	#382	—	89	1	no	—
911	#381	—	89	1	no	—
912	#381	—	89	1	no	—
913	#380	—	89	1	no	—
914	#380	—	89	1	no	—
915	#380	—	89	1	no	—
916	#380	—	89	1	no	—
917	#380	—	89	1	no	—
918	#380	—	89	1	no	—
919	#380	—	89	1	no	—
920	#380	—	89	1	no	—
921	C₄×C₄⋊C₄	—	89	1	no	—
922	C₄×C₄⋊C₄	—	89	1	no	—
923	C₄×C₄⋊C₄	—	89	1	no	—
924	C₄×C₄⋊C₄	—	89	1	no	—
925	C₄×C₄⋊C₄	—	89	1	no	—
926	C₄×C₄⋊C₄	—	89	1	no	—
927	C₄×C₄⋊C₄	—	89	1	no	—
928	C₄×C₄⋊C₄	—	89	1	no	—
929	C₄×C₂²⋊C₄	—	89	1	no	—
930	C₄×C₂²⋊C₄	—	89	1	no	—
931	C₄×C₂²⋊C₄	—	89	1	no	—
932	C₄×C₂²⋊C₄	—	89	1	no	—
933	C₄×C₂²⋊C₄	—	89	1	no	—
934	C₄×C₂²⋊C₄	—	89	1	no	—
935	C₄×C₂²⋊C₄	—	89	1	no	—
936	C₄×C₂²⋊C₄	—	89	1	no	—
937	C₄×C₂²⋊C₄	—	89	1	no	—
938	C₄×C₂²⋊C₄	—	89	1	no	—
939	#376	—	89	1	no	—
940	C₂×#95	—	89	1	no	—
941	C₂×#95	—	89	1	no	—
942	C₂×#95	—	89	1	no	—
943	C₂×#95	—	89	1	no	—
944	C₂×#95	—	89	1	no	—
945	C₂×#95	—	89	1	no	—
946	C₂²×D₄	C₂²×D₈₉	1	1	yes	characteristic
947	C₂²×D₄	C₂²×D₈₉	1	1	yes	characteristic
948	C₂²×D₄	C₂²×D₈₉	1	1	yes	characteristic
949	C₂²×D₄	C₂²×D₈₉	1	1	yes	characteristic
950	C₂²×D₄	C₂²×D₈₉	1	1	yes	characteristic
951	C₂²×D₄	C₂²×D₈₉	1	1	yes	characteristic
952	C₂³×C₄	—	89	1	no	—
953	C₂³×C₄	—	89	1	no	—
954	C₂³×C₄	—	89	1	no	—
955	C₂³×C₄	—	89	1	no	—
956	C₂³×C₄	—	89	1	no	—
957	C₂³×C₄	—	89	1	no	—
958	C₂³×C₄	—	89	1	no	—
959	C₂³×C₄	—	89	1	no	—
960	C₂³×C₄	—	89	1	no	—
961	C₂³×C₄	—	89	1	no	—
962	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
963	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
964	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
965	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
966	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
967	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
968	#126	C₂×Dic₈₉	1	8	yes	complemented
969	#126	C₂×Dic₈₉	1	8	yes	complemented
970	#125	C₂×Dic₈₉	1	8	yes	complemented
971	#123	C₂×Dic₈₉	1	8	yes	complemented
972	#123	C₂×Dic₈₉	1	8	yes	complemented
973	#121	C₂×Dic₈₉	1	8	yes	complemented
974	#121	C₂×Dic₈₉	1	8	yes	complemented
975	#121	C₂×Dic₈₉	1	8	yes	complemented
976	#121	C₂×Dic₈₉	1	8	yes	complemented
977	C₄×D₄	—	356	2	no	—
978	C₄×D₄	—	356	2	no	—
979	C₄×D₄	—	356	2	no	—
980	C₄×D₄	—	356	2	no	—
981	C₄×D₄	—	356	2	no	—
982	C₄×D₄	—	356	2	no	—
983	C₄×D₄	—	356	2	no	—
984	C₄×D₄	—	356	2	no	—
985	C₄×D₄	C₂×Dic₈₉	1	8	yes	complemented
986	C₄×D₄	C₂×Dic₈₉	1	8	yes	complemented
987	C₄×D₄	C₂×Dic₈₉	1	8	yes	complemented
988	C₄×D₄	C₂×Dic₈₉	1	8	yes	complemented
989	#117	—	356	2	no	—
990	#117	C₂×Dic₈₉	1	8	yes	complemented
991	C₂×C₄⋊C₄	—	89	1	no	—
992	C₂×C₄⋊C₄	—	89	1	no	—
993	C₂×C₄⋊C₄	—	89	1	no	—
994	C₂×C₄⋊C₄	—	89	1	no	—
995	C₂×C₄⋊C₄	—	89	1	no	—
996	C₂×C₄⋊C₄	—	89	1	no	—
997	C₂×C₄⋊C₄	—	89	1	no	—
998	C₂×C₄⋊C₄	—	89	1	no	—
999	C₂×C₄⋊C₄	—	89	1	no	—
1000	C₂×C₄⋊C₄	—	89	1	no	—
1001	C₂×C₄⋊C₄	—	89	1	no	—
1002	C₂×C₄⋊C₄	—	89	1	no	—
1003	C₂×C₄⋊C₄	—	89	1	no	—
1004	C₂×C₄⋊C₄	—	89	1	no	—
1005	C₂×C₄⋊C₄	—	89	1	no	—
1006	C₂×C₄⋊C₄	—	89	1	no	—
1007	C₂×C₄⋊C₄	—	89	1	no	—
1008	C₂×C₄⋊C₄	—	89	1	no	—
1009	C₂×C₄⋊C₄	—	89	1	no	—
1010	C₂×C₄⋊C₄	—	89	1	no	—
1011	C₂×C₄⋊C₄	—	89	1	no	—
1012	C₂×C₄⋊C₄	—	89	1	no	—
1013	C₂×C₄⋊C₄	—	89	1	no	—
1014	C₂×C₄⋊C₄	—	89	1	no	—
1015	C₂×C₄⋊C₄	—	356	2	no	—
1016	C₂×C₄⋊C₄	—	356	2	no	—
1017	C₂×C₄⋊C₄	C₂×Dic₈₉	1	8	yes	complemented
1018	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1019	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1020	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1021	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1022	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1023	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1024	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1025	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1026	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1027	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1028	C₂×C₂²⋊C₄	—	89	1	no	—
1029	C₂×C₂²⋊C₄	—	89	1	no	—
1030	C₂×C₂²⋊C₄	—	89	1	no	—
1031	C₂×C₂²⋊C₄	—	89	1	no	—
1032	C₂×C₂²⋊C₄	—	89	1	no	—
1033	C₂×C₂²⋊C₄	—	89	1	no	—
1034	C₂×C₂²⋊C₄	—	89	1	no	—
1035	C₂×C₂²⋊C₄	—	89	1	no	—
1036	C₂×C₂²⋊C₄	—	89	1	no	—
1037	C₂×C₂²⋊C₄	—	89	1	no	—
1038	C₂×C₂²⋊C₄	—	89	1	no	—
1039	C₂×C₂²⋊C₄	—	89	1	no	—
1040	C₂×C₂²⋊C₄	—	89	1	no	—
1041	C₂×C₂²⋊C₄	—	89	1	no	—
1042	C₂×C₂²⋊C₄	—	89	1	no	—
1043	C₂×C₂²⋊C₄	—	89	1	no	—
1044	C₂×C₂²⋊C₄	—	89	1	no	—
1045	C₂×C₂²⋊C₄	—	89	1	no	—
1046	C₂×C₂²⋊C₄	—	89	1	no	—
1047	C₂×C₂²⋊C₄	—	89	1	no	—
1048	C₂×C₂²⋊C₄	—	89	1	no	—
1049	C₂×C₂²⋊C₄	—	89	1	no	—
1050	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1051	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1052	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1053	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1054	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1055	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1056	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1057	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1058	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1059	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1060	C₂×C₄²	—	89	1	no	—
1061	C₂×C₄²	—	89	1	no	—
1062	C₂×C₄²	—	89	1	no	—
1063	C₂×C₄²	—	89	1	no	—
1064	C₂×C₄²	—	89	1	no	—
1065	C₂×C₄²	—	89	1	no	—
1066	C₂×C₄²	—	89	1	no	—
1067	C₂×C₄²	—	89	1	no	—
1068	C₂×C₄²	—	89	1	no	—
1069	C₂×C₄²	—	89	1	no	—
1070	C₂×C₄²	—	89	1	no	—
1071	C₂×C₄²	—	89	1	no	—
1072	C₂×C₄²	—	89	1	no	—
1073	C₂×C₄²	—	89	1	no	—
1074	C₂×C₄²	—	89	1	no	—
1075	C₂×C₄²	—	89	1	no	—
1076	C₂×C₄²	—	356	2	no	—
1077	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1078	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1079	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1080	#95	—	89	1	no	—
1081	#95	—	89	1	no	—
1082	#95	—	89	1	no	—
1083	#95	—	89	1	no	—
1084	#95	—	89	1	no	—
1085	#95	—	89	1	no	—
1086	#95	—	89	1	no	—
1087	#95	—	89	1	no	—
1088	#95	—	89	1	no	—
1089	#95	—	89	1	no	—
1090	#95	—	89	1	no	—
1091	#95	—	89	1	no	—
1092	#95	—	89	1	no	—
1093	#95	—	89	1	no	—
1094	#95	—	89	1	no	—
1095	#95	—	89	1	no	—
1096	#95	—	89	1	no	—
1097	#95	—	89	1	no	—
1098	#95	—	89	1	no	—
1099	#95	—	89	1	no	—
1100	#95	—	89	1	no	—
1101	#95	—	89	1	no	—
1102	#95	—	89	1	no	—
1103	#95	—	89	1	no	—
1104	#95	—	89	1	no	—
1105	#95	—	89	1	no	—
1106	#95	—	89	1	no	—
1107	#95	—	89	1	no	—
1108	#95	—	89	1	no	—
1109	#95	—	89	1	no	—
1110	#95	—	89	1	no	—
1111	#95	—	89	1	no	—
1112	#95	—	89	1	no	—
1113	#95	—	89	1	no	—
1114	#95	—	89	1	no	—
1115	#95	—	89	1	no	—
1116	#95	—	89	1	no	—
1117	#95	—	89	1	no	—
1118	#95	—	89	1	no	—
1119	#95	—	89	1	no	—
1120	#95	—	89	1	no	—
1121	#95	—	89	1	no	—
1122	#95	—	89	1	no	—
1123	#95	—	89	1	no	—
1124	#95	—	89	1	no	—
1125	#95	—	89	1	no	—
1126	#95	—	89	1	no	—
1127	#95	—	89	1	no	—
1128	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
1129	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
1130	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
1131	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
1132	C₂×D₄	—	2	2	no	—
1133	C₂×D₄	—	2	2	no	—
1134	C₂×D₄	—	2	2	no	—
1135	C₂×D₄	—	2	2	no	—
1136	C₂×D₄	—	2	2	no	—
1137	C₂×D₄	—	2	2	no	—
1138	C₂×D₄	—	4	1	no	—
1139	C₂×D₄	—	4	1	no	—
1140	C₂×D₄	—	4	1	no	—
1141	C₂×D₄	—	4	1	no	—
1142	C₂×D₄	—	4	1	no	—
1143	C₂×D₄	—	4	1	no	—
1144	C₂×D₄	C₂²×Dic₈₉	1	4	yes	—
1145	C₂×D₄	C₂²×Dic₈₉	1	4	yes	—
1146	C₂×D₄	C₂²×Dic₈₉	1	4	yes	—
1147	C₂×D₄	C₂²×Dic₈₉	1	4	yes	—
1148	C₂×D₄	C₂²×Dic₈₉	1	4	yes	—
1149	C₂×D₄	C₂²×Dic₈₉	1	4	yes	—
1150	C₂²×C₄	—	4	1	no	—
1151	C₂²×C₄	—	4	1	no	—
1152	C₂²×C₄	—	4	1	no	—
1153	C₂²×C₄	—	4	1	no	—
1154	C₂²×C₄	—	4	1	no	—
1155	C₂²×C₄	—	4	1	no	—
1156	C₂²×C₄	—	4	1	no	—
1157	C₂²×C₄	—	4	1	no	—
1158	C₂²×C₄	—	4	1	no	—
1159	C₂²×C₄	—	4	1	no	—
1160	C₂²×C₄	—	4	1	no	—
1161	C₂²×C₄	—	4	1	no	—
1162	C₂²×C₄	—	89	1	no	—
1163	C₂²×C₄	—	89	1	no	—
1164	C₂²×C₄	—	89	1	no	—
1165	C₂²×C₄	—	89	1	no	—
1166	C₂²×C₄	—	89	1	no	—
1167	C₂²×C₄	—	89	1	no	—
1168	C₂²×C₄	—	89	1	no	—
1169	C₂²×C₄	—	89	1	no	—
1170	C₂²×C₄	—	89	1	no	—
1171	C₂²×C₄	—	89	1	no	—
1172	C₂²×C₄	—	89	1	no	—
1173	C₂²×C₄	—	89	1	no	—
1174	C₂²×C₄	—	89	1	no	—
1175	C₂²×C₄	—	89	1	no	—
1176	C₂²×C₄	—	89	1	no	—
1177	C₂²×C₄	—	89	1	no	—
1178	C₂²×C₄	—	356	1	no	—
1179	C₂²×C₄	—	356	1	no	—
1180	C₂²×C₄	—	356	1	no	—
1181	C₂²×C₄	—	356	1	no	—
1182	C₂²×C₄	—	356	1	no	—
1183	C₂²×C₄	—	356	1	no	—
1184	C₂²×C₄	—	356	1	no	—
1185	C₂²×C₄	—	356	1	no	—
1186	C₂²×C₄	—	356	1	no	—
1187	C₂²×C₄	—	356	1	no	—
1188	C₂²×C₄	—	356	1	no	—
1189	C₂²×C₄	—	356	1	no	—
1190	C₂²×C₄	—	356	1	no	—
1191	C₂²×C₄	—	356	1	no	—
1192	C₂²×C₄	—	356	1	no	—
1193	C₂²×C₄	—	356	1	no	—
1194	C₂²×C₄	—	356	1	no	—
1195	C₂²×C₄	—	356	1	no	—
1196	C₂²×C₄	—	356	1	no	—
1197	C₂²×C₄	—	356	1	no	—
1198	C₂²×C₄	—	356	1	no	—
1199	C₂²×C₄	—	356	1	no	—
1200	C₂²×C₄	—	356	1	no	—
1201	C₂²×C₄	—	178	2	no	—
1202	C₂²×C₄	—	178	2	no	—
1203	C₂²×C₄	—	178	2	no	—
1204	C₂²×C₄	—	178	2	no	—
1205	C₂²×C₄	—	178	2	no	—
1206	C₂²×C₄	—	178	2	no	—
1207	C₂²×C₄	—	178	2	no	—
1208	C₂²×C₄	C₂²×Dic₈₉	1	4	yes	—
1209	C₂²×C₄	C₂²×Dic₈₉	1	4	yes	—
1210	C₂²×C₄	C₂²×Dic₈₉	1	4	yes	—
1211	C₂²×C₄	C₂²×Dic₈₉	1	4	yes	—
1212	C₂²×C₄	C₂²×Dic₈₉	1	4	yes	—
1213	C₂²×C₄	C₂²×Dic₈₉	1	4	yes	—
1214	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1215	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1216	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1217	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1218	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1219	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1220	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1221	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1222	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1223	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1224	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1225	C₄⋊C₄	—	356	1	no	—
1226	C₄⋊C₄	—	356	1	no	—
1227	C₄⋊C₄	—	356	1	no	—
1228	C₄⋊C₄	—	356	1	no	—
1229	C₄⋊C₄	—	356	1	no	—
1230	C₄⋊C₄	—	356	1	no	—
1231	C₄⋊C₄	—	356	1	no	—
1232	C₄⋊C₄	—	356	1	no	—
1233	C₄⋊C₄	—	356	1	no	—
1234	C₄⋊C₄	—	356	1	no	—
1235	C₄⋊C₄	—	356	1	no	—
1236	C₄⋊C₄	—	356	1	no	—
1237	C₄⋊C₄	—	356	1	no	—
1238	C₄⋊C₄	—	356	1	no	—
1239	C₄⋊C₄	—	356	1	no	—
1240	C₄⋊C₄	—	356	1	no	—
1241	C₄⋊C₄	—	356	1	no	—
1242	C₄⋊C₄	—	356	1	no	—
1243	C₄⋊C₄	—	356	1	no	—
1244	C₄⋊C₄	—	356	1	no	—
1245	C₄⋊C₄	—	356	1	no	—
1246	C₄⋊C₄	—	178	2	no	—
1247	C₄⋊C₄	—	178	2	no	—
1248	C₄⋊C₄	—	178	2	no	—
1249	C₄⋊C₄	C₂²×Dic₈₉	1	4	yes	—
1250	C₄⋊C₄	C₂²×Dic₈₉	1	4	yes	—
1251	C₄⋊C₄	C₂²×Dic₈₉	1	4	yes	—
1252	C₄⋊C₄	C₂²×Dic₈₉	1	4	yes	—
1253	C₄⋊C₄	C₂²×Dic₈₉	1	4	yes	—
1254	C₄⋊C₄	C₂²×Dic₈₉	1	4	yes	—
1255	C₄⋊C₄	C₂²×Dic₈₉	1	4	yes	—
1256	C₄⋊C₄	C₂²×Dic₈₉	1	4	yes	—
1257	C₄⋊C₄	C₂²×Dic₈₉	1	4	yes	—
1258	C₄⋊C₄	C₂²×Dic₈₉	1	4	yes	—
1259	C₂²⋊C₄	—	356	1	no	—
1260	C₂²⋊C₄	—	356	1	no	—
1261	C₂²⋊C₄	—	356	1	no	—
1262	C₂²⋊C₄	—	356	1	no	—
1263	C₂²⋊C₄	—	356	1	no	—
1264	C₂²⋊C₄	—	356	1	no	—
1265	C₂²⋊C₄	—	356	1	no	—
1266	C₂²⋊C₄	—	356	1	no	—
1267	C₂²⋊C₄	—	356	1	no	—
1268	C₂²⋊C₄	—	356	1	no	—
1269	C₂²⋊C₄	—	356	1	no	—
1270	C₂²⋊C₄	—	356	1	no	—
1271	C₂²⋊C₄	—	356	1	no	—
1272	C₂²⋊C₄	—	356	1	no	—
1273	C₂²⋊C₄	—	356	1	no	—
1274	C₂²⋊C₄	—	356	1	no	—
1275	C₂²⋊C₄	—	356	1	no	—
1276	C₂²⋊C₄	—	178	2	no	—
1277	C₂²⋊C₄	—	178	2	no	—
1278	C₂²⋊C₄	—	178	2	no	—
1279	C₂²⋊C₄	—	178	2	no	—
1280	C₂²⋊C₄	—	178	2	no	—
1281	C₂²⋊C₄	C₂²×Dic₈₉	1	4	yes	—
1282	C₂²⋊C₄	C₂²×Dic₈₉	1	4	yes	—
1283	C₂²⋊C₄	C₂²×Dic₈₉	1	4	yes	—
1284	C₂²⋊C₄	C₂²×Dic₈₉	1	4	yes	—
1285	C₂²⋊C₄	C₂²×Dic₈₉	1	4	yes	—
1286	C₂²⋊C₄	C₂²×Dic₈₉	1	4	yes	—
1287	C₂²⋊C₄	C₂²×Dic₈₉	1	4	yes	—
1288	C₂²⋊C₄	C₂²×Dic₈₉	1	4	yes	—
1289	C₂²⋊C₄	C₂²×Dic₈₉	1	4	yes	—
1290	C₂²⋊C₄	C₂²×Dic₈₉	1	4	yes	—
1291	C₄²	—	356	1	no	—
1292	C₄²	—	356	1	no	—
1293	C₄²	—	356	1	no	—
1294	C₄²	—	356	1	no	—
1295	C₄²	—	356	1	no	—
1296	C₄²	—	356	1	no	—
1297	C₄²	—	356	1	no	—
1298	C₄²	—	356	1	no	—
1299	C₄²	—	356	1	no	—
1300	C₄²	—	356	1	no	—
1301	C₄²	—	356	1	no	—
1302	C₄²	—	356	1	no	—
1303	C₄²	—	356	1	no	—
1304	C₄²	—	356	1	no	—
1305	C₄²	—	178	2	no	—
1306	C₄²	—	178	2	no	—
1307	C₄²	C₂²×Dic₈₉	1	4	yes	—
1308	C₄²	C₂²×Dic₈₉	1	4	yes	—
1309	C₄²	C₂²×Dic₈₉	1	4	yes	—
1310	C₂³	—	2	1	no	—
1311	C₂³	—	2	1	no	—
1312	C₂³	—	2	1	no	—
1313	C₂³	—	2	1	no	—
1314	C₂³	—	2	1	no	—
1315	C₂³	—	2	1	no	—
1316	C₂³	—	2	1	no	—
1317	C₂³	—	2	1	no	—
1318	C₂³	—	2	1	no	—
1319	C₂³	—	2	1	no	—
1320	C₂³	—	2	1	no	—
1321	C₂³	—	2	1	no	—
1322	C₂³	—	2	1	no	—
1323	C₂³	—	2	1	no	—
1324	C₂³	—	2	1	no	—
1325	C₂³	—	2	1	no	—
1326	C₂³	—	2	1	no	—
1327	C₂³	—	2	1	no	—
1328	C₂³	—	2	1	no	—
1329	C₂³	—	2	1	no	—
1330	C₂³	—	2	1	no	—
1331	C₂³	—	2	1	no	—
1332	C₂³	C₂³×Dic₈₉	1	2	yes	—
1333	C₂³	C₂³×Dic₈₉	1	2	yes	—
1334	C₂³	C₂³×Dic₈₉	1	2	yes	—
1335	C₂³	C₂³×Dic₈₉	1	2	yes	—
1336	C₂³	#15668058	1	2	yes	—
1337	C₂³	#15668059	1	2	yes	—
1338	C₂³	C₂⁴×D₈₉	1	1	yes	characteristic
1339	D₄	—	2	8	no	—
1340	D₄	—	2	8	no	—
1341	D₄	—	2	8	no	—
1342	D₄	—	4	4	no	—
1343	D₄	—	4	4	no	—
1344	D₄	—	4	4	no	—
1345	C₂×C₄	—	2	1	no	—
1346	C₂×C₄	—	2	1	no	—
1347	C₂×C₄	—	2	1	no	—
1348	C₂×C₄	—	2	1	no	—
1349	C₂×C₄	—	2	1	no	—
1350	C₂×C₄	—	2	1	no	—
1351	C₂×C₄	—	2	1	no	—
1352	C₂×C₄	—	2	1	no	—
1353	C₂×C₄	—	2	1	no	—
1354	C₂×C₄	—	2	1	no	—
1355	C₂×C₄	—	2	1	no	—
1356	C₂×C₄	—	2	1	no	—
1357	C₂×C₄	—	2	1	no	—
1358	C₂×C₄	—	2	1	no	—
1359	C₂×C₄	—	2	1	no	—
1360	C₂×C₄	—	2	1	no	—
1361	C₂×C₄	—	2	1	no	—
1362	C₂×C₄	—	2	1	no	—
1363	C₂×C₄	—	2	1	no	—
1364	C₂×C₄	—	2	1	no	—
1365	C₂×C₄	—	2	1	no	—
1366	C₂×C₄	—	2	1	no	—
1367	C₂×C₄	—	4	4	no	—
1368	C₂×C₄	—	4	4	no	—
1369	C₂×C₄	—	4	4	no	—
1370	C₂×C₄	—	4	4	no	—
1371	C₂×C₄	—	4	4	no	—
1372	C₂×C₄	—	4	4	no	—
1373	C₂×C₄	—	89	2	no	—
1374	C₂×C₄	—	356	4	no	—
1375	C₂×C₄	—	356	4	no	—
1376	C₂×C₄	—	178	1	no	—
1377	C₂×C₄	—	178	1	no	—
1378	C₂×C₄	—	178	1	no	—
1379	C₂×C₄	—	178	1	no	—
1380	C₂×C₄	—	178	1	no	—
1381	C₂×C₄	—	178	1	no	—
1382	C₂×C₄	—	178	1	no	—
1383	C₂×C₄	—	178	1	no	—
1384	C₂×C₄	—	178	1	no	—
1385	C₂×C₄	—	178	1	no	—
1386	C₂×C₄	—	178	1	no	—
1387	C₂×C₄	—	178	1	no	—
1388	C₂×C₄	—	178	1	no	—
1389	C₂×C₄	—	178	1	no	—
1390	C₂×C₄	—	178	1	no	—
1391	C₂×C₄	—	178	1	no	—
1392	C₂×C₄	—	178	1	no	—
1393	C₂×C₄	—	178	1	no	—
1394	C₂×C₄	—	178	1	no	—
1395	C₂×C₄	—	178	1	no	—
1396	C₂×C₄	—	178	1	no	—
1397	C₂×C₄	—	178	1	no	—
1398	C₂×C₄	—	178	1	no	—
1399	C₂×C₄	—	178	1	no	—
1400	C₂×C₄	—	178	1	no	—
1401	C₂×C₄	—	178	1	no	—
1402	C₂×C₄	—	178	1	no	—
1403	C₂×C₄	—	178	1	no	—
1404	C₂×C₄	—	178	1	no	—
1405	C₂×C₄	—	178	1	no	—
1406	C₂×C₄	—	178	1	no	—
1407	C₂×C₄	—	178	1	no	—
1408	C₂×C₄	—	178	1	no	—
1409	C₂×C₄	—	178	1	no	—
1410	C₂×C₄	—	178	1	no	—
1411	C₂×C₄	—	178	1	no	—
1412	C₂×C₄	—	178	1	no	—
1413	C₂×C₄	—	178	1	no	—
1414	C₂×C₄	—	178	1	no	—
1415	C₂×C₄	—	178	1	no	—
1416	C₂×C₄	—	178	1	no	—
1417	C₂×C₄	—	178	1	no	—
1418	C₂×C₄	—	178	1	no	—
1419	C₂×C₄	—	178	1	no	—
1420	C₂×C₄	—	178	1	no	—
1421	C₂×C₄	—	178	1	no	—
1422	C₂×C₄	—	178	1	no	—
1423	C₂×C₄	—	712	2	no	—
1424	C₂×C₄	—	712	2	no	—
1425	C₂×C₄	—	712	2	no	—
1426	C₂×C₄	—	712	2	no	—
1427	C₂×C₄	—	712	2	no	—
1428	C₂×C₄	—	712	2	no	—
1429	C₂×C₄	—	712	2	no	—
1430	C₂×C₄	—	712	2	no	—
1431	C₂×C₄	C₂³×Dic₈₉	1	2	yes	—
1432	C₂×C₄	C₂³×Dic₈₉	1	2	yes	—
1433	C₂×C₄	C₂³×Dic₈₉	1	2	yes	—
1434	C₂×C₄	C₂³×Dic₈₉	1	2	yes	—
1435	C₂×C₄	C₂³×Dic₈₉	1	2	yes	—
1436	C₂×C₄	C₂³×Dic₈₉	1	2	yes	—
1437	C₂×C₄	C₂³×Dic₈₉	1	2	yes	—
1438	C₂×C₄	C₂³×Dic₈₉	1	2	yes	—
1439	C₂×C₄	C₂³×Dic₈₉	1	2	yes	—
1440	C₂×C₄	C₂³×Dic₈₉	1	2	yes	—
1441	C₂×C₄	C₂³×Dic₈₉	1	2	yes	—
1442	C₂²	—	2	2	no	—
1443	C₂²	—	2	2	no	—
1444	C₂²	—	2	2	no	—
1445	C₂²	—	2	2	no	—
1446	C₂²	—	2	2	no	—
1447	C₂²	—	2	2	no	—
1448	C₂²	—	2	2	no	—
1449	C₂²	—	2	2	no	—
1450	C₂²	—	2	2	no	—
1451	C₂²	—	2	2	no	—
1452	C₂²	—	2	2	no	—
1453	C₂²	—	2	2	no	—
1454	C₂²	—	2	2	no	—
1455	C₂²	—	2	2	no	—
1456	C₂²	—	2	2	no	—
1457	C₂²	—	4	1	no	—
1458	C₂²	—	4	1	no	—
1459	C₂²	—	4	1	no	—
1460	C₂²	—	4	1	no	—
1461	C₂²	—	4	1	no	—
1462	C₂²	—	4	1	no	—
1463	C₂²	—	4	1	no	—
1464	C₂²	—	4	1	no	—
1465	C₂²	—	4	1	no	—
1466	C₂²	—	4	1	no	—
1467	C₂²	—	4	1	no	—
1468	C₂²	—	4	1	no	—
1469	C₂²	#19152081	1	4	yes	—
1470	C₂²	C₂⁴×Dic₈₉	1	1	yes	characteristic
1471	C₂²	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
1472	C₂²	C₂×#15668058	1	1	yes	characteristic
1473	C₂²	C₂×#15668059	1	1	yes	characteristic
1474	C₂²	#19152433	1	1	yes	characteristic
1475	C₂²	#19152434	1	1	yes	characteristic
1476	C₂²	#19152434	1	1	yes	characteristic
1477	C₄	—	2	2	no	—
1478	C₄	—	2	2	no	—
1479	C₄	—	2	2	no	—
1480	C₄	—	2	2	no	—
1481	C₄	—	2	2	no	—
1482	C₄	—	2	2	no	—
1483	C₄	—	2	2	no	—
1484	C₄	—	2	2	no	—
1485	C₄	—	2	2	no	—
1486	C₄	—	2	2	no	—
1487	C₄	—	2	2	no	—
1488	C₄	—	356	1	no	—
1489	C₄	—	356	1	no	—
1490	C₄	—	356	1	no	—
1491	C₄	—	356	1	no	—
1492	C₄	—	356	1	no	—
1493	C₄	—	356	1	no	—
1494	C₄	—	356	1	no	—
1495	C₄	—	356	1	no	—
1496	C₄	—	356	1	no	—
1497	C₄	—	356	1	no	—
1498	C₄	—	356	1	no	—
1499	C₄	—	356	1	no	—
1500	C₄	—	356	1	no	—
1501	C₄	—	356	1	no	—
1502	C₄	—	356	1	no	—
1503	C₄	—	178	2	no	—
1504	C₂	—	2	4	no	—
1505	C₂	—	4	2	no	—
1506	C₂	—	4	2	no	—
1507	C₂	—	4	2	no	—
1508	C₂	C₂×#19152081	1	1	yes	characteristic
1509	C₂	#26033455	1	1	yes	characteristic
1510	C₂	H(5,𝔽₂)×Dic₈₉	1	1	yes	characteristic
1511	C₂	#26034429	1	1	yes	characteristic
1512	C₂	#26034530	1	1	yes	characteristic
1513	C₂	#26034700	1	1	yes	characteristic
1514	C₂	#26034803	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₈₉
commutator	C₂²×C₈₉	C₂⁴×C₄
Fitting, prime radical	C₂×#553×C₈₉	C₂
socle, cosocle	C₂³×C₈₉	C₂⁵
hypercenter	C₂×#553	D₈₉
hypocenter	C₈₉	#34497
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×#553

Complements

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

N	H ≅ G/N	type
1. #26023444	C₂	semidirect
2. #26023438	C₂	semidirect
3. #26023409	C₂	semidirect
4. #26023400	C₂	semidirect
5. #26023376	C₂	semidirect
6. #26023304	C₂	semidirect
7. #26023304	C₂	semidirect
8. #26023272	C₂	semidirect
9. #26023248	C₂	semidirect
10. #26023181	C₂	semidirect
11. #26023162	C₂	semidirect
12. #26023162	C₂	semidirect
13. D₄×C₄⋊Dic₈₉	C₂	semidirect
14. #26023129	C₂	semidirect
15. #26023112	C₂	semidirect
16. #26023058	C₂	semidirect
17. #26023046	C₂	semidirect
18. #26023031	C₂	semidirect
19. #26023031	C₂	semidirect
20. #26022957	C₂	semidirect
21. #26022957	C₂	semidirect
22. #26022957	C₂	semidirect
23. #26022924	C₂	semidirect
24. #26022885	C₂	semidirect
25. #26022885	C₂	semidirect
26. #26022885	C₂	semidirect
27. #26022861	C₂	semidirect
28. #121×Dic₈₉	C₂	semidirect
29. #26022697	C₂	semidirect
30. C₂×#19151484	C₂	semidirect
172. #553×C₈₉	C₄	semidirect
332. #126×C₈₉	C₂×C₄	semidirect
333. #126×C₈₉	C₂×C₄	semidirect
334. #125×C₈₉	C₂×C₄	semidirect
335. #123×C₈₉	C₂×C₄	semidirect
336. #123×C₈₉	C₂×C₄	semidirect
337. #121×C₈₉	C₂×C₄	semidirect
338. #121×C₈₉	C₂×C₄	semidirect
339. #121×C₈₉	C₂×C₄	semidirect
340. #121×C₈₉	C₂×C₄	semidirect
341. C₄×D₄×C₈₉	C₂×C₄	semidirect
342. C₄×D₄×C₈₉	C₂×C₄	semidirect
343. C₄×D₄×C₈₉	C₂×C₄	semidirect
344. C₄×D₄×C₈₉	C₂×C₄	semidirect
345. #117×C₈₉	C₂×C₄	semidirect
346. C₂×C₄⋊C₄×C₈₉	C₂×C₄	semidirect
789. C₈₉	#34497	semidirect
790. #553	Dic₈₉	semidirect
968. #126	C₂×Dic₈₉	semidirect
969. #126	C₂×Dic₈₉	semidirect
970. #125	C₂×Dic₈₉	semidirect
971. #123	C₂×Dic₈₉	semidirect
972. #123	C₂×Dic₈₉	semidirect
973. #121	C₂×Dic₈₉	semidirect
974. #121	C₂×Dic₈₉	semidirect
975. #121	C₂×Dic₈₉	semidirect
976. #121	C₂×Dic₈₉	semidirect
985. C₄×D₄	C₂×Dic₈₉	semidirect
986. C₄×D₄	C₂×Dic₈₉	semidirect
987. C₄×D₄	C₂×Dic₈₉	semidirect
988. C₄×D₄	C₂×Dic₈₉	semidirect
990. #117	C₂×Dic₈₉	semidirect
1017. C₂×C₄⋊C₄	C₂×Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26023444	2
#26023438	2
#26023409	2
#26023400	2
#26023376	2
#26023304	2
#26023272	2
#26023248	2
#26023181	2
#26023162	2
D₄×C₄⋊Dic₈₉	2
#26023129	2
#26023112	2
#26023058	2
#26023046	2
#26023031	2
#26022957	2
#26022924	2
#26022885	2
#26022861	2
#121×Dic₈₉	2
#26022697	2
C₂×#19151484	2
C₂×#553×C₈₉	2
#34497	89