Subgroups — #36761236

Order 22784.

2326 conjugacy classes of subgroups.

The subgroup lattice has 1532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19152225	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂²⋊Q₈×D₈₉	C₂	1	1	yes	maximal, characteristic
3	#26028538	C₂	1	1	yes	maximal, characteristic
4	#26028536	C₂	1	1	yes	maximal, characteristic
5	#26026724	C₂	1	1	yes	maximal, characteristic, complemented
6	#26026722	C₂	1	1	yes	maximal, characteristic, complemented
7	#26026721	C₂	1	1	yes	maximal, characteristic, complemented
8	#26026719	C₂	1	1	yes	maximal, characteristic, complemented
9	#26026717	C₂	1	1	yes	maximal, characteristic, complemented
10	#26026716	C₂	1	1	yes	maximal, characteristic, complemented
11	#26026715	C₂	1	1	yes	maximal, characteristic, complemented
12	#26026714	C₂	1	1	yes	maximal, characteristic, complemented
13	#26026569	C₂	1	1	yes	maximal, characteristic, complemented
14	#26026568	C₂	1	1	yes	maximal, characteristic, complemented
15	#26026566	C₂	1	1	yes	maximal, characteristic, complemented
16	#26026563	C₂	1	1	yes	maximal, characteristic, complemented
17	#26026562	C₂	1	1	yes	maximal, characteristic, complemented
18	#26026562	C₂	1	1	yes	maximal, characteristic, complemented
19	#26026561	C₂	1	1	yes	maximal, characteristic, complemented
20	#26026070	C₂	1	1	yes	maximal, characteristic, complemented
21	#26026064	C₂	1	1	yes	maximal, characteristic, complemented
22	#26025408	C₂	1	1	yes	maximal, characteristic
23	#26025406	C₂	1	1	yes	maximal, characteristic
24	#26024537	C₂	1	1	yes	maximal, characteristic, complemented
25	#26024534	C₂	1	1	yes	maximal, characteristic, complemented
26	#26024527	C₂	1	1	yes	maximal, characteristic
27	#26024524	C₂	1	1	yes	maximal, characteristic
28	#26023893	C₂	1	1	yes	maximal, characteristic, complemented
29	#26023891	C₂	1	1	yes	maximal, characteristic, complemented
30	#26022851	C₂	1	1	yes	maximal, characteristic, complemented
31	C₈₉×#2677	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×Q₈×D₈₉	C₂²	1	1	yes	characteristic
33	C₂³×C₄×D₈₉	C₂²	1	1	yes	characteristic
34	#19152225	—	2	8	no	—
35	C₂×#15668011	C₂²	1	1	yes	characteristic, complemented
36	C₂×#15668011	C₂²	1	1	yes	characteristic, complemented
37	C₂×#15668011	C₂²	1	1	yes	characteristic, complemented
38	C₂×#15668010	C₂²	1	1	yes	characteristic, complemented
39	C₂×#15668010	C₂²	1	1	yes	characteristic, complemented
40	C₂×#15668010	C₂²	1	1	yes	characteristic, complemented
41	C₂×#15668004	C₂²	1	1	yes	characteristic, complemented
42	C₂×#15668003	C₂²	1	1	yes	characteristic, complemented
43	C₂×#15668002	C₂²	1	1	yes	characteristic, complemented
44	C₂×#15668002	C₂²	1	1	yes	characteristic, complemented
45	C₂×#15667992	C₂²	1	1	yes	characteristic
46	C₂×#15667991	C₂²	1	1	yes	characteristic
47	C₂×#15667990	C₂²	1	1	yes	characteristic
48	C₂×#15667990	C₂²	1	1	yes	characteristic
49	C₂×#15667990	C₂²	1	1	yes	characteristic
50	C₂×#15667990	C₂²	1	1	yes	characteristic
51	C₂×#15667990	C₂²	1	1	yes	characteristic
52	C₂×#15667989	C₂²	1	1	yes	characteristic
53	C₂×#15667989	C₂²	1	1	yes	characteristic
54	C₂×#15667989	C₂²	1	1	yes	characteristic
55	C₂×#15667988	C₂²	1	1	yes	characteristic
56	C₂×#15667988	C₂²	1	1	yes	characteristic
57	C₂×#15667988	C₂²	1	1	yes	characteristic
58	C₂×#15667988	C₂²	1	1	yes	characteristic
59	C₂²⋊Q₈×D₈₉	—	2	8	no	—
60	C₂×#15667970	C₂²	1	1	yes	characteristic
61	C₂×#15667969	C₂²	1	1	yes	characteristic
62	C₂×C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
63	C₂×C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
67	#19151540	C₂²	1	1	yes	characteristic, complemented
68	#19151540	C₂²	1	1	yes	characteristic, complemented
69	#19151539	C₂²	1	1	yes	characteristic, complemented
70	#19151539	C₂²	1	1	yes	characteristic, complemented
71	#19151538	C₂²	1	1	yes	characteristic, complemented
72	#19151538	C₂²	1	1	yes	characteristic, complemented
73	#19151537	C₂²	1	1	yes	characteristic, complemented
74	#19151537	C₂²	1	1	yes	characteristic, complemented
75	#19151534	C₂²	1	1	yes	characteristic
76	#19151533	C₂²	1	1	yes	characteristic
77	#19151533	C₂²	1	1	yes	characteristic
78	#19151532	C₂²	1	1	yes	characteristic, complemented
79	#19151532	C₂²	1	1	yes	characteristic, complemented
80	#19151532	C₂²	1	1	yes	characteristic, complemented
81	#19151531	C₂²	1	1	yes	characteristic, complemented
82	#19151531	C₂²	1	1	yes	characteristic, complemented
83	#19151531	C₂²	1	1	yes	characteristic, complemented
84	#19151529	C₂²	1	1	yes	characteristic, complemented
85	#19151529	C₂²	1	1	yes	characteristic, complemented
86	#19151529	C₂²	1	1	yes	characteristic, complemented
87	#19151528	C₂²	1	1	yes	characteristic, complemented
88	#19151527	C₂²	1	1	yes	characteristic
89	#19151527	C₂²	1	1	yes	characteristic
90	#19151526	C₂²	1	1	yes	characteristic
91	#19151526	C₂²	1	1	yes	characteristic
92	#19151525	C₂²	1	1	yes	characteristic
93	#19151525	C₂²	1	1	yes	characteristic
94	#19151523	C₂²	1	1	yes	characteristic
95	#19151523	C₂²	1	1	yes	characteristic
96	#19151519	C₂²	1	1	yes	characteristic, complemented
97	#19151519	C₂²	1	1	yes	characteristic, complemented
98	#19151518	C₂²	1	1	yes	characteristic, complemented
99	#19151518	C₂²	1	1	yes	characteristic, complemented
100	#19151518	C₂²	1	1	yes	characteristic, complemented
101	#19151518	C₂²	1	1	yes	characteristic, complemented
102	#19151518	C₂²	1	1	yes	characteristic, complemented
103	#19151518	C₂²	1	1	yes	characteristic, complemented
104	#19151517	C₂²	1	1	yes	characteristic, complemented
105	#19151517	C₂²	1	1	yes	characteristic, complemented
106	#19151511	C₂²	1	1	yes	characteristic
107	#19151510	C₂²	1	1	yes	characteristic
108	#19151509	C₂²	1	1	yes	characteristic
109	#19151505	C₂²	1	1	yes	characteristic, complemented
110	#19151504	C₂²	1	1	yes	characteristic, complemented
111	#19151502	C₂²	1	1	yes	characteristic, complemented
112	#19151502	C₂²	1	1	yes	characteristic, complemented
113	#19151492	C₂²	1	1	yes	characteristic
114	#19151492	C₂²	1	1	yes	characteristic
115	#19151492	C₂²	1	1	yes	characteristic
116	#19151490	C₂²	1	1	yes	characteristic
117	#19151489	C₂²	1	1	yes	characteristic
118	#19151489	C₂²	1	1	yes	characteristic
119	#19151488	C₂²	1	1	yes	characteristic
120	#19151488	C₂²	1	1	yes	characteristic
121	#19151488	C₂²	1	1	yes	characteristic
122	#19151487	C₂²	1	1	yes	characteristic
123	#19151487	C₂²	1	1	yes	characteristic
124	#19151486	C₂²	1	1	yes	characteristic
125	#19151486	C₂²	1	1	yes	characteristic
126	#19151486	C₂²	1	1	yes	characteristic
127	#19151485	C₂²	1	1	yes	characteristic, complemented
128	#19151484	C₂²	1	1	yes	characteristic, complemented
129	#19151484	C₂²	1	1	yes	characteristic, complemented
130	#19151484	C₂²	1	1	yes	characteristic, complemented
131	#19151483	C₂²	1	1	yes	characteristic, complemented
132	#19151483	C₂²	1	1	yes	characteristic, complemented
133	#19151482	C₂²	1	1	yes	characteristic, complemented
134	#19151482	C₂²	1	1	yes	characteristic, complemented
135	#19151481	C₂²	1	1	yes	characteristic, complemented
136	#19151480	C₂²	1	1	yes	characteristic, complemented
137	#19151480	C₂²	1	1	yes	characteristic, complemented
138	#19151480	C₂²	1	1	yes	characteristic, complemented
139	#19151479	C₂²	1	1	yes	characteristic, complemented
140	#19151479	C₂²	1	1	yes	characteristic, complemented
141	#19151472	C₂²	1	1	yes	characteristic
142	#19151472	C₂²	1	1	yes	characteristic
143	#19151472	C₂²	1	1	yes	characteristic
144	#19151471	C₂²	1	1	yes	characteristic
145	#19151470	C₂²	1	1	yes	characteristic
146	#19151470	C₂²	1	1	yes	characteristic
147	#19151469	C₂²	1	1	yes	characteristic
148	#19151469	C₂²	1	1	yes	characteristic
149	#19151469	C₂²	1	1	yes	characteristic
150	#19151469	C₂²	1	1	yes	characteristic
151	#19151469	C₂²	1	1	yes	characteristic
152	#19151469	C₂²	1	1	yes	characteristic
153	#19151469	C₂²	1	1	yes	characteristic
154	#19151469	C₂²	1	1	yes	characteristic
155	#19151469	C₂²	1	1	yes	characteristic
156	#19151460	C₂²	1	1	yes	characteristic
157	#19151460	C₂²	1	1	yes	characteristic
158	#19151460	C₂²	1	1	yes	characteristic
159	#19151460	C₂²	1	1	yes	characteristic
160	#19151460	C₂²	1	1	yes	characteristic
161	#19151460	C₂²	1	1	yes	characteristic
162	#19151458	C₂²	1	1	yes	characteristic
163	#19151457	C₂²	1	1	yes	characteristic
164	#19151457	C₂²	1	1	yes	characteristic
165	#19151456	C₂²	1	1	yes	characteristic
166	#19151455	C₂²	1	1	yes	characteristic
167	#19151455	C₂²	1	1	yes	characteristic
168	#19151453	C₂²	1	1	yes	characteristic
169	#19151453	C₂²	1	1	yes	characteristic
170	#19151453	C₂²	1	1	yes	characteristic
171	#19151453	C₂²	1	1	yes	characteristic
172	C₄×#13083551	C₂²	1	1	yes	characteristic
173	#19151445	C₂²	1	1	yes	characteristic
174	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
175	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
176	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
177	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
178	#399×C₈₉	C₂²	1	1	yes	characteristic
179	#398×C₈₉	C₂²	1	1	yes	characteristic, complemented
180	#398×C₈₉	C₂²	1	1	yes	characteristic, complemented
181	#395×C₈₉	C₂²	1	1	yes	characteristic, complemented
182	#395×C₈₉	C₂²	1	1	yes	characteristic, complemented
183	#393×C₈₉	C₂²	1	1	yes	characteristic
184	#388×C₈₉	C₂²	1	1	yes	characteristic
185	#388×C₈₉	C₂²	1	1	yes	characteristic
186	#387×C₈₉	C₂²	1	1	yes	characteristic, complemented
187	#387×C₈₉	C₂²	1	1	yes	characteristic, complemented
188	#385×C₈₉	C₂²	1	1	yes	characteristic
189	C₂⁴×D₈₉	C₂³	1	1	yes	characteristic
190	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
191	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
192	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
193	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
194	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
195	C₂×Q₈×D₈₉	—	2	4	no	—
196	C₂×Q₈×D₈₉	—	4	2	no	—
197	C₂×Q₈×D₈₉	—	4	2	no	—
198	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
199	C₂²×C₄×D₈₉	—	2	4	no	—
200	C₂²×C₄×D₈₉	—	4	2	no	—
201	C₂²×C₄×D₈₉	—	4	2	no	—
202	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
203	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
204	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
205	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
206	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
207	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
208	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
209	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
210	#15668011	—	2	4	no	—
211	#15668011	—	4	2	no	—
212	#15668011	—	4	2	no	—
213	#15668010	—	2	4	no	—
214	#15668010	—	2	4	no	—
215	#15668010	—	4	2	no	—
216	#15668004	—	2	4	no	—
217	#15668003	—	2	4	no	—
218	#15668002	—	2	4	no	—
219	#15668002	—	2	4	no	—
220	#15667992	—	2	4	no	—
221	#15667991	—	2	4	no	—
222	#15667990	—	2	4	no	—
223	#15667990	—	2	4	no	—
224	#15667990	—	2	4	no	—
225	#15667990	—	2	4	no	—
226	#15667990	—	4	2	no	—
227	#15667989	—	2	4	no	—
228	#15667989	—	2	4	no	—
229	#15667989	—	4	2	no	—
230	#15667988	—	2	4	no	—
231	#15667988	—	2	4	no	—
232	#15667988	—	2	4	no	—
233	#15667988	—	4	2	no	—
234	#15667970	—	2	4	no	—
235	#15667969	—	2	4	no	—
236	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
245	C₂×#13083553	C₂³	1	1	yes	characteristic
246	C₂×#13083553	C₂³	1	1	yes	characteristic
247	C₂×#13083553	C₂³	1	1	yes	characteristic
248	C₂×#13083553	C₂³	1	1	yes	characteristic
249	C₂×#13083553	C₂³	1	1	yes	characteristic
250	C₂×#13083553	C₂³	1	1	yes	characteristic
251	C₂×#13083553	C₂³	1	1	yes	characteristic
252	C₂×#13083553	C₂³	1	1	yes	characteristic
253	C₂×#13083553	C₂³	1	1	yes	characteristic
254	C₂×#13083553	C₂³	1	1	yes	characteristic
255	C₂×#13083553	C₂³	1	1	yes	characteristic
256	C₂×#13083553	C₂³	1	1	yes	characteristic
257	C₂×#13083553	C₂³	1	1	yes	characteristic
258	C₂×#13083553	C₂³	1	1	yes	characteristic
259	C₂×#13083553	C₂³	1	1	yes	characteristic
260	C₂×#13083553	C₂³	1	1	yes	characteristic
261	C₂×#13083553	C₂³	1	1	yes	characteristic
262	C₂×#13083553	C₂³	1	1	yes	characteristic
263	C₂×#13083553	C₂³	1	1	yes	characteristic
264	C₂×#13083553	C₂³	1	1	yes	characteristic
265	C₂×#13083553	C₂³	1	1	yes	characteristic
266	C₂×#13083553	C₂³	1	1	yes	characteristic
267	C₂×#13083553	C₂³	1	1	yes	characteristic
268	C₂×#13083553	C₂³	1	1	yes	characteristic
269	C₂×#13083553	C₂³	1	1	yes	characteristic
270	C₂×#13083553	C₂³	1	1	yes	characteristic
271	C₄⋊C₄×D₈₉	—	2	4	no	—
272	C₄⋊C₄×D₈₉	—	2	4	no	—
273	C₄⋊C₄×D₈₉	D₄	1	8	yes	—
274	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
280	C₂×#13083551	C₂³	1	1	yes	characteristic
281	C₂×#13083551	C₂³	1	1	yes	characteristic
282	C₂×#13083551	C₂³	1	1	yes	characteristic
283	C₂×#13083551	C₂³	1	1	yes	characteristic
284	C₂×#13083551	C₂³	1	1	yes	characteristic
285	C₂×#13083551	C₂³	1	1	yes	characteristic
286	C₂×#13083551	C₂³	1	1	yes	characteristic
287	C₂×#13083551	C₂³	1	1	yes	characteristic
288	C₂×#13083551	C₂³	1	1	yes	characteristic
289	C₂×#13083551	C₂³	1	1	yes	characteristic
290	C₂×#13083551	C₂³	1	1	yes	characteristic
291	C₂×#13083551	C₂³	1	1	yes	characteristic
292	C₂×#13083551	C₂³	1	1	yes	characteristic
293	C₂×#13083551	C₂³	1	1	yes	characteristic
294	C₂×#13083551	C₂³	1	1	yes	characteristic
295	C₂×#13083551	C₂³	1	1	yes	characteristic
296	C₂×#13083551	C₂³	1	1	yes	characteristic
297	C₂×#13083551	C₂³	1	1	yes	characteristic
298	C₂×#13083551	C₂³	1	1	yes	characteristic
299	C₂×#13083551	C₂³	1	1	yes	characteristic
300	C₂²⋊C₄×D₈₉	—	2	4	no	—
301	C₂²⋊C₄×D₈₉	—	2	4	no	—
302	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
303	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
304	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
305	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
306	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
307	C₂×C₄×Dic₈₉	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	#15667919	C₂³	1	1	yes	characteristic
321	#15667919	C₂³	1	1	yes	characteristic
322	#15667919	C₂³	1	1	yes	characteristic
323	#15667919	C₂³	1	1	yes	characteristic
324	#15667919	C₂³	1	1	yes	characteristic
325	#15667919	C₂³	1	1	yes	characteristic
326	#15667919	C₂³	1	1	yes	characteristic
327	#15667919	C₂³	1	1	yes	characteristic
328	#15667919	C₂³	1	1	yes	characteristic
329	#15667919	C₂³	1	1	yes	characteristic
330	#15667919	C₂³	1	1	yes	characteristic
331	#15667919	C₂³	1	1	yes	characteristic
332	#15667919	C₂³	1	1	yes	characteristic
333	#15667919	C₂³	1	1	yes	characteristic
334	#15667919	C₂³	1	1	yes	characteristic
335	#15667919	C₂³	1	1	yes	characteristic
336	#15667919	C₂³	1	1	yes	characteristic
337	#15667919	C₂³	1	1	yes	characteristic
338	#15667919	C₂³	1	1	yes	characteristic
339	#15667919	C₂³	1	1	yes	characteristic
340	#15667919	C₂³	1	1	yes	characteristic
341	#15667919	C₂³	1	1	yes	characteristic
342	#15667919	C₂³	1	1	yes	characteristic
343	#15667919	C₂³	1	1	yes	characteristic
344	#15667919	C₂³	1	1	yes	characteristic
345	#15667919	C₂³	1	1	yes	characteristic
346	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
347	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
348	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
349	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
350	C₄⋊Q₈×C₈₉	—	2	4	no	—
351	C₄⋊Q₈×C₈₉	—	4	2	no	—
352	C₂²⋊Q₈×C₈₉	—	2	4	no	—
353	C₂²⋊Q₈×C₈₉	—	4	2	no	—
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×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
358	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
359	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
360	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
361	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
362	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
363	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
364	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
365	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
366	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
367	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
368	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
369	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
370	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
371	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
372	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
373	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
374	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
375	#95×C₈₉	C₂³	1	1	yes	characteristic
376	#95×C₈₉	C₂³	1	1	yes	characteristic
377	#95×C₈₉	C₂³	1	1	yes	characteristic
378	#95×C₈₉	C₂³	1	1	yes	characteristic
379	#95×C₈₉	C₂³	1	1	yes	characteristic
380	#95×C₈₉	C₂³	1	1	yes	characteristic
381	#95×C₈₉	C₂³	1	1	yes	characteristic
382	#95×C₈₉	C₂³	1	1	yes	characteristic
383	#95×C₈₉	C₂³	1	1	yes	characteristic
384	#95×C₈₉	C₂³	1	1	yes	characteristic
385	C₂³×D₈₉	—	2	2	no	—
386	C₂³×D₈₉	—	2	2	no	—
387	C₂³×D₈₉	—	2	2	no	—
388	C₂³×D₈₉	—	2	2	no	—
389	C₂³×D₈₉	—	2	2	no	—
390	C₂³×D₈₉	—	4	1	no	—
391	C₂³×D₈₉	—	4	1	no	—
392	C₂³×D₈₉	C₂⁴	1	1	yes	characteristic
393	C₂³×D₈₉	C₂⁴	1	1	yes	characteristic
394	C₂×Dic₁₇₈	—	2	2	no	—
395	C₂×Dic₁₇₈	—	2	2	no	—
396	C₂×Dic₁₇₈	—	2	2	no	—
397	C₂×Dic₁₇₈	—	2	2	no	—
398	C₂×Dic₁₇₈	—	2	2	no	—
399	C₂×Dic₁₇₈	—	2	2	no	—
400	C₂×Dic₁₇₈	—	2	2	no	—
401	C₂×Dic₁₇₈	—	2	2	no	—
402	C₂×Dic₁₇₈	—	4	1	no	—
403	C₂×Dic₁₇₈	—	4	1	no	—
404	C₂×Dic₁₇₈	—	4	1	no	—
405	C₂×Dic₁₇₈	—	4	1	no	—
406	C₂×Dic₁₇₈	—	4	1	no	—
407	C₂×Dic₁₇₈	—	4	1	no	—
408	C₂×Dic₁₇₈	—	4	1	no	—
409	Q₈×D₈₉	—	4	16	no	—
410	C₂²×Dic₈₉	—	2	2	no	—
411	C₂²×Dic₈₉	—	2	2	no	—
412	C₂²×Dic₈₉	—	4	1	no	—
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	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
417	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
418	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
419	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
420	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
421	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
422	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
423	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
424	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
425	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
426	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
427	C₂×C₄×D₈₉	—	2	2	no	—
428	C₂×C₄×D₈₉	—	2	2	no	—
429	C₂×C₄×D₈₉	—	2	2	no	—
430	C₂×C₄×D₈₉	—	2	2	no	—
431	C₂×C₄×D₈₉	—	2	2	no	—
432	C₂×C₄×D₈₉	—	2	2	no	—
433	C₂×C₄×D₈₉	—	2	2	no	—
434	C₂×C₄×D₈₉	—	2	2	no	—
435	C₂×C₄×D₈₉	—	2	2	no	—
436	C₂×C₄×D₈₉	—	2	2	no	—
437	C₂×C₄×D₈₉	—	2	2	no	—
438	C₂×C₄×D₈₉	—	2	2	no	—
439	C₂×C₄×D₈₉	—	2	2	no	—
440	C₂×C₄×D₈₉	—	4	16	no	—
441	C₂×C₄×D₈₉	—	4	1	no	—
442	C₂×C₄×D₈₉	—	4	1	no	—
443	C₂×C₄×D₈₉	—	4	1	no	—
444	C₂×C₄×D₈₉	—	4	1	no	—
445	C₂×C₄×D₈₉	—	4	1	no	—
446	C₂×C₄×D₈₉	—	4	1	no	—
447	C₂×C₄×D₈₉	—	4	1	no	—
448	C₂×C₄×D₈₉	—	4	1	no	—
449	C₂×C₄×D₈₉	C₂×D₄	1	4	yes	—
450	C₂×C₄×D₈₉	C₂×D₄	1	4	yes	—
451	C₂×C₄×D₈₉	C₂×D₄	1	4	yes	—
452	C₄⋊Dic₈₉	—	2	2	no	—
453	C₄⋊Dic₈₉	—	2	2	no	—
454	C₄⋊Dic₈₉	—	2	2	no	—
455	C₄⋊Dic₈₉	—	2	2	no	—
456	C₄⋊Dic₈₉	—	2	2	no	—
457	C₄⋊Dic₈₉	—	2	2	no	—
458	C₄⋊Dic₈₉	—	4	1	no	—
459	C₄⋊Dic₈₉	—	4	1	no	—
460	C₄⋊Dic₈₉	C₂×D₄	1	4	yes	—
461	#13083553	—	2	2	no	—
462	#13083553	—	2	2	no	—
463	#13083553	—	2	2	no	—
464	#13083553	—	2	2	no	—
465	#13083553	—	2	2	no	—
466	#13083553	—	2	2	no	—
467	#13083553	—	2	2	no	—
468	#13083553	—	2	2	no	—
469	#13083553	—	2	2	no	—
470	#13083553	—	2	2	no	—
471	#13083553	—	2	2	no	—
472	#13083553	—	2	2	no	—
473	#13083553	—	2	2	no	—
474	#13083553	—	2	2	no	—
475	#13083553	—	2	2	no	—
476	#13083553	—	2	2	no	—
477	#13083553	—	2	2	no	—
478	#13083553	—	2	2	no	—
479	#13083553	—	4	1	no	—
480	#13083553	—	4	1	no	—
481	#13083553	—	4	1	no	—
482	#13083553	—	4	1	no	—
483	#13083553	—	4	1	no	—
484	#13083553	—	4	1	no	—
485	#13083553	C₂×D₄	1	4	yes	—
486	#13083553	C₂×D₄	1	4	yes	—
487	C₂²⋊Dic₈₉	—	2	2	no	—
488	C₂²⋊Dic₈₉	—	2	2	no	—
489	C₂²⋊Dic₈₉	—	2	2	no	—
490	C₂²⋊Dic₈₉	—	2	2	no	—
491	C₂²⋊Dic₈₉	—	2	2	no	—
492	C₂²⋊Dic₈₉	—	4	1	no	—
493	#13083551	—	2	2	no	—
494	#13083551	—	2	2	no	—
495	#13083551	—	2	2	no	—
496	#13083551	—	2	2	no	—
497	#13083551	—	2	2	no	—
498	#13083551	—	2	2	no	—
499	#13083551	—	2	2	no	—
500	#13083551	—	2	2	no	—
501	#13083551	—	2	2	no	—
502	#13083551	—	2	2	no	—
503	#13083551	—	2	2	no	—
504	#13083551	—	2	2	no	—
505	#13083551	—	2	2	no	—
506	#13083551	—	2	2	no	—
507	#13083551	—	2	2	no	—
508	#13083551	—	2	2	no	—
509	#13083551	—	4	1	no	—
510	#13083551	—	4	1	no	—
511	#13083551	—	4	1	no	—
512	#13083551	—	4	1	no	—
513	C₄×Dic₈₉	—	2	2	no	—
514	C₄×Dic₈₉	—	2	2	no	—
515	C₄×Dic₈₉	—	2	2	no	—
516	C₄×Dic₈₉	—	4	1	no	—
517	C₄×Dic₈₉	—	4	1	no	—
518	C₄×Dic₈₉	—	4	1	no	—
519	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
520	C₂×Q₈×C₈₉	—	2	2	no	—
521	C₂×Q₈×C₈₉	—	2	2	no	—
522	C₂×Q₈×C₈₉	—	2	2	no	—
523	C₂×Q₈×C₈₉	—	2	2	no	—
524	C₂×Q₈×C₈₉	—	4	1	no	—
525	C₂×Q₈×C₈₉	—	4	1	no	—
526	C₂×Q₈×C₈₉	—	4	1	no	—
527	C₂×Q₈×C₈₉	—	4	1	no	—
528	C₂×Q₈×C₈₉	—	4	1	no	—
529	C₂²×C₄×C₈₉	—	2	2	no	—
530	C₂²×C₄×C₈₉	—	2	2	no	—
531	C₂²×C₄×C₈₉	—	4	1	no	—
532	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
533	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
534	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
535	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
536	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
537	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
538	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
539	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
540	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
541	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
542	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
543	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
544	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
545	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
546	C₄⋊C₄×C₈₉	—	2	2	no	—
547	C₄⋊C₄×C₈₉	—	2	2	no	—
548	C₄⋊C₄×C₈₉	—	2	2	no	—
549	C₄⋊C₄×C₈₉	—	2	2	no	—
550	C₄⋊C₄×C₈₉	—	2	2	no	—
551	C₄⋊C₄×C₈₉	—	2	2	no	—
552	C₄⋊C₄×C₈₉	—	2	2	no	—
553	C₄⋊C₄×C₈₉	—	2	2	no	—
554	C₄⋊C₄×C₈₉	—	4	1	no	—
555	C₄⋊C₄×C₈₉	—	4	1	no	—
556	C₄⋊C₄×C₈₉	—	4	1	no	—
557	C₄⋊C₄×C₈₉	—	4	1	no	—
558	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
559	C₂²⋊C₄×C₈₉	—	2	2	no	—
560	C₂²⋊C₄×C₈₉	—	2	2	no	—
561	C₂²⋊C₄×C₈₉	—	2	2	no	—
562	C₂²⋊C₄×C₈₉	—	4	1	no	—
563	C₂²⋊C₄×C₈₉	—	4	1	no	—
564	C₂²⋊C₄×C₈₉	—	4	1	no	—
565	C₄²×C₈₉	—	2	2	no	—
566	C₄²×C₈₉	—	4	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⁺⁴	1	2	yes	—
574	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
575	C₂²×D₈₉	—	2	1	no	—
576	C₂²×D₈₉	—	2	1	no	—
577	C₂²×D₈₉	—	2	1	no	—
578	C₂²×D₈₉	—	2	1	no	—
579	C₂²×D₈₉	—	2	8	no	—
580	C₂²×D₈₉	—	2	1	no	—
581	C₂²×D₈₉	—	2	1	no	—
582	C₂²×D₈₉	—	2	1	no	—
583	C₂²×D₈₉	—	2	1	no	—
584	C₂²×D₈₉	—	2	1	no	—
585	C₂²×D₈₉	—	2	1	no	—
586	C₂²×D₈₉	—	4	4	no	—
587	C₂²×D₈₉	—	4	4	no	—
588	C₂²×D₈₉	—	4	4	no	—
589	C₂²×D₈₉	—	4	4	no	—
590	C₂²×D₈₉	—	4	4	no	—
591	C₂²×D₈₉	—	4	4	no	—
592	C₂²×D₈₉	C₂²×D₄	1	2	yes	—
593	C₂²×D₈₉	2₋¹⁺⁴	1	2	yes	—
594	C₂²×D₈₉	2₋¹⁺⁴	1	2	yes	—
595	C₂²×D₈₉	2₋¹⁺⁴	1	2	yes	—
596	Q₈×C₈₉	—	4	4	no	—
597	Q₈×C₈₉	—	8	2	no	—
598	Q₈×C₈₉	—	8	2	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	—	2	1	no	—
610	C₂×C₄×C₈₉	—	2	1	no	—
611	C₂×C₄×C₈₉	—	2	1	no	—
612	C₂×C₄×C₈₉	—	2	1	no	—
613	C₂×C₄×C₈₉	—	2	1	no	—
614	C₂×C₄×C₈₉	—	2	1	no	—
615	C₂×C₄×C₈₉	—	2	1	no	—
616	C₂×C₄×C₈₉	—	2	1	no	—
617	C₂×C₄×C₈₉	—	2	1	no	—
618	C₂×C₄×C₈₉	—	2	1	no	—
619	C₂×C₄×C₈₉	—	2	1	no	—
620	C₂×C₄×C₈₉	—	2	1	no	—
621	C₂×C₄×C₈₉	—	2	1	no	—
622	C₂×C₄×C₈₉	—	2	1	no	—
623	C₂×C₄×C₈₉	—	2	1	no	—
624	C₂×C₄×C₈₉	—	2	1	no	—
625	C₂×C₄×C₈₉	—	2	1	no	—
626	C₂×C₄×C₈₉	—	2	1	no	—
627	C₂×C₄×C₈₉	—	2	1	no	—
628	C₂×C₄×C₈₉	—	2	1	no	—
629	C₂×C₄×C₈₉	—	2	1	no	—
630	C₂×C₄×C₈₉	—	2	1	no	—
631	C₂×C₄×C₈₉	—	2	1	no	—
632	C₂×C₄×C₈₉	—	2	1	no	—
633	C₂×C₄×C₈₉	—	2	1	no	—
634	C₂×C₄×C₈₉	—	2	1	no	—
635	C₂×C₄×C₈₉	—	2	1	no	—
636	C₂×C₄×C₈₉	—	2	1	no	—
637	C₂×C₄×C₈₉	—	4	4	no	—
638	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
639	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
640	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
641	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
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	—	2	1	no	—
674	C₂×Dic₈₉	—	2	1	no	—
675	C₂×Dic₈₉	—	2	1	no	—
676	C₂×Dic₈₉	—	2	1	no	—
677	C₂×Dic₈₉	—	2	1	no	—
678	C₂×Dic₈₉	—	2	1	no	—
679	C₂×Dic₈₉	—	2	1	no	—
680	C₂×Dic₈₉	—	4	4	no	—
681	C₂×Dic₈₉	C₂²×D₄	1	2	yes	—
682	C₂×Dic₈₉	C₂²×D₄	1	2	yes	—
683	C₂×Dic₈₉	C₂²×D₄	1	2	yes	—
684	C₂×Dic₈₉	H(5,𝔽₂)	1	2	yes	—
685	C₄×D₈₉	—	2	8	no	—
686	C₄×D₈₉	—	2	8	no	—
687	C₄×D₈₉	—	4	4	no	—
688	C₄×D₈₉	—	4	4	no	—
689	C₄×D₈₉	—	4	4	no	—
690	C₄×D₈₉	—	4	4	no	—
691	C₄×D₈₉	—	4	4	no	—
692	C₄×D₈₉	—	4	4	no	—
693	Dic₁₇₈	—	4	4	no	—
694	Dic₁₇₈	—	4	4	no	—
695	Dic₁₇₈	—	4	4	no	—
696	Dic₁₇₈	—	8	2	no	—
697	Dic₁₇₈	—	8	2	no	—
698	C₂²×C₈₉	—	2	2	no	—
699	C₂²×C₈₉	—	2	2	no	—
700	C₂²×C₈₉	—	2	2	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	C₂³×D₄	1	1	yes	characteristic
706	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
707	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
708	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
709	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
710	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
711	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
712	C₂×D₈₉	—	2	2	no	—
713	C₂×D₈₉	—	2	2	no	—
714	C₂×D₈₉	—	2	2	no	—
715	C₂×D₈₉	—	2	2	no	—
716	C₂×D₈₉	—	2	2	no	—
717	C₂×D₈₉	—	2	2	no	—
718	C₂×D₈₉	—	2	2	no	—
719	C₂×D₈₉	—	2	2	no	—
720	C₂×D₈₉	—	2	2	no	—
721	C₂×D₈₉	—	4	16	no	—
722	C₂×D₈₉	—	4	1	no	—
723	C₂×D₈₉	—	4	1	no	—
724	C₂×D₈₉	—	4	1	no	—
725	C₂×D₈₉	—	4	1	no	—
726	C₂×D₈₉	#536	1	4	yes	—
727	C₄×C₈₉	—	2	2	no	—
728	C₄×C₈₉	—	2	2	no	—
729	C₄×C₈₉	—	2	2	no	—
730	C₄×C₈₉	—	2	2	no	—
731	C₄×C₈₉	—	4	1	no	—
732	C₄×C₈₉	—	4	1	no	—
733	C₄×C₈₉	—	4	1	no	—
734	C₄×C₈₉	—	4	1	no	—
735	C₄×C₈₉	—	4	1	no	—
736	C₄×C₈₉	—	4	1	no	—
737	C₄×C₈₉	—	4	1	no	—
738	C₄×C₈₉	—	4	1	no	—
739	C₄×C₈₉	—	4	1	no	—
740	C₄×C₈₉	—	4	1	no	—
741	Dic₈₉	—	2	2	no	—
742	Dic₈₉	—	2	2	no	—
743	Dic₈₉	—	2	2	no	—
744	Dic₈₉	—	2	2	no	—
745	Dic₈₉	—	4	1	no	—
746	Dic₈₉	—	4	1	no	—
747	Dic₈₉	—	4	1	no	—
748	Dic₈₉	—	4	1	no	—
749	Dic₈₉	—	4	1	no	—
750	Dic₈₉	—	4	1	no	—
751	Dic₈₉	—	4	1	no	—
752	Dic₈₉	—	4	1	no	—
753	Dic₈₉	—	4	1	no	—
754	Dic₈₉	—	4	1	no	—
755	#36708	—	89	1	no	maximal, Sylow
756	C₂×C₈₉	—	4	2	no	—
757	C₂×C₈₉	C₂×#536	1	1	yes	characteristic
758	C₂×C₈₉	#3484	1	1	yes	characteristic
759	C₂×C₈₉	#3486	1	1	yes	characteristic
760	C₂×C₈₉	#3538	1	1	yes	characteristic
761	C₂×C₈₉	#3538	1	1	yes	characteristic
762	C₂×C₈₉	#3538	1	1	yes	characteristic
763	C₂×C₈₉	#3538	1	1	yes	characteristic
764	D₈₉	—	2	4	no	—
765	D₈₉	—	4	2	no	—
766	C₂×#544	—	89	1	no	—
767	C₂²×C₂²⋊Q₈	—	89	1	no	—
768	#2848	—	89	1	no	—
769	#2848	—	89	1	no	—
770	#2690	—	89	1	no	—
771	#2690	—	89	1	no	—
772	#2690	—	89	1	no	—
773	#2690	—	89	1	no	—
774	#2690	—	89	1	no	—
775	#2690	—	89	1	no	—
776	#2690	—	89	1	no	—
777	#2690	—	89	1	no	—
778	#2677	—	89	1	no	—
779	#2677	—	89	1	no	—
780	#2677	—	89	1	no	—
781	#2677	—	89	1	no	—
782	#2677	—	89	1	no	—
783	#2677	—	89	1	no	—
784	#2677	—	89	1	no	—
785	#2677	D₈₉	1	1	yes	characteristic, complemented
786	#2627	—	89	1	no	—
787	#2627	—	89	1	no	—
788	#2561	—	89	1	no	—
789	#2561	—	89	1	no	—
790	#2484	—	89	1	no	—
791	#2484	—	89	1	no	—
792	#2482	—	89	1	no	—
793	#2482	—	89	1	no	—
794	#2434	—	89	1	no	—
795	#2434	—	89	1	no	—
796	#2313	—	89	1	no	—
797	C₈₉	#36708	1	1	yes	characteristic, complemented, Sylow
798	C₂³×Q₈	—	89	1	no	—
799	C₂⁴×C₄	—	89	1	no	—
800	#544	—	178	8	no	—
801	C₂×C₄⋊Q₈	—	89	1	no	—
802	C₂×C₄⋊Q₈	—	89	1	no	—
803	C₂×C₄⋊Q₈	—	89	1	no	—
804	C₂×C₄⋊Q₈	—	89	1	no	—
805	C₂×C₄⋊Q₈	—	89	1	no	—
806	C₂×C₄⋊Q₈	—	89	1	no	—
807	C₂×C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
808	C₂×C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
809	C₂×#125	—	89	1	no	—
810	C₂×#125	—	89	1	no	—
811	C₂×#125	—	89	1	no	—
812	C₂×#125	—	89	1	no	—
813	C₂×C₂²⋊Q₈	—	89	1	no	—
814	C₂×C₂²⋊Q₈	—	89	1	no	—
815	C₂×C₂²⋊Q₈	—	89	1	no	—
816	C₂×C₂²⋊Q₈	—	89	1	no	—
817	C₂×C₂²⋊Q₈	—	89	1	no	—
818	C₂×C₂²⋊Q₈	—	89	1	no	—
819	C₂×C₂²⋊Q₈	—	89	1	no	—
820	C₂×C₂²⋊Q₈	—	89	1	no	—
821	C₂×C₂²⋊Q₈	—	89	1	no	—
822	C₂×C₂²⋊Q₈	—	89	1	no	—
823	C₂×C₂²⋊Q₈	—	89	1	no	—
824	C₂×C₂²⋊Q₈	—	89	1	no	—
825	C₂×C₂²⋊Q₈	—	89	1	no	—
826	C₂×C₂²⋊Q₈	—	89	1	no	—
827	C₂×C₂²⋊Q₈	—	178	8	no	—
828	C₂×C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
829	C₂×C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
830	C₂×#117	—	89	1	no	—
831	C₂×#117	—	89	1	no	—
832	C₂²×C₄⋊C₄	—	89	1	no	—
833	C₂²×C₄⋊C₄	—	89	1	no	—
834	C₂²×C₄⋊C₄	—	89	1	no	—
835	C₂²×C₂²⋊C₄	—	89	1	no	—
836	C₂²×C₂²⋊C₄	—	89	1	no	—
837	#400	—	89	1	no	—
838	#400	—	89	1	no	—
839	#400	—	89	1	no	—
840	#400	—	89	1	no	—
841	#400	—	89	1	no	—
842	#400	—	89	1	no	—
843	#400	—	89	1	no	—
844	#400	—	89	1	no	—
845	#399	—	89	1	no	—
846	#399	—	89	1	no	—
847	#399	—	89	1	no	—
848	#399	C₂×D₈₉	1	1	yes	characteristic
849	#398	—	89	1	no	—
850	#398	—	89	1	no	—
851	#398	—	89	1	no	—
852	#398	—	89	1	no	—
853	#398	—	89	1	no	—
854	#398	—	89	1	no	—
855	#398	—	89	1	no	—
856	#398	—	89	1	no	—
857	#398	—	89	1	no	—
858	#398	—	89	1	no	—
859	#398	C₂×D₈₉	1	1	yes	characteristic, complemented
860	#398	C₂×D₈₉	1	1	yes	characteristic, complemented
861	#397	—	89	1	no	—
862	#397	—	89	1	no	—
863	#397	—	89	1	no	—
864	#397	—	89	1	no	—
865	#397	—	89	1	no	—
866	#397	—	89	1	no	—
867	#397	—	89	1	no	—
868	#397	—	89	1	no	—
869	#395	—	89	1	no	—
870	#395	—	89	1	no	—
871	#395	—	89	1	no	—
872	#395	—	89	1	no	—
873	#395	—	89	1	no	—
874	#395	—	89	1	no	—
875	#395	—	89	1	no	—
876	#395	—	89	1	no	—
877	#395	—	89	1	no	—
878	#395	—	89	1	no	—
879	#395	C₂×D₈₉	1	1	yes	characteristic, complemented
880	#395	C₂×D₈₉	1	1	yes	characteristic, complemented
881	#393	—	89	1	no	—
882	#393	—	89	1	no	—
883	#393	—	89	1	no	—
884	#393	C₂×D₈₉	1	1	yes	characteristic
885	#391	—	89	1	no	—
886	#391	—	89	1	no	—
887	#391	—	89	1	no	—
888	#391	—	89	1	no	—
889	#388	—	89	1	no	—
890	#388	—	89	1	no	—
891	#388	—	89	1	no	—
892	#388	—	89	1	no	—
893	#388	—	89	1	no	—
894	#388	—	89	1	no	—
895	#388	—	89	1	no	—
896	#388	—	89	1	no	—
897	#388	—	89	1	no	—
898	#388	—	89	1	no	—
899	#388	—	89	1	no	—
900	#388	—	89	1	no	—
901	#388	—	89	1	no	—
902	#388	—	89	1	no	—
903	#388	C₂×D₈₉	1	1	yes	characteristic
904	#388	C₂×D₈₉	1	1	yes	characteristic
905	#387	—	89	1	no	—
906	#387	—	89	1	no	—
907	#387	—	89	1	no	—
908	#387	—	89	1	no	—
909	#387	—	89	1	no	—
910	#387	—	89	1	no	—
911	#387	—	89	1	no	—
912	#387	—	89	1	no	—
913	#387	—	89	1	no	—
914	#387	—	89	1	no	—
915	#387	—	89	1	no	—
916	#387	—	89	1	no	—
917	#387	—	89	1	no	—
918	#387	—	89	1	no	—
919	#387	C₂×D₈₉	1	1	yes	characteristic, complemented
920	#387	C₂×D₈₉	1	1	yes	characteristic, complemented
921	#385	—	89	1	no	—
922	#385	—	89	1	no	—
923	#385	—	89	1	no	—
924	#385	—	89	1	no	—
925	#385	—	89	1	no	—
926	#385	—	89	1	no	—
927	#385	—	89	1	no	—
928	#385	—	89	1	no	—
929	#385	—	89	1	no	—
930	#385	—	89	1	no	—
931	#385	—	89	1	no	—
932	#385	—	89	1	no	—
933	#385	—	89	1	no	—
934	#385	—	89	1	no	—
935	#385	—	89	1	no	—
936	#385	C₂×D₈₉	1	1	yes	characteristic
937	#381	—	89	1	no	—
938	#381	—	89	1	no	—
939	#381	—	89	1	no	—
940	#381	—	89	1	no	—
941	#381	—	89	1	no	—
942	#381	—	89	1	no	—
943	#380	—	89	1	no	—
944	#380	—	89	1	no	—
945	#380	—	89	1	no	—
946	#380	—	89	1	no	—
947	#380	—	89	1	no	—
948	#380	—	89	1	no	—
949	#379	—	89	1	no	—
950	#379	—	89	1	no	—
951	#379	—	89	1	no	—
952	#379	—	89	1	no	—
953	C₄×C₂²⋊C₄	—	89	1	no	—
954	C₄×C₂²⋊C₄	—	89	1	no	—
955	C₂⁵	—	89	1	no	—
956	C₂²×Q₈	—	89	1	no	—
957	C₂²×Q₈	—	89	1	no	—
958	C₂²×Q₈	—	89	1	no	—
959	C₂²×Q₈	—	89	1	no	—
960	C₂²×Q₈	—	89	1	no	—
961	C₂²×Q₈	—	356	2	no	—
962	C₂²×Q₈	—	356	2	no	—
963	C₂²×Q₈	—	178	4	no	—
964	C₂²×Q₈	C₂²×D₈₉	1	1	yes	characteristic
965	C₂²×Q₈	C₂²×D₈₉	1	1	yes	characteristic
966	C₂²×Q₈	C₂²×D₈₉	1	1	yes	characteristic
967	C₂³×C₄	—	89	1	no	—
968	C₂³×C₄	—	89	1	no	—
969	C₂³×C₄	—	89	1	no	—
970	C₂³×C₄	—	89	1	no	—
971	C₂³×C₄	—	89	1	no	—
972	C₂³×C₄	—	89	1	no	—
973	C₂³×C₄	—	89	1	no	—
974	C₂³×C₄	—	89	1	no	—
975	C₂³×C₄	—	89	1	no	—
976	C₂³×C₄	—	356	2	no	—
977	C₂³×C₄	—	356	2	no	—
978	C₂³×C₄	—	178	4	no	—
979	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
980	C₄⋊Q₈	—	2	4	no	—
981	C₄⋊Q₈	—	4	2	no	—
982	C₄⋊Q₈	—	356	2	no	—
983	C₄⋊Q₈	—	356	2	no	—
984	C₄⋊Q₈	—	356	2	no	—
985	C₄⋊Q₈	—	178	4	no	—
986	C₄⋊Q₈	—	178	4	no	—
987	C₄⋊Q₈	—	178	4	no	—
988	#125	—	178	4	no	—
989	#125	—	178	4	no	—
990	#125	—	178	4	no	—
991	#125	—	178	4	no	—
992	C₂²⋊Q₈	—	2	4	no	—
993	C₂²⋊Q₈	—	4	2	no	—
994	C₂²⋊Q₈	—	356	2	no	—
995	C₂²⋊Q₈	—	356	2	no	—
996	C₂²⋊Q₈	—	356	2	no	—
997	C₂²⋊Q₈	—	178	4	no	—
998	C₂²⋊Q₈	—	178	4	no	—
999	C₂²⋊Q₈	—	178	4	no	—
1000	C₂²⋊Q₈	—	178	4	no	—
1001	C₂²⋊Q₈	—	178	4	no	—
1002	C₂²⋊Q₈	—	178	4	no	—
1003	C₂²⋊Q₈	—	178	4	no	—
1004	C₂²⋊Q₈	—	178	4	no	—
1005	C₂²⋊Q₈	—	178	4	no	—
1006	C₂²⋊Q₈	—	178	4	no	—
1007	C₂²⋊Q₈	—	178	4	no	—
1008	#117	—	178	4	no	—
1009	#117	—	178	4	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	8	no	—
1014	C₂×C₄⋊C₄	—	89	1	no	—
1015	C₂×C₄⋊C₄	—	89	1	no	—
1016	C₂×C₄⋊C₄	—	89	1	no	—
1017	C₂×C₄⋊C₄	—	89	1	no	—
1018	C₂×C₄⋊C₄	—	89	1	no	—
1019	C₂×C₄⋊C₄	—	89	1	no	—
1020	C₂×C₄⋊C₄	—	89	1	no	—
1021	C₂×C₄⋊C₄	—	89	1	no	—
1022	C₂×C₄⋊C₄	—	89	1	no	—
1023	C₂×C₄⋊C₄	—	89	1	no	—
1024	C₂×C₄⋊C₄	—	89	1	no	—
1025	C₂×C₄⋊C₄	—	89	1	no	—
1026	C₂×C₄⋊C₄	—	89	1	no	—
1027	C₂×C₄⋊C₄	—	89	1	no	—
1028	C₂×C₄⋊C₄	—	89	1	no	—
1029	C₂×C₄⋊C₄	—	89	1	no	—
1030	C₂×C₄⋊C₄	—	89	1	no	—
1031	C₂×C₄⋊C₄	—	89	1	no	—
1032	C₂×C₄⋊C₄	—	89	1	no	—
1033	C₂×C₄⋊C₄	—	89	1	no	—
1034	C₂×C₄⋊C₄	—	89	1	no	—
1035	C₂×C₄⋊C₄	—	89	1	no	—
1036	C₂×C₄⋊C₄	—	89	1	no	—
1037	C₂×C₄⋊C₄	—	89	1	no	—
1038	C₂×C₄⋊C₄	—	89	1	no	—
1039	C₂×C₄⋊C₄	—	89	1	no	—
1040	C₂×C₄⋊C₄	—	89	1	no	—
1041	C₂×C₄⋊C₄	—	89	1	no	—
1042	C₂×C₄⋊C₄	—	89	1	no	—
1043	C₂×C₄⋊C₄	—	89	1	no	—
1044	C₂×C₄⋊C₄	—	89	1	no	—
1045	C₂×C₄⋊C₄	—	89	1	no	—
1046	C₂×C₄⋊C₄	—	178	4	no	—
1047	C₂×C₄⋊C₄	—	178	4	no	—
1048	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1049	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1050	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1051	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1052	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1053	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1054	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1055	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1056	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1057	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1058	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1059	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1060	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1061	C₂×C₂²⋊C₄	—	89	1	no	—
1062	C₂×C₂²⋊C₄	—	89	1	no	—
1063	C₂×C₂²⋊C₄	—	89	1	no	—
1064	C₂×C₂²⋊C₄	—	89	1	no	—
1065	C₂×C₂²⋊C₄	—	89	1	no	—
1066	C₂×C₂²⋊C₄	—	89	1	no	—
1067	C₂×C₂²⋊C₄	—	89	1	no	—
1068	C₂×C₂²⋊C₄	—	89	1	no	—
1069	C₂×C₂²⋊C₄	—	89	1	no	—
1070	C₂×C₂²⋊C₄	—	89	1	no	—
1071	C₂×C₂²⋊C₄	—	89	1	no	—
1072	C₂×C₂²⋊C₄	—	89	1	no	—
1073	C₂×C₂²⋊C₄	—	89	1	no	—
1074	C₂×C₂²⋊C₄	—	89	1	no	—
1075	C₂×C₂²⋊C₄	—	89	1	no	—
1076	C₂×C₂²⋊C₄	—	89	1	no	—
1077	C₂×C₂²⋊C₄	—	89	1	no	—
1078	C₂×C₂²⋊C₄	—	89	1	no	—
1079	C₂×C₂²⋊C₄	—	89	1	no	—
1080	C₂×C₂²⋊C₄	—	89	1	no	—
1081	C₂×C₂²⋊C₄	—	89	1	no	—
1082	C₂×C₂²⋊C₄	—	89	1	no	—
1083	C₂×C₂²⋊C₄	—	89	1	no	—
1084	C₂×C₂²⋊C₄	—	89	1	no	—
1085	C₂×C₂²⋊C₄	—	89	1	no	—
1086	C₂×C₂²⋊C₄	—	89	1	no	—
1087	C₂×C₂²⋊C₄	—	178	4	no	—
1088	C₂×C₂²⋊C₄	—	178	4	no	—
1089	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1090	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1091	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1092	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1093	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1094	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1095	C₂×C₄²	—	89	1	no	—
1096	C₂×C₄²	—	89	1	no	—
1097	C₂×C₄²	—	89	1	no	—
1098	C₂×C₄²	—	89	1	no	—
1099	C₂×C₄²	—	89	1	no	—
1100	C₂×C₄²	—	89	1	no	—
1101	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1102	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
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	#95	—	89	1	no	—
1129	#95	—	89	1	no	—
1130	#95	—	89	1	no	—
1131	#95	—	89	1	no	—
1132	#95	—	89	1	no	—
1133	#95	—	89	1	no	—
1134	#95	—	89	1	no	—
1135	#95	—	89	1	no	—
1136	#95	—	89	1	no	—
1137	#95	—	89	1	no	—
1138	#95	—	89	1	no	—
1139	#95	—	89	1	no	—
1140	#95	—	89	1	no	—
1141	#95	C₂²×D₈₉	1	1	yes	characteristic
1142	#95	C₂²×D₈₉	1	1	yes	characteristic
1143	#95	C₂²×D₈₉	1	1	yes	characteristic
1144	#95	C₂²×D₈₉	1	1	yes	characteristic
1145	#95	C₂²×D₈₉	1	1	yes	characteristic
1146	#95	C₂²×D₈₉	1	1	yes	characteristic
1147	#95	C₂²×D₈₉	1	1	yes	characteristic
1148	#95	C₂²×D₈₉	1	1	yes	characteristic
1149	#95	C₂²×D₈₉	1	1	yes	characteristic
1150	#95	C₂²×D₈₉	1	1	yes	characteristic
1151	C₂⁴	—	89	1	no	—
1152	C₂⁴	—	89	1	no	—
1153	C₂⁴	—	356	1	no	—
1154	C₂⁴	—	356	1	no	—
1155	C₂⁴	—	178	2	no	—
1156	C₂⁴	—	178	2	no	—
1157	C₂⁴	—	178	2	no	—
1158	C₂⁴	—	178	2	no	—
1159	C₂⁴	—	178	2	no	—
1160	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
1161	C₂×Q₈	—	2	2	no	—
1162	C₂×Q₈	—	2	2	no	—
1163	C₂×Q₈	—	2	2	no	—
1164	C₂×Q₈	—	2	2	no	—
1165	C₂×Q₈	—	4	1	no	—
1166	C₂×Q₈	—	4	1	no	—
1167	C₂×Q₈	—	4	1	no	—
1168	C₂×Q₈	—	4	1	no	—
1169	C₂×Q₈	—	4	1	no	—
1170	C₂×Q₈	—	356	1	no	—
1171	C₂×Q₈	—	356	1	no	—
1172	C₂×Q₈	—	356	1	no	—
1173	C₂×Q₈	—	356	1	no	—
1174	C₂×Q₈	—	356	1	no	—
1175	C₂×Q₈	—	356	1	no	—
1176	C₂×Q₈	—	356	1	no	—
1177	C₂×Q₈	—	356	16	no	—
1178	C₂×Q₈	—	178	2	no	—
1179	C₂×Q₈	—	178	2	no	—
1180	C₂×Q₈	—	178	2	no	—
1181	C₂×Q₈	—	178	2	no	—
1182	C₂×Q₈	—	178	2	no	—
1183	C₂×Q₈	—	178	2	no	—
1184	C₂×Q₈	—	178	2	no	—
1185	C₂×Q₈	—	178	2	no	—
1186	C₂²×C₄	—	2	2	no	—
1187	C₂²×C₄	—	2	2	no	—
1188	C₂²×C₄	—	4	1	no	—
1189	C₂²×C₄	—	89	1	no	—
1190	C₂²×C₄	—	89	1	no	—
1191	C₂²×C₄	—	89	1	no	—
1192	C₂²×C₄	—	89	1	no	—
1193	C₂²×C₄	—	89	4	no	—
1194	C₂²×C₄	—	89	4	no	—
1195	C₂²×C₄	—	89	4	no	—
1196	C₂²×C₄	—	89	1	no	—
1197	C₂²×C₄	—	89	1	no	—
1198	C₂²×C₄	—	89	1	no	—
1199	C₂²×C₄	—	89	1	no	—
1200	C₂²×C₄	—	89	1	no	—
1201	C₂²×C₄	—	89	1	no	—
1202	C₂²×C₄	—	89	1	no	—
1203	C₂²×C₄	—	89	1	no	—
1204	C₂²×C₄	—	89	1	no	—
1205	C₂²×C₄	—	89	1	no	—
1206	C₂²×C₄	—	356	1	no	—
1207	C₂²×C₄	—	356	1	no	—
1208	C₂²×C₄	—	356	1	no	—
1209	C₂²×C₄	—	356	1	no	—
1210	C₂²×C₄	—	356	1	no	—
1211	C₂²×C₄	—	356	1	no	—
1212	C₂²×C₄	—	356	1	no	—
1213	C₂²×C₄	—	356	1	no	—
1214	C₂²×C₄	—	356	16	no	—
1215	C₂²×C₄	—	356	1	no	—
1216	C₂²×C₄	—	178	2	no	—
1217	C₂²×C₄	—	178	2	no	—
1218	C₂²×C₄	—	178	2	no	—
1219	C₂²×C₄	—	178	2	no	—
1220	C₂²×C₄	—	178	2	no	—
1221	C₂²×C₄	—	178	2	no	—
1222	C₂²×C₄	—	178	2	no	—
1223	C₂²×C₄	—	178	2	no	—
1224	C₂²×C₄	—	178	2	no	—
1225	C₂²×C₄	—	178	2	no	—
1226	C₂²×C₄	—	178	2	no	—
1227	C₂²×C₄	—	178	2	no	—
1228	C₂²×C₄	—	178	2	no	—
1229	C₂²×C₄	—	178	2	no	—
1230	C₂²×C₄	—	178	2	no	—
1231	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1232	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1233	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1234	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1235	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1236	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1237	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1238	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1239	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1240	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1241	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1242	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1243	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1244	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1245	C₄⋊C₄	—	2	2	no	—
1246	C₄⋊C₄	—	2	2	no	—
1247	C₄⋊C₄	—	2	2	no	—
1248	C₄⋊C₄	—	2	2	no	—
1249	C₄⋊C₄	—	2	2	no	—
1250	C₄⋊C₄	—	2	2	no	—
1251	C₄⋊C₄	—	2	2	no	—
1252	C₄⋊C₄	—	2	2	no	—
1253	C₄⋊C₄	—	4	1	no	—
1254	C₄⋊C₄	—	4	1	no	—
1255	C₄⋊C₄	—	4	1	no	—
1256	C₄⋊C₄	—	4	1	no	—
1257	C₄⋊C₄	—	89	4	no	—
1258	C₄⋊C₄	—	89	4	no	—
1259	C₄⋊C₄	—	89	4	no	—
1260	C₄⋊C₄	—	356	1	no	—
1261	C₄⋊C₄	—	356	1	no	—
1262	C₄⋊C₄	—	356	1	no	—
1263	C₄⋊C₄	—	356	1	no	—
1264	C₄⋊C₄	—	356	1	no	—
1265	C₄⋊C₄	—	356	1	no	—
1266	C₄⋊C₄	—	356	1	no	—
1267	C₄⋊C₄	—	356	1	no	—
1268	C₄⋊C₄	—	178	2	no	—
1269	C₄⋊C₄	—	178	2	no	—
1270	C₄⋊C₄	—	178	2	no	—
1271	C₄⋊C₄	—	178	2	no	—
1272	C₄⋊C₄	—	178	2	no	—
1273	C₄⋊C₄	—	178	2	no	—
1274	C₄⋊C₄	—	178	2	no	—
1275	C₄⋊C₄	—	178	2	no	—
1276	C₄⋊C₄	—	178	2	no	—
1277	C₄⋊C₄	—	178	2	no	—
1278	C₄⋊C₄	—	178	2	no	—
1279	C₄⋊C₄	—	178	2	no	—
1280	C₄⋊C₄	—	178	2	no	—
1281	C₄⋊C₄	—	178	2	no	—
1282	C₄⋊C₄	—	178	2	no	—
1283	C₄⋊C₄	—	178	2	no	—
1284	C₄⋊C₄	—	178	2	no	—
1285	C₄⋊C₄	—	178	2	no	—
1286	C₄⋊C₄	—	178	2	no	—
1287	C₄⋊C₄	—	178	2	no	—
1288	C₄⋊C₄	—	178	2	no	—
1289	C₄⋊C₄	—	178	2	no	—
1290	C₄⋊C₄	—	178	2	no	—
1291	C₄⋊C₄	—	178	2	no	—
1292	C₄⋊C₄	D₄×D₈₉	1	4	yes	—
1293	C₂²⋊C₄	—	2	2	no	—
1294	C₂²⋊C₄	—	2	2	no	—
1295	C₂²⋊C₄	—	2	2	no	—
1296	C₂²⋊C₄	—	4	1	no	—
1297	C₂²⋊C₄	—	4	1	no	—
1298	C₂²⋊C₄	—	4	1	no	—
1299	C₂²⋊C₄	—	356	1	no	—
1300	C₂²⋊C₄	—	356	1	no	—
1301	C₂²⋊C₄	—	356	1	no	—
1302	C₂²⋊C₄	—	356	1	no	—
1303	C₂²⋊C₄	—	356	1	no	—
1304	C₂²⋊C₄	—	178	2	no	—
1305	C₂²⋊C₄	—	178	2	no	—
1306	C₂²⋊C₄	—	178	2	no	—
1307	C₂²⋊C₄	—	178	2	no	—
1308	C₂²⋊C₄	—	178	2	no	—
1309	C₂²⋊C₄	—	178	2	no	—
1310	C₂²⋊C₄	—	178	2	no	—
1311	C₂²⋊C₄	—	178	2	no	—
1312	C₂²⋊C₄	—	178	2	no	—
1313	C₂²⋊C₄	—	178	2	no	—
1314	C₂²⋊C₄	—	178	2	no	—
1315	C₂²⋊C₄	—	178	2	no	—
1316	C₂²⋊C₄	—	178	2	no	—
1317	C₂²⋊C₄	—	178	2	no	—
1318	C₂²⋊C₄	—	178	2	no	—
1319	C₂²⋊C₄	—	178	2	no	—
1320	C₂²⋊C₄	—	178	2	no	—
1321	C₂²⋊C₄	—	178	2	no	—
1322	C₂²⋊C₄	—	178	2	no	—
1323	C₂²⋊C₄	—	178	2	no	—
1324	C₂²⋊C₄	—	178	2	no	—
1325	C₄²	—	2	2	no	—
1326	C₄²	—	4	1	no	—
1327	C₄²	—	356	1	no	—
1328	C₄²	—	356	1	no	—
1329	C₄²	—	356	1	no	—
1330	C₄²	—	178	2	no	—
1331	C₄²	—	178	2	no	—
1332	C₄²	—	178	2	no	—
1333	C₂³	—	2	1	no	—
1334	C₂³	—	2	1	no	—
1335	C₂³	—	2	1	no	—
1336	C₂³	—	2	1	no	—
1337	C₂³	—	2	1	no	—
1338	C₂³	—	2	1	no	—
1339	C₂³	—	89	2	no	—
1340	C₂³	—	89	2	no	—
1341	C₂³	—	89	2	no	—
1342	C₂³	—	89	2	no	—
1343	C₂³	—	356	4	no	—
1344	C₂³	—	356	4	no	—
1345	C₂³	—	356	4	no	—
1346	C₂³	—	356	4	no	—
1347	C₂³	—	356	4	no	—
1348	C₂³	—	356	4	no	—
1349	C₂³	—	178	8	no	—
1350	C₂³	—	178	1	no	—
1351	C₂³	—	178	1	no	—
1352	C₂³	—	178	1	no	—
1353	C₂³	—	178	1	no	—
1354	C₂³	—	178	1	no	—
1355	C₂³	—	178	1	no	—
1356	C₂³	—	178	1	no	—
1357	C₂³	—	178	1	no	—
1358	C₂³	—	178	1	no	—
1359	C₂³	—	178	1	no	—
1360	C₂³	#15668060	1	2	yes	—
1361	C₂³	C₂⁴×D₈₉	1	1	yes	characteristic
1362	Q₈	—	4	4	no	—
1363	Q₈	—	8	2	no	—
1364	Q₈	—	8	2	no	—
1365	Q₈	—	356	4	no	—
1366	Q₈	—	356	4	no	—
1367	Q₈	—	356	4	no	—
1368	Q₈	—	712	2	no	—
1369	Q₈	—	712	2	no	—
1370	C₂×C₄	—	2	1	no	—
1371	C₂×C₄	—	2	1	no	—
1372	C₂×C₄	—	2	1	no	—
1373	C₂×C₄	—	2	1	no	—
1374	C₂×C₄	—	2	1	no	—
1375	C₂×C₄	—	2	1	no	—
1376	C₂×C₄	—	2	1	no	—
1377	C₂×C₄	—	2	1	no	—
1378	C₂×C₄	—	2	1	no	—
1379	C₂×C₄	—	2	1	no	—
1380	C₂×C₄	—	2	1	no	—
1381	C₂×C₄	—	2	1	no	—
1382	C₂×C₄	—	2	1	no	—
1383	C₂×C₄	—	2	1	no	—
1384	C₂×C₄	—	2	1	no	—
1385	C₂×C₄	—	2	1	no	—
1386	C₂×C₄	—	2	1	no	—
1387	C₂×C₄	—	2	1	no	—
1388	C₂×C₄	—	2	1	no	—
1389	C₂×C₄	—	2	1	no	—
1390	C₂×C₄	—	2	1	no	—
1391	C₂×C₄	—	2	1	no	—
1392	C₂×C₄	—	2	1	no	—
1393	C₂×C₄	—	2	1	no	—
1394	C₂×C₄	—	2	1	no	—
1395	C₂×C₄	—	2	1	no	—
1396	C₂×C₄	—	2	1	no	—
1397	C₂×C₄	—	2	1	no	—
1398	C₂×C₄	—	2	1	no	—
1399	C₂×C₄	—	2	1	no	—
1400	C₂×C₄	—	2	1	no	—
1401	C₂×C₄	—	2	1	no	—
1402	C₂×C₄	—	2	1	no	—
1403	C₂×C₄	—	2	1	no	—
1404	C₂×C₄	—	2	1	no	—
1405	C₂×C₄	—	2	1	no	—
1406	C₂×C₄	—	2	1	no	—
1407	C₂×C₄	—	2	1	no	—
1408	C₂×C₄	—	4	4	no	—
1409	C₂×C₄	—	89	2	no	—
1410	C₂×C₄	—	89	2	no	—
1411	C₂×C₄	—	89	2	no	—
1412	C₂×C₄	—	89	2	no	—
1413	C₂×C₄	—	356	4	no	—
1414	C₂×C₄	—	356	4	no	—
1415	C₂×C₄	—	356	4	no	—
1416	C₂×C₄	—	356	4	no	—
1417	C₂×C₄	—	356	4	no	—
1418	C₂×C₄	—	356	4	no	—
1419	C₂×C₄	—	356	4	no	—
1420	C₂×C₄	—	178	8	no	—
1421	C₂×C₄	—	178	8	no	—
1422	C₂×C₄	—	178	1	no	—
1423	C₂×C₄	—	178	1	no	—
1424	C₂×C₄	—	178	1	no	—
1425	C₂×C₄	—	178	1	no	—
1426	C₂×C₄	—	178	1	no	—
1427	C₂×C₄	—	178	1	no	—
1428	C₂×C₄	—	178	1	no	—
1429	C₂×C₄	—	178	1	no	—
1430	C₂×C₄	—	178	1	no	—
1431	C₂×C₄	—	178	1	no	—
1432	C₂×C₄	—	178	1	no	—
1433	C₂×C₄	—	178	1	no	—
1434	C₂×C₄	—	178	1	no	—
1435	C₂×C₄	—	178	1	no	—
1436	C₂×C₄	—	178	1	no	—
1437	C₂×C₄	—	178	1	no	—
1438	C₂×C₄	—	178	1	no	—
1439	C₂×C₄	—	178	1	no	—
1440	C₂×C₄	—	178	1	no	—
1441	C₂×C₄	—	178	1	no	—
1442	C₂×C₄	—	178	1	no	—
1443	C₂×C₄	—	178	1	no	—
1444	C₂×C₄	—	178	1	no	—
1445	C₂×C₄	—	178	1	no	—
1446	C₂×C₄	—	178	1	no	—
1447	C₂×C₄	—	178	1	no	—
1448	C₂×C₄	—	178	1	no	—
1449	C₂×C₄	—	178	1	no	—
1450	C₂×C₄	—	178	1	no	—
1451	C₂×C₄	—	178	1	no	—
1452	C₂×C₄	—	178	1	no	—
1453	C₂×C₄	—	178	1	no	—
1454	C₂×C₄	—	178	1	no	—
1455	C₂×C₄	—	178	1	no	—
1456	C₂×C₄	—	178	1	no	—
1457	C₂×C₄	—	178	1	no	—
1458	C₂×C₄	—	178	1	no	—
1459	C₂×C₄	—	178	1	no	—
1460	C₂×C₄	C₂×D₄×D₈₉	1	2	yes	—
1461	C₂×C₄	C₂×D₄×D₈₉	1	2	yes	—
1462	C₂×C₄	C₂×D₄×D₈₉	1	2	yes	—
1463	C₂×C₄	#15668057	1	2	yes	—
1464	C₂²	—	2	2	no	—
1465	C₂²	—	2	2	no	—
1466	C₂²	—	2	2	no	—
1467	C₂²	—	4	1	no	—
1468	C₂²	—	4	1	no	—
1469	C₂²	—	4	1	no	—
1470	C₂²	—	4	1	no	—
1471	C₂²	—	89	4	no	—
1472	C₂²	—	356	16	no	—
1473	C₂²	—	356	1	no	—
1474	C₂²	—	356	1	no	—
1475	C₂²	—	356	1	no	—
1476	C₂²	—	356	1	no	—
1477	C₂²	—	178	2	no	—
1478	C₂²	—	178	2	no	—
1479	C₂²	—	178	2	no	—
1480	C₂²	—	178	2	no	—
1481	C₂²	—	178	2	no	—
1482	C₂²	—	178	2	no	—
1483	C₂²	—	178	2	no	—
1484	C₂²	—	178	2	no	—
1485	C₂²	—	178	2	no	—
1486	C₂²	C₂²×D₄×D₈₉	1	1	yes	characteristic
1487	C₂²	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
1488	C₂²	C₂×#15668057	1	1	yes	characteristic
1489	C₂²	2₋¹⁺⁴×D₈₉	1	1	yes	characteristic
1490	C₂²	2₋¹⁺⁴×D₈₉	1	1	yes	characteristic
1491	C₂²	2₋¹⁺⁴×D₈₉	1	1	yes	characteristic
1492	C₂²	C₂×#15668060	1	1	yes	characteristic
1493	C₄	—	2	2	no	—
1494	C₄	—	2	2	no	—
1495	C₄	—	2	2	no	—
1496	C₄	—	2	2	no	—
1497	C₄	—	4	1	no	—
1498	C₄	—	4	1	no	—
1499	C₄	—	4	1	no	—
1500	C₄	—	4	1	no	—
1501	C₄	—	4	1	no	—
1502	C₄	—	4	1	no	—
1503	C₄	—	4	1	no	—
1504	C₄	—	4	1	no	—
1505	C₄	—	4	1	no	—
1506	C₄	—	4	1	no	—
1507	C₄	—	356	1	no	—
1508	C₄	—	356	1	no	—
1509	C₄	—	356	1	no	—
1510	C₄	—	356	1	no	—
1511	C₄	—	356	1	no	—
1512	C₄	—	356	1	no	—
1513	C₄	—	356	1	no	—
1514	C₄	—	356	1	no	—
1515	C₄	—	356	1	no	—
1516	C₄	—	356	1	no	—
1517	C₄	—	178	2	no	—
1518	C₄	—	178	2	no	—
1519	C₄	—	178	2	no	—
1520	C₄	—	178	2	no	—
1521	C₂	—	4	2	no	—
1522	C₂	—	356	2	no	—
1523	C₂	—	178	4	no	—
1524	C₂	#536×D₈₉	1	1	yes	characteristic
1525	C₂	#26033880	1	1	yes	characteristic
1526	C₂	#26033902	1	1	yes	characteristic
1527	C₂	#26034493	1	1	yes	characteristic
1528	C₂	#26034494	1	1	yes	characteristic
1529	C₂	#26034495	1	1	yes	characteristic
1530	C₂	#26034496	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₈₉
commutator, socle, cosocle	C₂³×C₈₉	C₂⁵
Fitting	C₈₉×#2677	C₂
prime radical	C₂⁴×D₈₉	C₂³
hypercenter	#2677	D₈₉
hypocenter	C₈₉	#36708
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ #2677

Complements

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

N	H ≅ G/N	type
1. C₂×#19152225	C₂	semidirect
5. #26026724	C₂	semidirect
6. #26026722	C₂	semidirect
7. #26026721	C₂	semidirect
8. #26026719	C₂	semidirect
9. #26026717	C₂	semidirect
10. #26026716	C₂	semidirect
11. #26026715	C₂	semidirect
12. #26026714	C₂	semidirect
13. #26026569	C₂	semidirect
14. #26026568	C₂	semidirect
15. #26026566	C₂	semidirect
16. #26026563	C₂	semidirect
17. #26026562	C₂	semidirect
18. #26026562	C₂	semidirect
19. #26026561	C₂	semidirect
20. #26026070	C₂	semidirect
21. #26026064	C₂	semidirect
24. #26024537	C₂	semidirect
25. #26024534	C₂	semidirect
28. #26023893	C₂	semidirect
29. #26023891	C₂	semidirect
30. #26022851	C₂	semidirect
31. C₈₉×#2677	C₂	semidirect
35. C₂×#15668011	C₂²	semidirect
36. C₂×#15668011	C₂²	semidirect
37. C₂×#15668011	C₂²	semidirect
38. C₂×#15668010	C₂²	semidirect
39. C₂×#15668010	C₂²	semidirect
40. C₂×#15668010	C₂²	semidirect
41. C₂×#15668004	C₂²	semidirect
42. C₂×#15668003	C₂²	semidirect
43. C₂×#15668002	C₂²	semidirect
44. C₂×#15668002	C₂²	semidirect
67. #19151540	C₂²	semidirect
68. #19151540	C₂²	semidirect
69. #19151539	C₂²	semidirect
70. #19151539	C₂²	semidirect
71. #19151538	C₂²	semidirect
72. #19151538	C₂²	semidirect
73. #19151537	C₂²	semidirect
74. #19151537	C₂²	semidirect
78. #19151532	C₂²	semidirect
79. #19151532	C₂²	semidirect
80. #19151532	C₂²	semidirect
81. #19151531	C₂²	semidirect
82. #19151531	C₂²	semidirect
83. #19151531	C₂²	semidirect
84. #19151529	C₂²	semidirect
85. #19151529	C₂²	semidirect
86. #19151529	C₂²	semidirect
87. #19151528	C₂²	semidirect
96. #19151519	C₂²	semidirect
97. #19151519	C₂²	semidirect
98. #19151518	C₂²	semidirect
99. #19151518	C₂²	semidirect
100. #19151518	C₂²	semidirect
101. #19151518	C₂²	semidirect
102. #19151518	C₂²	semidirect
103. #19151518	C₂²	semidirect
104. #19151517	C₂²	semidirect
105. #19151517	C₂²	semidirect
109. #19151505	C₂²	semidirect
110. #19151504	C₂²	semidirect
111. #19151502	C₂²	semidirect
112. #19151502	C₂²	semidirect
127. #19151485	C₂²	semidirect
128. #19151484	C₂²	semidirect
129. #19151484	C₂²	semidirect
130. #19151484	C₂²	semidirect
131. #19151483	C₂²	semidirect
132. #19151483	C₂²	semidirect
133. #19151482	C₂²	semidirect
134. #19151482	C₂²	semidirect
135. #19151481	C₂²	semidirect
136. #19151480	C₂²	semidirect
137. #19151480	C₂²	semidirect
138. #19151480	C₂²	semidirect
139. #19151479	C₂²	semidirect
140. #19151479	C₂²	semidirect
174. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
175. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
179. #398×C₈₉	C₂²	semidirect
180. #398×C₈₉	C₂²	semidirect
181. #395×C₈₉	C₂²	semidirect
182. #395×C₈₉	C₂²	semidirect
186. #387×C₈₉	C₂²	semidirect
187. #387×C₈₉	C₂²	semidirect
785. #2677	D₈₉	semidirect
797. C₈₉	#36708	semidirect
807. C₂×C₄⋊Q₈	C₂×D₈₉	semidirect
808. C₂×C₄⋊Q₈	C₂×D₈₉	semidirect
859. #398	C₂×D₈₉	semidirect
860. #398	C₂×D₈₉	semidirect
879. #395	C₂×D₈₉	semidirect
880. #395	C₂×D₈₉	semidirect
919. #387	C₂×D₈₉	semidirect
920. #387	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19152225	2
C₂×C₂²⋊Q₈×D₈₉	2
#26028538	2
#26028536	2
#26026724	2
#26026722	2
#26026721	2
#26026719	2
#26026717	2
#26026716	2
#26026715	2
#26026714	2
#26026569	2
#26026568	2
#26026566	2
#26026563	2
#26026562	2
#26026561	2
#26026070	2
#26026064	2
#26025408	2
#26025406	2
#26024537	2
#26024534	2
#26024527	2
#26024524	2
#26023893	2
#26023891	2
#26022851	2
C₈₉×#2677	2
#36708	89