Subgroups — #36764293

Order 22784.

1462 conjugacy classes of subgroups.

The subgroup lattice has 1272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028587	C₂	1	1	yes	maximal, characteristic
2	#26028587	C₂	1	1	yes	maximal, characteristic
3	#26028213	C₂	1	1	yes	maximal, characteristic, complemented
4	#26028208	C₂	1	1	yes	maximal, characteristic, complemented
5	#26028177	C₂	1	1	yes	maximal, characteristic, complemented
6	#26028175	C₂	1	1	yes	maximal, characteristic, complemented
7	#26027839	C₂	1	1	yes	maximal, characteristic, complemented
8	#26027833	C₂	1	1	yes	maximal, characteristic, complemented
9	#26027809	C₂	1	1	yes	maximal, characteristic, complemented
10	#26027803	C₂	1	1	yes	maximal, characteristic, complemented
11	#26027426	C₂	1	1	yes	maximal, characteristic
12	#26027414	C₂	1	1	yes	maximal, characteristic
13	#26027327	C₂	1	1	yes	maximal, characteristic
14	#26027315	C₂	1	1	yes	maximal, characteristic
15	#26026831	C₂	1	1	yes	maximal, characteristic
16	#26026819	C₂	1	1	yes	maximal, characteristic
17	#26026708	C₂	1	1	yes	maximal, characteristic
18	#26026696	C₂	1	1	yes	maximal, characteristic
19	#26026339	C₂	1	1	yes	maximal, characteristic, complemented
20	#26025948	C₂	1	1	yes	maximal, characteristic
21	#26025902	C₂	1	1	yes	maximal, characteristic, complemented
22	#26025827	C₂	1	1	yes	maximal, characteristic
23	#26025687	C₂	1	1	yes	maximal, characteristic, complemented
24	#26025685	C₂	1	1	yes	maximal, characteristic, complemented
25	#26025638	C₂	1	1	yes	maximal, characteristic, complemented
26	#26024475	C₂	1	1	yes	maximal, characteristic
27	#26024473	C₂	1	1	yes	maximal, characteristic
28	#26023054	C₂	1	1	yes	maximal, characteristic, complemented
29	#26022901	C₂	1	1	yes	maximal, characteristic, complemented
30	#26022732	C₂	1	1	yes	maximal, characteristic
31	C₈₉×#2655	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#15668007	C₂²	1	1	yes	characteristic
33	C₂×#15668007	C₂²	1	1	yes	characteristic
34	C₂×#15668002	C₂²	1	1	yes	characteristic
35	C₂×#15667990	C₂²	1	1	yes	characteristic
36	C₂×#15667990	C₂²	1	1	yes	characteristic
37	C₂×#15667977	C₂²	1	1	yes	characteristic
38	C₂×#15667969	C₂²	1	1	yes	characteristic
39	C₂×#15667969	C₂²	1	1	yes	characteristic
40	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
41	C₈₉⋊#401	C₂²	1	1	yes	characteristic
42	#19151540	C₂²	1	1	yes	characteristic
43	#19151540	C₂²	1	1	yes	characteristic
44	#19151540	C₂²	1	1	yes	characteristic
45	#19151539	C₂²	1	1	yes	characteristic
46	#19151539	C₂²	1	1	yes	characteristic
47	#19151539	C₂²	1	1	yes	characteristic
48	#19151539	C₂²	1	1	yes	characteristic
49	#19151539	C₂²	1	1	yes	characteristic
50	#19151538	C₂²	1	1	yes	characteristic
51	#19151538	C₂²	1	1	yes	characteristic
52	#19151536	C₂²	1	1	yes	characteristic
53	#19151533	C₂²	1	1	yes	characteristic
54	#19151532	C₂²	1	1	yes	characteristic
55	#19151532	C₂²	1	1	yes	characteristic
56	#19151532	C₂²	1	1	yes	characteristic
57	#19151531	C₂²	1	1	yes	characteristic
58	#19151531	C₂²	1	1	yes	characteristic
59	#19151531	C₂²	1	1	yes	characteristic
60	#19151531	C₂²	1	1	yes	characteristic
61	#19151530	C₂²	1	1	yes	characteristic
62	#19151529	C₂²	1	1	yes	characteristic
63	#19151529	C₂²	1	1	yes	characteristic
64	#19151529	C₂²	1	1	yes	characteristic
65	#19151528	C₂²	1	1	yes	characteristic
66	#19151528	C₂²	1	1	yes	characteristic
67	#19151527	C₂²	1	1	yes	characteristic
68	#19151527	C₂²	1	1	yes	characteristic
69	#19151527	C₂²	1	1	yes	characteristic
70	#19151527	C₂²	1	1	yes	characteristic
71	#19151525	C₂²	1	1	yes	characteristic
72	#19151524	C₂²	1	1	yes	characteristic
73	#19151519	C₂²	1	1	yes	characteristic
74	#19151519	C₂²	1	1	yes	characteristic
75	#19151519	C₂²	1	1	yes	characteristic
76	#19151518	C₂²	1	1	yes	characteristic
77	#19151518	C₂²	1	1	yes	characteristic
78	#19151518	C₂²	1	1	yes	characteristic
79	#19151518	C₂²	1	1	yes	characteristic
80	#19151511	C₂²	1	1	yes	characteristic
81	#19151503	C₂²	1	1	yes	characteristic
82	#19151503	C₂²	1	1	yes	characteristic
83	#19151502	C₂²	1	1	yes	characteristic
84	#19151502	C₂²	1	1	yes	characteristic
85	#19151502	C₂²	1	1	yes	characteristic
86	#19151502	C₂²	1	1	yes	characteristic
87	#19151502	C₂²	1	1	yes	characteristic
88	#19151502	C₂²	1	1	yes	characteristic
89	#19151502	C₂²	1	1	yes	characteristic
90	#19151502	C₂²	1	1	yes	characteristic
91	#19151496	C₂²	1	1	yes	characteristic
92	#19151495	C₂²	1	1	yes	characteristic
93	#19151495	C₂²	1	1	yes	characteristic
94	#19151495	C₂²	1	1	yes	characteristic
95	#19151495	C₂²	1	1	yes	characteristic
96	#19151495	C₂²	1	1	yes	characteristic
97	#19151495	C₂²	1	1	yes	characteristic
98	#19151495	C₂²	1	1	yes	characteristic
99	#19151495	C₂²	1	1	yes	characteristic
100	#19151495	C₂²	1	1	yes	characteristic
101	#19151495	C₂²	1	1	yes	characteristic
102	#19151494	C₂²	1	1	yes	characteristic
103	#19151494	C₂²	1	1	yes	characteristic
104	#19151494	C₂²	1	1	yes	characteristic
105	#19151493	C₂²	1	1	yes	characteristic
106	#19151493	C₂²	1	1	yes	characteristic
107	#19151493	C₂²	1	1	yes	characteristic
108	#19151493	C₂²	1	1	yes	characteristic
109	#19151493	C₂²	1	1	yes	characteristic
110	#19151493	C₂²	1	1	yes	characteristic
111	#19151493	C₂²	1	1	yes	characteristic
112	#19151490	C₂²	1	1	yes	characteristic
113	#19151490	C₂²	1	1	yes	characteristic
114	#19151488	C₂²	1	1	yes	characteristic
115	#19151488	C₂²	1	1	yes	characteristic
116	#19151487	C₂²	1	1	yes	characteristic
117	#19151487	C₂²	1	1	yes	characteristic
118	#19151485	C₂²	1	1	yes	characteristic
119	#19151484	C₂²	1	1	yes	characteristic
120	#19151483	C₂²	1	1	yes	characteristic
121	#19151483	C₂²	1	1	yes	characteristic
122	#19151483	C₂²	1	1	yes	characteristic
123	#19151483	C₂²	1	1	yes	characteristic
124	#19151482	C₂²	1	1	yes	characteristic
125	#19151482	C₂²	1	1	yes	characteristic
126	#19151482	C₂²	1	1	yes	characteristic
127	#19151482	C₂²	1	1	yes	characteristic
128	#19151482	C₂²	1	1	yes	characteristic
129	#19151481	C₂²	1	1	yes	characteristic
130	#19151481	C₂²	1	1	yes	characteristic
131	#19151481	C₂²	1	1	yes	characteristic
132	#19151481	C₂²	1	1	yes	characteristic
133	#19151481	C₂²	1	1	yes	characteristic
134	#19151480	C₂²	1	1	yes	characteristic
135	#19151480	C₂²	1	1	yes	characteristic
136	#19151480	C₂²	1	1	yes	characteristic
137	#19151480	C₂²	1	1	yes	characteristic
138	#19151480	C₂²	1	1	yes	characteristic
139	#19151480	C₂²	1	1	yes	characteristic
140	#19151480	C₂²	1	1	yes	characteristic
141	#19151480	C₂²	1	1	yes	characteristic
142	#19151479	C₂²	1	1	yes	characteristic
143	#19151479	C₂²	1	1	yes	characteristic
144	#19151479	C₂²	1	1	yes	characteristic
145	#19151479	C₂²	1	1	yes	characteristic
146	#19151479	C₂²	1	1	yes	characteristic
147	#19151472	C₂²	1	1	yes	characteristic
148	#19151472	C₂²	1	1	yes	characteristic
149	#19151472	C₂²	1	1	yes	characteristic
150	#19151472	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	#19151465	C₂²	1	1	yes	characteristic
156	#19151465	C₂²	1	1	yes	characteristic
157	#19151465	C₂²	1	1	yes	characteristic
158	#19151463	C₂²	1	1	yes	characteristic
159	#19151462	C₂²	1	1	yes	characteristic
160	#19151460	C₂²	1	1	yes	characteristic
161	#19151460	C₂²	1	1	yes	characteristic
162	#19151460	C₂²	1	1	yes	characteristic
163	#19151460	C₂²	1	1	yes	characteristic
164	#19151457	C₂²	1	1	yes	characteristic
165	#19151457	C₂²	1	1	yes	characteristic
166	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
167	C₄×#13083553	C₂²	1	1	yes	characteristic
168	C₄×#13083553	C₂²	1	1	yes	characteristic
169	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
170	#19151449	C₂²	1	1	yes	characteristic
171	#19151443	C₂²	1	1	yes	characteristic
172	#401×C₈₉	C₂²	1	1	yes	characteristic
173	#400×C₈₉	C₂²	1	1	yes	characteristic
174	#400×C₈₉	C₂²	1	1	yes	characteristic
175	#400×C₈₉	C₂²	1	1	yes	characteristic
176	#400×C₈₉	C₂²	1	1	yes	characteristic
177	#398×C₈₉	C₂²	1	1	yes	characteristic
178	#398×C₈₉	C₂²	1	1	yes	characteristic
179	#398×C₈₉	C₂²	1	1	yes	characteristic
180	#389×C₈₉	C₂²	1	1	yes	characteristic
181	#387×C₈₉	C₂²	1	1	yes	characteristic
182	#387×C₈₉	C₂²	1	1	yes	characteristic
183	#387×C₈₉	C₂²	1	1	yes	characteristic
184	#387×C₈₉	C₂²	1	1	yes	characteristic
185	#387×C₈₉	C₂²	1	1	yes	characteristic
186	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
187	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
188	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
189	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
190	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
191	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
192	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
193	#15668007	—	4	2	no	—
194	#15668007	—	4	2	no	—
195	#15668002	—	2	4	no	—
196	#15667990	—	4	2	no	—
197	#15667990	—	4	2	no	—
198	#15667977	—	2	4	no	—
199	#15667969	—	2	4	no	—
200	#15667969	—	4	2	no	—
201	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
205	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
206	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
208	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
210	C₂×#13083553	C₂³	1	1	yes	characteristic
211	C₂×#13083553	C₂³	1	1	yes	characteristic
212	C₂×#13083553	C₂³	1	1	yes	characteristic
213	C₂×#13083553	C₂³	1	1	yes	characteristic
214	C₂×#13083553	C₂³	1	1	yes	characteristic
215	C₂×#13083553	C₂³	1	1	yes	characteristic
216	C₂×#13083553	C₂³	1	1	yes	characteristic
217	C₂×#13083553	C₂³	1	1	yes	characteristic
218	C₂×#13083553	C₂³	1	1	yes	characteristic
219	C₂×#13083553	C₂³	1	1	yes	characteristic
220	C₂×#13083553	C₂³	1	1	yes	characteristic
221	C₂×#13083553	C₂³	1	1	yes	characteristic
222	C₂×#13083553	C₂³	1	1	yes	characteristic
223	C₂×#13083553	C₂³	1	1	yes	characteristic
224	C₂×#13083553	C₂³	1	1	yes	characteristic
225	C₂×#13083553	C₂³	1	1	yes	characteristic
226	C₂×#13083553	C₂³	1	1	yes	characteristic
227	C₂×#13083553	C₂³	1	1	yes	characteristic
228	C₂×#13083553	C₂³	1	1	yes	characteristic
229	C₂×#13083553	C₂³	1	1	yes	characteristic
230	C₂×#13083553	C₂³	1	1	yes	characteristic
231	C₂×#13083553	C₂³	1	1	yes	characteristic
232	C₂×#13083553	C₂³	1	1	yes	characteristic
233	C₂×#13083553	C₂³	1	1	yes	characteristic
234	C₂×#13083553	C₂³	1	1	yes	characteristic
235	C₂×#13083553	C₂³	1	1	yes	characteristic
236	C₂×#13083553	C₂³	1	1	yes	characteristic
237	C₂×#13083553	C₂³	1	1	yes	characteristic
238	C₂×#13083553	C₂³	1	1	yes	characteristic
239	C₂×#13083553	C₂³	1	1	yes	characteristic
240	C₂×#13083551	C₂³	1	1	yes	characteristic
241	C₂×#13083551	C₂³	1	1	yes	characteristic
242	C₂×#13083551	C₂³	1	1	yes	characteristic
243	C₂×#13083551	C₂³	1	1	yes	characteristic
244	C₂×#13083551	C₂³	1	1	yes	characteristic
245	C₂×#13083551	C₂³	1	1	yes	characteristic
246	C₂×#13083551	C₂³	1	1	yes	characteristic
247	C₂×#13083551	C₂³	1	1	yes	characteristic
248	C₂×#13083551	C₂³	1	1	yes	characteristic
249	C₂×#13083551	C₂³	1	1	yes	characteristic
250	C₂×#13083551	C₂³	1	1	yes	characteristic
251	C₂×#13083551	C₂³	1	1	yes	characteristic
252	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
253	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
254	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
255	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
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	C₄²×D₈₉	—	4	2	no	—
266	#15667919	C₂³	1	1	yes	characteristic
267	#15667919	C₂³	1	1	yes	characteristic
268	#15667919	C₂³	1	1	yes	characteristic
269	#15667919	C₂³	1	1	yes	characteristic
270	#15667919	C₂³	1	1	yes	characteristic
271	#15667919	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	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
317	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
318	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
319	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
320	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
321	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
322	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
323	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
324	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
325	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
326	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
327	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
328	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
329	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
330	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
331	#95×C₈₉	C₂³	1	1	yes	characteristic
332	#95×C₈₉	C₂³	1	1	yes	characteristic
333	#95×C₈₉	C₂³	1	1	yes	characteristic
334	#95×C₈₉	C₂³	1	1	yes	characteristic
335	#95×C₈₉	C₂³	1	1	yes	characteristic
336	#95×C₈₉	C₂³	1	1	yes	characteristic
337	#95×C₈₉	C₂³	1	1	yes	characteristic
338	#95×C₈₉	C₂³	1	1	yes	characteristic
339	#95×C₈₉	C₂³	1	1	yes	characteristic
340	#95×C₈₉	C₂³	1	1	yes	characteristic
341	#95×C₈₉	C₂³	1	1	yes	characteristic
342	#95×C₈₉	C₂³	1	1	yes	characteristic
343	#95×C₈₉	C₂³	1	1	yes	characteristic
344	#95×C₈₉	C₂³	1	1	yes	characteristic
345	#95×C₈₉	C₂³	1	1	yes	characteristic
346	#95×C₈₉	C₂³	1	1	yes	characteristic
347	#95×C₈₉	C₂³	1	1	yes	characteristic
348	#95×C₈₉	C₂³	1	1	yes	characteristic
349	#95×C₈₉	C₂³	1	1	yes	characteristic
350	#95×C₈₉	C₂³	1	1	yes	characteristic
351	C₂³×D₈₉	C₂⁴	1	1	yes	characteristic
352	C₂×Dic₁₇₈	—	2	2	no	—
353	C₂×Dic₁₇₈	—	2	2	no	—
354	C₂×Dic₁₇₈	—	2	2	no	—
355	C₂×Dic₁₇₈	—	4	1	no	—
356	C₂×Dic₁₇₈	—	4	1	no	—
357	C₂×Dic₁₇₈	—	4	1	no	—
358	C₂×Dic₁₇₈	—	4	1	no	—
359	C₂×Dic₁₇₈	—	4	1	no	—
360	C₂×Dic₁₇₈	—	4	1	no	—
361	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
362	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
363	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
364	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
365	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
366	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
367	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
368	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
369	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
370	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
371	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
372	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
373	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
374	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
375	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
376	C₂×C₄×D₈₉	—	2	2	no	—
377	C₂×C₄×D₈₉	—	2	2	no	—
378	C₂×C₄×D₈₉	—	2	2	no	—
379	C₂×C₄×D₈₉	—	2	2	no	—
380	C₂×C₄×D₈₉	—	2	2	no	—
381	C₂×C₄×D₈₉	—	2	2	no	—
382	C₂×C₄×D₈₉	—	2	2	no	—
383	C₂×C₄×D₈₉	—	4	1	no	—
384	C₂×C₄×D₈₉	—	4	1	no	—
385	C₄⋊Dic₈₉	—	2	2	no	—
386	C₄⋊Dic₈₉	—	2	2	no	—
387	C₄⋊Dic₈₉	—	2	2	no	—
388	C₄⋊Dic₈₉	—	2	2	no	—
389	C₄⋊Dic₈₉	—	2	2	no	—
390	C₄⋊Dic₈₉	—	4	1	no	—
391	C₄⋊Dic₈₉	—	4	1	no	—
392	C₄⋊Dic₈₉	—	4	1	no	—
393	C₄⋊Dic₈₉	—	4	1	no	—
394	#13083553	—	2	2	no	—
395	#13083553	—	2	2	no	—
396	#13083553	—	2	2	no	—
397	#13083553	—	2	2	no	—
398	#13083553	—	2	2	no	—
399	#13083553	—	2	2	no	—
400	#13083553	—	2	2	no	—
401	#13083553	—	2	2	no	—
402	#13083553	—	2	2	no	—
403	#13083553	—	2	2	no	—
404	#13083553	—	2	2	no	—
405	#13083553	—	2	2	no	—
406	#13083553	—	2	2	no	—
407	#13083553	—	2	2	no	—
408	#13083553	—	4	1	no	—
409	#13083553	—	4	1	no	—
410	#13083553	—	4	1	no	—
411	#13083553	—	4	1	no	—
412	#13083553	—	4	1	no	—
413	#13083553	—	4	1	no	—
414	#13083553	—	4	1	no	—
415	#13083553	—	4	1	no	—
416	#13083553	—	4	1	no	—
417	#13083553	—	4	1	no	—
418	#13083553	—	4	1	no	—
419	#13083553	—	4	1	no	—
420	#13083553	—	4	1	no	—
421	#13083553	—	4	1	no	—
422	#13083553	—	4	1	no	—
423	#13083553	—	4	1	no	—
424	#13083551	—	2	2	no	—
425	#13083551	—	2	2	no	—
426	#13083551	—	2	2	no	—
427	#13083551	—	2	2	no	—
428	#13083551	—	2	2	no	—
429	#13083551	—	2	2	no	—
430	#13083551	—	2	2	no	—
431	#13083551	—	2	2	no	—
432	#13083551	—	4	1	no	—
433	#13083551	—	4	1	no	—
434	#13083551	—	4	1	no	—
435	#13083551	—	4	1	no	—
436	C₄×Dic₈₉	—	2	2	no	—
437	C₄×Dic₈₉	—	2	2	no	—
438	C₄×Dic₈₉	—	4	1	no	—
439	C₄×Dic₈₉	—	4	1	no	—
440	C₄×Dic₈₉	—	4	1	no	—
441	C₄×Dic₈₉	—	4	1	no	—
442	C₄×Dic₈₉	—	4	1	no	—
443	C₄×Dic₈₉	—	4	1	no	—
444	C₄×Dic₈₉	—	4	1	no	—
445	C₄×Dic₈₉	—	4	1	no	—
446	C₄×Dic₈₉	—	4	1	no	—
447	C₄×Dic₈₉	—	4	1	no	—
448	C₄×Dic₈₉	#41	1	4	yes	—
449	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
450	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
451	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
452	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
453	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
454	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
455	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
456	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
457	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
458	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
459	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
460	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
461	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
462	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
463	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
464	C₄⋊C₄×C₈₉	—	2	2	no	—
465	C₄⋊C₄×C₈₉	—	2	2	no	—
466	C₄⋊C₄×C₈₉	—	4	1	no	—
467	C₄⋊C₄×C₈₉	—	4	1	no	—
468	C₄⋊C₄×C₈₉	—	4	1	no	—
469	C₄⋊C₄×C₈₉	—	4	1	no	—
470	C₄⋊C₄×C₈₉	—	4	1	no	—
471	C₄⋊C₄×C₈₉	—	4	1	no	—
472	C₄⋊C₄×C₈₉	—	4	1	no	—
473	C₄⋊C₄×C₈₉	—	4	1	no	—
474	C₄⋊C₄×C₈₉	—	4	1	no	—
475	C₄⋊C₄×C₈₉	—	4	1	no	—
476	C₄²×C₈₉	—	2	2	no	—
477	C₄²×C₈₉	—	4	1	no	—
478	C₄²×C₈₉	—	4	1	no	—
479	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
480	C₂²×D₈₉	—	2	1	no	—
481	C₂²×D₈₉	—	2	1	no	—
482	C₂²×D₈₉	—	2	1	no	—
483	C₂²×D₈₉	—	2	1	no	—
484	C₂²×D₈₉	—	2	1	no	—
485	C₂²×D₈₉	—	2	1	no	—
486	C₂²×D₈₉	H(5,𝔽₂)	1	2	yes	—
487	C₂×C₄×C₈₉	—	2	1	no	—
488	C₂×C₄×C₈₉	—	2	1	no	—
489	C₂×C₄×C₈₉	—	2	1	no	—
490	C₂×C₄×C₈₉	—	2	1	no	—
491	C₂×C₄×C₈₉	—	2	1	no	—
492	C₂×C₄×C₈₉	—	2	1	no	—
493	C₂×C₄×C₈₉	—	2	1	no	—
494	C₂×C₄×C₈₉	—	2	1	no	—
495	C₂×C₄×C₈₉	—	2	1	no	—
496	C₂×C₄×C₈₉	—	2	1	no	—
497	C₂×C₄×C₈₉	—	2	1	no	—
498	C₂×C₄×C₈₉	—	2	1	no	—
499	C₂×C₄×C₈₉	—	2	1	no	—
500	C₂×C₄×C₈₉	—	2	1	no	—
501	C₂×C₄×C₈₉	—	2	1	no	—
502	C₂×C₄×C₈₉	—	2	1	no	—
503	C₂×C₄×C₈₉	—	2	1	no	—
504	C₂×C₄×C₈₉	—	2	1	no	—
505	C₂×C₄×C₈₉	—	2	1	no	—
506	C₂×C₄×C₈₉	—	2	1	no	—
507	C₂×C₄×C₈₉	—	2	1	no	—
508	C₂×C₄×C₈₉	—	2	1	no	—
509	C₂×C₄×C₈₉	—	2	1	no	—
510	C₂×C₄×C₈₉	—	2	1	no	—
511	C₂×C₄×C₈₉	—	2	1	no	—
512	C₂×C₄×C₈₉	—	2	1	no	—
513	C₂×C₄×C₈₉	—	2	1	no	—
514	C₂×C₄×C₈₉	—	2	1	no	—
515	C₂×C₄×C₈₉	—	2	1	no	—
516	C₂×C₄×C₈₉	—	2	1	no	—
517	C₂×C₄×C₈₉	—	2	1	no	—
518	C₂×C₄×C₈₉	—	2	1	no	—
519	C₂×C₄×C₈₉	—	2	1	no	—
520	C₂×C₄×C₈₉	—	2	1	no	—
521	C₂×C₄×C₈₉	—	2	1	no	—
522	C₂×C₄×C₈₉	—	2	1	no	—
523	C₂×C₄×C₈₉	—	2	1	no	—
524	C₂×C₄×C₈₉	—	2	1	no	—
525	C₂×C₄×C₈₉	—	2	1	no	—
526	C₂×C₄×C₈₉	—	2	1	no	—
527	C₂×C₄×C₈₉	—	2	1	no	—
528	C₂×C₄×C₈₉	—	2	1	no	—
529	C₂×C₄×C₈₉	—	2	1	no	—
530	C₂×C₄×C₈₉	—	2	1	no	—
531	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
532	C₂×Dic₈₉	—	2	1	no	—
533	C₂×Dic₈₉	—	2	1	no	—
534	C₂×Dic₈₉	—	2	1	no	—
535	C₂×Dic₈₉	—	2	1	no	—
536	C₂×Dic₈₉	—	2	1	no	—
537	C₂×Dic₈₉	—	2	1	no	—
538	C₂×Dic₈₉	—	2	1	no	—
539	C₂×Dic₈₉	—	2	1	no	—
540	C₂×Dic₈₉	—	2	1	no	—
541	C₂×Dic₈₉	—	2	1	no	—
542	C₂×Dic₈₉	—	2	1	no	—
543	C₂×Dic₈₉	—	2	1	no	—
544	C₂×Dic₈₉	—	2	1	no	—
545	C₂×Dic₈₉	—	2	1	no	—
546	C₂×Dic₈₉	—	2	1	no	—
547	C₂×Dic₈₉	—	2	1	no	—
548	C₂×Dic₈₉	—	2	1	no	—
549	C₂×Dic₈₉	—	2	1	no	—
550	C₂×Dic₈₉	—	2	1	no	—
551	C₂×Dic₈₉	—	2	1	no	—
552	C₂×Dic₈₉	—	2	1	no	—
553	C₂×Dic₈₉	—	2	1	no	—
554	C₂×Dic₈₉	—	2	1	no	—
555	C₂×Dic₈₉	—	2	1	no	—
556	C₂×Dic₈₉	—	2	1	no	—
557	C₂×Dic₈₉	—	2	1	no	—
558	C₂×Dic₈₉	—	2	1	no	—
559	C₂×Dic₈₉	—	2	1	no	—
560	C₂×Dic₈₉	—	2	1	no	—
561	C₂×Dic₈₉	—	2	1	no	—
562	C₂×Dic₈₉	—	2	1	no	—
563	C₂×Dic₈₉	—	2	1	no	—
564	C₂×Dic₈₉	—	2	1	no	—
565	C₂×Dic₈₉	—	2	1	no	—
566	C₂×Dic₈₉	—	2	1	no	—
567	C₂×Dic₈₉	—	2	1	no	—
568	C₂×Dic₈₉	—	2	1	no	—
569	C₂×Dic₈₉	—	2	1	no	—
570	C₂×Dic₈₉	—	2	1	no	—
571	C₂×Dic₈₉	—	2	1	no	—
572	C₂×Dic₈₉	C₂×#41	1	2	yes	—
573	C₂×Dic₈₉	C₂×#41	1	2	yes	—
574	C₂×Dic₈₉	2₋¹⁺⁴	1	2	yes	—
575	C₂×Dic₈₉	2₋¹⁺⁴	1	2	yes	—
576	C₂×Dic₈₉	2₋¹⁺⁴	1	2	yes	—
577	C₄×D₈₉	—	2	8	no	—
578	C₄×D₈₉	—	4	4	no	—
579	C₄×D₈₉	—	4	4	no	—
580	Dic₁₇₈	—	4	4	no	—
581	Dic₁₇₈	—	8	2	no	—
582	Dic₁₇₈	—	8	2	no	—
583	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
584	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
585	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
586	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
587	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
588	C₂²×C₈₉	#585	1	1	yes	characteristic
589	C₂²×C₈₉	#585	1	1	yes	characteristic
590	C₂×D₈₉	—	2	2	no	—
591	C₂×D₈₉	—	2	2	no	—
592	C₂×D₈₉	—	2	2	no	—
593	C₂×D₈₉	—	4	1	no	—
594	C₂×D₈₉	—	4	1	no	—
595	C₂×D₈₉	—	4	1	no	—
596	C₂×D₈₉	—	4	1	no	—
597	C₄×C₈₉	—	2	2	no	—
598	C₄×C₈₉	—	4	1	no	—
599	C₄×C₈₉	—	4	1	no	—
600	C₄×C₈₉	—	4	1	no	—
601	C₄×C₈₉	—	4	1	no	—
602	C₄×C₈₉	—	4	1	no	—
603	C₄×C₈₉	—	4	1	no	—
604	C₄×C₈₉	—	4	1	no	—
605	C₄×C₈₉	—	4	1	no	—
606	C₄×C₈₉	—	4	1	no	—
607	C₄×C₈₉	—	4	1	no	—
608	C₄×C₈₉	—	4	1	no	—
609	C₄×C₈₉	—	4	1	no	—
610	C₄×C₈₉	—	4	1	no	—
611	C₄×C₈₉	—	4	1	no	—
612	Dic₈₉	—	2	2	no	—
613	Dic₈₉	—	2	2	no	—
614	Dic₈₉	—	2	2	no	—
615	Dic₈₉	—	2	2	no	—
616	Dic₈₉	—	2	2	no	—
617	Dic₈₉	—	4	1	no	—
618	Dic₈₉	—	4	1	no	—
619	Dic₈₉	—	4	1	no	—
620	Dic₈₉	—	4	1	no	—
621	Dic₈₉	—	4	1	no	—
622	Dic₈₉	—	4	1	no	—
623	Dic₈₉	—	4	1	no	—
624	Dic₈₉	—	4	1	no	—
625	Dic₈₉	—	4	1	no	—
626	Dic₈₉	—	4	1	no	—
627	#36829	—	89	1	no	maximal, Sylow
628	C₂×C₈₉	#3455	1	1	yes	characteristic
629	C₂×C₈₉	#3492	1	1	yes	characteristic
630	C₂×C₈₉	#3509	1	1	yes	characteristic
631	C₂×C₈₉	#3535	1	1	yes	characteristic
632	C₂×C₈₉	#3535	1	1	yes	characteristic
633	C₂×C₈₉	#3555	1	1	yes	characteristic
634	C₂×C₈₉	#3555	1	1	yes	characteristic
635	D₈₉	—	4	2	no	—
636	#2855	—	89	1	no	—
637	#2855	—	89	1	no	—
638	#2806	—	89	1	no	—
639	#2806	—	89	1	no	—
640	#2802	—	89	1	no	—
641	#2802	—	89	1	no	—
642	#2776	—	89	1	no	—
643	#2776	—	89	1	no	—
644	#2774	—	89	1	no	—
645	#2774	—	89	1	no	—
646	#2745	—	89	1	no	—
647	#2745	—	89	1	no	—
648	#2738	—	89	1	no	—
649	#2738	—	89	1	no	—
650	#2698	—	89	1	no	—
651	#2698	—	89	1	no	—
652	#2689	—	89	1	no	—
653	#2689	—	89	1	no	—
654	#2655	—	89	1	no	—
655	#2655	D₈₉	1	1	yes	characteristic, complemented
656	#2611	—	89	1	no	—
657	#2605	—	89	1	no	—
658	#2599	—	89	1	no	—
659	#2588	—	89	1	no	—
660	#2588	—	89	1	no	—
661	#2584	—	89	1	no	—
662	#2478	—	89	1	no	—
663	#2478	—	89	1	no	—
664	#2336	—	89	1	no	—
665	#2320	—	89	1	no	—
666	#2296	—	89	1	no	—
667	C₈₉	#36829	1	1	yes	characteristic, complemented, Sylow
668	C₂×#126	—	89	1	no	—
669	C₂×#126	—	89	1	no	—
670	C₂×#125	—	89	1	no	—
671	C₂×C₂²⋊Q₈	—	89	1	no	—
672	C₂×C₂²⋊Q₈	—	89	1	no	—
673	C₂×C₄×Q₈	—	89	1	no	—
674	C₂×#117	—	89	1	no	—
675	C₂×#117	—	89	1	no	—
676	C₂²×C₄²	—	89	1	no	—
677	#401	—	89	1	no	—
678	#401	C₂×D₈₉	1	1	yes	characteristic
679	#400	—	89	1	no	—
680	#400	—	89	1	no	—
681	#400	—	89	1	no	—
682	#400	—	89	1	no	—
683	#400	—	89	1	no	—
684	#400	—	89	1	no	—
685	#400	—	89	1	no	—
686	#400	—	89	1	no	—
687	#400	—	89	1	no	—
688	#400	—	89	1	no	—
689	#400	—	89	1	no	—
690	#400	C₂×D₈₉	1	1	yes	characteristic
691	#400	C₂×D₈₉	1	1	yes	characteristic
692	#400	C₂×D₈₉	1	1	yes	characteristic
693	#400	C₂×D₈₉	1	1	yes	characteristic
694	#399	—	89	1	no	—
695	#398	—	89	1	no	—
696	#398	—	89	1	no	—
697	#398	—	89	1	no	—
698	#398	—	89	1	no	—
699	#398	—	89	1	no	—
700	#398	—	89	1	no	—
701	#398	—	89	1	no	—
702	#398	—	89	1	no	—
703	#398	—	89	1	no	—
704	#398	—	89	1	no	—
705	#398	—	89	1	no	—
706	#398	—	89	1	no	—
707	#398	—	89	1	no	—
708	#398	C₂×D₈₉	1	1	yes	characteristic
709	#398	C₂×D₈₉	1	1	yes	characteristic
710	#398	C₂×D₈₉	1	1	yes	characteristic
711	#397	—	89	1	no	—
712	#397	—	89	1	no	—
713	#397	—	89	1	no	—
714	#397	—	89	1	no	—
715	#397	—	89	1	no	—
716	#397	—	89	1	no	—
717	#395	—	89	1	no	—
718	#395	—	89	1	no	—
719	#395	—	89	1	no	—
720	#395	—	89	1	no	—
721	#395	—	89	1	no	—
722	#395	—	89	1	no	—
723	#395	—	89	1	no	—
724	#393	—	89	1	no	—
725	#391	—	89	1	no	—
726	#391	—	89	1	no	—
727	#391	—	89	1	no	—
728	#391	—	89	1	no	—
729	#391	—	89	1	no	—
730	#391	—	89	1	no	—
731	#391	—	89	1	no	—
732	#391	—	89	1	no	—
733	#391	—	89	1	no	—
734	#391	—	89	1	no	—
735	#389	—	89	1	no	—
736	#389	—	89	1	no	—
737	#389	—	89	1	no	—
738	#389	—	89	1	no	—
739	#389	—	89	1	no	—
740	#389	—	89	1	no	—
741	#389	—	89	1	no	—
742	#389	—	89	1	no	—
743	#389	—	89	1	no	—
744	#389	—	89	1	no	—
745	#389	—	89	1	no	—
746	#389	—	89	1	no	—
747	#389	—	89	1	no	—
748	#389	—	89	1	no	—
749	#389	—	89	1	no	—
750	#389	—	89	1	no	—
751	#389	—	89	1	no	—
752	#389	—	89	1	no	—
753	#389	—	89	1	no	—
754	#389	—	89	1	no	—
755	#389	—	89	1	no	—
756	#389	C₂×D₈₉	1	1	yes	characteristic
757	#388	—	89	1	no	—
758	#388	—	89	1	no	—
759	#388	—	89	1	no	—
760	#388	—	89	1	no	—
761	#388	—	89	1	no	—
762	#388	—	89	1	no	—
763	#387	—	89	1	no	—
764	#387	—	89	1	no	—
765	#387	—	89	1	no	—
766	#387	—	89	1	no	—
767	#387	—	89	1	no	—
768	#387	—	89	1	no	—
769	#387	—	89	1	no	—
770	#387	—	89	1	no	—
771	#387	—	89	1	no	—
772	#387	—	89	1	no	—
773	#387	—	89	1	no	—
774	#387	—	89	1	no	—
775	#387	—	89	1	no	—
776	#387	—	89	1	no	—
777	#387	—	89	1	no	—
778	#387	—	89	1	no	—
779	#387	—	89	1	no	—
780	#387	—	89	1	no	—
781	#387	—	89	1	no	—
782	#387	—	89	1	no	—
783	#387	—	89	1	no	—
784	#387	—	89	1	no	—
785	#387	—	89	1	no	—
786	#387	—	89	1	no	—
787	#387	—	89	1	no	—
788	#387	—	89	1	no	—
789	#387	—	89	1	no	—
790	#387	—	89	1	no	—
791	#387	—	89	1	no	—
792	#387	C₂×D₈₉	1	1	yes	characteristic
793	#387	C₂×D₈₉	1	1	yes	characteristic
794	#387	C₂×D₈₉	1	1	yes	characteristic
795	#387	C₂×D₈₉	1	1	yes	characteristic
796	#387	C₂×D₈₉	1	1	yes	characteristic
797	#385	—	89	1	no	—
798	#385	—	89	1	no	—
799	#385	—	89	1	no	—
800	#385	—	89	1	no	—
801	#385	—	89	1	no	—
802	#385	—	89	1	no	—
803	#385	—	89	1	no	—
804	#385	—	89	1	no	—
805	#383	—	89	1	no	—
806	#383	—	89	1	no	—
807	#383	—	89	1	no	—
808	#382	—	89	1	no	—
809	#382	—	89	1	no	—
810	#381	—	89	1	no	—
811	#381	—	89	1	no	—
812	#381	—	89	1	no	—
813	#381	—	89	1	no	—
814	#380	—	89	1	no	—
815	#380	—	89	1	no	—
816	C₄×C₄⋊C₄	—	89	1	no	—
817	C₄×C₄⋊C₄	—	89	1	no	—
818	C₄×C₄⋊C₄	—	89	1	no	—
819	C₄×C₄⋊C₄	—	89	1	no	—
820	C₄×C₄⋊C₄	—	89	1	no	—
821	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
822	#376	—	89	1	no	—
823	C₂²×Q₈	—	89	1	no	—
824	C₂²×Q₈	—	89	1	no	—
825	C₂²×Q₈	—	89	1	no	—
826	C₂³×C₄	—	89	1	no	—
827	C₂³×C₄	—	89	1	no	—
828	C₂³×C₄	—	89	1	no	—
829	#126	—	356	2	no	—
830	#126	—	356	2	no	—
831	#125	—	178	4	no	—
832	C₂²⋊Q₈	—	356	2	no	—
833	C₂²⋊Q₈	—	356	2	no	—
834	C₄×Q₈	—	178	4	no	—
835	#117	—	356	2	no	—
836	#117	—	178	4	no	—
837	C₂×C₄⋊C₄	—	89	1	no	—
838	C₂×C₄⋊C₄	—	89	1	no	—
839	C₂×C₄⋊C₄	—	89	1	no	—
840	C₂×C₄⋊C₄	—	89	1	no	—
841	C₂×C₄⋊C₄	—	89	1	no	—
842	C₂×C₄⋊C₄	—	89	1	no	—
843	C₂×C₄⋊C₄	—	89	1	no	—
844	C₂×C₄⋊C₄	—	89	1	no	—
845	C₂×C₄⋊C₄	—	89	1	no	—
846	C₂×C₄⋊C₄	—	89	1	no	—
847	C₂×C₄⋊C₄	—	89	1	no	—
848	C₂×C₄⋊C₄	—	89	1	no	—
849	C₂×C₄⋊C₄	—	89	1	no	—
850	C₂×C₄⋊C₄	—	89	1	no	—
851	C₂×C₄⋊C₄	—	89	1	no	—
852	C₂×C₄⋊C₄	—	89	1	no	—
853	C₂×C₄⋊C₄	—	89	1	no	—
854	C₂×C₄⋊C₄	—	89	1	no	—
855	C₂×C₄⋊C₄	—	89	1	no	—
856	C₂×C₄⋊C₄	—	89	1	no	—
857	C₂×C₄⋊C₄	—	89	1	no	—
858	C₂×C₄⋊C₄	—	89	1	no	—
859	C₂×C₄⋊C₄	—	89	1	no	—
860	C₂×C₄⋊C₄	—	89	1	no	—
861	C₂×C₄⋊C₄	—	89	1	no	—
862	C₂×C₄⋊C₄	—	89	1	no	—
863	C₂×C₄⋊C₄	—	89	1	no	—
864	C₂×C₄⋊C₄	—	89	1	no	—
865	C₂×C₄⋊C₄	—	89	1	no	—
866	C₂×C₄⋊C₄	—	89	1	no	—
867	C₂×C₄⋊C₄	—	89	1	no	—
868	C₂×C₄⋊C₄	—	89	1	no	—
869	C₂×C₄⋊C₄	—	89	1	no	—
870	C₂×C₄⋊C₄	—	89	1	no	—
871	C₂×C₄⋊C₄	—	89	1	no	—
872	C₂×C₄⋊C₄	—	89	1	no	—
873	C₂×C₄⋊C₄	—	89	1	no	—
874	C₂×C₄⋊C₄	—	89	1	no	—
875	C₂×C₄⋊C₄	—	89	1	no	—
876	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
877	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
878	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
879	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
880	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
881	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
882	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
883	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
884	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
885	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
886	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
887	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
888	C₂×C₂²⋊C₄	—	89	1	no	—
889	C₂×C₂²⋊C₄	—	89	1	no	—
890	C₂×C₂²⋊C₄	—	89	1	no	—
891	C₂×C₂²⋊C₄	—	89	1	no	—
892	C₂×C₂²⋊C₄	—	89	1	no	—
893	C₂×C₂²⋊C₄	—	89	1	no	—
894	C₂×C₂²⋊C₄	—	89	1	no	—
895	C₂×C₂²⋊C₄	—	89	1	no	—
896	C₂×C₂²⋊C₄	—	89	1	no	—
897	C₂×C₂²⋊C₄	—	89	1	no	—
898	C₂×C₂²⋊C₄	—	89	1	no	—
899	C₂×C₂²⋊C₄	—	89	1	no	—
900	C₂×C₄²	—	89	1	no	—
901	C₂×C₄²	—	89	1	no	—
902	C₂×C₄²	—	89	1	no	—
903	C₂×C₄²	—	89	1	no	—
904	C₂×C₄²	—	89	1	no	—
905	C₂×C₄²	—	89	1	no	—
906	C₂×C₄²	—	89	1	no	—
907	C₂×C₄²	—	89	1	no	—
908	C₂×C₄²	—	89	1	no	—
909	C₂×C₄²	—	89	1	no	—
910	C₂×C₄²	—	89	1	no	—
911	C₂×C₄²	—	89	1	no	—
912	C₂×C₄²	—	89	1	no	—
913	C₂×C₄²	—	356	2	no	—
914	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
915	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
916	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
917	#95	—	89	1	no	—
918	#95	—	89	1	no	—
919	#95	—	89	1	no	—
920	#95	—	89	1	no	—
921	#95	—	89	1	no	—
922	#95	—	89	1	no	—
923	#95	—	89	1	no	—
924	#95	—	89	1	no	—
925	#95	—	89	1	no	—
926	#95	—	89	1	no	—
927	#95	—	89	1	no	—
928	#95	—	89	1	no	—
929	#95	—	89	1	no	—
930	#95	—	89	1	no	—
931	#95	—	89	1	no	—
932	#95	—	89	1	no	—
933	#95	—	89	1	no	—
934	#95	—	89	1	no	—
935	#95	—	89	1	no	—
936	#95	—	89	1	no	—
937	#95	—	89	1	no	—
938	#95	—	89	1	no	—
939	#95	—	89	1	no	—
940	#95	—	89	1	no	—
941	#95	—	89	1	no	—
942	#95	—	89	1	no	—
943	#95	—	89	1	no	—
944	#95	—	89	1	no	—
945	#95	—	89	1	no	—
946	#95	—	89	1	no	—
947	#95	—	89	1	no	—
948	#95	—	89	1	no	—
949	#95	—	89	1	no	—
950	#95	—	89	1	no	—
951	#95	—	89	1	no	—
952	#95	—	89	1	no	—
953	#95	—	89	1	no	—
954	#95	—	89	1	no	—
955	#95	—	89	1	no	—
956	#95	—	89	1	no	—
957	#95	—	89	1	no	—
958	#95	—	89	1	no	—
959	#95	—	89	1	no	—
960	#95	—	89	1	no	—
961	#95	—	89	1	no	—
962	#95	—	89	1	no	—
963	#95	—	89	1	no	—
964	#95	—	89	1	no	—
965	#95	—	89	1	no	—
966	#95	—	89	1	no	—
967	#95	C₂²×D₈₉	1	1	yes	characteristic
968	#95	C₂²×D₈₉	1	1	yes	characteristic
969	#95	C₂²×D₈₉	1	1	yes	characteristic
970	#95	C₂²×D₈₉	1	1	yes	characteristic
971	#95	C₂²×D₈₉	1	1	yes	characteristic
972	#95	C₂²×D₈₉	1	1	yes	characteristic
973	#95	C₂²×D₈₉	1	1	yes	characteristic
974	#95	C₂²×D₈₉	1	1	yes	characteristic
975	#95	C₂²×D₈₉	1	1	yes	characteristic
976	#95	C₂²×D₈₉	1	1	yes	characteristic
977	#95	C₂²×D₈₉	1	1	yes	characteristic
978	#95	C₂²×D₈₉	1	1	yes	characteristic
979	#95	C₂²×D₈₉	1	1	yes	characteristic
980	#95	C₂²×D₈₉	1	1	yes	characteristic
981	#95	C₂²×D₈₉	1	1	yes	characteristic
982	#95	C₂²×D₈₉	1	1	yes	characteristic
983	#95	C₂²×D₈₉	1	1	yes	characteristic
984	#95	C₂²×D₈₉	1	1	yes	characteristic
985	#95	C₂²×D₈₉	1	1	yes	characteristic
986	#95	C₂²×D₈₉	1	1	yes	characteristic
987	C₂⁴	—	89	1	no	—
988	C₂×Q₈	—	356	1	no	—
989	C₂×Q₈	—	356	1	no	—
990	C₂×Q₈	—	356	1	no	—
991	C₂×Q₈	—	356	1	no	—
992	C₂×Q₈	—	356	1	no	—
993	C₂×Q₈	—	356	1	no	—
994	C₂×Q₈	—	178	2	no	—
995	C₂×Q₈	—	178	2	no	—
996	C₂×Q₈	—	178	2	no	—
997	C₂²×C₄	—	89	1	no	—
998	C₂²×C₄	—	89	1	no	—
999	C₂²×C₄	—	89	1	no	—
1000	C₂²×C₄	—	89	1	no	—
1001	C₂²×C₄	—	89	1	no	—
1002	C₂²×C₄	—	89	1	no	—
1003	C₂²×C₄	—	89	1	no	—
1004	C₂²×C₄	—	89	1	no	—
1005	C₂²×C₄	—	89	1	no	—
1006	C₂²×C₄	—	89	1	no	—
1007	C₂²×C₄	—	89	1	no	—
1008	C₂²×C₄	—	89	1	no	—
1009	C₂²×C₄	—	89	1	no	—
1010	C₂²×C₄	—	89	1	no	—
1011	C₂²×C₄	—	89	1	no	—
1012	C₂²×C₄	—	356	1	no	—
1013	C₂²×C₄	—	356	1	no	—
1014	C₂²×C₄	—	178	2	no	—
1015	C₂²×C₄	—	178	2	no	—
1016	C₂²×C₄	—	178	2	no	—
1017	C₂²×C₄	—	178	2	no	—
1018	C₂²×C₄	—	178	2	no	—
1019	C₂²×C₄	—	178	2	no	—
1020	C₂²×C₄	—	178	2	no	—
1021	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1022	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1023	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1024	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1025	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1026	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1027	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1028	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1029	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1030	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1031	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1032	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1033	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1034	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1035	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	4	1	no	—
1039	C₄⋊C₄	—	4	1	no	—
1040	C₄⋊C₄	—	4	1	no	—
1041	C₄⋊C₄	—	4	1	no	—
1042	C₄⋊C₄	—	4	1	no	—
1043	C₄⋊C₄	—	4	1	no	—
1044	C₄⋊C₄	—	4	1	no	—
1045	C₄⋊C₄	—	4	1	no	—
1046	C₄⋊C₄	—	4	1	no	—
1047	C₄⋊C₄	—	4	1	no	—
1048	C₄⋊C₄	—	356	1	no	—
1049	C₄⋊C₄	—	356	1	no	—
1050	C₄⋊C₄	—	356	1	no	—
1051	C₄⋊C₄	—	356	1	no	—
1052	C₄⋊C₄	—	356	1	no	—
1053	C₄⋊C₄	—	356	1	no	—
1054	C₄⋊C₄	—	356	1	no	—
1055	C₄⋊C₄	—	356	1	no	—
1056	C₄⋊C₄	—	356	1	no	—
1057	C₄⋊C₄	—	356	1	no	—
1058	C₄⋊C₄	—	356	1	no	—
1059	C₄⋊C₄	—	356	1	no	—
1060	C₄⋊C₄	—	356	1	no	—
1061	C₄⋊C₄	—	356	1	no	—
1062	C₄⋊C₄	—	356	1	no	—
1063	C₄⋊C₄	—	356	1	no	—
1064	C₄⋊C₄	—	356	1	no	—
1065	C₄⋊C₄	—	356	1	no	—
1066	C₄⋊C₄	—	356	1	no	—
1067	C₄⋊C₄	—	356	1	no	—
1068	C₄⋊C₄	—	178	2	no	—
1069	C₄⋊C₄	—	178	2	no	—
1070	C₄⋊C₄	—	178	2	no	—
1071	C₄⋊C₄	—	178	2	no	—
1072	C₄⋊C₄	—	178	2	no	—
1073	C₄⋊C₄	—	178	2	no	—
1074	C₄⋊C₄	—	178	2	no	—
1075	C₄⋊C₄	—	178	2	no	—
1076	C₄⋊C₄	—	178	2	no	—
1077	C₄⋊C₄	—	178	2	no	—
1078	C₄⋊C₄	—	178	2	no	—
1079	C₄⋊C₄	—	178	2	no	—
1080	C₄⋊C₄	—	178	2	no	—
1081	C₄⋊C₄	—	178	2	no	—
1082	C₄⋊C₄	—	178	2	no	—
1083	C₄⋊C₄	—	178	2	no	—
1084	C₄⋊C₄	—	178	2	no	—
1085	C₄⋊C₄	—	178	2	no	—
1086	C₄⋊C₄	—	178	2	no	—
1087	C₂²⋊C₄	—	356	1	no	—
1088	C₂²⋊C₄	—	356	1	no	—
1089	C₂²⋊C₄	—	356	1	no	—
1090	C₂²⋊C₄	—	356	1	no	—
1091	C₂²⋊C₄	—	178	2	no	—
1092	C₂²⋊C₄	—	178	2	no	—
1093	C₂²⋊C₄	—	178	2	no	—
1094	C₂²⋊C₄	—	178	2	no	—
1095	C₂²⋊C₄	—	178	2	no	—
1096	C₂²⋊C₄	—	178	2	no	—
1097	C₂²⋊C₄	—	178	2	no	—
1098	C₂²⋊C₄	—	178	2	no	—
1099	C₄²	—	2	2	no	—
1100	C₄²	—	4	1	no	—
1101	C₄²	—	4	1	no	—
1102	C₄²	—	89	4	no	—
1103	C₄²	—	356	1	no	—
1104	C₄²	—	356	1	no	—
1105	C₄²	—	356	1	no	—
1106	C₄²	—	356	1	no	—
1107	C₄²	—	356	1	no	—
1108	C₄²	—	356	1	no	—
1109	C₄²	—	356	1	no	—
1110	C₄²	—	356	1	no	—
1111	C₄²	—	356	1	no	—
1112	C₄²	—	356	1	no	—
1113	C₄²	—	178	2	no	—
1114	C₄²	—	178	2	no	—
1115	C₂³	—	89	2	no	—
1116	C₂³	—	178	1	no	—
1117	C₂³	—	178	1	no	—
1118	C₂³	—	178	1	no	—
1119	C₂³	—	178	1	no	—
1120	C₂³	—	178	1	no	—
1121	C₂³	—	178	1	no	—
1122	C₂³	C₂⁴×D₈₉	1	1	yes	characteristic
1123	Q₈	—	356	4	no	—
1124	Q₈	—	712	2	no	—
1125	Q₈	—	712	2	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	2	1	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	89	2	no	—
1171	C₂×C₄	—	89	2	no	—
1172	C₂×C₄	—	89	2	no	—
1173	C₂×C₄	—	89	2	no	—
1174	C₂×C₄	—	89	2	no	—
1175	C₂×C₄	—	356	4	no	—
1176	C₂×C₄	—	356	4	no	—
1177	C₂×C₄	—	178	8	no	—
1178	C₂×C₄	—	178	1	no	—
1179	C₂×C₄	—	178	1	no	—
1180	C₂×C₄	—	178	1	no	—
1181	C₂×C₄	—	178	1	no	—
1182	C₂×C₄	—	178	1	no	—
1183	C₂×C₄	—	178	1	no	—
1184	C₂×C₄	—	178	1	no	—
1185	C₂×C₄	—	178	1	no	—
1186	C₂×C₄	—	178	1	no	—
1187	C₂×C₄	—	178	1	no	—
1188	C₂×C₄	—	178	1	no	—
1189	C₂×C₄	—	178	1	no	—
1190	C₂×C₄	—	178	1	no	—
1191	C₂×C₄	—	178	1	no	—
1192	C₂×C₄	—	178	1	no	—
1193	C₂×C₄	—	178	1	no	—
1194	C₂×C₄	—	178	1	no	—
1195	C₂×C₄	—	178	1	no	—
1196	C₂×C₄	—	178	1	no	—
1197	C₂×C₄	—	178	1	no	—
1198	C₂×C₄	—	178	1	no	—
1199	C₂×C₄	—	178	1	no	—
1200	C₂×C₄	—	178	1	no	—
1201	C₂×C₄	—	178	1	no	—
1202	C₂×C₄	—	178	1	no	—
1203	C₂×C₄	—	178	1	no	—
1204	C₂×C₄	—	178	1	no	—
1205	C₂×C₄	—	178	1	no	—
1206	C₂×C₄	—	178	1	no	—
1207	C₂×C₄	—	178	1	no	—
1208	C₂×C₄	—	178	1	no	—
1209	C₂×C₄	—	178	1	no	—
1210	C₂×C₄	—	178	1	no	—
1211	C₂×C₄	—	178	1	no	—
1212	C₂×C₄	—	178	1	no	—
1213	C₂×C₄	—	178	1	no	—
1214	C₂×C₄	—	178	1	no	—
1215	C₂×C₄	—	178	1	no	—
1216	C₂×C₄	—	178	1	no	—
1217	C₂×C₄	—	178	1	no	—
1218	C₂×C₄	#41×D₈₉	1	2	yes	—
1219	C₂²	—	356	1	no	—
1220	C₂²	—	356	1	no	—
1221	C₂²	—	356	1	no	—
1222	C₂²	—	356	1	no	—
1223	C₂²	—	178	2	no	—
1224	C₂²	—	178	2	no	—
1225	C₂²	—	178	2	no	—
1226	C₂²	C₂×#41×D₈₉	1	1	yes	characteristic
1227	C₂²	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
1228	C₂²	2₋¹⁺⁴×D₈₉	1	1	yes	characteristic
1229	C₂²	2₋¹⁺⁴×D₈₉	1	1	yes	characteristic
1230	C₂²	2₋¹⁺⁴×D₈₉	1	1	yes	characteristic
1231	C₂²	#19152434	1	1	yes	characteristic
1232	C₂²	#19152434	1	1	yes	characteristic
1233	C₄	—	2	2	no	—
1234	C₄	—	4	1	no	—
1235	C₄	—	4	1	no	—
1236	C₄	—	4	1	no	—
1237	C₄	—	4	1	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	4	1	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	4	1	no	—
1242	C₄	—	4	1	no	—
1243	C₄	—	4	1	no	—
1244	C₄	—	4	1	no	—
1245	C₄	—	4	1	no	—
1246	C₄	—	4	1	no	—
1247	C₄	—	4	1	no	—
1248	C₄	—	356	1	no	—
1249	C₄	—	356	1	no	—
1250	C₄	—	356	1	no	—
1251	C₄	—	356	1	no	—
1252	C₄	—	356	1	no	—
1253	C₄	—	356	1	no	—
1254	C₄	—	356	1	no	—
1255	C₄	—	356	1	no	—
1256	C₄	—	356	1	no	—
1257	C₄	—	356	1	no	—
1258	C₄	—	178	2	no	—
1259	C₄	—	178	2	no	—
1260	C₄	—	178	2	no	—
1261	C₄	—	178	2	no	—
1262	C₄	—	178	2	no	—
1263	C₂	—	356	2	no	—
1264	C₂	#26033635	1	1	yes	characteristic
1265	C₂	#26033957	1	1	yes	characteristic
1266	C₂	#26034134	1	1	yes	characteristic
1267	C₂	#26034454	1	1	yes	characteristic
1268	C₂	#26034460	1	1	yes	characteristic
1269	C₂	#26034733	1	1	yes	characteristic
1270	C₂	#26034733	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₈₉
commutator, socle, cosocle	C₂³×C₈₉	C₂⁵
Fitting	C₈₉×#2655	C₂
prime radical	C₂³×D₈₉	C₂⁴
hypercenter	#2655	D₈₉
hypocenter	C₈₉	#36829
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ #2655

Complements

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

N	H ≅ G/N	type
3. #26028213	C₂	semidirect
4. #26028208	C₂	semidirect
5. #26028177	C₂	semidirect
6. #26028175	C₂	semidirect
7. #26027839	C₂	semidirect
8. #26027833	C₂	semidirect
9. #26027809	C₂	semidirect
10. #26027803	C₂	semidirect
19. #26026339	C₂	semidirect
21. #26025902	C₂	semidirect
23. #26025687	C₂	semidirect
24. #26025685	C₂	semidirect
25. #26025638	C₂	semidirect
28. #26023054	C₂	semidirect
29. #26022901	C₂	semidirect
31. C₈₉×#2655	C₂	semidirect
655. #2655	D₈₉	semidirect
667. C₈₉	#36829	semidirect

Maximal subgroups

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

subgroup	index
#26028587	2
#26028213	2
#26028208	2
#26028177	2
#26028175	2
#26027839	2
#26027833	2
#26027809	2
#26027803	2
#26027426	2
#26027414	2
#26027327	2
#26027315	2
#26026831	2
#26026819	2
#26026708	2
#26026696	2
#26026339	2
#26025948	2
#26025902	2
#26025827	2
#26025687	2
#26025685	2
#26025638	2
#26024475	2
#26024473	2
#26023054	2
#26022901	2
#26022732	2
C₈₉×#2655	2
#36829	89