Subgroups — #36762456

Order 22784.

1842 conjugacy classes of subgroups.

The subgroup lattice has 1536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028599	C₂	1	1	yes	maximal, characteristic, complemented
2	#26028550	C₂	1	1	yes	maximal, characteristic, complemented
3	#26028157	C₂	1	1	yes	maximal, characteristic, complemented
4	#26028156	C₂	1	1	yes	maximal, characteristic, complemented
5	#26028084	C₂	1	1	yes	maximal, characteristic, complemented
6	#26028084	C₂	1	1	yes	maximal, characteristic, complemented
7	#26027797	C₂	1	1	yes	maximal, characteristic, complemented
8	#26027789	C₂	1	1	yes	maximal, characteristic, complemented
9	#26027625	C₂	1	1	yes	maximal, characteristic, complemented
10	#26027618	C₂	1	1	yes	maximal, characteristic, complemented
11	#26027596	C₂	1	1	yes	maximal, characteristic, complemented
12	#26027590	C₂	1	1	yes	maximal, characteristic, complemented
13	#26027245	C₂	1	1	yes	maximal, characteristic, complemented
14	#26027243	C₂	1	1	yes	maximal, characteristic, complemented
15	#26026999	C₂	1	1	yes	maximal, characteristic, complemented
16	#26026990	C₂	1	1	yes	maximal, characteristic, complemented
17	#26026528	C₂	1	1	yes	maximal, characteristic, complemented
18	#26026062	C₂	1	1	yes	maximal, characteristic, complemented
19	#26025991	C₂	1	1	yes	maximal, characteristic
20	#26024809	C₂	1	1	yes	maximal, characteristic, complemented
21	#26024805	C₂	1	1	yes	maximal, characteristic, complemented
22	#26024381	C₂	1	1	yes	maximal, characteristic, complemented
23	#26024374	C₂	1	1	yes	maximal, characteristic, complemented
24	#26024058	C₂	1	1	yes	maximal, characteristic, complemented
25	#26024054	C₂	1	1	yes	maximal, characteristic, complemented
26	#26023717	C₂	1	1	yes	maximal, characteristic, complemented
27	#26023711	C₂	1	1	yes	maximal, characteristic, complemented
28	#26022986	C₂	1	1	yes	maximal, characteristic, complemented
29	#26022949	C₂	1	1	yes	maximal, characteristic, complemented
30	#388×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
31	C₈₉×#2674	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#15668001	C₂²	1	1	yes	characteristic
33	C₂×#15667998	C₂²	1	1	yes	characteristic, complemented
34	C₂×#15667997	C₂²	1	1	yes	characteristic
35	C₂×#15667990	C₂²	1	1	yes	characteristic
36	C₂×#15667988	C₂²	1	1	yes	characteristic
37	C₂×#15667988	C₂²	1	1	yes	characteristic
38	C₂×#15667988	C₂²	1	1	yes	characteristic, complemented
39	C₂×#15667985	C₂²	1	1	yes	characteristic
40	C₂×#15667982	C₂²	1	1	yes	characteristic
41	C₂×#15667980	C₂²	1	1	yes	characteristic
42	C₂×#15667974	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
48	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
49	C₈₉⋊#401	C₂²	1	1	yes	characteristic, complemented
50	C₈₉⋊#401	C₂²	1	1	yes	characteristic, complemented
51	#19151540	C₂²	1	1	yes	characteristic, complemented
52	#19151540	C₂²	1	1	yes	characteristic, complemented
53	#19151534	C₂²	1	1	yes	characteristic
54	#19151534	C₂²	1	1	yes	characteristic, complemented
55	#19151533	C₂²	1	1	yes	characteristic
56	#19151533	C₂²	1	1	yes	characteristic
57	#19151533	C₂²	1	1	yes	characteristic, complemented
58	#19151531	C₂²	1	1	yes	characteristic, complemented
59	#19151528	C₂²	1	1	yes	characteristic, complemented
60	#19151527	C₂²	1	1	yes	characteristic
61	#19151527	C₂²	1	1	yes	characteristic
62	#19151526	C₂²	1	1	yes	characteristic
63	#19151526	C₂²	1	1	yes	characteristic
64	#19151526	C₂²	1	1	yes	characteristic
65	#19151524	C₂²	1	1	yes	characteristic
66	#19151524	C₂²	1	1	yes	characteristic, complemented
67	#19151524	C₂²	1	1	yes	characteristic, complemented
68	#19151523	C₂²	1	1	yes	characteristic, complemented
69	#19151521	C₂²	1	1	yes	characteristic
70	#19151521	C₂²	1	1	yes	characteristic, complemented
71	#19151520	C₂²	1	1	yes	characteristic
72	#19151520	C₂²	1	1	yes	characteristic
73	#19151520	C₂²	1	1	yes	characteristic, complemented
74	#19151517	C₂²	1	1	yes	characteristic, complemented
75	#19151516	C₂²	1	1	yes	characteristic
76	#19151515	C₂²	1	1	yes	characteristic
77	#19151515	C₂²	1	1	yes	characteristic
78	#19151514	C₂²	1	1	yes	characteristic
79	#19151514	C₂²	1	1	yes	characteristic
80	#19151514	C₂²	1	1	yes	characteristic
81	#19151514	C₂²	1	1	yes	characteristic
82	#19151514	C₂²	1	1	yes	characteristic
83	#19151514	C₂²	1	1	yes	characteristic
84	#19151512	C₂²	1	1	yes	characteristic
85	#19151512	C₂²	1	1	yes	characteristic
86	#19151511	C₂²	1	1	yes	characteristic
87	#19151510	C₂²	1	1	yes	characteristic
88	#19151509	C₂²	1	1	yes	characteristic
89	#19151507	C₂²	1	1	yes	characteristic
90	#19151506	C₂²	1	1	yes	characteristic
91	#19151505	C₂²	1	1	yes	characteristic, complemented
92	#19151505	C₂²	1	1	yes	characteristic, complemented
93	#19151503	C₂²	1	1	yes	characteristic, complemented
94	#19151502	C₂²	1	1	yes	characteristic, complemented
95	#19151502	C₂²	1	1	yes	characteristic, complemented
96	#19151498	C₂²	1	1	yes	characteristic
97	#19151498	C₂²	1	1	yes	characteristic
98	#19151498	C₂²	1	1	yes	characteristic, complemented
99	#19151495	C₂²	1	1	yes	characteristic, complemented
100	#19151494	C₂²	1	1	yes	characteristic, complemented
101	#19151494	C₂²	1	1	yes	characteristic, complemented
102	#19151494	C₂²	1	1	yes	characteristic, complemented
103	#19151494	C₂²	1	1	yes	characteristic, complemented
104	#19151493	C₂²	1	1	yes	characteristic, complemented
105	#19151493	C₂²	1	1	yes	characteristic, complemented
106	#19151492	C₂²	1	1	yes	characteristic
107	#19151492	C₂²	1	1	yes	characteristic
108	#19151492	C₂²	1	1	yes	characteristic, complemented
109	#19151491	C₂²	1	1	yes	characteristic
110	#19151491	C₂²	1	1	yes	characteristic
111	#19151491	C₂²	1	1	yes	characteristic
112	#19151491	C₂²	1	1	yes	characteristic, complemented
113	#19151491	C₂²	1	1	yes	characteristic, complemented
114	#19151490	C₂²	1	1	yes	characteristic
115	#19151490	C₂²	1	1	yes	characteristic
116	#19151490	C₂²	1	1	yes	characteristic
117	#19151490	C₂²	1	1	yes	characteristic, complemented
118	#19151490	C₂²	1	1	yes	characteristic, complemented
119	#19151489	C₂²	1	1	yes	characteristic
120	#19151489	C₂²	1	1	yes	characteristic
121	#19151489	C₂²	1	1	yes	characteristic, complemented
122	#19151489	C₂²	1	1	yes	characteristic, complemented
123	#19151488	C₂²	1	1	yes	characteristic
124	#19151488	C₂²	1	1	yes	characteristic
125	#19151488	C₂²	1	1	yes	characteristic, complemented
126	#19151487	C₂²	1	1	yes	characteristic
127	#19151486	C₂²	1	1	yes	characteristic
128	#19151486	C₂²	1	1	yes	characteristic
129	#19151486	C₂²	1	1	yes	characteristic, complemented
130	#19151485	C₂²	1	1	yes	characteristic, complemented
131	#19151485	C₂²	1	1	yes	characteristic, complemented
132	#19151484	C₂²	1	1	yes	characteristic, complemented
133	#19151484	C₂²	1	1	yes	characteristic, complemented
134	#19151484	C₂²	1	1	yes	characteristic, complemented
135	#19151482	C₂²	1	1	yes	characteristic, complemented
136	#19151480	C₂²	1	1	yes	characteristic, complemented
137	#19151479	C₂²	1	1	yes	characteristic, complemented
138	#19151479	C₂²	1	1	yes	characteristic, complemented
139	#19151477	C₂²	1	1	yes	characteristic
140	#19151477	C₂²	1	1	yes	characteristic, complemented
141	#19151476	C₂²	1	1	yes	characteristic
142	#19151476	C₂²	1	1	yes	characteristic
143	#19151476	C₂²	1	1	yes	characteristic
144	#19151476	C₂²	1	1	yes	characteristic
145	#19151474	C₂²	1	1	yes	characteristic
146	#19151474	C₂²	1	1	yes	characteristic
147	#19151474	C₂²	1	1	yes	characteristic
148	#19151474	C₂²	1	1	yes	characteristic
149	#19151474	C₂²	1	1	yes	characteristic
150	#19151474	C₂²	1	1	yes	characteristic, complemented
151	#19151472	C₂²	1	1	yes	characteristic
152	#19151472	C₂²	1	1	yes	characteristic, complemented
153	#19151471	C₂²	1	1	yes	characteristic, complemented
154	#19151469	C₂²	1	1	yes	characteristic
155	#19151469	C₂²	1	1	yes	characteristic
156	#19151469	C₂²	1	1	yes	characteristic
157	#19151469	C₂²	1	1	yes	characteristic, complemented
158	#19151468	C₂²	1	1	yes	characteristic, complemented
159	#19151465	C₂²	1	1	yes	characteristic, complemented
160	#19151465	C₂²	1	1	yes	characteristic, complemented
161	#19151462	C₂²	1	1	yes	characteristic, complemented
162	#19151455	C₂²	1	1	yes	characteristic
163	#19151455	C₂²	1	1	yes	characteristic
164	#19151455	C₂²	1	1	yes	characteristic
165	#19151455	C₂²	1	1	yes	characteristic
166	#19151453	C₂²	1	1	yes	characteristic
167	#19151453	C₂²	1	1	yes	characteristic
168	C₄×#13083551	C₂²	1	1	yes	characteristic
169	#19151445	C₂²	1	1	yes	characteristic
170	#95×D₈₉	C₂²	1	1	yes	characteristic
171	#95×D₈₉	C₂²	1	1	yes	characteristic
172	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
173	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
174	C₂×#123×C₈₉	C₂²	1	1	yes	characteristic
175	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
176	#399×C₈₉	C₂²	1	1	yes	characteristic
177	#397×C₈₉	C₂²	1	1	yes	characteristic, complemented
178	#396×C₈₉	C₂²	1	1	yes	characteristic
179	#395×C₈₉	C₂²	1	1	yes	characteristic, complemented
180	#394×C₈₉	C₂²	1	1	yes	characteristic
181	#393×C₈₉	C₂²	1	1	yes	characteristic
182	#389×C₈₉	C₂²	1	1	yes	characteristic, complemented
183	#388×C₈₉	C₂²	1	1	yes	characteristic
184	#388×C₈₉	C₂²	1	1	yes	characteristic, complemented
185	#387×C₈₉	C₂²	1	1	yes	characteristic, complemented
186	#385×C₈₉	C₂²	1	1	yes	characteristic, complemented
187	C₂⁴×D₈₉	C₂³	1	1	yes	characteristic
188	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
189	C₂²×D₃₅₆	C₂³	1	1	yes	characteristic
190	C₂²×D₃₅₆	C₂³	1	1	yes	characteristic
191	C₂²×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
192	C₂²×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
193	C₂²×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
194	C₂²×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
195	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
196	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
197	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
198	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
199	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
200	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
201	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
202	#15668001	—	4	2	no	—
203	#15667998	—	4	2	no	—
204	#15667997	—	4	2	no	—
205	#15667990	—	2	4	no	—
206	#15667988	—	4	2	no	—
207	#15667988	—	4	2	no	—
208	#15667988	—	4	2	no	—
209	#15667985	—	2	4	no	—
210	#15667982	—	4	2	no	—
211	#15667980	—	4	2	no	—
212	#15667974	—	4	2	no	—
213	C₄×C₂²⋊D₈₉	—	4	2	no	—
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×#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	C₄⋊C₄×D₈₉	—	4	2	no	—
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×#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×#13083551	C₂³	1	1	yes	characteristic
253	C₂×#13083551	C₂³	1	1	yes	characteristic
254	C₂×#13083551	C₂³	1	1	yes	characteristic
255	C₂×#13083551	C₂³	1	1	yes	characteristic
256	C₂×#13083551	C₂³	1	1	yes	characteristic
257	C₂×#13083551	C₂³	1	1	yes	characteristic
258	C₂×#13083551	C₂³	1	1	yes	characteristic
259	C₂×#13083551	C₂³	1	1	yes	characteristic
260	C₂×#13083551	C₂³	1	1	yes	characteristic
261	C₂×#13083551	C₂³	1	1	yes	characteristic
262	C₂×#13083551	C₂³	1	1	yes	characteristic
263	C₂×#13083551	C₂³	1	1	yes	characteristic
264	C₂×#13083551	C₂³	1	1	yes	characteristic
265	C₂×#13083551	C₂³	1	1	yes	characteristic
266	C₂×#13083551	C₂³	1	1	yes	characteristic
267	C₂×#13083551	C₂³	1	1	yes	characteristic
268	C₂×#13083551	C₂³	1	1	yes	characteristic
269	C₂×#13083551	C₂³	1	1	yes	characteristic
270	C₂×#13083551	C₂³	1	1	yes	characteristic
271	C₂×#13083551	C₂³	1	1	yes	characteristic
272	C₂×#13083551	C₂³	1	1	yes	characteristic
273	C₂×#13083551	C₂³	1	1	yes	characteristic
274	C₂×#13083551	C₂³	1	1	yes	characteristic
275	C₂×#13083551	C₂³	1	1	yes	characteristic
276	C₂²⋊C₄×D₈₉	—	2	4	no	—
277	C₂²⋊C₄×D₈₉	—	4	2	no	—
278	C₂²⋊C₄×D₈₉	—	4	2	no	—
279	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
280	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
281	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
282	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
283	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
284	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
285	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
286	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
287	C₄²×D₈₉	—	4	2	no	—
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	#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	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
325	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
326	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
327	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
328	C₄⋊Q₈×C₈₉	—	4	2	no	—
329	#124×C₈₉	—	4	2	no	—
330	#123×C₈₉	—	4	2	no	—
331	C₂²⋊Q₈×C₈₉	—	4	2	no	—
332	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
333	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
334	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
335	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
336	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
337	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
338	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
339	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
340	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
341	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
342	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
343	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
344	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
346	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
347	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
348	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
349	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
350	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
351	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
352	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
353	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
354	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
355	#95×C₈₉	C₂³	1	1	yes	characteristic
356	#95×C₈₉	C₂³	1	1	yes	characteristic
357	#95×C₈₉	C₂³	1	1	yes	characteristic
358	#95×C₈₉	C₂³	1	1	yes	characteristic
359	#95×C₈₉	C₂³	1	1	yes	characteristic
360	#95×C₈₉	C₂³	1	1	yes	characteristic
361	#95×C₈₉	C₂³	1	1	yes	characteristic
362	#95×C₈₉	C₂³	1	1	yes	characteristic
363	C₂³×D₈₉	—	2	2	no	—
364	C₂³×D₈₉	—	2	2	no	—
365	C₂³×D₈₉	—	2	2	no	—
366	C₂³×D₈₉	—	4	1	no	—
367	C₂³×D₈₉	—	4	1	no	—
368	C₂³×D₈₉	—	4	1	no	—
369	C₂³×D₈₉	—	4	1	no	—
370	C₂³×D₈₉	C₂⁴	1	1	yes	characteristic
371	C₂³×D₈₉	C₂⁴	1	1	yes	characteristic
372	C₂³×D₈₉	C₂⁴	1	1	yes	characteristic
373	C₂×Dic₁₇₈	—	2	2	no	—
374	C₂×Dic₁₇₈	—	4	1	no	—
375	C₂×Dic₁₇₈	—	4	1	no	—
376	C₂×D₃₅₆	—	2	2	no	—
377	C₂×D₃₅₆	—	2	2	no	—
378	C₂×D₃₅₆	—	2	2	no	—
379	C₂×D₃₅₆	—	4	1	no	—
380	C₂×D₃₅₆	—	4	1	no	—
381	C₂×D₃₅₆	—	4	1	no	—
382	C₂×C₂²⋊D₈₉	—	2	2	no	—
383	C₂×C₂²⋊D₈₉	—	2	2	no	—
384	C₂×C₂²⋊D₈₉	—	2	2	no	—
385	C₂×C₂²⋊D₈₉	—	2	2	no	—
386	C₂×C₂²⋊D₈₉	—	4	1	no	—
387	C₂×C₂²⋊D₈₉	—	4	1	no	—
388	C₂×C₂²⋊D₈₉	—	4	1	no	—
389	C₂×C₂²⋊D₈₉	—	4	1	no	—
390	C₂×C₂²⋊D₈₉	—	4	1	no	—
391	C₂×C₂²⋊D₈₉	—	4	1	no	—
392	C₂×C₂²⋊D₈₉	—	4	1	no	—
393	C₂×C₂²⋊D₈₉	—	4	1	no	—
394	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
395	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
396	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
397	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
398	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
399	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
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	C₂×C₄×D₈₉	—	2	2	no	—
408	C₂×C₄×D₈₉	—	2	2	no	—
409	C₂×C₄×D₈₉	—	2	2	no	—
410	C₂×C₄×D₈₉	—	2	2	no	—
411	C₂×C₄×D₈₉	—	2	2	no	—
412	C₂×C₄×D₈₉	—	2	2	no	—
413	C₂×C₄×D₈₉	—	2	2	no	—
414	C₂×C₄×D₈₉	—	4	1	no	—
415	C₂×C₄×D₈₉	—	4	1	no	—
416	C₂×C₄×D₈₉	—	4	1	no	—
417	C₂×C₄×D₈₉	—	4	1	no	—
418	C₂×C₄×D₈₉	—	4	1	no	—
419	C₂×C₄×D₈₉	—	4	1	no	—
420	C₂×C₄×D₈₉	—	4	1	no	—
421	C₂×C₄×D₈₉	—	4	1	no	—
422	C₂×C₄×D₈₉	—	4	1	no	—
423	C₂×C₄×D₈₉	—	4	1	no	—
424	C₂×C₄×D₈₉	—	4	1	no	—
425	C₂×C₄×D₈₉	—	4	1	no	—
426	C₂×C₄×D₈₉	—	4	1	no	—
427	C₂×C₄×D₈₉	#41	1	4	yes	—
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	#13083553	—	2	2	no	—
437	#13083553	—	2	2	no	—
438	#13083553	—	2	2	no	—
439	#13083553	—	2	2	no	—
440	#13083553	—	4	1	no	—
441	#13083553	—	4	1	no	—
442	#13083553	—	4	1	no	—
443	#13083553	—	4	1	no	—
444	#13083553	—	4	1	no	—
445	#13083553	—	4	1	no	—
446	#13083553	—	4	1	no	—
447	#13083553	—	4	1	no	—
448	#13083553	—	4	1	no	—
449	#13083553	—	4	1	no	—
450	C₂²⋊Dic₈₉	—	2	2	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	#13083551	—	2	2	no	—
462	#13083551	—	2	2	no	—
463	#13083551	—	2	2	no	—
464	#13083551	—	2	2	no	—
465	#13083551	—	2	2	no	—
466	#13083551	—	2	2	no	—
467	#13083551	—	2	2	no	—
468	#13083551	—	2	2	no	—
469	#13083551	—	2	2	no	—
470	#13083551	—	2	2	no	—
471	#13083551	—	2	2	no	—
472	#13083551	—	2	2	no	—
473	#13083551	—	2	2	no	—
474	#13083551	—	4	1	no	—
475	#13083551	—	4	1	no	—
476	#13083551	—	4	1	no	—
477	#13083551	—	4	1	no	—
478	#13083551	—	4	1	no	—
479	#13083551	—	4	1	no	—
480	#13083551	—	4	1	no	—
481	#13083551	—	4	1	no	—
482	#13083551	—	4	1	no	—
483	#13083551	—	4	1	no	—
484	#13083551	—	4	1	no	—
485	#13083551	—	4	1	no	—
486	#13083551	—	4	1	no	—
487	#13083551	—	4	1	no	—
488	#13083551	—	4	1	no	—
489	C₄×Dic₈₉	—	2	2	no	—
490	C₄×Dic₈₉	—	4	1	no	—
491	C₄×Dic₈₉	—	4	1	no	—
492	C₄×Dic₈₉	—	4	1	no	—
493	C₄×Dic₈₉	—	4	1	no	—
494	C₄×Dic₈₉	—	4	1	no	—
495	C₄×Dic₈₉	—	4	1	no	—
496	C₄×Dic₈₉	—	4	1	no	—
497	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
498	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
499	C₂×Q₈×C₈₉	—	2	2	no	—
500	C₂×Q₈×C₈₉	—	2	2	no	—
501	C₂×Q₈×C₈₉	—	4	1	no	—
502	C₂×Q₈×C₈₉	—	4	1	no	—
503	C₂×Q₈×C₈₉	—	4	1	no	—
504	C₂×Q₈×C₈₉	—	4	1	no	—
505	C₂×D₄×C₈₉	—	4	1	no	—
506	C₂×D₄×C₈₉	—	4	1	no	—
507	C₂×D₄×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	C₂⁴	1	1	yes	characteristic
512	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
513	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
514	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
515	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
516	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
517	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₈₉	—	2	2	no	—
525	C₄⋊C₄×C₈₉	—	2	2	no	—
526	C₄⋊C₄×C₈₉	—	2	2	no	—
527	C₄⋊C₄×C₈₉	—	2	2	no	—
528	C₄⋊C₄×C₈₉	—	4	1	no	—
529	C₄⋊C₄×C₈₉	—	4	1	no	—
530	C₄⋊C₄×C₈₉	—	4	1	no	—
531	C₄⋊C₄×C₈₉	—	4	1	no	—
532	C₄⋊C₄×C₈₉	—	4	1	no	—
533	C₄⋊C₄×C₈₉	—	4	1	no	—
534	C₂²⋊C₄×C₈₉	—	2	2	no	—
535	C₂²⋊C₄×C₈₉	—	2	2	no	—
536	C₂²⋊C₄×C₈₉	—	2	2	no	—
537	C₂²⋊C₄×C₈₉	—	2	2	no	—
538	C₂²⋊C₄×C₈₉	—	2	2	no	—
539	C₂²⋊C₄×C₈₉	—	2	2	no	—
540	C₂²⋊C₄×C₈₉	—	4	1	no	—
541	C₂²⋊C₄×C₈₉	—	4	1	no	—
542	C₂²⋊C₄×C₈₉	—	4	1	no	—
543	C₂²⋊C₄×C₈₉	—	4	1	no	—
544	C₂²⋊C₄×C₈₉	—	4	1	no	—
545	C₄²×C₈₉	—	2	2	no	—
546	C₄²×C₈₉	—	4	1	no	—
547	C₂³×C₈₉	—	2	1	no	—
548	C₂³×C₈₉	—	2	1	no	—
549	C₂³×C₈₉	—	2	1	no	—
550	C₂³×C₈₉	—	2	1	no	—
551	C₂³×C₈₉	—	2	1	no	—
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	C₂⁵	1	1	yes	characteristic
562	C₂²×D₈₉	—	2	1	no	—
563	C₂²×D₈₉	—	2	1	no	—
564	C₂²×D₈₉	—	2	1	no	—
565	C₂²×D₈₉	—	2	1	no	—
566	C₂²×D₈₉	—	2	1	no	—
567	C₂²×D₈₉	—	2	1	no	—
568	C₂²×D₈₉	—	2	1	no	—
569	C₂²×D₈₉	—	2	1	no	—
570	C₂²×D₈₉	—	2	1	no	—
571	C₂²×D₈₉	—	2	1	no	—
572	C₂²×D₈₉	—	2	1	no	—
573	C₂²×D₈₉	—	2	1	no	—
574	C₂²×D₈₉	—	2	1	no	—
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	1	no	—
580	C₂²×D₈₉	—	4	4	no	—
581	C₂²×D₈₉	—	4	4	no	—
582	C₂²×D₈₉	—	4	4	no	—
583	C₂²×D₈₉	—	8	2	no	—
584	C₂²×D₈₉	—	8	2	no	—
585	C₂²×D₈₉	—	8	2	no	—
586	C₂²×D₈₉	—	8	2	no	—
587	C₂²×D₈₉	C₂×#41	1	2	yes	—
588	C₂²×D₈₉	H(5,𝔽₂)	1	2	yes	—
589	C₂²×D₈₉	2₋¹⁺⁴	1	2	yes	—
590	Q₈×C₈₉	—	8	2	no	—
591	Q₈×C₈₉	—	8	2	no	—
592	D₄×C₈₉	—	8	2	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	—	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	—	8	2	no	—
630	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
631	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
632	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
633	C₂²⋊D₈₉	—	4	4	no	—
634	C₂²⋊D₈₉	—	8	2	no	—
635	C₂²⋊D₈₉	—	8	2	no	—
636	C₂²⋊D₈₉	—	8	2	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	—	2	1	no	—
674	C₂×Dic₈₉	—	2	1	no	—
675	C₂×Dic₈₉	C₂×#41	1	2	yes	—
676	D₃₅₆	—	4	4	no	—
677	D₃₅₆	—	8	2	no	—
678	C₄×D₈₉	—	4	4	no	—
679	C₄×D₈₉	—	4	4	no	—
680	C₄×D₈₉	—	4	4	no	—
681	C₄×D₈₉	—	4	4	no	—
682	C₄×D₈₉	—	8	2	no	—
683	C₄×D₈₉	—	8	2	no	—
684	C₄×D₈₉	—	8	2	no	—
685	Dic₁₇₈	—	8	2	no	—
686	C₂²×C₈₉	—	4	1	no	—
687	C₂²×C₈₉	—	4	1	no	—
688	C₂²×C₈₉	—	4	1	no	—
689	C₂²×C₈₉	—	4	1	no	—
690	C₂²×C₈₉	—	4	1	no	—
691	C₂²×C₈₉	—	4	1	no	—
692	C₂²×C₈₉	—	4	1	no	—
693	C₂²×C₈₉	—	4	1	no	—
694	C₂²×C₈₉	—	4	1	no	—
695	C₂²×C₈₉	—	4	1	no	—
696	C₂²×C₈₉	—	4	1	no	—
697	C₂²×C₈₉	—	4	1	no	—
698	C₂²×C₈₉	—	4	1	no	—
699	C₂²×C₈₉	—	4	1	no	—
700	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
701	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
702	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
703	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
704	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
705	C₂²×C₈₉	#585	1	1	yes	characteristic
706	C₂²×C₈₉	#585	1	1	yes	characteristic
707	C₂×D₈₉	—	2	2	no	—
708	C₂×D₈₉	—	2	2	no	—
709	C₂×D₈₉	—	2	2	no	—
710	C₂×D₈₉	—	2	2	no	—
711	C₂×D₈₉	—	2	2	no	—
712	C₂×D₈₉	—	2	2	no	—
713	C₂×D₈₉	—	4	1	no	—
714	C₂×D₈₉	—	4	1	no	—
715	C₂×D₈₉	—	4	1	no	—
716	C₂×D₈₉	—	4	1	no	—
717	C₂×D₈₉	—	4	1	no	—
718	C₂×D₈₉	—	4	1	no	—
719	C₂×D₈₉	—	4	1	no	—
720	C₂×D₈₉	—	4	1	no	—
721	C₂×D₈₉	—	4	1	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	—	4	1	no	—
727	C₂×D₈₉	—	8	8	no	—
728	C₂×D₈₉	#542	1	4	yes	—
729	C₄×C₈₉	—	2	2	no	—
730	C₄×C₈₉	—	2	2	no	—
731	C₄×C₈₉	—	2	2	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	C₄×C₈₉	—	4	1	no	—
742	Dic₈₉	—	2	2	no	—
743	Dic₈₉	—	4	1	no	—
744	Dic₈₉	—	4	1	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	#36766	—	89	1	no	maximal, Sylow
756	C₂×C₈₉	—	8	1	no	—
757	C₂×C₈₉	—	8	1	no	—
758	C₂×C₈₉	C₂×#542	1	1	yes	characteristic
759	C₂×C₈₉	#3505	1	1	yes	characteristic
760	C₂×C₈₉	#3506	1	1	yes	characteristic
761	C₂×C₈₉	#3535	1	1	yes	characteristic
762	C₂×C₈₉	#3537	1	1	yes	characteristic
763	C₂×C₈₉	#3560	1	1	yes	characteristic
764	C₂×C₈₉	#3561	1	1	yes	characteristic
765	D₈₉	—	2	4	no	—
766	D₈₉	—	8	1	no	—
767	D₈₉	—	8	1	no	—
768	#2857	—	89	1	no	—
769	#2850	—	89	1	no	—
770	#2801	—	89	1	no	—
771	#2801	—	89	1	no	—
772	#2795	—	89	1	no	—
773	#2795	—	89	1	no	—
774	#2773	—	89	1	no	—
775	#2773	—	89	1	no	—
776	#2759	—	89	1	no	—
777	#2759	—	89	1	no	—
778	#2757	—	89	1	no	—
779	#2757	—	89	1	no	—
780	#2730	—	89	1	no	—
781	#2730	—	89	1	no	—
782	#2710	—	89	1	no	—
783	#2710	—	89	1	no	—
784	#2674	—	89	1	no	—
785	#2674	D₈₉	1	1	yes	characteristic, complemented
786	#2626	—	89	1	no	—
787	#2617	—	89	1	no	—
788	#2510	—	89	1	no	—
789	#2510	—	89	1	no	—
790	#2472	—	89	1	no	—
791	#2472	—	89	1	no	—
792	#2449	—	89	1	no	—
793	#2449	—	89	1	no	—
794	#2418	—	89	1	no	—
795	#2418	—	89	1	no	—
796	#2329	—	89	1	no	—
797	#2325	—	89	1	no	—
798	C₂×#388	—	89	1	no	—
799	C₈₉	#36766	1	1	yes	characteristic, complemented, Sylow
800	C₂×C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
801	C₂×#124	—	89	1	no	—
802	C₂×#124	—	89	1	no	—
803	C₂×#124	C₂×D₈₉	1	1	yes	characteristic
804	C₂×#123	—	89	1	no	—
805	C₂×#123	C₂×D₈₉	1	1	yes	characteristic
806	C₂×C₂²⋊Q₈	—	89	1	no	—
807	C₂×C₂²⋊Q₈	—	89	1	no	—
808	C₂×C₂²⋊Q₈	—	89	1	no	—
809	C₂×C₂²⋊Q₈	—	89	1	no	—
810	C₂×C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
811	C₂×#121	—	89	1	no	—
812	C₂×#120	—	89	1	no	—
813	C₂×#120	—	89	1	no	—
814	C₂×C₄×D₄	—	89	1	no	—
815	C₂×C₄×D₄	—	89	1	no	—
816	C₂²×C₄⋊C₄	—	89	1	no	—
817	C₂²×C₂²⋊C₄	—	89	1	no	—
818	C₂²×C₂²⋊C₄	—	89	1	no	—
819	C₂²×C₂²⋊C₄	—	89	1	no	—
820	C₂²×C₄²	—	89	1	no	—
821	#401	—	89	1	no	—
822	#401	—	89	1	no	—
823	#400	—	89	1	no	—
824	#400	—	89	1	no	—
825	#399	—	89	1	no	—
826	#399	—	89	1	no	—
827	#399	—	89	1	no	—
828	#399	—	89	1	no	—
829	#399	—	89	1	no	—
830	#399	C₂×D₈₉	1	1	yes	characteristic
831	#398	—	89	1	no	—
832	#398	—	89	1	no	—
833	#397	—	89	1	no	—
834	#397	—	89	1	no	—
835	#397	—	89	1	no	—
836	#397	—	89	1	no	—
837	#397	—	89	1	no	—
838	#397	—	89	1	no	—
839	#397	—	89	1	no	—
840	#397	—	89	1	no	—
841	#397	—	89	1	no	—
842	#397	C₂×D₈₉	1	1	yes	characteristic, complemented
843	#396	—	89	1	no	—
844	#396	—	89	1	no	—
845	#396	—	89	1	no	—
846	#396	—	89	1	no	—
847	#396	—	89	1	no	—
848	#396	C₂×D₈₉	1	1	yes	characteristic
849	#395	—	89	1	no	—
850	#395	C₂×D₈₉	1	1	yes	characteristic, complemented
851	#394	—	89	1	no	—
852	#394	—	89	1	no	—
853	#394	—	89	1	no	—
854	#394	—	89	1	no	—
855	#394	—	89	1	no	—
856	#394	—	89	1	no	—
857	#394	—	89	1	no	—
858	#394	—	89	1	no	—
859	#394	—	89	1	no	—
860	#394	—	89	1	no	—
861	#394	—	89	1	no	—
862	#394	C₂×D₈₉	1	1	yes	characteristic
863	#393	—	89	1	no	—
864	#393	—	89	1	no	—
865	#393	—	89	1	no	—
866	#393	C₂×D₈₉	1	1	yes	characteristic
867	#392	—	89	1	no	—
868	#392	—	89	1	no	—
869	#391	—	89	1	no	—
870	#391	—	89	1	no	—
871	#391	—	89	1	no	—
872	#391	—	89	1	no	—
873	#391	—	89	1	no	—
874	#390	—	89	1	no	—
875	#390	—	89	1	no	—
876	#390	—	89	1	no	—
877	#389	—	89	1	no	—
878	#389	—	89	1	no	—
879	#389	—	89	1	no	—
880	#389	—	89	1	no	—
881	#389	—	89	1	no	—
882	#389	—	89	1	no	—
883	#389	—	89	1	no	—
884	#389	C₂×D₈₉	1	1	yes	characteristic, complemented
885	#388	—	89	1	no	—
886	#388	—	89	1	no	—
887	#388	—	89	1	no	—
888	#388	—	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	—	89	1	no	—
904	#388	—	89	1	no	—
905	#388	—	89	1	no	—
906	#388	—	89	1	no	—
907	#388	—	89	1	no	—
908	#388	—	89	1	no	—
909	#388	C₂×D₈₉	1	1	yes	characteristic
910	#388	C₂×D₈₉	1	1	yes	characteristic, complemented
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	—	89	1	no	—
920	#387	C₂×D₈₉	1	1	yes	characteristic, complemented
921	#386	—	89	1	no	—
922	#386	—	89	1	no	—
923	#386	—	89	1	no	—
924	#386	—	89	1	no	—
925	#386	—	89	1	no	—
926	#386	—	89	1	no	—
927	#386	—	89	1	no	—
928	#386	—	89	1	no	—
929	#386	—	89	1	no	—
930	#386	—	89	1	no	—
931	#386	—	89	1	no	—
932	#386	—	89	1	no	—
933	#385	—	89	1	no	—
934	#385	—	89	1	no	—
935	#385	—	89	1	no	—
936	#385	—	89	1	no	—
937	#385	—	89	1	no	—
938	#385	—	89	1	no	—
939	#385	—	89	1	no	—
940	#385	C₂×D₈₉	1	1	yes	characteristic, complemented
941	#384	—	89	1	no	—
942	#383	—	89	1	no	—
943	#383	—	89	1	no	—
944	#382	—	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	C₄×C₂²⋊C₄	—	89	1	no	—
952	C₄×C₂²⋊C₄	—	89	1	no	—
953	C₂×#95	—	89	1	no	—
954	C₂×#95	—	89	1	no	—
955	C₂⁵	—	89	1	no	—
956	C₂²×Q₈	—	89	1	no	—
957	C₂²×Q₈	C₂²×D₈₉	1	1	yes	characteristic
958	C₂²×Q₈	C₂²×D₈₉	1	1	yes	characteristic
959	C₂²×D₄	—	89	1	no	—
960	C₂²×D₄	—	89	1	no	—
961	C₂²×D₄	—	89	1	no	—
962	C₂²×D₄	—	89	1	no	—
963	C₂²×D₄	—	89	1	no	—
964	C₂²×D₄	—	89	1	no	—
965	C₂²×D₄	C₂²×D₈₉	1	1	yes	characteristic
966	C₂³×C₄	—	89	1	no	—
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	C₂²×D₈₉	1	1	yes	characteristic
974	C₄⋊Q₈	—	4	2	no	—
975	#124	—	4	2	no	—
976	#124	—	356	2	no	—
977	#124	—	356	2	no	—
978	#123	—	4	2	no	—
979	#123	—	356	2	no	—
980	C₂²⋊Q₈	—	4	2	no	—
981	C₂²⋊Q₈	—	356	2	no	—
982	C₂²⋊Q₈	—	356	2	no	—
983	C₂²⋊Q₈	—	356	2	no	—
984	C₂²⋊Q₈	—	178	4	no	—
985	#121	—	178	4	no	—
986	#120	—	356	2	no	—
987	#120	—	356	2	no	—
988	C₄×D₄	—	356	2	no	—
989	C₄×D₄	—	356	2	no	—
990	C₂×C₄⋊C₄	—	89	1	no	—
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	—	356	2	no	—
1013	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1014	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1015	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1016	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1017	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
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×C₂²⋊C₄	—	89	1	no	—
1024	C₂×C₂²⋊C₄	—	89	1	no	—
1025	C₂×C₂²⋊C₄	—	89	1	no	—
1026	C₂×C₂²⋊C₄	—	89	1	no	—
1027	C₂×C₂²⋊C₄	—	89	1	no	—
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	—	89	1	no	—
1051	C₂×C₂²⋊C₄	—	89	1	no	—
1052	C₂×C₂²⋊C₄	—	89	1	no	—
1053	C₂×C₂²⋊C₄	—	89	1	no	—
1054	C₂×C₂²⋊C₄	—	89	1	no	—
1055	C₂×C₂²⋊C₄	—	89	1	no	—
1056	C₂×C₂²⋊C₄	—	89	1	no	—
1057	C₂×C₂²⋊C₄	—	89	1	no	—
1058	C₂×C₂²⋊C₄	—	89	1	no	—
1059	C₂×C₂²⋊C₄	—	89	1	no	—
1060	C₂×C₂²⋊C₄	—	89	1	no	—
1061	C₂×C₂²⋊C₄	—	89	1	no	—
1062	C₂×C₂²⋊C₄	—	356	2	no	—
1063	C₂×C₂²⋊C₄	—	356	2	no	—
1064	C₂×C₂²⋊C₄	—	178	4	no	—
1065	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1066	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1067	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1068	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1069	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1070	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1071	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1072	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1073	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1074	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1075	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1076	C₂×C₄²	—	89	1	no	—
1077	C₂×C₄²	—	89	1	no	—
1078	C₂×C₄²	—	89	1	no	—
1079	C₂×C₄²	—	89	1	no	—
1080	C₂×C₄²	—	89	1	no	—
1081	C₂×C₄²	—	89	1	no	—
1082	C₂×C₄²	—	89	1	no	—
1083	C₂×C₄²	—	89	1	no	—
1084	C₂×C₄²	—	356	2	no	—
1085	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1086	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
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	C₂²×D₈₉	1	1	yes	characteristic
1124	#95	C₂²×D₈₉	1	1	yes	characteristic
1125	#95	C₂²×D₈₉	1	1	yes	characteristic
1126	#95	C₂²×D₈₉	1	1	yes	characteristic
1127	#95	C₂²×D₈₉	1	1	yes	characteristic
1128	#95	C₂²×D₈₉	1	1	yes	characteristic
1129	#95	C₂²×D₈₉	1	1	yes	characteristic
1130	#95	C₂²×D₈₉	1	1	yes	characteristic
1131	C₂⁴	—	89	1	no	—
1132	C₂⁴	—	89	1	no	—
1133	C₂⁴	—	89	1	no	—
1134	C₂⁴	—	356	1	no	—
1135	C₂⁴	—	356	1	no	—
1136	C₂⁴	—	356	1	no	—
1137	C₂⁴	—	356	1	no	—
1138	C₂⁴	—	178	2	no	—
1139	C₂⁴	—	178	2	no	—
1140	C₂⁴	—	178	2	no	—
1141	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
1142	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
1143	C₂×Q₈	—	2	2	no	—
1144	C₂×Q₈	—	2	2	no	—
1145	C₂×Q₈	—	4	1	no	—
1146	C₂×Q₈	—	4	1	no	—
1147	C₂×Q₈	—	4	1	no	—
1148	C₂×Q₈	—	4	1	no	—
1149	C₂×Q₈	—	356	1	no	—
1150	C₂×Q₈	—	356	1	no	—
1151	C₂×Q₈	—	178	2	no	—
1152	C₂×D₄	—	4	1	no	—
1153	C₂×D₄	—	4	1	no	—
1154	C₂×D₄	—	4	1	no	—
1155	C₂×D₄	—	356	1	no	—
1156	C₂×D₄	—	356	1	no	—
1157	C₂×D₄	—	356	1	no	—
1158	C₂×D₄	—	356	1	no	—
1159	C₂×D₄	—	356	1	no	—
1160	C₂×D₄	—	356	1	no	—
1161	C₂×D₄	—	356	1	no	—
1162	C₂×D₄	—	356	1	no	—
1163	C₂×D₄	—	356	1	no	—
1164	C₂×D₄	—	356	1	no	—
1165	C₂×D₄	—	356	1	no	—
1166	C₂×D₄	—	178	2	no	—
1167	C₂×D₄	—	178	2	no	—
1168	C₂×D₄	—	178	2	no	—
1169	C₂×D₄	—	178	2	no	—
1170	C₂×D₄	—	178	2	no	—
1171	C₂×D₄	—	178	2	no	—
1172	C₂×D₄	—	178	2	no	—
1173	C₂²×C₄	—	4	1	no	—
1174	C₂²×C₄	—	4	1	no	—
1175	C₂²×C₄	—	4	1	no	—
1176	C₂²×C₄	—	89	1	no	—
1177	C₂²×C₄	—	89	4	no	—
1178	C₂²×C₄	—	89	1	no	—
1179	C₂²×C₄	—	89	1	no	—
1180	C₂²×C₄	—	89	1	no	—
1181	C₂²×C₄	—	89	1	no	—
1182	C₂²×C₄	—	89	1	no	—
1183	C₂²×C₄	—	89	1	no	—
1184	C₂²×C₄	—	89	1	no	—
1185	C₂²×C₄	—	89	1	no	—
1186	C₂²×C₄	—	89	1	no	—
1187	C₂²×C₄	—	89	1	no	—
1188	C₂²×C₄	—	89	1	no	—
1189	C₂²×C₄	—	89	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	—	356	1	no	—
1202	C₂²×C₄	—	356	1	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	—	178	2	no	—
1209	C₂²×C₄	—	178	2	no	—
1210	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1211	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1212	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1213	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
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	C₄⋊C₄	—	2	2	no	—
1224	C₄⋊C₄	—	2	2	no	—
1225	C₄⋊C₄	—	2	2	no	—
1226	C₄⋊C₄	—	2	2	no	—
1227	C₄⋊C₄	—	4	1	no	—
1228	C₄⋊C₄	—	4	1	no	—
1229	C₄⋊C₄	—	4	1	no	—
1230	C₄⋊C₄	—	4	1	no	—
1231	C₄⋊C₄	—	4	1	no	—
1232	C₄⋊C₄	—	4	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	—	356	1	no	—
1247	C₄⋊C₄	—	356	1	no	—
1248	C₄⋊C₄	—	356	1	no	—
1249	C₄⋊C₄	—	356	1	no	—
1250	C₄⋊C₄	—	356	1	no	—
1251	C₄⋊C₄	—	178	2	no	—
1252	C₄⋊C₄	—	178	2	no	—
1253	C₄⋊C₄	—	178	2	no	—
1254	C₄⋊C₄	—	178	2	no	—
1255	C₂²⋊C₄	—	2	2	no	—
1256	C₂²⋊C₄	—	2	2	no	—
1257	C₂²⋊C₄	—	2	2	no	—
1258	C₂²⋊C₄	—	2	2	no	—
1259	C₂²⋊C₄	—	2	2	no	—
1260	C₂²⋊C₄	—	2	2	no	—
1261	C₂²⋊C₄	—	4	1	no	—
1262	C₂²⋊C₄	—	4	1	no	—
1263	C₂²⋊C₄	—	4	1	no	—
1264	C₂²⋊C₄	—	4	1	no	—
1265	C₂²⋊C₄	—	4	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	—	356	1	no	—
1277	C₂²⋊C₄	—	356	1	no	—
1278	C₂²⋊C₄	—	356	1	no	—
1279	C₂²⋊C₄	—	356	1	no	—
1280	C₂²⋊C₄	—	356	1	no	—
1281	C₂²⋊C₄	—	356	1	no	—
1282	C₂²⋊C₄	—	356	1	no	—
1283	C₂²⋊C₄	—	356	1	no	—
1284	C₂²⋊C₄	—	356	1	no	—
1285	C₂²⋊C₄	—	356	1	no	—
1286	C₂²⋊C₄	—	356	1	no	—
1287	C₂²⋊C₄	—	356	1	no	—
1288	C₂²⋊C₄	—	356	1	no	—
1289	C₂²⋊C₄	—	356	1	no	—
1290	C₂²⋊C₄	—	356	1	no	—
1291	C₂²⋊C₄	—	178	2	no	—
1292	C₂²⋊C₄	—	178	2	no	—
1293	C₂²⋊C₄	—	178	2	no	—
1294	C₂²⋊C₄	—	178	2	no	—
1295	C₂²⋊C₄	—	178	2	no	—
1296	C₂²⋊C₄	—	178	2	no	—
1297	C₂²⋊C₄	—	178	2	no	—
1298	C₂²⋊C₄	—	178	2	no	—
1299	C₂²⋊C₄	—	178	2	no	—
1300	C₂²⋊C₄	—	178	2	no	—
1301	C₂²⋊C₄	—	178	2	no	—
1302	C₂²⋊C₄	—	178	2	no	—
1303	C₂²⋊C₄	—	178	2	no	—
1304	C₂²⋊C₄	—	178	2	no	—
1305	C₄²	—	2	2	no	—
1306	C₄²	—	4	1	no	—
1307	C₄²	—	356	1	no	—
1308	C₄²	—	356	1	no	—
1309	C₄²	—	356	1	no	—
1310	C₄²	—	356	1	no	—
1311	C₄²	—	356	1	no	—
1312	C₄²	—	356	1	no	—
1313	C₄²	—	356	1	no	—
1314	C₄²	—	178	2	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	—	89	2	no	—
1330	C₂³	—	89	2	no	—
1331	C₂³	—	89	2	no	—
1332	C₂³	—	356	4	no	—
1333	C₂³	—	356	4	no	—
1334	C₂³	—	356	4	no	—
1335	C₂³	—	178	1	no	—
1336	C₂³	—	178	1	no	—
1337	C₂³	—	178	1	no	—
1338	C₂³	—	178	1	no	—
1339	C₂³	—	178	1	no	—
1340	C₂³	—	178	1	no	—
1341	C₂³	—	178	1	no	—
1342	C₂³	—	178	1	no	—
1343	C₂³	—	178	1	no	—
1344	C₂³	—	178	1	no	—
1345	C₂³	—	178	1	no	—
1346	C₂³	—	178	1	no	—
1347	C₂³	—	178	1	no	—
1348	C₂³	—	178	1	no	—
1349	C₂³	—	178	1	no	—
1350	C₂³	—	178	1	no	—
1351	C₂³	—	178	1	no	—
1352	C₂³	—	178	1	no	—
1353	C₂³	—	712	2	no	—
1354	C₂³	—	712	2	no	—
1355	C₂³	—	712	2	no	—
1356	C₂³	—	712	2	no	—
1357	C₂³	C₂⁴×D₈₉	1	1	yes	characteristic
1358	Q₈	—	8	2	no	—
1359	Q₈	—	8	2	no	—
1360	Q₈	—	712	2	no	—
1361	D₄	—	8	2	no	—
1362	D₄	—	356	4	no	—
1363	D₄	—	356	4	no	—
1364	D₄	—	712	2	no	—
1365	D₄	—	712	2	no	—
1366	D₄	—	712	2	no	—
1367	D₄	—	712	2	no	—
1368	C₂×C₄	—	2	1	no	—
1369	C₂×C₄	—	2	1	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	—	8	2	no	—
1405	C₂×C₄	—	89	2	no	—
1406	C₂×C₄	—	356	4	no	—
1407	C₂×C₄	—	356	4	no	—
1408	C₂×C₄	—	356	4	no	—
1409	C₂×C₄	—	356	4	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	—	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	—	712	2	no	—
1449	C₂×C₄	—	712	2	no	—
1450	C₂×C₄	—	712	2	no	—
1451	C₂×C₄	#41×D₈₉	1	2	yes	—
1452	C₂×C₄	#15668057	1	2	yes	—
1453	C₂×C₄	#15668057	1	2	yes	—
1454	C₂²	—	4	1	no	—
1455	C₂²	—	4	1	no	—
1456	C₂²	—	4	1	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	—	89	4	no	—
1469	C₂²	—	356	1	no	—
1470	C₂²	—	356	1	no	—
1471	C₂²	—	356	1	no	—
1472	C₂²	—	356	1	no	—
1473	C₂²	—	356	1	no	—
1474	C₂²	—	356	1	no	—
1475	C₂²	—	356	1	no	—
1476	C₂²	—	356	1	no	—
1477	C₂²	—	356	1	no	—
1478	C₂²	—	356	1	no	—
1479	C₂²	—	356	1	no	—
1480	C₂²	—	356	1	no	—
1481	C₂²	—	356	1	no	—
1482	C₂²	—	356	1	no	—
1483	C₂²	—	178	2	no	—
1484	C₂²	—	178	2	no	—
1485	C₂²	—	178	2	no	—
1486	C₂²	—	178	2	no	—
1487	C₂²	—	178	2	no	—
1488	C₂²	—	178	2	no	—
1489	C₂²	—	712	8	no	—
1490	C₂²	C₂×#41×D₈₉	1	1	yes	characteristic
1491	C₂²	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
1492	C₂²	C₂×#15668057	1	1	yes	characteristic
1493	C₂²	C₂×#15668057	1	1	yes	characteristic
1494	C₂²	2₋¹⁺⁴×D₈₉	1	1	yes	characteristic
1495	C₂²	#19152435	1	1	yes	characteristic
1496	C₂²	#19152435	1	1	yes	characteristic
1497	C₄	—	2	2	no	—
1498	C₄	—	2	2	no	—
1499	C₄	—	2	2	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	—	4	1	no	—
1508	C₄	—	4	1	no	—
1509	C₄	—	4	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	—	356	1	no	—
1518	C₄	—	356	1	no	—
1519	C₄	—	356	1	no	—
1520	C₄	—	356	1	no	—
1521	C₄	—	356	1	no	—
1522	C₄	—	178	2	no	—
1523	C₂	—	8	1	no	—
1524	C₂	—	8	1	no	—
1525	C₂	—	178	4	no	—
1526	C₂	—	712	1	no	—
1527	C₂	—	712	1	no	—
1528	C₂	#542×D₈₉	1	1	yes	characteristic
1529	C₂	#26034088	1	1	yes	characteristic
1530	C₂	#26034102	1	1	yes	characteristic
1531	C₂	#26034451	1	1	yes	characteristic
1532	C₂	#26034483	1	1	yes	characteristic
1533	C₂	#26034795	1	1	yes	characteristic
1534	C₂	#26034813	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₈₉
commutator, socle, cosocle	C₂³×C₈₉	C₂⁵
Fitting	C₈₉×#2674	C₂
prime radical	#26025991	C₂
hypercenter	#2674	D₈₉
hypocenter	C₈₉	#36766
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ #2674

Complements

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

N	H ≅ G/N	type
1. #26028599	C₂	semidirect
2. #26028550	C₂	semidirect
3. #26028157	C₂	semidirect
4. #26028156	C₂	semidirect
5. #26028084	C₂	semidirect
6. #26028084	C₂	semidirect
7. #26027797	C₂	semidirect
8. #26027789	C₂	semidirect
9. #26027625	C₂	semidirect
10. #26027618	C₂	semidirect
11. #26027596	C₂	semidirect
12. #26027590	C₂	semidirect
13. #26027245	C₂	semidirect
14. #26027243	C₂	semidirect
15. #26026999	C₂	semidirect
16. #26026990	C₂	semidirect
17. #26026528	C₂	semidirect
18. #26026062	C₂	semidirect
20. #26024809	C₂	semidirect
21. #26024805	C₂	semidirect
22. #26024381	C₂	semidirect
23. #26024374	C₂	semidirect
24. #26024058	C₂	semidirect
25. #26024054	C₂	semidirect
26. #26023717	C₂	semidirect
27. #26023711	C₂	semidirect
28. #26022986	C₂	semidirect
29. #26022949	C₂	semidirect
30. #388×D₈₉	C₂	semidirect
31. C₈₉×#2674	C₂	semidirect
33. C₂×#15667998	C₂²	semidirect
38. C₂×#15667988	C₂²	semidirect
49. C₈₉⋊#401	C₂²	semidirect
50. C₈₉⋊#401	C₂²	semidirect
51. #19151540	C₂²	semidirect
52. #19151540	C₂²	semidirect
54. #19151534	C₂²	semidirect
57. #19151533	C₂²	semidirect
58. #19151531	C₂²	semidirect
59. #19151528	C₂²	semidirect
66. #19151524	C₂²	semidirect
67. #19151524	C₂²	semidirect
68. #19151523	C₂²	semidirect
70. #19151521	C₂²	semidirect
73. #19151520	C₂²	semidirect
74. #19151517	C₂²	semidirect
91. #19151505	C₂²	semidirect
92. #19151505	C₂²	semidirect
93. #19151503	C₂²	semidirect
94. #19151502	C₂²	semidirect
95. #19151502	C₂²	semidirect
98. #19151498	C₂²	semidirect
99. #19151495	C₂²	semidirect
100. #19151494	C₂²	semidirect
101. #19151494	C₂²	semidirect
102. #19151494	C₂²	semidirect
103. #19151494	C₂²	semidirect
104. #19151493	C₂²	semidirect
105. #19151493	C₂²	semidirect
108. #19151492	C₂²	semidirect
112. #19151491	C₂²	semidirect
113. #19151491	C₂²	semidirect
117. #19151490	C₂²	semidirect
118. #19151490	C₂²	semidirect
121. #19151489	C₂²	semidirect
122. #19151489	C₂²	semidirect
125. #19151488	C₂²	semidirect
129. #19151486	C₂²	semidirect
130. #19151485	C₂²	semidirect
131. #19151485	C₂²	semidirect
132. #19151484	C₂²	semidirect
133. #19151484	C₂²	semidirect
134. #19151484	C₂²	semidirect
135. #19151482	C₂²	semidirect
136. #19151480	C₂²	semidirect
137. #19151479	C₂²	semidirect
138. #19151479	C₂²	semidirect
140. #19151477	C₂²	semidirect
150. #19151474	C₂²	semidirect
152. #19151472	C₂²	semidirect
153. #19151471	C₂²	semidirect
157. #19151469	C₂²	semidirect
158. #19151468	C₂²	semidirect
159. #19151465	C₂²	semidirect
160. #19151465	C₂²	semidirect
161. #19151462	C₂²	semidirect
172. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
175. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
177. #397×C₈₉	C₂²	semidirect
179. #395×C₈₉	C₂²	semidirect
182. #389×C₈₉	C₂²	semidirect
184. #388×C₈₉	C₂²	semidirect
185. #387×C₈₉	C₂²	semidirect
186. #385×C₈₉	C₂²	semidirect
785. #2674	D₈₉	semidirect
799. C₈₉	#36766	semidirect
800. C₂×C₄⋊Q₈	C₂×D₈₉	semidirect
810. C₂×C₂²⋊Q₈	C₂×D₈₉	semidirect
842. #397	C₂×D₈₉	semidirect
850. #395	C₂×D₈₉	semidirect
884. #389	C₂×D₈₉	semidirect
910. #388	C₂×D₈₉	semidirect
920. #387	C₂×D₈₉	semidirect
940. #385	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26028599	2
#26028550	2
#26028157	2
#26028156	2
#26028084	2
#26027797	2
#26027789	2
#26027625	2
#26027618	2
#26027596	2
#26027590	2
#26027245	2
#26027243	2
#26026999	2
#26026990	2
#26026528	2
#26026062	2
#26025991	2
#26024809	2
#26024805	2
#26024381	2
#26024374	2
#26024058	2
#26024054	2
#26023717	2
#26023711	2
#26022986	2
#26022949	2
#388×D₈₉	2
C₈₉×#2674	2
#36766	89