Subgroups — #36763345

Order 22784.

1950 conjugacy classes of subgroups.

The subgroup lattice has 1590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028566	C₂	1	1	yes	maximal, characteristic, complemented
2	#26028548	C₂	1	1	yes	maximal, characteristic, complemented
3	#26028230	C₂	1	1	yes	maximal, characteristic, complemented
4	#26028191	C₂	1	1	yes	maximal, characteristic, complemented
5	#26028181	C₂	1	1	yes	maximal, characteristic, complemented
6	#26027973	C₂	1	1	yes	maximal, characteristic, complemented
7	#26027915	C₂	1	1	yes	maximal, characteristic, complemented
8	#26027886	C₂	1	1	yes	maximal, characteristic, complemented
9	#26027863	C₂	1	1	yes	maximal, characteristic, complemented
10	#26027828	C₂	1	1	yes	maximal, characteristic, complemented
11	#26027613	C₂	1	1	yes	maximal, characteristic, complemented
12	#26027576	C₂	1	1	yes	maximal, characteristic, complemented
13	#26027567	C₂	1	1	yes	maximal, characteristic, complemented
14	#26027499	C₂	1	1	yes	maximal, characteristic, complemented
15	#26027057	C₂	1	1	yes	maximal, characteristic, complemented
16	#26027050	C₂	1	1	yes	maximal, characteristic, complemented
17	#26026652	C₂	1	1	yes	maximal, characteristic, complemented
18	#26026024	C₂	1	1	yes	maximal, characteristic, complemented
19	#26025985	C₂	1	1	yes	maximal, characteristic, complemented
20	#26024811	C₂	1	1	yes	maximal, characteristic, complemented
21	#26024374	C₂	1	1	yes	maximal, characteristic, complemented
22	#26023995	C₂	1	1	yes	maximal, characteristic, complemented
23	#26023925	C₂	1	1	yes	maximal, characteristic, complemented
24	#26023855	C₂	1	1	yes	maximal, characteristic, complemented
25	#26023791	C₂	1	1	yes	maximal, characteristic, complemented
26	#26023634	C₂	1	1	yes	maximal, characteristic, complemented
27	#26023566	C₂	1	1	yes	maximal, characteristic, complemented
28	#26022922	C₂	1	1	yes	maximal, characteristic, complemented
29	#26022842	C₂	1	1	yes	maximal, characteristic, complemented
30	#388×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
31	C₈₉×#2733	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×#13083573	C₂²	1	1	yes	characteristic
33	C₂×#15668005	C₂²	1	1	yes	characteristic, complemented
34	C₂×#15667994	C₂²	1	1	yes	characteristic
35	C₂×#15667988	C₂²	1	1	yes	characteristic
36	C₂×#15667984	C₂²	1	1	yes	characteristic
37	C₂×#15667983	C₂²	1	1	yes	characteristic
38	C₂×#15667983	C₂²	1	1	yes	characteristic
39	C₂×#15667980	C₂²	1	1	yes	characteristic
40	C₂×#15667980	C₂²	1	1	yes	characteristic
41	C₂×#15667980	C₂²	1	1	yes	characteristic
42	C₂×#15667972	C₂²	1	1	yes	characteristic
43	C₂×#15667969	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	#19151540	C₂²	1	1	yes	characteristic, complemented
51	#19151539	C₂²	1	1	yes	characteristic, complemented
52	#19151536	C₂²	1	1	yes	characteristic, complemented
53	#19151532	C₂²	1	1	yes	characteristic, complemented
54	#19151528	C₂²	1	1	yes	characteristic, complemented
55	#19151527	C₂²	1	1	yes	characteristic
56	#19151526	C₂²	1	1	yes	characteristic
57	#19151526	C₂²	1	1	yes	characteristic
58	#19151526	C₂²	1	1	yes	characteristic, complemented
59	#19151526	C₂²	1	1	yes	characteristic, complemented
60	#19151526	C₂²	1	1	yes	characteristic, complemented
61	#19151526	C₂²	1	1	yes	characteristic, complemented
62	#19151525	C₂²	1	1	yes	characteristic
63	#19151524	C₂²	1	1	yes	characteristic
64	#19151523	C₂²	1	1	yes	characteristic
65	#19151523	C₂²	1	1	yes	characteristic
66	#19151521	C₂²	1	1	yes	characteristic
67	#19151521	C₂²	1	1	yes	characteristic
68	#19151520	C₂²	1	1	yes	characteristic
69	#19151519	C₂²	1	1	yes	characteristic, complemented
70	#19151517	C₂²	1	1	yes	characteristic, complemented
71	#19151514	C₂²	1	1	yes	characteristic
72	#19151514	C₂²	1	1	yes	characteristic
73	#19151514	C₂²	1	1	yes	characteristic
74	#19151513	C₂²	1	1	yes	characteristic
75	#19151513	C₂²	1	1	yes	characteristic
76	#19151513	C₂²	1	1	yes	characteristic
77	#19151513	C₂²	1	1	yes	characteristic
78	#19151513	C₂²	1	1	yes	characteristic
79	#19151512	C₂²	1	1	yes	characteristic
80	#19151512	C₂²	1	1	yes	characteristic
81	#19151512	C₂²	1	1	yes	characteristic
82	#19151512	C₂²	1	1	yes	characteristic
83	#19151512	C₂²	1	1	yes	characteristic
84	#19151512	C₂²	1	1	yes	characteristic, complemented
85	#19151511	C₂²	1	1	yes	characteristic
86	#19151510	C₂²	1	1	yes	characteristic
87	#19151510	C₂²	1	1	yes	characteristic, complemented
88	#19151509	C₂²	1	1	yes	characteristic
89	#19151506	C₂²	1	1	yes	characteristic
90	#19151506	C₂²	1	1	yes	characteristic
91	#19151505	C₂²	1	1	yes	characteristic, complemented
92	#19151504	C₂²	1	1	yes	characteristic, complemented
93	#19151503	C₂²	1	1	yes	characteristic, complemented
94	#19151501	C₂²	1	1	yes	characteristic
95	#19151501	C₂²	1	1	yes	characteristic, complemented
96	#19151501	C₂²	1	1	yes	characteristic, complemented
97	#19151498	C₂²	1	1	yes	characteristic
98	#19151498	C₂²	1	1	yes	characteristic
99	#19151496	C₂²	1	1	yes	characteristic, complemented
100	#19151495	C₂²	1	1	yes	characteristic, complemented
101	#19151493	C₂²	1	1	yes	characteristic, complemented
102	#19151492	C₂²	1	1	yes	characteristic
103	#19151492	C₂²	1	1	yes	characteristic
104	#19151492	C₂²	1	1	yes	characteristic, complemented
105	#19151492	C₂²	1	1	yes	characteristic, complemented
106	#19151492	C₂²	1	1	yes	characteristic, complemented
107	#19151491	C₂²	1	1	yes	characteristic
108	#19151491	C₂²	1	1	yes	characteristic
109	#19151491	C₂²	1	1	yes	characteristic, complemented
110	#19151490	C₂²	1	1	yes	characteristic
111	#19151490	C₂²	1	1	yes	characteristic
112	#19151489	C₂²	1	1	yes	characteristic
113	#19151489	C₂²	1	1	yes	characteristic
114	#19151489	C₂²	1	1	yes	characteristic
115	#19151488	C₂²	1	1	yes	characteristic
116	#19151487	C₂²	1	1	yes	characteristic
117	#19151486	C₂²	1	1	yes	characteristic
118	#19151486	C₂²	1	1	yes	characteristic, complemented
119	#19151486	C₂²	1	1	yes	characteristic, complemented
120	#19151486	C₂²	1	1	yes	characteristic, complemented
121	#19151486	C₂²	1	1	yes	characteristic, complemented
122	#19151486	C₂²	1	1	yes	characteristic, complemented
123	#19151485	C₂²	1	1	yes	characteristic, complemented
124	#19151485	C₂²	1	1	yes	characteristic, complemented
125	#19151484	C₂²	1	1	yes	characteristic, complemented
126	#19151484	C₂²	1	1	yes	characteristic, complemented
127	#19151482	C₂²	1	1	yes	characteristic, complemented
128	#19151482	C₂²	1	1	yes	characteristic, complemented
129	#19151482	C₂²	1	1	yes	characteristic, complemented
130	#19151481	C₂²	1	1	yes	characteristic, complemented
131	#19151481	C₂²	1	1	yes	characteristic, complemented
132	#19151478	C₂²	1	1	yes	characteristic
133	#19151478	C₂²	1	1	yes	characteristic
134	#19151478	C₂²	1	1	yes	characteristic
135	#19151478	C₂²	1	1	yes	characteristic, complemented
136	#19151478	C₂²	1	1	yes	characteristic, complemented
137	#19151478	C₂²	1	1	yes	characteristic, complemented
138	#19151475	C₂²	1	1	yes	characteristic
139	#19151475	C₂²	1	1	yes	characteristic
140	#19151474	C₂²	1	1	yes	characteristic
141	#19151474	C₂²	1	1	yes	characteristic
142	#19151474	C₂²	1	1	yes	characteristic
143	#19151474	C₂²	1	1	yes	characteristic
144	#19151474	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	#19151473	C₂²	1	1	yes	characteristic, complemented
151	#19151473	C₂²	1	1	yes	characteristic, complemented
152	#19151473	C₂²	1	1	yes	characteristic, complemented
153	#19151472	C₂²	1	1	yes	characteristic
154	#19151472	C₂²	1	1	yes	characteristic
155	#19151470	C₂²	1	1	yes	characteristic, complemented
156	#19151469	C₂²	1	1	yes	characteristic
157	#19151469	C₂²	1	1	yes	characteristic
158	#19151465	C₂²	1	1	yes	characteristic, complemented
159	#19151465	C₂²	1	1	yes	characteristic, complemented
160	#19151464	C₂²	1	1	yes	characteristic, complemented
161	#19151460	C₂²	1	1	yes	characteristic
162	#19151459	C₂²	1	1	yes	characteristic, complemented
163	#19151457	C₂²	1	1	yes	characteristic
164	#19151456	C₂²	1	1	yes	characteristic, complemented
165	#19151456	C₂²	1	1	yes	characteristic, complemented
166	#19151456	C₂²	1	1	yes	characteristic, complemented
167	#19151456	C₂²	1	1	yes	characteristic, complemented
168	#19151453	C₂²	1	1	yes	characteristic
169	C₄×#13083551	C₂²	1	1	yes	characteristic
170	#95×D₈₉	C₂²	1	1	yes	characteristic
171	#95×D₈₉	C₂²	1	1	yes	characteristic
172	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
173	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
174	#394×C₈₉	C₂²	1	1	yes	characteristic
175	#394×C₈₉	C₂²	1	1	yes	characteristic, complemented
176	#392×C₈₉	C₂²	1	1	yes	characteristic
177	#392×C₈₉	C₂²	1	1	yes	characteristic
178	#392×C₈₉	C₂²	1	1	yes	characteristic
179	#392×C₈₉	C₂²	1	1	yes	characteristic, complemented
180	#391×C₈₉	C₂²	1	1	yes	characteristic, complemented
181	#390×C₈₉	C₂²	1	1	yes	characteristic
182	#390×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	#388×C₈₉	C₂²	1	1	yes	characteristic, complemented
186	#388×C₈₉	C₂²	1	1	yes	characteristic, complemented
187	C₂⁴×D₈₉	C₂³	1	1	yes	characteristic
188	C₂×#13083573	—	2	4	no	—
189	C₂×#13083573	—	4	2	no	—
190	C₂×#13083573	—	4	2	no	—
191	C₂²×Dic₁₇₈	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×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
196	C₂²×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
197	C₂²×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
198	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
199	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
200	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
201	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
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	#15668005	—	4	2	no	—
208	#15667994	—	2	4	no	—
209	#15667988	—	4	2	no	—
210	#15667984	—	4	2	no	—
211	#15667983	—	4	2	no	—
212	#15667983	—	4	2	no	—
213	#15667980	—	4	2	no	—
214	#15667980	—	4	2	no	—
215	#15667980	—	4	2	no	—
216	#15667972	—	4	2	no	—
217	#15667969	—	4	2	no	—
218	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
225	C₂×#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	C₄⋊C₄×D₈₉	—	4	2	no	—
240	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
241	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
242	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
243	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
244	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
245	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
246	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
247	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
248	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
249	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
252	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
253	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
254	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
257	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊Dic₈₉	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	C₂×#13083551	C₂³	1	1	yes	characteristic
277	C₂×#13083551	C₂³	1	1	yes	characteristic
278	C₂²⋊C₄×D₈₉	—	2	4	no	—
279	C₂²⋊C₄×D₈₉	—	4	2	no	—
280	C₂²⋊C₄×D₈₉	—	4	2	no	—
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	#15667919	C₂³	1	1	yes	characteristic
325	#15667919	C₂³	1	1	yes	characteristic
326	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
327	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
328	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
329	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
330	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
331	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
332	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
333	#124×C₈₉	—	4	2	no	—
334	#124×C₈₉	—	4	2	no	—
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×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
339	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
340	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
341	C₂×C₂²⋊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×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
354	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
355	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
356	C₂×C₄²×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	#13083573	—	4	16	no	—
373	C₂×Dic₁₇₈	—	2	2	no	—
374	C₂×Dic₁₇₈	—	4	1	no	—
375	C₂×Dic₁₇₈	—	4	1	no	—
376	C₂×C₂²⋊D₈₉	—	2	2	no	—
377	C₂×C₂²⋊D₈₉	—	2	2	no	—
378	C₂×C₂²⋊D₈₉	—	2	2	no	—
379	C₂×C₂²⋊D₈₉	—	2	2	no	—
380	C₂×C₂²⋊D₈₉	—	2	2	no	—
381	C₂×C₂²⋊D₈₉	—	2	2	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	—	4	1	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	—	2	2	no	—
395	C₂²×Dic₈₉	—	2	2	no	—
396	C₂²×Dic₈₉	—	4	1	no	—
397	C₂²×Dic₈₉	—	4	1	no	—
398	C₂²×Dic₈₉	—	4	1	no	—
399	C₂²×Dic₈₉	—	4	1	no	—
400	C₂²×Dic₈₉	—	4	1	no	—
401	C₂²×Dic₈₉	—	4	1	no	—
402	C₂²×Dic₈₉	—	4	1	no	—
403	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
404	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
405	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
406	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
407	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
408	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
409	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
410	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
411	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
412	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
413	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
414	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
415	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
416	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
417	C₂×C₄×D₈₉	—	2	2	no	—
418	C₂×C₄×D₈₉	—	2	2	no	—
419	C₂×C₄×D₈₉	—	2	2	no	—
420	C₂×C₄×D₈₉	—	2	2	no	—
421	C₂×C₄×D₈₉	—	2	2	no	—
422	C₂×C₄×D₈₉	—	2	2	no	—
423	C₂×C₄×D₈₉	—	2	2	no	—
424	C₂×C₄×D₈₉	—	2	2	no	—
425	C₂×C₄×D₈₉	—	4	1	no	—
426	C₂×C₄×D₈₉	—	4	1	no	—
427	C₂×C₄×D₈₉	—	4	1	no	—
428	C₂×C₄×D₈₉	—	4	1	no	—
429	C₂×C₄×D₈₉	—	4	1	no	—
430	C₂×C₄×D₈₉	—	4	1	no	—
431	C₂×C₄×D₈₉	—	4	1	no	—
432	C₂×C₄×D₈₉	—	4	1	no	—
433	C₂×C₄×D₈₉	—	4	1	no	—
434	C₂×C₄×D₈₉	#41	1	4	yes	—
435	C₄⋊Dic₈₉	—	2	2	no	—
436	C₄⋊Dic₈₉	—	4	1	no	—
437	C₄⋊Dic₈₉	—	4	1	no	—
438	C₄⋊Dic₈₉	—	4	1	no	—
439	C₄⋊Dic₈₉	—	4	1	no	—
440	C₄⋊Dic₈₉	—	4	1	no	—
441	C₄⋊Dic₈₉	—	4	1	no	—
442	#13083553	—	2	2	no	—
443	#13083553	—	2	2	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	#13083553	—	4	1	no	—
451	#13083553	—	4	1	no	—
452	#13083553	—	4	1	no	—
453	#13083553	—	4	1	no	—
454	#13083553	—	4	1	no	—
455	#13083553	—	4	1	no	—
456	C₂²⋊Dic₈₉	—	2	2	no	—
457	C₂²⋊Dic₈₉	—	2	2	no	—
458	C₂²⋊Dic₈₉	—	4	1	no	—
459	C₂²⋊Dic₈₉	—	4	1	no	—
460	C₂²⋊Dic₈₉	—	4	1	no	—
461	C₂²⋊Dic₈₉	—	4	1	no	—
462	C₂²⋊Dic₈₉	—	4	1	no	—
463	C₂²⋊Dic₈₉	—	4	1	no	—
464	C₂²⋊Dic₈₉	—	4	1	no	—
465	C₂²⋊Dic₈₉	—	4	1	no	—
466	C₂²⋊Dic₈₉	—	4	1	no	—
467	C₂²⋊Dic₈₉	—	4	1	no	—
468	C₂²⋊Dic₈₉	—	4	1	no	—
469	C₂²⋊Dic₈₉	—	4	1	no	—
470	C₂²⋊Dic₈₉	—	4	1	no	—
471	C₂²⋊Dic₈₉	—	4	1	no	—
472	C₂²⋊Dic₈₉	—	4	1	no	—
473	C₂²⋊Dic₈₉	—	4	1	no	—
474	C₂²⋊Dic₈₉	—	4	1	no	—
475	C₂²⋊Dic₈₉	—	4	1	no	—
476	C₂²⋊Dic₈₉	—	4	1	no	—
477	C₂²⋊Dic₈₉	—	4	1	no	—
478	#13083551	—	2	2	no	—
479	#13083551	—	2	2	no	—
480	#13083551	—	2	2	no	—
481	#13083551	—	2	2	no	—
482	#13083551	—	2	2	no	—
483	#13083551	—	2	2	no	—
484	#13083551	—	2	2	no	—
485	#13083551	—	2	2	no	—
486	#13083551	—	4	1	no	—
487	#13083551	—	4	1	no	—
488	#13083551	—	4	1	no	—
489	#13083551	—	4	1	no	—
490	#13083551	—	4	1	no	—
491	#13083551	—	4	1	no	—
492	#13083551	—	4	1	no	—
493	#13083551	—	4	1	no	—
494	C₄×Dic₈₉	—	2	2	no	—
495	C₄×Dic₈₉	—	4	1	no	—
496	C₄×Dic₈₉	—	4	1	no	—
497	C₄×Dic₈₉	—	4	1	no	—
498	C₄×Dic₈₉	—	4	1	no	—
499	C₄×Dic₈₉	—	4	1	no	—
500	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
501	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
502	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
503	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
504	C₂×Q₈×C₈₉	—	2	2	no	—
505	C₂×Q₈×C₈₉	—	4	1	no	—
506	C₂×Q₈×C₈₉	—	4	1	no	—
507	C₂×D₄×C₈₉	—	2	2	no	—
508	C₂×D₄×C₈₉	—	2	2	no	—
509	C₂×D₄×C₈₉	—	4	1	no	—
510	C₂×D₄×C₈₉	—	4	1	no	—
511	C₂×D₄×C₈₉	—	4	1	no	—
512	C₂×D₄×C₈₉	—	4	1	no	—
513	C₂×D₄×C₈₉	—	4	1	no	—
514	C₂×D₄×C₈₉	—	4	1	no	—
515	C₂×D₄×C₈₉	—	4	1	no	—
516	C₂×D₄×C₈₉	—	4	1	no	—
517	C₂×D₄×C₈₉	—	4	1	no	—
518	C₂×D₄×C₈₉	—	4	1	no	—
519	C₂×D₄×C₈₉	—	4	1	no	—
520	C₂×D₄×C₈₉	—	4	1	no	—
521	C₂×D₄×C₈₉	—	4	1	no	—
522	C₂×D₄×C₈₉	—	4	1	no	—
523	C₂×D₄×C₈₉	—	4	1	no	—
524	C₂×D₄×C₈₉	—	4	1	no	—
525	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
526	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
527	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
528	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
529	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
530	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
531	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₈₉	—	4	1	no	—
537	C₄⋊C₄×C₈₉	—	4	1	no	—
538	C₄⋊C₄×C₈₉	—	4	1	no	—
539	C₂²⋊C₄×C₈₉	—	2	2	no	—
540	C₂²⋊C₄×C₈₉	—	2	2	no	—
541	C₂²⋊C₄×C₈₉	—	2	2	no	—
542	C₂²⋊C₄×C₈₉	—	2	2	no	—
543	C₂²⋊C₄×C₈₉	—	4	1	no	—
544	C₂²⋊C₄×C₈₉	—	4	1	no	—
545	C₂²⋊C₄×C₈₉	—	4	1	no	—
546	C₂²⋊C₄×C₈₉	—	4	1	no	—
547	C₂²⋊C₄×C₈₉	—	4	1	no	—
548	C₂²⋊C₄×C₈₉	—	4	1	no	—
549	C₂²⋊C₄×C₈₉	—	4	1	no	—
550	C₂²⋊C₄×C₈₉	—	4	1	no	—
551	C₂²⋊C₄×C₈₉	—	4	1	no	—
552	C₂²⋊C₄×C₈₉	—	4	1	no	—
553	C₂²⋊C₄×C₈₉	—	4	1	no	—
554	C₂²⋊C₄×C₈₉	—	4	1	no	—
555	C₄²×C₈₉	—	2	2	no	—
556	C₄²×C₈₉	—	4	1	no	—
557	C₄²×C₈₉	—	4	1	no	—
558	C₂³×C₈₉	—	2	1	no	—
559	C₂³×C₈₉	—	2	1	no	—
560	C₂³×C₈₉	—	2	1	no	—
561	C₂³×C₈₉	—	2	1	no	—
562	C₂³×C₈₉	—	2	1	no	—
563	C₂³×C₈₉	—	2	1	no	—
564	C₂³×C₈₉	—	2	1	no	—
565	C₂³×C₈₉	—	2	1	no	—
566	C₂³×C₈₉	—	2	1	no	—
567	C₂³×C₈₉	—	2	1	no	—
568	C₂³×C₈₉	—	2	1	no	—
569	C₂³×C₈₉	—	2	1	no	—
570	C₂³×C₈₉	—	2	1	no	—
571	C₂³×C₈₉	—	2	1	no	—
572	C₂³×C₈₉	—	2	1	no	—
573	C₂³×C₈₉	—	2	1	no	—
574	C₂³×C₈₉	—	2	1	no	—
575	C₂³×C₈₉	—	2	1	no	—
576	C₂³×C₈₉	—	2	1	no	—
577	C₂³×C₈₉	—	2	1	no	—
578	C₂³×C₈₉	—	2	1	no	—
579	C₂³×C₈₉	—	2	1	no	—
580	C₂³×C₈₉	—	2	1	no	—
581	C₂³×C₈₉	—	2	1	no	—
582	C₂³×C₈₉	—	2	1	no	—
583	C₂³×C₈₉	—	2	1	no	—
584	C₂³×C₈₉	—	2	1	no	—
585	C₂³×C₈₉	—	2	1	no	—
586	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
587	C₂²×D₈₉	—	2	1	no	—
588	C₂²×D₈₉	—	2	1	no	—
589	C₂²×D₈₉	—	2	1	no	—
590	C₂²×D₈₉	—	2	1	no	—
591	C₂²×D₈₉	—	2	1	no	—
592	C₂²×D₈₉	—	2	1	no	—
593	C₂²×D₈₉	—	2	1	no	—
594	C₂²×D₈₉	—	2	1	no	—
595	C₂²×D₈₉	—	2	1	no	—
596	C₂²×D₈₉	—	2	1	no	—
597	C₂²×D₈₉	—	2	1	no	—
598	C₂²×D₈₉	—	4	4	no	—
599	C₂²×D₈₉	—	4	4	no	—
600	C₂²×D₈₉	—	4	4	no	—
601	C₂²×D₈₉	—	8	2	no	—
602	C₂²×D₈₉	—	8	2	no	—
603	C₂²×D₈₉	—	8	2	no	—
604	C₂²×D₈₉	—	8	2	no	—
605	C₂²×D₈₉	C₂×#41	1	2	yes	—
606	C₂²×D₈₉	H(5,𝔽₂)	1	2	yes	—
607	C₂²×D₈₉	H(5,𝔽₂)	1	2	yes	—
608	Q₈×C₈₉	—	8	2	no	—
609	D₄×C₈₉	—	4	4	no	—
610	D₄×C₈₉	—	8	2	no	—
611	D₄×C₈₉	—	8	2	no	—
612	D₄×C₈₉	—	8	2	no	—
613	D₄×C₈₉	—	8	2	no	—
614	D₄×C₈₉	—	8	2	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	—	2	1	no	—
638	C₂×C₄×C₈₉	—	2	1	no	—
639	C₂×C₄×C₈₉	—	2	1	no	—
640	C₂×C₄×C₈₉	—	2	1	no	—
641	C₂×C₄×C₈₉	—	2	1	no	—
642	C₂×C₄×C₈₉	—	2	1	no	—
643	C₂×C₄×C₈₉	—	2	1	no	—
644	C₂×C₄×C₈₉	—	2	1	no	—
645	C₂×C₄×C₈₉	—	2	1	no	—
646	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
647	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
648	C₂²⋊D₈₉	—	4	4	no	—
649	C₂²⋊D₈₉	—	4	4	no	—
650	C₂²⋊D₈₉	—	4	4	no	—
651	C₂²⋊D₈₉	—	8	2	no	—
652	C₂²⋊D₈₉	—	8	2	no	—
653	C₂²⋊D₈₉	—	8	2	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	—	2	1	no	—
681	C₂×Dic₈₉	—	2	1	no	—
682	C₂×Dic₈₉	—	2	1	no	—
683	C₂×Dic₈₉	—	2	1	no	—
684	C₂×Dic₈₉	—	2	1	no	—
685	C₂×Dic₈₉	—	2	1	no	—
686	C₂×Dic₈₉	—	2	1	no	—
687	C₂×Dic₈₉	—	2	1	no	—
688	C₂×Dic₈₉	—	2	1	no	—
689	C₂×Dic₈₉	—	2	1	no	—
690	C₂×Dic₈₉	—	2	1	no	—
691	C₂×Dic₈₉	—	2	1	no	—
692	C₂×Dic₈₉	—	2	1	no	—
693	C₂×Dic₈₉	—	2	1	no	—
694	C₂×Dic₈₉	—	2	1	no	—
695	C₂×Dic₈₉	—	4	4	no	—
696	C₂×Dic₈₉	—	4	4	no	—
697	C₂×Dic₈₉	—	8	2	no	—
698	C₂×Dic₈₉	C₂×#41	1	2	yes	—
699	C₄×D₈₉	—	2	8	no	—
700	C₄×D₈₉	—	4	4	no	—
701	C₄×D₈₉	—	4	4	no	—
702	C₄×D₈₉	—	4	4	no	—
703	C₄×D₈₉	—	8	2	no	—
704	C₄×D₈₉	—	8	2	no	—
705	Dic₁₇₈	—	4	4	no	—
706	C₂²×C₈₉	—	4	1	no	—
707	C₂²×C₈₉	—	4	1	no	—
708	C₂²×C₈₉	—	4	1	no	—
709	C₂²×C₈₉	—	4	1	no	—
710	C₂²×C₈₉	—	4	1	no	—
711	C₂²×C₈₉	—	4	1	no	—
712	C₂²×C₈₉	—	4	1	no	—
713	C₂²×C₈₉	—	4	1	no	—
714	C₂²×C₈₉	—	4	1	no	—
715	C₂²×C₈₉	—	4	1	no	—
716	C₂²×C₈₉	—	4	1	no	—
717	C₂²×C₈₉	—	4	1	no	—
718	C₂²×C₈₉	—	4	1	no	—
719	C₂²×C₈₉	—	4	1	no	—
720	C₂²×C₈₉	—	4	1	no	—
721	C₂²×C₈₉	—	4	1	no	—
722	C₂²×C₈₉	—	4	1	no	—
723	C₂²×C₈₉	—	4	1	no	—
724	C₂²×C₈₉	—	4	1	no	—
725	C₂²×C₈₉	—	4	1	no	—
726	C₂²×C₈₉	—	4	1	no	—
727	C₂²×C₈₉	—	4	1	no	—
728	C₂²×C₈₉	—	4	1	no	—
729	C₂²×C₈₉	—	4	1	no	—
730	C₂²×C₈₉	—	4	1	no	—
731	C₂²×C₈₉	—	4	1	no	—
732	C₂²×C₈₉	—	4	1	no	—
733	C₂²×C₈₉	—	4	1	no	—
734	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
735	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
736	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
737	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
738	C₂²×C₈₉	#585	1	1	yes	characteristic
739	C₂²×C₈₉	#585	1	1	yes	characteristic
740	C₂²×C₈₉	#585	1	1	yes	characteristic
741	C₂×D₈₉	—	2	2	no	—
742	C₂×D₈₉	—	2	2	no	—
743	C₂×D₈₉	—	2	2	no	—
744	C₂×D₈₉	—	2	2	no	—
745	C₂×D₈₉	—	2	2	no	—
746	C₂×D₈₉	—	2	2	no	—
747	C₂×D₈₉	—	4	1	no	—
748	C₂×D₈₉	—	4	1	no	—
749	C₂×D₈₉	—	4	1	no	—
750	C₂×D₈₉	—	4	1	no	—
751	C₂×D₈₉	—	4	1	no	—
752	C₂×D₈₉	—	4	1	no	—
753	C₂×D₈₉	—	4	1	no	—
754	C₂×D₈₉	—	8	8	no	—
755	C₂×D₈₉	#538	1	4	yes	—
756	C₄×C₈₉	—	2	2	no	—
757	C₄×C₈₉	—	2	2	no	—
758	C₄×C₈₉	—	4	1	no	—
759	C₄×C₈₉	—	4	1	no	—
760	C₄×C₈₉	—	4	1	no	—
761	C₄×C₈₉	—	4	1	no	—
762	C₄×C₈₉	—	4	1	no	—
763	C₄×C₈₉	—	4	1	no	—
764	C₄×C₈₉	—	4	1	no	—
765	C₄×C₈₉	—	4	1	no	—
766	C₄×C₈₉	—	4	1	no	—
767	Dic₈₉	—	2	2	no	—
768	Dic₈₉	—	4	1	no	—
769	Dic₈₉	—	4	1	no	—
770	Dic₈₉	—	4	1	no	—
771	Dic₈₉	—	4	1	no	—
772	Dic₈₉	—	4	1	no	—
773	Dic₈₉	—	4	1	no	—
774	Dic₈₉	—	4	1	no	—
775	Dic₈₉	—	4	1	no	—
776	Dic₈₉	—	4	1	no	—
777	Dic₈₉	—	4	1	no	—
778	Dic₈₉	—	4	1	no	—
779	Dic₈₉	—	4	1	no	—
780	Dic₈₉	—	4	1	no	—
781	#36795	—	89	1	no	maximal, Sylow
782	C₂×C₈₉	—	8	1	no	—
783	C₂×C₈₉	—	8	1	no	—
784	C₂×C₈₉	—	8	1	no	—
785	C₂×C₈₉	—	8	1	no	—
786	C₂×C₈₉	C₂×#538	1	1	yes	characteristic
787	C₂×C₈₉	#3493	1	1	yes	characteristic
788	C₂×C₈₉	#3506	1	1	yes	characteristic
789	C₂×C₈₉	#3534	1	1	yes	characteristic
790	C₂×C₈₉	#3542	1	1	yes	characteristic
791	C₂×C₈₉	#3545	1	1	yes	characteristic
792	C₂×C₈₉	#3560	1	1	yes	characteristic
793	D₈₉	—	2	4	no	—
794	D₈₉	—	8	1	no	—
795	#2852	—	89	1	no	—
796	#2850	—	89	1	no	—
797	#2808	—	89	1	no	—
798	#2803	—	89	1	no	—
799	#2803	—	89	1	no	—
800	#2786	—	89	1	no	—
801	#2781	—	89	1	no	—
802	#2779	—	89	1	no	—
803	#2778	—	89	1	no	—
804	#2775	—	89	1	no	—
805	#2759	—	89	1	no	—
806	#2756	—	89	1	no	—
807	#2756	—	89	1	no	—
808	#2751	—	89	1	no	—
809	#2733	D₈₉	1	1	yes	characteristic, complemented
810	#2715	—	89	1	no	—
811	#2714	—	89	1	no	—
812	#2686	—	89	1	no	—
813	#2622	—	89	1	no	—
814	#2617	—	89	1	no	—
815	#2510	—	89	1	no	—
816	#2472	—	89	1	no	—
817	#2444	—	89	1	no	—
818	#2438	—	89	1	no	—
819	#2430	—	89	1	no	—
820	#2424	—	89	1	no	—
821	#2411	—	89	1	no	—
822	#2404	—	89	1	no	—
823	#2322	—	89	1	no	—
824	#2311	—	89	1	no	—
825	C₂×#388	—	89	1	no	—
826	C₈₉	#36795	1	1	yes	characteristic, complemented, Sylow
827	C₂²×#41	—	89	1	no	—
828	C₂×#126	—	89	1	no	—
829	C₂×#124	C₂×D₈₉	1	1	yes	characteristic
830	C₂×#124	C₂×D₈₉	1	1	yes	characteristic, complemented
831	C₂×#123	—	89	1	no	—
832	C₂×C₂²⋊Q₈	—	89	1	no	—
833	C₂×#121	—	89	1	no	—
834	C₂×#121	—	89	1	no	—
835	C₂×#121	—	89	1	no	—
836	C₂×#120	—	89	1	no	—
837	C₂×#120	—	89	1	no	—
838	C₂×#120	—	89	1	no	—
839	C₂×C₄×D₄	—	89	1	no	—
840	C₂×#117	—	89	1	no	—
841	C₂²×C₄⋊C₄	—	89	1	no	—
842	C₂²×C₂²⋊C₄	—	89	1	no	—
843	C₂²×C₂²⋊C₄	—	89	1	no	—
844	C₂²×C₂²⋊C₄	—	89	1	no	—
845	C₂²×C₄²	—	89	1	no	—
846	#401	—	89	1	no	—
847	#400	—	89	1	no	—
848	#400	—	89	1	no	—
849	#400	—	89	1	no	—
850	#398	—	89	1	no	—
851	#398	—	89	1	no	—
852	#397	—	89	1	no	—
853	#397	—	89	1	no	—
854	#397	—	89	1	no	—
855	#397	—	89	1	no	—
856	#397	—	89	1	no	—
857	#397	—	89	1	no	—
858	#397	—	89	1	no	—
859	#397	—	89	1	no	—
860	#397	—	89	1	no	—
861	#397	—	89	1	no	—
862	#397	—	89	1	no	—
863	#396	—	89	1	no	—
864	#396	—	89	1	no	—
865	#396	—	89	1	no	—
866	#395	—	89	1	no	—
867	#395	—	89	1	no	—
868	#394	—	89	1	no	—
869	#394	—	89	1	no	—
870	#394	—	89	1	no	—
871	#394	—	89	1	no	—
872	#394	—	89	1	no	—
873	#394	—	89	1	no	—
874	#394	—	89	1	no	—
875	#394	—	89	1	no	—
876	#394	—	89	1	no	—
877	#394	—	89	1	no	—
878	#394	—	89	1	no	—
879	#394	—	89	1	no	—
880	#394	—	89	1	no	—
881	#394	—	89	1	no	—
882	#394	C₂×D₈₉	1	1	yes	characteristic
883	#394	C₂×D₈₉	1	1	yes	characteristic, complemented
884	#393	—	89	1	no	—
885	#393	—	89	1	no	—
886	#393	—	89	1	no	—
887	#393	—	89	1	no	—
888	#392	—	89	1	no	—
889	#392	—	89	1	no	—
890	#392	C₂×D₈₉	1	1	yes	characteristic
891	#392	C₂×D₈₉	1	1	yes	characteristic
892	#392	C₂×D₈₉	1	1	yes	characteristic
893	#392	C₂×D₈₉	1	1	yes	characteristic, complemented
894	#391	—	89	1	no	—
895	#391	—	89	1	no	—
896	#391	—	89	1	no	—
897	#391	C₂×D₈₉	1	1	yes	characteristic, complemented
898	#390	—	89	1	no	—
899	#390	—	89	1	no	—
900	#390	—	89	1	no	—
901	#390	—	89	1	no	—
902	#390	—	89	1	no	—
903	#390	C₂×D₈₉	1	1	yes	characteristic
904	#390	C₂×D₈₉	1	1	yes	characteristic, complemented
905	#389	—	89	1	no	—
906	#389	—	89	1	no	—
907	#389	—	89	1	no	—
908	#388	—	89	1	no	—
909	#388	—	89	1	no	—
910	#388	—	89	1	no	—
911	#388	—	89	1	no	—
912	#388	—	89	1	no	—
913	#388	—	89	1	no	—
914	#388	—	89	1	no	—
915	#388	—	89	1	no	—
916	#388	—	89	1	no	—
917	#388	—	89	1	no	—
918	#388	—	89	1	no	—
919	#388	—	89	1	no	—
920	#388	—	89	1	no	—
921	#388	—	89	1	no	—
922	#388	—	89	1	no	—
923	#388	—	89	1	no	—
924	#388	—	89	1	no	—
925	#388	—	89	1	no	—
926	#388	—	89	1	no	—
927	#388	—	89	1	no	—
928	#388	—	89	1	no	—
929	#388	C₂×D₈₉	1	1	yes	characteristic
930	#388	C₂×D₈₉	1	1	yes	characteristic, complemented
931	#388	C₂×D₈₉	1	1	yes	characteristic, complemented
932	#388	C₂×D₈₉	1	1	yes	characteristic, complemented
933	#387	—	89	1	no	—
934	#387	—	89	1	no	—
935	#387	—	89	1	no	—
936	#387	—	89	1	no	—
937	#387	—	89	1	no	—
938	#387	—	89	1	no	—
939	#387	—	89	1	no	—
940	#387	—	89	1	no	—
941	#387	—	89	1	no	—
942	#386	—	89	1	no	—
943	#386	—	89	1	no	—
944	#386	—	89	1	no	—
945	#386	—	89	1	no	—
946	#386	—	89	1	no	—
947	#386	—	89	1	no	—
948	#386	—	89	1	no	—
949	#386	—	89	1	no	—
950	#386	—	89	1	no	—
951	#386	—	89	1	no	—
952	#386	—	89	1	no	—
953	#386	—	89	1	no	—
954	#386	—	89	1	no	—
955	#386	—	89	1	no	—
956	#386	—	89	1	no	—
957	#386	—	89	1	no	—
958	#386	—	89	1	no	—
959	#386	—	89	1	no	—
960	#385	—	89	1	no	—
961	#385	—	89	1	no	—
962	#385	—	89	1	no	—
963	#385	—	89	1	no	—
964	#385	—	89	1	no	—
965	#385	—	89	1	no	—
966	#385	—	89	1	no	—
967	#385	—	89	1	no	—
968	#383	—	89	1	no	—
969	#383	—	89	1	no	—
970	#382	—	89	1	no	—
971	#381	—	89	1	no	—
972	#381	—	89	1	no	—
973	#380	—	89	1	no	—
974	#380	—	89	1	no	—
975	#380	—	89	1	no	—
976	#380	—	89	1	no	—
977	#380	—	89	1	no	—
978	#379	—	89	1	no	—
979	C₄×C₂²⋊C₄	—	89	1	no	—
980	C₂×#95	—	89	1	no	—
981	C₂×#95	—	89	1	no	—
982	C₂⁵	—	89	1	no	—
983	C₂×#41	—	356	2	no	—
984	C₂×#41	—	356	2	no	—
985	C₂×#41	—	178	4	no	—
986	C₂²×Q₈	—	89	1	no	—
987	C₂²×Q₈	C₂²×D₈₉	1	1	yes	characteristic
988	C₂²×D₄	—	89	1	no	—
989	C₂²×D₄	—	89	1	no	—
990	C₂²×D₄	—	89	1	no	—
991	C₂²×D₄	—	89	1	no	—
992	C₂²×D₄	—	89	1	no	—
993	C₂²×D₄	—	89	1	no	—
994	C₂²×D₄	C₂²×D₈₉	1	1	yes	characteristic
995	C₂²×D₄	C₂²×D₈₉	1	1	yes	characteristic
996	C₂²×D₄	C₂²×D₈₉	1	1	yes	characteristic
997	C₂²×D₄	C₂²×D₈₉	1	1	yes	characteristic
998	C₂²×D₄	C₂²×D₈₉	1	1	yes	characteristic
999	C₂²×D₄	C₂²×D₈₉	1	1	yes	characteristic
1000	C₂³×C₄	—	89	1	no	—
1001	C₂³×C₄	—	89	1	no	—
1002	C₂³×C₄	—	89	1	no	—
1003	C₂³×C₄	—	89	1	no	—
1004	C₂³×C₄	—	89	1	no	—
1005	C₂³×C₄	—	89	1	no	—
1006	C₂³×C₄	—	89	1	no	—
1007	C₂³×C₄	—	89	1	no	—
1008	C₂³×C₄	—	89	1	no	—
1009	#126	—	356	2	no	—
1010	#124	—	4	2	no	—
1011	#124	—	4	2	no	—
1012	#123	—	178	4	no	—
1013	C₂²⋊Q₈	—	356	2	no	—
1014	#121	—	356	2	no	—
1015	#121	—	356	2	no	—
1016	#121	—	356	2	no	—
1017	#120	—	356	2	no	—
1018	#120	—	356	2	no	—
1019	#120	—	356	2	no	—
1020	C₄×D₄	—	356	2	no	—
1021	#117	—	356	2	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	—	356	2	no	—
1044	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1045	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1046	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
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	—	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	—	356	2	no	—
1086	C₂×C₂²⋊C₄	—	356	2	no	—
1087	C₂×C₂²⋊C₄	—	178	4	no	—
1088	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
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×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1096	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1097	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1098	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1099	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1100	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1101	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1102	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1103	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1104	C₂×C₄²	—	89	1	no	—
1105	C₂×C₄²	—	89	1	no	—
1106	C₂×C₄²	—	89	1	no	—
1107	C₂×C₄²	—	89	1	no	—
1108	C₂×C₄²	—	89	1	no	—
1109	C₂×C₄²	—	89	1	no	—
1110	C₂×C₄²	—	356	2	no	—
1111	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1112	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1113	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
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	—	89	1	no	—
1142	#95	—	89	1	no	—
1143	#95	—	89	1	no	—
1144	#95	—	89	1	no	—
1145	#95	—	89	1	no	—
1146	#95	—	89	1	no	—
1147	#95	—	89	1	no	—
1148	#95	—	89	1	no	—
1149	#95	—	89	1	no	—
1150	#95	—	89	1	no	—
1151	#95	—	89	1	no	—
1152	#95	C₂²×D₈₉	1	1	yes	characteristic
1153	#95	C₂²×D₈₉	1	1	yes	characteristic
1154	#95	C₂²×D₈₉	1	1	yes	characteristic
1155	#95	C₂²×D₈₉	1	1	yes	characteristic
1156	#95	C₂²×D₈₉	1	1	yes	characteristic
1157	#95	C₂²×D₈₉	1	1	yes	characteristic
1158	C₂⁴	—	89	1	no	—
1159	C₂⁴	—	89	1	no	—
1160	C₂⁴	—	356	1	no	—
1161	C₂⁴	—	356	1	no	—
1162	C₂⁴	—	356	1	no	—
1163	C₂⁴	—	356	1	no	—
1164	C₂⁴	—	178	2	no	—
1165	C₂⁴	—	178	2	no	—
1166	C₂⁴	—	178	2	no	—
1167	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
1168	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
1169	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
1170	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
1171	#41	—	356	16	no	—
1172	C₂×Q₈	—	2	2	no	—
1173	C₂×Q₈	—	4	1	no	—
1174	C₂×Q₈	—	4	1	no	—
1175	C₂×Q₈	—	356	1	no	—
1176	C₂×Q₈	—	356	1	no	—
1177	C₂×Q₈	—	178	2	no	—
1178	C₂×D₄	—	2	2	no	—
1179	C₂×D₄	—	2	2	no	—
1180	C₂×D₄	—	4	1	no	—
1181	C₂×D₄	—	4	1	no	—
1182	C₂×D₄	—	4	1	no	—
1183	C₂×D₄	—	4	1	no	—
1184	C₂×D₄	—	4	1	no	—
1185	C₂×D₄	—	4	1	no	—
1186	C₂×D₄	—	4	1	no	—
1187	C₂×D₄	—	4	1	no	—
1188	C₂×D₄	—	4	1	no	—
1189	C₂×D₄	—	4	1	no	—
1190	C₂×D₄	—	4	1	no	—
1191	C₂×D₄	—	4	1	no	—
1192	C₂×D₄	—	4	1	no	—
1193	C₂×D₄	—	4	1	no	—
1194	C₂×D₄	—	4	1	no	—
1195	C₂×D₄	—	4	1	no	—
1196	C₂×D₄	—	356	1	no	—
1197	C₂×D₄	—	356	1	no	—
1198	C₂×D₄	—	356	1	no	—
1199	C₂×D₄	—	356	1	no	—
1200	C₂×D₄	—	356	1	no	—
1201	C₂×D₄	—	356	1	no	—
1202	C₂×D₄	—	356	1	no	—
1203	C₂×D₄	—	356	1	no	—
1204	C₂×D₄	—	356	1	no	—
1205	C₂×D₄	—	178	2	no	—
1206	C₂×D₄	—	178	2	no	—
1207	C₂×D₄	—	178	2	no	—
1208	C₂×D₄	—	178	2	no	—
1209	C₂×D₄	—	178	2	no	—
1210	C₂×D₄	—	178	2	no	—
1211	C₂×D₄	—	178	2	no	—
1212	C₂×D₄	—	178	2	no	—
1213	C₂×D₄	—	178	2	no	—
1214	C₂²×C₄	—	89	1	no	—
1215	C₂²×C₄	—	89	4	no	—
1216	C₂²×C₄	—	89	1	no	—
1217	C₂²×C₄	—	89	1	no	—
1218	C₂²×C₄	—	89	1	no	—
1219	C₂²×C₄	—	89	1	no	—
1220	C₂²×C₄	—	89	1	no	—
1221	C₂²×C₄	—	89	1	no	—
1222	C₂²×C₄	—	89	1	no	—
1223	C₂²×C₄	—	89	1	no	—
1224	C₂²×C₄	—	89	1	no	—
1225	C₂²×C₄	—	89	1	no	—
1226	C₂²×C₄	—	89	1	no	—
1227	C₂²×C₄	—	89	1	no	—
1228	C₂²×C₄	—	89	1	no	—
1229	C₂²×C₄	—	356	1	no	—
1230	C₂²×C₄	—	356	1	no	—
1231	C₂²×C₄	—	356	1	no	—
1232	C₂²×C₄	—	356	1	no	—
1233	C₂²×C₄	—	356	1	no	—
1234	C₂²×C₄	—	356	1	no	—
1235	C₂²×C₄	—	356	1	no	—
1236	C₂²×C₄	—	356	1	no	—
1237	C₂²×C₄	—	356	1	no	—
1238	C₂²×C₄	—	356	1	no	—
1239	C₂²×C₄	—	356	1	no	—
1240	C₂²×C₄	—	356	1	no	—
1241	C₂²×C₄	—	356	1	no	—
1242	C₂²×C₄	—	356	1	no	—
1243	C₂²×C₄	—	356	1	no	—
1244	C₂²×C₄	—	356	1	no	—
1245	C₂²×C₄	—	178	2	no	—
1246	C₂²×C₄	—	178	2	no	—
1247	C₂²×C₄	—	178	2	no	—
1248	C₂²×C₄	—	178	2	no	—
1249	C₂²×C₄	—	178	2	no	—
1250	C₂²×C₄	—	178	2	no	—
1251	C₂²×C₄	—	178	2	no	—
1252	C₂²×C₄	—	178	2	no	—
1253	C₂²×C₄	—	178	2	no	—
1254	C₂²×C₄	—	178	2	no	—
1255	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1256	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1257	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1258	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1259	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1260	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1261	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1262	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1263	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1264	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1265	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1266	C₄⋊C₄	—	4	1	no	—
1267	C₄⋊C₄	—	4	1	no	—
1268	C₄⋊C₄	—	4	1	no	—
1269	C₄⋊C₄	—	356	1	no	—
1270	C₄⋊C₄	—	356	1	no	—
1271	C₄⋊C₄	—	356	1	no	—
1272	C₄⋊C₄	—	356	1	no	—
1273	C₄⋊C₄	—	356	1	no	—
1274	C₄⋊C₄	—	356	1	no	—
1275	C₄⋊C₄	—	356	1	no	—
1276	C₄⋊C₄	—	356	1	no	—
1277	C₄⋊C₄	—	356	1	no	—
1278	C₄⋊C₄	—	356	1	no	—
1279	C₄⋊C₄	—	356	1	no	—
1280	C₄⋊C₄	—	356	1	no	—
1281	C₄⋊C₄	—	356	1	no	—
1282	C₄⋊C₄	—	356	1	no	—
1283	C₄⋊C₄	—	356	1	no	—
1284	C₄⋊C₄	—	356	1	no	—
1285	C₄⋊C₄	—	356	1	no	—
1286	C₄⋊C₄	—	356	1	no	—
1287	C₄⋊C₄	—	178	2	no	—
1288	C₄⋊C₄	—	178	2	no	—
1289	C₄⋊C₄	—	178	2	no	—
1290	C₂²⋊C₄	—	2	2	no	—
1291	C₂²⋊C₄	—	2	2	no	—
1292	C₂²⋊C₄	—	2	2	no	—
1293	C₂²⋊C₄	—	2	2	no	—
1294	C₂²⋊C₄	—	4	1	no	—
1295	C₂²⋊C₄	—	4	1	no	—
1296	C₂²⋊C₄	—	4	1	no	—
1297	C₂²⋊C₄	—	4	1	no	—
1298	C₂²⋊C₄	—	4	1	no	—
1299	C₂²⋊C₄	—	4	1	no	—
1300	C₂²⋊C₄	—	4	1	no	—
1301	C₂²⋊C₄	—	4	1	no	—
1302	C₂²⋊C₄	—	4	1	no	—
1303	C₂²⋊C₄	—	4	1	no	—
1304	C₂²⋊C₄	—	4	1	no	—
1305	C₂²⋊C₄	—	4	1	no	—
1306	C₂²⋊C₄	—	356	1	no	—
1307	C₂²⋊C₄	—	356	1	no	—
1308	C₂²⋊C₄	—	356	1	no	—
1309	C₂²⋊C₄	—	356	1	no	—
1310	C₂²⋊C₄	—	356	1	no	—
1311	C₂²⋊C₄	—	356	1	no	—
1312	C₂²⋊C₄	—	356	1	no	—
1313	C₂²⋊C₄	—	356	1	no	—
1314	C₂²⋊C₄	—	356	1	no	—
1315	C₂²⋊C₄	—	356	1	no	—
1316	C₂²⋊C₄	—	356	1	no	—
1317	C₂²⋊C₄	—	356	1	no	—
1318	C₂²⋊C₄	—	356	1	no	—
1319	C₂²⋊C₄	—	356	1	no	—
1320	C₂²⋊C₄	—	356	1	no	—
1321	C₂²⋊C₄	—	356	1	no	—
1322	C₂²⋊C₄	—	356	1	no	—
1323	C₂²⋊C₄	—	356	1	no	—
1324	C₂²⋊C₄	—	356	1	no	—
1325	C₂²⋊C₄	—	356	1	no	—
1326	C₂²⋊C₄	—	356	1	no	—
1327	C₂²⋊C₄	—	356	1	no	—
1328	C₂²⋊C₄	—	356	1	no	—
1329	C₂²⋊C₄	—	356	1	no	—
1330	C₂²⋊C₄	—	356	1	no	—
1331	C₂²⋊C₄	—	356	1	no	—
1332	C₂²⋊C₄	—	356	1	no	—
1333	C₂²⋊C₄	—	356	1	no	—
1334	C₂²⋊C₄	—	178	2	no	—
1335	C₂²⋊C₄	—	178	2	no	—
1336	C₂²⋊C₄	—	178	2	no	—
1337	C₂²⋊C₄	—	178	2	no	—
1338	C₂²⋊C₄	—	178	2	no	—
1339	C₂²⋊C₄	—	178	2	no	—
1340	C₂²⋊C₄	—	178	2	no	—
1341	C₂²⋊C₄	—	178	2	no	—
1342	C₂²⋊C₄	—	178	2	no	—
1343	C₂²⋊C₄	—	178	2	no	—
1344	C₄²	—	2	2	no	—
1345	C₄²	—	4	1	no	—
1346	C₄²	—	4	1	no	—
1347	C₄²	—	356	1	no	—
1348	C₄²	—	356	1	no	—
1349	C₄²	—	356	1	no	—
1350	C₄²	—	356	1	no	—
1351	C₄²	—	356	1	no	—
1352	C₄²	—	178	2	no	—
1353	C₂³	—	2	1	no	—
1354	C₂³	—	2	1	no	—
1355	C₂³	—	2	1	no	—
1356	C₂³	—	2	1	no	—
1357	C₂³	—	2	1	no	—
1358	C₂³	—	2	1	no	—
1359	C₂³	—	2	1	no	—
1360	C₂³	—	2	1	no	—
1361	C₂³	—	2	1	no	—
1362	C₂³	—	2	1	no	—
1363	C₂³	—	2	1	no	—
1364	C₂³	—	2	1	no	—
1365	C₂³	—	2	1	no	—
1366	C₂³	—	2	1	no	—
1367	C₂³	—	2	1	no	—
1368	C₂³	—	2	1	no	—
1369	C₂³	—	2	1	no	—
1370	C₂³	—	2	1	no	—
1371	C₂³	—	2	1	no	—
1372	C₂³	—	2	1	no	—
1373	C₂³	—	2	1	no	—
1374	C₂³	—	2	1	no	—
1375	C₂³	—	2	1	no	—
1376	C₂³	—	2	1	no	—
1377	C₂³	—	2	1	no	—
1378	C₂³	—	2	1	no	—
1379	C₂³	—	2	1	no	—
1380	C₂³	—	2	1	no	—
1381	C₂³	—	89	2	no	—
1382	C₂³	—	89	2	no	—
1383	C₂³	—	89	2	no	—
1384	C₂³	—	356	4	no	—
1385	C₂³	—	356	4	no	—
1386	C₂³	—	356	4	no	—
1387	C₂³	—	178	1	no	—
1388	C₂³	—	178	1	no	—
1389	C₂³	—	178	1	no	—
1390	C₂³	—	178	1	no	—
1391	C₂³	—	178	1	no	—
1392	C₂³	—	178	1	no	—
1393	C₂³	—	178	1	no	—
1394	C₂³	—	178	1	no	—
1395	C₂³	—	178	1	no	—
1396	C₂³	—	178	1	no	—
1397	C₂³	—	178	1	no	—
1398	C₂³	—	712	2	no	—
1399	C₂³	—	712	2	no	—
1400	C₂³	—	712	2	no	—
1401	C₂³	—	712	2	no	—
1402	C₂³	C₂⁴×D₈₉	1	1	yes	characteristic
1403	Q₈	—	8	2	no	—
1404	Q₈	—	356	4	no	—
1405	D₄	—	4	4	no	—
1406	D₄	—	8	2	no	—
1407	D₄	—	8	2	no	—
1408	D₄	—	8	2	no	—
1409	D₄	—	8	2	no	—
1410	D₄	—	8	2	no	—
1411	D₄	—	356	4	no	—
1412	D₄	—	356	4	no	—
1413	D₄	—	356	4	no	—
1414	D₄	—	712	2	no	—
1415	D₄	—	712	2	no	—
1416	D₄	—	712	2	no	—
1417	C₂×C₄	—	2	1	no	—
1418	C₂×C₄	—	2	1	no	—
1419	C₂×C₄	—	2	1	no	—
1420	C₂×C₄	—	2	1	no	—
1421	C₂×C₄	—	2	1	no	—
1422	C₂×C₄	—	2	1	no	—
1423	C₂×C₄	—	2	1	no	—
1424	C₂×C₄	—	2	1	no	—
1425	C₂×C₄	—	2	1	no	—
1426	C₂×C₄	—	2	1	no	—
1427	C₂×C₄	—	2	1	no	—
1428	C₂×C₄	—	2	1	no	—
1429	C₂×C₄	—	2	1	no	—
1430	C₂×C₄	—	2	1	no	—
1431	C₂×C₄	—	2	1	no	—
1432	C₂×C₄	—	2	1	no	—
1433	C₂×C₄	—	2	1	no	—
1434	C₂×C₄	—	2	1	no	—
1435	C₂×C₄	—	2	1	no	—
1436	C₂×C₄	—	2	1	no	—
1437	C₂×C₄	—	2	1	no	—
1438	C₂×C₄	—	2	1	no	—
1439	C₂×C₄	—	2	1	no	—
1440	C₂×C₄	—	2	1	no	—
1441	C₂×C₄	—	2	1	no	—
1442	C₂×C₄	—	2	1	no	—
1443	C₂×C₄	—	2	1	no	—
1444	C₂×C₄	—	2	1	no	—
1445	C₂×C₄	—	2	1	no	—
1446	C₂×C₄	—	2	1	no	—
1447	C₂×C₄	—	2	1	no	—
1448	C₂×C₄	—	89	2	no	—
1449	C₂×C₄	—	356	4	no	—
1450	C₂×C₄	—	356	4	no	—
1451	C₂×C₄	—	356	4	no	—
1452	C₂×C₄	—	356	4	no	—
1453	C₂×C₄	—	356	4	no	—
1454	C₂×C₄	—	178	8	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	—	178	1	no	—
1461	C₂×C₄	—	178	1	no	—
1462	C₂×C₄	—	178	1	no	—
1463	C₂×C₄	—	178	1	no	—
1464	C₂×C₄	—	178	1	no	—
1465	C₂×C₄	—	178	1	no	—
1466	C₂×C₄	—	178	1	no	—
1467	C₂×C₄	—	178	1	no	—
1468	C₂×C₄	—	178	1	no	—
1469	C₂×C₄	—	178	1	no	—
1470	C₂×C₄	—	178	1	no	—
1471	C₂×C₄	—	178	1	no	—
1472	C₂×C₄	—	178	1	no	—
1473	C₂×C₄	—	178	1	no	—
1474	C₂×C₄	—	178	1	no	—
1475	C₂×C₄	—	178	1	no	—
1476	C₂×C₄	—	178	1	no	—
1477	C₂×C₄	—	178	1	no	—
1478	C₂×C₄	—	178	1	no	—
1479	C₂×C₄	—	178	1	no	—
1480	C₂×C₄	—	178	1	no	—
1481	C₂×C₄	—	178	1	no	—
1482	C₂×C₄	—	178	1	no	—
1483	C₂×C₄	—	178	1	no	—
1484	C₂×C₄	—	178	1	no	—
1485	C₂×C₄	—	178	1	no	—
1486	C₂×C₄	—	178	1	no	—
1487	C₂×C₄	—	178	1	no	—
1488	C₂×C₄	—	178	1	no	—
1489	C₂×C₄	—	178	1	no	—
1490	C₂×C₄	—	178	1	no	—
1491	C₂×C₄	—	178	1	no	—
1492	C₂×C₄	—	178	1	no	—
1493	C₂×C₄	—	178	1	no	—
1494	C₂×C₄	—	178	1	no	—
1495	C₂×C₄	—	178	1	no	—
1496	C₂×C₄	—	712	2	no	—
1497	C₂×C₄	—	712	2	no	—
1498	C₂×C₄	—	712	2	no	—
1499	C₂×C₄	#41×D₈₉	1	2	yes	—
1500	C₂×C₄	#15668057	1	2	yes	—
1501	C₂²	—	4	1	no	—
1502	C₂²	—	4	1	no	—
1503	C₂²	—	4	1	no	—
1504	C₂²	—	4	1	no	—
1505	C₂²	—	4	1	no	—
1506	C₂²	—	4	1	no	—
1507	C₂²	—	4	1	no	—
1508	C₂²	—	4	1	no	—
1509	C₂²	—	4	1	no	—
1510	C₂²	—	4	1	no	—
1511	C₂²	—	4	1	no	—
1512	C₂²	—	4	1	no	—
1513	C₂²	—	4	1	no	—
1514	C₂²	—	4	1	no	—
1515	C₂²	—	4	1	no	—
1516	C₂²	—	4	1	no	—
1517	C₂²	—	4	1	no	—
1518	C₂²	—	4	1	no	—
1519	C₂²	—	4	1	no	—
1520	C₂²	—	4	1	no	—
1521	C₂²	—	4	1	no	—
1522	C₂²	—	4	1	no	—
1523	C₂²	—	4	1	no	—
1524	C₂²	—	4	1	no	—
1525	C₂²	—	4	1	no	—
1526	C₂²	—	4	1	no	—
1527	C₂²	—	4	1	no	—
1528	C₂²	—	4	1	no	—
1529	C₂²	—	89	4	no	—
1530	C₂²	—	356	1	no	—
1531	C₂²	—	356	1	no	—
1532	C₂²	—	356	1	no	—
1533	C₂²	—	356	1	no	—
1534	C₂²	—	356	1	no	—
1535	C₂²	—	356	1	no	—
1536	C₂²	—	356	1	no	—
1537	C₂²	—	178	2	no	—
1538	C₂²	—	178	2	no	—
1539	C₂²	—	178	2	no	—
1540	C₂²	—	178	2	no	—
1541	C₂²	—	178	2	no	—
1542	C₂²	—	178	2	no	—
1543	C₂²	—	712	8	no	—
1544	C₂²	C₂×#41×D₈₉	1	1	yes	characteristic
1545	C₂²	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
1546	C₂²	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
1547	C₂²	C₂×#15668057	1	1	yes	characteristic
1548	C₂²	#19152433	1	1	yes	characteristic
1549	C₂²	#19152433	1	1	yes	characteristic
1550	C₂²	#19152434	1	1	yes	characteristic
1551	C₄	—	2	2	no	—
1552	C₄	—	2	2	no	—
1553	C₄	—	4	1	no	—
1554	C₄	—	4	1	no	—
1555	C₄	—	4	1	no	—
1556	C₄	—	4	1	no	—
1557	C₄	—	4	1	no	—
1558	C₄	—	4	1	no	—
1559	C₄	—	4	1	no	—
1560	C₄	—	4	1	no	—
1561	C₄	—	4	1	no	—
1562	C₄	—	356	1	no	—
1563	C₄	—	356	1	no	—
1564	C₄	—	356	1	no	—
1565	C₄	—	356	1	no	—
1566	C₄	—	356	1	no	—
1567	C₄	—	356	1	no	—
1568	C₄	—	356	1	no	—
1569	C₄	—	356	1	no	—
1570	C₄	—	356	1	no	—
1571	C₄	—	356	1	no	—
1572	C₄	—	356	1	no	—
1573	C₄	—	356	1	no	—
1574	C₄	—	356	1	no	—
1575	C₄	—	178	2	no	—
1576	C₂	—	8	1	no	—
1577	C₂	—	8	1	no	—
1578	C₂	—	8	1	no	—
1579	C₂	—	8	1	no	—
1580	C₂	—	178	4	no	—
1581	C₂	—	712	1	no	—
1582	C₂	#538×D₈₉	1	1	yes	characteristic
1583	C₂	#26033963	1	1	yes	characteristic
1584	C₂	#26034096	1	1	yes	characteristic
1585	C₂	#26034432	1	1	yes	characteristic
1586	C₂	#26034558	1	1	yes	characteristic
1587	C₂	#26034607	1	1	yes	characteristic
1588	C₂	#26034797	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₈₉
commutator, socle, cosocle	C₂³×C₈₉	C₂⁵
Fitting	C₈₉×#2733	C₂
hypercenter	#2733	D₈₉
hypocenter	C₈₉	#36795
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ #2733

Complements

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

N	H ≅ G/N	type
1. #26028566	C₂	semidirect
2. #26028548	C₂	semidirect
3. #26028230	C₂	semidirect
4. #26028191	C₂	semidirect
5. #26028181	C₂	semidirect
6. #26027973	C₂	semidirect
7. #26027915	C₂	semidirect
8. #26027886	C₂	semidirect
9. #26027863	C₂	semidirect
10. #26027828	C₂	semidirect
11. #26027613	C₂	semidirect
12. #26027576	C₂	semidirect
13. #26027567	C₂	semidirect
14. #26027499	C₂	semidirect
15. #26027057	C₂	semidirect
16. #26027050	C₂	semidirect
17. #26026652	C₂	semidirect
18. #26026024	C₂	semidirect
19. #26025985	C₂	semidirect
20. #26024811	C₂	semidirect
21. #26024374	C₂	semidirect
22. #26023995	C₂	semidirect
23. #26023925	C₂	semidirect
24. #26023855	C₂	semidirect
25. #26023791	C₂	semidirect
26. #26023634	C₂	semidirect
27. #26023566	C₂	semidirect
28. #26022922	C₂	semidirect
29. #26022842	C₂	semidirect
30. #388×D₈₉	C₂	semidirect
31. C₈₉×#2733	C₂	semidirect
33. C₂×#15668005	C₂²	semidirect
49. C₈₉⋊#401	C₂²	semidirect
50. #19151540	C₂²	semidirect
51. #19151539	C₂²	semidirect
52. #19151536	C₂²	semidirect
53. #19151532	C₂²	semidirect
54. #19151528	C₂²	semidirect
58. #19151526	C₂²	semidirect
59. #19151526	C₂²	semidirect
60. #19151526	C₂²	semidirect
61. #19151526	C₂²	semidirect
69. #19151519	C₂²	semidirect
70. #19151517	C₂²	semidirect
84. #19151512	C₂²	semidirect
87. #19151510	C₂²	semidirect
91. #19151505	C₂²	semidirect
92. #19151504	C₂²	semidirect
93. #19151503	C₂²	semidirect
95. #19151501	C₂²	semidirect
96. #19151501	C₂²	semidirect
99. #19151496	C₂²	semidirect
100. #19151495	C₂²	semidirect
101. #19151493	C₂²	semidirect
104. #19151492	C₂²	semidirect
105. #19151492	C₂²	semidirect
106. #19151492	C₂²	semidirect
109. #19151491	C₂²	semidirect
118. #19151486	C₂²	semidirect
119. #19151486	C₂²	semidirect
120. #19151486	C₂²	semidirect
121. #19151486	C₂²	semidirect
122. #19151486	C₂²	semidirect
123. #19151485	C₂²	semidirect
124. #19151485	C₂²	semidirect
125. #19151484	C₂²	semidirect
126. #19151484	C₂²	semidirect
127. #19151482	C₂²	semidirect
128. #19151482	C₂²	semidirect
129. #19151482	C₂²	semidirect
130. #19151481	C₂²	semidirect
131. #19151481	C₂²	semidirect
135. #19151478	C₂²	semidirect
136. #19151478	C₂²	semidirect
137. #19151478	C₂²	semidirect
150. #19151473	C₂²	semidirect
151. #19151473	C₂²	semidirect
152. #19151473	C₂²	semidirect
155. #19151470	C₂²	semidirect
158. #19151465	C₂²	semidirect
159. #19151465	C₂²	semidirect
160. #19151464	C₂²	semidirect
162. #19151459	C₂²	semidirect
164. #19151456	C₂²	semidirect
165. #19151456	C₂²	semidirect
166. #19151456	C₂²	semidirect
167. #19151456	C₂²	semidirect
173. C₂×#124×C₈₉	C₂²	semidirect
175. #394×C₈₉	C₂²	semidirect
179. #392×C₈₉	C₂²	semidirect
180. #391×C₈₉	C₂²	semidirect
182. #390×C₈₉	C₂²	semidirect
184. #388×C₈₉	C₂²	semidirect
185. #388×C₈₉	C₂²	semidirect
186. #388×C₈₉	C₂²	semidirect
809. #2733	D₈₉	semidirect
826. C₈₉	#36795	semidirect
830. C₂×#124	C₂×D₈₉	semidirect
883. #394	C₂×D₈₉	semidirect
893. #392	C₂×D₈₉	semidirect
897. #391	C₂×D₈₉	semidirect
904. #390	C₂×D₈₉	semidirect
930. #388	C₂×D₈₉	semidirect
931. #388	C₂×D₈₉	semidirect
932. #388	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26028566	2
#26028548	2
#26028230	2
#26028191	2
#26028181	2
#26027973	2
#26027915	2
#26027886	2
#26027863	2
#26027828	2
#26027613	2
#26027576	2
#26027567	2
#26027499	2
#26027057	2
#26027050	2
#26026652	2
#26026024	2
#26025985	2
#26024811	2
#26024374	2
#26023995	2
#26023925	2
#26023855	2
#26023791	2
#26023634	2
#26023566	2
#26022922	2
#26022842	2
#388×D₈₉	2
C₈₉×#2733	2
#36795	89