Subgroups — #36716954

Order 22784.

2500 conjugacy classes of subgroups.

The subgroup lattice has 1476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19152261	C₂	1	1	yes	maximal, characteristic
2	#26023340	C₂	1	1	yes	maximal, characteristic, complemented
3	#26023339	C₂	1	1	yes	maximal, characteristic, complemented
4	#26023336	C₂	1	1	yes	maximal, characteristic, complemented
5	#26023334	C₂	1	1	yes	maximal, characteristic, complemented
6	#26023330	C₂	1	1	yes	maximal, characteristic, complemented
7	#26023307	C₂	1	1	yes	maximal, characteristic, complemented
8	#26023260	C₂	1	1	yes	maximal, characteristic, complemented
9	#26023258	C₂	1	1	yes	maximal, characteristic, complemented
10	#26023206	C₂	1	1	yes	maximal, characteristic, complemented
11	#26023159	C₂	1	1	yes	maximal, characteristic
12	#26023158	C₂	1	1	yes	maximal, characteristic
13	#26023150	C₂	1	1	yes	maximal, characteristic
14	C₂²⋊C₄×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic, complemented
15	#26023086	C₂	1	1	yes	maximal, characteristic, complemented
16	#26022997	C₂	1	1	yes	maximal, characteristic, complemented
17	#26022995	C₂	1	1	yes	maximal, characteristic, complemented
18	#26022987	C₂	1	1	yes	maximal, characteristic, complemented
19	#26022983	C₂	1	1	yes	maximal, characteristic, complemented
20	#26022981	C₂	1	1	yes	maximal, characteristic, complemented
21	#26022979	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#15668011	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#15667990	C₂	1	1	yes	maximal, characteristic, complemented
24	#26022784	C₂	1	1	yes	maximal, characteristic, complemented
25	#26022725	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#19151502	C₂	1	1	yes	maximal, characteristic, complemented
27	#391×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
28	#26022611	C₂	1	1	yes	maximal, characteristic
29	#26022611	C₂	1	1	yes	maximal, characteristic
30	C₄×#15667972	C₂	1	1	yes	maximal, characteristic
31	C₈₉×#2368	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂³×Dic₁₇₈	C₂²	1	1	yes	characteristic
33	C₂²×Q₈×D₈₉	C₂²	1	1	yes	characteristic
34	#19152261	C₄	1	16	yes	complemented
35	C₂×#15668011	C₂²	1	1	yes	characteristic
36	C₂×#15668011	C₂²	1	1	yes	characteristic
37	C₂×#15668010	C₂²	1	1	yes	characteristic
38	C₂×#15667992	C₂²	1	1	yes	characteristic
39	C₂×#15667990	C₂²	1	1	yes	characteristic
40	C₂×#15667990	C₂²	1	1	yes	characteristic
41	C₂×#15667989	C₂²	1	1	yes	characteristic
42	C₂×#15667989	C₂²	1	1	yes	characteristic
43	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
44	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
45	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
46	C₂×#15667977	C₂²	1	1	yes	characteristic
47	C₂×#15667977	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
51	C₂×#15667972	C₂²	1	1	yes	characteristic
52	C₂×#15667972	C₂²	1	1	yes	characteristic
53	C₂×#15667972	C₂²	1	1	yes	characteristic
54	C₂×#15667972	C₂²	1	1	yes	characteristic
55	C₂²×#13083553	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
57	C₂²×C₄×Dic₈₉	C₂²	1	1	yes	characteristic
58	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
59	#19151505	C₂²	1	1	yes	characteristic
60	#19151505	C₂²	1	1	yes	characteristic
61	#19151504	C₂²	1	1	yes	characteristic
62	#19151504	C₂²	1	1	yes	characteristic
63	#19151504	C₂²	1	1	yes	characteristic
64	#19151503	C₂²	1	1	yes	characteristic
65	#19151502	C₂²	1	1	yes	characteristic
66	#19151502	C₂²	1	1	yes	characteristic
67	#19151502	C₂²	1	1	yes	characteristic
68	#19151502	C₂²	1	1	yes	characteristic
69	#19151502	C₂²	1	1	yes	characteristic
70	#19151502	C₂²	1	1	yes	characteristic
71	#19151502	C₂²	1	1	yes	characteristic
72	#19151502	C₂²	1	1	yes	characteristic
73	#19151502	C₂²	1	1	yes	characteristic
74	#19151502	C₂²	1	1	yes	characteristic
75	#19151502	C₂²	1	1	yes	characteristic
76	#19151502	C₂²	1	1	yes	characteristic
77	#19151502	C₂²	1	1	yes	characteristic
78	#19151502	C₂²	1	1	yes	characteristic
79	#19151502	C₂²	1	1	yes	characteristic
80	#19151502	C₂²	1	1	yes	characteristic
81	#19151497	C₂²	1	1	yes	characteristic
82	#19151497	C₂²	1	1	yes	characteristic
83	#19151496	C₂²	1	1	yes	characteristic
84	#19151495	C₂²	1	1	yes	characteristic
85	#19151495	C₂²	1	1	yes	characteristic
86	#19151495	C₂²	1	1	yes	characteristic
87	#19151495	C₂²	1	1	yes	characteristic
88	#19151495	C₂²	1	1	yes	characteristic
89	#19151495	C₂²	1	1	yes	characteristic
90	#19151494	C₂²	1	1	yes	characteristic
91	#19151493	C₂²	1	1	yes	characteristic
92	#19151493	C₂²	1	1	yes	characteristic
93	#19151493	C₂²	1	1	yes	characteristic
94	#19151493	C₂²	1	1	yes	characteristic
95	#19151485	C₂²	1	1	yes	characteristic
96	#19151485	C₂²	1	1	yes	characteristic
97	#19151484	C₂²	1	1	yes	characteristic
98	#19151484	C₂²	1	1	yes	characteristic
99	#19151484	C₂²	1	1	yes	characteristic
100	#19151484	C₂²	1	1	yes	characteristic
101	#19151483	C₂²	1	1	yes	characteristic
102	#19151483	C₂²	1	1	yes	characteristic
103	#19151482	C₂²	1	1	yes	characteristic
104	#19151482	C₂²	1	1	yes	characteristic
105	#19151481	C₂²	1	1	yes	characteristic
106	#19151481	C₂²	1	1	yes	characteristic
107	#19151480	C₂²	1	1	yes	characteristic
108	#19151480	C₂²	1	1	yes	characteristic
109	#19151479	C₂²	1	1	yes	characteristic
110	#19151479	C₂²	1	1	yes	characteristic
111	#19151473	C₂²	1	1	yes	characteristic
112	#19151473	C₂²	1	1	yes	characteristic
113	#19151472	C₂²	1	1	yes	characteristic
114	#19151472	C₂²	1	1	yes	characteristic
115	#19151472	C₂²	1	1	yes	characteristic
116	#19151472	C₂²	1	1	yes	characteristic
117	#19151471	C₂²	1	1	yes	characteristic
118	#19151471	C₂²	1	1	yes	characteristic
119	#19151469	C₂²	1	1	yes	characteristic
120	#19151469	C₂²	1	1	yes	characteristic
121	#19151467	C₂²	1	1	yes	characteristic
122	#19151462	C₂²	1	1	yes	characteristic
123	#19151462	C₂²	1	1	yes	characteristic
124	#19151458	C₂²	1	1	yes	characteristic
125	#19151457	C₂²	1	1	yes	characteristic
126	#19151457	C₂²	1	1	yes	characteristic
127	#19151456	C₂²	1	1	yes	characteristic
128	#19151456	C₂²	1	1	yes	characteristic
129	#19151455	C₂²	1	1	yes	characteristic
130	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
131	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
132	C₄×#13083553	C₂²	1	1	yes	characteristic
133	C₄×#13083553	C₂²	1	1	yes	characteristic
134	C₄×#13083553	C₂²	1	1	yes	characteristic
135	C₄×#13083553	C₂²	1	1	yes	characteristic
136	C₄×#13083553	C₂²	1	1	yes	characteristic
137	C₄×#13083553	C₂²	1	1	yes	characteristic
138	C₄×#13083553	C₂²	1	1	yes	characteristic
139	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
140	#19151449	C₂²	1	1	yes	characteristic
141	#19151449	C₂²	1	1	yes	characteristic
142	#19151449	C₂²	1	1	yes	characteristic
143	#19151449	C₂²	1	1	yes	characteristic
144	#19151449	C₂²	1	1	yes	characteristic
145	#19151449	C₂²	1	1	yes	characteristic
146	#19151449	C₂²	1	1	yes	characteristic
147	#19151449	C₂²	1	1	yes	characteristic
148	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
149	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
150	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
151	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
152	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
153	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
154	C₄×#13083551	C₂²	1	1	yes	characteristic
155	C₄×#13083551	C₂²	1	1	yes	characteristic
156	C₄×#13083551	C₂²	1	1	yes	characteristic
157	C₄×#13083551	C₂²	1	1	yes	characteristic
158	C₄×#13083551	C₂²	1	1	yes	characteristic
159	#19151445	C₂²	1	1	yes	characteristic
160	#19151445	C₂²	1	1	yes	characteristic
161	#19151445	C₂²	1	1	yes	characteristic
162	#19151445	C₂²	1	1	yes	characteristic
163	#19151443	C₂²	1	1	yes	characteristic
164	#19151443	C₂²	1	1	yes	characteristic
165	C₂×#15667919	C₂²	1	1	yes	characteristic
166	C₂×#15667919	C₂²	1	1	yes	characteristic
167	C₂×#15667919	C₂²	1	1	yes	characteristic
168	#95×D₈₉	C₂²	1	1	yes	characteristic
169	#95×D₈₉	C₂²	1	1	yes	characteristic
170	#95×D₈₉	C₂²	1	1	yes	characteristic
171	#95×D₈₉	C₂²	1	1	yes	characteristic
172	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
173	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
174	#391×C₈₉	C₂²	1	1	yes	characteristic
175	#391×C₈₉	C₂²	1	1	yes	characteristic
176	#387×C₈₉	C₂²	1	1	yes	characteristic
177	#387×C₈₉	C₂²	1	1	yes	characteristic
178	#387×C₈₉	C₂²	1	1	yes	characteristic
179	#387×C₈₉	C₂²	1	1	yes	characteristic
180	#385×C₈₉	C₂²	1	1	yes	characteristic
181	#385×C₈₉	C₂²	1	1	yes	characteristic
182	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
183	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
184	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
185	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
186	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
187	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
188	C₂²×Dic₁₇₈	—	4	2	no	—
189	C₂²×Dic₁₇₈	—	4	2	no	—
190	C₂²×Dic₁₇₈	C₂×C₄	1	8	yes	complemented
191	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
192	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
193	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
194	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
195	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
196	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
197	C₂×Q₈×D₈₉	—	4	2	no	—
198	C₂×Q₈×D₈₉	—	4	2	no	—
199	C₂×Q₈×D₈₉	C₂×C₄	1	8	yes	complemented
200	C₂²×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
201	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
202	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
203	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
204	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
205	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
206	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
207	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
208	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
209	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
210	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
211	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
212	#15668011	C₂×C₄	1	8	yes	complemented
213	#15668011	C₂×C₄	1	8	yes	complemented
214	#15668010	C₂×C₄	1	8	yes	complemented
215	#15667992	C₂×C₄	1	8	yes	complemented
216	#15667990	C₂×C₄	1	8	yes	complemented
217	#15667990	C₂×C₄	1	8	yes	complemented
218	#15667989	C₂×C₄	1	8	yes	complemented
219	#15667989	C₂×C₄	1	8	yes	complemented
220	C₄×Dic₁₇₈	—	4	2	no	—
221	C₄×Dic₁₇₈	—	4	2	no	—
222	C₄×Dic₁₇₈	—	4	2	no	—
223	#15667977	—	4	2	no	—
224	#15667977	C₂×C₄	1	8	yes	complemented
225	C₄×C₂²⋊D₈₉	—	2	4	no	—
226	C₄×C₂²⋊D₈₉	—	2	4	no	—
227	C₄×C₂²⋊D₈₉	C₂×C₄	1	8	yes	—
228	#15667972	—	2	4	no	—
229	#15667972	C₂×C₄	1	8	yes	—
230	#15667972	C₂×C₄	1	8	yes	—
231	#15667972	Q₈	1	8	yes	complemented
232	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
240	C₂×#13083553	—	4	2	no	—
241	C₂×#13083553	C₂³	1	1	yes	characteristic
242	C₂×#13083553	C₂³	1	1	yes	characteristic
243	C₂×#13083553	C₂³	1	1	yes	characteristic
244	C₂×#13083553	C₂³	1	1	yes	characteristic
245	C₂×#13083553	C₂³	1	1	yes	characteristic
246	C₂×#13083553	C₂³	1	1	yes	characteristic
247	C₂×#13083553	C₂³	1	1	yes	characteristic
248	C₂×#13083553	C₂³	1	1	yes	characteristic
249	C₂×#13083553	C₂³	1	1	yes	characteristic
250	C₂×#13083553	C₂³	1	1	yes	characteristic
251	C₂×#13083553	C₂³	1	1	yes	characteristic
252	C₂×#13083553	C₂³	1	1	yes	characteristic
253	C₂×#13083553	C₂³	1	1	yes	characteristic
254	C₂×#13083553	C₂³	1	1	yes	characteristic
255	C₂×#13083553	C₂³	1	1	yes	characteristic
256	C₂×#13083553	C₂³	1	1	yes	characteristic
257	C₂×#13083553	C₂³	1	1	yes	characteristic
258	C₂×#13083553	C₂³	1	1	yes	characteristic
259	C₂×#13083553	C₂³	1	1	yes	characteristic
260	C₂×#13083553	C₂³	1	1	yes	characteristic
261	C₂×#13083553	C₂³	1	1	yes	characteristic
262	C₂×#13083553	C₂³	1	1	yes	characteristic
263	C₂×#13083553	C₂³	1	1	yes	characteristic
264	C₄⋊C₄×D₈₉	—	4	2	no	—
265	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊Dic₈₉	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×C₄×Dic₈₉	—	4	2	no	—
276	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
277	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
278	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
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	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
288	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
289	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
290	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
291	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
292	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
293	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
294	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
295	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
296	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
297	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
298	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
299	C₄²×D₈₉	—	4	2	no	—
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	#15667919	C₂³	1	1	yes	characteristic
327	#15667919	C₂³	1	1	yes	characteristic
328	#15667919	C₂³	1	1	yes	characteristic
329	#15667919	C₂³	1	1	yes	characteristic
330	#15667919	C₂³	1	1	yes	characteristic
331	#15667919	C₂³	1	1	yes	characteristic
332	#15667919	C₂³	1	1	yes	characteristic
333	#15667919	C₂³	1	1	yes	characteristic
334	#15667919	C₂³	1	1	yes	characteristic
335	#15667919	C₂³	1	1	yes	characteristic
336	#15667919	C₂³	1	1	yes	characteristic
337	#15667919	C₂³	1	1	yes	characteristic
338	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
339	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
340	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
341	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
342	C₂²⋊Q₈×C₈₉	C₂×C₄	1	8	yes	complemented
343	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
344	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
345	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
346	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
347	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
348	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
349	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
350	C₂×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	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
358	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
359	C₂×C₄²×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	#95×C₈₉	C₂³	1	1	yes	characteristic
364	#95×C₈₉	C₂³	1	1	yes	characteristic
365	#95×C₈₉	C₂³	1	1	yes	characteristic
366	#95×C₈₉	C₂³	1	1	yes	characteristic
367	#95×C₈₉	C₂³	1	1	yes	characteristic
368	#95×C₈₉	C₂³	1	1	yes	characteristic
369	#95×C₈₉	C₂³	1	1	yes	characteristic
370	#95×C₈₉	C₂³	1	1	yes	characteristic
371	#95×C₈₉	C₂³	1	1	yes	characteristic
372	#95×C₈₉	C₂³	1	1	yes	characteristic
373	#95×C₈₉	C₂³	1	1	yes	characteristic
374	C₂³×D₈₉	C₂⁴	1	1	yes	characteristic
375	C₂×Dic₁₇₈	—	2	2	no	—
376	C₂×Dic₁₇₈	—	2	2	no	—
377	C₂×Dic₁₇₈	—	2	2	no	—
378	C₂×Dic₁₇₈	—	2	2	no	—
379	C₂×Dic₁₇₈	—	2	2	no	—
380	C₂×Dic₁₇₈	—	2	2	no	—
381	C₂×Dic₁₇₈	—	4	16	no	—
382	C₂×Dic₁₇₈	—	4	1	no	—
383	C₂×Dic₁₇₈	—	4	1	no	—
384	C₂×Dic₁₇₈	—	4	1	no	—
385	C₂×Dic₁₇₈	—	4	1	no	—
386	C₂×Dic₁₇₈	—	4	1	no	—
387	C₂×Dic₁₇₈	—	4	1	no	—
388	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
389	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
390	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
391	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
392	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
393	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
394	Q₈×D₈₉	—	4	16	no	—
395	C₂×C₂²⋊D₈₉	C₂²×C₄	1	4	yes	—
396	C₂×C₂²⋊D₈₉	C₂×Q₈	1	4	yes	—
397	C₂×C₂²⋊D₈₉	#41	1	4	yes	—
398	C₂²×Dic₈₉	—	2	2	no	—
399	C₂²×Dic₈₉	—	2	2	no	—
400	C₂²×Dic₈₉	—	2	2	no	—
401	C₂²×Dic₈₉	—	4	1	no	—
402	C₂²×Dic₈₉	—	4	1	no	—
403	C₂²×Dic₈₉	—	4	1	no	—
404	C₂²×Dic₈₉	—	4	1	no	—
405	C₂²×Dic₈₉	—	4	1	no	—
406	C₂²×Dic₈₉	—	4	1	no	—
407	C₂²×Dic₈₉	C₂²×C₄	1	4	yes	—
408	C₂²×Dic₈₉	C₂²×C₄	1	4	yes	—
409	C₂²×Dic₈₉	C₂×Q₈	1	4	yes	complemented
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	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
418	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
419	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
420	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
421	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
422	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
423	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
424	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
425	C₂×C₄×D₈₉	—	2	2	no	—
426	C₂×C₄×D₈₉	—	2	2	no	—
427	C₂×C₄×D₈₉	—	2	2	no	—
428	C₂×C₄×D₈₉	—	2	2	no	—
429	C₂×C₄×D₈₉	—	2	2	no	—
430	C₂×C₄×D₈₉	—	2	2	no	—
431	C₂×C₄×D₈₉	—	4	1	no	—
432	C₂×C₄×D₈₉	—	4	1	no	—
433	C₂×C₄×D₈₉	—	4	1	no	—
434	C₂×C₄×D₈₉	—	4	1	no	—
435	C₂×C₄×D₈₉	—	4	1	no	—
436	C₂×C₄×D₈₉	—	4	1	no	—
437	C₂×C₄×D₈₉	—	4	1	no	—
438	C₂×C₄×D₈₉	—	4	1	no	—
439	C₂×C₄×D₈₉	—	4	1	no	—
440	C₂×C₄×D₈₉	—	4	1	no	—
441	C₂×C₄×D₈₉	—	4	1	no	—
442	C₂×C₄×D₈₉	C₂²×C₄	1	4	yes	—
443	C₂×C₄×D₈₉	C₂²×C₄	1	4	yes	—
444	C₂×C₄×D₈₉	C₂²×C₄	1	4	yes	—
445	C₂×C₄×D₈₉	C₂×Q₈	1	4	yes	complemented
446	C₄⋊Dic₈₉	—	4	1	no	—
447	C₄⋊Dic₈₉	—	4	1	no	—
448	C₄⋊Dic₈₉	—	4	1	no	—
449	C₄⋊Dic₈₉	—	4	1	no	—
450	C₄⋊Dic₈₉	—	4	1	no	—
451	C₄⋊Dic₈₉	—	4	1	no	—
452	C₄⋊Dic₈₉	C₂²×C₄	1	4	yes	—
453	C₄⋊Dic₈₉	C₂²×C₄	1	4	yes	—
454	#13083553	—	2	2	no	—
455	#13083553	—	2	2	no	—
456	#13083553	—	2	2	no	—
457	#13083553	—	2	2	no	—
458	#13083553	—	2	2	no	—
459	#13083553	—	2	2	no	—
460	#13083553	—	2	2	no	—
461	#13083553	—	2	2	no	—
462	#13083553	—	4	1	no	—
463	#13083553	—	4	1	no	—
464	#13083553	—	4	1	no	—
465	#13083553	—	4	1	no	—
466	#13083553	—	4	1	no	—
467	#13083553	—	4	1	no	—
468	#13083553	—	4	1	no	—
469	#13083553	C₂²×C₄	1	4	yes	—
470	#13083553	C₂²×C₄	1	4	yes	—
471	#13083553	C₂²×C₄	1	4	yes	—
472	#13083553	C₂²×C₄	1	4	yes	—
473	#13083553	C₂²×C₄	1	4	yes	—
474	#13083553	C₂²×C₄	1	4	yes	—
475	#13083553	C₂²×C₄	1	4	yes	—
476	#13083553	C₂×Q₈	1	4	yes	complemented
477	C₂²⋊Dic₈₉	—	2	2	no	—
478	C₂²⋊Dic₈₉	—	2	2	no	—
479	C₂²⋊Dic₈₉	C₂²×C₄	1	4	yes	—
480	#13083551	—	2	2	no	—
481	#13083551	—	2	2	no	—
482	#13083551	—	2	2	no	—
483	#13083551	C₂²×C₄	1	4	yes	—
484	#13083551	C₂²×C₄	1	4	yes	—
485	#13083551	C₂²×C₄	1	4	yes	—
486	#13083551	C₂×Q₈	1	4	yes	complemented
487	C₄×Dic₈₉	—	2	2	no	—
488	C₄×Dic₈₉	—	2	2	no	—
489	C₄×Dic₈₉	—	2	2	no	—
490	C₄×Dic₈₉	—	2	2	no	—
491	C₄×Dic₈₉	—	2	2	no	—
492	C₄×Dic₈₉	—	2	2	no	—
493	C₄×Dic₈₉	—	2	2	no	—
494	C₄×Dic₈₉	—	4	1	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	C₄×Dic₈₉	—	4	1	no	—
501	C₄×Dic₈₉	—	4	1	no	—
502	C₄×Dic₈₉	—	4	1	no	—
503	C₄×Dic₈₉	—	4	1	no	—
504	C₄×Dic₈₉	—	4	1	no	—
505	C₄×Dic₈₉	—	4	1	no	—
506	C₄×Dic₈₉	C₂²×C₄	1	4	yes	—
507	C₄×Dic₈₉	C₂²×C₄	1	4	yes	—
508	C₄×Dic₈₉	C₂²×C₄	1	4	yes	—
509	C₄×Dic₈₉	C₂×Q₈	1	4	yes	complemented
510	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
511	C₂×Q₈×C₈₉	—	4	1	no	—
512	C₂×Q₈×C₈₉	—	4	1	no	—
513	C₂×Q₈×C₈₉	C₂²×C₄	1	4	yes	—
514	C₂²×C₄×C₈₉	—	2	2	no	—
515	C₂²×C₄×C₈₉	—	2	2	no	—
516	C₂²×C₄×C₈₉	—	2	2	no	—
517	C₂²×C₄×C₈₉	—	4	1	no	—
518	C₂²×C₄×C₈₉	—	4	1	no	—
519	C₂²×C₄×C₈₉	—	4	1	no	—
520	C₂²×C₄×C₈₉	—	4	1	no	—
521	C₂²×C₄×C₈₉	—	4	1	no	—
522	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
523	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
524	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
525	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
526	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
527	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
528	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
529	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	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
537	C₄⋊C₄×C₈₉	—	2	2	no	—
538	C₄⋊C₄×C₈₉	—	4	1	no	—
539	C₄⋊C₄×C₈₉	—	4	1	no	—
540	C₄⋊C₄×C₈₉	—	4	1	no	—
541	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
542	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
543	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
544	C₂²⋊C₄×C₈₉	—	2	2	no	—
545	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
546	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
547	C₂²⋊C₄×C₈₉	C₂×Q₈	1	4	yes	complemented
548	C₄²×C₈₉	—	2	2	no	—
549	C₄²×C₈₉	—	4	1	no	—
550	C₄²×C₈₉	—	4	1	no	—
551	C₄²×C₈₉	—	4	1	no	—
552	C₄²×C₈₉	—	4	1	no	—
553	C₄²×C₈₉	—	4	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	C₂³×C₄	1	2	yes	—
559	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
560	C₂³×C₈₉	C₂×#41	1	2	yes	—
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	C₂³×C₄	1	2	yes	—
567	C₂²×D₈₉	C₂²×Q₈	1	2	yes	—
568	C₂²×D₈₉	C₂×#41	1	2	yes	—
569	Q₈×C₈₉	—	4	4	no	—
570	C₂×C₄×C₈₉	—	2	1	no	—
571	C₂×C₄×C₈₉	—	2	1	no	—
572	C₂×C₄×C₈₉	—	2	1	no	—
573	C₂×C₄×C₈₉	—	2	1	no	—
574	C₂×C₄×C₈₉	—	2	1	no	—
575	C₂×C₄×C₈₉	—	2	1	no	—
576	C₂×C₄×C₈₉	—	2	1	no	—
577	C₂×C₄×C₈₉	—	2	1	no	—
578	C₂×C₄×C₈₉	—	2	1	no	—
579	C₂×C₄×C₈₉	—	2	1	no	—
580	C₂×C₄×C₈₉	—	2	1	no	—
581	C₂×C₄×C₈₉	—	2	1	no	—
582	C₂×C₄×C₈₉	—	2	1	no	—
583	C₂×C₄×C₈₉	—	2	1	no	—
584	C₂×C₄×C₈₉	—	2	1	no	—
585	C₂×C₄×C₈₉	—	2	1	no	—
586	C₂×C₄×C₈₉	—	2	1	no	—
587	C₂×C₄×C₈₉	—	2	1	no	—
588	C₂×C₄×C₈₉	—	2	1	no	—
589	C₂×C₄×C₈₉	—	2	1	no	—
590	C₂×C₄×C₈₉	—	2	1	no	—
591	C₂×C₄×C₈₉	—	2	1	no	—
592	C₂×C₄×C₈₉	—	2	1	no	—
593	C₂×C₄×C₈₉	—	2	1	no	—
594	C₂×C₄×C₈₉	—	2	1	no	—
595	C₂×C₄×C₈₉	—	2	1	no	—
596	C₂×C₄×C₈₉	—	2	1	no	—
597	C₂×C₄×C₈₉	—	2	1	no	—
598	C₂×C₄×C₈₉	—	2	1	no	—
599	C₂×C₄×C₈₉	—	2	1	no	—
600	C₂×C₄×C₈₉	—	2	1	no	—
601	C₂×C₄×C₈₉	—	2	1	no	—
602	C₂×C₄×C₈₉	—	2	1	no	—
603	C₂×C₄×C₈₉	—	4	4	no	—
604	C₂×C₄×C₈₉	—	4	4	no	—
605	C₂×C₄×C₈₉	—	8	2	no	—
606	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
607	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
608	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
609	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
610	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
611	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
612	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
613	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
614	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
615	C₂²⋊D₈₉	C₄×Q₈	1	16	yes	complemented
616	C₂×Dic₈₉	—	2	1	no	—
617	C₂×Dic₈₉	—	2	1	no	—
618	C₂×Dic₈₉	—	2	1	no	—
619	C₂×Dic₈₉	—	2	1	no	—
620	C₂×Dic₈₉	—	2	1	no	—
621	C₂×Dic₈₉	—	2	1	no	—
622	C₂×Dic₈₉	—	2	1	no	—
623	C₂×Dic₈₉	—	2	1	no	—
624	C₂×Dic₈₉	—	2	1	no	—
625	C₂×Dic₈₉	—	2	1	no	—
626	C₂×Dic₈₉	—	2	1	no	—
627	C₂×Dic₈₉	—	2	1	no	—
628	C₂×Dic₈₉	—	2	1	no	—
629	C₂×Dic₈₉	—	2	1	no	—
630	C₂×Dic₈₉	—	2	8	no	—
631	C₂×Dic₈₉	—	2	1	no	—
632	C₂×Dic₈₉	—	2	1	no	—
633	C₂×Dic₈₉	—	2	1	no	—
634	C₂×Dic₈₉	—	2	1	no	—
635	C₂×Dic₈₉	—	2	1	no	—
636	C₂×Dic₈₉	—	2	1	no	—
637	C₂×Dic₈₉	—	2	1	no	—
638	C₂×Dic₈₉	—	2	1	no	—
639	C₂×Dic₈₉	—	2	1	no	—
640	C₂×Dic₈₉	—	2	1	no	—
641	C₂×Dic₈₉	—	2	1	no	—
642	C₂×Dic₈₉	—	2	1	no	—
643	C₂×Dic₈₉	—	2	1	no	—
644	C₂×Dic₈₉	—	2	1	no	—
645	C₂×Dic₈₉	—	2	1	no	—
646	C₂×Dic₈₉	—	2	1	no	—
647	C₂×Dic₈₉	—	2	1	no	—
648	C₂×Dic₈₉	—	2	1	no	—
649	C₂×Dic₈₉	—	4	4	no	—
650	C₂×Dic₈₉	—	4	4	no	—
651	C₂×Dic₈₉	—	8	2	no	—
652	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
653	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
654	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
655	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
656	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
657	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
658	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
659	C₂×Dic₈₉	C₂²×Q₈	1	2	yes	—
660	C₂×Dic₈₉	C₂²×Q₈	1	2	yes	—
661	C₂×Dic₈₉	C₂²×Q₈	1	2	yes	—
662	C₂×Dic₈₉	C₂×#41	1	2	yes	—
663	C₂×Dic₈₉	H(5,𝔽₂)	1	2	yes	—
664	C₂×Dic₈₉	H(5,𝔽₂)	1	2	yes	—
665	C₄×D₈₉	—	2	8	no	—
666	C₄×D₈₉	—	4	4	no	—
667	C₄×D₈₉	—	4	4	no	—
668	C₄×D₈₉	—	4	4	no	—
669	C₄×D₈₉	—	4	4	no	—
670	C₄×D₈₉	—	8	2	no	—
671	C₄×D₈₉	—	8	2	no	—
672	Dic₁₇₈	—	2	8	no	—
673	Dic₁₇₈	—	2	8	no	—
674	Dic₁₇₈	—	2	8	no	—
675	Dic₁₇₈	—	4	4	no	—
676	Dic₁₇₈	—	4	4	no	—
677	Dic₁₇₈	—	4	4	no	—
678	C₂²×C₈₉	—	2	2	no	—
679	C₂²×C₈₉	—	2	2	no	—
680	C₂²×C₈₉	—	2	2	no	—
681	C₂²×C₈₉	—	2	2	no	—
682	C₂²×C₈₉	—	2	2	no	—
683	C₂²×C₈₉	—	2	2	no	—
684	C₂²×C₈₉	C₂×C₄×Q₈	1	4	yes	—
685	C₂²×C₈₉	C₂⁴×C₄	1	1	yes	characteristic
686	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
687	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
688	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
689	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
690	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
691	C₂²×C₈₉	#585	1	1	yes	characteristic
692	C₂×D₈₉	—	2	2	no	—
693	C₂×D₈₉	—	2	2	no	—
694	C₂×D₈₉	—	2	2	no	—
695	C₂×D₈₉	—	2	2	no	—
696	C₂×D₈₉	—	2	2	no	—
697	C₂×D₈₉	—	2	2	no	—
698	C₂×D₈₉	C₂×C₄×Q₈	1	4	yes	—
699	C₄×C₈₉	—	2	2	no	—
700	C₄×C₈₉	—	2	2	no	—
701	C₄×C₈₉	—	2	2	no	—
702	C₄×C₈₉	—	2	2	no	—
703	C₄×C₈₉	—	2	2	no	—
704	C₄×C₈₉	—	2	2	no	—
705	C₄×C₈₉	—	2	2	no	—
706	C₄×C₈₉	—	2	2	no	—
707	C₄×C₈₉	—	2	2	no	—
708	C₄×C₈₉	—	4	1	no	—
709	C₄×C₈₉	—	4	1	no	—
710	C₄×C₈₉	—	4	1	no	—
711	C₄×C₈₉	—	4	1	no	—
712	C₄×C₈₉	—	4	1	no	—
713	Dic₈₉	—	2	2	no	—
714	Dic₈₉	—	2	2	no	—
715	Dic₈₉	—	2	2	no	—
716	Dic₈₉	—	2	2	no	—
717	Dic₈₉	—	2	2	no	—
718	Dic₈₉	—	2	2	no	—
719	Dic₈₉	—	2	2	no	—
720	Dic₈₉	—	4	1	no	—
721	Dic₈₉	—	4	1	no	—
722	Dic₈₉	—	4	1	no	—
723	Dic₈₉	—	4	1	no	—
724	Dic₈₉	—	4	1	no	—
725	Dic₈₉	—	4	1	no	—
726	Dic₈₉	C₂×C₄×Q₈	1	4	yes	—
727	Dic₈₉	#518	1	4	yes	—
728	#34334	—	89	1	no	maximal, Sylow
729	C₂×C₈₉	—	2	4	no	—
730	C₂×C₈₉	C₂²×C₄×Q₈	1	1	yes	characteristic
731	C₂×C₈₉	C₂×#518	1	1	yes	characteristic
732	C₂×C₈₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic
733	C₂×C₈₉	#3501	1	1	yes	characteristic
734	C₂×C₈₉	#3503	1	1	yes	characteristic
735	C₂×C₈₉	#3514	1	1	yes	characteristic
736	C₂×C₈₉	#3520	1	1	yes	characteristic
737	D₈₉	—	2	4	no	—
738	C₂×D₄×Q₈	—	89	1	no	—
739	#2369	—	89	1	no	—
740	#2369	—	89	1	no	—
741	#2368	—	89	1	no	—
742	#2368	—	89	1	no	—
743	#2368	—	89	1	no	—
744	#2368	D₈₉	1	1	yes	characteristic, complemented
745	#2365	—	89	1	no	—
746	#2360	—	89	1	no	—
747	#2360	—	89	1	no	—
748	#2355	—	89	1	no	—
749	#2349	—	89	1	no	—
750	#2349	—	89	1	no	—
751	D₄×C₄⋊C₄	—	89	1	no	—
752	Q₈×C₂²⋊C₄	—	89	1	no	—
753	Q₈×C₂²⋊C₄	—	89	1	no	—
754	#2331	—	89	1	no	—
755	#2331	—	89	1	no	—
756	#2329	—	89	1	no	—
757	#2329	—	89	1	no	—
758	#2329	—	89	1	no	—
759	#2329	—	89	1	no	—
760	C₄×C₄⋊Q₈	—	89	1	no	—
761	C₄×C₂²⋊Q₈	—	89	1	no	—
762	C₄×C₂²⋊Q₈	—	89	1	no	—
763	#2295	—	89	1	no	—
764	C₂×#391	—	89	1	no	—
765	C₂×#391	—	89	1	no	—
766	#2275	—	89	1	no	—
767	#2275	—	89	1	no	—
768	C₄²×D₄	—	89	1	no	—
769	C₈₉	#34334	1	1	yes	characteristic, complemented, Sylow
770	C₂³×Q₈	—	89	1	no	—
771	C₂³×Q₈	—	89	1	no	—
772	D₄×Q₈	—	89	16	no	—
773	C₂×C₄⋊Q₈	—	89	1	no	—
774	C₂×C₄⋊Q₈	—	89	1	no	—
775	C₂×C₄⋊Q₈	—	89	1	no	—
776	C₂×C₂²⋊Q₈	—	89	1	no	—
777	C₂×C₂²⋊Q₈	—	89	1	no	—
778	C₂×C₂²⋊Q₈	—	89	1	no	—
779	C₂×C₂²⋊Q₈	—	89	1	no	—
780	C₂×C₂²⋊Q₈	—	89	1	no	—
781	C₂×C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
782	C₂×C₄×Q₈	—	89	1	no	—
783	C₂×C₄×Q₈	—	89	1	no	—
784	C₂×C₄×Q₈	—	89	1	no	—
785	C₂×C₄×Q₈	—	89	1	no	—
786	C₂×C₄×Q₈	—	89	1	no	—
787	C₂×C₄×D₄	—	89	1	no	—
788	C₂×C₄×D₄	—	89	1	no	—
789	C₂×C₄×D₄	—	89	1	no	—
790	C₂×C₄×D₄	—	89	1	no	—
791	C₂×C₄×D₄	—	89	1	no	—
792	C₂×C₄×D₄	—	89	1	no	—
793	C₂×C₄×D₄	—	89	1	no	—
794	C₂²×C₄⋊C₄	—	89	1	no	—
795	C₂²×C₄⋊C₄	—	89	1	no	—
796	C₂²×C₄²	—	89	1	no	—
797	C₂²×C₄²	—	89	1	no	—
798	#391	—	89	1	no	—
799	#391	—	89	1	no	—
800	#391	—	89	1	no	—
801	#391	—	89	1	no	—
802	#391	—	89	1	no	—
803	#391	—	89	1	no	—
804	#391	—	89	1	no	—
805	#391	—	89	1	no	—
806	#391	—	89	1	no	—
807	#391	—	89	1	no	—
808	#391	—	89	1	no	—
809	#391	—	89	1	no	—
810	#391	—	89	1	no	—
811	#391	—	89	1	no	—
812	#391	—	89	1	no	—
813	#391	—	89	1	no	—
814	#391	—	89	1	no	—
815	#391	—	89	1	no	—
816	#391	—	89	1	no	—
817	#391	—	89	1	no	—
818	#391	—	89	1	no	—
819	#391	—	89	1	no	—
820	#391	C₂×D₈₉	1	1	yes	characteristic
821	#391	C₂×D₈₉	1	1	yes	characteristic
822	#389	—	89	1	no	—
823	#389	—	89	1	no	—
824	#389	—	89	1	no	—
825	#389	—	89	1	no	—
826	#389	—	89	1	no	—
827	#389	—	89	1	no	—
828	#389	—	89	1	no	—
829	#389	—	89	1	no	—
830	#389	—	89	1	no	—
831	#389	—	89	1	no	—
832	#389	—	89	1	no	—
833	#389	—	89	1	no	—
834	#389	—	89	1	no	—
835	#389	—	89	1	no	—
836	#387	—	89	1	no	—
837	#387	—	89	1	no	—
838	#387	—	89	1	no	—
839	#387	—	89	1	no	—
840	#387	—	89	1	no	—
841	#387	—	89	1	no	—
842	#387	—	89	1	no	—
843	#387	—	89	1	no	—
844	#387	—	89	1	no	—
845	#387	—	89	1	no	—
846	#387	—	89	1	no	—
847	#387	—	89	1	no	—
848	#387	—	89	1	no	—
849	#387	—	89	1	no	—
850	#387	—	89	1	no	—
851	#387	—	89	1	no	—
852	#387	C₂×D₈₉	1	1	yes	characteristic
853	#387	C₂×D₈₉	1	1	yes	characteristic
854	#387	C₂×D₈₉	1	1	yes	characteristic
855	#387	C₂×D₈₉	1	1	yes	characteristic
856	#385	—	89	1	no	—
857	#385	—	89	1	no	—
858	#385	—	89	1	no	—
859	#385	—	89	1	no	—
860	#385	—	89	1	no	—
861	#385	—	89	1	no	—
862	#385	—	89	1	no	—
863	#385	—	89	1	no	—
864	#385	—	89	1	no	—
865	#385	—	89	1	no	—
866	#385	C₂×D₈₉	1	1	yes	characteristic
867	#385	C₂×D₈₉	1	1	yes	characteristic
868	#384	—	89	1	no	—
869	#382	—	89	1	no	—
870	#382	—	89	1	no	—
871	#380	—	89	1	no	—
872	#380	—	89	1	no	—
873	#380	—	89	1	no	—
874	#380	—	89	1	no	—
875	#380	—	89	1	no	—
876	#380	—	89	1	no	—
877	C₄×C₄⋊C₄	—	89	1	no	—
878	C₄×C₄⋊C₄	—	89	1	no	—
879	C₄×C₄⋊C₄	—	89	1	no	—
880	C₄×C₄⋊C₄	—	89	1	no	—
881	C₄×C₄⋊C₄	—	89	1	no	—
882	C₄×C₄⋊C₄	—	89	1	no	—
883	C₄×C₄⋊C₄	—	89	1	no	—
884	C₄×C₄⋊C₄	—	89	1	no	—
885	C₄×C₄⋊C₄	—	89	1	no	—
886	C₄×C₄⋊C₄	—	89	1	no	—
887	C₄×C₄⋊C₄	—	89	1	no	—
888	C₄×C₄⋊C₄	—	89	1	no	—
889	C₄×C₄⋊C₄	—	89	1	no	—
890	C₄×C₄⋊C₄	—	89	1	no	—
891	C₄×C₄⋊C₄	—	89	1	no	—
892	C₄×C₄⋊C₄	—	89	1	no	—
893	C₄×C₄⋊C₄	—	89	1	no	—
894	C₄×C₄⋊C₄	—	89	1	no	—
895	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
896	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
897	C₄×C₂²⋊C₄	—	89	1	no	—
898	C₄×C₂²⋊C₄	—	89	1	no	—
899	C₄×C₂²⋊C₄	—	89	1	no	—
900	C₄×C₂²⋊C₄	—	89	1	no	—
901	C₄×C₂²⋊C₄	—	89	1	no	—
902	C₄×C₂²⋊C₄	—	89	1	no	—
903	C₄×C₂²⋊C₄	—	89	1	no	—
904	C₄×C₂²⋊C₄	—	89	1	no	—
905	C₄×C₂²⋊C₄	—	89	1	no	—
906	C₄×C₂²⋊C₄	—	89	1	no	—
907	C₄×C₂²⋊C₄	—	89	1	no	—
908	C₄×C₂²⋊C₄	—	89	1	no	—
909	C₄×C₂²⋊C₄	—	89	1	no	—
910	C₄×C₂²⋊C₄	—	89	1	no	—
911	C₄×C₂²⋊C₄	—	89	1	no	—
912	C₄×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
913	C₄×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
914	C₄×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
915	#376	—	89	1	no	—
916	#376	—	89	1	no	—
917	C₂×#95	—	89	1	no	—
918	C₂×#95	—	89	1	no	—
919	C₂×#95	—	89	1	no	—
920	C₂×#95	—	89	1	no	—
921	C₂×#95	—	89	1	no	—
922	C₂×#95	—	89	1	no	—
923	C₂×#95	—	89	1	no	—
924	C₂×#95	C₂×D₈₉	1	1	yes	characteristic
925	C₄³	—	89	1	no	—
926	C₂²×Q₈	—	89	8	no	—
927	C₂²×Q₈	—	89	8	no	—
928	C₂²×Q₈	—	89	1	no	—
929	C₂²×Q₈	—	89	1	no	—
930	C₂²×Q₈	—	89	1	no	—
931	C₂²×Q₈	—	89	1	no	—
932	C₂²×Q₈	—	89	1	no	—
933	C₂²×Q₈	—	89	1	no	—
934	C₂²×Q₈	—	356	2	no	—
935	C₂²×Q₈	—	356	2	no	—
936	C₂²×Q₈	—	356	2	no	—
937	C₂²×Q₈	—	356	2	no	—
938	C₂²×Q₈	C₂²×D₈₉	1	1	yes	characteristic
939	C₂²×D₄	—	89	1	no	—
940	C₂³×C₄	—	89	1	no	—
941	C₂³×C₄	—	89	1	no	—
942	C₂³×C₄	—	89	1	no	—
943	C₂³×C₄	—	89	1	no	—
944	C₂³×C₄	—	89	1	no	—
945	C₂³×C₄	—	89	1	no	—
946	C₂³×C₄	—	89	1	no	—
947	C₂³×C₄	—	89	1	no	—
948	C₂³×C₄	—	89	1	no	—
949	C₂³×C₄	—	89	1	no	—
950	C₂³×C₄	—	89	1	no	—
951	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
952	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
953	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
954	C₄⋊Q₈	—	89	8	no	—
955	C₄⋊Q₈	—	89	8	no	—
956	C₄⋊Q₈	—	89	8	no	—
957	C₂²⋊Q₈	—	89	8	no	—
958	C₂²⋊Q₈	—	89	8	no	—
959	C₂²⋊Q₈	—	89	8	no	—
960	C₂²⋊Q₈	—	89	8	no	—
961	C₂²⋊Q₈	—	89	8	no	—
962	C₂²⋊Q₈	C₄×D₈₉	1	8	yes	complemented
963	C₄×Q₈	—	89	8	no	—
964	C₄×Q₈	—	356	2	no	—
965	C₄×Q₈	—	356	2	no	—
966	C₄×Q₈	—	356	2	no	—
967	C₄×Q₈	—	356	2	no	—
968	C₄×D₄	—	89	8	no	—
969	C₄×D₄	—	89	8	no	—
970	C₄×D₄	—	89	8	no	—
971	C₄×D₄	—	89	8	no	—
972	C₄×D₄	—	178	4	no	—
973	C₄×D₄	—	178	4	no	—
974	C₄×D₄	—	178	4	no	—
975	C₂×C₄⋊C₄	—	89	1	no	—
976	C₂×C₄⋊C₄	—	89	1	no	—
977	C₂×C₄⋊C₄	—	89	1	no	—
978	C₂×C₄⋊C₄	—	89	1	no	—
979	C₂×C₄⋊C₄	—	89	1	no	—
980	C₂×C₄⋊C₄	—	89	1	no	—
981	C₂×C₄⋊C₄	—	89	1	no	—
982	C₂×C₄⋊C₄	—	89	1	no	—
983	C₂×C₄⋊C₄	—	89	1	no	—
984	C₂×C₄⋊C₄	—	89	1	no	—
985	C₂×C₄⋊C₄	—	89	1	no	—
986	C₂×C₄⋊C₄	—	89	1	no	—
987	C₂×C₄⋊C₄	—	89	1	no	—
988	C₂×C₄⋊C₄	—	89	1	no	—
989	C₂×C₄⋊C₄	—	89	1	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	—	356	2	no	—
1007	C₂×C₄⋊C₄	—	356	2	no	—
1008	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1009	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1010	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1011	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1012	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1013	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1014	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1015	C₂×C₂²⋊C₄	—	89	1	no	—
1016	C₂×C₂²⋊C₄	—	89	1	no	—
1017	C₂×C₂²⋊C₄	—	89	1	no	—
1018	C₂×C₂²⋊C₄	—	89	1	no	—
1019	C₂×C₂²⋊C₄	—	89	1	no	—
1020	C₂×C₂²⋊C₄	—	89	1	no	—
1021	C₂×C₂²⋊C₄	—	89	1	no	—
1022	C₂×C₂²⋊C₄	—	89	1	no	—
1023	C₂×C₂²⋊C₄	—	89	1	no	—
1024	C₂×C₂²⋊C₄	—	89	1	no	—
1025	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1026	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1027	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1028	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1029	C₂×C₄²	—	89	1	no	—
1030	C₂×C₄²	—	89	1	no	—
1031	C₂×C₄²	—	89	1	no	—
1032	C₂×C₄²	—	89	1	no	—
1033	C₂×C₄²	—	89	1	no	—
1034	C₂×C₄²	—	89	1	no	—
1035	C₂×C₄²	—	89	1	no	—
1036	C₂×C₄²	—	89	1	no	—
1037	C₂×C₄²	—	89	1	no	—
1038	C₂×C₄²	—	89	1	no	—
1039	C₂×C₄²	—	89	1	no	—
1040	C₂×C₄²	—	89	1	no	—
1041	C₂×C₄²	—	89	1	no	—
1042	C₂×C₄²	—	89	1	no	—
1043	C₂×C₄²	—	89	1	no	—
1044	C₂×C₄²	—	89	1	no	—
1045	C₂×C₄²	—	89	1	no	—
1046	C₂×C₄²	—	89	1	no	—
1047	C₂×C₄²	—	89	1	no	—
1048	C₂×C₄²	—	89	1	no	—
1049	C₂×C₄²	—	89	1	no	—
1050	C₂×C₄²	—	89	1	no	—
1051	C₂×C₄²	—	89	1	no	—
1052	C₂×C₄²	—	356	2	no	—
1053	C₂×C₄²	—	356	2	no	—
1054	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1055	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1056	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1057	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1058	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1059	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1060	#95	—	89	1	no	—
1061	#95	—	89	1	no	—
1062	#95	—	89	1	no	—
1063	#95	—	89	1	no	—
1064	#95	—	89	1	no	—
1065	#95	—	89	1	no	—
1066	#95	—	89	1	no	—
1067	#95	—	89	1	no	—
1068	#95	—	89	1	no	—
1069	#95	—	89	1	no	—
1070	#95	—	89	1	no	—
1071	#95	—	89	1	no	—
1072	#95	—	89	1	no	—
1073	#95	—	89	1	no	—
1074	#95	—	89	1	no	—
1075	#95	—	89	1	no	—
1076	#95	—	89	1	no	—
1077	#95	—	89	1	no	—
1078	#95	—	89	1	no	—
1079	#95	—	89	1	no	—
1080	#95	—	89	1	no	—
1081	#95	—	89	1	no	—
1082	#95	—	89	1	no	—
1083	#95	—	89	1	no	—
1084	#95	—	89	1	no	—
1085	#95	—	89	1	no	—
1086	#95	—	89	1	no	—
1087	#95	—	89	1	no	—
1088	#95	—	89	1	no	—
1089	#95	—	89	1	no	—
1090	#95	—	89	1	no	—
1091	#95	—	89	1	no	—
1092	#95	—	89	1	no	—
1093	#95	—	89	1	no	—
1094	#95	—	89	1	no	—
1095	#95	—	89	1	no	—
1096	#95	—	89	1	no	—
1097	#95	—	89	1	no	—
1098	#95	C₂²×D₈₉	1	1	yes	characteristic
1099	#95	C₂²×D₈₉	1	1	yes	characteristic
1100	#95	C₂²×D₈₉	1	1	yes	characteristic
1101	#95	C₂²×D₈₉	1	1	yes	characteristic
1102	#95	C₂²×D₈₉	1	1	yes	characteristic
1103	#95	C₂²×D₈₉	1	1	yes	characteristic
1104	#95	C₂²×D₈₉	1	1	yes	characteristic
1105	#95	C₂²×D₈₉	1	1	yes	characteristic
1106	#95	C₂²×D₈₉	1	1	yes	characteristic
1107	#95	C₂²×D₈₉	1	1	yes	characteristic
1108	#95	C₂²×D₈₉	1	1	yes	characteristic
1109	#95	C₂²×D₈₉	1	1	yes	characteristic
1110	#95	C₂²×D₈₉	1	1	yes	characteristic
1111	#95	C₂²×D₈₉	1	1	yes	characteristic
1112	C₂⁴	—	89	1	no	—
1113	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
1114	C₂×Q₈	—	4	1	no	—
1115	C₂×Q₈	—	4	1	no	—
1116	C₂×Q₈	—	89	4	no	—
1117	C₂×Q₈	—	89	4	no	—
1118	C₂×Q₈	—	89	4	no	—
1119	C₂×Q₈	—	89	4	no	—
1120	C₂×Q₈	—	89	4	no	—
1121	C₂×Q₈	—	89	4	no	—
1122	C₂×Q₈	—	356	1	no	—
1123	C₂×Q₈	—	356	1	no	—
1124	C₂×Q₈	—	356	1	no	—
1125	C₂×Q₈	—	356	1	no	—
1126	C₂×Q₈	—	356	1	no	—
1127	C₂×Q₈	—	356	1	no	—
1128	C₂×Q₈	—	356	16	no	—
1129	C₂×Q₈	—	356	16	no	—
1130	C₂×Q₈	—	178	2	no	—
1131	C₂×Q₈	—	178	2	no	—
1132	C₂×Q₈	—	178	2	no	—
1133	C₂×Q₈	—	178	2	no	—
1134	C₂×Q₈	—	178	2	no	—
1135	C₂×Q₈	—	178	2	no	—
1136	C₂×Q₈	C₂×C₄×D₈₉	1	4	yes	—
1137	C₂×D₄	—	89	4	no	—
1138	C₂×D₄	—	89	4	no	—
1139	C₂×D₄	—	89	4	no	—
1140	C₂²×C₄	—	2	2	no	—
1141	C₂²×C₄	—	2	2	no	—
1142	C₂²×C₄	—	2	2	no	—
1143	C₂²×C₄	—	4	1	no	—
1144	C₂²×C₄	—	4	1	no	—
1145	C₂²×C₄	—	4	1	no	—
1146	C₂²×C₄	—	4	1	no	—
1147	C₂²×C₄	—	4	1	no	—
1148	C₂²×C₄	—	89	1	no	—
1149	C₂²×C₄	—	89	1	no	—
1150	C₂²×C₄	—	89	4	no	—
1151	C₂²×C₄	—	89	4	no	—
1152	C₂²×C₄	—	89	4	no	—
1153	C₂²×C₄	—	89	1	no	—
1154	C₂²×C₄	—	89	1	no	—
1155	C₂²×C₄	—	89	1	no	—
1156	C₂²×C₄	—	89	1	no	—
1157	C₂²×C₄	—	89	1	no	—
1158	C₂²×C₄	—	89	1	no	—
1159	C₂²×C₄	—	89	1	no	—
1160	C₂²×C₄	—	89	4	no	—
1161	C₂²×C₄	—	89	4	no	—
1162	C₂²×C₄	—	89	4	no	—
1163	C₂²×C₄	—	89	4	no	—
1164	C₂²×C₄	—	89	1	no	—
1165	C₂²×C₄	—	89	1	no	—
1166	C₂²×C₄	—	89	1	no	—
1167	C₂²×C₄	—	89	1	no	—
1168	C₂²×C₄	—	89	1	no	—
1169	C₂²×C₄	—	89	1	no	—
1170	C₂²×C₄	—	356	1	no	—
1171	C₂²×C₄	—	356	1	no	—
1172	C₂²×C₄	—	356	1	no	—
1173	C₂²×C₄	—	356	1	no	—
1174	C₂²×C₄	—	356	1	no	—
1175	C₂²×C₄	—	356	1	no	—
1176	C₂²×C₄	—	356	1	no	—
1177	C₂²×C₄	—	356	1	no	—
1178	C₂²×C₄	—	356	1	no	—
1179	C₂²×C₄	—	356	1	no	—
1180	C₂²×C₄	—	356	1	no	—
1181	C₂²×C₄	—	356	1	no	—
1182	C₂²×C₄	—	356	1	no	—
1183	C₂²×C₄	—	356	1	no	—
1184	C₂²×C₄	—	356	1	no	—
1185	C₂²×C₄	—	356	1	no	—
1186	C₂²×C₄	—	356	1	no	—
1187	C₂²×C₄	—	178	2	no	—
1188	C₂²×C₄	—	178	2	no	—
1189	C₂²×C₄	—	178	2	no	—
1190	C₂²×C₄	—	178	2	no	—
1191	C₂²×C₄	—	178	2	no	—
1192	C₂²×C₄	—	178	2	no	—
1193	C₂²×C₄	—	178	2	no	—
1194	C₂²×C₄	—	178	2	no	—
1195	C₂²×C₄	—	178	2	no	—
1196	C₂²×C₄	C₂×C₄×D₈₉	1	4	yes	—
1197	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1198	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1199	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1200	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1201	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1202	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1203	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1204	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1205	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1206	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1207	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1208	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1209	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1210	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1211	C₄⋊C₄	—	2	2	no	—
1212	C₄⋊C₄	—	4	1	no	—
1213	C₄⋊C₄	—	4	1	no	—
1214	C₄⋊C₄	—	4	1	no	—
1215	C₄⋊C₄	—	89	4	no	—
1216	C₄⋊C₄	—	89	4	no	—
1217	C₄⋊C₄	—	89	4	no	—
1218	C₄⋊C₄	—	89	4	no	—
1219	C₄⋊C₄	—	89	4	no	—
1220	C₄⋊C₄	—	89	4	no	—
1221	C₄⋊C₄	—	89	4	no	—
1222	C₄⋊C₄	—	89	4	no	—
1223	C₄⋊C₄	—	89	4	no	—
1224	C₄⋊C₄	—	89	4	no	—
1225	C₄⋊C₄	—	356	1	no	—
1226	C₄⋊C₄	—	356	1	no	—
1227	C₄⋊C₄	—	356	1	no	—
1228	C₄⋊C₄	—	356	1	no	—
1229	C₄⋊C₄	—	356	1	no	—
1230	C₄⋊C₄	—	356	1	no	—
1231	C₄⋊C₄	—	356	1	no	—
1232	C₄⋊C₄	—	356	1	no	—
1233	C₄⋊C₄	—	356	1	no	—
1234	C₄⋊C₄	—	356	1	no	—
1235	C₄⋊C₄	—	356	1	no	—
1236	C₄⋊C₄	—	356	1	no	—
1237	C₄⋊C₄	—	356	1	no	—
1238	C₄⋊C₄	—	178	2	no	—
1239	C₄⋊C₄	—	178	2	no	—
1240	C₄⋊C₄	—	178	2	no	—
1241	C₄⋊C₄	—	178	2	no	—
1242	C₄⋊C₄	—	178	2	no	—
1243	C₄⋊C₄	—	178	2	no	—
1244	C₄⋊C₄	—	178	2	no	—
1245	C₄⋊C₄	—	178	2	no	—
1246	C₄⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1247	C₄⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1248	C₄⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1249	C₂²⋊C₄	—	2	2	no	—
1250	C₂²⋊C₄	—	89	4	no	—
1251	C₂²⋊C₄	—	89	4	no	—
1252	C₂²⋊C₄	—	89	4	no	—
1253	C₂²⋊C₄	—	89	4	no	—
1254	C₂²⋊C₄	—	89	4	no	—
1255	C₂²⋊C₄	—	178	2	no	—
1256	C₂²⋊C₄	—	178	2	no	—
1257	C₂²⋊C₄	—	178	2	no	—
1258	C₂²⋊C₄	—	178	2	no	—
1259	C₂²⋊C₄	—	178	2	no	—
1260	C₂²⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1261	C₂²⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1262	C₂²⋊C₄	Q₈×D₈₉	1	4	yes	complemented
1263	C₄²	—	2	2	no	—
1264	C₄²	—	4	1	no	—
1265	C₄²	—	4	1	no	—
1266	C₄²	—	4	1	no	—
1267	C₄²	—	4	1	no	—
1268	C₄²	—	4	1	no	—
1269	C₄²	—	89	4	no	—
1270	C₄²	—	89	4	no	—
1271	C₄²	—	89	4	no	—
1272	C₄²	—	89	4	no	—
1273	C₄²	—	356	1	no	—
1274	C₄²	—	356	1	no	—
1275	C₄²	—	356	1	no	—
1276	C₄²	—	356	1	no	—
1277	C₄²	—	356	1	no	—
1278	C₄²	—	356	1	no	—
1279	C₄²	—	356	1	no	—
1280	C₄²	—	356	1	no	—
1281	C₄²	—	356	1	no	—
1282	C₄²	—	356	1	no	—
1283	C₄²	—	356	1	no	—
1284	C₄²	—	356	1	no	—
1285	C₄²	—	178	2	no	—
1286	C₄²	—	178	2	no	—
1287	C₄²	—	178	2	no	—
1288	C₄²	—	178	2	no	—
1289	C₄²	—	178	2	no	—
1290	C₄²	—	178	2	no	—
1291	C₄²	—	178	2	no	—
1292	C₂³	—	2	1	no	—
1293	C₂³	—	2	1	no	—
1294	C₂³	—	2	1	no	—
1295	C₂³	—	2	1	no	—
1296	C₂³	—	89	2	no	—
1297	C₂³	—	89	2	no	—
1298	C₂³	—	89	2	no	—
1299	C₂³	—	178	1	no	—
1300	C₂³	—	178	1	no	—
1301	C₂³	—	178	1	no	—
1302	C₂³	—	178	1	no	—
1303	C₂³	C₂²×C₄×D₈₉	1	2	yes	—
1304	C₂³	C₂×Q₈×D₈₉	1	2	yes	—
1305	C₂³	#41×D₈₉	1	2	yes	—
1306	C₂³	C₂⁴×D₈₉	1	1	yes	characteristic
1307	Q₈	—	4	4	no	—
1308	Q₈	—	356	4	no	—
1309	Q₈	—	356	4	no	—
1310	Q₈	—	356	4	no	—
1311	Q₈	—	178	8	no	—
1312	Q₈	—	178	8	no	—
1313	Q₈	—	178	8	no	—
1314	D₄	—	89	16	no	—
1315	C₂×C₄	—	2	1	no	—
1316	C₂×C₄	—	2	1	no	—
1317	C₂×C₄	—	2	1	no	—
1318	C₂×C₄	—	2	1	no	—
1319	C₂×C₄	—	2	1	no	—
1320	C₂×C₄	—	2	1	no	—
1321	C₂×C₄	—	2	1	no	—
1322	C₂×C₄	—	2	1	no	—
1323	C₂×C₄	—	2	1	no	—
1324	C₂×C₄	—	2	1	no	—
1325	C₂×C₄	—	2	1	no	—
1326	C₂×C₄	—	2	1	no	—
1327	C₂×C₄	—	2	1	no	—
1328	C₂×C₄	—	2	1	no	—
1329	C₂×C₄	—	2	1	no	—
1330	C₂×C₄	—	2	1	no	—
1331	C₂×C₄	—	2	1	no	—
1332	C₂×C₄	—	2	1	no	—
1333	C₂×C₄	—	2	1	no	—
1334	C₂×C₄	—	2	1	no	—
1335	C₂×C₄	—	2	1	no	—
1336	C₂×C₄	—	2	1	no	—
1337	C₂×C₄	—	2	1	no	—
1338	C₂×C₄	—	2	1	no	—
1339	C₂×C₄	—	2	1	no	—
1340	C₂×C₄	—	2	1	no	—
1341	C₂×C₄	—	2	1	no	—
1342	C₂×C₄	—	2	1	no	—
1343	C₂×C₄	—	2	1	no	—
1344	C₂×C₄	—	2	1	no	—
1345	C₂×C₄	—	2	1	no	—
1346	C₂×C₄	—	2	1	no	—
1347	C₂×C₄	—	2	1	no	—
1348	C₂×C₄	—	4	4	no	—
1349	C₂×C₄	—	4	4	no	—
1350	C₂×C₄	—	8	2	no	—
1351	C₂×C₄	—	89	2	no	—
1352	C₂×C₄	—	89	2	no	—
1353	C₂×C₄	—	89	2	no	—
1354	C₂×C₄	—	89	2	no	—
1355	C₂×C₄	—	89	2	no	—
1356	C₂×C₄	—	89	2	no	—
1357	C₂×C₄	—	89	2	no	—
1358	C₂×C₄	—	89	2	no	—
1359	C₂×C₄	—	89	2	no	—
1360	C₂×C₄	—	89	2	no	—
1361	C₂×C₄	—	89	2	no	—
1362	C₂×C₄	—	89	2	no	—
1363	C₂×C₄	—	89	2	no	—
1364	C₂×C₄	—	356	4	no	—
1365	C₂×C₄	—	356	4	no	—
1366	C₂×C₄	—	356	4	no	—
1367	C₂×C₄	—	356	4	no	—
1368	C₂×C₄	—	356	4	no	—
1369	C₂×C₄	—	356	4	no	—
1370	C₂×C₄	—	178	8	no	—
1371	C₂×C₄	—	178	8	no	—
1372	C₂×C₄	—	178	1	no	—
1373	C₂×C₄	—	178	1	no	—
1374	C₂×C₄	—	178	1	no	—
1375	C₂×C₄	—	178	1	no	—
1376	C₂×C₄	—	178	1	no	—
1377	C₂×C₄	—	178	1	no	—
1378	C₂×C₄	—	178	1	no	—
1379	C₂×C₄	—	178	1	no	—
1380	C₂×C₄	—	178	1	no	—
1381	C₂×C₄	—	178	1	no	—
1382	C₂×C₄	—	178	1	no	—
1383	C₂×C₄	—	178	1	no	—
1384	C₂×C₄	—	178	1	no	—
1385	C₂×C₄	—	178	1	no	—
1386	C₂×C₄	—	178	1	no	—
1387	C₂×C₄	—	178	1	no	—
1388	C₂×C₄	—	178	1	no	—
1389	C₂×C₄	—	178	1	no	—
1390	C₂×C₄	—	178	1	no	—
1391	C₂×C₄	—	178	1	no	—
1392	C₂×C₄	—	178	1	no	—
1393	C₂×C₄	—	178	1	no	—
1394	C₂×C₄	—	178	1	no	—
1395	C₂×C₄	—	178	1	no	—
1396	C₂×C₄	—	178	1	no	—
1397	C₂×C₄	—	178	1	no	—
1398	C₂×C₄	—	178	1	no	—
1399	C₂×C₄	—	178	1	no	—
1400	C₂×C₄	—	178	1	no	—
1401	C₂×C₄	—	178	1	no	—
1402	C₂×C₄	—	178	1	no	—
1403	C₂×C₄	—	178	1	no	—
1404	C₂×C₄	—	712	2	no	—
1405	C₂×C₄	—	712	2	no	—
1406	C₂×C₄	—	712	2	no	—
1407	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1408	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1409	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1410	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1411	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1412	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1413	C₂×C₄	C₂×Q₈×D₈₉	1	2	yes	—
1414	C₂×C₄	C₂×Q₈×D₈₉	1	2	yes	—
1415	C₂×C₄	#15668059	1	2	yes	—
1416	C₂²	—	2	2	no	—
1417	C₂²	—	2	2	no	—
1418	C₂²	—	2	2	no	—
1419	C₂²	—	2	2	no	—
1420	C₂²	—	2	2	no	—
1421	C₂²	—	2	2	no	—
1422	C₂²	—	89	4	no	—
1423	C₂²	—	178	2	no	—
1424	C₂²	—	178	2	no	—
1425	C₂²	—	178	2	no	—
1426	C₂²	—	178	2	no	—
1427	C₂²	—	178	2	no	—
1428	C₂²	—	178	2	no	—
1429	C₂²	C₄×Q₈×D₈₉	1	4	yes	—
1430	C₂²	C₂³×C₄×D₈₉	1	1	yes	characteristic
1431	C₂²	C₂²×Q₈×D₈₉	1	1	yes	characteristic
1432	C₂²	C₂×#41×D₈₉	1	1	yes	characteristic
1433	C₂²	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
1434	C₂²	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
1435	C₂²	C₂×#15668059	1	1	yes	characteristic
1436	C₂²	#19152434	1	1	yes	characteristic
1437	C₄	—	2	2	no	—
1438	C₄	—	2	2	no	—
1439	C₄	—	2	2	no	—
1440	C₄	—	2	2	no	—
1441	C₄	—	2	2	no	—
1442	C₄	—	2	2	no	—
1443	C₄	—	2	2	no	—
1444	C₄	—	2	2	no	—
1445	C₄	—	2	2	no	—
1446	C₄	—	4	1	no	—
1447	C₄	—	4	1	no	—
1448	C₄	—	4	1	no	—
1449	C₄	—	4	1	no	—
1450	C₄	—	4	1	no	—
1451	C₄	—	89	4	no	—
1452	C₄	—	89	4	no	—
1453	C₄	—	356	1	no	—
1454	C₄	—	356	1	no	—
1455	C₄	—	356	1	no	—
1456	C₄	—	356	1	no	—
1457	C₄	—	356	1	no	—
1458	C₄	—	356	1	no	—
1459	C₄	—	178	2	no	—
1460	C₄	—	178	2	no	—
1461	C₄	—	178	2	no	—
1462	C₄	—	178	2	no	—
1463	C₄	—	178	2	no	—
1464	C₄	—	178	2	no	—
1465	C₄	—	178	2	no	—
1466	C₂	—	2	4	no	—
1467	C₂	—	178	4	no	—
1468	C₂	C₂×C₄×Q₈×D₈₉	1	1	yes	characteristic
1469	C₂	#518×D₈₉	1	1	yes	characteristic
1470	C₂	C₄×#15668059	1	1	yes	characteristic
1471	C₂	#26034051	1	1	yes	characteristic
1472	C₂	#26034066	1	1	yes	characteristic
1473	C₂	#26034202	1	1	yes	characteristic
1474	C₂	#26034290	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₈₉
commutator	C₂²×C₈₉	C₂⁴×C₄
Fitting	C₈₉×#2368	C₂
socle, cosocle	C₂³×C₈₉	C₂⁵
prime radical	C₂²×C₂²⋊D₈₉	C₂³
hypercenter	#2368	D₈₉
hypocenter	C₈₉	#34334
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ #2368

Complements

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

N	H ≅ G/N	type
2. #26023340	C₂	semidirect
3. #26023339	C₂	semidirect
4. #26023336	C₂	semidirect
5. #26023334	C₂	semidirect
6. #26023330	C₂	semidirect
7. #26023307	C₂	semidirect
8. #26023260	C₂	semidirect
9. #26023258	C₂	semidirect
10. #26023206	C₂	semidirect
14. C₂²⋊C₄×Dic₁₇₈	C₂	semidirect
15. #26023086	C₂	semidirect
16. #26022997	C₂	semidirect
17. #26022995	C₂	semidirect
18. #26022987	C₂	semidirect
19. #26022983	C₂	semidirect
20. #26022981	C₂	semidirect
21. #26022979	C₂	semidirect
22. C₄×#15668011	C₂	semidirect
23. C₄×#15667990	C₂	semidirect
24. #26022784	C₂	semidirect
25. #26022725	C₂	semidirect
26. C₂×#19151502	C₂	semidirect
27. #391×D₈₉	C₂	semidirect
31. C₈₉×#2368	C₂	semidirect
34. #19152261	C₄	semidirect
190. C₂²×Dic₁₇₈	C₂×C₄	semidirect
199. C₂×Q₈×D₈₉	C₂×C₄	semidirect
212. #15668011	C₂×C₄	semidirect
213. #15668011	C₂×C₄	semidirect
214. #15668010	C₂×C₄	semidirect
215. #15667992	C₂×C₄	semidirect
216. #15667990	C₂×C₄	semidirect
217. #15667990	C₂×C₄	semidirect
218. #15667989	C₂×C₄	semidirect
219. #15667989	C₂×C₄	semidirect
224. #15667977	C₂×C₄	semidirect
231. #15667972	Q₈	semidirect
342. C₂²⋊Q₈×C₈₉	C₂×C₄	semidirect
409. C₂²×Dic₈₉	C₂×Q₈	semidirect
445. C₂×C₄×D₈₉	C₂×Q₈	semidirect
476. #13083553	C₂×Q₈	semidirect
486. #13083551	C₂×Q₈	semidirect
509. C₄×Dic₈₉	C₂×Q₈	semidirect
547. C₂²⋊C₄×C₈₉	C₂×Q₈	semidirect
615. C₂²⋊D₈₉	C₄×Q₈	semidirect
744. #2368	D₈₉	semidirect
769. C₈₉	#34334	semidirect
962. C₂²⋊Q₈	C₄×D₈₉	semidirect
1262. C₂²⋊C₄	Q₈×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19152261	2
#26023340	2
#26023339	2
#26023336	2
#26023334	2
#26023330	2
#26023307	2
#26023260	2
#26023258	2
#26023206	2
#26023159	2
#26023158	2
#26023150	2
C₂²⋊C₄×Dic₁₇₈	2
#26023086	2
#26022997	2
#26022995	2
#26022987	2
#26022983	2
#26022981	2
#26022979	2
C₄×#15668011	2
C₄×#15667990	2
#26022784	2
#26022725	2
C₂×#19151502	2
#391×D₈₉	2
#26022611	2
C₄×#15667972	2
C₈₉×#2368	2
#34334	89