Subgroups — #36716914

Order 22784.

2388 conjugacy classes of subgroups.

The subgroup lattice has 1464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19152302	C₂	1	1	yes	maximal, characteristic
2	#26023351	C₂	1	1	yes	maximal, characteristic, complemented
3	#26023349	C₂	1	1	yes	maximal, characteristic, complemented
4	#26023340	C₂	1	1	yes	maximal, characteristic, complemented
5	#26023260	C₂	1	1	yes	maximal, characteristic, complemented
6	#26023258	C₂	1	1	yes	maximal, characteristic, complemented
7	#26023258	C₂	1	1	yes	maximal, characteristic, complemented
8	#26023254	C₂	1	1	yes	maximal, characteristic, complemented
9	#26023253	C₂	1	1	yes	maximal, characteristic, complemented
10	#26023166	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄⋊C₄×C₂²⋊D₈₉	C₂	1	1	yes	maximal, characteristic
12	#26023150	C₂	1	1	yes	maximal, characteristic
13	#26023150	C₂	1	1	yes	maximal, characteristic
14	#26023130	C₂	1	1	yes	maximal, characteristic, complemented
15	#26023126	C₂	1	1	yes	maximal, characteristic, complemented
16	#26022990	C₂	1	1	yes	maximal, characteristic, complemented
17	#26022988	C₂	1	1	yes	maximal, characteristic, complemented
18	#26022987	C₂	1	1	yes	maximal, characteristic, complemented
19	#26022986	C₂	1	1	yes	maximal, characteristic, complemented
20	#26022984	C₂	1	1	yes	maximal, characteristic, complemented
21	#26022983	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#15668010	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×#19151493	C₂	1	1	yes	maximal, characteristic, complemented
27	#389×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×#2360	C₂	1	1	yes	maximal, characteristic, complemented
32	#19152302	C₄	1	16	yes	complemented
33	C₂×#15668010	C₂²	1	1	yes	characteristic
34	C₂×#15668002	C₂²	1	1	yes	characteristic
35	C₂×#15668002	C₂²	1	1	yes	characteristic
36	C₂×#15667990	C₂²	1	1	yes	characteristic
37	C₂×#15667990	C₂²	1	1	yes	characteristic
38	C₂×#15667989	C₂²	1	1	yes	characteristic
39	C₂×#15667989	C₂²	1	1	yes	characteristic
40	C₂×#15667988	C₂²	1	1	yes	characteristic
41	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
42	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
43	C₂×#15667977	C₂²	1	1	yes	characteristic
44	C₂×#15667977	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
48	C₂×#15667972	C₂²	1	1	yes	characteristic
49	C₂×#15667972	C₂²	1	1	yes	characteristic
50	C₂×#15667972	C₂²	1	1	yes	characteristic
51	C₂×#15667972	C₂²	1	1	yes	characteristic
52	C₂²×#13083553	C₂²	1	1	yes	characteristic
53	C₂²×#13083553	C₂²	1	1	yes	characteristic
54	C₂²×#13083553	C₂²	1	1	yes	characteristic
55	C₂×C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
57	C₂×C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
58	C₂×C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
59	C₂²×C₄×Dic₈₉	C₂²	1	1	yes	characteristic
60	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
61	#19151505	C₂²	1	1	yes	characteristic
62	#19151505	C₂²	1	1	yes	characteristic
63	#19151503	C₂²	1	1	yes	characteristic
64	#19151502	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	#19151497	C₂²	1	1	yes	characteristic
69	#19151497	C₂²	1	1	yes	characteristic
70	#19151496	C₂²	1	1	yes	characteristic
71	#19151496	C₂²	1	1	yes	characteristic
72	#19151495	C₂²	1	1	yes	characteristic
73	#19151495	C₂²	1	1	yes	characteristic
74	#19151495	C₂²	1	1	yes	characteristic
75	#19151495	C₂²	1	1	yes	characteristic
76	#19151495	C₂²	1	1	yes	characteristic
77	#19151495	C₂²	1	1	yes	characteristic
78	#19151495	C₂²	1	1	yes	characteristic
79	#19151495	C₂²	1	1	yes	characteristic
80	#19151494	C₂²	1	1	yes	characteristic
81	#19151493	C₂²	1	1	yes	characteristic
82	#19151493	C₂²	1	1	yes	characteristic
83	#19151493	C₂²	1	1	yes	characteristic
84	#19151493	C₂²	1	1	yes	characteristic
85	#19151493	C₂²	1	1	yes	characteristic
86	#19151493	C₂²	1	1	yes	characteristic
87	#19151493	C₂²	1	1	yes	characteristic
88	#19151493	C₂²	1	1	yes	characteristic
89	#19151493	C₂²	1	1	yes	characteristic
90	#19151493	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	#19151482	C₂²	1	1	yes	characteristic
106	#19151482	C₂²	1	1	yes	characteristic
107	#19151481	C₂²	1	1	yes	characteristic
108	#19151481	C₂²	1	1	yes	characteristic
109	#19151480	C₂²	1	1	yes	characteristic
110	#19151480	C₂²	1	1	yes	characteristic
111	#19151479	C₂²	1	1	yes	characteristic
112	#19151479	C₂²	1	1	yes	characteristic
113	#19151473	C₂²	1	1	yes	characteristic
114	#19151473	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	#19151469	C₂²	1	1	yes	characteristic
122	#19151469	C₂²	1	1	yes	characteristic
123	#19151467	C₂²	1	1	yes	characteristic
124	#19151467	C₂²	1	1	yes	characteristic
125	#19151467	C₂²	1	1	yes	characteristic
126	#19151458	C₂²	1	1	yes	characteristic
127	#19151457	C₂²	1	1	yes	characteristic
128	#19151457	C₂²	1	1	yes	characteristic
129	#19151456	C₂²	1	1	yes	characteristic
130	#19151456	C₂²	1	1	yes	characteristic
131	#19151455	C₂²	1	1	yes	characteristic
132	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
133	C₄⋊C₄×Dic₈₉	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×#13083553	C₂²	1	1	yes	characteristic
140	C₄×#13083553	C₂²	1	1	yes	characteristic
141	C₄×#13083553	C₂²	1	1	yes	characteristic
142	C₄×#13083553	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	#19151449	C₂²	1	1	yes	characteristic
149	#19151449	C₂²	1	1	yes	characteristic
150	#19151449	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	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
155	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
156	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
157	C₄×#13083551	C₂²	1	1	yes	characteristic
158	C₄×#13083551	C₂²	1	1	yes	characteristic
159	C₄×#13083551	C₂²	1	1	yes	characteristic
160	C₄×#13083551	C₂²	1	1	yes	characteristic
161	C₄×#13083551	C₂²	1	1	yes	characteristic
162	#19151445	C₂²	1	1	yes	characteristic
163	#19151445	C₂²	1	1	yes	characteristic
164	#19151445	C₂²	1	1	yes	characteristic
165	#19151445	C₂²	1	1	yes	characteristic
166	#19151443	C₂²	1	1	yes	characteristic
167	#19151443	C₂²	1	1	yes	characteristic
168	C₂×#15667919	C₂²	1	1	yes	characteristic
169	C₂×#15667919	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	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
175	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
176	#391×C₈₉	C₂²	1	1	yes	characteristic
177	#389×C₈₉	C₂²	1	1	yes	characteristic
178	#389×C₈₉	C₂²	1	1	yes	characteristic
179	#389×C₈₉	C₂²	1	1	yes	characteristic
180	#387×C₈₉	C₂²	1	1	yes	characteristic
181	#387×C₈₉	C₂²	1	1	yes	characteristic
182	#385×C₈₉	C₂²	1	1	yes	characteristic
183	#385×C₈₉	C₂²	1	1	yes	characteristic
184	C₄×C₄⋊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	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
188	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
189	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
190	C₂²×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
191	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
192	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
193	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
194	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
195	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
196	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
197	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
198	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
199	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
200	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
201	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
202	#15668010	C₂×C₄	1	8	yes	complemented
203	#15668002	C₂×C₄	1	8	yes	complemented
204	#15668002	C₂×C₄	1	8	yes	complemented
205	#15667990	C₂×C₄	1	8	yes	complemented
206	#15667990	C₂×C₄	1	8	yes	complemented
207	#15667989	C₂×C₄	1	8	yes	complemented
208	#15667989	C₂×C₄	1	8	yes	complemented
209	#15667988	C₂×C₄	1	8	yes	complemented
210	C₄×Dic₁₇₈	—	4	2	no	—
211	C₄×Dic₁₇₈	—	4	2	no	—
212	#15667977	—	4	2	no	—
213	#15667977	C₂×C₄	1	8	yes	complemented
214	C₄×C₂²⋊D₈₉	—	2	4	no	—
215	C₄×C₂²⋊D₈₉	—	2	4	no	—
216	C₄×C₂²⋊D₈₉	C₂×C₄	1	8	yes	—
217	#15667972	—	2	4	no	—
218	#15667972	C₂×C₄	1	8	yes	—
219	#15667972	C₂×C₄	1	8	yes	—
220	#15667972	Q₈	1	8	yes	complemented
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×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
229	C₂×#13083553	—	4	2	no	—
230	C₂×#13083553	—	4	2	no	—
231	C₂×#13083553	C₂×C₄	1	8	yes	complemented
232	C₂×#13083553	C₂³	1	1	yes	characteristic
233	C₂×#13083553	C₂³	1	1	yes	characteristic
234	C₂×#13083553	C₂³	1	1	yes	characteristic
235	C₂×#13083553	C₂³	1	1	yes	characteristic
236	C₂×#13083553	C₂³	1	1	yes	characteristic
237	C₂×#13083553	C₂³	1	1	yes	characteristic
238	C₂×#13083553	C₂³	1	1	yes	characteristic
239	C₂×#13083553	C₂³	1	1	yes	characteristic
240	C₂×#13083553	C₂³	1	1	yes	characteristic
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	C₄⋊C₄×D₈₉	—	4	2	no	—
264	C₄⋊C₄×D₈₉	—	4	2	no	—
265	C₄⋊C₄×D₈₉	—	4	2	no	—
266	C₄⋊C₄×D₈₉	C₂×C₄	1	8	yes	complemented
267	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊Dic₈₉	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×C₄×Dic₈₉	—	4	2	no	—
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	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
300	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
301	C₄²×D₈₉	—	4	2	no	—
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	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
337	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
338	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
339	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
340	C₂²⋊Q₈×C₈₉	C₂×C₄	1	8	yes	complemented
341	C₄×Q₈×C₈₉	—	4	2	no	—
342	C₂×C₄⋊C₄×C₈₉	—	4	2	no	—
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×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
351	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
352	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
353	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
354	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
355	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
356	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
357	C₂×C₂²⋊C₄×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	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
361	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
362	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
363	C₂×C₄²×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	—	4	1	no	—
378	C₂×Dic₁₇₈	—	4	1	no	—
379	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
380	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
381	C₂×C₂²⋊D₈₉	C₂²×C₄	1	4	yes	—
382	C₂×C₂²⋊D₈₉	C₂×Q₈	1	4	yes	—
383	C₂×C₂²⋊D₈₉	#41	1	4	yes	—
384	C₂²×Dic₈₉	—	2	2	no	—
385	C₂²×Dic₈₉	—	2	2	no	—
386	C₂²×Dic₈₉	—	2	2	no	—
387	C₂²×Dic₈₉	—	4	1	no	—
388	C₂²×Dic₈₉	—	4	1	no	—
389	C₂²×Dic₈₉	—	4	1	no	—
390	C₂²×Dic₈₉	—	4	1	no	—
391	C₂²×Dic₈₉	—	4	1	no	—
392	C₂²×Dic₈₉	—	4	1	no	—
393	C₂²×Dic₈₉	C₂²×C₄	1	4	yes	—
394	C₂²×Dic₈₉	C₂²×C₄	1	4	yes	—
395	C₂²×Dic₈₉	C₂×Q₈	1	4	yes	—
396	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
397	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
398	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
399	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
400	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
401	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
402	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
403	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
404	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
405	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
406	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
407	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	C₂×C₄×D₈₉	—	2	2	no	—
412	C₂×C₄×D₈₉	—	2	2	no	—
413	C₂×C₄×D₈₉	—	2	2	no	—
414	C₂×C₄×D₈₉	—	2	2	no	—
415	C₂×C₄×D₈₉	—	2	2	no	—
416	C₂×C₄×D₈₉	—	2	2	no	—
417	C₂×C₄×D₈₉	—	4	1	no	—
418	C₂×C₄×D₈₉	—	4	1	no	—
419	C₂×C₄×D₈₉	—	4	1	no	—
420	C₂×C₄×D₈₉	—	4	1	no	—
421	C₂×C₄×D₈₉	—	4	1	no	—
422	C₂×C₄×D₈₉	—	4	1	no	—
423	C₂×C₄×D₈₉	—	4	1	no	—
424	C₂×C₄×D₈₉	—	4	1	no	—
425	C₂×C₄×D₈₉	—	4	1	no	—
426	C₂×C₄×D₈₉	—	4	1	no	—
427	C₂×C₄×D₈₉	—	4	1	no	—
428	C₂×C₄×D₈₉	C₂²×C₄	1	4	yes	—
429	C₂×C₄×D₈₉	C₂²×C₄	1	4	yes	—
430	C₂×C₄×D₈₉	C₂²×C₄	1	4	yes	—
431	C₂×C₄×D₈₉	C₂×Q₈	1	4	yes	—
432	C₄⋊Dic₈₉	—	4	1	no	—
433	C₄⋊Dic₈₉	—	4	1	no	—
434	C₄⋊Dic₈₉	—	4	1	no	—
435	C₄⋊Dic₈₉	—	4	1	no	—
436	C₄⋊Dic₈₉	—	4	1	no	—
437	C₄⋊Dic₈₉	—	4	1	no	—
438	C₄⋊Dic₈₉	C₂²×C₄	1	4	yes	—
439	C₄⋊Dic₈₉	C₂²×C₄	1	4	yes	—
440	#13083553	—	2	2	no	—
441	#13083553	—	2	2	no	—
442	#13083553	—	2	2	no	—
443	#13083553	—	2	2	no	—
444	#13083553	—	2	2	no	—
445	#13083553	—	2	2	no	—
446	#13083553	—	2	2	no	—
447	#13083553	—	2	2	no	—
448	#13083553	—	2	2	no	—
449	#13083553	—	2	2	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	#13083553	—	4	1	no	—
457	#13083553	—	4	1	no	—
458	#13083553	—	4	1	no	—
459	#13083553	C₂²×C₄	1	4	yes	—
460	#13083553	C₂²×C₄	1	4	yes	—
461	#13083553	C₂²×C₄	1	4	yes	—
462	#13083553	C₂²×C₄	1	4	yes	—
463	#13083553	C₂²×C₄	1	4	yes	—
464	#13083553	C₂²×C₄	1	4	yes	—
465	#13083553	C₂²×C₄	1	4	yes	—
466	#13083553	C₂²×C₄	1	4	yes	—
467	#13083553	C₂²×C₄	1	4	yes	—
468	#13083553	C₂²×C₄	1	4	yes	—
469	#13083553	C₂²×C₄	1	4	yes	—
470	#13083553	C₂×Q₈	1	4	yes	—
471	C₂²⋊Dic₈₉	—	2	2	no	—
472	C₂²⋊Dic₈₉	—	2	2	no	—
473	C₂²⋊Dic₈₉	C₂²×C₄	1	4	yes	—
474	#13083551	—	2	2	no	—
475	#13083551	—	2	2	no	—
476	#13083551	—	2	2	no	—
477	#13083551	C₂²×C₄	1	4	yes	—
478	#13083551	C₂²×C₄	1	4	yes	—
479	#13083551	C₂²×C₄	1	4	yes	—
480	#13083551	C₂×Q₈	1	4	yes	—
481	C₄×Dic₈₉	—	2	2	no	—
482	C₄×Dic₈₉	—	2	2	no	—
483	C₄×Dic₈₉	—	2	2	no	—
484	C₄×Dic₈₉	—	2	2	no	—
485	C₄×Dic₈₉	—	2	2	no	—
486	C₄×Dic₈₉	—	2	2	no	—
487	C₄×Dic₈₉	—	2	2	no	—
488	C₄×Dic₈₉	—	4	1	no	—
489	C₄×Dic₈₉	—	4	1	no	—
490	C₄×Dic₈₉	—	4	1	no	—
491	C₄×Dic₈₉	—	4	1	no	—
492	C₄×Dic₈₉	—	4	1	no	—
493	C₄×Dic₈₉	—	4	1	no	—
494	C₄×Dic₈₉	—	4	1	no	—
495	C₄×Dic₈₉	—	4	1	no	—
496	C₄×Dic₈₉	—	4	1	no	—
497	C₄×Dic₈₉	—	4	1	no	—
498	C₄×Dic₈₉	—	4	1	no	—
499	C₄×Dic₈₉	—	4	1	no	—
500	C₄×Dic₈₉	C₂²×C₄	1	4	yes	—
501	C₄×Dic₈₉	C₂²×C₄	1	4	yes	—
502	C₄×Dic₈₉	C₂²×C₄	1	4	yes	—
503	C₄×Dic₈₉	C₂×Q₈	1	4	yes	—
504	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
505	C₂×Q₈×C₈₉	—	4	1	no	—
506	C₂×Q₈×C₈₉	—	4	1	no	—
507	C₂×Q₈×C₈₉	C₂²×C₄	1	4	yes	—
508	C₂²×C₄×C₈₉	—	2	2	no	—
509	C₂²×C₄×C₈₉	—	2	2	no	—
510	C₂²×C₄×C₈₉	—	2	2	no	—
511	C₂²×C₄×C₈₉	—	4	1	no	—
512	C₂²×C₄×C₈₉	—	4	1	no	—
513	C₂²×C₄×C₈₉	—	4	1	no	—
514	C₂²×C₄×C₈₉	—	4	1	no	—
515	C₂²×C₄×C₈₉	—	4	1	no	—
516	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
517	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
518	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
519	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
520	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
521	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
522	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
523	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
524	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	C₄⋊C₄×C₈₉	—	2	2	no	—
532	C₄⋊C₄×C₈₉	—	2	2	no	—
533	C₄⋊C₄×C₈₉	—	2	2	no	—
534	C₄⋊C₄×C₈₉	—	4	1	no	—
535	C₄⋊C₄×C₈₉	—	4	1	no	—
536	C₄⋊C₄×C₈₉	—	4	1	no	—
537	C₄⋊C₄×C₈₉	—	4	1	no	—
538	C₄⋊C₄×C₈₉	—	4	1	no	—
539	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
540	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
541	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
542	C₂²⋊C₄×C₈₉	—	2	2	no	—
543	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
544	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
545	C₂²⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
546	C₄²×C₈₉	—	2	2	no	—
547	C₄²×C₈₉	—	4	1	no	—
548	C₄²×C₈₉	—	4	1	no	—
549	C₄²×C₈₉	—	4	1	no	—
550	C₄²×C₈₉	—	4	1	no	—
551	C₄²×C₈₉	—	4	1	no	—
552	C₂³×C₈₉	—	2	1	no	—
553	C₂³×C₈₉	—	2	1	no	—
554	C₂³×C₈₉	—	2	1	no	—
555	C₂³×C₈₉	—	2	1	no	—
556	C₂³×C₈₉	C₂³×C₄	1	2	yes	—
557	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
558	C₂³×C₈₉	C₂×#41	1	2	yes	—
559	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
560	C₂²×D₈₉	—	2	1	no	—
561	C₂²×D₈₉	—	2	1	no	—
562	C₂²×D₈₉	—	2	1	no	—
563	C₂²×D₈₉	—	2	1	no	—
564	C₂²×D₈₉	C₂³×C₄	1	2	yes	—
565	C₂²×D₈₉	C₂²×Q₈	1	2	yes	—
566	C₂²×D₈₉	C₂×#41	1	2	yes	—
567	Q₈×C₈₉	—	4	4	no	—
568	C₂×C₄×C₈₉	—	2	1	no	—
569	C₂×C₄×C₈₉	—	2	1	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	—	4	4	no	—
602	C₂×C₄×C₈₉	—	4	4	no	—
603	C₂×C₄×C₈₉	—	8	2	no	—
604	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
605	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
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	C₂²×Q₈	1	2	yes	—
611	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
612	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
613	C₂²⋊D₈₉	C₄×Q₈	1	16	yes	complemented
614	C₂×Dic₈₉	—	2	1	no	—
615	C₂×Dic₈₉	—	2	1	no	—
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	8	no	—
629	C₂×Dic₈₉	—	2	1	no	—
630	C₂×Dic₈₉	—	2	1	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	—	4	4	no	—
648	C₂×Dic₈₉	—	4	4	no	—
649	C₂×Dic₈₉	—	8	2	no	—
650	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
651	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
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	C₂²×Q₈	1	2	yes	—
658	C₂×Dic₈₉	C₂²×Q₈	1	2	yes	—
659	C₂×Dic₈₉	C₂²×Q₈	1	2	yes	—
660	C₂×Dic₈₉	C₂×#41	1	2	yes	—
661	C₂×Dic₈₉	H(5,𝔽₂)	1	2	yes	—
662	C₂×Dic₈₉	2₋¹⁺⁴	1	2	yes	—
663	C₄×D₈₉	—	2	8	no	—
664	C₄×D₈₉	—	4	4	no	—
665	C₄×D₈₉	—	4	4	no	—
666	C₄×D₈₉	—	4	4	no	—
667	C₄×D₈₉	—	4	4	no	—
668	C₄×D₈₉	—	8	2	no	—
669	C₄×D₈₉	—	8	2	no	—
670	Dic₁₇₈	—	2	8	no	—
671	Dic₁₇₈	—	4	4	no	—
672	C₂²×C₈₉	—	2	2	no	—
673	C₂²×C₈₉	—	2	2	no	—
674	C₂²×C₈₉	—	2	2	no	—
675	C₂²×C₈₉	—	2	2	no	—
676	C₂²×C₈₉	—	2	2	no	—
677	C₂²×C₈₉	—	2	2	no	—
678	C₂²×C₈₉	C₂×C₄×Q₈	1	4	yes	—
679	C₂²×C₈₉	C₂⁴×C₄	1	1	yes	characteristic
680	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
681	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
682	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
683	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
684	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
685	C₂²×C₈₉	#585	1	1	yes	characteristic
686	C₂×D₈₉	—	2	2	no	—
687	C₂×D₈₉	—	2	2	no	—
688	C₂×D₈₉	—	2	2	no	—
689	C₂×D₈₉	—	2	2	no	—
690	C₂×D₈₉	—	2	2	no	—
691	C₂×D₈₉	—	2	2	no	—
692	C₂×D₈₉	C₂×C₄×Q₈	1	4	yes	—
693	C₄×C₈₉	—	2	2	no	—
694	C₄×C₈₉	—	2	2	no	—
695	C₄×C₈₉	—	2	2	no	—
696	C₄×C₈₉	—	2	2	no	—
697	C₄×C₈₉	—	2	2	no	—
698	C₄×C₈₉	—	2	2	no	—
699	C₄×C₈₉	—	2	2	no	—
700	C₄×C₈₉	—	2	2	no	—
701	C₄×C₈₉	—	2	2	no	—
702	C₄×C₈₉	—	4	1	no	—
703	C₄×C₈₉	—	4	1	no	—
704	C₄×C₈₉	—	4	1	no	—
705	C₄×C₈₉	—	4	1	no	—
706	C₄×C₈₉	—	4	1	no	—
707	Dic₈₉	—	2	2	no	—
708	Dic₈₉	—	2	2	no	—
709	Dic₈₉	—	2	2	no	—
710	Dic₈₉	—	2	2	no	—
711	Dic₈₉	—	2	2	no	—
712	Dic₈₉	—	2	2	no	—
713	Dic₈₉	—	2	2	no	—
714	Dic₈₉	—	4	1	no	—
715	Dic₈₉	—	4	1	no	—
716	Dic₈₉	—	4	1	no	—
717	Dic₈₉	—	4	1	no	—
718	Dic₈₉	—	4	1	no	—
719	Dic₈₉	—	4	1	no	—
720	Dic₈₉	C₂×C₄×Q₈	1	4	yes	—
721	Dic₈₉	#520	1	4	yes	—
722	#34332	—	89	1	no	maximal, Sylow
723	C₂×C₈₉	—	2	4	no	—
724	C₂×C₈₉	C₂²×C₄×Q₈	1	1	yes	characteristic
725	C₂×C₈₉	C₂×#520	1	1	yes	characteristic
726	C₂×C₈₉	C₄×H(5,𝔽₂)	1	1	yes	characteristic
727	C₂×C₈₉	#3501	1	1	yes	characteristic
728	C₂×C₈₉	#3503	1	1	yes	characteristic
729	C₂×C₈₉	#3515	1	1	yes	characteristic
730	C₂×C₈₉	#3519	1	1	yes	characteristic
731	D₈₉	—	2	4	no	—
732	C₂×#554	—	89	1	no	—
733	#2370	—	89	1	no	—
734	#2370	—	89	1	no	—
735	#2369	—	89	1	no	—
736	#2360	—	89	1	no	—
737	#2360	—	89	1	no	—
738	#2360	—	89	1	no	—
739	#2360	—	89	1	no	—
740	#2360	—	89	1	no	—
741	#2360	D₈₉	1	1	yes	characteristic, complemented
742	Q₈×C₄⋊C₄	—	89	1	no	—
743	D₄×C₄⋊C₄	—	89	1	no	—
744	D₄×C₄⋊C₄	—	89	1	no	—
745	D₄×C₄⋊C₄	—	89	1	no	—
746	#2345	—	89	1	no	—
747	#2345	—	89	1	no	—
748	#2330	—	89	1	no	—
749	#2330	—	89	1	no	—
750	#2329	—	89	1	no	—
751	#2329	—	89	1	no	—
752	#2329	—	89	1	no	—
753	#2329	—	89	1	no	—
754	C₄×C₄⋊Q₈	—	89	1	no	—
755	C₄×C₂²⋊Q₈	—	89	1	no	—
756	C₄×C₂²⋊Q₈	—	89	1	no	—
757	#2295	—	89	1	no	—
758	C₂×#389	—	89	1	no	—
759	C₂×#389	—	89	1	no	—
760	#2275	—	89	1	no	—
761	#2275	—	89	1	no	—
762	C₄²×D₄	—	89	1	no	—
763	C₈₉	#34332	1	1	yes	characteristic, complemented, Sylow
764	#554	—	89	16	no	—
765	C₂×C₄⋊Q₈	—	89	1	no	—
766	C₂×#125	—	89	1	no	—
767	C₂×#125	—	89	1	no	—
768	C₂×C₂²⋊Q₈	—	89	1	no	—
769	C₂×C₂²⋊Q₈	—	89	1	no	—
770	C₂×C₂²⋊Q₈	—	89	1	no	—
771	C₂×C₂²⋊Q₈	—	89	1	no	—
772	C₂×C₂²⋊Q₈	—	89	1	no	—
773	C₂×C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
774	C₂×C₄×Q₈	—	89	1	no	—
775	C₂×C₄×Q₈	—	89	1	no	—
776	C₂×C₄×Q₈	—	89	1	no	—
777	C₂×C₄×Q₈	—	89	1	no	—
778	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
779	C₂×C₄×D₄	—	89	1	no	—
780	C₂×C₄×D₄	—	89	1	no	—
781	C₂×C₄×D₄	—	89	1	no	—
782	C₂×C₄×D₄	—	89	1	no	—
783	C₂×C₄×D₄	—	89	1	no	—
784	C₂×C₄×D₄	—	89	1	no	—
785	C₂×C₄×D₄	—	89	1	no	—
786	C₂²×C₄⋊C₄	—	89	1	no	—
787	C₂²×C₄⋊C₄	—	89	1	no	—
788	C₂²×C₄⋊C₄	—	89	1	no	—
789	C₂²×C₄⋊C₄	—	89	1	no	—
790	C₂²×C₄⋊C₄	—	89	1	no	—
791	C₂²×C₄⋊C₄	—	89	1	no	—
792	C₂²×C₄⋊C₄	—	89	1	no	—
793	C₂²×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
794	C₂²×C₄²	—	89	1	no	—
795	C₂²×C₄²	—	89	1	no	—
796	#391	—	89	1	no	—
797	#391	—	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	C₂×D₈₉	1	1	yes	characteristic
804	#389	—	89	1	no	—
805	#389	—	89	1	no	—
806	#389	—	89	1	no	—
807	#389	—	89	1	no	—
808	#389	—	89	1	no	—
809	#389	—	89	1	no	—
810	#389	—	89	1	no	—
811	#389	—	89	1	no	—
812	#389	—	89	1	no	—
813	#389	—	89	1	no	—
814	#389	—	89	1	no	—
815	#389	—	89	1	no	—
816	#389	—	89	1	no	—
817	#389	—	89	1	no	—
818	#389	—	89	1	no	—
819	#389	—	89	1	no	—
820	#389	—	89	1	no	—
821	#389	—	89	1	no	—
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	C₂×D₈₉	1	1	yes	characteristic
832	#389	C₂×D₈₉	1	1	yes	characteristic
833	#389	C₂×D₈₉	1	1	yes	characteristic
834	#387	—	89	1	no	—
835	#387	—	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	#385	—	89	1	no	—
855	#385	—	89	1	no	—
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	C₂×D₈₉	1	1	yes	characteristic
865	#385	C₂×D₈₉	1	1	yes	characteristic
866	#384	—	89	1	no	—
867	#384	—	89	1	no	—
868	#384	—	89	1	no	—
869	#380	—	89	1	no	—
870	#380	—	89	1	no	—
871	#380	—	89	1	no	—
872	#380	—	89	1	no	—
873	#380	—	89	1	no	—
874	#380	—	89	1	no	—
875	C₄×C₄⋊C₄	—	89	1	no	—
876	C₄×C₄⋊C₄	—	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	C₂×D₈₉	1	1	yes	characteristic
895	C₄×C₂²⋊C₄	—	89	1	no	—
896	C₄×C₂²⋊C₄	—	89	1	no	—
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	C₂×D₈₉	1	1	yes	characteristic
911	C₄×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
912	C₄×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
913	#376	—	89	1	no	—
914	#376	—	89	1	no	—
915	C₂×#95	—	89	1	no	—
916	C₂×#95	—	89	1	no	—
917	C₂×#95	—	89	1	no	—
918	C₂×#95	—	89	1	no	—
919	C₄³	—	89	1	no	—
920	C₂²×Q₈	—	89	1	no	—
921	C₂²×Q₈	—	89	1	no	—
922	C₂²×Q₈	C₂²×D₈₉	1	1	yes	characteristic
923	C₂²×D₄	—	89	1	no	—
924	C₂³×C₄	—	89	1	no	—
925	C₂³×C₄	—	89	1	no	—
926	C₂³×C₄	—	89	1	no	—
927	C₂³×C₄	—	89	1	no	—
928	C₂³×C₄	—	89	1	no	—
929	C₂³×C₄	—	89	1	no	—
930	C₂³×C₄	—	89	1	no	—
931	C₂³×C₄	—	89	1	no	—
932	C₂³×C₄	—	89	1	no	—
933	C₂³×C₄	—	89	1	no	—
934	C₂³×C₄	—	89	1	no	—
935	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
936	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
937	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
938	C₄⋊Q₈	—	89	8	no	—
939	#125	—	89	8	no	—
940	#125	—	89	8	no	—
941	C₂²⋊Q₈	—	89	8	no	—
942	C₂²⋊Q₈	—	89	8	no	—
943	C₂²⋊Q₈	—	89	8	no	—
944	C₂²⋊Q₈	—	89	8	no	—
945	C₂²⋊Q₈	—	89	8	no	—
946	C₂²⋊Q₈	C₄×D₈₉	1	8	yes	complemented
947	C₄×Q₈	—	4	2	no	—
948	C₄×Q₈	—	89	8	no	—
949	C₄×Q₈	—	356	2	no	—
950	C₄×Q₈	—	356	2	no	—
951	C₄×Q₈	—	356	2	no	—
952	C₄×D₄	—	89	8	no	—
953	C₄×D₄	—	89	8	no	—
954	C₄×D₄	—	89	8	no	—
955	C₄×D₄	—	89	8	no	—
956	C₄×D₄	—	178	4	no	—
957	C₄×D₄	—	178	4	no	—
958	C₄×D₄	—	178	4	no	—
959	C₂×C₄⋊C₄	—	4	2	no	—
960	C₂×C₄⋊C₄	—	89	8	no	—
961	C₂×C₄⋊C₄	—	89	1	no	—
962	C₂×C₄⋊C₄	—	89	1	no	—
963	C₂×C₄⋊C₄	—	89	1	no	—
964	C₂×C₄⋊C₄	—	89	1	no	—
965	C₂×C₄⋊C₄	—	89	1	no	—
966	C₂×C₄⋊C₄	—	89	1	no	—
967	C₂×C₄⋊C₄	—	89	1	no	—
968	C₂×C₄⋊C₄	—	89	1	no	—
969	C₂×C₄⋊C₄	—	89	1	no	—
970	C₂×C₄⋊C₄	—	89	1	no	—
971	C₂×C₄⋊C₄	—	89	1	no	—
972	C₂×C₄⋊C₄	—	89	1	no	—
973	C₂×C₄⋊C₄	—	89	1	no	—
974	C₂×C₄⋊C₄	—	89	1	no	—
975	C₂×C₄⋊C₄	—	89	8	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	—	356	2	no	—
1002	C₂×C₄⋊C₄	—	356	2	no	—
1003	C₂×C₄⋊C₄	—	356	2	no	—
1004	C₂×C₄⋊C₄	—	356	2	no	—
1005	C₂×C₄⋊C₄	—	356	2	no	—
1006	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1007	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
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×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1016	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
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	—	89	1	no	—
1026	C₂×C₂²⋊C₄	—	89	1	no	—
1027	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1028	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1029	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1030	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
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	—	89	1	no	—
1053	C₂×C₄²	—	89	1	no	—
1054	C₂×C₄²	—	356	2	no	—
1055	C₂×C₄²	—	356	2	no	—
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	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1061	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
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	C₂²×D₈₉	1	1	yes	characteristic
1097	#95	C₂²×D₈₉	1	1	yes	characteristic
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	C₂⁴	—	89	1	no	—
1107	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
1108	C₂×Q₈	—	4	1	no	—
1109	C₂×Q₈	—	4	1	no	—
1110	C₂×Q₈	—	89	4	no	—
1111	C₂×Q₈	—	89	4	no	—
1112	C₂×Q₈	—	356	1	no	—
1113	C₂×Q₈	—	356	1	no	—
1114	C₂×Q₈	—	178	2	no	—
1115	C₂×Q₈	—	178	2	no	—
1116	C₂×Q₈	C₂×C₄×D₈₉	1	4	yes	—
1117	C₂×D₄	—	89	4	no	—
1118	C₂×D₄	—	89	4	no	—
1119	C₂×D₄	—	89	4	no	—
1120	C₂²×C₄	—	2	2	no	—
1121	C₂²×C₄	—	2	2	no	—
1122	C₂²×C₄	—	2	2	no	—
1123	C₂²×C₄	—	4	1	no	—
1124	C₂²×C₄	—	4	1	no	—
1125	C₂²×C₄	—	4	1	no	—
1126	C₂²×C₄	—	4	1	no	—
1127	C₂²×C₄	—	4	1	no	—
1128	C₂²×C₄	—	89	1	no	—
1129	C₂²×C₄	—	89	1	no	—
1130	C₂²×C₄	—	89	4	no	—
1131	C₂²×C₄	—	89	4	no	—
1132	C₂²×C₄	—	89	4	no	—
1133	C₂²×C₄	—	89	1	no	—
1134	C₂²×C₄	—	89	1	no	—
1135	C₂²×C₄	—	89	1	no	—
1136	C₂²×C₄	—	89	1	no	—
1137	C₂²×C₄	—	89	1	no	—
1138	C₂²×C₄	—	89	1	no	—
1139	C₂²×C₄	—	89	1	no	—
1140	C₂²×C₄	—	89	4	no	—
1141	C₂²×C₄	—	89	4	no	—
1142	C₂²×C₄	—	89	4	no	—
1143	C₂²×C₄	—	89	4	no	—
1144	C₂²×C₄	—	89	1	no	—
1145	C₂²×C₄	—	89	1	no	—
1146	C₂²×C₄	—	89	1	no	—
1147	C₂²×C₄	—	89	1	no	—
1148	C₂²×C₄	—	89	1	no	—
1149	C₂²×C₄	—	89	1	no	—
1150	C₂²×C₄	—	356	1	no	—
1151	C₂²×C₄	—	356	1	no	—
1152	C₂²×C₄	—	356	1	no	—
1153	C₂²×C₄	—	356	1	no	—
1154	C₂²×C₄	—	356	1	no	—
1155	C₂²×C₄	—	356	1	no	—
1156	C₂²×C₄	—	356	1	no	—
1157	C₂²×C₄	—	356	1	no	—
1158	C₂²×C₄	—	356	1	no	—
1159	C₂²×C₄	—	356	1	no	—
1160	C₂²×C₄	—	356	1	no	—
1161	C₂²×C₄	—	356	1	no	—
1162	C₂²×C₄	—	356	1	no	—
1163	C₂²×C₄	—	356	1	no	—
1164	C₂²×C₄	—	356	1	no	—
1165	C₂²×C₄	—	356	1	no	—
1166	C₂²×C₄	—	356	1	no	—
1167	C₂²×C₄	—	178	2	no	—
1168	C₂²×C₄	—	178	2	no	—
1169	C₂²×C₄	—	178	2	no	—
1170	C₂²×C₄	—	178	2	no	—
1171	C₂²×C₄	—	178	2	no	—
1172	C₂²×C₄	—	178	2	no	—
1173	C₂²×C₄	—	178	2	no	—
1174	C₂²×C₄	—	178	2	no	—
1175	C₂²×C₄	—	178	2	no	—
1176	C₂²×C₄	C₂×C₄×D₈₉	1	4	yes	—
1177	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1178	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1179	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1180	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1181	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1182	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1183	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1184	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1185	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1186	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1187	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1188	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1189	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1190	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1191	C₄⋊C₄	—	2	2	no	—
1192	C₄⋊C₄	—	2	2	no	—
1193	C₄⋊C₄	—	2	2	no	—
1194	C₄⋊C₄	—	4	1	no	—
1195	C₄⋊C₄	—	4	1	no	—
1196	C₄⋊C₄	—	4	1	no	—
1197	C₄⋊C₄	—	4	1	no	—
1198	C₄⋊C₄	—	4	1	no	—
1199	C₄⋊C₄	—	89	4	no	—
1200	C₄⋊C₄	—	89	4	no	—
1201	C₄⋊C₄	—	89	4	no	—
1202	C₄⋊C₄	—	89	4	no	—
1203	C₄⋊C₄	—	89	4	no	—
1204	C₄⋊C₄	—	89	4	no	—
1205	C₄⋊C₄	—	89	4	no	—
1206	C₄⋊C₄	—	89	4	no	—
1207	C₄⋊C₄	—	89	4	no	—
1208	C₄⋊C₄	—	89	4	no	—
1209	C₄⋊C₄	—	89	4	no	—
1210	C₄⋊C₄	—	89	4	no	—
1211	C₄⋊C₄	—	89	4	no	—
1212	C₄⋊C₄	—	89	4	no	—
1213	C₄⋊C₄	—	356	1	no	—
1214	C₄⋊C₄	—	356	1	no	—
1215	C₄⋊C₄	—	356	1	no	—
1216	C₄⋊C₄	—	356	1	no	—
1217	C₄⋊C₄	—	356	1	no	—
1218	C₄⋊C₄	—	356	1	no	—
1219	C₄⋊C₄	—	356	1	no	—
1220	C₄⋊C₄	—	356	1	no	—
1221	C₄⋊C₄	—	356	1	no	—
1222	C₄⋊C₄	—	356	1	no	—
1223	C₄⋊C₄	—	356	1	no	—
1224	C₄⋊C₄	—	356	1	no	—
1225	C₄⋊C₄	—	356	1	no	—
1226	C₄⋊C₄	—	356	1	no	—
1227	C₄⋊C₄	—	356	1	no	—
1228	C₄⋊C₄	—	178	2	no	—
1229	C₄⋊C₄	—	178	2	no	—
1230	C₄⋊C₄	—	178	2	no	—
1231	C₄⋊C₄	—	178	2	no	—
1232	C₄⋊C₄	—	178	2	no	—
1233	C₄⋊C₄	—	178	2	no	—
1234	C₄⋊C₄	—	178	2	no	—
1235	C₄⋊C₄	—	178	2	no	—
1236	C₄⋊C₄	—	178	2	no	—
1237	C₄⋊C₄	—	178	2	no	—
1238	C₄⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1239	C₄⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1240	C₄⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1241	C₂²⋊C₄	—	2	2	no	—
1242	C₂²⋊C₄	—	89	4	no	—
1243	C₂²⋊C₄	—	89	4	no	—
1244	C₂²⋊C₄	—	89	4	no	—
1245	C₂²⋊C₄	—	89	4	no	—
1246	C₂²⋊C₄	—	89	4	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	C₂×C₄×D₈₉	1	4	yes	—
1253	C₂²⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1254	C₂²⋊C₄	Q₈×D₈₉	1	4	yes	—
1255	C₄²	—	2	2	no	—
1256	C₄²	—	4	1	no	—
1257	C₄²	—	4	1	no	—
1258	C₄²	—	4	1	no	—
1259	C₄²	—	4	1	no	—
1260	C₄²	—	4	1	no	—
1261	C₄²	—	89	4	no	—
1262	C₄²	—	89	4	no	—
1263	C₄²	—	89	4	no	—
1264	C₄²	—	89	4	no	—
1265	C₄²	—	356	1	no	—
1266	C₄²	—	356	1	no	—
1267	C₄²	—	356	1	no	—
1268	C₄²	—	356	1	no	—
1269	C₄²	—	356	1	no	—
1270	C₄²	—	356	1	no	—
1271	C₄²	—	356	1	no	—
1272	C₄²	—	356	1	no	—
1273	C₄²	—	356	1	no	—
1274	C₄²	—	356	1	no	—
1275	C₄²	—	356	1	no	—
1276	C₄²	—	356	1	no	—
1277	C₄²	—	178	2	no	—
1278	C₄²	—	178	2	no	—
1279	C₄²	—	178	2	no	—
1280	C₄²	—	178	2	no	—
1281	C₄²	—	178	2	no	—
1282	C₄²	—	178	2	no	—
1283	C₄²	—	178	2	no	—
1284	C₂³	—	2	1	no	—
1285	C₂³	—	2	1	no	—
1286	C₂³	—	2	1	no	—
1287	C₂³	—	2	1	no	—
1288	C₂³	—	89	2	no	—
1289	C₂³	—	89	2	no	—
1290	C₂³	—	89	2	no	—
1291	C₂³	—	178	1	no	—
1292	C₂³	—	178	1	no	—
1293	C₂³	—	178	1	no	—
1294	C₂³	—	178	1	no	—
1295	C₂³	C₂²×C₄×D₈₉	1	2	yes	—
1296	C₂³	C₂×Q₈×D₈₉	1	2	yes	—
1297	C₂³	#41×D₈₉	1	2	yes	—
1298	C₂³	C₂⁴×D₈₉	1	1	yes	characteristic
1299	Q₈	—	4	4	no	—
1300	Q₈	—	356	4	no	—
1301	Q₈	—	178	8	no	—
1302	D₄	—	89	16	no	—
1303	C₂×C₄	—	2	1	no	—
1304	C₂×C₄	—	2	1	no	—
1305	C₂×C₄	—	2	1	no	—
1306	C₂×C₄	—	2	1	no	—
1307	C₂×C₄	—	2	1	no	—
1308	C₂×C₄	—	2	1	no	—
1309	C₂×C₄	—	2	1	no	—
1310	C₂×C₄	—	2	1	no	—
1311	C₂×C₄	—	2	1	no	—
1312	C₂×C₄	—	2	1	no	—
1313	C₂×C₄	—	2	1	no	—
1314	C₂×C₄	—	2	1	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	—	4	4	no	—
1337	C₂×C₄	—	4	4	no	—
1338	C₂×C₄	—	8	2	no	—
1339	C₂×C₄	—	89	2	no	—
1340	C₂×C₄	—	89	2	no	—
1341	C₂×C₄	—	89	2	no	—
1342	C₂×C₄	—	89	2	no	—
1343	C₂×C₄	—	89	2	no	—
1344	C₂×C₄	—	89	2	no	—
1345	C₂×C₄	—	89	2	no	—
1346	C₂×C₄	—	89	2	no	—
1347	C₂×C₄	—	89	2	no	—
1348	C₂×C₄	—	89	2	no	—
1349	C₂×C₄	—	89	2	no	—
1350	C₂×C₄	—	89	2	no	—
1351	C₂×C₄	—	89	2	no	—
1352	C₂×C₄	—	356	4	no	—
1353	C₂×C₄	—	356	4	no	—
1354	C₂×C₄	—	356	4	no	—
1355	C₂×C₄	—	356	4	no	—
1356	C₂×C₄	—	356	4	no	—
1357	C₂×C₄	—	356	4	no	—
1358	C₂×C₄	—	178	8	no	—
1359	C₂×C₄	—	178	8	no	—
1360	C₂×C₄	—	178	1	no	—
1361	C₂×C₄	—	178	1	no	—
1362	C₂×C₄	—	178	1	no	—
1363	C₂×C₄	—	178	1	no	—
1364	C₂×C₄	—	178	1	no	—
1365	C₂×C₄	—	178	1	no	—
1366	C₂×C₄	—	178	1	no	—
1367	C₂×C₄	—	178	1	no	—
1368	C₂×C₄	—	178	1	no	—
1369	C₂×C₄	—	178	1	no	—
1370	C₂×C₄	—	178	1	no	—
1371	C₂×C₄	—	178	1	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	—	712	2	no	—
1393	C₂×C₄	—	712	2	no	—
1394	C₂×C₄	—	712	2	no	—
1395	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1396	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1397	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1398	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1399	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1400	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1401	C₂×C₄	C₂×Q₈×D₈₉	1	2	yes	—
1402	C₂×C₄	C₂×Q₈×D₈₉	1	2	yes	—
1403	C₂×C₄	#15668057	1	2	yes	—
1404	C₂²	—	2	2	no	—
1405	C₂²	—	2	2	no	—
1406	C₂²	—	2	2	no	—
1407	C₂²	—	2	2	no	—
1408	C₂²	—	2	2	no	—
1409	C₂²	—	2	2	no	—
1410	C₂²	—	89	4	no	—
1411	C₂²	—	178	2	no	—
1412	C₂²	—	178	2	no	—
1413	C₂²	—	178	2	no	—
1414	C₂²	—	178	2	no	—
1415	C₂²	—	178	2	no	—
1416	C₂²	—	178	2	no	—
1417	C₂²	C₄×Q₈×D₈₉	1	4	yes	—
1418	C₂²	C₂³×C₄×D₈₉	1	1	yes	characteristic
1419	C₂²	C₂²×Q₈×D₈₉	1	1	yes	characteristic
1420	C₂²	C₂×#41×D₈₉	1	1	yes	characteristic
1421	C₂²	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
1422	C₂²	C₂×#15668057	1	1	yes	characteristic
1423	C₂²	2₋¹⁺⁴×D₈₉	1	1	yes	characteristic
1424	C₂²	#19152434	1	1	yes	characteristic
1425	C₄	—	2	2	no	—
1426	C₄	—	2	2	no	—
1427	C₄	—	2	2	no	—
1428	C₄	—	2	2	no	—
1429	C₄	—	2	2	no	—
1430	C₄	—	2	2	no	—
1431	C₄	—	2	2	no	—
1432	C₄	—	2	2	no	—
1433	C₄	—	2	2	no	—
1434	C₄	—	4	1	no	—
1435	C₄	—	4	1	no	—
1436	C₄	—	4	1	no	—
1437	C₄	—	4	1	no	—
1438	C₄	—	4	1	no	—
1439	C₄	—	89	4	no	—
1440	C₄	—	89	4	no	—
1441	C₄	—	356	1	no	—
1442	C₄	—	356	1	no	—
1443	C₄	—	356	1	no	—
1444	C₄	—	356	1	no	—
1445	C₄	—	356	1	no	—
1446	C₄	—	356	1	no	—
1447	C₄	—	178	2	no	—
1448	C₄	—	178	2	no	—
1449	C₄	—	178	2	no	—
1450	C₄	—	178	2	no	—
1451	C₄	—	178	2	no	—
1452	C₄	—	178	2	no	—
1453	C₄	—	178	2	no	—
1454	C₂	—	2	4	no	—
1455	C₂	—	178	4	no	—
1456	C₂	C₂×C₄×Q₈×D₈₉	1	1	yes	characteristic
1457	C₂	#520×D₈₉	1	1	yes	characteristic
1458	C₂	C₄×#15668057	1	1	yes	characteristic
1459	C₂	#26034051	1	1	yes	characteristic
1460	C₂	#26034063	1	1	yes	characteristic
1461	C₂	#26034219	1	1	yes	characteristic
1462	C₂	#26034273	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₈₉
commutator	C₂²×C₈₉	C₂⁴×C₄
Fitting	C₈₉×#2360	C₂
socle, cosocle	C₂³×C₈₉	C₂⁵
prime radical	C₂²×C₂²⋊D₈₉	C₂³
hypercenter	#2360	D₈₉
hypocenter	C₈₉	#34332
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ #2360

Complements

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

N	H ≅ G/N	type
2. #26023351	C₂	semidirect
3. #26023349	C₂	semidirect
4. #26023340	C₂	semidirect
5. #26023260	C₂	semidirect
6. #26023258	C₂	semidirect
7. #26023258	C₂	semidirect
8. #26023254	C₂	semidirect
9. #26023253	C₂	semidirect
10. #26023166	C₂	semidirect
14. #26023130	C₂	semidirect
15. #26023126	C₂	semidirect
16. #26022990	C₂	semidirect
17. #26022988	C₂	semidirect
18. #26022987	C₂	semidirect
19. #26022986	C₂	semidirect
20. #26022984	C₂	semidirect
21. #26022983	C₂	semidirect
22. C₄×#15668010	C₂	semidirect
23. C₄×#15667990	C₂	semidirect
24. #26022784	C₂	semidirect
25. #26022725	C₂	semidirect
26. C₂×#19151493	C₂	semidirect
27. #389×D₈₉	C₂	semidirect
31. C₈₉×#2360	C₂	semidirect
32. #19152302	C₄	semidirect
202. #15668010	C₂×C₄	semidirect
203. #15668002	C₂×C₄	semidirect
204. #15668002	C₂×C₄	semidirect
205. #15667990	C₂×C₄	semidirect
206. #15667990	C₂×C₄	semidirect
207. #15667989	C₂×C₄	semidirect
208. #15667989	C₂×C₄	semidirect
209. #15667988	C₂×C₄	semidirect
213. #15667977	C₂×C₄	semidirect
220. #15667972	Q₈	semidirect
231. C₂×#13083553	C₂×C₄	semidirect
266. C₄⋊C₄×D₈₉	C₂×C₄	semidirect
340. C₂²⋊Q₈×C₈₉	C₂×C₄	semidirect
613. C₂²⋊D₈₉	C₄×Q₈	semidirect
741. #2360	D₈₉	semidirect
763. C₈₉	#34332	semidirect
946. C₂²⋊Q₈	C₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19152302	2
#26023351	2
#26023349	2
#26023340	2
#26023260	2
#26023258	2
#26023254	2
#26023253	2
#26023166	2
C₄⋊C₄×C₂²⋊D₈₉	2
#26023150	2
#26023130	2
#26023126	2
#26022990	2
#26022988	2
#26022987	2
#26022986	2
#26022984	2
#26022983	2
C₄×#15668010	2
C₄×#15667990	2
#26022784	2
#26022725	2
C₂×#19151493	2
#389×D₈₉	2
#26022611	2
C₄×#15667972	2
C₈₉×#2360	2
#34332	89