Subgroups — #36719428

Order 22784.

2280 conjugacy classes of subgroups.

The subgroup lattice has 1428 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	#26023431	C₂	1	1	yes	maximal, characteristic, complemented
3	#26023430	C₂	1	1	yes	maximal, characteristic, complemented
4	#26023419	C₂	1	1	yes	maximal, characteristic, complemented
5	#26023334	C₂	1	1	yes	maximal, characteristic, complemented
6	#26023329	C₂	1	1	yes	maximal, characteristic, complemented
7	#26023305	C₂	1	1	yes	maximal, characteristic, complemented
8	#26023282	C₂	1	1	yes	maximal, characteristic, complemented
9	#26023254	C₂	1	1	yes	maximal, characteristic, complemented
10	#26023214	C₂	1	1	yes	maximal, characteristic, complemented
11	#26023189	C₂	1	1	yes	maximal, characteristic
12	#26023187	C₂	1	1	yes	maximal, characteristic
13	#26023180	C₂	1	1	yes	maximal, characteristic
14	#26023086	C₂	1	1	yes	maximal, characteristic, complemented
15	#26023084	C₂	1	1	yes	maximal, characteristic, complemented
16	#26023010	C₂	1	1	yes	maximal, characteristic, complemented
17	#26023009	C₂	1	1	yes	maximal, characteristic, complemented
18	#26022999	C₂	1	1	yes	maximal, characteristic, complemented
19	#26022995	C₂	1	1	yes	maximal, characteristic, complemented
20	#26022986	C₂	1	1	yes	maximal, characteristic, complemented
21	#26022981	C₂	1	1	yes	maximal, characteristic, complemented
22	#26022967	C₂	1	1	yes	maximal, characteristic, complemented
23	#26022927	C₂	1	1	yes	maximal, characteristic, complemented
24	#26022901	C₂	1	1	yes	maximal, characteristic, complemented
25	#26022887	C₂	1	1	yes	maximal, characteristic
26	#26022882	C₂	1	1	yes	maximal, characteristic
27	#26022837	C₂	1	1	yes	maximal, characteristic, complemented
28	#26022786	C₂	1	1	yes	maximal, characteristic, complemented
29	#391×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
30	#26022694	C₂	1	1	yes	maximal, characteristic
31	C₈₉×#2378	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×#15667977	C₂²	1	1	yes	characteristic
45	C₂×#15667977	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×#15667972	C₂²	1	1	yes	characteristic
50	C₂×#15667972	C₂²	1	1	yes	characteristic
51	C₂×#15667968	C₂²	1	1	yes	characteristic
52	C₂×#15667968	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
54	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
55	#19151505	C₂²	1	1	yes	characteristic
56	#19151505	C₂²	1	1	yes	characteristic
57	#19151504	C₂²	1	1	yes	characteristic
58	#19151503	C₂²	1	1	yes	characteristic
59	#19151503	C₂²	1	1	yes	characteristic
60	#19151503	C₂²	1	1	yes	characteristic
61	#19151502	C₂²	1	1	yes	characteristic
62	#19151502	C₂²	1	1	yes	characteristic
63	#19151502	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	#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	#19151496	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	#19151492	C₂²	1	1	yes	characteristic
84	#19151492	C₂²	1	1	yes	characteristic
85	#19151492	C₂²	1	1	yes	characteristic
86	#19151492	C₂²	1	1	yes	characteristic
87	#19151491	C₂²	1	1	yes	characteristic
88	#19151491	C₂²	1	1	yes	characteristic
89	#19151491	C₂²	1	1	yes	characteristic
90	#19151491	C₂²	1	1	yes	characteristic
91	#19151485	C₂²	1	1	yes	characteristic
92	#19151485	C₂²	1	1	yes	characteristic
93	#19151485	C₂²	1	1	yes	characteristic
94	#19151485	C₂²	1	1	yes	characteristic
95	#19151484	C₂²	1	1	yes	characteristic
96	#19151484	C₂²	1	1	yes	characteristic
97	#19151484	C₂²	1	1	yes	characteristic
98	#19151484	C₂²	1	1	yes	characteristic
99	#19151483	C₂²	1	1	yes	characteristic
100	#19151483	C₂²	1	1	yes	characteristic
101	#19151482	C₂²	1	1	yes	characteristic
102	#19151482	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	#19151480	C₂²	1	1	yes	characteristic
110	#19151480	C₂²	1	1	yes	characteristic
111	#19151480	C₂²	1	1	yes	characteristic
112	#19151480	C₂²	1	1	yes	characteristic
113	#19151479	C₂²	1	1	yes	characteristic
114	#19151479	C₂²	1	1	yes	characteristic
115	#19151479	C₂²	1	1	yes	characteristic
116	#19151479	C₂²	1	1	yes	characteristic
117	#19151479	C₂²	1	1	yes	characteristic
118	#19151479	C₂²	1	1	yes	characteristic
119	#19151474	C₂²	1	1	yes	characteristic
120	#19151474	C₂²	1	1	yes	characteristic
121	#19151474	C₂²	1	1	yes	characteristic
122	#19151474	C₂²	1	1	yes	characteristic
123	#19151472	C₂²	1	1	yes	characteristic
124	#19151472	C₂²	1	1	yes	characteristic
125	#19151469	C₂²	1	1	yes	characteristic
126	#19151469	C₂²	1	1	yes	characteristic
127	#19151469	C₂²	1	1	yes	characteristic
128	#19151469	C₂²	1	1	yes	characteristic
129	#19151465	C₂²	1	1	yes	characteristic
130	#19151465	C₂²	1	1	yes	characteristic
131	#19151465	C₂²	1	1	yes	characteristic
132	#19151465	C₂²	1	1	yes	characteristic
133	#19151463	C₂²	1	1	yes	characteristic
134	#19151462	C₂²	1	1	yes	characteristic
135	#19151462	C₂²	1	1	yes	characteristic
136	#19151461	C₂²	1	1	yes	characteristic
137	#19151459	C₂²	1	1	yes	characteristic
138	#19151459	C₂²	1	1	yes	characteristic
139	#19151457	C₂²	1	1	yes	characteristic
140	#19151457	C₂²	1	1	yes	characteristic
141	#19151456	C₂²	1	1	yes	characteristic
142	#19151456	C₂²	1	1	yes	characteristic
143	#19151455	C₂²	1	1	yes	characteristic
144	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
145	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
146	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
147	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
148	C₄×#13083553	C₂²	1	1	yes	characteristic
149	C₄×#13083553	C₂²	1	1	yes	characteristic
150	C₄×#13083553	C₂²	1	1	yes	characteristic
151	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
152	#19151449	C₂²	1	1	yes	characteristic
153	#19151449	C₂²	1	1	yes	characteristic
154	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
155	C₂²⋊C₄×Dic₈₉	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	C₄×C₂²⋊Dic₈₉	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	#19151445	C₂²	1	1	yes	characteristic
164	#19151445	C₂²	1	1	yes	characteristic
165	#19151445	C₂²	1	1	yes	characteristic
166	#19151444	C₂²	1	1	yes	characteristic
167	#19151443	C₂²	1	1	yes	characteristic
168	#19151443	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	#95×D₈₉	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	#389×C₈₉	C₂²	1	1	yes	characteristic
177	#389×C₈₉	C₂²	1	1	yes	characteristic
178	#388×C₈₉	C₂²	1	1	yes	characteristic
179	#388×C₈₉	C₂²	1	1	yes	characteristic
180	#388×C₈₉	C₂²	1	1	yes	characteristic
181	#388×C₈₉	C₂²	1	1	yes	characteristic
182	#387×C₈₉	C₂²	1	1	yes	characteristic
183	#387×C₈₉	C₂²	1	1	yes	characteristic
184	#387×C₈₉	C₂²	1	1	yes	characteristic
185	#387×C₈₉	C₂²	1	1	yes	characteristic
186	#381×C₈₉	C₂²	1	1	yes	characteristic
187	#380×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	—
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	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
204	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
205	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
206	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
207	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	#15668011	C₂×C₄	1	8	yes	complemented
211	#15668011	C₂×C₄	1	8	yes	complemented
212	#15668010	C₂×C₄	1	8	yes	complemented
213	#15667992	C₂×C₄	1	8	yes	—
214	#15667990	C₂×C₄	1	8	yes	—
215	#15667990	C₂×C₄	1	8	yes	—
216	#15667989	C₂×C₄	1	8	yes	complemented
217	#15667989	C₂×C₄	1	8	yes	complemented
218	C₄×Dic₁₇₈	—	4	2	no	—
219	#15667977	—	4	2	no	—
220	#15667977	—	4	2	no	—
221	#15667977	—	4	2	no	—
222	#15667977	C₂×C₄	1	8	yes	complemented
223	C₄×C₂²⋊D₈₉	C₂×C₄	1	8	yes	—
224	#15667972	C₂×C₄	1	8	yes	—
225	#15667972	C₂×C₄	1	8	yes	—
226	#15667968	—	4	2	no	—
227	#15667968	—	4	2	no	—
228	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊Dic₈₉	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	C₄⋊C₄×D₈₉	—	4	2	no	—
254	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
257	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
259	C₂×#13083551	C₂³	1	1	yes	characteristic
260	C₂×#13083551	C₂³	1	1	yes	characteristic
261	C₂×#13083551	C₂³	1	1	yes	characteristic
262	C₂×#13083551	C₂³	1	1	yes	characteristic
263	C₂×#13083551	C₂³	1	1	yes	characteristic
264	C₂×#13083551	C₂³	1	1	yes	characteristic
265	C₂×#13083551	C₂³	1	1	yes	characteristic
266	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
267	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
268	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
269	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
270	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
271	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
272	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
273	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
274	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
275	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
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	C₄²×D₈₉	—	4	2	no	—
288	#15667919	C₂³	1	1	yes	characteristic
289	#15667919	C₂³	1	1	yes	characteristic
290	#15667919	C₂³	1	1	yes	characteristic
291	#15667919	C₂³	1	1	yes	characteristic
292	#15667919	C₂³	1	1	yes	characteristic
293	#15667919	C₂³	1	1	yes	characteristic
294	#15667919	C₂³	1	1	yes	characteristic
295	#15667919	C₂³	1	1	yes	characteristic
296	#15667919	C₂³	1	1	yes	characteristic
297	#15667919	C₂³	1	1	yes	characteristic
298	#15667919	C₂³	1	1	yes	characteristic
299	#15667919	C₂³	1	1	yes	characteristic
300	#15667919	C₂³	1	1	yes	characteristic
301	#15667919	C₂³	1	1	yes	characteristic
302	#15667919	C₂³	1	1	yes	characteristic
303	#15667919	C₂³	1	1	yes	characteristic
304	#15667919	C₂³	1	1	yes	characteristic
305	#15667919	C₂³	1	1	yes	characteristic
306	#15667919	C₂³	1	1	yes	characteristic
307	#15667919	C₂³	1	1	yes	characteristic
308	#15667919	C₂³	1	1	yes	characteristic
309	#15667919	C₂³	1	1	yes	characteristic
310	#15667919	C₂³	1	1	yes	characteristic
311	#15667919	C₂³	1	1	yes	characteristic
312	#15667919	C₂³	1	1	yes	characteristic
313	#15667919	C₂³	1	1	yes	characteristic
314	#15667919	C₂³	1	1	yes	characteristic
315	#15667919	C₂³	1	1	yes	characteristic
316	#15667919	C₂³	1	1	yes	characteristic
317	#15667919	C₂³	1	1	yes	characteristic
318	#15667919	C₂³	1	1	yes	characteristic
319	#15667919	C₂³	1	1	yes	characteristic
320	#15667919	C₂³	1	1	yes	characteristic
321	#15667919	C₂³	1	1	yes	characteristic
322	#15667919	C₂³	1	1	yes	characteristic
323	#15667919	C₂³	1	1	yes	characteristic
324	#15667919	C₂³	1	1	yes	characteristic
325	#15667919	C₂³	1	1	yes	characteristic
326	#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	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
335	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
336	C₂²⋊Q₈×C₈₉	C₂×C₄	1	8	yes	complemented
337	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
338	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
339	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
340	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
341	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
342	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
347	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
348	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
349	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
350	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
351	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
352	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
353	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
354	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
355	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
356	#95×C₈₉	C₂³	1	1	yes	characteristic
357	#95×C₈₉	C₂³	1	1	yes	characteristic
358	#95×C₈₉	C₂³	1	1	yes	characteristic
359	#95×C₈₉	C₂³	1	1	yes	characteristic
360	#95×C₈₉	C₂³	1	1	yes	characteristic
361	#95×C₈₉	C₂³	1	1	yes	characteristic
362	#95×C₈₉	C₂³	1	1	yes	characteristic
363	#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	C₂³×D₈₉	C₂⁴	1	1	yes	characteristic
371	C₂×Dic₁₇₈	—	2	2	no	—
372	C₂×Dic₁₇₈	—	2	2	no	—
373	C₂×Dic₁₇₈	—	2	2	no	—
374	C₂×Dic₁₇₈	—	2	2	no	—
375	C₂×Dic₁₇₈	—	2	2	no	—
376	C₂×Dic₁₇₈	—	2	2	no	—
377	C₂×Dic₁₇₈	—	4	16	no	—
378	C₂×Dic₁₇₈	—	4	1	no	—
379	C₂×Dic₁₇₈	—	4	1	no	—
380	C₂×Dic₁₇₈	—	4	1	no	—
381	C₂×Dic₁₇₈	—	4	1	no	—
382	C₂×Dic₁₇₈	—	4	1	no	—
383	C₂×Dic₁₇₈	—	4	1	no	—
384	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
385	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
386	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
387	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
388	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
389	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
390	Q₈×D₈₉	—	4	16	no	—
391	C₂×C₂²⋊D₈₉	—	2	2	no	—
392	C₂×C₂²⋊D₈₉	—	2	2	no	—
393	C₂×C₂²⋊D₈₉	C₂²×C₄	1	4	yes	—
394	C₂²×Dic₈₉	—	2	2	no	—
395	C₂²×Dic₈₉	—	2	2	no	—
396	C₂²×Dic₈₉	—	4	1	no	—
397	C₂²×Dic₈₉	—	4	1	no	—
398	C₂²×Dic₈₉	C₂²×C₄	1	4	yes	—
399	C₂²×Dic₈₉	C₂²×C₄	1	4	yes	—
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	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	C₂×C₄×D₈₉	—	2	2	no	—
416	C₂×C₄×D₈₉	—	2	2	no	—
417	C₂×C₄×D₈₉	—	2	2	no	—
418	C₂×C₄×D₈₉	—	2	2	no	—
419	C₂×C₄×D₈₉	—	2	2	no	—
420	C₂×C₄×D₈₉	—	2	2	no	—
421	C₂×C₄×D₈₉	—	2	2	no	—
422	C₂×C₄×D₈₉	—	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	—	4	1	no	—
429	C₂×C₄×D₈₉	—	4	1	no	—
430	C₂×C₄×D₈₉	—	4	1	no	—
431	C₂×C₄×D₈₉	—	4	1	no	—
432	C₂×C₄×D₈₉	—	4	1	no	—
433	C₂×C₄×D₈₉	C₂²×C₄	1	4	yes	—
434	C₂×C₄×D₈₉	C₂²×C₄	1	4	yes	—
435	C₂×C₄×D₈₉	C₂²×C₄	1	4	yes	—
436	C₄⋊Dic₈₉	—	2	2	no	—
437	C₄⋊Dic₈₉	—	4	1	no	—
438	C₄⋊Dic₈₉	—	4	1	no	—
439	C₄⋊Dic₈₉	—	4	1	no	—
440	C₄⋊Dic₈₉	C₂²×C₄	1	4	yes	—
441	C₄⋊Dic₈₉	C₂²×C₄	1	4	yes	—
442	#13083553	—	2	2	no	—
443	#13083553	—	2	2	no	—
444	#13083553	—	2	2	no	—
445	#13083553	—	2	2	no	—
446	#13083553	—	4	1	no	—
447	#13083553	—	4	1	no	—
448	#13083553	—	4	1	no	—
449	#13083553	—	4	1	no	—
450	#13083553	—	4	1	no	—
451	#13083553	—	4	1	no	—
452	#13083553	—	4	1	no	—
453	#13083553	—	4	1	no	—
454	#13083553	C₂²×C₄	1	4	yes	—
455	#13083553	C₂²×C₄	1	4	yes	—
456	#13083553	C₂²×C₄	1	4	yes	—
457	#13083553	C₂²×C₄	1	4	yes	—
458	#13083553	C₂²×C₄	1	4	yes	—
459	#13083553	C₂²×C₄	1	4	yes	—
460	#13083553	C₂²×C₄	1	4	yes	—
461	C₂²⋊Dic₈₉	—	2	2	no	—
462	C₂²⋊Dic₈₉	—	4	1	no	—
463	C₂²⋊Dic₈₉	—	4	1	no	—
464	C₂²⋊Dic₈₉	—	4	1	no	—
465	C₂²⋊Dic₈₉	C₂²×C₄	1	4	yes	—
466	#13083551	—	2	2	no	—
467	#13083551	—	2	2	no	—
468	#13083551	—	2	2	no	—
469	#13083551	—	2	2	no	—
470	#13083551	C₂²×C₄	1	4	yes	—
471	#13083551	C₂²×C₄	1	4	yes	—
472	#13083551	C₂²×C₄	1	4	yes	—
473	C₄×Dic₈₉	—	2	2	no	—
474	C₄×Dic₈₉	—	2	2	no	—
475	C₄×Dic₈₉	—	2	2	no	—
476	C₄×Dic₈₉	—	2	2	no	—
477	C₄×Dic₈₉	—	2	2	no	—
478	C₄×Dic₈₉	—	2	2	no	—
479	C₄×Dic₈₉	—	4	1	no	—
480	C₄×Dic₈₉	—	4	1	no	—
481	C₄×Dic₈₉	—	4	1	no	—
482	C₄×Dic₈₉	—	4	1	no	—
483	C₄×Dic₈₉	—	4	1	no	—
484	C₄×Dic₈₉	—	4	1	no	—
485	C₄×Dic₈₉	—	4	1	no	—
486	C₄×Dic₈₉	—	4	1	no	—
487	C₄×Dic₈₉	—	4	1	no	—
488	C₄×Dic₈₉	—	4	1	no	—
489	C₄×Dic₈₉	—	4	1	no	—
490	C₄×Dic₈₉	—	4	1	no	—
491	C₄×Dic₈₉	C₂²×C₄	1	4	yes	—
492	C₄×Dic₈₉	C₂²×C₄	1	4	yes	—
493	C₄×Dic₈₉	C₂²×C₄	1	4	yes	—
494	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
495	C₂×Q₈×C₈₉	—	4	1	no	—
496	C₂×Q₈×C₈₉	—	4	1	no	—
497	C₂×Q₈×C₈₉	C₂²×C₄	1	4	yes	—
498	C₂²×C₄×C₈₉	—	4	1	no	—
499	C₂²×C₄×C₈₉	—	4	1	no	—
500	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
501	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
502	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
503	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
504	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
505	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
506	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
507	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
508	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
509	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
510	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
511	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
512	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
513	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
514	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
515	C₄⋊C₄×C₈₉	—	4	1	no	—
516	C₄⋊C₄×C₈₉	—	4	1	no	—
517	C₄⋊C₄×C₈₉	—	4	1	no	—
518	C₄⋊C₄×C₈₉	—	4	1	no	—
519	C₄⋊C₄×C₈₉	—	4	1	no	—
520	C₄⋊C₄×C₈₉	—	4	1	no	—
521	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
522	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
523	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
524	C₂²⋊C₄×C₈₉	—	4	1	no	—
525	C₂²⋊C₄×C₈₉	—	4	1	no	—
526	C₂²⋊C₄×C₈₉	—	4	1	no	—
527	C₂²⋊C₄×C₈₉	—	4	1	no	—
528	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
529	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
530	C₄²×C₈₉	—	4	1	no	—
531	C₄²×C₈₉	—	4	1	no	—
532	C₄²×C₈₉	—	4	1	no	—
533	C₄²×C₈₉	—	4	1	no	—
534	C₂³×C₈₉	—	2	1	no	—
535	C₂³×C₈₉	—	2	1	no	—
536	C₂³×C₈₉	—	2	1	no	—
537	C₂³×C₈₉	—	2	1	no	—
538	C₂³×C₈₉	—	2	1	no	—
539	C₂³×C₈₉	—	2	1	no	—
540	C₂³×C₈₉	C₂³×C₄	1	2	yes	—
541	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
542	C₂²×D₈₉	—	2	1	no	—
543	C₂²×D₈₉	—	2	1	no	—
544	C₂²×D₈₉	—	2	1	no	—
545	C₂²×D₈₉	—	2	1	no	—
546	C₂²×D₈₉	C₂³×C₄	1	2	yes	—
547	C₂²×D₈₉	2₋¹⁺⁴	1	2	yes	—
548	C₂²×D₈₉	2₋¹⁺⁴	1	2	yes	—
549	Q₈×C₈₉	—	4	4	no	—
550	C₂×C₄×C₈₉	—	2	1	no	—
551	C₂×C₄×C₈₉	—	2	1	no	—
552	C₂×C₄×C₈₉	—	2	1	no	—
553	C₂×C₄×C₈₉	—	2	1	no	—
554	C₂×C₄×C₈₉	—	2	1	no	—
555	C₂×C₄×C₈₉	—	2	1	no	—
556	C₂×C₄×C₈₉	—	2	1	no	—
557	C₂×C₄×C₈₉	—	2	1	no	—
558	C₂×C₄×C₈₉	—	2	1	no	—
559	C₂×C₄×C₈₉	—	2	1	no	—
560	C₂×C₄×C₈₉	—	2	1	no	—
561	C₂×C₄×C₈₉	—	2	1	no	—
562	C₂×C₄×C₈₉	—	2	1	no	—
563	C₂×C₄×C₈₉	—	2	1	no	—
564	C₂×C₄×C₈₉	—	2	1	no	—
565	C₂×C₄×C₈₉	—	2	1	no	—
566	C₂×C₄×C₈₉	—	2	1	no	—
567	C₂×C₄×C₈₉	—	2	1	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	—	4	4	no	—
587	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
588	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
589	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
590	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
591	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
592	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
593	C₂²⋊D₈₉	—	2	8	no	—
594	C₂×Dic₈₉	—	2	1	no	—
595	C₂×Dic₈₉	—	2	1	no	—
596	C₂×Dic₈₉	—	2	1	no	—
597	C₂×Dic₈₉	—	2	1	no	—
598	C₂×Dic₈₉	—	2	1	no	—
599	C₂×Dic₈₉	—	2	1	no	—
600	C₂×Dic₈₉	—	2	1	no	—
601	C₂×Dic₈₉	—	2	1	no	—
602	C₂×Dic₈₉	—	2	1	no	—
603	C₂×Dic₈₉	—	2	1	no	—
604	C₂×Dic₈₉	—	2	1	no	—
605	C₂×Dic₈₉	—	2	1	no	—
606	C₂×Dic₈₉	—	2	1	no	—
607	C₂×Dic₈₉	—	2	1	no	—
608	C₂×Dic₈₉	—	2	8	no	—
609	C₂×Dic₈₉	—	2	1	no	—
610	C₂×Dic₈₉	—	2	1	no	—
611	C₂×Dic₈₉	—	2	1	no	—
612	C₂×Dic₈₉	—	2	1	no	—
613	C₂×Dic₈₉	—	2	1	no	—
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	1	no	—
629	C₂×Dic₈₉	—	2	1	no	—
630	C₂×Dic₈₉	—	4	4	no	—
631	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
632	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
633	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
634	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
635	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
636	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
637	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
638	C₂×Dic₈₉	H(5,𝔽₂)	1	2	yes	—
639	C₂×Dic₈₉	H(5,𝔽₂)	1	2	yes	—
640	C₂×Dic₈₉	2₋¹⁺⁴	1	2	yes	—
641	C₄×D₈₉	—	2	8	no	—
642	C₄×D₈₉	—	4	4	no	—
643	C₄×D₈₉	—	4	4	no	—
644	C₄×D₈₉	—	4	4	no	—
645	C₄×D₈₉	—	4	4	no	—
646	C₄×D₈₉	—	8	2	no	—
647	C₄×D₈₉	—	8	2	no	—
648	Dic₁₇₈	—	2	8	no	—
649	Dic₁₇₈	—	2	8	no	—
650	Dic₁₇₈	—	2	8	no	—
651	Dic₁₇₈	—	4	4	no	—
652	Dic₁₇₈	—	4	4	no	—
653	Dic₁₇₈	—	4	4	no	—
654	C₂²×C₈₉	—	2	2	no	—
655	C₂²×C₈₉	—	2	2	no	—
656	C₂²×C₈₉	—	2	2	no	—
657	C₂²×C₈₉	—	4	1	no	—
658	C₂²×C₈₉	—	4	1	no	—
659	C₂²×C₈₉	—	4	1	no	—
660	C₂²×C₈₉	—	4	1	no	—
661	C₂²×C₈₉	C₂⁴×C₄	1	1	yes	characteristic
662	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
663	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
664	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
665	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
666	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
667	C₂²×C₈₉	#585	1	1	yes	characteristic
668	C₂×D₈₉	—	2	2	no	—
669	C₂×D₈₉	—	2	2	no	—
670	C₂×D₈₉	—	2	2	no	—
671	C₂×D₈₉	—	2	2	no	—
672	C₂×D₈₉	—	2	2	no	—
673	C₂×D₈₉	—	2	2	no	—
674	C₂×D₈₉	#519	1	4	yes	—
675	C₄×C₈₉	—	2	2	no	—
676	C₄×C₈₉	—	2	2	no	—
677	C₄×C₈₉	—	2	2	no	—
678	C₄×C₈₉	—	2	2	no	—
679	C₄×C₈₉	—	2	2	no	—
680	C₄×C₈₉	—	2	2	no	—
681	C₄×C₈₉	—	4	1	no	—
682	C₄×C₈₉	—	4	1	no	—
683	C₄×C₈₉	—	4	1	no	—
684	C₄×C₈₉	—	4	1	no	—
685	C₄×C₈₉	—	4	1	no	—
686	C₄×C₈₉	—	4	1	no	—
687	C₄×C₈₉	—	4	1	no	—
688	C₄×C₈₉	—	4	1	no	—
689	Dic₈₉	—	2	2	no	—
690	Dic₈₉	—	2	2	no	—
691	Dic₈₉	—	2	2	no	—
692	Dic₈₉	—	2	2	no	—
693	Dic₈₉	—	2	2	no	—
694	Dic₈₉	—	2	2	no	—
695	Dic₈₉	—	2	2	no	—
696	Dic₈₉	—	4	1	no	—
697	Dic₈₉	—	4	1	no	—
698	Dic₈₉	—	4	1	no	—
699	Dic₈₉	—	4	1	no	—
700	Dic₈₉	—	4	1	no	—
701	Dic₈₉	—	4	1	no	—
702	Dic₈₉	—	4	1	no	—
703	Dic₈₉	#518	1	4	yes	—
704	#34475	—	89	1	no	maximal, Sylow
705	C₂×C₈₉	—	4	2	no	—
706	C₂×C₈₉	C₂×#518	1	1	yes	characteristic
707	C₂×C₈₉	C₂×#519	1	1	yes	characteristic
708	C₂×C₈₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic
709	C₂×C₈₉	#3538	1	1	yes	characteristic
710	C₂×C₈₉	#3541	1	1	yes	characteristic
711	C₂×C₈₉	#3552	1	1	yes	characteristic
712	C₂×C₈₉	#3561	1	1	yes	characteristic
713	D₈₉	—	2	4	no	—
714	C₂×D₄×Q₈	—	89	1	no	—
715	#2381	—	89	1	no	—
716	#2381	—	89	1	no	—
717	#2378	—	89	1	no	—
718	#2378	D₈₉	1	1	yes	characteristic, complemented
719	#2368	—	89	1	no	—
720	#2368	—	89	1	no	—
721	#2365	—	89	1	no	—
722	#2362	—	89	1	no	—
723	#2360	—	89	1	no	—
724	#2356	—	89	1	no	—
725	#2353	—	89	1	no	—
726	#2353	—	89	1	no	—
727	#2352	—	89	1	no	—
728	Q₈×C₂²⋊C₄	—	89	1	no	—
729	Q₈×C₂²⋊C₄	—	89	1	no	—
730	#2332	—	89	1	no	—
731	#2332	—	89	1	no	—
732	#2331	—	89	1	no	—
733	#2331	—	89	1	no	—
734	#2329	—	89	1	no	—
735	#2329	—	89	1	no	—
736	#2327	—	89	1	no	—
737	#2323	—	89	1	no	—
738	#2320	—	89	1	no	—
739	#2318	—	89	1	no	—
740	#2318	—	89	1	no	—
741	#2310	—	89	1	no	—
742	C₄×C₂²⋊Q₈	—	89	1	no	—
743	C₂×#391	—	89	1	no	—
744	#2290	—	89	1	no	—
745	C₈₉	#34475	1	1	yes	characteristic, complemented, Sylow
746	C₂³×Q₈	—	89	1	no	—
747	C₂³×Q₈	—	89	1	no	—
748	D₄×Q₈	—	89	16	no	—
749	C₂×C₄⋊Q₈	—	89	1	no	—
750	C₂×C₄⋊Q₈	—	89	1	no	—
751	C₂×C₄⋊Q₈	—	89	1	no	—
752	C₂×C₂²⋊Q₈	—	89	1	no	—
753	C₂×C₂²⋊Q₈	—	89	1	no	—
754	C₂×C₂²⋊Q₈	—	89	1	no	—
755	C₂×C₂²⋊Q₈	—	89	1	no	—
756	C₂×C₂²⋊Q₈	—	89	1	no	—
757	C₂×C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
758	C₂×C₄×Q₈	—	89	1	no	—
759	C₂×C₄×Q₈	—	89	1	no	—
760	C₂×C₄×Q₈	—	89	1	no	—
761	C₂×C₄×Q₈	—	89	1	no	—
762	C₂×C₄×Q₈	—	89	1	no	—
763	C₂×C₄×D₄	—	89	1	no	—
764	C₂×C₄×D₄	—	89	1	no	—
765	C₂×C₄×D₄	—	89	1	no	—
766	C₂×#117	—	89	1	no	—
767	C₂×#117	—	89	1	no	—
768	C₂²×C₄⋊C₄	—	89	1	no	—
769	C₂²×C₄²	—	89	1	no	—
770	#391	—	89	1	no	—
771	#391	—	89	1	no	—
772	#391	—	89	1	no	—
773	#391	—	89	1	no	—
774	#391	—	89	1	no	—
775	#391	—	89	1	no	—
776	#391	—	89	1	no	—
777	#391	—	89	1	no	—
778	#391	—	89	1	no	—
779	#391	—	89	1	no	—
780	#391	—	89	1	no	—
781	#391	—	89	1	no	—
782	#391	—	89	1	no	—
783	#391	—	89	1	no	—
784	#391	—	89	1	no	—
785	#391	—	89	1	no	—
786	#391	—	89	1	no	—
787	#391	—	89	1	no	—
788	#391	—	89	1	no	—
789	#391	—	89	1	no	—
790	#391	—	89	1	no	—
791	#391	—	89	1	no	—
792	#391	C₂×D₈₉	1	1	yes	characteristic
793	#391	C₂×D₈₉	1	1	yes	characteristic
794	#389	—	89	1	no	—
795	#389	—	89	1	no	—
796	#389	—	89	1	no	—
797	#389	—	89	1	no	—
798	#389	—	89	1	no	—
799	#389	—	89	1	no	—
800	#389	C₂×D₈₉	1	1	yes	characteristic
801	#389	C₂×D₈₉	1	1	yes	characteristic
802	#388	—	89	1	no	—
803	#388	—	89	1	no	—
804	#388	—	89	1	no	—
805	#388	—	89	1	no	—
806	#388	—	89	1	no	—
807	#388	—	89	1	no	—
808	#388	—	89	1	no	—
809	#388	—	89	1	no	—
810	#388	C₂×D₈₉	1	1	yes	characteristic
811	#388	C₂×D₈₉	1	1	yes	characteristic
812	#388	C₂×D₈₉	1	1	yes	characteristic
813	#388	C₂×D₈₉	1	1	yes	characteristic
814	#387	—	89	1	no	—
815	#387	—	89	1	no	—
816	#387	—	89	1	no	—
817	#387	—	89	1	no	—
818	#387	—	89	1	no	—
819	#387	—	89	1	no	—
820	#387	—	89	1	no	—
821	#387	—	89	1	no	—
822	#387	—	89	1	no	—
823	#387	—	89	1	no	—
824	#387	—	89	1	no	—
825	#387	—	89	1	no	—
826	#387	—	89	1	no	—
827	#387	—	89	1	no	—
828	#387	—	89	1	no	—
829	#387	—	89	1	no	—
830	#387	—	89	1	no	—
831	#387	—	89	1	no	—
832	#387	—	89	1	no	—
833	#387	—	89	1	no	—
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	C₂×D₈₉	1	1	yes	characteristic
843	#387	C₂×D₈₉	1	1	yes	characteristic
844	#387	C₂×D₈₉	1	1	yes	characteristic
845	#387	C₂×D₈₉	1	1	yes	characteristic
846	#386	—	89	1	no	—
847	#386	—	89	1	no	—
848	#386	—	89	1	no	—
849	#386	—	89	1	no	—
850	#385	—	89	1	no	—
851	#385	—	89	1	no	—
852	#385	—	89	1	no	—
853	#385	—	89	1	no	—
854	#385	—	89	1	no	—
855	#385	—	89	1	no	—
856	#383	—	89	1	no	—
857	#383	—	89	1	no	—
858	#383	—	89	1	no	—
859	#383	—	89	1	no	—
860	#382	—	89	1	no	—
861	#382	—	89	1	no	—
862	#382	—	89	1	no	—
863	#381	—	89	1	no	—
864	#381	—	89	1	no	—
865	#381	—	89	1	no	—
866	#381	C₂×D₈₉	1	1	yes	characteristic
867	#380	—	89	1	no	—
868	#380	—	89	1	no	—
869	#380	—	89	1	no	—
870	#380	—	89	1	no	—
871	#380	—	89	1	no	—
872	#380	C₂×D₈₉	1	1	yes	characteristic
873	C₄×C₄⋊C₄	—	89	1	no	—
874	C₄×C₄⋊C₄	—	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×C₂²⋊C₄	—	89	1	no	—
884	C₄×C₂²⋊C₄	—	89	1	no	—
885	C₄×C₂²⋊C₄	—	89	1	no	—
886	C₄×C₂²⋊C₄	—	89	1	no	—
887	C₄×C₂²⋊C₄	—	89	1	no	—
888	C₄×C₂²⋊C₄	—	89	1	no	—
889	C₄×C₂²⋊C₄	—	89	1	no	—
890	C₄×C₂²⋊C₄	—	89	1	no	—
891	C₄×C₂²⋊C₄	—	89	1	no	—
892	C₄×C₂²⋊C₄	—	89	1	no	—
893	C₄×C₂²⋊C₄	—	89	1	no	—
894	C₄×C₂²⋊C₄	—	89	1	no	—
895	#376	—	89	1	no	—
896	#376	—	89	1	no	—
897	#376	—	89	1	no	—
898	C₂×#95	—	89	1	no	—
899	C₂×#95	—	89	1	no	—
900	C₂×#95	—	89	1	no	—
901	C₂×#95	—	89	1	no	—
902	C₂²×Q₈	—	89	8	no	—
903	C₂²×Q₈	—	89	8	no	—
904	C₂²×Q₈	—	89	1	no	—
905	C₂²×Q₈	—	89	1	no	—
906	C₂²×Q₈	—	89	1	no	—
907	C₂²×Q₈	—	89	1	no	—
908	C₂²×Q₈	—	89	1	no	—
909	C₂²×Q₈	—	89	1	no	—
910	C₂²×Q₈	—	356	2	no	—
911	C₂²×Q₈	—	356	2	no	—
912	C₂²×Q₈	—	356	2	no	—
913	C₂²×Q₈	—	356	2	no	—
914	C₂²×Q₈	C₂²×D₈₉	1	1	yes	characteristic
915	C₂²×D₄	—	89	1	no	—
916	C₂³×C₄	—	89	1	no	—
917	C₂³×C₄	—	89	1	no	—
918	C₂³×C₄	—	89	1	no	—
919	C₂³×C₄	—	89	1	no	—
920	C₂³×C₄	—	89	1	no	—
921	C₂³×C₄	—	89	1	no	—
922	C₂³×C₄	—	89	1	no	—
923	C₂³×C₄	—	89	1	no	—
924	C₂³×C₄	—	89	1	no	—
925	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
926	C₄⋊Q₈	—	89	8	no	—
927	C₄⋊Q₈	—	89	8	no	—
928	C₄⋊Q₈	—	89	8	no	—
929	C₂²⋊Q₈	—	89	8	no	—
930	C₂²⋊Q₈	—	89	8	no	—
931	C₂²⋊Q₈	—	89	8	no	—
932	C₂²⋊Q₈	—	89	8	no	—
933	C₂²⋊Q₈	—	89	8	no	—
934	C₂²⋊Q₈	C₄×D₈₉	1	8	yes	complemented
935	C₄×Q₈	—	89	8	no	—
936	C₄×Q₈	—	356	2	no	—
937	C₄×Q₈	—	356	2	no	—
938	C₄×Q₈	—	356	2	no	—
939	C₄×Q₈	—	356	2	no	—
940	C₄×D₄	—	89	8	no	—
941	C₄×D₄	—	89	8	no	—
942	C₄×D₄	—	89	8	no	—
943	#117	—	356	2	no	—
944	#117	—	356	2	no	—
945	C₂×C₄⋊C₄	—	89	1	no	—
946	C₂×C₄⋊C₄	—	89	1	no	—
947	C₂×C₄⋊C₄	—	89	1	no	—
948	C₂×C₄⋊C₄	—	89	1	no	—
949	C₂×C₄⋊C₄	—	89	1	no	—
950	C₂×C₄⋊C₄	—	89	1	no	—
951	C₂×C₄⋊C₄	—	89	1	no	—
952	C₂×C₄⋊C₄	—	89	1	no	—
953	C₂×C₄⋊C₄	—	89	1	no	—
954	C₂×C₄⋊C₄	—	89	1	no	—
955	C₂×C₄⋊C₄	—	89	1	no	—
956	C₂×C₄⋊C₄	—	89	1	no	—
957	C₂×C₄⋊C₄	—	89	1	no	—
958	C₂×C₄⋊C₄	—	89	1	no	—
959	C₂×C₄⋊C₄	—	89	1	no	—
960	C₂×C₄⋊C₄	—	89	1	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	—	356	2	no	—
971	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
972	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
973	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
974	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
975	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
976	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
977	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
978	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
979	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
980	C₂×C₂²⋊C₄	—	89	1	no	—
981	C₂×C₂²⋊C₄	—	89	1	no	—
982	C₂×C₂²⋊C₄	—	89	1	no	—
983	C₂×C₂²⋊C₄	—	89	1	no	—
984	C₂×C₂²⋊C₄	—	89	1	no	—
985	C₂×C₂²⋊C₄	—	89	1	no	—
986	C₂×C₂²⋊C₄	—	89	1	no	—
987	C₂×C₂²⋊C₄	—	89	1	no	—
988	C₂×C₂²⋊C₄	—	89	1	no	—
989	C₂×C₂²⋊C₄	—	89	1	no	—
990	C₂×C₂²⋊C₄	—	89	1	no	—
991	C₂×C₂²⋊C₄	—	89	1	no	—
992	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
993	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
994	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
995	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
996	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
997	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
998	C₂×C₄²	—	89	1	no	—
999	C₂×C₄²	—	89	1	no	—
1000	C₂×C₄²	—	89	1	no	—
1001	C₂×C₄²	—	89	1	no	—
1002	C₂×C₄²	—	89	1	no	—
1003	C₂×C₄²	—	89	1	no	—
1004	C₂×C₄²	—	89	1	no	—
1005	C₂×C₄²	—	89	1	no	—
1006	C₂×C₄²	—	89	1	no	—
1007	C₂×C₄²	—	89	1	no	—
1008	C₂×C₄²	—	89	1	no	—
1009	C₂×C₄²	—	89	1	no	—
1010	C₂×C₄²	—	89	1	no	—
1011	C₂×C₄²	—	89	1	no	—
1012	C₂×C₄²	—	89	1	no	—
1013	C₂×C₄²	—	89	1	no	—
1014	C₂×C₄²	—	89	1	no	—
1015	C₂×C₄²	—	89	1	no	—
1016	C₂×C₄²	—	89	1	no	—
1017	C₂×C₄²	—	89	1	no	—
1018	C₂×C₄²	—	89	1	no	—
1019	C₂×C₄²	—	356	2	no	—
1020	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1021	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1022	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1023	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1024	#95	—	89	1	no	—
1025	#95	—	89	1	no	—
1026	#95	—	89	1	no	—
1027	#95	—	89	1	no	—
1028	#95	—	89	1	no	—
1029	#95	—	89	1	no	—
1030	#95	—	89	1	no	—
1031	#95	—	89	1	no	—
1032	#95	—	89	1	no	—
1033	#95	—	89	1	no	—
1034	#95	—	89	1	no	—
1035	#95	—	89	1	no	—
1036	#95	—	89	1	no	—
1037	#95	—	89	1	no	—
1038	#95	—	89	1	no	—
1039	#95	—	89	1	no	—
1040	#95	—	89	1	no	—
1041	#95	—	89	1	no	—
1042	#95	—	89	1	no	—
1043	#95	—	89	1	no	—
1044	#95	—	89	1	no	—
1045	#95	—	89	1	no	—
1046	#95	—	89	1	no	—
1047	#95	—	89	1	no	—
1048	#95	—	89	1	no	—
1049	#95	—	89	1	no	—
1050	#95	—	89	1	no	—
1051	#95	—	89	1	no	—
1052	#95	—	89	1	no	—
1053	#95	—	89	1	no	—
1054	#95	—	89	1	no	—
1055	#95	—	89	1	no	—
1056	#95	—	89	1	no	—
1057	#95	—	89	1	no	—
1058	#95	—	89	1	no	—
1059	#95	—	89	1	no	—
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	C₂²×D₈₉	1	1	yes	characteristic
1071	#95	C₂²×D₈₉	1	1	yes	characteristic
1072	#95	C₂²×D₈₉	1	1	yes	characteristic
1073	#95	C₂²×D₈₉	1	1	yes	characteristic
1074	#95	C₂²×D₈₉	1	1	yes	characteristic
1075	#95	C₂²×D₈₉	1	1	yes	characteristic
1076	#95	C₂²×D₈₉	1	1	yes	characteristic
1077	#95	C₂²×D₈₉	1	1	yes	characteristic
1078	#95	C₂²×D₈₉	1	1	yes	characteristic
1079	#95	C₂²×D₈₉	1	1	yes	characteristic
1080	#95	C₂²×D₈₉	1	1	yes	characteristic
1081	#95	C₂²×D₈₉	1	1	yes	characteristic
1082	#95	C₂²×D₈₉	1	1	yes	characteristic
1083	#95	C₂²×D₈₉	1	1	yes	characteristic
1084	C₂⁴	—	89	1	no	—
1085	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
1086	C₂×Q₈	—	4	1	no	—
1087	C₂×Q₈	—	4	1	no	—
1088	C₂×Q₈	—	89	4	no	—
1089	C₂×Q₈	—	89	4	no	—
1090	C₂×Q₈	—	89	4	no	—
1091	C₂×Q₈	—	89	4	no	—
1092	C₂×Q₈	—	89	4	no	—
1093	C₂×Q₈	—	89	4	no	—
1094	C₂×Q₈	—	356	1	no	—
1095	C₂×Q₈	—	356	1	no	—
1096	C₂×Q₈	—	356	1	no	—
1097	C₂×Q₈	—	356	1	no	—
1098	C₂×Q₈	—	356	1	no	—
1099	C₂×Q₈	—	356	1	no	—
1100	C₂×Q₈	—	356	16	no	—
1101	C₂×Q₈	—	356	16	no	—
1102	C₂×Q₈	—	178	2	no	—
1103	C₂×Q₈	—	178	2	no	—
1104	C₂×Q₈	—	178	2	no	—
1105	C₂×Q₈	—	178	2	no	—
1106	C₂×Q₈	—	178	2	no	—
1107	C₂×Q₈	—	178	2	no	—
1108	C₂×Q₈	C₂×C₄×D₈₉	1	4	yes	—
1109	C₂×D₄	—	89	4	no	—
1110	C₂×D₄	—	178	2	no	—
1111	C₂×D₄	—	178	2	no	—
1112	C₂²×C₄	—	4	1	no	—
1113	C₂²×C₄	—	4	1	no	—
1114	C₂²×C₄	—	89	1	no	—
1115	C₂²×C₄	—	89	4	no	—
1116	C₂²×C₄	—	89	4	no	—
1117	C₂²×C₄	—	89	1	no	—
1118	C₂²×C₄	—	89	1	no	—
1119	C₂²×C₄	—	89	1	no	—
1120	C₂²×C₄	—	89	1	no	—
1121	C₂²×C₄	—	89	1	no	—
1122	C₂²×C₄	—	89	1	no	—
1123	C₂²×C₄	—	89	1	no	—
1124	C₂²×C₄	—	89	4	no	—
1125	C₂²×C₄	—	89	4	no	—
1126	C₂²×C₄	—	89	4	no	—
1127	C₂²×C₄	—	89	1	no	—
1128	C₂²×C₄	—	89	1	no	—
1129	C₂²×C₄	—	89	1	no	—
1130	C₂²×C₄	—	89	1	no	—
1131	C₂²×C₄	—	89	1	no	—
1132	C₂²×C₄	—	89	1	no	—
1133	C₂²×C₄	—	89	1	no	—
1134	C₂²×C₄	—	356	1	no	—
1135	C₂²×C₄	—	356	1	no	—
1136	C₂²×C₄	—	356	1	no	—
1137	C₂²×C₄	—	356	1	no	—
1138	C₂²×C₄	—	356	1	no	—
1139	C₂²×C₄	—	356	1	no	—
1140	C₂²×C₄	—	356	1	no	—
1141	C₂²×C₄	—	356	1	no	—
1142	C₂²×C₄	—	356	1	no	—
1143	C₂²×C₄	—	356	1	no	—
1144	C₂²×C₄	—	356	1	no	—
1145	C₂²×C₄	—	356	1	no	—
1146	C₂²×C₄	—	356	1	no	—
1147	C₂²×C₄	—	178	2	no	—
1148	C₂²×C₄	—	178	2	no	—
1149	C₂²×C₄	—	178	2	no	—
1150	C₂²×C₄	—	178	2	no	—
1151	C₂²×C₄	—	178	2	no	—
1152	C₂²×C₄	—	178	2	no	—
1153	C₂²×C₄	—	178	2	no	—
1154	C₂²×C₄	—	178	2	no	—
1155	C₂²×C₄	—	178	2	no	—
1156	C₂²×C₄	C₂×C₄×D₈₉	1	4	yes	—
1157	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1158	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1159	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1160	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1161	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1162	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1163	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1164	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1165	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1166	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1167	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1168	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1169	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1170	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1171	C₄⋊C₄	—	4	1	no	—
1172	C₄⋊C₄	—	4	1	no	—
1173	C₄⋊C₄	—	4	1	no	—
1174	C₄⋊C₄	—	4	1	no	—
1175	C₄⋊C₄	—	4	1	no	—
1176	C₄⋊C₄	—	4	1	no	—
1177	C₄⋊C₄	—	89	4	no	—
1178	C₄⋊C₄	—	89	4	no	—
1179	C₄⋊C₄	—	89	4	no	—
1180	C₄⋊C₄	—	89	4	no	—
1181	C₄⋊C₄	—	89	4	no	—
1182	C₄⋊C₄	—	89	4	no	—
1183	C₄⋊C₄	—	89	4	no	—
1184	C₄⋊C₄	—	89	4	no	—
1185	C₄⋊C₄	—	89	4	no	—
1186	C₄⋊C₄	—	356	1	no	—
1187	C₄⋊C₄	—	356	1	no	—
1188	C₄⋊C₄	—	356	1	no	—
1189	C₄⋊C₄	—	356	1	no	—
1190	C₄⋊C₄	—	356	1	no	—
1191	C₄⋊C₄	—	356	1	no	—
1192	C₄⋊C₄	—	356	1	no	—
1193	C₄⋊C₄	—	356	1	no	—
1194	C₄⋊C₄	—	356	1	no	—
1195	C₄⋊C₄	—	356	1	no	—
1196	C₄⋊C₄	—	356	1	no	—
1197	C₄⋊C₄	—	178	2	no	—
1198	C₄⋊C₄	—	178	2	no	—
1199	C₄⋊C₄	—	178	2	no	—
1200	C₄⋊C₄	—	178	2	no	—
1201	C₄⋊C₄	—	178	2	no	—
1202	C₄⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1203	C₄⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1204	C₄⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1205	C₂²⋊C₄	—	4	1	no	—
1206	C₂²⋊C₄	—	4	1	no	—
1207	C₂²⋊C₄	—	4	1	no	—
1208	C₂²⋊C₄	—	4	1	no	—
1209	C₂²⋊C₄	—	89	4	no	—
1210	C₂²⋊C₄	—	89	4	no	—
1211	C₂²⋊C₄	—	89	4	no	—
1212	C₂²⋊C₄	—	89	4	no	—
1213	C₂²⋊C₄	—	356	1	no	—
1214	C₂²⋊C₄	—	356	1	no	—
1215	C₂²⋊C₄	—	356	1	no	—
1216	C₂²⋊C₄	—	178	2	no	—
1217	C₂²⋊C₄	—	178	2	no	—
1218	C₂²⋊C₄	—	178	2	no	—
1219	C₂²⋊C₄	—	178	2	no	—
1220	C₂²⋊C₄	—	178	2	no	—
1221	C₂²⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1222	C₂²⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1223	C₄²	—	4	1	no	—
1224	C₄²	—	4	1	no	—
1225	C₄²	—	4	1	no	—
1226	C₄²	—	4	1	no	—
1227	C₄²	—	89	4	no	—
1228	C₄²	—	89	4	no	—
1229	C₄²	—	89	4	no	—
1230	C₄²	—	356	1	no	—
1231	C₄²	—	356	1	no	—
1232	C₄²	—	356	1	no	—
1233	C₄²	—	356	1	no	—
1234	C₄²	—	356	1	no	—
1235	C₄²	—	356	1	no	—
1236	C₄²	—	356	1	no	—
1237	C₄²	—	356	1	no	—
1238	C₄²	—	356	1	no	—
1239	C₄²	—	356	1	no	—
1240	C₄²	—	356	1	no	—
1241	C₄²	—	356	1	no	—
1242	C₄²	—	178	2	no	—
1243	C₄²	—	178	2	no	—
1244	C₄²	—	178	2	no	—
1245	C₄²	—	178	2	no	—
1246	C₄²	—	178	2	no	—
1247	C₄²	—	178	2	no	—
1248	C₂³	—	2	1	no	—
1249	C₂³	—	2	1	no	—
1250	C₂³	—	2	1	no	—
1251	C₂³	—	2	1	no	—
1252	C₂³	—	2	1	no	—
1253	C₂³	—	2	1	no	—
1254	C₂³	—	89	2	no	—
1255	C₂³	—	89	2	no	—
1256	C₂³	—	89	2	no	—
1257	C₂³	—	178	1	no	—
1258	C₂³	—	178	1	no	—
1259	C₂³	—	178	1	no	—
1260	C₂³	—	178	1	no	—
1261	C₂³	C₂²×C₄×D₈₉	1	2	yes	—
1262	C₂³	C₂⁴×D₈₉	1	1	yes	characteristic
1263	Q₈	—	4	4	no	—
1264	Q₈	—	356	4	no	—
1265	Q₈	—	356	4	no	—
1266	Q₈	—	356	4	no	—
1267	Q₈	—	178	8	no	—
1268	Q₈	—	178	8	no	—
1269	Q₈	—	178	8	no	—
1270	D₄	—	178	8	no	—
1271	C₂×C₄	—	2	1	no	—
1272	C₂×C₄	—	2	1	no	—
1273	C₂×C₄	—	2	1	no	—
1274	C₂×C₄	—	2	1	no	—
1275	C₂×C₄	—	2	1	no	—
1276	C₂×C₄	—	2	1	no	—
1277	C₂×C₄	—	2	1	no	—
1278	C₂×C₄	—	2	1	no	—
1279	C₂×C₄	—	2	1	no	—
1280	C₂×C₄	—	2	1	no	—
1281	C₂×C₄	—	2	1	no	—
1282	C₂×C₄	—	2	1	no	—
1283	C₂×C₄	—	2	1	no	—
1284	C₂×C₄	—	2	1	no	—
1285	C₂×C₄	—	2	1	no	—
1286	C₂×C₄	—	2	1	no	—
1287	C₂×C₄	—	2	1	no	—
1288	C₂×C₄	—	2	1	no	—
1289	C₂×C₄	—	2	1	no	—
1290	C₂×C₄	—	2	1	no	—
1291	C₂×C₄	—	2	1	no	—
1292	C₂×C₄	—	2	1	no	—
1293	C₂×C₄	—	2	1	no	—
1294	C₂×C₄	—	2	1	no	—
1295	C₂×C₄	—	2	1	no	—
1296	C₂×C₄	—	2	1	no	—
1297	C₂×C₄	—	2	1	no	—
1298	C₂×C₄	—	2	1	no	—
1299	C₂×C₄	—	2	1	no	—
1300	C₂×C₄	—	2	1	no	—
1301	C₂×C₄	—	2	1	no	—
1302	C₂×C₄	—	2	1	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	—	4	4	no	—
1308	C₂×C₄	—	89	2	no	—
1309	C₂×C₄	—	89	2	no	—
1310	C₂×C₄	—	89	2	no	—
1311	C₂×C₄	—	89	2	no	—
1312	C₂×C₄	—	89	2	no	—
1313	C₂×C₄	—	89	2	no	—
1314	C₂×C₄	—	89	2	no	—
1315	C₂×C₄	—	89	2	no	—
1316	C₂×C₄	—	89	2	no	—
1317	C₂×C₄	—	89	2	no	—
1318	C₂×C₄	—	356	4	no	—
1319	C₂×C₄	—	356	4	no	—
1320	C₂×C₄	—	356	4	no	—
1321	C₂×C₄	—	356	4	no	—
1322	C₂×C₄	—	356	4	no	—
1323	C₂×C₄	—	178	8	no	—
1324	C₂×C₄	—	178	8	no	—
1325	C₂×C₄	—	178	1	no	—
1326	C₂×C₄	—	178	1	no	—
1327	C₂×C₄	—	178	1	no	—
1328	C₂×C₄	—	178	1	no	—
1329	C₂×C₄	—	178	1	no	—
1330	C₂×C₄	—	178	1	no	—
1331	C₂×C₄	—	178	1	no	—
1332	C₂×C₄	—	178	1	no	—
1333	C₂×C₄	—	178	1	no	—
1334	C₂×C₄	—	178	1	no	—
1335	C₂×C₄	—	178	1	no	—
1336	C₂×C₄	—	178	1	no	—
1337	C₂×C₄	—	178	1	no	—
1338	C₂×C₄	—	178	1	no	—
1339	C₂×C₄	—	178	1	no	—
1340	C₂×C₄	—	178	1	no	—
1341	C₂×C₄	—	178	1	no	—
1342	C₂×C₄	—	178	1	no	—
1343	C₂×C₄	—	178	1	no	—
1344	C₂×C₄	—	178	1	no	—
1345	C₂×C₄	—	178	1	no	—
1346	C₂×C₄	—	178	1	no	—
1347	C₂×C₄	—	178	1	no	—
1348	C₂×C₄	—	178	1	no	—
1349	C₂×C₄	—	178	1	no	—
1350	C₂×C₄	—	178	1	no	—
1351	C₂×C₄	—	178	1	no	—
1352	C₂×C₄	—	178	1	no	—
1353	C₂×C₄	—	178	1	no	—
1354	C₂×C₄	—	178	1	no	—
1355	C₂×C₄	—	178	1	no	—
1356	C₂×C₄	—	178	1	no	—
1357	C₂×C₄	—	178	1	no	—
1358	C₂×C₄	—	178	1	no	—
1359	C₂×C₄	—	178	1	no	—
1360	C₂×C₄	—	712	2	no	—
1361	C₂×C₄	—	712	2	no	—
1362	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1363	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1364	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1365	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1366	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1367	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1368	C₂²	—	2	2	no	—
1369	C₂²	—	2	2	no	—
1370	C₂²	—	2	2	no	—
1371	C₂²	—	4	1	no	—
1372	C₂²	—	4	1	no	—
1373	C₂²	—	4	1	no	—
1374	C₂²	—	4	1	no	—
1375	C₂²	—	89	4	no	—
1376	C₂²	—	178	2	no	—
1377	C₂²	—	178	2	no	—
1378	C₂²	—	178	2	no	—
1379	C₂²	—	178	2	no	—
1380	C₂²	—	178	2	no	—
1381	C₂²	—	178	2	no	—
1382	C₂²	C₂³×C₄×D₈₉	1	1	yes	characteristic
1383	C₂²	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
1384	C₂²	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
1385	C₂²	2₋¹⁺⁴×D₈₉	1	1	yes	characteristic
1386	C₂²	2₋¹⁺⁴×D₈₉	1	1	yes	characteristic
1387	C₂²	2₋¹⁺⁴×D₈₉	1	1	yes	characteristic
1388	C₂²	#19152433	1	1	yes	characteristic
1389	C₄	—	2	2	no	—
1390	C₄	—	2	2	no	—
1391	C₄	—	2	2	no	—
1392	C₄	—	2	2	no	—
1393	C₄	—	2	2	no	—
1394	C₄	—	2	2	no	—
1395	C₄	—	4	1	no	—
1396	C₄	—	4	1	no	—
1397	C₄	—	4	1	no	—
1398	C₄	—	4	1	no	—
1399	C₄	—	4	1	no	—
1400	C₄	—	4	1	no	—
1401	C₄	—	4	1	no	—
1402	C₄	—	4	1	no	—
1403	C₄	—	89	4	no	—
1404	C₄	—	356	1	no	—
1405	C₄	—	356	1	no	—
1406	C₄	—	356	1	no	—
1407	C₄	—	356	1	no	—
1408	C₄	—	356	1	no	—
1409	C₄	—	356	1	no	—
1410	C₄	—	356	1	no	—
1411	C₄	—	178	2	no	—
1412	C₄	—	178	2	no	—
1413	C₄	—	178	2	no	—
1414	C₄	—	178	2	no	—
1415	C₄	—	178	2	no	—
1416	C₄	—	178	2	no	—
1417	C₄	—	178	2	no	—
1418	C₂	—	4	2	no	—
1419	C₂	—	178	4	no	—
1420	C₂	#518×D₈₉	1	1	yes	characteristic
1421	C₂	#519×D₈₉	1	1	yes	characteristic
1422	C₂	#26033463	1	1	yes	characteristic
1423	C₂	#26034496	1	1	yes	characteristic
1424	C₂	#26034534	1	1	yes	characteristic
1425	C₂	#26034686	1	1	yes	characteristic
1426	C₂	#26034814	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₈₉
commutator	C₂²×C₈₉	C₂⁴×C₄
Fitting	C₈₉×#2378	C₂
socle, cosocle	C₂³×C₈₉	C₂⁵
prime radical	C₂²×C₂²⋊D₈₉	C₂³
hypercenter	#2378	D₈₉
hypocenter	C₈₉	#34475
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ #2378

Complements

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

N	H ≅ G/N	type
2. #26023431	C₂	semidirect
3. #26023430	C₂	semidirect
4. #26023419	C₂	semidirect
5. #26023334	C₂	semidirect
6. #26023329	C₂	semidirect
7. #26023305	C₂	semidirect
8. #26023282	C₂	semidirect
9. #26023254	C₂	semidirect
10. #26023214	C₂	semidirect
14. #26023086	C₂	semidirect
15. #26023084	C₂	semidirect
16. #26023010	C₂	semidirect
17. #26023009	C₂	semidirect
18. #26022999	C₂	semidirect
19. #26022995	C₂	semidirect
20. #26022986	C₂	semidirect
21. #26022981	C₂	semidirect
22. #26022967	C₂	semidirect
23. #26022927	C₂	semidirect
24. #26022901	C₂	semidirect
27. #26022837	C₂	semidirect
28. #26022786	C₂	semidirect
29. #391×D₈₉	C₂	semidirect
31. C₈₉×#2378	C₂	semidirect
34. #19152261	C₄	semidirect
190. C₂²×Dic₁₇₈	C₂×C₄	semidirect
210. #15668011	C₂×C₄	semidirect
211. #15668011	C₂×C₄	semidirect
212. #15668010	C₂×C₄	semidirect
216. #15667989	C₂×C₄	semidirect
217. #15667989	C₂×C₄	semidirect
222. #15667977	C₂×C₄	semidirect
336. C₂²⋊Q₈×C₈₉	C₂×C₄	semidirect
718. #2378	D₈₉	semidirect
745. C₈₉	#34475	semidirect
934. 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×#19152261	2
#26023431	2
#26023430	2
#26023419	2
#26023334	2
#26023329	2
#26023305	2
#26023282	2
#26023254	2
#26023214	2
#26023189	2
#26023187	2
#26023180	2
#26023086	2
#26023084	2
#26023010	2
#26023009	2
#26022999	2
#26022995	2
#26022986	2
#26022981	2
#26022967	2
#26022927	2
#26022901	2
#26022887	2
#26022882	2
#26022837	2
#26022786	2
#391×D₈₉	2
#26022694	2
C₈₉×#2378	2
#34475	89