Subgroups — #36717832

Order 22784.

2314 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×#19152168	C₂	1	1	yes	maximal, characteristic
2	#26023432	C₂	1	1	yes	maximal, characteristic, complemented
3	#26023422	C₂	1	1	yes	maximal, characteristic, complemented
4	#26023419	C₂	1	1	yes	maximal, characteristic, complemented
5	#26023412	C₂	1	1	yes	maximal, characteristic, complemented
6	#26023361	C₂	1	1	yes	maximal, characteristic, complemented
7	#26023341	C₂	1	1	yes	maximal, characteristic, complemented
8	#26023333	C₂	1	1	yes	maximal, characteristic, complemented
9	#26023330	C₂	1	1	yes	maximal, characteristic, complemented
10	#26023247	C₂	1	1	yes	maximal, characteristic, complemented
11	#26023245	C₂	1	1	yes	maximal, characteristic, complemented
12	#26023243	C₂	1	1	yes	maximal, characteristic, complemented
13	#26023241	C₂	1	1	yes	maximal, characteristic, complemented
14	#26023115	C₂	1	1	yes	maximal, characteristic, complemented
15	#26023109	C₂	1	1	yes	maximal, characteristic, complemented
16	#26023078	C₂	1	1	yes	maximal, characteristic
17	#26023078	C₂	1	1	yes	maximal, characteristic
18	#26023067	C₂	1	1	yes	maximal, characteristic, complemented
19	#26023009	C₂	1	1	yes	maximal, characteristic, complemented
20	#26023002	C₂	1	1	yes	maximal, characteristic, complemented
21	#26022995	C₂	1	1	yes	maximal, characteristic, complemented
22	#26022995	C₂	1	1	yes	maximal, characteristic, complemented
23	#26022983	C₂	1	1	yes	maximal, characteristic, complemented
24	#26022980	C₂	1	1	yes	maximal, characteristic, complemented
25	#26022922	C₂	1	1	yes	maximal, characteristic, complemented
26	#26022919	C₂	1	1	yes	maximal, characteristic, complemented
27	#26022835	C₂	1	1	yes	maximal, characteristic, complemented
28	#26022779	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×#15667994	C₂	1	1	yes	maximal, characteristic, complemented
30	#391×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
31	C₈₉×#2337	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×#13083573	C₂²	1	1	yes	characteristic
33	C₂²×Q₈×D₈₉	C₂²	1	1	yes	characteristic
34	#19152168	C₄	1	16	yes	complemented
35	C₂×#15668012	C₂²	1	1	yes	characteristic
36	C₂×#15668010	C₂²	1	1	yes	characteristic
37	C₂×#15667999	C₂²	1	1	yes	characteristic
38	C₂×#15667994	C₂²	1	1	yes	characteristic
39	C₂×#15667994	C₂²	1	1	yes	characteristic
40	C₂×#15667994	C₂²	1	1	yes	characteristic
41	C₂×#15667994	C₂²	1	1	yes	characteristic
42	C₂×#15667989	C₂²	1	1	yes	characteristic
43	C₂×#15667989	C₂²	1	1	yes	characteristic
44	C₂×#15667989	C₂²	1	1	yes	characteristic
45	C₂×#15667989	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×#15667970	C₂²	1	1	yes	characteristic
51	C₂×#15667969	C₂²	1	1	yes	characteristic
52	C₂×#15667969	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	#19151504	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	#19151496	C₂²	1	1	yes	characteristic
74	#19151496	C₂²	1	1	yes	characteristic
75	#19151495	C₂²	1	1	yes	characteristic
76	#19151495	C₂²	1	1	yes	characteristic
77	#19151494	C₂²	1	1	yes	characteristic
78	#19151494	C₂²	1	1	yes	characteristic
79	#19151493	C₂²	1	1	yes	characteristic
80	#19151493	C₂²	1	1	yes	characteristic
81	#19151492	C₂²	1	1	yes	characteristic
82	#19151492	C₂²	1	1	yes	characteristic
83	#19151492	C₂²	1	1	yes	characteristic
84	#19151492	C₂²	1	1	yes	characteristic
85	#19151491	C₂²	1	1	yes	characteristic
86	#19151491	C₂²	1	1	yes	characteristic
87	#19151491	C₂²	1	1	yes	characteristic
88	#19151491	C₂²	1	1	yes	characteristic
89	#19151486	C₂²	1	1	yes	characteristic
90	#19151486	C₂²	1	1	yes	characteristic
91	#19151486	C₂²	1	1	yes	characteristic
92	#19151486	C₂²	1	1	yes	characteristic
93	#19151485	C₂²	1	1	yes	characteristic
94	#19151485	C₂²	1	1	yes	characteristic
95	#19151485	C₂²	1	1	yes	characteristic
96	#19151485	C₂²	1	1	yes	characteristic
97	#19151483	C₂²	1	1	yes	characteristic
98	#19151483	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	#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	#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	#19151478	C₂²	1	1	yes	characteristic
118	#19151478	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	#19151473	C₂²	1	1	yes	characteristic
124	#19151473	C₂²	1	1	yes	characteristic
125	#19151472	C₂²	1	1	yes	characteristic
126	#19151472	C₂²	1	1	yes	characteristic
127	#19151471	C₂²	1	1	yes	characteristic
128	#19151471	C₂²	1	1	yes	characteristic
129	#19151470	C₂²	1	1	yes	characteristic
130	#19151470	C₂²	1	1	yes	characteristic
131	#19151469	C₂²	1	1	yes	characteristic
132	#19151469	C₂²	1	1	yes	characteristic
133	#19151466	C₂²	1	1	yes	characteristic
134	#19151462	C₂²	1	1	yes	characteristic
135	#19151462	C₂²	1	1	yes	characteristic
136	#19151460	C₂²	1	1	yes	characteristic
137	#19151460	C₂²	1	1	yes	characteristic
138	#19151460	C₂²	1	1	yes	characteristic
139	#19151460	C₂²	1	1	yes	characteristic
140	#19151459	C₂²	1	1	yes	characteristic
141	#19151459	C₂²	1	1	yes	characteristic
142	#19151456	C₂²	1	1	yes	characteristic
143	#19151456	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×#13083553	C₂²	1	1	yes	characteristic
147	C₄×#13083553	C₂²	1	1	yes	characteristic
148	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
149	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
150	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
151	#19151449	C₂²	1	1	yes	characteristic
152	#19151449	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	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
158	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
159	C₄×#13083551	C₂²	1	1	yes	characteristic
160	C₄×#13083551	C₂²	1	1	yes	characteristic
161	C₄×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
162	C₄×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
163	#19151445	C₂²	1	1	yes	characteristic
164	#19151445	C₂²	1	1	yes	characteristic
165	#19151443	C₂²	1	1	yes	characteristic
166	#19151443	C₂²	1	1	yes	characteristic
167	C₂×#15667919	C₂²	1	1	yes	characteristic
168	C₂×#15667919	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×#124×C₈₉	C₂²	1	1	yes	characteristic
174	#391×C₈₉	C₂²	1	1	yes	characteristic
175	#391×C₈₉	C₂²	1	1	yes	characteristic
176	#388×C₈₉	C₂²	1	1	yes	characteristic
177	#388×C₈₉	C₂²	1	1	yes	characteristic
178	#388×C₈₉	C₂²	1	1	yes	characteristic
179	#388×C₈₉	C₂²	1	1	yes	characteristic
180	#386×C₈₉	C₂²	1	1	yes	characteristic
181	#386×C₈₉	C₂²	1	1	yes	characteristic
182	#385×C₈₉	C₂²	1	1	yes	characteristic
183	#385×C₈₉	C₂²	1	1	yes	characteristic
184	#383×C₈₉	C₂²	1	1	yes	characteristic
185	C₄×C₄⋊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	C₂×#13083573	—	4	2	no	—
189	C₂×#13083573	—	4	2	no	—
190	C₂×#13083573	C₂×C₄	1	8	yes	—
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	C₂×Q₈×D₈₉	—	4	2	no	—
196	C₂×Q₈×D₈₉	—	4	2	no	—
197	C₂×Q₈×D₈₉	C₂×C₄	1	8	yes	complemented
198	C₂²×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
199	C₂²×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
200	C₂³×Dic₈₉	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	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	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
211	#15668012	C₂×C₄	1	8	yes	complemented
212	#15668010	C₂×C₄	1	8	yes	complemented
213	#15667999	C₂×C₄	1	8	yes	complemented
214	#15667994	C₂×C₄	1	8	yes	complemented
215	#15667994	C₂×C₄	1	8	yes	complemented
216	#15667994	C₂×C₄	1	8	yes	complemented
217	#15667994	C₂×C₄	1	8	yes	complemented
218	#15667989	C₂×C₄	1	8	yes	complemented
219	#15667989	C₂×C₄	1	8	yes	complemented
220	#15667989	C₂×C₄	1	8	yes	complemented
221	#15667989	C₂×C₄	1	8	yes	complemented
222	C₄×C₂²⋊D₈₉	—	4	2	no	—
223	C₄×C₂²⋊D₈₉	—	4	2	no	—
224	#15667972	—	4	2	no	—
225	#15667972	—	4	2	no	—
226	#15667970	—	4	2	no	—
227	#15667969	—	4	2	no	—
228	#15667969	C₂×C₄	1	8	yes	complemented
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×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×#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	C₄⋊C₄×D₈₉	—	4	2	no	—
256	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
257	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
266	C₂×#13083551	C₂³	1	1	yes	characteristic
267	C₂×#13083551	C₂³	1	1	yes	characteristic
268	C₂×#13083551	C₂³	1	1	yes	characteristic
269	C₂×#13083551	C₂³	1	1	yes	characteristic
270	C₂×#13083551	C₂³	1	1	yes	characteristic
271	C₂×#13083551	C₂³	1	1	yes	characteristic
272	C₂×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	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
288	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
289	C₄²×D₈₉	—	4	2	no	—
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	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
336	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
337	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
338	#124×C₈₉	C₂×C₄	1	8	yes	complemented
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×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
344	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
346	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
347	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
348	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
349	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
350	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
351	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
352	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
353	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
354	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
355	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	#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	#13083573	—	4	16	no	—
372	C₂×Dic₁₇₈	—	4	1	no	—
373	C₂×Dic₁₇₈	—	4	1	no	—
374	C₂×Dic₁₇₈	—	4	1	no	—
375	C₂×Dic₁₇₈	—	4	1	no	—
376	C₂×Dic₁₇₈	—	4	1	no	—
377	C₂×Dic₁₇₈	—	4	1	no	—
378	C₂×Dic₁₇₈	—	4	1	no	—
379	C₂×Dic₁₇₈	—	4	1	no	—
380	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
381	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
382	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
383	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
384	Q₈×D₈₉	—	4	16	no	—
385	C₂×C₂²⋊D₈₉	—	2	2	no	—
386	C₂×C₂²⋊D₈₉	—	2	2	no	—
387	C₂×C₂²⋊D₈₉	—	2	2	no	—
388	C₂×C₂²⋊D₈₉	—	2	2	no	—
389	C₂×C₂²⋊D₈₉	C₂²×C₄	1	4	yes	—
390	C₂×C₂²⋊D₈₉	C₂²×C₄	1	4	yes	—
391	C₂²×Dic₈₉	—	2	2	no	—
392	C₂²×Dic₈₉	—	4	1	no	—
393	C₂²×Dic₈₉	—	4	1	no	—
394	C₂²×Dic₈₉	—	4	1	no	—
395	C₂²×Dic₈₉	—	4	1	no	—
396	C₂²×Dic₈₉	—	4	1	no	—
397	C₂²×Dic₈₉	—	4	1	no	—
398	C₂²×Dic₈₉	—	4	1	no	—
399	C₂²×Dic₈₉	—	4	1	no	—
400	C₂²×Dic₈₉	—	4	1	no	—
401	C₂²×Dic₈₉	C₂²×C₄	1	4	yes	—
402	C₂²×Dic₈₉	C₂²×C₄	1	4	yes	—
403	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
404	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
405	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
406	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
407	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
408	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
409	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
410	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
411	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
412	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
413	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
414	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
415	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
416	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
417	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
418	C₂×C₄×D₈₉	—	2	2	no	—
419	C₂×C₄×D₈₉	—	2	2	no	—
420	C₂×C₄×D₈₉	—	2	2	no	—
421	C₂×C₄×D₈₉	—	2	2	no	—
422	C₂×C₄×D₈₉	—	2	2	no	—
423	C₂×C₄×D₈₉	—	2	2	no	—
424	C₂×C₄×D₈₉	—	2	2	no	—
425	C₂×C₄×D₈₉	—	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	—	4	1	no	—
431	C₂×C₄×D₈₉	—	4	1	no	—
432	C₂×C₄×D₈₉	—	4	1	no	—
433	C₂×C₄×D₈₉	—	4	1	no	—
434	C₂×C₄×D₈₉	—	4	1	no	—
435	C₂×C₄×D₈₉	—	4	1	no	—
436	C₂×C₄×D₈₉	C₂²×C₄	1	4	yes	—
437	C₂×C₄×D₈₉	C₂²×C₄	1	4	yes	—
438	C₂×C₄×D₈₉	C₂²×C₄	1	4	yes	—
439	C₄⋊Dic₈₉	—	2	2	no	—
440	C₄⋊Dic₈₉	—	4	1	no	—
441	C₄⋊Dic₈₉	—	4	1	no	—
442	C₄⋊Dic₈₉	—	4	1	no	—
443	C₄⋊Dic₈₉	C₂²×C₄	1	4	yes	—
444	C₄⋊Dic₈₉	C₂²×C₄	1	4	yes	—
445	C₄⋊Dic₈₉	C₂²×C₄	1	4	yes	—
446	C₄⋊Dic₈₉	C₂²×C₄	1	4	yes	—
447	#13083553	—	4	1	no	—
448	#13083553	—	4	1	no	—
449	#13083553	—	4	1	no	—
450	#13083553	—	4	1	no	—
451	#13083553	—	4	1	no	—
452	#13083553	—	4	1	no	—
453	#13083553	—	4	1	no	—
454	#13083553	—	4	1	no	—
455	#13083553	—	4	1	no	—
456	#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	C₂²⋊Dic₈₉	—	2	2	no	—
466	C₂²⋊Dic₈₉	—	4	1	no	—
467	C₂²⋊Dic₈₉	—	4	1	no	—
468	C₂²⋊Dic₈₉	—	4	1	no	—
469	C₂²⋊Dic₈₉	—	4	1	no	—
470	C₂²⋊Dic₈₉	—	4	1	no	—
471	C₂²⋊Dic₈₉	C₂²×C₄	1	4	yes	—
472	C₂²⋊Dic₈₉	C₂²×C₄	1	4	yes	—
473	C₂²⋊Dic₈₉	C₂²×C₄	1	4	yes	—
474	C₂²⋊Dic₈₉	C₂²×C₄	1	4	yes	—
475	#13083551	—	2	2	no	—
476	#13083551	—	2	2	no	—
477	#13083551	—	2	2	no	—
478	#13083551	—	2	2	no	—
479	#13083551	C₂²×C₄	1	4	yes	—
480	#13083551	C₂²×C₄	1	4	yes	—
481	C₄×Dic₈₉	—	2	2	no	—
482	C₄×Dic₈₉	—	2	2	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	—	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	C₂²×C₄	1	4	yes	—
498	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
499	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
500	C₂×Q₈×C₈₉	—	4	1	no	—
501	C₂×Q₈×C₈₉	—	4	1	no	—
502	C₂×Q₈×C₈₉	C₂²×C₄	1	4	yes	—
503	C₂×D₄×C₈₉	—	4	1	no	—
504	C₂×D₄×C₈₉	—	4	1	no	—
505	C₂×D₄×C₈₉	C₂²×C₄	1	4	yes	—
506	C₂²×C₄×C₈₉	—	2	2	no	—
507	C₂²×C₄×C₈₉	—	4	1	no	—
508	C₂²×C₄×C₈₉	—	4	1	no	—
509	C₂²×C₄×C₈₉	—	4	1	no	—
510	C₂²×C₄×C₈₉	—	4	1	no	—
511	C₂²×C₄×C₈₉	—	4	1	no	—
512	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
513	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
514	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
515	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
516	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
517	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
518	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
519	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
520	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
521	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
522	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
523	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
524	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
525	C₄⋊C₄×C₈₉	—	2	2	no	—
526	C₄⋊C₄×C₈₉	—	4	1	no	—
527	C₄⋊C₄×C₈₉	—	4	1	no	—
528	C₄⋊C₄×C₈₉	—	4	1	no	—
529	C₂²⋊C₄×C₈₉	—	2	2	no	—
530	C₂²⋊C₄×C₈₉	—	4	1	no	—
531	C₂²⋊C₄×C₈₉	—	4	1	no	—
532	C₂²⋊C₄×C₈₉	—	4	1	no	—
533	C₂²⋊C₄×C₈₉	—	4	1	no	—
534	C₂²⋊C₄×C₈₉	—	4	1	no	—
535	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
536	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
537	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
538	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
539	C₄²×C₈₉	—	4	1	no	—
540	C₄²×C₈₉	—	4	1	no	—
541	C₄²×C₈₉	—	4	1	no	—
542	C₄²×C₈₉	—	4	1	no	—
543	C₄²×C₈₉	C₂²×C₄	1	4	yes	—
544	C₂³×C₈₉	—	2	1	no	—
545	C₂³×C₈₉	—	2	1	no	—
546	C₂³×C₈₉	—	2	1	no	—
547	C₂³×C₈₉	—	2	1	no	—
548	C₂³×C₈₉	—	2	1	no	—
549	C₂³×C₈₉	—	2	1	no	—
550	C₂³×C₈₉	—	2	1	no	—
551	C₂³×C₈₉	—	2	1	no	—
552	C₂³×C₈₉	—	2	1	no	—
553	C₂³×C₈₉	—	2	1	no	—
554	C₂³×C₈₉	—	2	1	no	—
555	C₂³×C₈₉	—	2	1	no	—
556	C₂³×C₈₉	C₂³×C₄	1	2	yes	—
557	C₂³×C₈₉	C₂³×C₄	1	2	yes	—
558	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
559	C₂²×D₈₉	—	2	1	no	—
560	C₂²×D₈₉	—	2	1	no	—
561	C₂²×D₈₉	—	2	1	no	—
562	C₂²×D₈₉	—	2	1	no	—
563	C₂²×D₈₉	C₂³×C₄	1	2	yes	—
564	C₂²×D₈₉	H(5,𝔽₂)	1	2	yes	—
565	C₂²×D₈₉	H(5,𝔽₂)	1	2	yes	—
566	Q₈×C₈₉	—	4	4	no	—
567	D₄×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	—	8	2	no	—
602	C₂×C₄×C₈₉	—	8	2	no	—
603	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
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	2₋¹⁺⁴	1	2	yes	—
609	C₂²⋊D₈₉	—	2	8	no	—
610	C₂²⋊D₈₉	—	2	8	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	—	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	—	2	1	no	—
648	C₂×Dic₈₉	—	4	4	no	—
649	C₂×Dic₈₉	—	4	4	no	—
650	C₂×Dic₈₉	—	8	2	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	2₋¹⁺⁴	1	2	yes	—
660	C₄×D₈₉	—	2	8	no	—
661	C₄×D₈₉	—	2	8	no	—
662	C₄×D₈₉	—	2	8	no	—
663	C₄×D₈₉	—	4	4	no	—
664	C₄×D₈₉	—	4	4	no	—
665	C₄×D₈₉	—	8	2	no	—
666	C₄×D₈₉	—	8	2	no	—
667	Dic₁₇₈	—	4	4	no	—
668	Dic₁₇₈	—	4	4	no	—
669	Dic₁₇₈	—	4	4	no	—
670	Dic₁₇₈	—	4	4	no	—
671	C₂²×C₈₉	—	2	2	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	—	4	1	no	—
678	C₂²×C₈₉	—	4	1	no	—
679	C₂²×C₈₉	—	4	1	no	—
680	C₂²×C₈₉	—	4	1	no	—
681	C₂²×C₈₉	—	4	1	no	—
682	C₂²×C₈₉	—	4	1	no	—
683	C₂²×C₈₉	—	4	1	no	—
684	C₂²×C₈₉	—	4	1	no	—
685	C₂²×C₈₉	C₂⁴×C₄	1	1	yes	characteristic
686	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
687	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
688	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
689	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
690	C₂²×C₈₉	#585	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	#518	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	—	4	1	no	—
706	C₄×C₈₉	—	4	1	no	—
707	C₄×C₈₉	—	4	1	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	Dic₈₉	—	2	2	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	—	4	1	no	—
727	#34409	—	89	1	no	maximal, Sylow
728	C₂×C₈₉	—	4	2	no	—
729	C₂×C₈₉	—	4	2	no	—
730	C₂×C₈₉	C₂×#518	1	1	yes	characteristic
731	C₂×C₈₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic
732	C₂×C₈₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic
733	C₂×C₈₉	#3535	1	1	yes	characteristic
734	C₂×C₈₉	#3535	1	1	yes	characteristic
735	C₂×C₈₉	#3544	1	1	yes	characteristic
736	C₂×C₈₉	#3545	1	1	yes	characteristic
737	D₈₉	—	2	4	no	—
738	C₂×#536	—	89	1	no	—
739	#2381	—	89	1	no	—
740	#2379	—	89	1	no	—
741	#2378	—	89	1	no	—
742	#2378	—	89	1	no	—
743	#2372	—	89	1	no	—
744	#2369	—	89	1	no	—
745	#2368	—	89	1	no	—
746	#2368	—	89	1	no	—
747	#2359	—	89	1	no	—
748	#2359	—	89	1	no	—
749	#2359	—	89	1	no	—
750	#2359	—	89	1	no	—
751	#2343	—	89	1	no	—
752	#2343	—	89	1	no	—
753	#2339	—	89	1	no	—
754	#2339	—	89	1	no	—
755	#2337	—	89	1	no	—
756	#2337	D₈₉	1	1	yes	characteristic, complemented
757	#2332	—	89	1	no	—
758	#2332	—	89	1	no	—
759	#2331	—	89	1	no	—
760	#2331	—	89	1	no	—
761	#2329	—	89	1	no	—
762	#2329	—	89	1	no	—
763	#2322	—	89	1	no	—
764	#2322	—	89	1	no	—
765	#2310	—	89	1	no	—
766	C₄×#123	—	89	1	no	—
767	C₄×#123	—	89	1	no	—
768	C₂×#391	—	89	1	no	—
769	C₈₉	#34409	1	1	yes	characteristic, complemented, Sylow
770	C₂²×#41	—	89	1	no	—
771	C₂³×Q₈	—	89	1	no	—
772	#536	—	89	16	no	—
773	C₂×C₄⋊Q₈	—	89	1	no	—
774	C₂×C₄⋊Q₈	—	89	1	no	—
775	C₂×#124	—	89	1	no	—
776	C₂×#124	C₂×D₈₉	1	1	yes	characteristic
777	C₂×#123	—	89	1	no	—
778	C₂×#123	—	89	1	no	—
779	C₂×#123	—	89	1	no	—
780	C₂×#123	—	89	1	no	—
781	C₂×C₂²⋊Q₈	—	89	1	no	—
782	C₂×C₂²⋊Q₈	—	89	1	no	—
783	C₂×C₂²⋊Q₈	—	89	1	no	—
784	C₂×C₂²⋊Q₈	—	89	1	no	—
785	C₂×C₄×D₄	—	89	1	no	—
786	C₂×C₄×D₄	—	89	1	no	—
787	C₂×C₄×D₄	—	89	1	no	—
788	C₂×C₄×D₄	—	89	1	no	—
789	C₂×#117	—	89	1	no	—
790	C₂×#117	—	89	1	no	—
791	C₂×#117	—	89	1	no	—
792	C₂²×C₄⋊C₄	—	89	1	no	—
793	C₂²×C₄²	—	89	1	no	—
794	#391	—	89	1	no	—
795	#391	—	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	—	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	C₂×D₈₉	1	1	yes	characteristic
813	#391	C₂×D₈₉	1	1	yes	characteristic
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	#388	—	89	1	no	—
823	#388	—	89	1	no	—
824	#388	—	89	1	no	—
825	#388	—	89	1	no	—
826	#388	—	89	1	no	—
827	#388	—	89	1	no	—
828	#388	—	89	1	no	—
829	#388	—	89	1	no	—
830	#388	—	89	1	no	—
831	#388	—	89	1	no	—
832	#388	—	89	1	no	—
833	#388	—	89	1	no	—
834	#388	C₂×D₈₉	1	1	yes	characteristic
835	#388	C₂×D₈₉	1	1	yes	characteristic
836	#388	C₂×D₈₉	1	1	yes	characteristic
837	#388	C₂×D₈₉	1	1	yes	characteristic
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	—	89	1	no	—
853	#387	—	89	1	no	—
854	#387	—	89	1	no	—
855	#387	—	89	1	no	—
856	#387	—	89	1	no	—
857	#387	—	89	1	no	—
858	#387	—	89	1	no	—
859	#387	—	89	1	no	—
860	#387	—	89	1	no	—
861	#387	—	89	1	no	—
862	#386	—	89	1	no	—
863	#386	—	89	1	no	—
864	#386	—	89	1	no	—
865	#386	—	89	1	no	—
866	#386	—	89	1	no	—
867	#386	—	89	1	no	—
868	#386	C₂×D₈₉	1	1	yes	characteristic
869	#386	C₂×D₈₉	1	1	yes	characteristic
870	#385	—	89	1	no	—
871	#385	—	89	1	no	—
872	#385	—	89	1	no	—
873	#385	—	89	1	no	—
874	#385	—	89	1	no	—
875	#385	—	89	1	no	—
876	#385	—	89	1	no	—
877	#385	—	89	1	no	—
878	#385	—	89	1	no	—
879	#385	—	89	1	no	—
880	#385	C₂×D₈₉	1	1	yes	characteristic
881	#385	C₂×D₈₉	1	1	yes	characteristic
882	#383	—	89	1	no	—
883	#383	C₂×D₈₉	1	1	yes	characteristic
884	#382	—	89	1	no	—
885	#382	—	89	1	no	—
886	#381	—	89	1	no	—
887	#381	—	89	1	no	—
888	#381	—	89	1	no	—
889	#381	—	89	1	no	—
890	#381	—	89	1	no	—
891	#381	—	89	1	no	—
892	#380	—	89	1	no	—
893	#380	—	89	1	no	—
894	C₄×C₄⋊C₄	—	89	1	no	—
895	C₄×C₄⋊C₄	—	89	1	no	—
896	C₄×C₄⋊C₄	—	89	1	no	—
897	C₄×C₄⋊C₄	—	89	1	no	—
898	C₄×C₄⋊C₄	—	89	1	no	—
899	C₄×C₄⋊C₄	—	89	1	no	—
900	C₄×C₄⋊C₄	—	89	1	no	—
901	C₄×C₄⋊C₄	—	89	1	no	—
902	C₄×C₄⋊C₄	—	89	1	no	—
903	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
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	—	89	1	no	—
913	C₄×C₂²⋊C₄	—	89	1	no	—
914	C₄×C₂²⋊C₄	—	89	1	no	—
915	C₄×C₂²⋊C₄	—	89	1	no	—
916	C₄×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
917	C₄×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
918	#376	—	89	1	no	—
919	#376	—	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	—	89	1	no	—
925	C₂×#95	—	89	1	no	—
926	C₂×#41	—	89	8	no	—
927	C₂×#41	—	356	2	no	—
928	C₂×#41	—	356	2	no	—
929	C₂²×Q₈	—	89	8	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	C₂²×D₈₉	1	1	yes	characteristic
937	C₂²×D₄	—	89	1	no	—
938	C₂²×D₄	—	89	1	no	—
939	C₂²×D₄	C₂²×D₈₉	1	1	yes	characteristic
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	C₄⋊Q₈	—	89	8	no	—
954	C₄⋊Q₈	—	89	8	no	—
955	#124	—	89	8	no	—
956	#124	C₄×D₈₉	1	8	yes	complemented
957	#123	—	89	8	no	—
958	#123	—	89	8	no	—
959	#123	—	89	8	no	—
960	#123	—	89	8	no	—
961	C₂²⋊Q₈	—	89	8	no	—
962	C₂²⋊Q₈	—	89	8	no	—
963	C₂²⋊Q₈	—	89	8	no	—
964	C₂²⋊Q₈	—	89	8	no	—
965	C₄×D₄	—	356	2	no	—
966	C₄×D₄	—	356	2	no	—
967	C₄×D₄	—	356	2	no	—
968	C₄×D₄	—	356	2	no	—
969	#117	—	89	8	no	—
970	#117	—	356	2	no	—
971	#117	—	356	2	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	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	—	356	2	no	—
999	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1000	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1001	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1002	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1003	C₂×C₂²⋊C₄	—	89	1	no	—
1004	C₂×C₂²⋊C₄	—	89	1	no	—
1005	C₂×C₂²⋊C₄	—	89	1	no	—
1006	C₂×C₂²⋊C₄	—	89	1	no	—
1007	C₂×C₂²⋊C₄	—	89	1	no	—
1008	C₂×C₂²⋊C₄	—	89	1	no	—
1009	C₂×C₂²⋊C₄	—	89	1	no	—
1010	C₂×C₂²⋊C₄	—	89	1	no	—
1011	C₂×C₂²⋊C₄	—	89	1	no	—
1012	C₂×C₂²⋊C₄	—	89	1	no	—
1013	C₂×C₂²⋊C₄	—	89	1	no	—
1014	C₂×C₂²⋊C₄	—	89	1	no	—
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	C₂²×D₈₉	1	1	yes	characteristic
1020	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1021	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1022	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1023	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1024	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
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	—	356	2	no	—
1047	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1048	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1049	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1050	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1051	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
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	—	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	#95	C₂²×D₈₉	1	1	yes	characteristic
1107	#95	C₂²×D₈₉	1	1	yes	characteristic
1108	C₂⁴	—	89	1	no	—
1109	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
1110	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
1111	#41	—	356	16	no	—
1112	C₂×Q₈	—	4	1	no	—
1113	C₂×Q₈	—	4	1	no	—
1114	C₂×Q₈	—	89	4	no	—
1115	C₂×Q₈	—	89	4	no	—
1116	C₂×Q₈	—	89	4	no	—
1117	C₂×Q₈	—	89	4	no	—
1118	C₂×Q₈	—	356	1	no	—
1119	C₂×Q₈	—	356	1	no	—
1120	C₂×Q₈	—	356	1	no	—
1121	C₂×Q₈	—	356	1	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	16	no	—
1127	C₂×Q₈	C₂×C₄×D₈₉	1	4	yes	—
1128	C₂×D₄	—	4	1	no	—
1129	C₂×D₄	—	4	1	no	—
1130	C₂×D₄	—	89	4	no	—
1131	C₂×D₄	—	89	4	no	—
1132	C₂×D₄	—	178	2	no	—
1133	C₂×D₄	—	178	2	no	—
1134	C₂×D₄	—	178	2	no	—
1135	C₂×D₄	—	178	2	no	—
1136	C₂×D₄	C₂×C₄×D₈₉	1	4	yes	—
1137	C₂²×C₄	—	2	2	no	—
1138	C₂²×C₄	—	4	1	no	—
1139	C₂²×C₄	—	4	1	no	—
1140	C₂²×C₄	—	4	1	no	—
1141	C₂²×C₄	—	4	1	no	—
1142	C₂²×C₄	—	4	1	no	—
1143	C₂²×C₄	—	89	4	no	—
1144	C₂²×C₄	—	89	4	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	—	89	1	no	—
1151	C₂²×C₄	—	89	1	no	—
1152	C₂²×C₄	—	89	1	no	—
1153	C₂²×C₄	—	89	4	no	—
1154	C₂²×C₄	—	89	4	no	—
1155	C₂²×C₄	—	89	4	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	1	no	—
1161	C₂²×C₄	—	89	1	no	—
1162	C₂²×C₄	—	89	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	—	356	1	no	—
1168	C₂²×C₄	—	356	1	no	—
1169	C₂²×C₄	—	356	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	—	178	2	no	—
1179	C₂²×C₄	—	178	2	no	—
1180	C₂²×C₄	—	178	2	no	—
1181	C₂²×C₄	—	178	2	no	—
1182	C₂²×C₄	—	178	2	no	—
1183	C₂²×C₄	—	178	2	no	—
1184	C₂²×C₄	—	178	2	no	—
1185	C₂²×C₄	—	178	2	no	—
1186	C₂²×C₄	—	178	2	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	C₂³×D₈₉	1	1	yes	characteristic
1192	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1193	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1194	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1195	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1196	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
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	C₄⋊C₄	—	2	2	no	—
1205	C₄⋊C₄	—	4	1	no	—
1206	C₄⋊C₄	—	4	1	no	—
1207	C₄⋊C₄	—	4	1	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	—	89	4	no	—
1214	C₄⋊C₄	—	89	4	no	—
1215	C₄⋊C₄	—	89	4	no	—
1216	C₄⋊C₄	—	89	4	no	—
1217	C₄⋊C₄	—	89	4	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	—	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	—	178	2	no	—
1234	C₂²⋊C₄	—	2	2	no	—
1235	C₂²⋊C₄	—	4	1	no	—
1236	C₂²⋊C₄	—	4	1	no	—
1237	C₂²⋊C₄	—	4	1	no	—
1238	C₂²⋊C₄	—	4	1	no	—
1239	C₂²⋊C₄	—	4	1	no	—
1240	C₂²⋊C₄	—	89	4	no	—
1241	C₂²⋊C₄	—	89	4	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	—	356	1	no	—
1247	C₂²⋊C₄	—	356	1	no	—
1248	C₂²⋊C₄	—	356	1	no	—
1249	C₂²⋊C₄	—	356	1	no	—
1250	C₂²⋊C₄	—	356	1	no	—
1251	C₂²⋊C₄	—	178	2	no	—
1252	C₂²⋊C₄	—	178	2	no	—
1253	C₂²⋊C₄	—	178	2	no	—
1254	C₂²⋊C₄	—	178	2	no	—
1255	C₂²⋊C₄	—	178	2	no	—
1256	C₂²⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1257	C₂²⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1258	C₂²⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1259	C₂²⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1260	C₄²	—	4	1	no	—
1261	C₄²	—	4	1	no	—
1262	C₄²	—	4	1	no	—
1263	C₄²	—	4	1	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	—	356	1	no	—
1278	C₄²	—	356	1	no	—
1279	C₄²	—	178	2	no	—
1280	C₄²	—	178	2	no	—
1281	C₄²	C₂×C₄×D₈₉	1	4	yes	—
1282	C₂³	—	2	1	no	—
1283	C₂³	—	2	1	no	—
1284	C₂³	—	2	1	no	—
1285	C₂³	—	2	1	no	—
1286	C₂³	—	2	1	no	—
1287	C₂³	—	2	1	no	—
1288	C₂³	—	2	1	no	—
1289	C₂³	—	2	1	no	—
1290	C₂³	—	2	1	no	—
1291	C₂³	—	2	1	no	—
1292	C₂³	—	2	1	no	—
1293	C₂³	—	2	1	no	—
1294	C₂³	—	89	2	no	—
1295	C₂³	—	89	2	no	—
1296	C₂³	—	89	2	no	—
1297	C₂³	—	178	1	no	—
1298	C₂³	—	178	1	no	—
1299	C₂³	—	178	1	no	—
1300	C₂³	—	178	1	no	—
1301	C₂³	C₂²×C₄×D₈₉	1	2	yes	—
1302	C₂³	C₂²×C₄×D₈₉	1	2	yes	—
1303	C₂³	C₂⁴×D₈₉	1	1	yes	characteristic
1304	Q₈	—	4	4	no	—
1305	Q₈	—	356	4	no	—
1306	Q₈	—	356	4	no	—
1307	Q₈	—	356	4	no	—
1308	Q₈	—	356	4	no	—
1309	D₄	—	4	4	no	—
1310	D₄	—	178	8	no	—
1311	D₄	—	178	8	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	—	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	—	8	2	no	—
1346	C₂×C₄	—	8	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	—	89	2	no	—
1353	C₂×C₄	—	89	2	no	—
1354	C₂×C₄	—	89	2	no	—
1355	C₂×C₄	—	356	4	no	—
1356	C₂×C₄	—	356	4	no	—
1357	C₂×C₄	—	356	4	no	—
1358	C₂×C₄	—	356	4	no	—
1359	C₂×C₄	—	178	8	no	—
1360	C₂×C₄	—	178	8	no	—
1361	C₂×C₄	—	178	8	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	—	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	—	712	2	no	—
1400	C₂×C₄	—	712	2	no	—
1401	C₂×C₄	—	712	2	no	—
1402	C₂×C₄	—	712	2	no	—
1403	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1404	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1405	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1406	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1407	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1408	C₂×C₄	#15668059	1	2	yes	—
1409	C₂²	—	2	2	no	—
1410	C₂²	—	2	2	no	—
1411	C₂²	—	2	2	no	—
1412	C₂²	—	2	2	no	—
1413	C₂²	—	2	2	no	—
1414	C₂²	—	2	2	no	—
1415	C₂²	—	4	1	no	—
1416	C₂²	—	4	1	no	—
1417	C₂²	—	4	1	no	—
1418	C₂²	—	4	1	no	—
1419	C₂²	—	4	1	no	—
1420	C₂²	—	4	1	no	—
1421	C₂²	—	4	1	no	—
1422	C₂²	—	4	1	no	—
1423	C₂²	—	89	4	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	—	178	2	no	—
1430	C₂²	C₂³×C₄×D₈₉	1	1	yes	characteristic
1431	C₂²	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
1432	C₂²	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
1433	C₂²	2₋¹⁺⁴×D₈₉	1	1	yes	characteristic
1434	C₂²	C₂×#15668059	1	1	yes	characteristic
1435	C₂²	#19152433	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	—	4	1	no	—
1444	C₄	—	4	1	no	—
1445	C₄	—	4	1	no	—
1446	C₄	—	4	1	no	—
1447	C₄	—	4	1	no	—
1448	C₄	—	4	1	no	—
1449	C₄	—	4	1	no	—
1450	C₄	—	356	1	no	—
1451	C₄	—	356	1	no	—
1452	C₄	—	356	1	no	—
1453	C₄	—	356	1	no	—
1454	C₄	—	356	1	no	—
1455	C₄	—	356	1	no	—
1456	C₄	—	356	1	no	—
1457	C₄	—	178	2	no	—
1458	C₄	—	178	2	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	C₂	—	4	2	no	—
1466	C₂	—	4	2	no	—
1467	C₂	—	178	4	no	—
1468	C₂	#518×D₈₉	1	1	yes	characteristic
1469	C₂	C₄×#15668059	1	1	yes	characteristic
1470	C₂	#26033463	1	1	yes	characteristic
1471	C₂	#26034450	1	1	yes	characteristic
1472	C₂	#26034454	1	1	yes	characteristic
1473	C₂	#26034589	1	1	yes	characteristic
1474	C₂	#26034603	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₈₉
commutator	C₂²×C₈₉	C₂⁴×C₄
Fitting	C₈₉×#2337	C₂
socle, cosocle	C₂³×C₈₉	C₂⁵
prime radical	C₂²×#13083573	C₂²
hypercenter	#2337	D₈₉
hypocenter	C₈₉	#34409
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ #2337

Complements

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

N	H ≅ G/N	type
2. #26023432	C₂	semidirect
3. #26023422	C₂	semidirect
4. #26023419	C₂	semidirect
5. #26023412	C₂	semidirect
6. #26023361	C₂	semidirect
7. #26023341	C₂	semidirect
8. #26023333	C₂	semidirect
9. #26023330	C₂	semidirect
10. #26023247	C₂	semidirect
11. #26023245	C₂	semidirect
12. #26023243	C₂	semidirect
13. #26023241	C₂	semidirect
14. #26023115	C₂	semidirect
15. #26023109	C₂	semidirect
18. #26023067	C₂	semidirect
19. #26023009	C₂	semidirect
20. #26023002	C₂	semidirect
21. #26022995	C₂	semidirect
22. #26022995	C₂	semidirect
23. #26022983	C₂	semidirect
24. #26022980	C₂	semidirect
25. #26022922	C₂	semidirect
26. #26022919	C₂	semidirect
27. #26022835	C₂	semidirect
28. #26022779	C₂	semidirect
29. C₄×#15667994	C₂	semidirect
30. #391×D₈₉	C₂	semidirect
31. C₈₉×#2337	C₂	semidirect
34. #19152168	C₄	semidirect
197. C₂×Q₈×D₈₉	C₂×C₄	semidirect
211. #15668012	C₂×C₄	semidirect
212. #15668010	C₂×C₄	semidirect
213. #15667999	C₂×C₄	semidirect
214. #15667994	C₂×C₄	semidirect
215. #15667994	C₂×C₄	semidirect
216. #15667994	C₂×C₄	semidirect
217. #15667994	C₂×C₄	semidirect
218. #15667989	C₂×C₄	semidirect
219. #15667989	C₂×C₄	semidirect
220. #15667989	C₂×C₄	semidirect
221. #15667989	C₂×C₄	semidirect
228. #15667969	C₂×C₄	semidirect
338. #124×C₈₉	C₂×C₄	semidirect
756. #2337	D₈₉	semidirect
769. C₈₉	#34409	semidirect
956. #124	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×#19152168	2
#26023432	2
#26023422	2
#26023419	2
#26023412	2
#26023361	2
#26023341	2
#26023333	2
#26023330	2
#26023247	2
#26023245	2
#26023243	2
#26023241	2
#26023115	2
#26023109	2
#26023078	2
#26023067	2
#26023009	2
#26023002	2
#26022995	2
#26022983	2
#26022980	2
#26022922	2
#26022919	2
#26022835	2
#26022779	2
C₄×#15667994	2
#391×D₈₉	2
C₈₉×#2337	2
#34409	89