Subgroups — #36723462

Order 22784.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26024979	C₂	1	1	yes	maximal, characteristic, complemented
2	#26024912	C₂	1	1	yes	maximal, characteristic, complemented
3	#26024895	C₂	1	1	yes	maximal, characteristic, complemented
4	#26024817	C₂	1	1	yes	maximal, characteristic, complemented
5	#26024811	C₂	1	1	yes	maximal, characteristic, complemented
6	#26024758	C₂	1	1	yes	maximal, characteristic, complemented
7	#26024752	C₂	1	1	yes	maximal, characteristic, complemented
8	#26024644	C₂	1	1	yes	maximal, characteristic, complemented
9	#26024634	C₂	1	1	yes	maximal, characteristic, complemented
10	#26024583	C₂	1	1	yes	maximal, characteristic, complemented
11	#26024577	C₂	1	1	yes	maximal, characteristic, complemented
12	#26024529	C₂	1	1	yes	maximal, characteristic, complemented
13	#26023914	C₂	1	1	yes	maximal, characteristic, complemented
14	#26023643	C₂	1	1	yes	maximal, characteristic
15	#26023643	C₂	1	1	yes	maximal, characteristic
16	#26023554	C₂	1	1	yes	maximal, characteristic, complemented
17	#26023549	C₂	1	1	yes	maximal, characteristic, complemented
18	#26023540	C₂	1	1	yes	maximal, characteristic, complemented
19	#26023508	C₂	1	1	yes	maximal, characteristic, complemented
20	#26022786	C₂	1	1	yes	maximal, characteristic, complemented
21	#26022782	C₂	1	1	yes	maximal, characteristic, complemented
22	#26022779	C₂	1	1	yes	maximal, characteristic, complemented
23	#26022779	C₂	1	1	yes	maximal, characteristic, complemented
24	#26022757	C₂	1	1	yes	maximal, characteristic
25	#26022694	C₂	1	1	yes	maximal, characteristic, complemented
26	#26022694	C₂	1	1	yes	maximal, characteristic, complemented
27	#26022649	C₂	1	1	yes	maximal, characteristic, complemented
28	#26022645	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×C₂²⋊C₄×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×C₂²⋊C₄×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
31	C₈₉×#2518	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂³×C₄×D₈₉	C₂²	1	1	yes	characteristic
33	C₂×#15667994	C₂²	1	1	yes	characteristic
34	C₂×#15667994	C₂²	1	1	yes	characteristic
35	C₂×#15667992	C₂²	1	1	yes	characteristic
36	C₂×#15667990	C₂²	1	1	yes	characteristic
37	C₂×#15667980	C₂²	1	1	yes	characteristic
38	C₂×#15667977	C₂²	1	1	yes	characteristic, complemented
39	C₂×D₄×Dic₈₉	C₂²	1	1	yes	characteristic
40	C₂×#15667972	C₂²	1	1	yes	characteristic
41	C₂×#15667972	C₂²	1	1	yes	characteristic
42	C₂×#15667968	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₂²⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
47	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
48	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
49	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
50	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
51	C₈₉⋊#401	C₂²	1	1	yes	characteristic, complemented
52	C₈₉⋊#401	C₂²	1	1	yes	characteristic, complemented
53	#19151540	C₂²	1	1	yes	characteristic, complemented
54	#19151540	C₂²	1	1	yes	characteristic, complemented
55	#19151539	C₂²	1	1	yes	characteristic, complemented
56	#19151538	C₂²	1	1	yes	characteristic, complemented
57	#19151537	C₂²	1	1	yes	characteristic, complemented
58	#19151537	C₂²	1	1	yes	characteristic, complemented
59	#19151537	C₂²	1	1	yes	characteristic, complemented
60	#19151537	C₂²	1	1	yes	characteristic, complemented
61	#19151536	C₂²	1	1	yes	characteristic, complemented
62	#19151534	C₂²	1	1	yes	characteristic
63	#19151531	C₂²	1	1	yes	characteristic, complemented
64	#19151526	C₂²	1	1	yes	characteristic
65	#19151526	C₂²	1	1	yes	characteristic
66	#19151526	C₂²	1	1	yes	characteristic
67	#19151526	C₂²	1	1	yes	characteristic
68	#19151526	C₂²	1	1	yes	characteristic, complemented
69	#19151526	C₂²	1	1	yes	characteristic, complemented
70	#19151523	C₂²	1	1	yes	characteristic
71	#19151523	C₂²	1	1	yes	characteristic
72	#19151523	C₂²	1	1	yes	characteristic
73	#19151523	C₂²	1	1	yes	characteristic, complemented
74	#19151521	C₂²	1	1	yes	characteristic
75	#19151512	C₂²	1	1	yes	characteristic
76	#19151512	C₂²	1	1	yes	characteristic
77	#19151510	C₂²	1	1	yes	characteristic
78	#19151510	C₂²	1	1	yes	characteristic, complemented
79	#19151504	C₂²	1	1	yes	characteristic, complemented
80	#19151502	C₂²	1	1	yes	characteristic, complemented
81	#19151495	C₂²	1	1	yes	characteristic, complemented
82	#19151491	C₂²	1	1	yes	characteristic, complemented
83	#19151491	C₂²	1	1	yes	characteristic, complemented
84	#19151486	C₂²	1	1	yes	characteristic, complemented
85	#19151486	C₂²	1	1	yes	characteristic, complemented
86	#19151483	C₂²	1	1	yes	characteristic, complemented
87	#19151483	C₂²	1	1	yes	characteristic, complemented
88	#19151482	C₂²	1	1	yes	characteristic, complemented
89	#19151482	C₂²	1	1	yes	characteristic, complemented
90	#19151482	C₂²	1	1	yes	characteristic, complemented
91	#19151482	C₂²	1	1	yes	characteristic, complemented
92	#19151482	C₂²	1	1	yes	characteristic, complemented
93	#19151481	C₂²	1	1	yes	characteristic, complemented
94	#19151481	C₂²	1	1	yes	characteristic, complemented
95	#19151480	C₂²	1	1	yes	characteristic, complemented
96	#19151480	C₂²	1	1	yes	characteristic, complemented
97	#19151474	C₂²	1	1	yes	characteristic
98	#19151474	C₂²	1	1	yes	characteristic
99	#19151474	C₂²	1	1	yes	characteristic
100	#19151474	C₂²	1	1	yes	characteristic
101	#19151474	C₂²	1	1	yes	characteristic
102	#19151474	C₂²	1	1	yes	characteristic
103	#19151474	C₂²	1	1	yes	characteristic
104	#19151474	C₂²	1	1	yes	characteristic
105	#19151472	C₂²	1	1	yes	characteristic
106	#19151472	C₂²	1	1	yes	characteristic
107	#19151472	C₂²	1	1	yes	characteristic
108	#19151472	C₂²	1	1	yes	characteristic
109	#19151472	C₂²	1	1	yes	characteristic
110	#19151471	C₂²	1	1	yes	characteristic
111	#19151469	C₂²	1	1	yes	characteristic
112	#19151469	C₂²	1	1	yes	characteristic
113	#19151469	C₂²	1	1	yes	characteristic
114	#19151469	C₂²	1	1	yes	characteristic
115	#19151469	C₂²	1	1	yes	characteristic
116	#19151469	C₂²	1	1	yes	characteristic
117	#19151469	C₂²	1	1	yes	characteristic
118	#19151466	C₂²	1	1	yes	characteristic, complemented
119	#19151465	C₂²	1	1	yes	characteristic, complemented
120	#19151465	C₂²	1	1	yes	characteristic, complemented
121	#19151464	C₂²	1	1	yes	characteristic, complemented
122	#19151462	C₂²	1	1	yes	characteristic, complemented
123	#19151462	C₂²	1	1	yes	characteristic, complemented
124	#19151460	C₂²	1	1	yes	characteristic
125	#19151460	C₂²	1	1	yes	characteristic
126	#19151460	C₂²	1	1	yes	characteristic
127	#19151460	C₂²	1	1	yes	characteristic
128	#19151460	C₂²	1	1	yes	characteristic
129	#19151460	C₂²	1	1	yes	characteristic
130	#19151457	C₂²	1	1	yes	characteristic
131	#19151457	C₂²	1	1	yes	characteristic
132	#19151457	C₂²	1	1	yes	characteristic
133	#19151455	C₂²	1	1	yes	characteristic
134	#19151455	C₂²	1	1	yes	characteristic
135	#19151455	C₂²	1	1	yes	characteristic
136	#19151453	C₂²	1	1	yes	characteristic
137	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
138	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
139	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
140	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
141	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
142	#19151449	C₂²	1	1	yes	characteristic, complemented
143	#19151449	C₂²	1	1	yes	characteristic, complemented
144	#19151449	C₂²	1	1	yes	characteristic, complemented
145	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
146	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
147	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
148	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
149	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
150	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
151	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
152	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
153	C₄×#13083551	C₂²	1	1	yes	characteristic
154	C₄×#13083551	C₂²	1	1	yes	characteristic
155	C₄×#13083551	C₂²	1	1	yes	characteristic
156	C₄×#13083551	C₂²	1	1	yes	characteristic
157	C₄×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
158	C₄×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
159	#19151445	C₂²	1	1	yes	characteristic
160	#19151445	C₂²	1	1	yes	characteristic
161	#19151445	C₂²	1	1	yes	characteristic
162	#19151445	C₂²	1	1	yes	characteristic
163	#19151445	C₂²	1	1	yes	characteristic
164	#19151445	C₂²	1	1	yes	characteristic
165	#19151443	C₂²	1	1	yes	characteristic, complemented
166	#19151443	C₂²	1	1	yes	characteristic, complemented
167	#19151443	C₂²	1	1	yes	characteristic, complemented
168	#95×D₈₉	C₂²	1	1	yes	characteristic
169	#95×D₈₉	C₂²	1	1	yes	characteristic
170	#95×D₈₉	C₂²	1	1	yes	characteristic
171	#95×D₈₉	C₂²	1	1	yes	characteristic
172	#397×C₈₉	C₂²	1	1	yes	characteristic
173	#396×C₈₉	C₂²	1	1	yes	characteristic
174	#394×C₈₉	C₂²	1	1	yes	characteristic
175	#394×C₈₉	C₂²	1	1	yes	characteristic
176	#389×C₈₉	C₂²	1	1	yes	characteristic, complemented
177	#388×C₈₉	C₂²	1	1	yes	characteristic, complemented
178	#388×C₈₉	C₂²	1	1	yes	characteristic, complemented
179	#388×C₈₉	C₂²	1	1	yes	characteristic, complemented
180	#388×C₈₉	C₂²	1	1	yes	characteristic, complemented
181	#387×C₈₉	C₂²	1	1	yes	characteristic, complemented
182	#386×C₈₉	C₂²	1	1	yes	characteristic
183	#383×C₈₉	C₂²	1	1	yes	characteristic, complemented
184	#382×C₈₉	C₂²	1	1	yes	characteristic, complemented
185	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
186	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
187	C₂⁴×D₈₉	C₂³	1	1	yes	characteristic
188	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
189	C₂²×C₂²⋊D₈₉	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	C₂²×C₄×D₈₉	—	2	4	no	—
194	C₂²×C₄×D₈₉	—	2	4	no	—
195	C₂²×C₄×D₈₉	—	4	2	no	—
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	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
203	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
204	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
205	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
206	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
207	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
208	#15667994	—	2	4	no	—
209	#15667994	—	2	4	no	—
210	#15667992	—	2	4	no	—
211	#15667990	—	2	4	no	—
212	#15667980	—	2	4	no	—
213	#15667977	—	4	2	no	—
214	D₄×Dic₈₉	—	4	2	no	—
215	#15667972	—	2	4	no	—
216	#15667972	—	2	4	no	—
217	#15667968	—	4	2	no	—
218	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
224	C₂×#13083553	C₂³	1	1	yes	characteristic
225	C₂×#13083553	C₂³	1	1	yes	characteristic
226	C₂×#13083553	C₂³	1	1	yes	characteristic
227	C₂×#13083553	C₂³	1	1	yes	characteristic
228	C₂×#13083553	C₂³	1	1	yes	characteristic
229	C₂×#13083553	C₂³	1	1	yes	characteristic
230	C₂×#13083553	C₂³	1	1	yes	characteristic
231	C₂×#13083553	C₂³	1	1	yes	characteristic
232	C₂×#13083553	C₂³	1	1	yes	characteristic
233	C₂×#13083553	C₂³	1	1	yes	characteristic
234	C₂×#13083553	C₂³	1	1	yes	characteristic
235	C₂×#13083553	C₂³	1	1	yes	characteristic
236	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
237	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
238	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
239	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
240	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
241	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
242	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
243	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
244	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
245	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
246	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
247	C₂×#13083551	C₂³	1	1	yes	characteristic
248	C₂×#13083551	C₂³	1	1	yes	characteristic
249	C₂×#13083551	C₂³	1	1	yes	characteristic
250	C₂×#13083551	C₂³	1	1	yes	characteristic
251	C₂×#13083551	C₂³	1	1	yes	characteristic
252	C₂×#13083551	C₂³	1	1	yes	characteristic
253	C₂×#13083551	C₂³	1	1	yes	characteristic
254	C₂×#13083551	C₂³	1	1	yes	characteristic
255	C₂×#13083551	C₂³	1	1	yes	characteristic
256	C₂×#13083551	C₂³	1	1	yes	characteristic
257	C₂×#13083551	C₂³	1	1	yes	characteristic
258	C₂×#13083551	C₂³	1	1	yes	characteristic
259	C₂×#13083551	C₂³	1	1	yes	characteristic
260	C₂×#13083551	C₂³	1	1	yes	characteristic
261	C₂²⋊C₄×D₈₉	—	2	4	no	—
262	C₂²⋊C₄×D₈₉	—	2	4	no	—
263	C₂²⋊C₄×D₈₉	—	2	4	no	—
264	C₂²⋊C₄×D₈₉	—	2	4	no	—
265	C₂×C₄×Dic₈₉	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	C₄²×D₈₉	—	2	4	no	—
281	C₄²×D₈₉	—	2	4	no	—
282	C₄²×D₈₉	—	4	2	no	—
283	C₄²×D₈₉	—	4	2	no	—
284	#15667919	C₂³	1	1	yes	characteristic
285	#15667919	C₂³	1	1	yes	characteristic
286	#15667919	C₂³	1	1	yes	characteristic
287	#15667919	C₂³	1	1	yes	characteristic
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	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
329	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
330	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
331	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
332	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
333	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
334	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
335	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
336	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
337	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
338	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
339	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
340	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
341	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
342	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
343	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
344	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
346	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
347	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
348	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
349	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
350	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
351	#95×C₈₉	C₂³	1	1	yes	characteristic
352	#95×C₈₉	C₂³	1	1	yes	characteristic
353	#95×C₈₉	C₂³	1	1	yes	characteristic
354	#95×C₈₉	C₂³	1	1	yes	characteristic
355	#95×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	C₂³×D₈₉	—	2	2	no	—
364	C₂³×D₈₉	—	2	2	no	—
365	C₂³×D₈₉	—	2	2	no	—
366	C₂³×D₈₉	—	2	2	no	—
367	C₂³×D₈₉	—	4	1	no	—
368	C₂³×D₈₉	—	4	1	no	—
369	C₂³×D₈₉	#41	1	4	yes	—
370	C₂³×D₈₉	C₂⁴	1	1	yes	characteristic
371	C₂³×D₈₉	C₂⁴	1	1	yes	characteristic
372	C₂×Dic₁₇₈	—	2	2	no	—
373	C₂×Dic₁₇₈	—	2	2	no	—
374	C₂×Dic₁₇₈	—	4	1	no	—
375	C₂×C₂²⋊D₈₉	—	2	2	no	—
376	C₂×C₂²⋊D₈₉	—	2	2	no	—
377	C₂×C₂²⋊D₈₉	—	2	2	no	—
378	C₂×C₂²⋊D₈₉	—	2	2	no	—
379	C₂×C₂²⋊D₈₉	—	2	2	no	—
380	C₂×C₂²⋊D₈₉	—	2	2	no	—
381	C₂²×Dic₈₉	—	2	2	no	—
382	C₂²×Dic₈₉	—	2	2	no	—
383	C₂²×Dic₈₉	—	2	2	no	—
384	C₂²×Dic₈₉	—	2	2	no	—
385	C₂²×Dic₈₉	—	2	2	no	—
386	C₂²×Dic₈₉	—	2	2	no	—
387	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
388	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
389	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
390	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
391	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
392	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
393	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
394	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
395	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
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	C₂×C₄×D₈₉	—	2	2	no	—
402	C₂×C₄×D₈₉	—	2	2	no	—
403	C₂×C₄×D₈₉	—	2	2	no	—
404	C₂×C₄×D₈₉	—	2	2	no	—
405	C₂×C₄×D₈₉	—	2	2	no	—
406	C₂×C₄×D₈₉	—	2	2	no	—
407	C₂×C₄×D₈₉	—	2	2	no	—
408	C₂×C₄×D₈₉	—	2	2	no	—
409	C₂×C₄×D₈₉	—	2	2	no	—
410	C₂×C₄×D₈₉	—	2	2	no	—
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	—	2	2	no	—
418	C₂×C₄×D₈₉	—	2	2	no	—
419	C₂×C₄×D₈₉	—	2	2	no	—
420	C₂×C₄×D₈₉	—	2	2	no	—
421	C₂×C₄×D₈₉	—	2	2	no	—
422	C₂×C₄×D₈₉	—	2	2	no	—
423	C₂×C₄×D₈₉	—	2	2	no	—
424	C₂×C₄×D₈₉	—	2	2	no	—
425	C₂×C₄×D₈₉	—	4	16	no	—
426	C₂×C₄×D₈₉	—	4	1	no	—
427	C₂×C₄×D₈₉	—	4	1	no	—
428	C₂×C₄×D₈₉	—	4	1	no	—
429	C₂×C₄×D₈₉	—	4	1	no	—
430	C₂×C₄×D₈₉	—	4	1	no	—
431	C₂×C₄×D₈₉	—	4	1	no	—
432	C₂×C₄×D₈₉	—	4	1	no	—
433	C₂×C₄×D₈₉	—	4	1	no	—
434	C₂×C₄×D₈₉	—	4	1	no	—
435	C₂×C₄×D₈₉	—	4	1	no	—
436	C₂×C₄×D₈₉	#41	1	4	yes	—
437	C₂×C₄×D₈₉	#41	1	4	yes	—
438	C₄⋊Dic₈₉	—	2	2	no	—
439	C₄⋊Dic₈₉	—	2	2	no	—
440	C₄⋊Dic₈₉	—	2	2	no	—
441	C₄⋊Dic₈₉	—	2	2	no	—
442	C₄⋊Dic₈₉	—	4	1	no	—
443	C₄⋊Dic₈₉	—	4	1	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	C₂²⋊Dic₈₉	—	2	2	no	—
457	C₂²⋊Dic₈₉	—	2	2	no	—
458	C₂²⋊Dic₈₉	—	2	2	no	—
459	C₂²⋊Dic₈₉	—	2	2	no	—
460	C₂²⋊Dic₈₉	—	2	2	no	—
461	C₂²⋊Dic₈₉	—	2	2	no	—
462	C₂²⋊Dic₈₉	—	2	2	no	—
463	C₂²⋊Dic₈₉	—	4	1	no	—
464	C₂²⋊Dic₈₉	—	4	1	no	—
465	C₂²⋊Dic₈₉	—	4	1	no	—
466	C₂²⋊Dic₈₉	—	4	1	no	—
467	#13083551	—	2	2	no	—
468	#13083551	—	2	2	no	—
469	#13083551	—	2	2	no	—
470	#13083551	—	2	2	no	—
471	#13083551	—	2	2	no	—
472	#13083551	—	2	2	no	—
473	#13083551	—	2	2	no	—
474	#13083551	—	2	2	no	—
475	#13083551	—	2	2	no	—
476	#13083551	—	2	2	no	—
477	#13083551	—	2	2	no	—
478	#13083551	—	2	2	no	—
479	#13083551	#41	1	4	yes	—
480	#13083551	#41	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	—	2	2	no	—
489	C₄×Dic₈₉	—	2	2	no	—
490	C₄×Dic₈₉	—	2	2	no	—
491	C₄×Dic₈₉	—	2	2	no	—
492	C₄×Dic₈₉	—	2	2	no	—
493	C₄×Dic₈₉	—	2	2	no	—
494	C₄×Dic₈₉	—	4	1	no	—
495	C₄×Dic₈₉	—	4	1	no	—
496	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
497	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
498	C₂×D₄×C₈₉	—	2	2	no	—
499	C₂×D₄×C₈₉	—	4	1	no	—
500	C₂×D₄×C₈₉	—	4	1	no	—
501	C₂²×C₄×C₈₉	—	2	2	no	—
502	C₂²×C₄×C₈₉	—	2	2	no	—
503	C₂²×C₄×C₈₉	—	4	1	no	—
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	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
516	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
517	C₄⋊C₄×C₈₉	—	2	2	no	—
518	C₄⋊C₄×C₈₉	—	2	2	no	—
519	C₄⋊C₄×C₈₉	—	4	1	no	—
520	C₄⋊C₄×C₈₉	—	4	1	no	—
521	C₄⋊C₄×C₈₉	—	4	1	no	—
522	C₄⋊C₄×C₈₉	—	4	1	no	—
523	C₂²⋊C₄×C₈₉	—	2	2	no	—
524	C₂²⋊C₄×C₈₉	—	2	2	no	—
525	C₂²⋊C₄×C₈₉	—	2	2	no	—
526	C₂²⋊C₄×C₈₉	—	2	2	no	—
527	C₂²⋊C₄×C₈₉	—	2	2	no	—
528	C₂²⋊C₄×C₈₉	—	2	2	no	—
529	C₂²⋊C₄×C₈₉	—	2	2	no	—
530	C₂²⋊C₄×C₈₉	—	2	2	no	—
531	C₂²⋊C₄×C₈₉	—	4	1	no	—
532	C₂²⋊C₄×C₈₉	—	4	1	no	—
533	C₂²⋊C₄×C₈₉	—	4	1	no	—
534	C₄²×C₈₉	—	2	2	no	—
535	C₄²×C₈₉	—	2	2	no	—
536	C₄²×C₈₉	—	4	1	no	—
537	C₄²×C₈₉	—	4	1	no	—
538	C₂³×C₈₉	—	2	1	no	—
539	C₂³×C₈₉	—	2	1	no	—
540	C₂³×C₈₉	—	2	1	no	—
541	C₂³×C₈₉	—	2	1	no	—
542	C₂³×C₈₉	—	2	1	no	—
543	C₂³×C₈₉	—	2	1	no	—
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	C₂×#41	1	2	yes	—
552	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
553	C₂²×D₈₉	—	2	1	no	—
554	C₂²×D₈₉	—	2	1	no	—
555	C₂²×D₈₉	—	2	1	no	—
556	C₂²×D₈₉	—	2	1	no	—
557	C₂²×D₈₉	—	2	1	no	—
558	C₂²×D₈₉	—	2	1	no	—
559	C₂²×D₈₉	—	2	1	no	—
560	C₂²×D₈₉	—	2	1	no	—
561	C₂²×D₈₉	—	2	8	no	—
562	C₂²×D₈₉	—	2	8	no	—
563	C₂²×D₈₉	—	4	4	no	—
564	C₂²×D₈₉	—	4	4	no	—
565	C₂²×D₈₉	—	4	4	no	—
566	C₂²×D₈₉	—	4	4	no	—
567	C₂²×D₈₉	—	4	4	no	—
568	C₂²×D₈₉	C₂×#41	1	2	yes	—
569	C₂²×D₈₉	C₂×#41	1	2	yes	—
570	C₂²×D₈₉	C₂×#41	1	2	yes	—
571	C₂²×D₈₉	C₂×#41	1	2	yes	—
572	C₂²×D₈₉	C₂×#41	1	2	yes	—
573	C₂²×D₈₉	C₂×#41	1	2	yes	—
574	D₄×C₈₉	—	4	4	no	—
575	C₂×C₄×C₈₉	—	2	1	no	—
576	C₂×C₄×C₈₉	—	2	1	no	—
577	C₂×C₄×C₈₉	—	2	1	no	—
578	C₂×C₄×C₈₉	—	2	1	no	—
579	C₂×C₄×C₈₉	—	2	1	no	—
580	C₂×C₄×C₈₉	—	2	1	no	—
581	C₂×C₄×C₈₉	—	2	1	no	—
582	C₂×C₄×C₈₉	—	2	1	no	—
583	C₂×C₄×C₈₉	—	2	1	no	—
584	C₂×C₄×C₈₉	—	2	1	no	—
585	C₂×C₄×C₈₉	—	2	1	no	—
586	C₂×C₄×C₈₉	—	2	1	no	—
587	C₂×C₄×C₈₉	—	2	1	no	—
588	C₂×C₄×C₈₉	—	2	1	no	—
589	C₂×C₄×C₈₉	—	2	1	no	—
590	C₂×C₄×C₈₉	—	2	1	no	—
591	C₂×C₄×C₈₉	—	2	1	no	—
592	C₂×C₄×C₈₉	—	2	1	no	—
593	C₂×C₄×C₈₉	—	2	1	no	—
594	C₂×C₄×C₈₉	—	2	1	no	—
595	C₂×C₄×C₈₉	—	2	1	no	—
596	C₂×C₄×C₈₉	—	2	1	no	—
597	C₂×C₄×C₈₉	—	2	1	no	—
598	C₂×C₄×C₈₉	—	2	1	no	—
599	C₂×C₄×C₈₉	—	2	1	no	—
600	C₂×C₄×C₈₉	—	2	1	no	—
601	C₂×C₄×C₈₉	—	2	1	no	—
602	C₂×C₄×C₈₉	—	2	1	no	—
603	C₂×C₄×C₈₉	—	2	1	no	—
604	C₂×C₄×C₈₉	—	2	1	no	—
605	C₂×C₄×C₈₉	—	2	1	no	—
606	C₂×C₄×C₈₉	—	2	1	no	—
607	C₂×C₄×C₈₉	—	2	1	no	—
608	C₂×C₄×C₈₉	—	2	1	no	—
609	C₂×C₄×C₈₉	—	2	1	no	—
610	C₂×C₄×C₈₉	—	4	4	no	—
611	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
612	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
613	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
614	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
615	C₂²⋊D₈₉	—	4	4	no	—
616	C₂²⋊D₈₉	—	4	4	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	—	2	1	no	—
649	C₂×Dic₈₉	—	2	1	no	—
650	C₂×Dic₈₉	—	2	1	no	—
651	C₂×Dic₈₉	—	2	1	no	—
652	C₂×Dic₈₉	—	2	1	no	—
653	C₂×Dic₈₉	—	2	1	no	—
654	C₂×Dic₈₉	—	4	4	no	—
655	C₂×Dic₈₉	—	4	4	no	—
656	C₂×Dic₈₉	C₂×#41	1	2	yes	—
657	C₂×Dic₈₉	C₂×#41	1	2	yes	—
658	C₂×Dic₈₉	C₂×#41	1	2	yes	—
659	C₂×Dic₈₉	C₂×#41	1	2	yes	—
660	C₂×Dic₈₉	H(5,𝔽₂)	1	2	yes	—
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	—	4	4	no	—
666	C₄×D₈₉	—	4	4	no	—
667	C₄×D₈₉	—	4	4	no	—
668	C₄×D₈₉	—	4	4	no	—
669	C₄×D₈₉	—	4	4	no	—
670	C₄×D₈₉	—	4	4	no	—
671	C₄×D₈₉	—	4	4	no	—
672	C₄×D₈₉	—	4	4	no	—
673	Dic₁₇₈	—	4	4	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	—	4	1	no	—
686	C₂²×C₈₉	—	4	1	no	—
687	C₂²×C₈₉	—	4	1	no	—
688	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
689	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
690	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
691	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
692	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
693	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
694	C₂²×C₈₉	#585	1	1	yes	characteristic
695	C₂×D₈₉	—	2	2	no	—
696	C₂×D₈₉	—	2	2	no	—
697	C₂×D₈₉	—	2	2	no	—
698	C₂×D₈₉	—	2	2	no	—
699	C₂×D₈₉	—	2	2	no	—
700	C₂×D₈₉	—	2	2	no	—
701	C₂×D₈₉	—	2	2	no	—
702	C₂×D₈₉	—	2	2	no	—
703	C₂×D₈₉	—	2	2	no	—
704	C₂×D₈₉	—	2	2	no	—
705	C₂×D₈₉	—	2	2	no	—
706	C₂×D₈₉	—	2	2	no	—
707	C₂×D₈₉	—	4	16	no	—
708	C₂×D₈₉	#529	1	4	yes	—
709	C₂×D₈₉	#529	1	4	yes	—
710	C₄×C₈₉	—	2	2	no	—
711	C₄×C₈₉	—	2	2	no	—
712	C₄×C₈₉	—	2	2	no	—
713	C₄×C₈₉	—	2	2	no	—
714	C₄×C₈₉	—	4	1	no	—
715	C₄×C₈₉	—	4	1	no	—
716	C₄×C₈₉	—	4	1	no	—
717	C₄×C₈₉	—	4	1	no	—
718	C₄×C₈₉	—	4	1	no	—
719	C₄×C₈₉	—	4	1	no	—
720	C₄×C₈₉	—	4	1	no	—
721	C₄×C₈₉	—	4	1	no	—
722	C₄×C₈₉	—	4	1	no	—
723	Dic₈₉	—	2	2	no	—
724	Dic₈₉	—	2	2	no	—
725	Dic₈₉	—	4	1	no	—
726	Dic₈₉	—	4	1	no	—
727	Dic₈₉	—	4	1	no	—
728	Dic₈₉	—	4	1	no	—
729	Dic₈₉	—	4	1	no	—
730	Dic₈₉	—	4	1	no	—
731	Dic₈₉	—	4	1	no	—
732	Dic₈₉	—	4	1	no	—
733	Dic₈₉	—	4	1	no	—
734	Dic₈₉	—	4	1	no	—
735	Dic₈₉	—	4	1	no	—
736	Dic₈₉	#551	1	4	yes	—
737	#34754	—	89	1	no	maximal, Sylow
738	C₂×C₈₉	—	4	2	no	—
739	C₂×C₈₉	—	8	1	no	—
740	C₂×C₈₉	C₂×#529	1	1	yes	characteristic
741	C₂×C₈₉	C₂×#529	1	1	yes	characteristic
742	C₂×C₈₉	#3459	1	1	yes	characteristic
743	C₂×C₈₉	C₂×#551	1	1	yes	characteristic
744	C₂×C₈₉	#3475	1	1	yes	characteristic
745	C₂×C₈₉	#3475	1	1	yes	characteristic
746	C₂×C₈₉	#3481	1	1	yes	characteristic
747	D₈₉	—	2	4	no	—
748	D₈₉	—	2	4	no	—
749	#2523	—	89	1	no	—
750	#2518	—	89	1	no	—
751	#2518	D₈₉	1	1	yes	characteristic, complemented
752	#2517	—	89	1	no	—
753	#2510	—	89	1	no	—
754	#2510	—	89	1	no	—
755	#2505	—	89	1	no	—
756	#2505	—	89	1	no	—
757	#2493	—	89	1	no	—
758	#2493	—	89	1	no	—
759	#2488	—	89	1	no	—
760	#2488	—	89	1	no	—
761	#2483	—	89	1	no	—
762	#2437	—	89	1	no	—
763	#2412	—	89	1	no	—
764	#2412	—	89	1	no	—
765	#2401	—	89	1	no	—
766	#2401	—	89	1	no	—
767	#2398	—	89	1	no	—
768	#2395	—	89	1	no	—
769	C₄×C₂²⋊Q₈	—	89	1	no	—
770	C₄×C₂²⋊Q₈	—	89	1	no	—
771	C₄×#123	—	89	1	no	—
772	C₄×#123	—	89	1	no	—
773	C₄×#120	—	89	1	no	—
774	#2290	—	89	1	no	—
775	#2290	—	89	1	no	—
776	#2283	—	89	1	no	—
777	#2283	—	89	1	no	—
778	C₂×C₄×C₂²⋊C₄	—	89	1	no	—
779	C₂×C₄×C₂²⋊C₄	—	89	1	no	—
780	C₈₉	#34754	1	1	yes	characteristic, complemented, Sylow
781	C₂⁴×C₄	—	89	1	no	—
782	C₂×#123	—	89	1	no	—
783	C₂×#123	—	89	1	no	—
784	C₂×C₂²⋊Q₈	—	89	1	no	—
785	C₂×C₂²⋊Q₈	—	89	1	no	—
786	C₂×#120	—	89	1	no	—
787	C₂×C₄×Q₈	—	89	1	no	—
788	C₂×C₄×D₄	—	89	1	no	—
789	C₂×C₄×D₄	—	89	1	no	—
790	C₂×C₄×D₄	—	89	1	no	—
791	C₂×#117	—	89	1	no	—
792	C₂²×C₂²⋊C₄	—	89	1	no	—
793	C₂²×C₂²⋊C₄	—	89	1	no	—
794	C₂²×C₂²⋊C₄	—	89	1	no	—
795	C₂²×C₂²⋊C₄	—	89	1	no	—
796	C₂²×C₄²	—	89	1	no	—
797	C₂²×C₄²	—	89	1	no	—
798	C₂²×C₄²	—	89	1	no	—
799	C₂²×C₄²	—	89	1	no	—
800	#401	—	89	1	no	—
801	#401	—	89	1	no	—
802	#400	—	89	1	no	—
803	#400	—	89	1	no	—
804	#400	—	89	1	no	—
805	#400	—	89	1	no	—
806	#400	—	89	1	no	—
807	#400	—	89	1	no	—
808	#400	—	89	1	no	—
809	#400	—	89	1	no	—
810	#400	—	89	1	no	—
811	#399	—	89	1	no	—
812	#398	—	89	1	no	—
813	#397	—	89	1	no	—
814	#397	—	89	1	no	—
815	#397	—	89	1	no	—
816	#397	—	89	1	no	—
817	#397	—	89	1	no	—
818	#397	—	89	1	no	—
819	#397	—	89	1	no	—
820	#397	—	89	1	no	—
821	#397	—	89	1	no	—
822	#397	—	89	1	no	—
823	#397	C₂×D₈₉	1	1	yes	characteristic
824	#396	—	89	1	no	—
825	#396	C₂×D₈₉	1	1	yes	characteristic
826	#394	—	89	1	no	—
827	#394	—	89	1	no	—
828	#394	C₂×D₈₉	1	1	yes	characteristic
829	#394	C₂×D₈₉	1	1	yes	characteristic
830	#393	—	89	1	no	—
831	#393	—	89	1	no	—
832	#391	—	89	1	no	—
833	#391	—	89	1	no	—
834	#389	—	89	1	no	—
835	#389	C₂×D₈₉	1	1	yes	characteristic, complemented
836	#388	—	89	1	no	—
837	#388	—	89	1	no	—
838	#388	—	89	1	no	—
839	#388	—	89	1	no	—
840	#388	C₂×D₈₉	1	1	yes	characteristic, complemented
841	#388	C₂×D₈₉	1	1	yes	characteristic, complemented
842	#388	C₂×D₈₉	1	1	yes	characteristic, complemented
843	#388	C₂×D₈₉	1	1	yes	characteristic, complemented
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	C₂×D₈₉	1	1	yes	characteristic, complemented
856	#386	—	89	1	no	—
857	#386	—	89	1	no	—
858	#386	—	89	1	no	—
859	#386	—	89	1	no	—
860	#386	—	89	1	no	—
861	#386	—	89	1	no	—
862	#386	—	89	1	no	—
863	#386	—	89	1	no	—
864	#386	C₂×D₈₉	1	1	yes	characteristic
865	#385	—	89	1	no	—
866	#385	—	89	1	no	—
867	#385	—	89	1	no	—
868	#385	—	89	1	no	—
869	#385	—	89	1	no	—
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	#383	—	89	1	no	—
879	#383	—	89	1	no	—
880	#383	—	89	1	no	—
881	#383	C₂×D₈₉	1	1	yes	characteristic, complemented
882	#382	—	89	1	no	—
883	#382	—	89	1	no	—
884	#382	—	89	1	no	—
885	#382	C₂×D₈₉	1	1	yes	characteristic, complemented
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	#380	—	89	1	no	—
895	#380	—	89	1	no	—
896	#380	—	89	1	no	—
897	#380	—	89	1	no	—
898	#379	—	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	—	89	1	no	—
904	C₄×C₄⋊C₄	—	89	1	no	—
905	C₄×C₄⋊C₄	—	89	1	no	—
906	C₄×C₄⋊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	—	89	1	no	—
917	C₄×C₂²⋊C₄	—	89	1	no	—
918	C₄×C₂²⋊C₄	—	89	1	no	—
919	C₄×C₂²⋊C₄	—	89	1	no	—
920	C₄×C₂²⋊C₄	—	89	1	no	—
921	C₄×C₂²⋊C₄	—	89	1	no	—
922	C₄×C₂²⋊C₄	—	89	1	no	—
923	C₄×C₂²⋊C₄	—	89	1	no	—
924	C₄×C₂²⋊C₄	—	89	1	no	—
925	C₄×C₂²⋊C₄	—	89	1	no	—
926	C₄×C₂²⋊C₄	—	89	1	no	—
927	C₄×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
928	C₄×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
929	#376	—	89	1	no	—
930	#376	—	89	1	no	—
931	#376	—	89	1	no	—
932	C₂×#95	—	89	1	no	—
933	C₂×#95	—	89	1	no	—
934	C₂×#95	—	89	1	no	—
935	C₂×#95	—	89	1	no	—
936	C₂⁵	—	89	1	no	—
937	C₂²×Q₈	—	89	1	no	—
938	C₂²×D₄	—	89	1	no	—
939	C₂²×D₄	—	89	1	no	—
940	C₂²×D₄	C₂²×D₈₉	1	1	yes	characteristic
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	—	89	1	no	—
952	C₂³×C₄	—	89	1	no	—
953	C₂³×C₄	—	89	1	no	—
954	C₂³×C₄	—	89	1	no	—
955	C₂³×C₄	—	356	2	no	—
956	C₂³×C₄	—	178	4	no	—
957	C₂³×C₄	—	178	4	no	—
958	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
959	#123	—	178	4	no	—
960	#123	—	178	4	no	—
961	C₂²⋊Q₈	—	178	4	no	—
962	C₂²⋊Q₈	—	178	4	no	—
963	#120	—	178	4	no	—
964	C₄×Q₈	—	356	2	no	—
965	C₄×D₄	—	356	2	no	—
966	C₄×D₄	—	178	4	no	—
967	C₄×D₄	—	178	4	no	—
968	#117	—	356	2	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	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	C₂²×D₈₉	1	1	yes	characteristic
988	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
989	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
990	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
991	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
992	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
993	C₂×C₂²⋊C₄	—	89	1	no	—
994	C₂×C₂²⋊C₄	—	89	1	no	—
995	C₂×C₂²⋊C₄	—	89	1	no	—
996	C₂×C₂²⋊C₄	—	89	1	no	—
997	C₂×C₂²⋊C₄	—	89	1	no	—
998	C₂×C₂²⋊C₄	—	89	1	no	—
999	C₂×C₂²⋊C₄	—	89	1	no	—
1000	C₂×C₂²⋊C₄	—	89	1	no	—
1001	C₂×C₂²⋊C₄	—	89	1	no	—
1002	C₂×C₂²⋊C₄	—	89	1	no	—
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	—	178	4	no	—
1019	C₂×C₂²⋊C₄	—	178	4	no	—
1020	C₂×C₂²⋊C₄	—	178	4	no	—
1021	C₂×C₂²⋊C₄	—	178	4	no	—
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×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1030	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1031	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1032	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
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	—	356	2	no	—
1049	C₂×C₄²	—	356	2	no	—
1050	C₂×C₄²	—	178	4	no	—
1051	C₂×C₄²	—	178	4	no	—
1052	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1053	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1054	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1055	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
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	—	89	1	no	—
1097	#95	—	89	1	no	—
1098	#95	—	89	1	no	—
1099	#95	—	89	1	no	—
1100	#95	C₂²×D₈₉	1	1	yes	characteristic
1101	#95	C₂²×D₈₉	1	1	yes	characteristic
1102	#95	C₂²×D₈₉	1	1	yes	characteristic
1103	#95	C₂²×D₈₉	1	1	yes	characteristic
1104	#95	C₂²×D₈₉	1	1	yes	characteristic
1105	#95	C₂²×D₈₉	1	1	yes	characteristic
1106	#95	C₂²×D₈₉	1	1	yes	characteristic
1107	#95	C₂²×D₈₉	1	1	yes	characteristic
1108	#95	C₂²×D₈₉	1	1	yes	characteristic
1109	#95	C₂²×D₈₉	1	1	yes	characteristic
1110	#95	C₂²×D₈₉	1	1	yes	characteristic
1111	#95	C₂²×D₈₉	1	1	yes	characteristic
1112	C₂⁴	—	89	1	no	—
1113	C₂⁴	—	89	1	no	—
1114	C₂⁴	—	89	4	no	—
1115	C₂⁴	—	356	1	no	—
1116	C₂⁴	—	356	1	no	—
1117	C₂⁴	—	178	2	no	—
1118	C₂⁴	—	178	2	no	—
1119	C₂⁴	—	178	2	no	—
1120	C₂⁴	—	178	2	no	—
1121	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
1122	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
1123	C₂×Q₈	—	356	1	no	—
1124	C₂×Q₈	—	178	2	no	—
1125	C₂×Q₈	—	178	2	no	—
1126	C₂×D₄	—	2	2	no	—
1127	C₂×D₄	—	4	1	no	—
1128	C₂×D₄	—	4	1	no	—
1129	C₂×D₄	—	178	2	no	—
1130	C₂×D₄	—	178	2	no	—
1131	C₂×D₄	—	178	2	no	—
1132	C₂×D₄	—	178	2	no	—
1133	C₂×D₄	—	178	2	no	—
1134	C₂×D₄	—	178	2	no	—
1135	C₂²×C₄	—	2	2	no	—
1136	C₂²×C₄	—	2	2	no	—
1137	C₂²×C₄	—	4	1	no	—
1138	C₂²×C₄	—	89	1	no	—
1139	C₂²×C₄	—	89	1	no	—
1140	C₂²×C₄	—	89	1	no	—
1141	C₂²×C₄	—	89	4	no	—
1142	C₂²×C₄	—	89	4	no	—
1143	C₂²×C₄	—	89	1	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	—	89	1	no	—
1151	C₂²×C₄	—	89	1	no	—
1152	C₂²×C₄	—	89	1	no	—
1153	C₂²×C₄	—	89	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	16	no	—
1165	C₂²×C₄	—	178	2	no	—
1166	C₂²×C₄	—	178	2	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	—	178	2	no	—
1177	C₂²×C₄	—	178	2	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	—	178	2	no	—
1192	C₂²×C₄	—	178	2	no	—
1193	C₂²×C₄	—	178	2	no	—
1194	C₂²×C₄	—	178	2	no	—
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	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1205	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1206	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1207	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1208	C₄⋊C₄	—	2	2	no	—
1209	C₄⋊C₄	—	2	2	no	—
1210	C₄⋊C₄	—	4	1	no	—
1211	C₄⋊C₄	—	4	1	no	—
1212	C₄⋊C₄	—	4	1	no	—
1213	C₄⋊C₄	—	4	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	—	178	2	no	—
1223	C₄⋊C₄	—	178	2	no	—
1224	C₄⋊C₄	—	178	2	no	—
1225	C₄⋊C₄	—	178	2	no	—
1226	C₄⋊C₄	—	178	2	no	—
1227	C₄⋊C₄	—	178	2	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	C₂²⋊C₄	—	2	2	no	—
1233	C₂²⋊C₄	—	2	2	no	—
1234	C₂²⋊C₄	—	2	2	no	—
1235	C₂²⋊C₄	—	2	2	no	—
1236	C₂²⋊C₄	—	2	2	no	—
1237	C₂²⋊C₄	—	2	2	no	—
1238	C₂²⋊C₄	—	2	2	no	—
1239	C₂²⋊C₄	—	2	2	no	—
1240	C₂²⋊C₄	—	4	1	no	—
1241	C₂²⋊C₄	—	4	1	no	—
1242	C₂²⋊C₄	—	4	1	no	—
1243	C₂²⋊C₄	—	89	4	no	—
1244	C₂²⋊C₄	—	89	4	no	—
1245	C₂²⋊C₄	—	356	1	no	—
1246	C₂²⋊C₄	—	356	1	no	—
1247	C₂²⋊C₄	—	356	1	no	—
1248	C₂²⋊C₄	—	356	1	no	—
1249	C₂²⋊C₄	—	178	2	no	—
1250	C₂²⋊C₄	—	178	2	no	—
1251	C₂²⋊C₄	—	178	2	no	—
1252	C₂²⋊C₄	—	178	2	no	—
1253	C₂²⋊C₄	—	178	2	no	—
1254	C₂²⋊C₄	—	178	2	no	—
1255	C₂²⋊C₄	—	178	2	no	—
1256	C₂²⋊C₄	—	178	2	no	—
1257	C₂²⋊C₄	—	178	2	no	—
1258	C₂²⋊C₄	—	178	2	no	—
1259	C₂²⋊C₄	—	178	2	no	—
1260	C₂²⋊C₄	—	178	2	no	—
1261	C₂²⋊C₄	—	178	2	no	—
1262	C₂²⋊C₄	—	178	2	no	—
1263	C₂²⋊C₄	—	178	2	no	—
1264	C₂²⋊C₄	—	178	2	no	—
1265	C₂²⋊C₄	—	178	2	no	—
1266	C₂²⋊C₄	—	178	2	no	—
1267	C₂²⋊C₄	—	178	2	no	—
1268	C₄²	—	2	2	no	—
1269	C₄²	—	2	2	no	—
1270	C₄²	—	4	1	no	—
1271	C₄²	—	4	1	no	—
1272	C₄²	—	356	1	no	—
1273	C₄²	—	356	1	no	—
1274	C₄²	—	178	2	no	—
1275	C₄²	—	178	2	no	—
1276	C₄²	—	178	2	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	C₄²	—	178	2	no	—
1285	C₄²	—	178	2	no	—
1286	C₄²	—	178	2	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	—	2	1	no	—
1295	C₂³	—	2	1	no	—
1296	C₂³	—	2	1	no	—
1297	C₂³	—	2	1	no	—
1298	C₂³	—	2	1	no	—
1299	C₂³	—	2	1	no	—
1300	C₂³	—	89	2	no	—
1301	C₂³	—	89	2	no	—
1302	C₂³	—	89	2	no	—
1303	C₂³	—	89	2	no	—
1304	C₂³	—	89	2	no	—
1305	C₂³	—	89	2	no	—
1306	C₂³	—	356	4	no	—
1307	C₂³	—	356	4	no	—
1308	C₂³	—	356	4	no	—
1309	C₂³	—	356	4	no	—
1310	C₂³	—	356	4	no	—
1311	C₂³	—	178	8	no	—
1312	C₂³	—	178	8	no	—
1313	C₂³	—	178	1	no	—
1314	C₂³	—	178	1	no	—
1315	C₂³	—	178	1	no	—
1316	C₂³	—	178	1	no	—
1317	C₂³	—	178	1	no	—
1318	C₂³	—	178	1	no	—
1319	C₂³	—	178	1	no	—
1320	C₂³	—	178	1	no	—
1321	C₂³	#41×D₈₉	1	2	yes	—
1322	C₂³	C₂⁴×D₈₉	1	1	yes	characteristic
1323	Q₈	—	356	4	no	—
1324	D₄	—	4	4	no	—
1325	D₄	—	356	4	no	—
1326	D₄	—	356	4	no	—
1327	C₂×C₄	—	2	1	no	—
1328	C₂×C₄	—	2	1	no	—
1329	C₂×C₄	—	2	1	no	—
1330	C₂×C₄	—	2	1	no	—
1331	C₂×C₄	—	2	1	no	—
1332	C₂×C₄	—	2	1	no	—
1333	C₂×C₄	—	2	1	no	—
1334	C₂×C₄	—	2	1	no	—
1335	C₂×C₄	—	2	1	no	—
1336	C₂×C₄	—	2	1	no	—
1337	C₂×C₄	—	2	1	no	—
1338	C₂×C₄	—	2	1	no	—
1339	C₂×C₄	—	2	1	no	—
1340	C₂×C₄	—	2	1	no	—
1341	C₂×C₄	—	2	1	no	—
1342	C₂×C₄	—	2	1	no	—
1343	C₂×C₄	—	2	1	no	—
1344	C₂×C₄	—	2	1	no	—
1345	C₂×C₄	—	2	1	no	—
1346	C₂×C₄	—	2	1	no	—
1347	C₂×C₄	—	2	1	no	—
1348	C₂×C₄	—	2	1	no	—
1349	C₂×C₄	—	2	1	no	—
1350	C₂×C₄	—	2	1	no	—
1351	C₂×C₄	—	2	1	no	—
1352	C₂×C₄	—	2	1	no	—
1353	C₂×C₄	—	2	1	no	—
1354	C₂×C₄	—	2	1	no	—
1355	C₂×C₄	—	2	1	no	—
1356	C₂×C₄	—	2	1	no	—
1357	C₂×C₄	—	2	1	no	—
1358	C₂×C₄	—	2	1	no	—
1359	C₂×C₄	—	2	1	no	—
1360	C₂×C₄	—	2	1	no	—
1361	C₂×C₄	—	2	1	no	—
1362	C₂×C₄	—	4	4	no	—
1363	C₂×C₄	—	89	2	no	—
1364	C₂×C₄	—	89	2	no	—
1365	C₂×C₄	—	89	2	no	—
1366	C₂×C₄	—	89	2	no	—
1367	C₂×C₄	—	89	2	no	—
1368	C₂×C₄	—	356	4	no	—
1369	C₂×C₄	—	356	4	no	—
1370	C₂×C₄	—	356	4	no	—
1371	C₂×C₄	—	356	4	no	—
1372	C₂×C₄	—	356	4	no	—
1373	C₂×C₄	—	356	4	no	—
1374	C₂×C₄	—	356	4	no	—
1375	C₂×C₄	—	356	4	no	—
1376	C₂×C₄	—	356	4	no	—
1377	C₂×C₄	—	356	4	no	—
1378	C₂×C₄	—	356	4	no	—
1379	C₂×C₄	—	356	4	no	—
1380	C₂×C₄	—	178	8	no	—
1381	C₂×C₄	—	178	8	no	—
1382	C₂×C₄	—	178	1	no	—
1383	C₂×C₄	—	178	1	no	—
1384	C₂×C₄	—	178	1	no	—
1385	C₂×C₄	—	178	1	no	—
1386	C₂×C₄	—	178	1	no	—
1387	C₂×C₄	—	178	1	no	—
1388	C₂×C₄	—	178	1	no	—
1389	C₂×C₄	—	178	1	no	—
1390	C₂×C₄	—	178	1	no	—
1391	C₂×C₄	—	178	1	no	—
1392	C₂×C₄	—	178	1	no	—
1393	C₂×C₄	—	178	1	no	—
1394	C₂×C₄	—	178	1	no	—
1395	C₂×C₄	—	178	1	no	—
1396	C₂×C₄	—	178	1	no	—
1397	C₂×C₄	—	178	1	no	—
1398	C₂×C₄	—	178	1	no	—
1399	C₂×C₄	—	178	1	no	—
1400	C₂×C₄	—	178	1	no	—
1401	C₂×C₄	—	178	1	no	—
1402	C₂×C₄	—	178	1	no	—
1403	C₂×C₄	—	178	1	no	—
1404	C₂×C₄	—	178	1	no	—
1405	C₂×C₄	—	178	1	no	—
1406	C₂×C₄	—	178	1	no	—
1407	C₂×C₄	—	178	1	no	—
1408	C₂×C₄	—	178	1	no	—
1409	C₂×C₄	—	178	1	no	—
1410	C₂×C₄	—	178	1	no	—
1411	C₂×C₄	—	178	1	no	—
1412	C₂×C₄	—	178	1	no	—
1413	C₂×C₄	—	178	1	no	—
1414	C₂×C₄	—	178	1	no	—
1415	C₂×C₄	—	178	1	no	—
1416	C₂×C₄	—	178	1	no	—
1417	C₂×C₄	—	178	1	no	—
1418	C₂×C₄	—	178	1	no	—
1419	C₂×C₄	#41×D₈₉	1	2	yes	—
1420	C₂×C₄	#41×D₈₉	1	2	yes	—
1421	C₂×C₄	#41×D₈₉	1	2	yes	—
1422	C₂×C₄	#41×D₈₉	1	2	yes	—
1423	C₂²	—	2	2	no	—
1424	C₂²	—	2	2	no	—
1425	C₂²	—	2	2	no	—
1426	C₂²	—	4	1	no	—
1427	C₂²	—	4	1	no	—
1428	C₂²	—	4	1	no	—
1429	C₂²	—	4	1	no	—
1430	C₂²	—	4	1	no	—
1431	C₂²	—	4	1	no	—
1432	C₂²	—	4	1	no	—
1433	C₂²	—	4	1	no	—
1434	C₂²	—	4	1	no	—
1435	C₂²	—	4	1	no	—
1436	C₂²	—	4	1	no	—
1437	C₂²	—	89	4	no	—
1438	C₂²	—	89	4	no	—
1439	C₂²	—	356	16	no	—
1440	C₂²	—	178	2	no	—
1441	C₂²	—	178	2	no	—
1442	C₂²	—	178	2	no	—
1443	C₂²	—	178	2	no	—
1444	C₂²	—	178	2	no	—
1445	C₂²	—	178	2	no	—
1446	C₂²	—	178	2	no	—
1447	C₂²	—	178	2	no	—
1448	C₂²	—	178	2	no	—
1449	C₂²	—	178	2	no	—
1450	C₂²	—	178	2	no	—
1451	C₂²	—	178	2	no	—
1452	C₂²	C₂×#41×D₈₉	1	1	yes	characteristic
1453	C₂²	C₂×#41×D₈₉	1	1	yes	characteristic
1454	C₂²	C₂×#41×D₈₉	1	1	yes	characteristic
1455	C₂²	C₂×#41×D₈₉	1	1	yes	characteristic
1456	C₂²	C₂×#41×D₈₉	1	1	yes	characteristic
1457	C₂²	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
1458	C₂²	#19152433	1	1	yes	characteristic
1459	C₄	—	2	2	no	—
1460	C₄	—	2	2	no	—
1461	C₄	—	2	2	no	—
1462	C₄	—	2	2	no	—
1463	C₄	—	4	1	no	—
1464	C₄	—	4	1	no	—
1465	C₄	—	4	1	no	—
1466	C₄	—	4	1	no	—
1467	C₄	—	4	1	no	—
1468	C₄	—	4	1	no	—
1469	C₄	—	4	1	no	—
1470	C₄	—	4	1	no	—
1471	C₄	—	4	1	no	—
1472	C₄	—	89	4	no	—
1473	C₄	—	356	1	no	—
1474	C₄	—	356	1	no	—
1475	C₄	—	356	1	no	—
1476	C₄	—	356	1	no	—
1477	C₄	—	356	1	no	—
1478	C₄	—	356	1	no	—
1479	C₄	—	356	1	no	—
1480	C₄	—	356	1	no	—
1481	C₄	—	356	1	no	—
1482	C₄	—	356	1	no	—
1483	C₄	—	356	1	no	—
1484	C₄	—	178	2	no	—
1485	C₄	—	178	2	no	—
1486	C₂	—	4	2	no	—
1487	C₂	—	8	1	no	—
1488	C₂	—	178	4	no	—
1489	C₂	—	178	4	no	—
1490	C₂	#529×D₈₉	1	1	yes	characteristic
1491	C₂	#529×D₈₉	1	1	yes	characteristic
1492	C₂	#26033663	1	1	yes	characteristic
1493	C₂	#551×D₈₉	1	1	yes	characteristic
1494	C₂	#26033809	1	1	yes	characteristic
1495	C₂	#26033811	1	1	yes	characteristic
1496	C₂	#26033859	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₈₉
commutator, socle, cosocle	C₂³×C₈₉	C₂⁵
Fitting	C₈₉×#2518	C₂
prime radical	C₂×#15667980	C₂²
hypercenter	#2518	D₈₉
hypocenter	C₈₉	#34754
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ #2518

Complements

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

N	H ≅ G/N	type
1. #26024979	C₂	semidirect
2. #26024912	C₂	semidirect
3. #26024895	C₂	semidirect
4. #26024817	C₂	semidirect
5. #26024811	C₂	semidirect
6. #26024758	C₂	semidirect
7. #26024752	C₂	semidirect
8. #26024644	C₂	semidirect
9. #26024634	C₂	semidirect
10. #26024583	C₂	semidirect
11. #26024577	C₂	semidirect
12. #26024529	C₂	semidirect
13. #26023914	C₂	semidirect
16. #26023554	C₂	semidirect
17. #26023549	C₂	semidirect
18. #26023540	C₂	semidirect
19. #26023508	C₂	semidirect
20. #26022786	C₂	semidirect
21. #26022782	C₂	semidirect
22. #26022779	C₂	semidirect
23. #26022779	C₂	semidirect
25. #26022694	C₂	semidirect
26. #26022694	C₂	semidirect
27. #26022649	C₂	semidirect
28. #26022645	C₂	semidirect
29. C₄×C₂²⋊C₄×D₈₉	C₂	semidirect
30. C₄×C₂²⋊C₄×D₈₉	C₂	semidirect
31. C₈₉×#2518	C₂	semidirect
38. C₂×#15667977	C₂²	semidirect
42. C₂×#15667968	C₂²	semidirect
51. C₈₉⋊#401	C₂²	semidirect
52. C₈₉⋊#401	C₂²	semidirect
53. #19151540	C₂²	semidirect
54. #19151540	C₂²	semidirect
55. #19151539	C₂²	semidirect
56. #19151538	C₂²	semidirect
57. #19151537	C₂²	semidirect
58. #19151537	C₂²	semidirect
59. #19151537	C₂²	semidirect
60. #19151537	C₂²	semidirect
61. #19151536	C₂²	semidirect
63. #19151531	C₂²	semidirect
68. #19151526	C₂²	semidirect
69. #19151526	C₂²	semidirect
73. #19151523	C₂²	semidirect
78. #19151510	C₂²	semidirect
79. #19151504	C₂²	semidirect
80. #19151502	C₂²	semidirect
81. #19151495	C₂²	semidirect
82. #19151491	C₂²	semidirect
83. #19151491	C₂²	semidirect
84. #19151486	C₂²	semidirect
85. #19151486	C₂²	semidirect
86. #19151483	C₂²	semidirect
87. #19151483	C₂²	semidirect
88. #19151482	C₂²	semidirect
89. #19151482	C₂²	semidirect
90. #19151482	C₂²	semidirect
91. #19151482	C₂²	semidirect
92. #19151482	C₂²	semidirect
93. #19151481	C₂²	semidirect
94. #19151481	C₂²	semidirect
95. #19151480	C₂²	semidirect
96. #19151480	C₂²	semidirect
118. #19151466	C₂²	semidirect
119. #19151465	C₂²	semidirect
120. #19151465	C₂²	semidirect
121. #19151464	C₂²	semidirect
122. #19151462	C₂²	semidirect
123. #19151462	C₂²	semidirect
137. C₄⋊C₄×Dic₈₉	C₂²	semidirect
138. C₄⋊C₄×Dic₈₉	C₂²	semidirect
139. C₄⋊C₄×Dic₈₉	C₂²	semidirect
140. C₄⋊C₄×Dic₈₉	C₂²	semidirect
141. C₄⋊C₄×Dic₈₉	C₂²	semidirect
142. #19151449	C₂²	semidirect
143. #19151449	C₂²	semidirect
144. #19151449	C₂²	semidirect
150. C₂²⋊C₄×Dic₈₉	C₂²	semidirect
151. C₂²⋊C₄×Dic₈₉	C₂²	semidirect
152. C₂²⋊C₄×Dic₈₉	C₂²	semidirect
165. #19151443	C₂²	semidirect
166. #19151443	C₂²	semidirect
167. #19151443	C₂²	semidirect
176. #389×C₈₉	C₂²	semidirect
177. #388×C₈₉	C₂²	semidirect
178. #388×C₈₉	C₂²	semidirect
179. #388×C₈₉	C₂²	semidirect
180. #388×C₈₉	C₂²	semidirect
181. #387×C₈₉	C₂²	semidirect
183. #383×C₈₉	C₂²	semidirect
184. #382×C₈₉	C₂²	semidirect
751. #2518	D₈₉	semidirect
780. C₈₉	#34754	semidirect
835. #389	C₂×D₈₉	semidirect
840. #388	C₂×D₈₉	semidirect
841. #388	C₂×D₈₉	semidirect
842. #388	C₂×D₈₉	semidirect
843. #388	C₂×D₈₉	semidirect
855. #387	C₂×D₈₉	semidirect
881. #383	C₂×D₈₉	semidirect
885. #382	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26024979	2
#26024912	2
#26024895	2
#26024817	2
#26024811	2
#26024758	2
#26024752	2
#26024644	2
#26024634	2
#26024583	2
#26024577	2
#26024529	2
#26023914	2
#26023643	2
#26023554	2
#26023549	2
#26023540	2
#26023508	2
#26022786	2
#26022782	2
#26022779	2
#26022757	2
#26022694	2
#26022649	2
#26022645	2
C₄×C₂²⋊C₄×D₈₉	2
C₈₉×#2518	2
#34754	89