Subgroups — #36722485

Order 22784.

2464 conjugacy classes of subgroups.

The subgroup lattice has 1484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19152152	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×Q₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#26024394	C₂	1	1	yes	maximal, characteristic, complemented
4	#26024386	C₂	1	1	yes	maximal, characteristic, complemented
5	#26024276	C₂	1	1	yes	maximal, characteristic, complemented
6	#26024268	C₂	1	1	yes	maximal, characteristic, complemented
7	#26024235	C₂	1	1	yes	maximal, characteristic, complemented
8	#26024227	C₂	1	1	yes	maximal, characteristic, complemented
9	#26024084	C₂	1	1	yes	maximal, characteristic, complemented
10	#26024056	C₂	1	1	yes	maximal, characteristic
11	#26024054	C₂	1	1	yes	maximal, characteristic
12	#26024021	C₂	1	1	yes	maximal, characteristic, complemented
13	#26023947	C₂	1	1	yes	maximal, characteristic, complemented
14	#26023891	C₂	1	1	yes	maximal, characteristic, complemented
15	#26023846	C₂	1	1	yes	maximal, characteristic, complemented
16	#26023772	C₂	1	1	yes	maximal, characteristic, complemented
17	#26023698	C₂	1	1	yes	maximal, characteristic
18	#26023612	C₂	1	1	yes	maximal, characteristic
19	#26023546	C₂	1	1	yes	maximal, characteristic, complemented
20	#26023528	C₂	1	1	yes	maximal, characteristic, complemented
21	#26023522	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#15668011	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#15667990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₄×#15667990	C₂	1	1	yes	maximal, characteristic, complemented
25	C₄×#15667990	C₂	1	1	yes	maximal, characteristic, complemented
26	C₄×#15667988	C₂	1	1	yes	maximal, characteristic, complemented
27	#26022724	C₂	1	1	yes	maximal, characteristic, complemented
28	#26022696	C₂	1	1	yes	maximal, characteristic
29	#26022693	C₂	1	1	yes	maximal, characteristic
30	C₄×#15667974	C₂	1	1	yes	maximal, characteristic
31	C₈₉×#2399	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×Q₈×D₈₉	C₂²	1	1	yes	characteristic
33	#19152152	—	2	8	no	—
34	C₂×#15668011	C₂²	1	1	yes	characteristic
35	C₂×#15668011	C₂²	1	1	yes	characteristic
36	C₂×#15668010	C₂²	1	1	yes	characteristic
37	C₂×#15668002	C₂²	1	1	yes	characteristic
38	C₂×#15668002	C₂²	1	1	yes	characteristic
39	C₂×#15667992	C₂²	1	1	yes	characteristic
40	C₂×#15667990	C₂²	1	1	yes	characteristic
41	C₂×#15667990	C₂²	1	1	yes	characteristic
42	C₂×#15667990	C₂²	1	1	yes	characteristic
43	C₂×#15667990	C₂²	1	1	yes	characteristic
44	C₂×#15667990	C₂²	1	1	yes	characteristic
45	C₂×#15667988	C₂²	1	1	yes	characteristic
46	C₂×#15667988	C₂²	1	1	yes	characteristic
47	C₂×Q₈×Dic₈₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
49	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
50	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
51	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
52	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
53	C₂×#15667977	C₂²	1	1	yes	characteristic
54	C₂×#15667977	C₂²	1	1	yes	characteristic
55	C₂×#15667977	C₂²	1	1	yes	characteristic
56	C₄×Q₈×D₈₉	—	2	8	no	—
57	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
58	C₂×#15667974	C₂²	1	1	yes	characteristic
59	C₂×#15667974	C₂²	1	1	yes	characteristic
60	C₂×#15667969	C₂²	1	1	yes	characteristic
61	C₂×#15667969	C₂²	1	1	yes	characteristic
62	C₂×C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
63	C₂×C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
65	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
66	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
67	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
68	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
69	#19151539	C₂²	1	1	yes	characteristic
70	#19151536	C₂²	1	1	yes	characteristic
71	#19151533	C₂²	1	1	yes	characteristic
72	#19151533	C₂²	1	1	yes	characteristic
73	#19151532	C₂²	1	1	yes	characteristic
74	#19151532	C₂²	1	1	yes	characteristic
75	#19151532	C₂²	1	1	yes	characteristic
76	#19151531	C₂²	1	1	yes	characteristic
77	#19151531	C₂²	1	1	yes	characteristic
78	#19151531	C₂²	1	1	yes	characteristic
79	#19151531	C₂²	1	1	yes	characteristic
80	#19151529	C₂²	1	1	yes	characteristic
81	#19151522	C₂²	1	1	yes	characteristic
82	#19151520	C₂²	1	1	yes	characteristic
83	#19151520	C₂²	1	1	yes	characteristic
84	#19151520	C₂²	1	1	yes	characteristic
85	#19151519	C₂²	1	1	yes	characteristic
86	#19151519	C₂²	1	1	yes	characteristic
87	#19151518	C₂²	1	1	yes	characteristic
88	#19151518	C₂²	1	1	yes	characteristic
89	#19151518	C₂²	1	1	yes	characteristic
90	#19151517	C₂²	1	1	yes	characteristic
91	#19151511	C₂²	1	1	yes	characteristic
92	#19151509	C₂²	1	1	yes	characteristic
93	#19151505	C₂²	1	1	yes	characteristic
94	#19151502	C₂²	1	1	yes	characteristic
95	#19151502	C₂²	1	1	yes	characteristic
96	#19151502	C₂²	1	1	yes	characteristic
97	#19151502	C₂²	1	1	yes	characteristic
98	#19151502	C₂²	1	1	yes	characteristic
99	#19151502	C₂²	1	1	yes	characteristic
100	#19151502	C₂²	1	1	yes	characteristic
101	#19151497	C₂²	1	1	yes	characteristic
102	#19151495	C₂²	1	1	yes	characteristic
103	#19151495	C₂²	1	1	yes	characteristic
104	#19151495	C₂²	1	1	yes	characteristic
105	#19151495	C₂²	1	1	yes	characteristic
106	#19151494	C₂²	1	1	yes	characteristic
107	#19151494	C₂²	1	1	yes	characteristic
108	#19151493	C₂²	1	1	yes	characteristic
109	#19151493	C₂²	1	1	yes	characteristic
110	#19151493	C₂²	1	1	yes	characteristic
111	#19151490	C₂²	1	1	yes	characteristic
112	#19151490	C₂²	1	1	yes	characteristic
113	#19151488	C₂²	1	1	yes	characteristic
114	#19151488	C₂²	1	1	yes	characteristic
115	#19151485	C₂²	1	1	yes	characteristic
116	#19151485	C₂²	1	1	yes	characteristic
117	#19151484	C₂²	1	1	yes	characteristic
118	#19151484	C₂²	1	1	yes	characteristic
119	#19151484	C₂²	1	1	yes	characteristic
120	#19151483	C₂²	1	1	yes	characteristic
121	#19151483	C₂²	1	1	yes	characteristic
122	#19151481	C₂²	1	1	yes	characteristic
123	#19151481	C₂²	1	1	yes	characteristic
124	#19151481	C₂²	1	1	yes	characteristic
125	#19151481	C₂²	1	1	yes	characteristic
126	#19151480	C₂²	1	1	yes	characteristic
127	#19151480	C₂²	1	1	yes	characteristic
128	#19151480	C₂²	1	1	yes	characteristic
129	#19151479	C₂²	1	1	yes	characteristic
130	#19151479	C₂²	1	1	yes	characteristic
131	#19151476	C₂²	1	1	yes	characteristic
132	#19151476	C₂²	1	1	yes	characteristic
133	#19151476	C₂²	1	1	yes	characteristic
134	#19151476	C₂²	1	1	yes	characteristic
135	#19151472	C₂²	1	1	yes	characteristic
136	#19151472	C₂²	1	1	yes	characteristic
137	#19151472	C₂²	1	1	yes	characteristic
138	#19151472	C₂²	1	1	yes	characteristic
139	#19151472	C₂²	1	1	yes	characteristic
140	#19151469	C₂²	1	1	yes	characteristic
141	#19151469	C₂²	1	1	yes	characteristic
142	#19151469	C₂²	1	1	yes	characteristic
143	#19151469	C₂²	1	1	yes	characteristic
144	#19151469	C₂²	1	1	yes	characteristic
145	#19151469	C₂²	1	1	yes	characteristic
146	#19151469	C₂²	1	1	yes	characteristic
147	#19151467	C₂²	1	1	yes	characteristic
148	#19151457	C₂²	1	1	yes	characteristic
149	#19151457	C₂²	1	1	yes	characteristic
150	#19151457	C₂²	1	1	yes	characteristic
151	#19151455	C₂²	1	1	yes	characteristic
152	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
153	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
154	C₄×#13083553	C₂²	1	1	yes	characteristic
155	C₄×#13083553	C₂²	1	1	yes	characteristic
156	C₄×#13083553	C₂²	1	1	yes	characteristic
157	C₄×#13083553	C₂²	1	1	yes	characteristic
158	C₄×#13083553	C₂²	1	1	yes	characteristic
159	C₄×#13083553	C₂²	1	1	yes	characteristic
160	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
161	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
162	C₄×#13083551	C₂²	1	1	yes	characteristic
163	C₄×#13083551	C₂²	1	1	yes	characteristic
164	C₄×#13083551	C₂²	1	1	yes	characteristic
165	C₄×#13083551	C₂²	1	1	yes	characteristic
166	C₄×#13083551	C₂²	1	1	yes	characteristic
167	C₄×#13083551	C₂²	1	1	yes	characteristic
168	#19151445	C₂²	1	1	yes	characteristic
169	#19151445	C₂²	1	1	yes	characteristic
170	#19151445	C₂²	1	1	yes	characteristic
171	#19151445	C₂²	1	1	yes	characteristic
172	#19151444	C₂²	1	1	yes	characteristic
173	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
174	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
175	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
176	#398×C₈₉	C₂²	1	1	yes	characteristic
177	#398×C₈₉	C₂²	1	1	yes	characteristic
178	#398×C₈₉	C₂²	1	1	yes	characteristic
179	#398×C₈₉	C₂²	1	1	yes	characteristic
180	#395×C₈₉	C₂²	1	1	yes	characteristic
181	#395×C₈₉	C₂²	1	1	yes	characteristic
182	#395×C₈₉	C₂²	1	1	yes	characteristic
183	#395×C₈₉	C₂²	1	1	yes	characteristic
184	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
185	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
186	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
187	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
188	#376×C₈₉	C₂²	1	1	yes	characteristic
189	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
190	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
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	C₂×Q₈×D₈₉	—	2	4	no	—
195	C₂×Q₈×D₈₉	—	2	4	no	—
196	C₂×Q₈×D₈₉	—	2	4	no	—
197	C₂²×D₃₅₆	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	#15668011	—	2	4	no	—
209	#15668011	—	2	4	no	—
210	#15668010	—	2	4	no	—
211	#15668002	—	2	4	no	—
212	#15668002	—	2	4	no	—
213	#15667992	—	2	4	no	—
214	#15667990	—	2	4	no	—
215	#15667990	—	2	4	no	—
216	#15667990	—	2	4	no	—
217	#15667990	—	2	4	no	—
218	#15667990	—	2	4	no	—
219	#15667988	—	2	4	no	—
220	#15667988	—	2	4	no	—
221	Q₈×Dic₈₉	—	2	4	no	—
222	C₄×Dic₁₇₈	—	2	4	no	—
223	C₄×Dic₁₇₈	—	2	4	no	—
224	C₄×Dic₁₇₈	—	2	4	no	—
225	C₄×Dic₁₇₈	—	2	4	no	—
226	C₄×Dic₁₇₈	D₄	1	8	yes	complemented
227	#15667977	—	2	4	no	—
228	#15667977	—	2	4	no	—
229	#15667977	—	2	4	no	—
230	C₄×D₃₅₆	Q₈	1	8	yes	complemented
231	#15667974	—	2	4	no	—
232	#15667974	—	2	4	no	—
233	#15667969	—	2	4	no	—
234	#15667969	—	2	4	no	—
235	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
245	C₂×#13083553	C₂³	1	1	yes	characteristic
246	C₂×#13083553	C₂³	1	1	yes	characteristic
247	C₂×#13083553	C₂³	1	1	yes	characteristic
248	C₂×#13083553	C₂³	1	1	yes	characteristic
249	C₂×#13083553	C₂³	1	1	yes	characteristic
250	C₂×#13083553	C₂³	1	1	yes	characteristic
251	C₂×#13083553	C₂³	1	1	yes	characteristic
252	C₂×#13083553	C₂³	1	1	yes	characteristic
253	C₂×#13083553	C₂³	1	1	yes	characteristic
254	C₂×#13083553	C₂³	1	1	yes	characteristic
255	C₂×#13083553	C₂³	1	1	yes	characteristic
256	C₂×#13083553	C₂³	1	1	yes	characteristic
257	C₂×#13083553	C₂³	1	1	yes	characteristic
258	C₂×#13083553	C₂³	1	1	yes	characteristic
259	C₂×#13083553	C₂³	1	1	yes	characteristic
260	C₂×#13083553	C₂³	1	1	yes	characteristic
261	C₂×#13083553	C₂³	1	1	yes	characteristic
262	C₂×#13083553	C₂³	1	1	yes	characteristic
263	C₂×#13083553	C₂³	1	1	yes	characteristic
264	C₂×#13083553	C₂³	1	1	yes	characteristic
265	C₂×#13083553	C₂³	1	1	yes	characteristic
266	C₂×#13083553	C₂³	1	1	yes	characteristic
267	C₂×#13083553	C₂³	1	1	yes	characteristic
268	C₂×#13083553	C₂³	1	1	yes	characteristic
269	C₂×#13083553	C₂³	1	1	yes	characteristic
270	C₂×#13083553	C₂³	1	1	yes	characteristic
271	C₄⋊C₄×D₈₉	—	2	4	no	—
272	C₄⋊C₄×D₈₉	—	2	4	no	—
273	C₄⋊C₄×D₈₉	—	2	4	no	—
274	C₂×#13083551	C₂³	1	1	yes	characteristic
275	C₂×#13083551	C₂³	1	1	yes	characteristic
276	C₂×#13083551	C₂³	1	1	yes	characteristic
277	C₂×#13083551	C₂³	1	1	yes	characteristic
278	C₂×#13083551	C₂³	1	1	yes	characteristic
279	C₂×#13083551	C₂³	1	1	yes	characteristic
280	C₂×#13083551	C₂³	1	1	yes	characteristic
281	C₂×#13083551	C₂³	1	1	yes	characteristic
282	C₂×#13083551	C₂³	1	1	yes	characteristic
283	C₂×#13083551	C₂³	1	1	yes	characteristic
284	C₂×#13083551	C₂³	1	1	yes	characteristic
285	C₂×#13083551	C₂³	1	1	yes	characteristic
286	C₂×#13083551	C₂³	1	1	yes	characteristic
287	C₂×#13083551	C₂³	1	1	yes	characteristic
288	C₂×#13083551	C₂³	1	1	yes	characteristic
289	C₂×#13083551	C₂³	1	1	yes	characteristic
290	C₂×#13083551	C₂³	1	1	yes	characteristic
291	C₂×#13083551	C₂³	1	1	yes	characteristic
292	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
293	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
294	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
295	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
296	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
297	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
298	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
299	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
300	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
301	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
302	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
303	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
304	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
305	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
306	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
307	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
308	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
309	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
310	C₄²×D₈₉	—	2	4	no	—
311	C₄²×D₈₉	—	2	4	no	—
312	C₄²×D₈₉	—	2	4	no	—
313	C₄²×D₈₉	—	2	4	no	—
314	#15667919	C₂³	1	1	yes	characteristic
315	#15667919	C₂³	1	1	yes	characteristic
316	#15667919	C₂³	1	1	yes	characteristic
317	#15667919	C₂³	1	1	yes	characteristic
318	#15667919	C₂³	1	1	yes	characteristic
319	#15667919	C₂³	1	1	yes	characteristic
320	#15667919	C₂³	1	1	yes	characteristic
321	#15667919	C₂³	1	1	yes	characteristic
322	#15667919	C₂³	1	1	yes	characteristic
323	#15667919	C₂³	1	1	yes	characteristic
324	#15667919	C₂³	1	1	yes	characteristic
325	#15667919	C₂³	1	1	yes	characteristic
326	#15667919	C₂³	1	1	yes	characteristic
327	#15667919	C₂³	1	1	yes	characteristic
328	#15667919	C₂³	1	1	yes	characteristic
329	#15667919	C₂³	1	1	yes	characteristic
330	#15667919	C₂³	1	1	yes	characteristic
331	#15667919	C₂³	1	1	yes	characteristic
332	#15667919	C₂³	1	1	yes	characteristic
333	#15667919	C₂³	1	1	yes	characteristic
334	#15667919	C₂³	1	1	yes	characteristic
335	#15667919	C₂³	1	1	yes	characteristic
336	#15667919	C₂³	1	1	yes	characteristic
337	#15667919	C₂³	1	1	yes	characteristic
338	#15667919	C₂³	1	1	yes	characteristic
339	#15667919	C₂³	1	1	yes	characteristic
340	#15667919	C₂³	1	1	yes	characteristic
341	#15667919	C₂³	1	1	yes	characteristic
342	#15667919	C₂³	1	1	yes	characteristic
343	#15667919	C₂³	1	1	yes	characteristic
344	#15667919	C₂³	1	1	yes	characteristic
345	#15667919	C₂³	1	1	yes	characteristic
346	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
347	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
348	C₄×Q₈×C₈₉	—	2	4	no	—
349	C₄×Q₈×C₈₉	—	2	4	no	—
350	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
351	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
352	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
353	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
354	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
355	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
356	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
357	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
358	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
359	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
360	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
361	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
362	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
363	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
364	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
365	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
366	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
367	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
368	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
369	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
370	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
371	#95×C₈₉	C₂³	1	1	yes	characteristic
372	#95×C₈₉	C₂³	1	1	yes	characteristic
373	#95×C₈₉	C₂³	1	1	yes	characteristic
374	#95×C₈₉	C₂³	1	1	yes	characteristic
375	#95×C₈₉	C₂³	1	1	yes	characteristic
376	#95×C₈₉	C₂³	1	1	yes	characteristic
377	#95×C₈₉	C₂³	1	1	yes	characteristic
378	#95×C₈₉	C₂³	1	1	yes	characteristic
379	#95×C₈₉	C₂³	1	1	yes	characteristic
380	#95×C₈₉	C₂³	1	1	yes	characteristic
381	#95×C₈₉	C₂³	1	1	yes	characteristic
382	#95×C₈₉	C₂³	1	1	yes	characteristic
383	C₂³×D₈₉	C₂⁴	1	1	yes	characteristic
384	C₂³×D₈₉	C₂⁴	1	1	yes	characteristic
385	C₂×Dic₁₇₈	—	2	2	no	—
386	C₂×Dic₁₇₈	—	2	2	no	—
387	C₂×Dic₁₇₈	—	2	2	no	—
388	C₂×Dic₁₇₈	—	2	2	no	—
389	C₂×Dic₁₇₈	—	2	2	no	—
390	C₂×Dic₁₇₈	—	2	2	no	—
391	C₂×Dic₁₇₈	—	2	2	no	—
392	C₂×Dic₁₇₈	—	2	2	no	—
393	C₂×Dic₁₇₈	—	2	2	no	—
394	C₂×Dic₁₇₈	—	2	2	no	—
395	C₂×Dic₁₇₈	—	2	2	no	—
396	C₂×Dic₁₇₈	—	2	2	no	—
397	C₂×Dic₁₇₈	—	4	1	no	—
398	C₂×Dic₁₇₈	C₂×D₄	1	4	yes	—
399	C₂×Dic₁₇₈	#41	1	4	yes	—
400	Q₈×D₈₉	—	2	32	no	—
401	C₂×D₃₅₆	—	2	2	no	—
402	C₂×D₃₅₆	—	2	2	no	—
403	C₂×D₃₅₆	C₂×Q₈	1	4	yes	—
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	—	2	2	no	—
431	C₂×C₄×D₈₉	—	2	2	no	—
432	C₂×C₄×D₈₉	—	2	2	no	—
433	C₂×C₄×D₈₉	—	2	2	no	—
434	C₂×C₄×D₈₉	—	2	2	no	—
435	C₂×C₄×D₈₉	—	2	2	no	—
436	C₂×C₄×D₈₉	—	2	2	no	—
437	C₂×C₄×D₈₉	—	2	2	no	—
438	C₂×C₄×D₈₉	—	2	2	no	—
439	C₂×C₄×D₈₉	—	2	2	no	—
440	C₂×C₄×D₈₉	—	2	2	no	—
441	C₂×C₄×D₈₉	—	4	1	no	—
442	C₂×C₄×D₈₉	—	4	1	no	—
443	C₂×C₄×D₈₉	—	4	1	no	—
444	C₂×C₄×D₈₉	—	4	1	no	—
445	C₂×C₄×D₈₉	C₂×Q₈	1	4	yes	—
446	C₂×C₄×D₈₉	C₂×Q₈	1	4	yes	complemented
447	C₂×C₄×D₈₉	#41	1	4	yes	—
448	C₄⋊Dic₈₉	—	2	2	no	—
449	C₄⋊Dic₈₉	—	2	2	no	—
450	C₄⋊Dic₈₉	—	2	2	no	—
451	C₄⋊Dic₈₉	—	2	2	no	—
452	C₄⋊Dic₈₉	—	2	2	no	—
453	C₄⋊Dic₈₉	—	2	2	no	—
454	C₄⋊Dic₈₉	—	4	1	no	—
455	C₄⋊Dic₈₉	—	4	1	no	—
456	C₄⋊Dic₈₉	C₂×D₄	1	4	yes	—
457	C₄⋊Dic₈₉	C₂×Q₈	1	4	yes	complemented
458	#13083553	—	2	2	no	—
459	#13083553	—	2	2	no	—
460	#13083553	—	2	2	no	—
461	#13083553	—	2	2	no	—
462	#13083553	—	2	2	no	—
463	#13083553	—	2	2	no	—
464	#13083553	—	2	2	no	—
465	#13083553	—	2	2	no	—
466	#13083553	—	2	2	no	—
467	#13083553	—	2	2	no	—
468	#13083553	—	2	2	no	—
469	#13083553	—	2	2	no	—
470	#13083553	—	2	2	no	—
471	#13083553	—	2	2	no	—
472	#13083553	—	2	2	no	—
473	#13083553	—	2	2	no	—
474	#13083553	—	2	2	no	—
475	#13083553	—	2	2	no	—
476	#13083553	—	2	2	no	—
477	#13083553	—	2	2	no	—
478	#13083553	—	2	2	no	—
479	#13083553	—	2	2	no	—
480	#13083553	—	4	1	no	—
481	#13083553	—	4	1	no	—
482	#13083553	C₂×D₄	1	4	yes	—
483	#13083553	C₂×D₄	1	4	yes	—
484	#13083551	—	2	2	no	—
485	#13083551	—	2	2	no	—
486	#13083551	—	2	2	no	—
487	#13083551	—	2	2	no	—
488	#13083551	—	2	2	no	—
489	#13083551	—	2	2	no	—
490	#13083551	—	2	2	no	—
491	#13083551	—	2	2	no	—
492	#13083551	—	2	2	no	—
493	#13083551	—	2	2	no	—
494	#13083551	—	2	2	no	—
495	#13083551	—	2	2	no	—
496	#13083551	—	2	2	no	—
497	#13083551	—	4	1	no	—
498	#13083551	—	4	1	no	—
499	#13083551	C₂×Q₈	1	4	yes	—
500	#13083551	C₂×Q₈	1	4	yes	complemented
501	#13083551	#41	1	4	yes	—
502	C₄×Dic₈₉	—	2	2	no	—
503	C₄×Dic₈₉	—	2	2	no	—
504	C₄×Dic₈₉	—	2	2	no	—
505	C₄×Dic₈₉	—	2	2	no	—
506	C₄×Dic₈₉	—	2	2	no	—
507	C₄×Dic₈₉	—	2	2	no	—
508	C₄×Dic₈₉	—	2	2	no	—
509	C₄×Dic₈₉	—	2	2	no	—
510	C₄×Dic₈₉	—	2	2	no	—
511	C₄×Dic₈₉	—	2	2	no	—
512	C₄×Dic₈₉	—	2	2	no	—
513	C₄×Dic₈₉	—	2	2	no	—
514	C₄×Dic₈₉	—	2	2	no	—
515	C₄×Dic₈₉	—	2	2	no	—
516	C₄×Dic₈₉	—	2	2	no	—
517	C₄×Dic₈₉	—	4	1	no	—
518	C₄×Dic₈₉	C₂×D₄	1	4	yes	—
519	C₄×Dic₈₉	C₂×D₄	1	4	yes	—
520	C₂×Q₈×C₈₉	—	2	2	no	—
521	C₂×Q₈×C₈₉	—	2	2	no	—
522	C₂×Q₈×C₈₉	—	2	2	no	—
523	C₂×Q₈×C₈₉	—	2	2	no	—
524	C₂×Q₈×C₈₉	—	2	2	no	—
525	C₂×Q₈×C₈₉	—	4	1	no	—
526	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
527	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
528	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
529	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
530	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
531	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
532	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
533	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
534	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
535	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
536	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
537	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
538	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
539	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
540	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
541	C₄⋊C₄×C₈₉	—	2	2	no	—
542	C₄⋊C₄×C₈₉	—	2	2	no	—
543	C₄⋊C₄×C₈₉	—	2	2	no	—
544	C₄⋊C₄×C₈₉	—	2	2	no	—
545	C₄⋊C₄×C₈₉	—	2	2	no	—
546	C₄⋊C₄×C₈₉	—	2	2	no	—
547	C₄⋊C₄×C₈₉	—	2	2	no	—
548	C₄⋊C₄×C₈₉	—	2	2	no	—
549	C₄⋊C₄×C₈₉	—	2	2	no	—
550	C₄⋊C₄×C₈₉	—	2	2	no	—
551	C₄⋊C₄×C₈₉	—	2	2	no	—
552	C₄⋊C₄×C₈₉	—	2	2	no	—
553	C₄⋊C₄×C₈₉	—	4	1	no	—
554	C₄⋊C₄×C₈₉	—	4	1	no	—
555	C₄²×C₈₉	—	2	2	no	—
556	C₄²×C₈₉	—	2	2	no	—
557	C₄²×C₈₉	—	2	2	no	—
558	C₄²×C₈₉	—	2	2	no	—
559	C₄²×C₈₉	—	2	2	no	—
560	C₄²×C₈₉	C₂×D₄	1	4	yes	—
561	C₄²×C₈₉	C₂×Q₈	1	4	yes	complemented
562	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
563	C₂²×D₈₉	—	2	1	no	—
564	C₂²×D₈₉	—	2	1	no	—
565	C₂²×D₈₉	—	2	1	no	—
566	C₂²×D₈₉	—	2	1	no	—
567	C₂²×D₈₉	—	2	1	no	—
568	C₂²×D₈₉	—	2	1	no	—
569	C₂²×D₈₉	—	2	1	no	—
570	C₂²×D₈₉	—	2	1	no	—
571	C₂²×D₈₉	—	2	1	no	—
572	C₂²×D₈₉	—	2	1	no	—
573	C₂²×D₈₉	C₂²×Q₈	1	2	yes	—
574	C₂²×D₈₉	C₂²×Q₈	1	2	yes	—
575	C₂²×D₈₉	C₂×#41	1	2	yes	—
576	C₂²×D₈₉	C₂×#41	1	2	yes	—
577	Q₈×C₈₉	—	2	8	no	—
578	Q₈×C₈₉	—	4	4	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	—	2	1	no	—
611	C₂×C₄×C₈₉	—	2	1	no	—
612	C₂×C₄×C₈₉	—	2	1	no	—
613	C₂×C₄×C₈₉	—	2	1	no	—
614	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
615	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
616	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
617	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
618	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
619	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
620	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
621	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
622	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
623	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
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	—	2	1	no	—
655	C₂×Dic₈₉	—	2	1	no	—
656	C₂×Dic₈₉	C₂²×D₄	1	2	yes	—
657	C₂×Dic₈₉	C₂²×D₄	1	2	yes	—
658	C₂×Dic₈₉	C₂²×D₄	1	2	yes	—
659	C₂×Dic₈₉	C₂²×D₄	1	2	yes	—
660	C₂×Dic₈₉	C₂²×Q₈	1	2	yes	—
661	C₂×Dic₈₉	C₂²×Q₈	1	2	yes	—
662	C₂×Dic₈₉	C₂×#41	1	2	yes	—
663	C₂×Dic₈₉	C₂×#41	1	2	yes	—
664	C₂×Dic₈₉	C₂×#41	1	2	yes	—
665	C₂×Dic₈₉	C₂×#41	1	2	yes	—
666	D₃₅₆	—	2	8	no	—
667	C₄×D₈₉	—	2	8	no	—
668	C₄×D₈₉	—	2	8	no	—
669	C₄×D₈₉	—	2	8	no	—
670	C₄×D₈₉	—	2	8	no	—
671	C₄×D₈₉	—	2	8	no	—
672	C₄×D₈₉	—	4	4	no	—
673	C₄×D₈₉	—	4	4	no	—
674	C₄×D₈₉	—	4	4	no	—
675	C₄×D₈₉	—	4	4	no	—
676	C₄×D₈₉	—	4	4	no	—
677	Dic₁₇₈	—	2	8	no	—
678	Dic₁₇₈	—	2	8	no	—
679	Dic₁₇₈	—	2	8	no	—
680	Dic₁₇₈	—	4	4	no	—
681	Dic₁₇₈	—	4	4	no	—
682	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
683	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
684	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
685	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
686	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
687	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
688	C₂²×C₈₉	#585	1	1	yes	characteristic
689	C₂×D₈₉	—	2	2	no	—
690	C₂×D₈₉	—	2	2	no	—
691	C₂×D₈₉	—	2	2	no	—
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	—	4	1	no	—
699	C₂×D₈₉	—	4	1	no	—
700	C₂×D₈₉	—	4	1	no	—
701	C₂×D₈₉	—	4	1	no	—
702	C₂×D₈₉	#533	1	4	yes	complemented
703	C₄×C₈₉	—	2	2	no	—
704	C₄×C₈₉	—	2	2	no	—
705	C₄×C₈₉	—	2	2	no	—
706	C₄×C₈₉	—	2	2	no	—
707	C₄×C₈₉	—	2	2	no	—
708	C₄×C₈₉	—	2	2	no	—
709	C₄×C₈₉	—	2	2	no	—
710	C₄×C₈₉	—	4	1	no	—
711	C₄×C₈₉	—	4	1	no	—
712	C₄×C₈₉	—	4	1	no	—
713	C₄×C₈₉	—	4	1	no	—
714	C₄×C₈₉	—	4	1	no	—
715	C₄×C₈₉	—	4	1	no	—
716	C₄×C₈₉	—	4	1	no	—
717	C₄×C₈₉	D₄×Q₈	1	4	yes	—
718	Dic₈₉	—	2	2	no	—
719	Dic₈₉	—	2	2	no	—
720	Dic₈₉	—	2	2	no	—
721	Dic₈₉	—	2	2	no	—
722	Dic₈₉	—	2	2	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	#525	1	4	yes	—
732	#34691	—	89	1	no	maximal, Sylow
733	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
734	C₂×C₈₉	C₂×#533	1	1	yes	characteristic
735	C₂×C₈₉	#3461	1	1	yes	characteristic
736	C₂×C₈₉	C₂×D₄×Q₈	1	1	yes	characteristic
737	C₂×C₈₉	D₄×#41	1	1	yes	characteristic
738	C₂×C₈₉	Q₈×#41	1	1	yes	characteristic
739	C₂×C₈₉	#3482	1	1	yes	characteristic
740	D₈₉	—	2	4	no	—
741	D₈₉	—	4	2	no	—
742	C₂×#533	—	89	1	no	—
743	C₂²×C₄×Q₈	—	89	1	no	—
744	#2473	—	89	1	no	—
745	#2473	—	89	1	no	—
746	#2465	—	89	1	no	—
747	#2465	—	89	1	no	—
748	#2462	—	89	1	no	—
749	#2462	—	89	1	no	—
750	#2451	—	89	1	no	—
751	#2449	—	89	1	no	—
752	#2449	—	89	1	no	—
753	#2446	—	89	1	no	—
754	#2440	—	89	1	no	—
755	#2434	—	89	1	no	—
756	#2429	—	89	1	no	—
757	#2423	—	89	1	no	—
758	#2417	—	89	1	no	—
759	#2409	—	89	1	no	—
760	#2399	—	89	1	no	—
761	#2399	D₈₉	1	1	yes	characteristic, complemented
762	#2396	—	89	1	no	—
763	#2396	—	89	1	no	—
764	C₄×C₄⋊Q₈	—	89	1	no	—
765	C₄×C₂²⋊Q₈	—	89	1	no	—
766	C₄×C₂²⋊Q₈	—	89	1	no	—
767	C₄×C₂²⋊Q₈	—	89	1	no	—
768	C₄×C₂²⋊Q₈	—	89	1	no	—
769	#2295	—	89	1	no	—
770	#2290	—	89	1	no	—
771	#2290	—	89	1	no	—
772	C₄²×D₄	—	89	1	no	—
773	C₈₉	#34691	1	1	yes	characteristic, complemented, Sylow
774	C₂³×Q₈	—	89	1	no	—
775	#533	—	178	8	no	—
776	C₂×C₄⋊Q₈	—	89	1	no	—
777	C₂×C₄⋊Q₈	—	89	1	no	—
778	C₂×C₄⋊Q₈	—	89	1	no	—
779	C₂×#125	—	89	1	no	—
780	C₂×#125	—	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×C₂²⋊Q₈	—	89	1	no	—
786	C₂×C₂²⋊Q₈	—	89	1	no	—
787	C₂×C₂²⋊Q₈	—	89	1	no	—
788	C₂×C₂²⋊Q₈	—	89	1	no	—
789	C₂×C₄×Q₈	—	89	1	no	—
790	C₂×C₄×Q₈	—	89	1	no	—
791	C₂×C₄×Q₈	—	89	1	no	—
792	C₂×C₄×Q₈	—	89	1	no	—
793	C₂×C₄×Q₈	—	89	1	no	—
794	C₂×C₄×Q₈	—	89	1	no	—
795	C₂×C₄×Q₈	—	89	1	no	—
796	C₂×C₄×Q₈	—	89	1	no	—
797	C₂×C₄×Q₈	—	89	1	no	—
798	C₂×C₄×Q₈	—	178	8	no	—
799	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
800	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
801	C₂×C₄×D₄	—	89	1	no	—
802	C₂×C₄×D₄	—	89	1	no	—
803	C₂×C₄×D₄	—	89	1	no	—
804	C₂×#117	—	89	1	no	—
805	C₂×#117	—	89	1	no	—
806	C₂²×C₄⋊C₄	—	89	1	no	—
807	C₂²×C₄⋊C₄	—	89	1	no	—
808	C₂²×C₄⋊C₄	—	89	1	no	—
809	C₂²×C₄²	—	89	1	no	—
810	C₂²×C₄²	—	89	1	no	—
811	C₂²×C₄²	—	89	1	no	—
812	C₂²×C₄²	—	89	1	no	—
813	#400	—	89	1	no	—
814	#400	—	89	1	no	—
815	#399	—	89	1	no	—
816	#399	—	89	1	no	—
817	#398	—	89	1	no	—
818	#398	—	89	1	no	—
819	#398	—	89	1	no	—
820	#398	—	89	1	no	—
821	#398	—	89	1	no	—
822	#398	—	89	1	no	—
823	#398	—	89	1	no	—
824	#398	—	89	1	no	—
825	#398	C₂×D₈₉	1	1	yes	characteristic
826	#398	C₂×D₈₉	1	1	yes	characteristic
827	#398	C₂×D₈₉	1	1	yes	characteristic
828	#398	C₂×D₈₉	1	1	yes	characteristic
829	#396	—	89	1	no	—
830	#396	—	89	1	no	—
831	#396	—	89	1	no	—
832	#396	—	89	1	no	—
833	#395	—	89	1	no	—
834	#395	—	89	1	no	—
835	#395	—	89	1	no	—
836	#395	—	89	1	no	—
837	#395	—	89	1	no	—
838	#395	—	89	1	no	—
839	#395	C₂×D₈₉	1	1	yes	characteristic
840	#395	C₂×D₈₉	1	1	yes	characteristic
841	#395	C₂×D₈₉	1	1	yes	characteristic
842	#395	C₂×D₈₉	1	1	yes	characteristic
843	#393	—	89	1	no	—
844	#393	—	89	1	no	—
845	#391	—	89	1	no	—
846	#391	—	89	1	no	—
847	#391	—	89	1	no	—
848	#391	—	89	1	no	—
849	#391	—	89	1	no	—
850	#391	—	89	1	no	—
851	#391	—	89	1	no	—
852	#391	—	89	1	no	—
853	#389	—	89	1	no	—
854	#389	—	89	1	no	—
855	#389	—	89	1	no	—
856	#389	—	89	1	no	—
857	#389	—	89	1	no	—
858	#389	—	89	1	no	—
859	#389	—	89	1	no	—
860	#389	—	89	1	no	—
861	#389	—	89	1	no	—
862	#389	—	89	1	no	—
863	#388	—	89	1	no	—
864	#388	—	89	1	no	—
865	#388	—	89	1	no	—
866	#388	—	89	1	no	—
867	#387	—	89	1	no	—
868	#387	—	89	1	no	—
869	#387	—	89	1	no	—
870	#387	—	89	1	no	—
871	#387	—	89	1	no	—
872	#387	—	89	1	no	—
873	#387	—	89	1	no	—
874	#387	—	89	1	no	—
875	#387	—	89	1	no	—
876	#387	—	89	1	no	—
877	#387	—	89	1	no	—
878	#387	—	89	1	no	—
879	#387	—	89	1	no	—
880	#387	—	89	1	no	—
881	#387	—	89	1	no	—
882	#387	—	89	1	no	—
883	#386	—	89	1	no	—
884	#386	—	89	1	no	—
885	#386	—	89	1	no	—
886	#386	—	89	1	no	—
887	#385	—	89	1	no	—
888	#385	—	89	1	no	—
889	#385	—	89	1	no	—
890	#385	—	89	1	no	—
891	#385	—	89	1	no	—
892	#385	—	89	1	no	—
893	#385	—	89	1	no	—
894	#385	—	89	1	no	—
895	#385	—	89	1	no	—
896	#385	—	89	1	no	—
897	#385	—	89	1	no	—
898	#385	—	89	1	no	—
899	#384	—	89	1	no	—
900	#380	—	89	1	no	—
901	#380	—	89	1	no	—
902	#380	—	89	1	no	—
903	#380	—	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×C₄⋊C₄	—	89	1	no	—
908	C₄×C₄⋊C₄	—	89	1	no	—
909	C₄×C₄⋊C₄	—	89	1	no	—
910	C₄×C₄⋊C₄	—	89	1	no	—
911	C₄×C₄⋊C₄	—	89	1	no	—
912	C₄×C₄⋊C₄	—	89	1	no	—
913	C₄×C₄⋊C₄	—	89	1	no	—
914	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
915	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
916	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
917	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
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	—	89	1	no	—
928	#376	—	89	1	no	—
929	#376	C₂×D₈₉	1	1	yes	characteristic
930	C₄³	—	89	1	no	—
931	C₂²×Q₈	—	89	1	no	—
932	C₂²×Q₈	—	89	1	no	—
933	C₂²×Q₈	—	89	1	no	—
934	C₂²×Q₈	—	89	1	no	—
935	C₂²×Q₈	—	89	1	no	—
936	C₂²×Q₈	—	178	4	no	—
937	C₂²×Q₈	—	178	4	no	—
938	C₂²×Q₈	—	178	4	no	—
939	C₂²×Q₈	C₂²×D₈₉	1	1	yes	characteristic
940	C₂²×Q₈	C₂²×D₈₉	1	1	yes	characteristic
941	C₂²×D₄	—	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	C₄⋊Q₈	—	178	4	no	—
953	C₄⋊Q₈	—	178	4	no	—
954	C₄⋊Q₈	—	178	4	no	—
955	#125	—	178	4	no	—
956	#125	—	178	4	no	—
957	C₂²⋊Q₈	—	178	4	no	—
958	C₂²⋊Q₈	—	178	4	no	—
959	C₂²⋊Q₈	—	178	4	no	—
960	C₂²⋊Q₈	—	178	4	no	—
961	C₂²⋊Q₈	—	178	4	no	—
962	C₂²⋊Q₈	—	178	4	no	—
963	C₂²⋊Q₈	—	178	4	no	—
964	C₂²⋊Q₈	—	178	4	no	—
965	C₄×Q₈	—	2	4	no	—
966	C₄×Q₈	—	2	4	no	—
967	C₄×Q₈	—	89	8	no	—
968	C₄×Q₈	—	178	4	no	—
969	C₄×Q₈	—	178	4	no	—
970	C₄×Q₈	—	178	4	no	—
971	C₄×Q₈	—	178	4	no	—
972	C₄×Q₈	—	178	4	no	—
973	C₄×Q₈	—	178	4	no	—
974	C₄×Q₈	—	178	4	no	—
975	C₄×Q₈	—	178	4	no	—
976	C₄×D₄	—	89	8	no	—
977	C₄×D₄	—	178	4	no	—
978	C₄×D₄	—	178	4	no	—
979	#117	—	178	4	no	—
980	#117	—	178	4	no	—
981	C₂×C₄⋊C₄	—	89	1	no	—
982	C₂×C₄⋊C₄	—	89	1	no	—
983	C₂×C₄⋊C₄	—	89	1	no	—
984	C₂×C₄⋊C₄	—	89	1	no	—
985	C₂×C₄⋊C₄	—	89	1	no	—
986	C₂×C₄⋊C₄	—	89	1	no	—
987	C₂×C₄⋊C₄	—	89	1	no	—
988	C₂×C₄⋊C₄	—	89	1	no	—
989	C₂×C₄⋊C₄	—	89	1	no	—
990	C₂×C₄⋊C₄	—	89	1	no	—
991	C₂×C₄⋊C₄	—	89	1	no	—
992	C₂×C₄⋊C₄	—	89	1	no	—
993	C₂×C₄⋊C₄	—	89	1	no	—
994	C₂×C₄⋊C₄	—	89	1	no	—
995	C₂×C₄⋊C₄	—	89	1	no	—
996	C₂×C₄⋊C₄	—	89	1	no	—
997	C₂×C₄⋊C₄	—	89	1	no	—
998	C₂×C₄⋊C₄	—	89	1	no	—
999	C₂×C₄⋊C₄	—	89	1	no	—
1000	C₂×C₄⋊C₄	—	89	1	no	—
1001	C₂×C₄⋊C₄	—	89	1	no	—
1002	C₂×C₄⋊C₄	—	89	1	no	—
1003	C₂×C₄⋊C₄	—	89	1	no	—
1004	C₂×C₄⋊C₄	—	89	1	no	—
1005	C₂×C₄⋊C₄	—	89	1	no	—
1006	C₂×C₄⋊C₄	—	89	1	no	—
1007	C₂×C₄⋊C₄	—	89	1	no	—
1008	C₂×C₄⋊C₄	—	89	1	no	—
1009	C₂×C₄⋊C₄	—	89	1	no	—
1010	C₂×C₄⋊C₄	—	89	1	no	—
1011	C₂×C₄⋊C₄	—	89	1	no	—
1012	C₂×C₄⋊C₄	—	89	1	no	—
1013	C₂×C₄⋊C₄	—	89	1	no	—
1014	C₂×C₄⋊C₄	—	89	1	no	—
1015	C₂×C₄⋊C₄	—	89	1	no	—
1016	C₂×C₄⋊C₄	—	89	1	no	—
1017	C₂×C₄⋊C₄	—	178	4	no	—
1018	C₂×C₄⋊C₄	—	178	4	no	—
1019	C₂×C₄⋊C₄	—	178	4	no	—
1020	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1021	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1022	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1023	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1024	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1025	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1026	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1027	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1028	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1029	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1030	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1031	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1032	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1033	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1034	C₂×C₂²⋊C₄	—	89	1	no	—
1035	C₂×C₂²⋊C₄	—	89	1	no	—
1036	C₂×C₂²⋊C₄	—	89	1	no	—
1037	C₂×C₂²⋊C₄	—	89	1	no	—
1038	C₂×C₂²⋊C₄	—	89	1	no	—
1039	C₂×C₂²⋊C₄	—	89	1	no	—
1040	C₂×C₂²⋊C₄	—	89	1	no	—
1041	C₂×C₂²⋊C₄	—	89	1	no	—
1042	C₂×C₂²⋊C₄	—	89	1	no	—
1043	C₂×C₂²⋊C₄	—	89	1	no	—
1044	C₂×C₂²⋊C₄	—	89	1	no	—
1045	C₂×C₂²⋊C₄	—	89	1	no	—
1046	C₂×C₂²⋊C₄	—	89	1	no	—
1047	C₂×C₂²⋊C₄	—	89	1	no	—
1048	C₂×C₂²⋊C₄	—	89	1	no	—
1049	C₂×C₂²⋊C₄	—	89	1	no	—
1050	C₂×C₂²⋊C₄	—	89	1	no	—
1051	C₂×C₂²⋊C₄	—	89	1	no	—
1052	C₂×C₄²	—	89	1	no	—
1053	C₂×C₄²	—	89	1	no	—
1054	C₂×C₄²	—	89	1	no	—
1055	C₂×C₄²	—	89	1	no	—
1056	C₂×C₄²	—	89	1	no	—
1057	C₂×C₄²	—	89	1	no	—
1058	C₂×C₄²	—	89	1	no	—
1059	C₂×C₄²	—	89	1	no	—
1060	C₂×C₄²	—	89	1	no	—
1061	C₂×C₄²	—	89	1	no	—
1062	C₂×C₄²	—	89	1	no	—
1063	C₂×C₄²	—	89	1	no	—
1064	C₂×C₄²	—	89	1	no	—
1065	C₂×C₄²	—	89	1	no	—
1066	C₂×C₄²	—	89	1	no	—
1067	C₂×C₄²	—	89	1	no	—
1068	C₂×C₄²	—	89	1	no	—
1069	C₂×C₄²	—	89	1	no	—
1070	C₂×C₄²	—	178	4	no	—
1071	C₂×C₄²	—	178	4	no	—
1072	C₂×C₄²	—	178	4	no	—
1073	C₂×C₄²	—	178	4	no	—
1074	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1075	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1076	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1077	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1078	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1079	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1080	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
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	—	89	1	no	—
1101	#95	—	89	1	no	—
1102	#95	—	89	1	no	—
1103	#95	—	89	1	no	—
1104	#95	—	89	1	no	—
1105	#95	—	89	1	no	—
1106	#95	—	89	1	no	—
1107	#95	—	89	1	no	—
1108	#95	—	89	1	no	—
1109	#95	—	89	1	no	—
1110	#95	—	89	1	no	—
1111	#95	—	89	1	no	—
1112	#95	—	89	1	no	—
1113	#95	C₂²×D₈₉	1	1	yes	characteristic
1114	#95	C₂²×D₈₉	1	1	yes	characteristic
1115	#95	C₂²×D₈₉	1	1	yes	characteristic
1116	#95	C₂²×D₈₉	1	1	yes	characteristic
1117	#95	C₂²×D₈₉	1	1	yes	characteristic
1118	#95	C₂²×D₈₉	1	1	yes	characteristic
1119	#95	C₂²×D₈₉	1	1	yes	characteristic
1120	#95	C₂²×D₈₉	1	1	yes	characteristic
1121	#95	C₂²×D₈₉	1	1	yes	characteristic
1122	#95	C₂²×D₈₉	1	1	yes	characteristic
1123	#95	C₂²×D₈₉	1	1	yes	characteristic
1124	#95	C₂²×D₈₉	1	1	yes	characteristic
1125	C₂⁴	—	89	1	no	—
1126	C₂⁴	—	89	1	no	—
1127	C₂×Q₈	—	2	2	no	—
1128	C₂×Q₈	—	2	2	no	—
1129	C₂×Q₈	—	2	2	no	—
1130	C₂×Q₈	—	2	2	no	—
1131	C₂×Q₈	—	2	2	no	—
1132	C₂×Q₈	—	4	1	no	—
1133	C₂×Q₈	—	89	4	no	—
1134	C₂×Q₈	—	89	4	no	—
1135	C₂×Q₈	—	356	1	no	—
1136	C₂×Q₈	—	178	2	no	—
1137	C₂×Q₈	—	178	2	no	—
1138	C₂×Q₈	—	178	2	no	—
1139	C₂×Q₈	—	178	2	no	—
1140	C₂×Q₈	—	178	2	no	—
1141	C₂×Q₈	—	178	2	no	—
1142	C₂×Q₈	—	178	2	no	—
1143	C₂×Q₈	—	178	2	no	—
1144	C₂×Q₈	—	178	2	no	—
1145	C₂×Q₈	—	178	2	no	—
1146	C₂×Q₈	—	178	32	no	—
1147	C₂×Q₈	—	178	2	no	—
1148	C₂×Q₈	—	178	2	no	—
1149	C₂×D₄	—	89	4	no	—
1150	C₂×D₄	—	178	2	no	—
1151	C₂×D₄	—	178	2	no	—
1152	C₂²×C₄	—	89	1	no	—
1153	C₂²×C₄	—	89	1	no	—
1154	C₂²×C₄	—	89	1	no	—
1155	C₂²×C₄	—	89	1	no	—
1156	C₂²×C₄	—	89	1	no	—
1157	C₂²×C₄	—	89	1	no	—
1158	C₂²×C₄	—	89	1	no	—
1159	C₂²×C₄	—	89	1	no	—
1160	C₂²×C₄	—	89	4	no	—
1161	C₂²×C₄	—	89	4	no	—
1162	C₂²×C₄	—	89	4	no	—
1163	C₂²×C₄	—	89	1	no	—
1164	C₂²×C₄	—	89	1	no	—
1165	C₂²×C₄	—	89	1	no	—
1166	C₂²×C₄	—	89	1	no	—
1167	C₂²×C₄	—	89	1	no	—
1168	C₂²×C₄	—	89	1	no	—
1169	C₂²×C₄	—	356	1	no	—
1170	C₂²×C₄	—	356	1	no	—
1171	C₂²×C₄	—	356	1	no	—
1172	C₂²×C₄	—	356	1	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	—	178	2	no	—
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	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1209	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1210	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1211	C₄⋊C₄	—	2	2	no	—
1212	C₄⋊C₄	—	2	2	no	—
1213	C₄⋊C₄	—	2	2	no	—
1214	C₄⋊C₄	—	2	2	no	—
1215	C₄⋊C₄	—	2	2	no	—
1216	C₄⋊C₄	—	2	2	no	—
1217	C₄⋊C₄	—	2	2	no	—
1218	C₄⋊C₄	—	2	2	no	—
1219	C₄⋊C₄	—	2	2	no	—
1220	C₄⋊C₄	—	2	2	no	—
1221	C₄⋊C₄	—	2	2	no	—
1222	C₄⋊C₄	—	2	2	no	—
1223	C₄⋊C₄	—	4	1	no	—
1224	C₄⋊C₄	—	4	1	no	—
1225	C₄⋊C₄	—	89	4	no	—
1226	C₄⋊C₄	—	89	4	no	—
1227	C₄⋊C₄	—	89	4	no	—
1228	C₄⋊C₄	—	89	4	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	C₄⋊C₄	—	178	2	no	—
1235	C₄⋊C₄	—	178	2	no	—
1236	C₄⋊C₄	—	178	2	no	—
1237	C₄⋊C₄	—	178	2	no	—
1238	C₄⋊C₄	—	178	2	no	—
1239	C₄⋊C₄	—	178	2	no	—
1240	C₄⋊C₄	—	178	2	no	—
1241	C₄⋊C₄	—	178	2	no	—
1242	C₄⋊C₄	—	178	2	no	—
1243	C₄⋊C₄	—	178	2	no	—
1244	C₄⋊C₄	—	178	2	no	—
1245	C₄⋊C₄	—	178	2	no	—
1246	C₄⋊C₄	—	178	2	no	—
1247	C₄⋊C₄	—	178	2	no	—
1248	C₄⋊C₄	—	178	2	no	—
1249	C₄⋊C₄	—	178	2	no	—
1250	C₄⋊C₄	—	178	2	no	—
1251	C₄⋊C₄	—	178	2	no	—
1252	C₄⋊C₄	—	178	2	no	—
1253	C₄⋊C₄	—	178	2	no	—
1254	C₄⋊C₄	—	178	2	no	—
1255	C₄⋊C₄	—	178	2	no	—
1256	C₄⋊C₄	—	178	2	no	—
1257	C₄⋊C₄	—	178	2	no	—
1258	C₄⋊C₄	—	178	2	no	—
1259	C₄⋊C₄	—	178	2	no	—
1260	C₄⋊C₄	—	178	2	no	—
1261	C₂²⋊C₄	—	89	4	no	—
1262	C₂²⋊C₄	—	89	4	no	—
1263	C₂²⋊C₄	—	89	4	no	—
1264	C₂²⋊C₄	—	356	1	no	—
1265	C₂²⋊C₄	—	356	1	no	—
1266	C₂²⋊C₄	—	178	2	no	—
1267	C₂²⋊C₄	—	178	2	no	—
1268	C₂²⋊C₄	—	178	2	no	—
1269	C₂²⋊C₄	—	178	2	no	—
1270	C₂²⋊C₄	—	178	2	no	—
1271	C₂²⋊C₄	—	178	2	no	—
1272	C₂²⋊C₄	—	178	2	no	—
1273	C₂²⋊C₄	—	178	2	no	—
1274	C₂²⋊C₄	—	178	2	no	—
1275	C₂²⋊C₄	—	178	2	no	—
1276	C₂²⋊C₄	—	178	2	no	—
1277	C₂²⋊C₄	—	178	2	no	—
1278	C₂²⋊C₄	—	178	2	no	—
1279	C₄²	—	2	2	no	—
1280	C₄²	—	2	2	no	—
1281	C₄²	—	2	2	no	—
1282	C₄²	—	2	2	no	—
1283	C₄²	—	2	2	no	—
1284	C₄²	—	89	4	no	—
1285	C₄²	—	89	4	no	—
1286	C₄²	—	356	1	no	—
1287	C₄²	—	178	2	no	—
1288	C₄²	—	178	2	no	—
1289	C₄²	—	178	2	no	—
1290	C₄²	—	178	2	no	—
1291	C₄²	—	178	2	no	—
1292	C₄²	—	178	2	no	—
1293	C₄²	—	178	2	no	—
1294	C₄²	—	178	2	no	—
1295	C₄²	—	178	2	no	—
1296	C₄²	—	178	2	no	—
1297	C₄²	—	178	2	no	—
1298	C₄²	—	178	2	no	—
1299	C₄²	—	178	2	no	—
1300	C₄²	—	178	2	no	—
1301	C₄²	—	178	2	no	—
1302	C₄²	D₄×D₈₉	1	4	yes	—
1303	C₄²	Q₈×D₈₉	1	4	yes	complemented
1304	C₂³	—	89	2	no	—
1305	C₂³	—	89	2	no	—
1306	C₂³	—	89	2	no	—
1307	C₂³	—	89	2	no	—
1308	C₂³	—	178	1	no	—
1309	C₂³	—	178	1	no	—
1310	C₂³	—	178	1	no	—
1311	C₂³	—	178	1	no	—
1312	C₂³	—	178	1	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	C₂⁴×D₈₉	1	1	yes	characteristic
1319	Q₈	—	2	8	no	—
1320	Q₈	—	4	4	no	—
1321	Q₈	—	356	4	no	—
1322	Q₈	—	356	4	no	—
1323	Q₈	—	178	8	no	—
1324	Q₈	—	178	8	no	—
1325	Q₈	—	178	8	no	—
1326	D₄	—	178	8	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	—	89	2	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	—	89	2	no	—
1369	C₂×C₄	—	89	2	no	—
1370	C₂×C₄	—	89	2	no	—
1371	C₂×C₄	—	89	2	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	—	178	8	no	—
1378	C₂×C₄	—	178	8	no	—
1379	C₂×C₄	—	178	8	no	—
1380	C₂×C₄	—	178	1	no	—
1381	C₂×C₄	—	178	1	no	—
1382	C₂×C₄	—	178	1	no	—
1383	C₂×C₄	—	178	1	no	—
1384	C₂×C₄	—	178	1	no	—
1385	C₂×C₄	—	178	1	no	—
1386	C₂×C₄	—	178	1	no	—
1387	C₂×C₄	—	178	1	no	—
1388	C₂×C₄	—	178	1	no	—
1389	C₂×C₄	—	178	1	no	—
1390	C₂×C₄	—	178	1	no	—
1391	C₂×C₄	—	178	1	no	—
1392	C₂×C₄	—	178	1	no	—
1393	C₂×C₄	—	178	1	no	—
1394	C₂×C₄	—	178	1	no	—
1395	C₂×C₄	—	178	1	no	—
1396	C₂×C₄	—	178	1	no	—
1397	C₂×C₄	—	178	1	no	—
1398	C₂×C₄	—	178	1	no	—
1399	C₂×C₄	—	178	1	no	—
1400	C₂×C₄	—	178	1	no	—
1401	C₂×C₄	—	178	1	no	—
1402	C₂×C₄	—	178	1	no	—
1403	C₂×C₄	—	178	1	no	—
1404	C₂×C₄	—	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	8	no	—
1413	C₂×C₄	—	178	8	no	—
1414	C₂×C₄	C₂×D₄×D₈₉	1	2	yes	—
1415	C₂×C₄	C₂×D₄×D₈₉	1	2	yes	—
1416	C₂×C₄	C₂×D₄×D₈₉	1	2	yes	—
1417	C₂×C₄	C₂×Q₈×D₈₉	1	2	yes	—
1418	C₂×C₄	C₂×Q₈×D₈₉	1	2	yes	—
1419	C₂×C₄	C₂×Q₈×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	C₂×C₄	#15668060	1	2	yes	—
1424	C₂²	—	89	4	no	—
1425	C₂²	—	356	1	no	—
1426	C₂²	—	356	1	no	—
1427	C₂²	—	356	1	no	—
1428	C₂²	—	356	1	no	—
1429	C₂²	—	178	2	no	—
1430	C₂²	—	178	2	no	—
1431	C₂²	—	178	2	no	—
1432	C₂²	—	178	2	no	—
1433	C₂²	—	178	2	no	—
1434	C₂²	—	178	2	no	—
1435	C₂²	—	178	2	no	—
1436	C₂²	—	178	2	no	—
1437	C₂²	—	178	2	no	—
1438	C₂²	C₂²×D₄×D₈₉	1	1	yes	characteristic
1439	C₂²	C₂²×Q₈×D₈₉	1	1	yes	characteristic
1440	C₂²	C₂×#41×D₈₉	1	1	yes	characteristic
1441	C₂²	C₂×#41×D₈₉	1	1	yes	characteristic
1442	C₂²	C₂×#41×D₈₉	1	1	yes	characteristic
1443	C₂²	C₂×#15668060	1	1	yes	characteristic
1444	C₂²	#19152434	1	1	yes	characteristic
1445	C₄	—	2	2	no	—
1446	C₄	—	2	2	no	—
1447	C₄	—	2	2	no	—
1448	C₄	—	2	2	no	—
1449	C₄	—	2	2	no	—
1450	C₄	—	2	2	no	—
1451	C₄	—	2	2	no	—
1452	C₄	—	4	1	no	—
1453	C₄	—	4	1	no	—
1454	C₄	—	4	1	no	—
1455	C₄	—	4	1	no	—
1456	C₄	—	4	1	no	—
1457	C₄	—	4	1	no	—
1458	C₄	—	4	1	no	—
1459	C₄	—	89	4	no	—
1460	C₄	—	356	1	no	—
1461	C₄	—	356	1	no	—
1462	C₄	—	356	1	no	—
1463	C₄	—	356	1	no	—
1464	C₄	—	356	1	no	—
1465	C₄	—	356	1	no	—
1466	C₄	—	178	2	no	—
1467	C₄	—	178	2	no	—
1468	C₄	—	178	2	no	—
1469	C₄	—	178	2	no	—
1470	C₄	—	178	2	no	—
1471	C₄	—	178	2	no	—
1472	C₄	—	178	2	no	—
1473	C₄	#19152263	1	4	yes	—
1474	C₂	—	356	2	no	—
1475	C₂	—	178	4	no	—
1476	C₂	#525×D₈₉	1	1	yes	characteristic
1477	C₂	#533×D₈₉	1	1	yes	characteristic
1478	C₂	#26033683	1	1	yes	characteristic
1479	C₂	C₂×#19152263	1	1	yes	characteristic
1480	C₂	#26033735	1	1	yes	characteristic
1481	C₂	#26033830	1	1	yes	characteristic
1482	C₂	#26033870	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₈₉
commutator, socle, cosocle	C₂³×C₈₉	C₂⁵
Frattini	C₂³	C₂⁴×D₈₉
Fitting	C₈₉×#2399	C₂
prime radical	C₂²×D₃₅₆	C₂³
hypercenter	#2399	D₈₉
hypocenter	C₈₉	#34691
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ #2399

Complements

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

N	H ≅ G/N	type
1. C₂×#19152152	C₂	semidirect
2. C₂×C₄×Q₈×D₈₉	C₂	semidirect
3. #26024394	C₂	semidirect
4. #26024386	C₂	semidirect
5. #26024276	C₂	semidirect
6. #26024268	C₂	semidirect
7. #26024235	C₂	semidirect
8. #26024227	C₂	semidirect
9. #26024084	C₂	semidirect
12. #26024021	C₂	semidirect
13. #26023947	C₂	semidirect
14. #26023891	C₂	semidirect
15. #26023846	C₂	semidirect
16. #26023772	C₂	semidirect
19. #26023546	C₂	semidirect
20. #26023528	C₂	semidirect
21. #26023522	C₂	semidirect
22. C₄×#15668011	C₂	semidirect
23. C₄×#15667990	C₂	semidirect
24. C₄×#15667990	C₂	semidirect
25. C₄×#15667990	C₂	semidirect
26. C₄×#15667988	C₂	semidirect
27. #26022724	C₂	semidirect
31. C₈₉×#2399	C₂	semidirect
226. C₄×Dic₁₇₈	D₄	semidirect
230. C₄×D₃₅₆	Q₈	semidirect
446. C₂×C₄×D₈₉	C₂×Q₈	semidirect
457. C₄⋊Dic₈₉	C₂×Q₈	semidirect
500. #13083551	C₂×Q₈	semidirect
561. C₄²×C₈₉	C₂×Q₈	semidirect
702. C₂×D₈₉	#533	semidirect
761. #2399	D₈₉	semidirect
773. C₈₉	#34691	semidirect
1303. C₄²	Q₈×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19152152	2
C₂×C₄×Q₈×D₈₉	2
#26024394	2
#26024386	2
#26024276	2
#26024268	2
#26024235	2
#26024227	2
#26024084	2
#26024056	2
#26024054	2
#26024021	2
#26023947	2
#26023891	2
#26023846	2
#26023772	2
#26023698	2
#26023612	2
#26023546	2
#26023528	2
#26023522	2
C₄×#15668011	2
C₄×#15667990	2
C₄×#15667988	2
#26022724	2
#26022696	2
#26022693	2
C₄×#15667974	2
C₈₉×#2399	2
#34691	89