Subgroups — #36715666

Order 22784.

2194 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19152227	C₂	1	1	yes	maximal, characteristic
2	#26023349	C₂	1	1	yes	maximal, characteristic, complemented
3	#26023345	C₂	1	1	yes	maximal, characteristic, complemented
4	#26023345	C₂	1	1	yes	maximal, characteristic, complemented
5	#26023343	C₂	1	1	yes	maximal, characteristic, complemented
6	#26023340	C₂	1	1	yes	maximal, characteristic, complemented
7	#26023339	C₂	1	1	yes	maximal, characteristic, complemented
8	#26023333	C₂	1	1	yes	maximal, characteristic
9	#26023332	C₂	1	1	yes	maximal, characteristic
10	#26023330	C₂	1	1	yes	maximal, characteristic
11	#26023309	C₂	1	1	yes	maximal, characteristic, complemented
12	#26023307	C₂	1	1	yes	maximal, characteristic, complemented
13	#26023261	C₂	1	1	yes	maximal, characteristic
14	#26023258	C₂	1	1	yes	maximal, characteristic
15	#26023255	C₂	1	1	yes	maximal, characteristic
16	#26023252	C₂	1	1	yes	maximal, characteristic
17	#26022997	C₂	1	1	yes	maximal, characteristic, complemented
18	#26022995	C₂	1	1	yes	maximal, characteristic, complemented
19	#26022988	C₂	1	1	yes	maximal, characteristic, complemented
20	#26022988	C₂	1	1	yes	maximal, characteristic, complemented
21	#26022871	C₂	1	1	yes	maximal, characteristic
22	C₄×#15668011	C₂	1	1	yes	maximal, characteristic, complemented
23	#26022821	C₂	1	1	yes	maximal, characteristic, complemented
24	#26022809	C₂	1	1	yes	maximal, characteristic, complemented
25	C₄×#15668002	C₂	1	1	yes	maximal, characteristic, complemented
26	#26022731	C₂	1	1	yes	maximal, characteristic
27	C₂×#19151495	C₂	1	1	yes	maximal, characteristic
28	#26022607	C₂	1	1	yes	maximal, characteristic
29	#26022607	C₂	1	1	yes	maximal, characteristic
30	C₄×#15667968	C₂	1	1	yes	maximal, characteristic
31	C₈₉×#2368	C₂	1	1	yes	maximal, characteristic
32	#19152227	C₄	1	16	yes	complemented
33	C₂×#15668011	C₂²	1	1	yes	characteristic
34	C₂×#15668011	C₂²	1	1	yes	characteristic
35	C₂×#15668010	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×#15668002	C₂²	1	1	yes	characteristic
40	C₂×#15668002	C₂²	1	1	yes	characteristic
41	C₂×#15667991	C₂²	1	1	yes	characteristic
42	C₂×#15667989	C₂²	1	1	yes	characteristic
43	C₂×#15667989	C₂²	1	1	yes	characteristic
44	C₂×Q₈×Dic₈₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
46	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
47	C₂×#15667977	C₂²	1	1	yes	characteristic
48	C₂×#15667968	C₂²	1	1	yes	characteristic
49	C₂×#15667968	C₂²	1	1	yes	characteristic
50	C₂×#15667968	C₂²	1	1	yes	characteristic
51	C₂×#15667968	C₂²	1	1	yes	characteristic
52	C₂²×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
53	C₂²×#13083553	C₂²	1	1	yes	characteristic
54	C₂²×#13083553	C₂²	1	1	yes	characteristic
55	C₂²×#13083553	C₂²	1	1	yes	characteristic
56	C₂²×C₄×Dic₈₉	C₂²	1	1	yes	characteristic
57	#19151505	C₂²	1	1	yes	characteristic
58	#19151504	C₂²	1	1	yes	characteristic
59	#19151504	C₂²	1	1	yes	characteristic
60	#19151503	C₂²	1	1	yes	characteristic
61	#19151502	C₂²	1	1	yes	characteristic
62	#19151502	C₂²	1	1	yes	characteristic
63	#19151502	C₂²	1	1	yes	characteristic
64	#19151502	C₂²	1	1	yes	characteristic
65	#19151502	C₂²	1	1	yes	characteristic
66	#19151502	C₂²	1	1	yes	characteristic
67	#19151497	C₂²	1	1	yes	characteristic
68	#19151497	C₂²	1	1	yes	characteristic
69	#19151497	C₂²	1	1	yes	characteristic
70	#19151496	C₂²	1	1	yes	characteristic
71	#19151496	C₂²	1	1	yes	characteristic
72	#19151495	C₂²	1	1	yes	characteristic
73	#19151495	C₂²	1	1	yes	characteristic
74	#19151495	C₂²	1	1	yes	characteristic
75	#19151495	C₂²	1	1	yes	characteristic
76	#19151495	C₂²	1	1	yes	characteristic
77	#19151495	C₂²	1	1	yes	characteristic
78	#19151495	C₂²	1	1	yes	characteristic
79	#19151495	C₂²	1	1	yes	characteristic
80	#19151495	C₂²	1	1	yes	characteristic
81	#19151495	C₂²	1	1	yes	characteristic
82	#19151495	C₂²	1	1	yes	characteristic
83	#19151495	C₂²	1	1	yes	characteristic
84	#19151495	C₂²	1	1	yes	characteristic
85	#19151495	C₂²	1	1	yes	characteristic
86	#19151495	C₂²	1	1	yes	characteristic
87	#19151495	C₂²	1	1	yes	characteristic
88	#19151494	C₂²	1	1	yes	characteristic
89	#19151493	C₂²	1	1	yes	characteristic
90	#19151493	C₂²	1	1	yes	characteristic
91	#19151493	C₂²	1	1	yes	characteristic
92	#19151493	C₂²	1	1	yes	characteristic
93	#19151493	C₂²	1	1	yes	characteristic
94	#19151493	C₂²	1	1	yes	characteristic
95	#19151485	C₂²	1	1	yes	characteristic
96	#19151485	C₂²	1	1	yes	characteristic
97	#19151485	C₂²	1	1	yes	characteristic
98	#19151485	C₂²	1	1	yes	characteristic
99	#19151484	C₂²	1	1	yes	characteristic
100	#19151484	C₂²	1	1	yes	characteristic
101	#19151483	C₂²	1	1	yes	characteristic
102	#19151483	C₂²	1	1	yes	characteristic
103	#19151483	C₂²	1	1	yes	characteristic
104	#19151483	C₂²	1	1	yes	characteristic
105	#19151482	C₂²	1	1	yes	characteristic
106	#19151482	C₂²	1	1	yes	characteristic
107	#19151481	C₂²	1	1	yes	characteristic
108	#19151481	C₂²	1	1	yes	characteristic
109	#19151480	C₂²	1	1	yes	characteristic
110	#19151480	C₂²	1	1	yes	characteristic
111	#19151480	C₂²	1	1	yes	characteristic
112	#19151480	C₂²	1	1	yes	characteristic
113	#19151479	C₂²	1	1	yes	characteristic
114	#19151479	C₂²	1	1	yes	characteristic
115	#19151473	C₂²	1	1	yes	characteristic
116	#19151473	C₂²	1	1	yes	characteristic
117	#19151471	C₂²	1	1	yes	characteristic
118	#19151471	C₂²	1	1	yes	characteristic
119	#19151470	C₂²	1	1	yes	characteristic
120	#19151470	C₂²	1	1	yes	characteristic
121	#19151467	C₂²	1	1	yes	characteristic
122	#19151467	C₂²	1	1	yes	characteristic
123	#19151462	C₂²	1	1	yes	characteristic
124	#19151462	C₂²	1	1	yes	characteristic
125	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
126	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
127	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
128	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
129	C₄×#13083553	C₂²	1	1	yes	characteristic
130	C₄×#13083553	C₂²	1	1	yes	characteristic
131	C₄×#13083553	C₂²	1	1	yes	characteristic
132	C₄×#13083553	C₂²	1	1	yes	characteristic
133	C₄×#13083553	C₂²	1	1	yes	characteristic
134	C₄×#13083553	C₂²	1	1	yes	characteristic
135	C₄×#13083553	C₂²	1	1	yes	characteristic
136	C₄×#13083553	C₂²	1	1	yes	characteristic
137	C₄×#13083553	C₂²	1	1	yes	characteristic
138	C₄×#13083553	C₂²	1	1	yes	characteristic
139	C₄×#13083553	C₂²	1	1	yes	characteristic
140	C₄×#13083553	C₂²	1	1	yes	characteristic
141	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
142	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
143	#19151449	C₂²	1	1	yes	characteristic
144	#19151449	C₂²	1	1	yes	characteristic
145	#19151449	C₂²	1	1	yes	characteristic
146	#19151449	C₂²	1	1	yes	characteristic
147	#19151449	C₂²	1	1	yes	characteristic
148	#19151449	C₂²	1	1	yes	characteristic
149	#19151449	C₂²	1	1	yes	characteristic
150	#19151449	C₂²	1	1	yes	characteristic
151	#19151449	C₂²	1	1	yes	characteristic
152	#19151449	C₂²	1	1	yes	characteristic
153	#19151449	C₂²	1	1	yes	characteristic
154	#19151449	C₂²	1	1	yes	characteristic
155	#19151449	C₂²	1	1	yes	characteristic
156	#19151449	C₂²	1	1	yes	characteristic
157	#19151449	C₂²	1	1	yes	characteristic
158	#19151449	C₂²	1	1	yes	characteristic
159	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
160	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
161	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
162	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
163	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
164	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic
165	C₄×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
166	C₄×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
167	C₄×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
168	#19151443	C₂²	1	1	yes	characteristic
169	#19151443	C₂²	1	1	yes	characteristic
170	C₂×#15667919	C₂²	1	1	yes	characteristic
171	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
172	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
173	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
174	#391×C₈₉	C₂²	1	1	yes	characteristic
175	#391×C₈₉	C₂²	1	1	yes	characteristic
176	#387×C₈₉	C₂²	1	1	yes	characteristic
177	#387×C₈₉	C₂²	1	1	yes	characteristic
178	#387×C₈₉	C₂²	1	1	yes	characteristic
179	#387×C₈₉	C₂²	1	1	yes	characteristic
180	#385×C₈₉	C₂²	1	1	yes	characteristic
181	#385×C₈₉	C₂²	1	1	yes	characteristic
182	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
183	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
184	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
185	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
186	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
187	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
188	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
189	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
190	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
191	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
192	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
193	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
194	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
195	#15668011	C₂×C₄	1	8	yes	complemented
196	#15668011	C₂×C₄	1	8	yes	complemented
197	#15668010	C₂×C₄	1	8	yes	complemented
198	#15668010	C₂×C₄	1	8	yes	complemented
199	#15668002	C₂×C₄	1	8	yes	complemented
200	#15668002	C₂×C₄	1	8	yes	complemented
201	#15668002	C₂×C₄	1	8	yes	complemented
202	#15668002	C₂×C₄	1	8	yes	complemented
203	#15667991	C₂×C₄	1	8	yes	—
204	#15667989	C₂×C₄	1	8	yes	—
205	#15667989	C₂×C₄	1	8	yes	—
206	Q₈×Dic₈₉	—	4	2	no	—
207	C₄×Dic₁₇₈	—	4	2	no	—
208	C₄×Dic₁₇₈	—	4	2	no	—
209	#15667977	—	4	2	no	—
210	#15667968	—	2	4	no	—
211	#15667968	C₂×C₄	1	8	yes	—
212	#15667968	C₂×C₄	1	8	yes	—
213	#15667968	Q₈	1	8	yes	complemented
214	C₂×C₄⋊Dic₈₉	—	4	2	no	—
215	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
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×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
226	C₂×#13083553	—	2	4	no	—
227	C₂×#13083553	—	4	2	no	—
228	C₂×#13083553	C₂×C₄	1	8	yes	—
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×#13083553	C₂³	1	1	yes	characteristic
237	C₂×#13083553	C₂³	1	1	yes	characteristic
238	C₂×#13083553	C₂³	1	1	yes	characteristic
239	C₂×#13083553	C₂³	1	1	yes	characteristic
240	C₂×#13083553	C₂³	1	1	yes	characteristic
241	C₂×#13083553	C₂³	1	1	yes	characteristic
242	C₂×#13083553	C₂³	1	1	yes	characteristic
243	C₂×#13083553	C₂³	1	1	yes	characteristic
244	C₂×#13083553	C₂³	1	1	yes	characteristic
245	C₂×#13083553	C₂³	1	1	yes	characteristic
246	C₂×#13083553	C₂³	1	1	yes	characteristic
247	C₂×#13083553	C₂³	1	1	yes	characteristic
248	C₂×#13083553	C₂³	1	1	yes	characteristic
249	C₂×#13083553	C₂³	1	1	yes	characteristic
250	C₂×#13083553	C₂³	1	1	yes	characteristic
251	C₂×#13083553	C₂³	1	1	yes	characteristic
252	C₂×#13083553	C₂³	1	1	yes	characteristic
253	C₂×#13083553	C₂³	1	1	yes	characteristic
254	C₂×#13083553	C₂³	1	1	yes	characteristic
255	C₂×#13083553	C₂³	1	1	yes	characteristic
256	C₂×#13083553	C₂³	1	1	yes	characteristic
257	C₂×#13083553	C₂³	1	1	yes	characteristic
258	C₂×#13083553	C₂³	1	1	yes	characteristic
259	C₂×#13083553	C₂³	1	1	yes	characteristic
260	C₂×#13083553	C₂³	1	1	yes	characteristic
261	C₂×#13083553	C₂³	1	1	yes	characteristic
262	C₂×#13083553	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
267	C₂×C₄×Dic₈₉	—	2	4	no	—
268	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
269	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
270	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
271	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
272	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
273	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
274	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
275	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
276	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
277	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
278	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
279	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
280	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
281	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
282	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
283	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
284	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
285	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
286	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
287	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
288	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
289	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
290	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
291	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
292	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
293	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
294	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
295	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
296	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
297	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
298	#15667919	C₂³	1	1	yes	characteristic
299	#15667919	C₂³	1	1	yes	characteristic
300	#15667919	C₂³	1	1	yes	characteristic
301	#15667919	C₂³	1	1	yes	characteristic
302	#15667919	C₂³	1	1	yes	characteristic
303	#15667919	C₂³	1	1	yes	characteristic
304	#15667919	C₂³	1	1	yes	characteristic
305	#15667919	C₂³	1	1	yes	characteristic
306	#15667919	C₂³	1	1	yes	characteristic
307	#15667919	C₂³	1	1	yes	characteristic
308	#15667919	C₂³	1	1	yes	characteristic
309	#15667919	C₂³	1	1	yes	characteristic
310	#15667919	C₂³	1	1	yes	characteristic
311	#15667919	C₂³	1	1	yes	characteristic
312	#15667919	C₂³	1	1	yes	characteristic
313	#15667919	C₂³	1	1	yes	characteristic
314	#15667919	C₂³	1	1	yes	characteristic
315	#15667919	C₂³	1	1	yes	characteristic
316	#15667919	C₂³	1	1	yes	characteristic
317	#15667919	C₂³	1	1	yes	characteristic
318	#15667919	C₂³	1	1	yes	characteristic
319	#15667919	C₂³	1	1	yes	characteristic
320	#15667919	C₂³	1	1	yes	characteristic
321	#15667919	C₂³	1	1	yes	characteristic
322	#15667919	C₂³	1	1	yes	characteristic
323	#15667919	C₂³	1	1	yes	characteristic
324	#15667919	C₂³	1	1	yes	characteristic
325	#15667919	C₂³	1	1	yes	characteristic
326	#15667919	C₂³	1	1	yes	characteristic
327	#15667919	C₂³	1	1	yes	characteristic
328	#15667919	C₂³	1	1	yes	characteristic
329	#15667919	C₂³	1	1	yes	characteristic
330	#15667919	C₂³	1	1	yes	characteristic
331	#15667919	C₂³	1	1	yes	characteristic
332	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
333	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
334	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
335	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
336	C₂²⋊Q₈×C₈₉	C₂×C₄	1	8	yes	—
337	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
338	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
339	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
340	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
341	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
342	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
343	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
344	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
346	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
347	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
348	C₂×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	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
352	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
353	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
354	#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	#95×C₈₉	C₂³	1	1	yes	characteristic
364	#95×C₈₉	C₂³	1	1	yes	characteristic
365	#95×C₈₉	C₂³	1	1	yes	characteristic
366	#95×C₈₉	C₂³	1	1	yes	characteristic
367	#95×C₈₉	C₂³	1	1	yes	characteristic
368	C₂×Dic₁₇₈	—	4	1	no	—
369	C₂×Dic₁₇₈	—	4	1	no	—
370	C₂×Dic₁₇₈	—	4	1	no	—
371	C₂×Dic₁₇₈	—	4	1	no	—
372	C₂×Dic₁₇₈	—	4	1	no	—
373	C₂×Dic₁₇₈	—	4	1	no	—
374	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
375	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
376	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
377	C₂²×Dic₈₉	—	2	2	no	—
378	C₂²×Dic₈₉	—	2	2	no	—
379	C₂²×Dic₈₉	—	2	2	no	—
380	C₂²×Dic₈₉	—	4	1	no	—
381	C₂²×Dic₈₉	—	4	1	no	—
382	C₂²×Dic₈₉	—	4	1	no	—
383	C₂²×Dic₈₉	—	4	1	no	—
384	C₂²×Dic₈₉	—	4	1	no	—
385	C₂²×Dic₈₉	C₂²×C₄	1	4	yes	—
386	C₂²×Dic₈₉	C₂²×C₄	1	4	yes	—
387	C₂²×Dic₈₉	C₂×Q₈	1	4	yes	—
388	C₂²×Dic₈₉	#41	1	4	yes	—
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	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
402	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
403	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
404	C₂²×Dic₈₉	C₂⁴	1	1	yes	characteristic
405	C₄⋊Dic₈₉	—	2	2	no	—
406	C₄⋊Dic₈₉	—	2	2	no	—
407	C₄⋊Dic₈₉	—	2	2	no	—
408	C₄⋊Dic₈₉	—	4	1	no	—
409	C₄⋊Dic₈₉	—	4	1	no	—
410	C₄⋊Dic₈₉	—	4	1	no	—
411	C₄⋊Dic₈₉	—	4	1	no	—
412	C₄⋊Dic₈₉	—	4	1	no	—
413	C₄⋊Dic₈₉	C₂²×C₄	1	4	yes	—
414	C₄⋊Dic₈₉	C₂²×C₄	1	4	yes	—
415	C₄⋊Dic₈₉	C₂²×C₄	1	4	yes	—
416	#13083553	—	2	2	no	—
417	#13083553	—	2	2	no	—
418	#13083553	—	2	2	no	—
419	#13083553	—	2	2	no	—
420	#13083553	—	2	2	no	—
421	#13083553	—	2	2	no	—
422	#13083553	—	2	2	no	—
423	#13083553	—	2	2	no	—
424	#13083553	—	2	2	no	—
425	#13083553	—	2	2	no	—
426	#13083553	—	4	1	no	—
427	#13083553	—	4	1	no	—
428	#13083553	—	4	1	no	—
429	#13083553	—	4	1	no	—
430	#13083553	—	4	1	no	—
431	#13083553	—	4	1	no	—
432	#13083553	—	4	1	no	—
433	#13083553	—	4	1	no	—
434	#13083553	C₂²×C₄	1	4	yes	—
435	#13083553	C₂²×C₄	1	4	yes	—
436	#13083553	C₂²×C₄	1	4	yes	—
437	#13083553	C₂²×C₄	1	4	yes	—
438	#13083553	C₂²×C₄	1	4	yes	—
439	#13083553	C₂²×C₄	1	4	yes	—
440	#13083553	C₂²×C₄	1	4	yes	—
441	#13083553	C₂²×C₄	1	4	yes	—
442	#13083553	C₂²×C₄	1	4	yes	—
443	#13083553	C₂²×C₄	1	4	yes	—
444	#13083553	C₂²×C₄	1	4	yes	—
445	#13083553	C₂²×C₄	1	4	yes	—
446	#13083553	C₂²×C₄	1	4	yes	—
447	#13083553	C₂²×C₄	1	4	yes	—
448	#13083553	C₂×Q₈	1	4	yes	—
449	#13083553	C₂×Q₈	1	4	yes	—
450	C₂²⋊Dic₈₉	—	2	2	no	—
451	C₂²⋊Dic₈₉	C₂²×C₄	1	4	yes	—
452	C₂²⋊Dic₈₉	C₂²×C₄	1	4	yes	—
453	C₂²⋊Dic₈₉	C₂×Q₈	1	4	yes	—
454	C₄×Dic₈₉	—	2	2	no	—
455	C₄×Dic₈₉	—	2	2	no	—
456	C₄×Dic₈₉	—	2	2	no	—
457	C₄×Dic₈₉	—	2	2	no	—
458	C₄×Dic₈₉	—	2	2	no	—
459	C₄×Dic₈₉	—	2	2	no	—
460	C₄×Dic₈₉	—	2	2	no	—
461	C₄×Dic₈₉	—	2	2	no	—
462	C₄×Dic₈₉	—	2	2	no	—
463	C₄×Dic₈₉	—	4	1	no	—
464	C₄×Dic₈₉	—	4	1	no	—
465	C₄×Dic₈₉	—	4	1	no	—
466	C₄×Dic₈₉	—	4	1	no	—
467	C₄×Dic₈₉	—	4	1	no	—
468	C₄×Dic₈₉	—	4	1	no	—
469	C₄×Dic₈₉	—	4	1	no	—
470	C₄×Dic₈₉	—	4	1	no	—
471	C₄×Dic₈₉	—	4	1	no	—
472	C₄×Dic₈₉	—	4	1	no	—
473	C₄×Dic₈₉	—	4	1	no	—
474	C₄×Dic₈₉	—	4	1	no	—
475	C₄×Dic₈₉	—	4	1	no	—
476	C₄×Dic₈₉	—	4	1	no	—
477	C₄×Dic₈₉	—	4	1	no	—
478	C₄×Dic₈₉	C₂²×C₄	1	4	yes	—
479	C₄×Dic₈₉	C₂²×C₄	1	4	yes	—
480	C₄×Dic₈₉	C₂²×C₄	1	4	yes	—
481	C₄×Dic₈₉	C₂²×C₄	1	4	yes	—
482	C₄×Dic₈₉	C₂×Q₈	1	4	yes	—
483	C₄×Dic₈₉	C₂×Q₈	1	4	yes	—
484	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
485	C₂×Q₈×C₈₉	—	4	1	no	—
486	C₂×Q₈×C₈₉	—	4	1	no	—
487	C₂×Q₈×C₈₉	C₂²×C₄	1	4	yes	—
488	C₂²×C₄×C₈₉	—	2	2	no	—
489	C₂²×C₄×C₈₉	—	2	2	no	—
490	C₂²×C₄×C₈₉	—	2	2	no	—
491	C₂²×C₄×C₈₉	—	4	1	no	—
492	C₂²×C₄×C₈₉	—	4	1	no	—
493	C₂²×C₄×C₈₉	—	4	1	no	—
494	C₂²×C₄×C₈₉	—	4	1	no	—
495	C₂²×C₄×C₈₉	—	4	1	no	—
496	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
497	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
498	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
499	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
500	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
501	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
502	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
503	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
504	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
505	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
506	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
507	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
508	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
509	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
510	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
511	C₄⋊C₄×C₈₉	—	2	2	no	—
512	C₄⋊C₄×C₈₉	—	4	1	no	—
513	C₄⋊C₄×C₈₉	—	4	1	no	—
514	C₄⋊C₄×C₈₉	—	4	1	no	—
515	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
516	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
517	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
518	C₂²⋊C₄×C₈₉	—	2	2	no	—
519	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
520	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
521	C₂²⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
522	C₄²×C₈₉	—	2	2	no	—
523	C₄²×C₈₉	—	4	1	no	—
524	C₄²×C₈₉	—	4	1	no	—
525	C₄²×C₈₉	—	4	1	no	—
526	C₄²×C₈₉	—	4	1	no	—
527	C₄²×C₈₉	—	4	1	no	—
528	C₂³×C₈₉	—	2	1	no	—
529	C₂³×C₈₉	—	2	1	no	—
530	C₂³×C₈₉	—	2	1	no	—
531	C₂³×C₈₉	—	2	1	no	—
532	C₂³×C₈₉	C₂³×C₄	1	2	yes	—
533	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
534	C₂³×C₈₉	C₂×#41	1	2	yes	—
535	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
536	Q₈×C₈₉	—	4	4	no	—
537	C₂×C₄×C₈₉	—	2	1	no	—
538	C₂×C₄×C₈₉	—	2	1	no	—
539	C₂×C₄×C₈₉	—	2	1	no	—
540	C₂×C₄×C₈₉	—	2	1	no	—
541	C₂×C₄×C₈₉	—	2	1	no	—
542	C₂×C₄×C₈₉	—	2	1	no	—
543	C₂×C₄×C₈₉	—	2	1	no	—
544	C₂×C₄×C₈₉	—	2	1	no	—
545	C₂×C₄×C₈₉	—	2	1	no	—
546	C₂×C₄×C₈₉	—	2	1	no	—
547	C₂×C₄×C₈₉	—	2	1	no	—
548	C₂×C₄×C₈₉	—	2	1	no	—
549	C₂×C₄×C₈₉	—	2	1	no	—
550	C₂×C₄×C₈₉	—	2	1	no	—
551	C₂×C₄×C₈₉	—	2	1	no	—
552	C₂×C₄×C₈₉	—	2	1	no	—
553	C₂×C₄×C₈₉	—	2	1	no	—
554	C₂×C₄×C₈₉	—	2	1	no	—
555	C₂×C₄×C₈₉	—	2	1	no	—
556	C₂×C₄×C₈₉	—	2	1	no	—
557	C₂×C₄×C₈₉	—	2	1	no	—
558	C₂×C₄×C₈₉	—	2	1	no	—
559	C₂×C₄×C₈₉	—	2	1	no	—
560	C₂×C₄×C₈₉	—	2	1	no	—
561	C₂×C₄×C₈₉	—	2	1	no	—
562	C₂×C₄×C₈₉	—	2	1	no	—
563	C₂×C₄×C₈₉	—	2	1	no	—
564	C₂×C₄×C₈₉	—	2	1	no	—
565	C₂×C₄×C₈₉	—	2	1	no	—
566	C₂×C₄×C₈₉	—	2	1	no	—
567	C₂×C₄×C₈₉	—	2	1	no	—
568	C₂×C₄×C₈₉	—	2	1	no	—
569	C₂×C₄×C₈₉	—	2	1	no	—
570	C₂×C₄×C₈₉	—	4	4	no	—
571	C₂×C₄×C₈₉	—	4	4	no	—
572	C₂×C₄×C₈₉	—	8	2	no	—
573	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
574	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
575	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
576	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
577	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
578	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
579	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
580	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
581	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
582	C₂×Dic₈₉	—	2	1	no	—
583	C₂×Dic₈₉	—	2	1	no	—
584	C₂×Dic₈₉	—	2	1	no	—
585	C₂×Dic₈₉	—	2	1	no	—
586	C₂×Dic₈₉	—	2	1	no	—
587	C₂×Dic₈₉	—	2	1	no	—
588	C₂×Dic₈₉	—	2	1	no	—
589	C₂×Dic₈₉	—	2	1	no	—
590	C₂×Dic₈₉	—	2	1	no	—
591	C₂×Dic₈₉	—	2	1	no	—
592	C₂×Dic₈₉	—	2	1	no	—
593	C₂×Dic₈₉	—	2	1	no	—
594	C₂×Dic₈₉	—	2	1	no	—
595	C₂×Dic₈₉	—	2	1	no	—
596	C₂×Dic₈₉	—	2	1	no	—
597	C₂×Dic₈₉	—	2	1	no	—
598	C₂×Dic₈₉	—	2	1	no	—
599	C₂×Dic₈₉	—	2	1	no	—
600	C₂×Dic₈₉	—	2	1	no	—
601	C₂×Dic₈₉	—	2	1	no	—
602	C₂×Dic₈₉	—	2	1	no	—
603	C₂×Dic₈₉	—	2	1	no	—
604	C₂×Dic₈₉	—	2	1	no	—
605	C₂×Dic₈₉	—	2	1	no	—
606	C₂×Dic₈₉	—	2	1	no	—
607	C₂×Dic₈₉	—	2	1	no	—
608	C₂×Dic₈₉	—	2	1	no	—
609	C₂×Dic₈₉	—	2	1	no	—
610	C₂×Dic₈₉	—	2	1	no	—
611	C₂×Dic₈₉	—	2	1	no	—
612	C₂×Dic₈₉	—	2	1	no	—
613	C₂×Dic₈₉	—	2	1	no	—
614	C₂×Dic₈₉	—	2	1	no	—
615	C₂×Dic₈₉	—	4	4	no	—
616	C₂×Dic₈₉	—	4	4	no	—
617	C₂×Dic₈₉	—	8	2	no	—
618	C₂×Dic₈₉	C₄×Q₈	1	16	yes	complemented
619	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
620	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
621	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
622	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
623	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
624	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
625	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
626	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
627	C₂×Dic₈₉	C₂²×Q₈	1	2	yes	—
628	C₂×Dic₈₉	C₂²×Q₈	1	2	yes	—
629	C₂×Dic₈₉	C₂²×Q₈	1	2	yes	—
630	C₂×Dic₈₉	C₂²×Q₈	1	2	yes	—
631	C₂×Dic₈₉	C₂×#41	1	2	yes	—
632	C₂×Dic₈₉	C₂×#41	1	2	yes	—
633	C₂×Dic₈₉	H(5,𝔽₂)	1	2	yes	—
634	Dic₁₇₈	—	4	4	no	—
635	Dic₁₇₈	—	4	4	no	—
636	Dic₁₇₈	—	4	4	no	—
637	C₂²×C₈₉	—	2	2	no	—
638	C₂²×C₈₉	—	2	2	no	—
639	C₂²×C₈₉	—	2	2	no	—
640	C₂²×C₈₉	—	2	2	no	—
641	C₂²×C₈₉	—	2	2	no	—
642	C₂²×C₈₉	—	2	2	no	—
643	C₂²×C₈₉	C₂×C₄×Q₈	1	4	yes	—
644	C₂²×C₈₉	C₂⁴×C₄	1	1	yes	characteristic
645	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
646	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
647	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
648	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
649	C₂²×C₈₉	#585	1	1	yes	characteristic
650	C₂²×C₈₉	#585	1	1	yes	characteristic
651	C₄×C₈₉	—	2	2	no	—
652	C₄×C₈₉	—	2	2	no	—
653	C₄×C₈₉	—	2	2	no	—
654	C₄×C₈₉	—	2	2	no	—
655	C₄×C₈₉	—	2	2	no	—
656	C₄×C₈₉	—	2	2	no	—
657	C₄×C₈₉	—	2	2	no	—
658	C₄×C₈₉	—	2	2	no	—
659	C₄×C₈₉	—	2	2	no	—
660	C₄×C₈₉	—	4	1	no	—
661	C₄×C₈₉	—	4	1	no	—
662	C₄×C₈₉	—	4	1	no	—
663	C₄×C₈₉	—	4	1	no	—
664	C₄×C₈₉	—	4	1	no	—
665	Dic₈₉	—	2	2	no	—
666	Dic₈₉	—	2	2	no	—
667	Dic₈₉	—	2	2	no	—
668	Dic₈₉	—	2	2	no	—
669	Dic₈₉	—	2	2	no	—
670	Dic₈₉	—	2	2	no	—
671	Dic₈₉	—	2	2	no	—
672	Dic₈₉	—	2	2	no	—
673	Dic₈₉	—	2	2	no	—
674	Dic₈₉	—	4	1	no	—
675	Dic₈₉	—	4	1	no	—
676	Dic₈₉	—	4	1	no	—
677	Dic₈₉	—	4	1	no	—
678	Dic₈₉	—	4	1	no	—
679	Dic₈₉	C₂×C₄×Q₈	1	4	yes	—
680	Dic₈₉	C₂×C₄×Q₈	1	4	yes	—
681	#34272	—	89	1	no	maximal, Sylow
682	C₂×C₈₉	—	2	4	no	—
683	C₂×C₈₉	C₂²×C₄×Q₈	1	1	yes	characteristic
684	C₂×C₈₉	C₄×H(5,𝔽₂)	1	1	yes	characteristic
685	C₂×C₈₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic
686	C₂×C₈₉	#3494	1	1	yes	characteristic
687	C₂×C₈₉	#3495	1	1	yes	characteristic
688	C₂×C₈₉	#3503	1	1	yes	characteristic
689	C₂×C₈₉	#3504	1	1	yes	characteristic
690	C₂×#544	—	89	1	no	—
691	#2370	—	89	1	no	—
692	#2370	—	89	1	no	—
693	#2370	—	89	1	no	—
694	#2370	—	89	1	no	—
695	#2369	—	89	1	no	—
696	#2369	—	89	1	no	—
697	#2368	—	89	1	no	—
698	#2368	—	89	1	no	—
699	#2368	—	89	1	no	—
700	#2368	D₈₉	1	1	yes	characteristic
701	#2365	—	89	1	no	—
702	#2365	—	89	1	no	—
703	#2360	—	89	1	no	—
704	#2360	—	89	1	no	—
705	#2360	—	89	1	no	—
706	#2360	—	89	1	no	—
707	#2331	—	89	1	no	—
708	#2331	—	89	1	no	—
709	#2330	—	89	1	no	—
710	#2330	—	89	1	no	—
711	#2317	—	89	1	no	—
712	C₄×C₄⋊Q₈	—	89	1	no	—
713	C₄×C₄⋊Q₈	—	89	1	no	—
714	C₄×#125	—	89	1	no	—
715	C₄×#125	—	89	1	no	—
716	#2296	—	89	1	no	—
717	C₂×#389	—	89	1	no	—
718	#2274	—	89	1	no	—
719	#2274	—	89	1	no	—
720	C₄×#117	—	89	1	no	—
721	C₈₉	#34272	1	1	yes	characteristic, complemented, Sylow
722	#544	—	89	16	no	—
723	C₂×C₄⋊Q₈	—	89	1	no	—
724	C₂×C₄⋊Q₈	—	89	1	no	—
725	C₂×C₄⋊Q₈	—	89	1	no	—
726	C₂×C₄⋊Q₈	—	89	1	no	—
727	C₂×#125	—	89	1	no	—
728	C₂×#125	—	89	1	no	—
729	C₂×#125	—	89	1	no	—
730	C₂×#125	—	89	1	no	—
731	C₂×C₂²⋊Q₈	—	89	1	no	—
732	C₂×C₂²⋊Q₈	—	89	1	no	—
733	C₂×C₂²⋊Q₈	—	89	1	no	—
734	C₂×C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
735	C₂×C₄×Q₈	—	89	1	no	—
736	C₂×C₄×Q₈	—	89	1	no	—
737	C₂×C₄×Q₈	—	89	1	no	—
738	C₂×C₄×Q₈	—	89	1	no	—
739	C₂×#117	—	89	1	no	—
740	C₂×#117	—	89	1	no	—
741	C₂×#117	—	89	1	no	—
742	C₂×#117	—	89	1	no	—
743	C₂²×C₄⋊C₄	—	89	1	no	—
744	C₂²×C₄⋊C₄	—	89	1	no	—
745	C₂²×C₄⋊C₄	—	89	1	no	—
746	C₂²×C₄⋊C₄	—	89	1	no	—
747	C₂²×C₄²	—	89	1	no	—
748	#391	—	89	1	no	—
749	#391	—	89	1	no	—
750	#391	—	89	1	no	—
751	#391	—	89	1	no	—
752	#391	—	89	1	no	—
753	#391	—	89	1	no	—
754	#391	—	89	1	no	—
755	#391	—	89	1	no	—
756	#391	—	89	1	no	—
757	#391	—	89	1	no	—
758	#391	C₂×D₈₉	1	1	yes	characteristic
759	#391	C₂×D₈₉	1	1	yes	characteristic
760	#389	—	89	1	no	—
761	#389	—	89	1	no	—
762	#389	—	89	1	no	—
763	#389	—	89	1	no	—
764	#389	—	89	1	no	—
765	#389	—	89	1	no	—
766	#389	—	89	1	no	—
767	#389	—	89	1	no	—
768	#389	—	89	1	no	—
769	#389	—	89	1	no	—
770	#389	—	89	1	no	—
771	#389	—	89	1	no	—
772	#389	—	89	1	no	—
773	#389	—	89	1	no	—
774	#389	—	89	1	no	—
775	#389	—	89	1	no	—
776	#389	—	89	1	no	—
777	#389	—	89	1	no	—
778	#389	—	89	1	no	—
779	#389	—	89	1	no	—
780	#389	—	89	1	no	—
781	#389	—	89	1	no	—
782	#389	—	89	1	no	—
783	#389	—	89	1	no	—
784	#389	—	89	1	no	—
785	#389	—	89	1	no	—
786	#389	—	89	1	no	—
787	#389	—	89	1	no	—
788	#387	—	89	1	no	—
789	#387	—	89	1	no	—
790	#387	—	89	1	no	—
791	#387	—	89	1	no	—
792	#387	—	89	1	no	—
793	#387	—	89	1	no	—
794	#387	—	89	1	no	—
795	#387	—	89	1	no	—
796	#387	—	89	1	no	—
797	#387	—	89	1	no	—
798	#387	—	89	1	no	—
799	#387	—	89	1	no	—
800	#387	—	89	1	no	—
801	#387	—	89	1	no	—
802	#387	—	89	1	no	—
803	#387	—	89	1	no	—
804	#387	—	89	1	no	—
805	#387	—	89	1	no	—
806	#387	—	89	1	no	—
807	#387	—	89	1	no	—
808	#387	C₂×D₈₉	1	1	yes	characteristic
809	#387	C₂×D₈₉	1	1	yes	characteristic
810	#387	C₂×D₈₉	1	1	yes	characteristic
811	#387	C₂×D₈₉	1	1	yes	characteristic
812	#385	—	89	1	no	—
813	#385	—	89	1	no	—
814	#385	—	89	1	no	—
815	#385	—	89	1	no	—
816	#385	—	89	1	no	—
817	#385	—	89	1	no	—
818	#385	C₂×D₈₉	1	1	yes	characteristic
819	#385	C₂×D₈₉	1	1	yes	characteristic
820	#384	—	89	1	no	—
821	#384	—	89	1	no	—
822	#382	—	89	1	no	—
823	#382	—	89	1	no	—
824	C₄×C₄⋊C₄	—	89	1	no	—
825	C₄×C₄⋊C₄	—	89	1	no	—
826	C₄×C₄⋊C₄	—	89	1	no	—
827	C₄×C₄⋊C₄	—	89	1	no	—
828	C₄×C₄⋊C₄	—	89	1	no	—
829	C₄×C₄⋊C₄	—	89	1	no	—
830	C₄×C₄⋊C₄	—	89	1	no	—
831	C₄×C₄⋊C₄	—	89	1	no	—
832	C₄×C₄⋊C₄	—	89	1	no	—
833	C₄×C₄⋊C₄	—	89	1	no	—
834	C₄×C₄⋊C₄	—	89	1	no	—
835	C₄×C₄⋊C₄	—	89	1	no	—
836	C₄×C₄⋊C₄	—	89	1	no	—
837	C₄×C₄⋊C₄	—	89	1	no	—
838	C₄×C₄⋊C₄	—	89	1	no	—
839	C₄×C₄⋊C₄	—	89	1	no	—
840	C₄×C₄⋊C₄	—	89	1	no	—
841	C₄×C₄⋊C₄	—	89	1	no	—
842	C₄×C₄⋊C₄	—	89	1	no	—
843	C₄×C₄⋊C₄	—	89	1	no	—
844	C₄×C₄⋊C₄	—	89	1	no	—
845	C₄×C₄⋊C₄	—	89	1	no	—
846	C₄×C₄⋊C₄	—	89	1	no	—
847	C₄×C₄⋊C₄	—	89	1	no	—
848	C₄×C₄⋊C₄	—	89	1	no	—
849	C₄×C₄⋊C₄	—	89	1	no	—
850	C₄×C₄⋊C₄	—	89	1	no	—
851	C₄×C₄⋊C₄	—	89	1	no	—
852	C₄×C₄⋊C₄	—	89	1	no	—
853	C₄×C₄⋊C₄	—	89	1	no	—
854	C₄×C₄⋊C₄	—	89	1	no	—
855	C₄×C₄⋊C₄	—	89	1	no	—
856	C₄×C₄⋊C₄	—	89	1	no	—
857	C₄×C₄⋊C₄	—	89	1	no	—
858	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
859	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
860	C₄×C₂²⋊C₄	—	89	1	no	—
861	C₄×C₂²⋊C₄	—	89	1	no	—
862	C₄×C₂²⋊C₄	—	89	1	no	—
863	C₄×C₂²⋊C₄	—	89	1	no	—
864	C₄×C₂²⋊C₄	—	89	1	no	—
865	C₄×C₂²⋊C₄	—	89	1	no	—
866	C₄×C₂²⋊C₄	—	89	1	no	—
867	C₄×C₂²⋊C₄	—	89	1	no	—
868	C₄×C₂²⋊C₄	—	89	1	no	—
869	C₄×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
870	C₄×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
871	C₄×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
872	#376	—	89	1	no	—
873	#376	—	89	1	no	—
874	C₂×#95	—	89	1	no	—
875	C₂×#95	C₂×D₈₉	1	1	yes	characteristic
876	C₄³	—	89	1	no	—
877	C₄³	—	89	1	no	—
878	C₂²×Q₈	—	89	1	no	—
879	C₂²×Q₈	—	89	1	no	—
880	C₂²×Q₈	—	89	1	no	—
881	C₂²×Q₈	C₂²×D₈₉	1	1	yes	characteristic
882	C₂³×C₄	—	89	1	no	—
883	C₂³×C₄	—	89	1	no	—
884	C₂³×C₄	—	89	1	no	—
885	C₂³×C₄	—	89	1	no	—
886	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
887	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
888	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
889	C₄⋊Q₈	—	89	8	no	—
890	C₄⋊Q₈	—	89	8	no	—
891	C₄⋊Q₈	—	89	8	no	—
892	C₄⋊Q₈	—	89	8	no	—
893	#125	—	89	8	no	—
894	#125	—	89	8	no	—
895	#125	—	89	8	no	—
896	#125	—	89	8	no	—
897	C₂²⋊Q₈	—	89	8	no	—
898	C₂²⋊Q₈	—	89	8	no	—
899	C₂²⋊Q₈	—	89	8	no	—
900	C₂²⋊Q₈	C₄×D₈₉	1	8	yes	—
901	C₄×Q₈	—	356	2	no	—
902	C₄×Q₈	—	356	2	no	—
903	C₄×Q₈	—	356	2	no	—
904	C₄×Q₈	—	356	2	no	—
905	#117	—	89	8	no	—
906	#117	—	89	8	no	—
907	#117	—	89	8	no	—
908	#117	—	178	4	no	—
909	C₂×C₄⋊C₄	—	89	8	no	—
910	C₂×C₄⋊C₄	—	89	1	no	—
911	C₂×C₄⋊C₄	—	89	1	no	—
912	C₂×C₄⋊C₄	—	89	1	no	—
913	C₂×C₄⋊C₄	—	89	1	no	—
914	C₂×C₄⋊C₄	—	89	1	no	—
915	C₂×C₄⋊C₄	—	89	1	no	—
916	C₂×C₄⋊C₄	—	89	1	no	—
917	C₂×C₄⋊C₄	—	89	1	no	—
918	C₂×C₄⋊C₄	—	89	1	no	—
919	C₂×C₄⋊C₄	—	89	1	no	—
920	C₂×C₄⋊C₄	—	89	1	no	—
921	C₂×C₄⋊C₄	—	89	1	no	—
922	C₂×C₄⋊C₄	—	89	1	no	—
923	C₂×C₄⋊C₄	—	89	1	no	—
924	C₂×C₄⋊C₄	—	89	1	no	—
925	C₂×C₄⋊C₄	—	89	1	no	—
926	C₂×C₄⋊C₄	—	89	1	no	—
927	C₂×C₄⋊C₄	—	89	1	no	—
928	C₂×C₄⋊C₄	—	89	1	no	—
929	C₂×C₄⋊C₄	—	89	1	no	—
930	C₂×C₄⋊C₄	—	89	1	no	—
931	C₂×C₄⋊C₄	—	89	1	no	—
932	C₂×C₄⋊C₄	—	89	1	no	—
933	C₂×C₄⋊C₄	—	89	1	no	—
934	C₂×C₄⋊C₄	—	89	1	no	—
935	C₂×C₄⋊C₄	—	89	1	no	—
936	C₂×C₄⋊C₄	—	89	1	no	—
937	C₂×C₄⋊C₄	—	89	1	no	—
938	C₂×C₄⋊C₄	—	89	1	no	—
939	C₂×C₄⋊C₄	—	89	1	no	—
940	C₂×C₄⋊C₄	—	89	1	no	—
941	C₂×C₄⋊C₄	—	89	1	no	—
942	C₂×C₄⋊C₄	—	89	1	no	—
943	C₂×C₄⋊C₄	—	89	1	no	—
944	C₂×C₄⋊C₄	—	89	1	no	—
945	C₂×C₄⋊C₄	—	89	1	no	—
946	C₂×C₄⋊C₄	—	89	1	no	—
947	C₂×C₄⋊C₄	—	89	1	no	—
948	C₂×C₄⋊C₄	—	89	1	no	—
949	C₂×C₄⋊C₄	—	89	1	no	—
950	C₂×C₄⋊C₄	—	89	1	no	—
951	C₂×C₄⋊C₄	—	89	1	no	—
952	C₂×C₄⋊C₄	—	89	1	no	—
953	C₂×C₄⋊C₄	—	89	1	no	—
954	C₂×C₄⋊C₄	—	89	1	no	—
955	C₂×C₄⋊C₄	—	356	2	no	—
956	C₂×C₄⋊C₄	—	356	2	no	—
957	C₂×C₄⋊C₄	—	178	4	no	—
958	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
959	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
960	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
961	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
962	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
963	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
964	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
965	C₂×C₂²⋊C₄	—	89	1	no	—
966	C₂×C₂²⋊C₄	—	89	1	no	—
967	C₂×C₂²⋊C₄	—	89	1	no	—
968	C₂×C₂²⋊C₄	—	89	1	no	—
969	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
970	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
971	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
972	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
973	C₂×C₄²	—	89	1	no	—
974	C₂×C₄²	—	89	1	no	—
975	C₂×C₄²	—	89	1	no	—
976	C₂×C₄²	—	89	1	no	—
977	C₂×C₄²	—	89	1	no	—
978	C₂×C₄²	—	89	1	no	—
979	C₂×C₄²	—	89	1	no	—
980	C₂×C₄²	—	89	1	no	—
981	C₂×C₄²	—	89	1	no	—
982	C₂×C₄²	—	89	1	no	—
983	C₂×C₄²	—	89	1	no	—
984	C₂×C₄²	—	89	1	no	—
985	C₂×C₄²	—	89	1	no	—
986	C₂×C₄²	—	89	1	no	—
987	C₂×C₄²	—	89	1	no	—
988	C₂×C₄²	—	89	1	no	—
989	C₂×C₄²	—	89	1	no	—
990	C₂×C₄²	—	89	1	no	—
991	C₂×C₄²	—	89	1	no	—
992	C₂×C₄²	—	89	1	no	—
993	C₂×C₄²	—	89	1	no	—
994	C₂×C₄²	—	89	1	no	—
995	C₂×C₄²	—	89	1	no	—
996	C₂×C₄²	—	89	1	no	—
997	C₂×C₄²	—	89	1	no	—
998	C₂×C₄²	—	89	1	no	—
999	C₂×C₄²	—	89	1	no	—
1000	C₂×C₄²	—	89	1	no	—
1001	C₂×C₄²	—	89	1	no	—
1002	C₂×C₄²	—	89	1	no	—
1003	C₂×C₄²	—	178	4	no	—
1004	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1005	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1006	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1007	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1008	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1009	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1010	#95	—	89	1	no	—
1011	#95	—	89	1	no	—
1012	#95	—	89	1	no	—
1013	#95	—	89	1	no	—
1014	#95	—	89	1	no	—
1015	#95	—	89	1	no	—
1016	#95	—	89	1	no	—
1017	#95	—	89	1	no	—
1018	#95	—	89	1	no	—
1019	#95	—	89	1	no	—
1020	#95	—	89	1	no	—
1021	#95	—	89	1	no	—
1022	#95	—	89	1	no	—
1023	#95	—	89	1	no	—
1024	#95	—	89	1	no	—
1025	#95	—	89	1	no	—
1026	#95	—	89	1	no	—
1027	#95	—	89	1	no	—
1028	#95	—	89	1	no	—
1029	#95	—	89	1	no	—
1030	#95	—	89	1	no	—
1031	#95	—	89	1	no	—
1032	#95	—	89	1	no	—
1033	#95	—	89	1	no	—
1034	#95	—	89	1	no	—
1035	#95	—	89	1	no	—
1036	#95	—	89	1	no	—
1037	#95	—	89	1	no	—
1038	#95	—	89	1	no	—
1039	#95	—	89	1	no	—
1040	#95	—	89	1	no	—
1041	#95	—	89	1	no	—
1042	#95	—	89	1	no	—
1043	#95	—	89	1	no	—
1044	#95	C₂²×D₈₉	1	1	yes	characteristic
1045	#95	C₂²×D₈₉	1	1	yes	characteristic
1046	#95	C₂²×D₈₉	1	1	yes	characteristic
1047	#95	C₂²×D₈₉	1	1	yes	characteristic
1048	#95	C₂²×D₈₉	1	1	yes	characteristic
1049	#95	C₂²×D₈₉	1	1	yes	characteristic
1050	#95	C₂²×D₈₉	1	1	yes	characteristic
1051	#95	C₂²×D₈₉	1	1	yes	characteristic
1052	#95	C₂²×D₈₉	1	1	yes	characteristic
1053	#95	C₂²×D₈₉	1	1	yes	characteristic
1054	#95	C₂²×D₈₉	1	1	yes	characteristic
1055	#95	C₂²×D₈₉	1	1	yes	characteristic
1056	#95	C₂²×D₈₉	1	1	yes	characteristic
1057	#95	C₂²×D₈₉	1	1	yes	characteristic
1058	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
1059	C₂×Q₈	—	4	1	no	—
1060	C₂×Q₈	—	4	1	no	—
1061	C₂×Q₈	—	89	4	no	—
1062	C₂×Q₈	—	89	4	no	—
1063	C₂×Q₈	—	89	4	no	—
1064	C₂×Q₈	—	356	1	no	—
1065	C₂×Q₈	—	356	1	no	—
1066	C₂×Q₈	—	356	1	no	—
1067	C₂×Q₈	—	356	1	no	—
1068	C₂×Q₈	—	356	1	no	—
1069	C₂×Q₈	—	356	1	no	—
1070	C₂×Q₈	C₂×C₄×D₈₉	1	4	yes	—
1071	C₂²×C₄	—	2	2	no	—
1072	C₂²×C₄	—	2	2	no	—
1073	C₂²×C₄	—	2	2	no	—
1074	C₂²×C₄	—	4	1	no	—
1075	C₂²×C₄	—	4	1	no	—
1076	C₂²×C₄	—	4	1	no	—
1077	C₂²×C₄	—	4	1	no	—
1078	C₂²×C₄	—	4	1	no	—
1079	C₂²×C₄	—	89	4	no	—
1080	C₂²×C₄	—	89	4	no	—
1081	C₂²×C₄	—	89	4	no	—
1082	C₂²×C₄	—	89	1	no	—
1083	C₂²×C₄	—	89	1	no	—
1084	C₂²×C₄	—	89	4	no	—
1085	C₂²×C₄	—	89	1	no	—
1086	C₂²×C₄	—	89	1	no	—
1087	C₂²×C₄	—	89	1	no	—
1088	C₂²×C₄	—	89	1	no	—
1089	C₂²×C₄	—	89	1	no	—
1090	C₂²×C₄	—	89	1	no	—
1091	C₂²×C₄	—	89	1	no	—
1092	C₂²×C₄	—	89	1	no	—
1093	C₂²×C₄	—	89	1	no	—
1094	C₂²×C₄	—	89	1	no	—
1095	C₂²×C₄	—	89	1	no	—
1096	C₂²×C₄	—	89	1	no	—
1097	C₂²×C₄	—	89	1	no	—
1098	C₂²×C₄	—	89	1	no	—
1099	C₂²×C₄	—	356	1	no	—
1100	C₂²×C₄	—	356	1	no	—
1101	C₂²×C₄	—	356	1	no	—
1102	C₂²×C₄	—	356	1	no	—
1103	C₂²×C₄	—	356	1	no	—
1104	C₂²×C₄	—	178	2	no	—
1105	C₂²×C₄	—	178	2	no	—
1106	C₂²×C₄	—	178	2	no	—
1107	C₂²×C₄	C₂×C₄×D₈₉	1	4	yes	—
1108	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1109	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1110	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1111	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1112	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1113	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1114	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1115	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1116	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1117	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1118	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1119	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1120	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1121	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1122	C₄⋊C₄	—	2	2	no	—
1123	C₄⋊C₄	—	4	1	no	—
1124	C₄⋊C₄	—	4	1	no	—
1125	C₄⋊C₄	—	4	1	no	—
1126	C₄⋊C₄	—	89	4	no	—
1127	C₄⋊C₄	—	89	4	no	—
1128	C₄⋊C₄	—	89	4	no	—
1129	C₄⋊C₄	—	89	4	no	—
1130	C₄⋊C₄	—	89	4	no	—
1131	C₄⋊C₄	—	89	4	no	—
1132	C₄⋊C₄	—	89	4	no	—
1133	C₄⋊C₄	—	89	4	no	—
1134	C₄⋊C₄	—	89	4	no	—
1135	C₄⋊C₄	—	89	4	no	—
1136	C₄⋊C₄	—	89	4	no	—
1137	C₄⋊C₄	—	89	4	no	—
1138	C₄⋊C₄	—	89	4	no	—
1139	C₄⋊C₄	—	89	4	no	—
1140	C₄⋊C₄	—	89	4	no	—
1141	C₄⋊C₄	—	89	4	no	—
1142	C₄⋊C₄	—	89	4	no	—
1143	C₄⋊C₄	—	89	4	no	—
1144	C₄⋊C₄	—	89	4	no	—
1145	C₄⋊C₄	—	356	1	no	—
1146	C₄⋊C₄	—	356	1	no	—
1147	C₄⋊C₄	—	356	1	no	—
1148	C₄⋊C₄	—	356	1	no	—
1149	C₄⋊C₄	—	356	1	no	—
1150	C₄⋊C₄	—	356	1	no	—
1151	C₄⋊C₄	—	356	1	no	—
1152	C₄⋊C₄	—	356	1	no	—
1153	C₄⋊C₄	—	356	1	no	—
1154	C₄⋊C₄	—	356	1	no	—
1155	C₄⋊C₄	—	356	1	no	—
1156	C₄⋊C₄	—	356	1	no	—
1157	C₄⋊C₄	—	356	1	no	—
1158	C₄⋊C₄	—	178	2	no	—
1159	C₄⋊C₄	—	178	2	no	—
1160	C₄⋊C₄	—	178	2	no	—
1161	C₄⋊C₄	—	178	2	no	—
1162	C₄⋊C₄	—	178	2	no	—
1163	C₄⋊C₄	—	178	2	no	—
1164	C₄⋊C₄	—	178	2	no	—
1165	C₄⋊C₄	—	178	2	no	—
1166	C₄⋊C₄	—	178	2	no	—
1167	C₄⋊C₄	—	178	2	no	—
1168	C₄⋊C₄	—	178	2	no	—
1169	C₄⋊C₄	—	178	2	no	—
1170	C₄⋊C₄	—	178	2	no	—
1171	C₄⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1172	C₄⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1173	C₄⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1174	C₂²⋊C₄	—	2	2	no	—
1175	C₂²⋊C₄	—	89	4	no	—
1176	C₂²⋊C₄	—	89	4	no	—
1177	C₂²⋊C₄	—	89	4	no	—
1178	C₂²⋊C₄	—	178	2	no	—
1179	C₂²⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1180	C₂²⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1181	C₂²⋊C₄	Q₈×D₈₉	1	4	yes	—
1182	C₄²	—	2	2	no	—
1183	C₄²	—	4	1	no	—
1184	C₄²	—	4	1	no	—
1185	C₄²	—	4	1	no	—
1186	C₄²	—	4	1	no	—
1187	C₄²	—	4	1	no	—
1188	C₄²	—	89	4	no	—
1189	C₄²	—	89	4	no	—
1190	C₄²	—	89	4	no	—
1191	C₄²	—	89	4	no	—
1192	C₄²	—	89	4	no	—
1193	C₄²	—	89	4	no	—
1194	C₄²	—	356	1	no	—
1195	C₄²	—	356	1	no	—
1196	C₄²	—	356	1	no	—
1197	C₄²	—	356	1	no	—
1198	C₄²	—	356	1	no	—
1199	C₄²	—	356	1	no	—
1200	C₄²	—	356	1	no	—
1201	C₄²	—	356	1	no	—
1202	C₄²	—	356	1	no	—
1203	C₄²	—	356	1	no	—
1204	C₄²	—	356	1	no	—
1205	C₄²	—	356	1	no	—
1206	C₄²	—	356	1	no	—
1207	C₄²	—	356	1	no	—
1208	C₄²	—	356	1	no	—
1209	C₄²	—	178	2	no	—
1210	C₄²	—	178	2	no	—
1211	C₄²	—	178	2	no	—
1212	C₄²	—	178	2	no	—
1213	C₄²	—	178	2	no	—
1214	C₄²	—	178	2	no	—
1215	C₄²	—	178	2	no	—
1216	C₄²	—	178	2	no	—
1217	C₄²	—	178	2	no	—
1218	C₂³	—	2	1	no	—
1219	C₂³	—	2	1	no	—
1220	C₂³	—	2	1	no	—
1221	C₂³	—	2	1	no	—
1222	C₂³	C₂²×C₄×D₈₉	1	2	yes	—
1223	C₂³	C₂×Q₈×D₈₉	1	2	yes	—
1224	C₂³	#41×D₈₉	1	2	yes	—
1225	C₂³	C₂⁴×D₈₉	1	1	yes	characteristic
1226	Q₈	—	4	4	no	—
1227	Q₈	—	356	4	no	—
1228	Q₈	—	356	4	no	—
1229	Q₈	—	356	4	no	—
1230	C₂×C₄	—	2	1	no	—
1231	C₂×C₄	—	2	1	no	—
1232	C₂×C₄	—	2	1	no	—
1233	C₂×C₄	—	2	1	no	—
1234	C₂×C₄	—	2	1	no	—
1235	C₂×C₄	—	2	1	no	—
1236	C₂×C₄	—	2	1	no	—
1237	C₂×C₄	—	2	1	no	—
1238	C₂×C₄	—	2	1	no	—
1239	C₂×C₄	—	2	1	no	—
1240	C₂×C₄	—	2	1	no	—
1241	C₂×C₄	—	2	1	no	—
1242	C₂×C₄	—	2	1	no	—
1243	C₂×C₄	—	2	1	no	—
1244	C₂×C₄	—	2	1	no	—
1245	C₂×C₄	—	2	1	no	—
1246	C₂×C₄	—	2	1	no	—
1247	C₂×C₄	—	2	1	no	—
1248	C₂×C₄	—	2	1	no	—
1249	C₂×C₄	—	2	1	no	—
1250	C₂×C₄	—	2	1	no	—
1251	C₂×C₄	—	2	1	no	—
1252	C₂×C₄	—	2	1	no	—
1253	C₂×C₄	—	2	1	no	—
1254	C₂×C₄	—	2	1	no	—
1255	C₂×C₄	—	2	1	no	—
1256	C₂×C₄	—	2	1	no	—
1257	C₂×C₄	—	2	1	no	—
1258	C₂×C₄	—	2	1	no	—
1259	C₂×C₄	—	2	1	no	—
1260	C₂×C₄	—	2	1	no	—
1261	C₂×C₄	—	2	1	no	—
1262	C₂×C₄	—	2	1	no	—
1263	C₂×C₄	—	4	4	no	—
1264	C₂×C₄	—	4	4	no	—
1265	C₂×C₄	—	8	2	no	—
1266	C₂×C₄	—	89	2	no	—
1267	C₂×C₄	—	89	2	no	—
1268	C₂×C₄	—	89	2	no	—
1269	C₂×C₄	—	89	2	no	—
1270	C₂×C₄	—	89	2	no	—
1271	C₂×C₄	—	89	2	no	—
1272	C₂×C₄	—	89	16	no	—
1273	C₂×C₄	—	89	2	no	—
1274	C₂×C₄	—	89	2	no	—
1275	C₂×C₄	—	89	2	no	—
1276	C₂×C₄	—	89	2	no	—
1277	C₂×C₄	—	89	2	no	—
1278	C₂×C₄	—	89	2	no	—
1279	C₂×C₄	—	89	2	no	—
1280	C₂×C₄	—	89	2	no	—
1281	C₂×C₄	—	89	2	no	—
1282	C₂×C₄	—	356	4	no	—
1283	C₂×C₄	—	356	4	no	—
1284	C₂×C₄	—	178	1	no	—
1285	C₂×C₄	—	178	1	no	—
1286	C₂×C₄	—	178	1	no	—
1287	C₂×C₄	—	178	1	no	—
1288	C₂×C₄	—	178	1	no	—
1289	C₂×C₄	—	178	1	no	—
1290	C₂×C₄	—	178	1	no	—
1291	C₂×C₄	—	178	1	no	—
1292	C₂×C₄	—	178	1	no	—
1293	C₂×C₄	—	178	1	no	—
1294	C₂×C₄	—	178	1	no	—
1295	C₂×C₄	—	178	1	no	—
1296	C₂×C₄	—	178	1	no	—
1297	C₂×C₄	—	178	1	no	—
1298	C₂×C₄	—	178	1	no	—
1299	C₂×C₄	—	178	1	no	—
1300	C₂×C₄	—	178	1	no	—
1301	C₂×C₄	—	178	1	no	—
1302	C₂×C₄	—	178	1	no	—
1303	C₂×C₄	—	178	1	no	—
1304	C₂×C₄	—	178	1	no	—
1305	C₂×C₄	—	178	1	no	—
1306	C₂×C₄	—	178	1	no	—
1307	C₂×C₄	—	178	1	no	—
1308	C₂×C₄	—	178	1	no	—
1309	C₂×C₄	—	178	1	no	—
1310	C₂×C₄	—	178	1	no	—
1311	C₂×C₄	—	178	1	no	—
1312	C₂×C₄	—	178	1	no	—
1313	C₂×C₄	—	178	1	no	—
1314	C₂×C₄	—	178	1	no	—
1315	C₂×C₄	—	178	1	no	—
1316	C₂×C₄	—	178	1	no	—
1317	C₂×C₄	—	712	2	no	—
1318	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1319	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1320	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1321	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1322	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1323	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1324	C₂×C₄	C₂×Q₈×D₈₉	1	2	yes	—
1325	C₂×C₄	C₂×Q₈×D₈₉	1	2	yes	—
1326	C₂×C₄	#15668059	1	2	yes	—
1327	C₂²	—	2	2	no	—
1328	C₂²	—	2	2	no	—
1329	C₂²	—	2	2	no	—
1330	C₂²	—	2	2	no	—
1331	C₂²	—	2	2	no	—
1332	C₂²	—	2	2	no	—
1333	C₂²	C₄×Q₈×D₈₉	1	4	yes	—
1334	C₂²	C₂³×C₄×D₈₉	1	1	yes	characteristic
1335	C₂²	C₂²×Q₈×D₈₉	1	1	yes	characteristic
1336	C₂²	C₂×#41×D₈₉	1	1	yes	characteristic
1337	C₂²	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
1338	C₂²	C₂×#15668059	1	1	yes	characteristic
1339	C₂²	#19152433	1	1	yes	characteristic
1340	C₂²	#19152434	1	1	yes	characteristic
1341	C₄	—	2	2	no	—
1342	C₄	—	2	2	no	—
1343	C₄	—	2	2	no	—
1344	C₄	—	2	2	no	—
1345	C₄	—	2	2	no	—
1346	C₄	—	2	2	no	—
1347	C₄	—	2	2	no	—
1348	C₄	—	2	2	no	—
1349	C₄	—	2	2	no	—
1350	C₄	—	4	1	no	—
1351	C₄	—	4	1	no	—
1352	C₄	—	4	1	no	—
1353	C₄	—	4	1	no	—
1354	C₄	—	4	1	no	—
1355	C₄	—	89	4	no	—
1356	C₄	—	89	4	no	—
1357	C₄	—	356	1	no	—
1358	C₄	—	356	1	no	—
1359	C₄	—	356	1	no	—
1360	C₄	—	356	1	no	—
1361	C₄	—	356	1	no	—
1362	C₄	—	178	2	no	—
1363	C₄	—	178	2	no	—
1364	C₄	—	178	2	no	—
1365	C₄	—	178	2	no	—
1366	C₄	—	178	2	no	—
1367	C₄	—	178	2	no	—
1368	C₄	—	178	2	no	—
1369	C₄	—	178	2	no	—
1370	C₄	—	178	2	no	—
1371	C₂	—	2	4	no	—
1372	C₂	C₂×C₄×Q₈×D₈₉	1	1	yes	characteristic
1373	C₂	#26033456	1	1	yes	characteristic
1374	C₂	C₄×#15668059	1	1	yes	characteristic
1375	C₂	#26033978	1	1	yes	characteristic
1376	C₂	#26033991	1	1	yes	characteristic
1377	C₂	#26034066	1	1	yes	characteristic
1378	C₂	#26034072	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₈₉
commutator	C₂²×C₈₉	C₂⁴×C₄
Fitting	C₈₉×#2368	C₂
socle, cosocle	C₂³×C₈₉	C₂⁵
prime radical	C₂⁴×C₈₉	C₂⁴
hypercenter	#2368	D₈₉
hypocenter	C₈₉	#34272
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ #2368

Complements

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

N	H ≅ G/N	type
2. #26023349	C₂	semidirect
3. #26023345	C₂	semidirect
4. #26023345	C₂	semidirect
5. #26023343	C₂	semidirect
6. #26023340	C₂	semidirect
7. #26023339	C₂	semidirect
11. #26023309	C₂	semidirect
12. #26023307	C₂	semidirect
17. #26022997	C₂	semidirect
18. #26022995	C₂	semidirect
19. #26022988	C₂	semidirect
20. #26022988	C₂	semidirect
22. C₄×#15668011	C₂	semidirect
23. #26022821	C₂	semidirect
24. #26022809	C₂	semidirect
25. C₄×#15668002	C₂	semidirect
32. #19152227	C₄	semidirect
195. #15668011	C₂×C₄	semidirect
196. #15668011	C₂×C₄	semidirect
197. #15668010	C₂×C₄	semidirect
198. #15668010	C₂×C₄	semidirect
199. #15668002	C₂×C₄	semidirect
200. #15668002	C₂×C₄	semidirect
201. #15668002	C₂×C₄	semidirect
202. #15668002	C₂×C₄	semidirect
213. #15667968	Q₈	semidirect
618. C₂×Dic₈₉	C₄×Q₈	semidirect
721. C₈₉	#34272	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19152227	2
#26023349	2
#26023345	2
#26023343	2
#26023340	2
#26023339	2
#26023333	2
#26023332	2
#26023330	2
#26023309	2
#26023307	2
#26023261	2
#26023258	2
#26023255	2
#26023252	2
#26022997	2
#26022995	2
#26022988	2
#26022871	2
C₄×#15668011	2
#26022821	2
#26022809	2
C₄×#15668002	2
#26022731	2
C₂×#19151495	2
#26022607	2
C₄×#15667968	2
C₈₉×#2368	2
#34272	89