Subgroups — #36719513

Order 22784.

2292 conjugacy classes of subgroups.

The subgroup lattice has 1522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19152279	C₂	1	1	yes	maximal, characteristic
2	#26023440	C₂	1	1	yes	maximal, characteristic, complemented
3	#26023422	C₂	1	1	yes	maximal, characteristic, complemented
4	#26023412	C₂	1	1	yes	maximal, characteristic, complemented
5	#26023395	C₂	1	1	yes	maximal, characteristic, complemented
6	#26023374	C₂	1	1	yes	maximal, characteristic, complemented
7	#26023333	C₂	1	1	yes	maximal, characteristic, complemented
8	#26023250	C₂	1	1	yes	maximal, characteristic, complemented
9	#26023238	C₂	1	1	yes	maximal, characteristic, complemented
10	#26023200	C₂	1	1	yes	maximal, characteristic, complemented
11	#26023157	C₂	1	1	yes	maximal, characteristic, complemented
12	#26023134	C₂	1	1	yes	maximal, characteristic, complemented
13	#26023106	C₂	1	1	yes	maximal, characteristic, complemented
14	#26023097	C₂	1	1	yes	maximal, characteristic, complemented
15	#26023097	C₂	1	1	yes	maximal, characteristic, complemented
16	#26023043	C₂	1	1	yes	maximal, characteristic, complemented
17	#26023039	C₂	1	1	yes	maximal, characteristic, complemented
18	#26023029	C₂	1	1	yes	maximal, characteristic, complemented
19	#26023022	C₂	1	1	yes	maximal, characteristic, complemented
20	#26022964	C₂	1	1	yes	maximal, characteristic, complemented
21	#26022931	C₂	1	1	yes	maximal, characteristic, complemented
22	#26022917	C₂	1	1	yes	maximal, characteristic, complemented
23	#26022913	C₂	1	1	yes	maximal, characteristic
24	#26022878	C₂	1	1	yes	maximal, characteristic, complemented
25	#26022871	C₂	1	1	yes	maximal, characteristic, complemented
26	#26022864	C₂	1	1	yes	maximal, characteristic, complemented
27	#26022856	C₂	1	1	yes	maximal, characteristic, complemented
28	C₄×#15667989	C₂	1	1	yes	maximal, characteristic, complemented
29	#26022692	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#19151486	C₂	1	1	yes	maximal, characteristic, complemented
31	C₈₉×#2358	C₂	1	1	yes	maximal, characteristic
32	#19152279	C₄	1	16	yes	complemented
33	C₂×#15668005	C₂²	1	1	yes	characteristic
34	C₂×#15668005	C₂²	1	1	yes	characteristic
35	C₂×#15667999	C₂²	1	1	yes	characteristic
36	C₂×#15667993	C₂²	1	1	yes	characteristic
37	C₂×#15667993	C₂²	1	1	yes	characteristic
38	C₂×#15667993	C₂²	1	1	yes	characteristic
39	C₂×#15667989	C₂²	1	1	yes	characteristic
40	C₂×#15667989	C₂²	1	1	yes	characteristic
41	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
42	C₂×D₄×Dic₈₉	C₂²	1	1	yes	characteristic
43	C₂×D₄×Dic₈₉	C₂²	1	1	yes	characteristic
44	C₂×D₄×Dic₈₉	C₂²	1	1	yes	characteristic
45	C₂×#15667968	C₂²	1	1	yes	characteristic
46	C₂×#15667968	C₂²	1	1	yes	characteristic
47	C₂×#15667968	C₂²	1	1	yes	characteristic
48	C₂×#15667968	C₂²	1	1	yes	characteristic
49	C₂×#15667968	C₂²	1	1	yes	characteristic, complemented
50	C₂²×#13083553	C₂²	1	1	yes	characteristic
51	C₂²×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
52	C₂²×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
53	C₂²×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
54	C₂²×C₄×Dic₈₉	C₂²	1	1	yes	characteristic
55	#19151503	C₂²	1	1	yes	characteristic, complemented
56	#19151502	C₂²	1	1	yes	characteristic, complemented
57	#19151502	C₂²	1	1	yes	characteristic, complemented
58	#19151501	C₂²	1	1	yes	characteristic
59	#19151501	C₂²	1	1	yes	characteristic
60	#19151496	C₂²	1	1	yes	characteristic, complemented
61	#19151495	C₂²	1	1	yes	characteristic, complemented
62	#19151495	C₂²	1	1	yes	characteristic, complemented
63	#19151495	C₂²	1	1	yes	characteristic, complemented
64	#19151495	C₂²	1	1	yes	characteristic, complemented
65	#19151494	C₂²	1	1	yes	characteristic, complemented
66	#19151493	C₂²	1	1	yes	characteristic, complemented
67	#19151493	C₂²	1	1	yes	characteristic, complemented
68	#19151493	C₂²	1	1	yes	characteristic, complemented
69	#19151493	C₂²	1	1	yes	characteristic, complemented
70	#19151492	C₂²	1	1	yes	characteristic
71	#19151492	C₂²	1	1	yes	characteristic
72	#19151492	C₂²	1	1	yes	characteristic
73	#19151492	C₂²	1	1	yes	characteristic
74	#19151492	C₂²	1	1	yes	characteristic, complemented
75	#19151492	C₂²	1	1	yes	characteristic, complemented
76	#19151492	C₂²	1	1	yes	characteristic, complemented
77	#19151492	C₂²	1	1	yes	characteristic, complemented
78	#19151491	C₂²	1	1	yes	characteristic
79	#19151491	C₂²	1	1	yes	characteristic
80	#19151491	C₂²	1	1	yes	characteristic
81	#19151491	C₂²	1	1	yes	characteristic
82	#19151486	C₂²	1	1	yes	characteristic
83	#19151486	C₂²	1	1	yes	characteristic
84	#19151486	C₂²	1	1	yes	characteristic
85	#19151486	C₂²	1	1	yes	characteristic
86	#19151486	C₂²	1	1	yes	characteristic
87	#19151486	C₂²	1	1	yes	characteristic
88	#19151486	C₂²	1	1	yes	characteristic
89	#19151486	C₂²	1	1	yes	characteristic
90	#19151486	C₂²	1	1	yes	characteristic
91	#19151486	C₂²	1	1	yes	characteristic
92	#19151486	C₂²	1	1	yes	characteristic
93	#19151486	C₂²	1	1	yes	characteristic
94	#19151486	C₂²	1	1	yes	characteristic, complemented
95	#19151486	C₂²	1	1	yes	characteristic, complemented
96	#19151485	C₂²	1	1	yes	characteristic, complemented
97	#19151485	C₂²	1	1	yes	characteristic, complemented
98	#19151483	C₂²	1	1	yes	characteristic, complemented
99	#19151483	C₂²	1	1	yes	characteristic, complemented
100	#19151482	C₂²	1	1	yes	characteristic, complemented
101	#19151482	C₂²	1	1	yes	characteristic, complemented
102	#19151482	C₂²	1	1	yes	characteristic, complemented
103	#19151482	C₂²	1	1	yes	characteristic, complemented
104	#19151481	C₂²	1	1	yes	characteristic, complemented
105	#19151481	C₂²	1	1	yes	characteristic, complemented
106	#19151480	C₂²	1	1	yes	characteristic, complemented
107	#19151480	C₂²	1	1	yes	characteristic, complemented
108	#19151480	C₂²	1	1	yes	characteristic, complemented
109	#19151480	C₂²	1	1	yes	characteristic, complemented
110	#19151479	C₂²	1	1	yes	characteristic, complemented
111	#19151479	C₂²	1	1	yes	characteristic, complemented
112	#19151478	C₂²	1	1	yes	characteristic
113	#19151478	C₂²	1	1	yes	characteristic
114	#19151478	C₂²	1	1	yes	characteristic
115	#19151473	C₂²	1	1	yes	characteristic
116	#19151471	C₂²	1	1	yes	characteristic
117	#19151471	C₂²	1	1	yes	characteristic
118	#19151471	C₂²	1	1	yes	characteristic
119	#19151471	C₂²	1	1	yes	characteristic
120	#19151471	C₂²	1	1	yes	characteristic
121	#19151471	C₂²	1	1	yes	characteristic
122	#19151471	C₂²	1	1	yes	characteristic
123	#19151471	C₂²	1	1	yes	characteristic
124	#19151471	C₂²	1	1	yes	characteristic, complemented
125	#19151471	C₂²	1	1	yes	characteristic, complemented
126	#19151471	C₂²	1	1	yes	characteristic, complemented
127	#19151470	C₂²	1	1	yes	characteristic
128	#19151470	C₂²	1	1	yes	characteristic
129	#19151470	C₂²	1	1	yes	characteristic
130	#19151470	C₂²	1	1	yes	characteristic
131	#19151470	C₂²	1	1	yes	characteristic, complemented
132	#19151470	C₂²	1	1	yes	characteristic, complemented
133	#19151467	C₂²	1	1	yes	characteristic, complemented
134	#19151467	C₂²	1	1	yes	characteristic, complemented
135	#19151465	C₂²	1	1	yes	characteristic, complemented
136	#19151463	C₂²	1	1	yes	characteristic, complemented
137	#19151462	C₂²	1	1	yes	characteristic, complemented
138	#19151462	C₂²	1	1	yes	characteristic, complemented
139	#19151462	C₂²	1	1	yes	characteristic, complemented
140	#19151459	C₂²	1	1	yes	characteristic
141	#19151459	C₂²	1	1	yes	characteristic
142	#19151456	C₂²	1	1	yes	characteristic
143	#19151456	C₂²	1	1	yes	characteristic
144	#19151456	C₂²	1	1	yes	characteristic
145	#19151456	C₂²	1	1	yes	characteristic
146	#19151456	C₂²	1	1	yes	characteristic
147	#19151456	C₂²	1	1	yes	characteristic
148	#19151456	C₂²	1	1	yes	characteristic, complemented
149	#19151454	C₂²	1	1	yes	characteristic
150	C₄⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
151	C₄×#13083553	C₂²	1	1	yes	characteristic, complemented
152	C₄×#13083553	C₂²	1	1	yes	characteristic, complemented
153	C₄×#13083553	C₂²	1	1	yes	characteristic, complemented
154	C₄×#13083553	C₂²	1	1	yes	characteristic, complemented
155	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic, complemented
156	#19151449	C₂²	1	1	yes	characteristic, complemented
157	#19151449	C₂²	1	1	yes	characteristic, complemented
158	#19151449	C₂²	1	1	yes	characteristic, complemented
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, complemented
163	C₂²⋊C₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
164	C₄×C₂²⋊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	#19151444	C₂²	1	1	yes	characteristic, complemented
169	#19151443	C₂²	1	1	yes	characteristic, complemented
170	C₂×#15667919	C₂²	1	1	yes	characteristic
171	C₂×#15667919	C₂²	1	1	yes	characteristic
172	C₂×#15667919	C₂²	1	1	yes	characteristic, complemented
173	C₂×#120×C₈₉	C₂²	1	1	yes	characteristic
174	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
175	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
176	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
177	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
178	#390×C₈₉	C₂²	1	1	yes	characteristic
179	#388×C₈₉	C₂²	1	1	yes	characteristic
180	#388×C₈₉	C₂²	1	1	yes	characteristic
181	#386×C₈₉	C₂²	1	1	yes	characteristic
182	#386×C₈₉	C₂²	1	1	yes	characteristic
183	#386×C₈₉	C₂²	1	1	yes	characteristic
184	#385×C₈₉	C₂²	1	1	yes	characteristic
185	#385×C₈₉	C₂²	1	1	yes	characteristic
186	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
187	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
188	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
189	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
190	C₂³×Dic₈₉	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	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
196	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
197	#15668005	C₂×C₄	1	8	yes	complemented
198	#15668005	C₂×C₄	1	8	yes	complemented
199	#15667999	C₂×C₄	1	8	yes	complemented
200	#15667993	C₂×C₄	1	8	yes	complemented
201	#15667993	C₂×C₄	1	8	yes	complemented
202	#15667993	C₂×C₄	1	8	yes	complemented
203	#15667989	C₂×C₄	1	8	yes	complemented
204	#15667989	C₂×C₄	1	8	yes	complemented
205	C₄×Dic₁₇₈	—	4	2	no	—
206	D₄×Dic₈₉	—	4	2	no	—
207	D₄×Dic₈₉	C₂×C₄	1	8	yes	complemented
208	D₄×Dic₈₉	C₂×C₄	1	8	yes	complemented
209	#15667968	—	4	2	no	—
210	#15667968	—	4	2	no	—
211	#15667968	—	4	2	no	—
212	#15667968	C₂×C₄	1	8	yes	complemented
213	#15667968	C₂×C₄	1	8	yes	complemented
214	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
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×#13083553	—	4	2	no	—
220	C₂×#13083553	C₂³	1	1	yes	characteristic
221	C₂×#13083553	C₂³	1	1	yes	characteristic
222	C₂×#13083553	C₂³	1	1	yes	characteristic
223	C₂×#13083553	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×#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×C₂²⋊Dic₈₉	—	4	2	no	—
247	C₂×C₂²⋊Dic₈₉	C₂×C₄	1	8	yes	complemented
248	C₂×C₂²⋊Dic₈₉	C₂×C₄	1	8	yes	complemented
249	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
252	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
253	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
254	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
257	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
273	C₂×C₄×Dic₈₉	—	4	2	no	—
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	#15667919	C₂³	1	1	yes	characteristic
293	#15667919	C₂³	1	1	yes	characteristic
294	#15667919	C₂³	1	1	yes	characteristic
295	#15667919	C₂³	1	1	yes	characteristic
296	#15667919	C₂³	1	1	yes	characteristic
297	#15667919	C₂³	1	1	yes	characteristic
298	#15667919	C₂³	1	1	yes	characteristic
299	#15667919	C₂³	1	1	yes	characteristic
300	#15667919	C₂³	1	1	yes	characteristic
301	#15667919	C₂³	1	1	yes	characteristic
302	#15667919	C₂³	1	1	yes	characteristic
303	#15667919	C₂³	1	1	yes	characteristic
304	#15667919	C₂³	1	1	yes	characteristic
305	#15667919	C₂³	1	1	yes	characteristic
306	#15667919	C₂³	1	1	yes	characteristic
307	#15667919	C₂³	1	1	yes	characteristic
308	#15667919	C₂³	1	1	yes	characteristic
309	#15667919	C₂³	1	1	yes	characteristic
310	#15667919	C₂³	1	1	yes	characteristic
311	#15667919	C₂³	1	1	yes	characteristic
312	#15667919	C₂³	1	1	yes	characteristic
313	#15667919	C₂³	1	1	yes	characteristic
314	#15667919	C₂³	1	1	yes	characteristic
315	#15667919	C₂³	1	1	yes	characteristic
316	#15667919	C₂³	1	1	yes	characteristic
317	#15667919	C₂³	1	1	yes	characteristic
318	#15667919	C₂³	1	1	yes	characteristic
319	#15667919	C₂³	1	1	yes	characteristic
320	#15667919	C₂³	1	1	yes	characteristic
321	#15667919	C₂³	1	1	yes	characteristic
322	#15667919	C₂³	1	1	yes	characteristic
323	#15667919	C₂³	1	1	yes	characteristic
324	#15667919	C₂³	1	1	yes	characteristic
325	#15667919	C₂³	1	1	yes	characteristic
326	#15667919	C₂³	1	1	yes	characteristic
327	#15667919	C₂³	1	1	yes	characteristic
328	#15667919	C₂³	1	1	yes	characteristic
329	#15667919	C₂³	1	1	yes	characteristic
330	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
331	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
332	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
333	C₂²×D₄×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	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
337	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
338	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
339	#120×C₈₉	C₂×C₄	1	8	yes	—
340	C₄×D₄×C₈₉	—	4	2	no	—
341	C₄×D₄×C₈₉	—	4	2	no	—
342	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
343	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
344	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×C₈₉	—	4	2	no	—
346	C₂×C₂²⋊C₄×C₈₉	—	4	2	no	—
347	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
348	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
349	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
350	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
351	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
352	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
353	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
354	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
355	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
356	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
357	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
358	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
359	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
360	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
361	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
362	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
363	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
364	#95×C₈₉	C₂³	1	1	yes	characteristic
365	#95×C₈₉	C₂³	1	1	yes	characteristic
366	#95×C₈₉	C₂³	1	1	yes	characteristic
367	#95×C₈₉	C₂³	1	1	yes	characteristic
368	#95×C₈₉	C₂³	1	1	yes	characteristic
369	#95×C₈₉	C₂³	1	1	yes	characteristic
370	C₂×Dic₁₇₈	—	4	1	no	—
371	C₂×Dic₁₇₈	—	4	1	no	—
372	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
373	C₂²×Dic₈₉	—	2	2	no	—
374	C₂²×Dic₈₉	—	2	2	no	—
375	C₂²×Dic₈₉	—	2	2	no	—
376	C₂²×Dic₈₉	—	2	2	no	—
377	C₂²×Dic₈₉	—	4	1	no	—
378	C₂²×Dic₈₉	—	4	1	no	—
379	C₂²×Dic₈₉	—	4	1	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	—	4	1	no	—
386	C₂²×Dic₈₉	—	4	1	no	—
387	C₂²×Dic₈₉	—	4	1	no	—
388	C₂²×Dic₈₉	—	4	1	no	—
389	C₂²×Dic₈₉	—	4	1	no	—
390	C₂²×Dic₈₉	—	4	1	no	—
391	C₂²×Dic₈₉	—	4	1	no	—
392	C₂²×Dic₈₉	C₂²×C₄	1	4	yes	—
393	C₂²×Dic₈₉	C₂²×C₄	1	4	yes	—
394	C₂²×Dic₈₉	C₂²×C₄	1	4	yes	—
395	C₂²×Dic₈₉	C₂²×C₄	1	4	yes	—
396	C₂²×Dic₈₉	C₂²×C₄	1	4	yes	—
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	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	C₄⋊Dic₈₉	—	4	1	no	—
414	C₄⋊Dic₈₉	—	4	1	no	—
415	C₄⋊Dic₈₉	—	4	1	no	—
416	C₄⋊Dic₈₉	C₂²×C₄	1	4	yes	—
417	C₄⋊Dic₈₉	C₂²×C₄	1	4	yes	—
418	#13083553	—	2	2	no	—
419	#13083553	—	4	1	no	—
420	#13083553	—	4	1	no	—
421	#13083553	—	4	1	no	—
422	#13083553	—	4	1	no	—
423	#13083553	—	4	1	no	—
424	#13083553	—	4	1	no	—
425	#13083553	—	4	1	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	—	4	1	no	—
435	#13083553	—	4	1	no	—
436	#13083553	—	4	1	no	—
437	#13083553	—	4	1	no	—
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	C₂²⋊Dic₈₉	—	2	2	no	—
445	C₂²⋊Dic₈₉	—	2	2	no	—
446	C₂²⋊Dic₈₉	—	4	1	no	—
447	C₂²⋊Dic₈₉	—	4	1	no	—
448	C₂²⋊Dic₈₉	—	4	1	no	—
449	C₂²⋊Dic₈₉	—	4	1	no	—
450	C₂²⋊Dic₈₉	—	4	1	no	—
451	C₂²⋊Dic₈₉	—	4	1	no	—
452	C₂²⋊Dic₈₉	—	4	1	no	—
453	C₂²⋊Dic₈₉	—	4	1	no	—
454	C₂²⋊Dic₈₉	—	4	1	no	—
455	C₂²⋊Dic₈₉	—	4	1	no	—
456	C₂²⋊Dic₈₉	—	4	1	no	—
457	C₂²⋊Dic₈₉	C₂²×C₄	1	4	yes	—
458	C₂²⋊Dic₈₉	C₂²×C₄	1	4	yes	—
459	C₂²⋊Dic₈₉	C₂²×C₄	1	4	yes	—
460	C₂²⋊Dic₈₉	C₂²×C₄	1	4	yes	—
461	C₂²⋊Dic₈₉	C₂²×C₄	1	4	yes	—
462	C₂²⋊Dic₈₉	C₂²×C₄	1	4	yes	—
463	C₂²⋊Dic₈₉	C₂²×C₄	1	4	yes	—
464	C₂²⋊Dic₈₉	C₂²×C₄	1	4	yes	—
465	C₂²⋊Dic₈₉	C₂²×C₄	1	4	yes	—
466	C₂²⋊Dic₈₉	C₂²×C₄	1	4	yes	—
467	C₂²⋊Dic₈₉	C₂²×C₄	1	4	yes	—
468	C₄×Dic₈₉	—	2	2	no	—
469	C₄×Dic₈₉	—	2	2	no	—
470	C₄×Dic₈₉	—	2	2	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	—	4	1	no	—
479	C₄×Dic₈₉	—	4	1	no	—
480	C₄×Dic₈₉	—	4	1	no	—
481	C₄×Dic₈₉	—	4	1	no	—
482	C₄×Dic₈₉	—	4	1	no	—
483	C₄×Dic₈₉	C₂²×C₄	1	4	yes	—
484	C₄×Dic₈₉	C₂²×C₄	1	4	yes	—
485	C₄×Dic₈₉	C₂²×C₄	1	4	yes	—
486	C₂⁴×C₈₉	—	2	2	no	—
487	C₂⁴×C₈₉	—	2	2	no	—
488	C₂⁴×C₈₉	—	4	1	no	—
489	C₂⁴×C₈₉	—	4	1	no	—
490	C₂⁴×C₈₉	—	4	1	no	—
491	C₂⁴×C₈₉	—	4	1	no	—
492	C₂⁴×C₈₉	C₂²×C₄	1	4	yes	—
493	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
494	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
495	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
496	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
497	C₂×D₄×C₈₉	—	2	2	no	—
498	C₂×D₄×C₈₉	—	2	2	no	—
499	C₂×D₄×C₈₉	—	4	1	no	—
500	C₂×D₄×C₈₉	—	4	1	no	—
501	C₂×D₄×C₈₉	—	4	1	no	—
502	C₂×D₄×C₈₉	—	4	1	no	—
503	C₂×D₄×C₈₉	C₂²×C₄	1	4	yes	—
504	C₂×D₄×C₈₉	C₂²×C₄	1	4	yes	—
505	C₂×D₄×C₈₉	C₂²×C₄	1	4	yes	—
506	C₂²×C₄×C₈₉	—	2	2	no	—
507	C₂²×C₄×C₈₉	—	2	2	no	—
508	C₂²×C₄×C₈₉	—	2	2	no	—
509	C₂²×C₄×C₈₉	—	4	1	no	—
510	C₂²×C₄×C₈₉	—	4	1	no	—
511	C₂²×C₄×C₈₉	—	4	1	no	—
512	C₂²×C₄×C₈₉	—	4	1	no	—
513	C₂²×C₄×C₈₉	—	4	1	no	—
514	C₂²×C₄×C₈₉	—	4	1	no	—
515	C₂²×C₄×C₈₉	—	4	1	no	—
516	C₂²×C₄×C₈₉	—	4	1	no	—
517	C₂²×C₄×C₈₉	—	4	1	no	—
518	C₂²×C₄×C₈₉	—	4	1	no	—
519	C₂²×C₄×C₈₉	—	4	1	no	—
520	C₂²×C₄×C₈₉	—	4	1	no	—
521	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
522	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
523	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
524	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
525	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₈₉	—	4	1	no	—
533	C₄⋊C₄×C₈₉	—	4	1	no	—
534	C₄⋊C₄×C₈₉	—	4	1	no	—
535	C₂²⋊C₄×C₈₉	—	2	2	no	—
536	C₂²⋊C₄×C₈₉	—	2	2	no	—
537	C₂²⋊C₄×C₈₉	—	2	2	no	—
538	C₂²⋊C₄×C₈₉	—	2	2	no	—
539	C₂²⋊C₄×C₈₉	—	2	2	no	—
540	C₂²⋊C₄×C₈₉	—	4	1	no	—
541	C₂²⋊C₄×C₈₉	—	4	1	no	—
542	C₂²⋊C₄×C₈₉	—	4	1	no	—
543	C₂²⋊C₄×C₈₉	—	4	1	no	—
544	C₂²⋊C₄×C₈₉	—	4	1	no	—
545	C₂²⋊C₄×C₈₉	—	4	1	no	—
546	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
547	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
548	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
549	C₄²×C₈₉	—	2	2	no	—
550	C₄²×C₈₉	—	4	1	no	—
551	C₄²×C₈₉	—	4	1	no	—
552	C₂³×C₈₉	—	2	1	no	—
553	C₂³×C₈₉	—	2	1	no	—
554	C₂³×C₈₉	—	2	1	no	—
555	C₂³×C₈₉	—	2	1	no	—
556	C₂³×C₈₉	—	2	1	no	—
557	C₂³×C₈₉	—	2	1	no	—
558	C₂³×C₈₉	—	2	1	no	—
559	C₂³×C₈₉	—	2	1	no	—
560	C₂³×C₈₉	—	2	1	no	—
561	C₂³×C₈₉	—	2	1	no	—
562	C₂³×C₈₉	—	2	1	no	—
563	C₂³×C₈₉	—	2	1	no	—
564	C₂³×C₈₉	—	2	1	no	—
565	C₂³×C₈₉	—	2	1	no	—
566	C₂³×C₈₉	—	2	1	no	—
567	C₂³×C₈₉	—	2	1	no	—
568	C₂³×C₈₉	—	2	1	no	—
569	C₂³×C₈₉	—	2	1	no	—
570	C₂³×C₈₉	—	2	1	no	—
571	C₂³×C₈₉	—	2	1	no	—
572	C₂³×C₈₉	—	2	1	no	—
573	C₂³×C₈₉	—	2	1	no	—
574	C₂³×C₈₉	—	2	8	no	—
575	C₂³×C₈₉	—	4	4	no	—
576	C₂³×C₈₉	—	4	4	no	—
577	C₂³×C₈₉	—	8	2	no	—
578	C₂³×C₈₉	—	8	2	no	—
579	C₂³×C₈₉	—	8	2	no	—
580	C₂³×C₈₉	—	8	2	no	—
581	C₂³×C₈₉	C₂³×C₄	1	2	yes	—
582	C₂³×C₈₉	C₂³×C₄	1	2	yes	—
583	C₂³×C₈₉	C₂³×C₄	1	2	yes	—
584	C₂³×C₈₉	C₂³×C₄	1	2	yes	—
585	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
586	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
587	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
588	D₄×C₈₉	—	2	8	no	—
589	D₄×C₈₉	—	4	4	no	—
590	D₄×C₈₉	—	4	4	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	—	2	1	no	—
615	C₂×C₄×C₈₉	—	2	1	no	—
616	C₂×C₄×C₈₉	—	2	1	no	—
617	C₂×C₄×C₈₉	—	2	1	no	—
618	C₂×C₄×C₈₉	—	2	1	no	—
619	C₂×C₄×C₈₉	—	2	1	no	—
620	C₂×C₄×C₈₉	—	4	4	no	—
621	C₂×C₄×C₈₉	—	8	2	no	—
622	C₂×C₄×C₈₉	—	8	2	no	—
623	C₂×C₄×C₈₉	—	8	2	no	—
624	C₂×C₄×C₈₉	—	8	2	no	—
625	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
626	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
627	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
628	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
629	C₂×Dic₈₉	—	2	8	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	—	2	1	no	—
657	C₂×Dic₈₉	—	2	1	no	—
658	C₂×Dic₈₉	—	2	1	no	—
659	C₂×Dic₈₉	—	2	1	no	—
660	C₂×Dic₈₉	—	2	1	no	—
661	C₂×Dic₈₉	—	2	1	no	—
662	C₂×Dic₈₉	—	2	1	no	—
663	C₂×Dic₈₉	—	2	1	no	—
664	C₂×Dic₈₉	—	2	1	no	—
665	C₂×Dic₈₉	—	2	1	no	—
666	C₂×Dic₈₉	—	2	1	no	—
667	C₂×Dic₈₉	—	2	1	no	—
668	C₂×Dic₈₉	—	2	1	no	—
669	C₂×Dic₈₉	—	2	1	no	—
670	C₂×Dic₈₉	—	4	4	no	—
671	C₂×Dic₈₉	—	4	4	no	—
672	C₂×Dic₈₉	—	4	4	no	—
673	C₂×Dic₈₉	—	4	4	no	—
674	C₂×Dic₈₉	—	4	4	no	—
675	C₂×Dic₈₉	—	8	2	no	—
676	C₂×Dic₈₉	—	8	2	no	—
677	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
678	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
679	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
680	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
681	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
682	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
683	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
684	C₂×Dic₈₉	C₂³×C₄	1	2	yes	—
685	Dic₁₇₈	—	4	4	no	—
686	C₂²×C₈₉	—	2	2	no	—
687	C₂²×C₈₉	—	2	2	no	—
688	C₂²×C₈₉	—	2	2	no	—
689	C₂²×C₈₉	—	2	2	no	—
690	C₂²×C₈₉	—	2	2	no	—
691	C₂²×C₈₉	—	2	2	no	—
692	C₂²×C₈₉	—	2	2	no	—
693	C₂²×C₈₉	—	2	2	no	—
694	C₂²×C₈₉	—	2	2	no	—
695	C₂²×C₈₉	—	2	2	no	—
696	C₂²×C₈₉	—	2	2	no	—
697	C₂²×C₈₉	—	2	2	no	—
698	C₂²×C₈₉	—	2	2	no	—
699	C₂²×C₈₉	—	2	2	no	—
700	C₂²×C₈₉	—	2	2	no	—
701	C₂²×C₈₉	—	4	1	no	—
702	C₂²×C₈₉	—	4	1	no	—
703	C₂²×C₈₉	—	4	1	no	—
704	C₂²×C₈₉	—	4	1	no	—
705	C₂²×C₈₉	—	4	1	no	—
706	C₂²×C₈₉	—	4	1	no	—
707	C₂²×C₈₉	—	4	1	no	—
708	C₂²×C₈₉	—	4	1	no	—
709	C₂²×C₈₉	—	4	1	no	—
710	C₂²×C₈₉	—	4	1	no	—
711	C₂²×C₈₉	—	4	1	no	—
712	C₂²×C₈₉	—	4	1	no	—
713	C₂²×C₈₉	—	8	8	no	—
714	C₂²×C₈₉	#520	1	4	yes	—
715	C₂²×C₈₉	C₂⁴×C₄	1	1	yes	characteristic
716	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
717	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
718	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
719	C₂²×C₈₉	#585	1	1	yes	characteristic
720	C₂²×C₈₉	#585	1	1	yes	characteristic
721	C₂²×C₈₉	#585	1	1	yes	characteristic
722	C₄×C₈₉	—	2	2	no	—
723	C₄×C₈₉	—	2	2	no	—
724	C₄×C₈₉	—	2	2	no	—
725	C₄×C₈₉	—	2	2	no	—
726	C₄×C₈₉	—	4	1	no	—
727	C₄×C₈₉	—	4	1	no	—
728	C₄×C₈₉	—	4	1	no	—
729	C₄×C₈₉	—	4	1	no	—
730	C₄×C₈₉	—	4	1	no	—
731	C₄×C₈₉	—	4	1	no	—
732	C₄×C₈₉	—	4	1	no	—
733	Dic₈₉	—	2	2	no	—
734	Dic₈₉	—	2	2	no	—
735	Dic₈₉	—	2	2	no	—
736	Dic₈₉	—	2	2	no	—
737	Dic₈₉	—	2	2	no	—
738	Dic₈₉	—	2	2	no	—
739	Dic₈₉	—	2	2	no	—
740	Dic₈₉	—	2	2	no	—
741	Dic₈₉	—	4	1	no	—
742	Dic₈₉	—	4	1	no	—
743	Dic₈₉	—	4	1	no	—
744	Dic₈₉	—	4	1	no	—
745	Dic₈₉	—	4	1	no	—
746	Dic₈₉	—	4	1	no	—
747	Dic₈₉	—	4	1	no	—
748	Dic₈₉	—	4	1	no	—
749	#34479	—	89	1	no	maximal, Sylow
750	C₂×C₈₉	—	2	4	no	—
751	C₂×C₈₉	—	4	2	no	—
752	C₂×C₈₉	—	4	2	no	—
753	C₂×C₈₉	—	4	2	no	—
754	C₂×C₈₉	C₂×#520	1	1	yes	characteristic
755	C₂×C₈₉	#3428	1	1	yes	characteristic
756	C₂×C₈₉	C₄×H(5,𝔽₂)	1	1	yes	characteristic
757	C₂×C₈₉	#3535	1	1	yes	characteristic
758	C₂×C₈₉	#3542	1	1	yes	characteristic
759	C₂×C₈₉	#3545	1	1	yes	characteristic
760	C₂×C₈₉	#3564	1	1	yes	characteristic
761	C₂×#551	—	89	1	no	—
762	#2383	—	89	1	no	—
763	#2379	—	89	1	no	—
764	#2378	—	89	1	no	—
765	#2376	—	89	1	no	—
766	#2373	—	89	1	no	—
767	#2368	—	89	1	no	—
768	#2359	—	89	1	no	—
769	#2359	—	89	1	no	—
770	#2358	D₈₉	1	1	yes	characteristic
771	#2354	—	89	1	no	—
772	#2349	—	89	1	no	—
773	#2346	—	89	1	no	—
774	#2343	—	89	1	no	—
775	#2342	—	89	1	no	—
776	#2342	—	89	1	no	—
777	#2335	—	89	1	no	—
778	#2335	—	89	1	no	—
779	#2334	—	89	1	no	—
780	#2334	—	89	1	no	—
781	#2326	—	89	1	no	—
782	#2323	—	89	1	no	—
783	#2322	—	89	1	no	—
784	#2321	—	89	1	no	—
785	#2318	—	89	1	no	—
786	#2317	—	89	1	no	—
787	#2315	—	89	1	no	—
788	#2314	—	89	1	no	—
789	C₄×C₂²⋊Q₈	—	89	1	no	—
790	#2290	—	89	1	no	—
791	C₂×#388	—	89	1	no	—
792	C₈₉	#34479	1	1	yes	characteristic, complemented, Sylow
793	#551	—	89	16	no	—
794	C₂×#126	—	89	1	no	—
795	C₂×#126	—	89	1	no	—
796	C₂×#124	—	89	1	no	—
797	C₂×#123	—	89	1	no	—
798	C₂×#123	—	89	1	no	—
799	C₂×#123	—	89	1	no	—
800	C₂×C₂²⋊Q₈	—	89	1	no	—
801	C₂×C₂²⋊Q₈	—	89	1	no	—
802	C₂×#120	C₂×D₈₉	1	1	yes	characteristic
803	C₂×C₄×Q₈	—	89	1	no	—
804	C₂×C₄×D₄	—	89	1	no	—
805	C₂×C₄×D₄	—	89	1	no	—
806	C₂×C₄×D₄	—	89	1	no	—
807	C₂×C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
808	C₂×C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
809	C₂×#117	—	89	1	no	—
810	C₂×#117	—	89	1	no	—
811	C₂×#117	—	89	1	no	—
812	C₂×#117	—	89	1	no	—
813	C₂×#117	—	89	1	no	—
814	C₂²×C₄⋊C₄	—	89	1	no	—
815	C₂²×C₂²⋊C₄	—	89	1	no	—
816	C₂²×C₂²⋊C₄	—	89	1	no	—
817	C₂²×C₂²⋊C₄	—	89	1	no	—
818	C₂²×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
819	C₂²×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
820	C₂²×C₄²	—	89	1	no	—
821	#391	—	89	1	no	—
822	#391	—	89	1	no	—
823	#391	—	89	1	no	—
824	#390	—	89	1	no	—
825	#390	—	89	1	no	—
826	#390	C₂×D₈₉	1	1	yes	characteristic
827	#389	—	89	1	no	—
828	#389	—	89	1	no	—
829	#389	—	89	1	no	—
830	#389	—	89	1	no	—
831	#389	—	89	1	no	—
832	#389	—	89	1	no	—
833	#389	—	89	1	no	—
834	#389	—	89	1	no	—
835	#389	—	89	1	no	—
836	#389	—	89	1	no	—
837	#388	—	89	1	no	—
838	#388	—	89	1	no	—
839	#388	—	89	1	no	—
840	#388	—	89	1	no	—
841	#388	—	89	1	no	—
842	#388	—	89	1	no	—
843	#388	—	89	1	no	—
844	#388	—	89	1	no	—
845	#388	—	89	1	no	—
846	#388	—	89	1	no	—
847	#388	—	89	1	no	—
848	#388	—	89	1	no	—
849	#388	—	89	1	no	—
850	#388	—	89	1	no	—
851	#388	—	89	1	no	—
852	#388	—	89	1	no	—
853	#388	—	89	1	no	—
854	#388	—	89	1	no	—
855	#388	—	89	1	no	—
856	#388	—	89	1	no	—
857	#388	—	89	1	no	—
858	#388	—	89	1	no	—
859	#388	—	89	1	no	—
860	#388	—	89	1	no	—
861	#388	—	89	1	no	—
862	#388	—	89	1	no	—
863	#388	C₂×D₈₉	1	1	yes	characteristic
864	#388	C₂×D₈₉	1	1	yes	characteristic
865	#387	—	89	1	no	—
866	#387	—	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	#386	—	89	1	no	—
882	#386	—	89	1	no	—
883	#386	—	89	1	no	—
884	#386	C₂×D₈₉	1	1	yes	characteristic
885	#386	C₂×D₈₉	1	1	yes	characteristic
886	#386	C₂×D₈₉	1	1	yes	characteristic
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	#385	—	89	1	no	—
900	#385	—	89	1	no	—
901	#385	—	89	1	no	—
902	#385	—	89	1	no	—
903	#385	—	89	1	no	—
904	#385	—	89	1	no	—
905	#385	C₂×D₈₉	1	1	yes	characteristic
906	#385	C₂×D₈₉	1	1	yes	characteristic
907	#384	—	89	1	no	—
908	#384	—	89	1	no	—
909	#383	—	89	1	no	—
910	#382	—	89	1	no	—
911	#382	—	89	1	no	—
912	#382	—	89	1	no	—
913	#382	—	89	1	no	—
914	#381	—	89	1	no	—
915	#381	—	89	1	no	—
916	#380	—	89	1	no	—
917	#380	—	89	1	no	—
918	#380	—	89	1	no	—
919	#380	—	89	1	no	—
920	#380	—	89	1	no	—
921	#380	—	89	1	no	—
922	#380	—	89	1	no	—
923	#379	—	89	1	no	—
924	C₄×C₄⋊C₄	—	89	1	no	—
925	C₄×C₄⋊C₄	—	89	1	no	—
926	C₄×C₄⋊C₄	—	89	1	no	—
927	C₄×C₄⋊C₄	—	89	1	no	—
928	C₄×C₄⋊C₄	—	89	1	no	—
929	C₄×C₄⋊C₄	—	89	1	no	—
930	C₄×C₄⋊C₄	—	89	1	no	—
931	C₄×C₄⋊C₄	—	89	1	no	—
932	C₄×C₄⋊C₄	—	89	1	no	—
933	C₄×C₂²⋊C₄	—	89	1	no	—
934	C₄×C₂²⋊C₄	—	89	1	no	—
935	C₄×C₂²⋊C₄	—	89	1	no	—
936	C₄×C₂²⋊C₄	—	89	1	no	—
937	C₄×C₂²⋊C₄	—	89	1	no	—
938	C₄×C₂²⋊C₄	—	89	1	no	—
939	C₄×C₂²⋊C₄	—	89	1	no	—
940	C₄×C₂²⋊C₄	—	89	1	no	—
941	C₄×C₂²⋊C₄	—	89	1	no	—
942	C₄×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
943	C₄×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
944	#376	—	89	1	no	—
945	#376	—	89	1	no	—
946	C₂×#95	—	89	1	no	—
947	C₂×#95	—	89	1	no	—
948	C₂×#95	—	89	1	no	—
949	C₂⁵	C₂²×D₈₉	1	1	yes	characteristic
950	C₂²×Q₈	—	89	1	no	—
951	C₂²×D₄	C₂²×D₈₉	1	1	yes	characteristic
952	C₂²×D₄	C₂²×D₈₉	1	1	yes	characteristic
953	C₂²×D₄	C₂²×D₈₉	1	1	yes	characteristic
954	C₂³×C₄	—	89	1	no	—
955	C₂³×C₄	—	89	1	no	—
956	C₂³×C₄	—	89	1	no	—
957	C₂³×C₄	—	89	1	no	—
958	C₂³×C₄	—	89	1	no	—
959	C₂³×C₄	—	89	1	no	—
960	C₂³×C₄	—	89	1	no	—
961	C₂³×C₄	—	89	1	no	—
962	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
963	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
964	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
965	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
966	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
967	#126	—	89	8	no	—
968	#126	—	89	8	no	—
969	#124	—	89	8	no	—
970	#123	—	89	8	no	—
971	#123	—	89	8	no	—
972	#123	—	89	8	no	—
973	C₂²⋊Q₈	—	89	8	no	—
974	C₂²⋊Q₈	—	89	8	no	—
975	#120	C₄×D₈₉	1	8	yes	—
976	C₄×Q₈	—	356	2	no	—
977	C₄×D₄	—	4	2	no	—
978	C₄×D₄	—	4	2	no	—
979	C₄×D₄	—	89	8	no	—
980	C₄×D₄	—	89	8	no	—
981	C₄×D₄	—	356	2	no	—
982	#117	—	89	8	no	—
983	#117	—	89	8	no	—
984	#117	—	356	2	no	—
985	#117	—	356	2	no	—
986	#117	—	356	2	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	—	89	1	no	—
1018	C₂×C₄⋊C₄	—	356	2	no	—
1019	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1020	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1021	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1022	C₂×C₂²⋊C₄	—	4	2	no	—
1023	C₂×C₂²⋊C₄	—	4	2	no	—
1024	C₂×C₂²⋊C₄	—	89	8	no	—
1025	C₂×C₂²⋊C₄	—	89	8	no	—
1026	C₂×C₂²⋊C₄	—	89	1	no	—
1027	C₂×C₂²⋊C₄	—	89	1	no	—
1028	C₂×C₂²⋊C₄	—	89	1	no	—
1029	C₂×C₂²⋊C₄	—	89	1	no	—
1030	C₂×C₂²⋊C₄	—	89	1	no	—
1031	C₂×C₂²⋊C₄	—	89	1	no	—
1032	C₂×C₂²⋊C₄	—	89	1	no	—
1033	C₂×C₂²⋊C₄	—	89	1	no	—
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	—	356	2	no	—
1051	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1052	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1053	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1054	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1055	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1056	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1057	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1058	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1059	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1060	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1061	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1062	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1063	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
1064	C₂×C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
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	—	89	1	no	—
1071	C₂×C₄²	—	89	1	no	—
1072	C₂×C₄²	—	89	1	no	—
1073	C₂×C₄²	—	89	1	no	—
1074	C₂×C₄²	—	89	1	no	—
1075	C₂×C₄²	—	89	1	no	—
1076	C₂×C₄²	—	89	1	no	—
1077	C₂×C₄²	—	89	1	no	—
1078	C₂×C₄²	—	89	1	no	—
1079	C₂×C₄²	—	89	1	no	—
1080	C₂×C₄²	—	89	1	no	—
1081	C₂×C₄²	—	89	1	no	—
1082	C₂×C₄²	—	89	1	no	—
1083	C₂×C₄²	—	356	2	no	—
1084	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1085	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
1086	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
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	—	89	1	no	—
1114	#95	—	89	1	no	—
1115	#95	—	89	1	no	—
1116	#95	—	89	1	no	—
1117	#95	—	89	1	no	—
1118	#95	—	89	1	no	—
1119	#95	—	89	1	no	—
1120	#95	—	89	1	no	—
1121	#95	—	89	1	no	—
1122	#95	—	89	1	no	—
1123	#95	—	89	1	no	—
1124	#95	—	89	1	no	—
1125	#95	C₂²×D₈₉	1	1	yes	characteristic
1126	#95	C₂²×D₈₉	1	1	yes	characteristic
1127	#95	C₂²×D₈₉	1	1	yes	characteristic
1128	#95	C₂²×D₈₉	1	1	yes	characteristic
1129	#95	C₂²×D₈₉	1	1	yes	characteristic
1130	#95	C₂²×D₈₉	1	1	yes	characteristic
1131	C₂⁴	—	2	2	no	—
1132	C₂⁴	—	2	2	no	—
1133	C₂⁴	—	4	1	no	—
1134	C₂⁴	—	4	1	no	—
1135	C₂⁴	—	4	1	no	—
1136	C₂⁴	—	4	1	no	—
1137	C₂⁴	C₂×C₄×D₈₉	1	4	yes	—
1138	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
1139	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
1140	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
1141	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
1142	C₂×Q₈	—	89	4	no	—
1143	C₂×Q₈	—	356	1	no	—
1144	C₂×Q₈	—	356	1	no	—
1145	C₂×D₄	—	2	2	no	—
1146	C₂×D₄	—	2	2	no	—
1147	C₂×D₄	—	4	1	no	—
1148	C₂×D₄	—	4	1	no	—
1149	C₂×D₄	—	4	1	no	—
1150	C₂×D₄	—	4	1	no	—
1151	C₂×D₄	C₂×C₄×D₈₉	1	4	yes	—
1152	C₂×D₄	C₂×C₄×D₈₉	1	4	yes	—
1153	C₂×D₄	C₂×C₄×D₈₉	1	4	yes	—
1154	C₂²×C₄	—	2	2	no	—
1155	C₂²×C₄	—	2	2	no	—
1156	C₂²×C₄	—	2	2	no	—
1157	C₂²×C₄	—	4	1	no	—
1158	C₂²×C₄	—	4	1	no	—
1159	C₂²×C₄	—	4	1	no	—
1160	C₂²×C₄	—	4	1	no	—
1161	C₂²×C₄	—	4	1	no	—
1162	C₂²×C₄	—	4	1	no	—
1163	C₂²×C₄	—	4	1	no	—
1164	C₂²×C₄	—	4	1	no	—
1165	C₂²×C₄	—	4	1	no	—
1166	C₂²×C₄	—	4	1	no	—
1167	C₂²×C₄	—	4	1	no	—
1168	C₂²×C₄	—	4	1	no	—
1169	C₂²×C₄	—	89	4	no	—
1170	C₂²×C₄	—	89	4	no	—
1171	C₂²×C₄	—	89	4	no	—
1172	C₂²×C₄	—	89	4	no	—
1173	C₂²×C₄	—	89	4	no	—
1174	C₂²×C₄	—	89	1	no	—
1175	C₂²×C₄	—	89	1	no	—
1176	C₂²×C₄	—	89	1	no	—
1177	C₂²×C₄	—	89	1	no	—
1178	C₂²×C₄	—	89	1	no	—
1179	C₂²×C₄	—	89	1	no	—
1180	C₂²×C₄	—	89	1	no	—
1181	C₂²×C₄	—	89	1	no	—
1182	C₂²×C₄	—	89	1	no	—
1183	C₂²×C₄	—	89	1	no	—
1184	C₂²×C₄	—	89	1	no	—
1185	C₂²×C₄	—	89	1	no	—
1186	C₂²×C₄	—	89	1	no	—
1187	C₂²×C₄	—	89	1	no	—
1188	C₂²×C₄	—	89	1	no	—
1189	C₂²×C₄	—	89	1	no	—
1190	C₂²×C₄	—	356	1	no	—
1191	C₂²×C₄	—	356	1	no	—
1192	C₂²×C₄	—	356	1	no	—
1193	C₂²×C₄	—	356	1	no	—
1194	C₂²×C₄	—	356	1	no	—
1195	C₂²×C₄	—	356	1	no	—
1196	C₂²×C₄	—	356	1	no	—
1197	C₂²×C₄	—	356	1	no	—
1198	C₂²×C₄	—	356	1	no	—
1199	C₂²×C₄	—	356	1	no	—
1200	C₂²×C₄	—	356	1	no	—
1201	C₂²×C₄	—	356	1	no	—
1202	C₂²×C₄	—	356	1	no	—
1203	C₂²×C₄	—	356	1	no	—
1204	C₂²×C₄	—	356	1	no	—
1205	C₂²×C₄	—	178	2	no	—
1206	C₂²×C₄	—	178	2	no	—
1207	C₂²×C₄	—	178	2	no	—
1208	C₂²×C₄	—	178	2	no	—
1209	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1210	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1211	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1212	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1213	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1214	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1215	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1216	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1217	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1218	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1219	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
1220	C₄⋊C₄	—	4	1	no	—
1221	C₄⋊C₄	—	4	1	no	—
1222	C₄⋊C₄	—	4	1	no	—
1223	C₄⋊C₄	—	89	4	no	—
1224	C₄⋊C₄	—	89	4	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	—	89	4	no	—
1230	C₄⋊C₄	—	89	4	no	—
1231	C₄⋊C₄	—	356	1	no	—
1232	C₄⋊C₄	—	356	1	no	—
1233	C₄⋊C₄	—	356	1	no	—
1234	C₄⋊C₄	—	356	1	no	—
1235	C₄⋊C₄	—	356	1	no	—
1236	C₄⋊C₄	—	356	1	no	—
1237	C₄⋊C₄	—	356	1	no	—
1238	C₄⋊C₄	—	356	1	no	—
1239	C₄⋊C₄	—	356	1	no	—
1240	C₄⋊C₄	—	356	1	no	—
1241	C₄⋊C₄	—	356	1	no	—
1242	C₄⋊C₄	—	356	1	no	—
1243	C₄⋊C₄	—	356	1	no	—
1244	C₄⋊C₄	—	356	1	no	—
1245	C₄⋊C₄	—	356	1	no	—
1246	C₄⋊C₄	—	356	1	no	—
1247	C₄⋊C₄	—	356	1	no	—
1248	C₄⋊C₄	—	356	1	no	—
1249	C₄⋊C₄	—	356	1	no	—
1250	C₄⋊C₄	—	356	1	no	—
1251	C₄⋊C₄	—	356	1	no	—
1252	C₄⋊C₄	—	356	1	no	—
1253	C₄⋊C₄	—	178	2	no	—
1254	C₂²⋊C₄	—	2	2	no	—
1255	C₂²⋊C₄	—	2	2	no	—
1256	C₂²⋊C₄	—	2	2	no	—
1257	C₂²⋊C₄	—	2	2	no	—
1258	C₂²⋊C₄	—	2	2	no	—
1259	C₂²⋊C₄	—	4	1	no	—
1260	C₂²⋊C₄	—	4	1	no	—
1261	C₂²⋊C₄	—	4	1	no	—
1262	C₂²⋊C₄	—	4	1	no	—
1263	C₂²⋊C₄	—	4	1	no	—
1264	C₂²⋊C₄	—	4	1	no	—
1265	C₂²⋊C₄	—	89	4	no	—
1266	C₂²⋊C₄	—	89	4	no	—
1267	C₂²⋊C₄	—	89	4	no	—
1268	C₂²⋊C₄	—	89	4	no	—
1269	C₂²⋊C₄	—	89	4	no	—
1270	C₂²⋊C₄	—	89	4	no	—
1271	C₂²⋊C₄	—	89	4	no	—
1272	C₂²⋊C₄	—	89	4	no	—
1273	C₂²⋊C₄	—	89	4	no	—
1274	C₂²⋊C₄	—	89	4	no	—
1275	C₂²⋊C₄	—	89	4	no	—
1276	C₂²⋊C₄	—	356	1	no	—
1277	C₂²⋊C₄	—	356	1	no	—
1278	C₂²⋊C₄	—	356	1	no	—
1279	C₂²⋊C₄	—	356	1	no	—
1280	C₂²⋊C₄	—	356	1	no	—
1281	C₂²⋊C₄	—	356	1	no	—
1282	C₂²⋊C₄	—	356	1	no	—
1283	C₂²⋊C₄	—	356	1	no	—
1284	C₂²⋊C₄	—	356	1	no	—
1285	C₂²⋊C₄	—	356	1	no	—
1286	C₂²⋊C₄	—	356	1	no	—
1287	C₂²⋊C₄	—	178	2	no	—
1288	C₂²⋊C₄	—	178	2	no	—
1289	C₂²⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1290	C₂²⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1291	C₂²⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
1292	C₄²	—	2	2	no	—
1293	C₄²	—	4	1	no	—
1294	C₄²	—	4	1	no	—
1295	C₄²	—	89	4	no	—
1296	C₄²	—	89	4	no	—
1297	C₄²	—	89	4	no	—
1298	C₄²	—	356	1	no	—
1299	C₄²	—	356	1	no	—
1300	C₄²	—	356	1	no	—
1301	C₄²	—	356	1	no	—
1302	C₄²	—	356	1	no	—
1303	C₄²	—	356	1	no	—
1304	C₄²	—	356	1	no	—
1305	C₄²	—	356	1	no	—
1306	C₄²	—	356	1	no	—
1307	C₄²	—	356	1	no	—
1308	C₄²	—	356	1	no	—
1309	C₄²	—	356	1	no	—
1310	C₄²	—	178	2	no	—
1311	C₄²	—	178	2	no	—
1312	C₄²	—	178	2	no	—
1313	C₂³	—	2	1	no	—
1314	C₂³	—	2	1	no	—
1315	C₂³	—	2	1	no	—
1316	C₂³	—	2	1	no	—
1317	C₂³	—	2	1	no	—
1318	C₂³	—	2	1	no	—
1319	C₂³	—	2	1	no	—
1320	C₂³	—	2	1	no	—
1321	C₂³	—	2	1	no	—
1322	C₂³	—	2	1	no	—
1323	C₂³	—	2	1	no	—
1324	C₂³	—	2	1	no	—
1325	C₂³	—	2	1	no	—
1326	C₂³	—	2	1	no	—
1327	C₂³	—	2	1	no	—
1328	C₂³	—	2	1	no	—
1329	C₂³	—	2	1	no	—
1330	C₂³	—	2	1	no	—
1331	C₂³	—	2	1	no	—
1332	C₂³	—	2	1	no	—
1333	C₂³	—	2	1	no	—
1334	C₂³	—	2	1	no	—
1335	C₂³	—	2	8	no	—
1336	C₂³	—	4	4	no	—
1337	C₂³	—	4	4	no	—
1338	C₂³	—	8	2	no	—
1339	C₂³	—	8	2	no	—
1340	C₂³	—	8	2	no	—
1341	C₂³	—	8	2	no	—
1342	C₂³	C₂²×C₄×D₈₉	1	2	yes	—
1343	C₂³	C₂²×C₄×D₈₉	1	2	yes	—
1344	C₂³	C₂²×C₄×D₈₉	1	2	yes	—
1345	C₂³	C₂²×C₄×D₈₉	1	2	yes	—
1346	C₂³	#15668057	1	2	yes	—
1347	C₂³	#15668059	1	2	yes	—
1348	C₂³	C₂⁴×D₈₉	1	1	yes	characteristic
1349	Q₈	—	356	4	no	—
1350	D₄	—	2	8	no	—
1351	D₄	—	4	4	no	—
1352	D₄	—	4	4	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	—	2	1	no	—
1363	C₂×C₄	—	2	1	no	—
1364	C₂×C₄	—	2	1	no	—
1365	C₂×C₄	—	2	1	no	—
1366	C₂×C₄	—	2	1	no	—
1367	C₂×C₄	—	2	1	no	—
1368	C₂×C₄	—	2	1	no	—
1369	C₂×C₄	—	2	1	no	—
1370	C₂×C₄	—	2	1	no	—
1371	C₂×C₄	—	2	1	no	—
1372	C₂×C₄	—	2	1	no	—
1373	C₂×C₄	—	2	1	no	—
1374	C₂×C₄	—	2	1	no	—
1375	C₂×C₄	—	2	1	no	—
1376	C₂×C₄	—	2	1	no	—
1377	C₂×C₄	—	2	1	no	—
1378	C₂×C₄	—	2	1	no	—
1379	C₂×C₄	—	2	1	no	—
1380	C₂×C₄	—	2	1	no	—
1381	C₂×C₄	—	2	1	no	—
1382	C₂×C₄	—	4	4	no	—
1383	C₂×C₄	—	8	2	no	—
1384	C₂×C₄	—	8	2	no	—
1385	C₂×C₄	—	8	2	no	—
1386	C₂×C₄	—	8	2	no	—
1387	C₂×C₄	—	89	2	no	—
1388	C₂×C₄	—	89	2	no	—
1389	C₂×C₄	—	89	2	no	—
1390	C₂×C₄	—	89	2	no	—
1391	C₂×C₄	—	89	2	no	—
1392	C₂×C₄	—	89	2	no	—
1393	C₂×C₄	—	89	2	no	—
1394	C₂×C₄	—	89	2	no	—
1395	C₂×C₄	—	356	4	no	—
1396	C₂×C₄	—	356	4	no	—
1397	C₂×C₄	—	356	4	no	—
1398	C₂×C₄	—	356	4	no	—
1399	C₂×C₄	—	356	4	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	—	178	1	no	—
1420	C₂×C₄	—	178	1	no	—
1421	C₂×C₄	—	178	1	no	—
1422	C₂×C₄	—	178	1	no	—
1423	C₂×C₄	—	178	1	no	—
1424	C₂×C₄	—	178	1	no	—
1425	C₂×C₄	—	178	1	no	—
1426	C₂×C₄	—	178	1	no	—
1427	C₂×C₄	—	178	1	no	—
1428	C₂×C₄	—	178	1	no	—
1429	C₂×C₄	—	178	1	no	—
1430	C₂×C₄	—	178	1	no	—
1431	C₂×C₄	—	178	1	no	—
1432	C₂×C₄	—	178	1	no	—
1433	C₂×C₄	—	178	1	no	—
1434	C₂×C₄	—	178	1	no	—
1435	C₂×C₄	—	178	1	no	—
1436	C₂×C₄	—	178	1	no	—
1437	C₂×C₄	—	178	1	no	—
1438	C₂×C₄	—	178	1	no	—
1439	C₂×C₄	—	178	1	no	—
1440	C₂×C₄	—	178	8	no	—
1441	C₂×C₄	—	712	2	no	—
1442	C₂×C₄	—	712	2	no	—
1443	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1444	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1445	C₂×C₄	C₂²×C₄×D₈₉	1	2	yes	—
1446	C₂×C₄	#15668057	1	2	yes	—
1447	C₂²	—	2	2	no	—
1448	C₂²	—	2	2	no	—
1449	C₂²	—	2	2	no	—
1450	C₂²	—	2	2	no	—
1451	C₂²	—	2	2	no	—
1452	C₂²	—	2	2	no	—
1453	C₂²	—	2	2	no	—
1454	C₂²	—	2	2	no	—
1455	C₂²	—	2	2	no	—
1456	C₂²	—	2	2	no	—
1457	C₂²	—	2	2	no	—
1458	C₂²	—	2	2	no	—
1459	C₂²	—	2	2	no	—
1460	C₂²	—	2	2	no	—
1461	C₂²	—	2	2	no	—
1462	C₂²	—	4	1	no	—
1463	C₂²	—	4	1	no	—
1464	C₂²	—	4	1	no	—
1465	C₂²	—	4	1	no	—
1466	C₂²	—	4	1	no	—
1467	C₂²	—	4	1	no	—
1468	C₂²	—	4	1	no	—
1469	C₂²	—	4	1	no	—
1470	C₂²	—	4	1	no	—
1471	C₂²	—	4	1	no	—
1472	C₂²	—	4	1	no	—
1473	C₂²	—	4	1	no	—
1474	C₂²	—	8	8	no	—
1475	C₂²	#19152077	1	4	yes	—
1476	C₂²	C₂³×C₄×D₈₉	1	1	yes	characteristic
1477	C₂²	C₂×#15668057	1	1	yes	characteristic
1478	C₂²	C₂×#15668057	1	1	yes	characteristic
1479	C₂²	C₂×#15668059	1	1	yes	characteristic
1480	C₂²	#19152433	1	1	yes	characteristic
1481	C₂²	#19152433	1	1	yes	characteristic
1482	C₂²	#19152434	1	1	yes	characteristic
1483	C₄	—	2	2	no	—
1484	C₄	—	2	2	no	—
1485	C₄	—	2	2	no	—
1486	C₄	—	2	2	no	—
1487	C₄	—	4	1	no	—
1488	C₄	—	4	1	no	—
1489	C₄	—	4	1	no	—
1490	C₄	—	4	1	no	—
1491	C₄	—	4	1	no	—
1492	C₄	—	4	1	no	—
1493	C₄	—	4	1	no	—
1494	C₄	—	356	1	no	—
1495	C₄	—	356	1	no	—
1496	C₄	—	356	1	no	—
1497	C₄	—	356	1	no	—
1498	C₄	—	356	1	no	—
1499	C₄	—	356	1	no	—
1500	C₄	—	356	1	no	—
1501	C₄	—	356	1	no	—
1502	C₄	—	178	2	no	—
1503	C₄	—	178	2	no	—
1504	C₄	—	178	2	no	—
1505	C₄	—	178	2	no	—
1506	C₄	—	178	2	no	—
1507	C₄	—	178	2	no	—
1508	C₄	—	178	2	no	—
1509	C₄	—	178	2	no	—
1510	C₂	—	2	4	no	—
1511	C₂	—	4	2	no	—
1512	C₂	—	4	2	no	—
1513	C₂	—	4	2	no	—
1514	C₂	C₂×#19152077	1	1	yes	characteristic
1515	C₂	#26033450	1	1	yes	characteristic
1516	C₂	C₄×#15668057	1	1	yes	characteristic
1517	C₂	#26034449	1	1	yes	characteristic
1518	C₂	#26034573	1	1	yes	characteristic
1519	C₂	#26034599	1	1	yes	characteristic
1520	C₂	#26034864	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₈₉
commutator	C₂²×C₈₉	C₂⁴×C₄
Fitting	C₈₉×#2358	C₂
socle, cosocle	C₂³×C₈₉	C₂⁵
prime radical	C₂×#120×C₈₉	C₂²
hypercenter	#2358	D₈₉
hypocenter	C₈₉	#34479
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ #2358

Complements

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

N	H ≅ G/N	type
2. #26023440	C₂	semidirect
3. #26023422	C₂	semidirect
4. #26023412	C₂	semidirect
5. #26023395	C₂	semidirect
6. #26023374	C₂	semidirect
7. #26023333	C₂	semidirect
8. #26023250	C₂	semidirect
9. #26023238	C₂	semidirect
10. #26023200	C₂	semidirect
11. #26023157	C₂	semidirect
12. #26023134	C₂	semidirect
13. #26023106	C₂	semidirect
14. #26023097	C₂	semidirect
15. #26023097	C₂	semidirect
16. #26023043	C₂	semidirect
17. #26023039	C₂	semidirect
18. #26023029	C₂	semidirect
19. #26023022	C₂	semidirect
20. #26022964	C₂	semidirect
21. #26022931	C₂	semidirect
22. #26022917	C₂	semidirect
24. #26022878	C₂	semidirect
25. #26022871	C₂	semidirect
26. #26022864	C₂	semidirect
27. #26022856	C₂	semidirect
28. C₄×#15667989	C₂	semidirect
29. #26022692	C₂	semidirect
30. C₂×#19151486	C₂	semidirect
32. #19152279	C₄	semidirect
41. C₂×C₄×Dic₁₇₈	C₂²	semidirect
49. C₂×#15667968	C₂²	semidirect
55. #19151503	C₂²	semidirect
56. #19151502	C₂²	semidirect
57. #19151502	C₂²	semidirect
60. #19151496	C₂²	semidirect
61. #19151495	C₂²	semidirect
62. #19151495	C₂²	semidirect
63. #19151495	C₂²	semidirect
64. #19151495	C₂²	semidirect
65. #19151494	C₂²	semidirect
66. #19151493	C₂²	semidirect
67. #19151493	C₂²	semidirect
68. #19151493	C₂²	semidirect
69. #19151493	C₂²	semidirect
74. #19151492	C₂²	semidirect
75. #19151492	C₂²	semidirect
76. #19151492	C₂²	semidirect
77. #19151492	C₂²	semidirect
94. #19151486	C₂²	semidirect
95. #19151486	C₂²	semidirect
96. #19151485	C₂²	semidirect
97. #19151485	C₂²	semidirect
98. #19151483	C₂²	semidirect
99. #19151483	C₂²	semidirect
100. #19151482	C₂²	semidirect
101. #19151482	C₂²	semidirect
102. #19151482	C₂²	semidirect
103. #19151482	C₂²	semidirect
104. #19151481	C₂²	semidirect
105. #19151481	C₂²	semidirect
106. #19151480	C₂²	semidirect
107. #19151480	C₂²	semidirect
108. #19151480	C₂²	semidirect
109. #19151480	C₂²	semidirect
110. #19151479	C₂²	semidirect
111. #19151479	C₂²	semidirect
124. #19151471	C₂²	semidirect
125. #19151471	C₂²	semidirect
126. #19151471	C₂²	semidirect
131. #19151470	C₂²	semidirect
132. #19151470	C₂²	semidirect
133. #19151467	C₂²	semidirect
134. #19151467	C₂²	semidirect
135. #19151465	C₂²	semidirect
136. #19151463	C₂²	semidirect
137. #19151462	C₂²	semidirect
138. #19151462	C₂²	semidirect
139. #19151462	C₂²	semidirect
148. #19151456	C₂²	semidirect
150. C₄⋊C₄×Dic₈₉	C₂²	semidirect
151. C₄×#13083553	C₂²	semidirect
152. C₄×#13083553	C₂²	semidirect
153. C₄×#13083553	C₂²	semidirect
154. C₄×#13083553	C₂²	semidirect
155. C₄×C₄⋊Dic₈₉	C₂²	semidirect
156. #19151449	C₂²	semidirect
157. #19151449	C₂²	semidirect
158. #19151449	C₂²	semidirect
162. C₂²⋊C₄×Dic₈₉	C₂²	semidirect
163. C₂²⋊C₄×Dic₈₉	C₂²	semidirect
168. #19151444	C₂²	semidirect
169. #19151443	C₂²	semidirect
172. C₂×#15667919	C₂²	semidirect
197. #15668005	C₂×C₄	semidirect
198. #15668005	C₂×C₄	semidirect
199. #15667999	C₂×C₄	semidirect
200. #15667993	C₂×C₄	semidirect
201. #15667993	C₂×C₄	semidirect
202. #15667993	C₂×C₄	semidirect
203. #15667989	C₂×C₄	semidirect
204. #15667989	C₂×C₄	semidirect
207. D₄×Dic₈₉	C₂×C₄	semidirect
208. D₄×Dic₈₉	C₂×C₄	semidirect
212. #15667968	C₂×C₄	semidirect
213. #15667968	C₂×C₄	semidirect
247. C₂×C₂²⋊Dic₈₉	C₂×C₄	semidirect
248. C₂×C₂²⋊Dic₈₉	C₂×C₄	semidirect
792. C₈₉	#34479	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19152279	2
#26023440	2
#26023422	2
#26023412	2
#26023395	2
#26023374	2
#26023333	2
#26023250	2
#26023238	2
#26023200	2
#26023157	2
#26023134	2
#26023106	2
#26023097	2
#26023043	2
#26023039	2
#26023029	2
#26023022	2
#26022964	2
#26022931	2
#26022917	2
#26022913	2
#26022878	2
#26022871	2
#26022864	2
#26022856	2
C₄×#15667989	2
#26022692	2
C₂×#19151486	2
C₈₉×#2358	2
#34479	89