Subgroups — C₈₉×#61974 #36439822

Order 22784.

1920 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3517	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3399	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3331	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3309	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3307	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3274	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3272	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3268	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3267	C₂	1	2	yes	maximal, complemented
15	C₈₉×#3256	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3219	C₂	1	2	yes	maximal, complemented
18	C₈₉×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3114	C₂	1	2	yes	maximal, complemented
20	C₈₉×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#3036	C₂	1	2	yes	maximal, complemented
22	C₈₉×#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2989	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
25	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
26	C₂×#135×C₈₉	C₂²	1	2	yes	—
27	#559×C₈₉	C₂²	1	1	yes	characteristic
28	#557×C₈₉	C₂²	1	1	yes	characteristic, complemented
29	#554×C₈₉	C₂²	1	1	yes	characteristic
30	#554×C₈₉	C₂²	1	1	yes	characteristic
31	#553×C₈₉	—	2	1	no	—
32	#553×C₈₉	—	2	1	no	—
33	#553×C₈₉	—	2	2	no	—
34	#553×C₈₉	C₂²	1	2	yes	—
35	#551×C₈₉	—	2	2	no	—
36	#550×C₈₉	—	2	1	no	—
37	#550×C₈₉	C₂²	1	1	yes	characteristic
38	#550×C₈₉	C₂²	1	2	yes	complemented
39	#550×C₈₉	C₂²	1	1	yes	characteristic, complemented
40	#547×C₈₉	C₂²	1	1	yes	characteristic
41	#547×C₈₉	C₂²	1	2	yes	complemented
42	#546×C₈₉	—	2	1	no	—
43	#546×C₈₉	C₂²	1	2	yes	—
44	D₄²×C₈₉	C₂²	1	1	yes	characteristic
45	#540×C₈₉	—	2	1	no	—
46	#540×C₈₉	—	2	2	no	—
47	#532×C₈₉	C₂²	1	1	yes	characteristic
48	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
49	#532×C₈₉	C₂²	1	2	yes	complemented
50	#529×C₈₉	—	2	1	no	—
51	#529×C₈₉	C₂²	1	2	yes	—
52	#529×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	#529×C₈₉	C₂²	1	2	yes	complemented
54	#525×C₈₉	—	2	2	no	—
55	#520×C₈₉	—	2	1	no	—
56	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
57	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₈₉	—	2	1	no	—
59	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
60	#497×C₈₉	C₂²	1	2	yes	complemented
61	#496×C₈₉	C₂²	1	2	yes	complemented
62	#493×C₈₉	C₂²	1	1	yes	characteristic
63	#492×C₈₉	C₂²	1	1	yes	characteristic
64	#491×C₈₉	C₂²	1	2	yes	complemented
65	#490×C₈₉	C₂²	1	2	yes	complemented
66	#487×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#486×C₈₉	C₂²	1	1	yes	characteristic, complemented
68	#485×C₈₉	C₂²	1	1	yes	characteristic, complemented
69	#483×C₈₉	C₂²	1	2	yes	complemented
70	#482×C₈₉	C₂²	1	1	yes	characteristic, complemented
71	#480×C₈₉	C₂²	1	2	yes	complemented
72	#479×C₈₉	C₂²	1	1	yes	characteristic, complemented
73	#479×C₈₉	C₂²	1	2	yes	complemented
74	#478×C₈₉	C₂²	1	1	yes	characteristic
75	#478×C₈₉	C₂²	1	2	yes	complemented
76	#478×C₈₉	C₂²	1	2	yes	complemented
77	#477×C₈₉	C₂²	1	1	yes	characteristic, complemented
78	#476×C₈₉	C₂²	1	1	yes	characteristic, complemented
79	#470×C₈₉	C₂²	1	2	yes	complemented
80	#469×C₈₉	C₂²	1	2	yes	—
81	#468×C₈₉	C₂²	1	2	yes	—
82	#468×C₈₉	C₂²	1	2	yes	complemented
83	#466×C₈₉	C₂²	1	2	yes	complemented
84	#465×C₈₉	C₂²	1	2	yes	complemented
85	#464×C₈₉	C₂²	1	1	yes	characteristic, complemented
86	#464×C₈₉	C₂²	1	2	yes	complemented
87	#464×C₈₉	C₂²	1	2	yes	complemented
88	#463×C₈₉	C₂²	1	1	yes	characteristic
89	#463×C₈₉	C₂²	1	2	yes	—
90	#463×C₈₉	C₂²	1	2	yes	complemented
91	#463×C₈₉	C₂²	1	2	yes	complemented
92	#463×C₈₉	C₂²	1	2	yes	complemented
93	#463×C₈₉	C₂²	1	2	yes	complemented
94	#462×C₈₉	C₂²	1	1	yes	characteristic, complemented
95	#461×C₈₉	C₂²	1	2	yes	—
96	#461×C₈₉	C₂²	1	1	yes	characteristic
97	#461×C₈₉	C₂²	1	2	yes	complemented
98	#460×C₈₉	C₂²	1	1	yes	characteristic
99	#460×C₈₉	C₂²	1	1	yes	characteristic, complemented
100	#459×C₈₉	C₂²	1	2	yes	—
101	#459×C₈₉	C₂²	1	1	yes	characteristic
102	#459×C₈₉	C₂²	1	1	yes	characteristic
103	#459×C₈₉	C₂²	1	2	yes	complemented
104	#452×C₈₉	C₂²	1	1	yes	characteristic
105	#452×C₈₉	C₂²	1	2	yes	complemented
106	#452×C₈₉	C₂²	1	2	yes	complemented
107	#450×C₈₉	C₂²	1	2	yes	—
108	#449×C₈₉	C₂²	1	1	yes	characteristic
109	#449×C₈₉	C₂²	1	2	yes	—
110	#449×C₈₉	C₂²	1	2	yes	—
111	#449×C₈₉	C₂²	1	2	yes	complemented
112	#449×C₈₉	C₂²	1	2	yes	complemented
113	#447×C₈₉	C₂²	1	2	yes	—
114	#446×C₈₉	C₂²	1	1	yes	characteristic, complemented
115	#446×C₈₉	C₂²	1	1	yes	characteristic, complemented
116	#442×C₈₉	C₂²	1	2	yes	—
117	#442×C₈₉	C₂²	1	2	yes	complemented
118	#440×C₈₉	C₂²	1	2	yes	—
119	#440×C₈₉	C₂²	1	2	yes	complemented
120	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
121	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
122	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
124	#436×C₈₉	C₂²	1	1	yes	characteristic
125	#436×C₈₉	C₂²	1	1	yes	characteristic
126	#435×C₈₉	C₂²	1	2	yes	complemented
127	#435×C₈₉	C₂²	1	2	yes	complemented
128	#432×C₈₉	C₂²	1	2	yes	complemented
129	#431×C₈₉	C₂²	1	1	yes	characteristic, complemented
130	#423×C₈₉	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
132	#417×C₈₉	C₂²	1	2	yes	complemented
133	#417×C₈₉	C₂²	1	2	yes	complemented
134	#416×C₈₉	C₂²	1	2	yes	complemented
135	C₂×#41×C₈₉	—	2	1	no	—
136	C₂×#41×C₈₉	—	2	1	no	—
137	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
138	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
139	C₂×#41×C₈₉	C₂³	1	2	yes	—
140	C₂×#41×C₈₉	C₂³	1	2	yes	—
141	C₂×#41×C₈₉	C₂³	1	2	yes	—
142	C₂²×D₄×C₈₉	—	2	1	no	—
143	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
144	C₂³×C₄×C₈₉	—	2	2	no	—
145	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
146	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
147	#135×C₈₉	—	4	4	no	—
148	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
149	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
153	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
157	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
158	C₂×D₈×C₈₉	C₂³	1	2	yes	—
159	C₂×D₈×C₈₉	C₂³	1	2	yes	—
160	C₂×D₈×C₈₉	C₂³	1	2	yes	—
161	C₂×D₈×C₈₉	C₂³	1	2	yes	—
162	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
163	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
164	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
166	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
168	#127×C₈₉	—	2	1	no	—
169	#127×C₈₉	—	2	2	no	—
170	#127×C₈₉	C₂³	1	2	yes	—
171	#127×C₈₉	C₂³	1	1	yes	characteristic
172	#127×C₈₉	C₂³	1	1	yes	characteristic
173	#126×C₈₉	—	2	2	no	—
174	#126×C₈₉	—	2	2	no	—
175	#126×C₈₉	—	2	1	no	—
176	#126×C₈₉	—	2	2	no	—
177	#125×C₈₉	—	2	1	no	—
178	#125×C₈₉	—	2	1	no	—
179	#125×C₈₉	—	2	2	no	—
180	#125×C₈₉	C₂³	1	1	yes	characteristic
181	#125×C₈₉	C₂³	1	2	yes	—
182	#124×C₈₉	—	2	1	no	—
183	#124×C₈₉	—	2	1	no	—
184	#124×C₈₉	C₂³	1	1	yes	characteristic
185	#124×C₈₉	C₂³	1	2	yes	—
186	#124×C₈₉	C₂³	1	2	yes	—
187	#123×C₈₉	—	2	2	no	—
188	#123×C₈₉	—	2	2	no	—
189	#123×C₈₉	—	2	1	no	—
190	#123×C₈₉	—	2	2	no	—
191	#123×C₈₉	—	2	2	no	—
192	#123×C₈₉	—	2	2	no	—
193	#123×C₈₉	—	2	2	no	—
194	#123×C₈₉	—	2	2	no	—
195	#123×C₈₉	—	2	2	no	—
196	C₂²⋊Q₈×C₈₉	—	2	1	no	—
197	C₂²⋊Q₈×C₈₉	—	2	2	no	—
198	C₂²⋊Q₈×C₈₉	—	2	2	no	—
199	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
201	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
202	#121×C₈₉	—	2	2	no	—
203	#121×C₈₉	—	2	1	no	—
204	#121×C₈₉	—	2	2	no	—
205	#121×C₈₉	—	2	1	no	—
206	#121×C₈₉	—	2	2	no	—
207	#121×C₈₉	—	2	1	no	—
208	#121×C₈₉	—	2	1	no	—
209	#121×C₈₉	—	2	2	no	—
210	#121×C₈₉	—	2	1	no	—
211	#121×C₈₉	—	2	1	no	—
212	#121×C₈₉	—	2	2	no	—
213	#121×C₈₉	—	2	2	no	—
214	#121×C₈₉	—	2	2	no	—
215	#121×C₈₉	—	2	2	no	—
216	#121×C₈₉	—	2	2	no	—
217	#121×C₈₉	C₂³	1	2	yes	—
218	#121×C₈₉	C₂³	1	2	yes	—
219	#121×C₈₉	C₂³	1	1	yes	characteristic
220	#121×C₈₉	C₂³	1	2	yes	—
221	#120×C₈₉	—	2	2	no	—
222	#120×C₈₉	—	2	2	no	—
223	C₄×Q₈×C₈₉	—	2	1	no	—
224	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
225	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
228	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₈₉	—	2	1	no	—
231	C₄×D₄×C₈₉	—	2	2	no	—
232	C₄×D₄×C₈₉	—	2	1	no	—
233	C₄×D₄×C₈₉	—	2	1	no	—
234	C₄×D₄×C₈₉	—	2	1	no	—
235	C₄×D₄×C₈₉	—	2	2	no	—
236	C₄×D₄×C₈₉	—	2	1	no	—
237	C₄×D₄×C₈₉	—	2	1	no	—
238	C₄×D₄×C₈₉	—	2	2	no	—
239	C₄×D₄×C₈₉	—	2	2	no	—
240	C₄×D₄×C₈₉	—	2	1	no	—
241	C₄×D₄×C₈₉	—	2	2	no	—
242	C₄×D₄×C₈₉	—	2	2	no	—
243	C₄×D₄×C₈₉	—	2	1	no	—
244	C₄×D₄×C₈₉	—	2	2	no	—
245	C₄×D₄×C₈₉	—	2	1	no	—
246	C₄×D₄×C₈₉	—	2	2	no	—
247	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
248	C₄×D₄×C₈₉	D₄	1	2	yes	—
249	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₈₉	C₂³	1	2	yes	—
252	C₄×D₄×C₈₉	C₂³	1	2	yes	—
253	C₄×D₄×C₈₉	C₂³	1	2	yes	—
254	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₈₉	C₂³	1	2	yes	—
256	C₄×D₄×C₈₉	C₂³	1	2	yes	—
257	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
258	#117×C₈₉	—	2	1	no	—
259	#117×C₈₉	—	2	1	no	—
260	#117×C₈₉	—	2	2	no	—
261	#117×C₈₉	—	2	2	no	—
262	#117×C₈₉	D₄	1	2	yes	—
263	#117×C₈₉	D₄	1	1	yes	characteristic
264	#117×C₈₉	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
266	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
267	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
268	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
269	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
270	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
271	C₂×C₄²×C₈₉	—	2	1	no	—
272	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
274	#107×C₈₉	C₂³	1	1	yes	characteristic
275	#107×C₈₉	C₂³	1	1	yes	characteristic
276	#107×C₈₉	C₂³	1	2	yes	—
277	#106×C₈₉	C₂³	1	1	yes	characteristic
278	#106×C₈₉	C₂³	1	1	yes	characteristic
279	#106×C₈₉	C₂³	1	2	yes	—
280	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
281	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
285	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
286	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
287	#103×C₈₉	C₂³	1	2	yes	—
288	#103×C₈₉	C₂³	1	2	yes	—
289	#103×C₈₉	C₂³	1	1	yes	characteristic
290	#103×C₈₉	C₂³	1	2	yes	—
291	#103×C₈₉	C₂³	1	2	yes	—
292	#103×C₈₉	C₂³	1	1	yes	characteristic
293	#103×C₈₉	C₂³	1	1	yes	characteristic
294	#103×C₈₉	C₂³	1	1	yes	characteristic
295	#103×C₈₉	C₂³	1	2	yes	—
296	#102×C₈₉	C₂³	1	2	yes	—
297	#102×C₈₉	C₂³	1	2	yes	—
298	#102×C₈₉	C₂³	1	1	yes	characteristic
299	#102×C₈₉	C₂³	1	2	yes	—
300	#102×C₈₉	C₂³	1	2	yes	—
301	#102×C₈₉	C₂³	1	1	yes	characteristic
302	#102×C₈₉	C₂³	1	1	yes	characteristic
303	#102×C₈₉	C₂³	1	1	yes	characteristic
304	#102×C₈₉	C₂³	1	2	yes	—
305	#102×C₈₉	C₂³	1	2	yes	—
306	#102×C₈₉	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
311	#97×C₈₉	C₂³	1	2	yes	—
312	#97×C₈₉	C₂³	1	2	yes	—
313	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
315	C₂⁴×C₈₉	—	2	2	no	—
316	#41×C₈₉	—	2	2	no	—
317	#41×C₈₉	—	4	2	no	—
318	#41×C₈₉	—	4	1	no	—
319	#41×C₈₉	—	4	2	no	—
320	#41×C₈₉	—	4	2	no	—
321	#41×C₈₉	—	4	2	no	—
322	#41×C₈₉	—	4	2	no	—
323	#41×C₈₉	—	4	2	no	—
324	#41×C₈₉	—	4	2	no	—
325	#41×C₈₉	—	4	4	no	—
326	#41×C₈₉	—	8	2	no	—
327	C₂×Q₈×C₈₉	—	2	1	no	—
328	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₈₉	—	2	4	no	—
333	C₂×D₄×C₈₉	—	2	1	no	—
334	C₂×D₄×C₈₉	—	2	2	no	—
335	C₂×D₄×C₈₉	—	2	2	no	—
336	C₂×D₄×C₈₉	—	2	1	no	—
337	C₂×D₄×C₈₉	—	2	2	no	—
338	C₂×D₄×C₈₉	—	2	2	no	—
339	C₂×D₄×C₈₉	—	2	2	no	—
340	C₂×D₄×C₈₉	—	2	2	no	—
341	C₂×D₄×C₈₉	—	2	2	no	—
342	C₂×D₄×C₈₉	—	2	1	no	—
343	C₂×D₄×C₈₉	—	2	2	no	—
344	C₂×D₄×C₈₉	—	2	1	no	—
345	C₂×D₄×C₈₉	—	2	2	no	—
346	C₂×D₄×C₈₉	—	2	1	no	—
347	C₂×D₄×C₈₉	—	2	1	no	—
348	C₂×D₄×C₈₉	—	4	2	no	—
349	C₂×D₄×C₈₉	—	4	4	no	—
350	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
351	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
354	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
355	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₈₉	—	2	2	no	—
357	C₂²×C₄×C₈₉	—	2	1	no	—
358	C₂²×C₄×C₈₉	—	2	1	no	—
359	C₂²×C₄×C₈₉	—	2	1	no	—
360	C₂²×C₄×C₈₉	—	2	2	no	—
361	C₂²×C₄×C₈₉	—	2	1	no	—
362	C₂²×C₄×C₈₉	—	2	2	no	—
363	C₂²×C₄×C₈₉	—	2	2	no	—
364	C₂²×C₄×C₈₉	—	2	2	no	—
365	C₂²×C₄×C₈₉	—	2	2	no	—
366	C₂²×C₄×C₈₉	—	2	2	no	—
367	C₂²×C₄×C₈₉	—	2	2	no	—
368	C₂²×C₄×C₈₉	—	8	4	no	—
369	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
371	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
372	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
374	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
375	Q₁₆×C₈₉	—	4	1	no	—
376	Q₁₆×C₈₉	—	4	2	no	—
377	SD₁₆×C₈₉	—	2	4	no	—
378	SD₁₆×C₈₉	—	2	2	no	—
379	SD₁₆×C₈₉	—	4	1	no	—
380	SD₁₆×C₈₉	—	4	2	no	—
381	SD₁₆×C₈₉	—	4	2	no	—
382	SD₁₆×C₈₉	—	4	2	no	—
383	SD₁₆×C₈₉	—	4	2	no	—
384	D₈×C₈₉	—	2	4	no	—
385	D₈×C₈₉	—	2	2	no	—
386	D₈×C₈₉	—	4	2	no	—
387	D₈×C₈₉	—	4	2	no	—
388	D₈×C₈₉	—	4	2	no	—
389	M₁₆×C₈₉	—	4	2	no	—
390	M₁₆×C₈₉	—	4	2	no	—
391	C₂×C₈×C₈₉	—	4	2	no	—
392	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
397	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
398	C₄⋊C₄×C₈₉	—	2	1	no	—
399	C₄⋊C₄×C₈₉	—	2	2	no	—
400	C₄⋊C₄×C₈₉	—	2	1	no	—
401	C₄⋊C₄×C₈₉	—	2	2	no	—
402	C₄⋊C₄×C₈₉	—	2	2	no	—
403	C₄⋊C₄×C₈₉	—	2	1	no	—
404	C₄⋊C₄×C₈₉	—	2	2	no	—
405	C₄⋊C₄×C₈₉	—	2	1	no	—
406	C₄⋊C₄×C₈₉	—	2	1	no	—
407	C₄⋊C₄×C₈₉	—	2	1	no	—
408	C₄⋊C₄×C₈₉	—	2	2	no	—
409	C₄⋊C₄×C₈₉	—	2	2	no	—
410	C₄⋊C₄×C₈₉	—	2	1	no	—
411	C₄⋊C₄×C₈₉	—	2	2	no	—
412	C₄⋊C₄×C₈₉	—	2	1	no	—
413	C₄⋊C₄×C₈₉	—	2	2	no	—
414	C₄⋊C₄×C₈₉	—	2	1	no	—
415	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
416	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
417	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
418	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
421	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
424	C₂²⋊C₄×C₈₉	—	2	2	no	—
425	C₂²⋊C₄×C₈₉	—	2	1	no	—
426	C₂²⋊C₄×C₈₉	—	2	2	no	—
427	C₂²⋊C₄×C₈₉	—	2	1	no	—
428	C₂²⋊C₄×C₈₉	—	2	1	no	—
429	C₂²⋊C₄×C₈₉	—	2	2	no	—
430	C₂²⋊C₄×C₈₉	—	2	2	no	—
431	C₂²⋊C₄×C₈₉	—	2	2	no	—
432	C₂²⋊C₄×C₈₉	—	2	2	no	—
433	C₂²⋊C₄×C₈₉	—	2	2	no	—
434	C₂²⋊C₄×C₈₉	—	2	1	no	—
435	C₂²⋊C₄×C₈₉	—	2	2	no	—
436	C₂²⋊C₄×C₈₉	—	2	1	no	—
437	C₂²⋊C₄×C₈₉	—	2	2	no	—
438	C₂²⋊C₄×C₈₉	—	2	1	no	—
439	C₂²⋊C₄×C₈₉	—	2	2	no	—
440	C₂²⋊C₄×C₈₉	—	2	2	no	—
441	C₂²⋊C₄×C₈₉	—	2	1	no	—
442	C₂²⋊C₄×C₈₉	—	2	2	no	—
443	C₂²⋊C₄×C₈₉	—	2	2	no	—
444	C₂²⋊C₄×C₈₉	—	2	1	no	—
445	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
447	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
448	C₄²×C₈₉	—	2	1	no	—
449	C₄²×C₈₉	—	2	1	no	—
450	C₄²×C₈₉	—	2	1	no	—
451	C₄²×C₈₉	—	2	2	no	—
452	C₄²×C₈₉	—	2	1	no	—
453	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₈₉	C₂×D₄	1	2	yes	—
455	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
456	C₄²×C₈₉	C₂×D₄	1	2	yes	—
457	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
458	C₄²×C₈₉	C₂⁴	1	2	yes	—
459	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
460	C₂³×C₈₉	—	2	1	no	—
461	C₂³×C₈₉	—	2	2	no	—
462	C₂³×C₈₉	—	2	1	no	—
463	C₂³×C₈₉	—	2	2	no	—
464	C₂³×C₈₉	—	4	4	no	—
465	C₂³×C₈₉	—	4	4	no	—
466	C₂³×C₈₉	—	8	2	no	—
467	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
468	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
469	Q₈×C₈₉	—	2	2	no	—
470	Q₈×C₈₉	—	2	1	no	—
471	Q₈×C₈₉	—	2	2	no	—
472	Q₈×C₈₉	—	2	1	no	—
473	Q₈×C₈₉	—	2	1	no	—
474	Q₈×C₈₉	—	2	2	no	—
475	Q₈×C₈₉	—	2	1	no	—
476	Q₈×C₈₉	—	8	1	no	—
477	D₄×C₈₉	—	2	2	no	—
478	D₄×C₈₉	—	2	1	no	—
479	D₄×C₈₉	—	2	2	no	—
480	D₄×C₈₉	—	2	2	no	—
481	D₄×C₈₉	—	2	1	no	—
482	D₄×C₈₉	—	2	2	no	—
483	D₄×C₈₉	—	2	2	no	—
484	D₄×C₈₉	—	2	1	no	—
485	D₄×C₈₉	—	4	2	no	—
486	D₄×C₈₉	—	4	4	no	—
487	D₄×C₈₉	—	4	4	no	—
488	D₄×C₈₉	—	4	2	no	—
489	D₄×C₈₉	—	4	4	no	—
490	D₄×C₈₉	—	4	2	no	—
491	D₄×C₈₉	—	4	2	no	—
492	D₄×C₈₉	—	8	2	no	—
493	D₄×C₈₉	—	8	1	no	—
494	D₄×C₈₉	—	8	1	no	—
495	D₄×C₈₉	—	8	2	no	—
496	D₄×C₈₉	—	8	1	no	—
497	D₄×C₈₉	—	8	2	no	—
498	D₄×C₈₉	—	8	2	no	—
499	D₄×C₈₉	—	8	2	no	—
500	D₄×C₈₉	—	8	2	no	—
501	D₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
502	C₂×C₄×C₈₉	—	2	2	no	—
503	C₂×C₄×C₈₉	—	2	1	no	—
504	C₂×C₄×C₈₉	—	2	2	no	—
505	C₂×C₄×C₈₉	—	2	2	no	—
506	C₂×C₄×C₈₉	—	2	1	no	—
507	C₂×C₄×C₈₉	—	2	1	no	—
508	C₂×C₄×C₈₉	—	2	1	no	—
509	C₂×C₄×C₈₉	—	2	1	no	—
510	C₂×C₄×C₈₉	—	2	1	no	—
511	C₂×C₄×C₈₉	—	2	1	no	—
512	C₂×C₄×C₈₉	—	2	2	no	—
513	C₂×C₄×C₈₉	—	2	1	no	—
514	C₂×C₄×C₈₉	—	2	2	no	—
515	C₂×C₄×C₈₉	—	4	2	no	—
516	C₂×C₄×C₈₉	—	4	2	no	—
517	C₂×C₄×C₈₉	—	4	1	no	—
518	C₂×C₄×C₈₉	—	4	2	no	—
519	C₂×C₄×C₈₉	—	4	2	no	—
520	C₂×C₄×C₈₉	—	4	4	no	—
521	C₂×C₄×C₈₉	—	4	4	no	—
522	C₂×C₄×C₈₉	—	4	2	no	—
523	C₂×C₄×C₈₉	—	4	2	no	—
524	C₂×C₄×C₈₉	—	8	2	no	—
525	C₂×C₄×C₈₉	—	8	2	no	—
526	C₂×C₄×C₈₉	—	8	2	no	—
527	C₂×C₄×C₈₉	—	8	2	no	—
528	C₂×C₄×C₈₉	—	8	2	no	—
529	C₂×C₄×C₈₉	—	8	2	no	—
530	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
533	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
535	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
536	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
539	C₈×C₈₉	—	2	2	no	—
540	C₈×C₈₉	—	2	2	no	—
541	C₈×C₈₉	—	2	1	no	—
542	C₈×C₈₉	—	2	1	no	—
543	C₈×C₈₉	—	2	1	no	—
544	C₈×C₈₉	—	2	1	no	—
545	C₂²×C₈₉	—	2	2	no	—
546	C₂²×C₈₉	—	2	1	no	—
547	C₂²×C₈₉	—	2	1	no	—
548	C₂²×C₈₉	—	2	2	no	—
549	C₂²×C₈₉	—	2	2	no	—
550	C₂²×C₈₉	—	2	1	no	—
551	C₂²×C₈₉	—	2	2	no	—
552	C₂²×C₈₉	—	4	1	no	—
553	C₂²×C₈₉	—	4	1	no	—
554	C₂²×C₈₉	—	4	2	no	—
555	C₂²×C₈₉	—	4	1	no	—
556	C₂²×C₈₉	—	4	2	no	—
557	C₂²×C₈₉	—	4	1	no	—
558	C₂²×C₈₉	—	4	2	no	—
559	C₂²×C₈₉	—	4	2	no	—
560	C₂²×C₈₉	—	4	2	no	—
561	C₂²×C₈₉	—	4	1	no	—
562	C₂²×C₈₉	—	4	2	no	—
563	C₂²×C₈₉	—	8	8	no	—
564	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
565	C₄×C₈₉	—	2	1	no	—
566	C₄×C₈₉	—	2	2	no	—
567	C₄×C₈₉	—	2	1	no	—
568	C₄×C₈₉	—	2	1	no	—
569	C₄×C₈₉	—	2	2	no	—
570	C₄×C₈₉	—	2	1	no	—
571	C₄×C₈₉	—	2	2	no	—
572	C₄×C₈₉	—	4	1	no	—
573	C₄×C₈₉	—	4	2	no	—
574	C₄×C₈₉	—	4	1	no	—
575	C₄×C₈₉	—	4	1	no	—
576	C₄×C₈₉	—	4	1	no	—
577	C₄×C₈₉	—	4	2	no	—
578	C₄×C₈₉	—	4	1	no	—
579	C₄×C₈₉	—	4	1	no	—
580	C₄×C₈₉	#575	1	2	yes	—
581	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
582	C₄×C₈₉	#585	1	1	yes	characteristic
583	#61974	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
584	C₂×C₈₉	—	4	1	no	—
585	C₂×C₈₉	—	4	2	no	—
586	C₂×C₈₉	—	4	2	no	—
587	C₂×C₈₉	—	8	1	no	—
588	C₂×C₈₉	—	8	2	no	—
589	C₂×C₈₉	—	8	2	no	—
590	C₂×C₈₉	#3488	1	1	yes	characteristic
591	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
592	C₂×C₈₉	#3585	1	1	yes	characteristic
593	#3517	C₂×C₈₉	1	1	yes	characteristic, complemented
594	#3481	C₂×C₈₉	1	1	yes	characteristic, complemented
595	#3400	C₂×C₈₉	1	1	yes	characteristic, complemented
596	#3399	C₂×C₈₉	1	1	yes	characteristic, complemented
597	#3372	C₂×C₈₉	1	1	yes	characteristic, complemented
598	#3366	C₂×C₈₉	1	1	yes	characteristic, complemented
599	#3333	C₂×C₈₉	1	1	yes	characteristic, complemented
600	#3331	C₂×C₈₉	1	1	yes	characteristic, complemented
601	#3309	C₂×C₈₉	1	2	yes	complemented
602	#3307	C₂×C₈₉	1	2	yes	complemented
603	#3274	C₂×C₈₉	1	1	yes	characteristic, complemented
604	#3272	C₂×C₈₉	1	1	yes	characteristic, complemented
605	#3268	C₂×C₈₉	1	2	yes	complemented
606	#3267	C₂×C₈₉	1	2	yes	complemented
607	#3256	C₂×C₈₉	1	2	yes	complemented
608	#3247	C₂×C₈₉	1	1	yes	characteristic, complemented
609	#3219	C₂×C₈₉	1	2	yes	complemented
610	#3207	C₂×C₈₉	1	1	yes	characteristic, complemented
611	#3114	C₂×C₈₉	1	2	yes	complemented
612	#3102	C₂×C₈₉	1	1	yes	characteristic, complemented
613	#3036	C₂×C₈₉	1	2	yes	complemented
614	#3035	C₂×C₈₉	1	1	yes	characteristic, complemented
615	#2989	C₂×C₈₉	1	1	yes	characteristic, complemented
616	C₈₉	#61974	1	1	yes	characteristic, direct product factor, Sylow
617	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
618	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
619	C₂×#135	C₂²×C₈₉	1	2	yes	—
620	#559	C₂²×C₈₉	1	1	yes	characteristic
621	#557	C₂²×C₈₉	1	1	yes	characteristic, complemented
622	#554	C₂²×C₈₉	1	1	yes	characteristic
623	#554	C₂²×C₈₉	1	1	yes	characteristic
624	#553	—	2	1	no	—
625	#553	—	2	1	no	—
626	#553	—	2	2	no	—
627	#553	C₂²×C₈₉	1	2	yes	—
628	#551	—	2	2	no	—
629	#550	—	2	1	no	—
630	#550	C₂²×C₈₉	1	1	yes	characteristic
631	#550	C₂²×C₈₉	1	2	yes	complemented
632	#550	C₂²×C₈₉	1	1	yes	characteristic, complemented
633	#547	C₂²×C₈₉	1	1	yes	characteristic
634	#547	C₂²×C₈₉	1	2	yes	complemented
635	#546	—	2	1	no	—
636	#546	C₂²×C₈₉	1	2	yes	—
637	D₄²	C₂²×C₈₉	1	1	yes	characteristic
638	#540	—	2	1	no	—
639	#540	—	2	2	no	—
640	#532	C₂²×C₈₉	1	1	yes	characteristic
641	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
642	#532	C₂²×C₈₉	1	2	yes	complemented
643	#529	—	2	1	no	—
644	#529	C₂²×C₈₉	1	2	yes	—
645	#529	C₂²×C₈₉	1	1	yes	characteristic, complemented
646	#529	C₂²×C₈₉	1	2	yes	complemented
647	#525	—	2	2	no	—
648	#520	—	2	1	no	—
649	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
650	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
651	C₂×C₄×D₄	—	2	1	no	—
652	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
653	#497	C₂²×C₈₉	1	2	yes	complemented
654	#496	C₂²×C₈₉	1	2	yes	complemented
655	#493	C₂²×C₈₉	1	1	yes	characteristic
656	#492	C₂²×C₈₉	1	1	yes	characteristic
657	#491	C₂²×C₈₉	1	2	yes	complemented
658	#490	C₂²×C₈₉	1	2	yes	complemented
659	#487	C₂²×C₈₉	1	1	yes	characteristic, complemented
660	#486	C₂²×C₈₉	1	1	yes	characteristic, complemented
661	#485	C₂²×C₈₉	1	1	yes	characteristic, complemented
662	#483	C₂²×C₈₉	1	2	yes	complemented
663	#482	C₂²×C₈₉	1	1	yes	characteristic, complemented
664	#480	C₂²×C₈₉	1	2	yes	complemented
665	#479	C₂²×C₈₉	1	1	yes	characteristic, complemented
666	#479	C₂²×C₈₉	1	2	yes	complemented
667	#478	C₂²×C₈₉	1	1	yes	characteristic
668	#478	C₂²×C₈₉	1	2	yes	complemented
669	#478	C₂²×C₈₉	1	2	yes	complemented
670	#477	C₂²×C₈₉	1	1	yes	characteristic, complemented
671	#476	C₂²×C₈₉	1	1	yes	characteristic, complemented
672	#470	C₂²×C₈₉	1	2	yes	complemented
673	#469	C₂²×C₈₉	1	2	yes	—
674	#468	C₂²×C₈₉	1	2	yes	—
675	#468	C₂²×C₈₉	1	2	yes	complemented
676	#466	C₂²×C₈₉	1	2	yes	complemented
677	#465	C₂²×C₈₉	1	2	yes	complemented
678	#464	C₂²×C₈₉	1	1	yes	characteristic, complemented
679	#464	C₂²×C₈₉	1	2	yes	complemented
680	#464	C₂²×C₈₉	1	2	yes	complemented
681	#463	C₂²×C₈₉	1	1	yes	characteristic
682	#463	C₂²×C₈₉	1	2	yes	—
683	#463	C₂²×C₈₉	1	2	yes	complemented
684	#463	C₂²×C₈₉	1	2	yes	complemented
685	#463	C₂²×C₈₉	1	2	yes	complemented
686	#463	C₂²×C₈₉	1	2	yes	complemented
687	#462	C₂²×C₈₉	1	1	yes	characteristic, complemented
688	#461	C₂²×C₈₉	1	2	yes	—
689	#461	C₂²×C₈₉	1	1	yes	characteristic
690	#461	C₂²×C₈₉	1	2	yes	complemented
691	#460	C₂²×C₈₉	1	1	yes	characteristic
692	#460	C₂²×C₈₉	1	1	yes	characteristic, complemented
693	#459	C₂²×C₈₉	1	2	yes	—
694	#459	C₂²×C₈₉	1	1	yes	characteristic
695	#459	C₂²×C₈₉	1	1	yes	characteristic
696	#459	C₂²×C₈₉	1	2	yes	complemented
697	#452	C₂²×C₈₉	1	1	yes	characteristic
698	#452	C₂²×C₈₉	1	2	yes	complemented
699	#452	C₂²×C₈₉	1	2	yes	complemented
700	#450	C₂²×C₈₉	1	2	yes	—
701	#449	C₂²×C₈₉	1	1	yes	characteristic
702	#449	C₂²×C₈₉	1	2	yes	—
703	#449	C₂²×C₈₉	1	2	yes	—
704	#449	C₂²×C₈₉	1	2	yes	complemented
705	#449	C₂²×C₈₉	1	2	yes	complemented
706	#447	C₂²×C₈₉	1	2	yes	—
707	#446	C₂²×C₈₉	1	1	yes	characteristic, complemented
708	#446	C₂²×C₈₉	1	1	yes	characteristic, complemented
709	#442	C₂²×C₈₉	1	2	yes	—
710	#442	C₂²×C₈₉	1	2	yes	complemented
711	#440	C₂²×C₈₉	1	2	yes	—
712	#440	C₂²×C₈₉	1	2	yes	complemented
713	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
714	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
715	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
716	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
717	#436	C₂²×C₈₉	1	1	yes	characteristic
718	#436	C₂²×C₈₉	1	1	yes	characteristic
719	#435	C₂²×C₈₉	1	2	yes	complemented
720	#435	C₂²×C₈₉	1	2	yes	complemented
721	#432	C₂²×C₈₉	1	2	yes	complemented
722	#431	C₂²×C₈₉	1	1	yes	characteristic, complemented
723	#423	C₂²×C₈₉	1	2	yes	complemented
724	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
725	#417	C₂²×C₈₉	1	2	yes	complemented
726	#417	C₂²×C₈₉	1	2	yes	complemented
727	#416	C₂²×C₈₉	1	2	yes	complemented
728	C₂×#41	—	2	1	no	—
729	C₂×#41	—	2	1	no	—
730	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
731	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
732	C₂×#41	C₂³×C₈₉	1	2	yes	—
733	C₂×#41	C₂³×C₈₉	1	2	yes	—
734	C₂×#41	C₂³×C₈₉	1	2	yes	—
735	C₂²×D₄	—	2	1	no	—
736	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
737	C₂³×C₄	—	2	2	no	—
738	AGL(1,ℤ/8)	—	4	4	no	—
739	AGL(1,ℤ/8)	—	4	4	no	—
740	#135	—	4	4	no	—
741	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
742	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
743	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
744	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
745	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
746	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
747	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
748	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
749	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
750	C₂×D₈	C₂³×C₈₉	1	2	yes	—
751	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
752	C₂×D₈	C₂³×C₈₉	1	2	yes	—
753	C₂×D₈	C₂³×C₈₉	1	2	yes	—
754	C₂×D₈	C₂³×C₈₉	1	2	yes	—
755	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
756	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
757	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
758	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
759	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
760	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
761	#127	—	2	1	no	—
762	#127	—	2	2	no	—
763	#127	C₂³×C₈₉	1	1	yes	characteristic
764	#127	C₂³×C₈₉	1	1	yes	characteristic
765	#127	C₂³×C₈₉	1	2	yes	—
766	#126	—	2	2	no	—
767	#126	—	2	2	no	—
768	#126	—	2	1	no	—
769	#126	—	2	2	no	—
770	#125	—	2	1	no	—
771	#125	—	2	1	no	—
772	#125	—	2	2	no	—
773	#125	C₂³×C₈₉	1	2	yes	—
774	#125	C₂³×C₈₉	1	1	yes	characteristic
775	#124	—	2	1	no	—
776	#124	—	2	1	no	—
777	#124	C₂³×C₈₉	1	2	yes	—
778	#124	C₂³×C₈₉	1	1	yes	characteristic
779	#124	C₂³×C₈₉	1	2	yes	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	1	no	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	#123	—	2	2	no	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	#123	—	2	2	no	—
789	C₂²⋊Q₈	—	2	1	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
793	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
794	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
795	#121	—	2	2	no	—
796	#121	—	2	1	no	—
797	#121	—	2	2	no	—
798	#121	—	2	1	no	—
799	#121	—	2	2	no	—
800	#121	—	2	1	no	—
801	#121	—	2	1	no	—
802	#121	—	2	2	no	—
803	#121	—	2	1	no	—
804	#121	—	2	1	no	—
805	#121	—	2	2	no	—
806	#121	—	2	2	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	C₂³×C₈₉	1	2	yes	—
811	#121	C₂³×C₈₉	1	2	yes	—
812	#121	C₂³×C₈₉	1	1	yes	characteristic
813	#121	C₂³×C₈₉	1	2	yes	—
814	#120	—	2	2	no	—
815	#120	—	2	2	no	—
816	C₄×Q₈	—	2	1	no	—
817	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
818	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
819	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
820	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
821	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
822	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	2	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	2	no	—
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	—	2	2	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	—	2	2	no	—
840	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
841	C₄×D₄	D₄×C₈₉	1	2	yes	—
842	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
843	C₄×D₄	C₂³×C₈₉	1	2	yes	—
844	C₄×D₄	C₂³×C₈₉	1	2	yes	—
845	C₄×D₄	C₂³×C₈₉	1	2	yes	—
846	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
847	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
848	C₄×D₄	C₂³×C₈₉	1	2	yes	—
849	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
850	C₄×D₄	C₂³×C₈₉	1	2	yes	—
851	#117	—	2	1	no	—
852	#117	—	2	1	no	—
853	#117	—	2	2	no	—
854	#117	—	2	2	no	—
855	#117	D₄×C₈₉	1	2	yes	—
856	#117	D₄×C₈₉	1	1	yes	characteristic
857	#117	C₂³×C₈₉	1	1	yes	characteristic
858	C₂×C₄⋊C₄	—	2	1	no	—
859	C₂×C₄⋊C₄	—	2	1	no	—
860	C₂×C₄⋊C₄	—	2	2	no	—
861	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
862	C₂×C₂²⋊C₄	—	2	2	no	—
863	C₂×C₂²⋊C₄	—	2	2	no	—
864	C₂×C₄²	—	2	1	no	—
865	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
866	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
867	#107	C₂³×C₈₉	1	1	yes	characteristic
868	#107	C₂³×C₈₉	1	1	yes	characteristic
869	#107	C₂³×C₈₉	1	2	yes	—
870	#106	C₂³×C₈₉	1	1	yes	characteristic
871	#106	C₂³×C₈₉	1	1	yes	characteristic
872	#106	C₂³×C₈₉	1	2	yes	—
873	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
874	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
875	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
876	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
877	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
878	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
879	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
880	#103	C₂³×C₈₉	1	2	yes	—
881	#103	C₂³×C₈₉	1	2	yes	—
882	#103	C₂³×C₈₉	1	1	yes	characteristic
883	#103	C₂³×C₈₉	1	2	yes	—
884	#103	C₂³×C₈₉	1	2	yes	—
885	#103	C₂³×C₈₉	1	1	yes	characteristic
886	#103	C₂³×C₈₉	1	1	yes	characteristic
887	#103	C₂³×C₈₉	1	1	yes	characteristic
888	#103	C₂³×C₈₉	1	2	yes	—
889	#102	C₂³×C₈₉	1	2	yes	—
890	#102	C₂³×C₈₉	1	2	yes	—
891	#102	C₂³×C₈₉	1	1	yes	characteristic
892	#102	C₂³×C₈₉	1	2	yes	—
893	#102	C₂³×C₈₉	1	2	yes	—
894	#102	C₂³×C₈₉	1	1	yes	characteristic
895	#102	C₂³×C₈₉	1	1	yes	characteristic
896	#102	C₂³×C₈₉	1	1	yes	characteristic
897	#102	C₂³×C₈₉	1	2	yes	—
898	#102	C₂³×C₈₉	1	2	yes	—
899	#102	C₂³×C₈₉	1	2	yes	—
900	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
901	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
902	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
903	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
904	#97	C₂³×C₈₉	1	2	yes	—
905	#97	C₂³×C₈₉	1	2	yes	—
906	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
907	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
908	C₂⁴	—	2	2	no	—
909	#41	—	2	2	no	—
910	#41	—	4	2	no	—
911	#41	—	4	1	no	—
912	#41	—	4	2	no	—
913	#41	—	4	2	no	—
914	#41	—	4	2	no	—
915	#41	—	4	2	no	—
916	#41	—	4	2	no	—
917	#41	—	4	2	no	—
918	#41	—	4	4	no	—
919	#41	—	8	2	no	—
920	C₂×Q₈	—	2	1	no	—
921	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
922	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
923	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
924	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
925	C₂×D₄	—	2	4	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	1	no	—
941	C₂×D₄	—	4	2	no	—
942	C₂×D₄	—	4	4	no	—
943	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
944	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
945	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
946	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
947	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
948	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	2	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	8	4	no	—
962	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
963	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
964	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
965	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
966	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
967	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
968	Q₁₆	—	4	2	no	—
969	Q₁₆	—	4	1	no	—
970	SD₁₆	—	2	4	no	—
971	SD₁₆	—	2	2	no	—
972	SD₁₆	—	4	2	no	—
973	SD₁₆	—	4	2	no	—
974	SD₁₆	—	4	2	no	—
975	SD₁₆	—	4	1	no	—
976	SD₁₆	—	4	2	no	—
977	D₈	—	2	4	no	—
978	D₈	—	2	2	no	—
979	D₈	—	4	2	no	—
980	D₈	—	4	2	no	—
981	D₈	—	4	2	no	—
982	M₁₆	—	4	2	no	—
983	M₁₆	—	4	2	no	—
984	C₂×C₈	—	4	2	no	—
985	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
986	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
987	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
988	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
989	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
990	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	1	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	1	no	—
1001	C₄⋊C₄	—	2	2	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1009	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1010	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1011	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1012	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1013	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1014	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1015	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1016	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	1	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1039	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1040	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	2	1	no	—
1043	C₄²	—	2	1	no	—
1044	C₄²	—	2	2	no	—
1045	C₄²	—	2	1	no	—
1046	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1047	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1048	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1049	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1050	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1051	C₄²	C₂⁴×C₈₉	1	2	yes	—
1052	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1053	C₂³	—	2	1	no	—
1054	C₂³	—	2	2	no	—
1055	C₂³	—	2	2	no	—
1056	C₂³	—	2	1	no	—
1057	C₂³	—	4	4	no	—
1058	C₂³	—	4	4	no	—
1059	C₂³	—	8	2	no	—
1060	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1061	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1062	Q₈	—	2	2	no	—
1063	Q₈	—	2	1	no	—
1064	Q₈	—	2	2	no	—
1065	Q₈	—	2	1	no	—
1066	Q₈	—	2	1	no	—
1067	Q₈	—	2	2	no	—
1068	Q₈	—	2	1	no	—
1069	Q₈	—	8	1	no	—
1070	D₄	—	2	2	no	—
1071	D₄	—	2	1	no	—
1072	D₄	—	2	2	no	—
1073	D₄	—	2	2	no	—
1074	D₄	—	2	1	no	—
1075	D₄	—	2	2	no	—
1076	D₄	—	2	2	no	—
1077	D₄	—	2	1	no	—
1078	D₄	—	4	2	no	—
1079	D₄	—	4	4	no	—
1080	D₄	—	4	4	no	—
1081	D₄	—	4	2	no	—
1082	D₄	—	4	4	no	—
1083	D₄	—	4	2	no	—
1084	D₄	—	4	2	no	—
1085	D₄	—	8	2	no	—
1086	D₄	—	8	1	no	—
1087	D₄	—	8	1	no	—
1088	D₄	—	8	2	no	—
1089	D₄	—	8	1	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	2	no	—
1092	D₄	—	8	2	no	—
1093	D₄	—	8	2	no	—
1094	D₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	4	2	no	—
1110	C₂×C₄	—	4	1	no	—
1111	C₂×C₄	—	4	2	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	4	4	no	—
1114	C₂×C₄	—	4	4	no	—
1115	C₂×C₄	—	4	2	no	—
1116	C₂×C₄	—	4	2	no	—
1117	C₂×C₄	—	8	2	no	—
1118	C₂×C₄	—	8	2	no	—
1119	C₂×C₄	—	8	2	no	—
1120	C₂×C₄	—	8	2	no	—
1121	C₂×C₄	—	8	2	no	—
1122	C₂×C₄	—	8	2	no	—
1123	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1124	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1125	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1126	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1127	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1128	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1129	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1130	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1131	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1132	C₈	—	2	2	no	—
1133	C₈	—	2	2	no	—
1134	C₈	—	2	1	no	—
1135	C₈	—	2	1	no	—
1136	C₈	—	2	1	no	—
1137	C₈	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	1	no	—
1142	C₂²	—	2	1	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	2	2	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	4	1	no	—
1149	C₂²	—	4	2	no	—
1150	C₂²	—	4	2	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	2	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	4	2	no	—
1155	C₂²	—	4	2	no	—
1156	C₂²	—	8	8	no	—
1157	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1158	C₄	—	2	1	no	—
1159	C₄	—	2	2	no	—
1160	C₄	—	2	1	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	1	no	—
1163	C₄	—	2	1	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	4	1	no	—
1166	C₄	—	4	1	no	—
1167	C₄	—	4	1	no	—
1168	C₄	—	4	2	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	1	no	—
1172	C₄	—	4	2	no	—
1173	C₄	#575×C₈₉	1	2	yes	—
1174	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1175	C₄	#585×C₈₉	1	1	yes	characteristic
1176	C₂	—	4	1	no	—
1177	C₂	—	4	2	no	—
1178	C₂	—	4	2	no	—
1179	C₂	—	8	2	no	—
1180	C₂	—	8	1	no	—
1181	C₂	—	8	2	no	—
1182	C₂	C₈₉×#3488	1	1	yes	characteristic
1183	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
1184	C₂	C₈₉×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3517	C₂	semidirect
2. C₈₉×#3481	C₂	semidirect
3. C₈₉×#3400	C₂	semidirect
4. C₈₉×#3399	C₂	semidirect
5. C₈₉×#3372	C₂	semidirect
6. C₈₉×#3366	C₂	semidirect
7. C₈₉×#3333	C₂	semidirect
8. C₈₉×#3331	C₂	semidirect
9. C₈₉×#3309	C₂	semidirect
10. C₈₉×#3307	C₂	semidirect
11. C₈₉×#3274	C₂	semidirect
12. C₈₉×#3272	C₂	semidirect
13. C₈₉×#3268	C₂	semidirect
14. C₈₉×#3267	C₂	semidirect
15. C₈₉×#3256	C₂	semidirect
16. C₈₉×#3247	C₂	semidirect
17. C₈₉×#3219	C₂	semidirect
18. C₈₉×#3207	C₂	semidirect
19. C₈₉×#3114	C₂	semidirect
20. C₈₉×#3102	C₂	semidirect
21. C₈₉×#3036	C₂	semidirect
22. C₈₉×#3035	C₂	semidirect
23. C₈₉×#2989	C₂	semidirect
28. #557×C₈₉	C₂²	semidirect
38. #550×C₈₉	C₂²	semidirect
39. #550×C₈₉	C₂²	semidirect
41. #547×C₈₉	C₂²	semidirect
48. #532×C₈₉	C₂²	semidirect
49. #532×C₈₉	C₂²	semidirect
52. #529×C₈₉	C₂²	semidirect
53. #529×C₈₉	C₂²	semidirect
60. #497×C₈₉	C₂²	semidirect
61. #496×C₈₉	C₂²	semidirect
64. #491×C₈₉	C₂²	semidirect
65. #490×C₈₉	C₂²	semidirect
66. #487×C₈₉	C₂²	semidirect
67. #486×C₈₉	C₂²	semidirect
68. #485×C₈₉	C₂²	semidirect
69. #483×C₈₉	C₂²	semidirect
70. #482×C₈₉	C₂²	semidirect
71. #480×C₈₉	C₂²	semidirect
72. #479×C₈₉	C₂²	semidirect
73. #479×C₈₉	C₂²	semidirect
75. #478×C₈₉	C₂²	semidirect
76. #478×C₈₉	C₂²	semidirect
77. #477×C₈₉	C₂²	semidirect
78. #476×C₈₉	C₂²	semidirect
79. #470×C₈₉	C₂²	semidirect
82. #468×C₈₉	C₂²	semidirect
83. #466×C₈₉	C₂²	semidirect
84. #465×C₈₉	C₂²	semidirect
85. #464×C₈₉	C₂²	semidirect
86. #464×C₈₉	C₂²	semidirect
87. #464×C₈₉	C₂²	semidirect
90. #463×C₈₉	C₂²	semidirect
91. #463×C₈₉	C₂²	semidirect
92. #463×C₈₉	C₂²	semidirect
93. #463×C₈₉	C₂²	semidirect
94. #462×C₈₉	C₂²	semidirect
97. #461×C₈₉	C₂²	semidirect
99. #460×C₈₉	C₂²	semidirect
103. #459×C₈₉	C₂²	semidirect
105. #452×C₈₉	C₂²	semidirect
106. #452×C₈₉	C₂²	semidirect
111. #449×C₈₉	C₂²	semidirect
112. #449×C₈₉	C₂²	semidirect
114. #446×C₈₉	C₂²	semidirect
115. #446×C₈₉	C₂²	semidirect
117. #442×C₈₉	C₂²	semidirect
119. #440×C₈₉	C₂²	semidirect
120. C₄×Q₁₆×C₈₉	C₂²	semidirect
122. C₄×SD₁₆×C₈₉	C₂²	semidirect
126. #435×C₈₉	C₂²	semidirect
127. #435×C₈₉	C₂²	semidirect
128. #432×C₈₉	C₂²	semidirect
129. #431×C₈₉	C₂²	semidirect
130. #423×C₈₉	C₂²	semidirect
131. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
132. #417×C₈₉	C₂²	semidirect
133. #417×C₈₉	C₂²	semidirect
134. #416×C₈₉	C₂²	semidirect
583. #61974	C₈₉	direct (N × H)
593. #3517	C₂×C₈₉	semidirect
594. #3481	C₂×C₈₉	semidirect
595. #3400	C₂×C₈₉	semidirect
596. #3399	C₂×C₈₉	semidirect
597. #3372	C₂×C₈₉	semidirect
598. #3366	C₂×C₈₉	semidirect
599. #3333	C₂×C₈₉	semidirect
600. #3331	C₂×C₈₉	semidirect
601. #3309	C₂×C₈₉	semidirect
602. #3307	C₂×C₈₉	semidirect
603. #3274	C₂×C₈₉	semidirect
604. #3272	C₂×C₈₉	semidirect
605. #3268	C₂×C₈₉	semidirect
606. #3267	C₂×C₈₉	semidirect
607. #3256	C₂×C₈₉	semidirect
608. #3247	C₂×C₈₉	semidirect
609. #3219	C₂×C₈₉	semidirect
610. #3207	C₂×C₈₉	semidirect
611. #3114	C₂×C₈₉	semidirect
612. #3102	C₂×C₈₉	semidirect
613. #3036	C₂×C₈₉	semidirect
614. #3035	C₂×C₈₉	semidirect
615. #2989	C₂×C₈₉	semidirect
616. C₈₉	#61974	direct (N × H)
621. #557	C₂²×C₈₉	semidirect
631. #550	C₂²×C₈₉	semidirect
632. #550	C₂²×C₈₉	semidirect
634. #547	C₂²×C₈₉	semidirect
641. #532	C₂²×C₈₉	semidirect
642. #532	C₂²×C₈₉	semidirect
645. #529	C₂²×C₈₉	semidirect
646. #529	C₂²×C₈₉	semidirect
653. #497	C₂²×C₈₉	semidirect
654. #496	C₂²×C₈₉	semidirect
657. #491	C₂²×C₈₉	semidirect
658. #490	C₂²×C₈₉	semidirect
659. #487	C₂²×C₈₉	semidirect
660. #486	C₂²×C₈₉	semidirect
661. #485	C₂²×C₈₉	semidirect
662. #483	C₂²×C₈₉	semidirect
663. #482	C₂²×C₈₉	semidirect
664. #480	C₂²×C₈₉	semidirect
665. #479	C₂²×C₈₉	semidirect
666. #479	C₂²×C₈₉	semidirect
668. #478	C₂²×C₈₉	semidirect
669. #478	C₂²×C₈₉	semidirect
670. #477	C₂²×C₈₉	semidirect
671. #476	C₂²×C₈₉	semidirect
672. #470	C₂²×C₈₉	semidirect
675. #468	C₂²×C₈₉	semidirect
676. #466	C₂²×C₈₉	semidirect
677. #465	C₂²×C₈₉	semidirect
678. #464	C₂²×C₈₉	semidirect
679. #464	C₂²×C₈₉	semidirect
680. #464	C₂²×C₈₉	semidirect
683. #463	C₂²×C₈₉	semidirect
684. #463	C₂²×C₈₉	semidirect
685. #463	C₂²×C₈₉	semidirect
686. #463	C₂²×C₈₉	semidirect
687. #462	C₂²×C₈₉	semidirect
690. #461	C₂²×C₈₉	semidirect
692. #460	C₂²×C₈₉	semidirect
696. #459	C₂²×C₈₉	semidirect
698. #452	C₂²×C₈₉	semidirect
699. #452	C₂²×C₈₉	semidirect
704. #449	C₂²×C₈₉	semidirect
705. #449	C₂²×C₈₉	semidirect
707. #446	C₂²×C₈₉	semidirect
708. #446	C₂²×C₈₉	semidirect
710. #442	C₂²×C₈₉	semidirect
712. #440	C₂²×C₈₉	semidirect
713. C₄×Q₁₆	C₂²×C₈₉	semidirect
715. C₄×SD₁₆	C₂²×C₈₉	semidirect
719. #435	C₂²×C₈₉	semidirect
720. #435	C₂²×C₈₉	semidirect
721. #432	C₂²×C₈₉	semidirect
722. #431	C₂²×C₈₉	semidirect
723. #423	C₂²×C₈₉	semidirect
724. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
725. #417	C₂²×C₈₉	semidirect
726. #417	C₂²×C₈₉	semidirect
727. #416	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3517	2
C₈₉×#3481	2
C₈₉×#3400	2
C₈₉×#3399	2
C₈₉×#3372	2
C₈₉×#3366	2
C₈₉×#3333	2
C₈₉×#3331	2
C₈₉×#3309	2
C₈₉×#3307	2
C₈₉×#3274	2
C₈₉×#3272	2
C₈₉×#3268	2
C₈₉×#3267	2
C₈₉×#3256	2
C₈₉×#3247	2
C₈₉×#3219	2
C₈₉×#3207	2
C₈₉×#3114	2
C₈₉×#3102	2
C₈₉×#3036	2
C₈₉×#3035	2
C₈₉×#2989	2
#61974	89

Subgroups — C89×#61974 #36439822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61974 #36439822