Subgroups — C₈₉×#62041 #36439889

Order 22784.

1896 conjugacy classes of subgroups.

The subgroup lattice has 1204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3393	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3333	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3330	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3314	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3294	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3283	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3273	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3268	C₂	1	2	yes	maximal, complemented
15	C₈₉×#3262	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3254	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3224	C₂	1	2	yes	maximal, complemented
18	C₈₉×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3124	C₂	1	2	yes	maximal, complemented
20	C₈₉×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#3045	C₂	1	2	yes	maximal, complemented
22	C₈₉×#3036	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2993	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	complemented
26	C₂×#135×C₈₉	C₂²	1	2	yes	complemented
27	#560×C₈₉	—	2	2	no	—
28	#556×C₈₉	C₂²	1	1	yes	characteristic, complemented
29	#556×C₈₉	C₂²	1	1	yes	characteristic, complemented
30	#554×C₈₉	C₂²	1	2	yes	complemented
31	#553×C₈₉	—	2	1	no	—
32	#552×C₈₉	—	2	1	no	—
33	#551×C₈₉	—	2	2	no	—
34	#550×C₈₉	C₂²	1	2	yes	—
35	#550×C₈₉	C₂²	1	1	yes	characteristic, complemented
36	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
37	#548×C₈₉	—	2	1	no	—
38	#547×C₈₉	C₂²	1	1	yes	characteristic
39	#547×C₈₉	C₂²	1	1	yes	characteristic
40	#547×C₈₉	C₂²	1	1	yes	characteristic, complemented
41	#546×C₈₉	—	2	1	no	—
42	#546×C₈₉	C₂²	1	2	yes	—
43	#546×C₈₉	C₂²	1	2	yes	complemented
44	D₄²×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	#542×C₈₉	C₂²	1	2	yes	complemented
46	#542×C₈₉	C₂²	1	2	yes	complemented
47	#539×C₈₉	—	2	2	no	—
48	#538×C₈₉	—	2	2	no	—
49	#537×C₈₉	—	2	1	no	—
50	#535×C₈₉	—	2	1	no	—
51	#535×C₈₉	C₂²	1	2	yes	complemented
52	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	#532×C₈₉	C₂²	1	1	yes	characteristic
54	#532×C₈₉	C₂²	1	1	yes	characteristic
55	#529×C₈₉	C₂²	1	1	yes	characteristic
56	#525×C₈₉	—	2	1	no	—
57	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
58	#520×C₈₉	C₂²	1	2	yes	complemented
59	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#496×C₈₉	C₂²	1	2	yes	complemented
61	#495×C₈₉	C₂²	1	2	yes	—
62	#494×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	#492×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	#489×C₈₉	C₂²	1	2	yes	complemented
65	#487×C₈₉	C₂²	1	1	yes	characteristic, complemented
66	#486×C₈₉	C₂²	1	2	yes	complemented
67	#486×C₈₉	C₂²	1	1	yes	characteristic, complemented
68	#484×C₈₉	C₂²	1	2	yes	complemented
69	#480×C₈₉	C₂²	1	1	yes	characteristic
70	#480×C₈₉	C₂²	1	1	yes	characteristic, complemented
71	#480×C₈₉	C₂²	1	2	yes	complemented
72	#477×C₈₉	C₂²	1	2	yes	complemented
73	#477×C₈₉	C₂²	1	2	yes	complemented
74	#474×C₈₉	C₂²	1	1	yes	characteristic, complemented
75	#474×C₈₉	C₂²	1	1	yes	characteristic, complemented
76	#474×C₈₉	C₂²	1	1	yes	characteristic, complemented
77	#474×C₈₉	C₂²	1	2	yes	complemented
78	#474×C₈₉	C₂²	1	1	yes	characteristic, complemented
79	#468×C₈₉	C₂²	1	2	yes	—
80	#468×C₈₉	C₂²	1	2	yes	complemented
81	#468×C₈₉	C₂²	1	2	yes	complemented
82	#468×C₈₉	C₂²	1	2	yes	complemented
83	#467×C₈₉	C₂²	1	2	yes	complemented
84	#466×C₈₉	C₂²	1	2	yes	—
85	#464×C₈₉	C₂²	1	2	yes	complemented
86	#464×C₈₉	C₂²	1	2	yes	complemented
87	#464×C₈₉	C₂²	1	2	yes	complemented
88	#464×C₈₉	C₂²	1	2	yes	complemented
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	#461×C₈₉	C₂²	1	1	yes	characteristic, complemented
94	#461×C₈₉	C₂²	1	1	yes	characteristic, complemented
95	#461×C₈₉	C₂²	1	1	yes	characteristic, complemented
96	#461×C₈₉	C₂²	1	1	yes	characteristic, complemented
97	#460×C₈₉	C₂²	1	2	yes	complemented
98	#460×C₈₉	C₂²	1	2	yes	complemented
99	#459×C₈₉	C₂²	1	1	yes	characteristic
100	#459×C₈₉	C₂²	1	1	yes	characteristic
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	2	yes	complemented
105	#452×C₈₉	C₂²	1	2	yes	complemented
106	#452×C₈₉	C₂²	1	2	yes	complemented
107	#452×C₈₉	C₂²	1	2	yes	complemented
108	#450×C₈₉	C₂²	1	2	yes	complemented
109	#449×C₈₉	C₂²	1	2	yes	—
110	#449×C₈₉	C₂²	1	2	yes	complemented
111	#447×C₈₉	C₂²	1	1	yes	characteristic
112	#447×C₈₉	C₂²	1	2	yes	—
113	#447×C₈₉	C₂²	1	1	yes	characteristic, complemented
114	#446×C₈₉	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
116	#440×C₈₉	C₂²	1	2	yes	complemented
117	#440×C₈₉	C₂²	1	2	yes	complemented
118	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
119	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
121	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
124	#436×C₈₉	C₂²	1	1	yes	characteristic, complemented
125	#436×C₈₉	C₂²	1	2	yes	complemented
126	#435×C₈₉	C₂²	1	2	yes	complemented
127	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
128	#433×C₈₉	C₂²	1	2	yes	complemented
129	#431×C₈₉	C₂²	1	1	yes	characteristic, complemented
130	#424×C₈₉	C₂²	1	2	yes	complemented
131	#423×C₈₉	C₂²	1	1	yes	characteristic, complemented
132	#417×C₈₉	C₂²	1	2	yes	complemented
133	#417×C₈₉	C₂²	1	2	yes	complemented
134	C₂×#102×C₈₉	C₂²	1	2	yes	complemented
135	C₂×#41×C₈₉	—	2	1	no	—
136	C₂×#41×C₈₉	—	2	1	no	—
137	C₂×#41×C₈₉	—	2	1	no	—
138	C₂×#41×C₈₉	C₂³	1	2	yes	—
139	C₂×#41×C₈₉	C₂³	1	2	yes	—
140	C₂×#41×C₈₉	C₂³	1	2	yes	—
141	C₂²×Q₈×C₈₉	—	2	1	no	—
142	C₂²×D₄×C₈₉	—	2	1	no	—
143	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
144	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
145	C₂³×C₄×C₈₉	—	2	1	no	—
146	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
147	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
148	#135×C₈₉	—	4	4	no	—
149	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
150	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
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	1	yes	characteristic
159	C₂×D₈×C₈₉	C₂³	1	2	yes	—
160	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
161	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
162	C₂×D₈×C₈₉	C₂³	1	2	yes	—
163	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
164	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
165	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
166	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
171	#127×C₈₉	—	2	2	no	—
172	#127×C₈₉	C₂³	1	1	yes	characteristic
173	#127×C₈₉	C₂³	1	1	yes	characteristic
174	#127×C₈₉	C₂³	1	2	yes	—
175	#126×C₈₉	—	2	2	no	—
176	#126×C₈₉	—	2	2	no	—
177	#126×C₈₉	—	2	2	no	—
178	#126×C₈₉	—	2	2	no	—
179	#126×C₈₉	D₄	1	2	yes	—
180	#125×C₈₉	—	2	2	no	—
181	#125×C₈₉	—	2	1	no	—
182	#125×C₈₉	D₄	1	1	yes	characteristic
183	#124×C₈₉	—	2	2	no	—
184	#124×C₈₉	—	2	2	no	—
185	#124×C₈₉	—	2	1	no	—
186	#124×C₈₉	D₄	1	1	yes	characteristic
187	#124×C₈₉	C₂³	1	2	yes	—
188	#124×C₈₉	C₂³	1	2	yes	—
189	#124×C₈₉	C₂³	1	2	yes	—
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	#123×C₈₉	—	2	2	no	—
197	#123×C₈₉	D₄	1	2	yes	—
198	C₂²⋊Q₈×C₈₉	—	2	1	no	—
199	C₂²⋊Q₈×C₈₉	—	2	1	no	—
200	C₂²⋊Q₈×C₈₉	—	2	1	no	—
201	C₂²⋊Q₈×C₈₉	—	2	2	no	—
202	C₂²⋊Q₈×C₈₉	—	2	1	no	—
203	C₂²⋊Q₈×C₈₉	—	2	1	no	—
204	C₂²⋊Q₈×C₈₉	—	2	2	no	—
205	C₂²⋊Q₈×C₈₉	—	2	2	no	—
206	C₂²⋊Q₈×C₈₉	—	2	2	no	—
207	C₂²⋊Q₈×C₈₉	—	2	2	no	—
208	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
209	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
212	#121×C₈₉	—	2	1	no	—
213	#121×C₈₉	—	2	1	no	—
214	#121×C₈₉	—	2	1	no	—
215	#121×C₈₉	—	2	1	no	—
216	#121×C₈₉	—	2	1	no	—
217	#121×C₈₉	—	2	1	no	—
218	#121×C₈₉	—	2	2	no	—
219	#121×C₈₉	—	2	2	no	—
220	#121×C₈₉	—	2	1	no	—
221	#121×C₈₉	—	2	2	no	—
222	#121×C₈₉	—	2	2	no	—
223	#121×C₈₉	—	2	2	no	—
224	#121×C₈₉	—	2	2	no	—
225	#121×C₈₉	—	2	2	no	—
226	#121×C₈₉	D₄	1	1	yes	characteristic
227	#121×C₈₉	C₂³	1	2	yes	—
228	#121×C₈₉	C₂³	1	1	yes	characteristic
229	#121×C₈₉	C₂³	1	1	yes	characteristic
230	#121×C₈₉	C₂³	1	2	yes	—
231	#120×C₈₉	—	2	2	no	—
232	#120×C₈₉	—	2	2	no	—
233	#120×C₈₉	—	2	2	no	—
234	#120×C₈₉	—	2	2	no	—
235	#120×C₈₉	—	2	2	no	—
236	C₄×Q₈×C₈₉	—	2	1	no	—
237	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
238	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
239	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
240	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₈₉	—	2	2	no	—
242	C₄×D₄×C₈₉	—	2	2	no	—
243	C₄×D₄×C₈₉	—	2	2	no	—
244	C₄×D₄×C₈₉	—	2	2	no	—
245	C₄×D₄×C₈₉	—	2	1	no	—
246	C₄×D₄×C₈₉	—	2	1	no	—
247	C₄×D₄×C₈₉	—	2	1	no	—
248	C₄×D₄×C₈₉	—	2	1	no	—
249	C₄×D₄×C₈₉	—	2	1	no	—
250	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₈₉	C₂³	1	2	yes	—
255	C₄×D₄×C₈₉	C₂³	1	2	yes	—
256	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₈₉	C₂³	1	2	yes	—
260	#117×C₈₉	—	2	1	no	—
261	#117×C₈₉	—	2	2	no	—
262	#117×C₈₉	—	2	1	no	—
263	#117×C₈₉	—	2	1	no	—
264	#117×C₈₉	C₂³	1	2	yes	—
265	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
266	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
267	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
268	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
271	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
272	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
273	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
274	#107×C₈₉	C₂³	1	1	yes	characteristic
275	#107×C₈₉	C₂³	1	1	yes	characteristic
276	#107×C₈₉	C₂³	1	1	yes	characteristic
277	#107×C₈₉	C₂³	1	1	yes	characteristic
278	#107×C₈₉	C₂³	1	2	yes	—
279	#107×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	2	yes	—
290	#103×C₈₉	C₂³	1	2	yes	—
291	#103×C₈₉	C₂³	1	2	yes	—
292	#103×C₈₉	C₂³	1	2	yes	—
293	#102×C₈₉	C₂³	1	1	yes	characteristic
294	#102×C₈₉	C₂³	1	2	yes	—
295	#102×C₈₉	C₂³	1	2	yes	—
296	#102×C₈₉	C₂³	1	2	yes	—
297	#102×C₈₉	C₂³	1	1	yes	characteristic
298	#102×C₈₉	C₂³	1	2	yes	—
299	#102×C₈₉	C₂³	1	2	yes	—
300	#102×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
306	#102×C₈₉	C₂³	1	1	yes	characteristic
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	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₈₉	C₂³	1	2	yes	—
315	C₂⁴×C₈₉	—	2	1	no	—
316	C₂⁴×C₈₉	—	2	2	no	—
317	#41×C₈₉	—	2	4	no	—
318	#41×C₈₉	—	4	2	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	—	8	2	no	—
324	#41×C₈₉	—	8	2	no	—
325	#41×C₈₉	—	8	2	no	—
326	C₂×Q₈×C₈₉	—	2	1	no	—
327	C₂×Q₈×C₈₉	—	2	2	no	—
328	C₂×Q₈×C₈₉	—	2	1	no	—
329	C₂×Q₈×C₈₉	—	8	2	no	—
330	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
333	C₂×D₄×C₈₉	—	2	2	no	—
334	C₂×D₄×C₈₉	—	2	2	no	—
335	C₂×D₄×C₈₉	—	2	1	no	—
336	C₂×D₄×C₈₉	—	2	2	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	1	no	—
341	C₂×D₄×C₈₉	—	2	1	no	—
342	C₂×D₄×C₈₉	—	2	1	no	—
343	C₂×D₄×C₈₉	—	2	1	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	2	no	—
348	C₂×D₄×C₈₉	—	2	2	no	—
349	C₂×D₄×C₈₉	—	4	1	no	—
350	C₂×D₄×C₈₉	—	4	2	no	—
351	C₂×D₄×C₈₉	—	4	2	no	—
352	C₂×D₄×C₈₉	—	8	2	no	—
353	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
354	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
355	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
356	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
357	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
359	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₈₉	—	2	1	no	—
361	C₂²×C₄×C₈₉	—	2	2	no	—
362	C₂²×C₄×C₈₉	—	2	2	no	—
363	C₂²×C₄×C₈₉	—	2	1	no	—
364	C₂²×C₄×C₈₉	—	2	1	no	—
365	C₂²×C₄×C₈₉	—	2	1	no	—
366	C₂²×C₄×C₈₉	—	2	1	no	—
367	C₂²×C₄×C₈₉	—	2	2	no	—
368	C₂²×C₄×C₈₉	—	2	2	no	—
369	C₂²×C₄×C₈₉	—	2	2	no	—
370	C₂²×C₄×C₈₉	—	2	1	no	—
371	C₂²×C₄×C₈₉	—	2	2	no	—
372	C₂²×C₄×C₈₉	—	2	1	no	—
373	C₂²×C₄×C₈₉	—	8	2	no	—
374	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
376	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
378	Q₁₆×C₈₉	—	4	2	no	—
379	Q₁₆×C₈₉	—	4	2	no	—
380	SD₁₆×C₈₉	—	2	4	no	—
381	SD₁₆×C₈₉	—	4	2	no	—
382	SD₁₆×C₈₉	—	4	2	no	—
383	SD₁₆×C₈₉	—	4	2	no	—
384	SD₁₆×C₈₉	—	4	2	no	—
385	SD₁₆×C₈₉	—	4	2	no	—
386	D₈×C₈₉	—	2	2	no	—
387	D₈×C₈₉	—	2	4	no	—
388	D₈×C₈₉	—	2	2	no	—
389	D₈×C₈₉	—	4	1	no	—
390	D₈×C₈₉	—	4	1	no	—
391	D₈×C₈₉	—	4	2	no	—
392	M₁₆×C₈₉	—	4	2	no	—
393	M₁₆×C₈₉	—	4	2	no	—
394	C₂×C₈×C₈₉	—	4	2	no	—
395	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
397	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
398	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
399	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
400	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₈₉	—	2	2	no	—
402	C₄⋊C₄×C₈₉	—	2	1	no	—
403	C₄⋊C₄×C₈₉	—	2	1	no	—
404	C₄⋊C₄×C₈₉	—	2	2	no	—
405	C₄⋊C₄×C₈₉	—	2	2	no	—
406	C₄⋊C₄×C₈₉	—	2	2	no	—
407	C₄⋊C₄×C₈₉	—	2	2	no	—
408	C₄⋊C₄×C₈₉	—	2	1	no	—
409	C₄⋊C₄×C₈₉	—	2	1	no	—
410	C₄⋊C₄×C₈₉	—	2	1	no	—
411	C₄⋊C₄×C₈₉	—	2	1	no	—
412	C₄⋊C₄×C₈₉	—	2	1	no	—
413	C₄⋊C₄×C₈₉	—	2	2	no	—
414	C₄⋊C₄×C₈₉	—	2	2	no	—
415	C₄⋊C₄×C₈₉	—	2	2	no	—
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	1	yes	characteristic
419	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
420	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
422	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
425	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
427	C₂²⋊C₄×C₈₉	—	2	2	no	—
428	C₂²⋊C₄×C₈₉	—	2	2	no	—
429	C₂²⋊C₄×C₈₉	—	2	2	no	—
430	C₂²⋊C₄×C₈₉	—	2	1	no	—
431	C₂²⋊C₄×C₈₉	—	2	1	no	—
432	C₂²⋊C₄×C₈₉	—	2	1	no	—
433	C₂²⋊C₄×C₈₉	—	2	1	no	—
434	C₂²⋊C₄×C₈₉	—	2	1	no	—
435	C₂²⋊C₄×C₈₉	—	2	2	no	—
436	C₂²⋊C₄×C₈₉	—	2	2	no	—
437	C₂²⋊C₄×C₈₉	—	2	2	no	—
438	C₂²⋊C₄×C₈₉	—	2	2	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	2	no	—
445	C₂²⋊C₄×C₈₉	—	2	1	no	—
446	C₂²⋊C₄×C₈₉	—	2	2	no	—
447	C₂²⋊C₄×C₈₉	—	2	1	no	—
448	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
449	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
451	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
452	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
453	C₄²×C₈₉	—	2	2	no	—
454	C₄²×C₈₉	—	2	2	no	—
455	C₄²×C₈₉	—	2	2	no	—
456	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
458	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
459	C₄²×C₈₉	C₂⁴	1	2	yes	—
460	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
461	C₂³×C₈₉	—	2	1	no	—
462	C₂³×C₈₉	—	2	1	no	—
463	C₂³×C₈₉	—	2	1	no	—
464	C₂³×C₈₉	—	2	2	no	—
465	C₂³×C₈₉	—	2	1	no	—
466	C₂³×C₈₉	—	4	2	no	—
467	C₂³×C₈₉	—	4	2	no	—
468	C₂³×C₈₉	—	8	1	no	—
469	C₂³×C₈₉	—	8	2	no	—
470	C₂³×C₈₉	—	8	2	no	—
471	C₂³×C₈₉	—	8	2	no	—
472	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
473	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
474	Q₈×C₈₉	—	2	2	no	—
475	Q₈×C₈₉	—	2	2	no	—
476	Q₈×C₈₉	—	2	2	no	—
477	Q₈×C₈₉	—	2	2	no	—
478	Q₈×C₈₉	—	2	2	no	—
479	Q₈×C₈₉	—	4	2	no	—
480	Q₈×C₈₉	—	8	2	no	—
481	Q₈×C₈₉	—	8	1	no	—
482	D₄×C₈₉	—	2	2	no	—
483	D₄×C₈₉	—	2	2	no	—
484	D₄×C₈₉	—	2	1	no	—
485	D₄×C₈₉	—	2	1	no	—
486	D₄×C₈₉	—	2	1	no	—
487	D₄×C₈₉	—	2	1	no	—
488	D₄×C₈₉	—	2	1	no	—
489	D₄×C₈₉	—	2	1	no	—
490	D₄×C₈₉	—	2	1	no	—
491	D₄×C₈₉	—	2	2	no	—
492	D₄×C₈₉	—	4	2	no	—
493	D₄×C₈₉	—	4	2	no	—
494	D₄×C₈₉	—	4	4	no	—
495	D₄×C₈₉	—	4	2	no	—
496	D₄×C₈₉	—	8	1	no	—
497	D₄×C₈₉	—	8	1	no	—
498	D₄×C₈₉	—	8	2	no	—
499	D₄×C₈₉	—	8	2	no	—
500	D₄×C₈₉	—	8	1	no	—
501	D₄×C₈₉	—	8	2	no	—
502	D₄×C₈₉	—	8	2	no	—
503	D₄×C₈₉	—	8	2	no	—
504	D₄×C₈₉	—	8	2	no	—
505	D₄×C₈₉	—	8	1	no	—
506	D₄×C₈₉	—	8	1	no	—
507	D₄×C₈₉	—	8	2	no	—
508	D₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
509	C₂×C₄×C₈₉	—	2	2	no	—
510	C₂×C₄×C₈₉	—	2	2	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	—	2	1	no	—
516	C₂×C₄×C₈₉	—	2	1	no	—
517	C₂×C₄×C₈₉	—	2	2	no	—
518	C₂×C₄×C₈₉	—	2	2	no	—
519	C₂×C₄×C₈₉	—	2	1	no	—
520	C₂×C₄×C₈₉	—	2	1	no	—
521	C₂×C₄×C₈₉	—	4	1	no	—
522	C₂×C₄×C₈₉	—	4	4	no	—
523	C₂×C₄×C₈₉	—	4	2	no	—
524	C₂×C₄×C₈₉	—	4	2	no	—
525	C₂×C₄×C₈₉	—	4	2	no	—
526	C₂×C₄×C₈₉	—	4	2	no	—
527	C₂×C₄×C₈₉	—	8	1	no	—
528	C₂×C₄×C₈₉	—	8	1	no	—
529	C₂×C₄×C₈₉	—	8	2	no	—
530	C₂×C₄×C₈₉	—	8	2	no	—
531	C₂×C₄×C₈₉	—	8	2	no	—
532	C₂×C₄×C₈₉	—	8	2	no	—
533	C₂×C₄×C₈₉	—	8	1	no	—
534	C₂×C₄×C₈₉	—	8	2	no	—
535	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
537	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
540	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
541	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
542	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
544	C₈×C₈₉	—	2	1	no	—
545	C₈×C₈₉	—	2	2	no	—
546	C₈×C₈₉	—	2	1	no	—
547	C₈×C₈₉	—	2	2	no	—
548	C₈×C₈₉	—	2	1	no	—
549	C₈×C₈₉	—	2	1	no	—
550	C₂²×C₈₉	—	2	1	no	—
551	C₂²×C₈₉	—	2	2	no	—
552	C₂²×C₈₉	—	2	2	no	—
553	C₂²×C₈₉	—	2	1	no	—
554	C₂²×C₈₉	—	2	2	no	—
555	C₂²×C₈₉	—	2	1	no	—
556	C₂²×C₈₉	—	2	2	no	—
557	C₂²×C₈₉	—	4	1	no	—
558	C₂²×C₈₉	—	4	1	no	—
559	C₂²×C₈₉	—	4	1	no	—
560	C₂²×C₈₉	—	4	2	no	—
561	C₂²×C₈₉	—	4	1	no	—
562	C₂²×C₈₉	—	4	1	no	—
563	C₂²×C₈₉	—	4	1	no	—
564	C₂²×C₈₉	—	4	2	no	—
565	C₂²×C₈₉	—	4	1	no	—
566	C₂²×C₈₉	—	4	1	no	—
567	C₂²×C₈₉	—	4	1	no	—
568	C₂²×C₈₉	—	4	1	no	—
569	C₂²×C₈₉	—	4	1	no	—
570	C₂²×C₈₉	—	4	2	no	—
571	C₂²×C₈₉	—	8	4	no	—
572	C₂²×C₈₉	—	16	4	no	—
573	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
574	C₄×C₈₉	—	2	1	no	—
575	C₄×C₈₉	—	2	1	no	—
576	C₄×C₈₉	—	2	2	no	—
577	C₄×C₈₉	—	2	2	no	—
578	C₄×C₈₉	—	2	1	no	—
579	C₄×C₈₉	—	2	1	no	—
580	C₄×C₈₉	—	2	2	no	—
581	C₄×C₈₉	—	4	2	no	—
582	C₄×C₈₉	—	4	2	no	—
583	C₄×C₈₉	—	4	1	no	—
584	C₄×C₈₉	—	4	1	no	—
585	C₄×C₈₉	—	4	1	no	—
586	C₄×C₈₉	—	4	1	no	—
587	C₄×C₈₉	—	4	2	no	—
588	C₄×C₈₉	#576	1	2	yes	—
589	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
590	C₄×C₈₉	#585	1	1	yes	characteristic
591	#62041	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
592	C₂×C₈₉	—	4	1	no	—
593	C₂×C₈₉	—	4	2	no	—
594	C₂×C₈₉	—	4	2	no	—
595	C₂×C₈₉	—	8	1	no	—
596	C₂×C₈₉	—	8	1	no	—
597	C₂×C₈₉	—	8	2	no	—
598	C₂×C₈₉	—	8	1	no	—
599	C₂×C₈₉	#3488	1	1	yes	characteristic
600	C₂×C₈₉	C₂×#576	1	1	yes	characteristic
601	C₂×C₈₉	#3586	1	1	yes	characteristic
602	#3546	C₂×C₈₉	1	1	yes	characteristic, complemented
603	#3520	C₂×C₈₉	1	1	yes	characteristic, complemented
604	#3397	C₂×C₈₉	1	1	yes	characteristic, complemented
605	#3393	C₂×C₈₉	1	1	yes	characteristic, complemented
606	#3367	C₂×C₈₉	1	1	yes	characteristic, complemented
607	#3358	C₂×C₈₉	1	1	yes	characteristic, complemented
608	#3333	C₂×C₈₉	1	2	yes	complemented
609	#3330	C₂×C₈₉	1	1	yes	characteristic, complemented
610	#3314	C₂×C₈₉	1	2	yes	complemented
611	#3294	C₂×C₈₉	1	1	yes	characteristic, complemented
612	#3283	C₂×C₈₉	1	1	yes	characteristic, complemented
613	#3273	C₂×C₈₉	1	2	yes	complemented
614	#3272	C₂×C₈₉	1	1	yes	characteristic, complemented
615	#3268	C₂×C₈₉	1	2	yes	complemented
616	#3262	C₂×C₈₉	1	2	yes	complemented
617	#3254	C₂×C₈₉	1	1	yes	characteristic, complemented
618	#3224	C₂×C₈₉	1	2	yes	complemented
619	#3210	C₂×C₈₉	1	1	yes	characteristic, complemented
620	#3124	C₂×C₈₉	1	2	yes	complemented
621	#3100	C₂×C₈₉	1	1	yes	characteristic, complemented
622	#3045	C₂×C₈₉	1	2	yes	complemented
623	#3036	C₂×C₈₉	1	1	yes	characteristic, complemented
624	#2993	C₂×C₈₉	1	1	yes	characteristic, complemented
625	C₈₉	#62041	1	1	yes	characteristic, direct product factor, Sylow
626	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
627	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	complemented
628	C₂×#135	C₂²×C₈₉	1	2	yes	complemented
629	#560	—	2	2	no	—
630	#556	C₂²×C₈₉	1	1	yes	characteristic, complemented
631	#556	C₂²×C₈₉	1	1	yes	characteristic, complemented
632	#554	C₂²×C₈₉	1	2	yes	complemented
633	#553	—	2	1	no	—
634	#552	—	2	1	no	—
635	#551	—	2	2	no	—
636	#550	C₂²×C₈₉	1	2	yes	—
637	#550	C₂²×C₈₉	1	1	yes	characteristic, complemented
638	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
639	#548	—	2	1	no	—
640	#547	C₂²×C₈₉	1	1	yes	characteristic
641	#547	C₂²×C₈₉	1	1	yes	characteristic
642	#547	C₂²×C₈₉	1	1	yes	characteristic, complemented
643	#546	—	2	1	no	—
644	#546	C₂²×C₈₉	1	2	yes	—
645	#546	C₂²×C₈₉	1	2	yes	complemented
646	D₄²	C₂²×C₈₉	1	1	yes	characteristic, complemented
647	#542	C₂²×C₈₉	1	2	yes	complemented
648	#542	C₂²×C₈₉	1	2	yes	complemented
649	#539	—	2	2	no	—
650	#538	—	2	2	no	—
651	#537	—	2	1	no	—
652	#535	—	2	1	no	—
653	#535	C₂²×C₈₉	1	2	yes	complemented
654	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
655	#532	C₂²×C₈₉	1	1	yes	characteristic
656	#532	C₂²×C₈₉	1	1	yes	characteristic
657	#529	C₂²×C₈₉	1	1	yes	characteristic
658	#525	—	2	1	no	—
659	C₂×C₂²⋊Q₈	—	2	1	no	—
660	#520	C₂²×C₈₉	1	2	yes	complemented
661	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
662	#496	C₂²×C₈₉	1	2	yes	complemented
663	#495	C₂²×C₈₉	1	2	yes	—
664	#494	C₂²×C₈₉	1	1	yes	characteristic, complemented
665	#492	C₂²×C₈₉	1	1	yes	characteristic, complemented
666	#489	C₂²×C₈₉	1	2	yes	complemented
667	#487	C₂²×C₈₉	1	1	yes	characteristic, complemented
668	#486	C₂²×C₈₉	1	2	yes	complemented
669	#486	C₂²×C₈₉	1	1	yes	characteristic, complemented
670	#484	C₂²×C₈₉	1	2	yes	complemented
671	#480	C₂²×C₈₉	1	1	yes	characteristic
672	#480	C₂²×C₈₉	1	1	yes	characteristic, complemented
673	#480	C₂²×C₈₉	1	2	yes	complemented
674	#477	C₂²×C₈₉	1	2	yes	complemented
675	#477	C₂²×C₈₉	1	2	yes	complemented
676	#474	C₂²×C₈₉	1	1	yes	characteristic, complemented
677	#474	C₂²×C₈₉	1	1	yes	characteristic, complemented
678	#474	C₂²×C₈₉	1	1	yes	characteristic, complemented
679	#474	C₂²×C₈₉	1	2	yes	complemented
680	#474	C₂²×C₈₉	1	1	yes	characteristic, complemented
681	#468	C₂²×C₈₉	1	2	yes	—
682	#468	C₂²×C₈₉	1	2	yes	complemented
683	#468	C₂²×C₈₉	1	2	yes	complemented
684	#468	C₂²×C₈₉	1	2	yes	complemented
685	#467	C₂²×C₈₉	1	2	yes	complemented
686	#466	C₂²×C₈₉	1	2	yes	—
687	#464	C₂²×C₈₉	1	2	yes	complemented
688	#464	C₂²×C₈₉	1	2	yes	complemented
689	#464	C₂²×C₈₉	1	2	yes	complemented
690	#464	C₂²×C₈₉	1	2	yes	complemented
691	#463	C₂²×C₈₉	1	2	yes	—
692	#463	C₂²×C₈₉	1	2	yes	complemented
693	#463	C₂²×C₈₉	1	2	yes	complemented
694	#463	C₂²×C₈₉	1	2	yes	complemented
695	#461	C₂²×C₈₉	1	1	yes	characteristic, complemented
696	#461	C₂²×C₈₉	1	1	yes	characteristic, complemented
697	#461	C₂²×C₈₉	1	1	yes	characteristic, complemented
698	#461	C₂²×C₈₉	1	1	yes	characteristic, complemented
699	#460	C₂²×C₈₉	1	2	yes	complemented
700	#460	C₂²×C₈₉	1	2	yes	complemented
701	#459	C₂²×C₈₉	1	1	yes	characteristic
702	#459	C₂²×C₈₉	1	1	yes	characteristic
703	#459	C₂²×C₈₉	1	1	yes	characteristic
704	#459	C₂²×C₈₉	1	1	yes	characteristic
705	#459	C₂²×C₈₉	1	2	yes	complemented
706	#452	C₂²×C₈₉	1	2	yes	complemented
707	#452	C₂²×C₈₉	1	2	yes	complemented
708	#452	C₂²×C₈₉	1	2	yes	complemented
709	#452	C₂²×C₈₉	1	2	yes	complemented
710	#450	C₂²×C₈₉	1	2	yes	complemented
711	#449	C₂²×C₈₉	1	2	yes	—
712	#449	C₂²×C₈₉	1	2	yes	complemented
713	#447	C₂²×C₈₉	1	1	yes	characteristic
714	#447	C₂²×C₈₉	1	2	yes	—
715	#447	C₂²×C₈₉	1	1	yes	characteristic, complemented
716	#446	C₂²×C₈₉	1	1	yes	characteristic, complemented
717	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
718	#440	C₂²×C₈₉	1	2	yes	complemented
719	#440	C₂²×C₈₉	1	2	yes	complemented
720	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
721	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
722	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
723	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
724	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
725	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
726	#436	C₂²×C₈₉	1	1	yes	characteristic, complemented
727	#436	C₂²×C₈₉	1	2	yes	complemented
728	#435	C₂²×C₈₉	1	2	yes	complemented
729	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
730	#433	C₂²×C₈₉	1	2	yes	complemented
731	#431	C₂²×C₈₉	1	1	yes	characteristic, complemented
732	#424	C₂²×C₈₉	1	2	yes	complemented
733	#423	C₂²×C₈₉	1	1	yes	characteristic, complemented
734	#417	C₂²×C₈₉	1	2	yes	complemented
735	#417	C₂²×C₈₉	1	2	yes	complemented
736	C₂×#102	C₂²×C₈₉	1	2	yes	complemented
737	C₂×#41	—	2	1	no	—
738	C₂×#41	—	2	1	no	—
739	C₂×#41	—	2	1	no	—
740	C₂×#41	C₂³×C₈₉	1	2	yes	—
741	C₂×#41	C₂³×C₈₉	1	2	yes	—
742	C₂×#41	C₂³×C₈₉	1	2	yes	—
743	C₂²×Q₈	—	2	1	no	—
744	C₂²×D₄	—	2	1	no	—
745	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
746	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
747	C₂³×C₄	—	2	1	no	—
748	AGL(1,ℤ/8)	—	4	4	no	—
749	AGL(1,ℤ/8)	—	4	4	no	—
750	#135	—	4	4	no	—
751	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
752	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
753	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
754	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
755	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
756	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
757	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
758	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
759	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
760	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
761	C₂×D₈	C₂³×C₈₉	1	2	yes	—
762	C₂×D₈	C₂³×C₈₉	1	2	yes	—
763	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
764	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
765	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
766	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
767	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
768	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
769	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
770	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
771	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
772	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
773	#127	—	2	2	no	—
774	#127	C₂³×C₈₉	1	1	yes	characteristic
775	#127	C₂³×C₈₉	1	1	yes	characteristic
776	#127	C₂³×C₈₉	1	2	yes	—
777	#126	—	2	2	no	—
778	#126	—	2	2	no	—
779	#126	—	2	2	no	—
780	#126	—	2	2	no	—
781	#126	D₄×C₈₉	1	2	yes	—
782	#125	—	2	2	no	—
783	#125	—	2	1	no	—
784	#125	D₄×C₈₉	1	1	yes	characteristic
785	#124	—	2	2	no	—
786	#124	—	2	2	no	—
787	#124	—	2	1	no	—
788	#124	D₄×C₈₉	1	1	yes	characteristic
789	#124	C₂³×C₈₉	1	2	yes	—
790	#124	C₂³×C₈₉	1	2	yes	—
791	#124	C₂³×C₈₉	1	2	yes	—
792	#123	—	2	2	no	—
793	#123	—	2	2	no	—
794	#123	—	2	2	no	—
795	#123	—	2	2	no	—
796	#123	—	2	2	no	—
797	#123	—	2	2	no	—
798	#123	—	2	2	no	—
799	#123	D₄×C₈₉	1	2	yes	—
800	C₂²⋊Q₈	—	2	1	no	—
801	C₂²⋊Q₈	—	2	1	no	—
802	C₂²⋊Q₈	—	2	1	no	—
803	C₂²⋊Q₈	—	2	2	no	—
804	C₂²⋊Q₈	—	2	1	no	—
805	C₂²⋊Q₈	—	2	1	no	—
806	C₂²⋊Q₈	—	2	2	no	—
807	C₂²⋊Q₈	—	2	2	no	—
808	C₂²⋊Q₈	—	2	2	no	—
809	C₂²⋊Q₈	—	2	2	no	—
810	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
811	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
812	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
813	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
814	#121	—	2	1	no	—
815	#121	—	2	1	no	—
816	#121	—	2	1	no	—
817	#121	—	2	1	no	—
818	#121	—	2	1	no	—
819	#121	—	2	1	no	—
820	#121	—	2	2	no	—
821	#121	—	2	2	no	—
822	#121	—	2	1	no	—
823	#121	—	2	2	no	—
824	#121	—	2	2	no	—
825	#121	—	2	2	no	—
826	#121	—	2	2	no	—
827	#121	—	2	2	no	—
828	#121	D₄×C₈₉	1	1	yes	characteristic
829	#121	C₂³×C₈₉	1	1	yes	characteristic
830	#121	C₂³×C₈₉	1	1	yes	characteristic
831	#121	C₂³×C₈₉	1	2	yes	—
832	#121	C₂³×C₈₉	1	2	yes	—
833	#120	—	2	2	no	—
834	#120	—	2	2	no	—
835	#120	—	2	2	no	—
836	#120	—	2	2	no	—
837	#120	—	2	2	no	—
838	C₄×Q₈	—	2	1	no	—
839	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
840	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
841	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
842	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
843	C₄×D₄	—	2	2	no	—
844	C₄×D₄	—	2	2	no	—
845	C₄×D₄	—	2	2	no	—
846	C₄×D₄	—	2	2	no	—
847	C₄×D₄	—	2	1	no	—
848	C₄×D₄	—	2	1	no	—
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	1	no	—
851	C₄×D₄	—	2	1	no	—
852	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
853	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
854	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
855	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
856	C₄×D₄	C₂³×C₈₉	1	2	yes	—
857	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
858	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
859	C₄×D₄	C₂³×C₈₉	1	2	yes	—
860	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
861	C₄×D₄	C₂³×C₈₉	1	2	yes	—
862	#117	—	2	1	no	—
863	#117	—	2	2	no	—
864	#117	—	2	1	no	—
865	#117	—	2	1	no	—
866	#117	C₂³×C₈₉	1	2	yes	—
867	C₂×C₄⋊C₄	—	2	2	no	—
868	C₂×C₄⋊C₄	—	2	1	no	—
869	C₂×C₄⋊C₄	—	2	1	no	—
870	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
871	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
872	C₂×C₂²⋊C₄	—	2	1	no	—
873	C₂×C₂²⋊C₄	—	2	2	no	—
874	C₂×C₂²⋊C₄	—	2	2	no	—
875	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
876	#107	C₂³×C₈₉	1	1	yes	characteristic
877	#107	C₂³×C₈₉	1	1	yes	characteristic
878	#107	C₂³×C₈₉	1	1	yes	characteristic
879	#107	C₂³×C₈₉	1	1	yes	characteristic
880	#107	C₂³×C₈₉	1	2	yes	—
881	#107	C₂³×C₈₉	1	2	yes	—
882	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
883	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
884	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
885	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
886	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
887	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
888	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
889	#103	C₂³×C₈₉	1	2	yes	—
890	#103	C₂³×C₈₉	1	2	yes	—
891	#103	C₂³×C₈₉	1	2	yes	—
892	#103	C₂³×C₈₉	1	2	yes	—
893	#103	C₂³×C₈₉	1	2	yes	—
894	#103	C₂³×C₈₉	1	2	yes	—
895	#102	C₂³×C₈₉	1	1	yes	characteristic
896	#102	C₂³×C₈₉	1	2	yes	—
897	#102	C₂³×C₈₉	1	2	yes	—
898	#102	C₂³×C₈₉	1	2	yes	—
899	#102	C₂³×C₈₉	1	1	yes	characteristic
900	#102	C₂³×C₈₉	1	2	yes	—
901	#102	C₂³×C₈₉	1	2	yes	—
902	#102	C₂³×C₈₉	1	1	yes	characteristic
903	#102	C₂³×C₈₉	1	1	yes	characteristic
904	#102	C₂³×C₈₉	1	1	yes	characteristic
905	#102	C₂³×C₈₉	1	1	yes	characteristic
906	#102	C₂³×C₈₉	1	2	yes	—
907	#102	C₂³×C₈₉	1	1	yes	characteristic
908	#102	C₂³×C₈₉	1	1	yes	characteristic
909	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
910	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
911	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
912	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
913	#97	C₂³×C₈₉	1	2	yes	—
914	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
915	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
916	C₄×C₈	C₂³×C₈₉	1	2	yes	—
917	C₂⁴	—	2	1	no	—
918	C₂⁴	—	2	2	no	—
919	#41	—	2	4	no	—
920	#41	—	4	2	no	—
921	#41	—	4	2	no	—
922	#41	—	4	2	no	—
923	#41	—	4	2	no	—
924	#41	—	4	2	no	—
925	#41	—	8	2	no	—
926	#41	—	8	2	no	—
927	#41	—	8	2	no	—
928	C₂×Q₈	—	2	1	no	—
929	C₂×Q₈	—	2	2	no	—
930	C₂×Q₈	—	2	1	no	—
931	C₂×Q₈	—	8	2	no	—
932	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
933	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
934	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	—	2	1	no	—
943	C₂×D₄	—	2	1	no	—
944	C₂×D₄	—	2	1	no	—
945	C₂×D₄	—	2	1	no	—
946	C₂×D₄	—	2	1	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	4	1	no	—
952	C₂×D₄	—	4	2	no	—
953	C₂×D₄	—	4	2	no	—
954	C₂×D₄	—	8	2	no	—
955	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
956	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
957	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
958	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
959	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
960	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
961	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	2	no	—
964	C₂²×C₄	—	2	2	no	—
965	C₂²×C₄	—	2	1	no	—
966	C₂²×C₄	—	2	1	no	—
967	C₂²×C₄	—	2	1	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	2	no	—
971	C₂²×C₄	—	2	2	no	—
972	C₂²×C₄	—	2	1	no	—
973	C₂²×C₄	—	2	2	no	—
974	C₂²×C₄	—	2	1	no	—
975	C₂²×C₄	—	8	2	no	—
976	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
977	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
978	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
979	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
980	Q₁₆	—	4	2	no	—
981	Q₁₆	—	4	2	no	—
982	SD₁₆	—	2	4	no	—
983	SD₁₆	—	4	2	no	—
984	SD₁₆	—	4	2	no	—
985	SD₁₆	—	4	2	no	—
986	SD₁₆	—	4	2	no	—
987	SD₁₆	—	4	2	no	—
988	D₈	—	2	2	no	—
989	D₈	—	2	4	no	—
990	D₈	—	2	2	no	—
991	D₈	—	4	2	no	—
992	D₈	—	4	1	no	—
993	D₈	—	4	1	no	—
994	M₁₆	—	4	2	no	—
995	M₁₆	—	4	2	no	—
996	C₂×C₈	—	4	2	no	—
997	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
998	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
999	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
1000	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
1001	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
1002	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	1	no	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	2	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	1	no	—
1014	C₄⋊C₄	—	2	1	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	2	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1019	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1020	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1021	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1022	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1023	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1024	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1025	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1026	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1027	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1028	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	1	no	—
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	1	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	1	no	—
1048	C₂²⋊C₄	—	2	2	no	—
1049	C₂²⋊C₄	—	2	1	no	—
1050	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1051	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1052	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1053	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1054	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1055	C₄²	—	2	2	no	—
1056	C₄²	—	2	2	no	—
1057	C₄²	—	2	2	no	—
1058	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1059	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1060	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1061	C₄²	C₂⁴×C₈₉	1	2	yes	—
1062	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1063	C₂³	—	2	1	no	—
1064	C₂³	—	2	1	no	—
1065	C₂³	—	2	1	no	—
1066	C₂³	—	2	2	no	—
1067	C₂³	—	2	1	no	—
1068	C₂³	—	4	2	no	—
1069	C₂³	—	4	2	no	—
1070	C₂³	—	8	1	no	—
1071	C₂³	—	8	2	no	—
1072	C₂³	—	8	2	no	—
1073	C₂³	—	8	2	no	—
1074	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1075	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1076	Q₈	—	2	2	no	—
1077	Q₈	—	2	2	no	—
1078	Q₈	—	2	2	no	—
1079	Q₈	—	2	2	no	—
1080	Q₈	—	2	2	no	—
1081	Q₈	—	4	2	no	—
1082	Q₈	—	8	2	no	—
1083	Q₈	—	8	1	no	—
1084	D₄	—	2	2	no	—
1085	D₄	—	2	2	no	—
1086	D₄	—	2	1	no	—
1087	D₄	—	2	1	no	—
1088	D₄	—	2	1	no	—
1089	D₄	—	2	1	no	—
1090	D₄	—	2	1	no	—
1091	D₄	—	2	1	no	—
1092	D₄	—	2	1	no	—
1093	D₄	—	2	2	no	—
1094	D₄	—	4	2	no	—
1095	D₄	—	4	2	no	—
1096	D₄	—	4	4	no	—
1097	D₄	—	4	2	no	—
1098	D₄	—	8	1	no	—
1099	D₄	—	8	1	no	—
1100	D₄	—	8	2	no	—
1101	D₄	—	8	2	no	—
1102	D₄	—	8	1	no	—
1103	D₄	—	8	2	no	—
1104	D₄	—	8	2	no	—
1105	D₄	—	8	2	no	—
1106	D₄	—	8	2	no	—
1107	D₄	—	8	1	no	—
1108	D₄	—	8	1	no	—
1109	D₄	—	8	2	no	—
1110	D₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	2	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	4	1	no	—
1124	C₂×C₄	—	4	4	no	—
1125	C₂×C₄	—	4	2	no	—
1126	C₂×C₄	—	4	2	no	—
1127	C₂×C₄	—	4	2	no	—
1128	C₂×C₄	—	4	2	no	—
1129	C₂×C₄	—	8	1	no	—
1130	C₂×C₄	—	8	1	no	—
1131	C₂×C₄	—	8	2	no	—
1132	C₂×C₄	—	8	2	no	—
1133	C₂×C₄	—	8	2	no	—
1134	C₂×C₄	—	8	2	no	—
1135	C₂×C₄	—	8	1	no	—
1136	C₂×C₄	—	8	2	no	—
1137	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1138	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1139	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1140	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1141	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1142	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1143	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1144	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1145	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1146	C₈	—	2	1	no	—
1147	C₈	—	2	2	no	—
1148	C₈	—	2	1	no	—
1149	C₈	—	2	2	no	—
1150	C₈	—	2	1	no	—
1151	C₈	—	2	1	no	—
1152	C₂²	—	2	1	no	—
1153	C₂²	—	2	2	no	—
1154	C₂²	—	2	1	no	—
1155	C₂²	—	2	2	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	2	1	no	—
1158	C₂²	—	2	2	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	1	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	4	1	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	4	2	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	8	4	no	—
1174	C₂²	—	16	4	no	—
1175	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1176	C₄	—	2	1	no	—
1177	C₄	—	2	2	no	—
1178	C₄	—	2	1	no	—
1179	C₄	—	2	1	no	—
1180	C₄	—	2	2	no	—
1181	C₄	—	2	2	no	—
1182	C₄	—	2	1	no	—
1183	C₄	—	4	1	no	—
1184	C₄	—	4	1	no	—
1185	C₄	—	4	1	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	2	no	—
1188	C₄	—	4	2	no	—
1189	C₄	—	4	2	no	—
1190	C₄	#576×C₈₉	1	2	yes	—
1191	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1192	C₄	#585×C₈₉	1	1	yes	characteristic
1193	C₂	—	4	1	no	—
1194	C₂	—	4	2	no	—
1195	C₂	—	4	2	no	—
1196	C₂	—	8	1	no	—
1197	C₂	—	8	1	no	—
1198	C₂	—	8	2	no	—
1199	C₂	—	8	1	no	—
1200	C₂	C₈₉×#3488	1	1	yes	characteristic
1201	C₂	C₂×#576×C₈₉	1	1	yes	characteristic
1202	C₂	C₈₉×#3586	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 ◁ #529×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3546	C₂	semidirect
2. C₈₉×#3520	C₂	semidirect
3. C₈₉×#3397	C₂	semidirect
4. C₈₉×#3393	C₂	semidirect
5. C₈₉×#3367	C₂	semidirect
6. C₈₉×#3358	C₂	semidirect
7. C₈₉×#3333	C₂	semidirect
8. C₈₉×#3330	C₂	semidirect
9. C₈₉×#3314	C₂	semidirect
10. C₈₉×#3294	C₂	semidirect
11. C₈₉×#3283	C₂	semidirect
12. C₈₉×#3273	C₂	semidirect
13. C₈₉×#3272	C₂	semidirect
14. C₈₉×#3268	C₂	semidirect
15. C₈₉×#3262	C₂	semidirect
16. C₈₉×#3254	C₂	semidirect
17. C₈₉×#3224	C₂	semidirect
18. C₈₉×#3210	C₂	semidirect
19. C₈₉×#3124	C₂	semidirect
20. C₈₉×#3100	C₂	semidirect
21. C₈₉×#3045	C₂	semidirect
22. C₈₉×#3036	C₂	semidirect
23. C₈₉×#2993	C₂	semidirect
25. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
26. C₂×#135×C₈₉	C₂²	semidirect
28. #556×C₈₉	C₂²	semidirect
29. #556×C₈₉	C₂²	semidirect
30. #554×C₈₉	C₂²	semidirect
35. #550×C₈₉	C₂²	semidirect
36. D₄×Q₈×C₈₉	C₂²	semidirect
40. #547×C₈₉	C₂²	semidirect
43. #546×C₈₉	C₂²	semidirect
44. D₄²×C₈₉	C₂²	semidirect
45. #542×C₈₉	C₂²	semidirect
46. #542×C₈₉	C₂²	semidirect
51. #535×C₈₉	C₂²	semidirect
52. #533×C₈₉	C₂²	semidirect
58. #520×C₈₉	C₂²	semidirect
59. C₂×C₄×D₄×C₈₉	C₂²	semidirect
60. #496×C₈₉	C₂²	semidirect
62. #494×C₈₉	C₂²	semidirect
63. #492×C₈₉	C₂²	semidirect
64. #489×C₈₉	C₂²	semidirect
65. #487×C₈₉	C₂²	semidirect
66. #486×C₈₉	C₂²	semidirect
67. #486×C₈₉	C₂²	semidirect
68. #484×C₈₉	C₂²	semidirect
70. #480×C₈₉	C₂²	semidirect
71. #480×C₈₉	C₂²	semidirect
72. #477×C₈₉	C₂²	semidirect
73. #477×C₈₉	C₂²	semidirect
74. #474×C₈₉	C₂²	semidirect
75. #474×C₈₉	C₂²	semidirect
76. #474×C₈₉	C₂²	semidirect
77. #474×C₈₉	C₂²	semidirect
78. #474×C₈₉	C₂²	semidirect
80. #468×C₈₉	C₂²	semidirect
81. #468×C₈₉	C₂²	semidirect
82. #468×C₈₉	C₂²	semidirect
83. #467×C₈₉	C₂²	semidirect
85. #464×C₈₉	C₂²	semidirect
86. #464×C₈₉	C₂²	semidirect
87. #464×C₈₉	C₂²	semidirect
88. #464×C₈₉	C₂²	semidirect
90. #463×C₈₉	C₂²	semidirect
91. #463×C₈₉	C₂²	semidirect
92. #463×C₈₉	C₂²	semidirect
93. #461×C₈₉	C₂²	semidirect
94. #461×C₈₉	C₂²	semidirect
95. #461×C₈₉	C₂²	semidirect
96. #461×C₈₉	C₂²	semidirect
97. #460×C₈₉	C₂²	semidirect
98. #460×C₈₉	C₂²	semidirect
103. #459×C₈₉	C₂²	semidirect
104. #452×C₈₉	C₂²	semidirect
105. #452×C₈₉	C₂²	semidirect
106. #452×C₈₉	C₂²	semidirect
107. #452×C₈₉	C₂²	semidirect
108. #450×C₈₉	C₂²	semidirect
110. #449×C₈₉	C₂²	semidirect
113. #447×C₈₉	C₂²	semidirect
114. #446×C₈₉	C₂²	semidirect
115. C₈×Q₈×C₈₉	C₂²	semidirect
116. #440×C₈₉	C₂²	semidirect
117. #440×C₈₉	C₂²	semidirect
118. C₄×Q₁₆×C₈₉	C₂²	semidirect
121. C₄×D₈×C₈₉	C₂²	semidirect
122. C₄×D₈×C₈₉	C₂²	semidirect
123. C₄×D₈×C₈₉	C₂²	semidirect
124. #436×C₈₉	C₂²	semidirect
125. #436×C₈₉	C₂²	semidirect
126. #435×C₈₉	C₂²	semidirect
127. C₈×D₄×C₈₉	C₂²	semidirect
128. #433×C₈₉	C₂²	semidirect
129. #431×C₈₉	C₂²	semidirect
130. #424×C₈₉	C₂²	semidirect
131. #423×C₈₉	C₂²	semidirect
132. #417×C₈₉	C₂²	semidirect
133. #417×C₈₉	C₂²	semidirect
134. C₂×#102×C₈₉	C₂²	semidirect
591. #62041	C₈₉	direct (N × H)
602. #3546	C₂×C₈₉	semidirect
603. #3520	C₂×C₈₉	semidirect
604. #3397	C₂×C₈₉	semidirect
605. #3393	C₂×C₈₉	semidirect
606. #3367	C₂×C₈₉	semidirect
607. #3358	C₂×C₈₉	semidirect
608. #3333	C₂×C₈₉	semidirect
609. #3330	C₂×C₈₉	semidirect
610. #3314	C₂×C₈₉	semidirect
611. #3294	C₂×C₈₉	semidirect
612. #3283	C₂×C₈₉	semidirect
613. #3273	C₂×C₈₉	semidirect
614. #3272	C₂×C₈₉	semidirect
615. #3268	C₂×C₈₉	semidirect
616. #3262	C₂×C₈₉	semidirect
617. #3254	C₂×C₈₉	semidirect
618. #3224	C₂×C₈₉	semidirect
619. #3210	C₂×C₈₉	semidirect
620. #3124	C₂×C₈₉	semidirect
621. #3100	C₂×C₈₉	semidirect
622. #3045	C₂×C₈₉	semidirect
623. #3036	C₂×C₈₉	semidirect
624. #2993	C₂×C₈₉	semidirect
625. C₈₉	#62041	direct (N × H)
627. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
628. C₂×#135	C₂²×C₈₉	semidirect
630. #556	C₂²×C₈₉	semidirect
631. #556	C₂²×C₈₉	semidirect
632. #554	C₂²×C₈₉	semidirect
637. #550	C₂²×C₈₉	semidirect
638. D₄×Q₈	C₂²×C₈₉	semidirect
642. #547	C₂²×C₈₉	semidirect
645. #546	C₂²×C₈₉	semidirect
646. D₄²	C₂²×C₈₉	semidirect
647. #542	C₂²×C₈₉	semidirect
648. #542	C₂²×C₈₉	semidirect
653. #535	C₂²×C₈₉	semidirect
654. #533	C₂²×C₈₉	semidirect
660. #520	C₂²×C₈₉	semidirect
661. C₂×C₄×D₄	C₂²×C₈₉	semidirect
662. #496	C₂²×C₈₉	semidirect
664. #494	C₂²×C₈₉	semidirect
665. #492	C₂²×C₈₉	semidirect
666. #489	C₂²×C₈₉	semidirect
667. #487	C₂²×C₈₉	semidirect
668. #486	C₂²×C₈₉	semidirect
669. #486	C₂²×C₈₉	semidirect
670. #484	C₂²×C₈₉	semidirect
672. #480	C₂²×C₈₉	semidirect
673. #480	C₂²×C₈₉	semidirect
674. #477	C₂²×C₈₉	semidirect
675. #477	C₂²×C₈₉	semidirect
676. #474	C₂²×C₈₉	semidirect
677. #474	C₂²×C₈₉	semidirect
678. #474	C₂²×C₈₉	semidirect
679. #474	C₂²×C₈₉	semidirect
680. #474	C₂²×C₈₉	semidirect
682. #468	C₂²×C₈₉	semidirect
683. #468	C₂²×C₈₉	semidirect
684. #468	C₂²×C₈₉	semidirect
685. #467	C₂²×C₈₉	semidirect
687. #464	C₂²×C₈₉	semidirect
688. #464	C₂²×C₈₉	semidirect
689. #464	C₂²×C₈₉	semidirect
690. #464	C₂²×C₈₉	semidirect
692. #463	C₂²×C₈₉	semidirect
693. #463	C₂²×C₈₉	semidirect
694. #463	C₂²×C₈₉	semidirect
695. #461	C₂²×C₈₉	semidirect
696. #461	C₂²×C₈₉	semidirect
697. #461	C₂²×C₈₉	semidirect
698. #461	C₂²×C₈₉	semidirect
699. #460	C₂²×C₈₉	semidirect
700. #460	C₂²×C₈₉	semidirect
705. #459	C₂²×C₈₉	semidirect
706. #452	C₂²×C₈₉	semidirect
707. #452	C₂²×C₈₉	semidirect
708. #452	C₂²×C₈₉	semidirect
709. #452	C₂²×C₈₉	semidirect
710. #450	C₂²×C₈₉	semidirect
712. #449	C₂²×C₈₉	semidirect
715. #447	C₂²×C₈₉	semidirect
716. #446	C₂²×C₈₉	semidirect
717. C₈×Q₈	C₂²×C₈₉	semidirect
718. #440	C₂²×C₈₉	semidirect
719. #440	C₂²×C₈₉	semidirect
720. C₄×Q₁₆	C₂²×C₈₉	semidirect
723. C₄×D₈	C₂²×C₈₉	semidirect
724. C₄×D₈	C₂²×C₈₉	semidirect
725. C₄×D₈	C₂²×C₈₉	semidirect
726. #436	C₂²×C₈₉	semidirect
727. #436	C₂²×C₈₉	semidirect
728. #435	C₂²×C₈₉	semidirect
729. C₈×D₄	C₂²×C₈₉	semidirect
730. #433	C₂²×C₈₉	semidirect
731. #431	C₂²×C₈₉	semidirect
732. #424	C₂²×C₈₉	semidirect
733. #423	C₂²×C₈₉	semidirect
734. #417	C₂²×C₈₉	semidirect
735. #417	C₂²×C₈₉	semidirect
736. C₂×#102	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×#3546	2
C₈₉×#3520	2
C₈₉×#3397	2
C₈₉×#3393	2
C₈₉×#3367	2
C₈₉×#3358	2
C₈₉×#3333	2
C₈₉×#3330	2
C₈₉×#3314	2
C₈₉×#3294	2
C₈₉×#3283	2
C₈₉×#3273	2
C₈₉×#3272	2
C₈₉×#3268	2
C₈₉×#3262	2
C₈₉×#3254	2
C₈₉×#3224	2
C₈₉×#3210	2
C₈₉×#3124	2
C₈₉×#3100	2
C₈₉×#3045	2
C₈₉×#3036	2
C₈₉×#2993	2
#62041	89

Subgroups — C89×#62041 #36439889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62041 #36439889