Subgroups — C₈₉×#61432 #36439280

Order 22784.

1926 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3482	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3394	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3337	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3301	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3299	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3296	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3294	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3282	C₂	1	2	yes	maximal, complemented
14	D₄×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3168	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3108	C₂	1	2	yes	maximal, complemented
18	C₈₉×#3107	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3106	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₉×#3105	C₂	1	2	yes	maximal, complemented
21	C₈×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#135×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×SD₁₆×C₈₉	C₂	1	2	yes	maximal, complemented
24	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
25	C₂²×SD₁₆×C₈₉	C₂²	1	2	yes	—
26	#559×C₈₉	C₂²	1	1	yes	characteristic
27	#557×C₈₉	C₂²	1	1	yes	characteristic, complemented
28	#556×C₈₉	—	2	1	no	—
29	#556×C₈₉	C₂²	1	1	yes	characteristic, complemented
30	#554×C₈₉	C₂²	1	1	yes	characteristic
31	#554×C₈₉	C₂²	1	1	yes	characteristic
32	#553×C₈₉	—	2	1	no	—
33	#553×C₈₉	C₂²	1	2	yes	—
34	#552×C₈₉	—	2	2	no	—
35	#552×C₈₉	C₂²	1	2	yes	complemented
36	#551×C₈₉	—	2	2	no	—
37	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
38	#548×C₈₉	C₂²	1	2	yes	complemented
39	#547×C₈₉	—	2	1	no	—
40	#547×C₈₉	C₂²	1	1	yes	characteristic
41	#546×C₈₉	—	2	1	no	—
42	#546×C₈₉	C₂²	1	2	yes	—
43	D₄²×C₈₉	C₂²	1	1	yes	characteristic
44	#533×C₈₉	—	2	1	no	—
45	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
46	#532×C₈₉	C₂²	1	1	yes	characteristic
47	#529×C₈₉	—	2	1	no	—
48	#529×C₈₉	—	2	2	no	—
49	#529×C₈₉	C₂²	1	2	yes	—
50	#529×C₈₉	C₂²	1	2	yes	complemented
51	#525×C₈₉	—	2	2	no	—
52	C₄×#41×C₈₉	—	2	1	no	—
53	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
54	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
55	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₈₉	—	2	1	no	—
58	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
59	#499×C₈₉	C₂²	1	2	yes	complemented
60	#498×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	#495×C₈₉	C₂²	1	2	yes	complemented
62	#492×C₈₉	C₂²	1	1	yes	characteristic
63	#488×C₈₉	C₂²	1	2	yes	complemented
64	#488×C₈₉	C₂²	1	2	yes	complemented
65	#487×C₈₉	C₂²	1	1	yes	characteristic, complemented
66	#486×C₈₉	C₂²	1	1	yes	characteristic
67	#485×C₈₉	C₂²	1	2	yes	complemented
68	#484×C₈₉	C₂²	1	2	yes	complemented
69	#483×C₈₉	C₂²	1	2	yes	complemented
70	#482×C₈₉	C₂²	1	2	yes	complemented
71	#481×C₈₉	C₂²	1	2	yes	complemented
72	#480×C₈₉	C₂²	1	2	yes	—
73	#479×C₈₉	C₂²	1	2	yes	complemented
74	#479×C₈₉	C₂²	1	2	yes	complemented
75	#478×C₈₉	C₂²	1	2	yes	—
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	#475×C₈₉	C₂²	1	1	yes	characteristic, complemented
80	#474×C₈₉	C₂²	1	1	yes	characteristic
81	#467×C₈₉	C₂²	1	2	yes	complemented
82	#466×C₈₉	C₂²	1	2	yes	—
83	#465×C₈₉	C₂²	1	2	yes	—
84	#465×C₈₉	C₂²	1	2	yes	complemented
85	#465×C₈₉	C₂²	1	2	yes	complemented
86	#465×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	#462×C₈₉	C₂²	1	1	yes	characteristic, complemented
92	#461×C₈₉	C₂²	1	1	yes	characteristic
93	#460×C₈₉	C₂²	1	1	yes	characteristic
94	#459×C₈₉	C₂²	1	1	yes	characteristic
95	#452×C₈₉	C₂²	1	2	yes	—
96	#451×C₈₉	C₂²	1	2	yes	complemented
97	#450×C₈₉	C₂²	1	2	yes	—
98	#449×C₈₉	C₂²	1	2	yes	complemented
99	#448×C₈₉	C₂²	1	2	yes	—
100	#447×C₈₉	C₂²	1	2	yes	—
101	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
103	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
105	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
106	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
107	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
108	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
109	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
110	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
111	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
112	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
113	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
114	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
116	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
121	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
122	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
123	C₈×D₄×C₈₉	C₂²	1	2	yes	complemented
124	C₈×D₄×C₈₉	C₂²	1	2	yes	complemented
125	#431×C₈₉	C₂²	1	2	yes	complemented
126	#431×C₈₉	C₂²	1	1	yes	characteristic, complemented
127	#427×C₈₉	C₂²	1	1	yes	characteristic, complemented
128	C₂×#106×C₈₉	C₂²	1	2	yes	complemented
129	#416×C₈₉	C₂²	1	1	yes	characteristic
130	#416×C₈₉	C₂²	1	1	yes	characteristic, complemented
131	C₂×#103×C₈₉	C₂²	1	2	yes	complemented
132	C₂×#102×C₈₉	C₂²	1	2	yes	—
133	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄×C₈×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	1	yes	characteristic
140	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
141	C₂²×D₄×C₈₉	—	2	1	no	—
142	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
143	C₂³×C₄×C₈₉	—	2	2	no	—
144	#135×C₈₉	—	2	4	no	—
145	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₈₉	—	2	8	no	—
148	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
154	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
155	C₂×D₈×C₈₉	C₂³	1	2	yes	—
156	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
157	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
158	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
159	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₈₉	—	2	1	no	—
161	C₄⋊Q₈×C₈₉	—	2	1	no	—
162	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
165	#127×C₈₉	C₂³	1	1	yes	characteristic
166	#126×C₈₉	—	2	2	no	—
167	#126×C₈₉	—	2	2	no	—
168	#126×C₈₉	—	2	2	no	—
169	#126×C₈₉	—	2	2	no	—
170	#126×C₈₉	—	2	2	no	—
171	#125×C₈₉	—	2	2	no	—
172	#125×C₈₉	—	2	1	no	—
173	#125×C₈₉	—	2	2	no	—
174	#125×C₈₉	—	2	1	no	—
175	#125×C₈₉	C₂³	1	2	yes	—
176	#125×C₈₉	C₂³	1	2	yes	—
177	#124×C₈₉	—	2	1	no	—
178	#124×C₈₉	—	2	2	no	—
179	#124×C₈₉	—	2	1	no	—
180	#124×C₈₉	C₂³	1	2	yes	—
181	#124×C₈₉	C₂³	1	2	yes	—
182	#123×C₈₉	—	2	2	no	—
183	#123×C₈₉	—	2	2	no	—
184	#123×C₈₉	—	2	2	no	—
185	#123×C₈₉	—	2	2	no	—
186	#123×C₈₉	—	2	2	no	—
187	#123×C₈₉	—	2	2	no	—
188	#123×C₈₉	—	2	2	no	—
189	C₂²⋊Q₈×C₈₉	—	2	1	no	—
190	C₂²⋊Q₈×C₈₉	—	2	1	no	—
191	C₂²⋊Q₈×C₈₉	—	2	1	no	—
192	C₂²⋊Q₈×C₈₉	—	2	2	no	—
193	C₂²⋊Q₈×C₈₉	—	2	1	no	—
194	C₂²⋊Q₈×C₈₉	—	2	2	no	—
195	C₂²⋊Q₈×C₈₉	—	2	2	no	—
196	C₂²⋊Q₈×C₈₉	—	2	2	no	—
197	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
198	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
199	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
200	#121×C₈₉	—	2	2	no	—
201	#121×C₈₉	—	2	2	no	—
202	#121×C₈₉	—	2	1	no	—
203	#121×C₈₉	—	2	1	no	—
204	#121×C₈₉	—	2	2	no	—
205	#121×C₈₉	C₂³	1	2	yes	—
206	#121×C₈₉	C₂³	1	2	yes	—
207	#121×C₈₉	C₂³	1	2	yes	—
208	#120×C₈₉	—	2	2	no	—
209	#120×C₈₉	—	2	2	no	—
210	C₄×Q₈×C₈₉	—	2	1	no	—
211	C₄×Q₈×C₈₉	—	2	2	no	—
212	C₄×Q₈×C₈₉	—	2	2	no	—
213	C₄×Q₈×C₈₉	—	2	1	no	—
214	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
215	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
217	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
218	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
219	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
223	C₄×D₄×C₈₉	—	2	1	no	—
224	C₄×D₄×C₈₉	—	2	1	no	—
225	C₄×D₄×C₈₉	—	2	2	no	—
226	C₄×D₄×C₈₉	—	2	2	no	—
227	C₄×D₄×C₈₉	—	2	1	no	—
228	C₄×D₄×C₈₉	—	2	1	no	—
229	C₄×D₄×C₈₉	—	2	1	no	—
230	C₄×D₄×C₈₉	—	2	1	no	—
231	C₄×D₄×C₈₉	—	2	1	no	—
232	C₄×D₄×C₈₉	—	2	2	no	—
233	C₄×D₄×C₈₉	—	2	2	no	—
234	C₄×D₄×C₈₉	—	2	1	no	—
235	C₄×D₄×C₈₉	—	2	2	no	—
236	C₄×D₄×C₈₉	—	2	2	no	—
237	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
238	C₄×D₄×C₈₉	D₄	1	2	yes	—
239	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₈₉	C₂³	1	2	yes	—
244	C₄×D₄×C₈₉	C₂³	1	2	yes	—
245	C₄×D₄×C₈₉	C₂³	1	2	yes	—
246	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₈₉	C₂³	1	2	yes	—
248	#117×C₈₉	—	2	1	no	—
249	#117×C₈₉	—	2	1	no	—
250	#117×C₈₉	—	2	2	no	—
251	#117×C₈₉	—	2	1	no	—
252	#117×C₈₉	—	2	1	no	—
253	#117×C₈₉	—	2	2	no	—
254	#117×C₈₉	—	2	2	no	—
255	#117×C₈₉	D₄	1	2	yes	—
256	#117×C₈₉	D₄	1	1	yes	characteristic
257	#117×C₈₉	C₂³	1	1	yes	characteristic
258	#117×C₈₉	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
260	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
261	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
263	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
264	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
265	C₂×C₄²×C₈₉	—	2	2	no	—
266	C₂×C₄²×C₈₉	—	2	1	no	—
267	C₂×C₄²×C₈₉	—	2	1	no	—
268	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
269	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
270	#107×C₈₉	C₂³	1	1	yes	characteristic
271	#107×C₈₉	C₂³	1	1	yes	characteristic
272	#107×C₈₉	C₂³	1	2	yes	—
273	#107×C₈₉	C₂³	1	2	yes	—
274	#106×C₈₉	C₂³	1	1	yes	characteristic
275	#106×C₈₉	C₂³	1	2	yes	—
276	#106×C₈₉	C₂³	1	2	yes	—
277	#106×C₈₉	C₂³	1	2	yes	—
278	#106×C₈₉	C₂³	1	1	yes	characteristic
279	#106×C₈₉	C₂³	1	2	yes	—
280	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
283	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
284	#103×C₈₉	C₂³	1	1	yes	characteristic
285	#103×C₈₉	C₂³	1	2	yes	—
286	#103×C₈₉	C₂³	1	2	yes	—
287	#103×C₈₉	C₂³	1	2	yes	—
288	#103×C₈₉	C₂³	1	1	yes	characteristic
289	#103×C₈₉	C₂³	1	1	yes	characteristic
290	#103×C₈₉	C₂³	1	1	yes	characteristic
291	#103×C₈₉	C₂³	1	2	yes	—
292	#103×C₈₉	C₂³	1	2	yes	—
293	#103×C₈₉	C₂³	1	2	yes	—
294	#102×C₈₉	C₂³	1	1	yes	characteristic
295	#102×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	1	yes	characteristic
300	#102×C₈₉	C₂³	1	1	yes	characteristic
301	#102×C₈₉	C₂³	1	2	yes	—
302	#102×C₈₉	C₂³	1	2	yes	—
303	#102×C₈₉	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
307	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₈₉	C₂³	1	2	yes	—
310	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₈₉	C₂³	1	2	yes	—
313	C₄×C₈×C₈₉	C₂³	1	2	yes	—
314	C₂⁴×C₈₉	—	2	2	no	—
315	#41×C₈₉	—	2	4	no	—
316	#41×C₈₉	—	2	2	no	—
317	#41×C₈₉	—	2	2	no	—
318	#41×C₈₉	—	4	1	no	—
319	#41×C₈₉	—	4	1	no	—
320	#41×C₈₉	—	4	4	no	—
321	#41×C₈₉	—	8	2	no	—
322	C₂×Q₈×C₈₉	—	2	2	no	—
323	C₂×Q₈×C₈₉	—	2	1	no	—
324	C₂×Q₈×C₈₉	—	2	1	no	—
325	C₂×Q₈×C₈₉	—	2	4	no	—
326	C₂×Q₈×C₈₉	—	4	2	no	—
327	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₈₉	—	2	4	no	—
332	C₂×D₄×C₈₉	—	2	1	no	—
333	C₂×D₄×C₈₉	—	2	2	no	—
334	C₂×D₄×C₈₉	—	2	1	no	—
335	C₂×D₄×C₈₉	—	2	2	no	—
336	C₂×D₄×C₈₉	—	2	2	no	—
337	C₂×D₄×C₈₉	—	2	2	no	—
338	C₂×D₄×C₈₉	—	2	1	no	—
339	C₂×D₄×C₈₉	—	2	1	no	—
340	C₂×D₄×C₈₉	—	4	2	no	—
341	C₂×D₄×C₈₉	—	4	4	no	—
342	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
343	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
344	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
345	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
346	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₈₉	—	2	2	no	—
348	C₂²×C₄×C₈₉	—	2	2	no	—
349	C₂²×C₄×C₈₉	—	2	2	no	—
350	C₂²×C₄×C₈₉	—	2	1	no	—
351	C₂²×C₄×C₈₉	—	2	1	no	—
352	C₂²×C₄×C₈₉	—	2	1	no	—
353	C₂²×C₄×C₈₉	—	2	1	no	—
354	C₂²×C₄×C₈₉	—	2	1	no	—
355	C₂²×C₄×C₈₉	—	2	1	no	—
356	C₂²×C₄×C₈₉	—	2	2	no	—
357	C₂²×C₄×C₈₉	—	2	2	no	—
358	C₂²×C₄×C₈₉	—	2	2	no	—
359	C₂²×C₄×C₈₉	—	8	4	no	—
360	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
361	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
363	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
365	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
366	Q₁₆×C₈₉	—	2	2	no	—
367	Q₁₆×C₈₉	—	4	2	no	—
368	SD₁₆×C₈₉	—	2	4	no	—
369	SD₁₆×C₈₉	—	2	4	no	—
370	SD₁₆×C₈₉	—	2	4	no	—
371	SD₁₆×C₈₉	—	2	2	no	—
372	SD₁₆×C₈₉	—	4	2	no	—
373	SD₁₆×C₈₉	#41	1	4	yes	complemented
374	D₈×C₈₉	—	2	2	no	—
375	D₈×C₈₉	—	4	2	no	—
376	C₂×C₈×C₈₉	—	2	4	no	—
377	C₂×C₈×C₈₉	—	2	2	no	—
378	C₂×C₈×C₈₉	—	4	2	no	—
379	C₂×C₈×C₈₉	—	4	1	no	—
380	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
382	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
385	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
386	C₄⋊C₄×C₈₉	—	2	1	no	—
387	C₄⋊C₄×C₈₉	—	2	1	no	—
388	C₄⋊C₄×C₈₉	—	2	2	no	—
389	C₄⋊C₄×C₈₉	—	2	2	no	—
390	C₄⋊C₄×C₈₉	—	2	2	no	—
391	C₄⋊C₄×C₈₉	—	2	2	no	—
392	C₄⋊C₄×C₈₉	—	2	2	no	—
393	C₄⋊C₄×C₈₉	—	2	2	no	—
394	C₄⋊C₄×C₈₉	—	2	1	no	—
395	C₄⋊C₄×C₈₉	—	2	2	no	—
396	C₄⋊C₄×C₈₉	—	2	2	no	—
397	C₄⋊C₄×C₈₉	—	2	1	no	—
398	C₄⋊C₄×C₈₉	—	2	1	no	—
399	C₄⋊C₄×C₈₉	—	2	1	no	—
400	C₄⋊C₄×C₈₉	—	2	2	no	—
401	C₄⋊C₄×C₈₉	—	2	2	no	—
402	C₄⋊C₄×C₈₉	—	2	1	no	—
403	C₄⋊C₄×C₈₉	—	2	2	no	—
404	C₄⋊C₄×C₈₉	—	2	1	no	—
405	C₄⋊C₄×C₈₉	—	2	2	no	—
406	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
412	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
415	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
416	C₂²⋊C₄×C₈₉	—	2	2	no	—
417	C₂²⋊C₄×C₈₉	—	2	2	no	—
418	C₂²⋊C₄×C₈₉	—	2	2	no	—
419	C₂²⋊C₄×C₈₉	—	2	1	no	—
420	C₂²⋊C₄×C₈₉	—	2	1	no	—
421	C₂²⋊C₄×C₈₉	—	2	1	no	—
422	C₂²⋊C₄×C₈₉	—	2	2	no	—
423	C₂²⋊C₄×C₈₉	—	2	2	no	—
424	C₂²⋊C₄×C₈₉	—	2	2	no	—
425	C₂²⋊C₄×C₈₉	—	2	2	no	—
426	C₂²⋊C₄×C₈₉	—	2	2	no	—
427	C₂²⋊C₄×C₈₉	—	2	2	no	—
428	C₂²⋊C₄×C₈₉	—	2	1	no	—
429	C₂²⋊C₄×C₈₉	—	2	1	no	—
430	C₂²⋊C₄×C₈₉	—	2	1	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	2	no	—
435	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
438	C₄²×C₈₉	—	2	1	no	—
439	C₄²×C₈₉	—	2	2	no	—
440	C₄²×C₈₉	—	2	1	no	—
441	C₄²×C₈₉	—	2	1	no	—
442	C₄²×C₈₉	—	2	1	no	—
443	C₄²×C₈₉	—	2	2	no	—
444	C₄²×C₈₉	—	2	1	no	—
445	C₄²×C₈₉	—	2	1	no	—
446	C₄²×C₈₉	—	2	2	no	—
447	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₈₉	C₂×D₄	1	2	yes	—
449	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
450	C₄²×C₈₉	C₂×D₄	1	2	yes	—
451	C₄²×C₈₉	C₂⁴	1	2	yes	—
452	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
453	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
454	C₂³×C₈₉	—	2	1	no	—
455	C₂³×C₈₉	—	2	1	no	—
456	C₂³×C₈₉	—	2	2	no	—
457	C₂³×C₈₉	—	4	4	no	—
458	C₂³×C₈₉	—	4	4	no	—
459	C₂³×C₈₉	—	8	2	no	—
460	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
461	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
462	Q₈×C₈₉	—	2	2	no	—
463	Q₈×C₈₉	—	2	1	no	—
464	Q₈×C₈₉	—	2	2	no	—
465	Q₈×C₈₉	—	2	1	no	—
466	Q₈×C₈₉	—	2	2	no	—
467	Q₈×C₈₉	—	2	1	no	—
468	Q₈×C₈₉	—	4	4	no	—
469	Q₈×C₈₉	—	4	2	no	—
470	Q₈×C₈₉	—	8	1	no	—
471	Q₈×C₈₉	C₂×#41	1	2	yes	—
472	D₄×C₈₉	—	2	4	no	—
473	D₄×C₈₉	—	2	1	no	—
474	D₄×C₈₉	—	2	2	no	—
475	D₄×C₈₉	—	2	1	no	—
476	D₄×C₈₉	—	2	1	no	—
477	D₄×C₈₉	—	2	2	no	—
478	D₄×C₈₉	—	4	4	no	—
479	D₄×C₈₉	—	4	2	no	—
480	D₄×C₈₉	—	4	2	no	—
481	D₄×C₈₉	—	4	4	no	—
482	D₄×C₈₉	—	4	4	no	—
483	D₄×C₈₉	—	4	2	no	—
484	D₄×C₈₉	—	8	1	no	—
485	D₄×C₈₉	—	8	2	no	—
486	D₄×C₈₉	#135	1	4	yes	complemented
487	D₄×C₈₉	C₂×#41	1	2	yes	—
488	C₂×C₄×C₈₉	—	2	4	no	—
489	C₂×C₄×C₈₉	—	2	1	no	—
490	C₂×C₄×C₈₉	—	2	2	no	—
491	C₂×C₄×C₈₉	—	2	4	no	—
492	C₂×C₄×C₈₉	—	2	2	no	—
493	C₂×C₄×C₈₉	—	2	2	no	—
494	C₂×C₄×C₈₉	—	2	1	no	—
495	C₂×C₄×C₈₉	—	2	2	no	—
496	C₂×C₄×C₈₉	—	2	1	no	—
497	C₂×C₄×C₈₉	—	2	1	no	—
498	C₂×C₄×C₈₉	—	2	1	no	—
499	C₂×C₄×C₈₉	—	2	1	no	—
500	C₂×C₄×C₈₉	—	2	2	no	—
501	C₂×C₄×C₈₉	—	2	1	no	—
502	C₂×C₄×C₈₉	—	2	1	no	—
503	C₂×C₄×C₈₉	—	2	2	no	—
504	C₂×C₄×C₈₉	—	2	2	no	—
505	C₂×C₄×C₈₉	—	4	2	no	—
506	C₂×C₄×C₈₉	—	4	4	no	—
507	C₂×C₄×C₈₉	—	4	2	no	—
508	C₂×C₄×C₈₉	—	4	4	no	—
509	C₂×C₄×C₈₉	—	4	2	no	—
510	C₂×C₄×C₈₉	—	4	2	no	—
511	C₂×C₄×C₈₉	—	4	2	no	—
512	C₂×C₄×C₈₉	—	4	2	no	—
513	C₂×C₄×C₈₉	—	4	4	no	—
514	C₂×C₄×C₈₉	—	8	2	no	—
515	C₂×C₄×C₈₉	—	8	2	no	—
516	C₂×C₄×C₈₉	—	8	2	no	—
517	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
519	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
526	C₈×C₈₉	—	2	1	no	—
527	C₈×C₈₉	—	2	2	no	—
528	C₈×C₈₉	—	2	1	no	—
529	C₈×C₈₉	—	2	2	no	—
530	C₈×C₈₉	—	2	1	no	—
531	C₈×C₈₉	C₂×#41	1	2	yes	—
532	C₂²×C₈₉	—	2	2	no	—
533	C₂²×C₈₉	—	2	2	no	—
534	C₂²×C₈₉	—	2	1	no	—
535	C₂²×C₈₉	—	2	2	no	—
536	C₂²×C₈₉	—	2	1	no	—
537	C₂²×C₈₉	—	2	1	no	—
538	C₂²×C₈₉	—	4	1	no	—
539	C₂²×C₈₉	—	4	1	no	—
540	C₂²×C₈₉	—	4	1	no	—
541	C₂²×C₈₉	—	4	2	no	—
542	C₂²×C₈₉	—	4	1	no	—
543	C₂²×C₈₉	—	4	2	no	—
544	C₂²×C₈₉	—	4	2	no	—
545	C₂²×C₈₉	—	4	1	no	—
546	C₂²×C₈₉	—	8	8	no	—
547	C₂²×C₈₉	C₂×#135	1	4	yes	—
548	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
549	C₄×C₈₉	—	2	1	no	—
550	C₄×C₈₉	—	2	2	no	—
551	C₄×C₈₉	—	2	2	no	—
552	C₄×C₈₉	—	2	1	no	—
553	C₄×C₈₉	—	2	2	no	—
554	C₄×C₈₉	—	2	2	no	—
555	C₄×C₈₉	—	2	1	no	—
556	C₄×C₈₉	—	4	1	no	—
557	C₄×C₈₉	—	4	2	no	—
558	C₄×C₈₉	—	4	1	no	—
559	C₄×C₈₉	—	4	1	no	—
560	C₄×C₈₉	—	4	2	no	—
561	C₄×C₈₉	—	4	1	no	—
562	C₄×C₈₉	—	4	1	no	—
563	C₄×C₈₉	—	4	2	no	—
564	C₄×C₈₉	C₂×#135	1	2	yes	—
565	C₄×C₈₉	#577	1	2	yes	—
566	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
567	C₄×C₈₉	#585	1	1	yes	characteristic
568	#61432	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
569	C₂×C₈₉	—	2	4	no	—
570	C₂×C₈₉	—	4	1	no	—
571	C₂×C₈₉	—	4	2	no	—
572	C₂×C₈₉	—	8	1	no	—
573	C₂×C₈₉	—	8	2	no	—
574	C₂×C₈₉	D₄×#41	1	1	yes	characteristic
575	C₂×C₈₉	C₂²×#135	1	1	yes	characteristic
576	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
577	#3482	C₂×C₈₉	1	1	yes	characteristic, complemented
578	#3481	C₂×C₈₉	1	1	yes	characteristic, complemented
579	#3394	C₂×C₈₉	1	1	yes	characteristic, complemented
580	#3381	C₂×C₈₉	1	1	yes	characteristic, complemented
581	#3365	C₂×C₈₉	1	1	yes	characteristic, complemented
582	#3360	C₂×C₈₉	1	1	yes	characteristic, complemented
583	#3337	C₂×C₈₉	1	2	yes	complemented
584	#3335	C₂×C₈₉	1	1	yes	characteristic, complemented
585	#3301	C₂×C₈₉	1	2	yes	complemented
586	#3299	C₂×C₈₉	1	1	yes	characteristic, complemented
587	#3296	C₂×C₈₉	1	2	yes	complemented
588	#3294	C₂×C₈₉	1	1	yes	characteristic, complemented
589	#3282	C₂×C₈₉	1	2	yes	complemented
590	D₄×SD₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
591	#3168	C₂×C₈₉	1	2	yes	complemented
592	#3167	C₂×C₈₉	1	1	yes	characteristic, complemented
593	#3108	C₂×C₈₉	1	2	yes	complemented
594	#3107	C₂×C₈₉	1	1	yes	characteristic, complemented
595	#3106	C₂×C₈₉	1	1	yes	characteristic, complemented
596	#3105	C₂×C₈₉	1	2	yes	complemented
597	C₈×#41	C₂×C₈₉	1	1	yes	characteristic, complemented
598	C₄×#135	C₂×C₈₉	1	1	yes	characteristic, complemented
599	C₂×C₄×SD₁₆	C₂×C₈₉	1	2	yes	complemented
600	C₈₉	#61432	1	1	yes	characteristic, direct product factor, Sylow
601	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
602	C₂²×SD₁₆	C₂²×C₈₉	1	2	yes	—
603	#559	C₂²×C₈₉	1	1	yes	characteristic
604	#557	C₂²×C₈₉	1	1	yes	characteristic, complemented
605	#556	—	2	1	no	—
606	#556	C₂²×C₈₉	1	1	yes	characteristic, complemented
607	#554	C₂²×C₈₉	1	1	yes	characteristic
608	#554	C₂²×C₈₉	1	1	yes	characteristic
609	#553	—	2	1	no	—
610	#553	C₂²×C₈₉	1	2	yes	—
611	#552	—	2	2	no	—
612	#552	C₂²×C₈₉	1	2	yes	complemented
613	#551	—	2	2	no	—
614	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
615	#548	C₂²×C₈₉	1	2	yes	complemented
616	#547	—	2	1	no	—
617	#547	C₂²×C₈₉	1	1	yes	characteristic
618	#546	—	2	1	no	—
619	#546	C₂²×C₈₉	1	2	yes	—
620	D₄²	C₂²×C₈₉	1	1	yes	characteristic
621	#533	—	2	1	no	—
622	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
623	#532	C₂²×C₈₉	1	1	yes	characteristic
624	#529	—	2	1	no	—
625	#529	—	2	2	no	—
626	#529	C₂²×C₈₉	1	2	yes	—
627	#529	C₂²×C₈₉	1	2	yes	complemented
628	#525	—	2	2	no	—
629	C₄×#41	—	2	1	no	—
630	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
631	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
632	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic, complemented
633	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	complemented
634	C₂×C₄×D₄	—	2	1	no	—
635	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
636	#499	C₂²×C₈₉	1	2	yes	complemented
637	#498	C₂²×C₈₉	1	1	yes	characteristic, complemented
638	#495	C₂²×C₈₉	1	2	yes	complemented
639	#492	C₂²×C₈₉	1	1	yes	characteristic
640	#488	C₂²×C₈₉	1	2	yes	complemented
641	#488	C₂²×C₈₉	1	2	yes	complemented
642	#487	C₂²×C₈₉	1	1	yes	characteristic, complemented
643	#486	C₂²×C₈₉	1	1	yes	characteristic
644	#485	C₂²×C₈₉	1	2	yes	complemented
645	#484	C₂²×C₈₉	1	2	yes	complemented
646	#483	C₂²×C₈₉	1	2	yes	complemented
647	#482	C₂²×C₈₉	1	2	yes	complemented
648	#481	C₂²×C₈₉	1	2	yes	complemented
649	#480	C₂²×C₈₉	1	2	yes	—
650	#479	C₂²×C₈₉	1	2	yes	complemented
651	#479	C₂²×C₈₉	1	2	yes	complemented
652	#478	C₂²×C₈₉	1	2	yes	—
653	#478	C₂²×C₈₉	1	2	yes	complemented
654	#477	C₂²×C₈₉	1	1	yes	characteristic, complemented
655	#476	C₂²×C₈₉	1	1	yes	characteristic, complemented
656	#475	C₂²×C₈₉	1	1	yes	characteristic, complemented
657	#474	C₂²×C₈₉	1	1	yes	characteristic
658	#467	C₂²×C₈₉	1	2	yes	complemented
659	#466	C₂²×C₈₉	1	2	yes	—
660	#465	C₂²×C₈₉	1	2	yes	—
661	#465	C₂²×C₈₉	1	2	yes	complemented
662	#465	C₂²×C₈₉	1	2	yes	complemented
663	#465	C₂²×C₈₉	1	2	yes	complemented
664	#464	C₂²×C₈₉	1	2	yes	complemented
665	#464	C₂²×C₈₉	1	2	yes	complemented
666	#463	C₂²×C₈₉	1	2	yes	—
667	#463	C₂²×C₈₉	1	2	yes	complemented
668	#462	C₂²×C₈₉	1	1	yes	characteristic, complemented
669	#461	C₂²×C₈₉	1	1	yes	characteristic
670	#460	C₂²×C₈₉	1	1	yes	characteristic
671	#459	C₂²×C₈₉	1	1	yes	characteristic
672	#452	C₂²×C₈₉	1	2	yes	—
673	#451	C₂²×C₈₉	1	2	yes	complemented
674	#450	C₂²×C₈₉	1	2	yes	—
675	#449	C₂²×C₈₉	1	2	yes	complemented
676	#448	C₂²×C₈₉	1	2	yes	—
677	#447	C₂²×C₈₉	1	2	yes	—
678	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
679	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
680	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
681	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
682	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
683	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
684	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
685	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
686	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
687	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
688	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
689	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
690	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
691	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
692	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
693	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
694	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
695	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
696	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
697	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
698	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic
699	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic
700	C₈×D₄	C₂²×C₈₉	1	2	yes	complemented
701	C₈×D₄	C₂²×C₈₉	1	2	yes	complemented
702	#431	C₂²×C₈₉	1	2	yes	complemented
703	#431	C₂²×C₈₉	1	1	yes	characteristic, complemented
704	#427	C₂²×C₈₉	1	1	yes	characteristic, complemented
705	C₂×#106	C₂²×C₈₉	1	2	yes	complemented
706	#416	C₂²×C₈₉	1	1	yes	characteristic
707	#416	C₂²×C₈₉	1	1	yes	characteristic, complemented
708	C₂×#103	C₂²×C₈₉	1	2	yes	complemented
709	C₂×#102	C₂²×C₈₉	1	2	yes	—
710	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
711	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	complemented
712	C₂×#41	—	2	1	no	—
713	C₂×#41	—	2	1	no	—
714	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
715	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
716	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
717	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
718	C₂²×D₄	—	2	1	no	—
719	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
720	C₂³×C₄	—	2	2	no	—
721	#135	—	2	4	no	—
722	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
723	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
724	C₂×SD₁₆	—	2	8	no	—
725	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
726	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
727	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
728	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
729	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
730	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
731	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
732	C₂×D₈	C₂³×C₈₉	1	2	yes	—
733	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
734	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
735	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
736	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
737	C₄⋊Q₈	—	2	1	no	—
738	C₄⋊Q₈	—	2	1	no	—
739	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
740	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
741	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
742	#127	C₂³×C₈₉	1	1	yes	characteristic
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#126	—	2	2	no	—
747	#126	—	2	2	no	—
748	#125	—	2	2	no	—
749	#125	—	2	1	no	—
750	#125	—	2	2	no	—
751	#125	—	2	1	no	—
752	#125	C₂³×C₈₉	1	2	yes	—
753	#125	C₂³×C₈₉	1	2	yes	—
754	#124	—	2	1	no	—
755	#124	—	2	2	no	—
756	#124	—	2	1	no	—
757	#124	C₂³×C₈₉	1	2	yes	—
758	#124	C₂³×C₈₉	1	2	yes	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	1	no	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	1	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
775	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
776	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
777	#121	—	2	2	no	—
778	#121	—	2	2	no	—
779	#121	—	2	1	no	—
780	#121	—	2	1	no	—
781	#121	—	2	2	no	—
782	#121	C₂³×C₈₉	1	2	yes	—
783	#121	C₂³×C₈₉	1	2	yes	—
784	#121	C₂³×C₈₉	1	2	yes	—
785	#120	—	2	2	no	—
786	#120	—	2	2	no	—
787	C₄×Q₈	—	2	1	no	—
788	C₄×Q₈	—	2	2	no	—
789	C₄×Q₈	—	2	2	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
792	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
793	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
794	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
795	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
796	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
798	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
799	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
815	C₄×D₄	D₄×C₈₉	1	2	yes	—
816	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
817	C₄×D₄	C₂³×C₈₉	1	2	yes	—
818	C₄×D₄	C₂³×C₈₉	1	2	yes	—
819	C₄×D₄	C₂³×C₈₉	1	2	yes	—
820	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
821	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
823	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₈₉	1	2	yes	—
825	#117	—	2	1	no	—
826	#117	—	2	1	no	—
827	#117	—	2	2	no	—
828	#117	—	2	1	no	—
829	#117	—	2	1	no	—
830	#117	—	2	2	no	—
831	#117	—	2	2	no	—
832	#117	D₄×C₈₉	1	2	yes	—
833	#117	D₄×C₈₉	1	1	yes	characteristic
834	#117	C₂³×C₈₉	1	1	yes	characteristic
835	#117	C₂³×C₈₉	1	1	yes	characteristic
836	C₂×C₄⋊C₄	—	2	2	no	—
837	C₂×C₄⋊C₄	—	2	1	no	—
838	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
839	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
840	C₂×C₂²⋊C₄	—	2	2	no	—
841	C₂×C₂²⋊C₄	—	2	2	no	—
842	C₂×C₄²	—	2	2	no	—
843	C₂×C₄²	—	2	1	no	—
844	C₂×C₄²	—	2	1	no	—
845	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
846	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
847	#107	C₂³×C₈₉	1	1	yes	characteristic
848	#107	C₂³×C₈₉	1	1	yes	characteristic
849	#107	C₂³×C₈₉	1	2	yes	—
850	#107	C₂³×C₈₉	1	2	yes	—
851	#106	C₂³×C₈₉	1	1	yes	characteristic
852	#106	C₂³×C₈₉	1	2	yes	—
853	#106	C₂³×C₈₉	1	2	yes	—
854	#106	C₂³×C₈₉	1	2	yes	—
855	#106	C₂³×C₈₉	1	1	yes	characteristic
856	#106	C₂³×C₈₉	1	2	yes	—
857	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
858	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
860	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
861	#103	C₂³×C₈₉	1	1	yes	characteristic
862	#103	C₂³×C₈₉	1	2	yes	—
863	#103	C₂³×C₈₉	1	2	yes	—
864	#103	C₂³×C₈₉	1	2	yes	—
865	#103	C₂³×C₈₉	1	1	yes	characteristic
866	#103	C₂³×C₈₉	1	1	yes	characteristic
867	#103	C₂³×C₈₉	1	1	yes	characteristic
868	#103	C₂³×C₈₉	1	2	yes	—
869	#103	C₂³×C₈₉	1	2	yes	—
870	#103	C₂³×C₈₉	1	2	yes	—
871	#102	C₂³×C₈₉	1	1	yes	characteristic
872	#102	C₂³×C₈₉	1	2	yes	—
873	#102	C₂³×C₈₉	1	2	yes	—
874	#102	C₂³×C₈₉	1	2	yes	—
875	#102	C₂³×C₈₉	1	1	yes	characteristic
876	#102	C₂³×C₈₉	1	1	yes	characteristic
877	#102	C₂³×C₈₉	1	1	yes	characteristic
878	#102	C₂³×C₈₉	1	2	yes	—
879	#102	C₂³×C₈₉	1	2	yes	—
880	#102	C₂³×C₈₉	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
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	1	yes	characteristic
888	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
889	C₄×C₈	C₂³×C₈₉	1	2	yes	—
890	C₄×C₈	C₂³×C₈₉	1	2	yes	—
891	C₂⁴	—	2	2	no	—
892	#41	—	2	4	no	—
893	#41	—	2	2	no	—
894	#41	—	2	2	no	—
895	#41	—	4	1	no	—
896	#41	—	4	1	no	—
897	#41	—	4	4	no	—
898	#41	—	8	2	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	2	1	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	—	2	4	no	—
903	C₂×Q₈	—	4	2	no	—
904	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
905	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
906	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
907	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
908	C₂×D₄	—	2	4	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	4	2	no	—
918	C₂×D₄	—	4	4	no	—
919	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
920	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
921	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
922	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
923	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	8	4	no	—
937	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
938	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
939	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
940	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
941	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
942	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
943	Q₁₆	—	2	2	no	—
944	Q₁₆	—	4	2	no	—
945	SD₁₆	—	2	4	no	—
946	SD₁₆	—	2	4	no	—
947	SD₁₆	—	2	4	no	—
948	SD₁₆	—	2	2	no	—
949	SD₁₆	—	4	2	no	—
950	SD₁₆	#41×C₈₉	1	4	yes	complemented
951	D₈	—	2	2	no	—
952	D₈	—	4	2	no	—
953	C₂×C₈	—	2	4	no	—
954	C₂×C₈	—	2	2	no	—
955	C₂×C₈	—	4	2	no	—
956	C₂×C₈	—	4	1	no	—
957	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
958	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
959	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
960	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
961	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
962	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
984	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
985	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
986	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
987	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
988	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
989	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
990	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
991	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
992	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1013	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1014	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	2	1	no	—
1018	C₄²	—	2	2	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	2	no	—
1024	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1025	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1026	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1027	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1028	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1029	C₄²	C₂⁴×C₈₉	1	2	yes	—
1030	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	2	no	—
1034	C₂³	—	4	4	no	—
1035	C₂³	—	4	4	no	—
1036	C₂³	—	8	2	no	—
1037	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1038	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1039	Q₈	—	2	2	no	—
1040	Q₈	—	2	1	no	—
1041	Q₈	—	2	2	no	—
1042	Q₈	—	2	1	no	—
1043	Q₈	—	2	2	no	—
1044	Q₈	—	2	1	no	—
1045	Q₈	—	4	4	no	—
1046	Q₈	—	4	2	no	—
1047	Q₈	—	8	1	no	—
1048	Q₈	C₂×#41×C₈₉	1	2	yes	—
1049	D₄	—	2	4	no	—
1050	D₄	—	2	1	no	—
1051	D₄	—	2	2	no	—
1052	D₄	—	2	1	no	—
1053	D₄	—	2	1	no	—
1054	D₄	—	2	2	no	—
1055	D₄	—	4	4	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	4	2	no	—
1058	D₄	—	4	4	no	—
1059	D₄	—	4	4	no	—
1060	D₄	—	4	2	no	—
1061	D₄	—	8	1	no	—
1062	D₄	—	8	2	no	—
1063	D₄	#135×C₈₉	1	4	yes	complemented
1064	D₄	C₂×#41×C₈₉	1	2	yes	—
1065	C₂×C₄	—	2	4	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	4	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	4	2	no	—
1083	C₂×C₄	—	4	4	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	4	4	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	4	no	—
1091	C₂×C₄	—	8	2	no	—
1092	C₂×C₄	—	8	2	no	—
1093	C₂×C₄	—	8	2	no	—
1094	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1095	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1096	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1097	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1098	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1099	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1100	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1102	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1103	C₈	—	2	1	no	—
1104	C₈	—	2	2	no	—
1105	C₈	—	2	1	no	—
1106	C₈	—	2	2	no	—
1107	C₈	—	2	1	no	—
1108	C₈	C₂×#41×C₈₉	1	2	yes	—
1109	C₂²	—	2	2	no	—
1110	C₂²	—	2	2	no	—
1111	C₂²	—	2	1	no	—
1112	C₂²	—	2	1	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	2	2	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	4	1	no	—
1117	C₂²	—	4	1	no	—
1118	C₂²	—	4	2	no	—
1119	C₂²	—	4	2	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	2	no	—
1123	C₂²	—	8	8	no	—
1124	C₂²	C₂×#135×C₈₉	1	4	yes	—
1125	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1126	C₄	—	2	1	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	2	no	—
1129	C₄	—	2	1	no	—
1130	C₄	—	2	1	no	—
1131	C₄	—	2	2	no	—
1132	C₄	—	2	2	no	—
1133	C₄	—	4	1	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	4	2	no	—
1136	C₄	—	4	1	no	—
1137	C₄	—	4	2	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	C₂×#135×C₈₉	1	2	yes	—
1142	C₄	#577×C₈₉	1	2	yes	—
1143	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
1144	C₄	#585×C₈₉	1	1	yes	characteristic
1145	C₂	—	2	4	no	—
1146	C₂	—	4	1	no	—
1147	C₂	—	4	2	no	—
1148	C₂	—	8	1	no	—
1149	C₂	—	8	2	no	—
1150	C₂	D₄×#41×C₈₉	1	1	yes	characteristic
1151	C₂	C₂²×#135×C₈₉	1	1	yes	characteristic
1152	C₂	C₂×#577×C₈₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3482	C₂	semidirect
2. C₈₉×#3481	C₂	semidirect
3. C₈₉×#3394	C₂	semidirect
4. C₈₉×#3381	C₂	semidirect
5. C₈₉×#3365	C₂	semidirect
6. C₈₉×#3360	C₂	semidirect
7. C₈₉×#3337	C₂	semidirect
8. C₈₉×#3335	C₂	semidirect
9. C₈₉×#3301	C₂	semidirect
10. C₈₉×#3299	C₂	semidirect
11. C₈₉×#3296	C₂	semidirect
12. C₈₉×#3294	C₂	semidirect
13. C₈₉×#3282	C₂	semidirect
14. D₄×SD₁₆×C₈₉	C₂	semidirect
15. C₈₉×#3168	C₂	semidirect
16. C₈₉×#3167	C₂	semidirect
17. C₈₉×#3108	C₂	semidirect
18. C₈₉×#3107	C₂	semidirect
19. C₈₉×#3106	C₂	semidirect
20. C₈₉×#3105	C₂	semidirect
21. C₈×#41×C₈₉	C₂	semidirect
22. C₄×#135×C₈₉	C₂	semidirect
23. C₂×C₄×SD₁₆×C₈₉	C₂	semidirect
27. #557×C₈₉	C₂²	semidirect
29. #556×C₈₉	C₂²	semidirect
35. #552×C₈₉	C₂²	semidirect
38. #548×C₈₉	C₂²	semidirect
45. #533×C₈₉	C₂²	semidirect
50. #529×C₈₉	C₂²	semidirect
55. C₄×#41×C₈₉	C₂²	semidirect
56. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
59. #499×C₈₉	C₂²	semidirect
60. #498×C₈₉	C₂²	semidirect
61. #495×C₈₉	C₂²	semidirect
63. #488×C₈₉	C₂²	semidirect
64. #488×C₈₉	C₂²	semidirect
65. #487×C₈₉	C₂²	semidirect
67. #485×C₈₉	C₂²	semidirect
68. #484×C₈₉	C₂²	semidirect
69. #483×C₈₉	C₂²	semidirect
70. #482×C₈₉	C₂²	semidirect
71. #481×C₈₉	C₂²	semidirect
73. #479×C₈₉	C₂²	semidirect
74. #479×C₈₉	C₂²	semidirect
76. #478×C₈₉	C₂²	semidirect
77. #477×C₈₉	C₂²	semidirect
78. #476×C₈₉	C₂²	semidirect
79. #475×C₈₉	C₂²	semidirect
81. #467×C₈₉	C₂²	semidirect
84. #465×C₈₉	C₂²	semidirect
85. #465×C₈₉	C₂²	semidirect
86. #465×C₈₉	C₂²	semidirect
87. #464×C₈₉	C₂²	semidirect
88. #464×C₈₉	C₂²	semidirect
90. #463×C₈₉	C₂²	semidirect
91. #462×C₈₉	C₂²	semidirect
96. #451×C₈₉	C₂²	semidirect
98. #449×C₈₉	C₂²	semidirect
101. C₈×Q₈×C₈₉	C₂²	semidirect
102. C₈×Q₈×C₈₉	C₂²	semidirect
103. C₄×Q₁₆×C₈₉	C₂²	semidirect
104. C₄×Q₁₆×C₈₉	C₂²	semidirect
105. C₄×Q₁₆×C₈₉	C₂²	semidirect
111. C₄×SD₁₆×C₈₉	C₂²	semidirect
112. C₄×SD₁₆×C₈₉	C₂²	semidirect
113. C₄×SD₁₆×C₈₉	C₂²	semidirect
114. C₄×SD₁₆×C₈₉	C₂²	semidirect
115. C₄×SD₁₆×C₈₉	C₂²	semidirect
116. C₄×SD₁₆×C₈₉	C₂²	semidirect
117. C₄×SD₁₆×C₈₉	C₂²	semidirect
120. C₄×D₈×C₈₉	C₂²	semidirect
123. C₈×D₄×C₈₉	C₂²	semidirect
124. C₈×D₄×C₈₉	C₂²	semidirect
125. #431×C₈₉	C₂²	semidirect
126. #431×C₈₉	C₂²	semidirect
127. #427×C₈₉	C₂²	semidirect
128. C₂×#106×C₈₉	C₂²	semidirect
130. #416×C₈₉	C₂²	semidirect
131. C₂×#103×C₈₉	C₂²	semidirect
133. C₂×C₄×C₈×C₈₉	C₂²	semidirect
134. C₂×C₄×C₈×C₈₉	C₂²	semidirect
373. SD₁₆×C₈₉	#41	semidirect
486. D₄×C₈₉	#135	semidirect
568. #61432	C₈₉	direct (N × H)
577. #3482	C₂×C₈₉	semidirect
578. #3481	C₂×C₈₉	semidirect
579. #3394	C₂×C₈₉	semidirect
580. #3381	C₂×C₈₉	semidirect
581. #3365	C₂×C₈₉	semidirect
582. #3360	C₂×C₈₉	semidirect
583. #3337	C₂×C₈₉	semidirect
584. #3335	C₂×C₈₉	semidirect
585. #3301	C₂×C₈₉	semidirect
586. #3299	C₂×C₈₉	semidirect
587. #3296	C₂×C₈₉	semidirect
588. #3294	C₂×C₈₉	semidirect
589. #3282	C₂×C₈₉	semidirect
590. D₄×SD₁₆	C₂×C₈₉	semidirect
591. #3168	C₂×C₈₉	semidirect
592. #3167	C₂×C₈₉	semidirect
593. #3108	C₂×C₈₉	semidirect
594. #3107	C₂×C₈₉	semidirect
595. #3106	C₂×C₈₉	semidirect
596. #3105	C₂×C₈₉	semidirect
597. C₈×#41	C₂×C₈₉	semidirect
598. C₄×#135	C₂×C₈₉	semidirect
599. C₂×C₄×SD₁₆	C₂×C₈₉	semidirect
600. C₈₉	#61432	direct (N × H)
604. #557	C₂²×C₈₉	semidirect
606. #556	C₂²×C₈₉	semidirect
612. #552	C₂²×C₈₉	semidirect
615. #548	C₂²×C₈₉	semidirect
622. #533	C₂²×C₈₉	semidirect
627. #529	C₂²×C₈₉	semidirect
632. C₄×#41	C₂²×C₈₉	semidirect
633. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
636. #499	C₂²×C₈₉	semidirect
637. #498	C₂²×C₈₉	semidirect
638. #495	C₂²×C₈₉	semidirect
640. #488	C₂²×C₈₉	semidirect
641. #488	C₂²×C₈₉	semidirect
642. #487	C₂²×C₈₉	semidirect
644. #485	C₂²×C₈₉	semidirect
645. #484	C₂²×C₈₉	semidirect
646. #483	C₂²×C₈₉	semidirect
647. #482	C₂²×C₈₉	semidirect
648. #481	C₂²×C₈₉	semidirect
650. #479	C₂²×C₈₉	semidirect
651. #479	C₂²×C₈₉	semidirect
653. #478	C₂²×C₈₉	semidirect
654. #477	C₂²×C₈₉	semidirect
655. #476	C₂²×C₈₉	semidirect
656. #475	C₂²×C₈₉	semidirect
658. #467	C₂²×C₈₉	semidirect
661. #465	C₂²×C₈₉	semidirect
662. #465	C₂²×C₈₉	semidirect
663. #465	C₂²×C₈₉	semidirect
664. #464	C₂²×C₈₉	semidirect
665. #464	C₂²×C₈₉	semidirect
667. #463	C₂²×C₈₉	semidirect
668. #462	C₂²×C₈₉	semidirect
673. #451	C₂²×C₈₉	semidirect
675. #449	C₂²×C₈₉	semidirect
678. C₈×Q₈	C₂²×C₈₉	semidirect
679. C₈×Q₈	C₂²×C₈₉	semidirect
680. C₄×Q₁₆	C₂²×C₈₉	semidirect
681. C₄×Q₁₆	C₂²×C₈₉	semidirect
682. C₄×Q₁₆	C₂²×C₈₉	semidirect
688. C₄×SD₁₆	C₂²×C₈₉	semidirect
689. C₄×SD₁₆	C₂²×C₈₉	semidirect
690. C₄×SD₁₆	C₂²×C₈₉	semidirect
691. C₄×SD₁₆	C₂²×C₈₉	semidirect
692. C₄×SD₁₆	C₂²×C₈₉	semidirect
693. C₄×SD₁₆	C₂²×C₈₉	semidirect
694. C₄×SD₁₆	C₂²×C₈₉	semidirect
697. C₄×D₈	C₂²×C₈₉	semidirect
700. C₈×D₄	C₂²×C₈₉	semidirect
701. C₈×D₄	C₂²×C₈₉	semidirect
702. #431	C₂²×C₈₉	semidirect
703. #431	C₂²×C₈₉	semidirect
704. #427	C₂²×C₈₉	semidirect
705. C₂×#106	C₂²×C₈₉	semidirect
707. #416	C₂²×C₈₉	semidirect
708. C₂×#103	C₂²×C₈₉	semidirect
710. C₂×C₄×C₈	C₂²×C₈₉	semidirect
711. C₂×C₄×C₈	C₂²×C₈₉	semidirect
950. SD₁₆	#41×C₈₉	semidirect
1063. D₄	#135×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3482	2
C₈₉×#3481	2
C₈₉×#3394	2
C₈₉×#3381	2
C₈₉×#3365	2
C₈₉×#3360	2
C₈₉×#3337	2
C₈₉×#3335	2
C₈₉×#3301	2
C₈₉×#3299	2
C₈₉×#3296	2
C₈₉×#3294	2
C₈₉×#3282	2
D₄×SD₁₆×C₈₉	2
C₈₉×#3168	2
C₈₉×#3167	2
C₈₉×#3108	2
C₈₉×#3107	2
C₈₉×#3106	2
C₈₉×#3105	2
C₈×#41×C₈₉	2
C₄×#135×C₈₉	2
C₂×C₄×SD₁₆×C₈₉	2
#61432	89

Subgroups — C89×#61432 #36439280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61432 #36439280