Subgroups — C₈₉×#60959 #36438807

Order 22784.

1836 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#529×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3250	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3240	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3236	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3234	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3219	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3215	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3213	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3190	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3188	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3181	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3180	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3117	C₂	1	2	yes	maximal, complemented
15	C₈₉×#3114	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3111	C₂	1	4	yes	maximal, complemented
17	C₂×#432×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#533×C₈₉	C₂²	1	1	yes	characteristic
19	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
20	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
21	#532×C₈₉	C₂²	1	1	yes	characteristic
22	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
23	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
24	#529×C₈₉	—	2	1	no	—
25	#529×C₈₉	—	2	1	no	—
26	#529×C₈₉	—	2	1	no	—
27	#529×C₈₉	—	2	1	no	—
28	#529×C₈₉	—	2	1	no	—
29	#529×C₈₉	—	2	1	no	—
30	#529×C₈₉	—	2	1	no	—
31	#529×C₈₉	—	2	1	no	—
32	#529×C₈₉	C₂²	1	2	yes	—
33	#529×C₈₉	C₂²	1	2	yes	—
34	#529×C₈₉	C₂²	1	2	yes	—
35	#529×C₈₉	C₂²	1	2	yes	—
36	#529×C₈₉	C₂²	1	2	yes	—
37	#529×C₈₉	C₂²	1	2	yes	complemented
38	C₂×#126×C₈₉	—	2	1	no	—
39	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
41	#525×C₈₉	—	2	1	no	—
42	#525×C₈₉	—	2	1	no	—
43	#525×C₈₉	C₂²	1	2	yes	—
44	C₂×#123×C₈₉	—	2	1	no	—
45	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
47	C₄×#41×C₈₉	—	2	1	no	—
48	C₄×#41×C₈₉	—	2	1	no	—
49	C₄×#41×C₈₉	C₂²	1	2	yes	complemented
50	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₈₉	—	2	1	no	—
52	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×#117×C₈₉	—	2	1	no	—
54	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
55	#501×C₈₉	C₂²	1	2	yes	complemented
56	#501×C₈₉	C₂²	1	2	yes	complemented
57	#497×C₈₉	C₂²	1	2	yes	complemented
58	#496×C₈₉	C₂²	1	2	yes	complemented
59	#491×C₈₉	C₂²	1	2	yes	complemented
60	#490×C₈₉	C₂²	1	2	yes	complemented
61	#489×C₈₉	C₂²	1	2	yes	complemented
62	#489×C₈₉	C₂²	1	2	yes	complemented
63	#485×C₈₉	C₂²	1	4	yes	complemented
64	#484×C₈₉	C₂²	1	2	yes	—
65	#483×C₈₉	C₂²	1	2	yes	—
66	#482×C₈₉	C₂²	1	4	yes	—
67	#481×C₈₉	C₂²	1	2	yes	—
68	#480×C₈₉	C₂²	1	2	yes	—
69	#479×C₈₉	C₂²	1	4	yes	complemented
70	#479×C₈₉	C₂²	1	4	yes	complemented
71	#478×C₈₉	C₂²	1	4	yes	complemented
72	#478×C₈₉	C₂²	1	4	yes	complemented
73	#467×C₈₉	C₂²	1	4	yes	complemented
74	#466×C₈₉	C₂²	1	4	yes	—
75	#465×C₈₉	C₂²	1	4	yes	—
76	#465×C₈₉	C₂²	1	4	yes	complemented
77	#464×C₈₉	C₂²	1	4	yes	complemented
78	#464×C₈₉	C₂²	1	4	yes	complemented
79	#463×C₈₉	C₂²	1	4	yes	complemented
80	#463×C₈₉	C₂²	1	4	yes	complemented
81	#452×C₈₉	C₂²	1	4	yes	complemented
82	#451×C₈₉	C₂²	1	2	yes	—
83	#450×C₈₉	C₂²	1	2	yes	—
84	#449×C₈₉	C₂²	1	4	yes	—
85	#448×C₈₉	C₂²	1	2	yes	—
86	#447×C₈₉	C₂²	1	2	yes	—
87	#442×C₈₉	C₂²	1	4	yes	complemented
88	#441×C₈₉	C₂²	1	4	yes	complemented
89	#440×C₈₉	C₂²	1	4	yes	complemented
90	#440×C₈₉	C₂²	1	4	yes	complemented
91	#432×C₈₉	C₂²	1	2	yes	—
92	#432×C₈₉	C₂²	1	1	yes	characteristic
93	#432×C₈₉	C₂²	1	1	yes	characteristic
94	#432×C₈₉	C₂²	1	2	yes	complemented
95	#432×C₈₉	C₂²	1	2	yes	complemented
96	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	complemented
97	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
98	C₂×#97×C₈₉	C₂²	1	2	yes	complemented
99	C₂×#41×C₈₉	—	2	1	no	—
100	C₂×#41×C₈₉	—	2	1	no	—
101	C₂×#41×C₈₉	C₂³	1	2	yes	—
102	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₈₉	—	2	1	no	—
104	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₈₉	—	2	1	no	—
106	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
107	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
108	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
112	C₂×D₈×C₈₉	C₂³	1	4	yes	—
113	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
114	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
116	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
117	#127×C₈₉	C₂³	1	1	yes	characteristic
118	#126×C₈₉	—	2	2	no	—
119	#126×C₈₉	—	2	2	no	—
120	#126×C₈₉	—	2	2	no	—
121	#126×C₈₉	—	2	2	no	—
122	#126×C₈₉	—	2	2	no	—
123	#126×C₈₉	—	2	2	no	—
124	#125×C₈₉	—	2	1	no	—
125	#125×C₈₉	—	2	1	no	—
126	#125×C₈₉	—	2	1	no	—
127	#125×C₈₉	—	2	1	no	—
128	#125×C₈₉	C₂³	1	2	yes	—
129	#125×C₈₉	C₂³	1	2	yes	—
130	#125×C₈₉	C₂³	1	2	yes	—
131	#124×C₈₉	—	2	1	no	—
132	#124×C₈₉	—	2	1	no	—
133	#124×C₈₉	—	2	1	no	—
134	#124×C₈₉	—	2	1	no	—
135	#124×C₈₉	C₂³	1	2	yes	—
136	#124×C₈₉	C₂³	1	2	yes	—
137	#124×C₈₉	C₂³	1	2	yes	—
138	#123×C₈₉	—	2	2	no	—
139	#123×C₈₉	—	2	2	no	—
140	#123×C₈₉	—	2	2	no	—
141	#123×C₈₉	—	2	2	no	—
142	#123×C₈₉	—	2	2	no	—
143	#123×C₈₉	—	2	2	no	—
144	#123×C₈₉	—	2	2	no	—
145	C₂²⋊Q₈×C₈₉	—	2	1	no	—
146	C₂²⋊Q₈×C₈₉	—	2	1	no	—
147	C₂²⋊Q₈×C₈₉	—	2	1	no	—
148	C₂²⋊Q₈×C₈₉	—	2	1	no	—
149	C₂²⋊Q₈×C₈₉	—	2	1	no	—
150	C₂²⋊Q₈×C₈₉	—	2	1	no	—
151	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
152	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
153	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
154	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
155	#121×C₈₉	—	2	1	no	—
156	#121×C₈₉	—	2	1	no	—
157	#121×C₈₉	—	2	1	no	—
158	#121×C₈₉	—	2	1	no	—
159	#121×C₈₉	—	2	1	no	—
160	#121×C₈₉	—	2	1	no	—
161	#121×C₈₉	C₂³	1	2	yes	—
162	#121×C₈₉	C₂³	1	2	yes	—
163	#121×C₈₉	C₂³	1	2	yes	—
164	#121×C₈₉	C₂³	1	2	yes	—
165	#120×C₈₉	—	2	2	no	—
166	C₄×Q₈×C₈₉	—	2	1	no	—
167	C₄×Q₈×C₈₉	—	2	1	no	—
168	C₄×Q₈×C₈₉	—	2	1	no	—
169	C₄×Q₈×C₈₉	—	2	1	no	—
170	C₄×Q₈×C₈₉	—	2	1	no	—
171	C₄×Q₈×C₈₉	—	2	1	no	—
172	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
173	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
174	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
175	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
176	C₄×D₄×C₈₉	—	2	2	no	—
177	C₄×D₄×C₈₉	—	2	2	no	—
178	C₄×D₄×C₈₉	—	2	2	no	—
179	C₄×D₄×C₈₉	—	2	2	no	—
180	C₄×D₄×C₈₉	—	2	2	no	—
181	C₄×D₄×C₈₉	—	2	2	no	—
182	C₄×D₄×C₈₉	—	2	2	no	—
183	C₄×D₄×C₈₉	—	2	2	no	—
184	C₄×D₄×C₈₉	—	2	2	no	—
185	C₄×D₄×C₈₉	—	2	2	no	—
186	C₄×D₄×C₈₉	—	2	1	no	—
187	C₄×D₄×C₈₉	—	2	1	no	—
188	C₄×D₄×C₈₉	—	2	1	no	—
189	C₄×D₄×C₈₉	—	2	1	no	—
190	C₄×D₄×C₈₉	—	2	1	no	—
191	C₄×D₄×C₈₉	—	2	1	no	—
192	C₄×D₄×C₈₉	C₂³	1	2	yes	—
193	C₄×D₄×C₈₉	C₂³	1	2	yes	—
194	C₄×D₄×C₈₉	C₂³	1	2	yes	—
195	C₄×D₄×C₈₉	C₂³	1	2	yes	—
196	#117×C₈₉	—	2	1	no	—
197	#117×C₈₉	—	2	1	no	—
198	#117×C₈₉	—	2	2	no	—
199	#117×C₈₉	—	2	2	no	—
200	#117×C₈₉	—	2	2	no	—
201	#117×C₈₉	—	2	2	no	—
202	#117×C₈₉	—	2	2	no	—
203	#117×C₈₉	—	2	2	no	—
204	#117×C₈₉	—	2	2	no	—
205	#117×C₈₉	C₂³	1	2	yes	—
206	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
207	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
208	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
209	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
210	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
213	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
214	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
215	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
216	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
217	C₂×C₄²×C₈₉	—	2	1	no	—
218	C₂×C₄²×C₈₉	—	2	2	no	—
219	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
220	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
221	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
222	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
223	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
224	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
225	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
231	#107×C₈₉	C₂³	1	4	yes	—
232	#107×C₈₉	C₂³	1	4	yes	—
233	#106×C₈₉	C₂³	1	4	yes	—
234	#106×C₈₉	C₂³	1	4	yes	—
235	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
236	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
237	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
238	#103×C₈₉	C₂³	1	4	yes	—
239	#103×C₈₉	C₂³	1	4	yes	—
240	#103×C₈₉	C₂³	1	4	yes	—
241	#103×C₈₉	C₂³	1	4	yes	—
242	#102×C₈₉	C₂³	1	4	yes	—
243	#102×C₈₉	C₂³	1	4	yes	—
244	#102×C₈₉	C₂³	1	4	yes	—
245	#102×C₈₉	C₂³	1	4	yes	—
246	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
247	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
248	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
249	#97×C₈₉	C₂³	1	4	yes	—
250	#97×C₈₉	C₂³	1	2	yes	—
251	#97×C₈₉	C₂³	1	2	yes	—
252	C₂⁴×C₈₉	—	2	1	no	—
253	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
254	#41×C₈₉	—	4	4	no	—
255	#41×C₈₉	—	4	4	no	—
256	#41×C₈₉	—	4	4	no	—
257	C₂×Q₈×C₈₉	—	2	1	no	—
258	C₂×Q₈×C₈₉	—	2	1	no	—
259	C₂×Q₈×C₈₉	—	2	1	no	—
260	C₂×Q₈×C₈₉	—	4	2	no	—
261	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
262	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
263	C₂×D₄×C₈₉	—	2	2	no	—
264	C₂×D₄×C₈₉	—	2	2	no	—
265	C₂×D₄×C₈₉	—	2	2	no	—
266	C₂×D₄×C₈₉	—	2	2	no	—
267	C₂×D₄×C₈₉	—	2	2	no	—
268	C₂×D₄×C₈₉	—	2	1	no	—
269	C₂×D₄×C₈₉	—	2	1	no	—
270	C₂×D₄×C₈₉	—	2	1	no	—
271	C₂×D₄×C₈₉	—	4	2	no	—
272	C₂×D₄×C₈₉	—	4	4	no	—
273	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
274	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₈₉	—	2	1	no	—
276	C₂²×C₄×C₈₉	—	2	1	no	—
277	C₂²×C₄×C₈₉	—	2	1	no	—
278	C₂²×C₄×C₈₉	—	2	2	no	—
279	C₂²×C₄×C₈₉	—	2	2	no	—
280	C₂²×C₄×C₈₉	—	2	2	no	—
281	C₂²×C₄×C₈₉	—	2	2	no	—
282	C₂²×C₄×C₈₉	—	2	2	no	—
283	C₂²×C₄×C₈₉	—	4	2	no	—
284	C₂²×C₄×C₈₉	—	4	2	no	—
285	C₂²×C₄×C₈₉	—	4	2	no	—
286	C₂²×C₄×C₈₉	—	4	4	no	—
287	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
293	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
294	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
295	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
299	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
305	Q₁₆×C₈₉	—	4	4	no	—
306	SD₁₆×C₈₉	—	4	4	no	—
307	SD₁₆×C₈₉	—	4	4	no	—
308	D₈×C₈₉	—	4	4	no	—
309	C₂×C₈×C₈₉	—	4	4	no	—
310	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
311	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
312	C₄⋊C₄×C₈₉	—	2	2	no	—
313	C₄⋊C₄×C₈₉	—	2	2	no	—
314	C₄⋊C₄×C₈₉	—	2	2	no	—
315	C₄⋊C₄×C₈₉	—	2	2	no	—
316	C₄⋊C₄×C₈₉	—	2	2	no	—
317	C₄⋊C₄×C₈₉	—	2	2	no	—
318	C₄⋊C₄×C₈₉	—	2	2	no	—
319	C₄⋊C₄×C₈₉	—	2	2	no	—
320	C₄⋊C₄×C₈₉	—	2	1	no	—
321	C₄⋊C₄×C₈₉	—	2	1	no	—
322	C₄⋊C₄×C₈₉	—	2	1	no	—
323	C₄⋊C₄×C₈₉	—	2	1	no	—
324	C₄⋊C₄×C₈₉	—	2	1	no	—
325	C₄⋊C₄×C₈₉	—	2	1	no	—
326	C₄⋊C₄×C₈₉	—	2	2	no	—
327	C₄⋊C₄×C₈₉	—	2	2	no	—
328	C₄⋊C₄×C₈₉	—	2	2	no	—
329	C₄⋊C₄×C₈₉	—	2	2	no	—
330	C₄⋊C₄×C₈₉	—	2	2	no	—
331	C₄⋊C₄×C₈₉	—	2	2	no	—
332	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
333	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
334	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
335	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
336	C₂²⋊C₄×C₈₉	—	2	2	no	—
337	C₂²⋊C₄×C₈₉	—	2	2	no	—
338	C₂²⋊C₄×C₈₉	—	2	2	no	—
339	C₂²⋊C₄×C₈₉	—	2	2	no	—
340	C₂²⋊C₄×C₈₉	—	2	2	no	—
341	C₂²⋊C₄×C₈₉	—	2	2	no	—
342	C₂²⋊C₄×C₈₉	—	2	2	no	—
343	C₂²⋊C₄×C₈₉	—	2	2	no	—
344	C₂²⋊C₄×C₈₉	—	2	2	no	—
345	C₂²⋊C₄×C₈₉	—	2	2	no	—
346	C₂²⋊C₄×C₈₉	—	2	2	no	—
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	2	no	—
351	C₂²⋊C₄×C₈₉	—	2	2	no	—
352	C₂²⋊C₄×C₈₉	—	2	2	no	—
353	C₂²⋊C₄×C₈₉	—	2	2	no	—
354	C₂²⋊C₄×C₈₉	—	2	2	no	—
355	C₄²×C₈₉	—	2	2	no	—
356	C₄²×C₈₉	—	2	2	no	—
357	C₄²×C₈₉	—	2	2	no	—
358	C₄²×C₈₉	—	2	2	no	—
359	C₄²×C₈₉	—	2	2	no	—
360	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
361	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
362	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
363	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
364	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
365	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
366	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
367	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
368	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
369	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
370	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
371	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
372	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
373	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
374	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
375	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
376	C₂³×C₈₉	—	2	2	no	—
377	C₂³×C₈₉	—	2	2	no	—
378	C₂³×C₈₉	—	2	2	no	—
379	C₂³×C₈₉	—	2	2	no	—
380	C₂³×C₈₉	—	4	1	no	—
381	C₂³×C₈₉	—	4	2	no	—
382	C₂³×C₈₉	—	4	2	no	—
383	C₂³×C₈₉	—	4	2	no	—
384	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
385	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
386	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
387	Q₈×C₈₉	—	2	4	no	—
388	Q₈×C₈₉	—	2	4	no	—
389	Q₈×C₈₉	—	4	2	no	—
390	Q₈×C₈₉	—	4	2	no	—
391	Q₈×C₈₉	—	4	2	no	—
392	D₄×C₈₉	—	2	4	no	—
393	D₄×C₈₉	—	2	4	no	—
394	D₄×C₈₉	—	4	2	no	—
395	D₄×C₈₉	—	4	2	no	—
396	D₄×C₈₉	—	4	2	no	—
397	D₄×C₈₉	—	4	4	no	—
398	D₄×C₈₉	—	4	4	no	—
399	D₄×C₈₉	—	4	4	no	—
400	D₄×C₈₉	—	4	4	no	—
401	D₄×C₈₉	—	4	4	no	—
402	C₂×C₄×C₈₉	—	2	2	no	—
403	C₂×C₄×C₈₉	—	2	2	no	—
404	C₂×C₄×C₈₉	—	2	2	no	—
405	C₂×C₄×C₈₉	—	2	2	no	—
406	C₂×C₄×C₈₉	—	2	2	no	—
407	C₂×C₄×C₈₉	—	2	2	no	—
408	C₂×C₄×C₈₉	—	2	2	no	—
409	C₂×C₄×C₈₉	—	2	2	no	—
410	C₂×C₄×C₈₉	—	2	2	no	—
411	C₂×C₄×C₈₉	—	2	2	no	—
412	C₂×C₄×C₈₉	—	2	2	no	—
413	C₂×C₄×C₈₉	—	2	2	no	—
414	C₂×C₄×C₈₉	—	2	2	no	—
415	C₂×C₄×C₈₉	—	4	1	no	—
416	C₂×C₄×C₈₉	—	4	1	no	—
417	C₂×C₄×C₈₉	—	4	1	no	—
418	C₂×C₄×C₈₉	—	4	1	no	—
419	C₂×C₄×C₈₉	—	4	1	no	—
420	C₂×C₄×C₈₉	—	4	1	no	—
421	C₂×C₄×C₈₉	—	4	1	no	—
422	C₂×C₄×C₈₉	—	4	1	no	—
423	C₂×C₄×C₈₉	—	4	1	no	—
424	C₂×C₄×C₈₉	—	4	1	no	—
425	C₂×C₄×C₈₉	—	4	1	no	—
426	C₂×C₄×C₈₉	—	4	4	no	—
427	C₂×C₄×C₈₉	—	4	4	no	—
428	C₂×C₄×C₈₉	—	4	4	no	—
429	C₂×C₄×C₈₉	—	4	4	no	—
430	C₂×C₄×C₈₉	—	4	4	no	—
431	C₂×C₄×C₈₉	—	4	2	no	—
432	C₂×C₄×C₈₉	—	4	2	no	—
433	C₂×C₄×C₈₉	—	4	2	no	—
434	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
436	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
446	C₈×C₈₉	—	2	4	no	—
447	C₈×C₈₉	—	2	4	no	—
448	C₂²×C₈₉	—	2	1	no	—
449	C₂²×C₈₉	—	2	1	no	—
450	C₂²×C₈₉	—	2	1	no	—
451	C₂²×C₈₉	—	2	1	no	—
452	C₂²×C₈₉	—	2	1	no	—
453	C₂²×C₈₉	—	2	1	no	—
454	C₂²×C₈₉	—	2	1	no	—
455	C₂²×C₈₉	—	4	4	no	—
456	C₂²×C₈₉	—	4	2	no	—
457	C₂²×C₈₉	—	4	2	no	—
458	C₂²×C₈₉	—	4	2	no	—
459	C₂²×C₈₉	—	4	2	no	—
460	C₂²×C₈₉	—	4	2	no	—
461	C₂²×C₈₉	—	4	2	no	—
462	C₂²×C₈₉	—	8	4	no	—
463	C₂²×C₈₉	#575	1	2	yes	—
464	C₂²×C₈₉	#575	1	2	yes	—
465	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
466	C₄×C₈₉	—	2	1	no	—
467	C₄×C₈₉	—	2	1	no	—
468	C₄×C₈₉	—	2	1	no	—
469	C₄×C₈₉	—	2	1	no	—
470	C₄×C₈₉	—	2	1	no	—
471	C₄×C₈₉	—	2	1	no	—
472	C₄×C₈₉	—	2	1	no	—
473	C₄×C₈₉	—	2	1	no	—
474	C₄×C₈₉	—	2	1	no	—
475	C₄×C₈₉	—	2	1	no	—
476	C₄×C₈₉	—	2	1	no	—
477	C₄×C₈₉	—	4	2	no	—
478	C₄×C₈₉	—	4	2	no	—
479	C₄×C₈₉	—	4	2	no	—
480	C₄×C₈₉	—	4	2	no	—
481	C₄×C₈₉	—	4	2	no	—
482	C₄×C₈₉	—	4	2	no	—
483	C₄×C₈₉	#585	1	2	yes	—
484	#60959	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
485	C₂×C₈₉	—	2	2	no	—
486	C₂×C₈₉	—	2	2	no	—
487	C₂×C₈₉	—	4	1	no	—
488	C₂×C₈₉	—	8	2	no	—
489	C₂×C₈₉	—	8	2	no	—
490	C₂×C₈₉	#3449	1	1	yes	characteristic
491	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
492	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
493	#3444	C₂×C₈₉	1	1	yes	characteristic, complemented
494	C₂×#529	C₂×C₈₉	1	1	yes	characteristic, complemented
495	#3250	C₂×C₈₉	1	4	yes	complemented
496	#3240	C₂×C₈₉	1	2	yes	complemented
497	#3236	C₂×C₈₉	1	1	yes	characteristic, complemented
498	#3234	C₂×C₈₉	1	1	yes	characteristic, complemented
499	#3219	C₂×C₈₉	1	2	yes	complemented
500	#3215	C₂×C₈₉	1	1	yes	characteristic, complemented
501	#3213	C₂×C₈₉	1	1	yes	characteristic, complemented
502	#3190	C₂×C₈₉	1	2	yes	complemented
503	#3188	C₂×C₈₉	1	2	yes	complemented
504	#3181	C₂×C₈₉	1	2	yes	complemented
505	#3180	C₂×C₈₉	1	2	yes	complemented
506	#3117	C₂×C₈₉	1	2	yes	complemented
507	#3114	C₂×C₈₉	1	2	yes	complemented
508	#3111	C₂×C₈₉	1	4	yes	complemented
509	C₂×#432	C₂×C₈₉	1	1	yes	characteristic, complemented
510	C₈₉	#60959	1	1	yes	characteristic, direct product factor, Sylow
511	#533	C₂²×C₈₉	1	1	yes	characteristic
512	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
513	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
514	#532	C₂²×C₈₉	1	1	yes	characteristic
515	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
516	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
517	#529	—	2	1	no	—
518	#529	—	2	1	no	—
519	#529	—	2	1	no	—
520	#529	—	2	1	no	—
521	#529	—	2	1	no	—
522	#529	—	2	1	no	—
523	#529	—	2	1	no	—
524	#529	—	2	1	no	—
525	#529	C₂²×C₈₉	1	2	yes	—
526	#529	C₂²×C₈₉	1	2	yes	—
527	#529	C₂²×C₈₉	1	2	yes	—
528	#529	C₂²×C₈₉	1	2	yes	—
529	#529	C₂²×C₈₉	1	2	yes	—
530	#529	C₂²×C₈₉	1	2	yes	complemented
531	C₂×#126	—	2	1	no	—
532	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
533	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
534	#525	—	2	1	no	—
535	#525	—	2	1	no	—
536	#525	C₂²×C₈₉	1	2	yes	—
537	C₂×#123	—	2	1	no	—
538	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
539	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
540	C₄×#41	—	2	1	no	—
541	C₄×#41	—	2	1	no	—
542	C₄×#41	C₂²×C₈₉	1	2	yes	complemented
543	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
544	C₂×C₄×D₄	—	2	1	no	—
545	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
546	C₂×#117	—	2	1	no	—
547	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
548	#501	C₂²×C₈₉	1	2	yes	complemented
549	#501	C₂²×C₈₉	1	2	yes	complemented
550	#497	C₂²×C₈₉	1	2	yes	complemented
551	#496	C₂²×C₈₉	1	2	yes	complemented
552	#491	C₂²×C₈₉	1	2	yes	complemented
553	#490	C₂²×C₈₉	1	2	yes	complemented
554	#489	C₂²×C₈₉	1	2	yes	complemented
555	#489	C₂²×C₈₉	1	2	yes	complemented
556	#485	C₂²×C₈₉	1	4	yes	complemented
557	#484	C₂²×C₈₉	1	2	yes	—
558	#483	C₂²×C₈₉	1	2	yes	—
559	#482	C₂²×C₈₉	1	4	yes	—
560	#481	C₂²×C₈₉	1	2	yes	—
561	#480	C₂²×C₈₉	1	2	yes	—
562	#479	C₂²×C₈₉	1	4	yes	complemented
563	#479	C₂²×C₈₉	1	4	yes	complemented
564	#478	C₂²×C₈₉	1	4	yes	complemented
565	#478	C₂²×C₈₉	1	4	yes	complemented
566	#467	C₂²×C₈₉	1	4	yes	complemented
567	#466	C₂²×C₈₉	1	4	yes	—
568	#465	C₂²×C₈₉	1	4	yes	—
569	#465	C₂²×C₈₉	1	4	yes	complemented
570	#464	C₂²×C₈₉	1	4	yes	complemented
571	#464	C₂²×C₈₉	1	4	yes	complemented
572	#463	C₂²×C₈₉	1	4	yes	complemented
573	#463	C₂²×C₈₉	1	4	yes	complemented
574	#452	C₂²×C₈₉	1	4	yes	complemented
575	#451	C₂²×C₈₉	1	2	yes	—
576	#450	C₂²×C₈₉	1	2	yes	—
577	#449	C₂²×C₈₉	1	4	yes	—
578	#448	C₂²×C₈₉	1	2	yes	—
579	#447	C₂²×C₈₉	1	2	yes	—
580	#442	C₂²×C₈₉	1	4	yes	complemented
581	#441	C₂²×C₈₉	1	4	yes	complemented
582	#440	C₂²×C₈₉	1	4	yes	complemented
583	#440	C₂²×C₈₉	1	4	yes	complemented
584	#432	C₂²×C₈₉	1	2	yes	—
585	#432	C₂²×C₈₉	1	1	yes	characteristic
586	#432	C₂²×C₈₉	1	1	yes	characteristic
587	#432	C₂²×C₈₉	1	2	yes	complemented
588	#432	C₂²×C₈₉	1	2	yes	complemented
589	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	complemented
590	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
591	C₂×#97	C₂²×C₈₉	1	2	yes	complemented
592	C₂×#41	—	2	1	no	—
593	C₂×#41	—	2	1	no	—
594	C₂×#41	C₂³×C₈₉	1	2	yes	—
595	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
596	C₂²×D₄	—	2	1	no	—
597	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
598	C₂³×C₄	—	2	1	no	—
599	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
600	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
601	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
602	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
603	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
604	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
605	C₂×D₈	C₂³×C₈₉	1	4	yes	—
606	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
607	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
608	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
609	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
610	#127	C₂³×C₈₉	1	1	yes	characteristic
611	#126	—	2	2	no	—
612	#126	—	2	2	no	—
613	#126	—	2	2	no	—
614	#126	—	2	2	no	—
615	#126	—	2	2	no	—
616	#126	—	2	2	no	—
617	#125	—	2	1	no	—
618	#125	—	2	1	no	—
619	#125	—	2	1	no	—
620	#125	—	2	1	no	—
621	#125	C₂³×C₈₉	1	2	yes	—
622	#125	C₂³×C₈₉	1	2	yes	—
623	#125	C₂³×C₈₉	1	2	yes	—
624	#124	—	2	1	no	—
625	#124	—	2	1	no	—
626	#124	—	2	1	no	—
627	#124	—	2	1	no	—
628	#124	C₂³×C₈₉	1	2	yes	—
629	#124	C₂³×C₈₉	1	2	yes	—
630	#124	C₂³×C₈₉	1	2	yes	—
631	#123	—	2	2	no	—
632	#123	—	2	2	no	—
633	#123	—	2	2	no	—
634	#123	—	2	2	no	—
635	#123	—	2	2	no	—
636	#123	—	2	2	no	—
637	#123	—	2	2	no	—
638	C₂²⋊Q₈	—	2	1	no	—
639	C₂²⋊Q₈	—	2	1	no	—
640	C₂²⋊Q₈	—	2	1	no	—
641	C₂²⋊Q₈	—	2	1	no	—
642	C₂²⋊Q₈	—	2	1	no	—
643	C₂²⋊Q₈	—	2	1	no	—
644	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
645	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
646	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
647	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
648	#121	—	2	1	no	—
649	#121	—	2	1	no	—
650	#121	—	2	1	no	—
651	#121	—	2	1	no	—
652	#121	—	2	1	no	—
653	#121	—	2	1	no	—
654	#121	C₂³×C₈₉	1	2	yes	—
655	#121	C₂³×C₈₉	1	2	yes	—
656	#121	C₂³×C₈₉	1	2	yes	—
657	#121	C₂³×C₈₉	1	2	yes	—
658	#120	—	2	2	no	—
659	C₄×Q₈	—	2	1	no	—
660	C₄×Q₈	—	2	1	no	—
661	C₄×Q₈	—	2	1	no	—
662	C₄×Q₈	—	2	1	no	—
663	C₄×Q₈	—	2	1	no	—
664	C₄×Q₈	—	2	1	no	—
665	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
666	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
667	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
668	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	—	2	2	no	—
678	C₄×D₄	—	2	2	no	—
679	C₄×D₄	—	2	1	no	—
680	C₄×D₄	—	2	1	no	—
681	C₄×D₄	—	2	1	no	—
682	C₄×D₄	—	2	1	no	—
683	C₄×D₄	—	2	1	no	—
684	C₄×D₄	—	2	1	no	—
685	C₄×D₄	C₂³×C₈₉	1	2	yes	—
686	C₄×D₄	C₂³×C₈₉	1	2	yes	—
687	C₄×D₄	C₂³×C₈₉	1	2	yes	—
688	C₄×D₄	C₂³×C₈₉	1	2	yes	—
689	#117	—	2	1	no	—
690	#117	—	2	1	no	—
691	#117	—	2	2	no	—
692	#117	—	2	2	no	—
693	#117	—	2	2	no	—
694	#117	—	2	2	no	—
695	#117	—	2	2	no	—
696	#117	—	2	2	no	—
697	#117	—	2	2	no	—
698	#117	C₂³×C₈₉	1	2	yes	—
699	C₂×C₄⋊C₄	—	2	1	no	—
700	C₂×C₄⋊C₄	—	2	1	no	—
701	C₂×C₄⋊C₄	—	2	1	no	—
702	C₂×C₄⋊C₄	—	2	1	no	—
703	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
704	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
705	C₂×C₂²⋊C₄	—	2	1	no	—
706	C₂×C₂²⋊C₄	—	2	1	no	—
707	C₂×C₂²⋊C₄	—	2	1	no	—
708	C₂×C₂²⋊C₄	—	2	1	no	—
709	C₂×C₂²⋊C₄	—	2	1	no	—
710	C₂×C₄²	—	2	1	no	—
711	C₂×C₄²	—	2	2	no	—
712	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
713	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
714	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
715	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
716	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
717	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
718	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
719	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
720	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
721	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
722	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
723	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
724	#107	C₂³×C₈₉	1	4	yes	—
725	#107	C₂³×C₈₉	1	4	yes	—
726	#106	C₂³×C₈₉	1	4	yes	—
727	#106	C₂³×C₈₉	1	4	yes	—
728	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
729	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
730	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
731	#103	C₂³×C₈₉	1	4	yes	—
732	#103	C₂³×C₈₉	1	4	yes	—
733	#103	C₂³×C₈₉	1	4	yes	—
734	#103	C₂³×C₈₉	1	4	yes	—
735	#102	C₂³×C₈₉	1	4	yes	—
736	#102	C₂³×C₈₉	1	4	yes	—
737	#102	C₂³×C₈₉	1	4	yes	—
738	#102	C₂³×C₈₉	1	4	yes	—
739	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
740	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
741	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
742	#97	C₂³×C₈₉	1	4	yes	—
743	#97	C₂³×C₈₉	1	2	yes	—
744	#97	C₂³×C₈₉	1	2	yes	—
745	C₂⁴	—	2	1	no	—
746	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
747	#41	—	4	4	no	—
748	#41	—	4	4	no	—
749	#41	—	4	4	no	—
750	C₂×Q₈	—	2	1	no	—
751	C₂×Q₈	—	2	1	no	—
752	C₂×Q₈	—	2	1	no	—
753	C₂×Q₈	—	4	2	no	—
754	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
755	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	2	no	—
758	C₂×D₄	—	2	2	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	1	no	—
762	C₂×D₄	—	2	1	no	—
763	C₂×D₄	—	2	1	no	—
764	C₂×D₄	—	4	2	no	—
765	C₂×D₄	—	4	4	no	—
766	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
767	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	2	1	no	—
770	C₂²×C₄	—	2	1	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	4	2	no	—
777	C₂²×C₄	—	4	2	no	—
778	C₂²×C₄	—	4	2	no	—
779	C₂²×C₄	—	4	4	no	—
780	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
781	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
782	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
783	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
784	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
785	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
786	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
787	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
788	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
789	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
790	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
791	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
792	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
793	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
794	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
798	Q₁₆	—	4	4	no	—
799	SD₁₆	—	4	4	no	—
800	SD₁₆	—	4	4	no	—
801	D₈	—	4	4	no	—
802	C₂×C₈	—	4	4	no	—
803	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
804	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	1	no	—
814	C₄⋊C₄	—	2	1	no	—
815	C₄⋊C₄	—	2	1	no	—
816	C₄⋊C₄	—	2	1	no	—
817	C₄⋊C₄	—	2	1	no	—
818	C₄⋊C₄	—	2	1	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
826	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
827	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
828	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	2	no	—
851	C₄²	—	2	2	no	—
852	C₄²	—	2	2	no	—
853	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
854	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
855	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
856	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
857	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
858	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
859	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
860	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
861	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
862	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
863	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
864	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
865	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
866	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
867	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
868	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
869	C₂³	—	2	2	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	4	1	no	—
874	C₂³	—	4	2	no	—
875	C₂³	—	4	2	no	—
876	C₂³	—	4	2	no	—
877	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
878	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
879	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
880	Q₈	—	2	4	no	—
881	Q₈	—	2	4	no	—
882	Q₈	—	4	2	no	—
883	Q₈	—	4	2	no	—
884	Q₈	—	4	2	no	—
885	D₄	—	2	4	no	—
886	D₄	—	2	4	no	—
887	D₄	—	4	2	no	—
888	D₄	—	4	2	no	—
889	D₄	—	4	2	no	—
890	D₄	—	4	4	no	—
891	D₄	—	4	4	no	—
892	D₄	—	4	4	no	—
893	D₄	—	4	4	no	—
894	D₄	—	4	4	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	4	1	no	—
909	C₂×C₄	—	4	1	no	—
910	C₂×C₄	—	4	1	no	—
911	C₂×C₄	—	4	1	no	—
912	C₂×C₄	—	4	1	no	—
913	C₂×C₄	—	4	1	no	—
914	C₂×C₄	—	4	1	no	—
915	C₂×C₄	—	4	1	no	—
916	C₂×C₄	—	4	1	no	—
917	C₂×C₄	—	4	1	no	—
918	C₂×C₄	—	4	1	no	—
919	C₂×C₄	—	4	4	no	—
920	C₂×C₄	—	4	4	no	—
921	C₂×C₄	—	4	4	no	—
922	C₂×C₄	—	4	4	no	—
923	C₂×C₄	—	4	4	no	—
924	C₂×C₄	—	4	2	no	—
925	C₂×C₄	—	4	2	no	—
926	C₂×C₄	—	4	2	no	—
927	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
928	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
929	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
930	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
931	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
932	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
933	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
934	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
935	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
936	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
937	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
938	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
939	C₈	—	2	4	no	—
940	C₈	—	2	4	no	—
941	C₂²	—	2	1	no	—
942	C₂²	—	2	1	no	—
943	C₂²	—	2	1	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	2	1	no	—
948	C₂²	—	4	4	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	8	4	no	—
956	C₂²	#575×C₈₉	1	2	yes	—
957	C₂²	#575×C₈₉	1	2	yes	—
958	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
959	C₄	—	2	1	no	—
960	C₄	—	2	1	no	—
961	C₄	—	2	1	no	—
962	C₄	—	2	1	no	—
963	C₄	—	2	1	no	—
964	C₄	—	2	1	no	—
965	C₄	—	2	1	no	—
966	C₄	—	2	1	no	—
967	C₄	—	2	1	no	—
968	C₄	—	2	1	no	—
969	C₄	—	2	1	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	2	no	—
972	C₄	—	4	2	no	—
973	C₄	—	4	2	no	—
974	C₄	—	4	2	no	—
975	C₄	—	4	2	no	—
976	C₄	#585×C₈₉	1	2	yes	—
977	C₂	—	2	2	no	—
978	C₂	—	2	2	no	—
979	C₂	—	4	1	no	—
980	C₂	—	8	2	no	—
981	C₂	—	8	2	no	—
982	C₂	C₈₉×#3449	1	1	yes	characteristic
983	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
984	C₂	C₂×#575×C₈₉	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 ◁ C₂²×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3444	C₂	semidirect
2. C₂×#529×C₈₉	C₂	semidirect
3. C₈₉×#3250	C₂	semidirect
4. C₈₉×#3240	C₂	semidirect
5. C₈₉×#3236	C₂	semidirect
6. C₈₉×#3234	C₂	semidirect
7. C₈₉×#3219	C₂	semidirect
8. C₈₉×#3215	C₂	semidirect
9. C₈₉×#3213	C₂	semidirect
10. C₈₉×#3190	C₂	semidirect
11. C₈₉×#3188	C₂	semidirect
12. C₈₉×#3181	C₂	semidirect
13. C₈₉×#3180	C₂	semidirect
14. C₈₉×#3117	C₂	semidirect
15. C₈₉×#3114	C₂	semidirect
16. C₈₉×#3111	C₂	semidirect
17. C₂×#432×C₈₉	C₂	semidirect
19. #533×C₈₉	C₂²	semidirect
20. #533×C₈₉	C₂²	semidirect
22. #532×C₈₉	C₂²	semidirect
23. #532×C₈₉	C₂²	semidirect
37. #529×C₈₉	C₂²	semidirect
49. C₄×#41×C₈₉	C₂²	semidirect
55. #501×C₈₉	C₂²	semidirect
56. #501×C₈₉	C₂²	semidirect
57. #497×C₈₉	C₂²	semidirect
58. #496×C₈₉	C₂²	semidirect
59. #491×C₈₉	C₂²	semidirect
60. #490×C₈₉	C₂²	semidirect
61. #489×C₈₉	C₂²	semidirect
62. #489×C₈₉	C₂²	semidirect
63. #485×C₈₉	C₂²	semidirect
69. #479×C₈₉	C₂²	semidirect
70. #479×C₈₉	C₂²	semidirect
71. #478×C₈₉	C₂²	semidirect
72. #478×C₈₉	C₂²	semidirect
73. #467×C₈₉	C₂²	semidirect
76. #465×C₈₉	C₂²	semidirect
77. #464×C₈₉	C₂²	semidirect
78. #464×C₈₉	C₂²	semidirect
79. #463×C₈₉	C₂²	semidirect
80. #463×C₈₉	C₂²	semidirect
81. #452×C₈₉	C₂²	semidirect
87. #442×C₈₉	C₂²	semidirect
88. #441×C₈₉	C₂²	semidirect
89. #440×C₈₉	C₂²	semidirect
90. #440×C₈₉	C₂²	semidirect
94. #432×C₈₉	C₂²	semidirect
95. #432×C₈₉	C₂²	semidirect
96. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
98. C₂×#97×C₈₉	C₂²	semidirect
484. #60959	C₈₉	direct (N × H)
493. #3444	C₂×C₈₉	semidirect
494. C₂×#529	C₂×C₈₉	semidirect
495. #3250	C₂×C₈₉	semidirect
496. #3240	C₂×C₈₉	semidirect
497. #3236	C₂×C₈₉	semidirect
498. #3234	C₂×C₈₉	semidirect
499. #3219	C₂×C₈₉	semidirect
500. #3215	C₂×C₈₉	semidirect
501. #3213	C₂×C₈₉	semidirect
502. #3190	C₂×C₈₉	semidirect
503. #3188	C₂×C₈₉	semidirect
504. #3181	C₂×C₈₉	semidirect
505. #3180	C₂×C₈₉	semidirect
506. #3117	C₂×C₈₉	semidirect
507. #3114	C₂×C₈₉	semidirect
508. #3111	C₂×C₈₉	semidirect
509. C₂×#432	C₂×C₈₉	semidirect
510. C₈₉	#60959	direct (N × H)
512. #533	C₂²×C₈₉	semidirect
513. #533	C₂²×C₈₉	semidirect
515. #532	C₂²×C₈₉	semidirect
516. #532	C₂²×C₈₉	semidirect
530. #529	C₂²×C₈₉	semidirect
542. C₄×#41	C₂²×C₈₉	semidirect
548. #501	C₂²×C₈₉	semidirect
549. #501	C₂²×C₈₉	semidirect
550. #497	C₂²×C₈₉	semidirect
551. #496	C₂²×C₈₉	semidirect
552. #491	C₂²×C₈₉	semidirect
553. #490	C₂²×C₈₉	semidirect
554. #489	C₂²×C₈₉	semidirect
555. #489	C₂²×C₈₉	semidirect
556. #485	C₂²×C₈₉	semidirect
562. #479	C₂²×C₈₉	semidirect
563. #479	C₂²×C₈₉	semidirect
564. #478	C₂²×C₈₉	semidirect
565. #478	C₂²×C₈₉	semidirect
566. #467	C₂²×C₈₉	semidirect
569. #465	C₂²×C₈₉	semidirect
570. #464	C₂²×C₈₉	semidirect
571. #464	C₂²×C₈₉	semidirect
572. #463	C₂²×C₈₉	semidirect
573. #463	C₂²×C₈₉	semidirect
574. #452	C₂²×C₈₉	semidirect
580. #442	C₂²×C₈₉	semidirect
581. #441	C₂²×C₈₉	semidirect
582. #440	C₂²×C₈₉	semidirect
583. #440	C₂²×C₈₉	semidirect
587. #432	C₂²×C₈₉	semidirect
588. #432	C₂²×C₈₉	semidirect
589. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
591. C₂×#97	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×#3444	2
C₂×#529×C₈₉	2
C₈₉×#3250	2
C₈₉×#3240	2
C₈₉×#3236	2
C₈₉×#3234	2
C₈₉×#3219	2
C₈₉×#3215	2
C₈₉×#3213	2
C₈₉×#3190	2
C₈₉×#3188	2
C₈₉×#3181	2
C₈₉×#3180	2
C₈₉×#3117	2
C₈₉×#3114	2
C₈₉×#3111	2
C₂×#432×C₈₉	2
#60959	89

Subgroups — C89×#60959 #36438807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60959 #36438807