Subgroups — C₈₉×#62604 #36440452

Order 22784.

1708 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3561	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3552	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3377	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3367	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3320	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3314	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3313	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3308	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3299	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3297	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3243	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3230	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3225	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3211	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3181	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#3175	C₂	1	2	yes	maximal, complemented
17	C₈₉×#3137	C₂	1	2	yes	maximal, complemented
18	C₂×#489×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2968	C₂	1	1	yes	maximal, characteristic, complemented
20	#563×C₈₉	—	2	2	no	—
21	#563×C₈₉	—	2	1	no	—
22	#562×C₈₉	—	2	1	no	—
23	#557×C₈₉	C₂²	1	1	yes	characteristic, complemented
24	#556×C₈₉	C₂²	1	2	yes	—
25	#556×C₈₉	C₂²	1	1	yes	characteristic, complemented
26	#554×C₈₉	C₂²	1	2	yes	—
27	#553×C₈₉	C₂²	1	2	yes	—
28	#551×C₈₉	—	2	2	no	—
29	D₄×Q₈×C₈₉	—	2	1	no	—
30	D₄×Q₈×C₈₉	C₂²	1	2	yes	—
31	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
32	#548×C₈₉	—	2	1	no	—
33	#548×C₈₉	C₂²	1	2	yes	—
34	#547×C₈₉	C₂²	1	1	yes	characteristic, complemented
35	#546×C₈₉	C₂²	1	2	yes	—
36	#544×C₈₉	C₂²	1	2	yes	complemented
37	#543×C₈₉	—	2	1	no	—
38	#542×C₈₉	—	2	2	no	—
39	#542×C₈₉	C₂²	1	2	yes	—
40	#542×C₈₉	C₂²	1	2	yes	complemented
41	#541×C₈₉	—	2	1	no	—
42	#539×C₈₉	—	2	2	no	—
43	#538×C₈₉	—	2	1	no	—
44	#536×C₈₉	—	2	1	no	—
45	#536×C₈₉	C₂²	1	2	yes	—
46	#533×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
48	#529×C₈₉	C₂²	1	1	yes	characteristic
49	#529×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
51	#501×C₈₉	C₂²	1	1	yes	characteristic, complemented
52	#500×C₈₉	C₂²	1	2	yes	complemented
53	#497×C₈₉	C₂²	1	1	yes	characteristic, complemented
54	#495×C₈₉	C₂²	1	2	yes	—
55	#491×C₈₉	C₂²	1	2	yes	complemented
56	#491×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	#489×C₈₉	C₂²	1	2	yes	—
58	#489×C₈₉	C₂²	1	2	yes	—
59	#489×C₈₉	C₂²	1	2	yes	—
60	#489×C₈₉	C₂²	1	2	yes	—
61	#489×C₈₉	C₂²	1	2	yes	—
62	#489×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	#488×C₈₉	C₂²	1	2	yes	—
64	#488×C₈₉	C₂²	1	2	yes	—
65	#487×C₈₉	C₂²	1	2	yes	complemented
66	#487×C₈₉	C₂²	1	2	yes	complemented
67	#485×C₈₉	C₂²	1	2	yes	complemented
68	#484×C₈₉	C₂²	1	2	yes	—
69	#484×C₈₉	C₂²	1	2	yes	—
70	#484×C₈₉	C₂²	1	2	yes	complemented
71	#482×C₈₉	C₂²	1	2	yes	—
72	#480×C₈₉	C₂²	1	2	yes	—
73	#479×C₈₉	C₂²	1	2	yes	complemented
74	#478×C₈₉	C₂²	1	2	yes	—
75	#477×C₈₉	C₂²	1	2	yes	complemented
76	#477×C₈₉	C₂²	1	2	yes	complemented
77	#477×C₈₉	C₂²	1	2	yes	complemented
78	#474×C₈₉	C₂²	1	2	yes	—
79	#468×C₈₉	C₂²	1	2	yes	—
80	#468×C₈₉	C₂²	1	2	yes	complemented
81	#467×C₈₉	C₂²	1	2	yes	—
82	#467×C₈₉	C₂²	1	2	yes	complemented
83	#466×C₈₉	C₂²	1	2	yes	—
84	#465×C₈₉	C₂²	1	2	yes	—
85	#464×C₈₉	C₂²	1	2	yes	—
86	#464×C₈₉	C₂²	1	2	yes	—
87	#463×C₈₉	C₂²	1	2	yes	—
88	#463×C₈₉	C₂²	1	2	yes	—
89	#462×C₈₉	C₂²	1	2	yes	complemented
90	#461×C₈₉	C₂²	1	2	yes	complemented
91	#452×C₈₉	C₂²	1	2	yes	—
92	#451×C₈₉	C₂²	1	1	yes	characteristic
93	#451×C₈₉	C₂²	1	2	yes	complemented
94	#450×C₈₉	C₂²	1	1	yes	characteristic
95	#449×C₈₉	C₂²	1	2	yes	—
96	#448×C₈₉	C₂²	1	1	yes	characteristic
97	#448×C₈₉	C₂²	1	2	yes	complemented
98	#447×C₈₉	C₂²	1	1	yes	characteristic
99	#446×C₈₉	C₂²	1	2	yes	complemented
100	#441×C₈₉	C₂²	1	2	yes	complemented
101	#440×C₈₉	C₂²	1	2	yes	—
102	#440×C₈₉	C₂²	1	2	yes	complemented
103	#440×C₈₉	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
105	C₄×D₈×C₈₉	C₂²	1	2	yes	—
106	#435×C₈₉	C₂²	1	2	yes	—
107	#435×C₈₉	C₂²	1	2	yes	complemented
108	C₈×D₄×C₈₉	C₂²	1	2	yes	—
109	#433×C₈₉	C₂²	1	2	yes	complemented
110	#431×C₈₉	C₂²	1	1	yes	characteristic
111	#419×C₈₉	C₂²	1	2	yes	complemented
112	#417×C₈₉	C₂²	1	2	yes	—
113	#416×C₈₉	C₂²	1	2	yes	—
114	C₂×#103×C₈₉	C₂²	1	2	yes	—
115	C₂×#103×C₈₉	C₂²	1	2	yes	complemented
116	C₂×#102×C₈₉	C₂²	1	2	yes	—
117	#405×C₈₉	C₂²	1	2	yes	complemented
118	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
119	C₂×#41×C₈₉	—	2	1	no	—
120	C₂×#41×C₈₉	C₂³	1	2	yes	—
121	C₂²×Q₈×C₈₉	—	2	1	no	—
122	C₂²×Q₈×C₈₉	—	2	1	no	—
123	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
125	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
126	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
127	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
131	C₂×D₈×C₈₉	C₂³	1	2	yes	—
132	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
133	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
134	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
135	C₄⋊Q₈×C₈₉	—	2	1	no	—
136	C₄⋊Q₈×C₈₉	—	2	2	no	—
137	C₄⋊Q₈×C₈₉	—	2	2	no	—
138	C₄⋊Q₈×C₈₉	—	2	1	no	—
139	C₄⋊Q₈×C₈₉	—	2	1	no	—
140	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
141	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
142	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
143	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
144	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
145	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
146	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
147	#126×C₈₉	—	2	2	no	—
148	#126×C₈₉	—	2	2	no	—
149	#126×C₈₉	—	2	2	no	—
150	#126×C₈₉	—	2	2	no	—
151	#126×C₈₉	—	2	2	no	—
152	#126×C₈₉	—	2	2	no	—
153	#126×C₈₉	—	2	1	no	—
154	#126×C₈₉	D₄	1	2	yes	—
155	#125×C₈₉	—	2	2	no	—
156	#125×C₈₉	—	2	2	no	—
157	#125×C₈₉	—	2	2	no	—
158	#125×C₈₉	—	2	1	no	—
159	#125×C₈₉	D₄	1	1	yes	characteristic
160	#125×C₈₉	C₂³	1	2	yes	—
161	#125×C₈₉	C₂³	1	1	yes	characteristic
162	#124×C₈₉	—	2	1	no	—
163	#124×C₈₉	—	2	2	no	—
164	#124×C₈₉	—	2	2	no	—
165	#124×C₈₉	—	2	2	no	—
166	#124×C₈₉	—	2	1	no	—
167	#124×C₈₉	—	2	1	no	—
168	#124×C₈₉	D₄	1	1	yes	characteristic
169	#124×C₈₉	C₂³	1	2	yes	—
170	#124×C₈₉	C₂³	1	2	yes	—
171	#124×C₈₉	C₂³	1	2	yes	—
172	#124×C₈₉	C₂³	1	1	yes	characteristic
173	#123×C₈₉	—	2	1	no	—
174	#123×C₈₉	—	2	2	no	—
175	#123×C₈₉	—	2	2	no	—
176	#123×C₈₉	—	2	2	no	—
177	#123×C₈₉	—	2	2	no	—
178	#123×C₈₉	—	2	2	no	—
179	#123×C₈₉	—	2	2	no	—
180	#123×C₈₉	—	2	2	no	—
181	#123×C₈₉	D₄	1	2	yes	—
182	C₂²⋊Q₈×C₈₉	—	2	2	no	—
183	C₂²⋊Q₈×C₈₉	—	2	1	no	—
184	C₂²⋊Q₈×C₈₉	—	2	2	no	—
185	C₂²⋊Q₈×C₈₉	—	2	2	no	—
186	C₂²⋊Q₈×C₈₉	—	2	2	no	—
187	C₂²⋊Q₈×C₈₉	—	2	1	no	—
188	C₂²⋊Q₈×C₈₉	—	2	1	no	—
189	C₂²⋊Q₈×C₈₉	—	2	2	no	—
190	C₂²⋊Q₈×C₈₉	—	2	2	no	—
191	C₂²⋊Q₈×C₈₉	—	2	2	no	—
192	C₂²⋊Q₈×C₈₉	—	2	2	no	—
193	C₂²⋊Q₈×C₈₉	—	2	2	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	—	2	2	no	—
198	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
199	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
200	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
201	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
202	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
203	#121×C₈₉	—	2	2	no	—
204	#121×C₈₉	—	2	2	no	—
205	#121×C₈₉	—	2	2	no	—
206	#121×C₈₉	D₄	1	1	yes	characteristic
207	#121×C₈₉	C₂³	1	1	yes	characteristic
208	#121×C₈₉	C₂³	1	2	yes	—
209	#121×C₈₉	C₂³	1	2	yes	—
210	#120×C₈₉	—	2	2	no	—
211	C₄×Q₈×C₈₉	—	2	1	no	—
212	C₄×Q₈×C₈₉	—	2	1	no	—
213	C₄×Q₈×C₈₉	—	2	1	no	—
214	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
215	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
216	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
217	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₈₉	—	2	2	no	—
220	C₄×D₄×C₈₉	—	2	2	no	—
221	C₄×D₄×C₈₉	—	2	1	no	—
222	C₄×D₄×C₈₉	—	2	2	no	—
223	C₄×D₄×C₈₉	—	2	2	no	—
224	C₄×D₄×C₈₉	C₂³	1	2	yes	—
225	C₄×D₄×C₈₉	C₂³	1	2	yes	—
226	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₈₉	C₂³	1	2	yes	—
228	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
229	#117×C₈₉	—	2	1	no	—
230	#117×C₈₉	—	2	2	no	—
231	#117×C₈₉	—	2	1	no	—
232	#117×C₈₉	C₂³	1	2	yes	—
233	#117×C₈₉	C₂³	1	2	yes	—
234	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
235	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
236	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
239	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
240	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
241	#107×C₈₉	C₂³	1	2	yes	—
242	#107×C₈₉	C₂³	1	2	yes	—
243	#107×C₈₉	C₂³	1	2	yes	—
244	#107×C₈₉	C₂³	1	2	yes	—
245	#107×C₈₉	C₂³	1	2	yes	—
246	#106×C₈₉	C₂³	1	2	yes	—
247	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
248	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
249	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
250	#103×C₈₉	C₂³	1	2	yes	—
251	#103×C₈₉	C₂³	1	2	yes	—
252	#103×C₈₉	C₂³	1	2	yes	—
253	#103×C₈₉	C₂³	1	2	yes	—
254	#103×C₈₉	C₂³	1	2	yes	—
255	#103×C₈₉	C₂³	1	2	yes	—
256	#103×C₈₉	C₂³	1	2	yes	—
257	#103×C₈₉	C₂³	1	2	yes	—
258	#103×C₈₉	C₂³	1	2	yes	—
259	#103×C₈₉	C₂³	1	2	yes	—
260	#103×C₈₉	C₂³	1	2	yes	—
261	#103×C₈₉	C₂³	1	2	yes	—
262	#103×C₈₉	C₂³	1	2	yes	—
263	#102×C₈₉	C₂³	1	2	yes	—
264	#102×C₈₉	C₂³	1	2	yes	—
265	#102×C₈₉	C₂³	1	2	yes	—
266	#102×C₈₉	C₂³	1	2	yes	—
267	#102×C₈₉	C₂³	1	2	yes	—
268	#102×C₈₉	C₂³	1	2	yes	—
269	#102×C₈₉	C₂³	1	2	yes	—
270	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
271	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
272	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
273	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
274	#97×C₈₉	C₂³	1	1	yes	characteristic
275	#97×C₈₉	C₂³	1	1	yes	characteristic
276	#97×C₈₉	C₂³	1	2	yes	—
277	#97×C₈₉	C₂³	1	2	yes	—
278	C₄×C₈×C₈₉	C₂³	1	2	yes	—
279	C₄×C₈×C₈₉	C₂³	1	2	yes	—
280	C₂⁴×C₈₉	—	2	1	no	—
281	#41×C₈₉	—	4	2	no	—
282	#41×C₈₉	—	4	2	no	—
283	#41×C₈₉	—	8	2	no	—
284	C₂×Q₈×C₈₉	—	2	1	no	—
285	C₂×Q₈×C₈₉	—	2	1	no	—
286	C₂×Q₈×C₈₉	—	2	1	no	—
287	C₂×Q₈×C₈₉	—	2	2	no	—
288	C₂×Q₈×C₈₉	—	2	2	no	—
289	C₂×Q₈×C₈₉	—	2	1	no	—
290	C₂×Q₈×C₈₉	—	2	2	no	—
291	C₂×Q₈×C₈₉	—	4	2	no	—
292	C₂×Q₈×C₈₉	—	4	2	no	—
293	C₂×Q₈×C₈₉	—	4	2	no	—
294	C₂×Q₈×C₈₉	—	8	2	no	—
295	C₂×Q₈×C₈₉	—	8	2	no	—
296	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
297	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
298	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
299	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
300	C₂×D₄×C₈₉	—	2	1	no	—
301	C₂×D₄×C₈₉	—	2	2	no	—
302	C₂×D₄×C₈₉	—	2	2	no	—
303	C₂×D₄×C₈₉	—	2	2	no	—
304	C₂×D₄×C₈₉	—	2	1	no	—
305	C₂×D₄×C₈₉	—	4	2	no	—
306	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
307	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
308	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
309	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₈₉	—	2	1	no	—
311	C₂²×C₄×C₈₉	—	2	2	no	—
312	C₂²×C₄×C₈₉	—	2	2	no	—
313	C₂²×C₄×C₈₉	—	2	2	no	—
314	C₂²×C₄×C₈₉	—	2	1	no	—
315	C₂²×C₄×C₈₉	—	2	2	no	—
316	C₂²×C₄×C₈₉	—	2	2	no	—
317	C₂²×C₄×C₈₉	—	2	2	no	—
318	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
322	Q₁₆×C₈₉	—	4	2	no	—
323	Q₁₆×C₈₉	—	4	2	no	—
324	SD₁₆×C₈₉	—	4	2	no	—
325	SD₁₆×C₈₉	—	4	2	no	—
326	SD₁₆×C₈₉	—	4	2	no	—
327	D₈×C₈₉	—	4	2	no	—
328	M₁₆×C₈₉	—	4	2	no	—
329	C₂×C₈×C₈₉	—	4	2	no	—
330	C₂×C₈×C₈₉	—	4	2	no	—
331	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
332	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
333	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
334	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
335	C₄⋊C₄×C₈₉	—	2	1	no	—
336	C₄⋊C₄×C₈₉	—	2	2	no	—
337	C₄⋊C₄×C₈₉	—	2	1	no	—
338	C₄⋊C₄×C₈₉	—	2	2	no	—
339	C₄⋊C₄×C₈₉	—	2	2	no	—
340	C₄⋊C₄×C₈₉	—	2	2	no	—
341	C₄⋊C₄×C₈₉	—	2	1	no	—
342	C₄⋊C₄×C₈₉	—	2	1	no	—
343	C₄⋊C₄×C₈₉	—	2	1	no	—
344	C₄⋊C₄×C₈₉	—	2	1	no	—
345	C₄⋊C₄×C₈₉	—	2	2	no	—
346	C₄⋊C₄×C₈₉	—	2	2	no	—
347	C₄⋊C₄×C₈₉	—	2	1	no	—
348	C₄⋊C₄×C₈₉	—	2	2	no	—
349	C₄⋊C₄×C₈₉	—	2	2	no	—
350	C₄⋊C₄×C₈₉	—	2	2	no	—
351	C₄⋊C₄×C₈₉	—	2	2	no	—
352	C₄⋊C₄×C₈₉	—	2	1	no	—
353	C₄⋊C₄×C₈₉	—	2	2	no	—
354	C₄⋊C₄×C₈₉	—	2	2	no	—
355	C₄⋊C₄×C₈₉	—	2	2	no	—
356	C₄⋊C₄×C₈₉	—	2	2	no	—
357	C₄⋊C₄×C₈₉	—	2	1	no	—
358	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
359	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
364	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
368	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
369	C₂²⋊C₄×C₈₉	—	2	2	no	—
370	C₂²⋊C₄×C₈₉	—	2	2	no	—
371	C₂²⋊C₄×C₈₉	—	2	1	no	—
372	C₂²⋊C₄×C₈₉	—	2	2	no	—
373	C₂²⋊C₄×C₈₉	—	2	2	no	—
374	C₂²⋊C₄×C₈₉	—	2	2	no	—
375	C₂²⋊C₄×C₈₉	—	2	2	no	—
376	C₂²⋊C₄×C₈₉	—	2	2	no	—
377	C₂²⋊C₄×C₈₉	—	2	2	no	—
378	C₂²⋊C₄×C₈₉	—	2	2	no	—
379	C₂²⋊C₄×C₈₉	—	2	2	no	—
380	C₂²⋊C₄×C₈₉	—	2	2	no	—
381	C₂²⋊C₄×C₈₉	—	2	1	no	—
382	C₂²⋊C₄×C₈₉	—	2	1	no	—
383	C₂²⋊C₄×C₈₉	—	2	2	no	—
384	C₂²⋊C₄×C₈₉	—	2	1	no	—
385	C₂²⋊C₄×C₈₉	—	2	2	no	—
386	C₂²⋊C₄×C₈₉	—	2	2	no	—
387	C₂²⋊C₄×C₈₉	—	2	1	no	—
388	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
389	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
390	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
391	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
392	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
393	C₄²×C₈₉	—	2	2	no	—
394	C₄²×C₈₉	—	2	1	no	—
395	C₄²×C₈₉	—	2	2	no	—
396	C₄²×C₈₉	—	2	2	no	—
397	C₄²×C₈₉	—	2	2	no	—
398	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
401	C₄²×C₈₉	C₂⁴	1	2	yes	—
402	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
403	C₂³×C₈₉	—	2	1	no	—
404	C₂³×C₈₉	—	2	2	no	—
405	C₂³×C₈₉	—	4	2	no	—
406	C₂³×C₈₉	—	8	1	no	—
407	C₂³×C₈₉	—	8	1	no	—
408	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
409	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
410	Q₈×C₈₉	—	2	2	no	—
411	Q₈×C₈₉	—	2	2	no	—
412	Q₈×C₈₉	—	2	2	no	—
413	Q₈×C₈₉	—	2	2	no	—
414	Q₈×C₈₉	—	2	2	no	—
415	Q₈×C₈₉	—	4	1	no	—
416	Q₈×C₈₉	—	4	2	no	—
417	Q₈×C₈₉	—	4	2	no	—
418	Q₈×C₈₉	—	8	1	no	—
419	Q₈×C₈₉	—	8	2	no	—
420	Q₈×C₈₉	—	8	1	no	—
421	Q₈×C₈₉	—	8	2	no	—
422	Q₈×C₈₉	—	8	2	no	—
423	D₄×C₈₉	—	2	4	no	—
424	D₄×C₈₉	—	2	2	no	—
425	D₄×C₈₉	—	2	2	no	—
426	D₄×C₈₉	—	2	2	no	—
427	D₄×C₈₉	—	4	1	no	—
428	D₄×C₈₉	—	4	2	no	—
429	D₄×C₈₉	—	8	1	no	—
430	D₄×C₈₉	—	8	2	no	—
431	D₄×C₈₉	—	8	2	no	—
432	D₄×C₈₉	—	8	2	no	—
433	C₂×C₄×C₈₉	—	2	2	no	—
434	C₂×C₄×C₈₉	—	2	2	no	—
435	C₂×C₄×C₈₉	—	2	2	no	—
436	C₂×C₄×C₈₉	—	2	2	no	—
437	C₂×C₄×C₈₉	—	2	1	no	—
438	C₂×C₄×C₈₉	—	2	1	no	—
439	C₂×C₄×C₈₉	—	2	2	no	—
440	C₂×C₄×C₈₉	—	2	2	no	—
441	C₂×C₄×C₈₉	—	2	2	no	—
442	C₂×C₄×C₈₉	—	2	2	no	—
443	C₂×C₄×C₈₉	—	2	2	no	—
444	C₂×C₄×C₈₉	—	2	1	no	—
445	C₂×C₄×C₈₉	—	4	1	no	—
446	C₂×C₄×C₈₉	—	4	2	no	—
447	C₂×C₄×C₈₉	—	8	2	no	—
448	C₂×C₄×C₈₉	—	8	2	no	—
449	C₂×C₄×C₈₉	—	8	2	no	—
450	C₂×C₄×C₈₉	—	8	2	no	—
451	C₂×C₄×C₈₉	—	8	1	no	—
452	C₂×C₄×C₈₉	—	8	2	no	—
453	C₂×C₄×C₈₉	—	8	2	no	—
454	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
456	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
458	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
462	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
463	C₈×C₈₉	—	2	2	no	—
464	C₈×C₈₉	—	2	2	no	—
465	C₈×C₈₉	—	2	2	no	—
466	C₈×C₈₉	—	2	2	no	—
467	C₂²×C₈₉	—	2	1	no	—
468	C₂²×C₈₉	—	2	1	no	—
469	C₂²×C₈₉	—	2	2	no	—
470	C₂²×C₈₉	—	2	2	no	—
471	C₂²×C₈₉	—	2	2	no	—
472	C₂²×C₈₉	—	4	1	no	—
473	C₂²×C₈₉	—	4	2	no	—
474	C₂²×C₈₉	—	4	2	no	—
475	C₂²×C₈₉	—	4	1	no	—
476	C₂²×C₈₉	—	4	1	no	—
477	C₂²×C₈₉	—	4	2	no	—
478	C₂²×C₈₉	—	16	2	no	—
479	C₂²×C₈₉	#578	1	2	yes	—
480	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
481	C₄×C₈₉	—	2	1	no	—
482	C₄×C₈₉	—	2	1	no	—
483	C₄×C₈₉	—	2	2	no	—
484	C₄×C₈₉	—	2	2	no	—
485	C₄×C₈₉	—	2	1	no	—
486	C₄×C₈₉	—	2	1	no	—
487	C₄×C₈₉	—	2	1	no	—
488	C₄×C₈₉	—	2	2	no	—
489	C₄×C₈₉	—	4	1	no	—
490	C₄×C₈₉	—	4	2	no	—
491	C₄×C₈₉	—	4	2	no	—
492	C₄×C₈₉	—	4	2	no	—
493	C₄×C₈₉	—	4	2	no	—
494	C₄×C₈₉	—	4	2	no	—
495	C₄×C₈₉	—	4	1	no	—
496	C₄×C₈₉	—	4	1	no	—
497	C₄×C₈₉	#585	1	2	yes	—
498	#62604	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
499	C₂×C₈₉	—	2	2	no	—
500	C₂×C₈₉	—	4	2	no	—
501	C₂×C₈₉	—	8	1	no	—
502	C₂×C₈₉	—	8	2	no	—
503	C₂×C₈₉	#3500	1	1	yes	characteristic
504	C₂×C₈₉	C₂×#578	1	1	yes	characteristic
505	C₂×C₈₉	#3585	1	1	yes	characteristic
506	#3561	C₂×C₈₉	1	1	yes	characteristic, complemented
507	#3552	C₂×C₈₉	1	1	yes	characteristic, complemented
508	#3377	C₂×C₈₉	1	2	yes	complemented
509	#3367	C₂×C₈₉	1	2	yes	complemented
510	#3320	C₂×C₈₉	1	2	yes	complemented
511	#3314	C₂×C₈₉	1	2	yes	complemented
512	#3313	C₂×C₈₉	1	2	yes	complemented
513	#3308	C₂×C₈₉	1	2	yes	complemented
514	#3299	C₂×C₈₉	1	2	yes	complemented
515	#3297	C₂×C₈₉	1	2	yes	complemented
516	#3243	C₂×C₈₉	1	2	yes	complemented
517	#3230	C₂×C₈₉	1	1	yes	characteristic, complemented
518	#3225	C₂×C₈₉	1	2	yes	complemented
519	#3211	C₂×C₈₉	1	1	yes	characteristic, complemented
520	#3181	C₂×C₈₉	1	1	yes	characteristic, complemented
521	#3175	C₂×C₈₉	1	2	yes	complemented
522	#3137	C₂×C₈₉	1	2	yes	complemented
523	C₂×#489	C₂×C₈₉	1	1	yes	characteristic, complemented
524	#2968	C₂×C₈₉	1	1	yes	characteristic, complemented
525	C₈₉	#62604	1	1	yes	characteristic, direct product factor, Sylow
526	#563	—	2	2	no	—
527	#563	—	2	1	no	—
528	#562	—	2	1	no	—
529	#557	C₂²×C₈₉	1	1	yes	characteristic, complemented
530	#556	C₂²×C₈₉	1	2	yes	—
531	#556	C₂²×C₈₉	1	1	yes	characteristic, complemented
532	#554	C₂²×C₈₉	1	2	yes	—
533	#553	C₂²×C₈₉	1	2	yes	—
534	#551	—	2	2	no	—
535	D₄×Q₈	—	2	1	no	—
536	D₄×Q₈	C₂²×C₈₉	1	2	yes	—
537	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
538	#548	—	2	1	no	—
539	#548	C₂²×C₈₉	1	2	yes	—
540	#547	C₂²×C₈₉	1	1	yes	characteristic, complemented
541	#546	C₂²×C₈₉	1	2	yes	—
542	#544	C₂²×C₈₉	1	2	yes	complemented
543	#543	—	2	1	no	—
544	#542	—	2	2	no	—
545	#542	C₂²×C₈₉	1	2	yes	—
546	#542	C₂²×C₈₉	1	2	yes	complemented
547	#541	—	2	1	no	—
548	#539	—	2	2	no	—
549	#538	—	2	1	no	—
550	#536	—	2	1	no	—
551	#536	C₂²×C₈₉	1	2	yes	—
552	#533	C₂²×C₈₉	1	1	yes	characteristic
553	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
554	#529	C₂²×C₈₉	1	1	yes	characteristic
555	#529	C₂²×C₈₉	1	1	yes	characteristic
556	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
557	#501	C₂²×C₈₉	1	1	yes	characteristic, complemented
558	#500	C₂²×C₈₉	1	2	yes	complemented
559	#497	C₂²×C₈₉	1	1	yes	characteristic, complemented
560	#495	C₂²×C₈₉	1	2	yes	—
561	#491	C₂²×C₈₉	1	2	yes	complemented
562	#491	C₂²×C₈₉	1	1	yes	characteristic, complemented
563	#489	C₂²×C₈₉	1	2	yes	—
564	#489	C₂²×C₈₉	1	2	yes	—
565	#489	C₂²×C₈₉	1	2	yes	—
566	#489	C₂²×C₈₉	1	2	yes	—
567	#489	C₂²×C₈₉	1	2	yes	—
568	#489	C₂²×C₈₉	1	1	yes	characteristic, complemented
569	#488	C₂²×C₈₉	1	2	yes	—
570	#488	C₂²×C₈₉	1	2	yes	—
571	#487	C₂²×C₈₉	1	2	yes	complemented
572	#487	C₂²×C₈₉	1	2	yes	complemented
573	#485	C₂²×C₈₉	1	2	yes	complemented
574	#484	C₂²×C₈₉	1	2	yes	—
575	#484	C₂²×C₈₉	1	2	yes	—
576	#484	C₂²×C₈₉	1	2	yes	complemented
577	#482	C₂²×C₈₉	1	2	yes	—
578	#480	C₂²×C₈₉	1	2	yes	—
579	#479	C₂²×C₈₉	1	2	yes	complemented
580	#478	C₂²×C₈₉	1	2	yes	—
581	#477	C₂²×C₈₉	1	2	yes	complemented
582	#477	C₂²×C₈₉	1	2	yes	complemented
583	#477	C₂²×C₈₉	1	2	yes	complemented
584	#474	C₂²×C₈₉	1	2	yes	—
585	#468	C₂²×C₈₉	1	2	yes	—
586	#468	C₂²×C₈₉	1	2	yes	complemented
587	#467	C₂²×C₈₉	1	2	yes	—
588	#467	C₂²×C₈₉	1	2	yes	complemented
589	#466	C₂²×C₈₉	1	2	yes	—
590	#465	C₂²×C₈₉	1	2	yes	—
591	#464	C₂²×C₈₉	1	2	yes	—
592	#464	C₂²×C₈₉	1	2	yes	—
593	#463	C₂²×C₈₉	1	2	yes	—
594	#463	C₂²×C₈₉	1	2	yes	—
595	#462	C₂²×C₈₉	1	2	yes	complemented
596	#461	C₂²×C₈₉	1	2	yes	complemented
597	#452	C₂²×C₈₉	1	2	yes	—
598	#451	C₂²×C₈₉	1	1	yes	characteristic
599	#451	C₂²×C₈₉	1	2	yes	complemented
600	#450	C₂²×C₈₉	1	1	yes	characteristic
601	#449	C₂²×C₈₉	1	2	yes	—
602	#448	C₂²×C₈₉	1	1	yes	characteristic
603	#448	C₂²×C₈₉	1	2	yes	complemented
604	#447	C₂²×C₈₉	1	1	yes	characteristic
605	#446	C₂²×C₈₉	1	2	yes	complemented
606	#441	C₂²×C₈₉	1	2	yes	complemented
607	#440	C₂²×C₈₉	1	2	yes	—
608	#440	C₂²×C₈₉	1	2	yes	complemented
609	#440	C₂²×C₈₉	1	2	yes	complemented
610	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
611	C₄×D₈	C₂²×C₈₉	1	2	yes	—
612	#435	C₂²×C₈₉	1	2	yes	—
613	#435	C₂²×C₈₉	1	2	yes	complemented
614	C₈×D₄	C₂²×C₈₉	1	2	yes	—
615	#433	C₂²×C₈₉	1	2	yes	complemented
616	#431	C₂²×C₈₉	1	1	yes	characteristic
617	#419	C₂²×C₈₉	1	2	yes	complemented
618	#417	C₂²×C₈₉	1	2	yes	—
619	#416	C₂²×C₈₉	1	2	yes	—
620	C₂×#103	C₂²×C₈₉	1	2	yes	—
621	C₂×#103	C₂²×C₈₉	1	2	yes	complemented
622	C₂×#102	C₂²×C₈₉	1	2	yes	—
623	#405	C₂²×C₈₉	1	2	yes	complemented
624	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
625	C₂×#41	—	2	1	no	—
626	C₂×#41	C₂³×C₈₉	1	2	yes	—
627	C₂²×Q₈	—	2	1	no	—
628	C₂²×Q₈	—	2	1	no	—
629	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
630	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
631	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
632	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
633	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
634	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
635	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
636	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
637	C₂×D₈	C₂³×C₈₉	1	2	yes	—
638	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
639	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
640	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
641	C₄⋊Q₈	—	2	1	no	—
642	C₄⋊Q₈	—	2	2	no	—
643	C₄⋊Q₈	—	2	2	no	—
644	C₄⋊Q₈	—	2	1	no	—
645	C₄⋊Q₈	—	2	1	no	—
646	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
647	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
648	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
649	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
650	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
651	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
652	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
653	#126	—	2	2	no	—
654	#126	—	2	2	no	—
655	#126	—	2	2	no	—
656	#126	—	2	2	no	—
657	#126	—	2	2	no	—
658	#126	—	2	2	no	—
659	#126	—	2	1	no	—
660	#126	D₄×C₈₉	1	2	yes	—
661	#125	—	2	2	no	—
662	#125	—	2	2	no	—
663	#125	—	2	2	no	—
664	#125	—	2	1	no	—
665	#125	D₄×C₈₉	1	1	yes	characteristic
666	#125	C₂³×C₈₉	1	1	yes	characteristic
667	#125	C₂³×C₈₉	1	2	yes	—
668	#124	—	2	1	no	—
669	#124	—	2	2	no	—
670	#124	—	2	2	no	—
671	#124	—	2	2	no	—
672	#124	—	2	1	no	—
673	#124	—	2	1	no	—
674	#124	D₄×C₈₉	1	1	yes	characteristic
675	#124	C₂³×C₈₉	1	2	yes	—
676	#124	C₂³×C₈₉	1	2	yes	—
677	#124	C₂³×C₈₉	1	1	yes	characteristic
678	#124	C₂³×C₈₉	1	2	yes	—
679	#123	—	2	1	no	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	#123	—	2	2	no	—
684	#123	—	2	2	no	—
685	#123	—	2	2	no	—
686	#123	—	2	2	no	—
687	#123	D₄×C₈₉	1	2	yes	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	1	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	—	2	2	no	—
693	C₂²⋊Q₈	—	2	1	no	—
694	C₂²⋊Q₈	—	2	1	no	—
695	C₂²⋊Q₈	—	2	2	no	—
696	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	—	2	2	no	—
698	C₂²⋊Q₈	—	2	2	no	—
699	C₂²⋊Q₈	—	2	2	no	—
700	C₂²⋊Q₈	—	2	2	no	—
701	C₂²⋊Q₈	—	2	2	no	—
702	C₂²⋊Q₈	—	2	2	no	—
703	C₂²⋊Q₈	—	2	2	no	—
704	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
705	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
706	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
707	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
708	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
709	#121	—	2	2	no	—
710	#121	—	2	2	no	—
711	#121	—	2	2	no	—
712	#121	D₄×C₈₉	1	1	yes	characteristic
713	#121	C₂³×C₈₉	1	1	yes	characteristic
714	#121	C₂³×C₈₉	1	2	yes	—
715	#121	C₂³×C₈₉	1	2	yes	—
716	#120	—	2	2	no	—
717	C₄×Q₈	—	2	1	no	—
718	C₄×Q₈	—	2	1	no	—
719	C₄×Q₈	—	2	1	no	—
720	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
721	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
722	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
723	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
724	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
725	C₄×D₄	—	2	2	no	—
726	C₄×D₄	—	2	2	no	—
727	C₄×D₄	—	2	1	no	—
728	C₄×D₄	—	2	2	no	—
729	C₄×D₄	—	2	2	no	—
730	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
731	C₄×D₄	C₂³×C₈₉	1	2	yes	—
732	C₄×D₄	C₂³×C₈₉	1	2	yes	—
733	C₄×D₄	C₂³×C₈₉	1	2	yes	—
734	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
735	#117	—	2	1	no	—
736	#117	—	2	2	no	—
737	#117	—	2	1	no	—
738	#117	C₂³×C₈₉	1	2	yes	—
739	#117	C₂³×C₈₉	1	2	yes	—
740	C₂×C₄⋊C₄	—	2	1	no	—
741	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
742	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
743	C₂×C₂²⋊C₄	—	2	1	no	—
744	C₂×C₂²⋊C₄	—	2	1	no	—
745	C₂×C₂²⋊C₄	—	2	2	no	—
746	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
747	#107	C₂³×C₈₉	1	2	yes	—
748	#107	C₂³×C₈₉	1	2	yes	—
749	#107	C₂³×C₈₉	1	2	yes	—
750	#107	C₂³×C₈₉	1	2	yes	—
751	#107	C₂³×C₈₉	1	2	yes	—
752	#106	C₂³×C₈₉	1	2	yes	—
753	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
754	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
755	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
756	#103	C₂³×C₈₉	1	2	yes	—
757	#103	C₂³×C₈₉	1	2	yes	—
758	#103	C₂³×C₈₉	1	2	yes	—
759	#103	C₂³×C₈₉	1	2	yes	—
760	#103	C₂³×C₈₉	1	2	yes	—
761	#103	C₂³×C₈₉	1	2	yes	—
762	#103	C₂³×C₈₉	1	2	yes	—
763	#103	C₂³×C₈₉	1	2	yes	—
764	#103	C₂³×C₈₉	1	2	yes	—
765	#103	C₂³×C₈₉	1	2	yes	—
766	#103	C₂³×C₈₉	1	2	yes	—
767	#103	C₂³×C₈₉	1	2	yes	—
768	#103	C₂³×C₈₉	1	2	yes	—
769	#102	C₂³×C₈₉	1	2	yes	—
770	#102	C₂³×C₈₉	1	2	yes	—
771	#102	C₂³×C₈₉	1	2	yes	—
772	#102	C₂³×C₈₉	1	2	yes	—
773	#102	C₂³×C₈₉	1	2	yes	—
774	#102	C₂³×C₈₉	1	2	yes	—
775	#102	C₂³×C₈₉	1	2	yes	—
776	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
777	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
778	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
779	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
780	#97	C₂³×C₈₉	1	1	yes	characteristic
781	#97	C₂³×C₈₉	1	1	yes	characteristic
782	#97	C₂³×C₈₉	1	2	yes	—
783	#97	C₂³×C₈₉	1	2	yes	—
784	C₄×C₈	C₂³×C₈₉	1	2	yes	—
785	C₄×C₈	C₂³×C₈₉	1	2	yes	—
786	C₂⁴	—	2	1	no	—
787	#41	—	4	2	no	—
788	#41	—	4	2	no	—
789	#41	—	8	2	no	—
790	C₂×Q₈	—	2	1	no	—
791	C₂×Q₈	—	2	1	no	—
792	C₂×Q₈	—	2	1	no	—
793	C₂×Q₈	—	2	2	no	—
794	C₂×Q₈	—	2	2	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	2	2	no	—
797	C₂×Q₈	—	4	2	no	—
798	C₂×Q₈	—	4	2	no	—
799	C₂×Q₈	—	4	2	no	—
800	C₂×Q₈	—	8	2	no	—
801	C₂×Q₈	—	8	2	no	—
802	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
803	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
804	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
805	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
806	C₂×D₄	—	2	1	no	—
807	C₂×D₄	—	2	2	no	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	1	no	—
811	C₂×D₄	—	4	2	no	—
812	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
813	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
814	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
815	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
816	C₂²×C₄	—	2	1	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	2	no	—
820	C₂²×C₄	—	2	1	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	2	2	no	—
824	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
825	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
826	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
828	Q₁₆	—	4	2	no	—
829	Q₁₆	—	4	2	no	—
830	SD₁₆	—	4	2	no	—
831	SD₁₆	—	4	2	no	—
832	SD₁₆	—	4	2	no	—
833	D₈	—	4	2	no	—
834	M₁₆	—	4	2	no	—
835	C₂×C₈	—	4	2	no	—
836	C₂×C₈	—	4	2	no	—
837	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
838	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
839	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
840	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
841	C₄⋊C₄	—	2	1	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	1	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	1	no	—
848	C₄⋊C₄	—	2	1	no	—
849	C₄⋊C₄	—	2	1	no	—
850	C₄⋊C₄	—	2	1	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	1	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	1	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	1	no	—
864	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
865	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
866	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
867	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
868	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
869	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
870	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
871	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
872	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
873	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
874	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	1	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	1	no	—
888	C₂²⋊C₄	—	2	1	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	1	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	1	no	—
894	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
895	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
896	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
897	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
898	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
899	C₄²	—	2	2	no	—
900	C₄²	—	2	1	no	—
901	C₄²	—	2	2	no	—
902	C₄²	—	2	2	no	—
903	C₄²	—	2	2	no	—
904	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
905	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
906	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
907	C₄²	C₂⁴×C₈₉	1	2	yes	—
908	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
909	C₂³	—	2	1	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	4	2	no	—
912	C₂³	—	8	1	no	—
913	C₂³	—	8	1	no	—
914	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
915	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
916	Q₈	—	2	2	no	—
917	Q₈	—	2	2	no	—
918	Q₈	—	2	2	no	—
919	Q₈	—	2	2	no	—
920	Q₈	—	2	2	no	—
921	Q₈	—	4	1	no	—
922	Q₈	—	4	2	no	—
923	Q₈	—	4	2	no	—
924	Q₈	—	8	1	no	—
925	Q₈	—	8	2	no	—
926	Q₈	—	8	1	no	—
927	Q₈	—	8	2	no	—
928	Q₈	—	8	2	no	—
929	D₄	—	2	4	no	—
930	D₄	—	2	2	no	—
931	D₄	—	2	2	no	—
932	D₄	—	2	2	no	—
933	D₄	—	4	1	no	—
934	D₄	—	4	2	no	—
935	D₄	—	8	1	no	—
936	D₄	—	8	2	no	—
937	D₄	—	8	2	no	—
938	D₄	—	8	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	4	1	no	—
952	C₂×C₄	—	4	2	no	—
953	C₂×C₄	—	8	2	no	—
954	C₂×C₄	—	8	2	no	—
955	C₂×C₄	—	8	2	no	—
956	C₂×C₄	—	8	2	no	—
957	C₂×C₄	—	8	1	no	—
958	C₂×C₄	—	8	2	no	—
959	C₂×C₄	—	8	2	no	—
960	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
961	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
962	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
963	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
964	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
965	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
966	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
967	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
968	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
969	C₈	—	2	2	no	—
970	C₈	—	2	2	no	—
971	C₈	—	2	2	no	—
972	C₈	—	2	2	no	—
973	C₂²	—	2	1	no	—
974	C₂²	—	2	1	no	—
975	C₂²	—	2	2	no	—
976	C₂²	—	2	2	no	—
977	C₂²	—	2	2	no	—
978	C₂²	—	4	1	no	—
979	C₂²	—	4	2	no	—
980	C₂²	—	4	1	no	—
981	C₂²	—	4	2	no	—
982	C₂²	—	4	2	no	—
983	C₂²	—	4	1	no	—
984	C₂²	—	16	2	no	—
985	C₂²	#578×C₈₉	1	2	yes	—
986	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
987	C₄	—	2	1	no	—
988	C₄	—	2	1	no	—
989	C₄	—	2	2	no	—
990	C₄	—	2	1	no	—
991	C₄	—	2	1	no	—
992	C₄	—	2	2	no	—
993	C₄	—	2	2	no	—
994	C₄	—	2	1	no	—
995	C₄	—	4	1	no	—
996	C₄	—	4	1	no	—
997	C₄	—	4	2	no	—
998	C₄	—	4	2	no	—
999	C₄	—	4	2	no	—
1000	C₄	—	4	2	no	—
1001	C₄	—	4	2	no	—
1002	C₄	—	4	1	no	—
1003	C₄	#585×C₈₉	1	2	yes	—
1004	C₂	—	2	2	no	—
1005	C₂	—	4	2	no	—
1006	C₂	—	8	1	no	—
1007	C₂	—	8	2	no	—
1008	C₂	C₈₉×#3500	1	1	yes	characteristic
1009	C₂	C₂×#578×C₈₉	1	1	yes	characteristic
1010	C₂	C₈₉×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ #529×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3561	C₂	semidirect
2. C₈₉×#3552	C₂	semidirect
3. C₈₉×#3377	C₂	semidirect
4. C₈₉×#3367	C₂	semidirect
5. C₈₉×#3320	C₂	semidirect
6. C₈₉×#3314	C₂	semidirect
7. C₈₉×#3313	C₂	semidirect
8. C₈₉×#3308	C₂	semidirect
9. C₈₉×#3299	C₂	semidirect
10. C₈₉×#3297	C₂	semidirect
11. C₈₉×#3243	C₂	semidirect
12. C₈₉×#3230	C₂	semidirect
13. C₈₉×#3225	C₂	semidirect
14. C₈₉×#3211	C₂	semidirect
15. C₈₉×#3181	C₂	semidirect
16. C₈₉×#3175	C₂	semidirect
17. C₈₉×#3137	C₂	semidirect
18. C₂×#489×C₈₉	C₂	semidirect
19. C₈₉×#2968	C₂	semidirect
23. #557×C₈₉	C₂²	semidirect
25. #556×C₈₉	C₂²	semidirect
31. D₄×Q₈×C₈₉	C₂²	semidirect
34. #547×C₈₉	C₂²	semidirect
36. #544×C₈₉	C₂²	semidirect
40. #542×C₈₉	C₂²	semidirect
51. #501×C₈₉	C₂²	semidirect
52. #500×C₈₉	C₂²	semidirect
53. #497×C₈₉	C₂²	semidirect
55. #491×C₈₉	C₂²	semidirect
56. #491×C₈₉	C₂²	semidirect
62. #489×C₈₉	C₂²	semidirect
65. #487×C₈₉	C₂²	semidirect
66. #487×C₈₉	C₂²	semidirect
67. #485×C₈₉	C₂²	semidirect
70. #484×C₈₉	C₂²	semidirect
73. #479×C₈₉	C₂²	semidirect
75. #477×C₈₉	C₂²	semidirect
76. #477×C₈₉	C₂²	semidirect
77. #477×C₈₉	C₂²	semidirect
80. #468×C₈₉	C₂²	semidirect
82. #467×C₈₉	C₂²	semidirect
89. #462×C₈₉	C₂²	semidirect
90. #461×C₈₉	C₂²	semidirect
93. #451×C₈₉	C₂²	semidirect
97. #448×C₈₉	C₂²	semidirect
99. #446×C₈₉	C₂²	semidirect
100. #441×C₈₉	C₂²	semidirect
102. #440×C₈₉	C₂²	semidirect
103. #440×C₈₉	C₂²	semidirect
104. C₄×Q₁₆×C₈₉	C₂²	semidirect
107. #435×C₈₉	C₂²	semidirect
109. #433×C₈₉	C₂²	semidirect
111. #419×C₈₉	C₂²	semidirect
115. C₂×#103×C₈₉	C₂²	semidirect
117. #405×C₈₉	C₂²	semidirect
498. #62604	C₈₉	direct (N × H)
506. #3561	C₂×C₈₉	semidirect
507. #3552	C₂×C₈₉	semidirect
508. #3377	C₂×C₈₉	semidirect
509. #3367	C₂×C₈₉	semidirect
510. #3320	C₂×C₈₉	semidirect
511. #3314	C₂×C₈₉	semidirect
512. #3313	C₂×C₈₉	semidirect
513. #3308	C₂×C₈₉	semidirect
514. #3299	C₂×C₈₉	semidirect
515. #3297	C₂×C₈₉	semidirect
516. #3243	C₂×C₈₉	semidirect
517. #3230	C₂×C₈₉	semidirect
518. #3225	C₂×C₈₉	semidirect
519. #3211	C₂×C₈₉	semidirect
520. #3181	C₂×C₈₉	semidirect
521. #3175	C₂×C₈₉	semidirect
522. #3137	C₂×C₈₉	semidirect
523. C₂×#489	C₂×C₈₉	semidirect
524. #2968	C₂×C₈₉	semidirect
525. C₈₉	#62604	direct (N × H)
529. #557	C₂²×C₈₉	semidirect
531. #556	C₂²×C₈₉	semidirect
537. D₄×Q₈	C₂²×C₈₉	semidirect
540. #547	C₂²×C₈₉	semidirect
542. #544	C₂²×C₈₉	semidirect
546. #542	C₂²×C₈₉	semidirect
557. #501	C₂²×C₈₉	semidirect
558. #500	C₂²×C₈₉	semidirect
559. #497	C₂²×C₈₉	semidirect
561. #491	C₂²×C₈₉	semidirect
562. #491	C₂²×C₈₉	semidirect
568. #489	C₂²×C₈₉	semidirect
571. #487	C₂²×C₈₉	semidirect
572. #487	C₂²×C₈₉	semidirect
573. #485	C₂²×C₈₉	semidirect
576. #484	C₂²×C₈₉	semidirect
579. #479	C₂²×C₈₉	semidirect
581. #477	C₂²×C₈₉	semidirect
582. #477	C₂²×C₈₉	semidirect
583. #477	C₂²×C₈₉	semidirect
586. #468	C₂²×C₈₉	semidirect
588. #467	C₂²×C₈₉	semidirect
595. #462	C₂²×C₈₉	semidirect
596. #461	C₂²×C₈₉	semidirect
599. #451	C₂²×C₈₉	semidirect
603. #448	C₂²×C₈₉	semidirect
605. #446	C₂²×C₈₉	semidirect
606. #441	C₂²×C₈₉	semidirect
608. #440	C₂²×C₈₉	semidirect
609. #440	C₂²×C₈₉	semidirect
610. C₄×Q₁₆	C₂²×C₈₉	semidirect
613. #435	C₂²×C₈₉	semidirect
615. #433	C₂²×C₈₉	semidirect
617. #419	C₂²×C₈₉	semidirect
621. C₂×#103	C₂²×C₈₉	semidirect
623. #405	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×#3561	2
C₈₉×#3552	2
C₈₉×#3377	2
C₈₉×#3367	2
C₈₉×#3320	2
C₈₉×#3314	2
C₈₉×#3313	2
C₈₉×#3308	2
C₈₉×#3299	2
C₈₉×#3297	2
C₈₉×#3243	2
C₈₉×#3230	2
C₈₉×#3225	2
C₈₉×#3211	2
C₈₉×#3181	2
C₈₉×#3175	2
C₈₉×#3137	2
C₂×#489×C₈₉	2
C₈₉×#2968	2
#62604	89

Subgroups — C89×#62604 #36440452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62604 #36440452