Subgroups — C₈₉×#62573 #36440421

Order 22784.

1772 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3376	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3366	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3332	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3322	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3318	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3309	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3307	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3306	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3244	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3234	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3220	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3214	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3184	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#3179	C₂	1	2	yes	maximal, complemented
17	C₈₉×#3142	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#3136	C₂	1	2	yes	maximal, complemented
19	C₈₉×#2967	C₂	1	1	yes	maximal, characteristic, complemented
20	#563×C₈₉	—	2	1	no	—
21	#562×C₈₉	—	2	1	no	—
22	#560×C₈₉	—	2	2	no	—
23	#556×C₈₉	C₂²	1	1	yes	characteristic
24	#554×C₈₉	C₂²	1	2	yes	complemented
25	#553×C₈₉	—	2	1	no	—
26	#553×C₈₉	C₂²	1	2	yes	—
27	#553×C₈₉	C₂²	1	2	yes	complemented
28	#550×C₈₉	C₂²	1	2	yes	—
29	#550×C₈₉	C₂²	1	1	yes	characteristic
30	#547×C₈₉	—	2	2	no	—
31	#547×C₈₉	C₂²	1	1	yes	characteristic
32	#547×C₈₉	C₂²	1	2	yes	complemented
33	#546×C₈₉	—	2	1	no	—
34	#546×C₈₉	C₂²	1	2	yes	—
35	D₄²×C₈₉	C₂²	1	1	yes	characteristic
36	#544×C₈₉	C₂²	1	2	yes	complemented
37	#542×C₈₉	C₂²	1	2	yes	—
38	#540×C₈₉	C₂²	1	2	yes	complemented
39	#539×C₈₉	—	2	2	no	—
40	#539×C₈₉	—	2	1	no	—
41	#538×C₈₉	—	2	2	no	—
42	#537×C₈₉	—	2	1	no	—
43	#537×C₈₉	—	2	1	no	—
44	#535×C₈₉	—	2	1	no	—
45	#535×C₈₉	C₂²	1	2	yes	—
46	#532×C₈₉	C₂²	1	1	yes	characteristic
47	#532×C₈₉	C₂²	1	1	yes	characteristic
48	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
49	#529×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic, complemented
51	#501×C₈₉	C₂²	1	2	yes	complemented
52	#498×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	#496×C₈₉	C₂²	1	2	yes	complemented
54	#493×C₈₉	C₂²	1	1	yes	characteristic
55	#491×C₈₉	C₂²	1	2	yes	complemented
56	#490×C₈₉	C₂²	1	2	yes	—
57	#490×C₈₉	C₂²	1	2	yes	—
58	#490×C₈₉	C₂²	1	2	yes	complemented
59	#489×C₈₉	C₂²	1	2	yes	—
60	#489×C₈₉	C₂²	1	2	yes	complemented
61	#488×C₈₉	C₂²	1	2	yes	—
62	#488×C₈₉	C₂²	1	2	yes	complemented
63	#488×C₈₉	C₂²	1	2	yes	complemented
64	#486×C₈₉	C₂²	1	1	yes	characteristic
65	#486×C₈₉	C₂²	1	2	yes	complemented
66	#486×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#485×C₈₉	C₂²	1	2	yes	complemented
68	#483×C₈₉	C₂²	1	2	yes	complemented
69	#482×C₈₉	C₂²	1	2	yes	—
70	#481×C₈₉	C₂²	1	2	yes	—
71	#481×C₈₉	C₂²	1	1	yes	characteristic
72	#481×C₈₉	C₂²	1	1	yes	characteristic, complemented
73	#480×C₈₉	C₂²	1	1	yes	characteristic
74	#480×C₈₉	C₂²	1	1	yes	characteristic, complemented
75	#479×C₈₉	C₂²	1	2	yes	complemented
76	#478×C₈₉	C₂²	1	2	yes	—
77	#478×C₈₉	C₂²	1	2	yes	complemented
78	#478×C₈₉	C₂²	1	2	yes	complemented
79	#476×C₈₉	C₂²	1	2	yes	complemented
80	#475×C₈₉	C₂²	1	2	yes	complemented
81	#469×C₈₉	C₂²	1	2	yes	—
82	#469×C₈₉	C₂²	1	2	yes	—
83	#469×C₈₉	C₂²	1	2	yes	complemented
84	#468×C₈₉	C₂²	1	2	yes	complemented
85	#466×C₈₉	C₂²	1	2	yes	—
86	#465×C₈₉	C₂²	1	2	yes	complemented
87	#463×C₈₉	C₂²	1	2	yes	—
88	#463×C₈₉	C₂²	1	2	yes	—
89	#461×C₈₉	C₂²	1	2	yes	complemented
90	#459×C₈₉	C₂²	1	2	yes	—
91	#459×C₈₉	C₂²	1	2	yes	complemented
92	#459×C₈₉	C₂²	1	2	yes	complemented
93	#449×C₈₉	C₂²	1	2	yes	complemented
94	#449×C₈₉	C₂²	1	2	yes	complemented
95	#449×C₈₉	C₂²	1	2	yes	complemented
96	#449×C₈₉	C₂²	1	2	yes	complemented
97	#447×C₈₉	C₂²	1	2	yes	—
98	#447×C₈₉	C₂²	1	2	yes	—
99	#446×C₈₉	C₂²	1	2	yes	complemented
100	#442×C₈₉	C₂²	1	2	yes	—
101	#442×C₈₉	C₂²	1	2	yes	complemented
102	#442×C₈₉	C₂²	1	2	yes	complemented
103	#440×C₈₉	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
105	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
106	#436×C₈₉	C₂²	1	2	yes	complemented
107	#435×C₈₉	C₂²	1	2	yes	—
108	#435×C₈₉	C₂²	1	2	yes	complemented
109	#433×C₈₉	C₂²	1	2	yes	complemented
110	#432×C₈₉	C₂²	1	1	yes	characteristic, complemented
111	#418×C₈₉	C₂²	1	2	yes	—
112	#417×C₈₉	C₂²	1	2	yes	complemented
113	#417×C₈₉	C₂²	1	2	yes	complemented
114	#417×C₈₉	C₂²	1	2	yes	complemented
115	#416×C₈₉	C₂²	1	2	yes	complemented
116	C₂×#102×C₈₉	C₂²	1	2	yes	—
117	#405×C₈₉	C₂²	1	2	yes	complemented
118	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	C₂×#41×C₈₉	—	2	1	no	—
120	C₂×#41×C₈₉	—	2	2	no	—
121	C₂×#41×C₈₉	—	2	1	no	—
122	C₂×#41×C₈₉	—	2	1	no	—
123	C₂×#41×C₈₉	C₂³	1	2	yes	—
124	C₂×#41×C₈₉	C₂³	1	2	yes	—
125	C₂²×D₄×C₈₉	—	2	1	no	—
126	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
129	C₂×D₈×C₈₉	C₂³	1	2	yes	—
130	C₂×D₈×C₈₉	C₂³	1	2	yes	—
131	C₂×D₈×C₈₉	C₂³	1	2	yes	—
132	C₂×D₈×C₈₉	C₂³	1	2	yes	—
133	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
134	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
135	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
136	C₄⋊Q₈×C₈₉	—	2	2	no	—
137	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
138	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
139	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
140	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
141	#127×C₈₉	—	2	2	no	—
142	#127×C₈₉	C₂³	1	1	yes	characteristic
143	#127×C₈₉	C₂³	1	2	yes	—
144	#127×C₈₉	C₂³	1	1	yes	characteristic
145	#127×C₈₉	C₂³	1	1	yes	characteristic
146	#126×C₈₉	—	2	2	no	—
147	#126×C₈₉	—	2	2	no	—
148	#126×C₈₉	—	2	2	no	—
149	#126×C₈₉	—	2	2	no	—
150	#126×C₈₉	D₄	1	2	yes	—
151	#125×C₈₉	—	2	2	no	—
152	#125×C₈₉	—	2	1	no	—
153	#125×C₈₉	—	2	1	no	—
154	#125×C₈₉	D₄	1	1	yes	characteristic
155	#125×C₈₉	C₂³	1	2	yes	—
156	#125×C₈₉	C₂³	1	2	yes	—
157	#125×C₈₉	C₂³	1	2	yes	—
158	#124×C₈₉	—	2	2	no	—
159	#124×C₈₉	—	2	1	no	—
160	#124×C₈₉	—	2	1	no	—
161	#124×C₈₉	D₄	1	1	yes	characteristic
162	#124×C₈₉	C₂³	1	2	yes	—
163	#124×C₈₉	C₂³	1	2	yes	—
164	#123×C₈₉	—	2	2	no	—
165	#123×C₈₉	—	2	2	no	—
166	#123×C₈₉	—	2	2	no	—
167	#123×C₈₉	—	2	2	no	—
168	#123×C₈₉	—	2	2	no	—
169	#123×C₈₉	—	2	2	no	—
170	#123×C₈₉	—	2	2	no	—
171	#123×C₈₉	—	2	2	no	—
172	#123×C₈₉	—	2	2	no	—
173	#123×C₈₉	D₄	1	2	yes	—
174	C₂²⋊Q₈×C₈₉	—	2	1	no	—
175	C₂²⋊Q₈×C₈₉	—	2	2	no	—
176	C₂²⋊Q₈×C₈₉	—	2	2	no	—
177	C₂²⋊Q₈×C₈₉	—	2	2	no	—
178	C₂²⋊Q₈×C₈₉	—	2	2	no	—
179	C₂²⋊Q₈×C₈₉	—	2	2	no	—
180	C₂²⋊Q₈×C₈₉	—	2	2	no	—
181	C₂²⋊Q₈×C₈₉	—	2	2	no	—
182	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
183	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
184	#121×C₈₉	—	2	1	no	—
185	#121×C₈₉	—	2	2	no	—
186	#121×C₈₉	—	2	2	no	—
187	#121×C₈₉	—	2	1	no	—
188	#121×C₈₉	—	2	1	no	—
189	#121×C₈₉	—	2	1	no	—
190	#121×C₈₉	—	2	1	no	—
191	#121×C₈₉	—	2	1	no	—
192	#121×C₈₉	—	2	2	no	—
193	#121×C₈₉	—	2	2	no	—
194	#121×C₈₉	—	2	1	no	—
195	#121×C₈₉	—	2	2	no	—
196	#121×C₈₉	—	2	2	no	—
197	#121×C₈₉	—	2	2	no	—
198	#121×C₈₉	—	2	2	no	—
199	#121×C₈₉	—	2	2	no	—
200	#121×C₈₉	—	2	2	no	—
201	#121×C₈₉	D₄	1	1	yes	characteristic
202	#121×C₈₉	C₂³	1	2	yes	—
203	#121×C₈₉	C₂³	1	2	yes	—
204	#121×C₈₉	C₂³	1	2	yes	—
205	#121×C₈₉	C₂³	1	2	yes	—
206	#121×C₈₉	C₂³	1	1	yes	characteristic
207	#121×C₈₉	C₂³	1	1	yes	characteristic
208	#120×C₈₉	—	2	2	no	—
209	#120×C₈₉	—	2	2	no	—
210	#120×C₈₉	—	2	2	no	—
211	#120×C₈₉	—	2	2	no	—
212	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
213	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
214	C₄×D₄×C₈₉	—	2	2	no	—
215	C₄×D₄×C₈₉	—	2	2	no	—
216	C₄×D₄×C₈₉	—	2	2	no	—
217	C₄×D₄×C₈₉	—	2	1	no	—
218	C₄×D₄×C₈₉	—	2	1	no	—
219	C₄×D₄×C₈₉	—	2	1	no	—
220	C₄×D₄×C₈₉	—	2	1	no	—
221	C₄×D₄×C₈₉	C₂³	1	2	yes	—
222	C₄×D₄×C₈₉	C₂³	1	2	yes	—
223	C₄×D₄×C₈₉	C₂³	1	2	yes	—
224	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₈₉	C₂³	1	2	yes	—
226	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₈₉	C₂³	1	2	yes	—
229	#117×C₈₉	—	2	1	no	—
230	#117×C₈₉	C₂³	1	2	yes	—
231	#117×C₈₉	C₂³	1	2	yes	—
232	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
233	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
234	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
235	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
236	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
237	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	#106×C₈₉	C₂³	1	2	yes	—
244	#106×C₈₉	C₂³	1	2	yes	—
245	#106×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	#102×C₈₉	C₂³	1	2	yes	—
257	#102×C₈₉	C₂³	1	2	yes	—
258	#102×C₈₉	C₂³	1	2	yes	—
259	#102×C₈₉	C₂³	1	2	yes	—
260	#102×C₈₉	C₂³	1	2	yes	—
261	#102×C₈₉	C₂³	1	2	yes	—
262	#102×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	2	yes	—
275	#97×C₈₉	C₂³	1	2	yes	—
276	#97×C₈₉	C₂³	1	2	yes	—
277	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
278	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
279	C₄×C₈×C₈₉	C₂³	1	2	yes	—
280	C₂⁴×C₈₉	—	2	2	no	—
281	#41×C₈₉	—	4	2	no	—
282	#41×C₈₉	—	4	2	no	—
283	#41×C₈₉	—	4	2	no	—
284	#41×C₈₉	—	4	2	no	—
285	#41×C₈₉	—	8	2	no	—
286	#41×C₈₉	—	8	2	no	—
287	#41×C₈₉	—	8	4	no	—
288	#41×C₈₉	—	8	2	no	—
289	C₂×Q₈×C₈₉	—	2	2	no	—
290	C₂×Q₈×C₈₉	—	2	1	no	—
291	C₂×Q₈×C₈₉	—	2	1	no	—
292	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
293	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
294	C₂×D₄×C₈₉	—	2	2	no	—
295	C₂×D₄×C₈₉	—	2	2	no	—
296	C₂×D₄×C₈₉	—	2	1	no	—
297	C₂×D₄×C₈₉	—	2	2	no	—
298	C₂×D₄×C₈₉	—	2	2	no	—
299	C₂×D₄×C₈₉	—	2	2	no	—
300	C₂×D₄×C₈₉	—	2	2	no	—
301	C₂×D₄×C₈₉	—	2	1	no	—
302	C₂×D₄×C₈₉	—	2	1	no	—
303	C₂×D₄×C₈₉	—	2	1	no	—
304	C₂×D₄×C₈₉	—	2	1	no	—
305	C₂×D₄×C₈₉	—	2	2	no	—
306	C₂×D₄×C₈₉	—	2	1	no	—
307	C₂×D₄×C₈₉	—	2	1	no	—
308	C₂×D₄×C₈₉	—	2	2	no	—
309	C₂×D₄×C₈₉	—	2	2	no	—
310	C₂×D₄×C₈₉	—	2	1	no	—
311	C₂×D₄×C₈₉	—	4	2	no	—
312	C₂×D₄×C₈₉	—	4	2	no	—
313	C₂×D₄×C₈₉	—	8	2	no	—
314	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
315	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
316	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
317	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
318	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
319	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₈₉	—	2	1	no	—
321	C₂²×C₄×C₈₉	—	2	1	no	—
322	C₂²×C₄×C₈₉	—	2	2	no	—
323	C₂²×C₄×C₈₉	—	2	1	no	—
324	C₂²×C₄×C₈₉	—	2	1	no	—
325	C₂²×C₄×C₈₉	—	2	2	no	—
326	C₂²×C₄×C₈₉	—	2	2	no	—
327	C₂²×C₄×C₈₉	—	2	2	no	—
328	C₂²×C₄×C₈₉	—	2	2	no	—
329	C₂²×C₄×C₈₉	—	2	2	no	—
330	C₂²×C₄×C₈₉	—	2	2	no	—
331	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
335	SD₁₆×C₈₉	—	4	2	no	—
336	SD₁₆×C₈₉	—	4	2	no	—
337	D₈×C₈₉	—	4	2	no	—
338	D₈×C₈₉	—	4	2	no	—
339	D₈×C₈₉	—	4	2	no	—
340	D₈×C₈₉	—	4	2	no	—
341	M₁₆×C₈₉	—	4	2	no	—
342	M₁₆×C₈₉	—	4	2	no	—
343	C₂×C₈×C₈₉	—	4	2	no	—
344	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
345	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
346	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
347	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
348	C₄⋊C₄×C₈₉	—	2	2	no	—
349	C₄⋊C₄×C₈₉	—	2	1	no	—
350	C₄⋊C₄×C₈₉	—	2	2	no	—
351	C₄⋊C₄×C₈₉	—	2	2	no	—
352	C₄⋊C₄×C₈₉	—	2	2	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	1	no	—
357	C₄⋊C₄×C₈₉	—	2	2	no	—
358	C₄⋊C₄×C₈₉	—	2	1	no	—
359	C₄⋊C₄×C₈₉	—	2	1	no	—
360	C₄⋊C₄×C₈₉	—	2	1	no	—
361	C₄⋊C₄×C₈₉	—	2	1	no	—
362	C₄⋊C₄×C₈₉	—	2	2	no	—
363	C₄⋊C₄×C₈₉	—	2	2	no	—
364	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
365	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
366	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
367	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
368	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
369	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
370	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
371	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
372	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
373	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
374	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
375	C₂²⋊C₄×C₈₉	—	2	2	no	—
376	C₂²⋊C₄×C₈₉	—	2	2	no	—
377	C₂²⋊C₄×C₈₉	—	2	1	no	—
378	C₂²⋊C₄×C₈₉	—	2	2	no	—
379	C₂²⋊C₄×C₈₉	—	2	2	no	—
380	C₂²⋊C₄×C₈₉	—	2	1	no	—
381	C₂²⋊C₄×C₈₉	—	2	2	no	—
382	C₂²⋊C₄×C₈₉	—	2	2	no	—
383	C₂²⋊C₄×C₈₉	—	2	2	no	—
384	C₂²⋊C₄×C₈₉	—	2	2	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	—	2	2	no	—
389	C₂²⋊C₄×C₈₉	—	2	1	no	—
390	C₂²⋊C₄×C₈₉	—	2	2	no	—
391	C₂²⋊C₄×C₈₉	—	2	2	no	—
392	C₂²⋊C₄×C₈₉	—	2	2	no	—
393	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
394	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
395	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
396	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
397	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
398	C₄²×C₈₉	—	2	2	no	—
399	C₄²×C₈₉	—	2	2	no	—
400	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
402	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
403	C₄²×C₈₉	C₂⁴	1	2	yes	—
404	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
405	C₂³×C₈₉	—	2	2	no	—
406	C₂³×C₈₉	—	2	1	no	—
407	C₂³×C₈₉	—	2	2	no	—
408	C₂³×C₈₉	—	2	1	no	—
409	C₂³×C₈₉	—	8	2	no	—
410	C₂³×C₈₉	—	8	2	no	—
411	C₂³×C₈₉	—	8	2	no	—
412	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
413	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
414	Q₈×C₈₉	—	2	2	no	—
415	Q₈×C₈₉	—	2	2	no	—
416	Q₈×C₈₉	—	4	1	no	—
417	Q₈×C₈₉	—	8	1	no	—
418	Q₈×C₈₉	—	8	1	no	—
419	Q₈×C₈₉	—	8	2	no	—
420	D₄×C₈₉	—	2	2	no	—
421	D₄×C₈₉	—	2	2	no	—
422	D₄×C₈₉	—	2	2	no	—
423	D₄×C₈₉	—	2	2	no	—
424	D₄×C₈₉	—	2	2	no	—
425	D₄×C₈₉	—	2	2	no	—
426	D₄×C₈₉	—	4	1	no	—
427	D₄×C₈₉	—	4	2	no	—
428	D₄×C₈₉	—	4	2	no	—
429	D₄×C₈₉	—	4	4	no	—
430	D₄×C₈₉	—	8	1	no	—
431	D₄×C₈₉	—	8	1	no	—
432	D₄×C₈₉	—	8	1	no	—
433	D₄×C₈₉	—	8	2	no	—
434	D₄×C₈₉	—	8	2	no	—
435	D₄×C₈₉	—	8	1	no	—
436	D₄×C₈₉	—	8	1	no	—
437	D₄×C₈₉	—	8	2	no	—
438	D₄×C₈₉	—	8	2	no	—
439	D₄×C₈₉	—	8	2	no	—
440	D₄×C₈₉	—	8	2	no	—
441	D₄×C₈₉	—	8	2	no	—
442	D₄×C₈₉	—	8	1	no	—
443	D₄×C₈₉	—	8	2	no	—
444	D₄×C₈₉	—	8	1	no	—
445	C₂×C₄×C₈₉	—	2	2	no	—
446	C₂×C₄×C₈₉	—	2	2	no	—
447	C₂×C₄×C₈₉	—	2	2	no	—
448	C₂×C₄×C₈₉	—	2	1	no	—
449	C₂×C₄×C₈₉	—	2	2	no	—
450	C₂×C₄×C₈₉	—	2	2	no	—
451	C₂×C₄×C₈₉	—	2	2	no	—
452	C₂×C₄×C₈₉	—	2	1	no	—
453	C₂×C₄×C₈₉	—	2	2	no	—
454	C₂×C₄×C₈₉	—	4	1	no	—
455	C₂×C₄×C₈₉	—	4	1	no	—
456	C₂×C₄×C₈₉	—	4	2	no	—
457	C₂×C₄×C₈₉	—	4	2	no	—
458	C₂×C₄×C₈₉	—	4	2	no	—
459	C₂×C₄×C₈₉	—	8	2	no	—
460	C₂×C₄×C₈₉	—	8	2	no	—
461	C₂×C₄×C₈₉	—	8	2	no	—
462	C₂×C₄×C₈₉	—	8	2	no	—
463	C₂×C₄×C₈₉	—	8	2	no	—
464	C₂×C₄×C₈₉	—	8	2	no	—
465	C₂×C₄×C₈₉	—	8	1	no	—
466	C₂×C₄×C₈₉	—	8	2	no	—
467	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
468	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
469	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
475	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
476	C₈×C₈₉	—	2	2	no	—
477	C₈×C₈₉	—	2	2	no	—
478	C₈×C₈₉	—	2	2	no	—
479	C₈×C₈₉	—	2	2	no	—
480	C₂²×C₈₉	—	2	1	no	—
481	C₂²×C₈₉	—	2	1	no	—
482	C₂²×C₈₉	—	2	2	no	—
483	C₂²×C₈₉	—	2	2	no	—
484	C₂²×C₈₉	—	2	1	no	—
485	C₂²×C₈₉	—	2	2	no	—
486	C₂²×C₈₉	—	4	1	no	—
487	C₂²×C₈₉	—	4	1	no	—
488	C₂²×C₈₉	—	4	2	no	—
489	C₂²×C₈₉	—	4	2	no	—
490	C₂²×C₈₉	—	4	2	no	—
491	C₂²×C₈₉	—	4	1	no	—
492	C₂²×C₈₉	—	4	2	no	—
493	C₂²×C₈₉	—	4	1	no	—
494	C₂²×C₈₉	—	4	1	no	—
495	C₂²×C₈₉	—	4	2	no	—
496	C₂²×C₈₉	—	4	1	no	—
497	C₂²×C₈₉	—	4	2	no	—
498	C₂²×C₈₉	—	16	4	no	—
499	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
500	C₄×C₈₉	—	2	1	no	—
501	C₄×C₈₉	—	2	1	no	—
502	C₄×C₈₉	—	2	1	no	—
503	C₄×C₈₉	—	2	1	no	—
504	C₄×C₈₉	—	2	2	no	—
505	C₄×C₈₉	—	2	2	no	—
506	C₄×C₈₉	—	2	1	no	—
507	C₄×C₈₉	—	2	2	no	—
508	C₄×C₈₉	—	4	1	no	—
509	C₄×C₈₉	—	4	2	no	—
510	C₄×C₈₉	—	4	1	no	—
511	C₄×C₈₉	—	4	2	no	—
512	C₄×C₈₉	—	4	2	no	—
513	C₄×C₈₉	—	4	2	no	—
514	C₄×C₈₉	#585	1	2	yes	—
515	#62573	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
516	C₂×C₈₉	—	4	1	no	—
517	C₂×C₈₉	—	4	2	no	—
518	C₂×C₈₉	—	8	1	no	—
519	C₂×C₈₉	—	8	2	no	—
520	C₂×C₈₉	—	8	2	no	—
521	C₂×C₈₉	—	8	1	no	—
522	C₂×C₈₉	#3500	1	1	yes	characteristic
523	C₂×C₈₉	#3585	1	1	yes	characteristic
524	C₂×C₈₉	#3585	1	1	yes	characteristic
525	#3559	C₂×C₈₉	1	1	yes	characteristic, complemented
526	#3546	C₂×C₈₉	1	1	yes	characteristic, complemented
527	#3376	C₂×C₈₉	1	2	yes	complemented
528	#3366	C₂×C₈₉	1	2	yes	complemented
529	#3332	C₂×C₈₉	1	2	yes	complemented
530	#3322	C₂×C₈₉	1	2	yes	complemented
531	#3318	C₂×C₈₉	1	2	yes	complemented
532	#3309	C₂×C₈₉	1	2	yes	complemented
533	#3307	C₂×C₈₉	1	2	yes	complemented
534	#3306	C₂×C₈₉	1	2	yes	complemented
535	#3244	C₂×C₈₉	1	2	yes	complemented
536	#3234	C₂×C₈₉	1	1	yes	characteristic, complemented
537	#3220	C₂×C₈₉	1	2	yes	complemented
538	#3214	C₂×C₈₉	1	1	yes	characteristic, complemented
539	#3184	C₂×C₈₉	1	1	yes	characteristic, complemented
540	#3179	C₂×C₈₉	1	2	yes	complemented
541	#3142	C₂×C₈₉	1	1	yes	characteristic, complemented
542	#3136	C₂×C₈₉	1	2	yes	complemented
543	#2967	C₂×C₈₉	1	1	yes	characteristic, complemented
544	C₈₉	#62573	1	1	yes	characteristic, direct product factor, Sylow
545	#563	—	2	1	no	—
546	#562	—	2	1	no	—
547	#560	—	2	2	no	—
548	#556	C₂²×C₈₉	1	1	yes	characteristic
549	#554	C₂²×C₈₉	1	2	yes	complemented
550	#553	—	2	1	no	—
551	#553	C₂²×C₈₉	1	2	yes	—
552	#553	C₂²×C₈₉	1	2	yes	complemented
553	#550	C₂²×C₈₉	1	2	yes	—
554	#550	C₂²×C₈₉	1	1	yes	characteristic
555	#547	—	2	2	no	—
556	#547	C₂²×C₈₉	1	1	yes	characteristic
557	#547	C₂²×C₈₉	1	2	yes	complemented
558	#546	—	2	1	no	—
559	#546	C₂²×C₈₉	1	2	yes	—
560	D₄²	C₂²×C₈₉	1	1	yes	characteristic
561	#544	C₂²×C₈₉	1	2	yes	complemented
562	#542	C₂²×C₈₉	1	2	yes	—
563	#540	C₂²×C₈₉	1	2	yes	complemented
564	#539	—	2	2	no	—
565	#539	—	2	1	no	—
566	#538	—	2	2	no	—
567	#537	—	2	1	no	—
568	#537	—	2	1	no	—
569	#535	—	2	1	no	—
570	#535	C₂²×C₈₉	1	2	yes	—
571	#532	C₂²×C₈₉	1	1	yes	characteristic
572	#532	C₂²×C₈₉	1	1	yes	characteristic
573	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
574	#529	C₂²×C₈₉	1	1	yes	characteristic
575	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic, complemented
576	#501	C₂²×C₈₉	1	2	yes	complemented
577	#498	C₂²×C₈₉	1	1	yes	characteristic, complemented
578	#496	C₂²×C₈₉	1	2	yes	complemented
579	#493	C₂²×C₈₉	1	1	yes	characteristic
580	#491	C₂²×C₈₉	1	2	yes	complemented
581	#490	C₂²×C₈₉	1	2	yes	—
582	#490	C₂²×C₈₉	1	2	yes	—
583	#490	C₂²×C₈₉	1	2	yes	complemented
584	#489	C₂²×C₈₉	1	2	yes	—
585	#489	C₂²×C₈₉	1	2	yes	complemented
586	#488	C₂²×C₈₉	1	2	yes	—
587	#488	C₂²×C₈₉	1	2	yes	complemented
588	#488	C₂²×C₈₉	1	2	yes	complemented
589	#486	C₂²×C₈₉	1	1	yes	characteristic
590	#486	C₂²×C₈₉	1	2	yes	complemented
591	#486	C₂²×C₈₉	1	1	yes	characteristic, complemented
592	#485	C₂²×C₈₉	1	2	yes	complemented
593	#483	C₂²×C₈₉	1	2	yes	complemented
594	#482	C₂²×C₈₉	1	2	yes	—
595	#481	C₂²×C₈₉	1	2	yes	—
596	#481	C₂²×C₈₉	1	1	yes	characteristic
597	#481	C₂²×C₈₉	1	1	yes	characteristic, complemented
598	#480	C₂²×C₈₉	1	1	yes	characteristic
599	#480	C₂²×C₈₉	1	1	yes	characteristic, complemented
600	#479	C₂²×C₈₉	1	2	yes	complemented
601	#478	C₂²×C₈₉	1	2	yes	—
602	#478	C₂²×C₈₉	1	2	yes	complemented
603	#478	C₂²×C₈₉	1	2	yes	complemented
604	#476	C₂²×C₈₉	1	2	yes	complemented
605	#475	C₂²×C₈₉	1	2	yes	complemented
606	#469	C₂²×C₈₉	1	2	yes	—
607	#469	C₂²×C₈₉	1	2	yes	—
608	#469	C₂²×C₈₉	1	2	yes	complemented
609	#468	C₂²×C₈₉	1	2	yes	complemented
610	#466	C₂²×C₈₉	1	2	yes	—
611	#465	C₂²×C₈₉	1	2	yes	complemented
612	#463	C₂²×C₈₉	1	2	yes	—
613	#463	C₂²×C₈₉	1	2	yes	—
614	#461	C₂²×C₈₉	1	2	yes	complemented
615	#459	C₂²×C₈₉	1	2	yes	—
616	#459	C₂²×C₈₉	1	2	yes	complemented
617	#459	C₂²×C₈₉	1	2	yes	complemented
618	#449	C₂²×C₈₉	1	2	yes	complemented
619	#449	C₂²×C₈₉	1	2	yes	complemented
620	#449	C₂²×C₈₉	1	2	yes	complemented
621	#449	C₂²×C₈₉	1	2	yes	complemented
622	#447	C₂²×C₈₉	1	2	yes	—
623	#447	C₂²×C₈₉	1	2	yes	—
624	#446	C₂²×C₈₉	1	2	yes	complemented
625	#442	C₂²×C₈₉	1	2	yes	—
626	#442	C₂²×C₈₉	1	2	yes	complemented
627	#442	C₂²×C₈₉	1	2	yes	complemented
628	#440	C₂²×C₈₉	1	2	yes	complemented
629	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
630	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
631	#436	C₂²×C₈₉	1	2	yes	complemented
632	#435	C₂²×C₈₉	1	2	yes	—
633	#435	C₂²×C₈₉	1	2	yes	complemented
634	#433	C₂²×C₈₉	1	2	yes	complemented
635	#432	C₂²×C₈₉	1	1	yes	characteristic, complemented
636	#418	C₂²×C₈₉	1	2	yes	—
637	#417	C₂²×C₈₉	1	2	yes	complemented
638	#417	C₂²×C₈₉	1	2	yes	complemented
639	#417	C₂²×C₈₉	1	2	yes	complemented
640	#416	C₂²×C₈₉	1	2	yes	complemented
641	C₂×#102	C₂²×C₈₉	1	2	yes	—
642	#405	C₂²×C₈₉	1	2	yes	complemented
643	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
644	C₂×#41	—	2	1	no	—
645	C₂×#41	—	2	2	no	—
646	C₂×#41	—	2	1	no	—
647	C₂×#41	—	2	1	no	—
648	C₂×#41	C₂³×C₈₉	1	2	yes	—
649	C₂×#41	C₂³×C₈₉	1	2	yes	—
650	C₂²×D₄	—	2	1	no	—
651	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
652	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
653	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
654	C₂×D₈	C₂³×C₈₉	1	2	yes	—
655	C₂×D₈	C₂³×C₈₉	1	2	yes	—
656	C₂×D₈	C₂³×C₈₉	1	2	yes	—
657	C₂×D₈	C₂³×C₈₉	1	2	yes	—
658	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
659	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
660	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
661	C₄⋊Q₈	—	2	2	no	—
662	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
663	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
664	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
665	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
666	#127	—	2	2	no	—
667	#127	C₂³×C₈₉	1	1	yes	characteristic
668	#127	C₂³×C₈₉	1	1	yes	characteristic
669	#127	C₂³×C₈₉	1	1	yes	characteristic
670	#127	C₂³×C₈₉	1	2	yes	—
671	#126	—	2	2	no	—
672	#126	—	2	2	no	—
673	#126	—	2	2	no	—
674	#126	—	2	2	no	—
675	#126	D₄×C₈₉	1	2	yes	—
676	#125	—	2	2	no	—
677	#125	—	2	1	no	—
678	#125	—	2	1	no	—
679	#125	D₄×C₈₉	1	1	yes	characteristic
680	#125	C₂³×C₈₉	1	2	yes	—
681	#125	C₂³×C₈₉	1	2	yes	—
682	#125	C₂³×C₈₉	1	2	yes	—
683	#124	—	2	2	no	—
684	#124	—	2	1	no	—
685	#124	—	2	1	no	—
686	#124	D₄×C₈₉	1	1	yes	characteristic
687	#124	C₂³×C₈₉	1	2	yes	—
688	#124	C₂³×C₈₉	1	2	yes	—
689	#123	—	2	2	no	—
690	#123	—	2	2	no	—
691	#123	—	2	2	no	—
692	#123	—	2	2	no	—
693	#123	—	2	2	no	—
694	#123	—	2	2	no	—
695	#123	—	2	2	no	—
696	#123	—	2	2	no	—
697	#123	—	2	2	no	—
698	#123	D₄×C₈₉	1	2	yes	—
699	C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
705	C₂²⋊Q₈	—	2	2	no	—
706	C₂²⋊Q₈	—	2	2	no	—
707	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
708	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
709	#121	—	2	1	no	—
710	#121	—	2	2	no	—
711	#121	—	2	2	no	—
712	#121	—	2	1	no	—
713	#121	—	2	1	no	—
714	#121	—	2	1	no	—
715	#121	—	2	1	no	—
716	#121	—	2	1	no	—
717	#121	—	2	2	no	—
718	#121	—	2	2	no	—
719	#121	—	2	1	no	—
720	#121	—	2	2	no	—
721	#121	—	2	2	no	—
722	#121	—	2	2	no	—
723	#121	—	2	2	no	—
724	#121	—	2	2	no	—
725	#121	—	2	2	no	—
726	#121	D₄×C₈₉	1	1	yes	characteristic
727	#121	C₂³×C₈₉	1	1	yes	characteristic
728	#121	C₂³×C₈₉	1	1	yes	characteristic
729	#121	C₂³×C₈₉	1	2	yes	—
730	#121	C₂³×C₈₉	1	2	yes	—
731	#121	C₂³×C₈₉	1	2	yes	—
732	#121	C₂³×C₈₉	1	2	yes	—
733	#120	—	2	2	no	—
734	#120	—	2	2	no	—
735	#120	—	2	2	no	—
736	#120	—	2	2	no	—
737	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
738	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
739	C₄×D₄	—	2	2	no	—
740	C₄×D₄	—	2	2	no	—
741	C₄×D₄	—	2	2	no	—
742	C₄×D₄	—	2	1	no	—
743	C₄×D₄	—	2	1	no	—
744	C₄×D₄	—	2	1	no	—
745	C₄×D₄	—	2	1	no	—
746	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
747	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
748	C₄×D₄	C₂³×C₈₉	1	2	yes	—
749	C₄×D₄	C₂³×C₈₉	1	2	yes	—
750	C₄×D₄	C₂³×C₈₉	1	2	yes	—
751	C₄×D₄	C₂³×C₈₉	1	2	yes	—
752	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
753	C₄×D₄	C₂³×C₈₉	1	2	yes	—
754	#117	—	2	1	no	—
755	#117	C₂³×C₈₉	1	2	yes	—
756	#117	C₂³×C₈₉	1	2	yes	—
757	C₂×C₄⋊C₄	—	2	1	no	—
758	C₂×C₄⋊C₄	—	2	1	no	—
759	C₂×C₄⋊C₄	—	2	1	no	—
760	C₂×C₄⋊C₄	—	2	2	no	—
761	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
762	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
763	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
764	C₂×C₂²⋊C₄	—	2	2	no	—
765	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
766	#107	C₂³×C₈₉	1	2	yes	—
767	#107	C₂³×C₈₉	1	2	yes	—
768	#106	C₂³×C₈₉	1	2	yes	—
769	#106	C₂³×C₈₉	1	2	yes	—
770	#106	C₂³×C₈₉	1	2	yes	—
771	#106	C₂³×C₈₉	1	2	yes	—
772	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
773	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
774	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
775	#103	C₂³×C₈₉	1	2	yes	—
776	#103	C₂³×C₈₉	1	2	yes	—
777	#103	C₂³×C₈₉	1	2	yes	—
778	#103	C₂³×C₈₉	1	2	yes	—
779	#103	C₂³×C₈₉	1	2	yes	—
780	#103	C₂³×C₈₉	1	2	yes	—
781	#102	C₂³×C₈₉	1	2	yes	—
782	#102	C₂³×C₈₉	1	2	yes	—
783	#102	C₂³×C₈₉	1	2	yes	—
784	#102	C₂³×C₈₉	1	2	yes	—
785	#102	C₂³×C₈₉	1	2	yes	—
786	#102	C₂³×C₈₉	1	2	yes	—
787	#102	C₂³×C₈₉	1	2	yes	—
788	#102	C₂³×C₈₉	1	2	yes	—
789	#102	C₂³×C₈₉	1	2	yes	—
790	#102	C₂³×C₈₉	1	2	yes	—
791	#102	C₂³×C₈₉	1	2	yes	—
792	#102	C₂³×C₈₉	1	2	yes	—
793	#102	C₂³×C₈₉	1	2	yes	—
794	#102	C₂³×C₈₉	1	2	yes	—
795	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
796	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
797	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
798	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
799	#97	C₂³×C₈₉	1	2	yes	—
800	#97	C₂³×C₈₉	1	2	yes	—
801	#97	C₂³×C₈₉	1	2	yes	—
802	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
803	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
804	C₄×C₈	C₂³×C₈₉	1	2	yes	—
805	C₂⁴	—	2	2	no	—
806	#41	—	4	2	no	—
807	#41	—	4	2	no	—
808	#41	—	4	2	no	—
809	#41	—	4	2	no	—
810	#41	—	8	2	no	—
811	#41	—	8	2	no	—
812	#41	—	8	4	no	—
813	#41	—	8	2	no	—
814	C₂×Q₈	—	2	2	no	—
815	C₂×Q₈	—	2	1	no	—
816	C₂×Q₈	—	2	1	no	—
817	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
818	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	2	1	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	—	2	2	no	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	1	no	—
827	C₂×D₄	—	2	1	no	—
828	C₂×D₄	—	2	1	no	—
829	C₂×D₄	—	2	1	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	1	no	—
832	C₂×D₄	—	2	1	no	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	1	no	—
836	C₂×D₄	—	4	2	no	—
837	C₂×D₄	—	4	2	no	—
838	C₂×D₄	—	8	2	no	—
839	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
840	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
841	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
842	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
843	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
844	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
845	C₂²×C₄	—	2	1	no	—
846	C₂²×C₄	—	2	1	no	—
847	C₂²×C₄	—	2	2	no	—
848	C₂²×C₄	—	2	1	no	—
849	C₂²×C₄	—	2	1	no	—
850	C₂²×C₄	—	2	2	no	—
851	C₂²×C₄	—	2	2	no	—
852	C₂²×C₄	—	2	2	no	—
853	C₂²×C₄	—	2	2	no	—
854	C₂²×C₄	—	2	2	no	—
855	C₂²×C₄	—	2	2	no	—
856	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
857	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
858	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
860	SD₁₆	—	4	2	no	—
861	SD₁₆	—	4	2	no	—
862	D₈	—	4	2	no	—
863	D₈	—	4	2	no	—
864	D₈	—	4	2	no	—
865	D₈	—	4	2	no	—
866	M₁₆	—	4	2	no	—
867	M₁₆	—	4	2	no	—
868	C₂×C₈	—	4	2	no	—
869	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
870	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
871	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
872	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	1	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	1	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	1	no	—
884	C₄⋊C₄	—	2	1	no	—
885	C₄⋊C₄	—	2	1	no	—
886	C₄⋊C₄	—	2	1	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
890	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
891	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
892	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
893	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
894	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
895	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
896	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
897	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
898	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
899	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	1	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	1	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	1	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	1	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
919	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
920	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
921	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
922	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
923	C₄²	—	2	2	no	—
924	C₄²	—	2	2	no	—
925	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
926	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
927	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
928	C₄²	C₂⁴×C₈₉	1	2	yes	—
929	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
930	C₂³	—	2	2	no	—
931	C₂³	—	2	1	no	—
932	C₂³	—	2	2	no	—
933	C₂³	—	2	1	no	—
934	C₂³	—	8	2	no	—
935	C₂³	—	8	2	no	—
936	C₂³	—	8	2	no	—
937	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
938	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
939	Q₈	—	2	2	no	—
940	Q₈	—	2	2	no	—
941	Q₈	—	4	1	no	—
942	Q₈	—	8	1	no	—
943	Q₈	—	8	1	no	—
944	Q₈	—	8	2	no	—
945	D₄	—	2	2	no	—
946	D₄	—	2	2	no	—
947	D₄	—	2	2	no	—
948	D₄	—	2	2	no	—
949	D₄	—	2	2	no	—
950	D₄	—	2	2	no	—
951	D₄	—	4	1	no	—
952	D₄	—	4	2	no	—
953	D₄	—	4	2	no	—
954	D₄	—	4	4	no	—
955	D₄	—	8	1	no	—
956	D₄	—	8	1	no	—
957	D₄	—	8	1	no	—
958	D₄	—	8	2	no	—
959	D₄	—	8	2	no	—
960	D₄	—	8	1	no	—
961	D₄	—	8	1	no	—
962	D₄	—	8	2	no	—
963	D₄	—	8	2	no	—
964	D₄	—	8	2	no	—
965	D₄	—	8	2	no	—
966	D₄	—	8	2	no	—
967	D₄	—	8	1	no	—
968	D₄	—	8	2	no	—
969	D₄	—	8	1	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	4	1	no	—
980	C₂×C₄	—	4	1	no	—
981	C₂×C₄	—	4	2	no	—
982	C₂×C₄	—	4	2	no	—
983	C₂×C₄	—	4	2	no	—
984	C₂×C₄	—	8	2	no	—
985	C₂×C₄	—	8	2	no	—
986	C₂×C₄	—	8	2	no	—
987	C₂×C₄	—	8	2	no	—
988	C₂×C₄	—	8	2	no	—
989	C₂×C₄	—	8	2	no	—
990	C₂×C₄	—	8	1	no	—
991	C₂×C₄	—	8	2	no	—
992	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
993	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
994	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
995	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
996	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
997	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
998	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
999	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1000	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1001	C₈	—	2	2	no	—
1002	C₈	—	2	2	no	—
1003	C₈	—	2	2	no	—
1004	C₈	—	2	2	no	—
1005	C₂²	—	2	1	no	—
1006	C₂²	—	2	1	no	—
1007	C₂²	—	2	2	no	—
1008	C₂²	—	2	2	no	—
1009	C₂²	—	2	1	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	4	1	no	—
1012	C₂²	—	4	1	no	—
1013	C₂²	—	4	2	no	—
1014	C₂²	—	4	2	no	—
1015	C₂²	—	4	2	no	—
1016	C₂²	—	4	1	no	—
1017	C₂²	—	4	2	no	—
1018	C₂²	—	4	1	no	—
1019	C₂²	—	4	1	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	4	1	no	—
1022	C₂²	—	4	2	no	—
1023	C₂²	—	16	4	no	—
1024	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1025	C₄	—	2	1	no	—
1026	C₄	—	2	1	no	—
1027	C₄	—	2	1	no	—
1028	C₄	—	2	1	no	—
1029	C₄	—	2	2	no	—
1030	C₄	—	2	2	no	—
1031	C₄	—	2	1	no	—
1032	C₄	—	2	2	no	—
1033	C₄	—	4	1	no	—
1034	C₄	—	4	2	no	—
1035	C₄	—	4	1	no	—
1036	C₄	—	4	2	no	—
1037	C₄	—	4	2	no	—
1038	C₄	—	4	2	no	—
1039	C₄	#585×C₈₉	1	2	yes	—
1040	C₂	—	4	1	no	—
1041	C₂	—	4	2	no	—
1042	C₂	—	8	1	no	—
1043	C₂	—	8	2	no	—
1044	C₂	—	8	2	no	—
1045	C₂	—	8	1	no	—
1046	C₂	C₈₉×#3500	1	1	yes	characteristic
1047	C₂	C₈₉×#3585	1	1	yes	characteristic
1048	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×#3559	C₂	semidirect
2. C₈₉×#3546	C₂	semidirect
3. C₈₉×#3376	C₂	semidirect
4. C₈₉×#3366	C₂	semidirect
5. C₈₉×#3332	C₂	semidirect
6. C₈₉×#3322	C₂	semidirect
7. C₈₉×#3318	C₂	semidirect
8. C₈₉×#3309	C₂	semidirect
9. C₈₉×#3307	C₂	semidirect
10. C₈₉×#3306	C₂	semidirect
11. C₈₉×#3244	C₂	semidirect
12. C₈₉×#3234	C₂	semidirect
13. C₈₉×#3220	C₂	semidirect
14. C₈₉×#3214	C₂	semidirect
15. C₈₉×#3184	C₂	semidirect
16. C₈₉×#3179	C₂	semidirect
17. C₈₉×#3142	C₂	semidirect
18. C₈₉×#3136	C₂	semidirect
19. C₈₉×#2967	C₂	semidirect
24. #554×C₈₉	C₂²	semidirect
27. #553×C₈₉	C₂²	semidirect
32. #547×C₈₉	C₂²	semidirect
36. #544×C₈₉	C₂²	semidirect
38. #540×C₈₉	C₂²	semidirect
48. #532×C₈₉	C₂²	semidirect
50. C₂×#125×C₈₉	C₂²	semidirect
51. #501×C₈₉	C₂²	semidirect
52. #498×C₈₉	C₂²	semidirect
53. #496×C₈₉	C₂²	semidirect
55. #491×C₈₉	C₂²	semidirect
58. #490×C₈₉	C₂²	semidirect
60. #489×C₈₉	C₂²	semidirect
62. #488×C₈₉	C₂²	semidirect
63. #488×C₈₉	C₂²	semidirect
65. #486×C₈₉	C₂²	semidirect
66. #486×C₈₉	C₂²	semidirect
67. #485×C₈₉	C₂²	semidirect
68. #483×C₈₉	C₂²	semidirect
72. #481×C₈₉	C₂²	semidirect
74. #480×C₈₉	C₂²	semidirect
75. #479×C₈₉	C₂²	semidirect
77. #478×C₈₉	C₂²	semidirect
78. #478×C₈₉	C₂²	semidirect
79. #476×C₈₉	C₂²	semidirect
80. #475×C₈₉	C₂²	semidirect
83. #469×C₈₉	C₂²	semidirect
84. #468×C₈₉	C₂²	semidirect
86. #465×C₈₉	C₂²	semidirect
89. #461×C₈₉	C₂²	semidirect
91. #459×C₈₉	C₂²	semidirect
92. #459×C₈₉	C₂²	semidirect
93. #449×C₈₉	C₂²	semidirect
94. #449×C₈₉	C₂²	semidirect
95. #449×C₈₉	C₂²	semidirect
96. #449×C₈₉	C₂²	semidirect
99. #446×C₈₉	C₂²	semidirect
101. #442×C₈₉	C₂²	semidirect
102. #442×C₈₉	C₂²	semidirect
103. #440×C₈₉	C₂²	semidirect
104. C₄×SD₁₆×C₈₉	C₂²	semidirect
105. C₄×D₈×C₈₉	C₂²	semidirect
106. #436×C₈₉	C₂²	semidirect
108. #435×C₈₉	C₂²	semidirect
109. #433×C₈₉	C₂²	semidirect
110. #432×C₈₉	C₂²	semidirect
112. #417×C₈₉	C₂²	semidirect
113. #417×C₈₉	C₂²	semidirect
114. #417×C₈₉	C₂²	semidirect
115. #416×C₈₉	C₂²	semidirect
117. #405×C₈₉	C₂²	semidirect
118. C₄×M₁₆×C₈₉	C₂²	semidirect
515. #62573	C₈₉	direct (N × H)
525. #3559	C₂×C₈₉	semidirect
526. #3546	C₂×C₈₉	semidirect
527. #3376	C₂×C₈₉	semidirect
528. #3366	C₂×C₈₉	semidirect
529. #3332	C₂×C₈₉	semidirect
530. #3322	C₂×C₈₉	semidirect
531. #3318	C₂×C₈₉	semidirect
532. #3309	C₂×C₈₉	semidirect
533. #3307	C₂×C₈₉	semidirect
534. #3306	C₂×C₈₉	semidirect
535. #3244	C₂×C₈₉	semidirect
536. #3234	C₂×C₈₉	semidirect
537. #3220	C₂×C₈₉	semidirect
538. #3214	C₂×C₈₉	semidirect
539. #3184	C₂×C₈₉	semidirect
540. #3179	C₂×C₈₉	semidirect
541. #3142	C₂×C₈₉	semidirect
542. #3136	C₂×C₈₉	semidirect
543. #2967	C₂×C₈₉	semidirect
544. C₈₉	#62573	direct (N × H)
549. #554	C₂²×C₈₉	semidirect
552. #553	C₂²×C₈₉	semidirect
557. #547	C₂²×C₈₉	semidirect
561. #544	C₂²×C₈₉	semidirect
563. #540	C₂²×C₈₉	semidirect
573. #532	C₂²×C₈₉	semidirect
575. C₂×#125	C₂²×C₈₉	semidirect
576. #501	C₂²×C₈₉	semidirect
577. #498	C₂²×C₈₉	semidirect
578. #496	C₂²×C₈₉	semidirect
580. #491	C₂²×C₈₉	semidirect
583. #490	C₂²×C₈₉	semidirect
585. #489	C₂²×C₈₉	semidirect
587. #488	C₂²×C₈₉	semidirect
588. #488	C₂²×C₈₉	semidirect
590. #486	C₂²×C₈₉	semidirect
591. #486	C₂²×C₈₉	semidirect
592. #485	C₂²×C₈₉	semidirect
593. #483	C₂²×C₈₉	semidirect
597. #481	C₂²×C₈₉	semidirect
599. #480	C₂²×C₈₉	semidirect
600. #479	C₂²×C₈₉	semidirect
602. #478	C₂²×C₈₉	semidirect
603. #478	C₂²×C₈₉	semidirect
604. #476	C₂²×C₈₉	semidirect
605. #475	C₂²×C₈₉	semidirect
608. #469	C₂²×C₈₉	semidirect
609. #468	C₂²×C₈₉	semidirect
611. #465	C₂²×C₈₉	semidirect
614. #461	C₂²×C₈₉	semidirect
616. #459	C₂²×C₈₉	semidirect
617. #459	C₂²×C₈₉	semidirect
618. #449	C₂²×C₈₉	semidirect
619. #449	C₂²×C₈₉	semidirect
620. #449	C₂²×C₈₉	semidirect
621. #449	C₂²×C₈₉	semidirect
624. #446	C₂²×C₈₉	semidirect
626. #442	C₂²×C₈₉	semidirect
627. #442	C₂²×C₈₉	semidirect
628. #440	C₂²×C₈₉	semidirect
629. C₄×SD₁₆	C₂²×C₈₉	semidirect
630. C₄×D₈	C₂²×C₈₉	semidirect
631. #436	C₂²×C₈₉	semidirect
633. #435	C₂²×C₈₉	semidirect
634. #433	C₂²×C₈₉	semidirect
635. #432	C₂²×C₈₉	semidirect
637. #417	C₂²×C₈₉	semidirect
638. #417	C₂²×C₈₉	semidirect
639. #417	C₂²×C₈₉	semidirect
640. #416	C₂²×C₈₉	semidirect
642. #405	C₂²×C₈₉	semidirect
643. C₄×M₁₆	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×#3559	2
C₈₉×#3546	2
C₈₉×#3376	2
C₈₉×#3366	2
C₈₉×#3332	2
C₈₉×#3322	2
C₈₉×#3318	2
C₈₉×#3309	2
C₈₉×#3307	2
C₈₉×#3306	2
C₈₉×#3244	2
C₈₉×#3234	2
C₈₉×#3220	2
C₈₉×#3214	2
C₈₉×#3184	2
C₈₉×#3179	2
C₈₉×#3142	2
C₈₉×#3136	2
C₈₉×#2967	2
#62573	89

Subgroups — C89×#62573 #36440421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62573 #36440421