Subgroups — C₈₉×#22423 #36400271

Order 22784.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#435×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#418×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#102×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2352	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#1982	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1961	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1895	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1875	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1804	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1786	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1786	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1762	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₈₉	—	2	1	no	—
17	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
20	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
21	D₄²×C₈₉	—	2	4	no	—
22	D₄²×C₈₉	C₄	1	8	yes	complemented
23	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#121×C₈₉	—	2	1	no	—
25	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#120×C₈₉	—	2	1	no	—
28	C₂×#120×C₈₉	—	2	1	no	—
29	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
33	#435×C₈₉	—	2	4	no	—
34	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
35	#418×C₈₉	—	2	4	no	—
36	C₂×#102×C₈₉	—	2	4	no	—
37	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
44	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
46	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
47	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
48	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
51	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic, complemented
52	#388×C₈₉	—	2	1	no	—
53	#387×C₈₉	—	2	1	no	—
54	#386×C₈₉	—	2	1	no	—
55	#382×C₈₉	C₂²	1	1	yes	characteristic, complemented
56	#380×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	#380×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
60	#340×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	#340×C₈₉	C₂²	1	1	yes	characteristic, complemented
62	#340×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	#340×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	C₂⁵×C₈₉	—	2	1	no	—
65	C₂⁵×C₈₉	—	2	1	no	—
66	C₂²×D₄×C₈₉	—	2	2	no	—
67	C₂²×D₄×C₈₉	—	2	2	no	—
68	C₂²×D₄×C₈₉	—	2	2	no	—
69	C₂²×D₄×C₈₉	—	2	2	no	—
70	C₂²×D₄×C₈₉	—	2	1	no	—
71	C₂²×D₄×C₈₉	—	2	1	no	—
72	C₂²×D₄×C₈₉	—	2	8	no	—
73	C₂²×D₄×C₈₉	—	2	1	no	—
74	C₂²×D₄×C₈₉	—	2	1	no	—
75	C₂²×D₄×C₈₉	—	2	1	no	—
76	C₂²×D₄×C₈₉	—	2	2	no	—
77	C₂²×D₄×C₈₉	—	2	2	no	—
78	C₂²×D₄×C₈₉	—	2	1	no	—
79	C₂²×D₄×C₈₉	—	4	1	no	—
80	C₂²×D₄×C₈₉	—	4	1	no	—
81	C₂²×D₄×C₈₉	—	4	1	no	—
82	C₂²×D₄×C₈₉	—	4	1	no	—
83	C₂²×D₄×C₈₉	—	4	4	no	—
84	C₂²×D₄×C₈₉	—	4	4	no	—
85	C₂²×D₄×C₈₉	C₂×C₄	1	4	yes	—
86	C₂²×D₄×C₈₉	C₂×C₄	1	4	yes	complemented
87	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
88	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₈₉	—	2	1	no	—
92	C₂³×C₄×C₈₉	—	2	1	no	—
93	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
95	C₂×M₁₆×C₈₉	—	2	2	no	—
96	C₂×M₁₆×C₈₉	—	2	2	no	—
97	C₂×M₁₆×C₈₉	—	4	1	no	—
98	C₂²×C₈×C₈₉	—	2	2	no	—
99	C₂²×C₈×C₈₉	—	2	2	no	—
100	C₂²×C₈×C₈₉	—	4	1	no	—
101	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
105	#127×C₈₉	—	2	2	no	—
106	#127×C₈₉	C₂×C₄	1	4	yes	complemented
107	#121×C₈₉	—	2	2	no	—
108	#121×C₈₉	—	2	2	no	—
109	#121×C₈₉	—	2	8	no	—
110	#121×C₈₉	C₂×C₄	1	4	yes	—
111	#121×C₈₉	C₂×C₄	1	4	yes	complemented
112	#120×C₈₉	—	2	8	no	—
113	#120×C₈₉	—	2	8	no	—
114	C₄×D₄×C₈₉	—	2	2	no	—
115	C₄×D₄×C₈₉	C₂×C₄	1	4	yes	—
116	C₄×D₄×C₈₉	C₂×C₄	1	4	yes	complemented
117	C₄×D₄×C₈₉	D₄	1	4	yes	—
118	#117×C₈₉	—	2	2	no	—
119	#117×C₈₉	—	4	1	no	—
120	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
121	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
122	C₂×C₄⋊C₄×C₈₉	—	4	1	no	—
123	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
131	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
133	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
134	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
135	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
136	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
137	C₂×C₄²×C₈₉	—	2	1	no	—
138	C₂×C₄²×C₈₉	—	2	1	no	—
139	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
140	C₄⋊C₈×C₈₉	—	2	2	no	—
141	#102×C₈₉	—	2	2	no	—
142	#102×C₈₉	—	2	2	no	—
143	#102×C₈₉	—	2	2	no	—
144	#102×C₈₉	—	2	2	no	—
145	#102×C₈₉	—	2	2	no	—
146	#102×C₈₉	—	2	2	no	—
147	#102×C₈₉	—	2	2	no	—
148	#102×C₈₉	—	4	1	no	—
149	#102×C₈₉	—	4	1	no	—
150	#102×C₈₉	—	4	1	no	—
151	#102×C₈₉	—	4	1	no	—
152	#102×C₈₉	D₄	1	4	yes	complemented
153	C₂²⋊C₈×C₈₉	—	2	2	no	—
154	C₂²⋊C₈×C₈₉	—	2	2	no	—
155	#97×C₈₉	—	2	2	no	—
156	#95×C₈₉	—	2	1	no	—
157	#95×C₈₉	—	2	1	no	—
158	#95×C₈₉	—	2	1	no	—
159	#95×C₈₉	—	2	1	no	—
160	#95×C₈₉	—	2	1	no	—
161	C₂⁴×C₈₉	—	2	1	no	—
162	C₂⁴×C₈₉	—	2	1	no	—
163	C₂⁴×C₈₉	—	2	1	no	—
164	C₂⁴×C₈₉	—	2	4	no	—
165	C₂⁴×C₈₉	—	2	4	no	—
166	C₂⁴×C₈₉	—	4	2	no	—
167	C₂⁴×C₈₉	—	4	2	no	—
168	C₂⁴×C₈₉	—	4	2	no	—
169	C₂⁴×C₈₉	—	4	2	no	—
170	C₂⁴×C₈₉	—	4	2	no	—
171	C₂⁴×C₈₉	—	4	2	no	—
172	C₂⁴×C₈₉	—	4	2	no	—
173	C₂⁴×C₈₉	—	4	2	no	—
174	C₂⁴×C₈₉	—	8	1	no	—
175	C₂⁴×C₈₉	—	8	1	no	—
176	C₂⁴×C₈₉	—	8	1	no	—
177	C₂⁴×C₈₉	—	8	1	no	—
178	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
179	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
180	C₂×D₄×C₈₉	—	2	2	no	—
181	C₂×D₄×C₈₉	—	2	2	no	—
182	C₂×D₄×C₈₉	—	2	8	no	—
183	C₂×D₄×C₈₉	—	2	8	no	—
184	C₂×D₄×C₈₉	—	2	4	no	—
185	C₂×D₄×C₈₉	—	2	4	no	—
186	C₂×D₄×C₈₉	—	2	4	no	—
187	C₂×D₄×C₈₉	—	2	4	no	—
188	C₂×D₄×C₈₉	—	2	4	no	—
189	C₂×D₄×C₈₉	—	2	4	no	—
190	C₂×D₄×C₈₉	—	2	1	no	—
191	C₂×D₄×C₈₉	—	2	1	no	—
192	C₂×D₄×C₈₉	—	2	1	no	—
193	C₂×D₄×C₈₉	—	2	1	no	—
194	C₂×D₄×C₈₉	—	2	1	no	—
195	C₂×D₄×C₈₉	—	2	1	no	—
196	C₂×D₄×C₈₉	—	2	1	no	—
197	C₂×D₄×C₈₉	—	2	1	no	—
198	C₂×D₄×C₈₉	—	2	1	no	—
199	C₂×D₄×C₈₉	—	2	1	no	—
200	C₂×D₄×C₈₉	—	2	1	no	—
201	C₂×D₄×C₈₉	—	2	1	no	—
202	C₂×D₄×C₈₉	—	2	1	no	—
203	C₂×D₄×C₈₉	—	4	4	no	—
204	C₂×D₄×C₈₉	—	4	4	no	—
205	C₂×D₄×C₈₉	—	4	4	no	—
206	C₂×D₄×C₈₉	—	4	4	no	—
207	C₂×D₄×C₈₉	—	4	4	no	—
208	C₂×D₄×C₈₉	—	4	4	no	—
209	C₂×D₄×C₈₉	—	4	2	no	—
210	C₂×D₄×C₈₉	—	4	2	no	—
211	C₂×D₄×C₈₉	—	4	2	no	—
212	C₂×D₄×C₈₉	—	4	2	no	—
213	C₂×D₄×C₈₉	—	4	2	no	—
214	C₂×D₄×C₈₉	—	4	2	no	—
215	C₂×D₄×C₈₉	—	4	32	no	—
216	C₂×D₄×C₈₉	—	4	2	no	—
217	C₂×D₄×C₈₉	—	4	2	no	—
218	C₂×D₄×C₈₉	—	4	2	no	—
219	C₂×D₄×C₈₉	—	4	2	no	—
220	C₂×D₄×C₈₉	—	8	1	no	—
221	C₂×D₄×C₈₉	—	8	1	no	—
222	C₂×D₄×C₈₉	C₂²⋊C₄	1	4	yes	—
223	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
224	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
225	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
226	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
227	C₂×D₄×C₈₉	#41	1	2	yes	—
228	C₂²×C₄×C₈₉	—	2	1	no	—
229	C₂²×C₄×C₈₉	—	2	1	no	—
230	C₂²×C₄×C₈₉	—	2	1	no	—
231	C₂²×C₄×C₈₉	—	2	1	no	—
232	C₂²×C₄×C₈₉	—	2	1	no	—
233	C₂²×C₄×C₈₉	—	2	1	no	—
234	C₂²×C₄×C₈₉	—	2	1	no	—
235	C₂²×C₄×C₈₉	—	2	1	no	—
236	C₂²×C₄×C₈₉	—	2	1	no	—
237	C₂²×C₄×C₈₉	—	2	1	no	—
238	C₂²×C₄×C₈₉	—	2	4	no	—
239	C₂²×C₄×C₈₉	—	2	1	no	—
240	C₂²×C₄×C₈₉	—	2	1	no	—
241	C₂²×C₄×C₈₉	—	2	1	no	—
242	C₂²×C₄×C₈₉	—	4	2	no	—
243	C₂²×C₄×C₈₉	—	4	2	no	—
244	C₂²×C₄×C₈₉	—	4	2	no	—
245	C₂²×C₄×C₈₉	—	4	2	no	—
246	C₂²×C₄×C₈₉	—	8	1	no	—
247	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
248	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
249	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
254	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
255	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
256	M₁₆×C₈₉	—	4	4	no	—
257	C₂×C₈×C₈₉	—	2	1	no	—
258	C₂×C₈×C₈₉	—	2	1	no	—
259	C₂×C₈×C₈₉	—	2	1	no	—
260	C₂×C₈×C₈₉	—	2	1	no	—
261	C₂×C₈×C₈₉	—	2	1	no	—
262	C₂×C₈×C₈₉	—	2	1	no	—
263	C₂×C₈×C₈₉	—	2	1	no	—
264	C₂×C₈×C₈₉	—	2	1	no	—
265	C₂×C₈×C₈₉	—	2	1	no	—
266	C₂×C₈×C₈₉	—	2	1	no	—
267	C₂×C₈×C₈₉	—	2	1	no	—
268	C₂×C₈×C₈₉	—	4	4	no	—
269	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	complemented
270	C₄⋊C₄×C₈₉	—	2	1	no	—
271	C₄⋊C₄×C₈₉	—	2	1	no	—
272	C₄⋊C₄×C₈₉	—	2	1	no	—
273	C₄⋊C₄×C₈₉	—	2	1	no	—
274	C₄⋊C₄×C₈₉	—	2	1	no	—
275	C₄⋊C₄×C₈₉	—	2	1	no	—
276	C₄⋊C₄×C₈₉	—	2	1	no	—
277	C₄⋊C₄×C₈₉	—	2	1	no	—
278	C₄⋊C₄×C₈₉	—	4	2	no	—
279	C₄⋊C₄×C₈₉	C₂²⋊C₄	1	4	yes	—
280	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
281	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	complemented
282	C₂²⋊C₄×C₈₉	—	2	4	no	—
283	C₂²⋊C₄×C₈₉	—	2	4	no	—
284	C₂²⋊C₄×C₈₉	—	2	4	no	—
285	C₂²⋊C₄×C₈₉	—	4	2	no	—
286	C₂²⋊C₄×C₈₉	—	4	2	no	—
287	C₂²⋊C₄×C₈₉	—	8	1	no	—
288	C₂²⋊C₄×C₈₉	C₂²⋊C₄	1	4	yes	—
289	C₂²⋊C₄×C₈₉	C₂²⋊C₄	1	4	yes	—
290	C₄²×C₈₉	—	4	2	no	—
291	C₄²×C₈₉	—	8	1	no	—
292	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
293	C₄²×C₈₉	C₂×D₄	1	2	yes	—
294	C₂³×C₈₉	—	2	1	no	—
295	C₂³×C₈₉	—	2	1	no	—
296	C₂³×C₈₉	—	2	1	no	—
297	C₂³×C₈₉	—	2	1	no	—
298	C₂³×C₈₉	—	2	2	no	—
299	C₂³×C₈₉	—	2	1	no	—
300	C₂³×C₈₉	—	2	2	no	—
301	C₂³×C₈₉	—	2	1	no	—
302	C₂³×C₈₉	—	2	2	no	—
303	C₂³×C₈₉	—	2	1	no	—
304	C₂³×C₈₉	—	2	1	no	—
305	C₂³×C₈₉	—	2	1	no	—
306	C₂³×C₈₉	—	2	1	no	—
307	C₂³×C₈₉	—	2	2	no	—
308	C₂³×C₈₉	—	2	2	no	—
309	C₂³×C₈₉	—	4	8	no	—
310	C₂³×C₈₉	—	4	8	no	—
311	C₂³×C₈₉	—	4	8	no	—
312	C₂³×C₈₉	—	4	1	no	—
313	C₂³×C₈₉	—	4	1	no	—
314	C₂³×C₈₉	—	4	1	no	—
315	C₂³×C₈₉	—	4	1	no	—
316	C₂³×C₈₉	—	4	1	no	—
317	C₂³×C₈₉	—	4	1	no	—
318	C₂³×C₈₉	—	4	1	no	—
319	C₂³×C₈₉	—	4	1	no	—
320	C₂³×C₈₉	—	4	1	no	—
321	C₂³×C₈₉	—	4	1	no	—
322	C₂³×C₈₉	—	4	1	no	—
323	C₂³×C₈₉	—	4	1	no	—
324	C₂³×C₈₉	—	4	1	no	—
325	C₂³×C₈₉	—	4	1	no	—
326	C₂³×C₈₉	—	4	1	no	—
327	C₂³×C₈₉	—	4	1	no	—
328	C₂³×C₈₉	—	4	8	no	—
329	C₂³×C₈₉	—	8	4	no	—
330	C₂³×C₈₉	—	8	4	no	—
331	C₂³×C₈₉	—	8	4	no	—
332	C₂³×C₈₉	—	8	4	no	—
333	C₂³×C₈₉	—	8	4	no	—
334	C₂³×C₈₉	—	8	4	no	—
335	C₂³×C₈₉	—	8	4	no	—
336	C₂³×C₈₉	—	8	4	no	—
337	C₂³×C₈₉	—	8	4	no	—
338	C₂³×C₈₉	—	8	4	no	—
339	C₂³×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
340	C₂³×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
341	C₂³×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
342	C₂³×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
343	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
344	D₄×C₈₉	—	2	8	no	—
345	D₄×C₈₉	—	2	2	no	—
346	D₄×C₈₉	—	2	2	no	—
347	D₄×C₈₉	—	2	2	no	—
348	D₄×C₈₉	—	2	2	no	—
349	D₄×C₈₉	—	2	2	no	—
350	D₄×C₈₉	—	2	2	no	—
351	D₄×C₈₉	—	2	2	no	—
352	D₄×C₈₉	—	4	8	no	—
353	D₄×C₈₉	—	4	8	no	—
354	D₄×C₈₉	—	4	8	no	—
355	D₄×C₈₉	—	4	8	no	—
356	D₄×C₈₉	—	4	8	no	—
357	D₄×C₈₉	—	4	1	no	—
358	D₄×C₈₉	—	4	1	no	—
359	D₄×C₈₉	—	4	1	no	—
360	D₄×C₈₉	—	4	1	no	—
361	D₄×C₈₉	—	8	4	no	—
362	D₄×C₈₉	C₄×D₄	1	4	yes	—
363	C₂×C₄×C₈₉	—	2	1	no	—
364	C₂×C₄×C₈₉	—	2	1	no	—
365	C₂×C₄×C₈₉	—	2	1	no	—
366	C₂×C₄×C₈₉	—	2	1	no	—
367	C₂×C₄×C₈₉	—	2	1	no	—
368	C₂×C₄×C₈₉	—	2	1	no	—
369	C₂×C₄×C₈₉	—	2	1	no	—
370	C₂×C₄×C₈₉	—	2	1	no	—
371	C₂×C₄×C₈₉	—	2	2	no	—
372	C₂×C₄×C₈₉	—	2	2	no	—
373	C₂×C₄×C₈₉	—	2	2	no	—
374	C₂×C₄×C₈₉	—	2	2	no	—
375	C₂×C₄×C₈₉	—	2	2	no	—
376	C₂×C₄×C₈₉	—	2	2	no	—
377	C₂×C₄×C₈₉	—	2	2	no	—
378	C₂×C₄×C₈₉	—	2	2	no	—
379	C₂×C₄×C₈₉	—	2	2	no	—
380	C₂×C₄×C₈₉	—	2	2	no	—
381	C₂×C₄×C₈₉	—	4	8	no	—
382	C₂×C₄×C₈₉	—	4	1	no	—
383	C₂×C₄×C₈₉	—	4	1	no	—
384	C₂×C₄×C₈₉	—	4	1	no	—
385	C₂×C₄×C₈₉	—	4	1	no	—
386	C₂×C₄×C₈₉	—	4	1	no	—
387	C₂×C₄×C₈₉	—	4	1	no	—
388	C₂×C₄×C₈₉	—	4	1	no	—
389	C₂×C₄×C₈₉	—	4	1	no	—
390	C₂×C₄×C₈₉	—	4	1	no	—
391	C₂×C₄×C₈₉	—	4	1	no	—
392	C₂×C₄×C₈₉	—	4	1	no	—
393	C₂×C₄×C₈₉	—	4	1	no	—
394	C₂×C₄×C₈₉	—	4	1	no	—
395	C₂×C₄×C₈₉	—	8	4	no	—
396	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
397	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
398	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
399	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
400	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
401	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
404	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
405	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
406	C₈×C₈₉	—	2	2	no	—
407	C₈×C₈₉	—	4	1	no	—
408	C₈×C₈₉	—	4	1	no	—
409	C₈×C₈₉	—	4	1	no	—
410	C₂²×C₈₉	—	2	2	no	—
411	C₂²×C₈₉	—	2	2	no	—
412	C₂²×C₈₉	—	2	2	no	—
413	C₂²×C₈₉	—	2	2	no	—
414	C₂²×C₈₉	—	2	2	no	—
415	C₂²×C₈₉	—	2	2	no	—
416	C₂²×C₈₉	—	2	2	no	—
417	C₂²×C₈₉	—	2	4	no	—
418	C₂²×C₈₉	—	2	2	no	—
419	C₂²×C₈₉	—	2	2	no	—
420	C₂²×C₈₉	—	4	2	no	—
421	C₂²×C₈₉	—	4	2	no	—
422	C₂²×C₈₉	—	4	1	no	—
423	C₂²×C₈₉	—	4	2	no	—
424	C₂²×C₈₉	—	4	1	no	—
425	C₂²×C₈₉	—	4	2	no	—
426	C₂²×C₈₉	—	4	1	no	—
427	C₂²×C₈₉	—	4	2	no	—
428	C₂²×C₈₉	—	4	1	no	—
429	C₂²×C₈₉	—	4	2	no	—
430	C₂²×C₈₉	—	4	2	no	—
431	C₂²×C₈₉	—	4	2	no	—
432	C₂²×C₈₉	—	4	2	no	—
433	C₂²×C₈₉	—	4	2	no	—
434	C₂²×C₈₉	—	4	2	no	—
435	C₂²×C₈₉	—	4	2	no	—
436	C₂²×C₈₉	—	8	16	no	—
437	C₂²×C₈₉	—	8	16	no	—
438	C₂²×C₈₉	—	8	1	no	—
439	C₂²×C₈₉	—	8	1	no	—
440	C₂²×C₈₉	—	8	1	no	—
441	C₂²×C₈₉	—	8	1	no	—
442	C₂²×C₈₉	—	8	1	no	—
443	C₂²×C₈₉	—	8	1	no	—
444	C₂²×C₈₉	—	8	1	no	—
445	C₂²×C₈₉	—	8	1	no	—
446	C₂²×C₈₉	#418	1	4	yes	complemented
447	C₂²×C₈₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
448	C₂²×C₈₉	D₄²	1	1	yes	characteristic
449	C₂²×C₈₉	#546	1	1	yes	characteristic
450	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
451	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
452	C₂²×C₈₉	#576	1	1	yes	characteristic
453	C₂²×C₈₉	#577	1	1	yes	characteristic
454	C₄×C₈₉	—	2	2	no	—
455	C₄×C₈₉	—	2	2	no	—
456	C₄×C₈₉	—	2	2	no	—
457	C₄×C₈₉	—	2	2	no	—
458	C₄×C₈₉	—	4	2	no	—
459	C₄×C₈₉	—	4	2	no	—
460	C₄×C₈₉	—	8	1	no	—
461	C₄×C₈₉	—	8	1	no	—
462	C₄×C₈₉	—	8	1	no	—
463	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
464	C₄×C₈₉	#518	1	1	yes	characteristic
465	C₄×C₈₉	D₄²	1	1	yes	characteristic
466	C₄×C₈₉	#546	1	1	yes	characteristic
467	#22423	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
468	C₂×C₈₉	—	2	4	no	—
469	C₂×C₈₉	—	4	2	no	—
470	C₂×C₈₉	—	4	4	no	—
471	C₂×C₈₉	—	8	2	no	—
472	C₂×C₈₉	—	8	2	no	—
473	C₂×C₈₉	D₄×C₂²⋊C₄	1	1	yes	characteristic
474	C₂×C₈₉	C₂×#418	1	1	yes	characteristic
475	C₂×C₈₉	#2897	1	1	yes	characteristic
476	C₂×C₈₉	#3264	1	1	yes	characteristic
477	C₂×C₈₉	#3265	1	1	yes	characteristic
478	C₂×C₈₉	#3310	1	1	yes	characteristic
479	C₂×C₈₉	#3318	1	1	yes	characteristic
480	C₂×D₄²	C₂×C₈₉	1	1	yes	characteristic
481	C₂×#435	C₂×C₈₉	1	1	yes	characteristic, complemented
482	C₂×#418	C₂×C₈₉	1	1	yes	characteristic, complemented
483	C₂²×#102	C₂×C₈₉	1	1	yes	characteristic, complemented
484	#2352	C₂×C₈₉	1	1	yes	characteristic, complemented
485	#1982	C₂×C₈₉	1	1	yes	characteristic, complemented
486	#1961	C₂×C₈₉	1	1	yes	characteristic, complemented
487	#1895	C₂×C₈₉	1	1	yes	characteristic, complemented
488	#1893	C₂×C₈₉	1	1	yes	characteristic, complemented
489	#1875	C₂×C₈₉	1	1	yes	characteristic, complemented
490	#1874	C₂×C₈₉	1	1	yes	characteristic, complemented
491	#1804	C₂×C₈₉	1	1	yes	characteristic, complemented
492	#1786	C₂×C₈₉	1	1	yes	characteristic, complemented
493	#1786	C₂×C₈₉	1	1	yes	characteristic, complemented
494	#1762	C₂×C₈₉	1	1	yes	characteristic, complemented
495	C₈₉	#22423	1	1	yes	characteristic, direct product factor, Sylow
496	C₂³×D₄	—	2	1	no	—
497	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
498	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
499	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
500	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
501	D₄²	—	2	4	no	—
502	D₄²	C₄×C₈₉	1	8	yes	complemented
503	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
504	C₂×#121	—	2	1	no	—
505	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
506	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
507	C₂×#120	—	2	1	no	—
508	C₂×#120	—	2	1	no	—
509	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
510	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
511	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic, complemented
512	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
513	#435	—	2	4	no	—
514	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
515	#418	—	2	4	no	—
516	C₂×#102	—	2	4	no	—
517	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
518	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
519	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
520	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
521	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
522	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
523	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
524	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
525	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
526	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
527	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
528	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
529	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
530	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
531	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic, complemented
532	#388	—	2	1	no	—
533	#387	—	2	1	no	—
534	#386	—	2	1	no	—
535	#382	C₂²×C₈₉	1	1	yes	characteristic, complemented
536	#380	C₂²×C₈₉	1	1	yes	characteristic, complemented
537	#380	C₂²×C₈₉	1	1	yes	characteristic, complemented
538	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
539	C₄×C₂²⋊C₄	—	2	1	no	—
540	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
541	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
542	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
543	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
544	C₂⁵	—	2	1	no	—
545	C₂⁵	—	2	1	no	—
546	C₂²×D₄	—	2	2	no	—
547	C₂²×D₄	—	2	2	no	—
548	C₂²×D₄	—	2	2	no	—
549	C₂²×D₄	—	2	2	no	—
550	C₂²×D₄	—	2	1	no	—
551	C₂²×D₄	—	2	1	no	—
552	C₂²×D₄	—	2	8	no	—
553	C₂²×D₄	—	2	1	no	—
554	C₂²×D₄	—	2	1	no	—
555	C₂²×D₄	—	2	1	no	—
556	C₂²×D₄	—	2	2	no	—
557	C₂²×D₄	—	2	2	no	—
558	C₂²×D₄	—	2	1	no	—
559	C₂²×D₄	—	4	1	no	—
560	C₂²×D₄	—	4	1	no	—
561	C₂²×D₄	—	4	1	no	—
562	C₂²×D₄	—	4	1	no	—
563	C₂²×D₄	—	4	4	no	—
564	C₂²×D₄	—	4	4	no	—
565	C₂²×D₄	C₂×C₄×C₈₉	1	4	yes	—
566	C₂²×D₄	C₂×C₄×C₈₉	1	4	yes	complemented
567	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
568	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
569	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
570	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
571	C₂³×C₄	—	2	1	no	—
572	C₂³×C₄	—	2	1	no	—
573	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
574	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
575	C₂×M₁₆	—	2	2	no	—
576	C₂×M₁₆	—	2	2	no	—
577	C₂×M₁₆	—	4	1	no	—
578	C₂²×C₈	—	2	2	no	—
579	C₂²×C₈	—	2	2	no	—
580	C₂²×C₈	—	4	1	no	—
581	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
582	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
583	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
584	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
585	#127	—	2	2	no	—
586	#127	C₂×C₄×C₈₉	1	4	yes	complemented
587	#121	—	2	2	no	—
588	#121	—	2	2	no	—
589	#121	—	2	8	no	—
590	#121	C₂×C₄×C₈₉	1	4	yes	—
591	#121	C₂×C₄×C₈₉	1	4	yes	complemented
592	#120	—	2	8	no	—
593	#120	—	2	8	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	C₂×C₄×C₈₉	1	4	yes	—
596	C₄×D₄	C₂×C₄×C₈₉	1	4	yes	complemented
597	C₄×D₄	D₄×C₈₉	1	4	yes	—
598	#117	—	2	2	no	—
599	#117	—	4	1	no	—
600	C₂×C₄⋊C₄	—	2	2	no	—
601	C₂×C₄⋊C₄	—	2	1	no	—
602	C₂×C₄⋊C₄	—	4	1	no	—
603	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
609	C₂×C₂²⋊C₄	—	2	1	no	—
610	C₂×C₂²⋊C₄	—	2	1	no	—
611	C₂×C₂²⋊C₄	—	2	1	no	—
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
616	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
617	C₂×C₄²	—	2	1	no	—
618	C₂×C₄²	—	2	1	no	—
619	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
620	C₄⋊C₈	—	2	2	no	—
621	#102	—	2	2	no	—
622	#102	—	2	2	no	—
623	#102	—	2	2	no	—
624	#102	—	2	2	no	—
625	#102	—	2	2	no	—
626	#102	—	2	2	no	—
627	#102	—	2	2	no	—
628	#102	—	4	1	no	—
629	#102	—	4	1	no	—
630	#102	—	4	1	no	—
631	#102	—	4	1	no	—
632	#102	D₄×C₈₉	1	4	yes	complemented
633	C₂²⋊C₈	—	2	2	no	—
634	C₂²⋊C₈	—	2	2	no	—
635	#97	—	2	2	no	—
636	#95	—	2	1	no	—
637	#95	—	2	1	no	—
638	#95	—	2	1	no	—
639	#95	—	2	1	no	—
640	#95	—	2	1	no	—
641	C₂⁴	—	2	1	no	—
642	C₂⁴	—	2	1	no	—
643	C₂⁴	—	2	1	no	—
644	C₂⁴	—	2	4	no	—
645	C₂⁴	—	2	4	no	—
646	C₂⁴	—	4	2	no	—
647	C₂⁴	—	4	2	no	—
648	C₂⁴	—	4	2	no	—
649	C₂⁴	—	4	2	no	—
650	C₂⁴	—	4	2	no	—
651	C₂⁴	—	4	2	no	—
652	C₂⁴	—	4	2	no	—
653	C₂⁴	—	4	2	no	—
654	C₂⁴	—	8	1	no	—
655	C₂⁴	—	8	1	no	—
656	C₂⁴	—	8	1	no	—
657	C₂⁴	—	8	1	no	—
658	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
659	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	2	2	no	—
662	C₂×D₄	—	2	8	no	—
663	C₂×D₄	—	2	8	no	—
664	C₂×D₄	—	2	4	no	—
665	C₂×D₄	—	2	4	no	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	4	no	—
668	C₂×D₄	—	2	4	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	—	2	1	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	4	4	no	—
684	C₂×D₄	—	4	4	no	—
685	C₂×D₄	—	4	4	no	—
686	C₂×D₄	—	4	4	no	—
687	C₂×D₄	—	4	4	no	—
688	C₂×D₄	—	4	4	no	—
689	C₂×D₄	—	4	2	no	—
690	C₂×D₄	—	4	2	no	—
691	C₂×D₄	—	4	2	no	—
692	C₂×D₄	—	4	2	no	—
693	C₂×D₄	—	4	2	no	—
694	C₂×D₄	—	4	2	no	—
695	C₂×D₄	—	4	32	no	—
696	C₂×D₄	—	4	2	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂×D₄	—	4	2	no	—
699	C₂×D₄	—	4	2	no	—
700	C₂×D₄	—	8	1	no	—
701	C₂×D₄	—	8	1	no	—
702	C₂×D₄	C₂²⋊C₄×C₈₉	1	4	yes	—
703	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
704	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
705	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
706	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
707	C₂×D₄	#41×C₈₉	1	2	yes	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	2	1	no	—
720	C₂²×C₄	—	2	1	no	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	4	2	no	—
723	C₂²×C₄	—	4	2	no	—
724	C₂²×C₄	—	4	2	no	—
725	C₂²×C₄	—	4	2	no	—
726	C₂²×C₄	—	8	1	no	—
727	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
728	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
729	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
730	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
731	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
732	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
733	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
734	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
736	M₁₆	—	4	4	no	—
737	C₂×C₈	—	2	1	no	—
738	C₂×C₈	—	2	1	no	—
739	C₂×C₈	—	2	1	no	—
740	C₂×C₈	—	2	1	no	—
741	C₂×C₈	—	2	1	no	—
742	C₂×C₈	—	2	1	no	—
743	C₂×C₈	—	2	1	no	—
744	C₂×C₈	—	2	1	no	—
745	C₂×C₈	—	2	1	no	—
746	C₂×C₈	—	2	1	no	—
747	C₂×C₈	—	2	1	no	—
748	C₂×C₈	—	4	4	no	—
749	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	complemented
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	1	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	—	2	1	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	2	1	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	4	2	no	—
759	C₄⋊C₄	C₂²⋊C₄×C₈₉	1	4	yes	—
760	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
761	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	complemented
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	4	2	no	—
766	C₂²⋊C₄	—	4	2	no	—
767	C₂²⋊C₄	—	8	1	no	—
768	C₂²⋊C₄	C₂²⋊C₄×C₈₉	1	4	yes	—
769	C₂²⋊C₄	C₂²⋊C₄×C₈₉	1	4	yes	—
770	C₄²	—	4	2	no	—
771	C₄²	—	8	1	no	—
772	C₄²	C₂²×C₄×C₈₉	1	2	yes	—
773	C₄²	C₂×D₄×C₈₉	1	2	yes	—
774	C₂³	—	2	1	no	—
775	C₂³	—	2	1	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	2	2	no	—
779	C₂³	—	2	1	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	1	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	1	no	—
784	C₂³	—	2	1	no	—
785	C₂³	—	2	1	no	—
786	C₂³	—	2	1	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	4	8	no	—
790	C₂³	—	4	8	no	—
791	C₂³	—	4	8	no	—
792	C₂³	—	4	1	no	—
793	C₂³	—	4	1	no	—
794	C₂³	—	4	1	no	—
795	C₂³	—	4	1	no	—
796	C₂³	—	4	8	no	—
797	C₂³	—	4	1	no	—
798	C₂³	—	4	1	no	—
799	C₂³	—	4	1	no	—
800	C₂³	—	4	1	no	—
801	C₂³	—	4	1	no	—
802	C₂³	—	4	1	no	—
803	C₂³	—	4	1	no	—
804	C₂³	—	4	1	no	—
805	C₂³	—	4	1	no	—
806	C₂³	—	4	1	no	—
807	C₂³	—	4	1	no	—
808	C₂³	—	4	1	no	—
809	C₂³	—	8	4	no	—
810	C₂³	—	8	4	no	—
811	C₂³	—	8	4	no	—
812	C₂³	—	8	4	no	—
813	C₂³	—	8	4	no	—
814	C₂³	—	8	4	no	—
815	C₂³	—	8	4	no	—
816	C₂³	—	8	4	no	—
817	C₂³	—	8	4	no	—
818	C₂³	—	8	4	no	—
819	C₂³	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
820	C₂³	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
821	C₂³	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
822	C₂³	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
823	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
824	D₄	—	2	8	no	—
825	D₄	—	2	2	no	—
826	D₄	—	2	2	no	—
827	D₄	—	2	2	no	—
828	D₄	—	2	2	no	—
829	D₄	—	2	2	no	—
830	D₄	—	2	2	no	—
831	D₄	—	2	2	no	—
832	D₄	—	4	8	no	—
833	D₄	—	4	8	no	—
834	D₄	—	4	8	no	—
835	D₄	—	4	8	no	—
836	D₄	—	4	8	no	—
837	D₄	—	4	1	no	—
838	D₄	—	4	1	no	—
839	D₄	—	4	1	no	—
840	D₄	—	4	1	no	—
841	D₄	—	8	4	no	—
842	D₄	C₄×D₄×C₈₉	1	4	yes	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	4	8	no	—
862	C₂×C₄	—	4	1	no	—
863	C₂×C₄	—	4	1	no	—
864	C₂×C₄	—	4	1	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	4	1	no	—
867	C₂×C₄	—	4	1	no	—
868	C₂×C₄	—	4	1	no	—
869	C₂×C₄	—	4	1	no	—
870	C₂×C₄	—	4	1	no	—
871	C₂×C₄	—	4	1	no	—
872	C₂×C₄	—	4	1	no	—
873	C₂×C₄	—	4	1	no	—
874	C₂×C₄	—	4	1	no	—
875	C₂×C₄	—	8	4	no	—
876	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
877	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
878	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
879	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
880	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
881	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
882	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
883	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
884	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
885	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
886	C₈	—	2	2	no	—
887	C₈	—	4	1	no	—
888	C₈	—	4	1	no	—
889	C₈	—	4	1	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	2	2	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	4	no	—
898	C₂²	—	2	2	no	—
899	C₂²	—	2	2	no	—
900	C₂²	—	4	1	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	1	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	1	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	1	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	2	no	—
911	C₂²	—	4	2	no	—
912	C₂²	—	4	2	no	—
913	C₂²	—	4	2	no	—
914	C₂²	—	4	2	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	8	16	no	—
917	C₂²	—	8	16	no	—
918	C₂²	—	8	1	no	—
919	C₂²	—	8	1	no	—
920	C₂²	—	8	1	no	—
921	C₂²	—	8	1	no	—
922	C₂²	—	8	1	no	—
923	C₂²	—	8	1	no	—
924	C₂²	—	8	1	no	—
925	C₂²	—	8	1	no	—
926	C₂²	#418×C₈₉	1	4	yes	complemented
927	C₂²	C₂²×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
928	C₂²	D₄²×C₈₉	1	1	yes	characteristic
929	C₂²	#546×C₈₉	1	1	yes	characteristic
930	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
931	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
932	C₂²	#576×C₈₉	1	1	yes	characteristic
933	C₂²	#577×C₈₉	1	1	yes	characteristic
934	C₄	—	2	2	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	2	no	—
937	C₄	—	2	2	no	—
938	C₄	—	4	2	no	—
939	C₄	—	4	2	no	—
940	C₄	—	8	1	no	—
941	C₄	—	8	1	no	—
942	C₄	—	8	1	no	—
943	C₄	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
944	C₄	#518×C₈₉	1	1	yes	characteristic
945	C₄	D₄²×C₈₉	1	1	yes	characteristic
946	C₄	#546×C₈₉	1	1	yes	characteristic
947	C₂	—	2	4	no	—
948	C₂	—	4	2	no	—
949	C₂	—	4	4	no	—
950	C₂	—	8	2	no	—
951	C₂	—	8	2	no	—
952	C₂	D₄×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
953	C₂	C₂×#418×C₈₉	1	1	yes	characteristic
954	C₂	C₈₉×#2897	1	1	yes	characteristic
955	C₂	C₈₉×#3264	1	1	yes	characteristic
956	C₂	C₈₉×#3265	1	1	yes	characteristic
957	C₂	C₈₉×#3310	1	1	yes	characteristic
958	C₂	C₈₉×#3318	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₈₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂×D₄²×C₈₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×C₄×D₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#435×C₈₉	C₂	semidirect
3. C₂×#418×C₈₉	C₂	semidirect
4. C₂²×#102×C₈₉	C₂	semidirect
5. C₈₉×#2352	C₂	semidirect
6. C₈₉×#1982	C₂	semidirect
7. C₈₉×#1961	C₂	semidirect
8. C₈₉×#1895	C₂	semidirect
9. C₈₉×#1893	C₂	semidirect
10. C₈₉×#1875	C₂	semidirect
11. C₈₉×#1874	C₂	semidirect
12. C₈₉×#1804	C₂	semidirect
13. C₈₉×#1786	C₂	semidirect
14. C₈₉×#1786	C₂	semidirect
15. C₈₉×#1762	C₂	semidirect
19. C₂²×M₁₆×C₈₉	C₂²	semidirect
20. C₂³×C₈×C₈₉	C₂²	semidirect
22. D₄²×C₈₉	C₄	semidirect
31. C₂×#117×C₈₉	C₂²	semidirect
32. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
34. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
41. C₂×#102×C₈₉	C₂²	semidirect
42. C₂×#102×C₈₉	C₂²	semidirect
43. C₂×#102×C₈₉	C₂²	semidirect
44. C₂×#102×C₈₉	C₂²	semidirect
45. C₂×#102×C₈₉	C₂²	semidirect
46. C₂×#102×C₈₉	C₂²	semidirect
47. C₂×#102×C₈₉	C₂²	semidirect
48. C₂×#102×C₈₉	C₂²	semidirect
49. C₂×C₂²⋊C₈×C₈₉	C₂²	semidirect
50. C₂×C₂²⋊C₈×C₈₉	C₂²	semidirect
51. C₂×#97×C₈₉	C₂²	semidirect
55. #382×C₈₉	C₂²	semidirect
56. #380×C₈₉	C₂²	semidirect
57. #380×C₈₉	C₂²	semidirect
58. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
60. #340×C₈₉	C₂²	semidirect
61. #340×C₈₉	C₂²	semidirect
62. #340×C₈₉	C₂²	semidirect
63. #340×C₈₉	C₂²	semidirect
86. C₂²×D₄×C₈₉	C₂×C₄	semidirect
106. #127×C₈₉	C₂×C₄	semidirect
111. #121×C₈₉	C₂×C₄	semidirect
116. C₄×D₄×C₈₉	C₂×C₄	semidirect
152. #102×C₈₉	D₄	semidirect
269. C₂×C₈×C₈₉	C₂×D₄	semidirect
281. C₄⋊C₄×C₈₉	C₂×D₄	semidirect
446. C₂²×C₈₉	#418	semidirect
467. #22423	C₈₉	direct (N × H)
481. C₂×#435	C₂×C₈₉	semidirect
482. C₂×#418	C₂×C₈₉	semidirect
483. C₂²×#102	C₂×C₈₉	semidirect
484. #2352	C₂×C₈₉	semidirect
485. #1982	C₂×C₈₉	semidirect
486. #1961	C₂×C₈₉	semidirect
487. #1895	C₂×C₈₉	semidirect
488. #1893	C₂×C₈₉	semidirect
489. #1875	C₂×C₈₉	semidirect
490. #1874	C₂×C₈₉	semidirect
491. #1804	C₂×C₈₉	semidirect
492. #1786	C₂×C₈₉	semidirect
493. #1786	C₂×C₈₉	semidirect
494. #1762	C₂×C₈₉	semidirect
495. C₈₉	#22423	direct (N × H)
499. C₂²×M₁₆	C₂²×C₈₉	semidirect
500. C₂³×C₈	C₂²×C₈₉	semidirect
502. D₄²	C₄×C₈₉	semidirect
511. C₂×#117	C₂²×C₈₉	semidirect
512. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
514. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
521. C₂×#102	C₂²×C₈₉	semidirect
522. C₂×#102	C₂²×C₈₉	semidirect
523. C₂×#102	C₂²×C₈₉	semidirect
524. C₂×#102	C₂²×C₈₉	semidirect
525. C₂×#102	C₂²×C₈₉	semidirect
526. C₂×#102	C₂²×C₈₉	semidirect
527. C₂×#102	C₂²×C₈₉	semidirect
528. C₂×#102	C₂²×C₈₉	semidirect
529. C₂×C₂²⋊C₈	C₂²×C₈₉	semidirect
530. C₂×C₂²⋊C₈	C₂²×C₈₉	semidirect
531. C₂×#97	C₂²×C₈₉	semidirect
535. #382	C₂²×C₈₉	semidirect
536. #380	C₂²×C₈₉	semidirect
537. #380	C₂²×C₈₉	semidirect
538. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
540. #340	C₂²×C₈₉	semidirect
541. #340	C₂²×C₈₉	semidirect
542. #340	C₂²×C₈₉	semidirect
543. #340	C₂²×C₈₉	semidirect
566. C₂²×D₄	C₂×C₄×C₈₉	semidirect
586. #127	C₂×C₄×C₈₉	semidirect
591. #121	C₂×C₄×C₈₉	semidirect
596. C₄×D₄	C₂×C₄×C₈₉	semidirect
632. #102	D₄×C₈₉	semidirect
749. C₂×C₈	C₂×D₄×C₈₉	semidirect
761. C₄⋊C₄	C₂×D₄×C₈₉	semidirect
926. C₂²	#418×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄²×C₈₉	2
C₂×#435×C₈₉	2
C₂×#418×C₈₉	2
C₂²×#102×C₈₉	2
C₈₉×#2352	2
C₈₉×#1982	2
C₈₉×#1961	2
C₈₉×#1895	2
C₈₉×#1893	2
C₈₉×#1875	2
C₈₉×#1874	2
C₈₉×#1804	2
C₈₉×#1786	2
C₈₉×#1762	2
#22423	89

Subgroups — C89×#22423 #36400271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#22423 #36400271