Subgroups — C₈₉×#22419 #36400267

Order 22784.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#546×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#435×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#417×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#102×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#1983	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1959	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1895	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1892	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1872	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1802	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1788	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	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
20	#546×C₈₉	—	2	4	no	—
21	#546×C₈₉	C₄	1	8	yes	complemented
22	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#123×C₈₉	—	2	1	no	—
24	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#121×C₈₉	—	2	1	no	—
26	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#120×C₈₉	—	2	1	no	—
28	C₂×C₄×D₄×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	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₂²⋊C₄×C₈₉	—	2	1	no	—
34	#435×C₈₉	—	2	4	no	—
35	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
36	#417×C₈₉	—	2	4	no	—
37	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
38	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×#102×C₈₉	—	2	4	no	—
42	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
52	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	#389×C₈₉	—	2	1	no	—
54	#385×C₈₉	—	2	1	no	—
55	#385×C₈₉	—	2	1	no	—
56	#384×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	#380×C₈₉	C₂²	1	1	yes	characteristic
58	#380×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
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	C₂×#41×C₈₉	—	2	2	no	—
66	C₂×#41×C₈₉	—	2	2	no	—
67	C₂×#41×C₈₉	—	2	2	no	—
68	C₂×#41×C₈₉	—	4	1	no	—
69	C₂×#41×C₈₉	—	4	1	no	—
70	C₂×#41×C₈₉	C₂×C₄	1	4	yes	complemented
71	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₈₉	—	2	2	no	—
73	C₂²×D₄×C₈₉	—	2	2	no	—
74	C₂²×D₄×C₈₉	—	2	1	no	—
75	C₂²×D₄×C₈₉	—	2	1	no	—
76	C₂²×D₄×C₈₉	—	2	1	no	—
77	C₂²×D₄×C₈₉	—	2	2	no	—
78	C₂²×D₄×C₈₉	—	4	1	no	—
79	C₂²×D₄×C₈₉	—	4	1	no	—
80	C₂²×D₄×C₈₉	C₂×C₄	1	4	yes	complemented
81	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
82	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₈₉	—	2	1	no	—
85	C₂³×C₄×C₈₉	—	2	1	no	—
86	C₂³×C₄×C₈₉	—	2	1	no	—
87	C₂³×C₄×C₈₉	—	2	1	no	—
88	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
90	C₂×M₁₆×C₈₉	—	2	2	no	—
91	C₂×M₁₆×C₈₉	—	2	2	no	—
92	C₂×M₁₆×C₈₉	—	4	1	no	—
93	C₂²×C₈×C₈₉	—	2	2	no	—
94	C₂²×C₈×C₈₉	—	2	2	no	—
95	C₂²×C₈×C₈₉	—	4	1	no	—
96	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
100	#124×C₈₉	—	2	2	no	—
101	#124×C₈₉	C₂×C₄	1	4	yes	complemented
102	#123×C₈₉	—	2	8	no	—
103	C₂²⋊Q₈×C₈₉	—	2	2	no	—
104	C₂²⋊Q₈×C₈₉	C₂×C₄	1	4	yes	complemented
105	#121×C₈₉	—	2	2	no	—
106	#121×C₈₉	—	2	8	no	—
107	#121×C₈₉	C₂×C₄	1	4	yes	complemented
108	#120×C₈₉	—	2	8	no	—
109	C₄×D₄×C₈₉	—	2	2	no	—
110	C₄×D₄×C₈₉	—	4	4	no	—
111	C₄×D₄×C₈₉	C₂×C₄	1	4	yes	—
112	C₄×D₄×C₈₉	C₂×C₄	1	4	yes	complemented
113	C₄×D₄×C₈₉	D₄	1	4	yes	—
114	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
115	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
116	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
117	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
118	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
119	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
120	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
121	C₂×C₄⋊C₄×C₈₉	—	4	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	8	no	—
135	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
136	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
137	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
138	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
139	C₂×C₄²×C₈₉	—	2	1	no	—
140	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
141	C₄⋊C₈×C₈₉	—	2	2	no	—
142	#103×C₈₉	—	2	2	no	—
143	#103×C₈₉	—	2	2	no	—
144	#103×C₈₉	—	4	1	no	—
145	#103×C₈₉	—	4	1	no	—
146	#102×C₈₉	—	2	2	no	—
147	#102×C₈₉	—	2	2	no	—
148	#102×C₈₉	—	2	2	no	—
149	#102×C₈₉	—	2	2	no	—
150	#102×C₈₉	—	2	2	no	—
151	#102×C₈₉	—	4	1	no	—
152	#102×C₈₉	—	4	1	no	—
153	#102×C₈₉	D₄	1	4	yes	complemented
154	C₂²⋊C₈×C₈₉	—	2	2	no	—
155	C₂²⋊C₈×C₈₉	—	2	2	no	—
156	#97×C₈₉	—	2	2	no	—
157	#95×C₈₉	—	2	1	no	—
158	#95×C₈₉	—	2	1	no	—
159	#95×C₈₉	—	2	1	no	—
160	C₂⁴×C₈₉	—	2	1	no	—
161	C₂⁴×C₈₉	—	2	1	no	—
162	C₂⁴×C₈₉	—	2	4	no	—
163	C₂⁴×C₈₉	—	4	2	no	—
164	C₂⁴×C₈₉	—	4	2	no	—
165	C₂⁴×C₈₉	—	4	2	no	—
166	C₂⁴×C₈₉	—	4	2	no	—
167	C₂⁴×C₈₉	—	8	1	no	—
168	C₂⁴×C₈₉	—	8	1	no	—
169	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
170	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
171	#41×C₈₉	—	2	8	no	—
172	#41×C₈₉	—	4	4	no	—
173	#41×C₈₉	—	4	4	no	—
174	#41×C₈₉	—	4	4	no	—
175	C₂×Q₈×C₈₉	—	2	1	no	—
176	C₂×Q₈×C₈₉	—	2	1	no	—
177	C₂×Q₈×C₈₉	—	2	1	no	—
178	C₂×Q₈×C₈₉	—	2	1	no	—
179	C₂×Q₈×C₈₉	—	2	1	no	—
180	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
181	C₂×D₄×C₈₉	—	2	2	no	—
182	C₂×D₄×C₈₉	—	2	2	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	1	no	—
188	C₂×D₄×C₈₉	—	2	1	no	—
189	C₂×D₄×C₈₉	—	2	1	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	—	4	4	no	—
196	C₂×D₄×C₈₉	—	4	4	no	—
197	C₂×D₄×C₈₉	—	4	4	no	—
198	C₂×D₄×C₈₉	—	4	2	no	—
199	C₂×D₄×C₈₉	—	4	2	no	—
200	C₂×D₄×C₈₉	—	4	2	no	—
201	C₂×D₄×C₈₉	—	4	2	no	—
202	C₂×D₄×C₈₉	—	8	1	no	—
203	C₂×D₄×C₈₉	—	8	1	no	—
204	C₂×D₄×C₈₉	C₂²⋊C₄	1	4	yes	—
205	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
206	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
207	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
208	C₂×D₄×C₈₉	#41	1	2	yes	—
209	C₂²×C₄×C₈₉	—	2	1	no	—
210	C₂²×C₄×C₈₉	—	2	1	no	—
211	C₂²×C₄×C₈₉	—	2	1	no	—
212	C₂²×C₄×C₈₉	—	2	1	no	—
213	C₂²×C₄×C₈₉	—	2	1	no	—
214	C₂²×C₄×C₈₉	—	2	1	no	—
215	C₂²×C₄×C₈₉	—	2	1	no	—
216	C₂²×C₄×C₈₉	—	2	1	no	—
217	C₂²×C₄×C₈₉	—	2	1	no	—
218	C₂²×C₄×C₈₉	—	2	1	no	—
219	C₂²×C₄×C₈₉	—	2	1	no	—
220	C₂²×C₄×C₈₉	—	2	4	no	—
221	C₂²×C₄×C₈₉	—	2	4	no	—
222	C₂²×C₄×C₈₉	—	2	1	no	—
223	C₂²×C₄×C₈₉	—	2	1	no	—
224	C₂²×C₄×C₈₉	—	2	1	no	—
225	C₂²×C₄×C₈₉	—	4	2	no	—
226	C₂²×C₄×C₈₉	—	4	2	no	—
227	C₂²×C₄×C₈₉	—	4	2	no	—
228	C₂²×C₄×C₈₉	—	4	2	no	—
229	C₂²×C₄×C₈₉	—	4	2	no	—
230	C₂²×C₄×C₈₉	—	4	2	no	—
231	C₂²×C₄×C₈₉	—	8	1	no	—
232	C₂²×C₄×C₈₉	—	8	1	no	—
233	C₂²×C₄×C₈₉	—	8	1	no	—
234	C₂²×C₄×C₈₉	—	8	1	no	—
235	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
236	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
237	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
242	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
243	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
244	M₁₆×C₈₉	—	4	4	no	—
245	C₂×C₈×C₈₉	—	2	1	no	—
246	C₂×C₈×C₈₉	—	2	1	no	—
247	C₂×C₈×C₈₉	—	2	1	no	—
248	C₂×C₈×C₈₉	—	2	1	no	—
249	C₂×C₈×C₈₉	—	2	1	no	—
250	C₂×C₈×C₈₉	—	2	1	no	—
251	C₂×C₈×C₈₉	—	2	1	no	—
252	C₂×C₈×C₈₉	—	2	1	no	—
253	C₂×C₈×C₈₉	—	2	1	no	—
254	C₂×C₈×C₈₉	—	2	1	no	—
255	C₂×C₈×C₈₉	—	2	1	no	—
256	C₂×C₈×C₈₉	—	4	4	no	—
257	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₈₉	—	2	4	no	—
259	C₄⋊C₄×C₈₉	—	2	1	no	—
260	C₄⋊C₄×C₈₉	—	2	1	no	—
261	C₄⋊C₄×C₈₉	—	2	1	no	—
262	C₄⋊C₄×C₈₉	—	2	1	no	—
263	C₄⋊C₄×C₈₉	—	2	1	no	—
264	C₄⋊C₄×C₈₉	—	2	1	no	—
265	C₄⋊C₄×C₈₉	—	2	1	no	—
266	C₄⋊C₄×C₈₉	—	2	1	no	—
267	C₄⋊C₄×C₈₉	—	4	2	no	—
268	C₄⋊C₄×C₈₉	—	4	2	no	—
269	C₄⋊C₄×C₈₉	—	4	2	no	—
270	C₄⋊C₄×C₈₉	—	8	1	no	—
271	C₄⋊C₄×C₈₉	C₂²⋊C₄	1	4	yes	—
272	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
273	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
274	C₂²⋊C₄×C₈₉	—	2	4	no	—
275	C₂²⋊C₄×C₈₉	—	2	4	no	—
276	C₂²⋊C₄×C₈₉	—	2	4	no	—
277	C₂²⋊C₄×C₈₉	—	2	4	no	—
278	C₂²⋊C₄×C₈₉	—	2	4	no	—
279	C₂²⋊C₄×C₈₉	—	4	2	no	—
280	C₂²⋊C₄×C₈₉	—	4	2	no	—
281	C₂²⋊C₄×C₈₉	C₂²⋊C₄	1	4	yes	—
282	C₂²⋊C₄×C₈₉	C₂²⋊C₄	1	4	yes	—
283	C₄²×C₈₉	—	4	2	no	—
284	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
285	C₄²×C₈₉	C₂×D₄	1	2	yes	—
286	C₂³×C₈₉	—	2	1	no	—
287	C₂³×C₈₉	—	2	1	no	—
288	C₂³×C₈₉	—	2	1	no	—
289	C₂³×C₈₉	—	2	1	no	—
290	C₂³×C₈₉	—	2	2	no	—
291	C₂³×C₈₉	—	2	1	no	—
292	C₂³×C₈₉	—	2	2	no	—
293	C₂³×C₈₉	—	2	1	no	—
294	C₂³×C₈₉	—	2	2	no	—
295	C₂³×C₈₉	—	2	1	no	—
296	C₂³×C₈₉	—	2	1	no	—
297	C₂³×C₈₉	—	2	1	no	—
298	C₂³×C₈₉	—	2	1	no	—
299	C₂³×C₈₉	—	2	2	no	—
300	C₂³×C₈₉	—	4	8	no	—
301	C₂³×C₈₉	—	4	1	no	—
302	C₂³×C₈₉	—	4	1	no	—
303	C₂³×C₈₉	—	4	1	no	—
304	C₂³×C₈₉	—	4	1	no	—
305	C₂³×C₈₉	—	4	1	no	—
306	C₂³×C₈₉	—	4	1	no	—
307	C₂³×C₈₉	—	4	1	no	—
308	C₂³×C₈₉	—	4	1	no	—
309	C₂³×C₈₉	—	4	1	no	—
310	C₂³×C₈₉	—	4	1	no	—
311	C₂³×C₈₉	—	4	8	no	—
312	C₂³×C₈₉	—	8	4	no	—
313	C₂³×C₈₉	—	8	4	no	—
314	C₂³×C₈₉	—	8	4	no	—
315	C₂³×C₈₉	—	8	4	no	—
316	C₂³×C₈₉	—	8	4	no	—
317	C₂³×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
318	C₂³×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
319	C₂³×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
320	C₂³×C₈₉	#137	1	2	yes	—
321	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
322	Q₈×C₈₉	—	2	2	no	—
323	Q₈×C₈₉	—	2	2	no	—
324	Q₈×C₈₉	—	4	1	no	—
325	Q₈×C₈₉	—	4	1	no	—
326	D₄×C₈₉	—	2	8	no	—
327	D₄×C₈₉	—	2	2	no	—
328	D₄×C₈₉	—	2	2	no	—
329	D₄×C₈₉	—	2	2	no	—
330	D₄×C₈₉	—	2	2	no	—
331	D₄×C₈₉	—	2	2	no	—
332	D₄×C₈₉	—	4	8	no	—
333	D₄×C₈₉	—	4	8	no	—
334	D₄×C₈₉	—	4	1	no	—
335	D₄×C₈₉	—	4	1	no	—
336	D₄×C₈₉	—	8	4	no	—
337	D₄×C₈₉	C₄×D₄	1	4	yes	complemented
338	C₂×C₄×C₈₉	—	2	1	no	—
339	C₂×C₄×C₈₉	—	2	1	no	—
340	C₂×C₄×C₈₉	—	2	1	no	—
341	C₂×C₄×C₈₉	—	2	1	no	—
342	C₂×C₄×C₈₉	—	2	1	no	—
343	C₂×C₄×C₈₉	—	2	1	no	—
344	C₂×C₄×C₈₉	—	2	1	no	—
345	C₂×C₄×C₈₉	—	2	1	no	—
346	C₂×C₄×C₈₉	—	2	2	no	—
347	C₂×C₄×C₈₉	—	2	2	no	—
348	C₂×C₄×C₈₉	—	2	2	no	—
349	C₂×C₄×C₈₉	—	2	2	no	—
350	C₂×C₄×C₈₉	—	2	2	no	—
351	C₂×C₄×C₈₉	—	2	2	no	—
352	C₂×C₄×C₈₉	—	2	2	no	—
353	C₂×C₄×C₈₉	—	2	2	no	—
354	C₂×C₄×C₈₉	—	2	2	no	—
355	C₂×C₄×C₈₉	—	2	2	no	—
356	C₂×C₄×C₈₉	—	2	2	no	—
357	C₂×C₄×C₈₉	—	4	8	no	—
358	C₂×C₄×C₈₉	—	4	1	no	—
359	C₂×C₄×C₈₉	—	4	1	no	—
360	C₂×C₄×C₈₉	—	4	1	no	—
361	C₂×C₄×C₈₉	—	4	1	no	—
362	C₂×C₄×C₈₉	—	4	1	no	—
363	C₂×C₄×C₈₉	—	4	1	no	—
364	C₂×C₄×C₈₉	—	4	1	no	—
365	C₂×C₄×C₈₉	—	4	1	no	—
366	C₂×C₄×C₈₉	—	4	1	no	—
367	C₂×C₄×C₈₉	—	4	1	no	—
368	C₂×C₄×C₈₉	—	4	1	no	—
369	C₂×C₄×C₈₉	—	4	1	no	—
370	C₂×C₄×C₈₉	—	4	1	no	—
371	C₂×C₄×C₈₉	—	4	1	no	—
372	C₂×C₄×C₈₉	—	4	1	no	—
373	C₂×C₄×C₈₉	—	8	4	no	—
374	C₂×C₄×C₈₉	—	8	4	no	—
375	C₂×C₄×C₈₉	—	8	4	no	—
376	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
377	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
378	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
379	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
380	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
381	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
384	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
385	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
386	C₈×C₈₉	—	2	2	no	—
387	C₈×C₈₉	—	4	1	no	—
388	C₈×C₈₉	—	4	1	no	—
389	C₈×C₈₉	—	4	1	no	—
390	C₂²×C₈₉	—	2	2	no	—
391	C₂²×C₈₉	—	2	2	no	—
392	C₂²×C₈₉	—	2	2	no	—
393	C₂²×C₈₉	—	2	2	no	—
394	C₂²×C₈₉	—	2	2	no	—
395	C₂²×C₈₉	—	2	2	no	—
396	C₂²×C₈₉	—	2	2	no	—
397	C₂²×C₈₉	—	2	4	no	—
398	C₂²×C₈₉	—	2	2	no	—
399	C₂²×C₈₉	—	2	2	no	—
400	C₂²×C₈₉	—	4	2	no	—
401	C₂²×C₈₉	—	4	2	no	—
402	C₂²×C₈₉	—	4	1	no	—
403	C₂²×C₈₉	—	4	2	no	—
404	C₂²×C₈₉	—	4	1	no	—
405	C₂²×C₈₉	—	4	2	no	—
406	C₂²×C₈₉	—	4	1	no	—
407	C₂²×C₈₉	—	4	2	no	—
408	C₂²×C₈₉	—	4	1	no	—
409	C₂²×C₈₉	—	4	2	no	—
410	C₂²×C₈₉	—	4	2	no	—
411	C₂²×C₈₉	—	4	2	no	—
412	C₂²×C₈₉	—	4	2	no	—
413	C₂²×C₈₉	—	8	16	no	—
414	C₂²×C₈₉	—	8	1	no	—
415	C₂²×C₈₉	—	8	1	no	—
416	C₂²×C₈₉	—	8	1	no	—
417	C₂²×C₈₉	—	8	1	no	—
418	C₂²×C₈₉	#417	1	4	yes	complemented
419	C₂²×C₈₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
420	C₂²×C₈₉	D₄²	1	1	yes	characteristic
421	C₂²×C₈₉	#546	1	1	yes	characteristic
422	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
423	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
424	C₂²×C₈₉	#576	1	1	yes	characteristic
425	C₂²×C₈₉	#577	1	1	yes	characteristic
426	C₄×C₈₉	—	2	2	no	—
427	C₄×C₈₉	—	2	2	no	—
428	C₄×C₈₉	—	2	2	no	—
429	C₄×C₈₉	—	2	2	no	—
430	C₄×C₈₉	—	4	2	no	—
431	C₄×C₈₉	—	4	2	no	—
432	C₄×C₈₉	—	4	2	no	—
433	C₄×C₈₉	—	8	1	no	—
434	C₄×C₈₉	—	8	1	no	—
435	C₄×C₈₉	—	8	1	no	—
436	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
437	C₄×C₈₉	#518	1	1	yes	characteristic
438	C₄×C₈₉	D₄²	1	1	yes	characteristic
439	C₄×C₈₉	#546	1	1	yes	characteristic
440	#22419	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
441	C₂×C₈₉	—	2	4	no	—
442	C₂×C₈₉	—	4	2	no	—
443	C₂×C₈₉	—	4	4	no	—
444	C₂×C₈₉	—	8	2	no	—
445	C₂×C₈₉	D₄×C₂²⋊C₄	1	1	yes	characteristic
446	C₂×C₈₉	C₂×#417	1	1	yes	characteristic
447	C₂×C₈₉	#2897	1	1	yes	characteristic
448	C₂×C₈₉	#3264	1	1	yes	characteristic
449	C₂×C₈₉	#3266	1	1	yes	characteristic
450	C₂×C₈₉	#3306	1	1	yes	characteristic
451	C₂×C₈₉	#3314	1	1	yes	characteristic
452	C₂×#546	C₂×C₈₉	1	1	yes	characteristic
453	C₂×#435	C₂×C₈₉	1	1	yes	characteristic, complemented
454	C₂×#417	C₂×C₈₉	1	1	yes	characteristic, complemented
455	C₂²×#102	C₂×C₈₉	1	1	yes	characteristic, complemented
456	D₄×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
457	#1983	C₂×C₈₉	1	1	yes	characteristic, complemented
458	#1959	C₂×C₈₉	1	1	yes	characteristic, complemented
459	#1895	C₂×C₈₉	1	1	yes	characteristic, complemented
460	#1892	C₂×C₈₉	1	1	yes	characteristic, complemented
461	#1874	C₂×C₈₉	1	1	yes	characteristic, complemented
462	#1872	C₂×C₈₉	1	1	yes	characteristic, complemented
463	#1802	C₂×C₈₉	1	1	yes	characteristic, complemented
464	#1788	C₂×C₈₉	1	1	yes	characteristic, complemented
465	#1786	C₂×C₈₉	1	1	yes	characteristic, complemented
466	#1762	C₂×C₈₉	1	1	yes	characteristic, complemented
467	C₈₉	#22419	1	1	yes	characteristic, direct product factor, Sylow
468	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
469	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
470	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
471	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
472	#546	—	2	4	no	—
473	#546	C₄×C₈₉	1	8	yes	complemented
474	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
475	C₂×#123	—	2	1	no	—
476	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
477	C₂×#121	—	2	1	no	—
478	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
479	C₂×#120	—	2	1	no	—
480	C₂×C₄×D₄	—	2	1	no	—
481	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
482	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
483	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
484	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
485	C₂²×C₂²⋊C₄	—	2	1	no	—
486	#435	—	2	4	no	—
487	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
488	#417	—	2	4	no	—
489	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
490	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
491	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
492	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
493	C₂×#102	—	2	4	no	—
494	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
495	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
496	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
497	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
498	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
499	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
500	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
501	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
502	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
503	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
504	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic, complemented
505	#389	—	2	1	no	—
506	#385	—	2	1	no	—
507	#385	—	2	1	no	—
508	#384	C₂²×C₈₉	1	1	yes	characteristic, complemented
509	#380	C₂²×C₈₉	1	1	yes	characteristic
510	#380	C₂²×C₈₉	1	1	yes	characteristic, complemented
511	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
512	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
513	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
514	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
515	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
516	C₂⁵	—	2	1	no	—
517	C₂×#41	—	2	2	no	—
518	C₂×#41	—	2	2	no	—
519	C₂×#41	—	2	2	no	—
520	C₂×#41	—	4	1	no	—
521	C₂×#41	—	4	1	no	—
522	C₂×#41	C₂×C₄×C₈₉	1	4	yes	complemented
523	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
524	C₂²×D₄	—	2	2	no	—
525	C₂²×D₄	—	2	2	no	—
526	C₂²×D₄	—	2	1	no	—
527	C₂²×D₄	—	2	1	no	—
528	C₂²×D₄	—	2	1	no	—
529	C₂²×D₄	—	2	2	no	—
530	C₂²×D₄	—	4	1	no	—
531	C₂²×D₄	—	4	1	no	—
532	C₂²×D₄	C₂×C₄×C₈₉	1	4	yes	complemented
533	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
534	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
535	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
536	C₂³×C₄	—	2	1	no	—
537	C₂³×C₄	—	2	1	no	—
538	C₂³×C₄	—	2	1	no	—
539	C₂³×C₄	—	2	1	no	—
540	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
542	C₂×M₁₆	—	2	2	no	—
543	C₂×M₁₆	—	2	2	no	—
544	C₂×M₁₆	—	4	1	no	—
545	C₂²×C₈	—	2	2	no	—
546	C₂²×C₈	—	2	2	no	—
547	C₂²×C₈	—	4	1	no	—
548	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
549	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
550	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
551	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
552	#124	—	2	2	no	—
553	#124	C₂×C₄×C₈₉	1	4	yes	complemented
554	#123	—	2	8	no	—
555	C₂²⋊Q₈	—	2	2	no	—
556	C₂²⋊Q₈	C₂×C₄×C₈₉	1	4	yes	complemented
557	#121	—	2	2	no	—
558	#121	—	2	8	no	—
559	#121	C₂×C₄×C₈₉	1	4	yes	complemented
560	#120	—	2	8	no	—
561	C₄×D₄	—	2	2	no	—
562	C₄×D₄	—	4	4	no	—
563	C₄×D₄	C₂×C₄×C₈₉	1	4	yes	—
564	C₄×D₄	C₂×C₄×C₈₉	1	4	yes	complemented
565	C₄×D₄	D₄×C₈₉	1	4	yes	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	2	no	—
568	C₂×C₄⋊C₄	—	2	2	no	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	4	1	no	—
574	C₂×C₄⋊C₄	—	4	1	no	—
575	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
581	C₂×C₂²⋊C₄	—	2	1	no	—
582	C₂×C₂²⋊C₄	—	2	1	no	—
583	C₂×C₂²⋊C₄	—	2	1	no	—
584	C₂×C₂²⋊C₄	—	2	1	no	—
585	C₂×C₂²⋊C₄	—	2	1	no	—
586	C₂×C₂²⋊C₄	—	2	8	no	—
587	C₂×C₂²⋊C₄	—	2	1	no	—
588	C₂×C₂²⋊C₄	—	2	1	no	—
589	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
590	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
591	C₂×C₄²	—	2	1	no	—
592	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
593	C₄⋊C₈	—	2	2	no	—
594	#103	—	2	2	no	—
595	#103	—	2	2	no	—
596	#103	—	4	1	no	—
597	#103	—	4	1	no	—
598	#102	—	2	2	no	—
599	#102	—	2	2	no	—
600	#102	—	2	2	no	—
601	#102	—	2	2	no	—
602	#102	—	2	2	no	—
603	#102	—	4	1	no	—
604	#102	—	4	1	no	—
605	#102	D₄×C₈₉	1	4	yes	complemented
606	C₂²⋊C₈	—	2	2	no	—
607	C₂²⋊C₈	—	2	2	no	—
608	#97	—	2	2	no	—
609	#95	—	2	1	no	—
610	#95	—	2	1	no	—
611	#95	—	2	1	no	—
612	C₂⁴	—	2	1	no	—
613	C₂⁴	—	2	1	no	—
614	C₂⁴	—	2	4	no	—
615	C₂⁴	—	4	2	no	—
616	C₂⁴	—	4	2	no	—
617	C₂⁴	—	4	2	no	—
618	C₂⁴	—	4	2	no	—
619	C₂⁴	—	8	1	no	—
620	C₂⁴	—	8	1	no	—
621	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
622	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
623	#41	—	2	8	no	—
624	#41	—	4	4	no	—
625	#41	—	4	4	no	—
626	#41	—	4	4	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	—	2	1	no	—
630	C₂×Q₈	—	2	1	no	—
631	C₂×Q₈	—	2	1	no	—
632	C₂×Q₈	C₂²×C₄×C₈₉	1	2	yes	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	8	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	1	no	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	1	no	—
647	C₂×D₄	—	4	4	no	—
648	C₂×D₄	—	4	4	no	—
649	C₂×D₄	—	4	4	no	—
650	C₂×D₄	—	4	2	no	—
651	C₂×D₄	—	4	2	no	—
652	C₂×D₄	—	4	2	no	—
653	C₂×D₄	—	4	2	no	—
654	C₂×D₄	—	8	1	no	—
655	C₂×D₄	—	8	1	no	—
656	C₂×D₄	C₂²⋊C₄×C₈₉	1	4	yes	—
657	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
658	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
659	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
660	C₂×D₄	#41×C₈₉	1	2	yes	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	1	no	—
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	4	no	—
673	C₂²×C₄	—	2	4	no	—
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	4	2	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	—	4	2	no	—
681	C₂²×C₄	—	4	2	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	—	8	1	no	—
684	C₂²×C₄	—	8	1	no	—
685	C₂²×C₄	—	8	1	no	—
686	C₂²×C₄	—	8	1	no	—
687	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
688	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
689	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
690	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
691	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
692	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
693	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
694	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
696	M₁₆	—	4	4	no	—
697	C₂×C₈	—	2	1	no	—
698	C₂×C₈	—	2	1	no	—
699	C₂×C₈	—	2	1	no	—
700	C₂×C₈	—	2	1	no	—
701	C₂×C₈	—	2	1	no	—
702	C₂×C₈	—	2	1	no	—
703	C₂×C₈	—	2	1	no	—
704	C₂×C₈	—	2	1	no	—
705	C₂×C₈	—	2	1	no	—
706	C₂×C₈	—	2	1	no	—
707	C₂×C₈	—	2	1	no	—
708	C₂×C₈	—	4	4	no	—
709	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	4	2	no	—
720	C₄⋊C₄	—	4	2	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₄⋊C₄	—	8	1	no	—
723	C₄⋊C₄	C₂²⋊C₄×C₈₉	1	4	yes	—
724	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
725	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	4	2	no	—
732	C₂²⋊C₄	—	4	2	no	—
733	C₂²⋊C₄	C₂²⋊C₄×C₈₉	1	4	yes	—
734	C₂²⋊C₄	C₂²⋊C₄×C₈₉	1	4	yes	—
735	C₄²	—	4	2	no	—
736	C₄²	C₂²×C₄×C₈₉	1	2	yes	—
737	C₄²	C₂×D₄×C₈₉	1	2	yes	—
738	C₂³	—	2	1	no	—
739	C₂³	—	2	1	no	—
740	C₂³	—	2	1	no	—
741	C₂³	—	2	1	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	1	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	1	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	1	no	—
748	C₂³	—	2	1	no	—
749	C₂³	—	2	1	no	—
750	C₂³	—	2	1	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	4	8	no	—
753	C₂³	—	4	1	no	—
754	C₂³	—	4	1	no	—
755	C₂³	—	4	1	no	—
756	C₂³	—	4	1	no	—
757	C₂³	—	4	8	no	—
758	C₂³	—	4	1	no	—
759	C₂³	—	4	1	no	—
760	C₂³	—	4	1	no	—
761	C₂³	—	4	1	no	—
762	C₂³	—	4	1	no	—
763	C₂³	—	4	1	no	—
764	C₂³	—	8	4	no	—
765	C₂³	—	8	4	no	—
766	C₂³	—	8	4	no	—
767	C₂³	—	8	4	no	—
768	C₂³	—	8	4	no	—
769	C₂³	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
770	C₂³	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
771	C₂³	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
772	C₂³	#137×C₈₉	1	2	yes	—
773	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
774	Q₈	—	2	2	no	—
775	Q₈	—	2	2	no	—
776	Q₈	—	4	1	no	—
777	Q₈	—	4	1	no	—
778	D₄	—	2	8	no	—
779	D₄	—	2	2	no	—
780	D₄	—	2	2	no	—
781	D₄	—	2	2	no	—
782	D₄	—	2	2	no	—
783	D₄	—	2	2	no	—
784	D₄	—	4	8	no	—
785	D₄	—	4	8	no	—
786	D₄	—	4	1	no	—
787	D₄	—	4	1	no	—
788	D₄	—	8	4	no	—
789	D₄	C₄×D₄×C₈₉	1	4	yes	complemented
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	4	8	no	—
810	C₂×C₄	—	4	1	no	—
811	C₂×C₄	—	4	1	no	—
812	C₂×C₄	—	4	1	no	—
813	C₂×C₄	—	4	1	no	—
814	C₂×C₄	—	4	1	no	—
815	C₂×C₄	—	4	1	no	—
816	C₂×C₄	—	4	1	no	—
817	C₂×C₄	—	4	1	no	—
818	C₂×C₄	—	4	1	no	—
819	C₂×C₄	—	4	1	no	—
820	C₂×C₄	—	4	1	no	—
821	C₂×C₄	—	4	1	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	8	4	no	—
826	C₂×C₄	—	8	4	no	—
827	C₂×C₄	—	8	4	no	—
828	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
829	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
830	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
831	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
832	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
833	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
834	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
835	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
836	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
837	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
838	C₈	—	2	2	no	—
839	C₈	—	4	1	no	—
840	C₈	—	4	1	no	—
841	C₈	—	4	1	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	2	2	no	—
846	C₂²	—	2	2	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	2	4	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	4	2	no	—
854	C₂²	—	4	1	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	8	16	no	—
866	C₂²	—	8	1	no	—
867	C₂²	—	8	1	no	—
868	C₂²	—	8	1	no	—
869	C₂²	—	8	1	no	—
870	C₂²	#417×C₈₉	1	4	yes	complemented
871	C₂²	C₂²×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
872	C₂²	D₄²×C₈₉	1	1	yes	characteristic
873	C₂²	#546×C₈₉	1	1	yes	characteristic
874	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
875	C₂²	C₂×#137×C₈₉	1	1	yes	characteristic
876	C₂²	#576×C₈₉	1	1	yes	characteristic
877	C₂²	#577×C₈₉	1	1	yes	characteristic
878	C₄	—	2	2	no	—
879	C₄	—	2	2	no	—
880	C₄	—	2	2	no	—
881	C₄	—	2	2	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	2	no	—
884	C₄	—	4	2	no	—
885	C₄	—	8	1	no	—
886	C₄	—	8	1	no	—
887	C₄	—	8	1	no	—
888	C₄	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
889	C₄	#518×C₈₉	1	1	yes	characteristic
890	C₄	D₄²×C₈₉	1	1	yes	characteristic
891	C₄	#546×C₈₉	1	1	yes	characteristic
892	C₂	—	2	4	no	—
893	C₂	—	4	2	no	—
894	C₂	—	4	4	no	—
895	C₂	—	8	2	no	—
896	C₂	D₄×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
897	C₂	C₂×#417×C₈₉	1	1	yes	characteristic
898	C₂	C₈₉×#2897	1	1	yes	characteristic
899	C₂	C₈₉×#3264	1	1	yes	characteristic
900	C₂	C₈₉×#3266	1	1	yes	characteristic
901	C₂	C₈₉×#3306	1	1	yes	characteristic
902	C₂	C₈₉×#3314	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×#546×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×#417×C₈₉	C₂	semidirect
4. C₂²×#102×C₈₉	C₂	semidirect
5. D₄×C₄⋊C₄×C₈₉	C₂	semidirect
6. C₈₉×#1983	C₂	semidirect
7. C₈₉×#1959	C₂	semidirect
8. C₈₉×#1895	C₂	semidirect
9. C₈₉×#1892	C₂	semidirect
10. C₈₉×#1874	C₂	semidirect
11. C₈₉×#1872	C₂	semidirect
12. C₈₉×#1802	C₂	semidirect
13. C₈₉×#1788	C₂	semidirect
14. C₈₉×#1786	C₂	semidirect
15. C₈₉×#1762	C₂	semidirect
18. C₂²×M₁₆×C₈₉	C₂²	semidirect
21. #546×C₈₉	C₄	semidirect
32. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
35. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
37. C₂×#103×C₈₉	C₂²	semidirect
38. C₂×#103×C₈₉	C₂²	semidirect
39. C₂×#103×C₈₉	C₂²	semidirect
40. C₂×#103×C₈₉	C₂²	semidirect
51. C₂×C₂²⋊C₈×C₈₉	C₂²	semidirect
52. C₂×#97×C₈₉	C₂²	semidirect
56. #384×C₈₉	C₂²	semidirect
58. #380×C₈₉	C₂²	semidirect
59. 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
70. C₂×#41×C₈₉	C₂×C₄	semidirect
80. C₂²×D₄×C₈₉	C₂×C₄	semidirect
101. #124×C₈₉	C₂×C₄	semidirect
104. C₂²⋊Q₈×C₈₉	C₂×C₄	semidirect
107. #121×C₈₉	C₂×C₄	semidirect
112. C₄×D₄×C₈₉	C₂×C₄	semidirect
153. #102×C₈₉	D₄	semidirect
337. D₄×C₈₉	C₄×D₄	semidirect
418. C₂²×C₈₉	#417	semidirect
440. #22419	C₈₉	direct (N × H)
453. C₂×#435	C₂×C₈₉	semidirect
454. C₂×#417	C₂×C₈₉	semidirect
455. C₂²×#102	C₂×C₈₉	semidirect
456. D₄×C₄⋊C₄	C₂×C₈₉	semidirect
457. #1983	C₂×C₈₉	semidirect
458. #1959	C₂×C₈₉	semidirect
459. #1895	C₂×C₈₉	semidirect
460. #1892	C₂×C₈₉	semidirect
461. #1874	C₂×C₈₉	semidirect
462. #1872	C₂×C₈₉	semidirect
463. #1802	C₂×C₈₉	semidirect
464. #1788	C₂×C₈₉	semidirect
465. #1786	C₂×C₈₉	semidirect
466. #1762	C₂×C₈₉	semidirect
467. C₈₉	#22419	direct (N × H)
470. C₂²×M₁₆	C₂²×C₈₉	semidirect
473. #546	C₄×C₈₉	semidirect
484. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
487. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
489. C₂×#103	C₂²×C₈₉	semidirect
490. C₂×#103	C₂²×C₈₉	semidirect
491. C₂×#103	C₂²×C₈₉	semidirect
492. C₂×#103	C₂²×C₈₉	semidirect
503. C₂×C₂²⋊C₈	C₂²×C₈₉	semidirect
504. C₂×#97	C₂²×C₈₉	semidirect
508. #384	C₂²×C₈₉	semidirect
510. #380	C₂²×C₈₉	semidirect
511. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
512. #340	C₂²×C₈₉	semidirect
513. #340	C₂²×C₈₉	semidirect
514. #340	C₂²×C₈₉	semidirect
515. #340	C₂²×C₈₉	semidirect
522. C₂×#41	C₂×C₄×C₈₉	semidirect
532. C₂²×D₄	C₂×C₄×C₈₉	semidirect
553. #124	C₂×C₄×C₈₉	semidirect
556. C₂²⋊Q₈	C₂×C₄×C₈₉	semidirect
559. #121	C₂×C₄×C₈₉	semidirect
564. C₄×D₄	C₂×C₄×C₈₉	semidirect
605. #102	D₄×C₈₉	semidirect
789. D₄	C₄×D₄×C₈₉	semidirect
870. C₂²	#417×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#546×C₈₉	2
C₂×#435×C₈₉	2
C₂×#417×C₈₉	2
C₂²×#102×C₈₉	2
D₄×C₄⋊C₄×C₈₉	2
C₈₉×#1983	2
C₈₉×#1959	2
C₈₉×#1895	2
C₈₉×#1892	2
C₈₉×#1874	2
C₈₉×#1872	2
C₈₉×#1802	2
C₈₉×#1788	2
C₈₉×#1786	2
C₈₉×#1762	2
#22419	89

Subgroups — C89×#22419 #36400267

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#22419 #36400267