Subgroups — C₈₉×#35578 #36413426

Order 22784.

1722 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2590	C₂	1	2	yes	maximal, complemented
2	C₈₉×#2589	C₂	1	2	yes	maximal
3	C₈₉×#2586	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2570	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2556	C₂	1	2	yes	maximal
6	C₈₉×#2552	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2551	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2550	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2465	C₂	1	2	yes	maximal
10	C₈₉×#2462	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2451	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2441	C₂	1	1	yes	maximal, characteristic
13	C₈₉×#2440	C₂	1	1	yes	maximal, characteristic
14	C₈₉×#2440	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#2439	C₂	1	1	yes	maximal, characteristic
16	C₈₉×#2429	C₂	1	2	yes	maximal
17	C₈₉×#2331	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#2330	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2314	C₂	1	1	yes	maximal, characteristic
20	C₄×C₄⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₄⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₉×#2298	C₂	1	1	yes	maximal, characteristic
23	C₈₉×#2274	C₂	1	1	yes	maximal, characteristic
24	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
28	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#125×C₈₉	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
31	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
34	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
37	#400×C₈₉	C₂²	1	2	yes	—
38	#399×C₈₉	C₂²	1	2	yes	—
39	#398×C₈₉	C₂²	1	2	yes	—
40	#398×C₈₉	C₂²	1	2	yes	—
41	#398×C₈₉	C₂²	1	2	yes	—
42	#398×C₈₉	C₂²	1	2	yes	—
43	#398×C₈₉	C₂²	1	2	yes	—
44	#398×C₈₉	C₂²	1	2	yes	—
45	#396×C₈₉	C₂²	1	2	yes	—
46	#396×C₈₉	C₂²	1	2	yes	—
47	#395×C₈₉	C₂²	1	2	yes	—
48	#395×C₈₉	C₂²	1	2	yes	—
49	#395×C₈₉	C₂²	1	2	yes	—
50	#395×C₈₉	C₂²	1	2	yes	—
51	#395×C₈₉	C₂²	1	2	yes	—
52	#393×C₈₉	C₂²	1	2	yes	—
53	#391×C₈₉	C₂²	1	2	yes	—
54	#391×C₈₉	C₂²	1	2	yes	—
55	#391×C₈₉	C₂²	1	2	yes	—
56	#391×C₈₉	C₂²	1	2	yes	—
57	#391×C₈₉	C₂²	1	2	yes	—
58	#391×C₈₉	C₂²	1	2	yes	—
59	#389×C₈₉	C₂²	1	1	yes	characteristic
60	#389×C₈₉	C₂²	1	1	yes	characteristic
61	#389×C₈₉	C₂²	1	2	yes	—
62	#389×C₈₉	C₂²	1	1	yes	characteristic
63	#389×C₈₉	C₂²	1	1	yes	characteristic
64	#389×C₈₉	C₂²	1	2	yes	—
65	#389×C₈₉	C₂²	1	1	yes	characteristic
66	#389×C₈₉	C₂²	1	2	yes	—
67	#389×C₈₉	C₂²	1	1	yes	characteristic
68	#389×C₈₉	C₂²	1	2	yes	—
69	#389×C₈₉	C₂²	1	2	yes	—
70	#389×C₈₉	C₂²	1	1	yes	characteristic
71	#389×C₈₉	C₂²	1	2	yes	—
72	#389×C₈₉	C₂²	1	1	yes	characteristic
73	#389×C₈₉	C₂²	1	2	yes	—
74	#389×C₈₉	C₂²	1	2	yes	—
75	#388×C₈₉	C₂²	1	1	yes	characteristic
76	#388×C₈₉	C₂²	1	1	yes	characteristic
77	#388×C₈₉	C₂²	1	1	yes	characteristic
78	#388×C₈₉	C₂²	1	1	yes	characteristic
79	#388×C₈₉	C₂²	1	2	yes	—
80	#388×C₈₉	C₂²	1	2	yes	—
81	#387×C₈₉	C₂²	1	1	yes	characteristic
82	#387×C₈₉	C₂²	1	1	yes	characteristic
83	#387×C₈₉	C₂²	1	1	yes	characteristic
84	#387×C₈₉	C₂²	1	1	yes	characteristic
85	#387×C₈₉	C₂²	1	2	yes	—
86	#387×C₈₉	C₂²	1	2	yes	—
87	#387×C₈₉	C₂²	1	2	yes	—
88	#387×C₈₉	C₂²	1	2	yes	—
89	#387×C₈₉	C₂²	1	2	yes	—
90	#387×C₈₉	C₂²	1	2	yes	—
91	#387×C₈₉	C₂²	1	2	yes	—
92	#387×C₈₉	C₂²	1	2	yes	—
93	#387×C₈₉	C₂²	1	2	yes	—
94	#387×C₈₉	C₂²	1	2	yes	—
95	#385×C₈₉	C₂²	1	2	yes	—
96	#385×C₈₉	C₂²	1	2	yes	—
97	#384×C₈₉	C₂²	1	1	yes	characteristic
98	#384×C₈₉	C₂²	1	1	yes	characteristic
99	#384×C₈₉	C₂²	1	1	yes	characteristic
100	#384×C₈₉	C₂²	1	1	yes	characteristic
101	#382×C₈₉	C₂²	1	1	yes	characteristic
102	#382×C₈₉	C₂²	1	1	yes	characteristic
103	#380×C₈₉	C₂²	1	1	yes	characteristic
104	#380×C₈₉	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
121	#376×C₈₉	C₂²	1	1	yes	characteristic
122	C₄³×C₈₉	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
124	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
125	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
126	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
128	C₄⋊Q₈×C₈₉	—	2	4	no	—
129	C₄⋊Q₈×C₈₉	—	2	4	no	—
130	C₄⋊Q₈×C₈₉	—	2	4	no	—
131	C₄⋊Q₈×C₈₉	—	4	4	no	—
132	#125×C₈₉	—	2	4	no	—
133	#125×C₈₉	—	4	4	no	—
134	C₂²⋊Q₈×C₈₉	—	4	4	no	—
135	C₂²⋊Q₈×C₈₉	—	4	4	no	—
136	C₄×Q₈×C₈₉	—	4	4	no	—
137	C₄×Q₈×C₈₉	—	4	4	no	—
138	#117×C₈₉	—	2	4	no	—
139	#117×C₈₉	Q₈	1	8	yes	complemented
140	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
141	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
195	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
196	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
197	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
198	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
199	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
200	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
201	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
203	#95×C₈₉	C₂³	1	1	yes	characteristic
204	#95×C₈₉	C₂³	1	1	yes	characteristic
205	#95×C₈₉	C₂³	1	1	yes	characteristic
206	#95×C₈₉	C₂³	1	1	yes	characteristic
207	#95×C₈₉	C₂³	1	2	yes	—
208	#95×C₈₉	C₂³	1	2	yes	—
209	#95×C₈₉	C₂³	1	2	yes	—
210	#95×C₈₉	C₂³	1	2	yes	—
211	#95×C₈₉	C₂³	1	1	yes	characteristic
212	#95×C₈₉	C₂³	1	1	yes	characteristic
213	#95×C₈₉	C₂³	1	1	yes	characteristic
214	#95×C₈₉	C₂³	1	1	yes	characteristic
215	#95×C₈₉	C₂³	1	2	yes	—
216	#95×C₈₉	C₂³	1	2	yes	—
217	#95×C₈₉	C₂³	1	1	yes	characteristic
218	#95×C₈₉	C₂³	1	1	yes	characteristic
219	#95×C₈₉	C₂³	1	2	yes	—
220	#95×C₈₉	C₂³	1	2	yes	—
221	#95×C₈₉	C₂³	1	1	yes	characteristic
222	#95×C₈₉	C₂³	1	1	yes	characteristic
223	#95×C₈₉	C₂³	1	2	yes	—
224	#95×C₈₉	C₂³	1	2	yes	—
225	#95×C₈₉	C₂³	1	2	yes	—
226	#95×C₈₉	C₂³	1	2	yes	—
227	#95×C₈₉	C₂³	1	2	yes	—
228	#95×C₈₉	C₂³	1	2	yes	—
229	#95×C₈₉	C₂³	1	2	yes	—
230	#95×C₈₉	C₂³	1	2	yes	—
231	#95×C₈₉	C₂³	1	2	yes	—
232	#95×C₈₉	C₂³	1	2	yes	—
233	#95×C₈₉	C₂³	1	2	yes	—
234	#95×C₈₉	C₂³	1	2	yes	—
235	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
236	C₂×Q₈×C₈₉	—	2	4	no	—
237	C₂×Q₈×C₈₉	—	2	4	no	—
238	C₂×Q₈×C₈₉	—	2	4	no	—
239	C₂×Q₈×C₈₉	—	2	4	no	—
240	C₂×Q₈×C₈₉	—	2	4	no	—
241	C₂×Q₈×C₈₉	—	4	2	no	—
242	C₂×Q₈×C₈₉	—	4	2	no	—
243	C₂×Q₈×C₈₉	—	4	2	no	—
244	C₂×Q₈×C₈₉	—	4	2	no	—
245	C₂²×C₄×C₈₉	—	2	2	no	—
246	C₂²×C₄×C₈₉	—	2	2	no	—
247	C₂²×C₄×C₈₉	—	2	4	no	—
248	C₂²×C₄×C₈₉	—	4	2	no	—
249	C₂²×C₄×C₈₉	—	4	2	no	—
250	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
251	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
273	C₄⋊C₄×C₈₉	—	2	4	no	—
274	C₄⋊C₄×C₈₉	—	2	2	no	—
275	C₄⋊C₄×C₈₉	—	2	2	no	—
276	C₄⋊C₄×C₈₉	—	2	4	no	—
277	C₄⋊C₄×C₈₉	—	2	4	no	—
278	C₄⋊C₄×C₈₉	—	2	2	no	—
279	C₄⋊C₄×C₈₉	—	2	4	no	—
280	C₄⋊C₄×C₈₉	—	2	4	no	—
281	C₄⋊C₄×C₈₉	—	2	4	no	—
282	C₄⋊C₄×C₈₉	—	2	2	no	—
283	C₄⋊C₄×C₈₉	—	2	2	no	—
284	C₄⋊C₄×C₈₉	—	2	2	no	—
285	C₄⋊C₄×C₈₉	—	2	4	no	—
286	C₄⋊C₄×C₈₉	—	2	4	no	—
287	C₄⋊C₄×C₈₉	—	2	4	no	—
288	C₄⋊C₄×C₈₉	—	2	4	no	—
289	C₄⋊C₄×C₈₉	—	2	4	no	—
290	C₄⋊C₄×C₈₉	—	2	2	no	—
291	C₄⋊C₄×C₈₉	—	2	2	no	—
292	C₄⋊C₄×C₈₉	—	2	2	no	—
293	C₄⋊C₄×C₈₉	—	2	2	no	—
294	C₄⋊C₄×C₈₉	—	2	4	no	—
295	C₄⋊C₄×C₈₉	—	4	2	no	—
296	C₄⋊C₄×C₈₉	—	4	2	no	—
297	C₄⋊C₄×C₈₉	—	4	2	no	—
298	C₄⋊C₄×C₈₉	—	4	2	no	—
299	C₄⋊C₄×C₈₉	—	4	2	no	—
300	C₄⋊C₄×C₈₉	—	4	2	no	—
301	C₄⋊C₄×C₈₉	—	4	2	no	—
302	C₄⋊C₄×C₈₉	—	4	2	no	—
303	C₄⋊C₄×C₈₉	—	4	2	no	—
304	C₄⋊C₄×C₈₉	—	4	2	no	—
305	C₄⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
306	C₄⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
307	C₄⋊C₄×C₈₉	#41	1	4	yes	—
308	C₄⋊C₄×C₈₉	#41	1	4	yes	—
309	C₂²⋊C₄×C₈₉	—	2	4	no	—
310	C₂²⋊C₄×C₈₉	—	2	2	no	—
311	C₂²⋊C₄×C₈₉	—	2	2	no	—
312	C₂²⋊C₄×C₈₉	—	2	2	no	—
313	C₂²⋊C₄×C₈₉	—	2	2	no	—
314	C₂²⋊C₄×C₈₉	—	4	2	no	—
315	C₂²⋊C₄×C₈₉	—	4	2	no	—
316	C₂²⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
317	C₂²⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
318	C₄²×C₈₉	—	2	4	no	—
319	C₄²×C₈₉	—	2	2	no	—
320	C₄²×C₈₉	—	2	2	no	—
321	C₄²×C₈₉	—	2	2	no	—
322	C₄²×C₈₉	—	2	2	no	—
323	C₄²×C₈₉	—	2	2	no	—
324	C₄²×C₈₉	—	2	2	no	—
325	C₄²×C₈₉	—	2	2	no	—
326	C₄²×C₈₉	—	2	2	no	—
327	C₄²×C₈₉	—	4	2	no	—
328	C₄²×C₈₉	—	4	2	no	—
329	C₄²×C₈₉	—	4	2	no	—
330	C₄²×C₈₉	—	4	2	no	—
331	C₄²×C₈₉	—	4	2	no	—
332	C₄²×C₈₉	—	4	2	no	—
333	C₄²×C₈₉	C₂×Q₈	1	4	yes	—
334	C₄²×C₈₉	C₂×Q₈	1	4	yes	—
335	C₂³×C₈₉	—	2	1	no	—
336	C₂³×C₈₉	—	2	1	no	—
337	C₂³×C₈₉	—	2	1	no	—
338	C₂³×C₈₉	—	2	1	no	—
339	C₂³×C₈₉	—	2	1	no	—
340	C₂³×C₈₉	—	2	1	no	—
341	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
342	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
343	Q₈×C₈₉	—	4	8	no	—
344	Q₈×C₈₉	—	4	8	no	—
345	Q₈×C₈₉	—	8	4	no	—
346	C₂×C₄×C₈₉	—	2	1	no	—
347	C₂×C₄×C₈₉	—	2	1	no	—
348	C₂×C₄×C₈₉	—	2	1	no	—
349	C₂×C₄×C₈₉	—	2	1	no	—
350	C₂×C₄×C₈₉	—	2	1	no	—
351	C₂×C₄×C₈₉	—	2	1	no	—
352	C₂×C₄×C₈₉	—	2	1	no	—
353	C₂×C₄×C₈₉	—	2	1	no	—
354	C₂×C₄×C₈₉	—	2	1	no	—
355	C₂×C₄×C₈₉	—	2	1	no	—
356	C₂×C₄×C₈₉	—	2	1	no	—
357	C₂×C₄×C₈₉	—	2	1	no	—
358	C₂×C₄×C₈₉	—	2	2	no	—
359	C₂×C₄×C₈₉	—	2	2	no	—
360	C₂×C₄×C₈₉	—	2	2	no	—
361	C₂×C₄×C₈₉	—	2	1	no	—
362	C₂×C₄×C₈₉	—	2	1	no	—
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	2	no	—
368	C₂×C₄×C₈₉	—	2	8	no	—
369	C₂×C₄×C₈₉	—	2	2	no	—
370	C₂×C₄×C₈₉	—	2	1	no	—
371	C₂×C₄×C₈₉	—	2	1	no	—
372	C₂×C₄×C₈₉	—	2	1	no	—
373	C₂×C₄×C₈₉	—	2	1	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	—	2	2	no	—
382	C₂×C₄×C₈₉	—	2	2	no	—
383	C₂×C₄×C₈₉	—	2	2	no	—
384	C₂×C₄×C₈₉	—	2	2	no	—
385	C₂×C₄×C₈₉	—	2	2	no	—
386	C₂×C₄×C₈₉	—	2	1	no	—
387	C₂×C₄×C₈₉	—	2	1	no	—
388	C₂×C₄×C₈₉	—	2	2	no	—
389	C₂×C₄×C₈₉	—	2	2	no	—
390	C₂×C₄×C₈₉	—	2	1	no	—
391	C₂×C₄×C₈₉	—	2	1	no	—
392	C₂×C₄×C₈₉	—	2	1	no	—
393	C₂×C₄×C₈₉	—	2	1	no	—
394	C₂×C₄×C₈₉	—	2	1	no	—
395	C₂×C₄×C₈₉	—	2	2	no	—
396	C₂×C₄×C₈₉	—	2	2	no	—
397	C₂×C₄×C₈₉	—	2	1	no	—
398	C₂×C₄×C₈₉	—	2	2	no	—
399	C₂×C₄×C₈₉	—	8	4	no	—
400	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
401	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
402	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
403	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
404	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
405	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
406	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
407	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
408	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
409	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
410	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
411	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
412	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
413	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
414	C₂²×C₈₉	—	2	2	no	—
415	C₂²×C₈₉	—	2	2	no	—
416	C₂²×C₈₉	—	2	2	no	—
417	C₂²×C₈₉	—	4	1	no	—
418	C₂²×C₈₉	—	4	1	no	—
419	C₂²×C₈₉	—	4	1	no	—
420	C₂²×C₈₉	—	4	1	no	—
421	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
422	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
423	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
424	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
425	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
426	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
427	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
428	C₄×C₈₉	—	2	2	no	—
429	C₄×C₈₉	—	2	2	no	—
430	C₄×C₈₉	—	2	2	no	—
431	C₄×C₈₉	—	2	2	no	—
432	C₄×C₈₉	—	2	2	no	—
433	C₄×C₈₉	—	2	4	no	—
434	C₄×C₈₉	—	2	2	no	—
435	C₄×C₈₉	—	2	4	no	—
436	C₄×C₈₉	—	2	2	no	—
437	C₄×C₈₉	—	2	2	no	—
438	C₄×C₈₉	—	2	2	no	—
439	C₄×C₈₉	—	4	2	no	—
440	C₄×C₈₉	—	4	2	no	—
441	C₄×C₈₉	—	4	2	no	—
442	C₄×C₈₉	—	4	1	no	—
443	C₄×C₈₉	—	4	1	no	—
444	C₄×C₈₉	—	4	2	no	—
445	C₄×C₈₉	—	4	2	no	—
446	C₄×C₈₉	—	4	1	no	—
447	C₄×C₈₉	—	4	2	no	—
448	C₄×C₈₉	—	4	1	no	—
449	C₄×C₈₉	#533	1	4	yes	—
450	#35578	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
451	C₂×C₈₉	—	4	2	no	—
452	C₂×C₈₉	C₂×#533	1	1	yes	characteristic
453	C₂×C₈₉	#3503	1	1	yes	characteristic
454	C₂×C₈₉	#3503	1	1	yes	characteristic
455	C₂×C₈₉	#3519	1	1	yes	characteristic
456	C₂×C₈₉	#3520	1	1	yes	characteristic
457	C₂×C₈₉	#3522	1	1	yes	characteristic
458	C₂×C₈₉	#3523	1	1	yes	characteristic
459	#2590	C₂×C₈₉	1	2	yes	complemented
460	#2589	C₂×C₈₉	1	2	yes	—
461	#2586	C₂×C₈₉	1	2	yes	complemented
462	#2570	C₂×C₈₉	1	1	yes	characteristic, complemented
463	#2556	C₂×C₈₉	1	2	yes	—
464	#2552	C₂×C₈₉	1	1	yes	characteristic, complemented
465	#2551	C₂×C₈₉	1	1	yes	characteristic, complemented
466	#2550	C₂×C₈₉	1	1	yes	characteristic, complemented
467	#2465	C₂×C₈₉	1	2	yes	—
468	#2462	C₂×C₈₉	1	2	yes	complemented
469	#2451	C₂×C₈₉	1	2	yes	complemented
470	#2441	C₂×C₈₉	1	1	yes	characteristic
471	#2440	C₂×C₈₉	1	1	yes	characteristic
472	#2440	C₂×C₈₉	1	1	yes	characteristic
473	#2439	C₂×C₈₉	1	1	yes	characteristic
474	#2429	C₂×C₈₉	1	2	yes	—
475	#2331	C₂×C₈₉	1	1	yes	characteristic, complemented
476	#2330	C₂×C₈₉	1	1	yes	characteristic, complemented
477	#2314	C₂×C₈₉	1	1	yes	characteristic
478	C₄×C₄⋊Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
479	C₄×C₄⋊Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
480	#2298	C₂×C₈₉	1	1	yes	characteristic
481	#2274	C₂×C₈₉	1	1	yes	characteristic
482	C₈₉	#35578	1	1	yes	characteristic, direct product factor, Sylow
483	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
484	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
485	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
486	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
487	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
488	C₂×#125	C₂²×C₈₉	1	2	yes	—
489	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
490	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
491	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
492	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
493	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
494	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
495	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
496	#400	C₂²×C₈₉	1	2	yes	—
497	#399	C₂²×C₈₉	1	2	yes	—
498	#398	C₂²×C₈₉	1	2	yes	—
499	#398	C₂²×C₈₉	1	2	yes	—
500	#398	C₂²×C₈₉	1	2	yes	—
501	#398	C₂²×C₈₉	1	2	yes	—
502	#398	C₂²×C₈₉	1	2	yes	—
503	#398	C₂²×C₈₉	1	2	yes	—
504	#396	C₂²×C₈₉	1	2	yes	—
505	#396	C₂²×C₈₉	1	2	yes	—
506	#395	C₂²×C₈₉	1	2	yes	—
507	#395	C₂²×C₈₉	1	2	yes	—
508	#395	C₂²×C₈₉	1	2	yes	—
509	#395	C₂²×C₈₉	1	2	yes	—
510	#395	C₂²×C₈₉	1	2	yes	—
511	#393	C₂²×C₈₉	1	2	yes	—
512	#391	C₂²×C₈₉	1	2	yes	—
513	#391	C₂²×C₈₉	1	2	yes	—
514	#391	C₂²×C₈₉	1	2	yes	—
515	#391	C₂²×C₈₉	1	2	yes	—
516	#391	C₂²×C₈₉	1	2	yes	—
517	#391	C₂²×C₈₉	1	2	yes	—
518	#389	C₂²×C₈₉	1	1	yes	characteristic
519	#389	C₂²×C₈₉	1	2	yes	—
520	#389	C₂²×C₈₉	1	2	yes	—
521	#389	C₂²×C₈₉	1	1	yes	characteristic
522	#389	C₂²×C₈₉	1	1	yes	characteristic
523	#389	C₂²×C₈₉	1	1	yes	characteristic
524	#389	C₂²×C₈₉	1	1	yes	characteristic
525	#389	C₂²×C₈₉	1	2	yes	—
526	#389	C₂²×C₈₉	1	1	yes	characteristic
527	#389	C₂²×C₈₉	1	2	yes	—
528	#389	C₂²×C₈₉	1	2	yes	—
529	#389	C₂²×C₈₉	1	1	yes	characteristic
530	#389	C₂²×C₈₉	1	1	yes	characteristic
531	#389	C₂²×C₈₉	1	2	yes	—
532	#389	C₂²×C₈₉	1	2	yes	—
533	#389	C₂²×C₈₉	1	2	yes	—
534	#388	C₂²×C₈₉	1	2	yes	—
535	#388	C₂²×C₈₉	1	2	yes	—
536	#388	C₂²×C₈₉	1	1	yes	characteristic
537	#388	C₂²×C₈₉	1	1	yes	characteristic
538	#388	C₂²×C₈₉	1	1	yes	characteristic
539	#388	C₂²×C₈₉	1	1	yes	characteristic
540	#387	C₂²×C₈₉	1	2	yes	—
541	#387	C₂²×C₈₉	1	2	yes	—
542	#387	C₂²×C₈₉	1	2	yes	—
543	#387	C₂²×C₈₉	1	2	yes	—
544	#387	C₂²×C₈₉	1	2	yes	—
545	#387	C₂²×C₈₉	1	2	yes	—
546	#387	C₂²×C₈₉	1	1	yes	characteristic
547	#387	C₂²×C₈₉	1	2	yes	—
548	#387	C₂²×C₈₉	1	2	yes	—
549	#387	C₂²×C₈₉	1	2	yes	—
550	#387	C₂²×C₈₉	1	1	yes	characteristic
551	#387	C₂²×C₈₉	1	2	yes	—
552	#387	C₂²×C₈₉	1	1	yes	characteristic
553	#387	C₂²×C₈₉	1	1	yes	characteristic
554	#385	C₂²×C₈₉	1	2	yes	—
555	#385	C₂²×C₈₉	1	2	yes	—
556	#384	C₂²×C₈₉	1	1	yes	characteristic
557	#384	C₂²×C₈₉	1	1	yes	characteristic
558	#384	C₂²×C₈₉	1	1	yes	characteristic
559	#384	C₂²×C₈₉	1	1	yes	characteristic
560	#382	C₂²×C₈₉	1	1	yes	characteristic
561	#382	C₂²×C₈₉	1	1	yes	characteristic
562	#380	C₂²×C₈₉	1	1	yes	characteristic
563	#380	C₂²×C₈₉	1	1	yes	characteristic
564	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
565	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
566	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
567	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
568	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
569	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
570	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
571	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
572	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
573	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
574	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
575	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
576	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
577	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
578	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
579	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
580	#376	C₂²×C₈₉	1	1	yes	characteristic
581	C₄³	C₂²×C₈₉	1	1	yes	characteristic
582	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
583	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
584	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
585	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
586	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
587	C₄⋊Q₈	—	2	4	no	—
588	C₄⋊Q₈	—	2	4	no	—
589	C₄⋊Q₈	—	2	4	no	—
590	C₄⋊Q₈	—	4	4	no	—
591	#125	—	2	4	no	—
592	#125	—	4	4	no	—
593	C₂²⋊Q₈	—	4	4	no	—
594	C₂²⋊Q₈	—	4	4	no	—
595	C₄×Q₈	—	4	4	no	—
596	C₄×Q₈	—	4	4	no	—
597	#117	—	2	4	no	—
598	#117	Q₈×C₈₉	1	8	yes	complemented
599	C₂×C₄⋊C₄	—	2	4	no	—
600	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
636	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
638	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
639	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
640	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
641	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
644	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
646	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
655	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
656	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
657	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
658	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
659	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
660	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
662	#95	C₂³×C₈₉	1	1	yes	characteristic
663	#95	C₂³×C₈₉	1	1	yes	characteristic
664	#95	C₂³×C₈₉	1	1	yes	characteristic
665	#95	C₂³×C₈₉	1	1	yes	characteristic
666	#95	C₂³×C₈₉	1	2	yes	—
667	#95	C₂³×C₈₉	1	2	yes	—
668	#95	C₂³×C₈₉	1	2	yes	—
669	#95	C₂³×C₈₉	1	2	yes	—
670	#95	C₂³×C₈₉	1	1	yes	characteristic
671	#95	C₂³×C₈₉	1	1	yes	characteristic
672	#95	C₂³×C₈₉	1	1	yes	characteristic
673	#95	C₂³×C₈₉	1	1	yes	characteristic
674	#95	C₂³×C₈₉	1	2	yes	—
675	#95	C₂³×C₈₉	1	2	yes	—
676	#95	C₂³×C₈₉	1	1	yes	characteristic
677	#95	C₂³×C₈₉	1	1	yes	characteristic
678	#95	C₂³×C₈₉	1	2	yes	—
679	#95	C₂³×C₈₉	1	2	yes	—
680	#95	C₂³×C₈₉	1	1	yes	characteristic
681	#95	C₂³×C₈₉	1	1	yes	characteristic
682	#95	C₂³×C₈₉	1	2	yes	—
683	#95	C₂³×C₈₉	1	2	yes	—
684	#95	C₂³×C₈₉	1	2	yes	—
685	#95	C₂³×C₈₉	1	2	yes	—
686	#95	C₂³×C₈₉	1	2	yes	—
687	#95	C₂³×C₈₉	1	2	yes	—
688	#95	C₂³×C₈₉	1	2	yes	—
689	#95	C₂³×C₈₉	1	2	yes	—
690	#95	C₂³×C₈₉	1	2	yes	—
691	#95	C₂³×C₈₉	1	2	yes	—
692	#95	C₂³×C₈₉	1	2	yes	—
693	#95	C₂³×C₈₉	1	2	yes	—
694	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
695	C₂×Q₈	—	2	4	no	—
696	C₂×Q₈	—	2	4	no	—
697	C₂×Q₈	—	2	4	no	—
698	C₂×Q₈	—	2	4	no	—
699	C₂×Q₈	—	2	4	no	—
700	C₂×Q₈	—	4	2	no	—
701	C₂×Q₈	—	4	2	no	—
702	C₂×Q₈	—	4	2	no	—
703	C₂×Q₈	—	4	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	4	2	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
710	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	4	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	4	2	no	—
755	C₄⋊C₄	—	4	2	no	—
756	C₄⋊C₄	—	4	2	no	—
757	C₄⋊C₄	—	4	2	no	—
758	C₄⋊C₄	—	4	2	no	—
759	C₄⋊C₄	—	4	2	no	—
760	C₄⋊C₄	—	4	2	no	—
761	C₄⋊C₄	—	4	2	no	—
762	C₄⋊C₄	—	4	2	no	—
763	C₄⋊C₄	—	4	2	no	—
764	C₄⋊C₄	C₂×Q₈×C₈₉	1	4	yes	—
765	C₄⋊C₄	C₂×Q₈×C₈₉	1	4	yes	—
766	C₄⋊C₄	#41×C₈₉	1	4	yes	—
767	C₄⋊C₄	#41×C₈₉	1	4	yes	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	C₂×Q₈×C₈₉	1	4	yes	—
776	C₂²⋊C₄	C₂×Q₈×C₈₉	1	4	yes	—
777	C₄²	—	2	4	no	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	2	no	—
780	C₄²	—	2	2	no	—
781	C₄²	—	2	2	no	—
782	C₄²	—	2	2	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	4	2	no	—
787	C₄²	—	4	2	no	—
788	C₄²	—	4	2	no	—
789	C₄²	—	4	2	no	—
790	C₄²	—	4	2	no	—
791	C₄²	—	4	2	no	—
792	C₄²	C₂×Q₈×C₈₉	1	4	yes	—
793	C₄²	C₂×Q₈×C₈₉	1	4	yes	—
794	C₂³	—	2	1	no	—
795	C₂³	—	2	1	no	—
796	C₂³	—	2	1	no	—
797	C₂³	—	2	1	no	—
798	C₂³	—	2	1	no	—
799	C₂³	—	2	1	no	—
800	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
801	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
802	Q₈	—	4	8	no	—
803	Q₈	—	4	8	no	—
804	Q₈	—	8	4	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	8	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	8	4	no	—
859	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
860	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
861	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
862	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
863	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
864	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
865	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
866	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
867	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
868	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
869	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
870	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
871	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
872	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
873	C₂²	—	2	2	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	4	1	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	1	no	—
880	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
881	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
882	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
883	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
884	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
885	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
886	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
887	C₄	—	2	2	no	—
888	C₄	—	2	2	no	—
889	C₄	—	2	2	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	2	no	—
892	C₄	—	2	4	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	4	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	1	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	1	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	1	no	—
908	C₄	#533×C₈₉	1	4	yes	—
909	C₂	—	4	2	no	—
910	C₂	C₂×#533×C₈₉	1	1	yes	characteristic
911	C₂	C₈₉×#3503	1	1	yes	characteristic
912	C₂	C₈₉×#3503	1	1	yes	characteristic
913	C₂	C₈₉×#3519	1	1	yes	characteristic
914	C₂	C₈₉×#3520	1	1	yes	characteristic
915	C₂	C₈₉×#3522	1	1	yes	characteristic
916	C₂	C₈₉×#3523	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂⁴×C₈₉	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#2590	C₂	semidirect
3. C₈₉×#2586	C₂	semidirect
4. C₈₉×#2570	C₂	semidirect
6. C₈₉×#2552	C₂	semidirect
7. C₈₉×#2551	C₂	semidirect
8. C₈₉×#2550	C₂	semidirect
10. C₈₉×#2462	C₂	semidirect
11. C₈₉×#2451	C₂	semidirect
17. C₈₉×#2331	C₂	semidirect
18. C₈₉×#2330	C₂	semidirect
20. C₄×C₄⋊Q₈×C₈₉	C₂	semidirect
21. C₄×C₄⋊Q₈×C₈₉	C₂	semidirect
139. #117×C₈₉	Q₈	semidirect
450. #35578	C₈₉	direct (N × H)
459. #2590	C₂×C₈₉	semidirect
461. #2586	C₂×C₈₉	semidirect
462. #2570	C₂×C₈₉	semidirect
464. #2552	C₂×C₈₉	semidirect
465. #2551	C₂×C₈₉	semidirect
466. #2550	C₂×C₈₉	semidirect
468. #2462	C₂×C₈₉	semidirect
469. #2451	C₂×C₈₉	semidirect
475. #2331	C₂×C₈₉	semidirect
476. #2330	C₂×C₈₉	semidirect
478. C₄×C₄⋊Q₈	C₂×C₈₉	semidirect
479. C₄×C₄⋊Q₈	C₂×C₈₉	semidirect
482. C₈₉	#35578	direct (N × H)
598. #117	Q₈×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#2590	2
C₈₉×#2589	2
C₈₉×#2586	2
C₈₉×#2570	2
C₈₉×#2556	2
C₈₉×#2552	2
C₈₉×#2551	2
C₈₉×#2550	2
C₈₉×#2465	2
C₈₉×#2462	2
C₈₉×#2451	2
C₈₉×#2441	2
C₈₉×#2440	2
C₈₉×#2439	2
C₈₉×#2429	2
C₈₉×#2331	2
C₈₉×#2330	2
C₈₉×#2314	2
C₄×C₄⋊Q₈×C₈₉	2
C₈₉×#2298	2
C₈₉×#2274	2
#35578	89

Subgroups — C89×#35578 #36413426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35578 #36413426