Subgroups — C₈₉×#35553 #36413401

Order 22784.

1878 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2575	C₂	1	2	yes	maximal, complemented
2	C₈₉×#2570	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2563	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2560	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2542	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2535	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#2517	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2497	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2496	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2488	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2477	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2471	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2467	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2450	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2422	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2420	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2331	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#2324	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2314	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#121×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#2290	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₉×#2285	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2275	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#126×C₈₉	C₂²	1	2	yes	—
26	C₂×#123×C₈₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
29	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
36	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#117×C₈₉	C₂²	1	2	yes	—
38	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
39	#400×C₈₉	C₂²	1	2	yes	—
40	#400×C₈₉	C₂²	1	2	yes	—
41	#400×C₈₉	C₂²	1	2	yes	—
42	#399×C₈₉	C₂²	1	2	yes	—
43	#399×C₈₉	C₂²	1	2	yes	—
44	#398×C₈₉	C₂²	1	2	yes	—
45	#397×C₈₉	C₂²	1	2	yes	—
46	#397×C₈₉	C₂²	1	2	yes	—
47	#397×C₈₉	C₂²	1	2	yes	—
48	#397×C₈₉	C₂²	1	2	yes	—
49	#396×C₈₉	C₂²	1	2	yes	—
50	#394×C₈₉	C₂²	1	2	yes	—
51	#394×C₈₉	C₂²	1	2	yes	—
52	#393×C₈₉	C₂²	1	2	yes	—
53	#393×C₈₉	C₂²	1	2	yes	—
54	#392×C₈₉	C₂²	1	2	yes	—
55	#391×C₈₉	C₂²	1	2	yes	—
56	#391×C₈₉	C₂²	1	2	yes	—
57	#390×C₈₉	C₂²	1	1	yes	characteristic
58	#390×C₈₉	C₂²	1	2	yes	—
59	#390×C₈₉	C₂²	1	2	yes	—
60	#390×C₈₉	C₂²	1	1	yes	characteristic
61	#389×C₈₉	C₂²	1	1	yes	characteristic
62	#389×C₈₉	C₂²	1	1	yes	characteristic
63	#389×C₈₉	C₂²	1	1	yes	characteristic
64	#389×C₈₉	C₂²	1	1	yes	characteristic
65	#388×C₈₉	C₂²	1	2	yes	—
66	#388×C₈₉	C₂²	1	1	yes	characteristic
67	#388×C₈₉	C₂²	1	2	yes	—
68	#388×C₈₉	C₂²	1	2	yes	—
69	#388×C₈₉	C₂²	1	2	yes	—
70	#388×C₈₉	C₂²	1	2	yes	—
71	#388×C₈₉	C₂²	1	1	yes	characteristic
72	#387×C₈₉	C₂²	1	2	yes	—
73	#387×C₈₉	C₂²	1	2	yes	—
74	#387×C₈₉	C₂²	1	2	yes	—
75	#387×C₈₉	C₂²	1	2	yes	—
76	#387×C₈₉	C₂²	1	2	yes	—
77	#387×C₈₉	C₂²	1	1	yes	characteristic
78	#387×C₈₉	C₂²	1	2	yes	—
79	#387×C₈₉	C₂²	1	2	yes	—
80	#387×C₈₉	C₂²	1	2	yes	—
81	#387×C₈₉	C₂²	1	1	yes	characteristic
82	#386×C₈₉	C₂²	1	2	yes	—
83	#386×C₈₉	C₂²	1	2	yes	—
84	#386×C₈₉	C₂²	1	2	yes	—
85	#386×C₈₉	C₂²	1	2	yes	—
86	#386×C₈₉	C₂²	1	2	yes	—
87	#386×C₈₉	C₂²	1	1	yes	characteristic
88	#386×C₈₉	C₂²	1	1	yes	characteristic
89	#385×C₈₉	C₂²	1	2	yes	—
90	#385×C₈₉	C₂²	1	2	yes	—
91	#385×C₈₉	C₂²	1	1	yes	characteristic
92	#385×C₈₉	C₂²	1	1	yes	characteristic
93	#384×C₈₉	C₂²	1	1	yes	characteristic
94	#384×C₈₉	C₂²	1	1	yes	characteristic
95	#384×C₈₉	C₂²	1	1	yes	characteristic
96	#382×C₈₉	C₂²	1	2	yes	—
97	#382×C₈₉	C₂²	1	1	yes	characteristic
98	#382×C₈₉	C₂²	1	1	yes	characteristic
99	#382×C₈₉	C₂²	1	2	yes	—
100	#381×C₈₉	C₂²	1	2	yes	—
101	#380×C₈₉	C₂²	1	1	yes	characteristic
102	#380×C₈₉	C₂²	1	1	yes	characteristic
103	#380×C₈₉	C₂²	1	1	yes	characteristic
104	#380×C₈₉	C₂²	1	1	yes	characteristic
105	#380×C₈₉	C₂²	1	1	yes	characteristic
106	#380×C₈₉	C₂²	1	2	yes	—
107	#380×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	1	yes	characteristic
114	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
121	#376×C₈₉	C₂²	1	1	yes	characteristic
122	C₂×#95×C₈₉	C₂²	1	2	yes	—
123	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
124	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
125	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
128	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
133	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
134	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
135	C₄⋊Q₈×C₈₉	—	2	4	no	—
136	#126×C₈₉	—	4	4	no	—
137	#123×C₈₉	—	4	4	no	—
138	C₂²⋊Q₈×C₈₉	—	4	4	no	—
139	C₂²⋊Q₈×C₈₉	—	4	4	no	—
140	#121×C₈₉	—	2	4	no	—
141	#121×C₈₉	—	2	4	no	—
142	C₄×D₄×C₈₉	—	2	4	no	—
143	C₄×D₄×C₈₉	—	2	4	no	—
144	C₄×D₄×C₈₉	—	2	4	no	—
145	C₄×D₄×C₈₉	—	2	4	no	—
146	C₄×D₄×C₈₉	—	4	4	no	—
147	#117×C₈₉	—	2	4	no	—
148	#117×C₈₉	—	4	4	no	—
149	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
156	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
164	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
195	C₂×C₄²×C₈₉	—	2	4	no	—
196	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
202	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
203	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
204	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
205	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
206	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
208	#95×C₈₉	C₂³	1	1	yes	characteristic
209	#95×C₈₉	C₂³	1	2	yes	—
210	#95×C₈₉	C₂³	1	2	yes	—
211	#95×C₈₉	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
221	#95×C₈₉	C₂³	1	2	yes	—
222	#95×C₈₉	C₂³	1	2	yes	—
223	#95×C₈₉	C₂³	1	2	yes	—
224	#95×C₈₉	C₂³	1	1	yes	characteristic
225	#95×C₈₉	C₂³	1	1	yes	characteristic
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	#95×C₈₉	C₂³	1	2	yes	—
236	#95×C₈₉	C₂³	1	2	yes	—
237	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
238	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
239	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
240	C₂×Q₈×C₈₉	—	2	4	no	—
241	C₂×Q₈×C₈₉	—	4	2	no	—
242	C₂×Q₈×C₈₉	—	4	2	no	—
243	C₂×D₄×C₈₉	—	2	4	no	—
244	C₂×D₄×C₈₉	—	2	2	no	—
245	C₂×D₄×C₈₉	—	2	4	no	—
246	C₂×D₄×C₈₉	—	2	4	no	—
247	C₂×D₄×C₈₉	—	2	2	no	—
248	C₂×D₄×C₈₉	—	2	2	no	—
249	C₂×D₄×C₈₉	—	2	2	no	—
250	C₂×D₄×C₈₉	—	4	2	no	—
251	C₂×D₄×C₈₉	—	4	1	no	—
252	C₂×D₄×C₈₉	—	4	2	no	—
253	C₂×D₄×C₈₉	—	4	2	no	—
254	C₂×D₄×C₈₉	#41	1	4	yes	—
255	C₂²×C₄×C₈₉	—	2	2	no	—
256	C₂²×C₄×C₈₉	—	2	2	no	—
257	C₂²×C₄×C₈₉	—	2	2	no	—
258	C₂²×C₄×C₈₉	—	2	4	no	—
259	C₂²×C₄×C₈₉	—	2	2	no	—
260	C₂²×C₄×C₈₉	—	2	2	no	—
261	C₂²×C₄×C₈₉	—	2	2	no	—
262	C₂²×C₄×C₈₉	—	2	2	no	—
263	C₂²×C₄×C₈₉	—	2	2	no	—
264	C₂²×C₄×C₈₉	—	2	2	no	—
265	C₂²×C₄×C₈₉	—	2	2	no	—
266	C₂²×C₄×C₈₉	—	2	2	no	—
267	C₂²×C₄×C₈₉	—	2	4	no	—
268	C₂²×C₄×C₈₉	—	2	4	no	—
269	C₂²×C₄×C₈₉	—	4	1	no	—
270	C₂²×C₄×C₈₉	—	4	2	no	—
271	C₂²×C₄×C₈₉	—	4	2	no	—
272	C₂²×C₄×C₈₉	—	4	2	no	—
273	C₂²×C₄×C₈₉	—	4	2	no	—
274	C₂²×C₄×C₈₉	—	4	2	no	—
275	C₂²×C₄×C₈₉	—	4	2	no	—
276	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
296	C₄⋊C₄×C₈₉	—	2	2	no	—
297	C₄⋊C₄×C₈₉	—	2	2	no	—
298	C₄⋊C₄×C₈₉	—	2	2	no	—
299	C₄⋊C₄×C₈₉	—	2	2	no	—
300	C₄⋊C₄×C₈₉	—	2	2	no	—
301	C₄⋊C₄×C₈₉	—	2	2	no	—
302	C₄⋊C₄×C₈₉	—	2	2	no	—
303	C₄⋊C₄×C₈₉	—	2	2	no	—
304	C₄⋊C₄×C₈₉	—	2	4	no	—
305	C₄⋊C₄×C₈₉	—	2	2	no	—
306	C₄⋊C₄×C₈₉	—	2	2	no	—
307	C₄⋊C₄×C₈₉	—	2	4	no	—
308	C₄⋊C₄×C₈₉	—	2	4	no	—
309	C₄⋊C₄×C₈₉	—	2	4	no	—
310	C₄⋊C₄×C₈₉	—	2	2	no	—
311	C₄⋊C₄×C₈₉	—	2	2	no	—
312	C₄⋊C₄×C₈₉	—	2	4	no	—
313	C₄⋊C₄×C₈₉	—	4	2	no	—
314	C₄⋊C₄×C₈₉	—	4	2	no	—
315	C₄⋊C₄×C₈₉	—	4	2	no	—
316	C₄⋊C₄×C₈₉	—	4	2	no	—
317	C₄⋊C₄×C₈₉	—	4	2	no	—
318	C₄⋊C₄×C₈₉	—	4	2	no	—
319	C₂²⋊C₄×C₈₉	—	2	4	no	—
320	C₂²⋊C₄×C₈₉	—	2	4	no	—
321	C₂²⋊C₄×C₈₉	—	2	4	no	—
322	C₂²⋊C₄×C₈₉	—	2	2	no	—
323	C₂²⋊C₄×C₈₉	—	2	2	no	—
324	C₂²⋊C₄×C₈₉	—	2	2	no	—
325	C₂²⋊C₄×C₈₉	—	2	4	no	—
326	C₂²⋊C₄×C₈₉	—	2	4	no	—
327	C₂²⋊C₄×C₈₉	—	2	2	no	—
328	C₂²⋊C₄×C₈₉	—	2	2	no	—
329	C₂²⋊C₄×C₈₉	—	2	4	no	—
330	C₂²⋊C₄×C₈₉	—	2	4	no	—
331	C₂²⋊C₄×C₈₉	—	2	2	no	—
332	C₂²⋊C₄×C₈₉	—	2	2	no	—
333	C₂²⋊C₄×C₈₉	—	4	1	no	—
334	C₂²⋊C₄×C₈₉	—	4	2	no	—
335	C₂²⋊C₄×C₈₉	—	4	2	no	—
336	C₂²⋊C₄×C₈₉	—	4	2	no	—
337	C₂²⋊C₄×C₈₉	—	4	2	no	—
338	C₂²⋊C₄×C₈₉	—	4	2	no	—
339	C₂²⋊C₄×C₈₉	—	4	2	no	—
340	C₂²⋊C₄×C₈₉	—	4	2	no	—
341	C₂²⋊C₄×C₈₉	—	4	2	no	—
342	C₄²×C₈₉	—	2	2	no	—
343	C₄²×C₈₉	—	2	2	no	—
344	C₄²×C₈₉	—	2	2	no	—
345	C₄²×C₈₉	—	2	2	no	—
346	C₄²×C₈₉	—	2	2	no	—
347	C₄²×C₈₉	—	4	2	no	—
348	C₄²×C₈₉	—	4	2	no	—
349	C₄²×C₈₉	—	4	2	no	—
350	C₄²×C₈₉	—	4	2	no	—
351	C₄²×C₈₉	—	4	2	no	—
352	C₄²×C₈₉	#41	1	4	yes	—
353	C₄²×C₈₉	#41	1	4	yes	—
354	C₂³×C₈₉	—	2	2	no	—
355	C₂³×C₈₉	—	2	2	no	—
356	C₂³×C₈₉	—	2	1	no	—
357	C₂³×C₈₉	—	2	1	no	—
358	C₂³×C₈₉	—	2	1	no	—
359	C₂³×C₈₉	—	2	2	no	—
360	C₂³×C₈₉	—	2	2	no	—
361	C₂³×C₈₉	—	2	1	no	—
362	C₂³×C₈₉	—	2	1	no	—
363	C₂³×C₈₉	—	2	2	no	—
364	C₂³×C₈₉	—	2	1	no	—
365	C₂³×C₈₉	—	2	2	no	—
366	C₂³×C₈₉	—	2	1	no	—
367	C₂³×C₈₉	—	2	1	no	—
368	C₂³×C₈₉	—	2	1	no	—
369	C₂³×C₈₉	—	2	1	no	—
370	C₂³×C₈₉	—	2	1	no	—
371	C₂³×C₈₉	—	2	1	no	—
372	C₂³×C₈₉	—	2	1	no	—
373	C₂³×C₈₉	C₂×#41	1	4	yes	—
374	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
375	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
376	Q₈×C₈₉	—	8	4	no	—
377	D₄×C₈₉	—	2	8	no	—
378	D₄×C₈₉	—	4	4	no	—
379	D₄×C₈₉	—	4	8	no	—
380	D₄×C₈₉	—	8	4	no	—
381	C₂×C₄×C₈₉	—	2	8	no	—
382	C₂×C₄×C₈₉	—	2	1	no	—
383	C₂×C₄×C₈₉	—	2	1	no	—
384	C₂×C₄×C₈₉	—	2	1	no	—
385	C₂×C₄×C₈₉	—	2	1	no	—
386	C₂×C₄×C₈₉	—	2	1	no	—
387	C₂×C₄×C₈₉	—	2	1	no	—
388	C₂×C₄×C₈₉	—	2	1	no	—
389	C₂×C₄×C₈₉	—	2	1	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	1	no	—
396	C₂×C₄×C₈₉	—	2	1	no	—
397	C₂×C₄×C₈₉	—	2	1	no	—
398	C₂×C₄×C₈₉	—	2	1	no	—
399	C₂×C₄×C₈₉	—	2	1	no	—
400	C₂×C₄×C₈₉	—	2	1	no	—
401	C₂×C₄×C₈₉	—	2	1	no	—
402	C₂×C₄×C₈₉	—	2	1	no	—
403	C₂×C₄×C₈₉	—	2	2	no	—
404	C₂×C₄×C₈₉	—	2	2	no	—
405	C₂×C₄×C₈₉	—	2	2	no	—
406	C₂×C₄×C₈₉	—	2	2	no	—
407	C₂×C₄×C₈₉	—	2	2	no	—
408	C₂×C₄×C₈₉	—	2	1	no	—
409	C₂×C₄×C₈₉	—	2	2	no	—
410	C₂×C₄×C₈₉	—	2	2	no	—
411	C₂×C₄×C₈₉	—	2	1	no	—
412	C₂×C₄×C₈₉	—	2	2	no	—
413	C₂×C₄×C₈₉	—	2	2	no	—
414	C₂×C₄×C₈₉	—	2	2	no	—
415	C₂×C₄×C₈₉	—	2	2	no	—
416	C₂×C₄×C₈₉	—	2	2	no	—
417	C₂×C₄×C₈₉	—	2	2	no	—
418	C₂×C₄×C₈₉	—	2	2	no	—
419	C₂×C₄×C₈₉	—	2	2	no	—
420	C₂×C₄×C₈₉	—	2	2	no	—
421	C₂×C₄×C₈₉	—	2	1	no	—
422	C₂×C₄×C₈₉	—	2	1	no	—
423	C₂×C₄×C₈₉	—	2	1	no	—
424	C₂×C₄×C₈₉	—	2	2	no	—
425	C₂×C₄×C₈₉	—	2	1	no	—
426	C₂×C₄×C₈₉	—	2	1	no	—
427	C₂×C₄×C₈₉	—	2	2	no	—
428	C₂×C₄×C₈₉	—	2	2	no	—
429	C₂×C₄×C₈₉	—	2	2	no	—
430	C₂×C₄×C₈₉	—	2	1	no	—
431	C₂×C₄×C₈₉	—	2	1	no	—
432	C₂×C₄×C₈₉	—	2	2	no	—
433	C₂×C₄×C₈₉	—	4	4	no	—
434	C₂×C₄×C₈₉	—	4	4	no	—
435	C₂×C₄×C₈₉	—	4	4	no	—
436	C₂×C₄×C₈₉	—	8	4	no	—
437	C₂×C₄×C₈₉	—	8	4	no	—
438	C₂×C₄×C₈₉	—	8	4	no	—
439	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
440	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
441	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
442	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
443	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
444	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
445	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
446	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
447	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
448	C₂²×C₈₉	—	2	4	no	—
449	C₂²×C₈₉	—	2	2	no	—
450	C₂²×C₈₉	—	2	2	no	—
451	C₂²×C₈₉	—	2	4	no	—
452	C₂²×C₈₉	—	2	2	no	—
453	C₂²×C₈₉	—	2	4	no	—
454	C₂²×C₈₉	—	4	1	no	—
455	C₂²×C₈₉	—	4	2	no	—
456	C₂²×C₈₉	—	4	1	no	—
457	C₂²×C₈₉	—	4	2	no	—
458	C₂²×C₈₉	—	4	2	no	—
459	C₂²×C₈₉	—	4	2	no	—
460	C₂²×C₈₉	—	4	1	no	—
461	C₂²×C₈₉	—	4	1	no	—
462	C₂²×C₈₉	—	4	1	no	—
463	C₂²×C₈₉	—	4	1	no	—
464	C₂²×C₈₉	—	4	1	no	—
465	C₂²×C₈₉	—	4	1	no	—
466	C₂²×C₈₉	—	4	1	no	—
467	C₂²×C₈₉	—	4	1	no	—
468	C₂²×C₈₉	—	4	1	no	—
469	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
470	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
471	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
472	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
473	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
474	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
475	C₂²×C₈₉	#585	1	1	yes	characteristic
476	C₄×C₈₉	—	2	2	no	—
477	C₄×C₈₉	—	2	2	no	—
478	C₄×C₈₉	—	2	2	no	—
479	C₄×C₈₉	—	2	2	no	—
480	C₄×C₈₉	—	2	2	no	—
481	C₄×C₈₉	—	2	2	no	—
482	C₄×C₈₉	—	4	1	no	—
483	C₄×C₈₉	—	4	1	no	—
484	C₄×C₈₉	—	4	1	no	—
485	C₄×C₈₉	—	4	1	no	—
486	C₄×C₈₉	—	4	2	no	—
487	C₄×C₈₉	—	4	2	no	—
488	C₄×C₈₉	—	4	2	no	—
489	C₄×C₈₉	—	4	2	no	—
490	C₄×C₈₉	—	4	2	no	—
491	C₄×C₈₉	—	4	1	no	—
492	C₄×C₈₉	—	4	2	no	—
493	C₄×C₈₉	—	4	1	no	—
494	C₄×C₈₉	—	4	2	no	—
495	C₄×C₈₉	#529	1	4	yes	—
496	#35553	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
497	C₂×C₈₉	—	4	4	no	—
498	C₂×C₈₉	—	4	2	no	—
499	C₂×C₈₉	—	8	1	no	—
500	C₂×C₈₉	C₂×#529	1	1	yes	characteristic
501	C₂×C₈₉	#3492	1	1	yes	characteristic
502	C₂×C₈₉	#3494	1	1	yes	characteristic
503	C₂×C₈₉	#3495	1	1	yes	characteristic
504	C₂×C₈₉	#3508	1	1	yes	characteristic
505	C₂×C₈₉	#3514	1	1	yes	characteristic
506	C₂×C₈₉	#3520	1	1	yes	characteristic
507	#2575	C₂×C₈₉	1	2	yes	complemented
508	#2570	C₂×C₈₉	1	1	yes	characteristic, complemented
509	#2563	C₂×C₈₉	1	1	yes	characteristic, complemented
510	#2560	C₂×C₈₉	1	2	yes	complemented
511	#2542	C₂×C₈₉	1	1	yes	characteristic, complemented
512	#2535	C₂×C₈₉	1	1	yes	characteristic
513	#2517	C₂×C₈₉	1	2	yes	complemented
514	#2497	C₂×C₈₉	1	1	yes	characteristic, complemented
515	#2496	C₂×C₈₉	1	1	yes	characteristic, complemented
516	#2488	C₂×C₈₉	1	2	yes	complemented
517	#2477	C₂×C₈₉	1	2	yes	complemented
518	#2471	C₂×C₈₉	1	2	yes	complemented
519	#2467	C₂×C₈₉	1	2	yes	complemented
520	#2450	C₂×C₈₉	1	2	yes	complemented
521	#2422	C₂×C₈₉	1	1	yes	characteristic, complemented
522	#2420	C₂×C₈₉	1	1	yes	characteristic, complemented
523	#2331	C₂×C₈₉	1	1	yes	characteristic, complemented
524	#2324	C₂×C₈₉	1	1	yes	characteristic, complemented
525	#2314	C₂×C₈₉	1	1	yes	characteristic, complemented
526	C₄×#121	C₂×C₈₉	1	1	yes	characteristic, complemented
527	#2290	C₂×C₈₉	1	1	yes	characteristic, complemented
528	#2285	C₂×C₈₉	1	1	yes	characteristic, complemented
529	#2275	C₂×C₈₉	1	1	yes	characteristic, complemented
530	C₈₉	#35553	1	1	yes	characteristic, direct product factor, Sylow
531	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
532	C₂×#126	C₂²×C₈₉	1	2	yes	—
533	C₂×#123	C₂²×C₈₉	1	2	yes	—
534	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
535	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
536	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
537	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
538	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
539	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
540	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
541	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
542	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
543	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
544	C₂×#117	C₂²×C₈₉	1	2	yes	—
545	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
546	#400	C₂²×C₈₉	1	2	yes	—
547	#400	C₂²×C₈₉	1	2	yes	—
548	#400	C₂²×C₈₉	1	2	yes	—
549	#399	C₂²×C₈₉	1	2	yes	—
550	#399	C₂²×C₈₉	1	2	yes	—
551	#398	C₂²×C₈₉	1	2	yes	—
552	#397	C₂²×C₈₉	1	2	yes	—
553	#397	C₂²×C₈₉	1	2	yes	—
554	#397	C₂²×C₈₉	1	2	yes	—
555	#397	C₂²×C₈₉	1	2	yes	—
556	#396	C₂²×C₈₉	1	2	yes	—
557	#394	C₂²×C₈₉	1	2	yes	—
558	#394	C₂²×C₈₉	1	2	yes	—
559	#393	C₂²×C₈₉	1	2	yes	—
560	#393	C₂²×C₈₉	1	2	yes	—
561	#392	C₂²×C₈₉	1	2	yes	—
562	#391	C₂²×C₈₉	1	2	yes	—
563	#391	C₂²×C₈₉	1	2	yes	—
564	#390	C₂²×C₈₉	1	2	yes	—
565	#390	C₂²×C₈₉	1	2	yes	—
566	#390	C₂²×C₈₉	1	1	yes	characteristic
567	#390	C₂²×C₈₉	1	1	yes	characteristic
568	#389	C₂²×C₈₉	1	1	yes	characteristic
569	#389	C₂²×C₈₉	1	1	yes	characteristic
570	#389	C₂²×C₈₉	1	1	yes	characteristic
571	#389	C₂²×C₈₉	1	1	yes	characteristic
572	#388	C₂²×C₈₉	1	1	yes	characteristic
573	#388	C₂²×C₈₉	1	2	yes	—
574	#388	C₂²×C₈₉	1	2	yes	—
575	#388	C₂²×C₈₉	1	2	yes	—
576	#388	C₂²×C₈₉	1	2	yes	—
577	#388	C₂²×C₈₉	1	2	yes	—
578	#388	C₂²×C₈₉	1	1	yes	characteristic
579	#387	C₂²×C₈₉	1	2	yes	—
580	#387	C₂²×C₈₉	1	2	yes	—
581	#387	C₂²×C₈₉	1	2	yes	—
582	#387	C₂²×C₈₉	1	2	yes	—
583	#387	C₂²×C₈₉	1	2	yes	—
584	#387	C₂²×C₈₉	1	1	yes	characteristic
585	#387	C₂²×C₈₉	1	2	yes	—
586	#387	C₂²×C₈₉	1	2	yes	—
587	#387	C₂²×C₈₉	1	2	yes	—
588	#387	C₂²×C₈₉	1	1	yes	characteristic
589	#386	C₂²×C₈₉	1	2	yes	—
590	#386	C₂²×C₈₉	1	2	yes	—
591	#386	C₂²×C₈₉	1	2	yes	—
592	#386	C₂²×C₈₉	1	2	yes	—
593	#386	C₂²×C₈₉	1	1	yes	characteristic
594	#386	C₂²×C₈₉	1	1	yes	characteristic
595	#386	C₂²×C₈₉	1	2	yes	—
596	#385	C₂²×C₈₉	1	2	yes	—
597	#385	C₂²×C₈₉	1	2	yes	—
598	#385	C₂²×C₈₉	1	1	yes	characteristic
599	#385	C₂²×C₈₉	1	1	yes	characteristic
600	#384	C₂²×C₈₉	1	1	yes	characteristic
601	#384	C₂²×C₈₉	1	1	yes	characteristic
602	#384	C₂²×C₈₉	1	1	yes	characteristic
603	#382	C₂²×C₈₉	1	2	yes	—
604	#382	C₂²×C₈₉	1	1	yes	characteristic
605	#382	C₂²×C₈₉	1	1	yes	characteristic
606	#382	C₂²×C₈₉	1	2	yes	—
607	#381	C₂²×C₈₉	1	2	yes	—
608	#380	C₂²×C₈₉	1	1	yes	characteristic
609	#380	C₂²×C₈₉	1	1	yes	characteristic
610	#380	C₂²×C₈₉	1	1	yes	characteristic
611	#380	C₂²×C₈₉	1	1	yes	characteristic
612	#380	C₂²×C₈₉	1	1	yes	characteristic
613	#380	C₂²×C₈₉	1	2	yes	—
614	#380	C₂²×C₈₉	1	1	yes	characteristic
615	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
616	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
617	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
618	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
619	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
620	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
621	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
622	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
623	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
624	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
625	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
626	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
627	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
628	#376	C₂²×C₈₉	1	1	yes	characteristic
629	C₂×#95	C₂²×C₈₉	1	2	yes	—
630	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
631	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
632	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
633	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
634	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
635	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
636	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
637	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
638	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
639	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
640	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
641	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
642	C₄⋊Q₈	—	2	4	no	—
643	#126	—	4	4	no	—
644	#123	—	4	4	no	—
645	C₂²⋊Q₈	—	4	4	no	—
646	C₂²⋊Q₈	—	4	4	no	—
647	#121	—	2	4	no	—
648	#121	—	2	4	no	—
649	C₄×D₄	—	2	4	no	—
650	C₄×D₄	—	2	4	no	—
651	C₄×D₄	—	2	4	no	—
652	C₄×D₄	—	2	4	no	—
653	C₄×D₄	—	4	4	no	—
654	#117	—	2	4	no	—
655	#117	—	4	4	no	—
656	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
672	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
673	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
674	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
675	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
676	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
677	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
678	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
680	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
681	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
686	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
687	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
691	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
692	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
693	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
702	C₂×C₄²	—	2	4	no	—
703	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
704	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
705	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
706	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
707	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
708	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
709	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
710	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
711	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
712	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
713	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
714	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
715	#95	C₂³×C₈₉	1	1	yes	characteristic
716	#95	C₂³×C₈₉	1	2	yes	—
717	#95	C₂³×C₈₉	1	2	yes	—
718	#95	C₂³×C₈₉	1	2	yes	—
719	#95	C₂³×C₈₉	1	1	yes	characteristic
720	#95	C₂³×C₈₉	1	1	yes	characteristic
721	#95	C₂³×C₈₉	1	1	yes	characteristic
722	#95	C₂³×C₈₉	1	2	yes	—
723	#95	C₂³×C₈₉	1	1	yes	characteristic
724	#95	C₂³×C₈₉	1	1	yes	characteristic
725	#95	C₂³×C₈₉	1	1	yes	characteristic
726	#95	C₂³×C₈₉	1	2	yes	—
727	#95	C₂³×C₈₉	1	1	yes	characteristic
728	#95	C₂³×C₈₉	1	2	yes	—
729	#95	C₂³×C₈₉	1	2	yes	—
730	#95	C₂³×C₈₉	1	2	yes	—
731	#95	C₂³×C₈₉	1	1	yes	characteristic
732	#95	C₂³×C₈₉	1	1	yes	characteristic
733	#95	C₂³×C₈₉	1	2	yes	—
734	#95	C₂³×C₈₉	1	2	yes	—
735	#95	C₂³×C₈₉	1	2	yes	—
736	#95	C₂³×C₈₉	1	2	yes	—
737	#95	C₂³×C₈₉	1	2	yes	—
738	#95	C₂³×C₈₉	1	2	yes	—
739	#95	C₂³×C₈₉	1	2	yes	—
740	#95	C₂³×C₈₉	1	2	yes	—
741	#95	C₂³×C₈₉	1	2	yes	—
742	#95	C₂³×C₈₉	1	2	yes	—
743	#95	C₂³×C₈₉	1	2	yes	—
744	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
745	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
746	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
747	C₂×Q₈	—	2	4	no	—
748	C₂×Q₈	—	4	2	no	—
749	C₂×Q₈	—	4	2	no	—
750	C₂×D₄	—	2	4	no	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	2	4	no	—
753	C₂×D₄	—	2	4	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	4	2	no	—
758	C₂×D₄	—	4	1	no	—
759	C₂×D₄	—	4	2	no	—
760	C₂×D₄	—	4	2	no	—
761	C₂×D₄	#41×C₈₉	1	4	yes	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	4	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	2	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	—	2	2	no	—
774	C₂²×C₄	—	2	4	no	—
775	C₂²×C₄	—	2	4	no	—
776	C₂²×C₄	—	4	1	no	—
777	C₂²×C₄	—	4	2	no	—
778	C₂²×C₄	—	4	2	no	—
779	C₂²×C₄	—	4	2	no	—
780	C₂²×C₄	—	4	2	no	—
781	C₂²×C₄	—	4	2	no	—
782	C₂²×C₄	—	4	2	no	—
783	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
785	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
790	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
792	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
795	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
796	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
801	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
802	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	4	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	4	no	—
815	C₄⋊C₄	—	2	4	no	—
816	C₄⋊C₄	—	2	4	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	4	no	—
820	C₄⋊C₄	—	4	2	no	—
821	C₄⋊C₄	—	4	2	no	—
822	C₄⋊C₄	—	4	2	no	—
823	C₄⋊C₄	—	4	2	no	—
824	C₄⋊C₄	—	4	2	no	—
825	C₄⋊C₄	—	4	2	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	2	4	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	4	no	—
833	C₂²⋊C₄	—	2	4	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	4	no	—
837	C₂²⋊C₄	—	2	4	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	4	2	no	—
841	C₂²⋊C₄	—	4	2	no	—
842	C₂²⋊C₄	—	4	2	no	—
843	C₂²⋊C₄	—	4	2	no	—
844	C₂²⋊C₄	—	4	2	no	—
845	C₂²⋊C₄	—	4	2	no	—
846	C₂²⋊C₄	—	4	2	no	—
847	C₂²⋊C₄	—	4	2	no	—
848	C₂²⋊C₄	—	4	1	no	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	2	no	—
851	C₄²	—	2	2	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	2	no	—
854	C₄²	—	4	2	no	—
855	C₄²	—	4	2	no	—
856	C₄²	—	4	2	no	—
857	C₄²	—	4	2	no	—
858	C₄²	—	4	2	no	—
859	C₄²	#41×C₈₉	1	4	yes	—
860	C₄²	#41×C₈₉	1	4	yes	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	1	no	—
865	C₂³	—	2	1	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	2	2	no	—
868	C₂³	—	2	1	no	—
869	C₂³	—	2	1	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	1	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	2	1	no	—
874	C₂³	—	2	1	no	—
875	C₂³	—	2	1	no	—
876	C₂³	—	2	1	no	—
877	C₂³	—	2	1	no	—
878	C₂³	—	2	1	no	—
879	C₂³	—	2	1	no	—
880	C₂³	C₂×#41×C₈₉	1	4	yes	—
881	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
882	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
883	Q₈	—	8	4	no	—
884	D₄	—	2	8	no	—
885	D₄	—	4	4	no	—
886	D₄	—	4	8	no	—
887	D₄	—	8	4	no	—
888	C₂×C₄	—	2	8	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	4	4	no	—
941	C₂×C₄	—	4	4	no	—
942	C₂×C₄	—	4	4	no	—
943	C₂×C₄	—	8	4	no	—
944	C₂×C₄	—	8	4	no	—
945	C₂×C₄	—	8	4	no	—
946	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
947	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
948	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
949	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
950	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
951	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
952	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
953	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
954	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
955	C₂²	—	2	4	no	—
956	C₂²	—	2	2	no	—
957	C₂²	—	2	2	no	—
958	C₂²	—	2	4	no	—
959	C₂²	—	2	2	no	—
960	C₂²	—	2	4	no	—
961	C₂²	—	4	1	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	1	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	2	no	—
966	C₂²	—	4	2	no	—
967	C₂²	—	4	1	no	—
968	C₂²	—	4	1	no	—
969	C₂²	—	4	1	no	—
970	C₂²	—	4	1	no	—
971	C₂²	—	4	1	no	—
972	C₂²	—	4	1	no	—
973	C₂²	—	4	1	no	—
974	C₂²	—	4	1	no	—
975	C₂²	—	4	1	no	—
976	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
977	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
978	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
979	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
980	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
981	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
982	C₂²	#585×C₈₉	1	1	yes	characteristic
983	C₄	—	2	2	no	—
984	C₄	—	2	2	no	—
985	C₄	—	2	2	no	—
986	C₄	—	2	2	no	—
987	C₄	—	2	2	no	—
988	C₄	—	2	2	no	—
989	C₄	—	4	1	no	—
990	C₄	—	4	1	no	—
991	C₄	—	4	1	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	1	no	—
994	C₄	—	4	2	no	—
995	C₄	—	4	2	no	—
996	C₄	—	4	2	no	—
997	C₄	—	4	1	no	—
998	C₄	—	4	2	no	—
999	C₄	—	4	2	no	—
1000	C₄	—	4	2	no	—
1001	C₄	—	4	1	no	—
1002	C₄	#529×C₈₉	1	4	yes	—
1003	C₂	—	4	4	no	—
1004	C₂	—	4	2	no	—
1005	C₂	—	8	1	no	—
1006	C₂	C₂×#529×C₈₉	1	1	yes	characteristic
1007	C₂	C₈₉×#3492	1	1	yes	characteristic
1008	C₂	C₈₉×#3494	1	1	yes	characteristic
1009	C₂	C₈₉×#3495	1	1	yes	characteristic
1010	C₂	C₈₉×#3508	1	1	yes	characteristic
1011	C₂	C₈₉×#3514	1	1	yes	characteristic
1012	C₂	C₈₉×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₈₉×#2535	C₂
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×#2575	C₂	semidirect
2. C₈₉×#2570	C₂	semidirect
3. C₈₉×#2563	C₂	semidirect
4. C₈₉×#2560	C₂	semidirect
5. C₈₉×#2542	C₂	semidirect
7. C₈₉×#2517	C₂	semidirect
8. C₈₉×#2497	C₂	semidirect
9. C₈₉×#2496	C₂	semidirect
10. C₈₉×#2488	C₂	semidirect
11. C₈₉×#2477	C₂	semidirect
12. C₈₉×#2471	C₂	semidirect
13. C₈₉×#2467	C₂	semidirect
14. C₈₉×#2450	C₂	semidirect
15. C₈₉×#2422	C₂	semidirect
16. C₈₉×#2420	C₂	semidirect
17. C₈₉×#2331	C₂	semidirect
18. C₈₉×#2324	C₂	semidirect
19. C₈₉×#2314	C₂	semidirect
20. C₄×#121×C₈₉	C₂	semidirect
21. C₈₉×#2290	C₂	semidirect
22. C₈₉×#2285	C₂	semidirect
23. C₈₉×#2275	C₂	semidirect
496. #35553	C₈₉	direct (N × H)
507. #2575	C₂×C₈₉	semidirect
508. #2570	C₂×C₈₉	semidirect
509. #2563	C₂×C₈₉	semidirect
510. #2560	C₂×C₈₉	semidirect
511. #2542	C₂×C₈₉	semidirect
513. #2517	C₂×C₈₉	semidirect
514. #2497	C₂×C₈₉	semidirect
515. #2496	C₂×C₈₉	semidirect
516. #2488	C₂×C₈₉	semidirect
517. #2477	C₂×C₈₉	semidirect
518. #2471	C₂×C₈₉	semidirect
519. #2467	C₂×C₈₉	semidirect
520. #2450	C₂×C₈₉	semidirect
521. #2422	C₂×C₈₉	semidirect
522. #2420	C₂×C₈₉	semidirect
523. #2331	C₂×C₈₉	semidirect
524. #2324	C₂×C₈₉	semidirect
525. #2314	C₂×C₈₉	semidirect
526. C₄×#121	C₂×C₈₉	semidirect
527. #2290	C₂×C₈₉	semidirect
528. #2285	C₂×C₈₉	semidirect
529. #2275	C₂×C₈₉	semidirect
530. C₈₉	#35553	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#2575	2
C₈₉×#2570	2
C₈₉×#2563	2
C₈₉×#2560	2
C₈₉×#2542	2
C₈₉×#2535	2
C₈₉×#2517	2
C₈₉×#2497	2
C₈₉×#2496	2
C₈₉×#2488	2
C₈₉×#2477	2
C₈₉×#2471	2
C₈₉×#2467	2
C₈₉×#2450	2
C₈₉×#2422	2
C₈₉×#2420	2
C₈₉×#2331	2
C₈₉×#2324	2
C₈₉×#2314	2
C₄×#121×C₈₉	2
C₈₉×#2290	2
C₈₉×#2285	2
C₈₉×#2275	2
#35553	89

Subgroups — C89×#35553 #36413401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35553 #36413401