Subgroups — C₈₉×#35229 #36413077

Order 22784.

1886 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2854	C₂	1	2	yes	maximal, complemented
2	C₈₉×#2853	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2654	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2651	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2522	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2516	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2513	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2507	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2501	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2497	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2490	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2486	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#2442	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2425	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2419	C₂	1	2	yes	maximal, complemented
16	C₈₉×#2416	C₂	1	1	yes	maximal, characteristic
17	C₈₉×#2330	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#2324	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2319	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₉×#2314	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#121×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₉×#2290	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#123×C₈₉	C₂²	1	2	yes	—
26	C₂×#123×C₈₉	C₂²	1	2	yes	—
27	C₂×#123×C₈₉	C₂²	1	2	yes	—
28	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#121×C₈₉	C₂²	1	2	yes	—
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	2	yes	—
34	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
39	#400×C₈₉	C₂²	1	2	yes	—
40	#400×C₈₉	C₂²	1	2	yes	—
41	#399×C₈₉	C₂²	1	2	yes	—
42	#399×C₈₉	C₂²	1	2	yes	—
43	#398×C₈₉	C₂²	1	2	yes	—
44	#398×C₈₉	C₂²	1	2	yes	—
45	#398×C₈₉	C₂²	1	2	yes	—
46	#398×C₈₉	C₂²	1	2	yes	—
47	#397×C₈₉	C₂²	1	2	yes	—
48	#397×C₈₉	C₂²	1	2	yes	—
49	#397×C₈₉	C₂²	1	2	yes	—
50	#397×C₈₉	C₂²	1	2	yes	—
51	#396×C₈₉	C₂²	1	2	yes	—
52	#396×C₈₉	C₂²	1	2	yes	—
53	#394×C₈₉	C₂²	1	2	yes	—
54	#394×C₈₉	C₂²	1	2	yes	—
55	#390×C₈₉	C₂²	1	1	yes	characteristic
56	#390×C₈₉	C₂²	1	1	yes	characteristic
57	#390×C₈₉	C₂²	1	1	yes	characteristic
58	#390×C₈₉	C₂²	1	2	yes	—
59	#390×C₈₉	C₂²	1	1	yes	characteristic
60	#390×C₈₉	C₂²	1	2	yes	—
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	#389×C₈₉	C₂²	1	2	yes	—
66	#389×C₈₉	C₂²	1	1	yes	characteristic
67	#389×C₈₉	C₂²	1	2	yes	—
68	#389×C₈₉	C₂²	1	1	yes	characteristic
69	#389×C₈₉	C₂²	1	2	yes	—
70	#388×C₈₉	C₂²	1	2	yes	—
71	#388×C₈₉	C₂²	1	2	yes	—
72	#388×C₈₉	C₂²	1	2	yes	—
73	#388×C₈₉	C₂²	1	2	yes	—
74	#388×C₈₉	C₂²	1	2	yes	—
75	#388×C₈₉	C₂²	1	2	yes	—
76	#388×C₈₉	C₂²	1	2	yes	—
77	#388×C₈₉	C₂²	1	2	yes	—
78	#388×C₈₉	C₂²	1	2	yes	—
79	#388×C₈₉	C₂²	1	2	yes	—
80	#388×C₈₉	C₂²	1	1	yes	characteristic
81	#388×C₈₉	C₂²	1	1	yes	characteristic
82	#387×C₈₉	C₂²	1	2	yes	—
83	#387×C₈₉	C₂²	1	2	yes	—
84	#387×C₈₉	C₂²	1	2	yes	—
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	1	yes	characteristic
89	#387×C₈₉	C₂²	1	1	yes	characteristic
90	#386×C₈₉	C₂²	1	2	yes	—
91	#386×C₈₉	C₂²	1	2	yes	—
92	#386×C₈₉	C₂²	1	2	yes	—
93	#386×C₈₉	C₂²	1	1	yes	characteristic
94	#386×C₈₉	C₂²	1	1	yes	characteristic
95	#385×C₈₉	C₂²	1	2	yes	—
96	#385×C₈₉	C₂²	1	1	yes	characteristic
97	#385×C₈₉	C₂²	1	2	yes	—
98	#385×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	#381×C₈₉	C₂²	1	2	yes	—
103	#381×C₈₉	C₂²	1	2	yes	—
104	#380×C₈₉	C₂²	1	1	yes	characteristic
105	#380×C₈₉	C₂²	1	1	yes	characteristic
106	#380×C₈₉	C₂²	1	1	yes	characteristic
107	#380×C₈₉	C₂²	1	2	yes	—
108	#380×C₈₉	C₂²	1	1	yes	characteristic
109	#380×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	1	yes	characteristic
116	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
121	#376×C₈₉	C₂²	1	1	yes	characteristic
122	C₂×#95×C₈₉	C₂²	1	2	yes	—
123	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
125	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
127	C₂³×C₄×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	2	yes	—
132	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
134	#125×C₈₉	—	2	4	no	—
135	#123×C₈₉	—	4	4	no	—
136	#123×C₈₉	—	4	4	no	—
137	#123×C₈₉	—	4	4	no	—
138	#121×C₈₉	—	2	4	no	—
139	#121×C₈₉	—	2	4	no	—
140	#121×C₈₉	—	4	4	no	—
141	C₄×D₄×C₈₉	—	2	4	no	—
142	C₄×D₄×C₈₉	—	2	4	no	—
143	C₄×D₄×C₈₉	—	4	4	no	—
144	#117×C₈₉	—	2	4	no	—
145	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
146	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
147	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
160	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
178	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
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	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	2	yes	—
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×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
196	C₂×C₄²×C₈₉	—	2	4	no	—
197	C₂×C₄²×C₈₉	—	4	4	no	—
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	1	yes	characteristic
202	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
205	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
206	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
207	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
208	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
209	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
210	#95×C₈₉	C₂³	1	2	yes	—
211	#95×C₈₉	C₂³	1	2	yes	—
212	#95×C₈₉	C₂³	1	2	yes	—
213	#95×C₈₉	C₂³	1	2	yes	—
214	#95×C₈₉	C₂³	1	1	yes	characteristic
215	#95×C₈₉	C₂³	1	1	yes	characteristic
216	#95×C₈₉	C₂³	1	1	yes	characteristic
217	#95×C₈₉	C₂³	1	1	yes	characteristic
218	#95×C₈₉	C₂³	1	2	yes	—
219	#95×C₈₉	C₂³	1	1	yes	characteristic
220	#95×C₈₉	C₂³	1	1	yes	characteristic
221	#95×C₈₉	C₂³	1	2	yes	—
222	#95×C₈₉	C₂³	1	1	yes	characteristic
223	#95×C₈₉	C₂³	1	1	yes	characteristic
224	#95×C₈₉	C₂³	1	2	yes	—
225	#95×C₈₉	C₂³	1	1	yes	characteristic
226	#95×C₈₉	C₂³	1	1	yes	characteristic
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×D₄×C₈₉	—	2	2	no	—
241	C₂×D₄×C₈₉	—	2	4	no	—
242	C₂×D₄×C₈₉	—	2	4	no	—
243	C₂×D₄×C₈₉	—	2	2	no	—
244	C₂×D₄×C₈₉	—	2	4	no	—
245	C₂×D₄×C₈₉	—	2	2	no	—
246	C₂×D₄×C₈₉	—	2	2	no	—
247	C₂×D₄×C₈₉	—	2	2	no	—
248	C₂×D₄×C₈₉	—	2	2	no	—
249	C₂×D₄×C₈₉	—	2	4	no	—
250	C₂×D₄×C₈₉	—	4	2	no	—
251	C₂×D₄×C₈₉	—	4	2	no	—
252	C₂²×C₄×C₈₉	—	2	2	no	—
253	C₂²×C₄×C₈₉	—	2	2	no	—
254	C₂²×C₄×C₈₉	—	2	2	no	—
255	C₂²×C₄×C₈₉	—	2	2	no	—
256	C₂²×C₄×C₈₉	—	2	2	no	—
257	C₂²×C₄×C₈₉	—	2	4	no	—
258	C₂²×C₄×C₈₉	—	2	4	no	—
259	C₂²×C₄×C₈₉	—	2	4	no	—
260	C₂²×C₄×C₈₉	—	2	2	no	—
261	C₂²×C₄×C₈₉	—	2	4	no	—
262	C₂²×C₄×C₈₉	—	2	2	no	—
263	C₂²×C₄×C₈₉	—	2	4	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	—	4	2	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	#41	1	4	yes	—
273	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
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	1	yes	characteristic
285	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
293	C₄⋊C₄×C₈₉	—	2	4	no	—
294	C₄⋊C₄×C₈₉	—	2	4	no	—
295	C₄⋊C₄×C₈₉	—	2	2	no	—
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	4	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	—	4	2	no	—
308	C₄⋊C₄×C₈₉	—	4	1	no	—
309	C₄⋊C₄×C₈₉	—	4	2	no	—
310	C₄⋊C₄×C₈₉	—	4	2	no	—
311	C₄⋊C₄×C₈₉	—	4	2	no	—
312	C₄⋊C₄×C₈₉	—	4	2	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	#41	1	4	yes	—
319	C₂²⋊C₄×C₈₉	—	2	2	no	—
320	C₂²⋊C₄×C₈₉	—	2	4	no	—
321	C₂²⋊C₄×C₈₉	—	2	2	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	2	no	—
326	C₂²⋊C₄×C₈₉	—	2	4	no	—
327	C₂²⋊C₄×C₈₉	—	2	4	no	—
328	C₂²⋊C₄×C₈₉	—	2	4	no	—
329	C₂²⋊C₄×C₈₉	—	2	4	no	—
330	C₂²⋊C₄×C₈₉	—	2	2	no	—
331	C₂²⋊C₄×C₈₉	—	4	2	no	—
332	C₂²⋊C₄×C₈₉	—	4	1	no	—
333	C₂²⋊C₄×C₈₉	—	4	2	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	—	2	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	—	4	2	no	—
353	C₄²×C₈₉	#41	1	4	yes	—
354	C₂³×C₈₉	—	2	1	no	—
355	C₂³×C₈₉	—	2	1	no	—
356	C₂³×C₈₉	—	2	1	no	—
357	C₂³×C₈₉	—	2	1	no	—
358	C₂³×C₈₉	—	2	1	no	—
359	C₂³×C₈₉	—	2	1	no	—
360	C₂³×C₈₉	—	2	2	no	—
361	C₂³×C₈₉	—	2	2	no	—
362	C₂³×C₈₉	—	2	2	no	—
363	C₂³×C₈₉	—	2	1	no	—
364	C₂³×C₈₉	—	2	1	no	—
365	C₂³×C₈₉	—	2	2	no	—
366	C₂³×C₈₉	—	2	2	no	—
367	C₂³×C₈₉	—	2	1	no	—
368	C₂³×C₈₉	—	2	1	no	—
369	C₂³×C₈₉	—	2	2	no	—
370	C₂³×C₈₉	—	2	2	no	—
371	C₂³×C₈₉	—	2	1	no	—
372	C₂³×C₈₉	C₂×#41	1	2	yes	—
373	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
374	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
375	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
376	D₄×C₈₉	—	4	4	no	—
377	D₄×C₈₉	—	4	8	no	—
378	D₄×C₈₉	—	4	4	no	—
379	D₄×C₈₉	—	8	4	no	—
380	C₂×C₄×C₈₉	—	2	8	no	—
381	C₂×C₄×C₈₉	—	2	1	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	2	no	—
387	C₂×C₄×C₈₉	—	2	1	no	—
388	C₂×C₄×C₈₉	—	2	1	no	—
389	C₂×C₄×C₈₉	—	2	2	no	—
390	C₂×C₄×C₈₉	—	2	1	no	—
391	C₂×C₄×C₈₉	—	2	8	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	2	no	—
402	C₂×C₄×C₈₉	—	2	2	no	—
403	C₂×C₄×C₈₉	—	2	2	no	—
404	C₂×C₄×C₈₉	—	2	1	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	2	no	—
409	C₂×C₄×C₈₉	—	2	2	no	—
410	C₂×C₄×C₈₉	—	2	2	no	—
411	C₂×C₄×C₈₉	—	2	2	no	—
412	C₂×C₄×C₈₉	—	2	2	no	—
413	C₂×C₄×C₈₉	—	2	1	no	—
414	C₂×C₄×C₈₉	—	2	1	no	—
415	C₂×C₄×C₈₉	—	2	1	no	—
416	C₂×C₄×C₈₉	—	2	1	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	1	no	—
421	C₂×C₄×C₈₉	—	2	1	no	—
422	C₂×C₄×C₈₉	—	2	2	no	—
423	C₂×C₄×C₈₉	—	2	1	no	—
424	C₂×C₄×C₈₉	—	2	1	no	—
425	C₂×C₄×C₈₉	—	2	2	no	—
426	C₂×C₄×C₈₉	—	2	1	no	—
427	C₂×C₄×C₈₉	—	2	1	no	—
428	C₂×C₄×C₈₉	—	2	1	no	—
429	C₂×C₄×C₈₉	—	2	1	no	—
430	C₂×C₄×C₈₉	—	2	1	no	—
431	C₂×C₄×C₈₉	—	2	2	no	—
432	C₂×C₄×C₈₉	—	2	1	no	—
433	C₂×C₄×C₈₉	—	2	2	no	—
434	C₂×C₄×C₈₉	—	4	4	no	—
435	C₂×C₄×C₈₉	—	4	8	no	—
436	C₂×C₄×C₈₉	—	4	8	no	—
437	C₂×C₄×C₈₉	—	4	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	4	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	2₋¹⁺⁴	1	2	yes	—
447	C₂²×C₈₉	—	2	2	no	—
448	C₂²×C₈₉	—	2	2	no	—
449	C₂²×C₈₉	—	2	2	no	—
450	C₂²×C₈₉	—	2	2	no	—
451	C₂²×C₈₉	—	2	2	no	—
452	C₂²×C₈₉	—	2	2	no	—
453	C₂²×C₈₉	—	4	1	no	—
454	C₂²×C₈₉	—	4	2	no	—
455	C₂²×C₈₉	—	4	1	no	—
456	C₂²×C₈₉	—	4	2	no	—
457	C₂²×C₈₉	—	4	1	no	—
458	C₂²×C₈₉	—	4	2	no	—
459	C₂²×C₈₉	—	4	1	no	—
460	C₂²×C₈₉	—	4	2	no	—
461	C₂²×C₈₉	—	4	2	no	—
462	C₂²×C₈₉	—	4	1	no	—
463	C₂²×C₈₉	—	4	1	no	—
464	C₂²×C₈₉	—	4	2	no	—
465	C₂²×C₈₉	—	4	2	no	—
466	C₂²×C₈₉	—	4	1	no	—
467	C₂²×C₈₉	#540	1	4	yes	—
468	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
469	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
470	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
471	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
472	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
473	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
474	C₂²×C₈₉	#585	1	1	yes	characteristic
475	C₄×C₈₉	—	2	2	no	—
476	C₄×C₈₉	—	2	2	no	—
477	C₄×C₈₉	—	2	2	no	—
478	C₄×C₈₉	—	2	2	no	—
479	C₄×C₈₉	—	2	4	no	—
480	C₄×C₈₉	—	4	1	no	—
481	C₄×C₈₉	—	4	2	no	—
482	C₄×C₈₉	—	4	2	no	—
483	C₄×C₈₉	—	4	1	no	—
484	C₄×C₈₉	—	4	2	no	—
485	C₄×C₈₉	—	4	1	no	—
486	C₄×C₈₉	—	4	1	no	—
487	C₄×C₈₉	—	4	1	no	—
488	C₄×C₈₉	—	4	1	no	—
489	C₄×C₈₉	—	4	2	no	—
490	C₄×C₈₉	—	4	1	no	—
491	C₄×C₈₉	—	4	2	no	—
492	C₄×C₈₉	—	4	1	no	—
493	C₄×C₈₉	—	4	2	no	—
494	C₄×C₈₉	#529	1	4	yes	—
495	#35229	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
496	C₂×C₈₉	—	2	4	no	—
497	C₂×C₈₉	—	8	1	no	—
498	C₂×C₈₉	—	8	2	no	—
499	C₂×C₈₉	C₂×#529	1	1	yes	characteristic
500	C₂×C₈₉	C₂×#540	1	1	yes	characteristic
501	C₂×C₈₉	#3461	1	1	yes	characteristic
502	C₂×C₈₉	#3492	1	1	yes	characteristic
503	C₂×C₈₉	#3494	1	1	yes	characteristic
504	C₂×C₈₉	#3513	1	1	yes	characteristic
505	C₂×C₈₉	#3522	1	1	yes	characteristic
506	#2854	C₂×C₈₉	1	2	yes	complemented
507	#2853	C₂×C₈₉	1	2	yes	complemented
508	#2654	C₂×C₈₉	1	2	yes	complemented
509	#2651	C₂×C₈₉	1	2	yes	complemented
510	#2522	C₂×C₈₉	1	2	yes	complemented
511	#2516	C₂×C₈₉	1	2	yes	complemented
512	#2513	C₂×C₈₉	1	1	yes	characteristic, complemented
513	#2507	C₂×C₈₉	1	1	yes	characteristic, complemented
514	#2501	C₂×C₈₉	1	1	yes	characteristic, complemented
515	#2497	C₂×C₈₉	1	1	yes	characteristic, complemented
516	#2490	C₂×C₈₉	1	1	yes	characteristic, complemented
517	#2486	C₂×C₈₉	1	1	yes	characteristic, complemented
518	#2442	C₂×C₈₉	1	1	yes	characteristic, complemented
519	#2425	C₂×C₈₉	1	2	yes	complemented
520	#2419	C₂×C₈₉	1	2	yes	complemented
521	#2416	C₂×C₈₉	1	1	yes	characteristic
522	#2330	C₂×C₈₉	1	1	yes	characteristic, complemented
523	#2324	C₂×C₈₉	1	1	yes	characteristic, complemented
524	#2319	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	C₂×C₄×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
529	C₈₉	#35229	1	1	yes	characteristic, direct product factor, Sylow
530	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
531	C₂×#123	C₂²×C₈₉	1	2	yes	—
532	C₂×#123	C₂²×C₈₉	1	2	yes	—
533	C₂×#123	C₂²×C₈₉	1	2	yes	—
534	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
535	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
536	C₂×#121	C₂²×C₈₉	1	2	yes	—
537	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
538	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
539	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
540	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
541	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
542	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
543	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
544	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
545	#400	C₂²×C₈₉	1	2	yes	—
546	#400	C₂²×C₈₉	1	2	yes	—
547	#399	C₂²×C₈₉	1	2	yes	—
548	#399	C₂²×C₈₉	1	2	yes	—
549	#398	C₂²×C₈₉	1	2	yes	—
550	#398	C₂²×C₈₉	1	2	yes	—
551	#398	C₂²×C₈₉	1	2	yes	—
552	#398	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	#397	C₂²×C₈₉	1	2	yes	—
557	#396	C₂²×C₈₉	1	2	yes	—
558	#396	C₂²×C₈₉	1	2	yes	—
559	#394	C₂²×C₈₉	1	2	yes	—
560	#394	C₂²×C₈₉	1	2	yes	—
561	#390	C₂²×C₈₉	1	1	yes	characteristic
562	#390	C₂²×C₈₉	1	1	yes	characteristic
563	#390	C₂²×C₈₉	1	2	yes	—
564	#390	C₂²×C₈₉	1	1	yes	characteristic
565	#390	C₂²×C₈₉	1	2	yes	—
566	#390	C₂²×C₈₉	1	1	yes	characteristic
567	#389	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	2	yes	—
571	#389	C₂²×C₈₉	1	1	yes	characteristic
572	#389	C₂²×C₈₉	1	2	yes	—
573	#389	C₂²×C₈₉	1	1	yes	characteristic
574	#389	C₂²×C₈₉	1	2	yes	—
575	#389	C₂²×C₈₉	1	1	yes	characteristic
576	#388	C₂²×C₈₉	1	2	yes	—
577	#388	C₂²×C₈₉	1	2	yes	—
578	#388	C₂²×C₈₉	1	2	yes	—
579	#388	C₂²×C₈₉	1	2	yes	—
580	#388	C₂²×C₈₉	1	2	yes	—
581	#388	C₂²×C₈₉	1	2	yes	—
582	#388	C₂²×C₈₉	1	2	yes	—
583	#388	C₂²×C₈₉	1	2	yes	—
584	#388	C₂²×C₈₉	1	2	yes	—
585	#388	C₂²×C₈₉	1	1	yes	characteristic
586	#388	C₂²×C₈₉	1	2	yes	—
587	#388	C₂²×C₈₉	1	1	yes	characteristic
588	#387	C₂²×C₈₉	1	2	yes	—
589	#387	C₂²×C₈₉	1	2	yes	—
590	#387	C₂²×C₈₉	1	2	yes	—
591	#387	C₂²×C₈₉	1	2	yes	—
592	#387	C₂²×C₈₉	1	2	yes	—
593	#387	C₂²×C₈₉	1	2	yes	—
594	#387	C₂²×C₈₉	1	1	yes	characteristic
595	#387	C₂²×C₈₉	1	1	yes	characteristic
596	#386	C₂²×C₈₉	1	2	yes	—
597	#386	C₂²×C₈₉	1	2	yes	—
598	#386	C₂²×C₈₉	1	2	yes	—
599	#386	C₂²×C₈₉	1	1	yes	characteristic
600	#386	C₂²×C₈₉	1	1	yes	characteristic
601	#385	C₂²×C₈₉	1	2	yes	—
602	#385	C₂²×C₈₉	1	1	yes	characteristic
603	#385	C₂²×C₈₉	1	2	yes	—
604	#385	C₂²×C₈₉	1	1	yes	characteristic
605	#384	C₂²×C₈₉	1	1	yes	characteristic
606	#384	C₂²×C₈₉	1	1	yes	characteristic
607	#382	C₂²×C₈₉	1	1	yes	characteristic
608	#381	C₂²×C₈₉	1	2	yes	—
609	#381	C₂²×C₈₉	1	2	yes	—
610	#380	C₂²×C₈₉	1	1	yes	characteristic
611	#380	C₂²×C₈₉	1	1	yes	characteristic
612	#380	C₂²×C₈₉	1	2	yes	—
613	#380	C₂²×C₈₉	1	1	yes	characteristic
614	#380	C₂²×C₈₉	1	2	yes	—
615	#380	C₂²×C₈₉	1	1	yes	characteristic
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	2	yes	—
620	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
621	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
622	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
623	C₄×C₄⋊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	#376	C₂²×C₈₉	1	1	yes	characteristic
628	C₂×#95	C₂²×C₈₉	1	2	yes	—
629	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
630	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
631	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
632	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
633	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
634	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
635	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
636	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
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	#125	—	2	4	no	—
641	#123	—	4	4	no	—
642	#123	—	4	4	no	—
643	#123	—	4	4	no	—
644	#121	—	2	4	no	—
645	#121	—	2	4	no	—
646	#121	—	4	4	no	—
647	C₄×D₄	—	2	4	no	—
648	C₄×D₄	—	2	4	no	—
649	C₄×D₄	—	4	4	no	—
650	#117	—	2	4	no	—
651	C₂×C₄⋊C₄	—	2	4	no	—
652	C₂×C₄⋊C₄	—	2	4	no	—
653	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
669	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
671	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
683	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
685	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
688	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
689	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
690	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
692	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
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	1	yes	characteristic
701	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
702	C₂×C₄²	—	2	4	no	—
703	C₂×C₄²	—	4	4	no	—
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	1	yes	characteristic
709	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
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	2	yes	—
714	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
715	C₂×C₄²	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	2	yes	—
720	#95	C₂³×C₈₉	1	1	yes	characteristic
721	#95	C₂³×C₈₉	1	1	yes	characteristic
722	#95	C₂³×C₈₉	1	1	yes	characteristic
723	#95	C₂³×C₈₉	1	1	yes	characteristic
724	#95	C₂³×C₈₉	1	2	yes	—
725	#95	C₂³×C₈₉	1	1	yes	characteristic
726	#95	C₂³×C₈₉	1	1	yes	characteristic
727	#95	C₂³×C₈₉	1	2	yes	—
728	#95	C₂³×C₈₉	1	1	yes	characteristic
729	#95	C₂³×C₈₉	1	1	yes	characteristic
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	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
744	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
745	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	4	no	—
748	C₂×D₄	—	2	4	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	4	no	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	2	2	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	4	no	—
756	C₂×D₄	—	4	2	no	—
757	C₂×D₄	—	4	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	2	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	4	no	—
764	C₂²×C₄	—	2	4	no	—
765	C₂²×C₄	—	2	4	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	4	no	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	4	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	4	no	—
774	C₂²×C₄	—	4	2	no	—
775	C₂²×C₄	—	4	1	no	—
776	C₂²×C₄	—	4	2	no	—
777	C₂²×C₄	—	4	2	no	—
778	C₂²×C₄	#41×C₈₉	1	4	yes	—
779	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
780	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
781	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
786	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
792	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
797	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
799	C₄⋊C₄	—	2	4	no	—
800	C₄⋊C₄	—	2	4	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
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	4	no	—
810	C₄⋊C₄	—	2	4	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	4	2	no	—
814	C₄⋊C₄	—	4	2	no	—
815	C₄⋊C₄	—	4	2	no	—
816	C₄⋊C₄	—	4	2	no	—
817	C₄⋊C₄	—	4	2	no	—
818	C₄⋊C₄	—	4	2	no	—
819	C₄⋊C₄	—	4	2	no	—
820	C₄⋊C₄	—	4	2	no	—
821	C₄⋊C₄	—	4	2	no	—
822	C₄⋊C₄	—	4	1	no	—
823	C₄⋊C₄	—	4	2	no	—
824	C₄⋊C₄	#41×C₈₉	1	4	yes	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	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	4	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	4	no	—
837	C₂²⋊C₄	—	4	2	no	—
838	C₂²⋊C₄	—	4	2	no	—
839	C₂²⋊C₄	—	4	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	1	no	—
848	C₄²	—	2	2	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	C₂³	—	2	1	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	1	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	2	no	—
869	C₂³	—	2	1	no	—
870	C₂³	—	2	1	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	2	1	no	—
874	C₂³	—	2	1	no	—
875	C₂³	—	2	2	no	—
876	C₂³	—	2	2	no	—
877	C₂³	—	2	1	no	—
878	C₂³	C₂×#41×C₈₉	1	2	yes	—
879	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
880	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
881	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
882	D₄	—	4	4	no	—
883	D₄	—	4	8	no	—
884	D₄	—	4	4	no	—
885	D₄	—	8	4	no	—
886	C₂×C₄	—	2	8	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	8	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	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	1	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	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	2	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	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	4	4	no	—
941	C₂×C₄	—	4	8	no	—
942	C₂×C₄	—	4	8	no	—
943	C₂×C₄	—	4	4	no	—
944	C₂×C₄	—	8	4	no	—
945	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
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	4	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	2₋¹⁺⁴×C₈₉	1	2	yes	—
953	C₂²	—	2	2	no	—
954	C₂²	—	2	2	no	—
955	C₂²	—	2	2	no	—
956	C₂²	—	2	2	no	—
957	C₂²	—	2	2	no	—
958	C₂²	—	2	2	no	—
959	C₂²	—	4	1	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	1	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	1	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	1	no	—
966	C₂²	—	4	2	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	1	no	—
969	C₂²	—	4	1	no	—
970	C₂²	—	4	2	no	—
971	C₂²	—	4	2	no	—
972	C₂²	—	4	1	no	—
973	C₂²	#540×C₈₉	1	4	yes	—
974	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
975	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
976	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
977	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
978	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
979	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
980	C₂²	#585×C₈₉	1	1	yes	characteristic
981	C₄	—	2	2	no	—
982	C₄	—	2	2	no	—
983	C₄	—	2	2	no	—
984	C₄	—	2	2	no	—
985	C₄	—	2	4	no	—
986	C₄	—	4	1	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	1	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	1	no	—
992	C₄	—	4	1	no	—
993	C₄	—	4	1	no	—
994	C₄	—	4	2	no	—
995	C₄	—	4	1	no	—
996	C₄	—	4	2	no	—
997	C₄	—	4	1	no	—
998	C₄	—	4	1	no	—
999	C₄	—	4	2	no	—
1000	C₄	#529×C₈₉	1	4	yes	—
1001	C₂	—	2	4	no	—
1002	C₂	—	8	1	no	—
1003	C₂	—	8	2	no	—
1004	C₂	C₂×#529×C₈₉	1	1	yes	characteristic
1005	C₂	C₂×#540×C₈₉	1	1	yes	characteristic
1006	C₂	C₈₉×#3461	1	1	yes	characteristic
1007	C₂	C₈₉×#3492	1	1	yes	characteristic
1008	C₂	C₈₉×#3494	1	1	yes	characteristic
1009	C₂	C₈₉×#3513	1	1	yes	characteristic
1010	C₂	C₈₉×#3522	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₈₉×#2416	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×#2854	C₂	semidirect
2. C₈₉×#2853	C₂	semidirect
3. C₈₉×#2654	C₂	semidirect
4. C₈₉×#2651	C₂	semidirect
5. C₈₉×#2522	C₂	semidirect
6. C₈₉×#2516	C₂	semidirect
7. C₈₉×#2513	C₂	semidirect
8. C₈₉×#2507	C₂	semidirect
9. C₈₉×#2501	C₂	semidirect
10. C₈₉×#2497	C₂	semidirect
11. C₈₉×#2490	C₂	semidirect
12. C₈₉×#2486	C₂	semidirect
13. C₈₉×#2442	C₂	semidirect
14. C₈₉×#2425	C₂	semidirect
15. C₈₉×#2419	C₂	semidirect
17. C₈₉×#2330	C₂	semidirect
18. C₈₉×#2324	C₂	semidirect
19. C₈₉×#2319	C₂	semidirect
20. C₈₉×#2314	C₂	semidirect
21. C₄×#121×C₈₉	C₂	semidirect
22. C₈₉×#2290	C₂	semidirect
23. C₂×C₄×C₄⋊C₄×C₈₉	C₂	semidirect
495. #35229	C₈₉	direct (N × H)
506. #2854	C₂×C₈₉	semidirect
507. #2853	C₂×C₈₉	semidirect
508. #2654	C₂×C₈₉	semidirect
509. #2651	C₂×C₈₉	semidirect
510. #2522	C₂×C₈₉	semidirect
511. #2516	C₂×C₈₉	semidirect
512. #2513	C₂×C₈₉	semidirect
513. #2507	C₂×C₈₉	semidirect
514. #2501	C₂×C₈₉	semidirect
515. #2497	C₂×C₈₉	semidirect
516. #2490	C₂×C₈₉	semidirect
517. #2486	C₂×C₈₉	semidirect
518. #2442	C₂×C₈₉	semidirect
519. #2425	C₂×C₈₉	semidirect
520. #2419	C₂×C₈₉	semidirect
522. #2330	C₂×C₈₉	semidirect
523. #2324	C₂×C₈₉	semidirect
524. #2319	C₂×C₈₉	semidirect
525. #2314	C₂×C₈₉	semidirect
526. C₄×#121	C₂×C₈₉	semidirect
527. #2290	C₂×C₈₉	semidirect
528. C₂×C₄×C₄⋊C₄	C₂×C₈₉	semidirect
529. C₈₉	#35229	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×#2854	2
C₈₉×#2853	2
C₈₉×#2654	2
C₈₉×#2651	2
C₈₉×#2522	2
C₈₉×#2516	2
C₈₉×#2513	2
C₈₉×#2507	2
C₈₉×#2501	2
C₈₉×#2497	2
C₈₉×#2490	2
C₈₉×#2486	2
C₈₉×#2442	2
C₈₉×#2425	2
C₈₉×#2419	2
C₈₉×#2416	2
C₈₉×#2330	2
C₈₉×#2324	2
C₈₉×#2319	2
C₈₉×#2314	2
C₄×#121×C₈₉	2
C₈₉×#2290	2
C₂×C₄×C₄⋊C₄×C₈₉	2
#35229	89

Subgroups — C89×#35229 #36413077

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35229 #36413077