Subgroups — C₈₉×#34465 #36412313

Order 22784.

2160 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#552×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2383	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2382	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2370	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2360	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2359	C₂	1	2	yes	maximal
8	Q₈×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic
10	C₈₉×#2346	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2344	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2343	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2334	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2330	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2330	C₂	1	2	yes	maximal, complemented
16	C₈₉×#2323	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2322	C₂	1	2	yes	maximal
18	C₈₉×#2320	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2317	C₂	1	2	yes	maximal, complemented
20	C₈₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂²⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#389×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2290	C₂	1	1	yes	maximal, characteristic
24	#552×C₈₉	C₄	1	16	yes	complemented
25	C₂×#126×C₈₉	C₂²	1	2	yes	—
26	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#125×C₈₉	C₂²	1	2	yes	—
28	C₂×#123×C₈₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#117×C₈₉	C₂²	1	2	yes	—
38	C₂×#117×C₈₉	C₂²	1	2	yes	—
39	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
40	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
41	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
45	#391×C₈₉	C₂²	1	1	yes	characteristic
46	#391×C₈₉	C₂²	1	1	yes	characteristic
47	#389×C₈₉	C₂²	1	1	yes	characteristic
48	#389×C₈₉	C₂²	1	1	yes	characteristic
49	#389×C₈₉	C₂²	1	2	yes	—
50	#389×C₈₉	C₂²	1	2	yes	—
51	#389×C₈₉	C₂²	1	1	yes	characteristic
52	#389×C₈₉	C₂²	1	1	yes	characteristic
53	#389×C₈₉	C₂²	1	2	yes	—
54	#389×C₈₉	C₂²	1	2	yes	—
55	#389×C₈₉	C₂²	1	1	yes	characteristic
56	#389×C₈₉	C₂²	1	2	yes	—
57	#389×C₈₉	C₂²	1	2	yes	—
58	#389×C₈₉	C₂²	1	1	yes	characteristic
59	#389×C₈₉	C₂²	1	2	yes	—
60	#389×C₈₉	C₂²	1	2	yes	—
61	#389×C₈₉	C₂²	1	2	yes	—
62	#389×C₈₉	C₂²	1	2	yes	—
63	#389×C₈₉	C₂²	1	1	yes	characteristic
64	#389×C₈₉	C₂²	1	1	yes	characteristic
65	#389×C₈₉	C₂²	1	2	yes	—
66	#388×C₈₉	C₂²	1	2	yes	—
67	#388×C₈₉	C₂²	1	2	yes	—
68	#388×C₈₉	C₂²	1	2	yes	—
69	#388×C₈₉	C₂²	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
86	#386×C₈₉	C₂²	1	1	yes	characteristic
87	#386×C₈₉	C₂²	1	1	yes	characteristic
88	#385×C₈₉	C₂²	1	2	yes	—
89	#385×C₈₉	C₂²	1	1	yes	characteristic
90	#385×C₈₉	C₂²	1	2	yes	—
91	#385×C₈₉	C₂²	1	2	yes	—
92	#385×C₈₉	C₂²	1	2	yes	—
93	#385×C₈₉	C₂²	1	2	yes	—
94	#385×C₈₉	C₂²	1	2	yes	—
95	#385×C₈₉	C₂²	1	2	yes	—
96	#385×C₈₉	C₂²	1	1	yes	characteristic
97	#384×C₈₉	C₂²	1	2	yes	—
98	#384×C₈₉	C₂²	1	2	yes	—
99	#384×C₈₉	C₂²	1	1	yes	characteristic
100	#383×C₈₉	C₂²	1	2	yes	—
101	#382×C₈₉	C₂²	1	2	yes	—
102	#382×C₈₉	C₂²	1	2	yes	—
103	#382×C₈₉	C₂²	1	2	yes	—
104	#381×C₈₉	C₂²	1	2	yes	—
105	#380×C₈₉	C₂²	1	1	yes	characteristic
106	#380×C₈₉	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
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	2	yes	—
115	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
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	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	#376×C₈₉	C₂²	1	2	yes	—
123	C₂×#95×C₈₉	C₂²	1	2	yes	—
124	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
131	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
133	#126×C₈₉	C₂×C₄	1	16	yes	complemented
134	#125×C₈₉	C₂×C₄	1	16	yes	complemented
135	#125×C₈₉	C₂×C₄	1	8	yes	complemented
136	#123×C₈₉	C₂×C₄	1	16	yes	—
137	C₂²⋊Q₈×C₈₉	C₂×C₄	1	8	yes	complemented
138	C₂²⋊Q₈×C₈₉	C₂×C₄	1	8	yes	complemented
139	C₄×Q₈×C₈₉	—	4	2	no	—
140	C₄×Q₈×C₈₉	—	4	2	no	—
141	C₄×Q₈×C₈₉	C₂×C₄	1	8	yes	complemented
142	C₄×D₄×C₈₉	—	4	4	no	—
143	C₄×D₄×C₈₉	C₂×C₄	1	8	yes	—
144	#117×C₈₉	—	4	2	no	—
145	#117×C₈₉	—	4	4	no	—
146	#117×C₈₉	C₂×C₄	1	8	yes	complemented
147	#117×C₈₉	C₂×C₄	1	16	yes	complemented
148	C₂×C₄⋊C₄×C₈₉	—	4	2	no	—
149	C₂×C₄⋊C₄×C₈₉	—	4	2	no	—
150	C₂×C₄⋊C₄×C₈₉	—	4	4	no	—
151	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	8	yes	complemented
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	1	yes	characteristic
157	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
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	2	yes	—
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	2	yes	—
177	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
183	C₂×C₄⋊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	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₈₉	—	4	2	no	—
198	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
209	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
210	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
213	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
214	#95×C₈₉	C₂³	1	2	yes	—
215	#95×C₈₉	C₂³	1	2	yes	—
216	#95×C₈₉	C₂³	1	2	yes	—
217	#95×C₈₉	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
232	#95×C₈₉	C₂³	1	1	yes	characteristic
233	#95×C₈₉	C₂³	1	1	yes	characteristic
234	#95×C₈₉	C₂³	1	2	yes	—
235	#95×C₈₉	C₂³	1	2	yes	—
236	#95×C₈₉	C₂³	1	2	yes	—
237	#95×C₈₉	C₂³	1	2	yes	—
238	#95×C₈₉	C₂³	1	2	yes	—
239	#95×C₈₉	C₂³	1	2	yes	—
240	#95×C₈₉	C₂³	1	2	yes	—
241	#95×C₈₉	C₂³	1	2	yes	—
242	#95×C₈₉	C₂³	1	1	yes	characteristic
243	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
244	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
245	C₂×Q₈×C₈₉	—	2	2	no	—
246	C₂×Q₈×C₈₉	—	2	2	no	—
247	C₂×Q₈×C₈₉	C₂²×C₄	1	4	yes	—
248	C₂×D₄×C₈₉	—	2	2	no	—
249	C₂×D₄×C₈₉	—	2	2	no	—
250	C₂×D₄×C₈₉	C₂²×C₄	1	4	yes	—
251	C₂²×C₄×C₈₉	—	2	4	no	—
252	C₂²×C₄×C₈₉	—	2	4	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	2	no	—
258	C₂²×C₄×C₈₉	—	2	2	no	—
259	C₂²×C₄×C₈₉	—	2	4	no	—
260	C₂²×C₄×C₈₉	—	2	2	no	—
261	C₂²×C₄×C₈₉	—	4	1	no	—
262	C₂²×C₄×C₈₉	—	4	1	no	—
263	C₂²×C₄×C₈₉	—	4	1	no	—
264	C₂²×C₄×C₈₉	—	4	2	no	—
265	C₂²×C₄×C₈₉	—	4	2	no	—
266	C₂²×C₄×C₈₉	—	4	2	no	—
267	C₂²×C₄×C₈₉	—	4	2	no	—
268	C₂²×C₄×C₈₉	—	4	2	no	—
269	C₂²×C₄×C₈₉	C₂²×C₄	1	8	yes	—
270	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
271	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
272	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
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	2	yes	—
281	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
289	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
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	C₄⋊C₄×C₈₉	—	2	2	no	—
294	C₄⋊C₄×C₈₉	—	2	2	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	—	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	—	4	2	no	—
306	C₄⋊C₄×C₈₉	—	4	2	no	—
307	C₄⋊C₄×C₈₉	—	4	1	no	—
308	C₄⋊C₄×C₈₉	—	4	1	no	—
309	C₄⋊C₄×C₈₉	—	4	1	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	C₂²×C₄	1	4	yes	—
316	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
317	C₄⋊C₄×C₈₉	C₂²×C₄	1	8	yes	—
318	C₄⋊C₄×C₈₉	C₂²×C₄	1	8	yes	—
319	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
320	C₄⋊C₄×C₈₉	C₂²×C₄	1	8	yes	—
321	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
322	C₄⋊C₄×C₈₉	C₂²×C₄	1	8	yes	—
323	C₄⋊C₄×C₈₉	C₂²×C₄	1	8	yes	—
324	C₄⋊C₄×C₈₉	C₂²×C₄	1	8	yes	—
325	C₂²⋊C₄×C₈₉	—	2	2	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	—	4	1	no	—
330	C₂²⋊C₄×C₈₉	—	4	1	no	—
331	C₂²⋊C₄×C₈₉	—	4	1	no	—
332	C₂²⋊C₄×C₈₉	—	4	2	no	—
333	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
334	C₂²⋊C₄×C₈₉	C₂²×C₄	1	8	yes	—
335	C₂²⋊C₄×C₈₉	C₂²×C₄	1	8	yes	—
336	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
337	C₂²⋊C₄×C₈₉	C₂²×C₄	1	8	yes	—
338	C₄²×C₈₉	—	2	2	no	—
339	C₄²×C₈₉	—	2	2	no	—
340	C₄²×C₈₉	—	2	2	no	—
341	C₄²×C₈₉	—	2	4	no	—
342	C₄²×C₈₉	—	2	2	no	—
343	C₄²×C₈₉	—	4	1	no	—
344	C₄²×C₈₉	—	4	1	no	—
345	C₄²×C₈₉	—	4	2	no	—
346	C₄²×C₈₉	—	4	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	C₂²×C₄	1	8	yes	—
352	C₄²×C₈₉	C₂²×C₄	1	8	yes	—
353	C₄²×C₈₉	C₂²×C₄	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	1	no	—
361	C₂³×C₈₉	—	2	1	no	—
362	C₂³×C₈₉	—	2	1	no	—
363	C₂³×C₈₉	—	2	1	no	—
364	C₂³×C₈₉	C₂³×C₄	1	2	yes	—
365	C₂³×C₈₉	C₂³×C₄	1	2	yes	—
366	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
367	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
368	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
369	Q₈×C₈₉	—	2	8	no	—
370	D₄×C₈₉	—	2	8	no	—
371	C₂×C₄×C₈₉	—	2	16	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	1	no	—
376	C₂×C₄×C₈₉	—	2	2	no	—
377	C₂×C₄×C₈₉	—	2	1	no	—
378	C₂×C₄×C₈₉	—	2	2	no	—
379	C₂×C₄×C₈₉	—	2	2	no	—
380	C₂×C₄×C₈₉	—	2	1	no	—
381	C₂×C₄×C₈₉	—	2	2	no	—
382	C₂×C₄×C₈₉	—	2	2	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	2	no	—
388	C₂×C₄×C₈₉	—	2	2	no	—
389	C₂×C₄×C₈₉	—	2	1	no	—
390	C₂×C₄×C₈₉	—	2	8	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	2	no	—
398	C₂×C₄×C₈₉	—	2	1	no	—
399	C₂×C₄×C₈₉	—	2	1	no	—
400	C₂×C₄×C₈₉	—	2	2	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	2	no	—
405	C₂×C₄×C₈₉	—	2	2	no	—
406	C₂×C₄×C₈₉	—	2	1	no	—
407	C₂×C₄×C₈₉	—	2	1	no	—
408	C₂×C₄×C₈₉	—	2	1	no	—
409	C₂×C₄×C₈₉	—	2	2	no	—
410	C₂×C₄×C₈₉	—	2	1	no	—
411	C₂×C₄×C₈₉	—	2	1	no	—
412	C₂×C₄×C₈₉	—	2	1	no	—
413	C₂×C₄×C₈₉	—	2	1	no	—
414	C₂×C₄×C₈₉	—	2	1	no	—
415	C₂×C₄×C₈₉	—	2	2	no	—
416	C₂×C₄×C₈₉	—	2	1	no	—
417	C₂×C₄×C₈₉	—	2	1	no	—
418	C₂×C₄×C₈₉	—	2	1	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	1	no	—
423	C₂×C₄×C₈₉	—	2	2	no	—
424	C₂×C₄×C₈₉	—	2	2	no	—
425	C₂×C₄×C₈₉	—	4	4	no	—
426	C₂×C₄×C₈₉	—	4	4	no	—
427	C₂×C₄×C₈₉	—	8	4	no	—
428	C₂×C₄×C₈₉	—	8	4	no	—
429	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
430	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
431	C₂×C₄×C₈₉	C₂³×C₄	1	4	yes	—
432	C₂×C₄×C₈₉	C₂³×C₄	1	4	yes	—
433	C₂×C₄×C₈₉	C₂³×C₄	1	4	yes	—
434	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
435	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
436	C₂×C₄×C₈₉	C₂³×C₄	1	4	yes	—
437	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
438	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
439	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
440	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
441	C₂²×C₈₉	—	2	2	no	—
442	C₂²×C₈₉	—	2	2	no	—
443	C₂²×C₈₉	—	2	2	no	—
444	C₂²×C₈₉	—	2	2	no	—
445	C₂²×C₈₉	—	2	2	no	—
446	C₂²×C₈₉	—	2	2	no	—
447	C₂²×C₈₉	—	2	2	no	—
448	C₂²×C₈₉	—	2	2	no	—
449	C₂²×C₈₉	—	2	2	no	—
450	C₂²×C₈₉	—	4	1	no	—
451	C₂²×C₈₉	—	4	1	no	—
452	C₂²×C₈₉	—	4	1	no	—
453	C₂²×C₈₉	—	4	1	no	—
454	C₂²×C₈₉	#520	1	4	yes	—
455	C₂²×C₈₉	C₂⁴×C₄	1	1	yes	characteristic
456	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
457	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
458	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
459	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
460	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
461	C₂²×C₈₉	#585	1	1	yes	characteristic
462	C₄×C₈₉	—	2	4	no	—
463	C₄×C₈₉	—	2	4	no	—
464	C₄×C₈₉	—	2	2	no	—
465	C₄×C₈₉	—	2	2	no	—
466	C₄×C₈₉	—	2	2	no	—
467	C₄×C₈₉	—	2	4	no	—
468	C₄×C₈₉	—	2	4	no	—
469	C₄×C₈₉	—	2	2	no	—
470	C₄×C₈₉	—	2	2	no	—
471	C₄×C₈₉	—	4	1	no	—
472	C₄×C₈₉	—	4	1	no	—
473	C₄×C₈₉	—	4	1	no	—
474	C₄×C₈₉	—	4	1	no	—
475	C₄×C₈₉	—	4	1	no	—
476	C₄×C₈₉	—	4	2	no	—
477	C₄×C₈₉	—	4	2	no	—
478	C₄×C₈₉	—	4	2	no	—
479	C₄×C₈₉	—	4	2	no	—
480	C₄×C₈₉	—	4	1	no	—
481	C₄×C₈₉	—	4	1	no	—
482	C₄×C₈₉	#520	1	4	yes	—
483	#34465	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
484	C₂×C₈₉	—	2	4	no	—
485	C₂×C₈₉	—	4	2	no	—
486	C₂×C₈₉	C₂×#520	1	1	yes	characteristic
487	C₂×C₈₉	C₂×#520	1	1	yes	characteristic
488	C₂×C₈₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic
489	C₂×C₈₉	#3538	1	1	yes	characteristic
490	C₂×C₈₉	#3542	1	1	yes	characteristic
491	C₂×C₈₉	#3544	1	1	yes	characteristic
492	C₂×C₈₉	#3563	1	1	yes	characteristic
493	C₂×#552	C₂×C₈₉	1	1	yes	characteristic
494	#2383	C₂×C₈₉	1	2	yes	complemented
495	#2382	C₂×C₈₉	1	2	yes	complemented
496	#2370	C₂×C₈₉	1	1	yes	characteristic, complemented
497	#2360	C₂×C₈₉	1	1	yes	characteristic, complemented
498	#2360	C₂×C₈₉	1	1	yes	characteristic, complemented
499	#2359	C₂×C₈₉	1	2	yes	—
500	Q₈×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
501	D₄×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic
502	#2346	C₂×C₈₉	1	1	yes	characteristic, complemented
503	#2344	C₂×C₈₉	1	1	yes	characteristic, complemented
504	#2343	C₂×C₈₉	1	2	yes	complemented
505	#2334	C₂×C₈₉	1	2	yes	complemented
506	#2330	C₂×C₈₉	1	1	yes	characteristic, complemented
507	#2330	C₂×C₈₉	1	2	yes	complemented
508	#2323	C₂×C₈₉	1	1	yes	characteristic, complemented
509	#2322	C₂×C₈₉	1	2	yes	—
510	#2320	C₂×C₈₉	1	1	yes	characteristic, complemented
511	#2317	C₂×C₈₉	1	2	yes	complemented
512	#2317	C₂×C₈₉	1	1	yes	characteristic, complemented
513	C₄×C₂²⋊Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
514	C₂×#389	C₂×C₈₉	1	1	yes	characteristic, complemented
515	#2290	C₂×C₈₉	1	1	yes	characteristic
516	C₈₉	#34465	1	1	yes	characteristic, direct product factor, Sylow
517	#552	C₄×C₈₉	1	16	yes	complemented
518	C₂×#126	C₂²×C₈₉	1	2	yes	—
519	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
520	C₂×#125	C₂²×C₈₉	1	2	yes	—
521	C₂×#123	C₂²×C₈₉	1	2	yes	—
522	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
523	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
524	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
525	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
526	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
527	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
528	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
529	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
530	C₂×#117	C₂²×C₈₉	1	2	yes	—
531	C₂×#117	C₂²×C₈₉	1	2	yes	—
532	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
533	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
534	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
535	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
536	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
537	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
538	#391	C₂²×C₈₉	1	1	yes	characteristic
539	#391	C₂²×C₈₉	1	1	yes	characteristic
540	#389	C₂²×C₈₉	1	1	yes	characteristic
541	#389	C₂²×C₈₉	1	2	yes	—
542	#389	C₂²×C₈₉	1	2	yes	—
543	#389	C₂²×C₈₉	1	1	yes	characteristic
544	#389	C₂²×C₈₉	1	1	yes	characteristic
545	#389	C₂²×C₈₉	1	1	yes	characteristic
546	#389	C₂²×C₈₉	1	2	yes	—
547	#389	C₂²×C₈₉	1	2	yes	—
548	#389	C₂²×C₈₉	1	1	yes	characteristic
549	#389	C₂²×C₈₉	1	2	yes	—
550	#389	C₂²×C₈₉	1	2	yes	—
551	#389	C₂²×C₈₉	1	1	yes	characteristic
552	#389	C₂²×C₈₉	1	2	yes	—
553	#389	C₂²×C₈₉	1	2	yes	—
554	#389	C₂²×C₈₉	1	2	yes	—
555	#389	C₂²×C₈₉	1	2	yes	—
556	#389	C₂²×C₈₉	1	1	yes	characteristic
557	#389	C₂²×C₈₉	1	1	yes	characteristic
558	#389	C₂²×C₈₉	1	2	yes	—
559	#388	C₂²×C₈₉	1	2	yes	—
560	#388	C₂²×C₈₉	1	2	yes	—
561	#388	C₂²×C₈₉	1	2	yes	—
562	#388	C₂²×C₈₉	1	1	yes	characteristic
563	#388	C₂²×C₈₉	1	2	yes	—
564	#388	C₂²×C₈₉	1	1	yes	characteristic
565	#387	C₂²×C₈₉	1	2	yes	—
566	#387	C₂²×C₈₉	1	2	yes	—
567	#387	C₂²×C₈₉	1	2	yes	—
568	#387	C₂²×C₈₉	1	2	yes	—
569	#387	C₂²×C₈₉	1	1	yes	characteristic
570	#387	C₂²×C₈₉	1	2	yes	—
571	#387	C₂²×C₈₉	1	2	yes	—
572	#387	C₂²×C₈₉	1	2	yes	—
573	#387	C₂²×C₈₉	1	2	yes	—
574	#387	C₂²×C₈₉	1	2	yes	—
575	#387	C₂²×C₈₉	1	2	yes	—
576	#387	C₂²×C₈₉	1	2	yes	—
577	#387	C₂²×C₈₉	1	1	yes	characteristic
578	#387	C₂²×C₈₉	1	2	yes	—
579	#386	C₂²×C₈₉	1	1	yes	characteristic
580	#386	C₂²×C₈₉	1	1	yes	characteristic
581	#385	C₂²×C₈₉	1	1	yes	characteristic
582	#385	C₂²×C₈₉	1	2	yes	—
583	#385	C₂²×C₈₉	1	2	yes	—
584	#385	C₂²×C₈₉	1	2	yes	—
585	#385	C₂²×C₈₉	1	2	yes	—
586	#385	C₂²×C₈₉	1	2	yes	—
587	#385	C₂²×C₈₉	1	2	yes	—
588	#385	C₂²×C₈₉	1	2	yes	—
589	#385	C₂²×C₈₉	1	1	yes	characteristic
590	#384	C₂²×C₈₉	1	2	yes	—
591	#384	C₂²×C₈₉	1	2	yes	—
592	#384	C₂²×C₈₉	1	1	yes	characteristic
593	#383	C₂²×C₈₉	1	2	yes	—
594	#382	C₂²×C₈₉	1	2	yes	—
595	#382	C₂²×C₈₉	1	2	yes	—
596	#382	C₂²×C₈₉	1	2	yes	—
597	#381	C₂²×C₈₉	1	2	yes	—
598	#380	C₂²×C₈₉	1	1	yes	characteristic
599	#380	C₂²×C₈₉	1	1	yes	characteristic
600	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
601	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
602	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
603	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
604	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
605	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
606	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
607	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
608	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
609	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
610	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
611	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
612	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
613	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
614	#376	C₂²×C₈₉	1	1	yes	characteristic
615	#376	C₂²×C₈₉	1	2	yes	—
616	C₂×#95	C₂²×C₈₉	1	2	yes	—
617	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
618	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
619	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
620	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
621	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
622	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
623	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
624	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
625	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
626	#126	C₂×C₄×C₈₉	1	16	yes	complemented
627	#125	C₂×C₄×C₈₉	1	16	yes	complemented
628	#125	C₂×C₄×C₈₉	1	8	yes	complemented
629	#123	C₂×C₄×C₈₉	1	16	yes	—
630	C₂²⋊Q₈	C₂×C₄×C₈₉	1	8	yes	complemented
631	C₂²⋊Q₈	C₂×C₄×C₈₉	1	8	yes	complemented
632	C₄×Q₈	—	4	2	no	—
633	C₄×Q₈	—	4	2	no	—
634	C₄×Q₈	C₂×C₄×C₈₉	1	8	yes	complemented
635	C₄×D₄	—	4	4	no	—
636	C₄×D₄	C₂×C₄×C₈₉	1	8	yes	—
637	#117	—	4	2	no	—
638	#117	—	4	4	no	—
639	#117	C₂×C₄×C₈₉	1	8	yes	complemented
640	#117	C₂×C₄×C₈₉	1	16	yes	complemented
641	C₂×C₄⋊C₄	—	4	2	no	—
642	C₂×C₄⋊C₄	—	4	2	no	—
643	C₂×C₄⋊C₄	—	4	4	no	—
644	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	8	yes	complemented
645	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
673	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
678	C₂×C₂²⋊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	1	yes	characteristic
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	1	yes	characteristic
686	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
689	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
690	C₂×C₄²	—	4	2	no	—
691	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
693	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
696	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
697	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
698	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
699	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
700	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
701	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
702	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
703	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
704	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
705	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
706	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
707	#95	C₂³×C₈₉	1	2	yes	—
708	#95	C₂³×C₈₉	1	2	yes	—
709	#95	C₂³×C₈₉	1	2	yes	—
710	#95	C₂³×C₈₉	1	2	yes	—
711	#95	C₂³×C₈₉	1	1	yes	characteristic
712	#95	C₂³×C₈₉	1	2	yes	—
713	#95	C₂³×C₈₉	1	2	yes	—
714	#95	C₂³×C₈₉	1	1	yes	characteristic
715	#95	C₂³×C₈₉	1	1	yes	characteristic
716	#95	C₂³×C₈₉	1	1	yes	characteristic
717	#95	C₂³×C₈₉	1	1	yes	characteristic
718	#95	C₂³×C₈₉	1	1	yes	characteristic
719	#95	C₂³×C₈₉	1	2	yes	—
720	#95	C₂³×C₈₉	1	2	yes	—
721	#95	C₂³×C₈₉	1	2	yes	—
722	#95	C₂³×C₈₉	1	2	yes	—
723	#95	C₂³×C₈₉	1	2	yes	—
724	#95	C₂³×C₈₉	1	1	yes	characteristic
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	2	yes	—
729	#95	C₂³×C₈₉	1	2	yes	—
730	#95	C₂³×C₈₉	1	2	yes	—
731	#95	C₂³×C₈₉	1	2	yes	—
732	#95	C₂³×C₈₉	1	2	yes	—
733	#95	C₂³×C₈₉	1	2	yes	—
734	#95	C₂³×C₈₉	1	2	yes	—
735	#95	C₂³×C₈₉	1	1	yes	characteristic
736	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
737	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
738	C₂×Q₈	—	2	2	no	—
739	C₂×Q₈	—	2	2	no	—
740	C₂×Q₈	C₂²×C₄×C₈₉	1	4	yes	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	2	2	no	—
743	C₂×D₄	C₂²×C₄×C₈₉	1	4	yes	—
744	C₂²×C₄	—	2	4	no	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	4	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	4	1	no	—
755	C₂²×C₄	—	4	1	no	—
756	C₂²×C₄	—	4	1	no	—
757	C₂²×C₄	—	4	2	no	—
758	C₂²×C₄	—	4	2	no	—
759	C₂²×C₄	—	4	2	no	—
760	C₂²×C₄	—	4	2	no	—
761	C₂²×C₄	—	4	2	no	—
762	C₂²×C₄	C₂²×C₄×C₈₉	1	8	yes	—
763	C₂²×C₄	C₂²×C₄×C₈₉	1	4	yes	—
764	C₂²×C₄	C₂²×C₄×C₈₉	1	4	yes	—
765	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
777	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
779	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
780	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
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	1	yes	characteristic
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	4	2	no	—
792	C₄⋊C₄	—	4	2	no	—
793	C₄⋊C₄	—	4	2	no	—
794	C₄⋊C₄	—	4	2	no	—
795	C₄⋊C₄	—	4	2	no	—
796	C₄⋊C₄	—	4	2	no	—
797	C₄⋊C₄	—	4	1	no	—
798	C₄⋊C₄	—	4	1	no	—
799	C₄⋊C₄	—	4	2	no	—
800	C₄⋊C₄	—	4	2	no	—
801	C₄⋊C₄	—	4	2	no	—
802	C₄⋊C₄	—	4	2	no	—
803	C₄⋊C₄	—	4	2	no	—
804	C₄⋊C₄	—	4	2	no	—
805	C₄⋊C₄	—	4	2	no	—
806	C₄⋊C₄	—	4	2	no	—
807	C₄⋊C₄	—	4	1	no	—
808	C₄⋊C₄	C₂²×C₄×C₈₉	1	4	yes	—
809	C₄⋊C₄	C₂²×C₄×C₈₉	1	4	yes	—
810	C₄⋊C₄	C₂²×C₄×C₈₉	1	8	yes	—
811	C₄⋊C₄	C₂²×C₄×C₈₉	1	8	yes	—
812	C₄⋊C₄	C₂²×C₄×C₈₉	1	4	yes	—
813	C₄⋊C₄	C₂²×C₄×C₈₉	1	8	yes	—
814	C₄⋊C₄	C₂²×C₄×C₈₉	1	4	yes	—
815	C₄⋊C₄	C₂²×C₄×C₈₉	1	8	yes	—
816	C₄⋊C₄	C₂²×C₄×C₈₉	1	8	yes	—
817	C₄⋊C₄	C₂²×C₄×C₈₉	1	8	yes	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	4	1	no	—
823	C₂²⋊C₄	—	4	1	no	—
824	C₂²⋊C₄	—	4	2	no	—
825	C₂²⋊C₄	—	4	1	no	—
826	C₂²⋊C₄	C₂²×C₄×C₈₉	1	4	yes	—
827	C₂²⋊C₄	C₂²×C₄×C₈₉	1	8	yes	—
828	C₂²⋊C₄	C₂²×C₄×C₈₉	1	8	yes	—
829	C₂²⋊C₄	C₂²×C₄×C₈₉	1	4	yes	—
830	C₂²⋊C₄	C₂²×C₄×C₈₉	1	8	yes	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	4	no	—
835	C₄²	—	2	2	no	—
836	C₄²	—	4	1	no	—
837	C₄²	—	4	1	no	—
838	C₄²	—	4	2	no	—
839	C₄²	—	4	2	no	—
840	C₄²	—	4	2	no	—
841	C₄²	—	4	2	no	—
842	C₄²	—	4	2	no	—
843	C₄²	—	4	2	no	—
844	C₄²	C₂²×C₄×C₈₉	1	8	yes	—
845	C₄²	C₂²×C₄×C₈₉	1	8	yes	—
846	C₄²	C₂²×C₄×C₈₉	1	4	yes	—
847	C₂³	—	2	1	no	—
848	C₂³	—	2	1	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	1	no	—
854	C₂³	—	2	1	no	—
855	C₂³	—	2	1	no	—
856	C₂³	—	2	1	no	—
857	C₂³	C₂³×C₄×C₈₉	1	2	yes	—
858	C₂³	C₂³×C₄×C₈₉	1	2	yes	—
859	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
860	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
861	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
862	Q₈	—	2	8	no	—
863	D₄	—	2	8	no	—
864	C₂×C₄	—	2	16	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	8	no	—
884	C₂×C₄	—	2	8	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	2	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	2	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	4	4	no	—
919	C₂×C₄	—	4	4	no	—
920	C₂×C₄	—	8	4	no	—
921	C₂×C₄	—	8	4	no	—
922	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
923	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
924	C₂×C₄	C₂³×C₄×C₈₉	1	4	yes	—
925	C₂×C₄	C₂³×C₄×C₈₉	1	4	yes	—
926	C₂×C₄	C₂³×C₄×C₈₉	1	4	yes	—
927	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
928	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
929	C₂×C₄	C₂³×C₄×C₈₉	1	4	yes	—
930	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
931	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
932	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
933	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
934	C₂²	—	2	2	no	—
935	C₂²	—	2	2	no	—
936	C₂²	—	2	2	no	—
937	C₂²	—	2	2	no	—
938	C₂²	—	2	2	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	4	1	no	—
944	C₂²	—	4	1	no	—
945	C₂²	—	4	1	no	—
946	C₂²	—	4	1	no	—
947	C₂²	#520×C₈₉	1	4	yes	—
948	C₂²	C₂⁴×C₄×C₈₉	1	1	yes	characteristic
949	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
950	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
951	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
952	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
953	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
954	C₂²	#585×C₈₉	1	1	yes	characteristic
955	C₄	—	2	4	no	—
956	C₄	—	2	4	no	—
957	C₄	—	2	2	no	—
958	C₄	—	2	2	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	4	no	—
961	C₄	—	2	4	no	—
962	C₄	—	2	2	no	—
963	C₄	—	2	2	no	—
964	C₄	—	4	1	no	—
965	C₄	—	4	1	no	—
966	C₄	—	4	1	no	—
967	C₄	—	4	1	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	1	no	—
972	C₄	—	4	2	no	—
973	C₄	—	4	1	no	—
974	C₄	—	4	1	no	—
975	C₄	#520×C₈₉	1	4	yes	—
976	C₂	—	2	4	no	—
977	C₂	—	4	2	no	—
978	C₂	C₂×#520×C₈₉	1	1	yes	characteristic
979	C₂	C₂×#520×C₈₉	1	1	yes	characteristic
980	C₂	C₄×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
981	C₂	C₈₉×#3538	1	1	yes	characteristic
982	C₂	C₈₉×#3542	1	1	yes	characteristic
983	C₂	C₈₉×#3544	1	1	yes	characteristic
984	C₂	C₈₉×#3563	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₈₉
Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂²×D₄×C₈₉	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₉×#2383	C₂	semidirect
3. C₈₉×#2382	C₂	semidirect
4. C₈₉×#2370	C₂	semidirect
5. C₈₉×#2360	C₂	semidirect
6. C₈₉×#2360	C₂	semidirect
8. Q₈×C₄⋊C₄×C₈₉	C₂	semidirect
10. C₈₉×#2346	C₂	semidirect
11. C₈₉×#2344	C₂	semidirect
12. C₈₉×#2343	C₂	semidirect
13. C₈₉×#2334	C₂	semidirect
14. C₈₉×#2330	C₂	semidirect
15. C₈₉×#2330	C₂	semidirect
16. C₈₉×#2323	C₂	semidirect
18. C₈₉×#2320	C₂	semidirect
19. C₈₉×#2317	C₂	semidirect
20. C₈₉×#2317	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₈₉	C₂	semidirect
22. C₂×#389×C₈₉	C₂	semidirect
24. #552×C₈₉	C₄	semidirect
133. #126×C₈₉	C₂×C₄	semidirect
134. #125×C₈₉	C₂×C₄	semidirect
135. #125×C₈₉	C₂×C₄	semidirect
137. C₂²⋊Q₈×C₈₉	C₂×C₄	semidirect
138. C₂²⋊Q₈×C₈₉	C₂×C₄	semidirect
141. C₄×Q₈×C₈₉	C₂×C₄	semidirect
146. #117×C₈₉	C₂×C₄	semidirect
147. #117×C₈₉	C₂×C₄	semidirect
151. C₂×C₄⋊C₄×C₈₉	C₂×C₄	semidirect
483. #34465	C₈₉	direct (N × H)
494. #2383	C₂×C₈₉	semidirect
495. #2382	C₂×C₈₉	semidirect
496. #2370	C₂×C₈₉	semidirect
497. #2360	C₂×C₈₉	semidirect
498. #2360	C₂×C₈₉	semidirect
500. Q₈×C₄⋊C₄	C₂×C₈₉	semidirect
502. #2346	C₂×C₈₉	semidirect
503. #2344	C₂×C₈₉	semidirect
504. #2343	C₂×C₈₉	semidirect
505. #2334	C₂×C₈₉	semidirect
506. #2330	C₂×C₈₉	semidirect
507. #2330	C₂×C₈₉	semidirect
508. #2323	C₂×C₈₉	semidirect
510. #2320	C₂×C₈₉	semidirect
511. #2317	C₂×C₈₉	semidirect
512. #2317	C₂×C₈₉	semidirect
513. C₄×C₂²⋊Q₈	C₂×C₈₉	semidirect
514. C₂×#389	C₂×C₈₉	semidirect
516. C₈₉	#34465	direct (N × H)
517. #552	C₄×C₈₉	semidirect
626. #126	C₂×C₄×C₈₉	semidirect
627. #125	C₂×C₄×C₈₉	semidirect
628. #125	C₂×C₄×C₈₉	semidirect
630. C₂²⋊Q₈	C₂×C₄×C₈₉	semidirect
631. C₂²⋊Q₈	C₂×C₄×C₈₉	semidirect
634. C₄×Q₈	C₂×C₄×C₈₉	semidirect
639. #117	C₂×C₄×C₈₉	semidirect
640. #117	C₂×C₄×C₈₉	semidirect
644. C₂×C₄⋊C₄	C₂×C₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#552×C₈₉	2
C₈₉×#2383	2
C₈₉×#2382	2
C₈₉×#2370	2
C₈₉×#2360	2
C₈₉×#2359	2
Q₈×C₄⋊C₄×C₈₉	2
D₄×C₄⋊C₄×C₈₉	2
C₈₉×#2346	2
C₈₉×#2344	2
C₈₉×#2343	2
C₈₉×#2334	2
C₈₉×#2330	2
C₈₉×#2323	2
C₈₉×#2322	2
C₈₉×#2320	2
C₈₉×#2317	2
C₄×C₂²⋊Q₈×C₈₉	2
C₂×#389×C₈₉	2
C₈₉×#2290	2
#34465	89

Subgroups — C89×#34465 #36412313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#34465 #36412313