Subgroups — C₈₉×#35194 #36413042

Order 22784.

1700 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2865	C₂	1	2	yes	maximal, complemented
2	C₈₉×#2861	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2651	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2650	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2597	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2589	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2513	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2506	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2497	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2491	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#2475	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2474	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2451	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2448	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2426	C₂	1	1	yes	maximal, characteristic
16	C₈₉×#2421	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2331	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#2326	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2324	C₂	1	1	yes	maximal, characteristic
20	C₈₉×#2323	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#2298	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₉×#2293	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#125×C₈₉	C₂²	1	2	yes	—
26	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#124×C₈₉	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×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×D₄×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#117×C₈₉	C₂²	1	2	yes	—
36	#400×C₈₉	C₂²	1	2	yes	—
37	#400×C₈₉	C₂²	1	2	yes	—
38	#400×C₈₉	C₂²	1	2	yes	—
39	#399×C₈₉	C₂²	1	2	yes	—
40	#398×C₈₉	C₂²	1	2	yes	—
41	#398×C₈₉	C₂²	1	2	yes	—
42	#397×C₈₉	C₂²	1	2	yes	—
43	#397×C₈₉	C₂²	1	2	yes	—
44	#397×C₈₉	C₂²	1	2	yes	—
45	#397×C₈₉	C₂²	1	2	yes	—
46	#396×C₈₉	C₂²	1	2	yes	—
47	#396×C₈₉	C₂²	1	2	yes	—
48	#395×C₈₉	C₂²	1	2	yes	—
49	#394×C₈₉	C₂²	1	2	yes	—
50	#394×C₈₉	C₂²	1	2	yes	—
51	#393×C₈₉	C₂²	1	2	yes	—
52	#391×C₈₉	C₂²	1	1	yes	characteristic
53	#391×C₈₉	C₂²	1	1	yes	characteristic
54	#391×C₈₉	C₂²	1	2	yes	—
55	#391×C₈₉	C₂²	1	2	yes	—
56	#391×C₈₉	C₂²	1	2	yes	—
57	#390×C₈₉	C₂²	1	2	yes	—
58	#390×C₈₉	C₂²	1	1	yes	characteristic
59	#390×C₈₉	C₂²	1	1	yes	characteristic
60	#390×C₈₉	C₂²	1	2	yes	—
61	#390×C₈₉	C₂²	1	1	yes	characteristic
62	#390×C₈₉	C₂²	1	1	yes	characteristic
63	#389×C₈₉	C₂²	1	2	yes	—
64	#389×C₈₉	C₂²	1	1	yes	characteristic
65	#389×C₈₉	C₂²	1	1	yes	characteristic
66	#389×C₈₉	C₂²	1	1	yes	characteristic
67	#389×C₈₉	C₂²	1	1	yes	characteristic
68	#389×C₈₉	C₂²	1	1	yes	characteristic
69	#389×C₈₉	C₂²	1	1	yes	characteristic
70	#388×C₈₉	C₂²	1	1	yes	characteristic
71	#388×C₈₉	C₂²	1	1	yes	characteristic
72	#388×C₈₉	C₂²	1	1	yes	characteristic
73	#388×C₈₉	C₂²	1	1	yes	characteristic
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	2	yes	—
81	#388×C₈₉	C₂²	1	2	yes	—
82	#388×C₈₉	C₂²	1	2	yes	—
83	#388×C₈₉	C₂²	1	2	yes	—
84	#388×C₈₉	C₂²	1	2	yes	—
85	#388×C₈₉	C₂²	1	2	yes	—
86	#388×C₈₉	C₂²	1	2	yes	—
87	#388×C₈₉	C₂²	1	2	yes	—
88	#388×C₈₉	C₂²	1	2	yes	—
89	#387×C₈₉	C₂²	1	1	yes	characteristic
90	#387×C₈₉	C₂²	1	1	yes	characteristic
91	#387×C₈₉	C₂²	1	1	yes	characteristic
92	#387×C₈₉	C₂²	1	1	yes	characteristic
93	#387×C₈₉	C₂²	1	2	yes	—
94	#387×C₈₉	C₂²	1	2	yes	—
95	#387×C₈₉	C₂²	1	2	yes	—
96	#387×C₈₉	C₂²	1	2	yes	—
97	#387×C₈₉	C₂²	1	2	yes	—
98	#387×C₈₉	C₂²	1	2	yes	—
99	#387×C₈₉	C₂²	1	2	yes	—
100	#386×C₈₉	C₂²	1	2	yes	—
101	#385×C₈₉	C₂²	1	2	yes	—
102	#385×C₈₉	C₂²	1	2	yes	—
103	#385×C₈₉	C₂²	1	2	yes	—
104	#384×C₈₉	C₂²	1	1	yes	characteristic
105	#382×C₈₉	C₂²	1	1	yes	characteristic
106	#380×C₈₉	C₂²	1	1	yes	characteristic
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	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	2	yes	—
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×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
120	#376×C₈₉	C₂²	1	1	yes	characteristic
121	C₄³×C₈₉	C₂²	1	1	yes	characteristic
122	C₄³×C₈₉	C₂²	1	2	yes	—
123	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×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	1	yes	characteristic
128	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
129	C₄⋊Q₈×C₈₉	—	2	4	no	—
130	#125×C₈₉	—	4	4	no	—
131	#124×C₈₉	—	2	4	no	—
132	#124×C₈₉	—	4	4	no	—
133	C₂²⋊Q₈×C₈₉	—	2	4	no	—
134	#121×C₈₉	—	2	4	no	—
135	C₄×Q₈×C₈₉	—	2	4	no	—
136	C₄×Q₈×C₈₉	—	2	4	no	—
137	C₄×Q₈×C₈₉	—	2	4	no	—
138	C₄×D₄×C₈₉	—	2	4	no	—
139	#117×C₈₉	—	2	4	no	—
140	#117×C₈₉	—	4	4	no	—
141	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
154	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
167	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
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	2	yes	—
184	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
187	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
192	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
193	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
194	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
195	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
201	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
202	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
203	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
204	#95×C₈₉	C₂³	1	1	yes	characteristic
205	#95×C₈₉	C₂³	1	1	yes	characteristic
206	#95×C₈₉	C₂³	1	1	yes	characteristic
207	#95×C₈₉	C₂³	1	1	yes	characteristic
208	#95×C₈₉	C₂³	1	1	yes	characteristic
209	#95×C₈₉	C₂³	1	1	yes	characteristic
210	#95×C₈₉	C₂³	1	2	yes	—
211	#95×C₈₉	C₂³	1	1	yes	characteristic
212	#95×C₈₉	C₂³	1	1	yes	characteristic
213	#95×C₈₉	C₂³	1	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	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	1	yes	characteristic
222	#95×C₈₉	C₂³	1	2	yes	—
223	#95×C₈₉	C₂³	1	2	yes	—
224	#95×C₈₉	C₂³	1	2	yes	—
225	#95×C₈₉	C₂³	1	2	yes	—
226	#95×C₈₉	C₂³	1	2	yes	—
227	#95×C₈₉	C₂³	1	2	yes	—
228	#95×C₈₉	C₂³	1	2	yes	—
229	#95×C₈₉	C₂³	1	2	yes	—
230	#95×C₈₉	C₂³	1	2	yes	—
231	#95×C₈₉	C₂³	1	2	yes	—
232	#95×C₈₉	C₂³	1	2	yes	—
233	#95×C₈₉	C₂³	1	2	yes	—
234	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
235	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
236	C₂×Q₈×C₈₉	—	2	2	no	—
237	C₂×Q₈×C₈₉	—	2	2	no	—
238	C₂×Q₈×C₈₉	—	2	4	no	—
239	C₂×Q₈×C₈₉	—	4	2	no	—
240	C₂×Q₈×C₈₉	—	4	2	no	—
241	C₂×Q₈×C₈₉	#41	1	4	yes	—
242	C₂×D₄×C₈₉	—	2	2	no	—
243	C₂×D₄×C₈₉	—	2	2	no	—
244	C₂×D₄×C₈₉	—	2	2	no	—
245	C₂×D₄×C₈₉	—	2	4	no	—
246	C₂×D₄×C₈₉	—	4	2	no	—
247	C₂×D₄×C₈₉	—	4	2	no	—
248	C₂²×C₄×C₈₉	—	2	2	no	—
249	C₂²×C₄×C₈₉	—	2	4	no	—
250	C₂²×C₄×C₈₉	—	2	2	no	—
251	C₂²×C₄×C₈₉	—	2	2	no	—
252	C₂²×C₄×C₈₉	—	4	2	no	—
253	C₂²×C₄×C₈₉	—	4	2	no	—
254	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₈₉	C₂⁴	1	2	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	C₄⋊C₄×C₈₉	—	2	2	no	—
276	C₄⋊C₄×C₈₉	—	2	2	no	—
277	C₄⋊C₄×C₈₉	—	2	2	no	—
278	C₄⋊C₄×C₈₉	—	2	4	no	—
279	C₄⋊C₄×C₈₉	—	2	4	no	—
280	C₄⋊C₄×C₈₉	—	2	4	no	—
281	C₄⋊C₄×C₈₉	—	2	2	no	—
282	C₄⋊C₄×C₈₉	—	2	2	no	—
283	C₄⋊C₄×C₈₉	—	2	2	no	—
284	C₄⋊C₄×C₈₉	—	2	4	no	—
285	C₄⋊C₄×C₈₉	—	2	4	no	—
286	C₄⋊C₄×C₈₉	—	2	2	no	—
287	C₄⋊C₄×C₈₉	—	2	4	no	—
288	C₄⋊C₄×C₈₉	—	2	2	no	—
289	C₄⋊C₄×C₈₉	—	2	2	no	—
290	C₄⋊C₄×C₈₉	—	4	1	no	—
291	C₄⋊C₄×C₈₉	—	4	1	no	—
292	C₄⋊C₄×C₈₉	—	4	2	no	—
293	C₄⋊C₄×C₈₉	—	4	2	no	—
294	C₄⋊C₄×C₈₉	—	4	2	no	—
295	C₄⋊C₄×C₈₉	—	4	2	no	—
296	C₄⋊C₄×C₈₉	—	4	2	no	—
297	C₄⋊C₄×C₈₉	—	4	2	no	—
298	C₄⋊C₄×C₈₉	—	4	2	no	—
299	C₄⋊C₄×C₈₉	#41	1	4	yes	—
300	C₂²⋊C₄×C₈₉	—	2	2	no	—
301	C₂²⋊C₄×C₈₉	—	2	2	no	—
302	C₂²⋊C₄×C₈₉	—	2	4	no	—
303	C₂²⋊C₄×C₈₉	—	2	4	no	—
304	C₂²⋊C₄×C₈₉	—	2	4	no	—
305	C₂²⋊C₄×C₈₉	—	2	4	no	—
306	C₂²⋊C₄×C₈₉	—	2	4	no	—
307	C₂²⋊C₄×C₈₉	—	2	4	no	—
308	C₂²⋊C₄×C₈₉	—	2	2	no	—
309	C₂²⋊C₄×C₈₉	—	2	2	no	—
310	C₂²⋊C₄×C₈₉	—	2	4	no	—
311	C₂²⋊C₄×C₈₉	—	4	2	no	—
312	C₂²⋊C₄×C₈₉	—	4	2	no	—
313	C₂²⋊C₄×C₈₉	—	4	2	no	—
314	C₂²⋊C₄×C₈₉	—	4	1	no	—
315	C₂²⋊C₄×C₈₉	—	4	2	no	—
316	C₂²⋊C₄×C₈₉	—	4	2	no	—
317	C₂²⋊C₄×C₈₉	—	4	1	no	—
318	C₂²⋊C₄×C₈₉	—	4	2	no	—
319	C₂²⋊C₄×C₈₉	—	4	2	no	—
320	C₂²⋊C₄×C₈₉	—	4	2	no	—
321	C₄²×C₈₉	—	2	2	no	—
322	C₄²×C₈₉	—	2	4	no	—
323	C₄²×C₈₉	—	2	4	no	—
324	C₄²×C₈₉	—	2	2	no	—
325	C₄²×C₈₉	—	2	2	no	—
326	C₄²×C₈₉	—	2	4	no	—
327	C₄²×C₈₉	—	2	2	no	—
328	C₄²×C₈₉	—	2	2	no	—
329	C₄²×C₈₉	—	2	2	no	—
330	C₄²×C₈₉	—	2	4	no	—
331	C₄²×C₈₉	—	2	2	no	—
332	C₄²×C₈₉	—	4	1	no	—
333	C₄²×C₈₉	—	4	2	no	—
334	C₄²×C₈₉	—	4	1	no	—
335	C₄²×C₈₉	—	4	2	no	—
336	C₄²×C₈₉	—	4	2	no	—
337	C₄²×C₈₉	#41	1	4	yes	—
338	C₂³×C₈₉	—	2	1	no	—
339	C₂³×C₈₉	—	2	1	no	—
340	C₂³×C₈₉	—	2	2	no	—
341	C₂³×C₈₉	—	2	2	no	—
342	C₂³×C₈₉	—	2	2	no	—
343	C₂³×C₈₉	—	2	1	no	—
344	C₂³×C₈₉	—	2	2	no	—
345	C₂³×C₈₉	—	2	1	no	—
346	C₂³×C₈₉	—	2	1	no	—
347	C₂³×C₈₉	—	2	2	no	—
348	C₂³×C₈₉	—	2	1	no	—
349	C₂³×C₈₉	—	2	2	no	—
350	C₂³×C₈₉	—	2	2	no	—
351	C₂³×C₈₉	—	2	1	no	—
352	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
353	Q₈×C₈₉	—	2	8	no	—
354	Q₈×C₈₉	—	8	4	no	—
355	D₄×C₈₉	—	4	4	no	—
356	D₄×C₈₉	—	8	4	no	—
357	C₂×C₄×C₈₉	—	2	1	no	—
358	C₂×C₄×C₈₉	—	2	1	no	—
359	C₂×C₄×C₈₉	—	2	2	no	—
360	C₂×C₄×C₈₉	—	2	2	no	—
361	C₂×C₄×C₈₉	—	2	1	no	—
362	C₂×C₄×C₈₉	—	2	2	no	—
363	C₂×C₄×C₈₉	—	2	1	no	—
364	C₂×C₄×C₈₉	—	2	1	no	—
365	C₂×C₄×C₈₉	—	2	1	no	—
366	C₂×C₄×C₈₉	—	2	1	no	—
367	C₂×C₄×C₈₉	—	2	1	no	—
368	C₂×C₄×C₈₉	—	2	2	no	—
369	C₂×C₄×C₈₉	—	2	1	no	—
370	C₂×C₄×C₈₉	—	2	1	no	—
371	C₂×C₄×C₈₉	—	2	1	no	—
372	C₂×C₄×C₈₉	—	2	1	no	—
373	C₂×C₄×C₈₉	—	2	2	no	—
374	C₂×C₄×C₈₉	—	2	1	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	1	no	—
379	C₂×C₄×C₈₉	—	2	1	no	—
380	C₂×C₄×C₈₉	—	2	2	no	—
381	C₂×C₄×C₈₉	—	2	2	no	—
382	C₂×C₄×C₈₉	—	2	1	no	—
383	C₂×C₄×C₈₉	—	2	1	no	—
384	C₂×C₄×C₈₉	—	2	2	no	—
385	C₂×C₄×C₈₉	—	2	2	no	—
386	C₂×C₄×C₈₉	—	2	1	no	—
387	C₂×C₄×C₈₉	—	2	2	no	—
388	C₂×C₄×C₈₉	—	2	2	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	2	no	—
393	C₂×C₄×C₈₉	—	2	1	no	—
394	C₂×C₄×C₈₉	—	2	2	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	2	no	—
400	C₂×C₄×C₈₉	—	2	1	no	—
401	C₂×C₄×C₈₉	—	2	1	no	—
402	C₂×C₄×C₈₉	—	2	2	no	—
403	C₂×C₄×C₈₉	—	2	1	no	—
404	C₂×C₄×C₈₉	—	2	1	no	—
405	C₂×C₄×C₈₉	—	2	1	no	—
406	C₂×C₄×C₈₉	—	2	1	no	—
407	C₂×C₄×C₈₉	—	2	2	no	—
408	C₂×C₄×C₈₉	—	2	2	no	—
409	C₂×C₄×C₈₉	—	2	1	no	—
410	C₂×C₄×C₈₉	—	2	1	no	—
411	C₂×C₄×C₈₉	—	4	8	no	—
412	C₂×C₄×C₈₉	—	4	4	no	—
413	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
414	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
415	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
416	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
417	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
418	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
419	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
420	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
421	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
422	C₂²×C₈₉	—	4	1	no	—
423	C₂²×C₈₉	—	4	2	no	—
424	C₂²×C₈₉	—	4	2	no	—
425	C₂²×C₈₉	—	4	1	no	—
426	C₂²×C₈₉	—	4	1	no	—
427	C₂²×C₈₉	—	4	2	no	—
428	C₂²×C₈₉	—	4	1	no	—
429	C₂²×C₈₉	—	4	2	no	—
430	C₂²×C₈₉	—	4	2	no	—
431	C₂²×C₈₉	—	4	1	no	—
432	C₂²×C₈₉	—	4	1	no	—
433	C₂²×C₈₉	—	4	2	no	—
434	C₂²×C₈₉	—	4	1	no	—
435	C₂²×C₈₉	—	4	2	no	—
436	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
437	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
438	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
439	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
440	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
441	C₂²×C₈₉	#585	1	1	yes	characteristic
442	C₂²×C₈₉	#585	1	1	yes	characteristic
443	C₄×C₈₉	—	2	4	no	—
444	C₄×C₈₉	—	2	2	no	—
445	C₄×C₈₉	—	2	2	no	—
446	C₄×C₈₉	—	2	4	no	—
447	C₄×C₈₉	—	2	2	no	—
448	C₄×C₈₉	—	2	2	no	—
449	C₄×C₈₉	—	4	1	no	—
450	C₄×C₈₉	—	4	1	no	—
451	C₄×C₈₉	—	4	2	no	—
452	C₄×C₈₉	—	4	2	no	—
453	C₄×C₈₉	—	4	1	no	—
454	C₄×C₈₉	—	4	1	no	—
455	C₄×C₈₉	—	4	2	no	—
456	C₄×C₈₉	—	4	1	no	—
457	C₄×C₈₉	—	4	1	no	—
458	C₄×C₈₉	—	4	1	no	—
459	C₄×C₈₉	—	4	2	no	—
460	C₄×C₈₉	—	4	1	no	—
461	C₄×C₈₉	—	4	2	no	—
462	C₄×C₈₉	—	4	1	no	—
463	C₄×C₈₉	#529	1	4	yes	—
464	#35194	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
465	C₂×C₈₉	—	8	1	no	—
466	C₂×C₈₉	—	8	2	no	—
467	C₂×C₈₉	C₂×#529	1	1	yes	characteristic
468	C₂×C₈₉	#3460	1	1	yes	characteristic
469	C₂×C₈₉	#3461	1	1	yes	characteristic
470	C₂×C₈₉	#3514	1	1	yes	characteristic
471	C₂×C₈₉	#3516	1	1	yes	characteristic
472	C₂×C₈₉	#3522	1	1	yes	characteristic
473	C₂×C₈₉	#3524	1	1	yes	characteristic
474	#2865	C₂×C₈₉	1	2	yes	complemented
475	#2861	C₂×C₈₉	1	2	yes	complemented
476	#2651	C₂×C₈₉	1	2	yes	complemented
477	#2650	C₂×C₈₉	1	2	yes	complemented
478	#2597	C₂×C₈₉	1	2	yes	complemented
479	#2589	C₂×C₈₉	1	2	yes	complemented
480	#2513	C₂×C₈₉	1	1	yes	characteristic, complemented
481	#2506	C₂×C₈₉	1	1	yes	characteristic, complemented
482	#2497	C₂×C₈₉	1	1	yes	characteristic, complemented
483	#2491	C₂×C₈₉	1	1	yes	characteristic
484	#2475	C₂×C₈₉	1	2	yes	complemented
485	#2474	C₂×C₈₉	1	2	yes	complemented
486	#2451	C₂×C₈₉	1	1	yes	characteristic, complemented
487	#2448	C₂×C₈₉	1	1	yes	characteristic, complemented
488	#2426	C₂×C₈₉	1	1	yes	characteristic
489	#2421	C₂×C₈₉	1	1	yes	characteristic, complemented
490	#2331	C₂×C₈₉	1	1	yes	characteristic, complemented
491	#2326	C₂×C₈₉	1	1	yes	characteristic, complemented
492	#2324	C₂×C₈₉	1	1	yes	characteristic
493	#2323	C₂×C₈₉	1	1	yes	characteristic, complemented
494	#2298	C₂×C₈₉	1	1	yes	characteristic, complemented
495	#2293	C₂×C₈₉	1	1	yes	characteristic, complemented
496	C₄²×Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
497	C₈₉	#35194	1	1	yes	characteristic, direct product factor, Sylow
498	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
499	C₂×#125	C₂²×C₈₉	1	2	yes	—
500	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
501	C₂×#124	C₂²×C₈₉	1	2	yes	—
502	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
503	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
504	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
505	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
506	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
507	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
508	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
509	C₂×#117	C₂²×C₈₉	1	2	yes	—
510	#400	C₂²×C₈₉	1	2	yes	—
511	#400	C₂²×C₈₉	1	2	yes	—
512	#400	C₂²×C₈₉	1	2	yes	—
513	#399	C₂²×C₈₉	1	2	yes	—
514	#398	C₂²×C₈₉	1	2	yes	—
515	#398	C₂²×C₈₉	1	2	yes	—
516	#397	C₂²×C₈₉	1	2	yes	—
517	#397	C₂²×C₈₉	1	2	yes	—
518	#397	C₂²×C₈₉	1	2	yes	—
519	#397	C₂²×C₈₉	1	2	yes	—
520	#396	C₂²×C₈₉	1	2	yes	—
521	#396	C₂²×C₈₉	1	2	yes	—
522	#395	C₂²×C₈₉	1	2	yes	—
523	#394	C₂²×C₈₉	1	2	yes	—
524	#394	C₂²×C₈₉	1	2	yes	—
525	#393	C₂²×C₈₉	1	2	yes	—
526	#391	C₂²×C₈₉	1	1	yes	characteristic
527	#391	C₂²×C₈₉	1	1	yes	characteristic
528	#391	C₂²×C₈₉	1	2	yes	—
529	#391	C₂²×C₈₉	1	2	yes	—
530	#391	C₂²×C₈₉	1	2	yes	—
531	#390	C₂²×C₈₉	1	2	yes	—
532	#390	C₂²×C₈₉	1	1	yes	characteristic
533	#390	C₂²×C₈₉	1	1	yes	characteristic
534	#390	C₂²×C₈₉	1	2	yes	—
535	#390	C₂²×C₈₉	1	1	yes	characteristic
536	#390	C₂²×C₈₉	1	1	yes	characteristic
537	#389	C₂²×C₈₉	1	2	yes	—
538	#389	C₂²×C₈₉	1	1	yes	characteristic
539	#389	C₂²×C₈₉	1	1	yes	characteristic
540	#389	C₂²×C₈₉	1	1	yes	characteristic
541	#389	C₂²×C₈₉	1	1	yes	characteristic
542	#389	C₂²×C₈₉	1	1	yes	characteristic
543	#389	C₂²×C₈₉	1	1	yes	characteristic
544	#388	C₂²×C₈₉	1	2	yes	—
545	#388	C₂²×C₈₉	1	2	yes	—
546	#388	C₂²×C₈₉	1	2	yes	—
547	#388	C₂²×C₈₉	1	2	yes	—
548	#388	C₂²×C₈₉	1	2	yes	—
549	#388	C₂²×C₈₉	1	2	yes	—
550	#388	C₂²×C₈₉	1	2	yes	—
551	#388	C₂²×C₈₉	1	1	yes	characteristic
552	#388	C₂²×C₈₉	1	2	yes	—
553	#388	C₂²×C₈₉	1	2	yes	—
554	#388	C₂²×C₈₉	1	1	yes	characteristic
555	#388	C₂²×C₈₉	1	2	yes	—
556	#388	C₂²×C₈₉	1	2	yes	—
557	#388	C₂²×C₈₉	1	2	yes	—
558	#388	C₂²×C₈₉	1	2	yes	—
559	#388	C₂²×C₈₉	1	2	yes	—
560	#388	C₂²×C₈₉	1	2	yes	—
561	#388	C₂²×C₈₉	1	1	yes	characteristic
562	#388	C₂²×C₈₉	1	1	yes	characteristic
563	#387	C₂²×C₈₉	1	2	yes	—
564	#387	C₂²×C₈₉	1	2	yes	—
565	#387	C₂²×C₈₉	1	2	yes	—
566	#387	C₂²×C₈₉	1	1	yes	characteristic
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	1	yes	characteristic
573	#387	C₂²×C₈₉	1	1	yes	characteristic
574	#386	C₂²×C₈₉	1	2	yes	—
575	#385	C₂²×C₈₉	1	2	yes	—
576	#385	C₂²×C₈₉	1	2	yes	—
577	#385	C₂²×C₈₉	1	2	yes	—
578	#384	C₂²×C₈₉	1	1	yes	characteristic
579	#382	C₂²×C₈₉	1	1	yes	characteristic
580	#380	C₂²×C₈₉	1	1	yes	characteristic
581	#380	C₂²×C₈₉	1	1	yes	characteristic
582	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
583	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
584	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
585	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
586	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
587	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
588	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
589	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
590	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
591	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
592	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
593	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
594	#376	C₂²×C₈₉	1	1	yes	characteristic
595	C₄³	C₂²×C₈₉	1	2	yes	—
596	C₄³	C₂²×C₈₉	1	1	yes	characteristic
597	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
598	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
599	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
600	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
601	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
602	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
603	C₄⋊Q₈	—	2	4	no	—
604	#125	—	4	4	no	—
605	#124	—	2	4	no	—
606	#124	—	4	4	no	—
607	C₂²⋊Q₈	—	2	4	no	—
608	#121	—	2	4	no	—
609	C₄×Q₈	—	2	4	no	—
610	C₄×Q₈	—	2	4	no	—
611	C₄×Q₈	—	2	4	no	—
612	C₄×D₄	—	2	4	no	—
613	#117	—	2	4	no	—
614	#117	—	4	4	no	—
615	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
640	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
642	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
643	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
656	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
661	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
664	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
665	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
666	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
667	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
668	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
669	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
670	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
671	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
672	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
673	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
674	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
675	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
676	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
677	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
678	#95	C₂³×C₈₉	1	1	yes	characteristic
679	#95	C₂³×C₈₉	1	1	yes	characteristic
680	#95	C₂³×C₈₉	1	1	yes	characteristic
681	#95	C₂³×C₈₉	1	1	yes	characteristic
682	#95	C₂³×C₈₉	1	1	yes	characteristic
683	#95	C₂³×C₈₉	1	1	yes	characteristic
684	#95	C₂³×C₈₉	1	2	yes	—
685	#95	C₂³×C₈₉	1	1	yes	characteristic
686	#95	C₂³×C₈₉	1	1	yes	characteristic
687	#95	C₂³×C₈₉	1	2	yes	—
688	#95	C₂³×C₈₉	1	2	yes	—
689	#95	C₂³×C₈₉	1	2	yes	—
690	#95	C₂³×C₈₉	1	2	yes	—
691	#95	C₂³×C₈₉	1	1	yes	characteristic
692	#95	C₂³×C₈₉	1	2	yes	—
693	#95	C₂³×C₈₉	1	1	yes	characteristic
694	#95	C₂³×C₈₉	1	1	yes	characteristic
695	#95	C₂³×C₈₉	1	1	yes	characteristic
696	#95	C₂³×C₈₉	1	2	yes	—
697	#95	C₂³×C₈₉	1	2	yes	—
698	#95	C₂³×C₈₉	1	2	yes	—
699	#95	C₂³×C₈₉	1	2	yes	—
700	#95	C₂³×C₈₉	1	2	yes	—
701	#95	C₂³×C₈₉	1	2	yes	—
702	#95	C₂³×C₈₉	1	2	yes	—
703	#95	C₂³×C₈₉	1	2	yes	—
704	#95	C₂³×C₈₉	1	2	yes	—
705	#95	C₂³×C₈₉	1	2	yes	—
706	#95	C₂³×C₈₉	1	2	yes	—
707	#95	C₂³×C₈₉	1	2	yes	—
708	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
709	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
710	C₂×Q₈	—	2	2	no	—
711	C₂×Q₈	—	2	2	no	—
712	C₂×Q₈	—	2	4	no	—
713	C₂×Q₈	—	4	2	no	—
714	C₂×Q₈	—	4	2	no	—
715	C₂×Q₈	#41×C₈₉	1	4	yes	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	4	no	—
720	C₂×D₄	—	4	2	no	—
721	C₂×D₄	—	4	2	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	4	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	4	2	no	—
727	C₂²×C₄	—	4	2	no	—
728	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	4	no	—
759	C₄⋊C₄	—	2	4	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	4	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	4	2	no	—
765	C₄⋊C₄	—	4	2	no	—
766	C₄⋊C₄	—	4	2	no	—
767	C₄⋊C₄	—	4	2	no	—
768	C₄⋊C₄	—	4	2	no	—
769	C₄⋊C₄	—	4	1	no	—
770	C₄⋊C₄	—	4	1	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₄⋊C₄	#41×C₈₉	1	4	yes	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	4	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	4	2	no	—
786	C₂²⋊C₄	—	4	2	no	—
787	C₂²⋊C₄	—	4	2	no	—
788	C₂²⋊C₄	—	4	2	no	—
789	C₂²⋊C₄	—	4	2	no	—
790	C₂²⋊C₄	—	4	2	no	—
791	C₂²⋊C₄	—	4	1	no	—
792	C₂²⋊C₄	—	4	2	no	—
793	C₂²⋊C₄	—	4	2	no	—
794	C₂²⋊C₄	—	4	1	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	4	no	—
797	C₄²	—	2	4	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	2	2	no	—
800	C₄²	—	2	4	no	—
801	C₄²	—	2	2	no	—
802	C₄²	—	2	2	no	—
803	C₄²	—	2	2	no	—
804	C₄²	—	2	4	no	—
805	C₄²	—	2	2	no	—
806	C₄²	—	4	2	no	—
807	C₄²	—	4	1	no	—
808	C₄²	—	4	2	no	—
809	C₄²	—	4	1	no	—
810	C₄²	—	4	2	no	—
811	C₄²	#41×C₈₉	1	4	yes	—
812	C₂³	—	2	1	no	—
813	C₂³	—	2	1	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	1	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	1	no	—
820	C₂³	—	2	1	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	1	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	2	no	—
825	C₂³	—	2	1	no	—
826	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
827	Q₈	—	2	8	no	—
828	Q₈	—	8	4	no	—
829	D₄	—	4	4	no	—
830	D₄	—	8	4	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	4	8	no	—
886	C₂×C₄	—	4	4	no	—
887	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
888	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
889	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
890	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
891	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
892	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
893	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
894	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
895	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
896	C₂²	—	4	1	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	1	no	—
900	C₂²	—	4	1	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	1	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	1	no	—
906	C₂²	—	4	1	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	1	no	—
909	C₂²	—	4	2	no	—
910	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
911	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
912	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
913	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
914	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
915	C₂²	#585×C₈₉	1	1	yes	characteristic
916	C₂²	#585×C₈₉	1	1	yes	characteristic
917	C₄	—	2	4	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	2	4	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	4	1	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	1	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	1	no	—
928	C₄	—	4	1	no	—
929	C₄	—	4	2	no	—
930	C₄	—	4	1	no	—
931	C₄	—	4	1	no	—
932	C₄	—	4	1	no	—
933	C₄	—	4	2	no	—
934	C₄	—	4	1	no	—
935	C₄	—	4	2	no	—
936	C₄	—	4	1	no	—
937	C₄	#529×C₈₉	1	4	yes	—
938	C₂	—	8	1	no	—
939	C₂	—	8	2	no	—
940	C₂	C₂×#529×C₈₉	1	1	yes	characteristic
941	C₂	C₈₉×#3460	1	1	yes	characteristic
942	C₂	C₈₉×#3461	1	1	yes	characteristic
943	C₂	C₈₉×#3514	1	1	yes	characteristic
944	C₂	C₈₉×#3516	1	1	yes	characteristic
945	C₂	C₈₉×#3522	1	1	yes	characteristic
946	C₂	C₈₉×#3524	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂×#121×C₈₉	C₂²
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×#2865	C₂	semidirect
2. C₈₉×#2861	C₂	semidirect
3. C₈₉×#2651	C₂	semidirect
4. C₈₉×#2650	C₂	semidirect
5. C₈₉×#2597	C₂	semidirect
6. C₈₉×#2589	C₂	semidirect
7. C₈₉×#2513	C₂	semidirect
8. C₈₉×#2506	C₂	semidirect
9. C₈₉×#2497	C₂	semidirect
11. C₈₉×#2475	C₂	semidirect
12. C₈₉×#2474	C₂	semidirect
13. C₈₉×#2451	C₂	semidirect
14. C₈₉×#2448	C₂	semidirect
16. C₈₉×#2421	C₂	semidirect
17. C₈₉×#2331	C₂	semidirect
18. C₈₉×#2326	C₂	semidirect
20. C₈₉×#2323	C₂	semidirect
21. C₈₉×#2298	C₂	semidirect
22. C₈₉×#2293	C₂	semidirect
23. C₄²×Q₈×C₈₉	C₂	semidirect
464. #35194	C₈₉	direct (N × H)
474. #2865	C₂×C₈₉	semidirect
475. #2861	C₂×C₈₉	semidirect
476. #2651	C₂×C₈₉	semidirect
477. #2650	C₂×C₈₉	semidirect
478. #2597	C₂×C₈₉	semidirect
479. #2589	C₂×C₈₉	semidirect
480. #2513	C₂×C₈₉	semidirect
481. #2506	C₂×C₈₉	semidirect
482. #2497	C₂×C₈₉	semidirect
484. #2475	C₂×C₈₉	semidirect
485. #2474	C₂×C₈₉	semidirect
486. #2451	C₂×C₈₉	semidirect
487. #2448	C₂×C₈₉	semidirect
489. #2421	C₂×C₈₉	semidirect
490. #2331	C₂×C₈₉	semidirect
491. #2326	C₂×C₈₉	semidirect
493. #2323	C₂×C₈₉	semidirect
494. #2298	C₂×C₈₉	semidirect
495. #2293	C₂×C₈₉	semidirect
496. C₄²×Q₈	C₂×C₈₉	semidirect
497. C₈₉	#35194	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×#2865	2
C₈₉×#2861	2
C₈₉×#2651	2
C₈₉×#2650	2
C₈₉×#2597	2
C₈₉×#2589	2
C₈₉×#2513	2
C₈₉×#2506	2
C₈₉×#2497	2
C₈₉×#2491	2
C₈₉×#2475	2
C₈₉×#2474	2
C₈₉×#2451	2
C₈₉×#2448	2
C₈₉×#2426	2
C₈₉×#2421	2
C₈₉×#2331	2
C₈₉×#2326	2
C₈₉×#2324	2
C₈₉×#2323	2
C₈₉×#2298	2
C₈₉×#2293	2
C₄²×Q₈×C₈₉	2
#35194	89

Subgroups — C89×#35194 #36413042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35194 #36413042