Subgroups — C₈₉×#35583 #36413431

Order 22784.

1596 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2612	C₂	1	2	yes	maximal
2	C₈₉×#2606	C₂	1	2	yes	maximal
3	C₈₉×#2605	C₂	1	2	yes	maximal
4	C₈₉×#2588	C₂	1	2	yes	maximal
5	C₈₉×#2585	C₂	1	2	yes	maximal
6	C₈₉×#2581	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#2567	C₂	1	1	yes	maximal, characteristic
8	C₈₉×#2550	C₂	1	1	yes	maximal, characteristic
9	C₈₉×#2550	C₂	1	2	yes	maximal
10	C₈₉×#2546	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#2507	C₂	1	1	yes	maximal, characteristic
12	C₈₉×#2506	C₂	1	1	yes	maximal, characteristic
13	C₈₉×#2462	C₂	1	2	yes	maximal
14	C₈₉×#2453	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#2451	C₂	1	1	yes	maximal, characteristic
16	C₈₉×#2451	C₂	1	2	yes	maximal
17	C₈₉×#2331	C₂	1	1	yes	maximal, characteristic
18	C₈₉×#2330	C₂	1	1	yes	maximal, characteristic
19	C₈₉×#2320	C₂	1	1	yes	maximal, characteristic
20	C₄×C₄⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic
21	C₈₉×#2295	C₂	1	1	yes	maximal, characteristic
22	C₈₉×#2295	C₂	1	1	yes	maximal, characteristic
23	C₈₉×#2276	C₂	1	1	yes	maximal, characteristic
24	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
27	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#125×C₈₉	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×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	2	yes	—
33	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
34	#400×C₈₉	C₂²	1	2	yes	—
35	#400×C₈₉	C₂²	1	2	yes	—
36	#400×C₈₉	C₂²	1	2	yes	—
37	#398×C₈₉	C₂²	1	2	yes	—
38	#398×C₈₉	C₂²	1	2	yes	—
39	#398×C₈₉	C₂²	1	2	yes	—
40	#398×C₈₉	C₂²	1	2	yes	—
41	#398×C₈₉	C₂²	1	2	yes	—
42	#398×C₈₉	C₂²	1	2	yes	—
43	#398×C₈₉	C₂²	1	2	yes	—
44	#398×C₈₉	C₂²	1	2	yes	—
45	#395×C₈₉	C₂²	1	2	yes	—
46	#395×C₈₉	C₂²	1	2	yes	—
47	#395×C₈₉	C₂²	1	2	yes	—
48	#395×C₈₉	C₂²	1	2	yes	—
49	#395×C₈₉	C₂²	1	2	yes	—
50	#391×C₈₉	C₂²	1	1	yes	characteristic
51	#391×C₈₉	C₂²	1	2	yes	—
52	#391×C₈₉	C₂²	1	2	yes	—
53	#391×C₈₉	C₂²	1	1	yes	characteristic
54	#391×C₈₉	C₂²	1	1	yes	characteristic
55	#391×C₈₉	C₂²	1	1	yes	characteristic
56	#391×C₈₉	C₂²	1	2	yes	—
57	#391×C₈₉	C₂²	1	1	yes	characteristic
58	#391×C₈₉	C₂²	1	1	yes	characteristic
59	#391×C₈₉	C₂²	1	2	yes	—
60	#391×C₈₉	C₂²	1	2	yes	—
61	#391×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	2	yes	—
65	#389×C₈₉	C₂²	1	1	yes	characteristic
66	#389×C₈₉	C₂²	1	2	yes	—
67	#389×C₈₉	C₂²	1	2	yes	—
68	#389×C₈₉	C₂²	1	1	yes	characteristic
69	#389×C₈₉	C₂²	1	1	yes	characteristic
70	#389×C₈₉	C₂²	1	1	yes	characteristic
71	#389×C₈₉	C₂²	1	1	yes	characteristic
72	#389×C₈₉	C₂²	1	1	yes	characteristic
73	#389×C₈₉	C₂²	1	2	yes	—
74	#389×C₈₉	C₂²	1	2	yes	—
75	#389×C₈₉	C₂²	1	1	yes	characteristic
76	#389×C₈₉	C₂²	1	1	yes	characteristic
77	#389×C₈₉	C₂²	1	2	yes	—
78	#389×C₈₉	C₂²	1	1	yes	characteristic
79	#389×C₈₉	C₂²	1	1	yes	characteristic
80	#389×C₈₉	C₂²	1	1	yes	characteristic
81	#389×C₈₉	C₂²	1	2	yes	—
82	#387×C₈₉	C₂²	1	1	yes	characteristic
83	#387×C₈₉	C₂²	1	2	yes	—
84	#387×C₈₉	C₂²	1	1	yes	characteristic
85	#387×C₈₉	C₂²	1	1	yes	characteristic
86	#387×C₈₉	C₂²	1	1	yes	characteristic
87	#387×C₈₉	C₂²	1	2	yes	—
88	#387×C₈₉	C₂²	1	2	yes	—
89	#387×C₈₉	C₂²	1	2	yes	—
90	#387×C₈₉	C₂²	1	2	yes	—
91	#387×C₈₉	C₂²	1	2	yes	—
92	#387×C₈₉	C₂²	1	2	yes	—
93	#387×C₈₉	C₂²	1	2	yes	—
94	#387×C₈₉	C₂²	1	2	yes	—
95	#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	#384×C₈₉	C₂²	1	1	yes	characteristic
101	#384×C₈₉	C₂²	1	1	yes	characteristic
102	#383×C₈₉	C₂²	1	2	yes	—
103	#382×C₈₉	C₂²	1	2	yes	—
104	#382×C₈₉	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
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	1	yes	characteristic
115	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
117	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
118	#376×C₈₉	C₂²	1	1	yes	characteristic
119	#376×C₈₉	C₂²	1	1	yes	characteristic
120	#376×C₈₉	C₂²	1	2	yes	—
121	#376×C₈₉	C₂²	1	2	yes	—
122	C₄³×C₈₉	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
124	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
127	C₄⋊Q₈×C₈₉	—	2	4	no	—
128	C₄⋊Q₈×C₈₉	—	2	4	no	—
129	C₄⋊Q₈×C₈₉	—	4	4	no	—
130	#125×C₈₉	—	2	4	no	—
131	#125×C₈₉	—	4	4	no	—
132	C₄×Q₈×C₈₉	—	2	4	no	—
133	C₄×Q₈×C₈₉	—	2	4	no	—
134	C₄×Q₈×C₈₉	—	2	4	no	—
135	C₄×Q₈×C₈₉	—	4	4	no	—
136	C₄×Q₈×C₈₉	Q₈	1	8	yes	complemented
137	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
144	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₈₉	C₂³	1	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×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
182	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
183	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
186	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
187	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
188	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
189	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
190	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
192	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
193	#95×C₈₉	C₂³	1	1	yes	characteristic
194	#95×C₈₉	C₂³	1	1	yes	characteristic
195	#95×C₈₉	C₂³	1	2	yes	—
196	#95×C₈₉	C₂³	1	1	yes	characteristic
197	#95×C₈₉	C₂³	1	1	yes	characteristic
198	#95×C₈₉	C₂³	1	2	yes	—
199	#95×C₈₉	C₂³	1	2	yes	—
200	#95×C₈₉	C₂³	1	1	yes	characteristic
201	#95×C₈₉	C₂³	1	1	yes	characteristic
202	#95×C₈₉	C₂³	1	1	yes	characteristic
203	#95×C₈₉	C₂³	1	1	yes	characteristic
204	#95×C₈₉	C₂³	1	2	yes	—
205	#95×C₈₉	C₂³	1	2	yes	—
206	#95×C₈₉	C₂³	1	2	yes	—
207	#95×C₈₉	C₂³	1	2	yes	—
208	#95×C₈₉	C₂³	1	2	yes	—
209	#95×C₈₉	C₂³	1	2	yes	—
210	#95×C₈₉	C₂³	1	1	yes	characteristic
211	#95×C₈₉	C₂³	1	1	yes	characteristic
212	#95×C₈₉	C₂³	1	2	yes	—
213	#95×C₈₉	C₂³	1	2	yes	—
214	#95×C₈₉	C₂³	1	2	yes	—
215	#95×C₈₉	C₂³	1	1	yes	characteristic
216	#95×C₈₉	C₂³	1	1	yes	characteristic
217	#95×C₈₉	C₂³	1	2	yes	—
218	#95×C₈₉	C₂³	1	1	yes	characteristic
219	#95×C₈₉	C₂³	1	1	yes	characteristic
220	#95×C₈₉	C₂³	1	2	yes	—
221	#95×C₈₉	C₂³	1	2	yes	—
222	#95×C₈₉	C₂³	1	2	yes	—
223	#95×C₈₉	C₂³	1	2	yes	—
224	#95×C₈₉	C₂³	1	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	C₂×Q₈×C₈₉	—	2	2	no	—
233	C₂×Q₈×C₈₉	—	2	2	no	—
234	C₂×Q₈×C₈₉	—	2	2	no	—
235	C₂×Q₈×C₈₉	—	2	4	no	—
236	C₂×Q₈×C₈₉	—	2	4	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	1	no	—
241	C₂×Q₈×C₈₉	—	4	2	no	—
242	C₂×Q₈×C₈₉	—	4	2	no	—
243	C₂×Q₈×C₈₉	C₂×Q₈	1	4	yes	—
244	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
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	1	yes	characteristic
264	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
267	C₄⋊C₄×C₈₉	—	2	2	no	—
268	C₄⋊C₄×C₈₉	—	2	4	no	—
269	C₄⋊C₄×C₈₉	—	2	4	no	—
270	C₄⋊C₄×C₈₉	—	2	2	no	—
271	C₄⋊C₄×C₈₉	—	2	2	no	—
272	C₄⋊C₄×C₈₉	—	2	2	no	—
273	C₄⋊C₄×C₈₉	—	2	4	no	—
274	C₄⋊C₄×C₈₉	—	2	4	no	—
275	C₄⋊C₄×C₈₉	—	2	2	no	—
276	C₄⋊C₄×C₈₉	—	2	4	no	—
277	C₄⋊C₄×C₈₉	—	2	4	no	—
278	C₄⋊C₄×C₈₉	—	2	2	no	—
279	C₄⋊C₄×C₈₉	—	2	2	no	—
280	C₄⋊C₄×C₈₉	—	2	2	no	—
281	C₄⋊C₄×C₈₉	—	2	4	no	—
282	C₄⋊C₄×C₈₉	—	2	4	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	2	no	—
288	C₄⋊C₄×C₈₉	—	2	2	no	—
289	C₄⋊C₄×C₈₉	—	2	2	no	—
290	C₄⋊C₄×C₈₉	—	4	2	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	—	4	2	no	—
300	C₄⋊C₄×C₈₉	—	4	2	no	—
301	C₄⋊C₄×C₈₉	C₂×Q₈	1	8	yes	—
302	C₄⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
303	C₄⋊C₄×C₈₉	#41	1	4	yes	—
304	C₄²×C₈₉	—	2	4	no	—
305	C₄²×C₈₉	—	2	4	no	—
306	C₄²×C₈₉	—	2	2	no	—
307	C₄²×C₈₉	—	2	2	no	—
308	C₄²×C₈₉	—	2	2	no	—
309	C₄²×C₈₉	—	2	2	no	—
310	C₄²×C₈₉	—	2	2	no	—
311	C₄²×C₈₉	—	2	2	no	—
312	C₄²×C₈₉	—	2	2	no	—
313	C₄²×C₈₉	—	2	2	no	—
314	C₄²×C₈₉	—	4	1	no	—
315	C₄²×C₈₉	—	4	2	no	—
316	C₄²×C₈₉	—	4	2	no	—
317	C₄²×C₈₉	—	4	2	no	—
318	C₄²×C₈₉	—	4	2	no	—
319	C₄²×C₈₉	—	4	2	no	—
320	C₄²×C₈₉	C₂×Q₈	1	8	yes	—
321	C₄²×C₈₉	C₂×Q₈	1	4	yes	—
322	C₄²×C₈₉	#41	1	4	yes	—
323	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
324	Q₈×C₈₉	—	2	8	no	—
325	Q₈×C₈₉	—	4	4	no	—
326	Q₈×C₈₉	—	4	8	no	—
327	Q₈×C₈₉	—	8	4	no	—
328	C₂×C₄×C₈₉	—	2	1	no	—
329	C₂×C₄×C₈₉	—	2	2	no	—
330	C₂×C₄×C₈₉	—	2	2	no	—
331	C₂×C₄×C₈₉	—	2	1	no	—
332	C₂×C₄×C₈₉	—	2	1	no	—
333	C₂×C₄×C₈₉	—	2	1	no	—
334	C₂×C₄×C₈₉	—	2	1	no	—
335	C₂×C₄×C₈₉	—	2	2	no	—
336	C₂×C₄×C₈₉	—	2	2	no	—
337	C₂×C₄×C₈₉	—	2	1	no	—
338	C₂×C₄×C₈₉	—	2	1	no	—
339	C₂×C₄×C₈₉	—	2	1	no	—
340	C₂×C₄×C₈₉	—	2	2	no	—
341	C₂×C₄×C₈₉	—	2	1	no	—
342	C₂×C₄×C₈₉	—	2	1	no	—
343	C₂×C₄×C₈₉	—	2	2	no	—
344	C₂×C₄×C₈₉	—	2	1	no	—
345	C₂×C₄×C₈₉	—	2	1	no	—
346	C₂×C₄×C₈₉	—	2	1	no	—
347	C₂×C₄×C₈₉	—	2	1	no	—
348	C₂×C₄×C₈₉	—	2	1	no	—
349	C₂×C₄×C₈₉	—	2	2	no	—
350	C₂×C₄×C₈₉	—	2	1	no	—
351	C₂×C₄×C₈₉	—	2	1	no	—
352	C₂×C₄×C₈₉	—	2	1	no	—
353	C₂×C₄×C₈₉	—	2	1	no	—
354	C₂×C₄×C₈₉	—	2	1	no	—
355	C₂×C₄×C₈₉	—	2	1	no	—
356	C₂×C₄×C₈₉	—	2	2	no	—
357	C₂×C₄×C₈₉	—	2	2	no	—
358	C₂×C₄×C₈₉	—	2	2	no	—
359	C₂×C₄×C₈₉	—	2	2	no	—
360	C₂×C₄×C₈₉	—	2	2	no	—
361	C₂×C₄×C₈₉	—	2	1	no	—
362	C₂×C₄×C₈₉	—	2	2	no	—
363	C₂×C₄×C₈₉	—	2	2	no	—
364	C₂×C₄×C₈₉	—	2	1	no	—
365	C₂×C₄×C₈₉	—	2	2	no	—
366	C₂×C₄×C₈₉	—	2	1	no	—
367	C₂×C₄×C₈₉	—	2	1	no	—
368	C₂×C₄×C₈₉	—	2	1	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	2	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	1	no	—
382	C₂×C₄×C₈₉	—	2	1	no	—
383	C₂×C₄×C₈₉	—	2	2	no	—
384	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
385	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
386	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
387	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
388	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
389	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
390	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
391	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
392	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
393	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
394	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
395	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
396	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
397	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
398	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
399	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
400	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
401	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
402	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
403	C₂²×C₈₉	#585	1	1	yes	characteristic
404	C₄×C₈₉	—	2	4	no	—
405	C₄×C₈₉	—	2	2	no	—
406	C₄×C₈₉	—	2	2	no	—
407	C₄×C₈₉	—	2	2	no	—
408	C₄×C₈₉	—	2	2	no	—
409	C₄×C₈₉	—	2	4	no	—
410	C₄×C₈₉	—	2	2	no	—
411	C₄×C₈₉	—	2	2	no	—
412	C₄×C₈₉	—	2	4	no	—
413	C₄×C₈₉	—	2	2	no	—
414	C₄×C₈₉	—	4	2	no	—
415	C₄×C₈₉	—	4	1	no	—
416	C₄×C₈₉	—	4	2	no	—
417	C₄×C₈₉	—	4	2	no	—
418	C₄×C₈₉	—	4	1	no	—
419	C₄×C₈₉	—	4	1	no	—
420	C₄×C₈₉	—	4	1	no	—
421	C₄×C₈₉	—	4	1	no	—
422	C₄×C₈₉	—	4	2	no	—
423	C₄×C₈₉	—	4	1	no	—
424	C₄×C₈₉	—	4	1	no	—
425	C₄×C₈₉	—	4	2	no	—
426	C₄×C₈₉	#533	1	4	yes	—
427	#35583	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
428	C₂×C₈₉	C₂×#533	1	1	yes	characteristic
429	C₂×C₈₉	#3494	1	1	yes	characteristic
430	C₂×C₈₉	#3502	1	1	yes	characteristic
431	C₂×C₈₉	#3503	1	1	yes	characteristic
432	C₂×C₈₉	#3509	1	1	yes	characteristic
433	C₂×C₈₉	#3516	1	1	yes	characteristic
434	C₂×C₈₉	#3520	1	1	yes	characteristic
435	#2612	C₂×C₈₉	1	2	yes	—
436	#2606	C₂×C₈₉	1	2	yes	—
437	#2605	C₂×C₈₉	1	2	yes	—
438	#2588	C₂×C₈₉	1	2	yes	—
439	#2585	C₂×C₈₉	1	2	yes	—
440	#2581	C₂×C₈₉	1	1	yes	characteristic
441	#2567	C₂×C₈₉	1	1	yes	characteristic
442	#2550	C₂×C₈₉	1	1	yes	characteristic
443	#2550	C₂×C₈₉	1	2	yes	—
444	#2546	C₂×C₈₉	1	1	yes	characteristic
445	#2507	C₂×C₈₉	1	1	yes	characteristic
446	#2506	C₂×C₈₉	1	1	yes	characteristic
447	#2462	C₂×C₈₉	1	2	yes	—
448	#2453	C₂×C₈₉	1	1	yes	characteristic
449	#2451	C₂×C₈₉	1	1	yes	characteristic
450	#2451	C₂×C₈₉	1	2	yes	—
451	#2331	C₂×C₈₉	1	1	yes	characteristic
452	#2330	C₂×C₈₉	1	1	yes	characteristic
453	#2320	C₂×C₈₉	1	1	yes	characteristic
454	C₄×C₄⋊Q₈	C₂×C₈₉	1	1	yes	characteristic
455	#2295	C₂×C₈₉	1	1	yes	characteristic
456	#2295	C₂×C₈₉	1	1	yes	characteristic
457	#2276	C₂×C₈₉	1	1	yes	characteristic
458	C₈₉	#35583	1	1	yes	characteristic, direct product factor, Sylow
459	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
460	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
461	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
462	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
463	C₂×#125	C₂²×C₈₉	1	2	yes	—
464	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
465	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
466	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
467	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
468	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
469	#400	C₂²×C₈₉	1	2	yes	—
470	#400	C₂²×C₈₉	1	2	yes	—
471	#400	C₂²×C₈₉	1	2	yes	—
472	#398	C₂²×C₈₉	1	2	yes	—
473	#398	C₂²×C₈₉	1	2	yes	—
474	#398	C₂²×C₈₉	1	2	yes	—
475	#398	C₂²×C₈₉	1	2	yes	—
476	#398	C₂²×C₈₉	1	2	yes	—
477	#398	C₂²×C₈₉	1	2	yes	—
478	#398	C₂²×C₈₉	1	2	yes	—
479	#398	C₂²×C₈₉	1	2	yes	—
480	#395	C₂²×C₈₉	1	2	yes	—
481	#395	C₂²×C₈₉	1	2	yes	—
482	#395	C₂²×C₈₉	1	2	yes	—
483	#395	C₂²×C₈₉	1	2	yes	—
484	#395	C₂²×C₈₉	1	2	yes	—
485	#391	C₂²×C₈₉	1	2	yes	—
486	#391	C₂²×C₈₉	1	1	yes	characteristic
487	#391	C₂²×C₈₉	1	1	yes	characteristic
488	#391	C₂²×C₈₉	1	1	yes	characteristic
489	#391	C₂²×C₈₉	1	1	yes	characteristic
490	#391	C₂²×C₈₉	1	2	yes	—
491	#391	C₂²×C₈₉	1	2	yes	—
492	#391	C₂²×C₈₉	1	2	yes	—
493	#391	C₂²×C₈₉	1	2	yes	—
494	#391	C₂²×C₈₉	1	2	yes	—
495	#391	C₂²×C₈₉	1	1	yes	characteristic
496	#391	C₂²×C₈₉	1	1	yes	characteristic
497	#389	C₂²×C₈₉	1	1	yes	characteristic
498	#389	C₂²×C₈₉	1	2	yes	—
499	#389	C₂²×C₈₉	1	1	yes	characteristic
500	#389	C₂²×C₈₉	1	2	yes	—
501	#389	C₂²×C₈₉	1	2	yes	—
502	#389	C₂²×C₈₉	1	1	yes	characteristic
503	#389	C₂²×C₈₉	1	1	yes	characteristic
504	#389	C₂²×C₈₉	1	1	yes	characteristic
505	#389	C₂²×C₈₉	1	2	yes	—
506	#389	C₂²×C₈₉	1	2	yes	—
507	#389	C₂²×C₈₉	1	2	yes	—
508	#389	C₂²×C₈₉	1	1	yes	characteristic
509	#389	C₂²×C₈₉	1	1	yes	characteristic
510	#389	C₂²×C₈₉	1	1	yes	characteristic
511	#389	C₂²×C₈₉	1	2	yes	—
512	#389	C₂²×C₈₉	1	1	yes	characteristic
513	#389	C₂²×C₈₉	1	2	yes	—
514	#389	C₂²×C₈₉	1	1	yes	characteristic
515	#389	C₂²×C₈₉	1	1	yes	characteristic
516	#389	C₂²×C₈₉	1	1	yes	characteristic
517	#387	C₂²×C₈₉	1	2	yes	—
518	#387	C₂²×C₈₉	1	2	yes	—
519	#387	C₂²×C₈₉	1	2	yes	—
520	#387	C₂²×C₈₉	1	2	yes	—
521	#387	C₂²×C₈₉	1	1	yes	characteristic
522	#387	C₂²×C₈₉	1	2	yes	—
523	#387	C₂²×C₈₉	1	2	yes	—
524	#387	C₂²×C₈₉	1	2	yes	—
525	#387	C₂²×C₈₉	1	2	yes	—
526	#387	C₂²×C₈₉	1	2	yes	—
527	#387	C₂²×C₈₉	1	2	yes	—
528	#387	C₂²×C₈₉	1	1	yes	characteristic
529	#387	C₂²×C₈₉	1	2	yes	—
530	#387	C₂²×C₈₉	1	2	yes	—
531	#387	C₂²×C₈₉	1	1	yes	characteristic
532	#387	C₂²×C₈₉	1	2	yes	—
533	#387	C₂²×C₈₉	1	1	yes	characteristic
534	#387	C₂²×C₈₉	1	2	yes	—
535	#384	C₂²×C₈₉	1	1	yes	characteristic
536	#384	C₂²×C₈₉	1	1	yes	characteristic
537	#383	C₂²×C₈₉	1	2	yes	—
538	#382	C₂²×C₈₉	1	2	yes	—
539	#382	C₂²×C₈₉	1	1	yes	characteristic
540	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
541	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
542	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
543	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
544	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
545	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
546	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
547	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
548	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
549	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
550	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
551	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
552	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
553	#376	C₂²×C₈₉	1	1	yes	characteristic
554	#376	C₂²×C₈₉	1	1	yes	characteristic
555	#376	C₂²×C₈₉	1	2	yes	—
556	#376	C₂²×C₈₉	1	2	yes	—
557	C₄³	C₂²×C₈₉	1	1	yes	characteristic
558	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
559	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
560	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
561	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
562	C₄⋊Q₈	—	2	4	no	—
563	C₄⋊Q₈	—	2	4	no	—
564	C₄⋊Q₈	—	4	4	no	—
565	#125	—	2	4	no	—
566	#125	—	4	4	no	—
567	C₄×Q₈	—	2	4	no	—
568	C₄×Q₈	—	2	4	no	—
569	C₄×Q₈	—	2	4	no	—
570	C₄×Q₈	—	4	4	no	—
571	C₄×Q₈	Q₈×C₈₉	1	8	yes	complemented
572	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
609	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
610	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
611	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
612	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
613	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
614	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
618	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
620	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
621	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
622	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
623	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
625	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
627	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
628	#95	C₂³×C₈₉	1	1	yes	characteristic
629	#95	C₂³×C₈₉	1	1	yes	characteristic
630	#95	C₂³×C₈₉	1	2	yes	—
631	#95	C₂³×C₈₉	1	1	yes	characteristic
632	#95	C₂³×C₈₉	1	1	yes	characteristic
633	#95	C₂³×C₈₉	1	2	yes	—
634	#95	C₂³×C₈₉	1	2	yes	—
635	#95	C₂³×C₈₉	1	1	yes	characteristic
636	#95	C₂³×C₈₉	1	1	yes	characteristic
637	#95	C₂³×C₈₉	1	1	yes	characteristic
638	#95	C₂³×C₈₉	1	1	yes	characteristic
639	#95	C₂³×C₈₉	1	2	yes	—
640	#95	C₂³×C₈₉	1	2	yes	—
641	#95	C₂³×C₈₉	1	2	yes	—
642	#95	C₂³×C₈₉	1	2	yes	—
643	#95	C₂³×C₈₉	1	2	yes	—
644	#95	C₂³×C₈₉	1	2	yes	—
645	#95	C₂³×C₈₉	1	1	yes	characteristic
646	#95	C₂³×C₈₉	1	1	yes	characteristic
647	#95	C₂³×C₈₉	1	2	yes	—
648	#95	C₂³×C₈₉	1	2	yes	—
649	#95	C₂³×C₈₉	1	2	yes	—
650	#95	C₂³×C₈₉	1	1	yes	characteristic
651	#95	C₂³×C₈₉	1	1	yes	characteristic
652	#95	C₂³×C₈₉	1	2	yes	—
653	#95	C₂³×C₈₉	1	1	yes	characteristic
654	#95	C₂³×C₈₉	1	1	yes	characteristic
655	#95	C₂³×C₈₉	1	2	yes	—
656	#95	C₂³×C₈₉	1	2	yes	—
657	#95	C₂³×C₈₉	1	2	yes	—
658	#95	C₂³×C₈₉	1	2	yes	—
659	#95	C₂³×C₈₉	1	2	yes	—
660	#95	C₂³×C₈₉	1	2	yes	—
661	#95	C₂³×C₈₉	1	2	yes	—
662	#95	C₂³×C₈₉	1	2	yes	—
663	#95	C₂³×C₈₉	1	2	yes	—
664	#95	C₂³×C₈₉	1	2	yes	—
665	#95	C₂³×C₈₉	1	2	yes	—
666	#95	C₂³×C₈₉	1	2	yes	—
667	C₂×Q₈	—	2	2	no	—
668	C₂×Q₈	—	2	2	no	—
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	—	2	4	no	—
671	C₂×Q₈	—	2	4	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	4	no	—
674	C₂×Q₈	—	4	2	no	—
675	C₂×Q₈	—	4	1	no	—
676	C₂×Q₈	—	4	2	no	—
677	C₂×Q₈	—	4	2	no	—
678	C₂×Q₈	C₂×Q₈×C₈₉	1	4	yes	—
679	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
680	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	4	2	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	2	no	—
730	C₄⋊C₄	—	4	2	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	1	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	C₂×Q₈×C₈₉	1	8	yes	—
737	C₄⋊C₄	C₂×Q₈×C₈₉	1	4	yes	—
738	C₄⋊C₄	#41×C₈₉	1	4	yes	—
739	C₄²	—	2	4	no	—
740	C₄²	—	2	4	no	—
741	C₄²	—	2	2	no	—
742	C₄²	—	2	2	no	—
743	C₄²	—	2	2	no	—
744	C₄²	—	2	2	no	—
745	C₄²	—	2	2	no	—
746	C₄²	—	2	2	no	—
747	C₄²	—	2	2	no	—
748	C₄²	—	2	2	no	—
749	C₄²	—	4	2	no	—
750	C₄²	—	4	2	no	—
751	C₄²	—	4	2	no	—
752	C₄²	—	4	2	no	—
753	C₄²	—	4	1	no	—
754	C₄²	—	4	2	no	—
755	C₄²	C₂×Q₈×C₈₉	1	8	yes	—
756	C₄²	C₂×Q₈×C₈₉	1	4	yes	—
757	C₄²	#41×C₈₉	1	4	yes	—
758	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
759	Q₈	—	2	8	no	—
760	Q₈	—	4	4	no	—
761	Q₈	—	4	8	no	—
762	Q₈	—	8	4	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
820	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
821	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
822	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
823	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
824	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
825	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
826	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
827	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
828	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
829	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
830	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
831	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
832	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
833	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
834	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
835	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
836	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
837	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
838	C₂²	#585×C₈₉	1	1	yes	characteristic
839	C₄	—	2	4	no	—
840	C₄	—	2	2	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	4	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	2	no	—
847	C₄	—	2	4	no	—
848	C₄	—	2	2	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	1	no	—
855	C₄	—	4	1	no	—
856	C₄	—	4	1	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	1	no	—
861	C₄	#533×C₈₉	1	4	yes	—
862	C₂	C₂×#533×C₈₉	1	1	yes	characteristic
863	C₂	C₈₉×#3494	1	1	yes	characteristic
864	C₂	C₈₉×#3502	1	1	yes	characteristic
865	C₂	C₈₉×#3503	1	1	yes	characteristic
866	C₂	C₈₉×#3509	1	1	yes	characteristic
867	C₂	C₈₉×#3516	1	1	yes	characteristic
868	C₂	C₈₉×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
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
136. C₄×Q₈×C₈₉	Q₈	semidirect
427. #35583	C₈₉	direct (N × H)
458. C₈₉	#35583	direct (N × H)
571. C₄×Q₈	Q₈×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#2612	2
C₈₉×#2606	2
C₈₉×#2605	2
C₈₉×#2588	2
C₈₉×#2585	2
C₈₉×#2581	2
C₈₉×#2567	2
C₈₉×#2550	2
C₈₉×#2546	2
C₈₉×#2507	2
C₈₉×#2506	2
C₈₉×#2462	2
C₈₉×#2453	2
C₈₉×#2451	2
C₈₉×#2331	2
C₈₉×#2330	2
C₈₉×#2320	2
C₄×C₄⋊Q₈×C₈₉	2
C₈₉×#2295	2
C₈₉×#2276	2
#35583	89

Subgroups — C89×#35583 #36413431

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35583 #36413431