Subgroups — C₈₉×#35221 #36413069

Order 22784.

1504 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2864	C₂	1	2	yes	maximal
2	C₈₉×#2863	C₂	1	2	yes	maximal
3	C₈₉×#2666	C₂	1	2	yes	maximal
4	C₈₉×#2666	C₂	1	2	yes	maximal
5	C₈₉×#2590	C₂	1	2	yes	maximal
6	C₈₉×#2588	C₂	1	2	yes	maximal
7	C₈₉×#2586	C₂	1	2	yes	maximal
8	C₈₉×#2585	C₂	1	2	yes	maximal
9	C₈₉×#2584	C₂	1	1	yes	maximal, characteristic
10	C₈₉×#2581	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#2565	C₂	1	1	yes	maximal, characteristic
12	C₈₉×#2550	C₂	1	1	yes	maximal, characteristic
13	C₈₉×#2509	C₂	1	1	yes	maximal, characteristic
14	C₈₉×#2507	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#2453	C₂	1	1	yes	maximal, characteristic
16	C₈₉×#2451	C₂	1	1	yes	maximal, characteristic
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	C₈₉×#2320	C₂	1	1	yes	maximal, characteristic
21	C₄×#125×C₈₉	C₂	1	1	yes	maximal, characteristic
22	C₈₉×#2295	C₂	1	1	yes	maximal, characteristic
23	C₄²×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic
24	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
31	#400×C₈₉	C₂²	1	2	yes	—
32	#400×C₈₉	C₂²	1	2	yes	—
33	#400×C₈₉	C₂²	1	2	yes	—
34	#400×C₈₉	C₂²	1	2	yes	—
35	#398×C₈₉	C₂²	1	2	yes	—
36	#398×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	#395×C₈₉	C₂²	1	2	yes	—
44	#395×C₈₉	C₂²	1	2	yes	—
45	#395×C₈₉	C₂²	1	2	yes	—
46	#395×C₈₉	C₂²	1	2	yes	—
47	#391×C₈₉	C₂²	1	2	yes	—
48	#391×C₈₉	C₂²	1	1	yes	characteristic
49	#391×C₈₉	C₂²	1	1	yes	characteristic
50	#391×C₈₉	C₂²	1	1	yes	characteristic
51	#391×C₈₉	C₂²	1	1	yes	characteristic
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	#389×C₈₉	C₂²	1	1	yes	characteristic
58	#389×C₈₉	C₂²	1	1	yes	characteristic
59	#389×C₈₉	C₂²	1	2	yes	—
60	#389×C₈₉	C₂²	1	1	yes	characteristic
61	#389×C₈₉	C₂²	1	1	yes	characteristic
62	#389×C₈₉	C₂²	1	1	yes	characteristic
63	#389×C₈₉	C₂²	1	1	yes	characteristic
64	#389×C₈₉	C₂²	1	1	yes	characteristic
65	#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	#389×C₈₉	C₂²	1	2	yes	—
71	#389×C₈₉	C₂²	1	2	yes	—
72	#389×C₈₉	C₂²	1	2	yes	—
73	#389×C₈₉	C₂²	1	2	yes	—
74	#389×C₈₉	C₂²	1	2	yes	—
75	#389×C₈₉	C₂²	1	2	yes	—
76	#389×C₈₉	C₂²	1	2	yes	—
77	#387×C₈₉	C₂²	1	1	yes	characteristic
78	#387×C₈₉	C₂²	1	1	yes	characteristic
79	#387×C₈₉	C₂²	1	1	yes	characteristic
80	#387×C₈₉	C₂²	1	1	yes	characteristic
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	2	yes	—
86	#387×C₈₉	C₂²	1	2	yes	—
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	#384×C₈₉	C₂²	1	1	yes	characteristic
100	#383×C₈₉	C₂²	1	2	yes	—
101	#383×C₈₉	C₂²	1	2	yes	—
102	#382×C₈₉	C₂²	1	1	yes	characteristic
103	#382×C₈₉	C₂²	1	1	yes	characteristic
104	#382×C₈₉	C₂²	1	2	yes	—
105	#382×C₈₉	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×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	2	yes	—
117	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
118	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
119	#376×C₈₉	C₂²	1	1	yes	characteristic
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×Q₈×C₈₉	C₂³	1	1	yes	characteristic
126	C₄⋊Q₈×C₈₉	—	2	4	no	—
127	#125×C₈₉	—	2	4	no	—
128	#125×C₈₉	—	2	4	no	—
129	C₄×Q₈×C₈₉	—	2	4	no	—
130	C₄×Q₈×C₈₉	—	2	4	no	—
131	C₄×Q₈×C₈₉	—	2	4	no	—
132	C₄×Q₈×C₈₉	Q₈	1	8	yes	complemented
133	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
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	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	2	yes	—
149	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
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	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	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	2	yes	—
166	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
172	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
173	C₂×C₄²×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	2	yes	—
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	2	yes	—
184	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
185	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
187	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
188	#95×C₈₉	C₂³	1	1	yes	characteristic
189	#95×C₈₉	C₂³	1	1	yes	characteristic
190	#95×C₈₉	C₂³	1	1	yes	characteristic
191	#95×C₈₉	C₂³	1	1	yes	characteristic
192	#95×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	1	yes	characteristic
196	#95×C₈₉	C₂³	1	2	yes	—
197	#95×C₈₉	C₂³	1	2	yes	—
198	#95×C₈₉	C₂³	1	2	yes	—
199	#95×C₈₉	C₂³	1	2	yes	—
200	#95×C₈₉	C₂³	1	2	yes	—
201	#95×C₈₉	C₂³	1	2	yes	—
202	#95×C₈₉	C₂³	1	2	yes	—
203	#95×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	2	yes	—
207	#95×C₈₉	C₂³	1	1	yes	characteristic
208	#95×C₈₉	C₂³	1	2	yes	—
209	#95×C₈₉	C₂³	1	1	yes	characteristic
210	#95×C₈₉	C₂³	1	1	yes	characteristic
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	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	2	yes	—
219	#95×C₈₉	C₂³	1	2	yes	—
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	C₂×Q₈×C₈₉	—	2	2	no	—
230	C₂×Q₈×C₈₉	—	2	2	no	—
231	C₂×Q₈×C₈₉	—	2	2	no	—
232	C₂×Q₈×C₈₉	—	2	4	no	—
233	C₂×Q₈×C₈₉	—	4	1	no	—
234	C₂×Q₈×C₈₉	—	4	1	no	—
235	C₂×Q₈×C₈₉	—	4	2	no	—
236	C₂×Q₈×C₈₉	—	4	2	no	—
237	C₂×Q₈×C₈₉	C₂×Q₈	1	4	yes	—
238	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
260	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
261	C₄⋊C₄×C₈₉	—	2	4	no	—
262	C₄⋊C₄×C₈₉	—	2	4	no	—
263	C₄⋊C₄×C₈₉	—	2	2	no	—
264	C₄⋊C₄×C₈₉	—	2	2	no	—
265	C₄⋊C₄×C₈₉	—	2	2	no	—
266	C₄⋊C₄×C₈₉	—	2	2	no	—
267	C₄⋊C₄×C₈₉	—	2	4	no	—
268	C₄⋊C₄×C₈₉	—	2	4	no	—
269	C₄⋊C₄×C₈₉	—	2	4	no	—
270	C₄⋊C₄×C₈₉	—	2	4	no	—
271	C₄⋊C₄×C₈₉	—	2	2	no	—
272	C₄⋊C₄×C₈₉	—	2	2	no	—
273	C₄⋊C₄×C₈₉	—	2	2	no	—
274	C₄⋊C₄×C₈₉	—	2	4	no	—
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	—	4	2	no	—
280	C₄⋊C₄×C₈₉	—	4	2	no	—
281	C₄⋊C₄×C₈₉	—	4	2	no	—
282	C₄⋊C₄×C₈₉	—	4	2	no	—
283	C₄⋊C₄×C₈₉	—	4	2	no	—
284	C₄⋊C₄×C₈₉	—	4	1	no	—
285	C₄⋊C₄×C₈₉	—	4	2	no	—
286	C₄⋊C₄×C₈₉	—	4	1	no	—
287	C₄⋊C₄×C₈₉	—	4	2	no	—
288	C₄⋊C₄×C₈₉	—	4	2	no	—
289	C₄⋊C₄×C₈₉	—	4	1	no	—
290	C₄⋊C₄×C₈₉	—	4	2	no	—
291	C₄⋊C₄×C₈₉	—	4	2	no	—
292	C₄⋊C₄×C₈₉	—	4	1	no	—
293	C₄⋊C₄×C₈₉	—	4	2	no	—
294	C₄⋊C₄×C₈₉	C₂×Q₈	1	8	yes	—
295	C₄⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
296	C₄⋊C₄×C₈₉	#41	1	4	yes	—
297	C₄²×C₈₉	—	2	4	no	—
298	C₄²×C₈₉	—	2	2	no	—
299	C₄²×C₈₉	—	2	4	no	—
300	C₄²×C₈₉	—	2	2	no	—
301	C₄²×C₈₉	—	2	2	no	—
302	C₄²×C₈₉	—	2	2	no	—
303	C₄²×C₈₉	—	2	2	no	—
304	C₄²×C₈₉	—	2	2	no	—
305	C₄²×C₈₉	—	4	1	no	—
306	C₄²×C₈₉	—	4	1	no	—
307	C₄²×C₈₉	—	4	2	no	—
308	C₄²×C₈₉	—	4	2	no	—
309	C₄²×C₈₉	—	4	1	no	—
310	C₄²×C₈₉	—	4	2	no	—
311	C₄²×C₈₉	—	4	2	no	—
312	C₄²×C₈₉	—	4	2	no	—
313	C₄²×C₈₉	C₂×Q₈	1	8	yes	—
314	C₄²×C₈₉	C₂×Q₈	1	4	yes	—
315	C₄²×C₈₉	#41	1	4	yes	—
316	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
317	Q₈×C₈₉	—	2	8	no	—
318	Q₈×C₈₉	—	4	4	no	—
319	Q₈×C₈₉	—	8	4	no	—
320	C₂×C₄×C₈₉	—	2	1	no	—
321	C₂×C₄×C₈₉	—	2	2	no	—
322	C₂×C₄×C₈₉	—	2	2	no	—
323	C₂×C₄×C₈₉	—	2	1	no	—
324	C₂×C₄×C₈₉	—	2	1	no	—
325	C₂×C₄×C₈₉	—	2	1	no	—
326	C₂×C₄×C₈₉	—	2	1	no	—
327	C₂×C₄×C₈₉	—	2	1	no	—
328	C₂×C₄×C₈₉	—	2	1	no	—
329	C₂×C₄×C₈₉	—	2	1	no	—
330	C₂×C₄×C₈₉	—	2	2	no	—
331	C₂×C₄×C₈₉	—	2	2	no	—
332	C₂×C₄×C₈₉	—	2	1	no	—
333	C₂×C₄×C₈₉	—	2	1	no	—
334	C₂×C₄×C₈₉	—	2	2	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	1	no	—
341	C₂×C₄×C₈₉	—	2	1	no	—
342	C₂×C₄×C₈₉	—	2	1	no	—
343	C₂×C₄×C₈₉	—	2	1	no	—
344	C₂×C₄×C₈₉	—	2	1	no	—
345	C₂×C₄×C₈₉	—	2	1	no	—
346	C₂×C₄×C₈₉	—	2	2	no	—
347	C₂×C₄×C₈₉	—	2	2	no	—
348	C₂×C₄×C₈₉	—	2	2	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	2	no	—
353	C₂×C₄×C₈₉	—	2	1	no	—
354	C₂×C₄×C₈₉	—	2	1	no	—
355	C₂×C₄×C₈₉	—	2	2	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	1	no	—
363	C₂×C₄×C₈₉	—	2	2	no	—
364	C₂×C₄×C₈₉	—	2	2	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	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	1	no	—
374	C₂×C₄×C₈₉	—	2	1	no	—
375	C₂×C₄×C₈₉	—	2	2	no	—
376	C₂×C₄×C₈₉	—	2	1	no	—
377	C₂×C₄×C₈₉	—	2	1	no	—
378	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
379	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
380	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
381	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
382	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
383	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
384	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
385	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
386	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
387	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
388	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
389	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
390	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
391	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
392	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
393	C₂²×C₈₉	#585	1	1	yes	characteristic
394	C₂²×C₈₉	#585	1	1	yes	characteristic
395	C₂²×C₈₉	#585	1	1	yes	characteristic
396	C₄×C₈₉	—	2	4	no	—
397	C₄×C₈₉	—	2	2	no	—
398	C₄×C₈₉	—	2	2	no	—
399	C₄×C₈₉	—	2	2	no	—
400	C₄×C₈₉	—	2	2	no	—
401	C₄×C₈₉	—	2	4	no	—
402	C₄×C₈₉	—	2	2	no	—
403	C₄×C₈₉	—	2	4	no	—
404	C₄×C₈₉	—	4	2	no	—
405	C₄×C₈₉	—	4	2	no	—
406	C₄×C₈₉	—	4	1	no	—
407	C₄×C₈₉	—	4	1	no	—
408	C₄×C₈₉	—	4	1	no	—
409	C₄×C₈₉	—	4	1	no	—
410	C₄×C₈₉	—	4	2	no	—
411	C₄×C₈₉	—	4	1	no	—
412	C₄×C₈₉	—	4	1	no	—
413	C₄×C₈₉	—	4	2	no	—
414	C₄×C₈₉	—	4	1	no	—
415	C₄×C₈₉	—	4	1	no	—
416	C₄×C₈₉	—	4	2	no	—
417	C₄×C₈₉	—	4	1	no	—
418	C₄×C₈₉	#533	1	4	yes	—
419	#35221	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
420	C₂×C₈₉	C₂×#533	1	1	yes	characteristic
421	C₂×C₈₉	#3455	1	1	yes	characteristic
422	C₂×C₈₉	#3461	1	1	yes	characteristic
423	C₂×C₈₉	#3502	1	1	yes	characteristic
424	C₂×C₈₉	#3504	1	1	yes	characteristic
425	C₂×C₈₉	#3516	1	1	yes	characteristic
426	C₂×C₈₉	#3521	1	1	yes	characteristic
427	#2864	C₂×C₈₉	1	2	yes	—
428	#2863	C₂×C₈₉	1	2	yes	—
429	#2666	C₂×C₈₉	1	2	yes	—
430	#2666	C₂×C₈₉	1	2	yes	—
431	#2590	C₂×C₈₉	1	2	yes	—
432	#2588	C₂×C₈₉	1	2	yes	—
433	#2586	C₂×C₈₉	1	2	yes	—
434	#2585	C₂×C₈₉	1	2	yes	—
435	#2584	C₂×C₈₉	1	1	yes	characteristic
436	#2581	C₂×C₈₉	1	1	yes	characteristic
437	#2565	C₂×C₈₉	1	1	yes	characteristic
438	#2550	C₂×C₈₉	1	1	yes	characteristic
439	#2509	C₂×C₈₉	1	1	yes	characteristic
440	#2507	C₂×C₈₉	1	1	yes	characteristic
441	#2453	C₂×C₈₉	1	1	yes	characteristic
442	#2451	C₂×C₈₉	1	1	yes	characteristic
443	#2331	C₂×C₈₉	1	1	yes	characteristic
444	#2330	C₂×C₈₉	1	1	yes	characteristic
445	#2320	C₂×C₈₉	1	1	yes	characteristic
446	#2320	C₂×C₈₉	1	1	yes	characteristic
447	C₄×#125	C₂×C₈₉	1	1	yes	characteristic
448	#2295	C₂×C₈₉	1	1	yes	characteristic
449	C₄²×Q₈	C₂×C₈₉	1	1	yes	characteristic
450	C₈₉	#35221	1	1	yes	characteristic, direct product factor, Sylow
451	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
452	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
453	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
454	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
455	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
456	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
457	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
458	#400	C₂²×C₈₉	1	2	yes	—
459	#400	C₂²×C₈₉	1	2	yes	—
460	#400	C₂²×C₈₉	1	2	yes	—
461	#400	C₂²×C₈₉	1	2	yes	—
462	#398	C₂²×C₈₉	1	2	yes	—
463	#398	C₂²×C₈₉	1	2	yes	—
464	#398	C₂²×C₈₉	1	2	yes	—
465	#398	C₂²×C₈₉	1	2	yes	—
466	#398	C₂²×C₈₉	1	2	yes	—
467	#398	C₂²×C₈₉	1	2	yes	—
468	#398	C₂²×C₈₉	1	2	yes	—
469	#398	C₂²×C₈₉	1	2	yes	—
470	#395	C₂²×C₈₉	1	2	yes	—
471	#395	C₂²×C₈₉	1	2	yes	—
472	#395	C₂²×C₈₉	1	2	yes	—
473	#395	C₂²×C₈₉	1	2	yes	—
474	#391	C₂²×C₈₉	1	1	yes	characteristic
475	#391	C₂²×C₈₉	1	1	yes	characteristic
476	#391	C₂²×C₈₉	1	1	yes	characteristic
477	#391	C₂²×C₈₉	1	1	yes	characteristic
478	#391	C₂²×C₈₉	1	1	yes	characteristic
479	#391	C₂²×C₈₉	1	2	yes	—
480	#391	C₂²×C₈₉	1	2	yes	—
481	#391	C₂²×C₈₉	1	2	yes	—
482	#391	C₂²×C₈₉	1	2	yes	—
483	#391	C₂²×C₈₉	1	1	yes	characteristic
484	#389	C₂²×C₈₉	1	1	yes	characteristic
485	#389	C₂²×C₈₉	1	1	yes	characteristic
486	#389	C₂²×C₈₉	1	1	yes	characteristic
487	#389	C₂²×C₈₉	1	1	yes	characteristic
488	#389	C₂²×C₈₉	1	1	yes	characteristic
489	#389	C₂²×C₈₉	1	1	yes	characteristic
490	#389	C₂²×C₈₉	1	1	yes	characteristic
491	#389	C₂²×C₈₉	1	1	yes	characteristic
492	#389	C₂²×C₈₉	1	1	yes	characteristic
493	#389	C₂²×C₈₉	1	1	yes	characteristic
494	#389	C₂²×C₈₉	1	2	yes	—
495	#389	C₂²×C₈₉	1	2	yes	—
496	#389	C₂²×C₈₉	1	1	yes	characteristic
497	#389	C₂²×C₈₉	1	2	yes	—
498	#389	C₂²×C₈₉	1	2	yes	—
499	#389	C₂²×C₈₉	1	2	yes	—
500	#389	C₂²×C₈₉	1	2	yes	—
501	#389	C₂²×C₈₉	1	2	yes	—
502	#389	C₂²×C₈₉	1	2	yes	—
503	#389	C₂²×C₈₉	1	1	yes	characteristic
504	#387	C₂²×C₈₉	1	2	yes	—
505	#387	C₂²×C₈₉	1	2	yes	—
506	#387	C₂²×C₈₉	1	2	yes	—
507	#387	C₂²×C₈₉	1	2	yes	—
508	#387	C₂²×C₈₉	1	2	yes	—
509	#387	C₂²×C₈₉	1	2	yes	—
510	#387	C₂²×C₈₉	1	2	yes	—
511	#387	C₂²×C₈₉	1	2	yes	—
512	#387	C₂²×C₈₉	1	2	yes	—
513	#387	C₂²×C₈₉	1	2	yes	—
514	#387	C₂²×C₈₉	1	2	yes	—
515	#387	C₂²×C₈₉	1	2	yes	—
516	#387	C₂²×C₈₉	1	2	yes	—
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	2	yes	—
522	#387	C₂²×C₈₉	1	1	yes	characteristic
523	#387	C₂²×C₈₉	1	1	yes	characteristic
524	#387	C₂²×C₈₉	1	1	yes	characteristic
525	#387	C₂²×C₈₉	1	1	yes	characteristic
526	#384	C₂²×C₈₉	1	1	yes	characteristic
527	#383	C₂²×C₈₉	1	2	yes	—
528	#383	C₂²×C₈₉	1	2	yes	—
529	#382	C₂²×C₈₉	1	1	yes	characteristic
530	#382	C₂²×C₈₉	1	1	yes	characteristic
531	#382	C₂²×C₈₉	1	2	yes	—
532	#382	C₂²×C₈₉	1	2	yes	—
533	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
534	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
535	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
536	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
537	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
538	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
539	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
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	2	yes	—
543	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
544	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
545	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
546	#376	C₂²×C₈₉	1	1	yes	characteristic
547	#376	C₂²×C₈₉	1	1	yes	characteristic
548	C₄³	C₂²×C₈₉	1	1	yes	characteristic
549	C₄³	C₂²×C₈₉	1	2	yes	—
550	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
551	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
552	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
553	C₄⋊Q₈	—	2	4	no	—
554	#125	—	2	4	no	—
555	#125	—	2	4	no	—
556	C₄×Q₈	—	2	4	no	—
557	C₄×Q₈	—	2	4	no	—
558	C₄×Q₈	—	2	4	no	—
559	C₄×Q₈	Q₈×C₈₉	1	8	yes	complemented
560	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
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	1	yes	characteristic
596	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
597	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
598	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
599	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
607	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
609	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
610	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
611	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
612	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
613	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
614	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
615	#95	C₂³×C₈₉	1	1	yes	characteristic
616	#95	C₂³×C₈₉	1	1	yes	characteristic
617	#95	C₂³×C₈₉	1	1	yes	characteristic
618	#95	C₂³×C₈₉	1	1	yes	characteristic
619	#95	C₂³×C₈₉	1	1	yes	characteristic
620	#95	C₂³×C₈₉	1	1	yes	characteristic
621	#95	C₂³×C₈₉	1	1	yes	characteristic
622	#95	C₂³×C₈₉	1	1	yes	characteristic
623	#95	C₂³×C₈₉	1	2	yes	—
624	#95	C₂³×C₈₉	1	2	yes	—
625	#95	C₂³×C₈₉	1	2	yes	—
626	#95	C₂³×C₈₉	1	2	yes	—
627	#95	C₂³×C₈₉	1	2	yes	—
628	#95	C₂³×C₈₉	1	2	yes	—
629	#95	C₂³×C₈₉	1	2	yes	—
630	#95	C₂³×C₈₉	1	1	yes	characteristic
631	#95	C₂³×C₈₉	1	1	yes	characteristic
632	#95	C₂³×C₈₉	1	2	yes	—
633	#95	C₂³×C₈₉	1	1	yes	characteristic
634	#95	C₂³×C₈₉	1	1	yes	characteristic
635	#95	C₂³×C₈₉	1	2	yes	—
636	#95	C₂³×C₈₉	1	1	yes	characteristic
637	#95	C₂³×C₈₉	1	1	yes	characteristic
638	#95	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
646	#95	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
651	#95	C₂³×C₈₉	1	2	yes	—
652	#95	C₂³×C₈₉	1	2	yes	—
653	#95	C₂³×C₈₉	1	2	yes	—
654	#95	C₂³×C₈₉	1	2	yes	—
655	#95	C₂³×C₈₉	1	2	yes	—
656	C₂×Q₈	—	2	2	no	—
657	C₂×Q₈	—	2	2	no	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	—	2	4	no	—
660	C₂×Q₈	—	4	1	no	—
661	C₂×Q₈	—	4	1	no	—
662	C₂×Q₈	—	4	2	no	—
663	C₂×Q₈	—	4	2	no	—
664	C₂×Q₈	C₂×Q₈×C₈₉	1	4	yes	—
665	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
666	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
667	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
668	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
669	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
670	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
677	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
680	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
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	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₄⋊C₄	—	4	2	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	—	4	2	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	—	4	1	no	—
712	C₄⋊C₄	—	4	2	no	—
713	C₄⋊C₄	—	4	1	no	—
714	C₄⋊C₄	—	4	2	no	—
715	C₄⋊C₄	—	4	2	no	—
716	C₄⋊C₄	—	4	1	no	—
717	C₄⋊C₄	—	4	2	no	—
718	C₄⋊C₄	—	4	2	no	—
719	C₄⋊C₄	—	4	1	no	—
720	C₄⋊C₄	—	4	2	no	—
721	C₄⋊C₄	C₂×Q₈×C₈₉	1	8	yes	—
722	C₄⋊C₄	C₂×Q₈×C₈₉	1	4	yes	—
723	C₄⋊C₄	#41×C₈₉	1	4	yes	—
724	C₄²	—	2	4	no	—
725	C₄²	—	2	2	no	—
726	C₄²	—	2	4	no	—
727	C₄²	—	2	2	no	—
728	C₄²	—	2	2	no	—
729	C₄²	—	2	2	no	—
730	C₄²	—	2	2	no	—
731	C₄²	—	2	2	no	—
732	C₄²	—	4	1	no	—
733	C₄²	—	4	1	no	—
734	C₄²	—	4	2	no	—
735	C₄²	—	4	2	no	—
736	C₄²	—	4	1	no	—
737	C₄²	—	4	2	no	—
738	C₄²	—	4	2	no	—
739	C₄²	—	4	2	no	—
740	C₄²	C₂×Q₈×C₈₉	1	8	yes	—
741	C₄²	C₂×Q₈×C₈₉	1	4	yes	—
742	C₄²	#41×C₈₉	1	4	yes	—
743	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
744	Q₈	—	2	8	no	—
745	Q₈	—	4	4	no	—
746	Q₈	—	8	4	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	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	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
806	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
807	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
808	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
809	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
810	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
811	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
812	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
813	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
814	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
815	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
816	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
817	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
818	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
819	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
820	C₂²	#585×C₈₉	1	1	yes	characteristic
821	C₂²	#585×C₈₉	1	1	yes	characteristic
822	C₂²	#585×C₈₉	1	1	yes	characteristic
823	C₄	—	2	4	no	—
824	C₄	—	2	2	no	—
825	C₄	—	2	2	no	—
826	C₄	—	2	2	no	—
827	C₄	—	2	2	no	—
828	C₄	—	2	4	no	—
829	C₄	—	2	2	no	—
830	C₄	—	2	4	no	—
831	C₄	—	4	1	no	—
832	C₄	—	4	1	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	1	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	1	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	1	no	—
844	C₄	—	4	1	no	—
845	C₄	#533×C₈₉	1	4	yes	—
846	C₂	C₂×#533×C₈₉	1	1	yes	characteristic
847	C₂	C₈₉×#3455	1	1	yes	characteristic
848	C₂	C₈₉×#3461	1	1	yes	characteristic
849	C₂	C₈₉×#3502	1	1	yes	characteristic
850	C₂	C₈₉×#3504	1	1	yes	characteristic
851	C₂	C₈₉×#3516	1	1	yes	characteristic
852	C₂	C₈₉×#3521	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
132. C₄×Q₈×C₈₉	Q₈	semidirect
419. #35221	C₈₉	direct (N × H)
450. C₈₉	#35221	direct (N × H)
559. 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×#2864	2
C₈₉×#2863	2
C₈₉×#2666	2
C₈₉×#2590	2
C₈₉×#2588	2
C₈₉×#2586	2
C₈₉×#2585	2
C₈₉×#2584	2
C₈₉×#2581	2
C₈₉×#2565	2
C₈₉×#2550	2
C₈₉×#2509	2
C₈₉×#2507	2
C₈₉×#2453	2
C₈₉×#2451	2
C₈₉×#2331	2
C₈₉×#2330	2
C₈₉×#2320	2
C₄×#125×C₈₉	2
C₈₉×#2295	2
C₄²×Q₈×C₈₉	2
#35221	89

Subgroups — C89×#35221 #36413069

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35221 #36413069