Subgroups — C₈₉×#35577 #36413425

Order 22784.

1638 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2588	C₂	1	2	yes	maximal, complemented
2	C₈₉×#2587	C₂	1	2	yes	maximal
3	C₈₉×#2586	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2574	C₂	1	2	yes	maximal
5	C₈₉×#2571	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2570	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2551	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2550	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2520	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2492	C₂	1	2	yes	maximal
11	C₈₉×#2465	C₂	1	2	yes	maximal
12	C₈₉×#2446	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2442	C₂	1	1	yes	maximal, characteristic
14	C₈₉×#2440	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#2439	C₂	1	1	yes	maximal, characteristic
16	C₈₉×#2439	C₂	1	1	yes	maximal, characteristic
17	C₈₉×#2331	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#2331	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2314	C₂	1	1	yes	maximal, characteristic
20	C₄×C₄⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#125×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₉×#2298	C₂	1	1	yes	maximal, characteristic
23	C₈₉×#2274	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	1	yes	characteristic
27	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
28	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
31	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×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	#400×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	#396×C₈₉	C₂²	1	2	yes	—
43	#396×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	#395×C₈₉	C₂²	1	2	yes	—
48	#393×C₈₉	C₂²	1	2	yes	—
49	#393×C₈₉	C₂²	1	2	yes	—
50	#391×C₈₉	C₂²	1	2	yes	—
51	#391×C₈₉	C₂²	1	2	yes	—
52	#391×C₈₉	C₂²	1	2	yes	—
53	#391×C₈₉	C₂²	1	2	yes	—
54	#391×C₈₉	C₂²	1	2	yes	—
55	#391×C₈₉	C₂²	1	2	yes	—
56	#391×C₈₉	C₂²	1	2	yes	—
57	#391×C₈₉	C₂²	1	2	yes	—
58	#389×C₈₉	C₂²	1	1	yes	characteristic
59	#389×C₈₉	C₂²	1	1	yes	characteristic
60	#389×C₈₉	C₂²	1	2	yes	—
61	#389×C₈₉	C₂²	1	1	yes	characteristic
62	#389×C₈₉	C₂²	1	1	yes	characteristic
63	#389×C₈₉	C₂²	1	2	yes	—
64	#389×C₈₉	C₂²	1	1	yes	characteristic
65	#389×C₈₉	C₂²	1	1	yes	characteristic
66	#389×C₈₉	C₂²	1	2	yes	—
67	#389×C₈₉	C₂²	1	1	yes	characteristic
68	#389×C₈₉	C₂²	1	2	yes	—
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	#387×C₈₉	C₂²	1	1	yes	characteristic
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	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	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	#385×C₈₉	C₂²	1	2	yes	—
93	#385×C₈₉	C₂²	1	2	yes	—
94	#384×C₈₉	C₂²	1	1	yes	characteristic
95	#384×C₈₉	C₂²	1	1	yes	characteristic
96	#382×C₈₉	C₂²	1	1	yes	characteristic
97	#382×C₈₉	C₂²	1	1	yes	characteristic
98	#382×C₈₉	C₂²	1	1	yes	characteristic
99	#382×C₈₉	C₂²	1	2	yes	—
100	#382×C₈₉	C₂²	1	1	yes	characteristic
101	#380×C₈₉	C₂²	1	1	yes	characteristic
102	#380×C₈₉	C₂²	1	1	yes	characteristic
103	#380×C₈₉	C₂²	1	2	yes	—
104	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
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	2	yes	—
109	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
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	1	yes	characteristic
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×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	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
121	#376×C₈₉	C₂²	1	1	yes	characteristic
122	C₄³×C₈₉	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
124	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
125	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
126	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
128	C₄⋊Q₈×C₈₉	—	2	4	no	—
129	C₄⋊Q₈×C₈₉	—	2	4	no	—
130	C₄⋊Q₈×C₈₉	—	2	4	no	—
131	C₄⋊Q₈×C₈₉	—	4	4	no	—
132	#125×C₈₉	—	2	4	no	—
133	C₂²⋊Q₈×C₈₉	—	4	4	no	—
134	C₄×Q₈×C₈₉	—	4	4	no	—
135	#117×C₈₉	—	2	4	no	—
136	#117×C₈₉	Q₈	1	8	yes	complemented
137	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
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	2	yes	—
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	2	yes	—
146	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	1	yes	characteristic
150	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	1	yes	characteristic
156	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₈₉	C₂³	1	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	1	yes	characteristic
167	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄×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	1	yes	characteristic
182	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
187	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
189	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
190	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
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	1	yes	characteristic
195	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
196	#95×C₈₉	C₂³	1	1	yes	characteristic
197	#95×C₈₉	C₂³	1	1	yes	characteristic
198	#95×C₈₉	C₂³	1	1	yes	characteristic
199	#95×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
209	#95×C₈₉	C₂³	1	2	yes	—
210	#95×C₈₉	C₂³	1	2	yes	—
211	#95×C₈₉	C₂³	1	2	yes	—
212	#95×C₈₉	C₂³	1	2	yes	—
213	#95×C₈₉	C₂³	1	1	yes	characteristic
214	#95×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	#95×C₈₉	C₂³	1	2	yes	—
230	#95×C₈₉	C₂³	1	2	yes	—
231	#95×C₈₉	C₂³	1	2	yes	—
232	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
233	C₂×Q₈×C₈₉	—	2	4	no	—
234	C₂×Q₈×C₈₉	—	2	4	no	—
235	C₂×Q₈×C₈₉	—	2	4	no	—
236	C₂×Q₈×C₈₉	—	2	4	no	—
237	C₂×Q₈×C₈₉	—	4	2	no	—
238	C₂×Q₈×C₈₉	—	4	2	no	—
239	C₂×Q₈×C₈₉	—	4	2	no	—
240	C₂×Q₈×C₈₉	—	4	2	no	—
241	C₂×Q₈×C₈₉	—	4	2	no	—
242	C₂²×C₄×C₈₉	—	2	2	no	—
243	C₂²×C₄×C₈₉	—	2	2	no	—
244	C₂²×C₄×C₈₉	—	2	4	no	—
245	C₂²×C₄×C₈₉	—	4	2	no	—
246	C₂²×C₄×C₈₉	—	4	2	no	—
247	C₂²×C₄×C₈₉	C₂×Q₈	1	4	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	1	yes	characteristic
252	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
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	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	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	4	no	—
279	C₄⋊C₄×C₈₉	—	2	2	no	—
280	C₄⋊C₄×C₈₉	—	2	2	no	—
281	C₄⋊C₄×C₈₉	—	2	2	no	—
282	C₄⋊C₄×C₈₉	—	2	4	no	—
283	C₄⋊C₄×C₈₉	—	2	4	no	—
284	C₄⋊C₄×C₈₉	—	2	2	no	—
285	C₄⋊C₄×C₈₉	—	2	2	no	—
286	C₄⋊C₄×C₈₉	—	2	4	no	—
287	C₄⋊C₄×C₈₉	—	4	1	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	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	C₂×Q₈	1	4	yes	—
299	C₄⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
300	C₄⋊C₄×C₈₉	#41	1	4	yes	—
301	C₄⋊C₄×C₈₉	#41	1	4	yes	—
302	C₂²⋊C₄×C₈₉	—	2	4	no	—
303	C₂²⋊C₄×C₈₉	—	2	2	no	—
304	C₂²⋊C₄×C₈₉	—	2	2	no	—
305	C₂²⋊C₄×C₈₉	—	4	1	no	—
306	C₂²⋊C₄×C₈₉	—	4	2	no	—
307	C₂²⋊C₄×C₈₉	—	4	1	no	—
308	C₂²⋊C₄×C₈₉	—	4	2	no	—
309	C₂²⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
310	C₂²⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
311	C₄²×C₈₉	—	2	4	no	—
312	C₄²×C₈₉	—	2	2	no	—
313	C₄²×C₈₉	—	2	2	no	—
314	C₄²×C₈₉	—	2	2	no	—
315	C₄²×C₈₉	—	2	2	no	—
316	C₄²×C₈₉	—	2	2	no	—
317	C₄²×C₈₉	—	2	2	no	—
318	C₄²×C₈₉	—	4	1	no	—
319	C₄²×C₈₉	—	4	2	no	—
320	C₄²×C₈₉	—	4	1	no	—
321	C₄²×C₈₉	—	4	2	no	—
322	C₄²×C₈₉	—	4	2	no	—
323	C₄²×C₈₉	—	4	2	no	—
324	C₄²×C₈₉	—	4	2	no	—
325	C₄²×C₈₉	—	4	2	no	—
326	C₄²×C₈₉	C₂×Q₈	1	4	yes	—
327	C₄²×C₈₉	C₂×Q₈	1	4	yes	—
328	C₂³×C₈₉	—	2	1	no	—
329	C₂³×C₈₉	—	2	1	no	—
330	C₂³×C₈₉	—	2	1	no	—
331	C₂³×C₈₉	—	2	1	no	—
332	C₂³×C₈₉	—	2	1	no	—
333	C₂³×C₈₉	—	2	1	no	—
334	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
335	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
336	Q₈×C₈₉	—	4	8	no	—
337	Q₈×C₈₉	—	8	4	no	—
338	Q₈×C₈₉	—	8	4	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	2	no	—
346	C₂×C₄×C₈₉	—	2	2	no	—
347	C₂×C₄×C₈₉	—	2	1	no	—
348	C₂×C₄×C₈₉	—	2	1	no	—
349	C₂×C₄×C₈₉	—	2	1	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	2	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	8	no	—
358	C₂×C₄×C₈₉	—	2	2	no	—
359	C₂×C₄×C₈₉	—	2	1	no	—
360	C₂×C₄×C₈₉	—	2	1	no	—
361	C₂×C₄×C₈₉	—	2	1	no	—
362	C₂×C₄×C₈₉	—	2	1	no	—
363	C₂×C₄×C₈₉	—	2	1	no	—
364	C₂×C₄×C₈₉	—	2	1	no	—
365	C₂×C₄×C₈₉	—	2	2	no	—
366	C₂×C₄×C₈₉	—	2	2	no	—
367	C₂×C₄×C₈₉	—	2	2	no	—
368	C₂×C₄×C₈₉	—	2	2	no	—
369	C₂×C₄×C₈₉	—	2	2	no	—
370	C₂×C₄×C₈₉	—	2	1	no	—
371	C₂×C₄×C₈₉	—	2	2	no	—
372	C₂×C₄×C₈₉	—	2	2	no	—
373	C₂×C₄×C₈₉	—	2	2	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	—	2	1	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	2	no	—
386	C₂×C₄×C₈₉	—	2	2	no	—
387	C₂×C₄×C₈₉	—	2	2	no	—
388	C₂×C₄×C₈₉	—	2	1	no	—
389	C₂×C₄×C₈₉	—	2	2	no	—
390	C₂×C₄×C₈₉	—	2	1	no	—
391	C₂×C₄×C₈₉	—	2	1	no	—
392	C₂×C₄×C₈₉	—	2	2	no	—
393	C₂×C₄×C₈₉	—	2	1	no	—
394	C₂×C₄×C₈₉	—	8	4	no	—
395	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
396	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
397	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
398	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
399	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
400	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
401	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
402	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
403	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
404	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
405	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
406	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
407	C₂²×C₈₉	—	2	2	no	—
408	C₂²×C₈₉	—	2	2	no	—
409	C₂²×C₈₉	—	2	2	no	—
410	C₂²×C₈₉	—	4	1	no	—
411	C₂²×C₈₉	—	4	1	no	—
412	C₂²×C₈₉	—	4	1	no	—
413	C₂²×C₈₉	—	4	1	no	—
414	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
415	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
416	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
417	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
418	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
419	C₂²×C₈₉	#585	1	1	yes	characteristic
420	C₂²×C₈₉	#585	1	1	yes	characteristic
421	C₄×C₈₉	—	2	2	no	—
422	C₄×C₈₉	—	2	2	no	—
423	C₄×C₈₉	—	2	2	no	—
424	C₄×C₈₉	—	2	2	no	—
425	C₄×C₈₉	—	2	2	no	—
426	C₄×C₈₉	—	2	4	no	—
427	C₄×C₈₉	—	2	2	no	—
428	C₄×C₈₉	—	2	4	no	—
429	C₄×C₈₉	—	2	2	no	—
430	C₄×C₈₉	—	4	2	no	—
431	C₄×C₈₉	—	4	2	no	—
432	C₄×C₈₉	—	4	1	no	—
433	C₄×C₈₉	—	4	1	no	—
434	C₄×C₈₉	—	4	2	no	—
435	C₄×C₈₉	—	4	2	no	—
436	C₄×C₈₉	—	4	1	no	—
437	C₄×C₈₉	—	4	2	no	—
438	C₄×C₈₉	—	4	1	no	—
439	C₄×C₈₉	—	4	1	no	—
440	C₄×C₈₉	—	4	1	no	—
441	C₄×C₈₉	—	4	2	no	—
442	C₄×C₈₉	#533	1	4	yes	—
443	#35577	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
444	C₂×C₈₉	—	4	2	no	—
445	C₂×C₈₉	C₂×#533	1	1	yes	characteristic
446	C₂×C₈₉	#3503	1	1	yes	characteristic
447	C₂×C₈₉	#3504	1	1	yes	characteristic
448	C₂×C₈₉	#3513	1	1	yes	characteristic
449	C₂×C₈₉	#3514	1	1	yes	characteristic
450	C₂×C₈₉	#3516	1	1	yes	characteristic
451	C₂×C₈₉	#3518	1	1	yes	characteristic
452	#2588	C₂×C₈₉	1	2	yes	complemented
453	#2587	C₂×C₈₉	1	2	yes	—
454	#2586	C₂×C₈₉	1	2	yes	complemented
455	#2574	C₂×C₈₉	1	2	yes	—
456	#2571	C₂×C₈₉	1	1	yes	characteristic, complemented
457	#2570	C₂×C₈₉	1	1	yes	characteristic, complemented
458	#2551	C₂×C₈₉	1	1	yes	characteristic, complemented
459	#2550	C₂×C₈₉	1	1	yes	characteristic, complemented
460	#2520	C₂×C₈₉	1	2	yes	complemented
461	#2492	C₂×C₈₉	1	2	yes	—
462	#2465	C₂×C₈₉	1	2	yes	—
463	#2446	C₂×C₈₉	1	2	yes	complemented
464	#2442	C₂×C₈₉	1	1	yes	characteristic
465	#2440	C₂×C₈₉	1	1	yes	characteristic
466	#2439	C₂×C₈₉	1	1	yes	characteristic
467	#2439	C₂×C₈₉	1	1	yes	characteristic
468	#2331	C₂×C₈₉	1	1	yes	characteristic, complemented
469	#2331	C₂×C₈₉	1	1	yes	characteristic, complemented
470	#2314	C₂×C₈₉	1	1	yes	characteristic
471	C₄×C₄⋊Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
472	C₄×#125	C₂×C₈₉	1	1	yes	characteristic, complemented
473	#2298	C₂×C₈₉	1	1	yes	characteristic
474	#2274	C₂×C₈₉	1	1	yes	characteristic
475	C₈₉	#35577	1	1	yes	characteristic, direct product factor, Sylow
476	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
477	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
478	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
479	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
480	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
481	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
482	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
483	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
484	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
485	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
486	#400	C₂²×C₈₉	1	2	yes	—
487	#400	C₂²×C₈₉	1	2	yes	—
488	#400	C₂²×C₈₉	1	2	yes	—
489	#400	C₂²×C₈₉	1	2	yes	—
490	#398	C₂²×C₈₉	1	2	yes	—
491	#398	C₂²×C₈₉	1	2	yes	—
492	#398	C₂²×C₈₉	1	2	yes	—
493	#398	C₂²×C₈₉	1	2	yes	—
494	#396	C₂²×C₈₉	1	2	yes	—
495	#396	C₂²×C₈₉	1	2	yes	—
496	#395	C₂²×C₈₉	1	2	yes	—
497	#395	C₂²×C₈₉	1	2	yes	—
498	#395	C₂²×C₈₉	1	2	yes	—
499	#395	C₂²×C₈₉	1	2	yes	—
500	#393	C₂²×C₈₉	1	2	yes	—
501	#393	C₂²×C₈₉	1	2	yes	—
502	#391	C₂²×C₈₉	1	2	yes	—
503	#391	C₂²×C₈₉	1	2	yes	—
504	#391	C₂²×C₈₉	1	2	yes	—
505	#391	C₂²×C₈₉	1	2	yes	—
506	#391	C₂²×C₈₉	1	2	yes	—
507	#391	C₂²×C₈₉	1	2	yes	—
508	#391	C₂²×C₈₉	1	2	yes	—
509	#391	C₂²×C₈₉	1	2	yes	—
510	#389	C₂²×C₈₉	1	1	yes	characteristic
511	#389	C₂²×C₈₉	1	1	yes	characteristic
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	2	yes	—
517	#389	C₂²×C₈₉	1	1	yes	characteristic
518	#389	C₂²×C₈₉	1	1	yes	characteristic
519	#389	C₂²×C₈₉	1	1	yes	characteristic
520	#389	C₂²×C₈₉	1	2	yes	—
521	#389	C₂²×C₈₉	1	2	yes	—
522	#388	C₂²×C₈₉	1	2	yes	—
523	#388	C₂²×C₈₉	1	2	yes	—
524	#388	C₂²×C₈₉	1	1	yes	characteristic
525	#388	C₂²×C₈₉	1	1	yes	characteristic
526	#388	C₂²×C₈₉	1	1	yes	characteristic
527	#388	C₂²×C₈₉	1	1	yes	characteristic
528	#387	C₂²×C₈₉	1	2	yes	—
529	#387	C₂²×C₈₉	1	2	yes	—
530	#387	C₂²×C₈₉	1	2	yes	—
531	#387	C₂²×C₈₉	1	2	yes	—
532	#387	C₂²×C₈₉	1	2	yes	—
533	#387	C₂²×C₈₉	1	2	yes	—
534	#387	C₂²×C₈₉	1	2	yes	—
535	#387	C₂²×C₈₉	1	1	yes	characteristic
536	#387	C₂²×C₈₉	1	2	yes	—
537	#387	C₂²×C₈₉	1	2	yes	—
538	#387	C₂²×C₈₉	1	2	yes	—
539	#387	C₂²×C₈₉	1	2	yes	—
540	#387	C₂²×C₈₉	1	1	yes	characteristic
541	#387	C₂²×C₈₉	1	2	yes	—
542	#387	C₂²×C₈₉	1	1	yes	characteristic
543	#387	C₂²×C₈₉	1	1	yes	characteristic
544	#385	C₂²×C₈₉	1	2	yes	—
545	#385	C₂²×C₈₉	1	2	yes	—
546	#384	C₂²×C₈₉	1	1	yes	characteristic
547	#384	C₂²×C₈₉	1	1	yes	characteristic
548	#382	C₂²×C₈₉	1	1	yes	characteristic
549	#382	C₂²×C₈₉	1	1	yes	characteristic
550	#382	C₂²×C₈₉	1	1	yes	characteristic
551	#382	C₂²×C₈₉	1	2	yes	—
552	#382	C₂²×C₈₉	1	1	yes	characteristic
553	#380	C₂²×C₈₉	1	1	yes	characteristic
554	#380	C₂²×C₈₉	1	1	yes	characteristic
555	#380	C₂²×C₈₉	1	2	yes	—
556	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
557	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
558	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
559	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
560	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
561	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
562	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
563	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
564	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
565	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
566	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
567	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
568	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
569	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
570	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
571	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
572	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
573	#376	C₂²×C₈₉	1	1	yes	characteristic
574	C₄³	C₂²×C₈₉	1	1	yes	characteristic
575	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
576	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
577	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
578	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
579	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
580	C₄⋊Q₈	—	2	4	no	—
581	C₄⋊Q₈	—	2	4	no	—
582	C₄⋊Q₈	—	2	4	no	—
583	C₄⋊Q₈	—	4	4	no	—
584	#125	—	2	4	no	—
585	C₂²⋊Q₈	—	4	4	no	—
586	C₄×Q₈	—	4	4	no	—
587	#117	—	2	4	no	—
588	#117	Q₈×C₈₉	1	8	yes	complemented
589	C₂×C₄⋊C₄	—	2	4	no	—
590	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
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	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
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	1	yes	characteristic
622	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
625	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
627	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
628	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
631	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
632	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
633	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
634	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
637	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
638	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
639	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
640	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
641	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
644	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
645	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
646	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
648	#95	C₂³×C₈₉	1	1	yes	characteristic
649	#95	C₂³×C₈₉	1	1	yes	characteristic
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	2	yes	—
654	#95	C₂³×C₈₉	1	2	yes	—
655	#95	C₂³×C₈₉	1	2	yes	—
656	#95	C₂³×C₈₉	1	1	yes	characteristic
657	#95	C₂³×C₈₉	1	1	yes	characteristic
658	#95	C₂³×C₈₉	1	1	yes	characteristic
659	#95	C₂³×C₈₉	1	1	yes	characteristic
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	1	yes	characteristic
666	#95	C₂³×C₈₉	1	1	yes	characteristic
667	#95	C₂³×C₈₉	1	2	yes	—
668	#95	C₂³×C₈₉	1	2	yes	—
669	#95	C₂³×C₈₉	1	1	yes	characteristic
670	#95	C₂³×C₈₉	1	1	yes	characteristic
671	#95	C₂³×C₈₉	1	2	yes	—
672	#95	C₂³×C₈₉	1	2	yes	—
673	#95	C₂³×C₈₉	1	2	yes	—
674	#95	C₂³×C₈₉	1	2	yes	—
675	#95	C₂³×C₈₉	1	2	yes	—
676	#95	C₂³×C₈₉	1	2	yes	—
677	#95	C₂³×C₈₉	1	2	yes	—
678	#95	C₂³×C₈₉	1	2	yes	—
679	#95	C₂³×C₈₉	1	2	yes	—
680	#95	C₂³×C₈₉	1	2	yes	—
681	#95	C₂³×C₈₉	1	2	yes	—
682	#95	C₂³×C₈₉	1	2	yes	—
683	#95	C₂³×C₈₉	1	2	yes	—
684	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
685	C₂×Q₈	—	2	4	no	—
686	C₂×Q₈	—	2	4	no	—
687	C₂×Q₈	—	2	4	no	—
688	C₂×Q₈	—	2	4	no	—
689	C₂×Q₈	—	4	2	no	—
690	C₂×Q₈	—	4	2	no	—
691	C₂×Q₈	—	4	2	no	—
692	C₂×Q₈	—	4	2	no	—
693	C₂×Q₈	—	4	2	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	4	no	—
697	C₂²×C₄	—	4	2	no	—
698	C₂²×C₄	—	4	2	no	—
699	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
700	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
702	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
704	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	4	no	—
726	C₄⋊C₄	—	2	4	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₄⋊C₄	—	4	2	no	—
743	C₄⋊C₄	—	4	2	no	—
744	C₄⋊C₄	—	4	1	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₄⋊C₄	—	4	1	no	—
747	C₄⋊C₄	—	4	2	no	—
748	C₄⋊C₄	—	4	2	no	—
749	C₄⋊C₄	—	4	2	no	—
750	C₄⋊C₄	C₂×Q₈×C₈₉	1	4	yes	—
751	C₄⋊C₄	C₂×Q₈×C₈₉	1	4	yes	—
752	C₄⋊C₄	#41×C₈₉	1	4	yes	—
753	C₄⋊C₄	#41×C₈₉	1	4	yes	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	4	2	no	—
758	C₂²⋊C₄	—	4	1	no	—
759	C₂²⋊C₄	—	4	2	no	—
760	C₂²⋊C₄	—	4	1	no	—
761	C₂²⋊C₄	C₂×Q₈×C₈₉	1	4	yes	—
762	C₂²⋊C₄	C₂×Q₈×C₈₉	1	4	yes	—
763	C₄²	—	2	4	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	2	no	—
766	C₄²	—	2	2	no	—
767	C₄²	—	2	2	no	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	4	2	no	—
771	C₄²	—	4	2	no	—
772	C₄²	—	4	2	no	—
773	C₄²	—	4	1	no	—
774	C₄²	—	4	2	no	—
775	C₄²	—	4	1	no	—
776	C₄²	—	4	2	no	—
777	C₄²	—	4	2	no	—
778	C₄²	C₂×Q₈×C₈₉	1	4	yes	—
779	C₄²	C₂×Q₈×C₈₉	1	4	yes	—
780	C₂³	—	2	1	no	—
781	C₂³	—	2	1	no	—
782	C₂³	—	2	1	no	—
783	C₂³	—	2	1	no	—
784	C₂³	—	2	1	no	—
785	C₂³	—	2	1	no	—
786	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
787	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
788	Q₈	—	4	8	no	—
789	Q₈	—	8	4	no	—
790	Q₈	—	8	4	no	—
791	C₂×C₄	—	2	1	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	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	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	2	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	8	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	2	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	1	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	8	4	no	—
847	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
848	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
849	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
850	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
851	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
852	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
853	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
854	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
855	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
856	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
857	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
858	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
859	C₂²	—	2	2	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	1	no	—
866	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
867	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
868	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
869	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
870	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
871	C₂²	#585×C₈₉	1	1	yes	characteristic
872	C₂²	#585×C₈₉	1	1	yes	characteristic
873	C₄	—	2	2	no	—
874	C₄	—	2	2	no	—
875	C₄	—	2	2	no	—
876	C₄	—	2	2	no	—
877	C₄	—	2	2	no	—
878	C₄	—	2	4	no	—
879	C₄	—	2	2	no	—
880	C₄	—	2	4	no	—
881	C₄	—	2	2	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	1	no	—
884	C₄	—	4	2	no	—
885	C₄	—	4	2	no	—
886	C₄	—	4	1	no	—
887	C₄	—	4	2	no	—
888	C₄	—	4	1	no	—
889	C₄	—	4	2	no	—
890	C₄	—	4	1	no	—
891	C₄	—	4	1	no	—
892	C₄	—	4	1	no	—
893	C₄	—	4	2	no	—
894	C₄	#533×C₈₉	1	4	yes	—
895	C₂	—	4	2	no	—
896	C₂	C₂×#533×C₈₉	1	1	yes	characteristic
897	C₂	C₈₉×#3503	1	1	yes	characteristic
898	C₂	C₈₉×#3504	1	1	yes	characteristic
899	C₂	C₈₉×#3513	1	1	yes	characteristic
900	C₂	C₈₉×#3514	1	1	yes	characteristic
901	C₂	C₈₉×#3516	1	1	yes	characteristic
902	C₂	C₈₉×#3518	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂⁴×C₈₉	C₂⁴
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×#2588	C₂	semidirect
3. C₈₉×#2586	C₂	semidirect
5. C₈₉×#2571	C₂	semidirect
6. C₈₉×#2570	C₂	semidirect
7. C₈₉×#2551	C₂	semidirect
8. C₈₉×#2550	C₂	semidirect
9. C₈₉×#2520	C₂	semidirect
12. C₈₉×#2446	C₂	semidirect
17. C₈₉×#2331	C₂	semidirect
18. C₈₉×#2331	C₂	semidirect
20. C₄×C₄⋊Q₈×C₈₉	C₂	semidirect
21. C₄×#125×C₈₉	C₂	semidirect
136. #117×C₈₉	Q₈	semidirect
443. #35577	C₈₉	direct (N × H)
452. #2588	C₂×C₈₉	semidirect
454. #2586	C₂×C₈₉	semidirect
456. #2571	C₂×C₈₉	semidirect
457. #2570	C₂×C₈₉	semidirect
458. #2551	C₂×C₈₉	semidirect
459. #2550	C₂×C₈₉	semidirect
460. #2520	C₂×C₈₉	semidirect
463. #2446	C₂×C₈₉	semidirect
468. #2331	C₂×C₈₉	semidirect
469. #2331	C₂×C₈₉	semidirect
471. C₄×C₄⋊Q₈	C₂×C₈₉	semidirect
472. C₄×#125	C₂×C₈₉	semidirect
475. C₈₉	#35577	direct (N × H)
588. #117	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×#2588	2
C₈₉×#2587	2
C₈₉×#2586	2
C₈₉×#2574	2
C₈₉×#2571	2
C₈₉×#2570	2
C₈₉×#2551	2
C₈₉×#2550	2
C₈₉×#2520	2
C₈₉×#2492	2
C₈₉×#2465	2
C₈₉×#2446	2
C₈₉×#2442	2
C₈₉×#2440	2
C₈₉×#2439	2
C₈₉×#2331	2
C₈₉×#2314	2
C₄×C₄⋊Q₈×C₈₉	2
C₄×#125×C₈₉	2
C₈₉×#2298	2
C₈₉×#2274	2
#35577	89

Subgroups — C89×#35577 #36413425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35577 #36413425