Subgroups — C₈₉×#35580 #36413428

Order 22784.

1772 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2607	C₂	1	2	yes	maximal, complemented
2	C₈₉×#2589	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2580	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#2567	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2556	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2550	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2549	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2542	C₂	1	1	yes	maximal, characteristic
9	C₈₉×#2507	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2506	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2465	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2454	C₂	1	1	yes	maximal, characteristic
13	C₈₉×#2452	C₂	1	1	yes	maximal, characteristic
14	C₈₉×#2441	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2438	C₂	1	2	yes	maximal, complemented
16	C₈₉×#2423	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2331	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#2330	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2319	C₂	1	1	yes	maximal, characteristic
20	C₄×C₄⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#2295	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₉×#2293	C₂	1	1	yes	maximal, characteristic
23	C₈₉×#2275	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×#125×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#125×C₈₉	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#117×C₈₉	C₂²	1	2	yes	—
37	#400×C₈₉	C₂²	1	2	yes	—
38	#399×C₈₉	C₂²	1	2	yes	—
39	#399×C₈₉	C₂²	1	2	yes	—
40	#399×C₈₉	C₂²	1	2	yes	—
41	#399×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	#398×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	#395×C₈₉	C₂²	1	2	yes	—
50	#395×C₈₉	C₂²	1	2	yes	—
51	#393×C₈₉	C₂²	1	2	yes	—
52	#393×C₈₉	C₂²	1	2	yes	—
53	#391×C₈₉	C₂²	1	2	yes	—
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	2	yes	—
58	#391×C₈₉	C₂²	1	2	yes	—
59	#391×C₈₉	C₂²	1	2	yes	—
60	#390×C₈₉	C₂²	1	1	yes	characteristic
61	#390×C₈₉	C₂²	1	1	yes	characteristic
62	#390×C₈₉	C₂²	1	1	yes	characteristic
63	#390×C₈₉	C₂²	1	1	yes	characteristic
64	#389×C₈₉	C₂²	1	1	yes	characteristic
65	#389×C₈₉	C₂²	1	2	yes	—
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	2	yes	—
70	#389×C₈₉	C₂²	1	1	yes	characteristic
71	#389×C₈₉	C₂²	1	1	yes	characteristic
72	#389×C₈₉	C₂²	1	2	yes	—
73	#389×C₈₉	C₂²	1	1	yes	characteristic
74	#389×C₈₉	C₂²	1	1	yes	characteristic
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	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	#387×C₈₉	C₂²	1	1	yes	characteristic
86	#387×C₈₉	C₂²	1	1	yes	characteristic
87	#387×C₈₉	C₂²	1	1	yes	characteristic
88	#387×C₈₉	C₂²	1	1	yes	characteristic
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	#385×C₈₉	C₂²	1	2	yes	—
96	#385×C₈₉	C₂²	1	2	yes	—
97	#385×C₈₉	C₂²	1	2	yes	—
98	#385×C₈₉	C₂²	1	2	yes	—
99	#384×C₈₉	C₂²	1	1	yes	characteristic
100	#384×C₈₉	C₂²	1	2	yes	—
101	#384×C₈₉	C₂²	1	1	yes	characteristic
102	#382×C₈₉	C₂²	1	1	yes	characteristic
103	#381×C₈₉	C₂²	1	2	yes	—
104	#380×C₈₉	C₂²	1	2	yes	—
105	#380×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	2	yes	—
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	1	yes	characteristic
114	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
119	#376×C₈₉	C₂²	1	1	yes	characteristic
120	#376×C₈₉	C₂²	1	1	yes	characteristic
121	C₂×#95×C₈₉	C₂²	1	2	yes	—
122	C₄³×C₈₉	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
125	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
126	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
128	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
129	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
130	C₄⋊Q₈×C₈₉	—	2	4	no	—
131	C₄⋊Q₈×C₈₉	—	2	4	no	—
132	#125×C₈₉	—	2	4	no	—
133	#125×C₈₉	—	4	4	no	—
134	C₂²⋊Q₈×C₈₉	—	4	4	no	—
135	C₂²⋊Q₈×C₈₉	—	4	4	no	—
136	C₂²⋊Q₈×C₈₉	—	4	4	no	—
137	C₄×Q₈×C₈₉	—	2	4	no	—
138	C₄×Q₈×C₈₉	—	4	4	no	—
139	C₄×D₄×C₈₉	—	2	4	no	—
140	C₄×D₄×C₈₉	—	2	4	no	—
141	C₄×D₄×C₈₉	Q₈	1	8	yes	complemented
142	#117×C₈₉	—	4	4	no	—
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	1	yes	characteristic
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	1	yes	characteristic
153	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₈₉	C₂³	1	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	1	yes	characteristic
160	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
173	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
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×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
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	1	yes	characteristic
192	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
198	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
199	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
200	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
201	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
202	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
204	#95×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
209	#95×C₈₉	C₂³	1	1	yes	characteristic
210	#95×C₈₉	C₂³	1	1	yes	characteristic
211	#95×C₈₉	C₂³	1	1	yes	characteristic
212	#95×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
223	#95×C₈₉	C₂³	1	2	yes	—
224	#95×C₈₉	C₂³	1	1	yes	characteristic
225	#95×C₈₉	C₂³	1	1	yes	characteristic
226	#95×C₈₉	C₂³	1	1	yes	characteristic
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	#95×C₈₉	C₂³	1	2	yes	—
235	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
236	C₂×Q₈×C₈₉	—	2	2	no	—
237	C₂×Q₈×C₈₉	—	2	4	no	—
238	C₂×Q₈×C₈₉	—	2	4	no	—
239	C₂×Q₈×C₈₉	—	2	4	no	—
240	C₂×Q₈×C₈₉	—	2	2	no	—
241	C₂×Q₈×C₈₉	—	4	1	no	—
242	C₂×Q₈×C₈₉	—	4	2	no	—
243	C₂×Q₈×C₈₉	—	4	2	no	—
244	C₂×Q₈×C₈₉	—	4	2	no	—
245	C₂×D₄×C₈₉	—	2	2	no	—
246	C₂×D₄×C₈₉	—	2	2	no	—
247	C₂×D₄×C₈₉	C₂×Q₈	1	4	yes	—
248	C₂²×C₄×C₈₉	—	2	4	no	—
249	C₂²×C₄×C₈₉	—	2	4	no	—
250	C₂²×C₄×C₈₉	—	4	2	no	—
251	C₂²×C₄×C₈₉	—	4	2	no	—
252	C₂²×C₄×C₈₉	—	4	2	no	—
253	C₂²×C₄×C₈₉	—	4	2	no	—
254	C₂²×C₄×C₈₉	—	4	2	no	—
255	C₂²×C₄×C₈₉	—	4	2	no	—
256	C₂²×C₄×C₈₉	C₂×Q₈	1	8	yes	—
257	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
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	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	2	yes	—
275	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	2	no	—
283	C₄⋊C₄×C₈₉	—	2	4	no	—
284	C₄⋊C₄×C₈₉	—	2	4	no	—
285	C₄⋊C₄×C₈₉	—	2	2	no	—
286	C₄⋊C₄×C₈₉	—	2	4	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	—	2	2	no	—
291	C₄⋊C₄×C₈₉	—	2	4	no	—
292	C₄⋊C₄×C₈₉	—	2	4	no	—
293	C₄⋊C₄×C₈₉	—	2	2	no	—
294	C₄⋊C₄×C₈₉	—	2	2	no	—
295	C₄⋊C₄×C₈₉	—	2	2	no	—
296	C₄⋊C₄×C₈₉	—	2	4	no	—
297	C₄⋊C₄×C₈₉	—	2	2	no	—
298	C₄⋊C₄×C₈₉	—	2	2	no	—
299	C₄⋊C₄×C₈₉	—	4	2	no	—
300	C₄⋊C₄×C₈₉	—	4	1	no	—
301	C₄⋊C₄×C₈₉	—	4	2	no	—
302	C₄⋊C₄×C₈₉	—	4	2	no	—
303	C₄⋊C₄×C₈₉	—	4	2	no	—
304	C₄⋊C₄×C₈₉	—	4	2	no	—
305	C₄⋊C₄×C₈₉	—	4	2	no	—
306	C₄⋊C₄×C₈₉	—	4	2	no	—
307	C₄⋊C₄×C₈₉	—	4	2	no	—
308	C₄⋊C₄×C₈₉	—	4	2	no	—
309	C₄⋊C₄×C₈₉	—	4	2	no	—
310	C₄⋊C₄×C₈₉	—	4	2	no	—
311	C₄⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
312	C₄⋊C₄×C₈₉	#41	1	4	yes	—
313	C₂²⋊C₄×C₈₉	—	2	4	no	—
314	C₂²⋊C₄×C₈₉	—	2	4	no	—
315	C₂²⋊C₄×C₈₉	—	2	4	no	—
316	C₂²⋊C₄×C₈₉	—	2	4	no	—
317	C₂²⋊C₄×C₈₉	—	2	4	no	—
318	C₂²⋊C₄×C₈₉	—	4	2	no	—
319	C₂²⋊C₄×C₈₉	—	4	2	no	—
320	C₂²⋊C₄×C₈₉	—	4	2	no	—
321	C₂²⋊C₄×C₈₉	—	4	2	no	—
322	C₂²⋊C₄×C₈₉	—	4	2	no	—
323	C₂²⋊C₄×C₈₉	C₂×Q₈	1	8	yes	—
324	C₄²×C₈₉	—	2	2	no	—
325	C₄²×C₈₉	—	2	2	no	—
326	C₄²×C₈₉	—	2	2	no	—
327	C₄²×C₈₉	—	2	2	no	—
328	C₄²×C₈₉	—	2	2	no	—
329	C₄²×C₈₉	—	2	2	no	—
330	C₄²×C₈₉	—	2	2	no	—
331	C₄²×C₈₉	—	2	2	no	—
332	C₄²×C₈₉	—	4	2	no	—
333	C₄²×C₈₉	—	4	1	no	—
334	C₄²×C₈₉	—	4	2	no	—
335	C₄²×C₈₉	—	4	2	no	—
336	C₄²×C₈₉	—	4	2	no	—
337	C₄²×C₈₉	—	4	2	no	—
338	C₄²×C₈₉	C₂×Q₈	1	4	yes	—
339	C₄²×C₈₉	#41	1	4	yes	—
340	C₂³×C₈₉	—	2	2	no	—
341	C₂³×C₈₉	—	2	2	no	—
342	C₂³×C₈₉	—	2	2	no	—
343	C₂³×C₈₉	—	2	2	no	—
344	C₂³×C₈₉	—	2	2	no	—
345	C₂³×C₈₉	—	2	2	no	—
346	C₂³×C₈₉	C₂²×Q₈	1	4	yes	—
347	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
348	Q₈×C₈₉	—	4	4	no	—
349	Q₈×C₈₉	—	4	8	no	—
350	Q₈×C₈₉	—	8	4	no	—
351	D₄×C₈₉	—	2	8	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	1	no	—
357	C₂×C₄×C₈₉	—	2	2	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	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	1	no	—
374	C₂×C₄×C₈₉	—	2	1	no	—
375	C₂×C₄×C₈₉	—	2	1	no	—
376	C₂×C₄×C₈₉	—	2	1	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	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	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	2	no	—
389	C₂×C₄×C₈₉	—	2	2	no	—
390	C₂×C₄×C₈₉	—	2	2	no	—
391	C₂×C₄×C₈₉	—	2	2	no	—
392	C₂×C₄×C₈₉	—	2	1	no	—
393	C₂×C₄×C₈₉	—	2	1	no	—
394	C₂×C₄×C₈₉	—	2	1	no	—
395	C₂×C₄×C₈₉	—	2	2	no	—
396	C₂×C₄×C₈₉	—	2	1	no	—
397	C₂×C₄×C₈₉	—	2	1	no	—
398	C₂×C₄×C₈₉	—	2	2	no	—
399	C₂×C₄×C₈₉	—	2	1	no	—
400	C₂×C₄×C₈₉	—	2	1	no	—
401	C₂×C₄×C₈₉	—	2	1	no	—
402	C₂×C₄×C₈₉	—	2	1	no	—
403	C₂×C₄×C₈₉	—	2	2	no	—
404	C₂×C₄×C₈₉	—	2	1	no	—
405	C₂×C₄×C₈₉	—	2	1	no	—
406	C₂×C₄×C₈₉	—	4	8	no	—
407	C₂×C₄×C₈₉	—	8	4	no	—
408	C₂×C₄×C₈₉	—	8	4	no	—
409	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
410	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
411	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
412	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
413	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
414	C₂×C₄×C₈₉	C₂×#41	1	2	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	H(5,𝔽₂)	1	2	yes	—
419	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
420	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
421	C₂²×C₈₉	—	2	4	no	—
422	C₂²×C₈₉	—	2	4	no	—
423	C₂²×C₈₉	—	2	4	no	—
424	C₂²×C₈₉	—	4	2	no	—
425	C₂²×C₈₉	—	4	2	no	—
426	C₂²×C₈₉	—	4	2	no	—
427	C₂²×C₈₉	—	4	2	no	—
428	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
429	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
430	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
431	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
432	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
433	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
434	C₂²×C₈₉	#585	1	1	yes	characteristic
435	C₄×C₈₉	—	2	2	no	—
436	C₄×C₈₉	—	2	2	no	—
437	C₄×C₈₉	—	2	2	no	—
438	C₄×C₈₉	—	2	4	no	—
439	C₄×C₈₉	—	2	2	no	—
440	C₄×C₈₉	—	2	2	no	—
441	C₄×C₈₉	—	2	4	no	—
442	C₄×C₈₉	—	2	2	no	—
443	C₄×C₈₉	—	2	2	no	—
444	C₄×C₈₉	—	4	1	no	—
445	C₄×C₈₉	—	4	1	no	—
446	C₄×C₈₉	—	4	1	no	—
447	C₄×C₈₉	—	4	2	no	—
448	C₄×C₈₉	—	4	2	no	—
449	C₄×C₈₉	—	4	2	no	—
450	C₄×C₈₉	—	4	1	no	—
451	C₄×C₈₉	—	4	1	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	#533	1	4	yes	—
457	#35580	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
458	C₂×C₈₉	—	4	4	no	—
459	C₂×C₈₉	C₂×#533	1	1	yes	characteristic
460	C₂×C₈₉	#3495	1	1	yes	characteristic
461	C₂×C₈₉	#3501	1	1	yes	characteristic
462	C₂×C₈₉	#3503	1	1	yes	characteristic
463	C₂×C₈₉	#3508	1	1	yes	characteristic
464	C₂×C₈₉	#3513	1	1	yes	characteristic
465	C₂×C₈₉	#3522	1	1	yes	characteristic
466	#2607	C₂×C₈₉	1	2	yes	complemented
467	#2589	C₂×C₈₉	1	2	yes	complemented
468	#2580	C₂×C₈₉	1	1	yes	characteristic
469	#2567	C₂×C₈₉	1	1	yes	characteristic, complemented
470	#2556	C₂×C₈₉	1	2	yes	complemented
471	#2550	C₂×C₈₉	1	1	yes	characteristic, complemented
472	#2549	C₂×C₈₉	1	2	yes	complemented
473	#2542	C₂×C₈₉	1	1	yes	characteristic
474	#2507	C₂×C₈₉	1	1	yes	characteristic, complemented
475	#2506	C₂×C₈₉	1	1	yes	characteristic, complemented
476	#2465	C₂×C₈₉	1	2	yes	complemented
477	#2454	C₂×C₈₉	1	1	yes	characteristic
478	#2452	C₂×C₈₉	1	1	yes	characteristic
479	#2441	C₂×C₈₉	1	2	yes	complemented
480	#2438	C₂×C₈₉	1	2	yes	complemented
481	#2423	C₂×C₈₉	1	2	yes	complemented
482	#2331	C₂×C₈₉	1	1	yes	characteristic, complemented
483	#2330	C₂×C₈₉	1	1	yes	characteristic, complemented
484	#2319	C₂×C₈₉	1	1	yes	characteristic
485	C₄×C₄⋊Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
486	#2295	C₂×C₈₉	1	1	yes	characteristic, complemented
487	#2293	C₂×C₈₉	1	1	yes	characteristic
488	#2275	C₂×C₈₉	1	1	yes	characteristic
489	C₈₉	#35580	1	1	yes	characteristic, direct product factor, Sylow
490	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
491	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
492	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
493	C₂×#125	C₂²×C₈₉	1	2	yes	—
494	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
495	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
496	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
497	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
498	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
499	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
500	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
501	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
502	C₂×#117	C₂²×C₈₉	1	2	yes	—
503	#400	C₂²×C₈₉	1	2	yes	—
504	#399	C₂²×C₈₉	1	2	yes	—
505	#399	C₂²×C₈₉	1	2	yes	—
506	#399	C₂²×C₈₉	1	2	yes	—
507	#399	C₂²×C₈₉	1	2	yes	—
508	#398	C₂²×C₈₉	1	2	yes	—
509	#398	C₂²×C₈₉	1	2	yes	—
510	#398	C₂²×C₈₉	1	2	yes	—
511	#398	C₂²×C₈₉	1	2	yes	—
512	#396	C₂²×C₈₉	1	2	yes	—
513	#396	C₂²×C₈₉	1	2	yes	—
514	#395	C₂²×C₈₉	1	2	yes	—
515	#395	C₂²×C₈₉	1	2	yes	—
516	#395	C₂²×C₈₉	1	2	yes	—
517	#393	C₂²×C₈₉	1	2	yes	—
518	#393	C₂²×C₈₉	1	2	yes	—
519	#391	C₂²×C₈₉	1	2	yes	—
520	#391	C₂²×C₈₉	1	2	yes	—
521	#391	C₂²×C₈₉	1	2	yes	—
522	#391	C₂²×C₈₉	1	2	yes	—
523	#391	C₂²×C₈₉	1	1	yes	characteristic
524	#391	C₂²×C₈₉	1	1	yes	characteristic
525	#391	C₂²×C₈₉	1	2	yes	—
526	#390	C₂²×C₈₉	1	1	yes	characteristic
527	#390	C₂²×C₈₉	1	1	yes	characteristic
528	#390	C₂²×C₈₉	1	1	yes	characteristic
529	#390	C₂²×C₈₉	1	1	yes	characteristic
530	#389	C₂²×C₈₉	1	1	yes	characteristic
531	#389	C₂²×C₈₉	1	1	yes	characteristic
532	#389	C₂²×C₈₉	1	2	yes	—
533	#389	C₂²×C₈₉	1	1	yes	characteristic
534	#389	C₂²×C₈₉	1	1	yes	characteristic
535	#389	C₂²×C₈₉	1	1	yes	characteristic
536	#389	C₂²×C₈₉	1	1	yes	characteristic
537	#389	C₂²×C₈₉	1	1	yes	characteristic
538	#389	C₂²×C₈₉	1	2	yes	—
539	#389	C₂²×C₈₉	1	2	yes	—
540	#389	C₂²×C₈₉	1	1	yes	characteristic
541	#389	C₂²×C₈₉	1	1	yes	characteristic
542	#389	C₂²×C₈₉	1	2	yes	—
543	#389	C₂²×C₈₉	1	2	yes	—
544	#389	C₂²×C₈₉	1	1	yes	characteristic
545	#389	C₂²×C₈₉	1	1	yes	characteristic
546	#389	C₂²×C₈₉	1	1	yes	characteristic
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	#387	C₂²×C₈₉	1	2	yes	—
552	#387	C₂²×C₈₉	1	2	yes	—
553	#387	C₂²×C₈₉	1	2	yes	—
554	#387	C₂²×C₈₉	1	2	yes	—
555	#387	C₂²×C₈₉	1	2	yes	—
556	#387	C₂²×C₈₉	1	2	yes	—
557	#387	C₂²×C₈₉	1	1	yes	characteristic
558	#387	C₂²×C₈₉	1	1	yes	characteristic
559	#387	C₂²×C₈₉	1	1	yes	characteristic
560	#387	C₂²×C₈₉	1	1	yes	characteristic
561	#385	C₂²×C₈₉	1	2	yes	—
562	#385	C₂²×C₈₉	1	2	yes	—
563	#385	C₂²×C₈₉	1	2	yes	—
564	#385	C₂²×C₈₉	1	2	yes	—
565	#384	C₂²×C₈₉	1	1	yes	characteristic
566	#384	C₂²×C₈₉	1	2	yes	—
567	#384	C₂²×C₈₉	1	1	yes	characteristic
568	#382	C₂²×C₈₉	1	1	yes	characteristic
569	#381	C₂²×C₈₉	1	2	yes	—
570	#380	C₂²×C₈₉	1	2	yes	—
571	#380	C₂²×C₈₉	1	2	yes	—
572	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
573	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
574	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
575	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
576	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
577	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
578	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
579	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
580	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
581	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
582	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
583	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
584	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
585	#376	C₂²×C₈₉	1	1	yes	characteristic
586	#376	C₂²×C₈₉	1	1	yes	characteristic
587	C₂×#95	C₂²×C₈₉	1	2	yes	—
588	C₄³	C₂²×C₈₉	1	1	yes	characteristic
589	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
590	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
591	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
592	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
593	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
594	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
595	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
596	C₄⋊Q₈	—	2	4	no	—
597	C₄⋊Q₈	—	2	4	no	—
598	#125	—	2	4	no	—
599	#125	—	4	4	no	—
600	C₂²⋊Q₈	—	4	4	no	—
601	C₂²⋊Q₈	—	4	4	no	—
602	C₂²⋊Q₈	—	4	4	no	—
603	C₄×Q₈	—	2	4	no	—
604	C₄×Q₈	—	4	4	no	—
605	C₄×D₄	—	2	4	no	—
606	C₄×D₄	—	2	4	no	—
607	C₄×D₄	Q₈×C₈₉	1	8	yes	complemented
608	#117	—	4	4	no	—
609	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
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×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
642	C₂×C₄⋊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	2	yes	—
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	2	yes	—
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×C₄²	C₂³×C₈₉	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
663	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
664	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
665	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
666	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
667	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
668	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
669	C₂×C₄²	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	1	yes	characteristic
675	#95	C₂³×C₈₉	1	1	yes	characteristic
676	#95	C₂³×C₈₉	1	1	yes	characteristic
677	#95	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	2	yes	—
682	#95	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
687	#95	C₂³×C₈₉	1	2	yes	—
688	#95	C₂³×C₈₉	1	1	yes	characteristic
689	#95	C₂³×C₈₉	1	2	yes	—
690	#95	C₂³×C₈₉	1	1	yes	characteristic
691	#95	C₂³×C₈₉	1	1	yes	characteristic
692	#95	C₂³×C₈₉	1	1	yes	characteristic
693	#95	C₂³×C₈₉	1	2	yes	—
694	#95	C₂³×C₈₉	1	2	yes	—
695	#95	C₂³×C₈₉	1	2	yes	—
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	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
702	C₂×Q₈	—	2	2	no	—
703	C₂×Q₈	—	2	4	no	—
704	C₂×Q₈	—	2	4	no	—
705	C₂×Q₈	—	2	4	no	—
706	C₂×Q₈	—	2	2	no	—
707	C₂×Q₈	—	4	1	no	—
708	C₂×Q₈	—	4	2	no	—
709	C₂×Q₈	—	4	2	no	—
710	C₂×Q₈	—	4	2	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	C₂×Q₈×C₈₉	1	4	yes	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	4	2	no	—
717	C₂²×C₄	—	4	2	no	—
718	C₂²×C₄	—	4	2	no	—
719	C₂²×C₄	—	4	2	no	—
720	C₂²×C₄	—	4	2	no	—
721	C₂²×C₄	—	4	2	no	—
722	C₂²×C₄	C₂×Q₈×C₈₉	1	8	yes	—
723	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
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	1	yes	characteristic
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	4	no	—
758	C₄⋊C₄	—	2	4	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	4	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	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	2	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₄⋊C₄	—	4	2	no	—
774	C₄⋊C₄	—	4	2	no	—
775	C₄⋊C₄	—	4	2	no	—
776	C₄⋊C₄	—	4	1	no	—
777	C₄⋊C₄	C₂×Q₈×C₈₉	1	4	yes	—
778	C₄⋊C₄	#41×C₈₉	1	4	yes	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	4	no	—
784	C₂²⋊C₄	—	4	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	C₂×Q₈×C₈₉	1	8	yes	—
790	C₄²	—	2	2	no	—
791	C₄²	—	2	2	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	2	no	—
797	C₄²	—	2	2	no	—
798	C₄²	—	4	2	no	—
799	C₄²	—	4	2	no	—
800	C₄²	—	4	2	no	—
801	C₄²	—	4	2	no	—
802	C₄²	—	4	2	no	—
803	C₄²	—	4	1	no	—
804	C₄²	C₂×Q₈×C₈₉	1	4	yes	—
805	C₄²	#41×C₈₉	1	4	yes	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	2	2	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	2	no	—
812	C₂³	C₂²×Q₈×C₈₉	1	4	yes	—
813	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
814	Q₈	—	4	4	no	—
815	Q₈	—	4	8	no	—
816	Q₈	—	8	4	no	—
817	D₄	—	2	8	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	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	1	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	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	1	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	4	8	no	—
873	C₂×C₄	—	8	4	no	—
874	C₂×C₄	—	8	4	no	—
875	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
876	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
877	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
878	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
879	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
880	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
881	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
882	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
883	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
884	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
885	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
886	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
887	C₂²	—	2	4	no	—
888	C₂²	—	2	4	no	—
889	C₂²	—	2	4	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
895	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
896	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
897	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
898	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
899	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
900	C₂²	#585×C₈₉	1	1	yes	characteristic
901	C₄	—	2	2	no	—
902	C₄	—	2	2	no	—
903	C₄	—	2	2	no	—
904	C₄	—	2	4	no	—
905	C₄	—	2	2	no	—
906	C₄	—	2	2	no	—
907	C₄	—	2	4	no	—
908	C₄	—	2	2	no	—
909	C₄	—	2	2	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	2	no	—
914	C₄	—	4	1	no	—
915	C₄	—	4	1	no	—
916	C₄	—	4	1	no	—
917	C₄	—	4	2	no	—
918	C₄	—	4	1	no	—
919	C₄	—	4	1	no	—
920	C₄	—	4	1	no	—
921	C₄	—	4	2	no	—
922	C₄	#533×C₈₉	1	4	yes	—
923	C₂	—	4	4	no	—
924	C₂	C₂×#533×C₈₉	1	1	yes	characteristic
925	C₂	C₈₉×#3495	1	1	yes	characteristic
926	C₂	C₈₉×#3501	1	1	yes	characteristic
927	C₂	C₈₉×#3503	1	1	yes	characteristic
928	C₂	C₈₉×#3508	1	1	yes	characteristic
929	C₂	C₈₉×#3513	1	1	yes	characteristic
930	C₂	C₈₉×#3522	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂²×D₄×C₈₉	C₂³
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×#2607	C₂	semidirect
2. C₈₉×#2589	C₂	semidirect
4. C₈₉×#2567	C₂	semidirect
5. C₈₉×#2556	C₂	semidirect
6. C₈₉×#2550	C₂	semidirect
7. C₈₉×#2549	C₂	semidirect
9. C₈₉×#2507	C₂	semidirect
10. C₈₉×#2506	C₂	semidirect
11. C₈₉×#2465	C₂	semidirect
14. C₈₉×#2441	C₂	semidirect
15. C₈₉×#2438	C₂	semidirect
16. C₈₉×#2423	C₂	semidirect
17. C₈₉×#2331	C₂	semidirect
18. C₈₉×#2330	C₂	semidirect
20. C₄×C₄⋊Q₈×C₈₉	C₂	semidirect
21. C₈₉×#2295	C₂	semidirect
141. C₄×D₄×C₈₉	Q₈	semidirect
457. #35580	C₈₉	direct (N × H)
466. #2607	C₂×C₈₉	semidirect
467. #2589	C₂×C₈₉	semidirect
469. #2567	C₂×C₈₉	semidirect
470. #2556	C₂×C₈₉	semidirect
471. #2550	C₂×C₈₉	semidirect
472. #2549	C₂×C₈₉	semidirect
474. #2507	C₂×C₈₉	semidirect
475. #2506	C₂×C₈₉	semidirect
476. #2465	C₂×C₈₉	semidirect
479. #2441	C₂×C₈₉	semidirect
480. #2438	C₂×C₈₉	semidirect
481. #2423	C₂×C₈₉	semidirect
482. #2331	C₂×C₈₉	semidirect
483. #2330	C₂×C₈₉	semidirect
485. C₄×C₄⋊Q₈	C₂×C₈₉	semidirect
486. #2295	C₂×C₈₉	semidirect
489. C₈₉	#35580	direct (N × H)
607. C₄×D₄	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×#2607	2
C₈₉×#2589	2
C₈₉×#2580	2
C₈₉×#2567	2
C₈₉×#2556	2
C₈₉×#2550	2
C₈₉×#2549	2
C₈₉×#2542	2
C₈₉×#2507	2
C₈₉×#2506	2
C₈₉×#2465	2
C₈₉×#2454	2
C₈₉×#2452	2
C₈₉×#2441	2
C₈₉×#2438	2
C₈₉×#2423	2
C₈₉×#2331	2
C₈₉×#2330	2
C₈₉×#2319	2
C₄×C₄⋊Q₈×C₈₉	2
C₈₉×#2295	2
C₈₉×#2293	2
C₈₉×#2275	2
#35580	89

Subgroups — C89×#35580 #36413428

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35580 #36413428