Subgroups — C₈₉×#24389 #36402237

Order 22784.

1568 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#525×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#470×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#468×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#452×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#407×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2848	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2036	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2034	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2001	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1895	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1894	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1788	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
19	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
20	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
22	#525×C₈₉	—	2	4	no	—
23	#525×C₈₉	—	2	4	no	—
24	C₂×#123×C₈₉	—	2	1	no	—
25	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#120×C₈₉	—	2	1	no	—
33	C₂×C₄×D₄×C₈₉	—	2	1	no	—
34	C₂×C₄×D₄×C₈₉	—	2	1	no	—
35	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
36	#470×C₈₉	—	2	4	no	—
37	#468×C₈₉	—	2	4	no	—
38	#452×C₈₉	—	2	4	no	—
39	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
44	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
46	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
47	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
48	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
49	#407×C₈₉	—	2	4	no	—
50	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
54	#385×C₈₉	—	2	1	no	—
55	#385×C₈₉	—	2	1	no	—
56	#385×C₈₉	—	2	1	no	—
57	#380×C₈₉	C₂²	1	1	yes	characteristic
58	#380×C₈₉	C₂²	1	1	yes	characteristic
59	#380×C₈₉	C₂²	1	1	yes	characteristic
60	#379×C₈₉	—	2	1	no	—
61	#340×C₈₉	C₂²	1	1	yes	characteristic, complemented
62	#340×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	#340×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	#340×C₈₉	C₂²	1	1	yes	characteristic, complemented
65	C₂⁵×C₈₉	D₄	1	1	yes	characteristic
66	C₂×#41×C₈₉	—	2	2	no	—
67	C₂×#41×C₈₉	—	2	2	no	—
68	C₂×#41×C₈₉	—	2	2	no	—
69	C₂×#41×C₈₉	—	2	2	no	—
70	C₂×#41×C₈₉	—	4	1	no	—
71	C₂×#41×C₈₉	—	4	1	no	—
72	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
73	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₈₉	—	2	1	no	—
75	C₂²×D₄×C₈₉	—	2	1	no	—
76	C₂²×D₄×C₈₉	—	2	1	no	—
77	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₈₉	—	2	2	no	—
79	C₂³×C₄×C₈₉	—	2	1	no	—
80	C₂³×C₄×C₈₉	—	2	2	no	—
81	C₂³×C₄×C₈₉	—	2	2	no	—
82	C₂³×C₄×C₈₉	—	2	2	no	—
83	C₂³×C₄×C₈₉	—	4	1	no	—
84	C₂³×C₄×C₈₉	—	4	1	no	—
85	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
86	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
87	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
88	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
91	C₂×Q₁₆×C₈₉	—	2	2	no	—
92	C₂×Q₁₆×C₈₉	—	2	2	no	—
93	C₂×Q₁₆×C₈₉	—	4	1	no	—
94	C₂×SD₁₆×C₈₉	—	2	2	no	—
95	C₂×SD₁₆×C₈₉	—	2	2	no	—
96	C₂×SD₁₆×C₈₉	—	4	1	no	—
97	C₂×M₁₆×C₈₉	—	2	2	no	—
98	C₂×M₁₆×C₈₉	—	2	2	no	—
99	C₂×M₁₆×C₈₉	—	2	2	no	—
100	C₂×M₁₆×C₈₉	—	2	2	no	—
101	C₂×M₁₆×C₈₉	—	4	1	no	—
102	C₂×M₁₆×C₈₉	—	4	1	no	—
103	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
107	#123×C₈₉	—	2	8	no	—
108	C₂²⋊Q₈×C₈₉	—	2	2	no	—
109	C₂²⋊Q₈×C₈₉	—	2	2	no	—
110	C₂²⋊Q₈×C₈₉	—	2	2	no	—
111	C₂²⋊Q₈×C₈₉	—	2	2	no	—
112	C₂²⋊Q₈×C₈₉	—	2	2	no	—
113	C₂²⋊Q₈×C₈₉	—	2	2	no	—
114	C₂²⋊Q₈×C₈₉	—	2	2	no	—
115	C₂²⋊Q₈×C₈₉	—	4	1	no	—
116	C₂²⋊Q₈×C₈₉	—	4	1	no	—
117	C₂²⋊Q₈×C₈₉	D₄	1	4	yes	—
118	#121×C₈₉	—	2	2	no	—
119	#121×C₈₉	—	2	2	no	—
120	#121×C₈₉	—	2	2	no	—
121	#121×C₈₉	D₄	1	4	yes	—
122	#120×C₈₉	—	2	8	no	—
123	C₄×D₄×C₈₉	—	2	8	no	—
124	C₄×D₄×C₈₉	—	2	8	no	—
125	#117×C₈₉	—	2	2	no	—
126	#117×C₈₉	—	2	2	no	—
127	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
128	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
129	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
130	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
131	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
132	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
138	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
139	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
140	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
141	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
142	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
143	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
144	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
145	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
146	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
147	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
148	C₂×C₄²×C₈₉	—	2	1	no	—
149	#107×C₈₉	—	2	2	no	—
150	#106×C₈₉	—	2	2	no	—
151	#103×C₈₉	—	2	2	no	—
152	#103×C₈₉	—	2	2	no	—
153	#103×C₈₉	—	2	2	no	—
154	#103×C₈₉	—	2	2	no	—
155	#103×C₈₉	—	4	1	no	—
156	#102×C₈₉	—	2	2	no	—
157	#102×C₈₉	—	2	2	no	—
158	#102×C₈₉	—	4	1	no	—
159	C₂²⋊C₈×C₈₉	—	2	2	no	—
160	C₂²⋊C₈×C₈₉	—	2	2	no	—
161	C₂²⋊C₈×C₈₉	—	2	2	no	—
162	C₂²⋊C₈×C₈₉	D₄	1	4	yes	complemented
163	#95×C₈₉	—	2	1	no	—
164	#95×C₈₉	—	2	1	no	—
165	#95×C₈₉	—	2	1	no	—
166	C₂⁴×C₈₉	—	2	2	no	—
167	C₂⁴×C₈₉	—	2	2	no	—
168	C₂⁴×C₈₉	—	2	2	no	—
169	C₂⁴×C₈₉	—	2	1	no	—
170	C₂⁴×C₈₉	—	4	1	no	—
171	C₂⁴×C₈₉	—	4	1	no	—
172	C₂⁴×C₈₉	—	4	1	no	—
173	C₂⁴×C₈₉	—	4	1	no	—
174	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
175	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
176	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
177	#41×C₈₉	—	4	4	no	—
178	#41×C₈₉	—	4	4	no	—
179	#41×C₈₉	—	4	4	no	—
180	#41×C₈₉	—	4	4	no	—
181	C₂×Q₈×C₈₉	—	2	1	no	—
182	C₂×Q₈×C₈₉	—	2	1	no	—
183	C₂×Q₈×C₈₉	—	2	1	no	—
184	C₂×Q₈×C₈₉	—	2	1	no	—
185	C₂×Q₈×C₈₉	—	2	1	no	—
186	C₂×Q₈×C₈₉	—	2	1	no	—
187	C₂×Q₈×C₈₉	—	2	1	no	—
188	C₂×Q₈×C₈₉	—	2	1	no	—
189	C₂×Q₈×C₈₉	—	2	1	no	—
190	C₂×Q₈×C₈₉	—	2	1	no	—
191	C₂×Q₈×C₈₉	—	2	1	no	—
192	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
193	C₂×D₄×C₈₉	—	2	4	no	—
194	C₂×D₄×C₈₉	—	2	4	no	—
195	C₂×D₄×C₈₉	—	2	4	no	—
196	C₂×D₄×C₈₉	—	2	1	no	—
197	C₂×D₄×C₈₉	—	2	1	no	—
198	C₂×D₄×C₈₉	—	2	1	no	—
199	C₂×D₄×C₈₉	—	2	1	no	—
200	C₂×D₄×C₈₉	—	2	1	no	—
201	C₂×D₄×C₈₉	—	4	2	no	—
202	C₂×D₄×C₈₉	—	4	2	no	—
203	C₂×D₄×C₈₉	—	4	2	no	—
204	C₂×D₄×C₈₉	—	4	2	no	—
205	C₂×D₄×C₈₉	—	4	2	no	—
206	C₂×D₄×C₈₉	—	4	2	no	—
207	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
208	C₂²×C₄×C₈₉	—	2	1	no	—
209	C₂²×C₄×C₈₉	—	2	1	no	—
210	C₂²×C₄×C₈₉	—	2	1	no	—
211	C₂²×C₄×C₈₉	—	2	1	no	—
212	C₂²×C₄×C₈₉	—	2	1	no	—
213	C₂²×C₄×C₈₉	—	2	1	no	—
214	C₂²×C₄×C₈₉	—	2	1	no	—
215	C₂²×C₄×C₈₉	—	2	1	no	—
216	C₂²×C₄×C₈₉	—	2	4	no	—
217	C₂²×C₄×C₈₉	—	2	2	no	—
218	C₂²×C₄×C₈₉	—	2	2	no	—
219	C₂²×C₄×C₈₉	—	2	1	no	—
220	C₂²×C₄×C₈₉	—	2	1	no	—
221	C₂²×C₄×C₈₉	—	2	1	no	—
222	C₂²×C₄×C₈₉	—	2	2	no	—
223	C₂²×C₄×C₈₉	—	2	2	no	—
224	C₂²×C₄×C₈₉	—	2	2	no	—
225	C₂²×C₄×C₈₉	—	2	2	no	—
226	C₂²×C₄×C₈₉	—	2	1	no	—
227	C₂²×C₄×C₈₉	—	2	1	no	—
228	C₂²×C₄×C₈₉	—	2	1	no	—
229	C₂²×C₄×C₈₉	—	2	1	no	—
230	C₂²×C₄×C₈₉	—	2	1	no	—
231	C₂²×C₄×C₈₉	—	2	1	no	—
232	C₂²×C₄×C₈₉	—	2	1	no	—
233	C₂²×C₄×C₈₉	—	2	1	no	—
234	C₂²×C₄×C₈₉	—	2	1	no	—
235	C₂²×C₄×C₈₉	—	2	1	no	—
236	C₂²×C₄×C₈₉	—	4	1	no	—
237	C₂²×C₄×C₈₉	—	4	1	no	—
238	C₂²×C₄×C₈₉	—	4	1	no	—
239	C₂²×C₄×C₈₉	—	4	4	no	—
240	C₂²×C₄×C₈₉	—	4	4	no	—
241	C₂²×C₄×C₈₉	—	4	4	no	—
242	C₂²×C₄×C₈₉	—	4	4	no	—
243	C₂²×C₄×C₈₉	—	4	2	no	—
244	C₂²×C₄×C₈₉	—	4	2	no	—
245	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
248	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
249	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
251	C₂²×C₄×C₈₉	#41	1	2	yes	—
252	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
253	Q₁₆×C₈₉	—	4	4	no	—
254	SD₁₆×C₈₉	—	4	4	no	—
255	M₁₆×C₈₉	—	4	4	no	—
256	M₁₆×C₈₉	—	4	4	no	—
257	C₂×C₈×C₈₉	—	2	1	no	—
258	C₂×C₈×C₈₉	—	2	1	no	—
259	C₂×C₈×C₈₉	—	2	1	no	—
260	C₂×C₈×C₈₉	—	2	1	no	—
261	C₂×C₈×C₈₉	—	2	1	no	—
262	C₂×C₈×C₈₉	—	2	1	no	—
263	C₂×C₈×C₈₉	—	2	1	no	—
264	C₂×C₈×C₈₉	—	2	1	no	—
265	C₂×C₈×C₈₉	—	2	1	no	—
266	C₂×C₈×C₈₉	—	2	1	no	—
267	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
268	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
269	C₄⋊C₄×C₈₉	—	2	4	no	—
270	C₄⋊C₄×C₈₉	—	2	4	no	—
271	C₄⋊C₄×C₈₉	—	2	1	no	—
272	C₄⋊C₄×C₈₉	—	2	1	no	—
273	C₄⋊C₄×C₈₉	—	2	1	no	—
274	C₄⋊C₄×C₈₉	—	2	1	no	—
275	C₄⋊C₄×C₈₉	—	2	1	no	—
276	C₄⋊C₄×C₈₉	—	2	1	no	—
277	C₄⋊C₄×C₈₉	—	2	1	no	—
278	C₄⋊C₄×C₈₉	—	2	1	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	C₂×D₄	1	2	yes	—
283	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
284	C₂²⋊C₄×C₈₉	—	2	4	no	—
285	C₂²⋊C₄×C₈₉	—	2	4	no	—
286	C₂²⋊C₄×C₈₉	—	2	4	no	—
287	C₂²⋊C₄×C₈₉	—	2	4	no	—
288	C₂²⋊C₄×C₈₉	—	2	4	no	—
289	C₂²⋊C₄×C₈₉	—	4	2	no	—
290	C₂²⋊C₄×C₈₉	—	4	2	no	—
291	C₂²⋊C₄×C₈₉	—	4	2	no	—
292	C₂²⋊C₄×C₈₉	—	4	2	no	—
293	C₂²⋊C₄×C₈₉	—	4	2	no	—
294	C₂²⋊C₄×C₈₉	—	4	2	no	—
295	C₄²×C₈₉	—	2	4	no	—
296	C₂³×C₈₉	—	2	1	no	—
297	C₂³×C₈₉	—	2	1	no	—
298	C₂³×C₈₉	—	2	1	no	—
299	C₂³×C₈₉	—	2	1	no	—
300	C₂³×C₈₉	—	2	1	no	—
301	C₂³×C₈₉	—	2	1	no	—
302	C₂³×C₈₉	—	2	1	no	—
303	C₂³×C₈₉	—	2	1	no	—
304	C₂³×C₈₉	—	2	1	no	—
305	C₂³×C₈₉	—	2	1	no	—
306	C₂³×C₈₉	—	2	1	no	—
307	C₂³×C₈₉	—	2	1	no	—
308	C₂³×C₈₉	—	2	1	no	—
309	C₂³×C₈₉	—	2	1	no	—
310	C₂³×C₈₉	—	2	1	no	—
311	C₂³×C₈₉	—	2	1	no	—
312	C₂³×C₈₉	—	2	1	no	—
313	C₂³×C₈₉	—	2	1	no	—
314	C₂³×C₈₉	—	2	2	no	—
315	C₂³×C₈₉	—	4	4	no	—
316	C₂³×C₈₉	—	4	4	no	—
317	C₂³×C₈₉	—	4	4	no	—
318	C₂³×C₈₉	—	4	4	no	—
319	C₂³×C₈₉	—	4	4	no	—
320	C₂³×C₈₉	—	4	4	no	—
321	C₂³×C₈₉	—	4	4	no	—
322	C₂³×C₈₉	—	4	1	no	—
323	C₂³×C₈₉	—	4	1	no	—
324	C₂³×C₈₉	—	4	1	no	—
325	C₂³×C₈₉	—	4	1	no	—
326	C₂³×C₈₉	—	4	1	no	—
327	C₂³×C₈₉	—	4	1	no	—
328	C₂³×C₈₉	#120	1	2	yes	—
329	C₂³×C₈₉	#121	1	2	yes	—
330	C₂³×C₈₉	#137	1	2	yes	—
331	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
332	Q₈×C₈₉	—	2	2	no	—
333	Q₈×C₈₉	—	2	2	no	—
334	Q₈×C₈₉	—	4	1	no	—
335	Q₈×C₈₉	—	4	1	no	—
336	Q₈×C₈₉	—	4	1	no	—
337	Q₈×C₈₉	—	4	1	no	—
338	Q₈×C₈₉	—	4	1	no	—
339	Q₈×C₈₉	—	4	1	no	—
340	D₄×C₈₉	—	2	2	no	—
341	D₄×C₈₉	—	2	2	no	—
342	D₄×C₈₉	—	4	8	no	—
343	D₄×C₈₉	—	4	8	no	—
344	D₄×C₈₉	—	4	8	no	—
345	D₄×C₈₉	—	4	1	no	—
346	D₄×C₈₉	—	4	1	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	2	no	—
352	C₂×C₄×C₈₉	—	2	2	no	—
353	C₂×C₄×C₈₉	—	2	2	no	—
354	C₂×C₄×C₈₉	—	2	2	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	2	no	—
363	C₂×C₄×C₈₉	—	2	1	no	—
364	C₂×C₄×C₈₉	—	2	1	no	—
365	C₂×C₄×C₈₉	—	4	4	no	—
366	C₂×C₄×C₈₉	—	4	4	no	—
367	C₂×C₄×C₈₉	—	4	4	no	—
368	C₂×C₄×C₈₉	—	4	8	no	—
369	C₂×C₄×C₈₉	—	4	1	no	—
370	C₂×C₄×C₈₉	—	4	1	no	—
371	C₂×C₄×C₈₉	—	4	1	no	—
372	C₂×C₄×C₈₉	—	4	1	no	—
373	C₂×C₄×C₈₉	—	4	1	no	—
374	C₂×C₄×C₈₉	—	4	1	no	—
375	C₂×C₄×C₈₉	—	4	1	no	—
376	C₂×C₄×C₈₉	—	4	1	no	—
377	C₂×C₄×C₈₉	—	4	1	no	—
378	C₂×C₄×C₈₉	—	4	1	no	—
379	C₂×C₄×C₈₉	—	4	1	no	—
380	C₂×C₄×C₈₉	—	4	1	no	—
381	C₂×C₄×C₈₉	—	4	1	no	—
382	C₂×C₄×C₈₉	—	4	1	no	—
383	C₂×C₄×C₈₉	—	4	1	no	—
384	C₂×C₄×C₈₉	—	4	1	no	—
385	C₂×C₄×C₈₉	—	4	1	no	—
386	C₂×C₄×C₈₉	—	4	1	no	—
387	C₂×C₄×C₈₉	—	4	1	no	—
388	C₂×C₄×C₈₉	—	4	1	no	—
389	C₂×C₄×C₈₉	—	4	1	no	—
390	C₂×C₄×C₈₉	—	4	1	no	—
391	C₂×C₄×C₈₉	#120	1	2	yes	—
392	C₂×C₄×C₈₉	#121	1	2	yes	—
393	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
397	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
398	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
399	C₈×C₈₉	—	2	2	no	—
400	C₈×C₈₉	—	2	2	no	—
401	C₈×C₈₉	—	4	1	no	—
402	C₈×C₈₉	—	4	1	no	—
403	C₂²×C₈₉	—	2	2	no	—
404	C₂²×C₈₉	—	2	2	no	—
405	C₂²×C₈₉	—	2	2	no	—
406	C₂²×C₈₉	—	2	2	no	—
407	C₂²×C₈₉	—	2	2	no	—
408	C₂²×C₈₉	—	2	2	no	—
409	C₂²×C₈₉	—	2	2	no	—
410	C₂²×C₈₉	—	2	2	no	—
411	C₂²×C₈₉	—	2	2	no	—
412	C₂²×C₈₉	—	4	16	no	—
413	C₂²×C₈₉	—	4	1	no	—
414	C₂²×C₈₉	—	4	1	no	—
415	C₂²×C₈₉	—	4	1	no	—
416	C₂²×C₈₉	—	4	1	no	—
417	C₂²×C₈₉	—	4	1	no	—
418	C₂²×C₈₉	—	4	1	no	—
419	C₂²×C₈₉	—	4	1	no	—
420	C₂²×C₈₉	—	4	1	no	—
421	C₂²×C₈₉	—	4	1	no	—
422	C₂²×C₈₉	—	4	1	no	—
423	C₂²×C₈₉	—	4	1	no	—
424	C₂²×C₈₉	—	4	1	no	—
425	C₂²×C₈₉	—	4	2	no	—
426	C₂²×C₈₉	—	4	2	no	—
427	C₂²×C₈₉	—	4	2	no	—
428	C₂²×C₈₉	—	8	1	no	—
429	C₂²×C₈₉	—	8	1	no	—
430	C₂²×C₈₉	—	8	1	no	—
431	C₂²×C₈₉	—	8	1	no	—
432	C₂²×C₈₉	C₂×#120	1	1	yes	characteristic
433	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
434	C₂²×C₈₉	#534	1	1	yes	characteristic
435	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
436	C₂²×C₈₉	#575	1	1	yes	characteristic
437	C₂²×C₈₉	#575	1	1	yes	characteristic
438	C₂²×C₈₉	#575	1	1	yes	characteristic
439	C₄×C₈₉	—	2	2	no	—
440	C₄×C₈₉	—	2	2	no	—
441	C₄×C₈₉	—	4	1	no	—
442	C₄×C₈₉	—	4	2	no	—
443	C₄×C₈₉	—	4	2	no	—
444	C₄×C₈₉	—	4	2	no	—
445	C₄×C₈₉	—	8	1	no	—
446	C₄×C₈₉	—	8	1	no	—
447	C₄×C₈₉	—	8	1	no	—
448	C₄×C₈₉	—	8	1	no	—
449	C₄×C₈₉	D₄²	1	1	yes	characteristic
450	C₄×C₈₉	D₄²	1	1	yes	characteristic
451	C₄×C₈₉	#546	1	1	yes	characteristic
452	C₄×C₈₉	#546	1	1	yes	characteristic
453	#24389	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
454	C₂×C₈₉	—	4	2	no	—
455	C₂×C₈₉	—	4	2	no	—
456	C₂×C₈₉	—	4	2	no	—
457	C₂×C₈₉	—	8	2	no	—
458	C₂×C₈₉	#2410	1	1	yes	characteristic
459	C₂×C₈₉	#3005	1	1	yes	characteristic
460	C₂×C₈₉	#3007	1	1	yes	characteristic
461	C₂×C₈₉	#3054	1	1	yes	characteristic
462	C₂×C₈₉	#3056	1	1	yes	characteristic
463	C₂×C₈₉	#3196	1	1	yes	characteristic
464	C₂×C₈₉	#3197	1	1	yes	characteristic
465	C₂×#525	C₂×C₈₉	1	1	yes	characteristic
466	C₂×#470	C₂×C₈₉	1	1	yes	characteristic, complemented
467	C₂×#468	C₂×C₈₉	1	1	yes	characteristic, complemented
468	C₂×#452	C₂×C₈₉	1	1	yes	characteristic, complemented
469	C₂×#407	C₂×C₈₉	1	1	yes	characteristic, complemented
470	#2848	C₂×C₈₉	1	1	yes	characteristic, complemented
471	#2036	C₂×C₈₉	1	1	yes	characteristic, complemented
472	#2034	C₂×C₈₉	1	1	yes	characteristic, complemented
473	#2001	C₂×C₈₉	1	1	yes	characteristic, complemented
474	#2000	C₂×C₈₉	1	1	yes	characteristic, complemented
475	#1895	C₂×C₈₉	1	1	yes	characteristic, complemented
476	#1894	C₂×C₈₉	1	1	yes	characteristic, complemented
477	#1873	C₂×C₈₉	1	1	yes	characteristic, complemented
478	#1854	C₂×C₈₉	1	1	yes	characteristic, complemented
479	#1788	C₂×C₈₉	1	1	yes	characteristic, complemented
480	C₈₉	#24389	1	1	yes	characteristic, direct product factor, Sylow
481	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
482	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
483	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
484	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
485	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
486	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
487	#525	—	2	4	no	—
488	#525	—	2	4	no	—
489	C₂×#123	—	2	1	no	—
490	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
491	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
492	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
493	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
494	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
495	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
496	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
497	C₂×#120	—	2	1	no	—
498	C₂×C₄×D₄	—	2	1	no	—
499	C₂×C₄×D₄	—	2	1	no	—
500	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
501	#470	—	2	4	no	—
502	#468	—	2	4	no	—
503	#452	—	2	4	no	—
504	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic, complemented
505	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic, complemented
506	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
507	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
508	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
509	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
510	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
511	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
512	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
513	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
514	#407	—	2	4	no	—
515	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
516	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
517	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
518	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
519	#385	—	2	1	no	—
520	#385	—	2	1	no	—
521	#385	—	2	1	no	—
522	#380	C₂²×C₈₉	1	1	yes	characteristic
523	#380	C₂²×C₈₉	1	1	yes	characteristic
524	#380	C₂²×C₈₉	1	1	yes	characteristic
525	#379	—	2	1	no	—
526	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
527	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
528	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
529	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
530	C₂⁵	D₄×C₈₉	1	1	yes	characteristic
531	C₂×#41	—	2	2	no	—
532	C₂×#41	—	2	2	no	—
533	C₂×#41	—	2	2	no	—
534	C₂×#41	—	2	2	no	—
535	C₂×#41	—	4	1	no	—
536	C₂×#41	—	4	1	no	—
537	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
538	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
539	C₂²×D₄	—	2	1	no	—
540	C₂²×D₄	—	2	1	no	—
541	C₂²×D₄	—	2	1	no	—
542	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
543	C₂³×C₄	—	2	1	no	—
544	C₂³×C₄	—	2	2	no	—
545	C₂³×C₄	—	2	2	no	—
546	C₂³×C₄	—	2	2	no	—
547	C₂³×C₄	—	2	2	no	—
548	C₂³×C₄	—	4	1	no	—
549	C₂³×C₄	—	4	1	no	—
550	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
551	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
552	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
553	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
554	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
555	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
556	C₂×Q₁₆	—	2	2	no	—
557	C₂×Q₁₆	—	2	2	no	—
558	C₂×Q₁₆	—	4	1	no	—
559	C₂×SD₁₆	—	2	2	no	—
560	C₂×SD₁₆	—	2	2	no	—
561	C₂×SD₁₆	—	4	1	no	—
562	C₂×M₁₆	—	2	2	no	—
563	C₂×M₁₆	—	2	2	no	—
564	C₂×M₁₆	—	2	2	no	—
565	C₂×M₁₆	—	2	2	no	—
566	C₂×M₁₆	—	4	1	no	—
567	C₂×M₁₆	—	4	1	no	—
568	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
569	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
570	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
571	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
572	#123	—	2	8	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	2	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	—	4	1	no	—
581	C₂²⋊Q₈	—	4	1	no	—
582	C₂²⋊Q₈	D₄×C₈₉	1	4	yes	—
583	#121	—	2	2	no	—
584	#121	—	2	2	no	—
585	#121	—	2	2	no	—
586	#121	D₄×C₈₉	1	4	yes	—
587	#120	—	2	8	no	—
588	C₄×D₄	—	2	8	no	—
589	C₄×D₄	—	2	8	no	—
590	#117	—	2	2	no	—
591	#117	—	2	2	no	—
592	C₂×C₄⋊C₄	—	2	1	no	—
593	C₂×C₄⋊C₄	—	2	1	no	—
594	C₂×C₄⋊C₄	—	2	1	no	—
595	C₂×C₄⋊C₄	—	2	1	no	—
596	C₂×C₄⋊C₄	—	2	1	no	—
597	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
603	C₂×C₂²⋊C₄	—	2	1	no	—
604	C₂×C₂²⋊C₄	—	2	1	no	—
605	C₂×C₂²⋊C₄	—	2	1	no	—
606	C₂×C₂²⋊C₄	—	2	1	no	—
607	C₂×C₂²⋊C₄	—	2	1	no	—
608	C₂×C₂²⋊C₄	—	2	1	no	—
609	C₂×C₂²⋊C₄	—	2	1	no	—
610	C₂×C₂²⋊C₄	—	2	1	no	—
611	C₂×C₂²⋊C₄	—	2	1	no	—
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₄²	—	2	1	no	—
614	#107	—	2	2	no	—
615	#106	—	2	2	no	—
616	#103	—	2	2	no	—
617	#103	—	2	2	no	—
618	#103	—	2	2	no	—
619	#103	—	2	2	no	—
620	#103	—	4	1	no	—
621	#102	—	2	2	no	—
622	#102	—	2	2	no	—
623	#102	—	4	1	no	—
624	C₂²⋊C₈	—	2	2	no	—
625	C₂²⋊C₈	—	2	2	no	—
626	C₂²⋊C₈	—	2	2	no	—
627	C₂²⋊C₈	D₄×C₈₉	1	4	yes	complemented
628	#95	—	2	1	no	—
629	#95	—	2	1	no	—
630	#95	—	2	1	no	—
631	C₂⁴	—	2	2	no	—
632	C₂⁴	—	2	2	no	—
633	C₂⁴	—	2	2	no	—
634	C₂⁴	—	2	1	no	—
635	C₂⁴	—	4	1	no	—
636	C₂⁴	—	4	1	no	—
637	C₂⁴	—	4	1	no	—
638	C₂⁴	—	4	1	no	—
639	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
640	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
641	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
642	#41	—	4	4	no	—
643	#41	—	4	4	no	—
644	#41	—	4	4	no	—
645	#41	—	4	4	no	—
646	C₂×Q₈	—	2	1	no	—
647	C₂×Q₈	—	2	1	no	—
648	C₂×Q₈	—	2	1	no	—
649	C₂×Q₈	—	2	1	no	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	2	1	no	—
653	C₂×Q₈	—	2	1	no	—
654	C₂×Q₈	—	2	1	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
658	C₂×D₄	—	2	4	no	—
659	C₂×D₄	—	2	4	no	—
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	4	2	no	—
667	C₂×D₄	—	4	2	no	—
668	C₂×D₄	—	4	2	no	—
669	C₂×D₄	—	4	2	no	—
670	C₂×D₄	—	4	2	no	—
671	C₂×D₄	—	4	2	no	—
672	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
673	C₂²×C₄	—	2	1	no	—
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	1	no	—
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	4	1	no	—
702	C₂²×C₄	—	4	1	no	—
703	C₂²×C₄	—	4	1	no	—
704	C₂²×C₄	—	4	4	no	—
705	C₂²×C₄	—	4	4	no	—
706	C₂²×C₄	—	4	4	no	—
707	C₂²×C₄	—	4	4	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	—	4	2	no	—
710	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
711	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
712	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
713	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
714	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
715	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
716	C₂²×C₄	#41×C₈₉	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
718	Q₁₆	—	4	4	no	—
719	SD₁₆	—	4	4	no	—
720	M₁₆	—	4	4	no	—
721	M₁₆	—	4	4	no	—
722	C₂×C₈	—	2	1	no	—
723	C₂×C₈	—	2	1	no	—
724	C₂×C₈	—	2	1	no	—
725	C₂×C₈	—	2	1	no	—
726	C₂×C₈	—	2	1	no	—
727	C₂×C₈	—	2	1	no	—
728	C₂×C₈	—	2	1	no	—
729	C₂×C₈	—	2	1	no	—
730	C₂×C₈	—	2	1	no	—
731	C₂×C₈	—	2	1	no	—
732	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
733	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	4	2	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₄⋊C₄	—	4	2	no	—
747	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
748	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	4	2	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	—	4	2	no	—
757	C₂²⋊C₄	—	4	2	no	—
758	C₂²⋊C₄	—	4	2	no	—
759	C₂²⋊C₄	—	4	2	no	—
760	C₄²	—	2	4	no	—
761	C₂³	—	2	1	no	—
762	C₂³	—	2	1	no	—
763	C₂³	—	2	1	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	2	1	no	—
768	C₂³	—	2	1	no	—
769	C₂³	—	2	1	no	—
770	C₂³	—	2	1	no	—
771	C₂³	—	2	1	no	—
772	C₂³	—	2	1	no	—
773	C₂³	—	2	1	no	—
774	C₂³	—	2	1	no	—
775	C₂³	—	2	1	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	2	1	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	4	4	no	—
781	C₂³	—	4	4	no	—
782	C₂³	—	4	4	no	—
783	C₂³	—	4	4	no	—
784	C₂³	—	4	4	no	—
785	C₂³	—	4	4	no	—
786	C₂³	—	4	4	no	—
787	C₂³	—	4	1	no	—
788	C₂³	—	4	1	no	—
789	C₂³	—	4	1	no	—
790	C₂³	—	4	1	no	—
791	C₂³	—	4	1	no	—
792	C₂³	—	4	1	no	—
793	C₂³	#120×C₈₉	1	2	yes	—
794	C₂³	#121×C₈₉	1	2	yes	—
795	C₂³	#137×C₈₉	1	2	yes	—
796	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
797	Q₈	—	2	2	no	—
798	Q₈	—	2	2	no	—
799	Q₈	—	4	1	no	—
800	Q₈	—	4	1	no	—
801	Q₈	—	4	1	no	—
802	Q₈	—	4	1	no	—
803	Q₈	—	4	1	no	—
804	Q₈	—	4	1	no	—
805	D₄	—	2	2	no	—
806	D₄	—	2	2	no	—
807	D₄	—	4	8	no	—
808	D₄	—	4	8	no	—
809	D₄	—	4	8	no	—
810	D₄	—	4	1	no	—
811	D₄	—	4	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	2	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	2	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	—	4	4	no	—
831	C₂×C₄	—	4	4	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	8	no	—
834	C₂×C₄	—	4	1	no	—
835	C₂×C₄	—	4	1	no	—
836	C₂×C₄	—	4	1	no	—
837	C₂×C₄	—	4	1	no	—
838	C₂×C₄	—	4	1	no	—
839	C₂×C₄	—	4	1	no	—
840	C₂×C₄	—	4	1	no	—
841	C₂×C₄	—	4	1	no	—
842	C₂×C₄	—	4	1	no	—
843	C₂×C₄	—	4	1	no	—
844	C₂×C₄	—	4	1	no	—
845	C₂×C₄	—	4	1	no	—
846	C₂×C₄	—	4	1	no	—
847	C₂×C₄	—	4	1	no	—
848	C₂×C₄	—	4	1	no	—
849	C₂×C₄	—	4	1	no	—
850	C₂×C₄	—	4	1	no	—
851	C₂×C₄	—	4	1	no	—
852	C₂×C₄	—	4	1	no	—
853	C₂×C₄	—	4	1	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	1	no	—
856	C₂×C₄	#120×C₈₉	1	2	yes	—
857	C₂×C₄	#121×C₈₉	1	2	yes	—
858	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
859	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
860	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
861	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
862	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
863	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
864	C₈	—	2	2	no	—
865	C₈	—	2	2	no	—
866	C₈	—	4	1	no	—
867	C₈	—	4	1	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	2	2	no	—
870	C₂²	—	2	2	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	2	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	2	2	no	—
877	C₂²	—	4	16	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	4	1	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	1	no	—
883	C₂²	—	4	1	no	—
884	C₂²	—	4	1	no	—
885	C₂²	—	4	1	no	—
886	C₂²	—	4	1	no	—
887	C₂²	—	4	1	no	—
888	C₂²	—	4	1	no	—
889	C₂²	—	4	1	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	8	1	no	—
894	C₂²	—	8	1	no	—
895	C₂²	—	8	1	no	—
896	C₂²	—	8	1	no	—
897	C₂²	C₂×#120×C₈₉	1	1	yes	characteristic
898	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
899	C₂²	#534×C₈₉	1	1	yes	characteristic
900	C₂²	C₂×#137×C₈₉	1	1	yes	characteristic
901	C₂²	#575×C₈₉	1	1	yes	characteristic
902	C₂²	#575×C₈₉	1	1	yes	characteristic
903	C₂²	#575×C₈₉	1	1	yes	characteristic
904	C₄	—	2	2	no	—
905	C₄	—	2	2	no	—
906	C₄	—	4	1	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	2	no	—
910	C₄	—	8	1	no	—
911	C₄	—	8	1	no	—
912	C₄	—	8	1	no	—
913	C₄	—	8	1	no	—
914	C₄	D₄²×C₈₉	1	1	yes	characteristic
915	C₄	D₄²×C₈₉	1	1	yes	characteristic
916	C₄	#546×C₈₉	1	1	yes	characteristic
917	C₄	#546×C₈₉	1	1	yes	characteristic
918	C₂	—	4	2	no	—
919	C₂	—	4	2	no	—
920	C₂	—	4	2	no	—
921	C₂	—	8	2	no	—
922	C₂	C₈₉×#2410	1	1	yes	characteristic
923	C₂	C₈₉×#3005	1	1	yes	characteristic
924	C₂	C₈₉×#3007	1	1	yes	characteristic
925	C₂	C₈₉×#3054	1	1	yes	characteristic
926	C₂	C₈₉×#3056	1	1	yes	characteristic
927	C₂	C₈₉×#3196	1	1	yes	characteristic
928	C₂	C₈₉×#3197	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂×#525×C₈₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂⁴×C₄×C₈₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×#470×C₈₉	C₂	semidirect
3. C₂×#468×C₈₉	C₂	semidirect
4. C₂×#452×C₈₉	C₂	semidirect
5. C₂×#407×C₈₉	C₂	semidirect
6. C₈₉×#2848	C₂	semidirect
7. C₈₉×#2036	C₂	semidirect
8. C₈₉×#2034	C₂	semidirect
9. C₈₉×#2001	C₂	semidirect
10. C₈₉×#2000	C₂	semidirect
11. C₈₉×#1895	C₂	semidirect
12. C₈₉×#1894	C₂	semidirect
13. C₈₉×#1873	C₂	semidirect
14. C₈₉×#1854	C₂	semidirect
15. C₈₉×#1788	C₂	semidirect
18. C₂²×Q₁₆×C₈₉	C₂²	semidirect
19. C₂²×SD₁₆×C₈₉	C₂²	semidirect
39. C₂×#107×C₈₉	C₂²	semidirect
40. C₂×#106×C₈₉	C₂²	semidirect
41. C₂×#103×C₈₉	C₂²	semidirect
42. C₂×#103×C₈₉	C₂²	semidirect
43. C₂×#103×C₈₉	C₂²	semidirect
44. C₂×#103×C₈₉	C₂²	semidirect
45. C₂×#103×C₈₉	C₂²	semidirect
46. C₂×#102×C₈₉	C₂²	semidirect
47. C₂×#102×C₈₉	C₂²	semidirect
48. C₂×#102×C₈₉	C₂²	semidirect
61. #340×C₈₉	C₂²	semidirect
62. #340×C₈₉	C₂²	semidirect
63. #340×C₈₉	C₂²	semidirect
64. #340×C₈₉	C₂²	semidirect
162. C₂²⋊C₈×C₈₉	D₄	semidirect
453. #24389	C₈₉	direct (N × H)
466. C₂×#470	C₂×C₈₉	semidirect
467. C₂×#468	C₂×C₈₉	semidirect
468. C₂×#452	C₂×C₈₉	semidirect
469. C₂×#407	C₂×C₈₉	semidirect
470. #2848	C₂×C₈₉	semidirect
471. #2036	C₂×C₈₉	semidirect
472. #2034	C₂×C₈₉	semidirect
473. #2001	C₂×C₈₉	semidirect
474. #2000	C₂×C₈₉	semidirect
475. #1895	C₂×C₈₉	semidirect
476. #1894	C₂×C₈₉	semidirect
477. #1873	C₂×C₈₉	semidirect
478. #1854	C₂×C₈₉	semidirect
479. #1788	C₂×C₈₉	semidirect
480. C₈₉	#24389	direct (N × H)
483. C₂²×Q₁₆	C₂²×C₈₉	semidirect
484. C₂²×SD₁₆	C₂²×C₈₉	semidirect
504. C₂×#107	C₂²×C₈₉	semidirect
505. C₂×#106	C₂²×C₈₉	semidirect
506. C₂×#103	C₂²×C₈₉	semidirect
507. C₂×#103	C₂²×C₈₉	semidirect
508. C₂×#103	C₂²×C₈₉	semidirect
509. C₂×#103	C₂²×C₈₉	semidirect
510. C₂×#103	C₂²×C₈₉	semidirect
511. C₂×#102	C₂²×C₈₉	semidirect
512. C₂×#102	C₂²×C₈₉	semidirect
513. C₂×#102	C₂²×C₈₉	semidirect
526. #340	C₂²×C₈₉	semidirect
527. #340	C₂²×C₈₉	semidirect
528. #340	C₂²×C₈₉	semidirect
529. #340	C₂²×C₈₉	semidirect
627. C₂²⋊C₈	D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#525×C₈₉	2
C₂×#470×C₈₉	2
C₂×#468×C₈₉	2
C₂×#452×C₈₉	2
C₂×#407×C₈₉	2
C₈₉×#2848	2
C₈₉×#2036	2
C₈₉×#2034	2
C₈₉×#2001	2
C₈₉×#2000	2
C₈₉×#1895	2
C₈₉×#1894	2
C₈₉×#1873	2
C₈₉×#1854	2
C₈₉×#1788	2
#24389	89

Subgroups — C89×#24389 #36402237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#24389 #36402237