Subgroups — C₈₉×#24388 #36402236

Order 22784.

1646 conjugacy classes of subgroups.

The subgroup lattice has 972 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, complemented
2	C₂×#469×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#468×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#449×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#407×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2847	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1999	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×#1875	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×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₈×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×#121×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#121×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×#120×C₈₉	—	2	1	no	—
34	C₂×C₄×D₄×C₈₉	—	2	1	no	—
35	C₂×C₄×D₄×C₈₉	—	2	1	no	—
36	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
37	#469×C₈₉	—	2	4	no	—
38	#468×C₈₉	—	2	4	no	—
39	#449×C₈₉	—	2	4	no	—
40	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×#106×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×#102×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	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
50	#407×C₈₉	—	2	4	no	—
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	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
55	#386×C₈₉	—	2	1	no	—
56	#386×C₈₉	—	2	1	no	—
57	#386×C₈₉	—	2	1	no	—
58	#380×C₈₉	C₂²	1	1	yes	characteristic
59	#380×C₈₉	C₂²	1	1	yes	characteristic
60	#380×C₈₉	C₂²	1	1	yes	characteristic
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×D₄×C₈₉	—	2	1	no	—
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	—	2	1	no	—
78	C₂²×D₄×C₈₉	—	2	1	no	—
79	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₈₉	—	2	2	no	—
82	C₂³×C₄×C₈₉	—	2	1	no	—
83	C₂³×C₄×C₈₉	—	2	2	no	—
84	C₂³×C₄×C₈₉	—	2	2	no	—
85	C₂³×C₄×C₈₉	—	2	2	no	—
86	C₂³×C₄×C₈₉	—	4	1	no	—
87	C₂³×C₄×C₈₉	—	4	1	no	—
88	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
89	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
90	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
91	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
94	C₂×SD₁₆×C₈₉	—	2	2	no	—
95	C₂×SD₁₆×C₈₉	—	2	2	no	—
96	C₂×SD₁₆×C₈₉	—	4	1	no	—
97	C₂×D₈×C₈₉	—	2	2	no	—
98	C₂×D₈×C₈₉	—	2	2	no	—
99	C₂×D₈×C₈₉	—	4	1	no	—
100	C₂×M₁₆×C₈₉	—	2	2	no	—
101	C₂×M₁₆×C₈₉	—	2	2	no	—
102	C₂×M₁₆×C₈₉	—	2	2	no	—
103	C₂×M₁₆×C₈₉	—	2	2	no	—
104	C₂×M₁₆×C₈₉	—	4	1	no	—
105	C₂×M₁₆×C₈₉	—	4	1	no	—
106	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
110	#123×C₈₉	—	2	8	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	D₄	1	4	yes	complemented
115	#121×C₈₉	—	2	2	no	—
116	#121×C₈₉	—	2	2	no	—
117	#121×C₈₉	—	2	2	no	—
118	#121×C₈₉	—	2	2	no	—
119	#121×C₈₉	—	2	2	no	—
120	#121×C₈₉	—	2	2	no	—
121	#121×C₈₉	—	2	2	no	—
122	#121×C₈₉	—	4	1	no	—
123	#121×C₈₉	—	4	1	no	—
124	#121×C₈₉	D₄	1	4	yes	complemented
125	#120×C₈₉	—	2	8	no	—
126	#120×C₈₉	—	4	4	no	—
127	C₄×D₄×C₈₉	—	2	8	no	—
128	C₄×D₄×C₈₉	—	2	8	no	—
129	#117×C₈₉	—	2	2	no	—
130	#117×C₈₉	—	2	2	no	—
131	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
132	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
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×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₈₉	—	2	1	no	—
149	C₂×C₄²×C₈₉	—	2	1	no	—
150	#107×C₈₉	—	2	2	no	—
151	#106×C₈₉	—	2	2	no	—
152	#103×C₈₉	—	2	2	no	—
153	#103×C₈₉	—	2	2	no	—
154	#103×C₈₉	—	4	1	no	—
155	#102×C₈₉	—	2	2	no	—
156	#102×C₈₉	—	2	2	no	—
157	#102×C₈₉	—	2	2	no	—
158	#102×C₈₉	—	2	2	no	—
159	#102×C₈₉	—	4	1	no	—
160	C₂²⋊C₈×C₈₉	—	2	2	no	—
161	C₂²⋊C₈×C₈₉	—	2	2	no	—
162	C₂²⋊C₈×C₈₉	—	2	2	no	—
163	C₂²⋊C₈×C₈₉	D₄	1	4	yes	complemented
164	#95×C₈₉	—	2	1	no	—
165	#95×C₈₉	—	2	1	no	—
166	#95×C₈₉	—	2	1	no	—
167	C₂⁴×C₈₉	—	2	2	no	—
168	C₂⁴×C₈₉	—	2	2	no	—
169	C₂⁴×C₈₉	—	2	2	no	—
170	C₂⁴×C₈₉	—	2	1	no	—
171	C₂⁴×C₈₉	—	2	1	no	—
172	C₂⁴×C₈₉	—	4	1	no	—
173	C₂⁴×C₈₉	—	4	1	no	—
174	C₂⁴×C₈₉	—	4	1	no	—
175	C₂⁴×C₈₉	—	4	1	no	—
176	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
177	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
178	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
179	#41×C₈₉	—	4	4	no	—
180	#41×C₈₉	—	4	4	no	—
181	#41×C₈₉	—	4	4	no	—
182	#41×C₈₉	—	4	4	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	C₂×D₄	1	2	yes	—
189	C₂×D₄×C₈₉	—	2	4	no	—
190	C₂×D₄×C₈₉	—	2	4	no	—
191	C₂×D₄×C₈₉	—	2	4	no	—
192	C₂×D₄×C₈₉	—	2	1	no	—
193	C₂×D₄×C₈₉	—	2	1	no	—
194	C₂×D₄×C₈₉	—	2	1	no	—
195	C₂×D₄×C₈₉	—	2	1	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	—	2	1	no	—
202	C₂×D₄×C₈₉	—	2	1	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	—	4	2	no	—
208	C₂×D₄×C₈₉	—	4	2	no	—
209	C₂×D₄×C₈₉	—	4	2	no	—
210	C₂×D₄×C₈₉	—	4	2	no	—
211	C₂×D₄×C₈₉	—	4	2	no	—
212	C₂×D₄×C₈₉	—	4	2	no	—
213	C₂×D₄×C₈₉	—	4	2	no	—
214	C₂×D₄×C₈₉	—	4	2	no	—
215	C₂×D₄×C₈₉	—	4	2	no	—
216	C₂×D₄×C₈₉	—	4	2	no	—
217	C₂×D₄×C₈₉	—	4	2	no	—
218	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
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	1	no	—
223	C₂²×C₄×C₈₉	—	2	1	no	—
224	C₂²×C₄×C₈₉	—	2	1	no	—
225	C₂²×C₄×C₈₉	—	2	1	no	—
226	C₂²×C₄×C₈₉	—	2	1	no	—
227	C₂²×C₄×C₈₉	—	2	4	no	—
228	C₂²×C₄×C₈₉	—	2	2	no	—
229	C₂²×C₄×C₈₉	—	2	2	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	2	no	—
234	C₂²×C₄×C₈₉	—	2	2	no	—
235	C₂²×C₄×C₈₉	—	2	2	no	—
236	C₂²×C₄×C₈₉	—	2	2	no	—
237	C₂²×C₄×C₈₉	—	2	1	no	—
238	C₂²×C₄×C₈₉	—	2	1	no	—
239	C₂²×C₄×C₈₉	—	2	1	no	—
240	C₂²×C₄×C₈₉	—	2	1	no	—
241	C₂²×C₄×C₈₉	—	2	1	no	—
242	C₂²×C₄×C₈₉	—	2	1	no	—
243	C₂²×C₄×C₈₉	—	2	1	no	—
244	C₂²×C₄×C₈₉	—	2	1	no	—
245	C₂²×C₄×C₈₉	—	2	1	no	—
246	C₂²×C₄×C₈₉	—	4	1	no	—
247	C₂²×C₄×C₈₉	—	4	1	no	—
248	C₂²×C₄×C₈₉	—	4	1	no	—
249	C₂²×C₄×C₈₉	—	4	4	no	—
250	C₂²×C₄×C₈₉	—	4	4	no	—
251	C₂²×C₄×C₈₉	—	4	4	no	—
252	C₂²×C₄×C₈₉	—	4	4	no	—
253	C₂²×C₄×C₈₉	—	4	2	no	—
254	C₂²×C₄×C₈₉	—	4	2	no	—
255	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
258	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
259	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₈₉	#41	1	2	yes	—
262	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
263	SD₁₆×C₈₉	—	4	4	no	—
264	D₈×C₈₉	—	4	4	no	—
265	M₁₆×C₈₉	—	4	4	no	—
266	M₁₆×C₈₉	—	4	4	no	—
267	C₂×C₈×C₈₉	—	2	1	no	—
268	C₂×C₈×C₈₉	—	2	1	no	—
269	C₂×C₈×C₈₉	—	2	1	no	—
270	C₂×C₈×C₈₉	—	2	1	no	—
271	C₂×C₈×C₈₉	—	2	1	no	—
272	C₂×C₈×C₈₉	—	2	1	no	—
273	C₂×C₈×C₈₉	—	2	1	no	—
274	C₂×C₈×C₈₉	—	2	1	no	—
275	C₂×C₈×C₈₉	—	2	1	no	—
276	C₂×C₈×C₈₉	—	2	1	no	—
277	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
278	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₈₉	—	2	4	no	—
280	C₄⋊C₄×C₈₉	—	2	4	no	—
281	C₄⋊C₄×C₈₉	—	2	1	no	—
282	C₄⋊C₄×C₈₉	—	2	1	no	—
283	C₄⋊C₄×C₈₉	—	2	1	no	—
284	C₄⋊C₄×C₈₉	—	2	1	no	—
285	C₄⋊C₄×C₈₉	—	2	1	no	—
286	C₄⋊C₄×C₈₉	—	2	1	no	—
287	C₄⋊C₄×C₈₉	—	2	1	no	—
288	C₄⋊C₄×C₈₉	—	2	1	no	—
289	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
290	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
291	C₂²⋊C₄×C₈₉	—	2	4	no	—
292	C₂²⋊C₄×C₈₉	—	2	4	no	—
293	C₂²⋊C₄×C₈₉	—	2	4	no	—
294	C₂²⋊C₄×C₈₉	—	2	4	no	—
295	C₂²⋊C₄×C₈₉	—	2	4	no	—
296	C₂²⋊C₄×C₈₉	—	4	2	no	—
297	C₂²⋊C₄×C₈₉	—	4	2	no	—
298	C₂²⋊C₄×C₈₉	—	4	2	no	—
299	C₂²⋊C₄×C₈₉	—	4	2	no	—
300	C₂²⋊C₄×C₈₉	—	4	2	no	—
301	C₂²⋊C₄×C₈₉	—	4	2	no	—
302	C₄²×C₈₉	—	2	4	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	1	no	—
315	C₂³×C₈₉	—	2	1	no	—
316	C₂³×C₈₉	—	2	1	no	—
317	C₂³×C₈₉	—	2	1	no	—
318	C₂³×C₈₉	—	2	1	no	—
319	C₂³×C₈₉	—	2	1	no	—
320	C₂³×C₈₉	—	2	1	no	—
321	C₂³×C₈₉	—	2	2	no	—
322	C₂³×C₈₉	—	4	4	no	—
323	C₂³×C₈₉	—	4	4	no	—
324	C₂³×C₈₉	—	4	4	no	—
325	C₂³×C₈₉	—	4	4	no	—
326	C₂³×C₈₉	—	4	4	no	—
327	C₂³×C₈₉	—	4	4	no	—
328	C₂³×C₈₉	—	4	4	no	—
329	C₂³×C₈₉	—	4	1	no	—
330	C₂³×C₈₉	—	4	1	no	—
331	C₂³×C₈₉	—	4	1	no	—
332	C₂³×C₈₉	—	4	1	no	—
333	C₂³×C₈₉	—	4	1	no	—
334	C₂³×C₈₉	—	4	1	no	—
335	C₂³×C₈₉	—	4	1	no	—
336	C₂³×C₈₉	—	4	1	no	—
337	C₂³×C₈₉	—	4	1	no	—
338	C₂³×C₈₉	—	4	1	no	—
339	C₂³×C₈₉	—	4	1	no	—
340	C₂³×C₈₉	—	4	1	no	—
341	C₂³×C₈₉	—	4	1	no	—
342	C₂³×C₈₉	#120	1	2	yes	—
343	C₂³×C₈₉	#121	1	2	yes	—
344	C₂³×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
345	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
346	Q₈×C₈₉	—	2	2	no	—
347	Q₈×C₈₉	—	2	2	no	—
348	Q₈×C₈₉	—	4	1	no	—
349	Q₈×C₈₉	—	4	1	no	—
350	D₄×C₈₉	—	2	2	no	—
351	D₄×C₈₉	—	2	2	no	—
352	D₄×C₈₉	—	4	8	no	—
353	D₄×C₈₉	—	4	8	no	—
354	D₄×C₈₉	—	4	8	no	—
355	D₄×C₈₉	—	4	1	no	—
356	D₄×C₈₉	—	4	1	no	—
357	D₄×C₈₉	—	4	1	no	—
358	D₄×C₈₉	—	4	1	no	—
359	D₄×C₈₉	—	4	1	no	—
360	D₄×C₈₉	—	4	1	no	—
361	D₄×C₈₉	—	8	4	no	—
362	D₄×C₈₉	—	8	4	no	—
363	D₄×C₈₉	—	8	4	no	—
364	C₂×C₄×C₈₉	—	2	1	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	2	no	—
369	C₂×C₄×C₈₉	—	2	2	no	—
370	C₂×C₄×C₈₉	—	2	2	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	2	no	—
375	C₂×C₄×C₈₉	—	2	2	no	—
376	C₂×C₄×C₈₉	—	2	2	no	—
377	C₂×C₄×C₈₉	—	2	2	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	1	no	—
382	C₂×C₄×C₈₉	—	4	4	no	—
383	C₂×C₄×C₈₉	—	4	4	no	—
384	C₂×C₄×C₈₉	—	4	4	no	—
385	C₂×C₄×C₈₉	—	4	8	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	—	4	1	no	—
392	C₂×C₄×C₈₉	—	4	1	no	—
393	C₂×C₄×C₈₉	—	4	1	no	—
394	C₂×C₄×C₈₉	—	4	1	no	—
395	C₂×C₄×C₈₉	—	4	1	no	—
396	C₂×C₄×C₈₉	—	4	1	no	—
397	C₂×C₄×C₈₉	—	4	1	no	—
398	C₂×C₄×C₈₉	—	4	1	no	—
399	C₂×C₄×C₈₉	—	4	1	no	—
400	C₂×C₄×C₈₉	—	4	1	no	—
401	C₂×C₄×C₈₉	—	4	1	no	—
402	C₂×C₄×C₈₉	—	4	1	no	—
403	C₂×C₄×C₈₉	—	4	1	no	—
404	C₂×C₄×C₈₉	—	4	1	no	—
405	C₂×C₄×C₈₉	#120	1	2	yes	—
406	C₂×C₄×C₈₉	#121	1	2	yes	—
407	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
411	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
412	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
413	C₈×C₈₉	—	2	2	no	—
414	C₈×C₈₉	—	2	2	no	—
415	C₈×C₈₉	—	4	1	no	—
416	C₈×C₈₉	—	4	1	no	—
417	C₂²×C₈₉	—	2	2	no	—
418	C₂²×C₈₉	—	2	2	no	—
419	C₂²×C₈₉	—	2	2	no	—
420	C₂²×C₈₉	—	2	2	no	—
421	C₂²×C₈₉	—	2	2	no	—
422	C₂²×C₈₉	—	2	2	no	—
423	C₂²×C₈₉	—	2	2	no	—
424	C₂²×C₈₉	—	2	2	no	—
425	C₂²×C₈₉	—	2	2	no	—
426	C₂²×C₈₉	—	4	16	no	—
427	C₂²×C₈₉	—	4	1	no	—
428	C₂²×C₈₉	—	4	1	no	—
429	C₂²×C₈₉	—	4	1	no	—
430	C₂²×C₈₉	—	4	1	no	—
431	C₂²×C₈₉	—	4	1	no	—
432	C₂²×C₈₉	—	4	1	no	—
433	C₂²×C₈₉	—	4	1	no	—
434	C₂²×C₈₉	—	4	1	no	—
435	C₂²×C₈₉	—	4	1	no	—
436	C₂²×C₈₉	—	4	1	no	—
437	C₂²×C₈₉	—	4	1	no	—
438	C₂²×C₈₉	—	4	1	no	—
439	C₂²×C₈₉	—	4	2	no	—
440	C₂²×C₈₉	—	4	2	no	—
441	C₂²×C₈₉	—	4	2	no	—
442	C₂²×C₈₉	—	8	1	no	—
443	C₂²×C₈₉	—	8	1	no	—
444	C₂²×C₈₉	—	8	1	no	—
445	C₂²×C₈₉	—	8	1	no	—
446	C₂²×C₈₉	—	8	1	no	—
447	C₂²×C₈₉	—	8	1	no	—
448	C₂²×C₈₉	—	8	1	no	—
449	C₂²×C₈₉	—	8	1	no	—
450	C₂²×C₈₉	—	8	1	no	—
451	C₂²×C₈₉	—	8	1	no	—
452	C₂²×C₈₉	—	8	1	no	—
453	C₂²×C₈₉	C₂×#120	1	1	yes	characteristic
454	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
455	C₂²×C₈₉	#534	1	1	yes	characteristic
456	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
457	C₂²×C₈₉	#575	1	1	yes	characteristic
458	C₂²×C₈₉	#575	1	1	yes	characteristic
459	C₂²×C₈₉	#575	1	1	yes	characteristic
460	C₄×C₈₉	—	2	2	no	—
461	C₄×C₈₉	—	2	2	no	—
462	C₄×C₈₉	—	4	1	no	—
463	C₄×C₈₉	—	4	2	no	—
464	C₄×C₈₉	—	4	2	no	—
465	C₄×C₈₉	—	4	2	no	—
466	C₄×C₈₉	—	8	1	no	—
467	C₄×C₈₉	—	8	1	no	—
468	C₄×C₈₉	—	8	1	no	—
469	C₄×C₈₉	D₄²	1	1	yes	characteristic
470	C₄×C₈₉	D₄²	1	1	yes	characteristic
471	C₄×C₈₉	#546	1	1	yes	characteristic
472	C₄×C₈₉	#546	1	1	yes	characteristic
473	#24388	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
474	C₂×C₈₉	—	4	2	no	—
475	C₂×C₈₉	—	4	2	no	—
476	C₂×C₈₉	—	4	2	no	—
477	C₂×C₈₉	—	8	2	no	—
478	C₂×C₈₉	—	16	1	no	—
479	C₂×C₈₉	#2410	1	1	yes	characteristic
480	C₂×C₈₉	#3005	1	1	yes	characteristic
481	C₂×C₈₉	#3006	1	1	yes	characteristic
482	C₂×C₈₉	#3054	1	1	yes	characteristic
483	C₂×C₈₉	#3055	1	1	yes	characteristic
484	C₂×C₈₉	#3194	1	1	yes	characteristic
485	C₂×C₈₉	#3197	1	1	yes	characteristic
486	C₂×#525	C₂×C₈₉	1	1	yes	characteristic, complemented
487	C₂×#469	C₂×C₈₉	1	1	yes	characteristic, complemented
488	C₂×#468	C₂×C₈₉	1	1	yes	characteristic, complemented
489	C₂×#449	C₂×C₈₉	1	1	yes	characteristic, complemented
490	C₂×#407	C₂×C₈₉	1	1	yes	characteristic, complemented
491	#2847	C₂×C₈₉	1	1	yes	characteristic, complemented
492	#2035	C₂×C₈₉	1	1	yes	characteristic, complemented
493	#2033	C₂×C₈₉	1	1	yes	characteristic, complemented
494	#2000	C₂×C₈₉	1	1	yes	characteristic, complemented
495	#1999	C₂×C₈₉	1	1	yes	characteristic, complemented
496	#1895	C₂×C₈₉	1	1	yes	characteristic, complemented
497	#1894	C₂×C₈₉	1	1	yes	characteristic, complemented
498	#1875	C₂×C₈₉	1	1	yes	characteristic, complemented
499	#1854	C₂×C₈₉	1	1	yes	characteristic, complemented
500	#1788	C₂×C₈₉	1	1	yes	characteristic, complemented
501	C₈₉	#24388	1	1	yes	characteristic, direct product factor, Sylow
502	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
503	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
504	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
505	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
506	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
507	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
508	#525	—	2	4	no	—
509	#525	—	2	4	no	—
510	C₂×#123	—	2	1	no	—
511	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
512	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
513	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
514	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
515	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
516	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
517	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
518	C₂×#120	—	2	1	no	—
519	C₂×#120	—	2	1	no	—
520	C₂×C₄×D₄	—	2	1	no	—
521	C₂×C₄×D₄	—	2	1	no	—
522	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
523	#469	—	2	4	no	—
524	#468	—	2	4	no	—
525	#449	—	2	4	no	—
526	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic, complemented
527	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic, complemented
528	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
529	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
530	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
531	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
532	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
533	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
534	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
535	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
536	#407	—	2	4	no	—
537	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
538	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
539	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
540	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
541	#386	—	2	1	no	—
542	#386	—	2	1	no	—
543	#386	—	2	1	no	—
544	#380	C₂²×C₈₉	1	1	yes	characteristic
545	#380	C₂²×C₈₉	1	1	yes	characteristic
546	#380	C₂²×C₈₉	1	1	yes	characteristic
547	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
548	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
549	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
550	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
551	C₂⁵	D₄×C₈₉	1	1	yes	characteristic
552	C₂×#41	—	2	2	no	—
553	C₂×#41	—	2	2	no	—
554	C₂×#41	—	2	2	no	—
555	C₂×#41	—	2	2	no	—
556	C₂×#41	—	4	1	no	—
557	C₂×#41	—	4	1	no	—
558	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
559	C₂²×D₄	—	2	1	no	—
560	C₂²×D₄	—	2	1	no	—
561	C₂²×D₄	—	2	1	no	—
562	C₂²×D₄	—	2	1	no	—
563	C₂²×D₄	—	2	1	no	—
564	C₂²×D₄	—	2	1	no	—
565	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
566	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
567	C₂³×C₄	—	2	1	no	—
568	C₂³×C₄	—	2	2	no	—
569	C₂³×C₄	—	2	2	no	—
570	C₂³×C₄	—	2	2	no	—
571	C₂³×C₄	—	2	2	no	—
572	C₂³×C₄	—	4	1	no	—
573	C₂³×C₄	—	4	1	no	—
574	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
575	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
576	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
577	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
578	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
579	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
580	C₂×SD₁₆	—	2	2	no	—
581	C₂×SD₁₆	—	2	2	no	—
582	C₂×SD₁₆	—	4	1	no	—
583	C₂×D₈	—	2	2	no	—
584	C₂×D₈	—	2	2	no	—
585	C₂×D₈	—	4	1	no	—
586	C₂×M₁₆	—	2	2	no	—
587	C₂×M₁₆	—	2	2	no	—
588	C₂×M₁₆	—	2	2	no	—
589	C₂×M₁₆	—	2	2	no	—
590	C₂×M₁₆	—	4	1	no	—
591	C₂×M₁₆	—	4	1	no	—
592	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
593	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
594	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
595	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
596	#123	—	2	8	no	—
597	C₂²⋊Q₈	—	2	2	no	—
598	C₂²⋊Q₈	—	2	2	no	—
599	C₂²⋊Q₈	—	2	2	no	—
600	C₂²⋊Q₈	D₄×C₈₉	1	4	yes	complemented
601	#121	—	2	2	no	—
602	#121	—	2	2	no	—
603	#121	—	2	2	no	—
604	#121	—	2	2	no	—
605	#121	—	2	2	no	—
606	#121	—	2	2	no	—
607	#121	—	2	2	no	—
608	#121	—	4	1	no	—
609	#121	—	4	1	no	—
610	#121	D₄×C₈₉	1	4	yes	complemented
611	#120	—	2	8	no	—
612	#120	—	4	4	no	—
613	C₄×D₄	—	2	8	no	—
614	C₄×D₄	—	2	8	no	—
615	#117	—	2	2	no	—
616	#117	—	2	2	no	—
617	C₂×C₄⋊C₄	—	2	1	no	—
618	C₂×C₄⋊C₄	—	2	1	no	—
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×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₂²⋊C₄	—	2	1	no	—
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	1	no	—
629	C₂×C₂²⋊C₄	—	2	1	no	—
630	C₂×C₂²⋊C₄	—	2	1	no	—
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	1	no	—
633	C₂×C₂²⋊C₄	—	2	1	no	—
634	C₂×C₂²⋊C₄	—	2	1	no	—
635	C₂×C₄²	—	2	1	no	—
636	#107	—	2	2	no	—
637	#106	—	2	2	no	—
638	#103	—	2	2	no	—
639	#103	—	2	2	no	—
640	#103	—	4	1	no	—
641	#102	—	2	2	no	—
642	#102	—	2	2	no	—
643	#102	—	2	2	no	—
644	#102	—	2	2	no	—
645	#102	—	4	1	no	—
646	C₂²⋊C₈	—	2	2	no	—
647	C₂²⋊C₈	—	2	2	no	—
648	C₂²⋊C₈	—	2	2	no	—
649	C₂²⋊C₈	D₄×C₈₉	1	4	yes	complemented
650	#95	—	2	1	no	—
651	#95	—	2	1	no	—
652	#95	—	2	1	no	—
653	C₂⁴	—	2	2	no	—
654	C₂⁴	—	2	2	no	—
655	C₂⁴	—	2	2	no	—
656	C₂⁴	—	2	1	no	—
657	C₂⁴	—	2	1	no	—
658	C₂⁴	—	4	1	no	—
659	C₂⁴	—	4	1	no	—
660	C₂⁴	—	4	1	no	—
661	C₂⁴	—	4	1	no	—
662	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
663	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
664	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
665	#41	—	4	4	no	—
666	#41	—	4	4	no	—
667	#41	—	4	4	no	—
668	#41	—	4	4	no	—
669	C₂×Q₈	—	2	1	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
675	C₂×D₄	—	2	4	no	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	4	2	no	—
690	C₂×D₄	—	4	2	no	—
691	C₂×D₄	—	4	2	no	—
692	C₂×D₄	—	4	2	no	—
693	C₂×D₄	—	4	2	no	—
694	C₂×D₄	—	4	2	no	—
695	C₂×D₄	—	4	2	no	—
696	C₂×D₄	—	4	2	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂×D₄	—	4	2	no	—
699	C₂×D₄	—	4	2	no	—
700	C₂×D₄	—	4	2	no	—
701	C₂×D₄	—	4	2	no	—
702	C₂×D₄	—	4	2	no	—
703	C₂×D₄	—	4	2	no	—
704	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	1	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	1	no	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	2	1	no	—
726	C₂²×C₄	—	2	1	no	—
727	C₂²×C₄	—	2	1	no	—
728	C₂²×C₄	—	2	1	no	—
729	C₂²×C₄	—	2	1	no	—
730	C₂²×C₄	—	2	1	no	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	4	1	no	—
733	C₂²×C₄	—	4	1	no	—
734	C₂²×C₄	—	4	1	no	—
735	C₂²×C₄	—	4	4	no	—
736	C₂²×C₄	—	4	4	no	—
737	C₂²×C₄	—	4	4	no	—
738	C₂²×C₄	—	4	4	no	—
739	C₂²×C₄	—	4	2	no	—
740	C₂²×C₄	—	4	2	no	—
741	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
742	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
743	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
744	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
745	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
746	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
747	C₂²×C₄	#41×C₈₉	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
749	SD₁₆	—	4	4	no	—
750	D₈	—	4	4	no	—
751	M₁₆	—	4	4	no	—
752	M₁₆	—	4	4	no	—
753	C₂×C₈	—	2	1	no	—
754	C₂×C₈	—	2	1	no	—
755	C₂×C₈	—	2	1	no	—
756	C₂×C₈	—	2	1	no	—
757	C₂×C₈	—	2	1	no	—
758	C₂×C₈	—	2	1	no	—
759	C₂×C₈	—	2	1	no	—
760	C₂×C₈	—	2	1	no	—
761	C₂×C₈	—	2	1	no	—
762	C₂×C₈	—	2	1	no	—
763	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
764	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
765	C₄⋊C₄	—	2	4	no	—
766	C₄⋊C₄	—	2	4	no	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	—	2	1	no	—
769	C₄⋊C₄	—	2	1	no	—
770	C₄⋊C₄	—	2	1	no	—
771	C₄⋊C₄	—	2	1	no	—
772	C₄⋊C₄	—	2	1	no	—
773	C₄⋊C₄	—	2	1	no	—
774	C₄⋊C₄	—	2	1	no	—
775	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
776	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	4	2	no	—
783	C₂²⋊C₄	—	4	2	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	C₄²	—	2	4	no	—
789	C₂³	—	2	1	no	—
790	C₂³	—	2	1	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	1	no	—
793	C₂³	—	2	1	no	—
794	C₂³	—	2	1	no	—
795	C₂³	—	2	1	no	—
796	C₂³	—	2	1	no	—
797	C₂³	—	2	1	no	—
798	C₂³	—	2	1	no	—
799	C₂³	—	2	1	no	—
800	C₂³	—	2	1	no	—
801	C₂³	—	2	1	no	—
802	C₂³	—	2	1	no	—
803	C₂³	—	2	1	no	—
804	C₂³	—	2	1	no	—
805	C₂³	—	2	1	no	—
806	C₂³	—	2	1	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	4	4	no	—
809	C₂³	—	4	4	no	—
810	C₂³	—	4	4	no	—
811	C₂³	—	4	4	no	—
812	C₂³	—	4	4	no	—
813	C₂³	—	4	4	no	—
814	C₂³	—	4	4	no	—
815	C₂³	—	4	1	no	—
816	C₂³	—	4	1	no	—
817	C₂³	—	4	1	no	—
818	C₂³	—	4	1	no	—
819	C₂³	—	4	1	no	—
820	C₂³	—	4	1	no	—
821	C₂³	—	4	1	no	—
822	C₂³	—	4	1	no	—
823	C₂³	—	4	1	no	—
824	C₂³	—	4	1	no	—
825	C₂³	—	4	1	no	—
826	C₂³	—	4	1	no	—
827	C₂³	—	4	1	no	—
828	C₂³	#120×C₈₉	1	2	yes	—
829	C₂³	#121×C₈₉	1	2	yes	—
830	C₂³	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
831	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
832	Q₈	—	2	2	no	—
833	Q₈	—	2	2	no	—
834	Q₈	—	4	1	no	—
835	Q₈	—	4	1	no	—
836	D₄	—	2	2	no	—
837	D₄	—	2	2	no	—
838	D₄	—	4	8	no	—
839	D₄	—	4	8	no	—
840	D₄	—	4	8	no	—
841	D₄	—	4	1	no	—
842	D₄	—	4	1	no	—
843	D₄	—	4	1	no	—
844	D₄	—	4	1	no	—
845	D₄	—	4	1	no	—
846	D₄	—	4	1	no	—
847	D₄	—	8	4	no	—
848	D₄	—	8	4	no	—
849	D₄	—	8	4	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	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	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	4	4	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	4	4	no	—
871	C₂×C₄	—	4	8	no	—
872	C₂×C₄	—	4	1	no	—
873	C₂×C₄	—	4	1	no	—
874	C₂×C₄	—	4	1	no	—
875	C₂×C₄	—	4	1	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	1	no	—
882	C₂×C₄	—	4	1	no	—
883	C₂×C₄	—	4	1	no	—
884	C₂×C₄	—	4	1	no	—
885	C₂×C₄	—	4	1	no	—
886	C₂×C₄	—	4	1	no	—
887	C₂×C₄	—	4	1	no	—
888	C₂×C₄	—	4	1	no	—
889	C₂×C₄	—	4	1	no	—
890	C₂×C₄	—	4	1	no	—
891	C₂×C₄	#120×C₈₉	1	2	yes	—
892	C₂×C₄	#121×C₈₉	1	2	yes	—
893	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
894	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
895	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
896	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
897	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
898	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
899	C₈	—	2	2	no	—
900	C₈	—	2	2	no	—
901	C₈	—	4	1	no	—
902	C₈	—	4	1	no	—
903	C₂²	—	2	2	no	—
904	C₂²	—	2	2	no	—
905	C₂²	—	2	2	no	—
906	C₂²	—	2	2	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	2	2	no	—
909	C₂²	—	2	2	no	—
910	C₂²	—	2	2	no	—
911	C₂²	—	2	2	no	—
912	C₂²	—	4	16	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	4	1	no	—
915	C₂²	—	4	1	no	—
916	C₂²	—	4	1	no	—
917	C₂²	—	4	1	no	—
918	C₂²	—	4	1	no	—
919	C₂²	—	4	1	no	—
920	C₂²	—	4	1	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	4	1	no	—
924	C₂²	—	4	1	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	8	1	no	—
929	C₂²	—	8	1	no	—
930	C₂²	—	8	1	no	—
931	C₂²	—	8	1	no	—
932	C₂²	—	8	1	no	—
933	C₂²	—	8	1	no	—
934	C₂²	—	8	1	no	—
935	C₂²	—	8	1	no	—
936	C₂²	—	8	1	no	—
937	C₂²	—	8	1	no	—
938	C₂²	—	8	1	no	—
939	C₂²	C₂×#120×C₈₉	1	1	yes	characteristic
940	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
941	C₂²	#534×C₈₉	1	1	yes	characteristic
942	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
943	C₂²	#575×C₈₉	1	1	yes	characteristic
944	C₂²	#575×C₈₉	1	1	yes	characteristic
945	C₂²	#575×C₈₉	1	1	yes	characteristic
946	C₄	—	2	2	no	—
947	C₄	—	2	2	no	—
948	C₄	—	4	1	no	—
949	C₄	—	4	2	no	—
950	C₄	—	4	2	no	—
951	C₄	—	4	2	no	—
952	C₄	—	8	1	no	—
953	C₄	—	8	1	no	—
954	C₄	—	8	1	no	—
955	C₄	D₄²×C₈₉	1	1	yes	characteristic
956	C₄	D₄²×C₈₉	1	1	yes	characteristic
957	C₄	#546×C₈₉	1	1	yes	characteristic
958	C₄	#546×C₈₉	1	1	yes	characteristic
959	C₂	—	4	2	no	—
960	C₂	—	4	2	no	—
961	C₂	—	4	2	no	—
962	C₂	—	8	2	no	—
963	C₂	—	16	1	no	—
964	C₂	C₈₉×#2410	1	1	yes	characteristic
965	C₂	C₈₉×#3005	1	1	yes	characteristic
966	C₂	C₈₉×#3006	1	1	yes	characteristic
967	C₂	C₈₉×#3054	1	1	yes	characteristic
968	C₂	C₈₉×#3055	1	1	yes	characteristic
969	C₂	C₈₉×#3194	1	1	yes	characteristic
970	C₂	C₈₉×#3197	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
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
1. C₂×#525×C₈₉	C₂	semidirect
2. C₂×#469×C₈₉	C₂	semidirect
3. C₂×#468×C₈₉	C₂	semidirect
4. C₂×#449×C₈₉	C₂	semidirect
5. C₂×#407×C₈₉	C₂	semidirect
6. C₈₉×#2847	C₂	semidirect
7. C₈₉×#2035	C₂	semidirect
8. C₈₉×#2033	C₂	semidirect
9. C₈₉×#2000	C₂	semidirect
10. C₈₉×#1999	C₂	semidirect
11. C₈₉×#1895	C₂	semidirect
12. C₈₉×#1894	C₂	semidirect
13. C₈₉×#1875	C₂	semidirect
14. C₈₉×#1854	C₂	semidirect
15. C₈₉×#1788	C₂	semidirect
18. C₂²×SD₁₆×C₈₉	C₂²	semidirect
19. C₂²×D₈×C₈₉	C₂²	semidirect
40. C₂×#107×C₈₉	C₂²	semidirect
41. C₂×#106×C₈₉	C₂²	semidirect
42. C₂×#103×C₈₉	C₂²	semidirect
43. C₂×#103×C₈₉	C₂²	semidirect
44. C₂×#103×C₈₉	C₂²	semidirect
45. C₂×#102×C₈₉	C₂²	semidirect
46. C₂×#102×C₈₉	C₂²	semidirect
47. C₂×#102×C₈₉	C₂²	semidirect
48. C₂×#102×C₈₉	C₂²	semidirect
49. 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
114. C₂²⋊Q₈×C₈₉	D₄	semidirect
124. #121×C₈₉	D₄	semidirect
163. C₂²⋊C₈×C₈₉	D₄	semidirect
473. #24388	C₈₉	direct (N × H)
486. C₂×#525	C₂×C₈₉	semidirect
487. C₂×#469	C₂×C₈₉	semidirect
488. C₂×#468	C₂×C₈₉	semidirect
489. C₂×#449	C₂×C₈₉	semidirect
490. C₂×#407	C₂×C₈₉	semidirect
491. #2847	C₂×C₈₉	semidirect
492. #2035	C₂×C₈₉	semidirect
493. #2033	C₂×C₈₉	semidirect
494. #2000	C₂×C₈₉	semidirect
495. #1999	C₂×C₈₉	semidirect
496. #1895	C₂×C₈₉	semidirect
497. #1894	C₂×C₈₉	semidirect
498. #1875	C₂×C₈₉	semidirect
499. #1854	C₂×C₈₉	semidirect
500. #1788	C₂×C₈₉	semidirect
501. C₈₉	#24388	direct (N × H)
504. C₂²×SD₁₆	C₂²×C₈₉	semidirect
505. C₂²×D₈	C₂²×C₈₉	semidirect
526. C₂×#107	C₂²×C₈₉	semidirect
527. C₂×#106	C₂²×C₈₉	semidirect
528. C₂×#103	C₂²×C₈₉	semidirect
529. C₂×#103	C₂²×C₈₉	semidirect
530. C₂×#103	C₂²×C₈₉	semidirect
531. C₂×#102	C₂²×C₈₉	semidirect
532. C₂×#102	C₂²×C₈₉	semidirect
533. C₂×#102	C₂²×C₈₉	semidirect
534. C₂×#102	C₂²×C₈₉	semidirect
535. C₂×#102	C₂²×C₈₉	semidirect
547. #340	C₂²×C₈₉	semidirect
548. #340	C₂²×C₈₉	semidirect
549. #340	C₂²×C₈₉	semidirect
550. #340	C₂²×C₈₉	semidirect
600. C₂²⋊Q₈	D₄×C₈₉	semidirect
610. #121	D₄×C₈₉	semidirect
649. 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×#469×C₈₉	2
C₂×#468×C₈₉	2
C₂×#449×C₈₉	2
C₂×#407×C₈₉	2
C₈₉×#2847	2
C₈₉×#2035	2
C₈₉×#2033	2
C₈₉×#2000	2
C₈₉×#1999	2
C₈₉×#1895	2
C₈₉×#1894	2
C₈₉×#1875	2
C₈₉×#1854	2
C₈₉×#1788	2
#24388	89

Subgroups — C89×#24388 #36402236

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#24388 #36402236