Subgroups — C₈₉×#60871 #36438719

Order 22784.

1742 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3494	C₂	1	1	yes	maximal, characteristic
2	C₂×#544×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3243	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3241	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3238	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3234	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3232	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3226	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3164	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3136	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3094	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3092	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3091	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#480×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3083	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3081	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	#555×C₈₉	—	2	1	no	—
19	#553×C₈₉	—	2	1	no	—
20	#553×C₈₉	—	2	1	no	—
21	#551×C₈₉	—	2	2	no	—
22	#547×C₈₉	—	2	1	no	—
23	#546×C₈₉	—	2	2	no	—
24	#544×C₈₉	—	2	2	no	—
25	#544×C₈₉	—	2	1	no	—
26	#544×C₈₉	—	2	1	no	—
27	#544×C₈₉	C₂²	1	2	yes	—
28	#544×C₈₉	C₂²	1	2	yes	—
29	#544×C₈₉	C₂²	1	1	yes	characteristic
30	#544×C₈₉	C₂²	1	4	yes	complemented
31	#542×C₈₉	C₂²	1	2	yes	—
32	#540×C₈₉	C₂²	1	2	yes	—
33	#535×C₈₉	C₂²	1	1	yes	characteristic
34	#532×C₈₉	C₂²	1	2	yes	—
35	C₂×C₄⋊Q₈×C₈₉	—	2	1	no	—
36	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
37	#529×C₈₉	C₂²	1	2	yes	—
38	C₂×#125×C₈₉	—	2	1	no	—
39	C₂×#125×C₈₉	C₂²	1	2	yes	complemented
40	#525×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊Q₈×C₈₉	—	2	2	no	—
42	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
43	#520×C₈₉	C₂²	1	1	yes	characteristic
44	#518×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
47	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
48	#501×C₈₉	C₂²	1	4	yes	complemented
49	#501×C₈₉	C₂²	1	4	yes	complemented
50	#500×C₈₉	C₂²	1	4	yes	complemented
51	#499×C₈₉	C₂²	1	4	yes	complemented
52	#490×C₈₉	C₂²	1	4	yes	complemented
53	#489×C₈₉	C₂²	1	4	yes	complemented
54	#488×C₈₉	C₂²	1	4	yes	complemented
55	#486×C₈₉	C₂²	1	4	yes	complemented
56	#485×C₈₉	C₂²	1	2	yes	complemented
57	#484×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#484×C₈₉	C₂²	1	2	yes	complemented
59	#483×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#483×C₈₉	C₂²	1	2	yes	complemented
61	#482×C₈₉	C₂²	1	4	yes	—
62	#482×C₈₉	C₂²	1	2	yes	complemented
63	#481×C₈₉	C₂²	1	2	yes	—
64	#481×C₈₉	C₂²	1	1	yes	characteristic, complemented
65	#481×C₈₉	C₂²	1	2	yes	complemented
66	#480×C₈₉	C₂²	1	2	yes	—
67	#480×C₈₉	C₂²	1	2	yes	—
68	#480×C₈₉	C₂²	1	4	yes	—
69	#480×C₈₉	C₂²	1	2	yes	—
70	#480×C₈₉	C₂²	1	1	yes	characteristic, complemented
71	#480×C₈₉	C₂²	1	2	yes	complemented
72	#479×C₈₉	C₂²	1	4	yes	complemented
73	#478×C₈₉	C₂²	1	4	yes	complemented
74	#478×C₈₉	C₂²	1	4	yes	complemented
75	#478×C₈₉	C₂²	1	4	yes	complemented
76	#477×C₈₉	C₂²	1	4	yes	complemented
77	#476×C₈₉	C₂²	1	4	yes	complemented
78	#474×C₈₉	C₂²	1	4	yes	complemented
79	#474×C₈₉	C₂²	1	4	yes	complemented
80	#433×C₈₉	C₂²	1	4	yes	complemented
81	#432×C₈₉	C₂²	1	2	yes	complemented
82	#431×C₈₉	C₂²	1	2	yes	complemented
83	#428×C₈₉	C₂²	1	2	yes	—
84	#428×C₈₉	C₂²	1	2	yes	—
85	#427×C₈₉	C₂²	1	2	yes	—
86	C₂×#107×C₈₉	C₂²	1	2	yes	—
87	#424×C₈₉	C₂²	1	2	yes	—
88	#418×C₈₉	C₂²	1	2	yes	—
89	#417×C₈₉	C₂²	1	2	yes	—
90	#416×C₈₉	C₂²	1	2	yes	—
91	C₂×#102×C₈₉	C₂²	1	2	yes	—
92	#407×C₈₉	C₂²	1	1	yes	characteristic
93	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
94	#405×C₈₉	C₂²	1	2	yes	—
95	C₂×#41×C₈₉	—	2	2	no	—
96	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₈₉	—	2	2	no	—
98	C₂²×D₄×C₈₉	—	2	1	no	—
99	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₈₉	—	2	1	no	—
101	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
102	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
103	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
104	C₄⋊Q₈×C₈₉	—	2	2	no	—
105	C₄⋊Q₈×C₈₉	—	2	2	no	—
106	C₄⋊Q₈×C₈₉	—	2	4	no	—
107	C₄⋊Q₈×C₈₉	—	2	1	no	—
108	C₄⋊Q₈×C₈₉	—	2	2	no	—
109	C₄⋊Q₈×C₈₉	—	2	2	no	—
110	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
111	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
112	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
113	#127×C₈₉	C₂³	1	2	yes	—
114	#126×C₈₉	—	2	2	no	—
115	#126×C₈₉	—	2	2	no	—
116	#125×C₈₉	—	2	2	no	—
117	#125×C₈₉	—	2	2	no	—
118	#125×C₈₉	—	2	4	no	—
119	#125×C₈₉	—	2	1	no	—
120	#125×C₈₉	—	2	2	no	—
121	#125×C₈₉	—	2	2	no	—
122	#125×C₈₉	C₂³	1	4	yes	—
123	#125×C₈₉	C₂³	1	4	yes	—
124	#125×C₈₉	C₂³	1	2	yes	—
125	#124×C₈₉	—	2	2	no	—
126	#124×C₈₉	—	2	2	no	—
127	#124×C₈₉	C₂³	1	2	yes	—
128	#123×C₈₉	—	2	1	no	—
129	#123×C₈₉	—	2	2	no	—
130	#123×C₈₉	—	2	2	no	—
131	#123×C₈₉	—	2	2	no	—
132	#123×C₈₉	—	2	2	no	—
133	C₂²⋊Q₈×C₈₉	—	2	2	no	—
134	C₂²⋊Q₈×C₈₉	—	2	4	no	—
135	C₂²⋊Q₈×C₈₉	—	2	4	no	—
136	C₂²⋊Q₈×C₈₉	—	2	4	no	—
137	C₂²⋊Q₈×C₈₉	—	2	4	no	—
138	C₂²⋊Q₈×C₈₉	—	2	2	no	—
139	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
140	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
141	#121×C₈₉	—	2	1	no	—
142	#121×C₈₉	—	2	1	no	—
143	#121×C₈₉	—	2	2	no	—
144	#121×C₈₉	—	2	1	no	—
145	#121×C₈₉	—	2	1	no	—
146	#121×C₈₉	—	2	2	no	—
147	#121×C₈₉	—	2	2	no	—
148	#121×C₈₉	C₂³	1	2	yes	—
149	#121×C₈₉	C₂³	1	2	yes	—
150	#121×C₈₉	C₂³	1	1	yes	characteristic
151	#121×C₈₉	C₂³	1	1	yes	characteristic
152	#120×C₈₉	—	2	1	no	—
153	#120×C₈₉	—	2	2	no	—
154	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
155	C₄×D₄×C₈₉	—	2	1	no	—
156	C₄×D₄×C₈₉	—	2	1	no	—
157	C₄×D₄×C₈₉	—	2	2	no	—
158	C₄×D₄×C₈₉	—	2	1	no	—
159	C₄×D₄×C₈₉	—	2	1	no	—
160	C₄×D₄×C₈₉	—	2	2	no	—
161	C₄×D₄×C₈₉	—	2	2	no	—
162	C₄×D₄×C₈₉	C₂³	1	2	yes	—
163	C₄×D₄×C₈₉	C₂³	1	2	yes	—
164	C₄×D₄×C₈₉	C₂³	1	2	yes	—
165	#117×C₈₉	—	2	1	no	—
166	#117×C₈₉	—	2	1	no	—
167	#117×C₈₉	—	2	1	no	—
168	#117×C₈₉	—	2	2	no	—
169	#117×C₈₉	D₄	1	2	yes	—
170	#117×C₈₉	D₄	1	1	yes	characteristic
171	#117×C₈₉	D₄	1	1	yes	characteristic
172	#117×C₈₉	C₂³	1	2	yes	—
173	#117×C₈₉	C₂³	1	1	yes	characteristic
174	#117×C₈₉	C₂³	1	2	yes	—
175	#117×C₈₉	C₂³	1	1	yes	characteristic
176	#117×C₈₉	C₂³	1	1	yes	characteristic
177	#117×C₈₉	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
179	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
180	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
181	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
182	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
183	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
184	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
185	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
194	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
195	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
196	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
197	C₂×C₄²×C₈₉	—	2	1	no	—
198	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
199	#107×C₈₉	C₂³	1	4	yes	—
200	#107×C₈₉	C₂³	1	4	yes	—
201	#107×C₈₉	C₂³	1	2	yes	—
202	#107×C₈₉	C₂³	1	2	yes	—
203	#107×C₈₉	C₂³	1	4	yes	—
204	#107×C₈₉	C₂³	1	4	yes	—
205	#106×C₈₉	C₂³	1	2	yes	—
206	#106×C₈₉	C₂³	1	2	yes	—
207	#106×C₈₉	C₂³	1	4	yes	—
208	#106×C₈₉	C₂³	1	4	yes	—
209	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
210	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
211	#103×C₈₉	C₂³	1	2	yes	—
212	#103×C₈₉	C₂³	1	2	yes	—
213	#103×C₈₉	C₂³	1	4	yes	—
214	#102×C₈₉	C₂³	1	4	yes	—
215	#102×C₈₉	C₂³	1	4	yes	—
216	#102×C₈₉	C₂³	1	2	yes	—
217	#102×C₈₉	C₂³	1	2	yes	—
218	#102×C₈₉	C₂³	1	4	yes	—
219	#102×C₈₉	C₂³	1	4	yes	—
220	#102×C₈₉	C₂³	1	4	yes	—
221	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
222	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
223	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
224	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
225	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
226	#97×C₈₉	C₂³	1	4	yes	—
227	C₄×C₈×C₈₉	C₂³	1	4	yes	—
228	C₂⁴×C₈₉	—	2	1	no	—
229	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
230	#41×C₈₉	—	2	4	no	—
231	#41×C₈₉	—	8	4	no	—
232	C₂×Q₈×C₈₉	—	2	2	no	—
233	C₂×Q₈×C₈₉	—	2	4	no	—
234	C₂×Q₈×C₈₉	—	2	4	no	—
235	C₂×Q₈×C₈₉	—	8	4	no	—
236	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
237	C₂×D₄×C₈₉	—	2	1	no	—
238	C₂×D₄×C₈₉	—	2	1	no	—
239	C₂×D₄×C₈₉	—	2	2	no	—
240	C₂×D₄×C₈₉	—	2	1	no	—
241	C₂×D₄×C₈₉	—	2	2	no	—
242	C₂×D₄×C₈₉	—	2	1	no	—
243	C₂×D₄×C₈₉	—	2	2	no	—
244	C₂×D₄×C₈₉	—	2	2	no	—
245	C₂×D₄×C₈₉	—	2	4	no	—
246	C₂×D₄×C₈₉	—	8	2	no	—
247	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
248	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₈₉	—	2	4	no	—
250	C₂²×C₄×C₈₉	—	2	1	no	—
251	C₂²×C₄×C₈₉	—	2	1	no	—
252	C₂²×C₄×C₈₉	—	2	2	no	—
253	C₂²×C₄×C₈₉	—	2	1	no	—
254	C₂²×C₄×C₈₉	—	2	2	no	—
255	C₂²×C₄×C₈₉	—	2	2	no	—
256	C₂²×C₄×C₈₉	—	2	1	no	—
257	C₂²×C₄×C₈₉	—	2	2	no	—
258	C₂²×C₄×C₈₉	—	2	2	no	—
259	C₂²×C₄×C₈₉	—	2	2	no	—
260	C₂²×C₄×C₈₉	—	8	2	no	—
261	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
266	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
269	M₁₆×C₈₉	—	2	4	no	—
270	C₂×C₈×C₈₉	—	2	4	no	—
271	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
272	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
273	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
274	C₄⋊C₄×C₈₉	—	2	2	no	—
275	C₄⋊C₄×C₈₉	—	2	2	no	—
276	C₄⋊C₄×C₈₉	—	2	2	no	—
277	C₄⋊C₄×C₈₉	—	2	1	no	—
278	C₄⋊C₄×C₈₉	—	2	2	no	—
279	C₄⋊C₄×C₈₉	—	2	4	no	—
280	C₄⋊C₄×C₈₉	—	2	4	no	—
281	C₄⋊C₄×C₈₉	—	2	4	no	—
282	C₄⋊C₄×C₈₉	—	2	4	no	—
283	C₄⋊C₄×C₈₉	—	2	4	no	—
284	C₄⋊C₄×C₈₉	—	2	4	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	2	no	—
289	C₄⋊C₄×C₈₉	—	2	2	no	—
290	C₄⋊C₄×C₈₉	—	2	2	no	—
291	C₄⋊C₄×C₈₉	—	2	1	no	—
292	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
293	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
294	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
295	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
296	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
300	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
304	C₂²⋊C₄×C₈₉	—	2	1	no	—
305	C₂²⋊C₄×C₈₉	—	2	2	no	—
306	C₂²⋊C₄×C₈₉	—	2	2	no	—
307	C₂²⋊C₄×C₈₉	—	2	1	no	—
308	C₂²⋊C₄×C₈₉	—	2	1	no	—
309	C₂²⋊C₄×C₈₉	—	2	2	no	—
310	C₂²⋊C₄×C₈₉	—	2	2	no	—
311	C₂²⋊C₄×C₈₉	—	2	2	no	—
312	C₂²⋊C₄×C₈₉	—	2	2	no	—
313	C₂²⋊C₄×C₈₉	—	2	2	no	—
314	C₂²⋊C₄×C₈₉	—	2	2	no	—
315	C₂²⋊C₄×C₈₉	—	2	1	no	—
316	C₂²⋊C₄×C₈₉	—	2	2	no	—
317	C₂²⋊C₄×C₈₉	—	2	1	no	—
318	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
319	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
320	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
321	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
322	C₄²×C₈₉	—	2	2	no	—
323	C₄²×C₈₉	—	2	2	no	—
324	C₄²×C₈₉	—	2	2	no	—
325	C₄²×C₈₉	—	2	1	no	—
326	C₄²×C₈₉	C₂×D₄	1	2	yes	—
327	C₄²×C₈₉	C₂×D₄	1	2	yes	—
328	C₄²×C₈₉	C₂⁴	1	2	yes	—
329	C₄²×C₈₉	C₂⁴	1	2	yes	—
330	C₂³×C₈₉	—	2	2	no	—
331	C₂³×C₈₉	—	2	2	no	—
332	C₂³×C₈₉	—	2	2	no	—
333	C₂³×C₈₉	—	2	1	no	—
334	C₂³×C₈₉	—	4	1	no	—
335	C₂³×C₈₉	—	4	2	no	—
336	C₂³×C₈₉	—	8	1	no	—
337	C₂³×C₈₉	—	8	1	no	—
338	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
339	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
340	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
341	Q₈×C₈₉	—	2	2	no	—
342	Q₈×C₈₉	—	8	4	no	—
343	Q₈×C₈₉	—	8	4	no	—
344	Q₈×C₈₉	—	8	2	no	—
345	D₄×C₈₉	—	2	4	no	—
346	D₄×C₈₉	—	2	2	no	—
347	D₄×C₈₉	—	4	2	no	—
348	D₄×C₈₉	—	4	4	no	—
349	D₄×C₈₉	—	4	2	no	—
350	D₄×C₈₉	—	4	2	no	—
351	D₄×C₈₉	—	8	2	no	—
352	D₄×C₈₉	—	8	2	no	—
353	D₄×C₈₉	—	8	1	no	—
354	D₄×C₈₉	—	8	2	no	—
355	C₂×C₄×C₈₉	—	2	2	no	—
356	C₂×C₄×C₈₉	—	2	4	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	2	no	—
364	C₂×C₄×C₈₉	—	2	1	no	—
365	C₂×C₄×C₈₉	—	2	1	no	—
366	C₂×C₄×C₈₉	—	2	2	no	—
367	C₂×C₄×C₈₉	—	2	4	no	—
368	C₂×C₄×C₈₉	—	4	2	no	—
369	C₂×C₄×C₈₉	—	4	2	no	—
370	C₂×C₄×C₈₉	—	4	4	no	—
371	C₂×C₄×C₈₉	—	4	2	no	—
372	C₂×C₄×C₈₉	—	4	2	no	—
373	C₂×C₄×C₈₉	—	8	2	no	—
374	C₂×C₄×C₈₉	—	8	2	no	—
375	C₂×C₄×C₈₉	—	8	2	no	—
376	C₂×C₄×C₈₉	—	8	2	no	—
377	C₂×C₄×C₈₉	—	8	2	no	—
378	C₂×C₄×C₈₉	—	8	1	no	—
379	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
381	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
387	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
388	C₈×C₈₉	—	2	2	no	—
389	C₈×C₈₉	—	2	2	no	—
390	C₈×C₈₉	—	2	4	no	—
391	C₂²×C₈₉	—	2	1	no	—
392	C₂²×C₈₉	—	2	1	no	—
393	C₂²×C₈₉	—	2	1	no	—
394	C₂²×C₈₉	—	2	1	no	—
395	C₂²×C₈₉	—	2	1	no	—
396	C₂²×C₈₉	—	2	1	no	—
397	C₂²×C₈₉	—	2	1	no	—
398	C₂²×C₈₉	—	4	4	no	—
399	C₂²×C₈₉	—	4	2	no	—
400	C₂²×C₈₉	—	4	1	no	—
401	C₂²×C₈₉	—	4	1	no	—
402	C₂²×C₈₉	—	4	2	no	—
403	C₂²×C₈₉	—	4	1	no	—
404	C₂²×C₈₉	—	4	2	no	—
405	C₂²×C₈₉	—	16	2	no	—
406	C₂²×C₈₉	#536	1	2	yes	—
407	C₂²×C₈₉	#576	1	2	yes	—
408	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
409	C₄×C₈₉	—	2	2	no	—
410	C₄×C₈₉	—	2	2	no	—
411	C₄×C₈₉	—	2	1	no	—
412	C₄×C₈₉	—	2	1	no	—
413	C₄×C₈₉	—	2	2	no	—
414	C₄×C₈₉	—	2	2	no	—
415	C₄×C₈₉	—	4	2	no	—
416	C₄×C₈₉	—	4	1	no	—
417	C₄×C₈₉	—	4	1	no	—
418	C₄×C₈₉	—	4	4	no	—
419	C₄×C₈₉	—	4	2	no	—
420	C₄×C₈₉	—	4	2	no	—
421	C₄×C₈₉	—	4	1	no	—
422	C₄×C₈₉	#536	1	2	yes	—
423	C₄×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
424	#60871	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
425	C₂×C₈₉	—	2	2	no	—
426	C₂×C₈₉	—	2	2	no	—
427	C₂×C₈₉	—	4	1	no	—
428	C₂×C₈₉	—	8	1	no	—
429	C₂×C₈₉	—	8	2	no	—
430	C₂×C₈₉	C₂×#536	1	1	yes	characteristic
431	C₂×C₈₉	C₂×#576	1	1	yes	characteristic
432	C₂×C₈₉	#3586	1	1	yes	characteristic
433	#3494	C₂×C₈₉	1	1	yes	characteristic
434	C₂×#544	C₂×C₈₉	1	1	yes	characteristic, complemented
435	#3243	C₂×C₈₉	1	4	yes	complemented
436	#3241	C₂×C₈₉	1	4	yes	complemented
437	#3238	C₂×C₈₉	1	2	yes	complemented
438	#3234	C₂×C₈₉	1	2	yes	complemented
439	#3232	C₂×C₈₉	1	2	yes	complemented
440	#3226	C₂×C₈₉	1	2	yes	complemented
441	#3164	C₂×C₈₉	1	2	yes	complemented
442	#3136	C₂×C₈₉	1	2	yes	complemented
443	#3094	C₂×C₈₉	1	1	yes	characteristic, complemented
444	#3092	C₂×C₈₉	1	1	yes	characteristic, complemented
445	#3091	C₂×C₈₉	1	1	yes	characteristic, complemented
446	C₂×#480	C₂×C₈₉	1	1	yes	characteristic, complemented
447	#3083	C₂×C₈₉	1	2	yes	complemented
448	#3081	C₂×C₈₉	1	2	yes	complemented
449	#2924	C₂×C₈₉	1	1	yes	characteristic, complemented
450	C₈₉	#60871	1	1	yes	characteristic, direct product factor, Sylow
451	#555	—	2	1	no	—
452	#553	—	2	1	no	—
453	#553	—	2	1	no	—
454	#551	—	2	2	no	—
455	#547	—	2	1	no	—
456	#546	—	2	2	no	—
457	#544	—	2	2	no	—
458	#544	—	2	1	no	—
459	#544	—	2	1	no	—
460	#544	C₂²×C₈₉	1	2	yes	—
461	#544	C₂²×C₈₉	1	2	yes	—
462	#544	C₂²×C₈₉	1	1	yes	characteristic
463	#544	C₂²×C₈₉	1	4	yes	complemented
464	#542	C₂²×C₈₉	1	2	yes	—
465	#540	C₂²×C₈₉	1	2	yes	—
466	#535	C₂²×C₈₉	1	1	yes	characteristic
467	#532	C₂²×C₈₉	1	2	yes	—
468	C₂×C₄⋊Q₈	—	2	1	no	—
469	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
470	#529	C₂²×C₈₉	1	2	yes	—
471	C₂×#125	—	2	1	no	—
472	C₂×#125	C₂²×C₈₉	1	2	yes	complemented
473	#525	C₂²×C₈₉	1	1	yes	characteristic
474	C₂×C₂²⋊Q₈	—	2	2	no	—
475	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
476	#520	C₂²×C₈₉	1	1	yes	characteristic
477	#518	C₂²×C₈₉	1	1	yes	characteristic
478	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
479	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
480	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
481	#501	C₂²×C₈₉	1	4	yes	complemented
482	#501	C₂²×C₈₉	1	4	yes	complemented
483	#500	C₂²×C₈₉	1	4	yes	complemented
484	#499	C₂²×C₈₉	1	4	yes	complemented
485	#490	C₂²×C₈₉	1	4	yes	complemented
486	#489	C₂²×C₈₉	1	4	yes	complemented
487	#488	C₂²×C₈₉	1	4	yes	complemented
488	#486	C₂²×C₈₉	1	4	yes	complemented
489	#485	C₂²×C₈₉	1	2	yes	complemented
490	#484	C₂²×C₈₉	1	1	yes	characteristic, complemented
491	#484	C₂²×C₈₉	1	2	yes	complemented
492	#483	C₂²×C₈₉	1	1	yes	characteristic, complemented
493	#483	C₂²×C₈₉	1	2	yes	complemented
494	#482	C₂²×C₈₉	1	4	yes	—
495	#482	C₂²×C₈₉	1	2	yes	complemented
496	#481	C₂²×C₈₉	1	2	yes	—
497	#481	C₂²×C₈₉	1	1	yes	characteristic, complemented
498	#481	C₂²×C₈₉	1	2	yes	complemented
499	#480	C₂²×C₈₉	1	2	yes	—
500	#480	C₂²×C₈₉	1	2	yes	—
501	#480	C₂²×C₈₉	1	4	yes	—
502	#480	C₂²×C₈₉	1	2	yes	—
503	#480	C₂²×C₈₉	1	1	yes	characteristic, complemented
504	#480	C₂²×C₈₉	1	2	yes	complemented
505	#479	C₂²×C₈₉	1	4	yes	complemented
506	#478	C₂²×C₈₉	1	4	yes	complemented
507	#478	C₂²×C₈₉	1	4	yes	complemented
508	#478	C₂²×C₈₉	1	4	yes	complemented
509	#477	C₂²×C₈₉	1	4	yes	complemented
510	#476	C₂²×C₈₉	1	4	yes	complemented
511	#474	C₂²×C₈₉	1	4	yes	complemented
512	#474	C₂²×C₈₉	1	4	yes	complemented
513	#433	C₂²×C₈₉	1	4	yes	complemented
514	#432	C₂²×C₈₉	1	2	yes	complemented
515	#431	C₂²×C₈₉	1	2	yes	complemented
516	#428	C₂²×C₈₉	1	2	yes	—
517	#428	C₂²×C₈₉	1	2	yes	—
518	#427	C₂²×C₈₉	1	2	yes	—
519	C₂×#107	C₂²×C₈₉	1	2	yes	—
520	#424	C₂²×C₈₉	1	2	yes	—
521	#418	C₂²×C₈₉	1	2	yes	—
522	#417	C₂²×C₈₉	1	2	yes	—
523	#416	C₂²×C₈₉	1	2	yes	—
524	C₂×#102	C₂²×C₈₉	1	2	yes	—
525	#407	C₂²×C₈₉	1	1	yes	characteristic
526	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
527	#405	C₂²×C₈₉	1	2	yes	—
528	C₂×#41	—	2	2	no	—
529	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
530	C₂²×Q₈	—	2	2	no	—
531	C₂²×D₄	—	2	1	no	—
532	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
533	C₂³×C₄	—	2	1	no	—
534	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
535	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
536	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
537	C₄⋊Q₈	—	2	2	no	—
538	C₄⋊Q₈	—	2	2	no	—
539	C₄⋊Q₈	—	2	4	no	—
540	C₄⋊Q₈	—	2	1	no	—
541	C₄⋊Q₈	—	2	2	no	—
542	C₄⋊Q₈	—	2	2	no	—
543	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
544	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
545	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
546	#127	C₂³×C₈₉	1	2	yes	—
547	#126	—	2	2	no	—
548	#126	—	2	2	no	—
549	#125	—	2	2	no	—
550	#125	—	2	2	no	—
551	#125	—	2	4	no	—
552	#125	—	2	1	no	—
553	#125	—	2	2	no	—
554	#125	—	2	2	no	—
555	#125	C₂³×C₈₉	1	4	yes	—
556	#125	C₂³×C₈₉	1	4	yes	—
557	#125	C₂³×C₈₉	1	2	yes	—
558	#124	—	2	2	no	—
559	#124	—	2	2	no	—
560	#124	C₂³×C₈₉	1	2	yes	—
561	#123	—	2	1	no	—
562	#123	—	2	2	no	—
563	#123	—	2	2	no	—
564	#123	—	2	2	no	—
565	#123	—	2	2	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	4	no	—
568	C₂²⋊Q₈	—	2	4	no	—
569	C₂²⋊Q₈	—	2	4	no	—
570	C₂²⋊Q₈	—	2	4	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
573	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
574	#121	—	2	1	no	—
575	#121	—	2	1	no	—
576	#121	—	2	2	no	—
577	#121	—	2	1	no	—
578	#121	—	2	1	no	—
579	#121	—	2	2	no	—
580	#121	—	2	2	no	—
581	#121	C₂³×C₈₉	1	2	yes	—
582	#121	C₂³×C₈₉	1	2	yes	—
583	#121	C₂³×C₈₉	1	1	yes	characteristic
584	#121	C₂³×C₈₉	1	1	yes	characteristic
585	#120	—	2	1	no	—
586	#120	—	2	2	no	—
587	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
588	C₄×D₄	—	2	1	no	—
589	C₄×D₄	—	2	1	no	—
590	C₄×D₄	—	2	2	no	—
591	C₄×D₄	—	2	1	no	—
592	C₄×D₄	—	2	1	no	—
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	C₂³×C₈₉	1	2	yes	—
596	C₄×D₄	C₂³×C₈₉	1	2	yes	—
597	C₄×D₄	C₂³×C₈₉	1	2	yes	—
598	#117	—	2	1	no	—
599	#117	—	2	1	no	—
600	#117	—	2	1	no	—
601	#117	—	2	2	no	—
602	#117	D₄×C₈₉	1	2	yes	—
603	#117	D₄×C₈₉	1	1	yes	characteristic
604	#117	D₄×C₈₉	1	1	yes	characteristic
605	#117	C₂³×C₈₉	1	2	yes	—
606	#117	C₂³×C₈₉	1	2	yes	—
607	#117	C₂³×C₈₉	1	1	yes	characteristic
608	#117	C₂³×C₈₉	1	1	yes	characteristic
609	#117	C₂³×C₈₉	1	1	yes	characteristic
610	#117	C₂³×C₈₉	1	2	yes	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	—	2	2	no	—
615	C₂×C₄⋊C₄	—	2	2	no	—
616	C₂×C₄⋊C₄	—	2	2	no	—
617	C₂×C₄⋊C₄	—	2	1	no	—
618	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
619	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
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×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	2	no	—
629	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
630	C₂×C₄²	—	2	1	no	—
631	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
632	#107	C₂³×C₈₉	1	4	yes	—
633	#107	C₂³×C₈₉	1	4	yes	—
634	#107	C₂³×C₈₉	1	2	yes	—
635	#107	C₂³×C₈₉	1	2	yes	—
636	#107	C₂³×C₈₉	1	4	yes	—
637	#107	C₂³×C₈₉	1	4	yes	—
638	#106	C₂³×C₈₉	1	2	yes	—
639	#106	C₂³×C₈₉	1	2	yes	—
640	#106	C₂³×C₈₉	1	4	yes	—
641	#106	C₂³×C₈₉	1	4	yes	—
642	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
643	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
644	#103	C₂³×C₈₉	1	2	yes	—
645	#103	C₂³×C₈₉	1	2	yes	—
646	#103	C₂³×C₈₉	1	4	yes	—
647	#102	C₂³×C₈₉	1	4	yes	—
648	#102	C₂³×C₈₉	1	4	yes	—
649	#102	C₂³×C₈₉	1	2	yes	—
650	#102	C₂³×C₈₉	1	2	yes	—
651	#102	C₂³×C₈₉	1	4	yes	—
652	#102	C₂³×C₈₉	1	4	yes	—
653	#102	C₂³×C₈₉	1	4	yes	—
654	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
655	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
656	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
657	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
658	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
659	#97	C₂³×C₈₉	1	4	yes	—
660	C₄×C₈	C₂³×C₈₉	1	4	yes	—
661	C₂⁴	—	2	1	no	—
662	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
663	#41	—	2	4	no	—
664	#41	—	8	4	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	4	no	—
667	C₂×Q₈	—	2	4	no	—
668	C₂×Q₈	—	8	4	no	—
669	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	8	2	no	—
680	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
681	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
682	C₂²×C₄	—	2	4	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	8	2	no	—
694	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
695	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
696	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
697	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
698	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
702	M₁₆	—	2	4	no	—
703	C₂×C₈	—	2	4	no	—
704	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
705	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
706	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
726	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
727	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
728	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
729	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
730	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
731	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
732	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
733	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
734	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
735	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
736	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
737	C₂²⋊C₄	—	2	1	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	1	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
752	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
753	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
754	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	1	no	—
759	C₄²	C₂×D₄×C₈₉	1	2	yes	—
760	C₄²	C₂×D₄×C₈₉	1	2	yes	—
761	C₄²	C₂⁴×C₈₉	1	2	yes	—
762	C₄²	C₂⁴×C₈₉	1	2	yes	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	4	1	no	—
768	C₂³	—	4	2	no	—
769	C₂³	—	8	1	no	—
770	C₂³	—	8	1	no	—
771	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
772	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
773	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
774	Q₈	—	2	2	no	—
775	Q₈	—	8	4	no	—
776	Q₈	—	8	4	no	—
777	Q₈	—	8	2	no	—
778	D₄	—	2	4	no	—
779	D₄	—	2	2	no	—
780	D₄	—	4	2	no	—
781	D₄	—	4	4	no	—
782	D₄	—	4	2	no	—
783	D₄	—	4	2	no	—
784	D₄	—	8	2	no	—
785	D₄	—	8	2	no	—
786	D₄	—	8	1	no	—
787	D₄	—	8	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	4	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	4	2	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	4	4	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	8	2	no	—
807	C₂×C₄	—	8	2	no	—
808	C₂×C₄	—	8	2	no	—
809	C₂×C₄	—	8	2	no	—
810	C₂×C₄	—	8	2	no	—
811	C₂×C₄	—	8	1	no	—
812	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
813	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
814	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
816	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
817	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
818	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
819	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
820	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
821	C₈	—	2	2	no	—
822	C₈	—	2	2	no	—
823	C₈	—	2	4	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	2	1	no	—
830	C₂²	—	2	1	no	—
831	C₂²	—	4	4	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	16	2	no	—
839	C₂²	#536×C₈₉	1	2	yes	—
840	C₂²	#576×C₈₉	1	2	yes	—
841	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	1	no	—
847	C₄	—	2	1	no	—
848	C₄	—	4	4	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	1	no	—
855	C₄	#536×C₈₉	1	2	yes	—
856	C₄	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
857	C₂	—	2	2	no	—
858	C₂	—	2	2	no	—
859	C₂	—	4	1	no	—
860	C₂	—	8	1	no	—
861	C₂	—	8	2	no	—
862	C₂	C₂×#536×C₈₉	1	1	yes	characteristic
863	C₂	C₂×#576×C₈₉	1	1	yes	characteristic
864	C₂	C₈₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₈₉×#3494	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×#117×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#544×C₈₉	C₂	semidirect
3. C₈₉×#3243	C₂	semidirect
4. C₈₉×#3241	C₂	semidirect
5. C₈₉×#3238	C₂	semidirect
6. C₈₉×#3234	C₂	semidirect
7. C₈₉×#3232	C₂	semidirect
8. C₈₉×#3226	C₂	semidirect
9. C₈₉×#3164	C₂	semidirect
10. C₈₉×#3136	C₂	semidirect
11. C₈₉×#3094	C₂	semidirect
12. C₈₉×#3092	C₂	semidirect
13. C₈₉×#3091	C₂	semidirect
14. C₂×#480×C₈₉	C₂	semidirect
15. C₈₉×#3083	C₂	semidirect
16. C₈₉×#3081	C₂	semidirect
17. C₈₉×#2924	C₂	semidirect
30. #544×C₈₉	C₂²	semidirect
36. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
39. C₂×#125×C₈₉	C₂²	semidirect
48. #501×C₈₉	C₂²	semidirect
49. #501×C₈₉	C₂²	semidirect
50. #500×C₈₉	C₂²	semidirect
51. #499×C₈₉	C₂²	semidirect
52. #490×C₈₉	C₂²	semidirect
53. #489×C₈₉	C₂²	semidirect
54. #488×C₈₉	C₂²	semidirect
55. #486×C₈₉	C₂²	semidirect
56. #485×C₈₉	C₂²	semidirect
57. #484×C₈₉	C₂²	semidirect
58. #484×C₈₉	C₂²	semidirect
59. #483×C₈₉	C₂²	semidirect
60. #483×C₈₉	C₂²	semidirect
62. #482×C₈₉	C₂²	semidirect
64. #481×C₈₉	C₂²	semidirect
65. #481×C₈₉	C₂²	semidirect
70. #480×C₈₉	C₂²	semidirect
71. #480×C₈₉	C₂²	semidirect
72. #479×C₈₉	C₂²	semidirect
73. #478×C₈₉	C₂²	semidirect
74. #478×C₈₉	C₂²	semidirect
75. #478×C₈₉	C₂²	semidirect
76. #477×C₈₉	C₂²	semidirect
77. #476×C₈₉	C₂²	semidirect
78. #474×C₈₉	C₂²	semidirect
79. #474×C₈₉	C₂²	semidirect
80. #433×C₈₉	C₂²	semidirect
81. #432×C₈₉	C₂²	semidirect
82. #431×C₈₉	C₂²	semidirect
424. #60871	C₈₉	direct (N × H)
434. C₂×#544	C₂×C₈₉	semidirect
435. #3243	C₂×C₈₉	semidirect
436. #3241	C₂×C₈₉	semidirect
437. #3238	C₂×C₈₉	semidirect
438. #3234	C₂×C₈₉	semidirect
439. #3232	C₂×C₈₉	semidirect
440. #3226	C₂×C₈₉	semidirect
441. #3164	C₂×C₈₉	semidirect
442. #3136	C₂×C₈₉	semidirect
443. #3094	C₂×C₈₉	semidirect
444. #3092	C₂×C₈₉	semidirect
445. #3091	C₂×C₈₉	semidirect
446. C₂×#480	C₂×C₈₉	semidirect
447. #3083	C₂×C₈₉	semidirect
448. #3081	C₂×C₈₉	semidirect
449. #2924	C₂×C₈₉	semidirect
450. C₈₉	#60871	direct (N × H)
463. #544	C₂²×C₈₉	semidirect
469. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
472. C₂×#125	C₂²×C₈₉	semidirect
481. #501	C₂²×C₈₉	semidirect
482. #501	C₂²×C₈₉	semidirect
483. #500	C₂²×C₈₉	semidirect
484. #499	C₂²×C₈₉	semidirect
485. #490	C₂²×C₈₉	semidirect
486. #489	C₂²×C₈₉	semidirect
487. #488	C₂²×C₈₉	semidirect
488. #486	C₂²×C₈₉	semidirect
489. #485	C₂²×C₈₉	semidirect
490. #484	C₂²×C₈₉	semidirect
491. #484	C₂²×C₈₉	semidirect
492. #483	C₂²×C₈₉	semidirect
493. #483	C₂²×C₈₉	semidirect
495. #482	C₂²×C₈₉	semidirect
497. #481	C₂²×C₈₉	semidirect
498. #481	C₂²×C₈₉	semidirect
503. #480	C₂²×C₈₉	semidirect
504. #480	C₂²×C₈₉	semidirect
505. #479	C₂²×C₈₉	semidirect
506. #478	C₂²×C₈₉	semidirect
507. #478	C₂²×C₈₉	semidirect
508. #478	C₂²×C₈₉	semidirect
509. #477	C₂²×C₈₉	semidirect
510. #476	C₂²×C₈₉	semidirect
511. #474	C₂²×C₈₉	semidirect
512. #474	C₂²×C₈₉	semidirect
513. #433	C₂²×C₈₉	semidirect
514. #432	C₂²×C₈₉	semidirect
515. #431	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3494	2
C₂×#544×C₈₉	2
C₈₉×#3243	2
C₈₉×#3241	2
C₈₉×#3238	2
C₈₉×#3234	2
C₈₉×#3232	2
C₈₉×#3226	2
C₈₉×#3164	2
C₈₉×#3136	2
C₈₉×#3094	2
C₈₉×#3092	2
C₈₉×#3091	2
C₂×#480×C₈₉	2
C₈₉×#3083	2
C₈₉×#3081	2
C₈₉×#2924	2
#60871	89

Subgroups — C89×#60871 #36438719

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60871 #36438719