Subgroups — C₈₉×#61159 #36439007

Order 22784.

2120 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#547×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3331	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3330	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3315	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3307	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3303	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3302	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3095	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3077	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3056	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3039	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3005	C₂	1	2	yes	maximal, complemented
15	C₄×AGL(1,ℤ/8)×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×M₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2896	C₂	1	2	yes	maximal, complemented
18	C₂²×#41×C₈₉	C₂²	1	2	yes	—
19	C₂×#137×C₈₉	C₂²	1	2	yes	—
20	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₈₉	C₂²	1	2	yes	—
22	#556×C₈₉	C₂²	1	1	yes	characteristic, complemented
23	#555×C₈₉	C₂²	1	1	yes	characteristic, complemented
24	#554×C₈₉	C₂²	1	1	yes	characteristic, complemented
25	#553×C₈₉	C₂²	1	2	yes	complemented
26	#552×C₈₉	—	2	1	no	—
27	#552×C₈₉	C₂²	1	2	yes	complemented
28	#551×C₈₉	—	2	2	no	—
29	#547×C₈₉	—	2	1	no	—
30	#547×C₈₉	—	2	1	no	—
31	#547×C₈₉	—	2	2	no	—
32	#547×C₈₉	C₂²	1	2	yes	—
33	#547×C₈₉	C₂²	1	2	yes	—
34	#547×C₈₉	C₂²	1	4	yes	—
35	#547×C₈₉	C₂²	1	1	yes	characteristic, complemented
36	#546×C₈₉	—	2	1	no	—
37	#533×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
39	#529×C₈₉	—	2	2	no	—
40	#529×C₈₉	—	2	1	no	—
41	#525×C₈₉	C₂²	1	2	yes	—
42	C₂×#123×C₈₉	—	2	2	no	—
43	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
44	C₂×#121×C₈₉	—	2	1	no	—
45	C₄×#41×C₈₉	—	2	1	no	—
46	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×#117×C₈₉	C₂²	1	2	yes	—
50	C₂²×C₄⋊C₄×C₈₉	—	2	1	no	—
51	#491×C₈₉	C₂²	1	4	yes	complemented
52	#487×C₈₉	C₂²	1	2	yes	complemented
53	#487×C₈₉	C₂²	1	2	yes	complemented
54	#485×C₈₉	C₂²	1	4	yes	complemented
55	#485×C₈₉	C₂²	1	4	yes	complemented
56	#484×C₈₉	C₂²	1	4	yes	complemented
57	#483×C₈₉	C₂²	1	4	yes	complemented
58	#478×C₈₉	C₂²	1	4	yes	complemented
59	#476×C₈₉	C₂²	1	2	yes	complemented
60	#474×C₈₉	C₂²	1	2	yes	complemented
61	#470×C₈₉	C₂²	1	4	yes	complemented
62	#468×C₈₉	C₂²	1	4	yes	complemented
63	#467×C₈₉	C₂²	1	4	yes	complemented
64	#465×C₈₉	C₂²	1	4	yes	complemented
65	#462×C₈₉	C₂²	1	2	yes	complemented
66	#462×C₈₉	C₂²	1	2	yes	complemented
67	#461×C₈₉	C₂²	1	2	yes	complemented
68	#461×C₈₉	C₂²	1	2	yes	complemented
69	#452×C₈₉	C₂²	1	4	yes	complemented
70	#452×C₈₉	C₂²	1	4	yes	complemented
71	#449×C₈₉	C₂²	1	4	yes	complemented
72	#449×C₈₉	C₂²	1	4	yes	complemented
73	#442×C₈₉	C₂²	1	2	yes	complemented
74	#440×C₈₉	C₂²	1	2	yes	complemented
75	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
76	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
77	#436×C₈₉	C₂²	1	2	yes	complemented
78	#435×C₈₉	C₂²	1	4	yes	complemented
79	C₈×D₄×C₈₉	C₂²	1	2	yes	complemented
80	#428×C₈₉	C₂²	1	2	yes	—
81	#428×C₈₉	C₂²	1	1	yes	characteristic
82	#423×C₈₉	C₂²	1	1	yes	characteristic
83	#419×C₈₉	C₂²	1	2	yes	—
84	#419×C₈₉	C₂²	1	2	yes	—
85	#419×C₈₉	C₂²	1	2	yes	—
86	#418×C₈₉	C₂²	1	2	yes	—
87	#418×C₈₉	C₂²	1	1	yes	characteristic
88	#417×C₈₉	C₂²	1	1	yes	characteristic
89	#417×C₈₉	C₂²	1	4	yes	complemented
90	#417×C₈₉	C₂²	1	4	yes	complemented
91	#416×C₈₉	C₂²	1	4	yes	complemented
92	#416×C₈₉	C₂²	1	4	yes	complemented
93	#407×C₈₉	C₂²	1	2	yes	—
94	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
95	C₂×#41×C₈₉	—	2	1	no	—
96	C₂×#41×C₈₉	—	2	2	no	—
97	C₂×#41×C₈₉	—	2	2	no	—
98	C₂×#41×C₈₉	—	2	8	no	—
99	C₂×#41×C₈₉	—	4	4	no	—
100	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
101	C₂×#41×C₈₉	C₂³	1	4	yes	—
102	C₂×#41×C₈₉	C₂³	1	4	yes	—
103	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
104	C₂²×D₄×C₈₉	—	2	2	no	—
105	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
106	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₈₉	—	2	1	no	—
108	C₂³×C₄×C₈₉	—	2	2	no	—
109	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
110	#137×C₈₉	—	4	4	no	—
111	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
112	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
113	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
114	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
115	C₂×D₈×C₈₉	C₂³	1	2	yes	—
116	C₂×M₁₆×C₈₉	—	4	4	no	—
117	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
119	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
120	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
121	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
122	C₄⋊Q₈×C₈₉	—	2	1	no	—
123	C₄⋊Q₈×C₈₉	—	2	1	no	—
124	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
125	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
126	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
127	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
128	#126×C₈₉	—	2	2	no	—
129	#126×C₈₉	—	2	2	no	—
130	#126×C₈₉	—	2	2	no	—
131	#125×C₈₉	—	2	2	no	—
132	#125×C₈₉	—	2	1	no	—
133	#125×C₈₉	C₂³	1	2	yes	—
134	#124×C₈₉	—	2	1	no	—
135	#124×C₈₉	—	2	2	no	—
136	#123×C₈₉	—	2	2	no	—
137	#123×C₈₉	—	2	2	no	—
138	#123×C₈₉	—	2	4	no	—
139	#123×C₈₉	—	2	4	no	—
140	#123×C₈₉	—	2	4	no	—
141	#123×C₈₉	—	2	4	no	—
142	#123×C₈₉	—	2	2	no	—
143	#123×C₈₉	—	2	2	no	—
144	C₂²⋊Q₈×C₈₉	—	2	2	no	—
145	C₂²⋊Q₈×C₈₉	—	2	2	no	—
146	C₂²⋊Q₈×C₈₉	—	2	1	no	—
147	C₂²⋊Q₈×C₈₉	—	2	1	no	—
148	C₂²⋊Q₈×C₈₉	—	2	1	no	—
149	C₂²⋊Q₈×C₈₉	—	2	2	no	—
150	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
151	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
152	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
153	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
154	#121×C₈₉	—	2	2	no	—
155	#121×C₈₉	—	2	2	no	—
156	#121×C₈₉	—	2	4	no	—
157	#121×C₈₉	—	2	2	no	—
158	#121×C₈₉	—	2	1	no	—
159	#121×C₈₉	C₂³	1	2	yes	—
160	#121×C₈₉	C₂³	1	2	yes	—
161	#120×C₈₉	—	2	2	no	—
162	C₄×Q₈×C₈₉	—	2	1	no	—
163	C₄×Q₈×C₈₉	—	2	1	no	—
164	C₄×Q₈×C₈₉	—	2	1	no	—
165	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₈₉	—	2	1	no	—
168	C₄×D₄×C₈₉	—	2	2	no	—
169	C₄×D₄×C₈₉	—	2	1	no	—
170	C₄×D₄×C₈₉	—	2	1	no	—
171	C₄×D₄×C₈₉	—	2	2	no	—
172	C₄×D₄×C₈₉	—	2	2	no	—
173	C₄×D₄×C₈₉	—	2	1	no	—
174	C₄×D₄×C₈₉	—	2	1	no	—
175	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
176	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
177	C₄×D₄×C₈₉	D₄	1	2	yes	—
178	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₈₉	C₂³	1	2	yes	—
180	C₄×D₄×C₈₉	C₂³	1	2	yes	—
181	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₈₉	C₂³	1	2	yes	—
184	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
185	#117×C₈₉	—	2	2	no	—
186	#117×C₈₉	—	2	2	no	—
187	#117×C₈₉	—	2	1	no	—
188	#117×C₈₉	—	2	2	no	—
189	#117×C₈₉	—	2	1	no	—
190	#117×C₈₉	C₂³	1	2	yes	—
191	#117×C₈₉	C₂³	1	2	yes	—
192	#117×C₈₉	C₂³	1	1	yes	characteristic
193	#117×C₈₉	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
195	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
196	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
197	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
198	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
199	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
200	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
203	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
205	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
206	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
207	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
208	C₂×C₄²×C₈₉	—	2	2	no	—
209	C₂×C₄²×C₈₉	—	2	1	no	—
210	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
211	#107×C₈₉	C₂³	1	2	yes	—
212	#107×C₈₉	C₂³	1	4	yes	—
213	#106×C₈₉	C₂³	1	2	yes	—
214	#106×C₈₉	C₂³	1	4	yes	—
215	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
216	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
217	#103×C₈₉	C₂³	1	4	yes	—
218	#103×C₈₉	C₂³	1	4	yes	—
219	#103×C₈₉	C₂³	1	4	yes	—
220	#103×C₈₉	C₂³	1	4	yes	—
221	#103×C₈₉	C₂³	1	2	yes	—
222	#103×C₈₉	C₂³	1	4	yes	—
223	#103×C₈₉	C₂³	1	4	yes	—
224	#102×C₈₉	C₂³	1	2	yes	—
225	#102×C₈₉	C₂³	1	2	yes	—
226	#102×C₈₉	C₂³	1	4	yes	—
227	#102×C₈₉	C₂³	1	4	yes	—
228	#102×C₈₉	C₂³	1	2	yes	—
229	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
230	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
231	#97×C₈₉	C₂³	1	2	yes	—
232	C₄×C₈×C₈₉	C₂³	1	2	yes	—
233	C₂⁴×C₈₉	—	2	1	no	—
234	C₂⁴×C₈₉	C₂×D₄	1	2	yes	—
235	#41×C₈₉	—	2	8	no	—
236	#41×C₈₉	—	2	8	no	—
237	#41×C₈₉	—	2	2	no	—
238	#41×C₈₉	—	2	2	no	—
239	#41×C₈₉	—	4	4	no	—
240	#41×C₈₉	—	4	4	no	—
241	#41×C₈₉	—	4	8	no	—
242	#41×C₈₉	—	4	8	no	—
243	#41×C₈₉	—	4	4	no	—
244	C₂×Q₈×C₈₉	—	2	1	no	—
245	C₂×Q₈×C₈₉	—	2	2	no	—
246	C₂×Q₈×C₈₉	—	2	1	no	—
247	C₂×Q₈×C₈₉	—	2	4	no	—
248	C₂×Q₈×C₈₉	—	2	4	no	—
249	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
250	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
251	C₂×D₄×C₈₉	—	2	1	no	—
252	C₂×D₄×C₈₉	—	2	2	no	—
253	C₂×D₄×C₈₉	—	2	4	no	—
254	C₂×D₄×C₈₉	—	2	4	no	—
255	C₂×D₄×C₈₉	—	2	2	no	—
256	C₂×D₄×C₈₉	—	2	1	no	—
257	C₂×D₄×C₈₉	—	2	2	no	—
258	C₂×D₄×C₈₉	—	4	2	no	—
259	C₂×D₄×C₈₉	—	4	8	no	—
260	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
261	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
262	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
263	C₂×D₄×C₈₉	#41	1	4	yes	complemented
264	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
265	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₈₉	—	2	4	no	—
267	C₂²×C₄×C₈₉	—	2	4	no	—
268	C₂²×C₄×C₈₉	—	2	2	no	—
269	C₂²×C₄×C₈₉	—	2	1	no	—
270	C₂²×C₄×C₈₉	—	2	2	no	—
271	C₂²×C₄×C₈₉	—	2	2	no	—
272	C₂²×C₄×C₈₉	—	2	1	no	—
273	C₂²×C₄×C₈₉	—	2	1	no	—
274	C₂²×C₄×C₈₉	—	2	2	no	—
275	C₂²×C₄×C₈₉	—	2	2	no	—
276	C₂²×C₄×C₈₉	—	2	4	no	—
277	C₂²×C₄×C₈₉	—	2	4	no	—
278	C₂²×C₄×C₈₉	—	2	1	no	—
279	C₂²×C₄×C₈₉	—	4	8	no	—
280	C₂²×C₄×C₈₉	—	4	4	no	—
281	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
282	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
284	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
285	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
289	Q₁₆×C₈₉	—	4	4	no	—
290	SD₁₆×C₈₉	—	2	4	no	—
291	SD₁₆×C₈₉	—	4	4	no	—
292	D₈×C₈₉	—	2	4	no	—
293	M₁₆×C₈₉	—	2	2	no	—
294	M₁₆×C₈₉	—	2	2	no	—
295	M₁₆×C₈₉	—	2	4	no	—
296	M₁₆×C₈₉	—	4	4	no	—
297	C₂×C₈×C₈₉	—	4	4	no	—
298	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
299	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
300	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
301	C₄⋊C₄×C₈₉	—	2	2	no	—
302	C₄⋊C₄×C₈₉	—	2	2	no	—
303	C₄⋊C₄×C₈₉	—	2	4	no	—
304	C₄⋊C₄×C₈₉	—	2	4	no	—
305	C₄⋊C₄×C₈₉	—	2	2	no	—
306	C₄⋊C₄×C₈₉	—	2	2	no	—
307	C₄⋊C₄×C₈₉	—	2	2	no	—
308	C₄⋊C₄×C₈₉	—	2	2	no	—
309	C₄⋊C₄×C₈₉	—	2	1	no	—
310	C₄⋊C₄×C₈₉	—	2	1	no	—
311	C₄⋊C₄×C₈₉	—	2	2	no	—
312	C₄⋊C₄×C₈₉	—	2	2	no	—
313	C₄⋊C₄×C₈₉	—	2	1	no	—
314	C₄⋊C₄×C₈₉	—	2	1	no	—
315	C₄⋊C₄×C₈₉	—	2	2	no	—
316	C₄⋊C₄×C₈₉	—	2	2	no	—
317	C₄⋊C₄×C₈₉	—	2	1	no	—
318	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
319	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
320	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
321	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
322	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
323	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
324	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
325	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
326	C₂²⋊C₄×C₈₉	—	2	1	no	—
327	C₂²⋊C₄×C₈₉	—	2	2	no	—
328	C₂²⋊C₄×C₈₉	—	2	2	no	—
329	C₂²⋊C₄×C₈₉	—	2	2	no	—
330	C₂²⋊C₄×C₈₉	—	2	4	no	—
331	C₂²⋊C₄×C₈₉	—	2	4	no	—
332	C₂²⋊C₄×C₈₉	—	2	2	no	—
333	C₂²⋊C₄×C₈₉	—	2	2	no	—
334	C₂²⋊C₄×C₈₉	—	2	2	no	—
335	C₂²⋊C₄×C₈₉	—	2	2	no	—
336	C₂²⋊C₄×C₈₉	—	2	2	no	—
337	C₂²⋊C₄×C₈₉	—	2	1	no	—
338	C₂²⋊C₄×C₈₉	—	2	1	no	—
339	C₂²⋊C₄×C₈₉	—	2	2	no	—
340	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
341	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
342	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
343	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
344	C₄²×C₈₉	—	2	1	no	—
345	C₄²×C₈₉	—	2	2	no	—
346	C₄²×C₈₉	—	2	1	no	—
347	C₄²×C₈₉	—	2	2	no	—
348	C₄²×C₈₉	—	2	2	no	—
349	C₄²×C₈₉	—	2	1	no	—
350	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
351	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
352	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
353	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
354	C₂³×C₈₉	—	2	4	no	—
355	C₂³×C₈₉	—	2	2	no	—
356	C₂³×C₈₉	—	2	4	no	—
357	C₂³×C₈₉	—	2	1	no	—
358	C₂³×C₈₉	—	4	2	no	—
359	C₂³×C₈₉	—	4	2	no	—
360	C₂³×C₈₉	—	4	2	no	—
361	C₂³×C₈₉	—	4	2	no	—
362	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
363	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
364	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
365	Q₈×C₈₉	—	2	1	no	—
366	Q₈×C₈₉	—	2	4	no	—
367	Q₈×C₈₉	—	2	4	no	—
368	Q₈×C₈₉	—	2	1	no	—
369	Q₈×C₈₉	—	4	4	no	—
370	Q₈×C₈₉	—	4	2	no	—
371	Q₈×C₈₉	—	8	1	no	—
372	D₄×C₈₉	—	2	4	no	—
373	D₄×C₈₉	—	2	2	no	—
374	D₄×C₈₉	—	2	2	no	—
375	D₄×C₈₉	—	2	1	no	—
376	D₄×C₈₉	—	2	2	no	—
377	D₄×C₈₉	—	2	1	no	—
378	D₄×C₈₉	—	4	2	no	—
379	D₄×C₈₉	—	4	8	no	—
380	D₄×C₈₉	—	4	8	no	—
381	D₄×C₈₉	—	4	4	no	—
382	D₄×C₈₉	—	4	2	no	—
383	D₄×C₈₉	—	8	2	no	—
384	D₄×C₈₉	C₂×#41	1	4	yes	—
385	C₂×C₄×C₈₉	—	2	4	no	—
386	C₂×C₄×C₈₉	—	2	4	no	—
387	C₂×C₄×C₈₉	—	2	4	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	2	no	—
393	C₂×C₄×C₈₉	—	2	1	no	—
394	C₂×C₄×C₈₉	—	2	1	no	—
395	C₂×C₄×C₈₉	—	2	1	no	—
396	C₂×C₄×C₈₉	—	2	2	no	—
397	C₂×C₄×C₈₉	—	2	2	no	—
398	C₂×C₄×C₈₉	—	2	2	no	—
399	C₂×C₄×C₈₉	—	2	4	no	—
400	C₂×C₄×C₈₉	—	4	1	no	—
401	C₂×C₄×C₈₉	—	4	8	no	—
402	C₂×C₄×C₈₉	—	4	8	no	—
403	C₂×C₄×C₈₉	—	4	4	no	—
404	C₂×C₄×C₈₉	—	4	2	no	—
405	C₂×C₄×C₈₉	—	4	4	no	—
406	C₂×C₄×C₈₉	—	4	4	no	—
407	C₂×C₄×C₈₉	—	4	2	no	—
408	C₂×C₄×C₈₉	—	4	4	no	—
409	C₂×C₄×C₈₉	—	4	2	no	—
410	C₂×C₄×C₈₉	—	8	1	no	—
411	C₂×C₄×C₈₉	—	8	2	no	—
412	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
417	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
420	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
421	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
422	C₈×C₈₉	—	2	2	no	—
423	C₈×C₈₉	—	2	2	no	—
424	C₈×C₈₉	—	2	4	no	—
425	C₂²×C₈₉	—	2	1	no	—
426	C₂²×C₈₉	—	2	1	no	—
427	C₂²×C₈₉	—	2	2	no	—
428	C₂²×C₈₉	—	2	2	no	—
429	C₂²×C₈₉	—	2	2	no	—
430	C₂²×C₈₉	—	2	2	no	—
431	C₂²×C₈₉	—	2	4	no	—
432	C₂²×C₈₉	—	2	2	no	—
433	C₂²×C₈₉	—	2	2	no	—
434	C₂²×C₈₉	—	4	8	no	—
435	C₂²×C₈₉	—	4	2	no	—
436	C₂²×C₈₉	—	4	2	no	—
437	C₂²×C₈₉	—	4	1	no	—
438	C₂²×C₈₉	—	4	1	no	—
439	C₂²×C₈₉	—	4	1	no	—
440	C₂²×C₈₉	—	8	4	no	—
441	C₂²×C₈₉	#546	1	2	yes	—
442	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
443	C₄×C₈₉	—	2	1	no	—
444	C₄×C₈₉	—	2	1	no	—
445	C₄×C₈₉	—	2	2	no	—
446	C₄×C₈₉	—	2	2	no	—
447	C₄×C₈₉	—	2	1	no	—
448	C₄×C₈₉	—	4	1	no	—
449	C₄×C₈₉	—	4	2	no	—
450	C₄×C₈₉	—	4	4	no	—
451	C₄×C₈₉	—	4	1	no	—
452	C₄×C₈₉	—	4	1	no	—
453	C₄×C₈₉	—	4	2	no	—
454	C₄×C₈₉	—	4	2	no	—
455	C₄×C₈₉	#546	1	2	yes	—
456	C₄×C₈₉	#575	1	2	yes	—
457	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
458	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
459	#61159	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
460	C₂×C₈₉	—	2	2	no	—
461	C₂×C₈₉	—	4	2	no	—
462	C₂×C₈₉	—	4	2	no	—
463	C₂×C₈₉	—	4	4	no	—
464	C₂×C₈₉	—	8	1	no	—
465	C₂×C₈₉	C₂×#546	1	1	yes	characteristic
466	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
467	C₂×C₈₉	#3586	1	1	yes	characteristic
468	#3475	C₂×C₈₉	1	1	yes	characteristic, complemented
469	C₂×#547	C₂×C₈₉	1	1	yes	characteristic, complemented
470	#3331	C₂×C₈₉	1	2	yes	complemented
471	#3330	C₂×C₈₉	1	2	yes	complemented
472	#3315	C₂×C₈₉	1	4	yes	complemented
473	#3307	C₂×C₈₉	1	4	yes	complemented
474	#3303	C₂×C₈₉	1	2	yes	complemented
475	#3302	C₂×C₈₉	1	2	yes	complemented
476	#3139	C₂×C₈₉	1	1	yes	characteristic, complemented
477	#3095	C₂×C₈₉	1	2	yes	complemented
478	#3077	C₂×C₈₉	1	1	yes	characteristic, complemented
479	#3056	C₂×C₈₉	1	2	yes	complemented
480	#3039	C₂×C₈₉	1	1	yes	characteristic, complemented
481	#3005	C₂×C₈₉	1	2	yes	complemented
482	C₄×AGL(1,ℤ/8)	C₂×C₈₉	1	1	yes	characteristic, complemented
483	D₄×M₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
484	#2896	C₂×C₈₉	1	2	yes	complemented
485	C₈₉	#61159	1	1	yes	characteristic, direct product factor, Sylow
486	C₂²×#41	C₂²×C₈₉	1	2	yes	—
487	C₂×#137	C₂²×C₈₉	1	2	yes	—
488	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
489	C₂²×M₁₆	C₂²×C₈₉	1	2	yes	—
490	#556	C₂²×C₈₉	1	1	yes	characteristic, complemented
491	#555	C₂²×C₈₉	1	1	yes	characteristic, complemented
492	#554	C₂²×C₈₉	1	1	yes	characteristic, complemented
493	#553	C₂²×C₈₉	1	2	yes	complemented
494	#552	—	2	1	no	—
495	#552	C₂²×C₈₉	1	2	yes	complemented
496	#551	—	2	2	no	—
497	#547	—	2	1	no	—
498	#547	—	2	1	no	—
499	#547	—	2	2	no	—
500	#547	C₂²×C₈₉	1	2	yes	—
501	#547	C₂²×C₈₉	1	2	yes	—
502	#547	C₂²×C₈₉	1	4	yes	—
503	#547	C₂²×C₈₉	1	1	yes	characteristic, complemented
504	#546	—	2	1	no	—
505	#533	C₂²×C₈₉	1	1	yes	characteristic
506	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
507	#529	—	2	2	no	—
508	#529	—	2	1	no	—
509	#525	C₂²×C₈₉	1	2	yes	—
510	C₂×#123	—	2	2	no	—
511	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
512	C₂×#121	—	2	1	no	—
513	C₄×#41	—	2	1	no	—
514	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
515	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
516	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
517	C₂×#117	C₂²×C₈₉	1	2	yes	—
518	C₂²×C₄⋊C₄	—	2	1	no	—
519	#491	C₂²×C₈₉	1	4	yes	complemented
520	#487	C₂²×C₈₉	1	2	yes	complemented
521	#487	C₂²×C₈₉	1	2	yes	complemented
522	#485	C₂²×C₈₉	1	4	yes	complemented
523	#485	C₂²×C₈₉	1	4	yes	complemented
524	#484	C₂²×C₈₉	1	4	yes	complemented
525	#483	C₂²×C₈₉	1	4	yes	complemented
526	#478	C₂²×C₈₉	1	4	yes	complemented
527	#476	C₂²×C₈₉	1	2	yes	complemented
528	#474	C₂²×C₈₉	1	2	yes	complemented
529	#470	C₂²×C₈₉	1	4	yes	complemented
530	#468	C₂²×C₈₉	1	4	yes	complemented
531	#467	C₂²×C₈₉	1	4	yes	complemented
532	#465	C₂²×C₈₉	1	4	yes	complemented
533	#462	C₂²×C₈₉	1	2	yes	complemented
534	#462	C₂²×C₈₉	1	2	yes	complemented
535	#461	C₂²×C₈₉	1	2	yes	complemented
536	#461	C₂²×C₈₉	1	2	yes	complemented
537	#452	C₂²×C₈₉	1	4	yes	complemented
538	#452	C₂²×C₈₉	1	4	yes	complemented
539	#449	C₂²×C₈₉	1	4	yes	complemented
540	#449	C₂²×C₈₉	1	4	yes	complemented
541	#442	C₂²×C₈₉	1	2	yes	complemented
542	#440	C₂²×C₈₉	1	2	yes	complemented
543	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
544	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
545	#436	C₂²×C₈₉	1	2	yes	complemented
546	#435	C₂²×C₈₉	1	4	yes	complemented
547	C₈×D₄	C₂²×C₈₉	1	2	yes	complemented
548	#428	C₂²×C₈₉	1	2	yes	—
549	#428	C₂²×C₈₉	1	1	yes	characteristic
550	#423	C₂²×C₈₉	1	1	yes	characteristic
551	#419	C₂²×C₈₉	1	2	yes	—
552	#419	C₂²×C₈₉	1	2	yes	—
553	#419	C₂²×C₈₉	1	2	yes	—
554	#418	C₂²×C₈₉	1	2	yes	—
555	#418	C₂²×C₈₉	1	1	yes	characteristic
556	#417	C₂²×C₈₉	1	1	yes	characteristic
557	#417	C₂²×C₈₉	1	4	yes	complemented
558	#417	C₂²×C₈₉	1	4	yes	complemented
559	#416	C₂²×C₈₉	1	4	yes	complemented
560	#416	C₂²×C₈₉	1	4	yes	complemented
561	#407	C₂²×C₈₉	1	2	yes	—
562	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
563	C₂×#41	—	2	1	no	—
564	C₂×#41	—	2	2	no	—
565	C₂×#41	—	2	2	no	—
566	C₂×#41	—	2	8	no	—
567	C₂×#41	—	4	4	no	—
568	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
569	C₂×#41	C₂³×C₈₉	1	4	yes	—
570	C₂×#41	C₂³×C₈₉	1	4	yes	—
571	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
572	C₂²×D₄	—	2	2	no	—
573	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
574	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
575	C₂³×C₄	—	2	1	no	—
576	C₂³×C₄	—	2	2	no	—
577	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
578	#137	—	4	4	no	—
579	AGL(1,ℤ/8)	—	2	4	no	—
580	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
581	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
582	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
583	C₂×D₈	C₂³×C₈₉	1	2	yes	—
584	C₂×M₁₆	—	4	4	no	—
585	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
586	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
587	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
588	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
589	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
590	C₄⋊Q₈	—	2	1	no	—
591	C₄⋊Q₈	—	2	1	no	—
592	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
593	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
594	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
595	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
596	#126	—	2	2	no	—
597	#126	—	2	2	no	—
598	#126	—	2	2	no	—
599	#125	—	2	2	no	—
600	#125	—	2	1	no	—
601	#125	C₂³×C₈₉	1	2	yes	—
602	#124	—	2	1	no	—
603	#124	—	2	2	no	—
604	#123	—	2	2	no	—
605	#123	—	2	2	no	—
606	#123	—	2	4	no	—
607	#123	—	2	4	no	—
608	#123	—	2	4	no	—
609	#123	—	2	4	no	—
610	#123	—	2	2	no	—
611	#123	—	2	2	no	—
612	C₂²⋊Q₈	—	2	2	no	—
613	C₂²⋊Q₈	—	2	2	no	—
614	C₂²⋊Q₈	—	2	1	no	—
615	C₂²⋊Q₈	—	2	1	no	—
616	C₂²⋊Q₈	—	2	1	no	—
617	C₂²⋊Q₈	—	2	2	no	—
618	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
619	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
620	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
621	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
622	#121	—	2	2	no	—
623	#121	—	2	2	no	—
624	#121	—	2	4	no	—
625	#121	—	2	2	no	—
626	#121	—	2	1	no	—
627	#121	C₂³×C₈₉	1	2	yes	—
628	#121	C₂³×C₈₉	1	2	yes	—
629	#120	—	2	2	no	—
630	C₄×Q₈	—	2	1	no	—
631	C₄×Q₈	—	2	1	no	—
632	C₄×Q₈	—	2	1	no	—
633	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
634	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
635	C₄×D₄	—	2	1	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	—	2	1	no	—
638	C₄×D₄	—	2	1	no	—
639	C₄×D₄	—	2	2	no	—
640	C₄×D₄	—	2	2	no	—
641	C₄×D₄	—	2	1	no	—
642	C₄×D₄	—	2	1	no	—
643	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
644	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
645	C₄×D₄	D₄×C₈₉	1	2	yes	—
646	C₄×D₄	C₂³×C₈₉	1	2	yes	—
647	C₄×D₄	C₂³×C₈₉	1	2	yes	—
648	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
649	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
650	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
651	C₄×D₄	C₂³×C₈₉	1	2	yes	—
652	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
653	#117	—	2	2	no	—
654	#117	—	2	2	no	—
655	#117	—	2	1	no	—
656	#117	—	2	2	no	—
657	#117	—	2	1	no	—
658	#117	C₂³×C₈₉	1	1	yes	characteristic
659	#117	C₂³×C₈₉	1	2	yes	—
660	#117	C₂³×C₈₉	1	2	yes	—
661	#117	C₂³×C₈₉	1	2	yes	—
662	C₂×C₄⋊C₄	—	2	1	no	—
663	C₂×C₄⋊C₄	—	2	2	no	—
664	C₂×C₄⋊C₄	—	2	1	no	—
665	C₂×C₄⋊C₄	—	2	2	no	—
666	C₂×C₄⋊C₄	—	2	2	no	—
667	C₂×C₄⋊C₄	—	2	4	no	—
668	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
671	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
672	C₂×C₂²⋊C₄	—	2	2	no	—
673	C₂×C₂²⋊C₄	—	2	2	no	—
674	C₂×C₂²⋊C₄	—	2	1	no	—
675	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
676	C₂×C₄²	—	2	2	no	—
677	C₂×C₄²	—	2	1	no	—
678	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
679	#107	C₂³×C₈₉	1	2	yes	—
680	#107	C₂³×C₈₉	1	4	yes	—
681	#106	C₂³×C₈₉	1	2	yes	—
682	#106	C₂³×C₈₉	1	4	yes	—
683	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
684	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
685	#103	C₂³×C₈₉	1	4	yes	—
686	#103	C₂³×C₈₉	1	4	yes	—
687	#103	C₂³×C₈₉	1	4	yes	—
688	#103	C₂³×C₈₉	1	4	yes	—
689	#103	C₂³×C₈₉	1	2	yes	—
690	#103	C₂³×C₈₉	1	4	yes	—
691	#103	C₂³×C₈₉	1	4	yes	—
692	#102	C₂³×C₈₉	1	2	yes	—
693	#102	C₂³×C₈₉	1	2	yes	—
694	#102	C₂³×C₈₉	1	4	yes	—
695	#102	C₂³×C₈₉	1	4	yes	—
696	#102	C₂³×C₈₉	1	2	yes	—
697	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
698	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
699	#97	C₂³×C₈₉	1	2	yes	—
700	C₄×C₈	C₂³×C₈₉	1	2	yes	—
701	C₂⁴	—	2	1	no	—
702	C₂⁴	C₂×D₄×C₈₉	1	2	yes	—
703	#41	—	2	8	no	—
704	#41	—	2	8	no	—
705	#41	—	2	2	no	—
706	#41	—	2	2	no	—
707	#41	—	4	4	no	—
708	#41	—	4	4	no	—
709	#41	—	4	8	no	—
710	#41	—	4	8	no	—
711	#41	—	4	4	no	—
712	C₂×Q₈	—	2	1	no	—
713	C₂×Q₈	—	2	2	no	—
714	C₂×Q₈	—	2	1	no	—
715	C₂×Q₈	—	2	4	no	—
716	C₂×Q₈	—	2	4	no	—
717	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
718	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
719	C₂×D₄	—	2	1	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	4	2	no	—
727	C₂×D₄	—	4	8	no	—
728	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
729	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
730	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
731	C₂×D₄	#41×C₈₉	1	4	yes	complemented
732	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
733	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
734	C₂²×C₄	—	2	4	no	—
735	C₂²×C₄	—	2	4	no	—
736	C₂²×C₄	—	2	2	no	—
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	4	no	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	2	1	no	—
747	C₂²×C₄	—	4	8	no	—
748	C₂²×C₄	—	4	4	no	—
749	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
750	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
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	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
757	Q₁₆	—	4	4	no	—
758	SD₁₆	—	2	4	no	—
759	SD₁₆	—	4	4	no	—
760	D₈	—	2	4	no	—
761	M₁₆	—	2	2	no	—
762	M₁₆	—	2	2	no	—
763	M₁₆	—	2	4	no	—
764	M₁₆	—	4	4	no	—
765	C₂×C₈	—	4	4	no	—
766	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
767	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
768	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	4	no	—
772	C₄⋊C₄	—	2	4	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	1	no	—
778	C₄⋊C₄	—	2	1	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	1	no	—
782	C₄⋊C₄	—	2	1	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	1	no	—
786	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
787	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
788	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
789	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
790	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
791	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
792	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
793	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
794	C₂²⋊C₄	—	2	1	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	1	no	—
806	C₂²⋊C₄	—	2	1	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
809	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
810	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
811	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
812	C₄²	—	2	1	no	—
813	C₄²	—	2	2	no	—
814	C₄²	—	2	1	no	—
815	C₄²	—	2	2	no	—
816	C₄²	—	2	2	no	—
817	C₄²	—	2	1	no	—
818	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
819	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
820	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
821	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
822	C₂³	—	2	4	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	4	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	4	2	no	—
827	C₂³	—	4	2	no	—
828	C₂³	—	4	2	no	—
829	C₂³	—	4	2	no	—
830	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
831	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
832	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
833	Q₈	—	2	1	no	—
834	Q₈	—	2	4	no	—
835	Q₈	—	2	4	no	—
836	Q₈	—	2	1	no	—
837	Q₈	—	4	4	no	—
838	Q₈	—	4	2	no	—
839	Q₈	—	8	1	no	—
840	D₄	—	2	4	no	—
841	D₄	—	2	2	no	—
842	D₄	—	2	2	no	—
843	D₄	—	2	1	no	—
844	D₄	—	2	2	no	—
845	D₄	—	2	1	no	—
846	D₄	—	4	2	no	—
847	D₄	—	4	8	no	—
848	D₄	—	4	8	no	—
849	D₄	—	4	4	no	—
850	D₄	—	4	2	no	—
851	D₄	—	8	2	no	—
852	D₄	C₂×#41×C₈₉	1	4	yes	—
853	C₂×C₄	—	2	4	no	—
854	C₂×C₄	—	2	4	no	—
855	C₂×C₄	—	2	4	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	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	4	no	—
868	C₂×C₄	—	4	1	no	—
869	C₂×C₄	—	4	8	no	—
870	C₂×C₄	—	4	8	no	—
871	C₂×C₄	—	4	4	no	—
872	C₂×C₄	—	4	2	no	—
873	C₂×C₄	—	4	4	no	—
874	C₂×C₄	—	4	4	no	—
875	C₂×C₄	—	4	2	no	—
876	C₂×C₄	—	4	4	no	—
877	C₂×C₄	—	4	2	no	—
878	C₂×C₄	—	8	1	no	—
879	C₂×C₄	—	8	2	no	—
880	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
881	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
882	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
883	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
884	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
885	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
886	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
887	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
888	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
889	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
890	C₈	—	2	2	no	—
891	C₈	—	2	2	no	—
892	C₈	—	2	4	no	—
893	C₂²	—	2	1	no	—
894	C₂²	—	2	1	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	2	no	—
898	C₂²	—	2	2	no	—
899	C₂²	—	2	2	no	—
900	C₂²	—	2	2	no	—
901	C₂²	—	2	4	no	—
902	C₂²	—	4	8	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	1	no	—
906	C₂²	—	4	1	no	—
907	C₂²	—	4	1	no	—
908	C₂²	—	8	4	no	—
909	C₂²	#546×C₈₉	1	2	yes	—
910	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
911	C₄	—	2	1	no	—
912	C₄	—	2	1	no	—
913	C₄	—	2	1	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	2	no	—
916	C₄	—	4	1	no	—
917	C₄	—	4	2	no	—
918	C₄	—	4	2	no	—
919	C₄	—	4	1	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	4	no	—
922	C₄	—	4	1	no	—
923	C₄	#546×C₈₉	1	2	yes	—
924	C₄	#575×C₈₉	1	2	yes	—
925	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
926	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
927	C₂	—	2	2	no	—
928	C₂	—	4	2	no	—
929	C₂	—	4	2	no	—
930	C₂	—	4	4	no	—
931	C₂	—	8	1	no	—
932	C₂	C₂×#546×C₈₉	1	1	yes	characteristic
933	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
934	C₂	C₈₉×#3586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3475	C₂	semidirect
2. C₂×#547×C₈₉	C₂	semidirect
3. C₈₉×#3331	C₂	semidirect
4. C₈₉×#3330	C₂	semidirect
5. C₈₉×#3315	C₂	semidirect
6. C₈₉×#3307	C₂	semidirect
7. C₈₉×#3303	C₂	semidirect
8. C₈₉×#3302	C₂	semidirect
9. C₈₉×#3139	C₂	semidirect
10. C₈₉×#3095	C₂	semidirect
11. C₈₉×#3077	C₂	semidirect
12. C₈₉×#3056	C₂	semidirect
13. C₈₉×#3039	C₂	semidirect
14. C₈₉×#3005	C₂	semidirect
15. C₄×AGL(1,ℤ/8)×C₈₉	C₂	semidirect
16. D₄×M₁₆×C₈₉	C₂	semidirect
17. C₈₉×#2896	C₂	semidirect
22. #556×C₈₉	C₂²	semidirect
23. #555×C₈₉	C₂²	semidirect
24. #554×C₈₉	C₂²	semidirect
25. #553×C₈₉	C₂²	semidirect
27. #552×C₈₉	C₂²	semidirect
35. #547×C₈₉	C₂²	semidirect
51. #491×C₈₉	C₂²	semidirect
52. #487×C₈₉	C₂²	semidirect
53. #487×C₈₉	C₂²	semidirect
54. #485×C₈₉	C₂²	semidirect
55. #485×C₈₉	C₂²	semidirect
56. #484×C₈₉	C₂²	semidirect
57. #483×C₈₉	C₂²	semidirect
58. #478×C₈₉	C₂²	semidirect
59. #476×C₈₉	C₂²	semidirect
60. #474×C₈₉	C₂²	semidirect
61. #470×C₈₉	C₂²	semidirect
62. #468×C₈₉	C₂²	semidirect
63. #467×C₈₉	C₂²	semidirect
64. #465×C₈₉	C₂²	semidirect
65. #462×C₈₉	C₂²	semidirect
66. #462×C₈₉	C₂²	semidirect
67. #461×C₈₉	C₂²	semidirect
68. #461×C₈₉	C₂²	semidirect
69. #452×C₈₉	C₂²	semidirect
70. #452×C₈₉	C₂²	semidirect
71. #449×C₈₉	C₂²	semidirect
72. #449×C₈₉	C₂²	semidirect
73. #442×C₈₉	C₂²	semidirect
74. #440×C₈₉	C₂²	semidirect
75. C₄×SD₁₆×C₈₉	C₂²	semidirect
76. C₄×D₈×C₈₉	C₂²	semidirect
77. #436×C₈₉	C₂²	semidirect
78. #435×C₈₉	C₂²	semidirect
79. C₈×D₄×C₈₉	C₂²	semidirect
89. #417×C₈₉	C₂²	semidirect
90. #417×C₈₉	C₂²	semidirect
91. #416×C₈₉	C₂²	semidirect
92. #416×C₈₉	C₂²	semidirect
263. C₂×D₄×C₈₉	#41	semidirect
459. #61159	C₈₉	direct (N × H)
468. #3475	C₂×C₈₉	semidirect
469. C₂×#547	C₂×C₈₉	semidirect
470. #3331	C₂×C₈₉	semidirect
471. #3330	C₂×C₈₉	semidirect
472. #3315	C₂×C₈₉	semidirect
473. #3307	C₂×C₈₉	semidirect
474. #3303	C₂×C₈₉	semidirect
475. #3302	C₂×C₈₉	semidirect
476. #3139	C₂×C₈₉	semidirect
477. #3095	C₂×C₈₉	semidirect
478. #3077	C₂×C₈₉	semidirect
479. #3056	C₂×C₈₉	semidirect
480. #3039	C₂×C₈₉	semidirect
481. #3005	C₂×C₈₉	semidirect
482. C₄×AGL(1,ℤ/8)	C₂×C₈₉	semidirect
483. D₄×M₁₆	C₂×C₈₉	semidirect
484. #2896	C₂×C₈₉	semidirect
485. C₈₉	#61159	direct (N × H)
490. #556	C₂²×C₈₉	semidirect
491. #555	C₂²×C₈₉	semidirect
492. #554	C₂²×C₈₉	semidirect
493. #553	C₂²×C₈₉	semidirect
495. #552	C₂²×C₈₉	semidirect
503. #547	C₂²×C₈₉	semidirect
519. #491	C₂²×C₈₉	semidirect
520. #487	C₂²×C₈₉	semidirect
521. #487	C₂²×C₈₉	semidirect
522. #485	C₂²×C₈₉	semidirect
523. #485	C₂²×C₈₉	semidirect
524. #484	C₂²×C₈₉	semidirect
525. #483	C₂²×C₈₉	semidirect
526. #478	C₂²×C₈₉	semidirect
527. #476	C₂²×C₈₉	semidirect
528. #474	C₂²×C₈₉	semidirect
529. #470	C₂²×C₈₉	semidirect
530. #468	C₂²×C₈₉	semidirect
531. #467	C₂²×C₈₉	semidirect
532. #465	C₂²×C₈₉	semidirect
533. #462	C₂²×C₈₉	semidirect
534. #462	C₂²×C₈₉	semidirect
535. #461	C₂²×C₈₉	semidirect
536. #461	C₂²×C₈₉	semidirect
537. #452	C₂²×C₈₉	semidirect
538. #452	C₂²×C₈₉	semidirect
539. #449	C₂²×C₈₉	semidirect
540. #449	C₂²×C₈₉	semidirect
541. #442	C₂²×C₈₉	semidirect
542. #440	C₂²×C₈₉	semidirect
543. C₄×SD₁₆	C₂²×C₈₉	semidirect
544. C₄×D₈	C₂²×C₈₉	semidirect
545. #436	C₂²×C₈₉	semidirect
546. #435	C₂²×C₈₉	semidirect
547. C₈×D₄	C₂²×C₈₉	semidirect
557. #417	C₂²×C₈₉	semidirect
558. #417	C₂²×C₈₉	semidirect
559. #416	C₂²×C₈₉	semidirect
560. #416	C₂²×C₈₉	semidirect
731. C₂×D₄	#41×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3475	2
C₂×#547×C₈₉	2
C₈₉×#3331	2
C₈₉×#3330	2
C₈₉×#3315	2
C₈₉×#3307	2
C₈₉×#3303	2
C₈₉×#3302	2
C₈₉×#3139	2
C₈₉×#3095	2
C₈₉×#3077	2
C₈₉×#3056	2
C₈₉×#3039	2
C₈₉×#3005	2
C₄×AGL(1,ℤ/8)×C₈₉	2
D₄×M₁₆×C₈₉	2
C₈₉×#2896	2
#61159	89

Subgroups — C89×#61159 #36439007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61159 #36439007