Subgroups — C₈₉×#62039 #36439887

Order 22784.

1896 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3392	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3329	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3326	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3307	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3305	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3274	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3272	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3265	C₂	1	2	yes	maximal, complemented
15	C₈₉×#3257	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3254	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3221	C₂	1	2	yes	maximal, complemented
18	C₈₉×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3118	C₂	1	2	yes	maximal, complemented
20	C₈₉×#3101	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#3042	C₂	1	2	yes	maximal, complemented
22	C₈₉×#3036	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
25	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
26	C₂²×SD₁₆×C₈₉	C₂²	1	2	yes	—
27	#562×C₈₉	—	2	2	no	—
28	#559×C₈₉	—	2	1	no	—
29	#559×C₈₉	C₂²	1	1	yes	characteristic, complemented
30	#557×C₈₉	C₂²	1	1	yes	characteristic, complemented
31	#555×C₈₉	C₂²	1	1	yes	characteristic
32	#554×C₈₉	—	2	1	no	—
33	#554×C₈₉	C₂²	1	1	yes	characteristic
34	#553×C₈₉	—	2	1	no	—
35	#553×C₈₉	C₂²	1	2	yes	—
36	#550×C₈₉	C₂²	1	1	yes	characteristic
37	#550×C₈₉	C₂²	1	1	yes	characteristic, complemented
38	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	#548×C₈₉	C₂²	1	2	yes	complemented
40	#547×C₈₉	C₂²	1	2	yes	complemented
41	#546×C₈₉	—	2	1	no	—
42	#546×C₈₉	—	2	2	no	—
43	D₄²×C₈₉	C₂²	1	2	yes	—
44	D₄²×C₈₉	C₂²	1	1	yes	characteristic
45	#542×C₈₉	—	2	1	no	—
46	#542×C₈₉	C₂²	1	2	yes	complemented
47	#540×C₈₉	—	2	1	no	—
48	#540×C₈₉	C₂²	1	2	yes	—
49	#539×C₈₉	—	2	2	no	—
50	#538×C₈₉	—	2	2	no	—
51	#536×C₈₉	C₂²	1	2	yes	complemented
52	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	#532×C₈₉	C₂²	1	1	yes	characteristic
54	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	#529×C₈₉	C₂²	1	1	yes	characteristic
56	#525×C₈₉	—	2	1	no	—
57	C₂×#121×C₈₉	—	2	1	no	—
58	#518×C₈₉	C₂²	1	2	yes	—
59	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
60	#496×C₈₉	C₂²	1	2	yes	complemented
61	#493×C₈₉	C₂²	1	1	yes	characteristic, complemented
62	#492×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	#492×C₈₉	C₂²	1	2	yes	complemented
64	#491×C₈₉	C₂²	1	2	yes	complemented
65	#488×C₈₉	C₂²	1	2	yes	complemented
66	#487×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#486×C₈₉	C₂²	1	1	yes	characteristic, complemented
68	#485×C₈₉	C₂²	1	2	yes	complemented
69	#483×C₈₉	C₂²	1	1	yes	characteristic, complemented
70	#483×C₈₉	C₂²	1	1	yes	characteristic, complemented
71	#482×C₈₉	C₂²	1	2	yes	complemented
72	#479×C₈₉	C₂²	1	2	yes	complemented
73	#478×C₈₉	C₂²	1	2	yes	complemented
74	#477×C₈₉	C₂²	1	1	yes	characteristic, complemented
75	#477×C₈₉	C₂²	1	1	yes	characteristic, complemented
76	#476×C₈₉	C₂²	1	1	yes	characteristic
77	#476×C₈₉	C₂²	1	1	yes	characteristic, complemented
78	#474×C₈₉	C₂²	1	2	yes	complemented
79	#469×C₈₉	C₂²	1	2	yes	complemented
80	#468×C₈₉	C₂²	1	2	yes	complemented
81	#468×C₈₉	C₂²	1	2	yes	complemented
82	#468×C₈₉	C₂²	1	2	yes	complemented
83	#466×C₈₉	C₂²	1	2	yes	complemented
84	#465×C₈₉	C₂²	1	2	yes	complemented
85	#463×C₈₉	C₂²	1	2	yes	—
86	#463×C₈₉	C₂²	1	2	yes	—
87	#463×C₈₉	C₂²	1	2	yes	complemented
88	#463×C₈₉	C₂²	1	2	yes	complemented
89	#463×C₈₉	C₂²	1	2	yes	complemented
90	#463×C₈₉	C₂²	1	2	yes	complemented
91	#461×C₈₉	C₂²	1	1	yes	characteristic
92	#461×C₈₉	C₂²	1	2	yes	—
93	#461×C₈₉	C₂²	1	1	yes	characteristic
94	#461×C₈₉	C₂²	1	1	yes	characteristic, complemented
95	#461×C₈₉	C₂²	1	1	yes	characteristic, complemented
96	#461×C₈₉	C₂²	1	2	yes	complemented
97	#461×C₈₉	C₂²	1	2	yes	complemented
98	#460×C₈₉	C₂²	1	1	yes	characteristic, complemented
99	#460×C₈₉	C₂²	1	2	yes	complemented
100	#460×C₈₉	C₂²	1	1	yes	characteristic, complemented
101	#459×C₈₉	C₂²	1	1	yes	characteristic
102	#459×C₈₉	C₂²	1	2	yes	complemented
103	#459×C₈₉	C₂²	1	1	yes	characteristic, complemented
104	#450×C₈₉	C₂²	1	1	yes	characteristic
105	#450×C₈₉	C₂²	1	1	yes	characteristic
106	#450×C₈₉	C₂²	1	2	yes	—
107	#449×C₈₉	C₂²	1	2	yes	complemented
108	#449×C₈₉	C₂²	1	2	yes	complemented
109	#449×C₈₉	C₂²	1	2	yes	complemented
110	#449×C₈₉	C₂²	1	2	yes	complemented
111	#448×C₈₉	C₂²	1	2	yes	complemented
112	#448×C₈₉	C₂²	1	2	yes	complemented
113	#447×C₈₉	C₂²	1	2	yes	—
114	#446×C₈₉	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
116	#442×C₈₉	C₂²	1	2	yes	complemented
117	#440×C₈₉	C₂²	1	2	yes	—
118	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
121	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
122	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₈×C₈₉	C₂²	1	2	yes	—
124	#436×C₈₉	C₂²	1	2	yes	complemented
125	#436×C₈₉	C₂²	1	1	yes	characteristic, complemented
126	#435×C₈₉	C₂²	1	2	yes	complemented
127	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
128	#433×C₈₉	C₂²	1	2	yes	complemented
129	#431×C₈₉	C₂²	1	1	yes	characteristic, complemented
130	#424×C₈₉	C₂²	1	2	yes	complemented
131	#423×C₈₉	C₂²	1	1	yes	characteristic, complemented
132	#419×C₈₉	C₂²	1	2	yes	complemented
133	#417×C₈₉	C₂²	1	2	yes	complemented
134	#416×C₈₉	C₂²	1	2	yes	complemented
135	C₂×#41×C₈₉	—	2	1	no	—
136	C₂×#41×C₈₉	—	2	1	no	—
137	C₂×#41×C₈₉	C₂³	1	2	yes	—
138	C₂×#41×C₈₉	C₂³	1	2	yes	—
139	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
140	C₂²×D₄×C₈₉	—	2	1	no	—
141	C₂²×D₄×C₈₉	—	2	2	no	—
142	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
143	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₈₉	—	2	1	no	—
145	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
146	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
147	C₂×SD₁₆×C₈₉	—	4	4	no	—
148	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
154	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
158	C₂×D₈×C₈₉	C₂³	1	2	yes	—
159	C₂×D₈×C₈₉	C₂³	1	2	yes	—
160	C₂×D₈×C₈₉	C₂³	1	2	yes	—
161	C₂×D₈×C₈₉	C₂³	1	2	yes	—
162	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
163	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
164	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₈₉	—	2	1	no	—
166	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
169	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
171	#127×C₈₉	—	2	1	no	—
172	#127×C₈₉	C₂³	1	1	yes	characteristic
173	#127×C₈₉	C₂³	1	2	yes	—
174	#127×C₈₉	C₂³	1	1	yes	characteristic
175	#126×C₈₉	—	2	2	no	—
176	#126×C₈₉	—	2	2	no	—
177	#126×C₈₉	D₄	1	2	yes	—
178	#125×C₈₉	—	2	2	no	—
179	#125×C₈₉	—	2	1	no	—
180	#125×C₈₉	—	2	1	no	—
181	#125×C₈₉	D₄	1	1	yes	characteristic
182	#125×C₈₉	C₂³	1	2	yes	—
183	#124×C₈₉	—	2	1	no	—
184	#124×C₈₉	—	2	2	no	—
185	#124×C₈₉	—	2	2	no	—
186	#124×C₈₉	—	2	2	no	—
187	#124×C₈₉	—	2	1	no	—
188	#124×C₈₉	D₄	1	1	yes	characteristic
189	#124×C₈₉	C₂³	1	2	yes	—
190	#124×C₈₉	C₂³	1	2	yes	—
191	#123×C₈₉	—	2	2	no	—
192	#123×C₈₉	—	2	2	no	—
193	#123×C₈₉	—	2	2	no	—
194	#123×C₈₉	—	2	2	no	—
195	#123×C₈₉	—	2	2	no	—
196	#123×C₈₉	—	2	2	no	—
197	#123×C₈₉	—	2	2	no	—
198	#123×C₈₉	—	2	2	no	—
199	#123×C₈₉	—	2	2	no	—
200	#123×C₈₉	D₄	1	2	yes	—
201	C₂²⋊Q₈×C₈₉	—	2	1	no	—
202	C₂²⋊Q₈×C₈₉	—	2	1	no	—
203	C₂²⋊Q₈×C₈₉	—	2	2	no	—
204	C₂²⋊Q₈×C₈₉	—	2	2	no	—
205	C₂²⋊Q₈×C₈₉	—	2	2	no	—
206	C₂²⋊Q₈×C₈₉	—	2	2	no	—
207	C₂²⋊Q₈×C₈₉	—	2	2	no	—
208	C₂²⋊Q₈×C₈₉	—	2	2	no	—
209	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
210	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
212	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
213	#121×C₈₉	—	2	2	no	—
214	#121×C₈₉	—	2	1	no	—
215	#121×C₈₉	—	2	2	no	—
216	#121×C₈₉	—	2	2	no	—
217	#121×C₈₉	—	2	1	no	—
218	#121×C₈₉	—	2	1	no	—
219	#121×C₈₉	—	2	1	no	—
220	#121×C₈₉	—	2	1	no	—
221	#121×C₈₉	—	2	1	no	—
222	#121×C₈₉	—	2	2	no	—
223	#121×C₈₉	—	2	2	no	—
224	#121×C₈₉	—	2	2	no	—
225	#121×C₈₉	—	2	2	no	—
226	#121×C₈₉	—	2	2	no	—
227	#121×C₈₉	D₄	1	1	yes	characteristic
228	#121×C₈₉	C₂³	1	2	yes	—
229	#121×C₈₉	C₂³	1	2	yes	—
230	#121×C₈₉	C₂³	1	2	yes	—
231	#121×C₈₉	C₂³	1	2	yes	—
232	#120×C₈₉	—	2	2	no	—
233	#120×C₈₉	—	2	2	no	—
234	#120×C₈₉	—	2	2	no	—
235	C₄×Q₈×C₈₉	—	2	1	no	—
236	C₄×Q₈×C₈₉	—	2	1	no	—
237	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
240	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₈₉	—	2	1	no	—
242	C₄×D₄×C₈₉	—	2	2	no	—
243	C₄×D₄×C₈₉	—	2	2	no	—
244	C₄×D₄×C₈₉	—	2	1	no	—
245	C₄×D₄×C₈₉	—	2	1	no	—
246	C₄×D₄×C₈₉	—	2	2	no	—
247	C₄×D₄×C₈₉	—	2	2	no	—
248	C₄×D₄×C₈₉	—	2	1	no	—
249	C₄×D₄×C₈₉	—	2	1	no	—
250	C₄×D₄×C₈₉	—	2	1	no	—
251	C₄×D₄×C₈₉	—	2	1	no	—
252	C₄×D₄×C₈₉	—	2	1	no	—
253	C₄×D₄×C₈₉	C₂³	1	2	yes	—
254	C₄×D₄×C₈₉	C₂³	1	2	yes	—
255	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₈₉	C₂³	1	2	yes	—
258	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₈₉	C₂³	1	2	yes	—
260	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₈₉	C₂³	1	2	yes	—
263	#117×C₈₉	—	2	1	no	—
264	#117×C₈₉	—	2	1	no	—
265	#117×C₈₉	C₂³	1	2	yes	—
266	#117×C₈₉	C₂³	1	2	yes	—
267	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
268	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
269	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
271	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
272	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
273	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
274	#107×C₈₉	C₂³	1	2	yes	—
275	#107×C₈₉	C₂³	1	2	yes	—
276	#106×C₈₉	C₂³	1	1	yes	characteristic
277	#106×C₈₉	C₂³	1	1	yes	characteristic
278	#106×C₈₉	C₂³	1	1	yes	characteristic
279	#106×C₈₉	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
281	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
285	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
286	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
287	#103×C₈₉	C₂³	1	1	yes	characteristic
288	#103×C₈₉	C₂³	1	2	yes	—
289	#103×C₈₉	C₂³	1	2	yes	—
290	#103×C₈₉	C₂³	1	2	yes	—
291	#103×C₈₉	C₂³	1	1	yes	characteristic
292	#103×C₈₉	C₂³	1	2	yes	—
293	#103×C₈₉	C₂³	1	2	yes	—
294	#103×C₈₉	C₂³	1	1	yes	characteristic
295	#103×C₈₉	C₂³	1	1	yes	characteristic
296	#103×C₈₉	C₂³	1	2	yes	—
297	#102×C₈₉	C₂³	1	2	yes	—
298	#102×C₈₉	C₂³	1	2	yes	—
299	#102×C₈₉	C₂³	1	2	yes	—
300	#102×C₈₉	C₂³	1	1	yes	characteristic
301	#102×C₈₉	C₂³	1	2	yes	—
302	#102×C₈₉	C₂³	1	1	yes	characteristic
303	#102×C₈₉	C₂³	1	2	yes	—
304	#102×C₈₉	C₂³	1	1	yes	characteristic
305	#102×C₈₉	C₂³	1	1	yes	characteristic
306	#102×C₈₉	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
311	#97×C₈₉	C₂³	1	2	yes	—
312	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₈₉	C₂³	1	2	yes	—
315	C₂⁴×C₈₉	—	2	1	no	—
316	C₂⁴×C₈₉	—	2	2	no	—
317	#41×C₈₉	—	4	2	no	—
318	#41×C₈₉	—	4	2	no	—
319	#41×C₈₉	—	4	2	no	—
320	#41×C₈₉	—	4	2	no	—
321	#41×C₈₉	—	8	2	no	—
322	#41×C₈₉	—	8	2	no	—
323	C₂×Q₈×C₈₉	—	2	1	no	—
324	C₂×Q₈×C₈₉	—	2	2	no	—
325	C₂×Q₈×C₈₉	—	2	1	no	—
326	C₂×Q₈×C₈₉	—	4	2	no	—
327	C₂×Q₈×C₈₉	—	4	2	no	—
328	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₈₉	—	2	4	no	—
333	C₂×D₄×C₈₉	—	2	2	no	—
334	C₂×D₄×C₈₉	—	2	2	no	—
335	C₂×D₄×C₈₉	—	2	2	no	—
336	C₂×D₄×C₈₉	—	2	2	no	—
337	C₂×D₄×C₈₉	—	2	2	no	—
338	C₂×D₄×C₈₉	—	2	2	no	—
339	C₂×D₄×C₈₉	—	2	2	no	—
340	C₂×D₄×C₈₉	—	2	1	no	—
341	C₂×D₄×C₈₉	—	2	2	no	—
342	C₂×D₄×C₈₉	—	2	1	no	—
343	C₂×D₄×C₈₉	—	2	1	no	—
344	C₂×D₄×C₈₉	—	2	1	no	—
345	C₂×D₄×C₈₉	—	2	2	no	—
346	C₂×D₄×C₈₉	—	2	1	no	—
347	C₂×D₄×C₈₉	—	2	2	no	—
348	C₂×D₄×C₈₉	—	4	2	no	—
349	C₂×D₄×C₈₉	—	4	1	no	—
350	C₂×D₄×C₈₉	—	8	2	no	—
351	C₂×D₄×C₈₉	—	8	4	no	—
352	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
353	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
354	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
355	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
356	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
357	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₈₉	—	2	1	no	—
359	C₂²×C₄×C₈₉	—	2	2	no	—
360	C₂²×C₄×C₈₉	—	2	1	no	—
361	C₂²×C₄×C₈₉	—	2	1	no	—
362	C₂²×C₄×C₈₉	—	2	1	no	—
363	C₂²×C₄×C₈₉	—	2	2	no	—
364	C₂²×C₄×C₈₉	—	2	2	no	—
365	C₂²×C₄×C₈₉	—	2	2	no	—
366	C₂²×C₄×C₈₉	—	2	2	no	—
367	C₂²×C₄×C₈₉	—	2	2	no	—
368	C₂²×C₄×C₈₉	—	2	2	no	—
369	C₂²×C₄×C₈₉	—	2	1	no	—
370	C₂²×C₄×C₈₉	—	8	2	no	—
371	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
372	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
375	SD₁₆×C₈₉	—	2	2	no	—
376	SD₁₆×C₈₉	—	2	4	no	—
377	SD₁₆×C₈₉	—	2	2	no	—
378	SD₁₆×C₈₉	—	4	2	no	—
379	SD₁₆×C₈₉	—	4	2	no	—
380	SD₁₆×C₈₉	—	4	1	no	—
381	SD₁₆×C₈₉	—	4	2	no	—
382	SD₁₆×C₈₉	—	4	1	no	—
383	SD₁₆×C₈₉	—	4	2	no	—
384	SD₁₆×C₈₉	—	4	2	no	—
385	D₈×C₈₉	—	2	4	no	—
386	D₈×C₈₉	—	4	2	no	—
387	D₈×C₈₉	—	4	2	no	—
388	D₈×C₈₉	—	4	2	no	—
389	M₁₆×C₈₉	—	4	2	no	—
390	M₁₆×C₈₉	—	4	2	no	—
391	C₂×C₈×C₈₉	—	4	2	no	—
392	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
396	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
397	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
398	C₄⋊C₄×C₈₉	—	2	1	no	—
399	C₄⋊C₄×C₈₉	—	2	1	no	—
400	C₄⋊C₄×C₈₉	—	2	2	no	—
401	C₄⋊C₄×C₈₉	—	2	2	no	—
402	C₄⋊C₄×C₈₉	—	2	2	no	—
403	C₄⋊C₄×C₈₉	—	2	1	no	—
404	C₄⋊C₄×C₈₉	—	2	1	no	—
405	C₄⋊C₄×C₈₉	—	2	1	no	—
406	C₄⋊C₄×C₈₉	—	2	1	no	—
407	C₄⋊C₄×C₈₉	—	2	1	no	—
408	C₄⋊C₄×C₈₉	—	2	2	no	—
409	C₄⋊C₄×C₈₉	—	2	1	no	—
410	C₄⋊C₄×C₈₉	—	2	1	no	—
411	C₄⋊C₄×C₈₉	—	2	2	no	—
412	C₄⋊C₄×C₈₉	—	2	1	no	—
413	C₄⋊C₄×C₈₉	—	2	2	no	—
414	C₄⋊C₄×C₈₉	—	2	1	no	—
415	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
416	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
418	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
420	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
426	C₂²⋊C₄×C₈₉	—	2	2	no	—
427	C₂²⋊C₄×C₈₉	—	2	1	no	—
428	C₂²⋊C₄×C₈₉	—	2	1	no	—
429	C₂²⋊C₄×C₈₉	—	2	2	no	—
430	C₂²⋊C₄×C₈₉	—	2	1	no	—
431	C₂²⋊C₄×C₈₉	—	2	2	no	—
432	C₂²⋊C₄×C₈₉	—	2	1	no	—
433	C₂²⋊C₄×C₈₉	—	2	2	no	—
434	C₂²⋊C₄×C₈₉	—	2	1	no	—
435	C₂²⋊C₄×C₈₉	—	2	2	no	—
436	C₂²⋊C₄×C₈₉	—	2	1	no	—
437	C₂²⋊C₄×C₈₉	—	2	2	no	—
438	C₂²⋊C₄×C₈₉	—	2	2	no	—
439	C₂²⋊C₄×C₈₉	—	2	2	no	—
440	C₂²⋊C₄×C₈₉	—	2	2	no	—
441	C₂²⋊C₄×C₈₉	—	2	2	no	—
442	C₂²⋊C₄×C₈₉	—	2	2	no	—
443	C₂²⋊C₄×C₈₉	—	2	2	no	—
444	C₂²⋊C₄×C₈₉	—	2	2	no	—
445	C₂²⋊C₄×C₈₉	—	2	2	no	—
446	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
447	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
448	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
449	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
451	C₄²×C₈₉	—	2	2	no	—
452	C₄²×C₈₉	—	2	1	no	—
453	C₄²×C₈₉	—	2	1	no	—
454	C₄²×C₈₉	—	2	2	no	—
455	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
456	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
458	C₄²×C₈₉	C₂⁴	1	2	yes	—
459	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
460	C₂³×C₈₉	—	2	1	no	—
461	C₂³×C₈₉	—	2	2	no	—
462	C₂³×C₈₉	—	2	2	no	—
463	C₂³×C₈₉	—	2	1	no	—
464	C₂³×C₈₉	—	4	2	no	—
465	C₂³×C₈₉	—	4	4	no	—
466	C₂³×C₈₉	—	4	2	no	—
467	C₂³×C₈₉	—	8	1	no	—
468	C₂³×C₈₉	—	8	2	no	—
469	C₂³×C₈₉	—	8	2	no	—
470	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
471	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
472	Q₈×C₈₉	—	2	2	no	—
473	Q₈×C₈₉	—	2	1	no	—
474	Q₈×C₈₉	—	2	2	no	—
475	Q₈×C₈₉	—	2	1	no	—
476	Q₈×C₈₉	—	2	1	no	—
477	Q₈×C₈₉	—	2	2	no	—
478	Q₈×C₈₉	—	2	1	no	—
479	Q₈×C₈₉	—	8	1	no	—
480	Q₈×C₈₉	—	8	2	no	—
481	Q₈×C₈₉	—	8	1	no	—
482	D₄×C₈₉	—	2	2	no	—
483	D₄×C₈₉	—	2	2	no	—
484	D₄×C₈₉	—	2	1	no	—
485	D₄×C₈₉	—	2	2	no	—
486	D₄×C₈₉	—	2	1	no	—
487	D₄×C₈₉	—	2	2	no	—
488	D₄×C₈₉	—	2	2	no	—
489	D₄×C₈₉	—	2	1	no	—
490	D₄×C₈₉	—	4	2	no	—
491	D₄×C₈₉	—	4	2	no	—
492	D₄×C₈₉	—	4	4	no	—
493	D₄×C₈₉	—	4	4	no	—
494	D₄×C₈₉	—	4	2	no	—
495	D₄×C₈₉	—	4	2	no	—
496	D₄×C₈₉	—	8	1	no	—
497	D₄×C₈₉	—	8	2	no	—
498	D₄×C₈₉	—	8	1	no	—
499	D₄×C₈₉	—	8	2	no	—
500	D₄×C₈₉	—	8	2	no	—
501	D₄×C₈₉	—	8	2	no	—
502	D₄×C₈₉	—	8	2	no	—
503	D₄×C₈₉	—	8	2	no	—
504	D₄×C₈₉	—	8	2	no	—
505	D₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
506	C₂×C₄×C₈₉	—	2	2	no	—
507	C₂×C₄×C₈₉	—	2	2	no	—
508	C₂×C₄×C₈₉	—	2	1	no	—
509	C₂×C₄×C₈₉	—	2	2	no	—
510	C₂×C₄×C₈₉	—	2	1	no	—
511	C₂×C₄×C₈₉	—	2	1	no	—
512	C₂×C₄×C₈₉	—	2	1	no	—
513	C₂×C₄×C₈₉	—	2	1	no	—
514	C₂×C₄×C₈₉	—	2	1	no	—
515	C₂×C₄×C₈₉	—	2	2	no	—
516	C₂×C₄×C₈₉	—	2	2	no	—
517	C₂×C₄×C₈₉	—	2	1	no	—
518	C₂×C₄×C₈₉	—	2	1	no	—
519	C₂×C₄×C₈₉	—	4	1	no	—
520	C₂×C₄×C₈₉	—	4	2	no	—
521	C₂×C₄×C₈₉	—	4	2	no	—
522	C₂×C₄×C₈₉	—	8	2	no	—
523	C₂×C₄×C₈₉	—	8	1	no	—
524	C₂×C₄×C₈₉	—	8	1	no	—
525	C₂×C₄×C₈₉	—	8	2	no	—
526	C₂×C₄×C₈₉	—	8	2	no	—
527	C₂×C₄×C₈₉	—	8	2	no	—
528	C₂×C₄×C₈₉	—	8	2	no	—
529	C₂×C₄×C₈₉	—	8	2	no	—
530	C₂×C₄×C₈₉	—	8	1	no	—
531	C₂×C₄×C₈₉	—	8	2	no	—
532	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
533	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
534	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
539	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
540	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
541	C₈×C₈₉	—	2	1	no	—
542	C₈×C₈₉	—	2	2	no	—
543	C₈×C₈₉	—	2	2	no	—
544	C₈×C₈₉	—	2	1	no	—
545	C₈×C₈₉	—	2	1	no	—
546	C₈×C₈₉	—	2	1	no	—
547	C₂²×C₈₉	—	2	1	no	—
548	C₂²×C₈₉	—	2	2	no	—
549	C₂²×C₈₉	—	2	2	no	—
550	C₂²×C₈₉	—	2	1	no	—
551	C₂²×C₈₉	—	2	2	no	—
552	C₂²×C₈₉	—	2	1	no	—
553	C₂²×C₈₉	—	2	2	no	—
554	C₂²×C₈₉	—	4	1	no	—
555	C₂²×C₈₉	—	4	1	no	—
556	C₂²×C₈₉	—	4	2	no	—
557	C₂²×C₈₉	—	4	2	no	—
558	C₂²×C₈₉	—	4	1	no	—
559	C₂²×C₈₉	—	4	2	no	—
560	C₂²×C₈₉	—	4	1	no	—
561	C₂²×C₈₉	—	4	2	no	—
562	C₂²×C₈₉	—	4	1	no	—
563	C₂²×C₈₉	—	4	2	no	—
564	C₂²×C₈₉	—	4	2	no	—
565	C₂²×C₈₉	—	8	4	no	—
566	C₂²×C₈₉	—	16	4	no	—
567	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
568	C₄×C₈₉	—	2	1	no	—
569	C₄×C₈₉	—	2	1	no	—
570	C₄×C₈₉	—	2	2	no	—
571	C₄×C₈₉	—	2	1	no	—
572	C₄×C₈₉	—	2	2	no	—
573	C₄×C₈₉	—	2	1	no	—
574	C₄×C₈₉	—	2	2	no	—
575	C₄×C₈₉	—	4	2	no	—
576	C₄×C₈₉	—	4	1	no	—
577	C₄×C₈₉	—	4	1	no	—
578	C₄×C₈₉	—	4	1	no	—
579	C₄×C₈₉	—	4	2	no	—
580	C₄×C₈₉	—	4	1	no	—
581	C₄×C₈₉	—	4	1	no	—
582	C₄×C₈₉	—	4	1	no	—
583	C₄×C₈₉	#577	1	2	yes	—
584	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
585	C₄×C₈₉	#585	1	1	yes	characteristic
586	#62039	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
587	C₂×C₈₉	—	4	1	no	—
588	C₂×C₈₉	—	4	2	no	—
589	C₂×C₈₉	—	4	2	no	—
590	C₂×C₈₉	—	8	2	no	—
591	C₂×C₈₉	—	8	1	no	—
592	C₂×C₈₉	—	8	2	no	—
593	C₂×C₈₉	#3488	1	1	yes	characteristic
594	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
595	C₂×C₈₉	#3585	1	1	yes	characteristic
596	#3554	C₂×C₈₉	1	1	yes	characteristic, complemented
597	#3519	C₂×C₈₉	1	1	yes	characteristic, complemented
598	#3399	C₂×C₈₉	1	1	yes	characteristic, complemented
599	#3392	C₂×C₈₉	1	1	yes	characteristic, complemented
600	#3372	C₂×C₈₉	1	1	yes	characteristic, complemented
601	#3361	C₂×C₈₉	1	1	yes	characteristic, complemented
602	#3329	C₂×C₈₉	1	1	yes	characteristic, complemented
603	#3326	C₂×C₈₉	1	2	yes	complemented
604	#3307	C₂×C₈₉	1	2	yes	complemented
605	#3305	C₂×C₈₉	1	1	yes	characteristic, complemented
606	D₄×SD₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
607	#3274	C₂×C₈₉	1	1	yes	characteristic, complemented
608	#3272	C₂×C₈₉	1	2	yes	complemented
609	#3265	C₂×C₈₉	1	2	yes	complemented
610	#3257	C₂×C₈₉	1	2	yes	complemented
611	#3254	C₂×C₈₉	1	1	yes	characteristic, complemented
612	#3221	C₂×C₈₉	1	2	yes	complemented
613	#3207	C₂×C₈₉	1	1	yes	characteristic, complemented
614	#3118	C₂×C₈₉	1	2	yes	complemented
615	#3101	C₂×C₈₉	1	1	yes	characteristic, complemented
616	#3042	C₂×C₈₉	1	2	yes	complemented
617	#3036	C₂×C₈₉	1	1	yes	characteristic, complemented
618	#2993	C₂×C₈₉	1	1	yes	characteristic, complemented
619	C₈₉	#62039	1	1	yes	characteristic, direct product factor, Sylow
620	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
621	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
622	C₂²×SD₁₆	C₂²×C₈₉	1	2	yes	—
623	#562	—	2	2	no	—
624	#559	—	2	1	no	—
625	#559	C₂²×C₈₉	1	1	yes	characteristic, complemented
626	#557	C₂²×C₈₉	1	1	yes	characteristic, complemented
627	#555	C₂²×C₈₉	1	1	yes	characteristic
628	#554	—	2	1	no	—
629	#554	C₂²×C₈₉	1	1	yes	characteristic
630	#553	—	2	1	no	—
631	#553	C₂²×C₈₉	1	2	yes	—
632	#550	C₂²×C₈₉	1	1	yes	characteristic
633	#550	C₂²×C₈₉	1	1	yes	characteristic, complemented
634	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
635	#548	C₂²×C₈₉	1	2	yes	complemented
636	#547	C₂²×C₈₉	1	2	yes	complemented
637	#546	—	2	1	no	—
638	#546	—	2	2	no	—
639	D₄²	C₂²×C₈₉	1	2	yes	—
640	D₄²	C₂²×C₈₉	1	1	yes	characteristic
641	#542	—	2	1	no	—
642	#542	C₂²×C₈₉	1	2	yes	complemented
643	#540	—	2	1	no	—
644	#540	C₂²×C₈₉	1	2	yes	—
645	#539	—	2	2	no	—
646	#538	—	2	2	no	—
647	#536	C₂²×C₈₉	1	2	yes	complemented
648	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
649	#532	C₂²×C₈₉	1	1	yes	characteristic
650	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
651	#529	C₂²×C₈₉	1	1	yes	characteristic
652	#525	—	2	1	no	—
653	C₂×#121	—	2	1	no	—
654	#518	C₂²×C₈₉	1	2	yes	—
655	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
656	#496	C₂²×C₈₉	1	2	yes	complemented
657	#493	C₂²×C₈₉	1	1	yes	characteristic, complemented
658	#492	C₂²×C₈₉	1	1	yes	characteristic, complemented
659	#492	C₂²×C₈₉	1	2	yes	complemented
660	#491	C₂²×C₈₉	1	2	yes	complemented
661	#488	C₂²×C₈₉	1	2	yes	complemented
662	#487	C₂²×C₈₉	1	1	yes	characteristic, complemented
663	#486	C₂²×C₈₉	1	1	yes	characteristic, complemented
664	#485	C₂²×C₈₉	1	2	yes	complemented
665	#483	C₂²×C₈₉	1	1	yes	characteristic, complemented
666	#483	C₂²×C₈₉	1	1	yes	characteristic, complemented
667	#482	C₂²×C₈₉	1	2	yes	complemented
668	#479	C₂²×C₈₉	1	2	yes	complemented
669	#478	C₂²×C₈₉	1	2	yes	complemented
670	#477	C₂²×C₈₉	1	1	yes	characteristic, complemented
671	#477	C₂²×C₈₉	1	1	yes	characteristic, complemented
672	#476	C₂²×C₈₉	1	1	yes	characteristic
673	#476	C₂²×C₈₉	1	1	yes	characteristic, complemented
674	#474	C₂²×C₈₉	1	2	yes	complemented
675	#469	C₂²×C₈₉	1	2	yes	complemented
676	#468	C₂²×C₈₉	1	2	yes	complemented
677	#468	C₂²×C₈₉	1	2	yes	complemented
678	#468	C₂²×C₈₉	1	2	yes	complemented
679	#466	C₂²×C₈₉	1	2	yes	complemented
680	#465	C₂²×C₈₉	1	2	yes	complemented
681	#463	C₂²×C₈₉	1	2	yes	—
682	#463	C₂²×C₈₉	1	2	yes	—
683	#463	C₂²×C₈₉	1	2	yes	complemented
684	#463	C₂²×C₈₉	1	2	yes	complemented
685	#463	C₂²×C₈₉	1	2	yes	complemented
686	#463	C₂²×C₈₉	1	2	yes	complemented
687	#461	C₂²×C₈₉	1	1	yes	characteristic
688	#461	C₂²×C₈₉	1	2	yes	—
689	#461	C₂²×C₈₉	1	1	yes	characteristic
690	#461	C₂²×C₈₉	1	1	yes	characteristic, complemented
691	#461	C₂²×C₈₉	1	1	yes	characteristic, complemented
692	#461	C₂²×C₈₉	1	2	yes	complemented
693	#461	C₂²×C₈₉	1	2	yes	complemented
694	#460	C₂²×C₈₉	1	1	yes	characteristic, complemented
695	#460	C₂²×C₈₉	1	2	yes	complemented
696	#460	C₂²×C₈₉	1	1	yes	characteristic, complemented
697	#459	C₂²×C₈₉	1	1	yes	characteristic
698	#459	C₂²×C₈₉	1	2	yes	complemented
699	#459	C₂²×C₈₉	1	1	yes	characteristic, complemented
700	#450	C₂²×C₈₉	1	1	yes	characteristic
701	#450	C₂²×C₈₉	1	1	yes	characteristic
702	#450	C₂²×C₈₉	1	2	yes	—
703	#449	C₂²×C₈₉	1	2	yes	complemented
704	#449	C₂²×C₈₉	1	2	yes	complemented
705	#449	C₂²×C₈₉	1	2	yes	complemented
706	#449	C₂²×C₈₉	1	2	yes	complemented
707	#448	C₂²×C₈₉	1	2	yes	complemented
708	#448	C₂²×C₈₉	1	2	yes	complemented
709	#447	C₂²×C₈₉	1	2	yes	—
710	#446	C₂²×C₈₉	1	1	yes	characteristic, complemented
711	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
712	#442	C₂²×C₈₉	1	2	yes	complemented
713	#440	C₂²×C₈₉	1	2	yes	—
714	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
715	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
716	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
717	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
718	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
719	C₄×D₈	C₂²×C₈₉	1	2	yes	—
720	#436	C₂²×C₈₉	1	1	yes	characteristic, complemented
721	#436	C₂²×C₈₉	1	2	yes	complemented
722	#435	C₂²×C₈₉	1	2	yes	complemented
723	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
724	#433	C₂²×C₈₉	1	2	yes	complemented
725	#431	C₂²×C₈₉	1	1	yes	characteristic, complemented
726	#424	C₂²×C₈₉	1	2	yes	complemented
727	#423	C₂²×C₈₉	1	1	yes	characteristic, complemented
728	#419	C₂²×C₈₉	1	2	yes	complemented
729	#417	C₂²×C₈₉	1	2	yes	complemented
730	#416	C₂²×C₈₉	1	2	yes	complemented
731	C₂×#41	—	2	1	no	—
732	C₂×#41	—	2	1	no	—
733	C₂×#41	C₂³×C₈₉	1	2	yes	—
734	C₂×#41	C₂³×C₈₉	1	2	yes	—
735	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
736	C₂²×D₄	—	2	1	no	—
737	C₂²×D₄	—	2	2	no	—
738	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
739	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
740	C₂³×C₄	—	2	1	no	—
741	AGL(1,ℤ/8)	—	4	4	no	—
742	AGL(1,ℤ/8)	—	4	4	no	—
743	C₂×SD₁₆	—	4	4	no	—
744	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
745	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
746	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
747	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
748	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
749	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
750	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
751	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
752	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
753	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
754	C₂×D₈	C₂³×C₈₉	1	2	yes	—
755	C₂×D₈	C₂³×C₈₉	1	2	yes	—
756	C₂×D₈	C₂³×C₈₉	1	2	yes	—
757	C₂×D₈	C₂³×C₈₉	1	2	yes	—
758	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
759	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
760	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
761	C₄⋊Q₈	—	2	1	no	—
762	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
763	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
764	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
765	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
766	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
767	#127	—	2	1	no	—
768	#127	C₂³×C₈₉	1	1	yes	characteristic
769	#127	C₂³×C₈₉	1	1	yes	characteristic
770	#127	C₂³×C₈₉	1	2	yes	—
771	#126	—	2	2	no	—
772	#126	—	2	2	no	—
773	#126	D₄×C₈₉	1	2	yes	—
774	#125	—	2	2	no	—
775	#125	—	2	1	no	—
776	#125	—	2	1	no	—
777	#125	D₄×C₈₉	1	1	yes	characteristic
778	#125	C₂³×C₈₉	1	2	yes	—
779	#124	—	2	1	no	—
780	#124	—	2	2	no	—
781	#124	—	2	2	no	—
782	#124	—	2	2	no	—
783	#124	—	2	1	no	—
784	#124	D₄×C₈₉	1	1	yes	characteristic
785	#124	C₂³×C₈₉	1	2	yes	—
786	#124	C₂³×C₈₉	1	2	yes	—
787	#123	—	2	2	no	—
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	no	—
791	#123	—	2	2	no	—
792	#123	—	2	2	no	—
793	#123	—	2	2	no	—
794	#123	—	2	2	no	—
795	#123	—	2	2	no	—
796	#123	D₄×C₈₉	1	2	yes	—
797	C₂²⋊Q₈	—	2	1	no	—
798	C₂²⋊Q₈	—	2	1	no	—
799	C₂²⋊Q₈	—	2	2	no	—
800	C₂²⋊Q₈	—	2	2	no	—
801	C₂²⋊Q₈	—	2	2	no	—
802	C₂²⋊Q₈	—	2	2	no	—
803	C₂²⋊Q₈	—	2	2	no	—
804	C₂²⋊Q₈	—	2	2	no	—
805	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
806	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
807	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
808	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
809	#121	—	2	2	no	—
810	#121	—	2	1	no	—
811	#121	—	2	2	no	—
812	#121	—	2	2	no	—
813	#121	—	2	1	no	—
814	#121	—	2	1	no	—
815	#121	—	2	1	no	—
816	#121	—	2	1	no	—
817	#121	—	2	1	no	—
818	#121	—	2	2	no	—
819	#121	—	2	2	no	—
820	#121	—	2	2	no	—
821	#121	—	2	2	no	—
822	#121	—	2	2	no	—
823	#121	D₄×C₈₉	1	1	yes	characteristic
824	#121	C₂³×C₈₉	1	2	yes	—
825	#121	C₂³×C₈₉	1	2	yes	—
826	#121	C₂³×C₈₉	1	2	yes	—
827	#121	C₂³×C₈₉	1	2	yes	—
828	#120	—	2	2	no	—
829	#120	—	2	2	no	—
830	#120	—	2	2	no	—
831	C₄×Q₈	—	2	1	no	—
832	C₄×Q₈	—	2	1	no	—
833	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
834	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
835	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
836	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	—	2	2	no	—
839	C₄×D₄	—	2	2	no	—
840	C₄×D₄	—	2	1	no	—
841	C₄×D₄	—	2	1	no	—
842	C₄×D₄	—	2	2	no	—
843	C₄×D₄	—	2	2	no	—
844	C₄×D₄	—	2	1	no	—
845	C₄×D₄	—	2	1	no	—
846	C₄×D₄	—	2	1	no	—
847	C₄×D₄	—	2	1	no	—
848	C₄×D₄	—	2	1	no	—
849	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
850	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
851	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
852	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
853	C₄×D₄	C₂³×C₈₉	1	2	yes	—
854	C₄×D₄	C₂³×C₈₉	1	2	yes	—
855	C₄×D₄	C₂³×C₈₉	1	2	yes	—
856	C₄×D₄	C₂³×C₈₉	1	2	yes	—
857	C₄×D₄	C₂³×C₈₉	1	2	yes	—
858	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
859	#117	—	2	1	no	—
860	#117	—	2	1	no	—
861	#117	C₂³×C₈₉	1	2	yes	—
862	#117	C₂³×C₈₉	1	2	yes	—
863	C₂×C₄⋊C₄	—	2	1	no	—
864	C₂×C₄⋊C₄	—	2	2	no	—
865	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
866	C₂×C₂²⋊C₄	—	2	1	no	—
867	C₂×C₂²⋊C₄	—	2	2	no	—
868	C₂×C₂²⋊C₄	—	2	2	no	—
869	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
870	#107	C₂³×C₈₉	1	2	yes	—
871	#107	C₂³×C₈₉	1	2	yes	—
872	#106	C₂³×C₈₉	1	1	yes	characteristic
873	#106	C₂³×C₈₉	1	1	yes	characteristic
874	#106	C₂³×C₈₉	1	1	yes	characteristic
875	#106	C₂³×C₈₉	1	1	yes	characteristic
876	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
877	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
878	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
879	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
880	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
881	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
882	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
883	#103	C₂³×C₈₉	1	1	yes	characteristic
884	#103	C₂³×C₈₉	1	2	yes	—
885	#103	C₂³×C₈₉	1	2	yes	—
886	#103	C₂³×C₈₉	1	2	yes	—
887	#103	C₂³×C₈₉	1	1	yes	characteristic
888	#103	C₂³×C₈₉	1	2	yes	—
889	#103	C₂³×C₈₉	1	2	yes	—
890	#103	C₂³×C₈₉	1	1	yes	characteristic
891	#103	C₂³×C₈₉	1	1	yes	characteristic
892	#103	C₂³×C₈₉	1	2	yes	—
893	#102	C₂³×C₈₉	1	2	yes	—
894	#102	C₂³×C₈₉	1	2	yes	—
895	#102	C₂³×C₈₉	1	2	yes	—
896	#102	C₂³×C₈₉	1	1	yes	characteristic
897	#102	C₂³×C₈₉	1	2	yes	—
898	#102	C₂³×C₈₉	1	1	yes	characteristic
899	#102	C₂³×C₈₉	1	2	yes	—
900	#102	C₂³×C₈₉	1	1	yes	characteristic
901	#102	C₂³×C₈₉	1	1	yes	characteristic
902	#102	C₂³×C₈₉	1	2	yes	—
903	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
904	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
905	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
906	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
907	#97	C₂³×C₈₉	1	2	yes	—
908	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
909	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
910	C₄×C₈	C₂³×C₈₉	1	2	yes	—
911	C₂⁴	—	2	1	no	—
912	C₂⁴	—	2	2	no	—
913	#41	—	4	2	no	—
914	#41	—	4	2	no	—
915	#41	—	4	2	no	—
916	#41	—	4	2	no	—
917	#41	—	8	2	no	—
918	#41	—	8	2	no	—
919	C₂×Q₈	—	2	1	no	—
920	C₂×Q₈	—	2	2	no	—
921	C₂×Q₈	—	2	1	no	—
922	C₂×Q₈	—	4	2	no	—
923	C₂×Q₈	—	4	2	no	—
924	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
925	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
926	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
927	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
928	C₂×D₄	—	2	4	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	1	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	1	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	1	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	—	2	1	no	—
943	C₂×D₄	—	2	2	no	—
944	C₂×D₄	—	4	2	no	—
945	C₂×D₄	—	4	1	no	—
946	C₂×D₄	—	8	2	no	—
947	C₂×D₄	—	8	4	no	—
948	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
949	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
950	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
951	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
952	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
953	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	1	no	—
958	C₂²×C₄	—	2	1	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	—	2	2	no	—
963	C₂²×C₄	—	2	2	no	—
964	C₂²×C₄	—	2	2	no	—
965	C₂²×C₄	—	2	1	no	—
966	C₂²×C₄	—	8	2	no	—
967	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
968	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
969	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
970	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
971	SD₁₆	—	2	2	no	—
972	SD₁₆	—	2	4	no	—
973	SD₁₆	—	2	2	no	—
974	SD₁₆	—	4	2	no	—
975	SD₁₆	—	4	2	no	—
976	SD₁₆	—	4	2	no	—
977	SD₁₆	—	4	2	no	—
978	SD₁₆	—	4	1	no	—
979	SD₁₆	—	4	2	no	—
980	SD₁₆	—	4	1	no	—
981	D₈	—	2	4	no	—
982	D₈	—	4	2	no	—
983	D₈	—	4	2	no	—
984	D₈	—	4	2	no	—
985	M₁₆	—	4	2	no	—
986	M₁₆	—	4	2	no	—
987	C₂×C₈	—	4	2	no	—
988	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
989	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
990	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
991	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
992	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
993	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	1	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	1	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	1	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1012	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1013	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1014	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1015	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1016	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1017	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1018	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1019	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1020	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1021	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	1	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	1	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1043	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1044	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1045	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1046	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1047	C₄²	—	2	2	no	—
1048	C₄²	—	2	1	no	—
1049	C₄²	—	2	1	no	—
1050	C₄²	—	2	2	no	—
1051	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1052	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1053	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1054	C₄²	C₂⁴×C₈₉	1	2	yes	—
1055	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1056	C₂³	—	2	1	no	—
1057	C₂³	—	2	2	no	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	2	no	—
1060	C₂³	—	4	2	no	—
1061	C₂³	—	4	4	no	—
1062	C₂³	—	4	2	no	—
1063	C₂³	—	8	1	no	—
1064	C₂³	—	8	2	no	—
1065	C₂³	—	8	2	no	—
1066	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1067	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1068	Q₈	—	2	2	no	—
1069	Q₈	—	2	1	no	—
1070	Q₈	—	2	2	no	—
1071	Q₈	—	2	1	no	—
1072	Q₈	—	2	1	no	—
1073	Q₈	—	2	2	no	—
1074	Q₈	—	2	1	no	—
1075	Q₈	—	8	1	no	—
1076	Q₈	—	8	2	no	—
1077	Q₈	—	8	1	no	—
1078	D₄	—	2	2	no	—
1079	D₄	—	2	2	no	—
1080	D₄	—	2	1	no	—
1081	D₄	—	2	2	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	2	no	—
1084	D₄	—	2	2	no	—
1085	D₄	—	2	1	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	4	2	no	—
1088	D₄	—	4	4	no	—
1089	D₄	—	4	4	no	—
1090	D₄	—	4	2	no	—
1091	D₄	—	4	2	no	—
1092	D₄	—	8	1	no	—
1093	D₄	—	8	2	no	—
1094	D₄	—	8	2	no	—
1095	D₄	—	8	1	no	—
1096	D₄	—	8	2	no	—
1097	D₄	—	8	2	no	—
1098	D₄	—	8	2	no	—
1099	D₄	—	8	2	no	—
1100	D₄	—	8	2	no	—
1101	D₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	4	1	no	—
1116	C₂×C₄	—	4	2	no	—
1117	C₂×C₄	—	4	2	no	—
1118	C₂×C₄	—	8	2	no	—
1119	C₂×C₄	—	8	1	no	—
1120	C₂×C₄	—	8	1	no	—
1121	C₂×C₄	—	8	2	no	—
1122	C₂×C₄	—	8	2	no	—
1123	C₂×C₄	—	8	2	no	—
1124	C₂×C₄	—	8	2	no	—
1125	C₂×C₄	—	8	2	no	—
1126	C₂×C₄	—	8	1	no	—
1127	C₂×C₄	—	8	2	no	—
1128	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1129	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1130	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1131	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1132	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1133	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1134	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1135	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1136	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1137	C₈	—	2	1	no	—
1138	C₈	—	2	2	no	—
1139	C₈	—	2	2	no	—
1140	C₈	—	2	1	no	—
1141	C₈	—	2	1	no	—
1142	C₈	—	2	1	no	—
1143	C₂²	—	2	1	no	—
1144	C₂²	—	2	2	no	—
1145	C₂²	—	2	1	no	—
1146	C₂²	—	2	2	no	—
1147	C₂²	—	2	2	no	—
1148	C₂²	—	2	1	no	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	4	1	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	1	no	—
1153	C₂²	—	4	2	no	—
1154	C₂²	—	4	2	no	—
1155	C₂²	—	4	2	no	—
1156	C₂²	—	4	2	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	2	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	2	no	—
1161	C₂²	—	8	4	no	—
1162	C₂²	—	16	4	no	—
1163	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1164	C₄	—	2	1	no	—
1165	C₄	—	2	2	no	—
1166	C₄	—	2	1	no	—
1167	C₄	—	2	1	no	—
1168	C₄	—	2	2	no	—
1169	C₄	—	2	1	no	—
1170	C₄	—	2	2	no	—
1171	C₄	—	4	1	no	—
1172	C₄	—	4	1	no	—
1173	C₄	—	4	2	no	—
1174	C₄	—	4	1	no	—
1175	C₄	—	4	1	no	—
1176	C₄	—	4	1	no	—
1177	C₄	—	4	2	no	—
1178	C₄	—	4	1	no	—
1179	C₄	#577×C₈₉	1	2	yes	—
1180	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1181	C₄	#585×C₈₉	1	1	yes	characteristic
1182	C₂	—	4	1	no	—
1183	C₂	—	4	2	no	—
1184	C₂	—	4	2	no	—
1185	C₂	—	8	2	no	—
1186	C₂	—	8	1	no	—
1187	C₂	—	8	2	no	—
1188	C₂	C₈₉×#3488	1	1	yes	characteristic
1189	C₂	C₂×#577×C₈₉	1	1	yes	characteristic
1190	C₂	C₈₉×#3585	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 ◁ #529×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3554	C₂	semidirect
2. C₈₉×#3519	C₂	semidirect
3. C₈₉×#3399	C₂	semidirect
4. C₈₉×#3392	C₂	semidirect
5. C₈₉×#3372	C₂	semidirect
6. C₈₉×#3361	C₂	semidirect
7. C₈₉×#3329	C₂	semidirect
8. C₈₉×#3326	C₂	semidirect
9. C₈₉×#3307	C₂	semidirect
10. C₈₉×#3305	C₂	semidirect
11. D₄×SD₁₆×C₈₉	C₂	semidirect
12. C₈₉×#3274	C₂	semidirect
13. C₈₉×#3272	C₂	semidirect
14. C₈₉×#3265	C₂	semidirect
15. C₈₉×#3257	C₂	semidirect
16. C₈₉×#3254	C₂	semidirect
17. C₈₉×#3221	C₂	semidirect
18. C₈₉×#3207	C₂	semidirect
19. C₈₉×#3118	C₂	semidirect
20. C₈₉×#3101	C₂	semidirect
21. C₈₉×#3042	C₂	semidirect
22. C₈₉×#3036	C₂	semidirect
23. C₈₉×#2993	C₂	semidirect
29. #559×C₈₉	C₂²	semidirect
30. #557×C₈₉	C₂²	semidirect
37. #550×C₈₉	C₂²	semidirect
38. D₄×Q₈×C₈₉	C₂²	semidirect
39. #548×C₈₉	C₂²	semidirect
40. #547×C₈₉	C₂²	semidirect
46. #542×C₈₉	C₂²	semidirect
51. #536×C₈₉	C₂²	semidirect
52. #533×C₈₉	C₂²	semidirect
54. #532×C₈₉	C₂²	semidirect
60. #496×C₈₉	C₂²	semidirect
61. #493×C₈₉	C₂²	semidirect
62. #492×C₈₉	C₂²	semidirect
63. #492×C₈₉	C₂²	semidirect
64. #491×C₈₉	C₂²	semidirect
65. #488×C₈₉	C₂²	semidirect
66. #487×C₈₉	C₂²	semidirect
67. #486×C₈₉	C₂²	semidirect
68. #485×C₈₉	C₂²	semidirect
69. #483×C₈₉	C₂²	semidirect
70. #483×C₈₉	C₂²	semidirect
71. #482×C₈₉	C₂²	semidirect
72. #479×C₈₉	C₂²	semidirect
73. #478×C₈₉	C₂²	semidirect
74. #477×C₈₉	C₂²	semidirect
75. #477×C₈₉	C₂²	semidirect
77. #476×C₈₉	C₂²	semidirect
78. #474×C₈₉	C₂²	semidirect
79. #469×C₈₉	C₂²	semidirect
80. #468×C₈₉	C₂²	semidirect
81. #468×C₈₉	C₂²	semidirect
82. #468×C₈₉	C₂²	semidirect
83. #466×C₈₉	C₂²	semidirect
84. #465×C₈₉	C₂²	semidirect
87. #463×C₈₉	C₂²	semidirect
88. #463×C₈₉	C₂²	semidirect
89. #463×C₈₉	C₂²	semidirect
90. #463×C₈₉	C₂²	semidirect
94. #461×C₈₉	C₂²	semidirect
95. #461×C₈₉	C₂²	semidirect
96. #461×C₈₉	C₂²	semidirect
97. #461×C₈₉	C₂²	semidirect
98. #460×C₈₉	C₂²	semidirect
99. #460×C₈₉	C₂²	semidirect
100. #460×C₈₉	C₂²	semidirect
102. #459×C₈₉	C₂²	semidirect
103. #459×C₈₉	C₂²	semidirect
107. #449×C₈₉	C₂²	semidirect
108. #449×C₈₉	C₂²	semidirect
109. #449×C₈₉	C₂²	semidirect
110. #449×C₈₉	C₂²	semidirect
111. #448×C₈₉	C₂²	semidirect
112. #448×C₈₉	C₂²	semidirect
114. #446×C₈₉	C₂²	semidirect
115. C₈×Q₈×C₈₉	C₂²	semidirect
116. #442×C₈₉	C₂²	semidirect
120. C₄×SD₁₆×C₈₉	C₂²	semidirect
121. C₄×SD₁₆×C₈₉	C₂²	semidirect
122. C₄×SD₁₆×C₈₉	C₂²	semidirect
124. #436×C₈₉	C₂²	semidirect
125. #436×C₈₉	C₂²	semidirect
126. #435×C₈₉	C₂²	semidirect
127. C₈×D₄×C₈₉	C₂²	semidirect
128. #433×C₈₉	C₂²	semidirect
129. #431×C₈₉	C₂²	semidirect
130. #424×C₈₉	C₂²	semidirect
131. #423×C₈₉	C₂²	semidirect
132. #419×C₈₉	C₂²	semidirect
133. #417×C₈₉	C₂²	semidirect
134. #416×C₈₉	C₂²	semidirect
586. #62039	C₈₉	direct (N × H)
596. #3554	C₂×C₈₉	semidirect
597. #3519	C₂×C₈₉	semidirect
598. #3399	C₂×C₈₉	semidirect
599. #3392	C₂×C₈₉	semidirect
600. #3372	C₂×C₈₉	semidirect
601. #3361	C₂×C₈₉	semidirect
602. #3329	C₂×C₈₉	semidirect
603. #3326	C₂×C₈₉	semidirect
604. #3307	C₂×C₈₉	semidirect
605. #3305	C₂×C₈₉	semidirect
606. D₄×SD₁₆	C₂×C₈₉	semidirect
607. #3274	C₂×C₈₉	semidirect
608. #3272	C₂×C₈₉	semidirect
609. #3265	C₂×C₈₉	semidirect
610. #3257	C₂×C₈₉	semidirect
611. #3254	C₂×C₈₉	semidirect
612. #3221	C₂×C₈₉	semidirect
613. #3207	C₂×C₈₉	semidirect
614. #3118	C₂×C₈₉	semidirect
615. #3101	C₂×C₈₉	semidirect
616. #3042	C₂×C₈₉	semidirect
617. #3036	C₂×C₈₉	semidirect
618. #2993	C₂×C₈₉	semidirect
619. C₈₉	#62039	direct (N × H)
625. #559	C₂²×C₈₉	semidirect
626. #557	C₂²×C₈₉	semidirect
633. #550	C₂²×C₈₉	semidirect
634. D₄×Q₈	C₂²×C₈₉	semidirect
635. #548	C₂²×C₈₉	semidirect
636. #547	C₂²×C₈₉	semidirect
642. #542	C₂²×C₈₉	semidirect
647. #536	C₂²×C₈₉	semidirect
648. #533	C₂²×C₈₉	semidirect
650. #532	C₂²×C₈₉	semidirect
656. #496	C₂²×C₈₉	semidirect
657. #493	C₂²×C₈₉	semidirect
658. #492	C₂²×C₈₉	semidirect
659. #492	C₂²×C₈₉	semidirect
660. #491	C₂²×C₈₉	semidirect
661. #488	C₂²×C₈₉	semidirect
662. #487	C₂²×C₈₉	semidirect
663. #486	C₂²×C₈₉	semidirect
664. #485	C₂²×C₈₉	semidirect
665. #483	C₂²×C₈₉	semidirect
666. #483	C₂²×C₈₉	semidirect
667. #482	C₂²×C₈₉	semidirect
668. #479	C₂²×C₈₉	semidirect
669. #478	C₂²×C₈₉	semidirect
670. #477	C₂²×C₈₉	semidirect
671. #477	C₂²×C₈₉	semidirect
673. #476	C₂²×C₈₉	semidirect
674. #474	C₂²×C₈₉	semidirect
675. #469	C₂²×C₈₉	semidirect
676. #468	C₂²×C₈₉	semidirect
677. #468	C₂²×C₈₉	semidirect
678. #468	C₂²×C₈₉	semidirect
679. #466	C₂²×C₈₉	semidirect
680. #465	C₂²×C₈₉	semidirect
683. #463	C₂²×C₈₉	semidirect
684. #463	C₂²×C₈₉	semidirect
685. #463	C₂²×C₈₉	semidirect
686. #463	C₂²×C₈₉	semidirect
690. #461	C₂²×C₈₉	semidirect
691. #461	C₂²×C₈₉	semidirect
692. #461	C₂²×C₈₉	semidirect
693. #461	C₂²×C₈₉	semidirect
694. #460	C₂²×C₈₉	semidirect
695. #460	C₂²×C₈₉	semidirect
696. #460	C₂²×C₈₉	semidirect
698. #459	C₂²×C₈₉	semidirect
699. #459	C₂²×C₈₉	semidirect
703. #449	C₂²×C₈₉	semidirect
704. #449	C₂²×C₈₉	semidirect
705. #449	C₂²×C₈₉	semidirect
706. #449	C₂²×C₈₉	semidirect
707. #448	C₂²×C₈₉	semidirect
708. #448	C₂²×C₈₉	semidirect
710. #446	C₂²×C₈₉	semidirect
711. C₈×Q₈	C₂²×C₈₉	semidirect
712. #442	C₂²×C₈₉	semidirect
716. C₄×SD₁₆	C₂²×C₈₉	semidirect
717. C₄×SD₁₆	C₂²×C₈₉	semidirect
718. C₄×SD₁₆	C₂²×C₈₉	semidirect
720. #436	C₂²×C₈₉	semidirect
721. #436	C₂²×C₈₉	semidirect
722. #435	C₂²×C₈₉	semidirect
723. C₈×D₄	C₂²×C₈₉	semidirect
724. #433	C₂²×C₈₉	semidirect
725. #431	C₂²×C₈₉	semidirect
726. #424	C₂²×C₈₉	semidirect
727. #423	C₂²×C₈₉	semidirect
728. #419	C₂²×C₈₉	semidirect
729. #417	C₂²×C₈₉	semidirect
730. #416	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×#3554	2
C₈₉×#3519	2
C₈₉×#3399	2
C₈₉×#3392	2
C₈₉×#3372	2
C₈₉×#3361	2
C₈₉×#3329	2
C₈₉×#3326	2
C₈₉×#3307	2
C₈₉×#3305	2
D₄×SD₁₆×C₈₉	2
C₈₉×#3274	2
C₈₉×#3272	2
C₈₉×#3265	2
C₈₉×#3257	2
C₈₉×#3254	2
C₈₉×#3221	2
C₈₉×#3207	2
C₈₉×#3118	2
C₈₉×#3101	2
C₈₉×#3042	2
C₈₉×#3036	2
C₈₉×#2993	2
#62039	89

Subgroups — C89×#62039 #36439887

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62039 #36439887