Subgroups — C₈₉×#62035 #36439883

Order 22784.

1894 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3394	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3325	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3324	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3311	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×#3278	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3275	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×#3252	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3224	C₂	1	2	yes	maximal, complemented
18	C₈₉×#3208	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3126	C₂	1	2	yes	maximal, complemented
20	C₈₉×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#3043	C₂	1	2	yes	maximal, complemented
22	C₈₉×#3038	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₈₉	C₂²	1	2	yes	complemented
25	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
27	#560×C₈₉	—	2	2	no	—
28	#559×C₈₉	C₂²	1	1	yes	characteristic
29	Q₈²×C₈₉	C₂²	1	1	yes	characteristic, complemented
30	#556×C₈₉	—	2	2	no	—
31	#556×C₈₉	—	2	1	no	—
32	#556×C₈₉	C₂²	1	1	yes	characteristic, complemented
33	#556×C₈₉	C₂²	1	2	yes	complemented
34	#555×C₈₉	—	2	1	no	—
35	#555×C₈₉	C₂²	1	1	yes	characteristic, complemented
36	#550×C₈₉	C₂²	1	1	yes	characteristic
37	#550×C₈₉	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	#548×C₈₉	C₂²	1	2	yes	complemented
40	#546×C₈₉	—	2	1	no	—
41	#546×C₈₉	C₂²	1	2	yes	—
42	D₄²×C₈₉	—	2	1	no	—
43	D₄²×C₈₉	C₂²	1	2	yes	—
44	D₄²×C₈₉	C₂²	1	1	yes	characteristic
45	#542×C₈₉	—	2	2	no	—
46	#542×C₈₉	C₂²	1	2	yes	complemented
47	#540×C₈₉	—	2	1	no	—
48	#540×C₈₉	C₂²	1	2	yes	—
49	#535×C₈₉	—	2	1	no	—
50	#535×C₈₉	C₂²	1	2	yes	—
51	#534×C₈₉	—	2	2	no	—
52	#533×C₈₉	—	2	1	no	—
53	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
54	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
55	#529×C₈₉	—	2	1	no	—
56	#529×C₈₉	C₂²	1	1	yes	characteristic
57	#529×C₈₉	C₂²	1	1	yes	characteristic
58	#519×C₈₉	C₂²	1	2	yes	complemented
59	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#496×C₈₉	C₂²	1	2	yes	complemented
61	#495×C₈₉	C₂²	1	2	yes	complemented
62	#492×C₈₉	C₂²	1	1	yes	characteristic
63	#492×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	#489×C₈₉	C₂²	1	2	yes	complemented
65	#486×C₈₉	C₂²	1	1	yes	characteristic
66	#486×C₈₉	C₂²	1	2	yes	complemented
67	#486×C₈₉	C₂²	1	1	yes	characteristic, complemented
68	#485×C₈₉	C₂²	1	1	yes	characteristic, complemented
69	#482×C₈₉	C₂²	1	1	yes	characteristic
70	#482×C₈₉	C₂²	1	2	yes	complemented
71	#482×C₈₉	C₂²	1	2	yes	complemented
72	#479×C₈₉	C₂²	1	1	yes	characteristic, complemented
73	#479×C₈₉	C₂²	1	2	yes	complemented
74	#478×C₈₉	C₂²	1	1	yes	characteristic, complemented
75	#477×C₈₉	C₂²	1	1	yes	characteristic, complemented
76	#476×C₈₉	C₂²	1	1	yes	characteristic, complemented
77	#476×C₈₉	C₂²	1	2	yes	complemented
78	#474×C₈₉	C₂²	1	2	yes	complemented
79	#470×C₈₉	C₂²	1	2	yes	complemented
80	#469×C₈₉	C₂²	1	2	yes	complemented
81	#468×C₈₉	C₂²	1	2	yes	—
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	#464×C₈₉	C₂²	1	1	yes	characteristic, complemented
86	#464×C₈₉	C₂²	1	2	yes	complemented
87	#464×C₈₉	C₂²	1	2	yes	complemented
88	#464×C₈₉	C₂²	1	2	yes	complemented
89	#463×C₈₉	C₂²	1	1	yes	characteristic, complemented
90	#463×C₈₉	C₂²	1	2	yes	complemented
91	#463×C₈₉	C₂²	1	2	yes	complemented
92	#462×C₈₉	C₂²	1	1	yes	characteristic, complemented
93	#461×C₈₉	C₂²	1	1	yes	characteristic, complemented
94	#460×C₈₉	C₂²	1	1	yes	characteristic
95	#460×C₈₉	C₂²	1	2	yes	complemented
96	#460×C₈₉	C₂²	1	2	yes	complemented
97	#460×C₈₉	C₂²	1	1	yes	characteristic, complemented
98	#460×C₈₉	C₂²	1	2	yes	complemented
99	#460×C₈₉	C₂²	1	2	yes	complemented
100	#460×C₈₉	C₂²	1	2	yes	complemented
101	#459×C₈₉	C₂²	1	1	yes	characteristic
102	#459×C₈₉	C₂²	1	1	yes	characteristic, complemented
103	#459×C₈₉	C₂²	1	2	yes	complemented
104	#452×C₈₉	C₂²	1	1	yes	characteristic, complemented
105	#452×C₈₉	C₂²	1	2	yes	complemented
106	#450×C₈₉	C₂²	1	2	yes	complemented
107	#450×C₈₉	C₂²	1	2	yes	complemented
108	#450×C₈₉	C₂²	1	2	yes	complemented
109	#449×C₈₉	C₂²	1	1	yes	characteristic
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	complemented
114	#446×C₈₉	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
116	#440×C₈₉	C₂²	1	2	yes	complemented
117	#440×C₈₉	C₂²	1	2	yes	complemented
118	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
121	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
122	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
123	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
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	#418×C₈₉	C₂²	1	2	yes	complemented
133	#418×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	C₂³	1	1	yes	characteristic
137	C₂×#41×C₈₉	C₂³	1	2	yes	—
138	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
139	C₂²×D₄×C₈₉	—	2	2	no	—
140	C₂²×D₄×C₈₉	—	2	1	no	—
141	C₂²×D₄×C₈₉	—	2	1	no	—
142	C₂²×D₄×C₈₉	—	2	1	no	—
143	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
144	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
145	#137×C₈₉	—	4	4	no	—
146	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
147	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₈₉	—	4	4	no	—
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	2	yes	—
154	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
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×SD₁₆×C₈₉	C₂³	1	2	yes	—
159	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
167	C₄⋊Q₈×C₈₉	—	2	2	no	—
168	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
170	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
171	#127×C₈₉	—	2	1	no	—
172	#127×C₈₉	—	2	1	no	—
173	#127×C₈₉	—	2	1	no	—
174	#127×C₈₉	C₂³	1	1	yes	characteristic
175	#127×C₈₉	C₂³	1	2	yes	—
176	#127×C₈₉	C₂³	1	1	yes	characteristic
177	#127×C₈₉	C₂³	1	2	yes	—
178	#126×C₈₉	—	2	2	no	—
179	#126×C₈₉	—	2	2	no	—
180	#126×C₈₉	—	2	2	no	—
181	#126×C₈₉	—	2	2	no	—
182	#126×C₈₉	—	2	1	no	—
183	#126×C₈₉	D₄	1	2	yes	—
184	#125×C₈₉	—	2	1	no	—
185	#125×C₈₉	D₄	1	1	yes	characteristic
186	#125×C₈₉	C₂³	1	1	yes	characteristic
187	#124×C₈₉	—	2	1	no	—
188	#124×C₈₉	—	2	2	no	—
189	#124×C₈₉	—	2	2	no	—
190	#124×C₈₉	—	2	2	no	—
191	#124×C₈₉	—	2	2	no	—
192	#124×C₈₉	D₄	1	1	yes	characteristic
193	#124×C₈₉	C₂³	1	2	yes	—
194	#124×C₈₉	C₂³	1	1	yes	characteristic
195	#124×C₈₉	C₂³	1	2	yes	—
196	#123×C₈₉	—	2	1	no	—
197	#123×C₈₉	—	2	2	no	—
198	#123×C₈₉	—	2	2	no	—
199	#123×C₈₉	—	2	2	no	—
200	#123×C₈₉	—	2	2	no	—
201	#123×C₈₉	—	2	2	no	—
202	#123×C₈₉	D₄	1	2	yes	—
203	C₂²⋊Q₈×C₈₉	—	2	1	no	—
204	C₂²⋊Q₈×C₈₉	—	2	1	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	D₄	1	1	yes	characteristic
209	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
212	#121×C₈₉	—	2	1	no	—
213	#121×C₈₉	—	2	2	no	—
214	#121×C₈₉	—	2	2	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	2	no	—
220	#121×C₈₉	—	2	2	no	—
221	#121×C₈₉	—	2	2	no	—
222	#121×C₈₉	—	2	2	no	—
223	#121×C₈₉	—	2	2	no	—
224	#121×C₈₉	D₄	1	1	yes	characteristic
225	#121×C₈₉	C₂³	1	2	yes	—
226	#121×C₈₉	C₂³	1	2	yes	—
227	#121×C₈₉	C₂³	1	2	yes	—
228	#121×C₈₉	C₂³	1	1	yes	characteristic
229	#120×C₈₉	—	2	2	no	—
230	#120×C₈₉	—	2	2	no	—
231	#120×C₈₉	—	2	2	no	—
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	2	no	—
237	C₄×Q₈×C₈₉	—	2	2	no	—
238	C₄×Q₈×C₈₉	—	2	2	no	—
239	C₄×Q₈×C₈₉	—	2	1	no	—
240	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
243	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
244	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
245	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
246	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₈₉	—	2	1	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	—	2	2	no	—
254	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₈₉	C₂³	1	2	yes	—
257	C₄×D₄×C₈₉	C₂³	1	2	yes	—
258	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₈₉	C₂³	1	2	yes	—
261	#117×C₈₉	—	2	1	no	—
262	#117×C₈₉	—	2	1	no	—
263	#117×C₈₉	—	2	1	no	—
264	#117×C₈₉	—	2	2	no	—
265	#117×C₈₉	—	2	2	no	—
266	#117×C₈₉	—	2	1	no	—
267	#117×C₈₉	—	2	1	no	—
268	#117×C₈₉	C₂³	1	2	yes	—
269	#117×C₈₉	C₂³	1	1	yes	characteristic
270	#117×C₈₉	C₂³	1	2	yes	—
271	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
272	C₂×C₄²×C₈₉	—	2	1	no	—
273	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
274	#107×C₈₉	C₂³	1	1	yes	characteristic
275	#107×C₈₉	C₂³	1	1	yes	characteristic
276	#107×C₈₉	C₂³	1	2	yes	—
277	#106×C₈₉	C₂³	1	1	yes	characteristic
278	#106×C₈₉	C₂³	1	1	yes	characteristic
279	#106×C₈₉	C₂³	1	2	yes	—
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	1	yes	characteristic
290	#103×C₈₉	C₂³	1	2	yes	—
291	#103×C₈₉	C₂³	1	1	yes	characteristic
292	#103×C₈₉	C₂³	1	1	yes	characteristic
293	#103×C₈₉	C₂³	1	2	yes	—
294	#102×C₈₉	C₂³	1	2	yes	—
295	#102×C₈₉	C₂³	1	2	yes	—
296	#102×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
301	#102×C₈₉	C₂³	1	2	yes	—
302	#102×C₈₉	C₂³	1	1	yes	characteristic
303	#102×C₈₉	C₂³	1	1	yes	characteristic
304	#102×C₈₉	C₂³	1	2	yes	—
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	2	no	—
316	C₂⁴×C₈₉	—	2	2	no	—
317	#41×C₈₉	—	2	2	no	—
318	#41×C₈₉	—	4	1	no	—
319	#41×C₈₉	—	4	2	no	—
320	#41×C₈₉	—	4	2	no	—
321	#41×C₈₉	—	8	2	no	—
322	C₂×Q₈×C₈₉	—	2	2	no	—
323	C₂×Q₈×C₈₉	—	2	1	no	—
324	C₂×Q₈×C₈₉	—	2	2	no	—
325	C₂×Q₈×C₈₉	—	2	4	no	—
326	C₂×Q₈×C₈₉	—	4	2	no	—
327	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₈₉	—	2	1	no	—
332	C₂×D₄×C₈₉	—	2	1	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	1	no	—
338	C₂×D₄×C₈₉	—	2	1	no	—
339	C₂×D₄×C₈₉	—	2	2	no	—
340	C₂×D₄×C₈₉	—	2	2	no	—
341	C₂×D₄×C₈₉	—	2	1	no	—
342	C₂×D₄×C₈₉	—	2	2	no	—
343	C₂×D₄×C₈₉	—	2	2	no	—
344	C₂×D₄×C₈₉	—	2	2	no	—
345	C₂×D₄×C₈₉	—	2	2	no	—
346	C₂×D₄×C₈₉	—	2	1	no	—
347	C₂×D₄×C₈₉	—	4	2	no	—
348	C₂×D₄×C₈₉	—	4	2	no	—
349	C₂×D₄×C₈₉	—	4	2	no	—
350	C₂×D₄×C₈₉	—	4	2	no	—
351	C₂×D₄×C₈₉	—	8	2	no	—
352	C₂×D₄×C₈₉	—	8	2	no	—
353	C₂×D₄×C₈₉	—	8	2	no	—
354	C₂×D₄×C₈₉	—	8	4	no	—
355	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
356	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
357	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
358	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
359	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
360	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₈₉	—	2	2	no	—
362	C₂²×C₄×C₈₉	—	2	1	no	—
363	C₂²×C₄×C₈₉	—	2	1	no	—
364	C₂²×C₄×C₈₉	—	2	1	no	—
365	C₂²×C₄×C₈₉	—	2	1	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	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
373	Q₁₆×C₈₉	—	2	2	no	—
374	Q₁₆×C₈₉	—	4	2	no	—
375	SD₁₆×C₈₉	—	2	2	no	—
376	SD₁₆×C₈₉	—	2	4	no	—
377	SD₁₆×C₈₉	—	2	4	no	—
378	SD₁₆×C₈₉	—	4	2	no	—
379	SD₁₆×C₈₉	—	4	2	no	—
380	SD₁₆×C₈₉	—	4	2	no	—
381	SD₁₆×C₈₉	—	4	1	no	—
382	SD₁₆×C₈₉	—	4	2	no	—
383	SD₁₆×C₈₉	—	4	2	no	—
384	D₈×C₈₉	—	4	1	no	—
385	D₈×C₈₉	—	4	2	no	—
386	D₈×C₈₉	—	4	2	no	—
387	M₁₆×C₈₉	—	4	2	no	—
388	M₁₆×C₈₉	—	4	2	no	—
389	C₂×C₈×C₈₉	—	4	2	no	—
390	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
395	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
396	C₄⋊C₄×C₈₉	—	2	1	no	—
397	C₄⋊C₄×C₈₉	—	2	1	no	—
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	2	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	2	no	—
410	C₄⋊C₄×C₈₉	—	2	1	no	—
411	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
412	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
413	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
414	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
415	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
416	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
420	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
422	C₂²⋊C₄×C₈₉	—	2	1	no	—
423	C₂²⋊C₄×C₈₉	—	2	2	no	—
424	C₂²⋊C₄×C₈₉	—	2	2	no	—
425	C₂²⋊C₄×C₈₉	—	2	1	no	—
426	C₂²⋊C₄×C₈₉	—	2	2	no	—
427	C₂²⋊C₄×C₈₉	—	2	2	no	—
428	C₂²⋊C₄×C₈₉	—	2	2	no	—
429	C₂²⋊C₄×C₈₉	—	2	1	no	—
430	C₂²⋊C₄×C₈₉	—	2	1	no	—
431	C₂²⋊C₄×C₈₉	—	2	1	no	—
432	C₂²⋊C₄×C₈₉	—	2	1	no	—
433	C₂²⋊C₄×C₈₉	—	2	2	no	—
434	C₂²⋊C₄×C₈₉	—	2	2	no	—
435	C₂²⋊C₄×C₈₉	—	2	1	no	—
436	C₂²⋊C₄×C₈₉	—	2	2	no	—
437	C₂²⋊C₄×C₈₉	—	2	2	no	—
438	C₂²⋊C₄×C₈₉	—	2	2	no	—
439	C₂²⋊C₄×C₈₉	—	2	1	no	—
440	C₂²⋊C₄×C₈₉	—	2	2	no	—
441	C₂²⋊C₄×C₈₉	—	2	2	no	—
442	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
447	C₄²×C₈₉	—	2	1	no	—
448	C₄²×C₈₉	—	2	1	no	—
449	C₄²×C₈₉	—	2	1	no	—
450	C₄²×C₈₉	—	2	2	no	—
451	C₄²×C₈₉	—	2	2	no	—
452	C₄²×C₈₉	—	2	2	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	1	no	—
463	C₂³×C₈₉	—	2	2	no	—
464	C₂³×C₈₉	—	4	4	no	—
465	C₂³×C₈₉	—	8	2	no	—
466	C₂³×C₈₉	—	8	2	no	—
467	C₂³×C₈₉	—	8	2	no	—
468	C₂³×C₈₉	—	8	2	no	—
469	C₂³×C₈₉	—	8	2	no	—
470	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
471	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
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	2	no	—
477	Q₈×C₈₉	—	2	1	no	—
478	Q₈×C₈₉	—	4	4	no	—
479	Q₈×C₈₉	—	8	1	no	—
480	Q₈×C₈₉	—	8	2	no	—
481	Q₈×C₈₉	H(5,𝔽₂)	1	2	yes	—
482	D₄×C₈₉	—	2	2	no	—
483	D₄×C₈₉	—	2	1	no	—
484	D₄×C₈₉	—	2	2	no	—
485	D₄×C₈₉	—	2	2	no	—
486	D₄×C₈₉	—	2	1	no	—
487	D₄×C₈₉	—	2	1	no	—
488	D₄×C₈₉	—	2	1	no	—
489	D₄×C₈₉	—	2	2	no	—
490	D₄×C₈₉	—	2	2	no	—
491	D₄×C₈₉	—	4	2	no	—
492	D₄×C₈₉	—	4	2	no	—
493	D₄×C₈₉	—	4	2	no	—
494	D₄×C₈₉	—	4	2	no	—
495	D₄×C₈₉	—	4	2	no	—
496	D₄×C₈₉	—	8	2	no	—
497	D₄×C₈₉	—	8	2	no	—
498	D₄×C₈₉	—	8	2	no	—
499	D₄×C₈₉	—	8	1	no	—
500	D₄×C₈₉	—	8	1	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	—	8	2	no	—
506	D₄×C₈₉	—	8	2	no	—
507	D₄×C₈₉	—	8	2	no	—
508	C₂×C₄×C₈₉	—	2	1	no	—
509	C₂×C₄×C₈₉	—	2	2	no	—
510	C₂×C₄×C₈₉	—	2	2	no	—
511	C₂×C₄×C₈₉	—	2	1	no	—
512	C₂×C₄×C₈₉	—	2	1	no	—
513	C₂×C₄×C₈₉	—	2	2	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	—	2	1	no	—
520	C₂×C₄×C₈₉	—	2	1	no	—
521	C₂×C₄×C₈₉	—	4	1	no	—
522	C₂×C₄×C₈₉	—	4	2	no	—
523	C₂×C₄×C₈₉	—	4	4	no	—
524	C₂×C₄×C₈₉	—	4	2	no	—
525	C₂×C₄×C₈₉	—	4	2	no	—
526	C₂×C₄×C₈₉	—	8	1	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	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
534	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
535	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
536	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
539	C₈×C₈₉	—	2	1	no	—
540	C₈×C₈₉	—	2	2	no	—
541	C₈×C₈₉	—	2	2	no	—
542	C₈×C₈₉	—	2	1	no	—
543	C₈×C₈₉	—	2	1	no	—
544	C₈×C₈₉	—	2	1	no	—
545	C₂²×C₈₉	—	2	1	no	—
546	C₂²×C₈₉	—	2	2	no	—
547	C₂²×C₈₉	—	2	2	no	—
548	C₂²×C₈₉	—	2	1	no	—
549	C₂²×C₈₉	—	2	1	no	—
550	C₂²×C₈₉	—	2	2	no	—
551	C₂²×C₈₉	—	4	1	no	—
552	C₂²×C₈₉	—	4	2	no	—
553	C₂²×C₈₉	—	4	1	no	—
554	C₂²×C₈₉	—	4	2	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	1	no	—
560	C₂²×C₈₉	—	4	1	no	—
561	C₂²×C₈₉	—	4	2	no	—
562	C₂²×C₈₉	—	4	2	no	—
563	C₂²×C₈₉	—	16	4	no	—
564	C₂²×C₈₉	—	16	4	no	—
565	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
566	C₄×C₈₉	—	2	1	no	—
567	C₄×C₈₉	—	2	1	no	—
568	C₄×C₈₉	—	2	2	no	—
569	C₄×C₈₉	—	2	1	no	—
570	C₄×C₈₉	—	2	2	no	—
571	C₄×C₈₉	—	2	2	no	—
572	C₄×C₈₉	—	2	1	no	—
573	C₄×C₈₉	—	2	2	no	—
574	C₄×C₈₉	—	4	1	no	—
575	C₄×C₈₉	—	4	1	no	—
576	C₄×C₈₉	—	4	2	no	—
577	C₄×C₈₉	—	4	2	no	—
578	C₄×C₈₉	—	4	1	no	—
579	C₄×C₈₉	—	4	1	no	—
580	C₄×C₈₉	—	4	1	no	—
581	C₄×C₈₉	#577	1	2	yes	—
582	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
583	C₄×C₈₉	#585	1	1	yes	characteristic
584	#62035	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
585	C₂×C₈₉	—	4	2	no	—
586	C₂×C₈₉	—	4	1	no	—
587	C₂×C₈₉	—	8	1	no	—
588	C₂×C₈₉	—	8	2	no	—
589	C₂×C₈₉	—	8	2	no	—
590	C₂×C₈₉	—	8	1	no	—
591	C₂×C₈₉	#3488	1	1	yes	characteristic
592	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
593	C₂×C₈₉	#3585	1	1	yes	characteristic
594	#3543	C₂×C₈₉	1	1	yes	characteristic, complemented
595	#3518	C₂×C₈₉	1	1	yes	characteristic, complemented
596	#3397	C₂×C₈₉	1	1	yes	characteristic, complemented
597	#3394	C₂×C₈₉	1	1	yes	characteristic, complemented
598	#3375	C₂×C₈₉	1	1	yes	characteristic, complemented
599	#3362	C₂×C₈₉	1	1	yes	characteristic, complemented
600	#3325	C₂×C₈₉	1	1	yes	characteristic, complemented
601	#3324	C₂×C₈₉	1	2	yes	complemented
602	#3311	C₂×C₈₉	1	2	yes	complemented
603	#3305	C₂×C₈₉	1	1	yes	characteristic, complemented
604	D₄×SD₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
605	#3278	C₂×C₈₉	1	1	yes	characteristic, complemented
606	#3275	C₂×C₈₉	1	2	yes	complemented
607	#3265	C₂×C₈₉	1	2	yes	complemented
608	#3257	C₂×C₈₉	1	2	yes	complemented
609	#3252	C₂×C₈₉	1	1	yes	characteristic, complemented
610	#3224	C₂×C₈₉	1	2	yes	complemented
611	#3208	C₂×C₈₉	1	1	yes	characteristic, complemented
612	#3126	C₂×C₈₉	1	2	yes	complemented
613	#3102	C₂×C₈₉	1	1	yes	characteristic, complemented
614	#3043	C₂×C₈₉	1	2	yes	complemented
615	#3038	C₂×C₈₉	1	1	yes	characteristic, complemented
616	#2993	C₂×C₈₉	1	1	yes	characteristic, complemented
617	C₈₉	#62035	1	1	yes	characteristic, direct product factor, Sylow
618	C₂×#137	C₂²×C₈₉	1	2	yes	complemented
619	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	complemented
620	C₂²×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
621	#560	—	2	2	no	—
622	#559	C₂²×C₈₉	1	1	yes	characteristic
623	Q₈²	C₂²×C₈₉	1	1	yes	characteristic, complemented
624	#556	—	2	2	no	—
625	#556	—	2	1	no	—
626	#556	C₂²×C₈₉	1	1	yes	characteristic, complemented
627	#556	C₂²×C₈₉	1	2	yes	complemented
628	#555	—	2	1	no	—
629	#555	C₂²×C₈₉	1	1	yes	characteristic, complemented
630	#550	C₂²×C₈₉	1	1	yes	characteristic
631	#550	C₂²×C₈₉	1	1	yes	characteristic
632	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
633	#548	C₂²×C₈₉	1	2	yes	complemented
634	#546	—	2	1	no	—
635	#546	C₂²×C₈₉	1	2	yes	—
636	D₄²	—	2	1	no	—
637	D₄²	C₂²×C₈₉	1	2	yes	—
638	D₄²	C₂²×C₈₉	1	1	yes	characteristic
639	#542	—	2	2	no	—
640	#542	C₂²×C₈₉	1	2	yes	complemented
641	#540	—	2	1	no	—
642	#540	C₂²×C₈₉	1	2	yes	—
643	#535	—	2	1	no	—
644	#535	C₂²×C₈₉	1	2	yes	—
645	#534	—	2	2	no	—
646	#533	—	2	1	no	—
647	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
648	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
649	#529	—	2	1	no	—
650	#529	C₂²×C₈₉	1	1	yes	characteristic
651	#529	C₂²×C₈₉	1	1	yes	characteristic
652	#519	C₂²×C₈₉	1	2	yes	complemented
653	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic, complemented
654	#496	C₂²×C₈₉	1	2	yes	complemented
655	#495	C₂²×C₈₉	1	2	yes	complemented
656	#492	C₂²×C₈₉	1	1	yes	characteristic
657	#492	C₂²×C₈₉	1	1	yes	characteristic, complemented
658	#489	C₂²×C₈₉	1	2	yes	complemented
659	#486	C₂²×C₈₉	1	1	yes	characteristic
660	#486	C₂²×C₈₉	1	1	yes	characteristic, complemented
661	#486	C₂²×C₈₉	1	2	yes	complemented
662	#485	C₂²×C₈₉	1	1	yes	characteristic, complemented
663	#482	C₂²×C₈₉	1	1	yes	characteristic
664	#482	C₂²×C₈₉	1	2	yes	complemented
665	#482	C₂²×C₈₉	1	2	yes	complemented
666	#479	C₂²×C₈₉	1	1	yes	characteristic, complemented
667	#479	C₂²×C₈₉	1	2	yes	complemented
668	#478	C₂²×C₈₉	1	1	yes	characteristic, complemented
669	#477	C₂²×C₈₉	1	1	yes	characteristic, complemented
670	#476	C₂²×C₈₉	1	1	yes	characteristic, complemented
671	#476	C₂²×C₈₉	1	2	yes	complemented
672	#474	C₂²×C₈₉	1	2	yes	complemented
673	#470	C₂²×C₈₉	1	2	yes	complemented
674	#469	C₂²×C₈₉	1	2	yes	complemented
675	#468	C₂²×C₈₉	1	2	yes	—
676	#468	C₂²×C₈₉	1	2	yes	complemented
677	#466	C₂²×C₈₉	1	2	yes	complemented
678	#465	C₂²×C₈₉	1	2	yes	complemented
679	#464	C₂²×C₈₉	1	1	yes	characteristic, complemented
680	#464	C₂²×C₈₉	1	2	yes	complemented
681	#464	C₂²×C₈₉	1	2	yes	complemented
682	#464	C₂²×C₈₉	1	2	yes	complemented
683	#463	C₂²×C₈₉	1	1	yes	characteristic, complemented
684	#463	C₂²×C₈₉	1	2	yes	complemented
685	#463	C₂²×C₈₉	1	2	yes	complemented
686	#462	C₂²×C₈₉	1	1	yes	characteristic, complemented
687	#461	C₂²×C₈₉	1	1	yes	characteristic, complemented
688	#460	C₂²×C₈₉	1	1	yes	characteristic
689	#460	C₂²×C₈₉	1	2	yes	complemented
690	#460	C₂²×C₈₉	1	1	yes	characteristic, complemented
691	#460	C₂²×C₈₉	1	2	yes	complemented
692	#460	C₂²×C₈₉	1	2	yes	complemented
693	#460	C₂²×C₈₉	1	2	yes	complemented
694	#460	C₂²×C₈₉	1	2	yes	complemented
695	#459	C₂²×C₈₉	1	1	yes	characteristic
696	#459	C₂²×C₈₉	1	1	yes	characteristic, complemented
697	#459	C₂²×C₈₉	1	2	yes	complemented
698	#452	C₂²×C₈₉	1	1	yes	characteristic, complemented
699	#452	C₂²×C₈₉	1	2	yes	complemented
700	#450	C₂²×C₈₉	1	2	yes	complemented
701	#450	C₂²×C₈₉	1	2	yes	complemented
702	#450	C₂²×C₈₉	1	2	yes	complemented
703	#449	C₂²×C₈₉	1	1	yes	characteristic
704	#449	C₂²×C₈₉	1	2	yes	complemented
705	#448	C₂²×C₈₉	1	2	yes	complemented
706	#448	C₂²×C₈₉	1	2	yes	complemented
707	#447	C₂²×C₈₉	1	2	yes	complemented
708	#446	C₂²×C₈₉	1	1	yes	characteristic, complemented
709	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
710	#440	C₂²×C₈₉	1	2	yes	complemented
711	#440	C₂²×C₈₉	1	2	yes	complemented
712	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
713	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
714	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
715	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
716	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
717	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
718	#436	C₂²×C₈₉	1	2	yes	complemented
719	#436	C₂²×C₈₉	1	1	yes	characteristic, complemented
720	#435	C₂²×C₈₉	1	2	yes	complemented
721	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
722	#433	C₂²×C₈₉	1	2	yes	complemented
723	#431	C₂²×C₈₉	1	1	yes	characteristic, complemented
724	#424	C₂²×C₈₉	1	2	yes	complemented
725	#423	C₂²×C₈₉	1	1	yes	characteristic, complemented
726	#418	C₂²×C₈₉	1	2	yes	complemented
727	#418	C₂²×C₈₉	1	2	yes	complemented
728	#416	C₂²×C₈₉	1	2	yes	complemented
729	C₂×#41	—	2	1	no	—
730	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
731	C₂×#41	C₂³×C₈₉	1	2	yes	—
732	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
733	C₂²×D₄	—	2	2	no	—
734	C₂²×D₄	—	2	1	no	—
735	C₂²×D₄	—	2	1	no	—
736	C₂²×D₄	—	2	1	no	—
737	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
738	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
739	#137	—	4	4	no	—
740	AGL(1,ℤ/8)	—	4	4	no	—
741	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
742	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
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×D₈	C₂³×C₈₉	1	2	yes	—
754	C₂×D₈	C₂³×C₈₉	1	2	yes	—
755	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
756	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
757	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
758	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
759	C₄⋊Q₈	—	2	1	no	—
760	C₄⋊Q₈	—	2	1	no	—
761	C₄⋊Q₈	—	2	2	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	#127	—	2	1	no	—
766	#127	—	2	1	no	—
767	#127	—	2	1	no	—
768	#127	C₂³×C₈₉	1	2	yes	—
769	#127	C₂³×C₈₉	1	1	yes	characteristic
770	#127	C₂³×C₈₉	1	1	yes	characteristic
771	#127	C₂³×C₈₉	1	2	yes	—
772	#126	—	2	2	no	—
773	#126	—	2	2	no	—
774	#126	—	2	2	no	—
775	#126	—	2	2	no	—
776	#126	—	2	1	no	—
777	#126	D₄×C₈₉	1	2	yes	—
778	#125	—	2	1	no	—
779	#125	D₄×C₈₉	1	1	yes	characteristic
780	#125	C₂³×C₈₉	1	1	yes	characteristic
781	#124	—	2	1	no	—
782	#124	—	2	2	no	—
783	#124	—	2	2	no	—
784	#124	—	2	2	no	—
785	#124	—	2	2	no	—
786	#124	D₄×C₈₉	1	1	yes	characteristic
787	#124	C₂³×C₈₉	1	1	yes	characteristic
788	#124	C₂³×C₈₉	1	2	yes	—
789	#124	C₂³×C₈₉	1	2	yes	—
790	#123	—	2	1	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	D₄×C₈₉	1	1	yes	characteristic
803	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
804	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
805	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
806	#121	—	2	1	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	—	2	1	no	—
812	#121	—	2	1	no	—
813	#121	—	2	2	no	—
814	#121	—	2	2	no	—
815	#121	—	2	2	no	—
816	#121	—	2	2	no	—
817	#121	—	2	2	no	—
818	#121	D₄×C₈₉	1	1	yes	characteristic
819	#121	C₂³×C₈₉	1	1	yes	characteristic
820	#121	C₂³×C₈₉	1	2	yes	—
821	#121	C₂³×C₈₉	1	2	yes	—
822	#121	C₂³×C₈₉	1	2	yes	—
823	#120	—	2	2	no	—
824	#120	—	2	2	no	—
825	#120	—	2	2	no	—
826	#120	—	2	2	no	—
827	#120	—	2	2	no	—
828	#120	—	2	2	no	—
829	C₄×Q₈	—	2	1	no	—
830	C₄×Q₈	—	2	2	no	—
831	C₄×Q₈	—	2	2	no	—
832	C₄×Q₈	—	2	2	no	—
833	C₄×Q₈	—	2	1	no	—
834	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
835	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
836	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
837	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
838	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
839	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
840	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
841	C₄×D₄	—	2	1	no	—
842	C₄×D₄	—	2	1	no	—
843	C₄×D₄	—	2	1	no	—
844	C₄×D₄	—	2	1	no	—
845	C₄×D₄	—	2	1	no	—
846	C₄×D₄	—	2	1	no	—
847	C₄×D₄	—	2	2	no	—
848	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
849	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
850	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
851	C₄×D₄	C₂³×C₈₉	1	2	yes	—
852	C₄×D₄	C₂³×C₈₉	1	2	yes	—
853	C₄×D₄	C₂³×C₈₉	1	2	yes	—
854	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
855	#117	—	2	1	no	—
856	#117	—	2	1	no	—
857	#117	—	2	1	no	—
858	#117	—	2	2	no	—
859	#117	—	2	2	no	—
860	#117	—	2	1	no	—
861	#117	—	2	1	no	—
862	#117	C₂³×C₈₉	1	1	yes	characteristic
863	#117	C₂³×C₈₉	1	2	yes	—
864	#117	C₂³×C₈₉	1	2	yes	—
865	C₂×C₂²⋊C₄	—	2	2	no	—
866	C₂×C₄²	—	2	1	no	—
867	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
868	#107	C₂³×C₈₉	1	1	yes	characteristic
869	#107	C₂³×C₈₉	1	1	yes	characteristic
870	#107	C₂³×C₈₉	1	2	yes	—
871	#106	C₂³×C₈₉	1	1	yes	characteristic
872	#106	C₂³×C₈₉	1	1	yes	characteristic
873	#106	C₂³×C₈₉	1	2	yes	—
874	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
875	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
876	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
877	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
878	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
879	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
880	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
881	#103	C₂³×C₈₉	1	1	yes	characteristic
882	#103	C₂³×C₈₉	1	2	yes	—
883	#103	C₂³×C₈₉	1	1	yes	characteristic
884	#103	C₂³×C₈₉	1	2	yes	—
885	#103	C₂³×C₈₉	1	1	yes	characteristic
886	#103	C₂³×C₈₉	1	1	yes	characteristic
887	#103	C₂³×C₈₉	1	2	yes	—
888	#102	C₂³×C₈₉	1	2	yes	—
889	#102	C₂³×C₈₉	1	2	yes	—
890	#102	C₂³×C₈₉	1	1	yes	characteristic
891	#102	C₂³×C₈₉	1	2	yes	—
892	#102	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	1	yes	characteristic
898	#102	C₂³×C₈₉	1	2	yes	—
899	#102	C₂³×C₈₉	1	1	yes	characteristic
900	#102	C₂³×C₈₉	1	2	yes	—
901	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
902	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
903	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
904	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
905	#97	C₂³×C₈₉	1	2	yes	—
906	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
907	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
908	C₄×C₈	C₂³×C₈₉	1	2	yes	—
909	C₂⁴	—	2	2	no	—
910	C₂⁴	—	2	2	no	—
911	#41	—	2	2	no	—
912	#41	—	4	1	no	—
913	#41	—	4	2	no	—
914	#41	—	4	2	no	—
915	#41	—	8	2	no	—
916	C₂×Q₈	—	2	2	no	—
917	C₂×Q₈	—	2	1	no	—
918	C₂×Q₈	—	2	2	no	—
919	C₂×Q₈	—	2	4	no	—
920	C₂×Q₈	—	4	2	no	—
921	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
922	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
923	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
924	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	1	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	1	no	—
941	C₂×D₄	—	4	2	no	—
942	C₂×D₄	—	4	2	no	—
943	C₂×D₄	—	4	2	no	—
944	C₂×D₄	—	4	2	no	—
945	C₂×D₄	—	8	2	no	—
946	C₂×D₄	—	8	2	no	—
947	C₂×D₄	—	8	2	no	—
948	C₂×D₄	—	8	4	no	—
949	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
950	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
951	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
952	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
953	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
954	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
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	1	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	—	2	2	no	—
963	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
964	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
965	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
966	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
967	Q₁₆	—	2	2	no	—
968	Q₁₆	—	4	2	no	—
969	SD₁₆	—	2	2	no	—
970	SD₁₆	—	2	4	no	—
971	SD₁₆	—	2	4	no	—
972	SD₁₆	—	4	2	no	—
973	SD₁₆	—	4	2	no	—
974	SD₁₆	—	4	2	no	—
975	SD₁₆	—	4	2	no	—
976	SD₁₆	—	4	1	no	—
977	SD₁₆	—	4	2	no	—
978	D₈	—	4	2	no	—
979	D₈	—	4	2	no	—
980	D₈	—	4	1	no	—
981	M₁₆	—	4	2	no	—
982	M₁₆	—	4	2	no	—
983	C₂×C₈	—	4	2	no	—
984	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
985	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
986	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
987	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
988	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
989	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	—	2	1	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	1	no	—
1005	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1006	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1007	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1008	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1009	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1010	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1011	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1012	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1013	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1014	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1015	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	1	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1037	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1038	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1039	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1040	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	2	1	no	—
1043	C₄²	—	2	1	no	—
1044	C₄²	—	2	2	no	—
1045	C₄²	—	2	2	no	—
1046	C₄²	—	2	2	no	—
1047	C₄²	—	2	1	no	—
1048	C₄²	—	2	2	no	—
1049	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1050	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1051	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1052	C₄²	C₂⁴×C₈₉	1	2	yes	—
1053	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1054	C₂³	—	2	1	no	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	2	2	no	—
1057	C₂³	—	2	2	no	—
1058	C₂³	—	4	4	no	—
1059	C₂³	—	8	2	no	—
1060	C₂³	—	8	2	no	—
1061	C₂³	—	8	2	no	—
1062	C₂³	—	8	2	no	—
1063	C₂³	—	8	2	no	—
1064	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1065	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1066	Q₈	—	2	2	no	—
1067	Q₈	—	2	1	no	—
1068	Q₈	—	2	2	no	—
1069	Q₈	—	2	1	no	—
1070	Q₈	—	2	2	no	—
1071	Q₈	—	2	1	no	—
1072	Q₈	—	4	4	no	—
1073	Q₈	—	8	1	no	—
1074	Q₈	—	8	2	no	—
1075	Q₈	H(5,𝔽₂)×C₈₉	1	2	yes	—
1076	D₄	—	2	2	no	—
1077	D₄	—	2	1	no	—
1078	D₄	—	2	2	no	—
1079	D₄	—	2	2	no	—
1080	D₄	—	2	1	no	—
1081	D₄	—	2	1	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	2	no	—
1084	D₄	—	2	2	no	—
1085	D₄	—	4	2	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	4	2	no	—
1088	D₄	—	4	2	no	—
1089	D₄	—	4	2	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	2	no	—
1092	D₄	—	8	2	no	—
1093	D₄	—	8	2	no	—
1094	D₄	—	8	1	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	—	8	2	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	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	4	no	—
1118	C₂×C₄	—	4	2	no	—
1119	C₂×C₄	—	4	2	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	C₂²×D₄×C₈₉	1	1	yes	characteristic
1125	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1126	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1127	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
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	C₂⁵×C₈₉	1	1	yes	characteristic
1133	C₈	—	2	1	no	—
1134	C₈	—	2	2	no	—
1135	C₈	—	2	2	no	—
1136	C₈	—	2	1	no	—
1137	C₈	—	2	1	no	—
1138	C₈	—	2	1	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	1	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	2	1	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	4	2	no	—
1150	C₂²	—	4	1	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	2	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	4	2	no	—
1155	C₂²	—	4	2	no	—
1156	C₂²	—	4	1	no	—
1157	C₂²	—	16	4	no	—
1158	C₂²	—	16	4	no	—
1159	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1160	C₄	—	2	1	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	1	no	—
1163	C₄	—	2	1	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	2	1	no	—
1166	C₄	—	2	2	no	—
1167	C₄	—	2	2	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	1	no	—
1172	C₄	—	4	2	no	—
1173	C₄	—	4	2	no	—
1174	C₄	—	4	1	no	—
1175	C₄	#577×C₈₉	1	2	yes	—
1176	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1177	C₄	#585×C₈₉	1	1	yes	characteristic
1178	C₂	—	4	2	no	—
1179	C₂	—	4	1	no	—
1180	C₂	—	8	1	no	—
1181	C₂	—	8	2	no	—
1182	C₂	—	8	1	no	—
1183	C₂	—	8	2	no	—
1184	C₂	C₈₉×#3488	1	1	yes	characteristic
1185	C₂	C₂×#577×C₈₉	1	1	yes	characteristic
1186	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×#3543	C₂	semidirect
2. C₈₉×#3518	C₂	semidirect
3. C₈₉×#3397	C₂	semidirect
4. C₈₉×#3394	C₂	semidirect
5. C₈₉×#3375	C₂	semidirect
6. C₈₉×#3362	C₂	semidirect
7. C₈₉×#3325	C₂	semidirect
8. C₈₉×#3324	C₂	semidirect
9. C₈₉×#3311	C₂	semidirect
10. C₈₉×#3305	C₂	semidirect
11. D₄×SD₁₆×C₈₉	C₂	semidirect
12. C₈₉×#3278	C₂	semidirect
13. C₈₉×#3275	C₂	semidirect
14. C₈₉×#3265	C₂	semidirect
15. C₈₉×#3257	C₂	semidirect
16. C₈₉×#3252	C₂	semidirect
17. C₈₉×#3224	C₂	semidirect
18. C₈₉×#3208	C₂	semidirect
19. C₈₉×#3126	C₂	semidirect
20. C₈₉×#3102	C₂	semidirect
21. C₈₉×#3043	C₂	semidirect
22. C₈₉×#3038	C₂	semidirect
23. C₈₉×#2993	C₂	semidirect
24. C₂×#137×C₈₉	C₂²	semidirect
25. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
26. C₂²×SD₁₆×C₈₉	C₂²	semidirect
29. Q₈²×C₈₉	C₂²	semidirect
32. #556×C₈₉	C₂²	semidirect
33. #556×C₈₉	C₂²	semidirect
35. #555×C₈₉	C₂²	semidirect
38. D₄×Q₈×C₈₉	C₂²	semidirect
39. #548×C₈₉	C₂²	semidirect
46. #542×C₈₉	C₂²	semidirect
53. #533×C₈₉	C₂²	semidirect
58. #519×C₈₉	C₂²	semidirect
59. C₄×#41×C₈₉	C₂²	semidirect
60. #496×C₈₉	C₂²	semidirect
61. #495×C₈₉	C₂²	semidirect
63. #492×C₈₉	C₂²	semidirect
64. #489×C₈₉	C₂²	semidirect
66. #486×C₈₉	C₂²	semidirect
67. #486×C₈₉	C₂²	semidirect
68. #485×C₈₉	C₂²	semidirect
70. #482×C₈₉	C₂²	semidirect
71. #482×C₈₉	C₂²	semidirect
72. #479×C₈₉	C₂²	semidirect
73. #479×C₈₉	C₂²	semidirect
74. #478×C₈₉	C₂²	semidirect
75. #477×C₈₉	C₂²	semidirect
76. #476×C₈₉	C₂²	semidirect
77. #476×C₈₉	C₂²	semidirect
78. #474×C₈₉	C₂²	semidirect
79. #470×C₈₉	C₂²	semidirect
80. #469×C₈₉	C₂²	semidirect
82. #468×C₈₉	C₂²	semidirect
83. #466×C₈₉	C₂²	semidirect
84. #465×C₈₉	C₂²	semidirect
85. #464×C₈₉	C₂²	semidirect
86. #464×C₈₉	C₂²	semidirect
87. #464×C₈₉	C₂²	semidirect
88. #464×C₈₉	C₂²	semidirect
89. #463×C₈₉	C₂²	semidirect
90. #463×C₈₉	C₂²	semidirect
91. #463×C₈₉	C₂²	semidirect
92. #462×C₈₉	C₂²	semidirect
93. #461×C₈₉	C₂²	semidirect
95. #460×C₈₉	C₂²	semidirect
96. #460×C₈₉	C₂²	semidirect
97. #460×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
104. #452×C₈₉	C₂²	semidirect
105. #452×C₈₉	C₂²	semidirect
106. #450×C₈₉	C₂²	semidirect
107. #450×C₈₉	C₂²	semidirect
108. #450×C₈₉	C₂²	semidirect
110. #449×C₈₉	C₂²	semidirect
111. #448×C₈₉	C₂²	semidirect
112. #448×C₈₉	C₂²	semidirect
113. #447×C₈₉	C₂²	semidirect
114. #446×C₈₉	C₂²	semidirect
115. C₈×Q₈×C₈₉	C₂²	semidirect
116. #440×C₈₉	C₂²	semidirect
117. #440×C₈₉	C₂²	semidirect
118. C₄×Q₁₆×C₈₉	C₂²	semidirect
119. C₄×SD₁₆×C₈₉	C₂²	semidirect
120. C₄×SD₁₆×C₈₉	C₂²	semidirect
121. C₄×SD₁₆×C₈₉	C₂²	semidirect
122. C₄×SD₁₆×C₈₉	C₂²	semidirect
123. C₄×D₈×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. #418×C₈₉	C₂²	semidirect
133. #418×C₈₉	C₂²	semidirect
134. #416×C₈₉	C₂²	semidirect
584. #62035	C₈₉	direct (N × H)
594. #3543	C₂×C₈₉	semidirect
595. #3518	C₂×C₈₉	semidirect
596. #3397	C₂×C₈₉	semidirect
597. #3394	C₂×C₈₉	semidirect
598. #3375	C₂×C₈₉	semidirect
599. #3362	C₂×C₈₉	semidirect
600. #3325	C₂×C₈₉	semidirect
601. #3324	C₂×C₈₉	semidirect
602. #3311	C₂×C₈₉	semidirect
603. #3305	C₂×C₈₉	semidirect
604. D₄×SD₁₆	C₂×C₈₉	semidirect
605. #3278	C₂×C₈₉	semidirect
606. #3275	C₂×C₈₉	semidirect
607. #3265	C₂×C₈₉	semidirect
608. #3257	C₂×C₈₉	semidirect
609. #3252	C₂×C₈₉	semidirect
610. #3224	C₂×C₈₉	semidirect
611. #3208	C₂×C₈₉	semidirect
612. #3126	C₂×C₈₉	semidirect
613. #3102	C₂×C₈₉	semidirect
614. #3043	C₂×C₈₉	semidirect
615. #3038	C₂×C₈₉	semidirect
616. #2993	C₂×C₈₉	semidirect
617. C₈₉	#62035	direct (N × H)
618. C₂×#137	C₂²×C₈₉	semidirect
619. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
620. C₂²×SD₁₆	C₂²×C₈₉	semidirect
623. Q₈²	C₂²×C₈₉	semidirect
626. #556	C₂²×C₈₉	semidirect
627. #556	C₂²×C₈₉	semidirect
629. #555	C₂²×C₈₉	semidirect
632. D₄×Q₈	C₂²×C₈₉	semidirect
633. #548	C₂²×C₈₉	semidirect
640. #542	C₂²×C₈₉	semidirect
647. #533	C₂²×C₈₉	semidirect
652. #519	C₂²×C₈₉	semidirect
653. C₄×#41	C₂²×C₈₉	semidirect
654. #496	C₂²×C₈₉	semidirect
655. #495	C₂²×C₈₉	semidirect
657. #492	C₂²×C₈₉	semidirect
658. #489	C₂²×C₈₉	semidirect
660. #486	C₂²×C₈₉	semidirect
661. #486	C₂²×C₈₉	semidirect
662. #485	C₂²×C₈₉	semidirect
664. #482	C₂²×C₈₉	semidirect
665. #482	C₂²×C₈₉	semidirect
666. #479	C₂²×C₈₉	semidirect
667. #479	C₂²×C₈₉	semidirect
668. #478	C₂²×C₈₉	semidirect
669. #477	C₂²×C₈₉	semidirect
670. #476	C₂²×C₈₉	semidirect
671. #476	C₂²×C₈₉	semidirect
672. #474	C₂²×C₈₉	semidirect
673. #470	C₂²×C₈₉	semidirect
674. #469	C₂²×C₈₉	semidirect
676. #468	C₂²×C₈₉	semidirect
677. #466	C₂²×C₈₉	semidirect
678. #465	C₂²×C₈₉	semidirect
679. #464	C₂²×C₈₉	semidirect
680. #464	C₂²×C₈₉	semidirect
681. #464	C₂²×C₈₉	semidirect
682. #464	C₂²×C₈₉	semidirect
683. #463	C₂²×C₈₉	semidirect
684. #463	C₂²×C₈₉	semidirect
685. #463	C₂²×C₈₉	semidirect
686. #462	C₂²×C₈₉	semidirect
687. #461	C₂²×C₈₉	semidirect
689. #460	C₂²×C₈₉	semidirect
690. #460	C₂²×C₈₉	semidirect
691. #460	C₂²×C₈₉	semidirect
692. #460	C₂²×C₈₉	semidirect
693. #460	C₂²×C₈₉	semidirect
694. #460	C₂²×C₈₉	semidirect
696. #459	C₂²×C₈₉	semidirect
697. #459	C₂²×C₈₉	semidirect
698. #452	C₂²×C₈₉	semidirect
699. #452	C₂²×C₈₉	semidirect
700. #450	C₂²×C₈₉	semidirect
701. #450	C₂²×C₈₉	semidirect
702. #450	C₂²×C₈₉	semidirect
704. #449	C₂²×C₈₉	semidirect
705. #448	C₂²×C₈₉	semidirect
706. #448	C₂²×C₈₉	semidirect
707. #447	C₂²×C₈₉	semidirect
708. #446	C₂²×C₈₉	semidirect
709. C₈×Q₈	C₂²×C₈₉	semidirect
710. #440	C₂²×C₈₉	semidirect
711. #440	C₂²×C₈₉	semidirect
712. C₄×Q₁₆	C₂²×C₈₉	semidirect
713. C₄×SD₁₆	C₂²×C₈₉	semidirect
714. C₄×SD₁₆	C₂²×C₈₉	semidirect
715. C₄×SD₁₆	C₂²×C₈₉	semidirect
716. C₄×SD₁₆	C₂²×C₈₉	semidirect
717. C₄×D₈	C₂²×C₈₉	semidirect
718. #436	C₂²×C₈₉	semidirect
719. #436	C₂²×C₈₉	semidirect
720. #435	C₂²×C₈₉	semidirect
721. C₈×D₄	C₂²×C₈₉	semidirect
722. #433	C₂²×C₈₉	semidirect
723. #431	C₂²×C₈₉	semidirect
724. #424	C₂²×C₈₉	semidirect
725. #423	C₂²×C₈₉	semidirect
726. #418	C₂²×C₈₉	semidirect
727. #418	C₂²×C₈₉	semidirect
728. #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×#3543	2
C₈₉×#3518	2
C₈₉×#3397	2
C₈₉×#3394	2
C₈₉×#3375	2
C₈₉×#3362	2
C₈₉×#3325	2
C₈₉×#3324	2
C₈₉×#3311	2
C₈₉×#3305	2
D₄×SD₁₆×C₈₉	2
C₈₉×#3278	2
C₈₉×#3275	2
C₈₉×#3265	2
C₈₉×#3257	2
C₈₉×#3252	2
C₈₉×#3224	2
C₈₉×#3208	2
C₈₉×#3126	2
C₈₉×#3102	2
C₈₉×#3043	2
C₈₉×#3038	2
C₈₉×#2993	2
#62035	89

Subgroups — C89×#62035 #36439883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62035 #36439883