Subgroups — C₈₉×#62006 #36439854

Order 22784.

1868 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3396	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3394	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3328	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3326	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3324	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3322	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3278	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3277	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3275	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3274	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3256	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3211	C₂	1	2	yes	maximal, complemented
18	C₈₉×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3108	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₉×#3102	C₂	1	2	yes	maximal, complemented
21	C₈₉×#3040	C₂	1	2	yes	maximal, complemented
22	C₈₉×#3037	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2991	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₈₉	C₂²	1	2	yes	complemented
25	C₂×#137×C₈₉	C₂²	1	2	yes	complemented
26	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
27	#559×C₈₉	—	2	1	no	—
28	#559×C₈₉	C₂²	1	1	yes	characteristic
29	#559×C₈₉	C₂²	1	1	yes	characteristic, complemented
30	#557×C₈₉	C₂²	1	1	yes	characteristic, complemented
31	#556×C₈₉	—	2	1	no	—
32	#556×C₈₉	C₂²	1	1	yes	characteristic
33	#556×C₈₉	C₂²	1	1	yes	characteristic
34	#555×C₈₉	—	2	1	no	—
35	#553×C₈₉	—	2	2	no	—
36	#553×C₈₉	C₂²	1	2	yes	complemented
37	#551×C₈₉	—	2	2	no	—
38	#550×C₈₉	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
40	#548×C₈₉	C₂²	1	2	yes	—
41	#548×C₈₉	C₂²	1	2	yes	complemented
42	#546×C₈₉	—	2	1	no	—
43	#546×C₈₉	C₂²	1	2	yes	—
44	D₄²×C₈₉	C₂²	1	1	yes	characteristic
45	#542×C₈₉	—	2	1	no	—
46	#538×C₈₉	—	2	2	no	—
47	#532×C₈₉	—	2	1	no	—
48	#532×C₈₉	C₂²	1	1	yes	characteristic
49	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
50	#529×C₈₉	—	2	2	no	—
51	#529×C₈₉	C₂²	1	2	yes	—
52	#529×C₈₉	C₂²	1	1	yes	characteristic
53	#529×C₈₉	C₂²	1	2	yes	complemented
54	C₂×#124×C₈₉	C₂²	1	2	yes	—
55	#518×C₈₉	—	2	1	no	—
56	C₄×#41×C₈₉	—	2	1	no	—
57	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
58	C₄×#41×C₈₉	C₂²	1	2	yes	complemented
59	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#495×C₈₉	C₂²	1	2	yes	—
61	#495×C₈₉	C₂²	1	2	yes	complemented
62	#493×C₈₉	C₂²	1	1	yes	characteristic
63	#492×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	#488×C₈₉	C₂²	1	2	yes	—
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
68	#485×C₈₉	C₂²	1	2	yes	complemented
69	#483×C₈₉	C₂²	1	1	yes	characteristic, complemented
70	#482×C₈₉	C₂²	1	2	yes	—
71	#480×C₈₉	C₂²	1	1	yes	characteristic
72	#479×C₈₉	C₂²	1	2	yes	complemented
73	#479×C₈₉	C₂²	1	1	yes	characteristic, complemented
74	#479×C₈₉	C₂²	1	1	yes	characteristic, complemented
75	#478×C₈₉	C₂²	1	2	yes	complemented
76	#478×C₈₉	C₂²	1	2	yes	complemented
77	#475×C₈₉	C₂²	1	1	yes	characteristic, complemented
78	#474×C₈₉	C₂²	1	1	yes	characteristic
79	#470×C₈₉	C₂²	1	2	yes	complemented
80	#469×C₈₉	C₂²	1	2	yes	—
81	#469×C₈₉	C₂²	1	2	yes	—
82	#468×C₈₉	C₂²	1	2	yes	—
83	#468×C₈₉	C₂²	1	2	yes	complemented
84	#468×C₈₉	C₂²	1	2	yes	complemented
85	#464×C₈₉	C₂²	1	2	yes	—
86	#464×C₈₉	C₂²	1	1	yes	characteristic
87	#464×C₈₉	C₂²	1	1	yes	characteristic
88	#464×C₈₉	C₂²	1	2	yes	complemented
89	#464×C₈₉	C₂²	1	2	yes	complemented
90	#464×C₈₉	C₂²	1	2	yes	complemented
91	#464×C₈₉	C₂²	1	2	yes	complemented
92	#463×C₈₉	C₂²	1	2	yes	—
93	#463×C₈₉	C₂²	1	2	yes	—
94	#463×C₈₉	C₂²	1	2	yes	complemented
95	#463×C₈₉	C₂²	1	2	yes	complemented
96	#463×C₈₉	C₂²	1	2	yes	complemented
97	#463×C₈₉	C₂²	1	2	yes	complemented
98	#462×C₈₉	C₂²	1	1	yes	characteristic, complemented
99	#462×C₈₉	C₂²	1	1	yes	characteristic, complemented
100	#460×C₈₉	C₂²	1	1	yes	characteristic
101	#460×C₈₉	C₂²	1	1	yes	characteristic
102	#460×C₈₉	C₂²	1	1	yes	characteristic, complemented
103	#459×C₈₉	C₂²	1	1	yes	characteristic
104	#452×C₈₉	C₂²	1	2	yes	complemented
105	#451×C₈₉	C₂²	1	2	yes	complemented
106	#451×C₈₉	C₂²	1	1	yes	characteristic, complemented
107	#450×C₈₉	C₂²	1	2	yes	—
108	#449×C₈₉	C₂²	1	2	yes	—
109	#449×C₈₉	C₂²	1	2	yes	complemented
110	#449×C₈₉	C₂²	1	2	yes	complemented
111	#448×C₈₉	C₂²	1	1	yes	characteristic
112	#448×C₈₉	C₂²	1	2	yes	complemented
113	#447×C₈₉	C₂²	1	2	yes	—
114	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
116	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
117	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
118	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
121	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
122	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
123	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
124	#436×C₈₉	C₂²	1	1	yes	characteristic
125	#436×C₈₉	C₂²	1	1	yes	characteristic
126	#436×C₈₉	C₂²	1	2	yes	complemented
127	#436×C₈₉	C₂²	1	2	yes	complemented
128	#431×C₈₉	C₂²	1	2	yes	complemented
129	#431×C₈₉	C₂²	1	1	yes	characteristic, complemented
130	#423×C₈₉	C₂²	1	1	yes	characteristic, complemented
131	#423×C₈₉	C₂²	1	2	yes	complemented
132	#419×C₈₉	C₂²	1	2	yes	complemented
133	#418×C₈₉	C₂²	1	2	yes	—
134	#417×C₈₉	C₂²	1	2	yes	complemented
135	C₂×#41×C₈₉	—	2	1	no	—
136	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
137	C₂×#41×C₈₉	C₂³	1	2	yes	—
138	C₂×#41×C₈₉	C₂³	1	2	yes	—
139	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
140	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
141	C₂²×D₄×C₈₉	—	2	1	no	—
142	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
143	#137×C₈₉	—	4	4	no	—
144	#137×C₈₉	—	4	4	no	—
145	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
146	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
149	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
153	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
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×D₈×C₈₉	C₂³	1	2	yes	—
158	C₂×D₈×C₈₉	C₂³	1	2	yes	—
159	C₂×D₈×C₈₉	C₂³	1	2	yes	—
160	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
161	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
162	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
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	#127×C₈₉	—	2	1	no	—
168	#127×C₈₉	C₂³	1	1	yes	characteristic
169	#127×C₈₉	C₂³	1	1	yes	characteristic
170	#126×C₈₉	—	2	2	no	—
171	#126×C₈₉	—	2	2	no	—
172	#126×C₈₉	—	2	2	no	—
173	#126×C₈₉	—	2	2	no	—
174	#126×C₈₉	—	2	1	no	—
175	#126×C₈₉	—	2	2	no	—
176	#125×C₈₉	—	2	2	no	—
177	#125×C₈₉	C₂³	1	1	yes	characteristic
178	#125×C₈₉	C₂³	1	2	yes	—
179	#124×C₈₉	—	2	1	no	—
180	#124×C₈₉	—	2	1	no	—
181	#124×C₈₉	—	2	1	no	—
182	#124×C₈₉	—	2	2	no	—
183	#124×C₈₉	—	2	2	no	—
184	#124×C₈₉	—	2	2	no	—
185	#124×C₈₉	—	2	2	no	—
186	#124×C₈₉	—	2	1	no	—
187	#124×C₈₉	C₂³	1	1	yes	characteristic
188	#124×C₈₉	C₂³	1	2	yes	—
189	#124×C₈₉	C₂³	1	2	yes	—
190	#124×C₈₉	C₂³	1	2	yes	—
191	#124×C₈₉	C₂³	1	2	yes	—
192	#123×C₈₉	—	2	1	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	C₂²⋊Q₈×C₈₉	—	2	1	no	—
200	C₂²⋊Q₈×C₈₉	—	2	2	no	—
201	C₂²⋊Q₈×C₈₉	—	2	2	no	—
202	C₂²⋊Q₈×C₈₉	—	2	2	no	—
203	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
204	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
205	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
206	#121×C₈₉	—	2	2	no	—
207	#121×C₈₉	—	2	2	no	—
208	#121×C₈₉	—	2	2	no	—
209	#121×C₈₉	—	2	1	no	—
210	#121×C₈₉	—	2	1	no	—
211	#121×C₈₉	—	2	1	no	—
212	#121×C₈₉	—	2	1	no	—
213	#121×C₈₉	—	2	2	no	—
214	#121×C₈₉	—	2	2	no	—
215	#121×C₈₉	C₂³	1	2	yes	—
216	#121×C₈₉	C₂³	1	1	yes	characteristic
217	#121×C₈₉	C₂³	1	2	yes	—
218	#121×C₈₉	C₂³	1	2	yes	—
219	#120×C₈₉	—	2	2	no	—
220	#120×C₈₉	—	2	2	no	—
221	C₄×Q₈×C₈₉	—	2	1	no	—
222	C₄×Q₈×C₈₉	—	2	1	no	—
223	C₄×Q₈×C₈₉	—	2	1	no	—
224	C₄×Q₈×C₈₉	—	2	1	no	—
225	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
226	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
229	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
230	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₈₉	—	2	1	no	—
235	C₄×D₄×C₈₉	—	2	2	no	—
236	C₄×D₄×C₈₉	—	2	2	no	—
237	C₄×D₄×C₈₉	—	2	2	no	—
238	C₄×D₄×C₈₉	—	2	2	no	—
239	C₄×D₄×C₈₉	—	2	1	no	—
240	C₄×D₄×C₈₉	—	2	1	no	—
241	C₄×D₄×C₈₉	—	2	1	no	—
242	C₄×D₄×C₈₉	—	2	1	no	—
243	C₄×D₄×C₈₉	—	2	2	no	—
244	C₄×D₄×C₈₉	—	2	2	no	—
245	C₄×D₄×C₈₉	—	2	2	no	—
246	C₄×D₄×C₈₉	—	2	1	no	—
247	C₄×D₄×C₈₉	—	2	1	no	—
248	C₄×D₄×C₈₉	—	2	1	no	—
249	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
250	C₄×D₄×C₈₉	D₄	1	2	yes	—
251	C₄×D₄×C₈₉	C₂³	1	2	yes	—
252	C₄×D₄×C₈₉	C₂³	1	2	yes	—
253	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₈₉	C₂³	1	2	yes	—
255	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₈₉	C₂³	1	2	yes	—
257	#117×C₈₉	—	2	1	no	—
258	#117×C₈₉	—	2	2	no	—
259	#117×C₈₉	—	2	2	no	—
260	#117×C₈₉	—	2	1	no	—
261	#117×C₈₉	—	2	2	no	—
262	#117×C₈₉	D₄	1	1	yes	characteristic
263	#117×C₈₉	D₄	1	2	yes	—
264	#117×C₈₉	C₂³	1	2	yes	—
265	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
266	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
268	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
269	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
270	C₂×C₄²×C₈₉	—	2	1	no	—
271	C₂×C₄²×C₈₉	—	2	2	no	—
272	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
274	#107×C₈₉	C₂³	1	1	yes	characteristic
275	#107×C₈₉	C₂³	1	2	yes	—
276	#107×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	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	2	yes	—
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	2	yes	—
292	#103×C₈₉	C₂³	1	1	yes	characteristic
293	#103×C₈₉	C₂³	1	1	yes	characteristic
294	#103×C₈₉	C₂³	1	1	yes	characteristic
295	#103×C₈₉	C₂³	1	1	yes	characteristic
296	#103×C₈₉	C₂³	1	1	yes	characteristic
297	#103×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	2	yes	—
303	#102×C₈₉	C₂³	1	2	yes	—
304	#102×C₈₉	C₂³	1	1	yes	characteristic
305	#102×C₈₉	C₂³	1	2	yes	—
306	#102×C₈₉	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
310	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₈₉	C₂³	1	2	yes	—
314	C₄×C₈×C₈₉	C₂³	1	2	yes	—
315	C₂⁴×C₈₉	—	2	2	no	—
316	#41×C₈₉	—	2	4	no	—
317	#41×C₈₉	—	4	2	no	—
318	#41×C₈₉	—	4	2	no	—
319	#41×C₈₉	—	4	4	no	—
320	#41×C₈₉	—	4	2	no	—
321	#41×C₈₉	—	4	2	no	—
322	C₂×Q₈×C₈₉	—	2	1	no	—
323	C₂×Q₈×C₈₉	—	2	1	no	—
324	C₂×Q₈×C₈₉	—	2	2	no	—
325	C₂×Q₈×C₈₉	—	2	2	no	—
326	C₂×Q₈×C₈₉	—	4	1	no	—
327	C₂×Q₈×C₈₉	—	4	2	no	—
328	C₂×Q₈×C₈₉	—	4	2	no	—
329	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
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	2	no	—
339	C₂×D₄×C₈₉	—	2	2	no	—
340	C₂×D₄×C₈₉	—	2	1	no	—
341	C₂×D₄×C₈₉	—	2	1	no	—
342	C₂×D₄×C₈₉	—	2	1	no	—
343	C₂×D₄×C₈₉	—	2	1	no	—
344	C₂×D₄×C₈₉	—	2	2	no	—
345	C₂×D₄×C₈₉	—	4	2	no	—
346	C₂×D₄×C₈₉	—	4	2	no	—
347	C₂×D₄×C₈₉	—	4	4	no	—
348	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
349	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
350	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
352	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
353	C₂²×C₄×C₈₉	—	2	1	no	—
354	C₂²×C₄×C₈₉	—	2	1	no	—
355	C₂²×C₄×C₈₉	—	2	2	no	—
356	C₂²×C₄×C₈₉	—	2	2	no	—
357	C₂²×C₄×C₈₉	—	2	2	no	—
358	C₂²×C₄×C₈₉	—	2	1	no	—
359	C₂²×C₄×C₈₉	—	2	2	no	—
360	C₂²×C₄×C₈₉	—	2	2	no	—
361	C₂²×C₄×C₈₉	—	2	2	no	—
362	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
364	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
365	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
368	Q₁₆×C₈₉	—	2	2	no	—
369	Q₁₆×C₈₉	—	2	4	no	—
370	Q₁₆×C₈₉	—	4	1	no	—
371	Q₁₆×C₈₉	—	4	2	no	—
372	SD₁₆×C₈₉	—	2	2	no	—
373	SD₁₆×C₈₉	—	2	4	no	—
374	SD₁₆×C₈₉	—	4	2	no	—
375	SD₁₆×C₈₉	—	4	1	no	—
376	SD₁₆×C₈₉	—	4	2	no	—
377	SD₁₆×C₈₉	—	4	2	no	—
378	SD₁₆×C₈₉	—	4	2	no	—
379	D₈×C₈₉	—	4	2	no	—
380	D₈×C₈₉	—	4	2	no	—
381	D₈×C₈₉	—	4	2	no	—
382	M₁₆×C₈₉	—	4	2	no	—
383	M₁₆×C₈₉	—	4	2	no	—
384	M₁₆×C₈₉	—	4	2	no	—
385	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
389	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
390	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
391	C₄⋊C₄×C₈₉	—	2	1	no	—
392	C₄⋊C₄×C₈₉	—	2	1	no	—
393	C₄⋊C₄×C₈₉	—	2	1	no	—
394	C₄⋊C₄×C₈₉	—	2	1	no	—
395	C₄⋊C₄×C₈₉	—	2	1	no	—
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	2	no	—
404	C₄⋊C₄×C₈₉	—	2	1	no	—
405	C₄⋊C₄×C₈₉	—	2	1	no	—
406	C₄⋊C₄×C₈₉	—	2	2	no	—
407	C₄⋊C₄×C₈₉	—	2	2	no	—
408	C₄⋊C₄×C₈₉	—	2	1	no	—
409	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
411	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
416	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
418	C₂²⋊C₄×C₈₉	—	2	2	no	—
419	C₂²⋊C₄×C₈₉	—	2	2	no	—
420	C₂²⋊C₄×C₈₉	—	2	1	no	—
421	C₂²⋊C₄×C₈₉	—	2	2	no	—
422	C₂²⋊C₄×C₈₉	—	2	2	no	—
423	C₂²⋊C₄×C₈₉	—	2	1	no	—
424	C₂²⋊C₄×C₈₉	—	2	1	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	2	no	—
430	C₂²⋊C₄×C₈₉	—	2	2	no	—
431	C₂²⋊C₄×C₈₉	—	2	2	no	—
432	C₂²⋊C₄×C₈₉	—	2	2	no	—
433	C₂²⋊C₄×C₈₉	—	2	2	no	—
434	C₂²⋊C₄×C₈₉	—	2	2	no	—
435	C₂²⋊C₄×C₈₉	—	2	2	no	—
436	C₂²⋊C₄×C₈₉	—	2	2	no	—
437	C₂²⋊C₄×C₈₉	—	2	2	no	—
438	C₂²⋊C₄×C₈₉	—	2	1	no	—
439	C₂²⋊C₄×C₈₉	—	2	2	no	—
440	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
443	C₄²×C₈₉	—	2	1	no	—
444	C₄²×C₈₉	—	2	1	no	—
445	C₄²×C₈₉	—	2	2	no	—
446	C₄²×C₈₉	—	2	2	no	—
447	C₄²×C₈₉	—	2	1	no	—
448	C₄²×C₈₉	—	2	1	no	—
449	C₄²×C₈₉	—	2	2	no	—
450	C₄²×C₈₉	—	2	1	no	—
451	C₄²×C₈₉	C₂×D₄	1	2	yes	—
452	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₈₉	C₂×D₄	1	2	yes	—
454	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₈₉	C₂⁴	1	2	yes	—
456	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
457	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
458	C₂³×C₈₉	—	2	1	no	—
459	C₂³×C₈₉	—	2	2	no	—
460	C₂³×C₈₉	—	2	2	no	—
461	C₂³×C₈₉	—	4	4	no	—
462	C₂³×C₈₉	—	8	2	no	—
463	C₂³×C₈₉	—	8	2	no	—
464	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
465	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
466	Q₈×C₈₉	—	2	2	no	—
467	Q₈×C₈₉	—	2	1	no	—
468	Q₈×C₈₉	—	2	1	no	—
469	Q₈×C₈₉	—	2	1	no	—
470	Q₈×C₈₉	—	2	2	no	—
471	Q₈×C₈₉	—	2	1	no	—
472	Q₈×C₈₉	—	2	2	no	—
473	Q₈×C₈₉	—	2	1	no	—
474	Q₈×C₈₉	—	4	2	no	—
475	Q₈×C₈₉	—	4	2	no	—
476	Q₈×C₈₉	—	8	2	no	—
477	Q₈×C₈₉	H(5,𝔽₂)	1	2	yes	—
478	D₄×C₈₉	—	2	2	no	—
479	D₄×C₈₉	—	2	1	no	—
480	D₄×C₈₉	—	2	2	no	—
481	D₄×C₈₉	—	2	2	no	—
482	D₄×C₈₉	—	2	2	no	—
483	D₄×C₈₉	—	2	2	no	—
484	D₄×C₈₉	—	2	1	no	—
485	D₄×C₈₉	—	4	2	no	—
486	D₄×C₈₉	—	4	4	no	—
487	D₄×C₈₉	—	4	4	no	—
488	D₄×C₈₉	—	4	4	no	—
489	D₄×C₈₉	—	4	2	no	—
490	D₄×C₈₉	—	4	2	no	—
491	D₄×C₈₉	—	8	1	no	—
492	D₄×C₈₉	—	8	1	no	—
493	D₄×C₈₉	—	8	2	no	—
494	D₄×C₈₉	—	8	1	no	—
495	D₄×C₈₉	—	8	2	no	—
496	D₄×C₈₉	—	8	2	no	—
497	C₂×C₄×C₈₉	—	2	1	no	—
498	C₂×C₄×C₈₉	—	2	2	no	—
499	C₂×C₄×C₈₉	—	2	2	no	—
500	C₂×C₄×C₈₉	—	2	1	no	—
501	C₂×C₄×C₈₉	—	2	2	no	—
502	C₂×C₄×C₈₉	—	2	1	no	—
503	C₂×C₄×C₈₉	—	2	1	no	—
504	C₂×C₄×C₈₉	—	2	1	no	—
505	C₂×C₄×C₈₉	—	2	1	no	—
506	C₂×C₄×C₈₉	—	2	2	no	—
507	C₂×C₄×C₈₉	—	2	1	no	—
508	C₂×C₄×C₈₉	—	2	1	no	—
509	C₂×C₄×C₈₉	—	2	1	no	—
510	C₂×C₄×C₈₉	—	2	2	no	—
511	C₂×C₄×C₈₉	—	4	2	no	—
512	C₂×C₄×C₈₉	—	4	1	no	—
513	C₂×C₄×C₈₉	—	4	2	no	—
514	C₂×C₄×C₈₉	—	4	4	no	—
515	C₂×C₄×C₈₉	—	4	2	no	—
516	C₂×C₄×C₈₉	—	4	4	no	—
517	C₂×C₄×C₈₉	—	4	2	no	—
518	C₂×C₄×C₈₉	—	8	2	no	—
519	C₂×C₄×C₈₉	—	8	2	no	—
520	C₂×C₄×C₈₉	—	8	2	no	—
521	C₂×C₄×C₈₉	—	8	1	no	—
522	C₂×C₄×C₈₉	—	8	2	no	—
523	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
532	C₈×C₈₉	—	2	1	no	—
533	C₈×C₈₉	—	2	2	no	—
534	C₈×C₈₉	—	2	1	no	—
535	C₈×C₈₉	—	2	2	no	—
536	C₈×C₈₉	—	2	1	no	—
537	C₈×C₈₉	—	2	1	no	—
538	C₂²×C₈₉	—	2	1	no	—
539	C₂²×C₈₉	—	2	2	no	—
540	C₂²×C₈₉	—	2	1	no	—
541	C₂²×C₈₉	—	2	2	no	—
542	C₂²×C₈₉	—	2	1	no	—
543	C₂²×C₈₉	—	2	2	no	—
544	C₂²×C₈₉	—	4	2	no	—
545	C₂²×C₈₉	—	4	2	no	—
546	C₂²×C₈₉	—	4	1	no	—
547	C₂²×C₈₉	—	4	2	no	—
548	C₂²×C₈₉	—	4	2	no	—
549	C₂²×C₈₉	—	4	1	no	—
550	C₂²×C₈₉	—	4	2	no	—
551	C₂²×C₈₉	—	4	1	no	—
552	C₂²×C₈₉	—	4	2	no	—
553	C₂²×C₈₉	—	16	4	no	—
554	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
555	C₄×C₈₉	—	2	1	no	—
556	C₄×C₈₉	—	2	2	no	—
557	C₄×C₈₉	—	2	1	no	—
558	C₄×C₈₉	—	2	2	no	—
559	C₄×C₈₉	—	2	1	no	—
560	C₄×C₈₉	—	2	2	no	—
561	C₄×C₈₉	—	2	1	no	—
562	C₄×C₈₉	—	2	2	no	—
563	C₄×C₈₉	—	4	1	no	—
564	C₄×C₈₉	—	4	1	no	—
565	C₄×C₈₉	—	4	1	no	—
566	C₄×C₈₉	—	4	1	no	—
567	C₄×C₈₉	—	4	2	no	—
568	C₄×C₈₉	—	4	1	no	—
569	C₄×C₈₉	—	4	1	no	—
570	C₄×C₈₉	—	4	2	no	—
571	C₄×C₈₉	#575	1	2	yes	—
572	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
573	C₄×C₈₉	#585	1	1	yes	characteristic
574	#62006	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
575	C₂×C₈₉	—	4	1	no	—
576	C₂×C₈₉	—	4	2	no	—
577	C₂×C₈₉	—	8	2	no	—
578	C₂×C₈₉	—	8	2	no	—
579	C₂×C₈₉	—	8	1	no	—
580	C₂×C₈₉	#3488	1	1	yes	characteristic
581	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
582	C₂×C₈₉	#3584	1	1	yes	characteristic
583	#3514	C₂×C₈₉	1	1	yes	characteristic, complemented
584	#3480	C₂×C₈₉	1	1	yes	characteristic, complemented
585	#3396	C₂×C₈₉	1	1	yes	characteristic, complemented
586	#3394	C₂×C₈₉	1	1	yes	characteristic, complemented
587	#3365	C₂×C₈₉	1	1	yes	characteristic, complemented
588	#3364	C₂×C₈₉	1	1	yes	characteristic, complemented
589	#3328	C₂×C₈₉	1	1	yes	characteristic, complemented
590	#3326	C₂×C₈₉	1	2	yes	complemented
591	#3324	C₂×C₈₉	1	1	yes	characteristic, complemented
592	#3322	C₂×C₈₉	1	2	yes	complemented
593	#3278	C₂×C₈₉	1	1	yes	characteristic, complemented
594	#3277	C₂×C₈₉	1	2	yes	complemented
595	#3275	C₂×C₈₉	1	2	yes	complemented
596	#3274	C₂×C₈₉	1	1	yes	characteristic, complemented
597	#3256	C₂×C₈₉	1	2	yes	complemented
598	#3251	C₂×C₈₉	1	1	yes	characteristic, complemented
599	#3211	C₂×C₈₉	1	2	yes	complemented
600	#3207	C₂×C₈₉	1	1	yes	characteristic, complemented
601	#3108	C₂×C₈₉	1	1	yes	characteristic, complemented
602	#3102	C₂×C₈₉	1	2	yes	complemented
603	#3040	C₂×C₈₉	1	2	yes	complemented
604	#3037	C₂×C₈₉	1	1	yes	characteristic, complemented
605	#2991	C₂×C₈₉	1	1	yes	characteristic, complemented
606	C₈₉	#62006	1	1	yes	characteristic, direct product factor, Sylow
607	C₂×#137	C₂²×C₈₉	1	2	yes	complemented
608	C₂×#137	C₂²×C₈₉	1	2	yes	complemented
609	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
610	#559	—	2	1	no	—
611	#559	C₂²×C₈₉	1	1	yes	characteristic
612	#559	C₂²×C₈₉	1	1	yes	characteristic, complemented
613	#557	C₂²×C₈₉	1	1	yes	characteristic, complemented
614	#556	—	2	1	no	—
615	#556	C₂²×C₈₉	1	1	yes	characteristic
616	#556	C₂²×C₈₉	1	1	yes	characteristic
617	#555	—	2	1	no	—
618	#553	—	2	2	no	—
619	#553	C₂²×C₈₉	1	2	yes	complemented
620	#551	—	2	2	no	—
621	#550	C₂²×C₈₉	1	1	yes	characteristic
622	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
623	#548	C₂²×C₈₉	1	2	yes	—
624	#548	C₂²×C₈₉	1	2	yes	complemented
625	#546	—	2	1	no	—
626	#546	C₂²×C₈₉	1	2	yes	—
627	D₄²	C₂²×C₈₉	1	1	yes	characteristic
628	#542	—	2	1	no	—
629	#538	—	2	2	no	—
630	#532	—	2	1	no	—
631	#532	C₂²×C₈₉	1	1	yes	characteristic
632	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
633	#529	—	2	2	no	—
634	#529	C₂²×C₈₉	1	2	yes	—
635	#529	C₂²×C₈₉	1	1	yes	characteristic
636	#529	C₂²×C₈₉	1	2	yes	complemented
637	C₂×#124	C₂²×C₈₉	1	2	yes	—
638	#518	—	2	1	no	—
639	C₄×#41	—	2	1	no	—
640	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
641	C₄×#41	C₂²×C₈₉	1	2	yes	complemented
642	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
643	#495	C₂²×C₈₉	1	2	yes	—
644	#495	C₂²×C₈₉	1	2	yes	complemented
645	#493	C₂²×C₈₉	1	1	yes	characteristic
646	#492	C₂²×C₈₉	1	1	yes	characteristic, complemented
647	#488	C₂²×C₈₉	1	2	yes	—
648	#488	C₂²×C₈₉	1	2	yes	complemented
649	#487	C₂²×C₈₉	1	1	yes	characteristic, complemented
650	#486	C₂²×C₈₉	1	1	yes	characteristic
651	#485	C₂²×C₈₉	1	2	yes	complemented
652	#483	C₂²×C₈₉	1	1	yes	characteristic, complemented
653	#482	C₂²×C₈₉	1	2	yes	—
654	#480	C₂²×C₈₉	1	1	yes	characteristic
655	#479	C₂²×C₈₉	1	1	yes	characteristic, complemented
656	#479	C₂²×C₈₉	1	1	yes	characteristic, complemented
657	#479	C₂²×C₈₉	1	2	yes	complemented
658	#478	C₂²×C₈₉	1	2	yes	complemented
659	#478	C₂²×C₈₉	1	2	yes	complemented
660	#475	C₂²×C₈₉	1	1	yes	characteristic, complemented
661	#474	C₂²×C₈₉	1	1	yes	characteristic
662	#470	C₂²×C₈₉	1	2	yes	complemented
663	#469	C₂²×C₈₉	1	2	yes	—
664	#469	C₂²×C₈₉	1	2	yes	—
665	#468	C₂²×C₈₉	1	2	yes	—
666	#468	C₂²×C₈₉	1	2	yes	complemented
667	#468	C₂²×C₈₉	1	2	yes	complemented
668	#464	C₂²×C₈₉	1	1	yes	characteristic
669	#464	C₂²×C₈₉	1	1	yes	characteristic
670	#464	C₂²×C₈₉	1	2	yes	—
671	#464	C₂²×C₈₉	1	2	yes	complemented
672	#464	C₂²×C₈₉	1	2	yes	complemented
673	#464	C₂²×C₈₉	1	2	yes	complemented
674	#464	C₂²×C₈₉	1	2	yes	complemented
675	#463	C₂²×C₈₉	1	2	yes	—
676	#463	C₂²×C₈₉	1	2	yes	—
677	#463	C₂²×C₈₉	1	2	yes	complemented
678	#463	C₂²×C₈₉	1	2	yes	complemented
679	#463	C₂²×C₈₉	1	2	yes	complemented
680	#463	C₂²×C₈₉	1	2	yes	complemented
681	#462	C₂²×C₈₉	1	1	yes	characteristic, complemented
682	#462	C₂²×C₈₉	1	1	yes	characteristic, complemented
683	#460	C₂²×C₈₉	1	1	yes	characteristic
684	#460	C₂²×C₈₉	1	1	yes	characteristic
685	#460	C₂²×C₈₉	1	1	yes	characteristic, complemented
686	#459	C₂²×C₈₉	1	1	yes	characteristic
687	#452	C₂²×C₈₉	1	2	yes	complemented
688	#451	C₂²×C₈₉	1	2	yes	complemented
689	#451	C₂²×C₈₉	1	1	yes	characteristic, complemented
690	#450	C₂²×C₈₉	1	2	yes	—
691	#449	C₂²×C₈₉	1	2	yes	—
692	#449	C₂²×C₈₉	1	2	yes	complemented
693	#449	C₂²×C₈₉	1	2	yes	complemented
694	#448	C₂²×C₈₉	1	1	yes	characteristic
695	#448	C₂²×C₈₉	1	2	yes	complemented
696	#447	C₂²×C₈₉	1	2	yes	—
697	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
698	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
699	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
700	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
701	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
702	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
703	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
704	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
705	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
706	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
707	#436	C₂²×C₈₉	1	1	yes	characteristic
708	#436	C₂²×C₈₉	1	1	yes	characteristic
709	#436	C₂²×C₈₉	1	2	yes	complemented
710	#436	C₂²×C₈₉	1	2	yes	complemented
711	#431	C₂²×C₈₉	1	2	yes	complemented
712	#431	C₂²×C₈₉	1	1	yes	characteristic, complemented
713	#423	C₂²×C₈₉	1	1	yes	characteristic, complemented
714	#423	C₂²×C₈₉	1	2	yes	complemented
715	#419	C₂²×C₈₉	1	2	yes	complemented
716	#418	C₂²×C₈₉	1	2	yes	—
717	#417	C₂²×C₈₉	1	2	yes	complemented
718	C₂×#41	—	2	1	no	—
719	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
720	C₂×#41	C₂³×C₈₉	1	2	yes	—
721	C₂×#41	C₂³×C₈₉	1	2	yes	—
722	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
723	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
724	C₂²×D₄	—	2	1	no	—
725	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
726	#137	—	4	4	no	—
727	#137	—	4	4	no	—
728	AGL(1,ℤ/8)	—	4	4	no	—
729	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
730	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
731	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
732	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
733	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
734	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
737	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
738	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
739	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
740	C₂×D₈	C₂³×C₈₉	1	2	yes	—
741	C₂×D₈	C₂³×C₈₉	1	2	yes	—
742	C₂×D₈	C₂³×C₈₉	1	2	yes	—
743	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
744	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
745	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
746	C₄⋊Q₈	—	2	1	no	—
747	C₄⋊Q₈	—	2	1	no	—
748	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
749	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
750	#127	—	2	1	no	—
751	#127	C₂³×C₈₉	1	1	yes	characteristic
752	#127	C₂³×C₈₉	1	1	yes	characteristic
753	#126	—	2	2	no	—
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	1	no	—
758	#126	—	2	2	no	—
759	#125	—	2	2	no	—
760	#125	C₂³×C₈₉	1	1	yes	characteristic
761	#125	C₂³×C₈₉	1	2	yes	—
762	#124	—	2	1	no	—
763	#124	—	2	1	no	—
764	#124	—	2	1	no	—
765	#124	—	2	2	no	—
766	#124	—	2	2	no	—
767	#124	—	2	2	no	—
768	#124	—	2	2	no	—
769	#124	—	2	1	no	—
770	#124	C₂³×C₈₉	1	1	yes	characteristic
771	#124	C₂³×C₈₉	1	2	yes	—
772	#124	C₂³×C₈₉	1	2	yes	—
773	#124	C₂³×C₈₉	1	2	yes	—
774	#124	C₂³×C₈₉	1	2	yes	—
775	#123	—	2	1	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	C₂²⋊Q₈	—	2	1	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
787	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
788	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	—	2	1	no	—
793	#121	—	2	1	no	—
794	#121	—	2	1	no	—
795	#121	—	2	1	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	C₂³×C₈₉	1	2	yes	—
799	#121	C₂³×C₈₉	1	1	yes	characteristic
800	#121	C₂³×C₈₉	1	2	yes	—
801	#121	C₂³×C₈₉	1	2	yes	—
802	#120	—	2	2	no	—
803	#120	—	2	2	no	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	—	2	1	no	—
806	C₄×Q₈	—	2	1	no	—
807	C₄×Q₈	—	2	1	no	—
808	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
810	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
812	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
813	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
814	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
815	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
816	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
833	C₄×D₄	D₄×C₈₉	1	2	yes	—
834	C₄×D₄	C₂³×C₈₉	1	2	yes	—
835	C₄×D₄	C₂³×C₈₉	1	2	yes	—
836	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
837	C₄×D₄	C₂³×C₈₉	1	2	yes	—
838	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₈₉	1	2	yes	—
840	#117	—	2	1	no	—
841	#117	—	2	2	no	—
842	#117	—	2	2	no	—
843	#117	—	2	1	no	—
844	#117	—	2	2	no	—
845	#117	D₄×C₈₉	1	1	yes	characteristic
846	#117	D₄×C₈₉	1	2	yes	—
847	#117	C₂³×C₈₉	1	2	yes	—
848	C₂×C₄⋊C₄	—	2	1	no	—
849	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
850	C₂×C₂²⋊C₄	—	2	2	no	—
851	C₂×C₂²⋊C₄	—	2	2	no	—
852	C₂×C₂²⋊C₄	—	2	2	no	—
853	C₂×C₄²	—	2	1	no	—
854	C₂×C₄²	—	2	2	no	—
855	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
856	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
857	#107	C₂³×C₈₉	1	1	yes	characteristic
858	#107	C₂³×C₈₉	1	2	yes	—
859	#107	C₂³×C₈₉	1	1	yes	characteristic
860	#106	C₂³×C₈₉	1	1	yes	characteristic
861	#106	C₂³×C₈₉	1	1	yes	characteristic
862	#106	C₂³×C₈₉	1	2	yes	—
863	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
864	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
865	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
866	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
867	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
868	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
869	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
870	#103	C₂³×C₈₉	1	2	yes	—
871	#103	C₂³×C₈₉	1	2	yes	—
872	#103	C₂³×C₈₉	1	1	yes	characteristic
873	#103	C₂³×C₈₉	1	2	yes	—
874	#103	C₂³×C₈₉	1	2	yes	—
875	#103	C₂³×C₈₉	1	1	yes	characteristic
876	#103	C₂³×C₈₉	1	1	yes	characteristic
877	#103	C₂³×C₈₉	1	1	yes	characteristic
878	#103	C₂³×C₈₉	1	1	yes	characteristic
879	#103	C₂³×C₈₉	1	1	yes	characteristic
880	#103	C₂³×C₈₉	1	2	yes	—
881	#102	C₂³×C₈₉	1	2	yes	—
882	#102	C₂³×C₈₉	1	2	yes	—
883	#102	C₂³×C₈₉	1	1	yes	characteristic
884	#102	C₂³×C₈₉	1	2	yes	—
885	#102	C₂³×C₈₉	1	2	yes	—
886	#102	C₂³×C₈₉	1	2	yes	—
887	#102	C₂³×C₈₉	1	1	yes	characteristic
888	#102	C₂³×C₈₉	1	2	yes	—
889	#102	C₂³×C₈₉	1	2	yes	—
890	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
891	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
892	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
893	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
894	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
895	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
896	C₄×C₈	C₂³×C₈₉	1	2	yes	—
897	C₄×C₈	C₂³×C₈₉	1	2	yes	—
898	C₂⁴	—	2	2	no	—
899	#41	—	2	4	no	—
900	#41	—	4	2	no	—
901	#41	—	4	2	no	—
902	#41	—	4	4	no	—
903	#41	—	4	2	no	—
904	#41	—	4	2	no	—
905	C₂×Q₈	—	2	1	no	—
906	C₂×Q₈	—	2	1	no	—
907	C₂×Q₈	—	2	2	no	—
908	C₂×Q₈	—	2	2	no	—
909	C₂×Q₈	—	4	1	no	—
910	C₂×Q₈	—	4	2	no	—
911	C₂×Q₈	—	4	2	no	—
912	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
913	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
914	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
915	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
916	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	4	2	no	—
929	C₂×D₄	—	4	2	no	—
930	C₂×D₄	—	4	4	no	—
931	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
932	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
933	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
934	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
935	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
946	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
947	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
948	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
949	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
950	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
951	Q₁₆	—	2	2	no	—
952	Q₁₆	—	2	4	no	—
953	Q₁₆	—	4	2	no	—
954	Q₁₆	—	4	1	no	—
955	SD₁₆	—	2	2	no	—
956	SD₁₆	—	2	4	no	—
957	SD₁₆	—	4	2	no	—
958	SD₁₆	—	4	2	no	—
959	SD₁₆	—	4	2	no	—
960	SD₁₆	—	4	2	no	—
961	SD₁₆	—	4	1	no	—
962	D₈	—	4	2	no	—
963	D₈	—	4	2	no	—
964	D₈	—	4	2	no	—
965	M₁₆	—	4	2	no	—
966	M₁₆	—	4	2	no	—
967	M₁₆	—	4	2	no	—
968	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
969	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
972	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
973	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
993	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
994	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
995	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
996	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
998	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
999	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	—	2	1	no	—
1034	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1035	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1036	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1037	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1038	C₄²	C₂⁴×C₈₉	1	2	yes	—
1039	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1040	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	2	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	4	4	no	—
1045	C₂³	—	8	2	no	—
1046	C₂³	—	8	2	no	—
1047	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1048	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	1	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	2	2	no	—
1054	Q₈	—	2	1	no	—
1055	Q₈	—	2	2	no	—
1056	Q₈	—	2	1	no	—
1057	Q₈	—	4	2	no	—
1058	Q₈	—	4	2	no	—
1059	Q₈	—	8	2	no	—
1060	Q₈	H(5,𝔽₂)×C₈₉	1	2	yes	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	4	no	—
1070	D₄	—	4	4	no	—
1071	D₄	—	4	4	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	2	no	—
1074	D₄	—	8	1	no	—
1075	D₄	—	8	1	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	1	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	4	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	4	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	1	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1108	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1109	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1110	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1111	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1112	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1113	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1114	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1115	C₈	—	2	1	no	—
1116	C₈	—	2	2	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	2	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	1	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	2	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	2	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	4	2	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	2	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	16	4	no	—
1137	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1138	C₄	—	2	1	no	—
1139	C₄	—	2	2	no	—
1140	C₄	—	2	1	no	—
1141	C₄	—	2	2	no	—
1142	C₄	—	2	1	no	—
1143	C₄	—	2	2	no	—
1144	C₄	—	2	1	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	2	no	—
1148	C₄	—	4	1	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	4	1	no	—
1152	C₄	—	4	2	no	—
1153	C₄	—	4	1	no	—
1154	C₄	#575×C₈₉	1	2	yes	—
1155	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1156	C₄	#585×C₈₉	1	1	yes	characteristic
1157	C₂	—	4	1	no	—
1158	C₂	—	4	2	no	—
1159	C₂	—	8	2	no	—
1160	C₂	—	8	2	no	—
1161	C₂	—	8	1	no	—
1162	C₂	C₈₉×#3488	1	1	yes	characteristic
1163	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
1164	C₂	C₈₉×#3584	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 ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3514	C₂	semidirect
2. C₈₉×#3480	C₂	semidirect
3. C₈₉×#3396	C₂	semidirect
4. C₈₉×#3394	C₂	semidirect
5. C₈₉×#3365	C₂	semidirect
6. C₈₉×#3364	C₂	semidirect
7. C₈₉×#3328	C₂	semidirect
8. C₈₉×#3326	C₂	semidirect
9. C₈₉×#3324	C₂	semidirect
10. C₈₉×#3322	C₂	semidirect
11. C₈₉×#3278	C₂	semidirect
12. C₈₉×#3277	C₂	semidirect
13. C₈₉×#3275	C₂	semidirect
14. C₈₉×#3274	C₂	semidirect
15. C₈₉×#3256	C₂	semidirect
16. C₈₉×#3251	C₂	semidirect
17. C₈₉×#3211	C₂	semidirect
18. C₈₉×#3207	C₂	semidirect
19. C₈₉×#3108	C₂	semidirect
20. C₈₉×#3102	C₂	semidirect
21. C₈₉×#3040	C₂	semidirect
22. C₈₉×#3037	C₂	semidirect
23. C₈₉×#2991	C₂	semidirect
24. C₂×#137×C₈₉	C₂²	semidirect
25. C₂×#137×C₈₉	C₂²	semidirect
29. #559×C₈₉	C₂²	semidirect
30. #557×C₈₉	C₂²	semidirect
36. #553×C₈₉	C₂²	semidirect
41. #548×C₈₉	C₂²	semidirect
49. #532×C₈₉	C₂²	semidirect
53. #529×C₈₉	C₂²	semidirect
58. C₄×#41×C₈₉	C₂²	semidirect
59. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
61. #495×C₈₉	C₂²	semidirect
63. #492×C₈₉	C₂²	semidirect
65. #488×C₈₉	C₂²	semidirect
66. #487×C₈₉	C₂²	semidirect
68. #485×C₈₉	C₂²	semidirect
69. #483×C₈₉	C₂²	semidirect
72. #479×C₈₉	C₂²	semidirect
73. #479×C₈₉	C₂²	semidirect
74. #479×C₈₉	C₂²	semidirect
75. #478×C₈₉	C₂²	semidirect
76. #478×C₈₉	C₂²	semidirect
77. #475×C₈₉	C₂²	semidirect
79. #470×C₈₉	C₂²	semidirect
83. #468×C₈₉	C₂²	semidirect
84. #468×C₈₉	C₂²	semidirect
88. #464×C₈₉	C₂²	semidirect
89. #464×C₈₉	C₂²	semidirect
90. #464×C₈₉	C₂²	semidirect
91. #464×C₈₉	C₂²	semidirect
94. #463×C₈₉	C₂²	semidirect
95. #463×C₈₉	C₂²	semidirect
96. #463×C₈₉	C₂²	semidirect
97. #463×C₈₉	C₂²	semidirect
98. #462×C₈₉	C₂²	semidirect
99. #462×C₈₉	C₂²	semidirect
102. #460×C₈₉	C₂²	semidirect
104. #452×C₈₉	C₂²	semidirect
105. #451×C₈₉	C₂²	semidirect
106. #451×C₈₉	C₂²	semidirect
109. #449×C₈₉	C₂²	semidirect
110. #449×C₈₉	C₂²	semidirect
112. #448×C₈₉	C₂²	semidirect
114. C₈×Q₈×C₈₉	C₂²	semidirect
115. C₈×Q₈×C₈₉	C₂²	semidirect
116. C₄×Q₁₆×C₈₉	C₂²	semidirect
117. C₄×Q₁₆×C₈₉	C₂²	semidirect
118. C₄×Q₁₆×C₈₉	C₂²	semidirect
121. C₄×SD₁₆×C₈₉	C₂²	semidirect
122. C₄×SD₁₆×C₈₉	C₂²	semidirect
123. C₄×D₈×C₈₉	C₂²	semidirect
126. #436×C₈₉	C₂²	semidirect
127. #436×C₈₉	C₂²	semidirect
128. #431×C₈₉	C₂²	semidirect
129. #431×C₈₉	C₂²	semidirect
130. #423×C₈₉	C₂²	semidirect
131. #423×C₈₉	C₂²	semidirect
132. #419×C₈₉	C₂²	semidirect
134. #417×C₈₉	C₂²	semidirect
574. #62006	C₈₉	direct (N × H)
583. #3514	C₂×C₈₉	semidirect
584. #3480	C₂×C₈₉	semidirect
585. #3396	C₂×C₈₉	semidirect
586. #3394	C₂×C₈₉	semidirect
587. #3365	C₂×C₈₉	semidirect
588. #3364	C₂×C₈₉	semidirect
589. #3328	C₂×C₈₉	semidirect
590. #3326	C₂×C₈₉	semidirect
591. #3324	C₂×C₈₉	semidirect
592. #3322	C₂×C₈₉	semidirect
593. #3278	C₂×C₈₉	semidirect
594. #3277	C₂×C₈₉	semidirect
595. #3275	C₂×C₈₉	semidirect
596. #3274	C₂×C₈₉	semidirect
597. #3256	C₂×C₈₉	semidirect
598. #3251	C₂×C₈₉	semidirect
599. #3211	C₂×C₈₉	semidirect
600. #3207	C₂×C₈₉	semidirect
601. #3108	C₂×C₈₉	semidirect
602. #3102	C₂×C₈₉	semidirect
603. #3040	C₂×C₈₉	semidirect
604. #3037	C₂×C₈₉	semidirect
605. #2991	C₂×C₈₉	semidirect
606. C₈₉	#62006	direct (N × H)
607. C₂×#137	C₂²×C₈₉	semidirect
608. C₂×#137	C₂²×C₈₉	semidirect
612. #559	C₂²×C₈₉	semidirect
613. #557	C₂²×C₈₉	semidirect
619. #553	C₂²×C₈₉	semidirect
624. #548	C₂²×C₈₉	semidirect
632. #532	C₂²×C₈₉	semidirect
636. #529	C₂²×C₈₉	semidirect
641. C₄×#41	C₂²×C₈₉	semidirect
642. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
644. #495	C₂²×C₈₉	semidirect
646. #492	C₂²×C₈₉	semidirect
648. #488	C₂²×C₈₉	semidirect
649. #487	C₂²×C₈₉	semidirect
651. #485	C₂²×C₈₉	semidirect
652. #483	C₂²×C₈₉	semidirect
655. #479	C₂²×C₈₉	semidirect
656. #479	C₂²×C₈₉	semidirect
657. #479	C₂²×C₈₉	semidirect
658. #478	C₂²×C₈₉	semidirect
659. #478	C₂²×C₈₉	semidirect
660. #475	C₂²×C₈₉	semidirect
662. #470	C₂²×C₈₉	semidirect
666. #468	C₂²×C₈₉	semidirect
667. #468	C₂²×C₈₉	semidirect
671. #464	C₂²×C₈₉	semidirect
672. #464	C₂²×C₈₉	semidirect
673. #464	C₂²×C₈₉	semidirect
674. #464	C₂²×C₈₉	semidirect
677. #463	C₂²×C₈₉	semidirect
678. #463	C₂²×C₈₉	semidirect
679. #463	C₂²×C₈₉	semidirect
680. #463	C₂²×C₈₉	semidirect
681. #462	C₂²×C₈₉	semidirect
682. #462	C₂²×C₈₉	semidirect
685. #460	C₂²×C₈₉	semidirect
687. #452	C₂²×C₈₉	semidirect
688. #451	C₂²×C₈₉	semidirect
689. #451	C₂²×C₈₉	semidirect
692. #449	C₂²×C₈₉	semidirect
693. #449	C₂²×C₈₉	semidirect
695. #448	C₂²×C₈₉	semidirect
697. C₈×Q₈	C₂²×C₈₉	semidirect
698. C₈×Q₈	C₂²×C₈₉	semidirect
699. C₄×Q₁₆	C₂²×C₈₉	semidirect
700. C₄×Q₁₆	C₂²×C₈₉	semidirect
701. C₄×Q₁₆	C₂²×C₈₉	semidirect
704. C₄×SD₁₆	C₂²×C₈₉	semidirect
705. C₄×SD₁₆	C₂²×C₈₉	semidirect
706. C₄×D₈	C₂²×C₈₉	semidirect
709. #436	C₂²×C₈₉	semidirect
710. #436	C₂²×C₈₉	semidirect
711. #431	C₂²×C₈₉	semidirect
712. #431	C₂²×C₈₉	semidirect
713. #423	C₂²×C₈₉	semidirect
714. #423	C₂²×C₈₉	semidirect
715. #419	C₂²×C₈₉	semidirect
717. #417	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×#3514	2
C₈₉×#3480	2
C₈₉×#3396	2
C₈₉×#3394	2
C₈₉×#3365	2
C₈₉×#3364	2
C₈₉×#3328	2
C₈₉×#3326	2
C₈₉×#3324	2
C₈₉×#3322	2
C₈₉×#3278	2
C₈₉×#3277	2
C₈₉×#3275	2
C₈₉×#3274	2
C₈₉×#3256	2
C₈₉×#3251	2
C₈₉×#3211	2
C₈₉×#3207	2
C₈₉×#3108	2
C₈₉×#3102	2
C₈₉×#3040	2
C₈₉×#3037	2
C₈₉×#2991	2
#62006	89

Subgroups — C89×#62006 #36439854

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62006 #36439854