Subgroups — C₈₉×#61967 #36439815

Order 22784.

1856 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3402	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3376	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3327	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3321	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3315	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3275	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3269	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3267	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3255	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3251	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3248	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3218	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3216	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#3212	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3115	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#3110	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3107	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₉×#3039	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#3036	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₉×#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2989	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₈₉	C₂²	1	2	yes	—
25	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
26	C₂×#135×C₈₉	C₂²	1	2	yes	—
27	#556×C₈₉	C₂²	1	1	yes	characteristic
28	#556×C₈₉	C₂²	1	2	yes	complemented
29	#555×C₈₉	—	2	1	no	—
30	#555×C₈₉	C₂²	1	1	yes	characteristic
31	#554×C₈₉	—	2	1	no	—
32	#554×C₈₉	C₂²	1	1	yes	characteristic
33	#553×C₈₉	—	2	1	no	—
34	#553×C₈₉	—	2	1	no	—
35	#553×C₈₉	—	2	1	no	—
36	#552×C₈₉	—	2	1	no	—
37	#552×C₈₉	C₂²	1	1	yes	characteristic
38	#552×C₈₉	C₂²	1	1	yes	characteristic
39	#551×C₈₉	—	2	1	no	—
40	#551×C₈₉	—	2	1	no	—
41	#548×C₈₉	C₂²	1	2	yes	—
42	#548×C₈₉	C₂²	1	2	yes	complemented
43	#547×C₈₉	C₂²	1	1	yes	characteristic
44	#547×C₈₉	C₂²	1	2	yes	—
45	#546×C₈₉	C₂²	1	1	yes	characteristic
46	#546×C₈₉	C₂²	1	1	yes	characteristic
47	#542×C₈₉	—	2	1	no	—
48	#542×C₈₉	—	2	1	no	—
49	#537×C₈₉	—	2	1	no	—
50	#533×C₈₉	C₂²	1	1	yes	characteristic
51	#533×C₈₉	C₂²	1	1	yes	characteristic
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	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	#529×C₈₉	—	2	1	no	—
58	#529×C₈₉	—	2	1	no	—
59	#529×C₈₉	C₂²	1	1	yes	characteristic
60	#529×C₈₉	C₂²	1	1	yes	characteristic
61	#525×C₈₉	—	2	1	no	—
62	#520×C₈₉	—	2	1	no	—
63	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
64	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
65	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
66	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×#117×C₈₉	—	2	1	no	—
68	#497×C₈₉	C₂²	1	2	yes	—
69	#497×C₈₉	C₂²	1	2	yes	complemented
70	#495×C₈₉	C₂²	1	2	yes	—
71	#491×C₈₉	C₂²	1	2	yes	complemented
72	#489×C₈₉	C₂²	1	2	yes	complemented
73	#488×C₈₉	C₂²	1	2	yes	complemented
74	#485×C₈₉	C₂²	1	2	yes	complemented
75	#484×C₈₉	C₂²	1	2	yes	—
76	#482×C₈₉	C₂²	1	2	yes	complemented
77	#479×C₈₉	C₂²	1	2	yes	complemented
78	#478×C₈₉	C₂²	1	2	yes	complemented
79	#475×C₈₉	C₂²	1	2	yes	complemented
80	#475×C₈₉	C₂²	1	1	yes	characteristic, complemented
81	#475×C₈₉	C₂²	1	1	yes	characteristic, complemented
82	#474×C₈₉	C₂²	1	1	yes	characteristic
83	#474×C₈₉	C₂²	1	1	yes	characteristic
84	#470×C₈₉	C₂²	1	2	yes	—
85	#470×C₈₉	C₂²	1	2	yes	—
86	#469×C₈₉	C₂²	1	2	yes	—
87	#468×C₈₉	C₂²	1	2	yes	complemented
88	#467×C₈₉	C₂²	1	2	yes	complemented
89	#465×C₈₉	C₂²	1	2	yes	—
90	#464×C₈₉	C₂²	1	2	yes	—
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	—
95	#463×C₈₉	C₂²	1	2	yes	—
96	#462×C₈₉	C₂²	1	1	yes	characteristic, complemented
97	#462×C₈₉	C₂²	1	2	yes	complemented
98	#462×C₈₉	C₂²	1	2	yes	complemented
99	#462×C₈₉	C₂²	1	1	yes	characteristic, complemented
100	#462×C₈₉	C₂²	1	1	yes	characteristic, complemented
101	#462×C₈₉	C₂²	1	1	yes	characteristic, complemented
102	#461×C₈₉	C₂²	1	1	yes	characteristic
103	#461×C₈₉	C₂²	1	1	yes	characteristic
104	#461×C₈₉	C₂²	1	1	yes	characteristic
105	#461×C₈₉	C₂²	1	2	yes	—
106	#461×C₈₉	C₂²	1	1	yes	characteristic
107	#460×C₈₉	C₂²	1	1	yes	characteristic, complemented
108	#460×C₈₉	C₂²	1	1	yes	characteristic, complemented
109	#459×C₈₉	C₂²	1	1	yes	characteristic
110	#459×C₈₉	C₂²	1	1	yes	characteristic
111	#452×C₈₉	C₂²	1	2	yes	—
112	#452×C₈₉	C₂²	1	2	yes	—
113	#452×C₈₉	C₂²	1	2	yes	—
114	#452×C₈₉	C₂²	1	2	yes	complemented
115	#451×C₈₉	C₂²	1	2	yes	complemented
116	#450×C₈₉	C₂²	1	2	yes	—
117	#449×C₈₉	C₂²	1	2	yes	—
118	#449×C₈₉	C₂²	1	2	yes	—
119	#448×C₈₉	C₂²	1	2	yes	—
120	#446×C₈₉	C₂²	1	2	yes	complemented
121	#442×C₈₉	C₂²	1	2	yes	—
122	#440×C₈₉	C₂²	1	2	yes	—
123	#440×C₈₉	C₂²	1	2	yes	—
124	#440×C₈₉	C₂²	1	2	yes	complemented
125	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
126	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
127	#436×C₈₉	C₂²	1	2	yes	—
128	#435×C₈₉	C₂²	1	2	yes	—
129	#435×C₈₉	C₂²	1	2	yes	complemented
130	#432×C₈₉	C₂²	1	1	yes	characteristic
131	#432×C₈₉	C₂²	1	1	yes	characteristic, complemented
132	#431×C₈₉	C₂²	1	1	yes	characteristic, complemented
133	#423×C₈₉	C₂²	1	1	yes	characteristic
134	#423×C₈₉	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
136	#419×C₈₉	C₂²	1	2	yes	complemented
137	#417×C₈₉	C₂²	1	2	yes	—
138	#416×C₈₉	C₂²	1	2	yes	complemented
139	C₂×#41×C₈₉	—	2	1	no	—
140	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
141	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
142	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
143	C₂×#41×C₈₉	C₂³	1	2	yes	—
144	C₂×#41×C₈₉	C₂³	1	2	yes	—
145	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
146	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₈₉	—	2	1	no	—
148	#137×C₈₉	—	4	4	no	—
149	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
150	#135×C₈₉	—	4	4	no	—
151	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
152	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
153	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
154	C₂×Q₁₆×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×SD₁₆×C₈₉	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
161	C₂×D₈×C₈₉	C₂³	1	2	yes	—
162	C₂×D₈×C₈₉	C₂³	1	2	yes	—
163	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
164	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
165	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
166	C₄⋊Q₈×C₈₉	—	2	1	no	—
167	C₄⋊Q₈×C₈₉	—	2	1	no	—
168	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
171	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
172	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
173	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
174	#127×C₈₉	C₂³	1	1	yes	characteristic
175	#126×C₈₉	—	2	1	no	—
176	#126×C₈₉	—	2	1	no	—
177	#126×C₈₉	—	2	2	no	—
178	#126×C₈₉	—	2	2	no	—
179	#126×C₈₉	—	2	1	no	—
180	#126×C₈₉	—	2	1	no	—
181	#126×C₈₉	—	2	1	no	—
182	#126×C₈₉	—	2	1	no	—
183	#125×C₈₉	—	2	1	no	—
184	#125×C₈₉	—	2	1	no	—
185	#125×C₈₉	—	2	1	no	—
186	#125×C₈₉	—	2	1	no	—
187	#125×C₈₉	—	2	1	no	—
188	#125×C₈₉	C₂³	1	1	yes	characteristic
189	#125×C₈₉	C₂³	1	1	yes	characteristic
190	#124×C₈₉	—	2	1	no	—
191	#124×C₈₉	—	2	1	no	—
192	#124×C₈₉	—	2	2	no	—
193	#124×C₈₉	—	2	2	no	—
194	#124×C₈₉	—	2	1	no	—
195	#124×C₈₉	C₂³	1	2	yes	—
196	#124×C₈₉	C₂³	1	1	yes	characteristic
197	#124×C₈₉	C₂³	1	2	yes	—
198	#124×C₈₉	C₂³	1	1	yes	characteristic
199	#123×C₈₉	—	2	1	no	—
200	#123×C₈₉	—	2	1	no	—
201	#123×C₈₉	—	2	1	no	—
202	#123×C₈₉	—	2	1	no	—
203	#123×C₈₉	—	2	1	no	—
204	#123×C₈₉	—	2	1	no	—
205	#123×C₈₉	—	2	1	no	—
206	#123×C₈₉	—	2	1	no	—
207	#123×C₈₉	—	2	2	no	—
208	#123×C₈₉	—	2	2	no	—
209	C₂²⋊Q₈×C₈₉	—	2	1	no	—
210	C₂²⋊Q₈×C₈₉	—	2	1	no	—
211	C₂²⋊Q₈×C₈₉	—	2	2	no	—
212	C₂²⋊Q₈×C₈₉	—	2	1	no	—
213	C₂²⋊Q₈×C₈₉	—	2	1	no	—
214	C₂²⋊Q₈×C₈₉	—	2	1	no	—
215	C₂²⋊Q₈×C₈₉	—	2	1	no	—
216	C₂²⋊Q₈×C₈₉	—	2	1	no	—
217	C₂²⋊Q₈×C₈₉	—	2	2	no	—
218	C₂²⋊Q₈×C₈₉	—	2	2	no	—
219	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
220	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
221	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
222	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
223	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
224	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
225	#121×C₈₉	—	2	1	no	—
226	#121×C₈₉	—	2	1	no	—
227	#121×C₈₉	—	2	2	no	—
228	#121×C₈₉	—	2	2	no	—
229	#121×C₈₉	—	2	2	no	—
230	#121×C₈₉	—	2	1	no	—
231	#121×C₈₉	—	2	1	no	—
232	#121×C₈₉	—	2	1	no	—
233	#121×C₈₉	—	2	1	no	—
234	#121×C₈₉	—	2	1	no	—
235	#121×C₈₉	—	2	1	no	—
236	#121×C₈₉	—	2	1	no	—
237	#121×C₈₉	C₂³	1	1	yes	characteristic
238	#121×C₈₉	C₂³	1	1	yes	characteristic
239	#121×C₈₉	C₂³	1	2	yes	—
240	#120×C₈₉	—	2	1	no	—
241	#120×C₈₉	—	2	1	no	—
242	C₄×Q₈×C₈₉	—	2	1	no	—
243	C₄×Q₈×C₈₉	—	2	1	no	—
244	C₄×Q₈×C₈₉	—	2	1	no	—
245	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
246	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
247	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
248	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
249	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
250	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
251	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
252	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₈₉	—	2	1	no	—
254	C₄×D₄×C₈₉	—	2	1	no	—
255	C₄×D₄×C₈₉	—	2	1	no	—
256	C₄×D₄×C₈₉	—	2	1	no	—
257	C₄×D₄×C₈₉	—	2	1	no	—
258	C₄×D₄×C₈₉	—	2	1	no	—
259	C₄×D₄×C₈₉	—	2	2	no	—
260	C₄×D₄×C₈₉	—	2	2	no	—
261	C₄×D₄×C₈₉	—	2	1	no	—
262	C₄×D₄×C₈₉	—	2	1	no	—
263	C₄×D₄×C₈₉	—	2	1	no	—
264	C₄×D₄×C₈₉	—	2	1	no	—
265	C₄×D₄×C₈₉	—	2	1	no	—
266	C₄×D₄×C₈₉	—	2	1	no	—
267	C₄×D₄×C₈₉	—	2	1	no	—
268	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
269	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
270	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
271	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
272	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
273	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
274	C₄×D₄×C₈₉	C₂³	1	2	yes	—
275	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
276	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
277	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
278	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
279	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
280	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
281	#117×C₈₉	—	2	1	no	—
282	#117×C₈₉	—	2	1	no	—
283	#117×C₈₉	—	2	1	no	—
284	#117×C₈₉	—	2	1	no	—
285	#117×C₈₉	—	2	1	no	—
286	#117×C₈₉	—	2	2	no	—
287	#117×C₈₉	—	2	1	no	—
288	#117×C₈₉	—	2	1	no	—
289	#117×C₈₉	—	2	1	no	—
290	#117×C₈₉	—	2	1	no	—
291	#117×C₈₉	—	2	1	no	—
292	#117×C₈₉	—	2	1	no	—
293	#117×C₈₉	D₄	1	1	yes	characteristic
294	#117×C₈₉	D₄	1	1	yes	characteristic
295	#117×C₈₉	D₄	1	1	yes	characteristic
296	#117×C₈₉	C₂³	1	1	yes	characteristic
297	#117×C₈₉	C₂³	1	1	yes	characteristic
298	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
299	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
300	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
301	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
302	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
303	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
304	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
305	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
306	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
307	C₂×C₄²×C₈₉	—	2	1	no	—
308	C₂×C₄²×C₈₉	—	2	1	no	—
309	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
310	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
311	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
312	#107×C₈₉	C₂³	1	2	yes	—
313	#107×C₈₉	C₂³	1	2	yes	—
314	#106×C₈₉	C₂³	1	2	yes	—
315	#106×C₈₉	C₂³	1	2	yes	—
316	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
317	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
318	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
319	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
320	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
321	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
322	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
323	#103×C₈₉	C₂³	1	2	yes	—
324	#103×C₈₉	C₂³	1	2	yes	—
325	#103×C₈₉	C₂³	1	2	yes	—
326	#103×C₈₉	C₂³	1	2	yes	—
327	#103×C₈₉	C₂³	1	2	yes	—
328	#103×C₈₉	C₂³	1	2	yes	—
329	#103×C₈₉	C₂³	1	2	yes	—
330	#103×C₈₉	C₂³	1	2	yes	—
331	#103×C₈₉	C₂³	1	2	yes	—
332	#103×C₈₉	C₂³	1	2	yes	—
333	#102×C₈₉	C₂³	1	2	yes	—
334	#102×C₈₉	C₂³	1	2	yes	—
335	#102×C₈₉	C₂³	1	2	yes	—
336	#102×C₈₉	C₂³	1	2	yes	—
337	#102×C₈₉	C₂³	1	2	yes	—
338	#102×C₈₉	C₂³	1	2	yes	—
339	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
340	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
341	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
342	#97×C₈₉	C₂³	1	2	yes	—
343	#97×C₈₉	C₂³	1	2	yes	—
344	C₄×C₈×C₈₉	C₂³	1	2	yes	—
345	C₂⁴×C₈₉	—	2	1	no	—
346	#41×C₈₉	—	2	2	no	—
347	#41×C₈₉	—	2	2	no	—
348	#41×C₈₉	—	4	2	no	—
349	#41×C₈₉	—	4	1	no	—
350	#41×C₈₉	—	4	1	no	—
351	#41×C₈₉	—	4	4	no	—
352	#41×C₈₉	—	4	2	no	—
353	#41×C₈₉	—	4	2	no	—
354	#41×C₈₉	—	4	2	no	—
355	#41×C₈₉	—	4	2	no	—
356	C₂×Q₈×C₈₉	—	2	1	no	—
357	C₂×Q₈×C₈₉	—	2	1	no	—
358	C₂×Q₈×C₈₉	—	2	2	no	—
359	C₂×Q₈×C₈₉	—	4	2	no	—
360	C₂×Q₈×C₈₉	—	4	2	no	—
361	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
362	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
363	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
364	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
365	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
366	C₂×D₄×C₈₉	—	2	2	no	—
367	C₂×D₄×C₈₉	—	2	1	no	—
368	C₂×D₄×C₈₉	—	2	1	no	—
369	C₂×D₄×C₈₉	—	2	2	no	—
370	C₂×D₄×C₈₉	—	2	1	no	—
371	C₂×D₄×C₈₉	—	2	1	no	—
372	C₂×D₄×C₈₉	—	2	2	no	—
373	C₂×D₄×C₈₉	—	2	2	no	—
374	C₂×D₄×C₈₉	—	2	1	no	—
375	C₂×D₄×C₈₉	—	2	1	no	—
376	C₂×D₄×C₈₉	—	2	1	no	—
377	C₂×D₄×C₈₉	—	4	1	no	—
378	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
379	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
380	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
381	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
382	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
383	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₈₉	—	2	1	no	—
385	C₂²×C₄×C₈₉	—	2	2	no	—
386	C₂²×C₄×C₈₉	—	2	1	no	—
387	C₂²×C₄×C₈₉	—	2	1	no	—
388	C₂²×C₄×C₈₉	—	2	1	no	—
389	C₂²×C₄×C₈₉	—	2	1	no	—
390	C₂²×C₄×C₈₉	—	2	2	no	—
391	C₂²×C₄×C₈₉	—	2	1	no	—
392	C₂²×C₄×C₈₉	—	2	1	no	—
393	C₂²×C₄×C₈₉	—	2	1	no	—
394	C₂²×C₄×C₈₉	—	2	1	no	—
395	C₂²×C₄×C₈₉	—	2	2	no	—
396	C₂²×C₄×C₈₉	—	2	2	no	—
397	C₂²×C₄×C₈₉	—	4	4	no	—
398	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
404	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
407	Q₁₆×C₈₉	—	4	2	no	—
408	Q₁₆×C₈₉	—	4	2	no	—
409	Q₁₆×C₈₉	—	4	2	no	—
410	Q₁₆×C₈₉	—	4	2	no	—
411	SD₁₆×C₈₉	—	2	4	no	—
412	SD₁₆×C₈₉	—	2	4	no	—
413	SD₁₆×C₈₉	—	4	2	no	—
414	SD₁₆×C₈₉	—	4	2	no	—
415	SD₁₆×C₈₉	—	4	2	no	—
416	SD₁₆×C₈₉	—	4	2	no	—
417	D₈×C₈₉	—	2	4	no	—
418	D₈×C₈₉	—	4	2	no	—
419	M₁₆×C₈₉	—	4	2	no	—
420	M₁₆×C₈₉	—	4	2	no	—
421	C₂×C₈×C₈₉	—	4	2	no	—
422	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
423	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
424	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
425	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
426	C₄⋊C₄×C₈₉	—	2	2	no	—
427	C₄⋊C₄×C₈₉	—	2	1	no	—
428	C₄⋊C₄×C₈₉	—	2	1	no	—
429	C₄⋊C₄×C₈₉	—	2	1	no	—
430	C₄⋊C₄×C₈₉	—	2	1	no	—
431	C₄⋊C₄×C₈₉	—	2	1	no	—
432	C₄⋊C₄×C₈₉	—	2	1	no	—
433	C₄⋊C₄×C₈₉	—	2	1	no	—
434	C₄⋊C₄×C₈₉	—	2	1	no	—
435	C₄⋊C₄×C₈₉	—	2	1	no	—
436	C₄⋊C₄×C₈₉	—	2	1	no	—
437	C₄⋊C₄×C₈₉	—	2	2	no	—
438	C₄⋊C₄×C₈₉	—	2	2	no	—
439	C₄⋊C₄×C₈₉	—	2	2	no	—
440	C₄⋊C₄×C₈₉	—	2	1	no	—
441	C₄⋊C₄×C₈₉	—	2	1	no	—
442	C₄⋊C₄×C₈₉	—	2	1	no	—
443	C₄⋊C₄×C₈₉	—	2	1	no	—
444	C₄⋊C₄×C₈₉	—	2	1	no	—
445	C₄⋊C₄×C₈₉	—	2	1	no	—
446	C₄⋊C₄×C₈₉	—	2	1	no	—
447	C₄⋊C₄×C₈₉	—	2	1	no	—
448	C₄⋊C₄×C₈₉	—	2	1	no	—
449	C₄⋊C₄×C₈₉	—	2	1	no	—
450	C₄⋊C₄×C₈₉	—	2	1	no	—
451	C₄⋊C₄×C₈₉	—	2	2	no	—
452	C₄⋊C₄×C₈₉	—	2	2	no	—
453	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
454	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
455	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
456	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
457	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
458	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
459	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
460	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
461	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
462	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
463	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
464	C₂²⋊C₄×C₈₉	—	2	1	no	—
465	C₂²⋊C₄×C₈₉	—	2	1	no	—
466	C₂²⋊C₄×C₈₉	—	2	2	no	—
467	C₂²⋊C₄×C₈₉	—	2	2	no	—
468	C₂²⋊C₄×C₈₉	—	2	1	no	—
469	C₂²⋊C₄×C₈₉	—	2	1	no	—
470	C₂²⋊C₄×C₈₉	—	2	1	no	—
471	C₂²⋊C₄×C₈₉	—	2	1	no	—
472	C₂²⋊C₄×C₈₉	—	2	1	no	—
473	C₂²⋊C₄×C₈₉	—	2	1	no	—
474	C₂²⋊C₄×C₈₉	—	2	1	no	—
475	C₂²⋊C₄×C₈₉	—	2	1	no	—
476	C₂²⋊C₄×C₈₉	—	2	1	no	—
477	C₂²⋊C₄×C₈₉	—	2	1	no	—
478	C₂²⋊C₄×C₈₉	—	2	1	no	—
479	C₂²⋊C₄×C₈₉	—	2	1	no	—
480	C₂²⋊C₄×C₈₉	—	2	2	no	—
481	C₂²⋊C₄×C₈₉	—	2	2	no	—
482	C₂²⋊C₄×C₈₉	—	2	1	no	—
483	C₂²⋊C₄×C₈₉	—	2	1	no	—
484	C₂²⋊C₄×C₈₉	—	2	1	no	—
485	C₂²⋊C₄×C₈₉	—	2	1	no	—
486	C₂²⋊C₄×C₈₉	—	2	2	no	—
487	C₂²⋊C₄×C₈₉	—	2	2	no	—
488	C₂²⋊C₄×C₈₉	—	2	2	no	—
489	C₂²⋊C₄×C₈₉	—	2	2	no	—
490	C₂²⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
491	C₂²⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
492	C₂²⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
493	C₂²⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
494	C₂²⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
495	C₂²⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
496	C₄²×C₈₉	—	2	1	no	—
497	C₄²×C₈₉	—	2	1	no	—
498	C₄²×C₈₉	—	2	1	no	—
499	C₄²×C₈₉	—	2	1	no	—
500	C₄²×C₈₉	—	2	1	no	—
501	C₄²×C₈₉	—	2	1	no	—
502	C₄²×C₈₉	—	2	2	no	—
503	C₄²×C₈₉	—	2	2	no	—
504	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
505	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
506	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
507	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
508	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
509	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
510	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
511	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
512	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
513	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
514	C₂³×C₈₉	—	2	1	no	—
515	C₂³×C₈₉	—	2	1	no	—
516	C₂³×C₈₉	—	2	2	no	—
517	C₂³×C₈₉	—	4	2	no	—
518	C₂³×C₈₉	—	4	2	no	—
519	C₂³×C₈₉	—	8	1	no	—
520	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
521	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
522	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
523	Q₈×C₈₉	—	2	2	no	—
524	Q₈×C₈₉	—	2	2	no	—
525	Q₈×C₈₉	—	2	1	no	—
526	Q₈×C₈₉	—	2	1	no	—
527	Q₈×C₈₉	—	2	1	no	—
528	Q₈×C₈₉	—	2	2	no	—
529	Q₈×C₈₉	—	2	1	no	—
530	Q₈×C₈₉	—	2	2	no	—
531	Q₈×C₈₉	—	4	1	no	—
532	Q₈×C₈₉	—	4	2	no	—
533	Q₈×C₈₉	—	8	1	no	—
534	Q₈×C₈₉	—	8	2	no	—
535	D₄×C₈₉	—	2	2	no	—
536	D₄×C₈₉	—	2	1	no	—
537	D₄×C₈₉	—	2	1	no	—
538	D₄×C₈₉	—	2	1	no	—
539	D₄×C₈₉	—	2	2	no	—
540	D₄×C₈₉	—	4	1	no	—
541	D₄×C₈₉	—	4	1	no	—
542	D₄×C₈₉	—	4	1	no	—
543	D₄×C₈₉	—	4	2	no	—
544	D₄×C₈₉	—	4	2	no	—
545	D₄×C₈₉	—	4	2	no	—
546	D₄×C₈₉	—	4	2	no	—
547	D₄×C₈₉	—	4	4	no	—
548	D₄×C₈₉	—	4	2	no	—
549	D₄×C₈₉	—	8	1	no	—
550	D₄×C₈₉	—	8	1	no	—
551	D₄×C₈₉	—	8	2	no	—
552	D₄×C₈₉	—	8	2	no	—
553	D₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
554	C₂×C₄×C₈₉	—	2	2	no	—
555	C₂×C₄×C₈₉	—	2	2	no	—
556	C₂×C₄×C₈₉	—	2	2	no	—
557	C₂×C₄×C₈₉	—	2	1	no	—
558	C₂×C₄×C₈₉	—	2	1	no	—
559	C₂×C₄×C₈₉	—	2	1	no	—
560	C₂×C₄×C₈₉	—	2	1	no	—
561	C₂×C₄×C₈₉	—	2	1	no	—
562	C₂×C₄×C₈₉	—	2	1	no	—
563	C₂×C₄×C₈₉	—	2	1	no	—
564	C₂×C₄×C₈₉	—	2	1	no	—
565	C₂×C₄×C₈₉	—	2	1	no	—
566	C₂×C₄×C₈₉	—	2	1	no	—
567	C₂×C₄×C₈₉	—	2	1	no	—
568	C₂×C₄×C₈₉	—	2	2	no	—
569	C₂×C₄×C₈₉	—	2	2	no	—
570	C₂×C₄×C₈₉	—	2	2	no	—
571	C₂×C₄×C₈₉	—	2	1	no	—
572	C₂×C₄×C₈₉	—	4	1	no	—
573	C₂×C₄×C₈₉	—	4	1	no	—
574	C₂×C₄×C₈₉	—	4	1	no	—
575	C₂×C₄×C₈₉	—	4	2	no	—
576	C₂×C₄×C₈₉	—	4	2	no	—
577	C₂×C₄×C₈₉	—	4	2	no	—
578	C₂×C₄×C₈₉	—	4	2	no	—
579	C₂×C₄×C₈₉	—	4	4	no	—
580	C₂×C₄×C₈₉	—	4	2	no	—
581	C₂×C₄×C₈₉	—	4	2	no	—
582	C₂×C₄×C₈₉	—	4	2	no	—
583	C₂×C₄×C₈₉	—	8	1	no	—
584	C₂×C₄×C₈₉	—	8	1	no	—
585	C₂×C₄×C₈₉	—	8	2	no	—
586	C₂×C₄×C₈₉	—	8	2	no	—
587	C₂×C₄×C₈₉	—	8	2	no	—
588	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
589	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
590	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
591	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
592	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
593	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
594	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
595	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
596	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
597	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
598	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
599	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
600	C₈×C₈₉	—	2	2	no	—
601	C₈×C₈₉	—	2	2	no	—
602	C₈×C₈₉	—	2	2	no	—
603	C₈×C₈₉	—	2	2	no	—
604	C₂²×C₈₉	—	2	1	no	—
605	C₂²×C₈₉	—	2	1	no	—
606	C₂²×C₈₉	—	2	1	no	—
607	C₂²×C₈₉	—	2	1	no	—
608	C₂²×C₈₉	—	2	1	no	—
609	C₂²×C₈₉	—	2	1	no	—
610	C₂²×C₈₉	—	2	2	no	—
611	C₂²×C₈₉	—	2	1	no	—
612	C₂²×C₈₉	—	2	1	no	—
613	C₂²×C₈₉	—	2	1	no	—
614	C₂²×C₈₉	—	4	1	no	—
615	C₂²×C₈₉	—	4	1	no	—
616	C₂²×C₈₉	—	4	2	no	—
617	C₂²×C₈₉	—	4	1	no	—
618	C₂²×C₈₉	—	4	2	no	—
619	C₂²×C₈₉	—	4	1	no	—
620	C₂²×C₈₉	—	4	1	no	—
621	C₂²×C₈₉	—	4	2	no	—
622	C₂²×C₈₉	—	8	4	no	—
623	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
624	C₄×C₈₉	—	2	1	no	—
625	C₄×C₈₉	—	2	1	no	—
626	C₄×C₈₉	—	2	1	no	—
627	C₄×C₈₉	—	2	1	no	—
628	C₄×C₈₉	—	2	1	no	—
629	C₄×C₈₉	—	2	1	no	—
630	C₄×C₈₉	—	2	1	no	—
631	C₄×C₈₉	—	2	1	no	—
632	C₄×C₈₉	—	2	1	no	—
633	C₄×C₈₉	—	2	1	no	—
634	C₄×C₈₉	—	4	1	no	—
635	C₄×C₈₉	—	4	1	no	—
636	C₄×C₈₉	—	4	1	no	—
637	C₄×C₈₉	—	4	1	no	—
638	C₄×C₈₉	—	4	2	no	—
639	C₄×C₈₉	—	4	2	no	—
640	C₄×C₈₉	—	4	1	no	—
641	C₄×C₈₉	—	4	1	no	—
642	C₄×C₈₉	—	4	2	no	—
643	C₄×C₈₉	#575	1	2	yes	—
644	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
645	C₄×C₈₉	#585	1	1	yes	characteristic
646	#61967	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
647	C₂×C₈₉	—	4	1	no	—
648	C₂×C₈₉	—	4	1	no	—
649	C₂×C₈₉	—	4	1	no	—
650	C₂×C₈₉	—	4	2	no	—
651	C₂×C₈₉	—	8	2	no	—
652	C₂×C₈₉	—	8	1	no	—
653	C₂×C₈₉	#3488	1	1	yes	characteristic
654	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
655	C₂×C₈₉	#3586	1	1	yes	characteristic
656	#3511	C₂×C₈₉	1	1	yes	characteristic, complemented
657	#3475	C₂×C₈₉	1	1	yes	characteristic, complemented
658	#3402	C₂×C₈₉	1	2	yes	complemented
659	#3376	C₂×C₈₉	1	2	yes	complemented
660	#3327	C₂×C₈₉	1	2	yes	complemented
661	#3321	C₂×C₈₉	1	2	yes	complemented
662	#3315	C₂×C₈₉	1	2	yes	complemented
663	#3275	C₂×C₈₉	1	2	yes	complemented
664	#3269	C₂×C₈₉	1	2	yes	complemented
665	#3267	C₂×C₈₉	1	2	yes	complemented
666	#3255	C₂×C₈₉	1	1	yes	characteristic, complemented
667	#3251	C₂×C₈₉	1	1	yes	characteristic, complemented
668	#3248	C₂×C₈₉	1	1	yes	characteristic, complemented
669	#3218	C₂×C₈₉	1	1	yes	characteristic, complemented
670	#3216	C₂×C₈₉	1	1	yes	characteristic, complemented
671	#3212	C₂×C₈₉	1	1	yes	characteristic, complemented
672	#3115	C₂×C₈₉	1	1	yes	characteristic, complemented
673	#3110	C₂×C₈₉	1	1	yes	characteristic, complemented
674	#3107	C₂×C₈₉	1	1	yes	characteristic, complemented
675	#3039	C₂×C₈₉	1	1	yes	characteristic, complemented
676	#3036	C₂×C₈₉	1	1	yes	characteristic, complemented
677	#3035	C₂×C₈₉	1	1	yes	characteristic, complemented
678	#2989	C₂×C₈₉	1	1	yes	characteristic, complemented
679	C₈₉	#61967	1	1	yes	characteristic, direct product factor, Sylow
680	C₂×#137	C₂²×C₈₉	1	2	yes	—
681	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
682	C₂×#135	C₂²×C₈₉	1	2	yes	—
683	#556	C₂²×C₈₉	1	1	yes	characteristic
684	#556	C₂²×C₈₉	1	2	yes	complemented
685	#555	—	2	1	no	—
686	#555	C₂²×C₈₉	1	1	yes	characteristic
687	#554	—	2	1	no	—
688	#554	C₂²×C₈₉	1	1	yes	characteristic
689	#553	—	2	1	no	—
690	#553	—	2	1	no	—
691	#553	—	2	1	no	—
692	#552	—	2	1	no	—
693	#552	C₂²×C₈₉	1	1	yes	characteristic
694	#552	C₂²×C₈₉	1	1	yes	characteristic
695	#551	—	2	1	no	—
696	#551	—	2	1	no	—
697	#548	C₂²×C₈₉	1	2	yes	—
698	#548	C₂²×C₈₉	1	2	yes	complemented
699	#547	C₂²×C₈₉	1	1	yes	characteristic
700	#547	C₂²×C₈₉	1	2	yes	—
701	#546	C₂²×C₈₉	1	1	yes	characteristic
702	#546	C₂²×C₈₉	1	1	yes	characteristic
703	#542	—	2	1	no	—
704	#542	—	2	1	no	—
705	#537	—	2	1	no	—
706	#533	C₂²×C₈₉	1	1	yes	characteristic
707	#533	C₂²×C₈₉	1	1	yes	characteristic
708	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
709	#532	C₂²×C₈₉	1	1	yes	characteristic
710	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
711	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
712	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
713	#529	—	2	1	no	—
714	#529	—	2	1	no	—
715	#529	C₂²×C₈₉	1	1	yes	characteristic
716	#529	C₂²×C₈₉	1	1	yes	characteristic
717	#525	—	2	1	no	—
718	#520	—	2	1	no	—
719	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
720	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
721	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
722	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
723	C₂×#117	—	2	1	no	—
724	#497	C₂²×C₈₉	1	2	yes	—
725	#497	C₂²×C₈₉	1	2	yes	complemented
726	#495	C₂²×C₈₉	1	2	yes	—
727	#491	C₂²×C₈₉	1	2	yes	complemented
728	#489	C₂²×C₈₉	1	2	yes	complemented
729	#488	C₂²×C₈₉	1	2	yes	complemented
730	#485	C₂²×C₈₉	1	2	yes	complemented
731	#484	C₂²×C₈₉	1	2	yes	—
732	#482	C₂²×C₈₉	1	2	yes	complemented
733	#479	C₂²×C₈₉	1	2	yes	complemented
734	#478	C₂²×C₈₉	1	2	yes	complemented
735	#475	C₂²×C₈₉	1	1	yes	characteristic, complemented
736	#475	C₂²×C₈₉	1	1	yes	characteristic, complemented
737	#475	C₂²×C₈₉	1	2	yes	complemented
738	#474	C₂²×C₈₉	1	1	yes	characteristic
739	#474	C₂²×C₈₉	1	1	yes	characteristic
740	#470	C₂²×C₈₉	1	2	yes	—
741	#470	C₂²×C₈₉	1	2	yes	—
742	#469	C₂²×C₈₉	1	2	yes	—
743	#468	C₂²×C₈₉	1	2	yes	complemented
744	#467	C₂²×C₈₉	1	2	yes	complemented
745	#465	C₂²×C₈₉	1	2	yes	—
746	#464	C₂²×C₈₉	1	2	yes	—
747	#464	C₂²×C₈₉	1	2	yes	complemented
748	#463	C₂²×C₈₉	1	2	yes	—
749	#463	C₂²×C₈₉	1	2	yes	—
750	#463	C₂²×C₈₉	1	2	yes	—
751	#463	C₂²×C₈₉	1	2	yes	—
752	#462	C₂²×C₈₉	1	1	yes	characteristic, complemented
753	#462	C₂²×C₈₉	1	2	yes	complemented
754	#462	C₂²×C₈₉	1	2	yes	complemented
755	#462	C₂²×C₈₉	1	1	yes	characteristic, complemented
756	#462	C₂²×C₈₉	1	1	yes	characteristic, complemented
757	#462	C₂²×C₈₉	1	1	yes	characteristic, complemented
758	#461	C₂²×C₈₉	1	1	yes	characteristic
759	#461	C₂²×C₈₉	1	1	yes	characteristic
760	#461	C₂²×C₈₉	1	1	yes	characteristic
761	#461	C₂²×C₈₉	1	2	yes	—
762	#461	C₂²×C₈₉	1	1	yes	characteristic
763	#460	C₂²×C₈₉	1	1	yes	characteristic, complemented
764	#460	C₂²×C₈₉	1	1	yes	characteristic, complemented
765	#459	C₂²×C₈₉	1	1	yes	characteristic
766	#459	C₂²×C₈₉	1	1	yes	characteristic
767	#452	C₂²×C₈₉	1	2	yes	—
768	#452	C₂²×C₈₉	1	2	yes	—
769	#452	C₂²×C₈₉	1	2	yes	—
770	#452	C₂²×C₈₉	1	2	yes	complemented
771	#451	C₂²×C₈₉	1	2	yes	complemented
772	#450	C₂²×C₈₉	1	2	yes	—
773	#449	C₂²×C₈₉	1	2	yes	—
774	#449	C₂²×C₈₉	1	2	yes	—
775	#448	C₂²×C₈₉	1	2	yes	—
776	#446	C₂²×C₈₉	1	2	yes	complemented
777	#442	C₂²×C₈₉	1	2	yes	—
778	#440	C₂²×C₈₉	1	2	yes	—
779	#440	C₂²×C₈₉	1	2	yes	—
780	#440	C₂²×C₈₉	1	2	yes	complemented
781	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
782	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
783	#436	C₂²×C₈₉	1	2	yes	—
784	#435	C₂²×C₈₉	1	2	yes	—
785	#435	C₂²×C₈₉	1	2	yes	complemented
786	#432	C₂²×C₈₉	1	1	yes	characteristic
787	#432	C₂²×C₈₉	1	1	yes	characteristic, complemented
788	#431	C₂²×C₈₉	1	1	yes	characteristic, complemented
789	#423	C₂²×C₈₉	1	1	yes	characteristic
790	#423	C₂²×C₈₉	1	1	yes	characteristic, complemented
791	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
792	#419	C₂²×C₈₉	1	2	yes	complemented
793	#417	C₂²×C₈₉	1	2	yes	—
794	#416	C₂²×C₈₉	1	2	yes	complemented
795	C₂×#41	—	2	1	no	—
796	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
797	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
798	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
799	C₂×#41	C₂³×C₈₉	1	2	yes	—
800	C₂×#41	C₂³×C₈₉	1	2	yes	—
801	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
802	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
803	C₂³×C₄	—	2	1	no	—
804	#137	—	4	4	no	—
805	AGL(1,ℤ/8)	—	4	4	no	—
806	#135	—	4	4	no	—
807	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
808	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
809	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
810	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
811	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
812	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
813	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
814	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
815	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
816	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
817	C₂×D₈	C₂³×C₈₉	1	2	yes	—
818	C₂×D₈	C₂³×C₈₉	1	2	yes	—
819	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
820	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
821	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
822	C₄⋊Q₈	—	2	1	no	—
823	C₄⋊Q₈	—	2	1	no	—
824	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
825	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
826	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
827	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
828	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
829	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
830	#127	C₂³×C₈₉	1	1	yes	characteristic
831	#126	—	2	1	no	—
832	#126	—	2	1	no	—
833	#126	—	2	2	no	—
834	#126	—	2	2	no	—
835	#126	—	2	1	no	—
836	#126	—	2	1	no	—
837	#126	—	2	1	no	—
838	#126	—	2	1	no	—
839	#125	—	2	1	no	—
840	#125	—	2	1	no	—
841	#125	—	2	1	no	—
842	#125	—	2	1	no	—
843	#125	—	2	1	no	—
844	#125	C₂³×C₈₉	1	1	yes	characteristic
845	#125	C₂³×C₈₉	1	1	yes	characteristic
846	#124	—	2	1	no	—
847	#124	—	2	1	no	—
848	#124	—	2	2	no	—
849	#124	—	2	2	no	—
850	#124	—	2	1	no	—
851	#124	C₂³×C₈₉	1	1	yes	characteristic
852	#124	C₂³×C₈₉	1	1	yes	characteristic
853	#124	C₂³×C₈₉	1	2	yes	—
854	#124	C₂³×C₈₉	1	2	yes	—
855	#123	—	2	1	no	—
856	#123	—	2	1	no	—
857	#123	—	2	1	no	—
858	#123	—	2	1	no	—
859	#123	—	2	1	no	—
860	#123	—	2	1	no	—
861	#123	—	2	1	no	—
862	#123	—	2	1	no	—
863	#123	—	2	2	no	—
864	#123	—	2	2	no	—
865	C₂²⋊Q₈	—	2	1	no	—
866	C₂²⋊Q₈	—	2	1	no	—
867	C₂²⋊Q₈	—	2	2	no	—
868	C₂²⋊Q₈	—	2	1	no	—
869	C₂²⋊Q₈	—	2	1	no	—
870	C₂²⋊Q₈	—	2	1	no	—
871	C₂²⋊Q₈	—	2	1	no	—
872	C₂²⋊Q₈	—	2	1	no	—
873	C₂²⋊Q₈	—	2	2	no	—
874	C₂²⋊Q₈	—	2	2	no	—
875	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
876	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
877	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
878	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
879	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
880	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
881	#121	—	2	1	no	—
882	#121	—	2	1	no	—
883	#121	—	2	2	no	—
884	#121	—	2	2	no	—
885	#121	—	2	2	no	—
886	#121	—	2	1	no	—
887	#121	—	2	1	no	—
888	#121	—	2	1	no	—
889	#121	—	2	1	no	—
890	#121	—	2	1	no	—
891	#121	—	2	1	no	—
892	#121	—	2	1	no	—
893	#121	C₂³×C₈₉	1	1	yes	characteristic
894	#121	C₂³×C₈₉	1	1	yes	characteristic
895	#121	C₂³×C₈₉	1	2	yes	—
896	#120	—	2	1	no	—
897	#120	—	2	1	no	—
898	C₄×Q₈	—	2	1	no	—
899	C₄×Q₈	—	2	1	no	—
900	C₄×Q₈	—	2	1	no	—
901	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
902	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
903	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
904	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
905	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
906	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
907	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
908	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
909	C₄×D₄	—	2	1	no	—
910	C₄×D₄	—	2	1	no	—
911	C₄×D₄	—	2	1	no	—
912	C₄×D₄	—	2	1	no	—
913	C₄×D₄	—	2	1	no	—
914	C₄×D₄	—	2	1	no	—
915	C₄×D₄	—	2	2	no	—
916	C₄×D₄	—	2	2	no	—
917	C₄×D₄	—	2	1	no	—
918	C₄×D₄	—	2	1	no	—
919	C₄×D₄	—	2	1	no	—
920	C₄×D₄	—	2	1	no	—
921	C₄×D₄	—	2	1	no	—
922	C₄×D₄	—	2	1	no	—
923	C₄×D₄	—	2	1	no	—
924	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
925	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
926	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
927	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
928	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
929	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
930	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
931	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
932	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
933	C₄×D₄	C₂³×C₈₉	1	2	yes	—
934	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
935	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
936	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
937	#117	—	2	1	no	—
938	#117	—	2	1	no	—
939	#117	—	2	1	no	—
940	#117	—	2	1	no	—
941	#117	—	2	1	no	—
942	#117	—	2	2	no	—
943	#117	—	2	1	no	—
944	#117	—	2	1	no	—
945	#117	—	2	1	no	—
946	#117	—	2	1	no	—
947	#117	—	2	1	no	—
948	#117	—	2	1	no	—
949	#117	D₄×C₈₉	1	1	yes	characteristic
950	#117	D₄×C₈₉	1	1	yes	characteristic
951	#117	D₄×C₈₉	1	1	yes	characteristic
952	#117	C₂³×C₈₉	1	1	yes	characteristic
953	#117	C₂³×C₈₉	1	1	yes	characteristic
954	C₂×C₄⋊C₄	—	2	1	no	—
955	C₂×C₄⋊C₄	—	2	1	no	—
956	C₂×C₄⋊C₄	—	2	1	no	—
957	C₂×C₄⋊C₄	—	2	1	no	—
958	C₂×C₄⋊C₄	—	2	2	no	—
959	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
960	C₂×C₂²⋊C₄	—	2	1	no	—
961	C₂×C₂²⋊C₄	—	2	1	no	—
962	C₂×C₂²⋊C₄	—	2	1	no	—
963	C₂×C₄²	—	2	1	no	—
964	C₂×C₄²	—	2	1	no	—
965	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
966	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
967	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
968	#107	C₂³×C₈₉	1	2	yes	—
969	#107	C₂³×C₈₉	1	2	yes	—
970	#106	C₂³×C₈₉	1	2	yes	—
971	#106	C₂³×C₈₉	1	2	yes	—
972	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
973	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
974	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
975	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
976	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
977	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
978	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
979	#103	C₂³×C₈₉	1	2	yes	—
980	#103	C₂³×C₈₉	1	2	yes	—
981	#103	C₂³×C₈₉	1	2	yes	—
982	#103	C₂³×C₈₉	1	2	yes	—
983	#103	C₂³×C₈₉	1	2	yes	—
984	#103	C₂³×C₈₉	1	2	yes	—
985	#103	C₂³×C₈₉	1	2	yes	—
986	#103	C₂³×C₈₉	1	2	yes	—
987	#103	C₂³×C₈₉	1	2	yes	—
988	#103	C₂³×C₈₉	1	2	yes	—
989	#102	C₂³×C₈₉	1	2	yes	—
990	#102	C₂³×C₈₉	1	2	yes	—
991	#102	C₂³×C₈₉	1	2	yes	—
992	#102	C₂³×C₈₉	1	2	yes	—
993	#102	C₂³×C₈₉	1	2	yes	—
994	#102	C₂³×C₈₉	1	2	yes	—
995	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
996	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
997	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
998	#97	C₂³×C₈₉	1	2	yes	—
999	#97	C₂³×C₈₉	1	2	yes	—
1000	C₄×C₈	C₂³×C₈₉	1	2	yes	—
1001	C₂⁴	—	2	1	no	—
1002	#41	—	2	2	no	—
1003	#41	—	2	2	no	—
1004	#41	—	4	2	no	—
1005	#41	—	4	1	no	—
1006	#41	—	4	1	no	—
1007	#41	—	4	4	no	—
1008	#41	—	4	2	no	—
1009	#41	—	4	2	no	—
1010	#41	—	4	2	no	—
1011	#41	—	4	2	no	—
1012	C₂×Q₈	—	2	1	no	—
1013	C₂×Q₈	—	2	1	no	—
1014	C₂×Q₈	—	2	2	no	—
1015	C₂×Q₈	—	4	2	no	—
1016	C₂×Q₈	—	4	2	no	—
1017	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
1018	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
1019	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
1020	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
1021	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
1022	C₂×D₄	—	2	2	no	—
1023	C₂×D₄	—	2	1	no	—
1024	C₂×D₄	—	2	1	no	—
1025	C₂×D₄	—	2	2	no	—
1026	C₂×D₄	—	2	1	no	—
1027	C₂×D₄	—	2	1	no	—
1028	C₂×D₄	—	2	2	no	—
1029	C₂×D₄	—	2	2	no	—
1030	C₂×D₄	—	2	1	no	—
1031	C₂×D₄	—	2	1	no	—
1032	C₂×D₄	—	2	1	no	—
1033	C₂×D₄	—	4	1	no	—
1034	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1035	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1036	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1037	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
1038	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
1039	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
1040	C₂²×C₄	—	2	1	no	—
1041	C₂²×C₄	—	2	2	no	—
1042	C₂²×C₄	—	2	1	no	—
1043	C₂²×C₄	—	2	1	no	—
1044	C₂²×C₄	—	2	1	no	—
1045	C₂²×C₄	—	2	1	no	—
1046	C₂²×C₄	—	2	2	no	—
1047	C₂²×C₄	—	2	1	no	—
1048	C₂²×C₄	—	2	1	no	—
1049	C₂²×C₄	—	2	1	no	—
1050	C₂²×C₄	—	2	1	no	—
1051	C₂²×C₄	—	2	2	no	—
1052	C₂²×C₄	—	2	2	no	—
1053	C₂²×C₄	—	4	4	no	—
1054	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1055	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1056	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1057	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1058	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1059	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1060	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1061	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1062	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1063	Q₁₆	—	4	2	no	—
1064	Q₁₆	—	4	2	no	—
1065	Q₁₆	—	4	2	no	—
1066	Q₁₆	—	4	2	no	—
1067	SD₁₆	—	2	4	no	—
1068	SD₁₆	—	2	4	no	—
1069	SD₁₆	—	4	2	no	—
1070	SD₁₆	—	4	2	no	—
1071	SD₁₆	—	4	2	no	—
1072	SD₁₆	—	4	2	no	—
1073	D₈	—	2	4	no	—
1074	D₈	—	4	2	no	—
1075	M₁₆	—	4	2	no	—
1076	M₁₆	—	4	2	no	—
1077	C₂×C₈	—	4	2	no	—
1078	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
1079	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
1080	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
1081	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
1082	C₄⋊C₄	—	2	2	no	—
1083	C₄⋊C₄	—	2	1	no	—
1084	C₄⋊C₄	—	2	1	no	—
1085	C₄⋊C₄	—	2	1	no	—
1086	C₄⋊C₄	—	2	1	no	—
1087	C₄⋊C₄	—	2	1	no	—
1088	C₄⋊C₄	—	2	1	no	—
1089	C₄⋊C₄	—	2	1	no	—
1090	C₄⋊C₄	—	2	1	no	—
1091	C₄⋊C₄	—	2	1	no	—
1092	C₄⋊C₄	—	2	1	no	—
1093	C₄⋊C₄	—	2	2	no	—
1094	C₄⋊C₄	—	2	2	no	—
1095	C₄⋊C₄	—	2	2	no	—
1096	C₄⋊C₄	—	2	1	no	—
1097	C₄⋊C₄	—	2	1	no	—
1098	C₄⋊C₄	—	2	1	no	—
1099	C₄⋊C₄	—	2	1	no	—
1100	C₄⋊C₄	—	2	1	no	—
1101	C₄⋊C₄	—	2	1	no	—
1102	C₄⋊C₄	—	2	1	no	—
1103	C₄⋊C₄	—	2	1	no	—
1104	C₄⋊C₄	—	2	1	no	—
1105	C₄⋊C₄	—	2	1	no	—
1106	C₄⋊C₄	—	2	1	no	—
1107	C₄⋊C₄	—	2	2	no	—
1108	C₄⋊C₄	—	2	2	no	—
1109	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1110	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1111	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1112	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1113	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1114	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1115	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1116	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1117	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1118	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1119	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1120	C₂²⋊C₄	—	2	1	no	—
1121	C₂²⋊C₄	—	2	1	no	—
1122	C₂²⋊C₄	—	2	2	no	—
1123	C₂²⋊C₄	—	2	2	no	—
1124	C₂²⋊C₄	—	2	1	no	—
1125	C₂²⋊C₄	—	2	1	no	—
1126	C₂²⋊C₄	—	2	1	no	—
1127	C₂²⋊C₄	—	2	1	no	—
1128	C₂²⋊C₄	—	2	1	no	—
1129	C₂²⋊C₄	—	2	1	no	—
1130	C₂²⋊C₄	—	2	1	no	—
1131	C₂²⋊C₄	—	2	1	no	—
1132	C₂²⋊C₄	—	2	1	no	—
1133	C₂²⋊C₄	—	2	1	no	—
1134	C₂²⋊C₄	—	2	1	no	—
1135	C₂²⋊C₄	—	2	1	no	—
1136	C₂²⋊C₄	—	2	2	no	—
1137	C₂²⋊C₄	—	2	2	no	—
1138	C₂²⋊C₄	—	2	1	no	—
1139	C₂²⋊C₄	—	2	1	no	—
1140	C₂²⋊C₄	—	2	1	no	—
1141	C₂²⋊C₄	—	2	1	no	—
1142	C₂²⋊C₄	—	2	2	no	—
1143	C₂²⋊C₄	—	2	2	no	—
1144	C₂²⋊C₄	—	2	2	no	—
1145	C₂²⋊C₄	—	2	2	no	—
1146	C₂²⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1147	C₂²⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1148	C₂²⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1149	C₂²⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1150	C₂²⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1151	C₂²⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1152	C₄²	—	2	1	no	—
1153	C₄²	—	2	1	no	—
1154	C₄²	—	2	1	no	—
1155	C₄²	—	2	1	no	—
1156	C₄²	—	2	1	no	—
1157	C₄²	—	2	1	no	—
1158	C₄²	—	2	2	no	—
1159	C₄²	—	2	2	no	—
1160	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1161	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1162	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1163	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1164	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1165	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1166	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1167	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1168	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1169	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1170	C₂³	—	2	1	no	—
1171	C₂³	—	2	1	no	—
1172	C₂³	—	2	2	no	—
1173	C₂³	—	4	2	no	—
1174	C₂³	—	4	2	no	—
1175	C₂³	—	8	1	no	—
1176	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1177	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1178	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1179	Q₈	—	2	2	no	—
1180	Q₈	—	2	2	no	—
1181	Q₈	—	2	1	no	—
1182	Q₈	—	2	1	no	—
1183	Q₈	—	2	1	no	—
1184	Q₈	—	2	2	no	—
1185	Q₈	—	2	1	no	—
1186	Q₈	—	2	2	no	—
1187	Q₈	—	4	1	no	—
1188	Q₈	—	4	2	no	—
1189	Q₈	—	8	1	no	—
1190	Q₈	—	8	2	no	—
1191	D₄	—	2	2	no	—
1192	D₄	—	2	1	no	—
1193	D₄	—	2	1	no	—
1194	D₄	—	2	1	no	—
1195	D₄	—	2	2	no	—
1196	D₄	—	4	1	no	—
1197	D₄	—	4	1	no	—
1198	D₄	—	4	1	no	—
1199	D₄	—	4	2	no	—
1200	D₄	—	4	2	no	—
1201	D₄	—	4	2	no	—
1202	D₄	—	4	2	no	—
1203	D₄	—	4	4	no	—
1204	D₄	—	4	2	no	—
1205	D₄	—	8	1	no	—
1206	D₄	—	8	1	no	—
1207	D₄	—	8	2	no	—
1208	D₄	—	8	2	no	—
1209	D₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
1210	C₂×C₄	—	2	2	no	—
1211	C₂×C₄	—	2	2	no	—
1212	C₂×C₄	—	2	2	no	—
1213	C₂×C₄	—	2	1	no	—
1214	C₂×C₄	—	2	1	no	—
1215	C₂×C₄	—	2	1	no	—
1216	C₂×C₄	—	2	1	no	—
1217	C₂×C₄	—	2	1	no	—
1218	C₂×C₄	—	2	1	no	—
1219	C₂×C₄	—	2	1	no	—
1220	C₂×C₄	—	2	1	no	—
1221	C₂×C₄	—	2	1	no	—
1222	C₂×C₄	—	2	2	no	—
1223	C₂×C₄	—	2	1	no	—
1224	C₂×C₄	—	2	1	no	—
1225	C₂×C₄	—	2	2	no	—
1226	C₂×C₄	—	2	2	no	—
1227	C₂×C₄	—	2	1	no	—
1228	C₂×C₄	—	4	1	no	—
1229	C₂×C₄	—	4	1	no	—
1230	C₂×C₄	—	4	1	no	—
1231	C₂×C₄	—	4	2	no	—
1232	C₂×C₄	—	4	2	no	—
1233	C₂×C₄	—	4	2	no	—
1234	C₂×C₄	—	4	2	no	—
1235	C₂×C₄	—	4	4	no	—
1236	C₂×C₄	—	4	2	no	—
1237	C₂×C₄	—	4	2	no	—
1238	C₂×C₄	—	4	2	no	—
1239	C₂×C₄	—	8	1	no	—
1240	C₂×C₄	—	8	1	no	—
1241	C₂×C₄	—	8	2	no	—
1242	C₂×C₄	—	8	2	no	—
1243	C₂×C₄	—	8	2	no	—
1244	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1245	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1246	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1247	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1248	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1249	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1250	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1251	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1252	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1253	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1254	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1255	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1256	C₈	—	2	2	no	—
1257	C₈	—	2	2	no	—
1258	C₈	—	2	2	no	—
1259	C₈	—	2	2	no	—
1260	C₂²	—	2	1	no	—
1261	C₂²	—	2	1	no	—
1262	C₂²	—	2	1	no	—
1263	C₂²	—	2	1	no	—
1264	C₂²	—	2	1	no	—
1265	C₂²	—	2	1	no	—
1266	C₂²	—	2	1	no	—
1267	C₂²	—	2	1	no	—
1268	C₂²	—	2	1	no	—
1269	C₂²	—	2	2	no	—
1270	C₂²	—	4	1	no	—
1271	C₂²	—	4	1	no	—
1272	C₂²	—	4	1	no	—
1273	C₂²	—	4	2	no	—
1274	C₂²	—	4	2	no	—
1275	C₂²	—	4	1	no	—
1276	C₂²	—	4	2	no	—
1277	C₂²	—	4	1	no	—
1278	C₂²	—	8	4	no	—
1279	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1280	C₄	—	2	1	no	—
1281	C₄	—	2	1	no	—
1282	C₄	—	2	1	no	—
1283	C₄	—	2	1	no	—
1284	C₄	—	2	1	no	—
1285	C₄	—	2	1	no	—
1286	C₄	—	2	1	no	—
1287	C₄	—	2	1	no	—
1288	C₄	—	2	1	no	—
1289	C₄	—	2	1	no	—
1290	C₄	—	4	1	no	—
1291	C₄	—	4	1	no	—
1292	C₄	—	4	2	no	—
1293	C₄	—	4	1	no	—
1294	C₄	—	4	1	no	—
1295	C₄	—	4	1	no	—
1296	C₄	—	4	1	no	—
1297	C₄	—	4	2	no	—
1298	C₄	—	4	2	no	—
1299	C₄	#575×C₈₉	1	2	yes	—
1300	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1301	C₄	#585×C₈₉	1	1	yes	characteristic
1302	C₂	—	4	1	no	—
1303	C₂	—	4	1	no	—
1304	C₂	—	4	1	no	—
1305	C₂	—	4	2	no	—
1306	C₂	—	8	2	no	—
1307	C₂	—	8	1	no	—
1308	C₂	C₈₉×#3488	1	1	yes	characteristic
1309	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
1310	C₂	C₈₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3511	C₂	semidirect
2. C₈₉×#3475	C₂	semidirect
3. C₈₉×#3402	C₂	semidirect
4. C₈₉×#3376	C₂	semidirect
5. C₈₉×#3327	C₂	semidirect
6. C₈₉×#3321	C₂	semidirect
7. C₈₉×#3315	C₂	semidirect
8. C₈₉×#3275	C₂	semidirect
9. C₈₉×#3269	C₂	semidirect
10. C₈₉×#3267	C₂	semidirect
11. C₈₉×#3255	C₂	semidirect
12. C₈₉×#3251	C₂	semidirect
13. C₈₉×#3248	C₂	semidirect
14. C₈₉×#3218	C₂	semidirect
15. C₈₉×#3216	C₂	semidirect
16. C₈₉×#3212	C₂	semidirect
17. C₈₉×#3115	C₂	semidirect
18. C₈₉×#3110	C₂	semidirect
19. C₈₉×#3107	C₂	semidirect
20. C₈₉×#3039	C₂	semidirect
21. C₈₉×#3036	C₂	semidirect
22. C₈₉×#3035	C₂	semidirect
23. C₈₉×#2989	C₂	semidirect
28. #556×C₈₉	C₂²	semidirect
42. #548×C₈₉	C₂²	semidirect
52. #533×C₈₉	C₂²	semidirect
54. #532×C₈₉	C₂²	semidirect
55. #532×C₈₉	C₂²	semidirect
56. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
69. #497×C₈₉	C₂²	semidirect
71. #491×C₈₉	C₂²	semidirect
72. #489×C₈₉	C₂²	semidirect
73. #488×C₈₉	C₂²	semidirect
74. #485×C₈₉	C₂²	semidirect
76. #482×C₈₉	C₂²	semidirect
77. #479×C₈₉	C₂²	semidirect
78. #478×C₈₉	C₂²	semidirect
79. #475×C₈₉	C₂²	semidirect
80. #475×C₈₉	C₂²	semidirect
81. #475×C₈₉	C₂²	semidirect
87. #468×C₈₉	C₂²	semidirect
88. #467×C₈₉	C₂²	semidirect
91. #464×C₈₉	C₂²	semidirect
96. #462×C₈₉	C₂²	semidirect
97. #462×C₈₉	C₂²	semidirect
98. #462×C₈₉	C₂²	semidirect
99. #462×C₈₉	C₂²	semidirect
100. #462×C₈₉	C₂²	semidirect
101. #462×C₈₉	C₂²	semidirect
107. #460×C₈₉	C₂²	semidirect
108. #460×C₈₉	C₂²	semidirect
114. #452×C₈₉	C₂²	semidirect
115. #451×C₈₉	C₂²	semidirect
120. #446×C₈₉	C₂²	semidirect
124. #440×C₈₉	C₂²	semidirect
125. C₄×Q₁₆×C₈₉	C₂²	semidirect
129. #435×C₈₉	C₂²	semidirect
131. #432×C₈₉	C₂²	semidirect
132. #431×C₈₉	C₂²	semidirect
134. #423×C₈₉	C₂²	semidirect
135. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
136. #419×C₈₉	C₂²	semidirect
138. #416×C₈₉	C₂²	semidirect
646. #61967	C₈₉	direct (N × H)
656. #3511	C₂×C₈₉	semidirect
657. #3475	C₂×C₈₉	semidirect
658. #3402	C₂×C₈₉	semidirect
659. #3376	C₂×C₈₉	semidirect
660. #3327	C₂×C₈₉	semidirect
661. #3321	C₂×C₈₉	semidirect
662. #3315	C₂×C₈₉	semidirect
663. #3275	C₂×C₈₉	semidirect
664. #3269	C₂×C₈₉	semidirect
665. #3267	C₂×C₈₉	semidirect
666. #3255	C₂×C₈₉	semidirect
667. #3251	C₂×C₈₉	semidirect
668. #3248	C₂×C₈₉	semidirect
669. #3218	C₂×C₈₉	semidirect
670. #3216	C₂×C₈₉	semidirect
671. #3212	C₂×C₈₉	semidirect
672. #3115	C₂×C₈₉	semidirect
673. #3110	C₂×C₈₉	semidirect
674. #3107	C₂×C₈₉	semidirect
675. #3039	C₂×C₈₉	semidirect
676. #3036	C₂×C₈₉	semidirect
677. #3035	C₂×C₈₉	semidirect
678. #2989	C₂×C₈₉	semidirect
679. C₈₉	#61967	direct (N × H)
684. #556	C₂²×C₈₉	semidirect
698. #548	C₂²×C₈₉	semidirect
708. #533	C₂²×C₈₉	semidirect
710. #532	C₂²×C₈₉	semidirect
711. #532	C₂²×C₈₉	semidirect
712. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
725. #497	C₂²×C₈₉	semidirect
727. #491	C₂²×C₈₉	semidirect
728. #489	C₂²×C₈₉	semidirect
729. #488	C₂²×C₈₉	semidirect
730. #485	C₂²×C₈₉	semidirect
732. #482	C₂²×C₈₉	semidirect
733. #479	C₂²×C₈₉	semidirect
734. #478	C₂²×C₈₉	semidirect
735. #475	C₂²×C₈₉	semidirect
736. #475	C₂²×C₈₉	semidirect
737. #475	C₂²×C₈₉	semidirect
743. #468	C₂²×C₈₉	semidirect
744. #467	C₂²×C₈₉	semidirect
747. #464	C₂²×C₈₉	semidirect
752. #462	C₂²×C₈₉	semidirect
753. #462	C₂²×C₈₉	semidirect
754. #462	C₂²×C₈₉	semidirect
755. #462	C₂²×C₈₉	semidirect
756. #462	C₂²×C₈₉	semidirect
757. #462	C₂²×C₈₉	semidirect
763. #460	C₂²×C₈₉	semidirect
764. #460	C₂²×C₈₉	semidirect
770. #452	C₂²×C₈₉	semidirect
771. #451	C₂²×C₈₉	semidirect
776. #446	C₂²×C₈₉	semidirect
780. #440	C₂²×C₈₉	semidirect
781. C₄×Q₁₆	C₂²×C₈₉	semidirect
785. #435	C₂²×C₈₉	semidirect
787. #432	C₂²×C₈₉	semidirect
788. #431	C₂²×C₈₉	semidirect
790. #423	C₂²×C₈₉	semidirect
791. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
792. #419	C₂²×C₈₉	semidirect
794. #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×#3511	2
C₈₉×#3475	2
C₈₉×#3402	2
C₈₉×#3376	2
C₈₉×#3327	2
C₈₉×#3321	2
C₈₉×#3315	2
C₈₉×#3275	2
C₈₉×#3269	2
C₈₉×#3267	2
C₈₉×#3255	2
C₈₉×#3251	2
C₈₉×#3248	2
C₈₉×#3218	2
C₈₉×#3216	2
C₈₉×#3212	2
C₈₉×#3115	2
C₈₉×#3110	2
C₈₉×#3107	2
C₈₉×#3039	2
C₈₉×#3036	2
C₈₉×#3035	2
C₈₉×#2989	2
#61967	89

Subgroups — C89×#61967 #36439815

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61967 #36439815