Subgroups — C₈₉×#62137 #36439985

Order 22784.

1990 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3386	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3345	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3343	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3335	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3334	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3318	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3310	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3295	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3251	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#3247	C₂	1	2	yes	maximal, complemented
17	C₈₉×#3234	C₂	1	2	yes	maximal, complemented
18	C₈₉×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3114	C₂	1	2	yes	maximal, complemented
20	C₈₉×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#3077	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#478×C₈₉	C₂	1	2	yes	maximal, complemented
23	C₈₉×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₈₉	—	2	1	no	—
25	#557×C₈₉	C₂²	1	1	yes	characteristic, complemented
26	#554×C₈₉	C₂²	1	1	yes	characteristic, complemented
27	#554×C₈₉	C₂²	1	1	yes	characteristic, complemented
28	#553×C₈₉	C₂²	1	2	yes	complemented
29	#552×C₈₉	—	2	2	no	—
30	#552×C₈₉	—	2	1	no	—
31	#552×C₈₉	C₂²	1	2	yes	complemented
32	#550×C₈₉	C₂²	1	1	yes	characteristic
33	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
34	#548×C₈₉	—	2	1	no	—
35	#547×C₈₉	—	2	1	no	—
36	#547×C₈₉	C₂²	1	1	yes	characteristic
37	#547×C₈₉	C₂²	1	2	yes	—
38	#547×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	#546×C₈₉	—	2	1	no	—
40	#546×C₈₉	—	2	2	no	—
41	D₄²×C₈₉	C₂²	1	2	yes	—
42	D₄²×C₈₉	C₂²	1	1	yes	characteristic
43	#541×C₈₉	—	2	1	no	—
44	#539×C₈₉	—	2	2	no	—
45	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
46	#532×C₈₉	C₂²	1	1	yes	characteristic
47	#532×C₈₉	C₂²	1	2	yes	—
48	#529×C₈₉	C₂²	1	1	yes	characteristic, complemented
49	#529×C₈₉	C₂²	1	2	yes	complemented
50	C₂×#125×C₈₉	C₂²	1	2	yes	complemented
51	#525×C₈₉	—	2	1	no	—
52	#525×C₈₉	—	2	2	no	—
53	#520×C₈₉	—	2	1	no	—
54	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
57	#501×C₈₉	C₂²	1	2	yes	complemented
58	#501×C₈₉	C₂²	1	2	yes	complemented
59	#500×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#498×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	#490×C₈₉	C₂²	1	2	yes	complemented
62	#490×C₈₉	C₂²	1	2	yes	complemented
63	#486×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	#486×C₈₉	C₂²	1	1	yes	characteristic, complemented
65	#484×C₈₉	C₂²	1	1	yes	characteristic, complemented
66	#483×C₈₉	C₂²	1	2	yes	complemented
67	#482×C₈₉	C₂²	1	2	yes	complemented
68	#482×C₈₉	C₂²	1	2	yes	complemented
69	#481×C₈₉	C₂²	1	2	yes	complemented
70	#481×C₈₉	C₂²	1	1	yes	characteristic, complemented
71	#481×C₈₉	C₂²	1	2	yes	complemented
72	#480×C₈₉	C₂²	1	2	yes	complemented
73	#480×C₈₉	C₂²	1	2	yes	complemented
74	#480×C₈₉	C₂²	1	2	yes	complemented
75	#478×C₈₉	C₂²	1	2	yes	—
76	#478×C₈₉	C₂²	1	1	yes	characteristic
77	#478×C₈₉	C₂²	1	2	yes	—
78	#478×C₈₉	C₂²	1	2	yes	—
79	#478×C₈₉	C₂²	1	2	yes	complemented
80	#478×C₈₉	C₂²	1	2	yes	complemented
81	#478×C₈₉	C₂²	1	2	yes	complemented
82	#478×C₈₉	C₂²	1	2	yes	complemented
83	#478×C₈₉	C₂²	1	2	yes	complemented
84	#478×C₈₉	C₂²	1	1	yes	characteristic, complemented
85	#478×C₈₉	C₂²	1	2	yes	complemented
86	#477×C₈₉	C₂²	1	2	yes	complemented
87	#476×C₈₉	C₂²	1	1	yes	characteristic
88	#476×C₈₉	C₂²	1	1	yes	characteristic, complemented
89	#476×C₈₉	C₂²	1	2	yes	complemented
90	#475×C₈₉	C₂²	1	1	yes	characteristic, complemented
91	#474×C₈₉	C₂²	1	1	yes	characteristic
92	#474×C₈₉	C₂²	1	1	yes	characteristic, complemented
93	#474×C₈₉	C₂²	1	1	yes	characteristic, complemented
94	#469×C₈₉	C₂²	1	2	yes	complemented
95	#468×C₈₉	C₂²	1	2	yes	complemented
96	#466×C₈₉	C₂²	1	2	yes	complemented
97	#466×C₈₉	C₂²	1	2	yes	complemented
98	#465×C₈₉	C₂²	1	2	yes	complemented
99	#465×C₈₉	C₂²	1	2	yes	complemented
100	#463×C₈₉	C₂²	1	1	yes	characteristic
101	#463×C₈₉	C₂²	1	1	yes	characteristic, complemented
102	#463×C₈₉	C₂²	1	2	yes	complemented
103	#460×C₈₉	C₂²	1	2	yes	complemented
104	#460×C₈₉	C₂²	1	1	yes	characteristic, complemented
105	#459×C₈₉	C₂²	1	2	yes	complemented
106	#459×C₈₉	C₂²	1	1	yes	characteristic, complemented
107	#450×C₈₉	C₂²	1	1	yes	characteristic
108	#450×C₈₉	C₂²	1	2	yes	—
109	#447×C₈₉	C₂²	1	1	yes	characteristic
110	#447×C₈₉	C₂²	1	2	yes	—
111	#446×C₈₉	C₂²	1	1	yes	characteristic, complemented
112	#446×C₈₉	C₂²	1	1	yes	characteristic, complemented
113	#442×C₈₉	C₂²	1	2	yes	—
114	#442×C₈₉	C₂²	1	2	yes	complemented
115	#440×C₈₉	C₂²	1	2	yes	—
116	#440×C₈₉	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
121	#435×C₈₉	C₂²	1	2	yes	complemented
122	#435×C₈₉	C₂²	1	2	yes	complemented
123	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
125	#432×C₈₉	C₂²	1	2	yes	complemented
126	#431×C₈₉	C₂²	1	1	yes	characteristic, complemented
127	#428×C₈₉	C₂²	1	2	yes	complemented
128	C₂×#107×C₈₉	C₂²	1	2	yes	complemented
129	C₂×#106×C₈₉	C₂²	1	2	yes	complemented
130	#423×C₈₉	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	complemented
132	#418×C₈₉	C₂²	1	2	yes	—
133	C₂×#102×C₈₉	C₂²	1	2	yes	—
134	C₂×#102×C₈₉	C₂²	1	2	yes	—
135	C₂×#41×C₈₉	—	2	1	no	—
136	C₂×#41×C₈₉	—	2	1	no	—
137	C₂×#41×C₈₉	—	2	2	no	—
138	C₂×#41×C₈₉	—	2	1	no	—
139	C₂×#41×C₈₉	—	2	2	no	—
140	C₂×#41×C₈₉	—	2	1	no	—
141	C₂×#41×C₈₉	—	4	8	no	—
142	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
143	C₂²×Q₈×C₈₉	—	2	1	no	—
144	C₂²×D₄×C₈₉	—	2	2	no	—
145	C₂²×D₄×C₈₉	—	2	1	no	—
146	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
147	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₈₉	—	2	2	no	—
149	C₂³×C₄×C₈₉	—	2	1	no	—
150	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
153	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
154	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
155	C₂×D₈×C₈₉	C₂³	1	2	yes	—
156	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
157	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
158	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₈₉	—	2	1	no	—
160	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
164	#127×C₈₉	C₂³	1	1	yes	characteristic
165	#127×C₈₉	C₂³	1	2	yes	—
166	#126×C₈₉	—	2	2	no	—
167	#126×C₈₉	—	2	2	no	—
168	#126×C₈₉	—	2	2	no	—
169	#126×C₈₉	—	2	1	no	—
170	#125×C₈₉	—	2	2	no	—
171	#125×C₈₉	—	2	2	no	—
172	#125×C₈₉	—	2	1	no	—
173	#125×C₈₉	—	2	2	no	—
174	#125×C₈₉	—	2	2	no	—
175	#125×C₈₉	C₂³	1	1	yes	characteristic
176	#125×C₈₉	C₂³	1	2	yes	—
177	#125×C₈₉	C₂³	1	2	yes	—
178	#125×C₈₉	C₂³	1	2	yes	—
179	#124×C₈₉	—	2	1	no	—
180	#124×C₈₉	—	2	2	no	—
181	#124×C₈₉	C₂³	1	1	yes	characteristic
182	#123×C₈₉	—	2	2	no	—
183	#123×C₈₉	—	2	1	no	—
184	#123×C₈₉	—	2	2	no	—
185	#123×C₈₉	—	2	2	no	—
186	#123×C₈₉	—	2	2	no	—
187	#123×C₈₉	—	2	2	no	—
188	#123×C₈₉	—	2	2	no	—
189	#123×C₈₉	—	2	2	no	—
190	C₂²⋊Q₈×C₈₉	—	2	1	no	—
191	C₂²⋊Q₈×C₈₉	—	2	1	no	—
192	C₂²⋊Q₈×C₈₉	—	2	1	no	—
193	C₂²⋊Q₈×C₈₉	—	2	1	no	—
194	C₂²⋊Q₈×C₈₉	—	2	2	no	—
195	C₂²⋊Q₈×C₈₉	—	2	1	no	—
196	C₂²⋊Q₈×C₈₉	—	2	2	no	—
197	C₂²⋊Q₈×C₈₉	—	2	2	no	—
198	C₂²⋊Q₈×C₈₉	—	2	1	no	—
199	C₂²⋊Q₈×C₈₉	—	2	2	no	—
200	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
201	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
202	#121×C₈₉	—	2	2	no	—
203	#121×C₈₉	—	2	2	no	—
204	#121×C₈₉	—	2	1	no	—
205	#121×C₈₉	—	2	1	no	—
206	#121×C₈₉	—	2	2	no	—
207	#121×C₈₉	—	2	1	no	—
208	#121×C₈₉	—	2	2	no	—
209	#121×C₈₉	C₂³	1	2	yes	—
210	#121×C₈₉	C₂³	1	1	yes	characteristic
211	#121×C₈₉	C₂³	1	2	yes	—
212	#121×C₈₉	C₂³	1	2	yes	—
213	#121×C₈₉	C₂³	1	2	yes	—
214	#120×C₈₉	—	2	2	no	—
215	#120×C₈₉	—	2	2	no	—
216	#120×C₈₉	—	2	2	no	—
217	C₄×Q₈×C₈₉	—	2	1	no	—
218	C₄×Q₈×C₈₉	—	2	1	no	—
219	C₄×Q₈×C₈₉	—	2	1	no	—
220	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
221	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
223	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
224	C₄×D₄×C₈₉	—	2	1	no	—
225	C₄×D₄×C₈₉	—	2	2	no	—
226	C₄×D₄×C₈₉	—	2	1	no	—
227	C₄×D₄×C₈₉	—	2	2	no	—
228	C₄×D₄×C₈₉	—	2	2	no	—
229	C₄×D₄×C₈₉	—	2	1	no	—
230	C₄×D₄×C₈₉	—	2	1	no	—
231	C₄×D₄×C₈₉	—	2	2	no	—
232	C₄×D₄×C₈₉	—	2	2	no	—
233	C₄×D₄×C₈₉	—	2	1	no	—
234	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
235	C₄×D₄×C₈₉	D₄	1	2	yes	—
236	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₈₉	C₂³	1	2	yes	—
240	C₄×D₄×C₈₉	C₂³	1	2	yes	—
241	C₄×D₄×C₈₉	C₂³	1	2	yes	—
242	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₈₉	C₂³	1	2	yes	—
245	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₈₉	C₂³	1	2	yes	—
247	#117×C₈₉	—	2	2	no	—
248	#117×C₈₉	—	2	1	no	—
249	#117×C₈₉	—	2	2	no	—
250	#117×C₈₉	D₄	1	1	yes	characteristic
251	#117×C₈₉	D₄	1	2	yes	—
252	#117×C₈₉	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
254	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
255	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
256	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
261	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
262	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
263	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
264	#107×C₈₉	C₂³	1	1	yes	characteristic
265	#107×C₈₉	C₂³	1	2	yes	—
266	#107×C₈₉	C₂³	1	2	yes	—
267	#107×C₈₉	C₂³	1	2	yes	—
268	#107×C₈₉	C₂³	1	2	yes	—
269	#107×C₈₉	C₂³	1	1	yes	characteristic
270	#107×C₈₉	C₂³	1	2	yes	—
271	#106×C₈₉	C₂³	1	1	yes	characteristic
272	#106×C₈₉	C₂³	1	2	yes	—
273	#106×C₈₉	C₂³	1	2	yes	—
274	#106×C₈₉	C₂³	1	2	yes	—
275	#106×C₈₉	C₂³	1	2	yes	—
276	#106×C₈₉	C₂³	1	1	yes	characteristic
277	#106×C₈₉	C₂³	1	2	yes	—
278	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
280	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
281	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
282	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
285	#103×C₈₉	C₂³	1	1	yes	characteristic
286	#103×C₈₉	C₂³	1	1	yes	characteristic
287	#103×C₈₉	C₂³	1	2	yes	—
288	#102×C₈₉	C₂³	1	1	yes	characteristic
289	#102×C₈₉	C₂³	1	1	yes	characteristic
290	#102×C₈₉	C₂³	1	2	yes	—
291	#102×C₈₉	C₂³	1	2	yes	—
292	#102×C₈₉	C₂³	1	2	yes	—
293	#102×C₈₉	C₂³	1	2	yes	—
294	#102×C₈₉	C₂³	1	2	yes	—
295	#102×C₈₉	C₂³	1	2	yes	—
296	#102×C₈₉	C₂³	1	2	yes	—
297	#102×C₈₉	C₂³	1	2	yes	—
298	#102×C₈₉	C₂³	1	1	yes	characteristic
299	#102×C₈₉	C₂³	1	1	yes	characteristic
300	#102×C₈₉	C₂³	1	1	yes	characteristic
301	#102×C₈₉	C₂³	1	1	yes	characteristic
302	#102×C₈₉	C₂³	1	2	yes	—
303	#102×C₈₉	C₂³	1	2	yes	—
304	#102×C₈₉	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
309	#97×C₈₉	C₂³	1	2	yes	—
310	#97×C₈₉	C₂³	1	2	yes	—
311	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
313	C₂⁴×C₈₉	—	2	1	no	—
314	C₂⁴×C₈₉	—	2	2	no	—
315	#41×C₈₉	—	2	4	no	—
316	#41×C₈₉	—	4	8	no	—
317	#41×C₈₉	—	4	4	no	—
318	#41×C₈₉	—	4	8	no	—
319	#41×C₈₉	—	4	4	no	—
320	#41×C₈₉	—	4	4	no	—
321	#41×C₈₉	—	4	4	no	—
322	C₂×Q₈×C₈₉	—	2	1	no	—
323	C₂×Q₈×C₈₉	—	2	2	no	—
324	C₂×Q₈×C₈₉	—	2	1	no	—
325	C₂×Q₈×C₈₉	—	2	1	no	—
326	C₂×Q₈×C₈₉	—	4	4	no	—
327	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₈₉	—	2	4	no	—
330	C₂×D₄×C₈₉	—	2	2	no	—
331	C₂×D₄×C₈₉	—	2	2	no	—
332	C₂×D₄×C₈₉	—	2	2	no	—
333	C₂×D₄×C₈₉	—	2	2	no	—
334	C₂×D₄×C₈₉	—	2	2	no	—
335	C₂×D₄×C₈₉	—	2	1	no	—
336	C₂×D₄×C₈₉	—	2	1	no	—
337	C₂×D₄×C₈₉	—	2	2	no	—
338	C₂×D₄×C₈₉	—	2	2	no	—
339	C₂×D₄×C₈₉	—	2	1	no	—
340	C₂×D₄×C₈₉	—	2	2	no	—
341	C₂×D₄×C₈₉	—	2	1	no	—
342	C₂×D₄×C₈₉	—	4	2	no	—
343	C₂×D₄×C₈₉	—	4	1	no	—
344	C₂×D₄×C₈₉	—	4	8	no	—
345	C₂×D₄×C₈₉	—	4	4	no	—
346	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
347	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
348	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
349	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
350	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₈₉	—	2	1	no	—
353	C₂²×C₄×C₈₉	—	2	2	no	—
354	C₂²×C₄×C₈₉	—	2	2	no	—
355	C₂²×C₄×C₈₉	—	2	2	no	—
356	C₂²×C₄×C₈₉	—	2	1	no	—
357	C₂²×C₄×C₈₉	—	2	1	no	—
358	C₂²×C₄×C₈₉	—	2	2	no	—
359	C₂²×C₄×C₈₉	—	2	1	no	—
360	C₂²×C₄×C₈₉	—	2	2	no	—
361	C₂²×C₄×C₈₉	—	2	1	no	—
362	C₂²×C₄×C₈₉	—	2	2	no	—
363	C₂²×C₄×C₈₉	—	2	1	no	—
364	C₂²×C₄×C₈₉	—	2	2	no	—
365	C₂²×C₄×C₈₉	—	4	8	no	—
366	C₂²×C₄×C₈₉	—	4	4	no	—
367	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
368	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
370	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
372	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
373	SD₁₆×C₈₉	—	2	2	no	—
374	SD₁₆×C₈₉	—	4	1	no	—
375	SD₁₆×C₈₉	—	4	2	no	—
376	D₈×C₈₉	—	2	2	no	—
377	D₈×C₈₉	—	4	1	no	—
378	D₈×C₈₉	—	4	2	no	—
379	M₁₆×C₈₉	—	4	2	no	—
380	C₂×C₈×C₈₉	—	4	2	no	—
381	C₂×C₈×C₈₉	—	4	2	no	—
382	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
387	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
388	C₄⋊C₄×C₈₉	—	2	2	no	—
389	C₄⋊C₄×C₈₉	—	2	1	no	—
390	C₄⋊C₄×C₈₉	—	2	1	no	—
391	C₄⋊C₄×C₈₉	—	2	2	no	—
392	C₄⋊C₄×C₈₉	—	2	1	no	—
393	C₄⋊C₄×C₈₉	—	2	2	no	—
394	C₄⋊C₄×C₈₉	—	2	2	no	—
395	C₄⋊C₄×C₈₉	—	2	2	no	—
396	C₄⋊C₄×C₈₉	—	2	2	no	—
397	C₄⋊C₄×C₈₉	—	2	1	no	—
398	C₄⋊C₄×C₈₉	—	2	2	no	—
399	C₄⋊C₄×C₈₉	—	2	2	no	—
400	C₄⋊C₄×C₈₉	—	2	2	no	—
401	C₄⋊C₄×C₈₉	—	2	1	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	1	no	—
407	C₄⋊C₄×C₈₉	—	2	2	no	—
408	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
411	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
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	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
419	C₂²⋊C₄×C₈₉	—	2	2	no	—
420	C₂²⋊C₄×C₈₉	—	2	2	no	—
421	C₂²⋊C₄×C₈₉	—	2	1	no	—
422	C₂²⋊C₄×C₈₉	—	2	1	no	—
423	C₂²⋊C₄×C₈₉	—	2	2	no	—
424	C₂²⋊C₄×C₈₉	—	2	1	no	—
425	C₂²⋊C₄×C₈₉	—	2	2	no	—
426	C₂²⋊C₄×C₈₉	—	2	1	no	—
427	C₂²⋊C₄×C₈₉	—	2	2	no	—
428	C₂²⋊C₄×C₈₉	—	2	1	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	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	1	no	—
438	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
441	C₄²×C₈₉	—	2	2	no	—
442	C₄²×C₈₉	—	2	2	no	—
443	C₄²×C₈₉	—	2	1	no	—
444	C₄²×C₈₉	C₂×D₄	1	2	yes	—
445	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₈₉	C₂×D₄	1	2	yes	—
448	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
449	C₄²×C₈₉	C₂⁴	1	2	yes	—
450	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
451	C₂³×C₈₉	—	2	1	no	—
452	C₂³×C₈₉	—	2	1	no	—
453	C₂³×C₈₉	—	2	2	no	—
454	C₂³×C₈₉	—	2	1	no	—
455	C₂³×C₈₉	—	4	4	no	—
456	C₂³×C₈₉	—	4	2	no	—
457	C₂³×C₈₉	—	4	2	no	—
458	C₂³×C₈₉	—	4	4	no	—
459	C₂³×C₈₉	—	8	2	no	—
460	C₂³×C₈₉	—	8	1	no	—
461	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
462	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
463	Q₈×C₈₉	—	2	2	no	—
464	Q₈×C₈₉	—	2	1	no	—
465	Q₈×C₈₉	—	2	1	no	—
466	Q₈×C₈₉	—	4	4	no	—
467	Q₈×C₈₉	—	4	2	no	—
468	Q₈×C₈₉	—	4	2	no	—
469	Q₈×C₈₉	—	8	1	no	—
470	D₄×C₈₉	—	2	4	no	—
471	D₄×C₈₉	—	2	1	no	—
472	D₄×C₈₉	—	2	2	no	—
473	D₄×C₈₉	—	2	1	no	—
474	D₄×C₈₉	—	2	1	no	—
475	D₄×C₈₉	—	2	1	no	—
476	D₄×C₈₉	—	2	1	no	—
477	D₄×C₈₉	—	2	2	no	—
478	D₄×C₈₉	—	4	4	no	—
479	D₄×C₈₉	—	4	2	no	—
480	D₄×C₈₉	—	4	4	no	—
481	D₄×C₈₉	—	4	4	no	—
482	D₄×C₈₉	—	4	4	no	—
483	D₄×C₈₉	—	4	4	no	—
484	D₄×C₈₉	—	4	4	no	—
485	D₄×C₈₉	—	4	2	no	—
486	D₄×C₈₉	—	8	2	no	—
487	D₄×C₈₉	—	8	1	no	—
488	D₄×C₈₉	—	8	1	no	—
489	D₄×C₈₉	AGL(1,ℤ/8)	1	4	yes	—
490	D₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
491	C₂×C₄×C₈₉	—	2	4	no	—
492	C₂×C₄×C₈₉	—	2	2	no	—
493	C₂×C₄×C₈₉	—	2	2	no	—
494	C₂×C₄×C₈₉	—	2	1	no	—
495	C₂×C₄×C₈₉	—	2	2	no	—
496	C₂×C₄×C₈₉	—	2	1	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	1	no	—
502	C₂×C₄×C₈₉	—	2	2	no	—
503	C₂×C₄×C₈₉	—	2	1	no	—
504	C₂×C₄×C₈₉	—	2	1	no	—
505	C₂×C₄×C₈₉	—	4	2	no	—
506	C₂×C₄×C₈₉	—	4	1	no	—
507	C₂×C₄×C₈₉	—	4	2	no	—
508	C₂×C₄×C₈₉	—	4	4	no	—
509	C₂×C₄×C₈₉	—	4	4	no	—
510	C₂×C₄×C₈₉	—	4	2	no	—
511	C₂×C₄×C₈₉	—	4	4	no	—
512	C₂×C₄×C₈₉	—	4	2	no	—
513	C₂×C₄×C₈₉	—	4	4	no	—
514	C₂×C₄×C₈₉	—	4	4	no	—
515	C₂×C₄×C₈₉	—	4	2	no	—
516	C₂×C₄×C₈₉	—	4	2	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	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
526	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
529	C₈×C₈₉	—	2	1	no	—
530	C₈×C₈₉	—	2	1	no	—
531	C₈×C₈₉	—	2	1	no	—
532	C₈×C₈₉	—	2	1	no	—
533	C₈×C₈₉	—	2	2	no	—
534	C₈×C₈₉	—	2	2	no	—
535	C₂²×C₈₉	—	2	2	no	—
536	C₂²×C₈₉	—	2	2	no	—
537	C₂²×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	—	4	1	no	—
542	C₂²×C₈₉	—	4	1	no	—
543	C₂²×C₈₉	—	4	1	no	—
544	C₂²×C₈₉	—	4	2	no	—
545	C₂²×C₈₉	—	4	1	no	—
546	C₂²×C₈₉	—	4	2	no	—
547	C₂²×C₈₉	—	4	1	no	—
548	C₂²×C₈₉	—	4	1	no	—
549	C₂²×C₈₉	—	4	2	no	—
550	C₂²×C₈₉	—	4	1	no	—
551	C₂²×C₈₉	—	4	1	no	—
552	C₂²×C₈₉	—	8	8	no	—
553	C₂²×C₈₉	—	8	4	no	—
554	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	4	yes	—
555	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
556	C₄×C₈₉	—	2	1	no	—
557	C₄×C₈₉	—	2	2	no	—
558	C₄×C₈₉	—	2	1	no	—
559	C₄×C₈₉	—	2	2	no	—
560	C₄×C₈₉	—	2	1	no	—
561	C₄×C₈₉	—	2	1	no	—
562	C₄×C₈₉	—	2	2	no	—
563	C₄×C₈₉	—	4	1	no	—
564	C₄×C₈₉	—	4	2	no	—
565	C₄×C₈₉	—	4	1	no	—
566	C₄×C₈₉	—	4	1	no	—
567	C₄×C₈₉	—	4	1	no	—
568	C₄×C₈₉	—	4	2	no	—
569	C₄×C₈₉	—	4	1	no	—
570	C₄×C₈₉	—	4	2	no	—
571	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
572	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
573	C₄×C₈₉	#585	1	1	yes	characteristic
574	#62137	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
575	C₂×C₈₉	—	2	4	no	—
576	C₂×C₈₉	—	4	1	no	—
577	C₂×C₈₉	—	4	2	no	—
578	C₂×C₈₉	—	8	1	no	—
579	C₂×C₈₉	—	8	2	no	—
580	C₂×C₈₉	—	8	1	no	—
581	C₂×C₈₉	#3489	1	1	yes	characteristic
582	C₂×C₈₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
583	C₂×C₈₉	#3584	1	1	yes	characteristic
584	#3515	C₂×C₈₉	1	1	yes	characteristic, complemented
585	D₄×#41	C₂×C₈₉	1	1	yes	characteristic, complemented
586	#3386	C₂×C₈₉	1	1	yes	characteristic, complemented
587	#3384	C₂×C₈₉	1	1	yes	characteristic, complemented
588	#3368	C₂×C₈₉	1	1	yes	characteristic, complemented
589	#3366	C₂×C₈₉	1	1	yes	characteristic, complemented
590	#3345	C₂×C₈₉	1	2	yes	complemented
591	#3343	C₂×C₈₉	1	2	yes	complemented
592	#3335	C₂×C₈₉	1	1	yes	characteristic, complemented
593	#3334	C₂×C₈₉	1	1	yes	characteristic, complemented
594	#3318	C₂×C₈₉	1	2	yes	complemented
595	#3310	C₂×C₈₉	1	2	yes	complemented
596	#3295	C₂×C₈₉	1	1	yes	characteristic, complemented
597	#3294	C₂×C₈₉	1	1	yes	characteristic, complemented
598	#3251	C₂×C₈₉	1	1	yes	characteristic, complemented
599	#3247	C₂×C₈₉	1	2	yes	complemented
600	#3234	C₂×C₈₉	1	2	yes	complemented
601	#3228	C₂×C₈₉	1	1	yes	characteristic, complemented
602	#3114	C₂×C₈₉	1	2	yes	complemented
603	#3105	C₂×C₈₉	1	1	yes	characteristic, complemented
604	#3077	C₂×C₈₉	1	1	yes	characteristic, complemented
605	C₂×#478	C₂×C₈₉	1	2	yes	complemented
606	#2990	C₂×C₈₉	1	1	yes	characteristic, complemented
607	C₈₉	#62137	1	1	yes	characteristic, direct product factor, Sylow
608	C₂²×#41	—	2	1	no	—
609	#557	C₂²×C₈₉	1	1	yes	characteristic, complemented
610	#554	C₂²×C₈₉	1	1	yes	characteristic, complemented
611	#554	C₂²×C₈₉	1	1	yes	characteristic, complemented
612	#553	C₂²×C₈₉	1	2	yes	complemented
613	#552	—	2	2	no	—
614	#552	—	2	1	no	—
615	#552	C₂²×C₈₉	1	2	yes	complemented
616	#550	C₂²×C₈₉	1	1	yes	characteristic
617	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
618	#548	—	2	1	no	—
619	#547	—	2	1	no	—
620	#547	C₂²×C₈₉	1	1	yes	characteristic
621	#547	C₂²×C₈₉	1	2	yes	—
622	#547	C₂²×C₈₉	1	1	yes	characteristic, complemented
623	#546	—	2	1	no	—
624	#546	—	2	2	no	—
625	D₄²	C₂²×C₈₉	1	1	yes	characteristic
626	D₄²	C₂²×C₈₉	1	2	yes	—
627	#541	—	2	1	no	—
628	#539	—	2	2	no	—
629	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
630	#532	C₂²×C₈₉	1	1	yes	characteristic
631	#532	C₂²×C₈₉	1	2	yes	—
632	#529	C₂²×C₈₉	1	1	yes	characteristic, complemented
633	#529	C₂²×C₈₉	1	2	yes	complemented
634	C₂×#125	C₂²×C₈₉	1	2	yes	complemented
635	#525	—	2	1	no	—
636	#525	—	2	2	no	—
637	#520	—	2	1	no	—
638	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
639	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
640	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
641	#501	C₂²×C₈₉	1	2	yes	complemented
642	#501	C₂²×C₈₉	1	2	yes	complemented
643	#500	C₂²×C₈₉	1	1	yes	characteristic, complemented
644	#498	C₂²×C₈₉	1	1	yes	characteristic, complemented
645	#490	C₂²×C₈₉	1	2	yes	complemented
646	#490	C₂²×C₈₉	1	2	yes	complemented
647	#486	C₂²×C₈₉	1	1	yes	characteristic, complemented
648	#486	C₂²×C₈₉	1	1	yes	characteristic, complemented
649	#484	C₂²×C₈₉	1	1	yes	characteristic, complemented
650	#483	C₂²×C₈₉	1	2	yes	complemented
651	#482	C₂²×C₈₉	1	2	yes	complemented
652	#482	C₂²×C₈₉	1	2	yes	complemented
653	#481	C₂²×C₈₉	1	2	yes	complemented
654	#481	C₂²×C₈₉	1	1	yes	characteristic, complemented
655	#481	C₂²×C₈₉	1	2	yes	complemented
656	#480	C₂²×C₈₉	1	2	yes	complemented
657	#480	C₂²×C₈₉	1	2	yes	complemented
658	#480	C₂²×C₈₉	1	2	yes	complemented
659	#478	C₂²×C₈₉	1	1	yes	characteristic
660	#478	C₂²×C₈₉	1	2	yes	—
661	#478	C₂²×C₈₉	1	2	yes	—
662	#478	C₂²×C₈₉	1	2	yes	—
663	#478	C₂²×C₈₉	1	2	yes	complemented
664	#478	C₂²×C₈₉	1	2	yes	complemented
665	#478	C₂²×C₈₉	1	2	yes	complemented
666	#478	C₂²×C₈₉	1	2	yes	complemented
667	#478	C₂²×C₈₉	1	2	yes	complemented
668	#478	C₂²×C₈₉	1	1	yes	characteristic, complemented
669	#478	C₂²×C₈₉	1	2	yes	complemented
670	#477	C₂²×C₈₉	1	2	yes	complemented
671	#476	C₂²×C₈₉	1	1	yes	characteristic
672	#476	C₂²×C₈₉	1	1	yes	characteristic, complemented
673	#476	C₂²×C₈₉	1	2	yes	complemented
674	#475	C₂²×C₈₉	1	1	yes	characteristic, complemented
675	#474	C₂²×C₈₉	1	1	yes	characteristic
676	#474	C₂²×C₈₉	1	1	yes	characteristic, complemented
677	#474	C₂²×C₈₉	1	1	yes	characteristic, complemented
678	#469	C₂²×C₈₉	1	2	yes	complemented
679	#468	C₂²×C₈₉	1	2	yes	complemented
680	#466	C₂²×C₈₉	1	2	yes	complemented
681	#466	C₂²×C₈₉	1	2	yes	complemented
682	#465	C₂²×C₈₉	1	2	yes	complemented
683	#465	C₂²×C₈₉	1	2	yes	complemented
684	#463	C₂²×C₈₉	1	1	yes	characteristic
685	#463	C₂²×C₈₉	1	1	yes	characteristic, complemented
686	#463	C₂²×C₈₉	1	2	yes	complemented
687	#460	C₂²×C₈₉	1	2	yes	complemented
688	#460	C₂²×C₈₉	1	1	yes	characteristic, complemented
689	#459	C₂²×C₈₉	1	2	yes	complemented
690	#459	C₂²×C₈₉	1	1	yes	characteristic, complemented
691	#450	C₂²×C₈₉	1	1	yes	characteristic
692	#450	C₂²×C₈₉	1	2	yes	—
693	#447	C₂²×C₈₉	1	1	yes	characteristic
694	#447	C₂²×C₈₉	1	2	yes	—
695	#446	C₂²×C₈₉	1	1	yes	characteristic, complemented
696	#446	C₂²×C₈₉	1	1	yes	characteristic, complemented
697	#442	C₂²×C₈₉	1	2	yes	—
698	#442	C₂²×C₈₉	1	2	yes	complemented
699	#440	C₂²×C₈₉	1	2	yes	—
700	#440	C₂²×C₈₉	1	2	yes	complemented
701	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
702	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
703	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
704	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
705	#435	C₂²×C₈₉	1	2	yes	complemented
706	#435	C₂²×C₈₉	1	2	yes	complemented
707	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
708	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
709	#432	C₂²×C₈₉	1	2	yes	complemented
710	#431	C₂²×C₈₉	1	1	yes	characteristic, complemented
711	#428	C₂²×C₈₉	1	2	yes	complemented
712	C₂×#107	C₂²×C₈₉	1	2	yes	complemented
713	C₂×#106	C₂²×C₈₉	1	2	yes	complemented
714	#423	C₂²×C₈₉	1	1	yes	characteristic, complemented
715	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	complemented
716	#418	C₂²×C₈₉	1	2	yes	—
717	C₂×#102	C₂²×C₈₉	1	2	yes	—
718	C₂×#102	C₂²×C₈₉	1	2	yes	—
719	C₂×#41	—	2	1	no	—
720	C₂×#41	—	2	1	no	—
721	C₂×#41	—	2	2	no	—
722	C₂×#41	—	2	1	no	—
723	C₂×#41	—	2	2	no	—
724	C₂×#41	—	2	1	no	—
725	C₂×#41	—	4	8	no	—
726	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
727	C₂²×Q₈	—	2	1	no	—
728	C₂²×D₄	—	2	2	no	—
729	C₂²×D₄	—	2	1	no	—
730	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
731	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
732	C₂³×C₄	—	2	2	no	—
733	C₂³×C₄	—	2	1	no	—
734	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
735	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
736	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
737	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
738	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
739	C₂×D₈	C₂³×C₈₉	1	2	yes	—
740	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
741	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
742	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
743	C₄⋊Q₈	—	2	1	no	—
744	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
745	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
746	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
747	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
748	#127	C₂³×C₈₉	1	1	yes	characteristic
749	#127	C₂³×C₈₉	1	2	yes	—
750	#126	—	2	2	no	—
751	#126	—	2	2	no	—
752	#126	—	2	2	no	—
753	#126	—	2	1	no	—
754	#125	—	2	2	no	—
755	#125	—	2	2	no	—
756	#125	—	2	1	no	—
757	#125	—	2	2	no	—
758	#125	—	2	2	no	—
759	#125	C₂³×C₈₉	1	1	yes	characteristic
760	#125	C₂³×C₈₉	1	2	yes	—
761	#125	C₂³×C₈₉	1	2	yes	—
762	#125	C₂³×C₈₉	1	2	yes	—
763	#124	—	2	1	no	—
764	#124	—	2	2	no	—
765	#124	C₂³×C₈₉	1	1	yes	characteristic
766	#123	—	2	2	no	—
767	#123	—	2	1	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	C₂²⋊Q₈	—	2	1	no	—
775	C₂²⋊Q₈	—	2	1	no	—
776	C₂²⋊Q₈	—	2	1	no	—
777	C₂²⋊Q₈	—	2	1	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	1	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
785	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
786	#121	—	2	2	no	—
787	#121	—	2	2	no	—
788	#121	—	2	1	no	—
789	#121	—	2	1	no	—
790	#121	—	2	2	no	—
791	#121	—	2	1	no	—
792	#121	—	2	2	no	—
793	#121	C₂³×C₈₉	1	2	yes	—
794	#121	C₂³×C₈₉	1	1	yes	characteristic
795	#121	C₂³×C₈₉	1	2	yes	—
796	#121	C₂³×C₈₉	1	2	yes	—
797	#121	C₂³×C₈₉	1	2	yes	—
798	#120	—	2	2	no	—
799	#120	—	2	2	no	—
800	#120	—	2	2	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	—	2	1	no	—
803	C₄×Q₈	—	2	1	no	—
804	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
805	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
806	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
807	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
819	C₄×D₄	D₄×C₈₉	1	2	yes	—
820	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
821	C₄×D₄	C₂³×C₈₉	1	2	yes	—
822	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
823	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₈₉	1	2	yes	—
825	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
826	C₄×D₄	C₂³×C₈₉	1	2	yes	—
827	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₈₉	1	2	yes	—
829	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
830	C₄×D₄	C₂³×C₈₉	1	2	yes	—
831	#117	—	2	2	no	—
832	#117	—	2	1	no	—
833	#117	—	2	2	no	—
834	#117	D₄×C₈₉	1	1	yes	characteristic
835	#117	D₄×C₈₉	1	2	yes	—
836	#117	C₂³×C₈₉	1	2	yes	—
837	C₂×C₄⋊C₄	—	2	2	no	—
838	C₂×C₄⋊C₄	—	2	2	no	—
839	C₂×C₄⋊C₄	—	2	1	no	—
840	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
841	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
842	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
843	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
844	C₂×C₂²⋊C₄	—	2	2	no	—
845	C₂×C₂²⋊C₄	—	2	1	no	—
846	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
847	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
848	#107	C₂³×C₈₉	1	1	yes	characteristic
849	#107	C₂³×C₈₉	1	2	yes	—
850	#107	C₂³×C₈₉	1	2	yes	—
851	#107	C₂³×C₈₉	1	2	yes	—
852	#107	C₂³×C₈₉	1	2	yes	—
853	#107	C₂³×C₈₉	1	1	yes	characteristic
854	#107	C₂³×C₈₉	1	2	yes	—
855	#106	C₂³×C₈₉	1	1	yes	characteristic
856	#106	C₂³×C₈₉	1	2	yes	—
857	#106	C₂³×C₈₉	1	2	yes	—
858	#106	C₂³×C₈₉	1	2	yes	—
859	#106	C₂³×C₈₉	1	2	yes	—
860	#106	C₂³×C₈₉	1	1	yes	characteristic
861	#106	C₂³×C₈₉	1	2	yes	—
862	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
863	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
864	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
865	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
866	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
867	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
868	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
869	#103	C₂³×C₈₉	1	1	yes	characteristic
870	#103	C₂³×C₈₉	1	1	yes	characteristic
871	#103	C₂³×C₈₉	1	2	yes	—
872	#102	C₂³×C₈₉	1	1	yes	characteristic
873	#102	C₂³×C₈₉	1	1	yes	characteristic
874	#102	C₂³×C₈₉	1	2	yes	—
875	#102	C₂³×C₈₉	1	2	yes	—
876	#102	C₂³×C₈₉	1	2	yes	—
877	#102	C₂³×C₈₉	1	2	yes	—
878	#102	C₂³×C₈₉	1	2	yes	—
879	#102	C₂³×C₈₉	1	2	yes	—
880	#102	C₂³×C₈₉	1	2	yes	—
881	#102	C₂³×C₈₉	1	2	yes	—
882	#102	C₂³×C₈₉	1	1	yes	characteristic
883	#102	C₂³×C₈₉	1	1	yes	characteristic
884	#102	C₂³×C₈₉	1	1	yes	characteristic
885	#102	C₂³×C₈₉	1	1	yes	characteristic
886	#102	C₂³×C₈₉	1	2	yes	—
887	#102	C₂³×C₈₉	1	2	yes	—
888	#102	C₂³×C₈₉	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
890	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
891	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
892	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
893	#97	C₂³×C₈₉	1	2	yes	—
894	#97	C₂³×C₈₉	1	2	yes	—
895	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
896	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
897	C₂⁴	—	2	1	no	—
898	C₂⁴	—	2	2	no	—
899	#41	—	2	4	no	—
900	#41	—	4	8	no	—
901	#41	—	4	4	no	—
902	#41	—	4	8	no	—
903	#41	—	4	4	no	—
904	#41	—	4	4	no	—
905	#41	—	4	4	no	—
906	C₂×Q₈	—	2	1	no	—
907	C₂×Q₈	—	2	2	no	—
908	C₂×Q₈	—	2	1	no	—
909	C₂×Q₈	—	2	1	no	—
910	C₂×Q₈	—	4	4	no	—
911	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
912	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
913	C₂×D₄	—	2	4	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	1	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	2	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	4	2	no	—
927	C₂×D₄	—	4	1	no	—
928	C₂×D₄	—	4	8	no	—
929	C₂×D₄	—	4	4	no	—
930	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
931	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
932	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
933	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
934	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
935	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	4	8	no	—
950	C₂²×C₄	—	4	4	no	—
951	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
952	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
953	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
954	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
956	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
957	SD₁₆	—	2	2	no	—
958	SD₁₆	—	4	1	no	—
959	SD₁₆	—	4	2	no	—
960	D₈	—	2	2	no	—
961	D₈	—	4	1	no	—
962	D₈	—	4	2	no	—
963	M₁₆	—	4	2	no	—
964	C₂×C₈	—	4	2	no	—
965	C₂×C₈	—	4	2	no	—
966	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
967	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
968	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
969	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
971	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
993	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
994	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
995	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
996	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
998	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1000	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1001	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1002	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	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	C₂×D₄×C₈₉	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1025	C₄²	—	2	2	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1029	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1030	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1031	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1032	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1033	C₄²	C₂⁴×C₈₉	1	2	yes	—
1034	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	1	no	—
1037	C₂³	—	2	2	no	—
1038	C₂³	—	2	1	no	—
1039	C₂³	—	4	4	no	—
1040	C₂³	—	4	2	no	—
1041	C₂³	—	4	2	no	—
1042	C₂³	—	4	4	no	—
1043	C₂³	—	8	2	no	—
1044	C₂³	—	8	1	no	—
1045	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1046	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1047	Q₈	—	2	2	no	—
1048	Q₈	—	2	1	no	—
1049	Q₈	—	2	1	no	—
1050	Q₈	—	4	4	no	—
1051	Q₈	—	4	2	no	—
1052	Q₈	—	4	2	no	—
1053	Q₈	—	8	1	no	—
1054	D₄	—	2	4	no	—
1055	D₄	—	2	1	no	—
1056	D₄	—	2	2	no	—
1057	D₄	—	2	1	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	4	4	no	—
1063	D₄	—	4	2	no	—
1064	D₄	—	4	4	no	—
1065	D₄	—	4	4	no	—
1066	D₄	—	4	4	no	—
1067	D₄	—	4	4	no	—
1068	D₄	—	4	4	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	8	2	no	—
1071	D₄	—	8	1	no	—
1072	D₄	—	8	1	no	—
1073	D₄	AGL(1,ℤ/8)×C₈₉	1	4	yes	—
1074	D₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
1075	C₂×C₄	—	2	4	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	1	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	4	no	—
1093	C₂×C₄	—	4	4	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	4	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	4	no	—
1098	C₂×C₄	—	4	4	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	4	2	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1105	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1106	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
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	2	yes	—
1111	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1112	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1113	C₈	—	2	1	no	—
1114	C₈	—	2	1	no	—
1115	C₈	—	2	1	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	2	no	—
1118	C₈	—	2	2	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	1	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	4	1	no	—
1131	C₂²	—	4	2	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	2	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	8	8	no	—
1137	C₂²	—	8	4	no	—
1138	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	4	yes	—
1139	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
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	—	2	1	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	2	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	4	2	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	2	no	—
1154	C₄	—	4	1	no	—
1155	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	2	yes	—
1156	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
1157	C₄	#585×C₈₉	1	1	yes	characteristic
1158	C₂	—	2	4	no	—
1159	C₂	—	4	1	no	—
1160	C₂	—	4	2	no	—
1161	C₂	—	8	1	no	—
1162	C₂	—	8	2	no	—
1163	C₂	—	8	1	no	—
1164	C₂	C₈₉×#3489	1	1	yes	characteristic
1165	C₂	C₂²×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
1166	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×#3515	C₂	semidirect
2. D₄×#41×C₈₉	C₂	semidirect
3. C₈₉×#3386	C₂	semidirect
4. C₈₉×#3384	C₂	semidirect
5. C₈₉×#3368	C₂	semidirect
6. C₈₉×#3366	C₂	semidirect
7. C₈₉×#3345	C₂	semidirect
8. C₈₉×#3343	C₂	semidirect
9. C₈₉×#3335	C₂	semidirect
10. C₈₉×#3334	C₂	semidirect
11. C₈₉×#3318	C₂	semidirect
12. C₈₉×#3310	C₂	semidirect
13. C₈₉×#3295	C₂	semidirect
14. C₈₉×#3294	C₂	semidirect
15. C₈₉×#3251	C₂	semidirect
16. C₈₉×#3247	C₂	semidirect
17. C₈₉×#3234	C₂	semidirect
18. C₈₉×#3228	C₂	semidirect
19. C₈₉×#3114	C₂	semidirect
20. C₈₉×#3105	C₂	semidirect
21. C₈₉×#3077	C₂	semidirect
22. C₂×#478×C₈₉	C₂	semidirect
23. C₈₉×#2990	C₂	semidirect
25. #557×C₈₉	C₂²	semidirect
26. #554×C₈₉	C₂²	semidirect
27. #554×C₈₉	C₂²	semidirect
28. #553×C₈₉	C₂²	semidirect
31. #552×C₈₉	C₂²	semidirect
38. #547×C₈₉	C₂²	semidirect
45. #533×C₈₉	C₂²	semidirect
48. #529×C₈₉	C₂²	semidirect
49. #529×C₈₉	C₂²	semidirect
50. C₂×#125×C₈₉	C₂²	semidirect
57. #501×C₈₉	C₂²	semidirect
58. #501×C₈₉	C₂²	semidirect
59. #500×C₈₉	C₂²	semidirect
60. #498×C₈₉	C₂²	semidirect
61. #490×C₈₉	C₂²	semidirect
62. #490×C₈₉	C₂²	semidirect
63. #486×C₈₉	C₂²	semidirect
64. #486×C₈₉	C₂²	semidirect
65. #484×C₈₉	C₂²	semidirect
66. #483×C₈₉	C₂²	semidirect
67. #482×C₈₉	C₂²	semidirect
68. #482×C₈₉	C₂²	semidirect
69. #481×C₈₉	C₂²	semidirect
70. #481×C₈₉	C₂²	semidirect
71. #481×C₈₉	C₂²	semidirect
72. #480×C₈₉	C₂²	semidirect
73. #480×C₈₉	C₂²	semidirect
74. #480×C₈₉	C₂²	semidirect
79. #478×C₈₉	C₂²	semidirect
80. #478×C₈₉	C₂²	semidirect
81. #478×C₈₉	C₂²	semidirect
82. #478×C₈₉	C₂²	semidirect
83. #478×C₈₉	C₂²	semidirect
84. #478×C₈₉	C₂²	semidirect
85. #478×C₈₉	C₂²	semidirect
86. #477×C₈₉	C₂²	semidirect
88. #476×C₈₉	C₂²	semidirect
89. #476×C₈₉	C₂²	semidirect
90. #475×C₈₉	C₂²	semidirect
92. #474×C₈₉	C₂²	semidirect
93. #474×C₈₉	C₂²	semidirect
94. #469×C₈₉	C₂²	semidirect
95. #468×C₈₉	C₂²	semidirect
96. #466×C₈₉	C₂²	semidirect
97. #466×C₈₉	C₂²	semidirect
98. #465×C₈₉	C₂²	semidirect
99. #465×C₈₉	C₂²	semidirect
101. #463×C₈₉	C₂²	semidirect
102. #463×C₈₉	C₂²	semidirect
103. #460×C₈₉	C₂²	semidirect
104. #460×C₈₉	C₂²	semidirect
105. #459×C₈₉	C₂²	semidirect
106. #459×C₈₉	C₂²	semidirect
111. #446×C₈₉	C₂²	semidirect
112. #446×C₈₉	C₂²	semidirect
114. #442×C₈₉	C₂²	semidirect
116. #440×C₈₉	C₂²	semidirect
118. C₄×SD₁₆×C₈₉	C₂²	semidirect
120. C₄×D₈×C₈₉	C₂²	semidirect
121. #435×C₈₉	C₂²	semidirect
122. #435×C₈₉	C₂²	semidirect
123. C₈×D₄×C₈₉	C₂²	semidirect
124. C₈×D₄×C₈₉	C₂²	semidirect
125. #432×C₈₉	C₂²	semidirect
126. #431×C₈₉	C₂²	semidirect
127. #428×C₈₉	C₂²	semidirect
128. C₂×#107×C₈₉	C₂²	semidirect
129. C₂×#106×C₈₉	C₂²	semidirect
130. #423×C₈₉	C₂²	semidirect
131. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
574. #62137	C₈₉	direct (N × H)
584. #3515	C₂×C₈₉	semidirect
585. D₄×#41	C₂×C₈₉	semidirect
586. #3386	C₂×C₈₉	semidirect
587. #3384	C₂×C₈₉	semidirect
588. #3368	C₂×C₈₉	semidirect
589. #3366	C₂×C₈₉	semidirect
590. #3345	C₂×C₈₉	semidirect
591. #3343	C₂×C₈₉	semidirect
592. #3335	C₂×C₈₉	semidirect
593. #3334	C₂×C₈₉	semidirect
594. #3318	C₂×C₈₉	semidirect
595. #3310	C₂×C₈₉	semidirect
596. #3295	C₂×C₈₉	semidirect
597. #3294	C₂×C₈₉	semidirect
598. #3251	C₂×C₈₉	semidirect
599. #3247	C₂×C₈₉	semidirect
600. #3234	C₂×C₈₉	semidirect
601. #3228	C₂×C₈₉	semidirect
602. #3114	C₂×C₈₉	semidirect
603. #3105	C₂×C₈₉	semidirect
604. #3077	C₂×C₈₉	semidirect
605. C₂×#478	C₂×C₈₉	semidirect
606. #2990	C₂×C₈₉	semidirect
607. C₈₉	#62137	direct (N × H)
609. #557	C₂²×C₈₉	semidirect
610. #554	C₂²×C₈₉	semidirect
611. #554	C₂²×C₈₉	semidirect
612. #553	C₂²×C₈₉	semidirect
615. #552	C₂²×C₈₉	semidirect
622. #547	C₂²×C₈₉	semidirect
629. #533	C₂²×C₈₉	semidirect
632. #529	C₂²×C₈₉	semidirect
633. #529	C₂²×C₈₉	semidirect
634. C₂×#125	C₂²×C₈₉	semidirect
641. #501	C₂²×C₈₉	semidirect
642. #501	C₂²×C₈₉	semidirect
643. #500	C₂²×C₈₉	semidirect
644. #498	C₂²×C₈₉	semidirect
645. #490	C₂²×C₈₉	semidirect
646. #490	C₂²×C₈₉	semidirect
647. #486	C₂²×C₈₉	semidirect
648. #486	C₂²×C₈₉	semidirect
649. #484	C₂²×C₈₉	semidirect
650. #483	C₂²×C₈₉	semidirect
651. #482	C₂²×C₈₉	semidirect
652. #482	C₂²×C₈₉	semidirect
653. #481	C₂²×C₈₉	semidirect
654. #481	C₂²×C₈₉	semidirect
655. #481	C₂²×C₈₉	semidirect
656. #480	C₂²×C₈₉	semidirect
657. #480	C₂²×C₈₉	semidirect
658. #480	C₂²×C₈₉	semidirect
663. #478	C₂²×C₈₉	semidirect
664. #478	C₂²×C₈₉	semidirect
665. #478	C₂²×C₈₉	semidirect
666. #478	C₂²×C₈₉	semidirect
667. #478	C₂²×C₈₉	semidirect
668. #478	C₂²×C₈₉	semidirect
669. #478	C₂²×C₈₉	semidirect
670. #477	C₂²×C₈₉	semidirect
672. #476	C₂²×C₈₉	semidirect
673. #476	C₂²×C₈₉	semidirect
674. #475	C₂²×C₈₉	semidirect
676. #474	C₂²×C₈₉	semidirect
677. #474	C₂²×C₈₉	semidirect
678. #469	C₂²×C₈₉	semidirect
679. #468	C₂²×C₈₉	semidirect
680. #466	C₂²×C₈₉	semidirect
681. #466	C₂²×C₈₉	semidirect
682. #465	C₂²×C₈₉	semidirect
683. #465	C₂²×C₈₉	semidirect
685. #463	C₂²×C₈₉	semidirect
686. #463	C₂²×C₈₉	semidirect
687. #460	C₂²×C₈₉	semidirect
688. #460	C₂²×C₈₉	semidirect
689. #459	C₂²×C₈₉	semidirect
690. #459	C₂²×C₈₉	semidirect
695. #446	C₂²×C₈₉	semidirect
696. #446	C₂²×C₈₉	semidirect
698. #442	C₂²×C₈₉	semidirect
700. #440	C₂²×C₈₉	semidirect
702. C₄×SD₁₆	C₂²×C₈₉	semidirect
704. C₄×D₈	C₂²×C₈₉	semidirect
705. #435	C₂²×C₈₉	semidirect
706. #435	C₂²×C₈₉	semidirect
707. C₈×D₄	C₂²×C₈₉	semidirect
708. C₈×D₄	C₂²×C₈₉	semidirect
709. #432	C₂²×C₈₉	semidirect
710. #431	C₂²×C₈₉	semidirect
711. #428	C₂²×C₈₉	semidirect
712. C₂×#107	C₂²×C₈₉	semidirect
713. C₂×#106	C₂²×C₈₉	semidirect
714. #423	C₂²×C₈₉	semidirect
715. C₂×C₄⋊C₈	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×#3515	2
D₄×#41×C₈₉	2
C₈₉×#3386	2
C₈₉×#3384	2
C₈₉×#3368	2
C₈₉×#3366	2
C₈₉×#3345	2
C₈₉×#3343	2
C₈₉×#3335	2
C₈₉×#3334	2
C₈₉×#3318	2
C₈₉×#3310	2
C₈₉×#3295	2
C₈₉×#3294	2
C₈₉×#3251	2
C₈₉×#3247	2
C₈₉×#3234	2
C₈₉×#3228	2
C₈₉×#3114	2
C₈₉×#3105	2
C₈₉×#3077	2
C₂×#478×C₈₉	2
C₈₉×#2990	2
#62137	89

Subgroups — C89×#62137 #36439985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62137 #36439985