Subgroups — C₈₉×#61608 #36439456

Order 22784.

2132 conjugacy classes of subgroups.

The subgroup lattice has 1230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3328	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3324	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3321	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3319	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3304	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3302	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3287	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3284	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3278	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3274	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3269	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3267	C₂	1	2	yes	maximal, complemented
15	C₈₉×#3216	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#3207	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3197	C₂	1	2	yes	maximal, complemented
18	C₈₉×#3191	C₂	1	2	yes	maximal, complemented
19	C₈₉×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₉×#3107	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#3005	C₂	1	2	yes	maximal, complemented
22	C₈₉×#3002	C₂	1	2	yes	maximal, complemented
23	C₈₉×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₈₉	C₂²	1	2	yes	—
25	C₂×#137×C₈₉	C₂²	1	2	yes	complemented
26	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	complemented
27	C₂×#135×C₈₉	C₂²	1	2	yes	complemented
28	C₂×#135×C₈₉	C₂²	1	2	yes	complemented
29	#559×C₈₉	—	2	1	no	—
30	#559×C₈₉	—	2	1	no	—
31	#556×C₈₉	C₂²	1	1	yes	characteristic
32	#556×C₈₉	C₂²	1	1	yes	characteristic, complemented
33	#555×C₈₉	C₂²	1	2	yes	complemented
34	#553×C₈₉	—	2	2	no	—
35	#550×C₈₉	C₂²	1	1	yes	characteristic
36	#550×C₈₉	C₂²	1	1	yes	characteristic
37	#550×C₈₉	C₂²	1	1	yes	characteristic, complemented
38	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
39	#548×C₈₉	C₂²	1	2	yes	—
40	#547×C₈₉	—	2	1	no	—
41	#547×C₈₉	C₂²	1	1	yes	characteristic
42	#547×C₈₉	C₂²	1	2	yes	complemented
43	#546×C₈₉	—	2	2	no	—
44	#546×C₈₉	C₂²	1	2	yes	—
45	D₄²×C₈₉	—	2	1	no	—
46	D₄²×C₈₉	C₂²	1	1	yes	characteristic
47	#538×C₈₉	—	2	2	no	—
48	#535×C₈₉	—	2	1	no	—
49	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
50	#532×C₈₉	—	2	1	no	—
51	#532×C₈₉	C₂²	1	1	yes	characteristic
52	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	#525×C₈₉	—	2	2	no	—
54	#525×C₈₉	C₂²	1	2	yes	—
55	#525×C₈₉	C₂²	1	2	yes	complemented
56	#525×C₈₉	C₂²	1	2	yes	complemented
57	#520×C₈₉	—	2	1	no	—
58	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄×C₈₉	—	2	1	no	—
60	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
61	#497×C₈₉	C₂²	1	2	yes	complemented
62	#493×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	#492×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	#489×C₈₉	C₂²	1	2	yes	complemented
65	#487×C₈₉	C₂²	1	1	yes	characteristic, complemented
66	#486×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#485×C₈₉	C₂²	1	2	yes	complemented
68	#485×C₈₉	C₂²	1	2	yes	complemented
69	#485×C₈₉	C₂²	1	1	yes	characteristic, complemented
70	#485×C₈₉	C₂²	1	1	yes	characteristic, complemented
71	#482×C₈₉	C₂²	1	2	yes	complemented
72	#482×C₈₉	C₂²	1	2	yes	complemented
73	#482×C₈₉	C₂²	1	2	yes	complemented
74	#475×C₈₉	C₂²	1	1	yes	characteristic, complemented
75	#475×C₈₉	C₂²	1	1	yes	characteristic, complemented
76	#474×C₈₉	C₂²	1	1	yes	characteristic, complemented
77	#474×C₈₉	C₂²	1	1	yes	characteristic, complemented
78	#470×C₈₉	C₂²	1	2	yes	complemented
79	#469×C₈₉	C₂²	1	2	yes	complemented
80	#468×C₈₉	C₂²	1	2	yes	complemented
81	#468×C₈₉	C₂²	1	2	yes	complemented
82	#467×C₈₉	C₂²	1	2	yes	complemented
83	#466×C₈₉	C₂²	1	2	yes	complemented
84	#465×C₈₉	C₂²	1	2	yes	complemented
85	#465×C₈₉	C₂²	1	2	yes	complemented
86	#463×C₈₉	C₂²	1	2	yes	complemented
87	#463×C₈₉	C₂²	1	2	yes	complemented
88	#462×C₈₉	C₂²	1	1	yes	characteristic, complemented
89	#462×C₈₉	C₂²	1	1	yes	characteristic, complemented
90	#462×C₈₉	C₂²	1	1	yes	characteristic, complemented
91	#461×C₈₉	C₂²	1	1	yes	characteristic, complemented
92	#460×C₈₉	C₂²	1	1	yes	characteristic, complemented
93	#460×C₈₉	C₂²	1	1	yes	characteristic, complemented
94	#460×C₈₉	C₂²	1	1	yes	characteristic, complemented
95	#459×C₈₉	C₂²	1	1	yes	characteristic, complemented
96	#452×C₈₉	C₂²	1	1	yes	characteristic
97	#452×C₈₉	C₂²	1	1	yes	characteristic
98	#452×C₈₉	C₂²	1	2	yes	complemented
99	#452×C₈₉	C₂²	1	2	yes	complemented
100	#452×C₈₉	C₂²	1	2	yes	complemented
101	#452×C₈₉	C₂²	1	2	yes	complemented
102	#452×C₈₉	C₂²	1	2	yes	complemented
103	#452×C₈₉	C₂²	1	2	yes	complemented
104	#451×C₈₉	C₂²	1	2	yes	complemented
105	#450×C₈₉	C₂²	1	2	yes	complemented
106	#449×C₈₉	C₂²	1	2	yes	—
107	#449×C₈₉	C₂²	1	2	yes	complemented
108	#449×C₈₉	C₂²	1	2	yes	complemented
109	#449×C₈₉	C₂²	1	2	yes	complemented
110	#449×C₈₉	C₂²	1	2	yes	complemented
111	#449×C₈₉	C₂²	1	2	yes	complemented
112	#449×C₈₉	C₂²	1	2	yes	complemented
113	#448×C₈₉	C₂²	1	2	yes	complemented
114	#447×C₈₉	C₂²	1	2	yes	complemented
115	#442×C₈₉	C₂²	1	2	yes	complemented
116	#440×C₈₉	C₂²	1	2	yes	complemented
117	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
120	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
121	#436×C₈₉	C₂²	1	1	yes	characteristic
122	#436×C₈₉	C₂²	1	1	yes	characteristic
123	#435×C₈₉	C₂²	1	2	yes	complemented
124	#435×C₈₉	C₂²	1	2	yes	complemented
125	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
126	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
127	#432×C₈₉	C₂²	1	1	yes	characteristic, complemented
128	#431×C₈₉	C₂²	1	1	yes	characteristic, complemented
129	#419×C₈₉	C₂²	1	2	yes	complemented
130	#418×C₈₉	C₂²	1	2	yes	complemented
131	#416×C₈₉	C₂²	1	2	yes	complemented
132	#416×C₈₉	C₂²	1	2	yes	complemented
133	#407×C₈₉	C₂²	1	2	yes	complemented
134	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	complemented
135	C₂×#41×C₈₉	—	2	1	no	—
136	C₂×#41×C₈₉	—	2	2	no	—
137	C₂×#41×C₈₉	—	2	2	no	—
138	C₂×#41×C₈₉	—	4	4	no	—
139	C₂×#41×C₈₉	—	4	4	no	—
140	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
141	C₂×#41×C₈₉	C₂³	1	2	yes	—
142	C₂×#41×C₈₉	C₂³	1	2	yes	—
143	C₂×#41×C₈₉	C₂³	1	2	yes	—
144	C₂×#41×C₈₉	C₂³	1	2	yes	—
145	C₂×#41×C₈₉	C₂³	1	2	yes	—
146	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
147	C₂²×D₄×C₈₉	—	2	2	no	—
148	C₂²×D₄×C₈₉	—	2	1	no	—
149	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
150	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
151	C₂³×C₄×C₈₉	—	2	2	no	—
152	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
153	#137×C₈₉	—	4	4	no	—
154	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
155	#135×C₈₉	—	4	4	no	—
156	#135×C₈₉	—	4	4	no	—
157	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
158	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
159	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
160	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
162	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
163	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
167	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
168	C₂×D₈×C₈₉	C₂³	1	2	yes	—
169	C₂×D₈×C₈₉	C₂³	1	2	yes	—
170	C₂×D₈×C₈₉	C₂³	1	2	yes	—
171	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
172	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
173	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
174	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
175	C₄⋊Q₈×C₈₉	—	2	1	no	—
176	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
177	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
178	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
179	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
180	#127×C₈₉	—	2	1	no	—
181	#127×C₈₉	—	2	1	no	—
182	#127×C₈₉	—	2	1	no	—
183	#127×C₈₉	C₂³	1	1	yes	characteristic
184	#127×C₈₉	C₂³	1	1	yes	characteristic
185	#126×C₈₉	—	2	2	no	—
186	#126×C₈₉	—	2	2	no	—
187	#125×C₈₉	—	2	1	no	—
188	#124×C₈₉	—	2	1	no	—
189	#124×C₈₉	—	2	1	no	—
190	#124×C₈₉	—	2	2	no	—
191	#124×C₈₉	—	2	2	no	—
192	#124×C₈₉	—	2	2	no	—
193	#124×C₈₉	—	2	1	no	—
194	#124×C₈₉	C₂³	1	2	yes	—
195	#123×C₈₉	—	2	2	no	—
196	#123×C₈₉	—	2	2	no	—
197	#123×C₈₉	—	2	2	no	—
198	#123×C₈₉	—	2	2	no	—
199	#123×C₈₉	—	2	2	no	—
200	#123×C₈₉	—	2	2	no	—
201	#123×C₈₉	—	2	2	no	—
202	C₂²⋊Q₈×C₈₉	—	2	1	no	—
203	C₂²⋊Q₈×C₈₉	—	2	2	no	—
204	C₂²⋊Q₈×C₈₉	—	2	2	no	—
205	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
206	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
207	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
208	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
209	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
211	#121×C₈₉	—	2	2	no	—
212	#121×C₈₉	—	2	1	no	—
213	#121×C₈₉	—	2	2	no	—
214	#121×C₈₉	—	2	2	no	—
215	#121×C₈₉	—	2	1	no	—
216	#121×C₈₉	—	2	1	no	—
217	#121×C₈₉	—	2	1	no	—
218	#121×C₈₉	—	2	1	no	—
219	#121×C₈₉	—	2	2	no	—
220	#121×C₈₉	—	2	2	no	—
221	#121×C₈₉	—	2	2	no	—
222	#121×C₈₉	—	2	2	no	—
223	#121×C₈₉	C₂³	1	2	yes	—
224	#121×C₈₉	C₂³	1	2	yes	—
225	#121×C₈₉	C₂³	1	2	yes	—
226	#121×C₈₉	C₂³	1	2	yes	—
227	#121×C₈₉	C₂³	1	2	yes	—
228	#120×C₈₉	—	2	2	no	—
229	#120×C₈₉	—	2	2	no	—
230	#120×C₈₉	—	2	2	no	—
231	#120×C₈₉	—	2	2	no	—
232	#120×C₈₉	—	2	2	no	—
233	C₄×Q₈×C₈₉	—	2	1	no	—
234	C₄×Q₈×C₈₉	—	2	1	no	—
235	C₄×Q₈×C₈₉	—	2	1	no	—
236	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₈₉	—	2	1	no	—
241	C₄×D₄×C₈₉	—	2	2	no	—
242	C₄×D₄×C₈₉	—	2	1	no	—
243	C₄×D₄×C₈₉	—	2	1	no	—
244	C₄×D₄×C₈₉	—	2	2	no	—
245	C₄×D₄×C₈₉	—	2	2	no	—
246	C₄×D₄×C₈₉	—	2	2	no	—
247	C₄×D₄×C₈₉	—	2	2	no	—
248	C₄×D₄×C₈₉	—	2	2	no	—
249	C₄×D₄×C₈₉	—	2	1	no	—
250	C₄×D₄×C₈₉	—	2	1	no	—
251	C₄×D₄×C₈₉	—	2	1	no	—
252	C₄×D₄×C₈₉	—	2	2	no	—
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	D₄	1	1	yes	characteristic
257	C₄×D₄×C₈₉	D₄	1	2	yes	—
258	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
259	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₈₉	C₂³	1	2	yes	—
261	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
263	C₄×D₄×C₈₉	C₂³	1	2	yes	—
264	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
265	#117×C₈₉	—	2	1	no	—
266	#117×C₈₉	—	2	2	no	—
267	#117×C₈₉	—	2	1	no	—
268	#117×C₈₉	C₂³	1	2	yes	—
269	#117×C₈₉	C₂³	1	2	yes	—
270	#117×C₈₉	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
272	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
273	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
275	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
276	C₂×C₄²×C₈₉	—	2	1	no	—
277	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
278	#107×C₈₉	C₂³	1	1	yes	characteristic
279	#107×C₈₉	C₂³	1	1	yes	characteristic
280	#107×C₈₉	C₂³	1	2	yes	—
281	#106×C₈₉	C₂³	1	1	yes	characteristic
282	#106×C₈₉	C₂³	1	1	yes	characteristic
283	#106×C₈₉	C₂³	1	2	yes	—
284	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
285	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
286	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
288	#103×C₈₉	C₂³	1	1	yes	characteristic
289	#103×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
294	#103×C₈₉	C₂³	1	2	yes	—
295	#103×C₈₉	C₂³	1	1	yes	characteristic
296	#103×C₈₉	C₂³	1	1	yes	characteristic
297	#103×C₈₉	C₂³	1	1	yes	characteristic
298	#103×C₈₉	C₂³	1	1	yes	characteristic
299	#102×C₈₉	C₂³	1	1	yes	characteristic
300	#102×C₈₉	C₂³	1	2	yes	—
301	#102×C₈₉	C₂³	1	2	yes	—
302	#102×C₈₉	C₂³	1	2	yes	—
303	#102×C₈₉	C₂³	1	1	yes	characteristic
304	#102×C₈₉	C₂³	1	2	yes	—
305	#102×C₈₉	C₂³	1	2	yes	—
306	#102×C₈₉	C₂³	1	2	yes	—
307	#102×C₈₉	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
312	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
313	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
314	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
315	#97×C₈₉	C₂³	1	2	yes	—
316	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
318	C₂⁴×C₈₉	—	2	2	no	—
319	C₂⁴×C₈₉	C₂×D₄	1	2	yes	—
320	#41×C₈₉	—	2	2	no	—
321	#41×C₈₉	—	2	2	no	—
322	#41×C₈₉	—	2	4	no	—
323	#41×C₈₉	—	2	4	no	—
324	#41×C₈₉	—	4	2	no	—
325	#41×C₈₉	—	4	2	no	—
326	#41×C₈₉	—	4	2	no	—
327	#41×C₈₉	—	4	2	no	—
328	#41×C₈₉	—	4	4	no	—
329	#41×C₈₉	—	4	8	no	—
330	#41×C₈₉	—	4	2	no	—
331	#41×C₈₉	—	4	2	no	—
332	#41×C₈₉	—	4	2	no	—
333	#41×C₈₉	—	4	2	no	—
334	#41×C₈₉	—	4	8	no	—
335	C₂×Q₈×C₈₉	—	2	1	no	—
336	C₂×Q₈×C₈₉	—	2	2	no	—
337	C₂×Q₈×C₈₉	—	2	1	no	—
338	C₂×Q₈×C₈₉	—	2	4	no	—
339	C₂×Q₈×C₈₉	—	4	2	no	—
340	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
341	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
342	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
343	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
344	C₂×D₄×C₈₉	—	2	1	no	—
345	C₂×D₄×C₈₉	—	2	4	no	—
346	C₂×D₄×C₈₉	—	2	2	no	—
347	C₂×D₄×C₈₉	—	2	2	no	—
348	C₂×D₄×C₈₉	—	2	2	no	—
349	C₂×D₄×C₈₉	—	2	2	no	—
350	C₂×D₄×C₈₉	—	2	2	no	—
351	C₂×D₄×C₈₉	—	2	2	no	—
352	C₂×D₄×C₈₉	—	2	2	no	—
353	C₂×D₄×C₈₉	—	2	2	no	—
354	C₂×D₄×C₈₉	—	2	2	no	—
355	C₂×D₄×C₈₉	—	2	2	no	—
356	C₂×D₄×C₈₉	—	2	1	no	—
357	C₂×D₄×C₈₉	—	2	1	no	—
358	C₂×D₄×C₈₉	—	2	2	no	—
359	C₂×D₄×C₈₉	—	2	1	no	—
360	C₂×D₄×C₈₉	—	2	1	no	—
361	C₂×D₄×C₈₉	—	4	2	no	—
362	C₂×D₄×C₈₉	—	4	2	no	—
363	C₂×D₄×C₈₉	—	4	4	no	—
364	C₂×D₄×C₈₉	—	4	8	no	—
365	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
366	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
367	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
368	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
369	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
370	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₈₉	—	2	1	no	—
372	C₂²×C₄×C₈₉	—	2	2	no	—
373	C₂²×C₄×C₈₉	—	2	1	no	—
374	C₂²×C₄×C₈₉	—	2	2	no	—
375	C₂²×C₄×C₈₉	—	2	2	no	—
376	C₂²×C₄×C₈₉	—	2	2	no	—
377	C₂²×C₄×C₈₉	—	2	2	no	—
378	C₂²×C₄×C₈₉	—	2	1	no	—
379	C₂²×C₄×C₈₉	—	2	2	no	—
380	C₂²×C₄×C₈₉	—	2	2	no	—
381	C₂²×C₄×C₈₉	—	4	2	no	—
382	C₂²×C₄×C₈₉	—	4	2	no	—
383	C₂²×C₄×C₈₉	—	4	8	no	—
384	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
387	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
388	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
389	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
391	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
392	Q₁₆×C₈₉	—	2	2	no	—
393	Q₁₆×C₈₉	—	2	2	no	—
394	Q₁₆×C₈₉	—	4	2	no	—
395	Q₁₆×C₈₉	—	4	2	no	—
396	SD₁₆×C₈₉	—	2	4	no	—
397	SD₁₆×C₈₉	—	2	2	no	—
398	SD₁₆×C₈₉	—	2	2	no	—
399	SD₁₆×C₈₉	—	4	2	no	—
400	SD₁₆×C₈₉	—	4	2	no	—
401	SD₁₆×C₈₉	—	4	2	no	—
402	SD₁₆×C₈₉	—	4	2	no	—
403	D₈×C₈₉	—	2	4	no	—
404	D₈×C₈₉	—	4	2	no	—
405	D₈×C₈₉	—	4	2	no	—
406	M₁₆×C₈₉	—	4	2	no	—
407	M₁₆×C₈₉	—	4	2	no	—
408	C₂×C₈×C₈₉	—	4	2	no	—
409	C₂×C₈×C₈₉	—	4	2	no	—
410	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
411	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
412	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
413	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
414	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
415	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
416	C₄⋊C₄×C₈₉	—	2	1	no	—
417	C₄⋊C₄×C₈₉	—	2	1	no	—
418	C₄⋊C₄×C₈₉	—	2	2	no	—
419	C₄⋊C₄×C₈₉	—	2	2	no	—
420	C₄⋊C₄×C₈₉	—	2	2	no	—
421	C₄⋊C₄×C₈₉	—	2	1	no	—
422	C₄⋊C₄×C₈₉	—	2	1	no	—
423	C₄⋊C₄×C₈₉	—	2	1	no	—
424	C₄⋊C₄×C₈₉	—	2	1	no	—
425	C₄⋊C₄×C₈₉	—	2	1	no	—
426	C₄⋊C₄×C₈₉	—	2	1	no	—
427	C₄⋊C₄×C₈₉	—	2	2	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	C₂×D₄	1	2	yes	—
433	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
434	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
435	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
436	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
440	C₂²⋊C₄×C₈₉	—	2	2	no	—
441	C₂²⋊C₄×C₈₉	—	2	1	no	—
442	C₂²⋊C₄×C₈₉	—	2	1	no	—
443	C₂²⋊C₄×C₈₉	—	2	1	no	—
444	C₂²⋊C₄×C₈₉	—	2	2	no	—
445	C₂²⋊C₄×C₈₉	—	2	2	no	—
446	C₂²⋊C₄×C₈₉	—	2	2	no	—
447	C₂²⋊C₄×C₈₉	—	2	2	no	—
448	C₂²⋊C₄×C₈₉	—	2	2	no	—
449	C₂²⋊C₄×C₈₉	—	2	2	no	—
450	C₂²⋊C₄×C₈₉	—	2	2	no	—
451	C₂²⋊C₄×C₈₉	—	2	2	no	—
452	C₂²⋊C₄×C₈₉	—	2	2	no	—
453	C₂²⋊C₄×C₈₉	—	2	1	no	—
454	C₂²⋊C₄×C₈₉	—	2	1	no	—
455	C₂²⋊C₄×C₈₉	—	2	2	no	—
456	C₂²⋊C₄×C₈₉	—	2	2	no	—
457	C₂²⋊C₄×C₈₉	—	2	2	no	—
458	C₂²⋊C₄×C₈₉	—	2	2	no	—
459	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
460	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
461	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
463	C₄²×C₈₉	—	2	1	no	—
464	C₄²×C₈₉	—	2	1	no	—
465	C₄²×C₈₉	—	2	1	no	—
466	C₄²×C₈₉	—	2	2	no	—
467	C₄²×C₈₉	—	2	2	no	—
468	C₄²×C₈₉	—	2	1	no	—
469	C₄²×C₈₉	—	2	1	no	—
470	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
471	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
472	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
473	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
474	C₂³×C₈₉	—	2	1	no	—
475	C₂³×C₈₉	—	2	2	no	—
476	C₂³×C₈₉	—	2	2	no	—
477	C₂³×C₈₉	—	4	2	no	—
478	C₂³×C₈₉	—	4	2	no	—
479	C₂³×C₈₉	—	4	2	no	—
480	C₂³×C₈₉	—	4	4	no	—
481	C₂³×C₈₉	—	4	4	no	—
482	C₂³×C₈₉	—	8	2	no	—
483	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
484	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
485	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
486	Q₈×C₈₉	—	2	1	no	—
487	Q₈×C₈₉	—	2	1	no	—
488	Q₈×C₈₉	—	2	1	no	—
489	Q₈×C₈₉	—	2	1	no	—
490	Q₈×C₈₉	—	2	2	no	—
491	Q₈×C₈₉	—	2	2	no	—
492	Q₈×C₈₉	—	2	1	no	—
493	Q₈×C₈₉	—	4	4	no	—
494	Q₈×C₈₉	—	4	2	no	—
495	Q₈×C₈₉	—	8	1	no	—
496	Q₈×C₈₉	H(5,𝔽₂)	1	2	yes	—
497	D₄×C₈₉	—	2	4	no	—
498	D₄×C₈₉	—	2	2	no	—
499	D₄×C₈₉	—	2	2	no	—
500	D₄×C₈₉	—	2	1	no	—
501	D₄×C₈₉	—	2	2	no	—
502	D₄×C₈₉	—	2	2	no	—
503	D₄×C₈₉	—	2	2	no	—
504	D₄×C₈₉	—	2	2	no	—
505	D₄×C₈₉	—	4	2	no	—
506	D₄×C₈₉	—	4	4	no	—
507	D₄×C₈₉	—	4	4	no	—
508	D₄×C₈₉	—	4	4	no	—
509	D₄×C₈₉	—	4	4	no	—
510	D₄×C₈₉	—	4	4	no	—
511	D₄×C₈₉	—	4	4	no	—
512	D₄×C₈₉	—	4	2	no	—
513	D₄×C₈₉	—	4	2	no	—
514	D₄×C₈₉	—	8	1	no	—
515	D₄×C₈₉	—	8	1	no	—
516	D₄×C₈₉	—	8	2	no	—
517	D₄×C₈₉	—	8	2	no	—
518	D₄×C₈₉	—	8	2	no	—
519	D₄×C₈₉	—	8	2	no	—
520	D₄×C₈₉	—	8	2	no	—
521	D₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
522	C₂×C₄×C₈₉	—	2	4	no	—
523	C₂×C₄×C₈₉	—	2	1	no	—
524	C₂×C₄×C₈₉	—	2	2	no	—
525	C₂×C₄×C₈₉	—	2	2	no	—
526	C₂×C₄×C₈₉	—	2	2	no	—
527	C₂×C₄×C₈₉	—	2	2	no	—
528	C₂×C₄×C₈₉	—	2	2	no	—
529	C₂×C₄×C₈₉	—	2	1	no	—
530	C₂×C₄×C₈₉	—	2	1	no	—
531	C₂×C₄×C₈₉	—	2	1	no	—
532	C₂×C₄×C₈₉	—	2	1	no	—
533	C₂×C₄×C₈₉	—	2	1	no	—
534	C₂×C₄×C₈₉	—	2	1	no	—
535	C₂×C₄×C₈₉	—	2	2	no	—
536	C₂×C₄×C₈₉	—	2	1	no	—
537	C₂×C₄×C₈₉	—	2	1	no	—
538	C₂×C₄×C₈₉	—	2	2	no	—
539	C₂×C₄×C₈₉	—	4	2	no	—
540	C₂×C₄×C₈₉	—	4	2	no	—
541	C₂×C₄×C₈₉	—	4	2	no	—
542	C₂×C₄×C₈₉	—	4	1	no	—
543	C₂×C₄×C₈₉	—	4	4	no	—
544	C₂×C₄×C₈₉	—	4	4	no	—
545	C₂×C₄×C₈₉	—	4	4	no	—
546	C₂×C₄×C₈₉	—	4	4	no	—
547	C₂×C₄×C₈₉	—	4	4	no	—
548	C₂×C₄×C₈₉	—	4	2	no	—
549	C₂×C₄×C₈₉	—	8	1	no	—
550	C₂×C₄×C₈₉	—	8	2	no	—
551	C₂×C₄×C₈₉	—	8	2	no	—
552	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
555	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
556	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
560	C₈×C₈₉	—	2	1	no	—
561	C₈×C₈₉	—	2	1	no	—
562	C₈×C₈₉	—	2	2	no	—
563	C₈×C₈₉	—	2	2	no	—
564	C₈×C₈₉	—	2	1	no	—
565	C₈×C₈₉	—	2	1	no	—
566	C₂²×C₈₉	—	2	1	no	—
567	C₂²×C₈₉	—	2	2	no	—
568	C₂²×C₈₉	—	2	2	no	—
569	C₂²×C₈₉	—	2	2	no	—
570	C₂²×C₈₉	—	2	1	no	—
571	C₂²×C₈₉	—	2	2	no	—
572	C₂²×C₈₉	—	2	2	no	—
573	C₂²×C₈₉	—	2	1	no	—
574	C₂²×C₈₉	—	2	2	no	—
575	C₂²×C₈₉	—	2	2	no	—
576	C₂²×C₈₉	—	4	1	no	—
577	C₂²×C₈₉	—	4	1	no	—
578	C₂²×C₈₉	—	4	2	no	—
579	C₂²×C₈₉	—	4	2	no	—
580	C₂²×C₈₉	—	4	2	no	—
581	C₂²×C₈₉	—	4	2	no	—
582	C₂²×C₈₉	—	4	2	no	—
583	C₂²×C₈₉	—	4	2	no	—
584	C₂²×C₈₉	—	8	4	no	—
585	C₂²×C₈₉	—	8	8	no	—
586	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
587	C₄×C₈₉	—	2	1	no	—
588	C₄×C₈₉	—	2	1	no	—
589	C₄×C₈₉	—	2	1	no	—
590	C₄×C₈₉	—	2	2	no	—
591	C₄×C₈₉	—	2	2	no	—
592	C₄×C₈₉	—	2	2	no	—
593	C₄×C₈₉	—	2	1	no	—
594	C₄×C₈₉	—	4	1	no	—
595	C₄×C₈₉	—	4	1	no	—
596	C₄×C₈₉	—	4	1	no	—
597	C₄×C₈₉	—	4	2	no	—
598	C₄×C₈₉	—	4	1	no	—
599	C₄×C₈₉	—	4	1	no	—
600	C₄×C₈₉	—	4	1	no	—
601	C₄×C₈₉	—	4	2	no	—
602	C₄×C₈₉	#575	1	2	yes	—
603	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
604	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
605	#61608	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
606	C₂×C₈₉	—	4	2	no	—
607	C₂×C₈₉	—	4	1	no	—
608	C₂×C₈₉	—	4	2	no	—
609	C₂×C₈₉	—	4	2	no	—
610	C₂×C₈₉	—	8	2	no	—
611	C₂×C₈₉	—	8	2	no	—
612	C₂×C₈₉	#3484	1	1	yes	characteristic
613	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
614	C₂×C₈₉	#3584	1	1	yes	characteristic
615	#3506	C₂×C₈₉	1	1	yes	characteristic, complemented
616	D₄×#41	C₂×C₈₉	1	1	yes	characteristic, complemented
617	#3328	C₂×C₈₉	1	1	yes	characteristic, complemented
618	#3324	C₂×C₈₉	1	1	yes	characteristic, complemented
619	#3321	C₂×C₈₉	1	2	yes	complemented
620	#3319	C₂×C₈₉	1	2	yes	complemented
621	#3304	C₂×C₈₉	1	1	yes	characteristic, complemented
622	#3302	C₂×C₈₉	1	1	yes	characteristic, complemented
623	#3287	C₂×C₈₉	1	1	yes	characteristic, complemented
624	#3284	C₂×C₈₉	1	1	yes	characteristic, complemented
625	#3278	C₂×C₈₉	1	1	yes	characteristic, complemented
626	#3274	C₂×C₈₉	1	1	yes	characteristic, complemented
627	#3269	C₂×C₈₉	1	2	yes	complemented
628	#3267	C₂×C₈₉	1	2	yes	complemented
629	#3216	C₂×C₈₉	1	1	yes	characteristic, complemented
630	#3207	C₂×C₈₉	1	1	yes	characteristic, complemented
631	#3197	C₂×C₈₉	1	2	yes	complemented
632	#3191	C₂×C₈₉	1	2	yes	complemented
633	#3115	C₂×C₈₉	1	1	yes	characteristic, complemented
634	#3107	C₂×C₈₉	1	1	yes	characteristic, complemented
635	#3005	C₂×C₈₉	1	2	yes	complemented
636	#3002	C₂×C₈₉	1	2	yes	complemented
637	#2974	C₂×C₈₉	1	1	yes	characteristic, complemented
638	C₈₉	#61608	1	1	yes	characteristic, direct product factor, Sylow
639	C₂²×#41	C₂²×C₈₉	1	2	yes	—
640	C₂×#137	C₂²×C₈₉	1	2	yes	complemented
641	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	complemented
642	C₂×#135	C₂²×C₈₉	1	2	yes	complemented
643	C₂×#135	C₂²×C₈₉	1	2	yes	complemented
644	#559	—	2	1	no	—
645	#559	—	2	1	no	—
646	#556	C₂²×C₈₉	1	1	yes	characteristic
647	#556	C₂²×C₈₉	1	1	yes	characteristic, complemented
648	#555	C₂²×C₈₉	1	2	yes	complemented
649	#553	—	2	2	no	—
650	#550	C₂²×C₈₉	1	1	yes	characteristic
651	#550	C₂²×C₈₉	1	1	yes	characteristic
652	#550	C₂²×C₈₉	1	1	yes	characteristic, complemented
653	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
654	#548	C₂²×C₈₉	1	2	yes	—
655	#547	—	2	1	no	—
656	#547	C₂²×C₈₉	1	1	yes	characteristic
657	#547	C₂²×C₈₉	1	2	yes	complemented
658	#546	—	2	2	no	—
659	#546	C₂²×C₈₉	1	2	yes	—
660	D₄²	—	2	1	no	—
661	D₄²	C₂²×C₈₉	1	1	yes	characteristic
662	#538	—	2	2	no	—
663	#535	—	2	1	no	—
664	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
665	#532	—	2	1	no	—
666	#532	C₂²×C₈₉	1	1	yes	characteristic
667	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
668	#525	—	2	2	no	—
669	#525	C₂²×C₈₉	1	2	yes	—
670	#525	C₂²×C₈₉	1	2	yes	complemented
671	#525	C₂²×C₈₉	1	2	yes	complemented
672	#520	—	2	1	no	—
673	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
674	C₂×C₄×D₄	—	2	1	no	—
675	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
676	#497	C₂²×C₈₉	1	2	yes	complemented
677	#493	C₂²×C₈₉	1	1	yes	characteristic, complemented
678	#492	C₂²×C₈₉	1	1	yes	characteristic, complemented
679	#489	C₂²×C₈₉	1	2	yes	complemented
680	#487	C₂²×C₈₉	1	1	yes	characteristic, complemented
681	#486	C₂²×C₈₉	1	1	yes	characteristic, complemented
682	#485	C₂²×C₈₉	1	2	yes	complemented
683	#485	C₂²×C₈₉	1	1	yes	characteristic, complemented
684	#485	C₂²×C₈₉	1	1	yes	characteristic, complemented
685	#485	C₂²×C₈₉	1	2	yes	complemented
686	#482	C₂²×C₈₉	1	2	yes	complemented
687	#482	C₂²×C₈₉	1	2	yes	complemented
688	#482	C₂²×C₈₉	1	2	yes	complemented
689	#475	C₂²×C₈₉	1	1	yes	characteristic, complemented
690	#475	C₂²×C₈₉	1	1	yes	characteristic, complemented
691	#474	C₂²×C₈₉	1	1	yes	characteristic, complemented
692	#474	C₂²×C₈₉	1	1	yes	characteristic, complemented
693	#470	C₂²×C₈₉	1	2	yes	complemented
694	#469	C₂²×C₈₉	1	2	yes	complemented
695	#468	C₂²×C₈₉	1	2	yes	complemented
696	#468	C₂²×C₈₉	1	2	yes	complemented
697	#467	C₂²×C₈₉	1	2	yes	complemented
698	#466	C₂²×C₈₉	1	2	yes	complemented
699	#465	C₂²×C₈₉	1	2	yes	complemented
700	#465	C₂²×C₈₉	1	2	yes	complemented
701	#463	C₂²×C₈₉	1	2	yes	complemented
702	#463	C₂²×C₈₉	1	2	yes	complemented
703	#462	C₂²×C₈₉	1	1	yes	characteristic, complemented
704	#462	C₂²×C₈₉	1	1	yes	characteristic, complemented
705	#462	C₂²×C₈₉	1	1	yes	characteristic, complemented
706	#461	C₂²×C₈₉	1	1	yes	characteristic, complemented
707	#460	C₂²×C₈₉	1	1	yes	characteristic, complemented
708	#460	C₂²×C₈₉	1	1	yes	characteristic, complemented
709	#460	C₂²×C₈₉	1	1	yes	characteristic, complemented
710	#459	C₂²×C₈₉	1	1	yes	characteristic, complemented
711	#452	C₂²×C₈₉	1	1	yes	characteristic
712	#452	C₂²×C₈₉	1	1	yes	characteristic
713	#452	C₂²×C₈₉	1	2	yes	complemented
714	#452	C₂²×C₈₉	1	2	yes	complemented
715	#452	C₂²×C₈₉	1	2	yes	complemented
716	#452	C₂²×C₈₉	1	2	yes	complemented
717	#452	C₂²×C₈₉	1	2	yes	complemented
718	#452	C₂²×C₈₉	1	2	yes	complemented
719	#451	C₂²×C₈₉	1	2	yes	complemented
720	#450	C₂²×C₈₉	1	2	yes	complemented
721	#449	C₂²×C₈₉	1	2	yes	—
722	#449	C₂²×C₈₉	1	2	yes	complemented
723	#449	C₂²×C₈₉	1	2	yes	complemented
724	#449	C₂²×C₈₉	1	2	yes	complemented
725	#449	C₂²×C₈₉	1	2	yes	complemented
726	#449	C₂²×C₈₉	1	2	yes	complemented
727	#449	C₂²×C₈₉	1	2	yes	complemented
728	#448	C₂²×C₈₉	1	2	yes	complemented
729	#447	C₂²×C₈₉	1	2	yes	complemented
730	#442	C₂²×C₈₉	1	2	yes	complemented
731	#440	C₂²×C₈₉	1	2	yes	complemented
732	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
733	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
734	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
735	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
736	#436	C₂²×C₈₉	1	1	yes	characteristic
737	#436	C₂²×C₈₉	1	1	yes	characteristic
738	#435	C₂²×C₈₉	1	2	yes	complemented
739	#435	C₂²×C₈₉	1	2	yes	complemented
740	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
741	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
742	#432	C₂²×C₈₉	1	1	yes	characteristic, complemented
743	#431	C₂²×C₈₉	1	1	yes	characteristic, complemented
744	#419	C₂²×C₈₉	1	2	yes	complemented
745	#418	C₂²×C₈₉	1	2	yes	complemented
746	#416	C₂²×C₈₉	1	2	yes	complemented
747	#416	C₂²×C₈₉	1	2	yes	complemented
748	#407	C₂²×C₈₉	1	2	yes	complemented
749	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	complemented
750	C₂×#41	—	2	1	no	—
751	C₂×#41	—	2	2	no	—
752	C₂×#41	—	2	2	no	—
753	C₂×#41	—	4	4	no	—
754	C₂×#41	—	4	4	no	—
755	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
756	C₂×#41	C₂³×C₈₉	1	2	yes	—
757	C₂×#41	C₂³×C₈₉	1	2	yes	—
758	C₂×#41	C₂³×C₈₉	1	2	yes	—
759	C₂×#41	C₂³×C₈₉	1	2	yes	—
760	C₂×#41	C₂³×C₈₉	1	2	yes	—
761	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
762	C₂²×D₄	—	2	2	no	—
763	C₂²×D₄	—	2	1	no	—
764	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
765	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
766	C₂³×C₄	—	2	2	no	—
767	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
768	#137	—	4	4	no	—
769	AGL(1,ℤ/8)	—	4	4	no	—
770	#135	—	4	4	no	—
771	#135	—	4	4	no	—
772	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
773	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
774	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
775	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
776	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
777	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
778	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
779	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
780	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
781	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
782	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
783	C₂×D₈	C₂³×C₈₉	1	2	yes	—
784	C₂×D₈	C₂³×C₈₉	1	2	yes	—
785	C₂×D₈	C₂³×C₈₉	1	2	yes	—
786	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
787	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
788	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
789	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
790	C₄⋊Q₈	—	2	1	no	—
791	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
792	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
793	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
794	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
795	#127	—	2	1	no	—
796	#127	—	2	1	no	—
797	#127	—	2	1	no	—
798	#127	C₂³×C₈₉	1	1	yes	characteristic
799	#127	C₂³×C₈₉	1	1	yes	characteristic
800	#126	—	2	2	no	—
801	#126	—	2	2	no	—
802	#125	—	2	1	no	—
803	#124	—	2	1	no	—
804	#124	—	2	1	no	—
805	#124	—	2	2	no	—
806	#124	—	2	2	no	—
807	#124	—	2	2	no	—
808	#124	—	2	1	no	—
809	#124	C₂³×C₈₉	1	2	yes	—
810	#123	—	2	2	no	—
811	#123	—	2	2	no	—
812	#123	—	2	2	no	—
813	#123	—	2	2	no	—
814	#123	—	2	2	no	—
815	#123	—	2	2	no	—
816	#123	—	2	2	no	—
817	C₂²⋊Q₈	—	2	1	no	—
818	C₂²⋊Q₈	—	2	2	no	—
819	C₂²⋊Q₈	—	2	2	no	—
820	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
821	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
822	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
823	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
824	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
825	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
826	#121	—	2	2	no	—
827	#121	—	2	1	no	—
828	#121	—	2	2	no	—
829	#121	—	2	2	no	—
830	#121	—	2	1	no	—
831	#121	—	2	1	no	—
832	#121	—	2	1	no	—
833	#121	—	2	1	no	—
834	#121	—	2	2	no	—
835	#121	—	2	2	no	—
836	#121	—	2	2	no	—
837	#121	—	2	2	no	—
838	#121	C₂³×C₈₉	1	2	yes	—
839	#121	C₂³×C₈₉	1	2	yes	—
840	#121	C₂³×C₈₉	1	2	yes	—
841	#121	C₂³×C₈₉	1	2	yes	—
842	#121	C₂³×C₈₉	1	2	yes	—
843	#120	—	2	2	no	—
844	#120	—	2	2	no	—
845	#120	—	2	2	no	—
846	#120	—	2	2	no	—
847	#120	—	2	2	no	—
848	C₄×Q₈	—	2	1	no	—
849	C₄×Q₈	—	2	1	no	—
850	C₄×Q₈	—	2	1	no	—
851	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
852	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
853	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
854	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
855	C₄×D₄	—	2	1	no	—
856	C₄×D₄	—	2	2	no	—
857	C₄×D₄	—	2	1	no	—
858	C₄×D₄	—	2	1	no	—
859	C₄×D₄	—	2	2	no	—
860	C₄×D₄	—	2	2	no	—
861	C₄×D₄	—	2	2	no	—
862	C₄×D₄	—	2	2	no	—
863	C₄×D₄	—	2	2	no	—
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	—	2	1	no	—
866	C₄×D₄	—	2	1	no	—
867	C₄×D₄	—	2	2	no	—
868	C₄×D₄	—	2	1	no	—
869	C₄×D₄	—	2	1	no	—
870	C₄×D₄	—	2	1	no	—
871	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
872	C₄×D₄	D₄×C₈₉	1	2	yes	—
873	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
874	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
875	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
876	C₄×D₄	C₂³×C₈₉	1	2	yes	—
877	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
878	C₄×D₄	C₂³×C₈₉	1	2	yes	—
879	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
880	#117	—	2	1	no	—
881	#117	—	2	2	no	—
882	#117	—	2	1	no	—
883	#117	C₂³×C₈₉	1	1	yes	characteristic
884	#117	C₂³×C₈₉	1	2	yes	—
885	#117	C₂³×C₈₉	1	2	yes	—
886	C₂×C₄⋊C₄	—	2	1	no	—
887	C₂×C₄⋊C₄	—	2	2	no	—
888	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
889	C₂×C₂²⋊C₄	—	2	2	no	—
890	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
891	C₂×C₄²	—	2	1	no	—
892	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
893	#107	C₂³×C₈₉	1	1	yes	characteristic
894	#107	C₂³×C₈₉	1	1	yes	characteristic
895	#107	C₂³×C₈₉	1	2	yes	—
896	#106	C₂³×C₈₉	1	1	yes	characteristic
897	#106	C₂³×C₈₉	1	1	yes	characteristic
898	#106	C₂³×C₈₉	1	2	yes	—
899	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
900	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
901	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
902	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
903	#103	C₂³×C₈₉	1	1	yes	characteristic
904	#103	C₂³×C₈₉	1	2	yes	—
905	#103	C₂³×C₈₉	1	2	yes	—
906	#103	C₂³×C₈₉	1	2	yes	—
907	#103	C₂³×C₈₉	1	1	yes	characteristic
908	#103	C₂³×C₈₉	1	2	yes	—
909	#103	C₂³×C₈₉	1	2	yes	—
910	#103	C₂³×C₈₉	1	1	yes	characteristic
911	#103	C₂³×C₈₉	1	1	yes	characteristic
912	#103	C₂³×C₈₉	1	1	yes	characteristic
913	#103	C₂³×C₈₉	1	1	yes	characteristic
914	#102	C₂³×C₈₉	1	1	yes	characteristic
915	#102	C₂³×C₈₉	1	2	yes	—
916	#102	C₂³×C₈₉	1	2	yes	—
917	#102	C₂³×C₈₉	1	2	yes	—
918	#102	C₂³×C₈₉	1	1	yes	characteristic
919	#102	C₂³×C₈₉	1	2	yes	—
920	#102	C₂³×C₈₉	1	2	yes	—
921	#102	C₂³×C₈₉	1	2	yes	—
922	#102	C₂³×C₈₉	1	2	yes	—
923	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
924	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
925	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
926	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
927	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
928	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
929	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
930	#97	C₂³×C₈₉	1	2	yes	—
931	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
932	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
933	C₂⁴	—	2	2	no	—
934	C₂⁴	C₂×D₄×C₈₉	1	2	yes	—
935	#41	—	2	2	no	—
936	#41	—	2	2	no	—
937	#41	—	2	4	no	—
938	#41	—	2	4	no	—
939	#41	—	4	2	no	—
940	#41	—	4	2	no	—
941	#41	—	4	2	no	—
942	#41	—	4	2	no	—
943	#41	—	4	8	no	—
944	#41	—	4	4	no	—
945	#41	—	4	2	no	—
946	#41	—	4	2	no	—
947	#41	—	4	2	no	—
948	#41	—	4	2	no	—
949	#41	—	4	8	no	—
950	C₂×Q₈	—	2	1	no	—
951	C₂×Q₈	—	2	2	no	—
952	C₂×Q₈	—	2	1	no	—
953	C₂×Q₈	—	2	4	no	—
954	C₂×Q₈	—	4	2	no	—
955	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
956	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
957	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
958	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
959	C₂×D₄	—	2	1	no	—
960	C₂×D₄	—	2	4	no	—
961	C₂×D₄	—	2	2	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	2	no	—
964	C₂×D₄	—	2	2	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	2	no	—
967	C₂×D₄	—	2	2	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	1	no	—
972	C₂×D₄	—	2	1	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	1	no	—
975	C₂×D₄	—	2	1	no	—
976	C₂×D₄	—	4	2	no	—
977	C₂×D₄	—	4	2	no	—
978	C₂×D₄	—	4	8	no	—
979	C₂×D₄	—	4	4	no	—
980	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
981	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
982	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
983	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
984	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
985	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
986	C₂²×C₄	—	2	1	no	—
987	C₂²×C₄	—	2	2	no	—
988	C₂²×C₄	—	2	1	no	—
989	C₂²×C₄	—	2	2	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	2	2	no	—
993	C₂²×C₄	—	2	1	no	—
994	C₂²×C₄	—	2	2	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	4	2	no	—
997	C₂²×C₄	—	4	2	no	—
998	C₂²×C₄	—	4	8	no	—
999	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1000	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1001	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
1002	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
1003	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
1004	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1005	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
1006	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
1007	Q₁₆	—	2	2	no	—
1008	Q₁₆	—	2	2	no	—
1009	Q₁₆	—	4	2	no	—
1010	Q₁₆	—	4	2	no	—
1011	SD₁₆	—	2	4	no	—
1012	SD₁₆	—	2	2	no	—
1013	SD₁₆	—	2	2	no	—
1014	SD₁₆	—	4	2	no	—
1015	SD₁₆	—	4	2	no	—
1016	SD₁₆	—	4	2	no	—
1017	SD₁₆	—	4	2	no	—
1018	D₈	—	2	4	no	—
1019	D₈	—	4	2	no	—
1020	D₈	—	4	2	no	—
1021	M₁₆	—	4	2	no	—
1022	M₁₆	—	4	2	no	—
1023	C₂×C₈	—	4	2	no	—
1024	C₂×C₈	—	4	2	no	—
1025	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
1026	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
1027	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
1028	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
1029	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
1030	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	2	2	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	1	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1048	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1049	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1050	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1051	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1052	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1053	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1054	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	1	no	—
1057	C₂²⋊C₄	—	2	1	no	—
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	1	no	—
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1075	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1076	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1077	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1078	C₄²	—	2	1	no	—
1079	C₄²	—	2	1	no	—
1080	C₄²	—	2	1	no	—
1081	C₄²	—	2	2	no	—
1082	C₄²	—	2	2	no	—
1083	C₄²	—	2	1	no	—
1084	C₄²	—	2	1	no	—
1085	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1086	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1087	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1088	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1089	C₂³	—	2	1	no	—
1090	C₂³	—	2	2	no	—
1091	C₂³	—	2	2	no	—
1092	C₂³	—	4	2	no	—
1093	C₂³	—	4	2	no	—
1094	C₂³	—	4	2	no	—
1095	C₂³	—	4	4	no	—
1096	C₂³	—	4	4	no	—
1097	C₂³	—	8	2	no	—
1098	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1099	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1100	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1101	Q₈	—	2	1	no	—
1102	Q₈	—	2	1	no	—
1103	Q₈	—	2	1	no	—
1104	Q₈	—	2	1	no	—
1105	Q₈	—	2	2	no	—
1106	Q₈	—	2	2	no	—
1107	Q₈	—	2	1	no	—
1108	Q₈	—	4	4	no	—
1109	Q₈	—	4	2	no	—
1110	Q₈	—	8	1	no	—
1111	Q₈	H(5,𝔽₂)×C₈₉	1	2	yes	—
1112	D₄	—	2	4	no	—
1113	D₄	—	2	2	no	—
1114	D₄	—	2	2	no	—
1115	D₄	—	2	1	no	—
1116	D₄	—	2	2	no	—
1117	D₄	—	2	2	no	—
1118	D₄	—	2	2	no	—
1119	D₄	—	2	2	no	—
1120	D₄	—	4	2	no	—
1121	D₄	—	4	4	no	—
1122	D₄	—	4	4	no	—
1123	D₄	—	4	4	no	—
1124	D₄	—	4	4	no	—
1125	D₄	—	4	4	no	—
1126	D₄	—	4	4	no	—
1127	D₄	—	4	2	no	—
1128	D₄	—	4	2	no	—
1129	D₄	—	8	1	no	—
1130	D₄	—	8	1	no	—
1131	D₄	—	8	2	no	—
1132	D₄	—	8	2	no	—
1133	D₄	—	8	2	no	—
1134	D₄	—	8	2	no	—
1135	D₄	—	8	2	no	—
1136	D₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
1137	C₂×C₄	—	2	4	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	2	no	—
1140	C₂×C₄	—	2	2	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	2	no	—
1154	C₂×C₄	—	4	2	no	—
1155	C₂×C₄	—	4	2	no	—
1156	C₂×C₄	—	4	2	no	—
1157	C₂×C₄	—	4	1	no	—
1158	C₂×C₄	—	4	4	no	—
1159	C₂×C₄	—	4	4	no	—
1160	C₂×C₄	—	4	4	no	—
1161	C₂×C₄	—	4	4	no	—
1162	C₂×C₄	—	4	4	no	—
1163	C₂×C₄	—	4	2	no	—
1164	C₂×C₄	—	8	1	no	—
1165	C₂×C₄	—	8	2	no	—
1166	C₂×C₄	—	8	2	no	—
1167	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1168	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1169	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1170	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1171	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1172	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1173	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1174	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1175	C₈	—	2	1	no	—
1176	C₈	—	2	1	no	—
1177	C₈	—	2	2	no	—
1178	C₈	—	2	2	no	—
1179	C₈	—	2	1	no	—
1180	C₈	—	2	1	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	2	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	2	1	no	—
1185	C₂²	—	2	2	no	—
1186	C₂²	—	2	2	no	—
1187	C₂²	—	2	2	no	—
1188	C₂²	—	2	1	no	—
1189	C₂²	—	2	2	no	—
1190	C₂²	—	2	2	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	2	no	—
1194	C₂²	—	4	2	no	—
1195	C₂²	—	4	2	no	—
1196	C₂²	—	4	2	no	—
1197	C₂²	—	4	2	no	—
1198	C₂²	—	4	2	no	—
1199	C₂²	—	8	4	no	—
1200	C₂²	—	8	8	no	—
1201	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1202	C₄	—	2	1	no	—
1203	C₄	—	2	1	no	—
1204	C₄	—	2	1	no	—
1205	C₄	—	2	1	no	—
1206	C₄	—	2	2	no	—
1207	C₄	—	2	2	no	—
1208	C₄	—	2	2	no	—
1209	C₄	—	4	1	no	—
1210	C₄	—	4	2	no	—
1211	C₄	—	4	1	no	—
1212	C₄	—	4	1	no	—
1213	C₄	—	4	1	no	—
1214	C₄	—	4	2	no	—
1215	C₄	—	4	1	no	—
1216	C₄	—	4	1	no	—
1217	C₄	#575×C₈₉	1	2	yes	—
1218	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1219	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1220	C₂	—	4	2	no	—
1221	C₂	—	4	1	no	—
1222	C₂	—	4	2	no	—
1223	C₂	—	4	2	no	—
1224	C₂	—	8	2	no	—
1225	C₂	—	8	2	no	—
1226	C₂	C₈₉×#3484	1	1	yes	characteristic
1227	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
1228	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 ◁ C₂×C₄×D₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3506	C₂	semidirect
2. D₄×#41×C₈₉	C₂	semidirect
3. C₈₉×#3328	C₂	semidirect
4. C₈₉×#3324	C₂	semidirect
5. C₈₉×#3321	C₂	semidirect
6. C₈₉×#3319	C₂	semidirect
7. C₈₉×#3304	C₂	semidirect
8. C₈₉×#3302	C₂	semidirect
9. C₈₉×#3287	C₂	semidirect
10. C₈₉×#3284	C₂	semidirect
11. C₈₉×#3278	C₂	semidirect
12. C₈₉×#3274	C₂	semidirect
13. C₈₉×#3269	C₂	semidirect
14. C₈₉×#3267	C₂	semidirect
15. C₈₉×#3216	C₂	semidirect
16. C₈₉×#3207	C₂	semidirect
17. C₈₉×#3197	C₂	semidirect
18. C₈₉×#3191	C₂	semidirect
19. C₈₉×#3115	C₂	semidirect
20. C₈₉×#3107	C₂	semidirect
21. C₈₉×#3005	C₂	semidirect
22. C₈₉×#3002	C₂	semidirect
23. C₈₉×#2974	C₂	semidirect
25. C₂×#137×C₈₉	C₂²	semidirect
26. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
27. C₂×#135×C₈₉	C₂²	semidirect
28. C₂×#135×C₈₉	C₂²	semidirect
32. #556×C₈₉	C₂²	semidirect
33. #555×C₈₉	C₂²	semidirect
37. #550×C₈₉	C₂²	semidirect
42. #547×C₈₉	C₂²	semidirect
49. #533×C₈₉	C₂²	semidirect
52. #532×C₈₉	C₂²	semidirect
55. #525×C₈₉	C₂²	semidirect
56. #525×C₈₉	C₂²	semidirect
61. #497×C₈₉	C₂²	semidirect
62. #493×C₈₉	C₂²	semidirect
63. #492×C₈₉	C₂²	semidirect
64. #489×C₈₉	C₂²	semidirect
65. #487×C₈₉	C₂²	semidirect
66. #486×C₈₉	C₂²	semidirect
67. #485×C₈₉	C₂²	semidirect
68. #485×C₈₉	C₂²	semidirect
69. #485×C₈₉	C₂²	semidirect
70. #485×C₈₉	C₂²	semidirect
71. #482×C₈₉	C₂²	semidirect
72. #482×C₈₉	C₂²	semidirect
73. #482×C₈₉	C₂²	semidirect
74. #475×C₈₉	C₂²	semidirect
75. #475×C₈₉	C₂²	semidirect
76. #474×C₈₉	C₂²	semidirect
77. #474×C₈₉	C₂²	semidirect
78. #470×C₈₉	C₂²	semidirect
79. #469×C₈₉	C₂²	semidirect
80. #468×C₈₉	C₂²	semidirect
81. #468×C₈₉	C₂²	semidirect
82. #467×C₈₉	C₂²	semidirect
83. #466×C₈₉	C₂²	semidirect
84. #465×C₈₉	C₂²	semidirect
85. #465×C₈₉	C₂²	semidirect
86. #463×C₈₉	C₂²	semidirect
87. #463×C₈₉	C₂²	semidirect
88. #462×C₈₉	C₂²	semidirect
89. #462×C₈₉	C₂²	semidirect
90. #462×C₈₉	C₂²	semidirect
91. #461×C₈₉	C₂²	semidirect
92. #460×C₈₉	C₂²	semidirect
93. #460×C₈₉	C₂²	semidirect
94. #460×C₈₉	C₂²	semidirect
95. #459×C₈₉	C₂²	semidirect
98. #452×C₈₉	C₂²	semidirect
99. #452×C₈₉	C₂²	semidirect
100. #452×C₈₉	C₂²	semidirect
101. #452×C₈₉	C₂²	semidirect
102. #452×C₈₉	C₂²	semidirect
103. #452×C₈₉	C₂²	semidirect
104. #451×C₈₉	C₂²	semidirect
105. #450×C₈₉	C₂²	semidirect
107. #449×C₈₉	C₂²	semidirect
108. #449×C₈₉	C₂²	semidirect
109. #449×C₈₉	C₂²	semidirect
110. #449×C₈₉	C₂²	semidirect
111. #449×C₈₉	C₂²	semidirect
112. #449×C₈₉	C₂²	semidirect
113. #448×C₈₉	C₂²	semidirect
114. #447×C₈₉	C₂²	semidirect
115. #442×C₈₉	C₂²	semidirect
116. #440×C₈₉	C₂²	semidirect
117. C₄×Q₁₆×C₈₉	C₂²	semidirect
118. C₄×Q₁₆×C₈₉	C₂²	semidirect
119. C₄×SD₁₆×C₈₉	C₂²	semidirect
120. C₄×SD₁₆×C₈₉	C₂²	semidirect
123. #435×C₈₉	C₂²	semidirect
124. #435×C₈₉	C₂²	semidirect
125. C₈×D₄×C₈₉	C₂²	semidirect
126. C₈×D₄×C₈₉	C₂²	semidirect
127. #432×C₈₉	C₂²	semidirect
128. #431×C₈₉	C₂²	semidirect
129. #419×C₈₉	C₂²	semidirect
130. #418×C₈₉	C₂²	semidirect
131. #416×C₈₉	C₂²	semidirect
132. #416×C₈₉	C₂²	semidirect
133. #407×C₈₉	C₂²	semidirect
134. C₂×C₂²⋊C₈×C₈₉	C₂²	semidirect
605. #61608	C₈₉	direct (N × H)
615. #3506	C₂×C₈₉	semidirect
616. D₄×#41	C₂×C₈₉	semidirect
617. #3328	C₂×C₈₉	semidirect
618. #3324	C₂×C₈₉	semidirect
619. #3321	C₂×C₈₉	semidirect
620. #3319	C₂×C₈₉	semidirect
621. #3304	C₂×C₈₉	semidirect
622. #3302	C₂×C₈₉	semidirect
623. #3287	C₂×C₈₉	semidirect
624. #3284	C₂×C₈₉	semidirect
625. #3278	C₂×C₈₉	semidirect
626. #3274	C₂×C₈₉	semidirect
627. #3269	C₂×C₈₉	semidirect
628. #3267	C₂×C₈₉	semidirect
629. #3216	C₂×C₈₉	semidirect
630. #3207	C₂×C₈₉	semidirect
631. #3197	C₂×C₈₉	semidirect
632. #3191	C₂×C₈₉	semidirect
633. #3115	C₂×C₈₉	semidirect
634. #3107	C₂×C₈₉	semidirect
635. #3005	C₂×C₈₉	semidirect
636. #3002	C₂×C₈₉	semidirect
637. #2974	C₂×C₈₉	semidirect
638. C₈₉	#61608	direct (N × H)
640. C₂×#137	C₂²×C₈₉	semidirect
641. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
642. C₂×#135	C₂²×C₈₉	semidirect
643. C₂×#135	C₂²×C₈₉	semidirect
647. #556	C₂²×C₈₉	semidirect
648. #555	C₂²×C₈₉	semidirect
652. #550	C₂²×C₈₉	semidirect
657. #547	C₂²×C₈₉	semidirect
664. #533	C₂²×C₈₉	semidirect
667. #532	C₂²×C₈₉	semidirect
670. #525	C₂²×C₈₉	semidirect
671. #525	C₂²×C₈₉	semidirect
676. #497	C₂²×C₈₉	semidirect
677. #493	C₂²×C₈₉	semidirect
678. #492	C₂²×C₈₉	semidirect
679. #489	C₂²×C₈₉	semidirect
680. #487	C₂²×C₈₉	semidirect
681. #486	C₂²×C₈₉	semidirect
682. #485	C₂²×C₈₉	semidirect
683. #485	C₂²×C₈₉	semidirect
684. #485	C₂²×C₈₉	semidirect
685. #485	C₂²×C₈₉	semidirect
686. #482	C₂²×C₈₉	semidirect
687. #482	C₂²×C₈₉	semidirect
688. #482	C₂²×C₈₉	semidirect
689. #475	C₂²×C₈₉	semidirect
690. #475	C₂²×C₈₉	semidirect
691. #474	C₂²×C₈₉	semidirect
692. #474	C₂²×C₈₉	semidirect
693. #470	C₂²×C₈₉	semidirect
694. #469	C₂²×C₈₉	semidirect
695. #468	C₂²×C₈₉	semidirect
696. #468	C₂²×C₈₉	semidirect
697. #467	C₂²×C₈₉	semidirect
698. #466	C₂²×C₈₉	semidirect
699. #465	C₂²×C₈₉	semidirect
700. #465	C₂²×C₈₉	semidirect
701. #463	C₂²×C₈₉	semidirect
702. #463	C₂²×C₈₉	semidirect
703. #462	C₂²×C₈₉	semidirect
704. #462	C₂²×C₈₉	semidirect
705. #462	C₂²×C₈₉	semidirect
706. #461	C₂²×C₈₉	semidirect
707. #460	C₂²×C₈₉	semidirect
708. #460	C₂²×C₈₉	semidirect
709. #460	C₂²×C₈₉	semidirect
710. #459	C₂²×C₈₉	semidirect
713. #452	C₂²×C₈₉	semidirect
714. #452	C₂²×C₈₉	semidirect
715. #452	C₂²×C₈₉	semidirect
716. #452	C₂²×C₈₉	semidirect
717. #452	C₂²×C₈₉	semidirect
718. #452	C₂²×C₈₉	semidirect
719. #451	C₂²×C₈₉	semidirect
720. #450	C₂²×C₈₉	semidirect
722. #449	C₂²×C₈₉	semidirect
723. #449	C₂²×C₈₉	semidirect
724. #449	C₂²×C₈₉	semidirect
725. #449	C₂²×C₈₉	semidirect
726. #449	C₂²×C₈₉	semidirect
727. #449	C₂²×C₈₉	semidirect
728. #448	C₂²×C₈₉	semidirect
729. #447	C₂²×C₈₉	semidirect
730. #442	C₂²×C₈₉	semidirect
731. #440	C₂²×C₈₉	semidirect
732. C₄×Q₁₆	C₂²×C₈₉	semidirect
733. C₄×Q₁₆	C₂²×C₈₉	semidirect
734. C₄×SD₁₆	C₂²×C₈₉	semidirect
735. C₄×SD₁₆	C₂²×C₈₉	semidirect
738. #435	C₂²×C₈₉	semidirect
739. #435	C₂²×C₈₉	semidirect
740. C₈×D₄	C₂²×C₈₉	semidirect
741. C₈×D₄	C₂²×C₈₉	semidirect
742. #432	C₂²×C₈₉	semidirect
743. #431	C₂²×C₈₉	semidirect
744. #419	C₂²×C₈₉	semidirect
745. #418	C₂²×C₈₉	semidirect
746. #416	C₂²×C₈₉	semidirect
747. #416	C₂²×C₈₉	semidirect
748. #407	C₂²×C₈₉	semidirect
749. C₂×C₂²⋊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×#3506	2
D₄×#41×C₈₉	2
C₈₉×#3328	2
C₈₉×#3324	2
C₈₉×#3321	2
C₈₉×#3319	2
C₈₉×#3304	2
C₈₉×#3302	2
C₈₉×#3287	2
C₈₉×#3284	2
C₈₉×#3278	2
C₈₉×#3274	2
C₈₉×#3269	2
C₈₉×#3267	2
C₈₉×#3216	2
C₈₉×#3207	2
C₈₉×#3197	2
C₈₉×#3191	2
C₈₉×#3115	2
C₈₉×#3107	2
C₈₉×#3005	2
C₈₉×#3002	2
C₈₉×#2974	2
#61608	89

Subgroups — C89×#61608 #36439456

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61608 #36439456