Subgroups — C₈₉×#61449 #36439297

Order 22784.

1958 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3483	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3385	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3347	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3333	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3325	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3319	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3309	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3268	C₂	1	2	yes	maximal, complemented
15	C₈₉×#3171	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3169	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3106	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#3106	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3102	C₂	1	2	yes	maximal, complemented
20	C₈₉×#3100	C₂	1	2	yes	maximal, complemented
21	C₈₉×#2965	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×AGL(1,ℤ/8)×C₈₉	C₂	1	2	yes	maximal, complemented
23	C₄×#135×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
25	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
26	#559×C₈₉	C₂²	1	1	yes	characteristic
27	Q₈²×C₈₉	C₂²	1	1	yes	characteristic, complemented
28	#555×C₈₉	—	2	1	no	—
29	#555×C₈₉	—	2	2	no	—
30	#555×C₈₉	C₂²	1	1	yes	characteristic
31	#555×C₈₉	C₂²	1	2	yes	complemented
32	#554×C₈₉	C₂²	1	1	yes	characteristic
33	#554×C₈₉	C₂²	1	1	yes	characteristic
34	#553×C₈₉	—	2	1	no	—
35	#553×C₈₉	C₂²	1	2	yes	—
36	#551×C₈₉	—	2	2	no	—
37	#550×C₈₉	—	2	1	no	—
38	#550×C₈₉	C₂²	1	1	yes	characteristic
39	#550×C₈₉	C₂²	1	2	yes	complemented
40	#550×C₈₉	C₂²	1	1	yes	characteristic, complemented
41	#546×C₈₉	—	2	1	no	—
42	#546×C₈₉	C₂²	1	2	yes	—
43	D₄²×C₈₉	C₂²	1	1	yes	characteristic
44	#532×C₈₉	—	2	1	no	—
45	#532×C₈₉	—	2	2	no	—
46	#532×C₈₉	C₂²	1	1	yes	characteristic
47	#532×C₈₉	C₂²	1	2	yes	complemented
48	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
49	#529×C₈₉	—	2	1	no	—
50	#529×C₈₉	C₂²	1	2	yes	—
51	#525×C₈₉	—	2	2	no	—
52	C₄×#41×C₈₉	—	2	1	no	—
53	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
54	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
55	C₄×#41×C₈₉	C₂²	1	2	yes	complemented
56	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×D₄×C₈₉	—	2	1	no	—
58	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
59	#501×C₈₉	C₂²	1	2	yes	complemented
60	#500×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	#496×C₈₉	C₂²	1	2	yes	complemented
62	#493×C₈₉	C₂²	1	1	yes	characteristic
63	#490×C₈₉	C₂²	1	2	yes	complemented
64	#489×C₈₉	C₂²	1	2	yes	complemented
65	#486×C₈₉	C₂²	1	1	yes	characteristic
66	#486×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#485×C₈₉	C₂²	1	2	yes	complemented
68	#482×C₈₉	C₂²	1	2	yes	—
69	#482×C₈₉	C₂²	1	2	yes	complemented
70	#482×C₈₉	C₂²	1	2	yes	complemented
71	#480×C₈₉	C₂²	1	2	yes	complemented
72	#480×C₈₉	C₂²	1	2	yes	complemented
73	#479×C₈₉	C₂²	1	2	yes	complemented
74	#478×C₈₉	C₂²	1	2	yes	complemented
75	#477×C₈₉	C₂²	1	1	yes	characteristic, complemented
76	#477×C₈₉	C₂²	1	1	yes	characteristic, complemented
77	#476×C₈₉	C₂²	1	1	yes	characteristic
78	#476×C₈₉	C₂²	1	1	yes	characteristic, complemented
79	#474×C₈₉	C₂²	1	2	yes	—
80	#474×C₈₉	C₂²	1	2	yes	complemented
81	#469×C₈₉	C₂²	1	2	yes	—
82	#469×C₈₉	C₂²	1	2	yes	—
83	#468×C₈₉	C₂²	1	2	yes	complemented
84	#468×C₈₉	C₂²	1	2	yes	complemented
85	#466×C₈₉	C₂²	1	2	yes	complemented
86	#466×C₈₉	C₂²	1	2	yes	complemented
87	#464×C₈₉	C₂²	1	2	yes	complemented
88	#463×C₈₉	C₂²	1	2	yes	complemented
89	#460×C₈₉	C₂²	1	1	yes	characteristic
90	#460×C₈₉	C₂²	1	1	yes	characteristic, complemented
91	#459×C₈₉	C₂²	1	1	yes	characteristic
92	#459×C₈₉	C₂²	1	2	yes	—
93	#459×C₈₉	C₂²	1	1	yes	characteristic
94	#459×C₈₉	C₂²	1	2	yes	complemented
95	#452×C₈₉	C₂²	1	2	yes	complemented
96	#449×C₈₉	C₂²	1	2	yes	—
97	#449×C₈₉	C₂²	1	2	yes	—
98	#449×C₈₉	C₂²	1	2	yes	complemented
99	#447×C₈₉	C₂²	1	2	yes	—
100	#447×C₈₉	C₂²	1	2	yes	—
101	#446×C₈₉	C₂²	1	1	yes	characteristic, complemented
102	#446×C₈₉	C₂²	1	1	yes	characteristic, complemented
103	#442×C₈₉	C₂²	1	2	yes	—
104	#442×C₈₉	C₂²	1	2	yes	complemented
105	#440×C₈₉	C₂²	1	2	yes	—
106	#440×C₈₉	C₂²	1	2	yes	complemented
107	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
108	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
109	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
110	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
111	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
112	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
113	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
114	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
116	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
117	C₄×D₈×C₈₉	C₂²	1	2	yes	—
118	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
119	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
120	C₄×D₈×C₈₉	C₂²	1	2	yes	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	#431×C₈₉	C₂²	1	2	yes	complemented
126	#431×C₈₉	C₂²	1	1	yes	characteristic, complemented
127	#428×C₈₉	C₂²	1	2	yes	complemented
128	#427×C₈₉	C₂²	1	1	yes	characteristic, complemented
129	#418×C₈₉	C₂²	1	2	yes	—
130	#417×C₈₉	C₂²	1	2	yes	complemented
131	#416×C₈₉	C₂²	1	1	yes	characteristic
132	#416×C₈₉	C₂²	1	1	yes	characteristic, complemented
133	C₄×M₁₆×C₈₉	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
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	D₄	1	1	yes	characteristic
140	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
141	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
142	C₂×#41×C₈₉	C₂³	1	2	yes	—
143	C₂²×D₄×C₈₉	—	2	1	no	—
144	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
145	C₂³×C₄×C₈₉	—	2	2	no	—
146	AGL(1,ℤ/8)×C₈₉	—	2	8	no	—
147	#135×C₈₉	—	2	4	no	—
148	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
154	C₂×D₈×C₈₉	C₂³	1	2	yes	—
155	C₂×D₈×C₈₉	C₂³	1	2	yes	—
156	C₂×D₈×C₈₉	C₂³	1	2	yes	—
157	C₂×D₈×C₈₉	C₂³	1	2	yes	—
158	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
159	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
160	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
161	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₈₉	—	2	1	no	—
163	C₄⋊Q₈×C₈₉	—	2	2	no	—
164	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
167	#127×C₈₉	—	2	1	no	—
168	#127×C₈₉	—	2	2	no	—
169	#127×C₈₉	C₂³	1	2	yes	—
170	#127×C₈₉	C₂³	1	1	yes	characteristic
171	#127×C₈₉	C₂³	1	1	yes	characteristic
172	#126×C₈₉	—	2	2	no	—
173	#126×C₈₉	—	2	2	no	—
174	#125×C₈₉	—	2	1	no	—
175	#125×C₈₉	C₂³	1	2	yes	—
176	#124×C₈₉	—	2	1	no	—
177	#124×C₈₉	—	2	2	no	—
178	#124×C₈₉	—	2	2	no	—
179	#124×C₈₉	—	2	2	no	—
180	#124×C₈₉	—	2	1	no	—
181	#124×C₈₉	—	2	1	no	—
182	#124×C₈₉	—	2	2	no	—
183	#124×C₈₉	C₂³	1	2	yes	—
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	C₂²⋊Q₈×C₈₉	—	2	1	no	—
189	C₂²⋊Q₈×C₈₉	—	2	2	no	—
190	C₂²⋊Q₈×C₈₉	—	2	2	no	—
191	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
192	#121×C₈₉	—	2	2	no	—
193	#121×C₈₉	—	2	1	no	—
194	#121×C₈₉	—	2	2	no	—
195	#121×C₈₉	—	2	1	no	—
196	#121×C₈₉	—	2	1	no	—
197	#121×C₈₉	—	2	2	no	—
198	#121×C₈₉	—	2	1	no	—
199	#121×C₈₉	—	2	1	no	—
200	#121×C₈₉	—	2	2	no	—
201	#121×C₈₉	—	2	2	no	—
202	#121×C₈₉	—	2	2	no	—
203	#121×C₈₉	—	2	2	no	—
204	#121×C₈₉	—	2	2	no	—
205	#121×C₈₉	C₂³	1	2	yes	—
206	#121×C₈₉	C₂³	1	2	yes	—
207	#121×C₈₉	C₂³	1	2	yes	—
208	#121×C₈₉	C₂³	1	2	yes	—
209	#121×C₈₉	C₂³	1	2	yes	—
210	#120×C₈₉	—	2	2	no	—
211	#120×C₈₉	—	2	2	no	—
212	C₄×Q₈×C₈₉	—	2	1	no	—
213	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
214	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
219	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₈₉	—	2	1	no	—
221	C₄×D₄×C₈₉	—	2	2	no	—
222	C₄×D₄×C₈₉	—	2	1	no	—
223	C₄×D₄×C₈₉	—	2	1	no	—
224	C₄×D₄×C₈₉	—	2	2	no	—
225	C₄×D₄×C₈₉	—	2	1	no	—
226	C₄×D₄×C₈₉	—	2	1	no	—
227	C₄×D₄×C₈₉	—	2	2	no	—
228	C₄×D₄×C₈₉	—	2	1	no	—
229	C₄×D₄×C₈₉	—	2	1	no	—
230	C₄×D₄×C₈₉	—	2	2	no	—
231	C₄×D₄×C₈₉	—	2	2	no	—
232	C₄×D₄×C₈₉	—	2	1	no	—
233	C₄×D₄×C₈₉	—	2	2	no	—
234	C₄×D₄×C₈₉	—	2	2	no	—
235	C₄×D₄×C₈₉	—	2	1	no	—
236	C₄×D₄×C₈₉	—	2	2	no	—
237	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
238	C₄×D₄×C₈₉	D₄	1	2	yes	—
239	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
246	C₄×D₄×C₈₉	C₂³	1	2	yes	—
247	C₄×D₄×C₈₉	C₂³	1	2	yes	—
248	C₄×D₄×C₈₉	C₂³	1	2	yes	—
249	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
250	#117×C₈₉	—	2	1	no	—
251	#117×C₈₉	—	2	2	no	—
252	#117×C₈₉	—	2	1	no	—
253	#117×C₈₉	—	2	1	no	—
254	#117×C₈₉	—	2	2	no	—
255	#117×C₈₉	—	2	2	no	—
256	#117×C₈₉	D₄	1	2	yes	—
257	#117×C₈₉	D₄	1	1	yes	characteristic
258	#117×C₈₉	C₂³	1	1	yes	characteristic
259	#117×C₈₉	C₂³	1	1	yes	characteristic
260	#117×C₈₉	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
262	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
263	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
264	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
265	C₂×C₄²×C₈₉	—	2	1	no	—
266	C₂×C₄²×C₈₉	—	2	1	no	—
267	C₂×C₄²×C₈₉	—	2	2	no	—
268	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
269	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
270	#107×C₈₉	C₂³	1	1	yes	characteristic
271	#107×C₈₉	C₂³	1	1	yes	characteristic
272	#107×C₈₉	C₂³	1	2	yes	—
273	#107×C₈₉	C₂³	1	2	yes	—
274	#107×C₈₉	C₂³	1	2	yes	—
275	#107×C₈₉	C₂³	1	2	yes	—
276	#106×C₈₉	C₂³	1	1	yes	characteristic
277	#106×C₈₉	C₂³	1	1	yes	characteristic
278	#106×C₈₉	C₂³	1	2	yes	—
279	#106×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	#103×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	1	yes	characteristic
288	#103×C₈₉	C₂³	1	2	yes	—
289	#103×C₈₉	C₂³	1	2	yes	—
290	#102×C₈₉	C₂³	1	1	yes	characteristic
291	#102×C₈₉	C₂³	1	1	yes	characteristic
292	#102×C₈₉	C₂³	1	1	yes	characteristic
293	#102×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
299	#102×C₈₉	C₂³	1	2	yes	—
300	#102×C₈₉	C₂³	1	2	yes	—
301	#102×C₈₉	C₂³	1	2	yes	—
302	#102×C₈₉	C₂³	1	2	yes	—
303	#102×C₈₉	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
307	#97×C₈₉	C₂³	1	2	yes	—
308	#97×C₈₉	C₂³	1	2	yes	—
309	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₈₉	C₂³	1	2	yes	—
314	C₂⁴×C₈₉	—	2	2	no	—
315	#41×C₈₉	—	2	2	no	—
316	#41×C₈₉	—	2	4	no	—
317	#41×C₈₉	—	2	2	no	—
318	#41×C₈₉	—	4	2	no	—
319	#41×C₈₉	—	4	1	no	—
320	#41×C₈₉	—	4	1	no	—
321	#41×C₈₉	—	4	2	no	—
322	#41×C₈₉	—	4	4	no	—
323	#41×C₈₉	—	8	4	no	—
324	#41×C₈₉	—	8	2	no	—
325	#41×C₈₉	—	8	2	no	—
326	C₂×Q₈×C₈₉	—	2	1	no	—
327	C₂×Q₈×C₈₉	—	2	2	no	—
328	C₂×Q₈×C₈₉	—	2	1	no	—
329	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₈₉	—	2	4	no	—
333	C₂×D₄×C₈₉	—	2	1	no	—
334	C₂×D₄×C₈₉	—	2	2	no	—
335	C₂×D₄×C₈₉	—	2	2	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	2	no	—
340	C₂×D₄×C₈₉	—	2	2	no	—
341	C₂×D₄×C₈₉	—	2	2	no	—
342	C₂×D₄×C₈₉	—	2	1	no	—
343	C₂×D₄×C₈₉	—	2	2	no	—
344	C₂×D₄×C₈₉	—	2	1	no	—
345	C₂×D₄×C₈₉	—	2	1	no	—
346	C₂×D₄×C₈₉	—	2	2	no	—
347	C₂×D₄×C₈₉	—	2	1	no	—
348	C₂×D₄×C₈₉	—	4	2	no	—
349	C₂×D₄×C₈₉	—	4	4	no	—
350	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
351	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
353	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
354	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
355	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₈₉	—	2	2	no	—
357	C₂²×C₄×C₈₉	—	2	1	no	—
358	C₂²×C₄×C₈₉	—	2	1	no	—
359	C₂²×C₄×C₈₉	—	2	1	no	—
360	C₂²×C₄×C₈₉	—	2	2	no	—
361	C₂²×C₄×C₈₉	—	2	2	no	—
362	C₂²×C₄×C₈₉	—	2	1	no	—
363	C₂²×C₄×C₈₉	—	2	1	no	—
364	C₂²×C₄×C₈₉	—	2	1	no	—
365	C₂²×C₄×C₈₉	—	2	2	no	—
366	C₂²×C₄×C₈₉	—	2	2	no	—
367	C₂²×C₄×C₈₉	—	2	2	no	—
368	C₂²×C₄×C₈₉	—	2	2	no	—
369	C₂²×C₄×C₈₉	—	8	4	no	—
370	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
372	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
374	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
375	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
376	Q₁₆×C₈₉	—	2	2	no	—
377	SD₁₆×C₈₉	—	2	4	no	—
378	SD₁₆×C₈₉	—	2	2	no	—
379	SD₁₆×C₈₉	—	4	2	no	—
380	SD₁₆×C₈₉	#41	1	4	yes	complemented
381	D₈×C₈₉	—	2	2	no	—
382	D₈×C₈₉	—	2	4	no	—
383	D₈×C₈₉	—	2	4	no	—
384	D₈×C₈₉	—	4	2	no	—
385	D₈×C₈₉	—	4	2	no	—
386	M₁₆×C₈₉	—	2	4	no	—
387	M₁₆×C₈₉	—	4	2	no	—
388	C₂×C₈×C₈₉	—	2	2	no	—
389	C₂×C₈×C₈₉	—	4	1	no	—
390	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
394	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
395	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
396	C₄⋊C₄×C₈₉	—	2	1	no	—
397	C₄⋊C₄×C₈₉	—	2	2	no	—
398	C₄⋊C₄×C₈₉	—	2	2	no	—
399	C₄⋊C₄×C₈₉	—	2	1	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	1	no	—
404	C₄⋊C₄×C₈₉	—	2	1	no	—
405	C₄⋊C₄×C₈₉	—	2	1	no	—
406	C₄⋊C₄×C₈₉	—	2	2	no	—
407	C₄⋊C₄×C₈₉	—	2	2	no	—
408	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
416	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
418	C₂²⋊C₄×C₈₉	—	2	2	no	—
419	C₂²⋊C₄×C₈₉	—	2	1	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	2	no	—
425	C₂²⋊C₄×C₈₉	—	2	2	no	—
426	C₂²⋊C₄×C₈₉	—	2	2	no	—
427	C₂²⋊C₄×C₈₉	—	2	2	no	—
428	C₂²⋊C₄×C₈₉	—	2	2	no	—
429	C₂²⋊C₄×C₈₉	—	2	2	no	—
430	C₂²⋊C₄×C₈₉	—	2	2	no	—
431	C₂²⋊C₄×C₈₉	—	2	1	no	—
432	C₂²⋊C₄×C₈₉	—	2	2	no	—
433	C₂²⋊C₄×C₈₉	—	2	1	no	—
434	C₂²⋊C₄×C₈₉	—	2	1	no	—
435	C₂²⋊C₄×C₈₉	—	2	2	no	—
436	C₂²⋊C₄×C₈₉	—	2	2	no	—
437	C₂²⋊C₄×C₈₉	—	2	2	no	—
438	C₂²⋊C₄×C₈₉	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	1	no	—
442	C₄²×C₈₉	—	2	2	no	—
443	C₄²×C₈₉	—	2	1	no	—
444	C₄²×C₈₉	—	2	1	no	—
445	C₄²×C₈₉	—	2	2	no	—
446	C₄²×C₈₉	—	2	1	no	—
447	C₄²×C₈₉	—	2	1	no	—
448	C₄²×C₈₉	—	2	1	no	—
449	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
450	C₄²×C₈₉	C₂×D₄	1	2	yes	—
451	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₈₉	C₂×D₄	1	2	yes	—
453	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
454	C₄²×C₈₉	C₂⁴	1	2	yes	—
455	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
456	C₂³×C₈₉	—	2	1	no	—
457	C₂³×C₈₉	—	2	2	no	—
458	C₂³×C₈₉	—	2	2	no	—
459	C₂³×C₈₉	—	2	1	no	—
460	C₂³×C₈₉	—	4	4	no	—
461	C₂³×C₈₉	—	4	4	no	—
462	C₂³×C₈₉	—	8	2	no	—
463	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
464	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
465	Q₈×C₈₉	—	2	2	no	—
466	Q₈×C₈₉	—	2	1	no	—
467	Q₈×C₈₉	—	2	1	no	—
468	Q₈×C₈₉	—	2	1	no	—
469	Q₈×C₈₉	—	8	2	no	—
470	Q₈×C₈₉	—	8	1	no	—
471	Q₈×C₈₉	—	8	1	no	—
472	Q₈×C₈₉	C₂×#41	1	2	yes	—
473	D₄×C₈₉	—	2	2	no	—
474	D₄×C₈₉	—	2	2	no	—
475	D₄×C₈₉	—	2	2	no	—
476	D₄×C₈₉	—	2	1	no	—
477	D₄×C₈₉	—	2	1	no	—
478	D₄×C₈₉	—	2	2	no	—
479	D₄×C₈₉	—	2	1	no	—
480	D₄×C₈₉	—	2	2	no	—
481	D₄×C₈₉	—	4	2	no	—
482	D₄×C₈₉	—	4	4	no	—
483	D₄×C₈₉	—	4	2	no	—
484	D₄×C₈₉	—	4	4	no	—
485	D₄×C₈₉	—	4	4	no	—
486	D₄×C₈₉	—	4	2	no	—
487	D₄×C₈₉	—	4	4	no	—
488	D₄×C₈₉	—	4	2	no	—
489	D₄×C₈₉	—	4	2	no	—
490	D₄×C₈₉	—	8	2	no	—
491	D₄×C₈₉	—	8	1	no	—
492	D₄×C₈₉	—	8	1	no	—
493	D₄×C₈₉	—	8	2	no	—
494	D₄×C₈₉	—	8	2	no	—
495	D₄×C₈₉	—	8	2	no	—
496	D₄×C₈₉	—	8	2	no	—
497	D₄×C₈₉	C₂×#41	1	2	yes	—
498	C₂×C₄×C₈₉	—	2	1	no	—
499	C₂×C₄×C₈₉	—	2	2	no	—
500	C₂×C₄×C₈₉	—	2	4	no	—
501	C₂×C₄×C₈₉	—	2	2	no	—
502	C₂×C₄×C₈₉	—	2	1	no	—
503	C₂×C₄×C₈₉	—	2	2	no	—
504	C₂×C₄×C₈₉	—	2	1	no	—
505	C₂×C₄×C₈₉	—	2	2	no	—
506	C₂×C₄×C₈₉	—	2	1	no	—
507	C₂×C₄×C₈₉	—	2	1	no	—
508	C₂×C₄×C₈₉	—	2	1	no	—
509	C₂×C₄×C₈₉	—	2	1	no	—
510	C₂×C₄×C₈₉	—	2	1	no	—
511	C₂×C₄×C₈₉	—	2	2	no	—
512	C₂×C₄×C₈₉	—	2	2	no	—
513	C₂×C₄×C₈₉	—	4	2	no	—
514	C₂×C₄×C₈₉	—	4	2	no	—
515	C₂×C₄×C₈₉	—	4	4	no	—
516	C₂×C₄×C₈₉	—	4	2	no	—
517	C₂×C₄×C₈₉	—	4	4	no	—
518	C₂×C₄×C₈₉	—	4	2	no	—
519	C₂×C₄×C₈₉	—	4	2	no	—
520	C₂×C₄×C₈₉	—	4	2	no	—
521	C₂×C₄×C₈₉	—	4	4	no	—
522	C₂×C₄×C₈₉	—	4	2	no	—
523	C₂×C₄×C₈₉	—	4	4	no	—
524	C₂×C₄×C₈₉	—	8	2	no	—
525	C₂×C₄×C₈₉	—	8	2	no	—
526	C₂×C₄×C₈₉	—	8	2	no	—
527	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
536	C₈×C₈₉	—	2	1	no	—
537	C₈×C₈₉	—	2	2	no	—
538	C₈×C₈₉	—	2	1	no	—
539	C₈×C₈₉	—	2	1	no	—
540	C₈×C₈₉	—	2	2	no	—
541	C₈×C₈₉	C₂×#41	1	2	yes	—
542	C₂²×C₈₉	—	2	1	no	—
543	C₂²×C₈₉	—	2	2	no	—
544	C₂²×C₈₉	—	2	2	no	—
545	C₂²×C₈₉	—	2	1	no	—
546	C₂²×C₈₉	—	2	2	no	—
547	C₂²×C₈₉	—	2	2	no	—
548	C₂²×C₈₉	—	2	1	no	—
549	C₂²×C₈₉	—	4	1	no	—
550	C₂²×C₈₉	—	4	1	no	—
551	C₂²×C₈₉	—	4	2	no	—
552	C₂²×C₈₉	—	4	1	no	—
553	C₂²×C₈₉	—	4	2	no	—
554	C₂²×C₈₉	—	4	2	no	—
555	C₂²×C₈₉	—	4	1	no	—
556	C₂²×C₈₉	—	4	2	no	—
557	C₂²×C₈₉	—	4	2	no	—
558	C₂²×C₈₉	—	4	1	no	—
559	C₂²×C₈₉	—	4	2	no	—
560	C₂²×C₈₉	—	8	8	no	—
561	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
562	C₄×C₈₉	—	2	1	no	—
563	C₄×C₈₉	—	2	2	no	—
564	C₄×C₈₉	—	2	2	no	—
565	C₄×C₈₉	—	2	1	no	—
566	C₄×C₈₉	—	2	2	no	—
567	C₄×C₈₉	—	2	2	no	—
568	C₄×C₈₉	—	2	1	no	—
569	C₄×C₈₉	—	4	1	no	—
570	C₄×C₈₉	—	4	1	no	—
571	C₄×C₈₉	—	4	1	no	—
572	C₄×C₈₉	—	4	1	no	—
573	C₄×C₈₉	—	4	2	no	—
574	C₄×C₈₉	—	4	1	no	—
575	C₄×C₈₉	—	4	2	no	—
576	C₄×C₈₉	#575	1	2	yes	—
577	C₄×C₈₉	#576	1	2	yes	—
578	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
579	C₄×C₈₉	#585	1	1	yes	characteristic
580	#61449	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
581	C₂×C₈₉	—	4	1	no	—
582	C₂×C₈₉	—	4	2	no	—
583	C₂×C₈₉	—	4	2	no	—
584	C₂×C₈₉	—	8	2	no	—
585	C₂×C₈₉	—	8	1	no	—
586	C₂×C₈₉	—	8	2	no	—
587	C₂×C₈₉	D₄×#41	1	1	yes	characteristic
588	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
589	C₂×C₈₉	C₂×#576	1	1	yes	characteristic
590	#3483	C₂×C₈₉	1	1	yes	characteristic, complemented
591	#3481	C₂×C₈₉	1	1	yes	characteristic, complemented
592	#3399	C₂×C₈₉	1	1	yes	characteristic, complemented
593	#3385	C₂×C₈₉	1	1	yes	characteristic, complemented
594	#3375	C₂×C₈₉	1	1	yes	characteristic, complemented
595	#3366	C₂×C₈₉	1	1	yes	characteristic, complemented
596	#3357	C₂×C₈₉	1	1	yes	characteristic, complemented
597	#3347	C₂×C₈₉	1	2	yes	complemented
598	#3333	C₂×C₈₉	1	1	yes	characteristic, complemented
599	#3325	C₂×C₈₉	1	1	yes	characteristic, complemented
600	#3319	C₂×C₈₉	1	2	yes	complemented
601	#3309	C₂×C₈₉	1	2	yes	complemented
602	#3274	C₂×C₈₉	1	1	yes	characteristic, complemented
603	#3268	C₂×C₈₉	1	2	yes	complemented
604	#3171	C₂×C₈₉	1	2	yes	complemented
605	#3169	C₂×C₈₉	1	1	yes	characteristic, complemented
606	#3106	C₂×C₈₉	1	1	yes	characteristic, complemented
607	#3106	C₂×C₈₉	1	1	yes	characteristic, complemented
608	#3102	C₂×C₈₉	1	2	yes	complemented
609	#3100	C₂×C₈₉	1	2	yes	complemented
610	#2965	C₂×C₈₉	1	1	yes	characteristic, complemented
611	C₄×AGL(1,ℤ/8)	C₂×C₈₉	1	2	yes	complemented
612	C₄×#135	C₂×C₈₉	1	1	yes	characteristic, complemented
613	C₈₉	#61449	1	1	yes	characteristic, direct product factor, Sylow
614	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
615	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
616	#559	C₂²×C₈₉	1	1	yes	characteristic
617	Q₈²	C₂²×C₈₉	1	1	yes	characteristic, complemented
618	#555	—	2	1	no	—
619	#555	—	2	2	no	—
620	#555	C₂²×C₈₉	1	1	yes	characteristic
621	#555	C₂²×C₈₉	1	2	yes	complemented
622	#554	C₂²×C₈₉	1	1	yes	characteristic
623	#554	C₂²×C₈₉	1	1	yes	characteristic
624	#553	—	2	1	no	—
625	#553	C₂²×C₈₉	1	2	yes	—
626	#551	—	2	2	no	—
627	#550	—	2	1	no	—
628	#550	C₂²×C₈₉	1	1	yes	characteristic
629	#550	C₂²×C₈₉	1	2	yes	complemented
630	#550	C₂²×C₈₉	1	1	yes	characteristic, complemented
631	#546	—	2	1	no	—
632	#546	C₂²×C₈₉	1	2	yes	—
633	D₄²	C₂²×C₈₉	1	1	yes	characteristic
634	#532	—	2	1	no	—
635	#532	—	2	2	no	—
636	#532	C₂²×C₈₉	1	1	yes	characteristic
637	#532	C₂²×C₈₉	1	2	yes	complemented
638	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
639	#529	—	2	1	no	—
640	#529	C₂²×C₈₉	1	2	yes	—
641	#525	—	2	2	no	—
642	C₄×#41	—	2	1	no	—
643	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
644	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
645	C₄×#41	C₂²×C₈₉	1	2	yes	complemented
646	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic, complemented
647	C₂×C₄×D₄	—	2	1	no	—
648	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
649	#501	C₂²×C₈₉	1	2	yes	complemented
650	#500	C₂²×C₈₉	1	1	yes	characteristic, complemented
651	#496	C₂²×C₈₉	1	2	yes	complemented
652	#493	C₂²×C₈₉	1	1	yes	characteristic
653	#490	C₂²×C₈₉	1	2	yes	complemented
654	#489	C₂²×C₈₉	1	2	yes	complemented
655	#486	C₂²×C₈₉	1	1	yes	characteristic
656	#486	C₂²×C₈₉	1	1	yes	characteristic, complemented
657	#485	C₂²×C₈₉	1	2	yes	complemented
658	#482	C₂²×C₈₉	1	2	yes	—
659	#482	C₂²×C₈₉	1	2	yes	complemented
660	#482	C₂²×C₈₉	1	2	yes	complemented
661	#480	C₂²×C₈₉	1	2	yes	complemented
662	#480	C₂²×C₈₉	1	2	yes	complemented
663	#479	C₂²×C₈₉	1	2	yes	complemented
664	#478	C₂²×C₈₉	1	2	yes	complemented
665	#477	C₂²×C₈₉	1	1	yes	characteristic, complemented
666	#477	C₂²×C₈₉	1	1	yes	characteristic, complemented
667	#476	C₂²×C₈₉	1	1	yes	characteristic
668	#476	C₂²×C₈₉	1	1	yes	characteristic, complemented
669	#474	C₂²×C₈₉	1	2	yes	—
670	#474	C₂²×C₈₉	1	2	yes	complemented
671	#469	C₂²×C₈₉	1	2	yes	—
672	#469	C₂²×C₈₉	1	2	yes	—
673	#468	C₂²×C₈₉	1	2	yes	complemented
674	#468	C₂²×C₈₉	1	2	yes	complemented
675	#466	C₂²×C₈₉	1	2	yes	complemented
676	#466	C₂²×C₈₉	1	2	yes	complemented
677	#464	C₂²×C₈₉	1	2	yes	complemented
678	#463	C₂²×C₈₉	1	2	yes	complemented
679	#460	C₂²×C₈₉	1	1	yes	characteristic
680	#460	C₂²×C₈₉	1	1	yes	characteristic, complemented
681	#459	C₂²×C₈₉	1	2	yes	—
682	#459	C₂²×C₈₉	1	1	yes	characteristic
683	#459	C₂²×C₈₉	1	1	yes	characteristic
684	#459	C₂²×C₈₉	1	2	yes	complemented
685	#452	C₂²×C₈₉	1	2	yes	complemented
686	#449	C₂²×C₈₉	1	2	yes	—
687	#449	C₂²×C₈₉	1	2	yes	—
688	#449	C₂²×C₈₉	1	2	yes	complemented
689	#447	C₂²×C₈₉	1	2	yes	—
690	#447	C₂²×C₈₉	1	2	yes	—
691	#446	C₂²×C₈₉	1	1	yes	characteristic, complemented
692	#446	C₂²×C₈₉	1	1	yes	characteristic, complemented
693	#442	C₂²×C₈₉	1	2	yes	—
694	#442	C₂²×C₈₉	1	2	yes	complemented
695	#440	C₂²×C₈₉	1	2	yes	—
696	#440	C₂²×C₈₉	1	2	yes	complemented
697	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
698	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
699	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
700	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
701	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
702	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
703	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
704	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
705	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
706	C₄×D₈	C₂²×C₈₉	1	2	yes	—
707	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
708	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
709	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
710	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
711	#436	C₂²×C₈₉	1	1	yes	characteristic
712	#436	C₂²×C₈₉	1	1	yes	characteristic
713	#435	C₂²×C₈₉	1	2	yes	complemented
714	#435	C₂²×C₈₉	1	2	yes	complemented
715	#431	C₂²×C₈₉	1	2	yes	complemented
716	#431	C₂²×C₈₉	1	1	yes	characteristic, complemented
717	#428	C₂²×C₈₉	1	2	yes	complemented
718	#427	C₂²×C₈₉	1	1	yes	characteristic, complemented
719	#418	C₂²×C₈₉	1	2	yes	—
720	#417	C₂²×C₈₉	1	2	yes	complemented
721	#416	C₂²×C₈₉	1	1	yes	characteristic
722	#416	C₂²×C₈₉	1	1	yes	characteristic, complemented
723	C₄×M₁₆	C₂²×C₈₉	1	2	yes	complemented
724	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
725	C₂×#41	—	2	1	no	—
726	C₂×#41	—	2	1	no	—
727	C₂×#41	—	2	2	no	—
728	C₂×#41	—	2	1	no	—
729	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
730	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
731	C₂×#41	C₂³×C₈₉	1	2	yes	—
732	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
733	C₂²×D₄	—	2	1	no	—
734	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
735	C₂³×C₄	—	2	2	no	—
736	AGL(1,ℤ/8)	—	2	8	no	—
737	#135	—	2	4	no	—
738	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
739	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
740	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
741	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
742	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
743	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
744	C₂×D₈	C₂³×C₈₉	1	2	yes	—
745	C₂×D₈	C₂³×C₈₉	1	2	yes	—
746	C₂×D₈	C₂³×C₈₉	1	2	yes	—
747	C₂×D₈	C₂³×C₈₉	1	2	yes	—
748	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
749	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
750	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
751	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
752	C₄⋊Q₈	—	2	1	no	—
753	C₄⋊Q₈	—	2	2	no	—
754	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
755	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
756	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
757	#127	—	2	1	no	—
758	#127	—	2	2	no	—
759	#127	C₂³×C₈₉	1	1	yes	characteristic
760	#127	C₂³×C₈₉	1	1	yes	characteristic
761	#127	C₂³×C₈₉	1	2	yes	—
762	#126	—	2	2	no	—
763	#126	—	2	2	no	—
764	#125	—	2	1	no	—
765	#125	C₂³×C₈₉	1	2	yes	—
766	#124	—	2	1	no	—
767	#124	—	2	2	no	—
768	#124	—	2	2	no	—
769	#124	—	2	2	no	—
770	#124	—	2	1	no	—
771	#124	—	2	1	no	—
772	#124	—	2	2	no	—
773	#124	C₂³×C₈₉	1	2	yes	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
782	#121	—	2	2	no	—
783	#121	—	2	1	no	—
784	#121	—	2	2	no	—
785	#121	—	2	1	no	—
786	#121	—	2	1	no	—
787	#121	—	2	2	no	—
788	#121	—	2	1	no	—
789	#121	—	2	1	no	—
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	—	2	2	no	—
793	#121	—	2	2	no	—
794	#121	—	2	2	no	—
795	#121	C₂³×C₈₉	1	2	yes	—
796	#121	C₂³×C₈₉	1	2	yes	—
797	#121	C₂³×C₈₉	1	2	yes	—
798	#121	C₂³×C₈₉	1	2	yes	—
799	#121	C₂³×C₈₉	1	2	yes	—
800	#120	—	2	2	no	—
801	#120	—	2	2	no	—
802	C₄×Q₈	—	2	1	no	—
803	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
804	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
805	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
806	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
807	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
808	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
809	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
828	C₄×D₄	D₄×C₈₉	1	2	yes	—
829	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
830	C₄×D₄	C₂³×C₈₉	1	2	yes	—
831	C₄×D₄	C₂³×C₈₉	1	2	yes	—
832	C₄×D₄	C₂³×C₈₉	1	2	yes	—
833	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
834	C₄×D₄	C₂³×C₈₉	1	2	yes	—
835	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
836	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
837	C₄×D₄	C₂³×C₈₉	1	2	yes	—
838	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₈₉	1	2	yes	—
840	#117	—	2	1	no	—
841	#117	—	2	2	no	—
842	#117	—	2	1	no	—
843	#117	—	2	1	no	—
844	#117	—	2	2	no	—
845	#117	—	2	2	no	—
846	#117	D₄×C₈₉	1	2	yes	—
847	#117	D₄×C₈₉	1	1	yes	characteristic
848	#117	C₂³×C₈₉	1	1	yes	characteristic
849	#117	C₂³×C₈₉	1	2	yes	—
850	#117	C₂³×C₈₉	1	1	yes	characteristic
851	C₂×C₄⋊C₄	—	2	1	no	—
852	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
853	C₂×C₂²⋊C₄	—	2	2	no	—
854	C₂×C₂²⋊C₄	—	2	2	no	—
855	C₂×C₄²	—	2	1	no	—
856	C₂×C₄²	—	2	1	no	—
857	C₂×C₄²	—	2	2	no	—
858	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
859	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
860	#107	C₂³×C₈₉	1	1	yes	characteristic
861	#107	C₂³×C₈₉	1	1	yes	characteristic
862	#107	C₂³×C₈₉	1	2	yes	—
863	#107	C₂³×C₈₉	1	2	yes	—
864	#107	C₂³×C₈₉	1	2	yes	—
865	#107	C₂³×C₈₉	1	2	yes	—
866	#106	C₂³×C₈₉	1	1	yes	characteristic
867	#106	C₂³×C₈₉	1	1	yes	characteristic
868	#106	C₂³×C₈₉	1	2	yes	—
869	#106	C₂³×C₈₉	1	2	yes	—
870	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
871	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
872	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
873	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
874	#103	C₂³×C₈₉	1	1	yes	characteristic
875	#103	C₂³×C₈₉	1	1	yes	characteristic
876	#103	C₂³×C₈₉	1	1	yes	characteristic
877	#103	C₂³×C₈₉	1	1	yes	characteristic
878	#103	C₂³×C₈₉	1	2	yes	—
879	#103	C₂³×C₈₉	1	2	yes	—
880	#102	C₂³×C₈₉	1	1	yes	characteristic
881	#102	C₂³×C₈₉	1	1	yes	characteristic
882	#102	C₂³×C₈₉	1	1	yes	characteristic
883	#102	C₂³×C₈₉	1	1	yes	characteristic
884	#102	C₂³×C₈₉	1	2	yes	—
885	#102	C₂³×C₈₉	1	2	yes	—
886	#102	C₂³×C₈₉	1	2	yes	—
887	#102	C₂³×C₈₉	1	2	yes	—
888	#102	C₂³×C₈₉	1	2	yes	—
889	#102	C₂³×C₈₉	1	2	yes	—
890	#102	C₂³×C₈₉	1	2	yes	—
891	#102	C₂³×C₈₉	1	2	yes	—
892	#102	C₂³×C₈₉	1	2	yes	—
893	#102	C₂³×C₈₉	1	2	yes	—
894	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
895	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
896	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
897	#97	C₂³×C₈₉	1	2	yes	—
898	#97	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	C₄×C₈	C₂³×C₈₉	1	2	yes	—
904	C₂⁴	—	2	2	no	—
905	#41	—	2	2	no	—
906	#41	—	2	4	no	—
907	#41	—	2	2	no	—
908	#41	—	4	2	no	—
909	#41	—	4	1	no	—
910	#41	—	4	1	no	—
911	#41	—	4	2	no	—
912	#41	—	4	4	no	—
913	#41	—	8	4	no	—
914	#41	—	8	2	no	—
915	#41	—	8	2	no	—
916	C₂×Q₈	—	2	1	no	—
917	C₂×Q₈	—	2	2	no	—
918	C₂×Q₈	—	2	1	no	—
919	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
920	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
921	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
922	C₂×D₄	—	2	4	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	1	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	4	2	no	—
939	C₂×D₄	—	4	4	no	—
940	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
941	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
942	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
943	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
944	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
945	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	2	2	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	1	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	2	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	8	4	no	—
960	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
961	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
962	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
963	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
964	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
965	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
966	Q₁₆	—	2	2	no	—
967	SD₁₆	—	2	4	no	—
968	SD₁₆	—	2	2	no	—
969	SD₁₆	—	4	2	no	—
970	SD₁₆	#41×C₈₉	1	4	yes	complemented
971	D₈	—	2	2	no	—
972	D₈	—	2	4	no	—
973	D₈	—	2	4	no	—
974	D₈	—	4	2	no	—
975	D₈	—	4	2	no	—
976	M₁₆	—	2	4	no	—
977	M₁₆	—	4	2	no	—
978	C₂×C₈	—	2	2	no	—
979	C₂×C₈	—	4	1	no	—
980	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
981	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
982	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
983	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
984	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
985	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
999	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
1000	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1001	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1002	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1003	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1004	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1005	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1006	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1007	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1029	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1030	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	1	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	2	2	no	—
1038	C₄²	—	2	1	no	—
1039	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1040	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1041	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1042	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1043	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1044	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1045	C₄²	C₂⁴×C₈₉	1	2	yes	—
1046	C₂³	—	2	1	no	—
1047	C₂³	—	2	2	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	4	4	no	—
1051	C₂³	—	4	4	no	—
1052	C₂³	—	8	2	no	—
1053	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1054	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1055	Q₈	—	2	2	no	—
1056	Q₈	—	2	1	no	—
1057	Q₈	—	2	1	no	—
1058	Q₈	—	2	1	no	—
1059	Q₈	—	8	2	no	—
1060	Q₈	—	8	1	no	—
1061	Q₈	—	8	1	no	—
1062	Q₈	C₂×#41×C₈₉	1	2	yes	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	2	1	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	2	2	no	—
1069	D₄	—	2	1	no	—
1070	D₄	—	2	2	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	4	4	no	—
1073	D₄	—	4	2	no	—
1074	D₄	—	4	4	no	—
1075	D₄	—	4	4	no	—
1076	D₄	—	4	2	no	—
1077	D₄	—	4	4	no	—
1078	D₄	—	4	2	no	—
1079	D₄	—	4	2	no	—
1080	D₄	—	8	2	no	—
1081	D₄	—	8	1	no	—
1082	D₄	—	8	1	no	—
1083	D₄	—	8	2	no	—
1084	D₄	—	8	2	no	—
1085	D₄	—	8	2	no	—
1086	D₄	—	8	2	no	—
1087	D₄	C₂×#41×C₈₉	1	2	yes	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	4	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	4	2	no	—
1104	C₂×C₄	—	4	2	no	—
1105	C₂×C₄	—	4	4	no	—
1106	C₂×C₄	—	4	2	no	—
1107	C₂×C₄	—	4	4	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	4	2	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	4	4	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	4	4	no	—
1114	C₂×C₄	—	8	2	no	—
1115	C₂×C₄	—	8	2	no	—
1116	C₂×C₄	—	8	2	no	—
1117	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1118	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1119	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1120	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1121	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1122	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1123	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1124	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1125	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1126	C₈	—	2	1	no	—
1127	C₈	—	2	2	no	—
1128	C₈	—	2	1	no	—
1129	C₈	—	2	1	no	—
1130	C₈	—	2	2	no	—
1131	C₈	C₂×#41×C₈₉	1	2	yes	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	2	no	—
1135	C₂²	—	2	1	no	—
1136	C₂²	—	2	1	no	—
1137	C₂²	—	2	2	no	—
1138	C₂²	—	2	2	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	4	2	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	2	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	4	1	no	—
1149	C₂²	—	4	2	no	—
1150	C₂²	—	8	8	no	—
1151	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1152	C₄	—	2	1	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	2	no	—
1155	C₄	—	2	1	no	—
1156	C₄	—	2	1	no	—
1157	C₄	—	2	2	no	—
1158	C₄	—	2	2	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	1	no	—
1161	C₄	—	4	1	no	—
1162	C₄	—	4	2	no	—
1163	C₄	—	4	1	no	—
1164	C₄	—	4	2	no	—
1165	C₄	—	4	1	no	—
1166	C₄	#575×C₈₉	1	2	yes	—
1167	C₄	#576×C₈₉	1	2	yes	—
1168	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
1169	C₄	#585×C₈₉	1	1	yes	characteristic
1170	C₂	—	4	1	no	—
1171	C₂	—	4	2	no	—
1172	C₂	—	4	2	no	—
1173	C₂	—	8	2	no	—
1174	C₂	—	8	1	no	—
1175	C₂	—	8	2	no	—
1176	C₂	D₄×#41×C₈₉	1	1	yes	characteristic
1177	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
1178	C₂	C₂×#576×C₈₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3483	C₂	semidirect
2. C₈₉×#3481	C₂	semidirect
3. C₈₉×#3399	C₂	semidirect
4. C₈₉×#3385	C₂	semidirect
5. C₈₉×#3375	C₂	semidirect
6. C₈₉×#3366	C₂	semidirect
7. C₈₉×#3357	C₂	semidirect
8. C₈₉×#3347	C₂	semidirect
9. C₈₉×#3333	C₂	semidirect
10. C₈₉×#3325	C₂	semidirect
11. C₈₉×#3319	C₂	semidirect
12. C₈₉×#3309	C₂	semidirect
13. C₈₉×#3274	C₂	semidirect
14. C₈₉×#3268	C₂	semidirect
15. C₈₉×#3171	C₂	semidirect
16. C₈₉×#3169	C₂	semidirect
17. C₈₉×#3106	C₂	semidirect
18. C₈₉×#3106	C₂	semidirect
19. C₈₉×#3102	C₂	semidirect
20. C₈₉×#3100	C₂	semidirect
21. C₈₉×#2965	C₂	semidirect
22. C₄×AGL(1,ℤ/8)×C₈₉	C₂	semidirect
23. C₄×#135×C₈₉	C₂	semidirect
27. Q₈²×C₈₉	C₂²	semidirect
31. #555×C₈₉	C₂²	semidirect
39. #550×C₈₉	C₂²	semidirect
40. #550×C₈₉	C₂²	semidirect
47. #532×C₈₉	C₂²	semidirect
48. #532×C₈₉	C₂²	semidirect
55. C₄×#41×C₈₉	C₂²	semidirect
56. C₄×#41×C₈₉	C₂²	semidirect
59. #501×C₈₉	C₂²	semidirect
60. #500×C₈₉	C₂²	semidirect
61. #496×C₈₉	C₂²	semidirect
63. #490×C₈₉	C₂²	semidirect
64. #489×C₈₉	C₂²	semidirect
66. #486×C₈₉	C₂²	semidirect
67. #485×C₈₉	C₂²	semidirect
69. #482×C₈₉	C₂²	semidirect
70. #482×C₈₉	C₂²	semidirect
71. #480×C₈₉	C₂²	semidirect
72. #480×C₈₉	C₂²	semidirect
73. #479×C₈₉	C₂²	semidirect
74. #478×C₈₉	C₂²	semidirect
75. #477×C₈₉	C₂²	semidirect
76. #477×C₈₉	C₂²	semidirect
78. #476×C₈₉	C₂²	semidirect
80. #474×C₈₉	C₂²	semidirect
83. #468×C₈₉	C₂²	semidirect
84. #468×C₈₉	C₂²	semidirect
85. #466×C₈₉	C₂²	semidirect
86. #466×C₈₉	C₂²	semidirect
87. #464×C₈₉	C₂²	semidirect
88. #463×C₈₉	C₂²	semidirect
90. #460×C₈₉	C₂²	semidirect
94. #459×C₈₉	C₂²	semidirect
95. #452×C₈₉	C₂²	semidirect
98. #449×C₈₉	C₂²	semidirect
101. #446×C₈₉	C₂²	semidirect
102. #446×C₈₉	C₂²	semidirect
104. #442×C₈₉	C₂²	semidirect
106. #440×C₈₉	C₂²	semidirect
107. C₄×Q₁₆×C₈₉	C₂²	semidirect
108. C₄×Q₁₆×C₈₉	C₂²	semidirect
111. C₄×SD₁₆×C₈₉	C₂²	semidirect
112. C₄×SD₁₆×C₈₉	C₂²	semidirect
113. C₄×SD₁₆×C₈₉	C₂²	semidirect
114. C₄×SD₁₆×C₈₉	C₂²	semidirect
118. C₄×D₈×C₈₉	C₂²	semidirect
119. C₄×D₈×C₈₉	C₂²	semidirect
120. C₄×D₈×C₈₉	C₂²	semidirect
123. #435×C₈₉	C₂²	semidirect
124. #435×C₈₉	C₂²	semidirect
125. #431×C₈₉	C₂²	semidirect
126. #431×C₈₉	C₂²	semidirect
127. #428×C₈₉	C₂²	semidirect
128. #427×C₈₉	C₂²	semidirect
130. #417×C₈₉	C₂²	semidirect
132. #416×C₈₉	C₂²	semidirect
133. C₄×M₁₆×C₈₉	C₂²	semidirect
134. C₂×C₄×C₈×C₈₉	C₂²	semidirect
380. SD₁₆×C₈₉	#41	semidirect
580. #61449	C₈₉	direct (N × H)
590. #3483	C₂×C₈₉	semidirect
591. #3481	C₂×C₈₉	semidirect
592. #3399	C₂×C₈₉	semidirect
593. #3385	C₂×C₈₉	semidirect
594. #3375	C₂×C₈₉	semidirect
595. #3366	C₂×C₈₉	semidirect
596. #3357	C₂×C₈₉	semidirect
597. #3347	C₂×C₈₉	semidirect
598. #3333	C₂×C₈₉	semidirect
599. #3325	C₂×C₈₉	semidirect
600. #3319	C₂×C₈₉	semidirect
601. #3309	C₂×C₈₉	semidirect
602. #3274	C₂×C₈₉	semidirect
603. #3268	C₂×C₈₉	semidirect
604. #3171	C₂×C₈₉	semidirect
605. #3169	C₂×C₈₉	semidirect
606. #3106	C₂×C₈₉	semidirect
607. #3106	C₂×C₈₉	semidirect
608. #3102	C₂×C₈₉	semidirect
609. #3100	C₂×C₈₉	semidirect
610. #2965	C₂×C₈₉	semidirect
611. C₄×AGL(1,ℤ/8)	C₂×C₈₉	semidirect
612. C₄×#135	C₂×C₈₉	semidirect
613. C₈₉	#61449	direct (N × H)
617. Q₈²	C₂²×C₈₉	semidirect
621. #555	C₂²×C₈₉	semidirect
629. #550	C₂²×C₈₉	semidirect
630. #550	C₂²×C₈₉	semidirect
637. #532	C₂²×C₈₉	semidirect
638. #532	C₂²×C₈₉	semidirect
645. C₄×#41	C₂²×C₈₉	semidirect
646. C₄×#41	C₂²×C₈₉	semidirect
649. #501	C₂²×C₈₉	semidirect
650. #500	C₂²×C₈₉	semidirect
651. #496	C₂²×C₈₉	semidirect
653. #490	C₂²×C₈₉	semidirect
654. #489	C₂²×C₈₉	semidirect
656. #486	C₂²×C₈₉	semidirect
657. #485	C₂²×C₈₉	semidirect
659. #482	C₂²×C₈₉	semidirect
660. #482	C₂²×C₈₉	semidirect
661. #480	C₂²×C₈₉	semidirect
662. #480	C₂²×C₈₉	semidirect
663. #479	C₂²×C₈₉	semidirect
664. #478	C₂²×C₈₉	semidirect
665. #477	C₂²×C₈₉	semidirect
666. #477	C₂²×C₈₉	semidirect
668. #476	C₂²×C₈₉	semidirect
670. #474	C₂²×C₈₉	semidirect
673. #468	C₂²×C₈₉	semidirect
674. #468	C₂²×C₈₉	semidirect
675. #466	C₂²×C₈₉	semidirect
676. #466	C₂²×C₈₉	semidirect
677. #464	C₂²×C₈₉	semidirect
678. #463	C₂²×C₈₉	semidirect
680. #460	C₂²×C₈₉	semidirect
684. #459	C₂²×C₈₉	semidirect
685. #452	C₂²×C₈₉	semidirect
688. #449	C₂²×C₈₉	semidirect
691. #446	C₂²×C₈₉	semidirect
692. #446	C₂²×C₈₉	semidirect
694. #442	C₂²×C₈₉	semidirect
696. #440	C₂²×C₈₉	semidirect
697. C₄×Q₁₆	C₂²×C₈₉	semidirect
698. C₄×Q₁₆	C₂²×C₈₉	semidirect
701. C₄×SD₁₆	C₂²×C₈₉	semidirect
702. C₄×SD₁₆	C₂²×C₈₉	semidirect
703. C₄×SD₁₆	C₂²×C₈₉	semidirect
704. C₄×SD₁₆	C₂²×C₈₉	semidirect
708. C₄×D₈	C₂²×C₈₉	semidirect
709. C₄×D₈	C₂²×C₈₉	semidirect
710. C₄×D₈	C₂²×C₈₉	semidirect
713. #435	C₂²×C₈₉	semidirect
714. #435	C₂²×C₈₉	semidirect
715. #431	C₂²×C₈₉	semidirect
716. #431	C₂²×C₈₉	semidirect
717. #428	C₂²×C₈₉	semidirect
718. #427	C₂²×C₈₉	semidirect
720. #417	C₂²×C₈₉	semidirect
722. #416	C₂²×C₈₉	semidirect
723. C₄×M₁₆	C₂²×C₈₉	semidirect
724. C₂×C₄×C₈	C₂²×C₈₉	semidirect
970. SD₁₆	#41×C₈₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₈₉×#3483	2
C₈₉×#3481	2
C₈₉×#3399	2
C₈₉×#3385	2
C₈₉×#3375	2
C₈₉×#3366	2
C₈₉×#3357	2
C₈₉×#3347	2
C₈₉×#3333	2
C₈₉×#3325	2
C₈₉×#3319	2
C₈₉×#3309	2
C₈₉×#3274	2
C₈₉×#3268	2
C₈₉×#3171	2
C₈₉×#3169	2
C₈₉×#3106	2
C₈₉×#3102	2
C₈₉×#3100	2
C₈₉×#2965	2
C₄×AGL(1,ℤ/8)×C₈₉	2
C₄×#135×C₈₉	2
#61449	89

Subgroups — C89×#61449 #36439297

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61449 #36439297