Subgroups — C₈₉×#60707 #36438555

Order 22784.

1980 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3494	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3180	C₂	1	4	yes	maximal, complemented
3	C₈₉×#3179	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3176	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3175	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3169	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3168	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3155	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3136	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3055	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3050	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#466×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2951	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2948	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2946	C₂	1	2	yes	maximal, complemented
17	C₂×#405×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
19	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
23	#555×C₈₉	—	2	2	no	—
24	#553×C₈₉	—	2	2	no	—
25	#553×C₈₉	—	2	2	no	—
26	#551×C₈₉	—	2	4	no	—
27	#547×C₈₉	—	2	2	no	—
28	#546×C₈₉	—	2	4	no	—
29	#544×C₈₉	C₂²	1	2	yes	—
30	#542×C₈₉	C₂²	1	4	yes	complemented
31	#540×C₈₉	C₂²	1	4	yes	complemented
32	#535×C₈₉	C₂²	1	2	yes	—
33	#532×C₈₉	C₂²	1	4	yes	complemented
34	#529×C₈₉	C₂²	1	4	yes	complemented
35	#525×C₈₉	C₂²	1	2	yes	—
36	C₂×#121×C₈₉	C₂²	1	2	yes	—
37	#520×C₈₉	C₂²	1	2	yes	—
38	#518×C₈₉	C₂²	1	2	yes	—
39	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
40	#501×C₈₉	C₂²	1	4	yes	complemented
41	#500×C₈₉	C₂²	1	2	yes	complemented
42	#499×C₈₉	C₂²	1	2	yes	complemented
43	#496×C₈₉	C₂²	1	4	yes	complemented
44	#495×C₈₉	C₂²	1	2	yes	complemented
45	#493×C₈₉	C₂²	1	2	yes	complemented
46	#490×C₈₉	C₂²	1	4	yes	complemented
47	#489×C₈₉	C₂²	1	4	yes	complemented
48	#488×C₈₉	C₂²	1	4	yes	complemented
49	#486×C₈₉	C₂²	1	4	yes	complemented
50	#469×C₈₉	C₂²	1	4	yes	complemented
51	#468×C₈₉	C₂²	1	4	yes	complemented
52	#467×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	#467×C₈₉	C₂²	1	1	yes	characteristic, complemented
54	#466×C₈₉	C₂²	1	2	yes	—
55	#466×C₈₉	C₂²	1	2	yes	—
56	#466×C₈₉	C₂²	1	2	yes	—
57	#466×C₈₉	C₂²	1	2	yes	—
58	#466×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#466×C₈₉	C₂²	1	4	yes	complemented
60	#466×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	#465×C₈₉	C₂²	1	4	yes	complemented
62	#465×C₈₉	C₂²	1	2	yes	complemented
63	#465×C₈₉	C₂²	1	2	yes	complemented
64	#442×C₈₉	C₂²	1	4	yes	complemented
65	#442×C₈₉	C₂²	1	4	yes	complemented
66	#440×C₈₉	C₂²	1	4	yes	complemented
67	#440×C₈₉	C₂²	1	4	yes	complemented
68	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
69	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	complemented
70	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
71	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
72	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
73	C₄×D₈×C₈₉	C₂²	1	4	yes	complemented
74	#428×C₈₉	C₂²	1	2	yes	—
75	#427×C₈₉	C₂²	1	1	yes	characteristic
76	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
77	#418×C₈₉	C₂²	1	2	yes	—
78	#417×C₈₉	C₂²	1	2	yes	—
79	#416×C₈₉	C₂²	1	2	yes	—
80	C₂×#102×C₈₉	C₂²	1	2	yes	—
81	#405×C₈₉	C₂²	1	1	yes	characteristic
82	#405×C₈₉	C₂²	1	1	yes	characteristic
83	#405×C₈₉	C₂²	1	1	yes	characteristic
84	#405×C₈₉	C₂²	1	1	yes	characteristic
85	#405×C₈₉	C₂²	1	2	yes	complemented
86	#405×C₈₉	C₂²	1	2	yes	complemented
87	C₂×#97×C₈₉	C₂²	1	2	yes	complemented
88	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	complemented
89	C₂×#41×C₈₉	—	2	4	no	—
90	C₂×#41×C₈₉	C₂³	1	2	yes	—
91	C₂²×D₄×C₈₉	—	2	2	no	—
92	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
93	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
94	AGL(1,ℤ/8)×C₈₉	—	2	8	no	—
95	#135×C₈₉	—	2	4	no	—
96	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
97	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
99	C₂×D₈×C₈₉	—	2	4	no	—
100	C₂×D₈×C₈₉	C₂³	1	2	yes	—
101	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
102	C₂×D₈×C₈₉	C₂³	1	4	yes	—
103	C₂×D₈×C₈₉	C₂³	1	2	yes	—
104	C₂×M₁₆×C₈₉	—	2	4	no	—
105	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
106	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
107	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₈₉	—	2	4	no	—
109	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
111	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
116	C₄⋊Q₈×C₈₉	—	2	2	no	—
117	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
118	#127×C₈₉	C₂³	1	4	yes	—
119	#126×C₈₉	—	2	4	no	—
120	#126×C₈₉	—	2	4	no	—
121	#125×C₈₉	—	2	2	no	—
122	#125×C₈₉	C₂³	1	4	yes	—
123	#124×C₈₉	—	2	4	no	—
124	#124×C₈₉	—	2	4	no	—
125	#124×C₈₉	C₂³	1	4	yes	—
126	#123×C₈₉	—	2	2	no	—
127	#123×C₈₉	—	2	4	no	—
128	#123×C₈₉	—	2	4	no	—
129	#123×C₈₉	—	2	4	no	—
130	#123×C₈₉	—	2	4	no	—
131	C₂²⋊Q₈×C₈₉	—	2	4	no	—
132	C₂²⋊Q₈×C₈₉	—	2	4	no	—
133	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
134	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
135	#121×C₈₉	—	2	2	no	—
136	#121×C₈₉	—	2	2	no	—
137	#121×C₈₉	—	2	4	no	—
138	#121×C₈₉	—	2	2	no	—
139	#121×C₈₉	—	2	2	no	—
140	#121×C₈₉	—	2	4	no	—
141	#121×C₈₉	—	2	4	no	—
142	#121×C₈₉	C₂³	1	4	yes	—
143	#121×C₈₉	C₂³	1	2	yes	—
144	#121×C₈₉	C₂³	1	2	yes	—
145	#121×C₈₉	C₂³	1	4	yes	—
146	#120×C₈₉	—	2	2	no	—
147	#120×C₈₉	—	2	4	no	—
148	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
149	C₄×D₄×C₈₉	—	2	2	no	—
150	C₄×D₄×C₈₉	—	2	2	no	—
151	C₄×D₄×C₈₉	—	2	4	no	—
152	C₄×D₄×C₈₉	—	2	2	no	—
153	C₄×D₄×C₈₉	—	2	2	no	—
154	C₄×D₄×C₈₉	—	2	4	no	—
155	C₄×D₄×C₈₉	—	2	4	no	—
156	C₄×D₄×C₈₉	C₂³	1	4	yes	—
157	C₄×D₄×C₈₉	C₂³	1	4	yes	—
158	C₄×D₄×C₈₉	C₂³	1	4	yes	—
159	#117×C₈₉	—	2	2	no	—
160	#117×C₈₉	—	2	4	no	—
161	#117×C₈₉	D₄	1	2	yes	—
162	#117×C₈₉	D₄	1	1	yes	characteristic
163	#117×C₈₉	D₄	1	1	yes	characteristic
164	#117×C₈₉	C₂³	1	2	yes	—
165	#117×C₈₉	C₂³	1	1	yes	characteristic
166	#117×C₈₉	C₂³	1	1	yes	characteristic
167	#117×C₈₉	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
169	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
173	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
174	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
175	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
176	#107×C₈₉	C₂³	1	2	yes	—
177	#107×C₈₉	C₂³	1	2	yes	—
178	#107×C₈₉	C₂³	1	1	yes	characteristic
179	#107×C₈₉	C₂³	1	1	yes	characteristic
180	#107×C₈₉	C₂³	1	4	yes	—
181	#106×C₈₉	C₂³	1	2	yes	—
182	#106×C₈₉	C₂³	1	4	yes	—
183	#103×C₈₉	C₂³	1	2	yes	—
184	#103×C₈₉	C₂³	1	2	yes	—
185	#103×C₈₉	C₂³	1	4	yes	—
186	#102×C₈₉	C₂³	1	4	yes	—
187	#102×C₈₉	C₂³	1	4	yes	—
188	#102×C₈₉	C₂³	1	2	yes	—
189	#102×C₈₉	C₂³	1	2	yes	—
190	#102×C₈₉	C₂³	1	4	yes	—
191	#102×C₈₉	C₂³	1	4	yes	—
192	#102×C₈₉	C₂³	1	4	yes	—
193	#97×C₈₉	C₂³	1	2	yes	—
194	#97×C₈₉	C₂³	1	2	yes	—
195	#97×C₈₉	C₂³	1	2	yes	—
196	#97×C₈₉	C₂³	1	2	yes	—
197	C₄×C₈×C₈₉	C₂³	1	2	yes	—
198	C₄×C₈×C₈₉	C₂³	1	2	yes	—
199	C₄×C₈×C₈₉	C₂³	1	2	yes	—
200	C₄×C₈×C₈₉	C₂³	1	2	yes	—
201	C₂⁴×C₈₉	—	2	2	no	—
202	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
203	#41×C₈₉	—	2	4	no	—
204	#41×C₈₉	—	2	4	no	—
205	#41×C₈₉	—	8	8	no	—
206	C₂×Q₈×C₈₉	—	2	4	no	—
207	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
208	C₂×D₄×C₈₉	—	2	2	no	—
209	C₂×D₄×C₈₉	—	2	2	no	—
210	C₂×D₄×C₈₉	—	2	4	no	—
211	C₂×D₄×C₈₉	—	2	2	no	—
212	C₂×D₄×C₈₉	—	2	4	no	—
213	C₂×D₄×C₈₉	—	2	2	no	—
214	C₂×D₄×C₈₉	—	2	4	no	—
215	C₂×D₄×C₈₉	—	2	4	no	—
216	C₂×D₄×C₈₉	—	2	4	no	—
217	C₂×D₄×C₈₉	—	2	4	no	—
218	C₂×D₄×C₈₉	—	8	4	no	—
219	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
220	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₈₉	—	2	2	no	—
222	C₂²×C₄×C₈₉	—	2	2	no	—
223	C₂²×C₄×C₈₉	—	2	2	no	—
224	C₂²×C₄×C₈₉	—	2	2	no	—
225	C₂²×C₄×C₈₉	—	2	4	no	—
226	C₂²×C₄×C₈₉	—	2	4	no	—
227	C₂²×C₄×C₈₉	—	2	4	no	—
228	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
229	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
233	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
236	Q₁₆×C₈₉	—	2	2	no	—
237	SD₁₆×C₈₉	—	2	4	no	—
238	SD₁₆×C₈₉	—	2	8	no	—
239	D₈×C₈₉	—	2	4	no	—
240	D₈×C₈₉	—	2	4	no	—
241	D₈×C₈₉	—	2	2	no	—
242	D₈×C₈₉	—	2	8	no	—
243	M₁₆×C₈₉	—	2	2	no	—
244	M₁₆×C₈₉	—	2	4	no	—
245	M₁₆×C₈₉	#41	1	4	yes	complemented
246	C₂×C₈×C₈₉	—	2	2	no	—
247	C₂×C₈×C₈₉	—	2	2	no	—
248	C₂×C₈×C₈₉	—	2	2	no	—
249	C₂×C₈×C₈₉	—	2	2	no	—
250	C₂×C₈×C₈₉	—	2	2	no	—
251	C₂×C₈×C₈₉	—	2	4	no	—
252	C₂×C₈×C₈₉	#41	1	4	yes	complemented
253	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
254	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
255	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
256	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
257	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
258	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
259	C₄⋊C₄×C₈₉	—	2	2	no	—
260	C₄⋊C₄×C₈₉	—	2	4	no	—
261	C₄⋊C₄×C₈₉	—	2	2	no	—
262	C₄⋊C₄×C₈₉	—	2	4	no	—
263	C₄⋊C₄×C₈₉	—	2	4	no	—
264	C₄⋊C₄×C₈₉	—	2	4	no	—
265	C₄⋊C₄×C₈₉	—	2	2	no	—
266	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
267	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
268	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
269	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
270	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
271	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
272	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
273	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
274	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
275	C₂²⋊C₄×C₈₉	—	2	2	no	—
276	C₂²⋊C₄×C₈₉	—	2	2	no	—
277	C₂²⋊C₄×C₈₉	—	2	2	no	—
278	C₂²⋊C₄×C₈₉	—	2	4	no	—
279	C₂²⋊C₄×C₈₉	—	2	4	no	—
280	C₂²⋊C₄×C₈₉	—	2	4	no	—
281	C₂²⋊C₄×C₈₉	—	2	4	no	—
282	C₂²⋊C₄×C₈₉	—	2	4	no	—
283	C₂²⋊C₄×C₈₉	—	2	4	no	—
284	C₂²⋊C₄×C₈₉	—	2	2	no	—
285	C₂²⋊C₄×C₈₉	—	2	4	no	—
286	C₂²⋊C₄×C₈₉	—	2	2	no	—
287	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
288	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
289	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
290	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
291	C₄²×C₈₉	—	2	4	no	—
292	C₄²×C₈₉	—	2	2	no	—
293	C₄²×C₈₉	C₂×D₄	1	2	yes	—
294	C₄²×C₈₉	C₂×D₄	1	2	yes	—
295	C₄²×C₈₉	C₂⁴	1	2	yes	—
296	C₄²×C₈₉	C₂⁴	1	2	yes	—
297	C₂³×C₈₉	—	2	2	no	—
298	C₂³×C₈₉	—	2	2	no	—
299	C₂³×C₈₉	—	2	4	no	—
300	C₂³×C₈₉	—	2	2	no	—
301	C₂³×C₈₉	—	4	1	no	—
302	C₂³×C₈₉	—	4	4	no	—
303	C₂³×C₈₉	—	8	2	no	—
304	C₂³×C₈₉	—	8	2	no	—
305	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
306	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
307	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
308	Q₈×C₈₉	—	2	2	no	—
309	Q₈×C₈₉	—	2	2	no	—
310	Q₈×C₈₉	—	8	4	no	—
311	D₄×C₈₉	—	2	4	no	—
312	D₄×C₈₉	—	2	2	no	—
313	D₄×C₈₉	—	2	4	no	—
314	D₄×C₈₉	—	2	2	no	—
315	D₄×C₈₉	—	4	4	no	—
316	D₄×C₈₉	—	4	8	no	—
317	D₄×C₈₉	—	4	4	no	—
318	D₄×C₈₉	—	4	4	no	—
319	D₄×C₈₉	—	8	4	no	—
320	D₄×C₈₉	—	8	4	no	—
321	D₄×C₈₉	—	8	2	no	—
322	D₄×C₈₉	—	8	4	no	—
323	C₂×C₄×C₈₉	—	2	2	no	—
324	C₂×C₄×C₈₉	—	2	4	no	—
325	C₂×C₄×C₈₉	—	2	2	no	—
326	C₂×C₄×C₈₉	—	2	2	no	—
327	C₂×C₄×C₈₉	—	2	1	no	—
328	C₂×C₄×C₈₉	—	2	1	no	—
329	C₂×C₄×C₈₉	—	2	1	no	—
330	C₂×C₄×C₈₉	—	2	1	no	—
331	C₂×C₄×C₈₉	—	2	2	no	—
332	C₂×C₄×C₈₉	—	2	2	no	—
333	C₂×C₄×C₈₉	—	2	2	no	—
334	C₂×C₄×C₈₉	—	2	4	no	—
335	C₂×C₄×C₈₉	—	4	2	no	—
336	C₂×C₄×C₈₉	—	4	4	no	—
337	C₂×C₄×C₈₉	—	8	4	no	—
338	C₂×C₄×C₈₉	—	8	4	no	—
339	C₂×C₄×C₈₉	—	8	4	no	—
340	C₂×C₄×C₈₉	—	8	2	no	—
341	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
345	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
349	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
350	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
351	C₈×C₈₉	—	2	1	no	—
352	C₈×C₈₉	—	2	1	no	—
353	C₈×C₈₉	—	2	2	no	—
354	C₈×C₈₉	C₂×#41	1	2	yes	—
355	C₈×C₈₉	C₂×#41	1	2	yes	—
356	C₈×C₈₉	C₂×#41	1	4	yes	—
357	C₂²×C₈₉	—	2	1	no	—
358	C₂²×C₈₉	—	2	1	no	—
359	C₂²×C₈₉	—	2	1	no	—
360	C₂²×C₈₉	—	2	1	no	—
361	C₂²×C₈₉	—	2	1	no	—
362	C₂²×C₈₉	—	2	1	no	—
363	C₂²×C₈₉	—	2	1	no	—
364	C₂²×C₈₉	—	4	4	no	—
365	C₂²×C₈₉	—	4	4	no	—
366	C₂²×C₈₉	—	4	2	no	—
367	C₂²×C₈₉	—	4	2	no	—
368	C₂²×C₈₉	—	4	4	no	—
369	C₂²×C₈₉	—	4	2	no	—
370	C₂²×C₈₉	—	4	4	no	—
371	C₂²×C₈₉	—	16	4	no	—
372	C₂²×C₈₉	#532	1	2	yes	—
373	C₂²×C₈₉	#576	1	2	yes	—
374	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
375	C₄×C₈₉	—	2	2	no	—
376	C₄×C₈₉	—	2	2	no	—
377	C₄×C₈₉	—	2	1	no	—
378	C₄×C₈₉	—	2	1	no	—
379	C₄×C₈₉	—	2	2	no	—
380	C₄×C₈₉	—	2	2	no	—
381	C₄×C₈₉	—	4	2	no	—
382	C₄×C₈₉	—	4	2	no	—
383	C₄×C₈₉	—	4	4	no	—
384	C₄×C₈₉	—	4	2	no	—
385	C₄×C₈₉	#532	1	2	yes	—
386	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
387	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
388	#60707	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
389	C₂×C₈₉	—	2	2	no	—
390	C₂×C₈₉	—	2	2	no	—
391	C₂×C₈₉	—	4	1	no	—
392	C₂×C₈₉	—	8	2	no	—
393	C₂×C₈₉	—	8	4	no	—
394	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
395	C₂×C₈₉	C₂×#576	1	1	yes	characteristic
396	C₂×C₈₉	#3584	1	1	yes	characteristic
397	#3494	C₂×C₈₉	1	2	yes	complemented
398	#3180	C₂×C₈₉	1	4	yes	complemented
399	#3179	C₂×C₈₉	1	4	yes	complemented
400	#3176	C₂×C₈₉	1	2	yes	complemented
401	#3175	C₂×C₈₉	1	2	yes	complemented
402	#3169	C₂×C₈₉	1	2	yes	complemented
403	#3168	C₂×C₈₉	1	2	yes	complemented
404	#3164	C₂×C₈₉	1	1	yes	characteristic, complemented
405	#3155	C₂×C₈₉	1	1	yes	characteristic, complemented
406	#3136	C₂×C₈₉	1	2	yes	complemented
407	#3055	C₂×C₈₉	1	2	yes	complemented
408	#3050	C₂×C₈₉	1	1	yes	characteristic, complemented
409	C₂×#466	C₂×C₈₉	1	1	yes	characteristic, complemented
410	#2951	C₂×C₈₉	1	1	yes	characteristic, complemented
411	#2948	C₂×C₈₉	1	1	yes	characteristic, complemented
412	#2946	C₂×C₈₉	1	2	yes	complemented
413	C₂×#405	C₂×C₈₉	1	1	yes	characteristic, complemented
414	C₈₉	#60707	1	1	yes	characteristic, direct product factor, Sylow
415	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
416	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
417	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
418	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
419	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
420	#555	—	2	2	no	—
421	#553	—	2	2	no	—
422	#553	—	2	2	no	—
423	#551	—	2	4	no	—
424	#547	—	2	2	no	—
425	#546	—	2	4	no	—
426	#544	C₂²×C₈₉	1	2	yes	—
427	#542	C₂²×C₈₉	1	4	yes	complemented
428	#540	C₂²×C₈₉	1	4	yes	complemented
429	#535	C₂²×C₈₉	1	2	yes	—
430	#532	C₂²×C₈₉	1	4	yes	complemented
431	#529	C₂²×C₈₉	1	4	yes	complemented
432	#525	C₂²×C₈₉	1	2	yes	—
433	C₂×#121	C₂²×C₈₉	1	2	yes	—
434	#520	C₂²×C₈₉	1	2	yes	—
435	#518	C₂²×C₈₉	1	2	yes	—
436	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
437	#501	C₂²×C₈₉	1	4	yes	complemented
438	#500	C₂²×C₈₉	1	2	yes	complemented
439	#499	C₂²×C₈₉	1	2	yes	complemented
440	#496	C₂²×C₈₉	1	4	yes	complemented
441	#495	C₂²×C₈₉	1	2	yes	complemented
442	#493	C₂²×C₈₉	1	2	yes	complemented
443	#490	C₂²×C₈₉	1	4	yes	complemented
444	#489	C₂²×C₈₉	1	4	yes	complemented
445	#488	C₂²×C₈₉	1	4	yes	complemented
446	#486	C₂²×C₈₉	1	4	yes	complemented
447	#469	C₂²×C₈₉	1	4	yes	complemented
448	#468	C₂²×C₈₉	1	4	yes	complemented
449	#467	C₂²×C₈₉	1	1	yes	characteristic, complemented
450	#467	C₂²×C₈₉	1	1	yes	characteristic, complemented
451	#466	C₂²×C₈₉	1	2	yes	—
452	#466	C₂²×C₈₉	1	2	yes	—
453	#466	C₂²×C₈₉	1	2	yes	—
454	#466	C₂²×C₈₉	1	2	yes	—
455	#466	C₂²×C₈₉	1	1	yes	characteristic, complemented
456	#466	C₂²×C₈₉	1	4	yes	complemented
457	#466	C₂²×C₈₉	1	1	yes	characteristic, complemented
458	#465	C₂²×C₈₉	1	4	yes	complemented
459	#465	C₂²×C₈₉	1	2	yes	complemented
460	#465	C₂²×C₈₉	1	2	yes	complemented
461	#442	C₂²×C₈₉	1	4	yes	complemented
462	#442	C₂²×C₈₉	1	4	yes	complemented
463	#440	C₂²×C₈₉	1	4	yes	complemented
464	#440	C₂²×C₈₉	1	4	yes	complemented
465	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
466	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	complemented
467	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
468	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
469	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
470	C₄×D₈	C₂²×C₈₉	1	4	yes	complemented
471	#428	C₂²×C₈₉	1	2	yes	—
472	#427	C₂²×C₈₉	1	1	yes	characteristic
473	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
474	#418	C₂²×C₈₉	1	2	yes	—
475	#417	C₂²×C₈₉	1	2	yes	—
476	#416	C₂²×C₈₉	1	2	yes	—
477	C₂×#102	C₂²×C₈₉	1	2	yes	—
478	#405	C₂²×C₈₉	1	1	yes	characteristic
479	#405	C₂²×C₈₉	1	1	yes	characteristic
480	#405	C₂²×C₈₉	1	1	yes	characteristic
481	#405	C₂²×C₈₉	1	1	yes	characteristic
482	#405	C₂²×C₈₉	1	2	yes	complemented
483	#405	C₂²×C₈₉	1	2	yes	complemented
484	C₂×#97	C₂²×C₈₉	1	2	yes	complemented
485	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	complemented
486	C₂×#41	—	2	4	no	—
487	C₂×#41	C₂³×C₈₉	1	2	yes	—
488	C₂²×D₄	—	2	2	no	—
489	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
490	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
491	AGL(1,ℤ/8)	—	2	8	no	—
492	#135	—	2	4	no	—
493	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
494	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
495	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
496	C₂×D₈	—	2	4	no	—
497	C₂×D₈	C₂³×C₈₉	1	2	yes	—
498	C₂×D₈	C₂³×C₈₉	1	2	yes	—
499	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
500	C₂×D₈	C₂³×C₈₉	1	4	yes	—
501	C₂×M₁₆	—	2	4	no	—
502	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
503	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
504	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
505	C₂²×C₈	—	2	4	no	—
506	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
507	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
508	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
509	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
510	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
511	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
512	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
513	C₄⋊Q₈	—	2	2	no	—
514	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
515	#127	C₂³×C₈₉	1	4	yes	—
516	#126	—	2	4	no	—
517	#126	—	2	4	no	—
518	#125	—	2	2	no	—
519	#125	C₂³×C₈₉	1	4	yes	—
520	#124	—	2	4	no	—
521	#124	—	2	4	no	—
522	#124	C₂³×C₈₉	1	4	yes	—
523	#123	—	2	2	no	—
524	#123	—	2	4	no	—
525	#123	—	2	4	no	—
526	#123	—	2	4	no	—
527	#123	—	2	4	no	—
528	C₂²⋊Q₈	—	2	4	no	—
529	C₂²⋊Q₈	—	2	4	no	—
530	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
531	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
532	#121	—	2	2	no	—
533	#121	—	2	2	no	—
534	#121	—	2	4	no	—
535	#121	—	2	2	no	—
536	#121	—	2	2	no	—
537	#121	—	2	4	no	—
538	#121	—	2	4	no	—
539	#121	C₂³×C₈₉	1	4	yes	—
540	#121	C₂³×C₈₉	1	4	yes	—
541	#121	C₂³×C₈₉	1	2	yes	—
542	#121	C₂³×C₈₉	1	2	yes	—
543	#120	—	2	2	no	—
544	#120	—	2	4	no	—
545	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	—	2	2	no	—
548	C₄×D₄	—	2	4	no	—
549	C₄×D₄	—	2	2	no	—
550	C₄×D₄	—	2	2	no	—
551	C₄×D₄	—	2	4	no	—
552	C₄×D₄	—	2	4	no	—
553	C₄×D₄	C₂³×C₈₉	1	4	yes	—
554	C₄×D₄	C₂³×C₈₉	1	4	yes	—
555	C₄×D₄	C₂³×C₈₉	1	4	yes	—
556	#117	—	2	2	no	—
557	#117	—	2	4	no	—
558	#117	D₄×C₈₉	1	2	yes	—
559	#117	D₄×C₈₉	1	1	yes	characteristic
560	#117	D₄×C₈₉	1	1	yes	characteristic
561	#117	C₂³×C₈₉	1	2	yes	—
562	#117	C₂³×C₈₉	1	1	yes	characteristic
563	#117	C₂³×C₈₉	1	1	yes	characteristic
564	#117	C₂³×C₈₉	1	2	yes	—
565	C₂×C₄⋊C₄	—	2	2	no	—
566	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
567	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
569	C₂×C₂²⋊C₄	—	2	2	no	—
570	C₂×C₂²⋊C₄	—	2	4	no	—
571	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
572	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
573	#107	C₂³×C₈₉	1	2	yes	—
574	#107	C₂³×C₈₉	1	2	yes	—
575	#107	C₂³×C₈₉	1	1	yes	characteristic
576	#107	C₂³×C₈₉	1	1	yes	characteristic
577	#107	C₂³×C₈₉	1	4	yes	—
578	#106	C₂³×C₈₉	1	2	yes	—
579	#106	C₂³×C₈₉	1	4	yes	—
580	#103	C₂³×C₈₉	1	2	yes	—
581	#103	C₂³×C₈₉	1	2	yes	—
582	#103	C₂³×C₈₉	1	4	yes	—
583	#102	C₂³×C₈₉	1	4	yes	—
584	#102	C₂³×C₈₉	1	4	yes	—
585	#102	C₂³×C₈₉	1	2	yes	—
586	#102	C₂³×C₈₉	1	2	yes	—
587	#102	C₂³×C₈₉	1	4	yes	—
588	#102	C₂³×C₈₉	1	4	yes	—
589	#102	C₂³×C₈₉	1	4	yes	—
590	#97	C₂³×C₈₉	1	2	yes	—
591	#97	C₂³×C₈₉	1	2	yes	—
592	#97	C₂³×C₈₉	1	2	yes	—
593	#97	C₂³×C₈₉	1	2	yes	—
594	C₄×C₈	C₂³×C₈₉	1	2	yes	—
595	C₄×C₈	C₂³×C₈₉	1	2	yes	—
596	C₄×C₈	C₂³×C₈₉	1	2	yes	—
597	C₄×C₈	C₂³×C₈₉	1	2	yes	—
598	C₂⁴	—	2	2	no	—
599	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
600	#41	—	2	4	no	—
601	#41	—	2	4	no	—
602	#41	—	8	8	no	—
603	C₂×Q₈	—	2	4	no	—
604	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
605	C₂×D₄	—	2	2	no	—
606	C₂×D₄	—	2	2	no	—
607	C₂×D₄	—	2	4	no	—
608	C₂×D₄	—	2	2	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	2	no	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	8	4	no	—
616	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
617	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
626	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
627	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
628	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
629	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
630	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
631	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
632	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
633	Q₁₆	—	2	2	no	—
634	SD₁₆	—	2	4	no	—
635	SD₁₆	—	2	8	no	—
636	D₈	—	2	4	no	—
637	D₈	—	2	4	no	—
638	D₈	—	2	2	no	—
639	D₈	—	2	8	no	—
640	M₁₆	—	2	2	no	—
641	M₁₆	—	2	4	no	—
642	M₁₆	#41×C₈₉	1	4	yes	complemented
643	C₂×C₈	—	2	2	no	—
644	C₂×C₈	—	2	2	no	—
645	C₂×C₈	—	2	2	no	—
646	C₂×C₈	—	2	2	no	—
647	C₂×C₈	—	2	2	no	—
648	C₂×C₈	—	2	4	no	—
649	C₂×C₈	#41×C₈₉	1	4	yes	complemented
650	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
651	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
652	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
653	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
654	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
655	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
664	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
665	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
666	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
667	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
668	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
669	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
670	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
671	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
672	C₂²⋊C₄	—	2	2	no	—
673	C₂²⋊C₄	—	2	2	no	—
674	C₂²⋊C₄	—	2	2	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	2	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
685	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
686	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
687	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
688	C₄²	—	2	4	no	—
689	C₄²	—	2	2	no	—
690	C₄²	C₂×D₄×C₈₉	1	2	yes	—
691	C₄²	C₂×D₄×C₈₉	1	2	yes	—
692	C₄²	C₂⁴×C₈₉	1	2	yes	—
693	C₄²	C₂⁴×C₈₉	1	2	yes	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	4	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	4	1	no	—
699	C₂³	—	4	4	no	—
700	C₂³	—	8	2	no	—
701	C₂³	—	8	2	no	—
702	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
703	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
704	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
705	Q₈	—	2	2	no	—
706	Q₈	—	2	2	no	—
707	Q₈	—	8	4	no	—
708	D₄	—	2	4	no	—
709	D₄	—	2	2	no	—
710	D₄	—	2	4	no	—
711	D₄	—	2	2	no	—
712	D₄	—	4	4	no	—
713	D₄	—	4	8	no	—
714	D₄	—	4	4	no	—
715	D₄	—	4	4	no	—
716	D₄	—	8	4	no	—
717	D₄	—	8	4	no	—
718	D₄	—	8	2	no	—
719	D₄	—	8	4	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	4	no	—
732	C₂×C₄	—	4	2	no	—
733	C₂×C₄	—	4	4	no	—
734	C₂×C₄	—	8	4	no	—
735	C₂×C₄	—	8	4	no	—
736	C₂×C₄	—	8	4	no	—
737	C₂×C₄	—	8	2	no	—
738	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
739	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
740	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
741	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
742	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
743	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
744	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
745	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
746	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
747	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
748	C₈	—	2	1	no	—
749	C₈	—	2	1	no	—
750	C₈	—	2	2	no	—
751	C₈	C₂×#41×C₈₉	1	2	yes	—
752	C₈	C₂×#41×C₈₉	1	2	yes	—
753	C₈	C₂×#41×C₈₉	1	4	yes	—
754	C₂²	—	2	1	no	—
755	C₂²	—	2	1	no	—
756	C₂²	—	2	1	no	—
757	C₂²	—	2	1	no	—
758	C₂²	—	2	1	no	—
759	C₂²	—	2	1	no	—
760	C₂²	—	2	1	no	—
761	C₂²	—	4	4	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	4	no	—
764	C₂²	—	4	4	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	4	no	—
768	C₂²	—	16	4	no	—
769	C₂²	#532×C₈₉	1	2	yes	—
770	C₂²	#576×C₈₉	1	2	yes	—
771	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
772	C₄	—	2	2	no	—
773	C₄	—	2	2	no	—
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	1	no	—
777	C₄	—	2	1	no	—
778	C₄	—	4	4	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	2	no	—
782	C₄	#532×C₈₉	1	2	yes	—
783	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
784	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
785	C₂	—	2	2	no	—
786	C₂	—	2	2	no	—
787	C₂	—	4	1	no	—
788	C₂	—	8	2	no	—
789	C₂	—	8	4	no	—
790	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
791	C₂	C₂×#576×C₈₉	1	1	yes	characteristic
792	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×#117×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3494	C₂	semidirect
2. C₈₉×#3180	C₂	semidirect
3. C₈₉×#3179	C₂	semidirect
4. C₈₉×#3176	C₂	semidirect
5. C₈₉×#3175	C₂	semidirect
6. C₈₉×#3169	C₂	semidirect
7. C₈₉×#3168	C₂	semidirect
8. C₈₉×#3164	C₂	semidirect
9. C₈₉×#3155	C₂	semidirect
10. C₈₉×#3136	C₂	semidirect
11. C₈₉×#3055	C₂	semidirect
12. C₈₉×#3050	C₂	semidirect
13. C₂×#466×C₈₉	C₂	semidirect
14. C₈₉×#2951	C₂	semidirect
15. C₈₉×#2948	C₂	semidirect
16. C₈₉×#2946	C₂	semidirect
17. C₂×#405×C₈₉	C₂	semidirect
30. #542×C₈₉	C₂²	semidirect
31. #540×C₈₉	C₂²	semidirect
33. #532×C₈₉	C₂²	semidirect
34. #529×C₈₉	C₂²	semidirect
40. #501×C₈₉	C₂²	semidirect
41. #500×C₈₉	C₂²	semidirect
42. #499×C₈₉	C₂²	semidirect
43. #496×C₈₉	C₂²	semidirect
44. #495×C₈₉	C₂²	semidirect
45. #493×C₈₉	C₂²	semidirect
46. #490×C₈₉	C₂²	semidirect
47. #489×C₈₉	C₂²	semidirect
48. #488×C₈₉	C₂²	semidirect
49. #486×C₈₉	C₂²	semidirect
50. #469×C₈₉	C₂²	semidirect
51. #468×C₈₉	C₂²	semidirect
52. #467×C₈₉	C₂²	semidirect
53. #467×C₈₉	C₂²	semidirect
58. #466×C₈₉	C₂²	semidirect
59. #466×C₈₉	C₂²	semidirect
60. #466×C₈₉	C₂²	semidirect
61. #465×C₈₉	C₂²	semidirect
62. #465×C₈₉	C₂²	semidirect
63. #465×C₈₉	C₂²	semidirect
64. #442×C₈₉	C₂²	semidirect
65. #442×C₈₉	C₂²	semidirect
66. #440×C₈₉	C₂²	semidirect
67. #440×C₈₉	C₂²	semidirect
68. C₄×Q₁₆×C₈₉	C₂²	semidirect
69. C₄×SD₁₆×C₈₉	C₂²	semidirect
70. C₄×D₈×C₈₉	C₂²	semidirect
71. C₄×D₈×C₈₉	C₂²	semidirect
72. C₄×D₈×C₈₉	C₂²	semidirect
73. C₄×D₈×C₈₉	C₂²	semidirect
85. #405×C₈₉	C₂²	semidirect
86. #405×C₈₉	C₂²	semidirect
87. C₂×#97×C₈₉	C₂²	semidirect
88. C₂×C₄×C₈×C₈₉	C₂²	semidirect
245. M₁₆×C₈₉	#41	semidirect
252. C₂×C₈×C₈₉	#41	semidirect
388. #60707	C₈₉	direct (N × H)
397. #3494	C₂×C₈₉	semidirect
398. #3180	C₂×C₈₉	semidirect
399. #3179	C₂×C₈₉	semidirect
400. #3176	C₂×C₈₉	semidirect
401. #3175	C₂×C₈₉	semidirect
402. #3169	C₂×C₈₉	semidirect
403. #3168	C₂×C₈₉	semidirect
404. #3164	C₂×C₈₉	semidirect
405. #3155	C₂×C₈₉	semidirect
406. #3136	C₂×C₈₉	semidirect
407. #3055	C₂×C₈₉	semidirect
408. #3050	C₂×C₈₉	semidirect
409. C₂×#466	C₂×C₈₉	semidirect
410. #2951	C₂×C₈₉	semidirect
411. #2948	C₂×C₈₉	semidirect
412. #2946	C₂×C₈₉	semidirect
413. C₂×#405	C₂×C₈₉	semidirect
414. C₈₉	#60707	direct (N × H)
427. #542	C₂²×C₈₉	semidirect
428. #540	C₂²×C₈₉	semidirect
430. #532	C₂²×C₈₉	semidirect
431. #529	C₂²×C₈₉	semidirect
437. #501	C₂²×C₈₉	semidirect
438. #500	C₂²×C₈₉	semidirect
439. #499	C₂²×C₈₉	semidirect
440. #496	C₂²×C₈₉	semidirect
441. #495	C₂²×C₈₉	semidirect
442. #493	C₂²×C₈₉	semidirect
443. #490	C₂²×C₈₉	semidirect
444. #489	C₂²×C₈₉	semidirect
445. #488	C₂²×C₈₉	semidirect
446. #486	C₂²×C₈₉	semidirect
447. #469	C₂²×C₈₉	semidirect
448. #468	C₂²×C₈₉	semidirect
449. #467	C₂²×C₈₉	semidirect
450. #467	C₂²×C₈₉	semidirect
455. #466	C₂²×C₈₉	semidirect
456. #466	C₂²×C₈₉	semidirect
457. #466	C₂²×C₈₉	semidirect
458. #465	C₂²×C₈₉	semidirect
459. #465	C₂²×C₈₉	semidirect
460. #465	C₂²×C₈₉	semidirect
461. #442	C₂²×C₈₉	semidirect
462. #442	C₂²×C₈₉	semidirect
463. #440	C₂²×C₈₉	semidirect
464. #440	C₂²×C₈₉	semidirect
465. C₄×Q₁₆	C₂²×C₈₉	semidirect
466. C₄×SD₁₆	C₂²×C₈₉	semidirect
467. C₄×D₈	C₂²×C₈₉	semidirect
468. C₄×D₈	C₂²×C₈₉	semidirect
469. C₄×D₈	C₂²×C₈₉	semidirect
470. C₄×D₈	C₂²×C₈₉	semidirect
482. #405	C₂²×C₈₉	semidirect
483. #405	C₂²×C₈₉	semidirect
484. C₂×#97	C₂²×C₈₉	semidirect
485. C₂×C₄×C₈	C₂²×C₈₉	semidirect
642. M₁₆	#41×C₈₉	semidirect
649. C₂×C₈	#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×#3494	2
C₈₉×#3180	2
C₈₉×#3179	2
C₈₉×#3176	2
C₈₉×#3175	2
C₈₉×#3169	2
C₈₉×#3168	2
C₈₉×#3164	2
C₈₉×#3155	2
C₈₉×#3136	2
C₈₉×#3055	2
C₈₉×#3050	2
C₂×#466×C₈₉	2
C₈₉×#2951	2
C₈₉×#2948	2
C₈₉×#2946	2
C₂×#405×C₈₉	2
#60707	89

Subgroups — C89×#60707 #36438555

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60707 #36438555