Subgroups — C₈₉×#61258 #36439106

Order 22784.

1866 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3492	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3346	C₂	1	4	yes	maximal, complemented
3	C₈₉×#3343	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3339	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3338	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3336	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3334	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3098	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3092	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3083	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3061	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3050	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2951	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2929	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2913	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#107×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
21	#554×C₈₉	—	2	2	no	—
22	#554×C₈₉	C₂²	1	4	yes	—
23	#553×C₈₉	—	2	2	no	—
24	#553×C₈₉	C₂²	1	4	yes	—
25	#552×C₈₉	—	2	2	no	—
26	#552×C₈₉	C₂²	1	4	yes	—
27	#547×C₈₉	—	2	2	no	—
28	#547×C₈₉	C₂²	1	4	yes	—
29	#544×C₈₉	C₂²	1	2	yes	—
30	#539×C₈₉	—	2	4	no	—
31	#537×C₈₉	C₂²	1	2	yes	—
32	#525×C₈₉	—	2	4	no	—
33	#525×C₈₉	C₂²	1	2	yes	—
34	#525×C₈₉	C₂²	1	1	yes	characteristic
35	#520×C₈₉	C₂²	1	2	yes	—
36	#520×C₈₉	C₂²	1	2	yes	—
37	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
38	#501×C₈₉	C₂²	1	4	yes	complemented
39	#500×C₈₉	C₂²	1	2	yes	complemented
40	#499×C₈₉	C₂²	1	2	yes	complemented
41	#485×C₈₉	C₂²	1	4	yes	complemented
42	#484×C₈₉	C₂²	1	4	yes	—
43	#484×C₈₉	C₂²	1	4	yes	complemented
44	#483×C₈₉	C₂²	1	4	yes	—
45	#482×C₈₉	C₂²	1	4	yes	complemented
46	#481×C₈₉	C₂²	1	4	yes	—
47	#480×C₈₉	C₂²	1	4	yes	—
48	#480×C₈₉	C₂²	1	4	yes	complemented
49	#479×C₈₉	C₂²	1	4	yes	complemented
50	#478×C₈₉	C₂²	1	4	yes	complemented
51	#477×C₈₉	C₂²	1	4	yes	complemented
52	#474×C₈₉	C₂²	1	4	yes	complemented
53	#468×C₈₉	C₂²	1	4	yes	complemented
54	#467×C₈₉	C₂²	1	1	yes	characteristic
55	#467×C₈₉	C₂²	1	1	yes	characteristic
56	#467×C₈₉	C₂²	1	2	yes	complemented
57	#466×C₈₉	C₂²	1	1	yes	characteristic
58	#466×C₈₉	C₂²	1	1	yes	characteristic
59	#466×C₈₉	C₂²	1	2	yes	complemented
60	#465×C₈₉	C₂²	1	2	yes	—
61	#465×C₈₉	C₂²	1	2	yes	—
62	#440×C₈₉	C₂²	1	4	yes	complemented
63	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
64	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
65	#435×C₈₉	C₂²	1	2	yes	—
66	#435×C₈₉	C₂²	1	2	yes	—
67	C₈×D₄×C₈₉	C₂²	1	2	yes	—
68	C₈×D₄×C₈₉	C₂²	1	2	yes	—
69	#428×C₈₉	C₂²	1	2	yes	—
70	#428×C₈₉	C₂²	1	2	yes	—
71	#428×C₈₉	C₂²	1	4	yes	complemented
72	#427×C₈₉	C₂²	1	1	yes	characteristic
73	#427×C₈₉	C₂²	1	2	yes	complemented
74	C₂×#107×C₈₉	C₂²	1	2	yes	—
75	C₂×#107×C₈₉	C₂²	1	2	yes	—
76	C₂×#107×C₈₉	C₂²	1	2	yes	—
77	C₂×#107×C₈₉	C₂²	1	2	yes	—
78	C₂×#107×C₈₉	C₂²	1	2	yes	—
79	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
80	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
81	C₂×#107×C₈₉	C₂²	1	2	yes	complemented
82	#424×C₈₉	C₂²	1	1	yes	characteristic
83	#417×C₈₉	C₂²	1	2	yes	—
84	#417×C₈₉	C₂²	1	2	yes	—
85	#416×C₈₉	C₂²	1	2	yes	—
86	#408×C₈₉	C₂²	1	1	yes	characteristic
87	#407×C₈₉	C₂²	1	1	yes	characteristic
88	#405×C₈₉	C₂²	1	1	yes	characteristic
89	C₂×#41×C₈₉	—	2	4	no	—
90	C₂×#41×C₈₉	C₂³	1	2	yes	—
91	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₈₉	—	2	2	no	—
93	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
94	#135×C₈₉	—	2	4	no	—
95	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
96	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
97	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
98	#131×C₈₉	—	2	4	no	—
99	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
101	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
102	C₂²×C₈×C₈₉	—	2	4	no	—
103	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
109	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
110	C₄⋊Q₈×C₈₉	—	2	2	no	—
111	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
112	#126×C₈₉	—	2	4	no	—
113	#126×C₈₉	—	2	4	no	—
114	#125×C₈₉	—	2	4	no	—
115	#125×C₈₉	—	2	4	no	—
116	#125×C₈₉	—	2	2	no	—
117	#125×C₈₉	C₂³	1	4	yes	—
118	#123×C₈₉	—	2	4	no	—
119	#123×C₈₉	—	2	2	no	—
120	#123×C₈₉	—	2	4	no	—
121	#123×C₈₉	—	2	4	no	—
122	#123×C₈₉	—	2	4	no	—
123	#123×C₈₉	D₄	1	2	yes	—
124	C₂²⋊Q₈×C₈₉	—	2	2	no	—
125	C₂²⋊Q₈×C₈₉	—	2	4	no	—
126	C₂²⋊Q₈×C₈₉	—	2	4	no	—
127	C₂²⋊Q₈×C₈₉	—	2	4	no	—
128	C₂²⋊Q₈×C₈₉	—	2	4	no	—
129	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
130	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
131	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
132	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
133	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
134	#121×C₈₉	—	2	4	no	—
135	#121×C₈₉	—	2	4	no	—
136	#121×C₈₉	—	2	2	no	—
137	#121×C₈₉	D₄	1	1	yes	characteristic
138	#121×C₈₉	D₄	1	1	yes	characteristic
139	#121×C₈₉	C₂³	1	2	yes	—
140	#121×C₈₉	C₂³	1	2	yes	—
141	#121×C₈₉	C₂³	1	4	yes	—
142	#120×C₈₉	—	2	2	no	—
143	#120×C₈₉	D₄	1	2	yes	—
144	C₄×Q₈×C₈₉	—	2	2	no	—
145	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
146	C₄×D₄×C₈₉	—	2	4	no	—
147	C₄×D₄×C₈₉	—	2	2	no	—
148	C₄×D₄×C₈₉	—	2	4	no	—
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	4	no	—
153	C₄×D₄×C₈₉	C₂³	1	4	yes	—
154	C₄×D₄×C₈₉	C₂³	1	2	yes	—
155	C₄×D₄×C₈₉	C₂³	1	2	yes	—
156	#117×C₈₉	—	2	2	no	—
157	#117×C₈₉	—	2	4	no	—
158	#117×C₈₉	C₂³	1	2	yes	—
159	#117×C₈₉	C₂³	1	4	yes	—
160	#117×C₈₉	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
162	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
163	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
164	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
165	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
168	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
169	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
170	#107×C₈₉	C₂³	1	2	yes	—
171	#107×C₈₉	C₂³	1	2	yes	—
172	#107×C₈₉	C₂³	1	2	yes	—
173	#107×C₈₉	C₂³	1	2	yes	—
174	#107×C₈₉	C₂³	1	4	yes	—
175	#107×C₈₉	C₂³	1	4	yes	—
176	#107×C₈₉	C₂³	1	1	yes	characteristic
177	#107×C₈₉	C₂³	1	4	yes	—
178	#107×C₈₉	C₂³	1	1	yes	characteristic
179	#107×C₈₉	C₂³	1	4	yes	—
180	#106×C₈₉	C₂³	1	2	yes	—
181	#106×C₈₉	C₂³	1	4	yes	—
182	#106×C₈₉	C₂³	1	4	yes	—
183	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
184	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
185	#103×C₈₉	C₂³	1	2	yes	—
186	#103×C₈₉	C₂³	1	2	yes	—
187	#103×C₈₉	C₂³	1	4	yes	—
188	#103×C₈₉	C₂³	1	4	yes	—
189	#102×C₈₉	C₂³	1	2	yes	—
190	#102×C₈₉	C₂³	1	2	yes	—
191	#102×C₈₉	C₂³	1	4	yes	—
192	#102×C₈₉	C₂³	1	4	yes	—
193	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
194	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
195	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
196	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
197	#97×C₈₉	C₂³	1	2	yes	—
198	C₄×C₈×C₈₉	C₂³	1	2	yes	—
199	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
200	#41×C₈₉	—	2	2	no	—
201	#41×C₈₉	—	2	2	no	—
202	#41×C₈₉	—	2	4	no	—
203	#41×C₈₉	—	2	4	no	—
204	#41×C₈₉	—	8	8	no	—
205	C₂×Q₈×C₈₉	—	2	4	no	—
206	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
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	2	no	—
211	C₂×D₄×C₈₉	—	2	4	no	—
212	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
213	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
214	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
215	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
216	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₈₉	—	2	2	no	—
218	C₂²×C₄×C₈₉	—	2	2	no	—
219	C₂²×C₄×C₈₉	—	2	4	no	—
220	C₂²×C₄×C₈₉	—	2	2	no	—
221	C₂²×C₄×C₈₉	—	2	4	no	—
222	C₂²×C₄×C₈₉	—	2	2	no	—
223	C₂²×C₄×C₈₉	—	2	4	no	—
224	C₂²×C₄×C₈₉	—	2	2	no	—
225	C₂²×C₄×C₈₉	—	2	4	no	—
226	C₂²×C₄×C₈₉	—	8	4	no	—
227	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
234	Q₁₆×C₈₉	—	2	2	no	—
235	SD₁₆×C₈₉	—	2	4	no	—
236	D₈×C₈₉	—	2	2	no	—
237	M₁₆×C₈₉	—	2	2	no	—
238	M₁₆×C₈₉	—	2	2	no	—
239	M₁₆×C₈₉	—	2	4	no	—
240	C₂×C₈×C₈₉	—	2	2	no	—
241	C₂×C₈×C₈₉	—	2	2	no	—
242	C₂×C₈×C₈₉	—	2	2	no	—
243	C₂×C₈×C₈₉	—	2	2	no	—
244	C₂×C₈×C₈₉	—	2	2	no	—
245	C₂×C₈×C₈₉	—	2	4	no	—
246	C₂×C₈×C₈₉	#41	1	4	yes	complemented
247	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
248	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
249	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
251	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
252	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
253	C₄⋊C₄×C₈₉	—	2	2	no	—
254	C₄⋊C₄×C₈₉	—	2	2	no	—
255	C₄⋊C₄×C₈₉	—	2	4	no	—
256	C₄⋊C₄×C₈₉	—	2	4	no	—
257	C₄⋊C₄×C₈₉	—	2	4	no	—
258	C₄⋊C₄×C₈₉	—	2	4	no	—
259	C₄⋊C₄×C₈₉	—	2	4	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	2	no	—
265	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
266	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
267	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
268	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
269	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
270	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
271	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
272	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
273	C₂²⋊C₄×C₈₉	—	2	2	no	—
274	C₂²⋊C₄×C₈₉	—	2	2	no	—
275	C₂²⋊C₄×C₈₉	—	2	4	no	—
276	C₂²⋊C₄×C₈₉	—	2	2	no	—
277	C₂²⋊C₄×C₈₉	—	2	4	no	—
278	C₂²⋊C₄×C₈₉	—	2	4	no	—
279	C₂²⋊C₄×C₈₉	—	2	4	no	—
280	C₂²⋊C₄×C₈₉	—	2	2	no	—
281	C₂²⋊C₄×C₈₉	—	2	2	no	—
282	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
283	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
284	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
285	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
286	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
287	C₄²×C₈₉	—	2	4	no	—
288	C₄²×C₈₉	—	2	4	no	—
289	C₄²×C₈₉	—	2	2	no	—
290	C₄²×C₈₉	C₂⁴	1	2	yes	—
291	C₂³×C₈₉	—	2	2	no	—
292	C₂³×C₈₉	—	2	2	no	—
293	C₂³×C₈₉	—	2	2	no	—
294	C₂³×C₈₉	—	2	2	no	—
295	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
296	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
297	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
298	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
299	Q₈×C₈₉	—	2	2	no	—
300	Q₈×C₈₉	—	2	2	no	—
301	Q₈×C₈₉	—	2	2	no	—
302	Q₈×C₈₉	—	8	4	no	—
303	D₄×C₈₉	—	2	4	no	—
304	D₄×C₈₉	—	2	4	no	—
305	D₄×C₈₉	—	2	4	no	—
306	D₄×C₈₉	—	2	2	no	—
307	D₄×C₈₉	—	2	2	no	—
308	D₄×C₈₉	—	2	2	no	—
309	D₄×C₈₉	—	4	4	no	—
310	D₄×C₈₉	—	4	4	no	—
311	D₄×C₈₉	—	4	4	no	—
312	D₄×C₈₉	—	8	4	no	—
313	C₂×C₄×C₈₉	—	2	2	no	—
314	C₂×C₄×C₈₉	—	2	2	no	—
315	C₂×C₄×C₈₉	—	2	2	no	—
316	C₂×C₄×C₈₉	—	2	1	no	—
317	C₂×C₄×C₈₉	—	2	1	no	—
318	C₂×C₄×C₈₉	—	2	2	no	—
319	C₂×C₄×C₈₉	—	2	1	no	—
320	C₂×C₄×C₈₉	—	2	1	no	—
321	C₂×C₄×C₈₉	—	2	2	no	—
322	C₂×C₄×C₈₉	—	2	2	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	4	no	—
327	C₂×C₄×C₈₉	—	4	8	no	—
328	C₂×C₄×C₈₉	—	4	4	no	—
329	C₂×C₄×C₈₉	—	8	4	no	—
330	C₂×C₄×C₈₉	—	8	2	no	—
331	C₂×C₄×C₈₉	—	8	4	no	—
332	C₂×C₄×C₈₉	—	8	2	no	—
333	C₂×C₄×C₈₉	—	8	4	no	—
334	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
341	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
342	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
343	C₈×C₈₉	—	2	1	no	—
344	C₈×C₈₉	—	2	1	no	—
345	C₈×C₈₉	—	2	2	no	—
346	C₈×C₈₉	—	2	2	no	—
347	C₈×C₈₉	C₂×#41	1	2	yes	—
348	C₈×C₈₉	C₂×#41	1	2	yes	—
349	C₂²×C₈₉	—	2	8	no	—
350	C₂²×C₈₉	—	2	1	no	—
351	C₂²×C₈₉	—	2	1	no	—
352	C₂²×C₈₉	—	2	1	no	—
353	C₂²×C₈₉	—	2	1	no	—
354	C₂²×C₈₉	—	2	1	no	—
355	C₂²×C₈₉	—	2	1	no	—
356	C₂²×C₈₉	—	2	2	no	—
357	C₂²×C₈₉	—	2	2	no	—
358	C₂²×C₈₉	—	2	2	no	—
359	C₂²×C₈₉	—	4	2	no	—
360	C₂²×C₈₉	—	4	2	no	—
361	C₂²×C₈₉	—	4	2	no	—
362	C₂²×C₈₉	#547	1	2	yes	—
363	C₂²×C₈₉	#576	1	2	yes	—
364	C₂²×C₈₉	#578	1	2	yes	—
365	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
366	C₄×C₈₉	—	2	1	no	—
367	C₄×C₈₉	—	2	1	no	—
368	C₄×C₈₉	—	2	2	no	—
369	C₄×C₈₉	—	2	2	no	—
370	C₄×C₈₉	—	2	2	no	—
371	C₄×C₈₉	—	4	2	no	—
372	C₄×C₈₉	—	4	4	no	—
373	C₄×C₈₉	—	4	4	no	—
374	C₄×C₈₉	—	4	2	no	—
375	C₄×C₈₉	—	4	2	no	—
376	C₄×C₈₉	#547	1	2	yes	—
377	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
378	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
379	#61258	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
380	C₂×C₈₉	—	2	2	no	—
381	C₂×C₈₉	—	2	2	no	—
382	C₂×C₈₉	—	2	2	no	—
383	C₂×C₈₉	—	4	2	no	—
384	C₂×C₈₉	—	8	2	no	—
385	C₂×C₈₉	C₂×#547	1	1	yes	characteristic
386	C₂×C₈₉	C₂×#576	1	1	yes	characteristic
387	C₂×C₈₉	C₂×#578	1	1	yes	characteristic
388	#3492	C₂×C₈₉	1	2	yes	complemented
389	#3346	C₂×C₈₉	1	4	yes	complemented
390	#3343	C₂×C₈₉	1	4	yes	complemented
391	#3339	C₂×C₈₉	1	2	yes	complemented
392	#3338	C₂×C₈₉	1	2	yes	complemented
393	#3336	C₂×C₈₉	1	2	yes	complemented
394	#3334	C₂×C₈₉	1	2	yes	complemented
395	#3164	C₂×C₈₉	1	1	yes	characteristic, complemented
396	#3098	C₂×C₈₉	1	2	yes	complemented
397	#3092	C₂×C₈₉	1	2	yes	complemented
398	#3083	C₂×C₈₉	1	2	yes	complemented
399	#3061	C₂×C₈₉	1	1	yes	characteristic, complemented
400	#3050	C₂×C₈₉	1	1	yes	characteristic, complemented
401	#2951	C₂×C₈₉	1	1	yes	characteristic, complemented
402	#2929	C₂×C₈₉	1	1	yes	characteristic, complemented
403	#2913	C₂×C₈₉	1	1	yes	characteristic, complemented
404	C₂²×#107	C₂×C₈₉	1	1	yes	characteristic, complemented
405	C₈₉	#61258	1	1	yes	characteristic, direct product factor, Sylow
406	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
407	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
408	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
409	#554	—	2	2	no	—
410	#554	C₂²×C₈₉	1	4	yes	—
411	#553	—	2	2	no	—
412	#553	C₂²×C₈₉	1	4	yes	—
413	#552	—	2	2	no	—
414	#552	C₂²×C₈₉	1	4	yes	—
415	#547	—	2	2	no	—
416	#547	C₂²×C₈₉	1	4	yes	—
417	#544	C₂²×C₈₉	1	2	yes	—
418	#539	—	2	4	no	—
419	#537	C₂²×C₈₉	1	2	yes	—
420	#525	—	2	4	no	—
421	#525	C₂²×C₈₉	1	2	yes	—
422	#525	C₂²×C₈₉	1	1	yes	characteristic
423	#520	C₂²×C₈₉	1	2	yes	—
424	#520	C₂²×C₈₉	1	2	yes	—
425	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
426	#501	C₂²×C₈₉	1	4	yes	complemented
427	#500	C₂²×C₈₉	1	2	yes	complemented
428	#499	C₂²×C₈₉	1	2	yes	complemented
429	#485	C₂²×C₈₉	1	4	yes	complemented
430	#484	C₂²×C₈₉	1	4	yes	—
431	#484	C₂²×C₈₉	1	4	yes	complemented
432	#483	C₂²×C₈₉	1	4	yes	—
433	#482	C₂²×C₈₉	1	4	yes	complemented
434	#481	C₂²×C₈₉	1	4	yes	—
435	#480	C₂²×C₈₉	1	4	yes	—
436	#480	C₂²×C₈₉	1	4	yes	complemented
437	#479	C₂²×C₈₉	1	4	yes	complemented
438	#478	C₂²×C₈₉	1	4	yes	complemented
439	#477	C₂²×C₈₉	1	4	yes	complemented
440	#474	C₂²×C₈₉	1	4	yes	complemented
441	#468	C₂²×C₈₉	1	4	yes	complemented
442	#467	C₂²×C₈₉	1	1	yes	characteristic
443	#467	C₂²×C₈₉	1	1	yes	characteristic
444	#467	C₂²×C₈₉	1	2	yes	complemented
445	#466	C₂²×C₈₉	1	1	yes	characteristic
446	#466	C₂²×C₈₉	1	1	yes	characteristic
447	#466	C₂²×C₈₉	1	2	yes	complemented
448	#465	C₂²×C₈₉	1	2	yes	—
449	#465	C₂²×C₈₉	1	2	yes	—
450	#440	C₂²×C₈₉	1	4	yes	complemented
451	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
452	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
453	#435	C₂²×C₈₉	1	2	yes	—
454	#435	C₂²×C₈₉	1	2	yes	—
455	C₈×D₄	C₂²×C₈₉	1	2	yes	—
456	C₈×D₄	C₂²×C₈₉	1	2	yes	—
457	#428	C₂²×C₈₉	1	2	yes	—
458	#428	C₂²×C₈₉	1	2	yes	—
459	#428	C₂²×C₈₉	1	4	yes	complemented
460	#427	C₂²×C₈₉	1	1	yes	characteristic
461	#427	C₂²×C₈₉	1	2	yes	complemented
462	C₂×#107	C₂²×C₈₉	1	2	yes	—
463	C₂×#107	C₂²×C₈₉	1	2	yes	—
464	C₂×#107	C₂²×C₈₉	1	2	yes	—
465	C₂×#107	C₂²×C₈₉	1	2	yes	—
466	C₂×#107	C₂²×C₈₉	1	2	yes	—
467	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
468	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
469	C₂×#107	C₂²×C₈₉	1	2	yes	complemented
470	#424	C₂²×C₈₉	1	1	yes	characteristic
471	#417	C₂²×C₈₉	1	2	yes	—
472	#417	C₂²×C₈₉	1	2	yes	—
473	#416	C₂²×C₈₉	1	2	yes	—
474	#408	C₂²×C₈₉	1	1	yes	characteristic
475	#407	C₂²×C₈₉	1	1	yes	characteristic
476	#405	C₂²×C₈₉	1	1	yes	characteristic
477	C₂×#41	—	2	4	no	—
478	C₂×#41	C₂³×C₈₉	1	2	yes	—
479	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
480	C₂³×C₄	—	2	2	no	—
481	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
482	#135	—	2	4	no	—
483	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
484	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
485	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
486	#131	—	2	4	no	—
487	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
488	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
489	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
490	C₂²×C₈	—	2	4	no	—
491	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
492	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
496	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
497	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
498	C₄⋊Q₈	—	2	2	no	—
499	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
500	#126	—	2	4	no	—
501	#126	—	2	4	no	—
502	#125	—	2	4	no	—
503	#125	—	2	4	no	—
504	#125	—	2	2	no	—
505	#125	C₂³×C₈₉	1	4	yes	—
506	#123	—	2	4	no	—
507	#123	—	2	2	no	—
508	#123	—	2	4	no	—
509	#123	—	2	4	no	—
510	#123	—	2	4	no	—
511	#123	D₄×C₈₉	1	2	yes	—
512	C₂²⋊Q₈	—	2	2	no	—
513	C₂²⋊Q₈	—	2	4	no	—
514	C₂²⋊Q₈	—	2	4	no	—
515	C₂²⋊Q₈	—	2	4	no	—
516	C₂²⋊Q₈	—	2	4	no	—
517	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
518	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
519	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
520	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
521	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
522	#121	—	2	4	no	—
523	#121	—	2	4	no	—
524	#121	—	2	2	no	—
525	#121	D₄×C₈₉	1	1	yes	characteristic
526	#121	D₄×C₈₉	1	1	yes	characteristic
527	#121	C₂³×C₈₉	1	2	yes	—
528	#121	C₂³×C₈₉	1	2	yes	—
529	#121	C₂³×C₈₉	1	4	yes	—
530	#120	—	2	2	no	—
531	#120	D₄×C₈₉	1	2	yes	—
532	C₄×Q₈	—	2	2	no	—
533	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
534	C₄×D₄	—	2	4	no	—
535	C₄×D₄	—	2	2	no	—
536	C₄×D₄	—	2	4	no	—
537	C₄×D₄	—	2	2	no	—
538	C₄×D₄	—	2	2	no	—
539	C₄×D₄	—	2	4	no	—
540	C₄×D₄	—	2	4	no	—
541	C₄×D₄	C₂³×C₈₉	1	4	yes	—
542	C₄×D₄	C₂³×C₈₉	1	2	yes	—
543	C₄×D₄	C₂³×C₈₉	1	2	yes	—
544	#117	—	2	2	no	—
545	#117	—	2	4	no	—
546	#117	C₂³×C₈₉	1	2	yes	—
547	#117	C₂³×C₈₉	1	4	yes	—
548	#117	C₂³×C₈₉	1	1	yes	characteristic
549	C₂×C₄⋊C₄	—	2	2	no	—
550	C₂×C₄⋊C₄	—	2	2	no	—
551	C₂×C₄⋊C₄	—	2	2	no	—
552	C₂×C₄⋊C₄	—	2	2	no	—
553	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
556	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
557	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
558	#107	C₂³×C₈₉	1	2	yes	—
559	#107	C₂³×C₈₉	1	2	yes	—
560	#107	C₂³×C₈₉	1	2	yes	—
561	#107	C₂³×C₈₉	1	2	yes	—
562	#107	C₂³×C₈₉	1	4	yes	—
563	#107	C₂³×C₈₉	1	4	yes	—
564	#107	C₂³×C₈₉	1	1	yes	characteristic
565	#107	C₂³×C₈₉	1	4	yes	—
566	#107	C₂³×C₈₉	1	1	yes	characteristic
567	#107	C₂³×C₈₉	1	4	yes	—
568	#106	C₂³×C₈₉	1	2	yes	—
569	#106	C₂³×C₈₉	1	4	yes	—
570	#106	C₂³×C₈₉	1	4	yes	—
571	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
572	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
573	#103	C₂³×C₈₉	1	2	yes	—
574	#103	C₂³×C₈₉	1	2	yes	—
575	#103	C₂³×C₈₉	1	4	yes	—
576	#103	C₂³×C₈₉	1	4	yes	—
577	#102	C₂³×C₈₉	1	2	yes	—
578	#102	C₂³×C₈₉	1	2	yes	—
579	#102	C₂³×C₈₉	1	4	yes	—
580	#102	C₂³×C₈₉	1	4	yes	—
581	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
582	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
583	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
584	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
585	#97	C₂³×C₈₉	1	2	yes	—
586	C₄×C₈	C₂³×C₈₉	1	2	yes	—
587	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
588	#41	—	2	2	no	—
589	#41	—	2	2	no	—
590	#41	—	2	4	no	—
591	#41	—	2	4	no	—
592	#41	—	8	8	no	—
593	C₂×Q₈	—	2	4	no	—
594	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
595	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
601	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
602	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
603	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
604	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	8	4	no	—
615	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
616	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
617	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
622	Q₁₆	—	2	2	no	—
623	SD₁₆	—	2	4	no	—
624	D₈	—	2	2	no	—
625	M₁₆	—	2	2	no	—
626	M₁₆	—	2	2	no	—
627	M₁₆	—	2	4	no	—
628	C₂×C₈	—	2	2	no	—
629	C₂×C₈	—	2	2	no	—
630	C₂×C₈	—	2	2	no	—
631	C₂×C₈	—	2	2	no	—
632	C₂×C₈	—	2	2	no	—
633	C₂×C₈	—	2	4	no	—
634	C₂×C₈	#41×C₈₉	1	4	yes	complemented
635	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
636	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
637	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
638	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
639	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
640	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
654	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
655	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
656	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
657	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
658	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
659	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
660	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	2	2	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	2	no	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
671	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
672	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
673	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
674	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
675	C₄²	—	2	4	no	—
676	C₄²	—	2	4	no	—
677	C₄²	—	2	2	no	—
678	C₄²	C₂⁴×C₈₉	1	2	yes	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
684	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
685	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
686	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
687	Q₈	—	2	2	no	—
688	Q₈	—	2	2	no	—
689	Q₈	—	2	2	no	—
690	Q₈	—	8	4	no	—
691	D₄	—	2	4	no	—
692	D₄	—	2	4	no	—
693	D₄	—	2	4	no	—
694	D₄	—	2	2	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	2	no	—
697	D₄	—	4	4	no	—
698	D₄	—	4	4	no	—
699	D₄	—	4	4	no	—
700	D₄	—	8	4	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	4	8	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	8	4	no	—
718	C₂×C₄	—	8	2	no	—
719	C₂×C₄	—	8	4	no	—
720	C₂×C₄	—	8	2	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
723	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
724	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
725	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
726	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
727	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
728	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
729	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
730	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
731	C₈	—	2	1	no	—
732	C₈	—	2	1	no	—
733	C₈	—	2	2	no	—
734	C₈	—	2	2	no	—
735	C₈	C₂×#41×C₈₉	1	2	yes	—
736	C₈	C₂×#41×C₈₉	1	2	yes	—
737	C₂²	—	2	8	no	—
738	C₂²	—	2	1	no	—
739	C₂²	—	2	1	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	2	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	#547×C₈₉	1	2	yes	—
751	C₂²	#576×C₈₉	1	2	yes	—
752	C₂²	#578×C₈₉	1	2	yes	—
753	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
754	C₄	—	2	2	no	—
755	C₄	—	2	2	no	—
756	C₄	—	2	1	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	2	no	—
759	C₄	—	4	4	no	—
760	C₄	—	4	4	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	#547×C₈₉	1	2	yes	—
765	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
766	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
767	C₂	—	2	2	no	—
768	C₂	—	2	2	no	—
769	C₂	—	2	2	no	—
770	C₂	—	4	2	no	—
771	C₂	—	8	2	no	—
772	C₂	C₂×#547×C₈₉	1	1	yes	characteristic
773	C₂	C₂×#576×C₈₉	1	1	yes	characteristic
774	C₂	C₂×#578×C₈₉	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 ◁ #525×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3492	C₂	semidirect
2. C₈₉×#3346	C₂	semidirect
3. C₈₉×#3343	C₂	semidirect
4. C₈₉×#3339	C₂	semidirect
5. C₈₉×#3338	C₂	semidirect
6. C₈₉×#3336	C₂	semidirect
7. C₈₉×#3334	C₂	semidirect
8. C₈₉×#3164	C₂	semidirect
9. C₈₉×#3098	C₂	semidirect
10. C₈₉×#3092	C₂	semidirect
11. C₈₉×#3083	C₂	semidirect
12. C₈₉×#3061	C₂	semidirect
13. C₈₉×#3050	C₂	semidirect
14. C₈₉×#2951	C₂	semidirect
15. C₈₉×#2929	C₂	semidirect
16. C₈₉×#2913	C₂	semidirect
17. C₂²×#107×C₈₉	C₂	semidirect
38. #501×C₈₉	C₂²	semidirect
39. #500×C₈₉	C₂²	semidirect
40. #499×C₈₉	C₂²	semidirect
41. #485×C₈₉	C₂²	semidirect
43. #484×C₈₉	C₂²	semidirect
45. #482×C₈₉	C₂²	semidirect
48. #480×C₈₉	C₂²	semidirect
49. #479×C₈₉	C₂²	semidirect
50. #478×C₈₉	C₂²	semidirect
51. #477×C₈₉	C₂²	semidirect
52. #474×C₈₉	C₂²	semidirect
53. #468×C₈₉	C₂²	semidirect
56. #467×C₈₉	C₂²	semidirect
59. #466×C₈₉	C₂²	semidirect
62. #440×C₈₉	C₂²	semidirect
63. C₄×Q₁₆×C₈₉	C₂²	semidirect
64. C₄×D₈×C₈₉	C₂²	semidirect
71. #428×C₈₉	C₂²	semidirect
73. #427×C₈₉	C₂²	semidirect
81. C₂×#107×C₈₉	C₂²	semidirect
246. C₂×C₈×C₈₉	#41	semidirect
379. #61258	C₈₉	direct (N × H)
388. #3492	C₂×C₈₉	semidirect
389. #3346	C₂×C₈₉	semidirect
390. #3343	C₂×C₈₉	semidirect
391. #3339	C₂×C₈₉	semidirect
392. #3338	C₂×C₈₉	semidirect
393. #3336	C₂×C₈₉	semidirect
394. #3334	C₂×C₈₉	semidirect
395. #3164	C₂×C₈₉	semidirect
396. #3098	C₂×C₈₉	semidirect
397. #3092	C₂×C₈₉	semidirect
398. #3083	C₂×C₈₉	semidirect
399. #3061	C₂×C₈₉	semidirect
400. #3050	C₂×C₈₉	semidirect
401. #2951	C₂×C₈₉	semidirect
402. #2929	C₂×C₈₉	semidirect
403. #2913	C₂×C₈₉	semidirect
404. C₂²×#107	C₂×C₈₉	semidirect
405. C₈₉	#61258	direct (N × H)
426. #501	C₂²×C₈₉	semidirect
427. #500	C₂²×C₈₉	semidirect
428. #499	C₂²×C₈₉	semidirect
429. #485	C₂²×C₈₉	semidirect
431. #484	C₂²×C₈₉	semidirect
433. #482	C₂²×C₈₉	semidirect
436. #480	C₂²×C₈₉	semidirect
437. #479	C₂²×C₈₉	semidirect
438. #478	C₂²×C₈₉	semidirect
439. #477	C₂²×C₈₉	semidirect
440. #474	C₂²×C₈₉	semidirect
441. #468	C₂²×C₈₉	semidirect
444. #467	C₂²×C₈₉	semidirect
447. #466	C₂²×C₈₉	semidirect
450. #440	C₂²×C₈₉	semidirect
451. C₄×Q₁₆	C₂²×C₈₉	semidirect
452. C₄×D₈	C₂²×C₈₉	semidirect
459. #428	C₂²×C₈₉	semidirect
461. #427	C₂²×C₈₉	semidirect
469. C₂×#107	C₂²×C₈₉	semidirect
634. 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×#3492	2
C₈₉×#3346	2
C₈₉×#3343	2
C₈₉×#3339	2
C₈₉×#3338	2
C₈₉×#3336	2
C₈₉×#3334	2
C₈₉×#3164	2
C₈₉×#3098	2
C₈₉×#3092	2
C₈₉×#3083	2
C₈₉×#3061	2
C₈₉×#3050	2
C₈₉×#2951	2
C₈₉×#2929	2
C₈₉×#2913	2
C₂²×#107×C₈₉	2
#61258	89

Subgroups — C89×#61258 #36439106

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61258 #36439106