Subgroups — C₈₉×#60867 #36438715

Order 22784.

1686 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#544×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3455	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3244	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3243	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3242	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3241	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3166	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3165	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3142	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3093	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3092	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3080	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3079	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2921	C₂	1	1	yes	maximal, characteristic, complemented
16	#544×C₈₉	—	2	2	no	—
17	#544×C₈₉	—	2	2	no	—
18	#544×C₈₉	C₂²	1	4	yes	—
19	#544×C₈₉	C₂²	1	4	yes	—
20	#542×C₈₉	C₂²	1	2	yes	—
21	#542×C₈₉	C₂²	1	2	yes	—
22	#541×C₈₉	C₂²	1	2	yes	—
23	#540×C₈₉	C₂²	1	2	yes	—
24	#539×C₈₉	—	2	1	no	—
25	#539×C₈₉	—	2	1	no	—
26	#538×C₈₉	—	2	1	no	—
27	#538×C₈₉	—	2	1	no	—
28	#533×C₈₉	C₂²	1	1	yes	characteristic
29	#532×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊Q₈×C₈₉	—	2	1	no	—
31	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
33	#529×C₈₉	—	2	2	no	—
34	#529×C₈₉	—	2	2	no	—
35	C₂×#125×C₈₉	—	2	1	no	—
36	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
38	#525×C₈₉	C₂²	1	2	yes	—
39	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
40	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
41	C₄×#41×C₈₉	C₂²	1	2	yes	—
42	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
45	#501×C₈₉	C₂²	1	4	yes	complemented
46	#501×C₈₉	C₂²	1	2	yes	complemented
47	#501×C₈₉	C₂²	1	2	yes	complemented
48	#500×C₈₉	C₂²	1	2	yes	complemented
49	#499×C₈₉	C₂²	1	4	yes	complemented
50	#498×C₈₉	C₂²	1	2	yes	complemented
51	#491×C₈₉	C₂²	1	2	yes	complemented
52	#490×C₈₉	C₂²	1	2	yes	complemented
53	#489×C₈₉	C₂²	1	4	yes	complemented
54	#488×C₈₉	C₂²	1	4	yes	complemented
55	#487×C₈₉	C₂²	1	2	yes	complemented
56	#486×C₈₉	C₂²	1	2	yes	complemented
57	#485×C₈₉	C₂²	1	4	yes	—
58	#485×C₈₉	C₂²	1	4	yes	—
59	#484×C₈₉	C₂²	1	4	yes	—
60	#483×C₈₉	C₂²	1	4	yes	—
61	#482×C₈₉	C₂²	1	4	yes	—
62	#482×C₈₉	C₂²	1	4	yes	—
63	#481×C₈₉	C₂²	1	4	yes	—
64	#480×C₈₉	C₂²	1	4	yes	—
65	#479×C₈₉	C₂²	1	4	yes	complemented
66	#479×C₈₉	C₂²	1	4	yes	complemented
67	#478×C₈₉	C₂²	1	4	yes	complemented
68	#478×C₈₉	C₂²	1	4	yes	complemented
69	#477×C₈₉	C₂²	1	4	yes	complemented
70	#476×C₈₉	C₂²	1	4	yes	complemented
71	#475×C₈₉	C₂²	1	4	yes	complemented
72	#474×C₈₉	C₂²	1	4	yes	complemented
73	#433×C₈₉	C₂²	1	4	yes	—
74	#433×C₈₉	C₂²	1	4	yes	—
75	#428×C₈₉	C₂²	1	2	yes	—
76	#428×C₈₉	C₂²	1	2	yes	—
77	#428×C₈₉	C₂²	1	2	yes	—
78	#428×C₈₉	C₂²	1	2	yes	—
79	#423×C₈₉	C₂²	1	2	yes	—
80	#417×C₈₉	C₂²	1	2	yes	—
81	#417×C₈₉	C₂²	1	2	yes	—
82	#417×C₈₉	C₂²	1	2	yes	—
83	#417×C₈₉	C₂²	1	2	yes	—
84	#407×C₈₉	C₂²	1	2	yes	—
85	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
86	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
87	C₂×#41×C₈₉	C₂³	1	2	yes	—
88	C₂²×Q₈×C₈₉	—	2	1	no	—
89	C₂²×Q₈×C₈₉	—	2	1	no	—
90	C₂³×C₄×C₈₉	—	2	1	no	—
91	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
92	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
93	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
94	C₄⋊Q₈×C₈₉	—	2	4	no	—
95	C₄⋊Q₈×C₈₉	—	2	4	no	—
96	C₄⋊Q₈×C₈₉	—	2	2	no	—
97	C₄⋊Q₈×C₈₉	—	2	1	no	—
98	C₄⋊Q₈×C₈₉	—	2	1	no	—
99	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
100	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
101	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
102	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
103	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
104	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
105	#127×C₈₉	C₂³	1	1	yes	characteristic
106	#126×C₈₉	—	2	2	no	—
107	#126×C₈₉	—	2	2	no	—
108	#126×C₈₉	—	2	2	no	—
109	#126×C₈₉	—	2	2	no	—
110	#125×C₈₉	—	2	4	no	—
111	#125×C₈₉	—	2	4	no	—
112	#125×C₈₉	—	2	2	no	—
113	#125×C₈₉	—	2	2	no	—
114	#125×C₈₉	—	2	2	no	—
115	#125×C₈₉	—	2	1	no	—
116	#125×C₈₉	—	2	1	no	—
117	#125×C₈₉	C₂³	1	4	yes	—
118	#125×C₈₉	C₂³	1	2	yes	—
119	#125×C₈₉	C₂³	1	2	yes	—
120	#125×C₈₉	C₂³	1	2	yes	—
121	#124×C₈₉	—	2	2	no	—
122	#124×C₈₉	—	2	2	no	—
123	#124×C₈₉	C₂³	1	2	yes	—
124	#123×C₈₉	—	2	2	no	—
125	#123×C₈₉	—	2	2	no	—
126	#123×C₈₉	—	2	2	no	—
127	#123×C₈₉	—	2	2	no	—
128	#123×C₈₉	—	2	2	no	—
129	C₂²⋊Q₈×C₈₉	—	2	1	no	—
130	C₂²⋊Q₈×C₈₉	—	2	1	no	—
131	C₂²⋊Q₈×C₈₉	—	2	2	no	—
132	C₂²⋊Q₈×C₈₉	—	2	2	no	—
133	C₂²⋊Q₈×C₈₉	—	2	4	no	—
134	C₂²⋊Q₈×C₈₉	—	2	4	no	—
135	C₂²⋊Q₈×C₈₉	—	2	4	no	—
136	C₂²⋊Q₈×C₈₉	—	2	4	no	—
137	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
138	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
139	#121×C₈₉	—	2	1	no	—
140	#121×C₈₉	—	2	1	no	—
141	#121×C₈₉	—	2	2	no	—
142	#121×C₈₉	—	2	2	no	—
143	#121×C₈₉	C₂³	1	2	yes	—
144	#121×C₈₉	C₂³	1	2	yes	—
145	#120×C₈₉	—	2	2	no	—
146	C₄×Q₈×C₈₉	—	2	1	no	—
147	C₄×Q₈×C₈₉	—	2	1	no	—
148	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
149	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
150	C₄×D₄×C₈₉	—	2	2	no	—
151	C₄×D₄×C₈₉	—	2	2	no	—
152	C₄×D₄×C₈₉	—	2	2	no	—
153	C₄×D₄×C₈₉	—	2	2	no	—
154	C₄×D₄×C₈₉	—	2	1	no	—
155	C₄×D₄×C₈₉	—	2	1	no	—
156	C₄×D₄×C₈₉	C₂³	1	2	yes	—
157	C₄×D₄×C₈₉	C₂³	1	2	yes	—
158	#117×C₈₉	—	2	2	no	—
159	#117×C₈₉	—	2	2	no	—
160	#117×C₈₉	D₄	1	2	yes	—
161	#117×C₈₉	D₄	1	2	yes	—
162	#117×C₈₉	C₂³	1	2	yes	—
163	#117×C₈₉	C₂³	1	4	yes	—
164	#117×C₈₉	C₂³	1	2	yes	—
165	#117×C₈₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
167	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
168	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
169	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
170	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
171	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
172	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
173	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
174	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
181	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
182	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
184	C₂×C₄²×C₈₉	—	2	1	no	—
185	C₂×C₄²×C₈₉	—	2	2	no	—
186	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
188	#107×C₈₉	C₂³	1	4	yes	—
189	#107×C₈₉	C₂³	1	4	yes	—
190	#107×C₈₉	C₂³	1	4	yes	—
191	#107×C₈₉	C₂³	1	4	yes	—
192	#106×C₈₉	C₂³	1	4	yes	—
193	#106×C₈₉	C₂³	1	4	yes	—
194	#106×C₈₉	C₂³	1	4	yes	—
195	#106×C₈₉	C₂³	1	4	yes	—
196	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
197	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
198	#103×C₈₉	C₂³	1	4	yes	—
199	#103×C₈₉	C₂³	1	4	yes	—
200	#103×C₈₉	C₂³	1	4	yes	—
201	#103×C₈₉	C₂³	1	4	yes	—
202	#102×C₈₉	C₂³	1	4	yes	—
203	#102×C₈₉	C₂³	1	4	yes	—
204	#102×C₈₉	C₂³	1	4	yes	—
205	#102×C₈₉	C₂³	1	4	yes	—
206	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
207	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
208	#97×C₈₉	C₂³	1	2	yes	—
209	#97×C₈₉	C₂³	1	2	yes	—
210	C₄×C₈×C₈₉	C₂³	1	2	yes	—
211	C₄×C₈×C₈₉	C₂³	1	2	yes	—
212	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
213	#41×C₈₉	—	2	8	no	—
214	C₂×Q₈×C₈₉	—	2	1	no	—
215	C₂×Q₈×C₈₉	—	2	1	no	—
216	C₂×Q₈×C₈₉	—	2	4	no	—
217	C₂×Q₈×C₈₉	—	2	2	no	—
218	C₂×Q₈×C₈₉	—	2	2	no	—
219	C₂×Q₈×C₈₉	—	8	2	no	—
220	C₂×Q₈×C₈₉	—	8	2	no	—
221	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
222	C₂×D₄×C₈₉	—	2	2	no	—
223	C₂×D₄×C₈₉	—	2	2	no	—
224	C₂×D₄×C₈₉	—	2	2	no	—
225	C₂×D₄×C₈₉	—	2	1	no	—
226	C₂×D₄×C₈₉	—	2	1	no	—
227	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₈₉	—	2	4	no	—
229	C₂²×C₄×C₈₉	—	2	1	no	—
230	C₂²×C₄×C₈₉	—	2	1	no	—
231	C₂²×C₄×C₈₉	—	2	1	no	—
232	C₂²×C₄×C₈₉	—	2	1	no	—
233	C₂²×C₄×C₈₉	—	2	4	no	—
234	C₂²×C₄×C₈₉	—	2	2	no	—
235	C₂²×C₄×C₈₉	—	2	2	no	—
236	C₂²×C₄×C₈₉	—	2	2	no	—
237	C₂²×C₄×C₈₉	—	8	2	no	—
238	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
240	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
246	M₁₆×C₈₉	—	2	4	no	—
247	M₁₆×C₈₉	—	2	4	no	—
248	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
249	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
250	C₄⋊C₄×C₈₉	—	2	4	no	—
251	C₄⋊C₄×C₈₉	—	2	1	no	—
252	C₄⋊C₄×C₈₉	—	2	1	no	—
253	C₄⋊C₄×C₈₉	—	2	4	no	—
254	C₄⋊C₄×C₈₉	—	2	2	no	—
255	C₄⋊C₄×C₈₉	—	2	2	no	—
256	C₄⋊C₄×C₈₉	—	2	4	no	—
257	C₄⋊C₄×C₈₉	—	2	2	no	—
258	C₄⋊C₄×C₈₉	—	2	2	no	—
259	C₄⋊C₄×C₈₉	—	2	4	no	—
260	C₄⋊C₄×C₈₉	—	2	2	no	—
261	C₄⋊C₄×C₈₉	—	2	2	no	—
262	C₄⋊C₄×C₈₉	—	2	1	no	—
263	C₄⋊C₄×C₈₉	—	2	1	no	—
264	C₄⋊C₄×C₈₉	—	2	2	no	—
265	C₄⋊C₄×C₈₉	—	2	2	no	—
266	C₄⋊C₄×C₈₉	—	2	1	no	—
267	C₄⋊C₄×C₈₉	—	2	1	no	—
268	C₄⋊C₄×C₈₉	—	2	2	no	—
269	C₄⋊C₄×C₈₉	—	2	2	no	—
270	C₄⋊C₄×C₈₉	—	2	2	no	—
271	C₄⋊C₄×C₈₉	—	2	2	no	—
272	C₄⋊C₄×C₈₉	—	2	1	no	—
273	C₄⋊C₄×C₈₉	—	2	1	no	—
274	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
275	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
277	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
279	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
284	C₂²⋊C₄×C₈₉	—	2	4	no	—
285	C₂²⋊C₄×C₈₉	—	2	2	no	—
286	C₂²⋊C₄×C₈₉	—	2	2	no	—
287	C₂²⋊C₄×C₈₉	—	2	2	no	—
288	C₂²⋊C₄×C₈₉	—	2	2	no	—
289	C₂²⋊C₄×C₈₉	—	2	2	no	—
290	C₂²⋊C₄×C₈₉	—	2	2	no	—
291	C₂²⋊C₄×C₈₉	—	2	2	no	—
292	C₂²⋊C₄×C₈₉	—	2	2	no	—
293	C₂²⋊C₄×C₈₉	—	2	2	no	—
294	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
295	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
296	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
297	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
298	C₄²×C₈₉	—	2	2	no	—
299	C₄²×C₈₉	—	2	4	no	—
300	C₄²×C₈₉	—	2	2	no	—
301	C₄²×C₈₉	—	2	2	no	—
302	C₄²×C₈₉	C₂×D₄	1	2	yes	—
303	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
306	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
307	C₄²×C₈₉	C₂⁴	1	2	yes	—
308	C₂³×C₈₉	—	2	2	no	—
309	C₂³×C₈₉	—	2	2	no	—
310	C₂³×C₈₉	—	4	1	no	—
311	C₂³×C₈₉	—	4	1	no	—
312	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
313	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
314	Q₈×C₈₉	—	2	4	no	—
315	Q₈×C₈₉	—	8	1	no	—
316	Q₈×C₈₉	—	8	1	no	—
317	Q₈×C₈₉	—	8	4	no	—
318	Q₈×C₈₉	—	8	2	no	—
319	Q₈×C₈₉	—	8	2	no	—
320	D₄×C₈₉	—	2	4	no	—
321	D₄×C₈₉	—	4	4	no	—
322	D₄×C₈₉	—	8	1	no	—
323	D₄×C₈₉	—	8	1	no	—
324	D₄×C₈₉	—	8	2	no	—
325	D₄×C₈₉	—	8	2	no	—
326	C₂×C₄×C₈₉	—	2	2	no	—
327	C₂×C₄×C₈₉	—	2	4	no	—
328	C₂×C₄×C₈₉	—	2	4	no	—
329	C₂×C₄×C₈₉	—	2	2	no	—
330	C₂×C₄×C₈₉	—	2	2	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	2	no	—
335	C₂×C₄×C₈₉	—	2	2	no	—
336	C₂×C₄×C₈₉	—	4	1	no	—
337	C₂×C₄×C₈₉	—	4	1	no	—
338	C₂×C₄×C₈₉	—	4	1	no	—
339	C₂×C₄×C₈₉	—	4	1	no	—
340	C₂×C₄×C₈₉	—	4	2	no	—
341	C₂×C₄×C₈₉	—	4	2	no	—
342	C₂×C₄×C₈₉	—	4	2	no	—
343	C₂×C₄×C₈₉	—	4	2	no	—
344	C₂×C₄×C₈₉	—	4	4	no	—
345	C₂×C₄×C₈₉	—	8	2	no	—
346	C₂×C₄×C₈₉	—	8	2	no	—
347	C₂×C₄×C₈₉	—	8	4	no	—
348	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
349	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
350	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
351	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
357	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
358	C₈×C₈₉	—	2	4	no	—
359	C₈×C₈₉	—	2	4	no	—
360	C₂²×C₈₉	—	2	1	no	—
361	C₂²×C₈₉	—	2	1	no	—
362	C₂²×C₈₉	—	2	2	no	—
363	C₂²×C₈₉	—	2	2	no	—
364	C₂²×C₈₉	—	2	2	no	—
365	C₂²×C₈₉	—	4	4	no	—
366	C₂²×C₈₉	—	4	2	no	—
367	C₂²×C₈₉	—	4	2	no	—
368	C₂²×C₈₉	—	4	2	no	—
369	C₂²×C₈₉	#536	1	2	yes	—
370	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
371	C₄×C₈₉	—	2	2	no	—
372	C₄×C₈₉	—	2	1	no	—
373	C₄×C₈₉	—	2	1	no	—
374	C₄×C₈₉	—	2	2	no	—
375	C₄×C₈₉	—	2	1	no	—
376	C₄×C₈₉	—	2	1	no	—
377	C₄×C₈₉	—	2	2	no	—
378	C₄×C₈₉	—	4	2	no	—
379	C₄×C₈₉	—	4	2	no	—
380	C₄×C₈₉	—	4	2	no	—
381	C₄×C₈₉	—	4	2	no	—
382	C₄×C₈₉	—	4	2	no	—
383	C₄×C₈₉	—	4	2	no	—
384	C₄×C₈₉	—	4	2	no	—
385	C₄×C₈₉	#536	1	2	yes	—
386	C₄×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
387	#60867	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
388	C₂×C₈₉	—	2	2	no	—
389	C₂×C₈₉	—	4	2	no	—
390	C₂×C₈₉	—	8	2	no	—
391	C₂×C₈₉	C₂×#536	1	1	yes	characteristic
392	C₂×C₈₉	#3585	1	1	yes	characteristic
393	C₂×C₈₉	#3586	1	1	yes	characteristic
394	C₂×#544	C₂×C₈₉	1	1	yes	characteristic, complemented
395	#3455	C₂×C₈₉	1	1	yes	characteristic
396	#3244	C₂×C₈₉	1	4	yes	complemented
397	#3243	C₂×C₈₉	1	4	yes	complemented
398	#3242	C₂×C₈₉	1	4	yes	complemented
399	#3241	C₂×C₈₉	1	4	yes	complemented
400	#3166	C₂×C₈₉	1	1	yes	characteristic, complemented
401	#3165	C₂×C₈₉	1	1	yes	characteristic, complemented
402	#3142	C₂×C₈₉	1	1	yes	characteristic, complemented
403	#3141	C₂×C₈₉	1	1	yes	characteristic, complemented
404	#3093	C₂×C₈₉	1	2	yes	complemented
405	#3092	C₂×C₈₉	1	2	yes	complemented
406	#3080	C₂×C₈₉	1	2	yes	complemented
407	#3079	C₂×C₈₉	1	2	yes	complemented
408	#2921	C₂×C₈₉	1	1	yes	characteristic, complemented
409	C₈₉	#60867	1	1	yes	characteristic, direct product factor, Sylow
410	#544	—	2	2	no	—
411	#544	—	2	2	no	—
412	#544	C₂²×C₈₉	1	4	yes	—
413	#544	C₂²×C₈₉	1	4	yes	—
414	#542	C₂²×C₈₉	1	2	yes	—
415	#542	C₂²×C₈₉	1	2	yes	—
416	#541	C₂²×C₈₉	1	2	yes	—
417	#540	C₂²×C₈₉	1	2	yes	—
418	#539	—	2	1	no	—
419	#539	—	2	1	no	—
420	#538	—	2	1	no	—
421	#538	—	2	1	no	—
422	#533	C₂²×C₈₉	1	1	yes	characteristic
423	#532	C₂²×C₈₉	1	1	yes	characteristic
424	C₂×C₄⋊Q₈	—	2	1	no	—
425	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
426	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
427	#529	—	2	2	no	—
428	#529	—	2	2	no	—
429	C₂×#125	—	2	1	no	—
430	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
431	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
432	#525	C₂²×C₈₉	1	2	yes	—
433	C₂×C₂²⋊Q₈	—	2	1	no	—
434	C₂×C₂²⋊Q₈	—	2	1	no	—
435	C₄×#41	C₂²×C₈₉	1	2	yes	—
436	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
437	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
438	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
439	#501	C₂²×C₈₉	1	4	yes	complemented
440	#501	C₂²×C₈₉	1	2	yes	complemented
441	#501	C₂²×C₈₉	1	2	yes	complemented
442	#500	C₂²×C₈₉	1	2	yes	complemented
443	#499	C₂²×C₈₉	1	4	yes	complemented
444	#498	C₂²×C₈₉	1	2	yes	complemented
445	#491	C₂²×C₈₉	1	2	yes	complemented
446	#490	C₂²×C₈₉	1	2	yes	complemented
447	#489	C₂²×C₈₉	1	4	yes	complemented
448	#488	C₂²×C₈₉	1	4	yes	complemented
449	#487	C₂²×C₈₉	1	2	yes	complemented
450	#486	C₂²×C₈₉	1	2	yes	complemented
451	#485	C₂²×C₈₉	1	4	yes	—
452	#485	C₂²×C₈₉	1	4	yes	—
453	#484	C₂²×C₈₉	1	4	yes	—
454	#483	C₂²×C₈₉	1	4	yes	—
455	#482	C₂²×C₈₉	1	4	yes	—
456	#482	C₂²×C₈₉	1	4	yes	—
457	#481	C₂²×C₈₉	1	4	yes	—
458	#480	C₂²×C₈₉	1	4	yes	—
459	#479	C₂²×C₈₉	1	4	yes	complemented
460	#479	C₂²×C₈₉	1	4	yes	complemented
461	#478	C₂²×C₈₉	1	4	yes	complemented
462	#478	C₂²×C₈₉	1	4	yes	complemented
463	#477	C₂²×C₈₉	1	4	yes	complemented
464	#476	C₂²×C₈₉	1	4	yes	complemented
465	#475	C₂²×C₈₉	1	4	yes	complemented
466	#474	C₂²×C₈₉	1	4	yes	complemented
467	#433	C₂²×C₈₉	1	4	yes	—
468	#433	C₂²×C₈₉	1	4	yes	—
469	#428	C₂²×C₈₉	1	2	yes	—
470	#428	C₂²×C₈₉	1	2	yes	—
471	#428	C₂²×C₈₉	1	2	yes	—
472	#428	C₂²×C₈₉	1	2	yes	—
473	#423	C₂²×C₈₉	1	2	yes	—
474	#417	C₂²×C₈₉	1	2	yes	—
475	#417	C₂²×C₈₉	1	2	yes	—
476	#417	C₂²×C₈₉	1	2	yes	—
477	#417	C₂²×C₈₉	1	2	yes	—
478	#407	C₂²×C₈₉	1	2	yes	—
479	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
480	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
481	C₂×#41	C₂³×C₈₉	1	2	yes	—
482	C₂²×Q₈	—	2	1	no	—
483	C₂²×Q₈	—	2	1	no	—
484	C₂³×C₄	—	2	1	no	—
485	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
486	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
487	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
488	C₄⋊Q₈	—	2	4	no	—
489	C₄⋊Q₈	—	2	4	no	—
490	C₄⋊Q₈	—	2	2	no	—
491	C₄⋊Q₈	—	2	1	no	—
492	C₄⋊Q₈	—	2	1	no	—
493	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
494	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
495	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
496	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
497	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
498	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
499	#127	C₂³×C₈₉	1	1	yes	characteristic
500	#126	—	2	2	no	—
501	#126	—	2	2	no	—
502	#126	—	2	2	no	—
503	#126	—	2	2	no	—
504	#125	—	2	4	no	—
505	#125	—	2	4	no	—
506	#125	—	2	2	no	—
507	#125	—	2	2	no	—
508	#125	—	2	2	no	—
509	#125	—	2	1	no	—
510	#125	—	2	1	no	—
511	#125	C₂³×C₈₉	1	4	yes	—
512	#125	C₂³×C₈₉	1	2	yes	—
513	#125	C₂³×C₈₉	1	2	yes	—
514	#125	C₂³×C₈₉	1	2	yes	—
515	#124	—	2	2	no	—
516	#124	—	2	2	no	—
517	#124	C₂³×C₈₉	1	2	yes	—
518	#123	—	2	2	no	—
519	#123	—	2	2	no	—
520	#123	—	2	2	no	—
521	#123	—	2	2	no	—
522	#123	—	2	2	no	—
523	C₂²⋊Q₈	—	2	1	no	—
524	C₂²⋊Q₈	—	2	1	no	—
525	C₂²⋊Q₈	—	2	2	no	—
526	C₂²⋊Q₈	—	2	2	no	—
527	C₂²⋊Q₈	—	2	4	no	—
528	C₂²⋊Q₈	—	2	4	no	—
529	C₂²⋊Q₈	—	2	4	no	—
530	C₂²⋊Q₈	—	2	4	no	—
531	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
532	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
533	#121	—	2	1	no	—
534	#121	—	2	1	no	—
535	#121	—	2	2	no	—
536	#121	—	2	2	no	—
537	#121	C₂³×C₈₉	1	2	yes	—
538	#121	C₂³×C₈₉	1	2	yes	—
539	#120	—	2	2	no	—
540	C₄×Q₈	—	2	1	no	—
541	C₄×Q₈	—	2	1	no	—
542	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
543	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
544	C₄×D₄	—	2	2	no	—
545	C₄×D₄	—	2	2	no	—
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	—	2	2	no	—
548	C₄×D₄	—	2	1	no	—
549	C₄×D₄	—	2	1	no	—
550	C₄×D₄	C₂³×C₈₉	1	2	yes	—
551	C₄×D₄	C₂³×C₈₉	1	2	yes	—
552	#117	—	2	2	no	—
553	#117	—	2	2	no	—
554	#117	D₄×C₈₉	1	2	yes	—
555	#117	D₄×C₈₉	1	2	yes	—
556	#117	C₂³×C₈₉	1	4	yes	—
557	#117	C₂³×C₈₉	1	2	yes	—
558	#117	C₂³×C₈₉	1	2	yes	—
559	#117	C₂³×C₈₉	1	2	yes	—
560	C₂×C₄⋊C₄	—	2	1	no	—
561	C₂×C₄⋊C₄	—	2	2	no	—
562	C₂×C₄⋊C₄	—	2	1	no	—
563	C₂×C₄⋊C₄	—	2	1	no	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
569	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
573	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
575	C₂×C₂²⋊C₄	—	2	1	no	—
576	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
577	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
578	C₂×C₄²	—	2	1	no	—
579	C₂×C₄²	—	2	2	no	—
580	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
581	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
582	#107	C₂³×C₈₉	1	4	yes	—
583	#107	C₂³×C₈₉	1	4	yes	—
584	#107	C₂³×C₈₉	1	4	yes	—
585	#107	C₂³×C₈₉	1	4	yes	—
586	#106	C₂³×C₈₉	1	4	yes	—
587	#106	C₂³×C₈₉	1	4	yes	—
588	#106	C₂³×C₈₉	1	4	yes	—
589	#106	C₂³×C₈₉	1	4	yes	—
590	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
591	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
592	#103	C₂³×C₈₉	1	4	yes	—
593	#103	C₂³×C₈₉	1	4	yes	—
594	#103	C₂³×C₈₉	1	4	yes	—
595	#103	C₂³×C₈₉	1	4	yes	—
596	#102	C₂³×C₈₉	1	4	yes	—
597	#102	C₂³×C₈₉	1	4	yes	—
598	#102	C₂³×C₈₉	1	4	yes	—
599	#102	C₂³×C₈₉	1	4	yes	—
600	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
601	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
602	#97	C₂³×C₈₉	1	2	yes	—
603	#97	C₂³×C₈₉	1	2	yes	—
604	C₄×C₈	C₂³×C₈₉	1	2	yes	—
605	C₄×C₈	C₂³×C₈₉	1	2	yes	—
606	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
607	#41	—	2	8	no	—
608	C₂×Q₈	—	2	1	no	—
609	C₂×Q₈	—	2	1	no	—
610	C₂×Q₈	—	2	4	no	—
611	C₂×Q₈	—	2	2	no	—
612	C₂×Q₈	—	2	2	no	—
613	C₂×Q₈	—	8	2	no	—
614	C₂×Q₈	—	8	2	no	—
615	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	2	2	no	—
618	C₂×D₄	—	2	2	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	8	2	no	—
632	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
633	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
634	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
635	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
636	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
637	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
640	M₁₆	—	2	4	no	—
641	M₁₆	—	2	4	no	—
642	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
643	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
669	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
670	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
671	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
672	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
673	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
674	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
675	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
676	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
677	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	2	no	—
681	C₂²⋊C₄	—	2	2	no	—
682	C₂²⋊C₄	—	2	2	no	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	2	2	no	—
687	C₂²⋊C₄	—	2	2	no	—
688	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
689	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
690	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
691	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
692	C₄²	—	2	2	no	—
693	C₄²	—	2	4	no	—
694	C₄²	—	2	2	no	—
695	C₄²	—	2	2	no	—
696	C₄²	C₂×D₄×C₈₉	1	2	yes	—
697	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
698	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
699	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
700	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
701	C₄²	C₂⁴×C₈₉	1	2	yes	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	4	1	no	—
705	C₂³	—	4	1	no	—
706	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
707	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
708	Q₈	—	2	4	no	—
709	Q₈	—	8	1	no	—
710	Q₈	—	8	1	no	—
711	Q₈	—	8	4	no	—
712	Q₈	—	8	2	no	—
713	Q₈	—	8	2	no	—
714	D₄	—	2	4	no	—
715	D₄	—	4	4	no	—
716	D₄	—	8	1	no	—
717	D₄	—	8	1	no	—
718	D₄	—	8	2	no	—
719	D₄	—	8	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	2	no	—
735	C₂×C₄	—	4	2	no	—
736	C₂×C₄	—	4	2	no	—
737	C₂×C₄	—	4	2	no	—
738	C₂×C₄	—	4	4	no	—
739	C₂×C₄	—	8	2	no	—
740	C₂×C₄	—	8	2	no	—
741	C₂×C₄	—	8	4	no	—
742	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
743	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
744	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
745	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
746	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
747	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
748	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
749	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
750	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
751	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
752	C₈	—	2	4	no	—
753	C₈	—	2	4	no	—
754	C₂²	—	2	1	no	—
755	C₂²	—	2	1	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	2	2	no	—
758	C₂²	—	2	2	no	—
759	C₂²	—	4	4	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	#536×C₈₉	1	2	yes	—
764	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
765	C₄	—	2	2	no	—
766	C₄	—	2	1	no	—
767	C₄	—	2	1	no	—
768	C₄	—	2	2	no	—
769	C₄	—	2	1	no	—
770	C₄	—	2	1	no	—
771	C₄	—	2	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	2	no	—
779	C₄	#536×C₈₉	1	2	yes	—
780	C₄	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
781	C₂	—	2	2	no	—
782	C₂	—	4	2	no	—
783	C₂	—	8	2	no	—
784	C₂	C₂×#536×C₈₉	1	1	yes	characteristic
785	C₂	C₈₉×#3585	1	1	yes	characteristic
786	C₂	C₈₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₈₉×#3455	C₂
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. C₂×#544×C₈₉	C₂	semidirect
3. C₈₉×#3244	C₂	semidirect
4. C₈₉×#3243	C₂	semidirect
5. C₈₉×#3242	C₂	semidirect
6. C₈₉×#3241	C₂	semidirect
7. C₈₉×#3166	C₂	semidirect
8. C₈₉×#3165	C₂	semidirect
9. C₈₉×#3142	C₂	semidirect
10. C₈₉×#3141	C₂	semidirect
11. C₈₉×#3093	C₂	semidirect
12. C₈₉×#3092	C₂	semidirect
13. C₈₉×#3080	C₂	semidirect
14. C₈₉×#3079	C₂	semidirect
15. C₈₉×#2921	C₂	semidirect
45. #501×C₈₉	C₂²	semidirect
46. #501×C₈₉	C₂²	semidirect
47. #501×C₈₉	C₂²	semidirect
48. #500×C₈₉	C₂²	semidirect
49. #499×C₈₉	C₂²	semidirect
50. #498×C₈₉	C₂²	semidirect
51. #491×C₈₉	C₂²	semidirect
52. #490×C₈₉	C₂²	semidirect
53. #489×C₈₉	C₂²	semidirect
54. #488×C₈₉	C₂²	semidirect
55. #487×C₈₉	C₂²	semidirect
56. #486×C₈₉	C₂²	semidirect
65. #479×C₈₉	C₂²	semidirect
66. #479×C₈₉	C₂²	semidirect
67. #478×C₈₉	C₂²	semidirect
68. #478×C₈₉	C₂²	semidirect
69. #477×C₈₉	C₂²	semidirect
70. #476×C₈₉	C₂²	semidirect
71. #475×C₈₉	C₂²	semidirect
72. #474×C₈₉	C₂²	semidirect
387. #60867	C₈₉	direct (N × H)
394. C₂×#544	C₂×C₈₉	semidirect
396. #3244	C₂×C₈₉	semidirect
397. #3243	C₂×C₈₉	semidirect
398. #3242	C₂×C₈₉	semidirect
399. #3241	C₂×C₈₉	semidirect
400. #3166	C₂×C₈₉	semidirect
401. #3165	C₂×C₈₉	semidirect
402. #3142	C₂×C₈₉	semidirect
403. #3141	C₂×C₈₉	semidirect
404. #3093	C₂×C₈₉	semidirect
405. #3092	C₂×C₈₉	semidirect
406. #3080	C₂×C₈₉	semidirect
407. #3079	C₂×C₈₉	semidirect
408. #2921	C₂×C₈₉	semidirect
409. C₈₉	#60867	direct (N × H)
439. #501	C₂²×C₈₉	semidirect
440. #501	C₂²×C₈₉	semidirect
441. #501	C₂²×C₈₉	semidirect
442. #500	C₂²×C₈₉	semidirect
443. #499	C₂²×C₈₉	semidirect
444. #498	C₂²×C₈₉	semidirect
445. #491	C₂²×C₈₉	semidirect
446. #490	C₂²×C₈₉	semidirect
447. #489	C₂²×C₈₉	semidirect
448. #488	C₂²×C₈₉	semidirect
449. #487	C₂²×C₈₉	semidirect
450. #486	C₂²×C₈₉	semidirect
459. #479	C₂²×C₈₉	semidirect
460. #479	C₂²×C₈₉	semidirect
461. #478	C₂²×C₈₉	semidirect
462. #478	C₂²×C₈₉	semidirect
463. #477	C₂²×C₈₉	semidirect
464. #476	C₂²×C₈₉	semidirect
465. #475	C₂²×C₈₉	semidirect
466. #474	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#544×C₈₉	2
C₈₉×#3455	2
C₈₉×#3244	2
C₈₉×#3243	2
C₈₉×#3242	2
C₈₉×#3241	2
C₈₉×#3166	2
C₈₉×#3165	2
C₈₉×#3142	2
C₈₉×#3141	2
C₈₉×#3093	2
C₈₉×#3092	2
C₈₉×#3080	2
C₈₉×#3079	2
C₈₉×#2921	2
#60867	89

Subgroups — C89×#60867 #36438715

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60867 #36438715