Subgroups — C₈₉×#25130 #36402978

Order 22784.

1166 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#468×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#448×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#435×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#103×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2416	C₂	1	1	yes	maximal, characteristic
6	C₈₉×#2409	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2036	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1973	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1935	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1894	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1852	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#121×C₈₉	—	2	1	no	—
24	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
28	#468×C₈₉	—	2	4	no	—
29	#448×C₈₉	—	2	4	no	—
30	#435×C₈₉	—	2	4	no	—
31	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#103×C₈₉	—	2	4	no	—
35	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
46	#396×C₈₉	—	2	1	no	—
47	#395×C₈₉	—	2	1	no	—
48	#394×C₈₉	—	2	1	no	—
49	#393×C₈₉	—	2	1	no	—
50	#391×C₈₉	C₂²	1	1	yes	characteristic
51	#391×C₈₉	C₂²	1	1	yes	characteristic
52	#390×C₈₉	C₂²	1	1	yes	characteristic
53	#389×C₈₉	C₂²	1	1	yes	characteristic
54	#386×C₈₉	—	2	1	no	—
55	#386×C₈₉	—	2	1	no	—
56	#385×C₈₉	—	2	1	no	—
57	#380×C₈₉	C₂²	1	1	yes	characteristic
58	#380×C₈₉	C₂²	1	1	yes	characteristic
59	#340×C₈₉	C₂²	1	1	yes	characteristic
60	#340×C₈₉	C₂²	1	1	yes	characteristic
61	#340×C₈₉	C₂²	1	1	yes	characteristic
62	#340×C₈₉	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₈₉	—	2	1	no	—
64	C₂²×Q₈×C₈₉	—	2	2	no	—
65	C₂²×Q₈×C₈₉	—	2	2	no	—
66	C₂²×Q₈×C₈₉	—	2	2	no	—
67	C₂²×Q₈×C₈₉	—	2	2	no	—
68	C₂²×Q₈×C₈₉	—	4	1	no	—
69	C₂²×Q₈×C₈₉	—	4	1	no	—
70	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₈₉	—	2	1	no	—
73	C₂²×D₄×C₈₉	—	2	1	no	—
74	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
75	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₈₉	—	2	1	no	—
77	C₂³×C₄×C₈₉	—	2	1	no	—
78	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
80	C₂×SD₁₆×C₈₉	—	2	2	no	—
81	C₂×SD₁₆×C₈₉	—	2	2	no	—
82	C₂×SD₁₆×C₈₉	—	2	2	no	—
83	C₂×SD₁₆×C₈₉	—	2	2	no	—
84	C₂×SD₁₆×C₈₉	—	4	1	no	—
85	C₂×SD₁₆×C₈₉	—	4	1	no	—
86	C₂×M₁₆×C₈₉	—	2	2	no	—
87	C₂×M₁₆×C₈₉	—	2	2	no	—
88	C₂×M₁₆×C₈₉	—	4	1	no	—
89	C₂²×C₈×C₈₉	—	2	2	no	—
90	C₂²×C₈×C₈₉	—	2	2	no	—
91	C₂²×C₈×C₈₉	—	4	1	no	—
92	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
96	C₂²⋊Q₈×C₈₉	—	2	2	no	—
97	C₂²⋊Q₈×C₈₉	—	2	2	no	—
98	C₂²⋊Q₈×C₈₉	—	4	1	no	—
99	C₂²⋊Q₈×C₈₉	—	4	1	no	—
100	#121×C₈₉	—	2	2	no	—
101	#121×C₈₉	—	2	2	no	—
102	#121×C₈₉	—	2	2	no	—
103	#121×C₈₉	—	4	1	no	—
104	#121×C₈₉	—	4	4	no	—
105	C₄×D₄×C₈₉	—	2	2	no	—
106	C₄×D₄×C₈₉	—	2	2	no	—
107	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
108	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₈₉	—	4	1	no	—
113	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
128	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
129	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
130	#107×C₈₉	—	2	2	no	—
131	#107×C₈₉	—	4	1	no	—
132	C₄⋊C₈×C₈₉	—	2	2	no	—
133	#103×C₈₉	—	2	2	no	—
134	#103×C₈₉	—	2	2	no	—
135	#103×C₈₉	—	2	2	no	—
136	#103×C₈₉	—	2	2	no	—
137	#103×C₈₉	—	2	2	no	—
138	#103×C₈₉	D₄	1	4	yes	complemented
139	#102×C₈₉	—	2	2	no	—
140	#102×C₈₉	—	4	1	no	—
141	C₂²⋊C₈×C₈₉	—	2	2	no	—
142	C₂²⋊C₈×C₈₉	D₄	1	4	yes	complemented
143	#97×C₈₉	—	2	2	no	—
144	#95×C₈₉	—	2	1	no	—
145	#95×C₈₉	—	2	1	no	—
146	#95×C₈₉	—	2	1	no	—
147	#95×C₈₉	—	2	1	no	—
148	#95×C₈₉	—	2	1	no	—
149	#95×C₈₉	—	2	1	no	—
150	#95×C₈₉	—	2	1	no	—
151	C₂⁴×C₈₉	—	2	1	no	—
152	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
153	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₈₉	—	2	1	no	—
155	C₂×Q₈×C₈₉	—	2	1	no	—
156	C₂×Q₈×C₈₉	—	2	8	no	—
157	C₂×Q₈×C₈₉	—	2	1	no	—
158	C₂×Q₈×C₈₉	—	2	1	no	—
159	C₂×Q₈×C₈₉	—	2	1	no	—
160	C₂×Q₈×C₈₉	—	2	1	no	—
161	C₂×Q₈×C₈₉	—	2	1	no	—
162	C₂×Q₈×C₈₉	—	2	1	no	—
163	C₂×Q₈×C₈₉	—	2	1	no	—
164	C₂×Q₈×C₈₉	—	2	1	no	—
165	C₂×Q₈×C₈₉	—	4	2	no	—
166	C₂×Q₈×C₈₉	—	4	2	no	—
167	C₂×Q₈×C₈₉	—	4	4	no	—
168	C₂×Q₈×C₈₉	—	4	4	no	—
169	C₂×Q₈×C₈₉	—	4	4	no	—
170	C₂×Q₈×C₈₉	—	4	2	no	—
171	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
172	C₂×Q₈×C₈₉	#41	1	2	yes	—
173	C₂×D₄×C₈₉	—	2	2	no	—
174	C₂×D₄×C₈₉	—	2	2	no	—
175	C₂×D₄×C₈₉	—	2	2	no	—
176	C₂×D₄×C₈₉	—	2	1	no	—
177	C₂×D₄×C₈₉	—	2	1	no	—
178	C₂×D₄×C₈₉	—	2	1	no	—
179	C₂×D₄×C₈₉	—	2	1	no	—
180	C₂×D₄×C₈₉	—	2	1	no	—
181	C₂×D₄×C₈₉	—	2	1	no	—
182	C₂×D₄×C₈₉	—	4	2	no	—
183	C₂×D₄×C₈₉	—	4	2	no	—
184	C₂×D₄×C₈₉	—	4	2	no	—
185	C₂×D₄×C₈₉	—	4	2	no	—
186	C₂×D₄×C₈₉	—	4	2	no	—
187	C₂×D₄×C₈₉	—	8	1	no	—
188	C₂²×C₄×C₈₉	—	2	1	no	—
189	C₂²×C₄×C₈₉	—	2	1	no	—
190	C₂²×C₄×C₈₉	—	2	1	no	—
191	C₂²×C₄×C₈₉	—	2	1	no	—
192	C₂²×C₄×C₈₉	—	2	1	no	—
193	C₂²×C₄×C₈₉	—	2	1	no	—
194	C₂²×C₄×C₈₉	—	2	1	no	—
195	C₂²×C₄×C₈₉	—	2	1	no	—
196	C₂²×C₄×C₈₉	—	2	1	no	—
197	C₂²×C₄×C₈₉	—	2	1	no	—
198	C₂²×C₄×C₈₉	—	2	1	no	—
199	C₂²×C₄×C₈₉	—	2	1	no	—
200	C₂²×C₄×C₈₉	—	2	1	no	—
201	C₂²×C₄×C₈₉	—	2	1	no	—
202	C₂²×C₄×C₈₉	—	2	1	no	—
203	C₂²×C₄×C₈₉	—	2	1	no	—
204	C₂²×C₄×C₈₉	—	2	1	no	—
205	C₂²×C₄×C₈₉	—	4	2	no	—
206	C₂²×C₄×C₈₉	—	4	2	no	—
207	C₂²×C₄×C₈₉	—	4	2	no	—
208	C₂²×C₄×C₈₉	—	4	2	no	—
209	C₂²×C₄×C₈₉	—	4	2	no	—
210	C₂²×C₄×C₈₉	—	8	1	no	—
211	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
216	C₂²×C₄×C₈₉	#41	1	2	yes	—
217	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
218	SD₁₆×C₈₉	—	4	4	no	—
219	SD₁₆×C₈₉	—	4	4	no	—
220	M₁₆×C₈₉	—	4	4	no	—
221	C₂×C₈×C₈₉	—	2	1	no	—
222	C₂×C₈×C₈₉	—	2	1	no	—
223	C₂×C₈×C₈₉	—	2	1	no	—
224	C₂×C₈×C₈₉	—	2	1	no	—
225	C₂×C₈×C₈₉	—	2	1	no	—
226	C₂×C₈×C₈₉	—	2	1	no	—
227	C₂×C₈×C₈₉	—	2	1	no	—
228	C₂×C₈×C₈₉	—	2	1	no	—
229	C₂×C₈×C₈₉	—	2	1	no	—
230	C₂×C₈×C₈₉	—	4	4	no	—
231	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
232	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
233	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
234	C₄⋊C₄×C₈₉	—	2	2	no	—
235	C₄⋊C₄×C₈₉	—	2	1	no	—
236	C₄⋊C₄×C₈₉	—	2	1	no	—
237	C₄⋊C₄×C₈₉	—	2	1	no	—
238	C₄⋊C₄×C₈₉	—	2	1	no	—
239	C₄⋊C₄×C₈₉	—	2	1	no	—
240	C₄⋊C₄×C₈₉	—	2	1	no	—
241	C₄⋊C₄×C₈₉	—	2	1	no	—
242	C₄⋊C₄×C₈₉	—	2	1	no	—
243	C₄⋊C₄×C₈₉	—	2	1	no	—
244	C₄⋊C₄×C₈₉	—	4	2	no	—
245	C₄⋊C₄×C₈₉	—	4	2	no	—
246	C₄⋊C₄×C₈₉	—	4	2	no	—
247	C₄⋊C₄×C₈₉	—	4	2	no	—
248	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
249	C₂²⋊C₄×C₈₉	—	2	2	no	—
250	C₂²⋊C₄×C₈₉	—	2	2	no	—
251	C₂²⋊C₄×C₈₉	—	4	2	no	—
252	C₂²⋊C₄×C₈₉	—	4	2	no	—
253	C₂²⋊C₄×C₈₉	—	4	2	no	—
254	C₂²⋊C₄×C₈₉	—	4	2	no	—
255	C₂²⋊C₄×C₈₉	—	4	2	no	—
256	C₂²⋊C₄×C₈₉	—	4	2	no	—
257	C₂²⋊C₄×C₈₉	—	4	2	no	—
258	C₂²⋊C₄×C₈₉	—	8	1	no	—
259	C₄²×C₈₉	—	2	1	no	—
260	C₄²×C₈₉	—	2	1	no	—
261	C₂³×C₈₉	—	2	1	no	—
262	C₂³×C₈₉	—	2	1	no	—
263	C₂³×C₈₉	—	2	1	no	—
264	C₂³×C₈₉	—	2	1	no	—
265	C₂³×C₈₉	—	2	1	no	—
266	C₂³×C₈₉	—	2	1	no	—
267	C₂³×C₈₉	—	2	1	no	—
268	C₂³×C₈₉	—	2	1	no	—
269	C₂³×C₈₉	—	2	1	no	—
270	C₂³×C₈₉	—	2	1	no	—
271	C₂³×C₈₉	—	2	1	no	—
272	C₂³×C₈₉	—	4	1	no	—
273	C₂³×C₈₉	—	4	1	no	—
274	C₂³×C₈₉	—	4	1	no	—
275	C₂³×C₈₉	—	4	1	no	—
276	C₂³×C₈₉	—	4	1	no	—
277	C₂³×C₈₉	—	4	1	no	—
278	C₂³×C₈₉	—	4	1	no	—
279	C₂³×C₈₉	#121	1	2	yes	—
280	C₂³×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
281	C₂³×C₈₉	#137	1	2	yes	—
282	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
283	Q₈×C₈₉	—	2	2	no	—
284	Q₈×C₈₉	—	2	2	no	—
285	Q₈×C₈₉	—	2	2	no	—
286	Q₈×C₈₉	—	2	2	no	—
287	Q₈×C₈₉	—	4	8	no	—
288	Q₈×C₈₉	—	4	1	no	—
289	Q₈×C₈₉	—	4	1	no	—
290	Q₈×C₈₉	—	4	1	no	—
291	Q₈×C₈₉	—	4	1	no	—
292	D₄×C₈₉	—	4	4	no	—
293	D₄×C₈₉	—	4	1	no	—
294	D₄×C₈₉	—	4	1	no	—
295	D₄×C₈₉	—	4	1	no	—
296	D₄×C₈₉	—	4	1	no	—
297	D₄×C₈₉	—	8	4	no	—
298	D₄×C₈₉	—	8	4	no	—
299	C₂×C₄×C₈₉	—	2	1	no	—
300	C₂×C₄×C₈₉	—	2	1	no	—
301	C₂×C₄×C₈₉	—	2	2	no	—
302	C₂×C₄×C₈₉	—	2	2	no	—
303	C₂×C₄×C₈₉	—	2	2	no	—
304	C₂×C₄×C₈₉	—	2	2	no	—
305	C₂×C₄×C₈₉	—	2	1	no	—
306	C₂×C₄×C₈₉	—	2	1	no	—
307	C₂×C₄×C₈₉	—	2	1	no	—
308	C₂×C₄×C₈₉	—	2	1	no	—
309	C₂×C₄×C₈₉	—	2	2	no	—
310	C₂×C₄×C₈₉	—	2	2	no	—
311	C₂×C₄×C₈₉	—	2	2	no	—
312	C₂×C₄×C₈₉	—	2	1	no	—
313	C₂×C₄×C₈₉	—	2	1	no	—
314	C₂×C₄×C₈₉	—	2	1	no	—
315	C₂×C₄×C₈₉	—	2	1	no	—
316	C₂×C₄×C₈₉	—	2	1	no	—
317	C₂×C₄×C₈₉	—	4	8	no	—
318	C₂×C₄×C₈₉	—	4	1	no	—
319	C₂×C₄×C₈₉	—	4	1	no	—
320	C₂×C₄×C₈₉	—	4	1	no	—
321	C₂×C₄×C₈₉	—	4	1	no	—
322	C₂×C₄×C₈₉	—	4	1	no	—
323	C₂×C₄×C₈₉	—	4	1	no	—
324	C₂×C₄×C₈₉	—	4	1	no	—
325	C₂×C₄×C₈₉	—	4	1	no	—
326	C₂×C₄×C₈₉	—	4	1	no	—
327	C₂×C₄×C₈₉	—	4	1	no	—
328	C₂×C₄×C₈₉	—	4	1	no	—
329	C₂×C₄×C₈₉	—	4	1	no	—
330	C₂×C₄×C₈₉	—	4	1	no	—
331	C₂×C₄×C₈₉	—	4	1	no	—
332	C₂×C₄×C₈₉	—	4	1	no	—
333	C₂×C₄×C₈₉	—	4	1	no	—
334	C₂×C₄×C₈₉	—	4	1	no	—
335	C₂×C₄×C₈₉	—	4	1	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	—	8	4	no	—
341	C₂×C₄×C₈₉	#121	1	2	yes	—
342	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
345	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
346	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
347	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
348	C₈×C₈₉	—	2	2	no	—
349	C₈×C₈₉	—	2	2	no	—
350	C₈×C₈₉	—	2	2	no	—
351	C₈×C₈₉	—	4	1	no	—
352	C₂²×C₈₉	—	2	2	no	—
353	C₂²×C₈₉	—	2	2	no	—
354	C₂²×C₈₉	—	2	2	no	—
355	C₂²×C₈₉	—	2	2	no	—
356	C₂²×C₈₉	—	2	2	no	—
357	C₂²×C₈₉	—	2	2	no	—
358	C₂²×C₈₉	—	4	1	no	—
359	C₂²×C₈₉	—	4	1	no	—
360	C₂²×C₈₉	—	4	1	no	—
361	C₂²×C₈₉	—	4	1	no	—
362	C₂²×C₈₉	—	4	1	no	—
363	C₂²×C₈₉	—	4	1	no	—
364	C₂²×C₈₉	—	4	1	no	—
365	C₂²×C₈₉	—	8	1	no	—
366	C₂²×C₈₉	—	8	1	no	—
367	C₂²×C₈₉	—	8	1	no	—
368	C₂²×C₈₉	—	8	1	no	—
369	C₂²×C₈₉	—	8	1	no	—
370	C₂²×C₈₉	—	8	1	no	—
371	C₂²×C₈₉	—	8	1	no	—
372	C₂²×C₈₉	#468	1	4	yes	complemented
373	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
374	C₂²×C₈₉	D₄²	1	1	yes	characteristic
375	C₂²×C₈₉	#546	1	1	yes	characteristic
376	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
377	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
378	C₂²×C₈₉	#577	1	1	yes	characteristic
379	C₂²×C₈₉	#578	1	1	yes	characteristic
380	C₄×C₈₉	—	2	2	no	—
381	C₄×C₈₉	—	4	1	no	—
382	C₄×C₈₉	—	4	2	no	—
383	C₄×C₈₉	—	4	2	no	—
384	C₄×C₈₉	—	4	2	no	—
385	C₄×C₈₉	—	4	1	no	—
386	C₄×C₈₉	—	4	1	no	—
387	C₄×C₈₉	—	8	1	no	—
388	C₄×C₈₉	—	8	1	no	—
389	C₄×C₈₉	—	8	1	no	—
390	C₄×C₈₉	—	8	1	no	—
391	C₄×C₈₉	#525	1	1	yes	characteristic
392	C₄×C₈₉	#538	1	1	yes	characteristic
393	C₄×C₈₉	D₄²	1	1	yes	characteristic
394	C₄×C₈₉	#546	1	1	yes	characteristic
395	#25130	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
396	C₂×C₈₉	—	2	4	no	—
397	C₂×C₈₉	—	8	1	no	—
398	C₂×C₈₉	—	16	1	no	—
399	C₂×C₈₉	#2424	1	1	yes	characteristic
400	C₂×C₈₉	C₂×#468	1	1	yes	characteristic
401	C₂×C₈₉	#3063	1	1	yes	characteristic
402	C₂×C₈₉	#3265	1	1	yes	characteristic
403	C₂×C₈₉	#3270	1	1	yes	characteristic
404	C₂×C₈₉	#3308	1	1	yes	characteristic
405	C₂×C₈₉	#3320	1	1	yes	characteristic
406	C₂×#468	C₂×C₈₉	1	1	yes	characteristic, complemented
407	C₂×#448	C₂×C₈₉	1	1	yes	characteristic, complemented
408	C₂×#435	C₂×C₈₉	1	1	yes	characteristic, complemented
409	C₂²×#103	C₂×C₈₉	1	1	yes	characteristic, complemented
410	#2416	C₂×C₈₉	1	1	yes	characteristic
411	#2409	C₂×C₈₉	1	1	yes	characteristic, complemented
412	#2068	C₂×C₈₉	1	1	yes	characteristic, complemented
413	#2055	C₂×C₈₉	1	1	yes	characteristic, complemented
414	#2036	C₂×C₈₉	1	1	yes	characteristic, complemented
415	#2000	C₂×C₈₉	1	1	yes	characteristic, complemented
416	#1973	C₂×C₈₉	1	1	yes	characteristic, complemented
417	#1935	C₂×C₈₉	1	1	yes	characteristic, complemented
418	#1894	C₂×C₈₉	1	1	yes	characteristic, complemented
419	#1893	C₂×C₈₉	1	1	yes	characteristic, complemented
420	#1852	C₂×C₈₉	1	1	yes	characteristic, complemented
421	C₈₉	#25130	1	1	yes	characteristic, direct product factor, Sylow
422	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
423	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
424	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
425	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
426	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
427	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
428	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
429	C₂×#121	—	2	1	no	—
430	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
431	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
432	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
433	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
434	#468	—	2	4	no	—
435	#448	—	2	4	no	—
436	#435	—	2	4	no	—
437	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
438	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
439	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
440	C₂×#103	—	2	4	no	—
441	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
442	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
443	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
444	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
445	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
446	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
447	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
448	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
449	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
450	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
451	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
452	#396	—	2	1	no	—
453	#395	—	2	1	no	—
454	#394	—	2	1	no	—
455	#393	—	2	1	no	—
456	#391	C₂²×C₈₉	1	1	yes	characteristic
457	#391	C₂²×C₈₉	1	1	yes	characteristic
458	#390	C₂²×C₈₉	1	1	yes	characteristic
459	#389	C₂²×C₈₉	1	1	yes	characteristic
460	#386	—	2	1	no	—
461	#386	—	2	1	no	—
462	#385	—	2	1	no	—
463	#380	C₂²×C₈₉	1	1	yes	characteristic
464	#380	C₂²×C₈₉	1	1	yes	characteristic
465	#340	C₂²×C₈₉	1	1	yes	characteristic
466	#340	C₂²×C₈₉	1	1	yes	characteristic
467	#340	C₂²×C₈₉	1	1	yes	characteristic
468	#340	C₂²×C₈₉	1	1	yes	characteristic
469	C₂²×Q₈	—	2	1	no	—
470	C₂²×Q₈	—	2	2	no	—
471	C₂²×Q₈	—	2	2	no	—
472	C₂²×Q₈	—	2	2	no	—
473	C₂²×Q₈	—	2	2	no	—
474	C₂²×Q₈	—	4	1	no	—
475	C₂²×Q₈	—	4	1	no	—
476	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
477	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
478	C₂²×D₄	—	2	1	no	—
479	C₂²×D₄	—	2	1	no	—
480	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
481	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
482	C₂³×C₄	—	2	1	no	—
483	C₂³×C₄	—	2	1	no	—
484	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
486	C₂×SD₁₆	—	2	2	no	—
487	C₂×SD₁₆	—	2	2	no	—
488	C₂×SD₁₆	—	2	2	no	—
489	C₂×SD₁₆	—	2	2	no	—
490	C₂×SD₁₆	—	4	1	no	—
491	C₂×SD₁₆	—	4	1	no	—
492	C₂×M₁₆	—	2	2	no	—
493	C₂×M₁₆	—	2	2	no	—
494	C₂×M₁₆	—	4	1	no	—
495	C₂²×C₈	—	2	2	no	—
496	C₂²×C₈	—	2	2	no	—
497	C₂²×C₈	—	4	1	no	—
498	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
499	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
500	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
501	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
502	C₂²⋊Q₈	—	2	2	no	—
503	C₂²⋊Q₈	—	2	2	no	—
504	C₂²⋊Q₈	—	4	1	no	—
505	C₂²⋊Q₈	—	4	1	no	—
506	#121	—	2	2	no	—
507	#121	—	2	2	no	—
508	#121	—	2	2	no	—
509	#121	—	4	1	no	—
510	#121	—	4	4	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	2	no	—
513	C₂×C₄⋊C₄	—	2	2	no	—
514	C₂×C₄⋊C₄	—	2	1	no	—
515	C₂×C₄⋊C₄	—	2	1	no	—
516	C₂×C₄⋊C₄	—	2	1	no	—
517	C₂×C₄⋊C₄	—	2	1	no	—
518	C₂×C₄⋊C₄	—	4	1	no	—
519	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₂²⋊C₄	—	2	1	no	—
527	C₂×C₂²⋊C₄	—	2	1	no	—
528	C₂×C₂²⋊C₄	—	2	1	no	—
529	C₂×C₂²⋊C₄	—	2	1	no	—
530	C₂×C₂²⋊C₄	—	2	1	no	—
531	C₂×C₂²⋊C₄	—	2	1	no	—
532	C₂×C₂²⋊C₄	—	2	1	no	—
533	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
534	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
535	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
536	#107	—	2	2	no	—
537	#107	—	4	1	no	—
538	C₄⋊C₈	—	2	2	no	—
539	#103	—	2	2	no	—
540	#103	—	2	2	no	—
541	#103	—	2	2	no	—
542	#103	—	2	2	no	—
543	#103	—	2	2	no	—
544	#103	D₄×C₈₉	1	4	yes	complemented
545	#102	—	2	2	no	—
546	#102	—	4	1	no	—
547	C₂²⋊C₈	—	2	2	no	—
548	C₂²⋊C₈	D₄×C₈₉	1	4	yes	complemented
549	#97	—	2	2	no	—
550	#95	—	2	1	no	—
551	#95	—	2	1	no	—
552	#95	—	2	1	no	—
553	#95	—	2	1	no	—
554	#95	—	2	1	no	—
555	#95	—	2	1	no	—
556	#95	—	2	1	no	—
557	C₂⁴	—	2	1	no	—
558	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
559	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	8	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	1	no	—
567	C₂×Q₈	—	2	1	no	—
568	C₂×Q₈	—	2	1	no	—
569	C₂×Q₈	—	2	1	no	—
570	C₂×Q₈	—	2	1	no	—
571	C₂×Q₈	—	4	2	no	—
572	C₂×Q₈	—	4	2	no	—
573	C₂×Q₈	—	4	4	no	—
574	C₂×Q₈	—	4	4	no	—
575	C₂×Q₈	—	4	4	no	—
576	C₂×Q₈	—	4	2	no	—
577	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
578	C₂×Q₈	#41×C₈₉	1	2	yes	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	1	no	—
583	C₂×D₄	—	2	1	no	—
584	C₂×D₄	—	2	1	no	—
585	C₂×D₄	—	2	1	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	4	2	no	—
589	C₂×D₄	—	4	2	no	—
590	C₂×D₄	—	4	2	no	—
591	C₂×D₄	—	4	2	no	—
592	C₂×D₄	—	4	2	no	—
593	C₂×D₄	—	8	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	4	2	no	—
612	C₂²×C₄	—	4	2	no	—
613	C₂²×C₄	—	4	2	no	—
614	C₂²×C₄	—	4	2	no	—
615	C₂²×C₄	—	4	2	no	—
616	C₂²×C₄	—	8	1	no	—
617	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
618	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
619	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
620	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
621	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
622	C₂²×C₄	#41×C₈₉	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
624	SD₁₆	—	4	4	no	—
625	SD₁₆	—	4	4	no	—
626	M₁₆	—	4	4	no	—
627	C₂×C₈	—	2	1	no	—
628	C₂×C₈	—	2	1	no	—
629	C₂×C₈	—	2	1	no	—
630	C₂×C₈	—	2	1	no	—
631	C₂×C₈	—	2	1	no	—
632	C₂×C₈	—	2	1	no	—
633	C₂×C₈	—	2	1	no	—
634	C₂×C₈	—	2	1	no	—
635	C₂×C₈	—	2	1	no	—
636	C₂×C₈	—	4	4	no	—
637	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
638	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
639	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	1	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	—	4	2	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₄⋊C₄	—	4	2	no	—
653	C₄⋊C₄	—	4	2	no	—
654	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	4	2	no	—
658	C₂²⋊C₄	—	4	2	no	—
659	C₂²⋊C₄	—	4	2	no	—
660	C₂²⋊C₄	—	4	2	no	—
661	C₂²⋊C₄	—	4	2	no	—
662	C₂²⋊C₄	—	4	2	no	—
663	C₂²⋊C₄	—	4	2	no	—
664	C₂²⋊C₄	—	8	1	no	—
665	C₄²	—	2	1	no	—
666	C₄²	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	1	no	—
678	C₂³	—	4	1	no	—
679	C₂³	—	4	1	no	—
680	C₂³	—	4	1	no	—
681	C₂³	—	4	1	no	—
682	C₂³	—	4	1	no	—
683	C₂³	—	4	1	no	—
684	C₂³	—	4	1	no	—
685	C₂³	#121×C₈₉	1	2	yes	—
686	C₂³	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
687	C₂³	#137×C₈₉	1	2	yes	—
688	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
689	Q₈	—	2	2	no	—
690	Q₈	—	2	2	no	—
691	Q₈	—	2	2	no	—
692	Q₈	—	2	2	no	—
693	Q₈	—	4	8	no	—
694	Q₈	—	4	1	no	—
695	Q₈	—	4	1	no	—
696	Q₈	—	4	1	no	—
697	Q₈	—	4	1	no	—
698	D₄	—	4	4	no	—
699	D₄	—	4	1	no	—
700	D₄	—	4	1	no	—
701	D₄	—	4	1	no	—
702	D₄	—	4	1	no	—
703	D₄	—	8	4	no	—
704	D₄	—	8	4	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	4	8	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	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	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	8	4	no	—
747	C₂×C₄	#121×C₈₉	1	2	yes	—
748	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
749	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
750	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
751	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
752	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
753	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
754	C₈	—	2	2	no	—
755	C₈	—	2	2	no	—
756	C₈	—	2	2	no	—
757	C₈	—	4	1	no	—
758	C₂²	—	2	2	no	—
759	C₂²	—	2	2	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	4	1	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	8	1	no	—
772	C₂²	—	8	1	no	—
773	C₂²	—	8	1	no	—
774	C₂²	—	8	1	no	—
775	C₂²	—	8	1	no	—
776	C₂²	—	8	1	no	—
777	C₂²	—	8	1	no	—
778	C₂²	#468×C₈₉	1	4	yes	complemented
779	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
780	C₂²	D₄²×C₈₉	1	1	yes	characteristic
781	C₂²	#546×C₈₉	1	1	yes	characteristic
782	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
783	C₂²	C₂×#137×C₈₉	1	1	yes	characteristic
784	C₂²	#577×C₈₉	1	1	yes	characteristic
785	C₂²	#578×C₈₉	1	1	yes	characteristic
786	C₄	—	2	2	no	—
787	C₄	—	4	1	no	—
788	C₄	—	4	1	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	1	no	—
793	C₄	—	8	1	no	—
794	C₄	—	8	1	no	—
795	C₄	—	8	1	no	—
796	C₄	—	8	1	no	—
797	C₄	#525×C₈₉	1	1	yes	characteristic
798	C₄	#538×C₈₉	1	1	yes	characteristic
799	C₄	D₄²×C₈₉	1	1	yes	characteristic
800	C₄	#546×C₈₉	1	1	yes	characteristic
801	C₂	—	2	4	no	—
802	C₂	—	8	1	no	—
803	C₂	—	16	1	no	—
804	C₂	C₈₉×#2424	1	1	yes	characteristic
805	C₂	C₂×#468×C₈₉	1	1	yes	characteristic
806	C₂	C₈₉×#3063	1	1	yes	characteristic
807	C₂	C₈₉×#3265	1	1	yes	characteristic
808	C₂	C₈₉×#3270	1	1	yes	characteristic
809	C₂	C₈₉×#3308	1	1	yes	characteristic
810	C₂	C₈₉×#3320	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₈₉×#2416	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×C₄×D₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#468×C₈₉	C₂	semidirect
2. C₂×#448×C₈₉	C₂	semidirect
3. C₂×#435×C₈₉	C₂	semidirect
4. C₂²×#103×C₈₉	C₂	semidirect
6. C₈₉×#2409	C₂	semidirect
7. C₈₉×#2068	C₂	semidirect
8. C₈₉×#2055	C₂	semidirect
9. C₈₉×#2036	C₂	semidirect
10. C₈₉×#2000	C₂	semidirect
11. C₈₉×#1973	C₂	semidirect
12. C₈₉×#1935	C₂	semidirect
13. C₈₉×#1894	C₂	semidirect
14. C₈₉×#1893	C₂	semidirect
15. C₈₉×#1852	C₂	semidirect
138. #103×C₈₉	D₄	semidirect
142. C₂²⋊C₈×C₈₉	D₄	semidirect
372. C₂²×C₈₉	#468	semidirect
395. #25130	C₈₉	direct (N × H)
406. C₂×#468	C₂×C₈₉	semidirect
407. C₂×#448	C₂×C₈₉	semidirect
408. C₂×#435	C₂×C₈₉	semidirect
409. C₂²×#103	C₂×C₈₉	semidirect
411. #2409	C₂×C₈₉	semidirect
412. #2068	C₂×C₈₉	semidirect
413. #2055	C₂×C₈₉	semidirect
414. #2036	C₂×C₈₉	semidirect
415. #2000	C₂×C₈₉	semidirect
416. #1973	C₂×C₈₉	semidirect
417. #1935	C₂×C₈₉	semidirect
418. #1894	C₂×C₈₉	semidirect
419. #1893	C₂×C₈₉	semidirect
420. #1852	C₂×C₈₉	semidirect
421. C₈₉	#25130	direct (N × H)
544. #103	D₄×C₈₉	semidirect
548. C₂²⋊C₈	D₄×C₈₉	semidirect
778. C₂²	#468×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#468×C₈₉	2
C₂×#448×C₈₉	2
C₂×#435×C₈₉	2
C₂²×#103×C₈₉	2
C₈₉×#2416	2
C₈₉×#2409	2
C₈₉×#2068	2
C₈₉×#2055	2
C₈₉×#2036	2
C₈₉×#2000	2
C₈₉×#1973	2
C₈₉×#1935	2
C₈₉×#1894	2
C₈₉×#1893	2
C₈₉×#1852	2
#25130	89

Subgroups — C89×#25130 #36402978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25130 #36402978