Subgroups — C₈₉×#25172 #36403020

Order 22784.

1310 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#463×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#450×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#447×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#442×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2427	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×C₂²⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2065	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1973	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1924	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1877	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1862	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×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×D₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₂²⋊C₄×C₈₉	—	2	1	no	—
28	#463×C₈₉	—	2	4	no	—
29	#450×C₈₉	—	2	4	no	—
30	#447×C₈₉	—	2	4	no	—
31	#442×C₈₉	—	2	4	no	—
32	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic, complemented
33	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
36	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
37	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
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, complemented
46	#397×C₈₉	—	2	1	no	—
47	#394×C₈₉	—	2	1	no	—
48	#391×C₈₉	C₂²	1	1	yes	characteristic, complemented
49	#390×C₈₉	C₂²	1	1	yes	characteristic
50	#390×C₈₉	C₂²	1	1	yes	characteristic
51	#389×C₈₉	C₂²	1	1	yes	characteristic, complemented
52	#386×C₈₉	—	2	1	no	—
53	#386×C₈₉	—	2	1	no	—
54	#386×C₈₉	—	2	1	no	—
55	#380×C₈₉	—	2	1	no	—
56	#380×C₈₉	C₂²	1	1	yes	characteristic
57	#379×C₈₉	—	2	1	no	—
58	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
59	#340×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#340×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	#336×C₈₉	C₂²	1	1	yes	characteristic, complemented
62	#336×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	C₂⁵×C₈₉	—	2	1	no	—
64	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₈₉	—	2	2	no	—
66	C₂²×D₄×C₈₉	—	2	2	no	—
67	C₂²×D₄×C₈₉	—	2	2	no	—
68	C₂²×D₄×C₈₉	—	2	2	no	—
69	C₂²×D₄×C₈₉	—	2	1	no	—
70	C₂²×D₄×C₈₉	—	2	1	no	—
71	C₂²×D₄×C₈₉	—	4	1	no	—
72	C₂²×D₄×C₈₉	—	4	1	no	—
73	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₈₉	C₂³	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	—	2	1	no	—
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	—	2	2	no	—
85	C₂×SD₁₆×C₈₉	—	4	1	no	—
86	C₂×D₈×C₈₉	—	2	2	no	—
87	C₂×D₈×C₈₉	—	2	2	no	—
88	C₂×D₈×C₈₉	—	2	2	no	—
89	C₂×D₈×C₈₉	—	2	2	no	—
90	C₂×D₈×C₈₉	—	4	1	no	—
91	C₂×D₈×C₈₉	D₄	1	4	yes	—
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	#124×C₈₉	—	2	2	no	—
97	#124×C₈₉	—	4	1	no	—
98	C₂²⋊Q₈×C₈₉	—	2	2	no	—
99	C₂²⋊Q₈×C₈₉	—	4	1	no	—
100	#121×C₈₉	—	2	2	no	—
101	#121×C₈₉	—	4	1	no	—
102	C₄×D₄×C₈₉	—	2	2	no	—
103	C₄×D₄×C₈₉	—	2	2	no	—
104	C₄×D₄×C₈₉	—	2	2	no	—
105	C₄×D₄×C₈₉	—	4	1	no	—
106	C₄×D₄×C₈₉	—	4	1	no	—
107	C₄×D₄×C₈₉	—	4	1	no	—
108	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
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	—	4	4	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	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
131	#107×C₈₉	—	4	1	no	—
132	#106×C₈₉	—	2	2	no	—
133	C₄⋊C₈×C₈₉	—	2	2	no	—
134	#103×C₈₉	—	2	2	no	—
135	#103×C₈₉	—	4	1	no	—
136	#102×C₈₉	—	2	2	no	—
137	#102×C₈₉	—	2	2	no	—
138	#102×C₈₉	—	2	2	no	—
139	#102×C₈₉	—	2	2	no	—
140	#102×C₈₉	—	2	2	no	—
141	#102×C₈₉	D₄	1	4	yes	complemented
142	C₂²⋊C₈×C₈₉	—	2	2	no	—
143	C₂²⋊C₈×C₈₉	—	2	2	no	—
144	#97×C₈₉	—	2	2	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	D₄	1	1	yes	characteristic
150	#95×C₈₉	D₄	1	1	yes	characteristic
151	C₂⁴×C₈₉	—	2	1	no	—
152	C₂⁴×C₈₉	—	2	4	no	—
153	C₂⁴×C₈₉	—	2	1	no	—
154	C₂⁴×C₈₉	—	2	1	no	—
155	C₂⁴×C₈₉	—	4	2	no	—
156	C₂⁴×C₈₉	—	4	2	no	—
157	C₂⁴×C₈₉	—	4	2	no	—
158	C₂⁴×C₈₉	—	4	2	no	—
159	C₂⁴×C₈₉	—	8	1	no	—
160	C₂⁴×C₈₉	—	8	1	no	—
161	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
166	C₂×Q₈×C₈₉	—	2	1	no	—
167	C₂×Q₈×C₈₉	—	2	1	no	—
168	C₂×D₄×C₈₉	—	2	4	no	—
169	C₂×D₄×C₈₉	—	2	1	no	—
170	C₂×D₄×C₈₉	—	2	1	no	—
171	C₂×D₄×C₈₉	—	2	1	no	—
172	C₂×D₄×C₈₉	—	2	1	no	—
173	C₂×D₄×C₈₉	—	2	1	no	—
174	C₂×D₄×C₈₉	—	2	1	no	—
175	C₂×D₄×C₈₉	—	2	1	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	4	no	—
185	C₂×D₄×C₈₉	—	4	4	no	—
186	C₂×D₄×C₈₉	—	4	4	no	—
187	C₂×D₄×C₈₉	—	4	4	no	—
188	C₂×D₄×C₈₉	—	4	2	no	—
189	C₂×D₄×C₈₉	—	4	2	no	—
190	C₂×D₄×C₈₉	—	8	1	no	—
191	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
192	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
193	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
194	C₂×D₄×C₈₉	#41	1	2	yes	—
195	C₂×D₄×C₈₉	#41	1	2	yes	—
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	—	2	1	no	—
206	C₂²×C₄×C₈₉	—	2	1	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	—	4	2	no	—
211	C₂²×C₄×C₈₉	—	4	2	no	—
212	C₂²×C₄×C₈₉	—	4	2	no	—
213	C₂²×C₄×C₈₉	—	8	1	no	—
214	C₂²×C₄×C₈₉	—	8	1	no	—
215	C₂²×C₄×C₈₉	—	8	1	no	—
216	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
222	SD₁₆×C₈₉	—	4	4	no	—
223	SD₁₆×C₈₉	—	4	4	no	—
224	D₈×C₈₉	—	2	8	no	—
225	D₈×C₈₉	—	4	4	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	—	2	1	no	—
231	C₂×C₈×C₈₉	—	2	1	no	—
232	C₂×C₈×C₈₉	—	2	1	no	—
233	C₂×C₈×C₈₉	—	2	1	no	—
234	C₂×C₈×C₈₉	—	2	1	no	—
235	C₂×C₈×C₈₉	—	2	1	no	—
236	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
237	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
245	C₄⋊C₄×C₈₉	—	4	2	no	—
246	C₄⋊C₄×C₈₉	—	8	1	no	—
247	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
248	C₂²⋊C₄×C₈₉	—	2	2	no	—
249	C₂²⋊C₄×C₈₉	—	4	1	no	—
250	C₂²⋊C₄×C₈₉	—	4	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	—	4	2	no	—
259	C₂²⋊C₄×C₈₉	—	4	2	no	—
260	C₂²⋊C₄×C₈₉	—	8	1	no	—
261	C₂²⋊C₄×C₈₉	—	8	1	no	—
262	C₄²×C₈₉	—	2	1	no	—
263	C₄²×C₈₉	—	2	1	no	—
264	C₄²×C₈₉	—	2	1	no	—
265	C₄²×C₈₉	—	2	1	no	—
266	C₂³×C₈₉	—	2	1	no	—
267	C₂³×C₈₉	—	2	2	no	—
268	C₂³×C₈₉	—	2	1	no	—
269	C₂³×C₈₉	—	2	2	no	—
270	C₂³×C₈₉	—	2	2	no	—
271	C₂³×C₈₉	—	2	1	no	—
272	C₂³×C₈₉	—	2	1	no	—
273	C₂³×C₈₉	—	2	1	no	—
274	C₂³×C₈₉	—	2	1	no	—
275	C₂³×C₈₉	—	2	2	no	—
276	C₂³×C₈₉	—	2	2	no	—
277	C₂³×C₈₉	—	4	8	no	—
278	C₂³×C₈₉	—	4	8	no	—
279	C₂³×C₈₉	—	4	1	no	—
280	C₂³×C₈₉	—	4	1	no	—
281	C₂³×C₈₉	—	4	1	no	—
282	C₂³×C₈₉	—	4	1	no	—
283	C₂³×C₈₉	—	4	1	no	—
284	C₂³×C₈₉	—	4	1	no	—
285	C₂³×C₈₉	—	4	1	no	—
286	C₂³×C₈₉	—	4	1	no	—
287	C₂³×C₈₉	—	4	1	no	—
288	C₂³×C₈₉	—	4	1	no	—
289	C₂³×C₈₉	—	4	1	no	—
290	C₂³×C₈₉	—	4	1	no	—
291	C₂³×C₈₉	—	4	1	no	—
292	C₂³×C₈₉	—	4	1	no	—
293	C₂³×C₈₉	—	4	1	no	—
294	C₂³×C₈₉	—	4	1	no	—
295	C₂³×C₈₉	—	8	4	no	—
296	C₂³×C₈₉	—	8	4	no	—
297	C₂³×C₈₉	—	8	4	no	—
298	C₂³×C₈₉	—	8	4	no	—
299	C₂³×C₈₉	—	8	4	no	—
300	C₂³×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
301	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
302	Q₈×C₈₉	—	4	1	no	—
303	Q₈×C₈₉	—	4	1	no	—
304	Q₈×C₈₉	—	4	1	no	—
305	Q₈×C₈₉	—	4	1	no	—
306	D₄×C₈₉	—	2	2	no	—
307	D₄×C₈₉	—	2	2	no	—
308	D₄×C₈₉	—	2	2	no	—
309	D₄×C₈₉	—	2	2	no	—
310	D₄×C₈₉	—	2	2	no	—
311	D₄×C₈₉	—	2	2	no	—
312	D₄×C₈₉	—	2	2	no	—
313	D₄×C₈₉	—	4	8	no	—
314	D₄×C₈₉	—	4	1	no	—
315	D₄×C₈₉	—	4	1	no	—
316	D₄×C₈₉	—	4	1	no	—
317	D₄×C₈₉	—	4	1	no	—
318	D₄×C₈₉	—	8	4	no	—
319	D₄×C₈₉	#121	1	4	yes	—
320	C₂×C₄×C₈₉	—	2	1	no	—
321	C₂×C₄×C₈₉	—	2	1	no	—
322	C₂×C₄×C₈₉	—	2	1	no	—
323	C₂×C₄×C₈₉	—	2	1	no	—
324	C₂×C₄×C₈₉	—	2	1	no	—
325	C₂×C₄×C₈₉	—	2	2	no	—
326	C₂×C₄×C₈₉	—	2	1	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	1	no	—
332	C₂×C₄×C₈₉	—	2	1	no	—
333	C₂×C₄×C₈₉	—	2	1	no	—
334	C₂×C₄×C₈₉	—	2	1	no	—
335	C₂×C₄×C₈₉	—	2	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	—	4	1	no	—
341	C₂×C₄×C₈₉	—	4	1	no	—
342	C₂×C₄×C₈₉	—	4	1	no	—
343	C₂×C₄×C₈₉	—	4	1	no	—
344	C₂×C₄×C₈₉	—	4	1	no	—
345	C₂×C₄×C₈₉	—	4	1	no	—
346	C₂×C₄×C₈₉	—	4	1	no	—
347	C₂×C₄×C₈₉	—	4	1	no	—
348	C₂×C₄×C₈₉	—	4	1	no	—
349	C₂×C₄×C₈₉	—	4	1	no	—
350	C₂×C₄×C₈₉	—	4	1	no	—
351	C₂×C₄×C₈₉	—	4	1	no	—
352	C₂×C₄×C₈₉	—	4	1	no	—
353	C₂×C₄×C₈₉	—	4	1	no	—
354	C₂×C₄×C₈₉	—	8	4	no	—
355	C₂×C₄×C₈₉	—	8	4	no	—
356	C₂×C₄×C₈₉	—	8	4	no	—
357	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
360	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
361	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
362	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
363	C₈×C₈₉	—	2	2	no	—
364	C₈×C₈₉	—	2	2	no	—
365	C₈×C₈₉	—	4	1	no	—
366	C₈×C₈₉	—	4	1	no	—
367	C₂²×C₈₉	—	2	2	no	—
368	C₂²×C₈₉	—	2	4	no	—
369	C₂²×C₈₉	—	2	2	no	—
370	C₂²×C₈₉	—	2	2	no	—
371	C₂²×C₈₉	—	4	2	no	—
372	C₂²×C₈₉	—	4	1	no	—
373	C₂²×C₈₉	—	4	2	no	—
374	C₂²×C₈₉	—	4	1	no	—
375	C₂²×C₈₉	—	4	2	no	—
376	C₂²×C₈₉	—	4	2	no	—
377	C₂²×C₈₉	—	4	1	no	—
378	C₂²×C₈₉	—	4	2	no	—
379	C₂²×C₈₉	—	4	1	no	—
380	C₂²×C₈₉	—	4	2	no	—
381	C₂²×C₈₉	—	4	2	no	—
382	C₂²×C₈₉	—	4	2	no	—
383	C₂²×C₈₉	—	4	2	no	—
384	C₂²×C₈₉	—	4	2	no	—
385	C₂²×C₈₉	—	4	2	no	—
386	C₂²×C₈₉	—	4	2	no	—
387	C₂²×C₈₉	—	8	16	no	—
388	C₂²×C₈₉	—	8	1	no	—
389	C₂²×C₈₉	—	8	1	no	—
390	C₂²×C₈₉	—	8	1	no	—
391	C₂²×C₈₉	—	8	1	no	—
392	C₂²×C₈₉	—	8	1	no	—
393	C₂²×C₈₉	—	8	1	no	—
394	C₂²×C₈₉	—	8	1	no	—
395	C₂²×C₈₉	—	8	1	no	—
396	C₂²×C₈₉	#525	1	1	yes	characteristic
397	C₂²×C₈₉	D₄²	1	1	yes	characteristic
398	C₂²×C₈₉	D₄²	1	1	yes	characteristic
399	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
400	C₂²×C₈₉	#575	1	1	yes	characteristic
401	C₂²×C₈₉	#576	1	1	yes	characteristic
402	C₂²×C₈₉	#577	1	1	yes	characteristic
403	C₄×C₈₉	—	4	1	no	—
404	C₄×C₈₉	—	4	1	no	—
405	C₄×C₈₉	—	4	1	no	—
406	C₄×C₈₉	—	4	1	no	—
407	C₄×C₈₉	—	4	1	no	—
408	C₄×C₈₉	—	4	2	no	—
409	C₄×C₈₉	—	8	1	no	—
410	C₄×C₈₉	—	8	1	no	—
411	C₄×C₈₉	—	8	1	no	—
412	C₄×C₈₉	—	8	1	no	—
413	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
414	C₄×C₈₉	#538	1	1	yes	characteristic
415	C₄×C₈₉	#546	1	1	yes	characteristic
416	C₄×C₈₉	#546	1	1	yes	characteristic
417	#25172	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
418	C₂×C₈₉	—	4	2	no	—
419	C₂×C₈₉	—	4	4	no	—
420	C₂×C₈₉	—	8	2	no	—
421	C₂×C₈₉	—	8	2	no	—
422	C₂×C₈₉	#2424	1	1	yes	characteristic
423	C₂×C₈₉	#3114	1	1	yes	characteristic
424	C₂×C₈₉	#3118	1	1	yes	characteristic
425	C₂×C₈₉	#3264	1	1	yes	characteristic
426	C₂×C₈₉	#3265	1	1	yes	characteristic
427	C₂×C₈₉	#3267	1	1	yes	characteristic
428	C₂×C₈₉	#3273	1	1	yes	characteristic
429	C₂×#463	C₂×C₈₉	1	1	yes	characteristic, complemented
430	C₂×#450	C₂×C₈₉	1	1	yes	characteristic, complemented
431	C₂×#447	C₂×C₈₉	1	1	yes	characteristic
432	C₂×#442	C₂×C₈₉	1	1	yes	characteristic, complemented
433	#2427	C₂×C₈₉	1	1	yes	characteristic, complemented
434	D₄×C₂²⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
435	#2065	C₂×C₈₉	1	1	yes	characteristic, complemented
436	#2035	C₂×C₈₉	1	1	yes	characteristic, complemented
437	#2033	C₂×C₈₉	1	1	yes	characteristic, complemented
438	#2012	C₂×C₈₉	1	1	yes	characteristic, complemented
439	#1973	C₂×C₈₉	1	1	yes	characteristic, complemented
440	#1924	C₂×C₈₉	1	1	yes	characteristic, complemented
441	#1879	C₂×C₈₉	1	1	yes	characteristic, complemented
442	#1877	C₂×C₈₉	1	1	yes	characteristic, complemented
443	#1862	C₂×C₈₉	1	1	yes	characteristic, complemented
444	C₈₉	#25172	1	1	yes	characteristic, direct product factor, Sylow
445	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
446	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
447	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
448	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
449	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
450	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic, complemented
451	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
452	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
453	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
454	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
455	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
456	C₂²×C₂²⋊C₄	—	2	1	no	—
457	#463	—	2	4	no	—
458	#450	—	2	4	no	—
459	#447	—	2	4	no	—
460	#442	—	2	4	no	—
461	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic, complemented
462	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic, complemented
463	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
464	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
465	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
466	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
467	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
468	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
469	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
470	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
471	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
472	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
473	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
474	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic, complemented
475	#397	—	2	1	no	—
476	#394	—	2	1	no	—
477	#391	C₂²×C₈₉	1	1	yes	characteristic, complemented
478	#390	C₂²×C₈₉	1	1	yes	characteristic
479	#390	C₂²×C₈₉	1	1	yes	characteristic
480	#389	C₂²×C₈₉	1	1	yes	characteristic, complemented
481	#386	—	2	1	no	—
482	#386	—	2	1	no	—
483	#386	—	2	1	no	—
484	#380	—	2	1	no	—
485	#380	C₂²×C₈₉	1	1	yes	characteristic
486	#379	—	2	1	no	—
487	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
488	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
489	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
490	#336	C₂²×C₈₉	1	1	yes	characteristic, complemented
491	#336	C₂²×C₈₉	1	1	yes	characteristic, complemented
492	C₂⁵	—	2	1	no	—
493	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
494	C₂²×D₄	—	2	2	no	—
495	C₂²×D₄	—	2	2	no	—
496	C₂²×D₄	—	2	2	no	—
497	C₂²×D₄	—	2	2	no	—
498	C₂²×D₄	—	2	1	no	—
499	C₂²×D₄	—	2	1	no	—
500	C₂²×D₄	—	4	1	no	—
501	C₂²×D₄	—	4	1	no	—
502	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
503	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
504	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
505	C₂³×C₄	—	2	1	no	—
506	C₂³×C₄	—	2	1	no	—
507	C₂³×C₄	—	2	1	no	—
508	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
509	C₂×SD₁₆	—	2	2	no	—
510	C₂×SD₁₆	—	2	2	no	—
511	C₂×SD₁₆	—	2	2	no	—
512	C₂×SD₁₆	—	2	2	no	—
513	C₂×SD₁₆	—	2	2	no	—
514	C₂×SD₁₆	—	4	1	no	—
515	C₂×D₈	—	2	2	no	—
516	C₂×D₈	—	2	2	no	—
517	C₂×D₈	—	2	2	no	—
518	C₂×D₈	—	2	2	no	—
519	C₂×D₈	—	4	1	no	—
520	C₂×D₈	D₄×C₈₉	1	4	yes	—
521	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
522	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
523	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
524	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
525	#124	—	2	2	no	—
526	#124	—	4	1	no	—
527	C₂²⋊Q₈	—	2	2	no	—
528	C₂²⋊Q₈	—	4	1	no	—
529	#121	—	2	2	no	—
530	#121	—	4	1	no	—
531	C₄×D₄	—	2	2	no	—
532	C₄×D₄	—	2	2	no	—
533	C₄×D₄	—	2	2	no	—
534	C₄×D₄	—	4	1	no	—
535	C₄×D₄	—	4	1	no	—
536	C₄×D₄	—	4	1	no	—
537	C₂×C₄⋊C₄	—	2	1	no	—
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
543	C₂×C₂²⋊C₄	—	2	1	no	—
544	C₂×C₂²⋊C₄	—	2	1	no	—
545	C₂×C₂²⋊C₄	—	2	1	no	—
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	—	2	1	no	—
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	C₂×C₂²⋊C₄	—	2	1	no	—
555	C₂×C₂²⋊C₄	—	4	4	no	—
556	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
558	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
559	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
560	#107	—	4	1	no	—
561	#106	—	2	2	no	—
562	C₄⋊C₈	—	2	2	no	—
563	#103	—	2	2	no	—
564	#103	—	4	1	no	—
565	#102	—	2	2	no	—
566	#102	—	2	2	no	—
567	#102	—	2	2	no	—
568	#102	—	2	2	no	—
569	#102	—	2	2	no	—
570	#102	D₄×C₈₉	1	4	yes	complemented
571	C₂²⋊C₈	—	2	2	no	—
572	C₂²⋊C₈	—	2	2	no	—
573	#97	—	2	2	no	—
574	#95	—	2	1	no	—
575	#95	—	2	1	no	—
576	#95	—	2	1	no	—
577	#95	—	2	1	no	—
578	#95	D₄×C₈₉	1	1	yes	characteristic
579	#95	D₄×C₈₉	1	1	yes	characteristic
580	C₂⁴	—	2	1	no	—
581	C₂⁴	—	2	4	no	—
582	C₂⁴	—	2	1	no	—
583	C₂⁴	—	2	1	no	—
584	C₂⁴	—	4	2	no	—
585	C₂⁴	—	4	2	no	—
586	C₂⁴	—	4	2	no	—
587	C₂⁴	—	4	2	no	—
588	C₂⁴	—	8	1	no	—
589	C₂⁴	—	8	1	no	—
590	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
591	C₂×Q₈	—	2	1	no	—
592	C₂×Q₈	—	2	1	no	—
593	C₂×Q₈	—	2	1	no	—
594	C₂×Q₈	—	2	1	no	—
595	C₂×Q₈	—	2	1	no	—
596	C₂×Q₈	—	2	1	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	1	no	—
599	C₂×D₄	—	2	1	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	2	1	no	—
604	C₂×D₄	—	2	1	no	—
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	—	2	1	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	2	1	no	—
609	C₂×D₄	—	2	1	no	—
610	C₂×D₄	—	2	1	no	—
611	C₂×D₄	—	4	2	no	—
612	C₂×D₄	—	4	2	no	—
613	C₂×D₄	—	4	4	no	—
614	C₂×D₄	—	4	4	no	—
615	C₂×D₄	—	4	4	no	—
616	C₂×D₄	—	4	4	no	—
617	C₂×D₄	—	4	2	no	—
618	C₂×D₄	—	4	2	no	—
619	C₂×D₄	—	8	1	no	—
620	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
621	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
622	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
623	C₂×D₄	#41×C₈₉	1	2	yes	—
624	C₂×D₄	#41×C₈₉	1	2	yes	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	4	2	no	—
637	C₂²×C₄	—	4	2	no	—
638	C₂²×C₄	—	4	2	no	—
639	C₂²×C₄	—	4	2	no	—
640	C₂²×C₄	—	4	2	no	—
641	C₂²×C₄	—	4	2	no	—
642	C₂²×C₄	—	8	1	no	—
643	C₂²×C₄	—	8	1	no	—
644	C₂²×C₄	—	8	1	no	—
645	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
646	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
647	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
648	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
649	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
650	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
651	SD₁₆	—	4	4	no	—
652	SD₁₆	—	4	4	no	—
653	D₈	—	2	8	no	—
654	D₈	—	4	4	no	—
655	C₂×C₈	—	2	1	no	—
656	C₂×C₈	—	2	1	no	—
657	C₂×C₈	—	2	1	no	—
658	C₂×C₈	—	2	1	no	—
659	C₂×C₈	—	2	1	no	—
660	C₂×C₈	—	2	1	no	—
661	C₂×C₈	—	2	1	no	—
662	C₂×C₈	—	2	1	no	—
663	C₂×C₈	—	2	1	no	—
664	C₂×C₈	—	2	1	no	—
665	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
666	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	4	2	no	—
675	C₄⋊C₄	—	8	1	no	—
676	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
677	C₂²⋊C₄	—	2	2	no	—
678	C₂²⋊C₄	—	4	1	no	—
679	C₂²⋊C₄	—	4	2	no	—
680	C₂²⋊C₄	—	4	2	no	—
681	C₂²⋊C₄	—	4	2	no	—
682	C₂²⋊C₄	—	4	2	no	—
683	C₂²⋊C₄	—	4	2	no	—
684	C₂²⋊C₄	—	4	2	no	—
685	C₂²⋊C₄	—	4	2	no	—
686	C₂²⋊C₄	—	4	2	no	—
687	C₂²⋊C₄	—	4	2	no	—
688	C₂²⋊C₄	—	4	2	no	—
689	C₂²⋊C₄	—	8	1	no	—
690	C₂²⋊C₄	—	8	1	no	—
691	C₄²	—	2	1	no	—
692	C₄²	—	2	1	no	—
693	C₄²	—	2	1	no	—
694	C₄²	—	2	1	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	1	no	—
701	C₂³	—	2	1	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	4	8	no	—
707	C₂³	—	4	8	no	—
708	C₂³	—	4	1	no	—
709	C₂³	—	4	1	no	—
710	C₂³	—	4	1	no	—
711	C₂³	—	4	1	no	—
712	C₂³	—	4	1	no	—
713	C₂³	—	4	1	no	—
714	C₂³	—	4	1	no	—
715	C₂³	—	4	1	no	—
716	C₂³	—	4	1	no	—
717	C₂³	—	4	1	no	—
718	C₂³	—	4	1	no	—
719	C₂³	—	4	1	no	—
720	C₂³	—	4	1	no	—
721	C₂³	—	4	1	no	—
722	C₂³	—	4	1	no	—
723	C₂³	—	4	1	no	—
724	C₂³	—	8	4	no	—
725	C₂³	—	8	4	no	—
726	C₂³	—	8	4	no	—
727	C₂³	—	8	4	no	—
728	C₂³	—	8	4	no	—
729	C₂³	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
730	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
731	Q₈	—	4	1	no	—
732	Q₈	—	4	1	no	—
733	Q₈	—	4	1	no	—
734	Q₈	—	4	1	no	—
735	D₄	—	2	2	no	—
736	D₄	—	2	2	no	—
737	D₄	—	2	2	no	—
738	D₄	—	2	2	no	—
739	D₄	—	2	2	no	—
740	D₄	—	2	2	no	—
741	D₄	—	2	2	no	—
742	D₄	—	4	8	no	—
743	D₄	—	4	1	no	—
744	D₄	—	4	1	no	—
745	D₄	—	4	1	no	—
746	D₄	—	4	1	no	—
747	D₄	—	8	4	no	—
748	D₄	#121×C₈₉	1	4	yes	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	—	4	1	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	8	4	no	—
784	C₂×C₄	—	8	4	no	—
785	C₂×C₄	—	8	4	no	—
786	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
787	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
788	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
789	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
790	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
791	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
792	C₈	—	2	2	no	—
793	C₈	—	2	2	no	—
794	C₈	—	4	1	no	—
795	C₈	—	4	1	no	—
796	C₂²	—	2	2	no	—
797	C₂²	—	2	4	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	1	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	8	16	no	—
817	C₂²	—	8	1	no	—
818	C₂²	—	8	1	no	—
819	C₂²	—	8	1	no	—
820	C₂²	—	8	1	no	—
821	C₂²	—	8	1	no	—
822	C₂²	—	8	1	no	—
823	C₂²	—	8	1	no	—
824	C₂²	—	8	1	no	—
825	C₂²	#525×C₈₉	1	1	yes	characteristic
826	C₂²	D₄²×C₈₉	1	1	yes	characteristic
827	C₂²	D₄²×C₈₉	1	1	yes	characteristic
828	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
829	C₂²	#575×C₈₉	1	1	yes	characteristic
830	C₂²	#576×C₈₉	1	1	yes	characteristic
831	C₂²	#577×C₈₉	1	1	yes	characteristic
832	C₄	—	4	1	no	—
833	C₄	—	4	1	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	2	no	—
838	C₄	—	8	1	no	—
839	C₄	—	8	1	no	—
840	C₄	—	8	1	no	—
841	C₄	—	8	1	no	—
842	C₄	C₂×#121×C₈₉	1	1	yes	characteristic
843	C₄	#538×C₈₉	1	1	yes	characteristic
844	C₄	#546×C₈₉	1	1	yes	characteristic
845	C₄	#546×C₈₉	1	1	yes	characteristic
846	C₂	—	4	2	no	—
847	C₂	—	4	4	no	—
848	C₂	—	8	2	no	—
849	C₂	—	8	2	no	—
850	C₂	C₈₉×#2424	1	1	yes	characteristic
851	C₂	C₈₉×#3114	1	1	yes	characteristic
852	C₂	C₈₉×#3118	1	1	yes	characteristic
853	C₂	C₈₉×#3264	1	1	yes	characteristic
854	C₂	C₈₉×#3265	1	1	yes	characteristic
855	C₂	C₈₉×#3267	1	1	yes	characteristic
856	C₂	C₈₉×#3273	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂×#447×C₈₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₄×C₂²⋊C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#463×C₈₉	C₂	semidirect
2. C₂×#450×C₈₉	C₂	semidirect
4. C₂×#442×C₈₉	C₂	semidirect
5. C₈₉×#2427	C₂	semidirect
6. D₄×C₂²⋊C₄×C₈₉	C₂	semidirect
7. C₈₉×#2065	C₂	semidirect
8. C₈₉×#2035	C₂	semidirect
9. C₈₉×#2033	C₂	semidirect
10. C₈₉×#2012	C₂	semidirect
11. C₈₉×#1973	C₂	semidirect
12. C₈₉×#1924	C₂	semidirect
13. C₈₉×#1879	C₂	semidirect
14. C₈₉×#1877	C₂	semidirect
15. C₈₉×#1862	C₂	semidirect
21. C₂×#124×C₈₉	C₂²	semidirect
26. C₂×C₄×D₄×C₈₉	C₂²	semidirect
32. C₂×#107×C₈₉	C₂²	semidirect
33. C₂×#106×C₈₉	C₂²	semidirect
34. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
35. C₂×#103×C₈₉	C₂²	semidirect
36. C₂×#103×C₈₉	C₂²	semidirect
41. C₂×#102×C₈₉	C₂²	semidirect
42. C₂×#102×C₈₉	C₂²	semidirect
45. C₂×#97×C₈₉	C₂²	semidirect
48. #391×C₈₉	C₂²	semidirect
51. #389×C₈₉	C₂²	semidirect
59. #340×C₈₉	C₂²	semidirect
60. #340×C₈₉	C₂²	semidirect
61. #336×C₈₉	C₂²	semidirect
62. #336×C₈₉	C₂²	semidirect
141. #102×C₈₉	D₄	semidirect
417. #25172	C₈₉	direct (N × H)
429. C₂×#463	C₂×C₈₉	semidirect
430. C₂×#450	C₂×C₈₉	semidirect
432. C₂×#442	C₂×C₈₉	semidirect
433. #2427	C₂×C₈₉	semidirect
434. D₄×C₂²⋊C₄	C₂×C₈₉	semidirect
435. #2065	C₂×C₈₉	semidirect
436. #2035	C₂×C₈₉	semidirect
437. #2033	C₂×C₈₉	semidirect
438. #2012	C₂×C₈₉	semidirect
439. #1973	C₂×C₈₉	semidirect
440. #1924	C₂×C₈₉	semidirect
441. #1879	C₂×C₈₉	semidirect
442. #1877	C₂×C₈₉	semidirect
443. #1862	C₂×C₈₉	semidirect
444. C₈₉	#25172	direct (N × H)
450. C₂×#124	C₂²×C₈₉	semidirect
455. C₂×C₄×D₄	C₂²×C₈₉	semidirect
461. C₂×#107	C₂²×C₈₉	semidirect
462. C₂×#106	C₂²×C₈₉	semidirect
463. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
464. C₂×#103	C₂²×C₈₉	semidirect
465. C₂×#103	C₂²×C₈₉	semidirect
470. C₂×#102	C₂²×C₈₉	semidirect
471. C₂×#102	C₂²×C₈₉	semidirect
474. C₂×#97	C₂²×C₈₉	semidirect
477. #391	C₂²×C₈₉	semidirect
480. #389	C₂²×C₈₉	semidirect
488. #340	C₂²×C₈₉	semidirect
489. #340	C₂²×C₈₉	semidirect
490. #336	C₂²×C₈₉	semidirect
491. #336	C₂²×C₈₉	semidirect
570. #102	D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#463×C₈₉	2
C₂×#450×C₈₉	2
C₂×#447×C₈₉	2
C₂×#442×C₈₉	2
C₈₉×#2427	2
D₄×C₂²⋊C₄×C₈₉	2
C₈₉×#2065	2
C₈₉×#2035	2
C₈₉×#2033	2
C₈₉×#2012	2
C₈₉×#1973	2
C₈₉×#1924	2
C₈₉×#1879	2
C₈₉×#1877	2
C₈₉×#1862	2
#25172	89

Subgroups — C89×#25172 #36403020

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25172 #36403020