Subgroups — C₈₉×#25088 #36402936

Order 22784.

1310 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#465×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#463×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#447×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×#102×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2435	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2065	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2054	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2042	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1983	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1926	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1872	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1850	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, complemented
18	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₈₉	—	2	1	no	—
26	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
28	#465×C₈₉	—	2	4	no	—
29	#463×C₈₉	—	2	4	no	—
30	#447×C₈₉	—	2	4	no	—
31	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×#103×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	—	2	4	no	—
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
42	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
46	#394×C₈₉	—	2	1	no	—
47	#394×C₈₉	—	2	1	no	—
48	#390×C₈₉	C₂²	1	1	yes	characteristic
49	#390×C₈₉	C₂²	1	1	yes	characteristic
50	#390×C₈₉	C₂²	1	1	yes	characteristic, complemented
51	#389×C₈₉	C₂²	1	1	yes	characteristic, complemented
52	#388×C₈₉	—	2	1	no	—
53	#386×C₈₉	—	2	1	no	—
54	#385×C₈₉	—	2	1	no	—
55	#379×C₈₉	—	2	1	no	—
56	#379×C₈₉	—	2	1	no	—
57	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
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	1	no	—
68	C₂²×D₄×C₈₉	—	2	2	no	—
69	C₂²×D₄×C₈₉	—	2	1	no	—
70	C₂²×D₄×C₈₉	—	2	2	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	C₂³	1	1	yes	characteristic
79	C₂×SD₁₆×C₈₉	—	2	2	no	—
80	C₂×SD₁₆×C₈₉	—	2	2	no	—
81	C₂×SD₁₆×C₈₉	—	4	1	no	—
82	C₂×D₈×C₈₉	—	2	2	no	—
83	C₂×D₈×C₈₉	—	2	2	no	—
84	C₂×D₈×C₈₉	—	2	2	no	—
85	C₂×D₈×C₈₉	—	2	2	no	—
86	C₂×D₈×C₈₉	—	4	1	no	—
87	C₂×D₈×C₈₉	—	4	1	no	—
88	C₂²×C₈×C₈₉	—	2	2	no	—
89	C₂²×C₈×C₈₉	—	2	2	no	—
90	C₂²×C₈×C₈₉	—	4	1	no	—
91	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
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	#124×C₈₉	—	2	2	no	—
96	#124×C₈₉	—	2	2	no	—
97	#124×C₈₉	—	4	1	no	—
98	#124×C₈₉	—	4	1	no	—
99	C₂²⋊Q₈×C₈₉	—	2	2	no	—
100	C₂²⋊Q₈×C₈₉	—	2	2	no	—
101	#121×C₈₉	—	2	2	no	—
102	#121×C₈₉	D₄	1	4	yes	—
103	C₄×D₄×C₈₉	—	2	2	no	—
104	C₄×D₄×C₈₉	—	4	1	no	—
105	C₄×D₄×C₈₉	—	4	4	no	—
106	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
107	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₈₉	—	4	1	no	—
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×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
130	C₂×C₄²×C₈₉	—	2	1	no	—
131	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
133	#106×C₈₉	—	2	2	no	—
134	C₄⋊C₈×C₈₉	—	2	2	no	—
135	C₄⋊C₈×C₈₉	—	4	1	no	—
136	#103×C₈₉	—	2	2	no	—
137	#103×C₈₉	—	2	2	no	—
138	#103×C₈₉	—	4	1	no	—
139	#102×C₈₉	—	2	2	no	—
140	#102×C₈₉	—	2	2	no	—
141	#102×C₈₉	—	2	2	no	—
142	#102×C₈₉	—	2	2	no	—
143	#102×C₈₉	—	2	2	no	—
144	#102×C₈₉	—	2	2	no	—
145	#102×C₈₉	D₄	1	4	yes	complemented
146	C₂²⋊C₈×C₈₉	—	2	2	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	1	no	—
153	C₂⁴×C₈₉	—	2	1	no	—
154	C₂⁴×C₈₉	—	4	2	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	8	no	—
169	C₂×D₄×C₈₉	—	2	4	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	—	2	1	no	—
183	C₂×D₄×C₈₉	—	2	1	no	—
184	C₂×D₄×C₈₉	—	2	1	no	—
185	C₂×D₄×C₈₉	—	4	4	no	—
186	C₂×D₄×C₈₉	—	4	4	no	—
187	C₂×D₄×C₈₉	—	4	2	no	—
188	C₂×D₄×C₈₉	—	4	2	no	—
189	C₂×D₄×C₈₉	—	4	4	no	—
190	C₂×D₄×C₈₉	—	4	2	no	—
191	C₂×D₄×C₈₉	—	4	2	no	—
192	C₂×D₄×C₈₉	—	4	2	no	—
193	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
194	C₂×D₄×C₈₉	C₂×D₄	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	—	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	—	8	1	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	1	yes	characteristic
216	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
217	C₂²×C₄×C₈₉	#41	1	2	yes	—
218	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
219	SD₁₆×C₈₉	—	4	4	no	—
220	D₈×C₈₉	—	4	4	no	—
221	D₈×C₈₉	—	4	4	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	—	2	1	no	—
231	C₂×C₈×C₈₉	—	2	1	no	—
232	C₂×C₈×C₈₉	—	2	1	no	—
233	C₂×C₈×C₈₉	—	4	4	no	—
234	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
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	—	4	2	no	—
242	C₄⋊C₄×C₈₉	—	4	2	no	—
243	C₄⋊C₄×C₈₉	—	4	2	no	—
244	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
245	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
246	C₂²⋊C₄×C₈₉	—	2	2	no	—
247	C₂²⋊C₄×C₈₉	—	2	2	no	—
248	C₂²⋊C₄×C₈₉	—	2	4	no	—
249	C₂²⋊C₄×C₈₉	—	4	2	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	—	8	1	no	—
257	C₂²⋊C₄×C₈₉	—	8	1	no	—
258	C₂²⋊C₄×C₈₉	—	8	1	no	—
259	C₂²⋊C₄×C₈₉	—	8	1	no	—
260	C₂²⋊C₄×C₈₉	—	8	1	no	—
261	C₄²×C₈₉	—	2	1	no	—
262	C₄²×C₈₉	—	2	1	no	—
263	C₄²×C₈₉	—	2	1	no	—
264	C₄²×C₈₉	—	2	1	no	—
265	C₄²×C₈₉	—	4	2	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	2	no	—
271	C₂³×C₈₉	—	2	2	no	—
272	C₂³×C₈₉	—	2	2	no	—
273	C₂³×C₈₉	—	4	8	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	—	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	—	8	4	no	—
293	C₂³×C₈₉	—	8	4	no	—
294	C₂³×C₈₉	—	8	4	no	—
295	C₂³×C₈₉	—	8	4	no	—
296	C₂³×C₈₉	—	8	4	no	—
297	C₂³×C₈₉	—	8	4	no	—
298	C₂³×C₈₉	#121	1	2	yes	—
299	C₂³×C₈₉	#135	1	2	yes	—
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	—	4	8	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	—	4	1	no	—
319	D₄×C₈₉	—	4	1	no	—
320	C₂×C₄×C₈₉	—	2	1	no	—
321	C₂×C₄×C₈₉	—	2	1	no	—
322	C₂×C₄×C₈₉	—	2	2	no	—
323	C₂×C₄×C₈₉	—	2	2	no	—
324	C₂×C₄×C₈₉	—	2	2	no	—
325	C₂×C₄×C₈₉	—	2	2	no	—
326	C₂×C₄×C₈₉	—	2	2	no	—
327	C₂×C₄×C₈₉	—	2	1	no	—
328	C₂×C₄×C₈₉	—	2	1	no	—
329	C₂×C₄×C₈₉	—	2	2	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	—	2	1	no	—
337	C₂×C₄×C₈₉	—	2	1	no	—
338	C₂×C₄×C₈₉	—	2	1	no	—
339	C₂×C₄×C₈₉	—	2	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	—	8	4	no	—
354	C₂×C₄×C₈₉	—	8	4	no	—
355	C₂×C₄×C₈₉	#121	1	2	yes	—
356	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
359	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
360	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
361	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
362	C₈×C₈₉	—	2	2	no	—
363	C₈×C₈₉	—	4	1	no	—
364	C₈×C₈₉	—	4	1	no	—
365	C₈×C₈₉	—	4	1	no	—
366	C₂²×C₈₉	—	2	2	no	—
367	C₂²×C₈₉	—	2	2	no	—
368	C₂²×C₈₉	—	2	2	no	—
369	C₂²×C₈₉	—	2	2	no	—
370	C₂²×C₈₉	—	2	2	no	—
371	C₂²×C₈₉	—	2	2	no	—
372	C₂²×C₈₉	—	4	2	no	—
373	C₂²×C₈₉	—	4	2	no	—
374	C₂²×C₈₉	—	4	2	no	—
375	C₂²×C₈₉	—	4	2	no	—
376	C₂²×C₈₉	—	4	2	no	—
377	C₂²×C₈₉	—	4	2	no	—
378	C₂²×C₈₉	—	4	2	no	—
379	C₂²×C₈₉	—	4	2	no	—
380	C₂²×C₈₉	—	4	2	no	—
381	C₂²×C₈₉	—	8	16	no	—
382	C₂²×C₈₉	—	8	1	no	—
383	C₂²×C₈₉	—	8	1	no	—
384	C₂²×C₈₉	—	8	1	no	—
385	C₂²×C₈₉	—	8	1	no	—
386	C₂²×C₈₉	—	8	1	no	—
387	C₂²×C₈₉	—	8	1	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	#463	1	4	yes	complemented
395	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
396	C₂²×C₈₉	D₄²	1	1	yes	characteristic
397	C₂²×C₈₉	#546	1	1	yes	characteristic
398	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
399	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
400	C₂²×C₈₉	#576	1	1	yes	characteristic
401	C₂²×C₈₉	#577	1	1	yes	characteristic
402	C₄×C₈₉	—	2	2	no	—
403	C₄×C₈₉	—	4	1	no	—
404	C₄×C₈₉	—	4	2	no	—
405	C₄×C₈₉	—	4	1	no	—
406	C₄×C₈₉	—	4	2	no	—
407	C₄×C₈₉	—	4	1	no	—
408	C₄×C₈₉	—	4	1	no	—
409	C₄×C₈₉	—	8	1	no	—
410	C₄×C₈₉	—	8	1	no	—
411	C₄×C₈₉	—	8	1	no	—
412	C₄×C₈₉	#525	1	1	yes	characteristic
413	C₄×C₈₉	#538	1	1	yes	characteristic
414	C₄×C₈₉	D₄²	1	1	yes	characteristic
415	C₄×C₈₉	#546	1	1	yes	characteristic
416	#25088	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
417	C₂×C₈₉	—	2	4	no	—
418	C₂×C₈₉	—	8	2	no	—
419	C₂×C₈₉	—	8	2	no	—
420	C₂×C₈₉	—	8	2	no	—
421	C₂×C₈₉	#2424	1	1	yes	characteristic
422	C₂×C₈₉	C₂×#463	1	1	yes	characteristic
423	C₂×C₈₉	#3045	1	1	yes	characteristic
424	C₂×C₈₉	#3264	1	1	yes	characteristic
425	C₂×C₈₉	#3282	1	1	yes	characteristic
426	C₂×C₈₉	#3297	1	1	yes	characteristic
427	C₂×C₈₉	#3306	1	1	yes	characteristic
428	C₂×#465	C₂×C₈₉	1	1	yes	characteristic, complemented
429	C₂×#463	C₂×C₈₉	1	1	yes	characteristic, complemented
430	C₂×#447	C₂×C₈₉	1	1	yes	characteristic
431	C₂²×#102	C₂×C₈₉	1	1	yes	characteristic, complemented
432	#2435	C₂×C₈₉	1	1	yes	characteristic, complemented
433	#2361	C₂×C₈₉	1	1	yes	characteristic, complemented
434	#2065	C₂×C₈₉	1	1	yes	characteristic, complemented
435	#2054	C₂×C₈₉	1	1	yes	characteristic, complemented
436	#2042	C₂×C₈₉	1	1	yes	characteristic, complemented
437	#2012	C₂×C₈₉	1	1	yes	characteristic, complemented
438	#1983	C₂×C₈₉	1	1	yes	characteristic, complemented
439	#1926	C₂×C₈₉	1	1	yes	characteristic, complemented
440	#1879	C₂×C₈₉	1	1	yes	characteristic, complemented
441	#1872	C₂×C₈₉	1	1	yes	characteristic, complemented
442	#1850	C₂×C₈₉	1	1	yes	characteristic, complemented
443	C₈₉	#25088	1	1	yes	characteristic, direct product factor, Sylow
444	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
445	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
446	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
447	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
448	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
449	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
450	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
451	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
452	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
453	C₂×C₄×D₄	—	2	1	no	—
454	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
455	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
456	#465	—	2	4	no	—
457	#463	—	2	4	no	—
458	#447	—	2	4	no	—
459	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic, complemented
460	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
461	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
462	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
463	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
464	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
465	C₂×#102	—	2	4	no	—
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
471	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
472	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
473	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
474	#394	—	2	1	no	—
475	#394	—	2	1	no	—
476	#390	C₂²×C₈₉	1	1	yes	characteristic
477	#390	C₂²×C₈₉	1	1	yes	characteristic
478	#390	C₂²×C₈₉	1	1	yes	characteristic, complemented
479	#389	C₂²×C₈₉	1	1	yes	characteristic, complemented
480	#388	—	2	1	no	—
481	#386	—	2	1	no	—
482	#385	—	2	1	no	—
483	#379	—	2	1	no	—
484	#379	—	2	1	no	—
485	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
486	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
487	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
488	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
489	#336	C₂²×C₈₉	1	1	yes	characteristic, complemented
490	#336	C₂²×C₈₉	1	1	yes	characteristic, complemented
491	C₂⁵	—	2	1	no	—
492	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
493	C₂²×D₄	—	2	2	no	—
494	C₂²×D₄	—	2	2	no	—
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	—	2	2	no	—
497	C₂²×D₄	—	2	1	no	—
498	C₂²×D₄	—	2	2	no	—
499	C₂²×D₄	—	4	1	no	—
500	C₂²×D₄	—	4	1	no	—
501	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
502	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
503	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
504	C₂³×C₄	—	2	1	no	—
505	C₂³×C₄	—	2	1	no	—
506	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
507	C₂×SD₁₆	—	2	2	no	—
508	C₂×SD₁₆	—	2	2	no	—
509	C₂×SD₁₆	—	4	1	no	—
510	C₂×D₈	—	2	2	no	—
511	C₂×D₈	—	2	2	no	—
512	C₂×D₈	—	2	2	no	—
513	C₂×D₈	—	2	2	no	—
514	C₂×D₈	—	4	1	no	—
515	C₂×D₈	—	4	1	no	—
516	C₂²×C₈	—	2	2	no	—
517	C₂²×C₈	—	2	2	no	—
518	C₂²×C₈	—	4	1	no	—
519	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
520	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
521	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
522	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
523	#124	—	2	2	no	—
524	#124	—	2	2	no	—
525	#124	—	4	1	no	—
526	#124	—	4	1	no	—
527	C₂²⋊Q₈	—	2	2	no	—
528	C₂²⋊Q₈	—	2	2	no	—
529	#121	—	2	2	no	—
530	#121	D₄×C₈₉	1	4	yes	—
531	C₄×D₄	—	2	2	no	—
532	C₄×D₄	—	4	1	no	—
533	C₄×D₄	—	4	4	no	—
534	C₂×C₄⋊C₄	—	2	2	no	—
535	C₂×C₄⋊C₄	—	2	1	no	—
536	C₂×C₄⋊C₄	—	2	1	no	—
537	C₂×C₄⋊C₄	—	2	1	no	—
538	C₂×C₄⋊C₄	—	4	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	—	2	1	no	—
556	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
558	C₂×C₄²	—	2	1	no	—
559	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
561	#106	—	2	2	no	—
562	C₄⋊C₈	—	2	2	no	—
563	C₄⋊C₈	—	4	1	no	—
564	#103	—	2	2	no	—
565	#103	—	2	2	no	—
566	#103	—	4	1	no	—
567	#102	—	2	2	no	—
568	#102	—	2	2	no	—
569	#102	—	2	2	no	—
570	#102	—	2	2	no	—
571	#102	—	2	2	no	—
572	#102	—	2	2	no	—
573	#102	D₄×C₈₉	1	4	yes	complemented
574	C₂²⋊C₈	—	2	2	no	—
575	#95	—	2	1	no	—
576	#95	—	2	1	no	—
577	#95	D₄×C₈₉	1	1	yes	characteristic
578	#95	D₄×C₈₉	1	1	yes	characteristic
579	C₂⁴	—	2	1	no	—
580	C₂⁴	—	2	1	no	—
581	C₂⁴	—	2	1	no	—
582	C₂⁴	—	4	2	no	—
583	C₂⁴	—	4	2	no	—
584	C₂⁴	—	4	2	no	—
585	C₂⁴	—	4	2	no	—
586	C₂⁴	—	4	2	no	—
587	C₂⁴	—	8	1	no	—
588	C₂⁴	—	8	1	no	—
589	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
590	C₂×Q₈	—	2	1	no	—
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×D₄	—	2	8	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	—	2	1	no	—
612	C₂×D₄	—	2	1	no	—
613	C₂×D₄	—	4	4	no	—
614	C₂×D₄	—	4	4	no	—
615	C₂×D₄	—	4	2	no	—
616	C₂×D₄	—	4	2	no	—
617	C₂×D₄	—	4	4	no	—
618	C₂×D₄	—	4	2	no	—
619	C₂×D₄	—	4	2	no	—
620	C₂×D₄	—	4	2	no	—
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	C₂²×C₄	—	2	1	no	—
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	—	4	2	no	—
634	C₂²×C₄	—	4	2	no	—
635	C₂²×C₄	—	4	2	no	—
636	C₂²×C₄	—	4	2	no	—
637	C₂²×C₄	—	8	1	no	—
638	C₂²×C₄	—	8	1	no	—
639	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
640	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
641	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
642	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
643	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
644	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
645	C₂²×C₄	#41×C₈₉	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
647	SD₁₆	—	4	4	no	—
648	D₈	—	4	4	no	—
649	D₈	—	4	4	no	—
650	C₂×C₈	—	2	1	no	—
651	C₂×C₈	—	2	1	no	—
652	C₂×C₈	—	2	1	no	—
653	C₂×C₈	—	2	1	no	—
654	C₂×C₈	—	2	1	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	—	4	4	no	—
662	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	4	2	no	—
670	C₄⋊C₄	—	4	2	no	—
671	C₄⋊C₄	—	4	2	no	—
672	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
673	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
674	C₂²⋊C₄	—	2	2	no	—
675	C₂²⋊C₄	—	2	2	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	4	2	no	—
678	C₂²⋊C₄	—	4	2	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	—	8	1	no	—
685	C₂²⋊C₄	—	8	1	no	—
686	C₂²⋊C₄	—	8	1	no	—
687	C₂²⋊C₄	—	8	1	no	—
688	C₂²⋊C₄	—	8	1	no	—
689	C₄²	—	2	1	no	—
690	C₄²	—	2	1	no	—
691	C₄²	—	2	1	no	—
692	C₄²	—	2	1	no	—
693	C₄²	—	4	2	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	4	8	no	—
702	C₂³	—	4	1	no	—
703	C₂³	—	4	1	no	—
704	C₂³	—	4	1	no	—
705	C₂³	—	4	1	no	—
706	C₂³	—	4	1	no	—
707	C₂³	—	4	1	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	—	8	4	no	—
721	C₂³	—	8	4	no	—
722	C₂³	—	8	4	no	—
723	C₂³	—	8	4	no	—
724	C₂³	—	8	4	no	—
725	C₂³	—	8	4	no	—
726	C₂³	#121×C₈₉	1	2	yes	—
727	C₂³	#135×C₈₉	1	2	yes	—
728	C₂³	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
729	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
730	Q₈	—	4	1	no	—
731	Q₈	—	4	1	no	—
732	Q₈	—	4	1	no	—
733	Q₈	—	4	1	no	—
734	D₄	—	2	2	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	—	4	8	no	—
741	D₄	—	4	8	no	—
742	D₄	—	4	1	no	—
743	D₄	—	4	1	no	—
744	D₄	—	4	1	no	—
745	D₄	—	4	1	no	—
746	D₄	—	4	1	no	—
747	D₄	—	4	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	2	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	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	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	—	8	4	no	—
782	C₂×C₄	—	8	4	no	—
783	C₂×C₄	#121×C₈₉	1	2	yes	—
784	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
785	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
786	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
787	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
788	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
789	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
790	C₈	—	2	2	no	—
791	C₈	—	4	1	no	—
792	C₈	—	4	1	no	—
793	C₈	—	4	1	no	—
794	C₂²	—	2	2	no	—
795	C₂²	—	2	2	no	—
796	C₂²	—	2	2	no	—
797	C₂²	—	2	2	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	8	16	no	—
810	C₂²	—	8	1	no	—
811	C₂²	—	8	1	no	—
812	C₂²	—	8	1	no	—
813	C₂²	—	8	1	no	—
814	C₂²	—	8	1	no	—
815	C₂²	—	8	1	no	—
816	C₂²	—	8	1	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	#463×C₈₉	1	4	yes	complemented
823	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
824	C₂²	D₄²×C₈₉	1	1	yes	characteristic
825	C₂²	#546×C₈₉	1	1	yes	characteristic
826	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
827	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
828	C₂²	#576×C₈₉	1	1	yes	characteristic
829	C₂²	#577×C₈₉	1	1	yes	characteristic
830	C₄	—	2	2	no	—
831	C₄	—	4	1	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	1	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	1	no	—
837	C₄	—	8	1	no	—
838	C₄	—	8	1	no	—
839	C₄	—	8	1	no	—
840	C₄	#525×C₈₉	1	1	yes	characteristic
841	C₄	#538×C₈₉	1	1	yes	characteristic
842	C₄	D₄²×C₈₉	1	1	yes	characteristic
843	C₄	#546×C₈₉	1	1	yes	characteristic
844	C₂	—	2	4	no	—
845	C₂	—	8	2	no	—
846	C₂	—	8	2	no	—
847	C₂	—	8	2	no	—
848	C₂	C₈₉×#2424	1	1	yes	characteristic
849	C₂	C₂×#463×C₈₉	1	1	yes	characteristic
850	C₂	C₈₉×#3045	1	1	yes	characteristic
851	C₂	C₈₉×#3264	1	1	yes	characteristic
852	C₂	C₈₉×#3282	1	1	yes	characteristic
853	C₂	C₈₉×#3297	1	1	yes	characteristic
854	C₂	C₈₉×#3306	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×#465×C₈₉	C₂	semidirect
2. C₂×#463×C₈₉	C₂	semidirect
4. C₂²×#102×C₈₉	C₂	semidirect
5. C₈₉×#2435	C₂	semidirect
6. C₈₉×#2361	C₂	semidirect
7. C₈₉×#2065	C₂	semidirect
8. C₈₉×#2054	C₂	semidirect
9. C₈₉×#2042	C₂	semidirect
10. C₈₉×#2012	C₂	semidirect
11. C₈₉×#1983	C₂	semidirect
12. C₈₉×#1926	C₂	semidirect
13. C₈₉×#1879	C₂	semidirect
14. C₈₉×#1872	C₂	semidirect
15. C₈₉×#1850	C₂	semidirect
17. C₂²×SD₁₆×C₈₉	C₂²	semidirect
26. C₂×C₄×D₄×C₈₉	C₂²	semidirect
31. C₂×#106×C₈₉	C₂²	semidirect
32. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
33. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
34. C₂×#103×C₈₉	C₂²	semidirect
35. C₂×#103×C₈₉	C₂²	semidirect
36. C₂×#103×C₈₉	C₂²	semidirect
44. C₂×#102×C₈₉	C₂²	semidirect
50. #390×C₈₉	C₂²	semidirect
51. #389×C₈₉	C₂²	semidirect
57. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
59. #340×C₈₉	C₂²	semidirect
60. #340×C₈₉	C₂²	semidirect
61. #336×C₈₉	C₂²	semidirect
62. #336×C₈₉	C₂²	semidirect
145. #102×C₈₉	D₄	semidirect
394. C₂²×C₈₉	#463	semidirect
416. #25088	C₈₉	direct (N × H)
428. C₂×#465	C₂×C₈₉	semidirect
429. C₂×#463	C₂×C₈₉	semidirect
431. C₂²×#102	C₂×C₈₉	semidirect
432. #2435	C₂×C₈₉	semidirect
433. #2361	C₂×C₈₉	semidirect
434. #2065	C₂×C₈₉	semidirect
435. #2054	C₂×C₈₉	semidirect
436. #2042	C₂×C₈₉	semidirect
437. #2012	C₂×C₈₉	semidirect
438. #1983	C₂×C₈₉	semidirect
439. #1926	C₂×C₈₉	semidirect
440. #1879	C₂×C₈₉	semidirect
441. #1872	C₂×C₈₉	semidirect
442. #1850	C₂×C₈₉	semidirect
443. C₈₉	#25088	direct (N × H)
445. C₂²×SD₁₆	C₂²×C₈₉	semidirect
454. C₂×C₄×D₄	C₂²×C₈₉	semidirect
459. C₂×#106	C₂²×C₈₉	semidirect
460. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
461. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
462. C₂×#103	C₂²×C₈₉	semidirect
463. C₂×#103	C₂²×C₈₉	semidirect
464. C₂×#103	C₂²×C₈₉	semidirect
472. C₂×#102	C₂²×C₈₉	semidirect
478. #390	C₂²×C₈₉	semidirect
479. #389	C₂²×C₈₉	semidirect
485. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
487. #340	C₂²×C₈₉	semidirect
488. #340	C₂²×C₈₉	semidirect
489. #336	C₂²×C₈₉	semidirect
490. #336	C₂²×C₈₉	semidirect
573. #102	D₄×C₈₉	semidirect
822. C₂²	#463×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#465×C₈₉	2
C₂×#463×C₈₉	2
C₂×#447×C₈₉	2
C₂²×#102×C₈₉	2
C₈₉×#2435	2
C₈₉×#2361	2
C₈₉×#2065	2
C₈₉×#2054	2
C₈₉×#2042	2
C₈₉×#2012	2
C₈₉×#1983	2
C₈₉×#1926	2
C₈₉×#1879	2
C₈₉×#1872	2
C₈₉×#1850	2
#25088	89

Subgroups — C89×#25088 #36402936

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25088 #36402936