Subgroups — C₈₉×#24044 #36401892

Order 22784.

1768 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#482×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#418×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2041	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2041	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2034	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1895	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1870	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1864	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1862	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1786	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1786	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1786	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₈₉	—	2	1	no	—
17	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
20	D₄²×C₈₉	—	2	4	no	—
21	D₄²×C₈₉	—	2	4	no	—
22	C₂×#127×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×#120×C₈₉	—	2	1	no	—
27	C₂×#120×C₈₉	—	2	1	no	—
28	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
31	#482×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	#418×C₈₉	—	2	4	no	—
35	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
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, complemented
40	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
44	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
46	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
50	#397×C₈₉	—	2	1	no	—
51	#394×C₈₉	—	2	1	no	—
52	#389×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	#389×C₈₉	C₂²	1	1	yes	characteristic, complemented
54	#388×C₈₉	—	2	1	no	—
55	#387×C₈₉	—	2	1	no	—
56	#380×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	#380×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#380×C₈₉	C₂²	1	1	yes	characteristic, complemented
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	C₂⁵×C₈₉	—	2	1	no	—
65	C₂²×D₄×C₈₉	—	2	2	no	—
66	C₂²×D₄×C₈₉	—	2	2	no	—
67	C₂²×D₄×C₈₉	—	2	8	no	—
68	C₂²×D₄×C₈₉	—	2	1	no	—
69	C₂²×D₄×C₈₉	—	2	1	no	—
70	C₂²×D₄×C₈₉	—	2	2	no	—
71	C₂²×D₄×C₈₉	—	2	2	no	—
72	C₂²×D₄×C₈₉	—	2	2	no	—
73	C₂²×D₄×C₈₉	—	2	2	no	—
74	C₂²×D₄×C₈₉	—	2	1	no	—
75	C₂²×D₄×C₈₉	—	2	1	no	—
76	C₂²×D₄×C₈₉	—	2	1	no	—
77	C₂²×D₄×C₈₉	—	2	2	no	—
78	C₂²×D₄×C₈₉	—	2	1	no	—
79	C₂²×D₄×C₈₉	—	4	1	no	—
80	C₂²×D₄×C₈₉	—	4	1	no	—
81	C₂²×D₄×C₈₉	—	4	1	no	—
82	C₂²×D₄×C₈₉	—	4	1	no	—
83	C₂²×D₄×C₈₉	—	4	4	no	—
84	C₂²×D₄×C₈₉	—	4	4	no	—
85	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
86	C₂²×D₄×C₈₉	D₄	1	4	yes	—
87	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₈₉	—	2	1	no	—
91	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
93	C₂×M₁₆×C₈₉	—	2	2	no	—
94	C₂×M₁₆×C₈₉	—	4	1	no	—
95	C₂×M₁₆×C₈₉	—	4	1	no	—
96	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
100	#127×C₈₉	—	2	2	no	—
101	#127×C₈₉	—	2	2	no	—
102	#121×C₈₉	—	2	8	no	—
103	#121×C₈₉	—	2	2	no	—
104	#121×C₈₉	—	2	2	no	—
105	#121×C₈₉	—	2	2	no	—
106	#121×C₈₉	D₄	1	4	yes	—
107	#120×C₈₉	—	2	8	no	—
108	#120×C₈₉	—	2	8	no	—
109	C₄×D₄×C₈₉	—	2	2	no	—
110	C₄×D₄×C₈₉	—	2	2	no	—
111	C₄×D₄×C₈₉	—	2	2	no	—
112	C₄×D₄×C₈₉	—	2	2	no	—
113	#117×C₈₉	—	2	2	no	—
114	#117×C₈₉	—	2	2	no	—
115	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
116	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
117	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
132	C₂×C₄²×C₈₉	—	2	1	no	—
133	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
134	#107×C₈₉	—	2	2	no	—
135	#106×C₈₉	—	2	2	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	—	2	2	no	—
142	#102×C₈₉	—	2	2	no	—
143	#102×C₈₉	—	2	2	no	—
144	#102×C₈₉	—	4	1	no	—
145	#102×C₈₉	—	4	1	no	—
146	#102×C₈₉	—	4	1	no	—
147	#102×C₈₉	—	4	1	no	—
148	C₂²⋊C₈×C₈₉	—	2	2	no	—
149	C₂²⋊C₈×C₈₉	—	4	1	no	—
150	C₂²⋊C₈×C₈₉	—	4	1	no	—
151	#95×C₈₉	—	2	1	no	—
152	#95×C₈₉	—	2	1	no	—
153	#95×C₈₉	—	2	1	no	—
154	#95×C₈₉	—	2	1	no	—
155	#95×C₈₉	—	2	1	no	—
156	C₂⁴×C₈₉	—	2	1	no	—
157	C₂⁴×C₈₉	—	2	4	no	—
158	C₂⁴×C₈₉	—	2	1	no	—
159	C₂⁴×C₈₉	—	2	1	no	—
160	C₂⁴×C₈₉	—	2	4	no	—
161	C₂⁴×C₈₉	—	4	2	no	—
162	C₂⁴×C₈₉	—	4	2	no	—
163	C₂⁴×C₈₉	—	4	2	no	—
164	C₂⁴×C₈₉	—	4	2	no	—
165	C₂⁴×C₈₉	—	4	2	no	—
166	C₂⁴×C₈₉	—	4	2	no	—
167	C₂⁴×C₈₉	—	4	2	no	—
168	C₂⁴×C₈₉	—	4	2	no	—
169	C₂⁴×C₈₉	—	8	1	no	—
170	C₂⁴×C₈₉	—	8	1	no	—
171	C₂⁴×C₈₉	—	8	1	no	—
172	C₂⁴×C₈₉	—	8	1	no	—
173	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
174	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
175	C₂×D₄×C₈₉	—	2	2	no	—
176	C₂×D₄×C₈₉	—	2	2	no	—
177	C₂×D₄×C₈₉	—	2	8	no	—
178	C₂×D₄×C₈₉	—	2	4	no	—
179	C₂×D₄×C₈₉	—	2	4	no	—
180	C₂×D₄×C₈₉	—	2	4	no	—
181	C₂×D₄×C₈₉	—	2	4	no	—
182	C₂×D₄×C₈₉	—	2	4	no	—
183	C₂×D₄×C₈₉	—	2	4	no	—
184	C₂×D₄×C₈₉	—	2	2	no	—
185	C₂×D₄×C₈₉	—	2	1	no	—
186	C₂×D₄×C₈₉	—	2	1	no	—
187	C₂×D₄×C₈₉	—	2	1	no	—
188	C₂×D₄×C₈₉	—	2	1	no	—
189	C₂×D₄×C₈₉	—	2	1	no	—
190	C₂×D₄×C₈₉	—	2	1	no	—
191	C₂×D₄×C₈₉	—	2	1	no	—
192	C₂×D₄×C₈₉	—	2	1	no	—
193	C₂×D₄×C₈₉	—	2	1	no	—
194	C₂×D₄×C₈₉	—	2	1	no	—
195	C₂×D₄×C₈₉	—	2	1	no	—
196	C₂×D₄×C₈₉	—	2	1	no	—
197	C₂×D₄×C₈₉	—	2	1	no	—
198	C₂×D₄×C₈₉	—	4	4	no	—
199	C₂×D₄×C₈₉	—	4	4	no	—
200	C₂×D₄×C₈₉	—	4	4	no	—
201	C₂×D₄×C₈₉	—	4	2	no	—
202	C₂×D₄×C₈₉	—	4	2	no	—
203	C₂×D₄×C₈₉	—	4	2	no	—
204	C₂×D₄×C₈₉	—	4	2	no	—
205	C₂×D₄×C₈₉	—	4	2	no	—
206	C₂×D₄×C₈₉	—	4	4	no	—
207	C₂×D₄×C₈₉	—	4	4	no	—
208	C₂×D₄×C₈₉	—	4	32	no	—
209	C₂×D₄×C₈₉	—	4	4	no	—
210	C₂×D₄×C₈₉	—	4	2	no	—
211	C₂×D₄×C₈₉	—	4	2	no	—
212	C₂×D₄×C₈₉	—	4	2	no	—
213	C₂×D₄×C₈₉	—	4	2	no	—
214	C₂×D₄×C₈₉	—	4	4	no	—
215	C₂×D₄×C₈₉	—	4	2	no	—
216	C₂×D₄×C₈₉	—	8	1	no	—
217	C₂×D₄×C₈₉	—	8	1	no	—
218	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
219	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
220	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
221	C₂×D₄×C₈₉	#41	1	2	yes	—
222	C₂×D₄×C₈₉	#41	1	2	yes	—
223	C₂²×C₄×C₈₉	—	2	1	no	—
224	C₂²×C₄×C₈₉	—	2	1	no	—
225	C₂²×C₄×C₈₉	—	2	1	no	—
226	C₂²×C₄×C₈₉	—	2	1	no	—
227	C₂²×C₄×C₈₉	—	2	4	no	—
228	C₂²×C₄×C₈₉	—	2	1	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	1	no	—
234	C₂²×C₄×C₈₉	—	2	1	no	—
235	C₂²×C₄×C₈₉	—	2	1	no	—
236	C₂²×C₄×C₈₉	—	2	1	no	—
237	C₂²×C₄×C₈₉	—	2	1	no	—
238	C₂²×C₄×C₈₉	—	2	1	no	—
239	C₂²×C₄×C₈₉	—	4	2	no	—
240	C₂²×C₄×C₈₉	—	4	2	no	—
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	C₂×D₄	1	2	yes	—
245	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
246	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
248	M₁₆×C₈₉	—	4	4	no	—
249	C₂×C₈×C₈₉	—	2	1	no	—
250	C₂×C₈×C₈₉	—	2	1	no	—
251	C₂×C₈×C₈₉	—	2	1	no	—
252	C₂×C₈×C₈₉	—	2	1	no	—
253	C₂×C₈×C₈₉	—	2	1	no	—
254	C₂×C₈×C₈₉	—	2	1	no	—
255	C₂×C₈×C₈₉	—	2	1	no	—
256	C₂×C₈×C₈₉	—	2	1	no	—
257	C₂×C₈×C₈₉	—	2	1	no	—
258	C₂×C₈×C₈₉	—	2	1	no	—
259	C₂×C₈×C₈₉	—	2	1	no	—
260	C₂×C₈×C₈₉	—	2	1	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	1	no	—
265	C₄⋊C₄×C₈₉	—	2	1	no	—
266	C₄⋊C₄×C₈₉	—	2	1	no	—
267	C₄⋊C₄×C₈₉	—	2	1	no	—
268	C₄⋊C₄×C₈₉	—	2	1	no	—
269	C₄⋊C₄×C₈₉	—	2	1	no	—
270	C₄⋊C₄×C₈₉	—	2	1	no	—
271	C₄⋊C₄×C₈₉	—	4	2	no	—
272	C₄⋊C₄×C₈₉	—	8	1	no	—
273	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
274	C₂²⋊C₄×C₈₉	—	2	4	no	—
275	C₂²⋊C₄×C₈₉	—	2	4	no	—
276	C₂²⋊C₄×C₈₉	—	2	2	no	—
277	C₂²⋊C₄×C₈₉	—	2	4	no	—
278	C₂²⋊C₄×C₈₉	—	2	2	no	—
279	C₂²⋊C₄×C₈₉	—	4	2	no	—
280	C₂²⋊C₄×C₈₉	—	4	2	no	—
281	C₂²⋊C₄×C₈₉	—	8	1	no	—
282	C₂²⋊C₄×C₈₉	—	8	1	no	—
283	C₄²×C₈₉	—	2	1	no	—
284	C₄²×C₈₉	—	2	1	no	—
285	C₄²×C₈₉	—	4	2	no	—
286	C₂³×C₈₉	—	2	1	no	—
287	C₂³×C₈₉	—	2	2	no	—
288	C₂³×C₈₉	—	2	1	no	—
289	C₂³×C₈₉	—	2	1	no	—
290	C₂³×C₈₉	—	2	1	no	—
291	C₂³×C₈₉	—	2	1	no	—
292	C₂³×C₈₉	—	2	2	no	—
293	C₂³×C₈₉	—	2	2	no	—
294	C₂³×C₈₉	—	2	1	no	—
295	C₂³×C₈₉	—	2	1	no	—
296	C₂³×C₈₉	—	2	1	no	—
297	C₂³×C₈₉	—	2	1	no	—
298	C₂³×C₈₉	—	2	1	no	—
299	C₂³×C₈₉	—	2	1	no	—
300	C₂³×C₈₉	—	2	1	no	—
301	C₂³×C₈₉	—	2	2	no	—
302	C₂³×C₈₉	—	2	2	no	—
303	C₂³×C₈₉	—	4	8	no	—
304	C₂³×C₈₉	—	4	8	no	—
305	C₂³×C₈₉	—	4	8	no	—
306	C₂³×C₈₉	—	4	8	no	—
307	C₂³×C₈₉	—	4	1	no	—
308	C₂³×C₈₉	—	4	1	no	—
309	C₂³×C₈₉	—	4	1	no	—
310	C₂³×C₈₉	—	4	1	no	—
311	C₂³×C₈₉	—	4	1	no	—
312	C₂³×C₈₉	—	4	1	no	—
313	C₂³×C₈₉	—	4	1	no	—
314	C₂³×C₈₉	—	4	1	no	—
315	C₂³×C₈₉	—	4	1	no	—
316	C₂³×C₈₉	—	4	1	no	—
317	C₂³×C₈₉	—	4	1	no	—
318	C₂³×C₈₉	—	4	1	no	—
319	C₂³×C₈₉	—	4	1	no	—
320	C₂³×C₈₉	—	4	1	no	—
321	C₂³×C₈₉	—	4	1	no	—
322	C₂³×C₈₉	—	4	1	no	—
323	C₂³×C₈₉	—	8	4	no	—
324	C₂³×C₈₉	—	8	4	no	—
325	C₂³×C₈₉	—	8	4	no	—
326	C₂³×C₈₉	—	8	4	no	—
327	C₂³×C₈₉	—	8	4	no	—
328	C₂³×C₈₉	—	8	4	no	—
329	C₂³×C₈₉	—	8	4	no	—
330	C₂³×C₈₉	—	8	4	no	—
331	C₂³×C₈₉	—	8	4	no	—
332	C₂³×C₈₉	—	8	4	no	—
333	C₂³×C₈₉	#120	1	2	yes	—
334	C₂³×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
335	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
336	D₄×C₈₉	—	2	8	no	—
337	D₄×C₈₉	—	2	2	no	—
338	D₄×C₈₉	—	2	2	no	—
339	D₄×C₈₉	—	2	2	no	—
340	D₄×C₈₉	—	2	2	no	—
341	D₄×C₈₉	—	2	2	no	—
342	D₄×C₈₉	—	2	2	no	—
343	D₄×C₈₉	—	2	2	no	—
344	D₄×C₈₉	—	4	8	no	—
345	D₄×C₈₉	—	4	8	no	—
346	D₄×C₈₉	—	4	8	no	—
347	D₄×C₈₉	—	4	8	no	—
348	D₄×C₈₉	—	4	8	no	—
349	D₄×C₈₉	—	4	1	no	—
350	D₄×C₈₉	—	4	1	no	—
351	D₄×C₈₉	—	4	1	no	—
352	D₄×C₈₉	—	4	1	no	—
353	D₄×C₈₉	—	8	4	no	—
354	D₄×C₈₉	#123	1	4	yes	—
355	C₂×C₄×C₈₉	—	2	1	no	—
356	C₂×C₄×C₈₉	—	2	1	no	—
357	C₂×C₄×C₈₉	—	2	1	no	—
358	C₂×C₄×C₈₉	—	2	1	no	—
359	C₂×C₄×C₈₉	—	2	2	no	—
360	C₂×C₄×C₈₉	—	2	2	no	—
361	C₂×C₄×C₈₉	—	2	2	no	—
362	C₂×C₄×C₈₉	—	2	2	no	—
363	C₂×C₄×C₈₉	—	2	1	no	—
364	C₂×C₄×C₈₉	—	2	1	no	—
365	C₂×C₄×C₈₉	—	2	2	no	—
366	C₂×C₄×C₈₉	—	2	1	no	—
367	C₂×C₄×C₈₉	—	2	1	no	—
368	C₂×C₄×C₈₉	—	2	1	no	—
369	C₂×C₄×C₈₉	—	2	1	no	—
370	C₂×C₄×C₈₉	—	4	8	no	—
371	C₂×C₄×C₈₉	—	4	1	no	—
372	C₂×C₄×C₈₉	—	4	1	no	—
373	C₂×C₄×C₈₉	—	4	1	no	—
374	C₂×C₄×C₈₉	—	4	1	no	—
375	C₂×C₄×C₈₉	—	4	1	no	—
376	C₂×C₄×C₈₉	—	4	1	no	—
377	C₂×C₄×C₈₉	—	4	1	no	—
378	C₂×C₄×C₈₉	—	4	1	no	—
379	C₂×C₄×C₈₉	—	4	1	no	—
380	C₂×C₄×C₈₉	—	4	1	no	—
381	C₂×C₄×C₈₉	—	4	1	no	—
382	C₂×C₄×C₈₉	—	4	1	no	—
383	C₂×C₄×C₈₉	—	4	1	no	—
384	C₂×C₄×C₈₉	—	4	1	no	—
385	C₂×C₄×C₈₉	—	4	1	no	—
386	C₂×C₄×C₈₉	—	4	1	no	—
387	C₂×C₄×C₈₉	—	4	1	no	—
388	C₂×C₄×C₈₉	—	4	1	no	—
389	C₂×C₄×C₈₉	#120	1	2	yes	—
390	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
391	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
394	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
395	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
396	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
397	C₈×C₈₉	—	4	1	no	—
398	C₈×C₈₉	—	4	1	no	—
399	C₈×C₈₉	—	4	1	no	—
400	C₈×C₈₉	—	4	1	no	—
401	C₂²×C₈₉	—	2	2	no	—
402	C₂²×C₈₉	—	2	4	no	—
403	C₂²×C₈₉	—	2	2	no	—
404	C₂²×C₈₉	—	2	2	no	—
405	C₂²×C₈₉	—	2	2	no	—
406	C₂²×C₈₉	—	2	2	no	—
407	C₂²×C₈₉	—	2	2	no	—
408	C₂²×C₈₉	—	4	1	no	—
409	C₂²×C₈₉	—	4	2	no	—
410	C₂²×C₈₉	—	4	1	no	—
411	C₂²×C₈₉	—	4	2	no	—
412	C₂²×C₈₉	—	4	1	no	—
413	C₂²×C₈₉	—	4	2	no	—
414	C₂²×C₈₉	—	4	1	no	—
415	C₂²×C₈₉	—	4	2	no	—
416	C₂²×C₈₉	—	4	1	no	—
417	C₂²×C₈₉	—	4	1	no	—
418	C₂²×C₈₉	—	4	2	no	—
419	C₂²×C₈₉	—	4	1	no	—
420	C₂²×C₈₉	—	4	1	no	—
421	C₂²×C₈₉	—	4	2	no	—
422	C₂²×C₈₉	—	4	2	no	—
423	C₂²×C₈₉	—	4	2	no	—
424	C₂²×C₈₉	—	4	2	no	—
425	C₂²×C₈₉	—	4	2	no	—
426	C₂²×C₈₉	—	4	2	no	—
427	C₂²×C₈₉	—	4	2	no	—
428	C₂²×C₈₉	—	8	16	no	—
429	C₂²×C₈₉	—	8	16	no	—
430	C₂²×C₈₉	—	8	1	no	—
431	C₂²×C₈₉	—	8	1	no	—
432	C₂²×C₈₉	—	8	1	no	—
433	C₂²×C₈₉	—	8	1	no	—
434	C₂²×C₈₉	—	8	1	no	—
435	C₂²×C₈₉	—	8	1	no	—
436	C₂²×C₈₉	—	8	1	no	—
437	C₂²×C₈₉	—	8	1	no	—
438	C₂²×C₈₉	C₂×#120	1	1	yes	characteristic
439	C₂²×C₈₉	#546	1	1	yes	characteristic
440	C₂²×C₈₉	#546	1	1	yes	characteristic
441	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
442	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
443	C₂²×C₈₉	#576	1	1	yes	characteristic
444	C₂²×C₈₉	#577	1	1	yes	characteristic
445	C₄×C₈₉	—	2	2	no	—
446	C₄×C₈₉	—	2	2	no	—
447	C₄×C₈₉	—	4	1	no	—
448	C₄×C₈₉	—	4	2	no	—
449	C₄×C₈₉	—	4	1	no	—
450	C₄×C₈₉	—	8	1	no	—
451	C₄×C₈₉	—	8	1	no	—
452	C₄×C₈₉	—	8	1	no	—
453	C₄×C₈₉	—	8	1	no	—
454	C₄×C₈₉	C₂×#123	1	1	yes	characteristic
455	C₄×C₈₉	#534	1	1	yes	characteristic
456	C₄×C₈₉	#546	1	1	yes	characteristic
457	C₄×C₈₉	#546	1	1	yes	characteristic
458	#24044	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
459	C₂×C₈₉	—	4	2	no	—
460	C₂×C₈₉	—	4	2	no	—
461	C₂×C₈₉	—	4	4	no	—
462	C₂×C₈₉	—	8	2	no	—
463	C₂×C₈₉	—	8	2	no	—
464	C₂×C₈₉	#2405	1	1	yes	characteristic
465	C₂×C₈₉	#3003	1	1	yes	characteristic
466	C₂×C₈₉	#3012	1	1	yes	characteristic
467	C₂×C₈₉	#3310	1	1	yes	characteristic
468	C₂×C₈₉	#3318	1	1	yes	characteristic
469	C₂×C₈₉	#3324	1	1	yes	characteristic
470	C₂×C₈₉	#3325	1	1	yes	characteristic
471	C₂×D₄²	C₂×C₈₉	1	1	yes	characteristic
472	C₂×#482	C₂×C₈₉	1	1	yes	characteristic, complemented
473	C₂×#418	C₂×C₈₉	1	1	yes	characteristic, complemented
474	#2485	C₂×C₈₉	1	1	yes	characteristic, complemented
475	#2041	C₂×C₈₉	1	1	yes	characteristic, complemented
476	#2041	C₂×C₈₉	1	1	yes	characteristic, complemented
477	#2034	C₂×C₈₉	1	1	yes	characteristic, complemented
478	#2033	C₂×C₈₉	1	1	yes	characteristic, complemented
479	#1895	C₂×C₈₉	1	1	yes	characteristic, complemented
480	#1870	C₂×C₈₉	1	1	yes	characteristic, complemented
481	#1864	C₂×C₈₉	1	1	yes	characteristic, complemented
482	#1862	C₂×C₈₉	1	1	yes	characteristic, complemented
483	#1786	C₂×C₈₉	1	1	yes	characteristic, complemented
484	#1786	C₂×C₈₉	1	1	yes	characteristic, complemented
485	#1786	C₂×C₈₉	1	1	yes	characteristic, complemented
486	C₈₉	#24044	1	1	yes	characteristic, direct product factor, Sylow
487	C₂³×D₄	—	2	1	no	—
488	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
489	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
490	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
491	D₄²	—	2	4	no	—
492	D₄²	—	2	4	no	—
493	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
494	C₂×#121	—	2	1	no	—
495	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
496	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
497	C₂×#120	—	2	1	no	—
498	C₂×#120	—	2	1	no	—
499	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
500	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
501	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic, complemented
502	#482	—	2	4	no	—
503	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic, complemented
504	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic, complemented
505	#418	—	2	4	no	—
506	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
507	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
508	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
509	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
510	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
511	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
512	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
513	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
514	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
515	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
516	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
517	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
518	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
519	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
520	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
521	#397	—	2	1	no	—
522	#394	—	2	1	no	—
523	#389	C₂²×C₈₉	1	1	yes	characteristic, complemented
524	#389	C₂²×C₈₉	1	1	yes	characteristic, complemented
525	#388	—	2	1	no	—
526	#387	—	2	1	no	—
527	#380	C₂²×C₈₉	1	1	yes	characteristic, complemented
528	#380	C₂²×C₈₉	1	1	yes	characteristic, complemented
529	#380	C₂²×C₈₉	1	1	yes	characteristic, complemented
530	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
531	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
532	#336	C₂²×C₈₉	1	1	yes	characteristic, complemented
533	#336	C₂²×C₈₉	1	1	yes	characteristic, complemented
534	C₂⁵	—	2	1	no	—
535	C₂⁵	—	2	1	no	—
536	C₂²×D₄	—	2	2	no	—
537	C₂²×D₄	—	2	2	no	—
538	C₂²×D₄	—	2	8	no	—
539	C₂²×D₄	—	2	1	no	—
540	C₂²×D₄	—	2	1	no	—
541	C₂²×D₄	—	2	2	no	—
542	C₂²×D₄	—	2	2	no	—
543	C₂²×D₄	—	2	2	no	—
544	C₂²×D₄	—	2	2	no	—
545	C₂²×D₄	—	2	1	no	—
546	C₂²×D₄	—	2	1	no	—
547	C₂²×D₄	—	2	1	no	—
548	C₂²×D₄	—	2	2	no	—
549	C₂²×D₄	—	2	1	no	—
550	C₂²×D₄	—	4	1	no	—
551	C₂²×D₄	—	4	1	no	—
552	C₂²×D₄	—	4	1	no	—
553	C₂²×D₄	—	4	1	no	—
554	C₂²×D₄	—	4	4	no	—
555	C₂²×D₄	—	4	4	no	—
556	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
557	C₂²×D₄	D₄×C₈₉	1	4	yes	—
558	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
559	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
560	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
561	C₂³×C₄	—	2	1	no	—
562	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
563	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
564	C₂×M₁₆	—	2	2	no	—
565	C₂×M₁₆	—	4	1	no	—
566	C₂×M₁₆	—	4	1	no	—
567	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
568	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
569	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
570	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
571	#127	—	2	2	no	—
572	#127	—	2	2	no	—
573	#121	—	2	8	no	—
574	#121	—	2	2	no	—
575	#121	—	2	2	no	—
576	#121	—	2	2	no	—
577	#121	D₄×C₈₉	1	4	yes	—
578	#120	—	2	8	no	—
579	#120	—	2	8	no	—
580	C₄×D₄	—	2	2	no	—
581	C₄×D₄	—	2	2	no	—
582	C₄×D₄	—	2	2	no	—
583	C₄×D₄	—	2	2	no	—
584	#117	—	2	2	no	—
585	#117	—	2	2	no	—
586	C₂×C₄⋊C₄	—	2	1	no	—
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
594	C₂×C₂²⋊C₄	—	2	1	no	—
595	C₂×C₂²⋊C₄	—	2	1	no	—
596	C₂×C₂²⋊C₄	—	2	1	no	—
597	C₂×C₂²⋊C₄	—	2	1	no	—
598	C₂×C₂²⋊C₄	—	2	1	no	—
599	C₂×C₂²⋊C₄	—	2	1	no	—
600	C₂×C₂²⋊C₄	—	2	1	no	—
601	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
602	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
603	C₂×C₄²	—	2	1	no	—
604	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
605	#107	—	2	2	no	—
606	#106	—	2	2	no	—
607	#102	—	2	2	no	—
608	#102	—	2	2	no	—
609	#102	—	2	2	no	—
610	#102	—	2	2	no	—
611	#102	—	2	2	no	—
612	#102	—	2	2	no	—
613	#102	—	2	2	no	—
614	#102	—	2	2	no	—
615	#102	—	4	1	no	—
616	#102	—	4	1	no	—
617	#102	—	4	1	no	—
618	#102	—	4	1	no	—
619	C₂²⋊C₈	—	2	2	no	—
620	C₂²⋊C₈	—	4	1	no	—
621	C₂²⋊C₈	—	4	1	no	—
622	#95	—	2	1	no	—
623	#95	—	2	1	no	—
624	#95	—	2	1	no	—
625	#95	—	2	1	no	—
626	#95	—	2	1	no	—
627	C₂⁴	—	2	1	no	—
628	C₂⁴	—	2	4	no	—
629	C₂⁴	—	2	1	no	—
630	C₂⁴	—	2	1	no	—
631	C₂⁴	—	2	4	no	—
632	C₂⁴	—	4	2	no	—
633	C₂⁴	—	4	2	no	—
634	C₂⁴	—	4	2	no	—
635	C₂⁴	—	4	2	no	—
636	C₂⁴	—	4	2	no	—
637	C₂⁴	—	4	2	no	—
638	C₂⁴	—	4	2	no	—
639	C₂⁴	—	4	2	no	—
640	C₂⁴	—	8	1	no	—
641	C₂⁴	—	8	1	no	—
642	C₂⁴	—	8	1	no	—
643	C₂⁴	—	8	1	no	—
644	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
645	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	8	no	—
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	2	4	no	—
652	C₂×D₄	—	2	4	no	—
653	C₂×D₄	—	2	4	no	—
654	C₂×D₄	—	2	4	no	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	1	no	—
657	C₂×D₄	—	2	1	no	—
658	C₂×D₄	—	2	1	no	—
659	C₂×D₄	—	2	1	no	—
660	C₂×D₄	—	2	1	no	—
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	4	4	no	—
670	C₂×D₄	—	4	4	no	—
671	C₂×D₄	—	4	4	no	—
672	C₂×D₄	—	4	2	no	—
673	C₂×D₄	—	4	2	no	—
674	C₂×D₄	—	4	2	no	—
675	C₂×D₄	—	4	2	no	—
676	C₂×D₄	—	4	2	no	—
677	C₂×D₄	—	4	4	no	—
678	C₂×D₄	—	4	4	no	—
679	C₂×D₄	—	4	32	no	—
680	C₂×D₄	—	4	4	no	—
681	C₂×D₄	—	4	2	no	—
682	C₂×D₄	—	4	2	no	—
683	C₂×D₄	—	4	2	no	—
684	C₂×D₄	—	4	2	no	—
685	C₂×D₄	—	4	4	no	—
686	C₂×D₄	—	4	2	no	—
687	C₂×D₄	—	8	1	no	—
688	C₂×D₄	—	8	1	no	—
689	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
690	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
691	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
692	C₂×D₄	#41×C₈₉	1	2	yes	—
693	C₂×D₄	#41×C₈₉	1	2	yes	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	1	no	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	2	no	—
712	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
713	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
714	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
715	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
716	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
717	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
719	M₁₆	—	4	4	no	—
720	C₂×C₈	—	2	1	no	—
721	C₂×C₈	—	2	1	no	—
722	C₂×C₈	—	2	1	no	—
723	C₂×C₈	—	2	1	no	—
724	C₂×C₈	—	2	1	no	—
725	C₂×C₈	—	2	1	no	—
726	C₂×C₈	—	2	1	no	—
727	C₂×C₈	—	2	1	no	—
728	C₂×C₈	—	2	1	no	—
729	C₂×C₈	—	2	1	no	—
730	C₂×C₈	—	2	1	no	—
731	C₂×C₈	—	2	1	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	4	2	no	—
743	C₄⋊C₄	—	8	1	no	—
744	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	—	8	1	no	—
753	C₂²⋊C₄	—	8	1	no	—
754	C₄²	—	2	1	no	—
755	C₄²	—	2	1	no	—
756	C₄²	—	4	2	no	—
757	C₂³	—	2	1	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	1	no	—
760	C₂³	—	2	1	no	—
761	C₂³	—	2	1	no	—
762	C₂³	—	2	1	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	2	1	no	—
768	C₂³	—	2	1	no	—
769	C₂³	—	2	1	no	—
770	C₂³	—	2	1	no	—
771	C₂³	—	2	1	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	4	8	no	—
775	C₂³	—	4	8	no	—
776	C₂³	—	4	8	no	—
777	C₂³	—	4	8	no	—
778	C₂³	—	4	1	no	—
779	C₂³	—	4	1	no	—
780	C₂³	—	4	1	no	—
781	C₂³	—	4	1	no	—
782	C₂³	—	4	1	no	—
783	C₂³	—	4	1	no	—
784	C₂³	—	4	1	no	—
785	C₂³	—	4	1	no	—
786	C₂³	—	4	1	no	—
787	C₂³	—	4	1	no	—
788	C₂³	—	4	1	no	—
789	C₂³	—	4	1	no	—
790	C₂³	—	4	1	no	—
791	C₂³	—	4	1	no	—
792	C₂³	—	4	1	no	—
793	C₂³	—	4	1	no	—
794	C₂³	—	8	4	no	—
795	C₂³	—	8	4	no	—
796	C₂³	—	8	4	no	—
797	C₂³	—	8	4	no	—
798	C₂³	—	8	4	no	—
799	C₂³	—	8	4	no	—
800	C₂³	—	8	4	no	—
801	C₂³	—	8	4	no	—
802	C₂³	—	8	4	no	—
803	C₂³	—	8	4	no	—
804	C₂³	#120×C₈₉	1	2	yes	—
805	C₂³	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
806	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
807	D₄	—	2	8	no	—
808	D₄	—	2	2	no	—
809	D₄	—	2	2	no	—
810	D₄	—	2	2	no	—
811	D₄	—	2	2	no	—
812	D₄	—	2	2	no	—
813	D₄	—	2	2	no	—
814	D₄	—	2	2	no	—
815	D₄	—	4	8	no	—
816	D₄	—	4	8	no	—
817	D₄	—	4	8	no	—
818	D₄	—	4	8	no	—
819	D₄	—	4	8	no	—
820	D₄	—	4	1	no	—
821	D₄	—	4	1	no	—
822	D₄	—	4	1	no	—
823	D₄	—	4	1	no	—
824	D₄	—	8	4	no	—
825	D₄	#123×C₈₉	1	4	yes	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	4	8	no	—
842	C₂×C₄	—	4	1	no	—
843	C₂×C₄	—	4	1	no	—
844	C₂×C₄	—	4	1	no	—
845	C₂×C₄	—	4	1	no	—
846	C₂×C₄	—	4	1	no	—
847	C₂×C₄	—	4	1	no	—
848	C₂×C₄	—	4	1	no	—
849	C₂×C₄	—	4	1	no	—
850	C₂×C₄	—	4	1	no	—
851	C₂×C₄	—	4	1	no	—
852	C₂×C₄	—	4	1	no	—
853	C₂×C₄	—	4	1	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	1	no	—
856	C₂×C₄	—	4	1	no	—
857	C₂×C₄	—	4	1	no	—
858	C₂×C₄	—	4	1	no	—
859	C₂×C₄	—	4	1	no	—
860	C₂×C₄	#120×C₈₉	1	2	yes	—
861	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
862	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
863	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
864	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
865	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
866	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
867	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
868	C₈	—	4	1	no	—
869	C₈	—	4	1	no	—
870	C₈	—	4	1	no	—
871	C₈	—	4	1	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	2	no	—
874	C₂²	—	2	4	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	2	2	no	—
877	C₂²	—	2	2	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	1	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	1	no	—
885	C₂²	—	4	1	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	1	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	4	1	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	1	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	8	16	no	—
900	C₂²	—	8	16	no	—
901	C₂²	—	8	1	no	—
902	C₂²	—	8	1	no	—
903	C₂²	—	8	1	no	—
904	C₂²	—	8	1	no	—
905	C₂²	—	8	1	no	—
906	C₂²	—	8	1	no	—
907	C₂²	—	8	1	no	—
908	C₂²	—	8	1	no	—
909	C₂²	C₂×#120×C₈₉	1	1	yes	characteristic
910	C₂²	#546×C₈₉	1	1	yes	characteristic
911	C₂²	#546×C₈₉	1	1	yes	characteristic
912	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
913	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
914	C₂²	#576×C₈₉	1	1	yes	characteristic
915	C₂²	#577×C₈₉	1	1	yes	characteristic
916	C₄	—	2	2	no	—
917	C₄	—	2	2	no	—
918	C₄	—	4	1	no	—
919	C₄	—	4	2	no	—
920	C₄	—	4	1	no	—
921	C₄	—	8	1	no	—
922	C₄	—	8	1	no	—
923	C₄	—	8	1	no	—
924	C₄	—	8	1	no	—
925	C₄	C₂×#123×C₈₉	1	1	yes	characteristic
926	C₄	#534×C₈₉	1	1	yes	characteristic
927	C₄	#546×C₈₉	1	1	yes	characteristic
928	C₄	#546×C₈₉	1	1	yes	characteristic
929	C₂	—	4	2	no	—
930	C₂	—	4	2	no	—
931	C₂	—	4	4	no	—
932	C₂	—	8	2	no	—
933	C₂	—	8	2	no	—
934	C₂	C₈₉×#2405	1	1	yes	characteristic
935	C₂	C₈₉×#3003	1	1	yes	characteristic
936	C₂	C₈₉×#3012	1	1	yes	characteristic
937	C₂	C₈₉×#3310	1	1	yes	characteristic
938	C₂	C₈₉×#3318	1	1	yes	characteristic
939	C₂	C₈₉×#3324	1	1	yes	characteristic
940	C₂	C₈₉×#3325	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂×D₄²×C₈₉	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
2. C₂×#482×C₈₉	C₂	semidirect
3. C₂×#418×C₈₉	C₂	semidirect
4. C₈₉×#2485	C₂	semidirect
5. C₈₉×#2041	C₂	semidirect
6. C₈₉×#2041	C₂	semidirect
7. C₈₉×#2034	C₂	semidirect
8. C₈₉×#2033	C₂	semidirect
9. C₈₉×#1895	C₂	semidirect
10. C₈₉×#1870	C₂	semidirect
11. C₈₉×#1864	C₂	semidirect
12. C₈₉×#1862	C₂	semidirect
13. C₈₉×#1786	C₂	semidirect
14. C₈₉×#1786	C₂	semidirect
15. C₈₉×#1786	C₂	semidirect
19. C₂²×M₁₆×C₈₉	C₂²	semidirect
30. C₂×#117×C₈₉	C₂²	semidirect
32. C₂×#107×C₈₉	C₂²	semidirect
33. C₂×#106×C₈₉	C₂²	semidirect
39. C₂×#102×C₈₉	C₂²	semidirect
40. C₂×#102×C₈₉	C₂²	semidirect
41. C₂×#102×C₈₉	C₂²	semidirect
42. C₂×#102×C₈₉	C₂²	semidirect
43. C₂×#102×C₈₉	C₂²	semidirect
44. C₂×#102×C₈₉	C₂²	semidirect
45. C₂×#102×C₈₉	C₂²	semidirect
46. C₂×#102×C₈₉	C₂²	semidirect
47. C₂×C₂²⋊C₈×C₈₉	C₂²	semidirect
48. C₂×C₂²⋊C₈×C₈₉	C₂²	semidirect
49. C₂×C₂²⋊C₈×C₈₉	C₂²	semidirect
52. #389×C₈₉	C₂²	semidirect
53. #389×C₈₉	C₂²	semidirect
56. #380×C₈₉	C₂²	semidirect
57. #380×C₈₉	C₂²	semidirect
58. #380×C₈₉	C₂²	semidirect
59. #340×C₈₉	C₂²	semidirect
60. #340×C₈₉	C₂²	semidirect
61. #336×C₈₉	C₂²	semidirect
62. #336×C₈₉	C₂²	semidirect
458. #24044	C₈₉	direct (N × H)
472. C₂×#482	C₂×C₈₉	semidirect
473. C₂×#418	C₂×C₈₉	semidirect
474. #2485	C₂×C₈₉	semidirect
475. #2041	C₂×C₈₉	semidirect
476. #2041	C₂×C₈₉	semidirect
477. #2034	C₂×C₈₉	semidirect
478. #2033	C₂×C₈₉	semidirect
479. #1895	C₂×C₈₉	semidirect
480. #1870	C₂×C₈₉	semidirect
481. #1864	C₂×C₈₉	semidirect
482. #1862	C₂×C₈₉	semidirect
483. #1786	C₂×C₈₉	semidirect
484. #1786	C₂×C₈₉	semidirect
485. #1786	C₂×C₈₉	semidirect
486. C₈₉	#24044	direct (N × H)
490. C₂²×M₁₆	C₂²×C₈₉	semidirect
501. C₂×#117	C₂²×C₈₉	semidirect
503. C₂×#107	C₂²×C₈₉	semidirect
504. C₂×#106	C₂²×C₈₉	semidirect
510. C₂×#102	C₂²×C₈₉	semidirect
511. C₂×#102	C₂²×C₈₉	semidirect
512. C₂×#102	C₂²×C₈₉	semidirect
513. C₂×#102	C₂²×C₈₉	semidirect
514. C₂×#102	C₂²×C₈₉	semidirect
515. C₂×#102	C₂²×C₈₉	semidirect
516. C₂×#102	C₂²×C₈₉	semidirect
517. C₂×#102	C₂²×C₈₉	semidirect
518. C₂×C₂²⋊C₈	C₂²×C₈₉	semidirect
519. C₂×C₂²⋊C₈	C₂²×C₈₉	semidirect
520. C₂×C₂²⋊C₈	C₂²×C₈₉	semidirect
523. #389	C₂²×C₈₉	semidirect
524. #389	C₂²×C₈₉	semidirect
527. #380	C₂²×C₈₉	semidirect
528. #380	C₂²×C₈₉	semidirect
529. #380	C₂²×C₈₉	semidirect
530. #340	C₂²×C₈₉	semidirect
531. #340	C₂²×C₈₉	semidirect
532. #336	C₂²×C₈₉	semidirect
533. #336	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×D₄²×C₈₉	2
C₂×#482×C₈₉	2
C₂×#418×C₈₉	2
C₈₉×#2485	2
C₈₉×#2041	2
C₈₉×#2034	2
C₈₉×#2033	2
C₈₉×#1895	2
C₈₉×#1870	2
C₈₉×#1864	2
C₈₉×#1862	2
C₈₉×#1786	2
#24044	89

Subgroups — C89×#24044 #36401892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#24044 #36401892