Subgroups — C₈₉×#25402 #36403250

Order 22784.

1120 conjugacy classes of subgroups.

The subgroup lattice has 836 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×#465×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#460×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#435×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2541	C₂	1	1	yes	maximal, characteristic
6	C₈₉×#2536	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×#2000	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1961	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1949	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1895	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1763	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#127×C₈₉	—	2	1	no	—
21	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×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×#121×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
30	#468×C₈₉	—	2	4	no	—
31	#465×C₈₉	—	2	4	no	—
32	#460×C₈₉	—	2	4	no	—
33	#435×C₈₉	—	2	4	no	—
34	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₈×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×#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
45	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
48	#398×C₈₉	—	2	1	no	—
49	#394×C₈₉	—	2	1	no	—
50	#392×C₈₉	—	2	1	no	—
51	#392×C₈₉	—	2	1	no	—
52	#390×C₈₉	—	2	1	no	—
53	#388×C₈₉	—	2	1	no	—
54	#388×C₈₉	—	2	1	no	—
55	#382×C₈₉	C₂²	1	1	yes	characteristic
56	#380×C₈₉	C₂²	1	1	yes	characteristic
57	#380×C₈₉	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×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	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₈₉	—	2	1	no	—
65	C₂²×D₄×C₈₉	—	2	1	no	—
66	C₂²×D₄×C₈₉	—	2	1	no	—
67	C₂²×D₄×C₈₉	—	2	1	no	—
68	C₂²×D₄×C₈₉	—	2	1	no	—
69	C₂²×D₄×C₈₉	—	2	1	no	—
70	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
71	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
75	C₂×SD₁₆×C₈₉	—	2	2	no	—
76	C₂×SD₁₆×C₈₉	—	2	2	no	—
77	C₂×SD₁₆×C₈₉	—	2	2	no	—
78	C₂×SD₁₆×C₈₉	—	2	2	no	—
79	C₂×SD₁₆×C₈₉	—	4	1	no	—
80	C₂×SD₁₆×C₈₉	—	4	1	no	—
81	C₂×M₁₆×C₈₉	—	2	2	no	—
82	C₂×M₁₆×C₈₉	—	2	2	no	—
83	C₂×M₁₆×C₈₉	—	4	1	no	—
84	C₂²×C₈×C₈₉	—	2	2	no	—
85	C₂²×C₈×C₈₉	—	2	2	no	—
86	C₂²×C₈×C₈₉	—	4	1	no	—
87	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
91	#127×C₈₉	—	2	2	no	—
92	#127×C₈₉	—	2	2	no	—
93	#127×C₈₉	—	4	4	no	—
94	C₂²⋊Q₈×C₈₉	—	2	2	no	—
95	C₂²⋊Q₈×C₈₉	—	2	2	no	—
96	C₂²⋊Q₈×C₈₉	—	4	1	no	—
97	C₂²⋊Q₈×C₈₉	—	4	1	no	—
98	#121×C₈₉	—	2	2	no	—
99	#121×C₈₉	—	2	2	no	—
100	#121×C₈₉	—	2	2	no	—
101	#121×C₈₉	—	2	2	no	—
102	#121×C₈₉	—	4	1	no	—
103	#121×C₈₉	—	4	1	no	—
104	#121×C₈₉	—	4	1	no	—
105	#121×C₈₉	—	4	1	no	—
106	C₄×Q₈×C₈₉	—	2	2	no	—
107	C₄×Q₈×C₈₉	—	2	2	no	—
108	C₄×D₄×C₈₉	—	2	2	no	—
109	C₄×D₄×C₈₉	—	2	2	no	—
110	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₈₉	—	2	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	—	2	1	no	—
130	C₂×C₄²×C₈₉	—	2	1	no	—
131	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
132	#107×C₈₉	—	2	2	no	—
133	#106×C₈₉	—	2	2	no	—
134	C₄⋊C₈×C₈₉	D₄	1	4	yes	complemented
135	#103×C₈₉	—	2	2	no	—
136	#103×C₈₉	D₄	1	4	yes	complemented
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	—	4	1	no	—
142	#102×C₈₉	—	4	1	no	—
143	C₂²⋊C₈×C₈₉	—	2	2	no	—
144	C₂²⋊C₈×C₈₉	—	2	2	no	—
145	#97×C₈₉	—	2	2	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	—	2	1	no	—
153	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₂×Q₈×C₈₉	—	2	1	no	—
156	C₂×Q₈×C₈₉	—	2	1	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	C₂×D₄	1	2	yes	—
161	C₂×D₄×C₈₉	—	2	2	no	—
162	C₂×D₄×C₈₉	—	2	2	no	—
163	C₂×D₄×C₈₉	—	2	1	no	—
164	C₂×D₄×C₈₉	—	2	1	no	—
165	C₂×D₄×C₈₉	—	2	1	no	—
166	C₂×D₄×C₈₉	—	2	1	no	—
167	C₂×D₄×C₈₉	—	2	1	no	—
168	C₂×D₄×C₈₉	—	2	1	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	—	4	1	no	—
176	C₂×D₄×C₈₉	—	4	2	no	—
177	C₂×D₄×C₈₉	—	4	2	no	—
178	C₂×D₄×C₈₉	—	4	2	no	—
179	C₂×D₄×C₈₉	—	4	2	no	—
180	C₂×D₄×C₈₉	—	4	2	no	—
181	C₂×D₄×C₈₉	—	4	2	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	—	4	2	no	—
188	C₂×D₄×C₈₉	—	8	1	no	—
189	C₂×D₄×C₈₉	—	8	1	no	—
190	C₂×D₄×C₈₉	—	8	1	no	—
191	C₂×D₄×C₈₉	—	8	1	no	—
192	C₂×D₄×C₈₉	—	8	1	no	—
193	C₂×D₄×C₈₉	—	8	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	—	2	1	no	—
206	C₂²×C₄×C₈₉	—	2	1	no	—
207	C₂²×C₄×C₈₉	—	2	1	no	—
208	C₂²×C₄×C₈₉	—	2	1	no	—
209	C₂²×C₄×C₈₉	—	2	1	no	—
210	C₂²×C₄×C₈₉	—	2	1	no	—
211	C₂²×C₄×C₈₉	—	2	1	no	—
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	C₂⁴	1	1	yes	characteristic
217	SD₁₆×C₈₉	—	4	4	no	—
218	SD₁₆×C₈₉	—	4	4	no	—
219	M₁₆×C₈₉	—	4	4	no	—
220	C₂×C₈×C₈₉	—	2	1	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	—	4	4	no	—
230	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
231	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
232	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
233	C₄⋊C₄×C₈₉	—	2	2	no	—
234	C₄⋊C₄×C₈₉	—	2	1	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	—	4	2	no	—
243	C₄⋊C₄×C₈₉	—	4	2	no	—
244	C₄⋊C₄×C₈₉	—	4	2	no	—
245	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
246	C₄⋊C₄×C₈₉	#41	1	2	yes	—
247	C₂²⋊C₄×C₈₉	—	2	2	no	—
248	C₂²⋊C₄×C₈₉	—	2	2	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	—	4	2	no	—
257	C₄²×C₈₉	—	4	2	no	—
258	C₄²×C₈₉	—	4	2	no	—
259	C₄²×C₈₉	C₂×D₄	1	2	yes	—
260	C₄²×C₈₉	#41	1	2	yes	—
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	—	2	1	no	—
273	C₂³×C₈₉	—	2	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	—	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	AGL(1,ℤ/8)	1	2	yes	—
289	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
290	Q₈×C₈₉	—	2	2	no	—
291	Q₈×C₈₉	—	2	2	no	—
292	Q₈×C₈₉	—	4	1	no	—
293	Q₈×C₈₉	—	4	1	no	—
294	D₄×C₈₉	—	4	4	no	—
295	D₄×C₈₉	—	4	1	no	—
296	D₄×C₈₉	—	4	1	no	—
297	D₄×C₈₉	—	4	1	no	—
298	D₄×C₈₉	—	4	1	no	—
299	D₄×C₈₉	—	4	1	no	—
300	D₄×C₈₉	—	4	1	no	—
301	D₄×C₈₉	—	4	1	no	—
302	D₄×C₈₉	—	4	1	no	—
303	D₄×C₈₉	—	8	4	no	—
304	D₄×C₈₉	—	8	4	no	—
305	D₄×C₈₉	—	8	4	no	—
306	D₄×C₈₉	—	8	4	no	—
307	D₄×C₈₉	—	8	4	no	—
308	D₄×C₈₉	—	8	4	no	—
309	C₂×C₄×C₈₉	—	2	1	no	—
310	C₂×C₄×C₈₉	—	2	1	no	—
311	C₂×C₄×C₈₉	—	2	1	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	2	no	—
316	C₂×C₄×C₈₉	—	2	1	no	—
317	C₂×C₄×C₈₉	—	2	1	no	—
318	C₂×C₄×C₈₉	—	2	2	no	—
319	C₂×C₄×C₈₉	—	2	2	no	—
320	C₂×C₄×C₈₉	—	2	1	no	—
321	C₂×C₄×C₈₉	—	2	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	—	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	#121	1	2	yes	—
346	C₂×C₄×C₈₉	#121	1	2	yes	—
347	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
350	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
351	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
352	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
353	C₈×C₈₉	—	2	2	no	—
354	C₈×C₈₉	—	2	2	no	—
355	C₈×C₈₉	—	2	2	no	—
356	C₈×C₈₉	—	4	1	no	—
357	C₂²×C₈₉	—	2	2	no	—
358	C₂²×C₈₉	—	2	2	no	—
359	C₂²×C₈₉	—	2	2	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	—	4	1	no	—
366	C₂²×C₈₉	—	4	1	no	—
367	C₂²×C₈₉	—	4	1	no	—
368	C₂²×C₈₉	—	4	1	no	—
369	C₂²×C₈₉	—	4	1	no	—
370	C₂²×C₈₉	—	4	1	no	—
371	C₂²×C₈₉	—	8	1	no	—
372	C₂²×C₈₉	—	8	1	no	—
373	C₂²×C₈₉	—	8	1	no	—
374	C₂²×C₈₉	—	8	1	no	—
375	C₂²×C₈₉	—	8	1	no	—
376	C₂²×C₈₉	—	8	1	no	—
377	C₂²×C₈₉	—	8	1	no	—
378	C₂²×C₈₉	—	8	1	no	—
379	C₂²×C₈₉	—	8	1	no	—
380	C₂²×C₈₉	—	8	1	no	—
381	C₂²×C₈₉	—	8	1	no	—
382	C₂²×C₈₉	—	8	1	no	—
383	C₂²×C₈₉	—	8	1	no	—
384	C₂²×C₈₉	—	8	1	no	—
385	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
386	C₂²×C₈₉	D₄²	1	1	yes	characteristic
387	C₂²×C₈₉	#546	1	1	yes	characteristic
388	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
389	C₂²×C₈₉	#575	1	1	yes	characteristic
390	C₂²×C₈₉	#577	1	1	yes	characteristic
391	C₂²×C₈₉	#577	1	1	yes	characteristic
392	C₄×C₈₉	—	2	2	no	—
393	C₄×C₈₉	—	2	2	no	—
394	C₄×C₈₉	—	4	1	no	—
395	C₄×C₈₉	—	4	1	no	—
396	C₄×C₈₉	—	4	2	no	—
397	C₄×C₈₉	—	4	2	no	—
398	C₄×C₈₉	—	4	2	no	—
399	C₄×C₈₉	—	8	1	no	—
400	C₄×C₈₉	—	8	1	no	—
401	C₄×C₈₉	—	8	1	no	—
402	C₄×C₈₉	#532	1	1	yes	characteristic
403	C₄×C₈₉	#540	1	1	yes	characteristic
404	C₄×C₈₉	D₄²	1	1	yes	characteristic
405	C₄×C₈₉	#550	1	1	yes	characteristic
406	#25402	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
407	C₂×C₈₉	—	4	2	no	—
408	C₂×C₈₉	—	8	1	no	—
409	C₂×C₈₉	—	16	1	no	—
410	C₂×C₈₉	—	16	1	no	—
411	C₂×C₈₉	#2428	1	1	yes	characteristic
412	C₂×C₈₉	#3055	1	1	yes	characteristic
413	C₂×C₈₉	#3057	1	1	yes	characteristic
414	C₂×C₈₉	#3265	1	1	yes	characteristic
415	C₂×C₈₉	#3271	1	1	yes	characteristic
416	C₂×C₈₉	#3310	1	1	yes	characteristic
417	C₂×C₈₉	#3317	1	1	yes	characteristic
418	C₂×#468	C₂×C₈₉	1	1	yes	characteristic, complemented
419	C₂×#465	C₂×C₈₉	1	1	yes	characteristic, complemented
420	C₂×#460	C₂×C₈₉	1	1	yes	characteristic, complemented
421	C₂×#435	C₂×C₈₉	1	1	yes	characteristic, complemented
422	#2541	C₂×C₈₉	1	1	yes	characteristic
423	#2536	C₂×C₈₉	1	1	yes	characteristic, complemented
424	#2034	C₂×C₈₉	1	1	yes	characteristic, complemented
425	#2033	C₂×C₈₉	1	1	yes	characteristic, complemented
426	#2000	C₂×C₈₉	1	1	yes	characteristic, complemented
427	#2000	C₂×C₈₉	1	1	yes	characteristic, complemented
428	#1961	C₂×C₈₉	1	1	yes	characteristic, complemented
429	#1949	C₂×C₈₉	1	1	yes	characteristic, complemented
430	#1895	C₂×C₈₉	1	1	yes	characteristic, complemented
431	#1893	C₂×C₈₉	1	1	yes	characteristic, complemented
432	#1763	C₂×C₈₉	1	1	yes	characteristic, complemented
433	C₈₉	#25402	1	1	yes	characteristic, direct product factor, Sylow
434	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
435	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
436	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
437	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
438	C₂×#127	—	2	1	no	—
439	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
440	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
441	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
442	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
443	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
444	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
445	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
446	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
447	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
448	#468	—	2	4	no	—
449	#465	—	2	4	no	—
450	#460	—	2	4	no	—
451	#435	—	2	4	no	—
452	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
453	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
454	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
455	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
456	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
457	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
458	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
459	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
460	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
461	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
462	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
463	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
464	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
465	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
466	#398	—	2	1	no	—
467	#394	—	2	1	no	—
468	#392	—	2	1	no	—
469	#392	—	2	1	no	—
470	#390	—	2	1	no	—
471	#388	—	2	1	no	—
472	#388	—	2	1	no	—
473	#382	C₂²×C₈₉	1	1	yes	characteristic
474	#380	C₂²×C₈₉	1	1	yes	characteristic
475	#380	C₂²×C₈₉	1	1	yes	characteristic
476	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
477	#340	C₂²×C₈₉	1	1	yes	characteristic
478	#340	C₂²×C₈₉	1	1	yes	characteristic
479	#340	C₂²×C₈₉	1	1	yes	characteristic
480	#340	C₂²×C₈₉	1	1	yes	characteristic
481	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
482	C₂²×D₄	—	2	1	no	—
483	C₂²×D₄	—	2	1	no	—
484	C₂²×D₄	—	2	1	no	—
485	C₂²×D₄	—	2	1	no	—
486	C₂²×D₄	—	2	1	no	—
487	C₂²×D₄	—	2	1	no	—
488	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
489	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
490	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
493	C₂×SD₁₆	—	2	2	no	—
494	C₂×SD₁₆	—	2	2	no	—
495	C₂×SD₁₆	—	2	2	no	—
496	C₂×SD₁₆	—	2	2	no	—
497	C₂×SD₁₆	—	4	1	no	—
498	C₂×SD₁₆	—	4	1	no	—
499	C₂×M₁₆	—	2	2	no	—
500	C₂×M₁₆	—	2	2	no	—
501	C₂×M₁₆	—	4	1	no	—
502	C₂²×C₈	—	2	2	no	—
503	C₂²×C₈	—	2	2	no	—
504	C₂²×C₈	—	4	1	no	—
505	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
506	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
507	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
508	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
509	#127	—	2	2	no	—
510	#127	—	2	2	no	—
511	#127	—	4	4	no	—
512	C₂²⋊Q₈	—	2	2	no	—
513	C₂²⋊Q₈	—	2	2	no	—
514	C₂²⋊Q₈	—	4	1	no	—
515	C₂²⋊Q₈	—	4	1	no	—
516	#121	—	2	2	no	—
517	#121	—	2	2	no	—
518	#121	—	2	2	no	—
519	#121	—	2	2	no	—
520	#121	—	4	1	no	—
521	#121	—	4	1	no	—
522	#121	—	4	1	no	—
523	#121	—	4	1	no	—
524	C₄×Q₈	—	2	2	no	—
525	C₄×Q₈	—	2	2	no	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	—	2	2	no	—
528	C₂×C₄⋊C₄	—	2	1	no	—
529	C₂×C₄⋊C₄	—	2	1	no	—
530	C₂×C₄⋊C₄	—	2	1	no	—
531	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
534	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
535	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
537	C₂×C₂²⋊C₄	—	2	1	no	—
538	C₂×C₂²⋊C₄	—	2	1	no	—
539	C₂×C₂²⋊C₄	—	2	1	no	—
540	C₂×C₂²⋊C₄	—	2	1	no	—
541	C₂×C₂²⋊C₄	—	2	1	no	—
542	C₂×C₂²⋊C₄	—	2	1	no	—
543	C₂×C₂²⋊C₄	—	2	1	no	—
544	C₂×C₂²⋊C₄	—	2	1	no	—
545	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
547	C₂×C₄²	—	2	1	no	—
548	C₂×C₄²	—	2	1	no	—
549	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
550	#107	—	2	2	no	—
551	#106	—	2	2	no	—
552	C₄⋊C₈	D₄×C₈₉	1	4	yes	complemented
553	#103	—	2	2	no	—
554	#103	D₄×C₈₉	1	4	yes	complemented
555	#102	—	2	2	no	—
556	#102	—	2	2	no	—
557	#102	—	2	2	no	—
558	#102	—	2	2	no	—
559	#102	—	4	1	no	—
560	#102	—	4	1	no	—
561	C₂²⋊C₈	—	2	2	no	—
562	C₂²⋊C₈	—	2	2	no	—
563	#97	—	2	2	no	—
564	#95	—	2	1	no	—
565	#95	—	2	1	no	—
566	#95	—	2	1	no	—
567	#95	—	2	1	no	—
568	#95	—	2	1	no	—
569	C₂⁴	—	2	1	no	—
570	C₂⁴	—	2	1	no	—
571	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
572	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
573	C₂×Q₈	—	2	1	no	—
574	C₂×Q₈	—	2	1	no	—
575	C₂×Q₈	—	2	1	no	—
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	1	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	—	2	1	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	4	1	no	—
594	C₂×D₄	—	4	2	no	—
595	C₂×D₄	—	4	2	no	—
596	C₂×D₄	—	4	2	no	—
597	C₂×D₄	—	4	2	no	—
598	C₂×D₄	—	4	2	no	—
599	C₂×D₄	—	4	2	no	—
600	C₂×D₄	—	4	2	no	—
601	C₂×D₄	—	4	2	no	—
602	C₂×D₄	—	4	2	no	—
603	C₂×D₄	—	4	2	no	—
604	C₂×D₄	—	4	2	no	—
605	C₂×D₄	—	4	2	no	—
606	C₂×D₄	—	8	1	no	—
607	C₂×D₄	—	8	1	no	—
608	C₂×D₄	—	8	1	no	—
609	C₂×D₄	—	8	1	no	—
610	C₂×D₄	—	8	1	no	—
611	C₂×D₄	—	8	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
631	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
632	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
633	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
634	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
635	SD₁₆	—	4	4	no	—
636	SD₁₆	—	4	4	no	—
637	M₁₆	—	4	4	no	—
638	C₂×C₈	—	2	1	no	—
639	C₂×C₈	—	2	1	no	—
640	C₂×C₈	—	2	1	no	—
641	C₂×C₈	—	2	1	no	—
642	C₂×C₈	—	2	1	no	—
643	C₂×C₈	—	2	1	no	—
644	C₂×C₈	—	2	1	no	—
645	C₂×C₈	—	2	1	no	—
646	C₂×C₈	—	2	1	no	—
647	C₂×C₈	—	4	4	no	—
648	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
649	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
650	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	4	2	no	—
661	C₄⋊C₄	—	4	2	no	—
662	C₄⋊C₄	—	4	2	no	—
663	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
664	C₄⋊C₄	#41×C₈₉	1	2	yes	—
665	C₂²⋊C₄	—	2	2	no	—
666	C₂²⋊C₄	—	2	2	no	—
667	C₂²⋊C₄	—	4	2	no	—
668	C₂²⋊C₄	—	4	2	no	—
669	C₂²⋊C₄	—	4	2	no	—
670	C₂²⋊C₄	—	4	2	no	—
671	C₂²⋊C₄	—	4	2	no	—
672	C₂²⋊C₄	—	4	2	no	—
673	C₂²⋊C₄	—	4	2	no	—
674	C₂²⋊C₄	—	4	2	no	—
675	C₄²	—	4	2	no	—
676	C₄²	—	4	2	no	—
677	C₄²	C₂×D₄×C₈₉	1	2	yes	—
678	C₄²	#41×C₈₉	1	2	yes	—
679	C₂³	—	2	1	no	—
680	C₂³	—	2	1	no	—
681	C₂³	—	2	1	no	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	1	no	—
684	C₂³	—	2	1	no	—
685	C₂³	—	2	1	no	—
686	C₂³	—	2	1	no	—
687	C₂³	—	2	1	no	—
688	C₂³	—	2	1	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	2	1	no	—
691	C₂³	—	2	1	no	—
692	C₂³	—	4	1	no	—
693	C₂³	—	4	1	no	—
694	C₂³	—	4	1	no	—
695	C₂³	—	4	1	no	—
696	C₂³	—	4	1	no	—
697	C₂³	—	4	1	no	—
698	C₂³	—	4	1	no	—
699	C₂³	—	4	1	no	—
700	C₂³	—	4	1	no	—
701	C₂³	—	4	1	no	—
702	C₂³	—	4	1	no	—
703	C₂³	—	4	1	no	—
704	C₂³	—	4	1	no	—
705	C₂³	—	4	1	no	—
706	C₂³	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
707	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
708	Q₈	—	2	2	no	—
709	Q₈	—	2	2	no	—
710	Q₈	—	4	1	no	—
711	Q₈	—	4	1	no	—
712	D₄	—	4	4	no	—
713	D₄	—	4	1	no	—
714	D₄	—	4	1	no	—
715	D₄	—	4	1	no	—
716	D₄	—	4	1	no	—
717	D₄	—	4	1	no	—
718	D₄	—	4	1	no	—
719	D₄	—	4	1	no	—
720	D₄	—	4	1	no	—
721	D₄	—	8	4	no	—
722	D₄	—	8	4	no	—
723	D₄	—	8	4	no	—
724	D₄	—	8	4	no	—
725	D₄	—	8	4	no	—
726	D₄	—	8	4	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	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	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	1	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	1	no	—
756	C₂×C₄	—	4	1	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	#121×C₈₉	1	2	yes	—
764	C₂×C₄	#121×C₈₉	1	2	yes	—
765	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
766	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
767	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
768	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
769	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
770	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
771	C₈	—	2	2	no	—
772	C₈	—	2	2	no	—
773	C₈	—	2	2	no	—
774	C₈	—	4	1	no	—
775	C₂²	—	2	2	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	4	1	no	—
779	C₂²	—	4	1	no	—
780	C₂²	—	4	1	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	1	no	—
786	C₂²	—	4	1	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	8	1	no	—
790	C₂²	—	8	1	no	—
791	C₂²	—	8	1	no	—
792	C₂²	—	8	1	no	—
793	C₂²	—	8	1	no	—
794	C₂²	—	8	1	no	—
795	C₂²	—	8	1	no	—
796	C₂²	—	8	1	no	—
797	C₂²	—	8	1	no	—
798	C₂²	—	8	1	no	—
799	C₂²	—	8	1	no	—
800	C₂²	—	8	1	no	—
801	C₂²	—	8	1	no	—
802	C₂²	—	8	1	no	—
803	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
804	C₂²	D₄²×C₈₉	1	1	yes	characteristic
805	C₂²	#546×C₈₉	1	1	yes	characteristic
806	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
807	C₂²	#575×C₈₉	1	1	yes	characteristic
808	C₂²	#577×C₈₉	1	1	yes	characteristic
809	C₂²	#577×C₈₉	1	1	yes	characteristic
810	C₄	—	2	2	no	—
811	C₄	—	2	2	no	—
812	C₄	—	4	1	no	—
813	C₄	—	4	1	no	—
814	C₄	—	4	2	no	—
815	C₄	—	4	2	no	—
816	C₄	—	4	2	no	—
817	C₄	—	8	1	no	—
818	C₄	—	8	1	no	—
819	C₄	—	8	1	no	—
820	C₄	#532×C₈₉	1	1	yes	characteristic
821	C₄	#540×C₈₉	1	1	yes	characteristic
822	C₄	D₄²×C₈₉	1	1	yes	characteristic
823	C₄	#550×C₈₉	1	1	yes	characteristic
824	C₂	—	4	2	no	—
825	C₂	—	8	1	no	—
826	C₂	—	16	1	no	—
827	C₂	—	16	1	no	—
828	C₂	C₈₉×#2428	1	1	yes	characteristic
829	C₂	C₈₉×#3055	1	1	yes	characteristic
830	C₂	C₈₉×#3057	1	1	yes	characteristic
831	C₂	C₈₉×#3265	1	1	yes	characteristic
832	C₂	C₈₉×#3271	1	1	yes	characteristic
833	C₂	C₈₉×#3310	1	1	yes	characteristic
834	C₂	C₈₉×#3317	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₈₉×#2541	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×#465×C₈₉	C₂	semidirect
3. C₂×#460×C₈₉	C₂	semidirect
4. C₂×#435×C₈₉	C₂	semidirect
6. C₈₉×#2536	C₂	semidirect
7. C₈₉×#2034	C₂	semidirect
8. C₈₉×#2033	C₂	semidirect
9. C₈₉×#2000	C₂	semidirect
10. C₈₉×#2000	C₂	semidirect
11. C₈₉×#1961	C₂	semidirect
12. C₈₉×#1949	C₂	semidirect
13. C₈₉×#1895	C₂	semidirect
14. C₈₉×#1893	C₂	semidirect
15. C₈₉×#1763	C₂	semidirect
134. C₄⋊C₈×C₈₉	D₄	semidirect
136. #103×C₈₉	D₄	semidirect
406. #25402	C₈₉	direct (N × H)
418. C₂×#468	C₂×C₈₉	semidirect
419. C₂×#465	C₂×C₈₉	semidirect
420. C₂×#460	C₂×C₈₉	semidirect
421. C₂×#435	C₂×C₈₉	semidirect
423. #2536	C₂×C₈₉	semidirect
424. #2034	C₂×C₈₉	semidirect
425. #2033	C₂×C₈₉	semidirect
426. #2000	C₂×C₈₉	semidirect
427. #2000	C₂×C₈₉	semidirect
428. #1961	C₂×C₈₉	semidirect
429. #1949	C₂×C₈₉	semidirect
430. #1895	C₂×C₈₉	semidirect
431. #1893	C₂×C₈₉	semidirect
432. #1763	C₂×C₈₉	semidirect
433. C₈₉	#25402	direct (N × H)
552. C₄⋊C₈	D₄×C₈₉	semidirect
554. #103	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×#468×C₈₉	2
C₂×#465×C₈₉	2
C₂×#460×C₈₉	2
C₂×#435×C₈₉	2
C₈₉×#2541	2
C₈₉×#2536	2
C₈₉×#2034	2
C₈₉×#2033	2
C₈₉×#2000	2
C₈₉×#1961	2
C₈₉×#1949	2
C₈₉×#1895	2
C₈₉×#1893	2
C₈₉×#1763	2
#25402	89

Subgroups — C89×#25402 #36403250

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25402 #36403250