Subgroups — C₈₉×#25093 #36402941

Order 22784.

1322 conjugacy classes of subgroups.

The subgroup lattice has 866 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×#460×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#450×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#418×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2433	C₂	1	1	yes	maximal, characteristic
6	C₈₉×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2067	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2041	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2014	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1982	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1925	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1875	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1851	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×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
20	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#127×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×#120×C₈₉	—	2	1	no	—
26	C₂×#120×C₈₉	—	2	1	no	—
27	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
29	#468×C₈₉	—	2	4	no	—
30	#460×C₈₉	—	2	4	no	—
31	#450×C₈₉	—	2	4	no	—
32	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
35	#418×C₈₉	—	2	4	no	—
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
42	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
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×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
47	#392×C₈₉	—	2	1	no	—
48	#392×C₈₉	—	2	1	no	—
49	#391×C₈₉	C₂²	1	1	yes	characteristic, complemented
50	#390×C₈₉	C₂²	1	1	yes	characteristic
51	#390×C₈₉	C₂²	1	1	yes	characteristic
52	#389×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	#388×C₈₉	—	2	1	no	—
54	#388×C₈₉	—	2	1	no	—
55	#387×C₈₉	—	2	1	no	—
56	C₄×C₄⋊C₄×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	1	no	—
71	C₂²×D₄×C₈₉	—	2	1	no	—
72	C₂²×D₄×C₈₉	—	2	1	no	—
73	C₂²×D₄×C₈₉	—	2	1	no	—
74	C₂²×D₄×C₈₉	—	2	2	no	—
75	C₂²×D₄×C₈₉	—	4	1	no	—
76	C₂²×D₄×C₈₉	—	4	1	no	—
77	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
86	C₂×SD₁₆×C₈₉	—	2	2	no	—
87	C₂×SD₁₆×C₈₉	—	4	1	no	—
88	C₂×SD₁₆×C₈₉	—	4	1	no	—
89	C₂×SD₁₆×C₈₉	—	4	1	no	—
90	C₂×M₁₆×C₈₉	—	2	2	no	—
91	C₂×M₁₆×C₈₉	—	2	2	no	—
92	C₂×M₁₆×C₈₉	—	4	1	no	—
93	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
97	#127×C₈₉	—	2	2	no	—
98	#127×C₈₉	—	2	2	no	—
99	#127×C₈₉	—	4	1	no	—
100	#127×C₈₉	—	4	1	no	—
101	C₂²⋊Q₈×C₈₉	—	2	2	no	—
102	C₂²⋊Q₈×C₈₉	D₄	1	4	yes	complemented
103	#121×C₈₉	—	2	2	no	—
104	#121×C₈₉	—	2	2	no	—
105	#120×C₈₉	—	4	4	no	—
106	#120×C₈₉	—	4	4	no	—
107	C₄×Q₈×C₈₉	—	2	2	no	—
108	C₄×Q₈×C₈₉	—	4	1	no	—
109	#117×C₈₉	—	2	2	no	—
110	#117×C₈₉	—	4	1	no	—
111	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
113	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
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×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	D₄	1	1	yes	characteristic
126	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
127	C₂×C₄²×C₈₉	—	2	1	no	—
128	C₂×C₄²×C₈₉	—	2	1	no	—
129	C₂×C₄²×C₈₉	—	2	1	no	—
130	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
132	#107×C₈₉	—	2	2	no	—
133	C₄⋊C₈×C₈₉	—	2	2	no	—
134	C₄⋊C₈×C₈₉	—	4	1	no	—
135	#103×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	—	4	1	no	—
144	#102×C₈₉	D₄	1	4	yes	complemented
145	C₂²⋊C₈×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	D₄	1	1	yes	characteristic
151	#95×C₈₉	D₄	1	1	yes	characteristic
152	C₂⁴×C₈₉	—	2	1	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	—	4	2	no	—
160	C₂⁴×C₈₉	—	8	1	no	—
161	C₂⁴×C₈₉	—	8	1	no	—
162	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
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×Q₈×C₈₉	C₂×D₄	1	2	yes	—
169	C₂×D₄×C₈₉	—	2	8	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	—	2	1	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	—	4	4	no	—
191	C₂×D₄×C₈₉	—	4	2	no	—
192	C₂×D₄×C₈₉	—	4	2	no	—
193	C₂×D₄×C₈₉	—	4	2	no	—
194	C₂×D₄×C₈₉	—	4	2	no	—
195	C₂×D₄×C₈₉	—	4	2	no	—
196	C₂×D₄×C₈₉	—	4	2	no	—
197	C₂×D₄×C₈₉	—	4	2	no	—
198	C₂×D₄×C₈₉	—	4	2	no	—
199	C₂×D₄×C₈₉	—	4	2	no	—
200	C₂×D₄×C₈₉	—	4	2	no	—
201	C₂×D₄×C₈₉	—	4	2	no	—
202	C₂×D₄×C₈₉	—	4	2	no	—
203	C₂×D₄×C₈₉	—	8	1	no	—
204	C₂×D₄×C₈₉	—	8	1	no	—
205	C₂×D₄×C₈₉	—	8	1	no	—
206	C₂×D₄×C₈₉	—	8	1	no	—
207	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
208	C₂×D₄×C₈₉	#41	1	2	yes	—
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	—	2	1	no	—
213	C₂²×C₄×C₈₉	—	2	1	no	—
214	C₂²×C₄×C₈₉	—	2	1	no	—
215	C₂²×C₄×C₈₉	—	2	1	no	—
216	C₂²×C₄×C₈₉	—	2	1	no	—
217	C₂²×C₄×C₈₉	—	2	1	no	—
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	C₂×D₄	1	2	yes	—
222	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₈₉	#41	1	2	yes	—
225	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
226	SD₁₆×C₈₉	—	4	4	no	—
227	SD₁₆×C₈₉	—	4	4	no	—
228	SD₁₆×C₈₉	—	4	4	no	—
229	M₁₆×C₈₉	—	4	4	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	—	2	1	no	—
237	C₂×C₈×C₈₉	—	2	1	no	—
238	C₂×C₈×C₈₉	—	2	1	no	—
239	C₂×C₈×C₈₉	—	2	1	no	—
240	C₂×C₈×C₈₉	—	2	1	no	—
241	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
242	C₄⋊C₄×C₈₉	—	2	4	no	—
243	C₄⋊C₄×C₈₉	—	2	1	no	—
244	C₄⋊C₄×C₈₉	—	2	1	no	—
245	C₄⋊C₄×C₈₉	—	2	1	no	—
246	C₄⋊C₄×C₈₉	—	2	1	no	—
247	C₄⋊C₄×C₈₉	—	2	1	no	—
248	C₄⋊C₄×C₈₉	—	2	1	no	—
249	C₄⋊C₄×C₈₉	—	4	2	no	—
250	C₄⋊C₄×C₈₉	—	4	2	no	—
251	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
252	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
253	C₂²⋊C₄×C₈₉	—	2	4	no	—
254	C₂²⋊C₄×C₈₉	—	2	2	no	—
255	C₂²⋊C₄×C₈₉	—	2	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	—	4	2	no	—
261	C₂²⋊C₄×C₈₉	—	4	2	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	C₄²×C₈₉	—	4	2	no	—
267	C₄²×C₈₉	—	4	2	no	—
268	C₄²×C₈₉	—	4	2	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	—	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	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	—	4	1	no	—
293	C₂³×C₈₉	—	4	1	no	—
294	C₂³×C₈₉	—	4	1	no	—
295	C₂³×C₈₉	—	4	1	no	—
296	C₂³×C₈₉	—	4	1	no	—
297	C₂³×C₈₉	—	8	4	no	—
298	C₂³×C₈₉	—	8	4	no	—
299	C₂³×C₈₉	—	8	4	no	—
300	C₂³×C₈₉	—	8	4	no	—
301	C₂³×C₈₉	—	8	4	no	—
302	C₂³×C₈₉	—	8	4	no	—
303	C₂³×C₈₉	#121	1	2	yes	—
304	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
305	Q₈×C₈₉	—	2	2	no	—
306	Q₈×C₈₉	—	2	2	no	—
307	Q₈×C₈₉	—	4	1	no	—
308	Q₈×C₈₉	—	4	1	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	—	4	1	no	—
319	D₄×C₈₉	—	4	1	no	—
320	D₄×C₈₉	—	4	1	no	—
321	D₄×C₈₉	—	4	1	no	—
322	D₄×C₈₉	—	8	4	no	—
323	D₄×C₈₉	—	8	4	no	—
324	D₄×C₈₉	—	8	4	no	—
325	D₄×C₈₉	—	8	4	no	—
326	D₄×C₈₉	—	8	4	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	2	no	—
334	C₂×C₄×C₈₉	—	2	2	no	—
335	C₂×C₄×C₈₉	—	2	2	no	—
336	C₂×C₄×C₈₉	—	2	2	no	—
337	C₂×C₄×C₈₉	—	2	2	no	—
338	C₂×C₄×C₈₉	—	2	2	no	—
339	C₂×C₄×C₈₉	—	2	1	no	—
340	C₂×C₄×C₈₉	—	2	2	no	—
341	C₂×C₄×C₈₉	—	2	1	no	—
342	C₂×C₄×C₈₉	—	2	1	no	—
343	C₂×C₄×C₈₉	—	2	1	no	—
344	C₂×C₄×C₈₉	—	2	1	no	—
345	C₂×C₄×C₈₉	—	2	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	—	4	1	no	—
355	C₂×C₄×C₈₉	—	4	1	no	—
356	C₂×C₄×C₈₉	—	4	1	no	—
357	C₂×C₄×C₈₉	—	4	1	no	—
358	C₂×C₄×C₈₉	#121	1	2	yes	—
359	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
360	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
361	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
364	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
365	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
366	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
367	C₈×C₈₉	—	2	2	no	—
368	C₈×C₈₉	—	4	1	no	—
369	C₈×C₈₉	—	4	1	no	—
370	C₈×C₈₉	—	4	1	no	—
371	C₂²×C₈₉	—	2	2	no	—
372	C₂²×C₈₉	—	2	2	no	—
373	C₂²×C₈₉	—	2	2	no	—
374	C₂²×C₈₉	—	4	1	no	—
375	C₂²×C₈₉	—	4	1	no	—
376	C₂²×C₈₉	—	4	1	no	—
377	C₂²×C₈₉	—	4	1	no	—
378	C₂²×C₈₉	—	4	2	no	—
379	C₂²×C₈₉	—	4	2	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	—	8	16	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	—	8	1	no	—
395	C₂²×C₈₉	—	8	1	no	—
396	C₂²×C₈₉	—	8	1	no	—
397	C₂²×C₈₉	—	8	1	no	—
398	C₂²×C₈₉	—	8	1	no	—
399	C₂²×C₈₉	—	8	1	no	—
400	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
401	C₂²×C₈₉	D₄²	1	1	yes	characteristic
402	C₂²×C₈₉	#546	1	1	yes	characteristic
403	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
404	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
405	C₂²×C₈₉	#577	1	1	yes	characteristic
406	C₂²×C₈₉	#577	1	1	yes	characteristic
407	C₄×C₈₉	—	2	2	no	—
408	C₄×C₈₉	—	2	2	no	—
409	C₄×C₈₉	—	2	2	no	—
410	C₄×C₈₉	—	4	2	no	—
411	C₄×C₈₉	—	4	1	no	—
412	C₄×C₈₉	—	4	2	no	—
413	C₄×C₈₉	—	4	2	no	—
414	C₄×C₈₉	—	4	1	no	—
415	C₄×C₈₉	—	8	1	no	—
416	C₄×C₈₉	—	8	1	no	—
417	C₄×C₈₉	#525	1	1	yes	characteristic
418	C₄×C₈₉	#538	1	1	yes	characteristic
419	C₄×C₈₉	D₄²	1	1	yes	characteristic
420	C₄×C₈₉	#546	1	1	yes	characteristic
421	#25093	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
422	C₂×C₈₉	—	4	2	no	—
423	C₂×C₈₉	—	8	2	no	—
424	C₂×C₈₉	—	8	2	no	—
425	C₂×C₈₉	—	16	1	no	—
426	C₂×C₈₉	#2424	1	1	yes	characteristic
427	C₂×C₈₉	#3038	1	1	yes	characteristic
428	C₂×C₈₉	#3043	1	1	yes	characteristic
429	C₂×C₈₉	#3265	1	1	yes	characteristic
430	C₂×C₈₉	#3272	1	1	yes	characteristic
431	C₂×C₈₉	#3310	1	1	yes	characteristic
432	C₂×C₈₉	#3324	1	1	yes	characteristic
433	C₂×#468	C₂×C₈₉	1	1	yes	characteristic, complemented
434	C₂×#460	C₂×C₈₉	1	1	yes	characteristic, complemented
435	C₂×#450	C₂×C₈₉	1	1	yes	characteristic, complemented
436	C₂×#418	C₂×C₈₉	1	1	yes	characteristic, complemented
437	#2433	C₂×C₈₉	1	1	yes	characteristic
438	#2362	C₂×C₈₉	1	1	yes	characteristic, complemented
439	#2067	C₂×C₈₉	1	1	yes	characteristic, complemented
440	#2055	C₂×C₈₉	1	1	yes	characteristic, complemented
441	#2041	C₂×C₈₉	1	1	yes	characteristic, complemented
442	#2014	C₂×C₈₉	1	1	yes	characteristic, complemented
443	#1982	C₂×C₈₉	1	1	yes	characteristic, complemented
444	#1925	C₂×C₈₉	1	1	yes	characteristic, complemented
445	#1880	C₂×C₈₉	1	1	yes	characteristic, complemented
446	#1875	C₂×C₈₉	1	1	yes	characteristic, complemented
447	#1851	C₂×C₈₉	1	1	yes	characteristic, complemented
448	C₈₉	#25093	1	1	yes	characteristic, direct product factor, Sylow
449	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
450	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
451	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
452	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
453	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
454	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
455	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
456	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
457	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
458	C₂×#120	—	2	1	no	—
459	C₂×#120	—	2	1	no	—
460	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
461	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
462	#468	—	2	4	no	—
463	#460	—	2	4	no	—
464	#450	—	2	4	no	—
465	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic, complemented
466	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
467	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
468	#418	—	2	4	no	—
469	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
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
473	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
474	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
475	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
476	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
477	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
478	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
479	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
480	#392	—	2	1	no	—
481	#392	—	2	1	no	—
482	#391	C₂²×C₈₉	1	1	yes	characteristic, complemented
483	#390	C₂²×C₈₉	1	1	yes	characteristic
484	#390	C₂²×C₈₉	1	1	yes	characteristic
485	#389	C₂²×C₈₉	1	1	yes	characteristic, complemented
486	#388	—	2	1	no	—
487	#388	—	2	1	no	—
488	#387	—	2	1	no	—
489	C₄×C₄⋊C₄	—	2	1	no	—
490	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
491	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
492	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
493	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
494	#336	C₂²×C₈₉	1	1	yes	characteristic, complemented
495	#336	C₂²×C₈₉	1	1	yes	characteristic, complemented
496	C₂⁵	—	2	1	no	—
497	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
498	C₂²×D₄	—	2	2	no	—
499	C₂²×D₄	—	2	2	no	—
500	C₂²×D₄	—	2	1	no	—
501	C₂²×D₄	—	2	2	no	—
502	C₂²×D₄	—	2	1	no	—
503	C₂²×D₄	—	2	1	no	—
504	C₂²×D₄	—	2	1	no	—
505	C₂²×D₄	—	2	1	no	—
506	C₂²×D₄	—	2	1	no	—
507	C₂²×D₄	—	2	2	no	—
508	C₂²×D₄	—	4	1	no	—
509	C₂²×D₄	—	4	1	no	—
510	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
511	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
512	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
514	C₂×SD₁₆	—	2	2	no	—
515	C₂×SD₁₆	—	2	2	no	—
516	C₂×SD₁₆	—	2	2	no	—
517	C₂×SD₁₆	—	2	2	no	—
518	C₂×SD₁₆	—	2	2	no	—
519	C₂×SD₁₆	—	2	2	no	—
520	C₂×SD₁₆	—	4	1	no	—
521	C₂×SD₁₆	—	4	1	no	—
522	C₂×SD₁₆	—	4	1	no	—
523	C₂×M₁₆	—	2	2	no	—
524	C₂×M₁₆	—	2	2	no	—
525	C₂×M₁₆	—	4	1	no	—
526	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
527	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
528	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
529	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
530	#127	—	2	2	no	—
531	#127	—	2	2	no	—
532	#127	—	4	1	no	—
533	#127	—	4	1	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	C₂²⋊Q₈	D₄×C₈₉	1	4	yes	complemented
536	#121	—	2	2	no	—
537	#121	—	2	2	no	—
538	#120	—	4	4	no	—
539	#120	—	4	4	no	—
540	C₄×Q₈	—	2	2	no	—
541	C₄×Q₈	—	4	1	no	—
542	#117	—	2	2	no	—
543	#117	—	4	1	no	—
544	C₂×C₄⋊C₄	—	2	1	no	—
545	C₂×C₄⋊C₄	—	2	1	no	—
546	C₂×C₄⋊C₄	—	2	1	no	—
547	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	—	2	1	no	—
557	C₂×C₂²⋊C₄	—	2	1	no	—
558	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
559	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
560	C₂×C₄²	—	2	1	no	—
561	C₂×C₄²	—	2	1	no	—
562	C₂×C₄²	—	2	1	no	—
563	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
564	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
565	#107	—	2	2	no	—
566	C₄⋊C₈	—	2	2	no	—
567	C₄⋊C₈	—	4	1	no	—
568	#103	—	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	—	2	2	no	—
574	#102	—	2	2	no	—
575	#102	—	2	2	no	—
576	#102	—	4	1	no	—
577	#102	D₄×C₈₉	1	4	yes	complemented
578	C₂²⋊C₈	—	2	2	no	—
579	#95	—	2	1	no	—
580	#95	—	2	1	no	—
581	#95	—	2	1	no	—
582	#95	—	2	1	no	—
583	#95	D₄×C₈₉	1	1	yes	characteristic
584	#95	D₄×C₈₉	1	1	yes	characteristic
585	C₂⁴	—	2	1	no	—
586	C₂⁴	—	2	1	no	—
587	C₂⁴	—	2	1	no	—
588	C₂⁴	—	4	2	no	—
589	C₂⁴	—	4	2	no	—
590	C₂⁴	—	4	2	no	—
591	C₂⁴	—	4	2	no	—
592	C₂⁴	—	4	2	no	—
593	C₂⁴	—	8	1	no	—
594	C₂⁴	—	8	1	no	—
595	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
596	C₂×Q₈	—	2	1	no	—
597	C₂×Q₈	—	2	1	no	—
598	C₂×Q₈	—	2	1	no	—
599	C₂×Q₈	—	2	1	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
602	C₂×D₄	—	2	8	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	—	2	1	no	—
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	4	4	no	—
620	C₂×D₄	—	4	4	no	—
621	C₂×D₄	—	4	2	no	—
622	C₂×D₄	—	4	2	no	—
623	C₂×D₄	—	4	4	no	—
624	C₂×D₄	—	4	2	no	—
625	C₂×D₄	—	4	2	no	—
626	C₂×D₄	—	4	2	no	—
627	C₂×D₄	—	4	2	no	—
628	C₂×D₄	—	4	2	no	—
629	C₂×D₄	—	4	2	no	—
630	C₂×D₄	—	4	2	no	—
631	C₂×D₄	—	4	2	no	—
632	C₂×D₄	—	4	2	no	—
633	C₂×D₄	—	4	2	no	—
634	C₂×D₄	—	4	2	no	—
635	C₂×D₄	—	4	2	no	—
636	C₂×D₄	—	8	1	no	—
637	C₂×D₄	—	8	1	no	—
638	C₂×D₄	—	8	1	no	—
639	C₂×D₄	—	8	1	no	—
640	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
641	C₂×D₄	#41×C₈₉	1	2	yes	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
652	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
653	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
654	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
655	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
657	C₂²×C₄	#41×C₈₉	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
659	SD₁₆	—	4	4	no	—
660	SD₁₆	—	4	4	no	—
661	SD₁₆	—	4	4	no	—
662	M₁₆	—	4	4	no	—
663	C₂×C₈	—	2	1	no	—
664	C₂×C₈	—	2	1	no	—
665	C₂×C₈	—	2	1	no	—
666	C₂×C₈	—	2	1	no	—
667	C₂×C₈	—	2	1	no	—
668	C₂×C₈	—	2	1	no	—
669	C₂×C₈	—	2	1	no	—
670	C₂×C₈	—	2	1	no	—
671	C₂×C₈	—	2	1	no	—
672	C₂×C₈	—	2	1	no	—
673	C₂×C₈	—	2	1	no	—
674	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	4	2	no	—
683	C₄⋊C₄	—	4	2	no	—
684	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
685	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	2	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	4	2	no	—
690	C₂²⋊C₄	—	4	2	no	—
691	C₂²⋊C₄	—	4	2	no	—
692	C₂²⋊C₄	—	4	2	no	—
693	C₂²⋊C₄	—	4	2	no	—
694	C₂²⋊C₄	—	4	2	no	—
695	C₄²	—	2	1	no	—
696	C₄²	—	2	1	no	—
697	C₄²	—	2	1	no	—
698	C₄²	—	2	1	no	—
699	C₄²	—	4	2	no	—
700	C₄²	—	4	2	no	—
701	C₄²	—	4	2	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	1	no	—
706	C₂³	—	2	1	no	—
707	C₂³	—	2	1	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	4	8	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	—	4	1	no	—
725	C₂³	—	4	1	no	—
726	C₂³	—	4	1	no	—
727	C₂³	—	4	1	no	—
728	C₂³	—	4	1	no	—
729	C₂³	—	4	1	no	—
730	C₂³	—	8	4	no	—
731	C₂³	—	8	4	no	—
732	C₂³	—	8	4	no	—
733	C₂³	—	8	4	no	—
734	C₂³	—	8	4	no	—
735	C₂³	—	8	4	no	—
736	C₂³	#121×C₈₉	1	2	yes	—
737	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
738	Q₈	—	2	2	no	—
739	Q₈	—	2	2	no	—
740	Q₈	—	4	1	no	—
741	Q₈	—	4	1	no	—
742	D₄	—	2	2	no	—
743	D₄	—	2	2	no	—
744	D₄	—	2	2	no	—
745	D₄	—	2	2	no	—
746	D₄	—	4	8	no	—
747	D₄	—	4	1	no	—
748	D₄	—	4	1	no	—
749	D₄	—	4	1	no	—
750	D₄	—	4	1	no	—
751	D₄	—	4	1	no	—
752	D₄	—	4	1	no	—
753	D₄	—	4	1	no	—
754	D₄	—	4	1	no	—
755	D₄	—	8	4	no	—
756	D₄	—	8	4	no	—
757	D₄	—	8	4	no	—
758	D₄	—	8	4	no	—
759	D₄	—	8	4	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	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	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	—	4	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	#121×C₈₉	1	2	yes	—
792	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
793	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
794	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
795	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
796	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
797	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
798	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
799	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
800	C₈	—	2	2	no	—
801	C₈	—	4	1	no	—
802	C₈	—	4	1	no	—
803	C₈	—	4	1	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	2	2	no	—
806	C₂²	—	2	2	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	1	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	—	4	2	no	—
817	C₂²	—	8	16	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	—	8	1	no	—
826	C₂²	—	8	1	no	—
827	C₂²	—	8	1	no	—
828	C₂²	—	8	1	no	—
829	C₂²	—	8	1	no	—
830	C₂²	—	8	1	no	—
831	C₂²	—	8	1	no	—
832	C₂²	—	8	1	no	—
833	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
834	C₂²	D₄²×C₈₉	1	1	yes	characteristic
835	C₂²	#546×C₈₉	1	1	yes	characteristic
836	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
837	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
838	C₂²	#577×C₈₉	1	1	yes	characteristic
839	C₂²	#577×C₈₉	1	1	yes	characteristic
840	C₄	—	2	2	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	4	1	no	—
844	C₄	—	4	2	no	—
845	C₄	—	4	1	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	2	no	—
848	C₄	—	8	1	no	—
849	C₄	—	8	1	no	—
850	C₄	#525×C₈₉	1	1	yes	characteristic
851	C₄	#538×C₈₉	1	1	yes	characteristic
852	C₄	D₄²×C₈₉	1	1	yes	characteristic
853	C₄	#546×C₈₉	1	1	yes	characteristic
854	C₂	—	4	2	no	—
855	C₂	—	8	2	no	—
856	C₂	—	8	2	no	—
857	C₂	—	16	1	no	—
858	C₂	C₈₉×#2424	1	1	yes	characteristic
859	C₂	C₈₉×#3038	1	1	yes	characteristic
860	C₂	C₈₉×#3043	1	1	yes	characteristic
861	C₂	C₈₉×#3265	1	1	yes	characteristic
862	C₂	C₈₉×#3272	1	1	yes	characteristic
863	C₂	C₈₉×#3310	1	1	yes	characteristic
864	C₂	C₈₉×#3324	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₈₉×#2433	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×#468×C₈₉	C₂	semidirect
2. C₂×#460×C₈₉	C₂	semidirect
3. C₂×#450×C₈₉	C₂	semidirect
4. C₂×#418×C₈₉	C₂	semidirect
6. C₈₉×#2362	C₂	semidirect
7. C₈₉×#2067	C₂	semidirect
8. C₈₉×#2055	C₂	semidirect
9. C₈₉×#2041	C₂	semidirect
10. C₈₉×#2014	C₂	semidirect
11. C₈₉×#1982	C₂	semidirect
12. C₈₉×#1925	C₂	semidirect
13. C₈₉×#1880	C₂	semidirect
14. C₈₉×#1875	C₂	semidirect
15. C₈₉×#1851	C₂	semidirect
19. C₂²×SD₁₆×C₈₉	C₂²	semidirect
27. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
32. C₂×#107×C₈₉	C₂²	semidirect
33. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
34. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
36. C₂×#103×C₈₉	C₂²	semidirect
43. C₂×#102×C₈₉	C₂²	semidirect
44. C₂×#102×C₈₉	C₂²	semidirect
45. C₂×#102×C₈₉	C₂²	semidirect
49. #391×C₈₉	C₂²	semidirect
52. #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
102. C₂²⋊Q₈×C₈₉	D₄	semidirect
144. #102×C₈₉	D₄	semidirect
421. #25093	C₈₉	direct (N × H)
433. C₂×#468	C₂×C₈₉	semidirect
434. C₂×#460	C₂×C₈₉	semidirect
435. C₂×#450	C₂×C₈₉	semidirect
436. C₂×#418	C₂×C₈₉	semidirect
438. #2362	C₂×C₈₉	semidirect
439. #2067	C₂×C₈₉	semidirect
440. #2055	C₂×C₈₉	semidirect
441. #2041	C₂×C₈₉	semidirect
442. #2014	C₂×C₈₉	semidirect
443. #1982	C₂×C₈₉	semidirect
444. #1925	C₂×C₈₉	semidirect
445. #1880	C₂×C₈₉	semidirect
446. #1875	C₂×C₈₉	semidirect
447. #1851	C₂×C₈₉	semidirect
448. C₈₉	#25093	direct (N × H)
452. C₂²×SD₁₆	C₂²×C₈₉	semidirect
460. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
465. C₂×#107	C₂²×C₈₉	semidirect
466. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
467. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
469. C₂×#103	C₂²×C₈₉	semidirect
476. C₂×#102	C₂²×C₈₉	semidirect
477. C₂×#102	C₂²×C₈₉	semidirect
478. C₂×#102	C₂²×C₈₉	semidirect
482. #391	C₂²×C₈₉	semidirect
485. #389	C₂²×C₈₉	semidirect
490. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
492. #340	C₂²×C₈₉	semidirect
493. #340	C₂²×C₈₉	semidirect
494. #336	C₂²×C₈₉	semidirect
495. #336	C₂²×C₈₉	semidirect
535. C₂²⋊Q₈	D₄×C₈₉	semidirect
577. #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×#468×C₈₉	2
C₂×#460×C₈₉	2
C₂×#450×C₈₉	2
C₂×#418×C₈₉	2
C₈₉×#2433	2
C₈₉×#2362	2
C₈₉×#2067	2
C₈₉×#2055	2
C₈₉×#2041	2
C₈₉×#2014	2
C₈₉×#1982	2
C₈₉×#1925	2
C₈₉×#1880	2
C₈₉×#1875	2
C₈₉×#1851	2
#25093	89

Subgroups — C89×#25093 #36402941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25093 #36402941