Subgroups — C₈₉×#21772 #36399620

Order 22784.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#537×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#408×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2311	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#1895	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#1894	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1892	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1875	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1872	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1824	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1823	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1788	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1788	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×#41×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	#537×C₈₉	—	2	4	no	—
21	#537×C₈₉	C₄	1	8	yes	complemented
22	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
23	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#121×C₈₉	—	2	1	no	—
26	C₂×#121×C₈₉	—	2	1	no	—
27	C₂×#121×C₈₉	—	2	1	no	—
28	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#103×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
40	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
41	#408×C₈₉	—	2	4	no	—
42	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
46	#391×C₈₉	—	2	1	no	—
47	#390×C₈₉	—	2	1	no	—
48	#386×C₈₉	—	2	1	no	—
49	#386×C₈₉	—	2	1	no	—
50	#380×C₈₉	C₂²	1	1	yes	characteristic
51	#380×C₈₉	C₂²	1	1	yes	characteristic
52	#380×C₈₉	C₂²	1	1	yes	characteristic
53	#380×C₈₉	C₂²	1	1	yes	characteristic
54	#340×C₈₉	C₂²	1	1	yes	characteristic
55	#340×C₈₉	C₂²	1	1	yes	characteristic
56	#340×C₈₉	C₂²	1	1	yes	characteristic
57	#340×C₈₉	C₂²	1	1	yes	characteristic
58	#340×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	C₂×#41×C₈₉	—	2	2	no	—
63	C₂×#41×C₈₉	—	4	1	no	—
64	C₂×#41×C₈₉	—	4	1	no	—
65	C₂×#41×C₈₉	—	4	1	no	—
66	C₂×#41×C₈₉	—	4	1	no	—
67	C₂×#41×C₈₉	—	4	1	no	—
68	C₂×#41×C₈₉	—	4	1	no	—
69	C₂×#41×C₈₉	—	4	1	no	—
70	C₂×#41×C₈₉	—	4	1	no	—
71	C₂×#41×C₈₉	C₂×C₄	1	4	yes	—
72	C₂×#41×C₈₉	C₂×C₄	1	4	yes	complemented
73	C₂×#41×C₈₉	D₄	1	4	yes	—
74	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
75	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₈₉	—	2	1	no	—
77	C₂²×D₄×C₈₉	—	2	1	no	—
78	C₂²×D₄×C₈₉	—	2	1	no	—
79	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
80	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
81	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
82	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₈₉	—	2	1	no	—
84	C₂³×C₄×C₈₉	—	2	1	no	—
85	C₂³×C₄×C₈₉	—	2	1	no	—
86	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
89	C₂×M₁₆×C₈₉	—	2	2	no	—
90	C₂×M₁₆×C₈₉	—	4	1	no	—
91	C₂×M₁₆×C₈₉	—	4	1	no	—
92	C₂²×C₈×C₈₉	—	2	2	no	—
93	C₂²×C₈×C₈₉	—	4	1	no	—
94	C₂²×C₈×C₈₉	—	4	1	no	—
95	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
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⋊Q₈×C₈₉	—	2	8	no	—
100	C₂²⋊Q₈×C₈₉	—	2	2	no	—
101	C₂²⋊Q₈×C₈₉	—	2	2	no	—
102	C₂²⋊Q₈×C₈₉	C₂×C₄	1	4	yes	—
103	C₂²⋊Q₈×C₈₉	C₂×C₄	1	4	yes	complemented
104	#121×C₈₉	—	2	8	no	—
105	#121×C₈₉	—	2	8	no	—
106	#121×C₈₉	—	2	8	no	—
107	#121×C₈₉	—	2	2	no	—
108	#121×C₈₉	—	2	2	no	—
109	#121×C₈₉	C₂×C₄	1	4	yes	—
110	#121×C₈₉	C₂×C₄	1	4	yes	complemented
111	#117×C₈₉	—	4	1	no	—
112	#117×C₈₉	—	4	1	no	—
113	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
114	C₂×C₄⋊C₄×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	—	2	1	no	—
118	C₂×C₄⋊C₄×C₈₉	—	4	1	no	—
119	C₂×C₄⋊C₄×C₈₉	—	4	1	no	—
120	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	4	yes	complemented
121	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
131	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
133	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
134	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
135	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
136	C₂×C₄²×C₈₉	—	2	1	no	—
137	#103×C₈₉	—	4	1	no	—
138	#103×C₈₉	—	4	1	no	—
139	#103×C₈₉	—	4	1	no	—
140	#103×C₈₉	—	4	1	no	—
141	#102×C₈₉	—	4	1	no	—
142	#102×C₈₉	—	4	1	no	—
143	#102×C₈₉	—	4	1	no	—
144	#102×C₈₉	—	4	1	no	—
145	C₂²⋊C₈×C₈₉	—	2	2	no	—
146	C₂²⋊C₈×C₈₉	—	2	2	no	—
147	C₂²⋊C₈×C₈₉	—	2	2	no	—
148	C₂²⋊C₈×C₈₉	—	2	2	no	—
149	#95×C₈₉	—	2	1	no	—
150	#95×C₈₉	—	2	1	no	—
151	#95×C₈₉	—	2	1	no	—
152	#95×C₈₉	—	2	1	no	—
153	C₂⁴×C₈₉	—	2	1	no	—
154	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
156	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
157	#41×C₈₉	—	4	4	no	—
158	#41×C₈₉	—	4	4	no	—
159	#41×C₈₉	—	4	4	no	—
160	#41×C₈₉	—	4	4	no	—
161	#41×C₈₉	—	4	4	no	—
162	#41×C₈₉	—	4	4	no	—
163	#41×C₈₉	—	4	4	no	—
164	#41×C₈₉	—	4	4	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	—	2	1	no	—
169	C₂×Q₈×C₈₉	—	2	1	no	—
170	C₂×Q₈×C₈₉	—	4	1	no	—
171	C₂×Q₈×C₈₉	—	4	1	no	—
172	C₂×Q₈×C₈₉	C₂²⋊C₄	1	4	yes	—
173	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
174	C₂×D₄×C₈₉	—	2	4	no	—
175	C₂×D₄×C₈₉	—	2	4	no	—
176	C₂×D₄×C₈₉	—	2	4	no	—
177	C₂×D₄×C₈₉	—	2	1	no	—
178	C₂×D₄×C₈₉	—	2	1	no	—
179	C₂×D₄×C₈₉	—	2	1	no	—
180	C₂×D₄×C₈₉	—	2	1	no	—
181	C₂×D₄×C₈₉	—	2	1	no	—
182	C₂×D₄×C₈₉	—	4	1	no	—
183	C₂×D₄×C₈₉	—	4	1	no	—
184	C₂×D₄×C₈₉	—	4	1	no	—
185	C₂×D₄×C₈₉	—	4	1	no	—
186	C₂×D₄×C₈₉	—	4	1	no	—
187	C₂×D₄×C₈₉	—	4	1	no	—
188	C₂×D₄×C₈₉	—	4	2	no	—
189	C₂×D₄×C₈₉	—	4	2	no	—
190	C₂×D₄×C₈₉	—	8	1	no	—
191	C₂×D₄×C₈₉	—	8	1	no	—
192	C₂×D₄×C₈₉	—	8	1	no	—
193	C₂×D₄×C₈₉	—	8	1	no	—
194	C₂×D₄×C₈₉	C₂²⋊C₄	1	4	yes	—
195	C₂×D₄×C₈₉	C₂²⋊C₄	1	4	yes	—
196	C₂×D₄×C₈₉	C₂²⋊C₄	1	4	yes	—
197	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
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	—	2	1	no	—
213	C₂²×C₄×C₈₉	—	2	4	no	—
214	C₂²×C₄×C₈₉	—	2	4	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	—	2	1	no	—
219	C₂²×C₄×C₈₉	—	4	2	no	—
220	C₂²×C₄×C₈₉	—	4	2	no	—
221	C₂²×C₄×C₈₉	—	4	2	no	—
222	C₂²×C₄×C₈₉	—	8	1	no	—
223	C₂²×C₄×C₈₉	—	8	1	no	—
224	C₂²×C₄×C₈₉	—	8	1	no	—
225	C₂²×C₄×C₈₉	—	8	1	no	—
226	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
227	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
228	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
229	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
233	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
234	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
235	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
236	M₁₆×C₈₉	—	4	4	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	—	2	1	no	—
242	C₂×C₈×C₈₉	—	2	1	no	—
243	C₂×C₈×C₈₉	—	2	1	no	—
244	C₂×C₈×C₈₉	—	2	1	no	—
245	C₂×C₈×C₈₉	—	2	1	no	—
246	C₂×C₈×C₈₉	—	2	1	no	—
247	C₂×C₈×C₈₉	—	2	1	no	—
248	C₂×C₈×C₈₉	—	2	1	no	—
249	C₂×C₈×C₈₉	—	4	4	no	—
250	C₄⋊C₄×C₈₉	—	2	4	no	—
251	C₄⋊C₄×C₈₉	—	2	4	no	—
252	C₄⋊C₄×C₈₉	—	2	4	no	—
253	C₄⋊C₄×C₈₉	—	2	1	no	—
254	C₄⋊C₄×C₈₉	—	2	1	no	—
255	C₄⋊C₄×C₈₉	—	2	1	no	—
256	C₄⋊C₄×C₈₉	—	2	1	no	—
257	C₄⋊C₄×C₈₉	—	2	1	no	—
258	C₄⋊C₄×C₈₉	—	2	1	no	—
259	C₄⋊C₄×C₈₉	—	2	1	no	—
260	C₄⋊C₄×C₈₉	—	2	1	no	—
261	C₄⋊C₄×C₈₉	—	2	1	no	—
262	C₄⋊C₄×C₈₉	—	2	1	no	—
263	C₄⋊C₄×C₈₉	—	4	2	no	—
264	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
265	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
266	C₂²⋊C₄×C₈₉	—	2	4	no	—
267	C₂²⋊C₄×C₈₉	—	2	4	no	—
268	C₂²⋊C₄×C₈₉	—	2	4	no	—
269	C₂²⋊C₄×C₈₉	—	2	4	no	—
270	C₂²⋊C₄×C₈₉	—	4	2	no	—
271	C₂²⋊C₄×C₈₉	—	8	1	no	—
272	C₂²⋊C₄×C₈₉	—	8	1	no	—
273	C₂²⋊C₄×C₈₉	—	8	1	no	—
274	C₂²⋊C₄×C₈₉	—	8	1	no	—
275	C₄²×C₈₉	—	4	2	no	—
276	C₂³×C₈₉	—	2	1	no	—
277	C₂³×C₈₉	—	2	1	no	—
278	C₂³×C₈₉	—	2	1	no	—
279	C₂³×C₈₉	—	2	1	no	—
280	C₂³×C₈₉	—	2	1	no	—
281	C₂³×C₈₉	—	2	1	no	—
282	C₂³×C₈₉	—	2	1	no	—
283	C₂³×C₈₉	—	2	1	no	—
284	C₂³×C₈₉	—	2	1	no	—
285	C₂³×C₈₉	—	2	1	no	—
286	C₂³×C₈₉	—	2	1	no	—
287	C₂³×C₈₉	—	2	1	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	1	no	—
293	C₂³×C₈₉	—	2	1	no	—
294	C₂³×C₈₉	—	2	2	no	—
295	C₂³×C₈₉	—	4	1	no	—
296	C₂³×C₈₉	—	4	1	no	—
297	C₂³×C₈₉	—	4	1	no	—
298	C₂³×C₈₉	—	4	1	no	—
299	C₂³×C₈₉	—	4	1	no	—
300	C₂³×C₈₉	—	4	1	no	—
301	C₂³×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
302	C₂³×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
303	C₂³×C₈₉	C₂×C₂²⋊C₄	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	4	no	—
308	Q₈×C₈₉	—	4	1	no	—
309	Q₈×C₈₉	—	4	1	no	—
310	D₄×C₈₉	—	2	2	no	—
311	D₄×C₈₉	—	2	2	no	—
312	D₄×C₈₉	—	4	4	no	—
313	D₄×C₈₉	—	4	4	no	—
314	D₄×C₈₉	—	4	4	no	—
315	D₄×C₈₉	—	4	8	no	—
316	D₄×C₈₉	—	4	1	no	—
317	D₄×C₈₉	—	4	1	no	—
318	D₄×C₈₉	—	8	4	no	—
319	D₄×C₈₉	—	8	4	no	—
320	C₂×C₄×C₈₉	—	2	1	no	—
321	C₂×C₄×C₈₉	—	2	1	no	—
322	C₂×C₄×C₈₉	—	2	1	no	—
323	C₂×C₄×C₈₉	—	2	1	no	—
324	C₂×C₄×C₈₉	—	2	1	no	—
325	C₂×C₄×C₈₉	—	2	1	no	—
326	C₂×C₄×C₈₉	—	2	2	no	—
327	C₂×C₄×C₈₉	—	2	2	no	—
328	C₂×C₄×C₈₉	—	2	2	no	—
329	C₂×C₄×C₈₉	—	2	2	no	—
330	C₂×C₄×C₈₉	—	2	2	no	—
331	C₂×C₄×C₈₉	—	2	2	no	—
332	C₂×C₄×C₈₉	—	2	2	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	2	no	—
340	C₂×C₄×C₈₉	—	2	2	no	—
341	C₂×C₄×C₈₉	—	4	8	no	—
342	C₂×C₄×C₈₉	—	4	1	no	—
343	C₂×C₄×C₈₉	—	4	1	no	—
344	C₂×C₄×C₈₉	—	4	1	no	—
345	C₂×C₄×C₈₉	—	4	1	no	—
346	C₂×C₄×C₈₉	—	4	1	no	—
347	C₂×C₄×C₈₉	—	4	1	no	—
348	C₂×C₄×C₈₉	—	4	1	no	—
349	C₂×C₄×C₈₉	—	4	1	no	—
350	C₂×C₄×C₈₉	—	4	1	no	—
351	C₂×C₄×C₈₉	—	4	1	no	—
352	C₂×C₄×C₈₉	—	4	1	no	—
353	C₂×C₄×C₈₉	—	4	1	no	—
354	C₂×C₄×C₈₉	—	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	—	4	1	no	—
359	C₂×C₄×C₈₉	—	4	1	no	—
360	C₂×C₄×C₈₉	—	8	4	no	—
361	C₂×C₄×C₈₉	—	8	4	no	—
362	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
363	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
364	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
365	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
366	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
368	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
369	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
370	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
371	C₈×C₈₉	—	4	1	no	—
372	C₈×C₈₉	—	4	1	no	—
373	C₈×C₈₉	—	4	1	no	—
374	C₈×C₈₉	—	4	1	no	—
375	C₂²×C₈₉	—	2	2	no	—
376	C₂²×C₈₉	—	2	2	no	—
377	C₂²×C₈₉	—	2	2	no	—
378	C₂²×C₈₉	—	2	2	no	—
379	C₂²×C₈₉	—	2	2	no	—
380	C₂²×C₈₉	—	2	2	no	—
381	C₂²×C₈₉	—	2	2	no	—
382	C₂²×C₈₉	—	2	2	no	—
383	C₂²×C₈₉	—	2	2	no	—
384	C₂²×C₈₉	—	4	1	no	—
385	C₂²×C₈₉	—	4	1	no	—
386	C₂²×C₈₉	—	4	1	no	—
387	C₂²×C₈₉	—	4	1	no	—
388	C₂²×C₈₉	—	4	1	no	—
389	C₂²×C₈₉	—	4	1	no	—
390	C₂²×C₈₉	—	4	1	no	—
391	C₂²×C₈₉	—	4	1	no	—
392	C₂²×C₈₉	—	4	1	no	—
393	C₂²×C₈₉	—	4	1	no	—
394	C₂²×C₈₉	—	4	1	no	—
395	C₂²×C₈₉	—	4	1	no	—
396	C₂²×C₈₉	—	4	2	no	—
397	C₂²×C₈₉	—	4	2	no	—
398	C₂²×C₈₉	—	4	2	no	—
399	C₂²×C₈₉	—	8	1	no	—
400	C₂²×C₈₉	—	8	1	no	—
401	C₂²×C₈₉	—	8	1	no	—
402	C₂²×C₈₉	—	8	1	no	—
403	C₂²×C₈₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
404	C₂²×C₈₉	#534	1	1	yes	characteristic
405	C₂²×C₈₉	#534	1	1	yes	characteristic
406	C₂²×C₈₉	#576	1	1	yes	characteristic
407	C₂²×C₈₉	#577	1	1	yes	characteristic
408	C₂²×C₈₉	#577	1	1	yes	characteristic
409	C₂²×C₈₉	#578	1	1	yes	characteristic
410	C₄×C₈₉	—	2	2	no	—
411	C₄×C₈₉	—	2	2	no	—
412	C₄×C₈₉	—	2	2	no	—
413	C₄×C₈₉	—	4	2	no	—
414	C₄×C₈₉	—	4	2	no	—
415	C₄×C₈₉	—	4	2	no	—
416	C₄×C₈₉	—	8	1	no	—
417	C₄×C₈₉	—	8	1	no	—
418	C₄×C₈₉	—	8	1	no	—
419	C₄×C₈₉	—	8	1	no	—
420	C₄×C₈₉	#518	1	1	yes	characteristic
421	C₄×C₈₉	#518	1	1	yes	characteristic
422	C₄×C₈₉	#534	1	1	yes	characteristic
423	C₄×C₈₉	#534	1	1	yes	characteristic
424	#21772	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
425	C₂×C₈₉	—	4	2	no	—
426	C₂×C₈₉	—	4	2	no	—
427	C₂×C₈₉	—	4	2	no	—
428	C₂×C₈₉	—	8	2	no	—
429	C₂×C₈₉	#2308	1	1	yes	characteristic
430	C₂×C₈₉	#2897	1	1	yes	characteristic
431	C₂×C₈₉	#2898	1	1	yes	characteristic
432	C₂×C₈₉	#3198	1	1	yes	characteristic
433	C₂×C₈₉	#3201	1	1	yes	characteristic
434	C₂×C₈₉	#3203	1	1	yes	characteristic
435	C₂×C₈₉	#3204	1	1	yes	characteristic
436	C₂×#537	C₂×C₈₉	1	1	yes	characteristic
437	C₂×#408	C₂×C₈₉	1	1	yes	characteristic, complemented
438	#2311	C₂×C₈₉	1	1	yes	characteristic, complemented
439	#1895	C₂×C₈₉	1	1	yes	characteristic, complemented
440	#1894	C₂×C₈₉	1	1	yes	characteristic, complemented
441	#1893	C₂×C₈₉	1	1	yes	characteristic, complemented
442	#1892	C₂×C₈₉	1	1	yes	characteristic, complemented
443	#1875	C₂×C₈₉	1	1	yes	characteristic, complemented
444	#1874	C₂×C₈₉	1	1	yes	characteristic, complemented
445	#1873	C₂×C₈₉	1	1	yes	characteristic, complemented
446	#1872	C₂×C₈₉	1	1	yes	characteristic, complemented
447	#1824	C₂×C₈₉	1	1	yes	characteristic, complemented
448	#1823	C₂×C₈₉	1	1	yes	characteristic, complemented
449	#1788	C₂×C₈₉	1	1	yes	characteristic, complemented
450	#1788	C₂×C₈₉	1	1	yes	characteristic, complemented
451	C₈₉	#21772	1	1	yes	characteristic, direct product factor, Sylow
452	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
453	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
454	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
455	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
456	#537	—	2	4	no	—
457	#537	C₄×C₈₉	1	8	yes	complemented
458	C₂×C₂²⋊Q₈	—	2	1	no	—
459	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
460	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
461	C₂×#121	—	2	1	no	—
462	C₂×#121	—	2	1	no	—
463	C₂×#121	—	2	1	no	—
464	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
465	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
466	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
467	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
468	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
469	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
470	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
471	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
472	C₂×#103	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
477	#408	—	2	4	no	—
478	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
479	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
480	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
481	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
482	#391	—	2	1	no	—
483	#390	—	2	1	no	—
484	#386	—	2	1	no	—
485	#386	—	2	1	no	—
486	#380	C₂²×C₈₉	1	1	yes	characteristic
487	#380	C₂²×C₈₉	1	1	yes	characteristic
488	#380	C₂²×C₈₉	1	1	yes	characteristic
489	#380	C₂²×C₈₉	1	1	yes	characteristic
490	#340	C₂²×C₈₉	1	1	yes	characteristic
491	#340	C₂²×C₈₉	1	1	yes	characteristic
492	#340	C₂²×C₈₉	1	1	yes	characteristic
493	#340	C₂²×C₈₉	1	1	yes	characteristic
494	#340	C₂²×C₈₉	1	1	yes	characteristic
495	#340	C₂²×C₈₉	1	1	yes	characteristic
496	#340	C₂²×C₈₉	1	1	yes	characteristic
497	#340	C₂²×C₈₉	1	1	yes	characteristic
498	C₂×#41	—	2	2	no	—
499	C₂×#41	—	4	1	no	—
500	C₂×#41	—	4	1	no	—
501	C₂×#41	—	4	1	no	—
502	C₂×#41	—	4	1	no	—
503	C₂×#41	—	4	1	no	—
504	C₂×#41	—	4	1	no	—
505	C₂×#41	—	4	1	no	—
506	C₂×#41	—	4	1	no	—
507	C₂×#41	C₂×C₄×C₈₉	1	4	yes	—
508	C₂×#41	C₂×C₄×C₈₉	1	4	yes	complemented
509	C₂×#41	D₄×C₈₉	1	4	yes	—
510	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
511	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
512	C₂²×D₄	—	2	1	no	—
513	C₂²×D₄	—	2	1	no	—
514	C₂²×D₄	—	2	1	no	—
515	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
516	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
517	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
518	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
519	C₂³×C₄	—	2	1	no	—
520	C₂³×C₄	—	2	1	no	—
521	C₂³×C₄	—	2	1	no	—
522	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
523	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
524	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
525	C₂×M₁₆	—	2	2	no	—
526	C₂×M₁₆	—	4	1	no	—
527	C₂×M₁₆	—	4	1	no	—
528	C₂²×C₈	—	2	2	no	—
529	C₂²×C₈	—	4	1	no	—
530	C₂²×C₈	—	4	1	no	—
531	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
532	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
533	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
534	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
535	C₂²⋊Q₈	—	2	8	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	2	no	—
538	C₂²⋊Q₈	C₂×C₄×C₈₉	1	4	yes	—
539	C₂²⋊Q₈	C₂×C₄×C₈₉	1	4	yes	complemented
540	#121	—	2	8	no	—
541	#121	—	2	8	no	—
542	#121	—	2	8	no	—
543	#121	—	2	2	no	—
544	#121	—	2	2	no	—
545	#121	C₂×C₄×C₈₉	1	4	yes	—
546	#121	C₂×C₄×C₈₉	1	4	yes	complemented
547	#117	—	4	1	no	—
548	#117	—	4	1	no	—
549	C₂×C₄⋊C₄	—	2	1	no	—
550	C₂×C₄⋊C₄	—	2	2	no	—
551	C₂×C₄⋊C₄	—	2	1	no	—
552	C₂×C₄⋊C₄	—	2	1	no	—
553	C₂×C₄⋊C₄	—	2	1	no	—
554	C₂×C₄⋊C₄	—	4	1	no	—
555	C₂×C₄⋊C₄	—	4	1	no	—
556	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	4	yes	complemented
557	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
563	C₂×C₂²⋊C₄	—	2	1	no	—
564	C₂×C₂²⋊C₄	—	2	1	no	—
565	C₂×C₂²⋊C₄	—	2	1	no	—
566	C₂×C₂²⋊C₄	—	2	1	no	—
567	C₂×C₂²⋊C₄	—	2	1	no	—
568	C₂×C₂²⋊C₄	—	2	1	no	—
569	C₂×C₂²⋊C₄	—	2	1	no	—
570	C₂×C₂²⋊C₄	—	2	1	no	—
571	C₂×C₂²⋊C₄	—	2	1	no	—
572	C₂×C₄²	—	2	1	no	—
573	#103	—	4	1	no	—
574	#103	—	4	1	no	—
575	#103	—	4	1	no	—
576	#103	—	4	1	no	—
577	#102	—	4	1	no	—
578	#102	—	4	1	no	—
579	#102	—	4	1	no	—
580	#102	—	4	1	no	—
581	C₂²⋊C₈	—	2	2	no	—
582	C₂²⋊C₈	—	2	2	no	—
583	C₂²⋊C₈	—	2	2	no	—
584	C₂²⋊C₈	—	2	2	no	—
585	#95	—	2	1	no	—
586	#95	—	2	1	no	—
587	#95	—	2	1	no	—
588	#95	—	2	1	no	—
589	C₂⁴	—	2	1	no	—
590	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
591	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
592	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
593	#41	—	4	4	no	—
594	#41	—	4	4	no	—
595	#41	—	4	4	no	—
596	#41	—	4	4	no	—
597	#41	—	4	4	no	—
598	#41	—	4	4	no	—
599	#41	—	4	4	no	—
600	#41	—	4	4	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	2	1	no	—
604	C₂×Q₈	—	2	1	no	—
605	C₂×Q₈	—	2	1	no	—
606	C₂×Q₈	—	4	1	no	—
607	C₂×Q₈	—	4	1	no	—
608	C₂×Q₈	C₂²⋊C₄×C₈₉	1	4	yes	—
609	C₂×Q₈	C₂²×C₄×C₈₉	1	2	yes	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	2	4	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	—	4	1	no	—
619	C₂×D₄	—	4	1	no	—
620	C₂×D₄	—	4	1	no	—
621	C₂×D₄	—	4	1	no	—
622	C₂×D₄	—	4	1	no	—
623	C₂×D₄	—	4	1	no	—
624	C₂×D₄	—	4	2	no	—
625	C₂×D₄	—	4	2	no	—
626	C₂×D₄	—	8	1	no	—
627	C₂×D₄	—	8	1	no	—
628	C₂×D₄	—	8	1	no	—
629	C₂×D₄	—	8	1	no	—
630	C₂×D₄	C₂²⋊C₄×C₈₉	1	4	yes	—
631	C₂×D₄	C₂²⋊C₄×C₈₉	1	4	yes	—
632	C₂×D₄	C₂²⋊C₄×C₈₉	1	4	yes	—
633	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
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	4	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	4	2	no	—
656	C₂²×C₄	—	4	2	no	—
657	C₂²×C₄	—	4	2	no	—
658	C₂²×C₄	—	8	1	no	—
659	C₂²×C₄	—	8	1	no	—
660	C₂²×C₄	—	8	1	no	—
661	C₂²×C₄	—	8	1	no	—
662	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
663	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
664	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
665	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
666	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
667	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
668	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
669	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
670	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
672	M₁₆	—	4	4	no	—
673	C₂×C₈	—	2	1	no	—
674	C₂×C₈	—	2	1	no	—
675	C₂×C₈	—	2	1	no	—
676	C₂×C₈	—	2	1	no	—
677	C₂×C₈	—	2	1	no	—
678	C₂×C₈	—	2	1	no	—
679	C₂×C₈	—	2	1	no	—
680	C₂×C₈	—	2	1	no	—
681	C₂×C₈	—	2	1	no	—
682	C₂×C₈	—	2	1	no	—
683	C₂×C₈	—	2	1	no	—
684	C₂×C₈	—	2	1	no	—
685	C₂×C₈	—	4	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	4	2	no	—
700	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
701	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	4	2	no	—
707	C₂²⋊C₄	—	8	1	no	—
708	C₂²⋊C₄	—	8	1	no	—
709	C₂²⋊C₄	—	8	1	no	—
710	C₂²⋊C₄	—	8	1	no	—
711	C₄²	—	4	2	no	—
712	C₂³	—	2	1	no	—
713	C₂³	—	2	1	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	1	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	1	no	—
723	C₂³	—	2	1	no	—
724	C₂³	—	2	1	no	—
725	C₂³	—	2	1	no	—
726	C₂³	—	2	1	no	—
727	C₂³	—	2	1	no	—
728	C₂³	—	2	1	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	4	1	no	—
732	C₂³	—	4	1	no	—
733	C₂³	—	4	1	no	—
734	C₂³	—	4	1	no	—
735	C₂³	—	4	1	no	—
736	C₂³	—	4	1	no	—
737	C₂³	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
738	C₂³	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
739	C₂³	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
740	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
741	Q₈	—	2	2	no	—
742	Q₈	—	2	2	no	—
743	Q₈	—	4	4	no	—
744	Q₈	—	4	1	no	—
745	Q₈	—	4	1	no	—
746	D₄	—	2	2	no	—
747	D₄	—	2	2	no	—
748	D₄	—	4	4	no	—
749	D₄	—	4	4	no	—
750	D₄	—	4	4	no	—
751	D₄	—	4	8	no	—
752	D₄	—	4	1	no	—
753	D₄	—	4	1	no	—
754	D₄	—	8	4	no	—
755	D₄	—	8	4	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	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	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	4	8	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	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	—	4	1	no	—
792	C₂×C₄	—	4	1	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	—	4	1	no	—
795	C₂×C₄	—	4	1	no	—
796	C₂×C₄	—	8	4	no	—
797	C₂×C₄	—	8	4	no	—
798	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
799	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
800	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
801	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
803	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
804	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
805	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
806	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
807	C₈	—	4	1	no	—
808	C₈	—	4	1	no	—
809	C₈	—	4	1	no	—
810	C₈	—	4	1	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	1	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	8	1	no	—
836	C₂²	—	8	1	no	—
837	C₂²	—	8	1	no	—
838	C₂²	—	8	1	no	—
839	C₂²	C₂²×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
840	C₂²	#534×C₈₉	1	1	yes	characteristic
841	C₂²	#534×C₈₉	1	1	yes	characteristic
842	C₂²	#576×C₈₉	1	1	yes	characteristic
843	C₂²	#577×C₈₉	1	1	yes	characteristic
844	C₂²	#577×C₈₉	1	1	yes	characteristic
845	C₂²	#578×C₈₉	1	1	yes	characteristic
846	C₄	—	2	2	no	—
847	C₄	—	2	2	no	—
848	C₄	—	2	2	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	8	1	no	—
853	C₄	—	8	1	no	—
854	C₄	—	8	1	no	—
855	C₄	—	8	1	no	—
856	C₄	#518×C₈₉	1	1	yes	characteristic
857	C₄	#518×C₈₉	1	1	yes	characteristic
858	C₄	#534×C₈₉	1	1	yes	characteristic
859	C₄	#534×C₈₉	1	1	yes	characteristic
860	C₂	—	4	2	no	—
861	C₂	—	4	2	no	—
862	C₂	—	4	2	no	—
863	C₂	—	8	2	no	—
864	C₂	C₈₉×#2308	1	1	yes	characteristic
865	C₂	C₈₉×#2897	1	1	yes	characteristic
866	C₂	C₈₉×#2898	1	1	yes	characteristic
867	C₂	C₈₉×#3198	1	1	yes	characteristic
868	C₂	C₈₉×#3201	1	1	yes	characteristic
869	C₂	C₈₉×#3203	1	1	yes	characteristic
870	C₂	C₈₉×#3204	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₈₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂×#537×C₈₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂²×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#408×C₈₉	C₂	semidirect
3. C₈₉×#2311	C₂	semidirect
4. C₈₉×#1895	C₂	semidirect
5. C₈₉×#1894	C₂	semidirect
6. C₈₉×#1893	C₂	semidirect
7. C₈₉×#1892	C₂	semidirect
8. C₈₉×#1875	C₂	semidirect
9. C₈₉×#1874	C₂	semidirect
10. C₈₉×#1873	C₂	semidirect
11. C₈₉×#1872	C₂	semidirect
12. C₈₉×#1824	C₂	semidirect
13. C₈₉×#1823	C₂	semidirect
14. C₈₉×#1788	C₂	semidirect
15. C₈₉×#1788	C₂	semidirect
21. #537×C₈₉	C₄	semidirect
72. C₂×#41×C₈₉	C₂×C₄	semidirect
103. C₂²⋊Q₈×C₈₉	C₂×C₄	semidirect
110. #121×C₈₉	C₂×C₄	semidirect
120. C₂×C₄⋊C₄×C₈₉	C₂×C₄	semidirect
424. #21772	C₈₉	direct (N × H)
437. C₂×#408	C₂×C₈₉	semidirect
438. #2311	C₂×C₈₉	semidirect
439. #1895	C₂×C₈₉	semidirect
440. #1894	C₂×C₈₉	semidirect
441. #1893	C₂×C₈₉	semidirect
442. #1892	C₂×C₈₉	semidirect
443. #1875	C₂×C₈₉	semidirect
444. #1874	C₂×C₈₉	semidirect
445. #1873	C₂×C₈₉	semidirect
446. #1872	C₂×C₈₉	semidirect
447. #1824	C₂×C₈₉	semidirect
448. #1823	C₂×C₈₉	semidirect
449. #1788	C₂×C₈₉	semidirect
450. #1788	C₂×C₈₉	semidirect
451. C₈₉	#21772	direct (N × H)
457. #537	C₄×C₈₉	semidirect
508. C₂×#41	C₂×C₄×C₈₉	semidirect
539. C₂²⋊Q₈	C₂×C₄×C₈₉	semidirect
546. #121	C₂×C₄×C₈₉	semidirect
556. C₂×C₄⋊C₄	C₂×C₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#537×C₈₉	2
C₂×#408×C₈₉	2
C₈₉×#2311	2
C₈₉×#1895	2
C₈₉×#1894	2
C₈₉×#1893	2
C₈₉×#1892	2
C₈₉×#1875	2
C₈₉×#1874	2
C₈₉×#1873	2
C₈₉×#1872	2
C₈₉×#1824	2
C₈₉×#1823	2
C₈₉×#1788	2
#21772	89

Subgroups — C89×#21772 #36399620

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#21772 #36399620