Subgroups — C₈₉×#35522 #36413370

Order 22784.

2712 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#518×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2580	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2538	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2537	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2535	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2485	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2485	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2480	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2472	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2467	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2463	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2460	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2456	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2424	C₂	1	2	yes	maximal, complemented
16	C₈₉×#2418	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2408	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#2408	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2324	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₉×#2324	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#2314	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#121×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
25	#529×C₈₉	—	2	8	no	—
26	C₂×#126×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#126×C₈₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#123×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#123×C₈₉	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
34	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×#121×C₈₉	C₂²	1	2	yes	complemented
40	C₂×#120×C₈₉	C₂²	1	2	yes	—
41	C₂×#120×C₈₉	C₂²	1	2	yes	—
42	#518×C₈₉	—	2	8	no	—
43	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
48	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
49	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
52	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
54	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
55	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
56	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
57	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
59	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
60	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	#399×C₈₉	C₂²	1	2	yes	complemented
62	#397×C₈₉	C₂²	1	2	yes	—
63	#397×C₈₉	C₂²	1	2	yes	—
64	#397×C₈₉	C₂²	1	2	yes	complemented
65	#396×C₈₉	C₂²	1	2	yes	complemented
66	#396×C₈₉	C₂²	1	2	yes	complemented
67	#394×C₈₉	C₂²	1	2	yes	—
68	#394×C₈₉	C₂²	1	2	yes	—
69	#394×C₈₉	C₂²	1	2	yes	—
70	#394×C₈₉	C₂²	1	2	yes	—
71	#394×C₈₉	C₂²	1	2	yes	complemented
72	#394×C₈₉	C₂²	1	2	yes	complemented
73	#393×C₈₉	C₂²	1	2	yes	complemented
74	#392×C₈₉	C₂²	1	2	yes	—
75	#392×C₈₉	C₂²	1	2	yes	—
76	#392×C₈₉	C₂²	1	2	yes	complemented
77	#390×C₈₉	C₂²	1	1	yes	characteristic
78	#390×C₈₉	C₂²	1	1	yes	characteristic
79	#390×C₈₉	C₂²	1	1	yes	characteristic
80	#390×C₈₉	C₂²	1	1	yes	characteristic
81	#390×C₈₉	C₂²	1	2	yes	complemented
82	#390×C₈₉	C₂²	1	2	yes	complemented
83	#389×C₈₉	C₂²	1	1	yes	characteristic, complemented
84	#389×C₈₉	C₂²	1	1	yes	characteristic, complemented
85	#389×C₈₉	C₂²	1	1	yes	characteristic, complemented
86	#389×C₈₉	C₂²	1	1	yes	characteristic, complemented
87	#388×C₈₉	C₂²	1	2	yes	—
88	#388×C₈₉	C₂²	1	2	yes	—
89	#388×C₈₉	C₂²	1	2	yes	complemented
90	#388×C₈₉	C₂²	1	2	yes	complemented
91	#388×C₈₉	C₂²	1	2	yes	complemented
92	#388×C₈₉	C₂²	1	2	yes	complemented
93	#388×C₈₉	C₂²	1	2	yes	complemented
94	#388×C₈₉	C₂²	1	2	yes	complemented
95	#387×C₈₉	C₂²	1	2	yes	complemented
96	#387×C₈₉	C₂²	1	2	yes	complemented
97	#387×C₈₉	C₂²	1	2	yes	complemented
98	#387×C₈₉	C₂²	1	2	yes	complemented
99	#386×C₈₉	C₂²	1	2	yes	complemented
100	#386×C₈₉	C₂²	1	2	yes	complemented
101	#386×C₈₉	C₂²	1	2	yes	complemented
102	#386×C₈₉	C₂²	1	2	yes	complemented
103	#386×C₈₉	C₂²	1	2	yes	complemented
104	#386×C₈₉	C₂²	1	2	yes	complemented
105	#385×C₈₉	C₂²	1	2	yes	complemented
106	#385×C₈₉	C₂²	1	2	yes	complemented
107	#385×C₈₉	C₂²	1	2	yes	complemented
108	#385×C₈₉	C₂²	1	2	yes	complemented
109	#384×C₈₉	C₂²	1	1	yes	characteristic, complemented
110	#382×C₈₉	C₂²	1	1	yes	characteristic, complemented
111	#380×C₈₉	C₂²	1	1	yes	characteristic
112	#380×C₈₉	C₂²	1	1	yes	characteristic
113	#380×C₈₉	C₂²	1	1	yes	characteristic, complemented
114	#380×C₈₉	C₂²	1	1	yes	characteristic, complemented
115	#380×C₈₉	C₂²	1	1	yes	characteristic, complemented
116	#380×C₈₉	C₂²	1	1	yes	characteristic, complemented
117	#380×C₈₉	C₂²	1	2	yes	complemented
118	#380×C₈₉	C₂²	1	2	yes	complemented
119	#379×C₈₉	C₂²	1	2	yes	—
120	#379×C₈₉	C₂²	1	2	yes	—
121	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
123	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
124	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
125	C₂⁵×C₈₉	C₂³	1	2	yes	—
126	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₈₉	—	2	4	no	—
128	C₂²×D₄×C₈₉	—	2	4	no	—
129	C₂²×D₄×C₈₉	—	2	4	no	—
130	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
131	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
132	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
133	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
139	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
140	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
146	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
147	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
148	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
149	#126×C₈₉	—	2	4	no	—
150	#126×C₈₉	—	2	4	no	—
151	#125×C₈₉	—	2	4	no	—
152	#124×C₈₉	—	2	4	no	—
153	#123×C₈₉	—	2	4	no	—
154	#123×C₈₉	—	2	4	no	—
155	C₂²⋊Q₈×C₈₉	—	2	4	no	—
156	C₂²⋊Q₈×C₈₉	—	4	4	no	—
157	#121×C₈₉	—	2	4	no	—
158	#121×C₈₉	—	2	4	no	—
159	#121×C₈₉	—	2	4	no	—
160	#121×C₈₉	—	2	4	no	—
161	#121×C₈₉	—	2	4	no	—
162	#121×C₈₉	—	4	4	no	—
163	#120×C₈₉	—	4	4	no	—
164	#120×C₈₉	—	4	4	no	—
165	C₄×Q₈×C₈₉	—	2	4	no	—
166	C₄×D₄×C₈₉	—	2	4	no	—
167	C₄×D₄×C₈₉	—	2	4	no	—
168	C₄×D₄×C₈₉	—	2	8	no	—
169	C₄×D₄×C₈₉	—	2	8	no	—
170	C₄×D₄×C₈₉	—	2	4	no	—
171	C₄×D₄×C₈₉	—	2	4	no	—
172	C₄×D₄×C₈₉	—	2	4	no	—
173	C₄×D₄×C₈₉	—	2	4	no	—
174	C₄×D₄×C₈₉	—	2	4	no	—
175	C₄×D₄×C₈₉	—	4	4	no	—
176	C₄×D₄×C₈₉	—	4	4	no	—
177	#117×C₈₉	—	2	4	no	—
178	#117×C₈₉	—	2	4	no	—
179	#117×C₈₉	D₄	1	8	yes	complemented
180	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
198	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
203	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
204	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
227	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
230	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
231	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
232	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
233	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
234	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
235	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
236	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₈₉	—	2	4	no	—
238	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
239	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
240	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
241	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
242	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
243	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
244	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
245	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
246	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
247	#95×C₈₉	C₂³	1	2	yes	—
248	#95×C₈₉	C₂³	1	2	yes	—
249	#95×C₈₉	C₂³	1	2	yes	—
250	#95×C₈₉	C₂³	1	2	yes	—
251	#95×C₈₉	C₂³	1	2	yes	—
252	#95×C₈₉	C₂³	1	2	yes	—
253	#95×C₈₉	C₂³	1	2	yes	—
254	#95×C₈₉	C₂³	1	2	yes	—
255	#95×C₈₉	C₂³	1	2	yes	—
256	#95×C₈₉	C₂³	1	2	yes	—
257	#95×C₈₉	C₂³	1	2	yes	—
258	#95×C₈₉	C₂³	1	2	yes	—
259	#95×C₈₉	C₂³	1	2	yes	—
260	#95×C₈₉	C₂³	1	2	yes	—
261	C₂⁴×C₈₉	—	2	4	no	—
262	C₂⁴×C₈₉	—	2	4	no	—
263	C₂⁴×C₈₉	—	2	4	no	—
264	C₂⁴×C₈₉	—	4	2	no	—
265	C₂⁴×C₈₉	—	4	2	no	—
266	C₂⁴×C₈₉	—	4	2	no	—
267	C₂⁴×C₈₉	—	4	2	no	—
268	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
269	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
270	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
271	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
272	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
273	C₂×Q₈×C₈₉	—	2	2	no	—
274	C₂×Q₈×C₈₉	—	2	2	no	—
275	C₂×Q₈×C₈₉	—	4	1	no	—
276	C₂×D₄×C₈₉	—	2	32	no	—
277	C₂×D₄×C₈₉	—	2	4	no	—
278	C₂×D₄×C₈₉	—	2	4	no	—
279	C₂×D₄×C₈₉	—	2	2	no	—
280	C₂×D₄×C₈₉	—	2	2	no	—
281	C₂×D₄×C₈₉	—	2	4	no	—
282	C₂×D₄×C₈₉	—	2	4	no	—
283	C₂×D₄×C₈₉	—	2	4	no	—
284	C₂×D₄×C₈₉	—	2	2	no	—
285	C₂×D₄×C₈₉	—	2	4	no	—
286	C₂×D₄×C₈₉	—	2	2	no	—
287	C₂×D₄×C₈₉	—	2	4	no	—
288	C₂×D₄×C₈₉	—	2	4	no	—
289	C₂×D₄×C₈₉	—	2	4	no	—
290	C₂×D₄×C₈₉	—	2	2	no	—
291	C₂×D₄×C₈₉	—	2	2	no	—
292	C₂×D₄×C₈₉	—	2	2	no	—
293	C₂×D₄×C₈₉	—	2	2	no	—
294	C₂×D₄×C₈₉	—	2	2	no	—
295	C₂×D₄×C₈₉	—	2	2	no	—
296	C₂×D₄×C₈₉	—	4	2	no	—
297	C₂×D₄×C₈₉	—	4	1	no	—
298	C₂×D₄×C₈₉	—	4	1	no	—
299	C₂×D₄×C₈₉	—	4	2	no	—
300	C₂×D₄×C₈₉	—	4	1	no	—
301	C₂×D₄×C₈₉	—	4	2	no	—
302	C₂×D₄×C₈₉	—	4	2	no	—
303	C₂×D₄×C₈₉	—	4	2	no	—
304	C₂×D₄×C₈₉	—	4	2	no	—
305	C₂×D₄×C₈₉	#41	1	4	yes	—
306	C₂×D₄×C₈₉	#41	1	4	yes	—
307	C₂²×C₄×C₈₉	—	2	2	no	—
308	C₂²×C₄×C₈₉	—	2	2	no	—
309	C₂²×C₄×C₈₉	—	2	2	no	—
310	C₂²×C₄×C₈₉	—	2	2	no	—
311	C₂²×C₄×C₈₉	—	2	2	no	—
312	C₂²×C₄×C₈₉	—	2	2	no	—
313	C₂²×C₄×C₈₉	—	2	2	no	—
314	C₂²×C₄×C₈₉	—	2	2	no	—
315	C₂²×C₄×C₈₉	—	2	2	no	—
316	C₂²×C₄×C₈₉	—	2	2	no	—
317	C₂²×C₄×C₈₉	—	2	2	no	—
318	C₂²×C₄×C₈₉	—	2	2	no	—
319	C₂²×C₄×C₈₉	—	2	4	no	—
320	C₂²×C₄×C₈₉	—	2	4	no	—
321	C₂²×C₄×C₈₉	—	2	4	no	—
322	C₂²×C₄×C₈₉	—	2	4	no	—
323	C₂²×C₄×C₈₉	—	4	1	no	—
324	C₂²×C₄×C₈₉	—	4	1	no	—
325	C₂²×C₄×C₈₉	—	4	2	no	—
326	C₂²×C₄×C₈₉	—	4	2	no	—
327	C₂²×C₄×C₈₉	—	4	2	no	—
328	C₂²×C₄×C₈₉	—	4	2	no	—
329	C₂²×C₄×C₈₉	—	4	2	no	—
330	C₂²×C₄×C₈₉	—	4	2	no	—
331	C₂²×C₄×C₈₉	—	4	2	no	—
332	C₂²×C₄×C₈₉	—	4	2	no	—
333	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
334	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
339	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
352	C₄⋊C₄×C₈₉	—	2	2	no	—
353	C₄⋊C₄×C₈₉	—	2	2	no	—
354	C₄⋊C₄×C₈₉	—	2	2	no	—
355	C₄⋊C₄×C₈₉	—	2	2	no	—
356	C₄⋊C₄×C₈₉	—	2	2	no	—
357	C₄⋊C₄×C₈₉	—	2	2	no	—
358	C₄⋊C₄×C₈₉	—	2	2	no	—
359	C₄⋊C₄×C₈₉	—	2	2	no	—
360	C₄⋊C₄×C₈₉	—	2	2	no	—
361	C₄⋊C₄×C₈₉	—	2	2	no	—
362	C₄⋊C₄×C₈₉	—	2	2	no	—
363	C₄⋊C₄×C₈₉	—	2	2	no	—
364	C₄⋊C₄×C₈₉	—	2	2	no	—
365	C₄⋊C₄×C₈₉	—	2	2	no	—
366	C₄⋊C₄×C₈₉	—	2	4	no	—
367	C₄⋊C₄×C₈₉	—	4	2	no	—
368	C₄⋊C₄×C₈₉	—	4	2	no	—
369	C₄⋊C₄×C₈₉	—	4	2	no	—
370	C₄⋊C₄×C₈₉	—	4	2	no	—
371	C₄⋊C₄×C₈₉	—	4	2	no	—
372	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
373	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
374	C₂²⋊C₄×C₈₉	—	2	4	no	—
375	C₂²⋊C₄×C₈₉	—	2	2	no	—
376	C₂²⋊C₄×C₈₉	—	2	2	no	—
377	C₂²⋊C₄×C₈₉	—	2	4	no	—
378	C₂²⋊C₄×C₈₉	—	2	4	no	—
379	C₂²⋊C₄×C₈₉	—	2	4	no	—
380	C₂²⋊C₄×C₈₉	—	2	4	no	—
381	C₂²⋊C₄×C₈₉	—	2	4	no	—
382	C₂²⋊C₄×C₈₉	—	2	4	no	—
383	C₂²⋊C₄×C₈₉	—	2	4	no	—
384	C₂²⋊C₄×C₈₉	—	2	4	no	—
385	C₂²⋊C₄×C₈₉	—	2	4	no	—
386	C₂²⋊C₄×C₈₉	—	2	2	no	—
387	C₂²⋊C₄×C₈₉	—	2	2	no	—
388	C₂²⋊C₄×C₈₉	—	2	2	no	—
389	C₂²⋊C₄×C₈₉	—	2	2	no	—
390	C₂²⋊C₄×C₈₉	—	2	2	no	—
391	C₂²⋊C₄×C₈₉	—	2	2	no	—
392	C₂²⋊C₄×C₈₉	—	2	4	no	—
393	C₂²⋊C₄×C₈₉	—	2	4	no	—
394	C₂²⋊C₄×C₈₉	—	4	2	no	—
395	C₂²⋊C₄×C₈₉	—	4	2	no	—
396	C₂²⋊C₄×C₈₉	—	4	2	no	—
397	C₂²⋊C₄×C₈₉	—	4	2	no	—
398	C₂²⋊C₄×C₈₉	—	4	2	no	—
399	C₂²⋊C₄×C₈₉	—	4	2	no	—
400	C₂²⋊C₄×C₈₉	—	4	2	no	—
401	C₂²⋊C₄×C₈₉	—	4	2	no	—
402	C₂²⋊C₄×C₈₉	—	4	2	no	—
403	C₂²⋊C₄×C₈₉	—	4	2	no	—
404	C₂²⋊C₄×C₈₉	—	4	2	no	—
405	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
406	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
407	C₄²×C₈₉	—	2	2	no	—
408	C₄²×C₈₉	—	2	2	no	—
409	C₄²×C₈₉	—	2	2	no	—
410	C₄²×C₈₉	—	2	4	no	—
411	C₄²×C₈₉	—	2	2	no	—
412	C₄²×C₈₉	—	4	2	no	—
413	C₄²×C₈₉	—	4	2	no	—
414	C₄²×C₈₉	C₂×D₄	1	4	yes	—
415	C₄²×C₈₉	C₂×D₄	1	4	yes	—
416	C₂³×C₈₉	—	2	16	no	—
417	C₂³×C₈₉	—	2	1	no	—
418	C₂³×C₈₉	—	2	2	no	—
419	C₂³×C₈₉	—	2	2	no	—
420	C₂³×C₈₉	—	2	1	no	—
421	C₂³×C₈₉	—	2	1	no	—
422	C₂³×C₈₉	—	2	1	no	—
423	C₂³×C₈₉	—	2	1	no	—
424	C₂³×C₈₉	—	2	2	no	—
425	C₂³×C₈₉	—	2	2	no	—
426	C₂³×C₈₉	—	2	2	no	—
427	C₂³×C₈₉	—	2	2	no	—
428	C₂³×C₈₉	—	2	1	no	—
429	C₂³×C₈₉	—	2	2	no	—
430	C₂³×C₈₉	—	2	1	no	—
431	C₂³×C₈₉	—	2	1	no	—
432	C₂³×C₈₉	—	2	2	no	—
433	C₂³×C₈₉	—	2	2	no	—
434	C₂³×C₈₉	—	2	2	no	—
435	C₂³×C₈₉	—	2	1	no	—
436	C₂³×C₈₉	—	2	1	no	—
437	C₂³×C₈₉	—	2	2	no	—
438	C₂³×C₈₉	—	2	2	no	—
439	C₂³×C₈₉	—	2	1	no	—
440	C₂³×C₈₉	—	2	1	no	—
441	C₂³×C₈₉	—	2	1	no	—
442	C₂³×C₈₉	—	2	1	no	—
443	C₂³×C₈₉	—	2	1	no	—
444	C₂³×C₈₉	—	2	1	no	—
445	C₂³×C₈₉	—	2	1	no	—
446	C₂³×C₈₉	—	2	1	no	—
447	C₂³×C₈₉	—	2	1	no	—
448	C₂³×C₈₉	—	8	4	no	—
449	C₂³×C₈₉	—	8	4	no	—
450	C₂³×C₈₉	—	8	4	no	—
451	C₂³×C₈₉	—	8	4	no	—
452	C₂³×C₈₉	—	8	4	no	—
453	C₂³×C₈₉	—	8	4	no	—
454	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
455	C₂³×C₈₉	C₂×#41	1	4	yes	—
456	C₂³×C₈₉	C₂×#41	1	4	yes	—
457	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
458	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
459	Q₈×C₈₉	—	4	4	no	—
460	D₄×C₈₉	—	2	16	no	—
461	D₄×C₈₉	—	2	8	no	—
462	D₄×C₈₉	—	2	8	no	—
463	D₄×C₈₉	—	4	4	no	—
464	D₄×C₈₉	—	4	4	no	—
465	D₄×C₈₉	—	4	4	no	—
466	D₄×C₈₉	—	4	8	no	—
467	D₄×C₈₉	—	4	8	no	—
468	D₄×C₈₉	—	8	4	no	—
469	D₄×C₈₉	—	8	4	no	—
470	C₂×C₄×C₈₉	—	2	1	no	—
471	C₂×C₄×C₈₉	—	2	1	no	—
472	C₂×C₄×C₈₉	—	2	1	no	—
473	C₂×C₄×C₈₉	—	2	1	no	—
474	C₂×C₄×C₈₉	—	2	1	no	—
475	C₂×C₄×C₈₉	—	2	1	no	—
476	C₂×C₄×C₈₉	—	2	1	no	—
477	C₂×C₄×C₈₉	—	2	1	no	—
478	C₂×C₄×C₈₉	—	2	1	no	—
479	C₂×C₄×C₈₉	—	2	1	no	—
480	C₂×C₄×C₈₉	—	2	1	no	—
481	C₂×C₄×C₈₉	—	2	1	no	—
482	C₂×C₄×C₈₉	—	2	8	no	—
483	C₂×C₄×C₈₉	—	2	1	no	—
484	C₂×C₄×C₈₉	—	2	1	no	—
485	C₂×C₄×C₈₉	—	2	1	no	—
486	C₂×C₄×C₈₉	—	2	2	no	—
487	C₂×C₄×C₈₉	—	2	2	no	—
488	C₂×C₄×C₈₉	—	2	1	no	—
489	C₂×C₄×C₈₉	—	2	1	no	—
490	C₂×C₄×C₈₉	—	2	1	no	—
491	C₂×C₄×C₈₉	—	2	1	no	—
492	C₂×C₄×C₈₉	—	2	1	no	—
493	C₂×C₄×C₈₉	—	2	1	no	—
494	C₂×C₄×C₈₉	—	2	2	no	—
495	C₂×C₄×C₈₉	—	2	2	no	—
496	C₂×C₄×C₈₉	—	2	2	no	—
497	C₂×C₄×C₈₉	—	2	2	no	—
498	C₂×C₄×C₈₉	—	2	2	no	—
499	C₂×C₄×C₈₉	—	2	2	no	—
500	C₂×C₄×C₈₉	—	2	2	no	—
501	C₂×C₄×C₈₉	—	2	2	no	—
502	C₂×C₄×C₈₉	—	2	2	no	—
503	C₂×C₄×C₈₉	—	2	2	no	—
504	C₂×C₄×C₈₉	—	2	1	no	—
505	C₂×C₄×C₈₉	—	2	2	no	—
506	C₂×C₄×C₈₉	—	2	1	no	—
507	C₂×C₄×C₈₉	—	2	1	no	—
508	C₂×C₄×C₈₉	—	2	2	no	—
509	C₂×C₄×C₈₉	—	2	1	no	—
510	C₂×C₄×C₈₉	—	2	2	no	—
511	C₂×C₄×C₈₉	—	2	1	no	—
512	C₂×C₄×C₈₉	—	2	2	no	—
513	C₂×C₄×C₈₉	—	2	2	no	—
514	C₂×C₄×C₈₉	—	2	1	no	—
515	C₂×C₄×C₈₉	—	2	2	no	—
516	C₂×C₄×C₈₉	—	4	4	no	—
517	C₂×C₄×C₈₉	—	4	4	no	—
518	C₂×C₄×C₈₉	—	4	4	no	—
519	C₂×C₄×C₈₉	—	4	4	no	—
520	C₂×C₄×C₈₉	—	8	4	no	—
521	C₂×C₄×C₈₉	—	8	4	no	—
522	C₂×C₄×C₈₉	—	8	4	no	—
523	C₂×C₄×C₈₉	—	8	4	no	—
524	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
531	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
532	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
533	C₂²×C₈₉	—	2	2	no	—
534	C₂²×C₈₉	—	2	4	no	—
535	C₂²×C₈₉	—	2	4	no	—
536	C₂²×C₈₉	—	2	2	no	—
537	C₂²×C₈₉	—	2	2	no	—
538	C₂²×C₈₉	—	2	2	no	—
539	C₂²×C₈₉	—	2	2	no	—
540	C₂²×C₈₉	—	2	4	no	—
541	C₂²×C₈₉	—	2	4	no	—
542	C₂²×C₈₉	—	2	2	no	—
543	C₂²×C₈₉	—	2	4	no	—
544	C₂²×C₈₉	—	2	4	no	—
545	C₂²×C₈₉	—	4	1	no	—
546	C₂²×C₈₉	—	4	1	no	—
547	C₂²×C₈₉	—	4	2	no	—
548	C₂²×C₈₉	—	4	2	no	—
549	C₂²×C₈₉	—	4	2	no	—
550	C₂²×C₈₉	—	4	2	no	—
551	C₂²×C₈₉	—	4	2	no	—
552	C₂²×C₈₉	—	4	1	no	—
553	C₂²×C₈₉	—	4	1	no	—
554	C₂²×C₈₉	—	4	2	no	—
555	C₂²×C₈₉	—	4	1	no	—
556	C₂²×C₈₉	—	4	2	no	—
557	C₂²×C₈₉	—	4	1	no	—
558	C₂²×C₈₉	—	4	1	no	—
559	C₂²×C₈₉	—	4	2	no	—
560	C₂²×C₈₉	—	4	1	no	—
561	C₂²×C₈₉	—	4	1	no	—
562	C₂²×C₈₉	—	4	1	no	—
563	C₂²×C₈₉	—	4	1	no	—
564	C₂²×C₈₉	—	4	1	no	—
565	C₂²×C₈₉	—	4	1	no	—
566	C₂²×C₈₉	—	4	1	no	—
567	C₂²×C₈₉	—	4	1	no	—
568	C₂²×C₈₉	—	8	16	no	—
569	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
570	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
571	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
572	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
573	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
574	C₂²×C₈₉	#585	1	1	yes	characteristic
575	C₂²×C₈₉	#585	1	1	yes	characteristic
576	C₄×C₈₉	—	2	2	no	—
577	C₄×C₈₉	—	2	2	no	—
578	C₄×C₈₉	—	2	2	no	—
579	C₄×C₈₉	—	2	2	no	—
580	C₄×C₈₉	—	2	2	no	—
581	C₄×C₈₉	—	2	2	no	—
582	C₄×C₈₉	—	4	1	no	—
583	C₄×C₈₉	—	4	1	no	—
584	C₄×C₈₉	—	4	1	no	—
585	C₄×C₈₉	—	4	2	no	—
586	C₄×C₈₉	—	4	2	no	—
587	C₄×C₈₉	—	4	1	no	—
588	C₄×C₈₉	—	4	1	no	—
589	C₄×C₈₉	—	4	2	no	—
590	C₄×C₈₉	—	4	2	no	—
591	C₄×C₈₉	—	4	2	no	—
592	C₄×C₈₉	—	4	2	no	—
593	C₄×C₈₉	#525	1	4	yes	—
594	#35522	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
595	C₂×C₈₉	—	4	2	no	—
596	C₂×C₈₉	—	4	4	no	—
597	C₂×C₈₉	—	4	4	no	—
598	C₂×C₈₉	—	4	2	no	—
599	C₂×C₈₉	—	8	1	no	—
600	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
601	C₂×C₈₉	#3488	1	1	yes	characteristic
602	C₂×C₈₉	#3488	1	1	yes	characteristic
603	C₂×C₈₉	#3513	1	1	yes	characteristic
604	C₂×C₈₉	#3514	1	1	yes	characteristic
605	C₂×C₈₉	#3519	1	1	yes	characteristic
606	C₂×C₈₉	#3521	1	1	yes	characteristic
607	C₂×#529	C₂×C₈₉	1	1	yes	characteristic, complemented
608	C₂×#518	C₂×C₈₉	1	1	yes	characteristic, complemented
609	#2580	C₂×C₈₉	1	1	yes	characteristic, complemented
610	#2538	C₂×C₈₉	1	1	yes	characteristic, complemented
611	#2537	C₂×C₈₉	1	1	yes	characteristic, complemented
612	#2535	C₂×C₈₉	1	1	yes	characteristic, complemented
613	#2485	C₂×C₈₉	1	1	yes	characteristic, complemented
614	#2485	C₂×C₈₉	1	1	yes	characteristic, complemented
615	#2480	C₂×C₈₉	1	2	yes	complemented
616	#2472	C₂×C₈₉	1	2	yes	complemented
617	#2467	C₂×C₈₉	1	2	yes	complemented
618	#2463	C₂×C₈₉	1	2	yes	complemented
619	#2460	C₂×C₈₉	1	2	yes	complemented
620	#2456	C₂×C₈₉	1	2	yes	complemented
621	#2424	C₂×C₈₉	1	2	yes	complemented
622	#2418	C₂×C₈₉	1	2	yes	complemented
623	#2408	C₂×C₈₉	1	1	yes	characteristic, complemented
624	#2408	C₂×C₈₉	1	1	yes	characteristic, complemented
625	#2324	C₂×C₈₉	1	1	yes	characteristic, complemented
626	#2324	C₂×C₈₉	1	1	yes	characteristic, complemented
627	#2314	C₂×C₈₉	1	1	yes	characteristic, complemented
628	C₄×#121	C₂×C₈₉	1	1	yes	characteristic, complemented
629	C₄×#121	C₂×C₈₉	1	1	yes	characteristic, complemented
630	C₈₉	#35522	1	1	yes	characteristic, direct product factor, Sylow
631	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
632	#529	—	2	8	no	—
633	C₂×#126	C₂²×C₈₉	1	1	yes	characteristic
634	C₂×#126	C₂²×C₈₉	1	1	yes	characteristic, complemented
635	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic, complemented
636	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
637	C₂×#123	C₂²×C₈₉	1	1	yes	characteristic
638	C₂×#123	C₂²×C₈₉	1	1	yes	characteristic, complemented
639	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
640	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
641	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
642	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
643	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
644	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
645	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
646	C₂×#121	C₂²×C₈₉	1	2	yes	complemented
647	C₂×#120	C₂²×C₈₉	1	2	yes	—
648	C₂×#120	C₂²×C₈₉	1	2	yes	—
649	#518	—	2	8	no	—
650	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
651	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
652	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
653	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
654	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
655	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
656	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
657	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
658	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
659	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
660	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
661	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
662	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
663	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
664	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic, complemented
665	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
666	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
667	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic, complemented
668	#399	C₂²×C₈₉	1	2	yes	complemented
669	#397	C₂²×C₈₉	1	2	yes	—
670	#397	C₂²×C₈₉	1	2	yes	—
671	#397	C₂²×C₈₉	1	2	yes	complemented
672	#396	C₂²×C₈₉	1	2	yes	complemented
673	#396	C₂²×C₈₉	1	2	yes	complemented
674	#394	C₂²×C₈₉	1	2	yes	—
675	#394	C₂²×C₈₉	1	2	yes	—
676	#394	C₂²×C₈₉	1	2	yes	—
677	#394	C₂²×C₈₉	1	2	yes	—
678	#394	C₂²×C₈₉	1	2	yes	complemented
679	#394	C₂²×C₈₉	1	2	yes	complemented
680	#393	C₂²×C₈₉	1	2	yes	complemented
681	#392	C₂²×C₈₉	1	2	yes	—
682	#392	C₂²×C₈₉	1	2	yes	—
683	#392	C₂²×C₈₉	1	2	yes	complemented
684	#390	C₂²×C₈₉	1	1	yes	characteristic
685	#390	C₂²×C₈₉	1	1	yes	characteristic
686	#390	C₂²×C₈₉	1	1	yes	characteristic
687	#390	C₂²×C₈₉	1	1	yes	characteristic
688	#390	C₂²×C₈₉	1	2	yes	complemented
689	#390	C₂²×C₈₉	1	2	yes	complemented
690	#389	C₂²×C₈₉	1	1	yes	characteristic, complemented
691	#389	C₂²×C₈₉	1	1	yes	characteristic, complemented
692	#389	C₂²×C₈₉	1	1	yes	characteristic, complemented
693	#389	C₂²×C₈₉	1	1	yes	characteristic, complemented
694	#388	C₂²×C₈₉	1	2	yes	—
695	#388	C₂²×C₈₉	1	2	yes	—
696	#388	C₂²×C₈₉	1	2	yes	complemented
697	#388	C₂²×C₈₉	1	2	yes	complemented
698	#388	C₂²×C₈₉	1	2	yes	complemented
699	#388	C₂²×C₈₉	1	2	yes	complemented
700	#388	C₂²×C₈₉	1	2	yes	complemented
701	#388	C₂²×C₈₉	1	2	yes	complemented
702	#387	C₂²×C₈₉	1	2	yes	complemented
703	#387	C₂²×C₈₉	1	2	yes	complemented
704	#387	C₂²×C₈₉	1	2	yes	complemented
705	#387	C₂²×C₈₉	1	2	yes	complemented
706	#386	C₂²×C₈₉	1	2	yes	complemented
707	#386	C₂²×C₈₉	1	2	yes	complemented
708	#386	C₂²×C₈₉	1	2	yes	complemented
709	#386	C₂²×C₈₉	1	2	yes	complemented
710	#386	C₂²×C₈₉	1	2	yes	complemented
711	#386	C₂²×C₈₉	1	2	yes	complemented
712	#385	C₂²×C₈₉	1	2	yes	complemented
713	#385	C₂²×C₈₉	1	2	yes	complemented
714	#385	C₂²×C₈₉	1	2	yes	complemented
715	#385	C₂²×C₈₉	1	2	yes	complemented
716	#384	C₂²×C₈₉	1	1	yes	characteristic, complemented
717	#382	C₂²×C₈₉	1	1	yes	characteristic, complemented
718	#380	C₂²×C₈₉	1	1	yes	characteristic
719	#380	C₂²×C₈₉	1	1	yes	characteristic
720	#380	C₂²×C₈₉	1	1	yes	characteristic, complemented
721	#380	C₂²×C₈₉	1	1	yes	characteristic, complemented
722	#380	C₂²×C₈₉	1	2	yes	complemented
723	#380	C₂²×C₈₉	1	2	yes	complemented
724	#380	C₂²×C₈₉	1	1	yes	characteristic, complemented
725	#380	C₂²×C₈₉	1	1	yes	characteristic, complemented
726	#379	C₂²×C₈₉	1	2	yes	—
727	#379	C₂²×C₈₉	1	2	yes	—
728	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
729	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
730	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
731	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
732	C₂⁵	C₂³×C₈₉	1	2	yes	—
733	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
734	C₂²×D₄	—	2	4	no	—
735	C₂²×D₄	—	2	4	no	—
736	C₂²×D₄	—	2	4	no	—
737	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
738	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
739	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
740	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
741	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
742	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
743	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
744	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
745	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
746	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
747	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
748	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
749	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
750	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
751	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
752	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
753	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
754	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
755	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
756	#126	—	2	4	no	—
757	#126	—	2	4	no	—
758	#125	—	2	4	no	—
759	#124	—	2	4	no	—
760	#123	—	2	4	no	—
761	#123	—	2	4	no	—
762	C₂²⋊Q₈	—	2	4	no	—
763	C₂²⋊Q₈	—	4	4	no	—
764	#121	—	2	4	no	—
765	#121	—	2	4	no	—
766	#121	—	2	4	no	—
767	#121	—	2	4	no	—
768	#121	—	2	4	no	—
769	#121	—	4	4	no	—
770	#120	—	4	4	no	—
771	#120	—	4	4	no	—
772	C₄×Q₈	—	2	4	no	—
773	C₄×D₄	—	2	4	no	—
774	C₄×D₄	—	2	4	no	—
775	C₄×D₄	—	2	8	no	—
776	C₄×D₄	—	2	8	no	—
777	C₄×D₄	—	2	4	no	—
778	C₄×D₄	—	2	4	no	—
779	C₄×D₄	—	2	4	no	—
780	C₄×D₄	—	2	4	no	—
781	C₄×D₄	—	2	4	no	—
782	C₄×D₄	—	4	4	no	—
783	C₄×D₄	—	4	4	no	—
784	#117	—	2	4	no	—
785	#117	—	2	4	no	—
786	#117	D₄×C₈₉	1	8	yes	complemented
787	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
788	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
789	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
790	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
791	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
792	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
793	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
794	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
795	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
796	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
797	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
798	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
799	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
800	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
801	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
802	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
803	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
804	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
805	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
806	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
807	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
808	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
809	C₂×C₂²⋊C₄	—	2	8	no	—
810	C₂×C₂²⋊C₄	—	2	8	no	—
811	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
812	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
813	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
814	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
815	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
816	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
817	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
818	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
819	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
820	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
821	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
822	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
823	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
824	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
825	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
826	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
827	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
828	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
829	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
830	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
831	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
832	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
833	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
834	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
835	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
836	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
837	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
838	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
839	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
840	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
841	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
842	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
843	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
844	C₂×C₄²	—	2	4	no	—
845	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
846	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
847	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
848	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
849	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
850	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
851	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
852	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
853	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
854	#95	C₂³×C₈₉	1	2	yes	—
855	#95	C₂³×C₈₉	1	2	yes	—
856	#95	C₂³×C₈₉	1	2	yes	—
857	#95	C₂³×C₈₉	1	2	yes	—
858	#95	C₂³×C₈₉	1	2	yes	—
859	#95	C₂³×C₈₉	1	2	yes	—
860	#95	C₂³×C₈₉	1	2	yes	—
861	#95	C₂³×C₈₉	1	2	yes	—
862	#95	C₂³×C₈₉	1	2	yes	—
863	#95	C₂³×C₈₉	1	2	yes	—
864	#95	C₂³×C₈₉	1	2	yes	—
865	#95	C₂³×C₈₉	1	2	yes	—
866	#95	C₂³×C₈₉	1	2	yes	—
867	#95	C₂³×C₈₉	1	2	yes	—
868	C₂⁴	—	2	4	no	—
869	C₂⁴	—	2	4	no	—
870	C₂⁴	—	2	4	no	—
871	C₂⁴	—	4	2	no	—
872	C₂⁴	—	4	2	no	—
873	C₂⁴	—	4	2	no	—
874	C₂⁴	—	4	2	no	—
875	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
876	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
877	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
878	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
879	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
880	C₂×Q₈	—	2	2	no	—
881	C₂×Q₈	—	2	2	no	—
882	C₂×Q₈	—	4	1	no	—
883	C₂×D₄	—	2	32	no	—
884	C₂×D₄	—	2	4	no	—
885	C₂×D₄	—	2	4	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	—	2	2	no	—
888	C₂×D₄	—	2	4	no	—
889	C₂×D₄	—	2	4	no	—
890	C₂×D₄	—	2	4	no	—
891	C₂×D₄	—	2	2	no	—
892	C₂×D₄	—	2	4	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	4	no	—
895	C₂×D₄	—	2	4	no	—
896	C₂×D₄	—	2	4	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	4	2	no	—
904	C₂×D₄	—	4	1	no	—
905	C₂×D₄	—	4	1	no	—
906	C₂×D₄	—	4	2	no	—
907	C₂×D₄	—	4	1	no	—
908	C₂×D₄	—	4	2	no	—
909	C₂×D₄	—	4	2	no	—
910	C₂×D₄	—	4	2	no	—
911	C₂×D₄	—	4	2	no	—
912	C₂×D₄	#41×C₈₉	1	4	yes	—
913	C₂×D₄	#41×C₈₉	1	4	yes	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	4	no	—
927	C₂²×C₄	—	2	4	no	—
928	C₂²×C₄	—	2	4	no	—
929	C₂²×C₄	—	2	4	no	—
930	C₂²×C₄	—	4	1	no	—
931	C₂²×C₄	—	4	1	no	—
932	C₂²×C₄	—	4	2	no	—
933	C₂²×C₄	—	4	2	no	—
934	C₂²×C₄	—	4	2	no	—
935	C₂²×C₄	—	4	2	no	—
936	C₂²×C₄	—	4	2	no	—
937	C₂²×C₄	—	4	2	no	—
938	C₂²×C₄	—	4	2	no	—
939	C₂²×C₄	—	4	2	no	—
940	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
941	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
942	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
943	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
944	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
945	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
946	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
947	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
948	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
949	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
950	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
951	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
952	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
953	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
954	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
956	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
957	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
958	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	4	no	—
974	C₄⋊C₄	—	4	2	no	—
975	C₄⋊C₄	—	4	2	no	—
976	C₄⋊C₄	—	4	2	no	—
977	C₄⋊C₄	—	4	2	no	—
978	C₄⋊C₄	—	4	2	no	—
979	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
980	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
981	C₂²⋊C₄	—	2	4	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	4	no	—
985	C₂²⋊C₄	—	2	4	no	—
986	C₂²⋊C₄	—	2	4	no	—
987	C₂²⋊C₄	—	2	4	no	—
988	C₂²⋊C₄	—	2	4	no	—
989	C₂²⋊C₄	—	2	4	no	—
990	C₂²⋊C₄	—	2	4	no	—
991	C₂²⋊C₄	—	2	4	no	—
992	C₂²⋊C₄	—	2	4	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	4	no	—
1000	C₂²⋊C₄	—	2	4	no	—
1001	C₂²⋊C₄	—	4	2	no	—
1002	C₂²⋊C₄	—	4	2	no	—
1003	C₂²⋊C₄	—	4	2	no	—
1004	C₂²⋊C₄	—	4	2	no	—
1005	C₂²⋊C₄	—	4	2	no	—
1006	C₂²⋊C₄	—	4	2	no	—
1007	C₂²⋊C₄	—	4	2	no	—
1008	C₂²⋊C₄	—	4	2	no	—
1009	C₂²⋊C₄	—	4	2	no	—
1010	C₂²⋊C₄	—	4	2	no	—
1011	C₂²⋊C₄	—	4	2	no	—
1012	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
1013	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	4	no	—
1018	C₄²	—	2	2	no	—
1019	C₄²	—	4	2	no	—
1020	C₄²	—	4	2	no	—
1021	C₄²	C₂×D₄×C₈₉	1	4	yes	—
1022	C₄²	C₂×D₄×C₈₉	1	4	yes	—
1023	C₂³	—	2	16	no	—
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	2	no	—
1026	C₂³	—	2	2	no	—
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	1	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	2	2	no	—
1032	C₂³	—	2	2	no	—
1033	C₂³	—	2	2	no	—
1034	C₂³	—	2	2	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	2	no	—
1040	C₂³	—	2	2	no	—
1041	C₂³	—	2	2	no	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	2	1	no	—
1044	C₂³	—	2	2	no	—
1045	C₂³	—	2	2	no	—
1046	C₂³	—	2	1	no	—
1047	C₂³	—	2	1	no	—
1048	C₂³	—	2	1	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	2	1	no	—
1051	C₂³	—	2	1	no	—
1052	C₂³	—	2	1	no	—
1053	C₂³	—	2	1	no	—
1054	C₂³	—	2	1	no	—
1055	C₂³	—	8	4	no	—
1056	C₂³	—	8	4	no	—
1057	C₂³	—	8	4	no	—
1058	C₂³	—	8	4	no	—
1059	C₂³	—	8	4	no	—
1060	C₂³	—	8	4	no	—
1061	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1062	C₂³	C₂×#41×C₈₉	1	4	yes	—
1063	C₂³	C₂×#41×C₈₉	1	4	yes	—
1064	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
1065	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
1066	Q₈	—	4	4	no	—
1067	D₄	—	2	16	no	—
1068	D₄	—	2	8	no	—
1069	D₄	—	2	8	no	—
1070	D₄	—	4	4	no	—
1071	D₄	—	4	4	no	—
1072	D₄	—	4	4	no	—
1073	D₄	—	4	8	no	—
1074	D₄	—	4	8	no	—
1075	D₄	—	8	4	no	—
1076	D₄	—	8	4	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	8	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	2	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	2	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	2	no	—
1123	C₂×C₄	—	4	4	no	—
1124	C₂×C₄	—	4	4	no	—
1125	C₂×C₄	—	4	4	no	—
1126	C₂×C₄	—	4	4	no	—
1127	C₂×C₄	—	8	4	no	—
1128	C₂×C₄	—	8	4	no	—
1129	C₂×C₄	—	8	4	no	—
1130	C₂×C₄	—	8	4	no	—
1131	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1132	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1133	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1134	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1135	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1136	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1137	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
1138	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
1139	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	4	no	—
1142	C₂²	—	2	4	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	2	2	no	—
1145	C₂²	—	2	2	no	—
1146	C₂²	—	2	2	no	—
1147	C₂²	—	2	4	no	—
1148	C₂²	—	2	4	no	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	4	no	—
1151	C₂²	—	2	4	no	—
1152	C₂²	—	4	1	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	4	2	no	—
1155	C₂²	—	4	2	no	—
1156	C₂²	—	4	2	no	—
1157	C₂²	—	4	2	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	2	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	2	no	—
1162	C₂²	—	4	1	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	4	1	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	4	1	no	—
1174	C₂²	—	4	1	no	—
1175	C₂²	—	8	16	no	—
1176	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1177	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
1178	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
1179	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1180	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1181	C₂²	#585×C₈₉	1	1	yes	characteristic
1182	C₂²	#585×C₈₉	1	1	yes	characteristic
1183	C₄	—	2	2	no	—
1184	C₄	—	2	2	no	—
1185	C₄	—	2	2	no	—
1186	C₄	—	2	2	no	—
1187	C₄	—	2	2	no	—
1188	C₄	—	2	2	no	—
1189	C₄	—	4	1	no	—
1190	C₄	—	4	1	no	—
1191	C₄	—	4	1	no	—
1192	C₄	—	4	2	no	—
1193	C₄	—	4	2	no	—
1194	C₄	—	4	1	no	—
1195	C₄	—	4	1	no	—
1196	C₄	—	4	2	no	—
1197	C₄	—	4	2	no	—
1198	C₄	—	4	2	no	—
1199	C₄	—	4	2	no	—
1200	C₄	#525×C₈₉	1	4	yes	—
1201	C₂	—	4	2	no	—
1202	C₂	—	4	4	no	—
1203	C₂	—	4	4	no	—
1204	C₂	—	4	2	no	—
1205	C₂	—	8	1	no	—
1206	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
1207	C₂	C₈₉×#3488	1	1	yes	characteristic
1208	C₂	C₈₉×#3488	1	1	yes	characteristic
1209	C₂	C₈₉×#3513	1	1	yes	characteristic
1210	C₂	C₈₉×#3514	1	1	yes	characteristic
1211	C₂	C₈₉×#3519	1	1	yes	characteristic
1212	C₂	C₈₉×#3521	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#529×C₈₉	C₂	semidirect
2. C₂×#518×C₈₉	C₂	semidirect
3. C₈₉×#2580	C₂	semidirect
4. C₈₉×#2538	C₂	semidirect
5. C₈₉×#2537	C₂	semidirect
6. C₈₉×#2535	C₂	semidirect
7. C₈₉×#2485	C₂	semidirect
8. C₈₉×#2485	C₂	semidirect
9. C₈₉×#2480	C₂	semidirect
10. C₈₉×#2472	C₂	semidirect
11. C₈₉×#2467	C₂	semidirect
12. C₈₉×#2463	C₂	semidirect
13. C₈₉×#2460	C₂	semidirect
14. C₈₉×#2456	C₂	semidirect
15. C₈₉×#2424	C₂	semidirect
16. C₈₉×#2418	C₂	semidirect
17. C₈₉×#2408	C₂	semidirect
18. C₈₉×#2408	C₂	semidirect
19. C₈₉×#2324	C₂	semidirect
20. C₈₉×#2324	C₂	semidirect
21. C₈₉×#2314	C₂	semidirect
22. C₄×#121×C₈₉	C₂	semidirect
23. C₄×#121×C₈₉	C₂	semidirect
27. C₂×#126×C₈₉	C₂²	semidirect
28. C₂×#125×C₈₉	C₂²	semidirect
31. C₂×#123×C₈₉	C₂²	semidirect
32. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
33. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
39. C₂×#121×C₈₉	C₂²	semidirect
43. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
52. C₂×C₄×D₄×C₈₉	C₂²	semidirect
53. C₂×C₄×D₄×C₈₉	C₂²	semidirect
54. C₂×C₄×D₄×C₈₉	C₂²	semidirect
57. C₂×#117×C₈₉	C₂²	semidirect
60. C₂²×C₄²×C₈₉	C₂²	semidirect
61. #399×C₈₉	C₂²	semidirect
64. #397×C₈₉	C₂²	semidirect
65. #396×C₈₉	C₂²	semidirect
66. #396×C₈₉	C₂²	semidirect
71. #394×C₈₉	C₂²	semidirect
72. #394×C₈₉	C₂²	semidirect
73. #393×C₈₉	C₂²	semidirect
76. #392×C₈₉	C₂²	semidirect
81. #390×C₈₉	C₂²	semidirect
82. #390×C₈₉	C₂²	semidirect
83. #389×C₈₉	C₂²	semidirect
84. #389×C₈₉	C₂²	semidirect
85. #389×C₈₉	C₂²	semidirect
86. #389×C₈₉	C₂²	semidirect
89. #388×C₈₉	C₂²	semidirect
90. #388×C₈₉	C₂²	semidirect
91. #388×C₈₉	C₂²	semidirect
92. #388×C₈₉	C₂²	semidirect
93. #388×C₈₉	C₂²	semidirect
94. #388×C₈₉	C₂²	semidirect
95. #387×C₈₉	C₂²	semidirect
96. #387×C₈₉	C₂²	semidirect
97. #387×C₈₉	C₂²	semidirect
98. #387×C₈₉	C₂²	semidirect
99. #386×C₈₉	C₂²	semidirect
100. #386×C₈₉	C₂²	semidirect
101. #386×C₈₉	C₂²	semidirect
102. #386×C₈₉	C₂²	semidirect
103. #386×C₈₉	C₂²	semidirect
104. #386×C₈₉	C₂²	semidirect
105. #385×C₈₉	C₂²	semidirect
106. #385×C₈₉	C₂²	semidirect
107. #385×C₈₉	C₂²	semidirect
108. #385×C₈₉	C₂²	semidirect
109. #384×C₈₉	C₂²	semidirect
110. #382×C₈₉	C₂²	semidirect
113. #380×C₈₉	C₂²	semidirect
114. #380×C₈₉	C₂²	semidirect
115. #380×C₈₉	C₂²	semidirect
116. #380×C₈₉	C₂²	semidirect
117. #380×C₈₉	C₂²	semidirect
118. #380×C₈₉	C₂²	semidirect
121. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
122. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
123. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
124. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
179. #117×C₈₉	D₄	semidirect
594. #35522	C₈₉	direct (N × H)
607. C₂×#529	C₂×C₈₉	semidirect
608. C₂×#518	C₂×C₈₉	semidirect
609. #2580	C₂×C₈₉	semidirect
610. #2538	C₂×C₈₉	semidirect
611. #2537	C₂×C₈₉	semidirect
612. #2535	C₂×C₈₉	semidirect
613. #2485	C₂×C₈₉	semidirect
614. #2485	C₂×C₈₉	semidirect
615. #2480	C₂×C₈₉	semidirect
616. #2472	C₂×C₈₉	semidirect
617. #2467	C₂×C₈₉	semidirect
618. #2463	C₂×C₈₉	semidirect
619. #2460	C₂×C₈₉	semidirect
620. #2456	C₂×C₈₉	semidirect
621. #2424	C₂×C₈₉	semidirect
622. #2418	C₂×C₈₉	semidirect
623. #2408	C₂×C₈₉	semidirect
624. #2408	C₂×C₈₉	semidirect
625. #2324	C₂×C₈₉	semidirect
626. #2324	C₂×C₈₉	semidirect
627. #2314	C₂×C₈₉	semidirect
628. C₄×#121	C₂×C₈₉	semidirect
629. C₄×#121	C₂×C₈₉	semidirect
630. C₈₉	#35522	direct (N × H)
634. C₂×#126	C₂²×C₈₉	semidirect
635. C₂×#125	C₂²×C₈₉	semidirect
638. C₂×#123	C₂²×C₈₉	semidirect
639. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
640. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
646. C₂×#121	C₂²×C₈₉	semidirect
650. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
659. C₂×C₄×D₄	C₂²×C₈₉	semidirect
660. C₂×C₄×D₄	C₂²×C₈₉	semidirect
661. C₂×C₄×D₄	C₂²×C₈₉	semidirect
664. C₂×#117	C₂²×C₈₉	semidirect
667. C₂²×C₄²	C₂²×C₈₉	semidirect
668. #399	C₂²×C₈₉	semidirect
671. #397	C₂²×C₈₉	semidirect
672. #396	C₂²×C₈₉	semidirect
673. #396	C₂²×C₈₉	semidirect
678. #394	C₂²×C₈₉	semidirect
679. #394	C₂²×C₈₉	semidirect
680. #393	C₂²×C₈₉	semidirect
683. #392	C₂²×C₈₉	semidirect
688. #390	C₂²×C₈₉	semidirect
689. #390	C₂²×C₈₉	semidirect
690. #389	C₂²×C₈₉	semidirect
691. #389	C₂²×C₈₉	semidirect
692. #389	C₂²×C₈₉	semidirect
693. #389	C₂²×C₈₉	semidirect
696. #388	C₂²×C₈₉	semidirect
697. #388	C₂²×C₈₉	semidirect
698. #388	C₂²×C₈₉	semidirect
699. #388	C₂²×C₈₉	semidirect
700. #388	C₂²×C₈₉	semidirect
701. #388	C₂²×C₈₉	semidirect
702. #387	C₂²×C₈₉	semidirect
703. #387	C₂²×C₈₉	semidirect
704. #387	C₂²×C₈₉	semidirect
705. #387	C₂²×C₈₉	semidirect
706. #386	C₂²×C₈₉	semidirect
707. #386	C₂²×C₈₉	semidirect
708. #386	C₂²×C₈₉	semidirect
709. #386	C₂²×C₈₉	semidirect
710. #386	C₂²×C₈₉	semidirect
711. #386	C₂²×C₈₉	semidirect
712. #385	C₂²×C₈₉	semidirect
713. #385	C₂²×C₈₉	semidirect
714. #385	C₂²×C₈₉	semidirect
715. #385	C₂²×C₈₉	semidirect
716. #384	C₂²×C₈₉	semidirect
717. #382	C₂²×C₈₉	semidirect
720. #380	C₂²×C₈₉	semidirect
721. #380	C₂²×C₈₉	semidirect
722. #380	C₂²×C₈₉	semidirect
723. #380	C₂²×C₈₉	semidirect
724. #380	C₂²×C₈₉	semidirect
725. #380	C₂²×C₈₉	semidirect
728. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
729. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
730. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
731. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
786. #117	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×#529×C₈₉	2
C₂×#518×C₈₉	2
C₈₉×#2580	2
C₈₉×#2538	2
C₈₉×#2537	2
C₈₉×#2535	2
C₈₉×#2485	2
C₈₉×#2480	2
C₈₉×#2472	2
C₈₉×#2467	2
C₈₉×#2463	2
C₈₉×#2460	2
C₈₉×#2456	2
C₈₉×#2424	2
C₈₉×#2418	2
C₈₉×#2408	2
C₈₉×#2324	2
C₈₉×#2314	2
C₄×#121×C₈₉	2
#35522	89

Subgroups — C89×#35522 #36413370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35522 #36413370