Subgroups — C₈₉×#35523 #36413371

Order 22784.

2576 conjugacy classes of subgroups.

The subgroup lattice has 1134 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×#2600	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2534	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2485	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2482	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2480	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2466	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2455	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2454	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2447	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2441	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#2435	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2427	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2422	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2418	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2415	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#2408	C₂	1	1	yes	maximal, characteristic
19	C₈₉×#2326	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₉×#2323	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#2319	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2290	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	2	yes	complemented
27	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#123×C₈₉	C₂²	1	2	yes	complemented
31	C₂×#123×C₈₉	C₂²	1	2	yes	complemented
32	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#120×C₈₉	C₂²	1	2	yes	—
37	#518×C₈₉	—	2	8	no	—
38	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
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	2	yes	complemented
47	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
48	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
51	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
52	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
53	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic, complemented
54	#399×C₈₉	C₂²	1	2	yes	—
55	#399×C₈₉	C₂²	1	2	yes	complemented
56	#397×C₈₉	C₂²	1	2	yes	—
57	#397×C₈₉	C₂²	1	2	yes	complemented
58	#397×C₈₉	C₂²	1	2	yes	complemented
59	#397×C₈₉	C₂²	1	2	yes	complemented
60	#397×C₈₉	C₂²	1	2	yes	complemented
61	#396×C₈₉	C₂²	1	2	yes	—
62	#396×C₈₉	C₂²	1	2	yes	complemented
63	#394×C₈₉	C₂²	1	2	yes	—
64	#394×C₈₉	C₂²	1	2	yes	—
65	#394×C₈₉	C₂²	1	2	yes	—
66	#394×C₈₉	C₂²	1	2	yes	—
67	#394×C₈₉	C₂²	1	2	yes	complemented
68	#394×C₈₉	C₂²	1	2	yes	complemented
69	#392×C₈₉	C₂²	1	2	yes	—
70	#391×C₈₉	C₂²	1	1	yes	characteristic, complemented
71	#391×C₈₉	C₂²	1	1	yes	characteristic, complemented
72	#390×C₈₉	C₂²	1	1	yes	characteristic
73	#390×C₈₉	C₂²	1	1	yes	characteristic
74	#390×C₈₉	C₂²	1	1	yes	characteristic
75	#390×C₈₉	C₂²	1	1	yes	characteristic
76	#389×C₈₉	C₂²	1	1	yes	characteristic, complemented
77	#389×C₈₉	C₂²	1	1	yes	characteristic, complemented
78	#389×C₈₉	C₂²	1	1	yes	characteristic, complemented
79	#389×C₈₉	C₂²	1	1	yes	characteristic, complemented
80	#389×C₈₉	C₂²	1	2	yes	complemented
81	#389×C₈₉	C₂²	1	2	yes	complemented
82	#389×C₈₉	C₂²	1	2	yes	complemented
83	#388×C₈₉	C₂²	1	2	yes	—
84	#388×C₈₉	C₂²	1	2	yes	—
85	#388×C₈₉	C₂²	1	1	yes	characteristic
86	#388×C₈₉	C₂²	1	1	yes	characteristic
87	#388×C₈₉	C₂²	1	2	yes	complemented
88	#388×C₈₉	C₂²	1	2	yes	complemented
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	#387×C₈₉	C₂²	1	2	yes	complemented
94	#387×C₈₉	C₂²	1	2	yes	complemented
95	#387×C₈₉	C₂²	1	1	yes	characteristic, complemented
96	#387×C₈₉	C₂²	1	1	yes	characteristic, complemented
97	#386×C₈₉	C₂²	1	1	yes	characteristic
98	#386×C₈₉	C₂²	1	1	yes	characteristic
99	#386×C₈₉	C₂²	1	2	yes	complemented
100	#386×C₈₉	C₂²	1	2	yes	complemented
101	#385×C₈₉	C₂²	1	2	yes	complemented
102	#385×C₈₉	C₂²	1	2	yes	complemented
103	#385×C₈₉	C₂²	1	1	yes	characteristic, complemented
104	#385×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	1	yes	characteristic, complemented
108	#384×C₈₉	C₂²	1	1	yes	characteristic, complemented
109	#381×C₈₉	C₂²	1	2	yes	complemented
110	#381×C₈₉	C₂²	1	2	yes	complemented
111	#380×C₈₉	C₂²	1	1	yes	characteristic
112	#380×C₈₉	C₂²	1	1	yes	characteristic, complemented
113	#380×C₈₉	C₂²	1	2	yes	complemented
114	#380×C₈₉	C₂²	1	2	yes	complemented
115	#380×C₈₉	C₂²	1	2	yes	complemented
116	#379×C₈₉	C₂²	1	2	yes	—
117	#379×C₈₉	C₂²	1	2	yes	—
118	#379×C₈₉	C₂²	1	2	yes	—
119	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
122	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
123	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
124	#376×C₈₉	C₂²	1	1	yes	characteristic, 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	1	yes	characteristic
132	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
133	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
134	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
140	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
141	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
142	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
144	#126×C₈₉	—	2	8	no	—
145	#125×C₈₉	—	2	4	no	—
146	#124×C₈₉	—	2	4	no	—
147	#124×C₈₉	—	2	4	no	—
148	#123×C₈₉	—	2	8	no	—
149	#123×C₈₉	—	4	4	no	—
150	C₂²⋊Q₈×C₈₉	—	2	4	no	—
151	C₂²⋊Q₈×C₈₉	—	2	4	no	—
152	#121×C₈₉	—	2	4	no	—
153	#121×C₈₉	—	2	4	no	—
154	#120×C₈₉	—	4	4	no	—
155	C₄×Q₈×C₈₉	—	2	4	no	—
156	C₄×D₄×C₈₉	—	2	4	no	—
157	C₄×D₄×C₈₉	—	2	8	no	—
158	C₄×D₄×C₈₉	—	2	8	no	—
159	C₄×D₄×C₈₉	—	2	4	no	—
160	C₄×D₄×C₈₉	—	2	4	no	—
161	C₄×D₄×C₈₉	—	2	8	no	—
162	C₄×D₄×C₈₉	—	2	4	no	—
163	C₄×D₄×C₈₉	—	4	4	no	—
164	C₄×D₄×C₈₉	D₄	1	8	yes	complemented
165	#117×C₈₉	—	2	8	no	—
166	#117×C₈₉	—	2	4	no	—
167	#117×C₈₉	—	2	4	no	—
168	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
183	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
190	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
191	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
208	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
220	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
222	C₂×C₄²×C₈₉	—	2	4	no	—
223	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
230	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
231	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
232	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
233	#95×C₈₉	C₂³	1	1	yes	characteristic
234	#95×C₈₉	C₂³	1	1	yes	characteristic
235	#95×C₈₉	C₂³	1	1	yes	characteristic
236	#95×C₈₉	C₂³	1	1	yes	characteristic
237	#95×C₈₉	C₂³	1	1	yes	characteristic
238	#95×C₈₉	C₂³	1	1	yes	characteristic
239	#95×C₈₉	C₂³	1	1	yes	characteristic
240	#95×C₈₉	C₂³	1	2	yes	—
241	#95×C₈₉	C₂³	1	2	yes	—
242	#95×C₈₉	C₂³	1	1	yes	characteristic
243	#95×C₈₉	C₂³	1	1	yes	characteristic
244	#95×C₈₉	C₂³	1	2	yes	—
245	#95×C₈₉	C₂³	1	1	yes	characteristic
246	#95×C₈₉	C₂³	1	2	yes	—
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	C₂⁴×C₈₉	—	2	4	no	—
255	C₂⁴×C₈₉	—	2	4	no	—
256	C₂⁴×C₈₉	—	2	4	no	—
257	C₂⁴×C₈₉	—	4	2	no	—
258	C₂⁴×C₈₉	—	4	2	no	—
259	C₂⁴×C₈₉	—	4	2	no	—
260	C₂⁴×C₈₉	—	4	2	no	—
261	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
262	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
263	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
264	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
265	C₂×Q₈×C₈₉	—	2	2	no	—
266	C₂×Q₈×C₈₉	—	2	2	no	—
267	C₂×Q₈×C₈₉	—	2	2	no	—
268	C₂×D₄×C₈₉	—	2	32	no	—
269	C₂×D₄×C₈₉	—	2	4	no	—
270	C₂×D₄×C₈₉	—	2	4	no	—
271	C₂×D₄×C₈₉	—	2	4	no	—
272	C₂×D₄×C₈₉	—	2	2	no	—
273	C₂×D₄×C₈₉	—	2	4	no	—
274	C₂×D₄×C₈₉	—	2	4	no	—
275	C₂×D₄×C₈₉	—	2	2	no	—
276	C₂×D₄×C₈₉	—	2	4	no	—
277	C₂×D₄×C₈₉	—	2	2	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	2	no	—
282	C₂×D₄×C₈₉	—	4	2	no	—
283	C₂×D₄×C₈₉	—	4	2	no	—
284	C₂×D₄×C₈₉	—	4	1	no	—
285	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
286	C₂×D₄×C₈₉	#41	1	4	yes	—
287	C₂²×C₄×C₈₉	—	2	2	no	—
288	C₂²×C₄×C₈₉	—	2	2	no	—
289	C₂²×C₄×C₈₉	—	2	2	no	—
290	C₂²×C₄×C₈₉	—	2	4	no	—
291	C₂²×C₄×C₈₉	—	2	2	no	—
292	C₂²×C₄×C₈₉	—	2	2	no	—
293	C₂²×C₄×C₈₉	—	2	2	no	—
294	C₂²×C₄×C₈₉	—	2	2	no	—
295	C₂²×C₄×C₈₉	—	2	2	no	—
296	C₂²×C₄×C₈₉	—	2	4	no	—
297	C₂²×C₄×C₈₉	—	2	4	no	—
298	C₂²×C₄×C₈₉	—	4	2	no	—
299	C₂²×C₄×C₈₉	—	4	2	no	—
300	C₂²×C₄×C₈₉	—	4	1	no	—
301	C₂²×C₄×C₈₉	—	4	1	no	—
302	C₂²×C₄×C₈₉	—	4	1	no	—
303	C₂²×C₄×C₈₉	—	4	2	no	—
304	C₂²×C₄×C₈₉	—	4	2	no	—
305	C₂²×C₄×C₈₉	—	4	2	no	—
306	C₂²×C₄×C₈₉	—	4	2	no	—
307	C₂²×C₄×C₈₉	—	4	2	no	—
308	C₂²×C₄×C₈₉	—	4	2	no	—
309	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
310	C₂²×C₄×C₈₉	#41	1	4	yes	—
311	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
328	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
330	C₄⋊C₄×C₈₉	—	2	2	no	—
331	C₄⋊C₄×C₈₉	—	2	2	no	—
332	C₄⋊C₄×C₈₉	—	2	2	no	—
333	C₄⋊C₄×C₈₉	—	2	4	no	—
334	C₄⋊C₄×C₈₉	—	2	4	no	—
335	C₄⋊C₄×C₈₉	—	2	4	no	—
336	C₄⋊C₄×C₈₉	—	2	2	no	—
337	C₄⋊C₄×C₈₉	—	2	4	no	—
338	C₄⋊C₄×C₈₉	—	2	2	no	—
339	C₄⋊C₄×C₈₉	—	2	2	no	—
340	C₄⋊C₄×C₈₉	—	2	2	no	—
341	C₄⋊C₄×C₈₉	—	2	4	no	—
342	C₄⋊C₄×C₈₉	—	4	2	no	—
343	C₄⋊C₄×C₈₉	—	4	2	no	—
344	C₄⋊C₄×C₈₉	—	4	1	no	—
345	C₄⋊C₄×C₈₉	—	4	1	no	—
346	C₄⋊C₄×C₈₉	—	4	2	no	—
347	C₄⋊C₄×C₈₉	—	4	2	no	—
348	C₄⋊C₄×C₈₉	—	4	2	no	—
349	C₄⋊C₄×C₈₉	—	4	2	no	—
350	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
351	C₂²⋊C₄×C₈₉	—	2	4	no	—
352	C₂²⋊C₄×C₈₉	—	2	4	no	—
353	C₂²⋊C₄×C₈₉	—	2	4	no	—
354	C₂²⋊C₄×C₈₉	—	2	4	no	—
355	C₂²⋊C₄×C₈₉	—	2	2	no	—
356	C₂²⋊C₄×C₈₉	—	2	4	no	—
357	C₂²⋊C₄×C₈₉	—	2	4	no	—
358	C₂²⋊C₄×C₈₉	—	2	4	no	—
359	C₂²⋊C₄×C₈₉	—	2	4	no	—
360	C₂²⋊C₄×C₈₉	—	2	4	no	—
361	C₂²⋊C₄×C₈₉	—	2	2	no	—
362	C₂²⋊C₄×C₈₉	—	2	2	no	—
363	C₂²⋊C₄×C₈₉	—	2	2	no	—
364	C₂²⋊C₄×C₈₉	—	2	4	no	—
365	C₂²⋊C₄×C₈₉	—	2	4	no	—
366	C₂²⋊C₄×C₈₉	—	2	4	no	—
367	C₂²⋊C₄×C₈₉	—	2	4	no	—
368	C₂²⋊C₄×C₈₉	—	2	2	no	—
369	C₂²⋊C₄×C₈₉	—	4	2	no	—
370	C₂²⋊C₄×C₈₉	—	4	1	no	—
371	C₂²⋊C₄×C₈₉	—	4	2	no	—
372	C₂²⋊C₄×C₈₉	—	4	2	no	—
373	C₂²⋊C₄×C₈₉	—	4	2	no	—
374	C₂²⋊C₄×C₈₉	—	4	1	no	—
375	C₂²⋊C₄×C₈₉	—	4	1	no	—
376	C₂²⋊C₄×C₈₉	—	4	2	no	—
377	C₂²⋊C₄×C₈₉	—	4	2	no	—
378	C₂²⋊C₄×C₈₉	—	4	2	no	—
379	C₂²⋊C₄×C₈₉	—	4	2	no	—
380	C₂²⋊C₄×C₈₉	—	4	2	no	—
381	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
382	C₄²×C₈₉	—	2	2	no	—
383	C₄²×C₈₉	—	2	2	no	—
384	C₄²×C₈₉	—	2	2	no	—
385	C₄²×C₈₉	—	2	4	no	—
386	C₄²×C₈₉	—	2	2	no	—
387	C₄²×C₈₉	—	2	4	no	—
388	C₄²×C₈₉	—	2	2	no	—
389	C₄²×C₈₉	—	2	2	no	—
390	C₄²×C₈₉	—	4	2	no	—
391	C₄²×C₈₉	C₂×D₄	1	4	yes	—
392	C₂³×C₈₉	—	2	16	no	—
393	C₂³×C₈₉	—	2	1	no	—
394	C₂³×C₈₉	—	2	1	no	—
395	C₂³×C₈₉	—	2	2	no	—
396	C₂³×C₈₉	—	2	1	no	—
397	C₂³×C₈₉	—	2	1	no	—
398	C₂³×C₈₉	—	2	1	no	—
399	C₂³×C₈₉	—	2	2	no	—
400	C₂³×C₈₉	—	2	2	no	—
401	C₂³×C₈₉	—	2	2	no	—
402	C₂³×C₈₉	—	2	2	no	—
403	C₂³×C₈₉	—	2	2	no	—
404	C₂³×C₈₉	—	2	1	no	—
405	C₂³×C₈₉	—	2	1	no	—
406	C₂³×C₈₉	—	2	2	no	—
407	C₂³×C₈₉	—	2	2	no	—
408	C₂³×C₈₉	—	2	2	no	—
409	C₂³×C₈₉	—	2	2	no	—
410	C₂³×C₈₉	—	2	1	no	—
411	C₂³×C₈₉	—	2	1	no	—
412	C₂³×C₈₉	—	2	1	no	—
413	C₂³×C₈₉	—	2	1	no	—
414	C₂³×C₈₉	—	2	2	no	—
415	C₂³×C₈₉	—	2	2	no	—
416	C₂³×C₈₉	—	2	1	no	—
417	C₂³×C₈₉	—	8	4	no	—
418	C₂³×C₈₉	—	8	4	no	—
419	C₂³×C₈₉	—	8	4	no	—
420	C₂³×C₈₉	—	8	4	no	—
421	C₂³×C₈₉	—	8	4	no	—
422	C₂³×C₈₉	—	8	4	no	—
423	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
424	C₂³×C₈₉	C₂×#41	1	2	yes	—
425	C₂³×C₈₉	C₂×#41	1	4	yes	—
426	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
427	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
428	Q₈×C₈₉	—	4	4	no	—
429	D₄×C₈₉	—	2	16	no	—
430	D₄×C₈₉	—	2	8	no	—
431	D₄×C₈₉	—	2	8	no	—
432	D₄×C₈₉	—	4	8	no	—
433	D₄×C₈₉	—	4	4	no	—
434	D₄×C₈₉	—	4	8	no	—
435	C₂×C₄×C₈₉	—	2	1	no	—
436	C₂×C₄×C₈₉	—	2	1	no	—
437	C₂×C₄×C₈₉	—	2	1	no	—
438	C₂×C₄×C₈₉	—	2	2	no	—
439	C₂×C₄×C₈₉	—	2	2	no	—
440	C₂×C₄×C₈₉	—	2	1	no	—
441	C₂×C₄×C₈₉	—	2	1	no	—
442	C₂×C₄×C₈₉	—	2	1	no	—
443	C₂×C₄×C₈₉	—	2	8	no	—
444	C₂×C₄×C₈₉	—	2	1	no	—
445	C₂×C₄×C₈₉	—	2	1	no	—
446	C₂×C₄×C₈₉	—	2	1	no	—
447	C₂×C₄×C₈₉	—	2	2	no	—
448	C₂×C₄×C₈₉	—	2	1	no	—
449	C₂×C₄×C₈₉	—	2	2	no	—
450	C₂×C₄×C₈₉	—	2	1	no	—
451	C₂×C₄×C₈₉	—	2	2	no	—
452	C₂×C₄×C₈₉	—	2	1	no	—
453	C₂×C₄×C₈₉	—	2	1	no	—
454	C₂×C₄×C₈₉	—	2	1	no	—
455	C₂×C₄×C₈₉	—	2	1	no	—
456	C₂×C₄×C₈₉	—	2	1	no	—
457	C₂×C₄×C₈₉	—	2	2	no	—
458	C₂×C₄×C₈₉	—	2	2	no	—
459	C₂×C₄×C₈₉	—	2	1	no	—
460	C₂×C₄×C₈₉	—	2	2	no	—
461	C₂×C₄×C₈₉	—	2	2	no	—
462	C₂×C₄×C₈₉	—	2	2	no	—
463	C₂×C₄×C₈₉	—	2	2	no	—
464	C₂×C₄×C₈₉	—	2	1	no	—
465	C₂×C₄×C₈₉	—	2	2	no	—
466	C₂×C₄×C₈₉	—	2	1	no	—
467	C₂×C₄×C₈₉	—	2	1	no	—
468	C₂×C₄×C₈₉	—	2	1	no	—
469	C₂×C₄×C₈₉	—	2	2	no	—
470	C₂×C₄×C₈₉	—	2	1	no	—
471	C₂×C₄×C₈₉	—	2	2	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	2	no	—
480	C₂×C₄×C₈₉	—	2	2	no	—
481	C₂×C₄×C₈₉	—	2	1	no	—
482	C₂×C₄×C₈₉	—	2	1	no	—
483	C₂×C₄×C₈₉	—	2	1	no	—
484	C₂×C₄×C₈₉	—	2	2	no	—
485	C₂×C₄×C₈₉	—	2	1	no	—
486	C₂×C₄×C₈₉	—	4	8	no	—
487	C₂×C₄×C₈₉	—	4	4	no	—
488	C₂×C₄×C₈₉	—	4	4	no	—
489	C₂×C₄×C₈₉	—	4	4	no	—
490	C₂×C₄×C₈₉	—	8	4	no	—
491	C₂×C₄×C₈₉	—	8	4	no	—
492	C₂×C₄×C₈₉	—	8	4	no	—
493	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
496	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
498	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
499	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
500	C₂²×C₈₉	—	2	2	no	—
501	C₂²×C₈₉	—	2	4	no	—
502	C₂²×C₈₉	—	2	4	no	—
503	C₂²×C₈₉	—	2	4	no	—
504	C₂²×C₈₉	—	2	2	no	—
505	C₂²×C₈₉	—	2	4	no	—
506	C₂²×C₈₉	—	2	2	no	—
507	C₂²×C₈₉	—	2	2	no	—
508	C₂²×C₈₉	—	2	2	no	—
509	C₂²×C₈₉	—	2	2	no	—
510	C₂²×C₈₉	—	2	4	no	—
511	C₂²×C₈₉	—	2	4	no	—
512	C₂²×C₈₉	—	4	1	no	—
513	C₂²×C₈₉	—	4	1	no	—
514	C₂²×C₈₉	—	4	2	no	—
515	C₂²×C₈₉	—	4	1	no	—
516	C₂²×C₈₉	—	4	2	no	—
517	C₂²×C₈₉	—	4	1	no	—
518	C₂²×C₈₉	—	4	2	no	—
519	C₂²×C₈₉	—	4	2	no	—
520	C₂²×C₈₉	—	4	1	no	—
521	C₂²×C₈₉	—	4	2	no	—
522	C₂²×C₈₉	—	4	2	no	—
523	C₂²×C₈₉	—	4	2	no	—
524	C₂²×C₈₉	—	4	1	no	—
525	C₂²×C₈₉	—	4	1	no	—
526	C₂²×C₈₉	—	4	2	no	—
527	C₂²×C₈₉	—	4	1	no	—
528	C₂²×C₈₉	—	8	16	no	—
529	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
530	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
531	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
532	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
533	C₂²×C₈₉	#585	1	1	yes	characteristic
534	C₂²×C₈₉	#585	1	1	yes	characteristic
535	C₂²×C₈₉	#585	1	1	yes	characteristic
536	C₄×C₈₉	—	2	2	no	—
537	C₄×C₈₉	—	2	2	no	—
538	C₄×C₈₉	—	2	4	no	—
539	C₄×C₈₉	—	2	2	no	—
540	C₄×C₈₉	—	4	1	no	—
541	C₄×C₈₉	—	4	2	no	—
542	C₄×C₈₉	—	4	1	no	—
543	C₄×C₈₉	—	4	1	no	—
544	C₄×C₈₉	—	4	1	no	—
545	C₄×C₈₉	—	4	2	no	—
546	C₄×C₈₉	—	4	1	no	—
547	C₄×C₈₉	—	4	2	no	—
548	C₄×C₈₉	—	4	2	no	—
549	C₄×C₈₉	—	4	1	no	—
550	C₄×C₈₉	—	4	1	no	—
551	C₄×C₈₉	—	4	1	no	—
552	C₄×C₈₉	—	4	2	no	—
553	C₄×C₈₉	—	4	1	no	—
554	C₄×C₈₉	#525	1	4	yes	—
555	#35523	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
556	C₂×C₈₉	—	4	2	no	—
557	C₂×C₈₉	—	4	4	no	—
558	C₂×C₈₉	—	4	4	no	—
559	C₂×C₈₉	—	4	2	no	—
560	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
561	C₂×C₈₉	#3485	1	1	yes	characteristic
562	C₂×C₈₉	#3488	1	1	yes	characteristic
563	C₂×C₈₉	#3494	1	1	yes	characteristic
564	C₂×C₈₉	#3510	1	1	yes	characteristic
565	C₂×C₈₉	#3513	1	1	yes	characteristic
566	C₂×C₈₉	#3521	1	1	yes	characteristic
567	C₂×#529	C₂×C₈₉	1	1	yes	characteristic, complemented
568	C₂×#518	C₂×C₈₉	1	1	yes	characteristic, complemented
569	#2600	C₂×C₈₉	1	2	yes	complemented
570	#2534	C₂×C₈₉	1	2	yes	complemented
571	#2485	C₂×C₈₉	1	2	yes	complemented
572	#2482	C₂×C₈₉	1	2	yes	complemented
573	#2480	C₂×C₈₉	1	2	yes	complemented
574	#2466	C₂×C₈₉	1	2	yes	complemented
575	#2455	C₂×C₈₉	1	2	yes	complemented
576	#2454	C₂×C₈₉	1	1	yes	characteristic, complemented
577	#2447	C₂×C₈₉	1	1	yes	characteristic, complemented
578	#2441	C₂×C₈₉	1	1	yes	characteristic, complemented
579	#2435	C₂×C₈₉	1	1	yes	characteristic, complemented
580	#2427	C₂×C₈₉	1	1	yes	characteristic, complemented
581	#2422	C₂×C₈₉	1	1	yes	characteristic, complemented
582	#2418	C₂×C₈₉	1	2	yes	complemented
583	#2415	C₂×C₈₉	1	1	yes	characteristic, complemented
584	#2408	C₂×C₈₉	1	1	yes	characteristic
585	#2326	C₂×C₈₉	1	1	yes	characteristic, complemented
586	#2323	C₂×C₈₉	1	1	yes	characteristic, complemented
587	#2319	C₂×C₈₉	1	1	yes	characteristic, complemented
588	C₄×#121	C₂×C₈₉	1	1	yes	characteristic, complemented
589	#2290	C₂×C₈₉	1	1	yes	characteristic, complemented
590	C₈₉	#35523	1	1	yes	characteristic, direct product factor, Sylow
591	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
592	#529	—	2	8	no	—
593	C₂×#126	C₂²×C₈₉	1	2	yes	complemented
594	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic, complemented
595	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
596	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
597	C₂×#123	C₂²×C₈₉	1	2	yes	complemented
598	C₂×#123	C₂²×C₈₉	1	2	yes	complemented
599	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
600	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
601	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
602	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
603	C₂×#120	C₂²×C₈₉	1	2	yes	—
604	#518	—	2	8	no	—
605	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
606	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
607	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
608	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
609	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
610	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
611	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
612	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
613	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
614	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
615	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
616	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
617	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
618	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
619	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
620	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic, complemented
621	#399	C₂²×C₈₉	1	2	yes	—
622	#399	C₂²×C₈₉	1	2	yes	complemented
623	#397	C₂²×C₈₉	1	2	yes	—
624	#397	C₂²×C₈₉	1	2	yes	complemented
625	#397	C₂²×C₈₉	1	2	yes	complemented
626	#397	C₂²×C₈₉	1	2	yes	complemented
627	#397	C₂²×C₈₉	1	2	yes	complemented
628	#396	C₂²×C₈₉	1	2	yes	—
629	#396	C₂²×C₈₉	1	2	yes	complemented
630	#394	C₂²×C₈₉	1	2	yes	—
631	#394	C₂²×C₈₉	1	2	yes	—
632	#394	C₂²×C₈₉	1	2	yes	—
633	#394	C₂²×C₈₉	1	2	yes	—
634	#394	C₂²×C₈₉	1	2	yes	complemented
635	#394	C₂²×C₈₉	1	2	yes	complemented
636	#392	C₂²×C₈₉	1	2	yes	—
637	#391	C₂²×C₈₉	1	1	yes	characteristic, complemented
638	#391	C₂²×C₈₉	1	1	yes	characteristic, complemented
639	#390	C₂²×C₈₉	1	1	yes	characteristic
640	#390	C₂²×C₈₉	1	1	yes	characteristic
641	#390	C₂²×C₈₉	1	1	yes	characteristic
642	#390	C₂²×C₈₉	1	1	yes	characteristic
643	#389	C₂²×C₈₉	1	1	yes	characteristic, complemented
644	#389	C₂²×C₈₉	1	1	yes	characteristic, complemented
645	#389	C₂²×C₈₉	1	1	yes	characteristic, complemented
646	#389	C₂²×C₈₉	1	2	yes	complemented
647	#389	C₂²×C₈₉	1	2	yes	complemented
648	#389	C₂²×C₈₉	1	1	yes	characteristic, complemented
649	#389	C₂²×C₈₉	1	2	yes	complemented
650	#388	C₂²×C₈₉	1	2	yes	—
651	#388	C₂²×C₈₉	1	2	yes	—
652	#388	C₂²×C₈₉	1	1	yes	characteristic
653	#388	C₂²×C₈₉	1	1	yes	characteristic
654	#388	C₂²×C₈₉	1	2	yes	complemented
655	#388	C₂²×C₈₉	1	2	yes	complemented
656	#388	C₂²×C₈₉	1	2	yes	complemented
657	#388	C₂²×C₈₉	1	2	yes	complemented
658	#388	C₂²×C₈₉	1	2	yes	complemented
659	#388	C₂²×C₈₉	1	2	yes	complemented
660	#387	C₂²×C₈₉	1	2	yes	complemented
661	#387	C₂²×C₈₉	1	2	yes	complemented
662	#387	C₂²×C₈₉	1	1	yes	characteristic, complemented
663	#387	C₂²×C₈₉	1	1	yes	characteristic, complemented
664	#386	C₂²×C₈₉	1	1	yes	characteristic
665	#386	C₂²×C₈₉	1	1	yes	characteristic
666	#386	C₂²×C₈₉	1	2	yes	complemented
667	#386	C₂²×C₈₉	1	2	yes	complemented
668	#385	C₂²×C₈₉	1	2	yes	complemented
669	#385	C₂²×C₈₉	1	2	yes	complemented
670	#385	C₂²×C₈₉	1	1	yes	characteristic, complemented
671	#385	C₂²×C₈₉	1	2	yes	complemented
672	#385	C₂²×C₈₉	1	2	yes	complemented
673	#385	C₂²×C₈₉	1	2	yes	complemented
674	#385	C₂²×C₈₉	1	1	yes	characteristic, complemented
675	#384	C₂²×C₈₉	1	1	yes	characteristic, complemented
676	#381	C₂²×C₈₉	1	2	yes	complemented
677	#381	C₂²×C₈₉	1	2	yes	complemented
678	#380	C₂²×C₈₉	1	1	yes	characteristic
679	#380	C₂²×C₈₉	1	2	yes	complemented
680	#380	C₂²×C₈₉	1	1	yes	characteristic, complemented
681	#380	C₂²×C₈₉	1	2	yes	complemented
682	#380	C₂²×C₈₉	1	2	yes	complemented
683	#379	C₂²×C₈₉	1	2	yes	—
684	#379	C₂²×C₈₉	1	2	yes	—
685	#379	C₂²×C₈₉	1	2	yes	—
686	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
687	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
688	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
689	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
690	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
691	#376	C₂²×C₈₉	1	1	yes	characteristic, complemented
692	C₂⁵	C₂³×C₈₉	1	2	yes	—
693	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
694	C₂²×D₄	—	2	4	no	—
695	C₂²×D₄	—	2	4	no	—
696	C₂²×D₄	—	2	4	no	—
697	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
698	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
699	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
700	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
701	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
702	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
703	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
704	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
705	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
706	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
707	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
708	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
709	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
710	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
711	#126	—	2	8	no	—
712	#125	—	2	4	no	—
713	#124	—	2	4	no	—
714	#124	—	2	4	no	—
715	#123	—	2	8	no	—
716	#123	—	4	4	no	—
717	C₂²⋊Q₈	—	2	4	no	—
718	C₂²⋊Q₈	—	2	4	no	—
719	#121	—	2	4	no	—
720	#121	—	2	4	no	—
721	#120	—	4	4	no	—
722	C₄×Q₈	—	2	4	no	—
723	C₄×D₄	—	2	4	no	—
724	C₄×D₄	—	2	8	no	—
725	C₄×D₄	—	2	8	no	—
726	C₄×D₄	—	2	4	no	—
727	C₄×D₄	—	2	4	no	—
728	C₄×D₄	—	2	8	no	—
729	C₄×D₄	—	2	4	no	—
730	C₄×D₄	—	4	4	no	—
731	C₄×D₄	D₄×C₈₉	1	8	yes	complemented
732	#117	—	2	8	no	—
733	#117	—	2	4	no	—
734	#117	—	2	4	no	—
735	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
736	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
737	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
738	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
739	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
740	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
741	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
742	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
743	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
744	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
745	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
746	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
747	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
748	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
749	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
750	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
751	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
752	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
753	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
754	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
755	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
756	C₂×C₂²⋊C₄	—	2	8	no	—
757	C₂×C₂²⋊C₄	—	2	8	no	—
758	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
759	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
760	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
762	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
765	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
766	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
767	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
768	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
769	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
774	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
776	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
777	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
780	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
781	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
782	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
783	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
784	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
785	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
786	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
787	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
788	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
789	C₂×C₄²	—	2	4	no	—
790	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
791	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
792	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
793	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
794	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
795	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
796	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
797	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
798	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
799	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
800	#95	C₂³×C₈₉	1	1	yes	characteristic
801	#95	C₂³×C₈₉	1	1	yes	characteristic
802	#95	C₂³×C₈₉	1	1	yes	characteristic
803	#95	C₂³×C₈₉	1	1	yes	characteristic
804	#95	C₂³×C₈₉	1	1	yes	characteristic
805	#95	C₂³×C₈₉	1	1	yes	characteristic
806	#95	C₂³×C₈₉	1	1	yes	characteristic
807	#95	C₂³×C₈₉	1	2	yes	—
808	#95	C₂³×C₈₉	1	2	yes	—
809	#95	C₂³×C₈₉	1	1	yes	characteristic
810	#95	C₂³×C₈₉	1	1	yes	characteristic
811	#95	C₂³×C₈₉	1	2	yes	—
812	#95	C₂³×C₈₉	1	1	yes	characteristic
813	#95	C₂³×C₈₉	1	2	yes	—
814	#95	C₂³×C₈₉	1	2	yes	—
815	#95	C₂³×C₈₉	1	2	yes	—
816	#95	C₂³×C₈₉	1	2	yes	—
817	#95	C₂³×C₈₉	1	2	yes	—
818	#95	C₂³×C₈₉	1	2	yes	—
819	#95	C₂³×C₈₉	1	2	yes	—
820	#95	C₂³×C₈₉	1	2	yes	—
821	C₂⁴	—	2	4	no	—
822	C₂⁴	—	2	4	no	—
823	C₂⁴	—	2	4	no	—
824	C₂⁴	—	4	2	no	—
825	C₂⁴	—	4	2	no	—
826	C₂⁴	—	4	2	no	—
827	C₂⁴	—	4	2	no	—
828	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
829	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
830	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
831	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
832	C₂×Q₈	—	2	2	no	—
833	C₂×Q₈	—	2	2	no	—
834	C₂×Q₈	—	2	2	no	—
835	C₂×D₄	—	2	32	no	—
836	C₂×D₄	—	2	4	no	—
837	C₂×D₄	—	2	4	no	—
838	C₂×D₄	—	2	4	no	—
839	C₂×D₄	—	2	2	no	—
840	C₂×D₄	—	2	4	no	—
841	C₂×D₄	—	2	4	no	—
842	C₂×D₄	—	2	2	no	—
843	C₂×D₄	—	2	4	no	—
844	C₂×D₄	—	2	2	no	—
845	C₂×D₄	—	2	4	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	2	no	—
849	C₂×D₄	—	4	2	no	—
850	C₂×D₄	—	4	2	no	—
851	C₂×D₄	—	4	1	no	—
852	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
853	C₂×D₄	#41×C₈₉	1	4	yes	—
854	C₂²×C₄	—	2	2	no	—
855	C₂²×C₄	—	2	2	no	—
856	C₂²×C₄	—	2	2	no	—
857	C₂²×C₄	—	2	4	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	2	no	—
863	C₂²×C₄	—	2	4	no	—
864	C₂²×C₄	—	2	4	no	—
865	C₂²×C₄	—	4	2	no	—
866	C₂²×C₄	—	4	2	no	—
867	C₂²×C₄	—	4	1	no	—
868	C₂²×C₄	—	4	1	no	—
869	C₂²×C₄	—	4	1	no	—
870	C₂²×C₄	—	4	2	no	—
871	C₂²×C₄	—	4	2	no	—
872	C₂²×C₄	—	4	2	no	—
873	C₂²×C₄	—	4	2	no	—
874	C₂²×C₄	—	4	2	no	—
875	C₂²×C₄	—	4	2	no	—
876	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
877	C₂²×C₄	#41×C₈₉	1	4	yes	—
878	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
880	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
882	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
883	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
884	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
885	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
886	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
887	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
888	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
889	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
890	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
891	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
892	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
893	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
894	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
895	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
896	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	4	no	—
901	C₄⋊C₄	—	2	4	no	—
902	C₄⋊C₄	—	2	4	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	4	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	4	no	—
909	C₄⋊C₄	—	4	2	no	—
910	C₄⋊C₄	—	4	2	no	—
911	C₄⋊C₄	—	4	2	no	—
912	C₄⋊C₄	—	4	2	no	—
913	C₄⋊C₄	—	4	2	no	—
914	C₄⋊C₄	—	4	1	no	—
915	C₄⋊C₄	—	4	1	no	—
916	C₄⋊C₄	—	4	2	no	—
917	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
918	C₂²⋊C₄	—	2	4	no	—
919	C₂²⋊C₄	—	2	4	no	—
920	C₂²⋊C₄	—	2	4	no	—
921	C₂²⋊C₄	—	2	4	no	—
922	C₂²⋊C₄	—	2	2	no	—
923	C₂²⋊C₄	—	2	4	no	—
924	C₂²⋊C₄	—	2	4	no	—
925	C₂²⋊C₄	—	2	4	no	—
926	C₂²⋊C₄	—	2	4	no	—
927	C₂²⋊C₄	—	2	4	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	4	no	—
932	C₂²⋊C₄	—	2	4	no	—
933	C₂²⋊C₄	—	2	4	no	—
934	C₂²⋊C₄	—	2	4	no	—
935	C₂²⋊C₄	—	2	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	—	4	2	no	—
941	C₂²⋊C₄	—	4	2	no	—
942	C₂²⋊C₄	—	4	1	no	—
943	C₂²⋊C₄	—	4	2	no	—
944	C₂²⋊C₄	—	4	2	no	—
945	C₂²⋊C₄	—	4	2	no	—
946	C₂²⋊C₄	—	4	1	no	—
947	C₂²⋊C₄	—	4	1	no	—
948	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
949	C₄²	—	2	2	no	—
950	C₄²	—	2	2	no	—
951	C₄²	—	2	2	no	—
952	C₄²	—	2	4	no	—
953	C₄²	—	2	2	no	—
954	C₄²	—	2	4	no	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	2	no	—
957	C₄²	—	4	2	no	—
958	C₄²	C₂×D₄×C₈₉	1	4	yes	—
959	C₂³	—	2	16	no	—
960	C₂³	—	2	1	no	—
961	C₂³	—	2	1	no	—
962	C₂³	—	2	2	no	—
963	C₂³	—	2	1	no	—
964	C₂³	—	2	1	no	—
965	C₂³	—	2	1	no	—
966	C₂³	—	2	2	no	—
967	C₂³	—	2	2	no	—
968	C₂³	—	2	2	no	—
969	C₂³	—	2	2	no	—
970	C₂³	—	2	2	no	—
971	C₂³	—	2	1	no	—
972	C₂³	—	2	1	no	—
973	C₂³	—	2	2	no	—
974	C₂³	—	2	2	no	—
975	C₂³	—	2	2	no	—
976	C₂³	—	2	2	no	—
977	C₂³	—	2	1	no	—
978	C₂³	—	2	1	no	—
979	C₂³	—	2	1	no	—
980	C₂³	—	2	1	no	—
981	C₂³	—	2	2	no	—
982	C₂³	—	2	2	no	—
983	C₂³	—	2	1	no	—
984	C₂³	—	8	4	no	—
985	C₂³	—	8	4	no	—
986	C₂³	—	8	4	no	—
987	C₂³	—	8	4	no	—
988	C₂³	—	8	4	no	—
989	C₂³	—	8	4	no	—
990	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
991	C₂³	C₂×#41×C₈₉	1	2	yes	—
992	C₂³	C₂×#41×C₈₉	1	4	yes	—
993	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
994	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
995	Q₈	—	4	4	no	—
996	D₄	—	2	16	no	—
997	D₄	—	2	8	no	—
998	D₄	—	2	8	no	—
999	D₄	—	4	8	no	—
1000	D₄	—	4	4	no	—
1001	D₄	—	4	8	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	8	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	4	8	no	—
1054	C₂×C₄	—	4	4	no	—
1055	C₂×C₄	—	4	4	no	—
1056	C₂×C₄	—	4	4	no	—
1057	C₂×C₄	—	8	4	no	—
1058	C₂×C₄	—	8	4	no	—
1059	C₂×C₄	—	8	4	no	—
1060	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1061	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1062	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
1063	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1064	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
1065	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
1066	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
1067	C₂²	—	2	2	no	—
1068	C₂²	—	2	4	no	—
1069	C₂²	—	2	4	no	—
1070	C₂²	—	2	4	no	—
1071	C₂²	—	2	2	no	—
1072	C₂²	—	2	4	no	—
1073	C₂²	—	2	2	no	—
1074	C₂²	—	2	2	no	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	2	2	no	—
1077	C₂²	—	2	4	no	—
1078	C₂²	—	2	4	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	2	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	2	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	4	2	no	—
1086	C₂²	—	4	2	no	—
1087	C₂²	—	4	2	no	—
1088	C₂²	—	4	2	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	2	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	8	16	no	—
1096	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1097	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
1098	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
1099	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1100	C₂²	#585×C₈₉	1	1	yes	characteristic
1101	C₂²	#585×C₈₉	1	1	yes	characteristic
1102	C₂²	#585×C₈₉	1	1	yes	characteristic
1103	C₄	—	2	2	no	—
1104	C₄	—	2	2	no	—
1105	C₄	—	2	4	no	—
1106	C₄	—	2	2	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	2	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	2	no	—
1115	C₄	—	4	1	no	—
1116	C₄	—	4	2	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	1	no	—
1121	C₄	#525×C₈₉	1	4	yes	—
1122	C₂	—	4	2	no	—
1123	C₂	—	4	4	no	—
1124	C₂	—	4	4	no	—
1125	C₂	—	4	2	no	—
1126	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
1127	C₂	C₈₉×#3485	1	1	yes	characteristic
1128	C₂	C₈₉×#3488	1	1	yes	characteristic
1129	C₂	C₈₉×#3494	1	1	yes	characteristic
1130	C₂	C₈₉×#3510	1	1	yes	characteristic
1131	C₂	C₈₉×#3513	1	1	yes	characteristic
1132	C₂	C₈₉×#3521	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₈₉×#2408	C₂
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×#2600	C₂	semidirect
4. C₈₉×#2534	C₂	semidirect
5. C₈₉×#2485	C₂	semidirect
6. C₈₉×#2482	C₂	semidirect
7. C₈₉×#2480	C₂	semidirect
8. C₈₉×#2466	C₂	semidirect
9. C₈₉×#2455	C₂	semidirect
10. C₈₉×#2454	C₂	semidirect
11. C₈₉×#2447	C₂	semidirect
12. C₈₉×#2441	C₂	semidirect
13. C₈₉×#2435	C₂	semidirect
14. C₈₉×#2427	C₂	semidirect
15. C₈₉×#2422	C₂	semidirect
16. C₈₉×#2418	C₂	semidirect
17. C₈₉×#2415	C₂	semidirect
19. C₈₉×#2326	C₂	semidirect
20. C₈₉×#2323	C₂	semidirect
21. C₈₉×#2319	C₂	semidirect
22. C₄×#121×C₈₉	C₂	semidirect
23. C₈₉×#2290	C₂	semidirect
26. C₂×#126×C₈₉	C₂²	semidirect
27. C₂×#125×C₈₉	C₂²	semidirect
30. C₂×#123×C₈₉	C₂²	semidirect
31. C₂×#123×C₈₉	C₂²	semidirect
33. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
38. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
46. C₂×C₄×D₄×C₈₉	C₂²	semidirect
47. C₂×C₄×D₄×C₈₉	C₂²	semidirect
50. C₂×#117×C₈₉	C₂²	semidirect
53. C₂²×C₄²×C₈₉	C₂²	semidirect
55. #399×C₈₉	C₂²	semidirect
57. #397×C₈₉	C₂²	semidirect
58. #397×C₈₉	C₂²	semidirect
59. #397×C₈₉	C₂²	semidirect
60. #397×C₈₉	C₂²	semidirect
62. #396×C₈₉	C₂²	semidirect
67. #394×C₈₉	C₂²	semidirect
68. #394×C₈₉	C₂²	semidirect
70. #391×C₈₉	C₂²	semidirect
71. #391×C₈₉	C₂²	semidirect
76. #389×C₈₉	C₂²	semidirect
77. #389×C₈₉	C₂²	semidirect
78. #389×C₈₉	C₂²	semidirect
79. #389×C₈₉	C₂²	semidirect
80. #389×C₈₉	C₂²	semidirect
81. #389×C₈₉	C₂²	semidirect
82. #389×C₈₉	C₂²	semidirect
87. #388×C₈₉	C₂²	semidirect
88. #388×C₈₉	C₂²	semidirect
89. #388×C₈₉	C₂²	semidirect
90. #388×C₈₉	C₂²	semidirect
91. #388×C₈₉	C₂²	semidirect
92. #388×C₈₉	C₂²	semidirect
93. #387×C₈₉	C₂²	semidirect
94. #387×C₈₉	C₂²	semidirect
95. #387×C₈₉	C₂²	semidirect
96. #387×C₈₉	C₂²	semidirect
99. #386×C₈₉	C₂²	semidirect
100. #386×C₈₉	C₂²	semidirect
101. #385×C₈₉	C₂²	semidirect
102. #385×C₈₉	C₂²	semidirect
103. #385×C₈₉	C₂²	semidirect
104. #385×C₈₉	C₂²	semidirect
105. #385×C₈₉	C₂²	semidirect
106. #385×C₈₉	C₂²	semidirect
107. #385×C₈₉	C₂²	semidirect
108. #384×C₈₉	C₂²	semidirect
109. #381×C₈₉	C₂²	semidirect
110. #381×C₈₉	C₂²	semidirect
112. #380×C₈₉	C₂²	semidirect
113. #380×C₈₉	C₂²	semidirect
114. #380×C₈₉	C₂²	semidirect
115. #380×C₈₉	C₂²	semidirect
119. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
120. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
123. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
124. #376×C₈₉	C₂²	semidirect
164. C₄×D₄×C₈₉	D₄	semidirect
555. #35523	C₈₉	direct (N × H)
567. C₂×#529	C₂×C₈₉	semidirect
568. C₂×#518	C₂×C₈₉	semidirect
569. #2600	C₂×C₈₉	semidirect
570. #2534	C₂×C₈₉	semidirect
571. #2485	C₂×C₈₉	semidirect
572. #2482	C₂×C₈₉	semidirect
573. #2480	C₂×C₈₉	semidirect
574. #2466	C₂×C₈₉	semidirect
575. #2455	C₂×C₈₉	semidirect
576. #2454	C₂×C₈₉	semidirect
577. #2447	C₂×C₈₉	semidirect
578. #2441	C₂×C₈₉	semidirect
579. #2435	C₂×C₈₉	semidirect
580. #2427	C₂×C₈₉	semidirect
581. #2422	C₂×C₈₉	semidirect
582. #2418	C₂×C₈₉	semidirect
583. #2415	C₂×C₈₉	semidirect
585. #2326	C₂×C₈₉	semidirect
586. #2323	C₂×C₈₉	semidirect
587. #2319	C₂×C₈₉	semidirect
588. C₄×#121	C₂×C₈₉	semidirect
589. #2290	C₂×C₈₉	semidirect
590. C₈₉	#35523	direct (N × H)
593. C₂×#126	C₂²×C₈₉	semidirect
594. C₂×#125	C₂²×C₈₉	semidirect
597. C₂×#123	C₂²×C₈₉	semidirect
598. C₂×#123	C₂²×C₈₉	semidirect
600. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
605. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
613. C₂×C₄×D₄	C₂²×C₈₉	semidirect
614. C₂×C₄×D₄	C₂²×C₈₉	semidirect
617. C₂×#117	C₂²×C₈₉	semidirect
620. C₂²×C₄²	C₂²×C₈₉	semidirect
622. #399	C₂²×C₈₉	semidirect
624. #397	C₂²×C₈₉	semidirect
625. #397	C₂²×C₈₉	semidirect
626. #397	C₂²×C₈₉	semidirect
627. #397	C₂²×C₈₉	semidirect
629. #396	C₂²×C₈₉	semidirect
634. #394	C₂²×C₈₉	semidirect
635. #394	C₂²×C₈₉	semidirect
637. #391	C₂²×C₈₉	semidirect
638. #391	C₂²×C₈₉	semidirect
643. #389	C₂²×C₈₉	semidirect
644. #389	C₂²×C₈₉	semidirect
645. #389	C₂²×C₈₉	semidirect
646. #389	C₂²×C₈₉	semidirect
647. #389	C₂²×C₈₉	semidirect
648. #389	C₂²×C₈₉	semidirect
649. #389	C₂²×C₈₉	semidirect
654. #388	C₂²×C₈₉	semidirect
655. #388	C₂²×C₈₉	semidirect
656. #388	C₂²×C₈₉	semidirect
657. #388	C₂²×C₈₉	semidirect
658. #388	C₂²×C₈₉	semidirect
659. #388	C₂²×C₈₉	semidirect
660. #387	C₂²×C₈₉	semidirect
661. #387	C₂²×C₈₉	semidirect
662. #387	C₂²×C₈₉	semidirect
663. #387	C₂²×C₈₉	semidirect
666. #386	C₂²×C₈₉	semidirect
667. #386	C₂²×C₈₉	semidirect
668. #385	C₂²×C₈₉	semidirect
669. #385	C₂²×C₈₉	semidirect
670. #385	C₂²×C₈₉	semidirect
671. #385	C₂²×C₈₉	semidirect
672. #385	C₂²×C₈₉	semidirect
673. #385	C₂²×C₈₉	semidirect
674. #385	C₂²×C₈₉	semidirect
675. #384	C₂²×C₈₉	semidirect
676. #381	C₂²×C₈₉	semidirect
677. #381	C₂²×C₈₉	semidirect
679. #380	C₂²×C₈₉	semidirect
680. #380	C₂²×C₈₉	semidirect
681. #380	C₂²×C₈₉	semidirect
682. #380	C₂²×C₈₉	semidirect
686. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
687. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
689. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
690. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
691. #376	C₂²×C₈₉	semidirect
731. C₄×D₄	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×#2600	2
C₈₉×#2534	2
C₈₉×#2485	2
C₈₉×#2482	2
C₈₉×#2480	2
C₈₉×#2466	2
C₈₉×#2455	2
C₈₉×#2454	2
C₈₉×#2447	2
C₈₉×#2441	2
C₈₉×#2435	2
C₈₉×#2427	2
C₈₉×#2422	2
C₈₉×#2418	2
C₈₉×#2415	2
C₈₉×#2408	2
C₈₉×#2326	2
C₈₉×#2323	2
C₈₉×#2319	2
C₄×#121×C₈₉	2
C₈₉×#2290	2
#35523	89

Subgroups — C89×#35523 #36413371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35523 #36413371