Subgroups — C₈₉×#35568 #36413416

Order 22784.

2308 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×#542×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#529×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2592	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2563	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2560	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2557	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2554	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2553	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2546	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2540	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2519	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2491	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2464	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2452	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2417	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2416	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2415	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#2414	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2324	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₉×#2323	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂²⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2274	C₂	1	1	yes	maximal, characteristic, complemented
24	#542×C₈₉	—	2	8	no	—
25	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
27	#529×C₈₉	—	2	8	no	—
28	C₂×#126×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#126×C₈₉	C₂²	1	2	yes	—
30	C₂×#126×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#124×C₈₉	C₂²	1	2	yes	—
33	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#123×C₈₉	C₂²	1	2	yes	—
36	C₂×#123×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#123×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
40	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#121×C₈₉	C₂²	1	2	yes	—
48	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×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
53	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
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
58	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
59	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
60	#399×C₈₉	C₂²	1	2	yes	—
61	#398×C₈₉	C₂²	1	2	yes	—
62	#398×C₈₉	C₂²	1	2	yes	—
63	#398×C₈₉	C₂²	1	2	yes	—
64	#397×C₈₉	C₂²	1	2	yes	—
65	#397×C₈₉	C₂²	1	2	yes	—
66	#396×C₈₉	C₂²	1	2	yes	—
67	#396×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	#393×C₈₉	C₂²	1	2	yes	—
72	#393×C₈₉	C₂²	1	2	yes	—
73	#393×C₈₉	C₂²	1	2	yes	—
74	#392×C₈₉	C₂²	1	2	yes	—
75	#392×C₈₉	C₂²	1	2	yes	—
76	#391×C₈₉	C₂²	1	2	yes	—
77	#391×C₈₉	C₂²	1	1	yes	characteristic
78	#391×C₈₉	C₂²	1	1	yes	characteristic
79	#390×C₈₉	C₂²	1	2	yes	—
80	#390×C₈₉	C₂²	1	2	yes	—
81	#390×C₈₉	C₂²	1	2	yes	—
82	#390×C₈₉	C₂²	1	1	yes	characteristic
83	#390×C₈₉	C₂²	1	2	yes	—
84	#390×C₈₉	C₂²	1	2	yes	—
85	#390×C₈₉	C₂²	1	1	yes	characteristic
86	#389×C₈₉	C₂²	1	2	yes	—
87	#389×C₈₉	C₂²	1	1	yes	characteristic
88	#389×C₈₉	C₂²	1	1	yes	characteristic
89	#389×C₈₉	C₂²	1	1	yes	characteristic
90	#389×C₈₉	C₂²	1	1	yes	characteristic
91	#389×C₈₉	C₂²	1	2	yes	—
92	#388×C₈₉	C₂²	1	2	yes	—
93	#388×C₈₉	C₂²	1	2	yes	—
94	#388×C₈₉	C₂²	1	2	yes	—
95	#388×C₈₉	C₂²	1	2	yes	—
96	#388×C₈₉	C₂²	1	2	yes	—
97	#388×C₈₉	C₂²	1	2	yes	—
98	#388×C₈₉	C₂²	1	2	yes	—
99	#388×C₈₉	C₂²	1	2	yes	—
100	#387×C₈₉	C₂²	1	2	yes	—
101	#387×C₈₉	C₂²	1	2	yes	—
102	#386×C₈₉	C₂²	1	2	yes	—
103	#386×C₈₉	C₂²	1	2	yes	—
104	#386×C₈₉	C₂²	1	2	yes	—
105	#386×C₈₉	C₂²	1	2	yes	—
106	#385×C₈₉	C₂²	1	2	yes	—
107	#385×C₈₉	C₂²	1	2	yes	—
108	#382×C₈₉	C₂²	1	2	yes	—
109	#380×C₈₉	C₂²	1	2	yes	—
110	#380×C₈₉	C₂²	1	1	yes	characteristic
111	#380×C₈₉	C₂²	1	1	yes	characteristic
112	#380×C₈₉	C₂²	1	1	yes	characteristic
113	#380×C₈₉	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
115	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
118	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
119	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
122	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
123	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
124	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
125	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
128	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
131	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
134	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
135	C₂³×C₄×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	1	yes	characteristic
140	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
141	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
142	C₄⋊Q₈×C₈₉	—	2	4	no	—
143	C₄⋊Q₈×C₈₉	—	4	4	no	—
144	#126×C₈₉	—	2	4	no	—
145	#126×C₈₉	—	2	8	no	—
146	#126×C₈₉	—	2	4	no	—
147	#125×C₈₉	—	2	4	no	—
148	#124×C₈₉	—	2	4	no	—
149	#124×C₈₉	—	2	8	no	—
150	#124×C₈₉	—	2	4	no	—
151	#123×C₈₉	—	2	4	no	—
152	#123×C₈₉	—	2	4	no	—
153	#123×C₈₉	—	2	8	no	—
154	C₂²⋊Q₈×C₈₉	—	2	4	no	—
155	C₂²⋊Q₈×C₈₉	—	2	4	no	—
156	C₂²⋊Q₈×C₈₉	—	2	8	no	—
157	C₂²⋊Q₈×C₈₉	—	2	4	no	—
158	C₂²⋊Q₈×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	—	2	4	no	—
163	#121×C₈₉	—	4	4	no	—
164	C₄×Q₈×C₈₉	—	2	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	4	no	—
169	C₄×D₄×C₈₉	—	2	4	no	—
170	C₄×D₄×C₈₉	—	4	4	no	—
171	#117×C₈₉	—	2	4	no	—
172	#117×C₈₉	—	2	4	no	—
173	#117×C₈₉	D₄	1	8	yes	complemented
174	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
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	2	yes	—
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	1	yes	characteristic
183	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
192	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
198	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
228	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₈₉	—	2	4	no	—
230	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
232	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
233	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
237	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
238	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
239	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
240	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
241	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
242	#95×C₈₉	C₂³	1	2	yes	—
243	#95×C₈₉	C₂³	1	2	yes	—
244	#95×C₈₉	C₂³	1	2	yes	—
245	#95×C₈₉	C₂³	1	2	yes	—
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	#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	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
259	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
260	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
261	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
262	C₂×Q₈×C₈₉	—	2	2	no	—
263	C₂×Q₈×C₈₉	—	2	2	no	—
264	C₂×Q₈×C₈₉	—	2	4	no	—
265	C₂×Q₈×C₈₉	—	2	2	no	—
266	C₂×Q₈×C₈₉	—	2	2	no	—
267	C₂×Q₈×C₈₉	—	2	2	no	—
268	C₂×Q₈×C₈₉	—	4	1	no	—
269	C₂×Q₈×C₈₉	—	4	2	no	—
270	C₂×Q₈×C₈₉	—	4	2	no	—
271	C₂×D₄×C₈₉	—	2	2	no	—
272	C₂×D₄×C₈₉	—	2	2	no	—
273	C₂×D₄×C₈₉	—	2	4	no	—
274	C₂×D₄×C₈₉	—	2	2	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	2	no	—
279	C₂×D₄×C₈₉	—	2	4	no	—
280	C₂×D₄×C₈₉	—	2	2	no	—
281	C₂×D₄×C₈₉	—	2	2	no	—
282	C₂×D₄×C₈₉	—	2	4	no	—
283	C₂×D₄×C₈₉	—	2	2	no	—
284	C₂×D₄×C₈₉	—	4	2	no	—
285	C₂×D₄×C₈₉	—	4	1	no	—
286	C₂×D₄×C₈₉	—	4	1	no	—
287	C₂×D₄×C₈₉	—	4	1	no	—
288	C₂×D₄×C₈₉	—	4	2	no	—
289	C₂×D₄×C₈₉	—	4	2	no	—
290	C₂×D₄×C₈₉	—	4	2	no	—
291	C₂×D₄×C₈₉	—	4	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	2	no	—
297	C₂²×C₄×C₈₉	—	2	2	no	—
298	C₂²×C₄×C₈₉	—	2	2	no	—
299	C₂²×C₄×C₈₉	—	2	2	no	—
300	C₂²×C₄×C₈₉	—	2	2	no	—
301	C₂²×C₄×C₈₉	—	2	2	no	—
302	C₂²×C₄×C₈₉	—	2	2	no	—
303	C₂²×C₄×C₈₉	—	2	2	no	—
304	C₂²×C₄×C₈₉	—	2	4	no	—
305	C₂²×C₄×C₈₉	—	2	4	no	—
306	C₂²×C₄×C₈₉	—	4	1	no	—
307	C₂²×C₄×C₈₉	—	4	1	no	—
308	C₂²×C₄×C₈₉	—	4	2	no	—
309	C₂²×C₄×C₈₉	—	4	2	no	—
310	C₂²×C₄×C₈₉	—	4	2	no	—
311	C₂²×C₄×C₈₉	—	4	2	no	—
312	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
313	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
325	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
329	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
330	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
332	C₄⋊C₄×C₈₉	—	2	2	no	—
333	C₄⋊C₄×C₈₉	—	2	2	no	—
334	C₄⋊C₄×C₈₉	—	2	2	no	—
335	C₄⋊C₄×C₈₉	—	2	2	no	—
336	C₄⋊C₄×C₈₉	—	2	2	no	—
337	C₄⋊C₄×C₈₉	—	2	2	no	—
338	C₄⋊C₄×C₈₉	—	2	2	no	—
339	C₄⋊C₄×C₈₉	—	2	2	no	—
340	C₄⋊C₄×C₈₉	—	2	4	no	—
341	C₄⋊C₄×C₈₉	—	2	2	no	—
342	C₄⋊C₄×C₈₉	—	2	2	no	—
343	C₄⋊C₄×C₈₉	—	2	4	no	—
344	C₄⋊C₄×C₈₉	—	2	4	no	—
345	C₄⋊C₄×C₈₉	—	2	4	no	—
346	C₄⋊C₄×C₈₉	—	2	2	no	—
347	C₄⋊C₄×C₈₉	—	2	2	no	—
348	C₄⋊C₄×C₈₉	—	2	4	no	—
349	C₄⋊C₄×C₈₉	—	2	4	no	—
350	C₄⋊C₄×C₈₉	—	2	4	no	—
351	C₄⋊C₄×C₈₉	—	2	4	no	—
352	C₄⋊C₄×C₈₉	—	4	2	no	—
353	C₄⋊C₄×C₈₉	—	4	2	no	—
354	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
355	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
356	C₄⋊C₄×C₈₉	#41	1	4	yes	—
357	C₄⋊C₄×C₈₉	#41	1	4	yes	—
358	C₂²⋊C₄×C₈₉	—	2	2	no	—
359	C₂²⋊C₄×C₈₉	—	2	2	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	2	no	—
365	C₂²⋊C₄×C₈₉	—	2	2	no	—
366	C₂²⋊C₄×C₈₉	—	2	2	no	—
367	C₂²⋊C₄×C₈₉	—	2	4	no	—
368	C₂²⋊C₄×C₈₉	—	2	4	no	—
369	C₂²⋊C₄×C₈₉	—	2	4	no	—
370	C₂²⋊C₄×C₈₉	—	2	4	no	—
371	C₂²⋊C₄×C₈₉	—	2	4	no	—
372	C₂²⋊C₄×C₈₉	—	2	4	no	—
373	C₂²⋊C₄×C₈₉	—	2	4	no	—
374	C₂²⋊C₄×C₈₉	—	2	4	no	—
375	C₂²⋊C₄×C₈₉	—	2	4	no	—
376	C₂²⋊C₄×C₈₉	—	2	4	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	—	4	2	no	—
382	C₂²⋊C₄×C₈₉	—	4	2	no	—
383	C₂²⋊C₄×C₈₉	—	4	2	no	—
384	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
385	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
386	C₄²×C₈₉	—	2	2	no	—
387	C₄²×C₈₉	—	2	2	no	—
388	C₄²×C₈₉	—	2	2	no	—
389	C₄²×C₈₉	—	2	2	no	—
390	C₄²×C₈₉	—	2	4	no	—
391	C₄²×C₈₉	—	2	4	no	—
392	C₄²×C₈₉	—	4	2	no	—
393	C₄²×C₈₉	—	4	2	no	—
394	C₄²×C₈₉	—	4	2	no	—
395	C₄²×C₈₉	—	4	2	no	—
396	C₄²×C₈₉	C₂×D₄	1	4	yes	—
397	C₄²×C₈₉	C₂×D₄	1	4	yes	—
398	C₂³×C₈₉	—	2	1	no	—
399	C₂³×C₈₉	—	2	1	no	—
400	C₂³×C₈₉	—	2	1	no	—
401	C₂³×C₈₉	—	2	1	no	—
402	C₂³×C₈₉	—	2	1	no	—
403	C₂³×C₈₉	—	2	1	no	—
404	C₂³×C₈₉	—	2	1	no	—
405	C₂³×C₈₉	—	2	1	no	—
406	C₂³×C₈₉	—	2	1	no	—
407	C₂³×C₈₉	—	2	1	no	—
408	C₂³×C₈₉	—	2	1	no	—
409	C₂³×C₈₉	—	2	1	no	—
410	C₂³×C₈₉	—	2	1	no	—
411	C₂³×C₈₉	—	2	2	no	—
412	C₂³×C₈₉	—	2	1	no	—
413	C₂³×C₈₉	—	2	2	no	—
414	C₂³×C₈₉	—	2	2	no	—
415	C₂³×C₈₉	—	2	1	no	—
416	C₂³×C₈₉	—	2	2	no	—
417	C₂³×C₈₉	—	2	1	no	—
418	C₂³×C₈₉	—	2	1	no	—
419	C₂³×C₈₉	—	2	2	no	—
420	C₂³×C₈₉	—	2	1	no	—
421	C₂³×C₈₉	—	2	2	no	—
422	C₂³×C₈₉	—	2	2	no	—
423	C₂³×C₈₉	—	2	1	no	—
424	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
425	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
426	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
427	Q₈×C₈₉	—	4	4	no	—
428	Q₈×C₈₉	—	4	4	no	—
429	Q₈×C₈₉	—	8	4	no	—
430	D₄×C₈₉	—	4	4	no	—
431	D₄×C₈₉	—	4	4	no	—
432	D₄×C₈₉	—	4	8	no	—
433	D₄×C₈₉	—	4	4	no	—
434	D₄×C₈₉	—	4	4	no	—
435	D₄×C₈₉	—	8	4	no	—
436	D₄×C₈₉	—	8	4	no	—
437	C₂×C₄×C₈₉	—	2	1	no	—
438	C₂×C₄×C₈₉	—	2	1	no	—
439	C₂×C₄×C₈₉	—	2	1	no	—
440	C₂×C₄×C₈₉	—	2	2	no	—
441	C₂×C₄×C₈₉	—	2	1	no	—
442	C₂×C₄×C₈₉	—	2	1	no	—
443	C₂×C₄×C₈₉	—	2	2	no	—
444	C₂×C₄×C₈₉	—	2	1	no	—
445	C₂×C₄×C₈₉	—	2	1	no	—
446	C₂×C₄×C₈₉	—	2	2	no	—
447	C₂×C₄×C₈₉	—	2	1	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	1	no	—
452	C₂×C₄×C₈₉	—	2	1	no	—
453	C₂×C₄×C₈₉	—	2	8	no	—
454	C₂×C₄×C₈₉	—	2	1	no	—
455	C₂×C₄×C₈₉	—	2	1	no	—
456	C₂×C₄×C₈₉	—	2	2	no	—
457	C₂×C₄×C₈₉	—	2	1	no	—
458	C₂×C₄×C₈₉	—	2	1	no	—
459	C₂×C₄×C₈₉	—	2	2	no	—
460	C₂×C₄×C₈₉	—	2	1	no	—
461	C₂×C₄×C₈₉	—	2	2	no	—
462	C₂×C₄×C₈₉	—	2	2	no	—
463	C₂×C₄×C₈₉	—	2	1	no	—
464	C₂×C₄×C₈₉	—	2	1	no	—
465	C₂×C₄×C₈₉	—	2	2	no	—
466	C₂×C₄×C₈₉	—	2	2	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	2	no	—
471	C₂×C₄×C₈₉	—	2	2	no	—
472	C₂×C₄×C₈₉	—	2	2	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	2	no	—
477	C₂×C₄×C₈₉	—	2	2	no	—
478	C₂×C₄×C₈₉	—	2	2	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	2	no	—
483	C₂×C₄×C₈₉	—	2	2	no	—
484	C₂×C₄×C₈₉	—	4	4	no	—
485	C₂×C₄×C₈₉	—	4	4	no	—
486	C₂×C₄×C₈₉	—	4	4	no	—
487	C₂×C₄×C₈₉	—	4	4	no	—
488	C₂×C₄×C₈₉	—	8	4	no	—
489	C₂×C₄×C₈₉	—	8	4	no	—
490	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
491	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
492	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
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	2	yes	—
496	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
497	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
498	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
499	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
500	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
501	C₂²×C₈₉	—	2	2	no	—
502	C₂²×C₈₉	—	2	2	no	—
503	C₂²×C₈₉	—	2	2	no	—
504	C₂²×C₈₉	—	2	2	no	—
505	C₂²×C₈₉	—	2	2	no	—
506	C₂²×C₈₉	—	2	2	no	—
507	C₂²×C₈₉	—	4	1	no	—
508	C₂²×C₈₉	—	4	1	no	—
509	C₂²×C₈₉	—	4	1	no	—
510	C₂²×C₈₉	—	4	1	no	—
511	C₂²×C₈₉	—	4	1	no	—
512	C₂²×C₈₉	—	4	1	no	—
513	C₂²×C₈₉	—	4	1	no	—
514	C₂²×C₈₉	—	4	1	no	—
515	C₂²×C₈₉	—	4	1	no	—
516	C₂²×C₈₉	—	4	2	no	—
517	C₂²×C₈₉	—	4	2	no	—
518	C₂²×C₈₉	—	4	1	no	—
519	C₂²×C₈₉	—	4	1	no	—
520	C₂²×C₈₉	—	4	2	no	—
521	C₂²×C₈₉	—	4	1	no	—
522	C₂²×C₈₉	—	4	2	no	—
523	C₂²×C₈₉	—	4	2	no	—
524	C₂²×C₈₉	—	4	1	no	—
525	C₂²×C₈₉	—	4	2	no	—
526	C₂²×C₈₉	—	4	1	no	—
527	C₂²×C₈₉	—	4	1	no	—
528	C₂²×C₈₉	—	4	2	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	C₂×2₋¹⁺⁴	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	2	no	—
539	C₄×C₈₉	—	2	2	no	—
540	C₄×C₈₉	—	2	2	no	—
541	C₄×C₈₉	—	2	2	no	—
542	C₄×C₈₉	—	2	4	no	—
543	C₄×C₈₉	—	2	4	no	—
544	C₄×C₈₉	—	4	1	no	—
545	C₄×C₈₉	—	4	1	no	—
546	C₄×C₈₉	—	4	2	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	2	no	—
554	C₄×C₈₉	#532	1	4	yes	—
555	#35568	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
556	C₂×C₈₉	—	4	2	no	—
557	C₂×C₈₉	—	4	2	no	—
558	C₂×C₈₉	—	8	1	no	—
559	C₂×C₈₉	—	8	2	no	—
560	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
561	C₂×C₈₉	#3488	1	1	yes	characteristic
562	C₂×C₈₉	#3489	1	1	yes	characteristic
563	C₂×C₈₉	#3514	1	1	yes	characteristic
564	C₂×C₈₉	#3516	1	1	yes	characteristic
565	C₂×C₈₉	#3520	1	1	yes	characteristic
566	C₂×C₈₉	#3524	1	1	yes	characteristic
567	C₂×#542	C₂×C₈₉	1	1	yes	characteristic, complemented
568	C₂×#529	C₂×C₈₉	1	1	yes	characteristic, complemented
569	#2592	C₂×C₈₉	1	1	yes	characteristic, complemented
570	#2563	C₂×C₈₉	1	1	yes	characteristic, complemented
571	#2560	C₂×C₈₉	1	2	yes	complemented
572	#2557	C₂×C₈₉	1	2	yes	complemented
573	#2554	C₂×C₈₉	1	2	yes	complemented
574	#2553	C₂×C₈₉	1	2	yes	complemented
575	#2546	C₂×C₈₉	1	1	yes	characteristic, complemented
576	#2540	C₂×C₈₉	1	1	yes	characteristic, complemented
577	#2519	C₂×C₈₉	1	2	yes	complemented
578	#2491	C₂×C₈₉	1	2	yes	complemented
579	#2464	C₂×C₈₉	1	2	yes	complemented
580	#2452	C₂×C₈₉	1	2	yes	complemented
581	#2417	C₂×C₈₉	1	1	yes	characteristic, complemented
582	#2416	C₂×C₈₉	1	1	yes	characteristic, complemented
583	#2415	C₂×C₈₉	1	1	yes	characteristic, complemented
584	#2414	C₂×C₈₉	1	1	yes	characteristic, complemented
585	#2324	C₂×C₈₉	1	1	yes	characteristic, complemented
586	#2323	C₂×C₈₉	1	1	yes	characteristic, complemented
587	C₄×C₂²⋊Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
588	C₄×#121	C₂×C₈₉	1	1	yes	characteristic, complemented
589	#2274	C₂×C₈₉	1	1	yes	characteristic, complemented
590	C₈₉	#35568	1	1	yes	characteristic, direct product factor, Sylow
591	#542	—	2	8	no	—
592	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
593	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
594	#529	—	2	8	no	—
595	C₂×#126	C₂²×C₈₉	1	1	yes	characteristic
596	C₂×#126	C₂²×C₈₉	1	1	yes	characteristic
597	C₂×#126	C₂²×C₈₉	1	2	yes	—
598	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
599	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
600	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
601	C₂×#124	C₂²×C₈₉	1	2	yes	—
602	C₂×#123	C₂²×C₈₉	1	1	yes	characteristic
603	C₂×#123	C₂²×C₈₉	1	1	yes	characteristic
604	C₂×#123	C₂²×C₈₉	1	2	yes	—
605	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
606	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
607	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
608	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
609	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
610	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
611	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
612	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
613	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
614	C₂×#121	C₂²×C₈₉	1	2	yes	—
615	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
616	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
617	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
618	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
619	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
620	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
621	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
622	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
623	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
624	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
625	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
626	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
627	#399	C₂²×C₈₉	1	2	yes	—
628	#398	C₂²×C₈₉	1	2	yes	—
629	#398	C₂²×C₈₉	1	2	yes	—
630	#398	C₂²×C₈₉	1	2	yes	—
631	#397	C₂²×C₈₉	1	2	yes	—
632	#397	C₂²×C₈₉	1	2	yes	—
633	#396	C₂²×C₈₉	1	2	yes	—
634	#396	C₂²×C₈₉	1	2	yes	—
635	#394	C₂²×C₈₉	1	2	yes	—
636	#394	C₂²×C₈₉	1	2	yes	—
637	#394	C₂²×C₈₉	1	2	yes	—
638	#393	C₂²×C₈₉	1	2	yes	—
639	#393	C₂²×C₈₉	1	2	yes	—
640	#393	C₂²×C₈₉	1	2	yes	—
641	#392	C₂²×C₈₉	1	2	yes	—
642	#392	C₂²×C₈₉	1	2	yes	—
643	#391	C₂²×C₈₉	1	2	yes	—
644	#391	C₂²×C₈₉	1	1	yes	characteristic
645	#391	C₂²×C₈₉	1	1	yes	characteristic
646	#390	C₂²×C₈₉	1	2	yes	—
647	#390	C₂²×C₈₉	1	2	yes	—
648	#390	C₂²×C₈₉	1	1	yes	characteristic
649	#390	C₂²×C₈₉	1	2	yes	—
650	#390	C₂²×C₈₉	1	1	yes	characteristic
651	#390	C₂²×C₈₉	1	2	yes	—
652	#390	C₂²×C₈₉	1	2	yes	—
653	#389	C₂²×C₈₉	1	1	yes	characteristic
654	#389	C₂²×C₈₉	1	2	yes	—
655	#389	C₂²×C₈₉	1	1	yes	characteristic
656	#389	C₂²×C₈₉	1	2	yes	—
657	#389	C₂²×C₈₉	1	1	yes	characteristic
658	#389	C₂²×C₈₉	1	1	yes	characteristic
659	#388	C₂²×C₈₉	1	2	yes	—
660	#388	C₂²×C₈₉	1	2	yes	—
661	#388	C₂²×C₈₉	1	2	yes	—
662	#388	C₂²×C₈₉	1	2	yes	—
663	#388	C₂²×C₈₉	1	2	yes	—
664	#388	C₂²×C₈₉	1	2	yes	—
665	#388	C₂²×C₈₉	1	2	yes	—
666	#388	C₂²×C₈₉	1	2	yes	—
667	#387	C₂²×C₈₉	1	2	yes	—
668	#387	C₂²×C₈₉	1	2	yes	—
669	#386	C₂²×C₈₉	1	2	yes	—
670	#386	C₂²×C₈₉	1	2	yes	—
671	#386	C₂²×C₈₉	1	2	yes	—
672	#386	C₂²×C₈₉	1	2	yes	—
673	#385	C₂²×C₈₉	1	2	yes	—
674	#385	C₂²×C₈₉	1	2	yes	—
675	#382	C₂²×C₈₉	1	2	yes	—
676	#380	C₂²×C₈₉	1	1	yes	characteristic
677	#380	C₂²×C₈₉	1	1	yes	characteristic
678	#380	C₂²×C₈₉	1	1	yes	characteristic
679	#380	C₂²×C₈₉	1	1	yes	characteristic
680	#380	C₂²×C₈₉	1	2	yes	—
681	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
682	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
683	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
684	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
685	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
686	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
687	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
688	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
689	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
690	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
691	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
692	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
693	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
694	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
695	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
696	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
697	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
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	2	yes	—
702	C₂³×C₄	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	1	yes	characteristic
707	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
708	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
709	C₄⋊Q₈	—	2	4	no	—
710	C₄⋊Q₈	—	4	4	no	—
711	#126	—	2	4	no	—
712	#126	—	2	8	no	—
713	#126	—	2	4	no	—
714	#125	—	2	4	no	—
715	#124	—	2	4	no	—
716	#124	—	2	8	no	—
717	#124	—	2	4	no	—
718	#123	—	2	4	no	—
719	#123	—	2	4	no	—
720	#123	—	2	8	no	—
721	C₂²⋊Q₈	—	2	4	no	—
722	C₂²⋊Q₈	—	2	4	no	—
723	C₂²⋊Q₈	—	2	8	no	—
724	C₂²⋊Q₈	—	2	4	no	—
725	C₂²⋊Q₈	—	2	4	no	—
726	#121	—	2	4	no	—
727	#121	—	2	4	no	—
728	#121	—	2	4	no	—
729	#121	—	2	4	no	—
730	#121	—	4	4	no	—
731	C₄×Q₈	—	2	4	no	—
732	C₄×Q₈	—	2	4	no	—
733	C₄×D₄	—	2	4	no	—
734	C₄×D₄	—	2	4	no	—
735	C₄×D₄	—	2	4	no	—
736	C₄×D₄	—	2	4	no	—
737	C₄×D₄	—	4	4	no	—
738	#117	—	2	4	no	—
739	#117	—	2	4	no	—
740	#117	D₄×C₈₉	1	8	yes	complemented
741	C₂×C₄⋊C₄	—	2	4	no	—
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	1	yes	characteristic
747	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
748	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
749	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
750	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
751	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
752	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
753	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
754	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
755	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
756	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
757	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
758	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
759	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
760	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
761	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
762	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
763	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
764	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
765	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
766	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
767	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
768	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
769	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	1	yes	characteristic
773	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
774	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
775	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
776	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
777	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	2	yes	—
782	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
783	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
784	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
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×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
790	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
791	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
792	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
793	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
794	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
795	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
796	C₂×C₄²	—	2	4	no	—
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	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
801	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
802	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
803	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
804	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
805	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
806	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
807	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
808	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
809	#95	C₂³×C₈₉	1	2	yes	—
810	#95	C₂³×C₈₉	1	2	yes	—
811	#95	C₂³×C₈₉	1	2	yes	—
812	#95	C₂³×C₈₉	1	2	yes	—
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	#95	C₂³×C₈₉	1	2	yes	—
822	#95	C₂³×C₈₉	1	2	yes	—
823	#95	C₂³×C₈₉	1	2	yes	—
824	#95	C₂³×C₈₉	1	2	yes	—
825	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
826	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
827	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
828	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
829	C₂×Q₈	—	2	2	no	—
830	C₂×Q₈	—	2	2	no	—
831	C₂×Q₈	—	2	4	no	—
832	C₂×Q₈	—	2	2	no	—
833	C₂×Q₈	—	2	2	no	—
834	C₂×Q₈	—	2	2	no	—
835	C₂×Q₈	—	4	1	no	—
836	C₂×Q₈	—	4	2	no	—
837	C₂×Q₈	—	4	2	no	—
838	C₂×D₄	—	2	2	no	—
839	C₂×D₄	—	2	2	no	—
840	C₂×D₄	—	2	2	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	2	no	—
846	C₂×D₄	—	2	4	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	2	no	—
849	C₂×D₄	—	2	4	no	—
850	C₂×D₄	—	2	2	no	—
851	C₂×D₄	—	4	2	no	—
852	C₂×D₄	—	4	1	no	—
853	C₂×D₄	—	4	1	no	—
854	C₂×D₄	—	4	1	no	—
855	C₂×D₄	—	4	2	no	—
856	C₂×D₄	—	4	2	no	—
857	C₂×D₄	—	4	2	no	—
858	C₂×D₄	—	4	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	2	no	—
864	C₂²×C₄	—	2	2	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	—	2	2	no	—
868	C₂²×C₄	—	2	2	no	—
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	4	no	—
872	C₂²×C₄	—	2	4	no	—
873	C₂²×C₄	—	4	1	no	—
874	C₂²×C₄	—	4	1	no	—
875	C₂²×C₄	—	4	2	no	—
876	C₂²×C₄	—	4	2	no	—
877	C₂²×C₄	—	4	2	no	—
878	C₂²×C₄	—	4	2	no	—
879	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
880	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
881	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
883	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
884	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
885	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
886	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
887	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
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	1	yes	characteristic
892	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
893	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
894	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
895	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
896	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
897	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
898	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	4	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	4	no	—
911	C₄⋊C₄	—	2	4	no	—
912	C₄⋊C₄	—	2	4	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	4	no	—
916	C₄⋊C₄	—	2	4	no	—
917	C₄⋊C₄	—	2	4	no	—
918	C₄⋊C₄	—	2	4	no	—
919	C₄⋊C₄	—	4	2	no	—
920	C₄⋊C₄	—	4	2	no	—
921	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
922	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
923	C₄⋊C₄	#41×C₈₉	1	4	yes	—
924	C₄⋊C₄	#41×C₈₉	1	4	yes	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	—	2	2	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	2	no	—
932	C₂²⋊C₄	—	2	2	no	—
933	C₂²⋊C₄	—	2	2	no	—
934	C₂²⋊C₄	—	2	4	no	—
935	C₂²⋊C₄	—	2	4	no	—
936	C₂²⋊C₄	—	2	4	no	—
937	C₂²⋊C₄	—	2	4	no	—
938	C₂²⋊C₄	—	2	4	no	—
939	C₂²⋊C₄	—	2	4	no	—
940	C₂²⋊C₄	—	2	4	no	—
941	C₂²⋊C₄	—	2	4	no	—
942	C₂²⋊C₄	—	2	4	no	—
943	C₂²⋊C₄	—	2	4	no	—
944	C₂²⋊C₄	—	4	2	no	—
945	C₂²⋊C₄	—	4	2	no	—
946	C₂²⋊C₄	—	4	2	no	—
947	C₂²⋊C₄	—	4	2	no	—
948	C₂²⋊C₄	—	4	2	no	—
949	C₂²⋊C₄	—	4	2	no	—
950	C₂²⋊C₄	—	4	2	no	—
951	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
952	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
953	C₄²	—	2	2	no	—
954	C₄²	—	2	2	no	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	2	no	—
957	C₄²	—	2	4	no	—
958	C₄²	—	2	4	no	—
959	C₄²	—	4	2	no	—
960	C₄²	—	4	2	no	—
961	C₄²	—	4	2	no	—
962	C₄²	—	4	2	no	—
963	C₄²	C₂×D₄×C₈₉	1	4	yes	—
964	C₄²	C₂×D₄×C₈₉	1	4	yes	—
965	C₂³	—	2	1	no	—
966	C₂³	—	2	1	no	—
967	C₂³	—	2	1	no	—
968	C₂³	—	2	1	no	—
969	C₂³	—	2	1	no	—
970	C₂³	—	2	1	no	—
971	C₂³	—	2	1	no	—
972	C₂³	—	2	1	no	—
973	C₂³	—	2	1	no	—
974	C₂³	—	2	1	no	—
975	C₂³	—	2	1	no	—
976	C₂³	—	2	1	no	—
977	C₂³	—	2	1	no	—
978	C₂³	—	2	2	no	—
979	C₂³	—	2	1	no	—
980	C₂³	—	2	2	no	—
981	C₂³	—	2	2	no	—
982	C₂³	—	2	1	no	—
983	C₂³	—	2	2	no	—
984	C₂³	—	2	1	no	—
985	C₂³	—	2	1	no	—
986	C₂³	—	2	2	no	—
987	C₂³	—	2	1	no	—
988	C₂³	—	2	2	no	—
989	C₂³	—	2	2	no	—
990	C₂³	—	2	1	no	—
991	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
992	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
993	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
994	Q₈	—	4	4	no	—
995	Q₈	—	4	4	no	—
996	Q₈	—	8	4	no	—
997	D₄	—	4	4	no	—
998	D₄	—	4	4	no	—
999	D₄	—	4	8	no	—
1000	D₄	—	4	4	no	—
1001	D₄	—	4	4	no	—
1002	D₄	—	8	4	no	—
1003	D₄	—	8	4	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	8	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	4	4	no	—
1052	C₂×C₄	—	4	4	no	—
1053	C₂×C₄	—	4	4	no	—
1054	C₂×C₄	—	4	4	no	—
1055	C₂×C₄	—	8	4	no	—
1056	C₂×C₄	—	8	4	no	—
1057	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1058	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1059	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
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	2	yes	—
1063	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
1064	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
1065	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
1066	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
1067	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
1068	C₂²	—	2	2	no	—
1069	C₂²	—	2	2	no	—
1070	C₂²	—	2	2	no	—
1071	C₂²	—	2	2	no	—
1072	C₂²	—	2	2	no	—
1073	C₂²	—	2	2	no	—
1074	C₂²	—	4	1	no	—
1075	C₂²	—	4	1	no	—
1076	C₂²	—	4	1	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	1	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	2	no	—
1084	C₂²	—	4	2	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	4	2	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	2	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	2	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	2	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	C₂×2₋¹⁺⁴×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	2	no	—
1106	C₄	—	2	2	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	2	4	no	—
1110	C₄	—	2	4	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	2	no	—
1114	C₄	—	4	2	no	—
1115	C₄	—	4	2	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	1	no	—
1119	C₄	—	4	2	no	—
1120	C₄	—	4	2	no	—
1121	C₄	#532×C₈₉	1	4	yes	—
1122	C₂	—	4	2	no	—
1123	C₂	—	4	2	no	—
1124	C₂	—	8	1	no	—
1125	C₂	—	8	2	no	—
1126	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
1127	C₂	C₈₉×#3488	1	1	yes	characteristic
1128	C₂	C₈₉×#3489	1	1	yes	characteristic
1129	C₂	C₈₉×#3514	1	1	yes	characteristic
1130	C₂	C₈₉×#3516	1	1	yes	characteristic
1131	C₂	C₈₉×#3520	1	1	yes	characteristic
1132	C₂	C₈₉×#3524	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×#542×C₈₉	C₂	semidirect
2. C₂×#529×C₈₉	C₂	semidirect
3. C₈₉×#2592	C₂	semidirect
4. C₈₉×#2563	C₂	semidirect
5. C₈₉×#2560	C₂	semidirect
6. C₈₉×#2557	C₂	semidirect
7. C₈₉×#2554	C₂	semidirect
8. C₈₉×#2553	C₂	semidirect
9. C₈₉×#2546	C₂	semidirect
10. C₈₉×#2540	C₂	semidirect
11. C₈₉×#2519	C₂	semidirect
12. C₈₉×#2491	C₂	semidirect
13. C₈₉×#2464	C₂	semidirect
14. C₈₉×#2452	C₂	semidirect
15. C₈₉×#2417	C₂	semidirect
16. C₈₉×#2416	C₂	semidirect
17. C₈₉×#2415	C₂	semidirect
18. C₈₉×#2414	C₂	semidirect
19. C₈₉×#2324	C₂	semidirect
20. C₈₉×#2323	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₈₉	C₂	semidirect
22. C₄×#121×C₈₉	C₂	semidirect
23. C₈₉×#2274	C₂	semidirect
173. #117×C₈₉	D₄	semidirect
555. #35568	C₈₉	direct (N × H)
567. C₂×#542	C₂×C₈₉	semidirect
568. C₂×#529	C₂×C₈₉	semidirect
569. #2592	C₂×C₈₉	semidirect
570. #2563	C₂×C₈₉	semidirect
571. #2560	C₂×C₈₉	semidirect
572. #2557	C₂×C₈₉	semidirect
573. #2554	C₂×C₈₉	semidirect
574. #2553	C₂×C₈₉	semidirect
575. #2546	C₂×C₈₉	semidirect
576. #2540	C₂×C₈₉	semidirect
577. #2519	C₂×C₈₉	semidirect
578. #2491	C₂×C₈₉	semidirect
579. #2464	C₂×C₈₉	semidirect
580. #2452	C₂×C₈₉	semidirect
581. #2417	C₂×C₈₉	semidirect
582. #2416	C₂×C₈₉	semidirect
583. #2415	C₂×C₈₉	semidirect
584. #2414	C₂×C₈₉	semidirect
585. #2324	C₂×C₈₉	semidirect
586. #2323	C₂×C₈₉	semidirect
587. C₄×C₂²⋊Q₈	C₂×C₈₉	semidirect
588. C₄×#121	C₂×C₈₉	semidirect
589. #2274	C₂×C₈₉	semidirect
590. C₈₉	#35568	direct (N × H)
740. #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×#542×C₈₉	2
C₂×#529×C₈₉	2
C₈₉×#2592	2
C₈₉×#2563	2
C₈₉×#2560	2
C₈₉×#2557	2
C₈₉×#2554	2
C₈₉×#2553	2
C₈₉×#2546	2
C₈₉×#2540	2
C₈₉×#2519	2
C₈₉×#2491	2
C₈₉×#2464	2
C₈₉×#2452	2
C₈₉×#2417	2
C₈₉×#2416	2
C₈₉×#2415	2
C₈₉×#2414	2
C₈₉×#2324	2
C₈₉×#2323	2
C₄×C₂²⋊Q₈×C₈₉	2
C₄×#121×C₈₉	2
C₈₉×#2274	2
#35568	89

Subgroups — C89×#35568 #36413416

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35568 #36413416