Subgroups — C₈₉×#35571 #36413419

Order 22784.

2750 conjugacy classes of subgroups.

The subgroup lattice has 1210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#540×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#532×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2602	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2557	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2555	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2550	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2543	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2541	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2541	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2535	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2491	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2490	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#2464	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2431	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2430	C₂	1	2	yes	maximal, complemented
16	C₈₉×#2428	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2428	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#2428	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2328	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₉×#2324	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#121×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₉×#2290	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2275	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₈₉	C₂²	1	2	yes	—
25	#540×C₈₉	—	2	8	no	—
26	#532×C₈₉	—	2	8	no	—
27	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#127×C₈₉	C₂²	1	2	yes	—
32	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#124×C₈₉	C₂²	1	2	yes	—
34	C₂×#124×C₈₉	C₂²	1	2	yes	—
35	C₂×#123×C₈₉	C₂²	1	2	yes	—
36	C₂×#123×C₈₉	C₂²	1	2	yes	—
37	C₂×#121×C₈₉	C₂²	1	2	yes	—
38	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#121×C₈₉	C₂²	1	2	yes	—
41	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×#121×C₈₉	C₂²	1	2	yes	—
45	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×#121×C₈₉	C₂²	1	2	yes	—
47	C₂×#121×C₈₉	C₂²	1	2	yes	—
48	C₂×#121×C₈₉	C₂²	1	2	yes	—
49	C₂×#121×C₈₉	C₂²	1	2	yes	—
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	2	yes	—
53	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
56	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
57	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
58	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
59	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
60	#398×C₈₉	C₂²	1	2	yes	—
61	#397×C₈₉	C₂²	1	2	yes	—
62	#397×C₈₉	C₂²	1	2	yes	—
63	#395×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	—
68	#393×C₈₉	C₂²	1	2	yes	—
69	#392×C₈₉	C₂²	1	2	yes	—
70	#392×C₈₉	C₂²	1	2	yes	—
71	#392×C₈₉	C₂²	1	2	yes	—
72	#392×C₈₉	C₂²	1	2	yes	—
73	#392×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	#390×C₈₉	C₂²	1	2	yes	—
78	#390×C₈₉	C₂²	1	1	yes	characteristic
79	#390×C₈₉	C₂²	1	2	yes	—
80	#390×C₈₉	C₂²	1	1	yes	characteristic
81	#390×C₈₉	C₂²	1	1	yes	characteristic
82	#390×C₈₉	C₂²	1	1	yes	characteristic
83	#390×C₈₉	C₂²	1	2	yes	—
84	#389×C₈₉	C₂²	1	1	yes	characteristic
85	#389×C₈₉	C₂²	1	1	yes	characteristic
86	#389×C₈₉	C₂²	1	2	yes	—
87	#388×C₈₉	C₂²	1	1	yes	characteristic
88	#388×C₈₉	C₂²	1	2	yes	—
89	#388×C₈₉	C₂²	1	2	yes	—
90	#388×C₈₉	C₂²	1	2	yes	—
91	#388×C₈₉	C₂²	1	2	yes	—
92	#388×C₈₉	C₂²	1	1	yes	characteristic
93	#387×C₈₉	C₂²	1	1	yes	characteristic
94	#387×C₈₉	C₂²	1	1	yes	characteristic
95	#386×C₈₉	C₂²	1	2	yes	—
96	#386×C₈₉	C₂²	1	2	yes	—
97	#386×C₈₉	C₂²	1	2	yes	—
98	#386×C₈₉	C₂²	1	2	yes	—
99	#386×C₈₉	C₂²	1	2	yes	—
100	#386×C₈₉	C₂²	1	2	yes	—
101	#386×C₈₉	C₂²	1	2	yes	—
102	#386×C₈₉	C₂²	1	2	yes	—
103	#386×C₈₉	C₂²	1	2	yes	—
104	#386×C₈₉	C₂²	1	1	yes	characteristic
105	#386×C₈₉	C₂²	1	2	yes	—
106	#386×C₈₉	C₂²	1	1	yes	characteristic
107	#385×C₈₉	C₂²	1	2	yes	—
108	#385×C₈₉	C₂²	1	1	yes	characteristic
109	#385×C₈₉	C₂²	1	1	yes	characteristic
110	#382×C₈₉	C₂²	1	1	yes	characteristic
111	#380×C₈₉	C₂²	1	1	yes	characteristic
112	#380×C₈₉	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
122	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
123	#376×C₈₉	C₂²	1	1	yes	characteristic
124	C₂×#95×C₈₉	C₂²	1	2	yes	—
125	C₂×#41×C₈₉	—	2	8	no	—
126	C₂×#41×C₈₉	—	4	4	no	—
127	C₂×#41×C₈₉	—	4	4	no	—
128	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
129	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
135	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
136	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
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	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
141	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
142	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
143	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
144	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
145	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
150	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
151	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
152	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
153	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
154	C₄⋊Q₈×C₈₉	—	2	4	no	—
155	#127×C₈₉	—	2	4	no	—
156	#127×C₈₉	—	2	4	no	—
157	#127×C₈₉	—	2	4	no	—
158	#127×C₈₉	—	4	4	no	—
159	#125×C₈₉	—	2	4	no	—
160	#124×C₈₉	—	2	8	no	—
161	#124×C₈₉	—	4	4	no	—
162	#123×C₈₉	—	2	8	no	—
163	#123×C₈₉	—	2	8	no	—
164	#121×C₈₉	—	2	4	no	—
165	#121×C₈₉	—	2	4	no	—
166	#121×C₈₉	—	2	8	no	—
167	#121×C₈₉	—	2	4	no	—
168	#121×C₈₉	—	2	4	no	—
169	#121×C₈₉	—	2	4	no	—
170	#121×C₈₉	—	2	4	no	—
171	#121×C₈₉	—	2	8	no	—
172	#121×C₈₉	—	2	8	no	—
173	#121×C₈₉	—	4	4	no	—
174	#121×C₈₉	—	4	4	no	—
175	#121×C₈₉	—	4	4	no	—
176	#121×C₈₉	—	4	4	no	—
177	C₄×D₄×C₈₉	—	2	8	no	—
178	C₄×D₄×C₈₉	—	2	4	no	—
179	C₄×D₄×C₈₉	—	2	4	no	—
180	C₄×D₄×C₈₉	—	2	4	no	—
181	C₄×D₄×C₈₉	—	2	4	no	—
182	C₄×D₄×C₈₉	—	2	4	no	—
183	C₄×D₄×C₈₉	—	4	4	no	—
184	C₄×D₄×C₈₉	D₄	1	8	yes	complemented
185	#117×C₈₉	—	2	4	no	—
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	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	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
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	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	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	2	yes	—
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×C₄²×C₈₉	—	2	4	no	—
231	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
240	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
241	#95×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	1	yes	characteristic
246	#95×C₈₉	C₂³	1	1	yes	characteristic
247	#95×C₈₉	C₂³	1	1	yes	characteristic
248	#95×C₈₉	C₂³	1	2	yes	—
249	#95×C₈₉	C₂³	1	1	yes	characteristic
250	#95×C₈₉	C₂³	1	1	yes	characteristic
251	#95×C₈₉	C₂³	1	1	yes	characteristic
252	#95×C₈₉	C₂³	1	2	yes	—
253	#95×C₈₉	C₂³	1	1	yes	characteristic
254	#95×C₈₉	C₂³	1	1	yes	characteristic
255	#95×C₈₉	C₂³	1	1	yes	characteristic
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	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
261	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
262	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
263	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
264	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
265	#41×C₈₉	—	4	32	no	—
266	C₂×Q₈×C₈₉	—	2	4	no	—
267	C₂×Q₈×C₈₉	—	2	4	no	—
268	C₂×Q₈×C₈₉	—	4	2	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	4	no	—
273	C₂×D₄×C₈₉	—	2	4	no	—
274	C₂×D₄×C₈₉	—	2	2	no	—
275	C₂×D₄×C₈₉	—	2	4	no	—
276	C₂×D₄×C₈₉	—	2	4	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	2	no	—
284	C₂×D₄×C₈₉	—	2	2	no	—
285	C₂×D₄×C₈₉	—	2	2	no	—
286	C₂×D₄×C₈₉	—	2	4	no	—
287	C₂×D₄×C₈₉	—	2	2	no	—
288	C₂×D₄×C₈₉	—	2	2	no	—
289	C₂×D₄×C₈₉	—	2	2	no	—
290	C₂×D₄×C₈₉	—	2	2	no	—
291	C₂×D₄×C₈₉	—	2	4	no	—
292	C₂×D₄×C₈₉	—	2	4	no	—
293	C₂×D₄×C₈₉	—	2	4	no	—
294	C₂×D₄×C₈₉	—	2	4	no	—
295	C₂×D₄×C₈₉	—	2	4	no	—
296	C₂×D₄×C₈₉	—	4	2	no	—
297	C₂×D₄×C₈₉	—	4	2	no	—
298	C₂×D₄×C₈₉	—	4	1	no	—
299	C₂×D₄×C₈₉	—	4	2	no	—
300	C₂×D₄×C₈₉	—	4	2	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	—	4	2	no	—
306	C₂×D₄×C₈₉	—	4	2	no	—
307	C₂×D₄×C₈₉	—	4	2	no	—
308	C₂×D₄×C₈₉	—	4	2	no	—
309	C₂×D₄×C₈₉	—	4	2	no	—
310	C₂×D₄×C₈₉	—	4	2	no	—
311	C₂×D₄×C₈₉	—	4	2	no	—
312	C₂×D₄×C₈₉	—	4	2	no	—
313	C₂×D₄×C₈₉	—	4	2	no	—
314	C₂×D₄×C₈₉	—	4	2	no	—
315	C₂×D₄×C₈₉	—	4	2	no	—
316	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
317	C₂²×C₄×C₈₉	—	2	2	no	—
318	C₂²×C₄×C₈₉	—	2	2	no	—
319	C₂²×C₄×C₈₉	—	2	2	no	—
320	C₂²×C₄×C₈₉	—	2	2	no	—
321	C₂²×C₄×C₈₉	—	2	2	no	—
322	C₂²×C₄×C₈₉	—	2	2	no	—
323	C₂²×C₄×C₈₉	—	2	4	no	—
324	C₂²×C₄×C₈₉	—	2	2	no	—
325	C₂²×C₄×C₈₉	—	2	2	no	—
326	C₂²×C₄×C₈₉	—	2	2	no	—
327	C₂²×C₄×C₈₉	—	2	2	no	—
328	C₂²×C₄×C₈₉	—	2	2	no	—
329	C₂²×C₄×C₈₉	—	2	4	no	—
330	C₂²×C₄×C₈₉	—	2	4	no	—
331	C₂²×C₄×C₈₉	—	2	4	no	—
332	C₂²×C₄×C₈₉	—	4	1	no	—
333	C₂²×C₄×C₈₉	—	4	2	no	—
334	C₂²×C₄×C₈₉	—	4	2	no	—
335	C₂²×C₄×C₈₉	—	4	2	no	—
336	C₂²×C₄×C₈₉	—	4	2	no	—
337	C₂²×C₄×C₈₉	—	4	2	no	—
338	C₂²×C₄×C₈₉	—	4	2	no	—
339	C₂²×C₄×C₈₉	—	4	2	no	—
340	C₂²×C₄×C₈₉	—	4	2	no	—
341	C₂²×C₄×C₈₉	—	4	2	no	—
342	C₂²×C₄×C₈₉	—	4	2	no	—
343	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
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	2	yes	—
348	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
352	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
356	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
359	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	4	no	—
366	C₄⋊C₄×C₈₉	—	2	2	no	—
367	C₄⋊C₄×C₈₉	—	2	4	no	—
368	C₄⋊C₄×C₈₉	—	2	4	no	—
369	C₄⋊C₄×C₈₉	—	2	2	no	—
370	C₄⋊C₄×C₈₉	—	2	2	no	—
371	C₄⋊C₄×C₈₉	—	2	4	no	—
372	C₄⋊C₄×C₈₉	—	2	2	no	—
373	C₄⋊C₄×C₈₉	—	2	2	no	—
374	C₄⋊C₄×C₈₉	—	4	2	no	—
375	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
376	C₄⋊C₄×C₈₉	#41	1	4	yes	complemented
377	C₂²⋊C₄×C₈₉	—	2	4	no	—
378	C₂²⋊C₄×C₈₉	—	2	4	no	—
379	C₂²⋊C₄×C₈₉	—	2	2	no	—
380	C₂²⋊C₄×C₈₉	—	2	2	no	—
381	C₂²⋊C₄×C₈₉	—	2	2	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	4	no	—
387	C₂²⋊C₄×C₈₉	—	2	4	no	—
388	C₂²⋊C₄×C₈₉	—	2	2	no	—
389	C₂²⋊C₄×C₈₉	—	2	2	no	—
390	C₂²⋊C₄×C₈₉	—	2	4	no	—
391	C₂²⋊C₄×C₈₉	—	2	4	no	—
392	C₂²⋊C₄×C₈₉	—	2	4	no	—
393	C₂²⋊C₄×C₈₉	—	2	2	no	—
394	C₂²⋊C₄×C₈₉	—	2	4	no	—
395	C₂²⋊C₄×C₈₉	—	2	2	no	—
396	C₂²⋊C₄×C₈₉	—	4	2	no	—
397	C₂²⋊C₄×C₈₉	—	4	1	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	8	yes	—
406	C₄²×C₈₉	—	2	2	no	—
407	C₄²×C₈₉	—	2	2	no	—
408	C₄²×C₈₉	—	2	2	no	—
409	C₄²×C₈₉	—	2	2	no	—
410	C₄²×C₈₉	—	2	2	no	—
411	C₄²×C₈₉	—	4	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	#41	1	4	yes	complemented
416	C₂³×C₈₉	—	2	1	no	—
417	C₂³×C₈₉	—	2	2	no	—
418	C₂³×C₈₉	—	2	2	no	—
419	C₂³×C₈₉	—	2	1	no	—
420	C₂³×C₈₉	—	2	1	no	—
421	C₂³×C₈₉	—	2	1	no	—
422	C₂³×C₈₉	—	2	1	no	—
423	C₂³×C₈₉	—	2	2	no	—
424	C₂³×C₈₉	—	2	2	no	—
425	C₂³×C₈₉	—	2	2	no	—
426	C₂³×C₈₉	—	2	1	no	—
427	C₂³×C₈₉	—	2	2	no	—
428	C₂³×C₈₉	—	2	1	no	—
429	C₂³×C₈₉	—	2	2	no	—
430	C₂³×C₈₉	—	2	2	no	—
431	C₂³×C₈₉	—	2	1	no	—
432	C₂³×C₈₉	—	2	2	no	—
433	C₂³×C₈₉	—	2	2	no	—
434	C₂³×C₈₉	—	2	1	no	—
435	C₂³×C₈₉	—	2	2	no	—
436	C₂³×C₈₉	—	2	2	no	—
437	C₂³×C₈₉	—	2	1	no	—
438	C₂³×C₈₉	—	2	2	no	—
439	C₂³×C₈₉	—	2	2	no	—
440	C₂³×C₈₉	—	2	1	no	—
441	C₂³×C₈₉	—	2	2	no	—
442	C₂³×C₈₉	—	2	2	no	—
443	C₂³×C₈₉	—	2	2	no	—
444	C₂³×C₈₉	—	2	2	no	—
445	C₂³×C₈₉	—	2	1	no	—
446	C₂³×C₈₉	—	2	2	no	—
447	C₂³×C₈₉	—	2	2	no	—
448	C₂³×C₈₉	—	2	1	no	—
449	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
450	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
451	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
452	Q₈×C₈₉	—	4	8	no	—
453	D₄×C₈₉	—	2	8	no	—
454	D₄×C₈₉	—	4	8	no	—
455	D₄×C₈₉	—	4	4	no	—
456	D₄×C₈₉	—	4	8	no	—
457	D₄×C₈₉	—	4	8	no	—
458	D₄×C₈₉	—	4	8	no	—
459	D₄×C₈₉	—	4	8	no	—
460	D₄×C₈₉	—	4	4	no	—
461	D₄×C₈₉	—	4	4	no	—
462	D₄×C₈₉	—	8	4	no	—
463	D₄×C₈₉	—	8	4	no	—
464	D₄×C₈₉	—	8	4	no	—
465	D₄×C₈₉	—	8	4	no	—
466	D₄×C₈₉	—	8	4	no	—
467	D₄×C₈₉	—	8	4	no	—
468	D₄×C₈₉	—	8	4	no	—
469	C₂×C₄×C₈₉	—	2	8	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	2	no	—
475	C₂×C₄×C₈₉	—	2	2	no	—
476	C₂×C₄×C₈₉	—	2	2	no	—
477	C₂×C₄×C₈₉	—	2	2	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	1	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	1	no	—
487	C₂×C₄×C₈₉	—	2	1	no	—
488	C₂×C₄×C₈₉	—	2	1	no	—
489	C₂×C₄×C₈₉	—	2	1	no	—
490	C₂×C₄×C₈₉	—	2	2	no	—
491	C₂×C₄×C₈₉	—	2	2	no	—
492	C₂×C₄×C₈₉	—	2	1	no	—
493	C₂×C₄×C₈₉	—	2	1	no	—
494	C₂×C₄×C₈₉	—	2	1	no	—
495	C₂×C₄×C₈₉	—	2	1	no	—
496	C₂×C₄×C₈₉	—	2	1	no	—
497	C₂×C₄×C₈₉	—	2	1	no	—
498	C₂×C₄×C₈₉	—	2	2	no	—
499	C₂×C₄×C₈₉	—	2	1	no	—
500	C₂×C₄×C₈₉	—	2	2	no	—
501	C₂×C₄×C₈₉	—	2	2	no	—
502	C₂×C₄×C₈₉	—	2	1	no	—
503	C₂×C₄×C₈₉	—	2	1	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	2	no	—
510	C₂×C₄×C₈₉	—	2	1	no	—
511	C₂×C₄×C₈₉	—	2	2	no	—
512	C₂×C₄×C₈₉	—	2	1	no	—
513	C₂×C₄×C₈₉	—	4	8	no	—
514	C₂×C₄×C₈₉	—	4	4	no	—
515	C₂×C₄×C₈₉	—	4	8	no	—
516	C₂×C₄×C₈₉	—	4	4	no	—
517	C₂×C₄×C₈₉	—	4	4	no	—
518	C₂×C₄×C₈₉	—	8	4	no	—
519	C₂×C₄×C₈₉	—	8	4	no	—
520	C₂×C₄×C₈₉	—	8	4	no	—
521	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
524	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
526	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
527	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
528	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
529	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
530	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
531	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
532	C₂²×C₈₉	—	2	4	no	—
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	—	4	1	no	—
539	C₂²×C₈₉	—	4	1	no	—
540	C₂²×C₈₉	—	4	2	no	—
541	C₂²×C₈₉	—	4	2	no	—
542	C₂²×C₈₉	—	4	1	no	—
543	C₂²×C₈₉	—	4	2	no	—
544	C₂²×C₈₉	—	4	1	no	—
545	C₂²×C₈₉	—	4	2	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	1	no	—
551	C₂²×C₈₉	—	4	2	no	—
552	C₂²×C₈₉	—	4	2	no	—
553	C₂²×C₈₉	—	4	2	no	—
554	C₂²×C₈₉	—	4	1	no	—
555	C₂²×C₈₉	—	4	1	no	—
556	C₂²×C₈₉	—	4	2	no	—
557	C₂²×C₈₉	—	4	2	no	—
558	C₂²×C₈₉	—	4	2	no	—
559	C₂²×C₈₉	—	4	2	no	—
560	C₂²×C₈₉	—	4	1	no	—
561	C₂²×C₈₉	—	4	2	no	—
562	C₂²×C₈₉	—	4	2	no	—
563	C₂²×C₈₉	—	4	1	no	—
564	C₂²×C₈₉	—	4	2	no	—
565	C₂²×C₈₉	—	4	1	no	—
566	C₂²×C₈₉	—	4	2	no	—
567	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
568	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
569	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
570	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
571	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
572	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
573	C₂²×C₈₉	#585	1	1	yes	characteristic
574	C₄×C₈₉	—	2	2	no	—
575	C₄×C₈₉	—	2	2	no	—
576	C₄×C₈₉	—	2	4	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	4	no	—
582	C₄×C₈₉	—	4	1	no	—
583	C₄×C₈₉	—	4	1	no	—
584	C₄×C₈₉	—	4	2	no	—
585	C₄×C₈₉	—	4	1	no	—
586	C₄×C₈₉	—	4	2	no	—
587	C₄×C₈₉	—	4	1	no	—
588	C₄×C₈₉	—	4	2	no	—
589	C₄×C₈₉	—	4	1	no	—
590	C₄×C₈₉	—	4	1	no	—
591	C₄×C₈₉	#532	1	4	yes	—
592	#35571	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
593	C₂×C₈₉	—	4	4	no	—
594	C₂×C₈₉	—	4	2	no	—
595	C₂×C₈₉	—	8	1	no	—
596	C₂×C₈₉	—	8	2	no	—
597	C₂×C₈₉	—	8	2	no	—
598	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
599	C₂×C₈₉	#3484	1	1	yes	characteristic
600	C₂×C₈₉	#3488	1	1	yes	characteristic
601	C₂×C₈₉	#3494	1	1	yes	characteristic
602	C₂×C₈₉	#3508	1	1	yes	characteristic
603	C₂×C₈₉	#3517	1	1	yes	characteristic
604	C₂×C₈₉	#3519	1	1	yes	characteristic
605	C₂×#540	C₂×C₈₉	1	1	yes	characteristic, complemented
606	C₂×#532	C₂×C₈₉	1	1	yes	characteristic, complemented
607	#2602	C₂×C₈₉	1	2	yes	complemented
608	#2557	C₂×C₈₉	1	2	yes	complemented
609	#2555	C₂×C₈₉	1	2	yes	complemented
610	#2550	C₂×C₈₉	1	1	yes	characteristic, complemented
611	#2543	C₂×C₈₉	1	2	yes	complemented
612	#2541	C₂×C₈₉	1	1	yes	characteristic, complemented
613	#2541	C₂×C₈₉	1	1	yes	characteristic, complemented
614	#2535	C₂×C₈₉	1	1	yes	characteristic, complemented
615	#2491	C₂×C₈₉	1	1	yes	characteristic, complemented
616	#2490	C₂×C₈₉	1	1	yes	characteristic, complemented
617	#2464	C₂×C₈₉	1	2	yes	complemented
618	#2431	C₂×C₈₉	1	2	yes	complemented
619	#2430	C₂×C₈₉	1	2	yes	complemented
620	#2428	C₂×C₈₉	1	1	yes	characteristic, complemented
621	#2428	C₂×C₈₉	1	1	yes	characteristic, complemented
622	#2428	C₂×C₈₉	1	2	yes	complemented
623	#2328	C₂×C₈₉	1	1	yes	characteristic, complemented
624	#2324	C₂×C₈₉	1	1	yes	characteristic, complemented
625	C₄×#121	C₂×C₈₉	1	1	yes	characteristic, complemented
626	#2290	C₂×C₈₉	1	1	yes	characteristic, complemented
627	#2275	C₂×C₈₉	1	1	yes	characteristic, complemented
628	C₈₉	#35571	1	1	yes	characteristic, direct product factor, Sylow
629	C₂²×#41	C₂²×C₈₉	1	2	yes	—
630	#540	—	2	8	no	—
631	#532	—	2	8	no	—
632	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
633	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
634	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
635	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
636	C₂×#127	C₂²×C₈₉	1	2	yes	—
637	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
638	C₂×#124	C₂²×C₈₉	1	2	yes	—
639	C₂×#124	C₂²×C₈₉	1	2	yes	—
640	C₂×#123	C₂²×C₈₉	1	2	yes	—
641	C₂×#123	C₂²×C₈₉	1	2	yes	—
642	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
643	C₂×#121	C₂²×C₈₉	1	2	yes	—
644	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
645	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
646	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
647	C₂×#121	C₂²×C₈₉	1	2	yes	—
648	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
649	C₂×#121	C₂²×C₈₉	1	2	yes	—
650	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
651	C₂×#121	C₂²×C₈₉	1	2	yes	—
652	C₂×#121	C₂²×C₈₉	1	2	yes	—
653	C₂×#121	C₂²×C₈₉	1	2	yes	—
654	C₂×#121	C₂²×C₈₉	1	2	yes	—
655	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
656	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
657	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
658	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
659	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
660	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
661	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
662	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
663	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
664	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
665	#398	C₂²×C₈₉	1	2	yes	—
666	#397	C₂²×C₈₉	1	2	yes	—
667	#397	C₂²×C₈₉	1	2	yes	—
668	#395	C₂²×C₈₉	1	2	yes	—
669	#394	C₂²×C₈₉	1	2	yes	—
670	#394	C₂²×C₈₉	1	2	yes	—
671	#394	C₂²×C₈₉	1	2	yes	—
672	#394	C₂²×C₈₉	1	2	yes	—
673	#393	C₂²×C₈₉	1	2	yes	—
674	#392	C₂²×C₈₉	1	2	yes	—
675	#392	C₂²×C₈₉	1	2	yes	—
676	#392	C₂²×C₈₉	1	2	yes	—
677	#392	C₂²×C₈₉	1	2	yes	—
678	#392	C₂²×C₈₉	1	2	yes	—
679	#392	C₂²×C₈₉	1	2	yes	—
680	#392	C₂²×C₈₉	1	2	yes	—
681	#391	C₂²×C₈₉	1	2	yes	—
682	#390	C₂²×C₈₉	1	2	yes	—
683	#390	C₂²×C₈₉	1	1	yes	characteristic
684	#390	C₂²×C₈₉	1	1	yes	characteristic
685	#390	C₂²×C₈₉	1	1	yes	characteristic
686	#390	C₂²×C₈₉	1	2	yes	—
687	#390	C₂²×C₈₉	1	2	yes	—
688	#390	C₂²×C₈₉	1	1	yes	characteristic
689	#389	C₂²×C₈₉	1	1	yes	characteristic
690	#389	C₂²×C₈₉	1	2	yes	—
691	#389	C₂²×C₈₉	1	1	yes	characteristic
692	#388	C₂²×C₈₉	1	2	yes	—
693	#388	C₂²×C₈₉	1	2	yes	—
694	#388	C₂²×C₈₉	1	2	yes	—
695	#388	C₂²×C₈₉	1	2	yes	—
696	#388	C₂²×C₈₉	1	1	yes	characteristic
697	#388	C₂²×C₈₉	1	1	yes	characteristic
698	#387	C₂²×C₈₉	1	1	yes	characteristic
699	#387	C₂²×C₈₉	1	1	yes	characteristic
700	#386	C₂²×C₈₉	1	2	yes	—
701	#386	C₂²×C₈₉	1	2	yes	—
702	#386	C₂²×C₈₉	1	2	yes	—
703	#386	C₂²×C₈₉	1	2	yes	—
704	#386	C₂²×C₈₉	1	2	yes	—
705	#386	C₂²×C₈₉	1	1	yes	characteristic
706	#386	C₂²×C₈₉	1	2	yes	—
707	#386	C₂²×C₈₉	1	2	yes	—
708	#386	C₂²×C₈₉	1	2	yes	—
709	#386	C₂²×C₈₉	1	2	yes	—
710	#386	C₂²×C₈₉	1	1	yes	characteristic
711	#386	C₂²×C₈₉	1	2	yes	—
712	#385	C₂²×C₈₉	1	2	yes	—
713	#385	C₂²×C₈₉	1	1	yes	characteristic
714	#385	C₂²×C₈₉	1	1	yes	characteristic
715	#382	C₂²×C₈₉	1	1	yes	characteristic
716	#380	C₂²×C₈₉	1	1	yes	characteristic
717	#380	C₂²×C₈₉	1	1	yes	characteristic
718	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
719	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
720	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
721	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
722	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
723	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
724	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
725	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
726	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
727	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
728	#376	C₂²×C₈₉	1	1	yes	characteristic
729	C₂×#95	C₂²×C₈₉	1	2	yes	—
730	C₂×#41	—	2	8	no	—
731	C₂×#41	—	4	4	no	—
732	C₂×#41	—	4	4	no	—
733	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
734	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
735	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
736	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
737	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
738	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
739	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
744	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
745	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
746	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
747	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
748	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
749	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
750	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
751	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
752	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
753	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
754	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
755	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
756	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
757	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
758	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
759	C₄⋊Q₈	—	2	4	no	—
760	#127	—	2	4	no	—
761	#127	—	2	4	no	—
762	#127	—	2	4	no	—
763	#127	—	4	4	no	—
764	#125	—	2	4	no	—
765	#124	—	2	8	no	—
766	#124	—	4	4	no	—
767	#123	—	2	8	no	—
768	#123	—	2	8	no	—
769	#121	—	2	4	no	—
770	#121	—	2	4	no	—
771	#121	—	2	8	no	—
772	#121	—	2	4	no	—
773	#121	—	2	4	no	—
774	#121	—	2	4	no	—
775	#121	—	2	4	no	—
776	#121	—	2	8	no	—
777	#121	—	2	8	no	—
778	#121	—	4	4	no	—
779	#121	—	4	4	no	—
780	#121	—	4	4	no	—
781	#121	—	4	4	no	—
782	C₄×D₄	—	2	8	no	—
783	C₄×D₄	—	2	4	no	—
784	C₄×D₄	—	2	4	no	—
785	C₄×D₄	—	2	4	no	—
786	C₄×D₄	—	2	4	no	—
787	C₄×D₄	—	2	4	no	—
788	C₄×D₄	—	4	4	no	—
789	C₄×D₄	D₄×C₈₉	1	8	yes	complemented
790	#117	—	2	4	no	—
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	1	yes	characteristic
794	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
795	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
796	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
805	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
806	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
807	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
808	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
809	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
810	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
820	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
821	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
833	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
834	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
835	C₂×C₄²	—	2	4	no	—
836	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
837	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
838	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
839	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
840	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
841	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
842	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
843	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
844	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
845	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
846	#95	C₂³×C₈₉	1	1	yes	characteristic
847	#95	C₂³×C₈₉	1	2	yes	—
848	#95	C₂³×C₈₉	1	2	yes	—
849	#95	C₂³×C₈₉	1	2	yes	—
850	#95	C₂³×C₈₉	1	1	yes	characteristic
851	#95	C₂³×C₈₉	1	1	yes	characteristic
852	#95	C₂³×C₈₉	1	1	yes	characteristic
853	#95	C₂³×C₈₉	1	2	yes	—
854	#95	C₂³×C₈₉	1	1	yes	characteristic
855	#95	C₂³×C₈₉	1	1	yes	characteristic
856	#95	C₂³×C₈₉	1	1	yes	characteristic
857	#95	C₂³×C₈₉	1	2	yes	—
858	#95	C₂³×C₈₉	1	1	yes	characteristic
859	#95	C₂³×C₈₉	1	1	yes	characteristic
860	#95	C₂³×C₈₉	1	1	yes	characteristic
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	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
866	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
867	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
868	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
869	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
870	#41	—	4	32	no	—
871	C₂×Q₈	—	2	4	no	—
872	C₂×Q₈	—	2	4	no	—
873	C₂×Q₈	—	4	2	no	—
874	C₂×D₄	—	2	4	no	—
875	C₂×D₄	—	2	4	no	—
876	C₂×D₄	—	2	4	no	—
877	C₂×D₄	—	2	4	no	—
878	C₂×D₄	—	2	4	no	—
879	C₂×D₄	—	2	2	no	—
880	C₂×D₄	—	2	4	no	—
881	C₂×D₄	—	2	4	no	—
882	C₂×D₄	—	2	4	no	—
883	C₂×D₄	—	2	4	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	2	2	no	—
886	C₂×D₄	—	2	4	no	—
887	C₂×D₄	—	2	4	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	4	no	—
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	4	no	—
897	C₂×D₄	—	2	4	no	—
898	C₂×D₄	—	2	4	no	—
899	C₂×D₄	—	2	4	no	—
900	C₂×D₄	—	2	4	no	—
901	C₂×D₄	—	4	2	no	—
902	C₂×D₄	—	4	2	no	—
903	C₂×D₄	—	4	2	no	—
904	C₂×D₄	—	4	2	no	—
905	C₂×D₄	—	4	2	no	—
906	C₂×D₄	—	4	1	no	—
907	C₂×D₄	—	4	2	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	—	4	2	no	—
913	C₂×D₄	—	4	2	no	—
914	C₂×D₄	—	4	2	no	—
915	C₂×D₄	—	4	2	no	—
916	C₂×D₄	—	4	2	no	—
917	C₂×D₄	—	4	2	no	—
918	C₂×D₄	—	4	2	no	—
919	C₂×D₄	—	4	2	no	—
920	C₂×D₄	—	4	2	no	—
921	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
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	2	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	4	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	—	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	1	no	—
942	C₂²×C₄	—	4	2	no	—
943	C₂²×C₄	—	4	2	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	C₂×D₄×C₈₉	1	8	yes	—
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	2	yes	—
953	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
954	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
956	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
957	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
958	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
959	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
960	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
961	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
962	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
963	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
964	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
965	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
966	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	4	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	4	no	—
973	C₄⋊C₄	—	2	4	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	4	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	4	2	no	—
980	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
981	C₄⋊C₄	#41×C₈₉	1	4	yes	complemented
982	C₂²⋊C₄	—	2	4	no	—
983	C₂²⋊C₄	—	2	4	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	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	4	no	—
996	C₂²⋊C₄	—	2	4	no	—
997	C₂²⋊C₄	—	2	4	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	4	no	—
1000	C₂²⋊C₄	—	2	2	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	1	no	—
1010	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
1011	C₄²	—	2	2	no	—
1012	C₄²	—	2	2	no	—
1013	C₄²	—	2	2	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	4	2	no	—
1017	C₄²	—	4	2	no	—
1018	C₄²	—	4	2	no	—
1019	C₄²	C₂×D₄×C₈₉	1	4	yes	—
1020	C₄²	#41×C₈₉	1	4	yes	complemented
1021	C₂³	—	2	1	no	—
1022	C₂³	—	2	2	no	—
1023	C₂³	—	2	2	no	—
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	2	no	—
1029	C₂³	—	2	2	no	—
1030	C₂³	—	2	2	no	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	2	no	—
1033	C₂³	—	2	1	no	—
1034	C₂³	—	2	2	no	—
1035	C₂³	—	2	2	no	—
1036	C₂³	—	2	1	no	—
1037	C₂³	—	2	2	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	2	no	—
1041	C₂³	—	2	2	no	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	2	2	no	—
1045	C₂³	—	2	1	no	—
1046	C₂³	—	2	2	no	—
1047	C₂³	—	2	2	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	2	no	—
1050	C₂³	—	2	1	no	—
1051	C₂³	—	2	2	no	—
1052	C₂³	—	2	2	no	—
1053	C₂³	—	2	1	no	—
1054	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
1055	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
1056	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
1057	Q₈	—	4	8	no	—
1058	D₄	—	2	8	no	—
1059	D₄	—	4	8	no	—
1060	D₄	—	4	4	no	—
1061	D₄	—	4	8	no	—
1062	D₄	—	4	8	no	—
1063	D₄	—	4	8	no	—
1064	D₄	—	4	8	no	—
1065	D₄	—	4	4	no	—
1066	D₄	—	4	4	no	—
1067	D₄	—	8	4	no	—
1068	D₄	—	8	4	no	—
1069	D₄	—	8	4	no	—
1070	D₄	—	8	4	no	—
1071	D₄	—	8	4	no	—
1072	D₄	—	8	4	no	—
1073	D₄	—	8	4	no	—
1074	C₂×C₄	—	2	8	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	2	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	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	2	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	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	4	8	no	—
1119	C₂×C₄	—	4	4	no	—
1120	C₂×C₄	—	4	8	no	—
1121	C₂×C₄	—	4	4	no	—
1122	C₂×C₄	—	4	4	no	—
1123	C₂×C₄	—	8	4	no	—
1124	C₂×C₄	—	8	4	no	—
1125	C₂×C₄	—	8	4	no	—
1126	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1127	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1128	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
1129	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1130	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
1131	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
1132	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
1133	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
1134	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
1135	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
1136	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
1137	C₂²	—	2	4	no	—
1138	C₂²	—	2	2	no	—
1139	C₂²	—	2	4	no	—
1140	C₂²	—	2	4	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	—	4	1	no	—
1145	C₂²	—	4	2	no	—
1146	C₂²	—	4	2	no	—
1147	C₂²	—	4	1	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	4	2	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	2	no	—
1153	C₂²	—	4	2	no	—
1154	C₂²	—	4	2	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	4	2	no	—
1157	C₂²	—	4	2	no	—
1158	C₂²	—	4	2	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	2	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	2	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	4	2	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	—	4	2	no	—
1172	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1173	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
1174	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
1175	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1176	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1177	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1178	C₂²	#585×C₈₉	1	1	yes	characteristic
1179	C₄	—	2	2	no	—
1180	C₄	—	2	2	no	—
1181	C₄	—	2	4	no	—
1182	C₄	—	2	2	no	—
1183	C₄	—	2	2	no	—
1184	C₄	—	2	2	no	—
1185	C₄	—	2	2	no	—
1186	C₄	—	2	4	no	—
1187	C₄	—	4	1	no	—
1188	C₄	—	4	1	no	—
1189	C₄	—	4	2	no	—
1190	C₄	—	4	1	no	—
1191	C₄	—	4	2	no	—
1192	C₄	—	4	1	no	—
1193	C₄	—	4	2	no	—
1194	C₄	—	4	1	no	—
1195	C₄	—	4	1	no	—
1196	C₄	#532×C₈₉	1	4	yes	—
1197	C₂	—	4	4	no	—
1198	C₂	—	4	2	no	—
1199	C₂	—	8	1	no	—
1200	C₂	—	8	2	no	—
1201	C₂	—	8	2	no	—
1202	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
1203	C₂	C₈₉×#3484	1	1	yes	characteristic
1204	C₂	C₈₉×#3488	1	1	yes	characteristic
1205	C₂	C₈₉×#3494	1	1	yes	characteristic
1206	C₂	C₈₉×#3508	1	1	yes	characteristic
1207	C₂	C₈₉×#3517	1	1	yes	characteristic
1208	C₂	C₈₉×#3519	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×#540×C₈₉	C₂	semidirect
2. C₂×#532×C₈₉	C₂	semidirect
3. C₈₉×#2602	C₂	semidirect
4. C₈₉×#2557	C₂	semidirect
5. C₈₉×#2555	C₂	semidirect
6. C₈₉×#2550	C₂	semidirect
7. C₈₉×#2543	C₂	semidirect
8. C₈₉×#2541	C₂	semidirect
9. C₈₉×#2541	C₂	semidirect
10. C₈₉×#2535	C₂	semidirect
11. C₈₉×#2491	C₂	semidirect
12. C₈₉×#2490	C₂	semidirect
13. C₈₉×#2464	C₂	semidirect
14. C₈₉×#2431	C₂	semidirect
15. C₈₉×#2430	C₂	semidirect
16. C₈₉×#2428	C₂	semidirect
17. C₈₉×#2428	C₂	semidirect
18. C₈₉×#2428	C₂	semidirect
19. C₈₉×#2328	C₂	semidirect
20. C₈₉×#2324	C₂	semidirect
21. C₄×#121×C₈₉	C₂	semidirect
22. C₈₉×#2290	C₂	semidirect
23. C₈₉×#2275	C₂	semidirect
184. C₄×D₄×C₈₉	D₄	semidirect
376. C₄⋊C₄×C₈₉	#41	semidirect
415. C₄²×C₈₉	#41	semidirect
592. #35571	C₈₉	direct (N × H)
605. C₂×#540	C₂×C₈₉	semidirect
606. C₂×#532	C₂×C₈₉	semidirect
607. #2602	C₂×C₈₉	semidirect
608. #2557	C₂×C₈₉	semidirect
609. #2555	C₂×C₈₉	semidirect
610. #2550	C₂×C₈₉	semidirect
611. #2543	C₂×C₈₉	semidirect
612. #2541	C₂×C₈₉	semidirect
613. #2541	C₂×C₈₉	semidirect
614. #2535	C₂×C₈₉	semidirect
615. #2491	C₂×C₈₉	semidirect
616. #2490	C₂×C₈₉	semidirect
617. #2464	C₂×C₈₉	semidirect
618. #2431	C₂×C₈₉	semidirect
619. #2430	C₂×C₈₉	semidirect
620. #2428	C₂×C₈₉	semidirect
621. #2428	C₂×C₈₉	semidirect
622. #2428	C₂×C₈₉	semidirect
623. #2328	C₂×C₈₉	semidirect
624. #2324	C₂×C₈₉	semidirect
625. C₄×#121	C₂×C₈₉	semidirect
626. #2290	C₂×C₈₉	semidirect
627. #2275	C₂×C₈₉	semidirect
628. C₈₉	#35571	direct (N × H)
789. C₄×D₄	D₄×C₈₉	semidirect
981. C₄⋊C₄	#41×C₈₉	semidirect
1020. C₄²	#41×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#540×C₈₉	2
C₂×#532×C₈₉	2
C₈₉×#2602	2
C₈₉×#2557	2
C₈₉×#2555	2
C₈₉×#2550	2
C₈₉×#2543	2
C₈₉×#2541	2
C₈₉×#2535	2
C₈₉×#2491	2
C₈₉×#2490	2
C₈₉×#2464	2
C₈₉×#2431	2
C₈₉×#2430	2
C₈₉×#2428	2
C₈₉×#2328	2
C₈₉×#2324	2
C₄×#121×C₈₉	2
C₈₉×#2290	2
C₈₉×#2275	2
#35571	89

Subgroups — C89×#35571 #36413419

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35571 #36413419