Subgroups — C₈₉×#36739 #36414587

Order 22784.

2782 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#538×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#534×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2856	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2850	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2718	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2710	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2706	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2703	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2685	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2678	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2670	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2669	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2656	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2639	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2543	C₂	1	2	yes	maximal, complemented
16	C₈₉×#2416	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2410	C₂	1	2	yes	maximal, complemented
18	C₈₉×#2410	C₂	1	2	yes	maximal, complemented
19	C₂×#388×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂³×D₄×C₈₉	C₂²	1	2	yes	—
21	#538×C₈₉	—	2	8	no	—
22	#534×C₈₉	—	2	8	no	—
23	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic, complemented
24	C₂×#126×C₈₉	C₂²	1	2	yes	complemented
25	C₂×#124×C₈₉	C₂²	1	2	yes	complemented
26	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
27	C₂×#123×C₈₉	C₂²	1	2	yes	—
28	C₂×#123×C₈₉	C₂²	1	2	yes	—
29	C₂×#123×C₈₉	C₂²	1	2	yes	complemented
30	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#121×C₈₉	C₂²	1	2	yes	—
34	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×#121×C₈₉	C₂²	1	2	yes	complemented
36	C₂×#121×C₈₉	C₂²	1	2	yes	complemented
37	C₂×#121×C₈₉	C₂²	1	2	yes	complemented
38	C₂×#121×C₈₉	C₂²	1	2	yes	complemented
39	C₂×#121×C₈₉	C₂²	1	2	yes	complemented
40	C₂×#121×C₈₉	C₂²	1	2	yes	complemented
41	C₂×#120×C₈₉	C₂²	1	2	yes	—
42	C₂×#120×C₈₉	C₂²	1	2	yes	—
43	C₂×#120×C₈₉	C₂²	1	2	yes	—
44	C₂×#120×C₈₉	C₂²	1	2	yes	complemented
45	C₂×#120×C₈₉	C₂²	1	2	yes	complemented
46	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
47	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
48	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
49	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
50	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
51	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic, complemented
52	#400×C₈₉	C₂²	1	2	yes	complemented
53	#399×C₈₉	C₂²	1	2	yes	complemented
54	#399×C₈₉	C₂²	1	2	yes	complemented
55	#398×C₈₉	C₂²	1	2	yes	complemented
56	#397×C₈₉	C₂²	1	2	yes	complemented
57	#397×C₈₉	C₂²	1	2	yes	complemented
58	#396×C₈₉	C₂²	1	2	yes	complemented
59	#396×C₈₉	C₂²	1	2	yes	complemented
60	#394×C₈₉	C₂²	1	2	yes	—
61	#394×C₈₉	C₂²	1	2	yes	—
62	#394×C₈₉	C₂²	1	2	yes	—
63	#394×C₈₉	C₂²	1	2	yes	—
64	#394×C₈₉	C₂²	1	2	yes	complemented
65	#394×C₈₉	C₂²	1	2	yes	complemented
66	#394×C₈₉	C₂²	1	2	yes	complemented
67	#394×C₈₉	C₂²	1	2	yes	complemented
68	#393×C₈₉	C₂²	1	2	yes	complemented
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	complemented
74	#392×C₈₉	C₂²	1	2	yes	complemented
75	#392×C₈₉	C₂²	1	2	yes	complemented
76	#391×C₈₉	C₂²	1	1	yes	characteristic, complemented
77	#390×C₈₉	C₂²	1	1	yes	characteristic, complemented
78	#390×C₈₉	C₂²	1	2	yes	complemented
79	#390×C₈₉	C₂²	1	2	yes	complemented
80	#390×C₈₉	C₂²	1	1	yes	characteristic, complemented
81	#390×C₈₉	C₂²	1	1	yes	characteristic, complemented
82	#390×C₈₉	C₂²	1	2	yes	complemented
83	#389×C₈₉	C₂²	1	2	yes	complemented
84	#388×C₈₉	C₂²	1	2	yes	complemented
85	#388×C₈₉	C₂²	1	2	yes	complemented
86	#388×C₈₉	C₂²	1	2	yes	complemented
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	#386×C₈₉	C₂²	1	2	yes	complemented
93	#386×C₈₉	C₂²	1	2	yes	complemented
94	#386×C₈₉	C₂²	1	2	yes	complemented
95	#386×C₈₉	C₂²	1	2	yes	complemented
96	#386×C₈₉	C₂²	1	2	yes	complemented
97	#386×C₈₉	C₂²	1	2	yes	complemented
98	#386×C₈₉	C₂²	1	2	yes	complemented
99	#386×C₈₉	C₂²	1	2	yes	complemented
100	#385×C₈₉	C₂²	1	2	yes	complemented
101	#385×C₈₉	C₂²	1	2	yes	complemented
102	#384×C₈₉	C₂²	1	1	yes	characteristic, complemented
103	#382×C₈₉	C₂²	1	1	yes	characteristic, complemented
104	#380×C₈₉	C₂²	1	2	yes	complemented
105	#379×C₈₉	C₂²	1	2	yes	complemented
106	#379×C₈₉	C₂²	1	2	yes	complemented
107	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic, complemented
108	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic, complemented
109	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
110	C₂⁵×C₈₉	C₂³	1	2	yes	—
111	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₈₉	—	2	8	no	—
113	C₂²×D₄×C₈₉	—	4	4	no	—
114	C₂²×D₄×C₈₉	—	4	4	no	—
115	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
116	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
117	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
118	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
119	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
120	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
121	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
122	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
123	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
125	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
127	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
128	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
129	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
130	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
135	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
136	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
138	#127×C₈₉	—	4	2	no	—
139	#126×C₈₉	—	2	8	no	—
140	#124×C₈₉	—	2	8	no	—
141	#124×C₈₉	—	4	2	no	—
142	#123×C₈₉	—	2	8	no	—
143	#123×C₈₉	—	2	8	no	—
144	#123×C₈₉	—	2	8	no	—
145	C₂²⋊Q₈×C₈₉	—	2	4	no	—
146	#121×C₈₉	—	2	8	no	—
147	#121×C₈₉	—	2	4	no	—
148	#121×C₈₉	—	2	4	no	—
149	#121×C₈₉	—	2	4	no	—
150	#121×C₈₉	—	2	8	no	—
151	#121×C₈₉	—	4	4	no	—
152	#121×C₈₉	—	4	4	no	—
153	#121×C₈₉	—	4	4	no	—
154	#121×C₈₉	—	4	4	no	—
155	#121×C₈₉	—	4	4	no	—
156	#120×C₈₉	—	2	8	no	—
157	#120×C₈₉	—	2	8	no	—
158	#120×C₈₉	—	2	8	no	—
159	#120×C₈₉	—	4	4	no	—
160	#120×C₈₉	—	4	4	no	—
161	C₄×D₄×C₈₉	—	2	8	no	—
162	C₂×C₄⋊C₄×C₈₉	—	4	2	no	—
163	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
176	C₂×C₂²⋊C₄×C₈₉	—	4	2	no	—
177	C₂×C₂²⋊C₄×C₈₉	—	4	2	no	—
178	C₂×C₂²⋊C₄×C₈₉	D₄	1	8	yes	complemented
179	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
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	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	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	2	yes	—
210	C₂×C₄²×C₈₉	—	4	2	no	—
211	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
214	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
216	#95×C₈₉	C₂³	1	2	yes	—
217	#95×C₈₉	C₂³	1	2	yes	—
218	#95×C₈₉	C₂³	1	2	yes	—
219	#95×C₈₉	C₂³	1	2	yes	—
220	#95×C₈₉	C₂³	1	2	yes	—
221	#95×C₈₉	C₂³	1	2	yes	—
222	#95×C₈₉	C₂³	1	2	yes	—
223	#95×C₈₉	C₂³	1	2	yes	—
224	#95×C₈₉	C₂³	1	2	yes	—
225	#95×C₈₉	C₂³	1	2	yes	—
226	#95×C₈₉	C₂³	1	2	yes	—
227	#95×C₈₉	C₂³	1	2	yes	—
228	C₂⁴×C₈₉	—	2	2	no	—
229	C₂⁴×C₈₉	—	2	2	no	—
230	C₂⁴×C₈₉	—	2	4	no	—
231	C₂⁴×C₈₉	—	4	1	no	—
232	C₂⁴×C₈₉	—	4	1	no	—
233	C₂⁴×C₈₉	—	4	2	no	—
234	C₂⁴×C₈₉	—	4	2	no	—
235	C₂⁴×C₈₉	—	4	1	no	—
236	C₂⁴×C₈₉	—	4	1	no	—
237	C₂⁴×C₈₉	—	4	2	no	—
238	C₂⁴×C₈₉	—	4	2	no	—
239	C₂⁴×C₈₉	—	4	2	no	—
240	C₂⁴×C₈₉	—	4	2	no	—
241	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
242	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
243	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
244	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
245	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
246	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
247	C₂×Q₈×C₈₉	—	2	2	no	—
248	C₂×Q₈×C₈₉	—	4	1	no	—
249	C₂×Q₈×C₈₉	—	4	1	no	—
250	C₂×D₄×C₈₉	—	2	4	no	—
251	C₂×D₄×C₈₉	—	2	4	no	—
252	C₂×D₄×C₈₉	—	2	4	no	—
253	C₂×D₄×C₈₉	—	2	4	no	—
254	C₂×D₄×C₈₉	—	2	4	no	—
255	C₂×D₄×C₈₉	—	2	4	no	—
256	C₂×D₄×C₈₉	—	2	4	no	—
257	C₂×D₄×C₈₉	—	2	4	no	—
258	C₂×D₄×C₈₉	—	2	4	no	—
259	C₂×D₄×C₈₉	—	2	4	no	—
260	C₂×D₄×C₈₉	—	2	4	no	—
261	C₂×D₄×C₈₉	—	2	4	no	—
262	C₂×D₄×C₈₉	—	2	4	no	—
263	C₂×D₄×C₈₉	—	2	4	no	—
264	C₂×D₄×C₈₉	—	2	2	no	—
265	C₂×D₄×C₈₉	—	2	2	no	—
266	C₂×D₄×C₈₉	—	2	2	no	—
267	C₂×D₄×C₈₉	—	2	4	no	—
268	C₂×D₄×C₈₉	—	2	4	no	—
269	C₂×D₄×C₈₉	—	4	2	no	—
270	C₂×D₄×C₈₉	—	4	2	no	—
271	C₂×D₄×C₈₉	—	4	2	no	—
272	C₂×D₄×C₈₉	—	4	2	no	—
273	C₂×D₄×C₈₉	—	4	2	no	—
274	C₂×D₄×C₈₉	—	4	2	no	—
275	C₂×D₄×C₈₉	—	4	2	no	—
276	C₂×D₄×C₈₉	—	4	2	no	—
277	C₂×D₄×C₈₉	—	4	2	no	—
278	C₂×D₄×C₈₉	—	4	2	no	—
279	C₂×D₄×C₈₉	—	4	2	no	—
280	C₂×D₄×C₈₉	—	4	2	no	—
281	C₂×D₄×C₈₉	—	4	2	no	—
282	C₂×D₄×C₈₉	—	4	2	no	—
283	C₂×D₄×C₈₉	—	4	1	no	—
284	C₂×D₄×C₈₉	—	4	1	no	—
285	C₂×D₄×C₈₉	—	4	2	no	—
286	C₂×D₄×C₈₉	—	4	1	no	—
287	C₂×D₄×C₈₉	—	4	2	no	—
288	C₂×D₄×C₈₉	—	4	1	no	—
289	C₂×D₄×C₈₉	—	4	2	no	—
290	C₂×D₄×C₈₉	—	4	1	no	—
291	C₂×D₄×C₈₉	—	4	1	no	—
292	C₂×D₄×C₈₉	—	4	2	no	—
293	C₂×D₄×C₈₉	—	4	2	no	—
294	C₂×D₄×C₈₉	—	4	2	no	—
295	C₂×D₄×C₈₉	—	4	32	no	—
296	C₂²×C₄×C₈₉	—	2	4	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	4	no	—
304	C₂²×C₄×C₈₉	—	4	1	no	—
305	C₂²×C₄×C₈₉	—	4	1	no	—
306	C₂²×C₄×C₈₉	—	4	1	no	—
307	C₂²×C₄×C₈₉	—	4	1	no	—
308	C₂²×C₄×C₈₉	—	4	1	no	—
309	C₂²×C₄×C₈₉	—	4	1	no	—
310	C₂²×C₄×C₈₉	—	4	2	no	—
311	C₂²×C₄×C₈₉	—	4	2	no	—
312	C₂²×C₄×C₈₉	—	4	1	no	—
313	C₂²×C₄×C₈₉	—	4	1	no	—
314	C₂²×C₄×C₈₉	—	4	1	no	—
315	C₂²×C₄×C₈₉	—	4	2	no	—
316	C₂²×C₄×C₈₉	—	4	2	no	—
317	C₂²×C₄×C₈₉	—	4	1	no	—
318	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
319	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
320	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
329	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
334	C₄⋊C₄×C₈₉	—	2	4	no	—
335	C₄⋊C₄×C₈₉	—	2	4	no	—
336	C₄⋊C₄×C₈₉	—	2	4	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	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	2	no	—
345	C₄⋊C₄×C₈₉	—	4	2	no	—
346	C₄⋊C₄×C₈₉	—	4	2	no	—
347	C₂²⋊C₄×C₈₉	—	2	4	no	—
348	C₂²⋊C₄×C₈₉	—	2	4	no	—
349	C₂²⋊C₄×C₈₉	—	2	4	no	—
350	C₂²⋊C₄×C₈₉	—	2	4	no	—
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	4	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	—	4	2	no	—
361	C₂²⋊C₄×C₈₉	—	4	2	no	—
362	C₂²⋊C₄×C₈₉	—	4	2	no	—
363	C₂²⋊C₄×C₈₉	—	4	2	no	—
364	C₂²⋊C₄×C₈₉	—	4	2	no	—
365	C₂²⋊C₄×C₈₉	—	4	2	no	—
366	C₂²⋊C₄×C₈₉	—	4	2	no	—
367	C₂²⋊C₄×C₈₉	—	4	2	no	—
368	C₂²⋊C₄×C₈₉	—	4	2	no	—
369	C₂²⋊C₄×C₈₉	—	4	2	no	—
370	C₂²⋊C₄×C₈₉	—	4	2	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	2	no	—
375	C₂²⋊C₄×C₈₉	—	4	2	no	—
376	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
377	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
378	C₄²×C₈₉	—	2	4	no	—
379	C₄²×C₈₉	—	2	2	no	—
380	C₄²×C₈₉	—	2	2	no	—
381	C₄²×C₈₉	—	4	1	no	—
382	C₄²×C₈₉	—	4	1	no	—
383	C₂³×C₈₉	—	2	1	no	—
384	C₂³×C₈₉	—	2	1	no	—
385	C₂³×C₈₉	—	2	1	no	—
386	C₂³×C₈₉	—	2	1	no	—
387	C₂³×C₈₉	—	2	2	no	—
388	C₂³×C₈₉	—	2	2	no	—
389	C₂³×C₈₉	—	2	2	no	—
390	C₂³×C₈₉	—	2	2	no	—
391	C₂³×C₈₉	—	2	2	no	—
392	C₂³×C₈₉	—	2	2	no	—
393	C₂³×C₈₉	—	2	8	no	—
394	C₂³×C₈₉	—	2	2	no	—
395	C₂³×C₈₉	—	2	2	no	—
396	C₂³×C₈₉	—	2	2	no	—
397	C₂³×C₈₉	—	2	2	no	—
398	C₂³×C₈₉	—	2	2	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	2	no	—
405	C₂³×C₈₉	—	2	2	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	2	no	—
411	C₂³×C₈₉	—	2	2	no	—
412	C₂³×C₈₉	—	2	2	no	—
413	C₂³×C₈₉	—	2	2	no	—
414	C₂³×C₈₉	—	2	2	no	—
415	C₂³×C₈₉	—	4	4	no	—
416	C₂³×C₈₉	—	4	4	no	—
417	C₂³×C₈₉	—	4	8	no	—
418	C₂³×C₈₉	—	8	2	no	—
419	C₂³×C₈₉	—	8	2	no	—
420	C₂³×C₈₉	—	8	2	no	—
421	C₂³×C₈₉	—	8	2	no	—
422	C₂³×C₈₉	—	8	4	no	—
423	C₂³×C₈₉	—	8	4	no	—
424	C₂³×C₈₉	—	8	4	no	—
425	C₂³×C₈₉	—	8	4	no	—
426	C₂³×C₈₉	—	8	4	no	—
427	C₂³×C₈₉	—	8	4	no	—
428	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
429	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
430	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
431	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
432	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
433	Q₈×C₈₉	—	8	2	no	—
434	D₄×C₈₉	—	4	8	no	—
435	D₄×C₈₉	—	4	8	no	—
436	D₄×C₈₉	—	4	8	no	—
437	D₄×C₈₉	—	4	8	no	—
438	D₄×C₈₉	—	4	8	no	—
439	D₄×C₈₉	—	8	4	no	—
440	D₄×C₈₉	—	8	2	no	—
441	D₄×C₈₉	—	8	2	no	—
442	D₄×C₈₉	—	8	2	no	—
443	D₄×C₈₉	—	8	4	no	—
444	D₄×C₈₉	—	8	4	no	—
445	D₄×C₈₉	—	8	4	no	—
446	D₄×C₈₉	—	8	4	no	—
447	D₄×C₈₉	—	8	4	no	—
448	D₄×C₈₉	—	8	4	no	—
449	C₂×C₄×C₈₉	—	2	1	no	—
450	C₂×C₄×C₈₉	—	2	1	no	—
451	C₂×C₄×C₈₉	—	2	1	no	—
452	C₂×C₄×C₈₉	—	2	2	no	—
453	C₂×C₄×C₈₉	—	2	1	no	—
454	C₂×C₄×C₈₉	—	2	1	no	—
455	C₂×C₄×C₈₉	—	2	2	no	—
456	C₂×C₄×C₈₉	—	2	1	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	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	1	no	—
466	C₂×C₄×C₈₉	—	2	2	no	—
467	C₂×C₄×C₈₉	—	2	2	no	—
468	C₂×C₄×C₈₉	—	2	2	no	—
469	C₂×C₄×C₈₉	—	2	2	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	2	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	2	no	—
479	C₂×C₄×C₈₉	—	2	2	no	—
480	C₂×C₄×C₈₉	—	2	2	no	—
481	C₂×C₄×C₈₉	—	2	2	no	—
482	C₂×C₄×C₈₉	—	2	1	no	—
483	C₂×C₄×C₈₉	—	2	2	no	—
484	C₂×C₄×C₈₉	—	2	2	no	—
485	C₂×C₄×C₈₉	—	2	2	no	—
486	C₂×C₄×C₈₉	—	4	4	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	—	4	8	no	—
491	C₂×C₄×C₈₉	—	8	4	no	—
492	C₂×C₄×C₈₉	—	8	2	no	—
493	C₂×C₄×C₈₉	—	8	2	no	—
494	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
495	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
498	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
499	C₂²×C₈₉	—	2	2	no	—
500	C₂²×C₈₉	—	2	2	no	—
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	4	no	—
506	C₂²×C₈₉	—	2	4	no	—
507	C₂²×C₈₉	—	2	4	no	—
508	C₂²×C₈₉	—	4	2	no	—
509	C₂²×C₈₉	—	4	2	no	—
510	C₂²×C₈₉	—	4	2	no	—
511	C₂²×C₈₉	—	4	2	no	—
512	C₂²×C₈₉	—	4	2	no	—
513	C₂²×C₈₉	—	4	2	no	—
514	C₂²×C₈₉	—	4	2	no	—
515	C₂²×C₈₉	—	4	2	no	—
516	C₂²×C₈₉	—	4	2	no	—
517	C₂²×C₈₉	—	4	2	no	—
518	C₂²×C₈₉	—	4	2	no	—
519	C₂²×C₈₉	—	4	2	no	—
520	C₂²×C₈₉	—	4	2	no	—
521	C₂²×C₈₉	—	4	2	no	—
522	C₂²×C₈₉	—	4	2	no	—
523	C₂²×C₈₉	—	4	2	no	—
524	C₂²×C₈₉	—	4	2	no	—
525	C₂²×C₈₉	—	4	2	no	—
526	C₂²×C₈₉	—	4	2	no	—
527	C₂²×C₈₉	—	4	2	no	—
528	C₂²×C₈₉	—	4	2	no	—
529	C₂²×C₈₉	—	4	2	no	—
530	C₂²×C₈₉	—	4	2	no	—
531	C₂²×C₈₉	—	4	2	no	—
532	C₂²×C₈₉	—	4	2	no	—
533	C₂²×C₈₉	—	8	8	no	—
534	C₂²×C₈₉	—	8	16	no	—
535	C₂²×C₈₉	#535	1	4	yes	—
536	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
537	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
538	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
539	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
540	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
541	C₂²×C₈₉	#585	1	1	yes	characteristic
542	C₂²×C₈₉	#585	1	1	yes	characteristic
543	C₄×C₈₉	—	2	4	no	—
544	C₄×C₈₉	—	2	2	no	—
545	C₄×C₈₉	—	2	2	no	—
546	C₄×C₈₉	—	2	2	no	—
547	C₄×C₈₉	—	2	2	no	—
548	C₄×C₈₉	—	4	2	no	—
549	C₄×C₈₉	—	4	2	no	—
550	C₄×C₈₉	—	4	2	no	—
551	C₄×C₈₉	—	4	2	no	—
552	C₄×C₈₉	—	4	2	no	—
553	C₄×C₈₉	—	4	1	no	—
554	C₄×C₈₉	—	4	1	no	—
555	C₄×C₈₉	—	4	2	no	—
556	C₄×C₈₉	—	4	2	no	—
557	#36739	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
558	C₂×C₈₉	—	2	4	no	—
559	C₂×C₈₉	—	4	4	no	—
560	C₂×C₈₉	—	8	2	no	—
561	C₂×C₈₉	—	8	2	no	—
562	C₂×C₈₉	—	8	2	no	—
563	C₂×C₈₉	C₂×#535	1	1	yes	characteristic
564	C₂×C₈₉	#3496	1	1	yes	characteristic
565	C₂×C₈₉	#3496	1	1	yes	characteristic
566	C₂×C₈₉	#3534	1	1	yes	characteristic
567	C₂×C₈₉	#3537	1	1	yes	characteristic
568	C₂×C₈₉	#3558	1	1	yes	characteristic
569	C₂×C₈₉	#3560	1	1	yes	characteristic
570	C₂×#538	C₂×C₈₉	1	1	yes	characteristic, complemented
571	C₂×#534	C₂×C₈₉	1	1	yes	characteristic, complemented
572	#2856	C₂×C₈₉	1	1	yes	characteristic, complemented
573	#2850	C₂×C₈₉	1	1	yes	characteristic, complemented
574	#2718	C₂×C₈₉	1	2	yes	complemented
575	#2710	C₂×C₈₉	1	2	yes	complemented
576	#2706	C₂×C₈₉	1	2	yes	complemented
577	#2703	C₂×C₈₉	1	2	yes	complemented
578	#2685	C₂×C₈₉	1	2	yes	complemented
579	#2678	C₂×C₈₉	1	2	yes	complemented
580	#2670	C₂×C₈₉	1	2	yes	complemented
581	#2669	C₂×C₈₉	1	2	yes	complemented
582	#2656	C₂×C₈₉	1	1	yes	characteristic, complemented
583	#2639	C₂×C₈₉	1	1	yes	characteristic, complemented
584	#2543	C₂×C₈₉	1	2	yes	complemented
585	#2416	C₂×C₈₉	1	2	yes	complemented
586	#2410	C₂×C₈₉	1	2	yes	complemented
587	#2410	C₂×C₈₉	1	2	yes	complemented
588	C₂×#388	C₂×C₈₉	1	1	yes	characteristic, complemented
589	C₈₉	#36739	1	1	yes	characteristic, direct product factor, Sylow
590	C₂³×D₄	C₂²×C₈₉	1	2	yes	—
591	#538	—	2	8	no	—
592	#534	—	2	8	no	—
593	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic, complemented
594	C₂×#126	C₂²×C₈₉	1	2	yes	complemented
595	C₂×#124	C₂²×C₈₉	1	2	yes	complemented
596	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic, complemented
597	C₂×#123	C₂²×C₈₉	1	2	yes	—
598	C₂×#123	C₂²×C₈₉	1	2	yes	—
599	C₂×#123	C₂²×C₈₉	1	2	yes	complemented
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×#121	C₂²×C₈₉	1	2	yes	—
604	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic, complemented
605	C₂×#121	C₂²×C₈₉	1	2	yes	complemented
606	C₂×#121	C₂²×C₈₉	1	2	yes	complemented
607	C₂×#121	C₂²×C₈₉	1	2	yes	complemented
608	C₂×#121	C₂²×C₈₉	1	2	yes	complemented
609	C₂×#121	C₂²×C₈₉	1	2	yes	complemented
610	C₂×#121	C₂²×C₈₉	1	2	yes	complemented
611	C₂×#120	C₂²×C₈₉	1	2	yes	—
612	C₂×#120	C₂²×C₈₉	1	2	yes	—
613	C₂×#120	C₂²×C₈₉	1	2	yes	—
614	C₂×#120	C₂²×C₈₉	1	2	yes	complemented
615	C₂×#120	C₂²×C₈₉	1	2	yes	complemented
616	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
617	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
618	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
619	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
620	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
621	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic, complemented
622	#400	C₂²×C₈₉	1	2	yes	complemented
623	#399	C₂²×C₈₉	1	2	yes	complemented
624	#399	C₂²×C₈₉	1	2	yes	complemented
625	#398	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	complemented
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	#394	C₂²×C₈₉	1	2	yes	complemented
637	#394	C₂²×C₈₉	1	2	yes	complemented
638	#393	C₂²×C₈₉	1	2	yes	complemented
639	#392	C₂²×C₈₉	1	2	yes	—
640	#392	C₂²×C₈₉	1	2	yes	—
641	#392	C₂²×C₈₉	1	2	yes	—
642	#392	C₂²×C₈₉	1	2	yes	—
643	#392	C₂²×C₈₉	1	2	yes	complemented
644	#392	C₂²×C₈₉	1	2	yes	complemented
645	#392	C₂²×C₈₉	1	2	yes	complemented
646	#391	C₂²×C₈₉	1	1	yes	characteristic, complemented
647	#390	C₂²×C₈₉	1	1	yes	characteristic, complemented
648	#390	C₂²×C₈₉	1	2	yes	complemented
649	#390	C₂²×C₈₉	1	2	yes	complemented
650	#390	C₂²×C₈₉	1	1	yes	characteristic, complemented
651	#390	C₂²×C₈₉	1	1	yes	characteristic, complemented
652	#390	C₂²×C₈₉	1	2	yes	complemented
653	#389	C₂²×C₈₉	1	2	yes	complemented
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	#388	C₂²×C₈₉	1	2	yes	complemented
661	#388	C₂²×C₈₉	1	2	yes	complemented
662	#386	C₂²×C₈₉	1	2	yes	complemented
663	#386	C₂²×C₈₉	1	2	yes	complemented
664	#386	C₂²×C₈₉	1	2	yes	complemented
665	#386	C₂²×C₈₉	1	2	yes	complemented
666	#386	C₂²×C₈₉	1	2	yes	complemented
667	#386	C₂²×C₈₉	1	2	yes	complemented
668	#386	C₂²×C₈₉	1	2	yes	complemented
669	#386	C₂²×C₈₉	1	2	yes	complemented
670	#385	C₂²×C₈₉	1	2	yes	complemented
671	#385	C₂²×C₈₉	1	2	yes	complemented
672	#384	C₂²×C₈₉	1	1	yes	characteristic, complemented
673	#382	C₂²×C₈₉	1	1	yes	characteristic, complemented
674	#380	C₂²×C₈₉	1	2	yes	complemented
675	#379	C₂²×C₈₉	1	2	yes	complemented
676	#379	C₂²×C₈₉	1	2	yes	complemented
677	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic, complemented
678	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic, complemented
679	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
680	C₂⁵	C₂³×C₈₉	1	2	yes	—
681	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
682	C₂²×D₄	—	2	8	no	—
683	C₂²×D₄	—	4	4	no	—
684	C₂²×D₄	—	4	4	no	—
685	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
686	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
687	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
688	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
689	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
690	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
691	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
692	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
693	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
694	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
695	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
696	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
697	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
698	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
699	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
700	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
701	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
702	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
703	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
704	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
705	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
706	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
707	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
708	#127	—	4	2	no	—
709	#126	—	2	8	no	—
710	#124	—	2	8	no	—
711	#124	—	4	2	no	—
712	#123	—	2	8	no	—
713	#123	—	2	8	no	—
714	#123	—	2	8	no	—
715	C₂²⋊Q₈	—	2	4	no	—
716	#121	—	2	8	no	—
717	#121	—	2	4	no	—
718	#121	—	2	4	no	—
719	#121	—	2	4	no	—
720	#121	—	2	8	no	—
721	#121	—	4	4	no	—
722	#121	—	4	4	no	—
723	#121	—	4	4	no	—
724	#121	—	4	4	no	—
725	#121	—	4	4	no	—
726	#120	—	2	8	no	—
727	#120	—	2	8	no	—
728	#120	—	2	8	no	—
729	#120	—	4	4	no	—
730	#120	—	4	4	no	—
731	C₄×D₄	—	2	8	no	—
732	C₂×C₄⋊C₄	—	4	2	no	—
733	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
734	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
735	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
743	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
744	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
745	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
746	C₂×C₂²⋊C₄	—	4	2	no	—
747	C₂×C₂²⋊C₄	—	4	2	no	—
748	C₂×C₂²⋊C₄	D₄×C₈₉	1	8	yes	complemented
749	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
759	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
767	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
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×C₄²	—	4	2	no	—
781	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
782	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
783	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
784	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
785	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
786	#95	C₂³×C₈₉	1	2	yes	—
787	#95	C₂³×C₈₉	1	2	yes	—
788	#95	C₂³×C₈₉	1	2	yes	—
789	#95	C₂³×C₈₉	1	2	yes	—
790	#95	C₂³×C₈₉	1	2	yes	—
791	#95	C₂³×C₈₉	1	2	yes	—
792	#95	C₂³×C₈₉	1	2	yes	—
793	#95	C₂³×C₈₉	1	2	yes	—
794	#95	C₂³×C₈₉	1	2	yes	—
795	#95	C₂³×C₈₉	1	2	yes	—
796	#95	C₂³×C₈₉	1	2	yes	—
797	#95	C₂³×C₈₉	1	2	yes	—
798	C₂⁴	—	2	2	no	—
799	C₂⁴	—	2	2	no	—
800	C₂⁴	—	2	4	no	—
801	C₂⁴	—	4	1	no	—
802	C₂⁴	—	4	1	no	—
803	C₂⁴	—	4	2	no	—
804	C₂⁴	—	4	2	no	—
805	C₂⁴	—	4	1	no	—
806	C₂⁴	—	4	1	no	—
807	C₂⁴	—	4	2	no	—
808	C₂⁴	—	4	2	no	—
809	C₂⁴	—	4	2	no	—
810	C₂⁴	—	4	2	no	—
811	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
812	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
813	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
814	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
815	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
816	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
817	C₂×Q₈	—	2	2	no	—
818	C₂×Q₈	—	4	1	no	—
819	C₂×Q₈	—	4	1	no	—
820	C₂×D₄	—	2	4	no	—
821	C₂×D₄	—	2	4	no	—
822	C₂×D₄	—	2	4	no	—
823	C₂×D₄	—	2	4	no	—
824	C₂×D₄	—	2	4	no	—
825	C₂×D₄	—	2	4	no	—
826	C₂×D₄	—	2	4	no	—
827	C₂×D₄	—	2	4	no	—
828	C₂×D₄	—	2	4	no	—
829	C₂×D₄	—	2	4	no	—
830	C₂×D₄	—	2	4	no	—
831	C₂×D₄	—	2	4	no	—
832	C₂×D₄	—	2	4	no	—
833	C₂×D₄	—	2	4	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	2	no	—
836	C₂×D₄	—	2	2	no	—
837	C₂×D₄	—	2	4	no	—
838	C₂×D₄	—	2	4	no	—
839	C₂×D₄	—	4	2	no	—
840	C₂×D₄	—	4	2	no	—
841	C₂×D₄	—	4	2	no	—
842	C₂×D₄	—	4	2	no	—
843	C₂×D₄	—	4	2	no	—
844	C₂×D₄	—	4	2	no	—
845	C₂×D₄	—	4	2	no	—
846	C₂×D₄	—	4	2	no	—
847	C₂×D₄	—	4	2	no	—
848	C₂×D₄	—	4	2	no	—
849	C₂×D₄	—	4	2	no	—
850	C₂×D₄	—	4	2	no	—
851	C₂×D₄	—	4	2	no	—
852	C₂×D₄	—	4	2	no	—
853	C₂×D₄	—	4	1	no	—
854	C₂×D₄	—	4	1	no	—
855	C₂×D₄	—	4	2	no	—
856	C₂×D₄	—	4	1	no	—
857	C₂×D₄	—	4	2	no	—
858	C₂×D₄	—	4	1	no	—
859	C₂×D₄	—	4	2	no	—
860	C₂×D₄	—	4	1	no	—
861	C₂×D₄	—	4	1	no	—
862	C₂×D₄	—	4	2	no	—
863	C₂×D₄	—	4	2	no	—
864	C₂×D₄	—	4	2	no	—
865	C₂×D₄	—	4	32	no	—
866	C₂²×C₄	—	2	4	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	2	no	—
872	C₂²×C₄	—	2	2	no	—
873	C₂²×C₄	—	2	4	no	—
874	C₂²×C₄	—	4	1	no	—
875	C₂²×C₄	—	4	1	no	—
876	C₂²×C₄	—	4	1	no	—
877	C₂²×C₄	—	4	2	no	—
878	C₂²×C₄	—	4	2	no	—
879	C₂²×C₄	—	4	1	no	—
880	C₂²×C₄	—	4	1	no	—
881	C₂²×C₄	—	4	1	no	—
882	C₂²×C₄	—	4	1	no	—
883	C₂²×C₄	—	4	1	no	—
884	C₂²×C₄	—	4	1	no	—
885	C₂²×C₄	—	4	2	no	—
886	C₂²×C₄	—	4	2	no	—
887	C₂²×C₄	—	4	1	no	—
888	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
889	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
890	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
891	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
892	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
893	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
894	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
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	2	yes	—
899	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
900	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
901	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
902	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
903	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
904	C₄⋊C₄	—	2	4	no	—
905	C₄⋊C₄	—	2	4	no	—
906	C₄⋊C₄	—	2	4	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	4	no	—
912	C₄⋊C₄	—	4	2	no	—
913	C₄⋊C₄	—	4	2	no	—
914	C₄⋊C₄	—	4	2	no	—
915	C₄⋊C₄	—	4	2	no	—
916	C₄⋊C₄	—	4	2	no	—
917	C₂²⋊C₄	—	2	4	no	—
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	4	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	4	no	—
929	C₂²⋊C₄	—	2	4	no	—
930	C₂²⋊C₄	—	4	2	no	—
931	C₂²⋊C₄	—	4	2	no	—
932	C₂²⋊C₄	—	4	2	no	—
933	C₂²⋊C₄	—	4	2	no	—
934	C₂²⋊C₄	—	4	2	no	—
935	C₂²⋊C₄	—	4	2	no	—
936	C₂²⋊C₄	—	4	2	no	—
937	C₂²⋊C₄	—	4	2	no	—
938	C₂²⋊C₄	—	4	2	no	—
939	C₂²⋊C₄	—	4	2	no	—
940	C₂²⋊C₄	—	4	2	no	—
941	C₂²⋊C₄	—	4	2	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	C₂×D₄×C₈₉	1	8	yes	—
947	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
948	C₄²	—	2	4	no	—
949	C₄²	—	2	2	no	—
950	C₄²	—	2	2	no	—
951	C₄²	—	4	1	no	—
952	C₄²	—	4	1	no	—
953	C₂³	—	2	1	no	—
954	C₂³	—	2	1	no	—
955	C₂³	—	2	1	no	—
956	C₂³	—	2	1	no	—
957	C₂³	—	2	2	no	—
958	C₂³	—	2	2	no	—
959	C₂³	—	2	2	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	2	2	no	—
962	C₂³	—	2	2	no	—
963	C₂³	—	2	8	no	—
964	C₂³	—	2	2	no	—
965	C₂³	—	2	2	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	2	no	—
972	C₂³	—	2	2	no	—
973	C₂³	—	2	2	no	—
974	C₂³	—	2	2	no	—
975	C₂³	—	2	2	no	—
976	C₂³	—	2	2	no	—
977	C₂³	—	2	2	no	—
978	C₂³	—	2	2	no	—
979	C₂³	—	2	2	no	—
980	C₂³	—	2	2	no	—
981	C₂³	—	2	2	no	—
982	C₂³	—	2	2	no	—
983	C₂³	—	2	2	no	—
984	C₂³	—	2	2	no	—
985	C₂³	—	4	4	no	—
986	C₂³	—	4	4	no	—
987	C₂³	—	4	8	no	—
988	C₂³	—	8	2	no	—
989	C₂³	—	8	2	no	—
990	C₂³	—	8	2	no	—
991	C₂³	—	8	2	no	—
992	C₂³	—	8	4	no	—
993	C₂³	—	8	4	no	—
994	C₂³	—	8	4	no	—
995	C₂³	—	8	4	no	—
996	C₂³	—	8	4	no	—
997	C₂³	—	8	4	no	—
998	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
999	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1000	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
1001	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
1002	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
1003	Q₈	—	8	2	no	—
1004	D₄	—	4	8	no	—
1005	D₄	—	4	8	no	—
1006	D₄	—	4	8	no	—
1007	D₄	—	4	8	no	—
1008	D₄	—	4	8	no	—
1009	D₄	—	8	4	no	—
1010	D₄	—	8	2	no	—
1011	D₄	—	8	2	no	—
1012	D₄	—	8	2	no	—
1013	D₄	—	8	4	no	—
1014	D₄	—	8	4	no	—
1015	D₄	—	8	4	no	—
1016	D₄	—	8	4	no	—
1017	D₄	—	8	4	no	—
1018	D₄	—	8	4	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	2	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	2	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	4	4	no	—
1057	C₂×C₄	—	4	4	no	—
1058	C₂×C₄	—	4	4	no	—
1059	C₂×C₄	—	4	4	no	—
1060	C₂×C₄	—	4	8	no	—
1061	C₂×C₄	—	8	4	no	—
1062	C₂×C₄	—	8	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
1065	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1066	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1067	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
1068	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
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	—	2	2	no	—
1075	C₂²	—	2	4	no	—
1076	C₂²	—	2	4	no	—
1077	C₂²	—	2	4	no	—
1078	C₂²	—	4	2	no	—
1079	C₂²	—	4	2	no	—
1080	C₂²	—	4	2	no	—
1081	C₂²	—	4	2	no	—
1082	C₂²	—	4	2	no	—
1083	C₂²	—	4	2	no	—
1084	C₂²	—	4	2	no	—
1085	C₂²	—	4	2	no	—
1086	C₂²	—	4	2	no	—
1087	C₂²	—	4	2	no	—
1088	C₂²	—	4	2	no	—
1089	C₂²	—	4	2	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	4	2	no	—
1092	C₂²	—	4	2	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	2	no	—
1095	C₂²	—	4	2	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	2	no	—
1098	C₂²	—	4	2	no	—
1099	C₂²	—	4	2	no	—
1100	C₂²	—	4	2	no	—
1101	C₂²	—	4	2	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	—	8	8	no	—
1104	C₂²	—	8	16	no	—
1105	C₂²	#535×C₈₉	1	4	yes	—
1106	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1107	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1108	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1109	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1110	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1111	C₂²	#585×C₈₉	1	1	yes	characteristic
1112	C₂²	#585×C₈₉	1	1	yes	characteristic
1113	C₄	—	2	4	no	—
1114	C₄	—	2	2	no	—
1115	C₄	—	2	2	no	—
1116	C₄	—	2	2	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	2	no	—
1120	C₄	—	4	2	no	—
1121	C₄	—	4	2	no	—
1122	C₄	—	4	2	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	2	no	—
1126	C₄	—	4	2	no	—
1127	C₂	—	2	4	no	—
1128	C₂	—	4	4	no	—
1129	C₂	—	8	2	no	—
1130	C₂	—	8	2	no	—
1131	C₂	—	8	2	no	—
1132	C₂	C₂×#535×C₈₉	1	1	yes	characteristic
1133	C₂	C₈₉×#3496	1	1	yes	characteristic
1134	C₂	C₈₉×#3496	1	1	yes	characteristic
1135	C₂	C₈₉×#3534	1	1	yes	characteristic
1136	C₂	C₈₉×#3537	1	1	yes	characteristic
1137	C₂	C₈₉×#3558	1	1	yes	characteristic
1138	C₂	C₈₉×#3560	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×#538×C₈₉	C₂	semidirect
2. C₂×#534×C₈₉	C₂	semidirect
3. C₈₉×#2856	C₂	semidirect
4. C₈₉×#2850	C₂	semidirect
5. C₈₉×#2718	C₂	semidirect
6. C₈₉×#2710	C₂	semidirect
7. C₈₉×#2706	C₂	semidirect
8. C₈₉×#2703	C₂	semidirect
9. C₈₉×#2685	C₂	semidirect
10. C₈₉×#2678	C₂	semidirect
11. C₈₉×#2670	C₂	semidirect
12. C₈₉×#2669	C₂	semidirect
13. C₈₉×#2656	C₂	semidirect
14. C₈₉×#2639	C₂	semidirect
15. C₈₉×#2543	C₂	semidirect
16. C₈₉×#2416	C₂	semidirect
17. C₈₉×#2410	C₂	semidirect
18. C₈₉×#2410	C₂	semidirect
19. C₂×#388×C₈₉	C₂	semidirect
23. C₂×#127×C₈₉	C₂²	semidirect
24. C₂×#126×C₈₉	C₂²	semidirect
25. C₂×#124×C₈₉	C₂²	semidirect
26. C₂×#124×C₈₉	C₂²	semidirect
29. C₂×#123×C₈₉	C₂²	semidirect
30. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
34. C₂×#121×C₈₉	C₂²	semidirect
35. C₂×#121×C₈₉	C₂²	semidirect
36. C₂×#121×C₈₉	C₂²	semidirect
37. C₂×#121×C₈₉	C₂²	semidirect
38. C₂×#121×C₈₉	C₂²	semidirect
39. C₂×#121×C₈₉	C₂²	semidirect
40. C₂×#121×C₈₉	C₂²	semidirect
44. C₂×#120×C₈₉	C₂²	semidirect
45. C₂×#120×C₈₉	C₂²	semidirect
46. C₂×C₄×D₄×C₈₉	C₂²	semidirect
47. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
51. C₂²×C₄²×C₈₉	C₂²	semidirect
52. #400×C₈₉	C₂²	semidirect
53. #399×C₈₉	C₂²	semidirect
54. #399×C₈₉	C₂²	semidirect
55. #398×C₈₉	C₂²	semidirect
56. #397×C₈₉	C₂²	semidirect
57. #397×C₈₉	C₂²	semidirect
58. #396×C₈₉	C₂²	semidirect
59. #396×C₈₉	C₂²	semidirect
64. #394×C₈₉	C₂²	semidirect
65. #394×C₈₉	C₂²	semidirect
66. #394×C₈₉	C₂²	semidirect
67. #394×C₈₉	C₂²	semidirect
68. #393×C₈₉	C₂²	semidirect
73. #392×C₈₉	C₂²	semidirect
74. #392×C₈₉	C₂²	semidirect
75. #392×C₈₉	C₂²	semidirect
76. #391×C₈₉	C₂²	semidirect
77. #390×C₈₉	C₂²	semidirect
78. #390×C₈₉	C₂²	semidirect
79. #390×C₈₉	C₂²	semidirect
80. #390×C₈₉	C₂²	semidirect
81. #390×C₈₉	C₂²	semidirect
82. #390×C₈₉	C₂²	semidirect
83. #389×C₈₉	C₂²	semidirect
84. #388×C₈₉	C₂²	semidirect
85. #388×C₈₉	C₂²	semidirect
86. #388×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. #386×C₈₉	C₂²	semidirect
93. #386×C₈₉	C₂²	semidirect
94. #386×C₈₉	C₂²	semidirect
95. #386×C₈₉	C₂²	semidirect
96. #386×C₈₉	C₂²	semidirect
97. #386×C₈₉	C₂²	semidirect
98. #386×C₈₉	C₂²	semidirect
99. #386×C₈₉	C₂²	semidirect
100. #385×C₈₉	C₂²	semidirect
101. #385×C₈₉	C₂²	semidirect
102. #384×C₈₉	C₂²	semidirect
103. #382×C₈₉	C₂²	semidirect
104. #380×C₈₉	C₂²	semidirect
105. #379×C₈₉	C₂²	semidirect
106. #379×C₈₉	C₂²	semidirect
107. C₂×#95×C₈₉	C₂²	semidirect
108. C₂×#95×C₈₉	C₂²	semidirect
178. C₂×C₂²⋊C₄×C₈₉	D₄	semidirect
557. #36739	C₈₉	direct (N × H)
570. C₂×#538	C₂×C₈₉	semidirect
571. C₂×#534	C₂×C₈₉	semidirect
572. #2856	C₂×C₈₉	semidirect
573. #2850	C₂×C₈₉	semidirect
574. #2718	C₂×C₈₉	semidirect
575. #2710	C₂×C₈₉	semidirect
576. #2706	C₂×C₈₉	semidirect
577. #2703	C₂×C₈₉	semidirect
578. #2685	C₂×C₈₉	semidirect
579. #2678	C₂×C₈₉	semidirect
580. #2670	C₂×C₈₉	semidirect
581. #2669	C₂×C₈₉	semidirect
582. #2656	C₂×C₈₉	semidirect
583. #2639	C₂×C₈₉	semidirect
584. #2543	C₂×C₈₉	semidirect
585. #2416	C₂×C₈₉	semidirect
586. #2410	C₂×C₈₉	semidirect
587. #2410	C₂×C₈₉	semidirect
588. C₂×#388	C₂×C₈₉	semidirect
589. C₈₉	#36739	direct (N × H)
593. C₂×#127	C₂²×C₈₉	semidirect
594. C₂×#126	C₂²×C₈₉	semidirect
595. C₂×#124	C₂²×C₈₉	semidirect
596. C₂×#124	C₂²×C₈₉	semidirect
599. C₂×#123	C₂²×C₈₉	semidirect
600. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
604. C₂×#121	C₂²×C₈₉	semidirect
605. C₂×#121	C₂²×C₈₉	semidirect
606. C₂×#121	C₂²×C₈₉	semidirect
607. C₂×#121	C₂²×C₈₉	semidirect
608. C₂×#121	C₂²×C₈₉	semidirect
609. C₂×#121	C₂²×C₈₉	semidirect
610. C₂×#121	C₂²×C₈₉	semidirect
614. C₂×#120	C₂²×C₈₉	semidirect
615. C₂×#120	C₂²×C₈₉	semidirect
616. C₂×C₄×D₄	C₂²×C₈₉	semidirect
617. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
621. C₂²×C₄²	C₂²×C₈₉	semidirect
622. #400	C₂²×C₈₉	semidirect
623. #399	C₂²×C₈₉	semidirect
624. #399	C₂²×C₈₉	semidirect
625. #398	C₂²×C₈₉	semidirect
626. #397	C₂²×C₈₉	semidirect
627. #397	C₂²×C₈₉	semidirect
628. #396	C₂²×C₈₉	semidirect
629. #396	C₂²×C₈₉	semidirect
634. #394	C₂²×C₈₉	semidirect
635. #394	C₂²×C₈₉	semidirect
636. #394	C₂²×C₈₉	semidirect
637. #394	C₂²×C₈₉	semidirect
638. #393	C₂²×C₈₉	semidirect
643. #392	C₂²×C₈₉	semidirect
644. #392	C₂²×C₈₉	semidirect
645. #392	C₂²×C₈₉	semidirect
646. #391	C₂²×C₈₉	semidirect
647. #390	C₂²×C₈₉	semidirect
648. #390	C₂²×C₈₉	semidirect
649. #390	C₂²×C₈₉	semidirect
650. #390	C₂²×C₈₉	semidirect
651. #390	C₂²×C₈₉	semidirect
652. #390	C₂²×C₈₉	semidirect
653. #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. #388	C₂²×C₈₉	semidirect
661. #388	C₂²×C₈₉	semidirect
662. #386	C₂²×C₈₉	semidirect
663. #386	C₂²×C₈₉	semidirect
664. #386	C₂²×C₈₉	semidirect
665. #386	C₂²×C₈₉	semidirect
666. #386	C₂²×C₈₉	semidirect
667. #386	C₂²×C₈₉	semidirect
668. #386	C₂²×C₈₉	semidirect
669. #386	C₂²×C₈₉	semidirect
670. #385	C₂²×C₈₉	semidirect
671. #385	C₂²×C₈₉	semidirect
672. #384	C₂²×C₈₉	semidirect
673. #382	C₂²×C₈₉	semidirect
674. #380	C₂²×C₈₉	semidirect
675. #379	C₂²×C₈₉	semidirect
676. #379	C₂²×C₈₉	semidirect
677. C₂×#95	C₂²×C₈₉	semidirect
678. C₂×#95	C₂²×C₈₉	semidirect
748. C₂×C₂²⋊C₄	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×#538×C₈₉	2
C₂×#534×C₈₉	2
C₈₉×#2856	2
C₈₉×#2850	2
C₈₉×#2718	2
C₈₉×#2710	2
C₈₉×#2706	2
C₈₉×#2703	2
C₈₉×#2685	2
C₈₉×#2678	2
C₈₉×#2670	2
C₈₉×#2669	2
C₈₉×#2656	2
C₈₉×#2639	2
C₈₉×#2543	2
C₈₉×#2416	2
C₈₉×#2410	2
C₂×#388×C₈₉	2
#36739	89

Subgroups — C89×#36739 #36414587

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#36739 #36414587