Subgroups — C₈₉×#35500 #36413348

Order 22784.

1608 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2610	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2606	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2599	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2595	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2592	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2577	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2554	C₂	1	2	yes	maximal
8	C₈₉×#2532	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2531	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2529	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2520	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2513	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2469	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2458	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2337	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2335	C₂	1	2	yes	maximal, complemented
17	C₄×#126×C₈₉	C₂	1	2	yes	maximal, complemented
18	C₈₉×#2298	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2276	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#126×C₈₉	C₂²	1	2	yes	—
21	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#123×C₈₉	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
25	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
26	#400×C₈₉	C₂²	1	2	yes	—
27	#400×C₈₉	C₂²	1	2	yes	—
28	#398×C₈₉	C₂²	1	2	yes	—
29	#398×C₈₉	C₂²	1	1	yes	characteristic
30	#398×C₈₉	C₂²	1	2	yes	—
31	#398×C₈₉	C₂²	1	2	yes	—
32	#397×C₈₉	C₂²	1	2	yes	—
33	#397×C₈₉	C₂²	1	2	yes	—
34	#397×C₈₉	C₂²	1	2	yes	—
35	#397×C₈₉	C₂²	1	1	yes	characteristic
36	#397×C₈₉	C₂²	1	2	yes	—
37	#396×C₈₉	C₂²	1	2	yes	—
38	#395×C₈₉	C₂²	1	1	yes	characteristic
39	#395×C₈₉	C₂²	1	1	yes	characteristic
40	#394×C₈₉	C₂²	1	2	yes	—
41	#394×C₈₉	C₂²	1	1	yes	characteristic
42	#393×C₈₉	C₂²	1	2	yes	—
43	#393×C₈₉	C₂²	1	1	yes	characteristic
44	#393×C₈₉	C₂²	1	1	yes	characteristic
45	#392×C₈₉	C₂²	1	1	yes	characteristic
46	#391×C₈₉	C₂²	1	2	yes	—
47	#391×C₈₉	C₂²	1	2	yes	—
48	#390×C₈₉	C₂²	1	2	yes	—
49	#390×C₈₉	C₂²	1	2	yes	—
50	#390×C₈₉	C₂²	1	2	yes	—
51	#390×C₈₉	C₂²	1	2	yes	—
52	#389×C₈₉	C₂²	1	2	yes	—
53	#389×C₈₉	C₂²	1	2	yes	—
54	#388×C₈₉	C₂²	1	2	yes	—
55	#388×C₈₉	C₂²	1	2	yes	—
56	#388×C₈₉	C₂²	1	2	yes	—
57	#388×C₈₉	C₂²	1	2	yes	—
58	#388×C₈₉	C₂²	1	2	yes	—
59	#388×C₈₉	C₂²	1	2	yes	—
60	#388×C₈₉	C₂²	1	2	yes	—
61	#388×C₈₉	C₂²	1	2	yes	—
62	#388×C₈₉	C₂²	1	2	yes	—
63	#388×C₈₉	C₂²	1	2	yes	—
64	#388×C₈₉	C₂²	1	2	yes	—
65	#388×C₈₉	C₂²	1	2	yes	—
66	#388×C₈₉	C₂²	1	2	yes	—
67	#388×C₈₉	C₂²	1	2	yes	—
68	#388×C₈₉	C₂²	1	2	yes	—
69	#388×C₈₉	C₂²	1	2	yes	—
70	#388×C₈₉	C₂²	1	2	yes	—
71	#387×C₈₉	C₂²	1	2	yes	—
72	#387×C₈₉	C₂²	1	2	yes	—
73	#387×C₈₉	C₂²	1	2	yes	—
74	#387×C₈₉	C₂²	1	2	yes	—
75	#387×C₈₉	C₂²	1	2	yes	—
76	#387×C₈₉	C₂²	1	2	yes	—
77	#387×C₈₉	C₂²	1	2	yes	—
78	#387×C₈₉	C₂²	1	2	yes	—
79	#387×C₈₉	C₂²	1	2	yes	—
80	#387×C₈₉	C₂²	1	2	yes	—
81	#387×C₈₉	C₂²	1	2	yes	—
82	#386×C₈₉	C₂²	1	2	yes	—
83	#386×C₈₉	C₂²	1	2	yes	—
84	#385×C₈₉	C₂²	1	2	yes	—
85	#385×C₈₉	C₂²	1	2	yes	—
86	#383×C₈₉	C₂²	1	2	yes	—
87	#383×C₈₉	C₂²	1	1	yes	characteristic
88	#382×C₈₉	C₂²	1	2	yes	—
89	#380×C₈₉	C₂²	1	2	yes	—
90	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
91	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
92	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
103	#376×C₈₉	C₂²	1	1	yes	characteristic
104	#376×C₈₉	C₂²	1	1	yes	characteristic
105	#376×C₈₉	C₂²	1	2	yes	—
106	C₄³×C₈₉	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
111	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
112	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
113	#126×C₈₉	—	2	8	no	—
114	#124×C₈₉	—	2	4	no	—
115	#123×C₈₉	—	2	8	no	—
116	C₄×Q₈×C₈₉	—	2	8	no	—
117	C₄×Q₈×C₈₉	—	2	4	no	—
118	#117×C₈₉	—	2	4	no	—
119	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
156	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
165	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
168	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
169	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
170	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
171	#95×C₈₉	C₂³	1	1	yes	characteristic
172	#95×C₈₉	C₂³	1	2	yes	—
173	#95×C₈₉	C₂³	1	2	yes	—
174	#95×C₈₉	C₂³	1	2	yes	—
175	#95×C₈₉	C₂³	1	1	yes	characteristic
176	#95×C₈₉	C₂³	1	2	yes	—
177	#95×C₈₉	C₂³	1	2	yes	—
178	#95×C₈₉	C₂³	1	2	yes	—
179	#95×C₈₉	C₂³	1	2	yes	—
180	#95×C₈₉	C₂³	1	2	yes	—
181	#95×C₈₉	C₂³	1	2	yes	—
182	#95×C₈₉	C₂³	1	2	yes	—
183	#95×C₈₉	C₂³	1	2	yes	—
184	#95×C₈₉	C₂³	1	2	yes	—
185	#95×C₈₉	C₂³	1	2	yes	—
186	#95×C₈₉	C₂³	1	2	yes	—
187	#95×C₈₉	C₂³	1	2	yes	—
188	#95×C₈₉	C₂³	1	2	yes	—
189	#95×C₈₉	C₂³	1	2	yes	—
190	#95×C₈₉	C₂³	1	2	yes	—
191	#95×C₈₉	C₂³	1	2	yes	—
192	#95×C₈₉	C₂³	1	2	yes	—
193	#95×C₈₉	C₂³	1	2	yes	—
194	#95×C₈₉	C₂³	1	1	yes	characteristic
195	#95×C₈₉	C₂³	1	2	yes	—
196	#95×C₈₉	C₂³	1	1	yes	characteristic
197	#95×C₈₉	C₂³	1	2	yes	—
198	#95×C₈₉	C₂³	1	2	yes	—
199	#95×C₈₉	C₂³	1	2	yes	—
200	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
201	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
202	C₂×Q₈×C₈₉	—	2	4	no	—
203	C₂×Q₈×C₈₉	—	2	2	no	—
204	C₂×Q₈×C₈₉	—	2	2	no	—
205	C₂×Q₈×C₈₉	—	4	2	no	—
206	C₂×D₄×C₈₉	—	2	4	no	—
207	C₂×D₄×C₈₉	—	2	2	no	—
208	C₂×D₄×C₈₉	—	4	2	no	—
209	C₂×D₄×C₈₉	—	4	2	no	—
210	C₂×D₄×C₈₉	—	4	2	no	—
211	C₂²×C₄×C₈₉	—	2	2	no	—
212	C₂²×C₄×C₈₉	—	2	4	no	—
213	C₂²×C₄×C₈₉	—	4	1	no	—
214	C₂²×C₄×C₈₉	—	4	1	no	—
215	C₂²×C₄×C₈₉	—	4	2	no	—
216	C₂²×C₄×C₈₉	—	4	2	no	—
217	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
234	C₄⋊C₄×C₈₉	—	2	2	no	—
235	C₄⋊C₄×C₈₉	—	2	2	no	—
236	C₄⋊C₄×C₈₉	—	2	4	no	—
237	C₄⋊C₄×C₈₉	—	2	4	no	—
238	C₄⋊C₄×C₈₉	—	2	4	no	—
239	C₄⋊C₄×C₈₉	—	2	2	no	—
240	C₄⋊C₄×C₈₉	—	2	4	no	—
241	C₄⋊C₄×C₈₉	—	2	4	no	—
242	C₄⋊C₄×C₈₉	—	2	4	no	—
243	C₄⋊C₄×C₈₉	—	4	2	no	—
244	C₄⋊C₄×C₈₉	—	4	2	no	—
245	C₄⋊C₄×C₈₉	—	4	2	no	—
246	C₄⋊C₄×C₈₉	—	4	2	no	—
247	C₄⋊C₄×C₈₉	—	4	2	no	—
248	C₄⋊C₄×C₈₉	—	4	2	no	—
249	C₄⋊C₄×C₈₉	—	4	2	no	—
250	C₄⋊C₄×C₈₉	—	4	2	no	—
251	C₄⋊C₄×C₈₉	#41	1	8	yes	—
252	C₂²⋊C₄×C₈₉	—	2	2	no	—
253	C₂²⋊C₄×C₈₉	—	2	2	no	—
254	C₂²⋊C₄×C₈₉	—	2	4	no	—
255	C₂²⋊C₄×C₈₉	—	2	4	no	—
256	C₂²⋊C₄×C₈₉	—	2	4	no	—
257	C₂²⋊C₄×C₈₉	—	2	4	no	—
258	C₂²⋊C₄×C₈₉	—	2	4	no	—
259	C₂²⋊C₄×C₈₉	—	2	4	no	—
260	C₂²⋊C₄×C₈₉	—	2	4	no	—
261	C₂²⋊C₄×C₈₉	—	2	4	no	—
262	C₂²⋊C₄×C₈₉	—	4	2	no	—
263	C₂²⋊C₄×C₈₉	—	4	2	no	—
264	C₂²⋊C₄×C₈₉	—	4	2	no	—
265	C₂²⋊C₄×C₈₉	—	4	2	no	—
266	C₂²⋊C₄×C₈₉	—	4	2	no	—
267	C₂²⋊C₄×C₈₉	—	4	2	no	—
268	C₂²⋊C₄×C₈₉	—	4	2	no	—
269	C₂²⋊C₄×C₈₉	—	4	2	no	—
270	C₂²⋊C₄×C₈₉	—	4	2	no	—
271	C₄²×C₈₉	—	2	2	no	—
272	C₄²×C₈₉	—	2	4	no	—
273	C₄²×C₈₉	—	2	4	no	—
274	C₄²×C₈₉	—	2	4	no	—
275	C₄²×C₈₉	—	2	4	no	—
276	C₄²×C₈₉	—	2	4	no	—
277	C₄²×C₈₉	—	4	1	no	—
278	C₄²×C₈₉	—	4	2	no	—
279	C₄²×C₈₉	—	4	1	no	—
280	C₄²×C₈₉	—	4	1	no	—
281	C₄²×C₈₉	—	4	2	no	—
282	C₄²×C₈₉	—	4	1	no	—
283	C₄²×C₈₉	—	4	2	no	—
284	C₄²×C₈₉	—	4	2	no	—
285	C₄²×C₈₉	#41	1	4	yes	—
286	C₂³×C₈₉	—	2	2	no	—
287	C₂³×C₈₉	—	2	1	no	—
288	C₂³×C₈₉	—	2	2	no	—
289	C₂³×C₈₉	—	2	2	no	—
290	C₂³×C₈₉	—	2	2	no	—
291	C₂³×C₈₉	—	2	2	no	—
292	C₂³×C₈₉	—	2	1	no	—
293	C₂³×C₈₉	—	2	2	no	—
294	C₂³×C₈₉	—	2	2	no	—
295	C₂³×C₈₉	—	2	2	no	—
296	C₂³×C₈₉	—	2	1	no	—
297	C₂³×C₈₉	—	2	2	no	—
298	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
299	Q₈×C₈₉	—	2	8	no	—
300	Q₈×C₈₉	—	8	2	no	—
301	D₄×C₈₉	—	8	2	no	—
302	D₄×C₈₉	—	8	4	no	—
303	C₂×C₄×C₈₉	—	2	2	no	—
304	C₂×C₄×C₈₉	—	2	2	no	—
305	C₂×C₄×C₈₉	—	2	2	no	—
306	C₂×C₄×C₈₉	—	2	1	no	—
307	C₂×C₄×C₈₉	—	2	1	no	—
308	C₂×C₄×C₈₉	—	2	2	no	—
309	C₂×C₄×C₈₉	—	2	2	no	—
310	C₂×C₄×C₈₉	—	2	2	no	—
311	C₂×C₄×C₈₉	—	2	2	no	—
312	C₂×C₄×C₈₉	—	2	2	no	—
313	C₂×C₄×C₈₉	—	2	2	no	—
314	C₂×C₄×C₈₉	—	2	1	no	—
315	C₂×C₄×C₈₉	—	2	2	no	—
316	C₂×C₄×C₈₉	—	2	1	no	—
317	C₂×C₄×C₈₉	—	2	2	no	—
318	C₂×C₄×C₈₉	—	2	2	no	—
319	C₂×C₄×C₈₉	—	2	2	no	—
320	C₂×C₄×C₈₉	—	2	2	no	—
321	C₂×C₄×C₈₉	—	2	2	no	—
322	C₂×C₄×C₈₉	—	2	2	no	—
323	C₂×C₄×C₈₉	—	2	2	no	—
324	C₂×C₄×C₈₉	—	2	1	no	—
325	C₂×C₄×C₈₉	—	2	2	no	—
326	C₂×C₄×C₈₉	—	2	2	no	—
327	C₂×C₄×C₈₉	—	2	2	no	—
328	C₂×C₄×C₈₉	—	2	2	no	—
329	C₂×C₄×C₈₉	—	2	2	no	—
330	C₂×C₄×C₈₉	—	2	2	no	—
331	C₂×C₄×C₈₉	—	2	2	no	—
332	C₂×C₄×C₈₉	—	2	2	no	—
333	C₂×C₄×C₈₉	—	2	2	no	—
334	C₂×C₄×C₈₉	—	2	2	no	—
335	C₂×C₄×C₈₉	—	2	2	no	—
336	C₂×C₄×C₈₉	—	2	1	no	—
337	C₂×C₄×C₈₉	—	2	2	no	—
338	C₂×C₄×C₈₉	—	2	2	no	—
339	C₂×C₄×C₈₉	—	2	2	no	—
340	C₂×C₄×C₈₉	—	2	2	no	—
341	C₂×C₄×C₈₉	—	2	1	no	—
342	C₂×C₄×C₈₉	—	2	2	no	—
343	C₂×C₄×C₈₉	—	2	2	no	—
344	C₂×C₄×C₈₉	—	4	4	no	—
345	C₂×C₄×C₈₉	—	8	4	no	—
346	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
347	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
348	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
349	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
350	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
351	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
352	C₂²×C₈₉	—	4	2	no	—
353	C₂²×C₈₉	—	4	1	no	—
354	C₂²×C₈₉	—	4	1	no	—
355	C₂²×C₈₉	—	4	2	no	—
356	C₂²×C₈₉	—	4	2	no	—
357	C₂²×C₈₉	—	4	1	no	—
358	C₂²×C₈₉	—	4	2	no	—
359	C₂²×C₈₉	—	4	2	no	—
360	C₂²×C₈₉	—	4	2	no	—
361	C₂²×C₈₉	—	4	2	no	—
362	C₂²×C₈₉	—	4	2	no	—
363	C₂²×C₈₉	—	4	2	no	—
364	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
365	C₂²×C₈₉	C₂²×#41	1	2	yes	—
366	C₂²×C₈₉	#585	1	1	yes	characteristic
367	C₂²×C₈₉	#585	1	1	yes	characteristic
368	C₂²×C₈₉	#585	1	2	yes	—
369	C₄×C₈₉	—	2	4	no	—
370	C₄×C₈₉	—	2	2	no	—
371	C₄×C₈₉	—	2	2	no	—
372	C₄×C₈₉	—	2	2	no	—
373	C₄×C₈₉	—	2	4	no	—
374	C₄×C₈₉	—	2	4	no	—
375	C₄×C₈₉	—	4	1	no	—
376	C₄×C₈₉	—	4	2	no	—
377	C₄×C₈₉	—	4	1	no	—
378	C₄×C₈₉	—	4	1	no	—
379	C₄×C₈₉	—	4	2	no	—
380	C₄×C₈₉	—	4	2	no	—
381	C₄×C₈₉	—	4	2	no	—
382	C₄×C₈₉	—	4	2	no	—
383	C₄×C₈₉	—	4	2	no	—
384	C₄×C₈₉	—	4	2	no	—
385	C₄×C₈₉	—	4	2	no	—
386	#35500	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
387	C₂×C₈₉	—	8	1	no	—
388	C₂×C₈₉	—	8	2	no	—
389	C₂×C₈₉	#3444	1	1	yes	characteristic
390	C₂×C₈₉	#3493	1	1	yes	characteristic
391	C₂×C₈₉	#3510	1	1	yes	characteristic
392	C₂×C₈₉	#3521	1	2	yes	—
393	C₂×C₈₉	#3524	1	2	yes	—
394	#2610	C₂×C₈₉	1	1	yes	characteristic
395	#2606	C₂×C₈₉	1	1	yes	characteristic, complemented
396	#2599	C₂×C₈₉	1	1	yes	characteristic, complemented
397	#2595	C₂×C₈₉	1	2	yes	complemented
398	#2592	C₂×C₈₉	1	1	yes	characteristic, complemented
399	#2577	C₂×C₈₉	1	2	yes	complemented
400	#2554	C₂×C₈₉	1	2	yes	—
401	#2532	C₂×C₈₉	1	2	yes	complemented
402	#2531	C₂×C₈₉	1	2	yes	complemented
403	#2529	C₂×C₈₉	1	2	yes	complemented
404	#2520	C₂×C₈₉	1	2	yes	complemented
405	#2513	C₂×C₈₉	1	2	yes	complemented
406	#2469	C₂×C₈₉	1	2	yes	complemented
407	#2458	C₂×C₈₉	1	2	yes	complemented
408	#2337	C₂×C₈₉	1	1	yes	characteristic, complemented
409	#2335	C₂×C₈₉	1	2	yes	complemented
410	C₄×#126	C₂×C₈₉	1	2	yes	complemented
411	#2298	C₂×C₈₉	1	1	yes	characteristic, complemented
412	#2276	C₂×C₈₉	1	1	yes	characteristic, complemented
413	C₈₉	#35500	1	1	yes	characteristic, direct product factor, Sylow
414	C₂×#126	C₂²×C₈₉	1	2	yes	—
415	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
416	C₂×#123	C₂²×C₈₉	1	2	yes	—
417	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
418	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
419	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
420	#400	C₂²×C₈₉	1	2	yes	—
421	#400	C₂²×C₈₉	1	2	yes	—
422	#398	C₂²×C₈₉	1	1	yes	characteristic
423	#398	C₂²×C₈₉	1	2	yes	—
424	#398	C₂²×C₈₉	1	2	yes	—
425	#398	C₂²×C₈₉	1	2	yes	—
426	#397	C₂²×C₈₉	1	2	yes	—
427	#397	C₂²×C₈₉	1	2	yes	—
428	#397	C₂²×C₈₉	1	2	yes	—
429	#397	C₂²×C₈₉	1	1	yes	characteristic
430	#397	C₂²×C₈₉	1	2	yes	—
431	#396	C₂²×C₈₉	1	2	yes	—
432	#395	C₂²×C₈₉	1	1	yes	characteristic
433	#395	C₂²×C₈₉	1	1	yes	characteristic
434	#394	C₂²×C₈₉	1	2	yes	—
435	#394	C₂²×C₈₉	1	1	yes	characteristic
436	#393	C₂²×C₈₉	1	2	yes	—
437	#393	C₂²×C₈₉	1	1	yes	characteristic
438	#393	C₂²×C₈₉	1	1	yes	characteristic
439	#392	C₂²×C₈₉	1	1	yes	characteristic
440	#391	C₂²×C₈₉	1	2	yes	—
441	#391	C₂²×C₈₉	1	2	yes	—
442	#390	C₂²×C₈₉	1	2	yes	—
443	#390	C₂²×C₈₉	1	2	yes	—
444	#390	C₂²×C₈₉	1	2	yes	—
445	#390	C₂²×C₈₉	1	2	yes	—
446	#389	C₂²×C₈₉	1	2	yes	—
447	#389	C₂²×C₈₉	1	2	yes	—
448	#388	C₂²×C₈₉	1	2	yes	—
449	#388	C₂²×C₈₉	1	2	yes	—
450	#388	C₂²×C₈₉	1	2	yes	—
451	#388	C₂²×C₈₉	1	2	yes	—
452	#388	C₂²×C₈₉	1	2	yes	—
453	#388	C₂²×C₈₉	1	2	yes	—
454	#388	C₂²×C₈₉	1	2	yes	—
455	#388	C₂²×C₈₉	1	2	yes	—
456	#388	C₂²×C₈₉	1	2	yes	—
457	#388	C₂²×C₈₉	1	2	yes	—
458	#388	C₂²×C₈₉	1	2	yes	—
459	#388	C₂²×C₈₉	1	2	yes	—
460	#388	C₂²×C₈₉	1	2	yes	—
461	#388	C₂²×C₈₉	1	2	yes	—
462	#388	C₂²×C₈₉	1	2	yes	—
463	#388	C₂²×C₈₉	1	2	yes	—
464	#388	C₂²×C₈₉	1	2	yes	—
465	#387	C₂²×C₈₉	1	2	yes	—
466	#387	C₂²×C₈₉	1	2	yes	—
467	#387	C₂²×C₈₉	1	2	yes	—
468	#387	C₂²×C₈₉	1	2	yes	—
469	#387	C₂²×C₈₉	1	2	yes	—
470	#387	C₂²×C₈₉	1	2	yes	—
471	#387	C₂²×C₈₉	1	2	yes	—
472	#387	C₂²×C₈₉	1	2	yes	—
473	#387	C₂²×C₈₉	1	2	yes	—
474	#387	C₂²×C₈₉	1	2	yes	—
475	#387	C₂²×C₈₉	1	2	yes	—
476	#386	C₂²×C₈₉	1	2	yes	—
477	#386	C₂²×C₈₉	1	2	yes	—
478	#385	C₂²×C₈₉	1	2	yes	—
479	#385	C₂²×C₈₉	1	2	yes	—
480	#383	C₂²×C₈₉	1	2	yes	—
481	#383	C₂²×C₈₉	1	1	yes	characteristic
482	#382	C₂²×C₈₉	1	2	yes	—
483	#380	C₂²×C₈₉	1	2	yes	—
484	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
485	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
486	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
487	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
488	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
489	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
490	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
491	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
492	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
493	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
494	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
495	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
496	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
497	#376	C₂²×C₈₉	1	1	yes	characteristic
498	#376	C₂²×C₈₉	1	1	yes	characteristic
499	#376	C₂²×C₈₉	1	2	yes	—
500	C₄³	C₂²×C₈₉	1	1	yes	characteristic
501	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
502	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
503	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
504	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
505	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
506	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
507	#126	—	2	8	no	—
508	#124	—	2	4	no	—
509	#123	—	2	8	no	—
510	C₄×Q₈	—	2	8	no	—
511	C₄×Q₈	—	2	4	no	—
512	#117	—	2	4	no	—
513	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
532	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
533	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
550	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
551	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
552	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
553	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
554	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
555	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
556	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
557	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
558	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
559	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
561	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
562	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
563	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
564	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
565	#95	C₂³×C₈₉	1	1	yes	characteristic
566	#95	C₂³×C₈₉	1	2	yes	—
567	#95	C₂³×C₈₉	1	2	yes	—
568	#95	C₂³×C₈₉	1	2	yes	—
569	#95	C₂³×C₈₉	1	1	yes	characteristic
570	#95	C₂³×C₈₉	1	2	yes	—
571	#95	C₂³×C₈₉	1	2	yes	—
572	#95	C₂³×C₈₉	1	2	yes	—
573	#95	C₂³×C₈₉	1	2	yes	—
574	#95	C₂³×C₈₉	1	2	yes	—
575	#95	C₂³×C₈₉	1	2	yes	—
576	#95	C₂³×C₈₉	1	2	yes	—
577	#95	C₂³×C₈₉	1	2	yes	—
578	#95	C₂³×C₈₉	1	2	yes	—
579	#95	C₂³×C₈₉	1	2	yes	—
580	#95	C₂³×C₈₉	1	2	yes	—
581	#95	C₂³×C₈₉	1	2	yes	—
582	#95	C₂³×C₈₉	1	2	yes	—
583	#95	C₂³×C₈₉	1	2	yes	—
584	#95	C₂³×C₈₉	1	2	yes	—
585	#95	C₂³×C₈₉	1	2	yes	—
586	#95	C₂³×C₈₉	1	2	yes	—
587	#95	C₂³×C₈₉	1	2	yes	—
588	#95	C₂³×C₈₉	1	1	yes	characteristic
589	#95	C₂³×C₈₉	1	2	yes	—
590	#95	C₂³×C₈₉	1	1	yes	characteristic
591	#95	C₂³×C₈₉	1	2	yes	—
592	#95	C₂³×C₈₉	1	2	yes	—
593	#95	C₂³×C₈₉	1	2	yes	—
594	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
595	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
596	C₂×Q₈	—	2	4	no	—
597	C₂×Q₈	—	2	2	no	—
598	C₂×Q₈	—	2	2	no	—
599	C₂×Q₈	—	4	2	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	4	2	no	—
603	C₂×D₄	—	4	2	no	—
604	C₂×D₄	—	4	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	4	1	no	—
608	C₂²×C₄	—	4	1	no	—
609	C₂²×C₄	—	4	2	no	—
610	C₂²×C₄	—	4	2	no	—
611	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
623	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
625	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	4	2	no	—
638	C₄⋊C₄	—	4	2	no	—
639	C₄⋊C₄	—	4	2	no	—
640	C₄⋊C₄	—	4	2	no	—
641	C₄⋊C₄	—	4	2	no	—
642	C₄⋊C₄	—	4	2	no	—
643	C₄⋊C₄	—	4	2	no	—
644	C₄⋊C₄	—	4	2	no	—
645	C₄⋊C₄	#41×C₈₉	1	8	yes	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	4	2	no	—
657	C₂²⋊C₄	—	4	2	no	—
658	C₂²⋊C₄	—	4	2	no	—
659	C₂²⋊C₄	—	4	2	no	—
660	C₂²⋊C₄	—	4	2	no	—
661	C₂²⋊C₄	—	4	2	no	—
662	C₂²⋊C₄	—	4	2	no	—
663	C₂²⋊C₄	—	4	2	no	—
664	C₂²⋊C₄	—	4	2	no	—
665	C₄²	—	2	2	no	—
666	C₄²	—	2	4	no	—
667	C₄²	—	2	4	no	—
668	C₄²	—	2	4	no	—
669	C₄²	—	2	4	no	—
670	C₄²	—	2	4	no	—
671	C₄²	—	4	1	no	—
672	C₄²	—	4	2	no	—
673	C₄²	—	4	1	no	—
674	C₄²	—	4	1	no	—
675	C₄²	—	4	2	no	—
676	C₄²	—	4	1	no	—
677	C₄²	—	4	2	no	—
678	C₄²	—	4	2	no	—
679	C₄²	#41×C₈₉	1	4	yes	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	1	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	1	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	1	no	—
691	C₂³	—	2	2	no	—
692	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
693	Q₈	—	2	8	no	—
694	Q₈	—	8	2	no	—
695	D₄	—	8	2	no	—
696	D₄	—	8	4	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	4	4	no	—
739	C₂×C₄	—	8	4	no	—
740	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
741	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
742	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
743	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
744	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
745	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	1	no	—
748	C₂²	—	4	1	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	1	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
759	C₂²	C₂²×#41×C₈₉	1	2	yes	—
760	C₂²	#585×C₈₉	1	1	yes	characteristic
761	C₂²	#585×C₈₉	1	1	yes	characteristic
762	C₂²	#585×C₈₉	1	2	yes	—
763	C₄	—	2	4	no	—
764	C₄	—	2	2	no	—
765	C₄	—	2	2	no	—
766	C₄	—	2	2	no	—
767	C₄	—	2	4	no	—
768	C₄	—	2	4	no	—
769	C₄	—	4	1	no	—
770	C₄	—	4	1	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	1	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	2	no	—
779	C₄	—	4	2	no	—
780	C₂	—	8	1	no	—
781	C₂	—	8	2	no	—
782	C₂	C₈₉×#3444	1	1	yes	characteristic
783	C₂	C₈₉×#3493	1	1	yes	characteristic
784	C₂	C₈₉×#3510	1	1	yes	characteristic
785	C₂	C₈₉×#3521	1	2	yes	—
786	C₂	C₈₉×#3524	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	#392×C₈₉	C₂²
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
2. C₈₉×#2606	C₂	semidirect
3. C₈₉×#2599	C₂	semidirect
4. C₈₉×#2595	C₂	semidirect
5. C₈₉×#2592	C₂	semidirect
6. C₈₉×#2577	C₂	semidirect
8. C₈₉×#2532	C₂	semidirect
9. C₈₉×#2531	C₂	semidirect
10. C₈₉×#2529	C₂	semidirect
11. C₈₉×#2520	C₂	semidirect
12. C₈₉×#2513	C₂	semidirect
13. C₈₉×#2469	C₂	semidirect
14. C₈₉×#2458	C₂	semidirect
15. C₈₉×#2337	C₂	semidirect
16. C₈₉×#2335	C₂	semidirect
17. C₄×#126×C₈₉	C₂	semidirect
18. C₈₉×#2298	C₂	semidirect
19. C₈₉×#2276	C₂	semidirect
386. #35500	C₈₉	direct (N × H)
395. #2606	C₂×C₈₉	semidirect
396. #2599	C₂×C₈₉	semidirect
397. #2595	C₂×C₈₉	semidirect
398. #2592	C₂×C₈₉	semidirect
399. #2577	C₂×C₈₉	semidirect
401. #2532	C₂×C₈₉	semidirect
402. #2531	C₂×C₈₉	semidirect
403. #2529	C₂×C₈₉	semidirect
404. #2520	C₂×C₈₉	semidirect
405. #2513	C₂×C₈₉	semidirect
406. #2469	C₂×C₈₉	semidirect
407. #2458	C₂×C₈₉	semidirect
408. #2337	C₂×C₈₉	semidirect
409. #2335	C₂×C₈₉	semidirect
410. C₄×#126	C₂×C₈₉	semidirect
411. #2298	C₂×C₈₉	semidirect
412. #2276	C₂×C₈₉	semidirect
413. C₈₉	#35500	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#2610	2
C₈₉×#2606	2
C₈₉×#2599	2
C₈₉×#2595	2
C₈₉×#2592	2
C₈₉×#2577	2
C₈₉×#2554	2
C₈₉×#2532	2
C₈₉×#2531	2
C₈₉×#2529	2
C₈₉×#2520	2
C₈₉×#2513	2
C₈₉×#2469	2
C₈₉×#2458	2
C₈₉×#2337	2
C₈₉×#2335	2
C₄×#126×C₈₉	2
C₈₉×#2298	2
C₈₉×#2276	2
#35500	89

Subgroups — C89×#35500 #36413348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35500 #36413348