Subgroups — C₈₉×#35488 #36413336

Order 22784.

1666 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2608	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#2589	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2577	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2573	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2561	C₂	1	1	yes	maximal, characteristic
6	C₈₉×#2530	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2523	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2517	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2515	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2499	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2496	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2482	C₂	1	1	yes	maximal, characteristic
13	C₈₉×#2480	C₂	1	2	yes	maximal
14	C₈₉×#2480	C₂	1	2	yes	maximal
15	C₈₉×#2334	C₂	1	2	yes	maximal, complemented
16	C₈₉×#2332	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#126×C₈₉	C₂	1	2	yes	maximal, complemented
18	C₈₉×#2298	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2273	C₂	1	1	yes	maximal, characteristic
20	C₂×#126×C₈₉	C₂²	1	2	yes	—
21	C₂×#126×C₈₉	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
26	#400×C₈₉	C₂²	1	2	yes	complemented
27	#400×C₈₉	C₂²	1	2	yes	complemented
28	#400×C₈₉	C₂²	1	2	yes	complemented
29	#399×C₈₉	C₂²	1	2	yes	—
30	#398×C₈₉	C₂²	1	2	yes	complemented
31	#397×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	2	yes	—
36	#397×C₈₉	C₂²	1	2	yes	—
37	#397×C₈₉	C₂²	1	2	yes	—
38	#397×C₈₉	C₂²	1	2	yes	—
39	#396×C₈₉	C₂²	1	2	yes	—
40	#396×C₈₉	C₂²	1	2	yes	—
41	#393×C₈₉	C₂²	1	2	yes	—
42	#391×C₈₉	C₂²	1	2	yes	complemented
43	#391×C₈₉	C₂²	1	1	yes	characteristic, complemented
44	#391×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	#389×C₈₉	C₂²	1	2	yes	complemented
46	#389×C₈₉	C₂²	1	2	yes	complemented
47	#389×C₈₉	C₂²	1	2	yes	complemented
48	#388×C₈₉	C₂²	1	2	yes	—
49	#388×C₈₉	C₂²	1	2	yes	—
50	#388×C₈₉	C₂²	1	2	yes	—
51	#388×C₈₉	C₂²	1	2	yes	—
52	#388×C₈₉	C₂²	1	2	yes	—
53	#388×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	#387×C₈₉	C₂²	1	2	yes	complemented
59	#387×C₈₉	C₂²	1	2	yes	complemented
60	#387×C₈₉	C₂²	1	2	yes	complemented
61	#387×C₈₉	C₂²	1	2	yes	complemented
62	#387×C₈₉	C₂²	1	2	yes	complemented
63	#387×C₈₉	C₂²	1	2	yes	complemented
64	#387×C₈₉	C₂²	1	2	yes	complemented
65	#387×C₈₉	C₂²	1	2	yes	complemented
66	#387×C₈₉	C₂²	1	2	yes	complemented
67	#387×C₈₉	C₂²	1	2	yes	complemented
68	#387×C₈₉	C₂²	1	2	yes	complemented
69	#387×C₈₉	C₂²	1	2	yes	complemented
70	#387×C₈₉	C₂²	1	2	yes	complemented
71	#387×C₈₉	C₂²	1	2	yes	complemented
72	#385×C₈₉	C₂²	1	1	yes	characteristic
73	#385×C₈₉	C₂²	1	2	yes	—
74	#385×C₈₉	C₂²	1	2	yes	—
75	#385×C₈₉	C₂²	1	2	yes	—
76	#385×C₈₉	C₂²	1	2	yes	—
77	#385×C₈₉	C₂²	1	1	yes	characteristic
78	#384×C₈₉	C₂²	1	1	yes	characteristic, complemented
79	#383×C₈₉	C₂²	1	2	yes	complemented
80	#383×C₈₉	C₂²	1	2	yes	complemented
81	#382×C₈₉	C₂²	1	2	yes	complemented
82	#382×C₈₉	C₂²	1	1	yes	characteristic, complemented
83	#381×C₈₉	C₂²	1	2	yes	—
84	#381×C₈₉	C₂²	1	1	yes	characteristic
85	#380×C₈₉	C₂²	1	2	yes	—
86	#380×C₈₉	C₂²	1	2	yes	—
87	#379×C₈₉	C₂²	1	2	yes	—
88	#379×C₈₉	C₂²	1	1	yes	characteristic
89	#379×C₈₉	C₂²	1	1	yes	characteristic
90	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
91	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
92	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
93	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
94	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
95	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
96	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
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	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
105	#376×C₈₉	C₂²	1	1	yes	characteristic, complemented
106	C₄³×C₈₉	C₂²	1	1	yes	characteristic, complemented
107	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
110	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
111	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
113	#126×C₈₉	—	2	8	no	—
114	#126×C₈₉	—	2	8	no	—
115	C₂²⋊Q₈×C₈₉	—	2	4	no	—
116	#117×C₈₉	—	2	4	no	—
117	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
123	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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×C₂²⋊C₄×C₈₉	—	2	4	no	—
136	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
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	2	yes	—
145	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
153	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
164	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
167	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
169	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
171	#95×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
195	#95×C₈₉	C₂³	1	2	yes	—
196	#95×C₈₉	C₂³	1	2	yes	—
197	#95×C₈₉	C₂³	1	2	yes	—
198	#95×C₈₉	C₂³	1	2	yes	—
199	#95×C₈₉	C₂³	1	2	yes	—
200	C₂⁴×C₈₉	—	2	2	no	—
201	C₂⁴×C₈₉	—	2	4	no	—
202	C₂⁴×C₈₉	—	4	1	no	—
203	C₂⁴×C₈₉	—	4	1	no	—
204	C₂⁴×C₈₉	—	4	2	no	—
205	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
206	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
207	C₂×Q₈×C₈₉	—	2	2	no	—
208	C₂×Q₈×C₈₉	—	4	1	no	—
209	C₂×Q₈×C₈₉	—	4	1	no	—
210	C₂²×C₄×C₈₉	—	2	2	no	—
211	C₂²×C₄×C₈₉	—	2	4	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	—	4	2	no	—
218	C₂²×C₄×C₈₉	—	4	2	no	—
219	C₂²×C₄×C₈₉	—	4	2	no	—
220	C₂²×C₄×C₈₉	#41	1	4	yes	—
221	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
238	C₄⋊C₄×C₈₉	—	2	2	no	—
239	C₄⋊C₄×C₈₉	—	2	2	no	—
240	C₄⋊C₄×C₈₉	—	2	2	no	—
241	C₄⋊C₄×C₈₉	—	2	4	no	—
242	C₄⋊C₄×C₈₉	—	2	4	no	—
243	C₄⋊C₄×C₈₉	—	2	4	no	—
244	C₄⋊C₄×C₈₉	—	2	4	no	—
245	C₄⋊C₄×C₈₉	—	2	4	no	—
246	C₄⋊C₄×C₈₉	—	2	4	no	—
247	C₄⋊C₄×C₈₉	—	2	4	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	—	4	2	no	—
252	C₄⋊C₄×C₈₉	—	4	2	no	—
253	C₄⋊C₄×C₈₉	—	4	2	no	—
254	C₄⋊C₄×C₈₉	—	4	2	no	—
255	C₄⋊C₄×C₈₉	—	4	2	no	—
256	C₂²⋊C₄×C₈₉	—	2	4	no	—
257	C₂²⋊C₄×C₈₉	—	2	2	no	—
258	C₂²⋊C₄×C₈₉	—	2	2	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	—	2	4	no	—
263	C₂²⋊C₄×C₈₉	—	2	4	no	—
264	C₂²⋊C₄×C₈₉	—	2	4	no	—
265	C₂²⋊C₄×C₈₉	—	2	4	no	—
266	C₂²⋊C₄×C₈₉	—	2	4	no	—
267	C₂²⋊C₄×C₈₉	—	2	4	no	—
268	C₂²⋊C₄×C₈₉	—	4	1	no	—
269	C₂²⋊C₄×C₈₉	—	4	2	no	—
270	C₂²⋊C₄×C₈₉	—	4	2	no	—
271	C₂²⋊C₄×C₈₉	—	4	2	no	—
272	C₂²⋊C₄×C₈₉	—	4	2	no	—
273	C₂²⋊C₄×C₈₉	—	4	1	no	—
274	C₂²⋊C₄×C₈₉	—	4	2	no	—
275	C₂²⋊C₄×C₈₉	#41	1	8	yes	—
276	C₄²×C₈₉	—	2	2	no	—
277	C₄²×C₈₉	—	2	2	no	—
278	C₄²×C₈₉	—	2	4	no	—
279	C₄²×C₈₉	—	2	4	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	1	no	—
285	C₄²×C₈₉	—	4	2	no	—
286	C₄²×C₈₉	—	4	1	no	—
287	C₄²×C₈₉	—	4	1	no	—
288	C₄²×C₈₉	—	4	1	no	—
289	C₄²×C₈₉	—	4	2	no	—
290	C₂³×C₈₉	—	2	8	no	—
291	C₂³×C₈₉	—	2	2	no	—
292	C₂³×C₈₉	—	2	2	no	—
293	C₂³×C₈₉	—	2	2	no	—
294	C₂³×C₈₉	—	2	1	no	—
295	C₂³×C₈₉	—	2	1	no	—
296	C₂³×C₈₉	—	2	2	no	—
297	C₂³×C₈₉	—	2	2	no	—
298	C₂³×C₈₉	—	2	2	no	—
299	C₂³×C₈₉	—	2	2	no	—
300	C₂³×C₈₉	—	2	2	no	—
301	C₂³×C₈₉	—	8	2	no	—
302	C₂³×C₈₉	—	8	2	no	—
303	C₂³×C₈₉	—	8	4	no	—
304	C₂³×C₈₉	—	8	4	no	—
305	C₂³×C₈₉	C₂×#41	1	4	yes	—
306	C₂³×C₈₉	C₂×#41	1	2	yes	—
307	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
308	Q₈×C₈₉	—	8	2	no	—
309	C₂×C₄×C₈₉	—	2	1	no	—
310	C₂×C₄×C₈₉	—	2	1	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	2	no	—
315	C₂×C₄×C₈₉	—	2	1	no	—
316	C₂×C₄×C₈₉	—	2	1	no	—
317	C₂×C₄×C₈₉	—	2	1	no	—
318	C₂×C₄×C₈₉	—	2	1	no	—
319	C₂×C₄×C₈₉	—	2	2	no	—
320	C₂×C₄×C₈₉	—	2	2	no	—
321	C₂×C₄×C₈₉	—	2	1	no	—
322	C₂×C₄×C₈₉	—	2	1	no	—
323	C₂×C₄×C₈₉	—	2	2	no	—
324	C₂×C₄×C₈₉	—	2	2	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	2	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	2	no	—
342	C₂×C₄×C₈₉	—	2	2	no	—
343	C₂×C₄×C₈₉	—	2	2	no	—
344	C₂×C₄×C₈₉	—	2	2	no	—
345	C₂×C₄×C₈₉	—	2	2	no	—
346	C₂×C₄×C₈₉	—	2	2	no	—
347	C₂×C₄×C₈₉	—	2	2	no	—
348	C₂×C₄×C₈₉	—	2	2	no	—
349	C₂×C₄×C₈₉	—	2	2	no	—
350	C₂×C₄×C₈₉	—	2	2	no	—
351	C₂×C₄×C₈₉	—	2	2	no	—
352	C₂×C₄×C₈₉	—	4	4	no	—
353	C₂×C₄×C₈₉	—	8	4	no	—
354	C₂×C₄×C₈₉	—	8	4	no	—
355	C₂×C₄×C₈₉	—	8	2	no	—
356	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
357	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
358	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
359	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
360	C₂²×C₈₉	—	2	2	no	—
361	C₂²×C₈₉	—	2	4	no	—
362	C₂²×C₈₉	—	2	2	no	—
363	C₂²×C₈₉	—	2	2	no	—
364	C₂²×C₈₉	—	2	4	no	—
365	C₂²×C₈₉	—	2	4	no	—
366	C₂²×C₈₉	—	4	2	no	—
367	C₂²×C₈₉	—	4	2	no	—
368	C₂²×C₈₉	—	4	2	no	—
369	C₂²×C₈₉	—	4	2	no	—
370	C₂²×C₈₉	—	4	2	no	—
371	C₂²×C₈₉	—	4	2	no	—
372	C₂²×C₈₉	—	8	8	no	—
373	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
374	C₂²×C₈₉	C₂²×#41	1	2	yes	—
375	C₂²×C₈₉	#585	1	1	yes	characteristic
376	C₂²×C₈₉	#585	1	1	yes	characteristic
377	C₂²×C₈₉	#585	1	2	yes	—
378	C₄×C₈₉	—	2	2	no	—
379	C₄×C₈₉	—	2	2	no	—
380	C₄×C₈₉	—	2	4	no	—
381	C₄×C₈₉	—	2	4	no	—
382	C₄×C₈₉	—	4	1	no	—
383	C₄×C₈₉	—	4	1	no	—
384	C₄×C₈₉	—	4	2	no	—
385	C₄×C₈₉	—	4	2	no	—
386	C₄×C₈₉	—	4	1	no	—
387	C₄×C₈₉	—	4	1	no	—
388	C₄×C₈₉	—	4	2	no	—
389	C₄×C₈₉	—	4	2	no	—
390	C₄×C₈₉	—	4	2	no	—
391	C₄×C₈₉	—	4	2	no	—
392	C₄×C₈₉	—	4	2	no	—
393	C₄×C₈₉	—	4	2	no	—
394	C₄×C₈₉	—	4	2	no	—
395	#35488	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
396	C₂×C₈₉	—	4	2	no	—
397	C₂×C₈₉	—	4	4	no	—
398	C₂×C₈₉	#3444	1	1	yes	characteristic
399	C₂×C₈₉	#3491	1	1	yes	characteristic
400	C₂×C₈₉	#3510	1	1	yes	characteristic
401	C₂×C₈₉	#3521	1	2	yes	—
402	C₂×C₈₉	#3521	1	2	yes	—
403	#2608	C₂×C₈₉	1	1	yes	characteristic, complemented
404	#2589	C₂×C₈₉	1	2	yes	complemented
405	#2577	C₂×C₈₉	1	2	yes	complemented
406	#2573	C₂×C₈₉	1	2	yes	complemented
407	#2561	C₂×C₈₉	1	1	yes	characteristic
408	#2530	C₂×C₈₉	1	2	yes	complemented
409	#2523	C₂×C₈₉	1	2	yes	complemented
410	#2517	C₂×C₈₉	1	2	yes	complemented
411	#2515	C₂×C₈₉	1	2	yes	complemented
412	#2499	C₂×C₈₉	1	1	yes	characteristic, complemented
413	#2496	C₂×C₈₉	1	2	yes	complemented
414	#2482	C₂×C₈₉	1	1	yes	characteristic
415	#2480	C₂×C₈₉	1	2	yes	—
416	#2480	C₂×C₈₉	1	2	yes	—
417	#2334	C₂×C₈₉	1	2	yes	complemented
418	#2332	C₂×C₈₉	1	1	yes	characteristic, complemented
419	C₄×#126	C₂×C₈₉	1	2	yes	complemented
420	#2298	C₂×C₈₉	1	1	yes	characteristic, complemented
421	#2273	C₂×C₈₉	1	1	yes	characteristic
422	C₈₉	#35488	1	1	yes	characteristic, direct product factor, Sylow
423	C₂×#126	C₂²×C₈₉	1	2	yes	—
424	C₂×#126	C₂²×C₈₉	1	2	yes	—
425	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
426	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
427	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
428	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
429	#400	C₂²×C₈₉	1	2	yes	complemented
430	#400	C₂²×C₈₉	1	2	yes	complemented
431	#400	C₂²×C₈₉	1	2	yes	complemented
432	#399	C₂²×C₈₉	1	2	yes	—
433	#398	C₂²×C₈₉	1	2	yes	complemented
434	#397	C₂²×C₈₉	1	2	yes	—
435	#397	C₂²×C₈₉	1	2	yes	—
436	#397	C₂²×C₈₉	1	2	yes	—
437	#397	C₂²×C₈₉	1	2	yes	—
438	#397	C₂²×C₈₉	1	2	yes	—
439	#397	C₂²×C₈₉	1	2	yes	—
440	#397	C₂²×C₈₉	1	2	yes	—
441	#397	C₂²×C₈₉	1	2	yes	—
442	#396	C₂²×C₈₉	1	2	yes	—
443	#396	C₂²×C₈₉	1	2	yes	—
444	#393	C₂²×C₈₉	1	2	yes	—
445	#391	C₂²×C₈₉	1	2	yes	complemented
446	#391	C₂²×C₈₉	1	1	yes	characteristic, complemented
447	#391	C₂²×C₈₉	1	1	yes	characteristic, complemented
448	#389	C₂²×C₈₉	1	2	yes	complemented
449	#389	C₂²×C₈₉	1	2	yes	complemented
450	#389	C₂²×C₈₉	1	2	yes	complemented
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	#387	C₂²×C₈₉	1	2	yes	complemented
462	#387	C₂²×C₈₉	1	2	yes	complemented
463	#387	C₂²×C₈₉	1	2	yes	complemented
464	#387	C₂²×C₈₉	1	2	yes	complemented
465	#387	C₂²×C₈₉	1	2	yes	complemented
466	#387	C₂²×C₈₉	1	2	yes	complemented
467	#387	C₂²×C₈₉	1	2	yes	complemented
468	#387	C₂²×C₈₉	1	2	yes	complemented
469	#387	C₂²×C₈₉	1	2	yes	complemented
470	#387	C₂²×C₈₉	1	2	yes	complemented
471	#387	C₂²×C₈₉	1	2	yes	complemented
472	#387	C₂²×C₈₉	1	2	yes	complemented
473	#387	C₂²×C₈₉	1	2	yes	complemented
474	#387	C₂²×C₈₉	1	2	yes	complemented
475	#385	C₂²×C₈₉	1	1	yes	characteristic
476	#385	C₂²×C₈₉	1	2	yes	—
477	#385	C₂²×C₈₉	1	2	yes	—
478	#385	C₂²×C₈₉	1	2	yes	—
479	#385	C₂²×C₈₉	1	2	yes	—
480	#385	C₂²×C₈₉	1	1	yes	characteristic
481	#384	C₂²×C₈₉	1	1	yes	characteristic, complemented
482	#383	C₂²×C₈₉	1	2	yes	complemented
483	#383	C₂²×C₈₉	1	2	yes	complemented
484	#382	C₂²×C₈₉	1	2	yes	complemented
485	#382	C₂²×C₈₉	1	1	yes	characteristic, complemented
486	#381	C₂²×C₈₉	1	2	yes	—
487	#381	C₂²×C₈₉	1	1	yes	characteristic
488	#380	C₂²×C₈₉	1	2	yes	—
489	#380	C₂²×C₈₉	1	2	yes	—
490	#379	C₂²×C₈₉	1	2	yes	—
491	#379	C₂²×C₈₉	1	1	yes	characteristic
492	#379	C₂²×C₈₉	1	1	yes	characteristic
493	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
494	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
495	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
496	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
497	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
498	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
499	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
500	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
501	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
502	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
503	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
504	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
505	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
506	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
507	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
508	#376	C₂²×C₈₉	1	1	yes	characteristic, complemented
509	C₄³	C₂²×C₈₉	1	1	yes	characteristic, complemented
510	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
511	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
513	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
514	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
516	#126	—	2	8	no	—
517	#126	—	2	8	no	—
518	C₂²⋊Q₈	—	2	4	no	—
519	#117	—	2	4	no	—
520	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
538	C₂×C₂²⋊C₄	—	2	4	no	—
539	C₂×C₂²⋊C₄	—	2	8	no	—
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	1	yes	characteristic
546	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
560	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
561	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
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	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
566	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
567	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
568	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
569	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
570	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
571	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
572	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
573	C₂×C₄²	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	2	yes	—
589	#95	C₂³×C₈₉	1	2	yes	—
590	#95	C₂³×C₈₉	1	2	yes	—
591	#95	C₂³×C₈₉	1	2	yes	—
592	#95	C₂³×C₈₉	1	2	yes	—
593	#95	C₂³×C₈₉	1	2	yes	—
594	#95	C₂³×C₈₉	1	2	yes	—
595	#95	C₂³×C₈₉	1	2	yes	—
596	#95	C₂³×C₈₉	1	2	yes	—
597	#95	C₂³×C₈₉	1	2	yes	—
598	#95	C₂³×C₈₉	1	2	yes	—
599	#95	C₂³×C₈₉	1	2	yes	—
600	#95	C₂³×C₈₉	1	2	yes	—
601	#95	C₂³×C₈₉	1	2	yes	—
602	#95	C₂³×C₈₉	1	2	yes	—
603	C₂⁴	—	2	2	no	—
604	C₂⁴	—	2	4	no	—
605	C₂⁴	—	4	1	no	—
606	C₂⁴	—	4	1	no	—
607	C₂⁴	—	4	2	no	—
608	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
609	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
610	C₂×Q₈	—	2	2	no	—
611	C₂×Q₈	—	4	1	no	—
612	C₂×Q₈	—	4	1	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	4	1	no	—
617	C₂²×C₄	—	4	1	no	—
618	C₂²×C₄	—	4	2	no	—
619	C₂²×C₄	—	4	2	no	—
620	C₂²×C₄	—	4	2	no	—
621	C₂²×C₄	—	4	2	no	—
622	C₂²×C₄	—	4	2	no	—
623	C₂²×C₄	#41×C₈₉	1	4	yes	—
624	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
629	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
630	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
633	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
635	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₄⋊C₄	—	4	2	no	—
653	C₄⋊C₄	—	4	2	no	—
654	C₄⋊C₄	—	4	2	no	—
655	C₄⋊C₄	—	4	2	no	—
656	C₄⋊C₄	—	4	2	no	—
657	C₄⋊C₄	—	4	2	no	—
658	C₄⋊C₄	—	4	2	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	4	1	no	—
672	C₂²⋊C₄	—	4	2	no	—
673	C₂²⋊C₄	—	4	2	no	—
674	C₂²⋊C₄	—	4	2	no	—
675	C₂²⋊C₄	—	4	2	no	—
676	C₂²⋊C₄	—	4	1	no	—
677	C₂²⋊C₄	—	4	2	no	—
678	C₂²⋊C₄	#41×C₈₉	1	8	yes	—
679	C₄²	—	2	2	no	—
680	C₄²	—	2	2	no	—
681	C₄²	—	2	4	no	—
682	C₄²	—	2	4	no	—
683	C₄²	—	4	1	no	—
684	C₄²	—	4	2	no	—
685	C₄²	—	4	1	no	—
686	C₄²	—	4	2	no	—
687	C₄²	—	4	1	no	—
688	C₄²	—	4	2	no	—
689	C₄²	—	4	1	no	—
690	C₄²	—	4	1	no	—
691	C₄²	—	4	1	no	—
692	C₄²	—	4	2	no	—
693	C₂³	—	2	8	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	1	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	8	2	no	—
705	C₂³	—	8	2	no	—
706	C₂³	—	8	4	no	—
707	C₂³	—	8	4	no	—
708	C₂³	C₂×#41×C₈₉	1	4	yes	—
709	C₂³	C₂×#41×C₈₉	1	2	yes	—
710	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
711	Q₈	—	8	2	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	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	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	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	2	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	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	4	4	no	—
756	C₂×C₄	—	8	4	no	—
757	C₂×C₄	—	8	4	no	—
758	C₂×C₄	—	8	2	no	—
759	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
760	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
761	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
762	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	4	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	4	no	—
768	C₂²	—	2	4	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	8	8	no	—
776	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
777	C₂²	C₂²×#41×C₈₉	1	2	yes	—
778	C₂²	#585×C₈₉	1	1	yes	characteristic
779	C₂²	#585×C₈₉	1	1	yes	characteristic
780	C₂²	#585×C₈₉	1	2	yes	—
781	C₄	—	2	2	no	—
782	C₄	—	2	2	no	—
783	C₄	—	2	4	no	—
784	C₄	—	2	4	no	—
785	C₄	—	4	1	no	—
786	C₄	—	4	1	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	1	no	—
791	C₄	—	4	1	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₂	—	4	2	no	—
799	C₂	—	4	4	no	—
800	C₂	C₈₉×#3444	1	1	yes	characteristic
801	C₂	C₈₉×#3491	1	1	yes	characteristic
802	C₂	C₈₉×#3510	1	1	yes	characteristic
803	C₂	C₈₉×#3521	1	2	yes	—
804	C₂	C₈₉×#3521	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂⁵×C₈₉	C₂³
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. C₈₉×#2608	C₂	semidirect
2. C₈₉×#2589	C₂	semidirect
3. C₈₉×#2577	C₂	semidirect
4. C₈₉×#2573	C₂	semidirect
6. C₈₉×#2530	C₂	semidirect
7. C₈₉×#2523	C₂	semidirect
8. C₈₉×#2517	C₂	semidirect
9. C₈₉×#2515	C₂	semidirect
10. C₈₉×#2499	C₂	semidirect
11. C₈₉×#2496	C₂	semidirect
15. C₈₉×#2334	C₂	semidirect
16. C₈₉×#2332	C₂	semidirect
17. C₄×#126×C₈₉	C₂	semidirect
18. C₈₉×#2298	C₂	semidirect
26. #400×C₈₉	C₂²	semidirect
27. #400×C₈₉	C₂²	semidirect
28. #400×C₈₉	C₂²	semidirect
30. #398×C₈₉	C₂²	semidirect
42. #391×C₈₉	C₂²	semidirect
43. #391×C₈₉	C₂²	semidirect
44. #391×C₈₉	C₂²	semidirect
45. #389×C₈₉	C₂²	semidirect
46. #389×C₈₉	C₂²	semidirect
47. #389×C₈₉	C₂²	semidirect
58. #387×C₈₉	C₂²	semidirect
59. #387×C₈₉	C₂²	semidirect
60. #387×C₈₉	C₂²	semidirect
61. #387×C₈₉	C₂²	semidirect
62. #387×C₈₉	C₂²	semidirect
63. #387×C₈₉	C₂²	semidirect
64. #387×C₈₉	C₂²	semidirect
65. #387×C₈₉	C₂²	semidirect
66. #387×C₈₉	C₂²	semidirect
67. #387×C₈₉	C₂²	semidirect
68. #387×C₈₉	C₂²	semidirect
69. #387×C₈₉	C₂²	semidirect
70. #387×C₈₉	C₂²	semidirect
71. #387×C₈₉	C₂²	semidirect
78. #384×C₈₉	C₂²	semidirect
79. #383×C₈₉	C₂²	semidirect
80. #383×C₈₉	C₂²	semidirect
81. #382×C₈₉	C₂²	semidirect
82. #382×C₈₉	C₂²	semidirect
90. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
91. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
92. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
93. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
94. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
105. #376×C₈₉	C₂²	semidirect
106. C₄³×C₈₉	C₂²	semidirect
395. #35488	C₈₉	direct (N × H)
403. #2608	C₂×C₈₉	semidirect
404. #2589	C₂×C₈₉	semidirect
405. #2577	C₂×C₈₉	semidirect
406. #2573	C₂×C₈₉	semidirect
408. #2530	C₂×C₈₉	semidirect
409. #2523	C₂×C₈₉	semidirect
410. #2517	C₂×C₈₉	semidirect
411. #2515	C₂×C₈₉	semidirect
412. #2499	C₂×C₈₉	semidirect
413. #2496	C₂×C₈₉	semidirect
417. #2334	C₂×C₈₉	semidirect
418. #2332	C₂×C₈₉	semidirect
419. C₄×#126	C₂×C₈₉	semidirect
420. #2298	C₂×C₈₉	semidirect
422. C₈₉	#35488	direct (N × H)
429. #400	C₂²×C₈₉	semidirect
430. #400	C₂²×C₈₉	semidirect
431. #400	C₂²×C₈₉	semidirect
433. #398	C₂²×C₈₉	semidirect
445. #391	C₂²×C₈₉	semidirect
446. #391	C₂²×C₈₉	semidirect
447. #391	C₂²×C₈₉	semidirect
448. #389	C₂²×C₈₉	semidirect
449. #389	C₂²×C₈₉	semidirect
450. #389	C₂²×C₈₉	semidirect
461. #387	C₂²×C₈₉	semidirect
462. #387	C₂²×C₈₉	semidirect
463. #387	C₂²×C₈₉	semidirect
464. #387	C₂²×C₈₉	semidirect
465. #387	C₂²×C₈₉	semidirect
466. #387	C₂²×C₈₉	semidirect
467. #387	C₂²×C₈₉	semidirect
468. #387	C₂²×C₈₉	semidirect
469. #387	C₂²×C₈₉	semidirect
470. #387	C₂²×C₈₉	semidirect
471. #387	C₂²×C₈₉	semidirect
472. #387	C₂²×C₈₉	semidirect
473. #387	C₂²×C₈₉	semidirect
474. #387	C₂²×C₈₉	semidirect
481. #384	C₂²×C₈₉	semidirect
482. #383	C₂²×C₈₉	semidirect
483. #383	C₂²×C₈₉	semidirect
484. #382	C₂²×C₈₉	semidirect
485. #382	C₂²×C₈₉	semidirect
493. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
494. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
495. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
496. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
497. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
508. #376	C₂²×C₈₉	semidirect
509. C₄³	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#2608	2
C₈₉×#2589	2
C₈₉×#2577	2
C₈₉×#2573	2
C₈₉×#2561	2
C₈₉×#2530	2
C₈₉×#2523	2
C₈₉×#2517	2
C₈₉×#2515	2
C₈₉×#2499	2
C₈₉×#2496	2
C₈₉×#2482	2
C₈₉×#2480	2
C₈₉×#2334	2
C₈₉×#2332	2
C₄×#126×C₈₉	2
C₈₉×#2298	2
C₈₉×#2273	2
#35488	89

Subgroups — C89×#35488 #36413336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35488 #36413336