Subgroups — C₈₉×#60030 #36437878

Order 22784.

1642 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2722	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2690	C₂	1	2	yes	maximal
3	C₈₉×#2677	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#2611	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#2606	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2599	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#2590	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2588	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2550	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2524	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2523	C₂	1	1	yes	maximal, characteristic
12	C₈₉×#2517	C₂	1	1	yes	maximal, characteristic
13	C₈₉×#2478	C₂	1	2	yes	maximal
14	C₈₉×#2462	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2373	C₂	1	2	yes	maximal
16	C₈₉×#2371	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2365	C₂	1	2	yes	maximal, complemented
18	C₄×C₂²⋊Q₈×C₈₉	C₂	1	2	yes	maximal
19	C₈₉×#2296	C₂	1	1	yes	maximal, characteristic
20	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
21	C₂×#126×C₈₉	C₂²	1	2	yes	—
22	C₂×#125×C₈₉	C₂²	1	2	yes	—
23	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
30	#400×C₈₉	C₂²	1	1	yes	characteristic
31	#400×C₈₉	C₂²	1	2	yes	—
32	#400×C₈₉	C₂²	1	2	yes	—
33	#399×C₈₉	C₂²	1	1	yes	characteristic
34	#398×C₈₉	C₂²	1	2	yes	—
35	#398×C₈₉	C₂²	1	2	yes	—
36	#398×C₈₉	C₂²	1	1	yes	characteristic
37	#398×C₈₉	C₂²	1	2	yes	—
38	#398×C₈₉	C₂²	1	2	yes	—
39	#398×C₈₉	C₂²	1	1	yes	characteristic
40	#398×C₈₉	C₂²	1	2	yes	—
41	#398×C₈₉	C₂²	1	2	yes	—
42	#397×C₈₉	C₂²	1	1	yes	characteristic
43	#397×C₈₉	C₂²	1	1	yes	characteristic
44	#397×C₈₉	C₂²	1	2	yes	—
45	#397×C₈₉	C₂²	1	2	yes	—
46	#395×C₈₉	C₂²	1	1	yes	characteristic
47	#395×C₈₉	C₂²	1	2	yes	—
48	#395×C₈₉	C₂²	1	2	yes	—
49	#393×C₈₉	C₂²	1	1	yes	characteristic
50	#391×C₈₉	C₂²	1	2	yes	—
51	#391×C₈₉	C₂²	1	2	yes	—
52	#391×C₈₉	C₂²	1	2	yes	—
53	#389×C₈₉	C₂²	1	2	yes	—
54	#389×C₈₉	C₂²	1	2	yes	—
55	#389×C₈₉	C₂²	1	2	yes	—
56	#389×C₈₉	C₂²	1	2	yes	—
57	#389×C₈₉	C₂²	1	2	yes	—
58	#389×C₈₉	C₂²	1	2	yes	—
59	#389×C₈₉	C₂²	1	2	yes	—
60	#389×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	#387×C₈₉	C₂²	1	2	yes	—
65	#387×C₈₉	C₂²	1	2	yes	—
66	#387×C₈₉	C₂²	1	2	yes	—
67	#387×C₈₉	C₂²	1	2	yes	—
68	#387×C₈₉	C₂²	1	2	yes	—
69	#387×C₈₉	C₂²	1	2	yes	—
70	#387×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	#387×C₈₉	C₂²	1	2	yes	—
83	#387×C₈₉	C₂²	1	2	yes	—
84	#385×C₈₉	C₂²	1	1	yes	characteristic
85	#385×C₈₉	C₂²	1	1	yes	characteristic
86	#385×C₈₉	C₂²	1	1	yes	characteristic
87	#385×C₈₉	C₂²	1	1	yes	characteristic
88	#385×C₈₉	C₂²	1	2	yes	—
89	#385×C₈₉	C₂²	1	2	yes	—
90	#383×C₈₉	C₂²	1	1	yes	characteristic
91	#383×C₈₉	C₂²	1	2	yes	—
92	#382×C₈₉	C₂²	1	2	yes	—
93	#380×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×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
102	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
105	#376×C₈₉	C₂²	1	2	yes	—
106	#376×C₈₉	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
109	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₈₉	—	2	8	no	—
113	#126×C₈₉	—	2	8	no	—
114	#125×C₈₉	—	2	8	no	—
115	#125×C₈₉	—	4	2	no	—
116	C₂²⋊Q₈×C₈₉	—	2	8	no	—
117	C₄×Q₈×C₈₉	—	4	4	no	—
118	C₄×Q₈×C₈₉	—	4	2	no	—
119	#117×C₈₉	—	2	4	no	—
120	#117×C₈₉	—	4	2	no	—
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	2	yes	—
124	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊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	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
155	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
156	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₈₉	—	4	2	no	—
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	1	yes	characteristic
162	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
163	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
164	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
165	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
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	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	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
197	#95×C₈₉	C₂³	1	2	yes	—
198	#95×C₈₉	C₂³	1	2	yes	—
199	#95×C₈₉	C₂³	1	2	yes	—
200	#95×C₈₉	C₂³	1	2	yes	—
201	#95×C₈₉	C₂³	1	2	yes	—
202	#95×C₈₉	C₂³	1	2	yes	—
203	#95×C₈₉	C₂³	1	2	yes	—
204	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
205	C₂×Q₈×C₈₉	—	2	4	no	—
206	C₂×Q₈×C₈₉	—	2	4	no	—
207	C₂×Q₈×C₈₉	—	2	4	no	—
208	C₂×Q₈×C₈₉	—	4	2	no	—
209	C₂×Q₈×C₈₉	—	4	1	no	—
210	C₂²×C₄×C₈₉	—	2	2	no	—
211	C₂²×C₄×C₈₉	—	2	2	no	—
212	C₂²×C₄×C₈₉	—	2	2	no	—
213	C₂²×C₄×C₈₉	—	2	4	no	—
214	C₂²×C₄×C₈₉	—	2	4	no	—
215	C₂²×C₄×C₈₉	—	4	1	no	—
216	C₂²×C₄×C₈₉	—	4	1	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	2	yes	—
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	1	yes	characteristic
227	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
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	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
235	C₄⋊C₄×C₈₉	—	2	4	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	4	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	—	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	—	2	4	no	—
249	C₄⋊C₄×C₈₉	—	2	4	no	—
250	C₄⋊C₄×C₈₉	—	2	4	no	—
251	C₄⋊C₄×C₈₉	—	2	4	no	—
252	C₄⋊C₄×C₈₉	—	2	4	no	—
253	C₄⋊C₄×C₈₉	—	2	4	no	—
254	C₄⋊C₄×C₈₉	—	2	4	no	—
255	C₄⋊C₄×C₈₉	—	4	1	no	—
256	C₄⋊C₄×C₈₉	—	4	1	no	—
257	C₄⋊C₄×C₈₉	—	4	2	no	—
258	C₄⋊C₄×C₈₉	—	4	1	no	—
259	C₄⋊C₄×C₈₉	—	4	1	no	—
260	C₄⋊C₄×C₈₉	—	4	2	no	—
261	C₄⋊C₄×C₈₉	—	4	1	no	—
262	C₄⋊C₄×C₈₉	#41	1	8	yes	—
263	C₂²⋊C₄×C₈₉	—	2	2	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	1	no	—
270	C₂²⋊C₄×C₈₉	#41	1	4	yes	—
271	C₄²×C₈₉	—	2	4	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	2	no	—
277	C₄²×C₈₉	—	2	2	no	—
278	C₄²×C₈₉	—	2	4	no	—
279	C₄²×C₈₉	—	2	4	no	—
280	C₄²×C₈₉	—	4	2	no	—
281	C₄²×C₈₉	—	4	2	no	—
282	C₄²×C₈₉	—	4	2	no	—
283	C₄²×C₈₉	—	4	2	no	—
284	C₂³×C₈₉	—	2	2	no	—
285	C₂³×C₈₉	—	2	1	no	—
286	C₂³×C₈₉	—	2	2	no	—
287	C₂³×C₈₉	—	2	1	no	—
288	C₂³×C₈₉	C₂×#41	1	2	yes	—
289	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
290	Q₈×C₈₉	—	4	8	no	—
291	Q₈×C₈₉	—	4	4	no	—
292	C₂×C₄×C₈₉	—	2	8	no	—
293	C₂×C₄×C₈₉	—	2	1	no	—
294	C₂×C₄×C₈₉	—	2	2	no	—
295	C₂×C₄×C₈₉	—	2	2	no	—
296	C₂×C₄×C₈₉	—	2	1	no	—
297	C₂×C₄×C₈₉	—	2	2	no	—
298	C₂×C₄×C₈₉	—	2	2	no	—
299	C₂×C₄×C₈₉	—	2	2	no	—
300	C₂×C₄×C₈₉	—	2	2	no	—
301	C₂×C₄×C₈₉	—	2	1	no	—
302	C₂×C₄×C₈₉	—	2	2	no	—
303	C₂×C₄×C₈₉	—	2	2	no	—
304	C₂×C₄×C₈₉	—	2	2	no	—
305	C₂×C₄×C₈₉	—	2	1	no	—
306	C₂×C₄×C₈₉	—	2	2	no	—
307	C₂×C₄×C₈₉	—	2	2	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	2	no	—
315	C₂×C₄×C₈₉	—	2	2	no	—
316	C₂×C₄×C₈₉	—	2	2	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	1	no	—
321	C₂×C₄×C₈₉	—	2	1	no	—
322	C₂×C₄×C₈₉	—	2	1	no	—
323	C₂×C₄×C₈₉	—	2	1	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	—	4	4	no	—
337	C₂×C₄×C₈₉	—	4	4	no	—
338	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
339	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
340	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
341	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
342	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
343	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
344	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
345	C₂²×C₈₉	—	2	4	no	—
346	C₂²×C₈₉	—	2	2	no	—
347	C₂²×C₈₉	—	4	1	no	—
348	C₂²×C₈₉	—	4	2	no	—
349	C₂²×C₈₉	—	4	1	no	—
350	C₂²×C₈₉	C₂²×#41	1	2	yes	—
351	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
352	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
353	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
354	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
355	C₄×C₈₉	—	2	4	no	—
356	C₄×C₈₉	—	2	4	no	—
357	C₄×C₈₉	—	2	4	no	—
358	C₄×C₈₉	—	2	2	no	—
359	C₄×C₈₉	—	2	2	no	—
360	C₄×C₈₉	—	2	4	no	—
361	C₄×C₈₉	—	2	4	no	—
362	C₄×C₈₉	—	4	1	no	—
363	C₄×C₈₉	—	4	2	no	—
364	C₄×C₈₉	—	4	1	no	—
365	C₄×C₈₉	—	4	2	no	—
366	C₄×C₈₉	—	4	2	no	—
367	C₄×C₈₉	—	4	2	no	—
368	C₄×C₈₉	—	4	2	no	—
369	C₄×C₈₉	—	4	2	no	—
370	C₄×C₈₉	—	4	2	no	—
371	C₄×C₈₉	—	4	1	no	—
372	C₄×C₈₉	—	4	1	no	—
373	#60030	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
374	C₂×C₈₉	—	4	2	no	—
375	C₂×C₈₉	#3481	1	1	yes	characteristic
376	C₂×C₈₉	#3482	1	2	yes	—
377	C₂×C₈₉	#3492	1	1	yes	characteristic
378	C₂×C₈₉	#3509	1	2	yes	—
379	C₂×C₈₉	#3538	1	1	yes	characteristic
380	#2722	C₂×C₈₉	1	1	yes	characteristic
381	#2690	C₂×C₈₉	1	2	yes	—
382	#2677	C₂×C₈₉	1	1	yes	characteristic
383	#2611	C₂×C₈₉	1	1	yes	characteristic
384	#2606	C₂×C₈₉	1	2	yes	complemented
385	#2599	C₂×C₈₉	1	1	yes	characteristic
386	#2590	C₂×C₈₉	1	2	yes	complemented
387	#2588	C₂×C₈₉	1	2	yes	complemented
388	#2550	C₂×C₈₉	1	2	yes	complemented
389	#2524	C₂×C₈₉	1	2	yes	complemented
390	#2523	C₂×C₈₉	1	1	yes	characteristic
391	#2517	C₂×C₈₉	1	1	yes	characteristic
392	#2478	C₂×C₈₉	1	2	yes	—
393	#2462	C₂×C₈₉	1	2	yes	complemented
394	#2373	C₂×C₈₉	1	2	yes	—
395	#2371	C₂×C₈₉	1	2	yes	complemented
396	#2365	C₂×C₈₉	1	2	yes	complemented
397	C₄×C₂²⋊Q₈	C₂×C₈₉	1	2	yes	—
398	#2296	C₂×C₈₉	1	1	yes	characteristic
399	C₈₉	#60030	1	1	yes	characteristic, direct product factor, Sylow
400	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
401	C₂×#126	C₂²×C₈₉	1	2	yes	—
402	C₂×#125	C₂²×C₈₉	1	2	yes	—
403	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
404	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
405	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
406	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
407	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
408	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
409	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
410	#400	C₂²×C₈₉	1	1	yes	characteristic
411	#400	C₂²×C₈₉	1	2	yes	—
412	#400	C₂²×C₈₉	1	2	yes	—
413	#399	C₂²×C₈₉	1	1	yes	characteristic
414	#398	C₂²×C₈₉	1	2	yes	—
415	#398	C₂²×C₈₉	1	1	yes	characteristic
416	#398	C₂²×C₈₉	1	2	yes	—
417	#398	C₂²×C₈₉	1	2	yes	—
418	#398	C₂²×C₈₉	1	1	yes	characteristic
419	#398	C₂²×C₈₉	1	2	yes	—
420	#398	C₂²×C₈₉	1	2	yes	—
421	#398	C₂²×C₈₉	1	2	yes	—
422	#397	C₂²×C₈₉	1	1	yes	characteristic
423	#397	C₂²×C₈₉	1	1	yes	characteristic
424	#397	C₂²×C₈₉	1	2	yes	—
425	#397	C₂²×C₈₉	1	2	yes	—
426	#395	C₂²×C₈₉	1	2	yes	—
427	#395	C₂²×C₈₉	1	1	yes	characteristic
428	#395	C₂²×C₈₉	1	2	yes	—
429	#393	C₂²×C₈₉	1	1	yes	characteristic
430	#391	C₂²×C₈₉	1	2	yes	—
431	#391	C₂²×C₈₉	1	2	yes	—
432	#391	C₂²×C₈₉	1	2	yes	—
433	#389	C₂²×C₈₉	1	2	yes	—
434	#389	C₂²×C₈₉	1	2	yes	—
435	#389	C₂²×C₈₉	1	2	yes	—
436	#389	C₂²×C₈₉	1	2	yes	—
437	#389	C₂²×C₈₉	1	2	yes	—
438	#389	C₂²×C₈₉	1	2	yes	—
439	#389	C₂²×C₈₉	1	2	yes	—
440	#389	C₂²×C₈₉	1	2	yes	—
441	#388	C₂²×C₈₉	1	2	yes	—
442	#388	C₂²×C₈₉	1	2	yes	—
443	#388	C₂²×C₈₉	1	2	yes	—
444	#387	C₂²×C₈₉	1	2	yes	—
445	#387	C₂²×C₈₉	1	2	yes	—
446	#387	C₂²×C₈₉	1	2	yes	—
447	#387	C₂²×C₈₉	1	2	yes	—
448	#387	C₂²×C₈₉	1	2	yes	—
449	#387	C₂²×C₈₉	1	2	yes	—
450	#387	C₂²×C₈₉	1	2	yes	—
451	#387	C₂²×C₈₉	1	2	yes	—
452	#387	C₂²×C₈₉	1	2	yes	—
453	#387	C₂²×C₈₉	1	2	yes	—
454	#387	C₂²×C₈₉	1	2	yes	—
455	#387	C₂²×C₈₉	1	2	yes	—
456	#387	C₂²×C₈₉	1	2	yes	—
457	#387	C₂²×C₈₉	1	2	yes	—
458	#387	C₂²×C₈₉	1	2	yes	—
459	#387	C₂²×C₈₉	1	2	yes	—
460	#387	C₂²×C₈₉	1	2	yes	—
461	#387	C₂²×C₈₉	1	2	yes	—
462	#387	C₂²×C₈₉	1	2	yes	—
463	#387	C₂²×C₈₉	1	2	yes	—
464	#385	C₂²×C₈₉	1	2	yes	—
465	#385	C₂²×C₈₉	1	2	yes	—
466	#385	C₂²×C₈₉	1	1	yes	characteristic
467	#385	C₂²×C₈₉	1	1	yes	characteristic
468	#385	C₂²×C₈₉	1	1	yes	characteristic
469	#385	C₂²×C₈₉	1	1	yes	characteristic
470	#383	C₂²×C₈₉	1	1	yes	characteristic
471	#383	C₂²×C₈₉	1	2	yes	—
472	#382	C₂²×C₈₉	1	2	yes	—
473	#380	C₂²×C₈₉	1	2	yes	—
474	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
475	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
476	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
477	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
478	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
479	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
480	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
481	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
482	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
483	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
484	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
485	#376	C₂²×C₈₉	1	2	yes	—
486	#376	C₂²×C₈₉	1	1	yes	characteristic
487	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
488	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
492	C₄⋊Q₈	—	2	8	no	—
493	#126	—	2	8	no	—
494	#125	—	2	8	no	—
495	#125	—	4	2	no	—
496	C₂²⋊Q₈	—	2	8	no	—
497	C₄×Q₈	—	4	4	no	—
498	C₄×Q₈	—	4	2	no	—
499	#117	—	2	4	no	—
500	#117	—	4	2	no	—
501	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
530	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
535	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
536	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
537	C₂×C₄²	—	4	2	no	—
538	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
541	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
542	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
543	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
544	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
545	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
546	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
547	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
548	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
549	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
550	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
551	#95	C₂³×C₈₉	1	2	yes	—
552	#95	C₂³×C₈₉	1	2	yes	—
553	#95	C₂³×C₈₉	1	2	yes	—
554	#95	C₂³×C₈₉	1	1	yes	characteristic
555	#95	C₂³×C₈₉	1	1	yes	characteristic
556	#95	C₂³×C₈₉	1	2	yes	—
557	#95	C₂³×C₈₉	1	2	yes	—
558	#95	C₂³×C₈₉	1	2	yes	—
559	#95	C₂³×C₈₉	1	2	yes	—
560	#95	C₂³×C₈₉	1	2	yes	—
561	#95	C₂³×C₈₉	1	2	yes	—
562	#95	C₂³×C₈₉	1	2	yes	—
563	#95	C₂³×C₈₉	1	2	yes	—
564	#95	C₂³×C₈₉	1	2	yes	—
565	#95	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
570	#95	C₂³×C₈₉	1	2	yes	—
571	#95	C₂³×C₈₉	1	2	yes	—
572	#95	C₂³×C₈₉	1	1	yes	characteristic
573	#95	C₂³×C₈₉	1	2	yes	—
574	#95	C₂³×C₈₉	1	1	yes	characteristic
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	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
585	C₂×Q₈	—	2	4	no	—
586	C₂×Q₈	—	2	4	no	—
587	C₂×Q₈	—	2	4	no	—
588	C₂×Q₈	—	4	2	no	—
589	C₂×Q₈	—	4	1	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	4	1	no	—
596	C₂²×C₄	—	4	1	no	—
597	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	4	1	no	—
636	C₄⋊C₄	—	4	1	no	—
637	C₄⋊C₄	—	4	2	no	—
638	C₄⋊C₄	—	4	1	no	—
639	C₄⋊C₄	—	4	1	no	—
640	C₄⋊C₄	—	4	2	no	—
641	C₄⋊C₄	—	4	1	no	—
642	C₄⋊C₄	#41×C₈₉	1	8	yes	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	4	1	no	—
649	C₂²⋊C₄	—	4	1	no	—
650	C₂²⋊C₄	#41×C₈₉	1	4	yes	—
651	C₄²	—	2	4	no	—
652	C₄²	—	2	4	no	—
653	C₄²	—	2	4	no	—
654	C₄²	—	2	4	no	—
655	C₄²	—	2	4	no	—
656	C₄²	—	2	2	no	—
657	C₄²	—	2	2	no	—
658	C₄²	—	2	4	no	—
659	C₄²	—	2	4	no	—
660	C₄²	—	4	2	no	—
661	C₄²	—	4	2	no	—
662	C₄²	—	4	2	no	—
663	C₄²	—	4	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	1	no	—
668	C₂³	C₂×#41×C₈₉	1	2	yes	—
669	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
670	Q₈	—	4	8	no	—
671	Q₈	—	4	4	no	—
672	C₂×C₄	—	2	8	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	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	1	no	—
703	C₂×C₄	—	2	1	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	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	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	—	4	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
719	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
720	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
721	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
722	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
723	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
724	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
725	C₂²	—	2	4	no	—
726	C₂²	—	2	2	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	1	no	—
730	C₂²	C₂²×#41×C₈₉	1	2	yes	—
731	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
732	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
733	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
734	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
735	C₄	—	2	4	no	—
736	C₄	—	2	4	no	—
737	C₄	—	2	4	no	—
738	C₄	—	2	2	no	—
739	C₄	—	2	2	no	—
740	C₄	—	2	4	no	—
741	C₄	—	2	4	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	1	no	—
744	C₄	—	4	1	no	—
745	C₄	—	4	2	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	2	no	—
748	C₄	—	4	2	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	1	no	—
752	C₄	—	4	1	no	—
753	C₂	—	4	2	no	—
754	C₂	C₈₉×#3481	1	1	yes	characteristic
755	C₂	C₈₉×#3482	1	2	yes	—
756	C₂	C₈₉×#3492	1	1	yes	characteristic
757	C₂	C₈₉×#3509	1	2	yes	—
758	C₂	C₈₉×#3538	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂⁴×C₈₉	C₂⁴
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
5. C₈₉×#2606	C₂	semidirect
7. C₈₉×#2590	C₂	semidirect
8. C₈₉×#2588	C₂	semidirect
9. C₈₉×#2550	C₂	semidirect
10. C₈₉×#2524	C₂	semidirect
14. C₈₉×#2462	C₂	semidirect
16. C₈₉×#2371	C₂	semidirect
17. C₈₉×#2365	C₂	semidirect
373. #60030	C₈₉	direct (N × H)
384. #2606	C₂×C₈₉	semidirect
386. #2590	C₂×C₈₉	semidirect
387. #2588	C₂×C₈₉	semidirect
388. #2550	C₂×C₈₉	semidirect
389. #2524	C₂×C₈₉	semidirect
393. #2462	C₂×C₈₉	semidirect
395. #2371	C₂×C₈₉	semidirect
396. #2365	C₂×C₈₉	semidirect
399. C₈₉	#60030	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×#2722	2
C₈₉×#2690	2
C₈₉×#2677	2
C₈₉×#2611	2
C₈₉×#2606	2
C₈₉×#2599	2
C₈₉×#2590	2
C₈₉×#2588	2
C₈₉×#2550	2
C₈₉×#2524	2
C₈₉×#2523	2
C₈₉×#2517	2
C₈₉×#2478	2
C₈₉×#2462	2
C₈₉×#2373	2
C₈₉×#2371	2
C₈₉×#2365	2
C₄×C₂²⋊Q₈×C₈₉	2
C₈₉×#2296	2
#60030	89

Subgroups — C89×#60030 #36437878

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60030 #36437878