Subgroups — C₈₉×#35354 #36413202

Order 22784.

2914 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#123×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#518×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2534	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2487	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2483	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2470	C₂	1	4	yes	maximal, complemented
7	C₈₉×#2457	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2455	C₂	1	4	yes	maximal, complemented
9	C₈₉×#2418	C₂	1	4	yes	maximal, complemented
10	C₈₉×#2405	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2405	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2403	C₂	1	1	yes	maximal, characteristic
13	C₈₉×#2322	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2312	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#120×C₈₉	C₂	1	2	yes	maximal, complemented
16	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
19	C₂×#123×C₈₉	—	2	8	no	—
20	C₂×#123×C₈₉	C₂²	1	2	yes	—
21	C₂×#123×C₈₉	C₂²	1	4	yes	—
22	C₂×#123×C₈₉	C₂²	1	4	yes	complemented
23	C₂×#123×C₈₉	C₂²	1	2	yes	complemented
24	C₂×#120×C₈₉	C₂²	1	2	yes	—
25	C₂×#120×C₈₉	C₂²	1	2	yes	—
26	#518×C₈₉	—	2	8	no	—
27	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
30	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
31	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
32	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
33	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
39	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
40	#400×C₈₉	C₂²	1	4	yes	complemented
41	#399×C₈₉	C₂²	1	4	yes	complemented
42	#397×C₈₉	C₂²	1	4	yes	complemented
43	#396×C₈₉	C₂²	1	4	yes	complemented
44	#394×C₈₉	C₂²	1	4	yes	—
45	#394×C₈₉	C₂²	1	4	yes	complemented
46	#394×C₈₉	C₂²	1	4	yes	complemented
47	#392×C₈₉	C₂²	1	4	yes	—
48	#389×C₈₉	C₂²	1	4	yes	complemented
49	#389×C₈₉	C₂²	1	4	yes	complemented
50	#388×C₈₉	C₂²	1	4	yes	complemented
51	#388×C₈₉	C₂²	1	4	yes	complemented
52	#388×C₈₉	C₂²	1	4	yes	complemented
53	#388×C₈₉	C₂²	1	4	yes	complemented
54	#387×C₈₉	C₂²	1	4	yes	complemented
55	#386×C₈₉	C₂²	1	2	yes	—
56	#386×C₈₉	C₂²	1	2	yes	—
57	#386×C₈₉	C₂²	1	2	yes	—
58	#386×C₈₉	C₂²	1	4	yes	complemented
59	#386×C₈₉	C₂²	1	2	yes	complemented
60	#386×C₈₉	C₂²	1	4	yes	complemented
61	#385×C₈₉	C₂²	1	4	yes	complemented
62	#385×C₈₉	C₂²	1	2	yes	complemented
63	#385×C₈₉	C₂²	1	2	yes	complemented
64	#385×C₈₉	C₂²	1	4	yes	complemented
65	#385×C₈₉	C₂²	1	2	yes	complemented
66	#385×C₈₉	C₂²	1	2	yes	complemented
67	#381×C₈₉	C₂²	1	2	yes	complemented
68	#381×C₈₉	C₂²	1	2	yes	complemented
69	#380×C₈₉	C₂²	1	2	yes	complemented
70	#380×C₈₉	C₂²	1	4	yes	complemented
71	#379×C₈₉	C₂²	1	1	yes	characteristic
72	#379×C₈₉	C₂²	1	1	yes	characteristic
73	#379×C₈₉	C₂²	1	2	yes	complemented
74	#379×C₈₉	C₂²	1	2	yes	complemented
75	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
76	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	complemented
77	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
78	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
79	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₈₉	—	2	4	no	—
81	C₂²×D₄×C₈₉	—	2	8	no	—
82	C₂²×D₄×C₈₉	—	2	4	no	—
83	C₂²×D₄×C₈₉	—	4	4	no	—
84	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
85	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
86	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
87	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
89	C₂³×C₄×C₈₉	—	2	4	no	—
90	C₂³×C₄×C₈₉	—	4	4	no	—
91	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
94	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
95	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
100	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
102	#123×C₈₉	—	2	8	no	—
103	#123×C₈₉	—	2	16	no	—
104	#123×C₈₉	—	2	16	no	—
105	#123×C₈₉	—	4	4	no	—
106	#120×C₈₉	—	2	8	no	—
107	#120×C₈₉	—	4	4	no	—
108	C₄×D₄×C₈₉	—	2	8	no	—
109	C₄×D₄×C₈₉	—	2	8	no	—
110	C₄×D₄×C₈₉	—	2	8	no	—
111	C₄×D₄×C₈₉	—	2	8	no	—
112	C₄×D₄×C₈₉	—	4	8	no	—
113	#117×C₈₉	—	2	8	no	—
114	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
115	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
116	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
125	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
126	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
127	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
128	C₂×C₂²⋊C₄×C₈₉	D₄	1	8	yes	complemented
129	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	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	4	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	4	yes	—
147	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
150	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
151	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
152	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
153	#95×C₈₉	C₂³	1	4	yes	—
154	#95×C₈₉	C₂³	1	4	yes	—
155	#95×C₈₉	C₂³	1	4	yes	—
156	#95×C₈₉	C₂³	1	4	yes	—
157	#95×C₈₉	C₂³	1	4	yes	—
158	#95×C₈₉	C₂³	1	4	yes	—
159	#95×C₈₉	C₂³	1	4	yes	—
160	#95×C₈₉	C₂³	1	4	yes	—
161	C₂⁴×C₈₉	—	2	2	no	—
162	C₂⁴×C₈₉	—	2	4	no	—
163	C₂⁴×C₈₉	—	2	2	no	—
164	C₂⁴×C₈₉	—	2	4	no	—
165	C₂⁴×C₈₉	—	2	4	no	—
166	C₂⁴×C₈₉	—	2	4	no	—
167	C₂⁴×C₈₉	—	4	2	no	—
168	C₂⁴×C₈₉	—	4	2	no	—
169	C₂⁴×C₈₉	—	4	2	no	—
170	C₂⁴×C₈₉	—	4	2	no	—
171	C₂⁴×C₈₉	—	4	2	no	—
172	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
173	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
174	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
175	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
176	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
177	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
178	C₂×D₄×C₈₉	—	2	32	no	—
179	C₂×D₄×C₈₉	—	2	4	no	—
180	C₂×D₄×C₈₉	—	2	4	no	—
181	C₂×D₄×C₈₉	—	2	4	no	—
182	C₂×D₄×C₈₉	—	2	4	no	—
183	C₂×D₄×C₈₉	—	2	4	no	—
184	C₂×D₄×C₈₉	—	2	4	no	—
185	C₂×D₄×C₈₉	—	2	8	no	—
186	C₂×D₄×C₈₉	—	2	8	no	—
187	C₂×D₄×C₈₉	—	2	4	no	—
188	C₂×D₄×C₈₉	—	2	4	no	—
189	C₂×D₄×C₈₉	—	2	4	no	—
190	C₂×D₄×C₈₉	—	4	2	no	—
191	C₂×D₄×C₈₉	—	4	2	no	—
192	C₂×D₄×C₈₉	—	4	4	no	—
193	C₂×D₄×C₈₉	—	4	16	no	—
194	C₂×D₄×C₈₉	#41	1	8	yes	—
195	C₂²×C₄×C₈₉	—	2	2	no	—
196	C₂²×C₄×C₈₉	—	2	4	no	—
197	C₂²×C₄×C₈₉	—	2	2	no	—
198	C₂²×C₄×C₈₉	—	2	2	no	—
199	C₂²×C₄×C₈₉	—	2	2	no	—
200	C₂²×C₄×C₈₉	—	2	4	no	—
201	C₂²×C₄×C₈₉	—	2	8	no	—
202	C₂²×C₄×C₈₉	—	2	2	no	—
203	C₂²×C₄×C₈₉	—	2	2	no	—
204	C₂²×C₄×C₈₉	—	2	8	no	—
205	C₂²×C₄×C₈₉	—	2	4	no	—
206	C₂²×C₄×C₈₉	—	2	4	no	—
207	C₂²×C₄×C₈₉	—	4	2	no	—
208	C₂²×C₄×C₈₉	—	4	4	no	—
209	C₂²×C₄×C₈₉	—	4	2	no	—
210	C₂²×C₄×C₈₉	—	4	2	no	—
211	C₂²×C₄×C₈₉	—	4	2	no	—
212	C₂²×C₄×C₈₉	—	4	4	no	—
213	C₂²×C₄×C₈₉	—	4	2	no	—
214	C₂²×C₄×C₈₉	—	4	4	no	—
215	C₂²×C₄×C₈₉	—	4	2	no	—
216	C₂²×C₄×C₈₉	—	4	16	no	—
217	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
218	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
219	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
220	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₈₉	C₂⁴	1	4	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	2	yes	—
226	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
229	C₄⋊C₄×C₈₉	—	2	8	no	—
230	C₄⋊C₄×C₈₉	—	2	8	no	—
231	C₄⋊C₄×C₈₉	—	2	4	no	—
232	C₄⋊C₄×C₈₉	—	2	4	no	—
233	C₄⋊C₄×C₈₉	—	2	8	no	—
234	C₄⋊C₄×C₈₉	—	4	4	no	—
235	C₄⋊C₄×C₈₉	—	4	4	no	—
236	C₄⋊C₄×C₈₉	—	4	4	no	—
237	C₂²⋊C₄×C₈₉	—	2	4	no	—
238	C₂²⋊C₄×C₈₉	—	2	4	no	—
239	C₂²⋊C₄×C₈₉	—	2	4	no	—
240	C₂²⋊C₄×C₈₉	—	2	4	no	—
241	C₂²⋊C₄×C₈₉	—	2	4	no	—
242	C₂²⋊C₄×C₈₉	—	2	4	no	—
243	C₂²⋊C₄×C₈₉	—	2	8	no	—
244	C₂²⋊C₄×C₈₉	—	2	8	no	—
245	C₂²⋊C₄×C₈₉	—	2	4	no	—
246	C₂²⋊C₄×C₈₉	—	2	4	no	—
247	C₂²⋊C₄×C₈₉	—	2	8	no	—
248	C₂²⋊C₄×C₈₉	—	2	8	no	—
249	C₂²⋊C₄×C₈₉	—	4	2	no	—
250	C₂²⋊C₄×C₈₉	—	4	4	no	—
251	C₂²⋊C₄×C₈₉	—	4	2	no	—
252	C₂²⋊C₄×C₈₉	—	4	4	no	—
253	C₂²⋊C₄×C₈₉	—	4	2	no	—
254	C₂²⋊C₄×C₈₉	—	4	4	no	—
255	C₂²⋊C₄×C₈₉	—	4	2	no	—
256	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
257	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
258	C₄²×C₈₉	—	2	4	no	—
259	C₄²×C₈₉	—	2	4	no	—
260	C₄²×C₈₉	—	4	4	no	—
261	C₂³×C₈₉	—	2	2	no	—
262	C₂³×C₈₉	—	2	2	no	—
263	C₂³×C₈₉	—	2	8	no	—
264	C₂³×C₈₉	—	2	8	no	—
265	C₂³×C₈₉	—	2	2	no	—
266	C₂³×C₈₉	—	2	2	no	—
267	C₂³×C₈₉	—	2	4	no	—
268	C₂³×C₈₉	—	2	2	no	—
269	C₂³×C₈₉	—	2	2	no	—
270	C₂³×C₈₉	—	2	2	no	—
271	C₂³×C₈₉	—	2	4	no	—
272	C₂³×C₈₉	—	2	2	no	—
273	C₂³×C₈₉	—	2	2	no	—
274	C₂³×C₈₉	—	2	2	no	—
275	C₂³×C₈₉	—	2	2	no	—
276	C₂³×C₈₉	—	2	4	no	—
277	C₂³×C₈₉	—	2	2	no	—
278	C₂³×C₈₉	—	2	4	no	—
279	C₂³×C₈₉	—	2	8	no	—
280	C₂³×C₈₉	—	4	4	no	—
281	C₂³×C₈₉	—	4	4	no	—
282	C₂³×C₈₉	—	4	16	no	—
283	C₂³×C₈₉	—	4	4	no	—
284	C₂³×C₈₉	—	4	4	no	—
285	C₂³×C₈₉	—	8	8	no	—
286	C₂³×C₈₉	—	8	2	no	—
287	C₂³×C₈₉	—	8	2	no	—
288	C₂³×C₈₉	—	8	8	no	—
289	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
290	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
291	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
292	C₂³×C₈₉	C₂×#41	1	4	yes	—
293	C₂³×C₈₉	C₂×#41	1	4	yes	—
294	C₂³×C₈₉	H(5,𝔽₂)	1	4	yes	—
295	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
296	D₄×C₈₉	—	2	16	no	—
297	D₄×C₈₉	—	2	16	no	—
298	D₄×C₈₉	—	4	16	no	—
299	D₄×C₈₉	—	4	8	no	—
300	D₄×C₈₉	—	4	8	no	—
301	C₂×C₄×C₈₉	—	2	8	no	—
302	C₂×C₄×C₈₉	—	2	2	no	—
303	C₂×C₄×C₈₉	—	2	2	no	—
304	C₂×C₄×C₈₉	—	2	4	no	—
305	C₂×C₄×C₈₉	—	2	4	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	4	no	—
312	C₂×C₄×C₈₉	—	2	4	no	—
313	C₂×C₄×C₈₉	—	2	4	no	—
314	C₂×C₄×C₈₉	—	2	4	no	—
315	C₂×C₄×C₈₉	—	2	4	no	—
316	C₂×C₄×C₈₉	—	2	4	no	—
317	C₂×C₄×C₈₉	—	2	2	no	—
318	C₂×C₄×C₈₉	—	2	4	no	—
319	C₂×C₄×C₈₉	—	2	2	no	—
320	C₂×C₄×C₈₉	—	2	4	no	—
321	C₂×C₄×C₈₉	—	2	4	no	—
322	C₂×C₄×C₈₉	—	2	4	no	—
323	C₂×C₄×C₈₉	—	4	4	no	—
324	C₂×C₄×C₈₉	—	4	4	no	—
325	C₂×C₄×C₈₉	—	4	16	no	—
326	C₂×C₄×C₈₉	—	4	4	no	—
327	C₂×C₄×C₈₉	—	4	4	no	—
328	C₂×C₄×C₈₉	—	4	4	no	—
329	C₂×C₄×C₈₉	—	8	4	no	—
330	C₂×C₄×C₈₉	—	8	4	no	—
331	C₂×C₄×C₈₉	—	8	2	no	—
332	C₂×C₄×C₈₉	—	8	2	no	—
333	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
334	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
335	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
336	C₂²×C₈₉	—	2	2	no	—
337	C₂²×C₈₉	—	2	2	no	—
338	C₂²×C₈₉	—	2	8	no	—
339	C₂²×C₈₉	—	2	2	no	—
340	C₂²×C₈₉	—	2	2	no	—
341	C₂²×C₈₉	—	2	4	no	—
342	C₂²×C₈₉	—	2	4	no	—
343	C₂²×C₈₉	—	2	2	no	—
344	C₂²×C₈₉	—	2	2	no	—
345	C₂²×C₈₉	—	2	2	no	—
346	C₂²×C₈₉	—	2	2	no	—
347	C₂²×C₈₉	—	2	8	no	—
348	C₂²×C₈₉	—	2	8	no	—
349	C₂²×C₈₉	—	4	16	no	—
350	C₂²×C₈₉	—	4	2	no	—
351	C₂²×C₈₉	—	4	2	no	—
352	C₂²×C₈₉	—	4	2	no	—
353	C₂²×C₈₉	—	4	2	no	—
354	C₂²×C₈₉	—	4	4	no	—
355	C₂²×C₈₉	—	4	4	no	—
356	C₂²×C₈₉	—	4	4	no	—
357	C₂²×C₈₉	—	4	4	no	—
358	C₂²×C₈₉	—	8	8	no	—
359	C₂²×C₈₉	—	8	8	no	—
360	C₂²×C₈₉	#525	1	4	yes	—
361	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
362	C₂²×C₈₉	C₂²×#41	1	2	yes	—
363	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
364	C₂²×C₈₉	#585	1	2	yes	—
365	C₄×C₈₉	—	2	4	no	—
366	C₄×C₈₉	—	2	4	no	—
367	C₄×C₈₉	—	2	4	no	—
368	C₄×C₈₉	—	4	2	no	—
369	C₄×C₈₉	—	4	2	no	—
370	C₄×C₈₉	—	4	2	no	—
371	C₄×C₈₉	—	4	2	no	—
372	C₄×C₈₉	—	4	2	no	—
373	C₄×C₈₉	—	4	4	no	—
374	C₄×C₈₉	—	4	4	no	—
375	#35354	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
376	C₂×C₈₉	—	2	4	no	—
377	C₂×C₈₉	—	4	4	no	—
378	C₂×C₈₉	—	4	2	no	—
379	C₂×C₈₉	—	4	4	no	—
380	C₂×C₈₉	—	4	2	no	—
381	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
382	C₂×C₈₉	#3484	1	1	yes	characteristic
383	C₂×C₈₉	#3485	1	1	yes	characteristic
384	C₂×C₈₉	#3513	1	4	yes	—
385	C₂²×#123	C₂×C₈₉	1	1	yes	characteristic, complemented
386	C₂×#518	C₂×C₈₉	1	1	yes	characteristic, complemented
387	#2534	C₂×C₈₉	1	2	yes	complemented
388	#2487	C₂×C₈₉	1	2	yes	complemented
389	#2483	C₂×C₈₉	1	1	yes	characteristic, complemented
390	#2470	C₂×C₈₉	1	4	yes	complemented
391	#2457	C₂×C₈₉	1	4	yes	complemented
392	#2455	C₂×C₈₉	1	4	yes	complemented
393	#2418	C₂×C₈₉	1	4	yes	complemented
394	#2405	C₂×C₈₉	1	1	yes	characteristic, complemented
395	#2405	C₂×C₈₉	1	1	yes	characteristic, complemented
396	#2403	C₂×C₈₉	1	1	yes	characteristic
397	#2322	C₂×C₈₉	1	2	yes	complemented
398	#2312	C₂×C₈₉	1	1	yes	characteristic, complemented
399	C₄×#120	C₂×C₈₉	1	2	yes	complemented
400	C₈₉	#35354	1	1	yes	characteristic, direct product factor, Sylow
401	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
402	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
403	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
404	C₂×#123	—	2	8	no	—
405	C₂×#123	C₂²×C₈₉	1	2	yes	—
406	C₂×#123	C₂²×C₈₉	1	4	yes	—
407	C₂×#123	C₂²×C₈₉	1	4	yes	complemented
408	C₂×#123	C₂²×C₈₉	1	2	yes	complemented
409	C₂×#120	C₂²×C₈₉	1	2	yes	—
410	C₂×#120	C₂²×C₈₉	1	2	yes	—
411	#518	—	2	8	no	—
412	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
413	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
414	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
415	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
416	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
417	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
418	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
419	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
420	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
421	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
422	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
423	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
424	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
425	#400	C₂²×C₈₉	1	4	yes	complemented
426	#399	C₂²×C₈₉	1	4	yes	complemented
427	#397	C₂²×C₈₉	1	4	yes	complemented
428	#396	C₂²×C₈₉	1	4	yes	complemented
429	#394	C₂²×C₈₉	1	4	yes	—
430	#394	C₂²×C₈₉	1	4	yes	complemented
431	#394	C₂²×C₈₉	1	4	yes	complemented
432	#392	C₂²×C₈₉	1	4	yes	—
433	#389	C₂²×C₈₉	1	4	yes	complemented
434	#389	C₂²×C₈₉	1	4	yes	complemented
435	#388	C₂²×C₈₉	1	4	yes	complemented
436	#388	C₂²×C₈₉	1	4	yes	complemented
437	#388	C₂²×C₈₉	1	4	yes	complemented
438	#388	C₂²×C₈₉	1	4	yes	complemented
439	#387	C₂²×C₈₉	1	4	yes	complemented
440	#386	C₂²×C₈₉	1	2	yes	—
441	#386	C₂²×C₈₉	1	2	yes	—
442	#386	C₂²×C₈₉	1	2	yes	—
443	#386	C₂²×C₈₉	1	2	yes	complemented
444	#386	C₂²×C₈₉	1	4	yes	complemented
445	#386	C₂²×C₈₉	1	4	yes	complemented
446	#385	C₂²×C₈₉	1	2	yes	complemented
447	#385	C₂²×C₈₉	1	4	yes	complemented
448	#385	C₂²×C₈₉	1	2	yes	complemented
449	#385	C₂²×C₈₉	1	2	yes	complemented
450	#385	C₂²×C₈₉	1	4	yes	complemented
451	#385	C₂²×C₈₉	1	2	yes	complemented
452	#381	C₂²×C₈₉	1	2	yes	complemented
453	#381	C₂²×C₈₉	1	2	yes	complemented
454	#380	C₂²×C₈₉	1	2	yes	complemented
455	#380	C₂²×C₈₉	1	4	yes	complemented
456	#379	C₂²×C₈₉	1	1	yes	characteristic
457	#379	C₂²×C₈₉	1	1	yes	characteristic
458	#379	C₂²×C₈₉	1	2	yes	complemented
459	#379	C₂²×C₈₉	1	2	yes	complemented
460	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
461	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	complemented
462	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
463	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
464	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
465	C₂²×D₄	—	2	4	no	—
466	C₂²×D₄	—	2	8	no	—
467	C₂²×D₄	—	2	4	no	—
468	C₂²×D₄	—	4	4	no	—
469	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
470	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
471	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
472	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
473	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
474	C₂³×C₄	—	2	4	no	—
475	C₂³×C₄	—	4	4	no	—
476	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
477	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
478	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
479	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
480	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
481	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
482	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
483	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
484	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
487	#123	—	2	8	no	—
488	#123	—	2	16	no	—
489	#123	—	2	16	no	—
490	#123	—	4	4	no	—
491	#120	—	2	8	no	—
492	#120	—	4	4	no	—
493	C₄×D₄	—	2	8	no	—
494	C₄×D₄	—	2	8	no	—
495	C₄×D₄	—	2	8	no	—
496	C₄×D₄	—	2	8	no	—
497	C₄×D₄	—	4	8	no	—
498	#117	—	2	8	no	—
499	C₂×C₄⋊C₄	—	2	4	no	—
500	C₂×C₄⋊C₄	—	2	4	no	—
501	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
502	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	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	4	yes	—
506	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
507	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
508	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
509	C₂×C₂²⋊C₄	—	2	4	no	—
510	C₂×C₂²⋊C₄	—	2	4	no	—
511	C₂×C₂²⋊C₄	—	2	4	no	—
512	C₂×C₂²⋊C₄	—	2	8	no	—
513	C₂×C₂²⋊C₄	D₄×C₈₉	1	8	yes	complemented
514	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	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	2	yes	—
535	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
536	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
537	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
538	#95	C₂³×C₈₉	1	4	yes	—
539	#95	C₂³×C₈₉	1	4	yes	—
540	#95	C₂³×C₈₉	1	4	yes	—
541	#95	C₂³×C₈₉	1	4	yes	—
542	#95	C₂³×C₈₉	1	4	yes	—
543	#95	C₂³×C₈₉	1	4	yes	—
544	#95	C₂³×C₈₉	1	4	yes	—
545	#95	C₂³×C₈₉	1	4	yes	—
546	C₂⁴	—	2	2	no	—
547	C₂⁴	—	2	4	no	—
548	C₂⁴	—	2	2	no	—
549	C₂⁴	—	2	4	no	—
550	C₂⁴	—	2	4	no	—
551	C₂⁴	—	2	4	no	—
552	C₂⁴	—	4	2	no	—
553	C₂⁴	—	4	2	no	—
554	C₂⁴	—	4	2	no	—
555	C₂⁴	—	4	2	no	—
556	C₂⁴	—	4	2	no	—
557	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
558	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
559	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
560	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
561	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
562	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
563	C₂×D₄	—	2	32	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	2	4	no	—
567	C₂×D₄	—	2	4	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	2	8	no	—
571	C₂×D₄	—	2	8	no	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	—	2	4	no	—
574	C₂×D₄	—	2	4	no	—
575	C₂×D₄	—	4	2	no	—
576	C₂×D₄	—	4	2	no	—
577	C₂×D₄	—	4	4	no	—
578	C₂×D₄	—	4	16	no	—
579	C₂×D₄	#41×C₈₉	1	8	yes	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	8	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	8	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	4	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	4	4	no	—
594	C₂²×C₄	—	4	2	no	—
595	C₂²×C₄	—	4	2	no	—
596	C₂²×C₄	—	4	2	no	—
597	C₂²×C₄	—	4	4	no	—
598	C₂²×C₄	—	4	2	no	—
599	C₂²×C₄	—	4	4	no	—
600	C₂²×C₄	—	4	2	no	—
601	C₂²×C₄	—	4	16	no	—
602	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
603	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
604	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
605	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
607	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
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	2	yes	—
613	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
614	C₄⋊C₄	—	2	8	no	—
615	C₄⋊C₄	—	2	8	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	8	no	—
619	C₄⋊C₄	—	4	4	no	—
620	C₄⋊C₄	—	4	4	no	—
621	C₄⋊C₄	—	4	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	8	no	—
629	C₂²⋊C₄	—	2	8	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	8	no	—
633	C₂²⋊C₄	—	2	8	no	—
634	C₂²⋊C₄	—	4	4	no	—
635	C₂²⋊C₄	—	4	2	no	—
636	C₂²⋊C₄	—	4	4	no	—
637	C₂²⋊C₄	—	4	2	no	—
638	C₂²⋊C₄	—	4	2	no	—
639	C₂²⋊C₄	—	4	4	no	—
640	C₂²⋊C₄	—	4	2	no	—
641	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
642	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
643	C₄²	—	2	4	no	—
644	C₄²	—	2	4	no	—
645	C₄²	—	4	4	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	8	no	—
649	C₂³	—	2	8	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	4	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	4	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	4	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	4	no	—
664	C₂³	—	2	8	no	—
665	C₂³	—	4	4	no	—
666	C₂³	—	4	4	no	—
667	C₂³	—	4	16	no	—
668	C₂³	—	4	4	no	—
669	C₂³	—	4	4	no	—
670	C₂³	—	8	8	no	—
671	C₂³	—	8	2	no	—
672	C₂³	—	8	2	no	—
673	C₂³	—	8	8	no	—
674	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
675	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
676	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
677	C₂³	C₂×#41×C₈₉	1	4	yes	—
678	C₂³	C₂×#41×C₈₉	1	4	yes	—
679	C₂³	H(5,𝔽₂)×C₈₉	1	4	yes	—
680	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
681	D₄	—	2	16	no	—
682	D₄	—	2	16	no	—
683	D₄	—	4	16	no	—
684	D₄	—	4	8	no	—
685	D₄	—	4	8	no	—
686	C₂×C₄	—	2	8	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	4	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	4	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	4	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	4	4	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	4	16	no	—
711	C₂×C₄	—	4	4	no	—
712	C₂×C₄	—	4	4	no	—
713	C₂×C₄	—	4	4	no	—
714	C₂×C₄	—	8	4	no	—
715	C₂×C₄	—	8	4	no	—
716	C₂×C₄	—	8	2	no	—
717	C₂×C₄	—	8	2	no	—
718	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
719	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
720	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	8	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	2	4	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	2	2	no	—
730	C₂²	—	2	2	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	2	8	no	—
733	C₂²	—	2	8	no	—
734	C₂²	—	4	16	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	4	no	—
740	C₂²	—	4	4	no	—
741	C₂²	—	4	4	no	—
742	C₂²	—	4	4	no	—
743	C₂²	—	8	8	no	—
744	C₂²	—	8	8	no	—
745	C₂²	#525×C₈₉	1	4	yes	—
746	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
747	C₂²	C₂²×#41×C₈₉	1	2	yes	—
748	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
749	C₂²	#585×C₈₉	1	2	yes	—
750	C₄	—	2	4	no	—
751	C₄	—	2	4	no	—
752	C₄	—	2	4	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	4	no	—
759	C₄	—	4	4	no	—
760	C₂	—	2	4	no	—
761	C₂	—	4	4	no	—
762	C₂	—	4	2	no	—
763	C₂	—	4	4	no	—
764	C₂	—	4	2	no	—
765	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
766	C₂	C₈₉×#3484	1	1	yes	characteristic
767	C₂	C₈₉×#3485	1	1	yes	characteristic
768	C₂	C₈₉×#3513	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₈₉×#2403	C₂
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. C₂²×#123×C₈₉	C₂	semidirect
2. C₂×#518×C₈₉	C₂	semidirect
3. C₈₉×#2534	C₂	semidirect
4. C₈₉×#2487	C₂	semidirect
5. C₈₉×#2483	C₂	semidirect
6. C₈₉×#2470	C₂	semidirect
7. C₈₉×#2457	C₂	semidirect
8. C₈₉×#2455	C₂	semidirect
9. C₈₉×#2418	C₂	semidirect
10. C₈₉×#2405	C₂	semidirect
11. C₈₉×#2405	C₂	semidirect
13. C₈₉×#2322	C₂	semidirect
14. C₈₉×#2312	C₂	semidirect
15. C₄×#120×C₈₉	C₂	semidirect
18. C₂⁴×C₄×C₈₉	C₂²	semidirect
22. C₂×#123×C₈₉	C₂²	semidirect
23. C₂×#123×C₈₉	C₂²	semidirect
29. C₂×C₄×D₄×C₈₉	C₂²	semidirect
30. C₂×C₄×D₄×C₈₉	C₂²	semidirect
31. C₂×C₄×D₄×C₈₉	C₂²	semidirect
32. C₂×#117×C₈₉	C₂²	semidirect
33. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
34. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
38. C₂²×C₂²⋊C₄×C₈₉	C₂²	semidirect
39. C₂²×C₂²⋊C₄×C₈₉	C₂²	semidirect
40. #400×C₈₉	C₂²	semidirect
41. #399×C₈₉	C₂²	semidirect
42. #397×C₈₉	C₂²	semidirect
43. #396×C₈₉	C₂²	semidirect
45. #394×C₈₉	C₂²	semidirect
46. #394×C₈₉	C₂²	semidirect
48. #389×C₈₉	C₂²	semidirect
49. #389×C₈₉	C₂²	semidirect
50. #388×C₈₉	C₂²	semidirect
51. #388×C₈₉	C₂²	semidirect
52. #388×C₈₉	C₂²	semidirect
53. #388×C₈₉	C₂²	semidirect
54. #387×C₈₉	C₂²	semidirect
58. #386×C₈₉	C₂²	semidirect
59. #386×C₈₉	C₂²	semidirect
60. #386×C₈₉	C₂²	semidirect
61. #385×C₈₉	C₂²	semidirect
62. #385×C₈₉	C₂²	semidirect
63. #385×C₈₉	C₂²	semidirect
64. #385×C₈₉	C₂²	semidirect
65. #385×C₈₉	C₂²	semidirect
66. #385×C₈₉	C₂²	semidirect
67. #381×C₈₉	C₂²	semidirect
68. #381×C₈₉	C₂²	semidirect
69. #380×C₈₉	C₂²	semidirect
70. #380×C₈₉	C₂²	semidirect
73. #379×C₈₉	C₂²	semidirect
74. #379×C₈₉	C₂²	semidirect
75. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
76. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
128. C₂×C₂²⋊C₄×C₈₉	D₄	semidirect
375. #35354	C₈₉	direct (N × H)
385. C₂²×#123	C₂×C₈₉	semidirect
386. C₂×#518	C₂×C₈₉	semidirect
387. #2534	C₂×C₈₉	semidirect
388. #2487	C₂×C₈₉	semidirect
389. #2483	C₂×C₈₉	semidirect
390. #2470	C₂×C₈₉	semidirect
391. #2457	C₂×C₈₉	semidirect
392. #2455	C₂×C₈₉	semidirect
393. #2418	C₂×C₈₉	semidirect
394. #2405	C₂×C₈₉	semidirect
395. #2405	C₂×C₈₉	semidirect
397. #2322	C₂×C₈₉	semidirect
398. #2312	C₂×C₈₉	semidirect
399. C₄×#120	C₂×C₈₉	semidirect
400. C₈₉	#35354	direct (N × H)
403. C₂⁴×C₄	C₂²×C₈₉	semidirect
407. C₂×#123	C₂²×C₈₉	semidirect
408. C₂×#123	C₂²×C₈₉	semidirect
414. C₂×C₄×D₄	C₂²×C₈₉	semidirect
415. C₂×C₄×D₄	C₂²×C₈₉	semidirect
416. C₂×C₄×D₄	C₂²×C₈₉	semidirect
417. C₂×#117	C₂²×C₈₉	semidirect
418. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
419. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
423. C₂²×C₂²⋊C₄	C₂²×C₈₉	semidirect
424. C₂²×C₂²⋊C₄	C₂²×C₈₉	semidirect
425. #400	C₂²×C₈₉	semidirect
426. #399	C₂²×C₈₉	semidirect
427. #397	C₂²×C₈₉	semidirect
428. #396	C₂²×C₈₉	semidirect
430. #394	C₂²×C₈₉	semidirect
431. #394	C₂²×C₈₉	semidirect
433. #389	C₂²×C₈₉	semidirect
434. #389	C₂²×C₈₉	semidirect
435. #388	C₂²×C₈₉	semidirect
436. #388	C₂²×C₈₉	semidirect
437. #388	C₂²×C₈₉	semidirect
438. #388	C₂²×C₈₉	semidirect
439. #387	C₂²×C₈₉	semidirect
443. #386	C₂²×C₈₉	semidirect
444. #386	C₂²×C₈₉	semidirect
445. #386	C₂²×C₈₉	semidirect
446. #385	C₂²×C₈₉	semidirect
447. #385	C₂²×C₈₉	semidirect
448. #385	C₂²×C₈₉	semidirect
449. #385	C₂²×C₈₉	semidirect
450. #385	C₂²×C₈₉	semidirect
451. #385	C₂²×C₈₉	semidirect
452. #381	C₂²×C₈₉	semidirect
453. #381	C₂²×C₈₉	semidirect
454. #380	C₂²×C₈₉	semidirect
455. #380	C₂²×C₈₉	semidirect
458. #379	C₂²×C₈₉	semidirect
459. #379	C₂²×C₈₉	semidirect
460. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
461. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
513. 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
C₂²×#123×C₈₉	2
C₂×#518×C₈₉	2
C₈₉×#2534	2
C₈₉×#2487	2
C₈₉×#2483	2
C₈₉×#2470	2
C₈₉×#2457	2
C₈₉×#2455	2
C₈₉×#2418	2
C₈₉×#2405	2
C₈₉×#2403	2
C₈₉×#2322	2
C₈₉×#2312	2
C₄×#120×C₈₉	2
#35354	89

Subgroups — C89×#35354 #36413202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35354 #36413202