Subgroups — C₈₉×#35516 #36413364

Order 22784.

2610 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#525×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#520×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2487	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2486	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2485	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2485	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2423	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2422	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2421	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2420	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2419	C₂	1	4	yes	maximal, complemented
12	C₈₉×#2418	C₂	1	4	yes	maximal, complemented
13	C₈₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2316	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2311	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2280	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#380×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
20	#525×C₈₉	—	2	8	no	—
21	C₂×#123×C₈₉	C₂²	1	2	yes	—
22	C₂×#123×C₈₉	C₂²	1	4	yes	—
23	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#120×C₈₉	C₂²	1	2	yes	—
28	#520×C₈₉	—	2	8	no	—
29	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
30	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
31	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
34	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
38	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
40	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
41	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
42	#400×C₈₉	C₂²	1	4	yes	complemented
43	#399×C₈₉	C₂²	1	4	yes	—
44	#398×C₈₉	C₂²	1	4	yes	complemented
45	#397×C₈₉	C₂²	1	4	yes	—
46	#397×C₈₉	C₂²	1	4	yes	complemented
47	#397×C₈₉	C₂²	1	4	yes	complemented
48	#394×C₈₉	C₂²	1	4	yes	—
49	#394×C₈₉	C₂²	1	4	yes	—
50	#391×C₈₉	C₂²	1	2	yes	complemented
51	#390×C₈₉	C₂²	1	2	yes	complemented
52	#389×C₈₉	C₂²	1	2	yes	complemented
53	#389×C₈₉	C₂²	1	2	yes	complemented
54	#389×C₈₉	C₂²	1	2	yes	complemented
55	#389×C₈₉	C₂²	1	2	yes	complemented
56	#389×C₈₉	C₂²	1	2	yes	complemented
57	#389×C₈₉	C₂²	1	2	yes	complemented
58	#388×C₈₉	C₂²	1	4	yes	—
59	#388×C₈₉	C₂²	1	4	yes	—
60	#387×C₈₉	C₂²	1	4	yes	complemented
61	#387×C₈₉	C₂²	1	4	yes	complemented
62	#386×C₈₉	C₂²	1	4	yes	—
63	#386×C₈₉	C₂²	1	4	yes	—
64	#385×C₈₉	C₂²	1	4	yes	—
65	#385×C₈₉	C₂²	1	4	yes	complemented
66	#384×C₈₉	C₂²	1	2	yes	complemented
67	#382×C₈₉	C₂²	1	2	yes	complemented
68	#381×C₈₉	C₂²	1	2	yes	—
69	#381×C₈₉	C₂²	1	4	yes	complemented
70	#380×C₈₉	C₂²	1	4	yes	—
71	#380×C₈₉	C₂²	1	2	yes	—
72	#380×C₈₉	C₂²	1	2	yes	—
73	#380×C₈₉	C₂²	1	1	yes	characteristic
74	#380×C₈₉	C₂²	1	1	yes	characteristic
75	#380×C₈₉	C₂²	1	2	yes	—
76	#380×C₈₉	C₂²	1	2	yes	—
77	#380×C₈₉	C₂²	1	1	yes	characteristic
78	#380×C₈₉	C₂²	1	1	yes	characteristic
79	#380×C₈₉	C₂²	1	2	yes	complemented
80	#380×C₈₉	C₂²	1	2	yes	complemented
81	#379×C₈₉	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
84	C₂×#95×C₈₉	C₂²	1	2	yes	—
85	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
86	C₂×#41×C₈₉	—	2	4	no	—
87	C₂×#41×C₈₉	—	2	4	no	—
88	C₂×#41×C₈₉	D₄	1	8	yes	—
89	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
91	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
93	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₈₉	—	2	4	no	—
95	C₂³×C₄×C₈₉	—	2	4	no	—
96	C₂³×C₄×C₈₉	—	2	4	no	—
97	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
104	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
105	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
106	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
107	#123×C₈₉	—	2	8	no	—
108	#123×C₈₉	—	4	8	no	—
109	C₂²⋊Q₈×C₈₉	—	2	4	no	—
110	C₂²⋊Q₈×C₈₉	—	2	4	no	—
111	#121×C₈₉	—	2	4	no	—
112	#121×C₈₉	—	2	4	no	—
113	#120×C₈₉	—	2	8	no	—
114	C₄×Q₈×C₈₉	—	2	8	no	—
115	C₄×D₄×C₈₉	—	2	16	no	—
116	C₄×D₄×C₈₉	—	2	8	no	—
117	C₄×D₄×C₈₉	—	2	8	no	—
118	C₄×D₄×C₈₉	—	2	8	no	—
119	#117×C₈₉	—	2	4	no	—
120	#117×C₈₉	—	2	4	no	—
121	#117×C₈₉	—	2	8	no	—
122	#117×C₈₉	—	2	4	no	—
123	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
124	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
125	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
126	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
133	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	4	yes	—
139	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
141	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
142	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₈₉	—	4	4	no	—
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	2	yes	—
148	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	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	4	yes	—
155	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
159	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
160	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
163	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
164	#95×C₈₉	C₂³	1	4	yes	—
165	#95×C₈₉	C₂³	1	4	yes	—
166	#95×C₈₉	C₂³	1	2	yes	—
167	#95×C₈₉	C₂³	1	2	yes	—
168	#95×C₈₉	C₂³	1	2	yes	—
169	#95×C₈₉	C₂³	1	2	yes	—
170	#95×C₈₉	C₂³	1	4	yes	—
171	#95×C₈₉	C₂³	1	4	yes	—
172	#95×C₈₉	C₂³	1	4	yes	—
173	#95×C₈₉	C₂³	1	4	yes	—
174	#95×C₈₉	C₂³	1	4	yes	—
175	#95×C₈₉	C₂³	1	4	yes	—
176	C₂⁴×C₈₉	—	2	2	no	—
177	C₂⁴×C₈₉	—	2	2	no	—
178	C₂⁴×C₈₉	—	2	2	no	—
179	C₂⁴×C₈₉	—	2	2	no	—
180	C₂⁴×C₈₉	—	2	2	no	—
181	C₂⁴×C₈₉	—	4	1	no	—
182	C₂⁴×C₈₉	—	4	1	no	—
183	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
184	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
185	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
186	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
187	#41×C₈₉	—	2	32	no	—
188	C₂×Q₈×C₈₉	—	2	2	no	—
189	C₂×Q₈×C₈₉	—	2	2	no	—
190	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
191	C₂×D₄×C₈₉	—	2	4	no	—
192	C₂×D₄×C₈₉	—	2	4	no	—
193	C₂×D₄×C₈₉	—	2	4	no	—
194	C₂×D₄×C₈₉	—	2	4	no	—
195	C₂×D₄×C₈₉	—	2	4	no	—
196	C₂×D₄×C₈₉	—	2	4	no	—
197	C₂×D₄×C₈₉	—	2	2	no	—
198	C₂×D₄×C₈₉	—	2	2	no	—
199	C₂×D₄×C₈₉	—	4	2	no	—
200	C₂×D₄×C₈₉	—	4	2	no	—
201	C₂×D₄×C₈₉	C₂×D₄	1	8	yes	—
202	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
203	C₂²×C₄×C₈₉	—	2	4	no	—
204	C₂²×C₄×C₈₉	—	2	4	no	—
205	C₂²×C₄×C₈₉	—	2	2	no	—
206	C₂²×C₄×C₈₉	—	2	2	no	—
207	C₂²×C₄×C₈₉	—	2	2	no	—
208	C₂²×C₄×C₈₉	—	2	8	no	—
209	C₂²×C₄×C₈₉	—	2	4	no	—
210	C₂²×C₄×C₈₉	—	2	4	no	—
211	C₂²×C₄×C₈₉	—	2	2	no	—
212	C₂²×C₄×C₈₉	—	2	2	no	—
213	C₂²×C₄×C₈₉	—	2	2	no	—
214	C₂²×C₄×C₈₉	—	2	2	no	—
215	C₂²×C₄×C₈₉	—	2	2	no	—
216	C₂²×C₄×C₈₉	—	2	2	no	—
217	C₂²×C₄×C₈₉	—	2	2	no	—
218	C₂²×C₄×C₈₉	—	2	2	no	—
219	C₂²×C₄×C₈₉	—	2	2	no	—
220	C₂²×C₄×C₈₉	—	2	2	no	—
221	C₂²×C₄×C₈₉	—	2	2	no	—
222	C₂²×C₄×C₈₉	—	2	2	no	—
223	C₂²×C₄×C₈₉	—	4	2	no	—
224	C₂²×C₄×C₈₉	—	4	2	no	—
225	C₂²×C₄×C₈₉	—	4	4	no	—
226	C₂²×C₄×C₈₉	—	4	2	no	—
227	C₂²×C₄×C₈₉	—	4	4	no	—
228	C₂²×C₄×C₈₉	—	4	2	no	—
229	C₂²×C₄×C₈₉	—	4	16	no	—
230	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
231	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
232	C₂²×C₄×C₈₉	#41	1	4	yes	—
233	C₂²×C₄×C₈₉	#41	1	4	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	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
240	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
242	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
247	C₄⋊C₄×C₈₉	—	2	4	no	—
248	C₄⋊C₄×C₈₉	—	2	2	no	—
249	C₄⋊C₄×C₈₉	—	2	8	no	—
250	C₄⋊C₄×C₈₉	—	2	4	no	—
251	C₄⋊C₄×C₈₉	—	2	2	no	—
252	C₄⋊C₄×C₈₉	—	2	2	no	—
253	C₄⋊C₄×C₈₉	—	2	2	no	—
254	C₄⋊C₄×C₈₉	—	2	4	no	—
255	C₄⋊C₄×C₈₉	—	2	4	no	—
256	C₄⋊C₄×C₈₉	—	2	4	no	—
257	C₄⋊C₄×C₈₉	—	2	4	no	—
258	C₄⋊C₄×C₈₉	—	2	2	no	—
259	C₄⋊C₄×C₈₉	—	2	2	no	—
260	C₄⋊C₄×C₈₉	—	4	4	no	—
261	C₄⋊C₄×C₈₉	—	4	4	no	—
262	C₄⋊C₄×C₈₉	—	4	4	no	—
263	C₄⋊C₄×C₈₉	—	4	4	no	—
264	C₂²⋊C₄×C₈₉	—	2	8	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	—	2	4	no	—
269	C₂²⋊C₄×C₈₉	—	2	4	no	—
270	C₂²⋊C₄×C₈₉	—	2	8	no	—
271	C₂²⋊C₄×C₈₉	—	2	4	no	—
272	C₂²⋊C₄×C₈₉	—	2	4	no	—
273	C₂²⋊C₄×C₈₉	—	2	4	no	—
274	C₂²⋊C₄×C₈₉	—	2	4	no	—
275	C₂²⋊C₄×C₈₉	—	4	4	no	—
276	C₂²⋊C₄×C₈₉	—	4	2	no	—
277	C₂²⋊C₄×C₈₉	—	4	4	no	—
278	C₂²⋊C₄×C₈₉	—	4	2	no	—
279	C₂²⋊C₄×C₈₉	—	4	4	no	—
280	C₄²×C₈₉	—	2	4	no	—
281	C₄²×C₈₉	—	2	8	no	—
282	C₄²×C₈₉	—	2	4	no	—
283	C₄²×C₈₉	—	2	4	no	—
284	C₂³×C₈₉	—	2	1	no	—
285	C₂³×C₈₉	—	2	1	no	—
286	C₂³×C₈₉	—	2	1	no	—
287	C₂³×C₈₉	—	2	1	no	—
288	C₂³×C₈₉	—	2	8	no	—
289	C₂³×C₈₉	—	2	1	no	—
290	C₂³×C₈₉	—	2	1	no	—
291	C₂³×C₈₉	—	2	1	no	—
292	C₂³×C₈₉	—	2	1	no	—
293	C₂³×C₈₉	—	2	1	no	—
294	C₂³×C₈₉	—	2	1	no	—
295	C₂³×C₈₉	—	2	2	no	—
296	C₂³×C₈₉	—	2	2	no	—
297	C₂³×C₈₉	—	2	1	no	—
298	C₂³×C₈₉	—	2	2	no	—
299	C₂³×C₈₉	—	2	2	no	—
300	C₂³×C₈₉	—	2	1	no	—
301	C₂³×C₈₉	—	2	2	no	—
302	C₂³×C₈₉	—	2	1	no	—
303	C₂³×C₈₉	—	2	1	no	—
304	C₂³×C₈₉	—	2	2	no	—
305	C₂³×C₈₉	—	2	1	no	—
306	C₂³×C₈₉	—	2	1	no	—
307	C₂³×C₈₉	—	4	4	no	—
308	C₂³×C₈₉	—	4	4	no	—
309	C₂³×C₈₉	—	4	4	no	—
310	C₂³×C₈₉	—	4	4	no	—
311	C₂³×C₈₉	—	4	4	no	—
312	C₂³×C₈₉	—	4	4	no	—
313	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
314	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
315	C₂³×C₈₉	C₂×#41	1	2	yes	—
316	C₂³×C₈₉	C₂×#41	1	2	yes	—
317	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
318	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
319	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
320	Q₈×C₈₉	—	2	8	no	—
321	D₄×C₈₉	—	2	16	no	—
322	D₄×C₈₉	—	2	8	no	—
323	D₄×C₈₉	—	4	8	no	—
324	D₄×C₈₉	—	4	8	no	—
325	C₂×C₄×C₈₉	—	2	2	no	—
326	C₂×C₄×C₈₉	—	2	2	no	—
327	C₂×C₄×C₈₉	—	2	16	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	4	no	—
332	C₂×C₄×C₈₉	—	2	2	no	—
333	C₂×C₄×C₈₉	—	2	1	no	—
334	C₂×C₄×C₈₉	—	2	1	no	—
335	C₂×C₄×C₈₉	—	2	2	no	—
336	C₂×C₄×C₈₉	—	2	2	no	—
337	C₂×C₄×C₈₉	—	2	4	no	—
338	C₂×C₄×C₈₉	—	2	1	no	—
339	C₂×C₄×C₈₉	—	2	1	no	—
340	C₂×C₄×C₈₉	—	2	1	no	—
341	C₂×C₄×C₈₉	—	2	1	no	—
342	C₂×C₄×C₈₉	—	2	2	no	—
343	C₂×C₄×C₈₉	—	2	4	no	—
344	C₂×C₄×C₈₉	—	2	4	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	—	2	2	no	—
353	C₂×C₄×C₈₉	—	2	4	no	—
354	C₂×C₄×C₈₉	—	2	2	no	—
355	C₂×C₄×C₈₉	—	2	2	no	—
356	C₂×C₄×C₈₉	—	2	2	no	—
357	C₂×C₄×C₈₉	—	2	4	no	—
358	C₂×C₄×C₈₉	—	4	4	no	—
359	C₂×C₄×C₈₉	—	4	4	no	—
360	C₂×C₄×C₈₉	—	4	4	no	—
361	C₂×C₄×C₈₉	—	4	4	no	—
362	C₂×C₄×C₈₉	—	4	4	no	—
363	C₂×C₄×C₈₉	—	8	4	no	—
364	C₂×C₄×C₈₉	—	8	8	no	—
365	C₂×C₄×C₈₉	—	8	4	no	—
366	C₂×C₄×C₈₉	#123	1	16	yes	complemented
367	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
368	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
369	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
370	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
371	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
372	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
373	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
374	C₂²×C₈₉	—	2	2	no	—
375	C₂²×C₈₉	—	2	2	no	—
376	C₂²×C₈₉	—	2	2	no	—
377	C₂²×C₈₉	—	2	2	no	—
378	C₂²×C₈₉	—	2	2	no	—
379	C₂²×C₈₉	—	2	2	no	—
380	C₂²×C₈₉	—	2	4	no	—
381	C₂²×C₈₉	—	2	4	no	—
382	C₂²×C₈₉	—	2	2	no	—
383	C₂²×C₈₉	—	2	2	no	—
384	C₂²×C₈₉	—	2	4	no	—
385	C₂²×C₈₉	—	2	2	no	—
386	C₂²×C₈₉	—	2	2	no	—
387	C₂²×C₈₉	—	2	2	no	—
388	C₂²×C₈₉	—	2	2	no	—
389	C₂²×C₈₉	—	4	16	no	—
390	C₂²×C₈₉	—	4	1	no	—
391	C₂²×C₈₉	—	4	1	no	—
392	C₂²×C₈₉	—	4	1	no	—
393	C₂²×C₈₉	—	4	1	no	—
394	C₂²×C₈₉	—	4	2	no	—
395	C₂²×C₈₉	—	4	2	no	—
396	C₂²×C₈₉	—	4	1	no	—
397	C₂²×C₈₉	—	4	1	no	—
398	C₂²×C₈₉	—	4	2	no	—
399	C₂²×C₈₉	—	4	1	no	—
400	C₂²×C₈₉	—	4	2	no	—
401	C₂²×C₈₉	—	4	1	no	—
402	C₂²×C₈₉	C₂×#123	1	4	yes	—
403	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
404	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
405	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
406	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
407	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
408	C₂²×C₈₉	#585	1	1	yes	characteristic
409	C₂²×C₈₉	#585	1	1	yes	characteristic
410	C₄×C₈₉	—	2	4	no	—
411	C₄×C₈₉	—	4	1	no	—
412	C₄×C₈₉	—	4	1	no	—
413	C₄×C₈₉	—	4	4	no	—
414	C₄×C₈₉	—	4	2	no	—
415	C₄×C₈₉	—	4	2	no	—
416	C₄×C₈₉	—	4	2	no	—
417	C₄×C₈₉	—	4	2	no	—
418	C₄×C₈₉	—	4	2	no	—
419	C₄×C₈₉	—	4	2	no	—
420	C₄×C₈₉	—	4	4	no	—
421	C₄×C₈₉	C₂×#123	1	4	yes	—
422	C₄×C₈₉	C₂×#123	1	4	yes	—
423	#35516	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
424	C₂×C₈₉	—	2	4	no	—
425	C₂×C₈₉	—	4	4	no	—
426	C₂×C₈₉	—	4	2	no	—
427	C₂×C₈₉	—	4	2	no	—
428	C₂×C₈₉	C₂²×#123	1	1	yes	characteristic
429	C₂×C₈₉	#3488	1	1	yes	characteristic
430	C₂×C₈₉	#3489	1	1	yes	characteristic
431	C₂×C₈₉	#3492	1	1	yes	characteristic
432	C₂×C₈₉	#3493	1	1	yes	characteristic
433	C₂×C₈₉	#3494	1	1	yes	characteristic
434	C₂×C₈₉	#3495	1	1	yes	characteristic
435	C₂×#525	C₂×C₈₉	1	1	yes	characteristic
436	C₂×#520	C₂×C₈₉	1	1	yes	characteristic, complemented
437	#2487	C₂×C₈₉	1	2	yes	complemented
438	#2486	C₂×C₈₉	1	2	yes	complemented
439	#2485	C₂×C₈₉	1	2	yes	complemented
440	#2485	C₂×C₈₉	1	2	yes	complemented
441	#2423	C₂×C₈₉	1	2	yes	complemented
442	#2422	C₂×C₈₉	1	2	yes	complemented
443	#2421	C₂×C₈₉	1	2	yes	complemented
444	#2420	C₂×C₈₉	1	2	yes	complemented
445	#2419	C₂×C₈₉	1	4	yes	complemented
446	#2418	C₂×C₈₉	1	4	yes	complemented
447	#2317	C₂×C₈₉	1	1	yes	characteristic, complemented
448	#2316	C₂×C₈₉	1	1	yes	characteristic, complemented
449	#2311	C₂×C₈₉	1	1	yes	characteristic, complemented
450	#2280	C₂×C₈₉	1	1	yes	characteristic, complemented
451	C₂×#380	C₂×C₈₉	1	1	yes	characteristic, complemented
452	C₈₉	#35516	1	1	yes	characteristic, direct product factor, Sylow
453	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
454	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
455	#525	—	2	8	no	—
456	C₂×#123	C₂²×C₈₉	1	2	yes	—
457	C₂×#123	C₂²×C₈₉	1	4	yes	—
458	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
459	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
460	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
461	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
462	C₂×#120	C₂²×C₈₉	1	2	yes	—
463	#520	—	2	8	no	—
464	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	complemented
465	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
466	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
467	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
468	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
469	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
470	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
471	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
472	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
473	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
474	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
475	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
476	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
477	#400	C₂²×C₈₉	1	4	yes	complemented
478	#399	C₂²×C₈₉	1	4	yes	—
479	#398	C₂²×C₈₉	1	4	yes	complemented
480	#397	C₂²×C₈₉	1	4	yes	—
481	#397	C₂²×C₈₉	1	4	yes	complemented
482	#397	C₂²×C₈₉	1	4	yes	complemented
483	#394	C₂²×C₈₉	1	4	yes	—
484	#394	C₂²×C₈₉	1	4	yes	—
485	#391	C₂²×C₈₉	1	2	yes	complemented
486	#390	C₂²×C₈₉	1	2	yes	complemented
487	#389	C₂²×C₈₉	1	2	yes	complemented
488	#389	C₂²×C₈₉	1	2	yes	complemented
489	#389	C₂²×C₈₉	1	2	yes	complemented
490	#389	C₂²×C₈₉	1	2	yes	complemented
491	#389	C₂²×C₈₉	1	2	yes	complemented
492	#389	C₂²×C₈₉	1	2	yes	complemented
493	#388	C₂²×C₈₉	1	4	yes	—
494	#388	C₂²×C₈₉	1	4	yes	—
495	#387	C₂²×C₈₉	1	4	yes	complemented
496	#387	C₂²×C₈₉	1	4	yes	complemented
497	#386	C₂²×C₈₉	1	4	yes	—
498	#386	C₂²×C₈₉	1	4	yes	—
499	#385	C₂²×C₈₉	1	4	yes	—
500	#385	C₂²×C₈₉	1	4	yes	complemented
501	#384	C₂²×C₈₉	1	2	yes	complemented
502	#382	C₂²×C₈₉	1	2	yes	complemented
503	#381	C₂²×C₈₉	1	2	yes	—
504	#381	C₂²×C₈₉	1	4	yes	complemented
505	#380	C₂²×C₈₉	1	4	yes	—
506	#380	C₂²×C₈₉	1	2	yes	—
507	#380	C₂²×C₈₉	1	2	yes	—
508	#380	C₂²×C₈₉	1	1	yes	characteristic
509	#380	C₂²×C₈₉	1	1	yes	characteristic
510	#380	C₂²×C₈₉	1	2	yes	—
511	#380	C₂²×C₈₉	1	2	yes	—
512	#380	C₂²×C₈₉	1	1	yes	characteristic
513	#380	C₂²×C₈₉	1	1	yes	characteristic
514	#380	C₂²×C₈₉	1	2	yes	complemented
515	#380	C₂²×C₈₉	1	2	yes	complemented
516	#379	C₂²×C₈₉	1	2	yes	—
517	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
518	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
519	C₂×#95	C₂²×C₈₉	1	2	yes	—
520	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
521	C₂×#41	—	2	4	no	—
522	C₂×#41	—	2	4	no	—
523	C₂×#41	D₄×C₈₉	1	8	yes	—
524	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
525	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
526	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
527	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
528	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
529	C₂³×C₄	—	2	4	no	—
530	C₂³×C₄	—	2	4	no	—
531	C₂³×C₄	—	2	4	no	—
532	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
533	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
535	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
536	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
537	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
538	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
539	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
540	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
541	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
542	#123	—	2	8	no	—
543	#123	—	4	8	no	—
544	C₂²⋊Q₈	—	2	4	no	—
545	C₂²⋊Q₈	—	2	4	no	—
546	#121	—	2	4	no	—
547	#121	—	2	4	no	—
548	#120	—	2	8	no	—
549	C₄×Q₈	—	2	8	no	—
550	C₄×D₄	—	2	16	no	—
551	C₄×D₄	—	2	8	no	—
552	C₄×D₄	—	2	8	no	—
553	C₄×D₄	—	2	8	no	—
554	#117	—	2	4	no	—
555	#117	—	2	4	no	—
556	#117	—	2	8	no	—
557	#117	—	2	4	no	—
558	C₂×C₄⋊C₄	—	2	4	no	—
559	C₂×C₄⋊C₄	—	2	8	no	—
560	C₂×C₄⋊C₄	—	2	4	no	—
561	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
567	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
575	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
576	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
577	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
578	C₂×C₂²⋊C₄	—	4	4	no	—
579	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
595	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
596	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
597	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
598	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
599	#95	C₂³×C₈₉	1	4	yes	—
600	#95	C₂³×C₈₉	1	4	yes	—
601	#95	C₂³×C₈₉	1	2	yes	—
602	#95	C₂³×C₈₉	1	2	yes	—
603	#95	C₂³×C₈₉	1	2	yes	—
604	#95	C₂³×C₈₉	1	2	yes	—
605	#95	C₂³×C₈₉	1	4	yes	—
606	#95	C₂³×C₈₉	1	4	yes	—
607	#95	C₂³×C₈₉	1	4	yes	—
608	#95	C₂³×C₈₉	1	4	yes	—
609	#95	C₂³×C₈₉	1	4	yes	—
610	#95	C₂³×C₈₉	1	4	yes	—
611	C₂⁴	—	2	2	no	—
612	C₂⁴	—	2	2	no	—
613	C₂⁴	—	2	2	no	—
614	C₂⁴	—	2	2	no	—
615	C₂⁴	—	2	2	no	—
616	C₂⁴	—	4	1	no	—
617	C₂⁴	—	4	1	no	—
618	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
619	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
620	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
621	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
622	#41	—	2	32	no	—
623	C₂×Q₈	—	2	2	no	—
624	C₂×Q₈	—	2	2	no	—
625	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
626	C₂×D₄	—	2	4	no	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	4	2	no	—
635	C₂×D₄	—	4	2	no	—
636	C₂×D₄	C₂×D₄×C₈₉	1	8	yes	—
637	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	8	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	4	2	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	—	4	4	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	4	no	—
663	C₂²×C₄	—	4	2	no	—
664	C₂²×C₄	—	4	16	no	—
665	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
666	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
667	C₂²×C₄	#41×C₈₉	1	4	yes	—
668	C₂²×C₄	#41×C₈₉	1	4	yes	—
669	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
670	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
675	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
677	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	8	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	4	4	no	—
696	C₄⋊C₄	—	4	4	no	—
697	C₄⋊C₄	—	4	4	no	—
698	C₄⋊C₄	—	4	4	no	—
699	C₂²⋊C₄	—	2	8	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	8	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	4	4	no	—
711	C₂²⋊C₄	—	4	4	no	—
712	C₂²⋊C₄	—	4	2	no	—
713	C₂²⋊C₄	—	4	4	no	—
714	C₂²⋊C₄	—	4	2	no	—
715	C₄²	—	2	4	no	—
716	C₄²	—	2	8	no	—
717	C₄²	—	2	4	no	—
718	C₄²	—	2	4	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	1	no	—
723	C₂³	—	2	8	no	—
724	C₂³	—	2	1	no	—
725	C₂³	—	2	1	no	—
726	C₂³	—	2	1	no	—
727	C₂³	—	2	1	no	—
728	C₂³	—	2	1	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	1	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	1	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	1	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	1	no	—
741	C₂³	—	2	1	no	—
742	C₂³	—	4	4	no	—
743	C₂³	—	4	4	no	—
744	C₂³	—	4	4	no	—
745	C₂³	—	4	4	no	—
746	C₂³	—	4	4	no	—
747	C₂³	—	4	4	no	—
748	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
749	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
750	C₂³	C₂×#41×C₈₉	1	2	yes	—
751	C₂³	C₂×#41×C₈₉	1	2	yes	—
752	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
753	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
754	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
755	Q₈	—	2	8	no	—
756	D₄	—	2	16	no	—
757	D₄	—	2	8	no	—
758	D₄	—	4	8	no	—
759	D₄	—	4	8	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	16	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	4	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	4	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	4	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	4	no	—
793	C₂×C₄	—	4	4	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	—	4	4	no	—
796	C₂×C₄	—	4	4	no	—
797	C₂×C₄	—	4	4	no	—
798	C₂×C₄	—	8	4	no	—
799	C₂×C₄	—	8	8	no	—
800	C₂×C₄	—	8	4	no	—
801	C₂×C₄	#123×C₈₉	1	16	yes	complemented
802	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
803	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
804	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
805	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
806	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
807	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
808	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
809	C₂²	—	2	2	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	4	no	—
816	C₂²	—	2	4	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	4	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	2	no	—
824	C₂²	—	4	16	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	2	no	—
837	C₂²	C₂×#123×C₈₉	1	4	yes	—
838	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
839	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
840	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
841	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
842	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
843	C₂²	#585×C₈₉	1	1	yes	characteristic
844	C₂²	#585×C₈₉	1	1	yes	characteristic
845	C₄	—	2	4	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	4	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	4	no	—
856	C₄	C₂×#123×C₈₉	1	4	yes	—
857	C₄	C₂×#123×C₈₉	1	4	yes	—
858	C₂	—	2	4	no	—
859	C₂	—	4	4	no	—
860	C₂	—	4	2	no	—
861	C₂	—	4	2	no	—
862	C₂	C₂²×#123×C₈₉	1	1	yes	characteristic
863	C₂	C₈₉×#3488	1	1	yes	characteristic
864	C₂	C₈₉×#3489	1	1	yes	characteristic
865	C₂	C₈₉×#3492	1	1	yes	characteristic
866	C₂	C₈₉×#3493	1	1	yes	characteristic
867	C₂	C₈₉×#3494	1	1	yes	characteristic
868	C₂	C₈₉×#3495	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂×#525×C₈₉	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
2. C₂×#520×C₈₉	C₂	semidirect
3. C₈₉×#2487	C₂	semidirect
4. C₈₉×#2486	C₂	semidirect
5. C₈₉×#2485	C₂	semidirect
6. C₈₉×#2485	C₂	semidirect
7. C₈₉×#2423	C₂	semidirect
8. C₈₉×#2422	C₂	semidirect
9. C₈₉×#2421	C₂	semidirect
10. C₈₉×#2420	C₂	semidirect
11. C₈₉×#2419	C₂	semidirect
12. C₈₉×#2418	C₂	semidirect
13. C₈₉×#2317	C₂	semidirect
14. C₈₉×#2316	C₂	semidirect
15. C₈₉×#2311	C₂	semidirect
16. C₈₉×#2280	C₂	semidirect
17. C₂×#380×C₈₉	C₂	semidirect
29. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
33. C₂×C₄×D₄×C₈₉	C₂²	semidirect
37. C₂×#117×C₈₉	C₂²	semidirect
40. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
42. #400×C₈₉	C₂²	semidirect
44. #398×C₈₉	C₂²	semidirect
46. #397×C₈₉	C₂²	semidirect
47. #397×C₈₉	C₂²	semidirect
50. #391×C₈₉	C₂²	semidirect
51. #390×C₈₉	C₂²	semidirect
52. #389×C₈₉	C₂²	semidirect
53. #389×C₈₉	C₂²	semidirect
54. #389×C₈₉	C₂²	semidirect
55. #389×C₈₉	C₂²	semidirect
56. #389×C₈₉	C₂²	semidirect
57. #389×C₈₉	C₂²	semidirect
60. #387×C₈₉	C₂²	semidirect
61. #387×C₈₉	C₂²	semidirect
65. #385×C₈₉	C₂²	semidirect
66. #384×C₈₉	C₂²	semidirect
67. #382×C₈₉	C₂²	semidirect
69. #381×C₈₉	C₂²	semidirect
79. #380×C₈₉	C₂²	semidirect
80. #380×C₈₉	C₂²	semidirect
366. C₂×C₄×C₈₉	#123	semidirect
423. #35516	C₈₉	direct (N × H)
436. C₂×#520	C₂×C₈₉	semidirect
437. #2487	C₂×C₈₉	semidirect
438. #2486	C₂×C₈₉	semidirect
439. #2485	C₂×C₈₉	semidirect
440. #2485	C₂×C₈₉	semidirect
441. #2423	C₂×C₈₉	semidirect
442. #2422	C₂×C₈₉	semidirect
443. #2421	C₂×C₈₉	semidirect
444. #2420	C₂×C₈₉	semidirect
445. #2419	C₂×C₈₉	semidirect
446. #2418	C₂×C₈₉	semidirect
447. #2317	C₂×C₈₉	semidirect
448. #2316	C₂×C₈₉	semidirect
449. #2311	C₂×C₈₉	semidirect
450. #2280	C₂×C₈₉	semidirect
451. C₂×#380	C₂×C₈₉	semidirect
452. C₈₉	#35516	direct (N × H)
464. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
468. C₂×C₄×D₄	C₂²×C₈₉	semidirect
472. C₂×#117	C₂²×C₈₉	semidirect
475. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
477. #400	C₂²×C₈₉	semidirect
479. #398	C₂²×C₈₉	semidirect
481. #397	C₂²×C₈₉	semidirect
482. #397	C₂²×C₈₉	semidirect
485. #391	C₂²×C₈₉	semidirect
486. #390	C₂²×C₈₉	semidirect
487. #389	C₂²×C₈₉	semidirect
488. #389	C₂²×C₈₉	semidirect
489. #389	C₂²×C₈₉	semidirect
490. #389	C₂²×C₈₉	semidirect
491. #389	C₂²×C₈₉	semidirect
492. #389	C₂²×C₈₉	semidirect
495. #387	C₂²×C₈₉	semidirect
496. #387	C₂²×C₈₉	semidirect
500. #385	C₂²×C₈₉	semidirect
501. #384	C₂²×C₈₉	semidirect
502. #382	C₂²×C₈₉	semidirect
504. #381	C₂²×C₈₉	semidirect
514. #380	C₂²×C₈₉	semidirect
515. #380	C₂²×C₈₉	semidirect
801. C₂×C₄	#123×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#525×C₈₉	2
C₂×#520×C₈₉	2
C₈₉×#2487	2
C₈₉×#2486	2
C₈₉×#2485	2
C₈₉×#2423	2
C₈₉×#2422	2
C₈₉×#2421	2
C₈₉×#2420	2
C₈₉×#2419	2
C₈₉×#2418	2
C₈₉×#2317	2
C₈₉×#2316	2
C₈₉×#2311	2
C₈₉×#2280	2
C₂×#380×C₈₉	2
#35516	89

Subgroups — C89×#35516 #36413364

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35516 #36413364