Subgroups — C₈₉×#35252 #36413100

Order 22784.

3602 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#535×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#525×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#121×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#117×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2856	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2850	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2620	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2619	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2416	C₂	1	4	yes	maximal, complemented
10	C₈₉×#2414	C₂	1	4	yes	maximal, complemented
11	C₈₉×#2411	C₂	1	4	yes	maximal, complemented
12	C₈₉×#2410	C₂	1	4	yes	maximal, complemented
13	C₈₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2311	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2309	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₈₉	C₂²	1	2	yes	—
19	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
20	#535×C₈₉	—	2	8	no	—
21	C₂×#127×C₈₉	C₂²	1	2	yes	complemented
22	C₂×#124×C₈₉	C₂²	1	2	yes	complemented
23	#525×C₈₉	—	2	8	no	—
24	C₂×#123×C₈₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
27	C₂×#121×C₈₉	—	2	8	no	—
28	C₂×#121×C₈₉	C₂²	1	2	yes	—
29	C₂×#121×C₈₉	C₂²	1	2	yes	—
30	C₂×#121×C₈₉	C₂²	1	2	yes	—
31	C₂×#121×C₈₉	C₂²	1	2	yes	—
32	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
33	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×#121×C₈₉	C₂²	1	4	yes	complemented
35	C₂×#121×C₈₉	C₂²	1	8	yes	complemented
36	C₂×#120×C₈₉	C₂²	1	2	yes	—
37	C₂×#120×C₈₉	C₂²	1	4	yes	—
38	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
39	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
40	C₂×#117×C₈₉	—	2	8	no	—
41	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#117×C₈₉	C₂²	1	2	yes	—
44	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
46	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
47	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
48	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
49	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
50	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
51	C₂²×C₄²×C₈₉	C₂²	1	2	yes	complemented
52	#396×C₈₉	C₂²	1	8	yes	complemented
53	#394×C₈₉	C₂²	1	8	yes	complemented
54	#394×C₈₉	C₂²	1	8	yes	complemented
55	#392×C₈₉	C₂²	1	8	yes	complemented
56	#391×C₈₉	C₂²	1	2	yes	complemented
57	#390×C₈₉	C₂²	1	2	yes	complemented
58	#390×C₈₉	C₂²	1	2	yes	complemented
59	#390×C₈₉	C₂²	1	4	yes	complemented
60	#390×C₈₉	C₂²	1	2	yes	complemented
61	#390×C₈₉	C₂²	1	8	yes	complemented
62	#389×C₈₉	C₂²	1	4	yes	complemented
63	#388×C₈₉	C₂²	1	8	yes	complemented
64	#386×C₈₉	C₂²	1	4	yes	—
65	#386×C₈₉	C₂²	1	8	yes	complemented
66	#385×C₈₉	C₂²	1	4	yes	—
67	#384×C₈₉	C₂²	1	2	yes	complemented
68	#382×C₈₉	C₂²	1	2	yes	complemented
69	#380×C₈₉	C₂²	1	4	yes	complemented
70	#379×C₈₉	C₂²	1	4	yes	—
71	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
72	C₂⁵×C₈₉	C₂³	1	2	yes	—
73	C₂×#41×C₈₉	—	2	4	no	—
74	C₂×#41×C₈₉	—	2	4	no	—
75	C₂×#41×C₈₉	—	2	4	no	—
76	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₈₉	—	2	8	no	—
78	C₂²×D₄×C₈₉	—	2	4	no	—
79	C₂²×D₄×C₈₉	—	2	4	no	—
80	C₂²×D₄×C₈₉	—	2	4	no	—
81	C₂²×D₄×C₈₉	—	4	8	no	—
82	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
83	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
84	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
85	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
86	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
89	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
90	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
91	C₂³×C₄×C₈₉	—	2	4	no	—
92	C₂³×C₄×C₈₉	—	2	4	no	—
93	C₂³×C₄×C₈₉	D₄	1	8	yes	complemented
94	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
95	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
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	1	yes	characteristic
100	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
102	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
103	#127×C₈₉	—	2	8	no	—
104	#124×C₈₉	—	2	8	no	—
105	#123×C₈₉	—	2	8	no	—
106	C₂²⋊Q₈×C₈₉	—	2	4	no	—
107	C₂²⋊Q₈×C₈₉	—	2	4	no	—
108	#121×C₈₉	—	2	8	no	—
109	#121×C₈₉	—	2	8	no	—
110	#121×C₈₉	—	2	8	no	—
111	#121×C₈₉	—	2	8	no	—
112	#121×C₈₉	—	2	4	no	—
113	#121×C₈₉	—	2	4	no	—
114	#121×C₈₉	—	2	16	no	—
115	#121×C₈₉	—	4	16	no	—
116	#120×C₈₉	—	2	8	no	—
117	#120×C₈₉	—	2	16	no	—
118	C₄×D₄×C₈₉	—	2	8	no	—
119	C₄×D₄×C₈₉	—	2	8	no	—
120	#117×C₈₉	—	2	4	no	—
121	#117×C₈₉	—	2	4	no	—
122	#117×C₈₉	—	2	8	no	—
123	#117×C₈₉	—	2	8	no	—
124	#117×C₈₉	—	2	8	no	—
125	#117×C₈₉	D₄	1	8	yes	complemented
126	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
127	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
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	1	yes	characteristic
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	2	yes	—
134	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
135	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
137	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
139	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
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	8	yes	—
144	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	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	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	8	yes	—
151	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
152	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
153	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
154	C₂×C₄²×C₈₉	—	2	8	no	—
155	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
156	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
159	#95×C₈₉	C₂³	1	8	yes	—
160	#95×C₈₉	C₂³	1	8	yes	—
161	C₂⁴×C₈₉	—	2	2	no	—
162	C₂⁴×C₈₉	—	2	2	no	—
163	C₂⁴×C₈₉	—	2	4	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	4	no	—
169	C₂⁴×C₈₉	—	4	4	no	—
170	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
171	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
172	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
173	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
174	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
175	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
176	#41×C₈₉	—	4	16	no	—
177	C₂×Q₈×C₈₉	—	2	2	no	—
178	C₂×Q₈×C₈₉	—	2	2	no	—
179	C₂×Q₈×C₈₉	—	2	2	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	8	no	—
185	C₂×D₄×C₈₉	—	2	8	no	—
186	C₂×D₄×C₈₉	—	2	4	no	—
187	C₂×D₄×C₈₉	—	2	8	no	—
188	C₂×D₄×C₈₉	—	2	16	no	—
189	C₂×D₄×C₈₉	—	2	4	no	—
190	C₂×D₄×C₈₉	—	2	4	no	—
191	C₂×D₄×C₈₉	—	2	4	no	—
192	C₂×D₄×C₈₉	—	2	2	no	—
193	C₂×D₄×C₈₉	—	2	4	no	—
194	C₂×D₄×C₈₉	—	2	2	no	—
195	C₂×D₄×C₈₉	—	2	16	no	—
196	C₂×D₄×C₈₉	—	2	4	no	—
197	C₂×D₄×C₈₉	—	2	4	no	—
198	C₂×D₄×C₈₉	—	2	2	no	—
199	C₂×D₄×C₈₉	—	4	8	no	—
200	C₂×D₄×C₈₉	—	4	4	no	—
201	C₂×D₄×C₈₉	—	4	8	no	—
202	C₂×D₄×C₈₉	—	4	8	no	—
203	C₂×D₄×C₈₉	—	4	32	no	—
204	C₂×D₄×C₈₉	—	4	16	no	—
205	C₂²×C₄×C₈₉	—	2	2	no	—
206	C₂²×C₄×C₈₉	—	2	2	no	—
207	C₂²×C₄×C₈₉	—	2	32	no	—
208	C₂²×C₄×C₈₉	—	2	2	no	—
209	C₂²×C₄×C₈₉	—	2	2	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	2	no	—
214	C₂²×C₄×C₈₉	—	2	2	no	—
215	C₂²×C₄×C₈₉	—	2	2	no	—
216	C₂²×C₄×C₈₉	—	2	4	no	—
217	C₂²×C₄×C₈₉	—	2	8	no	—
218	C₂²×C₄×C₈₉	—	2	8	no	—
219	C₂²×C₄×C₈₉	—	2	4	no	—
220	C₂²×C₄×C₈₉	—	2	4	no	—
221	C₂²×C₄×C₈₉	—	2	4	no	—
222	C₂²×C₄×C₈₉	—	4	4	no	—
223	C₂²×C₄×C₈₉	—	4	4	no	—
224	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
225	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
226	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
227	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
228	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
229	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
230	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
231	C₂²×C₄×C₈₉	#41	1	4	yes	—
232	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
235	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
236	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
238	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
242	C₄⋊C₄×C₈₉	—	2	8	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	2	no	—
247	C₄⋊C₄×C₈₉	—	2	2	no	—
248	C₄⋊C₄×C₈₉	—	2	4	no	—
249	C₄⋊C₄×C₈₉	—	2	4	no	—
250	C₄⋊C₄×C₈₉	—	4	8	no	—
251	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	complemented
252	C₂²⋊C₄×C₈₉	—	2	4	no	—
253	C₂²⋊C₄×C₈₉	—	2	4	no	—
254	C₂²⋊C₄×C₈₉	—	2	4	no	—
255	C₂²⋊C₄×C₈₉	—	2	4	no	—
256	C₂²⋊C₄×C₈₉	—	2	8	no	—
257	C₂²⋊C₄×C₈₉	—	2	8	no	—
258	C₂²⋊C₄×C₈₉	—	2	8	no	—
259	C₂²⋊C₄×C₈₉	—	2	4	no	—
260	C₂²⋊C₄×C₈₉	—	2	4	no	—
261	C₂²⋊C₄×C₈₉	—	2	16	no	—
262	C₂²⋊C₄×C₈₉	—	4	8	no	—
263	C₂²⋊C₄×C₈₉	—	4	8	no	—
264	C₂²⋊C₄×C₈₉	—	4	8	no	—
265	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
266	C₄²×C₈₉	—	2	8	no	—
267	C₄²×C₈₉	—	2	4	no	—
268	C₄²×C₈₉	—	2	4	no	—
269	C₄²×C₈₉	C₂×D₄	1	8	yes	complemented
270	C₂³×C₈₉	—	2	1	no	—
271	C₂³×C₈₉	—	2	1	no	—
272	C₂³×C₈₉	—	2	2	no	—
273	C₂³×C₈₉	—	2	2	no	—
274	C₂³×C₈₉	—	2	2	no	—
275	C₂³×C₈₉	—	2	8	no	—
276	C₂³×C₈₉	—	2	8	no	—
277	C₂³×C₈₉	—	2	1	no	—
278	C₂³×C₈₉	—	2	1	no	—
279	C₂³×C₈₉	—	2	2	no	—
280	C₂³×C₈₉	—	2	2	no	—
281	C₂³×C₈₉	—	2	2	no	—
282	C₂³×C₈₉	—	2	4	no	—
283	C₂³×C₈₉	—	2	4	no	—
284	C₂³×C₈₉	—	2	2	no	—
285	C₂³×C₈₉	—	2	2	no	—
286	C₂³×C₈₉	—	2	4	no	—
287	C₂³×C₈₉	—	2	4	no	—
288	C₂³×C₈₉	—	2	8	no	—
289	C₂³×C₈₉	—	2	8	no	—
290	C₂³×C₈₉	—	2	4	no	—
291	C₂³×C₈₉	—	4	4	no	—
292	C₂³×C₈₉	—	4	8	no	—
293	C₂³×C₈₉	—	4	8	no	—
294	C₂³×C₈₉	—	4	8	no	—
295	C₂³×C₈₉	—	4	8	no	—
296	C₂³×C₈₉	—	4	8	no	—
297	C₂³×C₈₉	—	8	8	no	—
298	C₂³×C₈₉	—	8	8	no	—
299	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
300	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
301	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
302	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
303	C₂³×C₈₉	C₂×#41	1	2	yes	—
304	C₂³×C₈₉	H(5,𝔽₂)	1	4	yes	—
305	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
306	Q₈×C₈₉	—	4	4	no	—
307	D₄×C₈₉	—	4	8	no	—
308	D₄×C₈₉	—	4	16	no	—
309	D₄×C₈₉	—	4	8	no	—
310	D₄×C₈₉	—	4	8	no	—
311	D₄×C₈₉	—	4	16	no	—
312	D₄×C₈₉	—	4	8	no	—
313	D₄×C₈₉	—	4	8	no	—
314	D₄×C₈₉	—	4	4	no	—
315	D₄×C₈₉	—	8	16	no	—
316	C₂×C₄×C₈₉	—	2	8	no	—
317	C₂×C₄×C₈₉	—	2	1	no	—
318	C₂×C₄×C₈₉	—	2	1	no	—
319	C₂×C₄×C₈₉	—	2	1	no	—
320	C₂×C₄×C₈₉	—	2	1	no	—
321	C₂×C₄×C₈₉	—	2	4	no	—
322	C₂×C₄×C₈₉	—	2	4	no	—
323	C₂×C₄×C₈₉	—	2	8	no	—
324	C₂×C₄×C₈₉	—	2	8	no	—
325	C₂×C₄×C₈₉	—	2	8	no	—
326	C₂×C₄×C₈₉	—	2	8	no	—
327	C₂×C₄×C₈₉	—	2	4	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	2	no	—
334	C₂×C₄×C₈₉	—	2	4	no	—
335	C₂×C₄×C₈₉	—	2	4	no	—
336	C₂×C₄×C₈₉	—	2	8	no	—
337	C₂×C₄×C₈₉	—	2	4	no	—
338	C₂×C₄×C₈₉	—	2	4	no	—
339	C₂×C₄×C₈₉	—	4	16	no	—
340	C₂×C₄×C₈₉	—	4	8	no	—
341	C₂×C₄×C₈₉	—	4	8	no	—
342	C₂×C₄×C₈₉	#121	1	16	yes	complemented
343	C₂×C₄×C₈₉	C₂²×D₄	1	8	yes	—
344	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
345	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
347	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
348	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
349	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
350	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
351	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
352	C₂²×C₈₉	—	2	2	no	—
353	C₂²×C₈₉	—	2	2	no	—
354	C₂²×C₈₉	—	2	2	no	—
355	C₂²×C₈₉	—	2	2	no	—
356	C₂²×C₈₉	—	2	4	no	—
357	C₂²×C₈₉	—	2	4	no	—
358	C₂²×C₈₉	—	2	4	no	—
359	C₂²×C₈₉	—	2	4	no	—
360	C₂²×C₈₉	—	2	2	no	—
361	C₂²×C₈₉	—	2	2	no	—
362	C₂²×C₈₉	—	2	2	no	—
363	C₂²×C₈₉	—	4	16	no	—
364	C₂²×C₈₉	—	4	2	no	—
365	C₂²×C₈₉	—	4	2	no	—
366	C₂²×C₈₉	—	4	2	no	—
367	C₂²×C₈₉	—	4	4	no	—
368	C₂²×C₈₉	—	4	4	no	—
369	C₂²×C₈₉	—	4	2	no	—
370	C₂²×C₈₉	—	4	2	no	—
371	C₂²×C₈₉	—	4	4	no	—
372	C₂²×C₈₉	—	4	4	no	—
373	C₂²×C₈₉	—	4	8	no	—
374	C₂²×C₈₉	—	4	4	no	—
375	C₂²×C₈₉	—	4	8	no	—
376	C₂²×C₈₉	—	8	16	no	—
377	C₂²×C₈₉	C₂×#121	1	4	yes	—
378	C₂²×C₈₉	#535	1	4	yes	complemented
379	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
380	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
381	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
382	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
383	C₂²×C₈₉	#585	1	2	yes	—
384	C₄×C₈₉	—	2	2	no	—
385	C₄×C₈₉	—	2	2	no	—
386	C₄×C₈₉	—	2	8	no	—
387	C₄×C₈₉	—	4	2	no	—
388	C₄×C₈₉	—	4	4	no	—
389	C₄×C₈₉	—	4	2	no	—
390	C₄×C₈₉	—	4	2	no	—
391	C₄×C₈₉	—	4	4	no	—
392	C₄×C₈₉	C₂×#121	1	4	yes	—
393	C₄×C₈₉	C₂×#121	1	4	yes	—
394	#35252	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
395	C₂×C₈₉	—	2	4	no	—
396	C₂×C₈₉	—	2	4	no	—
397	C₂×C₈₉	—	4	2	no	—
398	C₂×C₈₉	—	8	2	no	—
399	C₂×C₈₉	—	8	4	no	—
400	C₂×C₈₉	C₂²×#121	1	1	yes	characteristic
401	C₂×C₈₉	C₂×#535	1	1	yes	characteristic
402	C₂×C₈₉	#3449	1	1	yes	characteristic
403	C₂×C₈₉	#3488	1	2	yes	—
404	C₂×C₈₉	#3494	1	2	yes	—
405	C₂×#535	C₂×C₈₉	1	1	yes	characteristic, complemented
406	C₂×#525	C₂×C₈₉	1	1	yes	characteristic, complemented
407	C₂²×#121	C₂×C₈₉	1	1	yes	characteristic, complemented
408	C₂²×#117	C₂×C₈₉	1	1	yes	characteristic, complemented
409	#2856	C₂×C₈₉	1	2	yes	complemented
410	#2850	C₂×C₈₉	1	2	yes	complemented
411	#2620	C₂×C₈₉	1	2	yes	complemented
412	#2619	C₂×C₈₉	1	2	yes	complemented
413	#2416	C₂×C₈₉	1	4	yes	complemented
414	#2414	C₂×C₈₉	1	4	yes	complemented
415	#2411	C₂×C₈₉	1	4	yes	complemented
416	#2410	C₂×C₈₉	1	4	yes	complemented
417	#2317	C₂×C₈₉	1	1	yes	characteristic, complemented
418	#2311	C₂×C₈₉	1	1	yes	characteristic, complemented
419	#2309	C₂×C₈₉	1	1	yes	characteristic, complemented
420	C₈₉	#35252	1	1	yes	characteristic, direct product factor, Sylow
421	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
422	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
423	C₂³×D₄	C₂²×C₈₉	1	2	yes	—
424	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
425	#535	—	2	8	no	—
426	C₂×#127	C₂²×C₈₉	1	2	yes	complemented
427	C₂×#124	C₂²×C₈₉	1	2	yes	complemented
428	#525	—	2	8	no	—
429	C₂×#123	C₂²×C₈₉	1	2	yes	—
430	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
431	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
432	C₂×#121	—	2	8	no	—
433	C₂×#121	C₂²×C₈₉	1	2	yes	—
434	C₂×#121	C₂²×C₈₉	1	2	yes	—
435	C₂×#121	C₂²×C₈₉	1	2	yes	—
436	C₂×#121	C₂²×C₈₉	1	2	yes	—
437	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic, complemented
438	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic, complemented
439	C₂×#121	C₂²×C₈₉	1	4	yes	complemented
440	C₂×#121	C₂²×C₈₉	1	8	yes	complemented
441	C₂×#120	C₂²×C₈₉	1	2	yes	—
442	C₂×#120	C₂²×C₈₉	1	4	yes	—
443	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
444	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
445	C₂×#117	—	2	8	no	—
446	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
447	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
448	C₂×#117	C₂²×C₈₉	1	2	yes	—
449	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
450	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
451	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
452	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
453	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
454	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
455	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
456	C₂²×C₄²	C₂²×C₈₉	1	2	yes	complemented
457	#396	C₂²×C₈₉	1	8	yes	complemented
458	#394	C₂²×C₈₉	1	8	yes	complemented
459	#394	C₂²×C₈₉	1	8	yes	complemented
460	#392	C₂²×C₈₉	1	8	yes	complemented
461	#391	C₂²×C₈₉	1	2	yes	complemented
462	#390	C₂²×C₈₉	1	2	yes	complemented
463	#390	C₂²×C₈₉	1	2	yes	complemented
464	#390	C₂²×C₈₉	1	4	yes	complemented
465	#390	C₂²×C₈₉	1	2	yes	complemented
466	#390	C₂²×C₈₉	1	8	yes	complemented
467	#389	C₂²×C₈₉	1	4	yes	complemented
468	#388	C₂²×C₈₉	1	8	yes	complemented
469	#386	C₂²×C₈₉	1	4	yes	—
470	#386	C₂²×C₈₉	1	8	yes	complemented
471	#385	C₂²×C₈₉	1	4	yes	—
472	#384	C₂²×C₈₉	1	2	yes	complemented
473	#382	C₂²×C₈₉	1	2	yes	complemented
474	#380	C₂²×C₈₉	1	4	yes	complemented
475	#379	C₂²×C₈₉	1	4	yes	—
476	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
477	C₂⁵	C₂³×C₈₉	1	2	yes	—
478	C₂×#41	—	2	4	no	—
479	C₂×#41	—	2	4	no	—
480	C₂×#41	—	2	4	no	—
481	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
482	C₂²×D₄	—	2	8	no	—
483	C₂²×D₄	—	2	4	no	—
484	C₂²×D₄	—	2	4	no	—
485	C₂²×D₄	—	2	4	no	—
486	C₂²×D₄	—	4	8	no	—
487	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
488	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
489	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
490	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
491	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
492	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
493	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
494	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
495	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
496	C₂³×C₄	—	2	4	no	—
497	C₂³×C₄	—	2	4	no	—
498	C₂³×C₄	D₄×C₈₉	1	8	yes	complemented
499	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
500	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
501	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
502	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
503	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
504	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
505	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
506	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
507	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
508	#127	—	2	8	no	—
509	#124	—	2	8	no	—
510	#123	—	2	8	no	—
511	C₂²⋊Q₈	—	2	4	no	—
512	C₂²⋊Q₈	—	2	4	no	—
513	#121	—	2	8	no	—
514	#121	—	2	8	no	—
515	#121	—	2	8	no	—
516	#121	—	2	8	no	—
517	#121	—	2	4	no	—
518	#121	—	2	4	no	—
519	#121	—	2	16	no	—
520	#121	—	4	16	no	—
521	#120	—	2	8	no	—
522	#120	—	2	16	no	—
523	C₄×D₄	—	2	8	no	—
524	C₄×D₄	—	2	8	no	—
525	#117	—	2	4	no	—
526	#117	—	2	4	no	—
527	#117	—	2	8	no	—
528	#117	—	2	8	no	—
529	#117	—	2	8	no	—
530	#117	D₄×C₈₉	1	8	yes	complemented
531	C₂×C₄⋊C₄	—	2	4	no	—
532	C₂×C₄⋊C₄	—	2	8	no	—
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	4	yes	—
537	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
542	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
543	C₂×C₂²⋊C₄	—	2	8	no	—
544	C₂×C₂²⋊C₄	—	2	8	no	—
545	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	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	8	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
559	C₂×C₄²	—	2	8	no	—
560	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
561	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
562	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
563	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
564	#95	C₂³×C₈₉	1	8	yes	—
565	#95	C₂³×C₈₉	1	8	yes	—
566	C₂⁴	—	2	2	no	—
567	C₂⁴	—	2	2	no	—
568	C₂⁴	—	2	4	no	—
569	C₂⁴	—	2	4	no	—
570	C₂⁴	—	2	4	no	—
571	C₂⁴	—	2	4	no	—
572	C₂⁴	—	4	2	no	—
573	C₂⁴	—	4	4	no	—
574	C₂⁴	—	4	4	no	—
575	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
576	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
577	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
578	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
579	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
580	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
581	#41	—	4	16	no	—
582	C₂×Q₈	—	2	2	no	—
583	C₂×Q₈	—	2	2	no	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	8	no	—
590	C₂×D₄	—	2	8	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	8	no	—
593	C₂×D₄	—	2	16	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	16	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	2	no	—
604	C₂×D₄	—	4	8	no	—
605	C₂×D₄	—	4	4	no	—
606	C₂×D₄	—	4	8	no	—
607	C₂×D₄	—	4	8	no	—
608	C₂×D₄	—	4	32	no	—
609	C₂×D₄	—	4	16	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	32	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	8	no	—
623	C₂²×C₄	—	2	8	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	4	4	no	—
628	C₂²×C₄	—	4	4	no	—
629	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
630	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
631	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
632	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
633	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
634	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
635	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
636	C₂²×C₄	#41×C₈₉	1	4	yes	—
637	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
640	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
641	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
643	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
644	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
645	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
646	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
647	C₄⋊C₄	—	2	8	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	4	8	no	—
656	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	complemented
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	8	no	—
662	C₂²⋊C₄	—	2	8	no	—
663	C₂²⋊C₄	—	2	8	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	16	no	—
667	C₂²⋊C₄	—	4	8	no	—
668	C₂²⋊C₄	—	4	8	no	—
669	C₂²⋊C₄	—	4	8	no	—
670	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
671	C₄²	—	2	8	no	—
672	C₄²	—	2	4	no	—
673	C₄²	—	2	4	no	—
674	C₄²	C₂×D₄×C₈₉	1	8	yes	complemented
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	8	no	—
681	C₂³	—	2	8	no	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	1	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	4	no	—
688	C₂³	—	2	4	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	4	no	—
692	C₂³	—	2	4	no	—
693	C₂³	—	2	8	no	—
694	C₂³	—	2	8	no	—
695	C₂³	—	2	4	no	—
696	C₂³	—	4	4	no	—
697	C₂³	—	4	8	no	—
698	C₂³	—	4	8	no	—
699	C₂³	—	4	8	no	—
700	C₂³	—	4	8	no	—
701	C₂³	—	4	8	no	—
702	C₂³	—	8	8	no	—
703	C₂³	—	8	8	no	—
704	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
705	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
706	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
707	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
708	C₂³	C₂×#41×C₈₉	1	2	yes	—
709	C₂³	H(5,𝔽₂)×C₈₉	1	4	yes	—
710	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
711	Q₈	—	4	4	no	—
712	D₄	—	4	8	no	—
713	D₄	—	4	16	no	—
714	D₄	—	4	8	no	—
715	D₄	—	4	8	no	—
716	D₄	—	4	16	no	—
717	D₄	—	4	8	no	—
718	D₄	—	4	8	no	—
719	D₄	—	4	4	no	—
720	D₄	—	8	16	no	—
721	C₂×C₄	—	2	8	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	2	4	no	—
728	C₂×C₄	—	2	8	no	—
729	C₂×C₄	—	2	8	no	—
730	C₂×C₄	—	2	8	no	—
731	C₂×C₄	—	2	8	no	—
732	C₂×C₄	—	2	4	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	4	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	4	no	—
740	C₂×C₄	—	2	4	no	—
741	C₂×C₄	—	2	8	no	—
742	C₂×C₄	—	2	4	no	—
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	4	16	no	—
745	C₂×C₄	—	4	8	no	—
746	C₂×C₄	—	4	8	no	—
747	C₂×C₄	#121×C₈₉	1	16	yes	complemented
748	C₂×C₄	C₂²×D₄×C₈₉	1	8	yes	—
749	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
750	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
751	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
752	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
753	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
754	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
755	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
756	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
757	C₂²	—	2	2	no	—
758	C₂²	—	2	2	no	—
759	C₂²	—	2	2	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	4	no	—
762	C₂²	—	2	4	no	—
763	C₂²	—	2	4	no	—
764	C₂²	—	2	4	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	4	16	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	4	no	—
773	C₂²	—	4	4	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	4	no	—
777	C₂²	—	4	4	no	—
778	C₂²	—	4	8	no	—
779	C₂²	—	4	8	no	—
780	C₂²	—	4	4	no	—
781	C₂²	—	8	16	no	—
782	C₂²	C₂×#121×C₈₉	1	4	yes	—
783	C₂²	#535×C₈₉	1	4	yes	complemented
784	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
785	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
786	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
787	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
788	C₂²	#585×C₈₉	1	2	yes	—
789	C₄	—	2	2	no	—
790	C₄	—	2	2	no	—
791	C₄	—	2	8	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	4	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	4	no	—
797	C₄	C₂×#121×C₈₉	1	4	yes	—
798	C₄	C₂×#121×C₈₉	1	4	yes	—
799	C₂	—	2	4	no	—
800	C₂	—	2	4	no	—
801	C₂	—	4	2	no	—
802	C₂	—	8	2	no	—
803	C₂	—	8	4	no	—
804	C₂	C₂²×#121×C₈₉	1	1	yes	characteristic
805	C₂	C₂×#535×C₈₉	1	1	yes	characteristic
806	C₂	C₈₉×#3449	1	1	yes	characteristic
807	C₂	C₈₉×#3488	1	2	yes	—
808	C₂	C₈₉×#3494	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
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. C₂×#535×C₈₉	C₂	semidirect
2. C₂×#525×C₈₉	C₂	semidirect
3. C₂²×#121×C₈₉	C₂	semidirect
4. C₂²×#117×C₈₉	C₂	semidirect
5. C₈₉×#2856	C₂	semidirect
6. C₈₉×#2850	C₂	semidirect
7. C₈₉×#2620	C₂	semidirect
8. C₈₉×#2619	C₂	semidirect
9. C₈₉×#2416	C₂	semidirect
10. C₈₉×#2414	C₂	semidirect
11. C₈₉×#2411	C₂	semidirect
12. C₈₉×#2410	C₂	semidirect
13. C₈₉×#2317	C₂	semidirect
14. C₈₉×#2311	C₂	semidirect
15. C₈₉×#2309	C₂	semidirect
21. C₂×#127×C₈₉	C₂²	semidirect
22. C₂×#124×C₈₉	C₂²	semidirect
25. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
26. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
32. C₂×#121×C₈₉	C₂²	semidirect
33. C₂×#121×C₈₉	C₂²	semidirect
34. C₂×#121×C₈₉	C₂²	semidirect
35. C₂×#121×C₈₉	C₂²	semidirect
38. C₂×C₄×D₄×C₈₉	C₂²	semidirect
39. C₂×C₄×D₄×C₈₉	C₂²	semidirect
45. C₂×#117×C₈₉	C₂²	semidirect
46. C₂×#117×C₈₉	C₂²	semidirect
48. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
51. C₂²×C₄²×C₈₉	C₂²	semidirect
52. #396×C₈₉	C₂²	semidirect
53. #394×C₈₉	C₂²	semidirect
54. #394×C₈₉	C₂²	semidirect
55. #392×C₈₉	C₂²	semidirect
56. #391×C₈₉	C₂²	semidirect
57. #390×C₈₉	C₂²	semidirect
58. #390×C₈₉	C₂²	semidirect
59. #390×C₈₉	C₂²	semidirect
60. #390×C₈₉	C₂²	semidirect
61. #390×C₈₉	C₂²	semidirect
62. #389×C₈₉	C₂²	semidirect
63. #388×C₈₉	C₂²	semidirect
65. #386×C₈₉	C₂²	semidirect
67. #384×C₈₉	C₂²	semidirect
68. #382×C₈₉	C₂²	semidirect
69. #380×C₈₉	C₂²	semidirect
93. C₂³×C₄×C₈₉	D₄	semidirect
125. #117×C₈₉	D₄	semidirect
251. C₄⋊C₄×C₈₉	C₂×D₄	semidirect
269. C₄²×C₈₉	C₂×D₄	semidirect
342. C₂×C₄×C₈₉	#121	semidirect
378. C₂²×C₈₉	#535	semidirect
394. #35252	C₈₉	direct (N × H)
405. C₂×#535	C₂×C₈₉	semidirect
406. C₂×#525	C₂×C₈₉	semidirect
407. C₂²×#121	C₂×C₈₉	semidirect
408. C₂²×#117	C₂×C₈₉	semidirect
409. #2856	C₂×C₈₉	semidirect
410. #2850	C₂×C₈₉	semidirect
411. #2620	C₂×C₈₉	semidirect
412. #2619	C₂×C₈₉	semidirect
413. #2416	C₂×C₈₉	semidirect
414. #2414	C₂×C₈₉	semidirect
415. #2411	C₂×C₈₉	semidirect
416. #2410	C₂×C₈₉	semidirect
417. #2317	C₂×C₈₉	semidirect
418. #2311	C₂×C₈₉	semidirect
419. #2309	C₂×C₈₉	semidirect
420. C₈₉	#35252	direct (N × H)
426. C₂×#127	C₂²×C₈₉	semidirect
427. C₂×#124	C₂²×C₈₉	semidirect
430. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
431. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
437. C₂×#121	C₂²×C₈₉	semidirect
438. C₂×#121	C₂²×C₈₉	semidirect
439. C₂×#121	C₂²×C₈₉	semidirect
440. C₂×#121	C₂²×C₈₉	semidirect
443. C₂×C₄×D₄	C₂²×C₈₉	semidirect
444. C₂×C₄×D₄	C₂²×C₈₉	semidirect
450. C₂×#117	C₂²×C₈₉	semidirect
451. C₂×#117	C₂²×C₈₉	semidirect
453. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
456. C₂²×C₄²	C₂²×C₈₉	semidirect
457. #396	C₂²×C₈₉	semidirect
458. #394	C₂²×C₈₉	semidirect
459. #394	C₂²×C₈₉	semidirect
460. #392	C₂²×C₈₉	semidirect
461. #391	C₂²×C₈₉	semidirect
462. #390	C₂²×C₈₉	semidirect
463. #390	C₂²×C₈₉	semidirect
464. #390	C₂²×C₈₉	semidirect
465. #390	C₂²×C₈₉	semidirect
466. #390	C₂²×C₈₉	semidirect
467. #389	C₂²×C₈₉	semidirect
468. #388	C₂²×C₈₉	semidirect
470. #386	C₂²×C₈₉	semidirect
472. #384	C₂²×C₈₉	semidirect
473. #382	C₂²×C₈₉	semidirect
474. #380	C₂²×C₈₉	semidirect
498. C₂³×C₄	D₄×C₈₉	semidirect
530. #117	D₄×C₈₉	semidirect
656. C₄⋊C₄	C₂×D₄×C₈₉	semidirect
674. C₄²	C₂×D₄×C₈₉	semidirect
747. C₂×C₄	#121×C₈₉	semidirect
783. C₂²	#535×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#535×C₈₉	2
C₂×#525×C₈₉	2
C₂²×#121×C₈₉	2
C₂²×#117×C₈₉	2
C₈₉×#2856	2
C₈₉×#2850	2
C₈₉×#2620	2
C₈₉×#2619	2
C₈₉×#2416	2
C₈₉×#2414	2
C₈₉×#2411	2
C₈₉×#2410	2
C₈₉×#2317	2
C₈₉×#2311	2
C₈₉×#2309	2
#35252	89

Subgroups — C89×#35252 #36413100

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35252 #36413100