Subgroups — C₈₉×#36748 #36414596

Order 22784.

1858 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2848	C₂	1	2	yes	maximal
2	C₈₉×#2807	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2790	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2788	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2768	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2763	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2742	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2729	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2720	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2704	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2677	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2626	C₂	1	1	yes	maximal, characteristic
13	C₈₉×#2626	C₂	1	1	yes	maximal, characteristic
14	C₈₉×#2569	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2549	C₂	1	2	yes	maximal, complemented
16	C₈₉×#2442	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2440	C₂	1	2	yes	maximal, complemented
18	C₈₉×#2312	C₂	1	2	yes	maximal
19	C₂×#385×C₈₉	C₂	1	1	yes	maximal, characteristic
20	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
22	C₂×#125×C₈₉	C₂²	1	2	yes	complemented
23	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
31	#400×C₈₉	C₂²	1	2	yes	complemented
32	#400×C₈₉	C₂²	1	2	yes	complemented
33	#400×C₈₉	C₂²	1	2	yes	complemented
34	#400×C₈₉	C₂²	1	2	yes	complemented
35	#399×C₈₉	C₂²	1	1	yes	characteristic
36	#399×C₈₉	C₂²	1	1	yes	characteristic
37	#399×C₈₉	C₂²	1	1	yes	characteristic
38	#399×C₈₉	C₂²	1	1	yes	characteristic
39	#398×C₈₉	C₂²	1	2	yes	complemented
40	#398×C₈₉	C₂²	1	2	yes	complemented
41	#398×C₈₉	C₂²	1	2	yes	complemented
42	#398×C₈₉	C₂²	1	2	yes	complemented
43	#398×C₈₉	C₂²	1	2	yes	complemented
44	#398×C₈₉	C₂²	1	2	yes	complemented
45	#398×C₈₉	C₂²	1	2	yes	complemented
46	#398×C₈₉	C₂²	1	2	yes	complemented
47	#396×C₈₉	C₂²	1	2	yes	—
48	#396×C₈₉	C₂²	1	2	yes	—
49	#396×C₈₉	C₂²	1	2	yes	—
50	#396×C₈₉	C₂²	1	2	yes	—
51	#395×C₈₉	C₂²	1	2	yes	complemented
52	#395×C₈₉	C₂²	1	2	yes	complemented
53	#395×C₈₉	C₂²	1	2	yes	complemented
54	#395×C₈₉	C₂²	1	2	yes	complemented
55	#393×C₈₉	C₂²	1	1	yes	characteristic
56	#393×C₈₉	C₂²	1	1	yes	characteristic
57	#393×C₈₉	C₂²	1	1	yes	characteristic
58	#393×C₈₉	C₂²	1	1	yes	characteristic
59	#391×C₈₉	C₂²	1	2	yes	complemented
60	#391×C₈₉	C₂²	1	2	yes	complemented
61	#389×C₈₉	C₂²	1	2	yes	complemented
62	#389×C₈₉	C₂²	1	2	yes	complemented
63	#389×C₈₉	C₂²	1	2	yes	complemented
64	#389×C₈₉	C₂²	1	2	yes	complemented
65	#389×C₈₉	C₂²	1	2	yes	complemented
66	#389×C₈₉	C₂²	1	2	yes	complemented
67	#388×C₈₉	C₂²	1	2	yes	—
68	#388×C₈₉	C₂²	1	2	yes	—
69	#388×C₈₉	C₂²	1	2	yes	—
70	#388×C₈₉	C₂²	1	2	yes	—
71	#388×C₈₉	C₂²	1	2	yes	—
72	#388×C₈₉	C₂²	1	2	yes	—
73	#388×C₈₉	C₂²	1	2	yes	—
74	#388×C₈₉	C₂²	1	2	yes	—
75	#387×C₈₉	C₂²	1	2	yes	complemented
76	#387×C₈₉	C₂²	1	2	yes	complemented
77	#387×C₈₉	C₂²	1	2	yes	complemented
78	#387×C₈₉	C₂²	1	2	yes	complemented
79	#385×C₈₉	C₂²	1	2	yes	—
80	#385×C₈₉	C₂²	1	1	yes	characteristic
81	#385×C₈₉	C₂²	1	2	yes	—
82	#385×C₈₉	C₂²	1	2	yes	—
83	#385×C₈₉	C₂²	1	2	yes	—
84	#385×C₈₉	C₂²	1	2	yes	—
85	#385×C₈₉	C₂²	1	2	yes	—
86	#385×C₈₉	C₂²	1	2	yes	—
87	#385×C₈₉	C₂²	1	2	yes	—
88	#385×C₈₉	C₂²	1	1	yes	characteristic
89	#385×C₈₉	C₂²	1	1	yes	characteristic
90	#385×C₈₉	C₂²	1	2	yes	—
91	#385×C₈₉	C₂²	1	2	yes	—
92	#385×C₈₉	C₂²	1	1	yes	characteristic
93	#384×C₈₉	C₂²	1	2	yes	complemented
94	#382×C₈₉	C₂²	1	2	yes	complemented
95	#380×C₈₉	C₂²	1	2	yes	—
96	#380×C₈₉	C₂²	1	2	yes	—
97	#380×C₈₉	C₂²	1	1	yes	characteristic
98	#380×C₈₉	C₂²	1	2	yes	—
99	#380×C₈₉	C₂²	1	2	yes	—
100	#380×C₈₉	C₂²	1	2	yes	—
101	#380×C₈₉	C₂²	1	1	yes	characteristic
102	#379×C₈₉	C₂²	1	2	yes	—
103	#379×C₈₉	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
106	C₂×#95×C₈₉	C₂²	1	2	yes	—
107	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
109	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₈₉	—	4	4	no	—
112	C₂³×C₄×C₈₉	—	4	2	no	—
113	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
114	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
117	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
120	C₄⋊Q₈×C₈₉	—	4	4	no	—
121	#125×C₈₉	—	4	4	no	—
122	C₂²⋊Q₈×C₈₉	—	4	4	no	—
123	C₂²⋊Q₈×C₈₉	—	4	2	no	—
124	C₂²⋊Q₈×C₈₉	—	4	2	no	—
125	C₂²⋊Q₈×C₈₉	—	4	4	no	—
126	C₂²⋊Q₈×C₈₉	—	4	4	no	—
127	C₂×C₄⋊C₄×C₈₉	—	4	4	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	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	2	yes	—
143	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₈₉	—	4	2	no	—
156	C₂×C₂²⋊C₄×C₈₉	Q₈	1	8	yes	complemented
157	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
176	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
177	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
178	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
179	C₂×C₄²×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	1	yes	characteristic
189	#95×C₈₉	C₂³	1	2	yes	—
190	#95×C₈₉	C₂³	1	2	yes	—
191	#95×C₈₉	C₂³	1	2	yes	—
192	#95×C₈₉	C₂³	1	2	yes	—
193	#95×C₈₉	C₂³	1	2	yes	—
194	#95×C₈₉	C₂³	1	2	yes	—
195	#95×C₈₉	C₂³	1	2	yes	—
196	#95×C₈₉	C₂³	1	2	yes	—
197	#95×C₈₉	C₂³	1	1	yes	characteristic
198	#95×C₈₉	C₂³	1	1	yes	characteristic
199	#95×C₈₉	C₂³	1	2	yes	—
200	#95×C₈₉	C₂³	1	2	yes	—
201	#95×C₈₉	C₂³	1	1	yes	characteristic
202	#95×C₈₉	C₂³	1	2	yes	—
203	#95×C₈₉	C₂³	1	2	yes	—
204	#95×C₈₉	C₂³	1	2	yes	—
205	#95×C₈₉	C₂³	1	2	yes	—
206	C₂⁴×C₈₉	—	2	2	no	—
207	C₂⁴×C₈₉	—	2	2	no	—
208	C₂⁴×C₈₉	—	4	2	no	—
209	C₂⁴×C₈₉	—	4	2	no	—
210	C₂⁴×C₈₉	C₂×Q₈	1	4	yes	—
211	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
212	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
213	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
214	C₂×Q₈×C₈₉	—	2	4	no	—
215	C₂×Q₈×C₈₉	—	4	2	no	—
216	C₂×Q₈×C₈₉	—	4	2	no	—
217	C₂×Q₈×C₈₉	—	4	1	no	—
218	C₂×Q₈×C₈₉	—	4	1	no	—
219	C₂×Q₈×C₈₉	—	4	2	no	—
220	C₂×Q₈×C₈₉	—	4	2	no	—
221	C₂²×C₄×C₈₉	—	2	4	no	—
222	C₂²×C₄×C₈₉	—	2	2	no	—
223	C₂²×C₄×C₈₉	—	2	2	no	—
224	C₂²×C₄×C₈₉	—	2	4	no	—
225	C₂²×C₄×C₈₉	—	2	4	no	—
226	C₂²×C₄×C₈₉	—	2	4	no	—
227	C₂²×C₄×C₈₉	—	4	2	no	—
228	C₂²×C₄×C₈₉	—	4	1	no	—
229	C₂²×C₄×C₈₉	—	4	2	no	—
230	C₂²×C₄×C₈₉	—	4	2	no	—
231	C₂²×C₄×C₈₉	—	4	2	no	—
232	C₂²×C₄×C₈₉	—	4	2	no	—
233	C₂²×C₄×C₈₉	—	4	1	no	—
234	C₂²×C₄×C₈₉	—	4	2	no	—
235	C₂²×C₄×C₈₉	—	4	2	no	—
236	C₂²×C₄×C₈₉	—	4	2	no	—
237	C₂²×C₄×C₈₉	—	4	16	no	—
238	C₂²×C₄×C₈₉	C₂×Q₈	1	8	yes	—
239	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₈₉	C₂⁴	1	2	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	2	yes	—
247	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
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	4	no	—
259	C₄⋊C₄×C₈₉	—	2	4	no	—
260	C₄⋊C₄×C₈₉	—	4	2	no	—
261	C₄⋊C₄×C₈₉	—	4	2	no	—
262	C₄⋊C₄×C₈₉	—	4	2	no	—
263	C₄⋊C₄×C₈₉	—	4	2	no	—
264	C₄⋊C₄×C₈₉	—	4	2	no	—
265	C₄⋊C₄×C₈₉	—	4	2	no	—
266	C₄⋊C₄×C₈₉	—	4	2	no	—
267	C₄⋊C₄×C₈₉	—	4	2	no	—
268	C₄⋊C₄×C₈₉	—	4	2	no	—
269	C₄⋊C₄×C₈₉	—	4	2	no	—
270	C₄⋊C₄×C₈₉	—	4	2	no	—
271	C₄⋊C₄×C₈₉	—	4	1	no	—
272	C₄⋊C₄×C₈₉	—	4	2	no	—
273	C₄⋊C₄×C₈₉	—	4	2	no	—
274	C₄⋊C₄×C₈₉	—	4	2	no	—
275	C₄⋊C₄×C₈₉	—	4	1	no	—
276	C₄⋊C₄×C₈₉	—	4	2	no	—
277	C₄⋊C₄×C₈₉	—	4	2	no	—
278	C₄⋊C₄×C₈₉	—	4	2	no	—
279	C₄⋊C₄×C₈₉	—	4	2	no	—
280	C₄⋊C₄×C₈₉	—	4	2	no	—
281	C₄⋊C₄×C₈₉	—	4	2	no	—
282	C₂²⋊C₄×C₈₉	—	2	4	no	—
283	C₂²⋊C₄×C₈₉	—	2	4	no	—
284	C₂²⋊C₄×C₈₉	—	2	4	no	—
285	C₂²⋊C₄×C₈₉	—	2	4	no	—
286	C₂²⋊C₄×C₈₉	—	4	1	no	—
287	C₂²⋊C₄×C₈₉	—	4	1	no	—
288	C₂²⋊C₄×C₈₉	—	4	1	no	—
289	C₂²⋊C₄×C₈₉	—	4	1	no	—
290	C₂²⋊C₄×C₈₉	—	4	2	no	—
291	C₂²⋊C₄×C₈₉	—	4	2	no	—
292	C₂²⋊C₄×C₈₉	—	4	2	no	—
293	C₂²⋊C₄×C₈₉	—	4	2	no	—
294	C₂²⋊C₄×C₈₉	—	4	2	no	—
295	C₂²⋊C₄×C₈₉	—	4	2	no	—
296	C₂²⋊C₄×C₈₉	—	4	2	no	—
297	C₂²⋊C₄×C₈₉	—	4	2	no	—
298	C₂²⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
299	C₂²⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
300	C₂²⋊C₄×C₈₉	C₂×Q₈	1	8	yes	—
301	C₄²×C₈₉	—	4	2	no	—
302	C₄²×C₈₉	—	4	2	no	—
303	C₄²×C₈₉	—	4	2	no	—
304	C₄²×C₈₉	—	4	2	no	—
305	C₂³×C₈₉	—	2	2	no	—
306	C₂³×C₈₉	—	2	2	no	—
307	C₂³×C₈₉	—	2	8	no	—
308	C₂³×C₈₉	—	2	2	no	—
309	C₂³×C₈₉	—	2	2	no	—
310	C₂³×C₈₉	—	2	1	no	—
311	C₂³×C₈₉	—	2	1	no	—
312	C₂³×C₈₉	—	2	1	no	—
313	C₂³×C₈₉	—	2	1	no	—
314	C₂³×C₈₉	—	2	2	no	—
315	C₂³×C₈₉	—	2	2	no	—
316	C₂³×C₈₉	—	4	8	no	—
317	C₂³×C₈₉	—	4	4	no	—
318	C₂³×C₈₉	—	4	4	no	—
319	C₂³×C₈₉	—	4	8	no	—
320	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
321	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
322	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
323	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
324	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
325	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
326	Q₈×C₈₉	—	8	4	no	—
327	Q₈×C₈₉	—	8	2	no	—
328	Q₈×C₈₉	—	8	2	no	—
329	C₂×C₄×C₈₉	—	2	2	no	—
330	C₂×C₄×C₈₉	—	2	2	no	—
331	C₂×C₄×C₈₉	—	2	2	no	—
332	C₂×C₄×C₈₉	—	2	2	no	—
333	C₂×C₄×C₈₉	—	2	2	no	—
334	C₂×C₄×C₈₉	—	2	2	no	—
335	C₂×C₄×C₈₉	—	2	2	no	—
336	C₂×C₄×C₈₉	—	2	2	no	—
337	C₂×C₄×C₈₉	—	2	2	no	—
338	C₂×C₄×C₈₉	—	2	2	no	—
339	C₂×C₄×C₈₉	—	2	2	no	—
340	C₂×C₄×C₈₉	—	2	2	no	—
341	C₂×C₄×C₈₉	—	2	2	no	—
342	C₂×C₄×C₈₉	—	2	2	no	—
343	C₂×C₄×C₈₉	—	2	1	no	—
344	C₂×C₄×C₈₉	—	2	1	no	—
345	C₂×C₄×C₈₉	—	2	1	no	—
346	C₂×C₄×C₈₉	—	2	1	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	2	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	2	no	—
358	C₂×C₄×C₈₉	—	2	2	no	—
359	C₂×C₄×C₈₉	—	2	2	no	—
360	C₂×C₄×C₈₉	—	2	2	no	—
361	C₂×C₄×C₈₉	—	2	2	no	—
362	C₂×C₄×C₈₉	—	2	2	no	—
363	C₂×C₄×C₈₉	—	2	2	no	—
364	C₂×C₄×C₈₉	—	2	2	no	—
365	C₂×C₄×C₈₉	—	2	2	no	—
366	C₂×C₄×C₈₉	—	2	2	no	—
367	C₂×C₄×C₈₉	—	2	2	no	—
368	C₂×C₄×C₈₉	—	2	2	no	—
369	C₂×C₄×C₈₉	—	2	2	no	—
370	C₂×C₄×C₈₉	—	4	8	no	—
371	C₂×C₄×C₈₉	—	4	4	no	—
372	C₂×C₄×C₈₉	—	4	8	no	—
373	C₂×C₄×C₈₉	—	4	8	no	—
374	C₂×C₄×C₈₉	—	4	4	no	—
375	C₂×C₄×C₈₉	—	8	2	no	—
376	C₂×C₄×C₈₉	—	8	2	no	—
377	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
378	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
379	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
380	C₂²×C₈₉	—	2	4	no	—
381	C₂²×C₈₉	—	2	2	no	—
382	C₂²×C₈₉	—	2	2	no	—
383	C₂²×C₈₉	—	2	4	no	—
384	C₂²×C₈₉	—	2	2	no	—
385	C₂²×C₈₉	—	2	2	no	—
386	C₂²×C₈₉	—	2	4	no	—
387	C₂²×C₈₉	—	2	4	no	—
388	C₂²×C₈₉	—	4	16	no	—
389	C₂²×C₈₉	—	4	1	no	—
390	C₂²×C₈₉	—	4	1	no	—
391	C₂²×C₈₉	—	4	1	no	—
392	C₂²×C₈₉	—	4	1	no	—
393	C₂²×C₈₉	—	4	2	no	—
394	C₂²×C₈₉	—	4	2	no	—
395	C₂²×C₈₉	#544	1	4	yes	—
396	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
397	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
398	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
399	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
400	C₂²×C₈₉	#585	1	2	yes	—
401	C₄×C₈₉	—	2	4	no	—
402	C₄×C₈₉	—	2	4	no	—
403	C₄×C₈₉	—	2	4	no	—
404	C₄×C₈₉	—	4	2	no	—
405	C₄×C₈₉	—	4	1	no	—
406	C₄×C₈₉	—	4	1	no	—
407	C₄×C₈₉	—	4	2	no	—
408	C₄×C₈₉	—	4	2	no	—
409	C₄×C₈₉	—	4	2	no	—
410	C₄×C₈₉	—	4	1	no	—
411	C₄×C₈₉	—	4	1	no	—
412	C₄×C₈₉	—	4	2	no	—
413	C₄×C₈₉	—	4	2	no	—
414	C₄×C₈₉	—	4	2	no	—
415	C₄×C₈₉	—	4	2	no	—
416	C₄×C₈₉	—	4	2	no	—
417	#36748	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
418	C₂×C₈₉	—	2	4	no	—
419	C₂×C₈₉	—	4	2	no	—
420	C₂×C₈₉	—	4	2	no	—
421	C₂×C₈₉	C₂×#544	1	1	yes	characteristic
422	C₂×C₈₉	#3501	1	2	yes	—
423	C₂×C₈₉	#3532	1	1	yes	characteristic
424	C₂×C₈₉	#3533	1	1	yes	characteristic
425	C₂×C₈₉	#3541	1	2	yes	—
426	#2848	C₂×C₈₉	1	2	yes	—
427	#2807	C₂×C₈₉	1	1	yes	characteristic, complemented
428	#2790	C₂×C₈₉	1	2	yes	complemented
429	#2788	C₂×C₈₉	1	2	yes	complemented
430	#2768	C₂×C₈₉	1	2	yes	complemented
431	#2763	C₂×C₈₉	1	1	yes	characteristic, complemented
432	#2742	C₂×C₈₉	1	1	yes	characteristic, complemented
433	#2729	C₂×C₈₉	1	2	yes	complemented
434	#2720	C₂×C₈₉	1	2	yes	complemented
435	#2704	C₂×C₈₉	1	2	yes	complemented
436	#2677	C₂×C₈₉	1	1	yes	characteristic, complemented
437	#2626	C₂×C₈₉	1	1	yes	characteristic
438	#2626	C₂×C₈₉	1	1	yes	characteristic
439	#2569	C₂×C₈₉	1	2	yes	complemented
440	#2549	C₂×C₈₉	1	2	yes	complemented
441	#2442	C₂×C₈₉	1	2	yes	complemented
442	#2440	C₂×C₈₉	1	2	yes	complemented
443	#2312	C₂×C₈₉	1	2	yes	—
444	C₂×#385	C₂×C₈₉	1	1	yes	characteristic
445	C₈₉	#36748	1	1	yes	characteristic, direct product factor, Sylow
446	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
447	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
448	C₂×#125	C₂²×C₈₉	1	2	yes	complemented
449	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
450	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
451	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
452	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
453	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
454	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
455	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
456	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
457	#400	C₂²×C₈₉	1	2	yes	complemented
458	#400	C₂²×C₈₉	1	2	yes	complemented
459	#400	C₂²×C₈₉	1	2	yes	complemented
460	#400	C₂²×C₈₉	1	2	yes	complemented
461	#399	C₂²×C₈₉	1	1	yes	characteristic
462	#399	C₂²×C₈₉	1	1	yes	characteristic
463	#399	C₂²×C₈₉	1	1	yes	characteristic
464	#399	C₂²×C₈₉	1	1	yes	characteristic
465	#398	C₂²×C₈₉	1	2	yes	complemented
466	#398	C₂²×C₈₉	1	2	yes	complemented
467	#398	C₂²×C₈₉	1	2	yes	complemented
468	#398	C₂²×C₈₉	1	2	yes	complemented
469	#398	C₂²×C₈₉	1	2	yes	complemented
470	#398	C₂²×C₈₉	1	2	yes	complemented
471	#398	C₂²×C₈₉	1	2	yes	complemented
472	#398	C₂²×C₈₉	1	2	yes	complemented
473	#396	C₂²×C₈₉	1	2	yes	—
474	#396	C₂²×C₈₉	1	2	yes	—
475	#396	C₂²×C₈₉	1	2	yes	—
476	#396	C₂²×C₈₉	1	2	yes	—
477	#395	C₂²×C₈₉	1	2	yes	complemented
478	#395	C₂²×C₈₉	1	2	yes	complemented
479	#395	C₂²×C₈₉	1	2	yes	complemented
480	#395	C₂²×C₈₉	1	2	yes	complemented
481	#393	C₂²×C₈₉	1	1	yes	characteristic
482	#393	C₂²×C₈₉	1	1	yes	characteristic
483	#393	C₂²×C₈₉	1	1	yes	characteristic
484	#393	C₂²×C₈₉	1	1	yes	characteristic
485	#391	C₂²×C₈₉	1	2	yes	complemented
486	#391	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	2	yes	—
494	#388	C₂²×C₈₉	1	2	yes	—
495	#388	C₂²×C₈₉	1	2	yes	—
496	#388	C₂²×C₈₉	1	2	yes	—
497	#388	C₂²×C₈₉	1	2	yes	—
498	#388	C₂²×C₈₉	1	2	yes	—
499	#388	C₂²×C₈₉	1	2	yes	—
500	#388	C₂²×C₈₉	1	2	yes	—
501	#387	C₂²×C₈₉	1	2	yes	complemented
502	#387	C₂²×C₈₉	1	2	yes	complemented
503	#387	C₂²×C₈₉	1	2	yes	complemented
504	#387	C₂²×C₈₉	1	2	yes	complemented
505	#385	C₂²×C₈₉	1	2	yes	—
506	#385	C₂²×C₈₉	1	2	yes	—
507	#385	C₂²×C₈₉	1	2	yes	—
508	#385	C₂²×C₈₉	1	2	yes	—
509	#385	C₂²×C₈₉	1	2	yes	—
510	#385	C₂²×C₈₉	1	2	yes	—
511	#385	C₂²×C₈₉	1	2	yes	—
512	#385	C₂²×C₈₉	1	2	yes	—
513	#385	C₂²×C₈₉	1	1	yes	characteristic
514	#385	C₂²×C₈₉	1	1	yes	characteristic
515	#385	C₂²×C₈₉	1	2	yes	—
516	#385	C₂²×C₈₉	1	2	yes	—
517	#385	C₂²×C₈₉	1	1	yes	characteristic
518	#385	C₂²×C₈₉	1	1	yes	characteristic
519	#384	C₂²×C₈₉	1	2	yes	complemented
520	#382	C₂²×C₈₉	1	2	yes	complemented
521	#380	C₂²×C₈₉	1	2	yes	—
522	#380	C₂²×C₈₉	1	2	yes	—
523	#380	C₂²×C₈₉	1	1	yes	characteristic
524	#380	C₂²×C₈₉	1	2	yes	—
525	#380	C₂²×C₈₉	1	2	yes	—
526	#380	C₂²×C₈₉	1	2	yes	—
527	#380	C₂²×C₈₉	1	1	yes	characteristic
528	#379	C₂²×C₈₉	1	2	yes	—
529	#379	C₂²×C₈₉	1	2	yes	—
530	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
531	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
532	C₂×#95	C₂²×C₈₉	1	2	yes	—
533	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
534	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
535	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
536	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
537	C₂³×C₄	—	4	4	no	—
538	C₂³×C₄	—	4	2	no	—
539	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
540	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
543	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
544	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
545	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
546	C₄⋊Q₈	—	4	4	no	—
547	#125	—	4	4	no	—
548	C₂²⋊Q₈	—	4	4	no	—
549	C₂²⋊Q₈	—	4	2	no	—
550	C₂²⋊Q₈	—	4	2	no	—
551	C₂²⋊Q₈	—	4	4	no	—
552	C₂²⋊Q₈	—	4	4	no	—
553	C₂×C₄⋊C₄	—	4	4	no	—
554	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
581	C₂×C₂²⋊C₄	—	4	2	no	—
582	C₂×C₂²⋊C₄	Q₈×C₈₉	1	8	yes	complemented
583	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	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	1	yes	characteristic
588	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
589	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
590	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
591	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	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	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
600	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
601	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
602	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
603	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
604	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
605	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
606	#95	C₂³×C₈₉	1	2	yes	—
607	#95	C₂³×C₈₉	1	2	yes	—
608	#95	C₂³×C₈₉	1	2	yes	—
609	#95	C₂³×C₈₉	1	2	yes	—
610	#95	C₂³×C₈₉	1	2	yes	—
611	#95	C₂³×C₈₉	1	2	yes	—
612	#95	C₂³×C₈₉	1	2	yes	—
613	#95	C₂³×C₈₉	1	2	yes	—
614	#95	C₂³×C₈₉	1	1	yes	characteristic
615	#95	C₂³×C₈₉	1	2	yes	—
616	#95	C₂³×C₈₉	1	2	yes	—
617	#95	C₂³×C₈₉	1	2	yes	—
618	#95	C₂³×C₈₉	1	2	yes	—
619	#95	C₂³×C₈₉	1	2	yes	—
620	#95	C₂³×C₈₉	1	2	yes	—
621	#95	C₂³×C₈₉	1	2	yes	—
622	#95	C₂³×C₈₉	1	2	yes	—
623	#95	C₂³×C₈₉	1	1	yes	characteristic
624	#95	C₂³×C₈₉	1	1	yes	characteristic
625	#95	C₂³×C₈₉	1	2	yes	—
626	#95	C₂³×C₈₉	1	2	yes	—
627	#95	C₂³×C₈₉	1	1	yes	characteristic
628	#95	C₂³×C₈₉	1	2	yes	—
629	#95	C₂³×C₈₉	1	2	yes	—
630	#95	C₂³×C₈₉	1	2	yes	—
631	#95	C₂³×C₈₉	1	2	yes	—
632	C₂⁴	—	2	2	no	—
633	C₂⁴	—	2	2	no	—
634	C₂⁴	—	4	2	no	—
635	C₂⁴	—	4	2	no	—
636	C₂⁴	C₂×Q₈×C₈₉	1	4	yes	—
637	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
638	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
639	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
640	C₂×Q₈	—	2	4	no	—
641	C₂×Q₈	—	4	2	no	—
642	C₂×Q₈	—	4	2	no	—
643	C₂×Q₈	—	4	1	no	—
644	C₂×Q₈	—	4	1	no	—
645	C₂×Q₈	—	4	2	no	—
646	C₂×Q₈	—	4	2	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	2	4	no	—
652	C₂²×C₄	—	2	4	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	1	no	—
655	C₂²×C₄	—	4	2	no	—
656	C₂²×C₄	—	4	2	no	—
657	C₂²×C₄	—	4	2	no	—
658	C₂²×C₄	—	4	2	no	—
659	C₂²×C₄	—	4	1	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	2	no	—
663	C₂²×C₄	—	4	16	no	—
664	C₂²×C₄	C₂×Q₈×C₈₉	1	8	yes	—
665	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
666	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	4	2	no	—
687	C₄⋊C₄	—	4	2	no	—
688	C₄⋊C₄	—	4	2	no	—
689	C₄⋊C₄	—	4	2	no	—
690	C₄⋊C₄	—	4	2	no	—
691	C₄⋊C₄	—	4	2	no	—
692	C₄⋊C₄	—	4	1	no	—
693	C₄⋊C₄	—	4	2	no	—
694	C₄⋊C₄	—	4	2	no	—
695	C₄⋊C₄	—	4	2	no	—
696	C₄⋊C₄	—	4	1	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₄⋊C₄	—	4	2	no	—
700	C₄⋊C₄	—	4	2	no	—
701	C₄⋊C₄	—	4	2	no	—
702	C₄⋊C₄	—	4	2	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	4	2	no	—
705	C₄⋊C₄	—	4	2	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₄⋊C₄	—	4	2	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	4	1	no	—
713	C₂²⋊C₄	—	4	1	no	—
714	C₂²⋊C₄	—	4	1	no	—
715	C₂²⋊C₄	—	4	1	no	—
716	C₂²⋊C₄	—	4	2	no	—
717	C₂²⋊C₄	—	4	2	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	4	2	no	—
721	C₂²⋊C₄	—	4	2	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	—	4	2	no	—
724	C₂²⋊C₄	C₂×Q₈×C₈₉	1	4	yes	—
725	C₂²⋊C₄	C₂×Q₈×C₈₉	1	4	yes	—
726	C₂²⋊C₄	C₂×Q₈×C₈₉	1	8	yes	—
727	C₄²	—	4	2	no	—
728	C₄²	—	4	2	no	—
729	C₄²	—	4	2	no	—
730	C₄²	—	4	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	8	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	1	no	—
739	C₂³	—	2	1	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	4	8	no	—
743	C₂³	—	4	4	no	—
744	C₂³	—	4	4	no	—
745	C₂³	—	4	8	no	—
746	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
747	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
748	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
749	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
750	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
751	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
752	Q₈	—	8	4	no	—
753	Q₈	—	8	2	no	—
754	Q₈	—	8	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	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	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	4	8	no	—
797	C₂×C₄	—	4	4	no	—
798	C₂×C₄	—	4	8	no	—
799	C₂×C₄	—	4	8	no	—
800	C₂×C₄	—	4	4	no	—
801	C₂×C₄	—	8	2	no	—
802	C₂×C₄	—	8	2	no	—
803	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
804	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
805	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
806	C₂²	—	2	4	no	—
807	C₂²	—	2	2	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	4	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	4	no	—
813	C₂²	—	2	4	no	—
814	C₂²	—	4	16	no	—
815	C₂²	—	4	1	no	—
816	C₂²	—	4	1	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	#544×C₈₉	1	4	yes	—
822	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
823	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
824	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
825	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
826	C₂²	#585×C₈₉	1	2	yes	—
827	C₄	—	2	4	no	—
828	C₄	—	2	4	no	—
829	C₄	—	2	4	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	1	no	—
832	C₄	—	4	1	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	2	no	—
843	C₂	—	2	4	no	—
844	C₂	—	4	2	no	—
845	C₂	—	4	2	no	—
846	C₂	C₂×#544×C₈₉	1	1	yes	characteristic
847	C₂	C₈₉×#3501	1	2	yes	—
848	C₂	C₈₉×#3532	1	1	yes	characteristic
849	C₂	C₈₉×#3533	1	1	yes	characteristic
850	C₂	C₈₉×#3541	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂⁵×C₈₉	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₈₉×#2807	C₂	semidirect
3. C₈₉×#2790	C₂	semidirect
4. C₈₉×#2788	C₂	semidirect
5. C₈₉×#2768	C₂	semidirect
6. C₈₉×#2763	C₂	semidirect
7. C₈₉×#2742	C₂	semidirect
8. C₈₉×#2729	C₂	semidirect
9. C₈₉×#2720	C₂	semidirect
10. C₈₉×#2704	C₂	semidirect
11. C₈₉×#2677	C₂	semidirect
14. C₈₉×#2569	C₂	semidirect
15. C₈₉×#2549	C₂	semidirect
16. C₈₉×#2442	C₂	semidirect
17. C₈₉×#2440	C₂	semidirect
21. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
22. C₂×#125×C₈₉	C₂²	semidirect
31. #400×C₈₉	C₂²	semidirect
32. #400×C₈₉	C₂²	semidirect
33. #400×C₈₉	C₂²	semidirect
34. #400×C₈₉	C₂²	semidirect
39. #398×C₈₉	C₂²	semidirect
40. #398×C₈₉	C₂²	semidirect
41. #398×C₈₉	C₂²	semidirect
42. #398×C₈₉	C₂²	semidirect
43. #398×C₈₉	C₂²	semidirect
44. #398×C₈₉	C₂²	semidirect
45. #398×C₈₉	C₂²	semidirect
46. #398×C₈₉	C₂²	semidirect
51. #395×C₈₉	C₂²	semidirect
52. #395×C₈₉	C₂²	semidirect
53. #395×C₈₉	C₂²	semidirect
54. #395×C₈₉	C₂²	semidirect
59. #391×C₈₉	C₂²	semidirect
60. #391×C₈₉	C₂²	semidirect
61. #389×C₈₉	C₂²	semidirect
62. #389×C₈₉	C₂²	semidirect
63. #389×C₈₉	C₂²	semidirect
64. #389×C₈₉	C₂²	semidirect
65. #389×C₈₉	C₂²	semidirect
66. #389×C₈₉	C₂²	semidirect
75. #387×C₈₉	C₂²	semidirect
76. #387×C₈₉	C₂²	semidirect
77. #387×C₈₉	C₂²	semidirect
78. #387×C₈₉	C₂²	semidirect
93. #384×C₈₉	C₂²	semidirect
94. #382×C₈₉	C₂²	semidirect
156. C₂×C₂²⋊C₄×C₈₉	Q₈	semidirect
417. #36748	C₈₉	direct (N × H)
427. #2807	C₂×C₈₉	semidirect
428. #2790	C₂×C₈₉	semidirect
429. #2788	C₂×C₈₉	semidirect
430. #2768	C₂×C₈₉	semidirect
431. #2763	C₂×C₈₉	semidirect
432. #2742	C₂×C₈₉	semidirect
433. #2729	C₂×C₈₉	semidirect
434. #2720	C₂×C₈₉	semidirect
435. #2704	C₂×C₈₉	semidirect
436. #2677	C₂×C₈₉	semidirect
439. #2569	C₂×C₈₉	semidirect
440. #2549	C₂×C₈₉	semidirect
441. #2442	C₂×C₈₉	semidirect
442. #2440	C₂×C₈₉	semidirect
445. C₈₉	#36748	direct (N × H)
447. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
448. C₂×#125	C₂²×C₈₉	semidirect
457. #400	C₂²×C₈₉	semidirect
458. #400	C₂²×C₈₉	semidirect
459. #400	C₂²×C₈₉	semidirect
460. #400	C₂²×C₈₉	semidirect
465. #398	C₂²×C₈₉	semidirect
466. #398	C₂²×C₈₉	semidirect
467. #398	C₂²×C₈₉	semidirect
468. #398	C₂²×C₈₉	semidirect
469. #398	C₂²×C₈₉	semidirect
470. #398	C₂²×C₈₉	semidirect
471. #398	C₂²×C₈₉	semidirect
472. #398	C₂²×C₈₉	semidirect
477. #395	C₂²×C₈₉	semidirect
478. #395	C₂²×C₈₉	semidirect
479. #395	C₂²×C₈₉	semidirect
480. #395	C₂²×C₈₉	semidirect
485. #391	C₂²×C₈₉	semidirect
486. #391	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
501. #387	C₂²×C₈₉	semidirect
502. #387	C₂²×C₈₉	semidirect
503. #387	C₂²×C₈₉	semidirect
504. #387	C₂²×C₈₉	semidirect
519. #384	C₂²×C₈₉	semidirect
520. #382	C₂²×C₈₉	semidirect
582. C₂×C₂²⋊C₄	Q₈×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#2848	2
C₈₉×#2807	2
C₈₉×#2790	2
C₈₉×#2788	2
C₈₉×#2768	2
C₈₉×#2763	2
C₈₉×#2742	2
C₈₉×#2729	2
C₈₉×#2720	2
C₈₉×#2704	2
C₈₉×#2677	2
C₈₉×#2626	2
C₈₉×#2569	2
C₈₉×#2549	2
C₈₉×#2442	2
C₈₉×#2440	2
C₈₉×#2312	2
C₂×#385×C₈₉	2
#36748	89

Subgroups — C89×#36748 #36414596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#36748 #36414596