Subgroups — C₈₉×#35536 #36413384

Order 22784.

2682 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#542×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#518×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2563	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2544	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2544	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2542	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2500	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2499	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2472	C₂	1	4	yes	maximal, complemented
10	C₈₉×#2467	C₂	1	4	yes	maximal, complemented
11	C₈₉×#2463	C₂	1	4	yes	maximal, complemented
12	C₈₉×#2435	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#2433	C₂	1	1	yes	maximal, characteristic
14	C₈₉×#2418	C₂	1	4	yes	maximal, complemented
15	C₈₉×#2328	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2326	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#127×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#124×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2298	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
21	#542×C₈₉	—	2	8	no	—
22	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#126×C₈₉	C₂²	1	2	yes	complemented
26	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#124×C₈₉	C₂²	1	2	yes	—
29	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×#123×C₈₉	C₂²	1	2	yes	—
31	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
33	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
34	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#120×C₈₉	C₂²	1	4	yes	—
36	#518×C₈₉	—	2	8	no	—
37	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
46	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
48	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
49	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
50	#399×C₈₉	C₂²	1	4	yes	complemented
51	#397×C₈₉	C₂²	1	4	yes	—
52	#394×C₈₉	C₂²	1	4	yes	—
53	#394×C₈₉	C₂²	1	4	yes	—
54	#394×C₈₉	C₂²	1	4	yes	complemented
55	#394×C₈₉	C₂²	1	4	yes	complemented
56	#393×C₈₉	C₂²	1	4	yes	complemented
57	#392×C₈₉	C₂²	1	4	yes	—
58	#391×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#391×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#390×C₈₉	C₂²	1	1	yes	characteristic
61	#390×C₈₉	C₂²	1	1	yes	characteristic
62	#390×C₈₉	C₂²	1	1	yes	characteristic
63	#390×C₈₉	C₂²	1	1	yes	characteristic
64	#390×C₈₉	C₂²	1	4	yes	complemented
65	#390×C₈₉	C₂²	1	1	yes	characteristic, complemented
66	#390×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#388×C₈₉	C₂²	1	2	yes	—
68	#388×C₈₉	C₂²	1	2	yes	—
69	#388×C₈₉	C₂²	1	4	yes	complemented
70	#388×C₈₉	C₂²	1	4	yes	complemented
71	#388×C₈₉	C₂²	1	4	yes	complemented
72	#387×C₈₉	C₂²	1	2	yes	complemented
73	#387×C₈₉	C₂²	1	2	yes	complemented
74	#387×C₈₉	C₂²	1	4	yes	complemented
75	#386×C₈₉	C₂²	1	4	yes	complemented
76	#386×C₈₉	C₂²	1	4	yes	complemented
77	#386×C₈₉	C₂²	1	4	yes	complemented
78	#386×C₈₉	C₂²	1	4	yes	complemented
79	#385×C₈₉	C₂²	1	4	yes	complemented
80	#384×C₈₉	C₂²	1	1	yes	characteristic, complemented
81	#384×C₈₉	C₂²	1	1	yes	characteristic, complemented
82	#382×C₈₉	C₂²	1	1	yes	characteristic, complemented
83	#382×C₈₉	C₂²	1	1	yes	characteristic, complemented
84	#380×C₈₉	C₂²	1	4	yes	complemented
85	#379×C₈₉	C₂²	1	4	yes	—
86	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
87	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
88	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	complemented
91	#376×C₈₉	C₂²	1	1	yes	characteristic, complemented
92	C₄³×C₈₉	C₂²	1	1	yes	characteristic, complemented
93	C₂⁵×C₈₉	C₂³	1	2	yes	—
94	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
96	C₂²×D₄×C₈₉	—	2	4	no	—
97	C₂²×D₄×C₈₉	—	2	4	no	—
98	C₂²×D₄×C₈₉	—	2	4	no	—
99	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
101	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
102	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
105	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
106	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
108	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
109	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
110	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
111	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₈₉	—	2	4	no	—
113	#127×C₈₉	—	2	4	no	—
114	#127×C₈₉	—	2	4	no	—
115	#126×C₈₉	—	2	8	no	—
116	#124×C₈₉	—	2	4	no	—
117	#124×C₈₉	—	2	4	no	—
118	#124×C₈₉	—	2	8	no	—
119	#124×C₈₉	—	2	4	no	—
120	#123×C₈₉	—	2	8	no	—
121	C₂²⋊Q₈×C₈₉	—	2	4	no	—
122	C₂²⋊Q₈×C₈₉	—	2	8	no	—
123	C₂²⋊Q₈×C₈₉	—	4	8	no	—
124	#121×C₈₉	—	2	4	no	—
125	#120×C₈₉	—	4	8	no	—
126	C₄×Q₈×C₈₉	—	2	4	no	—
127	C₄×D₄×C₈₉	—	2	8	no	—
128	C₄×D₄×C₈₉	—	2	8	no	—
129	C₄×D₄×C₈₉	—	2	4	no	—
130	C₄×D₄×C₈₉	—	2	4	no	—
131	C₄×D₄×C₈₉	—	2	4	no	—
132	C₄×D₄×C₈₉	—	2	4	no	—
133	C₄×D₄×C₈₉	—	2	4	no	—
134	C₄×D₄×C₈₉	—	4	8	no	—
135	#117×C₈₉	—	2	4	no	—
136	#117×C₈₉	D₄	1	8	yes	complemented
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	1	yes	characteristic
140	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	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	4	yes	—
148	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
151	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
152	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	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	4	yes	—
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	4	yes	—
168	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
169	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
170	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
171	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
172	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
177	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
180	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
181	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
182	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
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	4	yes	—
189	#95×C₈₉	C₂³	1	4	yes	—
190	#95×C₈₉	C₂³	1	2	yes	—
191	#95×C₈₉	C₂³	1	2	yes	—
192	#95×C₈₉	C₂³	1	4	yes	—
193	#95×C₈₉	C₂³	1	4	yes	—
194	C₂⁴×C₈₉	—	2	4	no	—
195	C₂⁴×C₈₉	—	2	4	no	—
196	C₂⁴×C₈₉	—	2	4	no	—
197	C₂⁴×C₈₉	—	4	4	no	—
198	C₂⁴×C₈₉	—	4	4	no	—
199	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
200	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
201	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
202	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
203	C₂×Q₈×C₈₉	—	2	2	no	—
204	C₂×Q₈×C₈₉	—	2	4	no	—
205	C₂×Q₈×C₈₉	—	2	2	no	—
206	C₂×Q₈×C₈₉	—	2	2	no	—
207	C₂×Q₈×C₈₉	—	4	4	no	—
208	C₂×D₄×C₈₉	—	2	32	no	—
209	C₂×D₄×C₈₉	—	2	4	no	—
210	C₂×D₄×C₈₉	—	2	4	no	—
211	C₂×D₄×C₈₉	—	2	8	no	—
212	C₂×D₄×C₈₉	—	2	4	no	—
213	C₂×D₄×C₈₉	—	2	8	no	—
214	C₂×D₄×C₈₉	—	2	4	no	—
215	C₂×D₄×C₈₉	—	2	2	no	—
216	C₂×D₄×C₈₉	—	2	2	no	—
217	C₂×D₄×C₈₉	—	2	2	no	—
218	C₂×D₄×C₈₉	—	2	2	no	—
219	C₂×D₄×C₈₉	—	2	2	no	—
220	C₂×D₄×C₈₉	—	2	2	no	—
221	C₂×D₄×C₈₉	—	2	2	no	—
222	C₂×D₄×C₈₉	—	2	8	no	—
223	C₂×D₄×C₈₉	—	4	4	no	—
224	C₂×D₄×C₈₉	—	4	4	no	—
225	C₂×D₄×C₈₉	—	4	4	no	—
226	C₂×D₄×C₈₉	—	4	4	no	—
227	C₂×D₄×C₈₉	#41	1	4	yes	—
228	C₂×D₄×C₈₉	#41	1	4	yes	—
229	C₂²×C₄×C₈₉	—	2	2	no	—
230	C₂²×C₄×C₈₉	—	2	2	no	—
231	C₂²×C₄×C₈₉	—	2	4	no	—
232	C₂²×C₄×C₈₉	—	2	4	no	—
233	C₂²×C₄×C₈₉	—	2	4	no	—
234	C₂²×C₄×C₈₉	—	2	4	no	—
235	C₂²×C₄×C₈₉	—	2	4	no	—
236	C₂²×C₄×C₈₉	—	4	4	no	—
237	C₂²×C₄×C₈₉	—	4	4	no	—
238	C₂²×C₄×C₈₉	—	4	4	no	—
239	C₂²×C₄×C₈₉	—	4	4	no	—
240	C₂²×C₄×C₈₉	—	4	4	no	—
241	C₂²×C₄×C₈₉	C₂×D₄	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	2	yes	—
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	2	yes	—
250	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
257	C₄⋊C₄×C₈₉	—	2	2	no	—
258	C₄⋊C₄×C₈₉	—	2	2	no	—
259	C₄⋊C₄×C₈₉	—	2	2	no	—
260	C₄⋊C₄×C₈₉	—	2	2	no	—
261	C₄⋊C₄×C₈₉	—	2	4	no	—
262	C₄⋊C₄×C₈₉	—	2	4	no	—
263	C₄⋊C₄×C₈₉	—	2	4	no	—
264	C₄⋊C₄×C₈₉	—	2	8	no	—
265	C₄⋊C₄×C₈₉	—	2	4	no	—
266	C₄⋊C₄×C₈₉	—	4	2	no	—
267	C₄⋊C₄×C₈₉	—	4	4	no	—
268	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
269	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
270	C₂²⋊C₄×C₈₉	—	2	4	no	—
271	C₂²⋊C₄×C₈₉	—	2	4	no	—
272	C₂²⋊C₄×C₈₉	—	2	8	no	—
273	C₂²⋊C₄×C₈₉	—	2	8	no	—
274	C₂²⋊C₄×C₈₉	—	2	4	no	—
275	C₂²⋊C₄×C₈₉	—	2	4	no	—
276	C₂²⋊C₄×C₈₉	—	2	4	no	—
277	C₂²⋊C₄×C₈₉	—	2	4	no	—
278	C₂²⋊C₄×C₈₉	—	2	4	no	—
279	C₂²⋊C₄×C₈₉	—	2	4	no	—
280	C₂²⋊C₄×C₈₉	—	2	4	no	—
281	C₂²⋊C₄×C₈₉	—	2	4	no	—
282	C₂²⋊C₄×C₈₉	—	2	4	no	—
283	C₂²⋊C₄×C₈₉	—	2	8	no	—
284	C₂²⋊C₄×C₈₉	—	4	2	no	—
285	C₂²⋊C₄×C₈₉	—	4	4	no	—
286	C₂²⋊C₄×C₈₉	—	4	4	no	—
287	C₂²⋊C₄×C₈₉	—	4	4	no	—
288	C₂²⋊C₄×C₈₉	—	4	4	no	—
289	C₂²⋊C₄×C₈₉	—	4	4	no	—
290	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
291	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
292	C₄²×C₈₉	—	2	4	no	—
293	C₄²×C₈₉	—	2	4	no	—
294	C₄²×C₈₉	—	2	2	no	—
295	C₄²×C₈₉	—	2	2	no	—
296	C₄²×C₈₉	—	2	2	no	—
297	C₄²×C₈₉	—	2	2	no	—
298	C₄²×C₈₉	—	2	4	no	—
299	C₄²×C₈₉	—	4	2	no	—
300	C₄²×C₈₉	C₂×D₄	1	4	yes	—
301	C₄²×C₈₉	C₂×D₄	1	4	yes	—
302	C₂³×C₈₉	—	2	16	no	—
303	C₂³×C₈₉	—	2	2	no	—
304	C₂³×C₈₉	—	2	2	no	—
305	C₂³×C₈₉	—	2	1	no	—
306	C₂³×C₈₉	—	2	1	no	—
307	C₂³×C₈₉	—	2	2	no	—
308	C₂³×C₈₉	—	2	2	no	—
309	C₂³×C₈₉	—	2	4	no	—
310	C₂³×C₈₉	—	2	2	no	—
311	C₂³×C₈₉	—	2	4	no	—
312	C₂³×C₈₉	—	2	2	no	—
313	C₂³×C₈₉	—	2	4	no	—
314	C₂³×C₈₉	—	2	4	no	—
315	C₂³×C₈₉	—	2	2	no	—
316	C₂³×C₈₉	—	2	2	no	—
317	C₂³×C₈₉	—	2	2	no	—
318	C₂³×C₈₉	—	2	4	no	—
319	C₂³×C₈₉	—	2	4	no	—
320	C₂³×C₈₉	—	8	4	no	—
321	C₂³×C₈₉	—	8	4	no	—
322	C₂³×C₈₉	—	8	8	no	—
323	C₂³×C₈₉	—	8	8	no	—
324	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
325	C₂³×C₈₉	C₂×#41	1	4	yes	—
326	C₂³×C₈₉	C₂×#41	1	4	yes	—
327	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
328	Q₈×C₈₉	—	4	4	no	—
329	Q₈×C₈₉	—	8	4	no	—
330	D₄×C₈₉	—	2	16	no	—
331	D₄×C₈₉	—	2	8	no	—
332	D₄×C₈₉	—	2	8	no	—
333	D₄×C₈₉	—	4	16	no	—
334	D₄×C₈₉	—	4	4	no	—
335	D₄×C₈₉	—	8	4	no	—
336	D₄×C₈₉	—	8	8	no	—
337	C₂×C₄×C₈₉	—	2	2	no	—
338	C₂×C₄×C₈₉	—	2	1	no	—
339	C₂×C₄×C₈₉	—	2	1	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	2	no	—
344	C₂×C₄×C₈₉	—	2	2	no	—
345	C₂×C₄×C₈₉	—	2	8	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	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	4	no	—
359	C₂×C₄×C₈₉	—	2	2	no	—
360	C₂×C₄×C₈₉	—	2	4	no	—
361	C₂×C₄×C₈₉	—	2	4	no	—
362	C₂×C₄×C₈₉	—	2	2	no	—
363	C₂×C₄×C₈₉	—	2	2	no	—
364	C₂×C₄×C₈₉	—	2	4	no	—
365	C₂×C₄×C₈₉	—	2	2	no	—
366	C₂×C₄×C₈₉	—	8	4	no	—
367	C₂×C₄×C₈₉	—	8	4	no	—
368	C₂×C₄×C₈₉	—	8	4	no	—
369	C₂×C₄×C₈₉	—	8	4	no	—
370	C₂×C₄×C₈₉	—	8	4	no	—
371	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
372	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
373	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
374	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
378	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
379	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
380	C₂²×C₈₉	—	2	2	no	—
381	C₂²×C₈₉	—	2	4	no	—
382	C₂²×C₈₉	—	2	4	no	—
383	C₂²×C₈₉	—	2	2	no	—
384	C₂²×C₈₉	—	2	2	no	—
385	C₂²×C₈₉	—	2	8	no	—
386	C₂²×C₈₉	—	2	8	no	—
387	C₂²×C₈₉	—	4	2	no	—
388	C₂²×C₈₉	—	4	2	no	—
389	C₂²×C₈₉	—	4	2	no	—
390	C₂²×C₈₉	—	4	2	no	—
391	C₂²×C₈₉	—	4	4	no	—
392	C₂²×C₈₉	—	4	2	no	—
393	C₂²×C₈₉	—	4	4	no	—
394	C₂²×C₈₉	—	4	2	no	—
395	C₂²×C₈₉	—	4	2	no	—
396	C₂²×C₈₉	—	4	2	no	—
397	C₂²×C₈₉	—	4	2	no	—
398	C₂²×C₈₉	—	4	4	no	—
399	C₂²×C₈₉	—	4	4	no	—
400	C₂²×C₈₉	—	8	16	no	—
401	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
402	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
403	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
404	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
405	C₂²×C₈₉	#585	1	2	yes	—
406	C₄×C₈₉	—	2	2	no	—
407	C₄×C₈₉	—	2	2	no	—
408	C₄×C₈₉	—	2	2	no	—
409	C₄×C₈₉	—	2	2	no	—
410	C₄×C₈₉	—	2	2	no	—
411	C₄×C₈₉	—	2	4	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	C₄×C₈₉	—	4	2	no	—
418	C₄×C₈₉	—	4	2	no	—
419	C₄×C₈₉	—	4	2	no	—
420	C₄×C₈₉	#525	1	4	yes	—
421	#35536	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
422	C₂×C₈₉	—	4	4	no	—
423	C₂×C₈₉	—	4	4	no	—
424	C₂×C₈₉	—	4	2	no	—
425	C₂×C₈₉	—	8	2	no	—
426	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
427	C₂×C₈₉	#3498	1	1	yes	characteristic
428	C₂×C₈₉	#3500	1	1	yes	characteristic
429	C₂×C₈₉	#3513	1	2	yes	—
430	C₂×C₈₉	#3514	1	2	yes	—
431	C₂×#542	C₂×C₈₉	1	1	yes	characteristic, complemented
432	C₂×#518	C₂×C₈₉	1	1	yes	characteristic, complemented
433	#2563	C₂×C₈₉	1	1	yes	characteristic, complemented
434	#2544	C₂×C₈₉	1	1	yes	characteristic, complemented
435	#2544	C₂×C₈₉	1	1	yes	characteristic, complemented
436	#2542	C₂×C₈₉	1	1	yes	characteristic, complemented
437	#2500	C₂×C₈₉	1	1	yes	characteristic, complemented
438	#2499	C₂×C₈₉	1	1	yes	characteristic, complemented
439	#2472	C₂×C₈₉	1	4	yes	complemented
440	#2467	C₂×C₈₉	1	4	yes	complemented
441	#2463	C₂×C₈₉	1	4	yes	complemented
442	#2435	C₂×C₈₉	1	1	yes	characteristic, complemented
443	#2433	C₂×C₈₉	1	1	yes	characteristic
444	#2418	C₂×C₈₉	1	4	yes	complemented
445	#2328	C₂×C₈₉	1	1	yes	characteristic, complemented
446	#2326	C₂×C₈₉	1	1	yes	characteristic, complemented
447	C₄×#127	C₂×C₈₉	1	1	yes	characteristic, complemented
448	C₄×#124	C₂×C₈₉	1	1	yes	characteristic, complemented
449	#2298	C₂×C₈₉	1	1	yes	characteristic, complemented
450	C₈₉	#35536	1	1	yes	characteristic, direct product factor, Sylow
451	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
452	#542	—	2	8	no	—
453	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
454	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
455	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
456	C₂×#126	C₂²×C₈₉	1	2	yes	complemented
457	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
458	C₂×#124	C₂²×C₈₉	1	2	yes	—
459	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
460	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic, complemented
461	C₂×#123	C₂²×C₈₉	1	2	yes	—
462	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
463	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
464	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
465	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
466	C₂×#120	C₂²×C₈₉	1	4	yes	—
467	#518	—	2	8	no	—
468	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
469	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
470	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
471	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
472	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
473	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
474	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
475	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
476	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
477	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
478	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
479	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
480	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
481	#399	C₂²×C₈₉	1	4	yes	complemented
482	#397	C₂²×C₈₉	1	4	yes	—
483	#394	C₂²×C₈₉	1	4	yes	—
484	#394	C₂²×C₈₉	1	4	yes	—
485	#394	C₂²×C₈₉	1	4	yes	complemented
486	#394	C₂²×C₈₉	1	4	yes	complemented
487	#393	C₂²×C₈₉	1	4	yes	complemented
488	#392	C₂²×C₈₉	1	4	yes	—
489	#391	C₂²×C₈₉	1	1	yes	characteristic, complemented
490	#391	C₂²×C₈₉	1	1	yes	characteristic, complemented
491	#390	C₂²×C₈₉	1	1	yes	characteristic
492	#390	C₂²×C₈₉	1	1	yes	characteristic
493	#390	C₂²×C₈₉	1	1	yes	characteristic
494	#390	C₂²×C₈₉	1	1	yes	characteristic
495	#390	C₂²×C₈₉	1	4	yes	complemented
496	#390	C₂²×C₈₉	1	1	yes	characteristic, complemented
497	#390	C₂²×C₈₉	1	1	yes	characteristic, complemented
498	#388	C₂²×C₈₉	1	2	yes	—
499	#388	C₂²×C₈₉	1	2	yes	—
500	#388	C₂²×C₈₉	1	4	yes	complemented
501	#388	C₂²×C₈₉	1	4	yes	complemented
502	#388	C₂²×C₈₉	1	4	yes	complemented
503	#387	C₂²×C₈₉	1	2	yes	complemented
504	#387	C₂²×C₈₉	1	4	yes	complemented
505	#387	C₂²×C₈₉	1	2	yes	complemented
506	#386	C₂²×C₈₉	1	4	yes	complemented
507	#386	C₂²×C₈₉	1	4	yes	complemented
508	#386	C₂²×C₈₉	1	4	yes	complemented
509	#386	C₂²×C₈₉	1	4	yes	complemented
510	#385	C₂²×C₈₉	1	4	yes	complemented
511	#384	C₂²×C₈₉	1	1	yes	characteristic, complemented
512	#384	C₂²×C₈₉	1	1	yes	characteristic, complemented
513	#382	C₂²×C₈₉	1	1	yes	characteristic, complemented
514	#382	C₂²×C₈₉	1	1	yes	characteristic, complemented
515	#380	C₂²×C₈₉	1	4	yes	complemented
516	#379	C₂²×C₈₉	1	4	yes	—
517	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
518	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
519	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
520	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
521	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	complemented
522	#376	C₂²×C₈₉	1	1	yes	characteristic, complemented
523	C₄³	C₂²×C₈₉	1	1	yes	characteristic, complemented
524	C₂⁵	C₂³×C₈₉	1	2	yes	—
525	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
526	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
527	C₂²×D₄	—	2	4	no	—
528	C₂²×D₄	—	2	4	no	—
529	C₂²×D₄	—	2	4	no	—
530	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
531	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
532	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
533	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
534	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
535	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
536	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
537	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
539	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
540	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
541	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
542	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
543	C₄⋊Q₈	—	2	4	no	—
544	#127	—	2	4	no	—
545	#127	—	2	4	no	—
546	#126	—	2	8	no	—
547	#124	—	2	4	no	—
548	#124	—	2	4	no	—
549	#124	—	2	8	no	—
550	#124	—	2	4	no	—
551	#123	—	2	8	no	—
552	C₂²⋊Q₈	—	2	4	no	—
553	C₂²⋊Q₈	—	2	8	no	—
554	C₂²⋊Q₈	—	4	8	no	—
555	#121	—	2	4	no	—
556	#120	—	4	8	no	—
557	C₄×Q₈	—	2	4	no	—
558	C₄×D₄	—	2	8	no	—
559	C₄×D₄	—	2	8	no	—
560	C₄×D₄	—	2	4	no	—
561	C₄×D₄	—	2	4	no	—
562	C₄×D₄	—	2	4	no	—
563	C₄×D₄	—	2	4	no	—
564	C₄×D₄	—	2	4	no	—
565	C₄×D₄	—	4	8	no	—
566	#117	—	2	4	no	—
567	#117	D₄×C₈₉	1	8	yes	complemented
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	4	yes	—
572	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	4	yes	—
578	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
581	C₂×C₂²⋊C₄	—	2	8	no	—
582	C₂×C₂²⋊C₄	—	2	8	no	—
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	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	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	4	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
604	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
606	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
607	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
608	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
609	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
610	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
611	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
612	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
613	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
614	C₂×C₄²	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	4	yes	—
620	#95	C₂³×C₈₉	1	4	yes	—
621	#95	C₂³×C₈₉	1	2	yes	—
622	#95	C₂³×C₈₉	1	2	yes	—
623	#95	C₂³×C₈₉	1	4	yes	—
624	#95	C₂³×C₈₉	1	4	yes	—
625	C₂⁴	—	2	4	no	—
626	C₂⁴	—	2	4	no	—
627	C₂⁴	—	2	4	no	—
628	C₂⁴	—	4	4	no	—
629	C₂⁴	—	4	4	no	—
630	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
631	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
632	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
633	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
634	C₂×Q₈	—	2	2	no	—
635	C₂×Q₈	—	2	4	no	—
636	C₂×Q₈	—	2	2	no	—
637	C₂×Q₈	—	2	2	no	—
638	C₂×Q₈	—	4	4	no	—
639	C₂×D₄	—	2	32	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	8	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	8	no	—
645	C₂×D₄	—	2	4	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	2	no	—
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	2	2	no	—
653	C₂×D₄	—	2	8	no	—
654	C₂×D₄	—	4	4	no	—
655	C₂×D₄	—	4	4	no	—
656	C₂×D₄	—	4	4	no	—
657	C₂×D₄	—	4	4	no	—
658	C₂×D₄	#41×C₈₉	1	4	yes	—
659	C₂×D₄	#41×C₈₉	1	4	yes	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	2	4	no	—
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	4	4	no	—
668	C₂²×C₄	—	4	4	no	—
669	C₂²×C₄	—	4	4	no	—
670	C₂²×C₄	—	4	4	no	—
671	C₂²×C₄	—	4	4	no	—
672	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
673	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₈₉	1	2	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	2	yes	—
681	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
684	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	8	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	4	4	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
700	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	8	no	—
704	C₂²⋊C₄	—	2	8	no	—
705	C₂²⋊C₄	—	2	4	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	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	8	no	—
715	C₂²⋊C₄	—	4	4	no	—
716	C₂²⋊C₄	—	4	4	no	—
717	C₂²⋊C₄	—	4	4	no	—
718	C₂²⋊C₄	—	4	4	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	4	4	no	—
721	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
722	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
723	C₄²	—	2	4	no	—
724	C₄²	—	2	4	no	—
725	C₄²	—	2	2	no	—
726	C₄²	—	2	2	no	—
727	C₄²	—	2	2	no	—
728	C₄²	—	2	2	no	—
729	C₄²	—	2	4	no	—
730	C₄²	—	4	2	no	—
731	C₄²	C₂×D₄×C₈₉	1	4	yes	—
732	C₄²	C₂×D₄×C₈₉	1	4	yes	—
733	C₂³	—	2	16	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	4	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	4	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	4	no	—
745	C₂³	—	2	4	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	4	no	—
750	C₂³	—	2	4	no	—
751	C₂³	—	8	4	no	—
752	C₂³	—	8	4	no	—
753	C₂³	—	8	8	no	—
754	C₂³	—	8	8	no	—
755	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
756	C₂³	C₂×#41×C₈₉	1	4	yes	—
757	C₂³	C₂×#41×C₈₉	1	4	yes	—
758	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
759	Q₈	—	4	4	no	—
760	Q₈	—	8	4	no	—
761	D₄	—	2	16	no	—
762	D₄	—	2	8	no	—
763	D₄	—	2	8	no	—
764	D₄	—	4	16	no	—
765	D₄	—	4	4	no	—
766	D₄	—	8	4	no	—
767	D₄	—	8	8	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	8	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	4	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	4	no	—
792	C₂×C₄	—	2	4	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	8	4	no	—
798	C₂×C₄	—	8	4	no	—
799	C₂×C₄	—	8	4	no	—
800	C₂×C₄	—	8	4	no	—
801	C₂×C₄	—	8	4	no	—
802	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
803	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
804	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
805	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
806	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
807	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
808	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
809	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
810	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	4	no	—
813	C₂²	—	2	4	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	8	no	—
817	C₂²	—	2	8	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	4	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	4	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	4	no	—
830	C₂²	—	4	4	no	—
831	C₂²	—	8	16	no	—
832	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
833	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
834	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
835	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
836	C₂²	#585×C₈₉	1	2	yes	—
837	C₄	—	2	2	no	—
838	C₄	—	2	2	no	—
839	C₄	—	2	2	no	—
840	C₄	—	2	2	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	4	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	2	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	2	no	—
851	C₄	#525×C₈₉	1	4	yes	—
852	C₂	—	4	4	no	—
853	C₂	—	4	4	no	—
854	C₂	—	4	2	no	—
855	C₂	—	8	2	no	—
856	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
857	C₂	C₈₉×#3498	1	1	yes	characteristic
858	C₂	C₈₉×#3500	1	1	yes	characteristic
859	C₂	C₈₉×#3513	1	2	yes	—
860	C₂	C₈₉×#3514	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₈₉×#2433	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. C₂×#542×C₈₉	C₂	semidirect
2. C₂×#518×C₈₉	C₂	semidirect
3. C₈₉×#2563	C₂	semidirect
4. C₈₉×#2544	C₂	semidirect
5. C₈₉×#2544	C₂	semidirect
6. C₈₉×#2542	C₂	semidirect
7. C₈₉×#2500	C₂	semidirect
8. C₈₉×#2499	C₂	semidirect
9. C₈₉×#2472	C₂	semidirect
10. C₈₉×#2467	C₂	semidirect
11. C₈₉×#2463	C₂	semidirect
12. C₈₉×#2435	C₂	semidirect
14. C₈₉×#2418	C₂	semidirect
15. C₈₉×#2328	C₂	semidirect
16. C₈₉×#2326	C₂	semidirect
17. C₄×#127×C₈₉	C₂	semidirect
18. C₄×#124×C₈₉	C₂	semidirect
19. C₈₉×#2298	C₂	semidirect
22. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
25. C₂×#126×C₈₉	C₂²	semidirect
29. C₂×#124×C₈₉	C₂²	semidirect
32. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
33. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
37. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
44. C₂×C₄×D₄×C₈₉	C₂²	semidirect
45. C₂×C₄×D₄×C₈₉	C₂²	semidirect
50. #399×C₈₉	C₂²	semidirect
54. #394×C₈₉	C₂²	semidirect
55. #394×C₈₉	C₂²	semidirect
56. #393×C₈₉	C₂²	semidirect
58. #391×C₈₉	C₂²	semidirect
59. #391×C₈₉	C₂²	semidirect
64. #390×C₈₉	C₂²	semidirect
65. #390×C₈₉	C₂²	semidirect
66. #390×C₈₉	C₂²	semidirect
69. #388×C₈₉	C₂²	semidirect
70. #388×C₈₉	C₂²	semidirect
71. #388×C₈₉	C₂²	semidirect
72. #387×C₈₉	C₂²	semidirect
73. #387×C₈₉	C₂²	semidirect
74. #387×C₈₉	C₂²	semidirect
75. #386×C₈₉	C₂²	semidirect
76. #386×C₈₉	C₂²	semidirect
77. #386×C₈₉	C₂²	semidirect
78. #386×C₈₉	C₂²	semidirect
79. #385×C₈₉	C₂²	semidirect
80. #384×C₈₉	C₂²	semidirect
81. #384×C₈₉	C₂²	semidirect
82. #382×C₈₉	C₂²	semidirect
83. #382×C₈₉	C₂²	semidirect
84. #380×C₈₉	C₂²	semidirect
86. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
87. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
90. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
91. #376×C₈₉	C₂²	semidirect
92. C₄³×C₈₉	C₂²	semidirect
136. #117×C₈₉	D₄	semidirect
421. #35536	C₈₉	direct (N × H)
431. C₂×#542	C₂×C₈₉	semidirect
432. C₂×#518	C₂×C₈₉	semidirect
433. #2563	C₂×C₈₉	semidirect
434. #2544	C₂×C₈₉	semidirect
435. #2544	C₂×C₈₉	semidirect
436. #2542	C₂×C₈₉	semidirect
437. #2500	C₂×C₈₉	semidirect
438. #2499	C₂×C₈₉	semidirect
439. #2472	C₂×C₈₉	semidirect
440. #2467	C₂×C₈₉	semidirect
441. #2463	C₂×C₈₉	semidirect
442. #2435	C₂×C₈₉	semidirect
444. #2418	C₂×C₈₉	semidirect
445. #2328	C₂×C₈₉	semidirect
446. #2326	C₂×C₈₉	semidirect
447. C₄×#127	C₂×C₈₉	semidirect
448. C₄×#124	C₂×C₈₉	semidirect
449. #2298	C₂×C₈₉	semidirect
450. C₈₉	#35536	direct (N × H)
453. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
456. C₂×#126	C₂²×C₈₉	semidirect
460. C₂×#124	C₂²×C₈₉	semidirect
463. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
464. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
468. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
475. C₂×C₄×D₄	C₂²×C₈₉	semidirect
476. C₂×C₄×D₄	C₂²×C₈₉	semidirect
481. #399	C₂²×C₈₉	semidirect
485. #394	C₂²×C₈₉	semidirect
486. #394	C₂²×C₈₉	semidirect
487. #393	C₂²×C₈₉	semidirect
489. #391	C₂²×C₈₉	semidirect
490. #391	C₂²×C₈₉	semidirect
495. #390	C₂²×C₈₉	semidirect
496. #390	C₂²×C₈₉	semidirect
497. #390	C₂²×C₈₉	semidirect
500. #388	C₂²×C₈₉	semidirect
501. #388	C₂²×C₈₉	semidirect
502. #388	C₂²×C₈₉	semidirect
503. #387	C₂²×C₈₉	semidirect
504. #387	C₂²×C₈₉	semidirect
505. #387	C₂²×C₈₉	semidirect
506. #386	C₂²×C₈₉	semidirect
507. #386	C₂²×C₈₉	semidirect
508. #386	C₂²×C₈₉	semidirect
509. #386	C₂²×C₈₉	semidirect
510. #385	C₂²×C₈₉	semidirect
511. #384	C₂²×C₈₉	semidirect
512. #384	C₂²×C₈₉	semidirect
513. #382	C₂²×C₈₉	semidirect
514. #382	C₂²×C₈₉	semidirect
515. #380	C₂²×C₈₉	semidirect
517. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
518. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
521. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
522. #376	C₂²×C₈₉	semidirect
523. C₄³	C₂²×C₈₉	semidirect
567. #117	D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#542×C₈₉	2
C₂×#518×C₈₉	2
C₈₉×#2563	2
C₈₉×#2544	2
C₈₉×#2542	2
C₈₉×#2500	2
C₈₉×#2499	2
C₈₉×#2472	2
C₈₉×#2467	2
C₈₉×#2463	2
C₈₉×#2435	2
C₈₉×#2433	2
C₈₉×#2418	2
C₈₉×#2328	2
C₈₉×#2326	2
C₄×#127×C₈₉	2
C₄×#124×C₈₉	2
C₈₉×#2298	2
#35536	89

Subgroups — C89×#35536 #36413384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35536 #36413384