Subgroups — C₈₉×#35193 #36413041

Order 22784.

1916 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2853	C₂	1	2	yes	maximal, complemented
2	C₈₉×#2850	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2653	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2648	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2576	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2557	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2513	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2508	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2494	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2491	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2477	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2476	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2452	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2445	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2428	C₂	1	1	yes	maximal, characteristic
16	C₈₉×#2420	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2331	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#2328	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2324	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₉×#2324	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#2298	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₉×#2293	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#124×C₈₉	C₂²	1	2	yes	—
27	C₂×#123×C₈₉	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
29	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#121×C₈₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#117×C₈₉	C₂²	1	2	yes	—
38	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
39	#401×C₈₉	C₂²	1	2	yes	—
40	#400×C₈₉	C₂²	1	2	yes	—
41	#398×C₈₉	C₂²	1	2	yes	—
42	#397×C₈₉	C₂²	1	2	yes	—
43	#397×C₈₉	C₂²	1	2	yes	—
44	#397×C₈₉	C₂²	1	2	yes	—
45	#397×C₈₉	C₂²	1	2	yes	—
46	#396×C₈₉	C₂²	1	2	yes	—
47	#394×C₈₉	C₂²	1	2	yes	—
48	#394×C₈₉	C₂²	1	2	yes	—
49	#394×C₈₉	C₂²	1	2	yes	—
50	#394×C₈₉	C₂²	1	2	yes	—
51	#394×C₈₉	C₂²	1	2	yes	—
52	#393×C₈₉	C₂²	1	2	yes	—
53	#393×C₈₉	C₂²	1	2	yes	—
54	#392×C₈₉	C₂²	1	2	yes	—
55	#391×C₈₉	C₂²	1	2	yes	—
56	#391×C₈₉	C₂²	1	2	yes	—
57	#390×C₈₉	C₂²	1	2	yes	—
58	#390×C₈₉	C₂²	1	2	yes	—
59	#390×C₈₉	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
65	#389×C₈₉	C₂²	1	1	yes	characteristic
66	#389×C₈₉	C₂²	1	1	yes	characteristic
67	#389×C₈₉	C₂²	1	1	yes	characteristic
68	#389×C₈₉	C₂²	1	1	yes	characteristic
69	#389×C₈₉	C₂²	1	1	yes	characteristic
70	#389×C₈₉	C₂²	1	1	yes	characteristic
71	#388×C₈₉	C₂²	1	1	yes	characteristic
72	#388×C₈₉	C₂²	1	1	yes	characteristic
73	#388×C₈₉	C₂²	1	1	yes	characteristic
74	#388×C₈₉	C₂²	1	1	yes	characteristic
75	#388×C₈₉	C₂²	1	2	yes	—
76	#388×C₈₉	C₂²	1	2	yes	—
77	#388×C₈₉	C₂²	1	2	yes	—
78	#388×C₈₉	C₂²	1	2	yes	—
79	#388×C₈₉	C₂²	1	2	yes	—
80	#388×C₈₉	C₂²	1	2	yes	—
81	#388×C₈₉	C₂²	1	2	yes	—
82	#388×C₈₉	C₂²	1	2	yes	—
83	#387×C₈₉	C₂²	1	1	yes	characteristic
84	#387×C₈₉	C₂²	1	1	yes	characteristic
85	#387×C₈₉	C₂²	1	1	yes	characteristic
86	#387×C₈₉	C₂²	1	1	yes	characteristic
87	#387×C₈₉	C₂²	1	2	yes	—
88	#387×C₈₉	C₂²	1	2	yes	—
89	#387×C₈₉	C₂²	1	2	yes	—
90	#387×C₈₉	C₂²	1	2	yes	—
91	#386×C₈₉	C₂²	1	2	yes	—
92	#386×C₈₉	C₂²	1	2	yes	—
93	#386×C₈₉	C₂²	1	2	yes	—
94	#386×C₈₉	C₂²	1	2	yes	—
95	#386×C₈₉	C₂²	1	2	yes	—
96	#386×C₈₉	C₂²	1	2	yes	—
97	#386×C₈₉	C₂²	1	2	yes	—
98	#386×C₈₉	C₂²	1	2	yes	—
99	#386×C₈₉	C₂²	1	2	yes	—
100	#385×C₈₉	C₂²	1	2	yes	—
101	#385×C₈₉	C₂²	1	2	yes	—
102	#385×C₈₉	C₂²	1	2	yes	—
103	#382×C₈₉	C₂²	1	2	yes	—
104	#382×C₈₉	C₂²	1	1	yes	characteristic
105	#382×C₈₉	C₂²	1	1	yes	characteristic
106	#381×C₈₉	C₂²	1	2	yes	—
107	#380×C₈₉	C₂²	1	1	yes	characteristic
108	#380×C₈₉	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
121	#376×C₈₉	C₂²	1	1	yes	characteristic
122	C₄³×C₈₉	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
124	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
127	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
128	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
129	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
130	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
132	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
133	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
134	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
135	C₄⋊Q₈×C₈₉	—	2	4	no	—
136	#127×C₈₉	—	2	4	no	—
137	#124×C₈₉	—	4	4	no	—
138	#123×C₈₉	—	4	4	no	—
139	C₂²⋊Q₈×C₈₉	—	4	4	no	—
140	#121×C₈₉	—	2	4	no	—
141	#121×C₈₉	—	2	4	no	—
142	#121×C₈₉	—	4	4	no	—
143	C₄×D₄×C₈₉	—	2	4	no	—
144	C₄×D₄×C₈₉	—	2	4	no	—
145	C₄×D₄×C₈₉	—	2	4	no	—
146	C₄×D₄×C₈₉	—	2	4	no	—
147	#117×C₈₉	—	2	4	no	—
148	#117×C₈₉	—	4	4	no	—
149	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
155	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
194	C₂×C₄²×C₈₉	—	4	4	no	—
195	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
202	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
206	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
207	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
208	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
209	#95×C₈₉	C₂³	1	1	yes	characteristic
210	#95×C₈₉	C₂³	1	1	yes	characteristic
211	#95×C₈₉	C₂³	1	1	yes	characteristic
212	#95×C₈₉	C₂³	1	1	yes	characteristic
213	#95×C₈₉	C₂³	1	2	yes	—
214	#95×C₈₉	C₂³	1	2	yes	—
215	#95×C₈₉	C₂³	1	2	yes	—
216	#95×C₈₉	C₂³	1	1	yes	characteristic
217	#95×C₈₉	C₂³	1	2	yes	—
218	#95×C₈₉	C₂³	1	1	yes	characteristic
219	#95×C₈₉	C₂³	1	1	yes	characteristic
220	#95×C₈₉	C₂³	1	1	yes	characteristic
221	#95×C₈₉	C₂³	1	2	yes	—
222	#95×C₈₉	C₂³	1	1	yes	characteristic
223	#95×C₈₉	C₂³	1	1	yes	characteristic
224	#95×C₈₉	C₂³	1	2	yes	—
225	#95×C₈₉	C₂³	1	1	yes	characteristic
226	#95×C₈₉	C₂³	1	1	yes	characteristic
227	#95×C₈₉	C₂³	1	2	yes	—
228	#95×C₈₉	C₂³	1	2	yes	—
229	#95×C₈₉	C₂³	1	2	yes	—
230	#95×C₈₉	C₂³	1	2	yes	—
231	#95×C₈₉	C₂³	1	2	yes	—
232	#95×C₈₉	C₂³	1	2	yes	—
233	#95×C₈₉	C₂³	1	2	yes	—
234	#95×C₈₉	C₂³	1	2	yes	—
235	#95×C₈₉	C₂³	1	2	yes	—
236	#95×C₈₉	C₂³	1	2	yes	—
237	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
238	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
239	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
240	C₂×Q₈×C₈₉	—	2	4	no	—
241	C₂×Q₈×C₈₉	—	4	2	no	—
242	C₂×Q₈×C₈₉	—	4	2	no	—
243	C₂×D₄×C₈₉	—	2	4	no	—
244	C₂×D₄×C₈₉	—	2	4	no	—
245	C₂×D₄×C₈₉	—	2	4	no	—
246	C₂×D₄×C₈₉	—	2	2	no	—
247	C₂×D₄×C₈₉	—	2	2	no	—
248	C₂×D₄×C₈₉	—	2	2	no	—
249	C₂×D₄×C₈₉	—	2	2	no	—
250	C₂×D₄×C₈₉	—	2	2	no	—
251	C₂×D₄×C₈₉	—	2	4	no	—
252	C₂×D₄×C₈₉	—	4	2	no	—
253	C₂×D₄×C₈₉	—	4	2	no	—
254	C₂×D₄×C₈₉	—	4	2	no	—
255	C₂×D₄×C₈₉	—	4	2	no	—
256	C₂×D₄×C₈₉	—	4	2	no	—
257	C₂×D₄×C₈₉	—	4	2	no	—
258	C₂×D₄×C₈₉	—	4	2	no	—
259	C₂×D₄×C₈₉	—	4	2	no	—
260	C₂×D₄×C₈₉	#41	1	4	yes	—
261	C₂²×C₄×C₈₉	—	2	4	no	—
262	C₂²×C₄×C₈₉	—	2	2	no	—
263	C₂²×C₄×C₈₉	—	2	4	no	—
264	C₂²×C₄×C₈₉	—	2	4	no	—
265	C₂²×C₄×C₈₉	—	2	4	no	—
266	C₂²×C₄×C₈₉	—	2	2	no	—
267	C₂²×C₄×C₈₉	—	2	2	no	—
268	C₂²×C₄×C₈₉	—	2	4	no	—
269	C₂²×C₄×C₈₉	—	2	4	no	—
270	C₂²×C₄×C₈₉	—	4	2	no	—
271	C₂²×C₄×C₈₉	—	4	2	no	—
272	C₂²×C₄×C₈₉	—	4	2	no	—
273	C₂²×C₄×C₈₉	—	4	2	no	—
274	C₂²×C₄×C₈₉	—	4	2	no	—
275	C₂²×C₄×C₈₉	—	4	2	no	—
276	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
296	C₄⋊C₄×C₈₉	—	2	2	no	—
297	C₄⋊C₄×C₈₉	—	2	2	no	—
298	C₄⋊C₄×C₈₉	—	2	2	no	—
299	C₄⋊C₄×C₈₉	—	2	2	no	—
300	C₄⋊C₄×C₈₉	—	2	2	no	—
301	C₄⋊C₄×C₈₉	—	2	2	no	—
302	C₄⋊C₄×C₈₉	—	2	4	no	—
303	C₄⋊C₄×C₈₉	—	2	2	no	—
304	C₄⋊C₄×C₈₉	—	2	4	no	—
305	C₄⋊C₄×C₈₉	—	2	2	no	—
306	C₄⋊C₄×C₈₉	—	2	2	no	—
307	C₄⋊C₄×C₈₉	—	4	1	no	—
308	C₄⋊C₄×C₈₉	—	4	1	no	—
309	C₄⋊C₄×C₈₉	—	4	2	no	—
310	C₄⋊C₄×C₈₉	—	4	2	no	—
311	C₄⋊C₄×C₈₉	—	4	2	no	—
312	C₄⋊C₄×C₈₉	—	4	2	no	—
313	C₄⋊C₄×C₈₉	—	4	2	no	—
314	C₄⋊C₄×C₈₉	#41	1	4	yes	—
315	C₂²⋊C₄×C₈₉	—	2	4	no	—
316	C₂²⋊C₄×C₈₉	—	2	4	no	—
317	C₂²⋊C₄×C₈₉	—	2	2	no	—
318	C₂²⋊C₄×C₈₉	—	2	2	no	—
319	C₂²⋊C₄×C₈₉	—	2	4	no	—
320	C₂²⋊C₄×C₈₉	—	2	4	no	—
321	C₂²⋊C₄×C₈₉	—	2	4	no	—
322	C₂²⋊C₄×C₈₉	—	2	4	no	—
323	C₂²⋊C₄×C₈₉	—	2	4	no	—
324	C₂²⋊C₄×C₈₉	—	2	2	no	—
325	C₂²⋊C₄×C₈₉	—	2	4	no	—
326	C₂²⋊C₄×C₈₉	—	2	2	no	—
327	C₂²⋊C₄×C₈₉	—	4	2	no	—
328	C₂²⋊C₄×C₈₉	—	4	1	no	—
329	C₂²⋊C₄×C₈₉	—	4	1	no	—
330	C₂²⋊C₄×C₈₉	—	4	2	no	—
331	C₂²⋊C₄×C₈₉	—	4	2	no	—
332	C₂²⋊C₄×C₈₉	—	4	2	no	—
333	C₂²⋊C₄×C₈₉	—	4	2	no	—
334	C₂²⋊C₄×C₈₉	—	4	2	no	—
335	C₂²⋊C₄×C₈₉	—	4	2	no	—
336	C₂²⋊C₄×C₈₉	—	4	2	no	—
337	C₂²⋊C₄×C₈₉	—	4	2	no	—
338	C₂²⋊C₄×C₈₉	—	4	2	no	—
339	C₂²⋊C₄×C₈₉	—	4	2	no	—
340	C₂²⋊C₄×C₈₉	—	4	2	no	—
341	C₄²×C₈₉	—	2	2	no	—
342	C₄²×C₈₉	—	2	2	no	—
343	C₄²×C₈₉	—	2	2	no	—
344	C₄²×C₈₉	—	2	2	no	—
345	C₄²×C₈₉	—	2	2	no	—
346	C₄²×C₈₉	—	2	2	no	—
347	C₄²×C₈₉	—	2	4	no	—
348	C₄²×C₈₉	—	2	2	no	—
349	C₄²×C₈₉	—	4	2	no	—
350	C₄²×C₈₉	—	4	2	no	—
351	C₄²×C₈₉	—	4	1	no	—
352	C₄²×C₈₉	—	4	1	no	—
353	C₄²×C₈₉	—	4	2	no	—
354	C₄²×C₈₉	#41	1	4	yes	—
355	C₂³×C₈₉	—	2	2	no	—
356	C₂³×C₈₉	—	2	2	no	—
357	C₂³×C₈₉	—	2	2	no	—
358	C₂³×C₈₉	—	2	2	no	—
359	C₂³×C₈₉	—	2	2	no	—
360	C₂³×C₈₉	—	2	2	no	—
361	C₂³×C₈₉	—	2	1	no	—
362	C₂³×C₈₉	—	2	2	no	—
363	C₂³×C₈₉	—	2	2	no	—
364	C₂³×C₈₉	—	2	1	no	—
365	C₂³×C₈₉	—	2	1	no	—
366	C₂³×C₈₉	—	2	2	no	—
367	C₂³×C₈₉	—	2	2	no	—
368	C₂³×C₈₉	—	2	1	no	—
369	C₂³×C₈₉	—	2	2	no	—
370	C₂³×C₈₉	—	2	1	no	—
371	C₂³×C₈₉	—	2	1	no	—
372	C₂³×C₈₉	—	2	2	no	—
373	C₂³×C₈₉	—	2	2	no	—
374	C₂³×C₈₉	—	2	1	no	—
375	C₂³×C₈₉	C₂×#41	1	4	yes	—
376	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
377	Q₈×C₈₉	—	8	4	no	—
378	D₄×C₈₉	—	2	8	no	—
379	D₄×C₈₉	—	4	4	no	—
380	D₄×C₈₉	—	8	4	no	—
381	D₄×C₈₉	—	8	4	no	—
382	D₄×C₈₉	—	8	4	no	—
383	D₄×C₈₉	—	8	4	no	—
384	C₂×C₄×C₈₉	—	2	1	no	—
385	C₂×C₄×C₈₉	—	2	1	no	—
386	C₂×C₄×C₈₉	—	2	1	no	—
387	C₂×C₄×C₈₉	—	2	1	no	—
388	C₂×C₄×C₈₉	—	2	1	no	—
389	C₂×C₄×C₈₉	—	2	2	no	—
390	C₂×C₄×C₈₉	—	2	2	no	—
391	C₂×C₄×C₈₉	—	2	1	no	—
392	C₂×C₄×C₈₉	—	2	1	no	—
393	C₂×C₄×C₈₉	—	2	1	no	—
394	C₂×C₄×C₈₉	—	2	1	no	—
395	C₂×C₄×C₈₉	—	2	1	no	—
396	C₂×C₄×C₈₉	—	2	1	no	—
397	C₂×C₄×C₈₉	—	2	1	no	—
398	C₂×C₄×C₈₉	—	2	1	no	—
399	C₂×C₄×C₈₉	—	2	1	no	—
400	C₂×C₄×C₈₉	—	2	1	no	—
401	C₂×C₄×C₈₉	—	2	1	no	—
402	C₂×C₄×C₈₉	—	2	1	no	—
403	C₂×C₄×C₈₉	—	2	1	no	—
404	C₂×C₄×C₈₉	—	2	2	no	—
405	C₂×C₄×C₈₉	—	2	2	no	—
406	C₂×C₄×C₈₉	—	2	2	no	—
407	C₂×C₄×C₈₉	—	2	2	no	—
408	C₂×C₄×C₈₉	—	2	1	no	—
409	C₂×C₄×C₈₉	—	2	2	no	—
410	C₂×C₄×C₈₉	—	2	2	no	—
411	C₂×C₄×C₈₉	—	2	1	no	—
412	C₂×C₄×C₈₉	—	2	2	no	—
413	C₂×C₄×C₈₉	—	2	2	no	—
414	C₂×C₄×C₈₉	—	2	2	no	—
415	C₂×C₄×C₈₉	—	2	2	no	—
416	C₂×C₄×C₈₉	—	2	1	no	—
417	C₂×C₄×C₈₉	—	2	1	no	—
418	C₂×C₄×C₈₉	—	2	1	no	—
419	C₂×C₄×C₈₉	—	2	1	no	—
420	C₂×C₄×C₈₉	—	2	1	no	—
421	C₂×C₄×C₈₉	—	2	2	no	—
422	C₂×C₄×C₈₉	—	2	1	no	—
423	C₂×C₄×C₈₉	—	2	1	no	—
424	C₂×C₄×C₈₉	—	2	1	no	—
425	C₂×C₄×C₈₉	—	2	1	no	—
426	C₂×C₄×C₈₉	—	2	1	no	—
427	C₂×C₄×C₈₉	—	2	1	no	—
428	C₂×C₄×C₈₉	—	2	1	no	—
429	C₂×C₄×C₈₉	—	2	2	no	—
430	C₂×C₄×C₈₉	—	2	2	no	—
431	C₂×C₄×C₈₉	—	2	2	no	—
432	C₂×C₄×C₈₉	—	2	2	no	—
433	C₂×C₄×C₈₉	—	2	1	no	—
434	C₂×C₄×C₈₉	—	2	1	no	—
435	C₂×C₄×C₈₉	—	2	1	no	—
436	C₂×C₄×C₈₉	—	4	8	no	—
437	C₂×C₄×C₈₉	—	4	8	no	—
438	C₂×C₄×C₈₉	—	4	8	no	—
439	C₂×C₄×C₈₉	—	4	8	no	—
440	C₂×C₄×C₈₉	—	4	4	no	—
441	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
442	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
443	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
444	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
445	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
446	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
447	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
448	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
449	C₂²×C₈₉	—	2	4	no	—
450	C₂²×C₈₉	—	2	4	no	—
451	C₂²×C₈₉	—	2	4	no	—
452	C₂²×C₈₉	—	4	2	no	—
453	C₂²×C₈₉	—	4	2	no	—
454	C₂²×C₈₉	—	4	2	no	—
455	C₂²×C₈₉	—	4	2	no	—
456	C₂²×C₈₉	—	4	1	no	—
457	C₂²×C₈₉	—	4	2	no	—
458	C₂²×C₈₉	—	4	2	no	—
459	C₂²×C₈₉	—	4	1	no	—
460	C₂²×C₈₉	—	4	1	no	—
461	C₂²×C₈₉	—	4	2	no	—
462	C₂²×C₈₉	—	4	2	no	—
463	C₂²×C₈₉	—	4	1	no	—
464	C₂²×C₈₉	—	4	1	no	—
465	C₂²×C₈₉	—	4	2	no	—
466	C₂²×C₈₉	—	4	1	no	—
467	C₂²×C₈₉	—	4	2	no	—
468	C₂²×C₈₉	—	4	2	no	—
469	C₂²×C₈₉	—	4	1	no	—
470	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
471	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
472	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
473	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
474	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
475	C₂²×C₈₉	#585	1	1	yes	characteristic
476	C₂²×C₈₉	#585	1	1	yes	characteristic
477	C₄×C₈₉	—	2	2	no	—
478	C₄×C₈₉	—	2	2	no	—
479	C₄×C₈₉	—	2	2	no	—
480	C₄×C₈₉	—	2	2	no	—
481	C₄×C₈₉	—	2	4	no	—
482	C₄×C₈₉	—	4	1	no	—
483	C₄×C₈₉	—	4	1	no	—
484	C₄×C₈₉	—	4	1	no	—
485	C₄×C₈₉	—	4	2	no	—
486	C₄×C₈₉	—	4	2	no	—
487	C₄×C₈₉	—	4	2	no	—
488	C₄×C₈₉	—	4	1	no	—
489	C₄×C₈₉	—	4	1	no	—
490	C₄×C₈₉	—	4	2	no	—
491	C₄×C₈₉	—	4	1	no	—
492	C₄×C₈₉	—	4	2	no	—
493	C₄×C₈₉	—	4	1	no	—
494	C₄×C₈₉	—	4	1	no	—
495	C₄×C₈₉	—	4	1	no	—
496	C₄×C₈₉	#529	1	4	yes	—
497	#35193	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
498	C₂×C₈₉	—	4	4	no	—
499	C₂×C₈₉	—	8	1	no	—
500	C₂×C₈₉	—	8	2	no	—
501	C₂×C₈₉	C₂×#529	1	1	yes	characteristic
502	C₂×C₈₉	#3460	1	1	yes	characteristic
503	C₂×C₈₉	#3460	1	1	yes	characteristic
504	C₂×C₈₉	#3513	1	1	yes	characteristic
505	C₂×C₈₉	#3514	1	1	yes	characteristic
506	C₂×C₈₉	#3519	1	1	yes	characteristic
507	C₂×C₈₉	#3524	1	1	yes	characteristic
508	#2853	C₂×C₈₉	1	2	yes	complemented
509	#2850	C₂×C₈₉	1	2	yes	complemented
510	#2653	C₂×C₈₉	1	2	yes	complemented
511	#2648	C₂×C₈₉	1	2	yes	complemented
512	#2576	C₂×C₈₉	1	2	yes	complemented
513	#2557	C₂×C₈₉	1	2	yes	complemented
514	#2513	C₂×C₈₉	1	1	yes	characteristic, complemented
515	#2508	C₂×C₈₉	1	1	yes	characteristic, complemented
516	#2494	C₂×C₈₉	1	1	yes	characteristic, complemented
517	#2491	C₂×C₈₉	1	1	yes	characteristic, complemented
518	#2477	C₂×C₈₉	1	2	yes	complemented
519	#2476	C₂×C₈₉	1	2	yes	complemented
520	#2452	C₂×C₈₉	1	1	yes	characteristic, complemented
521	#2445	C₂×C₈₉	1	1	yes	characteristic, complemented
522	#2428	C₂×C₈₉	1	1	yes	characteristic
523	#2420	C₂×C₈₉	1	1	yes	characteristic, complemented
524	#2331	C₂×C₈₉	1	1	yes	characteristic, complemented
525	#2328	C₂×C₈₉	1	1	yes	characteristic, complemented
526	#2324	C₂×C₈₉	1	1	yes	characteristic, complemented
527	#2324	C₂×C₈₉	1	1	yes	characteristic, complemented
528	#2298	C₂×C₈₉	1	1	yes	characteristic, complemented
529	#2293	C₂×C₈₉	1	1	yes	characteristic, complemented
530	C₄²×D₄	C₂×C₈₉	1	1	yes	characteristic, complemented
531	C₈₉	#35193	1	1	yes	characteristic, direct product factor, Sylow
532	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
533	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
534	C₂×#124	C₂²×C₈₉	1	2	yes	—
535	C₂×#123	C₂²×C₈₉	1	2	yes	—
536	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
537	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
538	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
539	C₂×#121	C₂²×C₈₉	1	2	yes	—
540	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
541	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
542	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
543	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
544	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
545	C₂×#117	C₂²×C₈₉	1	2	yes	—
546	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
547	#401	C₂²×C₈₉	1	2	yes	—
548	#400	C₂²×C₈₉	1	2	yes	—
549	#398	C₂²×C₈₉	1	2	yes	—
550	#397	C₂²×C₈₉	1	2	yes	—
551	#397	C₂²×C₈₉	1	2	yes	—
552	#397	C₂²×C₈₉	1	2	yes	—
553	#397	C₂²×C₈₉	1	2	yes	—
554	#396	C₂²×C₈₉	1	2	yes	—
555	#394	C₂²×C₈₉	1	2	yes	—
556	#394	C₂²×C₈₉	1	2	yes	—
557	#394	C₂²×C₈₉	1	2	yes	—
558	#394	C₂²×C₈₉	1	2	yes	—
559	#394	C₂²×C₈₉	1	2	yes	—
560	#393	C₂²×C₈₉	1	2	yes	—
561	#393	C₂²×C₈₉	1	2	yes	—
562	#392	C₂²×C₈₉	1	2	yes	—
563	#391	C₂²×C₈₉	1	2	yes	—
564	#391	C₂²×C₈₉	1	2	yes	—
565	#390	C₂²×C₈₉	1	2	yes	—
566	#390	C₂²×C₈₉	1	1	yes	characteristic
567	#390	C₂²×C₈₉	1	1	yes	characteristic
568	#390	C₂²×C₈₉	1	2	yes	—
569	#390	C₂²×C₈₉	1	1	yes	characteristic
570	#390	C₂²×C₈₉	1	1	yes	characteristic
571	#390	C₂²×C₈₉	1	1	yes	characteristic
572	#390	C₂²×C₈₉	1	1	yes	characteristic
573	#389	C₂²×C₈₉	1	1	yes	characteristic
574	#389	C₂²×C₈₉	1	1	yes	characteristic
575	#389	C₂²×C₈₉	1	1	yes	characteristic
576	#389	C₂²×C₈₉	1	1	yes	characteristic
577	#389	C₂²×C₈₉	1	1	yes	characteristic
578	#389	C₂²×C₈₉	1	1	yes	characteristic
579	#388	C₂²×C₈₉	1	2	yes	—
580	#388	C₂²×C₈₉	1	2	yes	—
581	#388	C₂²×C₈₉	1	2	yes	—
582	#388	C₂²×C₈₉	1	1	yes	characteristic
583	#388	C₂²×C₈₉	1	2	yes	—
584	#388	C₂²×C₈₉	1	2	yes	—
585	#388	C₂²×C₈₉	1	2	yes	—
586	#388	C₂²×C₈₉	1	2	yes	—
587	#388	C₂²×C₈₉	1	1	yes	characteristic
588	#388	C₂²×C₈₉	1	2	yes	—
589	#388	C₂²×C₈₉	1	1	yes	characteristic
590	#388	C₂²×C₈₉	1	1	yes	characteristic
591	#387	C₂²×C₈₉	1	1	yes	characteristic
592	#387	C₂²×C₈₉	1	2	yes	—
593	#387	C₂²×C₈₉	1	2	yes	—
594	#387	C₂²×C₈₉	1	1	yes	characteristic
595	#387	C₂²×C₈₉	1	2	yes	—
596	#387	C₂²×C₈₉	1	2	yes	—
597	#387	C₂²×C₈₉	1	1	yes	characteristic
598	#387	C₂²×C₈₉	1	1	yes	characteristic
599	#386	C₂²×C₈₉	1	2	yes	—
600	#386	C₂²×C₈₉	1	2	yes	—
601	#386	C₂²×C₈₉	1	2	yes	—
602	#386	C₂²×C₈₉	1	2	yes	—
603	#386	C₂²×C₈₉	1	2	yes	—
604	#386	C₂²×C₈₉	1	2	yes	—
605	#386	C₂²×C₈₉	1	2	yes	—
606	#386	C₂²×C₈₉	1	2	yes	—
607	#386	C₂²×C₈₉	1	2	yes	—
608	#385	C₂²×C₈₉	1	2	yes	—
609	#385	C₂²×C₈₉	1	2	yes	—
610	#385	C₂²×C₈₉	1	2	yes	—
611	#382	C₂²×C₈₉	1	2	yes	—
612	#382	C₂²×C₈₉	1	1	yes	characteristic
613	#382	C₂²×C₈₉	1	1	yes	characteristic
614	#381	C₂²×C₈₉	1	2	yes	—
615	#380	C₂²×C₈₉	1	1	yes	characteristic
616	#380	C₂²×C₈₉	1	1	yes	characteristic
617	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
618	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
619	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
620	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
621	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
622	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
623	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
624	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
625	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
626	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
627	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
628	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
629	#376	C₂²×C₈₉	1	1	yes	characteristic
630	C₄³	C₂²×C₈₉	1	1	yes	characteristic
631	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
632	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
633	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
634	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
635	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
636	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
637	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
638	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
639	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
640	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
641	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
642	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
643	C₄⋊Q₈	—	2	4	no	—
644	#127	—	2	4	no	—
645	#124	—	4	4	no	—
646	#123	—	4	4	no	—
647	C₂²⋊Q₈	—	4	4	no	—
648	#121	—	2	4	no	—
649	#121	—	2	4	no	—
650	#121	—	4	4	no	—
651	C₄×D₄	—	2	4	no	—
652	C₄×D₄	—	2	4	no	—
653	C₄×D₄	—	2	4	no	—
654	C₄×D₄	—	2	4	no	—
655	#117	—	2	4	no	—
656	#117	—	4	4	no	—
657	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
669	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
671	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
673	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
675	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
676	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
678	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
679	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
684	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
688	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
692	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
696	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
697	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
702	C₂×C₄²	—	4	4	no	—
703	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
704	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
705	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
706	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
707	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
708	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
709	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
710	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
711	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
712	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
713	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
714	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
715	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
716	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
717	#95	C₂³×C₈₉	1	1	yes	characteristic
718	#95	C₂³×C₈₉	1	1	yes	characteristic
719	#95	C₂³×C₈₉	1	1	yes	characteristic
720	#95	C₂³×C₈₉	1	1	yes	characteristic
721	#95	C₂³×C₈₉	1	2	yes	—
722	#95	C₂³×C₈₉	1	2	yes	—
723	#95	C₂³×C₈₉	1	2	yes	—
724	#95	C₂³×C₈₉	1	1	yes	characteristic
725	#95	C₂³×C₈₉	1	2	yes	—
726	#95	C₂³×C₈₉	1	1	yes	characteristic
727	#95	C₂³×C₈₉	1	1	yes	characteristic
728	#95	C₂³×C₈₉	1	1	yes	characteristic
729	#95	C₂³×C₈₉	1	2	yes	—
730	#95	C₂³×C₈₉	1	1	yes	characteristic
731	#95	C₂³×C₈₉	1	1	yes	characteristic
732	#95	C₂³×C₈₉	1	2	yes	—
733	#95	C₂³×C₈₉	1	1	yes	characteristic
734	#95	C₂³×C₈₉	1	1	yes	characteristic
735	#95	C₂³×C₈₉	1	2	yes	—
736	#95	C₂³×C₈₉	1	2	yes	—
737	#95	C₂³×C₈₉	1	2	yes	—
738	#95	C₂³×C₈₉	1	2	yes	—
739	#95	C₂³×C₈₉	1	2	yes	—
740	#95	C₂³×C₈₉	1	2	yes	—
741	#95	C₂³×C₈₉	1	2	yes	—
742	#95	C₂³×C₈₉	1	2	yes	—
743	#95	C₂³×C₈₉	1	2	yes	—
744	#95	C₂³×C₈₉	1	2	yes	—
745	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
746	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
747	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
748	C₂×Q₈	—	2	4	no	—
749	C₂×Q₈	—	4	2	no	—
750	C₂×Q₈	—	4	2	no	—
751	C₂×D₄	—	2	4	no	—
752	C₂×D₄	—	2	4	no	—
753	C₂×D₄	—	2	4	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	2	no	—
758	C₂×D₄	—	2	2	no	—
759	C₂×D₄	—	2	4	no	—
760	C₂×D₄	—	4	2	no	—
761	C₂×D₄	—	4	2	no	—
762	C₂×D₄	—	4	2	no	—
763	C₂×D₄	—	4	2	no	—
764	C₂×D₄	—	4	2	no	—
765	C₂×D₄	—	4	2	no	—
766	C₂×D₄	—	4	2	no	—
767	C₂×D₄	—	4	2	no	—
768	C₂×D₄	#41×C₈₉	1	4	yes	—
769	C₂²×C₄	—	2	4	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	4	no	—
772	C₂²×C₄	—	2	4	no	—
773	C₂²×C₄	—	2	4	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	4	no	—
777	C₂²×C₄	—	2	4	no	—
778	C₂²×C₄	—	4	2	no	—
779	C₂²×C₄	—	4	2	no	—
780	C₂²×C₄	—	4	2	no	—
781	C₂²×C₄	—	4	2	no	—
782	C₂²×C₄	—	4	2	no	—
783	C₂²×C₄	—	4	2	no	—
784	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
790	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
792	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
794	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
798	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
801	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
802	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
803	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	4	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	4	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	4	2	no	—
816	C₄⋊C₄	—	4	2	no	—
817	C₄⋊C₄	—	4	2	no	—
818	C₄⋊C₄	—	4	2	no	—
819	C₄⋊C₄	—	4	1	no	—
820	C₄⋊C₄	—	4	1	no	—
821	C₄⋊C₄	—	4	2	no	—
822	C₄⋊C₄	#41×C₈₉	1	4	yes	—
823	C₂²⋊C₄	—	2	4	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	2	4	no	—
829	C₂²⋊C₄	—	2	4	no	—
830	C₂²⋊C₄	—	2	4	no	—
831	C₂²⋊C₄	—	2	4	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	4	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	4	2	no	—
836	C₂²⋊C₄	—	4	2	no	—
837	C₂²⋊C₄	—	4	2	no	—
838	C₂²⋊C₄	—	4	2	no	—
839	C₂²⋊C₄	—	4	2	no	—
840	C₂²⋊C₄	—	4	2	no	—
841	C₂²⋊C₄	—	4	2	no	—
842	C₂²⋊C₄	—	4	2	no	—
843	C₂²⋊C₄	—	4	1	no	—
844	C₂²⋊C₄	—	4	1	no	—
845	C₂²⋊C₄	—	4	2	no	—
846	C₂²⋊C₄	—	4	2	no	—
847	C₂²⋊C₄	—	4	2	no	—
848	C₂²⋊C₄	—	4	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	2	no	—
851	C₄²	—	2	2	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	2	no	—
854	C₄²	—	2	2	no	—
855	C₄²	—	2	4	no	—
856	C₄²	—	2	2	no	—
857	C₄²	—	4	2	no	—
858	C₄²	—	4	2	no	—
859	C₄²	—	4	2	no	—
860	C₄²	—	4	1	no	—
861	C₄²	—	4	1	no	—
862	C₄²	#41×C₈₉	1	4	yes	—
863	C₂³	—	2	2	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	2	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	2	2	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	2	1	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	1	no	—
873	C₂³	—	2	1	no	—
874	C₂³	—	2	2	no	—
875	C₂³	—	2	2	no	—
876	C₂³	—	2	1	no	—
877	C₂³	—	2	2	no	—
878	C₂³	—	2	1	no	—
879	C₂³	—	2	1	no	—
880	C₂³	—	2	2	no	—
881	C₂³	—	2	2	no	—
882	C₂³	—	2	1	no	—
883	C₂³	C₂×#41×C₈₉	1	4	yes	—
884	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
885	Q₈	—	8	4	no	—
886	D₄	—	2	8	no	—
887	D₄	—	4	4	no	—
888	D₄	—	8	4	no	—
889	D₄	—	8	4	no	—
890	D₄	—	8	4	no	—
891	D₄	—	8	4	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	4	8	no	—
945	C₂×C₄	—	4	8	no	—
946	C₂×C₄	—	4	8	no	—
947	C₂×C₄	—	4	8	no	—
948	C₂×C₄	—	4	4	no	—
949	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
950	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
951	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
952	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
953	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
954	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
955	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
956	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
957	C₂²	—	2	4	no	—
958	C₂²	—	2	4	no	—
959	C₂²	—	2	4	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	1	no	—
965	C₂²	—	4	2	no	—
966	C₂²	—	4	2	no	—
967	C₂²	—	4	1	no	—
968	C₂²	—	4	1	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	4	2	no	—
971	C₂²	—	4	1	no	—
972	C₂²	—	4	1	no	—
973	C₂²	—	4	2	no	—
974	C₂²	—	4	1	no	—
975	C₂²	—	4	2	no	—
976	C₂²	—	4	2	no	—
977	C₂²	—	4	1	no	—
978	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
979	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
980	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
981	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
982	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
983	C₂²	#585×C₈₉	1	1	yes	characteristic
984	C₂²	#585×C₈₉	1	1	yes	characteristic
985	C₄	—	2	2	no	—
986	C₄	—	2	2	no	—
987	C₄	—	2	2	no	—
988	C₄	—	2	2	no	—
989	C₄	—	2	4	no	—
990	C₄	—	4	1	no	—
991	C₄	—	4	2	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	1	no	—
994	C₄	—	4	1	no	—
995	C₄	—	4	2	no	—
996	C₄	—	4	1	no	—
997	C₄	—	4	1	no	—
998	C₄	—	4	2	no	—
999	C₄	—	4	1	no	—
1000	C₄	—	4	1	no	—
1001	C₄	—	4	2	no	—
1002	C₄	—	4	1	no	—
1003	C₄	—	4	1	no	—
1004	C₄	#529×C₈₉	1	4	yes	—
1005	C₂	—	4	4	no	—
1006	C₂	—	8	1	no	—
1007	C₂	—	8	2	no	—
1008	C₂	C₂×#529×C₈₉	1	1	yes	characteristic
1009	C₂	C₈₉×#3460	1	1	yes	characteristic
1010	C₂	C₈₉×#3460	1	1	yes	characteristic
1011	C₂	C₈₉×#3513	1	1	yes	characteristic
1012	C₂	C₈₉×#3514	1	1	yes	characteristic
1013	C₂	C₈₉×#3519	1	1	yes	characteristic
1014	C₂	C₈₉×#3524	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₈₉×#2428	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. C₈₉×#2853	C₂	semidirect
2. C₈₉×#2850	C₂	semidirect
3. C₈₉×#2653	C₂	semidirect
4. C₈₉×#2648	C₂	semidirect
5. C₈₉×#2576	C₂	semidirect
6. C₈₉×#2557	C₂	semidirect
7. C₈₉×#2513	C₂	semidirect
8. C₈₉×#2508	C₂	semidirect
9. C₈₉×#2494	C₂	semidirect
10. C₈₉×#2491	C₂	semidirect
11. C₈₉×#2477	C₂	semidirect
12. C₈₉×#2476	C₂	semidirect
13. C₈₉×#2452	C₂	semidirect
14. C₈₉×#2445	C₂	semidirect
16. C₈₉×#2420	C₂	semidirect
17. C₈₉×#2331	C₂	semidirect
18. C₈₉×#2328	C₂	semidirect
19. C₈₉×#2324	C₂	semidirect
20. C₈₉×#2324	C₂	semidirect
21. C₈₉×#2298	C₂	semidirect
22. C₈₉×#2293	C₂	semidirect
23. C₄²×D₄×C₈₉	C₂	semidirect
497. #35193	C₈₉	direct (N × H)
508. #2853	C₂×C₈₉	semidirect
509. #2850	C₂×C₈₉	semidirect
510. #2653	C₂×C₈₉	semidirect
511. #2648	C₂×C₈₉	semidirect
512. #2576	C₂×C₈₉	semidirect
513. #2557	C₂×C₈₉	semidirect
514. #2513	C₂×C₈₉	semidirect
515. #2508	C₂×C₈₉	semidirect
516. #2494	C₂×C₈₉	semidirect
517. #2491	C₂×C₈₉	semidirect
518. #2477	C₂×C₈₉	semidirect
519. #2476	C₂×C₈₉	semidirect
520. #2452	C₂×C₈₉	semidirect
521. #2445	C₂×C₈₉	semidirect
523. #2420	C₂×C₈₉	semidirect
524. #2331	C₂×C₈₉	semidirect
525. #2328	C₂×C₈₉	semidirect
526. #2324	C₂×C₈₉	semidirect
527. #2324	C₂×C₈₉	semidirect
528. #2298	C₂×C₈₉	semidirect
529. #2293	C₂×C₈₉	semidirect
530. C₄²×D₄	C₂×C₈₉	semidirect
531. C₈₉	#35193	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#2853	2
C₈₉×#2850	2
C₈₉×#2653	2
C₈₉×#2648	2
C₈₉×#2576	2
C₈₉×#2557	2
C₈₉×#2513	2
C₈₉×#2508	2
C₈₉×#2494	2
C₈₉×#2491	2
C₈₉×#2477	2
C₈₉×#2476	2
C₈₉×#2452	2
C₈₉×#2445	2
C₈₉×#2428	2
C₈₉×#2420	2
C₈₉×#2331	2
C₈₉×#2328	2
C₈₉×#2324	2
C₈₉×#2298	2
C₈₉×#2293	2
C₄²×D₄×C₈₉	2
#35193	89

Subgroups — C89×#35193 #36413041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35193 #36413041