Subgroups — C₈₉×#35270 #36413118

Order 22784.

1766 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#2855	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2854	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#2850	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#2647	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2645	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2644	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2640	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2532	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2530	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2529	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2527	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2510	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2488	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2450	C₂	1	2	yes	maximal, complemented
16	C₈₉×#2419	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2331	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#2326	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2320	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₉×#2319	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂²⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₈₉	C₂	1	1	yes	maximal, characteristic
23	C₂×#376×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#123×C₈₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
29	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
33	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
36	#401×C₈₉	C₂²	1	2	yes	—
37	#400×C₈₉	C₂²	1	2	yes	—
38	#400×C₈₉	C₂²	1	2	yes	—
39	#400×C₈₉	C₂²	1	2	yes	—
40	#400×C₈₉	C₂²	1	2	yes	—
41	#400×C₈₉	C₂²	1	2	yes	—
42	#398×C₈₉	C₂²	1	2	yes	—
43	#398×C₈₉	C₂²	1	2	yes	—
44	#397×C₈₉	C₂²	1	2	yes	—
45	#397×C₈₉	C₂²	1	2	yes	—
46	#397×C₈₉	C₂²	1	2	yes	—
47	#397×C₈₉	C₂²	1	2	yes	—
48	#397×C₈₉	C₂²	1	2	yes	—
49	#396×C₈₉	C₂²	1	2	yes	—
50	#393×C₈₉	C₂²	1	2	yes	—
51	#393×C₈₉	C₂²	1	2	yes	—
52	#391×C₈₉	C₂²	1	1	yes	characteristic
53	#391×C₈₉	C₂²	1	1	yes	characteristic
54	#391×C₈₉	C₂²	1	1	yes	characteristic
55	#391×C₈₉	C₂²	1	1	yes	characteristic
56	#391×C₈₉	C₂²	1	2	yes	—
57	#391×C₈₉	C₂²	1	2	yes	—
58	#391×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	#389×C₈₉	C₂²	1	1	yes	characteristic
64	#389×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	#389×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	#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	#387×C₈₉	C₂²	1	2	yes	—
82	#387×C₈₉	C₂²	1	2	yes	—
83	#387×C₈₉	C₂²	1	2	yes	—
84	#387×C₈₉	C₂²	1	2	yes	—
85	#387×C₈₉	C₂²	1	2	yes	—
86	#387×C₈₉	C₂²	1	2	yes	—
87	#387×C₈₉	C₂²	1	2	yes	—
88	#386×C₈₉	C₂²	1	2	yes	—
89	#386×C₈₉	C₂²	1	2	yes	—
90	#386×C₈₉	C₂²	1	2	yes	—
91	#386×C₈₉	C₂²	1	2	yes	—
92	#385×C₈₉	C₂²	1	2	yes	—
93	#385×C₈₉	C₂²	1	2	yes	—
94	#385×C₈₉	C₂²	1	2	yes	—
95	#385×C₈₉	C₂²	1	2	yes	—
96	#384×C₈₉	C₂²	1	1	yes	characteristic
97	#383×C₈₉	C₂²	1	2	yes	—
98	#382×C₈₉	C₂²	1	2	yes	—
99	#382×C₈₉	C₂²	1	1	yes	characteristic
100	#381×C₈₉	C₂²	1	2	yes	—
101	#381×C₈₉	C₂²	1	2	yes	—
102	#380×C₈₉	C₂²	1	1	yes	characteristic
103	#380×C₈₉	C₂²	1	1	yes	characteristic
104	#380×C₈₉	C₂²	1	2	yes	—
105	#380×C₈₉	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
109	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
110	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
111	#376×C₈₉	C₂²	1	1	yes	characteristic
112	#376×C₈₉	C₂²	1	1	yes	characteristic
113	#376×C₈₉	C₂²	1	1	yes	characteristic
114	#376×C₈₉	C₂²	1	1	yes	characteristic
115	#376×C₈₉	C₂²	1	1	yes	characteristic
116	#376×C₈₉	C₂²	1	1	yes	characteristic
117	#376×C₈₉	C₂²	1	1	yes	characteristic
118	#376×C₈₉	C₂²	1	1	yes	characteristic
119	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
120	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
121	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
122	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
125	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
126	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
135	C₄⋊Q₈×C₈₉	—	2	4	no	—
136	#124×C₈₉	—	2	4	no	—
137	#123×C₈₉	—	4	4	no	—
138	C₂²⋊Q₈×C₈₉	—	2	4	no	—
139	C₂²⋊Q₈×C₈₉	—	4	4	no	—
140	#121×C₈₉	—	2	4	no	—
141	C₄×Q₈×C₈₉	—	2	4	no	—
142	C₄×D₄×C₈₉	—	2	4	no	—
143	C₄×D₄×C₈₉	—	4	4	no	—
144	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
152	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
161	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
162	C₂×C₄⋊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	2	yes	—
170	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
178	C₂×C₄²×C₈₉	—	2	4	no	—
179	C₂×C₄²×C₈₉	—	2	4	no	—
180	C₂×C₄²×C₈₉	—	2	4	no	—
181	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
192	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
193	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
194	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
196	#95×C₈₉	C₂³	1	1	yes	characteristic
197	#95×C₈₉	C₂³	1	1	yes	characteristic
198	#95×C₈₉	C₂³	1	1	yes	characteristic
199	#95×C₈₉	C₂³	1	1	yes	characteristic
200	#95×C₈₉	C₂³	1	1	yes	characteristic
201	#95×C₈₉	C₂³	1	1	yes	characteristic
202	#95×C₈₉	C₂³	1	1	yes	characteristic
203	#95×C₈₉	C₂³	1	1	yes	characteristic
204	#95×C₈₉	C₂³	1	1	yes	characteristic
205	#95×C₈₉	C₂³	1	1	yes	characteristic
206	#95×C₈₉	C₂³	1	1	yes	characteristic
207	#95×C₈₉	C₂³	1	1	yes	characteristic
208	#95×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	2	yes	—
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	2	yes	—
217	#95×C₈₉	C₂³	1	2	yes	—
218	#95×C₈₉	C₂³	1	2	yes	—
219	#95×C₈₉	C₂³	1	2	yes	—
220	#95×C₈₉	C₂³	1	2	yes	—
221	#95×C₈₉	C₂³	1	2	yes	—
222	#95×C₈₉	C₂³	1	2	yes	—
223	#95×C₈₉	C₂³	1	2	yes	—
224	#95×C₈₉	C₂³	1	2	yes	—
225	#95×C₈₉	C₂³	1	2	yes	—
226	#95×C₈₉	C₂³	1	2	yes	—
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	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
235	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
236	C₂×Q₈×C₈₉	—	2	2	no	—
237	C₂×Q₈×C₈₉	—	2	2	no	—
238	C₂×Q₈×C₈₉	—	2	2	no	—
239	C₂×Q₈×C₈₉	—	2	4	no	—
240	C₂×Q₈×C₈₉	—	4	2	no	—
241	C₂×Q₈×C₈₉	—	4	2	no	—
242	C₂×D₄×C₈₉	—	2	4	no	—
243	C₂×D₄×C₈₉	—	2	4	no	—
244	C₂×D₄×C₈₉	—	2	4	no	—
245	C₂×D₄×C₈₉	—	2	2	no	—
246	C₂×D₄×C₈₉	—	2	2	no	—
247	C₂×D₄×C₈₉	—	2	2	no	—
248	C₂²×C₄×C₈₉	—	2	2	no	—
249	C₂²×C₄×C₈₉	—	2	2	no	—
250	C₂²×C₄×C₈₉	—	2	2	no	—
251	C₂²×C₄×C₈₉	—	2	2	no	—
252	C₂²×C₄×C₈₉	—	2	2	no	—
253	C₂²×C₄×C₈₉	—	2	2	no	—
254	C₂²×C₄×C₈₉	—	2	2	no	—
255	C₂²×C₄×C₈₉	—	2	2	no	—
256	C₂²×C₄×C₈₉	—	2	2	no	—
257	C₂²×C₄×C₈₉	—	2	2	no	—
258	C₂²×C₄×C₈₉	—	2	2	no	—
259	C₂²×C₄×C₈₉	—	2	2	no	—
260	C₂²×C₄×C₈₉	—	2	2	no	—
261	C₂²×C₄×C₈₉	—	2	2	no	—
262	C₂²×C₄×C₈₉	—	2	4	no	—
263	C₂²×C₄×C₈₉	—	4	1	no	—
264	C₂²×C₄×C₈₉	—	4	1	no	—
265	C₂²×C₄×C₈₉	—	4	1	no	—
266	C₂²×C₄×C₈₉	—	4	1	no	—
267	C₂²×C₄×C₈₉	—	4	1	no	—
268	C₂²×C₄×C₈₉	—	4	1	no	—
269	C₂²×C₄×C₈₉	—	4	2	no	—
270	C₂²×C₄×C₈₉	—	4	2	no	—
271	C₂²×C₄×C₈₉	#41	1	4	yes	—
272	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
293	C₄⋊C₄×C₈₉	—	2	2	no	—
294	C₄⋊C₄×C₈₉	—	2	2	no	—
295	C₄⋊C₄×C₈₉	—	2	4	no	—
296	C₄⋊C₄×C₈₉	—	2	2	no	—
297	C₄⋊C₄×C₈₉	—	2	2	no	—
298	C₄⋊C₄×C₈₉	—	2	4	no	—
299	C₄⋊C₄×C₈₉	—	2	4	no	—
300	C₄⋊C₄×C₈₉	—	2	2	no	—
301	C₄⋊C₄×C₈₉	—	2	2	no	—
302	C₄⋊C₄×C₈₉	—	4	2	no	—
303	C₄⋊C₄×C₈₉	—	4	2	no	—
304	C₄⋊C₄×C₈₉	—	4	2	no	—
305	C₄⋊C₄×C₈₉	—	4	2	no	—
306	C₄⋊C₄×C₈₉	—	4	2	no	—
307	C₄⋊C₄×C₈₉	—	4	2	no	—
308	C₄⋊C₄×C₈₉	—	4	2	no	—
309	C₄⋊C₄×C₈₉	—	4	2	no	—
310	C₄⋊C₄×C₈₉	—	4	2	no	—
311	C₄⋊C₄×C₈₉	—	4	2	no	—
312	C₂²⋊C₄×C₈₉	—	2	4	no	—
313	C₂²⋊C₄×C₈₉	—	2	4	no	—
314	C₂²⋊C₄×C₈₉	—	2	4	no	—
315	C₂²⋊C₄×C₈₉	—	2	4	no	—
316	C₂²⋊C₄×C₈₉	—	2	4	no	—
317	C₂²⋊C₄×C₈₉	—	2	4	no	—
318	C₂²⋊C₄×C₈₉	—	2	4	no	—
319	C₂²⋊C₄×C₈₉	—	4	2	no	—
320	C₂²⋊C₄×C₈₉	—	4	2	no	—
321	C₂²⋊C₄×C₈₉	—	4	2	no	—
322	C₂²⋊C₄×C₈₉	—	4	2	no	—
323	C₂²⋊C₄×C₈₉	—	4	2	no	—
324	C₂²⋊C₄×C₈₉	—	4	2	no	—
325	C₂²⋊C₄×C₈₉	—	4	2	no	—
326	C₂²⋊C₄×C₈₉	—	4	2	no	—
327	C₄²×C₈₉	—	2	2	no	—
328	C₄²×C₈₉	—	2	2	no	—
329	C₄²×C₈₉	—	2	2	no	—
330	C₄²×C₈₉	—	2	2	no	—
331	C₄²×C₈₉	—	2	2	no	—
332	C₄²×C₈₉	—	2	2	no	—
333	C₄²×C₈₉	—	2	2	no	—
334	C₄²×C₈₉	—	2	2	no	—
335	C₄²×C₈₉	—	2	2	no	—
336	C₄²×C₈₉	—	2	2	no	—
337	C₄²×C₈₉	—	2	4	no	—
338	C₄²×C₈₉	—	4	2	no	—
339	C₄²×C₈₉	—	4	2	no	—
340	C₄²×C₈₉	#41	1	4	yes	—
341	C₄²×C₈₉	#41	1	4	yes	—
342	C₂³×C₈₉	—	2	1	no	—
343	C₂³×C₈₉	—	2	1	no	—
344	C₂³×C₈₉	—	2	1	no	—
345	C₂³×C₈₉	—	2	1	no	—
346	C₂³×C₈₉	—	2	2	no	—
347	C₂³×C₈₉	—	2	2	no	—
348	C₂³×C₈₉	—	2	2	no	—
349	C₂³×C₈₉	—	2	2	no	—
350	C₂³×C₈₉	—	2	2	no	—
351	C₂³×C₈₉	—	2	2	no	—
352	C₂³×C₈₉	—	2	2	no	—
353	C₂³×C₈₉	C₂×#41	1	2	yes	—
354	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
355	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
356	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
357	Q₈×C₈₉	—	4	4	no	—
358	Q₈×C₈₉	—	8	4	no	—
359	D₄×C₈₉	—	4	8	no	—
360	D₄×C₈₉	—	4	4	no	—
361	C₂×C₄×C₈₉	—	2	1	no	—
362	C₂×C₄×C₈₉	—	2	1	no	—
363	C₂×C₄×C₈₉	—	2	1	no	—
364	C₂×C₄×C₈₉	—	2	1	no	—
365	C₂×C₄×C₈₉	—	2	1	no	—
366	C₂×C₄×C₈₉	—	2	1	no	—
367	C₂×C₄×C₈₉	—	2	1	no	—
368	C₂×C₄×C₈₉	—	2	1	no	—
369	C₂×C₄×C₈₉	—	2	1	no	—
370	C₂×C₄×C₈₉	—	2	1	no	—
371	C₂×C₄×C₈₉	—	2	8	no	—
372	C₂×C₄×C₈₉	—	2	1	no	—
373	C₂×C₄×C₈₉	—	2	1	no	—
374	C₂×C₄×C₈₉	—	2	1	no	—
375	C₂×C₄×C₈₉	—	2	1	no	—
376	C₂×C₄×C₈₉	—	2	1	no	—
377	C₂×C₄×C₈₉	—	2	1	no	—
378	C₂×C₄×C₈₉	—	2	1	no	—
379	C₂×C₄×C₈₉	—	2	1	no	—
380	C₂×C₄×C₈₉	—	2	2	no	—
381	C₂×C₄×C₈₉	—	2	2	no	—
382	C₂×C₄×C₈₉	—	2	2	no	—
383	C₂×C₄×C₈₉	—	2	2	no	—
384	C₂×C₄×C₈₉	—	2	2	no	—
385	C₂×C₄×C₈₉	—	2	2	no	—
386	C₂×C₄×C₈₉	—	2	2	no	—
387	C₂×C₄×C₈₉	—	2	2	no	—
388	C₂×C₄×C₈₉	—	2	2	no	—
389	C₂×C₄×C₈₉	—	2	2	no	—
390	C₂×C₄×C₈₉	—	2	2	no	—
391	C₂×C₄×C₈₉	—	2	2	no	—
392	C₂×C₄×C₈₉	—	2	2	no	—
393	C₂×C₄×C₈₉	—	2	2	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	2	no	—
403	C₂×C₄×C₈₉	—	2	2	no	—
404	C₂×C₄×C₈₉	—	2	2	no	—
405	C₂×C₄×C₈₉	—	2	1	no	—
406	C₂×C₄×C₈₉	—	2	1	no	—
407	C₂×C₄×C₈₉	—	2	1	no	—
408	C₂×C₄×C₈₉	—	2	1	no	—
409	C₂×C₄×C₈₉	—	2	1	no	—
410	C₂×C₄×C₈₉	—	2	2	no	—
411	C₂×C₄×C₈₉	—	2	2	no	—
412	C₂×C₄×C₈₉	—	2	2	no	—
413	C₂×C₄×C₈₉	—	2	1	no	—
414	C₂×C₄×C₈₉	—	2	1	no	—
415	C₂×C₄×C₈₉	—	2	1	no	—
416	C₂×C₄×C₈₉	—	2	2	no	—
417	C₂×C₄×C₈₉	—	4	4	no	—
418	C₂×C₄×C₈₉	—	4	4	no	—
419	C₂×C₄×C₈₉	—	4	4	no	—
420	C₂×C₄×C₈₉	—	4	4	no	—
421	C₂×C₄×C₈₉	—	4	4	no	—
422	C₂×C₄×C₈₉	—	4	4	no	—
423	C₂×C₄×C₈₉	—	8	4	no	—
424	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
425	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
426	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
427	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
428	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
429	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
430	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
431	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
432	C₂²×C₈₉	—	2	2	no	—
433	C₂²×C₈₉	—	2	2	no	—
434	C₂²×C₈₉	—	2	2	no	—
435	C₂²×C₈₉	—	2	2	no	—
436	C₂²×C₈₉	—	2	2	no	—
437	C₂²×C₈₉	—	2	2	no	—
438	C₂²×C₈₉	—	4	2	no	—
439	C₂²×C₈₉	—	4	2	no	—
440	C₂²×C₈₉	—	4	2	no	—
441	C₂²×C₈₉	—	4	2	no	—
442	C₂²×C₈₉	—	4	2	no	—
443	C₂²×C₈₉	—	4	2	no	—
444	C₂²×C₈₉	—	4	2	no	—
445	C₂²×C₈₉	#542	1	4	yes	—
446	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
447	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
448	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
449	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
450	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
451	C₂²×C₈₉	#585	1	1	yes	characteristic
452	C₂²×C₈₉	#585	1	1	yes	characteristic
453	C₄×C₈₉	—	2	2	no	—
454	C₄×C₈₉	—	2	2	no	—
455	C₄×C₈₉	—	2	2	no	—
456	C₄×C₈₉	—	2	2	no	—
457	C₄×C₈₉	—	2	2	no	—
458	C₄×C₈₉	—	4	2	no	—
459	C₄×C₈₉	—	4	1	no	—
460	C₄×C₈₉	—	4	1	no	—
461	C₄×C₈₉	—	4	2	no	—
462	C₄×C₈₉	—	4	2	no	—
463	C₄×C₈₉	—	4	1	no	—
464	C₄×C₈₉	—	4	1	no	—
465	C₄×C₈₉	—	4	2	no	—
466	C₄×C₈₉	—	4	1	no	—
467	C₄×C₈₉	—	4	1	no	—
468	C₄×C₈₉	—	4	2	no	—
469	C₄×C₈₉	—	4	2	no	—
470	C₄×C₈₉	—	4	2	no	—
471	C₄×C₈₉	—	4	1	no	—
472	C₄×C₈₉	—	4	1	no	—
473	C₄×C₈₉	#529	1	4	yes	—
474	#35270	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
475	C₂×C₈₉	—	2	4	no	—
476	C₂×C₈₉	—	8	2	no	—
477	C₂×C₈₉	C₂×#529	1	1	yes	characteristic
478	C₂×C₈₉	C₂×#542	1	1	yes	characteristic
479	C₂×C₈₉	#3455	1	1	yes	characteristic
480	C₂×C₈₉	#3494	1	1	yes	characteristic
481	C₂×C₈₉	#3494	1	1	yes	characteristic
482	C₂×C₈₉	#3495	1	1	yes	characteristic
483	C₂×C₈₉	#3495	1	1	yes	characteristic
484	#2857	C₂×C₈₉	1	1	yes	characteristic, complemented
485	#2855	C₂×C₈₉	1	1	yes	characteristic, complemented
486	#2854	C₂×C₈₉	1	1	yes	characteristic
487	#2850	C₂×C₈₉	1	1	yes	characteristic
488	#2647	C₂×C₈₉	1	1	yes	characteristic, complemented
489	#2645	C₂×C₈₉	1	1	yes	characteristic, complemented
490	#2644	C₂×C₈₉	1	1	yes	characteristic, complemented
491	#2640	C₂×C₈₉	1	1	yes	characteristic, complemented
492	#2532	C₂×C₈₉	1	2	yes	complemented
493	#2530	C₂×C₈₉	1	2	yes	complemented
494	#2529	C₂×C₈₉	1	2	yes	complemented
495	#2527	C₂×C₈₉	1	2	yes	complemented
496	#2510	C₂×C₈₉	1	2	yes	complemented
497	#2488	C₂×C₈₉	1	2	yes	complemented
498	#2450	C₂×C₈₉	1	2	yes	complemented
499	#2419	C₂×C₈₉	1	2	yes	complemented
500	#2331	C₂×C₈₉	1	1	yes	characteristic, complemented
501	#2326	C₂×C₈₉	1	1	yes	characteristic, complemented
502	#2320	C₂×C₈₉	1	1	yes	characteristic, complemented
503	#2319	C₂×C₈₉	1	1	yes	characteristic, complemented
504	C₄×C₂²⋊Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
505	C₄×#121	C₂×C₈₉	1	1	yes	characteristic
506	C₂×#376	C₂×C₈₉	1	1	yes	characteristic, complemented
507	C₈₉	#35270	1	1	yes	characteristic, direct product factor, Sylow
508	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
509	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
510	C₂×#123	C₂²×C₈₉	1	2	yes	—
511	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
512	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
513	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
514	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
515	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
516	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
517	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
518	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
519	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
520	#401	C₂²×C₈₉	1	2	yes	—
521	#400	C₂²×C₈₉	1	2	yes	—
522	#400	C₂²×C₈₉	1	2	yes	—
523	#400	C₂²×C₈₉	1	2	yes	—
524	#400	C₂²×C₈₉	1	2	yes	—
525	#400	C₂²×C₈₉	1	2	yes	—
526	#398	C₂²×C₈₉	1	2	yes	—
527	#398	C₂²×C₈₉	1	2	yes	—
528	#397	C₂²×C₈₉	1	2	yes	—
529	#397	C₂²×C₈₉	1	2	yes	—
530	#397	C₂²×C₈₉	1	2	yes	—
531	#397	C₂²×C₈₉	1	2	yes	—
532	#397	C₂²×C₈₉	1	2	yes	—
533	#396	C₂²×C₈₉	1	2	yes	—
534	#393	C₂²×C₈₉	1	2	yes	—
535	#393	C₂²×C₈₉	1	2	yes	—
536	#391	C₂²×C₈₉	1	1	yes	characteristic
537	#391	C₂²×C₈₉	1	1	yes	characteristic
538	#391	C₂²×C₈₉	1	1	yes	characteristic
539	#391	C₂²×C₈₉	1	2	yes	—
540	#391	C₂²×C₈₉	1	2	yes	—
541	#391	C₂²×C₈₉	1	2	yes	—
542	#391	C₂²×C₈₉	1	1	yes	characteristic
543	#390	C₂²×C₈₉	1	1	yes	characteristic
544	#390	C₂²×C₈₉	1	1	yes	characteristic
545	#390	C₂²×C₈₉	1	1	yes	characteristic
546	#390	C₂²×C₈₉	1	1	yes	characteristic
547	#389	C₂²×C₈₉	1	1	yes	characteristic
548	#389	C₂²×C₈₉	1	1	yes	characteristic
549	#389	C₂²×C₈₉	1	1	yes	characteristic
550	#389	C₂²×C₈₉	1	1	yes	characteristic
551	#389	C₂²×C₈₉	1	1	yes	characteristic
552	#389	C₂²×C₈₉	1	1	yes	characteristic
553	#389	C₂²×C₈₉	1	2	yes	—
554	#389	C₂²×C₈₉	1	1	yes	characteristic
555	#389	C₂²×C₈₉	1	1	yes	characteristic
556	#388	C₂²×C₈₉	1	2	yes	—
557	#388	C₂²×C₈₉	1	2	yes	—
558	#388	C₂²×C₈₉	1	2	yes	—
559	#388	C₂²×C₈₉	1	2	yes	—
560	#388	C₂²×C₈₉	1	2	yes	—
561	#388	C₂²×C₈₉	1	2	yes	—
562	#388	C₂²×C₈₉	1	2	yes	—
563	#388	C₂²×C₈₉	1	2	yes	—
564	#388	C₂²×C₈₉	1	2	yes	—
565	#387	C₂²×C₈₉	1	2	yes	—
566	#387	C₂²×C₈₉	1	2	yes	—
567	#387	C₂²×C₈₉	1	2	yes	—
568	#387	C₂²×C₈₉	1	2	yes	—
569	#387	C₂²×C₈₉	1	2	yes	—
570	#387	C₂²×C₈₉	1	2	yes	—
571	#387	C₂²×C₈₉	1	2	yes	—
572	#386	C₂²×C₈₉	1	2	yes	—
573	#386	C₂²×C₈₉	1	2	yes	—
574	#386	C₂²×C₈₉	1	2	yes	—
575	#386	C₂²×C₈₉	1	2	yes	—
576	#385	C₂²×C₈₉	1	2	yes	—
577	#385	C₂²×C₈₉	1	2	yes	—
578	#385	C₂²×C₈₉	1	2	yes	—
579	#385	C₂²×C₈₉	1	2	yes	—
580	#384	C₂²×C₈₉	1	1	yes	characteristic
581	#383	C₂²×C₈₉	1	2	yes	—
582	#382	C₂²×C₈₉	1	2	yes	—
583	#382	C₂²×C₈₉	1	1	yes	characteristic
584	#381	C₂²×C₈₉	1	2	yes	—
585	#381	C₂²×C₈₉	1	2	yes	—
586	#380	C₂²×C₈₉	1	2	yes	—
587	#380	C₂²×C₈₉	1	1	yes	characteristic
588	#380	C₂²×C₈₉	1	1	yes	characteristic
589	#380	C₂²×C₈₉	1	2	yes	—
590	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
591	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
592	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
593	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
594	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
595	#376	C₂²×C₈₉	1	1	yes	characteristic
596	#376	C₂²×C₈₉	1	1	yes	characteristic
597	#376	C₂²×C₈₉	1	1	yes	characteristic
598	#376	C₂²×C₈₉	1	1	yes	characteristic
599	#376	C₂²×C₈₉	1	1	yes	characteristic
600	#376	C₂²×C₈₉	1	1	yes	characteristic
601	#376	C₂²×C₈₉	1	1	yes	characteristic
602	#376	C₂²×C₈₉	1	1	yes	characteristic
603	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
604	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
605	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
606	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
607	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
608	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
609	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
610	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
612	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
613	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
614	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
615	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
616	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
617	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
618	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
619	C₄⋊Q₈	—	2	4	no	—
620	#124	—	2	4	no	—
621	#123	—	4	4	no	—
622	C₂²⋊Q₈	—	2	4	no	—
623	C₂²⋊Q₈	—	4	4	no	—
624	#121	—	2	4	no	—
625	C₄×Q₈	—	2	4	no	—
626	C₄×D₄	—	2	4	no	—
627	C₄×D₄	—	4	4	no	—
628	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
662	C₂×C₄²	—	2	4	no	—
663	C₂×C₄²	—	2	4	no	—
664	C₂×C₄²	—	2	4	no	—
665	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
666	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
667	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
668	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
669	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
670	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
671	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
672	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
673	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
674	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
675	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
676	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
677	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
678	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
679	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
680	#95	C₂³×C₈₉	1	1	yes	characteristic
681	#95	C₂³×C₈₉	1	1	yes	characteristic
682	#95	C₂³×C₈₉	1	1	yes	characteristic
683	#95	C₂³×C₈₉	1	1	yes	characteristic
684	#95	C₂³×C₈₉	1	1	yes	characteristic
685	#95	C₂³×C₈₉	1	1	yes	characteristic
686	#95	C₂³×C₈₉	1	1	yes	characteristic
687	#95	C₂³×C₈₉	1	1	yes	characteristic
688	#95	C₂³×C₈₉	1	1	yes	characteristic
689	#95	C₂³×C₈₉	1	1	yes	characteristic
690	#95	C₂³×C₈₉	1	1	yes	characteristic
691	#95	C₂³×C₈₉	1	1	yes	characteristic
692	#95	C₂³×C₈₉	1	1	yes	characteristic
693	#95	C₂³×C₈₉	1	1	yes	characteristic
694	#95	C₂³×C₈₉	1	1	yes	characteristic
695	#95	C₂³×C₈₉	1	1	yes	characteristic
696	#95	C₂³×C₈₉	1	2	yes	—
697	#95	C₂³×C₈₉	1	2	yes	—
698	#95	C₂³×C₈₉	1	2	yes	—
699	#95	C₂³×C₈₉	1	2	yes	—
700	#95	C₂³×C₈₉	1	2	yes	—
701	#95	C₂³×C₈₉	1	2	yes	—
702	#95	C₂³×C₈₉	1	2	yes	—
703	#95	C₂³×C₈₉	1	2	yes	—
704	#95	C₂³×C₈₉	1	2	yes	—
705	#95	C₂³×C₈₉	1	2	yes	—
706	#95	C₂³×C₈₉	1	2	yes	—
707	#95	C₂³×C₈₉	1	2	yes	—
708	#95	C₂³×C₈₉	1	2	yes	—
709	#95	C₂³×C₈₉	1	2	yes	—
710	#95	C₂³×C₈₉	1	2	yes	—
711	#95	C₂³×C₈₉	1	2	yes	—
712	#95	C₂³×C₈₉	1	2	yes	—
713	#95	C₂³×C₈₉	1	2	yes	—
714	#95	C₂³×C₈₉	1	2	yes	—
715	#95	C₂³×C₈₉	1	2	yes	—
716	#95	C₂³×C₈₉	1	2	yes	—
717	#95	C₂³×C₈₉	1	2	yes	—
718	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
719	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
720	C₂×Q₈	—	2	2	no	—
721	C₂×Q₈	—	2	2	no	—
722	C₂×Q₈	—	2	2	no	—
723	C₂×Q₈	—	2	4	no	—
724	C₂×Q₈	—	4	2	no	—
725	C₂×Q₈	—	4	2	no	—
726	C₂×D₄	—	2	4	no	—
727	C₂×D₄	—	2	4	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	4	no	—
747	C₂²×C₄	—	4	1	no	—
748	C₂²×C₄	—	4	1	no	—
749	C₂²×C₄	—	4	1	no	—
750	C₂²×C₄	—	4	1	no	—
751	C₂²×C₄	—	4	1	no	—
752	C₂²×C₄	—	4	1	no	—
753	C₂²×C₄	—	4	2	no	—
754	C₂²×C₄	—	4	2	no	—
755	C₂²×C₄	#41×C₈₉	1	4	yes	—
756	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	4	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	4	no	—
783	C₄⋊C₄	—	2	4	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	4	2	no	—
787	C₄⋊C₄	—	4	2	no	—
788	C₄⋊C₄	—	4	2	no	—
789	C₄⋊C₄	—	4	2	no	—
790	C₄⋊C₄	—	4	2	no	—
791	C₄⋊C₄	—	4	2	no	—
792	C₄⋊C₄	—	4	2	no	—
793	C₄⋊C₄	—	4	2	no	—
794	C₄⋊C₄	—	4	2	no	—
795	C₄⋊C₄	—	4	2	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	4	2	no	—
804	C₂²⋊C₄	—	4	2	no	—
805	C₂²⋊C₄	—	4	2	no	—
806	C₂²⋊C₄	—	4	2	no	—
807	C₂²⋊C₄	—	4	2	no	—
808	C₂²⋊C₄	—	4	2	no	—
809	C₂²⋊C₄	—	4	2	no	—
810	C₂²⋊C₄	—	4	2	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	2	no	—
813	C₄²	—	2	2	no	—
814	C₄²	—	2	2	no	—
815	C₄²	—	2	2	no	—
816	C₄²	—	2	2	no	—
817	C₄²	—	2	2	no	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	4	no	—
822	C₄²	—	4	2	no	—
823	C₄²	—	4	2	no	—
824	C₄²	#41×C₈₉	1	4	yes	—
825	C₄²	#41×C₈₉	1	4	yes	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	1	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	C₂×#41×C₈₉	1	2	yes	—
838	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
839	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
840	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
841	Q₈	—	4	4	no	—
842	Q₈	—	8	4	no	—
843	D₄	—	4	8	no	—
844	D₄	—	4	4	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	8	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	4	4	no	—
903	C₂×C₄	—	4	4	no	—
904	C₂×C₄	—	4	4	no	—
905	C₂×C₄	—	4	4	no	—
906	C₂×C₄	—	4	4	no	—
907	C₂×C₄	—	8	4	no	—
908	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
909	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
910	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
911	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
912	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
913	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
914	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
915	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	2	2	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	4	2	no	—
929	C₂²	#542×C₈₉	1	4	yes	—
930	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
931	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
932	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
933	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
934	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
935	C₂²	#585×C₈₉	1	1	yes	characteristic
936	C₂²	#585×C₈₉	1	1	yes	characteristic
937	C₄	—	2	2	no	—
938	C₄	—	2	2	no	—
939	C₄	—	2	2	no	—
940	C₄	—	2	2	no	—
941	C₄	—	2	2	no	—
942	C₄	—	4	2	no	—
943	C₄	—	4	1	no	—
944	C₄	—	4	1	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	1	no	—
947	C₄	—	4	1	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	1	no	—
950	C₄	—	4	1	no	—
951	C₄	—	4	2	no	—
952	C₄	—	4	2	no	—
953	C₄	—	4	2	no	—
954	C₄	—	4	2	no	—
955	C₄	—	4	1	no	—
956	C₄	—	4	1	no	—
957	C₄	#529×C₈₉	1	4	yes	—
958	C₂	—	2	4	no	—
959	C₂	—	8	2	no	—
960	C₂	C₂×#529×C₈₉	1	1	yes	characteristic
961	C₂	C₂×#542×C₈₉	1	1	yes	characteristic
962	C₂	C₈₉×#3455	1	1	yes	characteristic
963	C₂	C₈₉×#3494	1	1	yes	characteristic
964	C₂	C₈₉×#3494	1	1	yes	characteristic
965	C₂	C₈₉×#3495	1	1	yes	characteristic
966	C₂	C₈₉×#3495	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂×#121×C₈₉	C₂²
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×#2857	C₂	semidirect
2. C₈₉×#2855	C₂	semidirect
5. C₈₉×#2647	C₂	semidirect
6. C₈₉×#2645	C₂	semidirect
7. C₈₉×#2644	C₂	semidirect
8. C₈₉×#2640	C₂	semidirect
9. C₈₉×#2532	C₂	semidirect
10. C₈₉×#2530	C₂	semidirect
11. C₈₉×#2529	C₂	semidirect
12. C₈₉×#2527	C₂	semidirect
13. C₈₉×#2510	C₂	semidirect
14. C₈₉×#2488	C₂	semidirect
15. C₈₉×#2450	C₂	semidirect
16. C₈₉×#2419	C₂	semidirect
17. C₈₉×#2331	C₂	semidirect
18. C₈₉×#2326	C₂	semidirect
19. C₈₉×#2320	C₂	semidirect
20. C₈₉×#2319	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₈₉	C₂	semidirect
23. C₂×#376×C₈₉	C₂	semidirect
474. #35270	C₈₉	direct (N × H)
484. #2857	C₂×C₈₉	semidirect
485. #2855	C₂×C₈₉	semidirect
488. #2647	C₂×C₈₉	semidirect
489. #2645	C₂×C₈₉	semidirect
490. #2644	C₂×C₈₉	semidirect
491. #2640	C₂×C₈₉	semidirect
492. #2532	C₂×C₈₉	semidirect
493. #2530	C₂×C₈₉	semidirect
494. #2529	C₂×C₈₉	semidirect
495. #2527	C₂×C₈₉	semidirect
496. #2510	C₂×C₈₉	semidirect
497. #2488	C₂×C₈₉	semidirect
498. #2450	C₂×C₈₉	semidirect
499. #2419	C₂×C₈₉	semidirect
500. #2331	C₂×C₈₉	semidirect
501. #2326	C₂×C₈₉	semidirect
502. #2320	C₂×C₈₉	semidirect
503. #2319	C₂×C₈₉	semidirect
504. C₄×C₂²⋊Q₈	C₂×C₈₉	semidirect
506. C₂×#376	C₂×C₈₉	semidirect
507. C₈₉	#35270	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×#2857	2
C₈₉×#2855	2
C₈₉×#2854	2
C₈₉×#2850	2
C₈₉×#2647	2
C₈₉×#2645	2
C₈₉×#2644	2
C₈₉×#2640	2
C₈₉×#2532	2
C₈₉×#2530	2
C₈₉×#2529	2
C₈₉×#2527	2
C₈₉×#2510	2
C₈₉×#2488	2
C₈₉×#2450	2
C₈₉×#2419	2
C₈₉×#2331	2
C₈₉×#2326	2
C₈₉×#2320	2
C₈₉×#2319	2
C₄×C₂²⋊Q₈×C₈₉	2
C₄×#121×C₈₉	2
C₂×#376×C₈₉	2
#35270	89

Subgroups — C89×#35270 #36413118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35270 #36413118