Subgroups — C₈₉×#35204 #36413052

Order 22784.

1536 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2865	C₂	1	2	yes	maximal
2	C₈₉×#2864	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2655	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2654	C₂	1	2	yes	maximal
5	C₈₉×#2596	C₂	1	2	yes	maximal
6	C₈₉×#2590	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2529	C₂	1	2	yes	maximal
8	C₈₉×#2528	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2511	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2508	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2494	C₂	1	1	yes	maximal, characteristic
12	C₈₉×#2489	C₂	1	1	yes	maximal, characteristic
13	C₈₉×#2453	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2446	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2429	C₂	1	1	yes	maximal, characteristic
16	C₈₉×#2423	C₂	1	1	yes	maximal, characteristic
17	C₈₉×#2330	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#2327	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2323	C₂	1	1	yes	maximal, characteristic
20	C₈₉×#2323	C₂	1	1	yes	maximal, characteristic
21	C₈₉×#2298	C₂	1	1	yes	maximal, characteristic
22	C₈₉×#2295	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
33	#401×C₈₉	C₂²	1	2	yes	—
34	#400×C₈₉	C₂²	1	2	yes	—
35	#400×C₈₉	C₂²	1	2	yes	—
36	#400×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	#399×C₈₉	C₂²	1	2	yes	—
41	#398×C₈₉	C₂²	1	2	yes	—
42	#398×C₈₉	C₂²	1	2	yes	—
43	#398×C₈₉	C₂²	1	2	yes	—
44	#398×C₈₉	C₂²	1	2	yes	—
45	#398×C₈₉	C₂²	1	2	yes	—
46	#397×C₈₉	C₂²	1	2	yes	—
47	#397×C₈₉	C₂²	1	2	yes	—
48	#396×C₈₉	C₂²	1	2	yes	—
49	#391×C₈₉	C₂²	1	1	yes	characteristic
50	#391×C₈₉	C₂²	1	1	yes	characteristic
51	#391×C₈₉	C₂²	1	1	yes	characteristic
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	#389×C₈₉	C₂²	1	1	yes	characteristic
56	#389×C₈₉	C₂²	1	1	yes	characteristic
57	#389×C₈₉	C₂²	1	2	yes	—
58	#389×C₈₉	C₂²	1	2	yes	—
59	#389×C₈₉	C₂²	1	1	yes	characteristic
60	#389×C₈₉	C₂²	1	1	yes	characteristic
61	#389×C₈₉	C₂²	1	2	yes	—
62	#389×C₈₉	C₂²	1	2	yes	—
63	#389×C₈₉	C₂²	1	1	yes	characteristic
64	#389×C₈₉	C₂²	1	1	yes	characteristic
65	#389×C₈₉	C₂²	1	2	yes	—
66	#389×C₈₉	C₂²	1	2	yes	—
67	#388×C₈₉	C₂²	1	1	yes	characteristic
68	#388×C₈₉	C₂²	1	1	yes	characteristic
69	#388×C₈₉	C₂²	1	1	yes	characteristic
70	#388×C₈₉	C₂²	1	1	yes	characteristic
71	#388×C₈₉	C₂²	1	2	yes	—
72	#388×C₈₉	C₂²	1	2	yes	—
73	#388×C₈₉	C₂²	1	2	yes	—
74	#388×C₈₉	C₂²	1	2	yes	—
75	#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	#387×C₈₉	C₂²	1	2	yes	—
80	#387×C₈₉	C₂²	1	2	yes	—
81	#387×C₈₉	C₂²	1	1	yes	characteristic
82	#387×C₈₉	C₂²	1	1	yes	characteristic
83	#387×C₈₉	C₂²	1	1	yes	characteristic
84	#387×C₈₉	C₂²	1	1	yes	characteristic
85	#387×C₈₉	C₂²	1	2	yes	—
86	#387×C₈₉	C₂²	1	2	yes	—
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	#387×C₈₉	C₂²	1	2	yes	—
92	#387×C₈₉	C₂²	1	2	yes	—
93	#387×C₈₉	C₂²	1	2	yes	—
94	#387×C₈₉	C₂²	1	2	yes	—
95	#387×C₈₉	C₂²	1	2	yes	—
96	#387×C₈₉	C₂²	1	2	yes	—
97	#387×C₈₉	C₂²	1	2	yes	—
98	#387×C₈₉	C₂²	1	2	yes	—
99	#387×C₈₉	C₂²	1	2	yes	—
100	#387×C₈₉	C₂²	1	2	yes	—
101	#384×C₈₉	C₂²	1	1	yes	characteristic
102	#382×C₈₉	C₂²	1	1	yes	characteristic
103	#382×C₈₉	C₂²	1	2	yes	—
104	#382×C₈₉	C₂²	1	2	yes	—
105	#380×C₈₉	C₂²	1	1	yes	characteristic
106	#380×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×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	2	yes	—
113	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
119	#376×C₈₉	C₂²	1	2	yes	—
120	#376×C₈₉	C₂²	1	1	yes	characteristic
121	C₄³×C₈₉	C₂²	1	1	yes	characteristic
122	C₄³×C₈₉	C₂²	1	2	yes	—
123	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
126	C₄⋊Q₈×C₈₉	—	2	4	no	—
127	#125×C₈₉	—	2	4	no	—
128	C₂²⋊Q₈×C₈₉	—	2	4	no	—
129	C₂²⋊Q₈×C₈₉	—	2	4	no	—
130	C₄×Q₈×C₈₉	—	2	4	no	—
131	C₄×Q₈×C₈₉	—	2	4	no	—
132	C₄×Q₈×C₈₉	—	2	4	no	—
133	C₄×Q₈×C₈₉	—	2	4	no	—
134	#117×C₈₉	—	2	4	no	—
135	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₈₉	C₂³	1	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	2	yes	—
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	2	yes	—
147	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₈₉	C₂³	1	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	1	yes	characteristic
156	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
165	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
167	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
175	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
183	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
190	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
191	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
192	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
193	#95×C₈₉	C₂³	1	2	yes	—
194	#95×C₈₉	C₂³	1	2	yes	—
195	#95×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	2	yes	—
200	#95×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
206	#95×C₈₉	C₂³	1	2	yes	—
207	#95×C₈₉	C₂³	1	2	yes	—
208	#95×C₈₉	C₂³	1	1	yes	characteristic
209	#95×C₈₉	C₂³	1	1	yes	characteristic
210	#95×C₈₉	C₂³	1	2	yes	—
211	#95×C₈₉	C₂³	1	2	yes	—
212	#95×C₈₉	C₂³	1	1	yes	characteristic
213	#95×C₈₉	C₂³	1	1	yes	characteristic
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	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
232	C₂×Q₈×C₈₉	—	2	2	no	—
233	C₂×Q₈×C₈₉	—	2	2	no	—
234	C₂×Q₈×C₈₉	—	2	2	no	—
235	C₂×Q₈×C₈₉	—	2	2	no	—
236	C₂×Q₈×C₈₉	—	2	2	no	—
237	C₂×Q₈×C₈₉	#41	1	4	yes	—
238	C₂²×C₄×C₈₉	—	2	2	no	—
239	C₂²×C₄×C₈₉	—	2	2	no	—
240	C₂²×C₄×C₈₉	—	2	2	no	—
241	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
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	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
263	C₄⋊C₄×C₈₉	—	2	2	no	—
264	C₄⋊C₄×C₈₉	—	2	2	no	—
265	C₄⋊C₄×C₈₉	—	2	4	no	—
266	C₄⋊C₄×C₈₉	—	2	4	no	—
267	C₄⋊C₄×C₈₉	—	2	4	no	—
268	C₄⋊C₄×C₈₉	—	2	2	no	—
269	C₄⋊C₄×C₈₉	—	2	2	no	—
270	C₄⋊C₄×C₈₉	—	2	2	no	—
271	C₄⋊C₄×C₈₉	—	2	4	no	—
272	C₄⋊C₄×C₈₉	—	2	2	no	—
273	C₄⋊C₄×C₈₉	—	2	4	no	—
274	C₄⋊C₄×C₈₉	—	2	4	no	—
275	C₄⋊C₄×C₈₉	—	2	4	no	—
276	C₄⋊C₄×C₈₉	—	2	4	no	—
277	C₄⋊C₄×C₈₉	—	2	2	no	—
278	C₄⋊C₄×C₈₉	—	2	4	no	—
279	C₄⋊C₄×C₈₉	—	2	4	no	—
280	C₄⋊C₄×C₈₉	—	2	2	no	—
281	C₄⋊C₄×C₈₉	—	2	4	no	—
282	C₄⋊C₄×C₈₉	—	2	2	no	—
283	C₄⋊C₄×C₈₉	—	4	2	no	—
284	C₄⋊C₄×C₈₉	—	4	2	no	—
285	C₄⋊C₄×C₈₉	—	4	2	no	—
286	C₄⋊C₄×C₈₉	—	4	2	no	—
287	C₄⋊C₄×C₈₉	—	4	1	no	—
288	C₄⋊C₄×C₈₉	—	4	1	no	—
289	C₄⋊C₄×C₈₉	—	4	2	no	—
290	C₄⋊C₄×C₈₉	—	4	2	no	—
291	C₄⋊C₄×C₈₉	—	4	2	no	—
292	C₄⋊C₄×C₈₉	#41	1	4	yes	—
293	C₂²⋊C₄×C₈₉	—	2	2	no	—
294	C₂²⋊C₄×C₈₉	—	2	2	no	—
295	C₂²⋊C₄×C₈₉	—	2	4	no	—
296	C₂²⋊C₄×C₈₉	—	2	4	no	—
297	C₂²⋊C₄×C₈₉	—	2	2	no	—
298	C₂²⋊C₄×C₈₉	—	2	2	no	—
299	C₂²⋊C₄×C₈₉	—	4	2	no	—
300	C₂²⋊C₄×C₈₉	—	4	1	no	—
301	C₂²⋊C₄×C₈₉	—	4	1	no	—
302	C₂²⋊C₄×C₈₉	—	4	2	no	—
303	C₄²×C₈₉	—	2	2	no	—
304	C₄²×C₈₉	—	2	4	no	—
305	C₄²×C₈₉	—	2	4	no	—
306	C₄²×C₈₉	—	2	2	no	—
307	C₄²×C₈₉	—	2	2	no	—
308	C₄²×C₈₉	—	2	4	no	—
309	C₄²×C₈₉	—	2	4	no	—
310	C₄²×C₈₉	—	2	2	no	—
311	C₄²×C₈₉	—	2	2	no	—
312	C₄²×C₈₉	—	2	2	no	—
313	C₄²×C₈₉	—	2	2	no	—
314	C₄²×C₈₉	—	2	4	no	—
315	C₄²×C₈₉	—	4	1	no	—
316	C₄²×C₈₉	—	4	2	no	—
317	C₄²×C₈₉	—	4	1	no	—
318	C₄²×C₈₉	—	4	2	no	—
319	C₄²×C₈₉	—	4	2	no	—
320	C₄²×C₈₉	#41	1	4	yes	—
321	C₂³×C₈₉	—	2	1	no	—
322	C₂³×C₈₉	—	2	1	no	—
323	C₂³×C₈₉	—	2	1	no	—
324	C₂³×C₈₉	—	2	1	no	—
325	C₂³×C₈₉	—	2	1	no	—
326	C₂³×C₈₉	—	2	1	no	—
327	C₂³×C₈₉	—	2	1	no	—
328	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
329	Q₈×C₈₉	—	2	8	no	—
330	Q₈×C₈₉	—	4	4	no	—
331	C₂×C₄×C₈₉	—	2	1	no	—
332	C₂×C₄×C₈₉	—	2	1	no	—
333	C₂×C₄×C₈₉	—	2	2	no	—
334	C₂×C₄×C₈₉	—	2	2	no	—
335	C₂×C₄×C₈₉	—	2	1	no	—
336	C₂×C₄×C₈₉	—	2	1	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	1	no	—
341	C₂×C₄×C₈₉	—	2	1	no	—
342	C₂×C₄×C₈₉	—	2	2	no	—
343	C₂×C₄×C₈₉	—	2	1	no	—
344	C₂×C₄×C₈₉	—	2	1	no	—
345	C₂×C₄×C₈₉	—	2	2	no	—
346	C₂×C₄×C₈₉	—	2	2	no	—
347	C₂×C₄×C₈₉	—	2	1	no	—
348	C₂×C₄×C₈₉	—	2	1	no	—
349	C₂×C₄×C₈₉	—	2	1	no	—
350	C₂×C₄×C₈₉	—	2	1	no	—
351	C₂×C₄×C₈₉	—	2	2	no	—
352	C₂×C₄×C₈₉	—	2	1	no	—
353	C₂×C₄×C₈₉	—	2	1	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	1	no	—
359	C₂×C₄×C₈₉	—	2	1	no	—
360	C₂×C₄×C₈₉	—	2	1	no	—
361	C₂×C₄×C₈₉	—	2	2	no	—
362	C₂×C₄×C₈₉	—	2	2	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	2	no	—
369	C₂×C₄×C₈₉	—	2	1	no	—
370	C₂×C₄×C₈₉	—	2	2	no	—
371	C₂×C₄×C₈₉	—	2	1	no	—
372	C₂×C₄×C₈₉	—	2	2	no	—
373	C₂×C₄×C₈₉	—	2	1	no	—
374	C₂×C₄×C₈₉	—	2	2	no	—
375	C₂×C₄×C₈₉	—	2	2	no	—
376	C₂×C₄×C₈₉	—	2	1	no	—
377	C₂×C₄×C₈₉	—	2	1	no	—
378	C₂×C₄×C₈₉	—	2	2	no	—
379	C₂×C₄×C₈₉	—	2	2	no	—
380	C₂×C₄×C₈₉	—	2	2	no	—
381	C₂×C₄×C₈₉	—	2	1	no	—
382	C₂×C₄×C₈₉	—	2	1	no	—
383	C₂×C₄×C₈₉	—	2	1	no	—
384	C₂×C₄×C₈₉	—	2	1	no	—
385	C₂×C₄×C₈₉	—	2	1	no	—
386	C₂×C₄×C₈₉	—	2	2	no	—
387	C₂×C₄×C₈₉	—	2	1	no	—
388	C₂×C₄×C₈₉	—	4	4	no	—
389	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
390	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
391	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
392	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
393	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
394	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
395	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
396	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
397	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
398	C₂²×C₈₉	—	4	1	no	—
399	C₂²×C₈₉	—	4	1	no	—
400	C₂²×C₈₉	—	4	1	no	—
401	C₂²×C₈₉	—	4	1	no	—
402	C₂²×C₈₉	—	4	1	no	—
403	C₂²×C₈₉	—	4	1	no	—
404	C₂²×C₈₉	—	4	1	no	—
405	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
406	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
407	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
408	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
409	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
410	C₂²×C₈₉	#585	1	1	yes	characteristic
411	C₂²×C₈₉	#585	1	1	yes	characteristic
412	C₄×C₈₉	—	2	4	no	—
413	C₄×C₈₉	—	2	2	no	—
414	C₄×C₈₉	—	2	2	no	—
415	C₄×C₈₉	—	2	4	no	—
416	C₄×C₈₉	—	2	2	no	—
417	C₄×C₈₉	—	2	2	no	—
418	C₄×C₈₉	—	4	1	no	—
419	C₄×C₈₉	—	4	2	no	—
420	C₄×C₈₉	—	4	1	no	—
421	C₄×C₈₉	—	4	1	no	—
422	C₄×C₈₉	—	4	2	no	—
423	C₄×C₈₉	—	4	2	no	—
424	C₄×C₈₉	—	4	1	no	—
425	C₄×C₈₉	—	4	1	no	—
426	C₄×C₈₉	—	4	1	no	—
427	C₄×C₈₉	—	4	2	no	—
428	C₄×C₈₉	—	4	1	no	—
429	C₄×C₈₉	—	4	2	no	—
430	C₄×C₈₉	—	4	1	no	—
431	C₄×C₈₉	—	4	1	no	—
432	C₄×C₈₉	—	4	2	no	—
433	C₄×C₈₉	#529	1	4	yes	—
434	#35204	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
435	C₂×C₈₉	—	8	1	no	—
436	C₂×C₈₉	C₂×#529	1	1	yes	characteristic
437	C₂×C₈₉	#3461	1	1	yes	characteristic
438	C₂×C₈₉	#3461	1	1	yes	characteristic
439	C₂×C₈₉	#3515	1	1	yes	characteristic
440	C₂×C₈₉	#3516	1	1	yes	characteristic
441	C₂×C₈₉	#3523	1	1	yes	characteristic
442	C₂×C₈₉	#3524	1	1	yes	characteristic
443	#2865	C₂×C₈₉	1	2	yes	—
444	#2864	C₂×C₈₉	1	2	yes	complemented
445	#2655	C₂×C₈₉	1	2	yes	complemented
446	#2654	C₂×C₈₉	1	2	yes	—
447	#2596	C₂×C₈₉	1	2	yes	—
448	#2590	C₂×C₈₉	1	2	yes	complemented
449	#2529	C₂×C₈₉	1	2	yes	—
450	#2528	C₂×C₈₉	1	2	yes	complemented
451	#2511	C₂×C₈₉	1	1	yes	characteristic, complemented
452	#2508	C₂×C₈₉	1	1	yes	characteristic, complemented
453	#2494	C₂×C₈₉	1	1	yes	characteristic
454	#2489	C₂×C₈₉	1	1	yes	characteristic
455	#2453	C₂×C₈₉	1	1	yes	characteristic, complemented
456	#2446	C₂×C₈₉	1	1	yes	characteristic, complemented
457	#2429	C₂×C₈₉	1	1	yes	characteristic
458	#2423	C₂×C₈₉	1	1	yes	characteristic
459	#2330	C₂×C₈₉	1	1	yes	characteristic, complemented
460	#2327	C₂×C₈₉	1	1	yes	characteristic, complemented
461	#2323	C₂×C₈₉	1	1	yes	characteristic
462	#2323	C₂×C₈₉	1	1	yes	characteristic
463	#2298	C₂×C₈₉	1	1	yes	characteristic
464	#2295	C₂×C₈₉	1	1	yes	characteristic, complemented
465	C₄²×Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
466	C₈₉	#35204	1	1	yes	characteristic, direct product factor, Sylow
467	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
468	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
469	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
470	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
471	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
472	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
473	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
474	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
475	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
476	#401	C₂²×C₈₉	1	2	yes	—
477	#400	C₂²×C₈₉	1	2	yes	—
478	#400	C₂²×C₈₉	1	2	yes	—
479	#400	C₂²×C₈₉	1	2	yes	—
480	#400	C₂²×C₈₉	1	2	yes	—
481	#400	C₂²×C₈₉	1	2	yes	—
482	#400	C₂²×C₈₉	1	2	yes	—
483	#399	C₂²×C₈₉	1	2	yes	—
484	#398	C₂²×C₈₉	1	2	yes	—
485	#398	C₂²×C₈₉	1	2	yes	—
486	#398	C₂²×C₈₉	1	2	yes	—
487	#398	C₂²×C₈₉	1	2	yes	—
488	#398	C₂²×C₈₉	1	2	yes	—
489	#397	C₂²×C₈₉	1	2	yes	—
490	#397	C₂²×C₈₉	1	2	yes	—
491	#396	C₂²×C₈₉	1	2	yes	—
492	#391	C₂²×C₈₉	1	1	yes	characteristic
493	#391	C₂²×C₈₉	1	1	yes	characteristic
494	#391	C₂²×C₈₉	1	1	yes	characteristic
495	#391	C₂²×C₈₉	1	1	yes	characteristic
496	#391	C₂²×C₈₉	1	1	yes	characteristic
497	#391	C₂²×C₈₉	1	1	yes	characteristic
498	#389	C₂²×C₈₉	1	2	yes	—
499	#389	C₂²×C₈₉	1	2	yes	—
500	#389	C₂²×C₈₉	1	1	yes	characteristic
501	#389	C₂²×C₈₉	1	1	yes	characteristic
502	#389	C₂²×C₈₉	1	2	yes	—
503	#389	C₂²×C₈₉	1	2	yes	—
504	#389	C₂²×C₈₉	1	1	yes	characteristic
505	#389	C₂²×C₈₉	1	1	yes	characteristic
506	#389	C₂²×C₈₉	1	2	yes	—
507	#389	C₂²×C₈₉	1	2	yes	—
508	#389	C₂²×C₈₉	1	1	yes	characteristic
509	#389	C₂²×C₈₉	1	1	yes	characteristic
510	#388	C₂²×C₈₉	1	2	yes	—
511	#388	C₂²×C₈₉	1	2	yes	—
512	#388	C₂²×C₈₉	1	2	yes	—
513	#388	C₂²×C₈₉	1	2	yes	—
514	#388	C₂²×C₈₉	1	1	yes	characteristic
515	#388	C₂²×C₈₉	1	2	yes	—
516	#388	C₂²×C₈₉	1	2	yes	—
517	#388	C₂²×C₈₉	1	1	yes	characteristic
518	#388	C₂²×C₈₉	1	2	yes	—
519	#388	C₂²×C₈₉	1	2	yes	—
520	#388	C₂²×C₈₉	1	1	yes	characteristic
521	#388	C₂²×C₈₉	1	1	yes	characteristic
522	#387	C₂²×C₈₉	1	2	yes	—
523	#387	C₂²×C₈₉	1	2	yes	—
524	#387	C₂²×C₈₉	1	2	yes	—
525	#387	C₂²×C₈₉	1	2	yes	—
526	#387	C₂²×C₈₉	1	2	yes	—
527	#387	C₂²×C₈₉	1	2	yes	—
528	#387	C₂²×C₈₉	1	2	yes	—
529	#387	C₂²×C₈₉	1	2	yes	—
530	#387	C₂²×C₈₉	1	1	yes	characteristic
531	#387	C₂²×C₈₉	1	2	yes	—
532	#387	C₂²×C₈₉	1	2	yes	—
533	#387	C₂²×C₈₉	1	2	yes	—
534	#387	C₂²×C₈₉	1	2	yes	—
535	#387	C₂²×C₈₉	1	1	yes	characteristic
536	#387	C₂²×C₈₉	1	2	yes	—
537	#387	C₂²×C₈₉	1	2	yes	—
538	#387	C₂²×C₈₉	1	2	yes	—
539	#387	C₂²×C₈₉	1	2	yes	—
540	#387	C₂²×C₈₉	1	2	yes	—
541	#387	C₂²×C₈₉	1	2	yes	—
542	#387	C₂²×C₈₉	1	1	yes	characteristic
543	#387	C₂²×C₈₉	1	1	yes	characteristic
544	#384	C₂²×C₈₉	1	1	yes	characteristic
545	#382	C₂²×C₈₉	1	1	yes	characteristic
546	#382	C₂²×C₈₉	1	2	yes	—
547	#382	C₂²×C₈₉	1	2	yes	—
548	#380	C₂²×C₈₉	1	1	yes	characteristic
549	#380	C₂²×C₈₉	1	1	yes	characteristic
550	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
551	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
552	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
553	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
554	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
555	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
556	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
557	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
558	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
559	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
560	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
561	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
562	#376	C₂²×C₈₉	1	1	yes	characteristic
563	#376	C₂²×C₈₉	1	2	yes	—
564	C₄³	C₂²×C₈₉	1	2	yes	—
565	C₄³	C₂²×C₈₉	1	1	yes	characteristic
566	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
567	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
568	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
569	C₄⋊Q₈	—	2	4	no	—
570	#125	—	2	4	no	—
571	C₂²⋊Q₈	—	2	4	no	—
572	C₂²⋊Q₈	—	2	4	no	—
573	C₄×Q₈	—	2	4	no	—
574	C₄×Q₈	—	2	4	no	—
575	C₄×Q₈	—	2	4	no	—
576	C₄×Q₈	—	2	4	no	—
577	#117	—	2	4	no	—
578	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
608	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
609	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
610	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
614	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
615	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
616	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
618	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
622	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
623	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
624	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
625	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
629	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
630	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
631	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
632	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
633	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
634	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
635	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
636	#95	C₂³×C₈₉	1	2	yes	—
637	#95	C₂³×C₈₉	1	2	yes	—
638	#95	C₂³×C₈₉	1	1	yes	characteristic
639	#95	C₂³×C₈₉	1	1	yes	characteristic
640	#95	C₂³×C₈₉	1	1	yes	characteristic
641	#95	C₂³×C₈₉	1	1	yes	characteristic
642	#95	C₂³×C₈₉	1	2	yes	—
643	#95	C₂³×C₈₉	1	2	yes	—
644	#95	C₂³×C₈₉	1	1	yes	characteristic
645	#95	C₂³×C₈₉	1	1	yes	characteristic
646	#95	C₂³×C₈₉	1	1	yes	characteristic
647	#95	C₂³×C₈₉	1	1	yes	characteristic
648	#95	C₂³×C₈₉	1	2	yes	—
649	#95	C₂³×C₈₉	1	2	yes	—
650	#95	C₂³×C₈₉	1	2	yes	—
651	#95	C₂³×C₈₉	1	1	yes	characteristic
652	#95	C₂³×C₈₉	1	1	yes	characteristic
653	#95	C₂³×C₈₉	1	2	yes	—
654	#95	C₂³×C₈₉	1	2	yes	—
655	#95	C₂³×C₈₉	1	1	yes	characteristic
656	#95	C₂³×C₈₉	1	1	yes	characteristic
657	#95	C₂³×C₈₉	1	2	yes	—
658	#95	C₂³×C₈₉	1	2	yes	—
659	#95	C₂³×C₈₉	1	2	yes	—
660	#95	C₂³×C₈₉	1	2	yes	—
661	#95	C₂³×C₈₉	1	2	yes	—
662	#95	C₂³×C₈₉	1	2	yes	—
663	#95	C₂³×C₈₉	1	2	yes	—
664	#95	C₂³×C₈₉	1	2	yes	—
665	#95	C₂³×C₈₉	1	2	yes	—
666	#95	C₂³×C₈₉	1	2	yes	—
667	#95	C₂³×C₈₉	1	2	yes	—
668	#95	C₂³×C₈₉	1	2	yes	—
669	#95	C₂³×C₈₉	1	2	yes	—
670	#95	C₂³×C₈₉	1	2	yes	—
671	#95	C₂³×C₈₉	1	2	yes	—
672	#95	C₂³×C₈₉	1	2	yes	—
673	#95	C₂³×C₈₉	1	2	yes	—
674	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
675	C₂×Q₈	—	2	2	no	—
676	C₂×Q₈	—	2	2	no	—
677	C₂×Q₈	—	2	2	no	—
678	C₂×Q₈	—	2	2	no	—
679	C₂×Q₈	—	2	2	no	—
680	C₂×Q₈	#41×C₈₉	1	4	yes	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
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	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
704	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	4	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	2	no	—
730	C₄⋊C₄	—	4	1	no	—
731	C₄⋊C₄	—	4	1	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	#41×C₈₉	1	4	yes	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	4	2	no	—
743	C₂²⋊C₄	—	4	1	no	—
744	C₂²⋊C₄	—	4	1	no	—
745	C₂²⋊C₄	—	4	2	no	—
746	C₄²	—	2	2	no	—
747	C₄²	—	2	4	no	—
748	C₄²	—	2	4	no	—
749	C₄²	—	2	2	no	—
750	C₄²	—	2	2	no	—
751	C₄²	—	2	4	no	—
752	C₄²	—	2	4	no	—
753	C₄²	—	2	2	no	—
754	C₄²	—	2	2	no	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	4	no	—
758	C₄²	—	4	1	no	—
759	C₄²	—	4	2	no	—
760	C₄²	—	4	1	no	—
761	C₄²	—	4	2	no	—
762	C₄²	—	4	2	no	—
763	C₄²	#41×C₈₉	1	4	yes	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	2	1	no	—
768	C₂³	—	2	1	no	—
769	C₂³	—	2	1	no	—
770	C₂³	—	2	1	no	—
771	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
772	Q₈	—	2	8	no	—
773	Q₈	—	4	4	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	4	4	no	—
832	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
833	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
834	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
835	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
836	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
837	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
838	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
839	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
840	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
841	C₂²	—	4	1	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	1	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	1	no	—
848	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
849	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
850	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
851	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
852	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
853	C₂²	#585×C₈₉	1	1	yes	characteristic
854	C₂²	#585×C₈₉	1	1	yes	characteristic
855	C₄	—	2	4	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	2	no	—
858	C₄	—	2	4	no	—
859	C₄	—	2	2	no	—
860	C₄	—	2	2	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	1	no	—
868	C₄	—	4	1	no	—
869	C₄	—	4	1	no	—
870	C₄	—	4	2	no	—
871	C₄	—	4	1	no	—
872	C₄	—	4	2	no	—
873	C₄	—	4	1	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	2	no	—
876	C₄	#529×C₈₉	1	4	yes	—
877	C₂	—	8	1	no	—
878	C₂	C₂×#529×C₈₉	1	1	yes	characteristic
879	C₂	C₈₉×#3461	1	1	yes	characteristic
880	C₂	C₈₉×#3461	1	1	yes	characteristic
881	C₂	C₈₉×#3515	1	1	yes	characteristic
882	C₂	C₈₉×#3516	1	1	yes	characteristic
883	C₂	C₈₉×#3523	1	1	yes	characteristic
884	C₂	C₈₉×#3524	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂⁴×C₈₉	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₉×#2864	C₂	semidirect
3. C₈₉×#2655	C₂	semidirect
6. C₈₉×#2590	C₂	semidirect
8. C₈₉×#2528	C₂	semidirect
9. C₈₉×#2511	C₂	semidirect
10. C₈₉×#2508	C₂	semidirect
13. C₈₉×#2453	C₂	semidirect
14. C₈₉×#2446	C₂	semidirect
17. C₈₉×#2330	C₂	semidirect
18. C₈₉×#2327	C₂	semidirect
22. C₈₉×#2295	C₂	semidirect
23. C₄²×Q₈×C₈₉	C₂	semidirect
434. #35204	C₈₉	direct (N × H)
444. #2864	C₂×C₈₉	semidirect
445. #2655	C₂×C₈₉	semidirect
448. #2590	C₂×C₈₉	semidirect
450. #2528	C₂×C₈₉	semidirect
451. #2511	C₂×C₈₉	semidirect
452. #2508	C₂×C₈₉	semidirect
455. #2453	C₂×C₈₉	semidirect
456. #2446	C₂×C₈₉	semidirect
459. #2330	C₂×C₈₉	semidirect
460. #2327	C₂×C₈₉	semidirect
464. #2295	C₂×C₈₉	semidirect
465. C₄²×Q₈	C₂×C₈₉	semidirect
466. C₈₉	#35204	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×#2865	2
C₈₉×#2864	2
C₈₉×#2655	2
C₈₉×#2654	2
C₈₉×#2596	2
C₈₉×#2590	2
C₈₉×#2529	2
C₈₉×#2528	2
C₈₉×#2511	2
C₈₉×#2508	2
C₈₉×#2494	2
C₈₉×#2489	2
C₈₉×#2453	2
C₈₉×#2446	2
C₈₉×#2429	2
C₈₉×#2423	2
C₈₉×#2330	2
C₈₉×#2327	2
C₈₉×#2323	2
C₈₉×#2298	2
C₈₉×#2295	2
C₄²×Q₈×C₈₉	2
#35204	89

Subgroups — C89×#35204 #36413052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35204 #36413052