Subgroups — C₈₉×#35244 #36413092

Order 22784.

2242 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#541×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2852	C₂	1	2	yes	maximal
4	C₈₉×#2851	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2637	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2634	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2481	C₂	1	2	yes	maximal
8	C₈₉×#2473	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2469	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2462	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2453	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2446	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#2442	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2434	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2429	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2421	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2417	C₂	1	1	yes	maximal, characteristic
18	C₈₉×#2409	C₂	1	1	yes	maximal, characteristic
19	C₈₉×#2327	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₉×#2323	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#2320	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₂²⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2290	C₂	1	1	yes	maximal, characteristic
24	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	#541×C₈₉	—	2	8	no	—
26	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#126×C₈₉	C₂²	1	2	yes	—
29	C₂×#126×C₈₉	C₂²	1	2	yes	—
30	C₂×#125×C₈₉	C₂²	1	2	yes	—
31	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#125×C₈₉	C₂²	1	2	yes	—
33	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₈₉	—	2	8	no	—
38	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
41	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
44	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
47	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
48	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
49	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
50	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
51	#400×C₈₉	C₂²	1	2	yes	—
52	#400×C₈₉	C₂²	1	2	yes	—
53	#400×C₈₉	C₂²	1	2	yes	—
54	#400×C₈₉	C₂²	1	2	yes	—
55	#398×C₈₉	C₂²	1	2	yes	—
56	#398×C₈₉	C₂²	1	2	yes	—
57	#398×C₈₉	C₂²	1	2	yes	—
58	#398×C₈₉	C₂²	1	2	yes	—
59	#398×C₈₉	C₂²	1	2	yes	—
60	#397×C₈₉	C₂²	1	2	yes	—
61	#396×C₈₉	C₂²	1	2	yes	—
62	#396×C₈₉	C₂²	1	2	yes	—
63	#395×C₈₉	C₂²	1	2	yes	—
64	#395×C₈₉	C₂²	1	2	yes	—
65	#395×C₈₉	C₂²	1	2	yes	—
66	#393×C₈₉	C₂²	1	2	yes	—
67	#391×C₈₉	C₂²	1	1	yes	characteristic
68	#391×C₈₉	C₂²	1	1	yes	characteristic
69	#391×C₈₉	C₂²	1	1	yes	characteristic
70	#391×C₈₉	C₂²	1	1	yes	characteristic
71	#391×C₈₉	C₂²	1	1	yes	characteristic
72	#391×C₈₉	C₂²	1	1	yes	characteristic
73	#389×C₈₉	C₂²	1	1	yes	characteristic
74	#389×C₈₉	C₂²	1	1	yes	characteristic
75	#389×C₈₉	C₂²	1	1	yes	characteristic
76	#389×C₈₉	C₂²	1	1	yes	characteristic
77	#389×C₈₉	C₂²	1	2	yes	—
78	#389×C₈₉	C₂²	1	2	yes	—
79	#389×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	#388×C₈₉	C₂²	1	2	yes	—
84	#388×C₈₉	C₂²	1	1	yes	characteristic
85	#388×C₈₉	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
99	#387×C₈₉	C₂²	1	1	yes	characteristic
100	#386×C₈₉	C₂²	1	1	yes	characteristic
101	#386×C₈₉	C₂²	1	2	yes	—
102	#386×C₈₉	C₂²	1	2	yes	—
103	#386×C₈₉	C₂²	1	1	yes	characteristic
104	#385×C₈₉	C₂²	1	2	yes	—
105	#385×C₈₉	C₂²	1	1	yes	characteristic
106	#385×C₈₉	C₂²	1	2	yes	—
107	#385×C₈₉	C₂²	1	2	yes	—
108	#385×C₈₉	C₂²	1	2	yes	—
109	#385×C₈₉	C₂²	1	2	yes	—
110	#385×C₈₉	C₂²	1	1	yes	characteristic
111	#383×C₈₉	C₂²	1	2	yes	—
112	#382×C₈₉	C₂²	1	2	yes	—
113	#382×C₈₉	C₂²	1	1	yes	characteristic
114	#380×C₈₉	C₂²	1	1	yes	characteristic
115	#380×C₈₉	C₂²	1	1	yes	characteristic
116	#380×C₈₉	C₂²	1	2	yes	—
117	#380×C₈₉	C₂²	1	2	yes	—
118	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
119	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
120	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
122	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
123	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
124	#376×C₈₉	C₂²	1	1	yes	characteristic
125	C₂²×Q₈×C₈₉	—	2	4	no	—
126	C₂²×Q₈×C₈₉	—	2	4	no	—
127	C₂²×Q₈×C₈₉	—	2	4	no	—
128	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
129	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
130	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
136	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
138	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
139	C₄⋊Q₈×C₈₉	—	2	4	no	—
140	C₄⋊Q₈×C₈₉	—	2	4	no	—
141	#126×C₈₉	—	2	8	no	—
142	#126×C₈₉	—	2	8	no	—
143	#125×C₈₉	—	2	4	no	—
144	#125×C₈₉	—	2	8	no	—
145	#125×C₈₉	—	2	8	no	—
146	C₂²⋊Q₈×C₈₉	—	2	4	no	—
147	C₂²⋊Q₈×C₈₉	—	2	4	no	—
148	C₂²⋊Q₈×C₈₉	—	2	4	no	—
149	C₂²⋊Q₈×C₈₉	—	2	4	no	—
150	C₄×Q₈×C₈₉	—	2	4	no	—
151	C₄×Q₈×C₈₉	—	2	4	no	—
152	C₄×Q₈×C₈₉	—	2	8	no	—
153	C₄×Q₈×C₈₉	—	2	4	no	—
154	C₄×Q₈×C₈₉	—	2	8	no	—
155	C₄×Q₈×C₈₉	—	2	4	no	—
156	C₄×Q₈×C₈₉	D₄	1	8	yes	complemented
157	C₄×D₄×C₈₉	—	2	4	no	—
158	#117×C₈₉	—	2	4	no	—
159	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
160	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
161	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
205	C₂×C₄²×C₈₉	—	2	4	no	—
206	C₂×C₄²×C₈₉	—	2	8	no	—
207	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
210	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
215	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
216	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
217	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
218	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
220	#95×C₈₉	C₂³	1	1	yes	characteristic
221	#95×C₈₉	C₂³	1	1	yes	characteristic
222	#95×C₈₉	C₂³	1	1	yes	characteristic
223	#95×C₈₉	C₂³	1	1	yes	characteristic
224	#95×C₈₉	C₂³	1	1	yes	characteristic
225	#95×C₈₉	C₂³	1	1	yes	characteristic
226	#95×C₈₉	C₂³	1	1	yes	characteristic
227	#95×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
234	#95×C₈₉	C₂³	1	1	yes	characteristic
235	#95×C₈₉	C₂³	1	2	yes	—
236	#95×C₈₉	C₂³	1	2	yes	—
237	#95×C₈₉	C₂³	1	2	yes	—
238	#95×C₈₉	C₂³	1	2	yes	—
239	#95×C₈₉	C₂³	1	2	yes	—
240	#95×C₈₉	C₂³	1	2	yes	—
241	#95×C₈₉	C₂³	1	2	yes	—
242	#95×C₈₉	C₂³	1	2	yes	—
243	#95×C₈₉	C₂³	1	2	yes	—
244	#95×C₈₉	C₂³	1	2	yes	—
245	#95×C₈₉	C₂³	1	2	yes	—
246	#95×C₈₉	C₂³	1	2	yes	—
247	#95×C₈₉	C₂³	1	2	yes	—
248	#95×C₈₉	C₂³	1	2	yes	—
249	#95×C₈₉	C₂³	1	2	yes	—
250	#95×C₈₉	C₂³	1	2	yes	—
251	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
252	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
253	C₂×Q₈×C₈₉	—	2	32	no	—
254	C₂×Q₈×C₈₉	—	2	4	no	—
255	C₂×Q₈×C₈₉	—	2	2	no	—
256	C₂×Q₈×C₈₉	—	2	2	no	—
257	C₂×Q₈×C₈₉	—	2	4	no	—
258	C₂×Q₈×C₈₉	—	2	4	no	—
259	C₂×Q₈×C₈₉	—	2	2	no	—
260	C₂×Q₈×C₈₉	—	2	2	no	—
261	C₂×Q₈×C₈₉	—	2	2	no	—
262	C₂×Q₈×C₈₉	—	2	2	no	—
263	C₂×Q₈×C₈₉	—	2	2	no	—
264	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
265	C₂×Q₈×C₈₉	#41	1	4	yes	—
266	C₂×D₄×C₈₉	—	2	2	no	—
267	C₂×D₄×C₈₉	—	2	2	no	—
268	C₂×D₄×C₈₉	—	2	2	no	—
269	C₂²×C₄×C₈₉	—	2	4	no	—
270	C₂²×C₄×C₈₉	—	2	2	no	—
271	C₂²×C₄×C₈₉	—	2	2	no	—
272	C₂²×C₄×C₈₉	—	2	4	no	—
273	C₂²×C₄×C₈₉	—	2	2	no	—
274	C₂²×C₄×C₈₉	—	2	4	no	—
275	C₂²×C₄×C₈₉	—	2	2	no	—
276	C₂²×C₄×C₈₉	—	2	2	no	—
277	C₂²×C₄×C₈₉	—	2	2	no	—
278	C₂²×C₄×C₈₉	—	2	4	no	—
279	C₂²×C₄×C₈₉	—	2	2	no	—
280	C₂²×C₄×C₈₉	—	2	4	no	—
281	C₂²×C₄×C₈₉	—	2	2	no	—
282	C₂²×C₄×C₈₉	—	2	2	no	—
283	C₂²×C₄×C₈₉	—	2	2	no	—
284	C₂²×C₄×C₈₉	—	4	1	no	—
285	C₂²×C₄×C₈₉	—	4	2	no	—
286	C₂²×C₄×C₈₉	#41	1	4	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	2	yes	—
292	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
308	C₄⋊C₄×C₈₉	—	2	4	no	—
309	C₄⋊C₄×C₈₉	—	2	4	no	—
310	C₄⋊C₄×C₈₉	—	2	4	no	—
311	C₄⋊C₄×C₈₉	—	2	4	no	—
312	C₄⋊C₄×C₈₉	—	2	2	no	—
313	C₄⋊C₄×C₈₉	—	2	2	no	—
314	C₄⋊C₄×C₈₉	—	2	2	no	—
315	C₄⋊C₄×C₈₉	—	2	2	no	—
316	C₄⋊C₄×C₈₉	—	2	4	no	—
317	C₄⋊C₄×C₈₉	—	2	4	no	—
318	C₄⋊C₄×C₈₉	—	2	4	no	—
319	C₄⋊C₄×C₈₉	—	2	4	no	—
320	C₄⋊C₄×C₈₉	—	2	4	no	—
321	C₄⋊C₄×C₈₉	—	2	4	no	—
322	C₄⋊C₄×C₈₉	—	2	4	no	—
323	C₄⋊C₄×C₈₉	—	2	2	no	—
324	C₄⋊C₄×C₈₉	—	2	2	no	—
325	C₄⋊C₄×C₈₉	—	2	2	no	—
326	C₄⋊C₄×C₈₉	—	2	4	no	—
327	C₄⋊C₄×C₈₉	—	2	4	no	—
328	C₄⋊C₄×C₈₉	—	2	4	no	—
329	C₄⋊C₄×C₈₉	—	2	4	no	—
330	C₄⋊C₄×C₈₉	—	2	4	no	—
331	C₄⋊C₄×C₈₉	—	2	2	no	—
332	C₄⋊C₄×C₈₉	—	4	2	no	—
333	C₄⋊C₄×C₈₉	—	4	2	no	—
334	C₄⋊C₄×C₈₉	—	4	2	no	—
335	C₄⋊C₄×C₈₉	—	4	1	no	—
336	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
337	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
338	C₂²⋊C₄×C₈₉	—	2	2	no	—
339	C₂²⋊C₄×C₈₉	—	2	4	no	—
340	C₂²⋊C₄×C₈₉	—	2	4	no	—
341	C₂²⋊C₄×C₈₉	—	2	2	no	—
342	C₂²⋊C₄×C₈₉	—	2	2	no	—
343	C₂²⋊C₄×C₈₉	—	2	2	no	—
344	C₂²⋊C₄×C₈₉	—	2	2	no	—
345	C₂²⋊C₄×C₈₉	—	2	4	no	—
346	C₂²⋊C₄×C₈₉	—	2	4	no	—
347	C₂²⋊C₄×C₈₉	—	2	2	no	—
348	C₂²⋊C₄×C₈₉	—	2	4	no	—
349	C₂²⋊C₄×C₈₉	—	2	2	no	—
350	C₂²⋊C₄×C₈₉	—	4	2	no	—
351	C₂²⋊C₄×C₈₉	—	4	1	no	—
352	C₄²×C₈₉	—	2	2	no	—
353	C₄²×C₈₉	—	2	4	no	—
354	C₄²×C₈₉	—	2	4	no	—
355	C₄²×C₈₉	—	2	2	no	—
356	C₄²×C₈₉	—	2	2	no	—
357	C₄²×C₈₉	—	2	4	no	—
358	C₄²×C₈₉	—	2	2	no	—
359	C₄²×C₈₉	—	2	4	no	—
360	C₄²×C₈₉	—	2	2	no	—
361	C₄²×C₈₉	—	2	2	no	—
362	C₄²×C₈₉	—	4	2	no	—
363	C₄²×C₈₉	C₂×D₄	1	4	yes	—
364	C₄²×C₈₉	C₂×D₄	1	8	yes	—
365	C₂³×C₈₉	—	2	1	no	—
366	C₂³×C₈₉	—	2	1	no	—
367	C₂³×C₈₉	—	2	1	no	—
368	C₂³×C₈₉	—	2	1	no	—
369	C₂³×C₈₉	—	2	1	no	—
370	C₂³×C₈₉	—	2	1	no	—
371	C₂³×C₈₉	—	2	1	no	—
372	C₂³×C₈₉	—	2	1	no	—
373	C₂³×C₈₉	—	2	1	no	—
374	C₂³×C₈₉	—	2	1	no	—
375	C₂³×C₈₉	—	2	1	no	—
376	C₂³×C₈₉	C₂×#41	1	2	yes	—
377	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
378	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
379	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
380	Q₈×C₈₉	—	2	16	no	—
381	Q₈×C₈₉	—	2	8	no	—
382	Q₈×C₈₉	—	2	8	no	—
383	Q₈×C₈₉	—	4	4	no	—
384	D₄×C₈₉	—	4	4	no	—
385	C₂×C₄×C₈₉	—	2	8	no	—
386	C₂×C₄×C₈₉	—	2	16	no	—
387	C₂×C₄×C₈₉	—	2	1	no	—
388	C₂×C₄×C₈₉	—	2	2	no	—
389	C₂×C₄×C₈₉	—	2	1	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	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	2	no	—
399	C₂×C₄×C₈₉	—	2	1	no	—
400	C₂×C₄×C₈₉	—	2	2	no	—
401	C₂×C₄×C₈₉	—	2	8	no	—
402	C₂×C₄×C₈₉	—	2	2	no	—
403	C₂×C₄×C₈₉	—	2	1	no	—
404	C₂×C₄×C₈₉	—	2	1	no	—
405	C₂×C₄×C₈₉	—	2	2	no	—
406	C₂×C₄×C₈₉	—	2	1	no	—
407	C₂×C₄×C₈₉	—	2	2	no	—
408	C₂×C₄×C₈₉	—	2	1	no	—
409	C₂×C₄×C₈₉	—	2	1	no	—
410	C₂×C₄×C₈₉	—	2	1	no	—
411	C₂×C₄×C₈₉	—	2	1	no	—
412	C₂×C₄×C₈₉	—	2	1	no	—
413	C₂×C₄×C₈₉	—	2	2	no	—
414	C₂×C₄×C₈₉	—	2	2	no	—
415	C₂×C₄×C₈₉	—	2	1	no	—
416	C₂×C₄×C₈₉	—	2	2	no	—
417	C₂×C₄×C₈₉	—	2	1	no	—
418	C₂×C₄×C₈₉	—	2	2	no	—
419	C₂×C₄×C₈₉	—	2	1	no	—
420	C₂×C₄×C₈₉	—	2	2	no	—
421	C₂×C₄×C₈₉	—	2	1	no	—
422	C₂×C₄×C₈₉	—	2	1	no	—
423	C₂×C₄×C₈₉	—	2	2	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	2	no	—
428	C₂×C₄×C₈₉	—	2	1	no	—
429	C₂×C₄×C₈₉	—	2	2	no	—
430	C₂×C₄×C₈₉	—	2	1	no	—
431	C₂×C₄×C₈₉	—	2	2	no	—
432	C₂×C₄×C₈₉	—	2	1	no	—
433	C₂×C₄×C₈₉	—	2	1	no	—
434	C₂×C₄×C₈₉	—	2	2	no	—
435	C₂×C₄×C₈₉	—	2	2	no	—
436	C₂×C₄×C₈₉	—	2	1	no	—
437	C₂×C₄×C₈₉	—	2	2	no	—
438	C₂×C₄×C₈₉	—	2	1	no	—
439	C₂×C₄×C₈₉	—	2	1	no	—
440	C₂×C₄×C₈₉	—	2	1	no	—
441	C₂×C₄×C₈₉	—	4	4	no	—
442	C₂×C₄×C₈₉	—	4	8	no	—
443	C₂×C₄×C₈₉	—	4	4	no	—
444	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
446	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
447	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
448	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
449	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
450	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
451	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
452	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
453	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
454	C₂²×C₈₉	—	2	2	no	—
455	C₂²×C₈₉	—	2	2	no	—
456	C₂²×C₈₉	—	2	2	no	—
457	C₂²×C₈₉	—	2	2	no	—
458	C₂²×C₈₉	—	2	2	no	—
459	C₂²×C₈₉	—	2	2	no	—
460	C₂²×C₈₉	—	4	1	no	—
461	C₂²×C₈₉	—	4	1	no	—
462	C₂²×C₈₉	—	4	1	no	—
463	C₂²×C₈₉	—	4	1	no	—
464	C₂²×C₈₉	—	4	1	no	—
465	C₂²×C₈₉	—	4	1	no	—
466	C₂²×C₈₉	—	4	1	no	—
467	C₂²×C₈₉	#541	1	4	yes	complemented
468	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
469	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
470	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
471	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
472	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
473	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
474	C₂²×C₈₉	#585	1	1	yes	characteristic
475	C₄×C₈₉	—	2	4	no	—
476	C₄×C₈₉	—	2	4	no	—
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	2	no	—
484	C₄×C₈₉	—	4	1	no	—
485	C₄×C₈₉	—	4	1	no	—
486	C₄×C₈₉	—	4	2	no	—
487	C₄×C₈₉	—	4	1	no	—
488	C₄×C₈₉	—	4	2	no	—
489	C₄×C₈₉	—	4	1	no	—
490	C₄×C₈₉	—	4	2	no	—
491	C₄×C₈₉	—	4	1	no	—
492	C₄×C₈₉	—	4	1	no	—
493	C₄×C₈₉	—	4	2	no	—
494	C₄×C₈₉	—	4	1	no	—
495	C₄×C₈₉	#525	1	4	yes	—
496	#35244	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
497	C₂×C₈₉	—	2	4	no	—
498	C₂×C₈₉	—	8	1	no	—
499	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
500	C₂×C₈₉	C₂×#541	1	1	yes	characteristic
501	C₂×C₈₉	#3461	1	1	yes	characteristic
502	C₂×C₈₉	#3486	1	1	yes	characteristic
503	C₂×C₈₉	#3489	1	1	yes	characteristic
504	C₂×C₈₉	#3516	1	1	yes	characteristic
505	C₂×C₈₉	#3523	1	1	yes	characteristic
506	C₂×#541	C₂×C₈₉	1	1	yes	characteristic, complemented
507	C₂²×C₄×Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
508	#2852	C₂×C₈₉	1	2	yes	—
509	#2851	C₂×C₈₉	1	2	yes	complemented
510	#2637	C₂×C₈₉	1	2	yes	complemented
511	#2634	C₂×C₈₉	1	2	yes	complemented
512	#2481	C₂×C₈₉	1	2	yes	—
513	#2473	C₂×C₈₉	1	2	yes	complemented
514	#2469	C₂×C₈₉	1	2	yes	complemented
515	#2462	C₂×C₈₉	1	2	yes	complemented
516	#2453	C₂×C₈₉	1	1	yes	characteristic, complemented
517	#2446	C₂×C₈₉	1	1	yes	characteristic, complemented
518	#2442	C₂×C₈₉	1	1	yes	characteristic, complemented
519	#2434	C₂×C₈₉	1	1	yes	characteristic, complemented
520	#2429	C₂×C₈₉	1	1	yes	characteristic, complemented
521	#2421	C₂×C₈₉	1	1	yes	characteristic, complemented
522	#2417	C₂×C₈₉	1	1	yes	characteristic
523	#2409	C₂×C₈₉	1	1	yes	characteristic
524	#2327	C₂×C₈₉	1	1	yes	characteristic, complemented
525	#2323	C₂×C₈₉	1	1	yes	characteristic, complemented
526	#2320	C₂×C₈₉	1	1	yes	characteristic, complemented
527	C₄×C₂²⋊Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
528	#2290	C₂×C₈₉	1	1	yes	characteristic
529	C₈₉	#35244	1	1	yes	characteristic, direct product factor, Sylow
530	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
531	#541	—	2	8	no	—
532	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
533	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
534	C₂×#126	C₂²×C₈₉	1	2	yes	—
535	C₂×#126	C₂²×C₈₉	1	2	yes	—
536	C₂×#125	C₂²×C₈₉	1	2	yes	—
537	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
538	C₂×#125	C₂²×C₈₉	1	2	yes	—
539	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
540	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
541	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
542	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
543	C₂×C₄×Q₈	—	2	8	no	—
544	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
545	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
546	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
547	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
548	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
549	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
550	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
551	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
552	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
553	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
554	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
555	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
556	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
557	#400	C₂²×C₈₉	1	2	yes	—
558	#400	C₂²×C₈₉	1	2	yes	—
559	#400	C₂²×C₈₉	1	2	yes	—
560	#400	C₂²×C₈₉	1	2	yes	—
561	#398	C₂²×C₈₉	1	2	yes	—
562	#398	C₂²×C₈₉	1	2	yes	—
563	#398	C₂²×C₈₉	1	2	yes	—
564	#398	C₂²×C₈₉	1	2	yes	—
565	#398	C₂²×C₈₉	1	2	yes	—
566	#397	C₂²×C₈₉	1	2	yes	—
567	#396	C₂²×C₈₉	1	2	yes	—
568	#396	C₂²×C₈₉	1	2	yes	—
569	#395	C₂²×C₈₉	1	2	yes	—
570	#395	C₂²×C₈₉	1	2	yes	—
571	#395	C₂²×C₈₉	1	2	yes	—
572	#393	C₂²×C₈₉	1	2	yes	—
573	#391	C₂²×C₈₉	1	1	yes	characteristic
574	#391	C₂²×C₈₉	1	1	yes	characteristic
575	#391	C₂²×C₈₉	1	1	yes	characteristic
576	#391	C₂²×C₈₉	1	1	yes	characteristic
577	#391	C₂²×C₈₉	1	1	yes	characteristic
578	#391	C₂²×C₈₉	1	1	yes	characteristic
579	#389	C₂²×C₈₉	1	1	yes	characteristic
580	#389	C₂²×C₈₉	1	1	yes	characteristic
581	#389	C₂²×C₈₉	1	1	yes	characteristic
582	#389	C₂²×C₈₉	1	2	yes	—
583	#389	C₂²×C₈₉	1	2	yes	—
584	#389	C₂²×C₈₉	1	2	yes	—
585	#389	C₂²×C₈₉	1	1	yes	characteristic
586	#388	C₂²×C₈₉	1	2	yes	—
587	#388	C₂²×C₈₉	1	2	yes	—
588	#388	C₂²×C₈₉	1	2	yes	—
589	#388	C₂²×C₈₉	1	2	yes	—
590	#388	C₂²×C₈₉	1	1	yes	characteristic
591	#388	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	2	yes	—
595	#387	C₂²×C₈₉	1	2	yes	—
596	#387	C₂²×C₈₉	1	2	yes	—
597	#387	C₂²×C₈₉	1	2	yes	—
598	#387	C₂²×C₈₉	1	2	yes	—
599	#387	C₂²×C₈₉	1	2	yes	—
600	#387	C₂²×C₈₉	1	2	yes	—
601	#387	C₂²×C₈₉	1	2	yes	—
602	#387	C₂²×C₈₉	1	2	yes	—
603	#387	C₂²×C₈₉	1	1	yes	characteristic
604	#387	C₂²×C₈₉	1	2	yes	—
605	#387	C₂²×C₈₉	1	1	yes	characteristic
606	#386	C₂²×C₈₉	1	1	yes	characteristic
607	#386	C₂²×C₈₉	1	2	yes	—
608	#386	C₂²×C₈₉	1	2	yes	—
609	#386	C₂²×C₈₉	1	1	yes	characteristic
610	#385	C₂²×C₈₉	1	1	yes	characteristic
611	#385	C₂²×C₈₉	1	2	yes	—
612	#385	C₂²×C₈₉	1	2	yes	—
613	#385	C₂²×C₈₉	1	2	yes	—
614	#385	C₂²×C₈₉	1	2	yes	—
615	#385	C₂²×C₈₉	1	2	yes	—
616	#385	C₂²×C₈₉	1	1	yes	characteristic
617	#383	C₂²×C₈₉	1	2	yes	—
618	#382	C₂²×C₈₉	1	2	yes	—
619	#382	C₂²×C₈₉	1	1	yes	characteristic
620	#380	C₂²×C₈₉	1	1	yes	characteristic
621	#380	C₂²×C₈₉	1	2	yes	—
622	#380	C₂²×C₈₉	1	2	yes	—
623	#380	C₂²×C₈₉	1	1	yes	characteristic
624	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
625	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
626	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
627	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
628	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
629	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
630	#376	C₂²×C₈₉	1	1	yes	characteristic
631	C₂²×Q₈	—	2	4	no	—
632	C₂²×Q₈	—	2	4	no	—
633	C₂²×Q₈	—	2	4	no	—
634	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
635	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
636	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
637	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
638	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
639	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
640	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
641	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
642	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
643	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
644	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
645	C₄⋊Q₈	—	2	4	no	—
646	C₄⋊Q₈	—	2	4	no	—
647	#126	—	2	8	no	—
648	#126	—	2	8	no	—
649	#125	—	2	4	no	—
650	#125	—	2	8	no	—
651	#125	—	2	8	no	—
652	C₂²⋊Q₈	—	2	4	no	—
653	C₂²⋊Q₈	—	2	4	no	—
654	C₂²⋊Q₈	—	2	4	no	—
655	C₂²⋊Q₈	—	2	4	no	—
656	C₄×Q₈	—	2	4	no	—
657	C₄×Q₈	—	2	4	no	—
658	C₄×Q₈	—	2	8	no	—
659	C₄×Q₈	—	2	4	no	—
660	C₄×Q₈	—	2	8	no	—
661	C₄×Q₈	—	2	4	no	—
662	C₄×Q₈	D₄×C₈₉	1	8	yes	complemented
663	C₄×D₄	—	2	4	no	—
664	#117	—	2	4	no	—
665	C₂×C₄⋊C₄	—	2	4	no	—
666	C₂×C₄⋊C₄	—	2	8	no	—
667	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	1	yes	characteristic
675	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
676	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
677	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
678	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
679	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
680	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
681	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
682	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
683	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
684	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
685	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
688	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
689	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
692	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
693	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
694	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
695	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
696	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
698	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
699	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
700	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
701	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
706	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
708	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
709	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
710	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
711	C₂×C₄²	—	2	4	no	—
712	C₂×C₄²	—	2	8	no	—
713	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
714	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
715	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
716	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
717	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
718	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
719	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
720	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
721	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
722	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
723	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
724	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
725	C₂×C₄²	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	1	yes	characteristic
730	#95	C₂³×C₈₉	1	1	yes	characteristic
731	#95	C₂³×C₈₉	1	1	yes	characteristic
732	#95	C₂³×C₈₉	1	1	yes	characteristic
733	#95	C₂³×C₈₉	1	1	yes	characteristic
734	#95	C₂³×C₈₉	1	2	yes	—
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	1	yes	characteristic
740	#95	C₂³×C₈₉	1	1	yes	characteristic
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	#95	C₂³×C₈₉	1	2	yes	—
746	#95	C₂³×C₈₉	1	2	yes	—
747	#95	C₂³×C₈₉	1	2	yes	—
748	#95	C₂³×C₈₉	1	2	yes	—
749	#95	C₂³×C₈₉	1	2	yes	—
750	#95	C₂³×C₈₉	1	2	yes	—
751	#95	C₂³×C₈₉	1	2	yes	—
752	#95	C₂³×C₈₉	1	2	yes	—
753	#95	C₂³×C₈₉	1	2	yes	—
754	#95	C₂³×C₈₉	1	2	yes	—
755	#95	C₂³×C₈₉	1	2	yes	—
756	#95	C₂³×C₈₉	1	2	yes	—
757	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
758	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
759	C₂×Q₈	—	2	32	no	—
760	C₂×Q₈	—	2	4	no	—
761	C₂×Q₈	—	2	2	no	—
762	C₂×Q₈	—	2	2	no	—
763	C₂×Q₈	—	2	4	no	—
764	C₂×Q₈	—	2	4	no	—
765	C₂×Q₈	—	2	2	no	—
766	C₂×Q₈	—	2	2	no	—
767	C₂×Q₈	—	2	2	no	—
768	C₂×Q₈	—	2	2	no	—
769	C₂×Q₈	—	2	2	no	—
770	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
771	C₂×Q₈	#41×C₈₉	1	4	yes	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	2	no	—
774	C₂×D₄	—	2	2	no	—
775	C₂²×C₄	—	2	4	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	4	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	4	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	—	2	4	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	4	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	4	1	no	—
791	C₂²×C₄	—	4	2	no	—
792	C₂²×C₄	#41×C₈₉	1	4	yes	—
793	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
803	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
804	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
805	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
806	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
807	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
808	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
809	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
810	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
811	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
812	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
813	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
814	C₄⋊C₄	—	2	4	no	—
815	C₄⋊C₄	—	2	4	no	—
816	C₄⋊C₄	—	2	4	no	—
817	C₄⋊C₄	—	2	4	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	4	no	—
823	C₄⋊C₄	—	2	4	no	—
824	C₄⋊C₄	—	2	4	no	—
825	C₄⋊C₄	—	2	4	no	—
826	C₄⋊C₄	—	2	4	no	—
827	C₄⋊C₄	—	2	4	no	—
828	C₄⋊C₄	—	2	4	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	4	no	—
833	C₄⋊C₄	—	2	4	no	—
834	C₄⋊C₄	—	2	4	no	—
835	C₄⋊C₄	—	2	4	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	4	no	—
838	C₄⋊C₄	—	4	2	no	—
839	C₄⋊C₄	—	4	2	no	—
840	C₄⋊C₄	—	4	2	no	—
841	C₄⋊C₄	—	4	1	no	—
842	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
843	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	4	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	4	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	4	no	—
852	C₂²⋊C₄	—	2	4	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	4	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	4	2	no	—
857	C₂²⋊C₄	—	4	1	no	—
858	C₄²	—	2	2	no	—
859	C₄²	—	2	4	no	—
860	C₄²	—	2	4	no	—
861	C₄²	—	2	2	no	—
862	C₄²	—	2	2	no	—
863	C₄²	—	2	4	no	—
864	C₄²	—	2	2	no	—
865	C₄²	—	2	4	no	—
866	C₄²	—	2	2	no	—
867	C₄²	—	2	2	no	—
868	C₄²	—	4	2	no	—
869	C₄²	C₂×D₄×C₈₉	1	4	yes	—
870	C₄²	C₂×D₄×C₈₉	1	8	yes	—
871	C₂³	—	2	1	no	—
872	C₂³	—	2	1	no	—
873	C₂³	—	2	1	no	—
874	C₂³	—	2	1	no	—
875	C₂³	—	2	1	no	—
876	C₂³	—	2	1	no	—
877	C₂³	—	2	1	no	—
878	C₂³	—	2	1	no	—
879	C₂³	—	2	1	no	—
880	C₂³	—	2	1	no	—
881	C₂³	—	2	1	no	—
882	C₂³	C₂×#41×C₈₉	1	2	yes	—
883	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
884	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
885	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
886	Q₈	—	2	16	no	—
887	Q₈	—	2	8	no	—
888	Q₈	—	2	8	no	—
889	Q₈	—	4	4	no	—
890	D₄	—	4	4	no	—
891	C₂×C₄	—	2	8	no	—
892	C₂×C₄	—	2	16	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	2	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	2	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	8	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	2	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	2	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	4	4	no	—
948	C₂×C₄	—	4	8	no	—
949	C₂×C₄	—	4	4	no	—
950	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
951	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
952	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
953	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
954	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
955	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
956	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
957	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
958	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
959	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
960	C₂²	—	2	2	no	—
961	C₂²	—	2	2	no	—
962	C₂²	—	2	2	no	—
963	C₂²	—	2	2	no	—
964	C₂²	—	2	2	no	—
965	C₂²	—	2	2	no	—
966	C₂²	—	4	1	no	—
967	C₂²	—	4	1	no	—
968	C₂²	—	4	1	no	—
969	C₂²	—	4	1	no	—
970	C₂²	—	4	1	no	—
971	C₂²	—	4	1	no	—
972	C₂²	—	4	1	no	—
973	C₂²	#541×C₈₉	1	4	yes	complemented
974	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
975	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
976	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
977	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
978	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
979	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
980	C₂²	#585×C₈₉	1	1	yes	characteristic
981	C₄	—	2	4	no	—
982	C₄	—	2	4	no	—
983	C₄	—	2	2	no	—
984	C₄	—	2	2	no	—
985	C₄	—	2	2	no	—
986	C₄	—	2	2	no	—
987	C₄	—	2	4	no	—
988	C₄	—	4	1	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	1	no	—
991	C₄	—	4	1	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	1	no	—
994	C₄	—	4	2	no	—
995	C₄	—	4	2	no	—
996	C₄	—	4	1	no	—
997	C₄	—	4	1	no	—
998	C₄	—	4	1	no	—
999	C₄	—	4	2	no	—
1000	C₄	—	4	1	no	—
1001	C₄	#525×C₈₉	1	4	yes	—
1002	C₂	—	2	4	no	—
1003	C₂	—	8	1	no	—
1004	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
1005	C₂	C₂×#541×C₈₉	1	1	yes	characteristic
1006	C₂	C₈₉×#3461	1	1	yes	characteristic
1007	C₂	C₈₉×#3486	1	1	yes	characteristic
1008	C₂	C₈₉×#3489	1	1	yes	characteristic
1009	C₂	C₈₉×#3516	1	1	yes	characteristic
1010	C₂	C₈₉×#3523	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂²×D₄×C₈₉	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#541×C₈₉	C₂	semidirect
2. C₂²×C₄×Q₈×C₈₉	C₂	semidirect
4. C₈₉×#2851	C₂	semidirect
5. C₈₉×#2637	C₂	semidirect
6. C₈₉×#2634	C₂	semidirect
8. C₈₉×#2473	C₂	semidirect
9. C₈₉×#2469	C₂	semidirect
10. C₈₉×#2462	C₂	semidirect
11. C₈₉×#2453	C₂	semidirect
12. C₈₉×#2446	C₂	semidirect
13. C₈₉×#2442	C₂	semidirect
14. C₈₉×#2434	C₂	semidirect
15. C₈₉×#2429	C₂	semidirect
16. C₈₉×#2421	C₂	semidirect
19. C₈₉×#2327	C₂	semidirect
20. C₈₉×#2323	C₂	semidirect
21. C₈₉×#2320	C₂	semidirect
22. C₄×C₂²⋊Q₈×C₈₉	C₂	semidirect
156. C₄×Q₈×C₈₉	D₄	semidirect
467. C₂²×C₈₉	#541	semidirect
496. #35244	C₈₉	direct (N × H)
506. C₂×#541	C₂×C₈₉	semidirect
507. C₂²×C₄×Q₈	C₂×C₈₉	semidirect
509. #2851	C₂×C₈₉	semidirect
510. #2637	C₂×C₈₉	semidirect
511. #2634	C₂×C₈₉	semidirect
513. #2473	C₂×C₈₉	semidirect
514. #2469	C₂×C₈₉	semidirect
515. #2462	C₂×C₈₉	semidirect
516. #2453	C₂×C₈₉	semidirect
517. #2446	C₂×C₈₉	semidirect
518. #2442	C₂×C₈₉	semidirect
519. #2434	C₂×C₈₉	semidirect
520. #2429	C₂×C₈₉	semidirect
521. #2421	C₂×C₈₉	semidirect
524. #2327	C₂×C₈₉	semidirect
525. #2323	C₂×C₈₉	semidirect
526. #2320	C₂×C₈₉	semidirect
527. C₄×C₂²⋊Q₈	C₂×C₈₉	semidirect
529. C₈₉	#35244	direct (N × H)
662. C₄×Q₈	D₄×C₈₉	semidirect
973. C₂²	#541×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#541×C₈₉	2
C₂²×C₄×Q₈×C₈₉	2
C₈₉×#2852	2
C₈₉×#2851	2
C₈₉×#2637	2
C₈₉×#2634	2
C₈₉×#2481	2
C₈₉×#2473	2
C₈₉×#2469	2
C₈₉×#2462	2
C₈₉×#2453	2
C₈₉×#2446	2
C₈₉×#2442	2
C₈₉×#2434	2
C₈₉×#2429	2
C₈₉×#2421	2
C₈₉×#2417	2
C₈₉×#2409	2
C₈₉×#2327	2
C₈₉×#2323	2
C₈₉×#2320	2
C₄×C₂²⋊Q₈×C₈₉	2
C₈₉×#2290	2
#35244	89

Subgroups — C89×#35244 #36413092

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35244 #36413092