Subgroups — C₈₉×#62577 #36440425

Order 22784.

1706 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3515	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3374	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3372	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3320	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3312	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3299	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3298	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3237	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3236	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3218	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3218	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3181	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3172	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3139	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#491×C₈₉	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2970	C₂	1	1	yes	maximal, characteristic, complemented
18	Q₈²×C₈₉	—	2	1	no	—
19	#557×C₈₉	C₂²	1	2	yes	—
20	#557×C₈₉	C₂²	1	1	yes	characteristic
21	#554×C₈₉	—	2	1	no	—
22	#554×C₈₉	—	2	2	no	—
23	#554×C₈₉	C₂²	1	1	yes	characteristic
24	#554×C₈₉	C₂²	1	1	yes	characteristic
25	#553×C₈₉	C₂²	1	2	yes	—
26	#552×C₈₉	—	2	2	no	—
27	#552×C₈₉	—	2	1	no	—
28	#552×C₈₉	C₂²	1	2	yes	—
29	D₄×Q₈×C₈₉	C₂²	1	4	yes	—
30	D₄×Q₈×C₈₉	C₂²	1	2	yes	—
31	#547×C₈₉	—	2	1	no	—
32	#547×C₈₉	C₂²	1	1	yes	characteristic
33	#544×C₈₉	—	2	2	no	—
34	#544×C₈₉	—	2	1	no	—
35	#541×C₈₉	—	2	1	no	—
36	#539×C₈₉	—	2	2	no	—
37	#533×C₈₉	C₂²	1	1	yes	characteristic
38	#533×C₈₉	C₂²	1	2	yes	—
39	#533×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	#529×C₈₉	C₂²	1	1	yes	characteristic
43	#529×C₈₉	C₂²	1	2	yes	—
44	C₂×#125×C₈₉	C₂²	1	2	yes	—
45	#520×C₈₉	—	2	1	no	—
46	#520×C₈₉	—	2	1	no	—
47	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
48	#501×C₈₉	C₂²	1	1	yes	characteristic
49	#501×C₈₉	C₂²	1	2	yes	—
50	#497×C₈₉	C₂²	1	1	yes	characteristic
51	#497×C₈₉	C₂²	1	2	yes	—
52	#491×C₈₉	C₂²	1	4	yes	—
53	#491×C₈₉	C₂²	1	4	yes	—
54	#491×C₈₉	C₂²	1	1	yes	characteristic
55	#491×C₈₉	C₂²	1	2	yes	—
56	#491×C₈₉	C₂²	1	2	yes	—
57	#491×C₈₉	C₂²	1	2	yes	—
58	#491×C₈₉	C₂²	1	2	yes	—
59	#489×C₈₉	C₂²	1	1	yes	characteristic
60	#487×C₈₉	C₂²	1	2	yes	—
61	#487×C₈₉	C₂²	1	2	yes	—
62	#485×C₈₉	C₂²	1	4	yes	—
63	#484×C₈₉	C₂²	1	4	yes	—
64	#483×C₈₉	C₂²	1	4	yes	—
65	#479×C₈₉	C₂²	1	4	yes	—
66	#479×C₈₉	C₂²	1	4	yes	—
67	#477×C₈₉	C₂²	1	2	yes	—
68	#475×C₈₉	C₂²	1	2	yes	—
69	#470×C₈₉	C₂²	1	2	yes	—
70	#468×C₈₉	C₂²	1	2	yes	—
71	#467×C₈₉	C₂²	1	4	yes	—
72	#465×C₈₉	C₂²	1	4	yes	—
73	#462×C₈₉	C₂²	1	2	yes	—
74	#462×C₈₉	C₂²	1	4	yes	—
75	#461×C₈₉	C₂²	1	4	yes	—
76	#461×C₈₉	C₂²	1	2	yes	—
77	#451×C₈₉	C₂²	1	4	yes	—
78	#451×C₈₉	C₂²	1	2	yes	—
79	#448×C₈₉	C₂²	1	2	yes	—
80	#448×C₈₉	C₂²	1	4	yes	—
81	#446×C₈₉	C₂²	1	2	yes	—
82	#441×C₈₉	C₂²	1	4	yes	—
83	#440×C₈₉	C₂²	1	4	yes	—
84	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
85	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
86	#435×C₈₉	C₂²	1	4	yes	—
87	C₈×D₄×C₈₉	C₂²	1	2	yes	—
88	#432×C₈₉	C₂²	1	2	yes	—
89	#432×C₈₉	C₂²	1	1	yes	characteristic
90	#419×C₈₉	C₂²	1	4	yes	—
91	C₂×#103×C₈₉	C₂²	1	4	yes	—
92	C₂×#103×C₈₉	C₂²	1	4	yes	—
93	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
94	C₂×#97×C₈₉	C₂²	1	2	yes	—
95	C₂×#41×C₈₉	—	2	1	no	—
96	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
97	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
98	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
99	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
100	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
103	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
104	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
105	C₄⋊Q₈×C₈₉	—	2	1	no	—
106	C₄⋊Q₈×C₈₉	—	2	2	no	—
107	C₄⋊Q₈×C₈₉	—	2	4	no	—
108	C₄⋊Q₈×C₈₉	—	2	2	no	—
109	C₄⋊Q₈×C₈₉	—	2	1	no	—
110	C₄⋊Q₈×C₈₉	—	2	1	no	—
111	C₄⋊Q₈×C₈₉	—	2	2	no	—
112	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
114	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
116	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
117	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
118	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
119	#126×C₈₉	—	2	2	no	—
120	#126×C₈₉	—	2	2	no	—
121	#126×C₈₉	—	2	2	no	—
122	#126×C₈₉	—	2	1	no	—
123	#125×C₈₉	—	2	2	no	—
124	#125×C₈₉	—	2	2	no	—
125	#125×C₈₉	—	2	1	no	—
126	#125×C₈₉	—	2	2	no	—
127	#125×C₈₉	—	2	4	no	—
128	#125×C₈₉	—	2	2	no	—
129	#125×C₈₉	—	2	2	no	—
130	#125×C₈₉	—	2	2	no	—
131	#125×C₈₉	—	2	1	no	—
132	#125×C₈₉	C₂³	1	2	yes	—
133	#125×C₈₉	C₂³	1	2	yes	—
134	#125×C₈₉	C₂³	1	1	yes	characteristic
135	#125×C₈₉	C₂³	1	2	yes	—
136	#124×C₈₉	C₂³	1	1	yes	characteristic
137	#123×C₈₉	—	2	2	no	—
138	#123×C₈₉	—	2	1	no	—
139	#123×C₈₉	—	2	2	no	—
140	#123×C₈₉	—	2	2	no	—
141	#123×C₈₉	—	2	2	no	—
142	C₂²⋊Q₈×C₈₉	—	2	1	no	—
143	C₂²⋊Q₈×C₈₉	—	2	1	no	—
144	C₂²⋊Q₈×C₈₉	—	2	1	no	—
145	C₂²⋊Q₈×C₈₉	—	2	2	no	—
146	C₂²⋊Q₈×C₈₉	—	2	1	no	—
147	C₂²⋊Q₈×C₈₉	—	2	2	no	—
148	C₂²⋊Q₈×C₈₉	—	2	1	no	—
149	C₂²⋊Q₈×C₈₉	—	2	2	no	—
150	C₂²⋊Q₈×C₈₉	—	2	4	no	—
151	C₂²⋊Q₈×C₈₉	—	2	4	no	—
152	C₂²⋊Q₈×C₈₉	—	2	4	no	—
153	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
154	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
155	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
156	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
157	#121×C₈₉	—	2	2	no	—
158	#121×C₈₉	C₂³	1	2	yes	—
159	#121×C₈₉	C₂³	1	1	yes	characteristic
160	C₄×Q₈×C₈₉	—	2	2	no	—
161	C₄×Q₈×C₈₉	—	2	1	no	—
162	C₄×Q₈×C₈₉	—	2	1	no	—
163	C₄×Q₈×C₈₉	—	2	1	no	—
164	C₄×Q₈×C₈₉	—	2	1	no	—
165	C₄×Q₈×C₈₉	—	2	2	no	—
166	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
167	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
168	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
170	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
171	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₈₉	—	2	1	no	—
173	C₄×D₄×C₈₉	—	2	4	no	—
174	C₄×D₄×C₈₉	—	2	2	no	—
175	C₄×D₄×C₈₉	—	2	2	no	—
176	C₄×D₄×C₈₉	—	2	1	no	—
177	C₄×D₄×C₈₉	—	2	2	no	—
178	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
179	C₄×D₄×C₈₉	D₄	1	2	yes	—
180	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₈₉	C₂³	1	2	yes	—
182	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₈₉	C₂³	1	2	yes	—
184	#117×C₈₉	—	2	2	no	—
185	#117×C₈₉	—	2	1	no	—
186	#117×C₈₉	—	2	2	no	—
187	#117×C₈₉	—	2	1	no	—
188	#117×C₈₉	—	2	2	no	—
189	#117×C₈₉	D₄	1	1	yes	characteristic
190	#117×C₈₉	D₄	1	2	yes	—
191	#117×C₈₉	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
193	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
194	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
195	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
196	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
197	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
198	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
199	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
201	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
202	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
203	#107×C₈₉	C₂³	1	2	yes	—
204	#107×C₈₉	C₂³	1	4	yes	—
205	#106×C₈₉	C₂³	1	2	yes	—
206	#106×C₈₉	C₂³	1	4	yes	—
207	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
208	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
209	#103×C₈₉	C₂³	1	2	yes	—
210	#103×C₈₉	C₂³	1	2	yes	—
211	#103×C₈₉	C₂³	1	4	yes	—
212	#103×C₈₉	C₂³	1	4	yes	—
213	#103×C₈₉	C₂³	1	4	yes	—
214	#103×C₈₉	C₂³	1	4	yes	—
215	#103×C₈₉	C₂³	1	4	yes	—
216	#103×C₈₉	C₂³	1	4	yes	—
217	#103×C₈₉	C₂³	1	4	yes	—
218	#103×C₈₉	C₂³	1	4	yes	—
219	#103×C₈₉	C₂³	1	2	yes	—
220	#102×C₈₉	C₂³	1	2	yes	—
221	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
222	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
223	#97×C₈₉	C₂³	1	1	yes	characteristic
224	#97×C₈₉	C₂³	1	2	yes	—
225	#97×C₈₉	C₂³	1	4	yes	—
226	#97×C₈₉	C₂³	1	1	yes	characteristic
227	C₄×C₈×C₈₉	C₂³	1	2	yes	—
228	#41×C₈₉	—	2	4	no	—
229	#41×C₈₉	—	4	4	no	—
230	C₂×Q₈×C₈₉	—	2	1	no	—
231	C₂×Q₈×C₈₉	—	2	1	no	—
232	C₂×Q₈×C₈₉	—	2	1	no	—
233	C₂×Q₈×C₈₉	—	2	2	no	—
234	C₂×Q₈×C₈₉	—	2	4	no	—
235	C₂×Q₈×C₈₉	—	4	4	no	—
236	C₂×Q₈×C₈₉	—	4	4	no	—
237	C₂×Q₈×C₈₉	—	4	4	no	—
238	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
239	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
240	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
241	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
242	C₂×D₄×C₈₉	—	2	2	no	—
243	C₂×D₄×C₈₉	—	2	1	no	—
244	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
245	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
246	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₈₉	—	2	2	no	—
248	C₂²×C₄×C₈₉	—	2	2	no	—
249	C₂²×C₄×C₈₉	—	2	2	no	—
250	C₂²×C₄×C₈₉	—	2	4	no	—
251	C₂²×C₄×C₈₉	—	2	1	no	—
252	C₂²×C₄×C₈₉	—	2	2	no	—
253	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
254	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
256	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
259	Q₁₆×C₈₉	—	4	4	no	—
260	Q₁₆×C₈₉	—	4	2	no	—
261	SD₁₆×C₈₉	—	4	4	no	—
262	SD₁₆×C₈₉	—	4	2	no	—
263	M₁₆×C₈₉	—	4	2	no	—
264	C₂×C₈×C₈₉	—	4	4	no	—
265	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
266	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
267	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
268	C₄⋊C₄×C₈₉	—	2	2	no	—
269	C₄⋊C₄×C₈₉	—	2	1	no	—
270	C₄⋊C₄×C₈₉	—	2	1	no	—
271	C₄⋊C₄×C₈₉	—	2	2	no	—
272	C₄⋊C₄×C₈₉	—	2	1	no	—
273	C₄⋊C₄×C₈₉	—	2	1	no	—
274	C₄⋊C₄×C₈₉	—	2	2	no	—
275	C₄⋊C₄×C₈₉	—	2	2	no	—
276	C₄⋊C₄×C₈₉	—	2	1	no	—
277	C₄⋊C₄×C₈₉	—	2	2	no	—
278	C₄⋊C₄×C₈₉	—	2	2	no	—
279	C₄⋊C₄×C₈₉	—	2	4	no	—
280	C₄⋊C₄×C₈₉	—	2	2	no	—
281	C₄⋊C₄×C₈₉	—	2	2	no	—
282	C₄⋊C₄×C₈₉	—	2	2	no	—
283	C₄⋊C₄×C₈₉	—	2	4	no	—
284	C₄⋊C₄×C₈₉	—	2	2	no	—
285	C₄⋊C₄×C₈₉	—	2	2	no	—
286	C₄⋊C₄×C₈₉	—	2	2	no	—
287	C₄⋊C₄×C₈₉	—	2	1	no	—
288	C₄⋊C₄×C₈₉	—	2	1	no	—
289	C₄⋊C₄×C₈₉	—	2	2	no	—
290	C₄⋊C₄×C₈₉	—	2	2	no	—
291	C₄⋊C₄×C₈₉	—	2	4	no	—
292	C₄⋊C₄×C₈₉	—	2	1	no	—
293	C₄⋊C₄×C₈₉	—	2	4	no	—
294	C₄⋊C₄×C₈₉	—	2	2	no	—
295	C₄⋊C₄×C₈₉	—	2	1	no	—
296	C₄⋊C₄×C₈₉	—	2	2	no	—
297	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
298	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
300	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
304	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
305	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
306	C₂²⋊C₄×C₈₉	—	2	2	no	—
307	C₂²⋊C₄×C₈₉	—	2	4	no	—
308	C₂²⋊C₄×C₈₉	—	2	2	no	—
309	C₂²⋊C₄×C₈₉	—	2	2	no	—
310	C₂²⋊C₄×C₈₉	—	2	1	no	—
311	C₂²⋊C₄×C₈₉	—	2	1	no	—
312	C₂²⋊C₄×C₈₉	—	2	1	no	—
313	C₂²⋊C₄×C₈₉	—	2	1	no	—
314	C₂²⋊C₄×C₈₉	—	2	2	no	—
315	C₂²⋊C₄×C₈₉	—	2	2	no	—
316	C₂²⋊C₄×C₈₉	—	2	1	no	—
317	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
318	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
319	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
320	C₄²×C₈₉	—	2	2	no	—
321	C₄²×C₈₉	—	2	2	no	—
322	C₄²×C₈₉	—	2	1	no	—
323	C₄²×C₈₉	—	2	4	no	—
324	C₄²×C₈₉	—	2	2	no	—
325	C₄²×C₈₉	C₂×D₄	1	2	yes	—
326	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₈₉	C₂×D₄	1	2	yes	—
329	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
330	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
331	C₄²×C₈₉	C₂⁴	1	2	yes	—
332	C₂³×C₈₉	—	2	1	no	—
333	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
334	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
335	Q₈×C₈₉	—	2	2	no	—
336	Q₈×C₈₉	—	2	4	no	—
337	Q₈×C₈₉	—	2	2	no	—
338	Q₈×C₈₉	—	2	2	no	—
339	Q₈×C₈₉	—	2	4	no	—
340	Q₈×C₈₉	—	2	2	no	—
341	Q₈×C₈₉	—	4	2	no	—
342	Q₈×C₈₉	—	4	2	no	—
343	Q₈×C₈₉	—	8	1	no	—
344	Q₈×C₈₉	—	8	4	no	—
345	Q₈×C₈₉	—	8	2	no	—
346	D₄×C₈₉	—	2	4	no	—
347	D₄×C₈₉	—	2	2	no	—
348	D₄×C₈₉	—	4	4	no	—
349	D₄×C₈₉	—	8	1	no	—
350	D₄×C₈₉	#137	1	4	yes	—
351	C₂×C₄×C₈₉	—	2	4	no	—
352	C₂×C₄×C₈₉	—	2	2	no	—
353	C₂×C₄×C₈₉	—	2	4	no	—
354	C₂×C₄×C₈₉	—	2	2	no	—
355	C₂×C₄×C₈₉	—	2	1	no	—
356	C₂×C₄×C₈₉	—	2	2	no	—
357	C₂×C₄×C₈₉	—	2	2	no	—
358	C₂×C₄×C₈₉	—	2	2	no	—
359	C₂×C₄×C₈₉	—	2	1	no	—
360	C₂×C₄×C₈₉	—	2	4	no	—
361	C₂×C₄×C₈₉	—	2	2	no	—
362	C₂×C₄×C₈₉	—	2	1	no	—
363	C₂×C₄×C₈₉	—	4	2	no	—
364	C₂×C₄×C₈₉	—	4	1	no	—
365	C₂×C₄×C₈₉	—	4	4	no	—
366	C₂×C₄×C₈₉	—	4	2	no	—
367	C₂×C₄×C₈₉	—	8	2	no	—
368	C₂×C₄×C₈₉	—	8	2	no	—
369	C₂×C₄×C₈₉	—	8	4	no	—
370	C₂×C₄×C₈₉	—	8	2	no	—
371	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
373	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
374	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
380	C₈×C₈₉	—	2	2	no	—
381	C₈×C₈₉	—	2	4	no	—
382	C₈×C₈₉	—	2	2	no	—
383	C₂²×C₈₉	—	2	2	no	—
384	C₂²×C₈₉	—	2	2	no	—
385	C₂²×C₈₉	—	2	1	no	—
386	C₂²×C₈₉	—	2	1	no	—
387	C₂²×C₈₉	—	2	1	no	—
388	C₂²×C₈₉	—	4	1	no	—
389	C₂²×C₈₉	—	4	1	no	—
390	C₂²×C₈₉	—	4	1	no	—
391	C₂²×C₈₉	C₂×#137	1	4	yes	—
392	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
393	C₄×C₈₉	—	2	1	no	—
394	C₄×C₈₉	—	2	2	no	—
395	C₄×C₈₉	—	2	1	no	—
396	C₄×C₈₉	—	2	2	no	—
397	C₄×C₈₉	—	2	1	no	—
398	C₄×C₈₉	—	2	1	no	—
399	C₄×C₈₉	—	2	2	no	—
400	C₄×C₈₉	—	4	1	no	—
401	C₄×C₈₉	—	4	2	no	—
402	C₄×C₈₉	—	4	2	no	—
403	C₄×C₈₉	—	4	2	no	—
404	C₄×C₈₉	—	4	4	no	—
405	C₄×C₈₉	—	4	1	no	—
406	C₄×C₈₉	—	4	1	no	—
407	C₄×C₈₉	—	4	2	no	—
408	C₄×C₈₉	C₂×#137	1	2	yes	—
409	C₄×C₈₉	#585	1	2	yes	—
410	#62577	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
411	C₂×C₈₉	—	2	4	no	—
412	C₂×C₈₉	—	4	1	no	—
413	C₂×C₈₉	—	8	1	no	—
414	C₂×C₈₉	#3500	1	1	yes	characteristic
415	C₂×C₈₉	C₂²×#137	1	1	yes	characteristic
416	C₂×C₈₉	#3586	1	1	yes	characteristic
417	#3515	C₂×C₈₉	1	1	yes	characteristic
418	#3503	C₂×C₈₉	1	1	yes	characteristic, complemented
419	#3374	C₂×C₈₉	1	2	yes	complemented
420	#3372	C₂×C₈₉	1	2	yes	complemented
421	#3320	C₂×C₈₉	1	4	yes	complemented
422	#3312	C₂×C₈₉	1	4	yes	complemented
423	#3299	C₂×C₈₉	1	2	yes	complemented
424	#3298	C₂×C₈₉	1	2	yes	complemented
425	#3237	C₂×C₈₉	1	1	yes	characteristic, complemented
426	#3236	C₂×C₈₉	1	2	yes	complemented
427	#3218	C₂×C₈₉	1	1	yes	characteristic, complemented
428	#3218	C₂×C₈₉	1	2	yes	complemented
429	#3181	C₂×C₈₉	1	2	yes	complemented
430	#3172	C₂×C₈₉	1	1	yes	characteristic, complemented
431	#3139	C₂×C₈₉	1	1	yes	characteristic, complemented
432	C₂×#491	C₂×C₈₉	1	2	yes	complemented
433	#2970	C₂×C₈₉	1	1	yes	characteristic, complemented
434	C₈₉	#62577	1	1	yes	characteristic, direct product factor, Sylow
435	Q₈²	—	2	1	no	—
436	#557	C₂²×C₈₉	1	2	yes	—
437	#557	C₂²×C₈₉	1	1	yes	characteristic
438	#554	—	2	1	no	—
439	#554	—	2	2	no	—
440	#554	C₂²×C₈₉	1	1	yes	characteristic
441	#554	C₂²×C₈₉	1	1	yes	characteristic
442	#553	C₂²×C₈₉	1	2	yes	—
443	#552	—	2	2	no	—
444	#552	—	2	1	no	—
445	#552	C₂²×C₈₉	1	2	yes	—
446	D₄×Q₈	C₂²×C₈₉	1	2	yes	—
447	D₄×Q₈	C₂²×C₈₉	1	4	yes	—
448	#547	—	2	1	no	—
449	#547	C₂²×C₈₉	1	1	yes	characteristic
450	#544	—	2	2	no	—
451	#544	—	2	1	no	—
452	#541	—	2	1	no	—
453	#539	—	2	2	no	—
454	#533	C₂²×C₈₉	1	1	yes	characteristic
455	#533	C₂²×C₈₉	1	2	yes	—
456	#533	C₂²×C₈₉	1	1	yes	characteristic
457	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
458	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
459	#529	C₂²×C₈₉	1	1	yes	characteristic
460	#529	C₂²×C₈₉	1	2	yes	—
461	C₂×#125	C₂²×C₈₉	1	2	yes	—
462	#520	—	2	1	no	—
463	#520	—	2	1	no	—
464	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
465	#501	C₂²×C₈₉	1	1	yes	characteristic
466	#501	C₂²×C₈₉	1	2	yes	—
467	#497	C₂²×C₈₉	1	1	yes	characteristic
468	#497	C₂²×C₈₉	1	2	yes	—
469	#491	C₂²×C₈₉	1	4	yes	—
470	#491	C₂²×C₈₉	1	4	yes	—
471	#491	C₂²×C₈₉	1	1	yes	characteristic
472	#491	C₂²×C₈₉	1	2	yes	—
473	#491	C₂²×C₈₉	1	2	yes	—
474	#491	C₂²×C₈₉	1	2	yes	—
475	#491	C₂²×C₈₉	1	2	yes	—
476	#489	C₂²×C₈₉	1	1	yes	characteristic
477	#487	C₂²×C₈₉	1	2	yes	—
478	#487	C₂²×C₈₉	1	2	yes	—
479	#485	C₂²×C₈₉	1	4	yes	—
480	#484	C₂²×C₈₉	1	4	yes	—
481	#483	C₂²×C₈₉	1	4	yes	—
482	#479	C₂²×C₈₉	1	4	yes	—
483	#479	C₂²×C₈₉	1	4	yes	—
484	#477	C₂²×C₈₉	1	2	yes	—
485	#475	C₂²×C₈₉	1	2	yes	—
486	#470	C₂²×C₈₉	1	2	yes	—
487	#468	C₂²×C₈₉	1	2	yes	—
488	#467	C₂²×C₈₉	1	4	yes	—
489	#465	C₂²×C₈₉	1	4	yes	—
490	#462	C₂²×C₈₉	1	2	yes	—
491	#462	C₂²×C₈₉	1	4	yes	—
492	#461	C₂²×C₈₉	1	2	yes	—
493	#461	C₂²×C₈₉	1	4	yes	—
494	#451	C₂²×C₈₉	1	4	yes	—
495	#451	C₂²×C₈₉	1	2	yes	—
496	#448	C₂²×C₈₉	1	4	yes	—
497	#448	C₂²×C₈₉	1	2	yes	—
498	#446	C₂²×C₈₉	1	2	yes	—
499	#441	C₂²×C₈₉	1	4	yes	—
500	#440	C₂²×C₈₉	1	4	yes	—
501	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	—
502	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
503	#435	C₂²×C₈₉	1	4	yes	—
504	C₈×D₄	C₂²×C₈₉	1	2	yes	—
505	#432	C₂²×C₈₉	1	2	yes	—
506	#432	C₂²×C₈₉	1	1	yes	characteristic
507	#419	C₂²×C₈₉	1	4	yes	—
508	C₂×#103	C₂²×C₈₉	1	4	yes	—
509	C₂×#103	C₂²×C₈₉	1	4	yes	—
510	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
511	C₂×#97	C₂²×C₈₉	1	2	yes	—
512	C₂×#41	—	2	1	no	—
513	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
514	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
515	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
516	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
517	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
518	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
519	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
520	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
521	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
522	C₄⋊Q₈	—	2	1	no	—
523	C₄⋊Q₈	—	2	2	no	—
524	C₄⋊Q₈	—	2	4	no	—
525	C₄⋊Q₈	—	2	2	no	—
526	C₄⋊Q₈	—	2	1	no	—
527	C₄⋊Q₈	—	2	1	no	—
528	C₄⋊Q₈	—	2	2	no	—
529	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
530	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
531	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
532	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
533	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
534	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
535	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
536	#126	—	2	2	no	—
537	#126	—	2	2	no	—
538	#126	—	2	2	no	—
539	#126	—	2	1	no	—
540	#125	—	2	2	no	—
541	#125	—	2	2	no	—
542	#125	—	2	1	no	—
543	#125	—	2	2	no	—
544	#125	—	2	4	no	—
545	#125	—	2	2	no	—
546	#125	—	2	2	no	—
547	#125	—	2	2	no	—
548	#125	—	2	1	no	—
549	#125	C₂³×C₈₉	1	1	yes	characteristic
550	#125	C₂³×C₈₉	1	2	yes	—
551	#125	C₂³×C₈₉	1	2	yes	—
552	#125	C₂³×C₈₉	1	2	yes	—
553	#124	C₂³×C₈₉	1	1	yes	characteristic
554	#123	—	2	2	no	—
555	#123	—	2	1	no	—
556	#123	—	2	2	no	—
557	#123	—	2	2	no	—
558	#123	—	2	2	no	—
559	C₂²⋊Q₈	—	2	1	no	—
560	C₂²⋊Q₈	—	2	1	no	—
561	C₂²⋊Q₈	—	2	1	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	2	1	no	—
564	C₂²⋊Q₈	—	2	2	no	—
565	C₂²⋊Q₈	—	2	1	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	4	no	—
568	C₂²⋊Q₈	—	2	4	no	—
569	C₂²⋊Q₈	—	2	4	no	—
570	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
571	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
572	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
573	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
574	#121	—	2	2	no	—
575	#121	C₂³×C₈₉	1	2	yes	—
576	#121	C₂³×C₈₉	1	1	yes	characteristic
577	C₄×Q₈	—	2	2	no	—
578	C₄×Q₈	—	2	1	no	—
579	C₄×Q₈	—	2	1	no	—
580	C₄×Q₈	—	2	1	no	—
581	C₄×Q₈	—	2	1	no	—
582	C₄×Q₈	—	2	2	no	—
583	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
584	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
585	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
586	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
587	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
588	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
589	C₄×D₄	—	2	1	no	—
590	C₄×D₄	—	2	4	no	—
591	C₄×D₄	—	2	2	no	—
592	C₄×D₄	—	2	2	no	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
596	C₄×D₄	D₄×C₈₉	1	2	yes	—
597	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
598	C₄×D₄	C₂³×C₈₉	1	2	yes	—
599	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
600	C₄×D₄	C₂³×C₈₉	1	2	yes	—
601	#117	—	2	2	no	—
602	#117	—	2	1	no	—
603	#117	—	2	2	no	—
604	#117	—	2	1	no	—
605	#117	—	2	2	no	—
606	#117	D₄×C₈₉	1	1	yes	characteristic
607	#117	D₄×C₈₉	1	2	yes	—
608	#117	C₂³×C₈₉	1	2	yes	—
609	C₂×C₄⋊C₄	—	2	2	no	—
610	C₂×C₄⋊C₄	—	2	2	no	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	2	no	—
613	C₂×C₄⋊C₄	—	2	2	no	—
614	C₂×C₄⋊C₄	—	2	1	no	—
615	C₂×C₄⋊C₄	—	2	1	no	—
616	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
618	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
619	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
620	#107	C₂³×C₈₉	1	2	yes	—
621	#107	C₂³×C₈₉	1	4	yes	—
622	#106	C₂³×C₈₉	1	2	yes	—
623	#106	C₂³×C₈₉	1	4	yes	—
624	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
625	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
626	#103	C₂³×C₈₉	1	2	yes	—
627	#103	C₂³×C₈₉	1	2	yes	—
628	#103	C₂³×C₈₉	1	4	yes	—
629	#103	C₂³×C₈₉	1	4	yes	—
630	#103	C₂³×C₈₉	1	4	yes	—
631	#103	C₂³×C₈₉	1	4	yes	—
632	#103	C₂³×C₈₉	1	4	yes	—
633	#103	C₂³×C₈₉	1	4	yes	—
634	#103	C₂³×C₈₉	1	4	yes	—
635	#103	C₂³×C₈₉	1	4	yes	—
636	#103	C₂³×C₈₉	1	2	yes	—
637	#102	C₂³×C₈₉	1	2	yes	—
638	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
639	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
640	#97	C₂³×C₈₉	1	1	yes	characteristic
641	#97	C₂³×C₈₉	1	2	yes	—
642	#97	C₂³×C₈₉	1	4	yes	—
643	#97	C₂³×C₈₉	1	1	yes	characteristic
644	C₄×C₈	C₂³×C₈₉	1	2	yes	—
645	#41	—	2	4	no	—
646	#41	—	4	4	no	—
647	C₂×Q₈	—	2	1	no	—
648	C₂×Q₈	—	2	1	no	—
649	C₂×Q₈	—	2	1	no	—
650	C₂×Q₈	—	2	2	no	—
651	C₂×Q₈	—	2	4	no	—
652	C₂×Q₈	—	4	4	no	—
653	C₂×Q₈	—	4	4	no	—
654	C₂×Q₈	—	4	4	no	—
655	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
656	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
657	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
658	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	1	no	—
661	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
662	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
663	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
671	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
672	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
673	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
676	Q₁₆	—	4	4	no	—
677	Q₁₆	—	4	2	no	—
678	SD₁₆	—	4	4	no	—
679	SD₁₆	—	4	2	no	—
680	M₁₆	—	4	2	no	—
681	C₂×C₈	—	4	4	no	—
682	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
683	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
684	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
715	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
716	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
717	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
718	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
719	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
720	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
721	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
722	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	1	no	—
728	C₂²⋊C₄	—	2	1	no	—
729	C₂²⋊C₄	—	2	1	no	—
730	C₂²⋊C₄	—	2	1	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
735	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
736	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
737	C₄²	—	2	2	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	1	no	—
740	C₄²	—	2	4	no	—
741	C₄²	—	2	2	no	—
742	C₄²	C₂×D₄×C₈₉	1	2	yes	—
743	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
744	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
745	C₄²	C₂×D₄×C₈₉	1	2	yes	—
746	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
747	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
748	C₄²	C₂⁴×C₈₉	1	2	yes	—
749	C₂³	—	2	1	no	—
750	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
751	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
752	Q₈	—	2	2	no	—
753	Q₈	—	2	4	no	—
754	Q₈	—	2	2	no	—
755	Q₈	—	2	2	no	—
756	Q₈	—	2	4	no	—
757	Q₈	—	2	2	no	—
758	Q₈	—	4	2	no	—
759	Q₈	—	4	2	no	—
760	Q₈	—	8	1	no	—
761	Q₈	—	8	4	no	—
762	Q₈	—	8	2	no	—
763	D₄	—	2	4	no	—
764	D₄	—	2	2	no	—
765	D₄	—	4	4	no	—
766	D₄	—	8	1	no	—
767	D₄	#137×C₈₉	1	4	yes	—
768	C₂×C₄	—	2	4	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	4	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	4	2	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	4	no	—
783	C₂×C₄	—	4	2	no	—
784	C₂×C₄	—	8	2	no	—
785	C₂×C₄	—	8	2	no	—
786	C₂×C₄	—	8	4	no	—
787	C₂×C₄	—	8	2	no	—
788	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
789	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
790	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
791	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
793	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
794	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
795	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
796	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
797	C₈	—	2	2	no	—
798	C₈	—	2	4	no	—
799	C₈	—	2	2	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	1	no	—
808	C₂²	C₂×#137×C₈₉	1	4	yes	—
809	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
810	C₄	—	2	1	no	—
811	C₄	—	2	2	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	2	no	—
814	C₄	—	2	1	no	—
815	C₄	—	2	2	no	—
816	C₄	—	2	1	no	—
817	C₄	—	4	1	no	—
818	C₄	—	4	2	no	—
819	C₄	—	4	1	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	4	no	—
824	C₄	—	4	1	no	—
825	C₄	C₂×#137×C₈₉	1	2	yes	—
826	C₄	#585×C₈₉	1	2	yes	—
827	C₂	—	2	4	no	—
828	C₂	—	4	1	no	—
829	C₂	—	8	1	no	—
830	C₂	C₈₉×#3500	1	1	yes	characteristic
831	C₂	C₂²×#137×C₈₉	1	1	yes	characteristic
832	C₂	C₈₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₈₉×#3515	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₉×#3503	C₂	semidirect
3. C₈₉×#3374	C₂	semidirect
4. C₈₉×#3372	C₂	semidirect
5. C₈₉×#3320	C₂	semidirect
6. C₈₉×#3312	C₂	semidirect
7. C₈₉×#3299	C₂	semidirect
8. C₈₉×#3298	C₂	semidirect
9. C₈₉×#3237	C₂	semidirect
10. C₈₉×#3236	C₂	semidirect
11. C₈₉×#3218	C₂	semidirect
12. C₈₉×#3218	C₂	semidirect
13. C₈₉×#3181	C₂	semidirect
14. C₈₉×#3172	C₂	semidirect
15. C₈₉×#3139	C₂	semidirect
16. C₂×#491×C₈₉	C₂	semidirect
17. C₈₉×#2970	C₂	semidirect
410. #62577	C₈₉	direct (N × H)
418. #3503	C₂×C₈₉	semidirect
419. #3374	C₂×C₈₉	semidirect
420. #3372	C₂×C₈₉	semidirect
421. #3320	C₂×C₈₉	semidirect
422. #3312	C₂×C₈₉	semidirect
423. #3299	C₂×C₈₉	semidirect
424. #3298	C₂×C₈₉	semidirect
425. #3237	C₂×C₈₉	semidirect
426. #3236	C₂×C₈₉	semidirect
427. #3218	C₂×C₈₉	semidirect
428. #3218	C₂×C₈₉	semidirect
429. #3181	C₂×C₈₉	semidirect
430. #3172	C₂×C₈₉	semidirect
431. #3139	C₂×C₈₉	semidirect
432. C₂×#491	C₂×C₈₉	semidirect
433. #2970	C₂×C₈₉	semidirect
434. C₈₉	#62577	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×#3515	2
C₈₉×#3503	2
C₈₉×#3374	2
C₈₉×#3372	2
C₈₉×#3320	2
C₈₉×#3312	2
C₈₉×#3299	2
C₈₉×#3298	2
C₈₉×#3237	2
C₈₉×#3236	2
C₈₉×#3218	2
C₈₉×#3181	2
C₈₉×#3172	2
C₈₉×#3139	2
C₂×#491×C₈₉	2
C₈₉×#2970	2
#62577	89

Subgroups — C89×#62577 #36440425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62577 #36440425