Subgroups — C₈₉×#60955 #36438803

Order 22784.

1804 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3460	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3262	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3259	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3257	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3243	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3241	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3224	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3220	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3203	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3199	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3198	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3171	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3169	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3168	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3106	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3105	C₂	1	2	yes	maximal, complemented
17	C₈₉×#3102	C₂	1	2	yes	maximal, complemented
18	C₈₉×#3100	C₂	1	2	yes	maximal, complemented
19	C₈₉×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	#544×C₈₉	C₂²	1	2	yes	complemented
21	#542×C₈₉	—	2	2	no	—
22	#542×C₈₉	C₂²	1	2	yes	—
23	#542×C₈₉	C₂²	1	2	yes	complemented
24	#540×C₈₉	—	2	2	no	—
25	#540×C₈₉	C₂²	1	2	yes	—
26	#540×C₈₉	C₂²	1	2	yes	complemented
27	#538×C₈₉	—	2	2	no	—
28	#538×C₈₉	—	2	2	no	—
29	#537×C₈₉	C₂²	1	2	yes	—
30	#535×C₈₉	C₂²	1	2	yes	—
31	#535×C₈₉	C₂²	1	2	yes	complemented
32	#532×C₈₉	—	2	2	no	—
33	#532×C₈₉	C₂²	1	2	yes	—
34	#532×C₈₉	C₂²	1	2	yes	complemented
35	#529×C₈₉	—	2	2	no	—
36	#529×C₈₉	C₂²	1	2	yes	—
37	#529×C₈₉	C₂²	1	2	yes	complemented
38	#525×C₈₉	—	2	2	no	—
39	#525×C₈₉	—	2	2	no	—
40	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
41	C₄×#41×C₈₉	C₂²	1	2	yes	complemented
42	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
43	#501×C₈₉	C₂²	1	2	yes	complemented
44	#500×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	#499×C₈₉	C₂²	1	1	yes	characteristic, complemented
46	#496×C₈₉	C₂²	1	2	yes	—
47	#495×C₈₉	C₂²	1	1	yes	characteristic
48	#493×C₈₉	C₂²	1	1	yes	characteristic
49	#490×C₈₉	C₂²	1	2	yes	complemented
50	#489×C₈₉	C₂²	1	2	yes	complemented
51	#488×C₈₉	C₂²	1	2	yes	complemented
52	#486×C₈₉	C₂²	1	2	yes	complemented
53	#485×C₈₉	C₂²	1	2	yes	complemented
54	#484×C₈₉	C₂²	1	2	yes	complemented
55	#482×C₈₉	C₂²	1	2	yes	—
56	#482×C₈₉	C₂²	1	2	yes	—
57	#482×C₈₉	C₂²	1	2	yes	complemented
58	#481×C₈₉	C₂²	1	2	yes	—
59	#480×C₈₉	C₂²	1	2	yes	—
60	#480×C₈₉	C₂²	1	2	yes	complemented
61	#479×C₈₉	C₂²	1	2	yes	complemented
62	#478×C₈₉	C₂²	1	2	yes	complemented
63	#478×C₈₉	C₂²	1	2	yes	complemented
64	#478×C₈₉	C₂²	1	2	yes	complemented
65	#477×C₈₉	C₂²	1	2	yes	complemented
66	#476×C₈₉	C₂²	1	2	yes	complemented
67	#474×C₈₉	C₂²	1	2	yes	complemented
68	#474×C₈₉	C₂²	1	2	yes	complemented
69	#469×C₈₉	C₂²	1	2	yes	—
70	#469×C₈₉	C₂²	1	2	yes	complemented
71	#468×C₈₉	C₂²	1	2	yes	complemented
72	#468×C₈₉	C₂²	1	2	yes	complemented
73	#467×C₈₉	C₂²	1	1	yes	characteristic, complemented
74	#466×C₈₉	C₂²	1	1	yes	characteristic
75	#466×C₈₉	C₂²	1	1	yes	characteristic
76	#466×C₈₉	C₂²	1	2	yes	complemented
77	#466×C₈₉	C₂²	1	1	yes	characteristic, complemented
78	#465×C₈₉	C₂²	1	2	yes	complemented
79	#464×C₈₉	C₂²	1	2	yes	complemented
80	#463×C₈₉	C₂²	1	2	yes	—
81	#463×C₈₉	C₂²	1	2	yes	—
82	#463×C₈₉	C₂²	1	2	yes	complemented
83	#460×C₈₉	C₂²	1	2	yes	complemented
84	#459×C₈₉	C₂²	1	2	yes	—
85	#459×C₈₉	C₂²	1	2	yes	—
86	#459×C₈₉	C₂²	1	2	yes	complemented
87	#452×C₈₉	C₂²	1	2	yes	complemented
88	#450×C₈₉	C₂²	1	2	yes	complemented
89	#449×C₈₉	C₂²	1	2	yes	—
90	#449×C₈₉	C₂²	1	2	yes	—
91	#449×C₈₉	C₂²	1	2	yes	complemented
92	#447×C₈₉	C₂²	1	2	yes	—
93	#447×C₈₉	C₂²	1	2	yes	—
94	#447×C₈₉	C₂²	1	2	yes	complemented
95	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
96	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
97	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
98	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
99	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
100	C₄×D₈×C₈₉	C₂²	1	2	yes	—
101	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
102	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
103	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
104	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
105	#433×C₈₉	C₂²	1	2	yes	complemented
106	#433×C₈₉	C₂²	1	2	yes	complemented
107	#431×C₈₉	C₂²	1	2	yes	complemented
108	#431×C₈₉	C₂²	1	2	yes	complemented
109	#424×C₈₉	C₂²	1	1	yes	characteristic, complemented
110	#424×C₈₉	C₂²	1	1	yes	characteristic, complemented
111	#408×C₈₉	C₂²	1	1	yes	characteristic
112	#408×C₈₉	C₂²	1	1	yes	characteristic
113	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
115	C₂×#41×C₈₉	—	2	2	no	—
116	C₂×#41×C₈₉	—	2	2	no	—
117	C₂×#41×C₈₉	C₂³	1	2	yes	—
118	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
119	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
120	C₂³×C₄×C₈₉	—	2	2	no	—
121	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
122	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
125	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
126	C₂×D₈×C₈₉	C₂³	1	2	yes	—
127	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
128	C₂×D₈×C₈₉	C₂³	1	2	yes	—
129	C₂×D₈×C₈₉	C₂³	1	2	yes	—
130	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
131	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
132	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
135	C₄⋊Q₈×C₈₉	—	2	2	no	—
136	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
138	#127×C₈₉	—	2	2	no	—
139	#127×C₈₉	C₂³	1	2	yes	—
140	#127×C₈₉	C₂³	1	2	yes	—
141	#126×C₈₉	—	2	2	no	—
142	#126×C₈₉	—	2	2	no	—
143	#126×C₈₉	—	2	2	no	—
144	#126×C₈₉	—	2	2	no	—
145	#125×C₈₉	—	2	2	no	—
146	#125×C₈₉	C₂³	1	2	yes	—
147	#125×C₈₉	C₂³	1	2	yes	—
148	#124×C₈₉	—	2	2	no	—
149	#124×C₈₉	—	2	2	no	—
150	#124×C₈₉	—	2	2	no	—
151	#124×C₈₉	—	2	2	no	—
152	#124×C₈₉	—	2	2	no	—
153	#124×C₈₉	C₂³	1	2	yes	—
154	#124×C₈₉	C₂³	1	2	yes	—
155	#123×C₈₉	—	2	2	no	—
156	#123×C₈₉	—	2	2	no	—
157	#123×C₈₉	—	2	2	no	—
158	#123×C₈₉	—	2	2	no	—
159	#123×C₈₉	—	2	2	no	—
160	#123×C₈₉	—	2	2	no	—
161	#123×C₈₉	—	2	2	no	—
162	#123×C₈₉	—	2	2	no	—
163	C₂²⋊Q₈×C₈₉	—	2	2	no	—
164	C₂²⋊Q₈×C₈₉	—	2	2	no	—
165	C₂²⋊Q₈×C₈₉	—	2	2	no	—
166	C₂²⋊Q₈×C₈₉	—	2	2	no	—
167	C₂²⋊Q₈×C₈₉	—	2	2	no	—
168	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
169	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
170	#121×C₈₉	—	2	2	no	—
171	#121×C₈₉	—	2	2	no	—
172	#121×C₈₉	—	2	2	no	—
173	#121×C₈₉	—	2	2	no	—
174	#121×C₈₉	—	2	2	no	—
175	#121×C₈₉	—	2	2	no	—
176	#121×C₈₉	—	2	2	no	—
177	#121×C₈₉	—	2	2	no	—
178	#121×C₈₉	—	2	2	no	—
179	#121×C₈₉	—	2	2	no	—
180	#121×C₈₉	—	2	2	no	—
181	#121×C₈₉	C₂³	1	2	yes	—
182	#121×C₈₉	C₂³	1	2	yes	—
183	#121×C₈₉	C₂³	1	2	yes	—
184	#121×C₈₉	C₂³	1	2	yes	—
185	#121×C₈₉	C₂³	1	2	yes	—
186	#121×C₈₉	C₂³	1	2	yes	—
187	#120×C₈₉	—	2	2	no	—
188	#120×C₈₉	—	2	2	no	—
189	#120×C₈₉	—	2	2	no	—
190	#120×C₈₉	—	2	2	no	—
191	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
192	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
193	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
194	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
195	C₄×D₄×C₈₉	—	2	2	no	—
196	C₄×D₄×C₈₉	—	2	2	no	—
197	C₄×D₄×C₈₉	—	2	2	no	—
198	C₄×D₄×C₈₉	—	2	2	no	—
199	C₄×D₄×C₈₉	—	2	2	no	—
200	C₄×D₄×C₈₉	—	2	2	no	—
201	C₄×D₄×C₈₉	—	2	2	no	—
202	C₄×D₄×C₈₉	—	2	2	no	—
203	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
204	C₄×D₄×C₈₉	D₄	1	2	yes	—
205	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
206	C₄×D₄×C₈₉	D₄	1	2	yes	—
207	C₄×D₄×C₈₉	C₂³	1	2	yes	—
208	C₄×D₄×C₈₉	C₂³	1	2	yes	—
209	C₄×D₄×C₈₉	C₂³	1	2	yes	—
210	C₄×D₄×C₈₉	C₂³	1	2	yes	—
211	C₄×D₄×C₈₉	C₂³	1	2	yes	—
212	C₄×D₄×C₈₉	C₂³	1	2	yes	—
213	#117×C₈₉	—	2	2	no	—
214	#117×C₈₉	—	2	2	no	—
215	#117×C₈₉	—	2	2	no	—
216	#117×C₈₉	C₂³	1	2	yes	—
217	#117×C₈₉	C₂³	1	1	yes	characteristic
218	#117×C₈₉	C₂³	1	2	yes	—
219	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
221	C₂×C₄²×C₈₉	—	2	2	no	—
222	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
224	#107×C₈₉	C₂³	1	1	yes	characteristic
225	#107×C₈₉	C₂³	1	1	yes	characteristic
226	#107×C₈₉	C₂³	1	2	yes	—
227	#107×C₈₉	C₂³	1	1	yes	characteristic
228	#107×C₈₉	C₂³	1	2	yes	—
229	#107×C₈₉	C₂³	1	2	yes	—
230	#107×C₈₉	C₂³	1	1	yes	characteristic
231	#106×C₈₉	C₂³	1	2	yes	—
232	#106×C₈₉	C₂³	1	2	yes	—
233	#106×C₈₉	C₂³	1	2	yes	—
234	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
235	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
236	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
237	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
238	#103×C₈₉	C₂³	1	2	yes	—
239	#103×C₈₉	C₂³	1	2	yes	—
240	#103×C₈₉	C₂³	1	2	yes	—
241	#103×C₈₉	C₂³	1	2	yes	—
242	#102×C₈₉	C₂³	1	2	yes	—
243	#102×C₈₉	C₂³	1	2	yes	—
244	#102×C₈₉	C₂³	1	2	yes	—
245	#102×C₈₉	C₂³	1	2	yes	—
246	#102×C₈₉	C₂³	1	2	yes	—
247	#102×C₈₉	C₂³	1	2	yes	—
248	#102×C₈₉	C₂³	1	2	yes	—
249	#102×C₈₉	C₂³	1	2	yes	—
250	#102×C₈₉	C₂³	1	2	yes	—
251	#102×C₈₉	C₂³	1	2	yes	—
252	#102×C₈₉	C₂³	1	2	yes	—
253	#102×C₈₉	C₂³	1	2	yes	—
254	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
255	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
256	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
257	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
258	#97×C₈₉	C₂³	1	2	yes	—
259	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
260	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₈₉	C₂³	1	2	yes	—
264	C₂⁴×C₈₉	—	2	2	no	—
265	#41×C₈₉	—	4	1	no	—
266	#41×C₈₉	—	4	1	no	—
267	#41×C₈₉	—	4	2	no	—
268	#41×C₈₉	—	4	2	no	—
269	#41×C₈₉	—	8	4	no	—
270	#41×C₈₉	—	8	4	no	—
271	C₂×Q₈×C₈₉	—	2	2	no	—
272	C₂×Q₈×C₈₉	—	2	2	no	—
273	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
274	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
275	C₂×D₄×C₈₉	—	2	2	no	—
276	C₂×D₄×C₈₉	—	2	2	no	—
277	C₂×D₄×C₈₉	—	2	2	no	—
278	C₂×D₄×C₈₉	—	2	2	no	—
279	C₂×D₄×C₈₉	—	2	2	no	—
280	C₂×D₄×C₈₉	—	2	2	no	—
281	C₂×D₄×C₈₉	—	2	2	no	—
282	C₂×D₄×C₈₉	—	2	2	no	—
283	C₂×D₄×C₈₉	—	2	2	no	—
284	C₂×D₄×C₈₉	—	2	2	no	—
285	C₂×D₄×C₈₉	—	2	2	no	—
286	C₂×D₄×C₈₉	—	2	2	no	—
287	C₂×D₄×C₈₉	—	4	2	no	—
288	C₂×D₄×C₈₉	—	4	2	no	—
289	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
290	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
291	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
292	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
293	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₈₉	—	2	2	no	—
295	C₂²×C₄×C₈₉	—	2	2	no	—
296	C₂²×C₄×C₈₉	—	2	2	no	—
297	C₂²×C₄×C₈₉	—	2	2	no	—
298	C₂²×C₄×C₈₉	—	2	2	no	—
299	C₂²×C₄×C₈₉	—	2	2	no	—
300	C₂²×C₄×C₈₉	—	2	2	no	—
301	C₂²×C₄×C₈₉	—	2	2	no	—
302	C₂²×C₄×C₈₉	—	8	4	no	—
303	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
304	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
306	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
309	Q₁₆×C₈₉	—	4	1	no	—
310	SD₁₆×C₈₉	—	4	2	no	—
311	SD₁₆×C₈₉	—	4	2	no	—
312	SD₁₆×C₈₉	—	4	2	no	—
313	D₈×C₈₉	—	4	2	no	—
314	D₈×C₈₉	—	4	1	no	—
315	D₈×C₈₉	—	4	1	no	—
316	D₈×C₈₉	—	4	1	no	—
317	D₈×C₈₉	—	4	2	no	—
318	D₈×C₈₉	—	4	2	no	—
319	M₁₆×C₈₉	—	4	1	no	—
320	M₁₆×C₈₉	—	4	1	no	—
321	C₂×C₈×C₈₉	—	4	1	no	—
322	C₂×C₈×C₈₉	—	4	1	no	—
323	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
324	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
325	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
326	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
327	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
328	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
329	C₄⋊C₄×C₈₉	—	2	2	no	—
330	C₄⋊C₄×C₈₉	—	2	2	no	—
331	C₄⋊C₄×C₈₉	—	2	2	no	—
332	C₄⋊C₄×C₈₉	—	2	2	no	—
333	C₄⋊C₄×C₈₉	—	2	2	no	—
334	C₄⋊C₄×C₈₉	—	2	2	no	—
335	C₄⋊C₄×C₈₉	—	2	2	no	—
336	C₄⋊C₄×C₈₉	—	2	2	no	—
337	C₄⋊C₄×C₈₉	—	2	2	no	—
338	C₄⋊C₄×C₈₉	—	2	2	no	—
339	C₄⋊C₄×C₈₉	—	2	2	no	—
340	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
341	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
342	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
343	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
344	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
345	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
346	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
347	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
348	C₂²⋊C₄×C₈₉	—	2	2	no	—
349	C₂²⋊C₄×C₈₉	—	2	2	no	—
350	C₂²⋊C₄×C₈₉	—	2	2	no	—
351	C₂²⋊C₄×C₈₉	—	2	2	no	—
352	C₂²⋊C₄×C₈₉	—	2	2	no	—
353	C₂²⋊C₄×C₈₉	—	2	2	no	—
354	C₂²⋊C₄×C₈₉	—	2	2	no	—
355	C₂²⋊C₄×C₈₉	—	2	2	no	—
356	C₂²⋊C₄×C₈₉	—	2	2	no	—
357	C₂²⋊C₄×C₈₉	—	2	2	no	—
358	C₂²⋊C₄×C₈₉	—	2	2	no	—
359	C₂²⋊C₄×C₈₉	—	2	2	no	—
360	C₂²⋊C₄×C₈₉	—	2	2	no	—
361	C₂²⋊C₄×C₈₉	—	2	2	no	—
362	C₂²⋊C₄×C₈₉	—	2	2	no	—
363	C₂²⋊C₄×C₈₉	—	2	2	no	—
364	C₂²⋊C₄×C₈₉	—	2	2	no	—
365	C₂²⋊C₄×C₈₉	—	2	2	no	—
366	C₂²⋊C₄×C₈₉	—	2	2	no	—
367	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
368	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
369	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
370	C₄²×C₈₉	—	2	2	no	—
371	C₄²×C₈₉	—	2	2	no	—
372	C₄²×C₈₉	—	2	2	no	—
373	C₄²×C₈₉	C₂×D₄	1	2	yes	—
374	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
375	C₄²×C₈₉	C₂×D₄	1	2	yes	—
376	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
377	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
378	C₄²×C₈₉	C₂⁴	1	2	yes	—
379	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
380	C₂³×C₈₉	—	2	2	no	—
381	C₂³×C₈₉	—	2	2	no	—
382	C₂³×C₈₉	—	2	2	no	—
383	C₂³×C₈₉	—	4	4	no	—
384	C₂³×C₈₉	—	8	2	no	—
385	C₂³×C₈₉	—	8	2	no	—
386	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
387	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
388	Q₈×C₈₉	—	2	2	no	—
389	Q₈×C₈₉	—	2	2	no	—
390	Q₈×C₈₉	—	4	1	no	—
391	Q₈×C₈₉	—	8	2	no	—
392	Q₈×C₈₉	—	8	2	no	—
393	D₄×C₈₉	—	2	2	no	—
394	D₄×C₈₉	—	2	2	no	—
395	D₄×C₈₉	—	2	2	no	—
396	D₄×C₈₉	—	2	2	no	—
397	D₄×C₈₉	—	2	2	no	—
398	D₄×C₈₉	—	2	2	no	—
399	D₄×C₈₉	—	4	2	no	—
400	D₄×C₈₉	—	4	1	no	—
401	D₄×C₈₉	—	4	4	no	—
402	D₄×C₈₉	—	4	4	no	—
403	D₄×C₈₉	—	8	2	no	—
404	D₄×C₈₉	—	8	2	no	—
405	D₄×C₈₉	—	8	2	no	—
406	D₄×C₈₉	—	8	2	no	—
407	D₄×C₈₉	—	8	2	no	—
408	D₄×C₈₉	—	8	2	no	—
409	D₄×C₈₉	—	8	2	no	—
410	D₄×C₈₉	—	8	2	no	—
411	D₄×C₈₉	—	8	2	no	—
412	D₄×C₈₉	—	8	2	no	—
413	C₂×C₄×C₈₉	—	2	4	no	—
414	C₂×C₄×C₈₉	—	2	2	no	—
415	C₂×C₄×C₈₉	—	2	1	no	—
416	C₂×C₄×C₈₉	—	2	1	no	—
417	C₂×C₄×C₈₉	—	2	2	no	—
418	C₂×C₄×C₈₉	—	2	2	no	—
419	C₂×C₄×C₈₉	—	2	2	no	—
420	C₂×C₄×C₈₉	—	2	2	no	—
421	C₂×C₄×C₈₉	—	2	2	no	—
422	C₂×C₄×C₈₉	—	2	2	no	—
423	C₂×C₄×C₈₉	—	2	2	no	—
424	C₂×C₄×C₈₉	—	4	2	no	—
425	C₂×C₄×C₈₉	—	4	1	no	—
426	C₂×C₄×C₈₉	—	4	4	no	—
427	C₂×C₄×C₈₉	—	4	4	no	—
428	C₂×C₄×C₈₉	—	4	4	no	—
429	C₂×C₄×C₈₉	—	4	4	no	—
430	C₂×C₄×C₈₉	—	8	2	no	—
431	C₂×C₄×C₈₉	—	8	2	no	—
432	C₂×C₄×C₈₉	—	8	2	no	—
433	C₂×C₄×C₈₉	—	8	2	no	—
434	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
435	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
436	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
440	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
443	C₈×C₈₉	—	2	1	no	—
444	C₈×C₈₉	—	2	1	no	—
445	C₈×C₈₉	—	2	1	no	—
446	C₈×C₈₉	—	2	1	no	—
447	C₈×C₈₉	—	2	2	no	—
448	C₈×C₈₉	—	2	2	no	—
449	C₂²×C₈₉	—	2	1	no	—
450	C₂²×C₈₉	—	2	2	no	—
451	C₂²×C₈₉	—	2	2	no	—
452	C₂²×C₈₉	—	2	1	no	—
453	C₂²×C₈₉	—	2	2	no	—
454	C₂²×C₈₉	—	2	1	no	—
455	C₂²×C₈₉	—	4	2	no	—
456	C₂²×C₈₉	—	4	2	no	—
457	C₂²×C₈₉	—	4	2	no	—
458	C₂²×C₈₉	—	4	2	no	—
459	C₂²×C₈₉	—	4	2	no	—
460	C₂²×C₈₉	—	4	2	no	—
461	C₂²×C₈₉	—	4	2	no	—
462	C₂²×C₈₉	—	4	2	no	—
463	C₂²×C₈₉	—	4	2	no	—
464	C₂²×C₈₉	—	8	8	no	—
465	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
466	C₄×C₈₉	—	2	1	no	—
467	C₄×C₈₉	—	2	2	no	—
468	C₄×C₈₉	—	2	1	no	—
469	C₄×C₈₉	—	2	2	no	—
470	C₄×C₈₉	—	2	1	no	—
471	C₄×C₈₉	—	2	2	no	—
472	C₄×C₈₉	—	2	1	no	—
473	C₄×C₈₉	—	4	2	no	—
474	C₄×C₈₉	—	4	2	no	—
475	C₄×C₈₉	—	4	2	no	—
476	C₄×C₈₉	—	4	2	no	—
477	C₄×C₈₉	—	4	2	no	—
478	C₄×C₈₉	#576	1	2	yes	—
479	C₄×C₈₉	#585	1	1	yes	characteristic
480	C₄×C₈₉	#585	1	1	yes	characteristic
481	#60955	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
482	C₂×C₈₉	—	4	1	no	—
483	C₂×C₈₉	—	4	2	no	—
484	C₂×C₈₉	—	8	2	no	—
485	C₂×C₈₉	—	8	2	no	—
486	C₂×C₈₉	—	8	2	no	—
487	C₂×C₈₉	#3449	1	1	yes	characteristic
488	C₂×C₈₉	C₂×#576	1	1	yes	characteristic
489	C₂×C₈₉	#3584	1	1	yes	characteristic
490	#3460	C₂×C₈₉	1	2	yes	complemented
491	#3262	C₂×C₈₉	1	1	yes	characteristic, complemented
492	#3259	C₂×C₈₉	1	1	yes	characteristic, complemented
493	#3257	C₂×C₈₉	1	2	yes	complemented
494	#3243	C₂×C₈₉	1	2	yes	complemented
495	#3241	C₂×C₈₉	1	2	yes	complemented
496	#3224	C₂×C₈₉	1	2	yes	complemented
497	#3220	C₂×C₈₉	1	2	yes	complemented
498	#3203	C₂×C₈₉	1	1	yes	characteristic, complemented
499	#3199	C₂×C₈₉	1	1	yes	characteristic, complemented
500	#3198	C₂×C₈₉	1	2	yes	complemented
501	#3171	C₂×C₈₉	1	2	yes	complemented
502	#3169	C₂×C₈₉	1	1	yes	characteristic, complemented
503	#3168	C₂×C₈₉	1	1	yes	characteristic, complemented
504	#3106	C₂×C₈₉	1	2	yes	complemented
505	#3105	C₂×C₈₉	1	2	yes	complemented
506	#3102	C₂×C₈₉	1	2	yes	complemented
507	#3100	C₂×C₈₉	1	2	yes	complemented
508	#2922	C₂×C₈₉	1	1	yes	characteristic, complemented
509	C₈₉	#60955	1	1	yes	characteristic, direct product factor, Sylow
510	#544	C₂²×C₈₉	1	2	yes	complemented
511	#542	—	2	2	no	—
512	#542	C₂²×C₈₉	1	2	yes	—
513	#542	C₂²×C₈₉	1	2	yes	complemented
514	#540	—	2	2	no	—
515	#540	C₂²×C₈₉	1	2	yes	—
516	#540	C₂²×C₈₉	1	2	yes	complemented
517	#538	—	2	2	no	—
518	#538	—	2	2	no	—
519	#537	C₂²×C₈₉	1	2	yes	—
520	#535	C₂²×C₈₉	1	2	yes	—
521	#535	C₂²×C₈₉	1	2	yes	complemented
522	#532	—	2	2	no	—
523	#532	C₂²×C₈₉	1	2	yes	—
524	#532	C₂²×C₈₉	1	2	yes	complemented
525	#529	—	2	2	no	—
526	#529	C₂²×C₈₉	1	2	yes	—
527	#529	C₂²×C₈₉	1	2	yes	complemented
528	#525	—	2	2	no	—
529	#525	—	2	2	no	—
530	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
531	C₄×#41	C₂²×C₈₉	1	2	yes	complemented
532	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
533	#501	C₂²×C₈₉	1	2	yes	complemented
534	#500	C₂²×C₈₉	1	1	yes	characteristic, complemented
535	#499	C₂²×C₈₉	1	1	yes	characteristic, complemented
536	#496	C₂²×C₈₉	1	2	yes	—
537	#495	C₂²×C₈₉	1	1	yes	characteristic
538	#493	C₂²×C₈₉	1	1	yes	characteristic
539	#490	C₂²×C₈₉	1	2	yes	complemented
540	#489	C₂²×C₈₉	1	2	yes	complemented
541	#488	C₂²×C₈₉	1	2	yes	complemented
542	#486	C₂²×C₈₉	1	2	yes	complemented
543	#485	C₂²×C₈₉	1	2	yes	complemented
544	#484	C₂²×C₈₉	1	2	yes	complemented
545	#482	C₂²×C₈₉	1	2	yes	—
546	#482	C₂²×C₈₉	1	2	yes	—
547	#482	C₂²×C₈₉	1	2	yes	complemented
548	#481	C₂²×C₈₉	1	2	yes	—
549	#480	C₂²×C₈₉	1	2	yes	—
550	#480	C₂²×C₈₉	1	2	yes	complemented
551	#479	C₂²×C₈₉	1	2	yes	complemented
552	#478	C₂²×C₈₉	1	2	yes	complemented
553	#478	C₂²×C₈₉	1	2	yes	complemented
554	#478	C₂²×C₈₉	1	2	yes	complemented
555	#477	C₂²×C₈₉	1	2	yes	complemented
556	#476	C₂²×C₈₉	1	2	yes	complemented
557	#474	C₂²×C₈₉	1	2	yes	complemented
558	#474	C₂²×C₈₉	1	2	yes	complemented
559	#469	C₂²×C₈₉	1	2	yes	—
560	#469	C₂²×C₈₉	1	2	yes	complemented
561	#468	C₂²×C₈₉	1	2	yes	complemented
562	#468	C₂²×C₈₉	1	2	yes	complemented
563	#467	C₂²×C₈₉	1	1	yes	characteristic, complemented
564	#466	C₂²×C₈₉	1	1	yes	characteristic
565	#466	C₂²×C₈₉	1	1	yes	characteristic
566	#466	C₂²×C₈₉	1	2	yes	complemented
567	#466	C₂²×C₈₉	1	1	yes	characteristic, complemented
568	#465	C₂²×C₈₉	1	2	yes	complemented
569	#464	C₂²×C₈₉	1	2	yes	complemented
570	#463	C₂²×C₈₉	1	2	yes	—
571	#463	C₂²×C₈₉	1	2	yes	—
572	#463	C₂²×C₈₉	1	2	yes	complemented
573	#460	C₂²×C₈₉	1	2	yes	complemented
574	#459	C₂²×C₈₉	1	2	yes	—
575	#459	C₂²×C₈₉	1	2	yes	—
576	#459	C₂²×C₈₉	1	2	yes	complemented
577	#452	C₂²×C₈₉	1	2	yes	complemented
578	#450	C₂²×C₈₉	1	2	yes	complemented
579	#449	C₂²×C₈₉	1	2	yes	—
580	#449	C₂²×C₈₉	1	2	yes	—
581	#449	C₂²×C₈₉	1	2	yes	complemented
582	#447	C₂²×C₈₉	1	2	yes	—
583	#447	C₂²×C₈₉	1	2	yes	—
584	#447	C₂²×C₈₉	1	2	yes	complemented
585	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
586	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
587	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
588	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
589	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
590	C₄×D₈	C₂²×C₈₉	1	2	yes	—
591	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
592	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
593	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
594	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
595	#433	C₂²×C₈₉	1	2	yes	complemented
596	#433	C₂²×C₈₉	1	2	yes	complemented
597	#431	C₂²×C₈₉	1	2	yes	complemented
598	#431	C₂²×C₈₉	1	2	yes	complemented
599	#424	C₂²×C₈₉	1	1	yes	characteristic, complemented
600	#424	C₂²×C₈₉	1	1	yes	characteristic, complemented
601	#408	C₂²×C₈₉	1	1	yes	characteristic
602	#408	C₂²×C₈₉	1	1	yes	characteristic
603	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
604	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
605	C₂×#41	—	2	2	no	—
606	C₂×#41	—	2	2	no	—
607	C₂×#41	C₂³×C₈₉	1	2	yes	—
608	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
609	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
610	C₂³×C₄	—	2	2	no	—
611	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
612	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
613	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
614	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
615	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
616	C₂×D₈	C₂³×C₈₉	1	2	yes	—
617	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
618	C₂×D₈	C₂³×C₈₉	1	2	yes	—
619	C₂×D₈	C₂³×C₈₉	1	2	yes	—
620	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
621	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
622	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
623	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
624	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
625	C₄⋊Q₈	—	2	2	no	—
626	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
627	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
628	#127	—	2	2	no	—
629	#127	C₂³×C₈₉	1	2	yes	—
630	#127	C₂³×C₈₉	1	2	yes	—
631	#126	—	2	2	no	—
632	#126	—	2	2	no	—
633	#126	—	2	2	no	—
634	#126	—	2	2	no	—
635	#125	—	2	2	no	—
636	#125	C₂³×C₈₉	1	2	yes	—
637	#125	C₂³×C₈₉	1	2	yes	—
638	#124	—	2	2	no	—
639	#124	—	2	2	no	—
640	#124	—	2	2	no	—
641	#124	—	2	2	no	—
642	#124	—	2	2	no	—
643	#124	C₂³×C₈₉	1	2	yes	—
644	#124	C₂³×C₈₉	1	2	yes	—
645	#123	—	2	2	no	—
646	#123	—	2	2	no	—
647	#123	—	2	2	no	—
648	#123	—	2	2	no	—
649	#123	—	2	2	no	—
650	#123	—	2	2	no	—
651	#123	—	2	2	no	—
652	#123	—	2	2	no	—
653	C₂²⋊Q₈	—	2	2	no	—
654	C₂²⋊Q₈	—	2	2	no	—
655	C₂²⋊Q₈	—	2	2	no	—
656	C₂²⋊Q₈	—	2	2	no	—
657	C₂²⋊Q₈	—	2	2	no	—
658	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
659	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
660	#121	—	2	2	no	—
661	#121	—	2	2	no	—
662	#121	—	2	2	no	—
663	#121	—	2	2	no	—
664	#121	—	2	2	no	—
665	#121	—	2	2	no	—
666	#121	—	2	2	no	—
667	#121	—	2	2	no	—
668	#121	—	2	2	no	—
669	#121	—	2	2	no	—
670	#121	—	2	2	no	—
671	#121	C₂³×C₈₉	1	2	yes	—
672	#121	C₂³×C₈₉	1	2	yes	—
673	#121	C₂³×C₈₉	1	2	yes	—
674	#121	C₂³×C₈₉	1	2	yes	—
675	#121	C₂³×C₈₉	1	2	yes	—
676	#121	C₂³×C₈₉	1	2	yes	—
677	#120	—	2	2	no	—
678	#120	—	2	2	no	—
679	#120	—	2	2	no	—
680	#120	—	2	2	no	—
681	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
682	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
683	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
684	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
685	C₄×D₄	—	2	2	no	—
686	C₄×D₄	—	2	2	no	—
687	C₄×D₄	—	2	2	no	—
688	C₄×D₄	—	2	2	no	—
689	C₄×D₄	—	2	2	no	—
690	C₄×D₄	—	2	2	no	—
691	C₄×D₄	—	2	2	no	—
692	C₄×D₄	—	2	2	no	—
693	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
694	C₄×D₄	D₄×C₈₉	1	2	yes	—
695	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
696	C₄×D₄	D₄×C₈₉	1	2	yes	—
697	C₄×D₄	C₂³×C₈₉	1	2	yes	—
698	C₄×D₄	C₂³×C₈₉	1	2	yes	—
699	C₄×D₄	C₂³×C₈₉	1	2	yes	—
700	C₄×D₄	C₂³×C₈₉	1	2	yes	—
701	C₄×D₄	C₂³×C₈₉	1	2	yes	—
702	C₄×D₄	C₂³×C₈₉	1	2	yes	—
703	#117	—	2	2	no	—
704	#117	—	2	2	no	—
705	#117	—	2	2	no	—
706	#117	C₂³×C₈₉	1	2	yes	—
707	#117	C₂³×C₈₉	1	2	yes	—
708	#117	C₂³×C₈₉	1	1	yes	characteristic
709	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
710	C₂×C₂²⋊C₄	—	2	2	no	—
711	C₂×C₄²	—	2	2	no	—
712	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
713	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
714	#107	C₂³×C₈₉	1	1	yes	characteristic
715	#107	C₂³×C₈₉	1	1	yes	characteristic
716	#107	C₂³×C₈₉	1	2	yes	—
717	#107	C₂³×C₈₉	1	1	yes	characteristic
718	#107	C₂³×C₈₉	1	2	yes	—
719	#107	C₂³×C₈₉	1	2	yes	—
720	#107	C₂³×C₈₉	1	1	yes	characteristic
721	#106	C₂³×C₈₉	1	2	yes	—
722	#106	C₂³×C₈₉	1	2	yes	—
723	#106	C₂³×C₈₉	1	2	yes	—
724	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
725	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
726	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
727	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
728	#103	C₂³×C₈₉	1	2	yes	—
729	#103	C₂³×C₈₉	1	2	yes	—
730	#103	C₂³×C₈₉	1	2	yes	—
731	#103	C₂³×C₈₉	1	2	yes	—
732	#102	C₂³×C₈₉	1	2	yes	—
733	#102	C₂³×C₈₉	1	2	yes	—
734	#102	C₂³×C₈₉	1	2	yes	—
735	#102	C₂³×C₈₉	1	2	yes	—
736	#102	C₂³×C₈₉	1	2	yes	—
737	#102	C₂³×C₈₉	1	2	yes	—
738	#102	C₂³×C₈₉	1	2	yes	—
739	#102	C₂³×C₈₉	1	2	yes	—
740	#102	C₂³×C₈₉	1	2	yes	—
741	#102	C₂³×C₈₉	1	2	yes	—
742	#102	C₂³×C₈₉	1	2	yes	—
743	#102	C₂³×C₈₉	1	2	yes	—
744	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
745	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
746	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
747	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
748	#97	C₂³×C₈₉	1	2	yes	—
749	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
750	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
751	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
752	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
753	C₄×C₈	C₂³×C₈₉	1	2	yes	—
754	C₂⁴	—	2	2	no	—
755	#41	—	4	1	no	—
756	#41	—	4	1	no	—
757	#41	—	4	2	no	—
758	#41	—	4	2	no	—
759	#41	—	8	4	no	—
760	#41	—	8	4	no	—
761	C₂×Q₈	—	2	2	no	—
762	C₂×Q₈	—	2	2	no	—
763	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
764	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	2	no	—
774	C₂×D₄	—	2	2	no	—
775	C₂×D₄	—	2	2	no	—
776	C₂×D₄	—	2	2	no	—
777	C₂×D₄	—	4	2	no	—
778	C₂×D₄	—	4	2	no	—
779	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
780	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
781	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
782	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
783	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	2	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	8	4	no	—
793	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
794	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
795	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
796	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
798	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
799	Q₁₆	—	4	1	no	—
800	SD₁₆	—	4	2	no	—
801	SD₁₆	—	4	2	no	—
802	SD₁₆	—	4	2	no	—
803	D₈	—	4	2	no	—
804	D₈	—	4	1	no	—
805	D₈	—	4	1	no	—
806	D₈	—	4	1	no	—
807	D₈	—	4	2	no	—
808	D₈	—	4	2	no	—
809	M₁₆	—	4	1	no	—
810	M₁₆	—	4	1	no	—
811	C₂×C₈	—	4	1	no	—
812	C₂×C₈	—	4	1	no	—
813	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
814	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
815	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
816	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
817	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
818	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
831	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
832	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
833	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
834	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
835	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
836	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
837	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
858	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
859	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
860	C₄²	—	2	2	no	—
861	C₄²	—	2	2	no	—
862	C₄²	—	2	2	no	—
863	C₄²	C₂×D₄×C₈₉	1	2	yes	—
864	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
865	C₄²	C₂×D₄×C₈₉	1	2	yes	—
866	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
867	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
868	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
869	C₄²	C₂⁴×C₈₉	1	2	yes	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	4	4	no	—
874	C₂³	—	8	2	no	—
875	C₂³	—	8	2	no	—
876	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
877	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
878	Q₈	—	2	2	no	—
879	Q₈	—	2	2	no	—
880	Q₈	—	4	1	no	—
881	Q₈	—	8	2	no	—
882	Q₈	—	8	2	no	—
883	D₄	—	2	2	no	—
884	D₄	—	2	2	no	—
885	D₄	—	2	2	no	—
886	D₄	—	2	2	no	—
887	D₄	—	2	2	no	—
888	D₄	—	2	2	no	—
889	D₄	—	4	2	no	—
890	D₄	—	4	1	no	—
891	D₄	—	4	4	no	—
892	D₄	—	4	4	no	—
893	D₄	—	8	2	no	—
894	D₄	—	8	2	no	—
895	D₄	—	8	2	no	—
896	D₄	—	8	2	no	—
897	D₄	—	8	2	no	—
898	D₄	—	8	2	no	—
899	D₄	—	8	2	no	—
900	D₄	—	8	2	no	—
901	D₄	—	8	2	no	—
902	D₄	—	8	2	no	—
903	C₂×C₄	—	2	4	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	4	2	no	—
915	C₂×C₄	—	4	1	no	—
916	C₂×C₄	—	4	4	no	—
917	C₂×C₄	—	4	4	no	—
918	C₂×C₄	—	4	4	no	—
919	C₂×C₄	—	4	4	no	—
920	C₂×C₄	—	8	2	no	—
921	C₂×C₄	—	8	2	no	—
922	C₂×C₄	—	8	2	no	—
923	C₂×C₄	—	8	2	no	—
924	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
925	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
926	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
927	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
928	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
929	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
930	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
931	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
932	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
933	C₈	—	2	1	no	—
934	C₈	—	2	1	no	—
935	C₈	—	2	1	no	—
936	C₈	—	2	1	no	—
937	C₈	—	2	2	no	—
938	C₈	—	2	2	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	1	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	8	8	no	—
955	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
956	C₄	—	2	2	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	1	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	1	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	1	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	#576×C₈₉	1	2	yes	—
969	C₄	#585×C₈₉	1	1	yes	characteristic
970	C₄	#585×C₈₉	1	1	yes	characteristic
971	C₂	—	4	1	no	—
972	C₂	—	4	2	no	—
973	C₂	—	8	2	no	—
974	C₂	—	8	2	no	—
975	C₂	—	8	2	no	—
976	C₂	C₈₉×#3449	1	1	yes	characteristic
977	C₂	C₂×#576×C₈₉	1	1	yes	characteristic
978	C₂	C₈₉×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3460	C₂	semidirect
2. C₈₉×#3262	C₂	semidirect
3. C₈₉×#3259	C₂	semidirect
4. C₈₉×#3257	C₂	semidirect
5. C₈₉×#3243	C₂	semidirect
6. C₈₉×#3241	C₂	semidirect
7. C₈₉×#3224	C₂	semidirect
8. C₈₉×#3220	C₂	semidirect
9. C₈₉×#3203	C₂	semidirect
10. C₈₉×#3199	C₂	semidirect
11. C₈₉×#3198	C₂	semidirect
12. C₈₉×#3171	C₂	semidirect
13. C₈₉×#3169	C₂	semidirect
14. C₈₉×#3168	C₂	semidirect
15. C₈₉×#3106	C₂	semidirect
16. C₈₉×#3105	C₂	semidirect
17. C₈₉×#3102	C₂	semidirect
18. C₈₉×#3100	C₂	semidirect
19. C₈₉×#2922	C₂	semidirect
20. #544×C₈₉	C₂²	semidirect
23. #542×C₈₉	C₂²	semidirect
26. #540×C₈₉	C₂²	semidirect
31. #535×C₈₉	C₂²	semidirect
34. #532×C₈₉	C₂²	semidirect
37. #529×C₈₉	C₂²	semidirect
41. C₄×#41×C₈₉	C₂²	semidirect
42. C₂×C₄×D₄×C₈₉	C₂²	semidirect
43. #501×C₈₉	C₂²	semidirect
44. #500×C₈₉	C₂²	semidirect
45. #499×C₈₉	C₂²	semidirect
49. #490×C₈₉	C₂²	semidirect
50. #489×C₈₉	C₂²	semidirect
51. #488×C₈₉	C₂²	semidirect
52. #486×C₈₉	C₂²	semidirect
53. #485×C₈₉	C₂²	semidirect
54. #484×C₈₉	C₂²	semidirect
57. #482×C₈₉	C₂²	semidirect
60. #480×C₈₉	C₂²	semidirect
61. #479×C₈₉	C₂²	semidirect
62. #478×C₈₉	C₂²	semidirect
63. #478×C₈₉	C₂²	semidirect
64. #478×C₈₉	C₂²	semidirect
65. #477×C₈₉	C₂²	semidirect
66. #476×C₈₉	C₂²	semidirect
67. #474×C₈₉	C₂²	semidirect
68. #474×C₈₉	C₂²	semidirect
70. #469×C₈₉	C₂²	semidirect
71. #468×C₈₉	C₂²	semidirect
72. #468×C₈₉	C₂²	semidirect
73. #467×C₈₉	C₂²	semidirect
76. #466×C₈₉	C₂²	semidirect
77. #466×C₈₉	C₂²	semidirect
78. #465×C₈₉	C₂²	semidirect
79. #464×C₈₉	C₂²	semidirect
82. #463×C₈₉	C₂²	semidirect
83. #460×C₈₉	C₂²	semidirect
86. #459×C₈₉	C₂²	semidirect
87. #452×C₈₉	C₂²	semidirect
88. #450×C₈₉	C₂²	semidirect
91. #449×C₈₉	C₂²	semidirect
94. #447×C₈₉	C₂²	semidirect
95. C₄×Q₁₆×C₈₉	C₂²	semidirect
96. C₄×SD₁₆×C₈₉	C₂²	semidirect
97. C₄×SD₁₆×C₈₉	C₂²	semidirect
98. C₄×SD₁₆×C₈₉	C₂²	semidirect
102. C₄×D₈×C₈₉	C₂²	semidirect
103. C₄×D₈×C₈₉	C₂²	semidirect
104. C₄×D₈×C₈₉	C₂²	semidirect
105. #433×C₈₉	C₂²	semidirect
106. #433×C₈₉	C₂²	semidirect
107. #431×C₈₉	C₂²	semidirect
108. #431×C₈₉	C₂²	semidirect
109. #424×C₈₉	C₂²	semidirect
110. #424×C₈₉	C₂²	semidirect
113. C₄×M₁₆×C₈₉	C₂²	semidirect
114. C₂×C₄×C₈×C₈₉	C₂²	semidirect
481. #60955	C₈₉	direct (N × H)
490. #3460	C₂×C₈₉	semidirect
491. #3262	C₂×C₈₉	semidirect
492. #3259	C₂×C₈₉	semidirect
493. #3257	C₂×C₈₉	semidirect
494. #3243	C₂×C₈₉	semidirect
495. #3241	C₂×C₈₉	semidirect
496. #3224	C₂×C₈₉	semidirect
497. #3220	C₂×C₈₉	semidirect
498. #3203	C₂×C₈₉	semidirect
499. #3199	C₂×C₈₉	semidirect
500. #3198	C₂×C₈₉	semidirect
501. #3171	C₂×C₈₉	semidirect
502. #3169	C₂×C₈₉	semidirect
503. #3168	C₂×C₈₉	semidirect
504. #3106	C₂×C₈₉	semidirect
505. #3105	C₂×C₈₉	semidirect
506. #3102	C₂×C₈₉	semidirect
507. #3100	C₂×C₈₉	semidirect
508. #2922	C₂×C₈₉	semidirect
509. C₈₉	#60955	direct (N × H)
510. #544	C₂²×C₈₉	semidirect
513. #542	C₂²×C₈₉	semidirect
516. #540	C₂²×C₈₉	semidirect
521. #535	C₂²×C₈₉	semidirect
524. #532	C₂²×C₈₉	semidirect
527. #529	C₂²×C₈₉	semidirect
531. C₄×#41	C₂²×C₈₉	semidirect
532. C₂×C₄×D₄	C₂²×C₈₉	semidirect
533. #501	C₂²×C₈₉	semidirect
534. #500	C₂²×C₈₉	semidirect
535. #499	C₂²×C₈₉	semidirect
539. #490	C₂²×C₈₉	semidirect
540. #489	C₂²×C₈₉	semidirect
541. #488	C₂²×C₈₉	semidirect
542. #486	C₂²×C₈₉	semidirect
543. #485	C₂²×C₈₉	semidirect
544. #484	C₂²×C₈₉	semidirect
547. #482	C₂²×C₈₉	semidirect
550. #480	C₂²×C₈₉	semidirect
551. #479	C₂²×C₈₉	semidirect
552. #478	C₂²×C₈₉	semidirect
553. #478	C₂²×C₈₉	semidirect
554. #478	C₂²×C₈₉	semidirect
555. #477	C₂²×C₈₉	semidirect
556. #476	C₂²×C₈₉	semidirect
557. #474	C₂²×C₈₉	semidirect
558. #474	C₂²×C₈₉	semidirect
560. #469	C₂²×C₈₉	semidirect
561. #468	C₂²×C₈₉	semidirect
562. #468	C₂²×C₈₉	semidirect
563. #467	C₂²×C₈₉	semidirect
566. #466	C₂²×C₈₉	semidirect
567. #466	C₂²×C₈₉	semidirect
568. #465	C₂²×C₈₉	semidirect
569. #464	C₂²×C₈₉	semidirect
572. #463	C₂²×C₈₉	semidirect
573. #460	C₂²×C₈₉	semidirect
576. #459	C₂²×C₈₉	semidirect
577. #452	C₂²×C₈₉	semidirect
578. #450	C₂²×C₈₉	semidirect
581. #449	C₂²×C₈₉	semidirect
584. #447	C₂²×C₈₉	semidirect
585. C₄×Q₁₆	C₂²×C₈₉	semidirect
586. C₄×SD₁₆	C₂²×C₈₉	semidirect
587. C₄×SD₁₆	C₂²×C₈₉	semidirect
588. C₄×SD₁₆	C₂²×C₈₉	semidirect
592. C₄×D₈	C₂²×C₈₉	semidirect
593. C₄×D₈	C₂²×C₈₉	semidirect
594. C₄×D₈	C₂²×C₈₉	semidirect
595. #433	C₂²×C₈₉	semidirect
596. #433	C₂²×C₈₉	semidirect
597. #431	C₂²×C₈₉	semidirect
598. #431	C₂²×C₈₉	semidirect
599. #424	C₂²×C₈₉	semidirect
600. #424	C₂²×C₈₉	semidirect
603. C₄×M₁₆	C₂²×C₈₉	semidirect
604. C₂×C₄×C₈	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3460	2
C₈₉×#3262	2
C₈₉×#3259	2
C₈₉×#3257	2
C₈₉×#3243	2
C₈₉×#3241	2
C₈₉×#3224	2
C₈₉×#3220	2
C₈₉×#3203	2
C₈₉×#3199	2
C₈₉×#3198	2
C₈₉×#3171	2
C₈₉×#3169	2
C₈₉×#3168	2
C₈₉×#3106	2
C₈₉×#3105	2
C₈₉×#3102	2
C₈₉×#3100	2
C₈₉×#2922	2
#60955	89

Subgroups — C89×#60955 #36438803

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60955 #36438803