Subgroups — C₈₉×#62568 #36440416

Order 22784.

1720 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3558	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#3555	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3375	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3371	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3327	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3324	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3314	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3313	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3311	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3310	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3243	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3235	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3222	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3215	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#3178	C₂	1	2	yes	maximal, complemented
17	C₈₉×#3140	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#3136	C₂	1	2	yes	maximal, complemented
19	C₈₉×#2967	C₂	1	1	yes	maximal, characteristic, complemented
20	#563×C₈₉	—	2	2	no	—
21	#562×C₈₉	—	2	1	no	—
22	H(3,𝔽₄)×C₈₉	—	2	1	no	—
23	#559×C₈₉	C₂²	1	2	yes	—
24	Q₈²×C₈₉	C₂²	1	1	yes	characteristic, complemented
25	#557×C₈₉	—	2	1	no	—
26	#557×C₈₉	C₂²	1	1	yes	characteristic, complemented
27	#556×C₈₉	—	2	1	no	—
28	#556×C₈₉	C₂²	1	2	yes	complemented
29	#556×C₈₉	C₂²	1	1	yes	characteristic, complemented
30	#554×C₈₉	C₂²	1	1	yes	characteristic, complemented
31	#552×C₈₉	C₂²	1	2	yes	complemented
32	#548×C₈₉	C₂²	1	2	yes	—
33	#546×C₈₉	—	2	2	no	—
34	#546×C₈₉	C₂²	1	2	yes	—
35	D₄²×C₈₉	C₂²	1	2	yes	—
36	#544×C₈₉	C₂²	1	2	yes	complemented
37	#542×C₈₉	—	2	1	no	—
38	#542×C₈₉	C₂²	1	2	yes	—
39	#541×C₈₉	—	2	2	no	—
40	#541×C₈₉	—	2	1	no	—
41	#541×C₈₉	C₂²	1	2	yes	complemented
42	#538×C₈₉	—	2	2	no	—
43	#538×C₈₉	—	2	1	no	—
44	#535×C₈₉	C₂²	1	2	yes	—
45	#534×C₈₉	—	2	1	no	—
46	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
47	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
48	#532×C₈₉	C₂²	1	1	yes	characteristic
49	#529×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
51	#501×C₈₉	C₂²	1	2	yes	complemented
52	#500×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	#497×C₈₉	C₂²	1	2	yes	complemented
54	#492×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	#490×C₈₉	C₂²	1	2	yes	—
56	#490×C₈₉	C₂²	1	2	yes	complemented
57	#489×C₈₉	C₂²	1	2	yes	complemented
58	#489×C₈₉	C₂²	1	2	yes	complemented
59	#489×C₈₉	C₂²	1	2	yes	complemented
60	#489×C₈₉	C₂²	1	2	yes	complemented
61	#488×C₈₉	C₂²	1	2	yes	complemented
62	#488×C₈₉	C₂²	1	2	yes	complemented
63	#488×C₈₉	C₂²	1	2	yes	complemented
64	#487×C₈₉	C₂²	1	1	yes	characteristic, complemented
65	#486×C₈₉	C₂²	1	2	yes	—
66	#486×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#485×C₈₉	C₂²	1	2	yes	complemented
68	#484×C₈₉	C₂²	1	2	yes	complemented
69	#482×C₈₉	C₂²	1	2	yes	—
70	#482×C₈₉	C₂²	1	2	yes	complemented
71	#482×C₈₉	C₂²	1	2	yes	complemented
72	#480×C₈₉	C₂²	1	2	yes	—
73	#479×C₈₉	C₂²	1	2	yes	complemented
74	#478×C₈₉	C₂²	1	2	yes	complemented
75	#477×C₈₉	C₂²	1	2	yes	complemented
76	#476×C₈₉	C₂²	1	2	yes	complemented
77	#474×C₈₉	C₂²	1	2	yes	complemented
78	#474×C₈₉	C₂²	1	2	yes	complemented
79	#470×C₈₉	C₂²	1	2	yes	complemented
80	#468×C₈₉	C₂²	1	2	yes	—
81	#468×C₈₉	C₂²	1	2	yes	complemented
82	#468×C₈₉	C₂²	1	2	yes	complemented
83	#467×C₈₉	C₂²	1	2	yes	complemented
84	#465×C₈₉	C₂²	1	2	yes	—
85	#464×C₈₉	C₂²	1	2	yes	complemented
86	#464×C₈₉	C₂²	1	2	yes	complemented
87	#464×C₈₉	C₂²	1	2	yes	complemented
88	#464×C₈₉	C₂²	1	2	yes	complemented
89	#460×C₈₉	C₂²	1	2	yes	—
90	#460×C₈₉	C₂²	1	2	yes	—
91	#452×C₈₉	C₂²	1	2	yes	complemented
92	#452×C₈₉	C₂²	1	2	yes	complemented
93	#451×C₈₉	C₂²	1	1	yes	characteristic, complemented
94	#451×C₈₉	C₂²	1	1	yes	characteristic, complemented
95	#450×C₈₉	C₂²	1	1	yes	characteristic
96	#450×C₈₉	C₂²	1	1	yes	characteristic
97	#450×C₈₉	C₂²	1	2	yes	complemented
98	#450×C₈₉	C₂²	1	2	yes	complemented
99	#446×C₈₉	C₂²	1	2	yes	complemented
100	#441×C₈₉	C₂²	1	2	yes	complemented
101	#440×C₈₉	C₂²	1	2	yes	complemented
102	#440×C₈₉	C₂²	1	2	yes	complemented
103	#440×C₈₉	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
106	#436×C₈₉	C₂²	1	2	yes	complemented
107	#435×C₈₉	C₂²	1	2	yes	complemented
108	#435×C₈₉	C₂²	1	2	yes	complemented
109	#433×C₈₉	C₂²	1	2	yes	complemented
110	#432×C₈₉	C₂²	1	1	yes	characteristic, complemented
111	#419×C₈₉	C₂²	1	2	yes	complemented
112	#418×C₈₉	C₂²	1	2	yes	—
113	#418×C₈₉	C₂²	1	2	yes	complemented
114	#417×C₈₉	C₂²	1	2	yes	complemented
115	#416×C₈₉	C₂²	1	2	yes	complemented
116	C₂×#102×C₈₉	C₂²	1	2	yes	complemented
117	#405×C₈₉	C₂²	1	2	yes	complemented
118	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	C₂×#41×C₈₉	—	2	1	no	—
120	C₂×#41×C₈₉	C₂³	1	2	yes	—
121	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
122	C₂²×D₄×C₈₉	—	2	2	no	—
123	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
124	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
125	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
126	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
131	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
132	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
133	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
134	C₄⋊Q₈×C₈₉	—	2	1	no	—
135	C₄⋊Q₈×C₈₉	—	2	2	no	—
136	C₄⋊Q₈×C₈₉	—	2	1	no	—
137	C₄⋊Q₈×C₈₉	—	2	2	no	—
138	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
139	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
140	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
141	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
142	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
143	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
144	#127×C₈₉	C₂³	1	2	yes	—
145	#127×C₈₉	C₂³	1	1	yes	characteristic
146	#126×C₈₉	—	2	2	no	—
147	#126×C₈₉	—	2	2	no	—
148	#126×C₈₉	—	2	2	no	—
149	#126×C₈₉	—	2	2	no	—
150	#126×C₈₉	—	2	2	no	—
151	#126×C₈₉	—	2	2	no	—
152	#126×C₈₉	—	2	2	no	—
153	#126×C₈₉	D₄	1	2	yes	—
154	#125×C₈₉	—	2	2	no	—
155	#125×C₈₉	—	2	2	no	—
156	#125×C₈₉	—	2	2	no	—
157	#125×C₈₉	—	2	1	no	—
158	#125×C₈₉	—	2	2	no	—
159	#125×C₈₉	—	2	2	no	—
160	#125×C₈₉	—	2	1	no	—
161	#125×C₈₉	D₄	1	1	yes	characteristic
162	#125×C₈₉	C₂³	1	2	yes	—
163	#125×C₈₉	C₂³	1	2	yes	—
164	#124×C₈₉	—	2	2	no	—
165	#124×C₈₉	—	2	1	no	—
166	#124×C₈₉	—	2	2	no	—
167	#124×C₈₉	—	2	2	no	—
168	#124×C₈₉	—	2	2	no	—
169	#124×C₈₉	—	2	1	no	—
170	#124×C₈₉	—	2	1	no	—
171	#124×C₈₉	—	2	1	no	—
172	#124×C₈₉	D₄	1	1	yes	characteristic
173	#124×C₈₉	C₂³	1	2	yes	—
174	#124×C₈₉	C₂³	1	2	yes	—
175	#124×C₈₉	C₂³	1	2	yes	—
176	#123×C₈₉	—	2	2	no	—
177	#123×C₈₉	—	2	2	no	—
178	#123×C₈₉	—	2	2	no	—
179	#123×C₈₉	—	2	2	no	—
180	#123×C₈₉	—	2	2	no	—
181	#123×C₈₉	D₄	1	2	yes	—
182	C₂²⋊Q₈×C₈₉	—	2	1	no	—
183	C₂²⋊Q₈×C₈₉	—	2	1	no	—
184	C₂²⋊Q₈×C₈₉	—	2	1	no	—
185	C₂²⋊Q₈×C₈₉	—	2	2	no	—
186	C₂²⋊Q₈×C₈₉	—	2	2	no	—
187	C₂²⋊Q₈×C₈₉	—	2	2	no	—
188	C₂²⋊Q₈×C₈₉	—	2	2	no	—
189	C₂²⋊Q₈×C₈₉	—	2	2	no	—
190	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
191	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
192	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
193	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
194	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
195	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
196	#121×C₈₉	—	2	2	no	—
197	#121×C₈₉	—	2	1	no	—
198	#121×C₈₉	—	2	2	no	—
199	#121×C₈₉	—	2	2	no	—
200	#121×C₈₉	—	2	2	no	—
201	#121×C₈₉	—	2	2	no	—
202	#121×C₈₉	D₄	1	1	yes	characteristic
203	#121×C₈₉	C₂³	1	2	yes	—
204	#121×C₈₉	C₂³	1	2	yes	—
205	#120×C₈₉	—	2	2	no	—
206	#120×C₈₉	—	2	2	no	—
207	#120×C₈₉	—	2	2	no	—
208	#120×C₈₉	—	2	2	no	—
209	#120×C₈₉	—	2	2	no	—
210	C₄×Q₈×C₈₉	—	2	1	no	—
211	C₄×Q₈×C₈₉	—	2	2	no	—
212	C₄×Q₈×C₈₉	—	2	1	no	—
213	C₄×Q₈×C₈₉	—	2	1	no	—
214	C₄×Q₈×C₈₉	—	2	1	no	—
215	C₄×Q₈×C₈₉	—	2	1	no	—
216	C₄×Q₈×C₈₉	—	2	1	no	—
217	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
218	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
219	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
220	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
223	C₄×D₄×C₈₉	—	2	1	no	—
224	C₄×D₄×C₈₉	—	2	2	no	—
225	C₄×D₄×C₈₉	—	2	2	no	—
226	C₄×D₄×C₈₉	—	2	1	no	—
227	C₄×D₄×C₈₉	C₂³	1	2	yes	—
228	C₄×D₄×C₈₉	C₂³	1	2	yes	—
229	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₈₉	C₂³	1	2	yes	—
231	#117×C₈₉	—	2	1	no	—
232	#117×C₈₉	—	2	2	no	—
233	#117×C₈₉	C₂³	1	2	yes	—
234	#117×C₈₉	C₂³	1	2	yes	—
235	#117×C₈₉	C₂³	1	2	yes	—
236	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
239	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
240	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
241	#107×C₈₉	C₂³	1	2	yes	—
242	#107×C₈₉	C₂³	1	2	yes	—
243	#107×C₈₉	C₂³	1	2	yes	—
244	#107×C₈₉	C₂³	1	2	yes	—
245	#106×C₈₉	C₂³	1	2	yes	—
246	#106×C₈₉	C₂³	1	2	yes	—
247	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
248	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
249	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
250	#103×C₈₉	C₂³	1	2	yes	—
251	#103×C₈₉	C₂³	1	2	yes	—
252	#103×C₈₉	C₂³	1	2	yes	—
253	#103×C₈₉	C₂³	1	2	yes	—
254	#103×C₈₉	C₂³	1	2	yes	—
255	#103×C₈₉	C₂³	1	2	yes	—
256	#103×C₈₉	C₂³	1	2	yes	—
257	#103×C₈₉	C₂³	1	2	yes	—
258	#102×C₈₉	C₂³	1	2	yes	—
259	#102×C₈₉	C₂³	1	2	yes	—
260	#102×C₈₉	C₂³	1	2	yes	—
261	#102×C₈₉	C₂³	1	2	yes	—
262	#102×C₈₉	C₂³	1	2	yes	—
263	#102×C₈₉	C₂³	1	2	yes	—
264	#102×C₈₉	C₂³	1	2	yes	—
265	#102×C₈₉	C₂³	1	2	yes	—
266	#102×C₈₉	C₂³	1	2	yes	—
267	#102×C₈₉	C₂³	1	2	yes	—
268	#102×C₈₉	C₂³	1	2	yes	—
269	#102×C₈₉	C₂³	1	2	yes	—
270	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
271	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
272	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
273	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
274	#97×C₈₉	C₂³	1	2	yes	—
275	#97×C₈₉	C₂³	1	2	yes	—
276	#97×C₈₉	C₂³	1	2	yes	—
277	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
278	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
279	C₄×C₈×C₈₉	C₂³	1	2	yes	—
280	C₂⁴×C₈₉	—	2	1	no	—
281	C₂⁴×C₈₉	—	2	2	no	—
282	#41×C₈₉	—	4	2	no	—
283	#41×C₈₉	—	4	2	no	—
284	#41×C₈₉	—	8	2	no	—
285	C₂×Q₈×C₈₉	—	2	1	no	—
286	C₂×Q₈×C₈₉	—	2	1	no	—
287	C₂×Q₈×C₈₉	—	2	1	no	—
288	C₂×Q₈×C₈₉	—	2	2	no	—
289	C₂×Q₈×C₈₉	—	2	1	no	—
290	C₂×Q₈×C₈₉	—	2	1	no	—
291	C₂×Q₈×C₈₉	—	4	2	no	—
292	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
293	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
294	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
295	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
296	C₂×D₄×C₈₉	—	2	2	no	—
297	C₂×D₄×C₈₉	—	2	2	no	—
298	C₂×D₄×C₈₉	—	2	2	no	—
299	C₂×D₄×C₈₉	—	2	2	no	—
300	C₂×D₄×C₈₉	—	2	1	no	—
301	C₂×D₄×C₈₉	—	2	1	no	—
302	C₂×D₄×C₈₉	—	2	1	no	—
303	C₂×D₄×C₈₉	—	2	2	no	—
304	C₂×D₄×C₈₉	—	2	2	no	—
305	C₂×D₄×C₈₉	—	4	2	no	—
306	C₂×D₄×C₈₉	—	4	2	no	—
307	C₂×D₄×C₈₉	—	4	2	no	—
308	C₂×D₄×C₈₉	—	8	4	no	—
309	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
310	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
311	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
312	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
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	2	no	—
317	C₂²×C₄×C₈₉	—	2	2	no	—
318	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
322	Q₁₆×C₈₉	—	4	2	no	—
323	Q₁₆×C₈₉	—	4	2	no	—
324	SD₁₆×C₈₉	—	4	2	no	—
325	SD₁₆×C₈₉	—	4	2	no	—
326	SD₁₆×C₈₉	—	4	2	no	—
327	SD₁₆×C₈₉	—	4	2	no	—
328	M₁₆×C₈₉	—	4	2	no	—
329	M₁₆×C₈₉	—	4	2	no	—
330	C₂×C₈×C₈₉	—	4	2	no	—
331	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
332	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
333	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
334	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
335	C₄⋊C₄×C₈₉	—	2	2	no	—
336	C₄⋊C₄×C₈₉	—	2	1	no	—
337	C₄⋊C₄×C₈₉	—	2	1	no	—
338	C₄⋊C₄×C₈₉	—	2	2	no	—
339	C₄⋊C₄×C₈₉	—	2	1	no	—
340	C₄⋊C₄×C₈₉	—	2	1	no	—
341	C₄⋊C₄×C₈₉	—	2	2	no	—
342	C₄⋊C₄×C₈₉	—	2	1	no	—
343	C₄⋊C₄×C₈₉	—	2	1	no	—
344	C₄⋊C₄×C₈₉	—	2	2	no	—
345	C₄⋊C₄×C₈₉	—	2	2	no	—
346	C₄⋊C₄×C₈₉	—	2	2	no	—
347	C₄⋊C₄×C₈₉	—	2	2	no	—
348	C₄⋊C₄×C₈₉	—	2	1	no	—
349	C₄⋊C₄×C₈₉	—	2	1	no	—
350	C₄⋊C₄×C₈₉	—	2	2	no	—
351	C₄⋊C₄×C₈₉	—	2	2	no	—
352	C₄⋊C₄×C₈₉	—	2	2	no	—
353	C₄⋊C₄×C₈₉	—	2	1	no	—
354	C₄⋊C₄×C₈₉	—	2	1	no	—
355	C₄⋊C₄×C₈₉	—	2	2	no	—
356	C₄⋊C₄×C₈₉	—	2	2	no	—
357	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
358	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
359	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
363	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
367	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
368	C₂²⋊C₄×C₈₉	—	2	2	no	—
369	C₂²⋊C₄×C₈₉	—	2	1	no	—
370	C₂²⋊C₄×C₈₉	—	2	1	no	—
371	C₂²⋊C₄×C₈₉	—	2	2	no	—
372	C₂²⋊C₄×C₈₉	—	2	2	no	—
373	C₂²⋊C₄×C₈₉	—	2	2	no	—
374	C₂²⋊C₄×C₈₉	—	2	2	no	—
375	C₂²⋊C₄×C₈₉	—	2	2	no	—
376	C₂²⋊C₄×C₈₉	—	2	2	no	—
377	C₂²⋊C₄×C₈₉	—	2	2	no	—
378	C₂²⋊C₄×C₈₉	—	2	2	no	—
379	C₂²⋊C₄×C₈₉	—	2	2	no	—
380	C₂²⋊C₄×C₈₉	—	2	2	no	—
381	C₂²⋊C₄×C₈₉	—	2	2	no	—
382	C₂²⋊C₄×C₈₉	—	2	2	no	—
383	C₂²⋊C₄×C₈₉	—	2	2	no	—
384	C₂²⋊C₄×C₈₉	—	2	2	no	—
385	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
386	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
387	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
388	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
389	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
390	C₄²×C₈₉	—	2	2	no	—
391	C₄²×C₈₉	—	2	1	no	—
392	C₄²×C₈₉	—	2	1	no	—
393	C₄²×C₈₉	—	2	2	no	—
394	C₄²×C₈₉	—	2	2	no	—
395	C₄²×C₈₉	—	2	2	no	—
396	C₄²×C₈₉	—	2	2	no	—
397	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
400	C₄²×C₈₉	C₂⁴	1	2	yes	—
401	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
402	C₂³×C₈₉	—	2	2	no	—
403	C₂³×C₈₉	—	2	2	no	—
404	C₂³×C₈₉	—	4	2	no	—
405	C₂³×C₈₉	—	8	1	no	—
406	C₂³×C₈₉	—	8	2	no	—
407	C₂³×C₈₉	—	8	2	no	—
408	C₂³×C₈₉	—	8	1	no	—
409	C₂³×C₈₉	—	8	2	no	—
410	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
411	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
412	Q₈×C₈₉	—	2	2	no	—
413	Q₈×C₈₉	—	2	2	no	—
414	Q₈×C₈₉	—	2	2	no	—
415	Q₈×C₈₉	—	2	2	no	—
416	Q₈×C₈₉	—	4	1	no	—
417	Q₈×C₈₉	—	4	2	no	—
418	Q₈×C₈₉	—	8	1	no	—
419	Q₈×C₈₉	—	8	1	no	—
420	Q₈×C₈₉	—	8	2	no	—
421	Q₈×C₈₉	—	8	1	no	—
422	Q₈×C₈₉	—	8	1	no	—
423	D₄×C₈₉	—	2	2	no	—
424	D₄×C₈₉	—	2	2	no	—
425	D₄×C₈₉	—	2	2	no	—
426	D₄×C₈₉	—	2	2	no	—
427	D₄×C₈₉	—	4	2	no	—
428	D₄×C₈₉	—	4	1	no	—
429	D₄×C₈₉	—	4	4	no	—
430	D₄×C₈₉	—	8	1	no	—
431	D₄×C₈₉	—	8	2	no	—
432	D₄×C₈₉	—	8	2	no	—
433	D₄×C₈₉	—	8	1	no	—
434	D₄×C₈₉	—	8	2	no	—
435	D₄×C₈₉	—	8	1	no	—
436	D₄×C₈₉	—	8	2	no	—
437	D₄×C₈₉	—	8	2	no	—
438	C₂×C₄×C₈₉	—	2	2	no	—
439	C₂×C₄×C₈₉	—	2	2	no	—
440	C₂×C₄×C₈₉	—	2	2	no	—
441	C₂×C₄×C₈₉	—	2	1	no	—
442	C₂×C₄×C₈₉	—	2	1	no	—
443	C₂×C₄×C₈₉	—	2	2	no	—
444	C₂×C₄×C₈₉	—	2	1	no	—
445	C₂×C₄×C₈₉	—	2	2	no	—
446	C₂×C₄×C₈₉	—	2	2	no	—
447	C₂×C₄×C₈₉	—	2	2	no	—
448	C₂×C₄×C₈₉	—	2	1	no	—
449	C₂×C₄×C₈₉	—	4	1	no	—
450	C₂×C₄×C₈₉	—	4	1	no	—
451	C₂×C₄×C₈₉	—	8	2	no	—
452	C₂×C₄×C₈₉	—	8	2	no	—
453	C₂×C₄×C₈₉	—	8	2	no	—
454	C₂×C₄×C₈₉	—	8	2	no	—
455	C₂×C₄×C₈₉	—	8	1	no	—
456	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
459	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
460	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
461	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
465	C₈×C₈₉	—	2	2	no	—
466	C₈×C₈₉	—	2	2	no	—
467	C₈×C₈₉	—	2	2	no	—
468	C₈×C₈₉	—	2	2	no	—
469	C₂²×C₈₉	—	2	1	no	—
470	C₂²×C₈₉	—	2	2	no	—
471	C₂²×C₈₉	—	2	1	no	—
472	C₂²×C₈₉	—	2	2	no	—
473	C₂²×C₈₉	—	2	1	no	—
474	C₂²×C₈₉	—	2	2	no	—
475	C₂²×C₈₉	—	4	2	no	—
476	C₂²×C₈₉	—	4	2	no	—
477	C₂²×C₈₉	—	4	2	no	—
478	C₂²×C₈₉	—	4	2	no	—
479	C₂²×C₈₉	—	4	2	no	—
480	C₂²×C₈₉	—	4	2	no	—
481	C₂²×C₈₉	—	16	2	no	—
482	C₂²×C₈₉	—	16	4	no	—
483	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
484	C₄×C₈₉	—	2	1	no	—
485	C₄×C₈₉	—	2	1	no	—
486	C₄×C₈₉	—	2	2	no	—
487	C₄×C₈₉	—	2	1	no	—
488	C₄×C₈₉	—	2	1	no	—
489	C₄×C₈₉	—	2	2	no	—
490	C₄×C₈₉	—	2	2	no	—
491	C₄×C₈₉	—	2	1	no	—
492	C₄×C₈₉	—	4	2	no	—
493	C₄×C₈₉	—	4	1	no	—
494	C₄×C₈₉	—	4	2	no	—
495	C₄×C₈₉	—	4	1	no	—
496	C₄×C₈₉	—	4	2	no	—
497	C₄×C₈₉	—	4	2	no	—
498	C₄×C₈₉	—	4	1	no	—
499	C₄×C₈₉	—	4	1	no	—
500	C₄×C₈₉	#585	1	2	yes	—
501	#62568	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
502	C₂×C₈₉	—	4	1	no	—
503	C₂×C₈₉	—	4	2	no	—
504	C₂×C₈₉	—	8	2	no	—
505	C₂×C₈₉	—	8	2	no	—
506	C₂×C₈₉	#3500	1	1	yes	characteristic
507	C₂×C₈₉	#3585	1	1	yes	characteristic
508	C₂×C₈₉	#3586	1	1	yes	characteristic
509	#3558	C₂×C₈₉	1	1	yes	characteristic
510	#3555	C₂×C₈₉	1	1	yes	characteristic, complemented
511	#3375	C₂×C₈₉	1	2	yes	complemented
512	#3371	C₂×C₈₉	1	2	yes	complemented
513	#3327	C₂×C₈₉	1	2	yes	complemented
514	#3324	C₂×C₈₉	1	2	yes	complemented
515	#3314	C₂×C₈₉	1	2	yes	complemented
516	#3313	C₂×C₈₉	1	2	yes	complemented
517	#3311	C₂×C₈₉	1	2	yes	complemented
518	#3310	C₂×C₈₉	1	2	yes	complemented
519	#3243	C₂×C₈₉	1	2	yes	complemented
520	#3235	C₂×C₈₉	1	1	yes	characteristic, complemented
521	#3222	C₂×C₈₉	1	2	yes	complemented
522	#3215	C₂×C₈₉	1	1	yes	characteristic, complemented
523	#3182	C₂×C₈₉	1	1	yes	characteristic, complemented
524	#3178	C₂×C₈₉	1	2	yes	complemented
525	#3140	C₂×C₈₉	1	1	yes	characteristic, complemented
526	#3136	C₂×C₈₉	1	2	yes	complemented
527	#2967	C₂×C₈₉	1	1	yes	characteristic, complemented
528	C₈₉	#62568	1	1	yes	characteristic, direct product factor, Sylow
529	#563	—	2	2	no	—
530	#562	—	2	1	no	—
531	H(3,𝔽₄)	—	2	1	no	—
532	#559	C₂²×C₈₉	1	2	yes	—
533	Q₈²	C₂²×C₈₉	1	1	yes	characteristic, complemented
534	#557	—	2	1	no	—
535	#557	C₂²×C₈₉	1	1	yes	characteristic, complemented
536	#556	—	2	1	no	—
537	#556	C₂²×C₈₉	1	1	yes	characteristic, complemented
538	#556	C₂²×C₈₉	1	2	yes	complemented
539	#554	C₂²×C₈₉	1	1	yes	characteristic, complemented
540	#552	C₂²×C₈₉	1	2	yes	complemented
541	#548	C₂²×C₈₉	1	2	yes	—
542	#546	—	2	2	no	—
543	#546	C₂²×C₈₉	1	2	yes	—
544	D₄²	C₂²×C₈₉	1	2	yes	—
545	#544	C₂²×C₈₉	1	2	yes	complemented
546	#542	—	2	1	no	—
547	#542	C₂²×C₈₉	1	2	yes	—
548	#541	—	2	2	no	—
549	#541	—	2	1	no	—
550	#541	C₂²×C₈₉	1	2	yes	complemented
551	#538	—	2	2	no	—
552	#538	—	2	1	no	—
553	#535	C₂²×C₈₉	1	2	yes	—
554	#534	—	2	1	no	—
555	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
556	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
557	#532	C₂²×C₈₉	1	1	yes	characteristic
558	#529	C₂²×C₈₉	1	1	yes	characteristic
559	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
560	#501	C₂²×C₈₉	1	2	yes	complemented
561	#500	C₂²×C₈₉	1	1	yes	characteristic, complemented
562	#497	C₂²×C₈₉	1	2	yes	complemented
563	#492	C₂²×C₈₉	1	1	yes	characteristic, complemented
564	#490	C₂²×C₈₉	1	2	yes	—
565	#490	C₂²×C₈₉	1	2	yes	complemented
566	#489	C₂²×C₈₉	1	2	yes	complemented
567	#489	C₂²×C₈₉	1	2	yes	complemented
568	#489	C₂²×C₈₉	1	2	yes	complemented
569	#489	C₂²×C₈₉	1	2	yes	complemented
570	#488	C₂²×C₈₉	1	2	yes	complemented
571	#488	C₂²×C₈₉	1	2	yes	complemented
572	#488	C₂²×C₈₉	1	2	yes	complemented
573	#487	C₂²×C₈₉	1	1	yes	characteristic, complemented
574	#486	C₂²×C₈₉	1	2	yes	—
575	#486	C₂²×C₈₉	1	1	yes	characteristic, complemented
576	#485	C₂²×C₈₉	1	2	yes	complemented
577	#484	C₂²×C₈₉	1	2	yes	complemented
578	#482	C₂²×C₈₉	1	2	yes	—
579	#482	C₂²×C₈₉	1	2	yes	complemented
580	#482	C₂²×C₈₉	1	2	yes	complemented
581	#480	C₂²×C₈₉	1	2	yes	—
582	#479	C₂²×C₈₉	1	2	yes	complemented
583	#478	C₂²×C₈₉	1	2	yes	complemented
584	#477	C₂²×C₈₉	1	2	yes	complemented
585	#476	C₂²×C₈₉	1	2	yes	complemented
586	#474	C₂²×C₈₉	1	2	yes	complemented
587	#474	C₂²×C₈₉	1	2	yes	complemented
588	#470	C₂²×C₈₉	1	2	yes	complemented
589	#468	C₂²×C₈₉	1	2	yes	—
590	#468	C₂²×C₈₉	1	2	yes	complemented
591	#468	C₂²×C₈₉	1	2	yes	complemented
592	#467	C₂²×C₈₉	1	2	yes	complemented
593	#465	C₂²×C₈₉	1	2	yes	—
594	#464	C₂²×C₈₉	1	2	yes	complemented
595	#464	C₂²×C₈₉	1	2	yes	complemented
596	#464	C₂²×C₈₉	1	2	yes	complemented
597	#464	C₂²×C₈₉	1	2	yes	complemented
598	#460	C₂²×C₈₉	1	2	yes	—
599	#460	C₂²×C₈₉	1	2	yes	—
600	#452	C₂²×C₈₉	1	2	yes	complemented
601	#452	C₂²×C₈₉	1	2	yes	complemented
602	#451	C₂²×C₈₉	1	1	yes	characteristic, complemented
603	#451	C₂²×C₈₉	1	1	yes	characteristic, complemented
604	#450	C₂²×C₈₉	1	1	yes	characteristic
605	#450	C₂²×C₈₉	1	1	yes	characteristic
606	#450	C₂²×C₈₉	1	2	yes	complemented
607	#450	C₂²×C₈₉	1	2	yes	complemented
608	#446	C₂²×C₈₉	1	2	yes	complemented
609	#441	C₂²×C₈₉	1	2	yes	complemented
610	#440	C₂²×C₈₉	1	2	yes	complemented
611	#440	C₂²×C₈₉	1	2	yes	complemented
612	#440	C₂²×C₈₉	1	2	yes	complemented
613	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
614	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
615	#436	C₂²×C₈₉	1	2	yes	complemented
616	#435	C₂²×C₈₉	1	2	yes	complemented
617	#435	C₂²×C₈₉	1	2	yes	complemented
618	#433	C₂²×C₈₉	1	2	yes	complemented
619	#432	C₂²×C₈₉	1	1	yes	characteristic, complemented
620	#419	C₂²×C₈₉	1	2	yes	complemented
621	#418	C₂²×C₈₉	1	2	yes	—
622	#418	C₂²×C₈₉	1	2	yes	complemented
623	#417	C₂²×C₈₉	1	2	yes	complemented
624	#416	C₂²×C₈₉	1	2	yes	complemented
625	C₂×#102	C₂²×C₈₉	1	2	yes	complemented
626	#405	C₂²×C₈₉	1	2	yes	complemented
627	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
628	C₂×#41	—	2	1	no	—
629	C₂×#41	C₂³×C₈₉	1	2	yes	—
630	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
631	C₂²×D₄	—	2	2	no	—
632	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
633	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
634	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
635	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
636	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
637	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
638	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
639	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
640	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
641	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
642	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
643	C₄⋊Q₈	—	2	1	no	—
644	C₄⋊Q₈	—	2	2	no	—
645	C₄⋊Q₈	—	2	1	no	—
646	C₄⋊Q₈	—	2	2	no	—
647	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
648	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
649	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
650	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
651	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
652	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
653	#127	C₂³×C₈₉	1	1	yes	characteristic
654	#127	C₂³×C₈₉	1	2	yes	—
655	#126	—	2	2	no	—
656	#126	—	2	2	no	—
657	#126	—	2	2	no	—
658	#126	—	2	2	no	—
659	#126	—	2	2	no	—
660	#126	—	2	2	no	—
661	#126	—	2	2	no	—
662	#126	D₄×C₈₉	1	2	yes	—
663	#125	—	2	2	no	—
664	#125	—	2	2	no	—
665	#125	—	2	2	no	—
666	#125	—	2	1	no	—
667	#125	—	2	2	no	—
668	#125	—	2	2	no	—
669	#125	—	2	1	no	—
670	#125	D₄×C₈₉	1	1	yes	characteristic
671	#125	C₂³×C₈₉	1	2	yes	—
672	#125	C₂³×C₈₉	1	2	yes	—
673	#124	—	2	2	no	—
674	#124	—	2	1	no	—
675	#124	—	2	2	no	—
676	#124	—	2	2	no	—
677	#124	—	2	2	no	—
678	#124	—	2	1	no	—
679	#124	—	2	1	no	—
680	#124	—	2	1	no	—
681	#124	D₄×C₈₉	1	1	yes	characteristic
682	#124	C₂³×C₈₉	1	2	yes	—
683	#124	C₂³×C₈₉	1	2	yes	—
684	#124	C₂³×C₈₉	1	2	yes	—
685	#123	—	2	2	no	—
686	#123	—	2	2	no	—
687	#123	—	2	2	no	—
688	#123	—	2	2	no	—
689	#123	—	2	2	no	—
690	#123	D₄×C₈₉	1	2	yes	—
691	C₂²⋊Q₈	—	2	1	no	—
692	C₂²⋊Q₈	—	2	1	no	—
693	C₂²⋊Q₈	—	2	1	no	—
694	C₂²⋊Q₈	—	2	2	no	—
695	C₂²⋊Q₈	—	2	2	no	—
696	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	—	2	2	no	—
698	C₂²⋊Q₈	—	2	2	no	—
699	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
700	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
701	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
702	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
703	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
704	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
705	#121	—	2	2	no	—
706	#121	—	2	1	no	—
707	#121	—	2	2	no	—
708	#121	—	2	2	no	—
709	#121	—	2	2	no	—
710	#121	—	2	2	no	—
711	#121	D₄×C₈₉	1	1	yes	characteristic
712	#121	C₂³×C₈₉	1	2	yes	—
713	#121	C₂³×C₈₉	1	2	yes	—
714	#120	—	2	2	no	—
715	#120	—	2	2	no	—
716	#120	—	2	2	no	—
717	#120	—	2	2	no	—
718	#120	—	2	2	no	—
719	C₄×Q₈	—	2	1	no	—
720	C₄×Q₈	—	2	2	no	—
721	C₄×Q₈	—	2	1	no	—
722	C₄×Q₈	—	2	1	no	—
723	C₄×Q₈	—	2	1	no	—
724	C₄×Q₈	—	2	1	no	—
725	C₄×Q₈	—	2	1	no	—
726	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
727	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
728	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
729	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
730	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
731	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
732	C₄×D₄	—	2	1	no	—
733	C₄×D₄	—	2	2	no	—
734	C₄×D₄	—	2	2	no	—
735	C₄×D₄	—	2	1	no	—
736	C₄×D₄	C₂³×C₈₉	1	2	yes	—
737	C₄×D₄	C₂³×C₈₉	1	2	yes	—
738	C₄×D₄	C₂³×C₈₉	1	2	yes	—
739	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
740	#117	—	2	1	no	—
741	#117	—	2	2	no	—
742	#117	C₂³×C₈₉	1	2	yes	—
743	#117	C₂³×C₈₉	1	2	yes	—
744	#117	C₂³×C₈₉	1	2	yes	—
745	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
746	C₂×C₂²⋊C₄	—	2	1	no	—
747	C₂×C₂²⋊C₄	—	2	1	no	—
748	C₂×C₂²⋊C₄	—	2	2	no	—
749	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
750	#107	C₂³×C₈₉	1	2	yes	—
751	#107	C₂³×C₈₉	1	2	yes	—
752	#107	C₂³×C₈₉	1	2	yes	—
753	#107	C₂³×C₈₉	1	2	yes	—
754	#106	C₂³×C₈₉	1	2	yes	—
755	#106	C₂³×C₈₉	1	2	yes	—
756	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
757	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
758	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
759	#103	C₂³×C₈₉	1	2	yes	—
760	#103	C₂³×C₈₉	1	2	yes	—
761	#103	C₂³×C₈₉	1	2	yes	—
762	#103	C₂³×C₈₉	1	2	yes	—
763	#103	C₂³×C₈₉	1	2	yes	—
764	#103	C₂³×C₈₉	1	2	yes	—
765	#103	C₂³×C₈₉	1	2	yes	—
766	#103	C₂³×C₈₉	1	2	yes	—
767	#102	C₂³×C₈₉	1	2	yes	—
768	#102	C₂³×C₈₉	1	2	yes	—
769	#102	C₂³×C₈₉	1	2	yes	—
770	#102	C₂³×C₈₉	1	2	yes	—
771	#102	C₂³×C₈₉	1	2	yes	—
772	#102	C₂³×C₈₉	1	2	yes	—
773	#102	C₂³×C₈₉	1	2	yes	—
774	#102	C₂³×C₈₉	1	2	yes	—
775	#102	C₂³×C₈₉	1	2	yes	—
776	#102	C₂³×C₈₉	1	2	yes	—
777	#102	C₂³×C₈₉	1	2	yes	—
778	#102	C₂³×C₈₉	1	2	yes	—
779	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
780	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
781	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
782	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
783	#97	C₂³×C₈₉	1	2	yes	—
784	#97	C₂³×C₈₉	1	2	yes	—
785	#97	C₂³×C₈₉	1	2	yes	—
786	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
787	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
788	C₄×C₈	C₂³×C₈₉	1	2	yes	—
789	C₂⁴	—	2	1	no	—
790	C₂⁴	—	2	2	no	—
791	#41	—	4	2	no	—
792	#41	—	4	2	no	—
793	#41	—	8	2	no	—
794	C₂×Q₈	—	2	1	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	2	1	no	—
797	C₂×Q₈	—	2	2	no	—
798	C₂×Q₈	—	2	1	no	—
799	C₂×Q₈	—	2	1	no	—
800	C₂×Q₈	—	4	2	no	—
801	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
802	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
803	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
804	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
805	C₂×D₄	—	2	2	no	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	2	2	no	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	1	no	—
810	C₂×D₄	—	2	1	no	—
811	C₂×D₄	—	2	1	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	4	2	no	—
815	C₂×D₄	—	4	2	no	—
816	C₂×D₄	—	4	2	no	—
817	C₂×D₄	—	8	4	no	—
818	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
819	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
820	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
821	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
822	C₂²×C₄	—	2	1	no	—
823	C₂²×C₄	—	2	2	no	—
824	C₂²×C₄	—	2	2	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
828	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
831	Q₁₆	—	4	2	no	—
832	Q₁₆	—	4	2	no	—
833	SD₁₆	—	4	2	no	—
834	SD₁₆	—	4	2	no	—
835	SD₁₆	—	4	2	no	—
836	SD₁₆	—	4	2	no	—
837	M₁₆	—	4	2	no	—
838	M₁₆	—	4	2	no	—
839	C₂×C₈	—	4	2	no	—
840	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
841	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
842	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
843	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	1	no	—
846	C₄⋊C₄	—	2	1	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	1	no	—
849	C₄⋊C₄	—	2	1	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	1	no	—
852	C₄⋊C₄	—	2	1	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	1	no	—
858	C₄⋊C₄	—	2	1	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	1	no	—
863	C₄⋊C₄	—	2	1	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
867	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
868	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
869	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
870	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
871	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
872	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
873	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
874	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
875	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
876	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	1	no	—
879	C₂²⋊C₄	—	2	1	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
895	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
896	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
897	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
898	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
899	C₄²	—	2	2	no	—
900	C₄²	—	2	1	no	—
901	C₄²	—	2	1	no	—
902	C₄²	—	2	2	no	—
903	C₄²	—	2	2	no	—
904	C₄²	—	2	2	no	—
905	C₄²	—	2	2	no	—
906	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
907	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
908	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
909	C₄²	C₂⁴×C₈₉	1	2	yes	—
910	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
911	C₂³	—	2	2	no	—
912	C₂³	—	2	2	no	—
913	C₂³	—	4	2	no	—
914	C₂³	—	8	1	no	—
915	C₂³	—	8	2	no	—
916	C₂³	—	8	2	no	—
917	C₂³	—	8	1	no	—
918	C₂³	—	8	2	no	—
919	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
920	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
921	Q₈	—	2	2	no	—
922	Q₈	—	2	2	no	—
923	Q₈	—	2	2	no	—
924	Q₈	—	2	2	no	—
925	Q₈	—	4	1	no	—
926	Q₈	—	4	2	no	—
927	Q₈	—	8	1	no	—
928	Q₈	—	8	1	no	—
929	Q₈	—	8	2	no	—
930	Q₈	—	8	1	no	—
931	Q₈	—	8	1	no	—
932	D₄	—	2	2	no	—
933	D₄	—	2	2	no	—
934	D₄	—	2	2	no	—
935	D₄	—	2	2	no	—
936	D₄	—	4	2	no	—
937	D₄	—	4	1	no	—
938	D₄	—	4	4	no	—
939	D₄	—	8	1	no	—
940	D₄	—	8	2	no	—
941	D₄	—	8	2	no	—
942	D₄	—	8	1	no	—
943	D₄	—	8	2	no	—
944	D₄	—	8	1	no	—
945	D₄	—	8	2	no	—
946	D₄	—	8	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	4	1	no	—
959	C₂×C₄	—	4	1	no	—
960	C₂×C₄	—	8	2	no	—
961	C₂×C₄	—	8	2	no	—
962	C₂×C₄	—	8	2	no	—
963	C₂×C₄	—	8	2	no	—
964	C₂×C₄	—	8	1	no	—
965	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
966	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
967	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
968	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
969	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
970	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
971	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
972	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
973	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
974	C₈	—	2	2	no	—
975	C₈	—	2	2	no	—
976	C₈	—	2	2	no	—
977	C₈	—	2	2	no	—
978	C₂²	—	2	1	no	—
979	C₂²	—	2	2	no	—
980	C₂²	—	2	1	no	—
981	C₂²	—	2	2	no	—
982	C₂²	—	2	1	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	4	2	no	—
986	C₂²	—	4	2	no	—
987	C₂²	—	4	2	no	—
988	C₂²	—	4	2	no	—
989	C₂²	—	4	2	no	—
990	C₂²	—	16	2	no	—
991	C₂²	—	16	4	no	—
992	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
993	C₄	—	2	1	no	—
994	C₄	—	2	1	no	—
995	C₄	—	2	2	no	—
996	C₄	—	2	1	no	—
997	C₄	—	2	1	no	—
998	C₄	—	2	2	no	—
999	C₄	—	2	2	no	—
1000	C₄	—	2	1	no	—
1001	C₄	—	4	2	no	—
1002	C₄	—	4	1	no	—
1003	C₄	—	4	2	no	—
1004	C₄	—	4	1	no	—
1005	C₄	—	4	2	no	—
1006	C₄	—	4	2	no	—
1007	C₄	—	4	1	no	—
1008	C₄	—	4	1	no	—
1009	C₄	#585×C₈₉	1	2	yes	—
1010	C₂	—	4	1	no	—
1011	C₂	—	4	2	no	—
1012	C₂	—	8	2	no	—
1013	C₂	—	8	2	no	—
1014	C₂	C₈₉×#3500	1	1	yes	characteristic
1015	C₂	C₈₉×#3585	1	1	yes	characteristic
1016	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×#3558	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ #529×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₉×#3555	C₂	semidirect
3. C₈₉×#3375	C₂	semidirect
4. C₈₉×#3371	C₂	semidirect
5. C₈₉×#3327	C₂	semidirect
6. C₈₉×#3324	C₂	semidirect
7. C₈₉×#3314	C₂	semidirect
8. C₈₉×#3313	C₂	semidirect
9. C₈₉×#3311	C₂	semidirect
10. C₈₉×#3310	C₂	semidirect
11. C₈₉×#3243	C₂	semidirect
12. C₈₉×#3235	C₂	semidirect
13. C₈₉×#3222	C₂	semidirect
14. C₈₉×#3215	C₂	semidirect
15. C₈₉×#3182	C₂	semidirect
16. C₈₉×#3178	C₂	semidirect
17. C₈₉×#3140	C₂	semidirect
18. C₈₉×#3136	C₂	semidirect
19. C₈₉×#2967	C₂	semidirect
24. Q₈²×C₈₉	C₂²	semidirect
26. #557×C₈₉	C₂²	semidirect
28. #556×C₈₉	C₂²	semidirect
29. #556×C₈₉	C₂²	semidirect
30. #554×C₈₉	C₂²	semidirect
31. #552×C₈₉	C₂²	semidirect
36. #544×C₈₉	C₂²	semidirect
41. #541×C₈₉	C₂²	semidirect
46. #533×C₈₉	C₂²	semidirect
47. #533×C₈₉	C₂²	semidirect
51. #501×C₈₉	C₂²	semidirect
52. #500×C₈₉	C₂²	semidirect
53. #497×C₈₉	C₂²	semidirect
54. #492×C₈₉	C₂²	semidirect
56. #490×C₈₉	C₂²	semidirect
57. #489×C₈₉	C₂²	semidirect
58. #489×C₈₉	C₂²	semidirect
59. #489×C₈₉	C₂²	semidirect
60. #489×C₈₉	C₂²	semidirect
61. #488×C₈₉	C₂²	semidirect
62. #488×C₈₉	C₂²	semidirect
63. #488×C₈₉	C₂²	semidirect
64. #487×C₈₉	C₂²	semidirect
66. #486×C₈₉	C₂²	semidirect
67. #485×C₈₉	C₂²	semidirect
68. #484×C₈₉	C₂²	semidirect
70. #482×C₈₉	C₂²	semidirect
71. #482×C₈₉	C₂²	semidirect
73. #479×C₈₉	C₂²	semidirect
74. #478×C₈₉	C₂²	semidirect
75. #477×C₈₉	C₂²	semidirect
76. #476×C₈₉	C₂²	semidirect
77. #474×C₈₉	C₂²	semidirect
78. #474×C₈₉	C₂²	semidirect
79. #470×C₈₉	C₂²	semidirect
81. #468×C₈₉	C₂²	semidirect
82. #468×C₈₉	C₂²	semidirect
83. #467×C₈₉	C₂²	semidirect
85. #464×C₈₉	C₂²	semidirect
86. #464×C₈₉	C₂²	semidirect
87. #464×C₈₉	C₂²	semidirect
88. #464×C₈₉	C₂²	semidirect
91. #452×C₈₉	C₂²	semidirect
92. #452×C₈₉	C₂²	semidirect
93. #451×C₈₉	C₂²	semidirect
94. #451×C₈₉	C₂²	semidirect
97. #450×C₈₉	C₂²	semidirect
98. #450×C₈₉	C₂²	semidirect
99. #446×C₈₉	C₂²	semidirect
100. #441×C₈₉	C₂²	semidirect
101. #440×C₈₉	C₂²	semidirect
102. #440×C₈₉	C₂²	semidirect
103. #440×C₈₉	C₂²	semidirect
104. C₄×Q₁₆×C₈₉	C₂²	semidirect
105. C₄×SD₁₆×C₈₉	C₂²	semidirect
106. #436×C₈₉	C₂²	semidirect
107. #435×C₈₉	C₂²	semidirect
108. #435×C₈₉	C₂²	semidirect
109. #433×C₈₉	C₂²	semidirect
110. #432×C₈₉	C₂²	semidirect
111. #419×C₈₉	C₂²	semidirect
113. #418×C₈₉	C₂²	semidirect
114. #417×C₈₉	C₂²	semidirect
115. #416×C₈₉	C₂²	semidirect
116. C₂×#102×C₈₉	C₂²	semidirect
117. #405×C₈₉	C₂²	semidirect
118. C₄×M₁₆×C₈₉	C₂²	semidirect
501. #62568	C₈₉	direct (N × H)
510. #3555	C₂×C₈₉	semidirect
511. #3375	C₂×C₈₉	semidirect
512. #3371	C₂×C₈₉	semidirect
513. #3327	C₂×C₈₉	semidirect
514. #3324	C₂×C₈₉	semidirect
515. #3314	C₂×C₈₉	semidirect
516. #3313	C₂×C₈₉	semidirect
517. #3311	C₂×C₈₉	semidirect
518. #3310	C₂×C₈₉	semidirect
519. #3243	C₂×C₈₉	semidirect
520. #3235	C₂×C₈₉	semidirect
521. #3222	C₂×C₈₉	semidirect
522. #3215	C₂×C₈₉	semidirect
523. #3182	C₂×C₈₉	semidirect
524. #3178	C₂×C₈₉	semidirect
525. #3140	C₂×C₈₉	semidirect
526. #3136	C₂×C₈₉	semidirect
527. #2967	C₂×C₈₉	semidirect
528. C₈₉	#62568	direct (N × H)
533. Q₈²	C₂²×C₈₉	semidirect
535. #557	C₂²×C₈₉	semidirect
537. #556	C₂²×C₈₉	semidirect
538. #556	C₂²×C₈₉	semidirect
539. #554	C₂²×C₈₉	semidirect
540. #552	C₂²×C₈₉	semidirect
545. #544	C₂²×C₈₉	semidirect
550. #541	C₂²×C₈₉	semidirect
555. #533	C₂²×C₈₉	semidirect
556. #533	C₂²×C₈₉	semidirect
560. #501	C₂²×C₈₉	semidirect
561. #500	C₂²×C₈₉	semidirect
562. #497	C₂²×C₈₉	semidirect
563. #492	C₂²×C₈₉	semidirect
565. #490	C₂²×C₈₉	semidirect
566. #489	C₂²×C₈₉	semidirect
567. #489	C₂²×C₈₉	semidirect
568. #489	C₂²×C₈₉	semidirect
569. #489	C₂²×C₈₉	semidirect
570. #488	C₂²×C₈₉	semidirect
571. #488	C₂²×C₈₉	semidirect
572. #488	C₂²×C₈₉	semidirect
573. #487	C₂²×C₈₉	semidirect
575. #486	C₂²×C₈₉	semidirect
576. #485	C₂²×C₈₉	semidirect
577. #484	C₂²×C₈₉	semidirect
579. #482	C₂²×C₈₉	semidirect
580. #482	C₂²×C₈₉	semidirect
582. #479	C₂²×C₈₉	semidirect
583. #478	C₂²×C₈₉	semidirect
584. #477	C₂²×C₈₉	semidirect
585. #476	C₂²×C₈₉	semidirect
586. #474	C₂²×C₈₉	semidirect
587. #474	C₂²×C₈₉	semidirect
588. #470	C₂²×C₈₉	semidirect
590. #468	C₂²×C₈₉	semidirect
591. #468	C₂²×C₈₉	semidirect
592. #467	C₂²×C₈₉	semidirect
594. #464	C₂²×C₈₉	semidirect
595. #464	C₂²×C₈₉	semidirect
596. #464	C₂²×C₈₉	semidirect
597. #464	C₂²×C₈₉	semidirect
600. #452	C₂²×C₈₉	semidirect
601. #452	C₂²×C₈₉	semidirect
602. #451	C₂²×C₈₉	semidirect
603. #451	C₂²×C₈₉	semidirect
606. #450	C₂²×C₈₉	semidirect
607. #450	C₂²×C₈₉	semidirect
608. #446	C₂²×C₈₉	semidirect
609. #441	C₂²×C₈₉	semidirect
610. #440	C₂²×C₈₉	semidirect
611. #440	C₂²×C₈₉	semidirect
612. #440	C₂²×C₈₉	semidirect
613. C₄×Q₁₆	C₂²×C₈₉	semidirect
614. C₄×SD₁₆	C₂²×C₈₉	semidirect
615. #436	C₂²×C₈₉	semidirect
616. #435	C₂²×C₈₉	semidirect
617. #435	C₂²×C₈₉	semidirect
618. #433	C₂²×C₈₉	semidirect
619. #432	C₂²×C₈₉	semidirect
620. #419	C₂²×C₈₉	semidirect
622. #418	C₂²×C₈₉	semidirect
623. #417	C₂²×C₈₉	semidirect
624. #416	C₂²×C₈₉	semidirect
625. C₂×#102	C₂²×C₈₉	semidirect
626. #405	C₂²×C₈₉	semidirect
627. C₄×M₁₆	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×#3558	2
C₈₉×#3555	2
C₈₉×#3375	2
C₈₉×#3371	2
C₈₉×#3327	2
C₈₉×#3324	2
C₈₉×#3314	2
C₈₉×#3313	2
C₈₉×#3311	2
C₈₉×#3310	2
C₈₉×#3243	2
C₈₉×#3235	2
C₈₉×#3222	2
C₈₉×#3215	2
C₈₉×#3182	2
C₈₉×#3178	2
C₈₉×#3140	2
C₈₉×#3136	2
C₈₉×#2967	2
#62568	89

Subgroups — C89×#62568 #36440416

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62568 #36440416