Subgroups — C₈₉×#62144 #36439992

Order 22784.

1774 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3481	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3381	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3365	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3356	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3351	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3324	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3323	C₂	1	4	yes	maximal, complemented
9	C₈₉×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3252	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3233	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3227	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3107	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3101	C₂	1	2	yes	maximal, complemented
15	C₈₉×#3079	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#3077	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2991	C₂	1	1	yes	maximal, characteristic, complemented
18	#559×C₈₉	C₂²	1	1	yes	characteristic
19	#557×C₈₉	—	2	1	no	—
20	#557×C₈₉	C₂²	1	2	yes	complemented
21	#556×C₈₉	—	2	1	no	—
22	#556×C₈₉	C₂²	1	2	yes	—
23	#554×C₈₉	C₂²	1	1	yes	characteristic
24	#554×C₈₉	C₂²	1	1	yes	characteristic
25	#553×C₈₉	—	2	1	no	—
26	#553×C₈₉	C₂²	1	2	yes	—
27	#552×C₈₉	—	2	2	no	—
28	#552×C₈₉	C₂²	1	4	yes	complemented
29	#551×C₈₉	—	2	2	no	—
30	#546×C₈₉	—	2	1	no	—
31	#546×C₈₉	C₂²	1	2	yes	—
32	D₄²×C₈₉	C₂²	1	1	yes	characteristic
33	#541×C₈₉	—	2	2	no	—
34	#536×C₈₉	—	2	1	no	—
35	#533×C₈₉	C₂²	1	2	yes	complemented
36	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
37	#533×C₈₉	C₂²	1	2	yes	complemented
38	#532×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
40	#529×C₈₉	—	2	1	no	—
41	#529×C₈₉	C₂²	1	2	yes	—
42	#525×C₈₉	—	2	2	no	—
43	#519×C₈₉	—	2	1	no	—
44	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
45	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₈₉	—	2	1	no	—
47	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
48	#499×C₈₉	C₂²	1	4	yes	complemented
49	#498×C₈₉	C₂²	1	2	yes	complemented
50	#488×C₈₉	C₂²	1	4	yes	complemented
51	#486×C₈₉	C₂²	1	2	yes	—
52	#485×C₈₉	C₂²	1	4	yes	complemented
53	#485×C₈₉	C₂²	1	2	yes	complemented
54	#483×C₈₉	C₂²	1	4	yes	complemented
55	#482×C₈₉	C₂²	1	4	yes	—
56	#481×C₈₉	C₂²	1	4	yes	complemented
57	#479×C₈₉	C₂²	1	4	yes	complemented
58	#478×C₈₉	C₂²	1	4	yes	—
59	#478×C₈₉	C₂²	1	4	yes	complemented
60	#477×C₈₉	C₂²	1	2	yes	complemented
61	#477×C₈₉	C₂²	1	2	yes	complemented
62	#476×C₈₉	C₂²	1	2	yes	—
63	#476×C₈₉	C₂²	1	2	yes	complemented
64	#476×C₈₉	C₂²	1	2	yes	complemented
65	#475×C₈₉	C₂²	1	2	yes	complemented
66	#475×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#474×C₈₉	C₂²	1	2	yes	—
68	#474×C₈₉	C₂²	1	1	yes	characteristic
69	#474×C₈₉	C₂²	1	2	yes	complemented
70	#470×C₈₉	C₂²	1	4	yes	complemented
71	#468×C₈₉	C₂²	1	4	yes	—
72	#468×C₈₉	C₂²	1	4	yes	complemented
73	#464×C₈₉	C₂²	1	4	yes	complemented
74	#462×C₈₉	C₂²	1	1	yes	characteristic, complemented
75	#461×C₈₉	C₂²	1	1	yes	characteristic
76	#461×C₈₉	C₂²	1	2	yes	complemented
77	#460×C₈₉	C₂²	1	2	yes	—
78	#452×C₈₉	C₂²	1	2	yes	—
79	#450×C₈₉	C₂²	1	4	yes	—
80	C₈×Q₈×C₈₉	C₂²	1	2	yes	complemented
81	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
82	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	—
83	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
84	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	complemented
85	#436×C₈₉	C₂²	1	2	yes	—
86	#436×C₈₉	C₂²	1	4	yes	complemented
87	#431×C₈₉	C₂²	1	2	yes	complemented
88	#431×C₈₉	C₂²	1	1	yes	characteristic, complemented
89	#428×C₈₉	C₂²	1	4	yes	complemented
90	#428×C₈₉	C₂²	1	2	yes	complemented
91	#423×C₈₉	C₂²	1	2	yes	complemented
92	#423×C₈₉	C₂²	1	1	yes	characteristic, complemented
93	#418×C₈₉	C₂²	1	4	yes	—
94	#417×C₈₉	C₂²	1	2	yes	—
95	C₂×#41×C₈₉	—	2	1	no	—
96	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
97	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₈₉	—	2	1	no	—
99	C₂²×D₄×C₈₉	—	2	1	no	—
100	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
101	C₂³×C₄×C₈₉	—	2	2	no	—
102	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
105	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
106	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
107	C₄⋊Q₈×C₈₉	—	2	2	no	—
108	C₄⋊Q₈×C₈₉	—	2	1	no	—
109	C₄⋊Q₈×C₈₉	—	2	1	no	—
110	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
111	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
115	#127×C₈₉	C₂³	1	1	yes	characteristic
116	#126×C₈₉	—	2	2	no	—
117	#126×C₈₉	—	2	4	no	—
118	#126×C₈₉	—	2	4	no	—
119	#126×C₈₉	—	2	2	no	—
120	#125×C₈₉	—	2	1	no	—
121	#125×C₈₉	—	2	4	no	—
122	#125×C₈₉	—	2	4	no	—
123	#125×C₈₉	—	2	1	no	—
124	#125×C₈₉	—	2	2	no	—
125	#125×C₈₉	C₂³	1	4	yes	—
126	#125×C₈₉	C₂³	1	2	yes	—
127	#124×C₈₉	—	2	1	no	—
128	#124×C₈₉	—	2	2	no	—
129	#124×C₈₉	—	2	1	no	—
130	#124×C₈₉	C₂³	1	2	yes	—
131	#123×C₈₉	—	2	4	no	—
132	#123×C₈₉	—	2	2	no	—
133	#123×C₈₉	—	2	2	no	—
134	#123×C₈₉	—	2	2	no	—
135	#123×C₈₉	—	2	2	no	—
136	C₂²⋊Q₈×C₈₉	—	2	1	no	—
137	C₂²⋊Q₈×C₈₉	—	2	2	no	—
138	C₂²⋊Q₈×C₈₉	—	2	2	no	—
139	C₂²⋊Q₈×C₈₉	—	2	1	no	—
140	C₂²⋊Q₈×C₈₉	—	2	2	no	—
141	C₂²⋊Q₈×C₈₉	—	2	2	no	—
142	C₂²⋊Q₈×C₈₉	—	2	2	no	—
143	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
144	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
145	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
146	#121×C₈₉	—	2	2	no	—
147	#121×C₈₉	—	2	1	no	—
148	#121×C₈₉	—	2	1	no	—
149	#121×C₈₉	—	2	2	no	—
150	#121×C₈₉	C₂³	1	2	yes	—
151	#121×C₈₉	C₂³	1	2	yes	—
152	#120×C₈₉	—	2	2	no	—
153	#120×C₈₉	—	2	2	no	—
154	C₄×Q₈×C₈₉	—	2	2	no	—
155	C₄×Q₈×C₈₉	—	2	2	no	—
156	C₄×Q₈×C₈₉	—	2	2	no	—
157	C₄×Q₈×C₈₉	—	2	2	no	—
158	C₄×Q₈×C₈₉	—	2	2	no	—
159	C₄×Q₈×C₈₉	—	2	1	no	—
160	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
161	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
162	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
163	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
164	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
165	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
166	C₄×D₄×C₈₉	—	2	1	no	—
167	C₄×D₄×C₈₉	—	2	2	no	—
168	C₄×D₄×C₈₉	—	2	1	no	—
169	C₄×D₄×C₈₉	—	2	1	no	—
170	C₄×D₄×C₈₉	—	2	1	no	—
171	C₄×D₄×C₈₉	—	2	2	no	—
172	C₄×D₄×C₈₉	—	2	1	no	—
173	C₄×D₄×C₈₉	—	2	2	no	—
174	C₄×D₄×C₈₉	—	2	2	no	—
175	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
176	C₄×D₄×C₈₉	D₄	1	2	yes	—
177	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₈₉	C₂³	1	2	yes	—
179	C₄×D₄×C₈₉	C₂³	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	1	no	—
185	#117×C₈₉	—	2	2	no	—
186	#117×C₈₉	—	2	4	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	4	yes	—
192	#117×C₈₉	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
194	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
195	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
198	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
199	C₂×C₄²×C₈₉	—	2	1	no	—
200	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
201	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
202	#107×C₈₉	C₂³	1	2	yes	—
203	#107×C₈₉	C₂³	1	4	yes	—
204	#107×C₈₉	C₂³	1	4	yes	—
205	#106×C₈₉	C₂³	1	4	yes	—
206	#106×C₈₉	C₂³	1	4	yes	—
207	#106×C₈₉	C₂³	1	2	yes	—
208	#106×C₈₉	C₂³	1	4	yes	—
209	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
210	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
211	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
212	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
213	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
214	#103×C₈₉	C₂³	1	4	yes	—
215	#103×C₈₉	C₂³	1	4	yes	—
216	#103×C₈₉	C₂³	1	2	yes	—
217	#103×C₈₉	C₂³	1	2	yes	—
218	#103×C₈₉	C₂³	1	2	yes	—
219	#102×C₈₉	C₂³	1	4	yes	—
220	#102×C₈₉	C₂³	1	2	yes	—
221	#102×C₈₉	C₂³	1	4	yes	—
222	#102×C₈₉	C₂³	1	4	yes	—
223	#102×C₈₉	C₂³	1	4	yes	—
224	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
225	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
226	C₄×C₈×C₈₉	C₂³	1	2	yes	—
227	C₄×C₈×C₈₉	C₂³	1	4	yes	—
228	C₂⁴×C₈₉	—	2	2	no	—
229	#41×C₈₉	—	2	2	no	—
230	#41×C₈₉	—	4	2	no	—
231	#41×C₈₉	—	4	1	no	—
232	#41×C₈₉	—	8	2	no	—
233	C₂×Q₈×C₈₉	—	2	1	no	—
234	C₂×Q₈×C₈₉	—	2	2	no	—
235	C₂×Q₈×C₈₉	—	2	2	no	—
236	C₂×Q₈×C₈₉	—	2	1	no	—
237	C₂×Q₈×C₈₉	—	4	4	no	—
238	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
239	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
240	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
241	C₂×D₄×C₈₉	—	2	4	no	—
242	C₂×D₄×C₈₉	—	2	1	no	—
243	C₂×D₄×C₈₉	—	2	2	no	—
244	C₂×D₄×C₈₉	—	2	2	no	—
245	C₂×D₄×C₈₉	—	2	2	no	—
246	C₂×D₄×C₈₉	—	2	1	no	—
247	C₂×D₄×C₈₉	—	2	1	no	—
248	C₂×D₄×C₈₉	—	4	2	no	—
249	C₂×D₄×C₈₉	—	4	4	no	—
250	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
251	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
252	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
253	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₈₉	—	2	2	no	—
255	C₂²×C₄×C₈₉	—	2	2	no	—
256	C₂²×C₄×C₈₉	—	2	1	no	—
257	C₂²×C₄×C₈₉	—	2	1	no	—
258	C₂²×C₄×C₈₉	—	2	1	no	—
259	C₂²×C₄×C₈₉	—	2	2	no	—
260	C₂²×C₄×C₈₉	—	2	2	no	—
261	C₂²×C₄×C₈₉	—	2	2	no	—
262	C₂²×C₄×C₈₉	—	8	4	no	—
263	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
266	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
269	Q₁₆×C₈₉	—	4	2	no	—
270	SD₁₆×C₈₉	—	2	4	no	—
271	SD₁₆×C₈₉	—	4	4	no	—
272	M₁₆×C₈₉	—	4	2	no	—
273	M₁₆×C₈₉	—	4	4	no	—
274	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
275	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
276	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
277	C₄⋊C₄×C₈₉	—	2	2	no	—
278	C₄⋊C₄×C₈₉	—	2	1	no	—
279	C₄⋊C₄×C₈₉	—	2	2	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	1	no	—
284	C₄⋊C₄×C₈₉	—	2	1	no	—
285	C₄⋊C₄×C₈₉	—	2	1	no	—
286	C₄⋊C₄×C₈₉	—	2	1	no	—
287	C₄⋊C₄×C₈₉	—	2	1	no	—
288	C₄⋊C₄×C₈₉	—	2	4	no	—
289	C₄⋊C₄×C₈₉	—	2	4	no	—
290	C₄⋊C₄×C₈₉	—	2	2	no	—
291	C₄⋊C₄×C₈₉	—	2	2	no	—
292	C₄⋊C₄×C₈₉	—	2	4	no	—
293	C₄⋊C₄×C₈₉	—	2	2	no	—
294	C₄⋊C₄×C₈₉	—	2	4	no	—
295	C₄⋊C₄×C₈₉	—	2	2	no	—
296	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
297	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
299	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₈₉	C₂⁴	1	4	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	C₂²⋊C₄×C₈₉	—	2	2	no	—
306	C₂²⋊C₄×C₈₉	—	2	2	no	—
307	C₂²⋊C₄×C₈₉	—	2	4	no	—
308	C₂²⋊C₄×C₈₉	—	2	1	no	—
309	C₂²⋊C₄×C₈₉	—	2	4	no	—
310	C₂²⋊C₄×C₈₉	—	2	1	no	—
311	C₂²⋊C₄×C₈₉	—	2	2	no	—
312	C₂²⋊C₄×C₈₉	—	2	2	no	—
313	C₂²⋊C₄×C₈₉	—	2	2	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	—	2	2	no	—
318	C₂²⋊C₄×C₈₉	—	2	2	no	—
319	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
320	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
321	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
322	C₄²×C₈₉	—	2	1	no	—
323	C₄²×C₈₉	—	2	1	no	—
324	C₄²×C₈₉	—	2	1	no	—
325	C₄²×C₈₉	—	2	4	no	—
326	C₄²×C₈₉	—	2	4	no	—
327	C₄²×C₈₉	—	2	2	no	—
328	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₈₉	C₂×D₄	1	2	yes	—
331	C₄²×C₈₉	C₂×D₄	1	2	yes	—
332	C₄²×C₈₉	C₂⁴	1	2	yes	—
333	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
334	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
335	C₂³×C₈₉	—	2	1	no	—
336	C₂³×C₈₉	—	2	2	no	—
337	C₂³×C₈₉	—	4	4	no	—
338	C₂³×C₈₉	—	4	4	no	—
339	C₂³×C₈₉	—	8	2	no	—
340	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
341	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
342	Q₈×C₈₉	—	2	2	no	—
343	Q₈×C₈₉	—	2	2	no	—
344	Q₈×C₈₉	—	2	1	no	—
345	Q₈×C₈₉	—	2	2	no	—
346	Q₈×C₈₉	—	2	1	no	—
347	Q₈×C₈₉	—	4	4	no	—
348	Q₈×C₈₉	—	4	4	no	—
349	Q₈×C₈₉	—	4	2	no	—
350	Q₈×C₈₉	—	8	1	no	—
351	D₄×C₈₉	—	2	2	no	—
352	D₄×C₈₉	—	2	2	no	—
353	D₄×C₈₉	—	2	1	no	—
354	D₄×C₈₉	—	2	2	no	—
355	D₄×C₈₉	—	4	2	no	—
356	D₄×C₈₉	—	4	4	no	—
357	D₄×C₈₉	—	4	2	no	—
358	D₄×C₈₉	—	4	4	no	—
359	D₄×C₈₉	—	4	2	no	—
360	D₄×C₈₉	—	8	1	no	—
361	D₄×C₈₉	—	8	2	no	—
362	D₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
363	C₂×C₄×C₈₉	—	2	2	no	—
364	C₂×C₄×C₈₉	—	2	4	no	—
365	C₂×C₄×C₈₉	—	2	2	no	—
366	C₂×C₄×C₈₉	—	2	2	no	—
367	C₂×C₄×C₈₉	—	2	1	no	—
368	C₂×C₄×C₈₉	—	2	2	no	—
369	C₂×C₄×C₈₉	—	2	1	no	—
370	C₂×C₄×C₈₉	—	2	2	no	—
371	C₂×C₄×C₈₉	—	2	2	no	—
372	C₂×C₄×C₈₉	—	2	1	no	—
373	C₂×C₄×C₈₉	—	2	1	no	—
374	C₂×C₄×C₈₉	—	2	1	no	—
375	C₂×C₄×C₈₉	—	2	4	no	—
376	C₂×C₄×C₈₉	—	2	2	no	—
377	C₂×C₄×C₈₉	—	4	2	no	—
378	C₂×C₄×C₈₉	—	4	2	no	—
379	C₂×C₄×C₈₉	—	4	4	no	—
380	C₂×C₄×C₈₉	—	4	2	no	—
381	C₂×C₄×C₈₉	—	4	2	no	—
382	C₂×C₄×C₈₉	—	4	4	no	—
383	C₂×C₄×C₈₉	—	8	2	no	—
384	C₂×C₄×C₈₉	—	8	2	no	—
385	C₂×C₄×C₈₉	—	8	2	no	—
386	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
387	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
395	C₈×C₈₉	—	2	2	no	—
396	C₈×C₈₉	—	2	4	no	—
397	C₈×C₈₉	—	2	2	no	—
398	C₂²×C₈₉	—	2	1	no	—
399	C₂²×C₈₉	—	2	2	no	—
400	C₂²×C₈₉	—	2	2	no	—
401	C₂²×C₈₉	—	2	1	no	—
402	C₂²×C₈₉	—	2	2	no	—
403	C₂²×C₈₉	—	2	2	no	—
404	C₂²×C₈₉	—	2	1	no	—
405	C₂²×C₈₉	—	4	1	no	—
406	C₂²×C₈₉	—	4	1	no	—
407	C₂²×C₈₉	—	4	2	no	—
408	C₂²×C₈₉	—	4	2	no	—
409	C₂²×C₈₉	—	4	2	no	—
410	C₂²×C₈₉	—	8	8	no	—
411	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
412	C₄×C₈₉	—	2	1	no	—
413	C₄×C₈₉	—	2	2	no	—
414	C₄×C₈₉	—	2	1	no	—
415	C₄×C₈₉	—	2	2	no	—
416	C₄×C₈₉	—	2	2	no	—
417	C₄×C₈₉	—	2	1	no	—
418	C₄×C₈₉	—	4	1	no	—
419	C₄×C₈₉	—	4	2	no	—
420	C₄×C₈₉	—	4	1	no	—
421	C₄×C₈₉	—	4	4	no	—
422	C₄×C₈₉	—	4	1	no	—
423	C₄×C₈₉	—	4	2	no	—
424	C₄×C₈₉	—	4	2	no	—
425	C₄×C₈₉	#575	1	2	yes	—
426	C₄×C₈₉	#577	1	2	yes	—
427	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
428	C₄×C₈₉	#585	1	1	yes	characteristic
429	#62144	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
430	C₂×C₈₉	—	4	1	no	—
431	C₂×C₈₉	—	4	2	no	—
432	C₂×C₈₉	—	4	2	no	—
433	C₂×C₈₉	—	8	2	no	—
434	C₂×C₈₉	#3489	1	1	yes	characteristic
435	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
436	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
437	#3509	C₂×C₈₉	1	1	yes	characteristic, complemented
438	#3481	C₂×C₈₉	1	1	yes	characteristic
439	#3381	C₂×C₈₉	1	2	yes	complemented
440	#3365	C₂×C₈₉	1	2	yes	complemented
441	#3356	C₂×C₈₉	1	2	yes	complemented
442	#3351	C₂×C₈₉	1	4	yes	complemented
443	#3324	C₂×C₈₉	1	2	yes	complemented
444	#3323	C₂×C₈₉	1	4	yes	complemented
445	#3254	C₂×C₈₉	1	1	yes	characteristic, complemented
446	#3252	C₂×C₈₉	1	2	yes	complemented
447	#3233	C₂×C₈₉	1	2	yes	complemented
448	#3227	C₂×C₈₉	1	1	yes	characteristic, complemented
449	#3107	C₂×C₈₉	1	1	yes	characteristic, complemented
450	#3101	C₂×C₈₉	1	2	yes	complemented
451	#3079	C₂×C₈₉	1	1	yes	characteristic, complemented
452	#3077	C₂×C₈₉	1	2	yes	complemented
453	#2991	C₂×C₈₉	1	1	yes	characteristic, complemented
454	C₈₉	#62144	1	1	yes	characteristic, direct product factor, Sylow
455	#559	C₂²×C₈₉	1	1	yes	characteristic
456	#557	—	2	1	no	—
457	#557	C₂²×C₈₉	1	2	yes	complemented
458	#556	—	2	1	no	—
459	#556	C₂²×C₈₉	1	2	yes	—
460	#554	C₂²×C₈₉	1	1	yes	characteristic
461	#554	C₂²×C₈₉	1	1	yes	characteristic
462	#553	—	2	1	no	—
463	#553	C₂²×C₈₉	1	2	yes	—
464	#552	—	2	2	no	—
465	#552	C₂²×C₈₉	1	4	yes	complemented
466	#551	—	2	2	no	—
467	#546	—	2	1	no	—
468	#546	C₂²×C₈₉	1	2	yes	—
469	D₄²	C₂²×C₈₉	1	1	yes	characteristic
470	#541	—	2	2	no	—
471	#536	—	2	1	no	—
472	#533	C₂²×C₈₉	1	2	yes	complemented
473	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
474	#533	C₂²×C₈₉	1	2	yes	complemented
475	#532	C₂²×C₈₉	1	1	yes	characteristic
476	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
477	#529	—	2	1	no	—
478	#529	C₂²×C₈₉	1	2	yes	—
479	#525	—	2	2	no	—
480	#519	—	2	1	no	—
481	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
482	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
483	C₂×C₄×D₄	—	2	1	no	—
484	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
485	#499	C₂²×C₈₉	1	4	yes	complemented
486	#498	C₂²×C₈₉	1	2	yes	complemented
487	#488	C₂²×C₈₉	1	4	yes	complemented
488	#486	C₂²×C₈₉	1	2	yes	—
489	#485	C₂²×C₈₉	1	2	yes	complemented
490	#485	C₂²×C₈₉	1	4	yes	complemented
491	#483	C₂²×C₈₉	1	4	yes	complemented
492	#482	C₂²×C₈₉	1	4	yes	—
493	#481	C₂²×C₈₉	1	4	yes	complemented
494	#479	C₂²×C₈₉	1	4	yes	complemented
495	#478	C₂²×C₈₉	1	4	yes	—
496	#478	C₂²×C₈₉	1	4	yes	complemented
497	#477	C₂²×C₈₉	1	2	yes	complemented
498	#477	C₂²×C₈₉	1	2	yes	complemented
499	#476	C₂²×C₈₉	1	2	yes	—
500	#476	C₂²×C₈₉	1	2	yes	complemented
501	#476	C₂²×C₈₉	1	2	yes	complemented
502	#475	C₂²×C₈₉	1	2	yes	complemented
503	#475	C₂²×C₈₉	1	1	yes	characteristic, complemented
504	#474	C₂²×C₈₉	1	1	yes	characteristic
505	#474	C₂²×C₈₉	1	2	yes	—
506	#474	C₂²×C₈₉	1	2	yes	complemented
507	#470	C₂²×C₈₉	1	4	yes	complemented
508	#468	C₂²×C₈₉	1	4	yes	—
509	#468	C₂²×C₈₉	1	4	yes	complemented
510	#464	C₂²×C₈₉	1	4	yes	complemented
511	#462	C₂²×C₈₉	1	1	yes	characteristic, complemented
512	#461	C₂²×C₈₉	1	1	yes	characteristic
513	#461	C₂²×C₈₉	1	2	yes	complemented
514	#460	C₂²×C₈₉	1	2	yes	—
515	#452	C₂²×C₈₉	1	2	yes	—
516	#450	C₂²×C₈₉	1	4	yes	—
517	C₈×Q₈	C₂²×C₈₉	1	2	yes	complemented
518	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
519	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	—
520	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
521	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	complemented
522	#436	C₂²×C₈₉	1	2	yes	—
523	#436	C₂²×C₈₉	1	4	yes	complemented
524	#431	C₂²×C₈₉	1	2	yes	complemented
525	#431	C₂²×C₈₉	1	1	yes	characteristic, complemented
526	#428	C₂²×C₈₉	1	4	yes	complemented
527	#428	C₂²×C₈₉	1	2	yes	complemented
528	#423	C₂²×C₈₉	1	2	yes	complemented
529	#423	C₂²×C₈₉	1	1	yes	characteristic, complemented
530	#418	C₂²×C₈₉	1	4	yes	—
531	#417	C₂²×C₈₉	1	2	yes	—
532	C₂×#41	—	2	1	no	—
533	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
534	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
535	C₂²×Q₈	—	2	1	no	—
536	C₂²×D₄	—	2	1	no	—
537	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
538	C₂³×C₄	—	2	2	no	—
539	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
540	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
541	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
542	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
543	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
544	C₄⋊Q₈	—	2	2	no	—
545	C₄⋊Q₈	—	2	1	no	—
546	C₄⋊Q₈	—	2	1	no	—
547	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
548	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
549	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
550	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
551	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
552	#127	C₂³×C₈₉	1	1	yes	characteristic
553	#126	—	2	2	no	—
554	#126	—	2	4	no	—
555	#126	—	2	4	no	—
556	#126	—	2	2	no	—
557	#125	—	2	1	no	—
558	#125	—	2	4	no	—
559	#125	—	2	4	no	—
560	#125	—	2	1	no	—
561	#125	—	2	2	no	—
562	#125	C₂³×C₈₉	1	2	yes	—
563	#125	C₂³×C₈₉	1	4	yes	—
564	#124	—	2	1	no	—
565	#124	—	2	2	no	—
566	#124	—	2	1	no	—
567	#124	C₂³×C₈₉	1	2	yes	—
568	#123	—	2	4	no	—
569	#123	—	2	2	no	—
570	#123	—	2	2	no	—
571	#123	—	2	2	no	—
572	#123	—	2	2	no	—
573	C₂²⋊Q₈	—	2	1	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	1	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	2	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
581	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
582	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
583	#121	—	2	2	no	—
584	#121	—	2	1	no	—
585	#121	—	2	1	no	—
586	#121	—	2	2	no	—
587	#121	C₂³×C₈₉	1	2	yes	—
588	#121	C₂³×C₈₉	1	2	yes	—
589	#120	—	2	2	no	—
590	#120	—	2	2	no	—
591	C₄×Q₈	—	2	2	no	—
592	C₄×Q₈	—	2	2	no	—
593	C₄×Q₈	—	2	2	no	—
594	C₄×Q₈	—	2	2	no	—
595	C₄×Q₈	—	2	2	no	—
596	C₄×Q₈	—	2	1	no	—
597	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
598	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
599	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
601	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
602	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
613	C₄×D₄	D₄×C₈₉	1	2	yes	—
614	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
615	C₄×D₄	C₂³×C₈₉	1	2	yes	—
616	C₄×D₄	C₂³×C₈₉	1	2	yes	—
617	C₄×D₄	C₂³×C₈₉	1	2	yes	—
618	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
619	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
620	C₄×D₄	C₂³×C₈₉	1	2	yes	—
621	#117	—	2	1	no	—
622	#117	—	2	2	no	—
623	#117	—	2	4	no	—
624	#117	—	2	1	no	—
625	#117	—	2	2	no	—
626	#117	D₄×C₈₉	1	1	yes	characteristic
627	#117	D₄×C₈₉	1	2	yes	—
628	#117	C₂³×C₈₉	1	1	yes	characteristic
629	#117	C₂³×C₈₉	1	4	yes	—
630	C₂×C₄⋊C₄	—	2	1	no	—
631	C₂×C₄⋊C₄	—	2	1	no	—
632	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
634	C₂×C₂²⋊C₄	—	2	2	no	—
635	C₂×C₂²⋊C₄	—	2	2	no	—
636	C₂×C₄²	—	2	1	no	—
637	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
638	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
639	#107	C₂³×C₈₉	1	2	yes	—
640	#107	C₂³×C₈₉	1	4	yes	—
641	#107	C₂³×C₈₉	1	4	yes	—
642	#106	C₂³×C₈₉	1	4	yes	—
643	#106	C₂³×C₈₉	1	4	yes	—
644	#106	C₂³×C₈₉	1	2	yes	—
645	#106	C₂³×C₈₉	1	4	yes	—
646	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
647	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
648	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
649	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
650	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
651	#103	C₂³×C₈₉	1	4	yes	—
652	#103	C₂³×C₈₉	1	4	yes	—
653	#103	C₂³×C₈₉	1	2	yes	—
654	#103	C₂³×C₈₉	1	2	yes	—
655	#103	C₂³×C₈₉	1	2	yes	—
656	#102	C₂³×C₈₉	1	4	yes	—
657	#102	C₂³×C₈₉	1	2	yes	—
658	#102	C₂³×C₈₉	1	4	yes	—
659	#102	C₂³×C₈₉	1	4	yes	—
660	#102	C₂³×C₈₉	1	4	yes	—
661	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
662	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
663	C₄×C₈	C₂³×C₈₉	1	2	yes	—
664	C₄×C₈	C₂³×C₈₉	1	4	yes	—
665	C₂⁴	—	2	2	no	—
666	#41	—	2	2	no	—
667	#41	—	4	2	no	—
668	#41	—	4	1	no	—
669	#41	—	8	2	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	—	4	4	no	—
675	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
676	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
677	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	4	2	no	—
686	C₂×D₄	—	4	4	no	—
687	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
688	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
689	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
690	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	8	4	no	—
700	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
701	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
702	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
703	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
706	Q₁₆	—	4	2	no	—
707	SD₁₆	—	2	4	no	—
708	SD₁₆	—	4	4	no	—
709	M₁₆	—	4	2	no	—
710	M₁₆	—	4	4	no	—
711	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
712	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
713	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	4	no	—
726	C₄⋊C₄	—	2	4	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
734	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
735	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
736	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
738	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
739	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
740	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
741	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	1	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
757	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
758	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
759	C₄²	—	2	1	no	—
760	C₄²	—	2	1	no	—
761	C₄²	—	2	1	no	—
762	C₄²	—	2	4	no	—
763	C₄²	—	2	4	no	—
764	C₄²	—	2	2	no	—
765	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
766	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
767	C₄²	C₂×D₄×C₈₉	1	2	yes	—
768	C₄²	C₂×D₄×C₈₉	1	2	yes	—
769	C₄²	C₂⁴×C₈₉	1	2	yes	—
770	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
771	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
772	C₂³	—	2	1	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	4	4	no	—
775	C₂³	—	4	4	no	—
776	C₂³	—	8	2	no	—
777	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
778	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
779	Q₈	—	2	2	no	—
780	Q₈	—	2	2	no	—
781	Q₈	—	2	1	no	—
782	Q₈	—	2	2	no	—
783	Q₈	—	2	1	no	—
784	Q₈	—	4	4	no	—
785	Q₈	—	4	4	no	—
786	Q₈	—	4	2	no	—
787	Q₈	—	8	1	no	—
788	D₄	—	2	2	no	—
789	D₄	—	2	2	no	—
790	D₄	—	2	1	no	—
791	D₄	—	2	2	no	—
792	D₄	—	4	2	no	—
793	D₄	—	4	4	no	—
794	D₄	—	4	2	no	—
795	D₄	—	4	4	no	—
796	D₄	—	4	2	no	—
797	D₄	—	8	1	no	—
798	D₄	—	8	2	no	—
799	D₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	4	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	2	no	—
819	C₂×C₄	—	4	4	no	—
820	C₂×C₄	—	8	2	no	—
821	C₂×C₄	—	8	2	no	—
822	C₂×C₄	—	8	2	no	—
823	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
825	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
826	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
828	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
829	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
831	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
832	C₈	—	2	2	no	—
833	C₈	—	2	4	no	—
834	C₈	—	2	2	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	2	1	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	2	2	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	8	8	no	—
848	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
849	C₄	—	2	1	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	1	no	—
853	C₄	—	2	1	no	—
854	C₄	—	2	2	no	—
855	C₄	—	4	1	no	—
856	C₄	—	4	4	no	—
857	C₄	—	4	1	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	2	no	—
862	C₄	#575×C₈₉	1	2	yes	—
863	C₄	#577×C₈₉	1	2	yes	—
864	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
865	C₄	#585×C₈₉	1	1	yes	characteristic
866	C₂	—	4	1	no	—
867	C₂	—	4	2	no	—
868	C₂	—	4	2	no	—
869	C₂	—	8	2	no	—
870	C₂	C₈₉×#3489	1	1	yes	characteristic
871	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
872	C₂	C₂×#577×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₈₉×#3481	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
1. C₈₉×#3509	C₂	semidirect
3. C₈₉×#3381	C₂	semidirect
4. C₈₉×#3365	C₂	semidirect
5. C₈₉×#3356	C₂	semidirect
6. C₈₉×#3351	C₂	semidirect
7. C₈₉×#3324	C₂	semidirect
8. C₈₉×#3323	C₂	semidirect
9. C₈₉×#3254	C₂	semidirect
10. C₈₉×#3252	C₂	semidirect
11. C₈₉×#3233	C₂	semidirect
12. C₈₉×#3227	C₂	semidirect
13. C₈₉×#3107	C₂	semidirect
14. C₈₉×#3101	C₂	semidirect
15. C₈₉×#3079	C₂	semidirect
16. C₈₉×#3077	C₂	semidirect
17. C₈₉×#2991	C₂	semidirect
20. #557×C₈₉	C₂²	semidirect
28. #552×C₈₉	C₂²	semidirect
35. #533×C₈₉	C₂²	semidirect
36. #533×C₈₉	C₂²	semidirect
37. #533×C₈₉	C₂²	semidirect
39. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
48. #499×C₈₉	C₂²	semidirect
49. #498×C₈₉	C₂²	semidirect
50. #488×C₈₉	C₂²	semidirect
52. #485×C₈₉	C₂²	semidirect
53. #485×C₈₉	C₂²	semidirect
54. #483×C₈₉	C₂²	semidirect
56. #481×C₈₉	C₂²	semidirect
57. #479×C₈₉	C₂²	semidirect
59. #478×C₈₉	C₂²	semidirect
60. #477×C₈₉	C₂²	semidirect
61. #477×C₈₉	C₂²	semidirect
63. #476×C₈₉	C₂²	semidirect
64. #476×C₈₉	C₂²	semidirect
65. #475×C₈₉	C₂²	semidirect
66. #475×C₈₉	C₂²	semidirect
69. #474×C₈₉	C₂²	semidirect
70. #470×C₈₉	C₂²	semidirect
72. #468×C₈₉	C₂²	semidirect
73. #464×C₈₉	C₂²	semidirect
74. #462×C₈₉	C₂²	semidirect
76. #461×C₈₉	C₂²	semidirect
80. C₈×Q₈×C₈₉	C₂²	semidirect
81. C₄×Q₁₆×C₈₉	C₂²	semidirect
84. C₄×SD₁₆×C₈₉	C₂²	semidirect
86. #436×C₈₉	C₂²	semidirect
87. #431×C₈₉	C₂²	semidirect
88. #431×C₈₉	C₂²	semidirect
89. #428×C₈₉	C₂²	semidirect
90. #428×C₈₉	C₂²	semidirect
91. #423×C₈₉	C₂²	semidirect
92. #423×C₈₉	C₂²	semidirect
429. #62144	C₈₉	direct (N × H)
437. #3509	C₂×C₈₉	semidirect
439. #3381	C₂×C₈₉	semidirect
440. #3365	C₂×C₈₉	semidirect
441. #3356	C₂×C₈₉	semidirect
442. #3351	C₂×C₈₉	semidirect
443. #3324	C₂×C₈₉	semidirect
444. #3323	C₂×C₈₉	semidirect
445. #3254	C₂×C₈₉	semidirect
446. #3252	C₂×C₈₉	semidirect
447. #3233	C₂×C₈₉	semidirect
448. #3227	C₂×C₈₉	semidirect
449. #3107	C₂×C₈₉	semidirect
450. #3101	C₂×C₈₉	semidirect
451. #3079	C₂×C₈₉	semidirect
452. #3077	C₂×C₈₉	semidirect
453. #2991	C₂×C₈₉	semidirect
454. C₈₉	#62144	direct (N × H)
457. #557	C₂²×C₈₉	semidirect
465. #552	C₂²×C₈₉	semidirect
472. #533	C₂²×C₈₉	semidirect
473. #533	C₂²×C₈₉	semidirect
474. #533	C₂²×C₈₉	semidirect
476. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
485. #499	C₂²×C₈₉	semidirect
486. #498	C₂²×C₈₉	semidirect
487. #488	C₂²×C₈₉	semidirect
489. #485	C₂²×C₈₉	semidirect
490. #485	C₂²×C₈₉	semidirect
491. #483	C₂²×C₈₉	semidirect
493. #481	C₂²×C₈₉	semidirect
494. #479	C₂²×C₈₉	semidirect
496. #478	C₂²×C₈₉	semidirect
497. #477	C₂²×C₈₉	semidirect
498. #477	C₂²×C₈₉	semidirect
500. #476	C₂²×C₈₉	semidirect
501. #476	C₂²×C₈₉	semidirect
502. #475	C₂²×C₈₉	semidirect
503. #475	C₂²×C₈₉	semidirect
506. #474	C₂²×C₈₉	semidirect
507. #470	C₂²×C₈₉	semidirect
509. #468	C₂²×C₈₉	semidirect
510. #464	C₂²×C₈₉	semidirect
511. #462	C₂²×C₈₉	semidirect
513. #461	C₂²×C₈₉	semidirect
517. C₈×Q₈	C₂²×C₈₉	semidirect
518. C₄×Q₁₆	C₂²×C₈₉	semidirect
521. C₄×SD₁₆	C₂²×C₈₉	semidirect
523. #436	C₂²×C₈₉	semidirect
524. #431	C₂²×C₈₉	semidirect
525. #431	C₂²×C₈₉	semidirect
526. #428	C₂²×C₈₉	semidirect
527. #428	C₂²×C₈₉	semidirect
528. #423	C₂²×C₈₉	semidirect
529. #423	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×#3509	2
C₈₉×#3481	2
C₈₉×#3381	2
C₈₉×#3365	2
C₈₉×#3356	2
C₈₉×#3351	2
C₈₉×#3324	2
C₈₉×#3323	2
C₈₉×#3254	2
C₈₉×#3252	2
C₈₉×#3233	2
C₈₉×#3227	2
C₈₉×#3107	2
C₈₉×#3101	2
C₈₉×#3079	2
C₈₉×#3077	2
C₈₉×#2991	2
#62144	89

Subgroups — C89×#62144 #36439992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62144 #36439992