Subgroups — C₈₉×#60813 #36438661

Order 22784.

2086 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#536×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3225	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3221	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3218	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3213	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3211	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3206	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3154	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3137	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3046	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3042	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3006	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3004	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3002	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#448×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
19	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#137×C₈₉	C₂²	1	2	yes	complemented
21	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
22	C₂×#135×C₈₉	C₂²	1	2	yes	—
23	C₂²×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
24	#555×C₈₉	—	2	1	no	—
25	#553×C₈₉	—	2	1	no	—
26	#553×C₈₉	—	2	1	no	—
27	#551×C₈₉	—	2	2	no	—
28	#547×C₈₉	—	2	1	no	—
29	#546×C₈₉	—	2	2	no	—
30	#544×C₈₉	C₂²	1	1	yes	characteristic, complemented
31	#542×C₈₉	C₂²	1	2	yes	complemented
32	#540×C₈₉	C₂²	1	2	yes	complemented
33	#536×C₈₉	—	2	2	no	—
34	#536×C₈₉	—	2	1	no	—
35	#536×C₈₉	—	2	1	no	—
36	#536×C₈₉	C₂²	1	2	yes	—
37	#536×C₈₉	C₂²	1	2	yes	—
38	#536×C₈₉	C₂²	1	4	yes	complemented
39	#535×C₈₉	C₂²	1	1	yes	characteristic, complemented
40	#532×C₈₉	C₂²	1	2	yes	—
41	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
42	#529×C₈₉	C₂²	1	2	yes	—
43	C₂×#124×C₈₉	C₂²	1	2	yes	complemented
44	#525×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#123×C₈₉	—	2	2	no	—
46	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
47	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
48	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
49	#520×C₈₉	C₂²	1	1	yes	characteristic, complemented
50	#518×C₈₉	C₂²	1	1	yes	characteristic, complemented
51	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
52	#497×C₈₉	C₂²	1	4	yes	complemented
53	#496×C₈₉	C₂²	1	4	yes	complemented
54	#495×C₈₉	C₂²	1	4	yes	complemented
55	#492×C₈₉	C₂²	1	4	yes	complemented
56	#491×C₈₉	C₂²	1	4	yes	complemented
57	#489×C₈₉	C₂²	1	4	yes	complemented
58	#488×C₈₉	C₂²	1	4	yes	complemented
59	#487×C₈₉	C₂²	1	4	yes	complemented
60	#464×C₈₉	C₂²	1	4	yes	complemented
61	#463×C₈₉	C₂²	1	4	yes	complemented
62	#463×C₈₉	C₂²	1	4	yes	complemented
63	#463×C₈₉	C₂²	1	4	yes	complemented
64	#462×C₈₉	C₂²	1	4	yes	complemented
65	#461×C₈₉	C₂²	1	4	yes	complemented
66	#461×C₈₉	C₂²	1	4	yes	complemented
67	#461×C₈₉	C₂²	1	4	yes	complemented
68	#452×C₈₉	C₂²	1	2	yes	complemented
69	#451×C₈₉	C₂²	1	2	yes	complemented
70	#451×C₈₉	C₂²	1	1	yes	characteristic, complemented
71	#451×C₈₉	C₂²	1	2	yes	complemented
72	#450×C₈₉	C₂²	1	1	yes	characteristic, complemented
73	#449×C₈₉	C₂²	1	4	yes	—
74	#449×C₈₉	C₂²	1	2	yes	complemented
75	#448×C₈₉	C₂²	1	2	yes	—
76	#448×C₈₉	C₂²	1	2	yes	—
77	#448×C₈₉	C₂²	1	2	yes	—
78	#448×C₈₉	C₂²	1	1	yes	characteristic, complemented
79	#448×C₈₉	C₂²	1	2	yes	complemented
80	#448×C₈₉	C₂²	1	2	yes	complemented
81	#448×C₈₉	C₂²	1	4	yes	complemented
82	#447×C₈₉	C₂²	1	2	yes	—
83	#447×C₈₉	C₂²	1	1	yes	characteristic, complemented
84	#433×C₈₉	C₂²	1	4	yes	complemented
85	#432×C₈₉	C₂²	1	2	yes	complemented
86	#431×C₈₉	C₂²	1	2	yes	complemented
87	#424×C₈₉	C₂²	1	2	yes	complemented
88	#419×C₈₉	C₂²	1	2	yes	complemented
89	#417×C₈₉	C₂²	1	2	yes	—
90	#416×C₈₉	C₂²	1	2	yes	—
91	C₂×#103×C₈₉	C₂²	1	2	yes	complemented
92	#407×C₈₉	C₂²	1	1	yes	characteristic
93	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
94	#405×C₈₉	C₂²	1	2	yes	complemented
95	C₂×#41×C₈₉	—	2	1	no	—
96	C₂×#41×C₈₉	—	2	1	no	—
97	C₂×#41×C₈₉	—	2	2	no	—
98	C₂×#41×C₈₉	—	4	4	no	—
99	C₂×#41×C₈₉	C₂³	1	2	yes	—
100	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
101	C₂×#41×C₈₉	C₂³	1	2	yes	—
102	C₂²×Q₈×C₈₉	—	2	1	no	—
103	C₂²×Q₈×C₈₉	—	2	1	no	—
104	C₂²×Q₈×C₈₉	—	2	1	no	—
105	C₂²×Q₈×C₈₉	—	4	4	no	—
106	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
107	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
108	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
110	C₂²×D₄×C₈₉	—	2	1	no	—
111	C₂²×D₄×C₈₉	—	2	1	no	—
112	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₈₉	—	2	1	no	—
115	C₂³×C₄×C₈₉	—	2	1	no	—
116	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
117	#137×C₈₉	—	4	4	no	—
118	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
119	#135×C₈₉	—	4	4	no	—
120	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
121	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
122	C₂×SD₁₆×C₈₉	—	4	4	no	—
123	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
124	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
125	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
126	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
127	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
129	C₂×D₈×C₈₉	C₂³	1	4	yes	—
130	C₂×D₈×C₈₉	C₂³	1	2	yes	—
131	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
132	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
133	C₄⋊Q₈×C₈₉	—	2	1	no	—
134	C₄⋊Q₈×C₈₉	—	2	2	no	—
135	C₄⋊Q₈×C₈₉	—	2	2	no	—
136	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
137	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
138	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
139	#127×C₈₉	C₂³	1	2	yes	—
140	#126×C₈₉	—	2	2	no	—
141	#126×C₈₉	—	2	2	no	—
142	#125×C₈₉	—	2	1	no	—
143	#125×C₈₉	C₂³	1	2	yes	—
144	#124×C₈₉	—	2	2	no	—
145	#124×C₈₉	—	2	2	no	—
146	#124×C₈₉	—	2	2	no	—
147	#124×C₈₉	—	2	2	no	—
148	#124×C₈₉	C₂³	1	4	yes	—
149	#124×C₈₉	C₂³	1	4	yes	—
150	#124×C₈₉	C₂³	1	2	yes	—
151	#123×C₈₉	—	2	1	no	—
152	#123×C₈₉	—	2	2	no	—
153	#123×C₈₉	—	2	2	no	—
154	#123×C₈₉	—	2	2	no	—
155	#123×C₈₉	—	2	4	no	—
156	#123×C₈₉	—	2	4	no	—
157	#123×C₈₉	—	2	4	no	—
158	#123×C₈₉	—	2	4	no	—
159	#123×C₈₉	—	2	2	no	—
160	C₂²⋊Q₈×C₈₉	—	2	2	no	—
161	C₂²⋊Q₈×C₈₉	—	2	2	no	—
162	C₂²⋊Q₈×C₈₉	—	2	2	no	—
163	C₂²⋊Q₈×C₈₉	—	2	2	no	—
164	C₂²⋊Q₈×C₈₉	—	2	4	no	—
165	C₂²⋊Q₈×C₈₉	—	2	4	no	—
166	C₂²⋊Q₈×C₈₉	—	2	2	no	—
167	C₂²⋊Q₈×C₈₉	—	2	2	no	—
168	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
169	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
170	#121×C₈₉	—	2	1	no	—
171	#121×C₈₉	—	2	1	no	—
172	#121×C₈₉	—	2	2	no	—
173	#121×C₈₉	—	2	1	no	—
174	#121×C₈₉	—	2	1	no	—
175	#121×C₈₉	—	2	2	no	—
176	#121×C₈₉	—	2	2	no	—
177	#121×C₈₉	C₂³	1	2	yes	—
178	#121×C₈₉	C₂³	1	1	yes	characteristic
179	#121×C₈₉	C₂³	1	2	yes	—
180	#121×C₈₉	C₂³	1	1	yes	characteristic
181	#120×C₈₉	—	2	1	no	—
182	#120×C₈₉	—	2	2	no	—
183	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
184	C₄×D₄×C₈₉	—	2	1	no	—
185	C₄×D₄×C₈₉	—	2	1	no	—
186	C₄×D₄×C₈₉	—	2	2	no	—
187	C₄×D₄×C₈₉	—	2	1	no	—
188	C₄×D₄×C₈₉	—	2	1	no	—
189	C₄×D₄×C₈₉	—	2	2	no	—
190	C₄×D₄×C₈₉	—	2	2	no	—
191	C₄×D₄×C₈₉	C₂³	1	2	yes	—
192	C₄×D₄×C₈₉	C₂³	1	2	yes	—
193	C₄×D₄×C₈₉	C₂³	1	2	yes	—
194	#117×C₈₉	—	2	1	no	—
195	#117×C₈₉	—	2	2	no	—
196	#117×C₈₉	D₄	1	2	yes	—
197	#117×C₈₉	D₄	1	1	yes	characteristic
198	#117×C₈₉	D₄	1	1	yes	characteristic
199	#117×C₈₉	C₂³	1	1	yes	characteristic
200	#117×C₈₉	C₂³	1	1	yes	characteristic
201	#117×C₈₉	C₂³	1	1	yes	characteristic
202	#117×C₈₉	C₂³	1	2	yes	—
203	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
204	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
205	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
206	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
207	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
208	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
210	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
211	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
212	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
213	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
214	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
215	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
216	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
217	#103×C₈₉	C₂³	1	4	yes	—
218	#103×C₈₉	C₂³	1	4	yes	—
219	#103×C₈₉	C₂³	1	2	yes	—
220	#103×C₈₉	C₂³	1	2	yes	—
221	#103×C₈₉	C₂³	1	4	yes	—
222	#103×C₈₉	C₂³	1	4	yes	—
223	#103×C₈₉	C₂³	1	4	yes	—
224	#102×C₈₉	C₂³	1	2	yes	—
225	#102×C₈₉	C₂³	1	2	yes	—
226	#102×C₈₉	C₂³	1	4	yes	—
227	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
228	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
229	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
230	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
231	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
232	#97×C₈₉	C₂³	1	4	yes	—
233	C₄×C₈×C₈₉	C₂³	1	4	yes	—
234	C₂⁴×C₈₉	—	2	1	no	—
235	C₂⁴×C₈₉	—	2	1	no	—
236	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
237	#41×C₈₉	—	2	4	no	—
238	#41×C₈₉	—	2	4	no	—
239	#41×C₈₉	—	2	4	no	—
240	#41×C₈₉	—	4	2	no	—
241	#41×C₈₉	—	4	2	no	—
242	#41×C₈₉	—	4	4	no	—
243	#41×C₈₉	—	4	4	no	—
244	#41×C₈₉	—	8	4	no	—
245	C₂×Q₈×C₈₉	—	2	2	no	—
246	C₂×Q₈×C₈₉	—	2	2	no	—
247	C₂×Q₈×C₈₉	—	2	2	no	—
248	C₂×Q₈×C₈₉	—	2	1	no	—
249	C₂×Q₈×C₈₉	—	2	2	no	—
250	C₂×Q₈×C₈₉	—	2	4	no	—
251	C₂×Q₈×C₈₉	—	2	4	no	—
252	C₂×Q₈×C₈₉	—	4	4	no	—
253	C₂×Q₈×C₈₉	—	4	4	no	—
254	C₂×Q₈×C₈₉	—	4	2	no	—
255	C₂×Q₈×C₈₉	—	4	4	no	—
256	C₂×Q₈×C₈₉	—	4	4	no	—
257	C₂×Q₈×C₈₉	—	4	4	no	—
258	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
259	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
260	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
261	C₂×D₄×C₈₉	—	2	1	no	—
262	C₂×D₄×C₈₉	—	2	1	no	—
263	C₂×D₄×C₈₉	—	2	2	no	—
264	C₂×D₄×C₈₉	—	2	2	no	—
265	C₂×D₄×C₈₉	—	2	2	no	—
266	C₂×D₄×C₈₉	—	2	1	no	—
267	C₂×D₄×C₈₉	—	2	2	no	—
268	C₂×D₄×C₈₉	—	2	1	no	—
269	C₂×D₄×C₈₉	—	2	1	no	—
270	C₂×D₄×C₈₉	—	2	2	no	—
271	C₂×D₄×C₈₉	—	2	2	no	—
272	C₂×D₄×C₈₉	—	2	4	no	—
273	C₂×D₄×C₈₉	—	4	2	no	—
274	C₂×D₄×C₈₉	—	4	4	no	—
275	C₂×D₄×C₈₉	—	8	2	no	—
276	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
277	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
278	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₈₉	—	2	4	no	—
280	C₂²×C₄×C₈₉	—	2	2	no	—
281	C₂²×C₄×C₈₉	—	2	1	no	—
282	C₂²×C₄×C₈₉	—	2	2	no	—
283	C₂²×C₄×C₈₉	—	2	2	no	—
284	C₂²×C₄×C₈₉	—	2	1	no	—
285	C₂²×C₄×C₈₉	—	2	1	no	—
286	C₂²×C₄×C₈₉	—	2	2	no	—
287	C₂²×C₄×C₈₉	—	2	2	no	—
288	C₂²×C₄×C₈₉	—	2	2	no	—
289	C₂²×C₄×C₈₉	—	2	2	no	—
290	C₂²×C₄×C₈₉	—	2	2	no	—
291	C₂²×C₄×C₈₉	—	4	4	no	—
292	C₂²×C₄×C₈₉	—	4	4	no	—
293	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
294	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
295	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
298	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
301	Q₁₆×C₈₉	—	4	2	no	—
302	Q₁₆×C₈₉	—	4	4	no	—
303	SD₁₆×C₈₉	—	4	4	no	—
304	SD₁₆×C₈₉	—	4	4	no	—
305	SD₁₆×C₈₉	—	4	2	no	—
306	SD₁₆×C₈₉	—	4	2	no	—
307	SD₁₆×C₈₉	—	4	4	no	—
308	SD₁₆×C₈₉	—	4	4	no	—
309	D₈×C₈₉	—	4	2	no	—
310	D₈×C₈₉	—	4	4	no	—
311	M₁₆×C₈₉	—	2	4	no	—
312	C₂×C₈×C₈₉	—	2	4	no	—
313	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
314	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
315	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
316	C₄⋊C₄×C₈₉	—	2	1	no	—
317	C₄⋊C₄×C₈₉	—	2	2	no	—
318	C₄⋊C₄×C₈₉	—	2	4	no	—
319	C₄⋊C₄×C₈₉	—	2	4	no	—
320	C₄⋊C₄×C₈₉	—	2	4	no	—
321	C₄⋊C₄×C₈₉	—	2	4	no	—
322	C₄⋊C₄×C₈₉	—	2	1	no	—
323	C₄⋊C₄×C₈₉	—	2	2	no	—
324	C₄⋊C₄×C₈₉	—	2	2	no	—
325	C₄⋊C₄×C₈₉	—	2	2	no	—
326	C₄⋊C₄×C₈₉	—	2	1	no	—
327	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
328	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
329	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
330	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
331	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
332	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
333	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
334	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
335	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
336	C₂²⋊C₄×C₈₉	—	2	1	no	—
337	C₂²⋊C₄×C₈₉	—	2	1	no	—
338	C₂²⋊C₄×C₈₉	—	2	1	no	—
339	C₂²⋊C₄×C₈₉	—	2	2	no	—
340	C₂²⋊C₄×C₈₉	—	2	2	no	—
341	C₂²⋊C₄×C₈₉	—	2	2	no	—
342	C₂²⋊C₄×C₈₉	—	2	2	no	—
343	C₂²⋊C₄×C₈₉	—	2	4	no	—
344	C₂²⋊C₄×C₈₉	—	2	4	no	—
345	C₂²⋊C₄×C₈₉	—	2	4	no	—
346	C₂²⋊C₄×C₈₉	—	2	4	no	—
347	C₂²⋊C₄×C₈₉	—	2	2	no	—
348	C₂²⋊C₄×C₈₉	—	2	2	no	—
349	C₂²⋊C₄×C₈₉	—	2	1	no	—
350	C₂²⋊C₄×C₈₉	—	2	2	no	—
351	C₂²⋊C₄×C₈₉	—	2	1	no	—
352	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
353	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
354	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
355	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
356	C₄²×C₈₉	—	2	2	no	—
357	C₄²×C₈₉	—	2	1	no	—
358	C₄²×C₈₉	C₂×D₄	1	2	yes	—
359	C₄²×C₈₉	C₂×D₄	1	2	yes	—
360	C₄²×C₈₉	C₂⁴	1	2	yes	—
361	C₄²×C₈₉	C₂⁴	1	2	yes	—
362	C₂³×C₈₉	—	2	2	no	—
363	C₂³×C₈₉	—	2	2	no	—
364	C₂³×C₈₉	—	2	2	no	—
365	C₂³×C₈₉	—	2	2	no	—
366	C₂³×C₈₉	—	2	1	no	—
367	C₂³×C₈₉	—	4	1	no	—
368	C₂³×C₈₉	—	4	2	no	—
369	C₂³×C₈₉	—	4	2	no	—
370	C₂³×C₈₉	—	4	2	no	—
371	C₂³×C₈₉	—	4	2	no	—
372	C₂³×C₈₉	—	8	1	no	—
373	C₂³×C₈₉	—	8	1	no	—
374	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
375	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
376	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
377	Q₈×C₈₉	—	2	4	no	—
378	Q₈×C₈₉	—	2	2	no	—
379	Q₈×C₈₉	—	2	2	no	—
380	Q₈×C₈₉	—	2	4	no	—
381	Q₈×C₈₉	—	2	2	no	—
382	Q₈×C₈₉	—	4	4	no	—
383	Q₈×C₈₉	—	4	4	no	—
384	Q₈×C₈₉	—	4	2	no	—
385	Q₈×C₈₉	—	4	4	no	—
386	Q₈×C₈₉	—	8	2	no	—
387	D₄×C₈₉	—	2	2	no	—
388	D₄×C₈₉	—	2	4	no	—
389	D₄×C₈₉	—	2	2	no	—
390	D₄×C₈₉	—	2	2	no	—
391	D₄×C₈₉	—	4	2	no	—
392	D₄×C₈₉	—	4	4	no	—
393	D₄×C₈₉	—	4	4	no	—
394	D₄×C₈₉	—	4	2	no	—
395	D₄×C₈₉	—	4	4	no	—
396	D₄×C₈₉	—	4	2	no	—
397	D₄×C₈₉	—	4	2	no	—
398	D₄×C₈₉	—	8	2	no	—
399	D₄×C₈₉	—	8	2	no	—
400	D₄×C₈₉	—	8	1	no	—
401	D₄×C₈₉	—	8	2	no	—
402	C₂×C₄×C₈₉	—	2	2	no	—
403	C₂×C₄×C₈₉	—	2	4	no	—
404	C₂×C₄×C₈₉	—	2	2	no	—
405	C₂×C₄×C₈₉	—	2	2	no	—
406	C₂×C₄×C₈₉	—	2	2	no	—
407	C₂×C₄×C₈₉	—	2	2	no	—
408	C₂×C₄×C₈₉	—	2	1	no	—
409	C₂×C₄×C₈₉	—	2	1	no	—
410	C₂×C₄×C₈₉	—	2	1	no	—
411	C₂×C₄×C₈₉	—	2	2	no	—
412	C₂×C₄×C₈₉	—	2	4	no	—
413	C₂×C₄×C₈₉	—	2	2	no	—
414	C₂×C₄×C₈₉	—	4	2	no	—
415	C₂×C₄×C₈₉	—	4	4	no	—
416	C₂×C₄×C₈₉	—	4	2	no	—
417	C₂×C₄×C₈₉	—	4	4	no	—
418	C₂×C₄×C₈₉	—	4	4	no	—
419	C₂×C₄×C₈₉	—	4	4	no	—
420	C₂×C₄×C₈₉	—	4	4	no	—
421	C₂×C₄×C₈₉	—	4	2	no	—
422	C₂×C₄×C₈₉	—	8	2	no	—
423	C₂×C₄×C₈₉	—	8	2	no	—
424	C₂×C₄×C₈₉	—	8	2	no	—
425	C₂×C₄×C₈₉	—	8	1	no	—
426	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
427	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
429	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
434	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
435	C₈×C₈₉	—	2	2	no	—
436	C₈×C₈₉	—	2	2	no	—
437	C₈×C₈₉	—	2	4	no	—
438	C₂²×C₈₉	—	2	1	no	—
439	C₂²×C₈₉	—	2	1	no	—
440	C₂²×C₈₉	—	2	1	no	—
441	C₂²×C₈₉	—	2	1	no	—
442	C₂²×C₈₉	—	2	1	no	—
443	C₂²×C₈₉	—	2	1	no	—
444	C₂²×C₈₉	—	2	1	no	—
445	C₂²×C₈₉	—	4	4	no	—
446	C₂²×C₈₉	—	4	2	no	—
447	C₂²×C₈₉	—	4	1	no	—
448	C₂²×C₈₉	—	4	2	no	—
449	C₂²×C₈₉	—	4	2	no	—
450	C₂²×C₈₉	—	4	1	no	—
451	C₂²×C₈₉	—	4	2	no	—
452	C₂²×C₈₉	—	4	1	no	—
453	C₂²×C₈₉	—	4	2	no	—
454	C₂²×C₈₉	—	4	2	no	—
455	C₂²×C₈₉	—	8	4	no	—
456	C₂²×C₈₉	—	16	2	no	—
457	C₂²×C₈₉	#535	1	2	yes	—
458	C₂²×C₈₉	#577	1	2	yes	—
459	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
460	C₄×C₈₉	—	2	2	no	—
461	C₄×C₈₉	—	2	2	no	—
462	C₄×C₈₉	—	2	1	no	—
463	C₄×C₈₉	—	2	1	no	—
464	C₄×C₈₉	—	2	2	no	—
465	C₄×C₈₉	—	2	2	no	—
466	C₄×C₈₉	—	4	1	no	—
467	C₄×C₈₉	—	4	2	no	—
468	C₄×C₈₉	—	4	4	no	—
469	C₄×C₈₉	—	4	1	no	—
470	C₄×C₈₉	—	4	2	no	—
471	C₄×C₈₉	—	4	1	no	—
472	C₄×C₈₉	#535	1	2	yes	—
473	C₄×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
474	#60813	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
475	C₂×C₈₉	—	2	2	no	—
476	C₂×C₈₉	—	2	2	no	—
477	C₂×C₈₉	—	4	1	no	—
478	C₂×C₈₉	—	8	1	no	—
479	C₂×C₈₉	—	8	2	no	—
480	C₂×C₈₉	—	8	2	no	—
481	C₂×C₈₉	C₂×#535	1	1	yes	characteristic
482	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
483	C₂×C₈₉	#3586	1	1	yes	characteristic
484	#3494	C₂×C₈₉	1	1	yes	characteristic, complemented
485	C₂×#536	C₂×C₈₉	1	1	yes	characteristic, complemented
486	#3225	C₂×C₈₉	1	4	yes	complemented
487	#3221	C₂×C₈₉	1	4	yes	complemented
488	#3218	C₂×C₈₉	1	2	yes	complemented
489	#3213	C₂×C₈₉	1	2	yes	complemented
490	#3211	C₂×C₈₉	1	2	yes	complemented
491	#3206	C₂×C₈₉	1	2	yes	complemented
492	#3154	C₂×C₈₉	1	2	yes	complemented
493	#3137	C₂×C₈₉	1	2	yes	complemented
494	#3046	C₂×C₈₉	1	2	yes	complemented
495	#3042	C₂×C₈₉	1	2	yes	complemented
496	#3006	C₂×C₈₉	1	1	yes	characteristic, complemented
497	#3004	C₂×C₈₉	1	1	yes	characteristic, complemented
498	#3002	C₂×C₈₉	1	1	yes	characteristic, complemented
499	C₂×#448	C₂×C₈₉	1	1	yes	characteristic, complemented
500	#2924	C₂×C₈₉	1	1	yes	characteristic, complemented
501	C₈₉	#60813	1	1	yes	characteristic, direct product factor, Sylow
502	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
503	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
504	C₂×#137	C₂²×C₈₉	1	2	yes	complemented
505	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
506	C₂×#135	C₂²×C₈₉	1	2	yes	—
507	C₂²×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
508	#555	—	2	1	no	—
509	#553	—	2	1	no	—
510	#553	—	2	1	no	—
511	#551	—	2	2	no	—
512	#547	—	2	1	no	—
513	#546	—	2	2	no	—
514	#544	C₂²×C₈₉	1	1	yes	characteristic, complemented
515	#542	C₂²×C₈₉	1	2	yes	complemented
516	#540	C₂²×C₈₉	1	2	yes	complemented
517	#536	—	2	2	no	—
518	#536	—	2	1	no	—
519	#536	—	2	1	no	—
520	#536	C₂²×C₈₉	1	2	yes	—
521	#536	C₂²×C₈₉	1	2	yes	—
522	#536	C₂²×C₈₉	1	4	yes	complemented
523	#535	C₂²×C₈₉	1	1	yes	characteristic, complemented
524	#532	C₂²×C₈₉	1	2	yes	—
525	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
526	#529	C₂²×C₈₉	1	2	yes	—
527	C₂×#124	C₂²×C₈₉	1	2	yes	complemented
528	#525	C₂²×C₈₉	1	1	yes	characteristic
529	C₂×#123	—	2	2	no	—
530	C₂×C₂²⋊Q₈	—	2	1	no	—
531	C₂×C₂²⋊Q₈	—	2	1	no	—
532	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
533	#520	C₂²×C₈₉	1	1	yes	characteristic, complemented
534	#518	C₂²×C₈₉	1	1	yes	characteristic, complemented
535	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
536	#497	C₂²×C₈₉	1	4	yes	complemented
537	#496	C₂²×C₈₉	1	4	yes	complemented
538	#495	C₂²×C₈₉	1	4	yes	complemented
539	#492	C₂²×C₈₉	1	4	yes	complemented
540	#491	C₂²×C₈₉	1	4	yes	complemented
541	#489	C₂²×C₈₉	1	4	yes	complemented
542	#488	C₂²×C₈₉	1	4	yes	complemented
543	#487	C₂²×C₈₉	1	4	yes	complemented
544	#464	C₂²×C₈₉	1	4	yes	complemented
545	#463	C₂²×C₈₉	1	4	yes	complemented
546	#463	C₂²×C₈₉	1	4	yes	complemented
547	#463	C₂²×C₈₉	1	4	yes	complemented
548	#462	C₂²×C₈₉	1	4	yes	complemented
549	#461	C₂²×C₈₉	1	4	yes	complemented
550	#461	C₂²×C₈₉	1	4	yes	complemented
551	#461	C₂²×C₈₉	1	4	yes	complemented
552	#452	C₂²×C₈₉	1	2	yes	complemented
553	#451	C₂²×C₈₉	1	2	yes	complemented
554	#451	C₂²×C₈₉	1	1	yes	characteristic, complemented
555	#451	C₂²×C₈₉	1	2	yes	complemented
556	#450	C₂²×C₈₉	1	1	yes	characteristic, complemented
557	#449	C₂²×C₈₉	1	4	yes	—
558	#449	C₂²×C₈₉	1	2	yes	complemented
559	#448	C₂²×C₈₉	1	2	yes	—
560	#448	C₂²×C₈₉	1	2	yes	—
561	#448	C₂²×C₈₉	1	2	yes	—
562	#448	C₂²×C₈₉	1	1	yes	characteristic, complemented
563	#448	C₂²×C₈₉	1	2	yes	complemented
564	#448	C₂²×C₈₉	1	2	yes	complemented
565	#448	C₂²×C₈₉	1	4	yes	complemented
566	#447	C₂²×C₈₉	1	2	yes	—
567	#447	C₂²×C₈₉	1	1	yes	characteristic, complemented
568	#433	C₂²×C₈₉	1	4	yes	complemented
569	#432	C₂²×C₈₉	1	2	yes	complemented
570	#431	C₂²×C₈₉	1	2	yes	complemented
571	#424	C₂²×C₈₉	1	2	yes	complemented
572	#419	C₂²×C₈₉	1	2	yes	complemented
573	#417	C₂²×C₈₉	1	2	yes	—
574	#416	C₂²×C₈₉	1	2	yes	—
575	C₂×#103	C₂²×C₈₉	1	2	yes	complemented
576	#407	C₂²×C₈₉	1	1	yes	characteristic
577	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
578	#405	C₂²×C₈₉	1	2	yes	complemented
579	C₂×#41	—	2	1	no	—
580	C₂×#41	—	2	1	no	—
581	C₂×#41	—	2	2	no	—
582	C₂×#41	—	4	4	no	—
583	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
584	C₂×#41	C₂³×C₈₉	1	2	yes	—
585	C₂×#41	C₂³×C₈₉	1	2	yes	—
586	C₂²×Q₈	—	2	1	no	—
587	C₂²×Q₈	—	2	1	no	—
588	C₂²×Q₈	—	2	1	no	—
589	C₂²×Q₈	—	4	4	no	—
590	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
591	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
592	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
593	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
594	C₂²×D₄	—	2	1	no	—
595	C₂²×D₄	—	2	1	no	—
596	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
597	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
598	C₂³×C₄	—	2	1	no	—
599	C₂³×C₄	—	2	1	no	—
600	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
601	#137	—	4	4	no	—
602	AGL(1,ℤ/8)	—	4	4	no	—
603	#135	—	4	4	no	—
604	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
605	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
606	C₂×SD₁₆	—	4	4	no	—
607	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
608	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
609	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
610	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
611	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
612	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
613	C₂×D₈	C₂³×C₈₉	1	2	yes	—
614	C₂×D₈	C₂³×C₈₉	1	4	yes	—
615	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
616	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
617	C₄⋊Q₈	—	2	1	no	—
618	C₄⋊Q₈	—	2	2	no	—
619	C₄⋊Q₈	—	2	2	no	—
620	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
621	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
622	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
623	#127	C₂³×C₈₉	1	2	yes	—
624	#126	—	2	2	no	—
625	#126	—	2	2	no	—
626	#125	—	2	1	no	—
627	#125	C₂³×C₈₉	1	2	yes	—
628	#124	—	2	2	no	—
629	#124	—	2	2	no	—
630	#124	—	2	2	no	—
631	#124	—	2	2	no	—
632	#124	C₂³×C₈₉	1	4	yes	—
633	#124	C₂³×C₈₉	1	4	yes	—
634	#124	C₂³×C₈₉	1	2	yes	—
635	#123	—	2	1	no	—
636	#123	—	2	2	no	—
637	#123	—	2	2	no	—
638	#123	—	2	2	no	—
639	#123	—	2	4	no	—
640	#123	—	2	4	no	—
641	#123	—	2	4	no	—
642	#123	—	2	4	no	—
643	#123	—	2	2	no	—
644	C₂²⋊Q₈	—	2	2	no	—
645	C₂²⋊Q₈	—	2	2	no	—
646	C₂²⋊Q₈	—	2	2	no	—
647	C₂²⋊Q₈	—	2	2	no	—
648	C₂²⋊Q₈	—	2	4	no	—
649	C₂²⋊Q₈	—	2	4	no	—
650	C₂²⋊Q₈	—	2	2	no	—
651	C₂²⋊Q₈	—	2	2	no	—
652	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
653	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
654	#121	—	2	1	no	—
655	#121	—	2	1	no	—
656	#121	—	2	2	no	—
657	#121	—	2	1	no	—
658	#121	—	2	1	no	—
659	#121	—	2	2	no	—
660	#121	—	2	2	no	—
661	#121	C₂³×C₈₉	1	2	yes	—
662	#121	C₂³×C₈₉	1	2	yes	—
663	#121	C₂³×C₈₉	1	1	yes	characteristic
664	#121	C₂³×C₈₉	1	1	yes	characteristic
665	#120	—	2	1	no	—
666	#120	—	2	2	no	—
667	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
668	C₄×D₄	—	2	1	no	—
669	C₄×D₄	—	2	1	no	—
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	—	2	1	no	—
672	C₄×D₄	—	2	1	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	C₂³×C₈₉	1	2	yes	—
676	C₄×D₄	C₂³×C₈₉	1	2	yes	—
677	C₄×D₄	C₂³×C₈₉	1	2	yes	—
678	#117	—	2	1	no	—
679	#117	—	2	2	no	—
680	#117	D₄×C₈₉	1	2	yes	—
681	#117	D₄×C₈₉	1	1	yes	characteristic
682	#117	D₄×C₈₉	1	1	yes	characteristic
683	#117	C₂³×C₈₉	1	1	yes	characteristic
684	#117	C₂³×C₈₉	1	1	yes	characteristic
685	#117	C₂³×C₈₉	1	1	yes	characteristic
686	#117	C₂³×C₈₉	1	2	yes	—
687	C₂×C₄⋊C₄	—	2	2	no	—
688	C₂×C₄⋊C₄	—	2	2	no	—
689	C₂×C₄⋊C₄	—	2	1	no	—
690	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
691	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
692	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
693	C₂×C₂²⋊C₄	—	2	1	no	—
694	C₂×C₂²⋊C₄	—	2	2	no	—
695	C₂×C₂²⋊C₄	—	2	2	no	—
696	C₂×C₂²⋊C₄	—	2	2	no	—
697	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
698	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
699	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
700	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
701	#103	C₂³×C₈₉	1	4	yes	—
702	#103	C₂³×C₈₉	1	4	yes	—
703	#103	C₂³×C₈₉	1	2	yes	—
704	#103	C₂³×C₈₉	1	2	yes	—
705	#103	C₂³×C₈₉	1	4	yes	—
706	#103	C₂³×C₈₉	1	4	yes	—
707	#103	C₂³×C₈₉	1	4	yes	—
708	#102	C₂³×C₈₉	1	2	yes	—
709	#102	C₂³×C₈₉	1	2	yes	—
710	#102	C₂³×C₈₉	1	4	yes	—
711	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
712	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
713	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
714	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
715	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
716	#97	C₂³×C₈₉	1	4	yes	—
717	C₄×C₈	C₂³×C₈₉	1	4	yes	—
718	C₂⁴	—	2	1	no	—
719	C₂⁴	—	2	1	no	—
720	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
721	#41	—	2	4	no	—
722	#41	—	2	4	no	—
723	#41	—	2	4	no	—
724	#41	—	4	2	no	—
725	#41	—	4	2	no	—
726	#41	—	4	4	no	—
727	#41	—	4	4	no	—
728	#41	—	8	4	no	—
729	C₂×Q₈	—	2	2	no	—
730	C₂×Q₈	—	2	2	no	—
731	C₂×Q₈	—	2	2	no	—
732	C₂×Q₈	—	2	1	no	—
733	C₂×Q₈	—	2	2	no	—
734	C₂×Q₈	—	2	4	no	—
735	C₂×Q₈	—	2	4	no	—
736	C₂×Q₈	—	4	4	no	—
737	C₂×Q₈	—	4	4	no	—
738	C₂×Q₈	—	4	2	no	—
739	C₂×Q₈	—	4	4	no	—
740	C₂×Q₈	—	4	4	no	—
741	C₂×Q₈	—	4	4	no	—
742	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
743	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
744	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
745	C₂×D₄	—	2	1	no	—
746	C₂×D₄	—	2	1	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	1	no	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	2	1	no	—
753	C₂×D₄	—	2	1	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	4	no	—
757	C₂×D₄	—	4	2	no	—
758	C₂×D₄	—	4	4	no	—
759	C₂×D₄	—	8	2	no	—
760	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
761	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
762	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
763	C₂²×C₄	—	2	4	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	1	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	2	1	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	4	4	no	—
776	C₂²×C₄	—	4	4	no	—
777	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
778	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
779	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
780	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
781	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
782	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
785	Q₁₆	—	4	2	no	—
786	Q₁₆	—	4	4	no	—
787	SD₁₆	—	4	4	no	—
788	SD₁₆	—	4	4	no	—
789	SD₁₆	—	4	2	no	—
790	SD₁₆	—	4	2	no	—
791	SD₁₆	—	4	4	no	—
792	SD₁₆	—	4	4	no	—
793	D₈	—	4	2	no	—
794	D₈	—	4	4	no	—
795	M₁₆	—	2	4	no	—
796	C₂×C₈	—	2	4	no	—
797	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
798	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
799	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
800	C₄⋊C₄	—	2	1	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	4	no	—
803	C₄⋊C₄	—	2	4	no	—
804	C₄⋊C₄	—	2	4	no	—
805	C₄⋊C₄	—	2	4	no	—
806	C₄⋊C₄	—	2	1	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	1	no	—
811	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
812	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
813	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
814	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
815	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
816	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
817	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
818	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
819	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
820	C₂²⋊C₄	—	2	1	no	—
821	C₂²⋊C₄	—	2	1	no	—
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	—	2	4	no	—
828	C₂²⋊C₄	—	2	4	no	—
829	C₂²⋊C₄	—	2	4	no	—
830	C₂²⋊C₄	—	2	4	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	1	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	1	no	—
836	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
837	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
838	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
839	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
840	C₄²	—	2	2	no	—
841	C₄²	—	2	1	no	—
842	C₄²	C₂×D₄×C₈₉	1	2	yes	—
843	C₄²	C₂×D₄×C₈₉	1	2	yes	—
844	C₄²	C₂⁴×C₈₉	1	2	yes	—
845	C₄²	C₂⁴×C₈₉	1	2	yes	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	4	1	no	—
852	C₂³	—	4	2	no	—
853	C₂³	—	4	2	no	—
854	C₂³	—	4	2	no	—
855	C₂³	—	4	2	no	—
856	C₂³	—	8	1	no	—
857	C₂³	—	8	1	no	—
858	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
859	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
860	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
861	Q₈	—	2	4	no	—
862	Q₈	—	2	2	no	—
863	Q₈	—	2	2	no	—
864	Q₈	—	2	4	no	—
865	Q₈	—	2	2	no	—
866	Q₈	—	4	4	no	—
867	Q₈	—	4	4	no	—
868	Q₈	—	4	2	no	—
869	Q₈	—	4	4	no	—
870	Q₈	—	8	2	no	—
871	D₄	—	2	2	no	—
872	D₄	—	2	4	no	—
873	D₄	—	2	2	no	—
874	D₄	—	2	2	no	—
875	D₄	—	4	2	no	—
876	D₄	—	4	4	no	—
877	D₄	—	4	4	no	—
878	D₄	—	4	2	no	—
879	D₄	—	4	4	no	—
880	D₄	—	4	2	no	—
881	D₄	—	4	2	no	—
882	D₄	—	8	2	no	—
883	D₄	—	8	2	no	—
884	D₄	—	8	1	no	—
885	D₄	—	8	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	4	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	4	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	4	2	no	—
899	C₂×C₄	—	4	4	no	—
900	C₂×C₄	—	4	2	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	4	4	no	—
903	C₂×C₄	—	4	4	no	—
904	C₂×C₄	—	4	4	no	—
905	C₂×C₄	—	4	2	no	—
906	C₂×C₄	—	8	2	no	—
907	C₂×C₄	—	8	2	no	—
908	C₂×C₄	—	8	2	no	—
909	C₂×C₄	—	8	1	no	—
910	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
911	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
912	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
913	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
914	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
915	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
916	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
917	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
918	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
919	C₈	—	2	2	no	—
920	C₈	—	2	2	no	—
921	C₈	—	2	4	no	—
922	C₂²	—	2	1	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	4	4	no	—
930	C₂²	—	4	1	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	1	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	4	1	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	8	4	no	—
940	C₂²	—	16	2	no	—
941	C₂²	#535×C₈₉	1	2	yes	—
942	C₂²	#577×C₈₉	1	2	yes	—
943	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
944	C₄	—	2	2	no	—
945	C₄	—	2	2	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	4	2	no	—
951	C₄	—	4	1	no	—
952	C₄	—	4	1	no	—
953	C₄	—	4	2	no	—
954	C₄	—	4	4	no	—
955	C₄	—	4	1	no	—
956	C₄	#535×C₈₉	1	2	yes	—
957	C₄	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
958	C₂	—	2	2	no	—
959	C₂	—	2	2	no	—
960	C₂	—	4	1	no	—
961	C₂	—	8	1	no	—
962	C₂	—	8	2	no	—
963	C₂	—	8	2	no	—
964	C₂	C₂×#535×C₈₉	1	1	yes	characteristic
965	C₂	C₂×#577×C₈₉	1	1	yes	characteristic
966	C₂	C₈₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×#117×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3494	C₂	semidirect
2. C₂×#536×C₈₉	C₂	semidirect
3. C₈₉×#3225	C₂	semidirect
4. C₈₉×#3221	C₂	semidirect
5. C₈₉×#3218	C₂	semidirect
6. C₈₉×#3213	C₂	semidirect
7. C₈₉×#3211	C₂	semidirect
8. C₈₉×#3206	C₂	semidirect
9. C₈₉×#3154	C₂	semidirect
10. C₈₉×#3137	C₂	semidirect
11. C₈₉×#3046	C₂	semidirect
12. C₈₉×#3042	C₂	semidirect
13. C₈₉×#3006	C₂	semidirect
14. C₈₉×#3004	C₂	semidirect
15. C₈₉×#3002	C₂	semidirect
16. C₂×#448×C₈₉	C₂	semidirect
17. C₈₉×#2924	C₂	semidirect
20. C₂×#137×C₈₉	C₂²	semidirect
23. C₂²×SD₁₆×C₈₉	C₂²	semidirect
30. #544×C₈₉	C₂²	semidirect
31. #542×C₈₉	C₂²	semidirect
32. #540×C₈₉	C₂²	semidirect
38. #536×C₈₉	C₂²	semidirect
39. #535×C₈₉	C₂²	semidirect
41. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
43. C₂×#124×C₈₉	C₂²	semidirect
49. #520×C₈₉	C₂²	semidirect
50. #518×C₈₉	C₂²	semidirect
52. #497×C₈₉	C₂²	semidirect
53. #496×C₈₉	C₂²	semidirect
54. #495×C₈₉	C₂²	semidirect
55. #492×C₈₉	C₂²	semidirect
56. #491×C₈₉	C₂²	semidirect
57. #489×C₈₉	C₂²	semidirect
58. #488×C₈₉	C₂²	semidirect
59. #487×C₈₉	C₂²	semidirect
60. #464×C₈₉	C₂²	semidirect
61. #463×C₈₉	C₂²	semidirect
62. #463×C₈₉	C₂²	semidirect
63. #463×C₈₉	C₂²	semidirect
64. #462×C₈₉	C₂²	semidirect
65. #461×C₈₉	C₂²	semidirect
66. #461×C₈₉	C₂²	semidirect
67. #461×C₈₉	C₂²	semidirect
68. #452×C₈₉	C₂²	semidirect
69. #451×C₈₉	C₂²	semidirect
70. #451×C₈₉	C₂²	semidirect
71. #451×C₈₉	C₂²	semidirect
72. #450×C₈₉	C₂²	semidirect
74. #449×C₈₉	C₂²	semidirect
78. #448×C₈₉	C₂²	semidirect
79. #448×C₈₉	C₂²	semidirect
80. #448×C₈₉	C₂²	semidirect
81. #448×C₈₉	C₂²	semidirect
83. #447×C₈₉	C₂²	semidirect
84. #433×C₈₉	C₂²	semidirect
85. #432×C₈₉	C₂²	semidirect
86. #431×C₈₉	C₂²	semidirect
87. #424×C₈₉	C₂²	semidirect
88. #419×C₈₉	C₂²	semidirect
91. C₂×#103×C₈₉	C₂²	semidirect
94. #405×C₈₉	C₂²	semidirect
474. #60813	C₈₉	direct (N × H)
484. #3494	C₂×C₈₉	semidirect
485. C₂×#536	C₂×C₈₉	semidirect
486. #3225	C₂×C₈₉	semidirect
487. #3221	C₂×C₈₉	semidirect
488. #3218	C₂×C₈₉	semidirect
489. #3213	C₂×C₈₉	semidirect
490. #3211	C₂×C₈₉	semidirect
491. #3206	C₂×C₈₉	semidirect
492. #3154	C₂×C₈₉	semidirect
493. #3137	C₂×C₈₉	semidirect
494. #3046	C₂×C₈₉	semidirect
495. #3042	C₂×C₈₉	semidirect
496. #3006	C₂×C₈₉	semidirect
497. #3004	C₂×C₈₉	semidirect
498. #3002	C₂×C₈₉	semidirect
499. C₂×#448	C₂×C₈₉	semidirect
500. #2924	C₂×C₈₉	semidirect
501. C₈₉	#60813	direct (N × H)
504. C₂×#137	C₂²×C₈₉	semidirect
507. C₂²×SD₁₆	C₂²×C₈₉	semidirect
514. #544	C₂²×C₈₉	semidirect
515. #542	C₂²×C₈₉	semidirect
516. #540	C₂²×C₈₉	semidirect
522. #536	C₂²×C₈₉	semidirect
523. #535	C₂²×C₈₉	semidirect
525. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
527. C₂×#124	C₂²×C₈₉	semidirect
533. #520	C₂²×C₈₉	semidirect
534. #518	C₂²×C₈₉	semidirect
536. #497	C₂²×C₈₉	semidirect
537. #496	C₂²×C₈₉	semidirect
538. #495	C₂²×C₈₉	semidirect
539. #492	C₂²×C₈₉	semidirect
540. #491	C₂²×C₈₉	semidirect
541. #489	C₂²×C₈₉	semidirect
542. #488	C₂²×C₈₉	semidirect
543. #487	C₂²×C₈₉	semidirect
544. #464	C₂²×C₈₉	semidirect
545. #463	C₂²×C₈₉	semidirect
546. #463	C₂²×C₈₉	semidirect
547. #463	C₂²×C₈₉	semidirect
548. #462	C₂²×C₈₉	semidirect
549. #461	C₂²×C₈₉	semidirect
550. #461	C₂²×C₈₉	semidirect
551. #461	C₂²×C₈₉	semidirect
552. #452	C₂²×C₈₉	semidirect
553. #451	C₂²×C₈₉	semidirect
554. #451	C₂²×C₈₉	semidirect
555. #451	C₂²×C₈₉	semidirect
556. #450	C₂²×C₈₉	semidirect
558. #449	C₂²×C₈₉	semidirect
562. #448	C₂²×C₈₉	semidirect
563. #448	C₂²×C₈₉	semidirect
564. #448	C₂²×C₈₉	semidirect
565. #448	C₂²×C₈₉	semidirect
567. #447	C₂²×C₈₉	semidirect
568. #433	C₂²×C₈₉	semidirect
569. #432	C₂²×C₈₉	semidirect
570. #431	C₂²×C₈₉	semidirect
571. #424	C₂²×C₈₉	semidirect
572. #419	C₂²×C₈₉	semidirect
575. C₂×#103	C₂²×C₈₉	semidirect
578. #405	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×#3494	2
C₂×#536×C₈₉	2
C₈₉×#3225	2
C₈₉×#3221	2
C₈₉×#3218	2
C₈₉×#3213	2
C₈₉×#3211	2
C₈₉×#3206	2
C₈₉×#3154	2
C₈₉×#3137	2
C₈₉×#3046	2
C₈₉×#3042	2
C₈₉×#3006	2
C₈₉×#3004	2
C₈₉×#3002	2
C₂×#448×C₈₉	2
C₈₉×#2924	2
#60813	89

Subgroups — C89×#60813 #36438661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60813 #36438661