Subgroups — C₈₉×#60559 #36438407

Order 22784.

2170 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3116	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3115	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3111	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3107	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3106	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3102	C₂	1	4	yes	maximal, complemented
9	C₈₉×#3093	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3078	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3077	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3037	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3036	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3005	C₂	1	2	yes	maximal, complemented
15	C₄×#137×C₈₉	C₂	1	2	yes	maximal, complemented
16	C₄×AGL(1,ℤ/8)×C₈₉	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2920	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#137×C₈₉	C₂²	1	2	yes	—
20	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
21	#533×C₈₉	C₂²	1	1	yes	characteristic
22	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
23	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
24	#532×C₈₉	C₂²	1	1	yes	characteristic
25	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
26	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
27	#529×C₈₉	—	2	1	no	—
28	#529×C₈₉	—	2	1	no	—
29	#529×C₈₉	—	2	1	no	—
30	#529×C₈₉	—	2	1	no	—
31	#529×C₈₉	C₂²	1	2	yes	complemented
32	#529×C₈₉	C₂²	1	2	yes	complemented
33	#525×C₈₉	—	2	1	no	—
34	#525×C₈₉	—	2	1	no	—
35	#525×C₈₉	C₂²	1	2	yes	—
36	C₄×#41×C₈₉	—	2	1	no	—
37	C₄×#41×C₈₉	—	2	1	no	—
38	C₄×#41×C₈₉	—	2	1	no	—
39	C₄×#41×C₈₉	—	2	1	no	—
40	C₄×#41×C₈₉	—	2	1	no	—
41	C₄×#41×C₈₉	—	2	1	no	—
42	C₄×#41×C₈₉	C₂²	1	2	yes	—
43	C₄×#41×C₈₉	C₂²	1	2	yes	—
44	C₄×#41×C₈₉	C₂²	1	2	yes	—
45	C₄×#41×C₈₉	C₂²	1	2	yes	—
46	C₄×#41×C₈₉	C₂²	1	2	yes	—
47	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₈₉	—	2	1	no	—
50	C₂×C₄×D₄×C₈₉	—	2	1	no	—
51	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
52	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×#117×C₈₉	—	2	1	no	—
54	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
55	C₂²×C₄²×C₈₉	—	2	1	no	—
56	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
57	#485×C₈₉	C₂²	1	4	yes	complemented
58	#485×C₈₉	C₂²	1	4	yes	complemented
59	#482×C₈₉	C₂²	1	4	yes	complemented
60	#482×C₈₉	C₂²	1	4	yes	complemented
61	#479×C₈₉	C₂²	1	4	yes	complemented
62	#478×C₈₉	C₂²	1	4	yes	complemented
63	#477×C₈₉	C₂²	1	2	yes	complemented
64	#476×C₈₉	C₂²	1	2	yes	complemented
65	#475×C₈₉	C₂²	1	2	yes	complemented
66	#474×C₈₉	C₂²	1	2	yes	complemented
67	#464×C₈₉	C₂²	1	4	yes	complemented
68	#463×C₈₉	C₂²	1	4	yes	complemented
69	#462×C₈₉	C₂²	1	2	yes	complemented
70	#461×C₈₉	C₂²	1	2	yes	complemented
71	#460×C₈₉	C₂²	1	2	yes	complemented
72	#459×C₈₉	C₂²	1	2	yes	complemented
73	#452×C₈₉	C₂²	1	4	yes	—
74	#452×C₈₉	C₂²	1	4	yes	—
75	#449×C₈₉	C₂²	1	4	yes	—
76	#449×C₈₉	C₂²	1	4	yes	—
77	#442×C₈₉	C₂²	1	4	yes	complemented
78	#441×C₈₉	C₂²	1	4	yes	complemented
79	#440×C₈₉	C₂²	1	4	yes	complemented
80	#440×C₈₉	C₂²	1	4	yes	complemented
81	C₄×Q₁₆×C₈₉	C₂²	1	4	yes	complemented
82	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	complemented
83	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	complemented
84	C₄×D₈×C₈₉	C₂²	1	4	yes	complemented
85	#432×C₈₉	C₂²	1	2	yes	complemented
86	#432×C₈₉	C₂²	1	2	yes	complemented
87	#431×C₈₉	C₂²	1	2	yes	complemented
88	#431×C₈₉	C₂²	1	2	yes	complemented
89	#428×C₈₉	C₂²	1	2	yes	—
90	#428×C₈₉	C₂²	1	2	yes	—
91	#423×C₈₉	C₂²	1	1	yes	characteristic
92	#423×C₈₉	C₂²	1	1	yes	characteristic
93	#419×C₈₉	C₂²	1	2	yes	—
94	#418×C₈₉	C₂²	1	2	yes	—
95	#417×C₈₉	C₂²	1	2	yes	—
96	#417×C₈₉	C₂²	1	2	yes	—
97	#407×C₈₉	C₂²	1	2	yes	—
98	C₄×M₁₆×C₈₉	C₂²	1	2	yes	—
99	C₂×#41×C₈₉	—	2	4	no	—
100	C₂×#41×C₈₉	—	2	4	no	—
101	C₂×#41×C₈₉	—	2	1	no	—
102	C₂×#41×C₈₉	—	2	1	no	—
103	C₂×#41×C₈₉	—	2	1	no	—
104	C₂×#41×C₈₉	—	2	1	no	—
105	C₂×#41×C₈₉	C₂³	1	2	yes	—
106	C₂×#41×C₈₉	C₂³	1	2	yes	—
107	C₂×#41×C₈₉	C₂³	1	2	yes	—
108	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₈₉	—	2	1	no	—
110	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₈₉	—	2	1	no	—
112	C₂³×C₄×C₈₉	—	2	1	no	—
113	C₂³×C₄×C₈₉	—	2	1	no	—
114	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
115	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
116	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
117	#137×C₈₉	—	2	8	no	—
118	AGL(1,ℤ/8)×C₈₉	—	2	8	no	—
119	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
120	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
121	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
122	C₂×D₈×C₈₉	C₂³	1	4	yes	—
123	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
124	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
125	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
126	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
127	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
128	#127×C₈₉	C₂³	1	1	yes	characteristic
129	#126×C₈₉	—	2	2	no	—
130	#126×C₈₉	—	2	2	no	—
131	#125×C₈₉	—	2	1	no	—
132	#125×C₈₉	—	2	1	no	—
133	#125×C₈₉	C₂³	1	2	yes	—
134	#124×C₈₉	—	2	1	no	—
135	#124×C₈₉	—	2	1	no	—
136	#124×C₈₉	C₂³	1	2	yes	—
137	#123×C₈₉	—	2	2	no	—
138	#123×C₈₉	—	2	2	no	—
139	#123×C₈₉	—	2	2	no	—
140	C₂²⋊Q₈×C₈₉	—	2	1	no	—
141	C₂²⋊Q₈×C₈₉	—	2	1	no	—
142	C₂²⋊Q₈×C₈₉	—	2	1	no	—
143	C₂²⋊Q₈×C₈₉	—	2	1	no	—
144	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
145	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
146	#121×C₈₉	—	2	1	no	—
147	#121×C₈₉	—	2	1	no	—
148	#121×C₈₉	—	2	1	no	—
149	#121×C₈₉	—	2	1	no	—
150	#121×C₈₉	C₂³	1	2	yes	—
151	#121×C₈₉	C₂³	1	2	yes	—
152	#120×C₈₉	—	2	2	no	—
153	C₄×Q₈×C₈₉	—	2	1	no	—
154	C₄×Q₈×C₈₉	—	2	1	no	—
155	C₄×Q₈×C₈₉	—	2	1	no	—
156	C₄×Q₈×C₈₉	—	2	1	no	—
157	C₄×Q₈×C₈₉	—	2	1	no	—
158	C₄×Q₈×C₈₉	—	2	1	no	—
159	C₄×Q₈×C₈₉	—	2	1	no	—
160	C₄×Q₈×C₈₉	—	2	1	no	—
161	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
162	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
163	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
164	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
165	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
166	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
167	C₄×D₄×C₈₉	—	2	2	no	—
168	C₄×D₄×C₈₉	—	2	2	no	—
169	C₄×D₄×C₈₉	—	2	2	no	—
170	C₄×D₄×C₈₉	—	2	2	no	—
171	C₄×D₄×C₈₉	—	2	2	no	—
172	C₄×D₄×C₈₉	—	2	2	no	—
173	C₄×D₄×C₈₉	—	2	2	no	—
174	C₄×D₄×C₈₉	—	2	2	no	—
175	C₄×D₄×C₈₉	—	2	2	no	—
176	C₄×D₄×C₈₉	—	2	2	no	—
177	C₄×D₄×C₈₉	—	2	2	no	—
178	C₄×D₄×C₈₉	—	2	2	no	—
179	C₄×D₄×C₈₉	—	2	2	no	—
180	C₄×D₄×C₈₉	—	2	2	no	—
181	C₄×D₄×C₈₉	—	2	1	no	—
182	C₄×D₄×C₈₉	—	2	1	no	—
183	C₄×D₄×C₈₉	—	2	1	no	—
184	C₄×D₄×C₈₉	—	2	1	no	—
185	C₄×D₄×C₈₉	—	2	1	no	—
186	C₄×D₄×C₈₉	—	2	1	no	—
187	C₄×D₄×C₈₉	—	2	1	no	—
188	C₄×D₄×C₈₉	—	2	1	no	—
189	C₄×D₄×C₈₉	C₂³	1	2	yes	—
190	C₄×D₄×C₈₉	C₂³	1	2	yes	—
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	C₄×D₄×C₈₉	C₂³	1	2	yes	—
195	#117×C₈₉	—	2	1	no	—
196	#117×C₈₉	—	2	1	no	—
197	#117×C₈₉	—	2	1	no	—
198	#117×C₈₉	—	2	1	no	—
199	#117×C₈₉	—	2	2	no	—
200	#117×C₈₉	—	2	2	no	—
201	#117×C₈₉	—	2	2	no	—
202	#117×C₈₉	—	2	2	no	—
203	#117×C₈₉	—	2	2	no	—
204	#117×C₈₉	—	2	2	no	—
205	#117×C₈₉	—	2	2	no	—
206	#117×C₈₉	C₂³	1	2	yes	—
207	#117×C₈₉	C₂³	1	2	yes	—
208	#117×C₈₉	C₂³	1	2	yes	—
209	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
210	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
211	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
214	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
215	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
216	C₂×C₄²×C₈₉	—	2	1	no	—
217	C₂×C₄²×C₈₉	—	2	1	no	—
218	C₂×C₄²×C₈₉	—	2	1	no	—
219	C₂×C₄²×C₈₉	—	2	2	no	—
220	C₂×C₄²×C₈₉	—	2	2	no	—
221	C₂×C₄²×C₈₉	—	2	2	no	—
222	C₂×C₄²×C₈₉	—	2	2	no	—
223	C₂×C₄²×C₈₉	—	2	2	no	—
224	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
225	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
226	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
227	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
228	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
229	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
230	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
236	#107×C₈₉	C₂³	1	4	yes	—
237	#107×C₈₉	C₂³	1	4	yes	—
238	#106×C₈₉	C₂³	1	4	yes	—
239	#106×C₈₉	C₂³	1	4	yes	—
240	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
241	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
242	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
243	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
244	#103×C₈₉	C₂³	1	4	yes	—
245	#103×C₈₉	C₂³	1	4	yes	—
246	#103×C₈₉	C₂³	1	4	yes	—
247	#103×C₈₉	C₂³	1	4	yes	—
248	#102×C₈₉	C₂³	1	4	yes	—
249	#102×C₈₉	C₂³	1	4	yes	—
250	#102×C₈₉	C₂³	1	4	yes	—
251	#102×C₈₉	C₂³	1	4	yes	—
252	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
253	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
254	#97×C₈₉	C₂³	1	4	yes	—
255	C₄×C₈×C₈₉	C₂³	1	4	yes	—
256	C₂⁴×C₈₉	—	2	1	no	—
257	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
258	#41×C₈₉	—	2	8	no	—
259	#41×C₈₉	—	2	8	no	—
260	#41×C₈₉	—	2	4	no	—
261	#41×C₈₉	—	2	4	no	—
262	#41×C₈₉	—	2	4	no	—
263	#41×C₈₉	—	2	4	no	—
264	#41×C₈₉	—	2	4	no	—
265	#41×C₈₉	—	2	4	no	—
266	#41×C₈₉	—	4	4	no	—
267	#41×C₈₉	—	4	4	no	—
268	C₂×Q₈×C₈₉	—	2	1	no	—
269	C₂×Q₈×C₈₉	—	2	1	no	—
270	C₂×Q₈×C₈₉	—	2	1	no	—
271	C₂×Q₈×C₈₉	—	2	2	no	—
272	C₂×Q₈×C₈₉	#41	1	4	yes	complemented
273	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
274	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
275	C₂×D₄×C₈₉	—	2	8	no	—
276	C₂×D₄×C₈₉	—	2	2	no	—
277	C₂×D₄×C₈₉	—	2	2	no	—
278	C₂×D₄×C₈₉	—	2	2	no	—
279	C₂×D₄×C₈₉	—	2	2	no	—
280	C₂×D₄×C₈₉	—	2	2	no	—
281	C₂×D₄×C₈₉	—	2	1	no	—
282	C₂×D₄×C₈₉	—	2	1	no	—
283	C₂×D₄×C₈₉	—	2	1	no	—
284	C₂×D₄×C₈₉	—	2	2	no	—
285	C₂×D₄×C₈₉	#41	1	4	yes	complemented
286	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
287	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₈₉	—	2	8	no	—
289	C₂²×C₄×C₈₉	—	2	1	no	—
290	C₂²×C₄×C₈₉	—	2	2	no	—
291	C₂²×C₄×C₈₉	—	2	2	no	—
292	C₂²×C₄×C₈₉	—	2	2	no	—
293	C₂²×C₄×C₈₉	—	2	2	no	—
294	C₂²×C₄×C₈₉	—	2	1	no	—
295	C₂²×C₄×C₈₉	—	2	1	no	—
296	C₂²×C₄×C₈₉	—	2	2	no	—
297	C₂²×C₄×C₈₉	—	2	2	no	—
298	C₂²×C₄×C₈₉	—	2	2	no	—
299	C₂²×C₄×C₈₉	—	2	2	no	—
300	C₂²×C₄×C₈₉	—	2	2	no	—
301	C₂²×C₄×C₈₉	—	2	2	no	—
302	C₂²×C₄×C₈₉	—	2	2	no	—
303	C₂²×C₄×C₈₉	—	4	2	no	—
304	C₂²×C₄×C₈₉	—	4	2	no	—
305	C₂²×C₄×C₈₉	—	4	4	no	—
306	C₂²×C₄×C₈₉	—	4	4	no	—
307	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
310	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
314	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
315	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
316	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
317	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
318	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
321	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
322	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
325	Q₁₆×C₈₉	—	2	8	no	—
326	SD₁₆×C₈₉	—	2	8	no	—
327	SD₁₆×C₈₉	—	2	8	no	—
328	D₈×C₈₉	—	2	8	no	—
329	M₁₆×C₈₉	—	2	4	no	—
330	M₁₆×C₈₉	—	2	4	no	—
331	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
332	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
333	C₄⋊C₄×C₈₉	—	2	2	no	—
334	C₄⋊C₄×C₈₉	—	2	2	no	—
335	C₄⋊C₄×C₈₉	—	2	2	no	—
336	C₄⋊C₄×C₈₉	—	2	2	no	—
337	C₄⋊C₄×C₈₉	—	2	1	no	—
338	C₄⋊C₄×C₈₉	—	2	1	no	—
339	C₄⋊C₄×C₈₉	—	2	1	no	—
340	C₄⋊C₄×C₈₉	—	2	1	no	—
341	C₄⋊C₄×C₈₉	—	2	1	no	—
342	C₄⋊C₄×C₈₉	—	2	1	no	—
343	C₄⋊C₄×C₈₉	—	2	2	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	2	no	—
349	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
350	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
351	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
352	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
353	C₂²⋊C₄×C₈₉	—	2	2	no	—
354	C₂²⋊C₄×C₈₉	—	2	2	no	—
355	C₂²⋊C₄×C₈₉	—	2	2	no	—
356	C₂²⋊C₄×C₈₉	—	2	2	no	—
357	C₂²⋊C₄×C₈₉	—	2	2	no	—
358	C₂²⋊C₄×C₈₉	—	2	2	no	—
359	C₂²⋊C₄×C₈₉	—	2	2	no	—
360	C₂²⋊C₄×C₈₉	—	2	2	no	—
361	C₂²⋊C₄×C₈₉	—	2	2	no	—
362	C₂²⋊C₄×C₈₉	—	2	2	no	—
363	C₂²⋊C₄×C₈₉	—	2	2	no	—
364	C₂²⋊C₄×C₈₉	—	2	2	no	—
365	C₂²⋊C₄×C₈₉	—	2	2	no	—
366	C₂²⋊C₄×C₈₉	—	2	2	no	—
367	C₂²⋊C₄×C₈₉	—	2	2	no	—
368	C₄²×C₈₉	—	2	2	no	—
369	C₄²×C₈₉	—	2	2	no	—
370	C₄²×C₈₉	—	2	2	no	—
371	C₄²×C₈₉	—	2	2	no	—
372	C₄²×C₈₉	—	2	2	no	—
373	C₄²×C₈₉	—	2	2	no	—
374	C₄²×C₈₉	—	2	2	no	—
375	C₄²×C₈₉	—	2	2	no	—
376	C₄²×C₈₉	—	2	2	no	—
377	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
378	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
379	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
380	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
381	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
382	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
383	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
384	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
385	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
386	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
387	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
388	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
389	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
390	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
391	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
392	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
393	C₂³×C₈₉	—	2	2	no	—
394	C₂³×C₈₉	—	2	4	no	—
395	C₂³×C₈₉	—	2	2	no	—
396	C₂³×C₈₉	—	2	2	no	—
397	C₂³×C₈₉	—	4	1	no	—
398	C₂³×C₈₉	—	4	1	no	—
399	C₂³×C₈₉	—	4	2	no	—
400	C₂³×C₈₉	—	4	2	no	—
401	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
402	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
403	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
404	Q₈×C₈₉	—	2	4	no	—
405	Q₈×C₈₉	—	2	2	no	—
406	Q₈×C₈₉	—	2	2	no	—
407	Q₈×C₈₉	—	2	2	no	—
408	Q₈×C₈₉	—	4	2	no	—
409	Q₈×C₈₉	—	4	2	no	—
410	Q₈×C₈₉	C₂×#41	1	4	yes	—
411	D₄×C₈₉	—	2	8	no	—
412	D₄×C₈₉	—	2	8	no	—
413	D₄×C₈₉	—	2	4	no	—
414	D₄×C₈₉	—	2	2	no	—
415	D₄×C₈₉	—	2	2	no	—
416	D₄×C₈₉	—	2	2	no	—
417	D₄×C₈₉	—	4	2	no	—
418	D₄×C₈₉	—	4	4	no	—
419	D₄×C₈₉	—	4	4	no	—
420	D₄×C₈₉	—	4	4	no	—
421	D₄×C₈₉	—	4	2	no	—
422	D₄×C₈₉	C₂×#41	1	4	yes	—
423	C₂×C₄×C₈₉	—	2	8	no	—
424	C₂×C₄×C₈₉	—	2	8	no	—
425	C₂×C₄×C₈₉	—	2	2	no	—
426	C₂×C₄×C₈₉	—	2	4	no	—
427	C₂×C₄×C₈₉	—	2	2	no	—
428	C₂×C₄×C₈₉	—	2	2	no	—
429	C₂×C₄×C₈₉	—	2	2	no	—
430	C₂×C₄×C₈₉	—	2	2	no	—
431	C₂×C₄×C₈₉	—	2	2	no	—
432	C₂×C₄×C₈₉	—	2	2	no	—
433	C₂×C₄×C₈₉	—	2	2	no	—
434	C₂×C₄×C₈₉	—	2	2	no	—
435	C₂×C₄×C₈₉	—	2	2	no	—
436	C₂×C₄×C₈₉	—	2	1	no	—
437	C₂×C₄×C₈₉	—	2	1	no	—
438	C₂×C₄×C₈₉	—	2	1	no	—
439	C₂×C₄×C₈₉	—	2	1	no	—
440	C₂×C₄×C₈₉	—	2	2	no	—
441	C₂×C₄×C₈₉	—	2	2	no	—
442	C₂×C₄×C₈₉	—	2	2	no	—
443	C₂×C₄×C₈₉	—	2	2	no	—
444	C₂×C₄×C₈₉	—	2	2	no	—
445	C₂×C₄×C₈₉	—	4	1	no	—
446	C₂×C₄×C₈₉	—	4	1	no	—
447	C₂×C₄×C₈₉	—	4	1	no	—
448	C₂×C₄×C₈₉	—	4	1	no	—
449	C₂×C₄×C₈₉	—	4	1	no	—
450	C₂×C₄×C₈₉	—	4	1	no	—
451	C₂×C₄×C₈₉	—	4	4	no	—
452	C₂×C₄×C₈₉	—	4	4	no	—
453	C₂×C₄×C₈₉	—	4	4	no	—
454	C₂×C₄×C₈₉	—	4	2	no	—
455	C₂×C₄×C₈₉	—	4	2	no	—
456	C₂×C₄×C₈₉	—	4	4	no	—
457	C₂×C₄×C₈₉	—	4	4	no	—
458	C₂×C₄×C₈₉	—	4	4	no	—
459	C₂×C₄×C₈₉	—	4	4	no	—
460	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
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	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
472	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
473	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
474	C₈×C₈₉	—	2	4	no	—
475	C₈×C₈₉	—	2	4	no	—
476	C₂²×C₈₉	—	2	1	no	—
477	C₂²×C₈₉	—	2	1	no	—
478	C₂²×C₈₉	—	2	1	no	—
479	C₂²×C₈₉	—	2	1	no	—
480	C₂²×C₈₉	—	2	4	no	—
481	C₂²×C₈₉	—	2	1	no	—
482	C₂²×C₈₉	—	2	1	no	—
483	C₂²×C₈₉	—	2	1	no	—
484	C₂²×C₈₉	—	2	1	no	—
485	C₂²×C₈₉	—	4	4	no	—
486	C₂²×C₈₉	—	4	8	no	—
487	C₂²×C₈₉	—	4	2	no	—
488	C₂²×C₈₉	—	4	2	no	—
489	C₂²×C₈₉	—	4	2	no	—
490	C₂²×C₈₉	—	4	2	no	—
491	C₂²×C₈₉	—	4	2	no	—
492	C₂²×C₈₉	#525	1	2	yes	—
493	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
494	C₄×C₈₉	—	2	1	no	—
495	C₄×C₈₉	—	2	1	no	—
496	C₄×C₈₉	—	2	4	no	—
497	C₄×C₈₉	—	2	1	no	—
498	C₄×C₈₉	—	2	1	no	—
499	C₄×C₈₉	—	2	1	no	—
500	C₄×C₈₉	—	2	1	no	—
501	C₄×C₈₉	—	2	1	no	—
502	C₄×C₈₉	—	2	1	no	—
503	C₄×C₈₉	—	4	2	no	—
504	C₄×C₈₉	—	4	2	no	—
505	C₄×C₈₉	—	4	2	no	—
506	C₄×C₈₉	—	4	2	no	—
507	C₄×C₈₉	—	4	2	no	—
508	C₄×C₈₉	#525	1	2	yes	—
509	C₄×C₈₉	#575	1	2	yes	—
510	C₄×C₈₉	#575	1	2	yes	—
511	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
512	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
513	#60559	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
514	C₂×C₈₉	—	2	2	no	—
515	C₂×C₈₉	—	4	1	no	—
516	C₂×C₈₉	—	4	1	no	—
517	C₂×C₈₉	—	4	4	no	—
518	C₂×C₈₉	—	8	2	no	—
519	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
520	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
521	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
522	#3444	C₂×C₈₉	1	1	yes	characteristic, complemented
523	C₂×C₄×#41	C₂×C₈₉	1	1	yes	characteristic, complemented
524	#3116	C₂×C₈₉	1	2	yes	complemented
525	#3115	C₂×C₈₉	1	2	yes	complemented
526	#3111	C₂×C₈₉	1	4	yes	complemented
527	#3107	C₂×C₈₉	1	2	yes	complemented
528	#3106	C₂×C₈₉	1	2	yes	complemented
529	#3102	C₂×C₈₉	1	4	yes	complemented
530	#3093	C₂×C₈₉	1	2	yes	complemented
531	#3078	C₂×C₈₉	1	1	yes	characteristic, complemented
532	#3077	C₂×C₈₉	1	1	yes	characteristic, complemented
533	#3037	C₂×C₈₉	1	1	yes	characteristic, complemented
534	#3036	C₂×C₈₉	1	1	yes	characteristic, complemented
535	#3005	C₂×C₈₉	1	2	yes	complemented
536	C₄×#137	C₂×C₈₉	1	2	yes	complemented
537	C₄×AGL(1,ℤ/8)	C₂×C₈₉	1	2	yes	complemented
538	#2920	C₂×C₈₉	1	1	yes	characteristic, complemented
539	C₈₉	#60559	1	1	yes	characteristic, direct product factor, Sylow
540	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
541	C₂×#137	C₂²×C₈₉	1	2	yes	—
542	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
543	#533	C₂²×C₈₉	1	1	yes	characteristic
544	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
545	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
546	#532	C₂²×C₈₉	1	1	yes	characteristic
547	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
548	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
549	#529	—	2	1	no	—
550	#529	—	2	1	no	—
551	#529	—	2	1	no	—
552	#529	—	2	1	no	—
553	#529	C₂²×C₈₉	1	2	yes	complemented
554	#529	C₂²×C₈₉	1	2	yes	complemented
555	#525	—	2	1	no	—
556	#525	—	2	1	no	—
557	#525	C₂²×C₈₉	1	2	yes	—
558	C₄×#41	—	2	1	no	—
559	C₄×#41	—	2	1	no	—
560	C₄×#41	—	2	1	no	—
561	C₄×#41	—	2	1	no	—
562	C₄×#41	—	2	1	no	—
563	C₄×#41	—	2	1	no	—
564	C₄×#41	C₂²×C₈₉	1	2	yes	—
565	C₄×#41	C₂²×C₈₉	1	2	yes	—
566	C₄×#41	C₂²×C₈₉	1	2	yes	—
567	C₄×#41	C₂²×C₈₉	1	2	yes	—
568	C₄×#41	C₂²×C₈₉	1	2	yes	—
569	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
570	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
571	C₂×C₄×D₄	—	2	1	no	—
572	C₂×C₄×D₄	—	2	1	no	—
573	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
574	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
575	C₂×#117	—	2	1	no	—
576	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
577	C₂²×C₄²	—	2	1	no	—
578	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
579	#485	C₂²×C₈₉	1	4	yes	complemented
580	#485	C₂²×C₈₉	1	4	yes	complemented
581	#482	C₂²×C₈₉	1	4	yes	complemented
582	#482	C₂²×C₈₉	1	4	yes	complemented
583	#479	C₂²×C₈₉	1	4	yes	complemented
584	#478	C₂²×C₈₉	1	4	yes	complemented
585	#477	C₂²×C₈₉	1	2	yes	complemented
586	#476	C₂²×C₈₉	1	2	yes	complemented
587	#475	C₂²×C₈₉	1	2	yes	complemented
588	#474	C₂²×C₈₉	1	2	yes	complemented
589	#464	C₂²×C₈₉	1	4	yes	complemented
590	#463	C₂²×C₈₉	1	4	yes	complemented
591	#462	C₂²×C₈₉	1	2	yes	complemented
592	#461	C₂²×C₈₉	1	2	yes	complemented
593	#460	C₂²×C₈₉	1	2	yes	complemented
594	#459	C₂²×C₈₉	1	2	yes	complemented
595	#452	C₂²×C₈₉	1	4	yes	—
596	#452	C₂²×C₈₉	1	4	yes	—
597	#449	C₂²×C₈₉	1	4	yes	—
598	#449	C₂²×C₈₉	1	4	yes	—
599	#442	C₂²×C₈₉	1	4	yes	complemented
600	#441	C₂²×C₈₉	1	4	yes	complemented
601	#440	C₂²×C₈₉	1	4	yes	complemented
602	#440	C₂²×C₈₉	1	4	yes	complemented
603	C₄×Q₁₆	C₂²×C₈₉	1	4	yes	complemented
604	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	complemented
605	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	complemented
606	C₄×D₈	C₂²×C₈₉	1	4	yes	complemented
607	#432	C₂²×C₈₉	1	2	yes	complemented
608	#432	C₂²×C₈₉	1	2	yes	complemented
609	#431	C₂²×C₈₉	1	2	yes	complemented
610	#431	C₂²×C₈₉	1	2	yes	complemented
611	#428	C₂²×C₈₉	1	2	yes	—
612	#428	C₂²×C₈₉	1	2	yes	—
613	#423	C₂²×C₈₉	1	1	yes	characteristic
614	#423	C₂²×C₈₉	1	1	yes	characteristic
615	#419	C₂²×C₈₉	1	2	yes	—
616	#418	C₂²×C₈₉	1	2	yes	—
617	#417	C₂²×C₈₉	1	2	yes	—
618	#417	C₂²×C₈₉	1	2	yes	—
619	#407	C₂²×C₈₉	1	2	yes	—
620	C₄×M₁₆	C₂²×C₈₉	1	2	yes	—
621	C₂×#41	—	2	4	no	—
622	C₂×#41	—	2	4	no	—
623	C₂×#41	—	2	1	no	—
624	C₂×#41	—	2	1	no	—
625	C₂×#41	—	2	1	no	—
626	C₂×#41	—	2	1	no	—
627	C₂×#41	C₂³×C₈₉	1	2	yes	—
628	C₂×#41	C₂³×C₈₉	1	2	yes	—
629	C₂×#41	C₂³×C₈₉	1	2	yes	—
630	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
631	C₂²×D₄	—	2	1	no	—
632	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
633	C₂³×C₄	—	2	1	no	—
634	C₂³×C₄	—	2	1	no	—
635	C₂³×C₄	—	2	1	no	—
636	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
637	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
638	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
639	#137	—	2	8	no	—
640	AGL(1,ℤ/8)	—	2	8	no	—
641	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
642	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
643	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
644	C₂×D₈	C₂³×C₈₉	1	4	yes	—
645	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
646	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
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	#127	C₂³×C₈₉	1	1	yes	characteristic
651	#126	—	2	2	no	—
652	#126	—	2	2	no	—
653	#125	—	2	1	no	—
654	#125	—	2	1	no	—
655	#125	C₂³×C₈₉	1	2	yes	—
656	#124	—	2	1	no	—
657	#124	—	2	1	no	—
658	#124	C₂³×C₈₉	1	2	yes	—
659	#123	—	2	2	no	—
660	#123	—	2	2	no	—
661	#123	—	2	2	no	—
662	C₂²⋊Q₈	—	2	1	no	—
663	C₂²⋊Q₈	—	2	1	no	—
664	C₂²⋊Q₈	—	2	1	no	—
665	C₂²⋊Q₈	—	2	1	no	—
666	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
667	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
668	#121	—	2	1	no	—
669	#121	—	2	1	no	—
670	#121	—	2	1	no	—
671	#121	—	2	1	no	—
672	#121	C₂³×C₈₉	1	2	yes	—
673	#121	C₂³×C₈₉	1	2	yes	—
674	#120	—	2	2	no	—
675	C₄×Q₈	—	2	1	no	—
676	C₄×Q₈	—	2	1	no	—
677	C₄×Q₈	—	2	1	no	—
678	C₄×Q₈	—	2	1	no	—
679	C₄×Q₈	—	2	1	no	—
680	C₄×Q₈	—	2	1	no	—
681	C₄×Q₈	—	2	1	no	—
682	C₄×Q₈	—	2	1	no	—
683	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
684	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
685	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
686	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
687	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
688	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
689	C₄×D₄	—	2	2	no	—
690	C₄×D₄	—	2	2	no	—
691	C₄×D₄	—	2	2	no	—
692	C₄×D₄	—	2	2	no	—
693	C₄×D₄	—	2	2	no	—
694	C₄×D₄	—	2	2	no	—
695	C₄×D₄	—	2	2	no	—
696	C₄×D₄	—	2	2	no	—
697	C₄×D₄	—	2	2	no	—
698	C₄×D₄	—	2	2	no	—
699	C₄×D₄	—	2	2	no	—
700	C₄×D₄	—	2	2	no	—
701	C₄×D₄	—	2	2	no	—
702	C₄×D₄	—	2	2	no	—
703	C₄×D₄	—	2	1	no	—
704	C₄×D₄	—	2	1	no	—
705	C₄×D₄	—	2	1	no	—
706	C₄×D₄	—	2	1	no	—
707	C₄×D₄	—	2	1	no	—
708	C₄×D₄	—	2	1	no	—
709	C₄×D₄	—	2	1	no	—
710	C₄×D₄	—	2	1	no	—
711	C₄×D₄	C₂³×C₈₉	1	2	yes	—
712	C₄×D₄	C₂³×C₈₉	1	2	yes	—
713	C₄×D₄	C₂³×C₈₉	1	2	yes	—
714	C₄×D₄	C₂³×C₈₉	1	2	yes	—
715	C₄×D₄	C₂³×C₈₉	1	2	yes	—
716	C₄×D₄	C₂³×C₈₉	1	2	yes	—
717	#117	—	2	1	no	—
718	#117	—	2	1	no	—
719	#117	—	2	1	no	—
720	#117	—	2	1	no	—
721	#117	—	2	2	no	—
722	#117	—	2	2	no	—
723	#117	—	2	2	no	—
724	#117	—	2	2	no	—
725	#117	—	2	2	no	—
726	#117	—	2	2	no	—
727	#117	—	2	2	no	—
728	#117	C₂³×C₈₉	1	2	yes	—
729	#117	C₂³×C₈₉	1	2	yes	—
730	#117	C₂³×C₈₉	1	2	yes	—
731	C₂×C₄⋊C₄	—	2	1	no	—
732	C₂×C₄⋊C₄	—	2	1	no	—
733	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
734	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
735	C₂×C₂²⋊C₄	—	2	1	no	—
736	C₂×C₂²⋊C₄	—	2	1	no	—
737	C₂×C₂²⋊C₄	—	2	1	no	—
738	C₂×C₄²	—	2	1	no	—
739	C₂×C₄²	—	2	1	no	—
740	C₂×C₄²	—	2	1	no	—
741	C₂×C₄²	—	2	2	no	—
742	C₂×C₄²	—	2	2	no	—
743	C₂×C₄²	—	2	2	no	—
744	C₂×C₄²	—	2	2	no	—
745	C₂×C₄²	—	2	2	no	—
746	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
747	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
748	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
749	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
750	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
751	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
752	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
753	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
754	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
755	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
756	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
757	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
758	#107	C₂³×C₈₉	1	4	yes	—
759	#107	C₂³×C₈₉	1	4	yes	—
760	#106	C₂³×C₈₉	1	4	yes	—
761	#106	C₂³×C₈₉	1	4	yes	—
762	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
763	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
764	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
765	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
766	#103	C₂³×C₈₉	1	4	yes	—
767	#103	C₂³×C₈₉	1	4	yes	—
768	#103	C₂³×C₈₉	1	4	yes	—
769	#103	C₂³×C₈₉	1	4	yes	—
770	#102	C₂³×C₈₉	1	4	yes	—
771	#102	C₂³×C₈₉	1	4	yes	—
772	#102	C₂³×C₈₉	1	4	yes	—
773	#102	C₂³×C₈₉	1	4	yes	—
774	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
775	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
776	#97	C₂³×C₈₉	1	4	yes	—
777	C₄×C₈	C₂³×C₈₉	1	4	yes	—
778	C₂⁴	—	2	1	no	—
779	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
780	#41	—	2	8	no	—
781	#41	—	2	8	no	—
782	#41	—	2	4	no	—
783	#41	—	2	4	no	—
784	#41	—	2	4	no	—
785	#41	—	2	4	no	—
786	#41	—	2	4	no	—
787	#41	—	2	4	no	—
788	#41	—	4	4	no	—
789	#41	—	4	4	no	—
790	C₂×Q₈	—	2	1	no	—
791	C₂×Q₈	—	2	1	no	—
792	C₂×Q₈	—	2	1	no	—
793	C₂×Q₈	—	2	2	no	—
794	C₂×Q₈	#41×C₈₉	1	4	yes	complemented
795	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
796	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
797	C₂×D₄	—	2	8	no	—
798	C₂×D₄	—	2	2	no	—
799	C₂×D₄	—	2	2	no	—
800	C₂×D₄	—	2	2	no	—
801	C₂×D₄	—	2	2	no	—
802	C₂×D₄	—	2	2	no	—
803	C₂×D₄	—	2	1	no	—
804	C₂×D₄	—	2	1	no	—
805	C₂×D₄	—	2	1	no	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	#41×C₈₉	1	4	yes	complemented
808	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
809	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
810	C₂²×C₄	—	2	8	no	—
811	C₂²×C₄	—	2	1	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	1	no	—
817	C₂²×C₄	—	2	1	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	2	no	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	2	2	no	—
824	C₂²×C₄	—	2	2	no	—
825	C₂²×C₄	—	4	2	no	—
826	C₂²×C₄	—	4	2	no	—
827	C₂²×C₄	—	4	4	no	—
828	C₂²×C₄	—	4	4	no	—
829	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
830	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
831	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
832	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
833	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
834	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
835	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
836	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
837	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
838	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
839	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
840	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
841	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
842	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
843	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
845	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
846	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
847	Q₁₆	—	2	8	no	—
848	SD₁₆	—	2	8	no	—
849	SD₁₆	—	2	8	no	—
850	D₈	—	2	8	no	—
851	M₁₆	—	2	4	no	—
852	M₁₆	—	2	4	no	—
853	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
854	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	1	no	—
860	C₄⋊C₄	—	2	1	no	—
861	C₄⋊C₄	—	2	1	no	—
862	C₄⋊C₄	—	2	1	no	—
863	C₄⋊C₄	—	2	1	no	—
864	C₄⋊C₄	—	2	1	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
872	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
873	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
874	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	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	C₄²	—	2	2	no	—
891	C₄²	—	2	2	no	—
892	C₄²	—	2	2	no	—
893	C₄²	—	2	2	no	—
894	C₄²	—	2	2	no	—
895	C₄²	—	2	2	no	—
896	C₄²	—	2	2	no	—
897	C₄²	—	2	2	no	—
898	C₄²	—	2	2	no	—
899	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
900	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
901	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
902	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
903	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
904	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
905	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
906	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
907	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
908	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
909	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
910	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
911	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
912	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
913	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
914	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
915	C₂³	—	2	2	no	—
916	C₂³	—	2	4	no	—
917	C₂³	—	2	2	no	—
918	C₂³	—	2	2	no	—
919	C₂³	—	4	1	no	—
920	C₂³	—	4	1	no	—
921	C₂³	—	4	2	no	—
922	C₂³	—	4	2	no	—
923	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
924	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
925	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
926	Q₈	—	2	4	no	—
927	Q₈	—	2	2	no	—
928	Q₈	—	2	2	no	—
929	Q₈	—	2	2	no	—
930	Q₈	—	4	2	no	—
931	Q₈	—	4	2	no	—
932	Q₈	C₂×#41×C₈₉	1	4	yes	—
933	D₄	—	2	8	no	—
934	D₄	—	2	8	no	—
935	D₄	—	2	4	no	—
936	D₄	—	2	2	no	—
937	D₄	—	2	2	no	—
938	D₄	—	2	2	no	—
939	D₄	—	4	2	no	—
940	D₄	—	4	4	no	—
941	D₄	—	4	4	no	—
942	D₄	—	4	4	no	—
943	D₄	—	4	2	no	—
944	D₄	C₂×#41×C₈₉	1	4	yes	—
945	C₂×C₄	—	2	8	no	—
946	C₂×C₄	—	2	8	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	4	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	4	1	no	—
968	C₂×C₄	—	4	1	no	—
969	C₂×C₄	—	4	1	no	—
970	C₂×C₄	—	4	1	no	—
971	C₂×C₄	—	4	1	no	—
972	C₂×C₄	—	4	1	no	—
973	C₂×C₄	—	4	4	no	—
974	C₂×C₄	—	4	4	no	—
975	C₂×C₄	—	4	4	no	—
976	C₂×C₄	—	4	2	no	—
977	C₂×C₄	—	4	2	no	—
978	C₂×C₄	—	4	4	no	—
979	C₂×C₄	—	4	4	no	—
980	C₂×C₄	—	4	4	no	—
981	C₂×C₄	—	4	4	no	—
982	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
983	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
984	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
985	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
986	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
987	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
988	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
989	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
990	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
991	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
992	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
993	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
994	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
995	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
996	C₈	—	2	4	no	—
997	C₈	—	2	4	no	—
998	C₂²	—	2	1	no	—
999	C₂²	—	2	1	no	—
1000	C₂²	—	2	1	no	—
1001	C₂²	—	2	1	no	—
1002	C₂²	—	2	1	no	—
1003	C₂²	—	2	1	no	—
1004	C₂²	—	2	1	no	—
1005	C₂²	—	2	1	no	—
1006	C₂²	—	2	4	no	—
1007	C₂²	—	4	4	no	—
1008	C₂²	—	4	8	no	—
1009	C₂²	—	4	2	no	—
1010	C₂²	—	4	2	no	—
1011	C₂²	—	4	2	no	—
1012	C₂²	—	4	2	no	—
1013	C₂²	—	4	2	no	—
1014	C₂²	#525×C₈₉	1	2	yes	—
1015	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1016	C₄	—	2	1	no	—
1017	C₄	—	2	1	no	—
1018	C₄	—	2	1	no	—
1019	C₄	—	2	1	no	—
1020	C₄	—	2	1	no	—
1021	C₄	—	2	1	no	—
1022	C₄	—	2	1	no	—
1023	C₄	—	2	1	no	—
1024	C₄	—	2	4	no	—
1025	C₄	—	4	2	no	—
1026	C₄	—	4	2	no	—
1027	C₄	—	4	2	no	—
1028	C₄	—	4	2	no	—
1029	C₄	—	4	2	no	—
1030	C₄	#525×C₈₉	1	2	yes	—
1031	C₄	#575×C₈₉	1	2	yes	—
1032	C₄	#575×C₈₉	1	2	yes	—
1033	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
1034	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
1035	C₂	—	2	2	no	—
1036	C₂	—	4	1	no	—
1037	C₂	—	4	1	no	—
1038	C₂	—	4	4	no	—
1039	C₂	—	8	2	no	—
1040	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
1041	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
1042	C₂	C₂×#575×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
socle	C₂²×C₈₉	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₉ ◁ C₂²×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3444	C₂	semidirect
2. C₂×C₄×#41×C₈₉	C₂	semidirect
3. C₈₉×#3116	C₂	semidirect
4. C₈₉×#3115	C₂	semidirect
5. C₈₉×#3111	C₂	semidirect
6. C₈₉×#3107	C₂	semidirect
7. C₈₉×#3106	C₂	semidirect
8. C₈₉×#3102	C₂	semidirect
9. C₈₉×#3093	C₂	semidirect
10. C₈₉×#3078	C₂	semidirect
11. C₈₉×#3077	C₂	semidirect
12. C₈₉×#3037	C₂	semidirect
13. C₈₉×#3036	C₂	semidirect
14. C₈₉×#3005	C₂	semidirect
15. C₄×#137×C₈₉	C₂	semidirect
16. C₄×AGL(1,ℤ/8)×C₈₉	C₂	semidirect
17. C₈₉×#2920	C₂	semidirect
22. #533×C₈₉	C₂²	semidirect
23. #533×C₈₉	C₂²	semidirect
25. #532×C₈₉	C₂²	semidirect
26. #532×C₈₉	C₂²	semidirect
31. #529×C₈₉	C₂²	semidirect
32. #529×C₈₉	C₂²	semidirect
57. #485×C₈₉	C₂²	semidirect
58. #485×C₈₉	C₂²	semidirect
59. #482×C₈₉	C₂²	semidirect
60. #482×C₈₉	C₂²	semidirect
61. #479×C₈₉	C₂²	semidirect
62. #478×C₈₉	C₂²	semidirect
63. #477×C₈₉	C₂²	semidirect
64. #476×C₈₉	C₂²	semidirect
65. #475×C₈₉	C₂²	semidirect
66. #474×C₈₉	C₂²	semidirect
67. #464×C₈₉	C₂²	semidirect
68. #463×C₈₉	C₂²	semidirect
69. #462×C₈₉	C₂²	semidirect
70. #461×C₈₉	C₂²	semidirect
71. #460×C₈₉	C₂²	semidirect
72. #459×C₈₉	C₂²	semidirect
77. #442×C₈₉	C₂²	semidirect
78. #441×C₈₉	C₂²	semidirect
79. #440×C₈₉	C₂²	semidirect
80. #440×C₈₉	C₂²	semidirect
81. C₄×Q₁₆×C₈₉	C₂²	semidirect
82. C₄×SD₁₆×C₈₉	C₂²	semidirect
83. C₄×SD₁₆×C₈₉	C₂²	semidirect
84. C₄×D₈×C₈₉	C₂²	semidirect
85. #432×C₈₉	C₂²	semidirect
86. #432×C₈₉	C₂²	semidirect
87. #431×C₈₉	C₂²	semidirect
88. #431×C₈₉	C₂²	semidirect
272. C₂×Q₈×C₈₉	#41	semidirect
285. C₂×D₄×C₈₉	#41	semidirect
513. #60559	C₈₉	direct (N × H)
522. #3444	C₂×C₈₉	semidirect
523. C₂×C₄×#41	C₂×C₈₉	semidirect
524. #3116	C₂×C₈₉	semidirect
525. #3115	C₂×C₈₉	semidirect
526. #3111	C₂×C₈₉	semidirect
527. #3107	C₂×C₈₉	semidirect
528. #3106	C₂×C₈₉	semidirect
529. #3102	C₂×C₈₉	semidirect
530. #3093	C₂×C₈₉	semidirect
531. #3078	C₂×C₈₉	semidirect
532. #3077	C₂×C₈₉	semidirect
533. #3037	C₂×C₈₉	semidirect
534. #3036	C₂×C₈₉	semidirect
535. #3005	C₂×C₈₉	semidirect
536. C₄×#137	C₂×C₈₉	semidirect
537. C₄×AGL(1,ℤ/8)	C₂×C₈₉	semidirect
538. #2920	C₂×C₈₉	semidirect
539. C₈₉	#60559	direct (N × H)
544. #533	C₂²×C₈₉	semidirect
545. #533	C₂²×C₈₉	semidirect
547. #532	C₂²×C₈₉	semidirect
548. #532	C₂²×C₈₉	semidirect
553. #529	C₂²×C₈₉	semidirect
554. #529	C₂²×C₈₉	semidirect
579. #485	C₂²×C₈₉	semidirect
580. #485	C₂²×C₈₉	semidirect
581. #482	C₂²×C₈₉	semidirect
582. #482	C₂²×C₈₉	semidirect
583. #479	C₂²×C₈₉	semidirect
584. #478	C₂²×C₈₉	semidirect
585. #477	C₂²×C₈₉	semidirect
586. #476	C₂²×C₈₉	semidirect
587. #475	C₂²×C₈₉	semidirect
588. #474	C₂²×C₈₉	semidirect
589. #464	C₂²×C₈₉	semidirect
590. #463	C₂²×C₈₉	semidirect
591. #462	C₂²×C₈₉	semidirect
592. #461	C₂²×C₈₉	semidirect
593. #460	C₂²×C₈₉	semidirect
594. #459	C₂²×C₈₉	semidirect
599. #442	C₂²×C₈₉	semidirect
600. #441	C₂²×C₈₉	semidirect
601. #440	C₂²×C₈₉	semidirect
602. #440	C₂²×C₈₉	semidirect
603. C₄×Q₁₆	C₂²×C₈₉	semidirect
604. C₄×SD₁₆	C₂²×C₈₉	semidirect
605. C₄×SD₁₆	C₂²×C₈₉	semidirect
606. C₄×D₈	C₂²×C₈₉	semidirect
607. #432	C₂²×C₈₉	semidirect
608. #432	C₂²×C₈₉	semidirect
609. #431	C₂²×C₈₉	semidirect
610. #431	C₂²×C₈₉	semidirect
794. C₂×Q₈	#41×C₈₉	semidirect
807. C₂×D₄	#41×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3444	2
C₂×C₄×#41×C₈₉	2
C₈₉×#3116	2
C₈₉×#3115	2
C₈₉×#3111	2
C₈₉×#3107	2
C₈₉×#3106	2
C₈₉×#3102	2
C₈₉×#3093	2
C₈₉×#3078	2
C₈₉×#3077	2
C₈₉×#3037	2
C₈₉×#3036	2
C₈₉×#3005	2
C₄×#137×C₈₉	2
C₄×AGL(1,ℤ/8)×C₈₉	2
C₈₉×#2920	2
#60559	89

Subgroups — C89×#60559 #36438407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60559 #36438407