Subgroups — C₈₉×#60866 #36438714

Order 22784.

1788 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#529×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3240	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3239	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3238	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3233	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3232	C₂	1	4	yes	maximal, complemented
8	C₈₉×#3166	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3140	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3095	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3094	C₂	1	2	yes	maximal
12	C₈₉×#3078	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3077	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2920	C₂	1	1	yes	maximal, characteristic, complemented
15	#533×C₈₉	—	2	1	no	—
16	#533×C₈₉	—	2	1	no	—
17	#533×C₈₉	—	2	1	no	—
18	#533×C₈₉	—	2	1	no	—
19	#533×C₈₉	C₂²	1	2	yes	—
20	#533×C₈₉	C₂²	1	2	yes	—
21	#533×C₈₉	C₂²	1	2	yes	complemented
22	#533×C₈₉	C₂²	1	2	yes	complemented
23	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
25	#529×C₈₉	—	2	1	no	—
26	#529×C₈₉	—	2	1	no	—
27	#529×C₈₉	—	2	1	no	—
28	#529×C₈₉	—	2	1	no	—
29	#529×C₈₉	C₂²	1	2	yes	—
30	#529×C₈₉	C₂²	1	2	yes	—
31	#529×C₈₉	C₂²	1	2	yes	—
32	#529×C₈₉	C₂²	1	2	yes	—
33	C₂×#126×C₈₉	—	2	1	no	—
34	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#125×C₈₉	C₂²	1	2	yes	complemented
36	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#123×C₈₉	—	2	1	no	—
38	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
39	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
40	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
43	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
44	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₈₉	—	2	1	no	—
46	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#117×C₈₉	—	2	1	no	—
48	C₂×#117×C₈₉	C₂²	1	2	yes	—
49	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
50	#501×C₈₉	C₂²	1	4	yes	complemented
51	#501×C₈₉	C₂²	1	4	yes	complemented
52	#499×C₈₉	C₂²	1	8	yes	complemented
53	#489×C₈₉	C₂²	1	4	yes	complemented
54	#489×C₈₉	C₂²	1	4	yes	complemented
55	#488×C₈₉	C₂²	1	8	yes	complemented
56	#485×C₈₉	C₂²	1	8	yes	complemented
57	#484×C₈₉	C₂²	1	4	yes	complemented
58	#483×C₈₉	C₂²	1	4	yes	complemented
59	#482×C₈₉	C₂²	1	8	yes	—
60	#481×C₈₉	C₂²	1	4	yes	—
61	#480×C₈₉	C₂²	1	4	yes	—
62	#479×C₈₉	C₂²	1	8	yes	complemented
63	#478×C₈₉	C₂²	1	8	yes	complemented
64	#477×C₈₉	C₂²	1	4	yes	complemented
65	#476×C₈₉	C₂²	1	4	yes	complemented
66	#475×C₈₉	C₂²	1	4	yes	complemented
67	#474×C₈₉	C₂²	1	4	yes	complemented
68	#432×C₈₉	C₂²	1	2	yes	complemented
69	#432×C₈₉	C₂²	1	2	yes	complemented
70	#431×C₈₉	C₂²	1	2	yes	complemented
71	#431×C₈₉	C₂²	1	2	yes	complemented
72	#428×C₈₉	C₂²	1	4	yes	—
73	#428×C₈₉	C₂²	1	4	yes	—
74	#423×C₈₉	C₂²	1	2	yes	—
75	#419×C₈₉	C₂²	1	4	yes	—
76	#418×C₈₉	C₂²	1	4	yes	—
77	#407×C₈₉	C₂²	1	2	yes	—
78	C₄×M₁₆×C₈₉	C₂²	1	2	yes	—
79	C₂²×Q₈×C₈₉	—	2	1	no	—
80	C₂²×Q₈×C₈₉	—	2	1	no	—
81	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₈₉	—	2	1	no	—
83	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₈₉	—	2	1	no	—
85	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
86	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
87	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
88	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
89	C₄⋊Q₈×C₈₉	—	2	1	no	—
90	C₄⋊Q₈×C₈₉	—	2	1	no	—
91	C₄⋊Q₈×C₈₉	—	2	1	no	—
92	C₄⋊Q₈×C₈₉	—	2	1	no	—
93	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
94	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
95	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
96	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
97	#126×C₈₉	—	2	2	no	—
98	#126×C₈₉	—	2	2	no	—
99	#126×C₈₉	—	2	2	no	—
100	#126×C₈₉	—	2	2	no	—
101	#125×C₈₉	—	2	1	no	—
102	#125×C₈₉	—	2	1	no	—
103	#125×C₈₉	—	2	2	no	—
104	#125×C₈₉	—	2	2	no	—
105	#125×C₈₉	C₂³	1	4	yes	—
106	#125×C₈₉	C₂³	1	4	yes	—
107	#125×C₈₉	C₂³	1	2	yes	—
108	#125×C₈₉	C₂³	1	2	yes	—
109	#124×C₈₉	—	2	1	no	—
110	#124×C₈₉	—	2	1	no	—
111	#124×C₈₉	C₂³	1	2	yes	—
112	#124×C₈₉	C₂³	1	2	yes	—
113	#123×C₈₉	—	2	2	no	—
114	#123×C₈₉	—	2	2	no	—
115	#123×C₈₉	—	2	2	no	—
116	#123×C₈₉	—	2	2	no	—
117	C₂²⋊Q₈×C₈₉	—	2	2	no	—
118	C₂²⋊Q₈×C₈₉	—	2	2	no	—
119	C₂²⋊Q₈×C₈₉	—	2	2	no	—
120	C₂²⋊Q₈×C₈₉	—	2	2	no	—
121	C₂²⋊Q₈×C₈₉	—	2	2	no	—
122	C₂²⋊Q₈×C₈₉	—	2	2	no	—
123	C₂²⋊Q₈×C₈₉	—	2	2	no	—
124	C₂²⋊Q₈×C₈₉	—	2	2	no	—
125	C₂²⋊Q₈×C₈₉	—	2	1	no	—
126	C₂²⋊Q₈×C₈₉	—	2	1	no	—
127	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
128	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
129	#121×C₈₉	—	2	1	no	—
130	#121×C₈₉	—	2	1	no	—
131	#121×C₈₉	C₂³	1	2	yes	—
132	#121×C₈₉	C₂³	1	2	yes	—
133	C₄×Q₈×C₈₉	—	2	2	no	—
134	C₄×Q₈×C₈₉	—	2	2	no	—
135	C₄×Q₈×C₈₉	—	2	2	no	—
136	C₄×Q₈×C₈₉	—	2	2	no	—
137	C₄×Q₈×C₈₉	—	2	2	no	—
138	C₄×Q₈×C₈₉	—	2	2	no	—
139	C₄×Q₈×C₈₉	—	2	2	no	—
140	C₄×Q₈×C₈₉	—	2	2	no	—
141	C₄×Q₈×C₈₉	—	2	1	no	—
142	C₄×Q₈×C₈₉	—	2	1	no	—
143	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
144	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
145	C₄×D₄×C₈₉	—	2	2	no	—
146	C₄×D₄×C₈₉	—	2	2	no	—
147	C₄×D₄×C₈₉	—	2	2	no	—
148	C₄×D₄×C₈₉	—	2	2	no	—
149	C₄×D₄×C₈₉	—	2	1	no	—
150	C₄×D₄×C₈₉	—	2	1	no	—
151	C₄×D₄×C₈₉	C₂³	1	2	yes	—
152	C₄×D₄×C₈₉	C₂³	1	2	yes	—
153	#117×C₈₉	—	2	2	no	—
154	#117×C₈₉	—	2	2	no	—
155	#117×C₈₉	—	2	2	no	—
156	#117×C₈₉	—	2	2	no	—
157	#117×C₈₉	—	2	2	no	—
158	#117×C₈₉	—	2	2	no	—
159	#117×C₈₉	C₂³	1	4	yes	—
160	#117×C₈₉	C₂³	1	4	yes	—
161	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
162	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
163	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
164	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
165	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
166	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
167	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
168	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
169	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
174	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
175	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
176	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
177	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
178	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
179	C₂×C₄²×C₈₉	—	2	1	no	—
180	C₂×C₄²×C₈₉	—	2	2	no	—
181	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
182	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
183	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
184	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
185	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
186	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
193	#107×C₈₉	C₂³	1	8	yes	—
194	#107×C₈₉	C₂³	1	8	yes	—
195	#106×C₈₉	C₂³	1	8	yes	—
196	#106×C₈₉	C₂³	1	8	yes	—
197	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
198	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
199	#103×C₈₉	C₂³	1	8	yes	—
200	#103×C₈₉	C₂³	1	8	yes	—
201	#102×C₈₉	C₂³	1	8	yes	—
202	#102×C₈₉	C₂³	1	8	yes	—
203	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
204	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
205	#97×C₈₉	C₂³	1	4	yes	—
206	C₄×C₈×C₈₉	C₂³	1	4	yes	—
207	C₂⁴×C₈₉	—	2	1	no	—
208	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
209	C₂×Q₈×C₈₉	—	2	1	no	—
210	C₂×Q₈×C₈₉	—	2	2	no	—
211	C₂×Q₈×C₈₉	—	2	2	no	—
212	C₂×Q₈×C₈₉	—	2	2	no	—
213	C₂×Q₈×C₈₉	—	2	2	no	—
214	C₂×Q₈×C₈₉	—	2	4	no	—
215	C₂×Q₈×C₈₉	—	4	4	no	—
216	C₂×Q₈×C₈₉	—	4	4	no	—
217	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
218	C₂×D₄×C₈₉	—	2	2	no	—
219	C₂×D₄×C₈₉	—	2	2	no	—
220	C₂×D₄×C₈₉	—	2	1	no	—
221	C₂×D₄×C₈₉	—	2	4	no	—
222	C₂×D₄×C₈₉	—	4	4	no	—
223	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₈₉	—	2	4	no	—
225	C₂²×C₄×C₈₉	—	2	1	no	—
226	C₂²×C₄×C₈₉	—	2	1	no	—
227	C₂²×C₄×C₈₉	—	2	2	no	—
228	C₂²×C₄×C₈₉	—	2	2	no	—
229	C₂²×C₄×C₈₉	—	2	1	no	—
230	C₂²×C₄×C₈₉	—	2	2	no	—
231	C₂²×C₄×C₈₉	—	2	2	no	—
232	C₂²×C₄×C₈₉	—	4	2	no	—
233	C₂²×C₄×C₈₉	—	4	2	no	—
234	C₂²×C₄×C₈₉	—	4	4	no	—
235	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
253	M₁₆×C₈₉	—	2	8	no	—
254	C₂×C₈×C₈₉	C₂⁴	1	8	yes	—
255	C₄⋊C₄×C₈₉	—	2	2	no	—
256	C₄⋊C₄×C₈₉	—	2	2	no	—
257	C₄⋊C₄×C₈₉	—	2	2	no	—
258	C₄⋊C₄×C₈₉	—	2	2	no	—
259	C₄⋊C₄×C₈₉	—	2	2	no	—
260	C₄⋊C₄×C₈₉	—	2	2	no	—
261	C₄⋊C₄×C₈₉	—	2	4	no	—
262	C₄⋊C₄×C₈₉	—	2	4	no	—
263	C₄⋊C₄×C₈₉	—	2	4	no	—
264	C₄⋊C₄×C₈₉	—	2	4	no	—
265	C₄⋊C₄×C₈₉	—	2	2	no	—
266	C₄⋊C₄×C₈₉	—	2	2	no	—
267	C₄⋊C₄×C₈₉	—	2	2	no	—
268	C₄⋊C₄×C₈₉	—	2	2	no	—
269	C₄⋊C₄×C₈₉	—	2	2	no	—
270	C₄⋊C₄×C₈₉	—	2	2	no	—
271	C₄⋊C₄×C₈₉	—	2	2	no	—
272	C₄⋊C₄×C₈₉	—	2	2	no	—
273	C₄⋊C₄×C₈₉	—	2	1	no	—
274	C₄⋊C₄×C₈₉	—	2	1	no	—
275	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
276	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
277	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
278	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
279	C₂²⋊C₄×C₈₉	—	2	4	no	—
280	C₂²⋊C₄×C₈₉	—	2	4	no	—
281	C₂²⋊C₄×C₈₉	—	2	2	no	—
282	C₂²⋊C₄×C₈₉	—	2	2	no	—
283	C₂²⋊C₄×C₈₉	—	2	2	no	—
284	C₂²⋊C₄×C₈₉	—	2	2	no	—
285	C₂²⋊C₄×C₈₉	—	2	2	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	C₄²×C₈₉	—	2	2	no	—
292	C₄²×C₈₉	—	2	2	no	—
293	C₄²×C₈₉	—	2	4	no	—
294	C₄²×C₈₉	—	2	4	no	—
295	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
296	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
297	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
308	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
309	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
310	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
311	C₂³×C₈₉	—	2	2	no	—
312	C₂³×C₈₉	—	2	2	no	—
313	C₂³×C₈₉	—	2	2	no	—
314	C₂³×C₈₉	—	4	1	no	—
315	C₂³×C₈₉	—	4	2	no	—
316	C₂³×C₈₉	—	4	2	no	—
317	C₂³×C₈₉	—	4	2	no	—
318	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
319	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
320	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
321	Q₈×C₈₉	—	2	4	no	—
322	Q₈×C₈₉	—	4	4	no	—
323	Q₈×C₈₉	—	4	4	no	—
324	Q₈×C₈₉	—	4	4	no	—
325	Q₈×C₈₉	—	4	2	no	—
326	Q₈×C₈₉	—	4	4	no	—
327	D₄×C₈₉	—	2	4	no	—
328	D₄×C₈₉	—	4	4	no	—
329	D₄×C₈₉	—	4	4	no	—
330	D₄×C₈₉	—	4	2	no	—
331	C₂×C₄×C₈₉	—	2	2	no	—
332	C₂×C₄×C₈₉	—	2	2	no	—
333	C₂×C₄×C₈₉	—	2	2	no	—
334	C₂×C₄×C₈₉	—	2	2	no	—
335	C₂×C₄×C₈₉	—	2	2	no	—
336	C₂×C₄×C₈₉	—	2	2	no	—
337	C₂×C₄×C₈₉	—	2	2	no	—
338	C₂×C₄×C₈₉	—	2	2	no	—
339	C₂×C₄×C₈₉	—	2	2	no	—
340	C₂×C₄×C₈₉	—	2	2	no	—
341	C₂×C₄×C₈₉	—	2	2	no	—
342	C₂×C₄×C₈₉	—	2	2	no	—
343	C₂×C₄×C₈₉	—	2	4	no	—
344	C₂×C₄×C₈₉	—	2	4	no	—
345	C₂×C₄×C₈₉	—	2	2	no	—
346	C₂×C₄×C₈₉	—	4	1	no	—
347	C₂×C₄×C₈₉	—	4	1	no	—
348	C₂×C₄×C₈₉	—	4	1	no	—
349	C₂×C₄×C₈₉	—	4	1	no	—
350	C₂×C₄×C₈₉	—	4	1	no	—
351	C₂×C₄×C₈₉	—	4	1	no	—
352	C₂×C₄×C₈₉	—	4	1	no	—
353	C₂×C₄×C₈₉	—	4	4	no	—
354	C₂×C₄×C₈₉	—	4	2	no	—
355	C₂×C₄×C₈₉	—	4	2	no	—
356	C₂×C₄×C₈₉	—	4	4	no	—
357	C₂×C₄×C₈₉	—	4	2	no	—
358	C₂×C₄×C₈₉	—	4	4	no	—
359	C₂×C₄×C₈₉	—	4	4	no	—
360	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
372	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
373	C₈×C₈₉	—	2	8	no	—
374	C₂²×C₈₉	—	2	1	no	—
375	C₂²×C₈₉	—	2	1	no	—
376	C₂²×C₈₉	—	2	1	no	—
377	C₂²×C₈₉	—	2	1	no	—
378	C₂²×C₈₉	—	2	1	no	—
379	C₂²×C₈₉	—	2	1	no	—
380	C₂²×C₈₉	—	2	1	no	—
381	C₂²×C₈₉	—	4	4	no	—
382	C₂²×C₈₉	—	4	2	no	—
383	C₂²×C₈₉	—	4	2	no	—
384	C₂²×C₈₉	—	4	2	no	—
385	C₂²×C₈₉	—	8	4	no	—
386	C₂²×C₈₉	#536	1	2	yes	—
387	C₂²×C₈₉	#575	1	2	yes	—
388	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
389	C₄×C₈₉	—	2	1	no	—
390	C₄×C₈₉	—	2	1	no	—
391	C₄×C₈₉	—	2	1	no	—
392	C₄×C₈₉	—	2	1	no	—
393	C₄×C₈₉	—	2	1	no	—
394	C₄×C₈₉	—	2	1	no	—
395	C₄×C₈₉	—	2	1	no	—
396	C₄×C₈₉	—	2	1	no	—
397	C₄×C₈₉	—	2	1	no	—
398	C₄×C₈₉	—	4	2	no	—
399	C₄×C₈₉	—	4	2	no	—
400	C₄×C₈₉	—	4	2	no	—
401	C₄×C₈₉	—	4	4	no	—
402	C₄×C₈₉	—	4	4	no	—
403	C₄×C₈₉	#536	1	2	yes	—
404	C₄×C₈₉	#575	1	2	yes	—
405	C₄×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
406	#60866	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
407	C₂×C₈₉	—	2	2	no	—
408	C₂×C₈₉	—	2	2	no	—
409	C₂×C₈₉	—	4	1	no	—
410	C₂×C₈₉	—	8	2	no	—
411	C₂×C₈₉	C₂×#536	1	1	yes	characteristic
412	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
413	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
414	C₂×#533	C₂×C₈₉	1	1	yes	characteristic, complemented
415	C₂×#529	C₂×C₈₉	1	1	yes	characteristic
416	#3240	C₂×C₈₉	1	4	yes	complemented
417	#3239	C₂×C₈₉	1	2	yes	complemented
418	#3238	C₂×C₈₉	1	2	yes	complemented
419	#3233	C₂×C₈₉	1	4	yes	complemented
420	#3232	C₂×C₈₉	1	4	yes	complemented
421	#3166	C₂×C₈₉	1	2	yes	complemented
422	#3140	C₂×C₈₉	1	2	yes	complemented
423	#3095	C₂×C₈₉	1	2	yes	complemented
424	#3094	C₂×C₈₉	1	2	yes	—
425	#3078	C₂×C₈₉	1	2	yes	complemented
426	#3077	C₂×C₈₉	1	2	yes	complemented
427	#2920	C₂×C₈₉	1	1	yes	characteristic, complemented
428	C₈₉	#60866	1	1	yes	characteristic, direct product factor, Sylow
429	#533	—	2	1	no	—
430	#533	—	2	1	no	—
431	#533	—	2	1	no	—
432	#533	—	2	1	no	—
433	#533	C₂²×C₈₉	1	2	yes	—
434	#533	C₂²×C₈₉	1	2	yes	—
435	#533	C₂²×C₈₉	1	2	yes	complemented
436	#533	C₂²×C₈₉	1	2	yes	complemented
437	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
438	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
439	#529	—	2	1	no	—
440	#529	—	2	1	no	—
441	#529	—	2	1	no	—
442	#529	—	2	1	no	—
443	#529	C₂²×C₈₉	1	2	yes	—
444	#529	C₂²×C₈₉	1	2	yes	—
445	#529	C₂²×C₈₉	1	2	yes	—
446	#529	C₂²×C₈₉	1	2	yes	—
447	C₂×#126	—	2	1	no	—
448	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
449	C₂×#125	C₂²×C₈₉	1	2	yes	complemented
450	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
451	C₂×#123	—	2	1	no	—
452	C₂×C₂²⋊Q₈	—	2	1	no	—
453	C₂×C₂²⋊Q₈	—	2	1	no	—
454	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
455	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
456	C₂×C₄×Q₈	—	2	1	no	—
457	C₂×C₄×Q₈	—	2	1	no	—
458	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
459	C₂×C₄×D₄	—	2	1	no	—
460	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
461	C₂×#117	—	2	1	no	—
462	C₂×#117	C₂²×C₈₉	1	2	yes	—
463	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
464	#501	C₂²×C₈₉	1	4	yes	complemented
465	#501	C₂²×C₈₉	1	4	yes	complemented
466	#499	C₂²×C₈₉	1	8	yes	complemented
467	#489	C₂²×C₈₉	1	4	yes	complemented
468	#489	C₂²×C₈₉	1	4	yes	complemented
469	#488	C₂²×C₈₉	1	8	yes	complemented
470	#485	C₂²×C₈₉	1	8	yes	complemented
471	#484	C₂²×C₈₉	1	4	yes	complemented
472	#483	C₂²×C₈₉	1	4	yes	complemented
473	#482	C₂²×C₈₉	1	8	yes	—
474	#481	C₂²×C₈₉	1	4	yes	—
475	#480	C₂²×C₈₉	1	4	yes	—
476	#479	C₂²×C₈₉	1	8	yes	complemented
477	#478	C₂²×C₈₉	1	8	yes	complemented
478	#477	C₂²×C₈₉	1	4	yes	complemented
479	#476	C₂²×C₈₉	1	4	yes	complemented
480	#475	C₂²×C₈₉	1	4	yes	complemented
481	#474	C₂²×C₈₉	1	4	yes	complemented
482	#432	C₂²×C₈₉	1	2	yes	complemented
483	#432	C₂²×C₈₉	1	2	yes	complemented
484	#431	C₂²×C₈₉	1	2	yes	complemented
485	#431	C₂²×C₈₉	1	2	yes	complemented
486	#428	C₂²×C₈₉	1	4	yes	—
487	#428	C₂²×C₈₉	1	4	yes	—
488	#423	C₂²×C₈₉	1	2	yes	—
489	#419	C₂²×C₈₉	1	4	yes	—
490	#418	C₂²×C₈₉	1	4	yes	—
491	#407	C₂²×C₈₉	1	2	yes	—
492	C₄×M₁₆	C₂²×C₈₉	1	2	yes	—
493	C₂²×Q₈	—	2	1	no	—
494	C₂²×Q₈	—	2	1	no	—
495	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
496	C₂²×D₄	—	2	1	no	—
497	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
498	C₂³×C₄	—	2	1	no	—
499	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
500	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
501	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
502	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
503	C₄⋊Q₈	—	2	1	no	—
504	C₄⋊Q₈	—	2	1	no	—
505	C₄⋊Q₈	—	2	1	no	—
506	C₄⋊Q₈	—	2	1	no	—
507	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
508	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
509	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
510	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
511	#126	—	2	2	no	—
512	#126	—	2	2	no	—
513	#126	—	2	2	no	—
514	#126	—	2	2	no	—
515	#125	—	2	1	no	—
516	#125	—	2	1	no	—
517	#125	—	2	2	no	—
518	#125	—	2	2	no	—
519	#125	C₂³×C₈₉	1	2	yes	—
520	#125	C₂³×C₈₉	1	2	yes	—
521	#125	C₂³×C₈₉	1	4	yes	—
522	#125	C₂³×C₈₉	1	4	yes	—
523	#124	—	2	1	no	—
524	#124	—	2	1	no	—
525	#124	C₂³×C₈₉	1	2	yes	—
526	#124	C₂³×C₈₉	1	2	yes	—
527	#123	—	2	2	no	—
528	#123	—	2	2	no	—
529	#123	—	2	2	no	—
530	#123	—	2	2	no	—
531	C₂²⋊Q₈	—	2	2	no	—
532	C₂²⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	2	no	—
538	C₂²⋊Q₈	—	2	2	no	—
539	C₂²⋊Q₈	—	2	1	no	—
540	C₂²⋊Q₈	—	2	1	no	—
541	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
542	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
543	#121	—	2	1	no	—
544	#121	—	2	1	no	—
545	#121	C₂³×C₈₉	1	2	yes	—
546	#121	C₂³×C₈₉	1	2	yes	—
547	C₄×Q₈	—	2	2	no	—
548	C₄×Q₈	—	2	2	no	—
549	C₄×Q₈	—	2	2	no	—
550	C₄×Q₈	—	2	2	no	—
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	—	2	2	no	—
555	C₄×Q₈	—	2	1	no	—
556	C₄×Q₈	—	2	1	no	—
557	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
558	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	2	2	no	—
562	C₄×D₄	—	2	2	no	—
563	C₄×D₄	—	2	1	no	—
564	C₄×D₄	—	2	1	no	—
565	C₄×D₄	C₂³×C₈₉	1	2	yes	—
566	C₄×D₄	C₂³×C₈₉	1	2	yes	—
567	#117	—	2	2	no	—
568	#117	—	2	2	no	—
569	#117	—	2	2	no	—
570	#117	—	2	2	no	—
571	#117	—	2	2	no	—
572	#117	—	2	2	no	—
573	#117	C₂³×C₈₉	1	4	yes	—
574	#117	C₂³×C₈₉	1	4	yes	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	2	no	—
579	C₂×C₄⋊C₄	—	2	2	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
587	C₂×C₂²⋊C₄	—	2	2	no	—
588	C₂×C₂²⋊C₄	—	2	1	no	—
589	C₂×C₂²⋊C₄	—	2	1	no	—
590	C₂×C₂²⋊C₄	—	2	1	no	—
591	C₂×C₂²⋊C₄	—	2	1	no	—
592	C₂×C₂²⋊C₄	—	2	1	no	—
593	C₂×C₄²	—	2	1	no	—
594	C₂×C₄²	—	2	2	no	—
595	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
596	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
597	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
598	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
599	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
600	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
607	#107	C₂³×C₈₉	1	8	yes	—
608	#107	C₂³×C₈₉	1	8	yes	—
609	#106	C₂³×C₈₉	1	8	yes	—
610	#106	C₂³×C₈₉	1	8	yes	—
611	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
612	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
613	#103	C₂³×C₈₉	1	8	yes	—
614	#103	C₂³×C₈₉	1	8	yes	—
615	#102	C₂³×C₈₉	1	8	yes	—
616	#102	C₂³×C₈₉	1	8	yes	—
617	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
618	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
619	#97	C₂³×C₈₉	1	4	yes	—
620	C₄×C₈	C₂³×C₈₉	1	4	yes	—
621	C₂⁴	—	2	1	no	—
622	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
623	C₂×Q₈	—	2	1	no	—
624	C₂×Q₈	—	2	2	no	—
625	C₂×Q₈	—	2	2	no	—
626	C₂×Q₈	—	2	2	no	—
627	C₂×Q₈	—	2	2	no	—
628	C₂×Q₈	—	2	4	no	—
629	C₂×Q₈	—	4	4	no	—
630	C₂×Q₈	—	4	4	no	—
631	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	4	4	no	—
637	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	4	2	no	—
647	C₂²×C₄	—	4	2	no	—
648	C₂²×C₄	—	4	4	no	—
649	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
650	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
651	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
652	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
653	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
654	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
655	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
659	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
660	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
661	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
662	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
663	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
665	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
666	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
667	M₁₆	—	2	8	no	—
668	C₂×C₈	C₂⁴×C₈₉	1	8	yes	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	2	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
690	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
691	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
692	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	2	2	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₄²	—	2	2	no	—
706	C₄²	—	2	2	no	—
707	C₄²	—	2	4	no	—
708	C₄²	—	2	4	no	—
709	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
710	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
711	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
712	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
713	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
714	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
715	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
716	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
717	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
718	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
719	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
720	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
721	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
722	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
723	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
724	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	4	1	no	—
729	C₂³	—	4	2	no	—
730	C₂³	—	4	2	no	—
731	C₂³	—	4	2	no	—
732	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
733	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
734	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
735	Q₈	—	2	4	no	—
736	Q₈	—	4	4	no	—
737	Q₈	—	4	4	no	—
738	Q₈	—	4	4	no	—
739	Q₈	—	4	2	no	—
740	Q₈	—	4	4	no	—
741	D₄	—	2	4	no	—
742	D₄	—	4	4	no	—
743	D₄	—	4	4	no	—
744	D₄	—	4	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	4	no	—
758	C₂×C₄	—	2	4	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	4	no	—
768	C₂×C₄	—	4	2	no	—
769	C₂×C₄	—	4	2	no	—
770	C₂×C₄	—	4	4	no	—
771	C₂×C₄	—	4	2	no	—
772	C₂×C₄	—	4	4	no	—
773	C₂×C₄	—	4	4	no	—
774	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
775	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
776	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
777	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
778	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
779	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
780	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
781	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
782	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
784	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
785	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
786	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
787	C₈	—	2	8	no	—
788	C₂²	—	2	1	no	—
789	C₂²	—	2	1	no	—
790	C₂²	—	2	1	no	—
791	C₂²	—	2	1	no	—
792	C₂²	—	2	1	no	—
793	C₂²	—	2	1	no	—
794	C₂²	—	2	1	no	—
795	C₂²	—	4	4	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	8	4	no	—
800	C₂²	#536×C₈₉	1	2	yes	—
801	C₂²	#575×C₈₉	1	2	yes	—
802	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
803	C₄	—	2	1	no	—
804	C₄	—	2	1	no	—
805	C₄	—	2	1	no	—
806	C₄	—	2	1	no	—
807	C₄	—	2	1	no	—
808	C₄	—	2	1	no	—
809	C₄	—	2	1	no	—
810	C₄	—	2	1	no	—
811	C₄	—	2	1	no	—
812	C₄	—	4	2	no	—
813	C₄	—	4	2	no	—
814	C₄	—	4	4	no	—
815	C₄	—	4	4	no	—
816	C₄	—	4	2	no	—
817	C₄	#536×C₈₉	1	2	yes	—
818	C₄	#575×C₈₉	1	2	yes	—
819	C₄	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
820	C₂	—	2	2	no	—
821	C₂	—	2	2	no	—
822	C₂	—	4	1	no	—
823	C₂	—	8	2	no	—
824	C₂	C₂×#536×C₈₉	1	1	yes	characteristic
825	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
826	C₂	C₂×#575×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₂×#121×C₈₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂²×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#533×C₈₉	C₂	semidirect
3. C₈₉×#3240	C₂	semidirect
4. C₈₉×#3239	C₂	semidirect
5. C₈₉×#3238	C₂	semidirect
6. C₈₉×#3233	C₂	semidirect
7. C₈₉×#3232	C₂	semidirect
8. C₈₉×#3166	C₂	semidirect
9. C₈₉×#3140	C₂	semidirect
10. C₈₉×#3095	C₂	semidirect
12. C₈₉×#3078	C₂	semidirect
13. C₈₉×#3077	C₂	semidirect
14. C₈₉×#2920	C₂	semidirect
21. #533×C₈₉	C₂²	semidirect
22. #533×C₈₉	C₂²	semidirect
23. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
24. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
35. C₂×#125×C₈₉	C₂²	semidirect
50. #501×C₈₉	C₂²	semidirect
51. #501×C₈₉	C₂²	semidirect
52. #499×C₈₉	C₂²	semidirect
53. #489×C₈₉	C₂²	semidirect
54. #489×C₈₉	C₂²	semidirect
55. #488×C₈₉	C₂²	semidirect
56. #485×C₈₉	C₂²	semidirect
57. #484×C₈₉	C₂²	semidirect
58. #483×C₈₉	C₂²	semidirect
62. #479×C₈₉	C₂²	semidirect
63. #478×C₈₉	C₂²	semidirect
64. #477×C₈₉	C₂²	semidirect
65. #476×C₈₉	C₂²	semidirect
66. #475×C₈₉	C₂²	semidirect
67. #474×C₈₉	C₂²	semidirect
68. #432×C₈₉	C₂²	semidirect
69. #432×C₈₉	C₂²	semidirect
70. #431×C₈₉	C₂²	semidirect
71. #431×C₈₉	C₂²	semidirect
406. #60866	C₈₉	direct (N × H)
414. C₂×#533	C₂×C₈₉	semidirect
416. #3240	C₂×C₈₉	semidirect
417. #3239	C₂×C₈₉	semidirect
418. #3238	C₂×C₈₉	semidirect
419. #3233	C₂×C₈₉	semidirect
420. #3232	C₂×C₈₉	semidirect
421. #3166	C₂×C₈₉	semidirect
422. #3140	C₂×C₈₉	semidirect
423. #3095	C₂×C₈₉	semidirect
425. #3078	C₂×C₈₉	semidirect
426. #3077	C₂×C₈₉	semidirect
427. #2920	C₂×C₈₉	semidirect
428. C₈₉	#60866	direct (N × H)
435. #533	C₂²×C₈₉	semidirect
436. #533	C₂²×C₈₉	semidirect
437. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
438. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
449. C₂×#125	C₂²×C₈₉	semidirect
464. #501	C₂²×C₈₉	semidirect
465. #501	C₂²×C₈₉	semidirect
466. #499	C₂²×C₈₉	semidirect
467. #489	C₂²×C₈₉	semidirect
468. #489	C₂²×C₈₉	semidirect
469. #488	C₂²×C₈₉	semidirect
470. #485	C₂²×C₈₉	semidirect
471. #484	C₂²×C₈₉	semidirect
472. #483	C₂²×C₈₉	semidirect
476. #479	C₂²×C₈₉	semidirect
477. #478	C₂²×C₈₉	semidirect
478. #477	C₂²×C₈₉	semidirect
479. #476	C₂²×C₈₉	semidirect
480. #475	C₂²×C₈₉	semidirect
481. #474	C₂²×C₈₉	semidirect
482. #432	C₂²×C₈₉	semidirect
483. #432	C₂²×C₈₉	semidirect
484. #431	C₂²×C₈₉	semidirect
485. #431	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₈₉	2
C₂×#529×C₈₉	2
C₈₉×#3240	2
C₈₉×#3239	2
C₈₉×#3238	2
C₈₉×#3233	2
C₈₉×#3232	2
C₈₉×#3166	2
C₈₉×#3140	2
C₈₉×#3095	2
C₈₉×#3094	2
C₈₉×#3078	2
C₈₉×#3077	2
C₈₉×#2920	2
#60866	89

Subgroups — C89×#60866 #36438714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60866 #36438714