Subgroups — C₈₉×#60033 #36437881

Order 22784.

2184 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2735	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#2678	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2670	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2602	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2598	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2597	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2587	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2580	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2557	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2543	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2523	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2518	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2456	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2455	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2367	C₂	1	2	yes	maximal, complemented
16	C₈₉×#2363	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2359	C₂	1	2	yes	maximal, complemented
18	C₄×#120×C₈₉	C₂	1	2	yes	maximal, complemented
19	C₄×#120×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₈₉	C₂²	1	2	yes	—
22	C₂×#123×C₈₉	C₂²	1	2	yes	—
23	C₂×#123×C₈₉	C₂²	1	2	yes	complemented
24	C₂×#121×C₈₉	C₂²	1	2	yes	—
25	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
26	C₂×#120×C₈₉	C₂²	1	2	yes	—
27	C₂×#120×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
34	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
35	#400×C₈₉	C₂²	1	2	yes	complemented
36	#399×C₈₉	C₂²	1	1	yes	characteristic
37	#399×C₈₉	C₂²	1	1	yes	characteristic, complemented
38	#398×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	#397×C₈₉	C₂²	1	2	yes	—
40	#397×C₈₉	C₂²	1	2	yes	—
41	#397×C₈₉	C₂²	1	1	yes	characteristic
42	#397×C₈₉	C₂²	1	2	yes	complemented
43	#396×C₈₉	C₂²	1	2	yes	—
44	#396×C₈₉	C₂²	1	2	yes	—
45	#394×C₈₉	C₂²	1	2	yes	—
46	#394×C₈₉	C₂²	1	2	yes	—
47	#394×C₈₉	C₂²	1	2	yes	—
48	#394×C₈₉	C₂²	1	1	yes	characteristic, complemented
49	#393×C₈₉	C₂²	1	1	yes	characteristic
50	#393×C₈₉	C₂²	1	1	yes	characteristic, complemented
51	#392×C₈₉	C₂²	1	2	yes	—
52	#392×C₈₉	C₂²	1	2	yes	—
53	#392×C₈₉	C₂²	1	2	yes	—
54	#392×C₈₉	C₂²	1	1	yes	characteristic
55	#391×C₈₉	C₂²	1	2	yes	complemented
56	#390×C₈₉	C₂²	1	2	yes	—
57	#390×C₈₉	C₂²	1	2	yes	—
58	#390×C₈₉	C₂²	1	2	yes	—
59	#390×C₈₉	C₂²	1	2	yes	complemented
60	#389×C₈₉	C₂²	1	2	yes	complemented
61	#389×C₈₉	C₂²	1	2	yes	complemented
62	#389×C₈₉	C₂²	1	2	yes	complemented
63	#388×C₈₉	C₂²	1	2	yes	—
64	#388×C₈₉	C₂²	1	2	yes	—
65	#388×C₈₉	C₂²	1	2	yes	—
66	#388×C₈₉	C₂²	1	2	yes	—
67	#388×C₈₉	C₂²	1	2	yes	—
68	#388×C₈₉	C₂²	1	2	yes	complemented
69	#388×C₈₉	C₂²	1	2	yes	complemented
70	#388×C₈₉	C₂²	1	2	yes	complemented
71	#388×C₈₉	C₂²	1	2	yes	complemented
72	#388×C₈₉	C₂²	1	2	yes	complemented
73	#388×C₈₉	C₂²	1	2	yes	complemented
74	#387×C₈₉	C₂²	1	2	yes	complemented
75	#387×C₈₉	C₂²	1	2	yes	complemented
76	#387×C₈₉	C₂²	1	2	yes	complemented
77	#387×C₈₉	C₂²	1	2	yes	complemented
78	#386×C₈₉	C₂²	1	2	yes	—
79	#386×C₈₉	C₂²	1	2	yes	—
80	#386×C₈₉	C₂²	1	2	yes	—
81	#386×C₈₉	C₂²	1	1	yes	characteristic
82	#386×C₈₉	C₂²	1	2	yes	—
83	#386×C₈₉	C₂²	1	2	yes	—
84	#386×C₈₉	C₂²	1	2	yes	complemented
85	#386×C₈₉	C₂²	1	2	yes	complemented
86	#385×C₈₉	C₂²	1	2	yes	—
87	#385×C₈₉	C₂²	1	2	yes	—
88	#385×C₈₉	C₂²	1	2	yes	—
89	#385×C₈₉	C₂²	1	2	yes	—
90	#385×C₈₉	C₂²	1	1	yes	characteristic
91	#385×C₈₉	C₂²	1	2	yes	complemented
92	#385×C₈₉	C₂²	1	2	yes	complemented
93	#383×C₈₉	C₂²	1	2	yes	complemented
94	#382×C₈₉	C₂²	1	1	yes	characteristic, complemented
95	#379×C₈₉	C₂²	1	1	yes	characteristic
96	#379×C₈₉	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
98	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
99	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
105	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
106	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic, complemented
107	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
110	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
111	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
112	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
113	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
114	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₈₉	—	4	2	no	—
117	C₂³×C₄×C₈₉	—	4	4	no	—
118	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
119	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
120	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
123	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
125	#124×C₈₉	—	2	8	no	—
126	#123×C₈₉	—	2	8	no	—
127	#123×C₈₉	—	4	4	no	—
128	#121×C₈₉	—	2	8	no	—
129	#121×C₈₉	—	4	2	no	—
130	#120×C₈₉	—	2	4	no	—
131	#120×C₈₉	—	2	8	no	—
132	C₄×Q₈×C₈₉	—	4	2	no	—
133	C₄×D₄×C₈₉	—	4	4	no	—
134	C₄×D₄×C₈₉	—	4	2	no	—
135	C₄×D₄×C₈₉	—	4	4	no	—
136	C₄×D₄×C₈₉	—	4	4	no	—
137	C₄×D₄×C₈₉	—	4	4	no	—
138	#117×C₈₉	—	4	4	no	—
139	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
160	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
181	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
183	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
184	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
185	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
186	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
187	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
188	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
189	#95×C₈₉	C₂³	1	2	yes	—
190	#95×C₈₉	C₂³	1	1	yes	characteristic
191	#95×C₈₉	C₂³	1	1	yes	characteristic
192	#95×C₈₉	C₂³	1	2	yes	—
193	#95×C₈₉	C₂³	1	2	yes	—
194	#95×C₈₉	C₂³	1	2	yes	—
195	#95×C₈₉	C₂³	1	2	yes	—
196	#95×C₈₉	C₂³	1	2	yes	—
197	#95×C₈₉	C₂³	1	2	yes	—
198	#95×C₈₉	C₂³	1	2	yes	—
199	#95×C₈₉	C₂³	1	2	yes	—
200	#95×C₈₉	C₂³	1	2	yes	—
201	#95×C₈₉	C₂³	1	2	yes	—
202	#95×C₈₉	C₂³	1	2	yes	—
203	#95×C₈₉	C₂³	1	1	yes	characteristic
204	#95×C₈₉	C₂³	1	1	yes	characteristic
205	#95×C₈₉	C₂³	1	2	yes	—
206	#95×C₈₉	C₂³	1	2	yes	—
207	#95×C₈₉	C₂³	1	2	yes	—
208	#95×C₈₉	C₂³	1	2	yes	—
209	#95×C₈₉	C₂³	1	2	yes	—
210	C₂⁴×C₈₉	—	2	2	no	—
211	C₂⁴×C₈₉	—	2	4	no	—
212	C₂⁴×C₈₉	—	4	1	no	—
213	C₂⁴×C₈₉	—	4	2	no	—
214	C₂⁴×C₈₉	—	4	1	no	—
215	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
216	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
217	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
218	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
219	C₂×Q₈×C₈₉	—	2	4	no	—
220	C₂×Q₈×C₈₉	—	4	1	no	—
221	C₂×D₄×C₈₉	—	2	4	no	—
222	C₂×D₄×C₈₉	—	2	4	no	—
223	C₂×D₄×C₈₉	—	2	4	no	—
224	C₂×D₄×C₈₉	—	2	4	no	—
225	C₂×D₄×C₈₉	—	2	4	no	—
226	C₂×D₄×C₈₉	—	2	4	no	—
227	C₂×D₄×C₈₉	—	2	4	no	—
228	C₂×D₄×C₈₉	—	2	4	no	—
229	C₂×D₄×C₈₉	—	4	1	no	—
230	C₂×D₄×C₈₉	—	4	2	no	—
231	C₂×D₄×C₈₉	—	4	2	no	—
232	C₂×D₄×C₈₉	—	4	2	no	—
233	C₂×D₄×C₈₉	—	4	2	no	—
234	C₂×D₄×C₈₉	—	4	1	no	—
235	C₂×D₄×C₈₉	—	4	2	no	—
236	C₂×D₄×C₈₉	—	4	2	no	—
237	C₂×D₄×C₈₉	—	4	1	no	—
238	C₂×D₄×C₈₉	—	4	2	no	—
239	C₂×D₄×C₈₉	—	4	2	no	—
240	C₂×D₄×C₈₉	#41	1	4	yes	—
241	C₂²×C₄×C₈₉	—	2	4	no	—
242	C₂²×C₄×C₈₉	—	2	4	no	—
243	C₂²×C₄×C₈₉	—	2	4	no	—
244	C₂²×C₄×C₈₉	—	2	4	no	—
245	C₂²×C₄×C₈₉	—	2	4	no	—
246	C₂²×C₄×C₈₉	—	2	2	no	—
247	C₂²×C₄×C₈₉	—	2	4	no	—
248	C₂²×C₄×C₈₉	—	2	2	no	—
249	C₂²×C₄×C₈₉	—	2	4	no	—
250	C₂²×C₄×C₈₉	—	4	2	no	—
251	C₂²×C₄×C₈₉	—	4	1	no	—
252	C₂²×C₄×C₈₉	—	4	2	no	—
253	C₂²×C₄×C₈₉	—	4	2	no	—
254	C₂²×C₄×C₈₉	—	4	2	no	—
255	C₂²×C₄×C₈₉	—	4	2	no	—
256	C₂²×C₄×C₈₉	—	4	2	no	—
257	C₂²×C₄×C₈₉	—	4	2	no	—
258	C₂²×C₄×C₈₉	—	4	2	no	—
259	C₂²×C₄×C₈₉	—	4	16	no	—
260	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
275	C₄⋊C₄×C₈₉	—	2	4	no	—
276	C₄⋊C₄×C₈₉	—	2	4	no	—
277	C₄⋊C₄×C₈₉	—	2	4	no	—
278	C₄⋊C₄×C₈₉	—	2	4	no	—
279	C₄⋊C₄×C₈₉	—	2	4	no	—
280	C₄⋊C₄×C₈₉	—	2	4	no	—
281	C₄⋊C₄×C₈₉	—	4	2	no	—
282	C₄⋊C₄×C₈₉	—	4	2	no	—
283	C₄⋊C₄×C₈₉	—	4	2	no	—
284	C₄⋊C₄×C₈₉	—	4	1	no	—
285	C₄⋊C₄×C₈₉	—	4	2	no	—
286	C₄⋊C₄×C₈₉	—	4	1	no	—
287	C₄⋊C₄×C₈₉	—	4	1	no	—
288	C₄⋊C₄×C₈₉	—	4	2	no	—
289	C₂²⋊C₄×C₈₉	—	2	2	no	—
290	C₂²⋊C₄×C₈₉	—	2	4	no	—
291	C₂²⋊C₄×C₈₉	—	2	4	no	—
292	C₂²⋊C₄×C₈₉	—	2	4	no	—
293	C₂²⋊C₄×C₈₉	—	2	4	no	—
294	C₂²⋊C₄×C₈₉	—	2	4	no	—
295	C₂²⋊C₄×C₈₉	—	2	4	no	—
296	C₂²⋊C₄×C₈₉	—	2	4	no	—
297	C₂²⋊C₄×C₈₉	—	2	4	no	—
298	C₂²⋊C₄×C₈₉	—	2	4	no	—
299	C₂²⋊C₄×C₈₉	—	2	4	no	—
300	C₂²⋊C₄×C₈₉	—	2	4	no	—
301	C₂²⋊C₄×C₈₉	—	2	4	no	—
302	C₂²⋊C₄×C₈₉	—	2	4	no	—
303	C₂²⋊C₄×C₈₉	—	4	1	no	—
304	C₂²⋊C₄×C₈₉	—	4	2	no	—
305	C₂²⋊C₄×C₈₉	—	4	2	no	—
306	C₂²⋊C₄×C₈₉	—	4	2	no	—
307	C₂²⋊C₄×C₈₉	—	4	2	no	—
308	C₂²⋊C₄×C₈₉	—	4	2	no	—
309	C₂²⋊C₄×C₈₉	—	4	1	no	—
310	C₂²⋊C₄×C₈₉	—	4	1	no	—
311	C₂²⋊C₄×C₈₉	—	4	2	no	—
312	C₂²⋊C₄×C₈₉	—	4	2	no	—
313	C₂²⋊C₄×C₈₉	—	4	2	no	—
314	C₂²⋊C₄×C₈₉	—	4	2	no	—
315	C₂²⋊C₄×C₈₉	—	4	2	no	—
316	C₂²⋊C₄×C₈₉	#41	1	8	yes	—
317	C₄²×C₈₉	—	2	4	no	—
318	C₄²×C₈₉	—	2	4	no	—
319	C₄²×C₈₉	—	2	2	no	—
320	C₄²×C₈₉	—	4	2	no	—
321	C₄²×C₈₉	—	4	2	no	—
322	C₄²×C₈₉	—	4	2	no	—
323	C₄²×C₈₉	—	4	2	no	—
324	C₄²×C₈₉	—	4	2	no	—
325	C₂³×C₈₉	—	2	2	no	—
326	C₂³×C₈₉	—	2	2	no	—
327	C₂³×C₈₉	—	2	2	no	—
328	C₂³×C₈₉	—	2	2	no	—
329	C₂³×C₈₉	—	2	2	no	—
330	C₂³×C₈₉	—	2	2	no	—
331	C₂³×C₈₉	—	2	2	no	—
332	C₂³×C₈₉	—	2	2	no	—
333	C₂³×C₈₉	—	2	1	no	—
334	C₂³×C₈₉	—	2	2	no	—
335	C₂³×C₈₉	—	2	1	no	—
336	C₂³×C₈₉	—	2	1	no	—
337	C₂³×C₈₉	—	2	2	no	—
338	C₂³×C₈₉	—	2	1	no	—
339	C₂³×C₈₉	—	2	2	no	—
340	C₂³×C₈₉	—	2	2	no	—
341	C₂³×C₈₉	—	2	2	no	—
342	C₂³×C₈₉	—	2	2	no	—
343	C₂³×C₈₉	—	2	2	no	—
344	C₂³×C₈₉	—	2	2	no	—
345	C₂³×C₈₉	—	2	2	no	—
346	C₂³×C₈₉	—	4	4	no	—
347	C₂³×C₈₉	—	4	8	no	—
348	C₂³×C₈₉	—	4	4	no	—
349	C₂³×C₈₉	—	4	8	no	—
350	C₂³×C₈₉	—	4	4	no	—
351	C₂³×C₈₉	C₂×#41	1	2	yes	—
352	C₂³×C₈₉	C₂×#41	1	4	yes	—
353	C₂³×C₈₉	C₂×#41	1	2	yes	—
354	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
355	Q₈×C₈₉	—	4	4	no	—
356	D₄×C₈₉	—	4	4	no	—
357	D₄×C₈₉	—	4	8	no	—
358	D₄×C₈₉	—	4	8	no	—
359	D₄×C₈₉	—	4	8	no	—
360	D₄×C₈₉	—	4	8	no	—
361	D₄×C₈₉	—	8	4	no	—
362	D₄×C₈₉	—	8	2	no	—
363	C₂×C₄×C₈₉	—	2	2	no	—
364	C₂×C₄×C₈₉	—	2	2	no	—
365	C₂×C₄×C₈₉	—	2	1	no	—
366	C₂×C₄×C₈₉	—	2	2	no	—
367	C₂×C₄×C₈₉	—	2	2	no	—
368	C₂×C₄×C₈₉	—	2	2	no	—
369	C₂×C₄×C₈₉	—	2	2	no	—
370	C₂×C₄×C₈₉	—	2	2	no	—
371	C₂×C₄×C₈₉	—	2	1	no	—
372	C₂×C₄×C₈₉	—	2	2	no	—
373	C₂×C₄×C₈₉	—	2	2	no	—
374	C₂×C₄×C₈₉	—	2	2	no	—
375	C₂×C₄×C₈₉	—	2	2	no	—
376	C₂×C₄×C₈₉	—	2	2	no	—
377	C₂×C₄×C₈₉	—	2	2	no	—
378	C₂×C₄×C₈₉	—	2	2	no	—
379	C₂×C₄×C₈₉	—	2	2	no	—
380	C₂×C₄×C₈₉	—	2	2	no	—
381	C₂×C₄×C₈₉	—	2	2	no	—
382	C₂×C₄×C₈₉	—	2	1	no	—
383	C₂×C₄×C₈₉	—	2	2	no	—
384	C₂×C₄×C₈₉	—	2	2	no	—
385	C₂×C₄×C₈₉	—	2	2	no	—
386	C₂×C₄×C₈₉	—	2	2	no	—
387	C₂×C₄×C₈₉	—	2	2	no	—
388	C₂×C₄×C₈₉	—	2	2	no	—
389	C₂×C₄×C₈₉	—	2	2	no	—
390	C₂×C₄×C₈₉	—	2	2	no	—
391	C₂×C₄×C₈₉	—	2	2	no	—
392	C₂×C₄×C₈₉	—	2	1	no	—
393	C₂×C₄×C₈₉	—	2	1	no	—
394	C₂×C₄×C₈₉	—	2	2	no	—
395	C₂×C₄×C₈₉	—	2	2	no	—
396	C₂×C₄×C₈₉	—	2	2	no	—
397	C₂×C₄×C₈₉	—	2	2	no	—
398	C₂×C₄×C₈₉	—	2	2	no	—
399	C₂×C₄×C₈₉	—	4	4	no	—
400	C₂×C₄×C₈₉	—	4	8	no	—
401	C₂×C₄×C₈₉	—	4	8	no	—
402	C₂×C₄×C₈₉	—	4	8	no	—
403	C₂×C₄×C₈₉	—	4	4	no	—
404	C₂×C₄×C₈₉	—	8	4	no	—
405	C₂×C₄×C₈₉	—	8	2	no	—
406	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
407	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
408	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
409	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
410	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
411	C₂²×C₈₉	—	2	4	no	—
412	C₂²×C₈₉	—	2	4	no	—
413	C₂²×C₈₉	—	2	4	no	—
414	C₂²×C₈₉	—	2	4	no	—
415	C₂²×C₈₉	—	2	2	no	—
416	C₂²×C₈₉	—	2	2	no	—
417	C₂²×C₈₉	—	2	4	no	—
418	C₂²×C₈₉	—	4	16	no	—
419	C₂²×C₈₉	—	4	1	no	—
420	C₂²×C₈₉	—	4	1	no	—
421	C₂²×C₈₉	—	4	2	no	—
422	C₂²×C₈₉	—	4	2	no	—
423	C₂²×C₈₉	—	4	2	no	—
424	C₂²×C₈₉	—	4	2	no	—
425	C₂²×C₈₉	—	4	2	no	—
426	C₂²×C₈₉	—	4	1	no	—
427	C₂²×C₈₉	—	4	2	no	—
428	C₂²×C₈₉	—	4	1	no	—
429	C₂²×C₈₉	—	4	2	no	—
430	C₂²×C₈₉	—	4	2	no	—
431	C₂²×C₈₉	—	4	2	no	—
432	C₂²×C₈₉	—	4	2	no	—
433	C₂²×C₈₉	—	4	2	no	—
434	C₂²×C₈₉	—	4	2	no	—
435	C₂²×C₈₉	—	4	2	no	—
436	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
437	C₂²×C₈₉	C₂²×#41	1	2	yes	—
438	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
439	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
440	C₂²×C₈₉	#585	1	1	yes	characteristic
441	C₄×C₈₉	—	2	4	no	—
442	C₄×C₈₉	—	2	4	no	—
443	C₄×C₈₉	—	2	2	no	—
444	C₄×C₈₉	—	2	4	no	—
445	C₄×C₈₉	—	2	2	no	—
446	C₄×C₈₉	—	4	2	no	—
447	C₄×C₈₉	—	4	2	no	—
448	C₄×C₈₉	—	4	1	no	—
449	C₄×C₈₉	—	4	2	no	—
450	C₄×C₈₉	—	4	2	no	—
451	C₄×C₈₉	—	4	2	no	—
452	C₄×C₈₉	—	4	2	no	—
453	C₄×C₈₉	—	4	1	no	—
454	C₄×C₈₉	—	4	2	no	—
455	C₄×C₈₉	—	4	1	no	—
456	#60033	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
457	C₂×C₈₉	—	4	2	no	—
458	C₂×C₈₉	—	4	2	no	—
459	C₂×C₈₉	—	4	4	no	—
460	C₂×C₈₉	—	8	2	no	—
461	C₂×C₈₉	#3481	1	1	yes	characteristic
462	C₂×C₈₉	#3481	1	2	yes	—
463	C₂×C₈₉	#3505	1	1	yes	characteristic
464	C₂×C₈₉	#3506	1	2	yes	—
465	C₂×C₈₉	#3532	1	1	yes	characteristic
466	#2735	C₂×C₈₉	1	1	yes	characteristic, complemented
467	#2678	C₂×C₈₉	1	2	yes	complemented
468	#2670	C₂×C₈₉	1	1	yes	characteristic, complemented
469	#2602	C₂×C₈₉	1	2	yes	complemented
470	#2598	C₂×C₈₉	1	2	yes	complemented
471	#2597	C₂×C₈₉	1	2	yes	complemented
472	#2587	C₂×C₈₉	1	2	yes	complemented
473	#2580	C₂×C₈₉	1	1	yes	characteristic, complemented
474	#2557	C₂×C₈₉	1	2	yes	complemented
475	#2543	C₂×C₈₉	1	1	yes	characteristic, complemented
476	#2523	C₂×C₈₉	1	1	yes	characteristic, complemented
477	#2518	C₂×C₈₉	1	2	yes	complemented
478	#2456	C₂×C₈₉	1	2	yes	complemented
479	#2455	C₂×C₈₉	1	1	yes	characteristic, complemented
480	#2367	C₂×C₈₉	1	2	yes	complemented
481	#2363	C₂×C₈₉	1	2	yes	complemented
482	#2359	C₂×C₈₉	1	2	yes	complemented
483	C₄×#120	C₂×C₈₉	1	1	yes	characteristic, complemented
484	C₄×#120	C₂×C₈₉	1	2	yes	complemented
485	C₈₉	#60033	1	1	yes	characteristic, direct product factor, Sylow
486	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
487	C₂×#124	C₂²×C₈₉	1	2	yes	—
488	C₂×#123	C₂²×C₈₉	1	2	yes	—
489	C₂×#123	C₂²×C₈₉	1	2	yes	complemented
490	C₂×#121	C₂²×C₈₉	1	2	yes	—
491	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic, complemented
492	C₂×#120	C₂²×C₈₉	1	2	yes	—
493	C₂×#120	C₂²×C₈₉	1	1	yes	characteristic
494	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
495	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
496	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
497	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
498	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
499	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
500	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
501	#400	C₂²×C₈₉	1	2	yes	complemented
502	#399	C₂²×C₈₉	1	1	yes	characteristic
503	#399	C₂²×C₈₉	1	1	yes	characteristic, complemented
504	#398	C₂²×C₈₉	1	1	yes	characteristic, complemented
505	#397	C₂²×C₈₉	1	2	yes	—
506	#397	C₂²×C₈₉	1	2	yes	—
507	#397	C₂²×C₈₉	1	1	yes	characteristic
508	#397	C₂²×C₈₉	1	2	yes	complemented
509	#396	C₂²×C₈₉	1	2	yes	—
510	#396	C₂²×C₈₉	1	2	yes	—
511	#394	C₂²×C₈₉	1	2	yes	—
512	#394	C₂²×C₈₉	1	2	yes	—
513	#394	C₂²×C₈₉	1	2	yes	—
514	#394	C₂²×C₈₉	1	1	yes	characteristic, complemented
515	#393	C₂²×C₈₉	1	1	yes	characteristic
516	#393	C₂²×C₈₉	1	1	yes	characteristic, complemented
517	#392	C₂²×C₈₉	1	2	yes	—
518	#392	C₂²×C₈₉	1	2	yes	—
519	#392	C₂²×C₈₉	1	1	yes	characteristic
520	#392	C₂²×C₈₉	1	2	yes	—
521	#391	C₂²×C₈₉	1	2	yes	complemented
522	#390	C₂²×C₈₉	1	2	yes	—
523	#390	C₂²×C₈₉	1	2	yes	—
524	#390	C₂²×C₈₉	1	2	yes	—
525	#390	C₂²×C₈₉	1	2	yes	complemented
526	#389	C₂²×C₈₉	1	2	yes	complemented
527	#389	C₂²×C₈₉	1	2	yes	complemented
528	#389	C₂²×C₈₉	1	2	yes	complemented
529	#388	C₂²×C₈₉	1	2	yes	—
530	#388	C₂²×C₈₉	1	2	yes	—
531	#388	C₂²×C₈₉	1	2	yes	—
532	#388	C₂²×C₈₉	1	2	yes	—
533	#388	C₂²×C₈₉	1	2	yes	—
534	#388	C₂²×C₈₉	1	2	yes	complemented
535	#388	C₂²×C₈₉	1	2	yes	complemented
536	#388	C₂²×C₈₉	1	2	yes	complemented
537	#388	C₂²×C₈₉	1	2	yes	complemented
538	#388	C₂²×C₈₉	1	2	yes	complemented
539	#388	C₂²×C₈₉	1	2	yes	complemented
540	#387	C₂²×C₈₉	1	2	yes	complemented
541	#387	C₂²×C₈₉	1	2	yes	complemented
542	#387	C₂²×C₈₉	1	2	yes	complemented
543	#387	C₂²×C₈₉	1	2	yes	complemented
544	#386	C₂²×C₈₉	1	2	yes	—
545	#386	C₂²×C₈₉	1	2	yes	—
546	#386	C₂²×C₈₉	1	2	yes	—
547	#386	C₂²×C₈₉	1	2	yes	—
548	#386	C₂²×C₈₉	1	1	yes	characteristic
549	#386	C₂²×C₈₉	1	2	yes	—
550	#386	C₂²×C₈₉	1	2	yes	complemented
551	#386	C₂²×C₈₉	1	2	yes	complemented
552	#385	C₂²×C₈₉	1	2	yes	—
553	#385	C₂²×C₈₉	1	2	yes	—
554	#385	C₂²×C₈₉	1	2	yes	—
555	#385	C₂²×C₈₉	1	2	yes	—
556	#385	C₂²×C₈₉	1	1	yes	characteristic
557	#385	C₂²×C₈₉	1	2	yes	complemented
558	#385	C₂²×C₈₉	1	2	yes	complemented
559	#383	C₂²×C₈₉	1	2	yes	complemented
560	#382	C₂²×C₈₉	1	1	yes	characteristic, complemented
561	#379	C₂²×C₈₉	1	1	yes	characteristic
562	#379	C₂²×C₈₉	1	2	yes	—
563	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
564	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
565	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
566	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
567	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
568	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
569	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
570	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
571	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
572	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic, complemented
573	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
574	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
575	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
576	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
577	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
578	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
579	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
580	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
581	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
582	C₂³×C₄	—	4	2	no	—
583	C₂³×C₄	—	4	4	no	—
584	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
585	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
586	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
587	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
588	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
589	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
590	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
591	#124	—	2	8	no	—
592	#123	—	2	8	no	—
593	#123	—	4	4	no	—
594	#121	—	2	8	no	—
595	#121	—	4	2	no	—
596	#120	—	2	4	no	—
597	#120	—	2	8	no	—
598	C₄×Q₈	—	4	2	no	—
599	C₄×D₄	—	4	4	no	—
600	C₄×D₄	—	4	2	no	—
601	C₄×D₄	—	4	4	no	—
602	C₄×D₄	—	4	4	no	—
603	C₄×D₄	—	4	4	no	—
604	#117	—	4	4	no	—
605	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
639	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
640	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
644	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
647	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
648	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
650	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
651	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
652	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
653	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
654	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
655	#95	C₂³×C₈₉	1	2	yes	—
656	#95	C₂³×C₈₉	1	1	yes	characteristic
657	#95	C₂³×C₈₉	1	1	yes	characteristic
658	#95	C₂³×C₈₉	1	2	yes	—
659	#95	C₂³×C₈₉	1	2	yes	—
660	#95	C₂³×C₈₉	1	2	yes	—
661	#95	C₂³×C₈₉	1	2	yes	—
662	#95	C₂³×C₈₉	1	2	yes	—
663	#95	C₂³×C₈₉	1	2	yes	—
664	#95	C₂³×C₈₉	1	2	yes	—
665	#95	C₂³×C₈₉	1	2	yes	—
666	#95	C₂³×C₈₉	1	2	yes	—
667	#95	C₂³×C₈₉	1	2	yes	—
668	#95	C₂³×C₈₉	1	2	yes	—
669	#95	C₂³×C₈₉	1	1	yes	characteristic
670	#95	C₂³×C₈₉	1	1	yes	characteristic
671	#95	C₂³×C₈₉	1	2	yes	—
672	#95	C₂³×C₈₉	1	2	yes	—
673	#95	C₂³×C₈₉	1	2	yes	—
674	#95	C₂³×C₈₉	1	2	yes	—
675	#95	C₂³×C₈₉	1	2	yes	—
676	C₂⁴	—	2	2	no	—
677	C₂⁴	—	2	4	no	—
678	C₂⁴	—	4	1	no	—
679	C₂⁴	—	4	2	no	—
680	C₂⁴	—	4	1	no	—
681	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
682	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
683	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
684	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
685	C₂×Q₈	—	2	4	no	—
686	C₂×Q₈	—	4	1	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	4	no	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	2	4	no	—
693	C₂×D₄	—	2	4	no	—
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	4	1	no	—
696	C₂×D₄	—	4	2	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂×D₄	—	4	2	no	—
699	C₂×D₄	—	4	2	no	—
700	C₂×D₄	—	4	1	no	—
701	C₂×D₄	—	4	2	no	—
702	C₂×D₄	—	4	2	no	—
703	C₂×D₄	—	4	1	no	—
704	C₂×D₄	—	4	2	no	—
705	C₂×D₄	—	4	2	no	—
706	C₂×D₄	#41×C₈₉	1	4	yes	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	—	2	4	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	4	2	no	—
717	C₂²×C₄	—	4	1	no	—
718	C₂²×C₄	—	4	2	no	—
719	C₂²×C₄	—	4	2	no	—
720	C₂²×C₄	—	4	2	no	—
721	C₂²×C₄	—	4	2	no	—
722	C₂²×C₄	—	4	2	no	—
723	C₂²×C₄	—	4	2	no	—
724	C₂²×C₄	—	4	2	no	—
725	C₂²×C₄	—	4	16	no	—
726	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	4	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	4	2	no	—
748	C₄⋊C₄	—	4	1	no	—
749	C₄⋊C₄	—	4	2	no	—
750	C₄⋊C₄	—	4	1	no	—
751	C₄⋊C₄	—	4	1	no	—
752	C₄⋊C₄	—	4	2	no	—
753	C₄⋊C₄	—	4	2	no	—
754	C₄⋊C₄	—	4	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	4	2	no	—
770	C₂²⋊C₄	—	4	2	no	—
771	C₂²⋊C₄	—	4	2	no	—
772	C₂²⋊C₄	—	4	1	no	—
773	C₂²⋊C₄	—	4	1	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₂²⋊C₄	—	4	2	no	—
778	C₂²⋊C₄	—	4	2	no	—
779	C₂²⋊C₄	—	4	1	no	—
780	C₂²⋊C₄	—	4	2	no	—
781	C₂²⋊C₄	—	4	2	no	—
782	C₂²⋊C₄	#41×C₈₉	1	8	yes	—
783	C₄²	—	2	4	no	—
784	C₄²	—	2	4	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	4	2	no	—
787	C₄²	—	4	2	no	—
788	C₄²	—	4	2	no	—
789	C₄²	—	4	2	no	—
790	C₄²	—	4	2	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	1	no	—
800	C₂³	—	2	2	no	—
801	C₂³	—	2	1	no	—
802	C₂³	—	2	1	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	1	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	2	2	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	4	4	no	—
813	C₂³	—	4	8	no	—
814	C₂³	—	4	4	no	—
815	C₂³	—	4	8	no	—
816	C₂³	—	4	4	no	—
817	C₂³	C₂×#41×C₈₉	1	2	yes	—
818	C₂³	C₂×#41×C₈₉	1	4	yes	—
819	C₂³	C₂×#41×C₈₉	1	2	yes	—
820	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
821	Q₈	—	4	4	no	—
822	D₄	—	4	4	no	—
823	D₄	—	4	8	no	—
824	D₄	—	4	8	no	—
825	D₄	—	4	8	no	—
826	D₄	—	4	8	no	—
827	D₄	—	8	4	no	—
828	D₄	—	8	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	4	4	no	—
866	C₂×C₄	—	4	8	no	—
867	C₂×C₄	—	4	8	no	—
868	C₂×C₄	—	4	8	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	8	2	no	—
871	C₂×C₄	—	8	4	no	—
872	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
873	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
874	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
875	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
876	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
877	C₂²	—	2	4	no	—
878	C₂²	—	2	4	no	—
879	C₂²	—	2	4	no	—
880	C₂²	—	2	4	no	—
881	C₂²	—	2	2	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	2	4	no	—
884	C₂²	—	4	16	no	—
885	C₂²	—	4	1	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	1	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	1	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	1	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	2	no	—
902	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
903	C₂²	C₂²×#41×C₈₉	1	2	yes	—
904	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
905	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
906	C₂²	#585×C₈₉	1	1	yes	characteristic
907	C₄	—	2	4	no	—
908	C₄	—	2	4	no	—
909	C₄	—	2	2	no	—
910	C₄	—	2	4	no	—
911	C₄	—	2	2	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	2	no	—
914	C₄	—	4	1	no	—
915	C₄	—	4	2	no	—
916	C₄	—	4	2	no	—
917	C₄	—	4	2	no	—
918	C₄	—	4	2	no	—
919	C₄	—	4	1	no	—
920	C₄	—	4	1	no	—
921	C₄	—	4	2	no	—
922	C₂	—	4	2	no	—
923	C₂	—	4	2	no	—
924	C₂	—	4	4	no	—
925	C₂	—	8	2	no	—
926	C₂	C₈₉×#3481	1	1	yes	characteristic
927	C₂	C₈₉×#3481	1	2	yes	—
928	C₂	C₈₉×#3505	1	1	yes	characteristic
929	C₂	C₈₉×#3506	1	2	yes	—
930	C₂	C₈₉×#3532	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#2735	C₂	semidirect
2. C₈₉×#2678	C₂	semidirect
3. C₈₉×#2670	C₂	semidirect
4. C₈₉×#2602	C₂	semidirect
5. C₈₉×#2598	C₂	semidirect
6. C₈₉×#2597	C₂	semidirect
7. C₈₉×#2587	C₂	semidirect
8. C₈₉×#2580	C₂	semidirect
9. C₈₉×#2557	C₂	semidirect
10. C₈₉×#2543	C₂	semidirect
11. C₈₉×#2523	C₂	semidirect
12. C₈₉×#2518	C₂	semidirect
13. C₈₉×#2456	C₂	semidirect
14. C₈₉×#2455	C₂	semidirect
15. C₈₉×#2367	C₂	semidirect
16. C₈₉×#2363	C₂	semidirect
17. C₈₉×#2359	C₂	semidirect
18. C₄×#120×C₈₉	C₂	semidirect
19. C₄×#120×C₈₉	C₂	semidirect
23. C₂×#123×C₈₉	C₂²	semidirect
25. C₂×#121×C₈₉	C₂²	semidirect
28. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
34. C₂×#117×C₈₉	C₂²	semidirect
35. #400×C₈₉	C₂²	semidirect
37. #399×C₈₉	C₂²	semidirect
38. #398×C₈₉	C₂²	semidirect
42. #397×C₈₉	C₂²	semidirect
48. #394×C₈₉	C₂²	semidirect
50. #393×C₈₉	C₂²	semidirect
55. #391×C₈₉	C₂²	semidirect
59. #390×C₈₉	C₂²	semidirect
60. #389×C₈₉	C₂²	semidirect
61. #389×C₈₉	C₂²	semidirect
62. #389×C₈₉	C₂²	semidirect
68. #388×C₈₉	C₂²	semidirect
69. #388×C₈₉	C₂²	semidirect
70. #388×C₈₉	C₂²	semidirect
71. #388×C₈₉	C₂²	semidirect
72. #388×C₈₉	C₂²	semidirect
73. #388×C₈₉	C₂²	semidirect
74. #387×C₈₉	C₂²	semidirect
75. #387×C₈₉	C₂²	semidirect
76. #387×C₈₉	C₂²	semidirect
77. #387×C₈₉	C₂²	semidirect
84. #386×C₈₉	C₂²	semidirect
85. #386×C₈₉	C₂²	semidirect
91. #385×C₈₉	C₂²	semidirect
92. #385×C₈₉	C₂²	semidirect
93. #383×C₈₉	C₂²	semidirect
94. #382×C₈₉	C₂²	semidirect
97. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
98. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
106. C₂×#95×C₈₉	C₂²	semidirect
456. #60033	C₈₉	direct (N × H)
466. #2735	C₂×C₈₉	semidirect
467. #2678	C₂×C₈₉	semidirect
468. #2670	C₂×C₈₉	semidirect
469. #2602	C₂×C₈₉	semidirect
470. #2598	C₂×C₈₉	semidirect
471. #2597	C₂×C₈₉	semidirect
472. #2587	C₂×C₈₉	semidirect
473. #2580	C₂×C₈₉	semidirect
474. #2557	C₂×C₈₉	semidirect
475. #2543	C₂×C₈₉	semidirect
476. #2523	C₂×C₈₉	semidirect
477. #2518	C₂×C₈₉	semidirect
478. #2456	C₂×C₈₉	semidirect
479. #2455	C₂×C₈₉	semidirect
480. #2367	C₂×C₈₉	semidirect
481. #2363	C₂×C₈₉	semidirect
482. #2359	C₂×C₈₉	semidirect
483. C₄×#120	C₂×C₈₉	semidirect
484. C₄×#120	C₂×C₈₉	semidirect
485. C₈₉	#60033	direct (N × H)
489. C₂×#123	C₂²×C₈₉	semidirect
491. C₂×#121	C₂²×C₈₉	semidirect
494. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
500. C₂×#117	C₂²×C₈₉	semidirect
501. #400	C₂²×C₈₉	semidirect
503. #399	C₂²×C₈₉	semidirect
504. #398	C₂²×C₈₉	semidirect
508. #397	C₂²×C₈₉	semidirect
514. #394	C₂²×C₈₉	semidirect
516. #393	C₂²×C₈₉	semidirect
521. #391	C₂²×C₈₉	semidirect
525. #390	C₂²×C₈₉	semidirect
526. #389	C₂²×C₈₉	semidirect
527. #389	C₂²×C₈₉	semidirect
528. #389	C₂²×C₈₉	semidirect
534. #388	C₂²×C₈₉	semidirect
535. #388	C₂²×C₈₉	semidirect
536. #388	C₂²×C₈₉	semidirect
537. #388	C₂²×C₈₉	semidirect
538. #388	C₂²×C₈₉	semidirect
539. #388	C₂²×C₈₉	semidirect
540. #387	C₂²×C₈₉	semidirect
541. #387	C₂²×C₈₉	semidirect
542. #387	C₂²×C₈₉	semidirect
543. #387	C₂²×C₈₉	semidirect
550. #386	C₂²×C₈₉	semidirect
551. #386	C₂²×C₈₉	semidirect
557. #385	C₂²×C₈₉	semidirect
558. #385	C₂²×C₈₉	semidirect
559. #383	C₂²×C₈₉	semidirect
560. #382	C₂²×C₈₉	semidirect
563. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
564. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
570. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
571. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
572. C₂×#95	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×#2735	2
C₈₉×#2678	2
C₈₉×#2670	2
C₈₉×#2602	2
C₈₉×#2598	2
C₈₉×#2597	2
C₈₉×#2587	2
C₈₉×#2580	2
C₈₉×#2557	2
C₈₉×#2543	2
C₈₉×#2523	2
C₈₉×#2518	2
C₈₉×#2456	2
C₈₉×#2455	2
C₈₉×#2367	2
C₈₉×#2363	2
C₈₉×#2359	2
C₄×#120×C₈₉	2
#60033	89

Subgroups — C89×#60033 #36437881

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60033 #36437881