Subgroups — C₈₉×#36903 #36414751

Order 22784.

2230 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2847	C₂	1	2	yes	maximal, complemented
2	C₈₉×#2779	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2742	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2703	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2688	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2686	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2675	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2673	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2670	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2669	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2668	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2635	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#2631	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2578	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2555	C₂	1	2	yes	maximal, complemented
16	C₈₉×#2457	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2428	C₂	1	2	yes	maximal, complemented
18	C₈₉×#2333	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×#127×C₈₉	C₂²	1	2	yes	—
22	C₂×#124×C₈₉	C₂²	1	2	yes	—
23	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
24	C₂×#123×C₈₉	C₂²	1	2	yes	complemented
25	C₂×#121×C₈₉	C₂²	1	2	yes	—
26	C₂×#121×C₈₉	C₂²	1	2	yes	—
27	C₂×#121×C₈₉	C₂²	1	2	yes	—
28	C₂×#121×C₈₉	C₂²	1	2	yes	—
29	C₂×#121×C₈₉	C₂²	1	2	yes	—
30	C₂×#121×C₈₉	C₂²	1	2	yes	—
31	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
32	C₂×#121×C₈₉	C₂²	1	2	yes	complemented
33	C₂×#120×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#120×C₈₉	C₂²	1	2	yes	—
35	C₂×#120×C₈₉	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
38	#400×C₈₉	C₂²	1	2	yes	complemented
39	#400×C₈₉	C₂²	1	1	yes	characteristic, complemented
40	#400×C₈₉	C₂²	1	2	yes	complemented
41	#399×C₈₉	C₂²	1	1	yes	characteristic
42	#397×C₈₉	C₂²	1	2	yes	—
43	#397×C₈₉	C₂²	1	2	yes	complemented
44	#397×C₈₉	C₂²	1	2	yes	complemented
45	#396×C₈₉	C₂²	1	2	yes	complemented
46	#395×C₈₉	C₂²	1	2	yes	complemented
47	#394×C₈₉	C₂²	1	2	yes	—
48	#394×C₈₉	C₂²	1	2	yes	—
49	#394×C₈₉	C₂²	1	2	yes	—
50	#394×C₈₉	C₂²	1	2	yes	—
51	#394×C₈₉	C₂²	1	2	yes	complemented
52	#394×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	#394×C₈₉	C₂²	1	2	yes	complemented
54	#393×C₈₉	C₂²	1	1	yes	characteristic
55	#393×C₈₉	C₂²	1	1	yes	characteristic, complemented
56	#392×C₈₉	C₂²	1	2	yes	—
57	#392×C₈₉	C₂²	1	1	yes	characteristic
58	#392×C₈₉	C₂²	1	2	yes	—
59	#392×C₈₉	C₂²	1	2	yes	—
60	#392×C₈₉	C₂²	1	1	yes	characteristic
61	#392×C₈₉	C₂²	1	2	yes	—
62	#392×C₈₉	C₂²	1	2	yes	—
63	#392×C₈₉	C₂²	1	2	yes	complemented
64	#392×C₈₉	C₂²	1	1	yes	characteristic, complemented
65	#392×C₈₉	C₂²	1	2	yes	complemented
66	#390×C₈₉	C₂²	1	2	yes	—
67	#390×C₈₉	C₂²	1	2	yes	complemented
68	#389×C₈₉	C₂²	1	2	yes	complemented
69	#388×C₈₉	C₂²	1	2	yes	—
70	#388×C₈₉	C₂²	1	2	yes	—
71	#388×C₈₉	C₂²	1	2	yes	—
72	#388×C₈₉	C₂²	1	2	yes	complemented
73	#388×C₈₉	C₂²	1	2	yes	complemented
74	#388×C₈₉	C₂²	1	2	yes	complemented
75	#388×C₈₉	C₂²	1	2	yes	complemented
76	#387×C₈₉	C₂²	1	2	yes	complemented
77	#387×C₈₉	C₂²	1	2	yes	complemented
78	#387×C₈₉	C₂²	1	2	yes	complemented
79	#386×C₈₉	C₂²	1	2	yes	—
80	#386×C₈₉	C₂²	1	1	yes	characteristic
81	#386×C₈₉	C₂²	1	2	yes	—
82	#386×C₈₉	C₂²	1	2	yes	—
83	#386×C₈₉	C₂²	1	2	yes	—
84	#386×C₈₉	C₂²	1	2	yes	—
85	#386×C₈₉	C₂²	1	2	yes	—
86	#386×C₈₉	C₂²	1	2	yes	—
87	#386×C₈₉	C₂²	1	2	yes	—
88	#386×C₈₉	C₂²	1	2	yes	—
89	#386×C₈₉	C₂²	1	2	yes	—
90	#386×C₈₉	C₂²	1	2	yes	complemented
91	#386×C₈₉	C₂²	1	2	yes	complemented
92	#386×C₈₉	C₂²	1	2	yes	complemented
93	#385×C₈₉	C₂²	1	1	yes	characteristic
94	#385×C₈₉	C₂²	1	2	yes	—
95	#385×C₈₉	C₂²	1	2	yes	complemented
96	#383×C₈₉	C₂²	1	1	yes	characteristic, complemented
97	#381×C₈₉	C₂²	1	2	yes	complemented
98	#381×C₈₉	C₂²	1	1	yes	characteristic, complemented
99	#380×C₈₉	C₂²	1	2	yes	—
100	#380×C₈₉	C₂²	1	2	yes	—
101	#380×C₈₉	C₂²	1	2	yes	—
102	#379×C₈₉	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
105	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
106	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	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	2	yes	—
116	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
117	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
118	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
119	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
120	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
121	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
122	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
123	C₂³×C₄×C₈₉	—	4	4	no	—
124	C₂³×C₄×C₈₉	—	4	2	no	—
125	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
126	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
129	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
130	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
132	#127×C₈₉	—	4	4	no	—
133	#124×C₈₉	—	4	2	no	—
134	#124×C₈₉	—	4	4	no	—
135	#123×C₈₉	—	4	4	no	—
136	#121×C₈₉	—	2	8	no	—
137	#121×C₈₉	—	4	4	no	—
138	#121×C₈₉	—	4	4	no	—
139	#121×C₈₉	—	4	2	no	—
140	#121×C₈₉	—	4	4	no	—
141	#121×C₈₉	—	4	4	no	—
142	#121×C₈₉	—	4	4	no	—
143	#121×C₈₉	—	4	4	no	—
144	#120×C₈₉	—	2	4	no	—
145	#120×C₈₉	—	4	4	no	—
146	#120×C₈₉	—	4	4	no	—
147	C₄×D₄×C₈₉	—	4	2	no	—
148	C₄×D₄×C₈₉	—	4	4	no	—
149	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
159	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
168	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
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×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
191	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
192	C₂×C₄²×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	2	yes	—
204	#95×C₈₉	C₂³	1	2	yes	—
205	#95×C₈₉	C₂³	1	1	yes	characteristic
206	#95×C₈₉	C₂³	1	1	yes	characteristic
207	#95×C₈₉	C₂³	1	1	yes	characteristic
208	#95×C₈₉	C₂³	1	2	yes	—
209	#95×C₈₉	C₂³	1	1	yes	characteristic
210	#95×C₈₉	C₂³	1	2	yes	—
211	#95×C₈₉	C₂³	1	2	yes	—
212	#95×C₈₉	C₂³	1	2	yes	—
213	C₂⁴×C₈₉	—	2	2	no	—
214	C₂⁴×C₈₉	—	2	4	no	—
215	C₂⁴×C₈₉	—	4	1	no	—
216	C₂⁴×C₈₉	—	4	2	no	—
217	C₂⁴×C₈₉	—	4	1	no	—
218	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
219	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
220	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
221	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
222	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
223	C₂×Q₈×C₈₉	—	4	1	no	—
224	C₂×Q₈×C₈₉	—	4	2	no	—
225	C₂×D₄×C₈₉	—	2	2	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	—	2	4	no	—
230	C₂×D₄×C₈₉	—	2	4	no	—
231	C₂×D₄×C₈₉	—	2	4	no	—
232	C₂×D₄×C₈₉	—	2	4	no	—
233	C₂×D₄×C₈₉	—	2	4	no	—
234	C₂×D₄×C₈₉	—	2	4	no	—
235	C₂×D₄×C₈₉	—	2	4	no	—
236	C₂×D₄×C₈₉	—	4	2	no	—
237	C₂×D₄×C₈₉	—	4	1	no	—
238	C₂×D₄×C₈₉	—	4	1	no	—
239	C₂×D₄×C₈₉	—	4	2	no	—
240	C₂×D₄×C₈₉	—	4	2	no	—
241	C₂×D₄×C₈₉	—	4	2	no	—
242	C₂×D₄×C₈₉	—	4	2	no	—
243	C₂×D₄×C₈₉	—	4	2	no	—
244	C₂×D₄×C₈₉	—	4	2	no	—
245	C₂×D₄×C₈₉	—	4	2	no	—
246	C₂×D₄×C₈₉	—	4	2	no	—
247	C₂×D₄×C₈₉	—	4	2	no	—
248	C₂×D₄×C₈₉	—	4	2	no	—
249	C₂×D₄×C₈₉	—	4	2	no	—
250	C₂×D₄×C₈₉	—	4	2	no	—
251	C₂×D₄×C₈₉	—	4	2	no	—
252	C₂×D₄×C₈₉	—	4	2	no	—
253	C₂×D₄×C₈₉	—	4	2	no	—
254	C₂×D₄×C₈₉	—	4	2	no	—
255	C₂×D₄×C₈₉	—	4	2	no	—
256	C₂×D₄×C₈₉	—	4	1	no	—
257	C₂×D₄×C₈₉	—	4	2	no	—
258	C₂×D₄×C₈₉	—	4	1	no	—
259	C₂×D₄×C₈₉	—	4	2	no	—
260	C₂×D₄×C₈₉	—	4	2	no	—
261	C₂×D₄×C₈₉	—	4	2	no	—
262	C₂×D₄×C₈₉	—	4	2	no	—
263	C₂×D₄×C₈₉	—	4	2	no	—
264	C₂×D₄×C₈₉	—	4	2	no	—
265	C₂²×C₄×C₈₉	—	2	4	no	—
266	C₂²×C₄×C₈₉	—	2	2	no	—
267	C₂²×C₄×C₈₉	—	2	4	no	—
268	C₂²×C₄×C₈₉	—	2	4	no	—
269	C₂²×C₄×C₈₉	—	2	4	no	—
270	C₂²×C₄×C₈₉	—	2	4	no	—
271	C₂²×C₄×C₈₉	—	2	2	no	—
272	C₂²×C₄×C₈₉	—	4	2	no	—
273	C₂²×C₄×C₈₉	—	4	2	no	—
274	C₂²×C₄×C₈₉	—	4	1	no	—
275	C₂²×C₄×C₈₉	—	4	2	no	—
276	C₂²×C₄×C₈₉	—	4	2	no	—
277	C₂²×C₄×C₈₉	—	4	2	no	—
278	C₂²×C₄×C₈₉	—	4	2	no	—
279	C₂²×C₄×C₈₉	—	4	2	no	—
280	C₂²×C₄×C₈₉	—	4	2	no	—
281	C₂²×C₄×C₈₉	—	4	2	no	—
282	C₂²×C₄×C₈₉	—	4	2	no	—
283	C₂²×C₄×C₈₉	—	4	16	no	—
284	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
298	C₄⋊C₄×C₈₉	—	2	4	no	—
299	C₄⋊C₄×C₈₉	—	2	4	no	—
300	C₄⋊C₄×C₈₉	—	2	4	no	—
301	C₄⋊C₄×C₈₉	—	4	1	no	—
302	C₄⋊C₄×C₈₉	—	4	2	no	—
303	C₄⋊C₄×C₈₉	—	4	2	no	—
304	C₄⋊C₄×C₈₉	—	4	2	no	—
305	C₄⋊C₄×C₈₉	—	4	2	no	—
306	C₄⋊C₄×C₈₉	—	4	1	no	—
307	C₄⋊C₄×C₈₉	—	4	2	no	—
308	C₂²⋊C₄×C₈₉	—	2	4	no	—
309	C₂²⋊C₄×C₈₉	—	2	4	no	—
310	C₂²⋊C₄×C₈₉	—	2	4	no	—
311	C₂²⋊C₄×C₈₉	—	2	4	no	—
312	C₂²⋊C₄×C₈₉	—	2	4	no	—
313	C₂²⋊C₄×C₈₉	—	2	4	no	—
314	C₂²⋊C₄×C₈₉	—	2	4	no	—
315	C₂²⋊C₄×C₈₉	—	2	4	no	—
316	C₂²⋊C₄×C₈₉	—	2	4	no	—
317	C₂²⋊C₄×C₈₉	—	2	4	no	—
318	C₂²⋊C₄×C₈₉	—	4	1	no	—
319	C₂²⋊C₄×C₈₉	—	4	2	no	—
320	C₂²⋊C₄×C₈₉	—	4	2	no	—
321	C₂²⋊C₄×C₈₉	—	4	1	no	—
322	C₂²⋊C₄×C₈₉	—	4	1	no	—
323	C₂²⋊C₄×C₈₉	—	4	2	no	—
324	C₂²⋊C₄×C₈₉	—	4	2	no	—
325	C₂²⋊C₄×C₈₉	—	4	2	no	—
326	C₂²⋊C₄×C₈₉	—	4	2	no	—
327	C₂²⋊C₄×C₈₉	—	4	2	no	—
328	C₂²⋊C₄×C₈₉	—	4	2	no	—
329	C₂²⋊C₄×C₈₉	—	4	2	no	—
330	C₂²⋊C₄×C₈₉	—	4	2	no	—
331	C₂²⋊C₄×C₈₉	—	4	2	no	—
332	C₂²⋊C₄×C₈₉	—	4	2	no	—
333	C₂²⋊C₄×C₈₉	—	4	2	no	—
334	C₂²⋊C₄×C₈₉	—	4	2	no	—
335	C₂²⋊C₄×C₈₉	—	4	2	no	—
336	C₂²⋊C₄×C₈₉	—	4	2	no	—
337	C₂²⋊C₄×C₈₉	#41	1	4	yes	—
338	C₄²×C₈₉	—	2	2	no	—
339	C₄²×C₈₉	—	4	2	no	—
340	C₄²×C₈₉	—	4	2	no	—
341	C₄²×C₈₉	—	4	2	no	—
342	C₂³×C₈₉	—	2	2	no	—
343	C₂³×C₈₉	—	2	2	no	—
344	C₂³×C₈₉	—	2	2	no	—
345	C₂³×C₈₉	—	2	1	no	—
346	C₂³×C₈₉	—	2	2	no	—
347	C₂³×C₈₉	—	2	2	no	—
348	C₂³×C₈₉	—	2	2	no	—
349	C₂³×C₈₉	—	2	2	no	—
350	C₂³×C₈₉	—	2	1	no	—
351	C₂³×C₈₉	—	2	2	no	—
352	C₂³×C₈₉	—	2	2	no	—
353	C₂³×C₈₉	—	2	2	no	—
354	C₂³×C₈₉	—	2	1	no	—
355	C₂³×C₈₉	—	2	2	no	—
356	C₂³×C₈₉	—	2	2	no	—
357	C₂³×C₈₉	—	2	2	no	—
358	C₂³×C₈₉	—	2	2	no	—
359	C₂³×C₈₉	—	2	2	no	—
360	C₂³×C₈₉	—	2	2	no	—
361	C₂³×C₈₉	—	2	2	no	—
362	C₂³×C₈₉	—	2	1	no	—
363	C₂³×C₈₉	—	2	2	no	—
364	C₂³×C₈₉	—	2	2	no	—
365	C₂³×C₈₉	—	2	2	no	—
366	C₂³×C₈₉	—	2	2	no	—
367	C₂³×C₈₉	—	2	2	no	—
368	C₂³×C₈₉	—	2	2	no	—
369	C₂³×C₈₉	—	2	2	no	—
370	C₂³×C₈₉	—	2	1	no	—
371	C₂³×C₈₉	—	4	8	no	—
372	C₂³×C₈₉	—	4	4	no	—
373	C₂³×C₈₉	—	4	4	no	—
374	C₂³×C₈₉	—	4	8	no	—
375	C₂³×C₈₉	—	4	4	no	—
376	C₂³×C₈₉	C₂×#41	1	2	yes	—
377	C₂³×C₈₉	H(5,𝔽₂)	1	4	yes	—
378	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
379	Q₈×C₈₉	—	8	2	no	—
380	D₄×C₈₉	—	4	8	no	—
381	D₄×C₈₉	—	4	4	no	—
382	D₄×C₈₉	—	8	4	no	—
383	D₄×C₈₉	—	8	4	no	—
384	D₄×C₈₉	—	8	4	no	—
385	D₄×C₈₉	—	8	4	no	—
386	D₄×C₈₉	—	8	4	no	—
387	D₄×C₈₉	—	8	4	no	—
388	D₄×C₈₉	—	8	4	no	—
389	D₄×C₈₉	—	8	4	no	—
390	D₄×C₈₉	—	8	2	no	—
391	D₄×C₈₉	—	8	4	no	—
392	D₄×C₈₉	—	8	2	no	—
393	D₄×C₈₉	—	8	4	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	—	2	1	no	—
400	C₂×C₄×C₈₉	—	2	2	no	—
401	C₂×C₄×C₈₉	—	2	2	no	—
402	C₂×C₄×C₈₉	—	2	1	no	—
403	C₂×C₄×C₈₉	—	2	1	no	—
404	C₂×C₄×C₈₉	—	2	2	no	—
405	C₂×C₄×C₈₉	—	2	2	no	—
406	C₂×C₄×C₈₉	—	2	2	no	—
407	C₂×C₄×C₈₉	—	2	2	no	—
408	C₂×C₄×C₈₉	—	2	2	no	—
409	C₂×C₄×C₈₉	—	2	2	no	—
410	C₂×C₄×C₈₉	—	2	2	no	—
411	C₂×C₄×C₈₉	—	2	2	no	—
412	C₂×C₄×C₈₉	—	2	2	no	—
413	C₂×C₄×C₈₉	—	2	2	no	—
414	C₂×C₄×C₈₉	—	2	2	no	—
415	C₂×C₄×C₈₉	—	2	2	no	—
416	C₂×C₄×C₈₉	—	2	2	no	—
417	C₂×C₄×C₈₉	—	2	2	no	—
418	C₂×C₄×C₈₉	—	2	2	no	—
419	C₂×C₄×C₈₉	—	2	2	no	—
420	C₂×C₄×C₈₉	—	2	2	no	—
421	C₂×C₄×C₈₉	—	2	2	no	—
422	C₂×C₄×C₈₉	—	2	2	no	—
423	C₂×C₄×C₈₉	—	2	1	no	—
424	C₂×C₄×C₈₉	—	2	1	no	—
425	C₂×C₄×C₈₉	—	2	2	no	—
426	C₂×C₄×C₈₉	—	2	1	no	—
427	C₂×C₄×C₈₉	—	2	2	no	—
428	C₂×C₄×C₈₉	—	2	2	no	—
429	C₂×C₄×C₈₉	—	4	8	no	—
430	C₂×C₄×C₈₉	—	4	4	no	—
431	C₂×C₄×C₈₉	—	4	4	no	—
432	C₂×C₄×C₈₉	—	4	8	no	—
433	C₂×C₄×C₈₉	—	8	4	no	—
434	C₂×C₄×C₈₉	—	8	2	no	—
435	C₂×C₄×C₈₉	—	8	4	no	—
436	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
437	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
438	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
439	C₂²×C₈₉	—	2	2	no	—
440	C₂²×C₈₉	—	2	4	no	—
441	C₂²×C₈₉	—	2	4	no	—
442	C₂²×C₈₉	—	2	4	no	—
443	C₂²×C₈₉	—	2	4	no	—
444	C₂²×C₈₉	—	4	16	no	—
445	C₂²×C₈₉	—	4	2	no	—
446	C₂²×C₈₉	—	4	2	no	—
447	C₂²×C₈₉	—	4	1	no	—
448	C₂²×C₈₉	—	4	2	no	—
449	C₂²×C₈₉	—	4	1	no	—
450	C₂²×C₈₉	—	4	2	no	—
451	C₂²×C₈₉	—	4	2	no	—
452	C₂²×C₈₉	—	4	1	no	—
453	C₂²×C₈₉	—	4	2	no	—
454	C₂²×C₈₉	—	4	2	no	—
455	C₂²×C₈₉	—	4	2	no	—
456	C₂²×C₈₉	—	4	2	no	—
457	C₂²×C₈₉	—	4	2	no	—
458	C₂²×C₈₉	—	4	2	no	—
459	C₂²×C₈₉	—	4	2	no	—
460	C₂²×C₈₉	—	4	1	no	—
461	C₂²×C₈₉	—	4	2	no	—
462	C₂²×C₈₉	—	4	2	no	—
463	C₂²×C₈₉	—	4	2	no	—
464	C₂²×C₈₉	—	4	2	no	—
465	C₂²×C₈₉	—	4	1	no	—
466	C₂²×C₈₉	—	4	2	no	—
467	C₂²×C₈₉	—	4	2	no	—
468	C₂²×C₈₉	—	4	2	no	—
469	C₂²×C₈₉	—	4	2	no	—
470	C₂²×C₈₉	—	4	2	no	—
471	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
472	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
473	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
474	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
475	C₂²×C₈₉	#585	1	1	yes	characteristic
476	C₄×C₈₉	—	2	4	no	—
477	C₄×C₈₉	—	2	2	no	—
478	C₄×C₈₉	—	2	4	no	—
479	C₄×C₈₉	—	4	1	no	—
480	C₄×C₈₉	—	4	2	no	—
481	C₄×C₈₉	—	4	2	no	—
482	C₄×C₈₉	—	4	1	no	—
483	C₄×C₈₉	—	4	1	no	—
484	C₄×C₈₉	—	4	2	no	—
485	C₄×C₈₉	—	4	1	no	—
486	C₄×C₈₉	—	4	2	no	—
487	C₄×C₈₉	—	4	2	no	—
488	C₄×C₈₉	—	4	2	no	—
489	C₄×C₈₉	—	4	2	no	—
490	#36903	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
491	C₂×C₈₉	—	4	2	no	—
492	C₂×C₈₉	—	4	4	no	—
493	C₂×C₈₉	—	8	1	no	—
494	C₂×C₈₉	—	8	2	no	—
495	C₂×C₈₉	—	8	2	no	—
496	C₂×C₈₉	#3460	1	1	yes	characteristic
497	C₂×C₈₉	#3519	1	2	yes	—
498	C₂×C₈₉	#3532	1	1	yes	characteristic
499	C₂×C₈₉	#3537	1	1	yes	characteristic
500	C₂×C₈₉	#3542	1	2	yes	—
501	#2847	C₂×C₈₉	1	2	yes	complemented
502	#2779	C₂×C₈₉	1	2	yes	complemented
503	#2742	C₂×C₈₉	1	1	yes	characteristic, complemented
504	#2703	C₂×C₈₉	1	2	yes	complemented
505	#2688	C₂×C₈₉	1	2	yes	complemented
506	#2686	C₂×C₈₉	1	2	yes	complemented
507	#2675	C₂×C₈₉	1	1	yes	characteristic, complemented
508	#2673	C₂×C₈₉	1	2	yes	complemented
509	#2670	C₂×C₈₉	1	1	yes	characteristic, complemented
510	#2669	C₂×C₈₉	1	2	yes	complemented
511	#2668	C₂×C₈₉	1	1	yes	characteristic, complemented
512	#2635	C₂×C₈₉	1	1	yes	characteristic, complemented
513	#2631	C₂×C₈₉	1	1	yes	characteristic, complemented
514	#2578	C₂×C₈₉	1	2	yes	complemented
515	#2555	C₂×C₈₉	1	2	yes	complemented
516	#2457	C₂×C₈₉	1	2	yes	complemented
517	#2428	C₂×C₈₉	1	2	yes	complemented
518	#2333	C₂×C₈₉	1	2	yes	complemented
519	C₄×#120	C₂×C₈₉	1	1	yes	characteristic, complemented
520	C₈₉	#36903	1	1	yes	characteristic, direct product factor, Sylow
521	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
522	C₂×#127	C₂²×C₈₉	1	2	yes	—
523	C₂×#124	C₂²×C₈₉	1	2	yes	—
524	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic, complemented
525	C₂×#123	C₂²×C₈₉	1	2	yes	complemented
526	C₂×#121	C₂²×C₈₉	1	2	yes	—
527	C₂×#121	C₂²×C₈₉	1	2	yes	—
528	C₂×#121	C₂²×C₈₉	1	2	yes	—
529	C₂×#121	C₂²×C₈₉	1	2	yes	—
530	C₂×#121	C₂²×C₈₉	1	2	yes	—
531	C₂×#121	C₂²×C₈₉	1	2	yes	—
532	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic, complemented
533	C₂×#121	C₂²×C₈₉	1	2	yes	complemented
534	C₂×#120	C₂²×C₈₉	1	1	yes	characteristic
535	C₂×#120	C₂²×C₈₉	1	2	yes	—
536	C₂×#120	C₂²×C₈₉	1	2	yes	—
537	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
538	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
539	#400	C₂²×C₈₉	1	2	yes	complemented
540	#400	C₂²×C₈₉	1	1	yes	characteristic, complemented
541	#400	C₂²×C₈₉	1	2	yes	complemented
542	#399	C₂²×C₈₉	1	1	yes	characteristic
543	#397	C₂²×C₈₉	1	2	yes	—
544	#397	C₂²×C₈₉	1	2	yes	complemented
545	#397	C₂²×C₈₉	1	2	yes	complemented
546	#396	C₂²×C₈₉	1	2	yes	complemented
547	#395	C₂²×C₈₉	1	2	yes	complemented
548	#394	C₂²×C₈₉	1	2	yes	—
549	#394	C₂²×C₈₉	1	2	yes	—
550	#394	C₂²×C₈₉	1	2	yes	—
551	#394	C₂²×C₈₉	1	2	yes	—
552	#394	C₂²×C₈₉	1	2	yes	complemented
553	#394	C₂²×C₈₉	1	1	yes	characteristic, complemented
554	#394	C₂²×C₈₉	1	2	yes	complemented
555	#393	C₂²×C₈₉	1	1	yes	characteristic
556	#393	C₂²×C₈₉	1	1	yes	characteristic, complemented
557	#392	C₂²×C₈₉	1	1	yes	characteristic
558	#392	C₂²×C₈₉	1	2	yes	—
559	#392	C₂²×C₈₉	1	2	yes	—
560	#392	C₂²×C₈₉	1	1	yes	characteristic
561	#392	C₂²×C₈₉	1	2	yes	—
562	#392	C₂²×C₈₉	1	2	yes	—
563	#392	C₂²×C₈₉	1	2	yes	—
564	#392	C₂²×C₈₉	1	1	yes	characteristic, complemented
565	#392	C₂²×C₈₉	1	2	yes	complemented
566	#392	C₂²×C₈₉	1	2	yes	complemented
567	#390	C₂²×C₈₉	1	2	yes	—
568	#390	C₂²×C₈₉	1	2	yes	complemented
569	#389	C₂²×C₈₉	1	2	yes	complemented
570	#388	C₂²×C₈₉	1	2	yes	—
571	#388	C₂²×C₈₉	1	2	yes	—
572	#388	C₂²×C₈₉	1	2	yes	—
573	#388	C₂²×C₈₉	1	2	yes	complemented
574	#388	C₂²×C₈₉	1	2	yes	complemented
575	#388	C₂²×C₈₉	1	2	yes	complemented
576	#388	C₂²×C₈₉	1	2	yes	complemented
577	#387	C₂²×C₈₉	1	2	yes	complemented
578	#387	C₂²×C₈₉	1	2	yes	complemented
579	#387	C₂²×C₈₉	1	2	yes	complemented
580	#386	C₂²×C₈₉	1	2	yes	—
581	#386	C₂²×C₈₉	1	2	yes	—
582	#386	C₂²×C₈₉	1	2	yes	—
583	#386	C₂²×C₈₉	1	2	yes	—
584	#386	C₂²×C₈₉	1	2	yes	—
585	#386	C₂²×C₈₉	1	2	yes	—
586	#386	C₂²×C₈₉	1	2	yes	—
587	#386	C₂²×C₈₉	1	2	yes	—
588	#386	C₂²×C₈₉	1	2	yes	—
589	#386	C₂²×C₈₉	1	2	yes	—
590	#386	C₂²×C₈₉	1	1	yes	characteristic
591	#386	C₂²×C₈₉	1	2	yes	complemented
592	#386	C₂²×C₈₉	1	2	yes	complemented
593	#386	C₂²×C₈₉	1	2	yes	complemented
594	#385	C₂²×C₈₉	1	1	yes	characteristic
595	#385	C₂²×C₈₉	1	2	yes	—
596	#385	C₂²×C₈₉	1	2	yes	complemented
597	#383	C₂²×C₈₉	1	1	yes	characteristic, complemented
598	#381	C₂²×C₈₉	1	2	yes	complemented
599	#381	C₂²×C₈₉	1	1	yes	characteristic, complemented
600	#380	C₂²×C₈₉	1	2	yes	—
601	#380	C₂²×C₈₉	1	2	yes	—
602	#380	C₂²×C₈₉	1	2	yes	—
603	#379	C₂²×C₈₉	1	1	yes	characteristic
604	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
605	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
606	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
607	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
608	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
609	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
610	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
611	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
612	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
613	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
614	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
615	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
616	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
617	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
618	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
619	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
620	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
621	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
622	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
623	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
624	C₂³×C₄	—	4	4	no	—
625	C₂³×C₄	—	4	2	no	—
626	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
627	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
628	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
629	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
630	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
631	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
632	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
633	#127	—	4	4	no	—
634	#124	—	4	2	no	—
635	#124	—	4	4	no	—
636	#123	—	4	4	no	—
637	#121	—	2	8	no	—
638	#121	—	4	4	no	—
639	#121	—	4	4	no	—
640	#121	—	4	2	no	—
641	#121	—	4	4	no	—
642	#121	—	4	4	no	—
643	#121	—	4	4	no	—
644	#121	—	4	4	no	—
645	#120	—	2	4	no	—
646	#120	—	4	4	no	—
647	#120	—	4	4	no	—
648	C₄×D₄	—	4	2	no	—
649	C₄×D₄	—	4	4	no	—
650	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
672	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
673	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
687	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
690	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
691	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
692	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
693	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
694	#95	C₂³×C₈₉	1	2	yes	—
695	#95	C₂³×C₈₉	1	2	yes	—
696	#95	C₂³×C₈₉	1	2	yes	—
697	#95	C₂³×C₈₉	1	2	yes	—
698	#95	C₂³×C₈₉	1	2	yes	—
699	#95	C₂³×C₈₉	1	2	yes	—
700	#95	C₂³×C₈₉	1	2	yes	—
701	#95	C₂³×C₈₉	1	2	yes	—
702	#95	C₂³×C₈₉	1	2	yes	—
703	#95	C₂³×C₈₉	1	2	yes	—
704	#95	C₂³×C₈₉	1	2	yes	—
705	#95	C₂³×C₈₉	1	2	yes	—
706	#95	C₂³×C₈₉	1	1	yes	characteristic
707	#95	C₂³×C₈₉	1	1	yes	characteristic
708	#95	C₂³×C₈₉	1	1	yes	characteristic
709	#95	C₂³×C₈₉	1	2	yes	—
710	#95	C₂³×C₈₉	1	1	yes	characteristic
711	#95	C₂³×C₈₉	1	2	yes	—
712	#95	C₂³×C₈₉	1	2	yes	—
713	#95	C₂³×C₈₉	1	2	yes	—
714	C₂⁴	—	2	2	no	—
715	C₂⁴	—	2	4	no	—
716	C₂⁴	—	4	1	no	—
717	C₂⁴	—	4	2	no	—
718	C₂⁴	—	4	1	no	—
719	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
720	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
721	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
722	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
723	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
724	C₂×Q₈	—	4	1	no	—
725	C₂×Q₈	—	4	2	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	4	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	2	4	no	—
731	C₂×D₄	—	2	4	no	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	2	4	no	—
734	C₂×D₄	—	2	4	no	—
735	C₂×D₄	—	2	4	no	—
736	C₂×D₄	—	2	4	no	—
737	C₂×D₄	—	4	2	no	—
738	C₂×D₄	—	4	1	no	—
739	C₂×D₄	—	4	1	no	—
740	C₂×D₄	—	4	2	no	—
741	C₂×D₄	—	4	2	no	—
742	C₂×D₄	—	4	2	no	—
743	C₂×D₄	—	4	2	no	—
744	C₂×D₄	—	4	2	no	—
745	C₂×D₄	—	4	2	no	—
746	C₂×D₄	—	4	2	no	—
747	C₂×D₄	—	4	2	no	—
748	C₂×D₄	—	4	2	no	—
749	C₂×D₄	—	4	2	no	—
750	C₂×D₄	—	4	2	no	—
751	C₂×D₄	—	4	2	no	—
752	C₂×D₄	—	4	2	no	—
753	C₂×D₄	—	4	2	no	—
754	C₂×D₄	—	4	2	no	—
755	C₂×D₄	—	4	2	no	—
756	C₂×D₄	—	4	2	no	—
757	C₂×D₄	—	4	1	no	—
758	C₂×D₄	—	4	2	no	—
759	C₂×D₄	—	4	1	no	—
760	C₂×D₄	—	4	2	no	—
761	C₂×D₄	—	4	2	no	—
762	C₂×D₄	—	4	2	no	—
763	C₂×D₄	—	4	2	no	—
764	C₂×D₄	—	4	2	no	—
765	C₂×D₄	—	4	2	no	—
766	C₂²×C₄	—	2	4	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	4	no	—
769	C₂²×C₄	—	2	4	no	—
770	C₂²×C₄	—	2	4	no	—
771	C₂²×C₄	—	2	4	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	4	2	no	—
774	C₂²×C₄	—	4	2	no	—
775	C₂²×C₄	—	4	1	no	—
776	C₂²×C₄	—	4	2	no	—
777	C₂²×C₄	—	4	2	no	—
778	C₂²×C₄	—	4	2	no	—
779	C₂²×C₄	—	4	2	no	—
780	C₂²×C₄	—	4	2	no	—
781	C₂²×C₄	—	4	2	no	—
782	C₂²×C₄	—	4	2	no	—
783	C₂²×C₄	—	4	2	no	—
784	C₂²×C₄	—	4	16	no	—
785	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
791	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
792	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
794	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
795	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
797	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
799	C₄⋊C₄	—	2	4	no	—
800	C₄⋊C₄	—	2	4	no	—
801	C₄⋊C₄	—	2	4	no	—
802	C₄⋊C₄	—	4	1	no	—
803	C₄⋊C₄	—	4	2	no	—
804	C₄⋊C₄	—	4	2	no	—
805	C₄⋊C₄	—	4	2	no	—
806	C₄⋊C₄	—	4	2	no	—
807	C₄⋊C₄	—	4	1	no	—
808	C₄⋊C₄	—	4	2	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	4	no	—
812	C₂²⋊C₄	—	2	4	no	—
813	C₂²⋊C₄	—	2	4	no	—
814	C₂²⋊C₄	—	2	4	no	—
815	C₂²⋊C₄	—	2	4	no	—
816	C₂²⋊C₄	—	2	4	no	—
817	C₂²⋊C₄	—	2	4	no	—
818	C₂²⋊C₄	—	2	4	no	—
819	C₂²⋊C₄	—	4	1	no	—
820	C₂²⋊C₄	—	4	1	no	—
821	C₂²⋊C₄	—	4	2	no	—
822	C₂²⋊C₄	—	4	2	no	—
823	C₂²⋊C₄	—	4	2	no	—
824	C₂²⋊C₄	—	4	2	no	—
825	C₂²⋊C₄	—	4	2	no	—
826	C₂²⋊C₄	—	4	2	no	—
827	C₂²⋊C₄	—	4	2	no	—
828	C₂²⋊C₄	—	4	2	no	—
829	C₂²⋊C₄	—	4	2	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₂²⋊C₄	—	4	2	no	—
832	C₂²⋊C₄	—	4	2	no	—
833	C₂²⋊C₄	—	4	2	no	—
834	C₂²⋊C₄	—	4	2	no	—
835	C₂²⋊C₄	—	4	1	no	—
836	C₂²⋊C₄	—	4	2	no	—
837	C₂²⋊C₄	—	4	2	no	—
838	C₂²⋊C₄	#41×C₈₉	1	4	yes	—
839	C₄²	—	2	2	no	—
840	C₄²	—	4	2	no	—
841	C₄²	—	4	2	no	—
842	C₄²	—	4	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	1	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	2	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	1	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	2	2	no	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	2	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	2	2	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	1	no	—
872	C₂³	—	4	8	no	—
873	C₂³	—	4	4	no	—
874	C₂³	—	4	4	no	—
875	C₂³	—	4	8	no	—
876	C₂³	—	4	4	no	—
877	C₂³	C₂×#41×C₈₉	1	2	yes	—
878	C₂³	H(5,𝔽₂)×C₈₉	1	4	yes	—
879	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
880	Q₈	—	8	2	no	—
881	D₄	—	4	8	no	—
882	D₄	—	4	4	no	—
883	D₄	—	8	4	no	—
884	D₄	—	8	4	no	—
885	D₄	—	8	4	no	—
886	D₄	—	8	4	no	—
887	D₄	—	8	4	no	—
888	D₄	—	8	4	no	—
889	D₄	—	8	4	no	—
890	D₄	—	8	4	no	—
891	D₄	—	8	2	no	—
892	D₄	—	8	4	no	—
893	D₄	—	8	2	no	—
894	D₄	—	8	4	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	4	8	no	—
931	C₂×C₄	—	4	4	no	—
932	C₂×C₄	—	4	4	no	—
933	C₂×C₄	—	4	8	no	—
934	C₂×C₄	—	8	4	no	—
935	C₂×C₄	—	8	2	no	—
936	C₂×C₄	—	8	4	no	—
937	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
938	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
939	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	4	no	—
942	C₂²	—	2	4	no	—
943	C₂²	—	2	4	no	—
944	C₂²	—	2	4	no	—
945	C₂²	—	4	16	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	1	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	1	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	1	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	1	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	2	no	—
966	C₂²	—	4	1	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	4	2	no	—
971	C₂²	—	4	2	no	—
972	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
973	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
974	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
975	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
976	C₂²	#585×C₈₉	1	1	yes	characteristic
977	C₄	—	2	4	no	—
978	C₄	—	2	2	no	—
979	C₄	—	2	4	no	—
980	C₄	—	4	1	no	—
981	C₄	—	4	2	no	—
982	C₄	—	4	2	no	—
983	C₄	—	4	1	no	—
984	C₄	—	4	1	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	1	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	2	no	—
991	C₂	—	4	2	no	—
992	C₂	—	4	4	no	—
993	C₂	—	8	1	no	—
994	C₂	—	8	2	no	—
995	C₂	—	8	2	no	—
996	C₂	C₈₉×#3460	1	1	yes	characteristic
997	C₂	C₈₉×#3519	1	2	yes	—
998	C₂	C₈₉×#3532	1	1	yes	characteristic
999	C₂	C₈₉×#3537	1	1	yes	characteristic
1000	C₂	C₈₉×#3542	1	2	yes	—

	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×#2847	C₂	semidirect
2. C₈₉×#2779	C₂	semidirect
3. C₈₉×#2742	C₂	semidirect
4. C₈₉×#2703	C₂	semidirect
5. C₈₉×#2688	C₂	semidirect
6. C₈₉×#2686	C₂	semidirect
7. C₈₉×#2675	C₂	semidirect
8. C₈₉×#2673	C₂	semidirect
9. C₈₉×#2670	C₂	semidirect
10. C₈₉×#2669	C₂	semidirect
11. C₈₉×#2668	C₂	semidirect
12. C₈₉×#2635	C₂	semidirect
13. C₈₉×#2631	C₂	semidirect
14. C₈₉×#2578	C₂	semidirect
15. C₈₉×#2555	C₂	semidirect
16. C₈₉×#2457	C₂	semidirect
17. C₈₉×#2428	C₂	semidirect
18. C₈₉×#2333	C₂	semidirect
19. C₄×#120×C₈₉	C₂	semidirect
23. C₂×#124×C₈₉	C₂²	semidirect
24. C₂×#123×C₈₉	C₂²	semidirect
31. C₂×#121×C₈₉	C₂²	semidirect
32. C₂×#121×C₈₉	C₂²	semidirect
38. #400×C₈₉	C₂²	semidirect
39. #400×C₈₉	C₂²	semidirect
40. #400×C₈₉	C₂²	semidirect
43. #397×C₈₉	C₂²	semidirect
44. #397×C₈₉	C₂²	semidirect
45. #396×C₈₉	C₂²	semidirect
46. #395×C₈₉	C₂²	semidirect
51. #394×C₈₉	C₂²	semidirect
52. #394×C₈₉	C₂²	semidirect
53. #394×C₈₉	C₂²	semidirect
55. #393×C₈₉	C₂²	semidirect
63. #392×C₈₉	C₂²	semidirect
64. #392×C₈₉	C₂²	semidirect
65. #392×C₈₉	C₂²	semidirect
67. #390×C₈₉	C₂²	semidirect
68. #389×C₈₉	C₂²	semidirect
72. #388×C₈₉	C₂²	semidirect
73. #388×C₈₉	C₂²	semidirect
74. #388×C₈₉	C₂²	semidirect
75. #388×C₈₉	C₂²	semidirect
76. #387×C₈₉	C₂²	semidirect
77. #387×C₈₉	C₂²	semidirect
78. #387×C₈₉	C₂²	semidirect
90. #386×C₈₉	C₂²	semidirect
91. #386×C₈₉	C₂²	semidirect
92. #386×C₈₉	C₂²	semidirect
95. #385×C₈₉	C₂²	semidirect
96. #383×C₈₉	C₂²	semidirect
97. #381×C₈₉	C₂²	semidirect
98. #381×C₈₉	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
106. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
490. #36903	C₈₉	direct (N × H)
501. #2847	C₂×C₈₉	semidirect
502. #2779	C₂×C₈₉	semidirect
503. #2742	C₂×C₈₉	semidirect
504. #2703	C₂×C₈₉	semidirect
505. #2688	C₂×C₈₉	semidirect
506. #2686	C₂×C₈₉	semidirect
507. #2675	C₂×C₈₉	semidirect
508. #2673	C₂×C₈₉	semidirect
509. #2670	C₂×C₈₉	semidirect
510. #2669	C₂×C₈₉	semidirect
511. #2668	C₂×C₈₉	semidirect
512. #2635	C₂×C₈₉	semidirect
513. #2631	C₂×C₈₉	semidirect
514. #2578	C₂×C₈₉	semidirect
515. #2555	C₂×C₈₉	semidirect
516. #2457	C₂×C₈₉	semidirect
517. #2428	C₂×C₈₉	semidirect
518. #2333	C₂×C₈₉	semidirect
519. C₄×#120	C₂×C₈₉	semidirect
520. C₈₉	#36903	direct (N × H)
524. C₂×#124	C₂²×C₈₉	semidirect
525. C₂×#123	C₂²×C₈₉	semidirect
532. C₂×#121	C₂²×C₈₉	semidirect
533. C₂×#121	C₂²×C₈₉	semidirect
539. #400	C₂²×C₈₉	semidirect
540. #400	C₂²×C₈₉	semidirect
541. #400	C₂²×C₈₉	semidirect
544. #397	C₂²×C₈₉	semidirect
545. #397	C₂²×C₈₉	semidirect
546. #396	C₂²×C₈₉	semidirect
547. #395	C₂²×C₈₉	semidirect
552. #394	C₂²×C₈₉	semidirect
553. #394	C₂²×C₈₉	semidirect
554. #394	C₂²×C₈₉	semidirect
556. #393	C₂²×C₈₉	semidirect
564. #392	C₂²×C₈₉	semidirect
565. #392	C₂²×C₈₉	semidirect
566. #392	C₂²×C₈₉	semidirect
568. #390	C₂²×C₈₉	semidirect
569. #389	C₂²×C₈₉	semidirect
573. #388	C₂²×C₈₉	semidirect
574. #388	C₂²×C₈₉	semidirect
575. #388	C₂²×C₈₉	semidirect
576. #388	C₂²×C₈₉	semidirect
577. #387	C₂²×C₈₉	semidirect
578. #387	C₂²×C₈₉	semidirect
579. #387	C₂²×C₈₉	semidirect
591. #386	C₂²×C₈₉	semidirect
592. #386	C₂²×C₈₉	semidirect
593. #386	C₂²×C₈₉	semidirect
596. #385	C₂²×C₈₉	semidirect
597. #383	C₂²×C₈₉	semidirect
598. #381	C₂²×C₈₉	semidirect
599. #381	C₂²×C₈₉	semidirect
606. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
607. C₄×C₂²⋊C₄	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×#2847	2
C₈₉×#2779	2
C₈₉×#2742	2
C₈₉×#2703	2
C₈₉×#2688	2
C₈₉×#2686	2
C₈₉×#2675	2
C₈₉×#2673	2
C₈₉×#2670	2
C₈₉×#2669	2
C₈₉×#2668	2
C₈₉×#2635	2
C₈₉×#2631	2
C₈₉×#2578	2
C₈₉×#2555	2
C₈₉×#2457	2
C₈₉×#2428	2
C₈₉×#2333	2
C₄×#120×C₈₉	2
#36903	89

Subgroups — C89×#36903 #36414751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#36903 #36414751