Subgroups — C₈₉×#24008 #36401856

Order 22784.

1448 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#525×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#485×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#482×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2280	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2036	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2034	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1875	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1788	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1788	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1779	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
18	#525×C₈₉	—	2	4	no	—
19	#525×C₈₉	—	2	4	no	—
20	C₂×#123×C₈₉	—	2	1	no	—
21	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#120×C₈₉	—	2	1	no	—
26	C₂×C₄×D₄×C₈₉	—	2	1	no	—
27	C₂×C₄×D₄×C₈₉	—	2	1	no	—
28	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
31	#485×C₈₉	—	2	4	no	—
32	#482×C₈₉	—	2	4	no	—
33	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic, complemented
36	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic, complemented
37	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
38	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
44	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
51	#381×C₈₉	—	2	1	no	—
52	#380×C₈₉	C₂²	1	1	yes	characteristic
53	#380×C₈₉	C₂²	1	1	yes	characteristic
54	#380×C₈₉	C₂²	1	1	yes	characteristic
55	#380×C₈₉	C₂²	1	1	yes	characteristic
56	#379×C₈₉	—	2	1	no	—
57	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
58	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
59	#340×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#340×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	#340×C₈₉	C₂²	1	1	yes	characteristic, complemented
62	#340×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	C₂⁵×C₈₉	D₄	1	1	yes	characteristic
64	C₂×#41×C₈₉	—	2	2	no	—
65	C₂×#41×C₈₉	—	2	2	no	—
66	C₂×#41×C₈₉	—	2	2	no	—
67	C₂×#41×C₈₉	—	2	2	no	—
68	C₂×#41×C₈₉	—	4	1	no	—
69	C₂×#41×C₈₉	—	4	1	no	—
70	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₈₉	—	2	1	no	—
72	C₂²×D₄×C₈₉	—	2	1	no	—
73	C₂²×D₄×C₈₉	—	2	1	no	—
74	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₈₉	—	2	1	no	—
76	C₂³×C₄×C₈₉	—	2	2	no	—
77	C₂³×C₄×C₈₉	—	2	2	no	—
78	C₂³×C₄×C₈₉	—	2	2	no	—
79	C₂³×C₄×C₈₉	—	2	2	no	—
80	C₂³×C₄×C₈₉	—	4	1	no	—
81	C₂³×C₄×C₈₉	—	4	1	no	—
82	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
83	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
84	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
85	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
92	#123×C₈₉	—	2	8	no	—
93	C₂²⋊Q₈×C₈₉	—	2	2	no	—
94	C₂²⋊Q₈×C₈₉	—	2	2	no	—
95	C₂²⋊Q₈×C₈₉	—	2	2	no	—
96	C₂²⋊Q₈×C₈₉	D₄	1	4	yes	—
97	#121×C₈₉	—	2	2	no	—
98	#121×C₈₉	—	2	2	no	—
99	#121×C₈₉	—	2	2	no	—
100	#121×C₈₉	D₄	1	4	yes	—
101	#120×C₈₉	—	2	8	no	—
102	C₄×D₄×C₈₉	—	2	8	no	—
103	C₄×D₄×C₈₉	—	2	8	no	—
104	#117×C₈₉	—	2	2	no	—
105	#117×C₈₉	—	2	2	no	—
106	#117×C₈₉	—	2	2	no	—
107	#117×C₈₉	—	2	2	no	—
108	#117×C₈₉	—	4	1	no	—
109	#117×C₈₉	—	4	1	no	—
110	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
129	C₂×C₄²×C₈₉	—	2	1	no	—
130	C₂×C₄²×C₈₉	—	2	1	no	—
131	C₂×C₄²×C₈₉	—	2	1	no	—
132	#107×C₈₉	—	2	2	no	—
133	#107×C₈₉	—	2	2	no	—
134	#106×C₈₉	—	2	2	no	—
135	#106×C₈₉	—	2	2	no	—
136	#103×C₈₉	—	2	2	no	—
137	#103×C₈₉	—	2	2	no	—
138	#103×C₈₉	—	4	1	no	—
139	#103×C₈₉	—	4	1	no	—
140	#102×C₈₉	—	2	2	no	—
141	#102×C₈₉	—	2	2	no	—
142	#102×C₈₉	—	4	1	no	—
143	#102×C₈₉	—	4	1	no	—
144	C₂²⋊C₈×C₈₉	—	2	2	no	—
145	C₂²⋊C₈×C₈₉	—	2	2	no	—
146	C₂²⋊C₈×C₈₉	—	2	2	no	—
147	C₂²⋊C₈×C₈₉	—	2	2	no	—
148	C₂²⋊C₈×C₈₉	—	4	1	no	—
149	C₂²⋊C₈×C₈₉	—	4	1	no	—
150	#95×C₈₉	—	2	1	no	—
151	#95×C₈₉	—	2	1	no	—
152	#95×C₈₉	—	2	1	no	—
153	#95×C₈₉	—	2	1	no	—
154	C₂⁴×C₈₉	—	2	2	no	—
155	C₂⁴×C₈₉	—	2	2	no	—
156	C₂⁴×C₈₉	—	2	2	no	—
157	C₂⁴×C₈₉	—	2	1	no	—
158	C₂⁴×C₈₉	—	4	1	no	—
159	C₂⁴×C₈₉	—	4	1	no	—
160	C₂⁴×C₈₉	—	4	1	no	—
161	C₂⁴×C₈₉	—	4	1	no	—
162	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
163	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
164	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
165	#41×C₈₉	—	4	4	no	—
166	#41×C₈₉	—	4	4	no	—
167	#41×C₈₉	—	4	4	no	—
168	#41×C₈₉	—	4	4	no	—
169	C₂×Q₈×C₈₉	—	2	1	no	—
170	C₂×Q₈×C₈₉	—	2	1	no	—
171	C₂×Q₈×C₈₉	—	2	1	no	—
172	C₂×Q₈×C₈₉	—	2	1	no	—
173	C₂×Q₈×C₈₉	—	2	1	no	—
174	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
175	C₂×D₄×C₈₉	—	2	4	no	—
176	C₂×D₄×C₈₉	—	2	4	no	—
177	C₂×D₄×C₈₉	—	2	4	no	—
178	C₂×D₄×C₈₉	—	2	1	no	—
179	C₂×D₄×C₈₉	—	2	1	no	—
180	C₂×D₄×C₈₉	—	2	1	no	—
181	C₂×D₄×C₈₉	—	2	1	no	—
182	C₂×D₄×C₈₉	—	2	1	no	—
183	C₂×D₄×C₈₉	—	4	2	no	—
184	C₂×D₄×C₈₉	—	4	2	no	—
185	C₂×D₄×C₈₉	—	4	2	no	—
186	C₂×D₄×C₈₉	—	4	2	no	—
187	C₂×D₄×C₈₉	—	4	2	no	—
188	C₂×D₄×C₈₉	—	4	2	no	—
189	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
190	C₂²×C₄×C₈₉	—	2	1	no	—
191	C₂²×C₄×C₈₉	—	2	1	no	—
192	C₂²×C₄×C₈₉	—	2	1	no	—
193	C₂²×C₄×C₈₉	—	2	1	no	—
194	C₂²×C₄×C₈₉	—	2	1	no	—
195	C₂²×C₄×C₈₉	—	2	1	no	—
196	C₂²×C₄×C₈₉	—	2	1	no	—
197	C₂²×C₄×C₈₉	—	2	1	no	—
198	C₂²×C₄×C₈₉	—	2	4	no	—
199	C₂²×C₄×C₈₉	—	2	2	no	—
200	C₂²×C₄×C₈₉	—	2	2	no	—
201	C₂²×C₄×C₈₉	—	2	1	no	—
202	C₂²×C₄×C₈₉	—	2	1	no	—
203	C₂²×C₄×C₈₉	—	2	1	no	—
204	C₂²×C₄×C₈₉	—	2	2	no	—
205	C₂²×C₄×C₈₉	—	2	2	no	—
206	C₂²×C₄×C₈₉	—	2	2	no	—
207	C₂²×C₄×C₈₉	—	2	2	no	—
208	C₂²×C₄×C₈₉	—	2	1	no	—
209	C₂²×C₄×C₈₉	—	2	1	no	—
210	C₂²×C₄×C₈₉	—	2	1	no	—
211	C₂²×C₄×C₈₉	—	2	1	no	—
212	C₂²×C₄×C₈₉	—	2	1	no	—
213	C₂²×C₄×C₈₉	—	2	1	no	—
214	C₂²×C₄×C₈₉	—	2	1	no	—
215	C₂²×C₄×C₈₉	—	2	1	no	—
216	C₂²×C₄×C₈₉	—	2	1	no	—
217	C₂²×C₄×C₈₉	—	2	1	no	—
218	C₂²×C₄×C₈₉	—	4	1	no	—
219	C₂²×C₄×C₈₉	—	4	1	no	—
220	C₂²×C₄×C₈₉	—	4	1	no	—
221	C₂²×C₄×C₈₉	—	4	4	no	—
222	C₂²×C₄×C₈₉	—	4	4	no	—
223	C₂²×C₄×C₈₉	—	4	4	no	—
224	C₂²×C₄×C₈₉	—	4	4	no	—
225	C₂²×C₄×C₈₉	—	4	2	no	—
226	C₂²×C₄×C₈₉	—	4	2	no	—
227	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
230	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
231	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₈₉	#41	1	2	yes	—
233	C₂²×C₄×C₈₉	#41	1	2	yes	—
234	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
235	C₂×C₈×C₈₉	—	2	1	no	—
236	C₂×C₈×C₈₉	—	2	1	no	—
237	C₂×C₈×C₈₉	—	2	1	no	—
238	C₂×C₈×C₈₉	—	2	1	no	—
239	C₂×C₈×C₈₉	—	2	1	no	—
240	C₂×C₈×C₈₉	—	2	1	no	—
241	C₂×C₈×C₈₉	—	2	1	no	—
242	C₂×C₈×C₈₉	—	2	1	no	—
243	C₂×C₈×C₈₉	—	2	1	no	—
244	C₂×C₈×C₈₉	—	2	1	no	—
245	C₂×C₈×C₈₉	—	2	1	no	—
246	C₂×C₈×C₈₉	—	2	1	no	—
247	C₄⋊C₄×C₈₉	—	2	4	no	—
248	C₄⋊C₄×C₈₉	—	2	4	no	—
249	C₄⋊C₄×C₈₉	—	2	1	no	—
250	C₄⋊C₄×C₈₉	—	2	1	no	—
251	C₄⋊C₄×C₈₉	—	2	1	no	—
252	C₄⋊C₄×C₈₉	—	2	1	no	—
253	C₄⋊C₄×C₈₉	—	2	1	no	—
254	C₄⋊C₄×C₈₉	—	2	1	no	—
255	C₄⋊C₄×C₈₉	—	2	1	no	—
256	C₄⋊C₄×C₈₉	—	2	1	no	—
257	C₄⋊C₄×C₈₉	—	2	1	no	—
258	C₄⋊C₄×C₈₉	—	2	1	no	—
259	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
261	C₂²⋊C₄×C₈₉	—	2	4	no	—
262	C₂²⋊C₄×C₈₉	—	2	4	no	—
263	C₂²⋊C₄×C₈₉	—	2	4	no	—
264	C₂²⋊C₄×C₈₉	—	2	4	no	—
265	C₂²⋊C₄×C₈₉	—	2	4	no	—
266	C₂²⋊C₄×C₈₉	—	4	2	no	—
267	C₂²⋊C₄×C₈₉	—	4	2	no	—
268	C₂²⋊C₄×C₈₉	—	4	2	no	—
269	C₂²⋊C₄×C₈₉	—	4	2	no	—
270	C₂²⋊C₄×C₈₉	—	4	2	no	—
271	C₂²⋊C₄×C₈₉	—	4	2	no	—
272	C₄²×C₈₉	—	2	4	no	—
273	C₄²×C₈₉	—	4	2	no	—
274	C₄²×C₈₉	—	4	2	no	—
275	C₂³×C₈₉	—	2	1	no	—
276	C₂³×C₈₉	—	2	1	no	—
277	C₂³×C₈₉	—	2	1	no	—
278	C₂³×C₈₉	—	2	1	no	—
279	C₂³×C₈₉	—	2	1	no	—
280	C₂³×C₈₉	—	2	1	no	—
281	C₂³×C₈₉	—	2	1	no	—
282	C₂³×C₈₉	—	2	1	no	—
283	C₂³×C₈₉	—	2	1	no	—
284	C₂³×C₈₉	—	2	1	no	—
285	C₂³×C₈₉	—	2	1	no	—
286	C₂³×C₈₉	—	2	1	no	—
287	C₂³×C₈₉	—	2	1	no	—
288	C₂³×C₈₉	—	2	1	no	—
289	C₂³×C₈₉	—	2	1	no	—
290	C₂³×C₈₉	—	2	1	no	—
291	C₂³×C₈₉	—	2	1	no	—
292	C₂³×C₈₉	—	2	1	no	—
293	C₂³×C₈₉	—	2	2	no	—
294	C₂³×C₈₉	—	4	4	no	—
295	C₂³×C₈₉	—	4	4	no	—
296	C₂³×C₈₉	—	4	4	no	—
297	C₂³×C₈₉	—	4	4	no	—
298	C₂³×C₈₉	—	4	4	no	—
299	C₂³×C₈₉	—	4	4	no	—
300	C₂³×C₈₉	—	4	4	no	—
301	C₂³×C₈₉	—	4	1	no	—
302	C₂³×C₈₉	—	4	1	no	—
303	C₂³×C₈₉	—	4	1	no	—
304	C₂³×C₈₉	—	4	1	no	—
305	C₂³×C₈₉	—	4	1	no	—
306	C₂³×C₈₉	—	4	1	no	—
307	C₂³×C₈₉	#120	1	2	yes	—
308	C₂³×C₈₉	#123	1	2	yes	—
309	C₂³×C₈₉	#135	1	2	yes	—
310	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
311	Q₈×C₈₉	—	2	2	no	—
312	Q₈×C₈₉	—	2	2	no	—
313	Q₈×C₈₉	—	4	1	no	—
314	Q₈×C₈₉	—	4	1	no	—
315	D₄×C₈₉	—	2	2	no	—
316	D₄×C₈₉	—	2	2	no	—
317	D₄×C₈₉	—	4	8	no	—
318	D₄×C₈₉	—	4	8	no	—
319	D₄×C₈₉	—	4	8	no	—
320	D₄×C₈₉	—	4	1	no	—
321	D₄×C₈₉	—	4	1	no	—
322	C₂×C₄×C₈₉	—	2	1	no	—
323	C₂×C₄×C₈₉	—	2	1	no	—
324	C₂×C₄×C₈₉	—	2	1	no	—
325	C₂×C₄×C₈₉	—	2	1	no	—
326	C₂×C₄×C₈₉	—	2	2	no	—
327	C₂×C₄×C₈₉	—	2	2	no	—
328	C₂×C₄×C₈₉	—	2	2	no	—
329	C₂×C₄×C₈₉	—	2	2	no	—
330	C₂×C₄×C₈₉	—	2	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	1	no	—
337	C₂×C₄×C₈₉	—	2	2	no	—
338	C₂×C₄×C₈₉	—	2	1	no	—
339	C₂×C₄×C₈₉	—	2	1	no	—
340	C₂×C₄×C₈₉	—	4	4	no	—
341	C₂×C₄×C₈₉	—	4	4	no	—
342	C₂×C₄×C₈₉	—	4	4	no	—
343	C₂×C₄×C₈₉	—	4	8	no	—
344	C₂×C₄×C₈₉	—	4	1	no	—
345	C₂×C₄×C₈₉	—	4	1	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	1	no	—
354	C₂×C₄×C₈₉	—	4	1	no	—
355	C₂×C₄×C₈₉	—	4	1	no	—
356	C₂×C₄×C₈₉	—	4	1	no	—
357	C₂×C₄×C₈₉	—	4	1	no	—
358	C₂×C₄×C₈₉	—	4	1	no	—
359	C₂×C₄×C₈₉	—	4	1	no	—
360	C₂×C₄×C₈₉	—	4	1	no	—
361	C₂×C₄×C₈₉	—	4	1	no	—
362	C₂×C₄×C₈₉	—	4	1	no	—
363	C₂×C₄×C₈₉	—	4	1	no	—
364	C₂×C₄×C₈₉	—	4	1	no	—
365	C₂×C₄×C₈₉	—	4	1	no	—
366	C₂×C₄×C₈₉	#120	1	2	yes	—
367	C₂×C₄×C₈₉	#123	1	2	yes	—
368	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
371	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
372	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
373	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
374	C₈×C₈₉	—	4	1	no	—
375	C₈×C₈₉	—	4	1	no	—
376	C₈×C₈₉	—	4	1	no	—
377	C₈×C₈₉	—	4	1	no	—
378	C₂²×C₈₉	—	2	2	no	—
379	C₂²×C₈₉	—	2	2	no	—
380	C₂²×C₈₉	—	2	2	no	—
381	C₂²×C₈₉	—	2	2	no	—
382	C₂²×C₈₉	—	2	2	no	—
383	C₂²×C₈₉	—	2	2	no	—
384	C₂²×C₈₉	—	2	2	no	—
385	C₂²×C₈₉	—	2	2	no	—
386	C₂²×C₈₉	—	2	2	no	—
387	C₂²×C₈₉	—	4	16	no	—
388	C₂²×C₈₉	—	4	1	no	—
389	C₂²×C₈₉	—	4	1	no	—
390	C₂²×C₈₉	—	4	1	no	—
391	C₂²×C₈₉	—	4	1	no	—
392	C₂²×C₈₉	—	4	1	no	—
393	C₂²×C₈₉	—	4	1	no	—
394	C₂²×C₈₉	—	4	1	no	—
395	C₂²×C₈₉	—	4	1	no	—
396	C₂²×C₈₉	—	4	1	no	—
397	C₂²×C₈₉	—	4	1	no	—
398	C₂²×C₈₉	—	4	1	no	—
399	C₂²×C₈₉	—	4	1	no	—
400	C₂²×C₈₉	—	4	2	no	—
401	C₂²×C₈₉	—	4	2	no	—
402	C₂²×C₈₉	—	4	2	no	—
403	C₂²×C₈₉	—	8	1	no	—
404	C₂²×C₈₉	—	8	1	no	—
405	C₂²×C₈₉	—	8	1	no	—
406	C₂²×C₈₉	—	8	1	no	—
407	C₂²×C₈₉	C₂×#120	1	1	yes	characteristic
408	C₂²×C₈₉	C₂×#123	1	1	yes	characteristic
409	C₂²×C₈₉	#534	1	1	yes	characteristic
410	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
411	C₂²×C₈₉	#575	1	1	yes	characteristic
412	C₂²×C₈₉	#575	1	1	yes	characteristic
413	C₂²×C₈₉	#575	1	1	yes	characteristic
414	C₄×C₈₉	—	2	2	no	—
415	C₄×C₈₉	—	2	2	no	—
416	C₄×C₈₉	—	4	1	no	—
417	C₄×C₈₉	—	4	2	no	—
418	C₄×C₈₉	—	4	2	no	—
419	C₄×C₈₉	—	4	2	no	—
420	C₄×C₈₉	—	8	1	no	—
421	C₄×C₈₉	—	8	1	no	—
422	C₄×C₈₉	—	8	1	no	—
423	C₄×C₈₉	—	8	1	no	—
424	C₄×C₈₉	#546	1	1	yes	characteristic
425	C₄×C₈₉	#546	1	1	yes	characteristic
426	C₄×C₈₉	#546	1	1	yes	characteristic
427	C₄×C₈₉	#546	1	1	yes	characteristic
428	#24008	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
429	C₂×C₈₉	—	4	2	no	—
430	C₂×C₈₉	—	4	2	no	—
431	C₂×C₈₉	—	4	2	no	—
432	C₂×C₈₉	—	8	2	no	—
433	C₂×C₈₉	#2405	1	1	yes	characteristic
434	C₂×C₈₉	#3002	1	1	yes	characteristic
435	C₂×C₈₉	#3005	1	1	yes	characteristic
436	C₂×C₈₉	#3091	1	1	yes	characteristic
437	C₂×C₈₉	#3093	1	1	yes	characteristic
438	C₂×C₈₉	#3191	1	1	yes	characteristic
439	C₂×C₈₉	#3197	1	1	yes	characteristic
440	C₂×#525	C₂×C₈₉	1	1	yes	characteristic
441	C₂×#485	C₂×C₈₉	1	1	yes	characteristic, complemented
442	C₂×#482	C₂×C₈₉	1	1	yes	characteristic, complemented
443	#2280	C₂×C₈₉	1	1	yes	characteristic, complemented
444	#2036	C₂×C₈₉	1	1	yes	characteristic, complemented
445	#2035	C₂×C₈₉	1	1	yes	characteristic, complemented
446	#2034	C₂×C₈₉	1	1	yes	characteristic, complemented
447	#2033	C₂×C₈₉	1	1	yes	characteristic, complemented
448	#1875	C₂×C₈₉	1	1	yes	characteristic, complemented
449	#1873	C₂×C₈₉	1	1	yes	characteristic, complemented
450	#1854	C₂×C₈₉	1	1	yes	characteristic, complemented
451	#1854	C₂×C₈₉	1	1	yes	characteristic, complemented
452	#1788	C₂×C₈₉	1	1	yes	characteristic, complemented
453	#1788	C₂×C₈₉	1	1	yes	characteristic, complemented
454	#1779	C₂×C₈₉	1	1	yes	characteristic, complemented
455	C₈₉	#24008	1	1	yes	characteristic, direct product factor, Sylow
456	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
457	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
458	#525	—	2	4	no	—
459	#525	—	2	4	no	—
460	C₂×#123	—	2	1	no	—
461	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
462	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
463	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
464	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
465	C₂×#120	—	2	1	no	—
466	C₂×C₄×D₄	—	2	1	no	—
467	C₂×C₄×D₄	—	2	1	no	—
468	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
469	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
470	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
471	#485	—	2	4	no	—
472	#482	—	2	4	no	—
473	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic, complemented
474	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic, complemented
475	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic, complemented
476	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic, complemented
477	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
478	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
479	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
480	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
481	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
482	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
483	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
484	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
485	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
486	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
487	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
488	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
489	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
490	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
491	#381	—	2	1	no	—
492	#380	C₂²×C₈₉	1	1	yes	characteristic
493	#380	C₂²×C₈₉	1	1	yes	characteristic
494	#380	C₂²×C₈₉	1	1	yes	characteristic
495	#380	C₂²×C₈₉	1	1	yes	characteristic
496	#379	—	2	1	no	—
497	C₄×C₂²⋊C₄	—	2	1	no	—
498	C₄×C₂²⋊C₄	—	2	1	no	—
499	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
500	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
501	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
502	#340	C₂²×C₈₉	1	1	yes	characteristic, complemented
503	C₂⁵	D₄×C₈₉	1	1	yes	characteristic
504	C₂×#41	—	2	2	no	—
505	C₂×#41	—	2	2	no	—
506	C₂×#41	—	2	2	no	—
507	C₂×#41	—	2	2	no	—
508	C₂×#41	—	4	1	no	—
509	C₂×#41	—	4	1	no	—
510	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
511	C₂²×D₄	—	2	1	no	—
512	C₂²×D₄	—	2	1	no	—
513	C₂²×D₄	—	2	1	no	—
514	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
515	C₂³×C₄	—	2	1	no	—
516	C₂³×C₄	—	2	2	no	—
517	C₂³×C₄	—	2	2	no	—
518	C₂³×C₄	—	2	2	no	—
519	C₂³×C₄	—	2	2	no	—
520	C₂³×C₄	—	4	1	no	—
521	C₂³×C₄	—	4	1	no	—
522	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
523	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
524	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
525	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
526	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
527	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
528	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
529	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
530	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
531	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
532	#123	—	2	8	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	D₄×C₈₉	1	4	yes	—
537	#121	—	2	2	no	—
538	#121	—	2	2	no	—
539	#121	—	2	2	no	—
540	#121	D₄×C₈₉	1	4	yes	—
541	#120	—	2	8	no	—
542	C₄×D₄	—	2	8	no	—
543	C₄×D₄	—	2	8	no	—
544	#117	—	2	2	no	—
545	#117	—	2	2	no	—
546	#117	—	2	2	no	—
547	#117	—	2	2	no	—
548	#117	—	4	1	no	—
549	#117	—	4	1	no	—
550	C₂×C₄⋊C₄	—	2	1	no	—
551	C₂×C₄⋊C₄	—	2	1	no	—
552	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
558	C₂×C₂²⋊C₄	—	2	1	no	—
559	C₂×C₂²⋊C₄	—	2	1	no	—
560	C₂×C₂²⋊C₄	—	2	1	no	—
561	C₂×C₂²⋊C₄	—	2	1	no	—
562	C₂×C₂²⋊C₄	—	2	1	no	—
563	C₂×C₂²⋊C₄	—	2	1	no	—
564	C₂×C₂²⋊C₄	—	2	1	no	—
565	C₂×C₂²⋊C₄	—	2	1	no	—
566	C₂×C₂²⋊C₄	—	2	1	no	—
567	C₂×C₂²⋊C₄	—	2	1	no	—
568	C₂×C₂²⋊C₄	—	2	1	no	—
569	C₂×C₄²	—	2	1	no	—
570	C₂×C₄²	—	2	1	no	—
571	C₂×C₄²	—	2	1	no	—
572	#107	—	2	2	no	—
573	#107	—	2	2	no	—
574	#106	—	2	2	no	—
575	#106	—	2	2	no	—
576	#103	—	2	2	no	—
577	#103	—	2	2	no	—
578	#103	—	4	1	no	—
579	#103	—	4	1	no	—
580	#102	—	2	2	no	—
581	#102	—	2	2	no	—
582	#102	—	4	1	no	—
583	#102	—	4	1	no	—
584	C₂²⋊C₈	—	2	2	no	—
585	C₂²⋊C₈	—	2	2	no	—
586	C₂²⋊C₈	—	2	2	no	—
587	C₂²⋊C₈	—	2	2	no	—
588	C₂²⋊C₈	—	4	1	no	—
589	C₂²⋊C₈	—	4	1	no	—
590	#95	—	2	1	no	—
591	#95	—	2	1	no	—
592	#95	—	2	1	no	—
593	#95	—	2	1	no	—
594	C₂⁴	—	2	2	no	—
595	C₂⁴	—	2	2	no	—
596	C₂⁴	—	2	2	no	—
597	C₂⁴	—	2	1	no	—
598	C₂⁴	—	4	1	no	—
599	C₂⁴	—	4	1	no	—
600	C₂⁴	—	4	1	no	—
601	C₂⁴	—	4	1	no	—
602	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
603	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
604	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
605	#41	—	4	4	no	—
606	#41	—	4	4	no	—
607	#41	—	4	4	no	—
608	#41	—	4	4	no	—
609	C₂×Q₈	—	2	1	no	—
610	C₂×Q₈	—	2	1	no	—
611	C₂×Q₈	—	2	1	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	4	2	no	—
624	C₂×D₄	—	4	2	no	—
625	C₂×D₄	—	4	2	no	—
626	C₂×D₄	—	4	2	no	—
627	C₂×D₄	—	4	2	no	—
628	C₂×D₄	—	4	2	no	—
629	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	4	1	no	—
659	C₂²×C₄	—	4	1	no	—
660	C₂²×C₄	—	4	1	no	—
661	C₂²×C₄	—	4	4	no	—
662	C₂²×C₄	—	4	4	no	—
663	C₂²×C₄	—	4	4	no	—
664	C₂²×C₄	—	4	4	no	—
665	C₂²×C₄	—	4	2	no	—
666	C₂²×C₄	—	4	2	no	—
667	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
668	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
669	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
670	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
671	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
672	C₂²×C₄	#41×C₈₉	1	2	yes	—
673	C₂²×C₄	#41×C₈₉	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
675	C₂×C₈	—	2	1	no	—
676	C₂×C₈	—	2	1	no	—
677	C₂×C₈	—	2	1	no	—
678	C₂×C₈	—	2	1	no	—
679	C₂×C₈	—	2	1	no	—
680	C₂×C₈	—	2	1	no	—
681	C₂×C₈	—	2	1	no	—
682	C₂×C₈	—	2	1	no	—
683	C₂×C₈	—	2	1	no	—
684	C₂×C₈	—	2	1	no	—
685	C₂×C₈	—	2	1	no	—
686	C₂×C₈	—	2	1	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
700	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	4	2	no	—
707	C₂²⋊C₄	—	4	2	no	—
708	C₂²⋊C₄	—	4	2	no	—
709	C₂²⋊C₄	—	4	2	no	—
710	C₂²⋊C₄	—	4	2	no	—
711	C₂²⋊C₄	—	4	2	no	—
712	C₄²	—	2	4	no	—
713	C₄²	—	4	2	no	—
714	C₄²	—	4	2	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	1	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	1	no	—
723	C₂³	—	2	1	no	—
724	C₂³	—	2	1	no	—
725	C₂³	—	2	1	no	—
726	C₂³	—	2	1	no	—
727	C₂³	—	2	1	no	—
728	C₂³	—	2	1	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	1	no	—
731	C₂³	—	2	1	no	—
732	C₂³	—	2	1	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	4	4	no	—
735	C₂³	—	4	4	no	—
736	C₂³	—	4	4	no	—
737	C₂³	—	4	4	no	—
738	C₂³	—	4	4	no	—
739	C₂³	—	4	4	no	—
740	C₂³	—	4	4	no	—
741	C₂³	—	4	1	no	—
742	C₂³	—	4	1	no	—
743	C₂³	—	4	1	no	—
744	C₂³	—	4	1	no	—
745	C₂³	—	4	1	no	—
746	C₂³	—	4	1	no	—
747	C₂³	#120×C₈₉	1	2	yes	—
748	C₂³	#123×C₈₉	1	2	yes	—
749	C₂³	#135×C₈₉	1	2	yes	—
750	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
751	Q₈	—	2	2	no	—
752	Q₈	—	2	2	no	—
753	Q₈	—	4	1	no	—
754	Q₈	—	4	1	no	—
755	D₄	—	2	2	no	—
756	D₄	—	2	2	no	—
757	D₄	—	4	8	no	—
758	D₄	—	4	8	no	—
759	D₄	—	4	8	no	—
760	D₄	—	4	1	no	—
761	D₄	—	4	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	4	4	no	—
781	C₂×C₄	—	4	4	no	—
782	C₂×C₄	—	4	4	no	—
783	C₂×C₄	—	4	8	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	1	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	—	4	1	no	—
795	C₂×C₄	—	4	1	no	—
796	C₂×C₄	—	4	1	no	—
797	C₂×C₄	—	4	1	no	—
798	C₂×C₄	—	4	1	no	—
799	C₂×C₄	—	4	1	no	—
800	C₂×C₄	—	4	1	no	—
801	C₂×C₄	—	4	1	no	—
802	C₂×C₄	—	4	1	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	4	1	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	#120×C₈₉	1	2	yes	—
807	C₂×C₄	#123×C₈₉	1	2	yes	—
808	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
809	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
810	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
811	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
812	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
813	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
814	C₈	—	4	1	no	—
815	C₈	—	4	1	no	—
816	C₈	—	4	1	no	—
817	C₈	—	4	1	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	2	no	—
824	C₂²	—	2	2	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	4	16	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	8	1	no	—
844	C₂²	—	8	1	no	—
845	C₂²	—	8	1	no	—
846	C₂²	—	8	1	no	—
847	C₂²	C₂×#120×C₈₉	1	1	yes	characteristic
848	C₂²	C₂×#123×C₈₉	1	1	yes	characteristic
849	C₂²	#534×C₈₉	1	1	yes	characteristic
850	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
851	C₂²	#575×C₈₉	1	1	yes	characteristic
852	C₂²	#575×C₈₉	1	1	yes	characteristic
853	C₂²	#575×C₈₉	1	1	yes	characteristic
854	C₄	—	2	2	no	—
855	C₄	—	2	2	no	—
856	C₄	—	4	1	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	2	no	—
860	C₄	—	8	1	no	—
861	C₄	—	8	1	no	—
862	C₄	—	8	1	no	—
863	C₄	—	8	1	no	—
864	C₄	#546×C₈₉	1	1	yes	characteristic
865	C₄	#546×C₈₉	1	1	yes	characteristic
866	C₄	#546×C₈₉	1	1	yes	characteristic
867	C₄	#546×C₈₉	1	1	yes	characteristic
868	C₂	—	4	2	no	—
869	C₂	—	4	2	no	—
870	C₂	—	4	2	no	—
871	C₂	—	8	2	no	—
872	C₂	C₈₉×#2405	1	1	yes	characteristic
873	C₂	C₈₉×#3002	1	1	yes	characteristic
874	C₂	C₈₉×#3005	1	1	yes	characteristic
875	C₂	C₈₉×#3091	1	1	yes	characteristic
876	C₂	C₈₉×#3093	1	1	yes	characteristic
877	C₂	C₈₉×#3191	1	1	yes	characteristic
878	C₂	C₈₉×#3197	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂×#525×C₈₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂⁴×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#485×C₈₉	C₂	semidirect
3. C₂×#482×C₈₉	C₂	semidirect
4. C₈₉×#2280	C₂	semidirect
5. C₈₉×#2036	C₂	semidirect
6. C₈₉×#2035	C₂	semidirect
7. C₈₉×#2034	C₂	semidirect
8. C₈₉×#2033	C₂	semidirect
9. C₈₉×#1875	C₂	semidirect
10. C₈₉×#1873	C₂	semidirect
11. C₈₉×#1854	C₂	semidirect
12. C₈₉×#1854	C₂	semidirect
13. C₈₉×#1788	C₂	semidirect
14. C₈₉×#1788	C₂	semidirect
15. C₈₉×#1779	C₂	semidirect
33. C₂×#107×C₈₉	C₂²	semidirect
34. C₂×#107×C₈₉	C₂²	semidirect
35. C₂×#106×C₈₉	C₂²	semidirect
36. C₂×#106×C₈₉	C₂²	semidirect
37. C₂×#103×C₈₉	C₂²	semidirect
38. C₂×#103×C₈₉	C₂²	semidirect
39. C₂×#103×C₈₉	C₂²	semidirect
40. C₂×#103×C₈₉	C₂²	semidirect
41. C₂×#102×C₈₉	C₂²	semidirect
42. C₂×#102×C₈₉	C₂²	semidirect
43. C₂×#102×C₈₉	C₂²	semidirect
44. C₂×#102×C₈₉	C₂²	semidirect
59. #340×C₈₉	C₂²	semidirect
60. #340×C₈₉	C₂²	semidirect
61. #340×C₈₉	C₂²	semidirect
62. #340×C₈₉	C₂²	semidirect
428. #24008	C₈₉	direct (N × H)
441. C₂×#485	C₂×C₈₉	semidirect
442. C₂×#482	C₂×C₈₉	semidirect
443. #2280	C₂×C₈₉	semidirect
444. #2036	C₂×C₈₉	semidirect
445. #2035	C₂×C₈₉	semidirect
446. #2034	C₂×C₈₉	semidirect
447. #2033	C₂×C₈₉	semidirect
448. #1875	C₂×C₈₉	semidirect
449. #1873	C₂×C₈₉	semidirect
450. #1854	C₂×C₈₉	semidirect
451. #1854	C₂×C₈₉	semidirect
452. #1788	C₂×C₈₉	semidirect
453. #1788	C₂×C₈₉	semidirect
454. #1779	C₂×C₈₉	semidirect
455. C₈₉	#24008	direct (N × H)
473. C₂×#107	C₂²×C₈₉	semidirect
474. C₂×#107	C₂²×C₈₉	semidirect
475. C₂×#106	C₂²×C₈₉	semidirect
476. C₂×#106	C₂²×C₈₉	semidirect
477. C₂×#103	C₂²×C₈₉	semidirect
478. C₂×#103	C₂²×C₈₉	semidirect
479. C₂×#103	C₂²×C₈₉	semidirect
480. C₂×#103	C₂²×C₈₉	semidirect
481. C₂×#102	C₂²×C₈₉	semidirect
482. C₂×#102	C₂²×C₈₉	semidirect
483. C₂×#102	C₂²×C₈₉	semidirect
484. C₂×#102	C₂²×C₈₉	semidirect
499. #340	C₂²×C₈₉	semidirect
500. #340	C₂²×C₈₉	semidirect
501. #340	C₂²×C₈₉	semidirect
502. #340	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×#525×C₈₉	2
C₂×#485×C₈₉	2
C₂×#482×C₈₉	2
C₈₉×#2280	2
C₈₉×#2036	2
C₈₉×#2035	2
C₈₉×#2034	2
C₈₉×#2033	2
C₈₉×#1875	2
C₈₉×#1873	2
C₈₉×#1854	2
C₈₉×#1788	2
C₈₉×#1779	2
#24008	89

Subgroups — C89×#24008 #36401856

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#24008 #36401856