Subgroups — C₈₉×#23975 #36401823

Order 22784.

1326 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#449×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#417×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2407	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2026	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2025	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1999	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1895	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1875	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1870	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1823	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
20	#553×C₈₉	—	2	4	no	—
21	#553×C₈₉	—	2	4	no	—
22	C₂×#126×C₈₉	—	2	1	no	—
23	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#123×C₈₉	—	2	1	no	—
25	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#121×C₈₉	—	2	1	no	—
27	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₈₉	—	2	1	no	—
31	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
35	#449×C₈₉	—	2	4	no	—
36	#417×C₈₉	—	2	4	no	—
37	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
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	#394×C₈₉	—	2	1	no	—
49	#392×C₈₉	—	2	1	no	—
50	#391×C₈₉	C₂²	1	1	yes	characteristic
51	#390×C₈₉	C₂²	1	1	yes	characteristic
52	#386×C₈₉	—	2	1	no	—
53	#385×C₈₉	—	2	1	no	—
54	#380×C₈₉	C₂²	1	1	yes	characteristic
55	#340×C₈₉	C₂²	1	1	yes	characteristic
56	#340×C₈₉	C₂²	1	1	yes	characteristic
57	#340×C₈₉	C₂²	1	1	yes	characteristic
58	#340×C₈₉	C₂²	1	1	yes	characteristic
59	#340×C₈₉	C₂²	1	1	yes	characteristic
60	#340×C₈₉	C₂²	1	1	yes	characteristic
61	#336×C₈₉	C₂²	1	1	yes	characteristic
62	#336×C₈₉	C₂²	1	1	yes	characteristic
63	C₂×#41×C₈₉	—	2	2	no	—
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	—	4	1	no	—
68	C₂×#41×C₈₉	—	4	1	no	—
69	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₈₉	—	2	1	no	—
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	D₄	1	1	yes	characteristic
75	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₈₉	—	2	1	no	—
78	C₂³×C₄×C₈₉	—	2	1	no	—
79	C₂³×C₄×C₈₉	—	2	1	no	—
80	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
82	C₂×SD₁₆×C₈₉	—	2	2	no	—
83	C₂×SD₁₆×C₈₉	—	2	2	no	—
84	C₂×SD₁₆×C₈₉	—	4	1	no	—
85	C₂×D₈×C₈₉	—	2	2	no	—
86	C₂×D₈×C₈₉	—	2	2	no	—
87	C₂×D₈×C₈₉	—	4	1	no	—
88	C₂×M₁₆×C₈₉	—	2	2	no	—
89	C₂×M₁₆×C₈₉	—	4	1	no	—
90	C₂×M₁₆×C₈₉	—	4	1	no	—
91	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
95	#126×C₈₉	—	2	8	no	—
96	#125×C₈₉	—	2	2	no	—
97	#125×C₈₉	—	2	2	no	—
98	#123×C₈₉	—	2	8	no	—
99	C₂²⋊Q₈×C₈₉	—	2	2	no	—
100	C₂²⋊Q₈×C₈₉	—	4	1	no	—
101	#121×C₈₉	—	2	8	no	—
102	#121×C₈₉	—	2	2	no	—
103	#121×C₈₉	—	2	2	no	—
104	#121×C₈₉	—	2	2	no	—
105	#121×C₈₉	—	2	2	no	—
106	#121×C₈₉	—	4	1	no	—
107	#121×C₈₉	D₄	1	4	yes	complemented
108	C₄×D₄×C₈₉	—	2	8	no	—
109	C₄×D₄×C₈₉	—	2	2	no	—
110	C₄×D₄×C₈₉	—	2	2	no	—
111	C₄×D₄×C₈₉	—	2	2	no	—
112	C₄×D₄×C₈₉	—	2	2	no	—
113	#117×C₈₉	—	2	2	no	—
114	#117×C₈₉	—	2	2	no	—
115	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
116	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
117	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
118	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
119	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
120	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₈₉	D₄	1	4	yes	complemented
122	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
127	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
131	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
133	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
134	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
135	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
136	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
137	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
138	C₂×C₄²×C₈₉	—	2	1	no	—
139	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
140	#103×C₈₉	—	2	2	no	—
141	#103×C₈₉	—	2	2	no	—
142	#103×C₈₉	—	2	2	no	—
143	#102×C₈₉	—	2	2	no	—
144	#102×C₈₉	—	2	2	no	—
145	#102×C₈₉	—	2	2	no	—
146	#102×C₈₉	—	4	1	no	—
147	#102×C₈₉	—	4	1	no	—
148	C₂²⋊C₈×C₈₉	—	2	2	no	—
149	C₂²⋊C₈×C₈₉	—	4	1	no	—
150	C₂²⋊C₈×C₈₉	—	4	1	no	—
151	#95×C₈₉	—	2	1	no	—
152	#95×C₈₉	—	2	1	no	—
153	#95×C₈₉	—	2	1	no	—
154	C₂⁴×C₈₉	—	2	1	no	—
155	C₂⁴×C₈₉	—	2	1	no	—
156	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
158	#41×C₈₉	—	2	8	no	—
159	#41×C₈₉	—	4	4	no	—
160	#41×C₈₉	—	4	4	no	—
161	#41×C₈₉	—	4	4	no	—
162	C₂×Q₈×C₈₉	—	2	1	no	—
163	C₂×Q₈×C₈₉	—	2	1	no	—
164	C₂×Q₈×C₈₉	—	2	1	no	—
165	C₂×Q₈×C₈₉	—	2	1	no	—
166	C₂×Q₈×C₈₉	—	2	1	no	—
167	C₂×Q₈×C₈₉	#41	1	2	yes	—
168	C₂×D₄×C₈₉	—	2	2	no	—
169	C₂×D₄×C₈₉	—	2	4	no	—
170	C₂×D₄×C₈₉	—	2	4	no	—
171	C₂×D₄×C₈₉	—	2	1	no	—
172	C₂×D₄×C₈₉	—	2	1	no	—
173	C₂×D₄×C₈₉	—	2	1	no	—
174	C₂×D₄×C₈₉	—	2	1	no	—
175	C₂×D₄×C₈₉	—	2	1	no	—
176	C₂×D₄×C₈₉	—	2	1	no	—
177	C₂×D₄×C₈₉	—	2	1	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	—	4	1	no	—
182	C₂×D₄×C₈₉	—	4	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	—	4	2	no	—
190	C₂×D₄×C₈₉	—	8	1	no	—
191	C₂×D₄×C₈₉	—	8	1	no	—
192	C₂×D₄×C₈₉	—	8	1	no	—
193	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
194	C₂×D₄×C₈₉	#41	1	2	yes	—
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	1	no	—
199	C₂²×C₄×C₈₉	—	2	1	no	—
200	C₂²×C₄×C₈₉	—	2	1	no	—
201	C₂²×C₄×C₈₉	—	2	1	no	—
202	C₂²×C₄×C₈₉	—	2	1	no	—
203	C₂²×C₄×C₈₉	—	2	4	no	—
204	C₂²×C₄×C₈₉	—	2	4	no	—
205	C₂²×C₄×C₈₉	—	2	1	no	—
206	C₂²×C₄×C₈₉	—	2	1	no	—
207	C₂²×C₄×C₈₉	—	2	1	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	—	4	2	no	—
214	C₂²×C₄×C₈₉	—	4	2	no	—
215	C₂²×C₄×C₈₉	—	4	2	no	—
216	C₂²×C₄×C₈₉	—	8	1	no	—
217	C₂²×C₄×C₈₉	—	8	1	no	—
218	C₂²×C₄×C₈₉	—	8	1	no	—
219	C₂²×C₄×C₈₉	—	8	1	no	—
220	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
225	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
227	SD₁₆×C₈₉	—	4	4	no	—
228	D₈×C₈₉	—	4	4	no	—
229	M₁₆×C₈₉	—	4	4	no	—
230	C₂×C₈×C₈₉	—	2	1	no	—
231	C₂×C₈×C₈₉	—	2	1	no	—
232	C₂×C₈×C₈₉	—	2	1	no	—
233	C₂×C₈×C₈₉	—	2	1	no	—
234	C₂×C₈×C₈₉	—	2	1	no	—
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	C₄⋊C₄×C₈₉	—	2	4	no	—
243	C₄⋊C₄×C₈₉	—	2	4	no	—
244	C₄⋊C₄×C₈₉	—	2	4	no	—
245	C₄⋊C₄×C₈₉	—	2	2	no	—
246	C₄⋊C₄×C₈₉	—	2	1	no	—
247	C₄⋊C₄×C₈₉	—	2	1	no	—
248	C₄⋊C₄×C₈₉	—	2	1	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	—	4	2	no	—
254	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
255	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
257	C₂²⋊C₄×C₈₉	—	2	4	no	—
258	C₂²⋊C₄×C₈₉	—	2	4	no	—
259	C₂²⋊C₄×C₈₉	—	2	4	no	—
260	C₂²⋊C₄×C₈₉	—	2	2	no	—
261	C₂²⋊C₄×C₈₉	—	2	4	no	—
262	C₂²⋊C₄×C₈₉	—	2	2	no	—
263	C₂²⋊C₄×C₈₉	—	4	2	no	—
264	C₂²⋊C₄×C₈₉	—	4	2	no	—
265	C₂²⋊C₄×C₈₉	—	4	2	no	—
266	C₂²⋊C₄×C₈₉	—	8	1	no	—
267	C₂²⋊C₄×C₈₉	—	8	1	no	—
268	C₄²×C₈₉	—	2	4	no	—
269	C₄²×C₈₉	—	2	1	no	—
270	C₄²×C₈₉	—	2	1	no	—
271	C₂³×C₈₉	—	2	1	no	—
272	C₂³×C₈₉	—	2	1	no	—
273	C₂³×C₈₉	—	2	1	no	—
274	C₂³×C₈₉	—	2	1	no	—
275	C₂³×C₈₉	—	2	1	no	—
276	C₂³×C₈₉	—	2	1	no	—
277	C₂³×C₈₉	—	2	1	no	—
278	C₂³×C₈₉	—	2	2	no	—
279	C₂³×C₈₉	—	2	1	no	—
280	C₂³×C₈₉	—	2	2	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	—	4	1	no	—
287	C₂³×C₈₉	—	4	1	no	—
288	C₂³×C₈₉	—	4	1	no	—
289	C₂³×C₈₉	—	4	1	no	—
290	C₂³×C₈₉	—	4	1	no	—
291	C₂³×C₈₉	—	4	1	no	—
292	C₂³×C₈₉	—	4	1	no	—
293	C₂³×C₈₉	—	4	1	no	—
294	C₂³×C₈₉	—	4	1	no	—
295	C₂³×C₈₉	—	4	1	no	—
296	C₂³×C₈₉	—	4	1	no	—
297	C₂³×C₈₉	—	4	1	no	—
298	C₂³×C₈₉	#120	1	2	yes	—
299	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
300	Q₈×C₈₉	—	2	2	no	—
301	Q₈×C₈₉	—	2	2	no	—
302	Q₈×C₈₉	—	4	1	no	—
303	Q₈×C₈₉	—	4	1	no	—
304	D₄×C₈₉	—	2	2	no	—
305	D₄×C₈₉	—	2	2	no	—
306	D₄×C₈₉	—	2	2	no	—
307	D₄×C₈₉	—	2	2	no	—
308	D₄×C₈₉	—	4	4	no	—
309	D₄×C₈₉	—	4	8	no	—
310	D₄×C₈₉	—	4	8	no	—
311	D₄×C₈₉	—	4	1	no	—
312	D₄×C₈₉	—	4	1	no	—
313	D₄×C₈₉	—	4	1	no	—
314	D₄×C₈₉	—	4	1	no	—
315	D₄×C₈₉	—	8	4	no	—
316	D₄×C₈₉	—	8	4	no	—
317	C₂×C₄×C₈₉	—	2	1	no	—
318	C₂×C₄×C₈₉	—	2	1	no	—
319	C₂×C₄×C₈₉	—	2	2	no	—
320	C₂×C₄×C₈₉	—	2	2	no	—
321	C₂×C₄×C₈₉	—	2	2	no	—
322	C₂×C₄×C₈₉	—	2	2	no	—
323	C₂×C₄×C₈₉	—	2	1	no	—
324	C₂×C₄×C₈₉	—	2	1	no	—
325	C₂×C₄×C₈₉	—	2	2	no	—
326	C₂×C₄×C₈₉	—	2	1	no	—
327	C₂×C₄×C₈₉	—	2	2	no	—
328	C₂×C₄×C₈₉	—	2	2	no	—
329	C₂×C₄×C₈₉	—	2	1	no	—
330	C₂×C₄×C₈₉	—	2	2	no	—
331	C₂×C₄×C₈₉	—	2	1	no	—
332	C₂×C₄×C₈₉	—	2	1	no	—
333	C₂×C₄×C₈₉	—	2	1	no	—
334	C₂×C₄×C₈₉	—	2	1	no	—
335	C₂×C₄×C₈₉	—	2	1	no	—
336	C₂×C₄×C₈₉	—	4	8	no	—
337	C₂×C₄×C₈₉	—	4	1	no	—
338	C₂×C₄×C₈₉	—	4	1	no	—
339	C₂×C₄×C₈₉	—	4	1	no	—
340	C₂×C₄×C₈₉	—	4	1	no	—
341	C₂×C₄×C₈₉	—	4	1	no	—
342	C₂×C₄×C₈₉	—	4	1	no	—
343	C₂×C₄×C₈₉	—	4	1	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	—	8	4	no	—
356	C₂×C₄×C₈₉	—	8	4	no	—
357	C₂×C₄×C₈₉	#120	1	2	yes	—
358	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
361	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
362	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
363	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
364	C₈×C₈₉	—	4	1	no	—
365	C₈×C₈₉	—	4	1	no	—
366	C₈×C₈₉	—	4	1	no	—
367	C₈×C₈₉	—	4	1	no	—
368	C₂²×C₈₉	—	2	2	no	—
369	C₂²×C₈₉	—	2	2	no	—
370	C₂²×C₈₉	—	2	2	no	—
371	C₂²×C₈₉	—	4	1	no	—
372	C₂²×C₈₉	—	4	1	no	—
373	C₂²×C₈₉	—	4	1	no	—
374	C₂²×C₈₉	—	4	1	no	—
375	C₂²×C₈₉	—	4	2	no	—
376	C₂²×C₈₉	—	4	1	no	—
377	C₂²×C₈₉	—	4	2	no	—
378	C₂²×C₈₉	—	4	1	no	—
379	C₂²×C₈₉	—	4	2	no	—
380	C₂²×C₈₉	—	4	2	no	—
381	C₂²×C₈₉	—	4	1	no	—
382	C₂²×C₈₉	—	4	1	no	—
383	C₂²×C₈₉	—	4	2	no	—
384	C₂²×C₈₉	—	4	1	no	—
385	C₂²×C₈₉	—	4	1	no	—
386	C₂²×C₈₉	—	4	2	no	—
387	C₂²×C₈₉	—	4	1	no	—
388	C₂²×C₈₉	—	8	1	no	—
389	C₂²×C₈₉	—	8	1	no	—
390	C₂²×C₈₉	—	8	1	no	—
391	C₂²×C₈₉	—	8	1	no	—
392	C₂²×C₈₉	—	8	1	no	—
393	C₂²×C₈₉	—	8	1	no	—
394	C₂²×C₈₉	—	8	1	no	—
395	C₂²×C₈₉	—	8	1	no	—
396	C₂²×C₈₉	C₂×#120	1	1	yes	characteristic
397	C₂²×C₈₉	#546	1	1	yes	characteristic
398	C₂²×C₈₉	#546	1	1	yes	characteristic
399	C₂²×C₈₉	#575	1	1	yes	characteristic
400	C₂²×C₈₉	#575	1	1	yes	characteristic
401	C₂²×C₈₉	#576	1	1	yes	characteristic
402	C₂²×C₈₉	#577	1	1	yes	characteristic
403	C₄×C₈₉	—	2	2	no	—
404	C₄×C₈₉	—	4	1	no	—
405	C₄×C₈₉	—	4	2	no	—
406	C₄×C₈₉	—	4	1	no	—
407	C₄×C₈₉	—	4	2	no	—
408	C₄×C₈₉	—	4	1	no	—
409	C₄×C₈₉	—	4	2	no	—
410	C₄×C₈₉	—	4	2	no	—
411	C₄×C₈₉	—	8	1	no	—
412	C₄×C₈₉	—	8	1	no	—
413	C₄×C₈₉	#525	1	1	yes	characteristic
414	C₄×C₈₉	#535	1	1	yes	characteristic
415	C₄×C₈₉	#546	1	1	yes	characteristic
416	C₄×C₈₉	#546	1	1	yes	characteristic
417	#23975	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
418	C₂×C₈₉	—	4	2	no	—
419	C₂×C₈₉	—	8	1	no	—
420	C₂×C₈₉	—	8	2	no	—
421	C₂×C₈₉	—	8	2	no	—
422	C₂×C₈₉	#2404	1	1	yes	characteristic
423	C₂×C₈₉	#3005	1	1	yes	characteristic
424	C₂×C₈₉	#3012	1	1	yes	characteristic
425	C₂×C₈₉	#3307	1	1	yes	characteristic
426	C₂×C₈₉	#3309	1	1	yes	characteristic
427	C₂×C₈₉	#3322	1	1	yes	characteristic
428	C₂×C₈₉	#3326	1	1	yes	characteristic
429	C₂×#553	C₂×C₈₉	1	1	yes	characteristic, complemented
430	C₂×#449	C₂×C₈₉	1	1	yes	characteristic, complemented
431	C₂×#417	C₂×C₈₉	1	1	yes	characteristic, complemented
432	#2407	C₂×C₈₉	1	1	yes	characteristic, complemented
433	#2026	C₂×C₈₉	1	1	yes	characteristic, complemented
434	#2025	C₂×C₈₉	1	1	yes	characteristic, complemented
435	#2000	C₂×C₈₉	1	1	yes	characteristic, complemented
436	#1999	C₂×C₈₉	1	1	yes	characteristic, complemented
437	#1895	C₂×C₈₉	1	1	yes	characteristic, complemented
438	#1879	C₂×C₈₉	1	1	yes	characteristic, complemented
439	#1877	C₂×C₈₉	1	1	yes	characteristic, complemented
440	#1875	C₂×C₈₉	1	1	yes	characteristic, complemented
441	#1873	C₂×C₈₉	1	1	yes	characteristic, complemented
442	#1870	C₂×C₈₉	1	1	yes	characteristic, complemented
443	#1823	C₂×C₈₉	1	1	yes	characteristic, complemented
444	C₈₉	#23975	1	1	yes	characteristic, direct product factor, Sylow
445	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
446	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
447	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
448	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
449	#553	—	2	4	no	—
450	#553	—	2	4	no	—
451	C₂×#126	—	2	1	no	—
452	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
453	C₂×#123	—	2	1	no	—
454	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
455	C₂×#121	—	2	1	no	—
456	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
457	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
458	C₂×#121	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×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
462	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
463	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
464	#449	—	2	4	no	—
465	#417	—	2	4	no	—
466	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
467	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
468	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
469	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
470	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
471	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
472	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
473	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
474	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
475	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
476	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
477	#394	—	2	1	no	—
478	#392	—	2	1	no	—
479	#391	C₂²×C₈₉	1	1	yes	characteristic
480	#390	C₂²×C₈₉	1	1	yes	characteristic
481	#386	—	2	1	no	—
482	#385	—	2	1	no	—
483	#380	C₂²×C₈₉	1	1	yes	characteristic
484	#340	C₂²×C₈₉	1	1	yes	characteristic
485	#340	C₂²×C₈₉	1	1	yes	characteristic
486	#340	C₂²×C₈₉	1	1	yes	characteristic
487	#340	C₂²×C₈₉	1	1	yes	characteristic
488	#340	C₂²×C₈₉	1	1	yes	characteristic
489	#340	C₂²×C₈₉	1	1	yes	characteristic
490	#336	C₂²×C₈₉	1	1	yes	characteristic
491	#336	C₂²×C₈₉	1	1	yes	characteristic
492	C₂×#41	—	2	2	no	—
493	C₂×#41	—	2	2	no	—
494	C₂×#41	—	2	2	no	—
495	C₂×#41	—	2	2	no	—
496	C₂×#41	—	4	1	no	—
497	C₂×#41	—	4	1	no	—
498	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
499	C₂²×D₄	—	2	1	no	—
500	C₂²×D₄	—	2	1	no	—
501	C₂²×D₄	—	2	1	no	—
502	C₂²×D₄	—	2	1	no	—
503	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
504	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
505	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
506	C₂³×C₄	—	2	1	no	—
507	C₂³×C₄	—	2	1	no	—
508	C₂³×C₄	—	2	1	no	—
509	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
511	C₂×SD₁₆	—	2	2	no	—
512	C₂×SD₁₆	—	2	2	no	—
513	C₂×SD₁₆	—	4	1	no	—
514	C₂×D₈	—	2	2	no	—
515	C₂×D₈	—	2	2	no	—
516	C₂×D₈	—	4	1	no	—
517	C₂×M₁₆	—	2	2	no	—
518	C₂×M₁₆	—	4	1	no	—
519	C₂×M₁₆	—	4	1	no	—
520	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
521	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
522	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
523	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
524	#126	—	2	8	no	—
525	#125	—	2	2	no	—
526	#125	—	2	2	no	—
527	#123	—	2	8	no	—
528	C₂²⋊Q₈	—	2	2	no	—
529	C₂²⋊Q₈	—	4	1	no	—
530	#121	—	2	8	no	—
531	#121	—	2	2	no	—
532	#121	—	2	2	no	—
533	#121	—	2	2	no	—
534	#121	—	2	2	no	—
535	#121	—	4	1	no	—
536	#121	D₄×C₈₉	1	4	yes	complemented
537	C₄×D₄	—	2	8	no	—
538	C₄×D₄	—	2	2	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	2	2	no	—
541	C₄×D₄	—	2	2	no	—
542	#117	—	2	2	no	—
543	#117	—	2	2	no	—
544	C₂×C₄⋊C₄	—	2	1	no	—
545	C₂×C₄⋊C₄	—	2	2	no	—
546	C₂×C₄⋊C₄	—	2	1	no	—
547	C₂×C₄⋊C₄	—	2	1	no	—
548	C₂×C₄⋊C₄	—	2	1	no	—
549	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
550	C₂×C₄⋊C₄	D₄×C₈₉	1	4	yes	complemented
551	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
557	C₂×C₂²⋊C₄	—	2	1	no	—
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	D₄×C₈₉	1	1	yes	characteristic
566	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
567	C₂×C₄²	—	2	1	no	—
568	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
569	#103	—	2	2	no	—
570	#103	—	2	2	no	—
571	#103	—	2	2	no	—
572	#102	—	2	2	no	—
573	#102	—	2	2	no	—
574	#102	—	2	2	no	—
575	#102	—	4	1	no	—
576	#102	—	4	1	no	—
577	C₂²⋊C₈	—	2	2	no	—
578	C₂²⋊C₈	—	4	1	no	—
579	C₂²⋊C₈	—	4	1	no	—
580	#95	—	2	1	no	—
581	#95	—	2	1	no	—
582	#95	—	2	1	no	—
583	C₂⁴	—	2	1	no	—
584	C₂⁴	—	2	1	no	—
585	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
586	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
587	#41	—	2	8	no	—
588	#41	—	4	4	no	—
589	#41	—	4	4	no	—
590	#41	—	4	4	no	—
591	C₂×Q₈	—	2	1	no	—
592	C₂×Q₈	—	2	1	no	—
593	C₂×Q₈	—	2	1	no	—
594	C₂×Q₈	—	2	1	no	—
595	C₂×Q₈	—	2	1	no	—
596	C₂×Q₈	#41×C₈₉	1	2	yes	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	2	1	no	—
604	C₂×D₄	—	2	1	no	—
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	—	2	1	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	2	1	no	—
609	C₂×D₄	—	2	1	no	—
610	C₂×D₄	—	4	1	no	—
611	C₂×D₄	—	4	1	no	—
612	C₂×D₄	—	4	2	no	—
613	C₂×D₄	—	4	2	no	—
614	C₂×D₄	—	4	2	no	—
615	C₂×D₄	—	4	2	no	—
616	C₂×D₄	—	4	2	no	—
617	C₂×D₄	—	4	2	no	—
618	C₂×D₄	—	4	2	no	—
619	C₂×D₄	—	8	1	no	—
620	C₂×D₄	—	8	1	no	—
621	C₂×D₄	—	8	1	no	—
622	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
623	C₂×D₄	#41×C₈₉	1	2	yes	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	4	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	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	4	2	no	—
643	C₂²×C₄	—	4	2	no	—
644	C₂²×C₄	—	4	2	no	—
645	C₂²×C₄	—	8	1	no	—
646	C₂²×C₄	—	8	1	no	—
647	C₂²×C₄	—	8	1	no	—
648	C₂²×C₄	—	8	1	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	2	yes	—
654	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
656	SD₁₆	—	4	4	no	—
657	D₈	—	4	4	no	—
658	M₁₆	—	4	4	no	—
659	C₂×C₈	—	2	1	no	—
660	C₂×C₈	—	2	1	no	—
661	C₂×C₈	—	2	1	no	—
662	C₂×C₈	—	2	1	no	—
663	C₂×C₈	—	2	1	no	—
664	C₂×C₈	—	2	1	no	—
665	C₂×C₈	—	2	1	no	—
666	C₂×C₈	—	2	1	no	—
667	C₂×C₈	—	2	1	no	—
668	C₂×C₈	—	2	1	no	—
669	C₂×C₈	—	2	1	no	—
670	C₂×C₈	—	2	1	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	4	2	no	—
683	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
684	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
685	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	4	2	no	—
693	C₂²⋊C₄	—	4	2	no	—
694	C₂²⋊C₄	—	4	2	no	—
695	C₂²⋊C₄	—	8	1	no	—
696	C₂²⋊C₄	—	8	1	no	—
697	C₄²	—	2	4	no	—
698	C₄²	—	2	1	no	—
699	C₄²	—	2	1	no	—
700	C₂³	—	2	1	no	—
701	C₂³	—	2	1	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	1	no	—
706	C₂³	—	2	1	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	1	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	1	no	—
712	C₂³	—	2	1	no	—
713	C₂³	—	2	1	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	4	1	no	—
716	C₂³	—	4	1	no	—
717	C₂³	—	4	1	no	—
718	C₂³	—	4	1	no	—
719	C₂³	—	4	1	no	—
720	C₂³	—	4	1	no	—
721	C₂³	—	4	1	no	—
722	C₂³	—	4	1	no	—
723	C₂³	—	4	1	no	—
724	C₂³	—	4	1	no	—
725	C₂³	—	4	1	no	—
726	C₂³	—	4	1	no	—
727	C₂³	#120×C₈₉	1	2	yes	—
728	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
729	Q₈	—	2	2	no	—
730	Q₈	—	2	2	no	—
731	Q₈	—	4	1	no	—
732	Q₈	—	4	1	no	—
733	D₄	—	2	2	no	—
734	D₄	—	2	2	no	—
735	D₄	—	2	2	no	—
736	D₄	—	2	2	no	—
737	D₄	—	4	4	no	—
738	D₄	—	4	8	no	—
739	D₄	—	4	8	no	—
740	D₄	—	4	1	no	—
741	D₄	—	4	1	no	—
742	D₄	—	4	1	no	—
743	D₄	—	4	1	no	—
744	D₄	—	8	4	no	—
745	D₄	—	8	4	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	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	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	4	8	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	—	4	1	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	8	4	no	—
785	C₂×C₄	—	8	4	no	—
786	C₂×C₄	#120×C₈₉	1	2	yes	—
787	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
788	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
789	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
790	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
791	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
792	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
793	C₈	—	4	1	no	—
794	C₈	—	4	1	no	—
795	C₈	—	4	1	no	—
796	C₈	—	4	1	no	—
797	C₂²	—	2	2	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	4	1	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	4	1	no	—
803	C₂²	—	4	1	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	1	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	1	no	—
814	C₂²	—	4	1	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	1	no	—
817	C₂²	—	8	1	no	—
818	C₂²	—	8	1	no	—
819	C₂²	—	8	1	no	—
820	C₂²	—	8	1	no	—
821	C₂²	—	8	1	no	—
822	C₂²	—	8	1	no	—
823	C₂²	—	8	1	no	—
824	C₂²	—	8	1	no	—
825	C₂²	C₂×#120×C₈₉	1	1	yes	characteristic
826	C₂²	#546×C₈₉	1	1	yes	characteristic
827	C₂²	#546×C₈₉	1	1	yes	characteristic
828	C₂²	#575×C₈₉	1	1	yes	characteristic
829	C₂²	#575×C₈₉	1	1	yes	characteristic
830	C₂²	#576×C₈₉	1	1	yes	characteristic
831	C₂²	#577×C₈₉	1	1	yes	characteristic
832	C₄	—	2	2	no	—
833	C₄	—	4	1	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	1	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	8	1	no	—
841	C₄	—	8	1	no	—
842	C₄	#525×C₈₉	1	1	yes	characteristic
843	C₄	#535×C₈₉	1	1	yes	characteristic
844	C₄	#546×C₈₉	1	1	yes	characteristic
845	C₄	#546×C₈₉	1	1	yes	characteristic
846	C₂	—	4	2	no	—
847	C₂	—	8	1	no	—
848	C₂	—	8	2	no	—
849	C₂	—	8	2	no	—
850	C₂	C₈₉×#2404	1	1	yes	characteristic
851	C₂	C₈₉×#3005	1	1	yes	characteristic
852	C₂	C₈₉×#3012	1	1	yes	characteristic
853	C₂	C₈₉×#3307	1	1	yes	characteristic
854	C₂	C₈₉×#3309	1	1	yes	characteristic
855	C₂	C₈₉×#3322	1	1	yes	characteristic
856	C₂	C₈₉×#3326	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×#553×C₈₉	C₂	semidirect
2. C₂×#449×C₈₉	C₂	semidirect
3. C₂×#417×C₈₉	C₂	semidirect
4. C₈₉×#2407	C₂	semidirect
5. C₈₉×#2026	C₂	semidirect
6. C₈₉×#2025	C₂	semidirect
7. C₈₉×#2000	C₂	semidirect
8. C₈₉×#1999	C₂	semidirect
9. C₈₉×#1895	C₂	semidirect
10. C₈₉×#1879	C₂	semidirect
11. C₈₉×#1877	C₂	semidirect
12. C₈₉×#1875	C₂	semidirect
13. C₈₉×#1873	C₂	semidirect
14. C₈₉×#1870	C₂	semidirect
15. C₈₉×#1823	C₂	semidirect
107. #121×C₈₉	D₄	semidirect
121. C₂×C₄⋊C₄×C₈₉	D₄	semidirect
417. #23975	C₈₉	direct (N × H)
429. C₂×#553	C₂×C₈₉	semidirect
430. C₂×#449	C₂×C₈₉	semidirect
431. C₂×#417	C₂×C₈₉	semidirect
432. #2407	C₂×C₈₉	semidirect
433. #2026	C₂×C₈₉	semidirect
434. #2025	C₂×C₈₉	semidirect
435. #2000	C₂×C₈₉	semidirect
436. #1999	C₂×C₈₉	semidirect
437. #1895	C₂×C₈₉	semidirect
438. #1879	C₂×C₈₉	semidirect
439. #1877	C₂×C₈₉	semidirect
440. #1875	C₂×C₈₉	semidirect
441. #1873	C₂×C₈₉	semidirect
442. #1870	C₂×C₈₉	semidirect
443. #1823	C₂×C₈₉	semidirect
444. C₈₉	#23975	direct (N × H)
536. #121	D₄×C₈₉	semidirect
550. C₂×C₄⋊C₄	D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#553×C₈₉	2
C₂×#449×C₈₉	2
C₂×#417×C₈₉	2
C₈₉×#2407	2
C₈₉×#2026	2
C₈₉×#2025	2
C₈₉×#2000	2
C₈₉×#1999	2
C₈₉×#1895	2
C₈₉×#1879	2
C₈₉×#1877	2
C₈₉×#1875	2
C₈₉×#1873	2
C₈₉×#1870	2
C₈₉×#1823	2
#23975	89

Subgroups — C89×#23975 #36401823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#23975 #36401823