Subgroups — C₈₉×#22846 #36400694

Order 22784.

1320 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#435×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₈×D₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#407×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₂²⋊C₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#120×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₈₉×#1955	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1924	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1923	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1870	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1869	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1869	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1851	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1850	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1753	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1752	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×#120×C₈₉	C₄	1	1	yes	characteristic
23	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
26	#435×C₈₉	—	2	4	no	—
27	C₈×D₄×C₈₉	—	2	4	no	—
28	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
31	#407×C₈₉	—	2	4	no	—
32	C₂×C₂²⋊C₈×C₈₉	—	2	4	no	—
33	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
44	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
47	#386×C₈₉	C₄	1	1	yes	characteristic
48	#386×C₈₉	C₄	1	1	yes	characteristic
49	#386×C₈₉	C₄	1	1	yes	characteristic
50	#385×C₈₉	C₄	1	1	yes	characteristic
51	#385×C₈₉	C₄	1	1	yes	characteristic
52	#385×C₈₉	C₄	1	1	yes	characteristic
53	#379×C₈₉	C₄	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
55	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
57	#336×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#336×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#336×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#336×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	#336×C₈₉	C₂²	1	1	yes	characteristic, complemented
62	#336×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	C₂⁵×C₈₉	C₂×C₄	1	1	yes	characteristic
64	C₂²×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
65	C₂²×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
66	C₂²×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
67	C₂³×C₄×C₈₉	—	2	2	no	—
68	C₂³×C₄×C₈₉	—	2	2	no	—
69	C₂³×C₄×C₈₉	—	2	2	no	—
70	C₂³×C₄×C₈₉	—	2	2	no	—
71	C₂³×C₄×C₈₉	—	4	1	no	—
72	C₂³×C₄×C₈₉	—	4	1	no	—
73	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
74	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
75	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
76	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
80	C₂×M₁₆×C₈₉	—	2	2	no	—
81	C₂×M₁₆×C₈₉	—	2	2	no	—
82	C₂×M₁₆×C₈₉	—	2	2	no	—
83	C₂×M₁₆×C₈₉	—	2	2	no	—
84	C₂×M₁₆×C₈₉	—	4	1	no	—
85	C₂×M₁₆×C₈₉	—	4	1	no	—
86	C₂²×C₈×C₈₉	—	2	2	no	—
87	C₂²×C₈×C₈₉	—	2	2	no	—
88	C₂²×C₈×C₈₉	—	2	2	no	—
89	C₂²×C₈×C₈₉	—	2	2	no	—
90	C₂²×C₈×C₈₉	—	2	2	no	—
91	C₂²×C₈×C₈₉	—	2	2	no	—
92	C₂²×C₈×C₈₉	—	4	1	no	—
93	C₂²×C₈×C₈₉	—	4	1	no	—
94	C₂²×C₈×C₈₉	—	4	1	no	—
95	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
103	#120×C₈₉	—	2	4	no	—
104	C₄×D₄×C₈₉	—	2	2	no	—
105	C₄×D₄×C₈₉	—	2	2	no	—
106	C₄×D₄×C₈₉	—	2	2	no	—
107	C₄×D₄×C₈₉	—	2	2	no	—
108	C₄×D₄×C₈₉	—	4	1	no	—
109	C₄×D₄×C₈₉	—	4	1	no	—
110	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
113	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
115	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
121	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
123	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
124	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
125	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
128	C₄⋊C₈×C₈₉	—	2	2	no	—
129	C₄⋊C₈×C₈₉	—	2	2	no	—
130	C₄⋊C₈×C₈₉	—	4	1	no	—
131	C₂²⋊C₈×C₈₉	—	2	2	no	—
132	C₂²⋊C₈×C₈₉	—	2	2	no	—
133	C₂²⋊C₈×C₈₉	—	2	2	no	—
134	C₂²⋊C₈×C₈₉	—	2	2	no	—
135	C₂²⋊C₈×C₈₉	—	2	2	no	—
136	C₂²⋊C₈×C₈₉	—	2	2	no	—
137	C₂²⋊C₈×C₈₉	—	2	2	no	—
138	C₂²⋊C₈×C₈₉	—	2	2	no	—
139	C₂²⋊C₈×C₈₉	—	4	1	no	—
140	C₂²⋊C₈×C₈₉	D₄	1	4	yes	complemented
141	C₂²⋊C₈×C₈₉	D₄	1	4	yes	complemented
142	#97×C₈₉	—	2	2	no	—
143	#97×C₈₉	—	4	1	no	—
144	C₄×C₈×C₈₉	—	2	2	no	—
145	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
146	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
147	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
148	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
149	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
150	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
151	C₂⁴×C₈₉	—	2	2	no	—
152	C₂⁴×C₈₉	—	2	2	no	—
153	C₂⁴×C₈₉	—	2	2	no	—
154	C₂⁴×C₈₉	—	2	2	no	—
155	C₂⁴×C₈₉	—	2	2	no	—
156	C₂⁴×C₈₉	—	4	1	no	—
157	C₂⁴×C₈₉	—	4	1	no	—
158	C₂⁴×C₈₉	C₂²×C₄	1	1	yes	characteristic
159	C₂⁴×C₈₉	C₂²×C₄	1	1	yes	characteristic
160	C₂⁴×C₈₉	C₂²×C₄	1	1	yes	characteristic
161	C₂⁴×C₈₉	C₂²×C₄	1	1	yes	characteristic
162	C₂×D₄×C₈₉	—	2	2	no	—
163	C₂×D₄×C₈₉	—	2	2	no	—
164	C₂×D₄×C₈₉	—	2	2	no	—
165	C₂×D₄×C₈₉	—	2	2	no	—
166	C₂×D₄×C₈₉	—	2	2	no	—
167	C₂×D₄×C₈₉	—	2	2	no	—
168	C₂×D₄×C₈₉	—	4	1	no	—
169	C₂×D₄×C₈₉	—	4	1	no	—
170	C₂×D₄×C₈₉	M₁₆	1	4	yes	complemented
171	C₂²×C₄×C₈₉	—	2	1	no	—
172	C₂²×C₄×C₈₉	—	2	1	no	—
173	C₂²×C₄×C₈₉	—	2	1	no	—
174	C₂²×C₄×C₈₉	—	2	1	no	—
175	C₂²×C₄×C₈₉	—	2	1	no	—
176	C₂²×C₄×C₈₉	—	2	1	no	—
177	C₂²×C₄×C₈₉	—	2	1	no	—
178	C₂²×C₄×C₈₉	—	2	1	no	—
179	C₂²×C₄×C₈₉	—	2	2	no	—
180	C₂²×C₄×C₈₉	—	2	2	no	—
181	C₂²×C₄×C₈₉	—	2	2	no	—
182	C₂²×C₄×C₈₉	—	2	2	no	—
183	C₂²×C₄×C₈₉	—	2	2	no	—
184	C₂²×C₄×C₈₉	—	2	2	no	—
185	C₂²×C₄×C₈₉	—	2	1	no	—
186	C₂²×C₄×C₈₉	—	2	1	no	—
187	C₂²×C₄×C₈₉	—	2	1	no	—
188	C₂²×C₄×C₈₉	—	2	1	no	—
189	C₂²×C₄×C₈₉	—	2	1	no	—
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	—	4	1	no	—
198	C₂²×C₄×C₈₉	—	4	1	no	—
199	C₂²×C₄×C₈₉	—	4	1	no	—
200	C₂²×C₄×C₈₉	—	4	4	no	—
201	C₂²×C₄×C₈₉	—	4	4	no	—
202	C₂²×C₄×C₈₉	—	4	4	no	—
203	C₂²×C₄×C₈₉	—	4	4	no	—
204	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
206	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
207	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
208	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
209	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
210	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
211	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
212	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
213	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
214	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
215	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
216	C₂²×C₄×C₈₉	#41	1	2	yes	—
217	C₂²×C₄×C₈₉	#41	1	2	yes	—
218	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
219	M₁₆×C₈₉	—	4	4	no	—
220	M₁₆×C₈₉	—	4	4	no	—
221	C₂×C₈×C₈₉	—	2	1	no	—
222	C₂×C₈×C₈₉	—	2	1	no	—
223	C₂×C₈×C₈₉	—	2	1	no	—
224	C₂×C₈×C₈₉	—	2	1	no	—
225	C₂×C₈×C₈₉	—	2	1	no	—
226	C₂×C₈×C₈₉	—	2	1	no	—
227	C₂×C₈×C₈₉	—	2	1	no	—
228	C₂×C₈×C₈₉	—	2	1	no	—
229	C₂×C₈×C₈₉	—	2	1	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	—	4	4	no	—
242	C₂×C₈×C₈₉	—	4	4	no	—
243	C₂×C₈×C₈₉	—	4	4	no	—
244	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
245	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
246	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
247	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
248	C₄⋊C₄×C₈₉	—	2	2	no	—
249	C₄⋊C₄×C₈₉	—	2	2	no	—
250	C₄⋊C₄×C₈₉	—	4	1	no	—
251	C₂²⋊C₄×C₈₉	—	2	2	no	—
252	C₂²⋊C₄×C₈₉	—	2	2	no	—
253	C₂²⋊C₄×C₈₉	—	2	2	no	—
254	C₂²⋊C₄×C₈₉	—	2	2	no	—
255	C₂²⋊C₄×C₈₉	—	2	2	no	—
256	C₂²⋊C₄×C₈₉	—	2	2	no	—
257	C₂²⋊C₄×C₈₉	—	2	2	no	—
258	C₂²⋊C₄×C₈₉	—	2	2	no	—
259	C₂²⋊C₄×C₈₉	—	2	2	no	—
260	C₂²⋊C₄×C₈₉	—	4	1	no	—
261	C₂²⋊C₄×C₈₉	—	4	1	no	—
262	C₂²⋊C₄×C₈₉	—	4	1	no	—
263	C₄²×C₈₉	—	2	1	no	—
264	C₄²×C₈₉	—	2	1	no	—
265	C₄²×C₈₉	—	2	1	no	—
266	C₄²×C₈₉	—	2	1	no	—
267	C₄²×C₈₉	—	2	1	no	—
268	C₄²×C₈₉	—	2	1	no	—
269	C₂³×C₈₉	—	2	1	no	—
270	C₂³×C₈₉	—	2	1	no	—
271	C₂³×C₈₉	—	2	1	no	—
272	C₂³×C₈₉	—	2	1	no	—
273	C₂³×C₈₉	—	2	8	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	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	—	4	4	no	—
293	C₂³×C₈₉	—	4	4	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	C₄×D₄	1	2	yes	—
299	C₂³×C₈₉	C₄×D₄	1	2	yes	—
300	C₂³×C₈₉	C₂×M₁₆	1	2	yes	—
301	C₂³×C₈₉	C₂×M₁₆	1	2	yes	—
302	C₂³×C₈₉	#131	1	2	yes	—
303	C₂³×C₈₉	#131	1	2	yes	—
304	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
305	D₄×C₈₉	—	2	8	no	—
306	D₄×C₈₉	—	4	4	no	—
307	D₄×C₈₉	—	4	4	no	—
308	C₂×C₄×C₈₉	—	2	1	no	—
309	C₂×C₄×C₈₉	—	2	1	no	—
310	C₂×C₄×C₈₉	—	2	1	no	—
311	C₂×C₄×C₈₉	—	2	1	no	—
312	C₂×C₄×C₈₉	—	2	1	no	—
313	C₂×C₄×C₈₉	—	2	1	no	—
314	C₂×C₄×C₈₉	—	2	2	no	—
315	C₂×C₄×C₈₉	—	2	2	no	—
316	C₂×C₄×C₈₉	—	2	2	no	—
317	C₂×C₄×C₈₉	—	2	2	no	—
318	C₂×C₄×C₈₉	—	2	2	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	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	1	no	—
327	C₂×C₄×C₈₉	—	2	1	no	—
328	C₂×C₄×C₈₉	—	2	1	no	—
329	C₂×C₄×C₈₉	—	2	1	no	—
330	C₂×C₄×C₈₉	—	2	1	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	—	2	1	no	—
337	C₂×C₄×C₈₉	—	2	1	no	—
338	C₂×C₄×C₈₉	—	2	1	no	—
339	C₂×C₄×C₈₉	—	2	1	no	—
340	C₂×C₄×C₈₉	—	2	1	no	—
341	C₂×C₄×C₈₉	—	2	1	no	—
342	C₂×C₄×C₈₉	—	2	1	no	—
343	C₂×C₄×C₈₉	—	4	4	no	—
344	C₂×C₄×C₈₉	—	4	4	no	—
345	C₂×C₄×C₈₉	—	4	4	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	C₄×D₄	1	2	yes	—
355	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
356	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
357	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
360	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
361	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
362	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
363	C₈×C₈₉	—	2	2	no	—
364	C₈×C₈₉	—	2	2	no	—
365	C₈×C₈₉	—	2	2	no	—
366	C₈×C₈₉	—	2	2	no	—
367	C₈×C₈₉	—	4	1	no	—
368	C₈×C₈₉	—	4	1	no	—
369	C₈×C₈₉	—	4	1	no	—
370	C₈×C₈₉	—	4	1	no	—
371	C₂²×C₈₉	—	2	2	no	—
372	C₂²×C₈₉	—	2	2	no	—
373	C₂²×C₈₉	—	2	2	no	—
374	C₂²×C₈₉	—	2	2	no	—
375	C₂²×C₈₉	—	2	2	no	—
376	C₂²×C₈₉	—	2	2	no	—
377	C₂²×C₈₉	—	2	2	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	—	4	16	no	—
387	C₂²×C₈₉	—	4	1	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	#435	1	4	yes	complemented
400	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
401	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
402	C₂²×C₈₉	#518	1	1	yes	characteristic
403	C₂²×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
404	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
405	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
406	C₂²×C₈₉	#568	1	1	yes	characteristic
407	C₄×C₈₉	—	2	2	no	—
408	C₄×C₈₉	—	2	2	no	—
409	C₄×C₈₉	—	2	2	no	—
410	C₄×C₈₉	—	4	1	no	—
411	C₄×C₈₉	—	4	1	no	—
412	C₄×C₈₉	—	4	1	no	—
413	C₄×C₈₉	—	4	1	no	—
414	C₄×C₈₉	—	4	1	no	—
415	C₄×C₈₉	—	4	1	no	—
416	C₄×C₈₉	—	4	1	no	—
417	C₄×C₈₉	D₄²	1	1	yes	characteristic
418	C₄×C₈₉	#546	1	1	yes	characteristic
419	C₄×C₈₉	#546	1	1	yes	characteristic
420	C₄×C₈₉	#551	1	1	yes	characteristic
421	#22846	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
422	C₂×C₈₉	—	2	4	no	—
423	C₂×C₈₉	—	4	2	no	—
424	C₂×C₈₉	—	4	2	no	—
425	C₂×C₈₉	—	4	2	no	—
426	C₂×C₈₉	#2358	1	1	yes	characteristic
427	C₂×C₈₉	C₂×#435	1	1	yes	characteristic
428	C₂×C₈₉	#2929	1	1	yes	characteristic
429	C₂×C₈₉	#2933	1	1	yes	characteristic
430	C₂×C₈₉	D₄×M₁₆	1	1	yes	characteristic
431	C₂×C₈₉	#2974	1	1	yes	characteristic
432	C₂×C₈₉	#2976	1	1	yes	characteristic
433	C₂×#435	C₂×C₈₉	1	1	yes	characteristic, complemented
434	C₂×C₈×D₄	C₂×C₈₉	1	1	yes	characteristic, complemented
435	C₂×#407	C₂×C₈₉	1	1	yes	characteristic, complemented
436	C₂²×C₂²⋊C₈	C₂×C₈₉	1	1	yes	characteristic, complemented
437	C₄×#120	C₂×C₈₉	1	1	yes	characteristic
438	#1955	C₂×C₈₉	1	1	yes	characteristic, complemented
439	#1924	C₂×C₈₉	1	1	yes	characteristic, complemented
440	#1923	C₂×C₈₉	1	1	yes	characteristic, complemented
441	#1870	C₂×C₈₉	1	1	yes	characteristic, complemented
442	#1869	C₂×C₈₉	1	1	yes	characteristic, complemented
443	#1869	C₂×C₈₉	1	1	yes	characteristic, complemented
444	#1851	C₂×C₈₉	1	1	yes	characteristic, complemented
445	#1850	C₂×C₈₉	1	1	yes	characteristic, complemented
446	#1753	C₂×C₈₉	1	1	yes	characteristic, complemented
447	#1752	C₂×C₈₉	1	1	yes	characteristic, complemented
448	C₈₉	#22846	1	1	yes	characteristic, direct product factor, Sylow
449	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
450	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
451	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
452	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
453	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
454	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
455	C₂×#120	C₄×C₈₉	1	1	yes	characteristic
456	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
457	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
458	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
459	#435	—	2	4	no	—
460	C₈×D₄	—	2	4	no	—
461	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
462	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
463	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
464	#407	—	2	4	no	—
465	C₂×C₂²⋊C₈	—	2	4	no	—
466	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
467	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
468	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
469	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
470	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
471	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
472	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
473	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
474	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
475	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
476	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
477	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic, complemented
478	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic, complemented
479	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
480	#386	C₄×C₈₉	1	1	yes	characteristic
481	#386	C₄×C₈₉	1	1	yes	characteristic
482	#386	C₄×C₈₉	1	1	yes	characteristic
483	#385	C₄×C₈₉	1	1	yes	characteristic
484	#385	C₄×C₈₉	1	1	yes	characteristic
485	#385	C₄×C₈₉	1	1	yes	characteristic
486	#379	C₄×C₈₉	1	1	yes	characteristic
487	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
488	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
489	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
490	#336	C₂²×C₈₉	1	1	yes	characteristic, complemented
491	#336	C₂²×C₈₉	1	1	yes	characteristic, complemented
492	#336	C₂²×C₈₉	1	1	yes	characteristic, complemented
493	#336	C₂²×C₈₉	1	1	yes	characteristic, complemented
494	#336	C₂²×C₈₉	1	1	yes	characteristic, complemented
495	#336	C₂²×C₈₉	1	1	yes	characteristic, complemented
496	C₂⁵	C₂×C₄×C₈₉	1	1	yes	characteristic
497	C₂²×D₄	C₂×C₄×C₈₉	1	1	yes	characteristic
498	C₂²×D₄	C₂×C₄×C₈₉	1	1	yes	characteristic
499	C₂²×D₄	C₂×C₄×C₈₉	1	1	yes	characteristic
500	C₂³×C₄	—	2	2	no	—
501	C₂³×C₄	—	2	2	no	—
502	C₂³×C₄	—	2	2	no	—
503	C₂³×C₄	—	2	2	no	—
504	C₂³×C₄	—	4	1	no	—
505	C₂³×C₄	—	4	1	no	—
506	C₂³×C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
507	C₂³×C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
508	C₂³×C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
513	C₂×M₁₆	—	2	2	no	—
514	C₂×M₁₆	—	2	2	no	—
515	C₂×M₁₆	—	2	2	no	—
516	C₂×M₁₆	—	2	2	no	—
517	C₂×M₁₆	—	4	1	no	—
518	C₂×M₁₆	—	4	1	no	—
519	C₂²×C₈	—	2	2	no	—
520	C₂²×C₈	—	2	2	no	—
521	C₂²×C₈	—	2	2	no	—
522	C₂²×C₈	—	2	2	no	—
523	C₂²×C₈	—	2	2	no	—
524	C₂²×C₈	—	2	2	no	—
525	C₂²×C₈	—	4	1	no	—
526	C₂²×C₈	—	4	1	no	—
527	C₂²×C₈	—	4	1	no	—
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	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
533	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
534	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
535	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
536	#120	—	2	4	no	—
537	C₄×D₄	—	2	2	no	—
538	C₄×D₄	—	2	2	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	2	2	no	—
541	C₄×D₄	—	4	1	no	—
542	C₄×D₄	—	4	1	no	—
543	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
547	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
548	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
549	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
550	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
551	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
552	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
553	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
554	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
555	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
558	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
559	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
561	C₄⋊C₈	—	2	2	no	—
562	C₄⋊C₈	—	2	2	no	—
563	C₄⋊C₈	—	4	1	no	—
564	C₂²⋊C₈	—	2	2	no	—
565	C₂²⋊C₈	—	2	2	no	—
566	C₂²⋊C₈	—	2	2	no	—
567	C₂²⋊C₈	—	2	2	no	—
568	C₂²⋊C₈	—	2	2	no	—
569	C₂²⋊C₈	—	2	2	no	—
570	C₂²⋊C₈	—	2	2	no	—
571	C₂²⋊C₈	—	2	2	no	—
572	C₂²⋊C₈	—	4	1	no	—
573	C₂²⋊C₈	D₄×C₈₉	1	4	yes	complemented
574	C₂²⋊C₈	D₄×C₈₉	1	4	yes	complemented
575	#97	—	2	2	no	—
576	#97	—	4	1	no	—
577	C₄×C₈	—	2	2	no	—
578	#95	C₂×C₄×C₈₉	1	1	yes	characteristic
579	#95	C₂×C₄×C₈₉	1	1	yes	characteristic
580	#95	C₂×C₄×C₈₉	1	1	yes	characteristic
581	#95	C₂×C₄×C₈₉	1	1	yes	characteristic
582	#95	C₂×C₄×C₈₉	1	1	yes	characteristic
583	#95	C₂×C₄×C₈₉	1	1	yes	characteristic
584	C₂⁴	—	2	2	no	—
585	C₂⁴	—	2	2	no	—
586	C₂⁴	—	2	2	no	—
587	C₂⁴	—	2	2	no	—
588	C₂⁴	—	2	2	no	—
589	C₂⁴	—	4	1	no	—
590	C₂⁴	—	4	1	no	—
591	C₂⁴	C₂²×C₄×C₈₉	1	1	yes	characteristic
592	C₂⁴	C₂²×C₄×C₈₉	1	1	yes	characteristic
593	C₂⁴	C₂²×C₄×C₈₉	1	1	yes	characteristic
594	C₂⁴	C₂²×C₄×C₈₉	1	1	yes	characteristic
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	4	1	no	—
602	C₂×D₄	—	4	1	no	—
603	C₂×D₄	M₁₆×C₈₉	1	4	yes	complemented
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
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	—	4	1	no	—
631	C₂²×C₄	—	4	1	no	—
632	C₂²×C₄	—	4	1	no	—
633	C₂²×C₄	—	4	4	no	—
634	C₂²×C₄	—	4	4	no	—
635	C₂²×C₄	—	4	4	no	—
636	C₂²×C₄	—	4	4	no	—
637	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
638	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
639	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
640	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
641	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
642	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
643	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
644	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
645	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
646	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
647	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
648	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
649	C₂²×C₄	#41×C₈₉	1	2	yes	—
650	C₂²×C₄	#41×C₈₉	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
652	M₁₆	—	4	4	no	—
653	M₁₆	—	4	4	no	—
654	C₂×C₈	—	2	1	no	—
655	C₂×C₈	—	2	1	no	—
656	C₂×C₈	—	2	1	no	—
657	C₂×C₈	—	2	1	no	—
658	C₂×C₈	—	2	1	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	C₂×C₈	—	2	1	no	—
672	C₂×C₈	—	2	1	no	—
673	C₂×C₈	—	2	1	no	—
674	C₂×C₈	—	4	4	no	—
675	C₂×C₈	—	4	4	no	—
676	C₂×C₈	—	4	4	no	—
677	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
678	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
679	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
680	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	4	1	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	2	2	no	—
687	C₂²⋊C₄	—	2	2	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	4	1	no	—
694	C₂²⋊C₄	—	4	1	no	—
695	C₂²⋊C₄	—	4	1	no	—
696	C₄²	—	2	1	no	—
697	C₄²	—	2	1	no	—
698	C₄²	—	2	1	no	—
699	C₄²	—	2	1	no	—
700	C₄²	—	2	1	no	—
701	C₄²	—	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	8	no	—
707	C₂³	—	2	1	no	—
708	C₂³	—	2	1	no	—
709	C₂³	—	2	1	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	—	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	—	4	4	no	—
726	C₂³	—	4	4	no	—
727	C₂³	—	4	4	no	—
728	C₂³	—	4	4	no	—
729	C₂³	—	4	4	no	—
730	C₂³	—	4	4	no	—
731	C₂³	C₄×D₄×C₈₉	1	2	yes	—
732	C₂³	C₄×D₄×C₈₉	1	2	yes	—
733	C₂³	C₂×M₁₆×C₈₉	1	2	yes	—
734	C₂³	C₂×M₁₆×C₈₉	1	2	yes	—
735	C₂³	#131×C₈₉	1	2	yes	—
736	C₂³	#131×C₈₉	1	2	yes	—
737	C₂³	C₂³×C₄×C₈₉	1	1	yes	characteristic
738	D₄	—	2	8	no	—
739	D₄	—	4	4	no	—
740	D₄	—	4	4	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	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	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	4	4	no	—
777	C₂×C₄	—	4	4	no	—
778	C₂×C₄	—	4	4	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	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	C₄×D₄×C₈₉	1	2	yes	—
788	C₂×C₄	C₄×D₄×C₈₉	1	2	yes	—
789	C₂×C₄	C₂×M₁₆×C₈₉	1	2	yes	—
790	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
791	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
792	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
793	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
794	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
795	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
796	C₈	—	2	2	no	—
797	C₈	—	2	2	no	—
798	C₈	—	2	2	no	—
799	C₈	—	2	2	no	—
800	C₈	—	4	1	no	—
801	C₈	—	4	1	no	—
802	C₈	—	4	1	no	—
803	C₈	—	4	1	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	2	2	no	—
806	C₂²	—	2	2	no	—
807	C₂²	—	2	2	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	2	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	4	16	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	1	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	#435×C₈₉	1	4	yes	complemented
833	C₂²	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
834	C₂²	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
835	C₂²	#518×C₈₉	1	1	yes	characteristic
836	C₂²	C₂²×M₁₆×C₈₉	1	1	yes	characteristic
837	C₂²	C₂×#131×C₈₉	1	1	yes	characteristic
838	C₂²	C₂×#131×C₈₉	1	1	yes	characteristic
839	C₂²	#568×C₈₉	1	1	yes	characteristic
840	C₄	—	2	2	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	4	1	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	1	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	1	no	—
850	C₄	D₄²×C₈₉	1	1	yes	characteristic
851	C₄	#546×C₈₉	1	1	yes	characteristic
852	C₄	#546×C₈₉	1	1	yes	characteristic
853	C₄	#551×C₈₉	1	1	yes	characteristic
854	C₂	—	2	4	no	—
855	C₂	—	4	2	no	—
856	C₂	—	4	2	no	—
857	C₂	—	4	2	no	—
858	C₂	C₈₉×#2358	1	1	yes	characteristic
859	C₂	C₂×#435×C₈₉	1	1	yes	characteristic
860	C₂	C₈₉×#2929	1	1	yes	characteristic
861	C₂	C₈₉×#2933	1	1	yes	characteristic
862	C₂	D₄×M₁₆×C₈₉	1	1	yes	characteristic
863	C₂	C₈₉×#2974	1	1	yes	characteristic
864	C₂	C₈₉×#2976	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₈₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₈₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
socle	C₂³×C₈₉	C₂³×C₄
prime radical	C₂×#120×C₈₉	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#435×C₈₉	C₂	semidirect
2. C₂×C₈×D₄×C₈₉	C₂	semidirect
3. C₂×#407×C₈₉	C₂	semidirect
4. C₂²×C₂²⋊C₈×C₈₉	C₂	semidirect
6. C₈₉×#1955	C₂	semidirect
7. C₈₉×#1924	C₂	semidirect
8. C₈₉×#1923	C₂	semidirect
9. C₈₉×#1870	C₂	semidirect
10. C₈₉×#1869	C₂	semidirect
11. C₈₉×#1869	C₂	semidirect
12. C₈₉×#1851	C₂	semidirect
13. C₈₉×#1850	C₂	semidirect
14. C₈₉×#1753	C₂	semidirect
15. C₈₉×#1752	C₂	semidirect
21. C₂³×C₈×C₈₉	C₂²	semidirect
28. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
29. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
30. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
41. C₂×C₂²⋊C₈×C₈₉	C₂²	semidirect
42. C₂×C₂²⋊C₈×C₈₉	C₂²	semidirect
43. C₂×C₂²⋊C₈×C₈₉	C₂²	semidirect
44. C₂×#97×C₈₉	C₂²	semidirect
45. C₂×#97×C₈₉	C₂²	semidirect
46. C₂×C₄×C₈×C₈₉	C₂²	semidirect
57. #336×C₈₉	C₂²	semidirect
58. #336×C₈₉	C₂²	semidirect
59. #336×C₈₉	C₂²	semidirect
60. #336×C₈₉	C₂²	semidirect
61. #336×C₈₉	C₂²	semidirect
62. #336×C₈₉	C₂²	semidirect
140. C₂²⋊C₈×C₈₉	D₄	semidirect
141. C₂²⋊C₈×C₈₉	D₄	semidirect
170. C₂×D₄×C₈₉	M₁₆	semidirect
399. C₂²×C₈₉	#435	semidirect
421. #22846	C₈₉	direct (N × H)
433. C₂×#435	C₂×C₈₉	semidirect
434. C₂×C₈×D₄	C₂×C₈₉	semidirect
435. C₂×#407	C₂×C₈₉	semidirect
436. C₂²×C₂²⋊C₈	C₂×C₈₉	semidirect
438. #1955	C₂×C₈₉	semidirect
439. #1924	C₂×C₈₉	semidirect
440. #1923	C₂×C₈₉	semidirect
441. #1870	C₂×C₈₉	semidirect
442. #1869	C₂×C₈₉	semidirect
443. #1869	C₂×C₈₉	semidirect
444. #1851	C₂×C₈₉	semidirect
445. #1850	C₂×C₈₉	semidirect
446. #1753	C₂×C₈₉	semidirect
447. #1752	C₂×C₈₉	semidirect
448. C₈₉	#22846	direct (N × H)
454. C₂³×C₈	C₂²×C₈₉	semidirect
461. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
462. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
463. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
474. C₂×C₂²⋊C₈	C₂²×C₈₉	semidirect
475. C₂×C₂²⋊C₈	C₂²×C₈₉	semidirect
476. C₂×C₂²⋊C₈	C₂²×C₈₉	semidirect
477. C₂×#97	C₂²×C₈₉	semidirect
478. C₂×#97	C₂²×C₈₉	semidirect
479. C₂×C₄×C₈	C₂²×C₈₉	semidirect
490. #336	C₂²×C₈₉	semidirect
491. #336	C₂²×C₈₉	semidirect
492. #336	C₂²×C₈₉	semidirect
493. #336	C₂²×C₈₉	semidirect
494. #336	C₂²×C₈₉	semidirect
495. #336	C₂²×C₈₉	semidirect
573. C₂²⋊C₈	D₄×C₈₉	semidirect
574. C₂²⋊C₈	D₄×C₈₉	semidirect
603. C₂×D₄	M₁₆×C₈₉	semidirect
832. C₂²	#435×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#435×C₈₉	2
C₂×C₈×D₄×C₈₉	2
C₂×#407×C₈₉	2
C₂²×C₂²⋊C₈×C₈₉	2
C₄×#120×C₈₉	2
C₈₉×#1955	2
C₈₉×#1924	2
C₈₉×#1923	2
C₈₉×#1870	2
C₈₉×#1869	2
C₈₉×#1851	2
C₈₉×#1850	2
C₈₉×#1753	2
C₈₉×#1752	2
#22846	89

Subgroups — C89×#22846 #36400694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#22846 #36400694