Subgroups — C₈₉×#36581 #36414429

Order 22784.

2988 conjugacy classes of subgroups.

The subgroup lattice has 810 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	C₂³×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2847	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2847	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2591	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2579	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2504	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2487	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2481	C₂	1	4	yes	maximal, complemented
10	C₈₉×#2443	C₂	1	4	yes	maximal, complemented
11	C₈₉×#2442	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2416	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2361	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2352	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2345	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#120×C₈₉	C₂	1	2	yes	maximal, complemented
17	C₄×#120×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₈₉	C₂²	1	2	yes	—
20	#553×C₈₉	—	2	8	no	—
21	C₂×#126×C₈₉	C₂²	1	2	yes	complemented
22	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×#123×C₈₉	C₂²	1	2	yes	complemented
24	C₂×#121×C₈₉	C₂²	1	2	yes	—
25	C₂×#121×C₈₉	C₂²	1	2	yes	—
26	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#121×C₈₉	C₂²	1	4	yes	—
28	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×#120×C₈₉	C₂²	1	2	yes	—
30	C₂×#120×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
35	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
36	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₄⋊C₄×C₈₉	—	2	8	no	—
38	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
39	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
40	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
41	C₂²×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
42	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
44	#400×C₈₉	C₂²	1	4	yes	complemented
45	#400×C₈₉	C₂²	1	2	yes	complemented
46	#399×C₈₉	C₂²	1	2	yes	complemented
47	#398×C₈₉	C₂²	1	4	yes	complemented
48	#397×C₈₉	C₂²	1	4	yes	complemented
49	#396×C₈₉	C₂²	1	4	yes	complemented
50	#394×C₈₉	C₂²	1	4	yes	complemented
51	#390×C₈₉	C₂²	1	2	yes	complemented
52	#389×C₈₉	C₂²	1	2	yes	complemented
53	#389×C₈₉	C₂²	1	2	yes	complemented
54	#388×C₈₉	C₂²	1	4	yes	complemented
55	#388×C₈₉	C₂²	1	4	yes	complemented
56	#387×C₈₉	C₂²	1	4	yes	complemented
57	#387×C₈₉	C₂²	1	4	yes	complemented
58	#386×C₈₉	C₂²	1	1	yes	characteristic
59	#386×C₈₉	C₂²	1	2	yes	—
60	#386×C₈₉	C₂²	1	4	yes	—
61	#386×C₈₉	C₂²	1	2	yes	—
62	#386×C₈₉	C₂²	1	2	yes	—
63	#386×C₈₉	C₂²	1	2	yes	—
64	#386×C₈₉	C₂²	1	2	yes	—
65	#386×C₈₉	C₂²	1	4	yes	—
66	#386×C₈₉	C₂²	1	4	yes	—
67	#386×C₈₉	C₂²	1	4	yes	—
68	#385×C₈₉	C₂²	1	1	yes	characteristic
69	#385×C₈₉	C₂²	1	2	yes	—
70	#385×C₈₉	C₂²	1	4	yes	—
71	#385×C₈₉	C₂²	1	2	yes	—
72	#385×C₈₉	C₂²	1	4	yes	complemented
73	#382×C₈₉	C₂²	1	2	yes	complemented
74	#380×C₈₉	C₂²	1	2	yes	—
75	#380×C₈₉	C₂²	1	1	yes	characteristic
76	#380×C₈₉	C₂²	1	2	yes	—
77	#380×C₈₉	C₂²	1	4	yes	—
78	#380×C₈₉	C₂²	1	2	yes	complemented
79	#379×C₈₉	C₂²	1	1	yes	characteristic
80	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
84	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
85	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
89	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
90	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
92	C₂³×C₄×C₈₉	—	2	4	no	—
93	C₂³×C₄×C₈₉	—	2	8	no	—
94	C₂³×C₄×C₈₉	—	2	8	no	—
95	C₂³×C₄×C₈₉	—	4	8	no	—
96	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
99	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
100	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
101	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
104	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
105	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
106	#126×C₈₉	—	2	8	no	—
107	#125×C₈₉	—	2	4	no	—
108	#123×C₈₉	—	2	8	no	—
109	#121×C₈₉	—	2	8	no	—
110	#121×C₈₉	—	2	4	no	—
111	#121×C₈₉	—	2	8	no	—
112	#121×C₈₉	—	2	4	no	—
113	#121×C₈₉	—	4	8	no	—
114	#120×C₈₉	—	2	8	no	—
115	#120×C₈₉	—	2	4	no	—
116	C₄×D₄×C₈₉	—	2	8	no	—
117	C₄×D₄×C₈₉	—	2	4	no	—
118	C₄×D₄×C₈₉	—	2	8	no	—
119	C₄×D₄×C₈₉	—	2	4	no	—
120	C₄×D₄×C₈₉	—	4	8	no	—
121	#117×C₈₉	—	2	4	no	—
122	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
123	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
124	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
125	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
126	C₂×C₄⋊C₄×C₈₉	—	2	16	no	—
127	C₂×C₄⋊C₄×C₈₉	D₄	1	8	yes	complemented
128	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
136	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
139	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
159	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
160	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
161	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
163	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
165	#95×C₈₉	C₂³	1	4	yes	—
166	#95×C₈₉	C₂³	1	4	yes	—
167	#95×C₈₉	C₂³	1	2	yes	—
168	#95×C₈₉	C₂³	1	2	yes	—
169	#95×C₈₉	C₂³	1	4	yes	—
170	#95×C₈₉	C₂³	1	2	yes	—
171	#95×C₈₉	C₂³	1	4	yes	—
172	#95×C₈₉	C₂³	1	4	yes	—
173	#95×C₈₉	C₂³	1	2	yes	—
174	#95×C₈₉	C₂³	1	4	yes	—
175	#95×C₈₉	C₂³	1	4	yes	—
176	C₂⁴×C₈₉	—	2	2	no	—
177	C₂⁴×C₈₉	—	2	4	no	—
178	C₂⁴×C₈₉	—	2	4	no	—
179	C₂⁴×C₈₉	—	2	2	no	—
180	C₂⁴×C₈₉	#41	1	4	yes	—
181	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
182	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
183	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
184	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
185	C₂×D₄×C₈₉	—	2	4	no	—
186	C₂×D₄×C₈₉	—	2	2	no	—
187	C₂×D₄×C₈₉	—	2	4	no	—
188	C₂×D₄×C₈₉	—	2	2	no	—
189	C₂×D₄×C₈₉	—	2	4	no	—
190	C₂×D₄×C₈₉	—	2	4	no	—
191	C₂×D₄×C₈₉	—	2	8	no	—
192	C₂×D₄×C₈₉	—	2	8	no	—
193	C₂×D₄×C₈₉	—	2	8	no	—
194	C₂×D₄×C₈₉	—	2	4	no	—
195	C₂×D₄×C₈₉	—	2	2	no	—
196	C₂×D₄×C₈₉	—	2	4	no	—
197	C₂×D₄×C₈₉	—	2	2	no	—
198	C₂×D₄×C₈₉	—	2	4	no	—
199	C₂×D₄×C₈₉	—	2	4	no	—
200	C₂×D₄×C₈₉	—	4	4	no	—
201	C₂²×C₄×C₈₉	—	2	32	no	—
202	C₂²×C₄×C₈₉	—	2	2	no	—
203	C₂²×C₄×C₈₉	—	2	4	no	—
204	C₂²×C₄×C₈₉	—	2	4	no	—
205	C₂²×C₄×C₈₉	—	2	4	no	—
206	C₂²×C₄×C₈₉	—	2	4	no	—
207	C₂²×C₄×C₈₉	—	2	4	no	—
208	C₂²×C₄×C₈₉	—	2	4	no	—
209	C₂²×C₄×C₈₉	—	2	4	no	—
210	C₂²×C₄×C₈₉	—	2	4	no	—
211	C₂²×C₄×C₈₉	—	2	8	no	—
212	C₂²×C₄×C₈₉	—	2	8	no	—
213	C₂²×C₄×C₈₉	—	2	8	no	—
214	C₂²×C₄×C₈₉	—	2	8	no	—
215	C₂²×C₄×C₈₉	—	2	2	no	—
216	C₂²×C₄×C₈₉	—	2	4	no	—
217	C₂²×C₄×C₈₉	—	2	4	no	—
218	C₂²×C₄×C₈₉	—	4	4	no	—
219	C₂²×C₄×C₈₉	—	4	4	no	—
220	C₂²×C₄×C₈₉	—	4	4	no	—
221	C₂²×C₄×C₈₉	—	4	4	no	—
222	C₂²×C₄×C₈₉	—	4	4	no	—
223	C₂²×C₄×C₈₉	—	4	32	no	—
224	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
225	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
226	C₂²×C₄×C₈₉	#41	1	8	yes	—
227	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
232	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
234	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
240	C₄⋊C₄×C₈₉	—	2	8	no	—
241	C₄⋊C₄×C₈₉	—	2	8	no	—
242	C₄⋊C₄×C₈₉	—	2	4	no	—
243	C₄⋊C₄×C₈₉	—	2	4	no	—
244	C₄⋊C₄×C₈₉	—	2	2	no	—
245	C₄⋊C₄×C₈₉	—	2	4	no	—
246	C₄⋊C₄×C₈₉	—	2	2	no	—
247	C₄⋊C₄×C₈₉	—	2	4	no	—
248	C₄⋊C₄×C₈₉	—	2	4	no	—
249	C₄⋊C₄×C₈₉	—	2	4	no	—
250	C₄⋊C₄×C₈₉	—	4	4	no	—
251	C₄⋊C₄×C₈₉	—	4	4	no	—
252	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
253	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
254	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
255	C₂²⋊C₄×C₈₉	—	2	2	no	—
256	C₂²⋊C₄×C₈₉	—	2	4	no	—
257	C₂²⋊C₄×C₈₉	—	2	4	no	—
258	C₂²⋊C₄×C₈₉	—	2	2	no	—
259	C₂²⋊C₄×C₈₉	—	2	8	no	—
260	C₂²⋊C₄×C₈₉	—	2	4	no	—
261	C₂²⋊C₄×C₈₉	—	2	4	no	—
262	C₂²⋊C₄×C₈₉	—	2	2	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	—	2	2	no	—
267	C₂²⋊C₄×C₈₉	—	2	4	no	—
268	C₂²⋊C₄×C₈₉	—	2	4	no	—
269	C₂²⋊C₄×C₈₉	—	2	8	no	—
270	C₂²⋊C₄×C₈₉	—	4	4	no	—
271	C₂²⋊C₄×C₈₉	—	4	4	no	—
272	C₂²⋊C₄×C₈₉	—	4	4	no	—
273	C₄²×C₈₉	—	2	4	no	—
274	C₄²×C₈₉	—	2	2	no	—
275	C₄²×C₈₉	—	2	4	no	—
276	C₄²×C₈₉	—	4	4	no	—
277	C₂³×C₈₉	—	2	8	no	—
278	C₂³×C₈₉	—	2	8	no	—
279	C₂³×C₈₉	—	2	16	no	—
280	C₂³×C₈₉	—	2	8	no	—
281	C₂³×C₈₉	—	2	16	no	—
282	C₂³×C₈₉	—	2	2	no	—
283	C₂³×C₈₉	—	2	2	no	—
284	C₂³×C₈₉	—	2	2	no	—
285	C₂³×C₈₉	—	2	2	no	—
286	C₂³×C₈₉	—	2	2	no	—
287	C₂³×C₈₉	—	2	2	no	—
288	C₂³×C₈₉	—	2	1	no	—
289	C₂³×C₈₉	—	2	2	no	—
290	C₂³×C₈₉	—	2	2	no	—
291	C₂³×C₈₉	—	2	4	no	—
292	C₂³×C₈₉	—	2	1	no	—
293	C₂³×C₈₉	—	2	2	no	—
294	C₂³×C₈₉	—	2	4	no	—
295	C₂³×C₈₉	—	2	2	no	—
296	C₂³×C₈₉	—	2	1	no	—
297	C₂³×C₈₉	—	2	2	no	—
298	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
299	C₂³×C₈₉	C₂×#41	1	2	yes	—
300	C₂³×C₈₉	C₂×#41	1	4	yes	—
301	C₂³×C₈₉	C₂×#41	1	4	yes	—
302	C₂³×C₈₉	H(5,𝔽₂)	1	4	yes	—
303	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
304	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
305	D₄×C₈₉	—	4	8	no	—
306	D₄×C₈₉	—	4	4	no	—
307	D₄×C₈₉	—	4	8	no	—
308	D₄×C₈₉	—	4	16	no	—
309	D₄×C₈₉	—	4	4	no	—
310	D₄×C₈₉	—	8	4	no	—
311	C₂×C₄×C₈₉	—	2	16	no	—
312	C₂×C₄×C₈₉	—	2	8	no	—
313	C₂×C₄×C₈₉	—	2	2	no	—
314	C₂×C₄×C₈₉	—	2	2	no	—
315	C₂×C₄×C₈₉	—	2	2	no	—
316	C₂×C₄×C₈₉	—	2	4	no	—
317	C₂×C₄×C₈₉	—	2	4	no	—
318	C₂×C₄×C₈₉	—	2	8	no	—
319	C₂×C₄×C₈₉	—	2	16	no	—
320	C₂×C₄×C₈₉	—	2	1	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	4	no	—
325	C₂×C₄×C₈₉	—	2	2	no	—
326	C₂×C₄×C₈₉	—	2	2	no	—
327	C₂×C₄×C₈₉	—	2	2	no	—
328	C₂×C₄×C₈₉	—	2	1	no	—
329	C₂×C₄×C₈₉	—	2	2	no	—
330	C₂×C₄×C₈₉	—	2	4	no	—
331	C₂×C₄×C₈₉	—	2	2	no	—
332	C₂×C₄×C₈₉	—	2	4	no	—
333	C₂×C₄×C₈₉	—	2	2	no	—
334	C₂×C₄×C₈₉	—	2	4	no	—
335	C₂×C₄×C₈₉	—	2	2	no	—
336	C₂×C₄×C₈₉	—	2	2	no	—
337	C₂×C₄×C₈₉	—	2	4	no	—
338	C₂×C₄×C₈₉	—	2	4	no	—
339	C₂×C₄×C₈₉	—	2	2	no	—
340	C₂×C₄×C₈₉	—	2	2	no	—
341	C₂×C₄×C₈₉	—	2	1	no	—
342	C₂×C₄×C₈₉	—	4	8	no	—
343	C₂×C₄×C₈₉	—	4	16	no	—
344	C₂×C₄×C₈₉	—	4	16	no	—
345	C₂×C₄×C₈₉	—	4	8	no	—
346	C₂×C₄×C₈₉	—	4	4	no	—
347	C₂×C₄×C₈₉	—	8	4	no	—
348	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
349	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
350	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
351	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
352	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
353	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
354	C₂²×C₈₉	—	2	32	no	—
355	C₂²×C₈₉	—	2	2	no	—
356	C₂²×C₈₉	—	2	4	no	—
357	C₂²×C₈₉	—	2	4	no	—
358	C₂²×C₈₉	—	2	4	no	—
359	C₂²×C₈₉	—	2	4	no	—
360	C₂²×C₈₉	—	2	2	no	—
361	C₂²×C₈₉	—	2	4	no	—
362	C₂²×C₈₉	—	2	4	no	—
363	C₂²×C₈₉	—	2	4	no	—
364	C₂²×C₈₉	—	2	4	no	—
365	C₂²×C₈₉	—	4	1	no	—
366	C₂²×C₈₉	—	4	2	no	—
367	C₂²×C₈₉	—	4	1	no	—
368	C₂²×C₈₉	—	4	2	no	—
369	C₂²×C₈₉	—	4	2	no	—
370	C₂²×C₈₉	—	4	4	no	—
371	C₂²×C₈₉	—	4	2	no	—
372	C₂²×C₈₉	—	4	1	no	—
373	C₂²×C₈₉	—	4	2	no	—
374	C₂²×C₈₉	—	4	4	no	—
375	C₂²×C₈₉	#548	1	4	yes	—
376	C₂²×C₈₉	#553	1	8	yes	complemented
377	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
378	C₂²×C₈₉	C₂²×#41	1	2	yes	—
379	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
380	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
381	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
382	C₄×C₈₉	—	2	2	no	—
383	C₄×C₈₉	—	2	4	no	—
384	C₄×C₈₉	—	2	4	no	—
385	C₄×C₈₉	—	2	4	no	—
386	C₄×C₈₉	—	4	1	no	—
387	C₄×C₈₉	—	4	2	no	—
388	C₄×C₈₉	—	4	1	no	—
389	C₄×C₈₉	—	4	2	no	—
390	C₄×C₈₉	—	4	4	no	—
391	C₄×C₈₉	—	4	4	no	—
392	C₄×C₈₉	—	4	1	no	—
393	C₄×C₈₉	—	4	2	no	—
394	C₄×C₈₉	#525	1	4	yes	—
395	#36581	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
396	C₂×C₈₉	—	2	4	no	—
397	C₂×C₈₉	—	2	8	no	—
398	C₂×C₈₉	—	8	1	no	—
399	C₂×C₈₉	—	8	2	no	—
400	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
401	C₂×C₈₉	C₂×#548	1	1	yes	characteristic
402	C₂×C₈₉	C₂×#553	1	2	yes	—
403	C₂×C₈₉	#3484	1	1	yes	characteristic
404	C₂×C₈₉	#3492	1	2	yes	—
405	C₂×#553	C₂×C₈₉	1	1	yes	characteristic, complemented
406	C₂³×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
407	#2847	C₂×C₈₉	1	2	yes	complemented
408	#2847	C₂×C₈₉	1	1	yes	characteristic, complemented
409	#2591	C₂×C₈₉	1	2	yes	complemented
410	#2579	C₂×C₈₉	1	2	yes	complemented
411	#2504	C₂×C₈₉	1	1	yes	characteristic, complemented
412	#2487	C₂×C₈₉	1	1	yes	characteristic, complemented
413	#2481	C₂×C₈₉	1	4	yes	complemented
414	#2443	C₂×C₈₉	1	4	yes	complemented
415	#2442	C₂×C₈₉	1	2	yes	complemented
416	#2416	C₂×C₈₉	1	2	yes	complemented
417	#2361	C₂×C₈₉	1	2	yes	complemented
418	#2352	C₂×C₈₉	1	2	yes	complemented
419	#2345	C₂×C₈₉	1	1	yes	characteristic, complemented
420	C₄×#120	C₂×C₈₉	1	2	yes	complemented
421	C₄×#120	C₂×C₈₉	1	1	yes	characteristic, complemented
422	C₈₉	#36581	1	1	yes	characteristic, direct product factor, Sylow
423	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
424	C₂⁴×C₄	C₂²×C₈₉	1	2	yes	—
425	#553	—	2	8	no	—
426	C₂×#126	C₂²×C₈₉	1	2	yes	complemented
427	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic, complemented
428	C₂×#123	C₂²×C₈₉	1	2	yes	complemented
429	C₂×#121	C₂²×C₈₉	1	2	yes	—
430	C₂×#121	C₂²×C₈₉	1	2	yes	—
431	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
432	C₂×#121	C₂²×C₈₉	1	4	yes	—
433	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic, complemented
434	C₂×#120	C₂²×C₈₉	1	2	yes	—
435	C₂×#120	C₂²×C₈₉	1	1	yes	characteristic
436	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
437	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
438	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
439	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
440	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
441	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic, complemented
442	C₂²×C₄⋊C₄	—	2	8	no	—
443	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
444	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
445	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
446	C₂²×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
447	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
448	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
449	#400	C₂²×C₈₉	1	4	yes	complemented
450	#400	C₂²×C₈₉	1	2	yes	complemented
451	#399	C₂²×C₈₉	1	2	yes	complemented
452	#398	C₂²×C₈₉	1	4	yes	complemented
453	#397	C₂²×C₈₉	1	4	yes	complemented
454	#396	C₂²×C₈₉	1	4	yes	complemented
455	#394	C₂²×C₈₉	1	4	yes	complemented
456	#390	C₂²×C₈₉	1	2	yes	complemented
457	#389	C₂²×C₈₉	1	2	yes	complemented
458	#389	C₂²×C₈₉	1	2	yes	complemented
459	#388	C₂²×C₈₉	1	4	yes	complemented
460	#388	C₂²×C₈₉	1	4	yes	complemented
461	#387	C₂²×C₈₉	1	4	yes	complemented
462	#387	C₂²×C₈₉	1	4	yes	complemented
463	#386	C₂²×C₈₉	1	2	yes	—
464	#386	C₂²×C₈₉	1	2	yes	—
465	#386	C₂²×C₈₉	1	1	yes	characteristic
466	#386	C₂²×C₈₉	1	2	yes	—
467	#386	C₂²×C₈₉	1	2	yes	—
468	#386	C₂²×C₈₉	1	4	yes	—
469	#386	C₂²×C₈₉	1	4	yes	—
470	#386	C₂²×C₈₉	1	4	yes	—
471	#386	C₂²×C₈₉	1	4	yes	—
472	#386	C₂²×C₈₉	1	2	yes	—
473	#385	C₂²×C₈₉	1	1	yes	characteristic
474	#385	C₂²×C₈₉	1	2	yes	—
475	#385	C₂²×C₈₉	1	4	yes	—
476	#385	C₂²×C₈₉	1	2	yes	—
477	#385	C₂²×C₈₉	1	4	yes	complemented
478	#382	C₂²×C₈₉	1	2	yes	complemented
479	#380	C₂²×C₈₉	1	2	yes	—
480	#380	C₂²×C₈₉	1	1	yes	characteristic
481	#380	C₂²×C₈₉	1	2	yes	—
482	#380	C₂²×C₈₉	1	4	yes	—
483	#380	C₂²×C₈₉	1	2	yes	complemented
484	#379	C₂²×C₈₉	1	1	yes	characteristic
485	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
486	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
487	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
488	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
489	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
490	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
491	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
492	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
493	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
494	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
495	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
496	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
497	C₂³×C₄	—	2	4	no	—
498	C₂³×C₄	—	2	8	no	—
499	C₂³×C₄	—	2	8	no	—
500	C₂³×C₄	—	4	8	no	—
501	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
502	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
503	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
504	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
505	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
506	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
507	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
508	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
509	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
510	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
511	#126	—	2	8	no	—
512	#125	—	2	4	no	—
513	#123	—	2	8	no	—
514	#121	—	2	8	no	—
515	#121	—	2	4	no	—
516	#121	—	2	8	no	—
517	#121	—	2	4	no	—
518	#121	—	4	8	no	—
519	#120	—	2	8	no	—
520	#120	—	2	4	no	—
521	C₄×D₄	—	2	8	no	—
522	C₄×D₄	—	2	4	no	—
523	C₄×D₄	—	2	8	no	—
524	C₄×D₄	—	2	4	no	—
525	C₄×D₄	—	4	8	no	—
526	#117	—	2	4	no	—
527	C₂×C₄⋊C₄	—	2	8	no	—
528	C₂×C₄⋊C₄	—	2	4	no	—
529	C₂×C₄⋊C₄	—	2	8	no	—
530	C₂×C₄⋊C₄	—	2	8	no	—
531	C₂×C₄⋊C₄	—	2	16	no	—
532	C₂×C₄⋊C₄	D₄×C₈₉	1	8	yes	complemented
533	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
535	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
536	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
544	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
545	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
550	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
553	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
558	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
563	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
566	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
567	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
568	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
569	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
570	#95	C₂³×C₈₉	1	4	yes	—
571	#95	C₂³×C₈₉	1	4	yes	—
572	#95	C₂³×C₈₉	1	2	yes	—
573	#95	C₂³×C₈₉	1	2	yes	—
574	#95	C₂³×C₈₉	1	4	yes	—
575	#95	C₂³×C₈₉	1	2	yes	—
576	#95	C₂³×C₈₉	1	4	yes	—
577	#95	C₂³×C₈₉	1	4	yes	—
578	#95	C₂³×C₈₉	1	2	yes	—
579	#95	C₂³×C₈₉	1	4	yes	—
580	#95	C₂³×C₈₉	1	4	yes	—
581	C₂⁴	—	2	2	no	—
582	C₂⁴	—	2	4	no	—
583	C₂⁴	—	2	4	no	—
584	C₂⁴	—	2	2	no	—
585	C₂⁴	#41×C₈₉	1	4	yes	—
586	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
587	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
588	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
589	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	8	no	—
597	C₂×D₄	—	2	8	no	—
598	C₂×D₄	—	2	8	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	4	4	no	—
606	C₂²×C₄	—	2	32	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	8	no	—
617	C₂²×C₄	—	2	8	no	—
618	C₂²×C₄	—	2	8	no	—
619	C₂²×C₄	—	2	8	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	4	4	no	—
624	C₂²×C₄	—	4	4	no	—
625	C₂²×C₄	—	4	4	no	—
626	C₂²×C₄	—	4	4	no	—
627	C₂²×C₄	—	4	4	no	—
628	C₂²×C₄	—	4	32	no	—
629	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
630	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
631	C₂²×C₄	#41×C₈₉	1	8	yes	—
632	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
635	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
637	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
639	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
641	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
645	C₄⋊C₄	—	2	8	no	—
646	C₄⋊C₄	—	2	8	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	4	4	no	—
656	C₄⋊C₄	—	4	4	no	—
657	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
658	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
659	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	8	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	2	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	2	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	8	no	—
675	C₂²⋊C₄	—	4	4	no	—
676	C₂²⋊C₄	—	4	4	no	—
677	C₂²⋊C₄	—	4	4	no	—
678	C₄²	—	2	4	no	—
679	C₄²	—	2	2	no	—
680	C₄²	—	2	4	no	—
681	C₄²	—	4	4	no	—
682	C₂³	—	2	8	no	—
683	C₂³	—	2	8	no	—
684	C₂³	—	2	16	no	—
685	C₂³	—	2	8	no	—
686	C₂³	—	2	16	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	4	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	4	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	1	no	—
702	C₂³	—	2	2	no	—
703	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
704	C₂³	C₂×#41×C₈₉	1	2	yes	—
705	C₂³	C₂×#41×C₈₉	1	4	yes	—
706	C₂³	C₂×#41×C₈₉	1	4	yes	—
707	C₂³	H(5,𝔽₂)×C₈₉	1	4	yes	—
708	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
709	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
710	D₄	—	4	8	no	—
711	D₄	—	4	4	no	—
712	D₄	—	4	8	no	—
713	D₄	—	4	16	no	—
714	D₄	—	4	4	no	—
715	D₄	—	8	4	no	—
716	C₂×C₄	—	2	16	no	—
717	C₂×C₄	—	2	8	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	8	no	—
724	C₂×C₄	—	2	16	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	4	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	4	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	4	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	4	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	4	no	—
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	4	8	no	—
748	C₂×C₄	—	4	16	no	—
749	C₂×C₄	—	4	16	no	—
750	C₂×C₄	—	4	8	no	—
751	C₂×C₄	—	4	4	no	—
752	C₂×C₄	—	8	4	no	—
753	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
754	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
755	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
756	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
757	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
758	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
759	C₂²	—	2	32	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	4	no	—
762	C₂²	—	2	4	no	—
763	C₂²	—	2	4	no	—
764	C₂²	—	2	4	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	4	no	—
767	C₂²	—	2	4	no	—
768	C₂²	—	2	4	no	—
769	C₂²	—	2	4	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	4	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	1	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	4	no	—
780	C₂²	#548×C₈₉	1	4	yes	—
781	C₂²	#553×C₈₉	1	8	yes	complemented
782	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
783	C₂²	C₂²×#41×C₈₉	1	2	yes	—
784	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
785	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
786	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
787	C₄	—	2	2	no	—
788	C₄	—	2	4	no	—
789	C₄	—	2	4	no	—
790	C₄	—	2	4	no	—
791	C₄	—	4	1	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	1	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	4	no	—
796	C₄	—	4	4	no	—
797	C₄	—	4	1	no	—
798	C₄	—	4	2	no	—
799	C₄	#525×C₈₉	1	4	yes	—
800	C₂	—	2	4	no	—
801	C₂	—	2	8	no	—
802	C₂	—	8	1	no	—
803	C₂	—	8	2	no	—
804	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
805	C₂	C₂×#548×C₈₉	1	1	yes	characteristic
806	C₂	C₂×#553×C₈₉	1	2	yes	—
807	C₂	C₈₉×#3484	1	1	yes	characteristic
808	C₂	C₈₉×#3492	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. C₂×#553×C₈₉	C₂	semidirect
2. C₂³×C₄⋊C₄×C₈₉	C₂	semidirect
3. C₈₉×#2847	C₂	semidirect
4. C₈₉×#2847	C₂	semidirect
5. C₈₉×#2591	C₂	semidirect
6. C₈₉×#2579	C₂	semidirect
7. C₈₉×#2504	C₂	semidirect
8. C₈₉×#2487	C₂	semidirect
9. C₈₉×#2481	C₂	semidirect
10. C₈₉×#2443	C₂	semidirect
11. C₈₉×#2442	C₂	semidirect
12. C₈₉×#2416	C₂	semidirect
13. C₈₉×#2361	C₂	semidirect
14. C₈₉×#2352	C₂	semidirect
15. C₈₉×#2345	C₂	semidirect
16. C₄×#120×C₈₉	C₂	semidirect
17. C₄×#120×C₈₉	C₂	semidirect
21. C₂×#126×C₈₉	C₂²	semidirect
22. C₂×#125×C₈₉	C₂²	semidirect
23. C₂×#123×C₈₉	C₂²	semidirect
28. C₂×#121×C₈₉	C₂²	semidirect
35. C₂×C₄×D₄×C₈₉	C₂²	semidirect
36. C₂×#117×C₈₉	C₂²	semidirect
44. #400×C₈₉	C₂²	semidirect
45. #400×C₈₉	C₂²	semidirect
46. #399×C₈₉	C₂²	semidirect
47. #398×C₈₉	C₂²	semidirect
48. #397×C₈₉	C₂²	semidirect
49. #396×C₈₉	C₂²	semidirect
50. #394×C₈₉	C₂²	semidirect
51. #390×C₈₉	C₂²	semidirect
52. #389×C₈₉	C₂²	semidirect
53. #389×C₈₉	C₂²	semidirect
54. #388×C₈₉	C₂²	semidirect
55. #388×C₈₉	C₂²	semidirect
56. #387×C₈₉	C₂²	semidirect
57. #387×C₈₉	C₂²	semidirect
72. #385×C₈₉	C₂²	semidirect
73. #382×C₈₉	C₂²	semidirect
78. #380×C₈₉	C₂²	semidirect
80. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
127. C₂×C₄⋊C₄×C₈₉	D₄	semidirect
376. C₂²×C₈₉	#553	semidirect
395. #36581	C₈₉	direct (N × H)
405. C₂×#553	C₂×C₈₉	semidirect
406. C₂³×C₄⋊C₄	C₂×C₈₉	semidirect
407. #2847	C₂×C₈₉	semidirect
408. #2847	C₂×C₈₉	semidirect
409. #2591	C₂×C₈₉	semidirect
410. #2579	C₂×C₈₉	semidirect
411. #2504	C₂×C₈₉	semidirect
412. #2487	C₂×C₈₉	semidirect
413. #2481	C₂×C₈₉	semidirect
414. #2443	C₂×C₈₉	semidirect
415. #2442	C₂×C₈₉	semidirect
416. #2416	C₂×C₈₉	semidirect
417. #2361	C₂×C₈₉	semidirect
418. #2352	C₂×C₈₉	semidirect
419. #2345	C₂×C₈₉	semidirect
420. C₄×#120	C₂×C₈₉	semidirect
421. C₄×#120	C₂×C₈₉	semidirect
422. C₈₉	#36581	direct (N × H)
426. C₂×#126	C₂²×C₈₉	semidirect
427. C₂×#125	C₂²×C₈₉	semidirect
428. C₂×#123	C₂²×C₈₉	semidirect
433. C₂×#121	C₂²×C₈₉	semidirect
440. C₂×C₄×D₄	C₂²×C₈₉	semidirect
441. C₂×#117	C₂²×C₈₉	semidirect
449. #400	C₂²×C₈₉	semidirect
450. #400	C₂²×C₈₉	semidirect
451. #399	C₂²×C₈₉	semidirect
452. #398	C₂²×C₈₉	semidirect
453. #397	C₂²×C₈₉	semidirect
454. #396	C₂²×C₈₉	semidirect
455. #394	C₂²×C₈₉	semidirect
456. #390	C₂²×C₈₉	semidirect
457. #389	C₂²×C₈₉	semidirect
458. #389	C₂²×C₈₉	semidirect
459. #388	C₂²×C₈₉	semidirect
460. #388	C₂²×C₈₉	semidirect
461. #387	C₂²×C₈₉	semidirect
462. #387	C₂²×C₈₉	semidirect
477. #385	C₂²×C₈₉	semidirect
478. #382	C₂²×C₈₉	semidirect
483. #380	C₂²×C₈₉	semidirect
485. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
532. C₂×C₄⋊C₄	D₄×C₈₉	semidirect
781. C₂²	#553×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
C₂³×C₄⋊C₄×C₈₉	2
C₈₉×#2847	2
C₈₉×#2591	2
C₈₉×#2579	2
C₈₉×#2504	2
C₈₉×#2487	2
C₈₉×#2481	2
C₈₉×#2443	2
C₈₉×#2442	2
C₈₉×#2416	2
C₈₉×#2361	2
C₈₉×#2352	2
C₈₉×#2345	2
C₄×#120×C₈₉	2
#36581	89

Subgroups — C89×#36581 #36414429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#36581 #36414429