Subgroups — C₈₉×#35440 #36413288

Order 22784.

1876 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2609	C₂	1	2	yes	maximal, complemented
2	C₈₉×#2608	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2601	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2601	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2588	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2587	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2583	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2558	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2550	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2475	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2474	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2470	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2432	C₂	1	1	yes	maximal, characteristic
14	C₈₉×#2406	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#2334	C₂	1	2	yes	maximal, complemented
16	C₈₉×#2332	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2297	C₂	1	1	yes	maximal, characteristic
18	C₈₉×#2296	C₂	1	2	yes	maximal, complemented
19	C₈₉×#2274	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#126×C₈₉	C₂²	1	2	yes	—
23	C₂×#125×C₈₉	C₂²	1	2	yes	—
24	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#123×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#123×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#117×C₈₉	C₂²	1	2	yes	—
29	C₂×#117×C₈₉	C₂²	1	2	yes	—
30	C₂×#117×C₈₉	C₂²	1	2	yes	—
31	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
34	#400×C₈₉	C₂²	1	2	yes	—
35	#400×C₈₉	C₂²	1	2	yes	—
36	#398×C₈₉	C₂²	1	2	yes	—
37	#398×C₈₉	C₂²	1	2	yes	—
38	#398×C₈₉	C₂²	1	2	yes	—
39	#397×C₈₉	C₂²	1	2	yes	—
40	#396×C₈₉	C₂²	1	2	yes	—
41	#396×C₈₉	C₂²	1	2	yes	—
42	#396×C₈₉	C₂²	1	2	yes	—
43	#396×C₈₉	C₂²	1	2	yes	—
44	#396×C₈₉	C₂²	1	2	yes	—
45	#395×C₈₉	C₂²	1	2	yes	—
46	#395×C₈₉	C₂²	1	2	yes	—
47	#394×C₈₉	C₂²	1	2	yes	—
48	#394×C₈₉	C₂²	1	2	yes	—
49	#394×C₈₉	C₂²	1	2	yes	—
50	#391×C₈₉	C₂²	1	2	yes	—
51	#391×C₈₉	C₂²	1	2	yes	—
52	#391×C₈₉	C₂²	1	1	yes	characteristic
53	#390×C₈₉	C₂²	1	2	yes	—
54	#390×C₈₉	C₂²	1	1	yes	characteristic
55	#389×C₈₉	C₂²	1	2	yes	—
56	#389×C₈₉	C₂²	1	2	yes	—
57	#389×C₈₉	C₂²	1	2	yes	—
58	#389×C₈₉	C₂²	1	2	yes	—
59	#389×C₈₉	C₂²	1	2	yes	—
60	#389×C₈₉	C₂²	1	2	yes	—
61	#389×C₈₉	C₂²	1	2	yes	—
62	#389×C₈₉	C₂²	1	2	yes	—
63	#388×C₈₉	C₂²	1	2	yes	—
64	#388×C₈₉	C₂²	1	2	yes	—
65	#388×C₈₉	C₂²	1	2	yes	—
66	#388×C₈₉	C₂²	1	2	yes	—
67	#388×C₈₉	C₂²	1	2	yes	—
68	#388×C₈₉	C₂²	1	2	yes	—
69	#388×C₈₉	C₂²	1	2	yes	—
70	#388×C₈₉	C₂²	1	2	yes	—
71	#388×C₈₉	C₂²	1	2	yes	—
72	#387×C₈₉	C₂²	1	2	yes	—
73	#387×C₈₉	C₂²	1	2	yes	—
74	#387×C₈₉	C₂²	1	2	yes	—
75	#387×C₈₉	C₂²	1	2	yes	—
76	#387×C₈₉	C₂²	1	2	yes	—
77	#387×C₈₉	C₂²	1	2	yes	—
78	#387×C₈₉	C₂²	1	2	yes	—
79	#387×C₈₉	C₂²	1	2	yes	—
80	#386×C₈₉	C₂²	1	2	yes	—
81	#386×C₈₉	C₂²	1	2	yes	—
82	#386×C₈₉	C₂²	1	1	yes	characteristic
83	#386×C₈₉	C₂²	1	1	yes	characteristic
84	#385×C₈₉	C₂²	1	2	yes	—
85	#385×C₈₉	C₂²	1	2	yes	—
86	#385×C₈₉	C₂²	1	2	yes	—
87	#385×C₈₉	C₂²	1	2	yes	—
88	#385×C₈₉	C₂²	1	2	yes	—
89	#385×C₈₉	C₂²	1	2	yes	—
90	#385×C₈₉	C₂²	1	2	yes	—
91	#385×C₈₉	C₂²	1	2	yes	—
92	#382×C₈₉	C₂²	1	2	yes	—
93	#381×C₈₉	C₂²	1	1	yes	characteristic
94	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
105	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
106	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
107	C₂×#41×C₈₉	—	2	4	no	—
108	C₂×#41×C₈₉	—	4	2	no	—
109	C₂×#41×C₈₉	—	4	2	no	—
110	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
117	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
121	C₄⋊Q₈×C₈₉	—	4	2	no	—
122	#126×C₈₉	—	2	8	no	—
123	#125×C₈₉	—	4	4	no	—
124	#124×C₈₉	—	4	2	no	—
125	#123×C₈₉	—	4	2	no	—
126	#123×C₈₉	—	4	2	no	—
127	C₂²⋊Q₈×C₈₉	—	2	4	no	—
128	#117×C₈₉	—	2	8	no	—
129	#117×C₈₉	—	2	8	no	—
130	#117×C₈₉	—	4	4	no	—
131	#117×C₈₉	—	4	2	no	—
132	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
133	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
173	C₂×C₄²×C₈₉	—	4	2	no	—
174	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
175	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
176	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
181	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
183	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
185	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
186	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
187	#95×C₈₉	C₂³	1	2	yes	—
188	#95×C₈₉	C₂³	1	2	yes	—
189	#95×C₈₉	C₂³	1	2	yes	—
190	#95×C₈₉	C₂³	1	2	yes	—
191	#95×C₈₉	C₂³	1	2	yes	—
192	#95×C₈₉	C₂³	1	2	yes	—
193	#95×C₈₉	C₂³	1	2	yes	—
194	#95×C₈₉	C₂³	1	2	yes	—
195	#95×C₈₉	C₂³	1	2	yes	—
196	#95×C₈₉	C₂³	1	2	yes	—
197	#95×C₈₉	C₂³	1	2	yes	—
198	#95×C₈₉	C₂³	1	2	yes	—
199	#95×C₈₉	C₂³	1	2	yes	—
200	#95×C₈₉	C₂³	1	2	yes	—
201	#95×C₈₉	C₂³	1	2	yes	—
202	#95×C₈₉	C₂³	1	2	yes	—
203	#95×C₈₉	C₂³	1	2	yes	—
204	#95×C₈₉	C₂³	1	2	yes	—
205	#95×C₈₉	C₂³	1	2	yes	—
206	#95×C₈₉	C₂³	1	2	yes	—
207	#95×C₈₉	C₂³	1	2	yes	—
208	#95×C₈₉	C₂³	1	2	yes	—
209	#95×C₈₉	C₂³	1	2	yes	—
210	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
211	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
212	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
213	#41×C₈₉	—	4	16	no	—
214	C₂×Q₈×C₈₉	—	2	2	no	—
215	C₂×Q₈×C₈₉	—	2	2	no	—
216	C₂×Q₈×C₈₉	—	2	2	no	—
217	C₂×Q₈×C₈₉	—	4	1	no	—
218	C₂×Q₈×C₈₉	—	4	1	no	—
219	C₂×Q₈×C₈₉	—	4	1	no	—
220	C₂×D₄×C₈₉	—	2	2	no	—
221	C₂×D₄×C₈₉	—	2	2	no	—
222	C₂×D₄×C₈₉	—	2	2	no	—
223	C₂×D₄×C₈₉	—	2	2	no	—
224	C₂×D₄×C₈₉	—	2	2	no	—
225	C₂×D₄×C₈₉	—	2	2	no	—
226	C₂×D₄×C₈₉	—	4	1	no	—
227	C₂×D₄×C₈₉	—	4	1	no	—
228	C₂×D₄×C₈₉	—	4	1	no	—
229	C₂²×C₄×C₈₉	—	2	2	no	—
230	C₂²×C₄×C₈₉	—	2	4	no	—
231	C₂²×C₄×C₈₉	—	2	2	no	—
232	C₂²×C₄×C₈₉	—	2	4	no	—
233	C₂²×C₄×C₈₉	—	2	4	no	—
234	C₂²×C₄×C₈₉	—	2	2	no	—
235	C₂²×C₄×C₈₉	—	2	2	no	—
236	C₂²×C₄×C₈₉	—	2	4	no	—
237	C₂²×C₄×C₈₉	—	2	2	no	—
238	C₂²×C₄×C₈₉	—	2	2	no	—
239	C₂²×C₄×C₈₉	—	4	1	no	—
240	C₂²×C₄×C₈₉	—	4	1	no	—
241	C₂²×C₄×C₈₉	—	4	1	no	—
242	C₂²×C₄×C₈₉	—	4	1	no	—
243	C₂²×C₄×C₈₉	—	4	1	no	—
244	C₂²×C₄×C₈₉	—	4	1	no	—
245	C₂²×C₄×C₈₉	#41	1	4	yes	—
246	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₈₉	—	2	4	no	—
263	C₄⋊C₄×C₈₉	—	2	4	no	—
264	C₄⋊C₄×C₈₉	—	2	4	no	—
265	C₄⋊C₄×C₈₉	—	2	4	no	—
266	C₄⋊C₄×C₈₉	—	2	4	no	—
267	C₄⋊C₄×C₈₉	—	2	4	no	—
268	C₄⋊C₄×C₈₉	—	2	2	no	—
269	C₄⋊C₄×C₈₉	—	2	4	no	—
270	C₄⋊C₄×C₈₉	—	2	4	no	—
271	C₄⋊C₄×C₈₉	—	2	4	no	—
272	C₄⋊C₄×C₈₉	—	2	4	no	—
273	C₄⋊C₄×C₈₉	—	2	4	no	—
274	C₄⋊C₄×C₈₉	—	2	4	no	—
275	C₄⋊C₄×C₈₉	—	2	4	no	—
276	C₄⋊C₄×C₈₉	—	2	4	no	—
277	C₄⋊C₄×C₈₉	—	2	4	no	—
278	C₄⋊C₄×C₈₉	—	4	2	no	—
279	C₄⋊C₄×C₈₉	—	4	2	no	—
280	C₄⋊C₄×C₈₉	—	4	2	no	—
281	C₄⋊C₄×C₈₉	—	4	2	no	—
282	C₄⋊C₄×C₈₉	—	4	2	no	—
283	C₄⋊C₄×C₈₉	—	4	2	no	—
284	C₄⋊C₄×C₈₉	—	4	2	no	—
285	C₂²⋊C₄×C₈₉	—	2	4	no	—
286	C₂²⋊C₄×C₈₉	—	2	4	no	—
287	C₂²⋊C₄×C₈₉	—	2	4	no	—
288	C₂²⋊C₄×C₈₉	—	2	4	no	—
289	C₂²⋊C₄×C₈₉	—	2	4	no	—
290	C₂²⋊C₄×C₈₉	—	2	4	no	—
291	C₂²⋊C₄×C₈₉	—	2	4	no	—
292	C₂²⋊C₄×C₈₉	—	2	4	no	—
293	C₂²⋊C₄×C₈₉	—	2	4	no	—
294	C₂²⋊C₄×C₈₉	—	2	4	no	—
295	C₂²⋊C₄×C₈₉	—	2	4	no	—
296	C₂²⋊C₄×C₈₉	—	2	4	no	—
297	C₂²⋊C₄×C₈₉	—	4	2	no	—
298	C₂²⋊C₄×C₈₉	—	4	1	no	—
299	C₂²⋊C₄×C₈₉	—	4	2	no	—
300	C₂²⋊C₄×C₈₉	—	4	1	no	—
301	C₂²⋊C₄×C₈₉	—	4	2	no	—
302	C₄²×C₈₉	—	2	4	no	—
303	C₄²×C₈₉	—	2	4	no	—
304	C₄²×C₈₉	—	4	1	no	—
305	C₄²×C₈₉	—	4	2	no	—
306	C₄²×C₈₉	—	4	1	no	—
307	C₄²×C₈₉	—	4	2	no	—
308	C₄²×C₈₉	—	4	2	no	—
309	C₄²×C₈₉	—	4	1	no	—
310	C₄²×C₈₉	—	4	1	no	—
311	C₄²×C₈₉	—	4	1	no	—
312	C₄²×C₈₉	—	4	2	no	—
313	C₄²×C₈₉	—	4	1	no	—
314	C₄²×C₈₉	#41	1	8	yes	complemented
315	C₂³×C₈₉	—	2	2	no	—
316	C₂³×C₈₉	—	2	2	no	—
317	C₂³×C₈₉	—	2	1	no	—
318	C₂³×C₈₉	—	2	1	no	—
319	C₂³×C₈₉	—	2	1	no	—
320	C₂³×C₈₉	—	2	1	no	—
321	C₂³×C₈₉	—	2	2	no	—
322	C₂³×C₈₉	—	2	2	no	—
323	C₂³×C₈₉	—	2	2	no	—
324	C₂³×C₈₉	—	2	1	no	—
325	C₂³×C₈₉	—	2	1	no	—
326	C₂³×C₈₉	—	2	1	no	—
327	C₂³×C₈₉	—	2	2	no	—
328	C₂³×C₈₉	C₂×#41	1	2	yes	—
329	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
330	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
331	Q₈×C₈₉	—	4	4	no	—
332	Q₈×C₈₉	—	8	2	no	—
333	D₄×C₈₉	—	4	4	no	—
334	D₄×C₈₉	—	4	4	no	—
335	D₄×C₈₉	—	4	4	no	—
336	C₂×C₄×C₈₉	—	2	8	no	—
337	C₂×C₄×C₈₉	—	2	16	no	—
338	C₂×C₄×C₈₉	—	2	8	no	—
339	C₂×C₄×C₈₉	—	2	2	no	—
340	C₂×C₄×C₈₉	—	2	2	no	—
341	C₂×C₄×C₈₉	—	2	2	no	—
342	C₂×C₄×C₈₉	—	2	1	no	—
343	C₂×C₄×C₈₉	—	2	2	no	—
344	C₂×C₄×C₈₉	—	2	2	no	—
345	C₂×C₄×C₈₉	—	2	2	no	—
346	C₂×C₄×C₈₉	—	2	1	no	—
347	C₂×C₄×C₈₉	—	2	1	no	—
348	C₂×C₄×C₈₉	—	2	1	no	—
349	C₂×C₄×C₈₉	—	2	1	no	—
350	C₂×C₄×C₈₉	—	2	1	no	—
351	C₂×C₄×C₈₉	—	2	2	no	—
352	C₂×C₄×C₈₉	—	2	2	no	—
353	C₂×C₄×C₈₉	—	2	2	no	—
354	C₂×C₄×C₈₉	—	2	2	no	—
355	C₂×C₄×C₈₉	—	2	2	no	—
356	C₂×C₄×C₈₉	—	2	2	no	—
357	C₂×C₄×C₈₉	—	2	2	no	—
358	C₂×C₄×C₈₉	—	2	2	no	—
359	C₂×C₄×C₈₉	—	2	2	no	—
360	C₂×C₄×C₈₉	—	2	2	no	—
361	C₂×C₄×C₈₉	—	2	2	no	—
362	C₂×C₄×C₈₉	—	2	2	no	—
363	C₂×C₄×C₈₉	—	2	1	no	—
364	C₂×C₄×C₈₉	—	2	2	no	—
365	C₂×C₄×C₈₉	—	2	2	no	—
366	C₂×C₄×C₈₉	—	2	2	no	—
367	C₂×C₄×C₈₉	—	2	2	no	—
368	C₂×C₄×C₈₉	—	2	2	no	—
369	C₂×C₄×C₈₉	—	2	2	no	—
370	C₂×C₄×C₈₉	—	2	2	no	—
371	C₂×C₄×C₈₉	—	2	2	no	—
372	C₂×C₄×C₈₉	—	2	2	no	—
373	C₂×C₄×C₈₉	—	2	1	no	—
374	C₂×C₄×C₈₉	—	2	1	no	—
375	C₂×C₄×C₈₉	—	2	2	no	—
376	C₂×C₄×C₈₉	—	2	2	no	—
377	C₂×C₄×C₈₉	—	2	2	no	—
378	C₂×C₄×C₈₉	—	2	2	no	—
379	C₂×C₄×C₈₉	—	2	2	no	—
380	C₂×C₄×C₈₉	—	4	4	no	—
381	C₂×C₄×C₈₉	—	4	4	no	—
382	C₂×C₄×C₈₉	—	8	2	no	—
383	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
384	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
385	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
386	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
387	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
388	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
389	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
390	C₂²×C₈₉	—	2	2	no	—
391	C₂²×C₈₉	—	2	2	no	—
392	C₂²×C₈₉	—	2	2	no	—
393	C₂²×C₈₉	—	2	4	no	—
394	C₂²×C₈₉	—	2	2	no	—
395	C₂²×C₈₉	—	4	1	no	—
396	C₂²×C₈₉	—	4	2	no	—
397	C₂²×C₈₉	—	4	1	no	—
398	C₂²×C₈₉	—	4	2	no	—
399	C₂²×C₈₉	—	4	2	no	—
400	C₂²×C₈₉	—	4	1	no	—
401	C₂²×C₈₉	—	4	1	no	—
402	C₂²×C₈₉	—	4	2	no	—
403	C₂²×C₈₉	—	4	1	no	—
404	C₂²×C₈₉	—	4	2	no	—
405	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
406	C₂²×C₈₉	C₂²×#41	1	2	yes	—
407	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
408	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
409	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
410	C₄×C₈₉	—	2	4	no	—
411	C₄×C₈₉	—	2	2	no	—
412	C₄×C₈₉	—	2	2	no	—
413	C₄×C₈₉	—	2	2	no	—
414	C₄×C₈₉	—	2	4	no	—
415	C₄×C₈₉	—	2	4	no	—
416	C₄×C₈₉	—	2	4	no	—
417	C₄×C₈₉	—	4	2	no	—
418	C₄×C₈₉	—	4	1	no	—
419	C₄×C₈₉	—	4	2	no	—
420	C₄×C₈₉	—	4	2	no	—
421	C₄×C₈₉	—	4	2	no	—
422	C₄×C₈₉	—	4	2	no	—
423	C₄×C₈₉	—	4	2	no	—
424	C₄×C₈₉	—	4	2	no	—
425	C₄×C₈₉	—	4	2	no	—
426	#35440	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
427	C₂×C₈₉	—	4	2	no	—
428	C₂×C₈₉	—	4	2	no	—
429	C₂×C₈₉	—	8	1	no	—
430	C₂×C₈₉	#3444	1	1	yes	characteristic
431	C₂×C₈₉	#3490	1	1	yes	characteristic
432	C₂×C₈₉	#3492	1	2	yes	—
433	C₂×C₈₉	#3509	1	1	yes	characteristic
434	C₂×C₈₉	#3511	1	2	yes	—
435	#2609	C₂×C₈₉	1	2	yes	complemented
436	#2608	C₂×C₈₉	1	1	yes	characteristic, complemented
437	#2601	C₂×C₈₉	1	2	yes	complemented
438	#2601	C₂×C₈₉	1	2	yes	complemented
439	#2588	C₂×C₈₉	1	2	yes	complemented
440	#2587	C₂×C₈₉	1	2	yes	complemented
441	#2583	C₂×C₈₉	1	1	yes	characteristic, complemented
442	#2558	C₂×C₈₉	1	2	yes	complemented
443	#2550	C₂×C₈₉	1	2	yes	complemented
444	#2475	C₂×C₈₉	1	2	yes	complemented
445	#2474	C₂×C₈₉	1	2	yes	complemented
446	#2470	C₂×C₈₉	1	2	yes	complemented
447	#2432	C₂×C₈₉	1	1	yes	characteristic
448	#2406	C₂×C₈₉	1	1	yes	characteristic
449	#2334	C₂×C₈₉	1	2	yes	complemented
450	#2332	C₂×C₈₉	1	1	yes	characteristic, complemented
451	#2297	C₂×C₈₉	1	1	yes	characteristic
452	#2296	C₂×C₈₉	1	2	yes	complemented
453	#2274	C₂×C₈₉	1	1	yes	characteristic, complemented
454	C₈₉	#35440	1	1	yes	characteristic, direct product factor, Sylow
455	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
456	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
457	C₂×#126	C₂²×C₈₉	1	2	yes	—
458	C₂×#125	C₂²×C₈₉	1	2	yes	—
459	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
460	C₂×#123	C₂²×C₈₉	1	1	yes	characteristic
461	C₂×#123	C₂²×C₈₉	1	1	yes	characteristic
462	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
463	C₂×#117	C₂²×C₈₉	1	2	yes	—
464	C₂×#117	C₂²×C₈₉	1	2	yes	—
465	C₂×#117	C₂²×C₈₉	1	2	yes	—
466	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
467	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
468	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
469	#400	C₂²×C₈₉	1	2	yes	—
470	#400	C₂²×C₈₉	1	2	yes	—
471	#398	C₂²×C₈₉	1	2	yes	—
472	#398	C₂²×C₈₉	1	2	yes	—
473	#398	C₂²×C₈₉	1	2	yes	—
474	#397	C₂²×C₈₉	1	2	yes	—
475	#396	C₂²×C₈₉	1	2	yes	—
476	#396	C₂²×C₈₉	1	2	yes	—
477	#396	C₂²×C₈₉	1	2	yes	—
478	#396	C₂²×C₈₉	1	2	yes	—
479	#396	C₂²×C₈₉	1	2	yes	—
480	#395	C₂²×C₈₉	1	2	yes	—
481	#395	C₂²×C₈₉	1	2	yes	—
482	#394	C₂²×C₈₉	1	2	yes	—
483	#394	C₂²×C₈₉	1	2	yes	—
484	#394	C₂²×C₈₉	1	2	yes	—
485	#391	C₂²×C₈₉	1	2	yes	—
486	#391	C₂²×C₈₉	1	1	yes	characteristic
487	#391	C₂²×C₈₉	1	2	yes	—
488	#390	C₂²×C₈₉	1	1	yes	characteristic
489	#390	C₂²×C₈₉	1	2	yes	—
490	#389	C₂²×C₈₉	1	2	yes	—
491	#389	C₂²×C₈₉	1	2	yes	—
492	#389	C₂²×C₈₉	1	2	yes	—
493	#389	C₂²×C₈₉	1	2	yes	—
494	#389	C₂²×C₈₉	1	2	yes	—
495	#389	C₂²×C₈₉	1	2	yes	—
496	#389	C₂²×C₈₉	1	2	yes	—
497	#389	C₂²×C₈₉	1	2	yes	—
498	#388	C₂²×C₈₉	1	2	yes	—
499	#388	C₂²×C₈₉	1	2	yes	—
500	#388	C₂²×C₈₉	1	2	yes	—
501	#388	C₂²×C₈₉	1	2	yes	—
502	#388	C₂²×C₈₉	1	2	yes	—
503	#388	C₂²×C₈₉	1	2	yes	—
504	#388	C₂²×C₈₉	1	2	yes	—
505	#388	C₂²×C₈₉	1	2	yes	—
506	#388	C₂²×C₈₉	1	2	yes	—
507	#387	C₂²×C₈₉	1	2	yes	—
508	#387	C₂²×C₈₉	1	2	yes	—
509	#387	C₂²×C₈₉	1	2	yes	—
510	#387	C₂²×C₈₉	1	2	yes	—
511	#387	C₂²×C₈₉	1	2	yes	—
512	#387	C₂²×C₈₉	1	2	yes	—
513	#387	C₂²×C₈₉	1	2	yes	—
514	#387	C₂²×C₈₉	1	2	yes	—
515	#386	C₂²×C₈₉	1	1	yes	characteristic
516	#386	C₂²×C₈₉	1	2	yes	—
517	#386	C₂²×C₈₉	1	1	yes	characteristic
518	#386	C₂²×C₈₉	1	2	yes	—
519	#385	C₂²×C₈₉	1	2	yes	—
520	#385	C₂²×C₈₉	1	2	yes	—
521	#385	C₂²×C₈₉	1	2	yes	—
522	#385	C₂²×C₈₉	1	2	yes	—
523	#385	C₂²×C₈₉	1	2	yes	—
524	#385	C₂²×C₈₉	1	2	yes	—
525	#385	C₂²×C₈₉	1	2	yes	—
526	#385	C₂²×C₈₉	1	2	yes	—
527	#382	C₂²×C₈₉	1	2	yes	—
528	#381	C₂²×C₈₉	1	1	yes	characteristic
529	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
530	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
531	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
532	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
533	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
534	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
535	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
536	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
537	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
538	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
539	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
540	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
541	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
542	C₂×#41	—	2	4	no	—
543	C₂×#41	—	4	2	no	—
544	C₂×#41	—	4	2	no	—
545	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
546	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
547	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
548	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
549	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
550	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
551	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
552	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
553	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
554	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
555	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
556	C₄⋊Q₈	—	4	2	no	—
557	#126	—	2	8	no	—
558	#125	—	4	4	no	—
559	#124	—	4	2	no	—
560	#123	—	4	2	no	—
561	#123	—	4	2	no	—
562	C₂²⋊Q₈	—	2	4	no	—
563	#117	—	2	8	no	—
564	#117	—	2	8	no	—
565	#117	—	4	4	no	—
566	#117	—	4	2	no	—
567	C₂×C₄⋊C₄	—	2	4	no	—
568	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
605	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
606	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
608	C₂×C₄²	—	4	2	no	—
609	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
610	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
611	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
612	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
613	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
614	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
615	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
617	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
618	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
621	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
622	#95	C₂³×C₈₉	1	2	yes	—
623	#95	C₂³×C₈₉	1	2	yes	—
624	#95	C₂³×C₈₉	1	2	yes	—
625	#95	C₂³×C₈₉	1	2	yes	—
626	#95	C₂³×C₈₉	1	2	yes	—
627	#95	C₂³×C₈₉	1	2	yes	—
628	#95	C₂³×C₈₉	1	2	yes	—
629	#95	C₂³×C₈₉	1	2	yes	—
630	#95	C₂³×C₈₉	1	2	yes	—
631	#95	C₂³×C₈₉	1	2	yes	—
632	#95	C₂³×C₈₉	1	2	yes	—
633	#95	C₂³×C₈₉	1	2	yes	—
634	#95	C₂³×C₈₉	1	2	yes	—
635	#95	C₂³×C₈₉	1	2	yes	—
636	#95	C₂³×C₈₉	1	2	yes	—
637	#95	C₂³×C₈₉	1	2	yes	—
638	#95	C₂³×C₈₉	1	2	yes	—
639	#95	C₂³×C₈₉	1	2	yes	—
640	#95	C₂³×C₈₉	1	2	yes	—
641	#95	C₂³×C₈₉	1	2	yes	—
642	#95	C₂³×C₈₉	1	2	yes	—
643	#95	C₂³×C₈₉	1	2	yes	—
644	#95	C₂³×C₈₉	1	2	yes	—
645	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
646	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
647	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
648	#41	—	4	16	no	—
649	C₂×Q₈	—	2	2	no	—
650	C₂×Q₈	—	2	2	no	—
651	C₂×Q₈	—	2	2	no	—
652	C₂×Q₈	—	4	1	no	—
653	C₂×Q₈	—	4	1	no	—
654	C₂×Q₈	—	4	1	no	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	2	no	—
657	C₂×D₄	—	2	2	no	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	4	1	no	—
662	C₂×D₄	—	4	1	no	—
663	C₂×D₄	—	4	1	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	2	4	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	4	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	4	1	no	—
675	C₂²×C₄	—	4	1	no	—
676	C₂²×C₄	—	4	1	no	—
677	C₂²×C₄	—	4	1	no	—
678	C₂²×C₄	—	4	1	no	—
679	C₂²×C₄	—	4	1	no	—
680	C₂²×C₄	#41×C₈₉	1	4	yes	—
681	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
691	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	4	no	—
699	C₄⋊C₄	—	2	4	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	4	2	no	—
714	C₄⋊C₄	—	4	2	no	—
715	C₄⋊C₄	—	4	2	no	—
716	C₄⋊C₄	—	4	2	no	—
717	C₄⋊C₄	—	4	2	no	—
718	C₄⋊C₄	—	4	2	no	—
719	C₄⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	4	2	no	—
733	C₂²⋊C₄	—	4	1	no	—
734	C₂²⋊C₄	—	4	2	no	—
735	C₂²⋊C₄	—	4	1	no	—
736	C₂²⋊C₄	—	4	2	no	—
737	C₄²	—	2	4	no	—
738	C₄²	—	2	4	no	—
739	C₄²	—	4	1	no	—
740	C₄²	—	4	2	no	—
741	C₄²	—	4	1	no	—
742	C₄²	—	4	2	no	—
743	C₄²	—	4	2	no	—
744	C₄²	—	4	1	no	—
745	C₄²	—	4	1	no	—
746	C₄²	—	4	1	no	—
747	C₄²	—	4	2	no	—
748	C₄²	—	4	1	no	—
749	C₄²	#41×C₈₉	1	8	yes	complemented
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	1	no	—
753	C₂³	—	2	1	no	—
754	C₂³	—	2	1	no	—
755	C₂³	—	2	1	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	1	no	—
760	C₂³	—	2	1	no	—
761	C₂³	—	2	1	no	—
762	C₂³	—	2	2	no	—
763	C₂³	C₂×#41×C₈₉	1	2	yes	—
764	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
765	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
766	Q₈	—	4	4	no	—
767	Q₈	—	8	2	no	—
768	D₄	—	4	4	no	—
769	D₄	—	4	4	no	—
770	D₄	—	4	4	no	—
771	C₂×C₄	—	2	8	no	—
772	C₂×C₄	—	2	16	no	—
773	C₂×C₄	—	2	8	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	4	4	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	—	8	2	no	—
818	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
819	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
820	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
821	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
822	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
823	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
824	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	2	2	no	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	2	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	2	no	—
840	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
841	C₂²	C₂²×#41×C₈₉	1	2	yes	—
842	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
843	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
844	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
845	C₄	—	2	4	no	—
846	C₄	—	2	2	no	—
847	C₄	—	2	2	no	—
848	C₄	—	2	2	no	—
849	C₄	—	2	4	no	—
850	C₄	—	2	4	no	—
851	C₄	—	2	4	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	2	no	—
861	C₂	—	4	2	no	—
862	C₂	—	4	2	no	—
863	C₂	—	8	1	no	—
864	C₂	C₈₉×#3444	1	1	yes	characteristic
865	C₂	C₈₉×#3490	1	1	yes	characteristic
866	C₂	C₈₉×#3492	1	2	yes	—
867	C₂	C₈₉×#3509	1	1	yes	characteristic
868	C₂	C₈₉×#3511	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂²×#41×C₈₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#2609	C₂	semidirect
2. C₈₉×#2608	C₂	semidirect
3. C₈₉×#2601	C₂	semidirect
4. C₈₉×#2601	C₂	semidirect
5. C₈₉×#2588	C₂	semidirect
6. C₈₉×#2587	C₂	semidirect
7. C₈₉×#2583	C₂	semidirect
8. C₈₉×#2558	C₂	semidirect
9. C₈₉×#2550	C₂	semidirect
10. C₈₉×#2475	C₂	semidirect
11. C₈₉×#2474	C₂	semidirect
12. C₈₉×#2470	C₂	semidirect
15. C₈₉×#2334	C₂	semidirect
16. C₈₉×#2332	C₂	semidirect
18. C₈₉×#2296	C₂	semidirect
19. C₈₉×#2274	C₂	semidirect
314. C₄²×C₈₉	#41	semidirect
426. #35440	C₈₉	direct (N × H)
435. #2609	C₂×C₈₉	semidirect
436. #2608	C₂×C₈₉	semidirect
437. #2601	C₂×C₈₉	semidirect
438. #2601	C₂×C₈₉	semidirect
439. #2588	C₂×C₈₉	semidirect
440. #2587	C₂×C₈₉	semidirect
441. #2583	C₂×C₈₉	semidirect
442. #2558	C₂×C₈₉	semidirect
443. #2550	C₂×C₈₉	semidirect
444. #2475	C₂×C₈₉	semidirect
445. #2474	C₂×C₈₉	semidirect
446. #2470	C₂×C₈₉	semidirect
449. #2334	C₂×C₈₉	semidirect
450. #2332	C₂×C₈₉	semidirect
452. #2296	C₂×C₈₉	semidirect
453. #2274	C₂×C₈₉	semidirect
454. C₈₉	#35440	direct (N × H)
749. C₄²	#41×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#2609	2
C₈₉×#2608	2
C₈₉×#2601	2
C₈₉×#2588	2
C₈₉×#2587	2
C₈₉×#2583	2
C₈₉×#2558	2
C₈₉×#2550	2
C₈₉×#2475	2
C₈₉×#2474	2
C₈₉×#2470	2
C₈₉×#2432	2
C₈₉×#2406	2
C₈₉×#2334	2
C₈₉×#2332	2
C₈₉×#2297	2
C₈₉×#2296	2
C₈₉×#2274	2
#35440	89

Subgroups — C89×#35440 #36413288

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35440 #36413288