Subgroups — C₈₉×#35428 #36413276

Order 22784.

1730 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2610	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2605	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2599	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2594	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2594	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2592	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2586	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2527	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2526	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2474	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2465	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2461	C₂	1	2	yes	maximal
13	C₈₉×#2458	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2447	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2337	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2332	C₂	1	2	yes	maximal, complemented
17	C₄×#123×C₈₉	C₂	1	2	yes	maximal, complemented
18	C₈₉×#2296	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2276	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₈₉	C₂²	1	2	yes	—
22	C₂×#123×C₈₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
27	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
30	#401×C₈₉	C₂²	1	2	yes	—
31	#400×C₈₉	C₂²	1	2	yes	—
32	#398×C₈₉	C₂²	1	2	yes	—
33	#398×C₈₉	C₂²	1	1	yes	characteristic
34	#397×C₈₉	C₂²	1	2	yes	—
35	#397×C₈₉	C₂²	1	2	yes	—
36	#397×C₈₉	C₂²	1	1	yes	characteristic
37	#397×C₈₉	C₂²	1	2	yes	—
38	#396×C₈₉	C₂²	1	2	yes	—
39	#396×C₈₉	C₂²	1	2	yes	—
40	#395×C₈₉	C₂²	1	1	yes	characteristic
41	#395×C₈₉	C₂²	1	2	yes	—
42	#395×C₈₉	C₂²	1	2	yes	—
43	#395×C₈₉	C₂²	1	1	yes	characteristic
44	#394×C₈₉	C₂²	1	1	yes	characteristic
45	#394×C₈₉	C₂²	1	2	yes	—
46	#393×C₈₉	C₂²	1	2	yes	—
47	#393×C₈₉	C₂²	1	1	yes	characteristic
48	#393×C₈₉	C₂²	1	1	yes	characteristic
49	#392×C₈₉	C₂²	1	1	yes	characteristic
50	#391×C₈₉	C₂²	1	2	yes	—
51	#391×C₈₉	C₂²	1	2	yes	—
52	#391×C₈₉	C₂²	1	2	yes	—
53	#391×C₈₉	C₂²	1	2	yes	—
54	#391×C₈₉	C₂²	1	2	yes	—
55	#390×C₈₉	C₂²	1	2	yes	—
56	#390×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	#388×C₈₉	C₂²	1	2	yes	—
61	#388×C₈₉	C₂²	1	2	yes	—
62	#388×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	#388×C₈₉	C₂²	1	2	yes	—
73	#388×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	#387×C₈₉	C₂²	1	2	yes	—
81	#387×C₈₉	C₂²	1	2	yes	—
82	#387×C₈₉	C₂²	1	2	yes	—
83	#387×C₈₉	C₂²	1	2	yes	—
84	#386×C₈₉	C₂²	1	2	yes	—
85	#386×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	#383×C₈₉	C₂²	1	1	yes	characteristic
91	#381×C₈₉	C₂²	1	2	yes	—
92	#381×C₈₉	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
94	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
95	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
96	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
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×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
105	#376×C₈₉	C₂²	1	1	yes	characteristic
106	#376×C₈₉	C₂²	1	2	yes	—
107	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
110	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
111	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
114	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
115	#124×C₈₉	—	2	4	no	—
116	#124×C₈₉	—	4	4	no	—
117	#123×C₈₉	—	2	8	no	—
118	C₂²⋊Q₈×C₈₉	—	2	8	no	—
119	C₄×Q₈×C₈₉	—	2	8	no	—
120	C₄×Q₈×C₈₉	—	2	4	no	—
121	C₄×D₄×C₈₉	—	4	4	no	—
122	#117×C₈₉	—	2	4	no	—
123	#117×C₈₉	—	4	2	no	—
124	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	1	yes	characteristic
133	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
148	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	2	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	2	yes	—
158	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₈₉	—	4	2	no	—
161	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
163	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
164	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
165	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
168	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
169	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
171	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
172	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
175	#95×C₈₉	C₂³	1	1	yes	characteristic
176	#95×C₈₉	C₂³	1	2	yes	—
177	#95×C₈₉	C₂³	1	2	yes	—
178	#95×C₈₉	C₂³	1	2	yes	—
179	#95×C₈₉	C₂³	1	1	yes	characteristic
180	#95×C₈₉	C₂³	1	2	yes	—
181	#95×C₈₉	C₂³	1	2	yes	—
182	#95×C₈₉	C₂³	1	2	yes	—
183	#95×C₈₉	C₂³	1	2	yes	—
184	#95×C₈₉	C₂³	1	2	yes	—
185	#95×C₈₉	C₂³	1	2	yes	—
186	#95×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	1	yes	characteristic
195	#95×C₈₉	C₂³	1	2	yes	—
196	#95×C₈₉	C₂³	1	1	yes	characteristic
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	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
205	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
206	C₂×Q₈×C₈₉	—	2	4	no	—
207	C₂×Q₈×C₈₉	—	2	2	no	—
208	C₂×Q₈×C₈₉	—	2	4	no	—
209	C₂×Q₈×C₈₉	—	2	2	no	—
210	C₂×Q₈×C₈₉	—	4	2	no	—
211	C₂×Q₈×C₈₉	—	4	2	no	—
212	C₂×Q₈×C₈₉	—	4	2	no	—
213	C₂×D₄×C₈₉	—	2	4	no	—
214	C₂×D₄×C₈₉	—	2	4	no	—
215	C₂×D₄×C₈₉	—	2	2	no	—
216	C₂×D₄×C₈₉	—	4	2	no	—
217	C₂×D₄×C₈₉	—	4	2	no	—
218	C₂²×C₄×C₈₉	—	2	2	no	—
219	C₂²×C₄×C₈₉	—	2	2	no	—
220	C₂²×C₄×C₈₉	—	2	2	no	—
221	C₂²×C₄×C₈₉	—	2	4	no	—
222	C₂²×C₄×C₈₉	—	2	4	no	—
223	C₂²×C₄×C₈₉	—	2	4	no	—
224	C₂²×C₄×C₈₉	—	4	2	no	—
225	C₂²×C₄×C₈₉	—	4	2	no	—
226	C₂²×C₄×C₈₉	—	4	2	no	—
227	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
244	C₄⋊C₄×C₈₉	—	2	2	no	—
245	C₄⋊C₄×C₈₉	—	2	2	no	—
246	C₄⋊C₄×C₈₉	—	2	4	no	—
247	C₄⋊C₄×C₈₉	—	2	4	no	—
248	C₄⋊C₄×C₈₉	—	2	4	no	—
249	C₄⋊C₄×C₈₉	—	2	2	no	—
250	C₄⋊C₄×C₈₉	—	2	4	no	—
251	C₄⋊C₄×C₈₉	—	2	4	no	—
252	C₄⋊C₄×C₈₉	—	2	4	no	—
253	C₄⋊C₄×C₈₉	—	2	4	no	—
254	C₄⋊C₄×C₈₉	—	4	2	no	—
255	C₄⋊C₄×C₈₉	—	4	2	no	—
256	C₄⋊C₄×C₈₉	—	4	2	no	—
257	C₄⋊C₄×C₈₉	—	4	2	no	—
258	C₄⋊C₄×C₈₉	—	4	2	no	—
259	C₄⋊C₄×C₈₉	—	4	2	no	—
260	C₄⋊C₄×C₈₉	—	4	2	no	—
261	C₄⋊C₄×C₈₉	#41	1	8	yes	—
262	C₂²⋊C₄×C₈₉	—	2	4	no	—
263	C₂²⋊C₄×C₈₉	—	2	4	no	—
264	C₂²⋊C₄×C₈₉	—	2	2	no	—
265	C₂²⋊C₄×C₈₉	—	2	2	no	—
266	C₂²⋊C₄×C₈₉	—	2	4	no	—
267	C₂²⋊C₄×C₈₉	—	2	4	no	—
268	C₂²⋊C₄×C₈₉	—	2	4	no	—
269	C₂²⋊C₄×C₈₉	—	2	4	no	—
270	C₂²⋊C₄×C₈₉	—	2	4	no	—
271	C₂²⋊C₄×C₈₉	—	2	4	no	—
272	C₂²⋊C₄×C₈₉	—	2	4	no	—
273	C₂²⋊C₄×C₈₉	—	2	4	no	—
274	C₂²⋊C₄×C₈₉	—	4	2	no	—
275	C₂²⋊C₄×C₈₉	—	4	2	no	—
276	C₂²⋊C₄×C₈₉	—	4	2	no	—
277	C₂²⋊C₄×C₈₉	—	4	2	no	—
278	C₂²⋊C₄×C₈₉	—	4	2	no	—
279	C₂²⋊C₄×C₈₉	—	4	2	no	—
280	C₄²×C₈₉	—	2	2	no	—
281	C₄²×C₈₉	—	2	4	no	—
282	C₄²×C₈₉	—	2	4	no	—
283	C₄²×C₈₉	—	2	4	no	—
284	C₄²×C₈₉	—	2	4	no	—
285	C₄²×C₈₉	—	4	1	no	—
286	C₄²×C₈₉	—	4	1	no	—
287	C₄²×C₈₉	—	4	2	no	—
288	C₄²×C₈₉	—	4	2	no	—
289	C₄²×C₈₉	—	4	1	no	—
290	C₄²×C₈₉	—	4	1	no	—
291	C₄²×C₈₉	—	4	2	no	—
292	C₄²×C₈₉	—	4	2	no	—
293	C₄²×C₈₉	#41	1	4	yes	—
294	C₂³×C₈₉	—	2	1	no	—
295	C₂³×C₈₉	—	2	2	no	—
296	C₂³×C₈₉	—	2	1	no	—
297	C₂³×C₈₉	—	2	2	no	—
298	C₂³×C₈₉	—	2	2	no	—
299	C₂³×C₈₉	—	2	2	no	—
300	C₂³×C₈₉	—	2	2	no	—
301	C₂³×C₈₉	—	2	2	no	—
302	C₂³×C₈₉	—	2	2	no	—
303	C₂³×C₈₉	—	2	2	no	—
304	C₂³×C₈₉	—	2	2	no	—
305	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
306	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
307	Q₈×C₈₉	—	2	8	no	—
308	Q₈×C₈₉	—	8	2	no	—
309	Q₈×C₈₉	—	8	4	no	—
310	D₄×C₈₉	—	4	8	no	—
311	D₄×C₈₉	—	8	2	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	1	no	—
317	C₂×C₄×C₈₉	—	2	1	no	—
318	C₂×C₄×C₈₉	—	2	2	no	—
319	C₂×C₄×C₈₉	—	2	1	no	—
320	C₂×C₄×C₈₉	—	2	2	no	—
321	C₂×C₄×C₈₉	—	2	1	no	—
322	C₂×C₄×C₈₉	—	2	2	no	—
323	C₂×C₄×C₈₉	—	2	2	no	—
324	C₂×C₄×C₈₉	—	2	2	no	—
325	C₂×C₄×C₈₉	—	2	2	no	—
326	C₂×C₄×C₈₉	—	2	1	no	—
327	C₂×C₄×C₈₉	—	2	1	no	—
328	C₂×C₄×C₈₉	—	2	2	no	—
329	C₂×C₄×C₈₉	—	2	2	no	—
330	C₂×C₄×C₈₉	—	2	2	no	—
331	C₂×C₄×C₈₉	—	2	2	no	—
332	C₂×C₄×C₈₉	—	2	2	no	—
333	C₂×C₄×C₈₉	—	2	2	no	—
334	C₂×C₄×C₈₉	—	2	2	no	—
335	C₂×C₄×C₈₉	—	2	2	no	—
336	C₂×C₄×C₈₉	—	2	2	no	—
337	C₂×C₄×C₈₉	—	2	2	no	—
338	C₂×C₄×C₈₉	—	2	2	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	2	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	2	no	—
347	C₂×C₄×C₈₉	—	2	2	no	—
348	C₂×C₄×C₈₉	—	2	2	no	—
349	C₂×C₄×C₈₉	—	2	2	no	—
350	C₂×C₄×C₈₉	—	2	2	no	—
351	C₂×C₄×C₈₉	—	2	2	no	—
352	C₂×C₄×C₈₉	—	2	2	no	—
353	C₂×C₄×C₈₉	—	4	8	no	—
354	C₂×C₄×C₈₉	—	8	4	no	—
355	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
356	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
357	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
358	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
359	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
360	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
361	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
362	C₂²×C₈₉	—	2	2	no	—
363	C₂²×C₈₉	—	2	4	no	—
364	C₂²×C₈₉	—	4	1	no	—
365	C₂²×C₈₉	—	4	1	no	—
366	C₂²×C₈₉	—	4	2	no	—
367	C₂²×C₈₉	—	4	2	no	—
368	C₂²×C₈₉	—	4	2	no	—
369	C₂²×C₈₉	—	4	2	no	—
370	C₂²×C₈₉	—	4	2	no	—
371	C₂²×C₈₉	—	4	2	no	—
372	C₂²×C₈₉	—	4	2	no	—
373	C₂²×C₈₉	—	4	2	no	—
374	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
375	C₂²×C₈₉	C₂²×#41	1	2	yes	—
376	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
377	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
378	C₂²×C₈₉	#585	1	2	yes	—
379	C₄×C₈₉	—	2	4	no	—
380	C₄×C₈₉	—	2	2	no	—
381	C₄×C₈₉	—	2	2	no	—
382	C₄×C₈₉	—	2	2	no	—
383	C₄×C₈₉	—	2	2	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	2	no	—
391	C₄×C₈₉	—	4	2	no	—
392	C₄×C₈₉	—	4	2	no	—
393	C₄×C₈₉	—	4	2	no	—
394	C₄×C₈₉	—	4	2	no	—
395	C₄×C₈₉	—	4	2	no	—
396	#35428	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
397	C₂×C₈₉	—	4	2	no	—
398	C₂×C₈₉	—	8	2	no	—
399	C₂×C₈₉	#3444	1	1	yes	characteristic
400	C₂×C₈₉	#3492	1	1	yes	characteristic
401	C₂×C₈₉	#3510	1	1	yes	characteristic
402	C₂×C₈₉	#3513	1	2	yes	—
403	C₂×C₈₉	#3518	1	2	yes	—
404	#2610	C₂×C₈₉	1	1	yes	characteristic
405	#2605	C₂×C₈₉	1	1	yes	characteristic, complemented
406	#2599	C₂×C₈₉	1	1	yes	characteristic, complemented
407	#2594	C₂×C₈₉	1	2	yes	complemented
408	#2594	C₂×C₈₉	1	2	yes	complemented
409	#2592	C₂×C₈₉	1	1	yes	characteristic, complemented
410	#2586	C₂×C₈₉	1	2	yes	complemented
411	#2527	C₂×C₈₉	1	2	yes	complemented
412	#2526	C₂×C₈₉	1	2	yes	complemented
413	#2474	C₂×C₈₉	1	2	yes	complemented
414	#2465	C₂×C₈₉	1	2	yes	complemented
415	#2461	C₂×C₈₉	1	2	yes	—
416	#2458	C₂×C₈₉	1	2	yes	complemented
417	#2447	C₂×C₈₉	1	2	yes	complemented
418	#2337	C₂×C₈₉	1	1	yes	characteristic, complemented
419	#2332	C₂×C₈₉	1	2	yes	complemented
420	C₄×#123	C₂×C₈₉	1	2	yes	complemented
421	#2296	C₂×C₈₉	1	1	yes	characteristic, complemented
422	#2276	C₂×C₈₉	1	1	yes	characteristic, complemented
423	C₈₉	#35428	1	1	yes	characteristic, direct product factor, Sylow
424	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
425	C₂×#124	C₂²×C₈₉	1	2	yes	—
426	C₂×#123	C₂²×C₈₉	1	2	yes	—
427	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
428	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
429	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
430	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
431	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
432	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
433	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
434	#401	C₂²×C₈₉	1	2	yes	—
435	#400	C₂²×C₈₉	1	2	yes	—
436	#398	C₂²×C₈₉	1	2	yes	—
437	#398	C₂²×C₈₉	1	1	yes	characteristic
438	#397	C₂²×C₈₉	1	2	yes	—
439	#397	C₂²×C₈₉	1	2	yes	—
440	#397	C₂²×C₈₉	1	1	yes	characteristic
441	#397	C₂²×C₈₉	1	2	yes	—
442	#396	C₂²×C₈₉	1	2	yes	—
443	#396	C₂²×C₈₉	1	2	yes	—
444	#395	C₂²×C₈₉	1	1	yes	characteristic
445	#395	C₂²×C₈₉	1	2	yes	—
446	#395	C₂²×C₈₉	1	2	yes	—
447	#395	C₂²×C₈₉	1	1	yes	characteristic
448	#394	C₂²×C₈₉	1	1	yes	characteristic
449	#394	C₂²×C₈₉	1	2	yes	—
450	#393	C₂²×C₈₉	1	2	yes	—
451	#393	C₂²×C₈₉	1	1	yes	characteristic
452	#393	C₂²×C₈₉	1	1	yes	characteristic
453	#392	C₂²×C₈₉	1	1	yes	characteristic
454	#391	C₂²×C₈₉	1	2	yes	—
455	#391	C₂²×C₈₉	1	2	yes	—
456	#391	C₂²×C₈₉	1	2	yes	—
457	#391	C₂²×C₈₉	1	2	yes	—
458	#391	C₂²×C₈₉	1	2	yes	—
459	#390	C₂²×C₈₉	1	2	yes	—
460	#390	C₂²×C₈₉	1	2	yes	—
461	#389	C₂²×C₈₉	1	2	yes	—
462	#389	C₂²×C₈₉	1	2	yes	—
463	#389	C₂²×C₈₉	1	2	yes	—
464	#388	C₂²×C₈₉	1	2	yes	—
465	#388	C₂²×C₈₉	1	2	yes	—
466	#388	C₂²×C₈₉	1	2	yes	—
467	#388	C₂²×C₈₉	1	2	yes	—
468	#388	C₂²×C₈₉	1	2	yes	—
469	#388	C₂²×C₈₉	1	2	yes	—
470	#388	C₂²×C₈₉	1	2	yes	—
471	#388	C₂²×C₈₉	1	2	yes	—
472	#388	C₂²×C₈₉	1	2	yes	—
473	#388	C₂²×C₈₉	1	2	yes	—
474	#388	C₂²×C₈₉	1	2	yes	—
475	#388	C₂²×C₈₉	1	2	yes	—
476	#388	C₂²×C₈₉	1	2	yes	—
477	#388	C₂²×C₈₉	1	2	yes	—
478	#387	C₂²×C₈₉	1	2	yes	—
479	#387	C₂²×C₈₉	1	2	yes	—
480	#387	C₂²×C₈₉	1	2	yes	—
481	#387	C₂²×C₈₉	1	2	yes	—
482	#387	C₂²×C₈₉	1	2	yes	—
483	#387	C₂²×C₈₉	1	2	yes	—
484	#387	C₂²×C₈₉	1	2	yes	—
485	#387	C₂²×C₈₉	1	2	yes	—
486	#387	C₂²×C₈₉	1	2	yes	—
487	#387	C₂²×C₈₉	1	2	yes	—
488	#386	C₂²×C₈₉	1	2	yes	—
489	#386	C₂²×C₈₉	1	2	yes	—
490	#385	C₂²×C₈₉	1	2	yes	—
491	#385	C₂²×C₈₉	1	2	yes	—
492	#385	C₂²×C₈₉	1	2	yes	—
493	#385	C₂²×C₈₉	1	2	yes	—
494	#383	C₂²×C₈₉	1	1	yes	characteristic
495	#381	C₂²×C₈₉	1	2	yes	—
496	#381	C₂²×C₈₉	1	2	yes	—
497	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
498	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
499	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
500	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
501	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
502	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
503	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
504	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
505	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
506	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
507	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
508	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
509	#376	C₂²×C₈₉	1	1	yes	characteristic
510	#376	C₂²×C₈₉	1	2	yes	—
511	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
512	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
513	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
514	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
515	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
516	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
517	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
518	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
519	#124	—	2	4	no	—
520	#124	—	4	4	no	—
521	#123	—	2	8	no	—
522	C₂²⋊Q₈	—	2	8	no	—
523	C₄×Q₈	—	2	8	no	—
524	C₄×Q₈	—	2	4	no	—
525	C₄×D₄	—	4	4	no	—
526	#117	—	2	4	no	—
527	#117	—	4	2	no	—
528	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
534	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
548	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
549	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
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	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	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	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
564	C₂×C₄²	—	4	2	no	—
565	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
566	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
567	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
568	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
569	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
570	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
571	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
572	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
573	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
574	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
575	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
576	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
577	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
578	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
579	#95	C₂³×C₈₉	1	1	yes	characteristic
580	#95	C₂³×C₈₉	1	2	yes	—
581	#95	C₂³×C₈₉	1	2	yes	—
582	#95	C₂³×C₈₉	1	2	yes	—
583	#95	C₂³×C₈₉	1	1	yes	characteristic
584	#95	C₂³×C₈₉	1	2	yes	—
585	#95	C₂³×C₈₉	1	2	yes	—
586	#95	C₂³×C₈₉	1	2	yes	—
587	#95	C₂³×C₈₉	1	2	yes	—
588	#95	C₂³×C₈₉	1	2	yes	—
589	#95	C₂³×C₈₉	1	2	yes	—
590	#95	C₂³×C₈₉	1	2	yes	—
591	#95	C₂³×C₈₉	1	2	yes	—
592	#95	C₂³×C₈₉	1	2	yes	—
593	#95	C₂³×C₈₉	1	2	yes	—
594	#95	C₂³×C₈₉	1	2	yes	—
595	#95	C₂³×C₈₉	1	2	yes	—
596	#95	C₂³×C₈₉	1	2	yes	—
597	#95	C₂³×C₈₉	1	2	yes	—
598	#95	C₂³×C₈₉	1	1	yes	characteristic
599	#95	C₂³×C₈₉	1	2	yes	—
600	#95	C₂³×C₈₉	1	1	yes	characteristic
601	#95	C₂³×C₈₉	1	2	yes	—
602	#95	C₂³×C₈₉	1	2	yes	—
603	#95	C₂³×C₈₉	1	2	yes	—
604	#95	C₂³×C₈₉	1	2	yes	—
605	#95	C₂³×C₈₉	1	2	yes	—
606	#95	C₂³×C₈₉	1	2	yes	—
607	#95	C₂³×C₈₉	1	2	yes	—
608	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
609	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
610	C₂×Q₈	—	2	4	no	—
611	C₂×Q₈	—	2	2	no	—
612	C₂×Q₈	—	2	4	no	—
613	C₂×Q₈	—	2	2	no	—
614	C₂×Q₈	—	4	2	no	—
615	C₂×Q₈	—	4	2	no	—
616	C₂×Q₈	—	4	2	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	2	no	—
620	C₂×D₄	—	4	2	no	—
621	C₂×D₄	—	4	2	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	4	2	no	—
629	C₂²×C₄	—	4	2	no	—
630	C₂²×C₄	—	4	2	no	—
631	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
642	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
643	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
646	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	4	2	no	—
659	C₄⋊C₄	—	4	2	no	—
660	C₄⋊C₄	—	4	2	no	—
661	C₄⋊C₄	—	4	2	no	—
662	C₄⋊C₄	—	4	2	no	—
663	C₄⋊C₄	—	4	2	no	—
664	C₄⋊C₄	—	4	2	no	—
665	C₄⋊C₄	#41×C₈₉	1	8	yes	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	2	no	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	4	2	no	—
679	C₂²⋊C₄	—	4	2	no	—
680	C₂²⋊C₄	—	4	2	no	—
681	C₂²⋊C₄	—	4	2	no	—
682	C₂²⋊C₄	—	4	2	no	—
683	C₂²⋊C₄	—	4	2	no	—
684	C₄²	—	2	2	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	4	no	—
687	C₄²	—	2	4	no	—
688	C₄²	—	2	4	no	—
689	C₄²	—	4	1	no	—
690	C₄²	—	4	1	no	—
691	C₄²	—	4	2	no	—
692	C₄²	—	4	1	no	—
693	C₄²	—	4	1	no	—
694	C₄²	—	4	2	no	—
695	C₄²	—	4	2	no	—
696	C₄²	—	4	2	no	—
697	C₄²	#41×C₈₉	1	4	yes	—
698	C₂³	—	2	1	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	1	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	2	no	—
709	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
710	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
711	Q₈	—	2	8	no	—
712	Q₈	—	8	2	no	—
713	Q₈	—	8	4	no	—
714	D₄	—	4	8	no	—
715	D₄	—	8	2	no	—
716	C₂×C₄	—	2	8	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	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	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	4	8	no	—
758	C₂×C₄	—	8	4	no	—
759	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
760	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
761	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
762	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
763	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
764	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
765	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	4	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
779	C₂²	C₂²×#41×C₈₉	1	2	yes	—
780	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
781	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
782	C₂²	#585×C₈₉	1	2	yes	—
783	C₄	—	2	4	no	—
784	C₄	—	2	2	no	—
785	C₄	—	2	2	no	—
786	C₄	—	2	2	no	—
787	C₄	—	2	2	no	—
788	C₄	—	2	4	no	—
789	C₄	—	2	4	no	—
790	C₄	—	4	1	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	1	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	2	no	—
800	C₂	—	4	2	no	—
801	C₂	—	8	2	no	—
802	C₂	C₈₉×#3444	1	1	yes	characteristic
803	C₂	C₈₉×#3492	1	1	yes	characteristic
804	C₂	C₈₉×#3510	1	1	yes	characteristic
805	C₂	C₈₉×#3513	1	2	yes	—
806	C₂	C₈₉×#3518	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	#392×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
2. C₈₉×#2605	C₂	semidirect
3. C₈₉×#2599	C₂	semidirect
4. C₈₉×#2594	C₂	semidirect
5. C₈₉×#2594	C₂	semidirect
6. C₈₉×#2592	C₂	semidirect
7. C₈₉×#2586	C₂	semidirect
8. C₈₉×#2527	C₂	semidirect
9. C₈₉×#2526	C₂	semidirect
10. C₈₉×#2474	C₂	semidirect
11. C₈₉×#2465	C₂	semidirect
13. C₈₉×#2458	C₂	semidirect
14. C₈₉×#2447	C₂	semidirect
15. C₈₉×#2337	C₂	semidirect
16. C₈₉×#2332	C₂	semidirect
17. C₄×#123×C₈₉	C₂	semidirect
18. C₈₉×#2296	C₂	semidirect
19. C₈₉×#2276	C₂	semidirect
396. #35428	C₈₉	direct (N × H)
405. #2605	C₂×C₈₉	semidirect
406. #2599	C₂×C₈₉	semidirect
407. #2594	C₂×C₈₉	semidirect
408. #2594	C₂×C₈₉	semidirect
409. #2592	C₂×C₈₉	semidirect
410. #2586	C₂×C₈₉	semidirect
411. #2527	C₂×C₈₉	semidirect
412. #2526	C₂×C₈₉	semidirect
413. #2474	C₂×C₈₉	semidirect
414. #2465	C₂×C₈₉	semidirect
416. #2458	C₂×C₈₉	semidirect
417. #2447	C₂×C₈₉	semidirect
418. #2337	C₂×C₈₉	semidirect
419. #2332	C₂×C₈₉	semidirect
420. C₄×#123	C₂×C₈₉	semidirect
421. #2296	C₂×C₈₉	semidirect
422. #2276	C₂×C₈₉	semidirect
423. C₈₉	#35428	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#2610	2
C₈₉×#2605	2
C₈₉×#2599	2
C₈₉×#2594	2
C₈₉×#2592	2
C₈₉×#2586	2
C₈₉×#2527	2
C₈₉×#2526	2
C₈₉×#2474	2
C₈₉×#2465	2
C₈₉×#2461	2
C₈₉×#2458	2
C₈₉×#2447	2
C₈₉×#2337	2
C₈₉×#2332	2
C₄×#123×C₈₉	2
C₈₉×#2296	2
C₈₉×#2276	2
#35428	89

Subgroups — C89×#35428 #36413276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35428 #36413276