Subgroups — C₈₉×#35442 #36413290

Order 22784.

1758 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×#2611	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#2605	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2600	C₂	1	2	yes	maximal
4	C₈₉×#2598	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#2589	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2578	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2577	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2564	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2562	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2533	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2530	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2477	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2438	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2415	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2336	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2332	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2296	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#2290	C₂	1	2	yes	maximal, complemented
19	C₈₉×#2275	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
26	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#117×C₈₉	C₂²	1	2	yes	—
29	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
30	#400×C₈₉	C₂²	1	2	yes	—
31	#400×C₈₉	C₂²	1	2	yes	—
32	#400×C₈₉	C₂²	1	2	yes	—
33	#400×C₈₉	C₂²	1	1	yes	characteristic
34	#400×C₈₉	C₂²	1	1	yes	characteristic
35	#400×C₈₉	C₂²	1	2	yes	—
36	#399×C₈₉	C₂²	1	1	yes	characteristic
37	#399×C₈₉	C₂²	1	1	yes	characteristic
38	#398×C₈₉	C₂²	1	2	yes	—
39	#398×C₈₉	C₂²	1	1	yes	characteristic
40	#397×C₈₉	C₂²	1	2	yes	—
41	#397×C₈₉	C₂²	1	2	yes	—
42	#397×C₈₉	C₂²	1	1	yes	characteristic
43	#397×C₈₉	C₂²	1	2	yes	—
44	#395×C₈₉	C₂²	1	2	yes	—
45	#394×C₈₉	C₂²	1	2	yes	—
46	#394×C₈₉	C₂²	1	2	yes	—
47	#394×C₈₉	C₂²	1	1	yes	characteristic
48	#393×C₈₉	C₂²	1	2	yes	—
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	#389×C₈₉	C₂²	1	2	yes	—
54	#389×C₈₉	C₂²	1	2	yes	—
55	#389×C₈₉	C₂²	1	2	yes	—
56	#389×C₈₉	C₂²	1	2	yes	—
57	#388×C₈₉	C₂²	1	2	yes	—
58	#388×C₈₉	C₂²	1	2	yes	—
59	#388×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	#387×C₈₉	C₂²	1	2	yes	—
66	#387×C₈₉	C₂²	1	2	yes	—
67	#387×C₈₉	C₂²	1	2	yes	—
68	#387×C₈₉	C₂²	1	2	yes	—
69	#387×C₈₉	C₂²	1	2	yes	—
70	#387×C₈₉	C₂²	1	2	yes	—
71	#387×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	#386×C₈₉	C₂²	1	2	yes	—
79	#386×C₈₉	C₂²	1	2	yes	—
80	#386×C₈₉	C₂²	1	2	yes	—
81	#386×C₈₉	C₂²	1	2	yes	—
82	#385×C₈₉	C₂²	1	2	yes	—
83	#385×C₈₉	C₂²	1	2	yes	—
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	#383×C₈₉	C₂²	1	2	yes	—
89	#383×C₈₉	C₂²	1	1	yes	characteristic
90	#381×C₈₉	C₂²	1	2	yes	—
91	#380×C₈₉	C₂²	1	2	yes	—
92	#380×C₈₉	C₂²	1	2	yes	—
93	#380×C₈₉	C₂²	1	2	yes	—
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	1	yes	characteristic
98	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
101	C₄×C₂²⋊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	#376×C₈₉	C₂²	1	1	yes	characteristic
105	#376×C₈₉	C₂²	1	2	yes	—
106	C₂×#95×C₈₉	C₂²	1	2	yes	—
107	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
108	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
110	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
112	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
113	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
114	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
115	#125×C₈₉	—	2	4	no	—
116	C₂²⋊Q₈×C₈₉	—	2	8	no	—
117	C₂²⋊Q₈×C₈₉	—	4	4	no	—
118	C₄×D₄×C₈₉	—	2	8	no	—
119	C₄×D₄×C₈₉	—	2	8	no	—
120	C₄×D₄×C₈₉	—	2	4	no	—
121	#117×C₈₉	—	2	4	no	—
122	#117×C₈₉	—	4	4	no	—
123	#117×C₈₉	—	4	2	no	—
124	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	1	yes	characteristic
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	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	1	yes	characteristic
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×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	2	yes	—
149	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
165	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
166	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
169	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
170	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
173	#95×C₈₉	C₂³	1	1	yes	characteristic
174	#95×C₈₉	C₂³	1	2	yes	—
175	#95×C₈₉	C₂³	1	2	yes	—
176	#95×C₈₉	C₂³	1	2	yes	—
177	#95×C₈₉	C₂³	1	2	yes	—
178	#95×C₈₉	C₂³	1	1	yes	characteristic
179	#95×C₈₉	C₂³	1	2	yes	—
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	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	1	yes	characteristic
199	#95×C₈₉	C₂³	1	2	yes	—
200	#95×C₈₉	C₂³	1	1	yes	characteristic
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	—	4	2	no	—
208	C₂×Q₈×C₈₉	—	4	2	no	—
209	C₂×D₄×C₈₉	—	2	4	no	—
210	C₂×D₄×C₈₉	—	2	4	no	—
211	C₂×D₄×C₈₉	—	2	4	no	—
212	C₂×D₄×C₈₉	—	2	2	no	—
213	C₂×D₄×C₈₉	—	4	2	no	—
214	C₂²×C₄×C₈₉	—	2	2	no	—
215	C₂²×C₄×C₈₉	—	2	2	no	—
216	C₂²×C₄×C₈₉	—	2	2	no	—
217	C₂²×C₄×C₈₉	—	2	4	no	—
218	C₂²×C₄×C₈₉	—	2	4	no	—
219	C₂²×C₄×C₈₉	—	2	4	no	—
220	C₂²×C₄×C₈₉	—	4	2	no	—
221	C₂²×C₄×C₈₉	—	4	2	no	—
222	C₂²×C₄×C₈₉	—	4	2	no	—
223	C₂²×C₄×C₈₉	—	4	2	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	—	4	2	no	—
228	C₂²×C₄×C₈₉	#41	1	8	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	2	yes	—
234	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
246	C₄⋊C₄×C₈₉	—	2	2	no	—
247	C₄⋊C₄×C₈₉	—	2	2	no	—
248	C₄⋊C₄×C₈₉	—	2	4	no	—
249	C₄⋊C₄×C₈₉	—	2	4	no	—
250	C₄⋊C₄×C₈₉	—	2	2	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	—	2	4	no	—
255	C₄⋊C₄×C₈₉	—	2	4	no	—
256	C₄⋊C₄×C₈₉	—	2	2	no	—
257	C₄⋊C₄×C₈₉	—	2	2	no	—
258	C₄⋊C₄×C₈₉	—	2	4	no	—
259	C₄⋊C₄×C₈₉	—	2	4	no	—
260	C₄⋊C₄×C₈₉	—	4	2	no	—
261	C₄⋊C₄×C₈₉	—	4	2	no	—
262	C₄⋊C₄×C₈₉	—	4	2	no	—
263	C₄⋊C₄×C₈₉	—	4	2	no	—
264	C₄⋊C₄×C₈₉	—	4	2	no	—
265	C₄⋊C₄×C₈₉	—	4	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	2	no	—
272	C₂²⋊C₄×C₈₉	—	2	2	no	—
273	C₂²⋊C₄×C₈₉	—	2	4	no	—
274	C₂²⋊C₄×C₈₉	—	2	4	no	—
275	C₂²⋊C₄×C₈₉	—	2	4	no	—
276	C₂²⋊C₄×C₈₉	—	2	4	no	—
277	C₂²⋊C₄×C₈₉	—	4	2	no	—
278	C₂²⋊C₄×C₈₉	—	4	2	no	—
279	C₂²⋊C₄×C₈₉	—	4	2	no	—
280	C₂²⋊C₄×C₈₉	—	4	2	no	—
281	C₂²⋊C₄×C₈₉	—	4	2	no	—
282	C₄²×C₈₉	—	2	2	no	—
283	C₄²×C₈₉	—	2	4	no	—
284	C₄²×C₈₉	—	2	4	no	—
285	C₄²×C₈₉	—	2	4	no	—
286	C₄²×C₈₉	—	4	1	no	—
287	C₄²×C₈₉	—	4	1	no	—
288	C₄²×C₈₉	—	4	2	no	—
289	C₄²×C₈₉	—	4	2	no	—
290	C₄²×C₈₉	—	4	2	no	—
291	C₄²×C₈₉	—	4	1	no	—
292	C₄²×C₈₉	—	4	1	no	—
293	C₄²×C₈₉	#41	1	4	yes	—
294	C₂³×C₈₉	—	2	1	no	—
295	C₂³×C₈₉	—	2	2	no	—
296	C₂³×C₈₉	—	2	2	no	—
297	C₂³×C₈₉	—	2	2	no	—
298	C₂³×C₈₉	—	2	2	no	—
299	C₂³×C₈₉	—	2	1	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	C₂×#41	1	4	yes	—
305	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
306	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
307	Q₈×C₈₉	—	8	4	no	—
308	D₄×C₈₉	—	2	8	no	—
309	D₄×C₈₉	—	4	8	no	—
310	C₂×C₄×C₈₉	—	2	8	no	—
311	C₂×C₄×C₈₉	—	2	2	no	—
312	C₂×C₄×C₈₉	—	2	1	no	—
313	C₂×C₄×C₈₉	—	2	2	no	—
314	C₂×C₄×C₈₉	—	2	1	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	2	no	—
320	C₂×C₄×C₈₉	—	2	2	no	—
321	C₂×C₄×C₈₉	—	2	2	no	—
322	C₂×C₄×C₈₉	—	2	2	no	—
323	C₂×C₄×C₈₉	—	2	1	no	—
324	C₂×C₄×C₈₉	—	2	1	no	—
325	C₂×C₄×C₈₉	—	2	2	no	—
326	C₂×C₄×C₈₉	—	2	2	no	—
327	C₂×C₄×C₈₉	—	2	2	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	—	4	8	no	—
353	C₂×C₄×C₈₉	—	4	8	no	—
354	C₂×C₄×C₈₉	—	8	4	no	—
355	C₂×C₄×C₈₉	—	8	4	no	—
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	2	yes	—
360	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
361	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
362	C₂²×C₈₉	—	2	4	no	—
363	C₂²×C₈₉	—	2	2	no	—
364	C₂²×C₈₉	—	2	4	no	—
365	C₂²×C₈₉	—	2	4	no	—
366	C₂²×C₈₉	—	2	4	no	—
367	C₂²×C₈₉	—	4	1	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	1	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	2	no	—
380	C₄×C₈₉	—	2	2	no	—
381	C₄×C₈₉	—	2	2	no	—
382	C₄×C₈₉	—	2	4	no	—
383	C₄×C₈₉	—	2	4	no	—
384	C₄×C₈₉	—	2	2	no	—
385	C₄×C₈₉	—	4	2	no	—
386	C₄×C₈₉	—	4	1	no	—
387	C₄×C₈₉	—	4	2	no	—
388	C₄×C₈₉	—	4	2	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	1	no	—
395	C₄×C₈₉	—	4	2	no	—
396	#35442	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
397	C₂×C₈₉	—	4	4	no	—
398	C₂×C₈₉	—	4	2	no	—
399	C₂×C₈₉	#3444	1	1	yes	characteristic
400	C₂×C₈₉	#3492	1	1	yes	characteristic
401	C₂×C₈₉	#3495	1	2	yes	—
402	C₂×C₈₉	#3505	1	2	yes	—
403	C₂×C₈₉	#3510	1	1	yes	characteristic
404	#2611	C₂×C₈₉	1	1	yes	characteristic, complemented
405	#2605	C₂×C₈₉	1	1	yes	characteristic, complemented
406	#2600	C₂×C₈₉	1	2	yes	—
407	#2598	C₂×C₈₉	1	1	yes	characteristic
408	#2589	C₂×C₈₉	1	2	yes	complemented
409	#2578	C₂×C₈₉	1	2	yes	complemented
410	#2577	C₂×C₈₉	1	2	yes	complemented
411	#2564	C₂×C₈₉	1	2	yes	complemented
412	#2562	C₂×C₈₉	1	1	yes	characteristic, complemented
413	#2533	C₂×C₈₉	1	2	yes	complemented
414	#2530	C₂×C₈₉	1	2	yes	complemented
415	#2477	C₂×C₈₉	1	2	yes	complemented
416	#2438	C₂×C₈₉	1	2	yes	complemented
417	#2415	C₂×C₈₉	1	2	yes	complemented
418	#2336	C₂×C₈₉	1	1	yes	characteristic, complemented
419	#2332	C₂×C₈₉	1	2	yes	complemented
420	#2296	C₂×C₈₉	1	1	yes	characteristic, complemented
421	#2290	C₂×C₈₉	1	2	yes	complemented
422	#2275	C₂×C₈₉	1	1	yes	characteristic, complemented
423	C₈₉	#35442	1	1	yes	characteristic, direct product factor, Sylow
424	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
425	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
426	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
427	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
428	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
429	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
430	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
431	C₂×#117	C₂²×C₈₉	1	2	yes	—
432	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
433	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
434	#400	C₂²×C₈₉	1	2	yes	—
435	#400	C₂²×C₈₉	1	2	yes	—
436	#400	C₂²×C₈₉	1	2	yes	—
437	#400	C₂²×C₈₉	1	1	yes	characteristic
438	#400	C₂²×C₈₉	1	1	yes	characteristic
439	#400	C₂²×C₈₉	1	2	yes	—
440	#399	C₂²×C₈₉	1	1	yes	characteristic
441	#399	C₂²×C₈₉	1	1	yes	characteristic
442	#398	C₂²×C₈₉	1	2	yes	—
443	#398	C₂²×C₈₉	1	1	yes	characteristic
444	#397	C₂²×C₈₉	1	2	yes	—
445	#397	C₂²×C₈₉	1	2	yes	—
446	#397	C₂²×C₈₉	1	1	yes	characteristic
447	#397	C₂²×C₈₉	1	2	yes	—
448	#395	C₂²×C₈₉	1	2	yes	—
449	#394	C₂²×C₈₉	1	2	yes	—
450	#394	C₂²×C₈₉	1	2	yes	—
451	#394	C₂²×C₈₉	1	1	yes	characteristic
452	#393	C₂²×C₈₉	1	2	yes	—
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	#389	C₂²×C₈₉	1	2	yes	—
458	#389	C₂²×C₈₉	1	2	yes	—
459	#389	C₂²×C₈₉	1	2	yes	—
460	#389	C₂²×C₈₉	1	2	yes	—
461	#388	C₂²×C₈₉	1	2	yes	—
462	#388	C₂²×C₈₉	1	2	yes	—
463	#388	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	#387	C₂²×C₈₉	1	2	yes	—
470	#387	C₂²×C₈₉	1	2	yes	—
471	#387	C₂²×C₈₉	1	2	yes	—
472	#387	C₂²×C₈₉	1	2	yes	—
473	#387	C₂²×C₈₉	1	2	yes	—
474	#387	C₂²×C₈₉	1	2	yes	—
475	#387	C₂²×C₈₉	1	2	yes	—
476	#387	C₂²×C₈₉	1	2	yes	—
477	#387	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	#386	C₂²×C₈₉	1	2	yes	—
483	#386	C₂²×C₈₉	1	2	yes	—
484	#386	C₂²×C₈₉	1	2	yes	—
485	#386	C₂²×C₈₉	1	2	yes	—
486	#385	C₂²×C₈₉	1	2	yes	—
487	#385	C₂²×C₈₉	1	2	yes	—
488	#385	C₂²×C₈₉	1	2	yes	—
489	#385	C₂²×C₈₉	1	2	yes	—
490	#385	C₂²×C₈₉	1	2	yes	—
491	#385	C₂²×C₈₉	1	2	yes	—
492	#383	C₂²×C₈₉	1	2	yes	—
493	#383	C₂²×C₈₉	1	1	yes	characteristic
494	#381	C₂²×C₈₉	1	2	yes	—
495	#380	C₂²×C₈₉	1	2	yes	—
496	#380	C₂²×C₈₉	1	2	yes	—
497	#380	C₂²×C₈₉	1	2	yes	—
498	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
499	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
500	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
501	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
502	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
503	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
504	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
505	C₄×C₂²⋊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	#376	C₂²×C₈₉	1	1	yes	characteristic
509	#376	C₂²×C₈₉	1	2	yes	—
510	C₂×#95	C₂²×C₈₉	1	2	yes	—
511	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
512	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
513	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
514	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
516	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
517	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
518	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
519	#125	—	2	4	no	—
520	C₂²⋊Q₈	—	2	8	no	—
521	C₂²⋊Q₈	—	4	4	no	—
522	C₄×D₄	—	2	8	no	—
523	C₄×D₄	—	2	8	no	—
524	C₄×D₄	—	2	4	no	—
525	#117	—	2	4	no	—
526	#117	—	4	4	no	—
527	#117	—	4	2	no	—
528	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
566	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
567	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
568	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
569	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
570	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
571	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
572	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
573	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
574	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
575	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
576	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
577	#95	C₂³×C₈₉	1	1	yes	characteristic
578	#95	C₂³×C₈₉	1	2	yes	—
579	#95	C₂³×C₈₉	1	2	yes	—
580	#95	C₂³×C₈₉	1	2	yes	—
581	#95	C₂³×C₈₉	1	2	yes	—
582	#95	C₂³×C₈₉	1	1	yes	characteristic
583	#95	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
599	#95	C₂³×C₈₉	1	2	yes	—
600	#95	C₂³×C₈₉	1	2	yes	—
601	#95	C₂³×C₈₉	1	2	yes	—
602	#95	C₂³×C₈₉	1	1	yes	characteristic
603	#95	C₂³×C₈₉	1	2	yes	—
604	#95	C₂³×C₈₉	1	1	yes	characteristic
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	—	4	2	no	—
612	C₂×Q₈	—	4	2	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	4	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	4	2	no	—
625	C₂²×C₄	—	4	2	no	—
626	C₂²×C₄	—	4	2	no	—
627	C₂²×C₄	—	4	2	no	—
628	C₂²×C₄	—	4	2	no	—
629	C₂²×C₄	—	4	2	no	—
630	C₂²×C₄	—	4	2	no	—
631	C₂²×C₄	—	4	2	no	—
632	C₂²×C₄	#41×C₈₉	1	8	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	2	yes	—
638	C₂²×C₄	C₂⁴×C₈₉	1	2	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	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
647	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
648	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	2	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	4	2	no	—
665	C₄⋊C₄	—	4	2	no	—
666	C₄⋊C₄	—	4	2	no	—
667	C₄⋊C₄	—	4	2	no	—
668	C₄⋊C₄	—	4	2	no	—
669	C₄⋊C₄	—	4	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	2	no	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	4	2	no	—
682	C₂²⋊C₄	—	4	2	no	—
683	C₂²⋊C₄	—	4	2	no	—
684	C₂²⋊C₄	—	4	2	no	—
685	C₂²⋊C₄	—	4	2	no	—
686	C₄²	—	2	2	no	—
687	C₄²	—	2	4	no	—
688	C₄²	—	2	4	no	—
689	C₄²	—	2	4	no	—
690	C₄²	—	4	1	no	—
691	C₄²	—	4	1	no	—
692	C₄²	—	4	2	no	—
693	C₄²	—	4	1	no	—
694	C₄²	—	4	1	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	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	C₂×#41×C₈₉	1	4	yes	—
709	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
710	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
711	Q₈	—	8	4	no	—
712	D₄	—	2	8	no	—
713	D₄	—	4	8	no	—
714	C₂×C₄	—	2	8	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	1	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	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	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	—	4	8	no	—
757	C₂×C₄	—	4	8	no	—
758	C₂×C₄	—	8	4	no	—
759	C₂×C₄	—	8	4	no	—
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	2	yes	—
764	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
765	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
766	C₂²	—	2	4	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	2	4	no	—
769	C₂²	—	2	4	no	—
770	C₂²	—	2	4	no	—
771	C₂²	—	4	1	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	1	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	2	no	—
784	C₄	—	2	2	no	—
785	C₄	—	2	2	no	—
786	C₄	—	2	4	no	—
787	C₄	—	2	4	no	—
788	C₄	—	2	2	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	1	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	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	1	no	—
800	C₂	—	4	4	no	—
801	C₂	—	4	2	no	—
802	C₂	C₈₉×#3444	1	1	yes	characteristic
803	C₂	C₈₉×#3492	1	1	yes	characteristic
804	C₂	C₈₉×#3495	1	2	yes	—
805	C₂	C₈₉×#3505	1	2	yes	—
806	C₂	C₈₉×#3510	1	1	yes	characteristic

	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
1. C₈₉×#2611	C₂	semidirect
2. C₈₉×#2605	C₂	semidirect
5. C₈₉×#2589	C₂	semidirect
6. C₈₉×#2578	C₂	semidirect
7. C₈₉×#2577	C₂	semidirect
8. C₈₉×#2564	C₂	semidirect
9. C₈₉×#2562	C₂	semidirect
10. C₈₉×#2533	C₂	semidirect
11. C₈₉×#2530	C₂	semidirect
12. C₈₉×#2477	C₂	semidirect
13. C₈₉×#2438	C₂	semidirect
14. C₈₉×#2415	C₂	semidirect
15. C₈₉×#2336	C₂	semidirect
16. C₈₉×#2332	C₂	semidirect
17. C₈₉×#2296	C₂	semidirect
18. C₈₉×#2290	C₂	semidirect
19. C₈₉×#2275	C₂	semidirect
396. #35442	C₈₉	direct (N × H)
404. #2611	C₂×C₈₉	semidirect
405. #2605	C₂×C₈₉	semidirect
408. #2589	C₂×C₈₉	semidirect
409. #2578	C₂×C₈₉	semidirect
410. #2577	C₂×C₈₉	semidirect
411. #2564	C₂×C₈₉	semidirect
412. #2562	C₂×C₈₉	semidirect
413. #2533	C₂×C₈₉	semidirect
414. #2530	C₂×C₈₉	semidirect
415. #2477	C₂×C₈₉	semidirect
416. #2438	C₂×C₈₉	semidirect
417. #2415	C₂×C₈₉	semidirect
418. #2336	C₂×C₈₉	semidirect
419. #2332	C₂×C₈₉	semidirect
420. #2296	C₂×C₈₉	semidirect
421. #2290	C₂×C₈₉	semidirect
422. #2275	C₂×C₈₉	semidirect
423. C₈₉	#35442	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×#2611	2
C₈₉×#2605	2
C₈₉×#2600	2
C₈₉×#2598	2
C₈₉×#2589	2
C₈₉×#2578	2
C₈₉×#2577	2
C₈₉×#2564	2
C₈₉×#2562	2
C₈₉×#2533	2
C₈₉×#2530	2
C₈₉×#2477	2
C₈₉×#2438	2
C₈₉×#2415	2
C₈₉×#2336	2
C₈₉×#2332	2
C₈₉×#2296	2
C₈₉×#2290	2
C₈₉×#2275	2
#35442	89

Subgroups — C89×#35442 #36413290

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35442 #36413290