Subgroups — C₈₉×#35506 #36413354

Order 22784.

1622 conjugacy classes of subgroups.

The subgroup lattice has 796 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×#2595	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2594	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2591	C₂	1	1	yes	maximal, characteristic
8	C₈₉×#2576	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2570	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2529	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2528	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2526	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2500	C₂	1	1	yes	maximal, characteristic
14	C₈₉×#2484	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2334	C₂	1	2	yes	maximal, complemented
16	C₈₉×#2333	C₂	1	1	yes	maximal, characteristic
17	C₈₉×#2298	C₂	1	2	yes	maximal, complemented
18	C₈₉×#2298	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2274	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#126×C₈₉	C₂²	1	2	yes	—
21	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#117×C₈₉	C₂²	1	2	yes	—
23	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#117×C₈₉	C₂²	1	2	yes	—
25	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
26	#401×C₈₉	C₂²	1	2	yes	—
27	#400×C₈₉	C₂²	1	2	yes	—
28	#400×C₈₉	C₂²	1	2	yes	—
29	#400×C₈₉	C₂²	1	2	yes	—
30	#398×C₈₉	C₂²	1	2	yes	—
31	#398×C₈₉	C₂²	1	2	yes	—
32	#398×C₈₉	C₂²	1	2	yes	—
33	#397×C₈₉	C₂²	1	2	yes	—
34	#397×C₈₉	C₂²	1	2	yes	—
35	#396×C₈₉	C₂²	1	2	yes	—
36	#396×C₈₉	C₂²	1	2	yes	—
37	#396×C₈₉	C₂²	1	2	yes	—
38	#396×C₈₉	C₂²	1	2	yes	—
39	#394×C₈₉	C₂²	1	2	yes	—
40	#394×C₈₉	C₂²	1	2	yes	—
41	#394×C₈₉	C₂²	1	2	yes	—
42	#390×C₈₉	C₂²	1	2	yes	—
43	#390×C₈₉	C₂²	1	1	yes	characteristic
44	#390×C₈₉	C₂²	1	1	yes	characteristic
45	#389×C₈₉	C₂²	1	2	yes	—
46	#389×C₈₉	C₂²	1	2	yes	—
47	#389×C₈₉	C₂²	1	2	yes	—
48	#389×C₈₉	C₂²	1	2	yes	—
49	#388×C₈₉	C₂²	1	2	yes	—
50	#388×C₈₉	C₂²	1	2	yes	—
51	#388×C₈₉	C₂²	1	2	yes	—
52	#388×C₈₉	C₂²	1	2	yes	—
53	#388×C₈₉	C₂²	1	2	yes	—
54	#388×C₈₉	C₂²	1	2	yes	—
55	#388×C₈₉	C₂²	1	2	yes	—
56	#388×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	#387×C₈₉	C₂²	1	2	yes	—
64	#387×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	#386×C₈₉	C₂²	1	2	yes	—
77	#386×C₈₉	C₂²	1	2	yes	—
78	#386×C₈₉	C₂²	1	2	yes	—
79	#386×C₈₉	C₂²	1	2	yes	—
80	#385×C₈₉	C₂²	1	2	yes	—
81	#385×C₈₉	C₂²	1	2	yes	—
82	#385×C₈₉	C₂²	1	1	yes	characteristic
83	#385×C₈₉	C₂²	1	1	yes	characteristic
84	#384×C₈₉	C₂²	1	1	yes	characteristic
85	#382×C₈₉	C₂²	1	2	yes	—
86	#382×C₈₉	C₂²	1	2	yes	—
87	#382×C₈₉	C₂²	1	1	yes	characteristic
88	#381×C₈₉	C₂²	1	1	yes	characteristic
89	#381×C₈₉	C₂²	1	1	yes	characteristic
90	#381×C₈₉	C₂²	1	1	yes	characteristic
91	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
93	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
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×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
104	#376×C₈₉	C₂²	1	2	yes	—
105	#376×C₈₉	C₂²	1	1	yes	characteristic
106	C₄³×C₈₉	C₂²	1	1	yes	characteristic
107	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
108	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
112	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
113	#126×C₈₉	—	2	8	no	—
114	#121×C₈₉	—	2	4	no	—
115	#117×C₈₉	—	2	4	no	—
116	#117×C₈₉	—	2	8	no	—
117	#117×C₈₉	—	2	8	no	—
118	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
119	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	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	2	yes	—
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×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
152	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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×C₄²×C₈₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
168	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
171	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
173	#95×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
199	#95×C₈₉	C₂³	1	2	yes	—
200	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
201	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
202	C₂×D₄×C₈₉	—	2	4	no	—
203	C₂×D₄×C₈₉	—	2	2	no	—
204	C₂×D₄×C₈₉	—	4	1	no	—
205	C₂×D₄×C₈₉	—	4	1	no	—
206	C₂×D₄×C₈₉	—	4	2	no	—
207	C₂×D₄×C₈₉	—	4	2	no	—
208	C₂²×C₄×C₈₉	—	2	2	no	—
209	C₂²×C₄×C₈₉	—	2	4	no	—
210	C₂²×C₄×C₈₉	—	2	2	no	—
211	C₂²×C₄×C₈₉	—	2	4	no	—
212	C₂²×C₄×C₈₉	—	4	1	no	—
213	C₂²×C₄×C₈₉	—	4	1	no	—
214	C₂²×C₄×C₈₉	—	4	2	no	—
215	C₂²×C₄×C₈₉	—	4	2	no	—
216	C₂²×C₄×C₈₉	—	4	1	no	—
217	C₂²×C₄×C₈₉	—	4	1	no	—
218	C₂²×C₄×C₈₉	#41	1	4	yes	—
219	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
236	C₄⋊C₄×C₈₉	—	2	4	no	—
237	C₄⋊C₄×C₈₉	—	2	4	no	—
238	C₄⋊C₄×C₈₉	—	2	4	no	—
239	C₄⋊C₄×C₈₉	—	2	4	no	—
240	C₄⋊C₄×C₈₉	—	2	2	no	—
241	C₄⋊C₄×C₈₉	—	2	2	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	4	no	—
247	C₄⋊C₄×C₈₉	—	2	4	no	—
248	C₄⋊C₄×C₈₉	—	4	2	no	—
249	C₄⋊C₄×C₈₉	—	4	2	no	—
250	C₄⋊C₄×C₈₉	—	4	2	no	—
251	C₄⋊C₄×C₈₉	—	4	2	no	—
252	C₄⋊C₄×C₈₉	—	4	2	no	—
253	C₄⋊C₄×C₈₉	—	4	2	no	—
254	C₄⋊C₄×C₈₉	—	4	2	no	—
255	C₄⋊C₄×C₈₉	—	4	2	no	—
256	C₂²⋊C₄×C₈₉	—	2	2	no	—
257	C₂²⋊C₄×C₈₉	—	2	2	no	—
258	C₂²⋊C₄×C₈₉	—	2	4	no	—
259	C₂²⋊C₄×C₈₉	—	2	4	no	—
260	C₂²⋊C₄×C₈₉	—	2	4	no	—
261	C₂²⋊C₄×C₈₉	—	2	4	no	—
262	C₂²⋊C₄×C₈₉	—	2	4	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	—	4	2	no	—
267	C₂²⋊C₄×C₈₉	—	4	2	no	—
268	C₂²⋊C₄×C₈₉	—	4	2	no	—
269	C₂²⋊C₄×C₈₉	—	4	2	no	—
270	C₂²⋊C₄×C₈₉	—	4	2	no	—
271	C₂²⋊C₄×C₈₉	—	4	1	no	—
272	C₂²⋊C₄×C₈₉	—	4	2	no	—
273	C₂²⋊C₄×C₈₉	—	4	2	no	—
274	C₂²⋊C₄×C₈₉	—	4	1	no	—
275	C₄²×C₈₉	—	2	2	no	—
276	C₄²×C₈₉	—	2	2	no	—
277	C₄²×C₈₉	—	2	4	no	—
278	C₄²×C₈₉	—	2	4	no	—
279	C₄²×C₈₉	—	4	1	no	—
280	C₄²×C₈₉	—	4	2	no	—
281	C₄²×C₈₉	—	4	1	no	—
282	C₄²×C₈₉	—	4	1	no	—
283	C₄²×C₈₉	—	4	2	no	—
284	C₄²×C₈₉	—	4	1	no	—
285	C₄²×C₈₉	—	4	2	no	—
286	C₄²×C₈₉	—	4	1	no	—
287	C₄²×C₈₉	—	4	2	no	—
288	C₄²×C₈₉	—	4	1	no	—
289	C₄²×C₈₉	#41	1	8	yes	—
290	C₂³×C₈₉	—	2	2	no	—
291	C₂³×C₈₉	—	2	1	no	—
292	C₂³×C₈₉	—	2	1	no	—
293	C₂³×C₈₉	—	2	2	no	—
294	C₂³×C₈₉	—	2	2	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	2	no	—
300	C₂³×C₈₉	—	2	2	no	—
301	C₂³×C₈₉	C₂×#41	1	2	yes	—
302	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
303	D₄×C₈₉	—	8	2	no	—
304	D₄×C₈₉	—	8	4	no	—
305	C₂×C₄×C₈₉	—	2	8	no	—
306	C₂×C₄×C₈₉	—	2	2	no	—
307	C₂×C₄×C₈₉	—	2	2	no	—
308	C₂×C₄×C₈₉	—	2	2	no	—
309	C₂×C₄×C₈₉	—	2	1	no	—
310	C₂×C₄×C₈₉	—	2	1	no	—
311	C₂×C₄×C₈₉	—	2	2	no	—
312	C₂×C₄×C₈₉	—	2	2	no	—
313	C₂×C₄×C₈₉	—	2	1	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	1	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	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	—	4	4	no	—
349	C₂×C₄×C₈₉	—	4	8	no	—
350	C₂×C₄×C₈₉	—	8	2	no	—
351	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
352	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
353	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
354	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
355	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
356	C₂²×C₈₉	—	2	2	no	—
357	C₂²×C₈₉	—	2	2	no	—
358	C₂²×C₈₉	—	2	2	no	—
359	C₂²×C₈₉	—	4	2	no	—
360	C₂²×C₈₉	—	4	2	no	—
361	C₂²×C₈₉	—	4	2	no	—
362	C₂²×C₈₉	—	4	2	no	—
363	C₂²×C₈₉	—	4	2	no	—
364	C₂²×C₈₉	—	4	2	no	—
365	C₂²×C₈₉	—	4	2	no	—
366	C₂²×C₈₉	—	4	2	no	—
367	C₂²×C₈₉	—	4	2	no	—
368	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
369	C₂²×C₈₉	C₂²×#41	1	2	yes	—
370	C₂²×C₈₉	#585	1	1	yes	characteristic
371	C₂²×C₈₉	#585	1	1	yes	characteristic
372	C₂²×C₈₉	#585	1	2	yes	—
373	C₄×C₈₉	—	2	4	no	—
374	C₄×C₈₉	—	2	2	no	—
375	C₄×C₈₉	—	2	2	no	—
376	C₄×C₈₉	—	2	4	no	—
377	C₄×C₈₉	—	2	4	no	—
378	C₄×C₈₉	—	4	1	no	—
379	C₄×C₈₉	—	4	1	no	—
380	C₄×C₈₉	—	4	2	no	—
381	C₄×C₈₉	—	4	2	no	—
382	C₄×C₈₉	—	4	2	no	—
383	C₄×C₈₉	—	4	2	no	—
384	C₄×C₈₉	—	4	1	no	—
385	C₄×C₈₉	—	4	1	no	—
386	C₄×C₈₉	—	4	2	no	—
387	C₄×C₈₉	—	4	2	no	—
388	C₄×C₈₉	—	4	2	no	—
389	C₄×C₈₉	—	4	2	no	—
390	#35506	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
391	C₂×C₈₉	—	4	2	no	—
392	C₂×C₈₉	—	8	2	no	—
393	C₂×C₈₉	#3444	1	1	yes	characteristic
394	C₂×C₈₉	#3491	1	1	yes	characteristic
395	C₂×C₈₉	#3493	1	2	yes	—
396	C₂×C₈₉	#3510	1	1	yes	characteristic
397	C₂×C₈₉	#3512	1	2	yes	—
398	#2609	C₂×C₈₉	1	2	yes	complemented
399	#2608	C₂×C₈₉	1	1	yes	characteristic, complemented
400	#2601	C₂×C₈₉	1	2	yes	complemented
401	#2601	C₂×C₈₉	1	2	yes	complemented
402	#2595	C₂×C₈₉	1	2	yes	complemented
403	#2594	C₂×C₈₉	1	2	yes	complemented
404	#2591	C₂×C₈₉	1	1	yes	characteristic
405	#2576	C₂×C₈₉	1	2	yes	complemented
406	#2570	C₂×C₈₉	1	2	yes	complemented
407	#2529	C₂×C₈₉	1	2	yes	complemented
408	#2528	C₂×C₈₉	1	2	yes	complemented
409	#2526	C₂×C₈₉	1	2	yes	complemented
410	#2500	C₂×C₈₉	1	1	yes	characteristic
411	#2484	C₂×C₈₉	1	1	yes	characteristic, complemented
412	#2334	C₂×C₈₉	1	2	yes	complemented
413	#2333	C₂×C₈₉	1	1	yes	characteristic
414	#2298	C₂×C₈₉	1	2	yes	complemented
415	#2298	C₂×C₈₉	1	1	yes	characteristic, complemented
416	#2274	C₂×C₈₉	1	1	yes	characteristic, complemented
417	C₈₉	#35506	1	1	yes	characteristic, direct product factor, Sylow
418	C₂×#126	C₂²×C₈₉	1	2	yes	—
419	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
420	C₂×#117	C₂²×C₈₉	1	2	yes	—
421	C₂×#117	C₂²×C₈₉	1	2	yes	—
422	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
423	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
424	#401	C₂²×C₈₉	1	2	yes	—
425	#400	C₂²×C₈₉	1	2	yes	—
426	#400	C₂²×C₈₉	1	2	yes	—
427	#400	C₂²×C₈₉	1	2	yes	—
428	#398	C₂²×C₈₉	1	2	yes	—
429	#398	C₂²×C₈₉	1	2	yes	—
430	#398	C₂²×C₈₉	1	2	yes	—
431	#397	C₂²×C₈₉	1	2	yes	—
432	#397	C₂²×C₈₉	1	2	yes	—
433	#396	C₂²×C₈₉	1	2	yes	—
434	#396	C₂²×C₈₉	1	2	yes	—
435	#396	C₂²×C₈₉	1	2	yes	—
436	#396	C₂²×C₈₉	1	2	yes	—
437	#394	C₂²×C₈₉	1	2	yes	—
438	#394	C₂²×C₈₉	1	2	yes	—
439	#394	C₂²×C₈₉	1	2	yes	—
440	#390	C₂²×C₈₉	1	2	yes	—
441	#390	C₂²×C₈₉	1	1	yes	characteristic
442	#390	C₂²×C₈₉	1	1	yes	characteristic
443	#389	C₂²×C₈₉	1	2	yes	—
444	#389	C₂²×C₈₉	1	2	yes	—
445	#389	C₂²×C₈₉	1	2	yes	—
446	#389	C₂²×C₈₉	1	2	yes	—
447	#388	C₂²×C₈₉	1	2	yes	—
448	#388	C₂²×C₈₉	1	2	yes	—
449	#388	C₂²×C₈₉	1	2	yes	—
450	#388	C₂²×C₈₉	1	2	yes	—
451	#388	C₂²×C₈₉	1	2	yes	—
452	#388	C₂²×C₈₉	1	2	yes	—
453	#388	C₂²×C₈₉	1	2	yes	—
454	#388	C₂²×C₈₉	1	2	yes	—
455	#388	C₂²×C₈₉	1	2	yes	—
456	#388	C₂²×C₈₉	1	2	yes	—
457	#388	C₂²×C₈₉	1	2	yes	—
458	#388	C₂²×C₈₉	1	2	yes	—
459	#388	C₂²×C₈₉	1	2	yes	—
460	#388	C₂²×C₈₉	1	2	yes	—
461	#387	C₂²×C₈₉	1	2	yes	—
462	#387	C₂²×C₈₉	1	2	yes	—
463	#387	C₂²×C₈₉	1	2	yes	—
464	#387	C₂²×C₈₉	1	2	yes	—
465	#387	C₂²×C₈₉	1	2	yes	—
466	#387	C₂²×C₈₉	1	2	yes	—
467	#387	C₂²×C₈₉	1	2	yes	—
468	#387	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	#386	C₂²×C₈₉	1	2	yes	—
475	#386	C₂²×C₈₉	1	2	yes	—
476	#386	C₂²×C₈₉	1	2	yes	—
477	#386	C₂²×C₈₉	1	2	yes	—
478	#385	C₂²×C₈₉	1	2	yes	—
479	#385	C₂²×C₈₉	1	2	yes	—
480	#385	C₂²×C₈₉	1	1	yes	characteristic
481	#385	C₂²×C₈₉	1	1	yes	characteristic
482	#384	C₂²×C₈₉	1	1	yes	characteristic
483	#382	C₂²×C₈₉	1	2	yes	—
484	#382	C₂²×C₈₉	1	2	yes	—
485	#382	C₂²×C₈₉	1	1	yes	characteristic
486	#381	C₂²×C₈₉	1	1	yes	characteristic
487	#381	C₂²×C₈₉	1	1	yes	characteristic
488	#381	C₂²×C₈₉	1	1	yes	characteristic
489	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
490	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
491	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
492	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
493	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
494	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
495	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
496	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
497	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
498	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
499	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
500	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
501	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
502	#376	C₂²×C₈₉	1	2	yes	—
503	#376	C₂²×C₈₉	1	1	yes	characteristic
504	C₄³	C₂²×C₈₉	1	1	yes	characteristic
505	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
506	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
507	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
508	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
510	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
511	#126	—	2	8	no	—
512	#121	—	2	4	no	—
513	#117	—	2	4	no	—
514	#117	—	2	8	no	—
515	#117	—	2	8	no	—
516	C₂×C₄⋊C₄	—	2	4	no	—
517	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
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	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	2	yes	—
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×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
541	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
551	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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×C₄²	C₂³×C₈₉	1	2	yes	—
557	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
558	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
559	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
561	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
562	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
564	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
565	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
566	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
567	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
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	#95	C₂³×C₈₉	1	2	yes	—
572	#95	C₂³×C₈₉	1	2	yes	—
573	#95	C₂³×C₈₉	1	2	yes	—
574	#95	C₂³×C₈₉	1	2	yes	—
575	#95	C₂³×C₈₉	1	2	yes	—
576	#95	C₂³×C₈₉	1	2	yes	—
577	#95	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
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	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
599	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	4	1	no	—
603	C₂×D₄	—	4	1	no	—
604	C₂×D₄	—	4	2	no	—
605	C₂×D₄	—	4	2	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	—	4	1	no	—
611	C₂²×C₄	—	4	1	no	—
612	C₂²×C₄	—	4	2	no	—
613	C₂²×C₄	—	4	2	no	—
614	C₂²×C₄	—	4	1	no	—
615	C₂²×C₄	—	4	1	no	—
616	C₂²×C₄	#41×C₈₉	1	4	yes	—
617	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
621	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
624	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
630	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
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	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	4	2	no	—
647	C₄⋊C₄	—	4	2	no	—
648	C₄⋊C₄	—	4	2	no	—
649	C₄⋊C₄	—	4	2	no	—
650	C₄⋊C₄	—	4	2	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₄⋊C₄	—	4	2	no	—
653	C₄⋊C₄	—	4	2	no	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	4	2	no	—
665	C₂²⋊C₄	—	4	2	no	—
666	C₂²⋊C₄	—	4	2	no	—
667	C₂²⋊C₄	—	4	2	no	—
668	C₂²⋊C₄	—	4	2	no	—
669	C₂²⋊C₄	—	4	1	no	—
670	C₂²⋊C₄	—	4	2	no	—
671	C₂²⋊C₄	—	4	2	no	—
672	C₂²⋊C₄	—	4	1	no	—
673	C₄²	—	2	2	no	—
674	C₄²	—	2	2	no	—
675	C₄²	—	2	4	no	—
676	C₄²	—	2	4	no	—
677	C₄²	—	4	1	no	—
678	C₄²	—	4	2	no	—
679	C₄²	—	4	1	no	—
680	C₄²	—	4	1	no	—
681	C₄²	—	4	2	no	—
682	C₄²	—	4	1	no	—
683	C₄²	—	4	2	no	—
684	C₄²	—	4	1	no	—
685	C₄²	—	4	2	no	—
686	C₄²	—	4	1	no	—
687	C₄²	#41×C₈₉	1	8	yes	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	2	1	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	C₂×#41×C₈₉	1	2	yes	—
700	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
701	D₄	—	8	2	no	—
702	D₄	—	8	4	no	—
703	C₂×C₄	—	2	8	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	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	2	no	—
728	C₂×C₄	—	2	2	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	—	4	4	no	—
747	C₂×C₄	—	4	8	no	—
748	C₂×C₄	—	8	2	no	—
749	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
750	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
751	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
752	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
753	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
754	C₂²	—	2	2	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	2	no	—
766	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
767	C₂²	C₂²×#41×C₈₉	1	2	yes	—
768	C₂²	#585×C₈₉	1	1	yes	characteristic
769	C₂²	#585×C₈₉	1	1	yes	characteristic
770	C₂²	#585×C₈₉	1	2	yes	—
771	C₄	—	2	4	no	—
772	C₄	—	2	2	no	—
773	C₄	—	2	2	no	—
774	C₄	—	2	4	no	—
775	C₄	—	2	4	no	—
776	C₄	—	4	1	no	—
777	C₄	—	4	1	no	—
778	C₄	—	4	2	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	2	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	1	no	—
784	C₄	—	4	1	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₂	—	4	2	no	—
789	C₂	—	8	2	no	—
790	C₂	C₈₉×#3444	1	1	yes	characteristic
791	C₂	C₈₉×#3491	1	1	yes	characteristic
792	C₂	C₈₉×#3493	1	2	yes	—
793	C₂	C₈₉×#3510	1	1	yes	characteristic
794	C₂	C₈₉×#3512	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂×#121×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×#2595	C₂	semidirect
6. C₈₉×#2594	C₂	semidirect
8. C₈₉×#2576	C₂	semidirect
9. C₈₉×#2570	C₂	semidirect
10. C₈₉×#2529	C₂	semidirect
11. C₈₉×#2528	C₂	semidirect
12. C₈₉×#2526	C₂	semidirect
14. C₈₉×#2484	C₂	semidirect
15. C₈₉×#2334	C₂	semidirect
17. C₈₉×#2298	C₂	semidirect
18. C₈₉×#2298	C₂	semidirect
19. C₈₉×#2274	C₂	semidirect
390. #35506	C₈₉	direct (N × H)
398. #2609	C₂×C₈₉	semidirect
399. #2608	C₂×C₈₉	semidirect
400. #2601	C₂×C₈₉	semidirect
401. #2601	C₂×C₈₉	semidirect
402. #2595	C₂×C₈₉	semidirect
403. #2594	C₂×C₈₉	semidirect
405. #2576	C₂×C₈₉	semidirect
406. #2570	C₂×C₈₉	semidirect
407. #2529	C₂×C₈₉	semidirect
408. #2528	C₂×C₈₉	semidirect
409. #2526	C₂×C₈₉	semidirect
411. #2484	C₂×C₈₉	semidirect
412. #2334	C₂×C₈₉	semidirect
414. #2298	C₂×C₈₉	semidirect
415. #2298	C₂×C₈₉	semidirect
416. #2274	C₂×C₈₉	semidirect
417. C₈₉	#35506	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×#2609	2
C₈₉×#2608	2
C₈₉×#2601	2
C₈₉×#2595	2
C₈₉×#2594	2
C₈₉×#2591	2
C₈₉×#2576	2
C₈₉×#2570	2
C₈₉×#2529	2
C₈₉×#2528	2
C₈₉×#2526	2
C₈₉×#2500	2
C₈₉×#2484	2
C₈₉×#2334	2
C₈₉×#2333	2
C₈₉×#2298	2
C₈₉×#2274	2
#35506	89

Subgroups — C89×#35506 #36413354

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35506 #36413354