Subgroups — C₈₉×#36544 #36414392

Order 22784.

2504 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2851	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2584	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2580	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2567	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2538	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2465	C₂	1	4	yes	maximal, complemented
10	C₈₉×#2449	C₂	1	4	yes	maximal, complemented
11	C₈₉×#2423	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2409	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2360	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2355	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×C₄⋊C₄×C₈₉	C₂	1	2	yes	maximal, complemented
16	C₄×#121×C₈₉	C₂	1	1	yes	maximal, characteristic
17	C₄×#121×C₈₉	C₂	1	2	yes	maximal
18	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
19	#554×C₈₉	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#125×C₈₉	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
25	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
26	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₈₉	—	2	8	no	—
28	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
38	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
40	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
41	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
42	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
43	#399×C₈₉	C₂²	1	4	yes	—
44	#398×C₈₉	C₂²	1	4	yes	—
45	#396×C₈₉	C₂²	1	4	yes	—
46	#395×C₈₉	C₂²	1	4	yes	—
47	#395×C₈₉	C₂²	1	4	yes	—
48	#393×C₈₉	C₂²	1	4	yes	—
49	#391×C₈₉	C₂²	1	2	yes	—
50	#391×C₈₉	C₂²	1	2	yes	—
51	#391×C₈₉	C₂²	1	2	yes	—
52	#390×C₈₉	C₂²	1	1	yes	characteristic
53	#390×C₈₉	C₂²	1	2	yes	—
54	#389×C₈₉	C₂²	1	2	yes	—
55	#389×C₈₉	C₂²	1	1	yes	characteristic
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	4	yes	—
60	#389×C₈₉	C₂²	1	4	yes	—
61	#389×C₈₉	C₂²	1	2	yes	—
62	#388×C₈₉	C₂²	1	4	yes	—
63	#388×C₈₉	C₂²	1	2	yes	—
64	#387×C₈₉	C₂²	1	4	yes	—
65	#387×C₈₉	C₂²	1	4	yes	—
66	#387×C₈₉	C₂²	1	4	yes	—
67	#386×C₈₉	C₂²	1	4	yes	—
68	#386×C₈₉	C₂²	1	2	yes	—
69	#385×C₈₉	C₂²	1	4	yes	—
70	#385×C₈₉	C₂²	1	4	yes	—
71	#385×C₈₉	C₂²	1	4	yes	—
72	#385×C₈₉	C₂²	1	4	yes	—
73	#384×C₈₉	C₂²	1	2	yes	—
74	#384×C₈₉	C₂²	1	1	yes	characteristic
75	#382×C₈₉	C₂²	1	2	yes	—
76	#380×C₈₉	C₂²	1	1	yes	characteristic
77	#380×C₈₉	C₂²	1	2	yes	—
78	#380×C₈₉	C₂²	1	2	yes	—
79	#380×C₈₉	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
81	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
82	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
84	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
85	C₂²×Q₈×C₈₉	—	2	4	no	—
86	C₂²×Q₈×C₈₉	—	2	4	no	—
87	C₂²×Q₈×C₈₉	—	2	4	no	—
88	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
89	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
93	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
95	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
96	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
97	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
101	C₄⋊Q₈×C₈₉	—	2	4	no	—
102	#125×C₈₉	—	2	8	no	—
103	C₂²⋊Q₈×C₈₉	—	2	8	no	—
104	C₂²⋊Q₈×C₈₉	—	2	8	no	—
105	C₂²⋊Q₈×C₈₉	—	2	16	no	—
106	C₂²⋊Q₈×C₈₉	—	4	4	no	—
107	#121×C₈₉	Q₈	1	8	yes	complemented
108	C₄×Q₈×C₈₉	—	2	4	no	—
109	C₄×Q₈×C₈₉	—	2	4	no	—
110	C₄×Q₈×C₈₉	—	2	8	no	—
111	C₄×Q₈×C₈₉	—	2	8	no	—
112	C₄×Q₈×C₈₉	—	2	4	no	—
113	C₄×Q₈×C₈₉	D₄	1	8	yes	complemented
114	C₄×D₄×C₈₉	—	2	8	no	—
115	C₄×D₄×C₈₉	—	2	8	no	—
116	C₄×D₄×C₈₉	—	2	4	no	—
117	C₄×D₄×C₈₉	—	4	8	no	—
118	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
119	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
120	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
121	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
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	4	yes	—
131	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	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	4	yes	—
137	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
139	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	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	4	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	4	yes	—
151	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
152	C₂×C₄²×C₈₉	—	2	8	no	—
153	C₂×C₄²×C₈₉	—	2	4	no	—
154	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
162	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
163	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
164	#95×C₈₉	C₂³	1	2	yes	—
165	#95×C₈₉	C₂³	1	4	yes	—
166	#95×C₈₉	C₂³	1	2	yes	—
167	#95×C₈₉	C₂³	1	4	yes	—
168	#95×C₈₉	C₂³	1	4	yes	—
169	#95×C₈₉	C₂³	1	2	yes	—
170	#95×C₈₉	C₂³	1	4	yes	—
171	#95×C₈₉	C₂³	1	4	yes	—
172	#95×C₈₉	C₂³	1	4	yes	—
173	#95×C₈₉	C₂³	1	4	yes	—
174	#95×C₈₉	C₂³	1	4	yes	—
175	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
176	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
177	C₂×Q₈×C₈₉	—	2	32	no	—
178	C₂×Q₈×C₈₉	—	2	4	no	—
179	C₂×Q₈×C₈₉	—	2	2	no	—
180	C₂×Q₈×C₈₉	—	2	4	no	—
181	C₂×Q₈×C₈₉	—	2	4	no	—
182	C₂×Q₈×C₈₉	—	2	4	no	—
183	C₂×Q₈×C₈₉	—	2	2	no	—
184	C₂×Q₈×C₈₉	—	2	2	no	—
185	C₂×Q₈×C₈₉	—	2	2	no	—
186	C₂×Q₈×C₈₉	—	4	2	no	—
187	C₂×Q₈×C₈₉	—	4	2	no	—
188	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
189	C₂×Q₈×C₈₉	#41	1	4	yes	—
190	C₂×D₄×C₈₉	—	2	4	no	—
191	C₂×D₄×C₈₉	—	2	4	no	—
192	C₂×D₄×C₈₉	—	2	2	no	—
193	C₂×D₄×C₈₉	—	2	2	no	—
194	C₂×D₄×C₈₉	C₂×Q₈	1	8	yes	—
195	C₂×D₄×C₈₉	C₂×Q₈	1	4	yes	complemented
196	C₂²×C₄×C₈₉	—	2	4	no	—
197	C₂²×C₄×C₈₉	—	2	2	no	—
198	C₂²×C₄×C₈₉	—	2	4	no	—
199	C₂²×C₄×C₈₉	—	2	2	no	—
200	C₂²×C₄×C₈₉	—	2	4	no	—
201	C₂²×C₄×C₈₉	—	2	2	no	—
202	C₂²×C₄×C₈₉	—	2	2	no	—
203	C₂²×C₄×C₈₉	—	2	4	no	—
204	C₂²×C₄×C₈₉	—	2	2	no	—
205	C₂²×C₄×C₈₉	—	2	2	no	—
206	C₂²×C₄×C₈₉	—	2	4	no	—
207	C₂²×C₄×C₈₉	—	2	4	no	—
208	C₂²×C₄×C₈₉	—	2	4	no	—
209	C₂²×C₄×C₈₉	—	2	4	no	—
210	C₂²×C₄×C₈₉	—	2	8	no	—
211	C₂²×C₄×C₈₉	—	4	2	no	—
212	C₂²×C₄×C₈₉	—	4	1	no	—
213	C₂²×C₄×C₈₉	—	4	4	no	—
214	C₂²×C₄×C₈₉	—	4	4	no	—
215	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
216	C₂²×C₄×C₈₉	#41	1	4	yes	—
217	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₈₉	C₂⁴	1	4	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	1	yes	characteristic
227	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
232	C₄⋊C₄×C₈₉	—	2	4	no	—
233	C₄⋊C₄×C₈₉	—	2	4	no	—
234	C₄⋊C₄×C₈₉	—	2	4	no	—
235	C₄⋊C₄×C₈₉	—	2	4	no	—
236	C₄⋊C₄×C₈₉	—	2	2	no	—
237	C₄⋊C₄×C₈₉	—	2	8	no	—
238	C₄⋊C₄×C₈₉	—	2	4	no	—
239	C₄⋊C₄×C₈₉	—	2	2	no	—
240	C₄⋊C₄×C₈₉	—	2	4	no	—
241	C₄⋊C₄×C₈₉	—	2	8	no	—
242	C₄⋊C₄×C₈₉	—	2	4	no	—
243	C₄⋊C₄×C₈₉	—	2	4	no	—
244	C₄⋊C₄×C₈₉	—	2	8	no	—
245	C₄⋊C₄×C₈₉	—	2	2	no	—
246	C₄⋊C₄×C₈₉	—	2	4	no	—
247	C₄⋊C₄×C₈₉	—	4	4	no	—
248	C₄⋊C₄×C₈₉	—	4	4	no	—
249	C₄⋊C₄×C₈₉	—	4	2	no	—
250	C₄⋊C₄×C₈₉	—	4	4	no	—
251	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
252	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
253	C₄⋊C₄×C₈₉	C₂×Q₈	1	4	yes	complemented
254	C₂²⋊C₄×C₈₉	—	2	4	no	—
255	C₂²⋊C₄×C₈₉	—	2	8	no	—
256	C₂²⋊C₄×C₈₉	—	2	4	no	—
257	C₂²⋊C₄×C₈₉	—	2	8	no	—
258	C₂²⋊C₄×C₈₉	—	2	4	no	—
259	C₂²⋊C₄×C₈₉	—	2	8	no	—
260	C₂²⋊C₄×C₈₉	—	4	2	no	—
261	C₂²⋊C₄×C₈₉	—	4	4	no	—
262	C₂²⋊C₄×C₈₉	C₂×Q₈	1	8	yes	complemented
263	C₄²×C₈₉	—	2	2	no	—
264	C₄²×C₈₉	—	2	4	no	—
265	C₄²×C₈₉	—	2	4	no	—
266	C₄²×C₈₉	—	2	2	no	—
267	C₄²×C₈₉	—	2	4	no	—
268	C₄²×C₈₉	—	2	2	no	—
269	C₄²×C₈₉	—	2	4	no	—
270	C₄²×C₈₉	—	4	4	no	—
271	C₄²×C₈₉	C₂×D₄	1	8	yes	—
272	C₄²×C₈₉	C₂×D₄	1	4	yes	—
273	C₂³×C₈₉	—	2	1	no	—
274	C₂³×C₈₉	—	2	1	no	—
275	C₂³×C₈₉	—	2	1	no	—
276	C₂³×C₈₉	—	2	1	no	—
277	C₂³×C₈₉	—	2	2	no	—
278	C₂³×C₈₉	—	2	2	no	—
279	C₂³×C₈₉	—	2	2	no	—
280	C₂³×C₈₉	—	2	2	no	—
281	C₂³×C₈₉	—	2	2	no	—
282	C₂³×C₈₉	—	2	2	no	—
283	C₂³×C₈₉	C₂²×Q₈	1	4	yes	—
284	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
285	C₂³×C₈₉	C₂×#41	1	2	yes	—
286	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
287	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
288	Q₈×C₈₉	—	2	16	no	—
289	Q₈×C₈₉	—	2	8	no	—
290	Q₈×C₈₉	—	2	8	no	—
291	Q₈×C₈₉	—	8	4	no	—
292	D₄×C₈₉	—	2	16	no	—
293	D₄×C₈₉	—	2	8	no	—
294	C₂×C₄×C₈₉	—	2	16	no	—
295	C₂×C₄×C₈₉	—	2	1	no	—
296	C₂×C₄×C₈₉	—	2	2	no	—
297	C₂×C₄×C₈₉	—	2	1	no	—
298	C₂×C₄×C₈₉	—	2	2	no	—
299	C₂×C₄×C₈₉	—	2	2	no	—
300	C₂×C₄×C₈₉	—	2	2	no	—
301	C₂×C₄×C₈₉	—	2	2	no	—
302	C₂×C₄×C₈₉	—	2	1	no	—
303	C₂×C₄×C₈₉	—	2	2	no	—
304	C₂×C₄×C₈₉	—	2	2	no	—
305	C₂×C₄×C₈₉	—	2	1	no	—
306	C₂×C₄×C₈₉	—	2	1	no	—
307	C₂×C₄×C₈₉	—	2	2	no	—
308	C₂×C₄×C₈₉	—	2	1	no	—
309	C₂×C₄×C₈₉	—	2	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	4	no	—
315	C₂×C₄×C₈₉	—	2	2	no	—
316	C₂×C₄×C₈₉	—	2	4	no	—
317	C₂×C₄×C₈₉	—	2	2	no	—
318	C₂×C₄×C₈₉	—	2	2	no	—
319	C₂×C₄×C₈₉	—	2	4	no	—
320	C₂×C₄×C₈₉	—	2	4	no	—
321	C₂×C₄×C₈₉	—	2	2	no	—
322	C₂×C₄×C₈₉	—	2	1	no	—
323	C₂×C₄×C₈₉	—	2	2	no	—
324	C₂×C₄×C₈₉	—	2	4	no	—
325	C₂×C₄×C₈₉	—	2	1	no	—
326	C₂×C₄×C₈₉	—	2	2	no	—
327	C₂×C₄×C₈₉	—	2	2	no	—
328	C₂×C₄×C₈₉	—	2	4	no	—
329	C₂×C₄×C₈₉	—	4	8	no	—
330	C₂×C₄×C₈₉	—	4	4	no	—
331	C₂×C₄×C₈₉	—	4	8	no	—
332	C₂×C₄×C₈₉	—	8	8	no	—
333	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
334	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
336	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
339	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
340	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
341	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
342	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
343	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
344	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
345	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
346	C₂²×C₈₉	—	2	2	no	—
347	C₂²×C₈₉	—	2	2	no	—
348	C₂²×C₈₉	—	2	2	no	—
349	C₂²×C₈₉	—	2	2	no	—
350	C₂²×C₈₉	—	2	2	no	—
351	C₂²×C₈₉	—	2	2	no	—
352	C₂²×C₈₉	—	2	4	no	—
353	C₂²×C₈₉	—	2	4	no	—
354	C₂²×C₈₉	—	2	4	no	—
355	C₂²×C₈₉	—	4	2	no	—
356	C₂²×C₈₉	—	4	2	no	—
357	C₂²×C₈₉	—	4	2	no	—
358	C₂²×C₈₉	—	4	2	no	—
359	C₂²×C₈₉	#554	1	4	yes	complemented
360	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
361	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
362	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
363	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
364	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
365	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
366	C₂²×C₈₉	#585	1	1	yes	characteristic
367	C₄×C₈₉	—	2	4	no	—
368	C₄×C₈₉	—	2	4	no	—
369	C₄×C₈₉	—	2	2	no	—
370	C₄×C₈₉	—	2	2	no	—
371	C₄×C₈₉	—	2	4	no	—
372	C₄×C₈₉	—	2	4	no	—
373	C₄×C₈₉	—	2	2	no	—
374	C₄×C₈₉	—	4	2	no	—
375	C₄×C₈₉	—	4	2	no	—
376	C₄×C₈₉	—	4	1	no	—
377	C₄×C₈₉	—	4	4	no	—
378	C₄×C₈₉	—	4	2	no	—
379	C₄×C₈₉	—	4	4	no	—
380	C₄×C₈₉	#525	1	4	yes	—
381	C₄×C₈₉	D₄×Q₈	1	4	yes	—
382	#36544	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
383	C₂×C₈₉	—	2	4	no	—
384	C₂×C₈₉	—	4	4	no	—
385	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
386	C₂×C₈₉	C₂×D₄×Q₈	1	1	yes	characteristic
387	C₂×C₈₉	C₂×#554	1	1	yes	characteristic
388	C₂×C₈₉	Q₈×#41	1	1	yes	characteristic
389	C₂×C₈₉	#3488	1	1	yes	characteristic
390	C₂×C₈₉	#3507	1	1	yes	characteristic
391	C₂×C₈₉	#3522	1	1	yes	characteristic
392	C₂×#554	C₂×C₈₉	1	1	yes	characteristic, complemented
393	C₂²×C₄×Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
394	#2857	C₂×C₈₉	1	1	yes	characteristic, complemented
395	#2851	C₂×C₈₉	1	2	yes	complemented
396	#2584	C₂×C₈₉	1	2	yes	complemented
397	#2580	C₂×C₈₉	1	2	yes	complemented
398	#2567	C₂×C₈₉	1	1	yes	characteristic, complemented
399	#2538	C₂×C₈₉	1	1	yes	characteristic, complemented
400	#2465	C₂×C₈₉	1	4	yes	complemented
401	#2449	C₂×C₈₉	1	4	yes	complemented
402	#2423	C₂×C₈₉	1	2	yes	complemented
403	#2409	C₂×C₈₉	1	2	yes	complemented
404	#2360	C₂×C₈₉	1	2	yes	complemented
405	#2355	C₂×C₈₉	1	1	yes	characteristic, complemented
406	D₄×C₄⋊C₄	C₂×C₈₉	1	2	yes	complemented
407	C₄×#121	C₂×C₈₉	1	2	yes	—
408	C₄×#121	C₂×C₈₉	1	1	yes	characteristic
409	C₈₉	#36544	1	1	yes	characteristic, direct product factor, Sylow
410	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
411	#554	—	2	8	no	—
412	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
413	C₂×#125	C₂²×C₈₉	1	2	yes	—
414	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
415	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
416	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
417	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
418	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
419	C₂×C₄×Q₈	—	2	8	no	—
420	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
421	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
422	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
423	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
424	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
425	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
426	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
427	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
428	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
429	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
430	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
431	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
432	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
433	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
434	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
435	#399	C₂²×C₈₉	1	4	yes	—
436	#398	C₂²×C₈₉	1	4	yes	—
437	#396	C₂²×C₈₉	1	4	yes	—
438	#395	C₂²×C₈₉	1	4	yes	—
439	#395	C₂²×C₈₉	1	4	yes	—
440	#393	C₂²×C₈₉	1	4	yes	—
441	#391	C₂²×C₈₉	1	2	yes	—
442	#391	C₂²×C₈₉	1	2	yes	—
443	#391	C₂²×C₈₉	1	2	yes	—
444	#390	C₂²×C₈₉	1	1	yes	characteristic
445	#390	C₂²×C₈₉	1	2	yes	—
446	#389	C₂²×C₈₉	1	2	yes	—
447	#389	C₂²×C₈₉	1	2	yes	—
448	#389	C₂²×C₈₉	1	2	yes	—
449	#389	C₂²×C₈₉	1	1	yes	characteristic
450	#389	C₂²×C₈₉	1	2	yes	—
451	#389	C₂²×C₈₉	1	4	yes	—
452	#389	C₂²×C₈₉	1	4	yes	—
453	#389	C₂²×C₈₉	1	2	yes	—
454	#388	C₂²×C₈₉	1	4	yes	—
455	#388	C₂²×C₈₉	1	2	yes	—
456	#387	C₂²×C₈₉	1	4	yes	—
457	#387	C₂²×C₈₉	1	4	yes	—
458	#387	C₂²×C₈₉	1	4	yes	—
459	#386	C₂²×C₈₉	1	4	yes	—
460	#386	C₂²×C₈₉	1	2	yes	—
461	#385	C₂²×C₈₉	1	4	yes	—
462	#385	C₂²×C₈₉	1	4	yes	—
463	#385	C₂²×C₈₉	1	4	yes	—
464	#385	C₂²×C₈₉	1	4	yes	—
465	#384	C₂²×C₈₉	1	2	yes	—
466	#384	C₂²×C₈₉	1	1	yes	characteristic
467	#382	C₂²×C₈₉	1	2	yes	—
468	#380	C₂²×C₈₉	1	1	yes	characteristic
469	#380	C₂²×C₈₉	1	2	yes	—
470	#380	C₂²×C₈₉	1	2	yes	—
471	#380	C₂²×C₈₉	1	2	yes	—
472	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
473	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
474	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
475	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
476	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
477	C₂²×Q₈	—	2	4	no	—
478	C₂²×Q₈	—	2	4	no	—
479	C₂²×Q₈	—	2	4	no	—
480	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
481	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
482	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
483	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
484	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
485	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
487	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
488	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
489	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
493	C₄⋊Q₈	—	2	4	no	—
494	#125	—	2	8	no	—
495	C₂²⋊Q₈	—	2	8	no	—
496	C₂²⋊Q₈	—	2	8	no	—
497	C₂²⋊Q₈	—	2	16	no	—
498	C₂²⋊Q₈	—	4	4	no	—
499	#121	Q₈×C₈₉	1	8	yes	complemented
500	C₄×Q₈	—	2	4	no	—
501	C₄×Q₈	—	2	4	no	—
502	C₄×Q₈	—	2	8	no	—
503	C₄×Q₈	—	2	8	no	—
504	C₄×Q₈	—	2	4	no	—
505	C₄×Q₈	D₄×C₈₉	1	8	yes	complemented
506	C₄×D₄	—	2	8	no	—
507	C₄×D₄	—	2	8	no	—
508	C₄×D₄	—	2	4	no	—
509	C₄×D₄	—	4	8	no	—
510	C₂×C₄⋊C₄	—	2	4	no	—
511	C₂×C₄⋊C₄	—	2	8	no	—
512	C₂×C₄⋊C₄	—	2	8	no	—
513	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
519	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
524	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
526	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
529	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
531	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
532	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
535	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
544	C₂×C₄²	—	2	8	no	—
545	C₂×C₄²	—	2	4	no	—
546	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
547	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
548	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
549	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
550	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
551	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
552	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
554	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
555	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
556	#95	C₂³×C₈₉	1	2	yes	—
557	#95	C₂³×C₈₉	1	4	yes	—
558	#95	C₂³×C₈₉	1	2	yes	—
559	#95	C₂³×C₈₉	1	4	yes	—
560	#95	C₂³×C₈₉	1	4	yes	—
561	#95	C₂³×C₈₉	1	2	yes	—
562	#95	C₂³×C₈₉	1	4	yes	—
563	#95	C₂³×C₈₉	1	4	yes	—
564	#95	C₂³×C₈₉	1	4	yes	—
565	#95	C₂³×C₈₉	1	4	yes	—
566	#95	C₂³×C₈₉	1	4	yes	—
567	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
568	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
569	C₂×Q₈	—	2	32	no	—
570	C₂×Q₈	—	2	4	no	—
571	C₂×Q₈	—	2	2	no	—
572	C₂×Q₈	—	2	4	no	—
573	C₂×Q₈	—	2	4	no	—
574	C₂×Q₈	—	2	4	no	—
575	C₂×Q₈	—	2	2	no	—
576	C₂×Q₈	—	2	2	no	—
577	C₂×Q₈	—	2	2	no	—
578	C₂×Q₈	—	4	2	no	—
579	C₂×Q₈	—	4	2	no	—
580	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
581	C₂×Q₈	#41×C₈₉	1	4	yes	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	C₂×Q₈×C₈₉	1	8	yes	—
587	C₂×D₄	C₂×Q₈×C₈₉	1	4	yes	complemented
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	2	4	no	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	8	no	—
603	C₂²×C₄	—	4	2	no	—
604	C₂²×C₄	—	4	1	no	—
605	C₂²×C₄	—	4	4	no	—
606	C₂²×C₄	—	4	4	no	—
607	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
608	C₂²×C₄	#41×C₈₉	1	4	yes	—
609	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
611	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
613	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
615	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
623	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	8	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	2	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	8	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	8	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	4	4	no	—
640	C₄⋊C₄	—	4	2	no	—
641	C₄⋊C₄	—	4	4	no	—
642	C₄⋊C₄	—	4	4	no	—
643	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
644	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
645	C₄⋊C₄	C₂×Q₈×C₈₉	1	4	yes	complemented
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	8	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	8	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	8	no	—
652	C₂²⋊C₄	—	4	4	no	—
653	C₂²⋊C₄	—	4	2	no	—
654	C₂²⋊C₄	C₂×Q₈×C₈₉	1	8	yes	complemented
655	C₄²	—	2	2	no	—
656	C₄²	—	2	4	no	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	2	no	—
659	C₄²	—	2	4	no	—
660	C₄²	—	2	2	no	—
661	C₄²	—	2	4	no	—
662	C₄²	—	4	4	no	—
663	C₄²	C₂×D₄×C₈₉	1	8	yes	—
664	C₄²	C₂×D₄×C₈₉	1	4	yes	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	C₂²×Q₈×C₈₉	1	4	yes	—
676	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
677	C₂³	C₂×#41×C₈₉	1	2	yes	—
678	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
679	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
680	Q₈	—	2	16	no	—
681	Q₈	—	2	8	no	—
682	Q₈	—	2	8	no	—
683	Q₈	—	8	4	no	—
684	D₄	—	2	16	no	—
685	D₄	—	2	8	no	—
686	C₂×C₄	—	2	16	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	8	no	—
702	C₂×C₄	—	2	8	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	4	8	no	—
722	C₂×C₄	—	4	4	no	—
723	C₂×C₄	—	4	8	no	—
724	C₂×C₄	—	8	8	no	—
725	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
726	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
728	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
730	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
731	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
732	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
733	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
734	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
735	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
736	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
737	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	2	2	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	4	no	—
745	C₂²	—	2	4	no	—
746	C₂²	—	2	4	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	#554×C₈₉	1	4	yes	complemented
752	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
753	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
754	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
755	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
756	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
757	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
758	C₂²	#585×C₈₉	1	1	yes	characteristic
759	C₄	—	2	4	no	—
760	C₄	—	2	4	no	—
761	C₄	—	2	2	no	—
762	C₄	—	2	2	no	—
763	C₄	—	2	4	no	—
764	C₄	—	2	4	no	—
765	C₄	—	2	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	1	no	—
769	C₄	—	4	4	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	4	no	—
772	C₄	#525×C₈₉	1	4	yes	—
773	C₄	D₄×Q₈×C₈₉	1	4	yes	—
774	C₂	—	2	4	no	—
775	C₂	—	4	4	no	—
776	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
777	C₂	C₂×D₄×Q₈×C₈₉	1	1	yes	characteristic
778	C₂	C₂×#554×C₈₉	1	1	yes	characteristic
779	C₂	Q₈×#41×C₈₉	1	1	yes	characteristic
780	C₂	C₈₉×#3488	1	1	yes	characteristic
781	C₂	C₈₉×#3507	1	1	yes	characteristic
782	C₂	C₈₉×#3522	1	1	yes	characteristic

	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. C₂×#554×C₈₉	C₂	semidirect
2. C₂²×C₄×Q₈×C₈₉	C₂	semidirect
3. C₈₉×#2857	C₂	semidirect
4. C₈₉×#2851	C₂	semidirect
5. C₈₉×#2584	C₂	semidirect
6. C₈₉×#2580	C₂	semidirect
7. C₈₉×#2567	C₂	semidirect
8. C₈₉×#2538	C₂	semidirect
9. C₈₉×#2465	C₂	semidirect
10. C₈₉×#2449	C₂	semidirect
11. C₈₉×#2423	C₂	semidirect
12. C₈₉×#2409	C₂	semidirect
13. C₈₉×#2360	C₂	semidirect
14. C₈₉×#2355	C₂	semidirect
15. D₄×C₄⋊C₄×C₈₉	C₂	semidirect
107. #121×C₈₉	Q₈	semidirect
113. C₄×Q₈×C₈₉	D₄	semidirect
195. C₂×D₄×C₈₉	C₂×Q₈	semidirect
253. C₄⋊C₄×C₈₉	C₂×Q₈	semidirect
262. C₂²⋊C₄×C₈₉	C₂×Q₈	semidirect
359. C₂²×C₈₉	#554	semidirect
382. #36544	C₈₉	direct (N × H)
392. C₂×#554	C₂×C₈₉	semidirect
393. C₂²×C₄×Q₈	C₂×C₈₉	semidirect
394. #2857	C₂×C₈₉	semidirect
395. #2851	C₂×C₈₉	semidirect
396. #2584	C₂×C₈₉	semidirect
397. #2580	C₂×C₈₉	semidirect
398. #2567	C₂×C₈₉	semidirect
399. #2538	C₂×C₈₉	semidirect
400. #2465	C₂×C₈₉	semidirect
401. #2449	C₂×C₈₉	semidirect
402. #2423	C₂×C₈₉	semidirect
403. #2409	C₂×C₈₉	semidirect
404. #2360	C₂×C₈₉	semidirect
405. #2355	C₂×C₈₉	semidirect
406. D₄×C₄⋊C₄	C₂×C₈₉	semidirect
409. C₈₉	#36544	direct (N × H)
499. #121	Q₈×C₈₉	semidirect
505. C₄×Q₈	D₄×C₈₉	semidirect
587. C₂×D₄	C₂×Q₈×C₈₉	semidirect
645. C₄⋊C₄	C₂×Q₈×C₈₉	semidirect
654. C₂²⋊C₄	C₂×Q₈×C₈₉	semidirect
751. C₂²	#554×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#554×C₈₉	2
C₂²×C₄×Q₈×C₈₉	2
C₈₉×#2857	2
C₈₉×#2851	2
C₈₉×#2584	2
C₈₉×#2580	2
C₈₉×#2567	2
C₈₉×#2538	2
C₈₉×#2465	2
C₈₉×#2449	2
C₈₉×#2423	2
C₈₉×#2409	2
C₈₉×#2360	2
C₈₉×#2355	2
D₄×C₄⋊C₄×C₈₉	2
C₄×#121×C₈₉	2
#36544	89

Subgroups — C89×#36544 #36414392

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#36544 #36414392