Subgroups — C₈₉×#35535 #36413383

Order 22784.

2510 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#542×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#520×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2567	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2545	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2544	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2542	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2502	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2501	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2479	C₂	1	4	yes	maximal, complemented
10	C₈₉×#2461	C₂	1	4	yes	maximal, complemented
11	C₈₉×#2455	C₂	1	4	yes	maximal, complemented
12	C₈₉×#2449	C₂	1	4	yes	maximal, complemented
13	C₈₉×#2432	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2431	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#2326	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2326	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₄⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#127×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2298	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
21	#542×C₈₉	—	2	8	no	—
22	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#126×C₈₉	C₂²	1	2	yes	—
26	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#124×C₈₉	C₂²	1	2	yes	—
29	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#123×C₈₉	C₂²	1	2	yes	—
31	C₂×#123×C₈₉	C₂²	1	4	yes	—
32	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
34	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
35	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
36	#520×C₈₉	—	2	8	no	—
37	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
44	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
46	C₂×#117×C₈₉	C₂²	1	2	yes	—
47	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
48	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
49	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
50	#399×C₈₉	C₂²	1	4	yes	—
51	#399×C₈₉	C₂²	1	4	yes	—
52	#398×C₈₉	C₂²	1	4	yes	—
53	#396×C₈₉	C₂²	1	4	yes	—
54	#395×C₈₉	C₂²	1	4	yes	—
55	#394×C₈₉	C₂²	1	4	yes	—
56	#394×C₈₉	C₂²	1	4	yes	—
57	#392×C₈₉	C₂²	1	4	yes	—
58	#391×C₈₉	C₂²	1	1	yes	characteristic
59	#391×C₈₉	C₂²	1	1	yes	characteristic
60	#391×C₈₉	C₂²	1	1	yes	characteristic
61	#391×C₈₉	C₂²	1	1	yes	characteristic
62	#390×C₈₉	C₂²	1	1	yes	characteristic
63	#390×C₈₉	C₂²	1	4	yes	—
64	#390×C₈₉	C₂²	1	1	yes	characteristic
65	#390×C₈₉	C₂²	1	1	yes	characteristic
66	#390×C₈₉	C₂²	1	1	yes	characteristic
67	#389×C₈₉	C₂²	1	4	yes	—
68	#389×C₈₉	C₂²	1	4	yes	—
69	#388×C₈₉	C₂²	1	2	yes	—
70	#388×C₈₉	C₂²	1	2	yes	—
71	#388×C₈₉	C₂²	1	4	yes	—
72	#388×C₈₉	C₂²	1	4	yes	—
73	#388×C₈₉	C₂²	1	4	yes	—
74	#387×C₈₉	C₂²	1	2	yes	—
75	#387×C₈₉	C₂²	1	2	yes	—
76	#386×C₈₉	C₂²	1	4	yes	—
77	#386×C₈₉	C₂²	1	4	yes	—
78	#385×C₈₉	C₂²	1	4	yes	—
79	#385×C₈₉	C₂²	1	4	yes	—
80	#385×C₈₉	C₂²	1	4	yes	—
81	#385×C₈₉	C₂²	1	4	yes	—
82	#384×C₈₉	C₂²	1	1	yes	characteristic
83	#384×C₈₉	C₂²	1	1	yes	characteristic
84	#384×C₈₉	C₂²	1	1	yes	characteristic
85	#384×C₈₉	C₂²	1	1	yes	characteristic
86	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
87	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
88	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
89	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
91	#376×C₈₉	C₂²	1	1	yes	characteristic
92	C₄³×C₈₉	C₂²	1	1	yes	characteristic
93	C₂×#41×C₈₉	—	2	4	no	—
94	C₂×#41×C₈₉	—	2	4	no	—
95	C₂×#41×C₈₉	—	2	4	no	—
96	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
99	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
101	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
102	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
104	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
105	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
107	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
108	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
109	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
110	C₄⋊Q₈×C₈₉	—	2	4	no	—
111	C₄⋊Q₈×C₈₉	—	2	4	no	—
112	#127×C₈₉	—	2	4	no	—
113	#126×C₈₉	—	2	8	no	—
114	#124×C₈₉	—	2	4	no	—
115	#124×C₈₉	—	2	4	no	—
116	#124×C₈₉	—	2	8	no	—
117	#124×C₈₉	—	2	4	no	—
118	#123×C₈₉	—	2	8	no	—
119	#123×C₈₉	—	4	8	no	—
120	C₂²⋊Q₈×C₈₉	—	2	4	no	—
121	C₂²⋊Q₈×C₈₉	—	2	8	no	—
122	C₂²⋊Q₈×C₈₉	—	4	8	no	—
123	#121×C₈₉	—	2	4	no	—
124	C₄×Q₈×C₈₉	—	2	4	no	—
125	C₄×Q₈×C₈₉	—	2	4	no	—
126	C₄×Q₈×C₈₉	—	2	4	no	—
127	C₄×D₄×C₈₉	—	2	8	no	—
128	C₄×D₄×C₈₉	—	2	8	no	—
129	C₄×D₄×C₈₉	—	2	4	no	—
130	C₄×D₄×C₈₉	—	2	4	no	—
131	C₄×D₄×C₈₉	—	2	4	no	—
132	C₄×D₄×C₈₉	—	4	8	no	—
133	#117×C₈₉	—	2	8	no	—
134	#117×C₈₉	D₄	1	8	yes	complemented
135	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
136	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
137	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
138	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	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	1	yes	characteristic
142	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
152	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
153	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
154	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	4	yes	—
159	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
161	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
162	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
168	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
170	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
171	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×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	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
176	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
177	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
180	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
181	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
182	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
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	4	yes	—
189	#95×C₈₉	C₂³	1	2	yes	—
190	#95×C₈₉	C₂³	1	4	yes	—
191	#95×C₈₉	C₂³	1	2	yes	—
192	#95×C₈₉	C₂³	1	4	yes	—
193	#95×C₈₉	C₂³	1	4	yes	—
194	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
195	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
196	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
197	#41×C₈₉	—	2	32	no	—
198	C₂×Q₈×C₈₉	—	2	2	no	—
199	C₂×Q₈×C₈₉	—	2	2	no	—
200	C₂×Q₈×C₈₉	—	2	4	no	—
201	C₂×Q₈×C₈₉	—	2	2	no	—
202	C₂×Q₈×C₈₉	—	2	2	no	—
203	C₂×Q₈×C₈₉	—	2	2	no	—
204	C₂×Q₈×C₈₉	—	4	4	no	—
205	C₂×Q₈×C₈₉	#41	1	4	yes	—
206	C₂×D₄×C₈₉	—	2	4	no	—
207	C₂×D₄×C₈₉	—	2	4	no	—
208	C₂×D₄×C₈₉	—	2	8	no	—
209	C₂×D₄×C₈₉	—	2	4	no	—
210	C₂×D₄×C₈₉	—	2	2	no	—
211	C₂×D₄×C₈₉	—	2	2	no	—
212	C₂×D₄×C₈₉	—	2	4	no	—
213	C₂×D₄×C₈₉	—	2	2	no	—
214	C₂×D₄×C₈₉	—	2	2	no	—
215	C₂×D₄×C₈₉	—	2	2	no	—
216	C₂×D₄×C₈₉	—	2	8	no	—
217	C₂×D₄×C₈₉	—	4	4	no	—
218	C₂×D₄×C₈₉	—	4	4	no	—
219	C₂×D₄×C₈₉	#41	1	4	yes	—
220	C₂²×C₄×C₈₉	—	2	4	no	—
221	C₂²×C₄×C₈₉	—	2	4	no	—
222	C₂²×C₄×C₈₉	—	2	4	no	—
223	C₂²×C₄×C₈₉	—	2	2	no	—
224	C₂²×C₄×C₈₉	—	2	2	no	—
225	C₂²×C₄×C₈₉	—	2	4	no	—
226	C₂²×C₄×C₈₉	—	2	4	no	—
227	C₂²×C₄×C₈₉	—	2	4	no	—
228	C₂²×C₄×C₈₉	—	2	4	no	—
229	C₂²×C₄×C₈₉	—	4	4	no	—
230	C₂²×C₄×C₈₉	—	4	4	no	—
231	C₂²×C₄×C₈₉	—	4	4	no	—
232	C₂²×C₄×C₈₉	—	4	4	no	—
233	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
234	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
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	2	yes	—
241	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	2	no	—
254	C₄⋊C₄×C₈₉	—	2	2	no	—
255	C₄⋊C₄×C₈₉	—	2	2	no	—
256	C₄⋊C₄×C₈₉	—	2	2	no	—
257	C₄⋊C₄×C₈₉	—	2	4	no	—
258	C₄⋊C₄×C₈₉	—	2	4	no	—
259	C₄⋊C₄×C₈₉	—	2	4	no	—
260	C₄⋊C₄×C₈₉	—	2	8	no	—
261	C₄⋊C₄×C₈₉	—	2	4	no	—
262	C₄⋊C₄×C₈₉	—	2	8	no	—
263	C₄⋊C₄×C₈₉	—	2	4	no	—
264	C₄⋊C₄×C₈₉	—	4	4	no	—
265	C₄⋊C₄×C₈₉	—	4	4	no	—
266	C₄⋊C₄×C₈₉	—	4	4	no	—
267	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
268	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
269	C₂²⋊C₄×C₈₉	—	2	4	no	—
270	C₂²⋊C₄×C₈₉	—	2	8	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	—	2	4	no	—
275	C₂²⋊C₄×C₈₉	—	2	4	no	—
276	C₂²⋊C₄×C₈₉	—	2	4	no	—
277	C₂²⋊C₄×C₈₉	—	2	8	no	—
278	C₂²⋊C₄×C₈₉	—	2	8	no	—
279	C₂²⋊C₄×C₈₉	—	2	8	no	—
280	C₂²⋊C₄×C₈₉	—	2	4	no	—
281	C₂²⋊C₄×C₈₉	—	2	4	no	—
282	C₂²⋊C₄×C₈₉	—	4	4	no	—
283	C₂²⋊C₄×C₈₉	—	4	4	no	—
284	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
285	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
286	C₄²×C₈₉	—	2	4	no	—
287	C₄²×C₈₉	—	2	4	no	—
288	C₄²×C₈₉	—	2	4	no	—
289	C₄²×C₈₉	—	2	2	no	—
290	C₄²×C₈₉	—	2	2	no	—
291	C₄²×C₈₉	—	2	2	no	—
292	C₄²×C₈₉	—	2	2	no	—
293	C₄²×C₈₉	—	2	4	no	—
294	C₄²×C₈₉	—	2	4	no	—
295	C₄²×C₈₉	C₂×D₄	1	4	yes	—
296	C₄²×C₈₉	C₂×D₄	1	4	yes	—
297	C₂³×C₈₉	—	2	2	no	—
298	C₂³×C₈₉	—	2	1	no	—
299	C₂³×C₈₉	—	2	1	no	—
300	C₂³×C₈₉	—	2	2	no	—
301	C₂³×C₈₉	—	2	4	no	—
302	C₂³×C₈₉	—	2	2	no	—
303	C₂³×C₈₉	—	2	2	no	—
304	C₂³×C₈₉	—	2	4	no	—
305	C₂³×C₈₉	—	2	2	no	—
306	C₂³×C₈₉	—	2	2	no	—
307	C₂³×C₈₉	—	2	2	no	—
308	C₂³×C₈₉	—	2	4	no	—
309	C₂³×C₈₉	—	2	4	no	—
310	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
311	C₂³×C₈₉	C₂×#41	1	4	yes	—
312	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
313	Q₈×C₈₉	—	2	8	no	—
314	Q₈×C₈₉	—	4	4	no	—
315	Q₈×C₈₉	—	8	4	no	—
316	D₄×C₈₉	—	2	16	no	—
317	D₄×C₈₉	—	2	8	no	—
318	D₄×C₈₉	—	4	16	no	—
319	D₄×C₈₉	—	4	4	no	—
320	D₄×C₈₉	—	8	4	no	—
321	C₂×C₄×C₈₉	—	2	16	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	1	no	—
326	C₂×C₄×C₈₉	—	2	1	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	8	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	4	no	—
346	C₂×C₄×C₈₉	—	2	4	no	—
347	C₂×C₄×C₈₉	—	2	2	no	—
348	C₂×C₄×C₈₉	—	2	4	no	—
349	C₂×C₄×C₈₉	—	2	4	no	—
350	C₂×C₄×C₈₉	—	2	2	no	—
351	C₂×C₄×C₈₉	—	2	2	no	—
352	C₂×C₄×C₈₉	—	8	4	no	—
353	C₂×C₄×C₈₉	—	8	4	no	—
354	C₂×C₄×C₈₉	—	8	4	no	—
355	C₂×C₄×C₈₉	—	8	4	no	—
356	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
357	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
358	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
359	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
360	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
361	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
362	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
363	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
364	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
365	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
366	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
367	C₂²×C₈₉	—	2	2	no	—
368	C₂²×C₈₉	—	2	4	no	—
369	C₂²×C₈₉	—	2	2	no	—
370	C₂²×C₈₉	—	2	2	no	—
371	C₂²×C₈₉	—	2	8	no	—
372	C₂²×C₈₉	—	4	2	no	—
373	C₂²×C₈₉	—	4	2	no	—
374	C₂²×C₈₉	—	4	2	no	—
375	C₂²×C₈₉	—	4	4	no	—
376	C₂²×C₈₉	—	4	2	no	—
377	C₂²×C₈₉	—	4	2	no	—
378	C₂²×C₈₉	—	4	2	no	—
379	C₂²×C₈₉	—	4	2	no	—
380	C₂²×C₈₉	—	4	4	no	—
381	C₂²×C₈₉	—	4	4	no	—
382	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
383	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
384	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
385	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
386	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
387	C₄×C₈₉	—	2	2	no	—
388	C₄×C₈₉	—	2	4	no	—
389	C₄×C₈₉	—	2	2	no	—
390	C₄×C₈₉	—	2	2	no	—
391	C₄×C₈₉	—	2	2	no	—
392	C₄×C₈₉	—	2	2	no	—
393	C₄×C₈₉	—	2	4	no	—
394	C₄×C₈₉	—	2	4	no	—
395	C₄×C₈₉	—	4	2	no	—
396	C₄×C₈₉	—	4	2	no	—
397	C₄×C₈₉	—	4	2	no	—
398	C₄×C₈₉	—	4	2	no	—
399	C₄×C₈₉	—	4	2	no	—
400	C₄×C₈₉	—	4	2	no	—
401	C₄×C₈₉	—	4	2	no	—
402	C₄×C₈₉	#525	1	4	yes	—
403	#35535	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
404	C₂×C₈₉	—	4	2	no	—
405	C₂×C₈₉	—	4	4	no	—
406	C₂×C₈₉	—	8	2	no	—
407	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
408	C₂×C₈₉	#3498	1	1	yes	characteristic
409	C₂×C₈₉	#3499	1	1	yes	characteristic
410	C₂×C₈₉	#3520	1	2	yes	—
411	C₂×C₈₉	#3522	1	2	yes	—
412	C₂×#542	C₂×C₈₉	1	1	yes	characteristic, complemented
413	C₂×#520	C₂×C₈₉	1	1	yes	characteristic, complemented
414	#2567	C₂×C₈₉	1	1	yes	characteristic, complemented
415	#2545	C₂×C₈₉	1	1	yes	characteristic, complemented
416	#2544	C₂×C₈₉	1	1	yes	characteristic, complemented
417	#2542	C₂×C₈₉	1	1	yes	characteristic, complemented
418	#2502	C₂×C₈₉	1	1	yes	characteristic, complemented
419	#2501	C₂×C₈₉	1	1	yes	characteristic, complemented
420	#2479	C₂×C₈₉	1	4	yes	complemented
421	#2461	C₂×C₈₉	1	4	yes	complemented
422	#2455	C₂×C₈₉	1	4	yes	complemented
423	#2449	C₂×C₈₉	1	4	yes	complemented
424	#2432	C₂×C₈₉	1	1	yes	characteristic, complemented
425	#2431	C₂×C₈₉	1	1	yes	characteristic
426	#2326	C₂×C₈₉	1	1	yes	characteristic, complemented
427	#2326	C₂×C₈₉	1	1	yes	characteristic, complemented
428	C₄×C₄⋊Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
429	C₄×#127	C₂×C₈₉	1	1	yes	characteristic, complemented
430	#2298	C₂×C₈₉	1	1	yes	characteristic, complemented
431	C₈₉	#35535	1	1	yes	characteristic, direct product factor, Sylow
432	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
433	#542	—	2	8	no	—
434	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
435	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
436	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
437	C₂×#126	C₂²×C₈₉	1	2	yes	—
438	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
439	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
440	C₂×#124	C₂²×C₈₉	1	2	yes	—
441	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
442	C₂×#123	C₂²×C₈₉	1	2	yes	—
443	C₂×#123	C₂²×C₈₉	1	4	yes	—
444	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
445	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
446	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
447	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
448	#520	—	2	8	no	—
449	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
450	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
451	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
452	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
453	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
454	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
455	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
456	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
457	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
458	C₂×#117	C₂²×C₈₉	1	2	yes	—
459	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
460	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
461	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
462	#399	C₂²×C₈₉	1	4	yes	—
463	#399	C₂²×C₈₉	1	4	yes	—
464	#398	C₂²×C₈₉	1	4	yes	—
465	#396	C₂²×C₈₉	1	4	yes	—
466	#395	C₂²×C₈₉	1	4	yes	—
467	#394	C₂²×C₈₉	1	4	yes	—
468	#394	C₂²×C₈₉	1	4	yes	—
469	#392	C₂²×C₈₉	1	4	yes	—
470	#391	C₂²×C₈₉	1	1	yes	characteristic
471	#391	C₂²×C₈₉	1	1	yes	characteristic
472	#391	C₂²×C₈₉	1	1	yes	characteristic
473	#391	C₂²×C₈₉	1	1	yes	characteristic
474	#390	C₂²×C₈₉	1	1	yes	characteristic
475	#390	C₂²×C₈₉	1	4	yes	—
476	#390	C₂²×C₈₉	1	1	yes	characteristic
477	#390	C₂²×C₈₉	1	1	yes	characteristic
478	#390	C₂²×C₈₉	1	1	yes	characteristic
479	#389	C₂²×C₈₉	1	4	yes	—
480	#389	C₂²×C₈₉	1	4	yes	—
481	#388	C₂²×C₈₉	1	4	yes	—
482	#388	C₂²×C₈₉	1	4	yes	—
483	#388	C₂²×C₈₉	1	2	yes	—
484	#388	C₂²×C₈₉	1	4	yes	—
485	#388	C₂²×C₈₉	1	2	yes	—
486	#387	C₂²×C₈₉	1	2	yes	—
487	#387	C₂²×C₈₉	1	2	yes	—
488	#386	C₂²×C₈₉	1	4	yes	—
489	#386	C₂²×C₈₉	1	4	yes	—
490	#385	C₂²×C₈₉	1	4	yes	—
491	#385	C₂²×C₈₉	1	4	yes	—
492	#385	C₂²×C₈₉	1	4	yes	—
493	#385	C₂²×C₈₉	1	4	yes	—
494	#384	C₂²×C₈₉	1	1	yes	characteristic
495	#384	C₂²×C₈₉	1	1	yes	characteristic
496	#384	C₂²×C₈₉	1	1	yes	characteristic
497	#384	C₂²×C₈₉	1	1	yes	characteristic
498	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
499	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
500	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
501	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
502	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
503	#376	C₂²×C₈₉	1	1	yes	characteristic
504	C₄³	C₂²×C₈₉	1	1	yes	characteristic
505	C₂×#41	—	2	4	no	—
506	C₂×#41	—	2	4	no	—
507	C₂×#41	—	2	4	no	—
508	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
509	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
510	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
511	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
512	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
513	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
514	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
515	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
516	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
517	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
518	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
519	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
520	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
521	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
522	C₄⋊Q₈	—	2	4	no	—
523	C₄⋊Q₈	—	2	4	no	—
524	#127	—	2	4	no	—
525	#126	—	2	8	no	—
526	#124	—	2	4	no	—
527	#124	—	2	4	no	—
528	#124	—	2	8	no	—
529	#124	—	2	4	no	—
530	#123	—	2	8	no	—
531	#123	—	4	8	no	—
532	C₂²⋊Q₈	—	2	4	no	—
533	C₂²⋊Q₈	—	2	8	no	—
534	C₂²⋊Q₈	—	4	8	no	—
535	#121	—	2	4	no	—
536	C₄×Q₈	—	2	4	no	—
537	C₄×Q₈	—	2	4	no	—
538	C₄×Q₈	—	2	4	no	—
539	C₄×D₄	—	2	8	no	—
540	C₄×D₄	—	2	8	no	—
541	C₄×D₄	—	2	4	no	—
542	C₄×D₄	—	2	4	no	—
543	C₄×D₄	—	2	4	no	—
544	C₄×D₄	—	4	8	no	—
545	#117	—	2	8	no	—
546	#117	D₄×C₈₉	1	8	yes	complemented
547	C₂×C₄⋊C₄	—	2	4	no	—
548	C₂×C₄⋊C₄	—	2	8	no	—
549	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
551	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
560	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
562	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
564	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
565	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
566	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
568	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
584	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
585	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
586	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
587	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
588	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
589	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
590	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
591	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
592	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
593	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
594	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
595	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
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	4	yes	—
601	#95	C₂³×C₈₉	1	2	yes	—
602	#95	C₂³×C₈₉	1	4	yes	—
603	#95	C₂³×C₈₉	1	2	yes	—
604	#95	C₂³×C₈₉	1	4	yes	—
605	#95	C₂³×C₈₉	1	4	yes	—
606	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
607	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
608	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
609	#41	—	2	32	no	—
610	C₂×Q₈	—	2	2	no	—
611	C₂×Q₈	—	2	2	no	—
612	C₂×Q₈	—	2	4	no	—
613	C₂×Q₈	—	2	2	no	—
614	C₂×Q₈	—	2	2	no	—
615	C₂×Q₈	—	2	2	no	—
616	C₂×Q₈	—	4	4	no	—
617	C₂×Q₈	#41×C₈₉	1	4	yes	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	4	no	—
620	C₂×D₄	—	2	8	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	2	2	no	—
628	C₂×D₄	—	2	8	no	—
629	C₂×D₄	—	4	4	no	—
630	C₂×D₄	—	4	4	no	—
631	C₂×D₄	#41×C₈₉	1	4	yes	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	4	4	no	—
642	C₂²×C₄	—	4	4	no	—
643	C₂²×C₄	—	4	4	no	—
644	C₂²×C₄	—	4	4	no	—
645	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
646	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
648	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
649	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
650	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
654	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
655	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
656	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	8	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	8	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	4	4	no	—
677	C₄⋊C₄	—	4	4	no	—
678	C₄⋊C₄	—	4	4	no	—
679	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
680	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	8	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	8	no	—
690	C₂²⋊C₄	—	2	8	no	—
691	C₂²⋊C₄	—	2	8	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	4	4	no	—
695	C₂²⋊C₄	—	4	4	no	—
696	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
697	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
698	C₄²	—	2	4	no	—
699	C₄²	—	2	4	no	—
700	C₄²	—	2	4	no	—
701	C₄²	—	2	2	no	—
702	C₄²	—	2	2	no	—
703	C₄²	—	2	2	no	—
704	C₄²	—	2	2	no	—
705	C₄²	—	2	4	no	—
706	C₄²	—	2	4	no	—
707	C₄²	C₂×D₄×C₈₉	1	4	yes	—
708	C₄²	C₂×D₄×C₈₉	1	4	yes	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	1	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	4	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	4	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	4	no	—
721	C₂³	—	2	4	no	—
722	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
723	C₂³	C₂×#41×C₈₉	1	4	yes	—
724	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
725	Q₈	—	2	8	no	—
726	Q₈	—	4	4	no	—
727	Q₈	—	8	4	no	—
728	D₄	—	2	16	no	—
729	D₄	—	2	8	no	—
730	D₄	—	4	16	no	—
731	D₄	—	4	4	no	—
732	D₄	—	8	4	no	—
733	C₂×C₄	—	2	16	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	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	8	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	—	2	4	no	—
758	C₂×C₄	—	2	4	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	2	4	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	8	4	no	—
765	C₂×C₄	—	8	4	no	—
766	C₂×C₄	—	8	4	no	—
767	C₂×C₄	—	8	4	no	—
768	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
769	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
770	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
771	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
772	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
773	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
774	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
775	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
776	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
777	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
778	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
779	C₂²	—	2	2	no	—
780	C₂²	—	2	4	no	—
781	C₂²	—	2	2	no	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	8	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	4	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	4	4	no	—
793	C₂²	—	4	4	no	—
794	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
795	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
796	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
797	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
798	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
799	C₄	—	2	2	no	—
800	C₄	—	2	4	no	—
801	C₄	—	2	2	no	—
802	C₄	—	2	2	no	—
803	C₄	—	2	2	no	—
804	C₄	—	2	2	no	—
805	C₄	—	2	4	no	—
806	C₄	—	2	4	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	2	no	—
811	C₄	—	4	2	no	—
812	C₄	—	4	2	no	—
813	C₄	—	4	2	no	—
814	C₄	#525×C₈₉	1	4	yes	—
815	C₂	—	4	2	no	—
816	C₂	—	4	4	no	—
817	C₂	—	8	2	no	—
818	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
819	C₂	C₈₉×#3498	1	1	yes	characteristic
820	C₂	C₈₉×#3499	1	1	yes	characteristic
821	C₂	C₈₉×#3520	1	2	yes	—
822	C₂	C₈₉×#3522	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₈₉×#2431	C₂
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×#542×C₈₉	C₂	semidirect
2. C₂×#520×C₈₉	C₂	semidirect
3. C₈₉×#2567	C₂	semidirect
4. C₈₉×#2545	C₂	semidirect
5. C₈₉×#2544	C₂	semidirect
6. C₈₉×#2542	C₂	semidirect
7. C₈₉×#2502	C₂	semidirect
8. C₈₉×#2501	C₂	semidirect
9. C₈₉×#2479	C₂	semidirect
10. C₈₉×#2461	C₂	semidirect
11. C₈₉×#2455	C₂	semidirect
12. C₈₉×#2449	C₂	semidirect
13. C₈₉×#2432	C₂	semidirect
15. C₈₉×#2326	C₂	semidirect
16. C₈₉×#2326	C₂	semidirect
17. C₄×C₄⋊Q₈×C₈₉	C₂	semidirect
18. C₄×#127×C₈₉	C₂	semidirect
19. C₈₉×#2298	C₂	semidirect
134. #117×C₈₉	D₄	semidirect
403. #35535	C₈₉	direct (N × H)
412. C₂×#542	C₂×C₈₉	semidirect
413. C₂×#520	C₂×C₈₉	semidirect
414. #2567	C₂×C₈₉	semidirect
415. #2545	C₂×C₈₉	semidirect
416. #2544	C₂×C₈₉	semidirect
417. #2542	C₂×C₈₉	semidirect
418. #2502	C₂×C₈₉	semidirect
419. #2501	C₂×C₈₉	semidirect
420. #2479	C₂×C₈₉	semidirect
421. #2461	C₂×C₈₉	semidirect
422. #2455	C₂×C₈₉	semidirect
423. #2449	C₂×C₈₉	semidirect
424. #2432	C₂×C₈₉	semidirect
426. #2326	C₂×C₈₉	semidirect
427. #2326	C₂×C₈₉	semidirect
428. C₄×C₄⋊Q₈	C₂×C₈₉	semidirect
429. C₄×#127	C₂×C₈₉	semidirect
430. #2298	C₂×C₈₉	semidirect
431. C₈₉	#35535	direct (N × H)
546. #117	D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#542×C₈₉	2
C₂×#520×C₈₉	2
C₈₉×#2567	2
C₈₉×#2545	2
C₈₉×#2544	2
C₈₉×#2542	2
C₈₉×#2502	2
C₈₉×#2501	2
C₈₉×#2479	2
C₈₉×#2461	2
C₈₉×#2455	2
C₈₉×#2449	2
C₈₉×#2432	2
C₈₉×#2431	2
C₈₉×#2326	2
C₄×C₄⋊Q₈×C₈₉	2
C₄×#127×C₈₉	2
C₈₉×#2298	2
#35535	89

Subgroups — C89×#35535 #36413383

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35535 #36413383