Subgroups — C₈₉×#35534 #36413382

Order 22784.

2606 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#540×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#520×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2566	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2565	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2548	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2541	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2504	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2501	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2471	C₂	1	4	yes	maximal, complemented
10	C₈₉×#2464	C₂	1	4	yes	maximal, complemented
11	C₈₉×#2456	C₂	1	4	yes	maximal, complemented
12	C₈₉×#2443	C₂	1	4	yes	maximal, complemented
13	C₈₉×#2431	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2431	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2328	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2326	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#127×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#124×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	#540×C₈₉	—	2	8	no	—
22	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#123×C₈₉	C₂²	1	2	yes	—
29	C₂×#123×C₈₉	C₂²	1	2	yes	—
30	C₂×#123×C₈₉	C₂²	1	4	yes	—
31	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#121×C₈₉	C₂²	1	2	yes	—
34	C₂×#121×C₈₉	C₂²	1	2	yes	—
35	C₂×#121×C₈₉	C₂²	1	4	yes	—
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×D₄×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	1	yes	characteristic
43	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
44	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
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	#398×C₈₉	C₂²	1	4	yes	—
52	#397×C₈₉	C₂²	1	4	yes	—
53	#396×C₈₉	C₂²	1	4	yes	—
54	#394×C₈₉	C₂²	1	4	yes	—
55	#392×C₈₉	C₂²	1	4	yes	—
56	#392×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	#390×C₈₉	C₂²	1	1	yes	characteristic
61	#390×C₈₉	C₂²	1	1	yes	characteristic
62	#390×C₈₉	C₂²	1	4	yes	—
63	#390×C₈₉	C₂²	1	1	yes	characteristic
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	#390×C₈₉	C₂²	1	4	yes	—
68	#388×C₈₉	C₂²	1	2	yes	—
69	#388×C₈₉	C₂²	1	2	yes	—
70	#388×C₈₉	C₂²	1	4	yes	—
71	#388×C₈₉	C₂²	1	4	yes	—
72	#387×C₈₉	C₂²	1	2	yes	—
73	#387×C₈₉	C₂²	1	2	yes	—
74	#387×C₈₉	C₂²	1	4	yes	—
75	#386×C₈₉	C₂²	1	4	yes	—
76	#386×C₈₉	C₂²	1	4	yes	—
77	#386×C₈₉	C₂²	1	4	yes	—
78	#386×C₈₉	C₂²	1	4	yes	—
79	#386×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	#382×C₈₉	C₂²	1	1	yes	characteristic
85	#382×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×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
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×D₄×C₈₉	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
100	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
101	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
103	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
104	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
105	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
106	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
107	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
108	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
110	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
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	#127×C₈₉	—	2	4	no	—
115	#127×C₈₉	—	2	4	no	—
116	#127×C₈₉	—	2	4	no	—
117	#125×C₈₉	—	2	4	no	—
118	#124×C₈₉	—	2	4	no	—
119	#124×C₈₉	—	2	4	no	—
120	#123×C₈₉	—	2	8	no	—
121	#123×C₈₉	—	2	8	no	—
122	#123×C₈₉	—	4	8	no	—
123	#121×C₈₉	—	2	4	no	—
124	#121×C₈₉	—	2	4	no	—
125	#121×C₈₉	—	2	8	no	—
126	#121×C₈₉	—	2	8	no	—
127	#121×C₈₉	—	4	8	no	—
128	C₄×Q₈×C₈₉	—	2	4	no	—
129	C₄×Q₈×C₈₉	—	2	4	no	—
130	C₄×D₄×C₈₉	—	2	8	no	—
131	C₄×D₄×C₈₉	—	2	8	no	—
132	C₄×D₄×C₈₉	—	2	4	no	—
133	C₄×D₄×C₈₉	—	2	4	no	—
134	C₄×D₄×C₈₉	—	2	4	no	—
135	C₄×D₄×C₈₉	—	2	4	no	—
136	C₄×D₄×C₈₉	—	4	8	no	—
137	#117×C₈₉	—	2	8	no	—
138	#117×C₈₉	D₄	1	8	yes	complemented
139	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
140	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
141	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	1	yes	characteristic
146	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	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	2	yes	—
152	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	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	4	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	4	yes	—
160	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	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	4	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	4	yes	—
172	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
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	4	yes	—
187	#95×C₈₉	C₂³	1	2	yes	—
188	#95×C₈₉	C₂³	1	2	yes	—
189	#95×C₈₉	C₂³	1	4	yes	—
190	#95×C₈₉	C₂³	1	2	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	2	yes	—
196	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
197	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
198	#41×C₈₉	—	2	32	no	—
199	C₂×Q₈×C₈₉	—	2	2	no	—
200	C₂×Q₈×C₈₉	—	2	2	no	—
201	C₂×Q₈×C₈₉	#41	1	4	yes	—
202	C₂×D₄×C₈₉	—	2	4	no	—
203	C₂×D₄×C₈₉	—	2	4	no	—
204	C₂×D₄×C₈₉	—	2	8	no	—
205	C₂×D₄×C₈₉	—	2	4	no	—
206	C₂×D₄×C₈₉	—	2	4	no	—
207	C₂×D₄×C₈₉	—	2	8	no	—
208	C₂×D₄×C₈₉	—	2	2	no	—
209	C₂×D₄×C₈₉	—	2	2	no	—
210	C₂×D₄×C₈₉	—	2	2	no	—
211	C₂×D₄×C₈₉	—	2	4	no	—
212	C₂×D₄×C₈₉	—	2	4	no	—
213	C₂×D₄×C₈₉	—	2	4	no	—
214	C₂×D₄×C₈₉	—	2	2	no	—
215	C₂×D₄×C₈₉	—	2	2	no	—
216	C₂×D₄×C₈₉	—	2	2	no	—
217	C₂×D₄×C₈₉	—	2	2	no	—
218	C₂×D₄×C₈₉	—	2	2	no	—
219	C₂×D₄×C₈₉	—	2	8	no	—
220	C₂×D₄×C₈₉	—	4	4	no	—
221	C₂×D₄×C₈₉	—	4	4	no	—
222	C₂×D₄×C₈₉	—	4	4	no	—
223	C₂×D₄×C₈₉	—	4	4	no	—
224	C₂×D₄×C₈₉	—	4	4	no	—
225	C₂×D₄×C₈₉	—	4	4	no	—
226	C₂×D₄×C₈₉	—	4	4	no	—
227	C₂×D₄×C₈₉	#41	1	4	yes	—
228	C₂²×C₄×C₈₉	—	2	4	no	—
229	C₂²×C₄×C₈₉	—	2	4	no	—
230	C₂²×C₄×C₈₉	—	2	4	no	—
231	C₂²×C₄×C₈₉	—	2	2	no	—
232	C₂²×C₄×C₈₉	—	2	2	no	—
233	C₂²×C₄×C₈₉	—	2	4	no	—
234	C₂²×C₄×C₈₉	—	2	4	no	—
235	C₂²×C₄×C₈₉	—	2	4	no	—
236	C₂²×C₄×C₈₉	—	2	4	no	—
237	C₂²×C₄×C₈₉	—	2	4	no	—
238	C₂²×C₄×C₈₉	—	4	4	no	—
239	C₂²×C₄×C₈₉	—	4	4	no	—
240	C₂²×C₄×C₈₉	—	4	4	no	—
241	C₂²×C₄×C₈₉	—	4	4	no	—
242	C₂²×C₄×C₈₉	—	4	4	no	—
243	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
244	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
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	2	yes	—
250	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
259	C₄⋊C₄×C₈₉	—	2	4	no	—
260	C₄⋊C₄×C₈₉	—	2	4	no	—
261	C₄⋊C₄×C₈₉	—	2	4	no	—
262	C₄⋊C₄×C₈₉	—	2	2	no	—
263	C₄⋊C₄×C₈₉	—	2	2	no	—
264	C₄⋊C₄×C₈₉	—	2	2	no	—
265	C₄⋊C₄×C₈₉	—	2	2	no	—
266	C₄⋊C₄×C₈₉	—	2	4	no	—
267	C₄⋊C₄×C₈₉	—	2	4	no	—
268	C₄⋊C₄×C₈₉	—	2	8	no	—
269	C₄⋊C₄×C₈₉	—	2	4	no	—
270	C₄⋊C₄×C₈₉	—	4	2	no	—
271	C₄⋊C₄×C₈₉	—	4	4	no	—
272	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
273	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
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	4	no	—
278	C₂²⋊C₄×C₈₉	—	2	4	no	—
279	C₂²⋊C₄×C₈₉	—	2	4	no	—
280	C₂²⋊C₄×C₈₉	—	2	8	no	—
281	C₂²⋊C₄×C₈₉	—	2	8	no	—
282	C₂²⋊C₄×C₈₉	—	2	8	no	—
283	C₂²⋊C₄×C₈₉	—	2	4	no	—
284	C₂²⋊C₄×C₈₉	—	4	2	no	—
285	C₂²⋊C₄×C₈₉	—	4	4	no	—
286	C₂²⋊C₄×C₈₉	—	4	4	no	—
287	C₂²⋊C₄×C₈₉	—	4	4	no	—
288	C₂²⋊C₄×C₈₉	—	4	4	no	—
289	C₂²⋊C₄×C₈₉	—	4	4	no	—
290	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
291	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
292	C₄²×C₈₉	—	2	4	no	—
293	C₄²×C₈₉	—	2	4	no	—
294	C₄²×C₈₉	—	2	2	no	—
295	C₄²×C₈₉	—	2	2	no	—
296	C₄²×C₈₉	—	2	2	no	—
297	C₄²×C₈₉	—	2	2	no	—
298	C₄²×C₈₉	—	2	4	no	—
299	C₄²×C₈₉	—	4	2	no	—
300	C₄²×C₈₉	C₂×D₄	1	4	yes	—
301	C₄²×C₈₉	C₂×D₄	1	4	yes	—
302	C₂³×C₈₉	—	2	2	no	—
303	C₂³×C₈₉	—	2	1	no	—
304	C₂³×C₈₉	—	2	1	no	—
305	C₂³×C₈₉	—	2	2	no	—
306	C₂³×C₈₉	—	2	2	no	—
307	C₂³×C₈₉	—	2	4	no	—
308	C₂³×C₈₉	—	2	2	no	—
309	C₂³×C₈₉	—	2	4	no	—
310	C₂³×C₈₉	—	2	2	no	—
311	C₂³×C₈₉	—	2	2	no	—
312	C₂³×C₈₉	—	2	2	no	—
313	C₂³×C₈₉	—	2	2	no	—
314	C₂³×C₈₉	—	2	2	no	—
315	C₂³×C₈₉	—	2	2	no	—
316	C₂³×C₈₉	—	2	4	no	—
317	C₂³×C₈₉	—	2	4	no	—
318	C₂³×C₈₉	—	2	4	no	—
319	C₂³×C₈₉	—	2	4	no	—
320	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
321	C₂³×C₈₉	C₂×#41	1	4	yes	—
322	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
323	Q₈×C₈₉	—	2	8	no	—
324	D₄×C₈₉	—	2	16	no	—
325	D₄×C₈₉	—	2	8	no	—
326	D₄×C₈₉	—	4	16	no	—
327	D₄×C₈₉	—	4	4	no	—
328	D₄×C₈₉	—	4	4	no	—
329	D₄×C₈₉	—	8	4	no	—
330	D₄×C₈₉	—	8	4	no	—
331	D₄×C₈₉	—	8	4	no	—
332	D₄×C₈₉	—	8	4	no	—
333	D₄×C₈₉	—	8	8	no	—
334	C₂×C₄×C₈₉	—	2	16	no	—
335	C₂×C₄×C₈₉	—	2	2	no	—
336	C₂×C₄×C₈₉	—	2	2	no	—
337	C₂×C₄×C₈₉	—	2	1	no	—
338	C₂×C₄×C₈₉	—	2	1	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	8	no	—
346	C₂×C₄×C₈₉	—	2	2	no	—
347	C₂×C₄×C₈₉	—	2	2	no	—
348	C₂×C₄×C₈₉	—	2	2	no	—
349	C₂×C₄×C₈₉	—	2	2	no	—
350	C₂×C₄×C₈₉	—	2	2	no	—
351	C₂×C₄×C₈₉	—	2	2	no	—
352	C₂×C₄×C₈₉	—	2	2	no	—
353	C₂×C₄×C₈₉	—	2	2	no	—
354	C₂×C₄×C₈₉	—	2	2	no	—
355	C₂×C₄×C₈₉	—	2	4	no	—
356	C₂×C₄×C₈₉	—	2	4	no	—
357	C₂×C₄×C₈₉	—	2	2	no	—
358	C₂×C₄×C₈₉	—	2	4	no	—
359	C₂×C₄×C₈₉	—	2	2	no	—
360	C₂×C₄×C₈₉	—	2	2	no	—
361	C₂×C₄×C₈₉	—	2	4	no	—
362	C₂×C₄×C₈₉	—	2	2	no	—
363	C₂×C₄×C₈₉	—	8	4	no	—
364	C₂×C₄×C₈₉	—	8	4	no	—
365	C₂×C₄×C₈₉	—	8	4	no	—
366	C₂×C₄×C₈₉	—	8	4	no	—
367	C₂×C₄×C₈₉	—	8	4	no	—
368	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
369	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
370	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
371	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
372	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
373	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
374	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
375	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
376	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
377	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
378	C₂²×C₈₉	—	2	2	no	—
379	C₂²×C₈₉	—	2	4	no	—
380	C₂²×C₈₉	—	2	2	no	—
381	C₂²×C₈₉	—	2	2	no	—
382	C₂²×C₈₉	—	2	8	no	—
383	C₂²×C₈₉	—	4	2	no	—
384	C₂²×C₈₉	—	4	2	no	—
385	C₂²×C₈₉	—	4	2	no	—
386	C₂²×C₈₉	—	4	2	no	—
387	C₂²×C₈₉	—	4	4	no	—
388	C₂²×C₈₉	—	4	2	no	—
389	C₂²×C₈₉	—	4	2	no	—
390	C₂²×C₈₉	—	4	2	no	—
391	C₂²×C₈₉	—	4	2	no	—
392	C₂²×C₈₉	—	4	2	no	—
393	C₂²×C₈₉	—	4	2	no	—
394	C₂²×C₈₉	—	4	4	no	—
395	C₂²×C₈₉	—	4	4	no	—
396	C₂²×C₈₉	—	4	4	no	—
397	C₂²×C₈₉	—	4	4	no	—
398	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
399	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
400	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
401	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
402	C₂²×C₈₉	#585	1	2	yes	—
403	C₄×C₈₉	—	2	2	no	—
404	C₄×C₈₉	—	2	4	no	—
405	C₄×C₈₉	—	2	2	no	—
406	C₄×C₈₉	—	2	2	no	—
407	C₄×C₈₉	—	2	2	no	—
408	C₄×C₈₉	—	2	2	no	—
409	C₄×C₈₉	—	2	4	no	—
410	C₄×C₈₉	—	4	2	no	—
411	C₄×C₈₉	—	4	2	no	—
412	C₄×C₈₉	—	4	2	no	—
413	C₄×C₈₉	—	4	2	no	—
414	C₄×C₈₉	—	4	2	no	—
415	C₄×C₈₉	—	4	2	no	—
416	C₄×C₈₉	—	4	2	no	—
417	C₄×C₈₉	#525	1	4	yes	—
418	#35534	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
419	C₂×C₈₉	—	4	2	no	—
420	C₂×C₈₉	—	4	4	no	—
421	C₂×C₈₉	—	8	2	no	—
422	C₂×C₈₉	—	8	2	no	—
423	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
424	C₂×C₈₉	#3498	1	1	yes	characteristic
425	C₂×C₈₉	#3500	1	1	yes	characteristic
426	C₂×C₈₉	#3513	1	2	yes	—
427	C₂×C₈₉	#3517	1	2	yes	—
428	C₂×#540	C₂×C₈₉	1	1	yes	characteristic, complemented
429	C₂×#520	C₂×C₈₉	1	1	yes	characteristic, complemented
430	#2566	C₂×C₈₉	1	1	yes	characteristic, complemented
431	#2565	C₂×C₈₉	1	1	yes	characteristic, complemented
432	#2548	C₂×C₈₉	1	1	yes	characteristic, complemented
433	#2541	C₂×C₈₉	1	1	yes	characteristic, complemented
434	#2504	C₂×C₈₉	1	1	yes	characteristic, complemented
435	#2501	C₂×C₈₉	1	1	yes	characteristic, complemented
436	#2471	C₂×C₈₉	1	4	yes	complemented
437	#2464	C₂×C₈₉	1	4	yes	complemented
438	#2456	C₂×C₈₉	1	4	yes	complemented
439	#2443	C₂×C₈₉	1	4	yes	complemented
440	#2431	C₂×C₈₉	1	1	yes	characteristic, complemented
441	#2431	C₂×C₈₉	1	1	yes	characteristic, complemented
442	#2328	C₂×C₈₉	1	1	yes	characteristic, complemented
443	#2326	C₂×C₈₉	1	1	yes	characteristic, complemented
444	C₄×#127	C₂×C₈₉	1	1	yes	characteristic, complemented
445	C₄×#124	C₂×C₈₉	1	1	yes	characteristic, complemented
446	#2298	C₂×C₈₉	1	1	yes	characteristic, complemented
447	C₈₉	#35534	1	1	yes	characteristic, direct product factor, Sylow
448	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
449	#540	—	2	8	no	—
450	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
451	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
452	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
453	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
454	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
455	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
456	C₂×#123	C₂²×C₈₉	1	2	yes	—
457	C₂×#123	C₂²×C₈₉	1	2	yes	—
458	C₂×#123	C₂²×C₈₉	1	4	yes	—
459	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
460	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
461	C₂×#121	C₂²×C₈₉	1	2	yes	—
462	C₂×#121	C₂²×C₈₉	1	2	yes	—
463	C₂×#121	C₂²×C₈₉	1	4	yes	—
464	#520	—	2	8	no	—
465	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
466	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
467	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
468	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
469	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
470	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
471	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
472	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
473	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
474	C₂×#117	C₂²×C₈₉	1	2	yes	—
475	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
476	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
477	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
478	#399	C₂²×C₈₉	1	4	yes	—
479	#398	C₂²×C₈₉	1	4	yes	—
480	#397	C₂²×C₈₉	1	4	yes	—
481	#396	C₂²×C₈₉	1	4	yes	—
482	#394	C₂²×C₈₉	1	4	yes	—
483	#392	C₂²×C₈₉	1	4	yes	—
484	#392	C₂²×C₈₉	1	4	yes	—
485	#392	C₂²×C₈₉	1	4	yes	—
486	#391	C₂²×C₈₉	1	1	yes	characteristic
487	#391	C₂²×C₈₉	1	1	yes	characteristic
488	#390	C₂²×C₈₉	1	1	yes	characteristic
489	#390	C₂²×C₈₉	1	4	yes	—
490	#390	C₂²×C₈₉	1	1	yes	characteristic
491	#390	C₂²×C₈₉	1	1	yes	characteristic
492	#390	C₂²×C₈₉	1	1	yes	characteristic
493	#390	C₂²×C₈₉	1	1	yes	characteristic
494	#390	C₂²×C₈₉	1	4	yes	—
495	#390	C₂²×C₈₉	1	1	yes	characteristic
496	#388	C₂²×C₈₉	1	4	yes	—
497	#388	C₂²×C₈₉	1	4	yes	—
498	#388	C₂²×C₈₉	1	2	yes	—
499	#388	C₂²×C₈₉	1	2	yes	—
500	#387	C₂²×C₈₉	1	4	yes	—
501	#387	C₂²×C₈₉	1	2	yes	—
502	#387	C₂²×C₈₉	1	2	yes	—
503	#386	C₂²×C₈₉	1	4	yes	—
504	#386	C₂²×C₈₉	1	4	yes	—
505	#386	C₂²×C₈₉	1	4	yes	—
506	#386	C₂²×C₈₉	1	4	yes	—
507	#386	C₂²×C₈₉	1	4	yes	—
508	#385	C₂²×C₈₉	1	4	yes	—
509	#385	C₂²×C₈₉	1	4	yes	—
510	#384	C₂²×C₈₉	1	1	yes	characteristic
511	#384	C₂²×C₈₉	1	1	yes	characteristic
512	#382	C₂²×C₈₉	1	1	yes	characteristic
513	#382	C₂²×C₈₉	1	1	yes	characteristic
514	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
515	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
516	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
517	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
518	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
519	#376	C₂²×C₈₉	1	1	yes	characteristic
520	C₄³	C₂²×C₈₉	1	1	yes	characteristic
521	C₂×#41	—	2	4	no	—
522	C₂×#41	—	2	4	no	—
523	C₂×#41	—	2	4	no	—
524	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
525	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
526	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
527	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
528	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
529	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
530	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
531	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
532	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
533	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
534	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
535	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
536	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
537	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
538	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
539	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
540	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
541	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
542	#127	—	2	4	no	—
543	#127	—	2	4	no	—
544	#127	—	2	4	no	—
545	#125	—	2	4	no	—
546	#124	—	2	4	no	—
547	#124	—	2	4	no	—
548	#123	—	2	8	no	—
549	#123	—	2	8	no	—
550	#123	—	4	8	no	—
551	#121	—	2	4	no	—
552	#121	—	2	4	no	—
553	#121	—	2	8	no	—
554	#121	—	2	8	no	—
555	#121	—	4	8	no	—
556	C₄×Q₈	—	2	4	no	—
557	C₄×Q₈	—	2	4	no	—
558	C₄×D₄	—	2	8	no	—
559	C₄×D₄	—	2	8	no	—
560	C₄×D₄	—	2	4	no	—
561	C₄×D₄	—	2	4	no	—
562	C₄×D₄	—	2	4	no	—
563	C₄×D₄	—	2	4	no	—
564	C₄×D₄	—	4	8	no	—
565	#117	—	2	8	no	—
566	#117	D₄×C₈₉	1	8	yes	complemented
567	C₂×C₄⋊C₄	—	2	4	no	—
568	C₂×C₄⋊C₄	—	2	8	no	—
569	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
577	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
581	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
584	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
601	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
603	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
604	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
605	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
609	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
610	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
611	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
612	#95	C₂³×C₈₉	1	2	yes	—
613	#95	C₂³×C₈₉	1	2	yes	—
614	#95	C₂³×C₈₉	1	4	yes	—
615	#95	C₂³×C₈₉	1	2	yes	—
616	#95	C₂³×C₈₉	1	2	yes	—
617	#95	C₂³×C₈₉	1	4	yes	—
618	#95	C₂³×C₈₉	1	2	yes	—
619	#95	C₂³×C₈₉	1	2	yes	—
620	#95	C₂³×C₈₉	1	4	yes	—
621	#95	C₂³×C₈₉	1	4	yes	—
622	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
623	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
624	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
625	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
626	#41	—	2	32	no	—
627	C₂×Q₈	—	2	2	no	—
628	C₂×Q₈	—	2	2	no	—
629	C₂×Q₈	#41×C₈₉	1	4	yes	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	8	no	—
633	C₂×D₄	—	2	4	no	—
634	C₂×D₄	—	2	4	no	—
635	C₂×D₄	—	2	8	no	—
636	C₂×D₄	—	2	2	no	—
637	C₂×D₄	—	2	2	no	—
638	C₂×D₄	—	2	2	no	—
639	C₂×D₄	—	2	4	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	2	no	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	—	2	2	no	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	8	no	—
648	C₂×D₄	—	4	4	no	—
649	C₂×D₄	—	4	4	no	—
650	C₂×D₄	—	4	4	no	—
651	C₂×D₄	—	4	4	no	—
652	C₂×D₄	—	4	4	no	—
653	C₂×D₄	—	4	4	no	—
654	C₂×D₄	—	4	4	no	—
655	C₂×D₄	#41×C₈₉	1	4	yes	—
656	C₂²×C₄	—	2	4	no	—
657	C₂²×C₄	—	2	4	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	2	4	no	—
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	4	4	no	—
667	C₂²×C₄	—	4	4	no	—
668	C₂²×C₄	—	4	4	no	—
669	C₂²×C₄	—	4	4	no	—
670	C₂²×C₄	—	4	4	no	—
671	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
672	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
680	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
684	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	8	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	4	4	no	—
699	C₄⋊C₄	—	4	2	no	—
700	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
701	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	8	no	—
709	C₂²⋊C₄	—	2	8	no	—
710	C₂²⋊C₄	—	2	8	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	4	4	no	—
713	C₂²⋊C₄	—	4	4	no	—
714	C₂²⋊C₄	—	4	4	no	—
715	C₂²⋊C₄	—	4	4	no	—
716	C₂²⋊C₄	—	4	2	no	—
717	C₂²⋊C₄	—	4	4	no	—
718	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
719	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
720	C₄²	—	2	4	no	—
721	C₄²	—	2	4	no	—
722	C₄²	—	2	2	no	—
723	C₄²	—	2	2	no	—
724	C₄²	—	2	2	no	—
725	C₄²	—	2	2	no	—
726	C₄²	—	2	4	no	—
727	C₄²	—	4	2	no	—
728	C₄²	C₂×D₄×C₈₉	1	4	yes	—
729	C₄²	C₂×D₄×C₈₉	1	4	yes	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	1	no	—
732	C₂³	—	2	1	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	4	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	4	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	4	no	—
745	C₂³	—	2	4	no	—
746	C₂³	—	2	4	no	—
747	C₂³	—	2	4	no	—
748	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
749	C₂³	C₂×#41×C₈₉	1	4	yes	—
750	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
751	Q₈	—	2	8	no	—
752	D₄	—	2	16	no	—
753	D₄	—	2	8	no	—
754	D₄	—	4	16	no	—
755	D₄	—	4	4	no	—
756	D₄	—	4	4	no	—
757	D₄	—	8	4	no	—
758	D₄	—	8	4	no	—
759	D₄	—	8	4	no	—
760	D₄	—	8	4	no	—
761	D₄	—	8	8	no	—
762	C₂×C₄	—	2	16	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	8	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	4	no	—
784	C₂×C₄	—	2	4	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	4	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	4	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	8	4	no	—
792	C₂×C₄	—	8	4	no	—
793	C₂×C₄	—	8	4	no	—
794	C₂×C₄	—	8	4	no	—
795	C₂×C₄	—	8	4	no	—
796	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
797	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
798	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
799	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
800	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
801	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
802	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
803	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
804	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
805	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
806	C₂²	—	2	2	no	—
807	C₂²	—	2	4	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	2	no	—
810	C₂²	—	2	8	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	4	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	4	no	—
823	C₂²	—	4	4	no	—
824	C₂²	—	4	4	no	—
825	C₂²	—	4	4	no	—
826	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
827	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
828	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
829	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
830	C₂²	#585×C₈₉	1	2	yes	—
831	C₄	—	2	2	no	—
832	C₄	—	2	4	no	—
833	C₄	—	2	2	no	—
834	C₄	—	2	2	no	—
835	C₄	—	2	2	no	—
836	C₄	—	2	2	no	—
837	C₄	—	2	4	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	2	no	—
845	C₄	#525×C₈₉	1	4	yes	—
846	C₂	—	4	2	no	—
847	C₂	—	4	4	no	—
848	C₂	—	8	2	no	—
849	C₂	—	8	2	no	—
850	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
851	C₂	C₈₉×#3498	1	1	yes	characteristic
852	C₂	C₈₉×#3500	1	1	yes	characteristic
853	C₂	C₈₉×#3513	1	2	yes	—
854	C₂	C₈₉×#3517	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
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×#540×C₈₉	C₂	semidirect
2. C₂×#520×C₈₉	C₂	semidirect
3. C₈₉×#2566	C₂	semidirect
4. C₈₉×#2565	C₂	semidirect
5. C₈₉×#2548	C₂	semidirect
6. C₈₉×#2541	C₂	semidirect
7. C₈₉×#2504	C₂	semidirect
8. C₈₉×#2501	C₂	semidirect
9. C₈₉×#2471	C₂	semidirect
10. C₈₉×#2464	C₂	semidirect
11. C₈₉×#2456	C₂	semidirect
12. C₈₉×#2443	C₂	semidirect
13. C₈₉×#2431	C₂	semidirect
14. C₈₉×#2431	C₂	semidirect
15. C₈₉×#2328	C₂	semidirect
16. C₈₉×#2326	C₂	semidirect
17. C₄×#127×C₈₉	C₂	semidirect
18. C₄×#124×C₈₉	C₂	semidirect
19. C₈₉×#2298	C₂	semidirect
138. #117×C₈₉	D₄	semidirect
418. #35534	C₈₉	direct (N × H)
428. C₂×#540	C₂×C₈₉	semidirect
429. C₂×#520	C₂×C₈₉	semidirect
430. #2566	C₂×C₈₉	semidirect
431. #2565	C₂×C₈₉	semidirect
432. #2548	C₂×C₈₉	semidirect
433. #2541	C₂×C₈₉	semidirect
434. #2504	C₂×C₈₉	semidirect
435. #2501	C₂×C₈₉	semidirect
436. #2471	C₂×C₈₉	semidirect
437. #2464	C₂×C₈₉	semidirect
438. #2456	C₂×C₈₉	semidirect
439. #2443	C₂×C₈₉	semidirect
440. #2431	C₂×C₈₉	semidirect
441. #2431	C₂×C₈₉	semidirect
442. #2328	C₂×C₈₉	semidirect
443. #2326	C₂×C₈₉	semidirect
444. C₄×#127	C₂×C₈₉	semidirect
445. C₄×#124	C₂×C₈₉	semidirect
446. #2298	C₂×C₈₉	semidirect
447. C₈₉	#35534	direct (N × H)
566. #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×#540×C₈₉	2
C₂×#520×C₈₉	2
C₈₉×#2566	2
C₈₉×#2565	2
C₈₉×#2548	2
C₈₉×#2541	2
C₈₉×#2504	2
C₈₉×#2501	2
C₈₉×#2471	2
C₈₉×#2464	2
C₈₉×#2456	2
C₈₉×#2443	2
C₈₉×#2431	2
C₈₉×#2328	2
C₈₉×#2326	2
C₄×#127×C₈₉	2
C₄×#124×C₈₉	2
C₈₉×#2298	2
#35534	89

Subgroups — C89×#35534 #36413382

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35534 #36413382