Subgroups — C₈₉×#60708 #36438556

Order 22784.

1860 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3495	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3181	C₂	1	4	yes	maximal, complemented
3	C₈₉×#3178	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3177	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3175	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3170	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3168	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3156	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3137	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3056	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3050	C₂	1	1	yes	maximal, characteristic
13	C₂×#467×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2951	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2950	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2947	C₂	1	2	yes	maximal, complemented
17	C₂×#405×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#137×C₈₉	C₂²	1	2	yes	—
19	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
23	#556×C₈₉	—	2	2	no	—
24	#554×C₈₉	—	2	2	no	—
25	#552×C₈₉	—	2	4	no	—
26	#552×C₈₉	—	2	2	no	—
27	#552×C₈₉	—	2	2	no	—
28	#551×C₈₉	—	2	4	no	—
29	#544×C₈₉	C₂²	1	2	yes	—
30	#542×C₈₉	C₂²	1	4	yes	—
31	#541×C₈₉	C₂²	1	4	yes	—
32	#536×C₈₉	C₂²	1	2	yes	—
33	#533×C₈₉	C₂²	1	4	yes	—
34	#529×C₈₉	C₂²	1	4	yes	—
35	#525×C₈₉	C₂²	1	2	yes	—
36	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
37	#520×C₈₉	C₂²	1	2	yes	—
38	#519×C₈₉	C₂²	1	2	yes	—
39	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
40	#501×C₈₉	C₂²	1	4	yes	complemented
41	#500×C₈₉	C₂²	1	2	yes	complemented
42	#499×C₈₉	C₂²	1	2	yes	complemented
43	#497×C₈₉	C₂²	1	4	yes	complemented
44	#495×C₈₉	C₂²	1	2	yes	complemented
45	#494×C₈₉	C₂²	1	2	yes	complemented
46	#491×C₈₉	C₂²	1	4	yes	complemented
47	#489×C₈₉	C₂²	1	4	yes	complemented
48	#488×C₈₉	C₂²	1	4	yes	complemented
49	#487×C₈₉	C₂²	1	4	yes	complemented
50	#470×C₈₉	C₂²	1	4	yes	—
51	#468×C₈₉	C₂²	1	4	yes	—
52	#467×C₈₉	C₂²	1	2	yes	—
53	#467×C₈₉	C₂²	1	1	yes	characteristic
54	#467×C₈₉	C₂²	1	4	yes	—
55	#467×C₈₉	C₂²	1	2	yes	—
56	#467×C₈₉	C₂²	1	1	yes	characteristic
57	#467×C₈₉	C₂²	1	2	yes	—
58	#467×C₈₉	C₂²	1	2	yes	—
59	#466×C₈₉	C₂²	1	1	yes	characteristic
60	#466×C₈₉	C₂²	1	1	yes	characteristic
61	#465×C₈₉	C₂²	1	4	yes	—
62	#465×C₈₉	C₂²	1	2	yes	—
63	#465×C₈₉	C₂²	1	2	yes	—
64	#441×C₈₉	C₂²	1	4	yes	complemented
65	#441×C₈₉	C₂²	1	4	yes	complemented
66	#440×C₈₉	C₂²	1	4	yes	complemented
67	#440×C₈₉	C₂²	1	4	yes	complemented
68	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
69	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
70	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
71	C₄×Q₁₆×C₈₉	C₂²	1	4	yes	complemented
72	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	complemented
73	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
74	#428×C₈₉	C₂²	1	2	yes	—
75	#427×C₈₉	C₂²	1	1	yes	characteristic
76	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
77	#419×C₈₉	C₂²	1	2	yes	—
78	#417×C₈₉	C₂²	1	2	yes	—
79	#416×C₈₉	C₂²	1	2	yes	—
80	C₂×#103×C₈₉	C₂²	1	2	yes	—
81	#405×C₈₉	C₂²	1	1	yes	characteristic
82	#405×C₈₉	C₂²	1	1	yes	characteristic
83	#405×C₈₉	C₂²	1	2	yes	—
84	#405×C₈₉	C₂²	1	2	yes	—
85	#405×C₈₉	C₂²	1	1	yes	characteristic
86	#405×C₈₉	C₂²	1	1	yes	characteristic
87	C₂×#97×C₈₉	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
89	C₂×#41×C₈₉	C₂³	1	2	yes	—
90	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
91	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
92	#137×C₈₉	—	2	8	no	—
93	#135×C₈₉	—	2	4	no	—
94	C₂×Q₁₆×C₈₉	—	2	4	no	—
95	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
96	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
97	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
98	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
99	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
101	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
102	C₂×M₁₆×C₈₉	—	2	4	no	—
103	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
104	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
105	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₈₉	—	2	4	no	—
107	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
109	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₈₉	—	2	2	no	—
115	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
116	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
117	#126×C₈₉	—	2	4	no	—
118	#126×C₈₉	—	2	4	no	—
119	#126×C₈₉	—	2	4	no	—
120	#126×C₈₉	—	2	4	no	—
121	#125×C₈₉	—	2	4	no	—
122	#125×C₈₉	—	2	4	no	—
123	#125×C₈₉	—	2	2	no	—
124	#125×C₈₉	—	2	4	no	—
125	#125×C₈₉	C₂³	1	4	yes	—
126	#124×C₈₉	—	2	4	no	—
127	#124×C₈₉	C₂³	1	4	yes	—
128	#123×C₈₉	—	2	2	no	—
129	#123×C₈₉	—	2	4	no	—
130	#123×C₈₉	—	2	4	no	—
131	#123×C₈₉	—	2	4	no	—
132	C₂²⋊Q₈×C₈₉	—	2	2	no	—
133	C₂²⋊Q₈×C₈₉	—	2	2	no	—
134	C₂²⋊Q₈×C₈₉	—	2	4	no	—
135	C₂²⋊Q₈×C₈₉	—	2	2	no	—
136	C₂²⋊Q₈×C₈₉	—	2	2	no	—
137	C₂²⋊Q₈×C₈₉	—	2	4	no	—
138	C₂²⋊Q₈×C₈₉	—	2	4	no	—
139	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
140	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
141	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
142	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
143	#121×C₈₉	C₂³	1	2	yes	—
144	#121×C₈₉	C₂³	1	2	yes	—
145	#120×C₈₉	—	2	2	no	—
146	C₄×Q₈×C₈₉	—	2	2	no	—
147	C₄×Q₈×C₈₉	—	2	2	no	—
148	C₄×Q₈×C₈₉	—	2	4	no	—
149	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
150	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
151	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
152	C₄×D₄×C₈₉	—	2	2	no	—
153	C₄×D₄×C₈₉	—	2	2	no	—
154	C₄×D₄×C₈₉	—	2	4	no	—
155	C₄×D₄×C₈₉	—	2	4	no	—
156	C₄×D₄×C₈₉	C₂³	1	4	yes	—
157	#117×C₈₉	—	2	4	no	—
158	#117×C₈₉	—	2	2	no	—
159	#117×C₈₉	—	2	4	no	—
160	#117×C₈₉	—	2	4	no	—
161	#117×C₈₉	D₄	1	1	yes	characteristic
162	#117×C₈₉	D₄	1	2	yes	—
163	#117×C₈₉	D₄	1	1	yes	characteristic
164	#117×C₈₉	C₂³	1	2	yes	—
165	#117×C₈₉	C₂³	1	1	yes	characteristic
166	#117×C₈₉	C₂³	1	1	yes	characteristic
167	#117×C₈₉	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
169	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
170	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
174	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
175	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
176	#107×C₈₉	C₂³	1	2	yes	—
177	#107×C₈₉	C₂³	1	2	yes	—
178	#107×C₈₉	C₂³	1	1	yes	characteristic
179	#107×C₈₉	C₂³	1	1	yes	characteristic
180	#107×C₈₉	C₂³	1	4	yes	—
181	#106×C₈₉	C₂³	1	2	yes	—
182	#106×C₈₉	C₂³	1	4	yes	—
183	#103×C₈₉	C₂³	1	4	yes	—
184	#103×C₈₉	C₂³	1	4	yes	—
185	#103×C₈₉	C₂³	1	2	yes	—
186	#103×C₈₉	C₂³	1	2	yes	—
187	#103×C₈₉	C₂³	1	4	yes	—
188	#103×C₈₉	C₂³	1	4	yes	—
189	#103×C₈₉	C₂³	1	4	yes	—
190	#102×C₈₉	C₂³	1	2	yes	—
191	#102×C₈₉	C₂³	1	2	yes	—
192	#102×C₈₉	C₂³	1	4	yes	—
193	#97×C₈₉	C₂³	1	2	yes	—
194	#97×C₈₉	C₂³	1	2	yes	—
195	#97×C₈₉	C₂³	1	2	yes	—
196	#97×C₈₉	C₂³	1	2	yes	—
197	C₄×C₈×C₈₉	C₂³	1	2	yes	—
198	C₄×C₈×C₈₉	C₂³	1	2	yes	—
199	C₄×C₈×C₈₉	C₂³	1	2	yes	—
200	C₄×C₈×C₈₉	C₂³	1	2	yes	—
201	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
202	#41×C₈₉	—	2	4	no	—
203	#41×C₈₉	—	2	4	no	—
204	C₂×Q₈×C₈₉	—	2	2	no	—
205	C₂×Q₈×C₈₉	—	2	4	no	—
206	C₂×Q₈×C₈₉	—	2	4	no	—
207	C₂×Q₈×C₈₉	—	2	4	no	—
208	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
209	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
210	C₂×D₄×C₈₉	—	2	2	no	—
211	C₂×D₄×C₈₉	—	2	2	no	—
212	C₂×D₄×C₈₉	—	2	2	no	—
213	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₈₉	—	2	2	no	—
215	C₂²×C₄×C₈₉	—	2	2	no	—
216	C₂²×C₄×C₈₉	—	2	2	no	—
217	C₂²×C₄×C₈₉	—	2	2	no	—
218	C₂²×C₄×C₈₉	—	2	2	no	—
219	C₂²×C₄×C₈₉	—	2	4	no	—
220	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
221	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₈₉	C₂×D₄	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	1	yes	characteristic
228	Q₁₆×C₈₉	—	2	4	no	—
229	Q₁₆×C₈₉	—	2	4	no	—
230	Q₁₆×C₈₉	—	2	2	no	—
231	Q₁₆×C₈₉	—	2	8	no	—
232	SD₁₆×C₈₉	—	2	4	no	—
233	SD₁₆×C₈₉	—	2	8	no	—
234	D₈×C₈₉	—	2	2	no	—
235	M₁₆×C₈₉	—	2	2	no	—
236	M₁₆×C₈₉	—	2	4	no	—
237	M₁₆×C₈₉	#41	1	4	yes	—
238	C₂×C₈×C₈₉	—	2	2	no	—
239	C₂×C₈×C₈₉	—	2	2	no	—
240	C₂×C₈×C₈₉	—	2	2	no	—
241	C₂×C₈×C₈₉	—	2	2	no	—
242	C₂×C₈×C₈₉	—	2	2	no	—
243	C₂×C₈×C₈₉	—	2	4	no	—
244	C₂×C₈×C₈₉	#41	1	4	yes	—
245	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
247	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
250	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
251	C₄⋊C₄×C₈₉	—	2	2	no	—
252	C₄⋊C₄×C₈₉	—	2	4	no	—
253	C₄⋊C₄×C₈₉	—	2	4	no	—
254	C₄⋊C₄×C₈₉	—	2	4	no	—
255	C₄⋊C₄×C₈₉	—	2	4	no	—
256	C₄⋊C₄×C₈₉	—	2	4	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	2	no	—
261	C₄⋊C₄×C₈₉	—	2	4	no	—
262	C₄⋊C₄×C₈₉	—	2	2	no	—
263	C₄⋊C₄×C₈₉	—	2	4	no	—
264	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
265	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
266	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
267	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
268	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
269	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
270	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
271	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
272	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
273	C₂²⋊C₄×C₈₉	—	2	4	no	—
274	C₂²⋊C₄×C₈₉	—	2	4	no	—
275	C₂²⋊C₄×C₈₉	—	2	2	no	—
276	C₂²⋊C₄×C₈₉	—	2	2	no	—
277	C₂²⋊C₄×C₈₉	—	2	2	no	—
278	C₂²⋊C₄×C₈₉	—	2	2	no	—
279	C₂²⋊C₄×C₈₉	—	2	4	no	—
280	C₂²⋊C₄×C₈₉	—	2	4	no	—
281	C₂²⋊C₄×C₈₉	—	2	2	no	—
282	C₂²⋊C₄×C₈₉	—	2	4	no	—
283	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
284	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
285	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
286	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
287	C₄²×C₈₉	—	2	4	no	—
288	C₄²×C₈₉	—	2	4	no	—
289	C₄²×C₈₉	—	2	4	no	—
290	C₄²×C₈₉	—	2	2	no	—
291	C₄²×C₈₉	C₂×D₄	1	2	yes	—
292	C₄²×C₈₉	C₂×D₄	1	2	yes	—
293	C₄²×C₈₉	C₂⁴	1	2	yes	—
294	C₄²×C₈₉	C₂⁴	1	2	yes	—
295	C₂³×C₈₉	—	2	2	no	—
296	C₂³×C₈₉	—	2	2	no	—
297	C₂³×C₈₉	—	2	2	no	—
298	C₂³×C₈₉	—	4	1	no	—
299	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
300	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
301	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
302	Q₈×C₈₉	—	2	4	no	—
303	Q₈×C₈₉	—	2	2	no	—
304	Q₈×C₈₉	—	2	4	no	—
305	Q₈×C₈₉	—	2	2	no	—
306	Q₈×C₈₉	—	4	4	no	—
307	Q₈×C₈₉	—	8	4	no	—
308	D₄×C₈₉	—	2	2	no	—
309	D₄×C₈₉	—	2	2	no	—
310	D₄×C₈₉	—	4	4	no	—
311	D₄×C₈₉	—	4	4	no	—
312	D₄×C₈₉	—	8	2	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	2	no	—
317	C₂×C₄×C₈₉	—	2	1	no	—
318	C₂×C₄×C₈₉	—	2	1	no	—
319	C₂×C₄×C₈₉	—	2	1	no	—
320	C₂×C₄×C₈₉	—	2	1	no	—
321	C₂×C₄×C₈₉	—	2	2	no	—
322	C₂×C₄×C₈₉	—	2	2	no	—
323	C₂×C₄×C₈₉	—	2	4	no	—
324	C₂×C₄×C₈₉	—	2	2	no	—
325	C₂×C₄×C₈₉	—	2	4	no	—
326	C₂×C₄×C₈₉	—	4	2	no	—
327	C₂×C₄×C₈₉	—	4	4	no	—
328	C₂×C₄×C₈₉	—	4	4	no	—
329	C₂×C₄×C₈₉	—	8	4	no	—
330	C₂×C₄×C₈₉	—	8	2	no	—
331	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
339	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
340	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
341	C₈×C₈₉	—	2	1	no	—
342	C₈×C₈₉	—	2	1	no	—
343	C₈×C₈₉	—	2	2	no	—
344	C₈×C₈₉	C₂×#41	1	2	yes	—
345	C₈×C₈₉	C₂×#41	1	2	yes	—
346	C₈×C₈₉	C₂×#41	1	4	yes	—
347	C₂²×C₈₉	—	2	1	no	—
348	C₂²×C₈₉	—	2	1	no	—
349	C₂²×C₈₉	—	2	1	no	—
350	C₂²×C₈₉	—	2	1	no	—
351	C₂²×C₈₉	—	2	1	no	—
352	C₂²×C₈₉	—	2	1	no	—
353	C₂²×C₈₉	—	2	1	no	—
354	C₂²×C₈₉	—	4	4	no	—
355	C₂²×C₈₉	—	4	2	no	—
356	C₂²×C₈₉	—	4	2	no	—
357	C₂²×C₈₉	—	4	2	no	—
358	C₂²×C₈₉	#532	1	2	yes	—
359	C₂²×C₈₉	#578	1	2	yes	—
360	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
361	C₄×C₈₉	—	2	2	no	—
362	C₄×C₈₉	—	2	2	no	—
363	C₄×C₈₉	—	2	1	no	—
364	C₄×C₈₉	—	2	1	no	—
365	C₄×C₈₉	—	2	2	no	—
366	C₄×C₈₉	—	2	2	no	—
367	C₄×C₈₉	—	4	4	no	—
368	C₄×C₈₉	—	4	2	no	—
369	C₄×C₈₉	—	4	2	no	—
370	C₄×C₈₉	—	4	4	no	—
371	C₄×C₈₉	—	4	2	no	—
372	C₄×C₈₉	#532	1	2	yes	—
373	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
374	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
375	#60708	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
376	C₂×C₈₉	—	2	2	no	—
377	C₂×C₈₉	—	2	2	no	—
378	C₂×C₈₉	—	4	1	no	—
379	C₂×C₈₉	—	8	2	no	—
380	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
381	C₂×C₈₉	C₂×#578	1	1	yes	characteristic
382	C₂×C₈₉	#3584	1	1	yes	characteristic
383	#3495	C₂×C₈₉	1	2	yes	complemented
384	#3181	C₂×C₈₉	1	4	yes	complemented
385	#3178	C₂×C₈₉	1	4	yes	complemented
386	#3177	C₂×C₈₉	1	2	yes	complemented
387	#3175	C₂×C₈₉	1	2	yes	complemented
388	#3170	C₂×C₈₉	1	2	yes	complemented
389	#3168	C₂×C₈₉	1	2	yes	complemented
390	#3164	C₂×C₈₉	1	1	yes	characteristic, complemented
391	#3156	C₂×C₈₉	1	1	yes	characteristic, complemented
392	#3137	C₂×C₈₉	1	2	yes	complemented
393	#3056	C₂×C₈₉	1	2	yes	complemented
394	#3050	C₂×C₈₉	1	1	yes	characteristic
395	C₂×#467	C₂×C₈₉	1	1	yes	characteristic, complemented
396	#2951	C₂×C₈₉	1	1	yes	characteristic, complemented
397	#2950	C₂×C₈₉	1	1	yes	characteristic, complemented
398	#2947	C₂×C₈₉	1	2	yes	complemented
399	C₂×#405	C₂×C₈₉	1	1	yes	characteristic, complemented
400	C₈₉	#60708	1	1	yes	characteristic, direct product factor, Sylow
401	C₂×#137	C₂²×C₈₉	1	2	yes	—
402	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
403	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
404	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
405	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
406	#556	—	2	2	no	—
407	#554	—	2	2	no	—
408	#552	—	2	4	no	—
409	#552	—	2	2	no	—
410	#552	—	2	2	no	—
411	#551	—	2	4	no	—
412	#544	C₂²×C₈₉	1	2	yes	—
413	#542	C₂²×C₈₉	1	4	yes	—
414	#541	C₂²×C₈₉	1	4	yes	—
415	#536	C₂²×C₈₉	1	2	yes	—
416	#533	C₂²×C₈₉	1	4	yes	—
417	#529	C₂²×C₈₉	1	4	yes	—
418	#525	C₂²×C₈₉	1	2	yes	—
419	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
420	#520	C₂²×C₈₉	1	2	yes	—
421	#519	C₂²×C₈₉	1	2	yes	—
422	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
423	#501	C₂²×C₈₉	1	4	yes	complemented
424	#500	C₂²×C₈₉	1	2	yes	complemented
425	#499	C₂²×C₈₉	1	2	yes	complemented
426	#497	C₂²×C₈₉	1	4	yes	complemented
427	#495	C₂²×C₈₉	1	2	yes	complemented
428	#494	C₂²×C₈₉	1	2	yes	complemented
429	#491	C₂²×C₈₉	1	4	yes	complemented
430	#489	C₂²×C₈₉	1	4	yes	complemented
431	#488	C₂²×C₈₉	1	4	yes	complemented
432	#487	C₂²×C₈₉	1	4	yes	complemented
433	#470	C₂²×C₈₉	1	4	yes	—
434	#468	C₂²×C₈₉	1	4	yes	—
435	#467	C₂²×C₈₉	1	2	yes	—
436	#467	C₂²×C₈₉	1	1	yes	characteristic
437	#467	C₂²×C₈₉	1	4	yes	—
438	#467	C₂²×C₈₉	1	2	yes	—
439	#467	C₂²×C₈₉	1	1	yes	characteristic
440	#467	C₂²×C₈₉	1	2	yes	—
441	#467	C₂²×C₈₉	1	2	yes	—
442	#466	C₂²×C₈₉	1	1	yes	characteristic
443	#466	C₂²×C₈₉	1	1	yes	characteristic
444	#465	C₂²×C₈₉	1	4	yes	—
445	#465	C₂²×C₈₉	1	2	yes	—
446	#465	C₂²×C₈₉	1	2	yes	—
447	#441	C₂²×C₈₉	1	4	yes	complemented
448	#441	C₂²×C₈₉	1	4	yes	complemented
449	#440	C₂²×C₈₉	1	4	yes	complemented
450	#440	C₂²×C₈₉	1	4	yes	complemented
451	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
452	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
453	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
454	C₄×Q₁₆	C₂²×C₈₉	1	4	yes	complemented
455	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	complemented
456	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
457	#428	C₂²×C₈₉	1	2	yes	—
458	#427	C₂²×C₈₉	1	1	yes	characteristic
459	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
460	#419	C₂²×C₈₉	1	2	yes	—
461	#417	C₂²×C₈₉	1	2	yes	—
462	#416	C₂²×C₈₉	1	2	yes	—
463	C₂×#103	C₂²×C₈₉	1	2	yes	—
464	#405	C₂²×C₈₉	1	1	yes	characteristic
465	#405	C₂²×C₈₉	1	1	yes	characteristic
466	#405	C₂²×C₈₉	1	2	yes	—
467	#405	C₂²×C₈₉	1	2	yes	—
468	#405	C₂²×C₈₉	1	1	yes	characteristic
469	#405	C₂²×C₈₉	1	1	yes	characteristic
470	C₂×#97	C₂²×C₈₉	1	2	yes	—
471	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	—
472	C₂×#41	C₂³×C₈₉	1	2	yes	—
473	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
474	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
475	#137	—	2	8	no	—
476	#135	—	2	4	no	—
477	C₂×Q₁₆	—	2	4	no	—
478	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
479	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
480	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
481	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
482	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
483	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
484	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
485	C₂×M₁₆	—	2	4	no	—
486	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
487	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
488	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
489	C₂²×C₈	—	2	4	no	—
490	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
491	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
492	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
496	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
497	C₄⋊Q₈	—	2	2	no	—
498	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
499	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
500	#126	—	2	4	no	—
501	#126	—	2	4	no	—
502	#126	—	2	4	no	—
503	#126	—	2	4	no	—
504	#125	—	2	4	no	—
505	#125	—	2	4	no	—
506	#125	—	2	2	no	—
507	#125	—	2	4	no	—
508	#125	C₂³×C₈₉	1	4	yes	—
509	#124	—	2	4	no	—
510	#124	C₂³×C₈₉	1	4	yes	—
511	#123	—	2	2	no	—
512	#123	—	2	4	no	—
513	#123	—	2	4	no	—
514	#123	—	2	4	no	—
515	C₂²⋊Q₈	—	2	2	no	—
516	C₂²⋊Q₈	—	2	2	no	—
517	C₂²⋊Q₈	—	2	4	no	—
518	C₂²⋊Q₈	—	2	2	no	—
519	C₂²⋊Q₈	—	2	2	no	—
520	C₂²⋊Q₈	—	2	4	no	—
521	C₂²⋊Q₈	—	2	4	no	—
522	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
523	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
524	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
525	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
526	#121	C₂³×C₈₉	1	2	yes	—
527	#121	C₂³×C₈₉	1	2	yes	—
528	#120	—	2	2	no	—
529	C₄×Q₈	—	2	2	no	—
530	C₄×Q₈	—	2	2	no	—
531	C₄×Q₈	—	2	4	no	—
532	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
533	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
534	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
535	C₄×D₄	—	2	2	no	—
536	C₄×D₄	—	2	2	no	—
537	C₄×D₄	—	2	4	no	—
538	C₄×D₄	—	2	4	no	—
539	C₄×D₄	C₂³×C₈₉	1	4	yes	—
540	#117	—	2	4	no	—
541	#117	—	2	2	no	—
542	#117	—	2	4	no	—
543	#117	—	2	4	no	—
544	#117	D₄×C₈₉	1	1	yes	characteristic
545	#117	D₄×C₈₉	1	2	yes	—
546	#117	D₄×C₈₉	1	1	yes	characteristic
547	#117	C₂³×C₈₉	1	2	yes	—
548	#117	C₂³×C₈₉	1	1	yes	characteristic
549	#117	C₂³×C₈₉	1	1	yes	characteristic
550	#117	C₂³×C₈₉	1	2	yes	—
551	C₂×C₄⋊C₄	—	2	2	no	—
552	C₂×C₄⋊C₄	—	2	2	no	—
553	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
554	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
556	C₂×C₂²⋊C₄	—	2	2	no	—
557	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
558	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
559	#107	C₂³×C₈₉	1	2	yes	—
560	#107	C₂³×C₈₉	1	2	yes	—
561	#107	C₂³×C₈₉	1	1	yes	characteristic
562	#107	C₂³×C₈₉	1	1	yes	characteristic
563	#107	C₂³×C₈₉	1	4	yes	—
564	#106	C₂³×C₈₉	1	2	yes	—
565	#106	C₂³×C₈₉	1	4	yes	—
566	#103	C₂³×C₈₉	1	4	yes	—
567	#103	C₂³×C₈₉	1	4	yes	—
568	#103	C₂³×C₈₉	1	2	yes	—
569	#103	C₂³×C₈₉	1	2	yes	—
570	#103	C₂³×C₈₉	1	4	yes	—
571	#103	C₂³×C₈₉	1	4	yes	—
572	#103	C₂³×C₈₉	1	4	yes	—
573	#102	C₂³×C₈₉	1	2	yes	—
574	#102	C₂³×C₈₉	1	2	yes	—
575	#102	C₂³×C₈₉	1	4	yes	—
576	#97	C₂³×C₈₉	1	2	yes	—
577	#97	C₂³×C₈₉	1	2	yes	—
578	#97	C₂³×C₈₉	1	2	yes	—
579	#97	C₂³×C₈₉	1	2	yes	—
580	C₄×C₈	C₂³×C₈₉	1	2	yes	—
581	C₄×C₈	C₂³×C₈₉	1	2	yes	—
582	C₄×C₈	C₂³×C₈₉	1	2	yes	—
583	C₄×C₈	C₂³×C₈₉	1	2	yes	—
584	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
585	#41	—	2	4	no	—
586	#41	—	2	4	no	—
587	C₂×Q₈	—	2	2	no	—
588	C₂×Q₈	—	2	4	no	—
589	C₂×Q₈	—	2	4	no	—
590	C₂×Q₈	—	2	4	no	—
591	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
592	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
604	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
605	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
606	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
607	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
611	Q₁₆	—	2	4	no	—
612	Q₁₆	—	2	4	no	—
613	Q₁₆	—	2	2	no	—
614	Q₁₆	—	2	8	no	—
615	SD₁₆	—	2	4	no	—
616	SD₁₆	—	2	8	no	—
617	D₈	—	2	2	no	—
618	M₁₆	—	2	2	no	—
619	M₁₆	—	2	4	no	—
620	M₁₆	#41×C₈₉	1	4	yes	—
621	C₂×C₈	—	2	2	no	—
622	C₂×C₈	—	2	2	no	—
623	C₂×C₈	—	2	2	no	—
624	C₂×C₈	—	2	2	no	—
625	C₂×C₈	—	2	2	no	—
626	C₂×C₈	—	2	4	no	—
627	C₂×C₈	#41×C₈₉	1	4	yes	—
628	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
629	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
630	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
631	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
632	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
633	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
648	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
649	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
650	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
651	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
652	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
653	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
654	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
655	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
667	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
668	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
669	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
670	C₄²	—	2	4	no	—
671	C₄²	—	2	4	no	—
672	C₄²	—	2	4	no	—
673	C₄²	—	2	2	no	—
674	C₄²	C₂×D₄×C₈₉	1	2	yes	—
675	C₄²	C₂×D₄×C₈₉	1	2	yes	—
676	C₄²	C₂⁴×C₈₉	1	2	yes	—
677	C₄²	C₂⁴×C₈₉	1	2	yes	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	4	1	no	—
682	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
683	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
684	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
685	Q₈	—	2	4	no	—
686	Q₈	—	2	2	no	—
687	Q₈	—	2	4	no	—
688	Q₈	—	2	2	no	—
689	Q₈	—	4	4	no	—
690	Q₈	—	8	4	no	—
691	D₄	—	2	2	no	—
692	D₄	—	2	2	no	—
693	D₄	—	4	4	no	—
694	D₄	—	4	4	no	—
695	D₄	—	8	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	2	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	—	4	2	no	—
710	C₂×C₄	—	4	4	no	—
711	C₂×C₄	—	4	4	no	—
712	C₂×C₄	—	8	4	no	—
713	C₂×C₄	—	8	2	no	—
714	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
715	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
716	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
717	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
718	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
719	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
720	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
721	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
722	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
723	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
724	C₈	—	2	1	no	—
725	C₈	—	2	1	no	—
726	C₈	—	2	2	no	—
727	C₈	C₂×#41×C₈₉	1	2	yes	—
728	C₈	C₂×#41×C₈₉	1	2	yes	—
729	C₈	C₂×#41×C₈₉	1	4	yes	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	1	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	4	4	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	#532×C₈₉	1	2	yes	—
742	C₂²	#578×C₈₉	1	2	yes	—
743	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
744	C₄	—	2	2	no	—
745	C₄	—	2	2	no	—
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	1	no	—
749	C₄	—	2	1	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	4	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	4	no	—
755	C₄	#532×C₈₉	1	2	yes	—
756	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
757	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
758	C₂	—	2	2	no	—
759	C₂	—	2	2	no	—
760	C₂	—	4	1	no	—
761	C₂	—	8	2	no	—
762	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
763	C₂	C₂×#578×C₈₉	1	1	yes	characteristic
764	C₂	C₈₉×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₈₉×#3050	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×#117×C₈₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₈₉×#3495	C₂	semidirect
2. C₈₉×#3181	C₂	semidirect
3. C₈₉×#3178	C₂	semidirect
4. C₈₉×#3177	C₂	semidirect
5. C₈₉×#3175	C₂	semidirect
6. C₈₉×#3170	C₂	semidirect
7. C₈₉×#3168	C₂	semidirect
8. C₈₉×#3164	C₂	semidirect
9. C₈₉×#3156	C₂	semidirect
10. C₈₉×#3137	C₂	semidirect
11. C₈₉×#3056	C₂	semidirect
13. C₂×#467×C₈₉	C₂	semidirect
14. C₈₉×#2951	C₂	semidirect
15. C₈₉×#2950	C₂	semidirect
16. C₈₉×#2947	C₂	semidirect
17. C₂×#405×C₈₉	C₂	semidirect
40. #501×C₈₉	C₂²	semidirect
41. #500×C₈₉	C₂²	semidirect
42. #499×C₈₉	C₂²	semidirect
43. #497×C₈₉	C₂²	semidirect
44. #495×C₈₉	C₂²	semidirect
45. #494×C₈₉	C₂²	semidirect
46. #491×C₈₉	C₂²	semidirect
47. #489×C₈₉	C₂²	semidirect
48. #488×C₈₉	C₂²	semidirect
49. #487×C₈₉	C₂²	semidirect
64. #441×C₈₉	C₂²	semidirect
65. #441×C₈₉	C₂²	semidirect
66. #440×C₈₉	C₂²	semidirect
67. #440×C₈₉	C₂²	semidirect
68. C₄×Q₁₆×C₈₉	C₂²	semidirect
69. C₄×Q₁₆×C₈₉	C₂²	semidirect
70. C₄×Q₁₆×C₈₉	C₂²	semidirect
71. C₄×Q₁₆×C₈₉	C₂²	semidirect
72. C₄×SD₁₆×C₈₉	C₂²	semidirect
73. C₄×D₈×C₈₉	C₂²	semidirect
375. #60708	C₈₉	direct (N × H)
383. #3495	C₂×C₈₉	semidirect
384. #3181	C₂×C₈₉	semidirect
385. #3178	C₂×C₈₉	semidirect
386. #3177	C₂×C₈₉	semidirect
387. #3175	C₂×C₈₉	semidirect
388. #3170	C₂×C₈₉	semidirect
389. #3168	C₂×C₈₉	semidirect
390. #3164	C₂×C₈₉	semidirect
391. #3156	C₂×C₈₉	semidirect
392. #3137	C₂×C₈₉	semidirect
393. #3056	C₂×C₈₉	semidirect
395. C₂×#467	C₂×C₈₉	semidirect
396. #2951	C₂×C₈₉	semidirect
397. #2950	C₂×C₈₉	semidirect
398. #2947	C₂×C₈₉	semidirect
399. C₂×#405	C₂×C₈₉	semidirect
400. C₈₉	#60708	direct (N × H)
423. #501	C₂²×C₈₉	semidirect
424. #500	C₂²×C₈₉	semidirect
425. #499	C₂²×C₈₉	semidirect
426. #497	C₂²×C₈₉	semidirect
427. #495	C₂²×C₈₉	semidirect
428. #494	C₂²×C₈₉	semidirect
429. #491	C₂²×C₈₉	semidirect
430. #489	C₂²×C₈₉	semidirect
431. #488	C₂²×C₈₉	semidirect
432. #487	C₂²×C₈₉	semidirect
447. #441	C₂²×C₈₉	semidirect
448. #441	C₂²×C₈₉	semidirect
449. #440	C₂²×C₈₉	semidirect
450. #440	C₂²×C₈₉	semidirect
451. C₄×Q₁₆	C₂²×C₈₉	semidirect
452. C₄×Q₁₆	C₂²×C₈₉	semidirect
453. C₄×Q₁₆	C₂²×C₈₉	semidirect
454. C₄×Q₁₆	C₂²×C₈₉	semidirect
455. C₄×SD₁₆	C₂²×C₈₉	semidirect
456. C₄×D₈	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3495	2
C₈₉×#3181	2
C₈₉×#3178	2
C₈₉×#3177	2
C₈₉×#3175	2
C₈₉×#3170	2
C₈₉×#3168	2
C₈₉×#3164	2
C₈₉×#3156	2
C₈₉×#3137	2
C₈₉×#3056	2
C₈₉×#3050	2
C₂×#467×C₈₉	2
C₈₉×#2951	2
C₈₉×#2950	2
C₈₉×#2947	2
C₂×#405×C₈₉	2
#60708	89

Subgroups — C89×#60708 #36438556

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60708 #36438556