Subgroups — C₈₉×#60595 #36438443

Order 22784.

2014 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×2₋¹⁺⁴×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3125	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3124	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3121	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3121	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3117	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3111	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3108	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3102	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3097	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3096	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3078	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3076	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3040	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#464×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3011	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#3010	C₂	1	1	yes	maximal, characteristic
19	C₈₉×#2950	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₉×#2949	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#2947	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₉×#2946	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
27	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
29	#559×C₈₉	—	2	1	no	—
30	#559×C₈₉	—	2	1	no	—
31	#556×C₈₉	—	2	1	no	—
32	#556×C₈₉	—	2	1	no	—
33	#551×C₈₉	—	2	2	no	—
34	#551×C₈₉	—	2	2	no	—
35	#542×C₈₉	C₂²	1	2	yes	—
36	#542×C₈₉	C₂²	1	2	yes	—
37	#536×C₈₉	C₂²	1	1	yes	characteristic
38	#535×C₈₉	C₂²	1	1	yes	characteristic
39	#533×C₈₉	C₂²	1	1	yes	characteristic
40	#529×C₈₉	C₂²	1	2	yes	—
41	#529×C₈₉	C₂²	1	2	yes	—
42	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
43	#520×C₈₉	—	2	2	no	—
44	#520×C₈₉	—	2	1	no	—
45	#520×C₈₉	C₂²	1	1	yes	characteristic
46	#520×C₈₉	C₂²	1	1	yes	characteristic
47	#520×C₈₉	C₂²	1	2	yes	complemented
48	#519×C₈₉	—	2	1	no	—
49	#519×C₈₉	C₂²	1	1	yes	characteristic
50	#519×C₈₉	C₂²	1	1	yes	characteristic
51	#519×C₈₉	C₂²	1	2	yes	complemented
52	#518×C₈₉	C₂²	1	1	yes	characteristic
53	C₄×#41×C₈₉	—	2	2	no	—
54	C₄×#41×C₈₉	—	2	1	no	—
55	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
56	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
57	C₄×#41×C₈₉	C₂²	1	2	yes	complemented
58	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
59	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
60	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
61	#485×C₈₉	C₂²	1	2	yes	complemented
62	#485×C₈₉	C₂²	1	2	yes	complemented
63	#484×C₈₉	C₂²	1	2	yes	complemented
64	#483×C₈₉	C₂²	1	2	yes	complemented
65	#482×C₈₉	C₂²	1	2	yes	—
66	#482×C₈₉	C₂²	1	2	yes	—
67	#481×C₈₉	C₂²	1	2	yes	—
68	#480×C₈₉	C₂²	1	2	yes	—
69	#479×C₈₉	C₂²	1	1	yes	characteristic, complemented
70	#479×C₈₉	C₂²	1	1	yes	characteristic, complemented
71	#479×C₈₉	C₂²	1	2	yes	complemented
72	#479×C₈₉	C₂²	1	2	yes	complemented
73	#478×C₈₉	C₂²	1	1	yes	characteristic, complemented
74	#478×C₈₉	C₂²	1	1	yes	characteristic, complemented
75	#477×C₈₉	C₂²	1	1	yes	characteristic, complemented
76	#477×C₈₉	C₂²	1	2	yes	complemented
77	#476×C₈₉	C₂²	1	1	yes	characteristic, complemented
78	#475×C₈₉	C₂²	1	1	yes	characteristic, complemented
79	#475×C₈₉	C₂²	1	2	yes	complemented
80	#474×C₈₉	C₂²	1	1	yes	characteristic, complemented
81	#464×C₈₉	C₂²	1	2	yes	—
82	#464×C₈₉	C₂²	1	2	yes	—
83	#464×C₈₉	C₂²	1	2	yes	—
84	#464×C₈₉	C₂²	1	2	yes	—
85	#464×C₈₉	C₂²	1	2	yes	—
86	#464×C₈₉	C₂²	1	2	yes	—
87	#463×C₈₉	C₂²	1	2	yes	—
88	#463×C₈₉	C₂²	1	2	yes	—
89	#452×C₈₉	C₂²	1	2	yes	complemented
90	#452×C₈₉	C₂²	1	2	yes	complemented
91	#451×C₈₉	C₂²	1	2	yes	complemented
92	#451×C₈₉	C₂²	1	2	yes	complemented
93	#449×C₈₉	C₂²	1	2	yes	—
94	#449×C₈₉	C₂²	1	2	yes	—
95	#448×C₈₉	C₂²	1	2	yes	—
96	#448×C₈₉	C₂²	1	2	yes	—
97	#442×C₈₉	C₂²	1	2	yes	—
98	#441×C₈₉	C₂²	1	2	yes	complemented
99	#441×C₈₉	C₂²	1	2	yes	complemented
100	#441×C₈₉	C₂²	1	2	yes	complemented
101	#440×C₈₉	C₂²	1	2	yes	—
102	#440×C₈₉	C₂²	1	2	yes	—
103	#440×C₈₉	C₂²	1	2	yes	—
104	#440×C₈₉	C₂²	1	2	yes	complemented
105	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
106	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
107	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
108	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
109	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
110	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
111	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
112	C₄×D₈×C₈₉	C₂²	1	2	yes	—
113	#433×C₈₉	C₂²	1	2	yes	complemented
114	#433×C₈₉	C₂²	1	2	yes	complemented
115	#432×C₈₉	C₂²	1	2	yes	complemented
116	#431×C₈₉	C₂²	1	2	yes	complemented
117	#428×C₈₉	C₂²	1	1	yes	characteristic
118	#428×C₈₉	C₂²	1	1	yes	characteristic
119	#427×C₈₉	C₂²	1	1	yes	characteristic
120	#427×C₈₉	C₂²	1	1	yes	characteristic
121	#423×C₈₉	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
123	#419×C₈₉	C₂²	1	1	yes	characteristic
124	#419×C₈₉	C₂²	1	1	yes	characteristic
125	#419×C₈₉	C₂²	1	1	yes	characteristic
126	#418×C₈₉	C₂²	1	1	yes	characteristic
127	#416×C₈₉	C₂²	1	1	yes	characteristic
128	#416×C₈₉	C₂²	1	1	yes	characteristic
129	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
130	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
131	#408×C₈₉	C₂²	1	1	yes	characteristic
132	#408×C₈₉	C₂²	1	1	yes	characteristic
133	#405×C₈₉	C₂²	1	1	yes	characteristic
134	#405×C₈₉	C₂²	1	1	yes	characteristic
135	2₋¹⁺⁴×C₈₉	—	2	4	no	—
136	2₋¹⁺⁴×C₈₉	—	2	4	no	—
137	C₂×#41×C₈₉	—	2	2	no	—
138	C₂×#41×C₈₉	—	2	1	no	—
139	C₂×#41×C₈₉	C₂³	1	2	yes	—
140	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
141	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₈₉	—	2	1	no	—
143	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
144	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
145	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
146	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
147	#137×C₈₉	—	2	4	no	—
148	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
149	C₂×Q₁₆×C₈₉	—	2	4	no	—
150	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
151	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
152	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₈₉	—	2	4	no	—
154	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
158	C₂×D₈×C₈₉	C₂³	1	2	yes	—
159	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
160	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
161	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
162	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₈₉	—	2	1	no	—
164	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
166	#127×C₈₉	—	2	1	no	—
167	#126×C₈₉	—	2	2	no	—
168	#126×C₈₉	—	2	2	no	—
169	#126×C₈₉	—	2	2	no	—
170	#126×C₈₉	—	2	2	no	—
171	#125×C₈₉	C₂³	1	1	yes	characteristic
172	#125×C₈₉	C₂³	1	1	yes	characteristic
173	#124×C₈₉	—	2	1	no	—
174	#124×C₈₉	—	2	1	no	—
175	#124×C₈₉	—	2	2	no	—
176	#124×C₈₉	—	2	2	no	—
177	#124×C₈₉	—	2	1	no	—
178	#124×C₈₉	—	2	1	no	—
179	#124×C₈₉	C₂³	1	2	yes	—
180	#124×C₈₉	C₂³	1	2	yes	—
181	#123×C₈₉	—	2	2	no	—
182	#123×C₈₉	—	2	2	no	—
183	#123×C₈₉	—	2	2	no	—
184	#123×C₈₉	—	2	2	no	—
185	#123×C₈₉	—	2	2	no	—
186	C₂²⋊Q₈×C₈₉	—	2	1	no	—
187	C₂²⋊Q₈×C₈₉	—	2	1	no	—
188	C₂²⋊Q₈×C₈₉	—	2	2	no	—
189	C₂²⋊Q₈×C₈₉	—	2	2	no	—
190	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
191	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
192	#121×C₈₉	C₂³	1	2	yes	—
193	#121×C₈₉	C₂³	1	2	yes	—
194	#120×C₈₉	—	2	2	no	—
195	C₄×Q₈×C₈₉	—	2	1	no	—
196	C₄×Q₈×C₈₉	—	2	1	no	—
197	C₄×Q₈×C₈₉	—	2	2	no	—
198	C₄×Q₈×C₈₉	—	2	1	no	—
199	C₄×Q₈×C₈₉	—	2	2	no	—
200	C₄×Q₈×C₈₉	—	2	1	no	—
201	C₄×Q₈×C₈₉	—	2	1	no	—
202	C₄×Q₈×C₈₉	—	2	1	no	—
203	C₄×Q₈×C₈₉	—	2	2	no	—
204	C₄×Q₈×C₈₉	—	2	1	no	—
205	C₄×Q₈×C₈₉	—	2	2	no	—
206	C₄×Q₈×C₈₉	—	2	1	no	—
207	C₄×Q₈×C₈₉	—	2	1	no	—
208	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
209	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
210	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
211	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
212	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
213	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
214	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
215	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
216	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
218	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₈₉	—	2	2	no	—
220	C₄×D₄×C₈₉	—	2	1	no	—
221	C₄×D₄×C₈₉	—	2	1	no	—
222	C₄×D₄×C₈₉	—	2	2	no	—
223	C₄×D₄×C₈₉	—	2	1	no	—
224	C₄×D₄×C₈₉	—	2	2	no	—
225	C₄×D₄×C₈₉	—	2	2	no	—
226	C₄×D₄×C₈₉	—	2	2	no	—
227	C₄×D₄×C₈₉	—	2	1	no	—
228	C₄×D₄×C₈₉	—	2	1	no	—
229	C₄×D₄×C₈₉	—	2	2	no	—
230	C₄×D₄×C₈₉	—	2	2	no	—
231	C₄×D₄×C₈₉	—	2	2	no	—
232	C₄×D₄×C₈₉	D₄	1	2	yes	—
233	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
234	C₄×D₄×C₈₉	D₄	1	2	yes	—
235	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
236	C₄×D₄×C₈₉	C₂³	1	2	yes	—
237	C₄×D₄×C₈₉	C₂³	1	2	yes	—
238	C₄×D₄×C₈₉	C₂³	1	2	yes	—
239	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
241	#117×C₈₉	—	2	1	no	—
242	#117×C₈₉	—	2	2	no	—
243	#117×C₈₉	—	2	2	no	—
244	#117×C₈₉	—	2	2	no	—
245	#117×C₈₉	—	2	2	no	—
246	#117×C₈₉	—	2	2	no	—
247	#117×C₈₉	—	2	1	no	—
248	#117×C₈₉	—	2	2	no	—
249	#117×C₈₉	—	2	2	no	—
250	#117×C₈₉	—	2	2	no	—
251	#117×C₈₉	C₂³	1	1	yes	characteristic
252	#117×C₈₉	C₂³	1	1	yes	characteristic
253	#117×C₈₉	C₂³	1	1	yes	characteristic
254	#117×C₈₉	C₂³	1	2	yes	—
255	#117×C₈₉	C₂³	1	1	yes	characteristic
256	#117×C₈₉	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
258	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
259	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
260	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
261	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
263	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
265	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
266	C₂×C₄²×C₈₉	—	2	1	no	—
267	C₂×C₄²×C₈₉	—	2	2	no	—
268	C₂×C₄²×C₈₉	—	2	1	no	—
269	C₂×C₄²×C₈₉	—	2	2	no	—
270	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
271	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
272	#107×C₈₉	C₂³	1	1	yes	characteristic
273	#107×C₈₉	C₂³	1	1	yes	characteristic
274	#107×C₈₉	C₂³	1	1	yes	characteristic
275	#107×C₈₉	C₂³	1	1	yes	characteristic
276	#107×C₈₉	C₂³	1	2	yes	—
277	#107×C₈₉	C₂³	1	2	yes	—
278	#106×C₈₉	C₂³	1	1	yes	characteristic
279	#106×C₈₉	C₂³	1	1	yes	characteristic
280	#106×C₈₉	C₂³	1	1	yes	characteristic
281	#106×C₈₉	C₂³	1	1	yes	characteristic
282	#106×C₈₉	C₂³	1	2	yes	—
283	#106×C₈₉	C₂³	1	2	yes	—
284	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
285	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
286	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
288	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
289	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
290	#103×C₈₉	C₂³	1	2	yes	—
291	#103×C₈₉	C₂³	1	2	yes	—
292	#103×C₈₉	C₂³	1	1	yes	characteristic
293	#103×C₈₉	C₂³	1	1	yes	characteristic
294	#103×C₈₉	C₂³	1	1	yes	characteristic
295	#103×C₈₉	C₂³	1	1	yes	characteristic
296	#103×C₈₉	C₂³	1	2	yes	—
297	#103×C₈₉	C₂³	1	2	yes	—
298	#103×C₈₉	C₂³	1	2	yes	—
299	#103×C₈₉	C₂³	1	2	yes	—
300	#103×C₈₉	C₂³	1	2	yes	—
301	#103×C₈₉	C₂³	1	2	yes	—
302	#102×C₈₉	C₂³	1	2	yes	—
303	#102×C₈₉	C₂³	1	2	yes	—
304	#102×C₈₉	C₂³	1	1	yes	characteristic
305	#102×C₈₉	C₂³	1	1	yes	characteristic
306	#102×C₈₉	C₂³	1	1	yes	characteristic
307	#102×C₈₉	C₂³	1	1	yes	characteristic
308	#102×C₈₉	C₂³	1	2	yes	—
309	#102×C₈₉	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
312	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
313	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
314	#97×C₈₉	C₂³	1	2	yes	—
315	#97×C₈₉	C₂³	1	2	yes	—
316	C₄×C₈×C₈₉	C₂³	1	2	yes	—
317	C₄×C₈×C₈₉	C₂³	1	2	yes	—
318	C₂⁴×C₈₉	—	2	1	no	—
319	#41×C₈₉	—	2	16	no	—
320	#41×C₈₉	—	2	8	no	—
321	#41×C₈₉	—	2	4	no	—
322	#41×C₈₉	—	2	4	no	—
323	#41×C₈₉	—	2	2	no	—
324	#41×C₈₉	—	2	2	no	—
325	#41×C₈₉	—	2	2	no	—
326	#41×C₈₉	#41	1	4	yes	—
327	C₂×Q₈×C₈₉	—	2	8	no	—
328	C₂×Q₈×C₈₉	—	2	4	no	—
329	C₂×Q₈×C₈₉	—	2	4	no	—
330	C₂×Q₈×C₈₉	—	2	2	no	—
331	C₂×Q₈×C₈₉	—	2	1	no	—
332	C₂×Q₈×C₈₉	—	2	1	no	—
333	C₂×Q₈×C₈₉	—	2	1	no	—
334	C₂×Q₈×C₈₉	—	2	1	no	—
335	C₂×Q₈×C₈₉	—	2	2	no	—
336	C₂×Q₈×C₈₉	—	2	2	no	—
337	C₂×Q₈×C₈₉	—	2	2	no	—
338	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
339	C₂×Q₈×C₈₉	#41	1	4	yes	—
340	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
341	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
342	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
343	C₂×D₄×C₈₉	—	2	2	no	—
344	C₂×D₄×C₈₉	—	2	1	no	—
345	C₂×D₄×C₈₉	—	2	2	no	—
346	C₂×D₄×C₈₉	—	2	2	no	—
347	C₂×D₄×C₈₉	—	2	1	no	—
348	C₂×D₄×C₈₉	—	2	2	no	—
349	C₂×D₄×C₈₉	—	2	2	no	—
350	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
352	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
353	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₈₉	—	2	2	no	—
355	C₂²×C₄×C₈₉	—	2	1	no	—
356	C₂²×C₄×C₈₉	—	2	2	no	—
357	C₂²×C₄×C₈₉	—	2	1	no	—
358	C₂²×C₄×C₈₉	—	2	1	no	—
359	C₂²×C₄×C₈₉	—	2	2	no	—
360	C₂²×C₄×C₈₉	—	2	1	no	—
361	C₂²×C₄×C₈₉	—	2	1	no	—
362	C₂²×C₄×C₈₉	—	2	2	no	—
363	C₂²×C₄×C₈₉	—	2	1	no	—
364	C₂²×C₄×C₈₉	—	2	2	no	—
365	C₂²×C₄×C₈₉	—	2	2	no	—
366	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
368	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
370	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
371	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
372	Q₁₆×C₈₉	—	2	4	no	—
373	Q₁₆×C₈₉	—	2	4	no	—
374	Q₁₆×C₈₉	—	2	4	no	—
375	SD₁₆×C₈₉	—	2	4	no	—
376	SD₁₆×C₈₉	—	2	4	no	—
377	SD₁₆×C₈₉	—	2	4	no	—
378	SD₁₆×C₈₉	—	2	4	no	—
379	D₈×C₈₉	—	2	4	no	—
380	M₁₆×C₈₉	—	2	2	no	—
381	M₁₆×C₈₉	—	2	2	no	—
382	C₂×C₈×C₈₉	—	2	2	no	—
383	C₂×C₈×C₈₉	—	2	2	no	—
384	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
387	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
388	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
390	C₄⋊C₄×C₈₉	—	2	2	no	—
391	C₄⋊C₄×C₈₉	—	2	2	no	—
392	C₄⋊C₄×C₈₉	—	2	2	no	—
393	C₄⋊C₄×C₈₉	—	2	2	no	—
394	C₄⋊C₄×C₈₉	—	2	1	no	—
395	C₄⋊C₄×C₈₉	—	2	2	no	—
396	C₄⋊C₄×C₈₉	—	2	1	no	—
397	C₄⋊C₄×C₈₉	—	2	2	no	—
398	C₄⋊C₄×C₈₉	—	2	1	no	—
399	C₄⋊C₄×C₈₉	—	2	1	no	—
400	C₄⋊C₄×C₈₉	—	2	1	no	—
401	C₄⋊C₄×C₈₉	—	2	2	no	—
402	C₄⋊C₄×C₈₉	—	2	2	no	—
403	C₄⋊C₄×C₈₉	—	2	2	no	—
404	C₄⋊C₄×C₈₉	—	2	2	no	—
405	C₄⋊C₄×C₈₉	—	2	1	no	—
406	C₄⋊C₄×C₈₉	—	2	1	no	—
407	C₄⋊C₄×C₈₉	—	2	1	no	—
408	C₄⋊C₄×C₈₉	—	2	1	no	—
409	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
412	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
414	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
420	C₂²⋊C₄×C₈₉	—	2	1	no	—
421	C₂²⋊C₄×C₈₉	—	2	2	no	—
422	C₂²⋊C₄×C₈₉	—	2	1	no	—
423	C₂²⋊C₄×C₈₉	—	2	1	no	—
424	C₂²⋊C₄×C₈₉	—	2	2	no	—
425	C₂²⋊C₄×C₈₉	—	2	2	no	—
426	C₂²⋊C₄×C₈₉	—	2	2	no	—
427	C₂²⋊C₄×C₈₉	—	2	2	no	—
428	C₂²⋊C₄×C₈₉	—	2	2	no	—
429	C₂²⋊C₄×C₈₉	—	2	2	no	—
430	C₂²⋊C₄×C₈₉	—	2	2	no	—
431	C₂²⋊C₄×C₈₉	—	2	2	no	—
432	C₂²⋊C₄×C₈₉	—	2	1	no	—
433	C₂²⋊C₄×C₈₉	—	2	2	no	—
434	C₂²⋊C₄×C₈₉	—	2	1	no	—
435	C₂²⋊C₄×C₈₉	—	2	2	no	—
436	C₂²⋊C₄×C₈₉	—	2	2	no	—
437	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
440	C₄²×C₈₉	—	2	2	no	—
441	C₄²×C₈₉	—	2	1	no	—
442	C₄²×C₈₉	—	2	2	no	—
443	C₄²×C₈₉	—	2	1	no	—
444	C₄²×C₈₉	—	2	2	no	—
445	C₄²×C₈₉	—	2	2	no	—
446	C₄²×C₈₉	—	2	2	no	—
447	C₄²×C₈₉	—	2	2	no	—
448	C₄²×C₈₉	—	2	1	no	—
449	C₄²×C₈₉	—	2	2	no	—
450	C₄²×C₈₉	—	2	2	no	—
451	C₄²×C₈₉	—	2	1	no	—
452	C₄²×C₈₉	—	2	1	no	—
453	C₄²×C₈₉	C₂×D₄	1	2	yes	—
454	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₈₉	C₂×D₄	1	2	yes	—
456	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₈₉	C₂⁴	1	2	yes	—
458	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
459	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
460	C₂³×C₈₉	—	2	1	no	—
461	C₂³×C₈₉	—	2	2	no	—
462	C₂³×C₈₉	—	4	2	no	—
463	C₂³×C₈₉	—	8	1	no	—
464	C₂³×C₈₉	—	8	1	no	—
465	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
466	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
467	Q₈×C₈₉	—	2	8	no	—
468	Q₈×C₈₉	—	2	2	no	—
469	Q₈×C₈₉	—	2	4	no	—
470	Q₈×C₈₉	—	2	1	no	—
471	Q₈×C₈₉	—	2	2	no	—
472	Q₈×C₈₉	—	2	2	no	—
473	Q₈×C₈₉	—	2	2	no	—
474	Q₈×C₈₉	—	4	2	no	—
475	Q₈×C₈₉	—	8	1	no	—
476	Q₈×C₈₉	—	8	1	no	—
477	Q₈×C₈₉	C₂×#41	1	2	yes	—
478	Q₈×C₈₉	C₂×#41	1	4	yes	—
479	D₄×C₈₉	—	2	8	no	—
480	D₄×C₈₉	—	2	4	no	—
481	D₄×C₈₉	—	2	4	no	—
482	D₄×C₈₉	—	2	2	no	—
483	D₄×C₈₉	—	2	1	no	—
484	D₄×C₈₉	—	2	2	no	—
485	D₄×C₈₉	—	2	2	no	—
486	D₄×C₈₉	—	4	2	no	—
487	D₄×C₈₉	—	8	2	no	—
488	D₄×C₈₉	—	8	2	no	—
489	D₄×C₈₉	C₂×#41	1	2	yes	—
490	C₂×C₄×C₈₉	—	2	8	no	—
491	C₂×C₄×C₈₉	—	2	8	no	—
492	C₂×C₄×C₈₉	—	2	4	no	—
493	C₂×C₄×C₈₉	—	2	2	no	—
494	C₂×C₄×C₈₉	—	2	1	no	—
495	C₂×C₄×C₈₉	—	2	4	no	—
496	C₂×C₄×C₈₉	—	2	2	no	—
497	C₂×C₄×C₈₉	—	2	2	no	—
498	C₂×C₄×C₈₉	—	2	1	no	—
499	C₂×C₄×C₈₉	—	2	2	no	—
500	C₂×C₄×C₈₉	—	2	1	no	—
501	C₂×C₄×C₈₉	—	2	1	no	—
502	C₂×C₄×C₈₉	—	2	1	no	—
503	C₂×C₄×C₈₉	—	2	2	no	—
504	C₂×C₄×C₈₉	—	2	1	no	—
505	C₂×C₄×C₈₉	—	2	1	no	—
506	C₂×C₄×C₈₉	—	4	2	no	—
507	C₂×C₄×C₈₉	—	4	1	no	—
508	C₂×C₄×C₈₉	—	4	2	no	—
509	C₂×C₄×C₈₉	—	4	1	no	—
510	C₂×C₄×C₈₉	—	4	2	no	—
511	C₂×C₄×C₈₉	—	4	2	no	—
512	C₂×C₄×C₈₉	—	8	2	no	—
513	C₂×C₄×C₈₉	—	8	2	no	—
514	C₂×C₄×C₈₉	—	8	1	no	—
515	C₂×C₄×C₈₉	—	8	2	no	—
516	C₂×C₄×C₈₉	—	8	1	no	—
517	C₂×C₄×C₈₉	—	8	2	no	—
518	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
520	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
527	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
528	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
529	C₈×C₈₉	—	2	1	no	—
530	C₈×C₈₉	—	2	1	no	—
531	C₈×C₈₉	—	2	1	no	—
532	C₈×C₈₉	—	2	1	no	—
533	C₈×C₈₉	—	2	2	no	—
534	C₈×C₈₉	—	2	2	no	—
535	C₂²×C₈₉	—	2	1	no	—
536	C₂²×C₈₉	—	2	1	no	—
537	C₂²×C₈₉	—	2	2	no	—
538	C₂²×C₈₉	—	2	2	no	—
539	C₂²×C₈₉	—	2	2	no	—
540	C₂²×C₈₉	—	2	2	no	—
541	C₂²×C₈₉	—	4	1	no	—
542	C₂²×C₈₉	—	4	1	no	—
543	C₂²×C₈₉	—	4	2	no	—
544	C₂²×C₈₉	—	4	2	no	—
545	C₂²×C₈₉	—	4	2	no	—
546	C₂²×C₈₉	—	16	2	no	—
547	C₂²×C₈₉	#525	1	2	yes	—
548	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
549	C₄×C₈₉	—	2	1	no	—
550	C₄×C₈₉	—	2	2	no	—
551	C₄×C₈₉	—	2	1	no	—
552	C₄×C₈₉	—	2	1	no	—
553	C₄×C₈₉	—	2	2	no	—
554	C₄×C₈₉	—	2	1	no	—
555	C₄×C₈₉	—	2	4	no	—
556	C₄×C₈₉	—	2	2	no	—
557	C₄×C₈₉	—	2	2	no	—
558	C₄×C₈₉	—	4	2	no	—
559	C₄×C₈₉	—	4	1	no	—
560	C₄×C₈₉	—	4	1	no	—
561	C₄×C₈₉	—	4	1	no	—
562	C₄×C₈₉	—	4	1	no	—
563	C₄×C₈₉	—	4	1	no	—
564	C₄×C₈₉	—	4	1	no	—
565	C₄×C₈₉	—	4	2	no	—
566	C₄×C₈₉	#525	1	2	yes	—
567	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
568	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
569	#60595	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
570	C₂×C₈₉	—	2	2	no	—
571	C₂×C₈₉	—	4	2	no	—
572	C₂×C₈₉	—	4	2	no	—
573	C₂×C₈₉	—	8	2	no	—
574	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
575	C₂×C₈₉	#3584	1	1	yes	characteristic
576	C₂×C₈₉	#3586	1	1	yes	characteristic
577	#3510	C₂×C₈₉	1	1	yes	characteristic, complemented
578	C₄×2₋¹⁺⁴	C₂×C₈₉	1	1	yes	characteristic, complemented
579	#3125	C₂×C₈₉	1	2	yes	complemented
580	#3124	C₂×C₈₉	1	2	yes	complemented
581	#3121	C₂×C₈₉	1	2	yes	complemented
582	#3121	C₂×C₈₉	1	2	yes	complemented
583	#3117	C₂×C₈₉	1	2	yes	complemented
584	#3111	C₂×C₈₉	1	2	yes	complemented
585	#3108	C₂×C₈₉	1	2	yes	complemented
586	#3102	C₂×C₈₉	1	2	yes	complemented
587	#3097	C₂×C₈₉	1	1	yes	characteristic, complemented
588	#3096	C₂×C₈₉	1	1	yes	characteristic, complemented
589	#3078	C₂×C₈₉	1	1	yes	characteristic, complemented
590	#3076	C₂×C₈₉	1	1	yes	characteristic, complemented
591	#3040	C₂×C₈₉	1	1	yes	characteristic, complemented
592	C₂×#464	C₂×C₈₉	1	1	yes	characteristic, complemented
593	#3011	C₂×C₈₉	1	1	yes	characteristic, complemented
594	#3010	C₂×C₈₉	1	1	yes	characteristic
595	#2950	C₂×C₈₉	1	1	yes	characteristic, complemented
596	#2949	C₂×C₈₉	1	1	yes	characteristic, complemented
597	#2947	C₂×C₈₉	1	1	yes	characteristic, complemented
598	#2946	C₂×C₈₉	1	1	yes	characteristic, complemented
599	#2925	C₂×C₈₉	1	1	yes	characteristic, complemented
600	C₈₉	#60595	1	1	yes	characteristic, direct product factor, Sylow
601	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	1	yes	characteristic
602	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
603	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
604	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
605	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
606	#559	—	2	1	no	—
607	#559	—	2	1	no	—
608	#556	—	2	1	no	—
609	#556	—	2	1	no	—
610	#551	—	2	2	no	—
611	#551	—	2	2	no	—
612	#542	C₂²×C₈₉	1	2	yes	—
613	#542	C₂²×C₈₉	1	2	yes	—
614	#536	C₂²×C₈₉	1	1	yes	characteristic
615	#535	C₂²×C₈₉	1	1	yes	characteristic
616	#533	C₂²×C₈₉	1	1	yes	characteristic
617	#529	C₂²×C₈₉	1	2	yes	—
618	#529	C₂²×C₈₉	1	2	yes	—
619	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
620	#520	—	2	2	no	—
621	#520	—	2	1	no	—
622	#520	C₂²×C₈₉	1	1	yes	characteristic
623	#520	C₂²×C₈₉	1	1	yes	characteristic
624	#520	C₂²×C₈₉	1	2	yes	complemented
625	#519	—	2	1	no	—
626	#519	C₂²×C₈₉	1	1	yes	characteristic
627	#519	C₂²×C₈₉	1	1	yes	characteristic
628	#519	C₂²×C₈₉	1	2	yes	complemented
629	#518	C₂²×C₈₉	1	1	yes	characteristic
630	C₄×#41	—	2	2	no	—
631	C₄×#41	—	2	1	no	—
632	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
633	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
634	C₄×#41	C₂²×C₈₉	1	2	yes	complemented
635	C₂×C₄×Q₈	—	2	1	no	—
636	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
637	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	complemented
638	#485	C₂²×C₈₉	1	2	yes	complemented
639	#485	C₂²×C₈₉	1	2	yes	complemented
640	#484	C₂²×C₈₉	1	2	yes	complemented
641	#483	C₂²×C₈₉	1	2	yes	complemented
642	#482	C₂²×C₈₉	1	2	yes	—
643	#482	C₂²×C₈₉	1	2	yes	—
644	#481	C₂²×C₈₉	1	2	yes	—
645	#480	C₂²×C₈₉	1	2	yes	—
646	#479	C₂²×C₈₉	1	1	yes	characteristic, complemented
647	#479	C₂²×C₈₉	1	1	yes	characteristic, complemented
648	#479	C₂²×C₈₉	1	2	yes	complemented
649	#479	C₂²×C₈₉	1	2	yes	complemented
650	#478	C₂²×C₈₉	1	1	yes	characteristic, complemented
651	#478	C₂²×C₈₉	1	1	yes	characteristic, complemented
652	#477	C₂²×C₈₉	1	1	yes	characteristic, complemented
653	#477	C₂²×C₈₉	1	2	yes	complemented
654	#476	C₂²×C₈₉	1	1	yes	characteristic, complemented
655	#475	C₂²×C₈₉	1	1	yes	characteristic, complemented
656	#475	C₂²×C₈₉	1	2	yes	complemented
657	#474	C₂²×C₈₉	1	1	yes	characteristic, complemented
658	#464	C₂²×C₈₉	1	2	yes	—
659	#464	C₂²×C₈₉	1	2	yes	—
660	#464	C₂²×C₈₉	1	2	yes	—
661	#464	C₂²×C₈₉	1	2	yes	—
662	#464	C₂²×C₈₉	1	2	yes	—
663	#464	C₂²×C₈₉	1	2	yes	—
664	#463	C₂²×C₈₉	1	2	yes	—
665	#463	C₂²×C₈₉	1	2	yes	—
666	#452	C₂²×C₈₉	1	2	yes	complemented
667	#452	C₂²×C₈₉	1	2	yes	complemented
668	#451	C₂²×C₈₉	1	2	yes	complemented
669	#451	C₂²×C₈₉	1	2	yes	complemented
670	#449	C₂²×C₈₉	1	2	yes	—
671	#449	C₂²×C₈₉	1	2	yes	—
672	#448	C₂²×C₈₉	1	2	yes	—
673	#448	C₂²×C₈₉	1	2	yes	—
674	#442	C₂²×C₈₉	1	2	yes	—
675	#441	C₂²×C₈₉	1	2	yes	complemented
676	#441	C₂²×C₈₉	1	2	yes	complemented
677	#441	C₂²×C₈₉	1	2	yes	complemented
678	#440	C₂²×C₈₉	1	2	yes	—
679	#440	C₂²×C₈₉	1	2	yes	—
680	#440	C₂²×C₈₉	1	2	yes	—
681	#440	C₂²×C₈₉	1	2	yes	complemented
682	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
683	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
684	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
685	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
686	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
687	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
688	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
689	C₄×D₈	C₂²×C₈₉	1	2	yes	—
690	#433	C₂²×C₈₉	1	2	yes	complemented
691	#433	C₂²×C₈₉	1	2	yes	complemented
692	#432	C₂²×C₈₉	1	2	yes	complemented
693	#431	C₂²×C₈₉	1	2	yes	complemented
694	#428	C₂²×C₈₉	1	1	yes	characteristic
695	#428	C₂²×C₈₉	1	1	yes	characteristic
696	#427	C₂²×C₈₉	1	1	yes	characteristic
697	#427	C₂²×C₈₉	1	1	yes	characteristic
698	#423	C₂²×C₈₉	1	1	yes	characteristic
699	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
700	#419	C₂²×C₈₉	1	1	yes	characteristic
701	#419	C₂²×C₈₉	1	1	yes	characteristic
702	#419	C₂²×C₈₉	1	1	yes	characteristic
703	#418	C₂²×C₈₉	1	1	yes	characteristic
704	#416	C₂²×C₈₉	1	1	yes	characteristic
705	#416	C₂²×C₈₉	1	1	yes	characteristic
706	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
707	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
708	#408	C₂²×C₈₉	1	1	yes	characteristic
709	#408	C₂²×C₈₉	1	1	yes	characteristic
710	#405	C₂²×C₈₉	1	1	yes	characteristic
711	#405	C₂²×C₈₉	1	1	yes	characteristic
712	2₋¹⁺⁴	—	2	4	no	—
713	2₋¹⁺⁴	—	2	4	no	—
714	C₂×#41	—	2	2	no	—
715	C₂×#41	—	2	1	no	—
716	C₂×#41	C₂³×C₈₉	1	2	yes	—
717	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
718	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
719	C₂²×Q₈	—	2	1	no	—
720	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
721	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
722	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
723	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
724	#137	—	2	4	no	—
725	AGL(1,ℤ/8)	—	2	4	no	—
726	C₂×Q₁₆	—	2	4	no	—
727	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
728	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
729	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
730	C₂×SD₁₆	—	2	4	no	—
731	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
735	C₂×D₈	C₂³×C₈₉	1	2	yes	—
736	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
737	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
738	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
739	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
740	C₄⋊Q₈	—	2	1	no	—
741	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
742	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
743	#127	—	2	1	no	—
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#126	—	2	2	no	—
747	#126	—	2	2	no	—
748	#125	C₂³×C₈₉	1	1	yes	characteristic
749	#125	C₂³×C₈₉	1	1	yes	characteristic
750	#124	—	2	1	no	—
751	#124	—	2	1	no	—
752	#124	—	2	2	no	—
753	#124	—	2	2	no	—
754	#124	—	2	1	no	—
755	#124	—	2	1	no	—
756	#124	C₂³×C₈₉	1	2	yes	—
757	#124	C₂³×C₈₉	1	2	yes	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
768	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
769	#121	C₂³×C₈₉	1	2	yes	—
770	#121	C₂³×C₈₉	1	2	yes	—
771	#120	—	2	2	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	2	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	2	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	—	2	2	no	—
781	C₄×Q₈	—	2	1	no	—
782	C₄×Q₈	—	2	2	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
786	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
788	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
789	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
790	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
791	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
792	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
793	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
794	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
795	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	D₄×C₈₉	1	2	yes	—
810	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
811	C₄×D₄	D₄×C₈₉	1	2	yes	—
812	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
813	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₈₉	1	2	yes	—
816	C₄×D₄	C₂³×C₈₉	1	2	yes	—
817	C₄×D₄	C₂³×C₈₉	1	2	yes	—
818	#117	—	2	1	no	—
819	#117	—	2	2	no	—
820	#117	—	2	2	no	—
821	#117	—	2	2	no	—
822	#117	—	2	2	no	—
823	#117	—	2	2	no	—
824	#117	—	2	1	no	—
825	#117	—	2	2	no	—
826	#117	—	2	2	no	—
827	#117	—	2	2	no	—
828	#117	C₂³×C₈₉	1	1	yes	characteristic
829	#117	C₂³×C₈₉	1	2	yes	—
830	#117	C₂³×C₈₉	1	1	yes	characteristic
831	#117	C₂³×C₈₉	1	1	yes	characteristic
832	#117	C₂³×C₈₉	1	1	yes	characteristic
833	#117	C₂³×C₈₉	1	2	yes	—
834	C₂×C₄⋊C₄	—	2	1	no	—
835	C₂×C₄⋊C₄	—	2	2	no	—
836	C₂×C₄⋊C₄	—	2	1	no	—
837	C₂×C₄⋊C₄	—	2	2	no	—
838	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
839	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
840	C₂×C₂²⋊C₄	—	2	1	no	—
841	C₂×C₂²⋊C₄	—	2	1	no	—
842	C₂×C₂²⋊C₄	—	2	2	no	—
843	C₂×C₄²	—	2	1	no	—
844	C₂×C₄²	—	2	2	no	—
845	C₂×C₄²	—	2	1	no	—
846	C₂×C₄²	—	2	2	no	—
847	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
848	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
849	#107	C₂³×C₈₉	1	1	yes	characteristic
850	#107	C₂³×C₈₉	1	1	yes	characteristic
851	#107	C₂³×C₈₉	1	1	yes	characteristic
852	#107	C₂³×C₈₉	1	1	yes	characteristic
853	#107	C₂³×C₈₉	1	2	yes	—
854	#107	C₂³×C₈₉	1	2	yes	—
855	#106	C₂³×C₈₉	1	1	yes	characteristic
856	#106	C₂³×C₈₉	1	1	yes	characteristic
857	#106	C₂³×C₈₉	1	1	yes	characteristic
858	#106	C₂³×C₈₉	1	1	yes	characteristic
859	#106	C₂³×C₈₉	1	2	yes	—
860	#106	C₂³×C₈₉	1	2	yes	—
861	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
863	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
864	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
865	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
866	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
867	#103	C₂³×C₈₉	1	2	yes	—
868	#103	C₂³×C₈₉	1	2	yes	—
869	#103	C₂³×C₈₉	1	1	yes	characteristic
870	#103	C₂³×C₈₉	1	1	yes	characteristic
871	#103	C₂³×C₈₉	1	1	yes	characteristic
872	#103	C₂³×C₈₉	1	1	yes	characteristic
873	#103	C₂³×C₈₉	1	2	yes	—
874	#103	C₂³×C₈₉	1	2	yes	—
875	#103	C₂³×C₈₉	1	2	yes	—
876	#103	C₂³×C₈₉	1	2	yes	—
877	#103	C₂³×C₈₉	1	2	yes	—
878	#103	C₂³×C₈₉	1	2	yes	—
879	#102	C₂³×C₈₉	1	2	yes	—
880	#102	C₂³×C₈₉	1	2	yes	—
881	#102	C₂³×C₈₉	1	1	yes	characteristic
882	#102	C₂³×C₈₉	1	1	yes	characteristic
883	#102	C₂³×C₈₉	1	1	yes	characteristic
884	#102	C₂³×C₈₉	1	1	yes	characteristic
885	#102	C₂³×C₈₉	1	2	yes	—
886	#102	C₂³×C₈₉	1	2	yes	—
887	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
890	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
891	#97	C₂³×C₈₉	1	2	yes	—
892	#97	C₂³×C₈₉	1	2	yes	—
893	C₄×C₈	C₂³×C₈₉	1	2	yes	—
894	C₄×C₈	C₂³×C₈₉	1	2	yes	—
895	C₂⁴	—	2	1	no	—
896	#41	—	2	16	no	—
897	#41	—	2	8	no	—
898	#41	—	2	4	no	—
899	#41	—	2	4	no	—
900	#41	—	2	2	no	—
901	#41	—	2	2	no	—
902	#41	—	2	2	no	—
903	#41	#41×C₈₉	1	4	yes	—
904	C₂×Q₈	—	2	8	no	—
905	C₂×Q₈	—	2	4	no	—
906	C₂×Q₈	—	2	4	no	—
907	C₂×Q₈	—	2	2	no	—
908	C₂×Q₈	—	2	1	no	—
909	C₂×Q₈	—	2	1	no	—
910	C₂×Q₈	—	2	1	no	—
911	C₂×Q₈	—	2	1	no	—
912	C₂×Q₈	—	2	2	no	—
913	C₂×Q₈	—	2	2	no	—
914	C₂×Q₈	—	2	2	no	—
915	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
916	C₂×Q₈	#41×C₈₉	1	4	yes	—
917	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
918	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
919	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
928	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
929	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
930	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
944	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
945	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
946	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
947	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
948	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
949	Q₁₆	—	2	4	no	—
950	Q₁₆	—	2	4	no	—
951	Q₁₆	—	2	4	no	—
952	SD₁₆	—	2	4	no	—
953	SD₁₆	—	2	4	no	—
954	SD₁₆	—	2	4	no	—
955	SD₁₆	—	2	4	no	—
956	D₈	—	2	4	no	—
957	M₁₆	—	2	2	no	—
958	M₁₆	—	2	2	no	—
959	C₂×C₈	—	2	2	no	—
960	C₂×C₈	—	2	2	no	—
961	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
962	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
964	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
965	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
966	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
987	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
988	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
989	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
990	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
991	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
992	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
993	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
995	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1015	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1016	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	2	no	—
1023	C₄²	—	2	2	no	—
1024	C₄²	—	2	2	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1031	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1032	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1033	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1034	C₄²	C₂⁴×C₈₉	1	2	yes	—
1035	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1036	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	4	2	no	—
1040	C₂³	—	8	1	no	—
1041	C₂³	—	8	1	no	—
1042	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1043	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1044	Q₈	—	2	8	no	—
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	4	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	2	no	—
1051	Q₈	—	4	2	no	—
1052	Q₈	—	8	1	no	—
1053	Q₈	—	8	1	no	—
1054	Q₈	C₂×#41×C₈₉	1	2	yes	—
1055	Q₈	C₂×#41×C₈₉	1	4	yes	—
1056	D₄	—	2	8	no	—
1057	D₄	—	2	4	no	—
1058	D₄	—	2	4	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	2	no	—
1063	D₄	—	4	2	no	—
1064	D₄	—	8	2	no	—
1065	D₄	—	8	2	no	—
1066	D₄	C₂×#41×C₈₉	1	2	yes	—
1067	C₂×C₄	—	2	8	no	—
1068	C₂×C₄	—	2	8	no	—
1069	C₂×C₄	—	2	4	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	4	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	4	1	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	1	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	8	2	no	—
1090	C₂×C₄	—	8	2	no	—
1091	C₂×C₄	—	8	1	no	—
1092	C₂×C₄	—	8	2	no	—
1093	C₂×C₄	—	8	1	no	—
1094	C₂×C₄	—	8	2	no	—
1095	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1096	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1097	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1098	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1099	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1100	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1102	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1103	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
1104	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
1105	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1106	C₈	—	2	1	no	—
1107	C₈	—	2	1	no	—
1108	C₈	—	2	1	no	—
1109	C₈	—	2	1	no	—
1110	C₈	—	2	2	no	—
1111	C₈	—	2	2	no	—
1112	C₂²	—	2	1	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	2	2	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	4	1	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	2	no	—
1121	C₂²	—	4	2	no	—
1122	C₂²	—	4	2	no	—
1123	C₂²	—	16	2	no	—
1124	C₂²	#525×C₈₉	1	2	yes	—
1125	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1126	C₄	—	2	1	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	1	no	—
1129	C₄	—	2	1	no	—
1130	C₄	—	2	2	no	—
1131	C₄	—	2	1	no	—
1132	C₄	—	2	4	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	4	2	no	—
1136	C₄	—	4	1	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	2	no	—
1143	C₄	#525×C₈₉	1	2	yes	—
1144	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
1145	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
1146	C₂	—	2	2	no	—
1147	C₂	—	4	2	no	—
1148	C₂	—	4	2	no	—
1149	C₂	—	8	2	no	—
1150	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
1151	C₂	C₈₉×#3584	1	1	yes	characteristic
1152	C₂	C₈₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₈₉×#3010	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3510	C₂	semidirect
2. C₄×2₋¹⁺⁴×C₈₉	C₂	semidirect
3. C₈₉×#3125	C₂	semidirect
4. C₈₉×#3124	C₂	semidirect
5. C₈₉×#3121	C₂	semidirect
6. C₈₉×#3121	C₂	semidirect
7. C₈₉×#3117	C₂	semidirect
8. C₈₉×#3111	C₂	semidirect
9. C₈₉×#3108	C₂	semidirect
10. C₈₉×#3102	C₂	semidirect
11. C₈₉×#3097	C₂	semidirect
12. C₈₉×#3096	C₂	semidirect
13. C₈₉×#3078	C₂	semidirect
14. C₈₉×#3076	C₂	semidirect
15. C₈₉×#3040	C₂	semidirect
16. C₂×#464×C₈₉	C₂	semidirect
17. C₈₉×#3011	C₂	semidirect
19. C₈₉×#2950	C₂	semidirect
20. C₈₉×#2949	C₂	semidirect
21. C₈₉×#2947	C₂	semidirect
22. C₈₉×#2946	C₂	semidirect
23. C₈₉×#2925	C₂	semidirect
47. #520×C₈₉	C₂²	semidirect
51. #519×C₈₉	C₂²	semidirect
57. C₄×#41×C₈₉	C₂²	semidirect
60. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
61. #485×C₈₉	C₂²	semidirect
62. #485×C₈₉	C₂²	semidirect
63. #484×C₈₉	C₂²	semidirect
64. #483×C₈₉	C₂²	semidirect
69. #479×C₈₉	C₂²	semidirect
70. #479×C₈₉	C₂²	semidirect
71. #479×C₈₉	C₂²	semidirect
72. #479×C₈₉	C₂²	semidirect
73. #478×C₈₉	C₂²	semidirect
74. #478×C₈₉	C₂²	semidirect
75. #477×C₈₉	C₂²	semidirect
76. #477×C₈₉	C₂²	semidirect
77. #476×C₈₉	C₂²	semidirect
78. #475×C₈₉	C₂²	semidirect
79. #475×C₈₉	C₂²	semidirect
80. #474×C₈₉	C₂²	semidirect
89. #452×C₈₉	C₂²	semidirect
90. #452×C₈₉	C₂²	semidirect
91. #451×C₈₉	C₂²	semidirect
92. #451×C₈₉	C₂²	semidirect
98. #441×C₈₉	C₂²	semidirect
99. #441×C₈₉	C₂²	semidirect
100. #441×C₈₉	C₂²	semidirect
104. #440×C₈₉	C₂²	semidirect
105. C₄×Q₁₆×C₈₉	C₂²	semidirect
106. C₄×Q₁₆×C₈₉	C₂²	semidirect
107. C₄×Q₁₆×C₈₉	C₂²	semidirect
111. C₄×SD₁₆×C₈₉	C₂²	semidirect
113. #433×C₈₉	C₂²	semidirect
114. #433×C₈₉	C₂²	semidirect
115. #432×C₈₉	C₂²	semidirect
116. #431×C₈₉	C₂²	semidirect
569. #60595	C₈₉	direct (N × H)
577. #3510	C₂×C₈₉	semidirect
578. C₄×2₋¹⁺⁴	C₂×C₈₉	semidirect
579. #3125	C₂×C₈₉	semidirect
580. #3124	C₂×C₈₉	semidirect
581. #3121	C₂×C₈₉	semidirect
582. #3121	C₂×C₈₉	semidirect
583. #3117	C₂×C₈₉	semidirect
584. #3111	C₂×C₈₉	semidirect
585. #3108	C₂×C₈₉	semidirect
586. #3102	C₂×C₈₉	semidirect
587. #3097	C₂×C₈₉	semidirect
588. #3096	C₂×C₈₉	semidirect
589. #3078	C₂×C₈₉	semidirect
590. #3076	C₂×C₈₉	semidirect
591. #3040	C₂×C₈₉	semidirect
592. C₂×#464	C₂×C₈₉	semidirect
593. #3011	C₂×C₈₉	semidirect
595. #2950	C₂×C₈₉	semidirect
596. #2949	C₂×C₈₉	semidirect
597. #2947	C₂×C₈₉	semidirect
598. #2946	C₂×C₈₉	semidirect
599. #2925	C₂×C₈₉	semidirect
600. C₈₉	#60595	direct (N × H)
624. #520	C₂²×C₈₉	semidirect
628. #519	C₂²×C₈₉	semidirect
634. C₄×#41	C₂²×C₈₉	semidirect
637. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
638. #485	C₂²×C₈₉	semidirect
639. #485	C₂²×C₈₉	semidirect
640. #484	C₂²×C₈₉	semidirect
641. #483	C₂²×C₈₉	semidirect
646. #479	C₂²×C₈₉	semidirect
647. #479	C₂²×C₈₉	semidirect
648. #479	C₂²×C₈₉	semidirect
649. #479	C₂²×C₈₉	semidirect
650. #478	C₂²×C₈₉	semidirect
651. #478	C₂²×C₈₉	semidirect
652. #477	C₂²×C₈₉	semidirect
653. #477	C₂²×C₈₉	semidirect
654. #476	C₂²×C₈₉	semidirect
655. #475	C₂²×C₈₉	semidirect
656. #475	C₂²×C₈₉	semidirect
657. #474	C₂²×C₈₉	semidirect
666. #452	C₂²×C₈₉	semidirect
667. #452	C₂²×C₈₉	semidirect
668. #451	C₂²×C₈₉	semidirect
669. #451	C₂²×C₈₉	semidirect
675. #441	C₂²×C₈₉	semidirect
676. #441	C₂²×C₈₉	semidirect
677. #441	C₂²×C₈₉	semidirect
681. #440	C₂²×C₈₉	semidirect
682. C₄×Q₁₆	C₂²×C₈₉	semidirect
683. C₄×Q₁₆	C₂²×C₈₉	semidirect
684. C₄×Q₁₆	C₂²×C₈₉	semidirect
688. C₄×SD₁₆	C₂²×C₈₉	semidirect
690. #433	C₂²×C₈₉	semidirect
691. #433	C₂²×C₈₉	semidirect
692. #432	C₂²×C₈₉	semidirect
693. #431	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×#3510	2
C₄×2₋¹⁺⁴×C₈₉	2
C₈₉×#3125	2
C₈₉×#3124	2
C₈₉×#3121	2
C₈₉×#3117	2
C₈₉×#3111	2
C₈₉×#3108	2
C₈₉×#3102	2
C₈₉×#3097	2
C₈₉×#3096	2
C₈₉×#3078	2
C₈₉×#3076	2
C₈₉×#3040	2
C₂×#464×C₈₉	2
C₈₉×#3011	2
C₈₉×#3010	2
C₈₉×#2950	2
C₈₉×#2949	2
C₈₉×#2947	2
C₈₉×#2946	2
C₈₉×#2925	2
#60595	89

Subgroups — C89×#60595 #36438443

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60595 #36438443