Subgroups — C₈₉×#60703 #36438551

Order 22784.

1910 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3455	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#542×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3179	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3178	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3175	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3173	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3165	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3153	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3140	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3056	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3055	C₂	1	2	yes	maximal, complemented
13	C₄×#137×C₈₉	C₂	1	2	yes	maximal, complemented
14	C₄×AGL(1,ℤ/8)×C₈₉	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2873	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#137×C₈₉	C₂²	1	2	yes	—
17	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
18	C₂²×M₁₆×C₈₉	C₂²	1	2	yes	—
19	#542×C₈₉	—	2	2	no	—
20	#542×C₈₉	—	2	2	no	—
21	#542×C₈₉	C₂²	1	4	yes	—
22	#542×C₈₉	C₂²	1	4	yes	—
23	#542×C₈₉	C₂²	1	2	yes	complemented
24	#542×C₈₉	C₂²	1	2	yes	complemented
25	#541×C₈₉	C₂²	1	2	yes	complemented
26	#540×C₈₉	C₂²	1	2	yes	complemented
27	#539×C₈₉	—	2	1	no	—
28	#539×C₈₉	—	2	1	no	—
29	#538×C₈₉	—	2	1	no	—
30	#538×C₈₉	—	2	1	no	—
31	#533×C₈₉	C₂²	1	1	yes	characteristic
32	#532×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
34	#529×C₈₉	—	2	2	no	—
35	#529×C₈₉	—	2	2	no	—
36	C₂×#126×C₈₉	—	2	1	no	—
37	C₂×#124×C₈₉	—	2	1	no	—
38	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
39	#525×C₈₉	C₂²	1	2	yes	—
40	C₂×#123×C₈₉	—	2	1	no	—
41	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
42	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
44	C₄×#41×C₈₉	C₂²	1	2	yes	—
45	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
48	#501×C₈₉	C₂²	1	4	yes	complemented
49	#500×C₈₉	C₂²	1	2	yes	complemented
50	#498×C₈₉	C₂²	1	2	yes	complemented
51	#497×C₈₉	C₂²	1	2	yes	complemented
52	#496×C₈₉	C₂²	1	2	yes	complemented
53	#495×C₈₉	C₂²	1	4	yes	complemented
54	#489×C₈₉	C₂²	1	2	yes	complemented
55	#489×C₈₉	C₂²	1	2	yes	complemented
56	#489×C₈₉	C₂²	1	4	yes	complemented
57	#488×C₈₉	C₂²	1	4	yes	complemented
58	#487×C₈₉	C₂²	1	2	yes	complemented
59	#486×C₈₉	C₂²	1	2	yes	complemented
60	#470×C₈₉	C₂²	1	4	yes	complemented
61	#469×C₈₉	C₂²	1	4	yes	—
62	#468×C₈₉	C₂²	1	4	yes	—
63	#468×C₈₉	C₂²	1	4	yes	complemented
64	#467×C₈₉	C₂²	1	4	yes	complemented
65	#466×C₈₉	C₂²	1	4	yes	—
66	#465×C₈₉	C₂²	1	4	yes	—
67	#465×C₈₉	C₂²	1	4	yes	complemented
68	#442×C₈₉	C₂²	1	4	yes	complemented
69	#441×C₈₉	C₂²	1	4	yes	complemented
70	#440×C₈₉	C₂²	1	4	yes	complemented
71	#440×C₈₉	C₂²	1	4	yes	complemented
72	C₄×Q₁₆×C₈₉	C₂²	1	4	yes	complemented
73	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	complemented
74	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	complemented
75	C₄×D₈×C₈₉	C₂²	1	4	yes	complemented
76	#428×C₈₉	C₂²	1	2	yes	—
77	#428×C₈₉	C₂²	1	2	yes	—
78	#419×C₈₉	C₂²	1	2	yes	—
79	#418×C₈₉	C₂²	1	2	yes	—
80	#417×C₈₉	C₂²	1	2	yes	—
81	#417×C₈₉	C₂²	1	2	yes	—
82	#405×C₈₉	C₂²	1	4	yes	complemented
83	#405×C₈₉	C₂²	1	4	yes	complemented
84	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
85	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
86	C₄×M₁₆×C₈₉	C₂²	1	2	yes	—
87	C₂×#41×C₈₉	C₂³	1	2	yes	—
88	C₂²×Q₈×C₈₉	—	2	1	no	—
89	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₈₉	—	2	1	no	—
91	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₈₉	—	2	1	no	—
93	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
94	#137×C₈₉	—	2	8	no	—
95	AGL(1,ℤ/8)×C₈₉	—	2	8	no	—
96	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
97	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
99	C₂×D₈×C₈₉	C₂³	1	4	yes	—
100	C₂×M₁₆×C₈₉	—	2	8	no	—
101	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
102	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
103	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
104	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
105	C₄⋊Q₈×C₈₉	—	2	1	no	—
106	C₄⋊Q₈×C₈₉	—	2	1	no	—
107	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
109	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
110	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
111	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
112	#127×C₈₉	C₂³	1	1	yes	characteristic
113	#126×C₈₉	—	2	4	no	—
114	#126×C₈₉	—	2	4	no	—
115	#126×C₈₉	—	2	2	no	—
116	#126×C₈₉	—	2	2	no	—
117	#126×C₈₉	—	2	2	no	—
118	#126×C₈₉	—	2	2	no	—
119	#125×C₈₉	—	2	2	no	—
120	#125×C₈₉	—	2	2	no	—
121	#125×C₈₉	C₂³	1	2	yes	—
122	#124×C₈₉	—	2	4	no	—
123	#124×C₈₉	—	2	4	no	—
124	#124×C₈₉	—	2	2	no	—
125	#124×C₈₉	—	2	2	no	—
126	#124×C₈₉	—	2	1	no	—
127	#124×C₈₉	—	2	1	no	—
128	#124×C₈₉	C₂³	1	2	yes	—
129	#124×C₈₉	C₂³	1	2	yes	—
130	#124×C₈₉	C₂³	1	2	yes	—
131	#123×C₈₉	—	2	2	no	—
132	#123×C₈₉	—	2	2	no	—
133	#123×C₈₉	—	2	2	no	—
134	#123×C₈₉	—	2	4	no	—
135	#123×C₈₉	—	2	4	no	—
136	#123×C₈₉	—	2	2	no	—
137	#123×C₈₉	—	2	2	no	—
138	C₂²⋊Q₈×C₈₉	—	2	2	no	—
139	C₂²⋊Q₈×C₈₉	—	2	1	no	—
140	C₂²⋊Q₈×C₈₉	—	2	1	no	—
141	C₂²⋊Q₈×C₈₉	—	2	4	no	—
142	C₂²⋊Q₈×C₈₉	—	2	4	no	—
143	C₂²⋊Q₈×C₈₉	—	2	2	no	—
144	C₂²⋊Q₈×C₈₉	—	2	2	no	—
145	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
146	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
147	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
148	#121×C₈₉	—	2	2	no	—
149	#121×C₈₉	—	2	1	no	—
150	#121×C₈₉	—	2	1	no	—
151	#121×C₈₉	—	2	2	no	—
152	#121×C₈₉	—	2	2	no	—
153	#121×C₈₉	C₂³	1	4	yes	—
154	#121×C₈₉	C₂³	1	2	yes	—
155	#121×C₈₉	C₂³	1	2	yes	—
156	#120×C₈₉	—	2	2	no	—
157	C₄×Q₈×C₈₉	—	2	2	no	—
158	C₄×Q₈×C₈₉	—	2	1	no	—
159	C₄×Q₈×C₈₉	—	2	1	no	—
160	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
161	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
162	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
163	C₄×D₄×C₈₉	—	2	2	no	—
164	C₄×D₄×C₈₉	—	2	2	no	—
165	C₄×D₄×C₈₉	—	2	2	no	—
166	C₄×D₄×C₈₉	—	2	2	no	—
167	C₄×D₄×C₈₉	—	2	2	no	—
168	C₄×D₄×C₈₉	—	2	1	no	—
169	C₄×D₄×C₈₉	—	2	1	no	—
170	C₄×D₄×C₈₉	C₂³	1	2	yes	—
171	C₄×D₄×C₈₉	C₂³	1	4	yes	—
172	C₄×D₄×C₈₉	C₂³	1	2	yes	—
173	#117×C₈₉	—	2	2	no	—
174	#117×C₈₉	D₄	1	2	yes	—
175	#117×C₈₉	D₄	1	2	yes	—
176	#117×C₈₉	C₂³	1	2	yes	—
177	#117×C₈₉	C₂³	1	2	yes	—
178	#117×C₈₉	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
180	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
181	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
182	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
187	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
188	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
189	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
190	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
191	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₈₉	—	2	1	no	—
194	C₂×C₄²×C₈₉	—	2	2	no	—
195	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
197	#107×C₈₉	C₂³	1	4	yes	—
198	#107×C₈₉	C₂³	1	4	yes	—
199	#106×C₈₉	C₂³	1	4	yes	—
200	#106×C₈₉	C₂³	1	4	yes	—
201	#103×C₈₉	C₂³	1	4	yes	—
202	#103×C₈₉	C₂³	1	4	yes	—
203	#103×C₈₉	C₂³	1	4	yes	—
204	#103×C₈₉	C₂³	1	4	yes	—
205	#102×C₈₉	C₂³	1	4	yes	—
206	#102×C₈₉	C₂³	1	4	yes	—
207	#102×C₈₉	C₂³	1	4	yes	—
208	#102×C₈₉	C₂³	1	4	yes	—
209	#97×C₈₉	C₂³	1	4	yes	—
210	#97×C₈₉	C₂³	1	2	yes	—
211	#97×C₈₉	C₂³	1	2	yes	—
212	C₄×C₈×C₈₉	C₂³	1	4	yes	—
213	C₄×C₈×C₈₉	C₂³	1	2	yes	—
214	C₄×C₈×C₈₉	C₂³	1	2	yes	—
215	C₂⁴×C₈₉	—	2	1	no	—
216	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
217	#41×C₈₉	—	2	4	no	—
218	#41×C₈₉	—	2	4	no	—
219	C₂×Q₈×C₈₉	—	2	1	no	—
220	C₂×Q₈×C₈₉	—	2	1	no	—
221	C₂×Q₈×C₈₉	—	2	1	no	—
222	C₂×Q₈×C₈₉	—	2	2	no	—
223	C₂×Q₈×C₈₉	—	2	2	no	—
224	C₂×Q₈×C₈₉	—	2	4	no	—
225	C₂×Q₈×C₈₉	—	8	2	no	—
226	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
227	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
228	C₂×D₄×C₈₉	—	2	2	no	—
229	C₂×D₄×C₈₉	—	2	2	no	—
230	C₂×D₄×C₈₉	—	2	2	no	—
231	C₂×D₄×C₈₉	—	2	4	no	—
232	C₂×D₄×C₈₉	—	2	1	no	—
233	C₂×D₄×C₈₉	—	2	1	no	—
234	C₂×D₄×C₈₉	—	2	1	no	—
235	C₂×D₄×C₈₉	—	2	4	no	—
236	C₂×D₄×C₈₉	—	8	2	no	—
237	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
238	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₈₉	—	2	4	no	—
240	C₂²×C₄×C₈₉	—	2	1	no	—
241	C₂²×C₄×C₈₉	—	2	1	no	—
242	C₂²×C₄×C₈₉	—	2	1	no	—
243	C₂²×C₄×C₈₉	—	2	2	no	—
244	C₂²×C₄×C₈₉	—	2	2	no	—
245	C₂²×C₄×C₈₉	—	2	2	no	—
246	C₂²×C₄×C₈₉	—	2	4	no	—
247	C₂²×C₄×C₈₉	—	8	2	no	—
248	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
250	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
256	Q₁₆×C₈₉	—	2	8	no	—
257	SD₁₆×C₈₉	—	2	8	no	—
258	SD₁₆×C₈₉	—	2	8	no	—
259	D₈×C₈₉	—	2	8	no	—
260	M₁₆×C₈₉	—	2	4	no	—
261	M₁₆×C₈₉	—	2	8	no	—
262	M₁₆×C₈₉	#41	1	8	yes	—
263	C₂×C₈×C₈₉	—	2	8	no	—
264	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
265	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
266	C₄⋊C₄×C₈₉	—	2	4	no	—
267	C₄⋊C₄×C₈₉	—	2	4	no	—
268	C₄⋊C₄×C₈₉	—	2	2	no	—
269	C₄⋊C₄×C₈₉	—	2	2	no	—
270	C₄⋊C₄×C₈₉	—	2	1	no	—
271	C₄⋊C₄×C₈₉	—	2	1	no	—
272	C₄⋊C₄×C₈₉	—	2	2	no	—
273	C₄⋊C₄×C₈₉	—	2	2	no	—
274	C₄⋊C₄×C₈₉	—	2	1	no	—
275	C₄⋊C₄×C₈₉	—	2	1	no	—
276	C₄⋊C₄×C₈₉	—	2	2	no	—
277	C₄⋊C₄×C₈₉	—	2	2	no	—
278	C₄⋊C₄×C₈₉	—	2	2	no	—
279	C₄⋊C₄×C₈₉	—	2	2	no	—
280	C₄⋊C₄×C₈₉	—	2	1	no	—
281	C₄⋊C₄×C₈₉	—	2	1	no	—
282	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
283	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
284	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
285	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
286	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
287	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
289	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
290	C₂²⋊C₄×C₈₉	—	2	4	no	—
291	C₂²⋊C₄×C₈₉	—	2	2	no	—
292	C₂²⋊C₄×C₈₉	—	2	2	no	—
293	C₂²⋊C₄×C₈₉	—	2	2	no	—
294	C₂²⋊C₄×C₈₉	—	2	4	no	—
295	C₂²⋊C₄×C₈₉	—	2	4	no	—
296	C₂²⋊C₄×C₈₉	—	2	2	no	—
297	C₂²⋊C₄×C₈₉	—	2	2	no	—
298	C₂²⋊C₄×C₈₉	—	2	2	no	—
299	C₂²⋊C₄×C₈₉	—	2	2	no	—
300	C₂²⋊C₄×C₈₉	—	2	2	no	—
301	C₂²⋊C₄×C₈₉	—	2	2	no	—
302	C₂²⋊C₄×C₈₉	—	2	2	no	—
303	C₂²⋊C₄×C₈₉	—	2	2	no	—
304	C₂²⋊C₄×C₈₉	—	2	2	no	—
305	C₂²⋊C₄×C₈₉	—	2	2	no	—
306	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
307	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
308	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
309	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
310	C₄²×C₈₉	—	2	2	no	—
311	C₄²×C₈₉	—	2	2	no	—
312	C₄²×C₈₉	—	2	2	no	—
313	C₄²×C₈₉	—	2	4	no	—
314	C₄²×C₈₉	C₂×D₄	1	2	yes	—
315	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₈₉	C₂⁴	1	2	yes	—
318	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
319	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
320	C₂³×C₈₉	—	2	2	no	—
321	C₂³×C₈₉	—	2	2	no	—
322	C₂³×C₈₉	—	2	2	no	—
323	C₂³×C₈₉	—	4	1	no	—
324	C₂³×C₈₉	—	4	1	no	—
325	C₂³×C₈₉	—	4	2	no	—
326	C₂³×C₈₉	—	4	2	no	—
327	C₂³×C₈₉	—	4	2	no	—
328	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
329	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
330	Q₈×C₈₉	—	2	2	no	—
331	Q₈×C₈₉	—	2	4	no	—
332	Q₈×C₈₉	—	2	2	no	—
333	Q₈×C₈₉	—	4	2	no	—
334	Q₈×C₈₉	—	8	1	no	—
335	Q₈×C₈₉	—	8	1	no	—
336	Q₈×C₈₉	—	8	2	no	—
337	Q₈×C₈₉	—	8	2	no	—
338	D₄×C₈₉	—	2	2	no	—
339	D₄×C₈₉	—	2	4	no	—
340	D₄×C₈₉	—	2	2	no	—
341	D₄×C₈₉	—	4	4	no	—
342	D₄×C₈₉	—	4	2	no	—
343	D₄×C₈₉	—	8	1	no	—
344	D₄×C₈₉	—	8	1	no	—
345	D₄×C₈₉	—	8	2	no	—
346	D₄×C₈₉	—	8	2	no	—
347	D₄×C₈₉	—	8	4	no	—
348	C₂×C₄×C₈₉	—	2	2	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	—	2	2	no	—
353	C₂×C₄×C₈₉	—	2	2	no	—
354	C₂×C₄×C₈₉	—	2	2	no	—
355	C₂×C₄×C₈₉	—	2	2	no	—
356	C₂×C₄×C₈₉	—	2	2	no	—
357	C₂×C₄×C₈₉	—	2	2	no	—
358	C₂×C₄×C₈₉	—	4	1	no	—
359	C₂×C₄×C₈₉	—	4	1	no	—
360	C₂×C₄×C₈₉	—	4	1	no	—
361	C₂×C₄×C₈₉	—	4	1	no	—
362	C₂×C₄×C₈₉	—	4	2	no	—
363	C₂×C₄×C₈₉	—	4	2	no	—
364	C₂×C₄×C₈₉	—	4	2	no	—
365	C₂×C₄×C₈₉	—	4	4	no	—
366	C₂×C₄×C₈₉	—	8	2	no	—
367	C₂×C₄×C₈₉	—	8	2	no	—
368	C₂×C₄×C₈₉	—	8	4	no	—
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	1	yes	characteristic
372	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
378	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
379	C₈×C₈₉	—	2	4	no	—
380	C₈×C₈₉	C₂×#41	1	8	yes	—
381	C₂²×C₈₉	—	2	1	no	—
382	C₂²×C₈₉	—	2	1	no	—
383	C₂²×C₈₉	—	2	2	no	—
384	C₂²×C₈₉	—	2	2	no	—
385	C₂²×C₈₉	—	2	2	no	—
386	C₂²×C₈₉	—	4	2	no	—
387	C₂²×C₈₉	—	4	2	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	—	8	2	no	—
393	C₂²×C₈₉	—	8	4	no	—
394	C₂²×C₈₉	#532	1	2	yes	—
395	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
396	C₄×C₈₉	—	2	2	no	—
397	C₄×C₈₉	—	2	1	no	—
398	C₄×C₈₉	—	2	1	no	—
399	C₄×C₈₉	—	2	2	no	—
400	C₄×C₈₉	—	2	1	no	—
401	C₄×C₈₉	—	2	1	no	—
402	C₄×C₈₉	—	2	2	no	—
403	C₄×C₈₉	—	4	2	no	—
404	C₄×C₈₉	—	4	2	no	—
405	C₄×C₈₉	—	4	2	no	—
406	C₄×C₈₉	—	4	2	no	—
407	C₄×C₈₉	—	4	2	no	—
408	C₄×C₈₉	—	4	2	no	—
409	C₄×C₈₉	#532	1	2	yes	—
410	C₄×C₈₉	C₂²×#41	1	2	yes	—
411	#60703	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
412	C₂×C₈₉	—	2	2	no	—
413	C₂×C₈₉	—	4	2	no	—
414	C₂×C₈₉	—	8	2	no	—
415	C₂×C₈₉	—	8	2	no	—
416	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
417	C₂×C₈₉	#3585	1	1	yes	characteristic
418	C₂×C₈₉	#3586	1	1	yes	characteristic
419	#3455	C₂×C₈₉	1	1	yes	characteristic, complemented
420	C₂×#542	C₂×C₈₉	1	1	yes	characteristic, complemented
421	#3179	C₂×C₈₉	1	4	yes	complemented
422	#3178	C₂×C₈₉	1	4	yes	complemented
423	#3175	C₂×C₈₉	1	4	yes	complemented
424	#3173	C₂×C₈₉	1	4	yes	complemented
425	#3165	C₂×C₈₉	1	1	yes	characteristic, complemented
426	#3153	C₂×C₈₉	1	1	yes	characteristic, complemented
427	#3141	C₂×C₈₉	1	1	yes	characteristic, complemented
428	#3140	C₂×C₈₉	1	1	yes	characteristic, complemented
429	#3056	C₂×C₈₉	1	2	yes	complemented
430	#3055	C₂×C₈₉	1	2	yes	complemented
431	C₄×#137	C₂×C₈₉	1	2	yes	complemented
432	C₄×AGL(1,ℤ/8)	C₂×C₈₉	1	2	yes	complemented
433	#2873	C₂×C₈₉	1	1	yes	characteristic, complemented
434	C₈₉	#60703	1	1	yes	characteristic, direct product factor, Sylow
435	C₂×#137	C₂²×C₈₉	1	2	yes	—
436	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
437	C₂²×M₁₆	C₂²×C₈₉	1	2	yes	—
438	#542	—	2	2	no	—
439	#542	—	2	2	no	—
440	#542	C₂²×C₈₉	1	4	yes	—
441	#542	C₂²×C₈₉	1	4	yes	—
442	#542	C₂²×C₈₉	1	2	yes	complemented
443	#542	C₂²×C₈₉	1	2	yes	complemented
444	#541	C₂²×C₈₉	1	2	yes	complemented
445	#540	C₂²×C₈₉	1	2	yes	complemented
446	#539	—	2	1	no	—
447	#539	—	2	1	no	—
448	#538	—	2	1	no	—
449	#538	—	2	1	no	—
450	#533	C₂²×C₈₉	1	1	yes	characteristic
451	#532	C₂²×C₈₉	1	1	yes	characteristic
452	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
453	#529	—	2	2	no	—
454	#529	—	2	2	no	—
455	C₂×#126	—	2	1	no	—
456	C₂×#124	—	2	1	no	—
457	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
458	#525	C₂²×C₈₉	1	2	yes	—
459	C₂×#123	—	2	1	no	—
460	C₂×C₂²⋊Q₈	—	2	1	no	—
461	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
462	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
463	C₄×#41	C₂²×C₈₉	1	2	yes	—
464	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
465	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
466	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
467	#501	C₂²×C₈₉	1	4	yes	complemented
468	#500	C₂²×C₈₉	1	2	yes	complemented
469	#498	C₂²×C₈₉	1	2	yes	complemented
470	#497	C₂²×C₈₉	1	2	yes	complemented
471	#496	C₂²×C₈₉	1	2	yes	complemented
472	#495	C₂²×C₈₉	1	4	yes	complemented
473	#489	C₂²×C₈₉	1	2	yes	complemented
474	#489	C₂²×C₈₉	1	2	yes	complemented
475	#489	C₂²×C₈₉	1	4	yes	complemented
476	#488	C₂²×C₈₉	1	4	yes	complemented
477	#487	C₂²×C₈₉	1	2	yes	complemented
478	#486	C₂²×C₈₉	1	2	yes	complemented
479	#470	C₂²×C₈₉	1	4	yes	complemented
480	#469	C₂²×C₈₉	1	4	yes	—
481	#468	C₂²×C₈₉	1	4	yes	—
482	#468	C₂²×C₈₉	1	4	yes	complemented
483	#467	C₂²×C₈₉	1	4	yes	complemented
484	#466	C₂²×C₈₉	1	4	yes	—
485	#465	C₂²×C₈₉	1	4	yes	—
486	#465	C₂²×C₈₉	1	4	yes	complemented
487	#442	C₂²×C₈₉	1	4	yes	complemented
488	#441	C₂²×C₈₉	1	4	yes	complemented
489	#440	C₂²×C₈₉	1	4	yes	complemented
490	#440	C₂²×C₈₉	1	4	yes	complemented
491	C₄×Q₁₆	C₂²×C₈₉	1	4	yes	complemented
492	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	complemented
493	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	complemented
494	C₄×D₈	C₂²×C₈₉	1	4	yes	complemented
495	#428	C₂²×C₈₉	1	2	yes	—
496	#428	C₂²×C₈₉	1	2	yes	—
497	#419	C₂²×C₈₉	1	2	yes	—
498	#418	C₂²×C₈₉	1	2	yes	—
499	#417	C₂²×C₈₉	1	2	yes	—
500	#417	C₂²×C₈₉	1	2	yes	—
501	#405	C₂²×C₈₉	1	4	yes	complemented
502	#405	C₂²×C₈₉	1	4	yes	complemented
503	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
504	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
505	C₄×M₁₆	C₂²×C₈₉	1	2	yes	—
506	C₂×#41	C₂³×C₈₉	1	2	yes	—
507	C₂²×Q₈	—	2	1	no	—
508	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
509	C₂²×D₄	—	2	1	no	—
510	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
511	C₂³×C₄	—	2	1	no	—
512	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
513	#137	—	2	8	no	—
514	AGL(1,ℤ/8)	—	2	8	no	—
515	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
516	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
517	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
518	C₂×D₈	C₂³×C₈₉	1	4	yes	—
519	C₂×M₁₆	—	2	8	no	—
520	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
521	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
522	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
523	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
524	C₄⋊Q₈	—	2	1	no	—
525	C₄⋊Q₈	—	2	1	no	—
526	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
527	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
528	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
529	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
530	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
531	#127	C₂³×C₈₉	1	1	yes	characteristic
532	#126	—	2	4	no	—
533	#126	—	2	4	no	—
534	#126	—	2	2	no	—
535	#126	—	2	2	no	—
536	#126	—	2	2	no	—
537	#126	—	2	2	no	—
538	#125	—	2	2	no	—
539	#125	—	2	2	no	—
540	#125	C₂³×C₈₉	1	2	yes	—
541	#124	—	2	4	no	—
542	#124	—	2	4	no	—
543	#124	—	2	2	no	—
544	#124	—	2	2	no	—
545	#124	—	2	1	no	—
546	#124	—	2	1	no	—
547	#124	C₂³×C₈₉	1	2	yes	—
548	#124	C₂³×C₈₉	1	2	yes	—
549	#124	C₂³×C₈₉	1	2	yes	—
550	#123	—	2	2	no	—
551	#123	—	2	2	no	—
552	#123	—	2	2	no	—
553	#123	—	2	4	no	—
554	#123	—	2	4	no	—
555	#123	—	2	2	no	—
556	#123	—	2	2	no	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	—	2	1	no	—
559	C₂²⋊Q₈	—	2	1	no	—
560	C₂²⋊Q₈	—	2	4	no	—
561	C₂²⋊Q₈	—	2	4	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
565	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
566	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
567	#121	—	2	2	no	—
568	#121	—	2	1	no	—
569	#121	—	2	1	no	—
570	#121	—	2	2	no	—
571	#121	—	2	2	no	—
572	#121	C₂³×C₈₉	1	4	yes	—
573	#121	C₂³×C₈₉	1	2	yes	—
574	#121	C₂³×C₈₉	1	2	yes	—
575	#120	—	2	2	no	—
576	C₄×Q₈	—	2	2	no	—
577	C₄×Q₈	—	2	1	no	—
578	C₄×Q₈	—	2	1	no	—
579	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
580	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
581	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
582	C₄×D₄	—	2	2	no	—
583	C₄×D₄	—	2	2	no	—
584	C₄×D₄	—	2	2	no	—
585	C₄×D₄	—	2	2	no	—
586	C₄×D₄	—	2	2	no	—
587	C₄×D₄	—	2	1	no	—
588	C₄×D₄	—	2	1	no	—
589	C₄×D₄	C₂³×C₈₉	1	4	yes	—
590	C₄×D₄	C₂³×C₈₉	1	2	yes	—
591	C₄×D₄	C₂³×C₈₉	1	2	yes	—
592	#117	—	2	2	no	—
593	#117	D₄×C₈₉	1	2	yes	—
594	#117	D₄×C₈₉	1	2	yes	—
595	#117	C₂³×C₈₉	1	2	yes	—
596	#117	C₂³×C₈₉	1	2	yes	—
597	#117	C₂³×C₈₉	1	2	yes	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	2	1	no	—
601	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
602	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
605	C₂×C₂²⋊C₄	—	2	1	no	—
606	C₂×C₂²⋊C₄	—	2	1	no	—
607	C₂×C₂²⋊C₄	—	2	1	no	—
608	C₂×C₂²⋊C₄	—	2	1	no	—
609	C₂×C₂²⋊C₄	—	2	1	no	—
610	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
611	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
612	C₂×C₄²	—	2	1	no	—
613	C₂×C₄²	—	2	2	no	—
614	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
616	#107	C₂³×C₈₉	1	4	yes	—
617	#107	C₂³×C₈₉	1	4	yes	—
618	#106	C₂³×C₈₉	1	4	yes	—
619	#106	C₂³×C₈₉	1	4	yes	—
620	#103	C₂³×C₈₉	1	4	yes	—
621	#103	C₂³×C₈₉	1	4	yes	—
622	#103	C₂³×C₈₉	1	4	yes	—
623	#103	C₂³×C₈₉	1	4	yes	—
624	#102	C₂³×C₈₉	1	4	yes	—
625	#102	C₂³×C₈₉	1	4	yes	—
626	#102	C₂³×C₈₉	1	4	yes	—
627	#102	C₂³×C₈₉	1	4	yes	—
628	#97	C₂³×C₈₉	1	4	yes	—
629	#97	C₂³×C₈₉	1	2	yes	—
630	#97	C₂³×C₈₉	1	2	yes	—
631	C₄×C₈	C₂³×C₈₉	1	4	yes	—
632	C₄×C₈	C₂³×C₈₉	1	2	yes	—
633	C₄×C₈	C₂³×C₈₉	1	2	yes	—
634	C₂⁴	—	2	1	no	—
635	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
636	#41	—	2	4	no	—
637	#41	—	2	4	no	—
638	C₂×Q₈	—	2	1	no	—
639	C₂×Q₈	—	2	1	no	—
640	C₂×Q₈	—	2	1	no	—
641	C₂×Q₈	—	2	2	no	—
642	C₂×Q₈	—	2	2	no	—
643	C₂×Q₈	—	2	4	no	—
644	C₂×Q₈	—	8	2	no	—
645	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
646	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	4	no	—
655	C₂×D₄	—	8	2	no	—
656	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
657	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	8	2	no	—
667	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
668	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
669	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
670	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
671	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
672	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
675	Q₁₆	—	2	8	no	—
676	SD₁₆	—	2	8	no	—
677	SD₁₆	—	2	8	no	—
678	D₈	—	2	8	no	—
679	M₁₆	—	2	4	no	—
680	M₁₆	—	2	8	no	—
681	M₁₆	#41×C₈₉	1	8	yes	—
682	C₂×C₈	—	2	8	no	—
683	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
684	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
702	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
703	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
704	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
705	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
706	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
707	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
708	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	2	no	—
711	C₂²⋊C₄	—	2	2	no	—
712	C₂²⋊C₄	—	2	2	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	2	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
726	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
727	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
728	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
729	C₄²	—	2	2	no	—
730	C₄²	—	2	2	no	—
731	C₄²	—	2	2	no	—
732	C₄²	—	2	4	no	—
733	C₄²	C₂×D₄×C₈₉	1	2	yes	—
734	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
735	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
736	C₄²	C₂⁴×C₈₉	1	2	yes	—
737	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
738	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	4	1	no	—
743	C₂³	—	4	1	no	—
744	C₂³	—	4	2	no	—
745	C₂³	—	4	2	no	—
746	C₂³	—	4	2	no	—
747	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
748	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
749	Q₈	—	2	2	no	—
750	Q₈	—	2	4	no	—
751	Q₈	—	2	2	no	—
752	Q₈	—	4	2	no	—
753	Q₈	—	8	1	no	—
754	Q₈	—	8	1	no	—
755	Q₈	—	8	2	no	—
756	Q₈	—	8	2	no	—
757	D₄	—	2	2	no	—
758	D₄	—	2	4	no	—
759	D₄	—	2	2	no	—
760	D₄	—	4	4	no	—
761	D₄	—	4	2	no	—
762	D₄	—	8	1	no	—
763	D₄	—	8	1	no	—
764	D₄	—	8	2	no	—
765	D₄	—	8	2	no	—
766	D₄	—	8	4	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	4	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	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	2	no	—
782	C₂×C₄	—	4	2	no	—
783	C₂×C₄	—	4	2	no	—
784	C₂×C₄	—	4	4	no	—
785	C₂×C₄	—	8	2	no	—
786	C₂×C₄	—	8	2	no	—
787	C₂×C₄	—	8	4	no	—
788	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
789	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
790	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
791	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
793	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
794	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
795	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
796	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
797	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
798	C₈	—	2	4	no	—
799	C₈	C₂×#41×C₈₉	1	8	yes	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	2	no	—
803	C₂²	—	2	2	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	8	2	no	—
812	C₂²	—	8	4	no	—
813	C₂²	#532×C₈₉	1	2	yes	—
814	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
815	C₄	—	2	2	no	—
816	C₄	—	2	1	no	—
817	C₄	—	2	1	no	—
818	C₄	—	2	2	no	—
819	C₄	—	2	1	no	—
820	C₄	—	2	1	no	—
821	C₄	—	2	2	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	#532×C₈₉	1	2	yes	—
829	C₄	C₂²×#41×C₈₉	1	2	yes	—
830	C₂	—	2	2	no	—
831	C₂	—	4	2	no	—
832	C₂	—	8	2	no	—
833	C₂	—	8	2	no	—
834	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
835	C₂	C₈₉×#3585	1	1	yes	characteristic
836	C₂	C₈₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
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×#3455	C₂	semidirect
2. C₂×#542×C₈₉	C₂	semidirect
3. C₈₉×#3179	C₂	semidirect
4. C₈₉×#3178	C₂	semidirect
5. C₈₉×#3175	C₂	semidirect
6. C₈₉×#3173	C₂	semidirect
7. C₈₉×#3165	C₂	semidirect
8. C₈₉×#3153	C₂	semidirect
9. C₈₉×#3141	C₂	semidirect
10. C₈₉×#3140	C₂	semidirect
11. C₈₉×#3056	C₂	semidirect
12. C₈₉×#3055	C₂	semidirect
13. C₄×#137×C₈₉	C₂	semidirect
14. C₄×AGL(1,ℤ/8)×C₈₉	C₂	semidirect
15. C₈₉×#2873	C₂	semidirect
23. #542×C₈₉	C₂²	semidirect
24. #542×C₈₉	C₂²	semidirect
25. #541×C₈₉	C₂²	semidirect
26. #540×C₈₉	C₂²	semidirect
48. #501×C₈₉	C₂²	semidirect
49. #500×C₈₉	C₂²	semidirect
50. #498×C₈₉	C₂²	semidirect
51. #497×C₈₉	C₂²	semidirect
52. #496×C₈₉	C₂²	semidirect
53. #495×C₈₉	C₂²	semidirect
54. #489×C₈₉	C₂²	semidirect
55. #489×C₈₉	C₂²	semidirect
56. #489×C₈₉	C₂²	semidirect
57. #488×C₈₉	C₂²	semidirect
58. #487×C₈₉	C₂²	semidirect
59. #486×C₈₉	C₂²	semidirect
60. #470×C₈₉	C₂²	semidirect
63. #468×C₈₉	C₂²	semidirect
64. #467×C₈₉	C₂²	semidirect
67. #465×C₈₉	C₂²	semidirect
68. #442×C₈₉	C₂²	semidirect
69. #441×C₈₉	C₂²	semidirect
70. #440×C₈₉	C₂²	semidirect
71. #440×C₈₉	C₂²	semidirect
72. C₄×Q₁₆×C₈₉	C₂²	semidirect
73. C₄×SD₁₆×C₈₉	C₂²	semidirect
74. C₄×SD₁₆×C₈₉	C₂²	semidirect
75. C₄×D₈×C₈₉	C₂²	semidirect
82. #405×C₈₉	C₂²	semidirect
83. #405×C₈₉	C₂²	semidirect
411. #60703	C₈₉	direct (N × H)
419. #3455	C₂×C₈₉	semidirect
420. C₂×#542	C₂×C₈₉	semidirect
421. #3179	C₂×C₈₉	semidirect
422. #3178	C₂×C₈₉	semidirect
423. #3175	C₂×C₈₉	semidirect
424. #3173	C₂×C₈₉	semidirect
425. #3165	C₂×C₈₉	semidirect
426. #3153	C₂×C₈₉	semidirect
427. #3141	C₂×C₈₉	semidirect
428. #3140	C₂×C₈₉	semidirect
429. #3056	C₂×C₈₉	semidirect
430. #3055	C₂×C₈₉	semidirect
431. C₄×#137	C₂×C₈₉	semidirect
432. C₄×AGL(1,ℤ/8)	C₂×C₈₉	semidirect
433. #2873	C₂×C₈₉	semidirect
434. C₈₉	#60703	direct (N × H)
442. #542	C₂²×C₈₉	semidirect
443. #542	C₂²×C₈₉	semidirect
444. #541	C₂²×C₈₉	semidirect
445. #540	C₂²×C₈₉	semidirect
467. #501	C₂²×C₈₉	semidirect
468. #500	C₂²×C₈₉	semidirect
469. #498	C₂²×C₈₉	semidirect
470. #497	C₂²×C₈₉	semidirect
471. #496	C₂²×C₈₉	semidirect
472. #495	C₂²×C₈₉	semidirect
473. #489	C₂²×C₈₉	semidirect
474. #489	C₂²×C₈₉	semidirect
475. #489	C₂²×C₈₉	semidirect
476. #488	C₂²×C₈₉	semidirect
477. #487	C₂²×C₈₉	semidirect
478. #486	C₂²×C₈₉	semidirect
479. #470	C₂²×C₈₉	semidirect
482. #468	C₂²×C₈₉	semidirect
483. #467	C₂²×C₈₉	semidirect
486. #465	C₂²×C₈₉	semidirect
487. #442	C₂²×C₈₉	semidirect
488. #441	C₂²×C₈₉	semidirect
489. #440	C₂²×C₈₉	semidirect
490. #440	C₂²×C₈₉	semidirect
491. C₄×Q₁₆	C₂²×C₈₉	semidirect
492. C₄×SD₁₆	C₂²×C₈₉	semidirect
493. C₄×SD₁₆	C₂²×C₈₉	semidirect
494. C₄×D₈	C₂²×C₈₉	semidirect
501. #405	C₂²×C₈₉	semidirect
502. #405	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×#3455	2
C₂×#542×C₈₉	2
C₈₉×#3179	2
C₈₉×#3178	2
C₈₉×#3175	2
C₈₉×#3173	2
C₈₉×#3165	2
C₈₉×#3153	2
C₈₉×#3141	2
C₈₉×#3140	2
C₈₉×#3056	2
C₈₉×#3055	2
C₄×#137×C₈₉	2
C₄×AGL(1,ℤ/8)×C₈₉	2
C₈₉×#2873	2
#60703	89

Subgroups — C89×#60703 #36438551

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60703 #36438551