Subgroups — C₈₉×#61420 #36439268

Order 22784.

1908 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3401	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3400	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3398	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3397	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3393	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3392	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3154	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3152	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3046	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3043	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#461×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2947	C₂	1	2	yes	maximal, complemented
17	C₄×AGL(1,ℤ/8)×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#137×C₈₉	C₂²	1	2	yes	—
19	C₂×#137×C₈₉	C₂²	1	2	yes	—
20	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#135×C₈₉	C₂²	1	2	yes	—
22	C₂²×SD₁₆×C₈₉	C₂²	1	2	yes	—
23	#559×C₈₉	C₂²	1	4	yes	—
24	#557×C₈₉	C₂²	1	2	yes	complemented
25	#557×C₈₉	C₂²	1	2	yes	complemented
26	#556×C₈₉	C₂²	1	2	yes	—
27	#556×C₈₉	C₂²	1	2	yes	complemented
28	#556×C₈₉	C₂²	1	2	yes	complemented
29	#555×C₈₉	—	2	1	no	—
30	#553×C₈₉	—	2	2	no	—
31	#552×C₈₉	—	2	2	no	—
32	#552×C₈₉	—	2	2	no	—
33	#550×C₈₉	C₂²	1	2	yes	—
34	#547×C₈₉	—	2	1	no	—
35	#541×C₈₉	—	2	2	no	—
36	#538×C₈₉	—	2	2	no	—
37	#536×C₈₉	C₂²	1	2	yes	—
38	#535×C₈₉	C₂²	1	2	yes	—
39	#533×C₈₉	—	2	1	no	—
40	#533×C₈₉	—	2	1	no	—
41	#533×C₈₉	C₂²	1	1	yes	characteristic
42	#532×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
44	#525×C₈₉	—	2	2	no	—
45	#520×C₈₉	C₂²	1	2	yes	—
46	#519×C₈₉	C₂²	1	2	yes	—
47	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
49	#497×C₈₉	C₂²	1	4	yes	—
50	#497×C₈₉	C₂²	1	4	yes	complemented
51	#496×C₈₉	C₂²	1	4	yes	—
52	#495×C₈₉	C₂²	1	4	yes	—
53	#494×C₈₉	C₂²	1	2	yes	complemented
54	#492×C₈₉	C₂²	1	4	yes	—
55	#492×C₈₉	C₂²	1	2	yes	complemented
56	#464×C₈₉	C₂²	1	4	yes	—
57	#464×C₈₉	C₂²	1	4	yes	—
58	#464×C₈₉	C₂²	1	4	yes	complemented
59	#464×C₈₉	C₂²	1	2	yes	complemented
60	#463×C₈₉	C₂²	1	4	yes	complemented
61	#463×C₈₉	C₂²	1	2	yes	complemented
62	#462×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	#462×C₈₉	C₂²	1	4	yes	complemented
64	#461×C₈₉	C₂²	1	2	yes	—
65	#461×C₈₉	C₂²	1	2	yes	—
66	#461×C₈₉	C₂²	1	4	yes	—
67	#461×C₈₉	C₂²	1	4	yes	complemented
68	#461×C₈₉	C₂²	1	1	yes	characteristic, complemented
69	#460×C₈₉	C₂²	1	4	yes	—
70	#460×C₈₉	C₂²	1	4	yes	—
71	#460×C₈₉	C₂²	1	1	yes	characteristic, complemented
72	#459×C₈₉	C₂²	1	1	yes	characteristic, complemented
73	#446×C₈₉	C₂²	1	2	yes	complemented
74	#446×C₈₉	C₂²	1	4	yes	complemented
75	C₈×Q₈×C₈₉	C₂²	1	2	yes	complemented
76	#442×C₈₉	C₂²	1	2	yes	—
77	#441×C₈₉	C₂²	1	4	yes	complemented
78	#440×C₈₉	C₂²	1	2	yes	—
79	#440×C₈₉	C₂²	1	4	yes	complemented
80	C₄×Q₁₆×C₈₉	C₂²	1	4	yes	complemented
81	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
82	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	complemented
83	C₄×D₈×C₈₉	C₂²	1	2	yes	—
84	#428×C₈₉	C₂²	1	1	yes	characteristic
85	#424×C₈₉	C₂²	1	2	yes	—
86	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
87	#418×C₈₉	C₂²	1	1	yes	characteristic
88	#417×C₈₉	C₂²	1	1	yes	characteristic
89	#416×C₈₉	C₂²	1	2	yes	—
90	C₂×#103×C₈₉	C₂²	1	2	yes	—
91	#405×C₈₉	C₂²	1	2	yes	—
92	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
93	C₂×#41×C₈₉	—	2	2	no	—
94	C₂×#41×C₈₉	C₂³	1	2	yes	—
95	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
97	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₈₉	—	2	1	no	—
99	#137×C₈₉	—	2	8	no	—
100	#137×C₈₉	—	4	4	no	—
101	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
102	#135×C₈₉	—	4	4	no	—
103	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
104	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
105	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
106	C₂×SD₁₆×C₈₉	—	4	4	no	—
107	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
108	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
109	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
112	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
113	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
114	C₂×D₈×C₈₉	C₂³	1	2	yes	—
115	C₂×D₈×C₈₉	C₂³	1	2	yes	—
116	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
117	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
119	C₄⋊Q₈×C₈₉	—	2	1	no	—
120	C₄⋊Q₈×C₈₉	—	2	1	no	—
121	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
122	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
123	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
124	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
125	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
126	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
127	#127×C₈₉	C₂³	1	1	yes	characteristic
128	#127×C₈₉	C₂³	1	4	yes	—
129	#126×C₈₉	—	2	4	no	—
130	#126×C₈₉	—	2	4	no	—
131	#126×C₈₉	—	2	4	no	—
132	#125×C₈₉	—	2	2	no	—
133	#125×C₈₉	—	2	2	no	—
134	#125×C₈₉	—	2	4	no	—
135	#125×C₈₉	—	2	4	no	—
136	#125×C₈₉	D₄	1	2	yes	—
137	#124×C₈₉	—	2	4	no	—
138	#124×C₈₉	C₂³	1	4	yes	—
139	#124×C₈₉	C₂³	1	2	yes	—
140	#124×C₈₉	C₂³	1	4	yes	—
141	#123×C₈₉	—	2	4	no	—
142	#123×C₈₉	—	2	4	no	—
143	#123×C₈₉	—	2	4	no	—
144	C₂²⋊Q₈×C₈₉	—	2	2	no	—
145	C₂²⋊Q₈×C₈₉	—	2	2	no	—
146	C₂²⋊Q₈×C₈₉	—	2	2	no	—
147	C₂²⋊Q₈×C₈₉	—	2	2	no	—
148	C₂²⋊Q₈×C₈₉	—	2	2	no	—
149	C₂²⋊Q₈×C₈₉	D₄	1	2	yes	—
150	C₂²⋊Q₈×C₈₉	D₄	1	2	yes	—
151	#121×C₈₉	—	2	1	no	—
152	#121×C₈₉	—	2	1	no	—
153	#121×C₈₉	—	2	2	no	—
154	#121×C₈₉	—	2	2	no	—
155	#121×C₈₉	—	2	2	no	—
156	#121×C₈₉	—	2	4	no	—
157	#120×C₈₉	—	2	4	no	—
158	C₄×Q₈×C₈₉	—	2	2	no	—
159	C₄×Q₈×C₈₉	—	2	2	no	—
160	C₄×Q₈×C₈₉	—	2	2	no	—
161	C₄×Q₈×C₈₉	—	2	2	no	—
162	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
164	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
165	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
166	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
168	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
169	C₄×D₄×C₈₉	—	2	1	no	—
170	C₄×D₄×C₈₉	—	2	1	no	—
171	C₄×D₄×C₈₉	—	2	4	no	—
172	C₄×D₄×C₈₉	—	2	4	no	—
173	C₄×D₄×C₈₉	—	2	1	no	—
174	C₄×D₄×C₈₉	—	2	1	no	—
175	C₄×D₄×C₈₉	—	2	1	no	—
176	C₄×D₄×C₈₉	—	2	1	no	—
177	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₈₉	C₂³	1	2	yes	—
179	C₄×D₄×C₈₉	C₂³	1	4	yes	—
180	C₄×D₄×C₈₉	C₂³	1	2	yes	—
181	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
182	#117×C₈₉	—	2	2	no	—
183	#117×C₈₉	—	2	2	no	—
184	#117×C₈₉	—	2	2	no	—
185	#117×C₈₉	—	2	2	no	—
186	#117×C₈₉	—	2	4	no	—
187	#117×C₈₉	—	2	1	no	—
188	#117×C₈₉	C₂³	1	1	yes	characteristic
189	#117×C₈₉	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
191	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
192	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
193	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
195	C₂×C₄²×C₈₉	—	2	1	no	—
196	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
197	#107×C₈₉	C₂³	1	2	yes	—
198	#106×C₈₉	C₂³	1	2	yes	—
199	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
200	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
201	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
202	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
203	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
204	#103×C₈₉	C₂³	1	4	yes	—
205	#103×C₈₉	C₂³	1	4	yes	—
206	#103×C₈₉	C₂³	1	2	yes	—
207	#103×C₈₉	C₂³	1	2	yes	—
208	#103×C₈₉	C₂³	1	2	yes	—
209	#102×C₈₉	C₂³	1	2	yes	—
210	#102×C₈₉	C₂³	1	2	yes	—
211	#102×C₈₉	C₂³	1	2	yes	—
212	#102×C₈₉	C₂³	1	2	yes	—
213	#102×C₈₉	C₂³	1	2	yes	—
214	#97×C₈₉	C₂³	1	2	yes	—
215	#97×C₈₉	C₂³	1	4	yes	—
216	C₄×C₈×C₈₉	C₂³	1	2	yes	—
217	C₄×C₈×C₈₉	C₂³	1	4	yes	—
218	C₂⁴×C₈₉	—	2	1	no	—
219	#41×C₈₉	—	2	2	no	—
220	#41×C₈₉	—	2	4	no	—
221	#41×C₈₉	—	2	2	no	—
222	#41×C₈₉	—	2	4	no	—
223	#41×C₈₉	—	8	4	no	—
224	C₂×Q₈×C₈₉	—	2	2	no	—
225	C₂×Q₈×C₈₉	—	2	4	no	—
226	C₂×Q₈×C₈₉	—	2	4	no	—
227	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
229	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
230	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
231	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
232	C₂×D₄×C₈₉	—	2	2	no	—
233	C₂×D₄×C₈₉	—	2	1	no	—
234	C₂×D₄×C₈₉	—	2	1	no	—
235	C₂×D₄×C₈₉	—	2	1	no	—
236	C₂×D₄×C₈₉	—	2	4	no	—
237	C₂×D₄×C₈₉	—	2	1	no	—
238	C₂×D₄×C₈₉	—	2	4	no	—
239	C₂×D₄×C₈₉	—	2	2	no	—
240	C₂×D₄×C₈₉	—	2	2	no	—
241	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
242	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
243	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₈₉	—	2	2	no	—
245	C₂²×C₄×C₈₉	—	2	1	no	—
246	C₂²×C₄×C₈₉	—	2	1	no	—
247	C₂²×C₄×C₈₉	—	2	1	no	—
248	C₂²×C₄×C₈₉	—	2	1	no	—
249	C₂²×C₄×C₈₉	—	2	2	no	—
250	C₂²×C₄×C₈₉	—	2	2	no	—
251	C₂²×C₄×C₈₉	—	2	4	no	—
252	C₂²×C₄×C₈₉	—	2	2	no	—
253	C₂²×C₄×C₈₉	—	8	2	no	—
254	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
257	Q₁₆×C₈₉	—	2	8	no	—
258	Q₁₆×C₈₉	—	4	2	no	—
259	Q₁₆×C₈₉	—	4	4	no	—
260	SD₁₆×C₈₉	—	2	4	no	—
261	SD₁₆×C₈₉	—	2	8	no	—
262	SD₁₆×C₈₉	—	4	4	no	—
263	SD₁₆×C₈₉	—	4	4	no	—
264	SD₁₆×C₈₉	—	4	2	no	—
265	SD₁₆×C₈₉	—	4	2	no	—
266	SD₁₆×C₈₉	—	4	4	no	—
267	D₈×C₈₉	—	2	4	no	—
268	D₈×C₈₉	—	4	2	no	—
269	M₁₆×C₈₉	—	2	2	no	—
270	M₁₆×C₈₉	#41	1	4	yes	complemented
271	C₂×C₈×C₈₉	—	2	4	no	—
272	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
273	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
274	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
275	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
276	C₄⋊C₄×C₈₉	—	2	1	no	—
277	C₄⋊C₄×C₈₉	—	2	2	no	—
278	C₄⋊C₄×C₈₉	—	2	2	no	—
279	C₄⋊C₄×C₈₉	—	2	4	no	—
280	C₄⋊C₄×C₈₉	—	2	2	no	—
281	C₄⋊C₄×C₈₉	—	2	2	no	—
282	C₄⋊C₄×C₈₉	—	2	1	no	—
283	C₄⋊C₄×C₈₉	—	2	1	no	—
284	C₄⋊C₄×C₈₉	—	2	1	no	—
285	C₄⋊C₄×C₈₉	—	2	4	no	—
286	C₄⋊C₄×C₈₉	—	2	4	no	—
287	C₄⋊C₄×C₈₉	—	2	1	no	—
288	C₄⋊C₄×C₈₉	—	2	4	no	—
289	C₄⋊C₄×C₈₉	—	2	4	no	—
290	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
291	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
292	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
293	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
294	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
295	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
296	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
297	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
298	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
299	C₂²⋊C₄×C₈₉	—	2	1	no	—
300	C₂²⋊C₄×C₈₉	—	2	2	no	—
301	C₂²⋊C₄×C₈₉	—	2	2	no	—
302	C₂²⋊C₄×C₈₉	—	2	4	no	—
303	C₂²⋊C₄×C₈₉	—	2	1	no	—
304	C₂²⋊C₄×C₈₉	—	2	1	no	—
305	C₂²⋊C₄×C₈₉	—	2	4	no	—
306	C₂²⋊C₄×C₈₉	—	2	4	no	—
307	C₂²⋊C₄×C₈₉	—	2	4	no	—
308	C₂²⋊C₄×C₈₉	—	2	2	no	—
309	C₂²⋊C₄×C₈₉	—	2	4	no	—
310	C₂²⋊C₄×C₈₉	—	2	2	no	—
311	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
312	C₄²×C₈₉	—	2	1	no	—
313	C₄²×C₈₉	—	2	1	no	—
314	C₄²×C₈₉	—	2	1	no	—
315	C₄²×C₈₉	—	2	4	no	—
316	C₄²×C₈₉	—	2	4	no	—
317	C₄²×C₈₉	—	2	4	no	—
318	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
321	C₄²×C₈₉	C₂⁴	1	4	yes	—
322	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
323	C₂³×C₈₉	—	2	1	no	—
324	C₂³×C₈₉	—	2	2	no	—
325	C₂³×C₈₉	—	2	2	no	—
326	C₂³×C₈₉	—	4	2	no	—
327	C₂³×C₈₉	—	8	1	no	—
328	C₂³×C₈₉	—	8	1	no	—
329	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
330	Q₈×C₈₉	—	2	4	no	—
331	Q₈×C₈₉	—	2	1	no	—
332	Q₈×C₈₉	—	2	4	no	—
333	Q₈×C₈₉	—	2	2	no	—
334	Q₈×C₈₉	—	2	4	no	—
335	Q₈×C₈₉	—	2	1	no	—
336	Q₈×C₈₉	—	2	2	no	—
337	Q₈×C₈₉	—	4	2	no	—
338	Q₈×C₈₉	—	4	4	no	—
339	D₄×C₈₉	—	2	1	no	—
340	D₄×C₈₉	—	2	2	no	—
341	D₄×C₈₉	—	2	2	no	—
342	D₄×C₈₉	—	2	1	no	—
343	D₄×C₈₉	—	2	2	no	—
344	D₄×C₈₉	—	2	2	no	—
345	D₄×C₈₉	—	4	4	no	—
346	D₄×C₈₉	—	4	2	no	—
347	D₄×C₈₉	—	4	2	no	—
348	D₄×C₈₉	—	4	2	no	—
349	D₄×C₈₉	—	8	1	no	—
350	D₄×C₈₉	—	8	4	no	—
351	D₄×C₈₉	—	8	4	no	—
352	C₂×C₄×C₈₉	—	2	2	no	—
353	C₂×C₄×C₈₉	—	2	1	no	—
354	C₂×C₄×C₈₉	—	2	1	no	—
355	C₂×C₄×C₈₉	—	2	2	no	—
356	C₂×C₄×C₈₉	—	2	2	no	—
357	C₂×C₄×C₈₉	—	2	4	no	—
358	C₂×C₄×C₈₉	—	2	1	no	—
359	C₂×C₄×C₈₉	—	4	1	no	—
360	C₂×C₄×C₈₉	—	4	2	no	—
361	C₂×C₄×C₈₉	—	4	4	no	—
362	C₂×C₄×C₈₉	—	4	2	no	—
363	C₂×C₄×C₈₉	—	4	4	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	4	no	—
368	C₂×C₄×C₈₉	—	8	1	no	—
369	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
370	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
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	1	yes	characteristic
376	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
377	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
378	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
379	C₈×C₈₉	—	2	2	no	—
380	C₈×C₈₉	—	2	2	no	—
381	C₈×C₈₉	—	2	2	no	—
382	C₈×C₈₉	C₂×#41	1	4	yes	—
383	C₂²×C₈₉	—	2	1	no	—
384	C₂²×C₈₉	—	2	1	no	—
385	C₂²×C₈₉	—	4	1	no	—
386	C₂²×C₈₉	—	4	2	no	—
387	C₂²×C₈₉	—	4	2	no	—
388	C₂²×C₈₉	—	4	1	no	—
389	C₂²×C₈₉	—	4	2	no	—
390	C₂²×C₈₉	—	4	2	no	—
391	C₂²×C₈₉	—	4	2	no	—
392	C₂²×C₈₉	—	4	1	no	—
393	C₂²×C₈₉	—	4	2	no	—
394	C₂²×C₈₉	—	8	4	no	—
395	C₂²×C₈₉	#550	1	2	yes	—
396	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
397	C₄×C₈₉	—	2	1	no	—
398	C₄×C₈₉	—	2	1	no	—
399	C₄×C₈₉	—	2	4	no	—
400	C₄×C₈₉	—	2	1	no	—
401	C₄×C₈₉	—	2	4	no	—
402	C₄×C₈₉	—	4	1	no	—
403	C₄×C₈₉	—	4	2	no	—
404	C₄×C₈₉	—	4	1	no	—
405	C₄×C₈₉	—	4	4	no	—
406	C₄×C₈₉	—	4	1	no	—
407	C₄×C₈₉	—	4	2	no	—
408	C₄×C₈₉	#550	1	2	yes	—
409	C₄×C₈₉	#577	1	2	yes	—
410	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
411	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
412	#61420	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
413	C₂×C₈₉	—	2	2	no	—
414	C₂×C₈₉	—	8	1	no	—
415	C₂×C₈₉	—	8	2	no	—
416	C₂×C₈₉	—	8	2	no	—
417	C₂×C₈₉	C₂×#550	1	1	yes	characteristic
418	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
419	C₂×C₈₉	#3586	1	1	yes	characteristic
420	#3509	C₂×C₈₉	1	1	yes	characteristic, complemented
421	#3506	C₂×C₈₉	1	1	yes	characteristic, complemented
422	#3401	C₂×C₈₉	1	4	yes	complemented
423	#3400	C₂×C₈₉	1	4	yes	complemented
424	#3398	C₂×C₈₉	1	2	yes	complemented
425	#3397	C₂×C₈₉	1	2	yes	complemented
426	#3393	C₂×C₈₉	1	2	yes	complemented
427	#3392	C₂×C₈₉	1	2	yes	complemented
428	#3154	C₂×C₈₉	1	2	yes	complemented
429	#3152	C₂×C₈₉	1	1	yes	characteristic, complemented
430	#3046	C₂×C₈₉	1	2	yes	complemented
431	#3043	C₂×C₈₉	1	2	yes	complemented
432	#3035	C₂×C₈₉	1	1	yes	characteristic, complemented
433	C₂×#461	C₂×C₈₉	1	1	yes	characteristic, complemented
434	#2962	C₂×C₈₉	1	1	yes	characteristic, complemented
435	#2947	C₂×C₈₉	1	2	yes	complemented
436	C₄×AGL(1,ℤ/8)	C₂×C₈₉	1	1	yes	characteristic, complemented
437	C₈₉	#61420	1	1	yes	characteristic, direct product factor, Sylow
438	C₂×#137	C₂²×C₈₉	1	2	yes	—
439	C₂×#137	C₂²×C₈₉	1	2	yes	—
440	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
441	C₂×#135	C₂²×C₈₉	1	2	yes	—
442	C₂²×SD₁₆	C₂²×C₈₉	1	2	yes	—
443	#559	C₂²×C₈₉	1	4	yes	—
444	#557	C₂²×C₈₉	1	2	yes	complemented
445	#557	C₂²×C₈₉	1	2	yes	complemented
446	#556	C₂²×C₈₉	1	2	yes	—
447	#556	C₂²×C₈₉	1	2	yes	complemented
448	#556	C₂²×C₈₉	1	2	yes	complemented
449	#555	—	2	1	no	—
450	#553	—	2	2	no	—
451	#552	—	2	2	no	—
452	#552	—	2	2	no	—
453	#550	C₂²×C₈₉	1	2	yes	—
454	#547	—	2	1	no	—
455	#541	—	2	2	no	—
456	#538	—	2	2	no	—
457	#536	C₂²×C₈₉	1	2	yes	—
458	#535	C₂²×C₈₉	1	2	yes	—
459	#533	—	2	1	no	—
460	#533	—	2	1	no	—
461	#533	C₂²×C₈₉	1	1	yes	characteristic
462	#532	C₂²×C₈₉	1	1	yes	characteristic
463	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
464	#525	—	2	2	no	—
465	#520	C₂²×C₈₉	1	2	yes	—
466	#519	C₂²×C₈₉	1	2	yes	—
467	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
468	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
469	#497	C₂²×C₈₉	1	4	yes	—
470	#497	C₂²×C₈₉	1	4	yes	complemented
471	#496	C₂²×C₈₉	1	4	yes	—
472	#495	C₂²×C₈₉	1	4	yes	—
473	#494	C₂²×C₈₉	1	2	yes	complemented
474	#492	C₂²×C₈₉	1	4	yes	—
475	#492	C₂²×C₈₉	1	2	yes	complemented
476	#464	C₂²×C₈₉	1	4	yes	—
477	#464	C₂²×C₈₉	1	4	yes	—
478	#464	C₂²×C₈₉	1	4	yes	complemented
479	#464	C₂²×C₈₉	1	2	yes	complemented
480	#463	C₂²×C₈₉	1	4	yes	complemented
481	#463	C₂²×C₈₉	1	2	yes	complemented
482	#462	C₂²×C₈₉	1	1	yes	characteristic, complemented
483	#462	C₂²×C₈₉	1	4	yes	complemented
484	#461	C₂²×C₈₉	1	2	yes	—
485	#461	C₂²×C₈₉	1	2	yes	—
486	#461	C₂²×C₈₉	1	4	yes	—
487	#461	C₂²×C₈₉	1	4	yes	complemented
488	#461	C₂²×C₈₉	1	1	yes	characteristic, complemented
489	#460	C₂²×C₈₉	1	4	yes	—
490	#460	C₂²×C₈₉	1	4	yes	—
491	#460	C₂²×C₈₉	1	1	yes	characteristic, complemented
492	#459	C₂²×C₈₉	1	1	yes	characteristic, complemented
493	#446	C₂²×C₈₉	1	2	yes	complemented
494	#446	C₂²×C₈₉	1	4	yes	complemented
495	C₈×Q₈	C₂²×C₈₉	1	2	yes	complemented
496	#442	C₂²×C₈₉	1	2	yes	—
497	#441	C₂²×C₈₉	1	4	yes	complemented
498	#440	C₂²×C₈₉	1	2	yes	—
499	#440	C₂²×C₈₉	1	4	yes	complemented
500	C₄×Q₁₆	C₂²×C₈₉	1	4	yes	complemented
501	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
502	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	complemented
503	C₄×D₈	C₂²×C₈₉	1	2	yes	—
504	#428	C₂²×C₈₉	1	1	yes	characteristic
505	#424	C₂²×C₈₉	1	2	yes	—
506	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
507	#418	C₂²×C₈₉	1	1	yes	characteristic
508	#417	C₂²×C₈₉	1	1	yes	characteristic
509	#416	C₂²×C₈₉	1	2	yes	—
510	C₂×#103	C₂²×C₈₉	1	2	yes	—
511	#405	C₂²×C₈₉	1	2	yes	—
512	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
513	C₂×#41	—	2	2	no	—
514	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
515	C₂×#41	C₂³×C₈₉	1	2	yes	—
516	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
517	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
518	C₂³×C₄	—	2	1	no	—
519	#137	—	2	8	no	—
520	#137	—	4	4	no	—
521	AGL(1,ℤ/8)	—	2	4	no	—
522	#135	—	4	4	no	—
523	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
524	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
525	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
526	C₂×SD₁₆	—	4	4	no	—
527	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
528	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
529	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
530	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
531	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
532	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
533	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
534	C₂×D₈	C₂³×C₈₉	1	2	yes	—
535	C₂×D₈	C₂³×C₈₉	1	2	yes	—
536	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
537	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
538	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
539	C₄⋊Q₈	—	2	1	no	—
540	C₄⋊Q₈	—	2	1	no	—
541	C₄⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
542	C₄⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
543	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
544	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
545	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
546	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
547	#127	C₂³×C₈₉	1	1	yes	characteristic
548	#127	C₂³×C₈₉	1	4	yes	—
549	#126	—	2	4	no	—
550	#126	—	2	4	no	—
551	#126	—	2	4	no	—
552	#125	—	2	2	no	—
553	#125	—	2	2	no	—
554	#125	—	2	4	no	—
555	#125	—	2	4	no	—
556	#125	D₄×C₈₉	1	2	yes	—
557	#124	—	2	4	no	—
558	#124	C₂³×C₈₉	1	2	yes	—
559	#124	C₂³×C₈₉	1	4	yes	—
560	#124	C₂³×C₈₉	1	4	yes	—
561	#123	—	2	4	no	—
562	#123	—	2	4	no	—
563	#123	—	2	4	no	—
564	C₂²⋊Q₈	—	2	2	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	D₄×C₈₉	1	2	yes	—
570	C₂²⋊Q₈	D₄×C₈₉	1	2	yes	—
571	#121	—	2	1	no	—
572	#121	—	2	1	no	—
573	#121	—	2	2	no	—
574	#121	—	2	2	no	—
575	#121	—	2	2	no	—
576	#121	—	2	4	no	—
577	#120	—	2	4	no	—
578	C₄×Q₈	—	2	2	no	—
579	C₄×Q₈	—	2	2	no	—
580	C₄×Q₈	—	2	2	no	—
581	C₄×Q₈	—	2	2	no	—
582	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
583	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
584	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
585	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
586	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
587	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
588	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
589	C₄×D₄	—	2	1	no	—
590	C₄×D₄	—	2	1	no	—
591	C₄×D₄	—	2	4	no	—
592	C₄×D₄	—	2	4	no	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	C₂³×C₈₉	1	2	yes	—
598	C₄×D₄	C₂³×C₈₉	1	2	yes	—
599	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
600	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
601	C₄×D₄	C₂³×C₈₉	1	4	yes	—
602	#117	—	2	2	no	—
603	#117	—	2	2	no	—
604	#117	—	2	2	no	—
605	#117	—	2	2	no	—
606	#117	—	2	4	no	—
607	#117	—	2	1	no	—
608	#117	C₂³×C₈₉	1	1	yes	characteristic
609	#117	C₂³×C₈₉	1	2	yes	—
610	C₂×C₄⋊C₄	—	2	1	no	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	2	no	—
613	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₄²	—	2	1	no	—
616	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
617	#107	C₂³×C₈₉	1	2	yes	—
618	#106	C₂³×C₈₉	1	2	yes	—
619	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
620	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
621	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
622	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
623	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
624	#103	C₂³×C₈₉	1	4	yes	—
625	#103	C₂³×C₈₉	1	4	yes	—
626	#103	C₂³×C₈₉	1	2	yes	—
627	#103	C₂³×C₈₉	1	2	yes	—
628	#103	C₂³×C₈₉	1	2	yes	—
629	#102	C₂³×C₈₉	1	2	yes	—
630	#102	C₂³×C₈₉	1	2	yes	—
631	#102	C₂³×C₈₉	1	2	yes	—
632	#102	C₂³×C₈₉	1	2	yes	—
633	#102	C₂³×C₈₉	1	2	yes	—
634	#97	C₂³×C₈₉	1	2	yes	—
635	#97	C₂³×C₈₉	1	4	yes	—
636	C₄×C₈	C₂³×C₈₉	1	2	yes	—
637	C₄×C₈	C₂³×C₈₉	1	4	yes	—
638	C₂⁴	—	2	1	no	—
639	#41	—	2	2	no	—
640	#41	—	2	4	no	—
641	#41	—	2	2	no	—
642	#41	—	2	4	no	—
643	#41	—	8	4	no	—
644	C₂×Q₈	—	2	2	no	—
645	C₂×Q₈	—	2	4	no	—
646	C₂×Q₈	—	2	4	no	—
647	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
648	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
649	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
650	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
651	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
652	C₂×D₄	—	2	2	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	—	2	1	no	—
656	C₂×D₄	—	2	4	no	—
657	C₂×D₄	—	2	1	no	—
658	C₂×D₄	—	2	4	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
662	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
663	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	1	no	—
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	4	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	8	2	no	—
674	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
675	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
677	Q₁₆	—	2	8	no	—
678	Q₁₆	—	4	2	no	—
679	Q₁₆	—	4	4	no	—
680	SD₁₆	—	2	4	no	—
681	SD₁₆	—	2	8	no	—
682	SD₁₆	—	4	4	no	—
683	SD₁₆	—	4	4	no	—
684	SD₁₆	—	4	2	no	—
685	SD₁₆	—	4	2	no	—
686	SD₁₆	—	4	4	no	—
687	D₈	—	2	4	no	—
688	D₈	—	4	2	no	—
689	M₁₆	—	2	2	no	—
690	M₁₆	#41×C₈₉	1	4	yes	complemented
691	C₂×C₈	—	2	4	no	—
692	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
693	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
694	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
695	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	4	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
711	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
712	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
713	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
714	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
715	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
716	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
717	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
718	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
719	C₂²⋊C₄	—	2	1	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	1	no	—
724	C₂²⋊C₄	—	2	1	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
732	C₄²	—	2	1	no	—
733	C₄²	—	2	1	no	—
734	C₄²	—	2	1	no	—
735	C₄²	—	2	4	no	—
736	C₄²	—	2	4	no	—
737	C₄²	—	2	4	no	—
738	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
739	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
740	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
741	C₄²	C₂⁴×C₈₉	1	4	yes	—
742	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
743	C₂³	—	2	1	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	4	2	no	—
747	C₂³	—	8	1	no	—
748	C₂³	—	8	1	no	—
749	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
750	Q₈	—	2	4	no	—
751	Q₈	—	2	1	no	—
752	Q₈	—	2	4	no	—
753	Q₈	—	2	2	no	—
754	Q₈	—	2	4	no	—
755	Q₈	—	2	1	no	—
756	Q₈	—	2	2	no	—
757	Q₈	—	4	2	no	—
758	Q₈	—	4	4	no	—
759	D₄	—	2	1	no	—
760	D₄	—	2	2	no	—
761	D₄	—	2	2	no	—
762	D₄	—	2	1	no	—
763	D₄	—	2	2	no	—
764	D₄	—	2	2	no	—
765	D₄	—	4	4	no	—
766	D₄	—	4	2	no	—
767	D₄	—	4	2	no	—
768	D₄	—	4	2	no	—
769	D₄	—	8	1	no	—
770	D₄	—	8	4	no	—
771	D₄	—	8	4	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	2	no	—
781	C₂×C₄	—	4	4	no	—
782	C₂×C₄	—	4	2	no	—
783	C₂×C₄	—	4	4	no	—
784	C₂×C₄	—	4	2	no	—
785	C₂×C₄	—	4	4	no	—
786	C₂×C₄	—	8	2	no	—
787	C₂×C₄	—	8	4	no	—
788	C₂×C₄	—	8	1	no	—
789	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
790	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
791	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
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	1	yes	characteristic
795	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
796	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
797	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
798	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
799	C₈	—	2	2	no	—
800	C₈	—	2	2	no	—
801	C₈	—	2	2	no	—
802	C₈	C₂×#41×C₈₉	1	4	yes	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	1	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	8	4	no	—
815	C₂²	#550×C₈₉	1	2	yes	—
816	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
817	C₄	—	2	1	no	—
818	C₄	—	2	4	no	—
819	C₄	—	2	1	no	—
820	C₄	—	2	1	no	—
821	C₄	—	2	4	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	1	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	1	no	—
827	C₄	—	4	4	no	—
828	C₄	#550×C₈₉	1	2	yes	—
829	C₄	#577×C₈₉	1	2	yes	—
830	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
831	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
832	C₂	—	2	2	no	—
833	C₂	—	8	1	no	—
834	C₂	—	8	2	no	—
835	C₂	—	8	2	no	—
836	C₂	C₂×#550×C₈₉	1	1	yes	characteristic
837	C₂	C₂×#577×C₈₉	1	1	yes	characteristic
838	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 ◁ #533×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3509	C₂	semidirect
2. C₈₉×#3506	C₂	semidirect
3. C₈₉×#3401	C₂	semidirect
4. C₈₉×#3400	C₂	semidirect
5. C₈₉×#3398	C₂	semidirect
6. C₈₉×#3397	C₂	semidirect
7. C₈₉×#3393	C₂	semidirect
8. C₈₉×#3392	C₂	semidirect
9. C₈₉×#3154	C₂	semidirect
10. C₈₉×#3152	C₂	semidirect
11. C₈₉×#3046	C₂	semidirect
12. C₈₉×#3043	C₂	semidirect
13. C₈₉×#3035	C₂	semidirect
14. C₂×#461×C₈₉	C₂	semidirect
15. C₈₉×#2962	C₂	semidirect
16. C₈₉×#2947	C₂	semidirect
17. C₄×AGL(1,ℤ/8)×C₈₉	C₂	semidirect
24. #557×C₈₉	C₂²	semidirect
25. #557×C₈₉	C₂²	semidirect
27. #556×C₈₉	C₂²	semidirect
28. #556×C₈₉	C₂²	semidirect
50. #497×C₈₉	C₂²	semidirect
53. #494×C₈₉	C₂²	semidirect
55. #492×C₈₉	C₂²	semidirect
58. #464×C₈₉	C₂²	semidirect
59. #464×C₈₉	C₂²	semidirect
60. #463×C₈₉	C₂²	semidirect
61. #463×C₈₉	C₂²	semidirect
62. #462×C₈₉	C₂²	semidirect
63. #462×C₈₉	C₂²	semidirect
67. #461×C₈₉	C₂²	semidirect
68. #461×C₈₉	C₂²	semidirect
71. #460×C₈₉	C₂²	semidirect
72. #459×C₈₉	C₂²	semidirect
73. #446×C₈₉	C₂²	semidirect
74. #446×C₈₉	C₂²	semidirect
75. C₈×Q₈×C₈₉	C₂²	semidirect
77. #441×C₈₉	C₂²	semidirect
79. #440×C₈₉	C₂²	semidirect
80. C₄×Q₁₆×C₈₉	C₂²	semidirect
82. C₄×SD₁₆×C₈₉	C₂²	semidirect
270. M₁₆×C₈₉	#41	semidirect
412. #61420	C₈₉	direct (N × H)
420. #3509	C₂×C₈₉	semidirect
421. #3506	C₂×C₈₉	semidirect
422. #3401	C₂×C₈₉	semidirect
423. #3400	C₂×C₈₉	semidirect
424. #3398	C₂×C₈₉	semidirect
425. #3397	C₂×C₈₉	semidirect
426. #3393	C₂×C₈₉	semidirect
427. #3392	C₂×C₈₉	semidirect
428. #3154	C₂×C₈₉	semidirect
429. #3152	C₂×C₈₉	semidirect
430. #3046	C₂×C₈₉	semidirect
431. #3043	C₂×C₈₉	semidirect
432. #3035	C₂×C₈₉	semidirect
433. C₂×#461	C₂×C₈₉	semidirect
434. #2962	C₂×C₈₉	semidirect
435. #2947	C₂×C₈₉	semidirect
436. C₄×AGL(1,ℤ/8)	C₂×C₈₉	semidirect
437. C₈₉	#61420	direct (N × H)
444. #557	C₂²×C₈₉	semidirect
445. #557	C₂²×C₈₉	semidirect
447. #556	C₂²×C₈₉	semidirect
448. #556	C₂²×C₈₉	semidirect
470. #497	C₂²×C₈₉	semidirect
473. #494	C₂²×C₈₉	semidirect
475. #492	C₂²×C₈₉	semidirect
478. #464	C₂²×C₈₉	semidirect
479. #464	C₂²×C₈₉	semidirect
480. #463	C₂²×C₈₉	semidirect
481. #463	C₂²×C₈₉	semidirect
482. #462	C₂²×C₈₉	semidirect
483. #462	C₂²×C₈₉	semidirect
487. #461	C₂²×C₈₉	semidirect
488. #461	C₂²×C₈₉	semidirect
491. #460	C₂²×C₈₉	semidirect
492. #459	C₂²×C₈₉	semidirect
493. #446	C₂²×C₈₉	semidirect
494. #446	C₂²×C₈₉	semidirect
495. C₈×Q₈	C₂²×C₈₉	semidirect
497. #441	C₂²×C₈₉	semidirect
499. #440	C₂²×C₈₉	semidirect
500. C₄×Q₁₆	C₂²×C₈₉	semidirect
502. C₄×SD₁₆	C₂²×C₈₉	semidirect
690. M₁₆	#41×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3509	2
C₈₉×#3506	2
C₈₉×#3401	2
C₈₉×#3400	2
C₈₉×#3398	2
C₈₉×#3397	2
C₈₉×#3393	2
C₈₉×#3392	2
C₈₉×#3154	2
C₈₉×#3152	2
C₈₉×#3046	2
C₈₉×#3043	2
C₈₉×#3035	2
C₂×#461×C₈₉	2
C₈₉×#2962	2
C₈₉×#2947	2
C₄×AGL(1,ℤ/8)×C₈₉	2
#61420	89

Subgroups — C89×#61420 #36439268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61420 #36439268