Subgroups — C₈₉×#60812 #36438660

Order 22784.

2218 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#535×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3224	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3222	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3217	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3215	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3211	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3208	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3154	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3136	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3045	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3043	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3007	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3003	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3002	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#450×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#137×C₈₉	C₂²	1	2	yes	complemented
21	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	complemented
22	C₂×#135×C₈₉	C₂²	1	2	yes	complemented
23	C₂²×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
24	#556×C₈₉	—	2	1	no	—
25	#554×C₈₉	—	2	1	no	—
26	#552×C₈₉	—	2	2	no	—
27	#552×C₈₉	—	2	1	no	—
28	#552×C₈₉	—	2	1	no	—
29	#551×C₈₉	—	2	2	no	—
30	#544×C₈₉	C₂²	1	1	yes	characteristic, complemented
31	#542×C₈₉	C₂²	1	2	yes	complemented
32	#541×C₈₉	C₂²	1	2	yes	complemented
33	#536×C₈₉	C₂²	1	1	yes	characteristic, complemented
34	#535×C₈₉	—	2	1	no	—
35	#535×C₈₉	—	2	2	no	—
36	#535×C₈₉	—	2	1	no	—
37	#535×C₈₉	C₂²	1	2	yes	—
38	#535×C₈₉	C₂²	1	4	yes	—
39	#535×C₈₉	C₂²	1	2	yes	—
40	#533×C₈₉	C₂²	1	2	yes	complemented
41	C₂×#127×C₈₉	C₂²	1	2	yes	—
42	#529×C₈₉	C₂²	1	2	yes	complemented
43	C₂×#124×C₈₉	C₂²	1	2	yes	—
44	#525×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×#121×C₈₉	—	2	1	no	—
47	C₂×#121×C₈₉	—	2	1	no	—
48	C₂×#120×C₈₉	—	2	2	no	—
49	#520×C₈₉	C₂²	1	1	yes	characteristic, complemented
50	#519×C₈₉	C₂²	1	1	yes	characteristic, complemented
51	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
52	#497×C₈₉	C₂²	1	4	yes	complemented
53	#496×C₈₉	C₂²	1	4	yes	complemented
54	#495×C₈₉	C₂²	1	4	yes	complemented
55	#492×C₈₉	C₂²	1	4	yes	complemented
56	#490×C₈₉	C₂²	1	4	yes	complemented
57	#489×C₈₉	C₂²	1	4	yes	complemented
58	#488×C₈₉	C₂²	1	4	yes	complemented
59	#486×C₈₉	C₂²	1	4	yes	complemented
60	#464×C₈₉	C₂²	1	4	yes	complemented
61	#464×C₈₉	C₂²	1	4	yes	complemented
62	#464×C₈₉	C₂²	1	4	yes	complemented
63	#463×C₈₉	C₂²	1	4	yes	complemented
64	#460×C₈₉	C₂²	1	4	yes	complemented
65	#460×C₈₉	C₂²	1	4	yes	complemented
66	#460×C₈₉	C₂²	1	4	yes	complemented
67	#459×C₈₉	C₂²	1	4	yes	complemented
68	#452×C₈₉	C₂²	1	2	yes	complemented
69	#452×C₈₉	C₂²	1	4	yes	complemented
70	#451×C₈₉	C₂²	1	2	yes	complemented
71	#451×C₈₉	C₂²	1	1	yes	characteristic, complemented
72	#450×C₈₉	C₂²	1	2	yes	—
73	#450×C₈₉	C₂²	1	2	yes	—
74	#450×C₈₉	C₂²	1	2	yes	—
75	#450×C₈₉	C₂²	1	2	yes	complemented
76	#450×C₈₉	C₂²	1	4	yes	complemented
77	#450×C₈₉	C₂²	1	1	yes	characteristic, complemented
78	#450×C₈₉	C₂²	1	2	yes	complemented
79	#449×C₈₉	C₂²	1	2	yes	complemented
80	#448×C₈₉	C₂²	1	1	yes	characteristic, complemented
81	#447×C₈₉	C₂²	1	2	yes	—
82	#447×C₈₉	C₂²	1	2	yes	complemented
83	#447×C₈₉	C₂²	1	1	yes	characteristic, complemented
84	#433×C₈₉	C₂²	1	4	yes	complemented
85	#432×C₈₉	C₂²	1	2	yes	complemented
86	#431×C₈₉	C₂²	1	2	yes	complemented
87	#424×C₈₉	C₂²	1	2	yes	complemented
88	#418×C₈₉	C₂²	1	2	yes	complemented
89	#417×C₈₉	C₂²	1	2	yes	complemented
90	#416×C₈₉	C₂²	1	2	yes	complemented
91	C₂×#102×C₈₉	C₂²	1	2	yes	complemented
92	#407×C₈₉	C₂²	1	1	yes	characteristic
93	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
94	#405×C₈₉	C₂²	1	2	yes	complemented
95	C₂⁵×C₈₉	—	2	1	no	—
96	C₂×#41×C₈₉	—	2	1	no	—
97	C₂×#41×C₈₉	—	2	1	no	—
98	C₂×#41×C₈₉	—	4	4	no	—
99	C₂×#41×C₈₉	C₂³	1	2	yes	—
100	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
101	C₂×#41×C₈₉	C₂³	1	2	yes	—
102	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₈₉	—	2	1	no	—
105	C₂²×D₄×C₈₉	—	2	1	no	—
106	C₂²×D₄×C₈₉	—	2	1	no	—
107	C₂²×D₄×C₈₉	—	2	1	no	—
108	C₂²×D₄×C₈₉	—	2	2	no	—
109	C₂²×D₄×C₈₉	—	2	2	no	—
110	C₂²×D₄×C₈₉	—	4	4	no	—
111	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
112	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
113	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
115	C₂³×C₄×C₈₉	—	2	1	no	—
116	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
117	#137×C₈₉	—	4	4	no	—
118	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
119	#135×C₈₉	—	4	4	no	—
120	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	complemented
121	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	complemented
122	C₂×SD₁₆×C₈₉	—	4	4	no	—
123	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
124	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
125	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
126	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	complemented
127	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	complemented
128	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	complemented
129	C₂×D₈×C₈₉	C₂³	1	4	yes	—
130	C₂×D₈×C₈₉	C₂³	1	2	yes	complemented
131	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
132	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
133	C₄⋊Q₈×C₈₉	—	2	1	no	—
134	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	complemented
135	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	complemented
136	#127×C₈₉	—	2	2	no	—
137	#127×C₈₉	—	2	2	no	—
138	#127×C₈₉	C₂³	1	4	yes	—
139	#127×C₈₉	C₂³	1	4	yes	—
140	#126×C₈₉	—	2	2	no	—
141	#126×C₈₉	—	2	2	no	—
142	#126×C₈₉	—	2	2	no	—
143	#126×C₈₉	—	2	2	no	—
144	#125×C₈₉	—	2	2	no	—
145	#125×C₈₉	—	2	2	no	—
146	#125×C₈₉	—	2	1	no	—
147	#125×C₈₉	—	2	2	no	—
148	#125×C₈₉	C₂³	1	2	yes	complemented
149	#124×C₈₉	—	2	2	no	—
150	#124×C₈₉	—	2	2	no	—
151	#124×C₈₉	—	2	2	no	—
152	#124×C₈₉	C₂³	1	4	yes	—
153	#124×C₈₉	C₂³	1	4	yes	—
154	#124×C₈₉	C₂³	1	2	yes	complemented
155	#123×C₈₉	—	2	1	no	—
156	#123×C₈₉	—	2	2	no	—
157	#123×C₈₉	—	2	2	no	—
158	#123×C₈₉	—	2	2	no	—
159	C₂²⋊Q₈×C₈₉	—	2	1	no	—
160	C₂²⋊Q₈×C₈₉	—	2	1	no	—
161	C₂²⋊Q₈×C₈₉	—	2	2	no	—
162	C₂²⋊Q₈×C₈₉	—	2	1	no	—
163	C₂²⋊Q₈×C₈₉	—	2	1	no	—
164	C₂²⋊Q₈×C₈₉	—	2	2	no	—
165	C₂²⋊Q₈×C₈₉	—	2	2	no	—
166	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
167	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
168	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
169	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
170	#121×C₈₉	—	2	2	no	—
171	#121×C₈₉	—	2	2	no	—
172	#121×C₈₉	—	2	2	no	—
173	#121×C₈₉	—	2	4	no	—
174	#121×C₈₉	—	2	2	no	—
175	#121×C₈₉	—	2	4	no	—
176	#121×C₈₉	C₂³	1	1	yes	characteristic
177	#121×C₈₉	C₂³	1	1	yes	characteristic
178	#120×C₈₉	—	2	1	no	—
179	#120×C₈₉	—	2	4	no	—
180	#120×C₈₉	—	2	4	no	—
181	#120×C₈₉	—	2	4	no	—
182	#120×C₈₉	—	2	4	no	—
183	C₄×Q₈×C₈₉	—	2	1	no	—
184	C₄×Q₈×C₈₉	—	2	1	no	—
185	C₄×Q₈×C₈₉	—	2	2	no	—
186	C₄×Q₈×C₈₉	C₂³	1	2	yes	complemented
187	C₄×Q₈×C₈₉	C₂³	1	2	yes	complemented
188	C₄×Q₈×C₈₉	C₂³	1	2	yes	complemented
189	C₄×D₄×C₈₉	—	2	1	no	—
190	C₄×D₄×C₈₉	—	2	1	no	—
191	C₄×D₄×C₈₉	—	2	2	no	—
192	C₄×D₄×C₈₉	—	2	2	no	—
193	C₄×D₄×C₈₉	C₂³	1	2	yes	complemented
194	#117×C₈₉	—	2	2	no	—
195	#117×C₈₉	—	2	1	no	—
196	#117×C₈₉	—	2	2	no	—
197	#117×C₈₉	—	2	2	no	—
198	#117×C₈₉	D₄	1	1	yes	characteristic
199	#117×C₈₉	D₄	1	2	yes	—
200	#117×C₈₉	D₄	1	1	yes	characteristic
201	#117×C₈₉	C₂³	1	1	yes	characteristic
202	#117×C₈₉	C₂³	1	1	yes	characteristic
203	#117×C₈₉	C₂³	1	1	yes	characteristic
204	#117×C₈₉	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
206	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
207	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
208	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
209	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
211	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
212	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
213	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
214	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
215	C₄⋊C₈×C₈₉	C₂³	1	4	yes	complemented
216	C₄⋊C₈×C₈₉	C₂³	1	4	yes	complemented
217	#103×C₈₉	C₂³	1	2	yes	complemented
218	#103×C₈₉	C₂³	1	2	yes	complemented
219	#103×C₈₉	C₂³	1	4	yes	complemented
220	#102×C₈₉	C₂³	1	4	yes	—
221	#102×C₈₉	C₂³	1	4	yes	—
222	#102×C₈₉	C₂³	1	4	yes	—
223	#102×C₈₉	C₂³	1	4	yes	—
224	#102×C₈₉	C₂³	1	2	yes	complemented
225	#102×C₈₉	C₂³	1	2	yes	complemented
226	#102×C₈₉	C₂³	1	4	yes	complemented
227	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
228	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
229	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
230	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
231	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
232	#97×C₈₉	C₂³	1	4	yes	complemented
233	C₄×C₈×C₈₉	C₂³	1	4	yes	complemented
234	C₂⁴×C₈₉	—	2	2	no	—
235	C₂⁴×C₈₉	—	2	1	no	—
236	C₂⁴×C₈₉	—	2	2	no	—
237	C₂⁴×C₈₉	—	2	2	no	—
238	C₂⁴×C₈₉	—	4	4	no	—
239	C₂⁴×C₈₉	—	8	2	no	—
240	C₂⁴×C₈₉	—	8	2	no	—
241	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
242	#41×C₈₉	—	2	4	no	—
243	#41×C₈₉	—	2	4	no	—
244	#41×C₈₉	—	2	4	no	—
245	#41×C₈₉	—	4	2	no	—
246	#41×C₈₉	—	4	2	no	—
247	#41×C₈₉	—	4	4	no	—
248	#41×C₈₉	—	4	4	no	—
249	C₂×Q₈×C₈₉	—	2	1	no	—
250	C₂×Q₈×C₈₉	—	2	1	no	—
251	C₂×Q₈×C₈₉	—	2	2	no	—
252	C₂×Q₈×C₈₉	—	2	4	no	—
253	C₂×Q₈×C₈₉	—	4	2	no	—
254	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
255	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
256	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
257	C₂×D₄×C₈₉	—	2	1	no	—
258	C₂×D₄×C₈₉	—	2	1	no	—
259	C₂×D₄×C₈₉	—	2	2	no	—
260	C₂×D₄×C₈₉	—	2	2	no	—
261	C₂×D₄×C₈₉	—	2	1	no	—
262	C₂×D₄×C₈₉	—	2	2	no	—
263	C₂×D₄×C₈₉	—	2	2	no	—
264	C₂×D₄×C₈₉	—	2	2	no	—
265	C₂×D₄×C₈₉	—	2	1	no	—
266	C₂×D₄×C₈₉	—	2	4	no	—
267	C₂×D₄×C₈₉	—	2	4	no	—
268	C₂×D₄×C₈₉	—	2	4	no	—
269	C₂×D₄×C₈₉	—	2	4	no	—
270	C₂×D₄×C₈₉	—	2	4	no	—
271	C₂×D₄×C₈₉	—	2	4	no	—
272	C₂×D₄×C₈₉	—	4	4	no	—
273	C₂×D₄×C₈₉	—	4	4	no	—
274	C₂×D₄×C₈₉	—	4	2	no	—
275	C₂×D₄×C₈₉	—	4	4	no	—
276	C₂×D₄×C₈₉	—	4	4	no	—
277	C₂×D₄×C₈₉	—	4	4	no	—
278	C₂×D₄×C₈₉	—	4	4	no	—
279	C₂×D₄×C₈₉	—	8	4	no	—
280	C₂×D₄×C₈₉	—	8	4	no	—
281	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
282	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
283	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₈₉	—	2	4	no	—
285	C₂²×C₄×C₈₉	—	2	1	no	—
286	C₂²×C₄×C₈₉	—	2	1	no	—
287	C₂²×C₄×C₈₉	—	2	1	no	—
288	C₂²×C₄×C₈₉	—	2	1	no	—
289	C₂²×C₄×C₈₉	—	2	2	no	—
290	C₂²×C₄×C₈₉	—	2	2	no	—
291	C₂²×C₄×C₈₉	—	2	2	no	—
292	C₂²×C₄×C₈₉	—	4	4	no	—
293	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
294	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
295	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
298	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
301	Q₁₆×C₈₉	—	4	2	no	—
302	Q₁₆×C₈₉	—	4	4	no	—
303	SD₁₆×C₈₉	—	4	4	no	—
304	SD₁₆×C₈₉	—	4	4	no	—
305	SD₁₆×C₈₉	—	4	4	no	—
306	SD₁₆×C₈₉	—	4	2	no	—
307	SD₁₆×C₈₉	—	4	2	no	—
308	SD₁₆×C₈₉	—	4	4	no	—
309	D₈×C₈₉	—	4	4	no	—
310	D₈×C₈₉	—	4	2	no	—
311	M₁₆×C₈₉	—	2	4	no	—
312	C₂×C₈×C₈₉	—	2	4	no	—
313	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
314	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
315	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
316	C₄⋊C₄×C₈₉	—	2	1	no	—
317	C₄⋊C₄×C₈₉	—	2	2	no	—
318	C₄⋊C₄×C₈₉	—	2	2	no	—
319	C₄⋊C₄×C₈₉	—	2	2	no	—
320	C₄⋊C₄×C₈₉	—	2	2	no	—
321	C₄⋊C₄×C₈₉	—	2	2	no	—
322	C₄⋊C₄×C₈₉	—	2	2	no	—
323	C₄⋊C₄×C₈₉	—	2	2	no	—
324	C₄⋊C₄×C₈₉	—	2	2	no	—
325	C₄⋊C₄×C₈₉	—	2	1	no	—
326	C₄⋊C₄×C₈₉	—	2	2	no	—
327	C₄⋊C₄×C₈₉	—	2	1	no	—
328	C₄⋊C₄×C₈₉	—	2	2	no	—
329	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
330	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
331	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
332	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
333	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
334	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
335	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
336	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
337	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
338	C₂²⋊C₄×C₈₉	—	2	2	no	—
339	C₂²⋊C₄×C₈₉	—	2	2	no	—
340	C₂²⋊C₄×C₈₉	—	2	1	no	—
341	C₂²⋊C₄×C₈₉	—	2	1	no	—
342	C₂²⋊C₄×C₈₉	—	2	1	no	—
343	C₂²⋊C₄×C₈₉	—	2	4	no	—
344	C₂²⋊C₄×C₈₉	—	2	4	no	—
345	C₂²⋊C₄×C₈₉	—	2	4	no	—
346	C₂²⋊C₄×C₈₉	—	2	4	no	—
347	C₂²⋊C₄×C₈₉	—	2	1	no	—
348	C₂²⋊C₄×C₈₉	—	2	2	no	—
349	C₂²⋊C₄×C₈₉	—	2	2	no	—
350	C₂²⋊C₄×C₈₉	—	2	1	no	—
351	C₂²⋊C₄×C₈₉	—	2	2	no	—
352	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
353	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
354	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
355	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
356	C₄²×C₈₉	—	2	2	no	—
357	C₄²×C₈₉	—	2	2	no	—
358	C₄²×C₈₉	—	2	2	no	—
359	C₄²×C₈₉	—	2	1	no	—
360	C₄²×C₈₉	C₂×D₄	1	2	yes	—
361	C₄²×C₈₉	C₂×D₄	1	2	yes	—
362	C₄²×C₈₉	C₂⁴	1	2	yes	—
363	C₄²×C₈₉	C₂⁴	1	2	yes	—
364	C₂³×C₈₉	—	2	2	no	—
365	C₂³×C₈₉	—	2	2	no	—
366	C₂³×C₈₉	—	2	1	no	—
367	C₂³×C₈₉	—	2	4	no	—
368	C₂³×C₈₉	—	2	2	no	—
369	C₂³×C₈₉	—	4	1	no	—
370	C₂³×C₈₉	—	4	2	no	—
371	C₂³×C₈₉	—	4	4	no	—
372	C₂³×C₈₉	—	4	4	no	—
373	C₂³×C₈₉	—	4	2	no	—
374	C₂³×C₈₉	—	4	4	no	—
375	C₂³×C₈₉	—	4	4	no	—
376	C₂³×C₈₉	—	4	2	no	—
377	C₂³×C₈₉	—	4	4	no	—
378	C₂³×C₈₉	—	8	2	no	—
379	C₂³×C₈₉	—	8	2	no	—
380	C₂³×C₈₉	—	8	2	no	—
381	C₂³×C₈₉	—	8	2	no	—
382	C₂³×C₈₉	—	8	16	no	—
383	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
384	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
385	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
386	Q₈×C₈₉	—	2	4	no	—
387	Q₈×C₈₉	—	2	2	no	—
388	Q₈×C₈₉	—	2	2	no	—
389	Q₈×C₈₉	—	2	2	no	—
390	Q₈×C₈₉	—	4	2	no	—
391	Q₈×C₈₉	—	4	2	no	—
392	Q₈×C₈₉	—	8	2	no	—
393	D₄×C₈₉	—	2	2	no	—
394	D₄×C₈₉	—	2	4	no	—
395	D₄×C₈₉	—	2	2	no	—
396	D₄×C₈₉	—	2	4	no	—
397	D₄×C₈₉	—	2	2	no	—
398	D₄×C₈₉	—	4	4	no	—
399	D₄×C₈₉	—	4	4	no	—
400	D₄×C₈₉	—	4	2	no	—
401	D₄×C₈₉	—	4	4	no	—
402	D₄×C₈₉	—	4	4	no	—
403	D₄×C₈₉	—	4	2	no	—
404	D₄×C₈₉	—	4	2	no	—
405	D₄×C₈₉	—	4	4	no	—
406	D₄×C₈₉	—	8	4	no	—
407	D₄×C₈₉	—	8	4	no	—
408	D₄×C₈₉	—	8	4	no	—
409	D₄×C₈₉	—	8	4	no	—
410	D₄×C₈₉	—	8	1	no	—
411	C₂×C₄×C₈₉	—	2	2	no	—
412	C₂×C₄×C₈₉	—	2	4	no	—
413	C₂×C₄×C₈₉	—	2	2	no	—
414	C₂×C₄×C₈₉	—	2	2	no	—
415	C₂×C₄×C₈₉	—	2	2	no	—
416	C₂×C₄×C₈₉	—	2	2	no	—
417	C₂×C₄×C₈₉	—	2	1	no	—
418	C₂×C₄×C₈₉	—	2	1	no	—
419	C₂×C₄×C₈₉	—	2	2	no	—
420	C₂×C₄×C₈₉	—	2	1	no	—
421	C₂×C₄×C₈₉	—	2	2	no	—
422	C₂×C₄×C₈₉	—	2	2	no	—
423	C₂×C₄×C₈₉	—	4	2	no	—
424	C₂×C₄×C₈₉	—	4	4	no	—
425	C₂×C₄×C₈₉	—	4	2	no	—
426	C₂×C₄×C₈₉	—	4	2	no	—
427	C₂×C₄×C₈₉	—	4	4	no	—
428	C₂×C₄×C₈₉	—	4	2	no	—
429	C₂×C₄×C₈₉	—	8	2	no	—
430	C₂×C₄×C₈₉	—	8	1	no	—
431	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
433	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
435	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
436	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
439	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
440	C₈×C₈₉	—	2	2	no	—
441	C₈×C₈₉	—	2	2	no	—
442	C₈×C₈₉	—	2	4	no	—
443	C₂²×C₈₉	—	2	1	no	—
444	C₂²×C₈₉	—	2	1	no	—
445	C₂²×C₈₉	—	2	1	no	—
446	C₂²×C₈₉	—	2	1	no	—
447	C₂²×C₈₉	—	2	1	no	—
448	C₂²×C₈₉	—	2	1	no	—
449	C₂²×C₈₉	—	2	1	no	—
450	C₂²×C₈₉	—	4	4	no	—
451	C₂²×C₈₉	—	4	1	no	—
452	C₂²×C₈₉	—	4	2	no	—
453	C₂²×C₈₉	—	4	4	no	—
454	C₂²×C₈₉	—	4	2	no	—
455	C₂²×C₈₉	—	4	1	no	—
456	C₂²×C₈₉	—	4	4	no	—
457	C₂²×C₈₉	—	4	1	no	—
458	C₂²×C₈₉	—	4	2	no	—
459	C₂²×C₈₉	—	4	4	no	—
460	C₂²×C₈₉	—	8	4	no	—
461	C₂²×C₈₉	—	8	8	no	—
462	C₂²×C₈₉	—	8	8	no	—
463	C₂²×C₈₉	—	8	8	no	—
464	C₂²×C₈₉	#535	1	2	yes	—
465	C₂²×C₈₉	#577	1	2	yes	—
466	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
467	C₄×C₈₉	—	2	2	no	—
468	C₄×C₈₉	—	2	2	no	—
469	C₄×C₈₉	—	2	1	no	—
470	C₄×C₈₉	—	2	1	no	—
471	C₄×C₈₉	—	2	2	no	—
472	C₄×C₈₉	—	2	2	no	—
473	C₄×C₈₉	—	4	2	no	—
474	C₄×C₈₉	—	4	1	no	—
475	C₄×C₈₉	—	4	2	no	—
476	C₄×C₈₉	—	4	1	no	—
477	C₄×C₈₉	—	4	2	no	—
478	C₄×C₈₉	—	4	1	no	—
479	C₄×C₈₉	#535	1	2	yes	—
480	C₄×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
481	#60812	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
482	C₂×C₈₉	—	2	2	no	—
483	C₂×C₈₉	—	2	2	no	—
484	C₂×C₈₉	—	4	1	no	—
485	C₂×C₈₉	—	8	1	no	—
486	C₂×C₈₉	—	8	2	no	—
487	C₂×C₈₉	—	8	4	no	—
488	C₂×C₈₉	C₂×#535	1	1	yes	characteristic
489	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
490	C₂×C₈₉	#3585	1	1	yes	characteristic
491	#3495	C₂×C₈₉	1	1	yes	characteristic, complemented
492	C₂×#535	C₂×C₈₉	1	1	yes	characteristic, complemented
493	#3224	C₂×C₈₉	1	4	yes	complemented
494	#3222	C₂×C₈₉	1	4	yes	complemented
495	#3217	C₂×C₈₉	1	2	yes	complemented
496	#3215	C₂×C₈₉	1	2	yes	complemented
497	#3211	C₂×C₈₉	1	2	yes	complemented
498	#3208	C₂×C₈₉	1	2	yes	complemented
499	#3154	C₂×C₈₉	1	2	yes	complemented
500	#3136	C₂×C₈₉	1	2	yes	complemented
501	#3045	C₂×C₈₉	1	2	yes	complemented
502	#3043	C₂×C₈₉	1	2	yes	complemented
503	#3007	C₂×C₈₉	1	1	yes	characteristic, complemented
504	#3003	C₂×C₈₉	1	1	yes	characteristic, complemented
505	#3002	C₂×C₈₉	1	1	yes	characteristic, complemented
506	C₂×#450	C₂×C₈₉	1	1	yes	characteristic, complemented
507	#2924	C₂×C₈₉	1	1	yes	characteristic, complemented
508	C₈₉	#60812	1	1	yes	characteristic, direct product factor, Sylow
509	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
510	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
511	C₂×#137	C₂²×C₈₉	1	2	yes	complemented
512	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	complemented
513	C₂×#135	C₂²×C₈₉	1	2	yes	complemented
514	C₂²×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
515	#556	—	2	1	no	—
516	#554	—	2	1	no	—
517	#552	—	2	2	no	—
518	#552	—	2	1	no	—
519	#552	—	2	1	no	—
520	#551	—	2	2	no	—
521	#544	C₂²×C₈₉	1	1	yes	characteristic, complemented
522	#542	C₂²×C₈₉	1	2	yes	complemented
523	#541	C₂²×C₈₉	1	2	yes	complemented
524	#536	C₂²×C₈₉	1	1	yes	characteristic, complemented
525	#535	—	2	1	no	—
526	#535	—	2	2	no	—
527	#535	—	2	1	no	—
528	#535	C₂²×C₈₉	1	2	yes	—
529	#535	C₂²×C₈₉	1	4	yes	—
530	#535	C₂²×C₈₉	1	2	yes	—
531	#533	C₂²×C₈₉	1	2	yes	complemented
532	C₂×#127	C₂²×C₈₉	1	2	yes	—
533	#529	C₂²×C₈₉	1	2	yes	complemented
534	C₂×#124	C₂²×C₈₉	1	2	yes	—
535	#525	C₂²×C₈₉	1	1	yes	characteristic
536	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
537	C₂×#121	—	2	1	no	—
538	C₂×#121	—	2	1	no	—
539	C₂×#120	—	2	2	no	—
540	#520	C₂²×C₈₉	1	1	yes	characteristic, complemented
541	#519	C₂²×C₈₉	1	1	yes	characteristic, complemented
542	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
543	#497	C₂²×C₈₉	1	4	yes	complemented
544	#496	C₂²×C₈₉	1	4	yes	complemented
545	#495	C₂²×C₈₉	1	4	yes	complemented
546	#492	C₂²×C₈₉	1	4	yes	complemented
547	#490	C₂²×C₈₉	1	4	yes	complemented
548	#489	C₂²×C₈₉	1	4	yes	complemented
549	#488	C₂²×C₈₉	1	4	yes	complemented
550	#486	C₂²×C₈₉	1	4	yes	complemented
551	#464	C₂²×C₈₉	1	4	yes	complemented
552	#464	C₂²×C₈₉	1	4	yes	complemented
553	#464	C₂²×C₈₉	1	4	yes	complemented
554	#463	C₂²×C₈₉	1	4	yes	complemented
555	#460	C₂²×C₈₉	1	4	yes	complemented
556	#460	C₂²×C₈₉	1	4	yes	complemented
557	#460	C₂²×C₈₉	1	4	yes	complemented
558	#459	C₂²×C₈₉	1	4	yes	complemented
559	#452	C₂²×C₈₉	1	2	yes	complemented
560	#452	C₂²×C₈₉	1	4	yes	complemented
561	#451	C₂²×C₈₉	1	2	yes	complemented
562	#451	C₂²×C₈₉	1	1	yes	characteristic, complemented
563	#450	C₂²×C₈₉	1	2	yes	—
564	#450	C₂²×C₈₉	1	2	yes	—
565	#450	C₂²×C₈₉	1	2	yes	—
566	#450	C₂²×C₈₉	1	2	yes	complemented
567	#450	C₂²×C₈₉	1	4	yes	complemented
568	#450	C₂²×C₈₉	1	1	yes	characteristic, complemented
569	#450	C₂²×C₈₉	1	2	yes	complemented
570	#449	C₂²×C₈₉	1	2	yes	complemented
571	#448	C₂²×C₈₉	1	1	yes	characteristic, complemented
572	#447	C₂²×C₈₉	1	2	yes	—
573	#447	C₂²×C₈₉	1	2	yes	complemented
574	#447	C₂²×C₈₉	1	1	yes	characteristic, complemented
575	#433	C₂²×C₈₉	1	4	yes	complemented
576	#432	C₂²×C₈₉	1	2	yes	complemented
577	#431	C₂²×C₈₉	1	2	yes	complemented
578	#424	C₂²×C₈₉	1	2	yes	complemented
579	#418	C₂²×C₈₉	1	2	yes	complemented
580	#417	C₂²×C₈₉	1	2	yes	complemented
581	#416	C₂²×C₈₉	1	2	yes	complemented
582	C₂×#102	C₂²×C₈₉	1	2	yes	complemented
583	#407	C₂²×C₈₉	1	1	yes	characteristic
584	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
585	#405	C₂²×C₈₉	1	2	yes	complemented
586	C₂⁵	—	2	1	no	—
587	C₂×#41	—	2	1	no	—
588	C₂×#41	—	2	1	no	—
589	C₂×#41	—	4	4	no	—
590	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
591	C₂×#41	C₂³×C₈₉	1	2	yes	—
592	C₂×#41	C₂³×C₈₉	1	2	yes	—
593	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
594	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
595	C₂²×D₄	—	2	1	no	—
596	C₂²×D₄	—	2	1	no	—
597	C₂²×D₄	—	2	1	no	—
598	C₂²×D₄	—	2	1	no	—
599	C₂²×D₄	—	2	2	no	—
600	C₂²×D₄	—	2	2	no	—
601	C₂²×D₄	—	4	4	no	—
602	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
603	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
604	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
605	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
606	C₂³×C₄	—	2	1	no	—
607	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
608	#137	—	4	4	no	—
609	AGL(1,ℤ/8)	—	4	4	no	—
610	#135	—	4	4	no	—
611	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	complemented
612	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	complemented
613	C₂×SD₁₆	—	4	4	no	—
614	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
615	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
616	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
617	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	complemented
618	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	complemented
619	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	complemented
620	C₂×D₈	C₂³×C₈₉	1	4	yes	—
621	C₂×D₈	C₂³×C₈₉	1	2	yes	complemented
622	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
623	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
624	C₄⋊Q₈	—	2	1	no	—
625	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	complemented
626	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	complemented
627	#127	—	2	2	no	—
628	#127	—	2	2	no	—
629	#127	C₂³×C₈₉	1	4	yes	—
630	#127	C₂³×C₈₉	1	4	yes	—
631	#126	—	2	2	no	—
632	#126	—	2	2	no	—
633	#126	—	2	2	no	—
634	#126	—	2	2	no	—
635	#125	—	2	2	no	—
636	#125	—	2	2	no	—
637	#125	—	2	1	no	—
638	#125	—	2	2	no	—
639	#125	C₂³×C₈₉	1	2	yes	complemented
640	#124	—	2	2	no	—
641	#124	—	2	2	no	—
642	#124	—	2	2	no	—
643	#124	C₂³×C₈₉	1	4	yes	—
644	#124	C₂³×C₈₉	1	4	yes	—
645	#124	C₂³×C₈₉	1	2	yes	complemented
646	#123	—	2	1	no	—
647	#123	—	2	2	no	—
648	#123	—	2	2	no	—
649	#123	—	2	2	no	—
650	C₂²⋊Q₈	—	2	1	no	—
651	C₂²⋊Q₈	—	2	1	no	—
652	C₂²⋊Q₈	—	2	2	no	—
653	C₂²⋊Q₈	—	2	1	no	—
654	C₂²⋊Q₈	—	2	1	no	—
655	C₂²⋊Q₈	—	2	2	no	—
656	C₂²⋊Q₈	—	2	2	no	—
657	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
658	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
659	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
660	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
661	#121	—	2	2	no	—
662	#121	—	2	2	no	—
663	#121	—	2	2	no	—
664	#121	—	2	4	no	—
665	#121	—	2	2	no	—
666	#121	—	2	4	no	—
667	#121	C₂³×C₈₉	1	1	yes	characteristic
668	#121	C₂³×C₈₉	1	1	yes	characteristic
669	#120	—	2	1	no	—
670	#120	—	2	4	no	—
671	#120	—	2	4	no	—
672	#120	—	2	4	no	—
673	#120	—	2	4	no	—
674	C₄×Q₈	—	2	1	no	—
675	C₄×Q₈	—	2	1	no	—
676	C₄×Q₈	—	2	2	no	—
677	C₄×Q₈	C₂³×C₈₉	1	2	yes	complemented
678	C₄×Q₈	C₂³×C₈₉	1	2	yes	complemented
679	C₄×Q₈	C₂³×C₈₉	1	2	yes	complemented
680	C₄×D₄	—	2	1	no	—
681	C₄×D₄	—	2	1	no	—
682	C₄×D₄	—	2	2	no	—
683	C₄×D₄	—	2	2	no	—
684	C₄×D₄	C₂³×C₈₉	1	2	yes	complemented
685	#117	—	2	2	no	—
686	#117	—	2	1	no	—
687	#117	—	2	2	no	—
688	#117	—	2	2	no	—
689	#117	D₄×C₈₉	1	1	yes	characteristic
690	#117	D₄×C₈₉	1	2	yes	—
691	#117	D₄×C₈₉	1	1	yes	characteristic
692	#117	C₂³×C₈₉	1	1	yes	characteristic
693	#117	C₂³×C₈₉	1	1	yes	characteristic
694	#117	C₂³×C₈₉	1	1	yes	characteristic
695	#117	C₂³×C₈₉	1	2	yes	—
696	C₂×C₄⋊C₄	—	2	1	no	—
697	C₂×C₄⋊C₄	—	2	1	no	—
698	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
699	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
700	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
701	C₂×C₂²⋊C₄	—	2	1	no	—
702	C₂×C₂²⋊C₄	—	2	2	no	—
703	C₂×C₂²⋊C₄	—	2	2	no	—
704	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
705	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
706	C₄⋊C₈	C₂³×C₈₉	1	4	yes	complemented
707	C₄⋊C₈	C₂³×C₈₉	1	4	yes	complemented
708	#103	C₂³×C₈₉	1	2	yes	complemented
709	#103	C₂³×C₈₉	1	2	yes	complemented
710	#103	C₂³×C₈₉	1	4	yes	complemented
711	#102	C₂³×C₈₉	1	4	yes	—
712	#102	C₂³×C₈₉	1	4	yes	—
713	#102	C₂³×C₈₉	1	4	yes	—
714	#102	C₂³×C₈₉	1	4	yes	—
715	#102	C₂³×C₈₉	1	2	yes	complemented
716	#102	C₂³×C₈₉	1	2	yes	complemented
717	#102	C₂³×C₈₉	1	4	yes	complemented
718	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
719	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
720	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
721	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
722	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
723	#97	C₂³×C₈₉	1	4	yes	complemented
724	C₄×C₈	C₂³×C₈₉	1	4	yes	complemented
725	C₂⁴	—	2	2	no	—
726	C₂⁴	—	2	1	no	—
727	C₂⁴	—	2	2	no	—
728	C₂⁴	—	2	2	no	—
729	C₂⁴	—	4	4	no	—
730	C₂⁴	—	8	2	no	—
731	C₂⁴	—	8	2	no	—
732	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
733	#41	—	2	4	no	—
734	#41	—	2	4	no	—
735	#41	—	2	4	no	—
736	#41	—	4	2	no	—
737	#41	—	4	2	no	—
738	#41	—	4	4	no	—
739	#41	—	4	4	no	—
740	C₂×Q₈	—	2	1	no	—
741	C₂×Q₈	—	2	1	no	—
742	C₂×Q₈	—	2	2	no	—
743	C₂×Q₈	—	2	4	no	—
744	C₂×Q₈	—	4	2	no	—
745	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
746	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
747	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
748	C₂×D₄	—	2	1	no	—
749	C₂×D₄	—	2	1	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	2	1	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	1	no	—
757	C₂×D₄	—	2	4	no	—
758	C₂×D₄	—	2	4	no	—
759	C₂×D₄	—	2	4	no	—
760	C₂×D₄	—	2	4	no	—
761	C₂×D₄	—	2	4	no	—
762	C₂×D₄	—	2	4	no	—
763	C₂×D₄	—	4	4	no	—
764	C₂×D₄	—	4	4	no	—
765	C₂×D₄	—	4	2	no	—
766	C₂×D₄	—	4	4	no	—
767	C₂×D₄	—	4	4	no	—
768	C₂×D₄	—	4	4	no	—
769	C₂×D₄	—	4	4	no	—
770	C₂×D₄	—	8	4	no	—
771	C₂×D₄	—	8	4	no	—
772	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
773	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
774	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
775	C₂²×C₄	—	2	4	no	—
776	C₂²×C₄	—	2	1	no	—
777	C₂²×C₄	—	2	1	no	—
778	C₂²×C₄	—	2	1	no	—
779	C₂²×C₄	—	2	1	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	4	4	no	—
784	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
785	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
786	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
787	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
788	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
792	Q₁₆	—	4	2	no	—
793	Q₁₆	—	4	4	no	—
794	SD₁₆	—	4	4	no	—
795	SD₁₆	—	4	4	no	—
796	SD₁₆	—	4	4	no	—
797	SD₁₆	—	4	2	no	—
798	SD₁₆	—	4	2	no	—
799	SD₁₆	—	4	4	no	—
800	D₈	—	4	4	no	—
801	D₈	—	4	2	no	—
802	M₁₆	—	2	4	no	—
803	C₂×C₈	—	2	4	no	—
804	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
805	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
806	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
807	C₄⋊C₄	—	2	1	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	1	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	1	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
821	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
822	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
823	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
824	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
825	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
826	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
827	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
828	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	1	no	—
832	C₂²⋊C₄	—	2	1	no	—
833	C₂²⋊C₄	—	2	1	no	—
834	C₂²⋊C₄	—	2	4	no	—
835	C₂²⋊C₄	—	2	4	no	—
836	C₂²⋊C₄	—	2	4	no	—
837	C₂²⋊C₄	—	2	4	no	—
838	C₂²⋊C₄	—	2	1	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	1	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
844	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
845	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
846	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	1	no	—
851	C₄²	C₂×D₄×C₈₉	1	2	yes	—
852	C₄²	C₂×D₄×C₈₉	1	2	yes	—
853	C₄²	C₂⁴×C₈₉	1	2	yes	—
854	C₄²	C₂⁴×C₈₉	1	2	yes	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	1	no	—
858	C₂³	—	2	4	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	4	1	no	—
861	C₂³	—	4	2	no	—
862	C₂³	—	4	4	no	—
863	C₂³	—	4	4	no	—
864	C₂³	—	4	2	no	—
865	C₂³	—	4	4	no	—
866	C₂³	—	4	4	no	—
867	C₂³	—	4	2	no	—
868	C₂³	—	4	4	no	—
869	C₂³	—	8	2	no	—
870	C₂³	—	8	2	no	—
871	C₂³	—	8	2	no	—
872	C₂³	—	8	2	no	—
873	C₂³	—	8	16	no	—
874	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
875	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
876	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
877	Q₈	—	2	4	no	—
878	Q₈	—	2	2	no	—
879	Q₈	—	2	2	no	—
880	Q₈	—	2	2	no	—
881	Q₈	—	4	2	no	—
882	Q₈	—	4	2	no	—
883	Q₈	—	8	2	no	—
884	D₄	—	2	2	no	—
885	D₄	—	2	4	no	—
886	D₄	—	2	2	no	—
887	D₄	—	2	4	no	—
888	D₄	—	2	2	no	—
889	D₄	—	4	4	no	—
890	D₄	—	4	4	no	—
891	D₄	—	4	2	no	—
892	D₄	—	4	4	no	—
893	D₄	—	4	4	no	—
894	D₄	—	4	2	no	—
895	D₄	—	4	2	no	—
896	D₄	—	4	4	no	—
897	D₄	—	8	4	no	—
898	D₄	—	8	4	no	—
899	D₄	—	8	4	no	—
900	D₄	—	8	4	no	—
901	D₄	—	8	1	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	4	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	4	2	no	—
915	C₂×C₄	—	4	4	no	—
916	C₂×C₄	—	4	2	no	—
917	C₂×C₄	—	4	2	no	—
918	C₂×C₄	—	4	4	no	—
919	C₂×C₄	—	4	2	no	—
920	C₂×C₄	—	8	2	no	—
921	C₂×C₄	—	8	1	no	—
922	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
923	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
924	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
925	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
926	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
927	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
928	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
929	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
930	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
931	C₈	—	2	2	no	—
932	C₈	—	2	2	no	—
933	C₈	—	2	4	no	—
934	C₂²	—	2	1	no	—
935	C₂²	—	2	1	no	—
936	C₂²	—	2	1	no	—
937	C₂²	—	2	1	no	—
938	C₂²	—	2	1	no	—
939	C₂²	—	2	1	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	4	4	no	—
942	C₂²	—	4	1	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	4	no	—
945	C₂²	—	4	1	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	4	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	1	no	—
950	C₂²	—	4	4	no	—
951	C₂²	—	8	8	no	—
952	C₂²	—	8	4	no	—
953	C₂²	—	8	8	no	—
954	C₂²	—	8	8	no	—
955	C₂²	#535×C₈₉	1	2	yes	—
956	C₂²	#577×C₈₉	1	2	yes	—
957	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
958	C₄	—	2	2	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	1	no	—
963	C₄	—	2	1	no	—
964	C₄	—	4	1	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	1	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	1	no	—
969	C₄	—	4	2	no	—
970	C₄	#535×C₈₉	1	2	yes	—
971	C₄	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
972	C₂	—	2	2	no	—
973	C₂	—	2	2	no	—
974	C₂	—	4	1	no	—
975	C₂	—	8	1	no	—
976	C₂	—	8	2	no	—
977	C₂	—	8	4	no	—
978	C₂	C₂×#535×C₈₉	1	1	yes	characteristic
979	C₂	C₂×#577×C₈₉	1	1	yes	characteristic
980	C₂	C₈₉×#3585	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×#3495	C₂	semidirect
2. C₂×#535×C₈₉	C₂	semidirect
3. C₈₉×#3224	C₂	semidirect
4. C₈₉×#3222	C₂	semidirect
5. C₈₉×#3217	C₂	semidirect
6. C₈₉×#3215	C₂	semidirect
7. C₈₉×#3211	C₂	semidirect
8. C₈₉×#3208	C₂	semidirect
9. C₈₉×#3154	C₂	semidirect
10. C₈₉×#3136	C₂	semidirect
11. C₈₉×#3045	C₂	semidirect
12. C₈₉×#3043	C₂	semidirect
13. C₈₉×#3007	C₂	semidirect
14. C₈₉×#3003	C₂	semidirect
15. C₈₉×#3002	C₂	semidirect
16. C₂×#450×C₈₉	C₂	semidirect
17. C₈₉×#2924	C₂	semidirect
20. C₂×#137×C₈₉	C₂²	semidirect
21. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
22. C₂×#135×C₈₉	C₂²	semidirect
23. C₂²×SD₁₆×C₈₉	C₂²	semidirect
30. #544×C₈₉	C₂²	semidirect
31. #542×C₈₉	C₂²	semidirect
32. #541×C₈₉	C₂²	semidirect
33. #536×C₈₉	C₂²	semidirect
40. #533×C₈₉	C₂²	semidirect
42. #529×C₈₉	C₂²	semidirect
49. #520×C₈₉	C₂²	semidirect
50. #519×C₈₉	C₂²	semidirect
52. #497×C₈₉	C₂²	semidirect
53. #496×C₈₉	C₂²	semidirect
54. #495×C₈₉	C₂²	semidirect
55. #492×C₈₉	C₂²	semidirect
56. #490×C₈₉	C₂²	semidirect
57. #489×C₈₉	C₂²	semidirect
58. #488×C₈₉	C₂²	semidirect
59. #486×C₈₉	C₂²	semidirect
60. #464×C₈₉	C₂²	semidirect
61. #464×C₈₉	C₂²	semidirect
62. #464×C₈₉	C₂²	semidirect
63. #463×C₈₉	C₂²	semidirect
64. #460×C₈₉	C₂²	semidirect
65. #460×C₈₉	C₂²	semidirect
66. #460×C₈₉	C₂²	semidirect
67. #459×C₈₉	C₂²	semidirect
68. #452×C₈₉	C₂²	semidirect
69. #452×C₈₉	C₂²	semidirect
70. #451×C₈₉	C₂²	semidirect
71. #451×C₈₉	C₂²	semidirect
75. #450×C₈₉	C₂²	semidirect
76. #450×C₈₉	C₂²	semidirect
77. #450×C₈₉	C₂²	semidirect
78. #450×C₈₉	C₂²	semidirect
79. #449×C₈₉	C₂²	semidirect
80. #448×C₈₉	C₂²	semidirect
82. #447×C₈₉	C₂²	semidirect
83. #447×C₈₉	C₂²	semidirect
84. #433×C₈₉	C₂²	semidirect
85. #432×C₈₉	C₂²	semidirect
86. #431×C₈₉	C₂²	semidirect
87. #424×C₈₉	C₂²	semidirect
88. #418×C₈₉	C₂²	semidirect
89. #417×C₈₉	C₂²	semidirect
90. #416×C₈₉	C₂²	semidirect
91. C₂×#102×C₈₉	C₂²	semidirect
94. #405×C₈₉	C₂²	semidirect
120. C₂×Q₁₆×C₈₉	C₂³	semidirect
121. C₂×Q₁₆×C₈₉	C₂³	semidirect
126. C₂×SD₁₆×C₈₉	C₂³	semidirect
127. C₂×SD₁₆×C₈₉	C₂³	semidirect
128. C₂×SD₁₆×C₈₉	C₂³	semidirect
130. C₂×D₈×C₈₉	C₂³	semidirect
134. C₄⋊Q₈×C₈₉	C₂³	semidirect
135. C₄⋊Q₈×C₈₉	C₂³	semidirect
148. #125×C₈₉	C₂³	semidirect
154. #124×C₈₉	C₂³	semidirect
186. C₄×Q₈×C₈₉	C₂³	semidirect
187. C₄×Q₈×C₈₉	C₂³	semidirect
188. C₄×Q₈×C₈₉	C₂³	semidirect
193. C₄×D₄×C₈₉	C₂³	semidirect
215. C₄⋊C₈×C₈₉	C₂³	semidirect
216. C₄⋊C₈×C₈₉	C₂³	semidirect
217. #103×C₈₉	C₂³	semidirect
218. #103×C₈₉	C₂³	semidirect
219. #103×C₈₉	C₂³	semidirect
224. #102×C₈₉	C₂³	semidirect
225. #102×C₈₉	C₂³	semidirect
226. #102×C₈₉	C₂³	semidirect
232. #97×C₈₉	C₂³	semidirect
233. C₄×C₈×C₈₉	C₂³	semidirect
481. #60812	C₈₉	direct (N × H)
491. #3495	C₂×C₈₉	semidirect
492. C₂×#535	C₂×C₈₉	semidirect
493. #3224	C₂×C₈₉	semidirect
494. #3222	C₂×C₈₉	semidirect
495. #3217	C₂×C₈₉	semidirect
496. #3215	C₂×C₈₉	semidirect
497. #3211	C₂×C₈₉	semidirect
498. #3208	C₂×C₈₉	semidirect
499. #3154	C₂×C₈₉	semidirect
500. #3136	C₂×C₈₉	semidirect
501. #3045	C₂×C₈₉	semidirect
502. #3043	C₂×C₈₉	semidirect
503. #3007	C₂×C₈₉	semidirect
504. #3003	C₂×C₈₉	semidirect
505. #3002	C₂×C₈₉	semidirect
506. C₂×#450	C₂×C₈₉	semidirect
507. #2924	C₂×C₈₉	semidirect
508. C₈₉	#60812	direct (N × H)
511. C₂×#137	C₂²×C₈₉	semidirect
512. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
513. C₂×#135	C₂²×C₈₉	semidirect
514. C₂²×SD₁₆	C₂²×C₈₉	semidirect
521. #544	C₂²×C₈₉	semidirect
522. #542	C₂²×C₈₉	semidirect
523. #541	C₂²×C₈₉	semidirect
524. #536	C₂²×C₈₉	semidirect
531. #533	C₂²×C₈₉	semidirect
533. #529	C₂²×C₈₉	semidirect
540. #520	C₂²×C₈₉	semidirect
541. #519	C₂²×C₈₉	semidirect
543. #497	C₂²×C₈₉	semidirect
544. #496	C₂²×C₈₉	semidirect
545. #495	C₂²×C₈₉	semidirect
546. #492	C₂²×C₈₉	semidirect
547. #490	C₂²×C₈₉	semidirect
548. #489	C₂²×C₈₉	semidirect
549. #488	C₂²×C₈₉	semidirect
550. #486	C₂²×C₈₉	semidirect
551. #464	C₂²×C₈₉	semidirect
552. #464	C₂²×C₈₉	semidirect
553. #464	C₂²×C₈₉	semidirect
554. #463	C₂²×C₈₉	semidirect
555. #460	C₂²×C₈₉	semidirect
556. #460	C₂²×C₈₉	semidirect
557. #460	C₂²×C₈₉	semidirect
558. #459	C₂²×C₈₉	semidirect
559. #452	C₂²×C₈₉	semidirect
560. #452	C₂²×C₈₉	semidirect
561. #451	C₂²×C₈₉	semidirect
562. #451	C₂²×C₈₉	semidirect
566. #450	C₂²×C₈₉	semidirect
567. #450	C₂²×C₈₉	semidirect
568. #450	C₂²×C₈₉	semidirect
569. #450	C₂²×C₈₉	semidirect
570. #449	C₂²×C₈₉	semidirect
571. #448	C₂²×C₈₉	semidirect
573. #447	C₂²×C₈₉	semidirect
574. #447	C₂²×C₈₉	semidirect
575. #433	C₂²×C₈₉	semidirect
576. #432	C₂²×C₈₉	semidirect
577. #431	C₂²×C₈₉	semidirect
578. #424	C₂²×C₈₉	semidirect
579. #418	C₂²×C₈₉	semidirect
580. #417	C₂²×C₈₉	semidirect
581. #416	C₂²×C₈₉	semidirect
582. C₂×#102	C₂²×C₈₉	semidirect
585. #405	C₂²×C₈₉	semidirect
611. C₂×Q₁₆	C₂³×C₈₉	semidirect
612. C₂×Q₁₆	C₂³×C₈₉	semidirect
617. C₂×SD₁₆	C₂³×C₈₉	semidirect
618. C₂×SD₁₆	C₂³×C₈₉	semidirect
619. C₂×SD₁₆	C₂³×C₈₉	semidirect
621. C₂×D₈	C₂³×C₈₉	semidirect
625. C₄⋊Q₈	C₂³×C₈₉	semidirect
626. C₄⋊Q₈	C₂³×C₈₉	semidirect
639. #125	C₂³×C₈₉	semidirect
645. #124	C₂³×C₈₉	semidirect
677. C₄×Q₈	C₂³×C₈₉	semidirect
678. C₄×Q₈	C₂³×C₈₉	semidirect
679. C₄×Q₈	C₂³×C₈₉	semidirect
684. C₄×D₄	C₂³×C₈₉	semidirect
706. C₄⋊C₈	C₂³×C₈₉	semidirect
707. C₄⋊C₈	C₂³×C₈₉	semidirect
708. #103	C₂³×C₈₉	semidirect
709. #103	C₂³×C₈₉	semidirect
710. #103	C₂³×C₈₉	semidirect
715. #102	C₂³×C₈₉	semidirect
716. #102	C₂³×C₈₉	semidirect
717. #102	C₂³×C₈₉	semidirect
723. #97	C₂³×C₈₉	semidirect
724. C₄×C₈	C₂³×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3495	2
C₂×#535×C₈₉	2
C₈₉×#3224	2
C₈₉×#3222	2
C₈₉×#3217	2
C₈₉×#3215	2
C₈₉×#3211	2
C₈₉×#3208	2
C₈₉×#3154	2
C₈₉×#3136	2
C₈₉×#3045	2
C₈₉×#3043	2
C₈₉×#3007	2
C₈₉×#3003	2
C₈₉×#3002	2
C₂×#450×C₈₉	2
C₈₉×#2924	2
#60812	89

Subgroups — C89×#60812 #36438660

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60812 #36438660