Subgroups — C₈₉×#62590 #36440438

Order 22784.

1790 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3365	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3361	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3333	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3332	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3323	C₂	1	4	yes	maximal, complemented
8	C₈₉×#3322	C₂	1	4	yes	maximal, complemented
9	C₈₉×#3237	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3234	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3219	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3217	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3172	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3171	C₂	1	2	yes	maximal, complemented
15	C₈₉×#3142	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3138	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2971	C₂	1	1	yes	maximal, characteristic, complemented
18	#559×C₈₉	—	2	1	no	—
19	#559×C₈₉	C₂²	1	2	yes	—
20	#557×C₈₉	C₂²	1	1	yes	characteristic, complemented
21	#554×C₈₉	C₂²	1	1	yes	characteristic, complemented
22	#554×C₈₉	C₂²	1	1	yes	characteristic, complemented
23	#553×C₈₉	C₂²	1	2	yes	—
24	#552×C₈₉	—	2	2	no	—
25	#552×C₈₉	—	2	1	no	—
26	#552×C₈₉	C₂²	1	2	yes	—
27	#550×C₈₉	—	2	1	no	—
28	#550×C₈₉	C₂²	1	2	yes	—
29	#547×C₈₉	—	2	1	no	—
30	#547×C₈₉	C₂²	1	1	yes	characteristic, complemented
31	#546×C₈₉	—	2	2	no	—
32	#546×C₈₉	C₂²	1	4	yes	—
33	#541×C₈₉	—	2	1	no	—
34	#540×C₈₉	—	2	2	no	—
35	#539×C₈₉	—	2	2	no	—
36	#535×C₈₉	—	2	1	no	—
37	#533×C₈₉	C₂²	1	1	yes	characteristic
38	#533×C₈₉	C₂²	1	1	yes	characteristic
39	#532×C₈₉	C₂²	1	2	yes	—
40	#532×C₈₉	C₂²	1	2	yes	—
41	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
42	#529×C₈₉	C₂²	1	1	yes	characteristic
43	#529×C₈₉	C₂²	1	2	yes	complemented
44	C₂×#125×C₈₉	C₂²	1	2	yes	complemented
45	#520×C₈₉	—	2	1	no	—
46	#518×C₈₉	—	2	1	no	—
47	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
48	#501×C₈₉	C₂²	1	2	yes	complemented
49	#501×C₈₉	C₂²	1	1	yes	characteristic, complemented
50	#497×C₈₉	C₂²	1	1	yes	characteristic, complemented
51	#496×C₈₉	C₂²	1	2	yes	—
52	#491×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	#491×C₈₉	C₂²	1	2	yes	complemented
54	#490×C₈₉	C₂²	1	2	yes	—
55	#490×C₈₉	C₂²	1	2	yes	—
56	#490×C₈₉	C₂²	1	2	yes	—
57	#489×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#488×C₈₉	C₂²	1	4	yes	complemented
59	#488×C₈₉	C₂²	1	4	yes	complemented
60	#486×C₈₉	C₂²	1	2	yes	—
61	#486×C₈₉	C₂²	1	2	yes	—
62	#485×C₈₉	C₂²	1	4	yes	—
63	#481×C₈₉	C₂²	1	4	yes	complemented
64	#480×C₈₉	C₂²	1	4	yes	complemented
65	#478×C₈₉	C₂²	1	4	yes	complemented
66	#478×C₈₉	C₂²	1	4	yes	complemented
67	#477×C₈₉	C₂²	1	2	yes	complemented
68	#475×C₈₉	C₂²	1	2	yes	complemented
69	#470×C₈₉	C₂²	1	2	yes	—
70	#469×C₈₉	C₂²	1	4	yes	complemented
71	#468×C₈₉	C₂²	1	2	yes	—
72	#468×C₈₉	C₂²	1	4	yes	complemented
73	#464×C₈₉	C₂²	1	4	yes	complemented
74	#463×C₈₉	C₂²	1	4	yes	complemented
75	#460×C₈₉	C₂²	1	2	yes	—
76	#459×C₈₉	C₂²	1	2	yes	—
77	#452×C₈₉	C₂²	1	4	yes	complemented
78	#450×C₈₉	C₂²	1	2	yes	—
79	#449×C₈₉	C₂²	1	4	yes	complemented
80	#447×C₈₉	C₂²	1	2	yes	—
81	C₈×Q₈×C₈₉	C₂²	1	2	yes	complemented
82	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
83	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	complemented
84	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
85	C₄×D₈×C₈₉	C₂²	1	4	yes	complemented
86	#436×C₈₉	C₂²	1	4	yes	—
87	#436×C₈₉	C₂²	1	2	yes	complemented
88	#432×C₈₉	C₂²	1	1	yes	characteristic
89	#432×C₈₉	C₂²	1	2	yes	complemented
90	#418×C₈₉	C₂²	1	4	yes	—
91	#417×C₈₉	C₂²	1	4	yes	complemented
92	#417×C₈₉	C₂²	1	4	yes	complemented
93	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
94	C₄×M₁₆×C₈₉	C₂²	1	2	yes	complemented
95	C₂×#41×C₈₉	—	2	1	no	—
96	C₂×#41×C₈₉	—	2	2	no	—
97	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
98	C₂×#41×C₈₉	C₂³	1	4	yes	—
99	C₂²×D₄×C₈₉	—	2	1	no	—
100	C₂²×D₄×C₈₉	—	2	1	no	—
101	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
102	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
105	C₂×D₈×C₈₉	C₂³	1	4	yes	—
106	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
107	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
108	C₄⋊Q₈×C₈₉	—	2	1	no	—
109	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
110	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
111	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
113	#127×C₈₉	—	2	2	no	—
114	#127×C₈₉	—	2	1	no	—
115	#127×C₈₉	—	2	1	no	—
116	#127×C₈₉	C₂³	1	2	yes	—
117	#127×C₈₉	C₂³	1	2	yes	—
118	#126×C₈₉	—	2	2	no	—
119	#126×C₈₉	—	2	2	no	—
120	#126×C₈₉	—	2	1	no	—
121	#126×C₈₉	—	2	2	no	—
122	#125×C₈₉	—	2	2	no	—
123	#125×C₈₉	—	2	2	no	—
124	#125×C₈₉	—	2	1	no	—
125	#125×C₈₉	—	2	2	no	—
126	#125×C₈₉	—	2	2	no	—
127	#125×C₈₉	—	2	1	no	—
128	#125×C₈₉	C₂³	1	2	yes	—
129	#125×C₈₉	C₂³	1	2	yes	—
130	#125×C₈₉	C₂³	1	1	yes	characteristic
131	#125×C₈₉	C₂³	1	2	yes	—
132	#124×C₈₉	—	2	2	no	—
133	#124×C₈₉	—	2	2	no	—
134	#124×C₈₉	C₂³	1	4	yes	—
135	#124×C₈₉	C₂³	1	1	yes	characteristic
136	#123×C₈₉	—	2	2	no	—
137	#123×C₈₉	—	2	1	no	—
138	#123×C₈₉	—	2	2	no	—
139	#123×C₈₉	—	2	4	no	—
140	#123×C₈₉	—	2	4	no	—
141	#123×C₈₉	—	2	2	no	—
142	#123×C₈₉	—	2	2	no	—
143	C₂²⋊Q₈×C₈₉	—	2	1	no	—
144	C₂²⋊Q₈×C₈₉	—	2	1	no	—
145	C₂²⋊Q₈×C₈₉	—	2	1	no	—
146	C₂²⋊Q₈×C₈₉	—	2	1	no	—
147	C₂²⋊Q₈×C₈₉	—	2	2	no	—
148	C₂²⋊Q₈×C₈₉	—	2	1	no	—
149	C₂²⋊Q₈×C₈₉	—	2	2	no	—
150	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
151	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
152	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
153	#121×C₈₉	—	2	2	no	—
154	#121×C₈₉	—	2	2	no	—
155	#121×C₈₉	—	2	2	no	—
156	#121×C₈₉	—	2	2	no	—
157	#121×C₈₉	—	2	4	no	—
158	#121×C₈₉	—	2	4	no	—
159	#121×C₈₉	C₂³	1	1	yes	characteristic
160	#121×C₈₉	C₂³	1	2	yes	—
161	#121×C₈₉	C₂³	1	4	yes	—
162	#120×C₈₉	—	2	4	no	—
163	C₄×Q₈×C₈₉	—	2	1	no	—
164	C₄×Q₈×C₈₉	—	2	1	no	—
165	C₄×Q₈×C₈₉	—	2	1	no	—
166	C₄×Q₈×C₈₉	—	2	1	no	—
167	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
168	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
169	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
170	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₈₉	—	2	1	no	—
173	C₄×D₄×C₈₉	—	2	2	no	—
174	C₄×D₄×C₈₉	—	2	1	no	—
175	C₄×D₄×C₈₉	—	2	2	no	—
176	C₄×D₄×C₈₉	—	2	2	no	—
177	C₄×D₄×C₈₉	—	2	2	no	—
178	C₄×D₄×C₈₉	—	2	2	no	—
179	C₄×D₄×C₈₉	—	2	2	no	—
180	C₄×D₄×C₈₉	—	2	2	no	—
181	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
182	C₄×D₄×C₈₉	D₄	1	2	yes	—
183	C₄×D₄×C₈₉	C₂³	1	2	yes	—
184	C₄×D₄×C₈₉	C₂³	1	4	yes	—
185	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₈₉	C₂³	1	2	yes	—
187	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
188	#117×C₈₉	—	2	1	no	—
189	#117×C₈₉	—	2	2	no	—
190	#117×C₈₉	—	2	1	no	—
191	#117×C₈₉	—	2	2	no	—
192	#117×C₈₉	D₄	1	1	yes	characteristic
193	#117×C₈₉	D₄	1	2	yes	—
194	#117×C₈₉	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
196	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
197	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
198	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
201	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
203	#107×C₈₉	C₂³	1	4	yes	—
204	#107×C₈₉	C₂³	1	2	yes	—
205	#106×C₈₉	C₂³	1	4	yes	—
206	#106×C₈₉	C₂³	1	2	yes	—
207	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
208	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
209	#103×C₈₉	C₂³	1	2	yes	—
210	#103×C₈₉	C₂³	1	2	yes	—
211	#103×C₈₉	C₂³	1	4	yes	—
212	#103×C₈₉	C₂³	1	4	yes	—
213	#103×C₈₉	C₂³	1	2	yes	—
214	#102×C₈₉	C₂³	1	4	yes	—
215	#102×C₈₉	C₂³	1	4	yes	—
216	#102×C₈₉	C₂³	1	4	yes	—
217	#102×C₈₉	C₂³	1	4	yes	—
218	#102×C₈₉	C₂³	1	4	yes	—
219	#102×C₈₉	C₂³	1	4	yes	—
220	#102×C₈₉	C₂³	1	2	yes	—
221	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
222	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
223	#97×C₈₉	C₂³	1	1	yes	characteristic
224	#97×C₈₉	C₂³	1	1	yes	characteristic
225	#97×C₈₉	C₂³	1	2	yes	—
226	C₄×C₈×C₈₉	C₂³	1	2	yes	—
227	C₄×C₈×C₈₉	C₂³	1	4	yes	—
228	C₂⁴×C₈₉	—	2	2	no	—
229	#41×C₈₉	—	4	2	no	—
230	#41×C₈₉	—	4	4	no	—
231	#41×C₈₉	—	4	4	no	—
232	#41×C₈₉	—	4	4	no	—
233	#41×C₈₉	—	8	4	no	—
234	C₂×Q₈×C₈₉	—	2	1	no	—
235	C₂×Q₈×C₈₉	—	2	1	no	—
236	C₂×Q₈×C₈₉	—	2	1	no	—
237	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
238	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
239	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
240	C₂×D₄×C₈₉	—	2	2	no	—
241	C₂×D₄×C₈₉	—	2	1	no	—
242	C₂×D₄×C₈₉	—	2	4	no	—
243	C₂×D₄×C₈₉	—	2	4	no	—
244	C₂×D₄×C₈₉	—	2	2	no	—
245	C₂×D₄×C₈₉	—	2	2	no	—
246	C₂×D₄×C₈₉	—	2	2	no	—
247	C₂×D₄×C₈₉	—	2	2	no	—
248	C₂×D₄×C₈₉	—	2	2	no	—
249	C₂×D₄×C₈₉	—	4	4	no	—
250	C₂×D₄×C₈₉	—	4	4	no	—
251	C₂×D₄×C₈₉	—	8	2	no	—
252	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
253	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
254	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
255	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₈₉	—	2	2	no	—
257	C₂²×C₄×C₈₉	—	2	2	no	—
258	C₂²×C₄×C₈₉	—	2	1	no	—
259	C₂²×C₄×C₈₉	—	2	4	no	—
260	C₂²×C₄×C₈₉	—	2	4	no	—
261	C₂²×C₄×C₈₉	—	2	2	no	—
262	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
265	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
268	Q₁₆×C₈₉	—	4	2	no	—
269	SD₁₆×C₈₉	—	4	4	no	—
270	SD₁₆×C₈₉	—	4	2	no	—
271	D₈×C₈₉	—	4	4	no	—
272	M₁₆×C₈₉	—	4	4	no	—
273	M₁₆×C₈₉	—	4	2	no	—
274	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
275	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
276	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
277	C₄⋊C₄×C₈₉	—	2	2	no	—
278	C₄⋊C₄×C₈₉	—	2	1	no	—
279	C₄⋊C₄×C₈₉	—	2	1	no	—
280	C₄⋊C₄×C₈₉	—	2	2	no	—
281	C₄⋊C₄×C₈₉	—	2	1	no	—
282	C₄⋊C₄×C₈₉	—	2	2	no	—
283	C₄⋊C₄×C₈₉	—	2	2	no	—
284	C₄⋊C₄×C₈₉	—	2	2	no	—
285	C₄⋊C₄×C₈₉	—	2	2	no	—
286	C₄⋊C₄×C₈₉	—	2	2	no	—
287	C₄⋊C₄×C₈₉	—	2	2	no	—
288	C₄⋊C₄×C₈₉	—	2	1	no	—
289	C₄⋊C₄×C₈₉	—	2	1	no	—
290	C₄⋊C₄×C₈₉	—	2	1	no	—
291	C₄⋊C₄×C₈₉	—	2	2	no	—
292	C₄⋊C₄×C₈₉	—	2	1	no	—
293	C₄⋊C₄×C₈₉	—	2	2	no	—
294	C₄⋊C₄×C₈₉	—	2	1	no	—
295	C₄⋊C₄×C₈₉	—	2	2	no	—
296	C₄⋊C₄×C₈₉	—	2	1	no	—
297	C₄⋊C₄×C₈₉	—	2	2	no	—
298	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
299	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
300	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
304	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
305	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
306	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
307	C₂²⋊C₄×C₈₉	—	2	2	no	—
308	C₂²⋊C₄×C₈₉	—	2	2	no	—
309	C₂²⋊C₄×C₈₉	—	2	2	no	—
310	C₂²⋊C₄×C₈₉	—	2	1	no	—
311	C₂²⋊C₄×C₈₉	—	2	4	no	—
312	C₂²⋊C₄×C₈₉	—	2	4	no	—
313	C₂²⋊C₄×C₈₉	—	2	1	no	—
314	C₂²⋊C₄×C₈₉	—	2	1	no	—
315	C₂²⋊C₄×C₈₉	—	2	1	no	—
316	C₂²⋊C₄×C₈₉	—	2	2	no	—
317	C₂²⋊C₄×C₈₉	—	2	4	no	—
318	C₂²⋊C₄×C₈₉	—	2	4	no	—
319	C₂²⋊C₄×C₈₉	—	2	2	no	—
320	C₂²⋊C₄×C₈₉	—	2	1	no	—
321	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
322	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
323	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
324	C₄²×C₈₉	—	2	2	no	—
325	C₄²×C₈₉	—	2	2	no	—
326	C₄²×C₈₉	—	2	2	no	—
327	C₄²×C₈₉	—	2	1	no	—
328	C₄²×C₈₉	C₂×D₄	1	2	yes	—
329	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₈₉	C₂×D₄	1	2	yes	—
332	C₄²×C₈₉	C₂⁴	1	2	yes	—
333	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
334	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
335	C₂³×C₈₉	—	2	1	no	—
336	C₂³×C₈₉	—	2	4	no	—
337	C₂³×C₈₉	—	4	4	no	—
338	C₂³×C₈₉	—	8	2	no	—
339	C₂³×C₈₉	—	8	2	no	—
340	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
341	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
342	Q₈×C₈₉	—	2	2	no	—
343	Q₈×C₈₉	—	2	2	no	—
344	Q₈×C₈₉	—	2	2	no	—
345	Q₈×C₈₉	—	2	2	no	—
346	Q₈×C₈₉	—	4	2	no	—
347	Q₈×C₈₉	—	4	2	no	—
348	Q₈×C₈₉	—	8	1	no	—
349	D₄×C₈₉	—	2	2	no	—
350	D₄×C₈₉	—	2	2	no	—
351	D₄×C₈₉	—	2	4	no	—
352	D₄×C₈₉	—	2	4	no	—
353	D₄×C₈₉	—	4	2	no	—
354	D₄×C₈₉	—	4	4	no	—
355	D₄×C₈₉	—	4	4	no	—
356	D₄×C₈₉	—	4	4	no	—
357	D₄×C₈₉	—	4	4	no	—
358	D₄×C₈₉	—	8	2	no	—
359	D₄×C₈₉	—	8	2	no	—
360	D₄×C₈₉	—	8	1	no	—
361	D₄×C₈₉	—	8	4	no	—
362	D₄×C₈₉	—	8	4	no	—
363	C₂×C₄×C₈₉	—	2	2	no	—
364	C₂×C₄×C₈₉	—	2	2	no	—
365	C₂×C₄×C₈₉	—	2	4	no	—
366	C₂×C₄×C₈₉	—	2	1	no	—
367	C₂×C₄×C₈₉	—	2	2	no	—
368	C₂×C₄×C₈₉	—	2	2	no	—
369	C₂×C₄×C₈₉	—	2	2	no	—
370	C₂×C₄×C₈₉	—	2	2	no	—
371	C₂×C₄×C₈₉	—	2	1	no	—
372	C₂×C₄×C₈₉	—	2	1	no	—
373	C₂×C₄×C₈₉	—	4	1	no	—
374	C₂×C₄×C₈₉	—	4	2	no	—
375	C₂×C₄×C₈₉	—	4	2	no	—
376	C₂×C₄×C₈₉	—	4	4	no	—
377	C₂×C₄×C₈₉	—	4	2	no	—
378	C₂×C₄×C₈₉	—	8	2	no	—
379	C₂×C₄×C₈₉	—	8	4	no	—
380	C₂×C₄×C₈₉	—	8	4	no	—
381	C₂×C₄×C₈₉	—	8	2	no	—
382	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
387	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
391	C₈×C₈₉	—	2	2	no	—
392	C₈×C₈₉	—	2	4	no	—
393	C₈×C₈₉	—	2	2	no	—
394	C₂²×C₈₉	—	2	2	no	—
395	C₂²×C₈₉	—	2	1	no	—
396	C₂²×C₈₉	—	2	2	no	—
397	C₂²×C₈₉	—	2	1	no	—
398	C₂²×C₈₉	—	2	1	no	—
399	C₂²×C₈₉	—	2	2	no	—
400	C₂²×C₈₉	—	4	1	no	—
401	C₂²×C₈₉	—	4	4	no	—
402	C₂²×C₈₉	—	4	4	no	—
403	C₂²×C₈₉	—	4	1	no	—
404	C₂²×C₈₉	—	4	1	no	—
405	C₂²×C₈₉	—	4	4	no	—
406	C₂²×C₈₉	—	16	4	no	—
407	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
408	C₄×C₈₉	—	2	1	no	—
409	C₄×C₈₉	—	2	2	no	—
410	C₄×C₈₉	—	2	1	no	—
411	C₄×C₈₉	—	2	2	no	—
412	C₄×C₈₉	—	2	1	no	—
413	C₄×C₈₉	—	2	1	no	—
414	C₄×C₈₉	—	2	2	no	—
415	C₄×C₈₉	—	4	1	no	—
416	C₄×C₈₉	—	4	2	no	—
417	C₄×C₈₉	—	4	2	no	—
418	C₄×C₈₉	—	4	2	no	—
419	C₄×C₈₉	—	4	1	no	—
420	C₄×C₈₉	—	4	1	no	—
421	C₄×C₈₉	—	4	2	no	—
422	C₄×C₈₉	#575	1	2	yes	—
423	C₄×C₈₉	#585	1	2	yes	—
424	#62590	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
425	C₂×C₈₉	—	4	2	no	—
426	C₂×C₈₉	—	4	1	no	—
427	C₂×C₈₉	—	8	1	no	—
428	C₂×C₈₉	—	8	4	no	—
429	C₂×C₈₉	#3500	1	1	yes	characteristic
430	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
431	C₂×C₈₉	#3585	1	1	yes	characteristic
432	#3515	C₂×C₈₉	1	1	yes	characteristic, complemented
433	#3508	C₂×C₈₉	1	1	yes	characteristic, complemented
434	#3365	C₂×C₈₉	1	2	yes	complemented
435	#3361	C₂×C₈₉	1	2	yes	complemented
436	#3333	C₂×C₈₉	1	2	yes	complemented
437	#3332	C₂×C₈₉	1	2	yes	complemented
438	#3323	C₂×C₈₉	1	4	yes	complemented
439	#3322	C₂×C₈₉	1	4	yes	complemented
440	#3237	C₂×C₈₉	1	1	yes	characteristic, complemented
441	#3234	C₂×C₈₉	1	2	yes	complemented
442	#3219	C₂×C₈₉	1	2	yes	complemented
443	#3217	C₂×C₈₉	1	1	yes	characteristic, complemented
444	#3172	C₂×C₈₉	1	1	yes	characteristic, complemented
445	#3171	C₂×C₈₉	1	2	yes	complemented
446	#3142	C₂×C₈₉	1	2	yes	complemented
447	#3138	C₂×C₈₉	1	1	yes	characteristic, complemented
448	#2971	C₂×C₈₉	1	1	yes	characteristic, complemented
449	C₈₉	#62590	1	1	yes	characteristic, direct product factor, Sylow
450	#559	—	2	1	no	—
451	#559	C₂²×C₈₉	1	2	yes	—
452	#557	C₂²×C₈₉	1	1	yes	characteristic, complemented
453	#554	C₂²×C₈₉	1	1	yes	characteristic, complemented
454	#554	C₂²×C₈₉	1	1	yes	characteristic, complemented
455	#553	C₂²×C₈₉	1	2	yes	—
456	#552	—	2	2	no	—
457	#552	—	2	1	no	—
458	#552	C₂²×C₈₉	1	2	yes	—
459	#550	—	2	1	no	—
460	#550	C₂²×C₈₉	1	2	yes	—
461	#547	—	2	1	no	—
462	#547	C₂²×C₈₉	1	1	yes	characteristic, complemented
463	#546	—	2	2	no	—
464	#546	C₂²×C₈₉	1	4	yes	—
465	#541	—	2	1	no	—
466	#540	—	2	2	no	—
467	#539	—	2	2	no	—
468	#535	—	2	1	no	—
469	#533	C₂²×C₈₉	1	1	yes	characteristic
470	#533	C₂²×C₈₉	1	1	yes	characteristic
471	#532	C₂²×C₈₉	1	2	yes	—
472	#532	C₂²×C₈₉	1	2	yes	—
473	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
474	#529	C₂²×C₈₉	1	1	yes	characteristic
475	#529	C₂²×C₈₉	1	2	yes	complemented
476	C₂×#125	C₂²×C₈₉	1	2	yes	complemented
477	#520	—	2	1	no	—
478	#518	—	2	1	no	—
479	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
480	#501	C₂²×C₈₉	1	2	yes	complemented
481	#501	C₂²×C₈₉	1	1	yes	characteristic, complemented
482	#497	C₂²×C₈₉	1	1	yes	characteristic, complemented
483	#496	C₂²×C₈₉	1	2	yes	—
484	#491	C₂²×C₈₉	1	1	yes	characteristic, complemented
485	#491	C₂²×C₈₉	1	2	yes	complemented
486	#490	C₂²×C₈₉	1	2	yes	—
487	#490	C₂²×C₈₉	1	2	yes	—
488	#490	C₂²×C₈₉	1	2	yes	—
489	#489	C₂²×C₈₉	1	1	yes	characteristic, complemented
490	#488	C₂²×C₈₉	1	4	yes	complemented
491	#488	C₂²×C₈₉	1	4	yes	complemented
492	#486	C₂²×C₈₉	1	2	yes	—
493	#486	C₂²×C₈₉	1	2	yes	—
494	#485	C₂²×C₈₉	1	4	yes	—
495	#481	C₂²×C₈₉	1	4	yes	complemented
496	#480	C₂²×C₈₉	1	4	yes	complemented
497	#478	C₂²×C₈₉	1	4	yes	complemented
498	#478	C₂²×C₈₉	1	4	yes	complemented
499	#477	C₂²×C₈₉	1	2	yes	complemented
500	#475	C₂²×C₈₉	1	2	yes	complemented
501	#470	C₂²×C₈₉	1	2	yes	—
502	#469	C₂²×C₈₉	1	4	yes	complemented
503	#468	C₂²×C₈₉	1	2	yes	—
504	#468	C₂²×C₈₉	1	4	yes	complemented
505	#464	C₂²×C₈₉	1	4	yes	complemented
506	#463	C₂²×C₈₉	1	4	yes	complemented
507	#460	C₂²×C₈₉	1	2	yes	—
508	#459	C₂²×C₈₉	1	2	yes	—
509	#452	C₂²×C₈₉	1	4	yes	complemented
510	#450	C₂²×C₈₉	1	2	yes	—
511	#449	C₂²×C₈₉	1	4	yes	complemented
512	#447	C₂²×C₈₉	1	2	yes	—
513	C₈×Q₈	C₂²×C₈₉	1	2	yes	complemented
514	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
515	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
516	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	complemented
517	C₄×D₈	C₂²×C₈₉	1	4	yes	complemented
518	#436	C₂²×C₈₉	1	4	yes	—
519	#436	C₂²×C₈₉	1	2	yes	complemented
520	#432	C₂²×C₈₉	1	1	yes	characteristic
521	#432	C₂²×C₈₉	1	2	yes	complemented
522	#418	C₂²×C₈₉	1	4	yes	—
523	#417	C₂²×C₈₉	1	4	yes	complemented
524	#417	C₂²×C₈₉	1	4	yes	complemented
525	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
526	C₄×M₁₆	C₂²×C₈₉	1	2	yes	complemented
527	C₂×#41	—	2	1	no	—
528	C₂×#41	—	2	2	no	—
529	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
530	C₂×#41	C₂³×C₈₉	1	4	yes	—
531	C₂²×D₄	—	2	1	no	—
532	C₂²×D₄	—	2	1	no	—
533	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
534	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
535	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
536	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
537	C₂×D₈	C₂³×C₈₉	1	4	yes	—
538	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
539	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
540	C₄⋊Q₈	—	2	1	no	—
541	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
542	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
543	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
544	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
545	#127	—	2	2	no	—
546	#127	—	2	1	no	—
547	#127	—	2	1	no	—
548	#127	C₂³×C₈₉	1	2	yes	—
549	#127	C₂³×C₈₉	1	2	yes	—
550	#126	—	2	2	no	—
551	#126	—	2	2	no	—
552	#126	—	2	1	no	—
553	#126	—	2	2	no	—
554	#125	—	2	2	no	—
555	#125	—	2	2	no	—
556	#125	—	2	1	no	—
557	#125	—	2	2	no	—
558	#125	—	2	2	no	—
559	#125	—	2	1	no	—
560	#125	C₂³×C₈₉	1	1	yes	characteristic
561	#125	C₂³×C₈₉	1	2	yes	—
562	#125	C₂³×C₈₉	1	2	yes	—
563	#125	C₂³×C₈₉	1	2	yes	—
564	#124	—	2	2	no	—
565	#124	—	2	2	no	—
566	#124	C₂³×C₈₉	1	1	yes	characteristic
567	#124	C₂³×C₈₉	1	4	yes	—
568	#123	—	2	2	no	—
569	#123	—	2	1	no	—
570	#123	—	2	2	no	—
571	#123	—	2	4	no	—
572	#123	—	2	4	no	—
573	#123	—	2	2	no	—
574	#123	—	2	2	no	—
575	C₂²⋊Q₈	—	2	1	no	—
576	C₂²⋊Q₈	—	2	1	no	—
577	C₂²⋊Q₈	—	2	1	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	—	2	1	no	—
581	C₂²⋊Q₈	—	2	2	no	—
582	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
583	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
584	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
585	#121	—	2	2	no	—
586	#121	—	2	2	no	—
587	#121	—	2	2	no	—
588	#121	—	2	2	no	—
589	#121	—	2	4	no	—
590	#121	—	2	4	no	—
591	#121	C₂³×C₈₉	1	1	yes	characteristic
592	#121	C₂³×C₈₉	1	2	yes	—
593	#121	C₂³×C₈₉	1	4	yes	—
594	#120	—	2	4	no	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×Q₈	—	2	1	no	—
597	C₄×Q₈	—	2	1	no	—
598	C₄×Q₈	—	2	1	no	—
599	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
602	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
603	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
614	C₄×D₄	D₄×C₈₉	1	2	yes	—
615	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
616	C₄×D₄	C₂³×C₈₉	1	2	yes	—
617	C₄×D₄	C₂³×C₈₉	1	4	yes	—
618	C₄×D₄	C₂³×C₈₉	1	2	yes	—
619	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
620	#117	—	2	1	no	—
621	#117	—	2	2	no	—
622	#117	—	2	1	no	—
623	#117	—	2	2	no	—
624	#117	D₄×C₈₉	1	1	yes	characteristic
625	#117	D₄×C₈₉	1	2	yes	—
626	#117	C₂³×C₈₉	1	2	yes	—
627	C₂×C₄⋊C₄	—	2	2	no	—
628	C₂×C₄⋊C₄	—	2	2	no	—
629	C₂×C₄⋊C₄	—	2	1	no	—
630	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
632	C₂×C₂²⋊C₄	—	2	4	no	—
633	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
634	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
635	#107	C₂³×C₈₉	1	4	yes	—
636	#107	C₂³×C₈₉	1	2	yes	—
637	#106	C₂³×C₈₉	1	4	yes	—
638	#106	C₂³×C₈₉	1	2	yes	—
639	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
640	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
641	#103	C₂³×C₈₉	1	2	yes	—
642	#103	C₂³×C₈₉	1	2	yes	—
643	#103	C₂³×C₈₉	1	4	yes	—
644	#103	C₂³×C₈₉	1	4	yes	—
645	#103	C₂³×C₈₉	1	2	yes	—
646	#102	C₂³×C₈₉	1	4	yes	—
647	#102	C₂³×C₈₉	1	4	yes	—
648	#102	C₂³×C₈₉	1	4	yes	—
649	#102	C₂³×C₈₉	1	4	yes	—
650	#102	C₂³×C₈₉	1	4	yes	—
651	#102	C₂³×C₈₉	1	4	yes	—
652	#102	C₂³×C₈₉	1	2	yes	—
653	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
654	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
655	#97	C₂³×C₈₉	1	1	yes	characteristic
656	#97	C₂³×C₈₉	1	1	yes	characteristic
657	#97	C₂³×C₈₉	1	2	yes	—
658	C₄×C₈	C₂³×C₈₉	1	2	yes	—
659	C₄×C₈	C₂³×C₈₉	1	4	yes	—
660	C₂⁴	—	2	2	no	—
661	#41	—	4	2	no	—
662	#41	—	4	4	no	—
663	#41	—	4	4	no	—
664	#41	—	4	4	no	—
665	#41	—	8	4	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	2	1	no	—
669	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
670	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
671	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	4	no	—
675	C₂×D₄	—	2	4	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	4	4	no	—
682	C₂×D₄	—	4	4	no	—
683	C₂×D₄	—	8	2	no	—
684	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
685	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
686	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
687	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	1	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
695	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
696	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
697	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
700	Q₁₆	—	4	2	no	—
701	SD₁₆	—	4	4	no	—
702	SD₁₆	—	4	2	no	—
703	D₈	—	4	4	no	—
704	M₁₆	—	4	4	no	—
705	M₁₆	—	4	2	no	—
706	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
707	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
708	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
731	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
732	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
733	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
734	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
735	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
736	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
737	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
738	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	1	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
754	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
755	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	1	no	—
760	C₄²	C₂×D₄×C₈₉	1	2	yes	—
761	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
762	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
763	C₄²	C₂×D₄×C₈₉	1	2	yes	—
764	C₄²	C₂⁴×C₈₉	1	2	yes	—
765	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
766	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
767	C₂³	—	2	1	no	—
768	C₂³	—	2	4	no	—
769	C₂³	—	4	4	no	—
770	C₂³	—	8	2	no	—
771	C₂³	—	8	2	no	—
772	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
773	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
774	Q₈	—	2	2	no	—
775	Q₈	—	2	2	no	—
776	Q₈	—	2	2	no	—
777	Q₈	—	2	2	no	—
778	Q₈	—	4	2	no	—
779	Q₈	—	4	2	no	—
780	Q₈	—	8	1	no	—
781	D₄	—	2	2	no	—
782	D₄	—	2	2	no	—
783	D₄	—	2	4	no	—
784	D₄	—	2	4	no	—
785	D₄	—	4	2	no	—
786	D₄	—	4	4	no	—
787	D₄	—	4	4	no	—
788	D₄	—	4	4	no	—
789	D₄	—	4	4	no	—
790	D₄	—	8	2	no	—
791	D₄	—	8	2	no	—
792	D₄	—	8	1	no	—
793	D₄	—	8	4	no	—
794	D₄	—	8	4	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	4	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	—	4	2	no	—
807	C₂×C₄	—	4	2	no	—
808	C₂×C₄	—	4	4	no	—
809	C₂×C₄	—	4	2	no	—
810	C₂×C₄	—	8	2	no	—
811	C₂×C₄	—	8	4	no	—
812	C₂×C₄	—	8	4	no	—
813	C₂×C₄	—	8	2	no	—
814	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
816	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
817	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
819	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
820	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
821	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
822	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
823	C₈	—	2	2	no	—
824	C₈	—	2	4	no	—
825	C₈	—	2	2	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	2	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	1	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	4	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	4	no	—
836	C₂²	—	4	4	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	16	4	no	—
839	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
840	C₄	—	2	1	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	1	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	1	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	1	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	#575×C₈₉	1	2	yes	—
855	C₄	#585×C₈₉	1	2	yes	—
856	C₂	—	4	2	no	—
857	C₂	—	4	1	no	—
858	C₂	—	8	1	no	—
859	C₂	—	8	4	no	—
860	C₂	C₈₉×#3500	1	1	yes	characteristic
861	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
862	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 ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3515	C₂	semidirect
2. C₈₉×#3508	C₂	semidirect
3. C₈₉×#3365	C₂	semidirect
4. C₈₉×#3361	C₂	semidirect
5. C₈₉×#3333	C₂	semidirect
6. C₈₉×#3332	C₂	semidirect
7. C₈₉×#3323	C₂	semidirect
8. C₈₉×#3322	C₂	semidirect
9. C₈₉×#3237	C₂	semidirect
10. C₈₉×#3234	C₂	semidirect
11. C₈₉×#3219	C₂	semidirect
12. C₈₉×#3217	C₂	semidirect
13. C₈₉×#3172	C₂	semidirect
14. C₈₉×#3171	C₂	semidirect
15. C₈₉×#3142	C₂	semidirect
16. C₈₉×#3138	C₂	semidirect
17. C₈₉×#2971	C₂	semidirect
20. #557×C₈₉	C₂²	semidirect
21. #554×C₈₉	C₂²	semidirect
22. #554×C₈₉	C₂²	semidirect
30. #547×C₈₉	C₂²	semidirect
43. #529×C₈₉	C₂²	semidirect
44. C₂×#125×C₈₉	C₂²	semidirect
48. #501×C₈₉	C₂²	semidirect
49. #501×C₈₉	C₂²	semidirect
50. #497×C₈₉	C₂²	semidirect
52. #491×C₈₉	C₂²	semidirect
53. #491×C₈₉	C₂²	semidirect
57. #489×C₈₉	C₂²	semidirect
58. #488×C₈₉	C₂²	semidirect
59. #488×C₈₉	C₂²	semidirect
63. #481×C₈₉	C₂²	semidirect
64. #480×C₈₉	C₂²	semidirect
65. #478×C₈₉	C₂²	semidirect
66. #478×C₈₉	C₂²	semidirect
67. #477×C₈₉	C₂²	semidirect
68. #475×C₈₉	C₂²	semidirect
70. #469×C₈₉	C₂²	semidirect
72. #468×C₈₉	C₂²	semidirect
73. #464×C₈₉	C₂²	semidirect
74. #463×C₈₉	C₂²	semidirect
77. #452×C₈₉	C₂²	semidirect
79. #449×C₈₉	C₂²	semidirect
81. C₈×Q₈×C₈₉	C₂²	semidirect
82. C₄×Q₁₆×C₈₉	C₂²	semidirect
83. C₄×SD₁₆×C₈₉	C₂²	semidirect
84. C₄×SD₁₆×C₈₉	C₂²	semidirect
85. C₄×D₈×C₈₉	C₂²	semidirect
87. #436×C₈₉	C₂²	semidirect
89. #432×C₈₉	C₂²	semidirect
91. #417×C₈₉	C₂²	semidirect
92. #417×C₈₉	C₂²	semidirect
94. C₄×M₁₆×C₈₉	C₂²	semidirect
424. #62590	C₈₉	direct (N × H)
432. #3515	C₂×C₈₉	semidirect
433. #3508	C₂×C₈₉	semidirect
434. #3365	C₂×C₈₉	semidirect
435. #3361	C₂×C₈₉	semidirect
436. #3333	C₂×C₈₉	semidirect
437. #3332	C₂×C₈₉	semidirect
438. #3323	C₂×C₈₉	semidirect
439. #3322	C₂×C₈₉	semidirect
440. #3237	C₂×C₈₉	semidirect
441. #3234	C₂×C₈₉	semidirect
442. #3219	C₂×C₈₉	semidirect
443. #3217	C₂×C₈₉	semidirect
444. #3172	C₂×C₈₉	semidirect
445. #3171	C₂×C₈₉	semidirect
446. #3142	C₂×C₈₉	semidirect
447. #3138	C₂×C₈₉	semidirect
448. #2971	C₂×C₈₉	semidirect
449. C₈₉	#62590	direct (N × H)
452. #557	C₂²×C₈₉	semidirect
453. #554	C₂²×C₈₉	semidirect
454. #554	C₂²×C₈₉	semidirect
462. #547	C₂²×C₈₉	semidirect
475. #529	C₂²×C₈₉	semidirect
476. C₂×#125	C₂²×C₈₉	semidirect
480. #501	C₂²×C₈₉	semidirect
481. #501	C₂²×C₈₉	semidirect
482. #497	C₂²×C₈₉	semidirect
484. #491	C₂²×C₈₉	semidirect
485. #491	C₂²×C₈₉	semidirect
489. #489	C₂²×C₈₉	semidirect
490. #488	C₂²×C₈₉	semidirect
491. #488	C₂²×C₈₉	semidirect
495. #481	C₂²×C₈₉	semidirect
496. #480	C₂²×C₈₉	semidirect
497. #478	C₂²×C₈₉	semidirect
498. #478	C₂²×C₈₉	semidirect
499. #477	C₂²×C₈₉	semidirect
500. #475	C₂²×C₈₉	semidirect
502. #469	C₂²×C₈₉	semidirect
504. #468	C₂²×C₈₉	semidirect
505. #464	C₂²×C₈₉	semidirect
506. #463	C₂²×C₈₉	semidirect
509. #452	C₂²×C₈₉	semidirect
511. #449	C₂²×C₈₉	semidirect
513. C₈×Q₈	C₂²×C₈₉	semidirect
514. C₄×Q₁₆	C₂²×C₈₉	semidirect
515. C₄×SD₁₆	C₂²×C₈₉	semidirect
516. C₄×SD₁₆	C₂²×C₈₉	semidirect
517. C₄×D₈	C₂²×C₈₉	semidirect
519. #436	C₂²×C₈₉	semidirect
521. #432	C₂²×C₈₉	semidirect
523. #417	C₂²×C₈₉	semidirect
524. #417	C₂²×C₈₉	semidirect
526. C₄×M₁₆	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×#3515	2
C₈₉×#3508	2
C₈₉×#3365	2
C₈₉×#3361	2
C₈₉×#3333	2
C₈₉×#3332	2
C₈₉×#3323	2
C₈₉×#3322	2
C₈₉×#3237	2
C₈₉×#3234	2
C₈₉×#3219	2
C₈₉×#3217	2
C₈₉×#3172	2
C₈₉×#3171	2
C₈₉×#3142	2
C₈₉×#3138	2
C₈₉×#2971	2
#62590	89

Subgroups — C89×#62590 #36440438

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62590 #36440438