Subgroups — C₈₉×#62593 #36440441

Order 22784.

1734 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3514	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3365	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3364	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3328	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3327	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3324	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3323	C₂	1	4	yes	maximal, complemented
9	C₈₉×#3240	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3239	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3216	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3215	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3172	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3172	C₂	1	2	yes	maximal, complemented
15	C₈₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#3140	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2971	C₂	1	1	yes	maximal, characteristic, complemented
18	#559×C₈₉	C₂²	1	1	yes	characteristic
19	#557×C₈₉	—	2	1	no	—
20	#557×C₈₉	C₂²	1	2	yes	complemented
21	#556×C₈₉	—	2	1	no	—
22	#556×C₈₉	C₂²	1	1	yes	characteristic
23	#556×C₈₉	C₂²	1	2	yes	—
24	#555×C₈₉	—	2	1	no	—
25	#552×C₈₉	—	2	2	no	—
26	#552×C₈₉	C₂²	1	4	yes	complemented
27	#551×C₈₉	—	2	2	no	—
28	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
29	#548×C₈₉	C₂²	1	2	yes	—
30	#546×C₈₉	—	2	1	no	—
31	#546×C₈₉	C₂²	1	2	yes	—
32	D₄²×C₈₉	C₂²	1	1	yes	characteristic
33	#542×C₈₉	—	2	1	no	—
34	#541×C₈₉	—	2	2	no	—
35	#538×C₈₉	—	2	2	no	—
36	#536×C₈₉	—	2	1	no	—
37	#533×C₈₉	C₂²	1	2	yes	complemented
38	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	#533×C₈₉	C₂²	1	2	yes	complemented
40	#532×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	#529×C₈₉	C₂²	1	1	yes	characteristic
43	#529×C₈₉	C₂²	1	2	yes	—
44	C₂×#124×C₈₉	C₂²	1	2	yes	—
45	#519×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
51	#497×C₈₉	C₂²	1	2	yes	complemented
52	#491×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	#489×C₈₉	C₂²	1	1	yes	characteristic
54	#489×C₈₉	C₂²	1	2	yes	—
55	#489×C₈₉	C₂²	1	2	yes	complemented
56	#489×C₈₉	C₂²	1	2	yes	complemented
57	#489×C₈₉	C₂²	1	2	yes	complemented
58	#488×C₈₉	C₂²	1	4	yes	—
59	#488×C₈₉	C₂²	1	4	yes	complemented
60	#487×C₈₉	C₂²	1	2	yes	complemented
61	#486×C₈₉	C₂²	1	2	yes	—
62	#485×C₈₉	C₂²	1	4	yes	complemented
63	#484×C₈₉	C₂²	1	2	yes	complemented
64	#482×C₈₉	C₂²	1	4	yes	—
65	#481×C₈₉	C₂²	1	2	yes	—
66	#479×C₈₉	C₂²	1	4	yes	complemented
67	#478×C₈₉	C₂²	1	4	yes	complemented
68	#475×C₈₉	C₂²	1	2	yes	complemented
69	#474×C₈₉	C₂²	1	2	yes	—
70	#470×C₈₉	C₂²	1	4	yes	complemented
71	#470×C₈₉	C₂²	1	2	yes	complemented
72	#468×C₈₉	C₂²	1	2	yes	—
73	#468×C₈₉	C₂²	1	4	yes	—
74	#464×C₈₉	C₂²	1	4	yes	—
75	#464×C₈₉	C₂²	1	4	yes	complemented
76	#462×C₈₉	C₂²	1	2	yes	complemented
77	#460×C₈₉	C₂²	1	2	yes	—
78	#452×C₈₉	C₂²	1	4	yes	complemented
79	#451×C₈₉	C₂²	1	4	yes	complemented
80	#450×C₈₉	C₂²	1	4	yes	—
81	C₈×Q₈×C₈₉	C₂²	1	2	yes	complemented
82	C₄×Q₁₆×C₈₉	C₂²	1	4	yes	complemented
83	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
84	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
85	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	complemented
86	#436×C₈₉	C₂²	1	2	yes	—
87	#436×C₈₉	C₂²	1	4	yes	complemented
88	#432×C₈₉	C₂²	1	2	yes	complemented
89	#432×C₈₉	C₂²	1	1	yes	characteristic, complemented
90	#419×C₈₉	C₂²	1	4	yes	complemented
91	#418×C₈₉	C₂²	1	4	yes	—
92	#417×C₈₉	C₂²	1	4	yes	complemented
93	C₄×M₁₆×C₈₉	C₂²	1	2	yes	complemented
94	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
95	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
96	C₂×#41×C₈₉	C₂³	1	2	yes	—
97	C₂²×Q₈×C₈₉	—	2	1	no	—
98	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
99	C₂²×D₄×C₈₉	—	2	1	no	—
100	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
101	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
102	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
103	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
105	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
106	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
107	C₄⋊Q₈×C₈₉	—	2	2	no	—
108	C₄⋊Q₈×C₈₉	—	2	1	no	—
109	C₄⋊Q₈×C₈₉	—	2	1	no	—
110	C₄⋊Q₈×C₈₉	—	2	1	no	—
111	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
115	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
116	#127×C₈₉	C₂³	1	1	yes	characteristic
117	#126×C₈₉	—	2	2	no	—
118	#126×C₈₉	—	2	4	no	—
119	#126×C₈₉	—	2	4	no	—
120	#126×C₈₉	—	2	2	no	—
121	#126×C₈₉	—	2	1	no	—
122	#125×C₈₉	—	2	4	no	—
123	#125×C₈₉	—	2	4	no	—
124	#125×C₈₉	—	2	1	no	—
125	#125×C₈₉	—	2	2	no	—
126	#125×C₈₉	C₂³	1	4	yes	—
127	#125×C₈₉	C₂³	1	1	yes	characteristic
128	#124×C₈₉	—	2	1	no	—
129	#124×C₈₉	—	2	2	no	—
130	#124×C₈₉	—	2	2	no	—
131	#124×C₈₉	—	2	2	no	—
132	#124×C₈₉	—	2	2	no	—
133	#124×C₈₉	C₂³	1	2	yes	—
134	#124×C₈₉	C₂³	1	2	yes	—
135	#124×C₈₉	C₂³	1	1	yes	characteristic
136	#124×C₈₉	C₂³	1	2	yes	—
137	#123×C₈₉	—	2	4	no	—
138	#123×C₈₉	—	2	1	no	—
139	#123×C₈₉	—	2	2	no	—
140	#123×C₈₉	—	2	2	no	—
141	#123×C₈₉	—	2	2	no	—
142	C₂²⋊Q₈×C₈₉	—	2	1	no	—
143	C₂²⋊Q₈×C₈₉	—	2	2	no	—
144	C₂²⋊Q₈×C₈₉	—	2	2	no	—
145	C₂²⋊Q₈×C₈₉	—	2	1	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	C₂³	1	4	yes	—
150	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
151	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
152	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
153	#121×C₈₉	—	2	2	no	—
154	#121×C₈₉	—	2	1	no	—
155	#121×C₈₉	—	2	1	no	—
156	#121×C₈₉	—	2	1	no	—
157	#121×C₈₉	—	2	2	no	—
158	#121×C₈₉	C₂³	1	1	yes	characteristic
159	#121×C₈₉	C₂³	1	2	yes	—
160	#120×C₈₉	—	2	2	no	—
161	#120×C₈₉	—	2	2	no	—
162	C₄×Q₈×C₈₉	—	2	2	no	—
163	C₄×Q₈×C₈₉	—	2	2	no	—
164	C₄×Q₈×C₈₉	—	2	2	no	—
165	C₄×Q₈×C₈₉	—	2	2	no	—
166	C₄×Q₈×C₈₉	—	2	2	no	—
167	C₄×Q₈×C₈₉	—	2	1	no	—
168	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
169	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
170	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
171	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
172	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
173	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
174	C₄×D₄×C₈₉	—	2	1	no	—
175	C₄×D₄×C₈₉	—	2	2	no	—
176	C₄×D₄×C₈₉	—	2	1	no	—
177	C₄×D₄×C₈₉	—	2	1	no	—
178	C₄×D₄×C₈₉	—	2	2	no	—
179	C₄×D₄×C₈₉	—	2	1	no	—
180	C₄×D₄×C₈₉	—	2	1	no	—
181	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
182	C₄×D₄×C₈₉	D₄	1	2	yes	—
183	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₈₉	C₂³	1	2	yes	—
185	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₈₉	C₂³	1	2	yes	—
187	#117×C₈₉	—	2	1	no	—
188	#117×C₈₉	—	2	2	no	—
189	#117×C₈₉	—	2	1	no	—
190	#117×C₈₉	—	2	4	no	—
191	#117×C₈₉	—	2	1	no	—
192	#117×C₈₉	—	2	2	no	—
193	#117×C₈₉	D₄	1	1	yes	characteristic
194	#117×C₈₉	D₄	1	2	yes	—
195	#117×C₈₉	C₂³	1	4	yes	—
196	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
197	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
200	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
201	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
202	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
203	#107×C₈₉	C₂³	1	4	yes	—
204	#107×C₈₉	C₂³	1	2	yes	—
205	#106×C₈₉	C₂³	1	2	yes	—
206	#106×C₈₉	C₂³	1	4	yes	—
207	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
208	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
209	#103×C₈₉	C₂³	1	4	yes	—
210	#103×C₈₉	C₂³	1	4	yes	—
211	#103×C₈₉	C₂³	1	2	yes	—
212	#103×C₈₉	C₂³	1	4	yes	—
213	#103×C₈₉	C₂³	1	4	yes	—
214	#103×C₈₉	C₂³	1	2	yes	—
215	#103×C₈₉	C₂³	1	2	yes	—
216	#102×C₈₉	C₂³	1	4	yes	—
217	#102×C₈₉	C₂³	1	4	yes	—
218	#102×C₈₉	C₂³	1	2	yes	—
219	#102×C₈₉	C₂³	1	4	yes	—
220	#102×C₈₉	C₂³	1	4	yes	—
221	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
222	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
223	#97×C₈₉	C₂³	1	1	yes	characteristic
224	#97×C₈₉	C₂³	1	2	yes	—
225	#97×C₈₉	C₂³	1	1	yes	characteristic
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	C₂×Q₈×C₈₉	—	2	1	no	—
232	C₂×Q₈×C₈₉	—	2	2	no	—
233	C₂×Q₈×C₈₉	—	2	2	no	—
234	C₂×Q₈×C₈₉	—	2	2	no	—
235	C₂×Q₈×C₈₉	—	4	4	no	—
236	C₂×Q₈×C₈₉	—	4	4	no	—
237	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
238	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
239	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
240	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
241	C₂×D₄×C₈₉	—	2	2	no	—
242	C₂×D₄×C₈₉	—	2	1	no	—
243	C₂×D₄×C₈₉	—	2	2	no	—
244	C₂×D₄×C₈₉	—	2	1	no	—
245	C₂×D₄×C₈₉	—	2	1	no	—
246	C₂×D₄×C₈₉	—	2	2	no	—
247	C₂×D₄×C₈₉	—	4	4	no	—
248	C₂×D₄×C₈₉	—	4	4	no	—
249	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
250	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
251	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
252	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₈₉	—	2	2	no	—
254	C₂²×C₄×C₈₉	—	2	2	no	—
255	C₂²×C₄×C₈₉	—	2	1	no	—
256	C₂²×C₄×C₈₉	—	2	2	no	—
257	C₂²×C₄×C₈₉	—	2	2	no	—
258	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
260	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
264	Q₁₆×C₈₉	—	4	2	no	—
265	Q₁₆×C₈₉	—	4	4	no	—
266	SD₁₆×C₈₉	—	4	2	no	—
267	SD₁₆×C₈₉	—	4	4	no	—
268	M₁₆×C₈₉	—	4	4	no	—
269	M₁₆×C₈₉	—	4	2	no	—
270	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
271	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
272	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
273	C₄⋊C₄×C₈₉	—	2	2	no	—
274	C₄⋊C₄×C₈₉	—	2	2	no	—
275	C₄⋊C₄×C₈₉	—	2	2	no	—
276	C₄⋊C₄×C₈₉	—	2	1	no	—
277	C₄⋊C₄×C₈₉	—	2	1	no	—
278	C₄⋊C₄×C₈₉	—	2	1	no	—
279	C₄⋊C₄×C₈₉	—	2	1	no	—
280	C₄⋊C₄×C₈₉	—	2	1	no	—
281	C₄⋊C₄×C₈₉	—	2	1	no	—
282	C₄⋊C₄×C₈₉	—	2	1	no	—
283	C₄⋊C₄×C₈₉	—	2	4	no	—
284	C₄⋊C₄×C₈₉	—	2	4	no	—
285	C₄⋊C₄×C₈₉	—	2	2	no	—
286	C₄⋊C₄×C₈₉	—	2	1	no	—
287	C₄⋊C₄×C₈₉	—	2	4	no	—
288	C₄⋊C₄×C₈₉	—	2	2	no	—
289	C₄⋊C₄×C₈₉	—	2	2	no	—
290	C₄⋊C₄×C₈₉	—	2	1	no	—
291	C₄⋊C₄×C₈₉	—	2	4	no	—
292	C₄⋊C₄×C₈₉	—	2	2	no	—
293	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
294	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
295	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
296	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
298	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
300	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
301	C₂²⋊C₄×C₈₉	—	2	2	no	—
302	C₂²⋊C₄×C₈₉	—	2	2	no	—
303	C₂²⋊C₄×C₈₉	—	2	4	no	—
304	C₂²⋊C₄×C₈₉	—	2	4	no	—
305	C₂²⋊C₄×C₈₉	—	2	1	no	—
306	C₂²⋊C₄×C₈₉	—	2	2	no	—
307	C₂²⋊C₄×C₈₉	—	2	1	no	—
308	C₂²⋊C₄×C₈₉	—	2	1	no	—
309	C₂²⋊C₄×C₈₉	—	2	1	no	—
310	C₂²⋊C₄×C₈₉	—	2	2	no	—
311	C₂²⋊C₄×C₈₉	—	2	2	no	—
312	C₂²⋊C₄×C₈₉	—	2	2	no	—
313	C₂²⋊C₄×C₈₉	—	2	2	no	—
314	C₂²⋊C₄×C₈₉	—	2	2	no	—
315	C₂²⋊C₄×C₈₉	—	2	2	no	—
316	C₂²⋊C₄×C₈₉	—	2	1	no	—
317	C₂²⋊C₄×C₈₉	—	2	2	no	—
318	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
319	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
320	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
321	C₄²×C₈₉	—	2	2	no	—
322	C₄²×C₈₉	—	2	4	no	—
323	C₄²×C₈₉	—	2	4	no	—
324	C₄²×C₈₉	—	2	1	no	—
325	C₄²×C₈₉	—	2	2	no	—
326	C₄²×C₈₉	C₂×D₄	1	2	yes	—
327	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₈₉	C₂×D₄	1	2	yes	—
330	C₄²×C₈₉	C₂⁴	1	2	yes	—
331	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
332	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
333	C₂³×C₈₉	—	2	1	no	—
334	C₂³×C₈₉	—	2	2	no	—
335	C₂³×C₈₉	—	4	4	no	—
336	C₂³×C₈₉	—	8	2	no	—
337	C₂³×C₈₉	—	8	2	no	—
338	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
339	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
340	Q₈×C₈₉	—	2	2	no	—
341	Q₈×C₈₉	—	2	2	no	—
342	Q₈×C₈₉	—	2	2	no	—
343	Q₈×C₈₉	—	2	2	no	—
344	Q₈×C₈₉	—	2	4	no	—
345	Q₈×C₈₉	—	4	2	no	—
346	Q₈×C₈₉	—	4	4	no	—
347	Q₈×C₈₉	—	4	4	no	—
348	Q₈×C₈₉	—	8	2	no	—
349	D₄×C₈₉	—	2	2	no	—
350	D₄×C₈₉	—	2	2	no	—
351	D₄×C₈₉	—	2	4	no	—
352	D₄×C₈₉	—	4	2	no	—
353	D₄×C₈₉	—	4	4	no	—
354	D₄×C₈₉	—	4	2	no	—
355	D₄×C₈₉	—	8	1	no	—
356	D₄×C₈₉	—	8	2	no	—
357	D₄×C₈₉	—	8	1	no	—
358	D₄×C₈₉	—	8	2	no	—
359	C₂×C₄×C₈₉	—	2	2	no	—
360	C₂×C₄×C₈₉	—	2	4	no	—
361	C₂×C₄×C₈₉	—	2	2	no	—
362	C₂×C₄×C₈₉	—	2	2	no	—
363	C₂×C₄×C₈₉	—	2	2	no	—
364	C₂×C₄×C₈₉	—	2	1	no	—
365	C₂×C₄×C₈₉	—	2	4	no	—
366	C₂×C₄×C₈₉	—	2	1	no	—
367	C₂×C₄×C₈₉	—	2	1	no	—
368	C₂×C₄×C₈₉	—	2	2	no	—
369	C₂×C₄×C₈₉	—	4	2	no	—
370	C₂×C₄×C₈₉	—	4	1	no	—
371	C₂×C₄×C₈₉	—	4	2	no	—
372	C₂×C₄×C₈₉	—	4	4	no	—
373	C₂×C₄×C₈₉	—	4	2	no	—
374	C₂×C₄×C₈₉	—	8	2	no	—
375	C₂×C₄×C₈₉	—	8	2	no	—
376	C₂×C₄×C₈₉	—	8	2	no	—
377	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
378	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
379	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
386	C₈×C₈₉	—	2	2	no	—
387	C₈×C₈₉	—	2	2	no	—
388	C₈×C₈₉	—	2	4	no	—
389	C₂²×C₈₉	—	2	1	no	—
390	C₂²×C₈₉	—	2	2	no	—
391	C₂²×C₈₉	—	2	2	no	—
392	C₂²×C₈₉	—	2	1	no	—
393	C₂²×C₈₉	—	2	1	no	—
394	C₂²×C₈₉	—	2	2	no	—
395	C₂²×C₈₉	—	4	2	no	—
396	C₂²×C₈₉	—	4	1	no	—
397	C₂²×C₈₉	—	4	2	no	—
398	C₂²×C₈₉	—	4	1	no	—
399	C₂²×C₈₉	—	4	1	no	—
400	C₂²×C₈₉	—	4	2	no	—
401	C₂²×C₈₉	—	16	4	no	—
402	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
403	C₄×C₈₉	—	2	1	no	—
404	C₄×C₈₉	—	2	2	no	—
405	C₄×C₈₉	—	2	1	no	—
406	C₄×C₈₉	—	2	1	no	—
407	C₄×C₈₉	—	2	2	no	—
408	C₄×C₈₉	—	2	1	no	—
409	C₄×C₈₉	—	2	2	no	—
410	C₄×C₈₉	—	4	1	no	—
411	C₄×C₈₉	—	4	2	no	—
412	C₄×C₈₉	—	4	2	no	—
413	C₄×C₈₉	—	4	1	no	—
414	C₄×C₈₉	—	4	2	no	—
415	C₄×C₈₉	—	4	1	no	—
416	C₄×C₈₉	—	4	4	no	—
417	C₄×C₈₉	#575	1	2	yes	—
418	C₄×C₈₉	#585	1	2	yes	—
419	#62593	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
420	C₂×C₈₉	—	4	1	no	—
421	C₂×C₈₉	—	4	2	no	—
422	C₂×C₈₉	—	8	2	no	—
423	C₂×C₈₉	—	8	1	no	—
424	C₂×C₈₉	#3500	1	1	yes	characteristic
425	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
426	C₂×C₈₉	#3586	1	1	yes	characteristic
427	#3514	C₂×C₈₉	1	1	yes	characteristic
428	#3509	C₂×C₈₉	1	1	yes	characteristic, complemented
429	#3365	C₂×C₈₉	1	2	yes	complemented
430	#3364	C₂×C₈₉	1	2	yes	complemented
431	#3328	C₂×C₈₉	1	2	yes	complemented
432	#3327	C₂×C₈₉	1	4	yes	complemented
433	#3324	C₂×C₈₉	1	2	yes	complemented
434	#3323	C₂×C₈₉	1	4	yes	complemented
435	#3240	C₂×C₈₉	1	2	yes	complemented
436	#3239	C₂×C₈₉	1	1	yes	characteristic, complemented
437	#3216	C₂×C₈₉	1	1	yes	characteristic, complemented
438	#3215	C₂×C₈₉	1	2	yes	complemented
439	#3172	C₂×C₈₉	1	1	yes	characteristic, complemented
440	#3172	C₂×C₈₉	1	2	yes	complemented
441	#3141	C₂×C₈₉	1	1	yes	characteristic, complemented
442	#3140	C₂×C₈₉	1	2	yes	complemented
443	#2971	C₂×C₈₉	1	1	yes	characteristic, complemented
444	C₈₉	#62593	1	1	yes	characteristic, direct product factor, Sylow
445	#559	C₂²×C₈₉	1	1	yes	characteristic
446	#557	—	2	1	no	—
447	#557	C₂²×C₈₉	1	2	yes	complemented
448	#556	—	2	1	no	—
449	#556	C₂²×C₈₉	1	1	yes	characteristic
450	#556	C₂²×C₈₉	1	2	yes	—
451	#555	—	2	1	no	—
452	#552	—	2	2	no	—
453	#552	C₂²×C₈₉	1	4	yes	complemented
454	#551	—	2	2	no	—
455	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
456	#548	C₂²×C₈₉	1	2	yes	—
457	#546	—	2	1	no	—
458	#546	C₂²×C₈₉	1	2	yes	—
459	D₄²	C₂²×C₈₉	1	1	yes	characteristic
460	#542	—	2	1	no	—
461	#541	—	2	2	no	—
462	#538	—	2	2	no	—
463	#536	—	2	1	no	—
464	#533	C₂²×C₈₉	1	2	yes	complemented
465	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
466	#533	C₂²×C₈₉	1	2	yes	complemented
467	#532	C₂²×C₈₉	1	1	yes	characteristic
468	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
469	#529	C₂²×C₈₉	1	1	yes	characteristic
470	#529	C₂²×C₈₉	1	2	yes	—
471	C₂×#124	C₂²×C₈₉	1	2	yes	—
472	#519	—	2	1	no	—
473	#518	—	2	1	no	—
474	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
475	#501	C₂²×C₈₉	1	2	yes	complemented
476	#501	C₂²×C₈₉	1	1	yes	characteristic, complemented
477	#497	C₂²×C₈₉	1	1	yes	characteristic
478	#497	C₂²×C₈₉	1	2	yes	complemented
479	#491	C₂²×C₈₉	1	1	yes	characteristic, complemented
480	#489	C₂²×C₈₉	1	1	yes	characteristic
481	#489	C₂²×C₈₉	1	2	yes	—
482	#489	C₂²×C₈₉	1	2	yes	complemented
483	#489	C₂²×C₈₉	1	2	yes	complemented
484	#489	C₂²×C₈₉	1	2	yes	complemented
485	#488	C₂²×C₈₉	1	4	yes	—
486	#488	C₂²×C₈₉	1	4	yes	complemented
487	#487	C₂²×C₈₉	1	2	yes	complemented
488	#486	C₂²×C₈₉	1	2	yes	—
489	#485	C₂²×C₈₉	1	4	yes	complemented
490	#484	C₂²×C₈₉	1	2	yes	complemented
491	#482	C₂²×C₈₉	1	4	yes	—
492	#481	C₂²×C₈₉	1	2	yes	—
493	#479	C₂²×C₈₉	1	4	yes	complemented
494	#478	C₂²×C₈₉	1	4	yes	complemented
495	#475	C₂²×C₈₉	1	2	yes	complemented
496	#474	C₂²×C₈₉	1	2	yes	—
497	#470	C₂²×C₈₉	1	4	yes	complemented
498	#470	C₂²×C₈₉	1	2	yes	complemented
499	#468	C₂²×C₈₉	1	2	yes	—
500	#468	C₂²×C₈₉	1	4	yes	—
501	#464	C₂²×C₈₉	1	4	yes	—
502	#464	C₂²×C₈₉	1	4	yes	complemented
503	#462	C₂²×C₈₉	1	2	yes	complemented
504	#460	C₂²×C₈₉	1	2	yes	—
505	#452	C₂²×C₈₉	1	4	yes	complemented
506	#451	C₂²×C₈₉	1	4	yes	complemented
507	#450	C₂²×C₈₉	1	4	yes	—
508	C₈×Q₈	C₂²×C₈₉	1	2	yes	complemented
509	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
510	C₄×Q₁₆	C₂²×C₈₉	1	4	yes	complemented
511	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
512	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	complemented
513	#436	C₂²×C₈₉	1	2	yes	—
514	#436	C₂²×C₈₉	1	4	yes	complemented
515	#432	C₂²×C₈₉	1	2	yes	complemented
516	#432	C₂²×C₈₉	1	1	yes	characteristic, complemented
517	#419	C₂²×C₈₉	1	4	yes	complemented
518	#418	C₂²×C₈₉	1	4	yes	—
519	#417	C₂²×C₈₉	1	4	yes	complemented
520	C₄×M₁₆	C₂²×C₈₉	1	2	yes	complemented
521	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
522	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
523	C₂×#41	C₂³×C₈₉	1	2	yes	—
524	C₂²×Q₈	—	2	1	no	—
525	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
526	C₂²×D₄	—	2	1	no	—
527	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
528	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
529	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
530	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
531	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
532	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
533	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
534	C₄⋊Q₈	—	2	2	no	—
535	C₄⋊Q₈	—	2	1	no	—
536	C₄⋊Q₈	—	2	1	no	—
537	C₄⋊Q₈	—	2	1	no	—
538	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
539	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
540	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
541	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
542	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
543	#127	C₂³×C₈₉	1	1	yes	characteristic
544	#126	—	2	2	no	—
545	#126	—	2	4	no	—
546	#126	—	2	4	no	—
547	#126	—	2	2	no	—
548	#126	—	2	1	no	—
549	#125	—	2	4	no	—
550	#125	—	2	4	no	—
551	#125	—	2	1	no	—
552	#125	—	2	2	no	—
553	#125	C₂³×C₈₉	1	1	yes	characteristic
554	#125	C₂³×C₈₉	1	4	yes	—
555	#124	—	2	1	no	—
556	#124	—	2	2	no	—
557	#124	—	2	2	no	—
558	#124	—	2	2	no	—
559	#124	—	2	2	no	—
560	#124	C₂³×C₈₉	1	1	yes	characteristic
561	#124	C₂³×C₈₉	1	2	yes	—
562	#124	C₂³×C₈₉	1	2	yes	—
563	#124	C₂³×C₈₉	1	2	yes	—
564	#123	—	2	4	no	—
565	#123	—	2	1	no	—
566	#123	—	2	2	no	—
567	#123	—	2	2	no	—
568	#123	—	2	2	no	—
569	C₂²⋊Q₈	—	2	1	no	—
570	C₂²⋊Q₈	—	2	2	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	—	2	1	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
577	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
578	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
579	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
580	#121	—	2	2	no	—
581	#121	—	2	1	no	—
582	#121	—	2	1	no	—
583	#121	—	2	1	no	—
584	#121	—	2	2	no	—
585	#121	C₂³×C₈₉	1	2	yes	—
586	#121	C₂³×C₈₉	1	1	yes	characteristic
587	#120	—	2	2	no	—
588	#120	—	2	2	no	—
589	C₄×Q₈	—	2	2	no	—
590	C₄×Q₈	—	2	2	no	—
591	C₄×Q₈	—	2	2	no	—
592	C₄×Q₈	—	2	2	no	—
593	C₄×Q₈	—	2	2	no	—
594	C₄×Q₈	—	2	1	no	—
595	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
596	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
597	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
598	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
599	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
600	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
609	C₄×D₄	D₄×C₈₉	1	2	yes	—
610	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
611	C₄×D₄	C₂³×C₈₉	1	2	yes	—
612	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
613	C₄×D₄	C₂³×C₈₉	1	2	yes	—
614	#117	—	2	1	no	—
615	#117	—	2	2	no	—
616	#117	—	2	1	no	—
617	#117	—	2	4	no	—
618	#117	—	2	1	no	—
619	#117	—	2	2	no	—
620	#117	D₄×C₈₉	1	1	yes	characteristic
621	#117	D₄×C₈₉	1	2	yes	—
622	#117	C₂³×C₈₉	1	4	yes	—
623	C₂×C₄⋊C₄	—	2	1	no	—
624	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
625	C₂×C₂²⋊C₄	—	2	2	no	—
626	C₂×C₂²⋊C₄	—	2	2	no	—
627	C₂×C₂²⋊C₄	—	2	2	no	—
628	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
629	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
630	#107	C₂³×C₈₉	1	4	yes	—
631	#107	C₂³×C₈₉	1	2	yes	—
632	#106	C₂³×C₈₉	1	2	yes	—
633	#106	C₂³×C₈₉	1	4	yes	—
634	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
635	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
636	#103	C₂³×C₈₉	1	4	yes	—
637	#103	C₂³×C₈₉	1	4	yes	—
638	#103	C₂³×C₈₉	1	2	yes	—
639	#103	C₂³×C₈₉	1	4	yes	—
640	#103	C₂³×C₈₉	1	4	yes	—
641	#103	C₂³×C₈₉	1	2	yes	—
642	#103	C₂³×C₈₉	1	2	yes	—
643	#102	C₂³×C₈₉	1	4	yes	—
644	#102	C₂³×C₈₉	1	4	yes	—
645	#102	C₂³×C₈₉	1	2	yes	—
646	#102	C₂³×C₈₉	1	4	yes	—
647	#102	C₂³×C₈₉	1	4	yes	—
648	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
649	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
650	#97	C₂³×C₈₉	1	1	yes	characteristic
651	#97	C₂³×C₈₉	1	2	yes	—
652	#97	C₂³×C₈₉	1	1	yes	characteristic
653	C₄×C₈	C₂³×C₈₉	1	2	yes	—
654	C₄×C₈	C₂³×C₈₉	1	4	yes	—
655	C₂⁴	—	2	2	no	—
656	#41	—	4	2	no	—
657	#41	—	4	4	no	—
658	C₂×Q₈	—	2	1	no	—
659	C₂×Q₈	—	2	2	no	—
660	C₂×Q₈	—	2	2	no	—
661	C₂×Q₈	—	2	2	no	—
662	C₂×Q₈	—	4	4	no	—
663	C₂×Q₈	—	4	4	no	—
664	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
665	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
666	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
667	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	—	2	1	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	—	2	1	no	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	—	4	4	no	—
675	C₂×D₄	—	4	4	no	—
676	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
677	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
678	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
679	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
686	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
687	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
688	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
691	Q₁₆	—	4	2	no	—
692	Q₁₆	—	4	4	no	—
693	SD₁₆	—	4	2	no	—
694	SD₁₆	—	4	4	no	—
695	M₁₆	—	4	4	no	—
696	M₁₆	—	4	2	no	—
697	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
698	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
699	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
721	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
722	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
723	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
724	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
725	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
726	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
727	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	1	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	1	no	—
736	C₂²⋊C₄	—	2	1	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	1	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
746	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
747	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
748	C₄²	—	2	2	no	—
749	C₄²	—	2	4	no	—
750	C₄²	—	2	4	no	—
751	C₄²	—	2	1	no	—
752	C₄²	—	2	2	no	—
753	C₄²	C₂×D₄×C₈₉	1	2	yes	—
754	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
755	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
756	C₄²	C₂×D₄×C₈₉	1	2	yes	—
757	C₄²	C₂⁴×C₈₉	1	2	yes	—
758	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
759	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
760	C₂³	—	2	1	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	4	4	no	—
763	C₂³	—	8	2	no	—
764	C₂³	—	8	2	no	—
765	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
766	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
767	Q₈	—	2	2	no	—
768	Q₈	—	2	2	no	—
769	Q₈	—	2	2	no	—
770	Q₈	—	2	2	no	—
771	Q₈	—	2	4	no	—
772	Q₈	—	4	2	no	—
773	Q₈	—	4	4	no	—
774	Q₈	—	4	4	no	—
775	Q₈	—	8	2	no	—
776	D₄	—	2	2	no	—
777	D₄	—	2	2	no	—
778	D₄	—	2	4	no	—
779	D₄	—	4	2	no	—
780	D₄	—	4	4	no	—
781	D₄	—	4	2	no	—
782	D₄	—	8	1	no	—
783	D₄	—	8	2	no	—
784	D₄	—	8	1	no	—
785	D₄	—	8	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	4	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	4	2	no	—
797	C₂×C₄	—	4	1	no	—
798	C₂×C₄	—	4	2	no	—
799	C₂×C₄	—	4	4	no	—
800	C₂×C₄	—	4	2	no	—
801	C₂×C₄	—	8	2	no	—
802	C₂×C₄	—	8	2	no	—
803	C₂×C₄	—	8	2	no	—
804	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
805	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
806	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
808	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
809	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
810	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
811	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
812	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
813	C₈	—	2	2	no	—
814	C₈	—	2	2	no	—
815	C₈	—	2	4	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	1	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	16	4	no	—
829	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
830	C₄	—	2	1	no	—
831	C₄	—	2	2	no	—
832	C₄	—	2	1	no	—
833	C₄	—	2	2	no	—
834	C₄	—	2	1	no	—
835	C₄	—	2	1	no	—
836	C₄	—	2	2	no	—
837	C₄	—	4	1	no	—
838	C₄	—	4	4	no	—
839	C₄	—	4	1	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	1	no	—
843	C₄	—	4	2	no	—
844	C₄	#575×C₈₉	1	2	yes	—
845	C₄	#585×C₈₉	1	2	yes	—
846	C₂	—	4	1	no	—
847	C₂	—	4	2	no	—
848	C₂	—	8	2	no	—
849	C₂	—	8	1	no	—
850	C₂	C₈₉×#3500	1	1	yes	characteristic
851	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
852	C₂	C₈₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₈₉×#3514	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₉×#3509	C₂	semidirect
3. C₈₉×#3365	C₂	semidirect
4. C₈₉×#3364	C₂	semidirect
5. C₈₉×#3328	C₂	semidirect
6. C₈₉×#3327	C₂	semidirect
7. C₈₉×#3324	C₂	semidirect
8. C₈₉×#3323	C₂	semidirect
9. C₈₉×#3240	C₂	semidirect
10. C₈₉×#3239	C₂	semidirect
11. C₈₉×#3216	C₂	semidirect
12. C₈₉×#3215	C₂	semidirect
13. C₈₉×#3172	C₂	semidirect
14. C₈₉×#3172	C₂	semidirect
15. C₈₉×#3141	C₂	semidirect
16. C₈₉×#3140	C₂	semidirect
17. C₈₉×#2971	C₂	semidirect
20. #557×C₈₉	C₂²	semidirect
26. #552×C₈₉	C₂²	semidirect
37. #533×C₈₉	C₂²	semidirect
38. #533×C₈₉	C₂²	semidirect
39. #533×C₈₉	C₂²	semidirect
41. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
48. #501×C₈₉	C₂²	semidirect
49. #501×C₈₉	C₂²	semidirect
51. #497×C₈₉	C₂²	semidirect
52. #491×C₈₉	C₂²	semidirect
55. #489×C₈₉	C₂²	semidirect
56. #489×C₈₉	C₂²	semidirect
57. #489×C₈₉	C₂²	semidirect
59. #488×C₈₉	C₂²	semidirect
60. #487×C₈₉	C₂²	semidirect
62. #485×C₈₉	C₂²	semidirect
63. #484×C₈₉	C₂²	semidirect
66. #479×C₈₉	C₂²	semidirect
67. #478×C₈₉	C₂²	semidirect
68. #475×C₈₉	C₂²	semidirect
70. #470×C₈₉	C₂²	semidirect
71. #470×C₈₉	C₂²	semidirect
75. #464×C₈₉	C₂²	semidirect
76. #462×C₈₉	C₂²	semidirect
78. #452×C₈₉	C₂²	semidirect
79. #451×C₈₉	C₂²	semidirect
81. C₈×Q₈×C₈₉	C₂²	semidirect
82. C₄×Q₁₆×C₈₉	C₂²	semidirect
83. C₄×Q₁₆×C₈₉	C₂²	semidirect
85. C₄×SD₁₆×C₈₉	C₂²	semidirect
87. #436×C₈₉	C₂²	semidirect
88. #432×C₈₉	C₂²	semidirect
89. #432×C₈₉	C₂²	semidirect
90. #419×C₈₉	C₂²	semidirect
92. #417×C₈₉	C₂²	semidirect
93. C₄×M₁₆×C₈₉	C₂²	semidirect
94. C₄×M₁₆×C₈₉	C₂²	semidirect
419. #62593	C₈₉	direct (N × H)
428. #3509	C₂×C₈₉	semidirect
429. #3365	C₂×C₈₉	semidirect
430. #3364	C₂×C₈₉	semidirect
431. #3328	C₂×C₈₉	semidirect
432. #3327	C₂×C₈₉	semidirect
433. #3324	C₂×C₈₉	semidirect
434. #3323	C₂×C₈₉	semidirect
435. #3240	C₂×C₈₉	semidirect
436. #3239	C₂×C₈₉	semidirect
437. #3216	C₂×C₈₉	semidirect
438. #3215	C₂×C₈₉	semidirect
439. #3172	C₂×C₈₉	semidirect
440. #3172	C₂×C₈₉	semidirect
441. #3141	C₂×C₈₉	semidirect
442. #3140	C₂×C₈₉	semidirect
443. #2971	C₂×C₈₉	semidirect
444. C₈₉	#62593	direct (N × H)
447. #557	C₂²×C₈₉	semidirect
453. #552	C₂²×C₈₉	semidirect
464. #533	C₂²×C₈₉	semidirect
465. #533	C₂²×C₈₉	semidirect
466. #533	C₂²×C₈₉	semidirect
468. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
475. #501	C₂²×C₈₉	semidirect
476. #501	C₂²×C₈₉	semidirect
478. #497	C₂²×C₈₉	semidirect
479. #491	C₂²×C₈₉	semidirect
482. #489	C₂²×C₈₉	semidirect
483. #489	C₂²×C₈₉	semidirect
484. #489	C₂²×C₈₉	semidirect
486. #488	C₂²×C₈₉	semidirect
487. #487	C₂²×C₈₉	semidirect
489. #485	C₂²×C₈₉	semidirect
490. #484	C₂²×C₈₉	semidirect
493. #479	C₂²×C₈₉	semidirect
494. #478	C₂²×C₈₉	semidirect
495. #475	C₂²×C₈₉	semidirect
497. #470	C₂²×C₈₉	semidirect
498. #470	C₂²×C₈₉	semidirect
502. #464	C₂²×C₈₉	semidirect
503. #462	C₂²×C₈₉	semidirect
505. #452	C₂²×C₈₉	semidirect
506. #451	C₂²×C₈₉	semidirect
508. C₈×Q₈	C₂²×C₈₉	semidirect
509. C₄×Q₁₆	C₂²×C₈₉	semidirect
510. C₄×Q₁₆	C₂²×C₈₉	semidirect
512. C₄×SD₁₆	C₂²×C₈₉	semidirect
514. #436	C₂²×C₈₉	semidirect
515. #432	C₂²×C₈₉	semidirect
516. #432	C₂²×C₈₉	semidirect
517. #419	C₂²×C₈₉	semidirect
519. #417	C₂²×C₈₉	semidirect
520. C₄×M₁₆	C₂²×C₈₉	semidirect
521. 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×#3514	2
C₈₉×#3509	2
C₈₉×#3365	2
C₈₉×#3364	2
C₈₉×#3328	2
C₈₉×#3327	2
C₈₉×#3324	2
C₈₉×#3323	2
C₈₉×#3240	2
C₈₉×#3239	2
C₈₉×#3216	2
C₈₉×#3215	2
C₈₉×#3172	2
C₈₉×#3141	2
C₈₉×#3140	2
C₈₉×#2971	2
#62593	89

Subgroups — C89×#62593 #36440441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62593 #36440441