Subgroups — C₈₉×#60932 #36438780

Order 22784.

1768 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3261	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3260	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3258	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3257	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3256	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3252	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3250	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3248	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3084	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3083	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3080	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#479×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#3063	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3061	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#3060	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3046	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₉×#3046	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#3037	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₉×#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2906	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
30	#553×C₈₉	—	2	2	no	—
31	#553×C₈₉	—	2	2	no	—
32	#553×C₈₉	—	2	1	no	—
33	#553×C₈₉	—	2	1	no	—
34	#552×C₈₉	—	2	1	no	—
35	#552×C₈₉	—	2	1	no	—
36	#544×C₈₉	C₂²	1	1	yes	characteristic
37	#542×C₈₉	—	2	1	no	—
38	#542×C₈₉	C₂²	1	2	yes	—
39	#541×C₈₉	—	2	1	no	—
40	#541×C₈₉	C₂²	1	2	yes	—
41	#541×C₈₉	C₂²	1	2	yes	—
42	#540×C₈₉	C₂²	1	2	yes	—
43	#539×C₈₉	—	2	2	no	—
44	#537×C₈₉	C₂²	1	1	yes	characteristic
45	#537×C₈₉	C₂²	1	1	yes	characteristic
46	#537×C₈₉	C₂²	1	1	yes	characteristic
47	#536×C₈₉	C₂²	1	1	yes	characteristic
48	#536×C₈₉	C₂²	1	1	yes	characteristic
49	#533×C₈₉	—	2	1	no	—
50	#533×C₈₉	C₂²	1	2	yes	—
51	#532×C₈₉	C₂²	1	1	yes	characteristic
52	#529×C₈₉	—	2	2	no	—
53	#529×C₈₉	—	2	1	no	—
54	#529×C₈₉	C₂²	1	2	yes	—
55	#529×C₈₉	C₂²	1	2	yes	—
56	#529×C₈₉	C₂²	1	2	yes	—
57	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
58	#520×C₈₉	C₂²	1	1	yes	characteristic
59	#520×C₈₉	C₂²	1	1	yes	characteristic
60	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
61	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
62	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
63	#479×C₈₉	C₂²	1	2	yes	—
64	#479×C₈₉	C₂²	1	2	yes	—
65	#479×C₈₉	C₂²	1	2	yes	—
66	#479×C₈₉	C₂²	1	2	yes	—
67	#479×C₈₉	C₂²	1	2	yes	—
68	#479×C₈₉	C₂²	1	2	yes	—
69	#479×C₈₉	C₂²	1	2	yes	—
70	#479×C₈₉	C₂²	1	2	yes	—
71	#478×C₈₉	C₂²	1	2	yes	—
72	#478×C₈₉	C₂²	1	2	yes	—
73	#478×C₈₉	C₂²	1	2	yes	—
74	#478×C₈₉	C₂²	1	2	yes	—
75	#477×C₈₉	C₂²	1	2	yes	—
76	#476×C₈₉	C₂²	1	2	yes	—
77	#475×C₈₉	C₂²	1	2	yes	—
78	#474×C₈₉	C₂²	1	2	yes	—
79	#470×C₈₉	C₂²	1	2	yes	—
80	#470×C₈₉	C₂²	1	2	yes	—
81	#470×C₈₉	C₂²	1	2	yes	—
82	#469×C₈₉	C₂²	1	2	yes	—
83	#468×C₈₉	C₂²	1	2	yes	—
84	#468×C₈₉	C₂²	1	2	yes	—
85	#468×C₈₉	C₂²	1	2	yes	—
86	#468×C₈₉	C₂²	1	2	yes	—
87	#467×C₈₉	C₂²	1	2	yes	—
88	#467×C₈₉	C₂²	1	2	yes	—
89	#467×C₈₉	C₂²	1	2	yes	—
90	#466×C₈₉	C₂²	1	2	yes	—
91	#465×C₈₉	C₂²	1	2	yes	—
92	#465×C₈₉	C₂²	1	2	yes	—
93	#465×C₈₉	C₂²	1	2	yes	—
94	#465×C₈₉	C₂²	1	2	yes	—
95	#464×C₈₉	C₂²	1	1	yes	characteristic
96	#464×C₈₉	C₂²	1	2	yes	—
97	#464×C₈₉	C₂²	1	2	yes	—
98	#464×C₈₉	C₂²	1	2	yes	—
99	#464×C₈₉	C₂²	1	1	yes	characteristic
100	#464×C₈₉	C₂²	1	2	yes	—
101	#463×C₈₉	C₂²	1	1	yes	characteristic
102	#463×C₈₉	C₂²	1	2	yes	—
103	#463×C₈₉	C₂²	1	1	yes	characteristic
104	#463×C₈₉	C₂²	1	2	yes	—
105	#462×C₈₉	C₂²	1	2	yes	—
106	#462×C₈₉	C₂²	1	2	yes	—
107	#462×C₈₉	C₂²	1	2	yes	—
108	#462×C₈₉	C₂²	1	1	yes	characteristic
109	#461×C₈₉	C₂²	1	2	yes	—
110	#461×C₈₉	C₂²	1	2	yes	—
111	#461×C₈₉	C₂²	1	1	yes	characteristic
112	#460×C₈₉	C₂²	1	2	yes	—
113	#460×C₈₉	C₂²	1	1	yes	characteristic
114	#459×C₈₉	C₂²	1	1	yes	characteristic
115	#428×C₈₉	C₂²	1	1	yes	characteristic
116	#428×C₈₉	C₂²	1	1	yes	characteristic
117	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
118	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
119	#424×C₈₉	C₂²	1	1	yes	characteristic
120	#424×C₈₉	C₂²	1	1	yes	characteristic
121	#424×C₈₉	C₂²	1	2	yes	—
122	#424×C₈₉	C₂²	1	2	yes	—
123	#423×C₈₉	C₂²	1	1	yes	characteristic
124	#423×C₈₉	C₂²	1	2	yes	—
125	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
126	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
127	#417×C₈₉	C₂²	1	1	yes	characteristic
128	#417×C₈₉	C₂²	1	1	yes	characteristic
129	#417×C₈₉	C₂²	1	1	yes	characteristic
130	#417×C₈₉	C₂²	1	1	yes	characteristic
131	#416×C₈₉	C₂²	1	1	yes	characteristic
132	#416×C₈₉	C₂²	1	1	yes	characteristic
133	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
134	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
135	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
136	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
137	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
138	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
140	#137×C₈₉	—	4	2	no	—
141	#137×C₈₉	—	4	2	no	—
142	#135×C₈₉	—	4	2	no	—
143	#135×C₈₉	—	4	2	no	—
144	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
153	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
154	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
155	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
156	#131×C₈₉	—	4	2	no	—
157	#131×C₈₉	—	4	2	no	—
158	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
159	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
160	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
161	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
162	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
163	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
164	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
165	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
166	C₄⋊Q₈×C₈₉	—	2	1	no	—
167	C₄⋊Q₈×C₈₉	—	2	1	no	—
168	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
169	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
171	#127×C₈₉	C₂³	1	1	yes	characteristic
172	#126×C₈₉	—	2	2	no	—
173	#126×C₈₉	—	2	2	no	—
174	#126×C₈₉	—	2	2	no	—
175	#126×C₈₉	—	2	2	no	—
176	#126×C₈₉	—	2	2	no	—
177	#126×C₈₉	—	2	2	no	—
178	#126×C₈₉	—	2	2	no	—
179	#126×C₈₉	—	2	2	no	—
180	#125×C₈₉	—	2	2	no	—
181	#125×C₈₉	—	2	1	no	—
182	#125×C₈₉	—	2	2	no	—
183	#125×C₈₉	—	2	2	no	—
184	#125×C₈₉	—	2	2	no	—
185	#125×C₈₉	—	2	1	no	—
186	#125×C₈₉	—	2	1	no	—
187	#125×C₈₉	—	2	2	no	—
188	#125×C₈₉	C₂³	1	2	yes	—
189	#125×C₈₉	C₂³	1	2	yes	—
190	#125×C₈₉	C₂³	1	2	yes	—
191	#124×C₈₉	—	2	1	no	—
192	#124×C₈₉	—	2	2	no	—
193	#124×C₈₉	C₂³	1	2	yes	—
194	#124×C₈₉	C₂³	1	1	yes	characteristic
195	#124×C₈₉	C₂³	1	1	yes	characteristic
196	#123×C₈₉	—	2	2	no	—
197	#123×C₈₉	—	2	2	no	—
198	#123×C₈₉	—	2	2	no	—
199	#123×C₈₉	—	2	2	no	—
200	#123×C₈₉	—	2	2	no	—
201	#123×C₈₉	—	2	2	no	—
202	#123×C₈₉	—	2	2	no	—
203	#123×C₈₉	—	2	2	no	—
204	C₂²⋊Q₈×C₈₉	—	2	1	no	—
205	C₂²⋊Q₈×C₈₉	—	2	1	no	—
206	C₂²⋊Q₈×C₈₉	—	2	1	no	—
207	C₂²⋊Q₈×C₈₉	—	2	2	no	—
208	C₂²⋊Q₈×C₈₉	—	2	1	no	—
209	C₂²⋊Q₈×C₈₉	—	2	1	no	—
210	C₂²⋊Q₈×C₈₉	—	2	2	no	—
211	C₂²⋊Q₈×C₈₉	—	2	2	no	—
212	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
213	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
214	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
215	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
216	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
217	#121×C₈₉	—	2	2	no	—
218	#121×C₈₉	—	2	1	no	—
219	#121×C₈₉	—	2	1	no	—
220	#121×C₈₉	—	2	1	no	—
221	#121×C₈₉	—	2	2	no	—
222	#121×C₈₉	—	2	2	no	—
223	#121×C₈₉	—	2	1	no	—
224	#121×C₈₉	—	2	1	no	—
225	#121×C₈₉	—	2	2	no	—
226	#121×C₈₉	—	2	2	no	—
227	#121×C₈₉	C₂³	1	2	yes	—
228	#121×C₈₉	C₂³	1	2	yes	—
229	#121×C₈₉	C₂³	1	2	yes	—
230	C₄×Q₈×C₈₉	—	2	1	no	—
231	C₄×Q₈×C₈₉	—	2	1	no	—
232	C₄×Q₈×C₈₉	—	2	2	no	—
233	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
234	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
235	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
236	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
238	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
239	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
240	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₈₉	—	2	1	no	—
242	C₄×D₄×C₈₉	—	2	1	no	—
243	C₄×D₄×C₈₉	—	2	2	no	—
244	C₄×D₄×C₈₉	—	2	2	no	—
245	C₄×D₄×C₈₉	—	2	2	no	—
246	C₄×D₄×C₈₉	—	2	2	no	—
247	C₄×D₄×C₈₉	—	2	2	no	—
248	C₄×D₄×C₈₉	—	2	1	no	—
249	C₄×D₄×C₈₉	—	2	1	no	—
250	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
251	C₄×D₄×C₈₉	D₄	1	2	yes	—
252	C₄×D₄×C₈₉	D₄	1	2	yes	—
253	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
254	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₈₉	C₂³	1	2	yes	—
256	C₄×D₄×C₈₉	C₂³	1	2	yes	—
257	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
258	#117×C₈₉	—	2	2	no	—
259	#117×C₈₉	—	2	1	no	—
260	#117×C₈₉	—	2	1	no	—
261	#117×C₈₉	—	2	1	no	—
262	#117×C₈₉	—	2	2	no	—
263	#117×C₈₉	—	2	2	no	—
264	#117×C₈₉	—	2	2	no	—
265	#117×C₈₉	C₂³	1	1	yes	characteristic
266	#117×C₈₉	C₂³	1	1	yes	characteristic
267	#117×C₈₉	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
269	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
270	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
271	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
272	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
273	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
276	C₂×C₄²×C₈₉	—	2	1	no	—
277	C₂×C₄²×C₈₉	—	2	1	no	—
278	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
279	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
280	#107×C₈₉	C₂³	1	2	yes	—
281	#107×C₈₉	C₂³	1	2	yes	—
282	#107×C₈₉	C₂³	1	2	yes	—
283	#107×C₈₉	C₂³	1	2	yes	—
284	#106×C₈₉	C₂³	1	2	yes	—
285	#106×C₈₉	C₂³	1	2	yes	—
286	#106×C₈₉	C₂³	1	2	yes	—
287	#106×C₈₉	C₂³	1	2	yes	—
288	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
289	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
290	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
291	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
292	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
293	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
294	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
295	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
296	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
297	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
298	#103×C₈₉	C₂³	1	2	yes	—
299	#103×C₈₉	C₂³	1	2	yes	—
300	#103×C₈₉	C₂³	1	2	yes	—
301	#103×C₈₉	C₂³	1	2	yes	—
302	#103×C₈₉	C₂³	1	1	yes	characteristic
303	#103×C₈₉	C₂³	1	1	yes	characteristic
304	#103×C₈₉	C₂³	1	1	yes	characteristic
305	#103×C₈₉	C₂³	1	1	yes	characteristic
306	#103×C₈₉	C₂³	1	2	yes	—
307	#103×C₈₉	C₂³	1	2	yes	—
308	#103×C₈₉	C₂³	1	2	yes	—
309	#103×C₈₉	C₂³	1	2	yes	—
310	#102×C₈₉	C₂³	1	1	yes	characteristic
311	#102×C₈₉	C₂³	1	1	yes	characteristic
312	#102×C₈₉	C₂³	1	1	yes	characteristic
313	#102×C₈₉	C₂³	1	1	yes	characteristic
314	#102×C₈₉	C₂³	1	2	yes	—
315	#102×C₈₉	C₂³	1	2	yes	—
316	#102×C₈₉	C₂³	1	2	yes	—
317	#102×C₈₉	C₂³	1	2	yes	—
318	#41×C₈₉	—	2	2	no	—
319	#41×C₈₉	—	2	2	no	—
320	#41×C₈₉	—	2	2	no	—
321	#41×C₈₉	—	2	2	no	—
322	#41×C₈₉	—	2	2	no	—
323	#41×C₈₉	—	2	2	no	—
324	#41×C₈₉	—	2	2	no	—
325	#41×C₈₉	—	2	2	no	—
326	C₂×Q₈×C₈₉	—	2	1	no	—
327	C₂×Q₈×C₈₉	—	2	2	no	—
328	C₂×Q₈×C₈₉	—	2	2	no	—
329	C₂×Q₈×C₈₉	—	2	2	no	—
330	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₈₉	—	2	1	no	—
336	C₂×D₄×C₈₉	—	2	1	no	—
337	C₂×D₄×C₈₉	—	2	1	no	—
338	C₂×D₄×C₈₉	—	2	2	no	—
339	C₂×D₄×C₈₉	—	2	2	no	—
340	C₂×D₄×C₈₉	—	2	2	no	—
341	C₂×D₄×C₈₉	—	2	1	no	—
342	C₂×D₄×C₈₉	—	2	1	no	—
343	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
345	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
347	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₈₉	—	2	1	no	—
349	C₂²×C₄×C₈₉	—	2	1	no	—
350	C₂²×C₄×C₈₉	—	2	1	no	—
351	C₂²×C₄×C₈₉	—	2	1	no	—
352	C₂²×C₄×C₈₉	—	2	1	no	—
353	C₂²×C₄×C₈₉	—	2	1	no	—
354	C₂²×C₄×C₈₉	—	2	1	no	—
355	C₂²×C₄×C₈₉	—	2	1	no	—
356	C₂²×C₄×C₈₉	—	2	1	no	—
357	C₂²×C₄×C₈₉	—	2	2	no	—
358	C₂²×C₄×C₈₉	—	2	2	no	—
359	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
362	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
363	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
364	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
365	Q₁₆×C₈₉	—	4	1	no	—
366	Q₁₆×C₈₉	—	4	1	no	—
367	Q₁₆×C₈₉	—	4	2	no	—
368	Q₁₆×C₈₉	—	4	2	no	—
369	SD₁₆×C₈₉	—	4	1	no	—
370	SD₁₆×C₈₉	—	4	1	no	—
371	SD₁₆×C₈₉	—	4	1	no	—
372	SD₁₆×C₈₉	—	4	1	no	—
373	SD₁₆×C₈₉	—	4	2	no	—
374	SD₁₆×C₈₉	—	4	2	no	—
375	D₈×C₈₉	—	4	1	no	—
376	D₈×C₈₉	—	4	1	no	—
377	M₁₆×C₈₉	—	2	2	no	—
378	M₁₆×C₈₉	—	2	2	no	—
379	M₁₆×C₈₉	—	4	2	no	—
380	M₁₆×C₈₉	—	4	2	no	—
381	C₂×C₈×C₈₉	—	2	2	no	—
382	C₂×C₈×C₈₉	—	2	2	no	—
383	C₂×C₈×C₈₉	—	4	2	no	—
384	C₂×C₈×C₈₉	—	4	2	no	—
385	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
386	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
387	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
391	C₄⋊C₄×C₈₉	—	2	1	no	—
392	C₄⋊C₄×C₈₉	—	2	1	no	—
393	C₄⋊C₄×C₈₉	—	2	2	no	—
394	C₄⋊C₄×C₈₉	—	2	2	no	—
395	C₄⋊C₄×C₈₉	—	2	2	no	—
396	C₄⋊C₄×C₈₉	—	2	2	no	—
397	C₄⋊C₄×C₈₉	—	2	2	no	—
398	C₄⋊C₄×C₈₉	—	2	2	no	—
399	C₄⋊C₄×C₈₉	—	2	2	no	—
400	C₄⋊C₄×C₈₉	—	2	2	no	—
401	C₄⋊C₄×C₈₉	—	2	1	no	—
402	C₄⋊C₄×C₈₉	—	2	1	no	—
403	C₄⋊C₄×C₈₉	—	2	1	no	—
404	C₄⋊C₄×C₈₉	—	2	2	no	—
405	C₄⋊C₄×C₈₉	—	2	2	no	—
406	C₄⋊C₄×C₈₉	—	2	2	no	—
407	C₄⋊C₄×C₈₉	—	2	2	no	—
408	C₄⋊C₄×C₈₉	—	2	2	no	—
409	C₄⋊C₄×C₈₉	—	2	2	no	—
410	C₄⋊C₄×C₈₉	—	2	1	no	—
411	C₄⋊C₄×C₈₉	—	2	1	no	—
412	C₄⋊C₄×C₈₉	—	2	2	no	—
413	C₄⋊C₄×C₈₉	—	2	2	no	—
414	C₄⋊C₄×C₈₉	—	2	2	no	—
415	C₄⋊C₄×C₈₉	—	2	2	no	—
416	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
417	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
418	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
420	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
421	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
424	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
425	C₂²⋊C₄×C₈₉	—	2	2	no	—
426	C₂²⋊C₄×C₈₉	—	2	2	no	—
427	C₂²⋊C₄×C₈₉	—	2	1	no	—
428	C₂²⋊C₄×C₈₉	—	2	2	no	—
429	C₂²⋊C₄×C₈₉	—	2	2	no	—
430	C₂²⋊C₄×C₈₉	—	2	2	no	—
431	C₂²⋊C₄×C₈₉	—	2	1	no	—
432	C₂²⋊C₄×C₈₉	—	2	1	no	—
433	C₂²⋊C₄×C₈₉	—	2	2	no	—
434	C₂²⋊C₄×C₈₉	—	2	2	no	—
435	C₂²⋊C₄×C₈₉	—	2	1	no	—
436	C₂²⋊C₄×C₈₉	—	2	1	no	—
437	C₂²⋊C₄×C₈₉	—	2	2	no	—
438	C₂²⋊C₄×C₈₉	—	2	2	no	—
439	C₂²⋊C₄×C₈₉	—	2	2	no	—
440	C₂²⋊C₄×C₈₉	—	2	2	no	—
441	C₂²⋊C₄×C₈₉	—	2	1	no	—
442	C₂²⋊C₄×C₈₉	—	2	1	no	—
443	C₂²⋊C₄×C₈₉	—	2	2	no	—
444	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
447	C₄²×C₈₉	—	2	2	no	—
448	C₄²×C₈₉	—	2	1	no	—
449	C₄²×C₈₉	—	2	1	no	—
450	C₄²×C₈₉	—	2	1	no	—
451	C₄²×C₈₉	—	2	2	no	—
452	C₄²×C₈₉	—	2	2	no	—
453	C₄²×C₈₉	—	2	2	no	—
454	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₈₉	C₂×D₄	1	2	yes	—
456	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₈₉	C₂×D₄	1	2	yes	—
458	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
459	C₄²×C₈₉	C₂⁴	1	2	yes	—
460	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
461	C₂³×C₈₉	—	2	1	no	—
462	C₂³×C₈₉	—	2	1	no	—
463	C₂³×C₈₉	—	2	1	no	—
464	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
465	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
466	Q₈×C₈₉	—	2	2	no	—
467	Q₈×C₈₉	—	2	2	no	—
468	Q₈×C₈₉	—	2	1	no	—
469	Q₈×C₈₉	—	2	1	no	—
470	Q₈×C₈₉	—	2	1	no	—
471	Q₈×C₈₉	—	2	2	no	—
472	Q₈×C₈₉	—	2	1	no	—
473	Q₈×C₈₉	—	2	1	no	—
474	Q₈×C₈₉	—	2	1	no	—
475	Q₈×C₈₉	—	4	2	no	—
476	Q₈×C₈₉	—	8	2	no	—
477	D₄×C₈₉	—	2	4	no	—
478	D₄×C₈₉	—	2	2	no	—
479	D₄×C₈₉	—	2	1	no	—
480	D₄×C₈₉	—	2	1	no	—
481	D₄×C₈₉	—	2	1	no	—
482	D₄×C₈₉	—	2	1	no	—
483	D₄×C₈₉	—	2	1	no	—
484	D₄×C₈₉	—	2	1	no	—
485	D₄×C₈₉	—	4	2	no	—
486	D₄×C₈₉	—	4	2	no	—
487	D₄×C₈₉	—	4	2	no	—
488	D₄×C₈₉	—	8	1	no	—
489	D₄×C₈₉	—	8	1	no	—
490	D₄×C₈₉	—	8	2	no	—
491	D₄×C₈₉	—	8	2	no	—
492	D₄×C₈₉	—	8	2	no	—
493	C₂×C₄×C₈₉	—	2	2	no	—
494	C₂×C₄×C₈₉	—	2	2	no	—
495	C₂×C₄×C₈₉	—	2	1	no	—
496	C₂×C₄×C₈₉	—	2	1	no	—
497	C₂×C₄×C₈₉	—	2	1	no	—
498	C₂×C₄×C₈₉	—	2	2	no	—
499	C₂×C₄×C₈₉	—	2	1	no	—
500	C₂×C₄×C₈₉	—	2	1	no	—
501	C₂×C₄×C₈₉	—	2	2	no	—
502	C₂×C₄×C₈₉	—	2	2	no	—
503	C₂×C₄×C₈₉	—	2	2	no	—
504	C₂×C₄×C₈₉	—	4	1	no	—
505	C₂×C₄×C₈₉	—	4	2	no	—
506	C₂×C₄×C₈₉	—	4	2	no	—
507	C₂×C₄×C₈₉	—	4	1	no	—
508	C₂×C₄×C₈₉	—	4	2	no	—
509	C₂×C₄×C₈₉	—	4	2	no	—
510	C₂×C₄×C₈₉	—	4	2	no	—
511	C₂×C₄×C₈₉	—	4	2	no	—
512	C₂×C₄×C₈₉	—	4	2	no	—
513	C₂×C₄×C₈₉	—	8	1	no	—
514	C₂×C₄×C₈₉	—	8	2	no	—
515	C₂×C₄×C₈₉	—	8	2	no	—
516	C₂×C₄×C₈₉	—	8	1	no	—
517	C₂×C₄×C₈₉	—	8	1	no	—
518	C₂×C₄×C₈₉	—	8	1	no	—
519	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
528	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
529	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
530	C₈×C₈₉	—	2	1	no	—
531	C₈×C₈₉	—	2	1	no	—
532	C₈×C₈₉	—	2	1	no	—
533	C₈×C₈₉	—	2	1	no	—
534	C₈×C₈₉	—	2	2	no	—
535	C₈×C₈₉	—	2	2	no	—
536	C₂²×C₈₉	—	2	1	no	—
537	C₂²×C₈₉	—	2	1	no	—
538	C₂²×C₈₉	—	2	2	no	—
539	C₂²×C₈₉	—	2	2	no	—
540	C₂²×C₈₉	—	2	2	no	—
541	C₂²×C₈₉	—	4	1	no	—
542	C₂²×C₈₉	—	4	1	no	—
543	C₂²×C₈₉	—	4	1	no	—
544	C₂²×C₈₉	—	4	1	no	—
545	C₂²×C₈₉	—	4	1	no	—
546	C₂²×C₈₉	—	4	1	no	—
547	C₂²×C₈₉	—	4	1	no	—
548	C₂²×C₈₉	—	4	1	no	—
549	C₂²×C₈₉	—	4	1	no	—
550	C₂²×C₈₉	#537	1	2	yes	—
551	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
552	C₄×C₈₉	—	2	1	no	—
553	C₄×C₈₉	—	2	1	no	—
554	C₄×C₈₉	—	2	2	no	—
555	C₄×C₈₉	—	2	1	no	—
556	C₄×C₈₉	—	2	2	no	—
557	C₄×C₈₉	—	2	1	no	—
558	C₄×C₈₉	—	2	2	no	—
559	C₄×C₈₉	—	4	2	no	—
560	C₄×C₈₉	—	4	2	no	—
561	C₄×C₈₉	—	4	1	no	—
562	C₄×C₈₉	—	4	1	no	—
563	C₄×C₈₉	—	4	2	no	—
564	C₄×C₈₉	—	4	1	no	—
565	C₄×C₈₉	—	4	1	no	—
566	C₄×C₈₉	—	4	1	no	—
567	C₄×C₈₉	—	4	2	no	—
568	C₄×C₈₉	#537	1	2	yes	—
569	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
570	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
571	#60932	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
572	C₂×C₈₉	—	2	2	no	—
573	C₂×C₈₉	—	4	2	no	—
574	C₂×C₈₉	—	8	1	no	—
575	C₂×C₈₉	—	8	1	no	—
576	C₂×C₈₉	—	8	1	no	—
577	C₂×C₈₉	C₂×#537	1	1	yes	characteristic
578	C₂×C₈₉	#3584	1	1	yes	characteristic
579	C₂×C₈₉	#3586	1	1	yes	characteristic
580	#3512	C₂×C₈₉	1	1	yes	characteristic, complemented
581	#3461	C₂×C₈₉	1	1	yes	characteristic, complemented
582	#3261	C₂×C₈₉	1	2	yes	complemented
583	#3260	C₂×C₈₉	1	2	yes	complemented
584	#3258	C₂×C₈₉	1	2	yes	complemented
585	#3257	C₂×C₈₉	1	2	yes	complemented
586	#3256	C₂×C₈₉	1	2	yes	complemented
587	#3252	C₂×C₈₉	1	2	yes	complemented
588	#3250	C₂×C₈₉	1	2	yes	complemented
589	#3248	C₂×C₈₉	1	2	yes	complemented
590	#3084	C₂×C₈₉	1	1	yes	characteristic, complemented
591	#3083	C₂×C₈₉	1	1	yes	characteristic, complemented
592	#3080	C₂×C₈₉	1	1	yes	characteristic, complemented
593	C₂×#479	C₂×C₈₉	1	1	yes	characteristic, complemented
594	#3063	C₂×C₈₉	1	1	yes	characteristic, complemented
595	#3063	C₂×C₈₉	1	1	yes	characteristic, complemented
596	#3061	C₂×C₈₉	1	1	yes	characteristic, complemented
597	#3060	C₂×C₈₉	1	1	yes	characteristic, complemented
598	#3046	C₂×C₈₉	1	1	yes	characteristic, complemented
599	#3046	C₂×C₈₉	1	1	yes	characteristic, complemented
600	#3037	C₂×C₈₉	1	1	yes	characteristic, complemented
601	#3035	C₂×C₈₉	1	1	yes	characteristic, complemented
602	#2906	C₂×C₈₉	1	1	yes	characteristic, complemented
603	C₈₉	#60932	1	1	yes	characteristic, direct product factor, Sylow
604	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
605	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
606	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
607	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
608	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
609	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
610	#553	—	2	2	no	—
611	#553	—	2	2	no	—
612	#553	—	2	1	no	—
613	#553	—	2	1	no	—
614	#552	—	2	1	no	—
615	#552	—	2	1	no	—
616	#544	C₂²×C₈₉	1	1	yes	characteristic
617	#542	—	2	1	no	—
618	#542	C₂²×C₈₉	1	2	yes	—
619	#541	—	2	1	no	—
620	#541	C₂²×C₈₉	1	2	yes	—
621	#541	C₂²×C₈₉	1	2	yes	—
622	#540	C₂²×C₈₉	1	2	yes	—
623	#539	—	2	2	no	—
624	#537	C₂²×C₈₉	1	1	yes	characteristic
625	#537	C₂²×C₈₉	1	1	yes	characteristic
626	#537	C₂²×C₈₉	1	1	yes	characteristic
627	#536	C₂²×C₈₉	1	1	yes	characteristic
628	#536	C₂²×C₈₉	1	1	yes	characteristic
629	#533	—	2	1	no	—
630	#533	C₂²×C₈₉	1	2	yes	—
631	#532	C₂²×C₈₉	1	1	yes	characteristic
632	#529	—	2	2	no	—
633	#529	—	2	1	no	—
634	#529	C₂²×C₈₉	1	2	yes	—
635	#529	C₂²×C₈₉	1	2	yes	—
636	#529	C₂²×C₈₉	1	2	yes	—
637	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
638	#520	C₂²×C₈₉	1	1	yes	characteristic
639	#520	C₂²×C₈₉	1	1	yes	characteristic
640	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
641	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
642	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
643	#479	C₂²×C₈₉	1	2	yes	—
644	#479	C₂²×C₈₉	1	2	yes	—
645	#479	C₂²×C₈₉	1	2	yes	—
646	#479	C₂²×C₈₉	1	2	yes	—
647	#479	C₂²×C₈₉	1	2	yes	—
648	#479	C₂²×C₈₉	1	2	yes	—
649	#479	C₂²×C₈₉	1	2	yes	—
650	#479	C₂²×C₈₉	1	2	yes	—
651	#478	C₂²×C₈₉	1	2	yes	—
652	#478	C₂²×C₈₉	1	2	yes	—
653	#478	C₂²×C₈₉	1	2	yes	—
654	#478	C₂²×C₈₉	1	2	yes	—
655	#477	C₂²×C₈₉	1	2	yes	—
656	#476	C₂²×C₈₉	1	2	yes	—
657	#475	C₂²×C₈₉	1	2	yes	—
658	#474	C₂²×C₈₉	1	2	yes	—
659	#470	C₂²×C₈₉	1	2	yes	—
660	#470	C₂²×C₈₉	1	2	yes	—
661	#470	C₂²×C₈₉	1	2	yes	—
662	#469	C₂²×C₈₉	1	2	yes	—
663	#468	C₂²×C₈₉	1	2	yes	—
664	#468	C₂²×C₈₉	1	2	yes	—
665	#468	C₂²×C₈₉	1	2	yes	—
666	#468	C₂²×C₈₉	1	2	yes	—
667	#467	C₂²×C₈₉	1	2	yes	—
668	#467	C₂²×C₈₉	1	2	yes	—
669	#467	C₂²×C₈₉	1	2	yes	—
670	#466	C₂²×C₈₉	1	2	yes	—
671	#465	C₂²×C₈₉	1	2	yes	—
672	#465	C₂²×C₈₉	1	2	yes	—
673	#465	C₂²×C₈₉	1	2	yes	—
674	#465	C₂²×C₈₉	1	2	yes	—
675	#464	C₂²×C₈₉	1	1	yes	characteristic
676	#464	C₂²×C₈₉	1	2	yes	—
677	#464	C₂²×C₈₉	1	2	yes	—
678	#464	C₂²×C₈₉	1	2	yes	—
679	#464	C₂²×C₈₉	1	1	yes	characteristic
680	#464	C₂²×C₈₉	1	2	yes	—
681	#463	C₂²×C₈₉	1	1	yes	characteristic
682	#463	C₂²×C₈₉	1	2	yes	—
683	#463	C₂²×C₈₉	1	1	yes	characteristic
684	#463	C₂²×C₈₉	1	2	yes	—
685	#462	C₂²×C₈₉	1	2	yes	—
686	#462	C₂²×C₈₉	1	2	yes	—
687	#462	C₂²×C₈₉	1	2	yes	—
688	#462	C₂²×C₈₉	1	1	yes	characteristic
689	#461	C₂²×C₈₉	1	2	yes	—
690	#461	C₂²×C₈₉	1	2	yes	—
691	#461	C₂²×C₈₉	1	1	yes	characteristic
692	#460	C₂²×C₈₉	1	2	yes	—
693	#460	C₂²×C₈₉	1	1	yes	characteristic
694	#459	C₂²×C₈₉	1	1	yes	characteristic
695	#428	C₂²×C₈₉	1	1	yes	characteristic
696	#428	C₂²×C₈₉	1	1	yes	characteristic
697	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
698	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
699	#424	C₂²×C₈₉	1	1	yes	characteristic
700	#424	C₂²×C₈₉	1	1	yes	characteristic
701	#424	C₂²×C₈₉	1	2	yes	—
702	#424	C₂²×C₈₉	1	2	yes	—
703	#423	C₂²×C₈₉	1	1	yes	characteristic
704	#423	C₂²×C₈₉	1	2	yes	—
705	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
706	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
707	#417	C₂²×C₈₉	1	1	yes	characteristic
708	#417	C₂²×C₈₉	1	1	yes	characteristic
709	#417	C₂²×C₈₉	1	1	yes	characteristic
710	#417	C₂²×C₈₉	1	1	yes	characteristic
711	#416	C₂²×C₈₉	1	1	yes	characteristic
712	#416	C₂²×C₈₉	1	1	yes	characteristic
713	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
714	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
715	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
716	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
717	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
718	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
719	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
720	#137	—	4	2	no	—
721	#137	—	4	2	no	—
722	#135	—	4	2	no	—
723	#135	—	4	2	no	—
724	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
725	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
726	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
727	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
728	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
729	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
730	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
731	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
732	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
734	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
735	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
736	#131	—	4	2	no	—
737	#131	—	4	2	no	—
738	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
739	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
740	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
741	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
742	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
743	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
744	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
745	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
746	C₄⋊Q₈	—	2	1	no	—
747	C₄⋊Q₈	—	2	1	no	—
748	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
749	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
750	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
751	#127	C₂³×C₈₉	1	1	yes	characteristic
752	#126	—	2	2	no	—
753	#126	—	2	2	no	—
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	—	2	2	no	—
759	#126	—	2	2	no	—
760	#125	—	2	2	no	—
761	#125	—	2	1	no	—
762	#125	—	2	2	no	—
763	#125	—	2	2	no	—
764	#125	—	2	2	no	—
765	#125	—	2	1	no	—
766	#125	—	2	1	no	—
767	#125	—	2	2	no	—
768	#125	C₂³×C₈₉	1	2	yes	—
769	#125	C₂³×C₈₉	1	2	yes	—
770	#125	C₂³×C₈₉	1	2	yes	—
771	#124	—	2	1	no	—
772	#124	—	2	2	no	—
773	#124	C₂³×C₈₉	1	1	yes	characteristic
774	#124	C₂³×C₈₉	1	1	yes	characteristic
775	#124	C₂³×C₈₉	1	2	yes	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	C₂²⋊Q₈	—	2	1	no	—
785	C₂²⋊Q₈	—	2	1	no	—
786	C₂²⋊Q₈	—	2	1	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	1	no	—
789	C₂²⋊Q₈	—	2	1	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
793	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
794	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
795	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
796	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
797	#121	—	2	2	no	—
798	#121	—	2	1	no	—
799	#121	—	2	1	no	—
800	#121	—	2	1	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	—	2	1	no	—
804	#121	—	2	1	no	—
805	#121	—	2	2	no	—
806	#121	—	2	2	no	—
807	#121	C₂³×C₈₉	1	2	yes	—
808	#121	C₂³×C₈₉	1	2	yes	—
809	#121	C₂³×C₈₉	1	2	yes	—
810	C₄×Q₈	—	2	1	no	—
811	C₄×Q₈	—	2	1	no	—
812	C₄×Q₈	—	2	2	no	—
813	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
814	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
815	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
816	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
817	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
818	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
819	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
820	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
831	C₄×D₄	D₄×C₈₉	1	2	yes	—
832	C₄×D₄	D₄×C₈₉	1	2	yes	—
833	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
834	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
835	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
836	C₄×D₄	C₂³×C₈₉	1	2	yes	—
837	C₄×D₄	C₂³×C₈₉	1	2	yes	—
838	#117	—	2	2	no	—
839	#117	—	2	1	no	—
840	#117	—	2	1	no	—
841	#117	—	2	1	no	—
842	#117	—	2	2	no	—
843	#117	—	2	2	no	—
844	#117	—	2	2	no	—
845	#117	C₂³×C₈₉	1	1	yes	characteristic
846	#117	C₂³×C₈₉	1	1	yes	characteristic
847	#117	C₂³×C₈₉	1	2	yes	—
848	C₂×C₄⋊C₄	—	2	1	no	—
849	C₂×C₄⋊C₄	—	2	1	no	—
850	C₂×C₄⋊C₄	—	2	1	no	—
851	C₂×C₄⋊C₄	—	2	1	no	—
852	C₂×C₄⋊C₄	—	2	1	no	—
853	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
854	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
855	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
856	C₂×C₄²	—	2	1	no	—
857	C₂×C₄²	—	2	1	no	—
858	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
859	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
860	#107	C₂³×C₈₉	1	2	yes	—
861	#107	C₂³×C₈₉	1	2	yes	—
862	#107	C₂³×C₈₉	1	2	yes	—
863	#107	C₂³×C₈₉	1	2	yes	—
864	#106	C₂³×C₈₉	1	2	yes	—
865	#106	C₂³×C₈₉	1	2	yes	—
866	#106	C₂³×C₈₉	1	2	yes	—
867	#106	C₂³×C₈₉	1	2	yes	—
868	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
869	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
870	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
871	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
872	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
873	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
874	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
875	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
876	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
877	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
878	#103	C₂³×C₈₉	1	2	yes	—
879	#103	C₂³×C₈₉	1	2	yes	—
880	#103	C₂³×C₈₉	1	2	yes	—
881	#103	C₂³×C₈₉	1	2	yes	—
882	#103	C₂³×C₈₉	1	1	yes	characteristic
883	#103	C₂³×C₈₉	1	1	yes	characteristic
884	#103	C₂³×C₈₉	1	1	yes	characteristic
885	#103	C₂³×C₈₉	1	1	yes	characteristic
886	#103	C₂³×C₈₉	1	2	yes	—
887	#103	C₂³×C₈₉	1	2	yes	—
888	#103	C₂³×C₈₉	1	2	yes	—
889	#103	C₂³×C₈₉	1	2	yes	—
890	#102	C₂³×C₈₉	1	1	yes	characteristic
891	#102	C₂³×C₈₉	1	1	yes	characteristic
892	#102	C₂³×C₈₉	1	1	yes	characteristic
893	#102	C₂³×C₈₉	1	1	yes	characteristic
894	#102	C₂³×C₈₉	1	2	yes	—
895	#102	C₂³×C₈₉	1	2	yes	—
896	#102	C₂³×C₈₉	1	2	yes	—
897	#102	C₂³×C₈₉	1	2	yes	—
898	#41	—	2	2	no	—
899	#41	—	2	2	no	—
900	#41	—	2	2	no	—
901	#41	—	2	2	no	—
902	#41	—	2	2	no	—
903	#41	—	2	2	no	—
904	#41	—	2	2	no	—
905	#41	—	2	2	no	—
906	C₂×Q₈	—	2	1	no	—
907	C₂×Q₈	—	2	2	no	—
908	C₂×Q₈	—	2	2	no	—
909	C₂×Q₈	—	2	2	no	—
910	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
911	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
912	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
913	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
914	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
924	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
925	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
926	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
927	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
940	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
941	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
942	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
943	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
944	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
945	Q₁₆	—	4	1	no	—
946	Q₁₆	—	4	1	no	—
947	Q₁₆	—	4	2	no	—
948	Q₁₆	—	4	2	no	—
949	SD₁₆	—	4	1	no	—
950	SD₁₆	—	4	1	no	—
951	SD₁₆	—	4	1	no	—
952	SD₁₆	—	4	1	no	—
953	SD₁₆	—	4	2	no	—
954	SD₁₆	—	4	2	no	—
955	D₈	—	4	1	no	—
956	D₈	—	4	1	no	—
957	M₁₆	—	2	2	no	—
958	M₁₆	—	2	2	no	—
959	M₁₆	—	4	2	no	—
960	M₁₆	—	4	2	no	—
961	C₂×C₈	—	2	2	no	—
962	C₂×C₈	—	2	2	no	—
963	C₂×C₈	—	4	2	no	—
964	C₂×C₈	—	4	2	no	—
965	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
966	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
967	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
968	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
969	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
997	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
998	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
999	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1000	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1001	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1002	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1003	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1004	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	1	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	2	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1035	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1036	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1037	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1038	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1039	C₄²	C₂⁴×C₈₉	1	2	yes	—
1040	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	2	1	no	—
1044	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1045	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	2	no	—
1048	Q₈	—	2	1	no	—
1049	Q₈	—	2	1	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	2	1	no	—
1054	Q₈	—	2	1	no	—
1055	Q₈	—	4	2	no	—
1056	Q₈	—	8	2	no	—
1057	D₄	—	2	4	no	—
1058	D₄	—	2	2	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	8	1	no	—
1069	D₄	—	8	1	no	—
1070	D₄	—	8	2	no	—
1071	D₄	—	8	2	no	—
1072	D₄	—	8	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	4	1	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	4	1	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	8	1	no	—
1094	C₂×C₄	—	8	2	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	8	1	no	—
1097	C₂×C₄	—	8	1	no	—
1098	C₂×C₄	—	8	1	no	—
1099	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1100	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1102	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1103	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1104	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1105	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1106	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1107	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
1108	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
1109	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1110	C₈	—	2	1	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	2	1	no	—
1113	C₈	—	2	1	no	—
1114	C₈	—	2	2	no	—
1115	C₈	—	2	2	no	—
1116	C₂²	—	2	1	no	—
1117	C₂²	—	2	1	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	#537×C₈₉	1	2	yes	—
1131	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	4	2	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	2	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	1	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	2	no	—
1148	C₄	#537×C₈₉	1	2	yes	—
1149	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1150	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
1151	C₂	—	2	2	no	—
1152	C₂	—	4	2	no	—
1153	C₂	—	8	1	no	—
1154	C₂	—	8	1	no	—
1155	C₂	—	8	1	no	—
1156	C₂	C₂×#537×C₈₉	1	1	yes	characteristic
1157	C₂	C₈₉×#3584	1	1	yes	characteristic
1158	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 ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3512	C₂	semidirect
2. C₈₉×#3461	C₂	semidirect
3. C₈₉×#3261	C₂	semidirect
4. C₈₉×#3260	C₂	semidirect
5. C₈₉×#3258	C₂	semidirect
6. C₈₉×#3257	C₂	semidirect
7. C₈₉×#3256	C₂	semidirect
8. C₈₉×#3252	C₂	semidirect
9. C₈₉×#3250	C₂	semidirect
10. C₈₉×#3248	C₂	semidirect
11. C₈₉×#3084	C₂	semidirect
12. C₈₉×#3083	C₂	semidirect
13. C₈₉×#3080	C₂	semidirect
14. C₂×#479×C₈₉	C₂	semidirect
15. C₈₉×#3063	C₂	semidirect
16. C₈₉×#3063	C₂	semidirect
17. C₈₉×#3061	C₂	semidirect
18. C₈₉×#3060	C₂	semidirect
19. C₈₉×#3046	C₂	semidirect
20. C₈₉×#3046	C₂	semidirect
21. C₈₉×#3037	C₂	semidirect
22. C₈₉×#3035	C₂	semidirect
23. C₈₉×#2906	C₂	semidirect
571. #60932	C₈₉	direct (N × H)
580. #3512	C₂×C₈₉	semidirect
581. #3461	C₂×C₈₉	semidirect
582. #3261	C₂×C₈₉	semidirect
583. #3260	C₂×C₈₉	semidirect
584. #3258	C₂×C₈₉	semidirect
585. #3257	C₂×C₈₉	semidirect
586. #3256	C₂×C₈₉	semidirect
587. #3252	C₂×C₈₉	semidirect
588. #3250	C₂×C₈₉	semidirect
589. #3248	C₂×C₈₉	semidirect
590. #3084	C₂×C₈₉	semidirect
591. #3083	C₂×C₈₉	semidirect
592. #3080	C₂×C₈₉	semidirect
593. C₂×#479	C₂×C₈₉	semidirect
594. #3063	C₂×C₈₉	semidirect
595. #3063	C₂×C₈₉	semidirect
596. #3061	C₂×C₈₉	semidirect
597. #3060	C₂×C₈₉	semidirect
598. #3046	C₂×C₈₉	semidirect
599. #3046	C₂×C₈₉	semidirect
600. #3037	C₂×C₈₉	semidirect
601. #3035	C₂×C₈₉	semidirect
602. #2906	C₂×C₈₉	semidirect
603. C₈₉	#60932	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#3512	2
C₈₉×#3461	2
C₈₉×#3261	2
C₈₉×#3260	2
C₈₉×#3258	2
C₈₉×#3257	2
C₈₉×#3256	2
C₈₉×#3252	2
C₈₉×#3250	2
C₈₉×#3248	2
C₈₉×#3084	2
C₈₉×#3083	2
C₈₉×#3080	2
C₂×#479×C₈₉	2
C₈₉×#3063	2
C₈₉×#3061	2
C₈₉×#3060	2
C₈₉×#3046	2
C₈₉×#3037	2
C₈₉×#3035	2
C₈₉×#2906	2
#60932	89

Subgroups — C89×#60932 #36438780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60932 #36438780