Subgroups — C₈₉×#60887 #36438735

Order 22784.

1678 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3512	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3242	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3241	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3240	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3240	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3239	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3238	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3166	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#501×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3135	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3099	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3098	C₂	1	2	yes	maximal, complemented
15	C₈₉×#3084	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3083	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2923	C₂	1	1	yes	maximal, characteristic, complemented
18	Q₈²×C₈₉	—	2	1	no	—
19	#557×C₈₉	—	2	1	no	—
20	#554×C₈₉	—	2	2	no	—
21	#554×C₈₉	—	2	1	no	—
22	#553×C₈₉	—	2	2	no	—
23	#553×C₈₉	—	2	2	no	—
24	#553×C₈₉	—	2	1	no	—
25	#553×C₈₉	—	2	1	no	—
26	#552×C₈₉	—	2	1	no	—
27	#552×C₈₉	—	2	1	no	—
28	D₄×Q₈×C₈₉	—	2	2	no	—
29	D₄×Q₈×C₈₉	—	2	1	no	—
30	#544×C₈₉	C₂²	1	2	yes	—
31	#544×C₈₉	C₂²	1	4	yes	—
32	#541×C₈₉	C₂²	1	2	yes	—
33	#540×C₈₉	C₂²	1	2	yes	—
34	#537×C₈₉	C₂²	1	1	yes	characteristic
35	#537×C₈₉	C₂²	1	1	yes	characteristic
36	#533×C₈₉	C₂²	1	1	yes	characteristic
37	#533×C₈₉	C₂²	1	2	yes	—
38	#532×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
41	#529×C₈₉	C₂²	1	2	yes	—
42	#529×C₈₉	C₂²	1	2	yes	—
43	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
44	#520×C₈₉	C₂²	1	1	yes	characteristic
45	#520×C₈₉	C₂²	1	1	yes	characteristic
46	#520×C₈₉	C₂²	1	2	yes	—
47	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
48	#501×C₈₉	C₂²	1	2	yes	—
49	#501×C₈₉	C₂²	1	2	yes	—
50	#501×C₈₉	C₂²	1	4	yes	—
51	#501×C₈₉	C₂²	1	2	yes	—
52	#501×C₈₉	C₂²	1	2	yes	—
53	#499×C₈₉	C₂²	1	4	yes	—
54	#491×C₈₉	C₂²	1	2	yes	—
55	#490×C₈₉	C₂²	1	2	yes	—
56	#489×C₈₉	C₂²	1	1	yes	characteristic
57	#489×C₈₉	C₂²	1	1	yes	characteristic
58	#489×C₈₉	C₂²	1	1	yes	characteristic
59	#489×C₈₉	C₂²	1	1	yes	characteristic
60	#489×C₈₉	C₂²	1	2	yes	—
61	#489×C₈₉	C₂²	1	2	yes	—
62	#487×C₈₉	C₂²	1	2	yes	—
63	#486×C₈₉	C₂²	1	2	yes	—
64	#485×C₈₉	C₂²	1	4	yes	—
65	#485×C₈₉	C₂²	1	4	yes	—
66	#484×C₈₉	C₂²	1	4	yes	—
67	#483×C₈₉	C₂²	1	4	yes	—
68	#482×C₈₉	C₂²	1	4	yes	—
69	#482×C₈₉	C₂²	1	4	yes	—
70	#481×C₈₉	C₂²	1	4	yes	—
71	#480×C₈₉	C₂²	1	4	yes	—
72	#479×C₈₉	C₂²	1	4	yes	—
73	#479×C₈₉	C₂²	1	4	yes	—
74	#478×C₈₉	C₂²	1	4	yes	—
75	#478×C₈₉	C₂²	1	4	yes	—
76	#477×C₈₉	C₂²	1	4	yes	—
77	#476×C₈₉	C₂²	1	4	yes	—
78	#475×C₈₉	C₂²	1	4	yes	—
79	#474×C₈₉	C₂²	1	4	yes	—
80	#433×C₈₉	C₂²	1	4	yes	—
81	#432×C₈₉	C₂²	1	2	yes	—
82	#432×C₈₉	C₂²	1	2	yes	—
83	#428×C₈₉	C₂²	1	2	yes	—
84	#428×C₈₉	C₂²	1	2	yes	—
85	C₂×#107×C₈₉	C₂²	1	2	yes	—
86	C₂×#106×C₈₉	C₂²	1	2	yes	—
87	#424×C₈₉	C₂²	1	2	yes	—
88	#417×C₈₉	C₂²	1	2	yes	—
89	#417×C₈₉	C₂²	1	2	yes	—
90	#416×C₈₉	C₂²	1	2	yes	—
91	#416×C₈₉	C₂²	1	2	yes	—
92	#408×C₈₉	C₂²	1	2	yes	—
93	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
94	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
95	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
96	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
97	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₈₉	—	2	1	no	—
99	C₂²×Q₈×C₈₉	—	2	2	no	—
100	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
101	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
102	C₄⋊Q₈×C₈₉	—	2	2	no	—
103	C₄⋊Q₈×C₈₉	—	2	4	no	—
104	C₄⋊Q₈×C₈₉	—	2	2	no	—
105	C₄⋊Q₈×C₈₉	—	2	1	no	—
106	C₄⋊Q₈×C₈₉	—	2	2	no	—
107	C₄⋊Q₈×C₈₉	—	2	1	no	—
108	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
110	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
111	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
114	#127×C₈₉	C₂³	1	1	yes	characteristic
115	#126×C₈₉	—	2	2	no	—
116	#126×C₈₉	—	2	2	no	—
117	#126×C₈₉	—	2	2	no	—
118	#126×C₈₉	—	2	2	no	—
119	#125×C₈₉	—	2	2	no	—
120	#125×C₈₉	—	2	2	no	—
121	#125×C₈₉	—	2	2	no	—
122	#125×C₈₉	—	2	4	no	—
123	#125×C₈₉	—	2	1	no	—
124	#125×C₈₉	—	2	1	no	—
125	#125×C₈₉	C₂³	1	4	yes	—
126	#125×C₈₉	C₂³	1	2	yes	—
127	#125×C₈₉	C₂³	1	2	yes	—
128	#125×C₈₉	C₂³	1	2	yes	—
129	#124×C₈₉	C₂³	1	1	yes	characteristic
130	#124×C₈₉	C₂³	1	1	yes	characteristic
131	#123×C₈₉	—	2	2	no	—
132	#123×C₈₉	—	2	2	no	—
133	#123×C₈₉	—	2	2	no	—
134	#123×C₈₉	—	2	2	no	—
135	C₂²⋊Q₈×C₈₉	—	2	1	no	—
136	C₂²⋊Q₈×C₈₉	—	2	1	no	—
137	C₂²⋊Q₈×C₈₉	—	2	1	no	—
138	C₂²⋊Q₈×C₈₉	—	2	2	no	—
139	C₂²⋊Q₈×C₈₉	—	2	1	no	—
140	C₂²⋊Q₈×C₈₉	—	2	2	no	—
141	C₂²⋊Q₈×C₈₉	—	2	4	no	—
142	C₂²⋊Q₈×C₈₉	—	2	4	no	—
143	C₂²⋊Q₈×C₈₉	—	2	4	no	—
144	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
145	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
146	#121×C₈₉	—	2	1	no	—
147	#121×C₈₉	—	2	1	no	—
148	#121×C₈₉	—	2	2	no	—
149	#121×C₈₉	—	2	2	no	—
150	#121×C₈₉	—	2	1	no	—
151	#121×C₈₉	—	2	1	no	—
152	#121×C₈₉	—	2	2	no	—
153	#121×C₈₉	—	2	2	no	—
154	#121×C₈₉	C₂³	1	2	yes	—
155	#121×C₈₉	C₂³	1	2	yes	—
156	C₄×Q₈×C₈₉	—	2	2	no	—
157	C₄×Q₈×C₈₉	—	2	2	no	—
158	C₄×Q₈×C₈₉	—	2	1	no	—
159	C₄×Q₈×C₈₉	—	2	2	no	—
160	C₄×Q₈×C₈₉	—	2	1	no	—
161	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
162	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
163	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
164	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
165	C₄×D₄×C₈₉	—	2	4	no	—
166	C₄×D₄×C₈₉	—	2	2	no	—
167	C₄×D₄×C₈₉	—	2	2	no	—
168	C₄×D₄×C₈₉	—	2	2	no	—
169	C₄×D₄×C₈₉	—	2	2	no	—
170	C₄×D₄×C₈₉	—	2	2	no	—
171	C₄×D₄×C₈₉	—	2	1	no	—
172	C₄×D₄×C₈₉	—	2	1	no	—
173	C₄×D₄×C₈₉	D₄	1	2	yes	—
174	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
175	C₄×D₄×C₈₉	D₄	1	2	yes	—
176	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
177	C₄×D₄×C₈₉	C₂³	1	2	yes	—
178	C₄×D₄×C₈₉	C₂³	1	2	yes	—
179	#117×C₈₉	—	2	1	no	—
180	#117×C₈₉	—	2	1	no	—
181	#117×C₈₉	—	2	2	no	—
182	#117×C₈₉	—	2	2	no	—
183	#117×C₈₉	C₂³	1	2	yes	—
184	#117×C₈₉	C₂³	1	4	yes	—
185	#117×C₈₉	C₂³	1	1	yes	characteristic
186	#117×C₈₉	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
188	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
189	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
190	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
191	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
192	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
193	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
197	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
199	#107×C₈₉	C₂³	1	4	yes	—
200	#107×C₈₉	C₂³	1	4	yes	—
201	#107×C₈₉	C₂³	1	4	yes	—
202	#107×C₈₉	C₂³	1	4	yes	—
203	#106×C₈₉	C₂³	1	4	yes	—
204	#106×C₈₉	C₂³	1	4	yes	—
205	#106×C₈₉	C₂³	1	4	yes	—
206	#106×C₈₉	C₂³	1	4	yes	—
207	C₄⋊C₈×C₈₉	C₂³	1	4	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	2	yes	—
212	#103×C₈₉	C₂³	1	2	yes	—
213	#103×C₈₉	C₂³	1	4	yes	—
214	#103×C₈₉	C₂³	1	4	yes	—
215	#102×C₈₉	C₂³	1	2	yes	—
216	#102×C₈₉	C₂³	1	2	yes	—
217	#102×C₈₉	C₂³	1	2	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	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	#97×C₈₉	C₂³	1	2	yes	—
227	C₄×C₈×C₈₉	C₂³	1	2	yes	—
228	#41×C₈₉	—	2	4	no	—
229	#41×C₈₉	—	2	4	no	—
230	#41×C₈₉	—	2	4	no	—
231	C₂×Q₈×C₈₉	—	2	1	no	—
232	C₂×Q₈×C₈₉	—	2	2	no	—
233	C₂×Q₈×C₈₉	—	2	1	no	—
234	C₂×Q₈×C₈₉	—	2	4	no	—
235	C₂×Q₈×C₈₉	—	2	2	no	—
236	C₂×Q₈×C₈₉	—	8	4	no	—
237	C₂×Q₈×C₈₉	—	8	2	no	—
238	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
239	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
240	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
241	C₂×D₄×C₈₉	—	2	1	no	—
242	C₂×D₄×C₈₉	—	2	1	no	—
243	C₂×D₄×C₈₉	—	2	2	no	—
244	C₂×D₄×C₈₉	—	2	2	no	—
245	C₂×D₄×C₈₉	—	2	1	no	—
246	C₂×D₄×C₈₉	—	2	1	no	—
247	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
248	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
249	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
250	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₈₉	—	2	1	no	—
252	C₂²×C₄×C₈₉	—	2	1	no	—
253	C₂²×C₄×C₈₉	—	2	4	no	—
254	C₂²×C₄×C₈₉	—	2	2	no	—
255	C₂²×C₄×C₈₉	—	2	1	no	—
256	C₂²×C₄×C₈₉	—	2	1	no	—
257	C₂²×C₄×C₈₉	—	2	2	no	—
258	C₂²×C₄×C₈₉	—	2	2	no	—
259	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
265	M₁₆×C₈₉	—	2	4	no	—
266	C₂×C₈×C₈₉	—	2	4	no	—
267	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
268	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
269	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
270	C₄⋊C₄×C₈₉	—	2	2	no	—
271	C₄⋊C₄×C₈₉	—	2	1	no	—
272	C₄⋊C₄×C₈₉	—	2	1	no	—
273	C₄⋊C₄×C₈₉	—	2	1	no	—
274	C₄⋊C₄×C₈₉	—	2	2	no	—
275	C₄⋊C₄×C₈₉	—	2	2	no	—
276	C₄⋊C₄×C₈₉	—	2	2	no	—
277	C₄⋊C₄×C₈₉	—	2	2	no	—
278	C₄⋊C₄×C₈₉	—	2	2	no	—
279	C₄⋊C₄×C₈₉	—	2	2	no	—
280	C₄⋊C₄×C₈₉	—	2	4	no	—
281	C₄⋊C₄×C₈₉	—	2	2	no	—
282	C₄⋊C₄×C₈₉	—	2	4	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	1	no	—
287	C₄⋊C₄×C₈₉	—	2	1	no	—
288	C₄⋊C₄×C₈₉	—	2	1	no	—
289	C₄⋊C₄×C₈₉	—	2	4	no	—
290	C₄⋊C₄×C₈₉	—	2	2	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	1	yes	characteristic
295	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
298	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
299	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
300	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
302	C₂²⋊C₄×C₈₉	—	2	4	no	—
303	C₂²⋊C₄×C₈₉	—	2	2	no	—
304	C₂²⋊C₄×C₈₉	—	2	2	no	—
305	C₂²⋊C₄×C₈₉	—	2	2	no	—
306	C₂²⋊C₄×C₈₉	—	2	1	no	—
307	C₂²⋊C₄×C₈₉	—	2	1	no	—
308	C₂²⋊C₄×C₈₉	—	2	2	no	—
309	C₂²⋊C₄×C₈₉	—	2	2	no	—
310	C₂²⋊C₄×C₈₉	—	2	2	no	—
311	C₂²⋊C₄×C₈₉	—	2	2	no	—
312	C₂²⋊C₄×C₈₉	—	2	1	no	—
313	C₂²⋊C₄×C₈₉	—	2	1	no	—
314	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
315	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
316	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
317	C₄²×C₈₉	—	2	2	no	—
318	C₄²×C₈₉	—	2	2	no	—
319	C₄²×C₈₉	—	2	4	no	—
320	C₄²×C₈₉	—	2	2	no	—
321	C₄²×C₈₉	C₂×D₄	1	2	yes	—
322	C₄²×C₈₉	C₂×D₄	1	2	yes	—
323	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
326	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
327	C₄²×C₈₉	C₂⁴	1	2	yes	—
328	C₂³×C₈₉	—	2	1	no	—
329	C₂³×C₈₉	—	2	1	no	—
330	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
331	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
332	Q₈×C₈₉	—	2	2	no	—
333	Q₈×C₈₉	—	2	2	no	—
334	Q₈×C₈₉	—	2	2	no	—
335	Q₈×C₈₉	—	4	2	no	—
336	Q₈×C₈₉	—	4	4	no	—
337	Q₈×C₈₉	—	4	2	no	—
338	Q₈×C₈₉	—	8	4	no	—
339	Q₈×C₈₉	—	8	2	no	—
340	D₄×C₈₉	—	2	4	no	—
341	D₄×C₈₉	—	2	2	no	—
342	D₄×C₈₉	—	2	2	no	—
343	D₄×C₈₉	—	2	2	no	—
344	D₄×C₈₉	—	4	2	no	—
345	D₄×C₈₉	—	4	2	no	—
346	D₄×C₈₉	—	8	1	no	—
347	D₄×C₈₉	—	8	1	no	—
348	D₄×C₈₉	—	8	2	no	—
349	D₄×C₈₉	—	8	2	no	—
350	C₂×C₄×C₈₉	—	2	4	no	—
351	C₂×C₄×C₈₉	—	2	2	no	—
352	C₂×C₄×C₈₉	—	2	1	no	—
353	C₂×C₄×C₈₉	—	2	1	no	—
354	C₂×C₄×C₈₉	—	2	2	no	—
355	C₂×C₄×C₈₉	—	2	2	no	—
356	C₂×C₄×C₈₉	—	2	4	no	—
357	C₂×C₄×C₈₉	—	2	2	no	—
358	C₂×C₄×C₈₉	—	4	2	no	—
359	C₂×C₄×C₈₉	—	4	1	no	—
360	C₂×C₄×C₈₉	—	4	2	no	—
361	C₂×C₄×C₈₉	—	4	1	no	—
362	C₂×C₄×C₈₉	—	4	2	no	—
363	C₂×C₄×C₈₉	—	4	2	no	—
364	C₂×C₄×C₈₉	—	8	2	no	—
365	C₂×C₄×C₈₉	—	8	2	no	—
366	C₂×C₄×C₈₉	—	8	1	no	—
367	C₂×C₄×C₈₉	—	8	1	no	—
368	C₂×C₄×C₈₉	—	8	2	no	—
369	C₂×C₄×C₈₉	—	8	4	no	—
370	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
371	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
372	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
373	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
379	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
380	C₈×C₈₉	—	2	2	no	—
381	C₈×C₈₉	—	2	2	no	—
382	C₈×C₈₉	—	2	4	no	—
383	C₂²×C₈₉	—	2	1	no	—
384	C₂²×C₈₉	—	2	1	no	—
385	C₂²×C₈₉	—	2	2	no	—
386	C₂²×C₈₉	—	2	2	no	—
387	C₂²×C₈₉	—	2	2	no	—
388	C₂²×C₈₉	—	4	1	no	—
389	C₂²×C₈₉	—	4	1	no	—
390	C₂²×C₈₉	—	4	1	no	—
391	C₂²×C₈₉	—	4	1	no	—
392	C₂²×C₈₉	—	4	1	no	—
393	C₂²×C₈₉	—	4	1	no	—
394	C₂²×C₈₉	#536	1	2	yes	—
395	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
396	C₄×C₈₉	—	2	1	no	—
397	C₄×C₈₉	—	2	2	no	—
398	C₄×C₈₉	—	2	1	no	—
399	C₄×C₈₉	—	2	1	no	—
400	C₄×C₈₉	—	2	2	no	—
401	C₄×C₈₉	—	2	1	no	—
402	C₄×C₈₉	—	2	2	no	—
403	C₄×C₈₉	—	4	2	no	—
404	C₄×C₈₉	—	4	4	no	—
405	C₄×C₈₉	—	4	2	no	—
406	C₄×C₈₉	—	4	2	no	—
407	C₄×C₈₉	—	4	2	no	—
408	C₄×C₈₉	—	4	1	no	—
409	C₄×C₈₉	—	4	1	no	—
410	C₄×C₈₉	#536	1	2	yes	—
411	C₄×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
412	#60887	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
413	C₂×C₈₉	—	2	2	no	—
414	C₂×C₈₉	—	4	2	no	—
415	C₂×C₈₉	—	8	1	no	—
416	C₂×C₈₉	—	8	1	no	—
417	C₂×C₈₉	C₂×#536	1	1	yes	characteristic
418	C₂×C₈₉	#3585	1	1	yes	characteristic
419	C₂×C₈₉	#3586	1	1	yes	characteristic
420	#3512	C₂×C₈₉	1	1	yes	characteristic
421	#3503	C₂×C₈₉	1	1	yes	characteristic, complemented
422	#3242	C₂×C₈₉	1	4	yes	complemented
423	#3241	C₂×C₈₉	1	4	yes	complemented
424	#3240	C₂×C₈₉	1	2	yes	complemented
425	#3240	C₂×C₈₉	1	2	yes	complemented
426	#3239	C₂×C₈₉	1	2	yes	complemented
427	#3238	C₂×C₈₉	1	2	yes	complemented
428	#3166	C₂×C₈₉	1	1	yes	characteristic, complemented
429	C₂×#501	C₂×C₈₉	1	1	yes	characteristic, complemented
430	#3141	C₂×C₈₉	1	1	yes	characteristic, complemented
431	#3135	C₂×C₈₉	1	1	yes	characteristic, complemented
432	#3099	C₂×C₈₉	1	2	yes	complemented
433	#3098	C₂×C₈₉	1	2	yes	complemented
434	#3084	C₂×C₈₉	1	2	yes	complemented
435	#3083	C₂×C₈₉	1	2	yes	complemented
436	#2923	C₂×C₈₉	1	1	yes	characteristic, complemented
437	C₈₉	#60887	1	1	yes	characteristic, direct product factor, Sylow
438	Q₈²	—	2	1	no	—
439	#557	—	2	1	no	—
440	#554	—	2	2	no	—
441	#554	—	2	1	no	—
442	#553	—	2	2	no	—
443	#553	—	2	2	no	—
444	#553	—	2	1	no	—
445	#553	—	2	1	no	—
446	#552	—	2	1	no	—
447	#552	—	2	1	no	—
448	D₄×Q₈	—	2	2	no	—
449	D₄×Q₈	—	2	1	no	—
450	#544	C₂²×C₈₉	1	2	yes	—
451	#544	C₂²×C₈₉	1	4	yes	—
452	#541	C₂²×C₈₉	1	2	yes	—
453	#540	C₂²×C₈₉	1	2	yes	—
454	#537	C₂²×C₈₉	1	1	yes	characteristic
455	#537	C₂²×C₈₉	1	1	yes	characteristic
456	#533	C₂²×C₈₉	1	1	yes	characteristic
457	#533	C₂²×C₈₉	1	2	yes	—
458	#532	C₂²×C₈₉	1	1	yes	characteristic
459	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
460	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
461	#529	C₂²×C₈₉	1	2	yes	—
462	#529	C₂²×C₈₉	1	2	yes	—
463	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
464	#520	C₂²×C₈₉	1	1	yes	characteristic
465	#520	C₂²×C₈₉	1	1	yes	characteristic
466	#520	C₂²×C₈₉	1	2	yes	—
467	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
468	#501	C₂²×C₈₉	1	2	yes	—
469	#501	C₂²×C₈₉	1	2	yes	—
470	#501	C₂²×C₈₉	1	4	yes	—
471	#501	C₂²×C₈₉	1	2	yes	—
472	#501	C₂²×C₈₉	1	2	yes	—
473	#499	C₂²×C₈₉	1	4	yes	—
474	#491	C₂²×C₈₉	1	2	yes	—
475	#490	C₂²×C₈₉	1	2	yes	—
476	#489	C₂²×C₈₉	1	1	yes	characteristic
477	#489	C₂²×C₈₉	1	1	yes	characteristic
478	#489	C₂²×C₈₉	1	1	yes	characteristic
479	#489	C₂²×C₈₉	1	1	yes	characteristic
480	#489	C₂²×C₈₉	1	2	yes	—
481	#489	C₂²×C₈₉	1	2	yes	—
482	#487	C₂²×C₈₉	1	2	yes	—
483	#486	C₂²×C₈₉	1	2	yes	—
484	#485	C₂²×C₈₉	1	4	yes	—
485	#485	C₂²×C₈₉	1	4	yes	—
486	#484	C₂²×C₈₉	1	4	yes	—
487	#483	C₂²×C₈₉	1	4	yes	—
488	#482	C₂²×C₈₉	1	4	yes	—
489	#482	C₂²×C₈₉	1	4	yes	—
490	#481	C₂²×C₈₉	1	4	yes	—
491	#480	C₂²×C₈₉	1	4	yes	—
492	#479	C₂²×C₈₉	1	4	yes	—
493	#479	C₂²×C₈₉	1	4	yes	—
494	#478	C₂²×C₈₉	1	4	yes	—
495	#478	C₂²×C₈₉	1	4	yes	—
496	#477	C₂²×C₈₉	1	4	yes	—
497	#476	C₂²×C₈₉	1	4	yes	—
498	#475	C₂²×C₈₉	1	4	yes	—
499	#474	C₂²×C₈₉	1	4	yes	—
500	#433	C₂²×C₈₉	1	4	yes	—
501	#432	C₂²×C₈₉	1	2	yes	—
502	#432	C₂²×C₈₉	1	2	yes	—
503	#428	C₂²×C₈₉	1	2	yes	—
504	#428	C₂²×C₈₉	1	2	yes	—
505	C₂×#107	C₂²×C₈₉	1	2	yes	—
506	C₂×#106	C₂²×C₈₉	1	2	yes	—
507	#424	C₂²×C₈₉	1	2	yes	—
508	#417	C₂²×C₈₉	1	2	yes	—
509	#417	C₂²×C₈₉	1	2	yes	—
510	#416	C₂²×C₈₉	1	2	yes	—
511	#416	C₂²×C₈₉	1	2	yes	—
512	#408	C₂²×C₈₉	1	2	yes	—
513	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
514	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
515	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
516	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
517	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
518	C₂²×Q₈	—	2	1	no	—
519	C₂²×Q₈	—	2	2	no	—
520	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
521	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
522	C₄⋊Q₈	—	2	2	no	—
523	C₄⋊Q₈	—	2	4	no	—
524	C₄⋊Q₈	—	2	2	no	—
525	C₄⋊Q₈	—	2	1	no	—
526	C₄⋊Q₈	—	2	2	no	—
527	C₄⋊Q₈	—	2	1	no	—
528	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
529	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
530	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
531	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
532	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
533	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
534	#127	C₂³×C₈₉	1	1	yes	characteristic
535	#126	—	2	2	no	—
536	#126	—	2	2	no	—
537	#126	—	2	2	no	—
538	#126	—	2	2	no	—
539	#125	—	2	2	no	—
540	#125	—	2	2	no	—
541	#125	—	2	2	no	—
542	#125	—	2	4	no	—
543	#125	—	2	1	no	—
544	#125	—	2	1	no	—
545	#125	C₂³×C₈₉	1	2	yes	—
546	#125	C₂³×C₈₉	1	2	yes	—
547	#125	C₂³×C₈₉	1	4	yes	—
548	#125	C₂³×C₈₉	1	2	yes	—
549	#124	C₂³×C₈₉	1	1	yes	characteristic
550	#124	C₂³×C₈₉	1	1	yes	characteristic
551	#123	—	2	2	no	—
552	#123	—	2	2	no	—
553	#123	—	2	2	no	—
554	#123	—	2	2	no	—
555	C₂²⋊Q₈	—	2	1	no	—
556	C₂²⋊Q₈	—	2	1	no	—
557	C₂²⋊Q₈	—	2	1	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	—	2	1	no	—
560	C₂²⋊Q₈	—	2	2	no	—
561	C₂²⋊Q₈	—	2	4	no	—
562	C₂²⋊Q₈	—	2	4	no	—
563	C₂²⋊Q₈	—	2	4	no	—
564	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
565	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
566	#121	—	2	1	no	—
567	#121	—	2	1	no	—
568	#121	—	2	2	no	—
569	#121	—	2	2	no	—
570	#121	—	2	1	no	—
571	#121	—	2	1	no	—
572	#121	—	2	2	no	—
573	#121	—	2	2	no	—
574	#121	C₂³×C₈₉	1	2	yes	—
575	#121	C₂³×C₈₉	1	2	yes	—
576	C₄×Q₈	—	2	2	no	—
577	C₄×Q₈	—	2	2	no	—
578	C₄×Q₈	—	2	1	no	—
579	C₄×Q₈	—	2	2	no	—
580	C₄×Q₈	—	2	1	no	—
581	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
582	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
583	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
584	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
585	C₄×D₄	—	2	4	no	—
586	C₄×D₄	—	2	2	no	—
587	C₄×D₄	—	2	2	no	—
588	C₄×D₄	—	2	2	no	—
589	C₄×D₄	—	2	2	no	—
590	C₄×D₄	—	2	2	no	—
591	C₄×D₄	—	2	1	no	—
592	C₄×D₄	—	2	1	no	—
593	C₄×D₄	D₄×C₈₉	1	2	yes	—
594	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
595	C₄×D₄	D₄×C₈₉	1	2	yes	—
596	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
597	C₄×D₄	C₂³×C₈₉	1	2	yes	—
598	C₄×D₄	C₂³×C₈₉	1	2	yes	—
599	#117	—	2	1	no	—
600	#117	—	2	1	no	—
601	#117	—	2	2	no	—
602	#117	—	2	2	no	—
603	#117	C₂³×C₈₉	1	2	yes	—
604	#117	C₂³×C₈₉	1	4	yes	—
605	#117	C₂³×C₈₉	1	1	yes	characteristic
606	#117	C₂³×C₈₉	1	2	yes	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	—	2	1	no	—
610	C₂×C₄⋊C₄	—	2	2	no	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
617	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
618	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
619	#107	C₂³×C₈₉	1	4	yes	—
620	#107	C₂³×C₈₉	1	4	yes	—
621	#107	C₂³×C₈₉	1	4	yes	—
622	#107	C₂³×C₈₉	1	4	yes	—
623	#106	C₂³×C₈₉	1	4	yes	—
624	#106	C₂³×C₈₉	1	4	yes	—
625	#106	C₂³×C₈₉	1	4	yes	—
626	#106	C₂³×C₈₉	1	4	yes	—
627	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
628	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
629	#103	C₂³×C₈₉	1	2	yes	—
630	#103	C₂³×C₈₉	1	2	yes	—
631	#103	C₂³×C₈₉	1	2	yes	—
632	#103	C₂³×C₈₉	1	2	yes	—
633	#103	C₂³×C₈₉	1	4	yes	—
634	#103	C₂³×C₈₉	1	4	yes	—
635	#102	C₂³×C₈₉	1	2	yes	—
636	#102	C₂³×C₈₉	1	2	yes	—
637	#102	C₂³×C₈₉	1	2	yes	—
638	#102	C₂³×C₈₉	1	2	yes	—
639	#102	C₂³×C₈₉	1	4	yes	—
640	#102	C₂³×C₈₉	1	4	yes	—
641	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
642	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
643	#97	C₂³×C₈₉	1	1	yes	characteristic
644	#97	C₂³×C₈₉	1	1	yes	characteristic
645	#97	C₂³×C₈₉	1	2	yes	—
646	#97	C₂³×C₈₉	1	2	yes	—
647	C₄×C₈	C₂³×C₈₉	1	2	yes	—
648	#41	—	2	4	no	—
649	#41	—	2	4	no	—
650	#41	—	2	4	no	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	2	2	no	—
653	C₂×Q₈	—	2	1	no	—
654	C₂×Q₈	—	2	4	no	—
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	8	4	no	—
657	C₂×Q₈	—	8	2	no	—
658	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
659	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
660	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	2	2	no	—
664	C₂×D₄	—	2	2	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
668	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
669	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
670	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	4	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
681	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
682	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
685	M₁₆	—	2	4	no	—
686	C₂×C₈	—	2	4	no	—
687	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
688	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
689	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
714	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
715	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
716	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
717	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
718	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
719	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
720	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
721	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	1	no	—
727	C₂²⋊C₄	—	2	1	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	1	no	—
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
735	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
736	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
737	C₄²	—	2	2	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	4	no	—
740	C₄²	—	2	2	no	—
741	C₄²	C₂×D₄×C₈₉	1	2	yes	—
742	C₄²	C₂×D₄×C₈₉	1	2	yes	—
743	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
744	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
745	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
746	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
747	C₄²	C₂⁴×C₈₉	1	2	yes	—
748	C₂³	—	2	1	no	—
749	C₂³	—	2	1	no	—
750	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
751	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
752	Q₈	—	2	2	no	—
753	Q₈	—	2	2	no	—
754	Q₈	—	2	2	no	—
755	Q₈	—	4	2	no	—
756	Q₈	—	4	4	no	—
757	Q₈	—	4	2	no	—
758	Q₈	—	8	4	no	—
759	Q₈	—	8	2	no	—
760	D₄	—	2	4	no	—
761	D₄	—	2	2	no	—
762	D₄	—	2	2	no	—
763	D₄	—	2	2	no	—
764	D₄	—	4	2	no	—
765	D₄	—	4	2	no	—
766	D₄	—	8	1	no	—
767	D₄	—	8	1	no	—
768	D₄	—	8	2	no	—
769	D₄	—	8	2	no	—
770	C₂×C₄	—	2	4	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	4	2	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	2	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	2	no	—
783	C₂×C₄	—	4	2	no	—
784	C₂×C₄	—	8	2	no	—
785	C₂×C₄	—	8	2	no	—
786	C₂×C₄	—	8	1	no	—
787	C₂×C₄	—	8	1	no	—
788	C₂×C₄	—	8	2	no	—
789	C₂×C₄	—	8	4	no	—
790	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
791	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
792	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
793	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
794	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
795	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
796	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
797	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
798	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
799	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
800	C₈	—	2	2	no	—
801	C₈	—	2	2	no	—
802	C₈	—	2	4	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	2	no	—
806	C₂²	—	2	2	no	—
807	C₂²	—	2	2	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	1	no	—
811	C₂²	—	4	1	no	—
812	C₂²	—	4	1	no	—
813	C₂²	—	4	1	no	—
814	C₂²	#536×C₈₉	1	2	yes	—
815	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
816	C₄	—	2	1	no	—
817	C₄	—	2	2	no	—
818	C₄	—	2	1	no	—
819	C₄	—	2	1	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	1	no	—
822	C₄	—	2	2	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	4	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	1	no	—
829	C₄	—	4	1	no	—
830	C₄	#536×C₈₉	1	2	yes	—
831	C₄	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
832	C₂	—	2	2	no	—
833	C₂	—	4	2	no	—
834	C₂	—	8	1	no	—
835	C₂	—	8	1	no	—
836	C₂	C₂×#536×C₈₉	1	1	yes	characteristic
837	C₂	C₈₉×#3585	1	1	yes	characteristic
838	C₂	C₈₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₈₉×#3512	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×#3503	C₂	semidirect
3. C₈₉×#3242	C₂	semidirect
4. C₈₉×#3241	C₂	semidirect
5. C₈₉×#3240	C₂	semidirect
6. C₈₉×#3240	C₂	semidirect
7. C₈₉×#3239	C₂	semidirect
8. C₈₉×#3238	C₂	semidirect
9. C₈₉×#3166	C₂	semidirect
10. C₂×#501×C₈₉	C₂	semidirect
11. C₈₉×#3141	C₂	semidirect
12. C₈₉×#3135	C₂	semidirect
13. C₈₉×#3099	C₂	semidirect
14. C₈₉×#3098	C₂	semidirect
15. C₈₉×#3084	C₂	semidirect
16. C₈₉×#3083	C₂	semidirect
17. C₈₉×#2923	C₂	semidirect
412. #60887	C₈₉	direct (N × H)
421. #3503	C₂×C₈₉	semidirect
422. #3242	C₂×C₈₉	semidirect
423. #3241	C₂×C₈₉	semidirect
424. #3240	C₂×C₈₉	semidirect
425. #3240	C₂×C₈₉	semidirect
426. #3239	C₂×C₈₉	semidirect
427. #3238	C₂×C₈₉	semidirect
428. #3166	C₂×C₈₉	semidirect
429. C₂×#501	C₂×C₈₉	semidirect
430. #3141	C₂×C₈₉	semidirect
431. #3135	C₂×C₈₉	semidirect
432. #3099	C₂×C₈₉	semidirect
433. #3098	C₂×C₈₉	semidirect
434. #3084	C₂×C₈₉	semidirect
435. #3083	C₂×C₈₉	semidirect
436. #2923	C₂×C₈₉	semidirect
437. C₈₉	#60887	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×#3503	2
C₈₉×#3242	2
C₈₉×#3241	2
C₈₉×#3240	2
C₈₉×#3239	2
C₈₉×#3238	2
C₈₉×#3166	2
C₂×#501×C₈₉	2
C₈₉×#3141	2
C₈₉×#3135	2
C₈₉×#3099	2
C₈₉×#3098	2
C₈₉×#3084	2
C₈₉×#3083	2
C₈₉×#2923	2
#60887	89

Subgroups — C89×#60887 #36438735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60887 #36438735