Subgroups — C₈₉×#61842 #36439690

Order 22784.

1668 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3523	C₂	1	1	yes	maximal, characteristic
2	C₂×#557×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3390	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3386	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3383	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3377	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3374	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3364	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3239	C₂	1	1	yes	maximal, characteristic
10	C₈₉×#3236	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3232	C₂	1	2	yes	maximal
12	C₈₉×#3230	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3117	C₂	1	2	yes	maximal
14	C₈₉×#3113	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3108	C₂	1	1	yes	maximal, characteristic
16	C₈₉×#3104	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2984	C₂	1	1	yes	maximal, characteristic, complemented
18	#557×C₈₉	—	2	1	no	—
19	#557×C₈₉	—	2	1	no	—
20	#557×C₈₉	—	2	2	no	—
21	#557×C₈₉	C₂²	1	1	yes	characteristic
22	#557×C₈₉	C₂²	1	2	yes	—
23	#557×C₈₉	C₂²	1	2	yes	—
24	#557×C₈₉	C₂²	1	4	yes	—
25	#557×C₈₉	C₂²	1	1	yes	characteristic
26	#557×C₈₉	C₂²	1	2	yes	—
27	#556×C₈₉	C₂²	1	1	yes	characteristic
28	#556×C₈₉	C₂²	1	2	yes	—
29	#552×C₈₉	—	2	1	no	—
30	#552×C₈₉	—	2	2	no	—
31	D₄×Q₈×C₈₉	—	2	1	no	—
32	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
33	#541×C₈₉	—	2	2	no	—
34	#541×C₈₉	—	2	1	no	—
35	#533×C₈₉	C₂²	1	2	yes	—
36	#533×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊Q₈×C₈₉	—	2	1	no	—
38	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
39	#529×C₈₉	C₂²	1	1	yes	characteristic
40	#529×C₈₉	C₂²	1	2	yes	—
41	C₂×#125×C₈₉	—	2	2	no	—
42	C₂×#125×C₈₉	C₂²	1	2	yes	—
43	#519×C₈₉	—	2	1	no	—
44	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
45	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
48	#501×C₈₉	C₂²	1	4	yes	—
49	#501×C₈₉	C₂²	1	2	yes	—
50	#500×C₈₉	C₂²	1	2	yes	—
51	#499×C₈₉	C₂²	1	4	yes	—
52	#491×C₈₉	C₂²	1	4	yes	—
53	#489×C₈₉	C₂²	1	2	yes	—
54	#488×C₈₉	C₂²	1	4	yes	—
55	#487×C₈₉	C₂²	1	2	yes	—
56	#484×C₈₉	C₂²	1	2	yes	—
57	#484×C₈₉	C₂²	1	2	yes	—
58	#484×C₈₉	C₂²	1	2	yes	—
59	#483×C₈₉	C₂²	1	1	yes	characteristic
60	#483×C₈₉	C₂²	1	2	yes	—
61	#481×C₈₉	C₂²	1	2	yes	—
62	#480×C₈₉	C₂²	1	1	yes	characteristic
63	#479×C₈₉	C₂²	1	4	yes	—
64	#479×C₈₉	C₂²	1	2	yes	—
65	#479×C₈₉	C₂²	1	4	yes	—
66	#479×C₈₉	C₂²	1	4	yes	—
67	#479×C₈₉	C₂²	1	4	yes	—
68	#478×C₈₉	C₂²	1	4	yes	—
69	#477×C₈₉	C₂²	1	4	yes	—
70	#477×C₈₉	C₂²	1	4	yes	—
71	#475×C₈₉	C₂²	1	2	yes	—
72	#475×C₈₉	C₂²	1	2	yes	—
73	#474×C₈₉	C₂²	1	2	yes	—
74	#464×C₈₉	C₂²	1	4	yes	—
75	#464×C₈₉	C₂²	1	2	yes	—
76	#462×C₈₉	C₂²	1	4	yes	—
77	#462×C₈₉	C₂²	1	2	yes	—
78	#451×C₈₉	C₂²	1	1	yes	characteristic
79	#451×C₈₉	C₂²	1	2	yes	—
80	#448×C₈₉	C₂²	1	1	yes	characteristic
81	#446×C₈₉	C₂²	1	2	yes	—
82	#446×C₈₉	C₂²	1	4	yes	—
83	C₈×Q₈×C₈₉	C₂²	1	2	yes	—
84	#441×C₈₉	C₂²	1	4	yes	—
85	#441×C₈₉	C₂²	1	4	yes	—
86	#440×C₈₉	C₂²	1	4	yes	—
87	C₄×Q₁₆×C₈₉	C₂²	1	4	yes	—
88	C₄×Q₁₆×C₈₉	C₂²	1	4	yes	—
89	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
90	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
91	#432×C₈₉	C₂²	1	1	yes	characteristic
92	#432×C₈₉	C₂²	1	2	yes	—
93	#431×C₈₉	C₂²	1	2	yes	—
94	#431×C₈₉	C₂²	1	1	yes	characteristic
95	C₂²×Q₈×C₈₉	—	2	1	no	—
96	C₂²×Q₈×C₈₉	—	2	1	no	—
97	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
98	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
100	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
102	C₄⋊Q₈×C₈₉	—	2	2	no	—
103	C₄⋊Q₈×C₈₉	—	2	2	no	—
104	C₄⋊Q₈×C₈₉	—	2	4	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	—	2	1	no	—
109	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
110	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
111	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
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	#126×C₈₉	—	2	2	no	—
116	#126×C₈₉	—	2	2	no	—
117	#126×C₈₉	—	2	2	no	—
118	#126×C₈₉	—	2	2	no	—
119	#126×C₈₉	—	2	1	no	—
120	#125×C₈₉	—	2	4	no	—
121	#125×C₈₉	—	2	4	no	—
122	#125×C₈₉	—	2	4	no	—
123	#125×C₈₉	—	2	4	no	—
124	#125×C₈₉	—	2	2	no	—
125	#125×C₈₉	—	2	2	no	—
126	#125×C₈₉	—	2	2	no	—
127	#125×C₈₉	—	2	1	no	—
128	#125×C₈₉	—	2	2	no	—
129	#125×C₈₉	—	2	2	no	—
130	#125×C₈₉	—	2	2	no	—
131	#125×C₈₉	—	2	2	no	—
132	#125×C₈₉	—	2	1	no	—
133	#125×C₈₉	C₂³	1	4	yes	—
134	#125×C₈₉	C₂³	1	4	yes	—
135	#125×C₈₉	C₂³	1	2	yes	—
136	#125×C₈₉	C₂³	1	1	yes	characteristic
137	#124×C₈₉	C₂³	1	2	yes	—
138	#124×C₈₉	C₂³	1	1	yes	characteristic
139	#123×C₈₉	—	2	2	no	—
140	#123×C₈₉	—	2	1	no	—
141	C₂²⋊Q₈×C₈₉	—	2	1	no	—
142	C₂²⋊Q₈×C₈₉	—	2	2	no	—
143	C₂²⋊Q₈×C₈₉	—	2	1	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	C₂³	1	1	yes	characteristic
148	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
149	#121×C₈₉	C₂³	1	1	yes	characteristic
150	C₄×Q₈×C₈₉	—	2	1	no	—
151	C₄×Q₈×C₈₉	—	2	2	no	—
152	C₄×Q₈×C₈₉	—	2	2	no	—
153	C₄×Q₈×C₈₉	—	2	4	no	—
154	C₄×Q₈×C₈₉	—	2	1	no	—
155	C₄×Q₈×C₈₉	—	2	2	no	—
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	1	no	—
160	C₄×Q₈×C₈₉	—	2	2	no	—
161	C₄×Q₈×C₈₉	—	2	1	no	—
162	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
163	C₄×Q₈×C₈₉	D₄	1	2	yes	—
164	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
165	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
166	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
167	C₄×Q₈×C₈₉	C₂³	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	4	yes	—
171	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
172	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
173	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
174	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
175	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
176	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
177	C₄×D₄×C₈₉	—	2	1	no	—
178	C₄×D₄×C₈₉	—	2	2	no	—
179	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₈₉	C₂³	1	2	yes	—
181	#117×C₈₉	—	2	2	no	—
182	#117×C₈₉	—	2	1	no	—
183	#117×C₈₉	—	2	1	no	—
184	#117×C₈₉	—	2	2	no	—
185	#117×C₈₉	—	2	2	no	—
186	#117×C₈₉	—	2	1	no	—
187	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
188	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
189	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
190	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
191	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
192	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
194	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
196	C₂×C₄²×C₈₉	—	2	2	no	—
197	C₂×C₄²×C₈₉	—	2	1	no	—
198	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
199	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
200	#107×C₈₉	C₂³	1	4	yes	—
201	#107×C₈₉	C₂³	1	4	yes	—
202	#107×C₈₉	C₂³	1	2	yes	—
203	#107×C₈₉	C₂³	1	4	yes	—
204	#106×C₈₉	C₂³	1	2	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	2	yes	—
209	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
210	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
211	#103×C₈₉	C₂³	1	2	yes	—
212	#103×C₈₉	C₂³	1	4	yes	—
213	#103×C₈₉	C₂³	1	2	yes	—
214	#103×C₈₉	C₂³	1	4	yes	—
215	#103×C₈₉	C₂³	1	4	yes	—
216	#103×C₈₉	C₂³	1	2	yes	—
217	#103×C₈₉	C₂³	1	4	yes	—
218	#103×C₈₉	C₂³	1	4	yes	—
219	#102×C₈₉	C₂³	1	2	yes	—
220	#102×C₈₉	C₂³	1	4	yes	—
221	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
222	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
223	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
224	#97×C₈₉	C₂³	1	4	yes	—
225	#97×C₈₉	C₂³	1	2	yes	—
226	C₄×C₈×C₈₉	C₂³	1	2	yes	—
227	C₄×C₈×C₈₉	C₂³	1	4	yes	—
228	C₂×Q₈×C₈₉	—	2	4	no	—
229	C₂×Q₈×C₈₉	—	2	1	no	—
230	C₂×Q₈×C₈₉	—	2	2	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	—	4	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	C₂×D₄	1	1	yes	characteristic
239	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
240	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
241	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
242	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
243	C₂×D₄×C₈₉	—	2	1	no	—
244	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₈₉	—	2	1	no	—
246	C₂²×C₄×C₈₉	—	2	1	no	—
247	C₂²×C₄×C₈₉	—	2	2	no	—
248	C₂²×C₄×C₈₉	—	2	2	no	—
249	C₂²×C₄×C₈₉	—	2	1	no	—
250	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
251	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
254	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
255	Q₁₆×C₈₉	—	2	4	no	—
256	Q₁₆×C₈₉	—	2	8	no	—
257	SD₁₆×C₈₉	—	2	4	no	—
258	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
259	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
260	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₈₉	—	2	4	no	—
262	C₄⋊C₄×C₈₉	—	2	4	no	—
263	C₄⋊C₄×C₈₉	—	2	2	no	—
264	C₄⋊C₄×C₈₉	—	2	2	no	—
265	C₄⋊C₄×C₈₉	—	2	4	no	—
266	C₄⋊C₄×C₈₉	—	2	4	no	—
267	C₄⋊C₄×C₈₉	—	2	2	no	—
268	C₄⋊C₄×C₈₉	—	2	2	no	—
269	C₄⋊C₄×C₈₉	—	2	4	no	—
270	C₄⋊C₄×C₈₉	—	2	4	no	—
271	C₄⋊C₄×C₈₉	—	2	1	no	—
272	C₄⋊C₄×C₈₉	—	2	2	no	—
273	C₄⋊C₄×C₈₉	—	2	2	no	—
274	C₄⋊C₄×C₈₉	—	2	1	no	—
275	C₄⋊C₄×C₈₉	—	2	2	no	—
276	C₄⋊C₄×C₈₉	—	2	1	no	—
277	C₄⋊C₄×C₈₉	—	2	2	no	—
278	C₄⋊C₄×C₈₉	—	2	1	no	—
279	C₄⋊C₄×C₈₉	—	2	2	no	—
280	C₄⋊C₄×C₈₉	—	2	1	no	—
281	C₄⋊C₄×C₈₉	—	2	2	no	—
282	C₄⋊C₄×C₈₉	—	2	1	no	—
283	C₄⋊C₄×C₈₉	—	2	1	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	2	no	—
289	C₄⋊C₄×C₈₉	—	2	1	no	—
290	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
291	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
292	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
293	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
294	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
300	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
301	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
302	C₂²⋊C₄×C₈₉	—	2	1	no	—
303	C₂²⋊C₄×C₈₉	—	2	2	no	—
304	C₂²⋊C₄×C₈₉	—	2	1	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	1	no	—
311	C₄²×C₈₉	—	2	4	no	—
312	C₄²×C₈₉	—	2	4	no	—
313	C₄²×C₈₉	—	2	2	no	—
314	C₄²×C₈₉	—	2	2	no	—
315	C₄²×C₈₉	—	2	2	no	—
316	C₄²×C₈₉	—	2	2	no	—
317	C₄²×C₈₉	—	2	2	no	—
318	C₄²×C₈₉	—	2	2	no	—
319	C₄²×C₈₉	—	2	1	no	—
320	C₄²×C₈₉	C₂×D₄	1	2	yes	—
321	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₈₉	C₂×D₄	1	2	yes	—
323	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
325	C₄²×C₈₉	C₂⁴	1	2	yes	—
326	C₄²×C₈₉	C₂⁴	1	2	yes	—
327	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
328	C₂³×C₈₉	—	2	1	no	—
329	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
330	Q₈×C₈₉	—	2	4	no	—
331	Q₈×C₈₉	—	2	2	no	—
332	Q₈×C₈₉	—	2	2	no	—
333	Q₈×C₈₉	—	2	2	no	—
334	Q₈×C₈₉	—	2	2	no	—
335	Q₈×C₈₉	—	2	4	no	—
336	Q₈×C₈₉	—	4	2	no	—
337	Q₈×C₈₉	—	4	4	no	—
338	Q₈×C₈₉	—	4	4	no	—
339	Q₈×C₈₉	—	4	2	no	—
340	Q₈×C₈₉	—	4	4	no	—
341	Q₈×C₈₉	2₋¹⁺⁴	1	4	yes	—
342	D₄×C₈₉	—	2	2	no	—
343	D₄×C₈₉	—	4	2	no	—
344	C₂×C₄×C₈₉	—	2	4	no	—
345	C₂×C₄×C₈₉	—	2	4	no	—
346	C₂×C₄×C₈₉	—	2	2	no	—
347	C₂×C₄×C₈₉	—	2	2	no	—
348	C₂×C₄×C₈₉	—	2	2	no	—
349	C₂×C₄×C₈₉	—	2	2	no	—
350	C₂×C₄×C₈₉	—	2	1	no	—
351	C₂×C₄×C₈₉	—	2	2	no	—
352	C₂×C₄×C₈₉	—	2	1	no	—
353	C₂×C₄×C₈₉	—	2	2	no	—
354	C₂×C₄×C₈₉	—	2	1	no	—
355	C₂×C₄×C₈₉	—	2	2	no	—
356	C₂×C₄×C₈₉	—	2	4	no	—
357	C₂×C₄×C₈₉	—	4	2	no	—
358	C₂×C₄×C₈₉	—	4	4	no	—
359	C₂×C₄×C₈₉	—	4	4	no	—
360	C₂×C₄×C₈₉	—	4	2	no	—
361	C₂×C₄×C₈₉	—	4	2	no	—
362	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
363	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
364	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
367	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
370	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
372	C₈×C₈₉	—	2	2	no	—
373	C₈×C₈₉	—	2	2	no	—
374	C₈×C₈₉	—	2	4	no	—
375	C₂²×C₈₉	—	2	1	no	—
376	C₂²×C₈₉	—	2	1	no	—
377	C₂²×C₈₉	—	4	1	no	—
378	C₂²×C₈₉	—	4	1	no	—
379	C₂²×C₈₉	—	4	1	no	—
380	C₂²×C₈₉	#578	1	2	yes	—
381	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
382	C₄×C₈₉	—	2	4	no	—
383	C₄×C₈₉	—	2	1	no	—
384	C₄×C₈₉	—	2	1	no	—
385	C₄×C₈₉	—	2	2	no	—
386	C₄×C₈₉	—	2	2	no	—
387	C₄×C₈₉	—	2	2	no	—
388	C₄×C₈₉	—	2	2	no	—
389	C₄×C₈₉	—	2	1	no	—
390	C₄×C₈₉	—	2	1	no	—
391	C₄×C₈₉	—	4	1	no	—
392	C₄×C₈₉	—	4	2	no	—
393	C₄×C₈₉	—	4	2	no	—
394	C₄×C₈₉	—	4	1	no	—
395	C₄×C₈₉	—	4	4	no	—
396	C₄×C₈₉	—	4	2	no	—
397	C₄×C₈₉	—	4	1	no	—
398	C₄×C₈₉	#575	1	2	yes	—
399	C₄×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
400	#61842	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
401	C₂×C₈₉	—	2	2	no	—
402	C₂×C₈₉	—	8	1	no	—
403	C₂×C₈₉	#3486	1	1	yes	characteristic
404	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
405	C₂×C₈₉	C₂×#578	1	1	yes	characteristic
406	#3523	C₂×C₈₉	1	1	yes	characteristic
407	C₂×#557	C₂×C₈₉	1	1	yes	characteristic, complemented
408	#3390	C₂×C₈₉	1	4	yes	complemented
409	#3386	C₂×C₈₉	1	2	yes	complemented
410	#3383	C₂×C₈₉	1	2	yes	complemented
411	#3377	C₂×C₈₉	1	4	yes	complemented
412	#3374	C₂×C₈₉	1	2	yes	complemented
413	#3364	C₂×C₈₉	1	2	yes	complemented
414	#3239	C₂×C₈₉	1	1	yes	characteristic
415	#3236	C₂×C₈₉	1	2	yes	complemented
416	#3232	C₂×C₈₉	1	2	yes	—
417	#3230	C₂×C₈₉	1	1	yes	characteristic, complemented
418	#3117	C₂×C₈₉	1	2	yes	—
419	#3113	C₂×C₈₉	1	1	yes	characteristic, complemented
420	#3108	C₂×C₈₉	1	1	yes	characteristic
421	#3104	C₂×C₈₉	1	2	yes	complemented
422	#2984	C₂×C₈₉	1	1	yes	characteristic, complemented
423	C₈₉	#61842	1	1	yes	characteristic, direct product factor, Sylow
424	#557	—	2	1	no	—
425	#557	—	2	1	no	—
426	#557	—	2	2	no	—
427	#557	C₂²×C₈₉	1	1	yes	characteristic
428	#557	C₂²×C₈₉	1	2	yes	—
429	#557	C₂²×C₈₉	1	2	yes	—
430	#557	C₂²×C₈₉	1	4	yes	—
431	#557	C₂²×C₈₉	1	1	yes	characteristic
432	#557	C₂²×C₈₉	1	2	yes	—
433	#556	C₂²×C₈₉	1	1	yes	characteristic
434	#556	C₂²×C₈₉	1	2	yes	—
435	#552	—	2	1	no	—
436	#552	—	2	2	no	—
437	D₄×Q₈	—	2	1	no	—
438	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
439	#541	—	2	2	no	—
440	#541	—	2	1	no	—
441	#533	C₂²×C₈₉	1	2	yes	—
442	#533	C₂²×C₈₉	1	1	yes	characteristic
443	C₂×C₄⋊Q₈	—	2	1	no	—
444	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
445	#529	C₂²×C₈₉	1	1	yes	characteristic
446	#529	C₂²×C₈₉	1	2	yes	—
447	C₂×#125	—	2	2	no	—
448	C₂×#125	C₂²×C₈₉	1	2	yes	—
449	#519	—	2	1	no	—
450	C₂×C₄×Q₈	—	2	1	no	—
451	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
452	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
453	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
454	#501	C₂²×C₈₉	1	4	yes	—
455	#501	C₂²×C₈₉	1	2	yes	—
456	#500	C₂²×C₈₉	1	2	yes	—
457	#499	C₂²×C₈₉	1	4	yes	—
458	#491	C₂²×C₈₉	1	4	yes	—
459	#489	C₂²×C₈₉	1	2	yes	—
460	#488	C₂²×C₈₉	1	4	yes	—
461	#487	C₂²×C₈₉	1	2	yes	—
462	#484	C₂²×C₈₉	1	2	yes	—
463	#484	C₂²×C₈₉	1	2	yes	—
464	#484	C₂²×C₈₉	1	2	yes	—
465	#483	C₂²×C₈₉	1	1	yes	characteristic
466	#483	C₂²×C₈₉	1	2	yes	—
467	#481	C₂²×C₈₉	1	2	yes	—
468	#480	C₂²×C₈₉	1	1	yes	characteristic
469	#479	C₂²×C₈₉	1	2	yes	—
470	#479	C₂²×C₈₉	1	4	yes	—
471	#479	C₂²×C₈₉	1	4	yes	—
472	#479	C₂²×C₈₉	1	4	yes	—
473	#479	C₂²×C₈₉	1	4	yes	—
474	#478	C₂²×C₈₉	1	4	yes	—
475	#477	C₂²×C₈₉	1	4	yes	—
476	#477	C₂²×C₈₉	1	4	yes	—
477	#475	C₂²×C₈₉	1	2	yes	—
478	#475	C₂²×C₈₉	1	2	yes	—
479	#474	C₂²×C₈₉	1	2	yes	—
480	#464	C₂²×C₈₉	1	2	yes	—
481	#464	C₂²×C₈₉	1	4	yes	—
482	#462	C₂²×C₈₉	1	4	yes	—
483	#462	C₂²×C₈₉	1	2	yes	—
484	#451	C₂²×C₈₉	1	1	yes	characteristic
485	#451	C₂²×C₈₉	1	2	yes	—
486	#448	C₂²×C₈₉	1	1	yes	characteristic
487	#446	C₂²×C₈₉	1	2	yes	—
488	#446	C₂²×C₈₉	1	4	yes	—
489	C₈×Q₈	C₂²×C₈₉	1	2	yes	—
490	#441	C₂²×C₈₉	1	4	yes	—
491	#441	C₂²×C₈₉	1	4	yes	—
492	#440	C₂²×C₈₉	1	4	yes	—
493	C₄×Q₁₆	C₂²×C₈₉	1	4	yes	—
494	C₄×Q₁₆	C₂²×C₈₉	1	4	yes	—
495	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	—
496	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
497	#432	C₂²×C₈₉	1	1	yes	characteristic
498	#432	C₂²×C₈₉	1	2	yes	—
499	#431	C₂²×C₈₉	1	2	yes	—
500	#431	C₂²×C₈₉	1	1	yes	characteristic
501	C₂²×Q₈	—	2	1	no	—
502	C₂²×Q₈	—	2	1	no	—
503	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
504	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
505	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
506	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
507	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
508	C₄⋊Q₈	—	2	2	no	—
509	C₄⋊Q₈	—	2	2	no	—
510	C₄⋊Q₈	—	2	4	no	—
511	C₄⋊Q₈	—	2	1	no	—
512	C₄⋊Q₈	—	2	2	no	—
513	C₄⋊Q₈	—	2	1	no	—
514	C₄⋊Q₈	—	2	1	no	—
515	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
516	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
517	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
518	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
519	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
520	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
521	#126	—	2	2	no	—
522	#126	—	2	2	no	—
523	#126	—	2	2	no	—
524	#126	—	2	2	no	—
525	#126	—	2	1	no	—
526	#125	—	2	4	no	—
527	#125	—	2	4	no	—
528	#125	—	2	4	no	—
529	#125	—	2	4	no	—
530	#125	—	2	2	no	—
531	#125	—	2	2	no	—
532	#125	—	2	2	no	—
533	#125	—	2	1	no	—
534	#125	—	2	2	no	—
535	#125	—	2	2	no	—
536	#125	—	2	2	no	—
537	#125	—	2	2	no	—
538	#125	—	2	1	no	—
539	#125	C₂³×C₈₉	1	4	yes	—
540	#125	C₂³×C₈₉	1	4	yes	—
541	#125	C₂³×C₈₉	1	2	yes	—
542	#125	C₂³×C₈₉	1	1	yes	characteristic
543	#124	C₂³×C₈₉	1	2	yes	—
544	#124	C₂³×C₈₉	1	1	yes	characteristic
545	#123	—	2	2	no	—
546	#123	—	2	1	no	—
547	C₂²⋊Q₈	—	2	1	no	—
548	C₂²⋊Q₈	—	2	2	no	—
549	C₂²⋊Q₈	—	2	1	no	—
550	C₂²⋊Q₈	—	2	2	no	—
551	C₂²⋊Q₈	—	2	1	no	—
552	C₂²⋊Q₈	—	2	2	no	—
553	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
554	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
555	#121	C₂³×C₈₉	1	1	yes	characteristic
556	C₄×Q₈	—	2	1	no	—
557	C₄×Q₈	—	2	2	no	—
558	C₄×Q₈	—	2	2	no	—
559	C₄×Q₈	—	2	4	no	—
560	C₄×Q₈	—	2	1	no	—
561	C₄×Q₈	—	2	2	no	—
562	C₄×Q₈	—	2	2	no	—
563	C₄×Q₈	—	2	2	no	—
564	C₄×Q₈	—	2	1	no	—
565	C₄×Q₈	—	2	1	no	—
566	C₄×Q₈	—	2	2	no	—
567	C₄×Q₈	—	2	1	no	—
568	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
569	C₄×Q₈	D₄×C₈₉	1	2	yes	—
570	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
571	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
572	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
573	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
574	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
575	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
576	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
577	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
578	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
579	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
580	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
581	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
582	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
583	C₄×D₄	—	2	1	no	—
584	C₄×D₄	—	2	2	no	—
585	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
586	C₄×D₄	C₂³×C₈₉	1	2	yes	—
587	#117	—	2	2	no	—
588	#117	—	2	1	no	—
589	#117	—	2	1	no	—
590	#117	—	2	2	no	—
591	#117	—	2	2	no	—
592	#117	—	2	1	no	—
593	C₂×C₄⋊C₄	—	2	2	no	—
594	C₂×C₄⋊C₄	—	2	1	no	—
595	C₂×C₄⋊C₄	—	2	2	no	—
596	C₂×C₄⋊C₄	—	2	1	no	—
597	C₂×C₄⋊C₄	—	2	2	no	—
598	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
599	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
602	C₂×C₄²	—	2	2	no	—
603	C₂×C₄²	—	2	1	no	—
604	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
605	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
606	#107	C₂³×C₈₉	1	4	yes	—
607	#107	C₂³×C₈₉	1	4	yes	—
608	#107	C₂³×C₈₉	1	2	yes	—
609	#107	C₂³×C₈₉	1	4	yes	—
610	#106	C₂³×C₈₉	1	2	yes	—
611	#106	C₂³×C₈₉	1	4	yes	—
612	#106	C₂³×C₈₉	1	4	yes	—
613	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
614	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
615	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
616	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
617	#103	C₂³×C₈₉	1	2	yes	—
618	#103	C₂³×C₈₉	1	4	yes	—
619	#103	C₂³×C₈₉	1	2	yes	—
620	#103	C₂³×C₈₉	1	4	yes	—
621	#103	C₂³×C₈₉	1	4	yes	—
622	#103	C₂³×C₈₉	1	2	yes	—
623	#103	C₂³×C₈₉	1	4	yes	—
624	#103	C₂³×C₈₉	1	4	yes	—
625	#102	C₂³×C₈₉	1	2	yes	—
626	#102	C₂³×C₈₉	1	4	yes	—
627	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
628	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
629	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
630	#97	C₂³×C₈₉	1	4	yes	—
631	#97	C₂³×C₈₉	1	2	yes	—
632	C₄×C₈	C₂³×C₈₉	1	2	yes	—
633	C₄×C₈	C₂³×C₈₉	1	4	yes	—
634	C₂×Q₈	—	2	4	no	—
635	C₂×Q₈	—	2	1	no	—
636	C₂×Q₈	—	2	2	no	—
637	C₂×Q₈	—	2	1	no	—
638	C₂×Q₈	—	2	2	no	—
639	C₂×Q₈	—	2	2	no	—
640	C₂×Q₈	—	4	2	no	—
641	C₂×Q₈	—	4	4	no	—
642	C₂×Q₈	—	4	4	no	—
643	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
644	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
645	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
646	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
647	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
648	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
649	C₂×D₄	—	2	1	no	—
650	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
657	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
659	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
661	Q₁₆	—	2	4	no	—
662	Q₁₆	—	2	8	no	—
663	SD₁₆	—	2	4	no	—
664	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
665	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
666	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
697	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
698	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
699	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
700	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
701	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
702	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
703	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
704	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
705	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
706	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
707	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	2	no	—
710	C₂²⋊C₄	—	2	1	no	—
711	C₂²⋊C₄	—	2	2	no	—
712	C₂²⋊C₄	—	2	1	no	—
713	C₂²⋊C₄	—	2	1	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	1	no	—
717	C₄²	—	2	4	no	—
718	C₄²	—	2	4	no	—
719	C₄²	—	2	2	no	—
720	C₄²	—	2	2	no	—
721	C₄²	—	2	2	no	—
722	C₄²	—	2	2	no	—
723	C₄²	—	2	2	no	—
724	C₄²	—	2	2	no	—
725	C₄²	—	2	1	no	—
726	C₄²	C₂×D₄×C₈₉	1	2	yes	—
727	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
728	C₄²	C₂×D₄×C₈₉	1	2	yes	—
729	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
730	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
731	C₄²	C₂⁴×C₈₉	1	2	yes	—
732	C₄²	C₂⁴×C₈₉	1	2	yes	—
733	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
734	C₂³	—	2	1	no	—
735	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
736	Q₈	—	2	4	no	—
737	Q₈	—	2	2	no	—
738	Q₈	—	2	2	no	—
739	Q₈	—	2	2	no	—
740	Q₈	—	2	2	no	—
741	Q₈	—	2	4	no	—
742	Q₈	—	4	2	no	—
743	Q₈	—	4	4	no	—
744	Q₈	—	4	4	no	—
745	Q₈	—	4	2	no	—
746	Q₈	—	4	4	no	—
747	Q₈	2₋¹⁺⁴×C₈₉	1	4	yes	—
748	D₄	—	2	2	no	—
749	D₄	—	4	2	no	—
750	C₂×C₄	—	2	4	no	—
751	C₂×C₄	—	2	4	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	4	no	—
763	C₂×C₄	—	4	2	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	—	4	2	no	—
767	C₂×C₄	—	4	2	no	—
768	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
769	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
770	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
771	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
772	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
773	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
774	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
775	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
776	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
777	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
778	C₈	—	2	2	no	—
779	C₈	—	2	2	no	—
780	C₈	—	2	4	no	—
781	C₂²	—	2	1	no	—
782	C₂²	—	2	1	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	1	no	—
786	C₂²	#578×C₈₉	1	2	yes	—
787	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
788	C₄	—	2	1	no	—
789	C₄	—	2	2	no	—
790	C₄	—	2	2	no	—
791	C₄	—	2	2	no	—
792	C₄	—	2	2	no	—
793	C₄	—	2	1	no	—
794	C₄	—	2	1	no	—
795	C₄	—	2	4	no	—
796	C₄	—	2	1	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	1	no	—
799	C₄	—	4	4	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	1	no	—
802	C₄	—	4	1	no	—
803	C₄	—	4	2	no	—
804	C₄	#575×C₈₉	1	2	yes	—
805	C₄	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
806	C₂	—	2	2	no	—
807	C₂	—	8	1	no	—
808	C₂	C₈₉×#3486	1	1	yes	characteristic
809	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
810	C₂	C₂×#578×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	#121×C₈₉	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×C₄×Q₈×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#557×C₈₉	C₂	semidirect
3. C₈₉×#3390	C₂	semidirect
4. C₈₉×#3386	C₂	semidirect
5. C₈₉×#3383	C₂	semidirect
6. C₈₉×#3377	C₂	semidirect
7. C₈₉×#3374	C₂	semidirect
8. C₈₉×#3364	C₂	semidirect
10. C₈₉×#3236	C₂	semidirect
12. C₈₉×#3230	C₂	semidirect
14. C₈₉×#3113	C₂	semidirect
16. C₈₉×#3104	C₂	semidirect
17. C₈₉×#2984	C₂	semidirect
400. #61842	C₈₉	direct (N × H)
407. C₂×#557	C₂×C₈₉	semidirect
408. #3390	C₂×C₈₉	semidirect
409. #3386	C₂×C₈₉	semidirect
410. #3383	C₂×C₈₉	semidirect
411. #3377	C₂×C₈₉	semidirect
412. #3374	C₂×C₈₉	semidirect
413. #3364	C₂×C₈₉	semidirect
415. #3236	C₂×C₈₉	semidirect
417. #3230	C₂×C₈₉	semidirect
419. #3113	C₂×C₈₉	semidirect
421. #3104	C₂×C₈₉	semidirect
422. #2984	C₂×C₈₉	semidirect
423. C₈₉	#61842	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×#3523	2
C₂×#557×C₈₉	2
C₈₉×#3390	2
C₈₉×#3386	2
C₈₉×#3383	2
C₈₉×#3377	2
C₈₉×#3374	2
C₈₉×#3364	2
C₈₉×#3239	2
C₈₉×#3236	2
C₈₉×#3232	2
C₈₉×#3230	2
C₈₉×#3117	2
C₈₉×#3113	2
C₈₉×#3108	2
C₈₉×#3104	2
C₈₉×#2984	2
#61842	89

Subgroups — C89×#61842 #36439690

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61842 #36439690