Subgroups — C₈₉×#61966 #36439814

Order 22784.

1824 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3511	C₂	1	1	yes	maximal, characteristic
2	Q₈×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3398	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3369	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3331	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3316	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3276	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3270	C₂	1	4	yes	maximal, complemented
9	C₈₉×#3255	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3246	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3216	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3113	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3037	C₂	1	2	yes	maximal, complemented
16	C₂×#462×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2989	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#137×C₈₉	C₂²	1	4	yes	—
19	C₂²×Q₁₆×C₈₉	C₂²	1	2	yes	—
20	Q₈²×C₈₉	C₂²	1	1	yes	characteristic
21	#557×C₈₉	—	2	1	no	—
22	#557×C₈₉	C₂²	1	1	yes	characteristic
23	#556×C₈₉	C₂²	1	2	yes	—
24	#555×C₈₉	—	2	1	no	—
25	#554×C₈₉	—	2	1	no	—
26	#554×C₈₉	—	2	2	no	—
27	#554×C₈₉	—	2	1	no	—
28	#554×C₈₉	C₂²	1	1	yes	characteristic
29	#554×C₈₉	C₂²	1	2	yes	—
30	#553×C₈₉	—	2	2	no	—
31	D₄×Q₈×C₈₉	C₂²	1	2	yes	—
32	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
33	#548×C₈₉	C₂²	1	4	yes	—
34	#547×C₈₉	C₂²	1	2	yes	—
35	#542×C₈₉	—	2	2	no	—
36	#537×C₈₉	—	2	1	no	—
37	#533×C₈₉	—	2	1	no	—
38	#533×C₈₉	—	2	2	no	—
39	#533×C₈₉	C₂²	1	2	yes	—
40	#533×C₈₉	C₂²	1	1	yes	characteristic
41	#533×C₈₉	C₂²	1	2	yes	—
42	#532×C₈₉	C₂²	1	2	yes	—
43	#532×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
45	#520×C₈₉	—	2	1	no	—
46	C₄×#41×C₈₉	—	2	1	no	—
47	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
50	#497×C₈₉	C₂²	1	4	yes	—
51	#494×C₈₉	C₂²	1	2	yes	—
52	#489×C₈₉	C₂²	1	4	yes	—
53	#487×C₈₉	C₂²	1	2	yes	—
54	#483×C₈₉	C₂²	1	4	yes	—
55	#481×C₈₉	C₂²	1	2	yes	—
56	#476×C₈₉	C₂²	1	2	yes	—
57	#475×C₈₉	C₂²	1	1	yes	characteristic
58	#475×C₈₉	C₂²	1	1	yes	characteristic
59	#475×C₈₉	C₂²	1	4	yes	—
60	#475×C₈₉	C₂²	1	2	yes	—
61	#470×C₈₉	C₂²	1	4	yes	—
62	#470×C₈₉	C₂²	1	4	yes	—
63	#465×C₈₉	C₂²	1	4	yes	—
64	#464×C₈₉	C₂²	1	4	yes	—
65	#464×C₈₉	C₂²	1	4	yes	—
66	#462×C₈₉	C₂²	1	2	yes	—
67	#462×C₈₉	C₂²	1	2	yes	—
68	#462×C₈₉	C₂²	1	2	yes	—
69	#462×C₈₉	C₂²	1	2	yes	—
70	#462×C₈₉	C₂²	1	4	yes	—
71	#462×C₈₉	C₂²	1	2	yes	—
72	#462×C₈₉	C₂²	1	2	yes	—
73	#461×C₈₉	C₂²	1	2	yes	—
74	#460×C₈₉	C₂²	1	1	yes	characteristic
75	#460×C₈₉	C₂²	1	1	yes	characteristic
76	#460×C₈₉	C₂²	1	2	yes	—
77	#452×C₈₉	C₂²	1	4	yes	—
78	#452×C₈₉	C₂²	1	4	yes	—
79	#451×C₈₉	C₂²	1	4	yes	—
80	#451×C₈₉	C₂²	1	4	yes	—
81	#448×C₈₉	C₂²	1	2	yes	—
82	#446×C₈₉	C₂²	1	2	yes	—
83	#441×C₈₉	C₂²	1	4	yes	—
84	#441×C₈₉	C₂²	1	4	yes	—
85	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
86	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
87	#436×C₈₉	C₂²	1	2	yes	—
88	#435×C₈₉	C₂²	1	4	yes	—
89	#432×C₈₉	C₂²	1	2	yes	—
90	#431×C₈₉	C₂²	1	1	yes	characteristic
91	#423×C₈₉	C₂²	1	2	yes	—
92	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
93	#417×C₈₉	C₂²	1	4	yes	—
94	C₂×#103×C₈₉	C₂²	1	2	yes	—
95	C₂×#41×C₈₉	—	2	1	no	—
96	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
97	C₂×#41×C₈₉	C₂³	1	4	yes	—
98	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
100	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
101	#137×C₈₉	—	4	8	no	—
102	C₂×Q₁₆×C₈₉	—	4	4	no	—
103	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
104	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
105	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
106	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
107	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
108	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
110	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
111	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₈₉	—	2	1	no	—
113	C₄⋊Q₈×C₈₉	—	2	2	no	—
114	C₄⋊Q₈×C₈₉	—	2	1	no	—
115	C₄⋊Q₈×C₈₉	—	2	2	no	—
116	C₄⋊Q₈×C₈₉	—	2	1	no	—
117	C₄⋊Q₈×C₈₉	—	2	1	no	—
118	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
119	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
120	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
121	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
122	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
123	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
124	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
125	#127×C₈₉	C₂³	1	1	yes	characteristic
126	#126×C₈₉	—	2	4	no	—
127	#125×C₈₉	—	2	1	no	—
128	#125×C₈₉	—	2	2	no	—
129	#125×C₈₉	—	2	1	no	—
130	#125×C₈₉	—	2	2	no	—
131	#125×C₈₉	—	2	2	no	—
132	#125×C₈₉	—	2	2	no	—
133	#125×C₈₉	—	2	1	no	—
134	#124×C₈₉	—	2	4	no	—
135	#124×C₈₉	—	2	1	no	—
136	#124×C₈₉	C₂³	1	4	yes	—
137	#123×C₈₉	—	2	4	no	—
138	C₂²⋊Q₈×C₈₉	—	2	2	no	—
139	C₂²⋊Q₈×C₈₉	—	2	2	no	—
140	C₂²⋊Q₈×C₈₉	—	2	1	no	—
141	C₂²⋊Q₈×C₈₉	—	2	2	no	—
142	C₂²⋊Q₈×C₈₉	—	2	4	no	—
143	C₂²⋊Q₈×C₈₉	—	2	2	no	—
144	C₂²⋊Q₈×C₈₉	—	2	2	no	—
145	C₂²⋊Q₈×C₈₉	—	2	2	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	2	yes	—
150	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
151	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
152	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
153	#121×C₈₉	—	2	2	no	—
154	#121×C₈₉	—	2	4	no	—
155	#121×C₈₉	—	2	2	no	—
156	#121×C₈₉	—	2	1	no	—
157	#121×C₈₉	—	2	2	no	—
158	#121×C₈₉	C₂³	1	2	yes	—
159	C₄×Q₈×C₈₉	—	2	1	no	—
160	C₄×Q₈×C₈₉	—	2	1	no	—
161	C₄×Q₈×C₈₉	—	2	2	no	—
162	C₄×Q₈×C₈₉	—	2	1	no	—
163	C₄×Q₈×C₈₉	—	2	2	no	—
164	C₄×Q₈×C₈₉	—	2	1	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	1	yes	characteristic
170	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₈₉	C₂³	1	4	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×Q₈×C₈₉	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
182	C₄×D₄×C₈₉	—	2	4	no	—
183	C₄×D₄×C₈₉	—	2	2	no	—
184	C₄×D₄×C₈₉	—	2	2	no	—
185	C₄×D₄×C₈₉	—	2	1	no	—
186	C₄×D₄×C₈₉	D₄	1	2	yes	—
187	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
188	C₄×D₄×C₈₉	C₂³	1	2	yes	—
189	C₄×D₄×C₈₉	C₂³	1	2	yes	—
190	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
191	#117×C₈₉	—	2	2	no	—
192	#117×C₈₉	—	2	1	no	—
193	#117×C₈₉	—	2	2	no	—
194	#117×C₈₉	—	2	2	no	—
195	#117×C₈₉	D₄	1	1	yes	characteristic
196	#117×C₈₉	D₄	1	2	yes	—
197	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
198	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
199	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
200	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
201	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
202	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
204	C₂×C₄²×C₈₉	—	2	2	no	—
205	C₂×C₄²×C₈₉	—	2	1	no	—
206	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
208	#106×C₈₉	C₂³	1	2	yes	—
209	#106×C₈₉	C₂³	1	2	yes	—
210	#106×C₈₉	C₂³	1	4	yes	—
211	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
212	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
213	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
214	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
215	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
216	#103×C₈₉	C₂³	1	4	yes	—
217	#103×C₈₉	C₂³	1	4	yes	—
218	#103×C₈₉	C₂³	1	4	yes	—
219	#103×C₈₉	C₂³	1	2	yes	—
220	#103×C₈₉	C₂³	1	2	yes	—
221	#103×C₈₉	C₂³	1	4	yes	—
222	#103×C₈₉	C₂³	1	4	yes	—
223	#102×C₈₉	C₂³	1	2	yes	—
224	#102×C₈₉	C₂³	1	4	yes	—
225	#102×C₈₉	C₂³	1	2	yes	—
226	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
227	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
228	#97×C₈₉	C₂³	1	4	yes	—
229	C₄×C₈×C₈₉	C₂³	1	2	yes	—
230	#41×C₈₉	—	2	4	no	—
231	#41×C₈₉	—	4	4	no	—
232	#41×C₈₉	—	4	4	no	—
233	#41×C₈₉	—	4	4	no	—
234	C₂×Q₈×C₈₉	—	2	1	no	—
235	C₂×Q₈×C₈₉	—	2	1	no	—
236	C₂×Q₈×C₈₉	—	2	2	no	—
237	C₂×Q₈×C₈₉	—	2	2	no	—
238	C₂×Q₈×C₈₉	—	2	1	no	—
239	C₂×Q₈×C₈₉	—	2	2	no	—
240	C₂×Q₈×C₈₉	—	2	2	no	—
241	C₂×Q₈×C₈₉	—	2	4	no	—
242	C₂×Q₈×C₈₉	—	4	1	no	—
243	C₂×Q₈×C₈₉	—	4	2	no	—
244	C₂×Q₈×C₈₉	—	4	2	no	—
245	C₂×Q₈×C₈₉	—	4	2	no	—
246	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
247	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
248	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
249	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
250	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
251	C₂×D₄×C₈₉	—	2	2	no	—
252	C₂×D₄×C₈₉	—	2	4	no	—
253	C₂×D₄×C₈₉	—	2	1	no	—
254	C₂×D₄×C₈₉	—	2	1	no	—
255	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
256	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
257	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₈₉	—	2	2	no	—
259	C₂²×C₄×C₈₉	—	2	1	no	—
260	C₂²×C₄×C₈₉	—	2	2	no	—
261	C₂²×C₄×C₈₉	—	2	1	no	—
262	C₂²×C₄×C₈₉	—	2	2	no	—
263	C₂²×C₄×C₈₉	—	2	2	no	—
264	C₂²×C₄×C₈₉	—	2	4	no	—
265	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
266	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
271	Q₁₆×C₈₉	—	2	8	no	—
272	Q₁₆×C₈₉	—	4	4	no	—
273	Q₁₆×C₈₉	—	4	4	no	—
274	Q₁₆×C₈₉	—	4	4	no	—
275	SD₁₆×C₈₉	—	2	4	no	—
276	SD₁₆×C₈₉	—	4	2	no	—
277	SD₁₆×C₈₉	—	4	4	no	—
278	M₁₆×C₈₉	—	4	4	no	—
279	C₂×C₈×C₈₉	—	4	2	no	—
280	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
281	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
282	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
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	4	no	—
288	C₄⋊C₄×C₈₉	—	2	2	no	—
289	C₄⋊C₄×C₈₉	—	2	1	no	—
290	C₄⋊C₄×C₈₉	—	2	1	no	—
291	C₄⋊C₄×C₈₉	—	2	2	no	—
292	C₄⋊C₄×C₈₉	—	2	2	no	—
293	C₄⋊C₄×C₈₉	—	2	1	no	—
294	C₄⋊C₄×C₈₉	—	2	2	no	—
295	C₄⋊C₄×C₈₉	—	2	1	no	—
296	C₄⋊C₄×C₈₉	—	2	2	no	—
297	C₄⋊C₄×C₈₉	—	2	1	no	—
298	C₄⋊C₄×C₈₉	—	2	2	no	—
299	C₄⋊C₄×C₈₉	—	2	1	no	—
300	C₄⋊C₄×C₈₉	—	2	2	no	—
301	C₄⋊C₄×C₈₉	—	2	1	no	—
302	C₄⋊C₄×C₈₉	—	2	2	no	—
303	C₄⋊C₄×C₈₉	—	2	1	no	—
304	C₄⋊C₄×C₈₉	—	2	2	no	—
305	C₄⋊C₄×C₈₉	—	2	2	no	—
306	C₄⋊C₄×C₈₉	—	2	2	no	—
307	C₄⋊C₄×C₈₉	—	2	4	no	—
308	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
309	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
310	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
311	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
312	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
313	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
314	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
315	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
316	C₂²⋊C₄×C₈₉	—	2	2	no	—
317	C₂²⋊C₄×C₈₉	—	2	2	no	—
318	C₂²⋊C₄×C₈₉	—	2	2	no	—
319	C₂²⋊C₄×C₈₉	—	2	4	no	—
320	C₂²⋊C₄×C₈₉	—	2	4	no	—
321	C₂²⋊C₄×C₈₉	—	2	4	no	—
322	C₂²⋊C₄×C₈₉	—	2	2	no	—
323	C₂²⋊C₄×C₈₉	—	2	2	no	—
324	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
325	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
326	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
327	C₄²×C₈₉	—	2	1	no	—
328	C₄²×C₈₉	—	2	2	no	—
329	C₄²×C₈₉	—	2	1	no	—
330	C₄²×C₈₉	—	2	2	no	—
331	C₄²×C₈₉	—	2	1	no	—
332	C₄²×C₈₉	—	2	2	no	—
333	C₄²×C₈₉	—	2	1	no	—
334	C₄²×C₈₉	—	2	4	no	—
335	C₄²×C₈₉	C₂×D₄	1	2	yes	—
336	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₈₉	C₂×D₄	1	2	yes	—
338	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
340	C₄²×C₈₉	C₂⁴	1	2	yes	—
341	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
342	C₂³×C₈₉	—	2	2	no	—
343	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
344	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
345	Q₈×C₈₉	—	2	2	no	—
346	Q₈×C₈₉	—	2	1	no	—
347	Q₈×C₈₉	—	2	2	no	—
348	Q₈×C₈₉	—	2	4	no	—
349	Q₈×C₈₉	—	2	1	no	—
350	Q₈×C₈₉	—	2	1	no	—
351	Q₈×C₈₉	—	2	2	no	—
352	Q₈×C₈₉	—	2	4	no	—
353	Q₈×C₈₉	—	4	4	no	—
354	Q₈×C₈₉	—	4	2	no	—
355	Q₈×C₈₉	—	4	2	no	—
356	Q₈×C₈₉	—	8	2	no	—
357	Q₈×C₈₉	—	8	1	no	—
358	Q₈×C₈₉	—	8	2	no	—
359	Q₈×C₈₉	H(5,𝔽₂)	1	2	yes	—
360	D₄×C₈₉	—	2	4	no	—
361	D₄×C₈₉	—	2	2	no	—
362	D₄×C₈₉	—	2	2	no	—
363	D₄×C₈₉	—	2	2	no	—
364	D₄×C₈₉	—	4	2	no	—
365	D₄×C₈₉	—	4	4	no	—
366	D₄×C₈₉	—	4	2	no	—
367	D₄×C₈₉	—	8	4	no	—
368	C₂×C₄×C₈₉	—	2	1	no	—
369	C₂×C₄×C₈₉	—	2	4	no	—
370	C₂×C₄×C₈₉	—	2	1	no	—
371	C₂×C₄×C₈₉	—	2	2	no	—
372	C₂×C₄×C₈₉	—	2	1	no	—
373	C₂×C₄×C₈₉	—	2	2	no	—
374	C₂×C₄×C₈₉	—	2	1	no	—
375	C₂×C₄×C₈₉	—	2	2	no	—
376	C₂×C₄×C₈₉	—	2	2	no	—
377	C₂×C₄×C₈₉	—	2	1	no	—
378	C₂×C₄×C₈₉	—	2	2	no	—
379	C₂×C₄×C₈₉	—	2	1	no	—
380	C₂×C₄×C₈₉	—	2	4	no	—
381	C₂×C₄×C₈₉	—	4	1	no	—
382	C₂×C₄×C₈₉	—	4	2	no	—
383	C₂×C₄×C₈₉	—	4	2	no	—
384	C₂×C₄×C₈₉	—	4	4	no	—
385	C₂×C₄×C₈₉	—	4	4	no	—
386	C₂×C₄×C₈₉	—	8	4	no	—
387	C₂×C₄×C₈₉	—	8	1	no	—
388	C₂×C₄×C₈₉	—	8	2	no	—
389	C₂×C₄×C₈₉	—	8	2	no	—
390	C₂×C₄×C₈₉	#137	1	4	yes	complemented
391	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
393	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
400	C₈×C₈₉	—	2	4	no	—
401	C₈×C₈₉	—	2	2	no	—
402	C₈×C₈₉	—	2	2	no	—
403	C₂²×C₈₉	—	2	1	no	—
404	C₂²×C₈₉	—	2	1	no	—
405	C₂²×C₈₉	—	2	2	no	—
406	C₂²×C₈₉	—	2	2	no	—
407	C₂²×C₈₉	—	2	2	no	—
408	C₂²×C₈₉	—	4	2	no	—
409	C₂²×C₈₉	—	4	2	no	—
410	C₂²×C₈₉	—	4	2	no	—
411	C₂²×C₈₉	C₂×#137	1	2	yes	—
412	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
413	C₄×C₈₉	—	2	1	no	—
414	C₄×C₈₉	—	2	2	no	—
415	C₄×C₈₉	—	2	1	no	—
416	C₄×C₈₉	—	2	2	no	—
417	C₄×C₈₉	—	2	1	no	—
418	C₄×C₈₉	—	2	2	no	—
419	C₄×C₈₉	—	2	2	no	—
420	C₄×C₈₉	—	4	1	no	—
421	C₄×C₈₉	—	4	1	no	—
422	C₄×C₈₉	—	4	2	no	—
423	C₄×C₈₉	—	4	2	no	—
424	C₄×C₈₉	—	4	1	no	—
425	C₄×C₈₉	—	4	4	no	—
426	C₄×C₈₉	—	4	2	no	—
427	C₄×C₈₉	C₂×#137	1	2	yes	—
428	C₄×C₈₉	C₂×#137	1	2	yes	—
429	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
430	C₄×C₈₉	#585	1	1	yes	characteristic
431	#61966	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
432	C₂×C₈₉	—	2	2	no	—
433	C₂×C₈₉	—	4	2	no	—
434	C₂×C₈₉	—	8	2	no	—
435	C₂×C₈₉	#3488	1	1	yes	characteristic
436	C₂×C₈₉	C₂²×#137	1	1	yes	characteristic
437	C₂×C₈₉	#3586	1	1	yes	characteristic
438	#3511	C₂×C₈₉	1	1	yes	characteristic
439	Q₈×#41	C₂×C₈₉	1	1	yes	characteristic, complemented
440	#3398	C₂×C₈₉	1	2	yes	complemented
441	#3369	C₂×C₈₉	1	2	yes	complemented
442	#3331	C₂×C₈₉	1	2	yes	complemented
443	#3316	C₂×C₈₉	1	4	yes	complemented
444	#3276	C₂×C₈₉	1	2	yes	complemented
445	#3270	C₂×C₈₉	1	4	yes	complemented
446	#3255	C₂×C₈₉	1	2	yes	complemented
447	#3246	C₂×C₈₉	1	1	yes	characteristic, complemented
448	#3216	C₂×C₈₉	1	2	yes	complemented
449	#3209	C₂×C₈₉	1	1	yes	characteristic, complemented
450	#3113	C₂×C₈₉	1	2	yes	complemented
451	#3103	C₂×C₈₉	1	1	yes	characteristic, complemented
452	#3037	C₂×C₈₉	1	2	yes	complemented
453	C₂×#462	C₂×C₈₉	1	1	yes	characteristic, complemented
454	#2989	C₂×C₈₉	1	1	yes	characteristic, complemented
455	C₈₉	#61966	1	1	yes	characteristic, direct product factor, Sylow
456	C₂×#137	C₂²×C₈₉	1	4	yes	—
457	C₂²×Q₁₆	C₂²×C₈₉	1	2	yes	—
458	Q₈²	C₂²×C₈₉	1	1	yes	characteristic
459	#557	—	2	1	no	—
460	#557	C₂²×C₈₉	1	1	yes	characteristic
461	#556	C₂²×C₈₉	1	2	yes	—
462	#555	—	2	1	no	—
463	#554	—	2	1	no	—
464	#554	—	2	2	no	—
465	#554	—	2	1	no	—
466	#554	C₂²×C₈₉	1	1	yes	characteristic
467	#554	C₂²×C₈₉	1	2	yes	—
468	#553	—	2	2	no	—
469	D₄×Q₈	C₂²×C₈₉	1	2	yes	—
470	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
471	#548	C₂²×C₈₉	1	4	yes	—
472	#547	C₂²×C₈₉	1	2	yes	—
473	#542	—	2	2	no	—
474	#537	—	2	1	no	—
475	#533	—	2	1	no	—
476	#533	—	2	2	no	—
477	#533	C₂²×C₈₉	1	2	yes	—
478	#533	C₂²×C₈₉	1	1	yes	characteristic
479	#533	C₂²×C₈₉	1	2	yes	—
480	#532	C₂²×C₈₉	1	2	yes	—
481	#532	C₂²×C₈₉	1	1	yes	characteristic
482	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
483	#520	—	2	1	no	—
484	C₄×#41	—	2	1	no	—
485	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
486	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
487	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
488	#497	C₂²×C₈₉	1	4	yes	—
489	#494	C₂²×C₈₉	1	2	yes	—
490	#489	C₂²×C₈₉	1	4	yes	—
491	#487	C₂²×C₈₉	1	2	yes	—
492	#483	C₂²×C₈₉	1	4	yes	—
493	#481	C₂²×C₈₉	1	2	yes	—
494	#476	C₂²×C₈₉	1	2	yes	—
495	#475	C₂²×C₈₉	1	1	yes	characteristic
496	#475	C₂²×C₈₉	1	1	yes	characteristic
497	#475	C₂²×C₈₉	1	2	yes	—
498	#475	C₂²×C₈₉	1	4	yes	—
499	#470	C₂²×C₈₉	1	4	yes	—
500	#470	C₂²×C₈₉	1	4	yes	—
501	#465	C₂²×C₈₉	1	4	yes	—
502	#464	C₂²×C₈₉	1	4	yes	—
503	#464	C₂²×C₈₉	1	4	yes	—
504	#462	C₂²×C₈₉	1	2	yes	—
505	#462	C₂²×C₈₉	1	2	yes	—
506	#462	C₂²×C₈₉	1	2	yes	—
507	#462	C₂²×C₈₉	1	2	yes	—
508	#462	C₂²×C₈₉	1	4	yes	—
509	#462	C₂²×C₈₉	1	2	yes	—
510	#462	C₂²×C₈₉	1	2	yes	—
511	#461	C₂²×C₈₉	1	2	yes	—
512	#460	C₂²×C₈₉	1	1	yes	characteristic
513	#460	C₂²×C₈₉	1	1	yes	characteristic
514	#460	C₂²×C₈₉	1	2	yes	—
515	#452	C₂²×C₈₉	1	4	yes	—
516	#452	C₂²×C₈₉	1	4	yes	—
517	#451	C₂²×C₈₉	1	4	yes	—
518	#451	C₂²×C₈₉	1	4	yes	—
519	#448	C₂²×C₈₉	1	2	yes	—
520	#446	C₂²×C₈₉	1	2	yes	—
521	#441	C₂²×C₈₉	1	4	yes	—
522	#441	C₂²×C₈₉	1	4	yes	—
523	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
524	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
525	#436	C₂²×C₈₉	1	2	yes	—
526	#435	C₂²×C₈₉	1	4	yes	—
527	#432	C₂²×C₈₉	1	2	yes	—
528	#431	C₂²×C₈₉	1	1	yes	characteristic
529	#423	C₂²×C₈₉	1	2	yes	—
530	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
531	#417	C₂²×C₈₉	1	4	yes	—
532	C₂×#103	C₂²×C₈₉	1	2	yes	—
533	C₂×#41	—	2	1	no	—
534	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
535	C₂×#41	C₂³×C₈₉	1	4	yes	—
536	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
537	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
538	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
539	#137	—	4	8	no	—
540	C₂×Q₁₆	—	4	4	no	—
541	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
542	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
543	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
544	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
545	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
546	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
547	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
548	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
549	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
550	C₄⋊Q₈	—	2	1	no	—
551	C₄⋊Q₈	—	2	2	no	—
552	C₄⋊Q₈	—	2	1	no	—
553	C₄⋊Q₈	—	2	2	no	—
554	C₄⋊Q₈	—	2	1	no	—
555	C₄⋊Q₈	—	2	1	no	—
556	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
557	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
558	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
559	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
560	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
561	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
562	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
563	#127	C₂³×C₈₉	1	1	yes	characteristic
564	#126	—	2	4	no	—
565	#125	—	2	1	no	—
566	#125	—	2	2	no	—
567	#125	—	2	1	no	—
568	#125	—	2	2	no	—
569	#125	—	2	2	no	—
570	#125	—	2	2	no	—
571	#125	—	2	1	no	—
572	#124	—	2	4	no	—
573	#124	—	2	1	no	—
574	#124	C₂³×C₈₉	1	4	yes	—
575	#123	—	2	4	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	—	2	4	no	—
581	C₂²⋊Q₈	—	2	2	no	—
582	C₂²⋊Q₈	—	2	2	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
588	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
589	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
590	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
591	#121	—	2	2	no	—
592	#121	—	2	4	no	—
593	#121	—	2	2	no	—
594	#121	—	2	1	no	—
595	#121	—	2	2	no	—
596	#121	C₂³×C₈₉	1	2	yes	—
597	C₄×Q₈	—	2	1	no	—
598	C₄×Q₈	—	2	1	no	—
599	C₄×Q₈	—	2	2	no	—
600	C₄×Q₈	—	2	1	no	—
601	C₄×Q₈	—	2	2	no	—
602	C₄×Q₈	—	2	1	no	—
603	C₄×Q₈	—	2	2	no	—
604	C₄×Q₈	—	2	2	no	—
605	C₄×Q₈	—	2	1	no	—
606	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
607	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
608	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
609	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
610	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
611	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
612	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
613	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
614	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
615	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	4	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	1	no	—
624	C₄×D₄	D₄×C₈₉	1	2	yes	—
625	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
626	C₄×D₄	C₂³×C₈₉	1	2	yes	—
627	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
628	C₄×D₄	C₂³×C₈₉	1	2	yes	—
629	#117	—	2	2	no	—
630	#117	—	2	1	no	—
631	#117	—	2	2	no	—
632	#117	—	2	2	no	—
633	#117	D₄×C₈₉	1	1	yes	characteristic
634	#117	D₄×C₈₉	1	2	yes	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	—	2	2	no	—
637	C₂×C₄⋊C₄	—	2	1	no	—
638	C₂×C₄⋊C₄	—	2	1	no	—
639	C₂×C₄⋊C₄	—	2	2	no	—
640	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
642	C₂×C₄²	—	2	2	no	—
643	C₂×C₄²	—	2	1	no	—
644	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
646	#106	C₂³×C₈₉	1	2	yes	—
647	#106	C₂³×C₈₉	1	2	yes	—
648	#106	C₂³×C₈₉	1	4	yes	—
649	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
650	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
651	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
652	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
653	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
654	#103	C₂³×C₈₉	1	4	yes	—
655	#103	C₂³×C₈₉	1	4	yes	—
656	#103	C₂³×C₈₉	1	4	yes	—
657	#103	C₂³×C₈₉	1	2	yes	—
658	#103	C₂³×C₈₉	1	2	yes	—
659	#103	C₂³×C₈₉	1	4	yes	—
660	#103	C₂³×C₈₉	1	4	yes	—
661	#102	C₂³×C₈₉	1	2	yes	—
662	#102	C₂³×C₈₉	1	4	yes	—
663	#102	C₂³×C₈₉	1	2	yes	—
664	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
665	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
666	#97	C₂³×C₈₉	1	4	yes	—
667	C₄×C₈	C₂³×C₈₉	1	2	yes	—
668	#41	—	2	4	no	—
669	#41	—	4	4	no	—
670	#41	—	4	4	no	—
671	#41	—	4	4	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	2	no	—
676	C₂×Q₈	—	2	1	no	—
677	C₂×Q₈	—	2	2	no	—
678	C₂×Q₈	—	2	2	no	—
679	C₂×Q₈	—	2	4	no	—
680	C₂×Q₈	—	4	1	no	—
681	C₂×Q₈	—	4	2	no	—
682	C₂×Q₈	—	4	2	no	—
683	C₂×Q₈	—	4	2	no	—
684	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
685	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
686	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
687	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
688	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	4	no	—
691	C₂×D₄	—	2	1	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
694	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
695	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	1	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
704	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
705	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
706	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
709	Q₁₆	—	2	8	no	—
710	Q₁₆	—	4	4	no	—
711	Q₁₆	—	4	4	no	—
712	Q₁₆	—	4	4	no	—
713	SD₁₆	—	2	4	no	—
714	SD₁₆	—	4	4	no	—
715	SD₁₆	—	4	2	no	—
716	M₁₆	—	4	4	no	—
717	C₂×C₈	—	4	2	no	—
718	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
719	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
720	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	4	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
747	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
748	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
749	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
750	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
751	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
752	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
753	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
763	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
764	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
765	C₄²	—	2	1	no	—
766	C₄²	—	2	2	no	—
767	C₄²	—	2	1	no	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	1	no	—
770	C₄²	—	2	2	no	—
771	C₄²	—	2	1	no	—
772	C₄²	—	2	4	no	—
773	C₄²	C₂×D₄×C₈₉	1	2	yes	—
774	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
775	C₄²	C₂×D₄×C₈₉	1	2	yes	—
776	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
777	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
778	C₄²	C₂⁴×C₈₉	1	2	yes	—
779	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
780	C₂³	—	2	2	no	—
781	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
782	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
783	Q₈	—	2	2	no	—
784	Q₈	—	2	1	no	—
785	Q₈	—	2	2	no	—
786	Q₈	—	2	4	no	—
787	Q₈	—	2	1	no	—
788	Q₈	—	2	1	no	—
789	Q₈	—	2	2	no	—
790	Q₈	—	2	4	no	—
791	Q₈	—	4	4	no	—
792	Q₈	—	4	2	no	—
793	Q₈	—	4	2	no	—
794	Q₈	—	8	2	no	—
795	Q₈	—	8	1	no	—
796	Q₈	—	8	2	no	—
797	Q₈	H(5,𝔽₂)×C₈₉	1	2	yes	—
798	D₄	—	2	4	no	—
799	D₄	—	2	2	no	—
800	D₄	—	2	2	no	—
801	D₄	—	2	2	no	—
802	D₄	—	4	2	no	—
803	D₄	—	4	4	no	—
804	D₄	—	4	2	no	—
805	D₄	—	8	4	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	4	no	—
819	C₂×C₄	—	4	1	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	4	2	no	—
822	C₂×C₄	—	4	4	no	—
823	C₂×C₄	—	4	4	no	—
824	C₂×C₄	—	8	4	no	—
825	C₂×C₄	—	8	1	no	—
826	C₂×C₄	—	8	2	no	—
827	C₂×C₄	—	8	2	no	—
828	C₂×C₄	#137×C₈₉	1	4	yes	complemented
829	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
830	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
831	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
832	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
833	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
834	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
835	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
836	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
837	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
838	C₈	—	2	4	no	—
839	C₈	—	2	2	no	—
840	C₈	—	2	2	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	2	1	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	2	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	C₂×#137×C₈₉	1	2	yes	—
850	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
851	C₄	—	2	2	no	—
852	C₄	—	2	1	no	—
853	C₄	—	2	2	no	—
854	C₄	—	2	1	no	—
855	C₄	—	2	2	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	4	no	—
865	C₄	C₂×#137×C₈₉	1	2	yes	—
866	C₄	C₂×#137×C₈₉	1	2	yes	—
867	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
868	C₄	#585×C₈₉	1	1	yes	characteristic
869	C₂	—	2	2	no	—
870	C₂	—	4	2	no	—
871	C₂	—	8	2	no	—
872	C₂	C₈₉×#3488	1	1	yes	characteristic
873	C₂	C₂²×#137×C₈₉	1	1	yes	characteristic
874	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×#3511	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. Q₈×#41×C₈₉	C₂	semidirect
3. C₈₉×#3398	C₂	semidirect
4. C₈₉×#3369	C₂	semidirect
5. C₈₉×#3331	C₂	semidirect
6. C₈₉×#3316	C₂	semidirect
7. C₈₉×#3276	C₂	semidirect
8. C₈₉×#3270	C₂	semidirect
9. C₈₉×#3255	C₂	semidirect
10. C₈₉×#3246	C₂	semidirect
11. C₈₉×#3216	C₂	semidirect
12. C₈₉×#3209	C₂	semidirect
13. C₈₉×#3113	C₂	semidirect
14. C₈₉×#3103	C₂	semidirect
15. C₈₉×#3037	C₂	semidirect
16. C₂×#462×C₈₉	C₂	semidirect
17. C₈₉×#2989	C₂	semidirect
390. C₂×C₄×C₈₉	#137	semidirect
431. #61966	C₈₉	direct (N × H)
439. Q₈×#41	C₂×C₈₉	semidirect
440. #3398	C₂×C₈₉	semidirect
441. #3369	C₂×C₈₉	semidirect
442. #3331	C₂×C₈₉	semidirect
443. #3316	C₂×C₈₉	semidirect
444. #3276	C₂×C₈₉	semidirect
445. #3270	C₂×C₈₉	semidirect
446. #3255	C₂×C₈₉	semidirect
447. #3246	C₂×C₈₉	semidirect
448. #3216	C₂×C₈₉	semidirect
449. #3209	C₂×C₈₉	semidirect
450. #3113	C₂×C₈₉	semidirect
451. #3103	C₂×C₈₉	semidirect
452. #3037	C₂×C₈₉	semidirect
453. C₂×#462	C₂×C₈₉	semidirect
454. #2989	C₂×C₈₉	semidirect
455. C₈₉	#61966	direct (N × H)
828. C₂×C₄	#137×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3511	2
Q₈×#41×C₈₉	2
C₈₉×#3398	2
C₈₉×#3369	2
C₈₉×#3331	2
C₈₉×#3316	2
C₈₉×#3276	2
C₈₉×#3270	2
C₈₉×#3255	2
C₈₉×#3246	2
C₈₉×#3216	2
C₈₉×#3209	2
C₈₉×#3113	2
C₈₉×#3103	2
C₈₉×#3037	2
C₂×#462×C₈₉	2
C₈₉×#2989	2
#61966	89

Subgroups — C89×#61966 #36439814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61966 #36439814