Subgroups — C₈₉×#60819 #36438667

Order 22784.

2058 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3225	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3224	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3212	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3211	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3153	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#495×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3140	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3044	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3043	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3042	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3041	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3011	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#3010	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3009	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#3008	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic, complemented
26	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
27	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
29	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
30	#559×C₈₉	—	2	2	no	—
31	#556×C₈₉	—	2	2	no	—
32	#551×C₈₉	—	2	4	no	—
33	#548×C₈₉	—	2	2	no	—
34	#546×C₈₉	—	2	4	no	—
35	#546×C₈₉	—	2	2	no	—
36	#542×C₈₉	C₂²	1	4	yes	complemented
37	#536×C₈₉	C₂²	1	1	yes	characteristic
38	#536×C₈₉	C₂²	1	1	yes	characteristic
39	#536×C₈₉	C₂²	1	2	yes	complemented
40	#535×C₈₉	C₂²	1	1	yes	characteristic
41	#535×C₈₉	C₂²	1	1	yes	characteristic
42	#535×C₈₉	C₂²	1	2	yes	complemented
43	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
44	#532×C₈₉	C₂²	1	1	yes	characteristic
45	#532×C₈₉	C₂²	1	2	yes	complemented
46	#529×C₈₉	C₂²	1	4	yes	complemented
47	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
49	C₂×#124×C₈₉	C₂²	1	2	yes	complemented
50	#519×C₈₉	C₂²	1	1	yes	characteristic, complemented
51	#518×C₈₉	C₂²	1	1	yes	characteristic, complemented
52	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
53	#497×C₈₉	C₂²	1	2	yes	complemented
54	#496×C₈₉	C₂²	1	2	yes	complemented
55	#495×C₈₉	C₂²	1	4	yes	complemented
56	#495×C₈₉	C₂²	1	4	yes	complemented
57	#495×C₈₉	C₂²	1	2	yes	complemented
58	#495×C₈₉	C₂²	1	2	yes	complemented
59	#489×C₈₉	C₂²	1	4	yes	complemented
60	#488×C₈₉	C₂²	1	2	yes	complemented
61	#488×C₈₉	C₂²	1	2	yes	complemented
62	#488×C₈₉	C₂²	1	4	yes	complemented
63	#487×C₈₉	C₂²	1	2	yes	complemented
64	#486×C₈₉	C₂²	1	2	yes	complemented
65	#464×C₈₉	C₂²	1	4	yes	complemented
66	#464×C₈₉	C₂²	1	4	yes	complemented
67	#463×C₈₉	C₂²	1	4	yes	complemented
68	#463×C₈₉	C₂²	1	4	yes	complemented
69	#462×C₈₉	C₂²	1	4	yes	complemented
70	#461×C₈₉	C₂²	1	4	yes	complemented
71	#460×C₈₉	C₂²	1	4	yes	complemented
72	#459×C₈₉	C₂²	1	4	yes	complemented
73	#452×C₈₉	C₂²	1	4	yes	complemented
74	#452×C₈₉	C₂²	1	4	yes	complemented
75	#451×C₈₉	C₂²	1	4	yes	complemented
76	#450×C₈₉	C₂²	1	4	yes	complemented
77	#449×C₈₉	C₂²	1	4	yes	—
78	#449×C₈₉	C₂²	1	4	yes	complemented
79	#448×C₈₉	C₂²	1	4	yes	complemented
80	#447×C₈₉	C₂²	1	4	yes	—
81	#433×C₈₉	C₂²	1	4	yes	complemented
82	#431×C₈₉	C₂²	1	4	yes	complemented
83	#424×C₈₉	C₂²	1	1	yes	characteristic, complemented
84	#424×C₈₉	C₂²	1	1	yes	characteristic, complemented
85	#419×C₈₉	C₂²	1	1	yes	characteristic, complemented
86	#419×C₈₉	C₂²	1	1	yes	characteristic, complemented
87	#418×C₈₉	C₂²	1	1	yes	characteristic
88	#418×C₈₉	C₂²	1	1	yes	characteristic
89	#416×C₈₉	C₂²	1	1	yes	characteristic
90	#416×C₈₉	C₂²	1	1	yes	characteristic
91	#416×C₈₉	C₂²	1	1	yes	characteristic, complemented
92	#416×C₈₉	C₂²	1	1	yes	characteristic, complemented
93	#408×C₈₉	C₂²	1	1	yes	characteristic
94	#408×C₈₉	C₂²	1	1	yes	characteristic
95	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
96	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
97	2₋¹⁺⁴×C₈₉	—	4	2	no	—
98	2₋¹⁺⁴×C₈₉	—	4	2	no	—
99	H(5,𝔽₂)×C₈₉	—	4	2	no	—
100	H(5,𝔽₂)×C₈₉	—	4	2	no	—
101	C₂×#41×C₈₉	—	2	1	no	—
102	C₂×#41×C₈₉	—	2	2	no	—
103	C₂×#41×C₈₉	—	2	1	no	—
104	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
105	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
106	C₂×#41×C₈₉	C₂³	1	2	yes	—
107	C₂×#41×C₈₉	C₂³	1	2	yes	—
108	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₈₉	—	2	1	no	—
110	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
112	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
113	C₂²×D₄×C₈₉	—	2	2	no	—
114	C₂²×D₄×C₈₉	—	2	1	no	—
115	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
118	#137×C₈₉	—	4	2	no	—
119	#137×C₈₉	—	4	2	no	—
120	AGL(1,ℤ/8)×C₈₉	—	4	2	no	—
121	AGL(1,ℤ/8)×C₈₉	—	4	2	no	—
122	C₂×Q₁₆×C₈₉	—	4	2	no	—
123	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
124	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
125	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₈₉	—	4	2	no	—
127	C₂×SD₁₆×C₈₉	—	4	2	no	—
128	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
130	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
131	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
132	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
133	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
134	C₂×D₈×C₈₉	—	4	2	no	—
135	C₂×D₈×C₈₉	C₂³	1	2	yes	—
136	C₂×D₈×C₈₉	C₂³	1	4	yes	—
137	C₂×D₈×C₈₉	C₂³	1	2	yes	—
138	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
139	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
142	C₄⋊Q₈×C₈₉	—	2	1	no	—
143	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
144	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
145	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
146	#127×C₈₉	—	2	1	no	—
147	#127×C₈₉	C₂³	1	2	yes	—
148	#127×C₈₉	C₂³	1	1	yes	characteristic
149	#126×C₈₉	—	2	4	no	—
150	#126×C₈₉	—	2	4	no	—
151	#125×C₈₉	C₂³	1	2	yes	—
152	#124×C₈₉	—	2	1	no	—
153	#124×C₈₉	—	2	1	no	—
154	#124×C₈₉	—	2	4	no	—
155	#124×C₈₉	—	2	2	no	—
156	#124×C₈₉	—	2	4	no	—
157	#124×C₈₉	—	2	2	no	—
158	#124×C₈₉	C₂³	1	2	yes	—
159	#124×C₈₉	C₂³	1	2	yes	—
160	#124×C₈₉	C₂³	1	2	yes	—
161	#124×C₈₉	C₂³	1	1	yes	characteristic
162	#124×C₈₉	C₂³	1	1	yes	characteristic
163	#124×C₈₉	C₂³	1	2	yes	—
164	#124×C₈₉	C₂³	1	2	yes	—
165	#124×C₈₉	C₂³	1	2	yes	—
166	#123×C₈₉	—	2	2	no	—
167	#123×C₈₉	—	2	4	no	—
168	#123×C₈₉	—	2	2	no	—
169	#123×C₈₉	—	2	4	no	—
170	#123×C₈₉	—	2	4	no	—
171	C₂²⋊Q₈×C₈₉	—	2	2	no	—
172	C₂²⋊Q₈×C₈₉	—	2	2	no	—
173	C₂²⋊Q₈×C₈₉	—	2	4	no	—
174	C₂²⋊Q₈×C₈₉	—	2	4	no	—
175	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
176	#121×C₈₉	—	2	2	no	—
177	#121×C₈₉	—	2	4	no	—
178	#121×C₈₉	—	2	2	no	—
179	#121×C₈₉	—	2	4	no	—
180	#121×C₈₉	C₂³	1	4	yes	—
181	#120×C₈₉	—	2	2	no	—
182	#120×C₈₉	—	2	2	no	—
183	#120×C₈₉	—	2	4	no	—
184	C₄×Q₈×C₈₉	—	2	2	no	—
185	C₄×Q₈×C₈₉	—	2	2	no	—
186	C₄×Q₈×C₈₉	D₄	1	2	yes	—
187	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
188	C₄×D₄×C₈₉	—	2	4	no	—
189	C₄×D₄×C₈₉	—	2	2	no	—
190	C₄×D₄×C₈₉	—	2	2	no	—
191	C₄×D₄×C₈₉	—	2	4	no	—
192	C₄×D₄×C₈₉	D₄	1	4	yes	—
193	C₄×D₄×C₈₉	D₄	1	2	yes	—
194	C₄×D₄×C₈₉	C₂³	1	4	yes	—
195	#117×C₈₉	—	2	2	no	—
196	#117×C₈₉	—	2	4	no	—
197	#117×C₈₉	C₂³	1	1	yes	characteristic
198	#117×C₈₉	C₂³	1	1	yes	characteristic
199	#117×C₈₉	C₂³	1	1	yes	characteristic
200	#117×C₈₉	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
202	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
203	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
204	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
205	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₈₉	C₂³	1	2	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	2	yes	—
224	C₄×C₈×C₈₉	C₂³	1	2	yes	—
225	C₄×C₈×C₈₉	C₂³	1	2	yes	—
226	C₄×C₈×C₈₉	C₂³	1	2	yes	—
227	C₂⁴×C₈₉	—	2	1	no	—
228	C₂⁴×C₈₉	—	2	2	no	—
229	C₂⁴×C₈₉	—	2	1	no	—
230	#41×C₈₉	—	2	2	no	—
231	#41×C₈₉	—	2	2	no	—
232	#41×C₈₉	—	2	2	no	—
233	#41×C₈₉	—	2	2	no	—
234	#41×C₈₉	—	2	2	no	—
235	#41×C₈₉	—	2	2	no	—
236	#41×C₈₉	—	4	2	no	—
237	#41×C₈₉	—	4	2	no	—
238	#41×C₈₉	—	4	2	no	—
239	#41×C₈₉	—	4	2	no	—
240	#41×C₈₉	—	4	8	no	—
241	#41×C₈₉	—	4	4	no	—
242	#41×C₈₉	—	4	4	no	—
243	C₂×Q₈×C₈₉	—	2	1	no	—
244	C₂×Q₈×C₈₉	—	2	2	no	—
245	C₂×Q₈×C₈₉	—	2	1	no	—
246	C₂×Q₈×C₈₉	—	2	2	no	—
247	C₂×Q₈×C₈₉	—	2	2	no	—
248	C₂×Q₈×C₈₉	—	2	2	no	—
249	C₂×Q₈×C₈₉	—	2	2	no	—
250	C₂×Q₈×C₈₉	—	2	2	no	—
251	C₂×Q₈×C₈₉	—	4	2	no	—
252	C₂×Q₈×C₈₉	—	4	2	no	—
253	C₂×Q₈×C₈₉	—	4	4	no	—
254	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
255	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
256	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
257	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
258	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
259	C₂×D₄×C₈₉	—	2	2	no	—
260	C₂×D₄×C₈₉	—	2	1	no	—
261	C₂×D₄×C₈₉	—	2	2	no	—
262	C₂×D₄×C₈₉	—	2	1	no	—
263	C₂×D₄×C₈₉	—	2	4	no	—
264	C₂×D₄×C₈₉	—	2	1	no	—
265	C₂×D₄×C₈₉	—	2	2	no	—
266	C₂×D₄×C₈₉	—	2	1	no	—
267	C₂×D₄×C₈₉	—	2	4	no	—
268	C₂×D₄×C₈₉	—	2	2	no	—
269	C₂×D₄×C₈₉	—	2	2	no	—
270	C₂×D₄×C₈₉	—	2	2	no	—
271	C₂×D₄×C₈₉	—	2	2	no	—
272	C₂×D₄×C₈₉	—	2	2	no	—
273	C₂×D₄×C₈₉	—	4	2	no	—
274	C₂×D₄×C₈₉	—	4	2	no	—
275	C₂×D₄×C₈₉	—	4	8	no	—
276	C₂×D₄×C₈₉	—	4	4	no	—
277	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
278	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
279	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
280	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
281	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
282	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₈₉	—	2	1	no	—
284	C₂²×C₄×C₈₉	—	2	2	no	—
285	C₂²×C₄×C₈₉	—	2	1	no	—
286	C₂²×C₄×C₈₉	—	2	2	no	—
287	C₂²×C₄×C₈₉	—	2	1	no	—
288	C₂²×C₄×C₈₉	—	2	2	no	—
289	C₂²×C₄×C₈₉	—	2	1	no	—
290	C₂²×C₄×C₈₉	—	2	4	no	—
291	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
292	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
293	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
295	Q₁₆×C₈₉	—	4	4	no	—
296	Q₁₆×C₈₉	—	4	2	no	—
297	Q₁₆×C₈₉	—	4	2	no	—
298	SD₁₆×C₈₉	—	4	4	no	—
299	SD₁₆×C₈₉	—	4	4	no	—
300	SD₁₆×C₈₉	—	4	2	no	—
301	SD₁₆×C₈₉	—	4	2	no	—
302	SD₁₆×C₈₉	—	4	2	no	—
303	SD₁₆×C₈₉	—	4	2	no	—
304	D₈×C₈₉	—	4	4	no	—
305	D₈×C₈₉	—	4	2	no	—
306	D₈×C₈₉	—	4	2	no	—
307	M₁₆×C₈₉	—	2	2	no	—
308	M₁₆×C₈₉	—	2	2	no	—
309	C₂×C₈×C₈₉	—	2	2	no	—
310	C₂×C₈×C₈₉	—	2	2	no	—
311	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
312	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
313	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
314	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
315	C₄⋊C₄×C₈₉	—	2	2	no	—
316	C₄⋊C₄×C₈₉	—	2	4	no	—
317	C₄⋊C₄×C₈₉	—	2	4	no	—
318	C₄⋊C₄×C₈₉	—	2	2	no	—
319	C₄⋊C₄×C₈₉	—	2	4	no	—
320	C₄⋊C₄×C₈₉	—	2	2	no	—
321	C₄⋊C₄×C₈₉	—	2	2	no	—
322	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
323	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
324	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
325	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
326	C₂²⋊C₄×C₈₉	—	2	1	no	—
327	C₂²⋊C₄×C₈₉	—	2	1	no	—
328	C₂²⋊C₄×C₈₉	—	2	4	no	—
329	C₂²⋊C₄×C₈₉	—	2	4	no	—
330	C₂²⋊C₄×C₈₉	—	2	2	no	—
331	C₂²⋊C₄×C₈₉	—	2	4	no	—
332	C₂²⋊C₄×C₈₉	—	2	4	no	—
333	C₂²⋊C₄×C₈₉	—	2	4	no	—
334	C₂²⋊C₄×C₈₉	—	2	4	no	—
335	C₂²⋊C₄×C₈₉	—	2	4	no	—
336	C₂²⋊C₄×C₈₉	—	2	4	no	—
337	C₂²⋊C₄×C₈₉	—	2	4	no	—
338	C₂²⋊C₄×C₈₉	—	2	2	no	—
339	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
340	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
341	C₄²×C₈₉	—	2	4	no	—
342	C₄²×C₈₉	—	2	1	no	—
343	C₄²×C₈₉	—	2	1	no	—
344	C₄²×C₈₉	C₂×D₄	1	4	yes	—
345	C₄²×C₈₉	C₂×D₄	1	2	yes	—
346	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
347	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
348	C₄²×C₈₉	C₂⁴	1	2	yes	—
349	C₂³×C₈₉	—	2	2	no	—
350	C₂³×C₈₉	—	2	2	no	—
351	C₂³×C₈₉	—	2	1	no	—
352	C₂³×C₈₉	—	2	1	no	—
353	C₂³×C₈₉	—	4	4	no	—
354	C₂³×C₈₉	—	4	2	no	—
355	C₂³×C₈₉	—	4	2	no	—
356	C₂³×C₈₉	—	8	2	no	—
357	C₂³×C₈₉	—	8	2	no	—
358	C₂³×C₈₉	—	8	4	no	—
359	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
360	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
361	Q₈×C₈₉	—	2	2	no	—
362	Q₈×C₈₉	—	2	2	no	—
363	Q₈×C₈₉	—	2	2	no	—
364	Q₈×C₈₉	—	2	1	no	—
365	Q₈×C₈₉	—	2	1	no	—
366	Q₈×C₈₉	—	2	2	no	—
367	Q₈×C₈₉	—	2	2	no	—
368	Q₈×C₈₉	—	2	1	no	—
369	Q₈×C₈₉	—	2	1	no	—
370	Q₈×C₈₉	—	4	4	no	—
371	Q₈×C₈₉	—	4	2	no	—
372	Q₈×C₈₉	—	4	2	no	—
373	Q₈×C₈₉	—	8	2	no	—
374	D₄×C₈₉	—	2	4	no	—
375	D₄×C₈₉	—	2	2	no	—
376	D₄×C₈₉	—	2	2	no	—
377	D₄×C₈₉	—	2	2	no	—
378	D₄×C₈₉	—	2	1	no	—
379	D₄×C₈₉	—	2	1	no	—
380	D₄×C₈₉	—	2	2	no	—
381	D₄×C₈₉	—	2	2	no	—
382	D₄×C₈₉	—	2	1	no	—
383	D₄×C₈₉	—	2	1	no	—
384	D₄×C₈₉	—	4	4	no	—
385	D₄×C₈₉	—	4	4	no	—
386	D₄×C₈₉	—	4	4	no	—
387	D₄×C₈₉	—	4	2	no	—
388	D₄×C₈₉	—	4	2	no	—
389	D₄×C₈₉	—	4	2	no	—
390	D₄×C₈₉	—	4	2	no	—
391	D₄×C₈₉	—	8	4	no	—
392	D₄×C₈₉	—	8	2	no	—
393	D₄×C₈₉	—	8	4	no	—
394	C₂×C₄×C₈₉	—	2	2	no	—
395	C₂×C₄×C₈₉	—	2	2	no	—
396	C₂×C₄×C₈₉	—	2	2	no	—
397	C₂×C₄×C₈₉	—	2	2	no	—
398	C₂×C₄×C₈₉	—	2	2	no	—
399	C₂×C₄×C₈₉	—	2	2	no	—
400	C₂×C₄×C₈₉	—	2	1	no	—
401	C₂×C₄×C₈₉	—	2	1	no	—
402	C₂×C₄×C₈₉	—	4	4	no	—
403	C₂×C₄×C₈₉	—	4	2	no	—
404	C₂×C₄×C₈₉	—	4	4	no	—
405	C₂×C₄×C₈₉	—	4	4	no	—
406	C₂×C₄×C₈₉	—	4	4	no	—
407	C₂×C₄×C₈₉	—	4	2	no	—
408	C₂×C₄×C₈₉	—	4	2	no	—
409	C₂×C₄×C₈₉	—	4	2	no	—
410	C₂×C₄×C₈₉	—	4	2	no	—
411	C₂×C₄×C₈₉	—	8	4	no	—
412	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
413	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
418	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
419	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
420	C₈×C₈₉	—	2	2	no	—
421	C₈×C₈₉	—	2	2	no	—
422	C₈×C₈₉	—	2	2	no	—
423	C₈×C₈₉	—	2	2	no	—
424	C₂²×C₈₉	—	2	2	no	—
425	C₂²×C₈₉	—	2	4	no	—
426	C₂²×C₈₉	—	2	2	no	—
427	C₂²×C₈₉	—	4	4	no	—
428	C₂²×C₈₉	—	4	2	no	—
429	C₂²×C₈₉	—	4	4	no	—
430	C₂²×C₈₉	—	4	2	no	—
431	C₂²×C₈₉	—	4	1	no	—
432	C₂²×C₈₉	—	4	2	no	—
433	C₂²×C₈₉	—	4	1	no	—
434	C₂²×C₈₉	—	4	2	no	—
435	C₂²×C₈₉	—	16	2	no	—
436	C₂²×C₈₉	—	16	2	no	—
437	C₂²×C₈₉	—	16	4	no	—
438	C₂²×C₈₉	#535	1	2	yes	—
439	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
440	C₄×C₈₉	—	2	2	no	—
441	C₄×C₈₉	—	2	4	no	—
442	C₄×C₈₉	—	2	2	no	—
443	C₄×C₈₉	—	2	2	no	—
444	C₄×C₈₉	—	4	2	no	—
445	C₄×C₈₉	—	4	2	no	—
446	C₄×C₈₉	—	4	1	no	—
447	C₄×C₈₉	—	4	2	no	—
448	C₄×C₈₉	—	4	1	no	—
449	C₄×C₈₉	—	4	2	no	—
450	C₄×C₈₉	#535	1	2	yes	—
451	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
452	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
453	#60819	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
454	C₂×C₈₉	—	2	2	no	—
455	C₂×C₈₉	—	4	2	no	—
456	C₂×C₈₉	—	8	1	no	—
457	C₂×C₈₉	—	8	2	no	—
458	C₂×C₈₉	—	8	2	no	—
459	C₂×C₈₉	—	8	1	no	—
460	C₂×C₈₉	C₂×#535	1	1	yes	characteristic
461	C₂×C₈₉	#3584	1	2	yes	—
462	#3510	C₂×C₈₉	1	1	yes	characteristic, complemented
463	#3500	C₂×C₈₉	1	1	yes	characteristic, complemented
464	#3225	C₂×C₈₉	1	4	yes	complemented
465	#3224	C₂×C₈₉	1	4	yes	complemented
466	#3212	C₂×C₈₉	1	4	yes	complemented
467	#3211	C₂×C₈₉	1	4	yes	complemented
468	#3153	C₂×C₈₉	1	1	yes	characteristic, complemented
469	C₂×#495	C₂×C₈₉	1	1	yes	characteristic, complemented
470	#3140	C₂×C₈₉	1	1	yes	characteristic, complemented
471	#3131	C₂×C₈₉	1	1	yes	characteristic, complemented
472	#3044	C₂×C₈₉	1	1	yes	characteristic, complemented
473	#3043	C₂×C₈₉	1	1	yes	characteristic, complemented
474	#3042	C₂×C₈₉	1	1	yes	characteristic, complemented
475	#3041	C₂×C₈₉	1	1	yes	characteristic, complemented
476	#3011	C₂×C₈₉	1	1	yes	characteristic, complemented
477	#3010	C₂×C₈₉	1	1	yes	characteristic, complemented
478	#3009	C₂×C₈₉	1	1	yes	characteristic, complemented
479	#3008	C₂×C₈₉	1	1	yes	characteristic, complemented
480	#2922	C₂×C₈₉	1	1	yes	characteristic, complemented
481	C₈₉	#60819	1	1	yes	characteristic, direct product factor, Sylow
482	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	1	yes	characteristic
483	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	1	yes	characteristic
484	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
485	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic, complemented
486	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
487	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic, complemented
488	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
489	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
490	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
491	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
492	#559	—	2	2	no	—
493	#556	—	2	2	no	—
494	#551	—	2	4	no	—
495	#548	—	2	2	no	—
496	#546	—	2	4	no	—
497	#546	—	2	2	no	—
498	#542	C₂²×C₈₉	1	4	yes	complemented
499	#536	C₂²×C₈₉	1	1	yes	characteristic
500	#536	C₂²×C₈₉	1	1	yes	characteristic
501	#536	C₂²×C₈₉	1	2	yes	complemented
502	#535	C₂²×C₈₉	1	1	yes	characteristic
503	#535	C₂²×C₈₉	1	1	yes	characteristic
504	#535	C₂²×C₈₉	1	2	yes	complemented
505	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
506	#532	C₂²×C₈₉	1	1	yes	characteristic
507	#532	C₂²×C₈₉	1	2	yes	complemented
508	#529	C₂²×C₈₉	1	4	yes	complemented
509	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
510	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic, complemented
511	C₂×#124	C₂²×C₈₉	1	2	yes	complemented
512	#519	C₂²×C₈₉	1	1	yes	characteristic, complemented
513	#518	C₂²×C₈₉	1	1	yes	characteristic, complemented
514	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
515	#497	C₂²×C₈₉	1	2	yes	complemented
516	#496	C₂²×C₈₉	1	2	yes	complemented
517	#495	C₂²×C₈₉	1	4	yes	complemented
518	#495	C₂²×C₈₉	1	4	yes	complemented
519	#495	C₂²×C₈₉	1	2	yes	complemented
520	#495	C₂²×C₈₉	1	2	yes	complemented
521	#489	C₂²×C₈₉	1	4	yes	complemented
522	#488	C₂²×C₈₉	1	2	yes	complemented
523	#488	C₂²×C₈₉	1	2	yes	complemented
524	#488	C₂²×C₈₉	1	4	yes	complemented
525	#487	C₂²×C₈₉	1	2	yes	complemented
526	#486	C₂²×C₈₉	1	2	yes	complemented
527	#464	C₂²×C₈₉	1	4	yes	complemented
528	#464	C₂²×C₈₉	1	4	yes	complemented
529	#463	C₂²×C₈₉	1	4	yes	complemented
530	#463	C₂²×C₈₉	1	4	yes	complemented
531	#462	C₂²×C₈₉	1	4	yes	complemented
532	#461	C₂²×C₈₉	1	4	yes	complemented
533	#460	C₂²×C₈₉	1	4	yes	complemented
534	#459	C₂²×C₈₉	1	4	yes	complemented
535	#452	C₂²×C₈₉	1	4	yes	complemented
536	#452	C₂²×C₈₉	1	4	yes	complemented
537	#451	C₂²×C₈₉	1	4	yes	complemented
538	#450	C₂²×C₈₉	1	4	yes	complemented
539	#449	C₂²×C₈₉	1	4	yes	—
540	#449	C₂²×C₈₉	1	4	yes	complemented
541	#448	C₂²×C₈₉	1	4	yes	complemented
542	#447	C₂²×C₈₉	1	4	yes	—
543	#433	C₂²×C₈₉	1	4	yes	complemented
544	#431	C₂²×C₈₉	1	4	yes	complemented
545	#424	C₂²×C₈₉	1	1	yes	characteristic, complemented
546	#424	C₂²×C₈₉	1	1	yes	characteristic, complemented
547	#419	C₂²×C₈₉	1	1	yes	characteristic, complemented
548	#419	C₂²×C₈₉	1	1	yes	characteristic, complemented
549	#418	C₂²×C₈₉	1	1	yes	characteristic
550	#418	C₂²×C₈₉	1	1	yes	characteristic
551	#416	C₂²×C₈₉	1	1	yes	characteristic
552	#416	C₂²×C₈₉	1	1	yes	characteristic
553	#416	C₂²×C₈₉	1	1	yes	characteristic, complemented
554	#416	C₂²×C₈₉	1	1	yes	characteristic, complemented
555	#408	C₂²×C₈₉	1	1	yes	characteristic
556	#408	C₂²×C₈₉	1	1	yes	characteristic
557	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
558	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
559	2₋¹⁺⁴	—	4	2	no	—
560	2₋¹⁺⁴	—	4	2	no	—
561	H(5,𝔽₂)	—	4	2	no	—
562	H(5,𝔽₂)	—	4	2	no	—
563	C₂×#41	—	2	1	no	—
564	C₂×#41	—	2	2	no	—
565	C₂×#41	—	2	1	no	—
566	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
567	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
568	C₂×#41	C₂³×C₈₉	1	2	yes	—
569	C₂×#41	C₂³×C₈₉	1	2	yes	—
570	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
571	C₂²×Q₈	—	2	1	no	—
572	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
573	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
574	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
575	C₂²×D₄	—	2	2	no	—
576	C₂²×D₄	—	2	1	no	—
577	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
578	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
579	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
580	#137	—	4	2	no	—
581	#137	—	4	2	no	—
582	AGL(1,ℤ/8)	—	4	2	no	—
583	AGL(1,ℤ/8)	—	4	2	no	—
584	C₂×Q₁₆	—	4	2	no	—
585	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
586	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
587	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
588	C₂×SD₁₆	—	4	2	no	—
589	C₂×SD₁₆	—	4	2	no	—
590	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
591	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
592	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
593	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
594	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
595	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
596	C₂×D₈	—	4	2	no	—
597	C₂×D₈	C₂³×C₈₉	1	4	yes	—
598	C₂×D₈	C₂³×C₈₉	1	2	yes	—
599	C₂×D₈	C₂³×C₈₉	1	2	yes	—
600	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
601	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
602	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
603	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
604	C₄⋊Q₈	—	2	1	no	—
605	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
606	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
607	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
608	#127	—	2	1	no	—
609	#127	C₂³×C₈₉	1	1	yes	characteristic
610	#127	C₂³×C₈₉	1	2	yes	—
611	#126	—	2	4	no	—
612	#126	—	2	4	no	—
613	#125	C₂³×C₈₉	1	2	yes	—
614	#124	—	2	1	no	—
615	#124	—	2	1	no	—
616	#124	—	2	4	no	—
617	#124	—	2	2	no	—
618	#124	—	2	4	no	—
619	#124	—	2	2	no	—
620	#124	C₂³×C₈₉	1	2	yes	—
621	#124	C₂³×C₈₉	1	2	yes	—
622	#124	C₂³×C₈₉	1	1	yes	characteristic
623	#124	C₂³×C₈₉	1	2	yes	—
624	#124	C₂³×C₈₉	1	2	yes	—
625	#124	C₂³×C₈₉	1	2	yes	—
626	#124	C₂³×C₈₉	1	2	yes	—
627	#124	C₂³×C₈₉	1	1	yes	characteristic
628	#123	—	2	2	no	—
629	#123	—	2	4	no	—
630	#123	—	2	2	no	—
631	#123	—	2	4	no	—
632	#123	—	2	4	no	—
633	C₂²⋊Q₈	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	—	2	4	no	—
636	C₂²⋊Q₈	—	2	4	no	—
637	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
638	#121	—	2	2	no	—
639	#121	—	2	4	no	—
640	#121	—	2	2	no	—
641	#121	—	2	4	no	—
642	#121	C₂³×C₈₉	1	4	yes	—
643	#120	—	2	2	no	—
644	#120	—	2	2	no	—
645	#120	—	2	4	no	—
646	C₄×Q₈	—	2	2	no	—
647	C₄×Q₈	—	2	2	no	—
648	C₄×Q₈	D₄×C₈₉	1	2	yes	—
649	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
650	C₄×D₄	—	2	4	no	—
651	C₄×D₄	—	2	2	no	—
652	C₄×D₄	—	2	2	no	—
653	C₄×D₄	—	2	4	no	—
654	C₄×D₄	D₄×C₈₉	1	4	yes	—
655	C₄×D₄	D₄×C₈₉	1	2	yes	—
656	C₄×D₄	C₂³×C₈₉	1	4	yes	—
657	#117	—	2	2	no	—
658	#117	—	2	4	no	—
659	#117	C₂³×C₈₉	1	1	yes	characteristic
660	#117	C₂³×C₈₉	1	1	yes	characteristic
661	#117	C₂³×C₈₉	1	1	yes	characteristic
662	#117	C₂³×C₈₉	1	2	yes	—
663	C₂×C₂²⋊C₄	—	2	2	no	—
664	C₂×C₂²⋊C₄	—	2	4	no	—
665	C₂×C₂²⋊C₄	—	2	2	no	—
666	C₂×C₂²⋊C₄	—	2	2	no	—
667	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
668	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
669	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
670	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
671	#103	C₂³×C₈₉	1	2	yes	—
672	#103	C₂³×C₈₉	1	2	yes	—
673	#103	C₂³×C₈₉	1	2	yes	—
674	#103	C₂³×C₈₉	1	2	yes	—
675	#103	C₂³×C₈₉	1	4	yes	—
676	#103	C₂³×C₈₉	1	4	yes	—
677	#102	C₂³×C₈₉	1	2	yes	—
678	#102	C₂³×C₈₉	1	2	yes	—
679	#102	C₂³×C₈₉	1	2	yes	—
680	#102	C₂³×C₈₉	1	2	yes	—
681	#102	C₂³×C₈₉	1	4	yes	—
682	#102	C₂³×C₈₉	1	4	yes	—
683	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
684	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
685	#97	C₂³×C₈₉	1	2	yes	—
686	C₄×C₈	C₂³×C₈₉	1	2	yes	—
687	C₄×C₈	C₂³×C₈₉	1	2	yes	—
688	C₄×C₈	C₂³×C₈₉	1	2	yes	—
689	C₂⁴	—	2	1	no	—
690	C₂⁴	—	2	2	no	—
691	C₂⁴	—	2	1	no	—
692	#41	—	2	2	no	—
693	#41	—	2	2	no	—
694	#41	—	2	2	no	—
695	#41	—	2	2	no	—
696	#41	—	2	2	no	—
697	#41	—	2	2	no	—
698	#41	—	4	2	no	—
699	#41	—	4	2	no	—
700	#41	—	4	2	no	—
701	#41	—	4	2	no	—
702	#41	—	4	8	no	—
703	#41	—	4	4	no	—
704	#41	—	4	4	no	—
705	C₂×Q₈	—	2	1	no	—
706	C₂×Q₈	—	2	2	no	—
707	C₂×Q₈	—	2	1	no	—
708	C₂×Q₈	—	2	2	no	—
709	C₂×Q₈	—	2	2	no	—
710	C₂×Q₈	—	2	2	no	—
711	C₂×Q₈	—	2	2	no	—
712	C₂×Q₈	—	2	2	no	—
713	C₂×Q₈	—	4	2	no	—
714	C₂×Q₈	—	4	2	no	—
715	C₂×Q₈	—	4	4	no	—
716	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
717	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
718	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
719	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
720	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	1	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	4	no	—
726	C₂×D₄	—	2	1	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	4	2	no	—
736	C₂×D₄	—	4	2	no	—
737	C₂×D₄	—	4	8	no	—
738	C₂×D₄	—	4	4	no	—
739	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
740	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
741	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
742	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
743	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
744	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
745	C₂²×C₄	—	2	1	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	1	no	—
752	C₂²×C₄	—	2	4	no	—
753	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
754	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
755	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
757	Q₁₆	—	4	4	no	—
758	Q₁₆	—	4	2	no	—
759	Q₁₆	—	4	2	no	—
760	SD₁₆	—	4	4	no	—
761	SD₁₆	—	4	4	no	—
762	SD₁₆	—	4	2	no	—
763	SD₁₆	—	4	2	no	—
764	SD₁₆	—	4	2	no	—
765	SD₁₆	—	4	2	no	—
766	D₈	—	4	4	no	—
767	D₈	—	4	2	no	—
768	D₈	—	4	2	no	—
769	M₁₆	—	2	2	no	—
770	M₁₆	—	2	2	no	—
771	C₂×C₈	—	2	2	no	—
772	C₂×C₈	—	2	2	no	—
773	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
774	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
775	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
776	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	4	no	—
779	C₄⋊C₄	—	2	4	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	4	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
785	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
786	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
787	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
788	C₂²⋊C₄	—	2	1	no	—
789	C₂²⋊C₄	—	2	1	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
802	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
803	C₄²	—	2	4	no	—
804	C₄²	—	2	1	no	—
805	C₄²	—	2	1	no	—
806	C₄²	C₂×D₄×C₈₉	1	4	yes	—
807	C₄²	C₂×D₄×C₈₉	1	2	yes	—
808	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
809	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
810	C₄²	C₂⁴×C₈₉	1	2	yes	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	1	no	—
814	C₂³	—	2	1	no	—
815	C₂³	—	4	4	no	—
816	C₂³	—	4	2	no	—
817	C₂³	—	4	2	no	—
818	C₂³	—	8	2	no	—
819	C₂³	—	8	2	no	—
820	C₂³	—	8	4	no	—
821	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
822	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
823	Q₈	—	2	2	no	—
824	Q₈	—	2	2	no	—
825	Q₈	—	2	2	no	—
826	Q₈	—	2	1	no	—
827	Q₈	—	2	1	no	—
828	Q₈	—	2	2	no	—
829	Q₈	—	2	2	no	—
830	Q₈	—	2	1	no	—
831	Q₈	—	2	1	no	—
832	Q₈	—	4	4	no	—
833	Q₈	—	4	2	no	—
834	Q₈	—	4	2	no	—
835	Q₈	—	8	2	no	—
836	D₄	—	2	4	no	—
837	D₄	—	2	2	no	—
838	D₄	—	2	2	no	—
839	D₄	—	2	2	no	—
840	D₄	—	2	1	no	—
841	D₄	—	2	1	no	—
842	D₄	—	2	2	no	—
843	D₄	—	2	2	no	—
844	D₄	—	2	1	no	—
845	D₄	—	2	1	no	—
846	D₄	—	4	4	no	—
847	D₄	—	4	4	no	—
848	D₄	—	4	4	no	—
849	D₄	—	4	2	no	—
850	D₄	—	4	2	no	—
851	D₄	—	4	2	no	—
852	D₄	—	4	2	no	—
853	D₄	—	8	4	no	—
854	D₄	—	8	2	no	—
855	D₄	—	8	4	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	4	4	no	—
865	C₂×C₄	—	4	2	no	—
866	C₂×C₄	—	4	4	no	—
867	C₂×C₄	—	4	4	no	—
868	C₂×C₄	—	4	4	no	—
869	C₂×C₄	—	4	2	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	4	2	no	—
872	C₂×C₄	—	4	2	no	—
873	C₂×C₄	—	8	4	no	—
874	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
875	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
876	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
877	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
878	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
879	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
880	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
881	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
882	C₈	—	2	2	no	—
883	C₈	—	2	2	no	—
884	C₈	—	2	2	no	—
885	C₈	—	2	2	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	4	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	4	4	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	4	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	1	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	16	2	no	—
898	C₂²	—	16	2	no	—
899	C₂²	—	16	4	no	—
900	C₂²	#535×C₈₉	1	2	yes	—
901	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
902	C₄	—	2	2	no	—
903	C₄	—	2	4	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	2	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	2	no	—
912	C₄	#535×C₈₉	1	2	yes	—
913	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
914	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
915	C₂	—	2	2	no	—
916	C₂	—	4	2	no	—
917	C₂	—	8	1	no	—
918	C₂	—	8	2	no	—
919	C₂	—	8	2	no	—
920	C₂	—	8	1	no	—
921	C₂	C₂×#535×C₈₉	1	1	yes	characteristic
922	C₂	C₈₉×#3584	1	2	yes	—

	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×#3510	C₂	semidirect
2. C₈₉×#3500	C₂	semidirect
3. C₈₉×#3225	C₂	semidirect
4. C₈₉×#3224	C₂	semidirect
5. C₈₉×#3212	C₂	semidirect
6. C₈₉×#3211	C₂	semidirect
7. C₈₉×#3153	C₂	semidirect
8. C₂×#495×C₈₉	C₂	semidirect
9. C₈₉×#3140	C₂	semidirect
10. C₈₉×#3131	C₂	semidirect
11. C₈₉×#3044	C₂	semidirect
12. C₈₉×#3043	C₂	semidirect
13. C₈₉×#3042	C₂	semidirect
14. C₈₉×#3041	C₂	semidirect
15. C₈₉×#3011	C₂	semidirect
16. C₈₉×#3010	C₂	semidirect
17. C₈₉×#3009	C₂	semidirect
18. C₈₉×#3008	C₂	semidirect
19. C₈₉×#2922	C₂	semidirect
23. C₂×#137×C₈₉	C₂²	semidirect
25. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
26. C₂²×Q₁₆×C₈₉	C₂²	semidirect
28. C₂²×SD₁₆×C₈₉	C₂²	semidirect
36. #542×C₈₉	C₂²	semidirect
39. #536×C₈₉	C₂²	semidirect
42. #535×C₈₉	C₂²	semidirect
43. #533×C₈₉	C₂²	semidirect
45. #532×C₈₉	C₂²	semidirect
46. #529×C₈₉	C₂²	semidirect
48. C₂×#124×C₈₉	C₂²	semidirect
49. C₂×#124×C₈₉	C₂²	semidirect
50. #519×C₈₉	C₂²	semidirect
51. #518×C₈₉	C₂²	semidirect
53. #497×C₈₉	C₂²	semidirect
54. #496×C₈₉	C₂²	semidirect
55. #495×C₈₉	C₂²	semidirect
56. #495×C₈₉	C₂²	semidirect
57. #495×C₈₉	C₂²	semidirect
58. #495×C₈₉	C₂²	semidirect
59. #489×C₈₉	C₂²	semidirect
60. #488×C₈₉	C₂²	semidirect
61. #488×C₈₉	C₂²	semidirect
62. #488×C₈₉	C₂²	semidirect
63. #487×C₈₉	C₂²	semidirect
64. #486×C₈₉	C₂²	semidirect
65. #464×C₈₉	C₂²	semidirect
66. #464×C₈₉	C₂²	semidirect
67. #463×C₈₉	C₂²	semidirect
68. #463×C₈₉	C₂²	semidirect
69. #462×C₈₉	C₂²	semidirect
70. #461×C₈₉	C₂²	semidirect
71. #460×C₈₉	C₂²	semidirect
72. #459×C₈₉	C₂²	semidirect
73. #452×C₈₉	C₂²	semidirect
74. #452×C₈₉	C₂²	semidirect
75. #451×C₈₉	C₂²	semidirect
76. #450×C₈₉	C₂²	semidirect
78. #449×C₈₉	C₂²	semidirect
79. #448×C₈₉	C₂²	semidirect
81. #433×C₈₉	C₂²	semidirect
82. #431×C₈₉	C₂²	semidirect
83. #424×C₈₉	C₂²	semidirect
84. #424×C₈₉	C₂²	semidirect
85. #419×C₈₉	C₂²	semidirect
86. #419×C₈₉	C₂²	semidirect
91. #416×C₈₉	C₂²	semidirect
92. #416×C₈₉	C₂²	semidirect
95. C₄×M₁₆×C₈₉	C₂²	semidirect
96. C₂×C₄×C₈×C₈₉	C₂²	semidirect
453. #60819	C₈₉	direct (N × H)
462. #3510	C₂×C₈₉	semidirect
463. #3500	C₂×C₈₉	semidirect
464. #3225	C₂×C₈₉	semidirect
465. #3224	C₂×C₈₉	semidirect
466. #3212	C₂×C₈₉	semidirect
467. #3211	C₂×C₈₉	semidirect
468. #3153	C₂×C₈₉	semidirect
469. C₂×#495	C₂×C₈₉	semidirect
470. #3140	C₂×C₈₉	semidirect
471. #3131	C₂×C₈₉	semidirect
472. #3044	C₂×C₈₉	semidirect
473. #3043	C₂×C₈₉	semidirect
474. #3042	C₂×C₈₉	semidirect
475. #3041	C₂×C₈₉	semidirect
476. #3011	C₂×C₈₉	semidirect
477. #3010	C₂×C₈₉	semidirect
478. #3009	C₂×C₈₉	semidirect
479. #3008	C₂×C₈₉	semidirect
480. #2922	C₂×C₈₉	semidirect
481. C₈₉	#60819	direct (N × H)
485. C₂×#137	C₂²×C₈₉	semidirect
487. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
488. C₂²×Q₁₆	C₂²×C₈₉	semidirect
490. C₂²×SD₁₆	C₂²×C₈₉	semidirect
498. #542	C₂²×C₈₉	semidirect
501. #536	C₂²×C₈₉	semidirect
504. #535	C₂²×C₈₉	semidirect
505. #533	C₂²×C₈₉	semidirect
507. #532	C₂²×C₈₉	semidirect
508. #529	C₂²×C₈₉	semidirect
510. C₂×#124	C₂²×C₈₉	semidirect
511. C₂×#124	C₂²×C₈₉	semidirect
512. #519	C₂²×C₈₉	semidirect
513. #518	C₂²×C₈₉	semidirect
515. #497	C₂²×C₈₉	semidirect
516. #496	C₂²×C₈₉	semidirect
517. #495	C₂²×C₈₉	semidirect
518. #495	C₂²×C₈₉	semidirect
519. #495	C₂²×C₈₉	semidirect
520. #495	C₂²×C₈₉	semidirect
521. #489	C₂²×C₈₉	semidirect
522. #488	C₂²×C₈₉	semidirect
523. #488	C₂²×C₈₉	semidirect
524. #488	C₂²×C₈₉	semidirect
525. #487	C₂²×C₈₉	semidirect
526. #486	C₂²×C₈₉	semidirect
527. #464	C₂²×C₈₉	semidirect
528. #464	C₂²×C₈₉	semidirect
529. #463	C₂²×C₈₉	semidirect
530. #463	C₂²×C₈₉	semidirect
531. #462	C₂²×C₈₉	semidirect
532. #461	C₂²×C₈₉	semidirect
533. #460	C₂²×C₈₉	semidirect
534. #459	C₂²×C₈₉	semidirect
535. #452	C₂²×C₈₉	semidirect
536. #452	C₂²×C₈₉	semidirect
537. #451	C₂²×C₈₉	semidirect
538. #450	C₂²×C₈₉	semidirect
540. #449	C₂²×C₈₉	semidirect
541. #448	C₂²×C₈₉	semidirect
543. #433	C₂²×C₈₉	semidirect
544. #431	C₂²×C₈₉	semidirect
545. #424	C₂²×C₈₉	semidirect
546. #424	C₂²×C₈₉	semidirect
547. #419	C₂²×C₈₉	semidirect
548. #419	C₂²×C₈₉	semidirect
553. #416	C₂²×C₈₉	semidirect
554. #416	C₂²×C₈₉	semidirect
557. C₄×M₁₆	C₂²×C₈₉	semidirect
558. C₂×C₄×C₈	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3510	2
C₈₉×#3500	2
C₈₉×#3225	2
C₈₉×#3224	2
C₈₉×#3212	2
C₈₉×#3211	2
C₈₉×#3153	2
C₂×#495×C₈₉	2
C₈₉×#3140	2
C₈₉×#3131	2
C₈₉×#3044	2
C₈₉×#3043	2
C₈₉×#3042	2
C₈₉×#3041	2
C₈₉×#3011	2
C₈₉×#3010	2
C₈₉×#3009	2
C₈₉×#3008	2
C₈₉×#2922	2
#60819	89

Subgroups — C89×#60819 #36438667

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60819 #36438667