Subgroups — C₈₉×#61166 #36439014

Order 22784.

2182 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#555×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3329	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3325	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3321	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3319	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3305	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3303	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3093	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3079	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3055	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3036	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3006	C₂	1	2	yes	maximal, complemented
15	C₄×AGL(1,ℤ/8)×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×M₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2896	C₂	1	2	yes	maximal, complemented
18	C₂²×#41×C₈₉	C₂²	1	2	yes	—
19	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	complemented
21	C₂²×M₁₆×C₈₉	C₂²	1	2	yes	complemented
22	#555×C₈₉	—	2	1	no	—
23	#555×C₈₉	—	2	1	no	—
24	#555×C₈₉	—	2	2	no	—
25	#555×C₈₉	C₂²	1	2	yes	—
26	#555×C₈₉	C₂²	1	4	yes	complemented
27	#555×C₈₉	C₂²	1	2	yes	complemented
28	#550×C₈₉	C₂²	1	1	yes	characteristic, complemented
29	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
30	#548×C₈₉	C₂²	1	2	yes	complemented
31	#547×C₈₉	—	2	1	no	—
32	#547×C₈₉	C₂²	1	1	yes	characteristic, complemented
33	#546×C₈₉	—	2	2	no	—
34	#546×C₈₉	C₂²	1	2	yes	complemented
35	D₄²×C₈₉	—	2	1	no	—
36	D₄²×C₈₉	C₂²	1	1	yes	characteristic, complemented
37	#532×C₈₉	—	2	1	no	—
38	#532×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×#124×C₈₉	—	2	2	no	—
41	#525×C₈₉	—	2	2	no	—
42	#525×C₈₉	C₂²	1	2	yes	—
43	C₂×#121×C₈₉	—	2	1	no	—
44	C₂×#121×C₈₉	C₂²	1	2	yes	complemented
45	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₈₉	—	2	1	no	—
47	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
49	C₂×#117×C₈₉	—	2	1	no	—
50	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
51	#489×C₈₉	C₂²	1	4	yes	complemented
52	#487×C₈₉	C₂²	1	2	yes	complemented
53	#486×C₈₉	C₂²	1	2	yes	complemented
54	#485×C₈₉	C₂²	1	4	yes	complemented
55	#485×C₈₉	C₂²	1	4	yes	complemented
56	#482×C₈₉	C₂²	1	4	yes	complemented
57	#482×C₈₉	C₂²	1	4	yes	complemented
58	#477×C₈₉	C₂²	1	2	yes	complemented
59	#476×C₈₉	C₂²	1	2	yes	complemented
60	#475×C₈₉	C₂²	1	2	yes	complemented
61	#474×C₈₉	C₂²	1	2	yes	complemented
62	#469×C₈₉	C₂²	1	4	yes	complemented
63	#468×C₈₉	C₂²	1	4	yes	complemented
64	#466×C₈₉	C₂²	1	4	yes	complemented
65	#465×C₈₉	C₂²	1	4	yes	complemented
66	#463×C₈₉	C₂²	1	4	yes	complemented
67	#461×C₈₉	C₂²	1	2	yes	complemented
68	#459×C₈₉	C₂²	1	2	yes	complemented
69	#449×C₈₉	C₂²	1	4	yes	complemented
70	#449×C₈₉	C₂²	1	4	yes	complemented
71	#448×C₈₉	C₂²	1	4	yes	complemented
72	#447×C₈₉	C₂²	1	4	yes	complemented
73	#442×C₈₉	C₂²	1	2	yes	complemented
74	#440×C₈₉	C₂²	1	2	yes	complemented
75	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
76	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
77	#436×C₈₉	C₂²	1	2	yes	complemented
78	#435×C₈₉	C₂²	1	4	yes	complemented
79	C₈×D₄×C₈₉	C₂²	1	2	yes	complemented
80	#428×C₈₉	C₂²	1	2	yes	complemented
81	#428×C₈₉	C₂²	1	1	yes	characteristic, complemented
82	#423×C₈₉	C₂²	1	1	yes	characteristic, complemented
83	#419×C₈₉	C₂²	1	4	yes	complemented
84	#418×C₈₉	C₂²	1	4	yes	complemented
85	#418×C₈₉	C₂²	1	1	yes	characteristic, complemented
86	#417×C₈₉	C₂²	1	2	yes	—
87	#417×C₈₉	C₂²	1	1	yes	characteristic
88	#417×C₈₉	C₂²	1	2	yes	complemented
89	#417×C₈₉	C₂²	1	2	yes	complemented
90	#417×C₈₉	C₂²	1	2	yes	complemented
91	#416×C₈₉	C₂²	1	4	yes	complemented
92	#416×C₈₉	C₂²	1	4	yes	complemented
93	#407×C₈₉	C₂²	1	2	yes	complemented
94	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
95	C₂×#41×C₈₉	—	2	2	no	—
96	C₂×#41×C₈₉	—	2	2	no	—
97	C₂×#41×C₈₉	—	2	8	no	—
98	C₂×#41×C₈₉	—	4	4	no	—
99	C₂×#41×C₈₉	C₂³	1	2	yes	—
100	C₂×#41×C₈₉	C₂³	1	2	yes	—
101	C₂×#41×C₈₉	C₂³	1	2	yes	—
102	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₈₉	—	2	1	no	—
104	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
105	C₂²×D₄×C₈₉	—	2	2	no	—
106	C₂²×D₄×C₈₉	—	2	2	no	—
107	C₂²×D₄×C₈₉	—	2	1	no	—
108	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
109	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
111	C₂³×C₄×C₈₉	—	2	1	no	—
112	C₂³×C₄×C₈₉	—	2	2	no	—
113	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
114	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
115	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
116	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
117	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
118	C₂×D₈×C₈₉	C₂³	1	2	yes	—
119	C₂×D₈×C₈₉	C₂³	1	4	yes	—
120	C₂×M₁₆×C₈₉	—	4	4	no	—
121	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
122	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
123	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
124	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
125	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
126	C₄⋊Q₈×C₈₉	—	2	1	no	—
127	C₄⋊Q₈×C₈₉	—	2	1	no	—
128	C₄⋊Q₈×C₈₉	—	2	1	no	—
129	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
130	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
131	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
132	#127×C₈₉	—	2	1	no	—
133	#127×C₈₉	C₂³	1	1	yes	characteristic
134	#124×C₈₉	—	2	4	no	—
135	#124×C₈₉	—	2	4	no	—
136	#124×C₈₉	—	2	4	no	—
137	#124×C₈₉	—	2	4	no	—
138	#124×C₈₉	—	2	2	no	—
139	#124×C₈₉	C₂³	1	2	yes	—
140	#123×C₈₉	—	2	2	no	—
141	#123×C₈₉	—	2	2	no	—
142	#123×C₈₉	—	2	2	no	—
143	C₂²⋊Q₈×C₈₉	—	2	2	no	—
144	C₂²⋊Q₈×C₈₉	—	2	2	no	—
145	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
146	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
147	#121×C₈₉	—	2	2	no	—
148	#121×C₈₉	—	2	2	no	—
149	#121×C₈₉	—	2	4	no	—
150	#121×C₈₉	—	2	2	no	—
151	#121×C₈₉	—	2	1	no	—
152	#121×C₈₉	—	2	2	no	—
153	#121×C₈₉	—	2	2	no	—
154	#121×C₈₉	—	2	1	no	—
155	#121×C₈₉	—	2	1	no	—
156	#121×C₈₉	—	2	1	no	—
157	#121×C₈₉	—	2	2	no	—
158	#121×C₈₉	—	2	2	no	—
159	#121×C₈₉	C₂³	1	4	yes	—
160	#121×C₈₉	C₂³	1	4	yes	—
161	#121×C₈₉	C₂³	1	2	yes	—
162	#121×C₈₉	C₂³	1	2	yes	—
163	#120×C₈₉	—	2	2	no	—
164	#120×C₈₉	—	2	2	no	—
165	#120×C₈₉	—	2	2	no	—
166	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
168	C₄×D₄×C₈₉	—	2	1	no	—
169	C₄×D₄×C₈₉	—	2	2	no	—
170	C₄×D₄×C₈₉	—	2	1	no	—
171	C₄×D₄×C₈₉	—	2	1	no	—
172	C₄×D₄×C₈₉	—	2	2	no	—
173	C₄×D₄×C₈₉	—	2	1	no	—
174	C₄×D₄×C₈₉	—	2	2	no	—
175	C₄×D₄×C₈₉	—	2	1	no	—
176	C₄×D₄×C₈₉	—	2	1	no	—
177	C₄×D₄×C₈₉	—	2	1	no	—
178	C₄×D₄×C₈₉	—	2	1	no	—
179	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
180	C₄×D₄×C₈₉	D₄	1	2	yes	—
181	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
182	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₈₉	C₂³	1	2	yes	—
184	C₄×D₄×C₈₉	C₂³	1	2	yes	—
185	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₈₉	C₂³	1	2	yes	—
188	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
189	#117×C₈₉	—	2	2	no	—
190	#117×C₈₉	—	2	2	no	—
191	#117×C₈₉	—	2	2	no	—
192	#117×C₈₉	—	2	2	no	—
193	#117×C₈₉	—	2	4	no	—
194	#117×C₈₉	—	2	1	no	—
195	#117×C₈₉	C₂³	1	4	yes	—
196	#117×C₈₉	C₂³	1	4	yes	—
197	#117×C₈₉	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
199	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
200	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
204	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
205	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
206	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
207	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
208	C₂×C₄²×C₈₉	—	2	2	no	—
209	C₂×C₄²×C₈₉	—	2	1	no	—
210	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
211	#107×C₈₉	C₂³	1	2	yes	—
212	#107×C₈₉	C₂³	1	4	yes	—
213	#106×C₈₉	C₂³	1	2	yes	—
214	#106×C₈₉	C₂³	1	4	yes	—
215	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
216	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
217	#103×C₈₉	C₂³	1	2	yes	—
218	#103×C₈₉	C₂³	1	4	yes	—
219	#103×C₈₉	C₂³	1	4	yes	—
220	#103×C₈₉	C₂³	1	4	yes	—
221	#103×C₈₉	C₂³	1	4	yes	—
222	#102×C₈₉	C₂³	1	2	yes	—
223	#102×C₈₉	C₂³	1	4	yes	—
224	#102×C₈₉	C₂³	1	4	yes	—
225	#102×C₈₉	C₂³	1	4	yes	—
226	#102×C₈₉	C₂³	1	4	yes	—
227	#102×C₈₉	C₂³	1	2	yes	—
228	#102×C₈₉	C₂³	1	2	yes	—
229	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
230	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
231	#97×C₈₉	C₂³	1	2	yes	—
232	C₄×C₈×C₈₉	C₂³	1	2	yes	—
233	C₂⁴×C₈₉	—	2	1	no	—
234	C₂⁴×C₈₉	—	2	2	no	—
235	C₂⁴×C₈₉	C₂×D₄	1	2	yes	—
236	#41×C₈₉	—	2	2	no	—
237	#41×C₈₉	—	2	4	no	—
238	#41×C₈₉	—	2	4	no	—
239	#41×C₈₉	—	2	4	no	—
240	#41×C₈₉	—	2	4	no	—
241	#41×C₈₉	—	4	8	no	—
242	#41×C₈₉	—	4	2	no	—
243	#41×C₈₉	—	4	2	no	—
244	#41×C₈₉	—	4	8	no	—
245	#41×C₈₉	#41	1	4	yes	—
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	4	no	—
250	C₂×Q₈×C₈₉	—	4	2	no	—
251	C₂×Q₈×C₈₉	—	8	2	no	—
252	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
253	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
254	C₂×D₄×C₈₉	—	2	1	no	—
255	C₂×D₄×C₈₉	—	2	4	no	—
256	C₂×D₄×C₈₉	—	2	2	no	—
257	C₂×D₄×C₈₉	—	2	2	no	—
258	C₂×D₄×C₈₉	—	2	2	no	—
259	C₂×D₄×C₈₉	—	2	2	no	—
260	C₂×D₄×C₈₉	—	2	2	no	—
261	C₂×D₄×C₈₉	—	2	4	no	—
262	C₂×D₄×C₈₉	—	2	4	no	—
263	C₂×D₄×C₈₉	—	2	1	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	2	no	—
268	C₂×D₄×C₈₉	—	2	2	no	—
269	C₂×D₄×C₈₉	—	4	2	no	—
270	C₂×D₄×C₈₉	—	4	2	no	—
271	C₂×D₄×C₈₉	—	4	8	no	—
272	C₂×D₄×C₈₉	—	4	4	no	—
273	C₂×D₄×C₈₉	—	8	4	no	—
274	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
275	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
276	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
277	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
278	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
279	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₈₉	—	2	1	no	—
281	C₂²×C₄×C₈₉	—	2	4	no	—
282	C₂²×C₄×C₈₉	—	2	4	no	—
283	C₂²×C₄×C₈₉	—	2	1	no	—
284	C₂²×C₄×C₈₉	—	2	2	no	—
285	C₂²×C₄×C₈₉	—	2	2	no	—
286	C₂²×C₄×C₈₉	—	2	1	no	—
287	C₂²×C₄×C₈₉	—	2	2	no	—
288	C₂²×C₄×C₈₉	—	2	2	no	—
289	C₂²×C₄×C₈₉	—	2	2	no	—
290	C₂²×C₄×C₈₉	—	2	2	no	—
291	C₂²×C₄×C₈₉	—	2	2	no	—
292	C₂²×C₄×C₈₉	—	2	1	no	—
293	C₂²×C₄×C₈₉	—	4	8	no	—
294	C₂²×C₄×C₈₉	—	4	4	no	—
295	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
296	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
298	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
299	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
303	SD₁₆×C₈₉	—	2	4	no	—
304	SD₁₆×C₈₉	—	4	4	no	—
305	D₈×C₈₉	—	2	4	no	—
306	D₈×C₈₉	—	4	4	no	—
307	M₁₆×C₈₉	—	2	2	no	—
308	M₁₆×C₈₉	—	2	2	no	—
309	M₁₆×C₈₉	—	2	4	no	—
310	M₁₆×C₈₉	—	4	4	no	—
311	C₂×C₈×C₈₉	—	4	4	no	—
312	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
313	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
314	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
315	C₄⋊C₄×C₈₉	—	2	2	no	—
316	C₄⋊C₄×C₈₉	—	2	2	no	—
317	C₄⋊C₄×C₈₉	—	2	1	no	—
318	C₄⋊C₄×C₈₉	—	2	2	no	—
319	C₄⋊C₄×C₈₉	—	2	1	no	—
320	C₄⋊C₄×C₈₉	—	2	2	no	—
321	C₄⋊C₄×C₈₉	—	2	1	no	—
322	C₄⋊C₄×C₈₉	—	2	1	no	—
323	C₄⋊C₄×C₈₉	—	2	1	no	—
324	C₄⋊C₄×C₈₉	—	2	2	no	—
325	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
326	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
327	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
328	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
329	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
330	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
331	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
332	C₂²⋊C₄×C₈₉	—	2	4	no	—
333	C₂²⋊C₄×C₈₉	—	2	4	no	—
334	C₂²⋊C₄×C₈₉	—	2	2	no	—
335	C₂²⋊C₄×C₈₉	—	2	1	no	—
336	C₂²⋊C₄×C₈₉	—	2	2	no	—
337	C₂²⋊C₄×C₈₉	—	2	4	no	—
338	C₂²⋊C₄×C₈₉	—	2	4	no	—
339	C₂²⋊C₄×C₈₉	—	2	2	no	—
340	C₂²⋊C₄×C₈₉	—	2	2	no	—
341	C₂²⋊C₄×C₈₉	—	2	2	no	—
342	C₂²⋊C₄×C₈₉	—	2	2	no	—
343	C₂²⋊C₄×C₈₉	—	2	1	no	—
344	C₂²⋊C₄×C₈₉	—	2	1	no	—
345	C₂²⋊C₄×C₈₉	—	2	2	no	—
346	C₂²⋊C₄×C₈₉	—	2	2	no	—
347	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
348	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
349	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
350	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
351	C₄²×C₈₉	—	2	4	no	—
352	C₄²×C₈₉	—	2	4	no	—
353	C₄²×C₈₉	—	2	1	no	—
354	C₄²×C₈₉	—	2	1	no	—
355	C₄²×C₈₉	—	2	1	no	—
356	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
357	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
358	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
359	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
360	C₂³×C₈₉	—	2	1	no	—
361	C₂³×C₈₉	—	2	4	no	—
362	C₂³×C₈₉	—	2	2	no	—
363	C₂³×C₈₉	—	2	2	no	—
364	C₂³×C₈₉	—	4	2	no	—
365	C₂³×C₈₉	—	4	2	no	—
366	C₂³×C₈₉	—	4	4	no	—
367	C₂³×C₈₉	—	4	2	no	—
368	C₂³×C₈₉	—	4	4	no	—
369	C₂³×C₈₉	—	4	2	no	—
370	C₂³×C₈₉	—	4	2	no	—
371	C₂³×C₈₉	—	8	2	no	—
372	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
373	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
374	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
375	Q₈×C₈₉	—	2	1	no	—
376	Q₈×C₈₉	—	2	2	no	—
377	Q₈×C₈₉	—	2	2	no	—
378	Q₈×C₈₉	—	4	4	no	—
379	Q₈×C₈₉	—	8	2	no	—
380	Q₈×C₈₉	—	8	2	no	—
381	Q₈×C₈₉	C₂×#41	1	2	yes	—
382	D₄×C₈₉	—	2	4	no	—
383	D₄×C₈₉	—	2	2	no	—
384	D₄×C₈₉	—	2	2	no	—
385	D₄×C₈₉	—	2	2	no	—
386	D₄×C₈₉	—	2	2	no	—
387	D₄×C₈₉	—	2	1	no	—
388	D₄×C₈₉	—	2	2	no	—
389	D₄×C₈₉	—	2	2	no	—
390	D₄×C₈₉	—	4	2	no	—
391	D₄×C₈₉	—	4	4	no	—
392	D₄×C₈₉	—	4	4	no	—
393	D₄×C₈₉	—	4	4	no	—
394	D₄×C₈₉	—	4	4	no	—
395	D₄×C₈₉	—	4	4	no	—
396	D₄×C₈₉	—	4	2	no	—
397	D₄×C₈₉	—	4	2	no	—
398	D₄×C₈₉	—	8	1	no	—
399	D₄×C₈₉	—	8	2	no	—
400	D₄×C₈₉	—	8	4	no	—
401	D₄×C₈₉	—	8	4	no	—
402	D₄×C₈₉	C₂×#41	1	2	yes	—
403	C₂×C₄×C₈₉	—	2	4	no	—
404	C₂×C₄×C₈₉	—	2	1	no	—
405	C₂×C₄×C₈₉	—	2	4	no	—
406	C₂×C₄×C₈₉	—	2	4	no	—
407	C₂×C₄×C₈₉	—	2	4	no	—
408	C₂×C₄×C₈₉	—	2	2	no	—
409	C₂×C₄×C₈₉	—	2	2	no	—
410	C₂×C₄×C₈₉	—	2	2	no	—
411	C₂×C₄×C₈₉	—	2	2	no	—
412	C₂×C₄×C₈₉	—	2	2	no	—
413	C₂×C₄×C₈₉	—	2	2	no	—
414	C₂×C₄×C₈₉	—	2	1	no	—
415	C₂×C₄×C₈₉	—	2	1	no	—
416	C₂×C₄×C₈₉	—	2	4	no	—
417	C₂×C₄×C₈₉	—	2	2	no	—
418	C₂×C₄×C₈₉	—	4	1	no	—
419	C₂×C₄×C₈₉	—	4	4	no	—
420	C₂×C₄×C₈₉	—	4	4	no	—
421	C₂×C₄×C₈₉	—	4	4	no	—
422	C₂×C₄×C₈₉	—	4	4	no	—
423	C₂×C₄×C₈₉	—	4	2	no	—
424	C₂×C₄×C₈₉	—	4	4	no	—
425	C₂×C₄×C₈₉	—	4	4	no	—
426	C₂×C₄×C₈₉	—	4	4	no	—
427	C₂×C₄×C₈₉	—	4	2	no	—
428	C₂×C₄×C₈₉	—	8	1	no	—
429	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
436	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
437	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
438	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
439	C₈×C₈₉	—	2	2	no	—
440	C₈×C₈₉	—	2	2	no	—
441	C₈×C₈₉	—	2	4	no	—
442	C₂²×C₈₉	—	2	1	no	—
443	C₂²×C₈₉	—	2	1	no	—
444	C₂²×C₈₉	—	2	2	no	—
445	C₂²×C₈₉	—	2	2	no	—
446	C₂²×C₈₉	—	2	2	no	—
447	C₂²×C₈₉	—	2	2	no	—
448	C₂²×C₈₉	—	2	2	no	—
449	C₂²×C₈₉	—	2	2	no	—
450	C₂²×C₈₉	—	2	2	no	—
451	C₂²×C₈₉	—	4	1	no	—
452	C₂²×C₈₉	—	4	1	no	—
453	C₂²×C₈₉	—	4	2	no	—
454	C₂²×C₈₉	—	4	2	no	—
455	C₂²×C₈₉	—	4	2	no	—
456	C₂²×C₈₉	—	4	2	no	—
457	C₂²×C₈₉	—	4	2	no	—
458	C₂²×C₈₉	—	4	2	no	—
459	C₂²×C₈₉	—	8	4	no	—
460	C₂²×C₈₉	—	8	4	no	—
461	C₂²×C₈₉	—	8	8	no	—
462	C₂²×C₈₉	#546	1	2	yes	—
463	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
464	C₄×C₈₉	—	2	1	no	—
465	C₄×C₈₉	—	2	1	no	—
466	C₄×C₈₉	—	2	2	no	—
467	C₄×C₈₉	—	2	2	no	—
468	C₄×C₈₉	—	2	2	no	—
469	C₄×C₈₉	—	2	1	no	—
470	C₄×C₈₉	—	4	4	no	—
471	C₄×C₈₉	—	4	1	no	—
472	C₄×C₈₉	—	4	2	no	—
473	C₄×C₈₉	—	4	2	no	—
474	C₄×C₈₉	—	4	1	no	—
475	C₄×C₈₉	#546	1	2	yes	—
476	C₄×C₈₉	#575	1	2	yes	—
477	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
478	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
479	#61166	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
480	C₂×C₈₉	—	2	2	no	—
481	C₂×C₈₉	—	4	2	no	—
482	C₂×C₈₉	—	4	2	no	—
483	C₂×C₈₉	—	4	2	no	—
484	C₂×C₈₉	—	8	2	no	—
485	C₂×C₈₉	—	8	2	no	—
486	C₂×C₈₉	C₂×#546	1	1	yes	characteristic
487	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
488	C₂×C₈₉	#3585	1	1	yes	characteristic
489	C₂×#555	C₂×C₈₉	1	1	yes	characteristic, complemented
490	D₄×#41	C₂×C₈₉	1	1	yes	characteristic, complemented
491	#3329	C₂×C₈₉	1	2	yes	complemented
492	#3325	C₂×C₈₉	1	2	yes	complemented
493	#3321	C₂×C₈₉	1	4	yes	complemented
494	#3319	C₂×C₈₉	1	4	yes	complemented
495	#3305	C₂×C₈₉	1	2	yes	complemented
496	#3303	C₂×C₈₉	1	2	yes	complemented
497	#3141	C₂×C₈₉	1	1	yes	characteristic, complemented
498	#3093	C₂×C₈₉	1	2	yes	complemented
499	#3079	C₂×C₈₉	1	1	yes	characteristic, complemented
500	#3055	C₂×C₈₉	1	2	yes	complemented
501	#3036	C₂×C₈₉	1	1	yes	characteristic, complemented
502	#3006	C₂×C₈₉	1	2	yes	complemented
503	C₄×AGL(1,ℤ/8)	C₂×C₈₉	1	1	yes	characteristic, complemented
504	D₄×M₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
505	#2896	C₂×C₈₉	1	2	yes	complemented
506	C₈₉	#61166	1	1	yes	characteristic, direct product factor, Sylow
507	C₂²×#41	C₂²×C₈₉	1	2	yes	—
508	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
509	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	complemented
510	C₂²×M₁₆	C₂²×C₈₉	1	2	yes	complemented
511	#555	—	2	1	no	—
512	#555	—	2	1	no	—
513	#555	—	2	2	no	—
514	#555	C₂²×C₈₉	1	2	yes	—
515	#555	C₂²×C₈₉	1	2	yes	complemented
516	#555	C₂²×C₈₉	1	4	yes	complemented
517	#550	C₂²×C₈₉	1	1	yes	characteristic, complemented
518	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
519	#548	C₂²×C₈₉	1	2	yes	complemented
520	#547	—	2	1	no	—
521	#547	C₂²×C₈₉	1	1	yes	characteristic, complemented
522	#546	—	2	2	no	—
523	#546	C₂²×C₈₉	1	2	yes	complemented
524	D₄²	—	2	1	no	—
525	D₄²	C₂²×C₈₉	1	1	yes	characteristic, complemented
526	#532	—	2	1	no	—
527	#532	C₂²×C₈₉	1	1	yes	characteristic
528	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
529	C₂×#124	—	2	2	no	—
530	#525	—	2	2	no	—
531	#525	C₂²×C₈₉	1	2	yes	—
532	C₂×#121	—	2	1	no	—
533	C₂×#121	C₂²×C₈₉	1	2	yes	complemented
534	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
535	C₂×C₄×D₄	—	2	1	no	—
536	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
537	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
538	C₂×#117	—	2	1	no	—
539	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
540	#489	C₂²×C₈₉	1	4	yes	complemented
541	#487	C₂²×C₈₉	1	2	yes	complemented
542	#486	C₂²×C₈₉	1	2	yes	complemented
543	#485	C₂²×C₈₉	1	4	yes	complemented
544	#485	C₂²×C₈₉	1	4	yes	complemented
545	#482	C₂²×C₈₉	1	4	yes	complemented
546	#482	C₂²×C₈₉	1	4	yes	complemented
547	#477	C₂²×C₈₉	1	2	yes	complemented
548	#476	C₂²×C₈₉	1	2	yes	complemented
549	#475	C₂²×C₈₉	1	2	yes	complemented
550	#474	C₂²×C₈₉	1	2	yes	complemented
551	#469	C₂²×C₈₉	1	4	yes	complemented
552	#468	C₂²×C₈₉	1	4	yes	complemented
553	#466	C₂²×C₈₉	1	4	yes	complemented
554	#465	C₂²×C₈₉	1	4	yes	complemented
555	#463	C₂²×C₈₉	1	4	yes	complemented
556	#461	C₂²×C₈₉	1	2	yes	complemented
557	#459	C₂²×C₈₉	1	2	yes	complemented
558	#449	C₂²×C₈₉	1	4	yes	complemented
559	#449	C₂²×C₈₉	1	4	yes	complemented
560	#448	C₂²×C₈₉	1	4	yes	complemented
561	#447	C₂²×C₈₉	1	4	yes	complemented
562	#442	C₂²×C₈₉	1	2	yes	complemented
563	#440	C₂²×C₈₉	1	2	yes	complemented
564	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
565	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
566	#436	C₂²×C₈₉	1	2	yes	complemented
567	#435	C₂²×C₈₉	1	4	yes	complemented
568	C₈×D₄	C₂²×C₈₉	1	2	yes	complemented
569	#428	C₂²×C₈₉	1	2	yes	complemented
570	#428	C₂²×C₈₉	1	1	yes	characteristic, complemented
571	#423	C₂²×C₈₉	1	1	yes	characteristic, complemented
572	#419	C₂²×C₈₉	1	4	yes	complemented
573	#418	C₂²×C₈₉	1	4	yes	complemented
574	#418	C₂²×C₈₉	1	1	yes	characteristic, complemented
575	#417	C₂²×C₈₉	1	2	yes	—
576	#417	C₂²×C₈₉	1	1	yes	characteristic
577	#417	C₂²×C₈₉	1	2	yes	complemented
578	#417	C₂²×C₈₉	1	2	yes	complemented
579	#417	C₂²×C₈₉	1	2	yes	complemented
580	#416	C₂²×C₈₉	1	4	yes	complemented
581	#416	C₂²×C₈₉	1	4	yes	complemented
582	#407	C₂²×C₈₉	1	2	yes	complemented
583	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
584	C₂×#41	—	2	2	no	—
585	C₂×#41	—	2	2	no	—
586	C₂×#41	—	2	8	no	—
587	C₂×#41	—	4	4	no	—
588	C₂×#41	C₂³×C₈₉	1	2	yes	—
589	C₂×#41	C₂³×C₈₉	1	2	yes	—
590	C₂×#41	C₂³×C₈₉	1	2	yes	—
591	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
592	C₂²×Q₈	—	2	1	no	—
593	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
594	C₂²×D₄	—	2	2	no	—
595	C₂²×D₄	—	2	2	no	—
596	C₂²×D₄	—	2	1	no	—
597	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
598	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
599	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
600	C₂³×C₄	—	2	1	no	—
601	C₂³×C₄	—	2	2	no	—
602	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
603	AGL(1,ℤ/8)	—	2	4	no	—
604	AGL(1,ℤ/8)	—	4	4	no	—
605	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
606	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
607	C₂×D₈	C₂³×C₈₉	1	2	yes	—
608	C₂×D₈	C₂³×C₈₉	1	4	yes	—
609	C₂×M₁₆	—	4	4	no	—
610	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
611	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
612	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
613	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
614	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
615	C₄⋊Q₈	—	2	1	no	—
616	C₄⋊Q₈	—	2	1	no	—
617	C₄⋊Q₈	—	2	1	no	—
618	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
619	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
620	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
621	#127	—	2	1	no	—
622	#127	C₂³×C₈₉	1	1	yes	characteristic
623	#124	—	2	4	no	—
624	#124	—	2	4	no	—
625	#124	—	2	4	no	—
626	#124	—	2	4	no	—
627	#124	—	2	2	no	—
628	#124	C₂³×C₈₉	1	2	yes	—
629	#123	—	2	2	no	—
630	#123	—	2	2	no	—
631	#123	—	2	2	no	—
632	C₂²⋊Q₈	—	2	2	no	—
633	C₂²⋊Q₈	—	2	2	no	—
634	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
635	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
636	#121	—	2	2	no	—
637	#121	—	2	2	no	—
638	#121	—	2	4	no	—
639	#121	—	2	2	no	—
640	#121	—	2	1	no	—
641	#121	—	2	2	no	—
642	#121	—	2	2	no	—
643	#121	—	2	1	no	—
644	#121	—	2	1	no	—
645	#121	—	2	1	no	—
646	#121	—	2	2	no	—
647	#121	—	2	2	no	—
648	#121	C₂³×C₈₉	1	4	yes	—
649	#121	C₂³×C₈₉	1	4	yes	—
650	#121	C₂³×C₈₉	1	2	yes	—
651	#121	C₂³×C₈₉	1	2	yes	—
652	#120	—	2	2	no	—
653	#120	—	2	2	no	—
654	#120	—	2	2	no	—
655	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
656	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
657	C₄×D₄	—	2	1	no	—
658	C₄×D₄	—	2	2	no	—
659	C₄×D₄	—	2	1	no	—
660	C₄×D₄	—	2	1	no	—
661	C₄×D₄	—	2	2	no	—
662	C₄×D₄	—	2	1	no	—
663	C₄×D₄	—	2	2	no	—
664	C₄×D₄	—	2	1	no	—
665	C₄×D₄	—	2	1	no	—
666	C₄×D₄	—	2	1	no	—
667	C₄×D₄	—	2	1	no	—
668	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
669	C₄×D₄	D₄×C₈₉	1	2	yes	—
670	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
671	C₄×D₄	C₂³×C₈₉	1	2	yes	—
672	C₄×D₄	C₂³×C₈₉	1	2	yes	—
673	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
674	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
675	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
676	C₄×D₄	C₂³×C₈₉	1	2	yes	—
677	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
678	#117	—	2	2	no	—
679	#117	—	2	2	no	—
680	#117	—	2	2	no	—
681	#117	—	2	2	no	—
682	#117	—	2	4	no	—
683	#117	—	2	1	no	—
684	#117	C₂³×C₈₉	1	4	yes	—
685	#117	C₂³×C₈₉	1	4	yes	—
686	#117	C₂³×C₈₉	1	1	yes	characteristic
687	C₂×C₄⋊C₄	—	2	1	no	—
688	C₂×C₄⋊C₄	—	2	1	no	—
689	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
692	C₂×C₂²⋊C₄	—	2	2	no	—
693	C₂×C₂²⋊C₄	—	2	2	no	—
694	C₂×C₂²⋊C₄	—	2	1	no	—
695	C₂×C₂²⋊C₄	—	2	2	no	—
696	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
697	C₂×C₄²	—	2	2	no	—
698	C₂×C₄²	—	2	1	no	—
699	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
700	#107	C₂³×C₈₉	1	2	yes	—
701	#107	C₂³×C₈₉	1	4	yes	—
702	#106	C₂³×C₈₉	1	2	yes	—
703	#106	C₂³×C₈₉	1	4	yes	—
704	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
705	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
706	#103	C₂³×C₈₉	1	2	yes	—
707	#103	C₂³×C₈₉	1	4	yes	—
708	#103	C₂³×C₈₉	1	4	yes	—
709	#103	C₂³×C₈₉	1	4	yes	—
710	#103	C₂³×C₈₉	1	4	yes	—
711	#102	C₂³×C₈₉	1	2	yes	—
712	#102	C₂³×C₈₉	1	4	yes	—
713	#102	C₂³×C₈₉	1	4	yes	—
714	#102	C₂³×C₈₉	1	4	yes	—
715	#102	C₂³×C₈₉	1	4	yes	—
716	#102	C₂³×C₈₉	1	2	yes	—
717	#102	C₂³×C₈₉	1	2	yes	—
718	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
719	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
720	#97	C₂³×C₈₉	1	2	yes	—
721	C₄×C₈	C₂³×C₈₉	1	2	yes	—
722	C₂⁴	—	2	1	no	—
723	C₂⁴	—	2	2	no	—
724	C₂⁴	C₂×D₄×C₈₉	1	2	yes	—
725	#41	—	2	2	no	—
726	#41	—	2	4	no	—
727	#41	—	2	4	no	—
728	#41	—	2	4	no	—
729	#41	—	2	4	no	—
730	#41	—	4	8	no	—
731	#41	—	4	2	no	—
732	#41	—	4	2	no	—
733	#41	—	4	8	no	—
734	#41	#41×C₈₉	1	4	yes	—
735	C₂×Q₈	—	2	2	no	—
736	C₂×Q₈	—	2	2	no	—
737	C₂×Q₈	—	2	2	no	—
738	C₂×Q₈	—	2	4	no	—
739	C₂×Q₈	—	4	2	no	—
740	C₂×Q₈	—	8	2	no	—
741	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
742	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
743	C₂×D₄	—	2	1	no	—
744	C₂×D₄	—	2	4	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	4	no	—
751	C₂×D₄	—	2	4	no	—
752	C₂×D₄	—	2	1	no	—
753	C₂×D₄	—	2	1	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	1	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	2	no	—
758	C₂×D₄	—	4	2	no	—
759	C₂×D₄	—	4	2	no	—
760	C₂×D₄	—	4	8	no	—
761	C₂×D₄	—	4	4	no	—
762	C₂×D₄	—	8	4	no	—
763	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
764	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
765	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
766	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
767	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
768	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
769	C₂²×C₄	—	2	1	no	—
770	C₂²×C₄	—	2	4	no	—
771	C₂²×C₄	—	2	4	no	—
772	C₂²×C₄	—	2	1	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	1	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	1	no	—
782	C₂²×C₄	—	4	8	no	—
783	C₂²×C₄	—	4	4	no	—
784	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
785	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
786	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
787	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
788	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
790	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
791	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
792	SD₁₆	—	2	4	no	—
793	SD₁₆	—	4	4	no	—
794	D₈	—	2	4	no	—
795	D₈	—	4	4	no	—
796	M₁₆	—	2	2	no	—
797	M₁₆	—	2	2	no	—
798	M₁₆	—	2	4	no	—
799	M₁₆	—	4	4	no	—
800	C₂×C₈	—	4	4	no	—
801	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
802	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
803	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	1	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	1	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	1	no	—
811	C₄⋊C₄	—	2	1	no	—
812	C₄⋊C₄	—	2	1	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
815	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
816	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
817	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
818	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
819	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
820	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	4	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	1	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	1	no	—
833	C₂²⋊C₄	—	2	1	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
837	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
838	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
839	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
840	C₄²	—	2	4	no	—
841	C₄²	—	2	4	no	—
842	C₄²	—	2	1	no	—
843	C₄²	—	2	1	no	—
844	C₄²	—	2	1	no	—
845	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
846	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
847	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
848	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
849	C₂³	—	2	1	no	—
850	C₂³	—	2	4	no	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	4	2	no	—
854	C₂³	—	4	2	no	—
855	C₂³	—	4	4	no	—
856	C₂³	—	4	2	no	—
857	C₂³	—	4	4	no	—
858	C₂³	—	4	2	no	—
859	C₂³	—	4	2	no	—
860	C₂³	—	8	2	no	—
861	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
862	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
863	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
864	Q₈	—	2	1	no	—
865	Q₈	—	2	2	no	—
866	Q₈	—	2	2	no	—
867	Q₈	—	4	4	no	—
868	Q₈	—	8	2	no	—
869	Q₈	—	8	2	no	—
870	Q₈	C₂×#41×C₈₉	1	2	yes	—
871	D₄	—	2	4	no	—
872	D₄	—	2	2	no	—
873	D₄	—	2	2	no	—
874	D₄	—	2	2	no	—
875	D₄	—	2	2	no	—
876	D₄	—	2	1	no	—
877	D₄	—	2	2	no	—
878	D₄	—	2	2	no	—
879	D₄	—	4	2	no	—
880	D₄	—	4	4	no	—
881	D₄	—	4	4	no	—
882	D₄	—	4	4	no	—
883	D₄	—	4	4	no	—
884	D₄	—	4	4	no	—
885	D₄	—	4	2	no	—
886	D₄	—	4	2	no	—
887	D₄	—	8	1	no	—
888	D₄	—	8	2	no	—
889	D₄	—	8	4	no	—
890	D₄	—	8	4	no	—
891	D₄	C₂×#41×C₈₉	1	2	yes	—
892	C₂×C₄	—	2	4	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	4	no	—
895	C₂×C₄	—	2	4	no	—
896	C₂×C₄	—	2	4	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	4	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	4	1	no	—
908	C₂×C₄	—	4	4	no	—
909	C₂×C₄	—	4	4	no	—
910	C₂×C₄	—	4	4	no	—
911	C₂×C₄	—	4	4	no	—
912	C₂×C₄	—	4	2	no	—
913	C₂×C₄	—	4	4	no	—
914	C₂×C₄	—	4	4	no	—
915	C₂×C₄	—	4	4	no	—
916	C₂×C₄	—	4	2	no	—
917	C₂×C₄	—	8	1	no	—
918	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
919	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
920	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
921	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
922	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
923	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
924	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
925	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
926	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
927	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
928	C₈	—	2	2	no	—
929	C₈	—	2	2	no	—
930	C₈	—	2	4	no	—
931	C₂²	—	2	1	no	—
932	C₂²	—	2	1	no	—
933	C₂²	—	2	2	no	—
934	C₂²	—	2	2	no	—
935	C₂²	—	2	2	no	—
936	C₂²	—	2	2	no	—
937	C₂²	—	2	2	no	—
938	C₂²	—	2	2	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	4	1	no	—
941	C₂²	—	4	1	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	8	4	no	—
949	C₂²	—	8	4	no	—
950	C₂²	—	8	8	no	—
951	C₂²	#546×C₈₉	1	2	yes	—
952	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	2	no	—
957	C₄	—	2	2	no	—
958	C₄	—	2	2	no	—
959	C₄	—	4	2	no	—
960	C₄	—	4	1	no	—
961	C₄	—	4	4	no	—
962	C₄	—	4	1	no	—
963	C₄	—	4	2	no	—
964	C₄	#546×C₈₉	1	2	yes	—
965	C₄	#575×C₈₉	1	2	yes	—
966	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
967	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
968	C₂	—	2	2	no	—
969	C₂	—	4	2	no	—
970	C₂	—	4	2	no	—
971	C₂	—	4	2	no	—
972	C₂	—	8	2	no	—
973	C₂	—	8	2	no	—
974	C₂	C₂×#546×C₈₉	1	1	yes	characteristic
975	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
976	C₂	C₈₉×#3585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×#555×C₈₉	C₂	semidirect
2. D₄×#41×C₈₉	C₂	semidirect
3. C₈₉×#3329	C₂	semidirect
4. C₈₉×#3325	C₂	semidirect
5. C₈₉×#3321	C₂	semidirect
6. C₈₉×#3319	C₂	semidirect
7. C₈₉×#3305	C₂	semidirect
8. C₈₉×#3303	C₂	semidirect
9. C₈₉×#3141	C₂	semidirect
10. C₈₉×#3093	C₂	semidirect
11. C₈₉×#3079	C₂	semidirect
12. C₈₉×#3055	C₂	semidirect
13. C₈₉×#3036	C₂	semidirect
14. C₈₉×#3006	C₂	semidirect
15. C₄×AGL(1,ℤ/8)×C₈₉	C₂	semidirect
16. D₄×M₁₆×C₈₉	C₂	semidirect
17. C₈₉×#2896	C₂	semidirect
20. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
21. C₂²×M₁₆×C₈₉	C₂²	semidirect
26. #555×C₈₉	C₂²	semidirect
27. #555×C₈₉	C₂²	semidirect
28. #550×C₈₉	C₂²	semidirect
29. D₄×Q₈×C₈₉	C₂²	semidirect
30. #548×C₈₉	C₂²	semidirect
32. #547×C₈₉	C₂²	semidirect
34. #546×C₈₉	C₂²	semidirect
36. D₄²×C₈₉	C₂²	semidirect
39. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
44. C₂×#121×C₈₉	C₂²	semidirect
48. C₂×C₄×D₄×C₈₉	C₂²	semidirect
50. C₂×#117×C₈₉	C₂²	semidirect
51. #489×C₈₉	C₂²	semidirect
52. #487×C₈₉	C₂²	semidirect
53. #486×C₈₉	C₂²	semidirect
54. #485×C₈₉	C₂²	semidirect
55. #485×C₈₉	C₂²	semidirect
56. #482×C₈₉	C₂²	semidirect
57. #482×C₈₉	C₂²	semidirect
58. #477×C₈₉	C₂²	semidirect
59. #476×C₈₉	C₂²	semidirect
60. #475×C₈₉	C₂²	semidirect
61. #474×C₈₉	C₂²	semidirect
62. #469×C₈₉	C₂²	semidirect
63. #468×C₈₉	C₂²	semidirect
64. #466×C₈₉	C₂²	semidirect
65. #465×C₈₉	C₂²	semidirect
66. #463×C₈₉	C₂²	semidirect
67. #461×C₈₉	C₂²	semidirect
68. #459×C₈₉	C₂²	semidirect
69. #449×C₈₉	C₂²	semidirect
70. #449×C₈₉	C₂²	semidirect
71. #448×C₈₉	C₂²	semidirect
72. #447×C₈₉	C₂²	semidirect
73. #442×C₈₉	C₂²	semidirect
74. #440×C₈₉	C₂²	semidirect
75. C₄×SD₁₆×C₈₉	C₂²	semidirect
76. C₄×D₈×C₈₉	C₂²	semidirect
77. #436×C₈₉	C₂²	semidirect
78. #435×C₈₉	C₂²	semidirect
79. C₈×D₄×C₈₉	C₂²	semidirect
80. #428×C₈₉	C₂²	semidirect
81. #428×C₈₉	C₂²	semidirect
82. #423×C₈₉	C₂²	semidirect
83. #419×C₈₉	C₂²	semidirect
84. #418×C₈₉	C₂²	semidirect
85. #418×C₈₉	C₂²	semidirect
88. #417×C₈₉	C₂²	semidirect
89. #417×C₈₉	C₂²	semidirect
90. #417×C₈₉	C₂²	semidirect
91. #416×C₈₉	C₂²	semidirect
92. #416×C₈₉	C₂²	semidirect
93. #407×C₈₉	C₂²	semidirect
94. C₄×M₁₆×C₈₉	C₂²	semidirect
479. #61166	C₈₉	direct (N × H)
489. C₂×#555	C₂×C₈₉	semidirect
490. D₄×#41	C₂×C₈₉	semidirect
491. #3329	C₂×C₈₉	semidirect
492. #3325	C₂×C₈₉	semidirect
493. #3321	C₂×C₈₉	semidirect
494. #3319	C₂×C₈₉	semidirect
495. #3305	C₂×C₈₉	semidirect
496. #3303	C₂×C₈₉	semidirect
497. #3141	C₂×C₈₉	semidirect
498. #3093	C₂×C₈₉	semidirect
499. #3079	C₂×C₈₉	semidirect
500. #3055	C₂×C₈₉	semidirect
501. #3036	C₂×C₈₉	semidirect
502. #3006	C₂×C₈₉	semidirect
503. C₄×AGL(1,ℤ/8)	C₂×C₈₉	semidirect
504. D₄×M₁₆	C₂×C₈₉	semidirect
505. #2896	C₂×C₈₉	semidirect
506. C₈₉	#61166	direct (N × H)
509. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
510. C₂²×M₁₆	C₂²×C₈₉	semidirect
515. #555	C₂²×C₈₉	semidirect
516. #555	C₂²×C₈₉	semidirect
517. #550	C₂²×C₈₉	semidirect
518. D₄×Q₈	C₂²×C₈₉	semidirect
519. #548	C₂²×C₈₉	semidirect
521. #547	C₂²×C₈₉	semidirect
523. #546	C₂²×C₈₉	semidirect
525. D₄²	C₂²×C₈₉	semidirect
528. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
533. C₂×#121	C₂²×C₈₉	semidirect
537. C₂×C₄×D₄	C₂²×C₈₉	semidirect
539. C₂×#117	C₂²×C₈₉	semidirect
540. #489	C₂²×C₈₉	semidirect
541. #487	C₂²×C₈₉	semidirect
542. #486	C₂²×C₈₉	semidirect
543. #485	C₂²×C₈₉	semidirect
544. #485	C₂²×C₈₉	semidirect
545. #482	C₂²×C₈₉	semidirect
546. #482	C₂²×C₈₉	semidirect
547. #477	C₂²×C₈₉	semidirect
548. #476	C₂²×C₈₉	semidirect
549. #475	C₂²×C₈₉	semidirect
550. #474	C₂²×C₈₉	semidirect
551. #469	C₂²×C₈₉	semidirect
552. #468	C₂²×C₈₉	semidirect
553. #466	C₂²×C₈₉	semidirect
554. #465	C₂²×C₈₉	semidirect
555. #463	C₂²×C₈₉	semidirect
556. #461	C₂²×C₈₉	semidirect
557. #459	C₂²×C₈₉	semidirect
558. #449	C₂²×C₈₉	semidirect
559. #449	C₂²×C₈₉	semidirect
560. #448	C₂²×C₈₉	semidirect
561. #447	C₂²×C₈₉	semidirect
562. #442	C₂²×C₈₉	semidirect
563. #440	C₂²×C₈₉	semidirect
564. C₄×SD₁₆	C₂²×C₈₉	semidirect
565. C₄×D₈	C₂²×C₈₉	semidirect
566. #436	C₂²×C₈₉	semidirect
567. #435	C₂²×C₈₉	semidirect
568. C₈×D₄	C₂²×C₈₉	semidirect
569. #428	C₂²×C₈₉	semidirect
570. #428	C₂²×C₈₉	semidirect
571. #423	C₂²×C₈₉	semidirect
572. #419	C₂²×C₈₉	semidirect
573. #418	C₂²×C₈₉	semidirect
574. #418	C₂²×C₈₉	semidirect
577. #417	C₂²×C₈₉	semidirect
578. #417	C₂²×C₈₉	semidirect
579. #417	C₂²×C₈₉	semidirect
580. #416	C₂²×C₈₉	semidirect
581. #416	C₂²×C₈₉	semidirect
582. #407	C₂²×C₈₉	semidirect
583. C₄×M₁₆	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#555×C₈₉	2
D₄×#41×C₈₉	2
C₈₉×#3329	2
C₈₉×#3325	2
C₈₉×#3321	2
C₈₉×#3319	2
C₈₉×#3305	2
C₈₉×#3303	2
C₈₉×#3141	2
C₈₉×#3093	2
C₈₉×#3079	2
C₈₉×#3055	2
C₈₉×#3036	2
C₈₉×#3006	2
C₄×AGL(1,ℤ/8)×C₈₉	2
D₄×M₁₆×C₈₉	2
C₈₉×#2896	2
#61166	89

Subgroups — C89×#61166 #36439014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61166 #36439014