Subgroups — C₈₉×#60803 #36438651

Order 22784.

2444 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#532×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3214	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3213	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3207	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3206	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3205	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3151	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3141	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3036	C₂	1	4	yes	maximal, complemented
11	C₈₉×#3006	C₂	1	4	yes	maximal, complemented
12	C₈₉×#2920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₈₉	—	2	1	no	—
14	C₂²×#41×C₈₉	C₂²	1	2	yes	—
15	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	8	yes	complemented
16	#532×C₈₉	—	2	1	no	—
17	#532×C₈₉	—	2	1	no	—
18	#532×C₈₉	—	2	1	no	—
19	#532×C₈₉	—	2	1	no	—
20	#532×C₈₉	—	2	1	no	—
21	#532×C₈₉	—	2	1	no	—
22	#532×C₈₉	—	2	1	no	—
23	#532×C₈₉	—	2	1	no	—
24	#532×C₈₉	C₂²	1	2	yes	—
25	#532×C₈₉	C₂²	1	2	yes	—
26	#532×C₈₉	C₂²	1	2	yes	—
27	#532×C₈₉	C₂²	1	2	yes	—
28	#532×C₈₉	C₂²	1	2	yes	complemented
29	#532×C₈₉	C₂²	1	2	yes	complemented
30	#532×C₈₉	C₂²	1	2	yes	complemented
31	#532×C₈₉	C₂²	1	2	yes	complemented
32	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic, complemented
36	C₂×#124×C₈₉	—	2	1	no	—
37	C₂×#124×C₈₉	C₂²	1	2	yes	complemented
38	C₂×#121×C₈₉	—	2	1	no	—
39	C₂×#121×C₈₉	—	2	1	no	—
40	C₂×#121×C₈₉	—	2	1	no	—
41	C₂×#121×C₈₉	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₈₉	—	2	1	no	—
43	C₂×C₄×D₄×C₈₉	—	2	1	no	—
44	C₂×C₄×D₄×C₈₉	—	2	1	no	—
45	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
46	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
47	#496×C₈₉	C₂²	1	8	yes	complemented
48	#493×C₈₉	C₂²	1	4	yes	complemented
49	#492×C₈₉	C₂²	1	4	yes	complemented
50	#489×C₈₉	C₂²	1	8	yes	complemented
51	#487×C₈₉	C₂²	1	4	yes	complemented
52	#486×C₈₉	C₂²	1	4	yes	complemented
53	#463×C₈₉	C₂²	1	16	yes	complemented
54	#461×C₈₉	C₂²	1	8	yes	complemented
55	#459×C₈₉	C₂²	1	8	yes	complemented
56	#449×C₈₉	C₂²	1	16	yes	complemented
57	#448×C₈₉	C₂²	1	8	yes	complemented
58	#447×C₈₉	C₂²	1	8	yes	complemented
59	#432×C₈₉	C₂²	1	2	yes	complemented
60	#432×C₈₉	C₂²	1	2	yes	complemented
61	#431×C₈₉	C₂²	1	2	yes	complemented
62	#431×C₈₉	C₂²	1	2	yes	complemented
63	#423×C₈₉	C₂²	1	2	yes	complemented
64	#417×C₈₉	C₂²	1	8	yes	complemented
65	#407×C₈₉	C₂²	1	2	yes	—
66	C₄×M₁₆×C₈₉	C₂²	1	2	yes	complemented
67	C₂×#41×C₈₉	—	2	2	no	—
68	C₂×#41×C₈₉	—	2	2	no	—
69	C₂×#41×C₈₉	—	2	2	no	—
70	C₂×#41×C₈₉	—	2	2	no	—
71	C₂×#41×C₈₉	—	2	2	no	—
72	C₂×#41×C₈₉	—	2	2	no	—
73	C₂×#41×C₈₉	—	4	8	no	—
74	C₂×#41×C₈₉	—	4	8	no	—
75	C₂×#41×C₈₉	C₂³	1	4	yes	—
76	C₂×#41×C₈₉	C₂³	1	4	yes	—
77	C₂²×Q₈×C₈₉	—	2	1	no	—
78	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
79	C₂²×D₄×C₈₉	—	2	2	no	—
80	C₂²×D₄×C₈₉	—	2	2	no	—
81	C₂²×D₄×C₈₉	—	2	1	no	—
82	C₂²×D₄×C₈₉	—	2	1	no	—
83	C₂²×D₄×C₈₉	—	2	1	no	—
84	C₂²×D₄×C₈₉	—	2	1	no	—
85	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
86	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
87	C₂³×C₄×C₈₉	—	2	2	no	—
88	C₂³×C₄×C₈₉	—	2	2	no	—
89	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
90	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
91	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
92	AGL(1,ℤ/8)×C₈₉	—	4	16	no	—
93	C₂×SD₁₆×C₈₉	C₂³	1	16	yes	—
94	C₂×D₈×C₈₉	C₂³	1	16	yes	—
95	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
96	C₄⋊Q₈×C₈₉	—	2	1	no	—
97	C₄⋊Q₈×C₈₉	—	2	1	no	—
98	C₄⋊Q₈×C₈₉	—	2	1	no	—
99	C₄⋊Q₈×C₈₉	—	2	1	no	—
100	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
101	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
102	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
103	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
104	#127×C₈₉	—	2	1	no	—
105	#127×C₈₉	—	2	1	no	—
106	#127×C₈₉	—	2	1	no	—
107	#127×C₈₉	—	2	1	no	—
108	#127×C₈₉	C₂³	1	2	yes	—
109	#127×C₈₉	C₂³	1	2	yes	—
110	#127×C₈₉	C₂³	1	2	yes	—
111	#127×C₈₉	C₂³	1	2	yes	—
112	#124×C₈₉	—	2	2	no	—
113	#124×C₈₉	—	2	2	no	—
114	#124×C₈₉	—	2	2	no	—
115	#124×C₈₉	—	2	2	no	—
116	#124×C₈₉	—	2	2	no	—
117	#124×C₈₉	—	2	2	no	—
118	#124×C₈₉	C₂³	1	4	yes	—
119	#124×C₈₉	C₂³	1	4	yes	—
120	#121×C₈₉	—	2	2	no	—
121	#121×C₈₉	—	2	2	no	—
122	#121×C₈₉	—	2	2	no	—
123	#121×C₈₉	—	2	2	no	—
124	#121×C₈₉	—	2	2	no	—
125	#121×C₈₉	—	2	2	no	—
126	#121×C₈₉	—	2	2	no	—
127	#121×C₈₉	—	2	2	no	—
128	#121×C₈₉	—	2	2	no	—
129	#121×C₈₉	—	2	2	no	—
130	#121×C₈₉	—	2	2	no	—
131	#121×C₈₉	—	2	2	no	—
132	#121×C₈₉	—	2	2	no	—
133	#121×C₈₉	—	2	2	no	—
134	#121×C₈₉	C₂³	1	4	yes	—
135	#121×C₈₉	C₂³	1	4	yes	—
136	C₄×D₄×C₈₉	—	2	2	no	—
137	C₄×D₄×C₈₉	—	2	2	no	—
138	C₄×D₄×C₈₉	—	2	2	no	—
139	C₄×D₄×C₈₉	—	2	2	no	—
140	C₄×D₄×C₈₉	—	2	2	no	—
141	C₄×D₄×C₈₉	—	2	2	no	—
142	C₄×D₄×C₈₉	—	2	2	no	—
143	C₄×D₄×C₈₉	—	2	2	no	—
144	C₄×D₄×C₈₉	—	2	2	no	—
145	C₄×D₄×C₈₉	—	2	2	no	—
146	C₄×D₄×C₈₉	—	2	2	no	—
147	C₄×D₄×C₈₉	—	2	2	no	—
148	C₄×D₄×C₈₉	—	2	2	no	—
149	C₄×D₄×C₈₉	—	2	2	no	—
150	C₄×D₄×C₈₉	C₂³	1	4	yes	—
151	C₄×D₄×C₈₉	C₂³	1	4	yes	—
152	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
153	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
154	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
155	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
157	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
158	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
159	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
160	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
161	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
162	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
163	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
164	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
165	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
166	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
172	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
173	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
174	#103×C₈₉	C₂³	1	16	yes	—
175	#102×C₈₉	C₂³	1	16	yes	—
176	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
177	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
178	#97×C₈₉	C₂³	1	4	yes	—
179	C₄×C₈×C₈₉	C₂³	1	4	yes	—
180	C₂⁴×C₈₉	—	2	2	no	—
181	C₂⁴×C₈₉	—	2	2	no	—
182	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
183	#41×C₈₉	—	2	16	no	—
184	#41×C₈₉	—	4	8	no	—
185	#41×C₈₉	—	4	8	no	—
186	#41×C₈₉	—	4	8	no	—
187	#41×C₈₉	—	4	8	no	—
188	#41×C₈₉	—	4	8	no	—
189	#41×C₈₉	—	4	8	no	—
190	#41×C₈₉	—	4	8	no	—
191	C₂×Q₈×C₈₉	—	2	2	no	—
192	C₂×Q₈×C₈₉	—	2	2	no	—
193	C₂×Q₈×C₈₉	—	2	2	no	—
194	C₂×Q₈×C₈₉	—	4	4	no	—
195	C₂×Q₈×C₈₉	—	4	4	no	—
196	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
197	C₂×D₄×C₈₉	—	2	4	no	—
198	C₂×D₄×C₈₉	—	2	4	no	—
199	C₂×D₄×C₈₉	—	2	4	no	—
200	C₂×D₄×C₈₉	—	2	4	no	—
201	C₂×D₄×C₈₉	—	2	2	no	—
202	C₂×D₄×C₈₉	—	2	2	no	—
203	C₂×D₄×C₈₉	—	2	2	no	—
204	C₂×D₄×C₈₉	—	2	2	no	—
205	C₂×D₄×C₈₉	—	2	2	no	—
206	C₂×D₄×C₈₉	—	2	2	no	—
207	C₂×D₄×C₈₉	—	2	2	no	—
208	C₂×D₄×C₈₉	—	2	2	no	—
209	C₂×D₄×C₈₉	—	2	2	no	—
210	C₂×D₄×C₈₉	—	2	2	no	—
211	C₂×D₄×C₈₉	—	2	8	no	—
212	C₂×D₄×C₈₉	—	4	4	no	—
213	C₂×D₄×C₈₉	—	4	4	no	—
214	C₂×D₄×C₈₉	—	4	4	no	—
215	C₂×D₄×C₈₉	—	4	4	no	—
216	C₂×D₄×C₈₉	—	4	8	no	—
217	C₂×D₄×C₈₉	—	4	8	no	—
218	C₂×D₄×C₈₉	—	4	4	no	—
219	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
220	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
221	C₂²×C₄×C₈₉	—	2	4	no	—
222	C₂²×C₄×C₈₉	—	2	4	no	—
223	C₂²×C₄×C₈₉	—	2	2	no	—
224	C₂²×C₄×C₈₉	—	2	2	no	—
225	C₂²×C₄×C₈₉	—	2	4	no	—
226	C₂²×C₄×C₈₉	—	2	4	no	—
227	C₂²×C₄×C₈₉	—	2	4	no	—
228	C₂²×C₄×C₈₉	—	2	4	no	—
229	C₂²×C₄×C₈₉	—	4	2	no	—
230	C₂²×C₄×C₈₉	—	4	8	no	—
231	C₂²×C₄×C₈₉	—	4	8	no	—
232	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
250	SD₁₆×C₈₉	—	4	16	no	—
251	D₈×C₈₉	—	4	16	no	—
252	M₁₆×C₈₉	—	2	8	no	—
253	C₂×C₈×C₈₉	C₂⁴	1	8	yes	—
254	C₄⋊C₄×C₈₉	—	2	2	no	—
255	C₄⋊C₄×C₈₉	—	2	2	no	—
256	C₄⋊C₄×C₈₉	—	2	2	no	—
257	C₄⋊C₄×C₈₉	—	2	2	no	—
258	C₄⋊C₄×C₈₉	—	2	2	no	—
259	C₄⋊C₄×C₈₉	—	2	2	no	—
260	C₄⋊C₄×C₈₉	—	2	2	no	—
261	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
262	C₂²⋊C₄×C₈₉	—	2	4	no	—
263	C₂²⋊C₄×C₈₉	—	2	4	no	—
264	C₂²⋊C₄×C₈₉	—	2	4	no	—
265	C₂²⋊C₄×C₈₉	—	2	4	no	—
266	C₂²⋊C₄×C₈₉	—	2	4	no	—
267	C₂²⋊C₄×C₈₉	—	2	4	no	—
268	C₂²⋊C₄×C₈₉	—	2	4	no	—
269	C₂²⋊C₄×C₈₉	—	2	4	no	—
270	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
271	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
272	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
273	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
274	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
277	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
278	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
279	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
283	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
284	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
285	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
286	C₂³×C₈₉	—	2	2	no	—
287	C₂³×C₈₉	—	2	2	no	—
288	C₂³×C₈₉	—	2	4	no	—
289	C₂³×C₈₉	—	2	4	no	—
290	C₂³×C₈₉	—	4	1	no	—
291	C₂³×C₈₉	—	4	4	no	—
292	C₂³×C₈₉	—	4	4	no	—
293	C₂³×C₈₉	—	4	4	no	—
294	C₂³×C₈₉	—	4	4	no	—
295	C₂³×C₈₉	—	4	4	no	—
296	C₂³×C₈₉	—	4	4	no	—
297	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
298	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
299	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
300	Q₈×C₈₉	—	2	8	no	—
301	Q₈×C₈₉	—	4	4	no	—
302	Q₈×C₈₉	—	4	4	no	—
303	Q₈×C₈₉	—	4	4	no	—
304	D₄×C₈₉	—	2	8	no	—
305	D₄×C₈₉	—	2	8	no	—
306	D₄×C₈₉	—	4	4	no	—
307	D₄×C₈₉	—	4	4	no	—
308	D₄×C₈₉	—	4	4	no	—
309	D₄×C₈₉	—	4	4	no	—
310	D₄×C₈₉	—	4	8	no	—
311	D₄×C₈₉	—	4	8	no	—
312	D₄×C₈₉	—	4	8	no	—
313	D₄×C₈₉	—	4	8	no	—
314	D₄×C₈₉	—	4	4	no	—
315	D₄×C₈₉	—	4	4	no	—
316	D₄×C₈₉	—	4	4	no	—
317	D₄×C₈₉	—	4	4	no	—
318	D₄×C₈₉	—	4	4	no	—
319	D₄×C₈₉	—	4	4	no	—
320	C₂×C₄×C₈₉	—	2	2	no	—
321	C₂×C₄×C₈₉	—	2	2	no	—
322	C₂×C₄×C₈₉	—	2	2	no	—
323	C₂×C₄×C₈₉	—	2	2	no	—
324	C₂×C₄×C₈₉	—	2	2	no	—
325	C₂×C₄×C₈₉	—	2	2	no	—
326	C₂×C₄×C₈₉	—	2	2	no	—
327	C₂×C₄×C₈₉	—	2	2	no	—
328	C₂×C₄×C₈₉	—	2	2	no	—
329	C₂×C₄×C₈₉	—	2	2	no	—
330	C₂×C₄×C₈₉	—	2	2	no	—
331	C₂×C₄×C₈₉	—	2	2	no	—
332	C₂×C₄×C₈₉	—	2	2	no	—
333	C₂×C₄×C₈₉	—	2	4	no	—
334	C₂×C₄×C₈₉	—	2	4	no	—
335	C₂×C₄×C₈₉	—	4	1	no	—
336	C₂×C₄×C₈₉	—	4	1	no	—
337	C₂×C₄×C₈₉	—	4	1	no	—
338	C₂×C₄×C₈₉	—	4	8	no	—
339	C₂×C₄×C₈₉	—	4	8	no	—
340	C₂×C₄×C₈₉	—	4	4	no	—
341	C₂×C₄×C₈₉	—	4	4	no	—
342	C₂×C₄×C₈₉	—	4	8	no	—
343	C₂×C₄×C₈₉	—	4	8	no	—
344	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	4	yes	complemented
345	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
357	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
358	C₈×C₈₉	—	2	8	no	—
359	C₂²×C₈₉	—	2	1	no	—
360	C₂²×C₈₉	—	2	1	no	—
361	C₂²×C₈₉	—	2	1	no	—
362	C₂²×C₈₉	—	2	1	no	—
363	C₂²×C₈₉	—	2	1	no	—
364	C₂²×C₈₉	—	2	1	no	—
365	C₂²×C₈₉	—	2	1	no	—
366	C₂²×C₈₉	—	4	4	no	—
367	C₂²×C₈₉	—	4	4	no	—
368	C₂²×C₈₉	—	4	4	no	—
369	C₂²×C₈₉	—	4	4	no	—
370	C₂²×C₈₉	—	4	4	no	—
371	C₂²×C₈₉	—	4	4	no	—
372	C₂²×C₈₉	—	4	4	no	—
373	C₂²×C₈₉	—	8	8	no	—
374	C₂²×C₈₉	—	8	8	no	—
375	C₂²×C₈₉	#535	1	2	yes	—
376	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
377	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
378	C₄×C₈₉	—	2	1	no	—
379	C₄×C₈₉	—	2	1	no	—
380	C₄×C₈₉	—	2	1	no	—
381	C₄×C₈₉	—	2	1	no	—
382	C₄×C₈₉	—	2	1	no	—
383	C₄×C₈₉	—	2	1	no	—
384	C₄×C₈₉	—	2	1	no	—
385	C₄×C₈₉	—	4	4	no	—
386	C₄×C₈₉	—	4	4	no	—
387	C₄×C₈₉	#535	1	2	yes	—
388	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
389	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
390	C₄×C₈₉	#575	1	2	yes	—
391	C₄×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
392	#60803	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
393	C₂×C₈₉	—	2	2	no	—
394	C₂×C₈₉	—	2	2	no	—
395	C₂×C₈₉	—	4	1	no	—
396	C₂×C₈₉	—	8	4	no	—
397	C₂×C₈₉	—	8	4	no	—
398	C₂×C₈₉	C₂×#535	1	1	yes	characteristic
399	C₂×C₈₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
400	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
401	C₂×#532	C₂×C₈₉	1	1	yes	characteristic, complemented
402	C₂×#532	C₂×C₈₉	1	1	yes	characteristic, complemented
403	#3214	C₂×C₈₉	1	4	yes	complemented
404	#3213	C₂×C₈₉	1	4	yes	complemented
405	#3207	C₂×C₈₉	1	4	yes	complemented
406	#3206	C₂×C₈₉	1	2	yes	complemented
407	#3205	C₂×C₈₉	1	2	yes	complemented
408	#3151	C₂×C₈₉	1	2	yes	complemented
409	#3141	C₂×C₈₉	1	2	yes	complemented
410	#3036	C₂×C₈₉	1	4	yes	complemented
411	#3006	C₂×C₈₉	1	4	yes	complemented
412	#2920	C₂×C₈₉	1	1	yes	characteristic, complemented
413	C₈₉	#60803	1	1	yes	characteristic, direct product factor, Sylow
414	C₂²×#41	—	2	1	no	—
415	C₂²×#41	C₂²×C₈₉	1	2	yes	—
416	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	8	yes	complemented
417	#532	—	2	1	no	—
418	#532	—	2	1	no	—
419	#532	—	2	1	no	—
420	#532	—	2	1	no	—
421	#532	—	2	1	no	—
422	#532	—	2	1	no	—
423	#532	—	2	1	no	—
424	#532	—	2	1	no	—
425	#532	C₂²×C₈₉	1	2	yes	—
426	#532	C₂²×C₈₉	1	2	yes	—
427	#532	C₂²×C₈₉	1	2	yes	—
428	#532	C₂²×C₈₉	1	2	yes	—
429	#532	C₂²×C₈₉	1	2	yes	complemented
430	#532	C₂²×C₈₉	1	2	yes	complemented
431	#532	C₂²×C₈₉	1	2	yes	complemented
432	#532	C₂²×C₈₉	1	2	yes	complemented
433	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
434	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
435	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic, complemented
436	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic, complemented
437	C₂×#124	—	2	1	no	—
438	C₂×#124	C₂²×C₈₉	1	2	yes	complemented
439	C₂×#121	—	2	1	no	—
440	C₂×#121	—	2	1	no	—
441	C₂×#121	—	2	1	no	—
442	C₂×#121	C₂²×C₈₉	1	2	yes	—
443	C₂×C₄×D₄	—	2	1	no	—
444	C₂×C₄×D₄	—	2	1	no	—
445	C₂×C₄×D₄	—	2	1	no	—
446	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
447	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
448	#496	C₂²×C₈₉	1	8	yes	complemented
449	#493	C₂²×C₈₉	1	4	yes	complemented
450	#492	C₂²×C₈₉	1	4	yes	complemented
451	#489	C₂²×C₈₉	1	8	yes	complemented
452	#487	C₂²×C₈₉	1	4	yes	complemented
453	#486	C₂²×C₈₉	1	4	yes	complemented
454	#463	C₂²×C₈₉	1	16	yes	complemented
455	#461	C₂²×C₈₉	1	8	yes	complemented
456	#459	C₂²×C₈₉	1	8	yes	complemented
457	#449	C₂²×C₈₉	1	16	yes	complemented
458	#448	C₂²×C₈₉	1	8	yes	complemented
459	#447	C₂²×C₈₉	1	8	yes	complemented
460	#432	C₂²×C₈₉	1	2	yes	complemented
461	#432	C₂²×C₈₉	1	2	yes	complemented
462	#431	C₂²×C₈₉	1	2	yes	complemented
463	#431	C₂²×C₈₉	1	2	yes	complemented
464	#423	C₂²×C₈₉	1	2	yes	complemented
465	#417	C₂²×C₈₉	1	8	yes	complemented
466	#407	C₂²×C₈₉	1	2	yes	—
467	C₄×M₁₆	C₂²×C₈₉	1	2	yes	complemented
468	C₂×#41	—	2	2	no	—
469	C₂×#41	—	2	2	no	—
470	C₂×#41	—	2	2	no	—
471	C₂×#41	—	2	2	no	—
472	C₂×#41	—	2	2	no	—
473	C₂×#41	—	2	2	no	—
474	C₂×#41	—	4	8	no	—
475	C₂×#41	—	4	8	no	—
476	C₂×#41	C₂³×C₈₉	1	4	yes	—
477	C₂×#41	C₂³×C₈₉	1	4	yes	—
478	C₂²×Q₈	—	2	1	no	—
479	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
480	C₂²×D₄	—	2	2	no	—
481	C₂²×D₄	—	2	2	no	—
482	C₂²×D₄	—	2	1	no	—
483	C₂²×D₄	—	2	1	no	—
484	C₂²×D₄	—	2	1	no	—
485	C₂²×D₄	—	2	1	no	—
486	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
487	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
488	C₂³×C₄	—	2	2	no	—
489	C₂³×C₄	—	2	2	no	—
490	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
491	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
493	AGL(1,ℤ/8)	—	4	16	no	—
494	C₂×SD₁₆	C₂³×C₈₉	1	16	yes	—
495	C₂×D₈	C₂³×C₈₉	1	16	yes	—
496	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
497	C₄⋊Q₈	—	2	1	no	—
498	C₄⋊Q₈	—	2	1	no	—
499	C₄⋊Q₈	—	2	1	no	—
500	C₄⋊Q₈	—	2	1	no	—
501	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
502	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
503	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
504	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
505	#127	—	2	1	no	—
506	#127	—	2	1	no	—
507	#127	—	2	1	no	—
508	#127	—	2	1	no	—
509	#127	C₂³×C₈₉	1	2	yes	—
510	#127	C₂³×C₈₉	1	2	yes	—
511	#127	C₂³×C₈₉	1	2	yes	—
512	#127	C₂³×C₈₉	1	2	yes	—
513	#124	—	2	2	no	—
514	#124	—	2	2	no	—
515	#124	—	2	2	no	—
516	#124	—	2	2	no	—
517	#124	—	2	2	no	—
518	#124	—	2	2	no	—
519	#124	C₂³×C₈₉	1	4	yes	—
520	#124	C₂³×C₈₉	1	4	yes	—
521	#121	—	2	2	no	—
522	#121	—	2	2	no	—
523	#121	—	2	2	no	—
524	#121	—	2	2	no	—
525	#121	—	2	2	no	—
526	#121	—	2	2	no	—
527	#121	—	2	2	no	—
528	#121	—	2	2	no	—
529	#121	—	2	2	no	—
530	#121	—	2	2	no	—
531	#121	—	2	2	no	—
532	#121	—	2	2	no	—
533	#121	—	2	2	no	—
534	#121	—	2	2	no	—
535	#121	C₂³×C₈₉	1	4	yes	—
536	#121	C₂³×C₈₉	1	4	yes	—
537	C₄×D₄	—	2	2	no	—
538	C₄×D₄	—	2	2	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	2	2	no	—
541	C₄×D₄	—	2	2	no	—
542	C₄×D₄	—	2	2	no	—
543	C₄×D₄	—	2	2	no	—
544	C₄×D₄	—	2	2	no	—
545	C₄×D₄	—	2	2	no	—
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	—	2	2	no	—
548	C₄×D₄	—	2	2	no	—
549	C₄×D₄	—	2	2	no	—
550	C₄×D₄	—	2	2	no	—
551	C₄×D₄	C₂³×C₈₉	1	4	yes	—
552	C₄×D₄	C₂³×C₈₉	1	4	yes	—
553	C₂×C₄⋊C₄	—	2	1	no	—
554	C₂×C₄⋊C₄	—	2	1	no	—
555	C₂×C₄⋊C₄	—	2	1	no	—
556	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
557	C₂×C₂²⋊C₄	—	2	2	no	—
558	C₂×C₂²⋊C₄	—	2	2	no	—
559	C₂×C₂²⋊C₄	—	2	2	no	—
560	C₂×C₂²⋊C₄	—	2	2	no	—
561	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
562	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
563	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
564	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
565	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
566	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
567	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
568	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
569	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
570	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
571	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
572	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
573	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
574	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
575	#103	C₂³×C₈₉	1	16	yes	—
576	#102	C₂³×C₈₉	1	16	yes	—
577	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
578	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
579	#97	C₂³×C₈₉	1	4	yes	—
580	C₄×C₈	C₂³×C₈₉	1	4	yes	—
581	C₂⁴	—	2	2	no	—
582	C₂⁴	—	2	2	no	—
583	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
584	#41	—	2	16	no	—
585	#41	—	4	8	no	—
586	#41	—	4	8	no	—
587	#41	—	4	8	no	—
588	#41	—	4	8	no	—
589	#41	—	4	8	no	—
590	#41	—	4	8	no	—
591	#41	—	4	8	no	—
592	C₂×Q₈	—	2	2	no	—
593	C₂×Q₈	—	2	2	no	—
594	C₂×Q₈	—	2	2	no	—
595	C₂×Q₈	—	4	4	no	—
596	C₂×Q₈	—	4	4	no	—
597	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	2	no	—
604	C₂×D₄	—	2	2	no	—
605	C₂×D₄	—	2	2	no	—
606	C₂×D₄	—	2	2	no	—
607	C₂×D₄	—	2	2	no	—
608	C₂×D₄	—	2	2	no	—
609	C₂×D₄	—	2	2	no	—
610	C₂×D₄	—	2	2	no	—
611	C₂×D₄	—	2	2	no	—
612	C₂×D₄	—	2	8	no	—
613	C₂×D₄	—	4	4	no	—
614	C₂×D₄	—	4	4	no	—
615	C₂×D₄	—	4	4	no	—
616	C₂×D₄	—	4	4	no	—
617	C₂×D₄	—	4	8	no	—
618	C₂×D₄	—	4	8	no	—
619	C₂×D₄	—	4	4	no	—
620	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
621	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	2	4	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	4	2	no	—
631	C₂²×C₄	—	4	8	no	—
632	C₂²×C₄	—	4	8	no	—
633	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
634	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
635	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
636	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
637	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
638	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
639	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
640	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
641	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
642	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
643	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
644	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
645	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
646	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
647	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
648	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
650	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
651	SD₁₆	—	4	16	no	—
652	D₈	—	4	16	no	—
653	M₁₆	—	2	8	no	—
654	C₂×C₈	C₂⁴×C₈₉	1	8	yes	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	2	no	—
662	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
672	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
673	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
674	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
675	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
676	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
677	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
678	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
679	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
680	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
681	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
682	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
683	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
684	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
685	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
686	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	4	no	—
690	C₂³	—	2	4	no	—
691	C₂³	—	4	1	no	—
692	C₂³	—	4	4	no	—
693	C₂³	—	4	4	no	—
694	C₂³	—	4	4	no	—
695	C₂³	—	4	4	no	—
696	C₂³	—	4	4	no	—
697	C₂³	—	4	4	no	—
698	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
699	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
700	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
701	Q₈	—	2	8	no	—
702	Q₈	—	4	4	no	—
703	Q₈	—	4	4	no	—
704	Q₈	—	4	4	no	—
705	D₄	—	2	8	no	—
706	D₄	—	2	8	no	—
707	D₄	—	4	4	no	—
708	D₄	—	4	4	no	—
709	D₄	—	4	4	no	—
710	D₄	—	4	4	no	—
711	D₄	—	4	8	no	—
712	D₄	—	4	8	no	—
713	D₄	—	4	8	no	—
714	D₄	—	4	8	no	—
715	D₄	—	4	4	no	—
716	D₄	—	4	4	no	—
717	D₄	—	4	4	no	—
718	D₄	—	4	4	no	—
719	D₄	—	4	4	no	—
720	D₄	—	4	4	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	4	no	—
735	C₂×C₄	—	2	4	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	8	no	—
740	C₂×C₄	—	4	8	no	—
741	C₂×C₄	—	4	4	no	—
742	C₂×C₄	—	4	4	no	—
743	C₂×C₄	—	4	8	no	—
744	C₂×C₄	—	4	8	no	—
745	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	4	yes	complemented
746	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
747	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
748	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
749	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
750	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
751	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
752	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
753	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
754	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
755	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
756	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
757	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
758	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
759	C₈	—	2	8	no	—
760	C₂²	—	2	1	no	—
761	C₂²	—	2	1	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	2	1	no	—
765	C₂²	—	2	1	no	—
766	C₂²	—	2	1	no	—
767	C₂²	—	4	4	no	—
768	C₂²	—	4	4	no	—
769	C₂²	—	4	4	no	—
770	C₂²	—	4	4	no	—
771	C₂²	—	4	4	no	—
772	C₂²	—	4	4	no	—
773	C₂²	—	4	4	no	—
774	C₂²	—	8	8	no	—
775	C₂²	—	8	8	no	—
776	C₂²	#535×C₈₉	1	2	yes	—
777	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	2	yes	—
778	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
779	C₄	—	2	1	no	—
780	C₄	—	2	1	no	—
781	C₄	—	2	1	no	—
782	C₄	—	2	1	no	—
783	C₄	—	2	1	no	—
784	C₄	—	2	1	no	—
785	C₄	—	2	1	no	—
786	C₄	—	4	4	no	—
787	C₄	—	4	4	no	—
788	C₄	#535×C₈₉	1	2	yes	—
789	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	2	yes	—
790	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	2	yes	—
791	C₄	#575×C₈₉	1	2	yes	—
792	C₄	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
793	C₂	—	2	2	no	—
794	C₂	—	2	2	no	—
795	C₂	—	4	1	no	—
796	C₂	—	8	4	no	—
797	C₂	—	8	4	no	—
798	C₂	C₂×#535×C₈₉	1	1	yes	characteristic
799	C₂	C₂²×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
800	C₂	C₂×#575×C₈₉	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 ◁ C₂²×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#532×C₈₉	C₂	semidirect
2. C₂×#532×C₈₉	C₂	semidirect
3. C₈₉×#3214	C₂	semidirect
4. C₈₉×#3213	C₂	semidirect
5. C₈₉×#3207	C₂	semidirect
6. C₈₉×#3206	C₂	semidirect
7. C₈₉×#3205	C₂	semidirect
8. C₈₉×#3151	C₂	semidirect
9. C₈₉×#3141	C₂	semidirect
10. C₈₉×#3036	C₂	semidirect
11. C₈₉×#3006	C₂	semidirect
12. C₈₉×#2920	C₂	semidirect
15. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
28. #532×C₈₉	C₂²	semidirect
29. #532×C₈₉	C₂²	semidirect
30. #532×C₈₉	C₂²	semidirect
31. #532×C₈₉	C₂²	semidirect
32. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
33. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
34. C₂×#127×C₈₉	C₂²	semidirect
35. C₂×#127×C₈₉	C₂²	semidirect
37. C₂×#124×C₈₉	C₂²	semidirect
45. C₂×C₄×D₄×C₈₉	C₂²	semidirect
47. #496×C₈₉	C₂²	semidirect
48. #493×C₈₉	C₂²	semidirect
49. #492×C₈₉	C₂²	semidirect
50. #489×C₈₉	C₂²	semidirect
51. #487×C₈₉	C₂²	semidirect
52. #486×C₈₉	C₂²	semidirect
53. #463×C₈₉	C₂²	semidirect
54. #461×C₈₉	C₂²	semidirect
55. #459×C₈₉	C₂²	semidirect
56. #449×C₈₉	C₂²	semidirect
57. #448×C₈₉	C₂²	semidirect
58. #447×C₈₉	C₂²	semidirect
59. #432×C₈₉	C₂²	semidirect
60. #432×C₈₉	C₂²	semidirect
61. #431×C₈₉	C₂²	semidirect
62. #431×C₈₉	C₂²	semidirect
63. #423×C₈₉	C₂²	semidirect
64. #417×C₈₉	C₂²	semidirect
66. C₄×M₁₆×C₈₉	C₂²	semidirect
344. C₂×C₄×C₈₉	AGL(1,ℤ/8)	semidirect
392. #60803	C₈₉	direct (N × H)
401. C₂×#532	C₂×C₈₉	semidirect
402. C₂×#532	C₂×C₈₉	semidirect
403. #3214	C₂×C₈₉	semidirect
404. #3213	C₂×C₈₉	semidirect
405. #3207	C₂×C₈₉	semidirect
406. #3206	C₂×C₈₉	semidirect
407. #3205	C₂×C₈₉	semidirect
408. #3151	C₂×C₈₉	semidirect
409. #3141	C₂×C₈₉	semidirect
410. #3036	C₂×C₈₉	semidirect
411. #3006	C₂×C₈₉	semidirect
412. #2920	C₂×C₈₉	semidirect
413. C₈₉	#60803	direct (N × H)
416. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
429. #532	C₂²×C₈₉	semidirect
430. #532	C₂²×C₈₉	semidirect
431. #532	C₂²×C₈₉	semidirect
432. #532	C₂²×C₈₉	semidirect
433. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
434. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
435. C₂×#127	C₂²×C₈₉	semidirect
436. C₂×#127	C₂²×C₈₉	semidirect
438. C₂×#124	C₂²×C₈₉	semidirect
446. C₂×C₄×D₄	C₂²×C₈₉	semidirect
448. #496	C₂²×C₈₉	semidirect
449. #493	C₂²×C₈₉	semidirect
450. #492	C₂²×C₈₉	semidirect
451. #489	C₂²×C₈₉	semidirect
452. #487	C₂²×C₈₉	semidirect
453. #486	C₂²×C₈₉	semidirect
454. #463	C₂²×C₈₉	semidirect
455. #461	C₂²×C₈₉	semidirect
456. #459	C₂²×C₈₉	semidirect
457. #449	C₂²×C₈₉	semidirect
458. #448	C₂²×C₈₉	semidirect
459. #447	C₂²×C₈₉	semidirect
460. #432	C₂²×C₈₉	semidirect
461. #432	C₂²×C₈₉	semidirect
462. #431	C₂²×C₈₉	semidirect
463. #431	C₂²×C₈₉	semidirect
464. #423	C₂²×C₈₉	semidirect
465. #417	C₂²×C₈₉	semidirect
467. C₄×M₁₆	C₂²×C₈₉	semidirect
745. C₂×C₄	AGL(1,ℤ/8)×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#532×C₈₉	2
C₈₉×#3214	2
C₈₉×#3213	2
C₈₉×#3207	2
C₈₉×#3206	2
C₈₉×#3205	2
C₈₉×#3151	2
C₈₉×#3141	2
C₈₉×#3036	2
C₈₉×#3006	2
C₈₉×#2920	2
#60803	89

Subgroups — C89×#60803 #36438651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60803 #36438651