Subgroups — C₈₉×#61963 #36439811

Order 22784.

2168 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3399	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3368	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3324	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3318	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3274	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3265	C₂	1	4	yes	maximal, complemented
9	C₈₉×#3251	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3245	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3217	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3205	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3115	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3038	C₂	1	2	yes	maximal, complemented
16	C₂×#460×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2989	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×H(5,𝔽₂)×C₈₉	—	2	1	no	—
19	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	4	yes	complemented
20	C₂²×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
21	#559×C₈₉	—	2	1	no	—
22	#559×C₈₉	C₂²	1	1	yes	characteristic, complemented
23	#557×C₈₉	C₂²	1	1	yes	characteristic, complemented
24	#556×C₈₉	—	2	1	no	—
25	#556×C₈₉	C₂²	1	1	yes	characteristic, complemented
26	#553×C₈₉	—	2	2	no	—
27	#553×C₈₉	C₂²	1	2	yes	complemented
28	#550×C₈₉	—	2	1	no	—
29	#550×C₈₉	C₂²	1	2	yes	—
30	#550×C₈₉	C₂²	1	1	yes	characteristic, complemented
31	#548×C₈₉	C₂²	1	2	yes	complemented
32	D₄²×C₈₉	—	2	2	no	—
33	D₄²×C₈₉	—	2	1	no	—
34	D₄²×C₈₉	C₂²	1	4	yes	—
35	D₄²×C₈₉	C₂²	1	2	yes	—
36	#535×C₈₉	—	2	1	no	—
37	#535×C₈₉	—	2	2	no	—
38	#532×C₈₉	—	2	1	no	—
39	#532×C₈₉	C₂²	1	1	yes	characteristic
40	#532×C₈₉	C₂²	1	2	yes	—
41	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#127×C₈₉	C₂²	1	2	yes	—
44	#529×C₈₉	—	2	2	no	—
45	#529×C₈₉	C₂²	1	2	yes	complemented
46	C₄×#41×C₈₉	—	2	1	no	—
47	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
48	C₄×#41×C₈₉	C₂²	1	2	yes	complemented
49	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
50	#496×C₈₉	C₂²	1	4	yes	complemented
51	#493×C₈₉	C₂²	1	2	yes	complemented
52	#490×C₈₉	C₂²	1	4	yes	complemented
53	#486×C₈₉	C₂²	1	2	yes	complemented
54	#482×C₈₉	C₂²	1	4	yes	complemented
55	#481×C₈₉	C₂²	1	2	yes	complemented
56	#478×C₈₉	C₂²	1	4	yes	complemented
57	#475×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#475×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#474×C₈₉	C₂²	1	2	yes	complemented
60	#474×C₈₉	C₂²	1	2	yes	complemented
61	#469×C₈₉	C₂²	1	4	yes	complemented
62	#468×C₈₉	C₂²	1	4	yes	complemented
63	#466×C₈₉	C₂²	1	4	yes	complemented
64	#463×C₈₉	C₂²	1	4	yes	complemented
65	#460×C₈₉	C₂²	1	2	yes	complemented
66	#460×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#460×C₈₉	C₂²	1	1	yes	characteristic, complemented
68	#460×C₈₉	C₂²	1	4	yes	complemented
69	#460×C₈₉	C₂²	1	2	yes	complemented
70	#460×C₈₉	C₂²	1	2	yes	complemented
71	#460×C₈₉	C₂²	1	2	yes	complemented
72	#459×C₈₉	C₂²	1	4	yes	complemented
73	#459×C₈₉	C₂²	1	2	yes	complemented
74	#459×C₈₉	C₂²	1	2	yes	complemented
75	#459×C₈₉	C₂²	1	2	yes	complemented
76	#459×C₈₉	C₂²	1	2	yes	complemented
77	#450×C₈₉	C₂²	1	4	yes	complemented
78	#449×C₈₉	C₂²	1	4	yes	complemented
79	#448×C₈₉	C₂²	1	2	yes	complemented
80	#447×C₈₉	C₂²	1	4	yes	complemented
81	#447×C₈₉	C₂²	1	4	yes	complemented
82	#446×C₈₉	C₂²	1	2	yes	complemented
83	#442×C₈₉	C₂²	1	4	yes	complemented
84	#440×C₈₉	C₂²	1	4	yes	complemented
85	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
86	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
87	#436×C₈₉	C₂²	1	2	yes	complemented
88	#435×C₈₉	C₂²	1	4	yes	complemented
89	#432×C₈₉	C₂²	1	2	yes	complemented
90	#431×C₈₉	C₂²	1	1	yes	characteristic, complemented
91	#423×C₈₉	C₂²	1	2	yes	complemented
92	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
93	#418×C₈₉	C₂²	1	4	yes	complemented
94	C₂×#102×C₈₉	C₂²	1	2	yes	complemented
95	H(5,𝔽₂)×C₈₉	—	4	8	no	—
96	C₂×#41×C₈₉	—	2	2	no	—
97	C₂×#41×C₈₉	—	2	1	no	—
98	C₂×#41×C₈₉	—	2	2	no	—
99	C₂×#41×C₈₉	—	2	1	no	—
100	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
101	C₂×#41×C₈₉	C₂³	1	2	yes	—
102	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₈₉	—	2	4	no	—
104	C₂²×D₄×C₈₉	—	2	2	no	—
105	C₂²×D₄×C₈₉	—	2	2	no	—
106	C₂²×D₄×C₈₉	—	2	1	no	—
107	C₂²×D₄×C₈₉	—	2	1	no	—
108	C₂²×D₄×C₈₉	—	2	2	no	—
109	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
110	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
111	AGL(1,ℤ/8)×C₈₉	—	4	8	no	—
112	C₂×SD₁₆×C₈₉	—	4	4	no	—
113	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
114	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
115	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
116	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
117	C₂×D₈×C₈₉	C₂³	1	4	yes	—
118	C₂×D₈×C₈₉	C₂³	1	4	yes	—
119	C₂×D₈×C₈₉	C₂³	1	4	yes	—
120	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
121	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
122	C₄⋊Q₈×C₈₉	—	2	1	no	—
123	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
124	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
125	#127×C₈₉	—	2	1	no	—
126	#127×C₈₉	—	2	2	no	—
127	#127×C₈₉	—	2	1	no	—
128	#127×C₈₉	—	2	2	no	—
129	#127×C₈₉	—	2	1	no	—
130	#127×C₈₉	C₂³	1	2	yes	—
131	#127×C₈₉	C₂³	1	1	yes	characteristic
132	#127×C₈₉	C₂³	1	1	yes	characteristic
133	#127×C₈₉	C₂³	1	4	yes	—
134	#127×C₈₉	C₂³	1	2	yes	—
135	#126×C₈₉	—	2	2	no	—
136	#126×C₈₉	—	2	2	no	—
137	#126×C₈₉	—	2	2	no	—
138	#125×C₈₉	—	2	2	no	—
139	#125×C₈₉	C₂³	1	2	yes	—
140	#124×C₈₉	—	2	1	no	—
141	#124×C₈₉	—	2	1	no	—
142	#124×C₈₉	—	2	2	no	—
143	#124×C₈₉	—	2	2	no	—
144	#124×C₈₉	—	2	1	no	—
145	#124×C₈₉	—	2	1	no	—
146	#124×C₈₉	C₂³	1	2	yes	—
147	#123×C₈₉	—	2	2	no	—
148	#123×C₈₉	—	2	2	no	—
149	#123×C₈₉	—	2	2	no	—
150	C₂²⋊Q₈×C₈₉	—	2	2	no	—
151	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
152	#121×C₈₉	—	2	2	no	—
153	#121×C₈₉	—	2	2	no	—
154	#121×C₈₉	—	2	1	no	—
155	#121×C₈₉	—	2	2	no	—
156	#121×C₈₉	—	2	1	no	—
157	#121×C₈₉	—	2	2	no	—
158	#121×C₈₉	—	2	4	no	—
159	#121×C₈₉	—	2	2	no	—
160	#121×C₈₉	—	2	4	no	—
161	#121×C₈₉	—	2	2	no	—
162	#121×C₈₉	C₂³	1	2	yes	—
163	#121×C₈₉	C₂³	1	2	yes	—
164	#121×C₈₉	C₂³	1	2	yes	—
165	#121×C₈₉	C₂³	1	4	yes	—
166	#120×C₈₉	—	2	4	no	—
167	#120×C₈₉	—	2	4	no	—
168	#120×C₈₉	—	2	4	no	—
169	C₄×Q₈×C₈₉	—	2	1	no	—
170	C₄×Q₈×C₈₉	—	2	1	no	—
171	C₄×Q₈×C₈₉	—	2	1	no	—
172	C₄×Q₈×C₈₉	—	2	1	no	—
173	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
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×Q₈×C₈₉	C₂³	1	1	yes	characteristic
179	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₈₉	—	2	2	no	—
181	C₄×D₄×C₈₉	—	2	2	no	—
182	C₄×D₄×C₈₉	—	2	2	no	—
183	C₄×D₄×C₈₉	—	2	1	no	—
184	C₄×D₄×C₈₉	—	2	1	no	—
185	C₄×D₄×C₈₉	—	2	2	no	—
186	C₄×D₄×C₈₉	—	2	2	no	—
187	C₄×D₄×C₈₉	—	2	1	no	—
188	C₄×D₄×C₈₉	—	2	2	no	—
189	C₄×D₄×C₈₉	—	2	1	no	—
190	C₄×D₄×C₈₉	D₄	1	2	yes	—
191	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
192	C₄×D₄×C₈₉	C₂³	1	2	yes	—
193	C₄×D₄×C₈₉	C₂³	1	4	yes	—
194	C₄×D₄×C₈₉	C₂³	1	2	yes	—
195	C₄×D₄×C₈₉	C₂³	1	2	yes	—
196	C₄×D₄×C₈₉	C₂³	1	2	yes	—
197	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
198	#117×C₈₉	—	2	2	no	—
199	#117×C₈₉	—	2	2	no	—
200	#117×C₈₉	D₄	1	1	yes	characteristic
201	#117×C₈₉	D₄	1	2	yes	—
202	#117×C₈₉	C₂³	1	2	yes	—
203	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
204	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₈₉	—	2	1	no	—
206	C₂×C₄²×C₈₉	—	2	2	no	—
207	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
209	#107×C₈₉	C₂³	1	4	yes	—
210	#106×C₈₉	C₂³	1	2	yes	—
211	#106×C₈₉	C₂³	1	2	yes	—
212	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
213	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
214	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
215	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
216	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
217	#103×C₈₉	C₂³	1	2	yes	—
218	#103×C₈₉	C₂³	1	2	yes	—
219	#102×C₈₉	C₂³	1	4	yes	—
220	#102×C₈₉	C₂³	1	4	yes	—
221	#102×C₈₉	C₂³	1	2	yes	—
222	#102×C₈₉	C₂³	1	4	yes	—
223	#102×C₈₉	C₂³	1	4	yes	—
224	#102×C₈₉	C₂³	1	2	yes	—
225	#102×C₈₉	C₂³	1	4	yes	—
226	#102×C₈₉	C₂³	1	4	yes	—
227	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
228	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
229	#97×C₈₉	C₂³	1	4	yes	—
230	C₄×C₈×C₈₉	C₂³	1	2	yes	—
231	C₂⁴×C₈₉	—	2	4	no	—
232	C₂⁴×C₈₉	—	2	2	no	—
233	#41×C₈₉	—	2	4	no	—
234	#41×C₈₉	—	2	4	no	—
235	#41×C₈₉	—	4	2	no	—
236	#41×C₈₉	—	4	8	no	—
237	#41×C₈₉	—	4	8	no	—
238	#41×C₈₉	—	4	4	no	—
239	#41×C₈₉	—	4	4	no	—
240	C₂×Q₈×C₈₉	—	2	1	no	—
241	C₂×Q₈×C₈₉	—	2	1	no	—
242	C₂×Q₈×C₈₉	—	2	1	no	—
243	C₂×Q₈×C₈₉	—	2	2	no	—
244	C₂×Q₈×C₈₉	—	4	1	no	—
245	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
246	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
247	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
248	C₂×D₄×C₈₉	—	2	2	no	—
249	C₂×D₄×C₈₉	—	2	2	no	—
250	C₂×D₄×C₈₉	—	2	4	no	—
251	C₂×D₄×C₈₉	—	2	2	no	—
252	C₂×D₄×C₈₉	—	2	2	no	—
253	C₂×D₄×C₈₉	—	2	1	no	—
254	C₂×D₄×C₈₉	—	2	2	no	—
255	C₂×D₄×C₈₉	—	2	1	no	—
256	C₂×D₄×C₈₉	—	2	4	no	—
257	C₂×D₄×C₈₉	—	2	2	no	—
258	C₂×D₄×C₈₉	—	2	1	no	—
259	C₂×D₄×C₈₉	—	2	2	no	—
260	C₂×D₄×C₈₉	—	2	1	no	—
261	C₂×D₄×C₈₉	—	2	4	no	—
262	C₂×D₄×C₈₉	—	2	2	no	—
263	C₂×D₄×C₈₉	—	2	4	no	—
264	C₂×D₄×C₈₉	—	2	2	no	—
265	C₂×D₄×C₈₉	—	4	2	no	—
266	C₂×D₄×C₈₉	—	4	4	no	—
267	C₂×D₄×C₈₉	—	4	2	no	—
268	C₂×D₄×C₈₉	—	4	4	no	—
269	C₂×D₄×C₈₉	—	4	8	no	—
270	C₂×D₄×C₈₉	—	4	16	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	—	8	2	no	—
275	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
276	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
277	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
278	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
279	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₈₉	—	2	1	no	—
281	C₂²×C₄×C₈₉	—	2	1	no	—
282	C₂²×C₄×C₈₉	—	2	2	no	—
283	C₂²×C₄×C₈₉	—	2	2	no	—
284	C₂²×C₄×C₈₉	—	2	4	no	—
285	C₂²×C₄×C₈₉	—	2	2	no	—
286	C₂²×C₄×C₈₉	—	2	2	no	—
287	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
288	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
290	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
293	SD₁₆×C₈₉	—	2	8	no	—
294	SD₁₆×C₈₉	—	2	4	no	—
295	SD₁₆×C₈₉	—	4	4	no	—
296	SD₁₆×C₈₉	—	4	2	no	—
297	D₈×C₈₉	—	4	4	no	—
298	D₈×C₈₉	—	4	4	no	—
299	D₈×C₈₉	—	4	4	no	—
300	M₁₆×C₈₉	—	4	4	no	—
301	C₂×C₈×C₈₉	—	4	2	no	—
302	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
303	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
304	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
305	C₄⋊C₄×C₈₉	—	2	1	no	—
306	C₄⋊C₄×C₈₉	—	2	1	no	—
307	C₄⋊C₄×C₈₉	—	2	1	no	—
308	C₄⋊C₄×C₈₉	—	2	1	no	—
309	C₄⋊C₄×C₈₉	—	2	1	no	—
310	C₄⋊C₄×C₈₉	—	2	2	no	—
311	C₄⋊C₄×C₈₉	—	2	2	no	—
312	C₄⋊C₄×C₈₉	—	2	2	no	—
313	C₄⋊C₄×C₈₉	—	2	1	no	—
314	C₄⋊C₄×C₈₉	—	2	1	no	—
315	C₄⋊C₄×C₈₉	—	2	2	no	—
316	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
317	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
318	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
319	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
320	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
321	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
322	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
323	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
324	C₂²⋊C₄×C₈₉	—	2	2	no	—
325	C₂²⋊C₄×C₈₉	—	2	2	no	—
326	C₂²⋊C₄×C₈₉	—	2	2	no	—
327	C₂²⋊C₄×C₈₉	—	2	2	no	—
328	C₂²⋊C₄×C₈₉	—	2	2	no	—
329	C₂²⋊C₄×C₈₉	—	2	2	no	—
330	C₂²⋊C₄×C₈₉	—	2	4	no	—
331	C₂²⋊C₄×C₈₉	—	2	2	no	—
332	C₂²⋊C₄×C₈₉	—	2	2	no	—
333	C₂²⋊C₄×C₈₉	—	2	2	no	—
334	C₂²⋊C₄×C₈₉	—	2	4	no	—
335	C₂²⋊C₄×C₈₉	—	2	2	no	—
336	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
337	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
338	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
339	C₄²×C₈₉	—	2	1	no	—
340	C₄²×C₈₉	—	2	1	no	—
341	C₄²×C₈₉	—	2	2	no	—
342	C₄²×C₈₉	—	2	2	no	—
343	C₄²×C₈₉	—	2	1	no	—
344	C₄²×C₈₉	—	2	1	no	—
345	C₄²×C₈₉	C₂×D₄	1	2	yes	—
346	C₄²×C₈₉	C₂×D₄	1	2	yes	—
347	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
348	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
349	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
350	C₄²×C₈₉	C₂⁴	1	2	yes	—
351	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
352	C₂³×C₈₉	—	2	2	no	—
353	C₂³×C₈₉	—	2	2	no	—
354	C₂³×C₈₉	—	2	4	no	—
355	C₂³×C₈₉	—	4	8	no	—
356	C₂³×C₈₉	—	4	4	no	—
357	C₂³×C₈₉	—	8	2	no	—
358	C₂³×C₈₉	—	8	4	no	—
359	C₂³×C₈₉	—	8	2	no	—
360	C₂³×C₈₉	—	8	4	no	—
361	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
362	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
363	Q₈×C₈₉	—	2	2	no	—
364	Q₈×C₈₉	—	2	1	no	—
365	Q₈×C₈₉	—	2	1	no	—
366	Q₈×C₈₉	—	2	1	no	—
367	Q₈×C₈₉	—	4	2	no	—
368	Q₈×C₈₉	—	4	2	no	—
369	Q₈×C₈₉	—	4	2	no	—
370	Q₈×C₈₉	H(5,𝔽₂)	1	2	yes	complemented
371	D₄×C₈₉	—	2	4	no	—
372	D₄×C₈₉	—	2	2	no	—
373	D₄×C₈₉	—	2	2	no	—
374	D₄×C₈₉	—	2	2	no	—
375	D₄×C₈₉	—	2	4	no	—
376	D₄×C₈₉	—	2	2	no	—
377	D₄×C₈₉	—	2	4	no	—
378	D₄×C₈₉	—	2	2	no	—
379	D₄×C₈₉	—	4	4	no	—
380	D₄×C₈₉	—	4	8	no	—
381	D₄×C₈₉	—	4	4	no	—
382	D₄×C₈₉	—	4	2	no	—
383	D₄×C₈₉	—	4	8	no	—
384	D₄×C₈₉	—	4	4	no	—
385	D₄×C₈₉	—	4	4	no	—
386	D₄×C₈₉	—	4	2	no	—
387	D₄×C₈₉	—	4	4	no	—
388	D₄×C₈₉	—	4	4	no	—
389	D₄×C₈₉	—	4	2	no	—
390	D₄×C₈₉	—	8	1	no	—
391	D₄×C₈₉	—	8	4	no	—
392	D₄×C₈₉	—	8	2	no	—
393	D₄×C₈₉	—	8	4	no	—
394	D₄×C₈₉	—	8	2	no	—
395	D₄×C₈₉	—	8	2	no	—
396	C₂×C₄×C₈₉	—	2	1	no	—
397	C₂×C₄×C₈₉	—	2	4	no	—
398	C₂×C₄×C₈₉	—	2	1	no	—
399	C₂×C₄×C₈₉	—	2	2	no	—
400	C₂×C₄×C₈₉	—	2	1	no	—
401	C₂×C₄×C₈₉	—	2	2	no	—
402	C₂×C₄×C₈₉	—	2	1	no	—
403	C₂×C₄×C₈₉	—	2	1	no	—
404	C₂×C₄×C₈₉	—	2	2	no	—
405	C₂×C₄×C₈₉	—	2	1	no	—
406	C₂×C₄×C₈₉	—	2	2	no	—
407	C₂×C₄×C₈₉	—	4	2	no	—
408	C₂×C₄×C₈₉	—	4	1	no	—
409	C₂×C₄×C₈₉	—	4	4	no	—
410	C₂×C₄×C₈₉	—	4	2	no	—
411	C₂×C₄×C₈₉	—	4	8	no	—
412	C₂×C₄×C₈₉	—	4	4	no	—
413	C₂×C₄×C₈₉	—	4	4	no	—
414	C₂×C₄×C₈₉	—	8	2	no	—
415	C₂×C₄×C₈₉	—	8	1	no	—
416	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	4	yes	complemented
417	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
423	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
426	C₈×C₈₉	—	2	4	no	—
427	C₈×C₈₉	—	2	2	no	—
428	C₈×C₈₉	—	2	2	no	—
429	C₂²×C₈₉	—	2	1	no	—
430	C₂²×C₈₉	—	2	1	no	—
431	C₂²×C₈₉	—	2	2	no	—
432	C₂²×C₈₉	—	2	2	no	—
433	C₂²×C₈₉	—	2	2	no	—
434	C₂²×C₈₉	—	4	2	no	—
435	C₂²×C₈₉	—	4	4	no	—
436	C₂²×C₈₉	—	4	2	no	—
437	C₂²×C₈₉	—	4	2	no	—
438	C₂²×C₈₉	—	4	2	no	—
439	C₂²×C₈₉	—	4	4	no	—
440	C₂²×C₈₉	—	4	4	no	—
441	C₂²×C₈₉	—	4	2	no	—
442	C₂²×C₈₉	—	4	2	no	—
443	C₂²×C₈₉	—	16	4	no	—
444	C₂²×C₈₉	—	16	8	no	—
445	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
446	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
447	C₄×C₈₉	—	2	1	no	—
448	C₄×C₈₉	—	2	2	no	—
449	C₄×C₈₉	—	2	1	no	—
450	C₄×C₈₉	—	2	2	no	—
451	C₄×C₈₉	—	2	1	no	—
452	C₄×C₈₉	—	2	2	no	—
453	C₄×C₈₉	—	2	2	no	—
454	C₄×C₈₉	—	4	1	no	—
455	C₄×C₈₉	—	4	1	no	—
456	C₄×C₈₉	—	4	1	no	—
457	C₄×C₈₉	—	4	2	no	—
458	C₄×C₈₉	—	4	2	no	—
459	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
460	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
461	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
462	C₄×C₈₉	#585	1	1	yes	characteristic
463	#61963	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
464	C₂×C₈₉	—	2	2	no	—
465	C₂×C₈₉	—	4	2	no	—
466	C₂×C₈₉	—	8	2	no	—
467	C₂×C₈₉	—	8	4	no	—
468	C₂×C₈₉	—	8	2	no	—
469	C₂×C₈₉	#3488	1	1	yes	characteristic
470	C₂×C₈₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
471	C₂×C₈₉	#3585	1	1	yes	characteristic
472	#3498	C₂×C₈₉	1	1	yes	characteristic, complemented
473	#3480	C₂×C₈₉	1	1	yes	characteristic, complemented
474	#3399	C₂×C₈₉	1	2	yes	complemented
475	#3368	C₂×C₈₉	1	2	yes	complemented
476	#3324	C₂×C₈₉	1	2	yes	complemented
477	#3318	C₂×C₈₉	1	4	yes	complemented
478	#3274	C₂×C₈₉	1	2	yes	complemented
479	#3265	C₂×C₈₉	1	4	yes	complemented
480	#3251	C₂×C₈₉	1	2	yes	complemented
481	#3245	C₂×C₈₉	1	1	yes	characteristic, complemented
482	#3217	C₂×C₈₉	1	2	yes	complemented
483	#3205	C₂×C₈₉	1	1	yes	characteristic, complemented
484	#3115	C₂×C₈₉	1	2	yes	complemented
485	#3103	C₂×C₈₉	1	1	yes	characteristic, complemented
486	#3038	C₂×C₈₉	1	2	yes	complemented
487	C₂×#460	C₂×C₈₉	1	1	yes	characteristic, complemented
488	#2989	C₂×C₈₉	1	1	yes	characteristic, complemented
489	C₈₉	#61963	1	1	yes	characteristic, direct product factor, Sylow
490	C₂×H(5,𝔽₂)	—	2	1	no	—
491	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	4	yes	complemented
492	C₂²×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
493	#559	—	2	1	no	—
494	#559	C₂²×C₈₉	1	1	yes	characteristic, complemented
495	#557	C₂²×C₈₉	1	1	yes	characteristic, complemented
496	#556	—	2	1	no	—
497	#556	C₂²×C₈₉	1	1	yes	characteristic, complemented
498	#553	—	2	2	no	—
499	#553	C₂²×C₈₉	1	2	yes	complemented
500	#550	—	2	1	no	—
501	#550	C₂²×C₈₉	1	2	yes	—
502	#550	C₂²×C₈₉	1	1	yes	characteristic, complemented
503	#548	C₂²×C₈₉	1	2	yes	complemented
504	D₄²	—	2	2	no	—
505	D₄²	—	2	1	no	—
506	D₄²	C₂²×C₈₉	1	4	yes	—
507	D₄²	C₂²×C₈₉	1	2	yes	—
508	#535	—	2	1	no	—
509	#535	—	2	2	no	—
510	#532	—	2	1	no	—
511	#532	C₂²×C₈₉	1	1	yes	characteristic
512	#532	C₂²×C₈₉	1	2	yes	—
513	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
514	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
515	C₂×#127	C₂²×C₈₉	1	2	yes	—
516	#529	—	2	2	no	—
517	#529	C₂²×C₈₉	1	2	yes	complemented
518	C₄×#41	—	2	1	no	—
519	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
520	C₄×#41	C₂²×C₈₉	1	2	yes	complemented
521	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
522	#496	C₂²×C₈₉	1	4	yes	complemented
523	#493	C₂²×C₈₉	1	2	yes	complemented
524	#490	C₂²×C₈₉	1	4	yes	complemented
525	#486	C₂²×C₈₉	1	2	yes	complemented
526	#482	C₂²×C₈₉	1	4	yes	complemented
527	#481	C₂²×C₈₉	1	2	yes	complemented
528	#478	C₂²×C₈₉	1	4	yes	complemented
529	#475	C₂²×C₈₉	1	1	yes	characteristic, complemented
530	#475	C₂²×C₈₉	1	1	yes	characteristic, complemented
531	#474	C₂²×C₈₉	1	2	yes	complemented
532	#474	C₂²×C₈₉	1	2	yes	complemented
533	#469	C₂²×C₈₉	1	4	yes	complemented
534	#468	C₂²×C₈₉	1	4	yes	complemented
535	#466	C₂²×C₈₉	1	4	yes	complemented
536	#463	C₂²×C₈₉	1	4	yes	complemented
537	#460	C₂²×C₈₉	1	1	yes	characteristic, complemented
538	#460	C₂²×C₈₉	1	1	yes	characteristic, complemented
539	#460	C₂²×C₈₉	1	4	yes	complemented
540	#460	C₂²×C₈₉	1	2	yes	complemented
541	#460	C₂²×C₈₉	1	2	yes	complemented
542	#460	C₂²×C₈₉	1	2	yes	complemented
543	#460	C₂²×C₈₉	1	2	yes	complemented
544	#459	C₂²×C₈₉	1	2	yes	complemented
545	#459	C₂²×C₈₉	1	2	yes	complemented
546	#459	C₂²×C₈₉	1	4	yes	complemented
547	#459	C₂²×C₈₉	1	2	yes	complemented
548	#459	C₂²×C₈₉	1	2	yes	complemented
549	#450	C₂²×C₈₉	1	4	yes	complemented
550	#449	C₂²×C₈₉	1	4	yes	complemented
551	#448	C₂²×C₈₉	1	2	yes	complemented
552	#447	C₂²×C₈₉	1	4	yes	complemented
553	#447	C₂²×C₈₉	1	4	yes	complemented
554	#446	C₂²×C₈₉	1	2	yes	complemented
555	#442	C₂²×C₈₉	1	4	yes	complemented
556	#440	C₂²×C₈₉	1	4	yes	complemented
557	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
558	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
559	#436	C₂²×C₈₉	1	2	yes	complemented
560	#435	C₂²×C₈₉	1	4	yes	complemented
561	#432	C₂²×C₈₉	1	2	yes	complemented
562	#431	C₂²×C₈₉	1	1	yes	characteristic, complemented
563	#423	C₂²×C₈₉	1	2	yes	complemented
564	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
565	#418	C₂²×C₈₉	1	4	yes	complemented
566	C₂×#102	C₂²×C₈₉	1	2	yes	complemented
567	H(5,𝔽₂)	—	4	8	no	—
568	C₂×#41	—	2	2	no	—
569	C₂×#41	—	2	1	no	—
570	C₂×#41	—	2	2	no	—
571	C₂×#41	—	2	1	no	—
572	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
573	C₂×#41	C₂³×C₈₉	1	2	yes	—
574	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
575	C₂²×D₄	—	2	4	no	—
576	C₂²×D₄	—	2	2	no	—
577	C₂²×D₄	—	2	2	no	—
578	C₂²×D₄	—	2	1	no	—
579	C₂²×D₄	—	2	1	no	—
580	C₂²×D₄	—	2	2	no	—
581	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
582	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
583	AGL(1,ℤ/8)	—	4	8	no	—
584	C₂×SD₁₆	—	4	4	no	—
585	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
586	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
587	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
588	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
589	C₂×D₈	C₂³×C₈₉	1	4	yes	—
590	C₂×D₈	C₂³×C₈₉	1	4	yes	—
591	C₂×D₈	C₂³×C₈₉	1	4	yes	—
592	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
593	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
594	C₄⋊Q₈	—	2	1	no	—
595	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
596	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
597	#127	—	2	1	no	—
598	#127	—	2	2	no	—
599	#127	—	2	1	no	—
600	#127	—	2	2	no	—
601	#127	—	2	1	no	—
602	#127	C₂³×C₈₉	1	2	yes	—
603	#127	C₂³×C₈₉	1	1	yes	characteristic
604	#127	C₂³×C₈₉	1	4	yes	—
605	#127	C₂³×C₈₉	1	2	yes	—
606	#127	C₂³×C₈₉	1	1	yes	characteristic
607	#126	—	2	2	no	—
608	#126	—	2	2	no	—
609	#126	—	2	2	no	—
610	#125	—	2	2	no	—
611	#125	C₂³×C₈₉	1	2	yes	—
612	#124	—	2	1	no	—
613	#124	—	2	1	no	—
614	#124	—	2	2	no	—
615	#124	—	2	2	no	—
616	#124	—	2	1	no	—
617	#124	—	2	1	no	—
618	#124	C₂³×C₈₉	1	2	yes	—
619	#123	—	2	2	no	—
620	#123	—	2	2	no	—
621	#123	—	2	2	no	—
622	C₂²⋊Q₈	—	2	2	no	—
623	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
624	#121	—	2	2	no	—
625	#121	—	2	2	no	—
626	#121	—	2	1	no	—
627	#121	—	2	2	no	—
628	#121	—	2	1	no	—
629	#121	—	2	2	no	—
630	#121	—	2	4	no	—
631	#121	—	2	2	no	—
632	#121	—	2	4	no	—
633	#121	—	2	2	no	—
634	#121	C₂³×C₈₉	1	2	yes	—
635	#121	C₂³×C₈₉	1	2	yes	—
636	#121	C₂³×C₈₉	1	4	yes	—
637	#121	C₂³×C₈₉	1	2	yes	—
638	#120	—	2	4	no	—
639	#120	—	2	4	no	—
640	#120	—	2	4	no	—
641	C₄×Q₈	—	2	1	no	—
642	C₄×Q₈	—	2	1	no	—
643	C₄×Q₈	—	2	1	no	—
644	C₄×Q₈	—	2	1	no	—
645	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
646	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
647	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
648	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
649	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
650	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
651	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
652	C₄×D₄	—	2	2	no	—
653	C₄×D₄	—	2	2	no	—
654	C₄×D₄	—	2	2	no	—
655	C₄×D₄	—	2	1	no	—
656	C₄×D₄	—	2	1	no	—
657	C₄×D₄	—	2	2	no	—
658	C₄×D₄	—	2	2	no	—
659	C₄×D₄	—	2	1	no	—
660	C₄×D₄	—	2	2	no	—
661	C₄×D₄	—	2	1	no	—
662	C₄×D₄	D₄×C₈₉	1	2	yes	—
663	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
664	C₄×D₄	C₂³×C₈₉	1	2	yes	—
665	C₄×D₄	C₂³×C₈₉	1	2	yes	—
666	C₄×D₄	C₂³×C₈₉	1	2	yes	—
667	C₄×D₄	C₂³×C₈₉	1	4	yes	—
668	C₄×D₄	C₂³×C₈₉	1	2	yes	—
669	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
670	#117	—	2	2	no	—
671	#117	—	2	2	no	—
672	#117	D₄×C₈₉	1	1	yes	characteristic
673	#117	D₄×C₈₉	1	2	yes	—
674	#117	C₂³×C₈₉	1	2	yes	—
675	C₂×C₄⋊C₄	—	2	1	no	—
676	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
677	C₂×C₄²	—	2	1	no	—
678	C₂×C₄²	—	2	2	no	—
679	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
680	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
681	#107	C₂³×C₈₉	1	4	yes	—
682	#106	C₂³×C₈₉	1	2	yes	—
683	#106	C₂³×C₈₉	1	2	yes	—
684	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
685	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
686	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
687	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
688	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
689	#103	C₂³×C₈₉	1	2	yes	—
690	#103	C₂³×C₈₉	1	2	yes	—
691	#102	C₂³×C₈₉	1	4	yes	—
692	#102	C₂³×C₈₉	1	4	yes	—
693	#102	C₂³×C₈₉	1	2	yes	—
694	#102	C₂³×C₈₉	1	4	yes	—
695	#102	C₂³×C₈₉	1	4	yes	—
696	#102	C₂³×C₈₉	1	2	yes	—
697	#102	C₂³×C₈₉	1	4	yes	—
698	#102	C₂³×C₈₉	1	4	yes	—
699	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
700	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
701	#97	C₂³×C₈₉	1	4	yes	—
702	C₄×C₈	C₂³×C₈₉	1	2	yes	—
703	C₂⁴	—	2	4	no	—
704	C₂⁴	—	2	2	no	—
705	#41	—	2	4	no	—
706	#41	—	2	4	no	—
707	#41	—	4	2	no	—
708	#41	—	4	8	no	—
709	#41	—	4	8	no	—
710	#41	—	4	4	no	—
711	#41	—	4	4	no	—
712	C₂×Q₈	—	2	1	no	—
713	C₂×Q₈	—	2	1	no	—
714	C₂×Q₈	—	2	1	no	—
715	C₂×Q₈	—	2	2	no	—
716	C₂×Q₈	—	4	1	no	—
717	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
718	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
719	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	1	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	2	1	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	1	no	—
733	C₂×D₄	—	2	4	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	4	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	4	2	no	—
738	C₂×D₄	—	4	4	no	—
739	C₂×D₄	—	4	2	no	—
740	C₂×D₄	—	4	4	no	—
741	C₂×D₄	—	4	8	no	—
742	C₂×D₄	—	4	16	no	—
743	C₂×D₄	—	4	8	no	—
744	C₂×D₄	—	4	4	no	—
745	C₂×D₄	—	8	4	no	—
746	C₂×D₄	—	8	2	no	—
747	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
748	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
749	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
750	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
751	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
752	C₂²×C₄	—	2	1	no	—
753	C₂²×C₄	—	2	1	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	4	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
760	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
761	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
762	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
765	SD₁₆	—	2	8	no	—
766	SD₁₆	—	2	4	no	—
767	SD₁₆	—	4	4	no	—
768	SD₁₆	—	4	2	no	—
769	D₈	—	4	4	no	—
770	D₈	—	4	4	no	—
771	D₈	—	4	4	no	—
772	M₁₆	—	4	4	no	—
773	C₂×C₈	—	4	2	no	—
774	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
775	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
776	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
777	C₄⋊C₄	—	2	1	no	—
778	C₄⋊C₄	—	2	1	no	—
779	C₄⋊C₄	—	2	1	no	—
780	C₄⋊C₄	—	2	1	no	—
781	C₄⋊C₄	—	2	1	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	1	no	—
786	C₄⋊C₄	—	2	1	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
789	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
790	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
791	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
792	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
793	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
794	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
795	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
809	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
810	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
811	C₄²	—	2	1	no	—
812	C₄²	—	2	1	no	—
813	C₄²	—	2	2	no	—
814	C₄²	—	2	2	no	—
815	C₄²	—	2	1	no	—
816	C₄²	—	2	1	no	—
817	C₄²	C₂×D₄×C₈₉	1	2	yes	—
818	C₄²	C₂×D₄×C₈₉	1	2	yes	—
819	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
820	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
821	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
822	C₄²	C₂⁴×C₈₉	1	2	yes	—
823	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
824	C₂³	—	2	2	no	—
825	C₂³	—	2	4	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	4	8	no	—
828	C₂³	—	4	4	no	—
829	C₂³	—	8	2	no	—
830	C₂³	—	8	4	no	—
831	C₂³	—	8	2	no	—
832	C₂³	—	8	4	no	—
833	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
834	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
835	Q₈	—	2	2	no	—
836	Q₈	—	2	1	no	—
837	Q₈	—	2	1	no	—
838	Q₈	—	2	1	no	—
839	Q₈	—	4	2	no	—
840	Q₈	—	4	2	no	—
841	Q₈	—	4	2	no	—
842	Q₈	H(5,𝔽₂)×C₈₉	1	2	yes	complemented
843	D₄	—	2	4	no	—
844	D₄	—	2	2	no	—
845	D₄	—	2	2	no	—
846	D₄	—	2	2	no	—
847	D₄	—	2	4	no	—
848	D₄	—	2	2	no	—
849	D₄	—	2	4	no	—
850	D₄	—	2	2	no	—
851	D₄	—	4	4	no	—
852	D₄	—	4	8	no	—
853	D₄	—	4	4	no	—
854	D₄	—	4	2	no	—
855	D₄	—	4	8	no	—
856	D₄	—	4	4	no	—
857	D₄	—	4	4	no	—
858	D₄	—	4	2	no	—
859	D₄	—	4	4	no	—
860	D₄	—	4	4	no	—
861	D₄	—	4	2	no	—
862	D₄	—	8	1	no	—
863	D₄	—	8	4	no	—
864	D₄	—	8	2	no	—
865	D₄	—	8	4	no	—
866	D₄	—	8	2	no	—
867	D₄	—	8	2	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	4	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	4	2	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	4	no	—
882	C₂×C₄	—	4	2	no	—
883	C₂×C₄	—	4	8	no	—
884	C₂×C₄	—	4	4	no	—
885	C₂×C₄	—	4	4	no	—
886	C₂×C₄	—	8	2	no	—
887	C₂×C₄	—	8	1	no	—
888	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	4	yes	complemented
889	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
890	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
891	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
892	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
893	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
894	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
895	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
896	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
897	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
898	C₈	—	2	4	no	—
899	C₈	—	2	2	no	—
900	C₈	—	2	2	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	2	no	—
904	C₂²	—	2	2	no	—
905	C₂²	—	2	2	no	—
906	C₂²	—	4	4	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	4	no	—
911	C₂²	—	4	2	no	—
912	C₂²	—	4	2	no	—
913	C₂²	—	4	2	no	—
914	C₂²	—	4	4	no	—
915	C₂²	—	16	4	no	—
916	C₂²	—	16	8	no	—
917	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	2	yes	—
918	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
919	C₄	—	2	2	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	1	no	—
923	C₄	—	2	2	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	2	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	1	no	—
929	C₄	—	4	1	no	—
930	C₄	—	4	1	no	—
931	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	2	yes	—
932	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	2	yes	—
933	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
934	C₄	#585×C₈₉	1	1	yes	characteristic
935	C₂	—	2	2	no	—
936	C₂	—	4	2	no	—
937	C₂	—	8	2	no	—
938	C₂	—	8	4	no	—
939	C₂	—	8	2	no	—
940	C₂	C₈₉×#3488	1	1	yes	characteristic
941	C₂	C₂²×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
942	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 ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3498	C₂	semidirect
2. C₈₉×#3480	C₂	semidirect
3. C₈₉×#3399	C₂	semidirect
4. C₈₉×#3368	C₂	semidirect
5. C₈₉×#3324	C₂	semidirect
6. C₈₉×#3318	C₂	semidirect
7. C₈₉×#3274	C₂	semidirect
8. C₈₉×#3265	C₂	semidirect
9. C₈₉×#3251	C₂	semidirect
10. C₈₉×#3245	C₂	semidirect
11. C₈₉×#3217	C₂	semidirect
12. C₈₉×#3205	C₂	semidirect
13. C₈₉×#3115	C₂	semidirect
14. C₈₉×#3103	C₂	semidirect
15. C₈₉×#3038	C₂	semidirect
16. C₂×#460×C₈₉	C₂	semidirect
17. C₈₉×#2989	C₂	semidirect
19. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
20. C₂²×SD₁₆×C₈₉	C₂²	semidirect
22. #559×C₈₉	C₂²	semidirect
23. #557×C₈₉	C₂²	semidirect
25. #556×C₈₉	C₂²	semidirect
27. #553×C₈₉	C₂²	semidirect
30. #550×C₈₉	C₂²	semidirect
31. #548×C₈₉	C₂²	semidirect
41. #532×C₈₉	C₂²	semidirect
45. #529×C₈₉	C₂²	semidirect
48. C₄×#41×C₈₉	C₂²	semidirect
49. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
50. #496×C₈₉	C₂²	semidirect
51. #493×C₈₉	C₂²	semidirect
52. #490×C₈₉	C₂²	semidirect
53. #486×C₈₉	C₂²	semidirect
54. #482×C₈₉	C₂²	semidirect
55. #481×C₈₉	C₂²	semidirect
56. #478×C₈₉	C₂²	semidirect
57. #475×C₈₉	C₂²	semidirect
58. #475×C₈₉	C₂²	semidirect
59. #474×C₈₉	C₂²	semidirect
60. #474×C₈₉	C₂²	semidirect
61. #469×C₈₉	C₂²	semidirect
62. #468×C₈₉	C₂²	semidirect
63. #466×C₈₉	C₂²	semidirect
64. #463×C₈₉	C₂²	semidirect
65. #460×C₈₉	C₂²	semidirect
66. #460×C₈₉	C₂²	semidirect
67. #460×C₈₉	C₂²	semidirect
68. #460×C₈₉	C₂²	semidirect
69. #460×C₈₉	C₂²	semidirect
70. #460×C₈₉	C₂²	semidirect
71. #460×C₈₉	C₂²	semidirect
72. #459×C₈₉	C₂²	semidirect
73. #459×C₈₉	C₂²	semidirect
74. #459×C₈₉	C₂²	semidirect
75. #459×C₈₉	C₂²	semidirect
76. #459×C₈₉	C₂²	semidirect
77. #450×C₈₉	C₂²	semidirect
78. #449×C₈₉	C₂²	semidirect
79. #448×C₈₉	C₂²	semidirect
80. #447×C₈₉	C₂²	semidirect
81. #447×C₈₉	C₂²	semidirect
82. #446×C₈₉	C₂²	semidirect
83. #442×C₈₉	C₂²	semidirect
84. #440×C₈₉	C₂²	semidirect
85. C₄×SD₁₆×C₈₉	C₂²	semidirect
86. C₄×SD₁₆×C₈₉	C₂²	semidirect
87. #436×C₈₉	C₂²	semidirect
88. #435×C₈₉	C₂²	semidirect
89. #432×C₈₉	C₂²	semidirect
90. #431×C₈₉	C₂²	semidirect
91. #423×C₈₉	C₂²	semidirect
92. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
93. #418×C₈₉	C₂²	semidirect
94. C₂×#102×C₈₉	C₂²	semidirect
370. Q₈×C₈₉	H(5,𝔽₂)	semidirect
416. C₂×C₄×C₈₉	AGL(1,ℤ/8)	semidirect
463. #61963	C₈₉	direct (N × H)
472. #3498	C₂×C₈₉	semidirect
473. #3480	C₂×C₈₉	semidirect
474. #3399	C₂×C₈₉	semidirect
475. #3368	C₂×C₈₉	semidirect
476. #3324	C₂×C₈₉	semidirect
477. #3318	C₂×C₈₉	semidirect
478. #3274	C₂×C₈₉	semidirect
479. #3265	C₂×C₈₉	semidirect
480. #3251	C₂×C₈₉	semidirect
481. #3245	C₂×C₈₉	semidirect
482. #3217	C₂×C₈₉	semidirect
483. #3205	C₂×C₈₉	semidirect
484. #3115	C₂×C₈₉	semidirect
485. #3103	C₂×C₈₉	semidirect
486. #3038	C₂×C₈₉	semidirect
487. C₂×#460	C₂×C₈₉	semidirect
488. #2989	C₂×C₈₉	semidirect
489. C₈₉	#61963	direct (N × H)
491. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
492. C₂²×SD₁₆	C₂²×C₈₉	semidirect
494. #559	C₂²×C₈₉	semidirect
495. #557	C₂²×C₈₉	semidirect
497. #556	C₂²×C₈₉	semidirect
499. #553	C₂²×C₈₉	semidirect
502. #550	C₂²×C₈₉	semidirect
503. #548	C₂²×C₈₉	semidirect
513. #532	C₂²×C₈₉	semidirect
517. #529	C₂²×C₈₉	semidirect
520. C₄×#41	C₂²×C₈₉	semidirect
521. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
522. #496	C₂²×C₈₉	semidirect
523. #493	C₂²×C₈₉	semidirect
524. #490	C₂²×C₈₉	semidirect
525. #486	C₂²×C₈₉	semidirect
526. #482	C₂²×C₈₉	semidirect
527. #481	C₂²×C₈₉	semidirect
528. #478	C₂²×C₈₉	semidirect
529. #475	C₂²×C₈₉	semidirect
530. #475	C₂²×C₈₉	semidirect
531. #474	C₂²×C₈₉	semidirect
532. #474	C₂²×C₈₉	semidirect
533. #469	C₂²×C₈₉	semidirect
534. #468	C₂²×C₈₉	semidirect
535. #466	C₂²×C₈₉	semidirect
536. #463	C₂²×C₈₉	semidirect
537. #460	C₂²×C₈₉	semidirect
538. #460	C₂²×C₈₉	semidirect
539. #460	C₂²×C₈₉	semidirect
540. #460	C₂²×C₈₉	semidirect
541. #460	C₂²×C₈₉	semidirect
542. #460	C₂²×C₈₉	semidirect
543. #460	C₂²×C₈₉	semidirect
544. #459	C₂²×C₈₉	semidirect
545. #459	C₂²×C₈₉	semidirect
546. #459	C₂²×C₈₉	semidirect
547. #459	C₂²×C₈₉	semidirect
548. #459	C₂²×C₈₉	semidirect
549. #450	C₂²×C₈₉	semidirect
550. #449	C₂²×C₈₉	semidirect
551. #448	C₂²×C₈₉	semidirect
552. #447	C₂²×C₈₉	semidirect
553. #447	C₂²×C₈₉	semidirect
554. #446	C₂²×C₈₉	semidirect
555. #442	C₂²×C₈₉	semidirect
556. #440	C₂²×C₈₉	semidirect
557. C₄×SD₁₆	C₂²×C₈₉	semidirect
558. C₄×SD₁₆	C₂²×C₈₉	semidirect
559. #436	C₂²×C₈₉	semidirect
560. #435	C₂²×C₈₉	semidirect
561. #432	C₂²×C₈₉	semidirect
562. #431	C₂²×C₈₉	semidirect
563. #423	C₂²×C₈₉	semidirect
564. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
565. #418	C₂²×C₈₉	semidirect
566. C₂×#102	C₂²×C₈₉	semidirect
842. Q₈	H(5,𝔽₂)×C₈₉	semidirect
888. 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
C₈₉×#3498	2
C₈₉×#3480	2
C₈₉×#3399	2
C₈₉×#3368	2
C₈₉×#3324	2
C₈₉×#3318	2
C₈₉×#3274	2
C₈₉×#3265	2
C₈₉×#3251	2
C₈₉×#3245	2
C₈₉×#3217	2
C₈₉×#3205	2
C₈₉×#3115	2
C₈₉×#3103	2
C₈₉×#3038	2
C₂×#460×C₈₉	2
C₈₉×#2989	2
#61963	89

Subgroups — C89×#61963 #36439811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61963 #36439811