Subgroups — C₈₉×#60924 #36438772

Order 22784.

1868 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3260	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3257	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3254	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3251	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3247	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3246	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3081	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3078	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3062	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3057	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3042	C₂	1	2	yes	maximal, complemented
15	C₈₉×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#460×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2906	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
19	C₂²×SD₁₆×C₈₉	C₂²	1	2	yes	—
20	C₂×#131×C₈₉	C₂²	1	2	yes	—
21	#559×C₈₉	—	2	1	no	—
22	#559×C₈₉	—	2	1	no	—
23	#550×C₈₉	—	2	1	no	—
24	#550×C₈₉	—	2	1	no	—
25	#546×C₈₉	—	2	2	no	—
26	#546×C₈₉	—	2	2	no	—
27	#544×C₈₉	C₂²	1	1	yes	characteristic
28	#542×C₈₉	—	2	1	no	—
29	#542×C₈₉	C₂²	1	2	yes	complemented
30	#541×C₈₉	—	2	1	no	—
31	#541×C₈₉	C₂²	1	2	yes	complemented
32	#540×C₈₉	C₂²	1	4	yes	—
33	#539×C₈₉	—	2	2	no	—
34	#537×C₈₉	C₂²	1	1	yes	characteristic
35	#536×C₈₉	C₂²	1	1	yes	characteristic
36	#536×C₈₉	C₂²	1	1	yes	characteristic
37	#535×C₈₉	C₂²	1	2	yes	—
38	#533×C₈₉	—	2	1	no	—
39	#533×C₈₉	C₂²	1	1	yes	characteristic
40	#533×C₈₉	C₂²	1	2	yes	complemented
41	#532×C₈₉	C₂²	1	2	yes	—
42	#532×C₈₉	C₂²	1	2	yes	—
43	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
44	#529×C₈₉	—	2	2	no	—
45	#529×C₈₉	—	2	1	no	—
46	#529×C₈₉	C₂²	1	2	yes	complemented
47	#518×C₈₉	C₂²	1	2	yes	—
48	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
49	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
51	#479×C₈₉	C₂²	1	2	yes	complemented
52	#479×C₈₉	C₂²	1	4	yes	complemented
53	#478×C₈₉	C₂²	1	2	yes	complemented
54	#478×C₈₉	C₂²	1	4	yes	complemented
55	#478×C₈₉	C₂²	1	4	yes	complemented
56	#477×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	#477×C₈₉	C₂²	1	2	yes	complemented
58	#476×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#476×C₈₉	C₂²	1	4	yes	complemented
60	#475×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	#475×C₈₉	C₂²	1	2	yes	complemented
62	#474×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	#474×C₈₉	C₂²	1	4	yes	complemented
64	#469×C₈₉	C₂²	1	4	yes	complemented
65	#468×C₈₉	C₂²	1	4	yes	complemented
66	#468×C₈₉	C₂²	1	4	yes	complemented
67	#468×C₈₉	C₂²	1	4	yes	complemented
68	#466×C₈₉	C₂²	1	4	yes	complemented
69	#465×C₈₉	C₂²	1	4	yes	complemented
70	#465×C₈₉	C₂²	1	4	yes	complemented
71	#465×C₈₉	C₂²	1	4	yes	complemented
72	#463×C₈₉	C₂²	1	4	yes	complemented
73	#463×C₈₉	C₂²	1	4	yes	complemented
74	#461×C₈₉	C₂²	1	4	yes	complemented
75	#461×C₈₉	C₂²	1	4	yes	complemented
76	#460×C₈₉	C₂²	1	2	yes	—
77	#460×C₈₉	C₂²	1	2	yes	—
78	#460×C₈₉	C₂²	1	2	yes	—
79	#460×C₈₉	C₂²	1	4	yes	—
80	#460×C₈₉	C₂²	1	2	yes	—
81	#459×C₈₉	C₂²	1	2	yes	—
82	#459×C₈₉	C₂²	1	2	yes	—
83	#428×C₈₉	C₂²	1	2	yes	—
84	#427×C₈₉	C₂²	1	2	yes	—
85	#424×C₈₉	C₂²	1	2	yes	—
86	#424×C₈₉	C₂²	1	4	yes	complemented
87	#423×C₈₉	C₂²	1	1	yes	characteristic
88	#423×C₈₉	C₂²	1	2	yes	complemented
89	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
90	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	complemented
91	#419×C₈₉	C₂²	1	2	yes	—
92	#418×C₈₉	C₂²	1	2	yes	—
93	#416×C₈₉	C₂²	1	2	yes	—
94	C₂×#102×C₈₉	C₂²	1	2	yes	—
95	C₂×#41×C₈₉	—	2	2	no	—
96	C₂×#41×C₈₉	—	2	2	no	—
97	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
98	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
99	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₈₉	—	2	1	no	—
101	C₂²×D₄×C₈₉	—	2	1	no	—
102	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
103	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
104	C₂×SD₁₆×C₈₉	—	4	4	no	—
105	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
106	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
107	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
108	C₂×D₈×C₈₉	C₂³	1	4	yes	—
109	#131×C₈₉	—	4	4	no	—
110	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
111	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
112	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
113	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
114	C₄⋊Q₈×C₈₉	—	2	1	no	—
115	C₄⋊Q₈×C₈₉	—	2	1	no	—
116	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
117	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
118	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
119	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
120	#127×C₈₉	—	2	2	no	—
121	#127×C₈₉	—	2	1	no	—
122	#127×C₈₉	—	2	1	no	—
123	#127×C₈₉	C₂³	1	2	yes	—
124	#127×C₈₉	C₂³	1	2	yes	—
125	#126×C₈₉	—	2	2	no	—
126	#126×C₈₉	—	2	2	no	—
127	#126×C₈₉	—	2	2	no	—
128	#126×C₈₉	—	2	2	no	—
129	#125×C₈₉	—	2	2	no	—
130	#125×C₈₉	—	2	1	no	—
131	#125×C₈₉	—	2	2	no	—
132	#125×C₈₉	—	2	2	no	—
133	#125×C₈₉	C₂³	1	2	yes	—
134	#125×C₈₉	C₂³	1	2	yes	—
135	#124×C₈₉	—	2	2	no	—
136	#124×C₈₉	—	2	1	no	—
137	#124×C₈₉	—	2	2	no	—
138	#124×C₈₉	—	2	2	no	—
139	#124×C₈₉	—	2	2	no	—
140	#124×C₈₉	C₂³	1	2	yes	—
141	#123×C₈₉	—	2	2	no	—
142	#123×C₈₉	—	2	2	no	—
143	#123×C₈₉	—	2	4	no	—
144	#123×C₈₉	—	2	4	no	—
145	#123×C₈₉	—	2	2	no	—
146	#123×C₈₉	—	2	2	no	—
147	C₂²⋊Q₈×C₈₉	—	2	1	no	—
148	C₂²⋊Q₈×C₈₉	—	2	1	no	—
149	C₂²⋊Q₈×C₈₉	—	2	1	no	—
150	C₂²⋊Q₈×C₈₉	—	2	2	no	—
151	C₂²⋊Q₈×C₈₉	—	2	1	no	—
152	C₂²⋊Q₈×C₈₉	—	2	1	no	—
153	C₂²⋊Q₈×C₈₉	—	2	2	no	—
154	C₂²⋊Q₈×C₈₉	—	2	2	no	—
155	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
156	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
157	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
158	#121×C₈₉	—	2	2	no	—
159	#121×C₈₉	—	2	1	no	—
160	#121×C₈₉	—	2	2	no	—
161	#121×C₈₉	—	2	2	no	—
162	#121×C₈₉	—	2	4	no	—
163	#121×C₈₉	—	2	4	no	—
164	#121×C₈₉	C₂³	1	4	yes	—
165	#121×C₈₉	C₂³	1	4	yes	—
166	#121×C₈₉	C₂³	1	2	yes	—
167	#120×C₈₉	—	2	4	no	—
168	C₄×Q₈×C₈₉	—	2	1	no	—
169	C₄×Q₈×C₈₉	—	2	1	no	—
170	C₄×Q₈×C₈₉	—	2	2	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	D₄	1	1	yes	characteristic
175	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
176	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
177	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
178	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₈₉	—	2	1	no	—
180	C₄×D₄×C₈₉	—	2	1	no	—
181	C₄×D₄×C₈₉	—	2	2	no	—
182	C₄×D₄×C₈₉	—	2	2	no	—
183	C₄×D₄×C₈₉	—	2	2	no	—
184	C₄×D₄×C₈₉	—	2	2	no	—
185	C₄×D₄×C₈₉	—	2	2	no	—
186	C₄×D₄×C₈₉	D₄	1	2	yes	—
187	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
188	C₄×D₄×C₈₉	D₄	1	2	yes	—
189	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
190	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
192	C₄×D₄×C₈₉	C₂³	1	4	yes	—
193	C₄×D₄×C₈₉	C₂³	1	4	yes	—
194	#117×C₈₉	—	2	2	no	—
195	#117×C₈₉	—	2	1	no	—
196	#117×C₈₉	—	2	2	no	—
197	#117×C₈₉	C₂³	1	2	yes	—
198	#117×C₈₉	C₂³	1	1	yes	characteristic
199	#117×C₈₉	C₂³	1	1	yes	characteristic
200	#117×C₈₉	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
202	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
204	C₂×C₄²×C₈₉	—	2	1	no	—
205	C₂×C₄²×C₈₉	—	2	1	no	—
206	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
208	#107×C₈₉	C₂³	1	2	yes	—
209	#107×C₈₉	C₂³	1	2	yes	—
210	#107×C₈₉	C₂³	1	4	yes	—
211	#106×C₈₉	C₂³	1	2	yes	—
212	#106×C₈₉	C₂³	1	2	yes	—
213	#106×C₈₉	C₂³	1	4	yes	—
214	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
215	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
216	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
217	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
218	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
219	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
220	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
221	#103×C₈₉	C₂³	1	2	yes	—
222	#103×C₈₉	C₂³	1	2	yes	—
223	#103×C₈₉	C₂³	1	4	yes	—
224	#103×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	#102×C₈₉	C₂³	1	4	yes	—
230	#102×C₈₉	C₂³	1	4	yes	—
231	C₂⁴×C₈₉	—	2	2	no	—
232	#41×C₈₉	—	2	2	no	—
233	#41×C₈₉	—	2	2	no	—
234	#41×C₈₉	—	2	2	no	—
235	#41×C₈₉	—	2	2	no	—
236	#41×C₈₉	—	8	4	no	—
237	#41×C₈₉	—	8	4	no	—
238	C₂×Q₈×C₈₉	—	2	1	no	—
239	C₂×Q₈×C₈₉	—	2	1	no	—
240	C₂×Q₈×C₈₉	—	2	1	no	—
241	C₂×Q₈×C₈₉	—	2	2	no	—
242	C₂×Q₈×C₈₉	—	2	2	no	—
243	C₂×Q₈×C₈₉	—	2	2	no	—
244	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
245	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
246	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
247	C₂×D₄×C₈₉	—	2	1	no	—
248	C₂×D₄×C₈₉	—	2	2	no	—
249	C₂×D₄×C₈₉	—	2	4	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	2	no	—
254	C₂×D₄×C₈₉	—	2	2	no	—
255	C₂×D₄×C₈₉	—	2	2	no	—
256	C₂×D₄×C₈₉	—	2	4	no	—
257	C₂×D₄×C₈₉	—	2	4	no	—
258	C₂×D₄×C₈₉	—	8	2	no	—
259	C₂×D₄×C₈₉	—	8	2	no	—
260	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
261	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
262	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
263	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
264	C₂²×C₄×C₈₉	—	2	1	no	—
265	C₂²×C₄×C₈₉	—	2	1	no	—
266	C₂²×C₄×C₈₉	—	2	1	no	—
267	C₂²×C₄×C₈₉	—	2	1	no	—
268	C₂²×C₄×C₈₉	—	2	1	no	—
269	C₂²×C₄×C₈₉	—	2	4	no	—
270	C₂²×C₄×C₈₉	—	2	4	no	—
271	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
277	SD₁₆×C₈₉	—	4	4	no	—
278	SD₁₆×C₈₉	—	4	4	no	—
279	SD₁₆×C₈₉	—	4	4	no	—
280	D₈×C₈₉	—	4	4	no	—
281	M₁₆×C₈₉	—	2	4	no	—
282	M₁₆×C₈₉	—	4	4	no	—
283	C₂×C₈×C₈₉	—	2	4	no	—
284	C₂×C₈×C₈₉	—	4	4	no	—
285	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
286	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
287	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
288	C₄⋊C₄×C₈₉	—	2	2	no	—
289	C₄⋊C₄×C₈₉	—	2	2	no	—
290	C₄⋊C₄×C₈₉	—	2	1	no	—
291	C₄⋊C₄×C₈₉	—	2	1	no	—
292	C₄⋊C₄×C₈₉	—	2	1	no	—
293	C₄⋊C₄×C₈₉	—	2	2	no	—
294	C₄⋊C₄×C₈₉	—	2	2	no	—
295	C₄⋊C₄×C₈₉	—	2	2	no	—
296	C₄⋊C₄×C₈₉	—	2	2	no	—
297	C₄⋊C₄×C₈₉	—	2	1	no	—
298	C₄⋊C₄×C₈₉	—	2	1	no	—
299	C₄⋊C₄×C₈₉	—	2	2	no	—
300	C₄⋊C₄×C₈₉	—	2	2	no	—
301	C₄⋊C₄×C₈₉	—	2	2	no	—
302	C₄⋊C₄×C₈₉	—	2	2	no	—
303	C₄⋊C₄×C₈₉	—	2	2	no	—
304	C₄⋊C₄×C₈₉	—	2	2	no	—
305	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
306	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
307	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
308	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
309	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
310	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
311	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
312	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
313	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
314	C₂²⋊C₄×C₈₉	—	2	2	no	—
315	C₂²⋊C₄×C₈₉	—	2	2	no	—
316	C₂²⋊C₄×C₈₉	—	2	2	no	—
317	C₂²⋊C₄×C₈₉	—	2	1	no	—
318	C₂²⋊C₄×C₈₉	—	2	2	no	—
319	C₂²⋊C₄×C₈₉	—	2	4	no	—
320	C₂²⋊C₄×C₈₉	—	2	4	no	—
321	C₂²⋊C₄×C₈₉	—	2	1	no	—
322	C₂²⋊C₄×C₈₉	—	2	1	no	—
323	C₂²⋊C₄×C₈₉	—	2	2	no	—
324	C₂²⋊C₄×C₈₉	—	2	2	no	—
325	C₂²⋊C₄×C₈₉	—	2	4	no	—
326	C₂²⋊C₄×C₈₉	—	2	4	no	—
327	C₂²⋊C₄×C₈₉	—	2	2	no	—
328	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
329	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
330	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
331	C₄²×C₈₉	—	2	2	no	—
332	C₄²×C₈₉	—	2	1	no	—
333	C₄²×C₈₉	—	2	1	no	—
334	C₄²×C₈₉	—	2	1	no	—
335	C₄²×C₈₉	—	2	2	no	—
336	C₄²×C₈₉	—	2	2	no	—
337	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₈₉	C₂×D₄	1	2	yes	—
339	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₈₉	C₂×D₄	1	2	yes	—
341	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
342	C₄²×C₈₉	C₂⁴	1	2	yes	—
343	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
344	C₂³×C₈₉	—	2	1	no	—
345	C₂³×C₈₉	—	2	4	no	—
346	C₂³×C₈₉	—	4	4	no	—
347	C₂³×C₈₉	—	8	2	no	—
348	C₂³×C₈₉	—	8	2	no	—
349	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
350	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
351	Q₈×C₈₉	—	2	2	no	—
352	Q₈×C₈₉	—	2	2	no	—
353	Q₈×C₈₉	—	2	1	no	—
354	Q₈×C₈₉	—	2	2	no	—
355	Q₈×C₈₉	—	2	1	no	—
356	Q₈×C₈₉	—	4	2	no	—
357	Q₈×C₈₉	—	4	2	no	—
358	Q₈×C₈₉	—	4	2	no	—
359	Q₈×C₈₉	—	8	2	no	—
360	D₄×C₈₉	—	2	4	no	—
361	D₄×C₈₉	—	2	2	no	—
362	D₄×C₈₉	—	2	1	no	—
363	D₄×C₈₉	—	2	4	no	—
364	D₄×C₈₉	—	2	4	no	—
365	D₄×C₈₉	—	2	1	no	—
366	D₄×C₈₉	—	4	4	no	—
367	D₄×C₈₉	—	4	2	no	—
368	D₄×C₈₉	—	4	4	no	—
369	D₄×C₈₉	—	4	4	no	—
370	D₄×C₈₉	—	8	2	no	—
371	D₄×C₈₉	—	8	2	no	—
372	D₄×C₈₉	—	8	2	no	—
373	D₄×C₈₉	—	8	4	no	—
374	D₄×C₈₉	—	8	4	no	—
375	C₂×C₄×C₈₉	—	2	2	no	—
376	C₂×C₄×C₈₉	—	2	4	no	—
377	C₂×C₄×C₈₉	—	2	2	no	—
378	C₂×C₄×C₈₉	—	2	2	no	—
379	C₂×C₄×C₈₉	—	2	1	no	—
380	C₂×C₄×C₈₉	—	2	2	no	—
381	C₂×C₄×C₈₉	—	2	1	no	—
382	C₂×C₄×C₈₉	—	2	1	no	—
383	C₂×C₄×C₈₉	—	2	2	no	—
384	C₂×C₄×C₈₉	—	2	2	no	—
385	C₂×C₄×C₈₉	—	2	2	no	—
386	C₂×C₄×C₈₉	—	4	1	no	—
387	C₂×C₄×C₈₉	—	4	2	no	—
388	C₂×C₄×C₈₉	—	4	2	no	—
389	C₂×C₄×C₈₉	—	4	2	no	—
390	C₂×C₄×C₈₉	—	4	2	no	—
391	C₂×C₄×C₈₉	—	8	1	no	—
392	C₂×C₄×C₈₉	—	8	4	no	—
393	C₂×C₄×C₈₉	—	8	4	no	—
394	C₂×C₄×C₈₉	—	8	1	no	—
395	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
404	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
405	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
406	C₈×C₈₉	—	2	2	no	—
407	C₈×C₈₉	—	2	2	no	—
408	C₈×C₈₉	—	2	4	no	—
409	C₂²×C₈₉	—	2	1	no	—
410	C₂²×C₈₉	—	2	1	no	—
411	C₂²×C₈₉	—	2	2	no	—
412	C₂²×C₈₉	—	2	2	no	—
413	C₂²×C₈₉	—	2	2	no	—
414	C₂²×C₈₉	—	4	4	no	—
415	C₂²×C₈₉	—	4	1	no	—
416	C₂²×C₈₉	—	4	1	no	—
417	C₂²×C₈₉	—	4	4	no	—
418	C₂²×C₈₉	—	4	1	no	—
419	C₂²×C₈₉	—	4	4	no	—
420	C₂²×C₈₉	—	16	4	no	—
421	C₂²×C₈₉	#537	1	2	yes	—
422	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
423	C₄×C₈₉	—	2	1	no	—
424	C₄×C₈₉	—	2	2	no	—
425	C₄×C₈₉	—	2	1	no	—
426	C₄×C₈₉	—	2	2	no	—
427	C₄×C₈₉	—	2	2	no	—
428	C₄×C₈₉	—	2	1	no	—
429	C₄×C₈₉	—	4	2	no	—
430	C₄×C₈₉	—	4	2	no	—
431	C₄×C₈₉	—	4	1	no	—
432	C₄×C₈₉	—	4	1	no	—
433	C₄×C₈₉	—	4	2	no	—
434	C₄×C₈₉	—	4	1	no	—
435	C₄×C₈₉	—	4	2	no	—
436	C₄×C₈₉	#537	1	2	yes	—
437	C₄×C₈₉	#577	1	2	yes	—
438	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
439	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
440	#60924	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
441	C₂×C₈₉	—	2	2	no	—
442	C₂×C₈₉	—	4	2	no	—
443	C₂×C₈₉	—	8	1	no	—
444	C₂×C₈₉	—	8	4	no	—
445	C₂×C₈₉	C₂×#537	1	1	yes	characteristic
446	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
447	C₂×C₈₉	#3585	1	1	yes	characteristic
448	#3508	C₂×C₈₉	1	1	yes	characteristic, complemented
449	#3461	C₂×C₈₉	1	1	yes	characteristic, complemented
450	#3260	C₂×C₈₉	1	4	yes	complemented
451	#3257	C₂×C₈₉	1	4	yes	complemented
452	#3254	C₂×C₈₉	1	2	yes	complemented
453	#3251	C₂×C₈₉	1	2	yes	complemented
454	#3247	C₂×C₈₉	1	2	yes	complemented
455	#3246	C₂×C₈₉	1	2	yes	complemented
456	#3081	C₂×C₈₉	1	2	yes	complemented
457	#3078	C₂×C₈₉	1	1	yes	characteristic, complemented
458	#3076	C₂×C₈₉	1	1	yes	characteristic, complemented
459	#3062	C₂×C₈₉	1	2	yes	complemented
460	#3057	C₂×C₈₉	1	2	yes	complemented
461	#3042	C₂×C₈₉	1	2	yes	complemented
462	#3038	C₂×C₈₉	1	1	yes	characteristic, complemented
463	C₂×#460	C₂×C₈₉	1	1	yes	characteristic, complemented
464	#2906	C₂×C₈₉	1	1	yes	characteristic, complemented
465	C₈₉	#60924	1	1	yes	characteristic, direct product factor, Sylow
466	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
467	C₂²×SD₁₆	C₂²×C₈₉	1	2	yes	—
468	C₂×#131	C₂²×C₈₉	1	2	yes	—
469	#559	—	2	1	no	—
470	#559	—	2	1	no	—
471	#550	—	2	1	no	—
472	#550	—	2	1	no	—
473	#546	—	2	2	no	—
474	#546	—	2	2	no	—
475	#544	C₂²×C₈₉	1	1	yes	characteristic
476	#542	—	2	1	no	—
477	#542	C₂²×C₈₉	1	2	yes	complemented
478	#541	—	2	1	no	—
479	#541	C₂²×C₈₉	1	2	yes	complemented
480	#540	C₂²×C₈₉	1	4	yes	—
481	#539	—	2	2	no	—
482	#537	C₂²×C₈₉	1	1	yes	characteristic
483	#536	C₂²×C₈₉	1	1	yes	characteristic
484	#536	C₂²×C₈₉	1	1	yes	characteristic
485	#535	C₂²×C₈₉	1	2	yes	—
486	#533	—	2	1	no	—
487	#533	C₂²×C₈₉	1	1	yes	characteristic
488	#533	C₂²×C₈₉	1	2	yes	complemented
489	#532	C₂²×C₈₉	1	2	yes	—
490	#532	C₂²×C₈₉	1	2	yes	—
491	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
492	#529	—	2	2	no	—
493	#529	—	2	1	no	—
494	#529	C₂²×C₈₉	1	2	yes	complemented
495	#518	C₂²×C₈₉	1	2	yes	—
496	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
497	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
498	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
499	#479	C₂²×C₈₉	1	2	yes	complemented
500	#479	C₂²×C₈₉	1	4	yes	complemented
501	#478	C₂²×C₈₉	1	2	yes	complemented
502	#478	C₂²×C₈₉	1	4	yes	complemented
503	#478	C₂²×C₈₉	1	4	yes	complemented
504	#477	C₂²×C₈₉	1	1	yes	characteristic, complemented
505	#477	C₂²×C₈₉	1	2	yes	complemented
506	#476	C₂²×C₈₉	1	1	yes	characteristic, complemented
507	#476	C₂²×C₈₉	1	4	yes	complemented
508	#475	C₂²×C₈₉	1	1	yes	characteristic, complemented
509	#475	C₂²×C₈₉	1	2	yes	complemented
510	#474	C₂²×C₈₉	1	1	yes	characteristic, complemented
511	#474	C₂²×C₈₉	1	4	yes	complemented
512	#469	C₂²×C₈₉	1	4	yes	complemented
513	#468	C₂²×C₈₉	1	4	yes	complemented
514	#468	C₂²×C₈₉	1	4	yes	complemented
515	#468	C₂²×C₈₉	1	4	yes	complemented
516	#466	C₂²×C₈₉	1	4	yes	complemented
517	#465	C₂²×C₈₉	1	4	yes	complemented
518	#465	C₂²×C₈₉	1	4	yes	complemented
519	#465	C₂²×C₈₉	1	4	yes	complemented
520	#463	C₂²×C₈₉	1	4	yes	complemented
521	#463	C₂²×C₈₉	1	4	yes	complemented
522	#461	C₂²×C₈₉	1	4	yes	complemented
523	#461	C₂²×C₈₉	1	4	yes	complemented
524	#460	C₂²×C₈₉	1	2	yes	—
525	#460	C₂²×C₈₉	1	2	yes	—
526	#460	C₂²×C₈₉	1	2	yes	—
527	#460	C₂²×C₈₉	1	4	yes	—
528	#460	C₂²×C₈₉	1	2	yes	—
529	#459	C₂²×C₈₉	1	2	yes	—
530	#459	C₂²×C₈₉	1	2	yes	—
531	#428	C₂²×C₈₉	1	2	yes	—
532	#427	C₂²×C₈₉	1	2	yes	—
533	#424	C₂²×C₈₉	1	2	yes	—
534	#424	C₂²×C₈₉	1	4	yes	complemented
535	#423	C₂²×C₈₉	1	1	yes	characteristic
536	#423	C₂²×C₈₉	1	2	yes	complemented
537	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
538	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	complemented
539	#419	C₂²×C₈₉	1	2	yes	—
540	#418	C₂²×C₈₉	1	2	yes	—
541	#416	C₂²×C₈₉	1	2	yes	—
542	C₂×#102	C₂²×C₈₉	1	2	yes	—
543	C₂×#41	—	2	2	no	—
544	C₂×#41	—	2	2	no	—
545	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
546	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
547	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
548	C₂²×D₄	—	2	1	no	—
549	C₂²×D₄	—	2	1	no	—
550	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
551	AGL(1,ℤ/8)	—	4	4	no	—
552	C₂×SD₁₆	—	4	4	no	—
553	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
554	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
555	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
556	C₂×D₈	C₂³×C₈₉	1	4	yes	—
557	#131	—	4	4	no	—
558	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
559	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
560	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
561	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
562	C₄⋊Q₈	—	2	1	no	—
563	C₄⋊Q₈	—	2	1	no	—
564	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
565	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
566	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
567	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
568	#127	—	2	2	no	—
569	#127	—	2	1	no	—
570	#127	—	2	1	no	—
571	#127	C₂³×C₈₉	1	2	yes	—
572	#127	C₂³×C₈₉	1	2	yes	—
573	#126	—	2	2	no	—
574	#126	—	2	2	no	—
575	#126	—	2	2	no	—
576	#126	—	2	2	no	—
577	#125	—	2	2	no	—
578	#125	—	2	1	no	—
579	#125	—	2	2	no	—
580	#125	—	2	2	no	—
581	#125	C₂³×C₈₉	1	2	yes	—
582	#125	C₂³×C₈₉	1	2	yes	—
583	#124	—	2	2	no	—
584	#124	—	2	1	no	—
585	#124	—	2	2	no	—
586	#124	—	2	2	no	—
587	#124	—	2	2	no	—
588	#124	C₂³×C₈₉	1	2	yes	—
589	#123	—	2	2	no	—
590	#123	—	2	2	no	—
591	#123	—	2	4	no	—
592	#123	—	2	4	no	—
593	#123	—	2	2	no	—
594	#123	—	2	2	no	—
595	C₂²⋊Q₈	—	2	1	no	—
596	C₂²⋊Q₈	—	2	1	no	—
597	C₂²⋊Q₈	—	2	1	no	—
598	C₂²⋊Q₈	—	2	2	no	—
599	C₂²⋊Q₈	—	2	1	no	—
600	C₂²⋊Q₈	—	2	1	no	—
601	C₂²⋊Q₈	—	2	2	no	—
602	C₂²⋊Q₈	—	2	2	no	—
603	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
604	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
605	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
606	#121	—	2	2	no	—
607	#121	—	2	1	no	—
608	#121	—	2	2	no	—
609	#121	—	2	2	no	—
610	#121	—	2	4	no	—
611	#121	—	2	4	no	—
612	#121	C₂³×C₈₉	1	2	yes	—
613	#121	C₂³×C₈₉	1	4	yes	—
614	#121	C₂³×C₈₉	1	4	yes	—
615	#120	—	2	4	no	—
616	C₄×Q₈	—	2	1	no	—
617	C₄×Q₈	—	2	1	no	—
618	C₄×Q₈	—	2	2	no	—
619	C₄×Q₈	—	2	1	no	—
620	C₄×Q₈	—	2	1	no	—
621	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
622	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
623	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
624	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
625	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
626	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
627	C₄×D₄	—	2	1	no	—
628	C₄×D₄	—	2	1	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	D₄×C₈₉	1	2	yes	—
635	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
636	C₄×D₄	D₄×C₈₉	1	2	yes	—
637	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
638	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
639	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
640	C₄×D₄	C₂³×C₈₉	1	4	yes	—
641	C₄×D₄	C₂³×C₈₉	1	4	yes	—
642	#117	—	2	2	no	—
643	#117	—	2	1	no	—
644	#117	—	2	2	no	—
645	#117	C₂³×C₈₉	1	1	yes	characteristic
646	#117	C₂³×C₈₉	1	2	yes	—
647	#117	C₂³×C₈₉	1	1	yes	characteristic
648	#117	C₂³×C₈₉	1	2	yes	—
649	C₂×C₄⋊C₄	—	2	1	no	—
650	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	—	2	4	no	—
652	C₂×C₄²	—	2	1	no	—
653	C₂×C₄²	—	2	1	no	—
654	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
656	#107	C₂³×C₈₉	1	2	yes	—
657	#107	C₂³×C₈₉	1	2	yes	—
658	#107	C₂³×C₈₉	1	4	yes	—
659	#106	C₂³×C₈₉	1	2	yes	—
660	#106	C₂³×C₈₉	1	2	yes	—
661	#106	C₂³×C₈₉	1	4	yes	—
662	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
663	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
664	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
665	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
666	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
667	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
668	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
669	#103	C₂³×C₈₉	1	2	yes	—
670	#103	C₂³×C₈₉	1	2	yes	—
671	#103	C₂³×C₈₉	1	4	yes	—
672	#103	C₂³×C₈₉	1	4	yes	—
673	#102	C₂³×C₈₉	1	4	yes	—
674	#102	C₂³×C₈₉	1	4	yes	—
675	#102	C₂³×C₈₉	1	2	yes	—
676	#102	C₂³×C₈₉	1	2	yes	—
677	#102	C₂³×C₈₉	1	4	yes	—
678	#102	C₂³×C₈₉	1	4	yes	—
679	C₂⁴	—	2	2	no	—
680	#41	—	2	2	no	—
681	#41	—	2	2	no	—
682	#41	—	2	2	no	—
683	#41	—	2	2	no	—
684	#41	—	8	4	no	—
685	#41	—	8	4	no	—
686	C₂×Q₈	—	2	1	no	—
687	C₂×Q₈	—	2	1	no	—
688	C₂×Q₈	—	2	1	no	—
689	C₂×Q₈	—	2	2	no	—
690	C₂×Q₈	—	2	2	no	—
691	C₂×Q₈	—	2	2	no	—
692	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
693	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
694	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	4	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	4	no	—
705	C₂×D₄	—	2	4	no	—
706	C₂×D₄	—	8	2	no	—
707	C₂×D₄	—	8	2	no	—
708	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
709	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
710	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
711	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
720	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
721	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
722	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
725	SD₁₆	—	4	4	no	—
726	SD₁₆	—	4	4	no	—
727	SD₁₆	—	4	4	no	—
728	D₈	—	4	4	no	—
729	M₁₆	—	2	4	no	—
730	M₁₆	—	4	4	no	—
731	C₂×C₈	—	2	4	no	—
732	C₂×C₈	—	4	4	no	—
733	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
734	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
735	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
754	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
755	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
756	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
757	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
758	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
759	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
760	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
761	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	1	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	1	no	—
770	C₂²⋊C₄	—	2	1	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	4	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
777	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
778	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
779	C₄²	—	2	2	no	—
780	C₄²	—	2	1	no	—
781	C₄²	—	2	1	no	—
782	C₄²	—	2	1	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	2	no	—
785	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
786	C₄²	C₂×D₄×C₈₉	1	2	yes	—
787	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
788	C₄²	C₂×D₄×C₈₉	1	2	yes	—
789	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
790	C₄²	C₂⁴×C₈₉	1	2	yes	—
791	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
792	C₂³	—	2	1	no	—
793	C₂³	—	2	4	no	—
794	C₂³	—	4	4	no	—
795	C₂³	—	8	2	no	—
796	C₂³	—	8	2	no	—
797	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
798	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
799	Q₈	—	2	2	no	—
800	Q₈	—	2	2	no	—
801	Q₈	—	2	1	no	—
802	Q₈	—	2	2	no	—
803	Q₈	—	2	1	no	—
804	Q₈	—	4	2	no	—
805	Q₈	—	4	2	no	—
806	Q₈	—	4	2	no	—
807	Q₈	—	8	2	no	—
808	D₄	—	2	4	no	—
809	D₄	—	2	2	no	—
810	D₄	—	2	1	no	—
811	D₄	—	2	4	no	—
812	D₄	—	2	4	no	—
813	D₄	—	2	1	no	—
814	D₄	—	4	4	no	—
815	D₄	—	4	2	no	—
816	D₄	—	4	4	no	—
817	D₄	—	4	4	no	—
818	D₄	—	8	2	no	—
819	D₄	—	8	2	no	—
820	D₄	—	8	2	no	—
821	D₄	—	8	4	no	—
822	D₄	—	8	4	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	4	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	4	1	no	—
835	C₂×C₄	—	4	2	no	—
836	C₂×C₄	—	4	2	no	—
837	C₂×C₄	—	4	2	no	—
838	C₂×C₄	—	4	2	no	—
839	C₂×C₄	—	8	1	no	—
840	C₂×C₄	—	8	4	no	—
841	C₂×C₄	—	8	4	no	—
842	C₂×C₄	—	8	1	no	—
843	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
847	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
848	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
849	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
850	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
851	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
852	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
853	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
854	C₈	—	2	2	no	—
855	C₈	—	2	2	no	—
856	C₈	—	2	4	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	2	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	4	no	—
864	C₂²	—	4	4	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	4	no	—
868	C₂²	—	16	4	no	—
869	C₂²	#537×C₈₉	1	2	yes	—
870	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
871	C₄	—	2	2	no	—
872	C₄	—	2	1	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	2	no	—
875	C₄	—	2	1	no	—
876	C₄	—	2	2	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	1	no	—
882	C₄	—	4	1	no	—
883	C₄	—	4	2	no	—
884	C₄	#537×C₈₉	1	2	yes	—
885	C₄	#577×C₈₉	1	2	yes	—
886	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
887	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
888	C₂	—	2	2	no	—
889	C₂	—	4	2	no	—
890	C₂	—	8	1	no	—
891	C₂	—	8	4	no	—
892	C₂	C₂×#537×C₈₉	1	1	yes	characteristic
893	C₂	C₂×#577×C₈₉	1	1	yes	characteristic
894	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×#3508	C₂	semidirect
2. C₈₉×#3461	C₂	semidirect
3. C₈₉×#3260	C₂	semidirect
4. C₈₉×#3257	C₂	semidirect
5. C₈₉×#3254	C₂	semidirect
6. C₈₉×#3251	C₂	semidirect
7. C₈₉×#3247	C₂	semidirect
8. C₈₉×#3246	C₂	semidirect
9. C₈₉×#3081	C₂	semidirect
10. C₈₉×#3078	C₂	semidirect
11. C₈₉×#3076	C₂	semidirect
12. C₈₉×#3062	C₂	semidirect
13. C₈₉×#3057	C₂	semidirect
14. C₈₉×#3042	C₂	semidirect
15. C₈₉×#3038	C₂	semidirect
16. C₂×#460×C₈₉	C₂	semidirect
17. C₈₉×#2906	C₂	semidirect
29. #542×C₈₉	C₂²	semidirect
31. #541×C₈₉	C₂²	semidirect
40. #533×C₈₉	C₂²	semidirect
46. #529×C₈₉	C₂²	semidirect
51. #479×C₈₉	C₂²	semidirect
52. #479×C₈₉	C₂²	semidirect
53. #478×C₈₉	C₂²	semidirect
54. #478×C₈₉	C₂²	semidirect
55. #478×C₈₉	C₂²	semidirect
56. #477×C₈₉	C₂²	semidirect
57. #477×C₈₉	C₂²	semidirect
58. #476×C₈₉	C₂²	semidirect
59. #476×C₈₉	C₂²	semidirect
60. #475×C₈₉	C₂²	semidirect
61. #475×C₈₉	C₂²	semidirect
62. #474×C₈₉	C₂²	semidirect
63. #474×C₈₉	C₂²	semidirect
64. #469×C₈₉	C₂²	semidirect
65. #468×C₈₉	C₂²	semidirect
66. #468×C₈₉	C₂²	semidirect
67. #468×C₈₉	C₂²	semidirect
68. #466×C₈₉	C₂²	semidirect
69. #465×C₈₉	C₂²	semidirect
70. #465×C₈₉	C₂²	semidirect
71. #465×C₈₉	C₂²	semidirect
72. #463×C₈₉	C₂²	semidirect
73. #463×C₈₉	C₂²	semidirect
74. #461×C₈₉	C₂²	semidirect
75. #461×C₈₉	C₂²	semidirect
86. #424×C₈₉	C₂²	semidirect
88. #423×C₈₉	C₂²	semidirect
90. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
440. #60924	C₈₉	direct (N × H)
448. #3508	C₂×C₈₉	semidirect
449. #3461	C₂×C₈₉	semidirect
450. #3260	C₂×C₈₉	semidirect
451. #3257	C₂×C₈₉	semidirect
452. #3254	C₂×C₈₉	semidirect
453. #3251	C₂×C₈₉	semidirect
454. #3247	C₂×C₈₉	semidirect
455. #3246	C₂×C₈₉	semidirect
456. #3081	C₂×C₈₉	semidirect
457. #3078	C₂×C₈₉	semidirect
458. #3076	C₂×C₈₉	semidirect
459. #3062	C₂×C₈₉	semidirect
460. #3057	C₂×C₈₉	semidirect
461. #3042	C₂×C₈₉	semidirect
462. #3038	C₂×C₈₉	semidirect
463. C₂×#460	C₂×C₈₉	semidirect
464. #2906	C₂×C₈₉	semidirect
465. C₈₉	#60924	direct (N × H)
477. #542	C₂²×C₈₉	semidirect
479. #541	C₂²×C₈₉	semidirect
488. #533	C₂²×C₈₉	semidirect
494. #529	C₂²×C₈₉	semidirect
499. #479	C₂²×C₈₉	semidirect
500. #479	C₂²×C₈₉	semidirect
501. #478	C₂²×C₈₉	semidirect
502. #478	C₂²×C₈₉	semidirect
503. #478	C₂²×C₈₉	semidirect
504. #477	C₂²×C₈₉	semidirect
505. #477	C₂²×C₈₉	semidirect
506. #476	C₂²×C₈₉	semidirect
507. #476	C₂²×C₈₉	semidirect
508. #475	C₂²×C₈₉	semidirect
509. #475	C₂²×C₈₉	semidirect
510. #474	C₂²×C₈₉	semidirect
511. #474	C₂²×C₈₉	semidirect
512. #469	C₂²×C₈₉	semidirect
513. #468	C₂²×C₈₉	semidirect
514. #468	C₂²×C₈₉	semidirect
515. #468	C₂²×C₈₉	semidirect
516. #466	C₂²×C₈₉	semidirect
517. #465	C₂²×C₈₉	semidirect
518. #465	C₂²×C₈₉	semidirect
519. #465	C₂²×C₈₉	semidirect
520. #463	C₂²×C₈₉	semidirect
521. #463	C₂²×C₈₉	semidirect
522. #461	C₂²×C₈₉	semidirect
523. #461	C₂²×C₈₉	semidirect
534. #424	C₂²×C₈₉	semidirect
536. #423	C₂²×C₈₉	semidirect
538. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3508	2
C₈₉×#3461	2
C₈₉×#3260	2
C₈₉×#3257	2
C₈₉×#3254	2
C₈₉×#3251	2
C₈₉×#3247	2
C₈₉×#3246	2
C₈₉×#3081	2
C₈₉×#3078	2
C₈₉×#3076	2
C₈₉×#3062	2
C₈₉×#3057	2
C₈₉×#3042	2
C₈₉×#3038	2
C₂×#460×C₈₉	2
C₈₉×#2906	2
#60924	89

Subgroups — C89×#60924 #36438772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60924 #36438772