Subgroups — C₈₉×#61988 #36439836

Order 22784.

1960 conjugacy classes of subgroups.

The subgroup lattice has 926 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×#3483	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3399	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3375	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3319	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3305	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3287	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3268	C₂	1	4	yes	maximal, complemented
9	C₈₉×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3245	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3214	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×#3107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#3035	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2990	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
19	C₂×#135×C₈₉	C₂²	1	4	yes	complemented
20	#559×C₈₉	—	2	1	no	—
21	#559×C₈₉	C₂²	1	2	yes	—
22	Q₈²×C₈₉	C₂²	1	1	yes	characteristic, complemented
23	#555×C₈₉	—	2	2	no	—
24	#555×C₈₉	—	2	1	no	—
25	#555×C₈₉	C₂²	1	2	yes	—
26	#555×C₈₉	C₂²	1	1	yes	characteristic, complemented
27	#550×C₈₉	—	2	1	no	—
28	#550×C₈₉	—	2	1	no	—
29	#550×C₈₉	C₂²	1	2	yes	—
30	#550×C₈₉	C₂²	1	2	yes	—
31	#550×C₈₉	C₂²	1	1	yes	characteristic, complemented
32	#550×C₈₉	C₂²	1	1	yes	characteristic, complemented
33	#546×C₈₉	—	2	2	no	—
34	#546×C₈₉	C₂²	1	4	yes	—
35	#540×C₈₉	—	2	2	no	—
36	#535×C₈₉	—	2	1	no	—
37	#533×C₈₉	C₂²	1	1	yes	characteristic
38	#532×C₈₉	—	2	1	no	—
39	#532×C₈₉	—	2	2	no	—
40	#532×C₈₉	C₂²	1	2	yes	—
41	#532×C₈₉	C₂²	1	2	yes	—
42	#532×C₈₉	C₂²	1	1	yes	characteristic
43	#532×C₈₉	C₂²	1	2	yes	complemented
44	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
45	#518×C₈₉	—	2	1	no	—
46	C₄×#41×C₈₉	—	2	1	no	—
47	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
48	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
49	C₄×#41×C₈₉	C₂²	1	2	yes	complemented
50	#496×C₈₉	C₂²	1	4	yes	complemented
51	#493×C₈₉	C₂²	1	2	yes	—
52	#489×C₈₉	C₂²	1	4	yes	complemented
53	#486×C₈₉	C₂²	1	2	yes	—
54	#485×C₈₉	C₂²	1	2	yes	—
55	#482×C₈₉	C₂²	1	4	yes	complemented
56	#477×C₈₉	C₂²	1	2	yes	complemented
57	#475×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#474×C₈₉	C₂²	1	4	yes	complemented
59	#474×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#474×C₈₉	C₂²	1	2	yes	complemented
61	#468×C₈₉	C₂²	1	4	yes	—
62	#466×C₈₉	C₂²	1	4	yes	complemented
63	#466×C₈₉	C₂²	1	4	yes	complemented
64	#464×C₈₉	C₂²	1	4	yes	complemented
65	#463×C₈₉	C₂²	1	4	yes	complemented
66	#462×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#461×C₈₉	C₂²	1	1	yes	characteristic, complemented
68	#461×C₈₉	C₂²	1	2	yes	complemented
69	#460×C₈₉	C₂²	1	2	yes	—
70	#460×C₈₉	C₂²	1	2	yes	—
71	#460×C₈₉	C₂²	1	2	yes	complemented
72	#459×C₈₉	C₂²	1	2	yes	—
73	#459×C₈₉	C₂²	1	2	yes	—
74	#459×C₈₉	C₂²	1	2	yes	—
75	#459×C₈₉	C₂²	1	2	yes	—
76	#459×C₈₉	C₂²	1	4	yes	complemented
77	#452×C₈₉	C₂²	1	2	yes	—
78	#449×C₈₉	C₂²	1	4	yes	complemented
79	#449×C₈₉	C₂²	1	4	yes	complemented
80	#449×C₈₉	C₂²	1	4	yes	complemented
81	#447×C₈₉	C₂²	1	4	yes	—
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×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
86	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
87	#435×C₈₉	C₂²	1	4	yes	—
88	C₈×D₄×C₈₉	C₂²	1	2	yes	complemented
89	#432×C₈₉	C₂²	1	2	yes	complemented
90	#431×C₈₉	C₂²	1	1	yes	characteristic
91	#423×C₈₉	C₂²	1	1	yes	characteristic
92	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	complemented
93	#418×C₈₉	C₂²	1	2	yes	—
94	#416×C₈₉	C₂²	1	4	yes	complemented
95	C₂×#41×C₈₉	—	2	1	no	—
96	C₂×#41×C₈₉	—	2	1	no	—
97	C₂×#41×C₈₉	—	2	2	no	—
98	C₂×#41×C₈₉	—	2	2	no	—
99	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
100	C₂×#41×C₈₉	C₂³	1	2	yes	—
101	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
102	C₂×#41×C₈₉	C₂³	1	4	yes	—
103	C₂²×D₄×C₈₉	—	2	1	no	—
104	C₂²×D₄×C₈₉	—	2	1	no	—
105	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
106	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
107	#135×C₈₉	—	4	8	no	—
108	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
111	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
112	C₂×D₈×C₈₉	C₂³	1	4	yes	—
113	C₂×D₈×C₈₉	C₂³	1	4	yes	—
114	C₂×D₈×C₈₉	C₂³	1	4	yes	—
115	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
116	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
117	C₄⋊Q₈×C₈₉	—	2	1	no	—
118	C₄⋊Q₈×C₈₉	—	2	2	no	—
119	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
120	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
121	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
122	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
123	#127×C₈₉	—	2	2	no	—
124	#127×C₈₉	—	2	1	no	—
125	#127×C₈₉	—	2	2	no	—
126	#127×C₈₉	—	2	1	no	—
127	#127×C₈₉	—	2	1	no	—
128	#127×C₈₉	C₂³	1	2	yes	—
129	#127×C₈₉	C₂³	1	2	yes	—
130	#127×C₈₉	C₂³	1	2	yes	—
131	#127×C₈₉	C₂³	1	1	yes	characteristic
132	#125×C₈₉	—	2	1	no	—
133	#124×C₈₉	—	2	2	no	—
134	#124×C₈₉	—	2	2	no	—
135	#124×C₈₉	—	2	2	no	—
136	#124×C₈₉	—	2	2	no	—
137	#124×C₈₉	—	2	2	no	—
138	#124×C₈₉	—	2	1	no	—
139	#124×C₈₉	—	2	2	no	—
140	#124×C₈₉	C₂³	1	4	yes	—
141	#123×C₈₉	—	2	4	no	—
142	#123×C₈₉	—	2	4	no	—
143	C₂²⋊Q₈×C₈₉	—	2	1	no	—
144	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
145	#121×C₈₉	—	2	2	no	—
146	#121×C₈₉	—	2	1	no	—
147	#121×C₈₉	—	2	2	no	—
148	#121×C₈₉	—	2	2	no	—
149	#121×C₈₉	—	2	2	no	—
150	#121×C₈₉	—	2	1	no	—
151	#121×C₈₉	—	2	2	no	—
152	#121×C₈₉	—	2	1	no	—
153	#121×C₈₉	—	2	2	no	—
154	#121×C₈₉	—	2	2	no	—
155	#121×C₈₉	—	2	2	no	—
156	#121×C₈₉	—	2	2	no	—
157	#121×C₈₉	—	2	4	no	—
158	#121×C₈₉	—	2	4	no	—
159	#121×C₈₉	C₂³	1	2	yes	—
160	#121×C₈₉	C₂³	1	2	yes	—
161	#121×C₈₉	C₂³	1	2	yes	—
162	#121×C₈₉	C₂³	1	4	yes	—
163	#120×C₈₉	—	2	4	no	—
164	C₄×Q₈×C₈₉	—	2	1	no	—
165	C₄×Q₈×C₈₉	—	2	1	no	—
166	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
167	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
168	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
170	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₈₉	—	2	1	no	—
173	C₄×D₄×C₈₉	—	2	1	no	—
174	C₄×D₄×C₈₉	—	2	2	no	—
175	C₄×D₄×C₈₉	—	2	2	no	—
176	C₄×D₄×C₈₉	—	2	2	no	—
177	C₄×D₄×C₈₉	—	2	1	no	—
178	C₄×D₄×C₈₉	—	2	2	no	—
179	C₄×D₄×C₈₉	—	2	2	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	D₄	1	2	yes	—
186	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
187	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₈₉	C₂³	1	4	yes	—
189	C₄×D₄×C₈₉	C₂³	1	2	yes	—
190	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₈₉	C₂³	1	2	yes	—
192	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
193	C₄×D₄×C₈₉	C₂³	1	2	yes	—
194	#117×C₈₉	—	2	1	no	—
195	#117×C₈₉	—	2	2	no	—
196	#117×C₈₉	—	2	1	no	—
197	#117×C₈₉	—	2	1	no	—
198	#117×C₈₉	—	2	2	no	—
199	#117×C₈₉	D₄	1	1	yes	characteristic
200	#117×C₈₉	D₄	1	2	yes	—
201	#117×C₈₉	C₂³	1	2	yes	—
202	#117×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	2	no	—
206	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
207	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
208	#107×C₈₉	C₂³	1	2	yes	—
209	#107×C₈₉	C₂³	1	4	yes	—
210	#106×C₈₉	C₂³	1	2	yes	—
211	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
212	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
213	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
214	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
215	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
216	#103×C₈₉	C₂³	1	2	yes	—
217	#103×C₈₉	C₂³	1	4	yes	—
218	#103×C₈₉	C₂³	1	2	yes	—
219	#103×C₈₉	C₂³	1	2	yes	—
220	#102×C₈₉	C₂³	1	4	yes	—
221	#102×C₈₉	C₂³	1	4	yes	—
222	#102×C₈₉	C₂³	1	4	yes	—
223	#102×C₈₉	C₂³	1	2	yes	—
224	#102×C₈₉	C₂³	1	4	yes	—
225	#102×C₈₉	C₂³	1	4	yes	—
226	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
227	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
228	#97×C₈₉	C₂³	1	4	yes	—
229	C₄×C₈×C₈₉	C₂³	1	2	yes	—
230	C₂⁴×C₈₉	—	2	2	no	—
231	#41×C₈₉	—	2	4	no	—
232	#41×C₈₉	—	2	2	no	—
233	#41×C₈₉	—	4	2	no	—
234	#41×C₈₉	—	4	1	no	—
235	#41×C₈₉	—	4	2	no	—
236	#41×C₈₉	—	4	4	no	—
237	#41×C₈₉	—	4	4	no	—
238	#41×C₈₉	—	4	4	no	—
239	#41×C₈₉	—	8	2	no	—
240	#41×C₈₉	—	8	4	no	—
241	#41×C₈₉	—	8	4	no	—
242	C₂×Q₈×C₈₉	—	2	1	no	—
243	C₂×Q₈×C₈₉	—	2	2	no	—
244	C₂×Q₈×C₈₉	—	2	1	no	—
245	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
246	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
247	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
248	C₂×D₄×C₈₉	—	2	1	no	—
249	C₂×D₄×C₈₉	—	2	2	no	—
250	C₂×D₄×C₈₉	—	2	4	no	—
251	C₂×D₄×C₈₉	—	2	4	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	2	no	—
257	C₂×D₄×C₈₉	—	2	1	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	1	no	—
262	C₂×D₄×C₈₉	—	2	2	no	—
263	C₂×D₄×C₈₉	—	2	2	no	—
264	C₂×D₄×C₈₉	—	4	2	no	—
265	C₂×D₄×C₈₉	—	4	2	no	—
266	C₂×D₄×C₈₉	—	4	4	no	—
267	C₂×D₄×C₈₉	—	8	2	no	—
268	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
269	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
270	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
271	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
272	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₈₉	—	2	2	no	—
274	C₂²×C₄×C₈₉	—	2	1	no	—
275	C₂²×C₄×C₈₉	—	2	2	no	—
276	C₂²×C₄×C₈₉	—	2	1	no	—
277	C₂²×C₄×C₈₉	—	2	1	no	—
278	C₂²×C₄×C₈₉	—	2	2	no	—
279	C₂²×C₄×C₈₉	—	2	4	no	—
280	C₂²×C₄×C₈₉	—	2	4	no	—
281	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
283	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
285	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
287	Q₁₆×C₈₉	—	2	4	no	—
288	SD₁₆×C₈₉	—	2	8	no	—
289	SD₁₆×C₈₉	—	4	2	no	—
290	SD₁₆×C₈₉	—	4	4	no	—
291	D₈×C₈₉	—	4	4	no	—
292	D₈×C₈₉	—	4	4	no	—
293	D₈×C₈₉	—	4	4	no	—
294	M₁₆×C₈₉	—	4	2	no	—
295	C₂×C₈×C₈₉	—	4	4	no	—
296	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
297	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
298	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
299	C₄⋊C₄×C₈₉	—	2	1	no	—
300	C₄⋊C₄×C₈₉	—	2	1	no	—
301	C₄⋊C₄×C₈₉	—	2	1	no	—
302	C₄⋊C₄×C₈₉	—	2	2	no	—
303	C₄⋊C₄×C₈₉	—	2	1	no	—
304	C₄⋊C₄×C₈₉	—	2	2	no	—
305	C₄⋊C₄×C₈₉	—	2	1	no	—
306	C₄⋊C₄×C₈₉	—	2	1	no	—
307	C₄⋊C₄×C₈₉	—	2	2	no	—
308	C₄⋊C₄×C₈₉	—	2	2	no	—
309	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
310	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
311	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
312	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
313	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
314	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
315	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
316	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
317	C₂²⋊C₄×C₈₉	—	2	2	no	—
318	C₂²⋊C₄×C₈₉	—	2	1	no	—
319	C₂²⋊C₄×C₈₉	—	2	2	no	—
320	C₂²⋊C₄×C₈₉	—	2	4	no	—
321	C₂²⋊C₄×C₈₉	—	2	4	no	—
322	C₂²⋊C₄×C₈₉	—	2	2	no	—
323	C₂²⋊C₄×C₈₉	—	2	2	no	—
324	C₂²⋊C₄×C₈₉	—	2	2	no	—
325	C₂²⋊C₄×C₈₉	—	2	2	no	—
326	C₂²⋊C₄×C₈₉	—	2	1	no	—
327	C₂²⋊C₄×C₈₉	—	2	1	no	—
328	C₂²⋊C₄×C₈₉	—	2	2	no	—
329	C₂²⋊C₄×C₈₉	—	2	4	no	—
330	C₂²⋊C₄×C₈₉	—	2	4	no	—
331	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
332	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
333	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
334	C₄²×C₈₉	—	2	1	no	—
335	C₄²×C₈₉	—	2	2	no	—
336	C₄²×C₈₉	—	2	1	no	—
337	C₄²×C₈₉	—	2	2	no	—
338	C₄²×C₈₉	—	2	1	no	—
339	C₄²×C₈₉	—	2	2	no	—
340	C₄²×C₈₉	C₂×D₄	1	2	yes	—
341	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
342	C₄²×C₈₉	C₂×D₄	1	2	yes	—
343	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
344	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
345	C₄²×C₈₉	C₂⁴	1	2	yes	—
346	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
347	C₂³×C₈₉	—	2	1	no	—
348	C₂³×C₈₉	—	2	2	no	—
349	C₂³×C₈₉	—	2	4	no	—
350	C₂³×C₈₉	—	4	4	no	—
351	C₂³×C₈₉	—	8	2	no	—
352	C₂³×C₈₉	—	8	2	no	—
353	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
354	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
355	Q₈×C₈₉	—	2	2	no	—
356	Q₈×C₈₉	—	2	1	no	—
357	Q₈×C₈₉	—	2	2	no	—
358	Q₈×C₈₉	—	2	2	no	—
359	Q₈×C₈₉	—	4	2	no	—
360	Q₈×C₈₉	—	8	2	no	—
361	Q₈×C₈₉	—	8	1	no	—
362	Q₈×C₈₉	H(5,𝔽₂)	1	2	yes	—
363	D₄×C₈₉	—	2	2	no	—
364	D₄×C₈₉	—	2	1	no	—
365	D₄×C₈₉	—	2	4	no	—
366	D₄×C₈₉	—	2	2	no	—
367	D₄×C₈₉	—	2	2	no	—
368	D₄×C₈₉	—	2	4	no	—
369	D₄×C₈₉	—	2	1	no	—
370	D₄×C₈₉	—	4	2	no	—
371	D₄×C₈₉	—	4	4	no	—
372	D₄×C₈₉	—	4	2	no	—
373	D₄×C₈₉	—	4	4	no	—
374	D₄×C₈₉	—	4	4	no	—
375	D₄×C₈₉	—	4	4	no	—
376	D₄×C₈₉	—	4	2	no	—
377	D₄×C₈₉	—	4	4	no	—
378	D₄×C₈₉	—	8	2	no	—
379	D₄×C₈₉	—	8	2	no	—
380	D₄×C₈₉	—	8	2	no	—
381	D₄×C₈₉	—	8	1	no	—
382	D₄×C₈₉	—	8	4	no	—
383	D₄×C₈₉	—	8	2	no	—
384	D₄×C₈₉	—	8	2	no	—
385	D₄×C₈₉	—	8	2	no	—
386	D₄×C₈₉	—	8	4	no	—
387	C₂×C₄×C₈₉	—	2	1	no	—
388	C₂×C₄×C₈₉	—	2	2	no	—
389	C₂×C₄×C₈₉	—	2	2	no	—
390	C₂×C₄×C₈₉	—	2	4	no	—
391	C₂×C₄×C₈₉	—	2	2	no	—
392	C₂×C₄×C₈₉	—	2	1	no	—
393	C₂×C₄×C₈₉	—	2	1	no	—
394	C₂×C₄×C₈₉	—	2	2	no	—
395	C₂×C₄×C₈₉	—	2	1	no	—
396	C₂×C₄×C₈₉	—	2	2	no	—
397	C₂×C₄×C₈₉	—	2	1	no	—
398	C₂×C₄×C₈₉	—	2	2	no	—
399	C₂×C₄×C₈₉	—	2	2	no	—
400	C₂×C₄×C₈₉	—	4	2	no	—
401	C₂×C₄×C₈₉	—	4	4	no	—
402	C₂×C₄×C₈₉	—	4	2	no	—
403	C₂×C₄×C₈₉	—	4	4	no	—
404	C₂×C₄×C₈₉	—	4	2	no	—
405	C₂×C₄×C₈₉	—	4	2	no	—
406	C₂×C₄×C₈₉	—	4	4	no	—
407	C₂×C₄×C₈₉	—	8	4	no	—
408	C₂×C₄×C₈₉	—	8	4	no	—
409	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
410	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
418	C₈×C₈₉	—	2	2	no	—
419	C₈×C₈₉	—	2	4	no	—
420	C₈×C₈₉	—	2	2	no	—
421	C₂²×C₈₉	—	2	2	no	—
422	C₂²×C₈₉	—	2	1	no	—
423	C₂²×C₈₉	—	2	1	no	—
424	C₂²×C₈₉	—	2	2	no	—
425	C₂²×C₈₉	—	2	2	no	—
426	C₂²×C₈₉	—	2	1	no	—
427	C₂²×C₈₉	—	4	1	no	—
428	C₂²×C₈₉	—	4	2	no	—
429	C₂²×C₈₉	—	4	4	no	—
430	C₂²×C₈₉	—	4	2	no	—
431	C₂²×C₈₉	—	4	1	no	—
432	C₂²×C₈₉	—	4	4	no	—
433	C₂²×C₈₉	—	4	1	no	—
434	C₂²×C₈₉	—	4	2	no	—
435	C₂²×C₈₉	—	4	4	no	—
436	C₂²×C₈₉	—	16	4	no	—
437	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
438	C₄×C₈₉	—	2	2	no	—
439	C₄×C₈₉	—	2	1	no	—
440	C₄×C₈₉	—	2	2	no	—
441	C₄×C₈₉	—	2	1	no	—
442	C₄×C₈₉	—	2	2	no	—
443	C₄×C₈₉	—	2	2	no	—
444	C₄×C₈₉	—	2	1	no	—
445	C₄×C₈₉	—	4	2	no	—
446	C₄×C₈₉	—	4	1	no	—
447	C₄×C₈₉	—	4	1	no	—
448	C₄×C₈₉	—	4	2	no	—
449	C₄×C₈₉	—	4	2	no	—
450	C₄×C₈₉	#575	1	2	yes	—
451	C₄×C₈₉	#576	1	2	yes	—
452	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
453	C₄×C₈₉	#585	1	1	yes	characteristic
454	#61988	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
455	C₂×C₈₉	—	4	2	no	—
456	C₂×C₈₉	—	4	1	no	—
457	C₂×C₈₉	—	8	1	no	—
458	C₂×C₈₉	—	8	2	no	—
459	C₂×C₈₉	—	8	4	no	—
460	C₂×C₈₉	#3488	1	1	yes	characteristic
461	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
462	C₂×C₈₉	C₂×#576	1	1	yes	characteristic
463	#3508	C₂×C₈₉	1	1	yes	characteristic, complemented
464	#3483	C₂×C₈₉	1	1	yes	characteristic, complemented
465	#3399	C₂×C₈₉	1	2	yes	complemented
466	#3375	C₂×C₈₉	1	2	yes	complemented
467	#3319	C₂×C₈₉	1	4	yes	complemented
468	#3305	C₂×C₈₉	1	2	yes	complemented
469	#3287	C₂×C₈₉	1	2	yes	complemented
470	#3268	C₂×C₈₉	1	4	yes	complemented
471	#3254	C₂×C₈₉	1	1	yes	characteristic, complemented
472	#3245	C₂×C₈₉	1	2	yes	complemented
473	#3214	C₂×C₈₉	1	2	yes	complemented
474	#3205	C₂×C₈₉	1	1	yes	characteristic, complemented
475	#3115	C₂×C₈₉	1	2	yes	complemented
476	#3107	C₂×C₈₉	1	1	yes	characteristic, complemented
477	#3038	C₂×C₈₉	1	1	yes	characteristic, complemented
478	#3035	C₂×C₈₉	1	2	yes	complemented
479	#2990	C₂×C₈₉	1	1	yes	characteristic, complemented
480	C₈₉	#61988	1	1	yes	characteristic, direct product factor, Sylow
481	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
482	C₂×#135	C₂²×C₈₉	1	4	yes	complemented
483	#559	—	2	1	no	—
484	#559	C₂²×C₈₉	1	2	yes	—
485	Q₈²	C₂²×C₈₉	1	1	yes	characteristic, complemented
486	#555	—	2	2	no	—
487	#555	—	2	1	no	—
488	#555	C₂²×C₈₉	1	2	yes	—
489	#555	C₂²×C₈₉	1	1	yes	characteristic, complemented
490	#550	—	2	1	no	—
491	#550	—	2	1	no	—
492	#550	C₂²×C₈₉	1	2	yes	—
493	#550	C₂²×C₈₉	1	2	yes	—
494	#550	C₂²×C₈₉	1	1	yes	characteristic, complemented
495	#550	C₂²×C₈₉	1	1	yes	characteristic, complemented
496	#546	—	2	2	no	—
497	#546	C₂²×C₈₉	1	4	yes	—
498	#540	—	2	2	no	—
499	#535	—	2	1	no	—
500	#533	C₂²×C₈₉	1	1	yes	characteristic
501	#532	—	2	1	no	—
502	#532	—	2	2	no	—
503	#532	C₂²×C₈₉	1	2	yes	—
504	#532	C₂²×C₈₉	1	2	yes	—
505	#532	C₂²×C₈₉	1	1	yes	characteristic
506	#532	C₂²×C₈₉	1	2	yes	complemented
507	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
508	#518	—	2	1	no	—
509	C₄×#41	—	2	1	no	—
510	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
511	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
512	C₄×#41	C₂²×C₈₉	1	2	yes	complemented
513	#496	C₂²×C₈₉	1	4	yes	complemented
514	#493	C₂²×C₈₉	1	2	yes	—
515	#489	C₂²×C₈₉	1	4	yes	complemented
516	#486	C₂²×C₈₉	1	2	yes	—
517	#485	C₂²×C₈₉	1	2	yes	—
518	#482	C₂²×C₈₉	1	4	yes	complemented
519	#477	C₂²×C₈₉	1	2	yes	complemented
520	#475	C₂²×C₈₉	1	1	yes	characteristic, complemented
521	#474	C₂²×C₈₉	1	1	yes	characteristic, complemented
522	#474	C₂²×C₈₉	1	2	yes	complemented
523	#474	C₂²×C₈₉	1	4	yes	complemented
524	#468	C₂²×C₈₉	1	4	yes	—
525	#466	C₂²×C₈₉	1	4	yes	complemented
526	#466	C₂²×C₈₉	1	4	yes	complemented
527	#464	C₂²×C₈₉	1	4	yes	complemented
528	#463	C₂²×C₈₉	1	4	yes	complemented
529	#462	C₂²×C₈₉	1	1	yes	characteristic, complemented
530	#461	C₂²×C₈₉	1	1	yes	characteristic, complemented
531	#461	C₂²×C₈₉	1	2	yes	complemented
532	#460	C₂²×C₈₉	1	2	yes	—
533	#460	C₂²×C₈₉	1	2	yes	—
534	#460	C₂²×C₈₉	1	2	yes	complemented
535	#459	C₂²×C₈₉	1	2	yes	—
536	#459	C₂²×C₈₉	1	2	yes	—
537	#459	C₂²×C₈₉	1	2	yes	—
538	#459	C₂²×C₈₉	1	2	yes	—
539	#459	C₂²×C₈₉	1	4	yes	complemented
540	#452	C₂²×C₈₉	1	2	yes	—
541	#449	C₂²×C₈₉	1	4	yes	complemented
542	#449	C₂²×C₈₉	1	4	yes	complemented
543	#449	C₂²×C₈₉	1	4	yes	complemented
544	#447	C₂²×C₈₉	1	4	yes	—
545	#446	C₂²×C₈₉	1	2	yes	complemented
546	#442	C₂²×C₈₉	1	4	yes	complemented
547	#440	C₂²×C₈₉	1	4	yes	complemented
548	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
549	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
550	#435	C₂²×C₈₉	1	4	yes	—
551	C₈×D₄	C₂²×C₈₉	1	2	yes	complemented
552	#432	C₂²×C₈₉	1	2	yes	complemented
553	#431	C₂²×C₈₉	1	1	yes	characteristic
554	#423	C₂²×C₈₉	1	1	yes	characteristic
555	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	complemented
556	#418	C₂²×C₈₉	1	2	yes	—
557	#416	C₂²×C₈₉	1	4	yes	complemented
558	C₂×#41	—	2	1	no	—
559	C₂×#41	—	2	1	no	—
560	C₂×#41	—	2	2	no	—
561	C₂×#41	—	2	2	no	—
562	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
563	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
564	C₂×#41	C₂³×C₈₉	1	2	yes	—
565	C₂×#41	C₂³×C₈₉	1	4	yes	—
566	C₂²×D₄	—	2	1	no	—
567	C₂²×D₄	—	2	1	no	—
568	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
569	AGL(1,ℤ/8)	—	4	4	no	—
570	#135	—	4	8	no	—
571	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
572	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
573	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
574	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
575	C₂×D₈	C₂³×C₈₉	1	4	yes	—
576	C₂×D₈	C₂³×C₈₉	1	4	yes	—
577	C₂×D₈	C₂³×C₈₉	1	4	yes	—
578	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
579	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
580	C₄⋊Q₈	—	2	1	no	—
581	C₄⋊Q₈	—	2	2	no	—
582	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
583	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
584	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
585	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
586	#127	—	2	2	no	—
587	#127	—	2	1	no	—
588	#127	—	2	2	no	—
589	#127	—	2	1	no	—
590	#127	—	2	1	no	—
591	#127	C₂³×C₈₉	1	2	yes	—
592	#127	C₂³×C₈₉	1	2	yes	—
593	#127	C₂³×C₈₉	1	1	yes	characteristic
594	#127	C₂³×C₈₉	1	2	yes	—
595	#125	—	2	1	no	—
596	#124	—	2	2	no	—
597	#124	—	2	2	no	—
598	#124	—	2	2	no	—
599	#124	—	2	2	no	—
600	#124	—	2	2	no	—
601	#124	—	2	1	no	—
602	#124	—	2	2	no	—
603	#124	C₂³×C₈₉	1	4	yes	—
604	#123	—	2	4	no	—
605	#123	—	2	4	no	—
606	C₂²⋊Q₈	—	2	1	no	—
607	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
608	#121	—	2	2	no	—
609	#121	—	2	1	no	—
610	#121	—	2	2	no	—
611	#121	—	2	2	no	—
612	#121	—	2	2	no	—
613	#121	—	2	1	no	—
614	#121	—	2	2	no	—
615	#121	—	2	1	no	—
616	#121	—	2	2	no	—
617	#121	—	2	2	no	—
618	#121	—	2	2	no	—
619	#121	—	2	2	no	—
620	#121	—	2	4	no	—
621	#121	—	2	4	no	—
622	#121	C₂³×C₈₉	1	4	yes	—
623	#121	C₂³×C₈₉	1	2	yes	—
624	#121	C₂³×C₈₉	1	2	yes	—
625	#121	C₂³×C₈₉	1	2	yes	—
626	#120	—	2	4	no	—
627	C₄×Q₈	—	2	1	no	—
628	C₄×Q₈	—	2	1	no	—
629	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
630	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
631	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
632	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
633	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
634	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
635	C₄×D₄	—	2	1	no	—
636	C₄×D₄	—	2	1	no	—
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	—	2	2	no	—
639	C₄×D₄	—	2	2	no	—
640	C₄×D₄	—	2	1	no	—
641	C₄×D₄	—	2	2	no	—
642	C₄×D₄	—	2	2	no	—
643	C₄×D₄	—	2	1	no	—
644	C₄×D₄	—	2	2	no	—
645	C₄×D₄	—	2	2	no	—
646	C₄×D₄	—	2	2	no	—
647	C₄×D₄	—	2	2	no	—
648	C₄×D₄	D₄×C₈₉	1	2	yes	—
649	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
650	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
651	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
652	C₄×D₄	C₂³×C₈₉	1	2	yes	—
653	C₄×D₄	C₂³×C₈₉	1	2	yes	—
654	C₄×D₄	C₂³×C₈₉	1	4	yes	—
655	C₄×D₄	C₂³×C₈₉	1	2	yes	—
656	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
657	#117	—	2	1	no	—
658	#117	—	2	2	no	—
659	#117	—	2	1	no	—
660	#117	—	2	1	no	—
661	#117	—	2	2	no	—
662	#117	D₄×C₈₉	1	1	yes	characteristic
663	#117	D₄×C₈₉	1	2	yes	—
664	#117	C₂³×C₈₉	1	1	yes	characteristic
665	#117	C₂³×C₈₉	1	2	yes	—
666	C₂×C₂²⋊C₄	—	2	4	no	—
667	C₂×C₄²	—	2	1	no	—
668	C₂×C₄²	—	2	2	no	—
669	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
670	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
671	#107	C₂³×C₈₉	1	2	yes	—
672	#107	C₂³×C₈₉	1	4	yes	—
673	#106	C₂³×C₈₉	1	2	yes	—
674	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
675	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
676	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
677	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
678	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
679	#103	C₂³×C₈₉	1	2	yes	—
680	#103	C₂³×C₈₉	1	4	yes	—
681	#103	C₂³×C₈₉	1	2	yes	—
682	#103	C₂³×C₈₉	1	2	yes	—
683	#102	C₂³×C₈₉	1	4	yes	—
684	#102	C₂³×C₈₉	1	4	yes	—
685	#102	C₂³×C₈₉	1	4	yes	—
686	#102	C₂³×C₈₉	1	2	yes	—
687	#102	C₂³×C₈₉	1	4	yes	—
688	#102	C₂³×C₈₉	1	4	yes	—
689	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
690	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
691	#97	C₂³×C₈₉	1	4	yes	—
692	C₄×C₈	C₂³×C₈₉	1	2	yes	—
693	C₂⁴	—	2	2	no	—
694	#41	—	2	4	no	—
695	#41	—	2	2	no	—
696	#41	—	4	2	no	—
697	#41	—	4	1	no	—
698	#41	—	4	2	no	—
699	#41	—	4	4	no	—
700	#41	—	4	4	no	—
701	#41	—	4	4	no	—
702	#41	—	8	2	no	—
703	#41	—	8	4	no	—
704	#41	—	8	4	no	—
705	C₂×Q₈	—	2	1	no	—
706	C₂×Q₈	—	2	2	no	—
707	C₂×Q₈	—	2	1	no	—
708	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
709	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
710	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
711	C₂×D₄	—	2	1	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	2	4	no	—
714	C₂×D₄	—	2	4	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	1	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	4	2	no	—
728	C₂×D₄	—	4	2	no	—
729	C₂×D₄	—	4	4	no	—
730	C₂×D₄	—	8	2	no	—
731	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
732	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
733	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
734	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
735	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	1	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	1	no	—
740	C₂²×C₄	—	2	1	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	4	no	—
743	C₂²×C₄	—	2	4	no	—
744	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
745	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
746	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
747	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
749	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
750	Q₁₆	—	2	4	no	—
751	SD₁₆	—	2	8	no	—
752	SD₁₆	—	4	4	no	—
753	SD₁₆	—	4	2	no	—
754	D₈	—	4	4	no	—
755	D₈	—	4	4	no	—
756	D₈	—	4	4	no	—
757	M₁₆	—	4	2	no	—
758	C₂×C₈	—	4	4	no	—
759	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
760	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
761	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
762	C₄⋊C₄	—	2	1	no	—
763	C₄⋊C₄	—	2	1	no	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	1	no	—
769	C₄⋊C₄	—	2	1	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
773	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
774	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
775	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
776	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
777	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
778	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
779	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	1	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	4	no	—
784	C₂²⋊C₄	—	2	4	no	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	1	no	—
790	C₂²⋊C₄	—	2	1	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
795	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
796	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
797	C₄²	—	2	1	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	2	1	no	—
800	C₄²	—	2	2	no	—
801	C₄²	—	2	1	no	—
802	C₄²	—	2	2	no	—
803	C₄²	C₂×D₄×C₈₉	1	2	yes	—
804	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
805	C₄²	C₂×D₄×C₈₉	1	2	yes	—
806	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
807	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
808	C₄²	C₂⁴×C₈₉	1	2	yes	—
809	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
810	C₂³	—	2	2	no	—
811	C₂³	—	2	1	no	—
812	C₂³	—	2	4	no	—
813	C₂³	—	4	4	no	—
814	C₂³	—	8	2	no	—
815	C₂³	—	8	2	no	—
816	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
817	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
818	Q₈	—	2	2	no	—
819	Q₈	—	2	1	no	—
820	Q₈	—	2	2	no	—
821	Q₈	—	2	2	no	—
822	Q₈	—	4	2	no	—
823	Q₈	—	8	2	no	—
824	Q₈	—	8	1	no	—
825	Q₈	H(5,𝔽₂)×C₈₉	1	2	yes	—
826	D₄	—	2	2	no	—
827	D₄	—	2	1	no	—
828	D₄	—	2	4	no	—
829	D₄	—	2	2	no	—
830	D₄	—	2	2	no	—
831	D₄	—	2	4	no	—
832	D₄	—	2	1	no	—
833	D₄	—	4	2	no	—
834	D₄	—	4	4	no	—
835	D₄	—	4	2	no	—
836	D₄	—	4	4	no	—
837	D₄	—	4	4	no	—
838	D₄	—	4	4	no	—
839	D₄	—	4	2	no	—
840	D₄	—	4	4	no	—
841	D₄	—	8	2	no	—
842	D₄	—	8	2	no	—
843	D₄	—	8	2	no	—
844	D₄	—	8	1	no	—
845	D₄	—	8	4	no	—
846	D₄	—	8	2	no	—
847	D₄	—	8	2	no	—
848	D₄	—	8	2	no	—
849	D₄	—	8	4	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	4	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	4	4	no	—
865	C₂×C₄	—	4	2	no	—
866	C₂×C₄	—	4	4	no	—
867	C₂×C₄	—	4	2	no	—
868	C₂×C₄	—	4	2	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	8	4	no	—
871	C₂×C₄	—	8	4	no	—
872	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
873	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
875	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
876	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
877	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
878	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
879	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
880	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
881	C₈	—	2	2	no	—
882	C₈	—	2	4	no	—
883	C₈	—	2	2	no	—
884	C₂²	—	2	1	no	—
885	C₂²	—	2	2	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	1	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	1	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	1	no	—
892	C₂²	—	4	4	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	4	no	—
896	C₂²	—	4	1	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	4	no	—
899	C₂²	—	16	4	no	—
900	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
901	C₄	—	2	1	no	—
902	C₄	—	2	2	no	—
903	C₄	—	2	2	no	—
904	C₄	—	2	1	no	—
905	C₄	—	2	2	no	—
906	C₄	—	2	1	no	—
907	C₄	—	2	2	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	2	no	—
913	C₄	#575×C₈₉	1	2	yes	—
914	C₄	#576×C₈₉	1	2	yes	—
915	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
916	C₄	#585×C₈₉	1	1	yes	characteristic
917	C₂	—	4	2	no	—
918	C₂	—	4	1	no	—
919	C₂	—	8	2	no	—
920	C₂	—	8	1	no	—
921	C₂	—	8	4	no	—
922	C₂	C₈₉×#3488	1	1	yes	characteristic
923	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
924	C₂	C₂×#576×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 ◁ 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×#3483	C₂	semidirect
3. C₈₉×#3399	C₂	semidirect
4. C₈₉×#3375	C₂	semidirect
5. C₈₉×#3319	C₂	semidirect
6. C₈₉×#3305	C₂	semidirect
7. C₈₉×#3287	C₂	semidirect
8. C₈₉×#3268	C₂	semidirect
9. C₈₉×#3254	C₂	semidirect
10. C₈₉×#3245	C₂	semidirect
11. C₈₉×#3214	C₂	semidirect
12. C₈₉×#3205	C₂	semidirect
13. C₈₉×#3115	C₂	semidirect
14. C₈₉×#3107	C₂	semidirect
15. C₈₉×#3038	C₂	semidirect
16. C₈₉×#3035	C₂	semidirect
17. C₈₉×#2990	C₂	semidirect
19. C₂×#135×C₈₉	C₂²	semidirect
22. Q₈²×C₈₉	C₂²	semidirect
26. #555×C₈₉	C₂²	semidirect
31. #550×C₈₉	C₂²	semidirect
32. #550×C₈₉	C₂²	semidirect
43. #532×C₈₉	C₂²	semidirect
49. C₄×#41×C₈₉	C₂²	semidirect
50. #496×C₈₉	C₂²	semidirect
52. #489×C₈₉	C₂²	semidirect
55. #482×C₈₉	C₂²	semidirect
56. #477×C₈₉	C₂²	semidirect
57. #475×C₈₉	C₂²	semidirect
58. #474×C₈₉	C₂²	semidirect
59. #474×C₈₉	C₂²	semidirect
60. #474×C₈₉	C₂²	semidirect
62. #466×C₈₉	C₂²	semidirect
63. #466×C₈₉	C₂²	semidirect
64. #464×C₈₉	C₂²	semidirect
65. #463×C₈₉	C₂²	semidirect
66. #462×C₈₉	C₂²	semidirect
67. #461×C₈₉	C₂²	semidirect
68. #461×C₈₉	C₂²	semidirect
71. #460×C₈₉	C₂²	semidirect
76. #459×C₈₉	C₂²	semidirect
78. #449×C₈₉	C₂²	semidirect
79. #449×C₈₉	C₂²	semidirect
80. #449×C₈₉	C₂²	semidirect
82. #446×C₈₉	C₂²	semidirect
83. #442×C₈₉	C₂²	semidirect
84. #440×C₈₉	C₂²	semidirect
85. C₄×Q₁₆×C₈₉	C₂²	semidirect
86. C₄×SD₁₆×C₈₉	C₂²	semidirect
88. C₈×D₄×C₈₉	C₂²	semidirect
89. #432×C₈₉	C₂²	semidirect
92. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
94. #416×C₈₉	C₂²	semidirect
454. #61988	C₈₉	direct (N × H)
463. #3508	C₂×C₈₉	semidirect
464. #3483	C₂×C₈₉	semidirect
465. #3399	C₂×C₈₉	semidirect
466. #3375	C₂×C₈₉	semidirect
467. #3319	C₂×C₈₉	semidirect
468. #3305	C₂×C₈₉	semidirect
469. #3287	C₂×C₈₉	semidirect
470. #3268	C₂×C₈₉	semidirect
471. #3254	C₂×C₈₉	semidirect
472. #3245	C₂×C₈₉	semidirect
473. #3214	C₂×C₈₉	semidirect
474. #3205	C₂×C₈₉	semidirect
475. #3115	C₂×C₈₉	semidirect
476. #3107	C₂×C₈₉	semidirect
477. #3038	C₂×C₈₉	semidirect
478. #3035	C₂×C₈₉	semidirect
479. #2990	C₂×C₈₉	semidirect
480. C₈₉	#61988	direct (N × H)
482. C₂×#135	C₂²×C₈₉	semidirect
485. Q₈²	C₂²×C₈₉	semidirect
489. #555	C₂²×C₈₉	semidirect
494. #550	C₂²×C₈₉	semidirect
495. #550	C₂²×C₈₉	semidirect
506. #532	C₂²×C₈₉	semidirect
512. C₄×#41	C₂²×C₈₉	semidirect
513. #496	C₂²×C₈₉	semidirect
515. #489	C₂²×C₈₉	semidirect
518. #482	C₂²×C₈₉	semidirect
519. #477	C₂²×C₈₉	semidirect
520. #475	C₂²×C₈₉	semidirect
521. #474	C₂²×C₈₉	semidirect
522. #474	C₂²×C₈₉	semidirect
523. #474	C₂²×C₈₉	semidirect
525. #466	C₂²×C₈₉	semidirect
526. #466	C₂²×C₈₉	semidirect
527. #464	C₂²×C₈₉	semidirect
528. #463	C₂²×C₈₉	semidirect
529. #462	C₂²×C₈₉	semidirect
530. #461	C₂²×C₈₉	semidirect
531. #461	C₂²×C₈₉	semidirect
534. #460	C₂²×C₈₉	semidirect
539. #459	C₂²×C₈₉	semidirect
541. #449	C₂²×C₈₉	semidirect
542. #449	C₂²×C₈₉	semidirect
543. #449	C₂²×C₈₉	semidirect
545. #446	C₂²×C₈₉	semidirect
546. #442	C₂²×C₈₉	semidirect
547. #440	C₂²×C₈₉	semidirect
548. C₄×Q₁₆	C₂²×C₈₉	semidirect
549. C₄×SD₁₆	C₂²×C₈₉	semidirect
551. C₈×D₄	C₂²×C₈₉	semidirect
552. #432	C₂²×C₈₉	semidirect
555. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
557. #416	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×#3483	2
C₈₉×#3399	2
C₈₉×#3375	2
C₈₉×#3319	2
C₈₉×#3305	2
C₈₉×#3287	2
C₈₉×#3268	2
C₈₉×#3254	2
C₈₉×#3245	2
C₈₉×#3214	2
C₈₉×#3205	2
C₈₉×#3115	2
C₈₉×#3107	2
C₈₉×#3038	2
C₈₉×#3035	2
C₈₉×#2990	2
#61988	89

Subgroups — C89×#61988 #36439836

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61988 #36439836