Subgroups — C₈₉×#62610 #36440458

Order 22784.

1830 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3543	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3373	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3366	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3361	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3325	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3325	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3322	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3319	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3318	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3305	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3241	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3233	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3220	C₂	1	2	yes	maximal, complemented
18	C₈₉×#3205	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3176	C₂	1	2	yes	maximal, complemented
20	C₈₉×#3171	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#3138	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₉×#3136	C₂	1	2	yes	maximal, complemented
23	C₈₉×#2969	C₂	1	1	yes	maximal, characteristic, complemented
24	#562×C₈₉	—	2	2	no	—
25	#560×C₈₉	—	2	2	no	—
26	#559×C₈₉	C₂²	1	1	yes	characteristic
27	#555×C₈₉	C₂²	1	2	yes	complemented
28	#555×C₈₉	C₂²	1	1	yes	characteristic, complemented
29	#554×C₈₉	C₂²	1	1	yes	characteristic, complemented
30	#553×C₈₉	C₂²	1	2	yes	complemented
31	#552×C₈₉	—	2	1	no	—
32	#550×C₈₉	C₂²	1	1	yes	characteristic
33	#550×C₈₉	C₂²	1	1	yes	characteristic
34	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
35	#548×C₈₉	—	2	1	no	—
36	#547×C₈₉	C₂²	1	1	yes	characteristic, complemented
37	#546×C₈₉	—	2	1	no	—
38	#546×C₈₉	C₂²	1	2	yes	—
39	D₄²×C₈₉	—	2	1	no	—
40	D₄²×C₈₉	C₂²	1	2	yes	—
41	D₄²×C₈₉	C₂²	1	1	yes	characteristic
42	#544×C₈₉	C₂²	1	2	yes	complemented
43	#542×C₈₉	—	2	2	no	—
44	#540×C₈₉	—	2	1	no	—
45	#540×C₈₉	C₂²	1	2	yes	—
46	#540×C₈₉	C₂²	1	2	yes	complemented
47	#537×C₈₉	—	2	1	no	—
48	#536×C₈₉	—	2	1	no	—
49	#535×C₈₉	—	2	1	no	—
50	#535×C₈₉	C₂²	1	2	yes	—
51	#534×C₈₉	—	2	2	no	—
52	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
54	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
55	#529×C₈₉	C₂²	1	1	yes	characteristic
56	#529×C₈₉	C₂²	1	1	yes	characteristic
57	#501×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#499×C₈₉	C₂²	1	2	yes	complemented
59	#496×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#493×C₈₉	C₂²	1	2	yes	complemented
61	#490×C₈₉	C₂²	1	2	yes	complemented
62	#490×C₈₉	C₂²	1	2	yes	complemented
63	#490×C₈₉	C₂²	1	2	yes	complemented
64	#490×C₈₉	C₂²	1	1	yes	characteristic, complemented
65	#489×C₈₉	C₂²	1	2	yes	complemented
66	#489×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#488×C₈₉	C₂²	1	2	yes	complemented
68	#488×C₈₉	C₂²	1	2	yes	complemented
69	#486×C₈₉	C₂²	1	1	yes	characteristic
70	#486×C₈₉	C₂²	1	1	yes	characteristic
71	#486×C₈₉	C₂²	1	2	yes	complemented
72	#486×C₈₉	C₂²	1	1	yes	characteristic, complemented
73	#486×C₈₉	C₂²	1	1	yes	characteristic, complemented
74	#486×C₈₉	C₂²	1	2	yes	complemented
75	#485×C₈₉	C₂²	1	2	yes	complemented
76	#482×C₈₉	C₂²	1	2	yes	—
77	#482×C₈₉	C₂²	1	2	yes	complemented
78	#482×C₈₉	C₂²	1	2	yes	complemented
79	#481×C₈₉	C₂²	1	2	yes	complemented
80	#480×C₈₉	C₂²	1	2	yes	complemented
81	#478×C₈₉	C₂²	1	2	yes	complemented
82	#478×C₈₉	C₂²	1	2	yes	complemented
83	#477×C₈₉	C₂²	1	1	yes	characteristic, complemented
84	#476×C₈₉	C₂²	1	1	yes	characteristic, complemented
85	#476×C₈₉	C₂²	1	2	yes	complemented
86	#475×C₈₉	C₂²	1	1	yes	characteristic, complemented
87	#474×C₈₉	C₂²	1	2	yes	complemented
88	#474×C₈₉	C₂²	1	1	yes	characteristic, complemented
89	#469×C₈₉	C₂²	1	1	yes	characteristic
90	#469×C₈₉	C₂²	1	1	yes	characteristic
91	#469×C₈₉	C₂²	1	2	yes	complemented
92	#469×C₈₉	C₂²	1	2	yes	complemented
93	#468×C₈₉	C₂²	1	1	yes	characteristic, complemented
94	#468×C₈₉	C₂²	1	1	yes	characteristic, complemented
95	#466×C₈₉	C₂²	1	2	yes	complemented
96	#466×C₈₉	C₂²	1	2	yes	complemented
97	#463×C₈₉	C₂²	1	2	yes	complemented
98	#463×C₈₉	C₂²	1	2	yes	complemented
99	#459×C₈₉	C₂²	1	1	yes	characteristic
100	#459×C₈₉	C₂²	1	1	yes	characteristic
101	#459×C₈₉	C₂²	1	2	yes	complemented
102	#459×C₈₉	C₂²	1	2	yes	complemented
103	#459×C₈₉	C₂²	1	1	yes	characteristic, complemented
104	#459×C₈₉	C₂²	1	1	yes	characteristic, complemented
105	#449×C₈₉	C₂²	1	2	yes	complemented
106	#449×C₈₉	C₂²	1	2	yes	complemented
107	#447×C₈₉	C₂²	1	2	yes	complemented
108	#447×C₈₉	C₂²	1	2	yes	complemented
109	#447×C₈₉	C₂²	1	2	yes	complemented
110	#447×C₈₉	C₂²	1	2	yes	complemented
111	#446×C₈₉	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
113	#442×C₈₉	C₂²	1	2	yes	complemented
114	#442×C₈₉	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
118	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
120	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
121	#436×C₈₉	C₂²	1	2	yes	complemented
122	#436×C₈₉	C₂²	1	1	yes	characteristic, complemented
123	#435×C₈₉	C₂²	1	2	yes	complemented
124	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
125	#433×C₈₉	C₂²	1	2	yes	complemented
126	#431×C₈₉	C₂²	1	1	yes	characteristic, complemented
127	#418×C₈₉	C₂²	1	2	yes	complemented
128	#418×C₈₉	C₂²	1	2	yes	complemented
129	#418×C₈₉	C₂²	1	2	yes	complemented
130	#417×C₈₉	C₂²	1	2	yes	complemented
131	#416×C₈₉	C₂²	1	2	yes	complemented
132	C₂×#102×C₈₉	C₂²	1	2	yes	complemented
133	#405×C₈₉	C₂²	1	2	yes	complemented
134	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₈₉	—	2	1	no	—
136	C₂×#41×C₈₉	—	2	1	no	—
137	C₂×#41×C₈₉	—	2	1	no	—
138	C₂×#41×C₈₉	C₂³	1	2	yes	—
139	C₂²×Q₈×C₈₉	—	2	1	no	—
140	C₂²×D₄×C₈₉	—	2	2	no	—
141	C₂²×D₄×C₈₉	—	2	1	no	—
142	C₂²×D₄×C₈₉	—	2	1	no	—
143	C₂²×D₄×C₈₉	—	2	1	no	—
144	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
145	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×D₈×C₈₉	C₂³	1	2	yes	—
149	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
150	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
151	C₂×D₈×C₈₉	C₂³	1	2	yes	—
152	C₂×D₈×C₈₉	C₂³	1	2	yes	—
153	C₂×D₈×C₈₉	C₂³	1	2	yes	—
154	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
155	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
156	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
157	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
158	C₄⋊Q₈×C₈₉	—	2	2	no	—
159	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
161	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
163	#127×C₈₉	—	2	1	no	—
164	#127×C₈₉	—	2	1	no	—
165	#127×C₈₉	—	2	1	no	—
166	#127×C₈₉	C₂³	1	1	yes	characteristic
167	#127×C₈₉	C₂³	1	1	yes	characteristic
168	#127×C₈₉	C₂³	1	2	yes	—
169	#127×C₈₉	C₂³	1	2	yes	—
170	#127×C₈₉	C₂³	1	1	yes	characteristic
171	#126×C₈₉	—	2	2	no	—
172	#126×C₈₉	—	2	1	no	—
173	#126×C₈₉	D₄	1	2	yes	—
174	#125×C₈₉	—	2	2	no	—
175	#125×C₈₉	D₄	1	1	yes	characteristic
176	#125×C₈₉	C₂³	1	2	yes	—
177	#125×C₈₉	C₂³	1	2	yes	—
178	#125×C₈₉	C₂³	1	1	yes	characteristic
179	#124×C₈₉	—	2	1	no	—
180	#124×C₈₉	—	2	2	no	—
181	#124×C₈₉	—	2	2	no	—
182	#124×C₈₉	—	2	2	no	—
183	#124×C₈₉	—	2	1	no	—
184	#124×C₈₉	D₄	1	1	yes	characteristic
185	#124×C₈₉	C₂³	1	2	yes	—
186	#124×C₈₉	C₂³	1	1	yes	characteristic
187	#123×C₈₉	—	2	1	no	—
188	#123×C₈₉	—	2	2	no	—
189	#123×C₈₉	—	2	2	no	—
190	#123×C₈₉	—	2	2	no	—
191	#123×C₈₉	—	2	2	no	—
192	#123×C₈₉	—	2	2	no	—
193	#123×C₈₉	—	2	2	no	—
194	#123×C₈₉	—	2	2	no	—
195	#123×C₈₉	—	2	2	no	—
196	#123×C₈₉	D₄	1	2	yes	—
197	C₂²⋊Q₈×C₈₉	—	2	1	no	—
198	C₂²⋊Q₈×C₈₉	—	2	1	no	—
199	C₂²⋊Q₈×C₈₉	—	2	1	no	—
200	C₂²⋊Q₈×C₈₉	—	2	1	no	—
201	C₂²⋊Q₈×C₈₉	—	2	1	no	—
202	C₂²⋊Q₈×C₈₉	—	2	2	no	—
203	C₂²⋊Q₈×C₈₉	—	2	2	no	—
204	C₂²⋊Q₈×C₈₉	—	2	2	no	—
205	C₂²⋊Q₈×C₈₉	—	2	2	no	—
206	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
207	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
208	#121×C₈₉	—	2	1	no	—
209	#121×C₈₉	—	2	2	no	—
210	#121×C₈₉	—	2	2	no	—
211	#121×C₈₉	—	2	1	no	—
212	#121×C₈₉	—	2	2	no	—
213	#121×C₈₉	—	2	2	no	—
214	#121×C₈₉	—	2	2	no	—
215	#121×C₈₉	—	2	1	no	—
216	#121×C₈₉	—	2	1	no	—
217	#121×C₈₉	—	2	2	no	—
218	#121×C₈₉	—	2	2	no	—
219	#121×C₈₉	—	2	2	no	—
220	#121×C₈₉	—	2	2	no	—
221	#121×C₈₉	—	2	2	no	—
222	#121×C₈₉	—	2	2	no	—
223	#121×C₈₉	—	2	2	no	—
224	#121×C₈₉	D₄	1	1	yes	characteristic
225	#121×C₈₉	C₂³	1	1	yes	characteristic
226	#121×C₈₉	C₂³	1	1	yes	characteristic
227	#121×C₈₉	C₂³	1	2	yes	—
228	#121×C₈₉	C₂³	1	2	yes	—
229	#121×C₈₉	C₂³	1	2	yes	—
230	#121×C₈₉	C₂³	1	2	yes	—
231	#121×C₈₉	C₂³	1	1	yes	characteristic
232	#120×C₈₉	—	2	2	no	—
233	#120×C₈₉	—	2	2	no	—
234	#120×C₈₉	—	2	2	no	—
235	#120×C₈₉	—	2	2	no	—
236	#120×C₈₉	—	2	2	no	—
237	#120×C₈₉	—	2	2	no	—
238	C₄×Q₈×C₈₉	—	2	1	no	—
239	C₄×Q₈×C₈₉	—	2	1	no	—
240	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₈₉	—	2	1	no	—
243	C₄×D₄×C₈₉	—	2	1	no	—
244	C₄×D₄×C₈₉	—	2	1	no	—
245	C₄×D₄×C₈₉	—	2	2	no	—
246	C₄×D₄×C₈₉	—	2	1	no	—
247	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₈₉	C₂³	1	2	yes	—
251	C₄×D₄×C₈₉	C₂³	1	2	yes	—
252	C₄×D₄×C₈₉	C₂³	1	2	yes	—
253	C₄×D₄×C₈₉	C₂³	1	2	yes	—
254	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₈₉	C₂³	1	2	yes	—
256	#117×C₈₉	—	2	1	no	—
257	#117×C₈₉	—	2	2	no	—
258	#117×C₈₉	—	2	1	no	—
259	#117×C₈₉	C₂³	1	2	yes	—
260	#117×C₈₉	C₂³	1	2	yes	—
261	#117×C₈₉	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
263	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
265	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
266	#107×C₈₉	C₂³	1	2	yes	—
267	#107×C₈₉	C₂³	1	2	yes	—
268	#107×C₈₉	C₂³	1	1	yes	characteristic
269	#107×C₈₉	C₂³	1	1	yes	characteristic
270	#106×C₈₉	C₂³	1	1	yes	characteristic
271	#106×C₈₉	C₂³	1	1	yes	characteristic
272	#106×C₈₉	C₂³	1	2	yes	—
273	#106×C₈₉	C₂³	1	2	yes	—
274	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
275	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
276	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
277	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
278	#103×C₈₉	C₂³	1	1	yes	characteristic
279	#103×C₈₉	C₂³	1	2	yes	—
280	#103×C₈₉	C₂³	1	1	yes	characteristic
281	#103×C₈₉	C₂³	1	2	yes	—
282	#102×C₈₉	C₂³	1	1	yes	characteristic
283	#102×C₈₉	C₂³	1	2	yes	—
284	#102×C₈₉	C₂³	1	2	yes	—
285	#102×C₈₉	C₂³	1	2	yes	—
286	#102×C₈₉	C₂³	1	2	yes	—
287	#102×C₈₉	C₂³	1	2	yes	—
288	#102×C₈₉	C₂³	1	2	yes	—
289	#102×C₈₉	C₂³	1	2	yes	—
290	#102×C₈₉	C₂³	1	1	yes	characteristic
291	#102×C₈₉	C₂³	1	2	yes	—
292	#102×C₈₉	C₂³	1	2	yes	—
293	#102×C₈₉	C₂³	1	2	yes	—
294	#102×C₈₉	C₂³	1	2	yes	—
295	#102×C₈₉	C₂³	1	2	yes	—
296	#102×C₈₉	C₂³	1	2	yes	—
297	#102×C₈₉	C₂³	1	2	yes	—
298	#102×C₈₉	C₂³	1	1	yes	characteristic
299	#102×C₈₉	C₂³	1	1	yes	characteristic
300	#102×C₈₉	C₂³	1	1	yes	characteristic
301	#102×C₈₉	C₂³	1	1	yes	characteristic
302	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
303	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
305	#97×C₈₉	C₂³	1	1	yes	characteristic
306	#97×C₈₉	C₂³	1	1	yes	characteristic
307	#97×C₈₉	C₂³	1	2	yes	—
308	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₈₉	C₂³	1	2	yes	—
311	C₄×C₈×C₈₉	C₂³	1	2	yes	—
312	C₂⁴×C₈₉	—	2	2	no	—
313	C₂⁴×C₈₉	—	2	2	no	—
314	#41×C₈₉	—	4	2	no	—
315	#41×C₈₉	—	4	2	no	—
316	#41×C₈₉	—	8	2	no	—
317	#41×C₈₉	—	8	2	no	—
318	#41×C₈₉	—	8	2	no	—
319	C₂×Q₈×C₈₉	—	2	1	no	—
320	C₂×Q₈×C₈₉	—	2	1	no	—
321	C₂×Q₈×C₈₉	—	2	2	no	—
322	C₂×Q₈×C₈₉	—	2	1	no	—
323	C₂×Q₈×C₈₉	—	8	2	no	—
324	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
326	C₂×D₄×C₈₉	—	2	1	no	—
327	C₂×D₄×C₈₉	—	2	2	no	—
328	C₂×D₄×C₈₉	—	2	2	no	—
329	C₂×D₄×C₈₉	—	2	2	no	—
330	C₂×D₄×C₈₉	—	2	2	no	—
331	C₂×D₄×C₈₉	—	2	1	no	—
332	C₂×D₄×C₈₉	—	2	2	no	—
333	C₂×D₄×C₈₉	—	2	1	no	—
334	C₂×D₄×C₈₉	—	2	1	no	—
335	C₂×D₄×C₈₉	—	2	1	no	—
336	C₂×D₄×C₈₉	—	2	1	no	—
337	C₂×D₄×C₈₉	—	2	2	no	—
338	C₂×D₄×C₈₉	—	2	2	no	—
339	C₂×D₄×C₈₉	—	2	1	no	—
340	C₂×D₄×C₈₉	—	2	2	no	—
341	C₂×D₄×C₈₉	—	2	2	no	—
342	C₂×D₄×C₈₉	—	2	2	no	—
343	C₂×D₄×C₈₉	—	2	2	no	—
344	C₂×D₄×C₈₉	—	2	1	no	—
345	C₂×D₄×C₈₉	—	2	1	no	—
346	C₂×D₄×C₈₉	—	4	2	no	—
347	C₂×D₄×C₈₉	—	4	2	no	—
348	C₂×D₄×C₈₉	—	4	2	no	—
349	C₂×D₄×C₈₉	—	4	2	no	—
350	C₂×D₄×C₈₉	—	8	2	no	—
351	C₂×D₄×C₈₉	—	8	2	no	—
352	C₂×D₄×C₈₉	—	8	2	no	—
353	C₂×D₄×C₈₉	—	8	4	no	—
354	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
355	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
356	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
357	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
358	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
359	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
360	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₈₉	—	2	2	no	—
362	C₂²×C₄×C₈₉	—	2	1	no	—
363	C₂²×C₄×C₈₉	—	2	1	no	—
364	C₂²×C₄×C₈₉	—	2	1	no	—
365	C₂²×C₄×C₈₉	—	2	2	no	—
366	C₂²×C₄×C₈₉	—	2	2	no	—
367	C₂²×C₄×C₈₉	—	2	2	no	—
368	C₂²×C₄×C₈₉	—	2	2	no	—
369	C₂²×C₄×C₈₉	—	2	2	no	—
370	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
372	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
374	SD₁₆×C₈₉	—	4	1	no	—
375	SD₁₆×C₈₉	—	4	1	no	—
376	D₈×C₈₉	—	4	2	no	—
377	D₈×C₈₉	—	4	2	no	—
378	D₈×C₈₉	—	4	2	no	—
379	D₈×C₈₉	—	4	2	no	—
380	D₈×C₈₉	—	4	1	no	—
381	D₈×C₈₉	—	4	1	no	—
382	M₁₆×C₈₉	—	4	1	no	—
383	M₁₆×C₈₉	—	4	2	no	—
384	M₁₆×C₈₉	—	4	1	no	—
385	C₂×C₈×C₈₉	—	4	2	no	—
386	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
388	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
392	C₄⋊C₄×C₈₉	—	2	1	no	—
393	C₄⋊C₄×C₈₉	—	2	2	no	—
394	C₄⋊C₄×C₈₉	—	2	2	no	—
395	C₄⋊C₄×C₈₉	—	2	1	no	—
396	C₄⋊C₄×C₈₉	—	2	1	no	—
397	C₄⋊C₄×C₈₉	—	2	2	no	—
398	C₄⋊C₄×C₈₉	—	2	1	no	—
399	C₄⋊C₄×C₈₉	—	2	1	no	—
400	C₄⋊C₄×C₈₉	—	2	2	no	—
401	C₄⋊C₄×C₈₉	—	2	2	no	—
402	C₄⋊C₄×C₈₉	—	2	2	no	—
403	C₄⋊C₄×C₈₉	—	2	1	no	—
404	C₄⋊C₄×C₈₉	—	2	1	no	—
405	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
414	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
417	C₂²⋊C₄×C₈₉	—	2	1	no	—
418	C₂²⋊C₄×C₈₉	—	2	2	no	—
419	C₂²⋊C₄×C₈₉	—	2	2	no	—
420	C₂²⋊C₄×C₈₉	—	2	2	no	—
421	C₂²⋊C₄×C₈₉	—	2	2	no	—
422	C₂²⋊C₄×C₈₉	—	2	1	no	—
423	C₂²⋊C₄×C₈₉	—	2	1	no	—
424	C₂²⋊C₄×C₈₉	—	2	1	no	—
425	C₂²⋊C₄×C₈₉	—	2	2	no	—
426	C₂²⋊C₄×C₈₉	—	2	2	no	—
427	C₂²⋊C₄×C₈₉	—	2	1	no	—
428	C₂²⋊C₄×C₈₉	—	2	1	no	—
429	C₂²⋊C₄×C₈₉	—	2	2	no	—
430	C₂²⋊C₄×C₈₉	—	2	2	no	—
431	C₂²⋊C₄×C₈₉	—	2	1	no	—
432	C₂²⋊C₄×C₈₉	—	2	2	no	—
433	C₂²⋊C₄×C₈₉	—	2	2	no	—
434	C₂²⋊C₄×C₈₉	—	2	2	no	—
435	C₂²⋊C₄×C₈₉	—	2	1	no	—
436	C₂²⋊C₄×C₈₉	—	2	2	no	—
437	C₂²⋊C₄×C₈₉	—	2	1	no	—
438	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
443	C₄²×C₈₉	—	2	2	no	—
444	C₄²×C₈₉	—	2	2	no	—
445	C₄²×C₈₉	—	2	1	no	—
446	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
449	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
450	C₄²×C₈₉	C₂⁴	1	2	yes	—
451	C₂³×C₈₉	—	2	1	no	—
452	C₂³×C₈₉	—	2	1	no	—
453	C₂³×C₈₉	—	2	2	no	—
454	C₂³×C₈₉	—	2	1	no	—
455	C₂³×C₈₉	—	2	2	no	—
456	C₂³×C₈₉	—	4	4	no	—
457	C₂³×C₈₉	—	8	2	no	—
458	C₂³×C₈₉	—	8	2	no	—
459	C₂³×C₈₉	—	8	2	no	—
460	C₂³×C₈₉	—	8	2	no	—
461	C₂³×C₈₉	—	8	2	no	—
462	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
463	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
464	Q₈×C₈₉	—	2	2	no	—
465	Q₈×C₈₉	—	2	1	no	—
466	Q₈×C₈₉	—	2	1	no	—
467	Q₈×C₈₉	—	4	2	no	—
468	Q₈×C₈₉	—	8	1	no	—
469	Q₈×C₈₉	—	8	2	no	—
470	Q₈×C₈₉	—	8	1	no	—
471	D₄×C₈₉	—	2	2	no	—
472	D₄×C₈₉	—	2	1	no	—
473	D₄×C₈₉	—	2	1	no	—
474	D₄×C₈₉	—	2	1	no	—
475	D₄×C₈₉	—	2	1	no	—
476	D₄×C₈₉	—	2	2	no	—
477	D₄×C₈₉	—	2	1	no	—
478	D₄×C₈₉	—	2	2	no	—
479	D₄×C₈₉	—	2	1	no	—
480	D₄×C₈₉	—	2	2	no	—
481	D₄×C₈₉	—	2	2	no	—
482	D₄×C₈₉	—	4	2	no	—
483	D₄×C₈₉	—	4	2	no	—
484	D₄×C₈₉	—	4	2	no	—
485	D₄×C₈₉	—	4	2	no	—
486	D₄×C₈₉	—	8	1	no	—
487	D₄×C₈₉	—	8	2	no	—
488	D₄×C₈₉	—	8	2	no	—
489	D₄×C₈₉	—	8	2	no	—
490	D₄×C₈₉	—	8	1	no	—
491	D₄×C₈₉	—	8	1	no	—
492	D₄×C₈₉	—	8	2	no	—
493	D₄×C₈₉	—	8	2	no	—
494	D₄×C₈₉	—	8	1	no	—
495	D₄×C₈₉	—	8	2	no	—
496	D₄×C₈₉	—	8	2	no	—
497	D₄×C₈₉	—	8	2	no	—
498	D₄×C₈₉	—	8	2	no	—
499	D₄×C₈₉	—	8	2	no	—
500	D₄×C₈₉	—	8	1	no	—
501	D₄×C₈₉	—	8	1	no	—
502	D₄×C₈₉	—	8	2	no	—
503	C₂×C₄×C₈₉	—	2	2	no	—
504	C₂×C₄×C₈₉	—	2	2	no	—
505	C₂×C₄×C₈₉	—	2	1	no	—
506	C₂×C₄×C₈₉	—	2	1	no	—
507	C₂×C₄×C₈₉	—	2	2	no	—
508	C₂×C₄×C₈₉	—	2	2	no	—
509	C₂×C₄×C₈₉	—	2	1	no	—
510	C₂×C₄×C₈₉	—	2	1	no	—
511	C₂×C₄×C₈₉	—	2	1	no	—
512	C₂×C₄×C₈₉	—	2	2	no	—
513	C₂×C₄×C₈₉	—	2	1	no	—
514	C₂×C₄×C₈₉	—	2	1	no	—
515	C₂×C₄×C₈₉	—	4	1	no	—
516	C₂×C₄×C₈₉	—	4	2	no	—
517	C₂×C₄×C₈₉	—	4	2	no	—
518	C₂×C₄×C₈₉	—	4	2	no	—
519	C₂×C₄×C₈₉	—	8	2	no	—
520	C₂×C₄×C₈₉	—	8	2	no	—
521	C₂×C₄×C₈₉	—	8	2	no	—
522	C₂×C₄×C₈₉	—	8	2	no	—
523	C₂×C₄×C₈₉	—	8	2	no	—
524	C₂×C₄×C₈₉	—	8	2	no	—
525	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
531	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
534	C₈×C₈₉	—	2	1	no	—
535	C₈×C₈₉	—	2	2	no	—
536	C₈×C₈₉	—	2	1	no	—
537	C₈×C₈₉	—	2	2	no	—
538	C₈×C₈₉	—	2	1	no	—
539	C₈×C₈₉	—	2	1	no	—
540	C₂²×C₈₉	—	2	1	no	—
541	C₂²×C₈₉	—	2	2	no	—
542	C₂²×C₈₉	—	2	2	no	—
543	C₂²×C₈₉	—	2	1	no	—
544	C₂²×C₈₉	—	2	1	no	—
545	C₂²×C₈₉	—	2	2	no	—
546	C₂²×C₈₉	—	4	1	no	—
547	C₂²×C₈₉	—	4	2	no	—
548	C₂²×C₈₉	—	4	1	no	—
549	C₂²×C₈₉	—	4	2	no	—
550	C₂²×C₈₉	—	4	1	no	—
551	C₂²×C₈₉	—	4	2	no	—
552	C₂²×C₈₉	—	4	2	no	—
553	C₂²×C₈₉	—	4	1	no	—
554	C₂²×C₈₉	—	4	1	no	—
555	C₂²×C₈₉	—	4	1	no	—
556	C₂²×C₈₉	—	4	1	no	—
557	C₂²×C₈₉	—	4	1	no	—
558	C₂²×C₈₉	—	4	1	no	—
559	C₂²×C₈₉	—	4	2	no	—
560	C₂²×C₈₉	—	4	2	no	—
561	C₂²×C₈₉	—	16	4	no	—
562	C₂²×C₈₉	—	16	4	no	—
563	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
564	C₄×C₈₉	—	2	1	no	—
565	C₄×C₈₉	—	2	1	no	—
566	C₄×C₈₉	—	2	2	no	—
567	C₄×C₈₉	—	2	2	no	—
568	C₄×C₈₉	—	2	1	no	—
569	C₄×C₈₉	—	2	1	no	—
570	C₄×C₈₉	—	2	2	no	—
571	C₄×C₈₉	—	4	1	no	—
572	C₄×C₈₉	—	4	2	no	—
573	C₄×C₈₉	—	4	1	no	—
574	C₄×C₈₉	—	4	1	no	—
575	C₄×C₈₉	—	4	1	no	—
576	C₄×C₈₉	—	4	1	no	—
577	C₄×C₈₉	—	4	2	no	—
578	C₄×C₈₉	#576	1	2	yes	—
579	C₄×C₈₉	#585	1	1	yes	characteristic
580	C₄×C₈₉	#585	1	1	yes	characteristic
581	#62610	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
582	C₂×C₈₉	—	4	2	no	—
583	C₂×C₈₉	—	4	1	no	—
584	C₂×C₈₉	—	8	1	no	—
585	C₂×C₈₉	—	8	1	no	—
586	C₂×C₈₉	—	8	2	no	—
587	C₂×C₈₉	—	8	2	no	—
588	C₂×C₈₉	—	8	1	no	—
589	C₂×C₈₉	#3500	1	1	yes	characteristic
590	C₂×C₈₉	C₂×#576	1	1	yes	characteristic
591	C₂×C₈₉	#3585	1	1	yes	characteristic
592	#3547	C₂×C₈₉	1	1	yes	characteristic, complemented
593	#3543	C₂×C₈₉	1	1	yes	characteristic, complemented
594	#3373	C₂×C₈₉	1	1	yes	characteristic, complemented
595	#3366	C₂×C₈₉	1	1	yes	characteristic, complemented
596	#3361	C₂×C₈₉	1	1	yes	characteristic, complemented
597	#3358	C₂×C₈₉	1	1	yes	characteristic, complemented
598	#3332	C₂×C₈₉	1	1	yes	characteristic, complemented
599	#3325	C₂×C₈₉	1	1	yes	characteristic, complemented
600	#3325	C₂×C₈₉	1	2	yes	complemented
601	#3322	C₂×C₈₉	1	2	yes	complemented
602	#3319	C₂×C₈₉	1	2	yes	complemented
603	#3318	C₂×C₈₉	1	2	yes	complemented
604	#3305	C₂×C₈₉	1	1	yes	characteristic, complemented
605	#3294	C₂×C₈₉	1	1	yes	characteristic, complemented
606	#3241	C₂×C₈₉	1	2	yes	complemented
607	#3233	C₂×C₈₉	1	1	yes	characteristic, complemented
608	#3220	C₂×C₈₉	1	2	yes	complemented
609	#3205	C₂×C₈₉	1	1	yes	characteristic, complemented
610	#3176	C₂×C₈₉	1	2	yes	complemented
611	#3171	C₂×C₈₉	1	1	yes	characteristic, complemented
612	#3138	C₂×C₈₉	1	1	yes	characteristic, complemented
613	#3136	C₂×C₈₉	1	2	yes	complemented
614	#2969	C₂×C₈₉	1	1	yes	characteristic, complemented
615	C₈₉	#62610	1	1	yes	characteristic, direct product factor, Sylow
616	#562	—	2	2	no	—
617	#560	—	2	2	no	—
618	#559	C₂²×C₈₉	1	1	yes	characteristic
619	#555	C₂²×C₈₉	1	1	yes	characteristic, complemented
620	#555	C₂²×C₈₉	1	2	yes	complemented
621	#554	C₂²×C₈₉	1	1	yes	characteristic, complemented
622	#553	C₂²×C₈₉	1	2	yes	complemented
623	#552	—	2	1	no	—
624	#550	C₂²×C₈₉	1	1	yes	characteristic
625	#550	C₂²×C₈₉	1	1	yes	characteristic
626	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
627	#548	—	2	1	no	—
628	#547	C₂²×C₈₉	1	1	yes	characteristic, complemented
629	#546	—	2	1	no	—
630	#546	C₂²×C₈₉	1	2	yes	—
631	D₄²	—	2	1	no	—
632	D₄²	C₂²×C₈₉	1	1	yes	characteristic
633	D₄²	C₂²×C₈₉	1	2	yes	—
634	#544	C₂²×C₈₉	1	2	yes	complemented
635	#542	—	2	2	no	—
636	#540	—	2	1	no	—
637	#540	C₂²×C₈₉	1	2	yes	—
638	#540	C₂²×C₈₉	1	2	yes	complemented
639	#537	—	2	1	no	—
640	#536	—	2	1	no	—
641	#535	—	2	1	no	—
642	#535	C₂²×C₈₉	1	2	yes	—
643	#534	—	2	2	no	—
644	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
645	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
646	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
647	#529	C₂²×C₈₉	1	1	yes	characteristic
648	#529	C₂²×C₈₉	1	1	yes	characteristic
649	#501	C₂²×C₈₉	1	1	yes	characteristic, complemented
650	#499	C₂²×C₈₉	1	2	yes	complemented
651	#496	C₂²×C₈₉	1	1	yes	characteristic, complemented
652	#493	C₂²×C₈₉	1	2	yes	complemented
653	#490	C₂²×C₈₉	1	2	yes	complemented
654	#490	C₂²×C₈₉	1	2	yes	complemented
655	#490	C₂²×C₈₉	1	2	yes	complemented
656	#490	C₂²×C₈₉	1	1	yes	characteristic, complemented
657	#489	C₂²×C₈₉	1	2	yes	complemented
658	#489	C₂²×C₈₉	1	1	yes	characteristic, complemented
659	#488	C₂²×C₈₉	1	2	yes	complemented
660	#488	C₂²×C₈₉	1	2	yes	complemented
661	#486	C₂²×C₈₉	1	1	yes	characteristic
662	#486	C₂²×C₈₉	1	1	yes	characteristic
663	#486	C₂²×C₈₉	1	1	yes	characteristic, complemented
664	#486	C₂²×C₈₉	1	2	yes	complemented
665	#486	C₂²×C₈₉	1	1	yes	characteristic, complemented
666	#486	C₂²×C₈₉	1	2	yes	complemented
667	#485	C₂²×C₈₉	1	2	yes	complemented
668	#482	C₂²×C₈₉	1	2	yes	—
669	#482	C₂²×C₈₉	1	2	yes	complemented
670	#482	C₂²×C₈₉	1	2	yes	complemented
671	#481	C₂²×C₈₉	1	2	yes	complemented
672	#480	C₂²×C₈₉	1	2	yes	complemented
673	#478	C₂²×C₈₉	1	2	yes	complemented
674	#478	C₂²×C₈₉	1	2	yes	complemented
675	#477	C₂²×C₈₉	1	1	yes	characteristic, complemented
676	#476	C₂²×C₈₉	1	1	yes	characteristic, complemented
677	#476	C₂²×C₈₉	1	2	yes	complemented
678	#475	C₂²×C₈₉	1	1	yes	characteristic, complemented
679	#474	C₂²×C₈₉	1	1	yes	characteristic, complemented
680	#474	C₂²×C₈₉	1	2	yes	complemented
681	#469	C₂²×C₈₉	1	1	yes	characteristic
682	#469	C₂²×C₈₉	1	1	yes	characteristic
683	#469	C₂²×C₈₉	1	2	yes	complemented
684	#469	C₂²×C₈₉	1	2	yes	complemented
685	#468	C₂²×C₈₉	1	1	yes	characteristic, complemented
686	#468	C₂²×C₈₉	1	1	yes	characteristic, complemented
687	#466	C₂²×C₈₉	1	2	yes	complemented
688	#466	C₂²×C₈₉	1	2	yes	complemented
689	#463	C₂²×C₈₉	1	2	yes	complemented
690	#463	C₂²×C₈₉	1	2	yes	complemented
691	#459	C₂²×C₈₉	1	1	yes	characteristic
692	#459	C₂²×C₈₉	1	1	yes	characteristic
693	#459	C₂²×C₈₉	1	1	yes	characteristic, complemented
694	#459	C₂²×C₈₉	1	1	yes	characteristic, complemented
695	#459	C₂²×C₈₉	1	2	yes	complemented
696	#459	C₂²×C₈₉	1	2	yes	complemented
697	#449	C₂²×C₈₉	1	2	yes	complemented
698	#449	C₂²×C₈₉	1	2	yes	complemented
699	#447	C₂²×C₈₉	1	2	yes	complemented
700	#447	C₂²×C₈₉	1	2	yes	complemented
701	#447	C₂²×C₈₉	1	2	yes	complemented
702	#447	C₂²×C₈₉	1	2	yes	complemented
703	#446	C₂²×C₈₉	1	1	yes	characteristic, complemented
704	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
705	#442	C₂²×C₈₉	1	2	yes	complemented
706	#442	C₂²×C₈₉	1	2	yes	complemented
707	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
708	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
709	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
710	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
711	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
712	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
713	#436	C₂²×C₈₉	1	1	yes	characteristic, complemented
714	#436	C₂²×C₈₉	1	2	yes	complemented
715	#435	C₂²×C₈₉	1	2	yes	complemented
716	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
717	#433	C₂²×C₈₉	1	2	yes	complemented
718	#431	C₂²×C₈₉	1	1	yes	characteristic, complemented
719	#418	C₂²×C₈₉	1	2	yes	complemented
720	#418	C₂²×C₈₉	1	2	yes	complemented
721	#418	C₂²×C₈₉	1	2	yes	complemented
722	#417	C₂²×C₈₉	1	2	yes	complemented
723	#416	C₂²×C₈₉	1	2	yes	complemented
724	C₂×#102	C₂²×C₈₉	1	2	yes	complemented
725	#405	C₂²×C₈₉	1	2	yes	complemented
726	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
727	C₂×#41	—	2	1	no	—
728	C₂×#41	—	2	1	no	—
729	C₂×#41	—	2	1	no	—
730	C₂×#41	C₂³×C₈₉	1	2	yes	—
731	C₂²×Q₈	—	2	1	no	—
732	C₂²×D₄	—	2	2	no	—
733	C₂²×D₄	—	2	1	no	—
734	C₂²×D₄	—	2	1	no	—
735	C₂²×D₄	—	2	1	no	—
736	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
737	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
738	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
739	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
740	C₂×D₈	C₂³×C₈₉	1	2	yes	—
741	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
742	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
743	C₂×D₈	C₂³×C₈₉	1	2	yes	—
744	C₂×D₈	C₂³×C₈₉	1	2	yes	—
745	C₂×D₈	C₂³×C₈₉	1	2	yes	—
746	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
747	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
748	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
749	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
750	C₄⋊Q₈	—	2	2	no	—
751	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
752	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
753	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
754	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
755	#127	—	2	1	no	—
756	#127	—	2	1	no	—
757	#127	—	2	1	no	—
758	#127	C₂³×C₈₉	1	2	yes	—
759	#127	C₂³×C₈₉	1	1	yes	characteristic
760	#127	C₂³×C₈₉	1	1	yes	characteristic
761	#127	C₂³×C₈₉	1	1	yes	characteristic
762	#127	C₂³×C₈₉	1	2	yes	—
763	#126	—	2	2	no	—
764	#126	—	2	1	no	—
765	#126	D₄×C₈₉	1	2	yes	—
766	#125	—	2	2	no	—
767	#125	D₄×C₈₉	1	1	yes	characteristic
768	#125	C₂³×C₈₉	1	1	yes	characteristic
769	#125	C₂³×C₈₉	1	2	yes	—
770	#125	C₂³×C₈₉	1	2	yes	—
771	#124	—	2	1	no	—
772	#124	—	2	2	no	—
773	#124	—	2	2	no	—
774	#124	—	2	2	no	—
775	#124	—	2	1	no	—
776	#124	D₄×C₈₉	1	1	yes	characteristic
777	#124	C₂³×C₈₉	1	1	yes	characteristic
778	#124	C₂³×C₈₉	1	2	yes	—
779	#123	—	2	1	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	#123	—	2	2	no	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	#123	D₄×C₈₉	1	2	yes	—
789	C₂²⋊Q₈	—	2	1	no	—
790	C₂²⋊Q₈	—	2	1	no	—
791	C₂²⋊Q₈	—	2	1	no	—
792	C₂²⋊Q₈	—	2	1	no	—
793	C₂²⋊Q₈	—	2	1	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	—	2	2	no	—
796	C₂²⋊Q₈	—	2	2	no	—
797	C₂²⋊Q₈	—	2	2	no	—
798	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
799	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
800	#121	—	2	1	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	—	2	1	no	—
804	#121	—	2	2	no	—
805	#121	—	2	2	no	—
806	#121	—	2	2	no	—
807	#121	—	2	1	no	—
808	#121	—	2	1	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	—	2	2	no	—
812	#121	—	2	2	no	—
813	#121	—	2	2	no	—
814	#121	—	2	2	no	—
815	#121	—	2	2	no	—
816	#121	D₄×C₈₉	1	1	yes	characteristic
817	#121	C₂³×C₈₉	1	1	yes	characteristic
818	#121	C₂³×C₈₉	1	1	yes	characteristic
819	#121	C₂³×C₈₉	1	1	yes	characteristic
820	#121	C₂³×C₈₉	1	2	yes	—
821	#121	C₂³×C₈₉	1	2	yes	—
822	#121	C₂³×C₈₉	1	2	yes	—
823	#121	C₂³×C₈₉	1	2	yes	—
824	#120	—	2	2	no	—
825	#120	—	2	2	no	—
826	#120	—	2	2	no	—
827	#120	—	2	2	no	—
828	#120	—	2	2	no	—
829	#120	—	2	2	no	—
830	C₄×Q₈	—	2	1	no	—
831	C₄×Q₈	—	2	1	no	—
832	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
833	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	—	2	2	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
840	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
841	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
842	C₄×D₄	C₂³×C₈₉	1	2	yes	—
843	C₄×D₄	C₂³×C₈₉	1	2	yes	—
844	C₄×D₄	C₂³×C₈₉	1	2	yes	—
845	C₄×D₄	C₂³×C₈₉	1	2	yes	—
846	C₄×D₄	C₂³×C₈₉	1	2	yes	—
847	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
848	#117	—	2	1	no	—
849	#117	—	2	2	no	—
850	#117	—	2	1	no	—
851	#117	C₂³×C₈₉	1	2	yes	—
852	#117	C₂³×C₈₉	1	2	yes	—
853	#117	C₂³×C₈₉	1	2	yes	—
854	C₂×C₄⋊C₄	—	2	1	no	—
855	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
856	C₂×C₂²⋊C₄	—	2	2	no	—
857	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
858	#107	C₂³×C₈₉	1	2	yes	—
859	#107	C₂³×C₈₉	1	2	yes	—
860	#107	C₂³×C₈₉	1	1	yes	characteristic
861	#107	C₂³×C₈₉	1	1	yes	characteristic
862	#106	C₂³×C₈₉	1	1	yes	characteristic
863	#106	C₂³×C₈₉	1	1	yes	characteristic
864	#106	C₂³×C₈₉	1	2	yes	—
865	#106	C₂³×C₈₉	1	2	yes	—
866	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
867	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
868	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
869	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
870	#103	C₂³×C₈₉	1	1	yes	characteristic
871	#103	C₂³×C₈₉	1	2	yes	—
872	#103	C₂³×C₈₉	1	1	yes	characteristic
873	#103	C₂³×C₈₉	1	2	yes	—
874	#102	C₂³×C₈₉	1	1	yes	characteristic
875	#102	C₂³×C₈₉	1	2	yes	—
876	#102	C₂³×C₈₉	1	2	yes	—
877	#102	C₂³×C₈₉	1	2	yes	—
878	#102	C₂³×C₈₉	1	2	yes	—
879	#102	C₂³×C₈₉	1	2	yes	—
880	#102	C₂³×C₈₉	1	2	yes	—
881	#102	C₂³×C₈₉	1	2	yes	—
882	#102	C₂³×C₈₉	1	1	yes	characteristic
883	#102	C₂³×C₈₉	1	2	yes	—
884	#102	C₂³×C₈₉	1	2	yes	—
885	#102	C₂³×C₈₉	1	2	yes	—
886	#102	C₂³×C₈₉	1	2	yes	—
887	#102	C₂³×C₈₉	1	2	yes	—
888	#102	C₂³×C₈₉	1	2	yes	—
889	#102	C₂³×C₈₉	1	2	yes	—
890	#102	C₂³×C₈₉	1	1	yes	characteristic
891	#102	C₂³×C₈₉	1	1	yes	characteristic
892	#102	C₂³×C₈₉	1	1	yes	characteristic
893	#102	C₂³×C₈₉	1	1	yes	characteristic
894	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
895	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
896	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
897	#97	C₂³×C₈₉	1	1	yes	characteristic
898	#97	C₂³×C₈₉	1	1	yes	characteristic
899	#97	C₂³×C₈₉	1	2	yes	—
900	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
901	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
902	C₄×C₈	C₂³×C₈₉	1	2	yes	—
903	C₄×C₈	C₂³×C₈₉	1	2	yes	—
904	C₂⁴	—	2	2	no	—
905	C₂⁴	—	2	2	no	—
906	#41	—	4	2	no	—
907	#41	—	4	2	no	—
908	#41	—	8	2	no	—
909	#41	—	8	2	no	—
910	#41	—	8	2	no	—
911	C₂×Q₈	—	2	1	no	—
912	C₂×Q₈	—	2	1	no	—
913	C₂×Q₈	—	2	2	no	—
914	C₂×Q₈	—	2	1	no	—
915	C₂×Q₈	—	8	2	no	—
916	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
917	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	1	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	1	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	4	2	no	—
939	C₂×D₄	—	4	2	no	—
940	C₂×D₄	—	4	2	no	—
941	C₂×D₄	—	4	2	no	—
942	C₂×D₄	—	8	2	no	—
943	C₂×D₄	—	8	2	no	—
944	C₂×D₄	—	8	2	no	—
945	C₂×D₄	—	8	4	no	—
946	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
947	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
948	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
949	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
950	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
951	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
952	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	1	no	—
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
963	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
964	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
965	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
966	SD₁₆	—	4	1	no	—
967	SD₁₆	—	4	1	no	—
968	D₈	—	4	2	no	—
969	D₈	—	4	2	no	—
970	D₈	—	4	2	no	—
971	D₈	—	4	2	no	—
972	D₈	—	4	1	no	—
973	D₈	—	4	1	no	—
974	M₁₆	—	4	1	no	—
975	M₁₆	—	4	2	no	—
976	M₁₆	—	4	1	no	—
977	C₂×C₈	—	4	2	no	—
978	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
979	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
980	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
981	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
982	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
983	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	1	no	—
997	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
998	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
999	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1000	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1001	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1002	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1003	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1004	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1005	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1006	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1007	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1008	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1031	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1032	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1033	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1034	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1035	C₄²	—	2	2	no	—
1036	C₄²	—	2	2	no	—
1037	C₄²	—	2	1	no	—
1038	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1039	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1040	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1041	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1042	C₄²	C₂⁴×C₈₉	1	2	yes	—
1043	C₂³	—	2	1	no	—
1044	C₂³	—	2	1	no	—
1045	C₂³	—	2	1	no	—
1046	C₂³	—	2	2	no	—
1047	C₂³	—	2	2	no	—
1048	C₂³	—	4	4	no	—
1049	C₂³	—	8	2	no	—
1050	C₂³	—	8	2	no	—
1051	C₂³	—	8	2	no	—
1052	C₂³	—	8	2	no	—
1053	C₂³	—	8	2	no	—
1054	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1055	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1056	Q₈	—	2	2	no	—
1057	Q₈	—	2	1	no	—
1058	Q₈	—	2	1	no	—
1059	Q₈	—	4	2	no	—
1060	Q₈	—	8	1	no	—
1061	Q₈	—	8	2	no	—
1062	Q₈	—	8	1	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	2	1	no	—
1066	D₄	—	2	1	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	2	2	no	—
1069	D₄	—	2	1	no	—
1070	D₄	—	2	2	no	—
1071	D₄	—	2	1	no	—
1072	D₄	—	2	2	no	—
1073	D₄	—	2	2	no	—
1074	D₄	—	4	2	no	—
1075	D₄	—	4	2	no	—
1076	D₄	—	4	2	no	—
1077	D₄	—	4	2	no	—
1078	D₄	—	8	1	no	—
1079	D₄	—	8	2	no	—
1080	D₄	—	8	2	no	—
1081	D₄	—	8	2	no	—
1082	D₄	—	8	2	no	—
1083	D₄	—	8	1	no	—
1084	D₄	—	8	1	no	—
1085	D₄	—	8	2	no	—
1086	D₄	—	8	1	no	—
1087	D₄	—	8	2	no	—
1088	D₄	—	8	2	no	—
1089	D₄	—	8	2	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	2	no	—
1092	D₄	—	8	1	no	—
1093	D₄	—	8	1	no	—
1094	D₄	—	8	2	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	4	1	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	4	2	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	8	2	no	—
1112	C₂×C₄	—	8	2	no	—
1113	C₂×C₄	—	8	2	no	—
1114	C₂×C₄	—	8	2	no	—
1115	C₂×C₄	—	8	2	no	—
1116	C₂×C₄	—	8	2	no	—
1117	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1118	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1119	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1120	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1121	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1122	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1123	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1124	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1125	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1126	C₈	—	2	1	no	—
1127	C₈	—	2	2	no	—
1128	C₈	—	2	1	no	—
1129	C₈	—	2	2	no	—
1130	C₈	—	2	1	no	—
1131	C₈	—	2	1	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	2	no	—
1136	C₂²	—	2	2	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	4	2	no	—
1142	C₂²	—	4	2	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	2	no	—
1147	C₂²	—	4	1	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	4	2	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	1	no	—
1153	C₂²	—	16	4	no	—
1154	C₂²	—	16	4	no	—
1155	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1156	C₄	—	2	1	no	—
1157	C₄	—	2	2	no	—
1158	C₄	—	2	1	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	2	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	1	no	—
1163	C₄	—	4	1	no	—
1164	C₄	—	4	1	no	—
1165	C₄	—	4	1	no	—
1166	C₄	—	4	2	no	—
1167	C₄	—	4	1	no	—
1168	C₄	—	4	2	no	—
1169	C₄	—	4	1	no	—
1170	C₄	#576×C₈₉	1	2	yes	—
1171	C₄	#585×C₈₉	1	1	yes	characteristic
1172	C₄	#585×C₈₉	1	1	yes	characteristic
1173	C₂	—	4	2	no	—
1174	C₂	—	4	1	no	—
1175	C₂	—	8	1	no	—
1176	C₂	—	8	1	no	—
1177	C₂	—	8	2	no	—
1178	C₂	—	8	1	no	—
1179	C₂	—	8	2	no	—
1180	C₂	C₈₉×#3500	1	1	yes	characteristic
1181	C₂	C₂×#576×C₈₉	1	1	yes	characteristic
1182	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 ◁ #529×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3547	C₂	semidirect
2. C₈₉×#3543	C₂	semidirect
3. C₈₉×#3373	C₂	semidirect
4. C₈₉×#3366	C₂	semidirect
5. C₈₉×#3361	C₂	semidirect
6. C₈₉×#3358	C₂	semidirect
7. C₈₉×#3332	C₂	semidirect
8. C₈₉×#3325	C₂	semidirect
9. C₈₉×#3325	C₂	semidirect
10. C₈₉×#3322	C₂	semidirect
11. C₈₉×#3319	C₂	semidirect
12. C₈₉×#3318	C₂	semidirect
13. C₈₉×#3305	C₂	semidirect
14. C₈₉×#3294	C₂	semidirect
15. C₈₉×#3241	C₂	semidirect
16. C₈₉×#3233	C₂	semidirect
17. C₈₉×#3220	C₂	semidirect
18. C₈₉×#3205	C₂	semidirect
19. C₈₉×#3176	C₂	semidirect
20. C₈₉×#3171	C₂	semidirect
21. C₈₉×#3138	C₂	semidirect
22. C₈₉×#3136	C₂	semidirect
23. C₈₉×#2969	C₂	semidirect
27. #555×C₈₉	C₂²	semidirect
28. #555×C₈₉	C₂²	semidirect
29. #554×C₈₉	C₂²	semidirect
30. #553×C₈₉	C₂²	semidirect
34. D₄×Q₈×C₈₉	C₂²	semidirect
36. #547×C₈₉	C₂²	semidirect
42. #544×C₈₉	C₂²	semidirect
46. #540×C₈₉	C₂²	semidirect
52. #533×C₈₉	C₂²	semidirect
53. #532×C₈₉	C₂²	semidirect
57. #501×C₈₉	C₂²	semidirect
58. #499×C₈₉	C₂²	semidirect
59. #496×C₈₉	C₂²	semidirect
60. #493×C₈₉	C₂²	semidirect
61. #490×C₈₉	C₂²	semidirect
62. #490×C₈₉	C₂²	semidirect
63. #490×C₈₉	C₂²	semidirect
64. #490×C₈₉	C₂²	semidirect
65. #489×C₈₉	C₂²	semidirect
66. #489×C₈₉	C₂²	semidirect
67. #488×C₈₉	C₂²	semidirect
68. #488×C₈₉	C₂²	semidirect
71. #486×C₈₉	C₂²	semidirect
72. #486×C₈₉	C₂²	semidirect
73. #486×C₈₉	C₂²	semidirect
74. #486×C₈₉	C₂²	semidirect
75. #485×C₈₉	C₂²	semidirect
77. #482×C₈₉	C₂²	semidirect
78. #482×C₈₉	C₂²	semidirect
79. #481×C₈₉	C₂²	semidirect
80. #480×C₈₉	C₂²	semidirect
81. #478×C₈₉	C₂²	semidirect
82. #478×C₈₉	C₂²	semidirect
83. #477×C₈₉	C₂²	semidirect
84. #476×C₈₉	C₂²	semidirect
85. #476×C₈₉	C₂²	semidirect
86. #475×C₈₉	C₂²	semidirect
87. #474×C₈₉	C₂²	semidirect
88. #474×C₈₉	C₂²	semidirect
91. #469×C₈₉	C₂²	semidirect
92. #469×C₈₉	C₂²	semidirect
93. #468×C₈₉	C₂²	semidirect
94. #468×C₈₉	C₂²	semidirect
95. #466×C₈₉	C₂²	semidirect
96. #466×C₈₉	C₂²	semidirect
97. #463×C₈₉	C₂²	semidirect
98. #463×C₈₉	C₂²	semidirect
101. #459×C₈₉	C₂²	semidirect
102. #459×C₈₉	C₂²	semidirect
103. #459×C₈₉	C₂²	semidirect
104. #459×C₈₉	C₂²	semidirect
105. #449×C₈₉	C₂²	semidirect
106. #449×C₈₉	C₂²	semidirect
107. #447×C₈₉	C₂²	semidirect
108. #447×C₈₉	C₂²	semidirect
109. #447×C₈₉	C₂²	semidirect
110. #447×C₈₉	C₂²	semidirect
111. #446×C₈₉	C₂²	semidirect
112. C₈×Q₈×C₈₉	C₂²	semidirect
113. #442×C₈₉	C₂²	semidirect
114. #442×C₈₉	C₂²	semidirect
115. C₄×SD₁₆×C₈₉	C₂²	semidirect
116. C₄×SD₁₆×C₈₉	C₂²	semidirect
117. C₄×D₈×C₈₉	C₂²	semidirect
118. C₄×D₈×C₈₉	C₂²	semidirect
119. C₄×D₈×C₈₉	C₂²	semidirect
120. C₄×D₈×C₈₉	C₂²	semidirect
121. #436×C₈₉	C₂²	semidirect
122. #436×C₈₉	C₂²	semidirect
123. #435×C₈₉	C₂²	semidirect
124. C₈×D₄×C₈₉	C₂²	semidirect
125. #433×C₈₉	C₂²	semidirect
126. #431×C₈₉	C₂²	semidirect
127. #418×C₈₉	C₂²	semidirect
128. #418×C₈₉	C₂²	semidirect
129. #418×C₈₉	C₂²	semidirect
130. #417×C₈₉	C₂²	semidirect
131. #416×C₈₉	C₂²	semidirect
132. C₂×#102×C₈₉	C₂²	semidirect
133. #405×C₈₉	C₂²	semidirect
134. C₄×M₁₆×C₈₉	C₂²	semidirect
581. #62610	C₈₉	direct (N × H)
592. #3547	C₂×C₈₉	semidirect
593. #3543	C₂×C₈₉	semidirect
594. #3373	C₂×C₈₉	semidirect
595. #3366	C₂×C₈₉	semidirect
596. #3361	C₂×C₈₉	semidirect
597. #3358	C₂×C₈₉	semidirect
598. #3332	C₂×C₈₉	semidirect
599. #3325	C₂×C₈₉	semidirect
600. #3325	C₂×C₈₉	semidirect
601. #3322	C₂×C₈₉	semidirect
602. #3319	C₂×C₈₉	semidirect
603. #3318	C₂×C₈₉	semidirect
604. #3305	C₂×C₈₉	semidirect
605. #3294	C₂×C₈₉	semidirect
606. #3241	C₂×C₈₉	semidirect
607. #3233	C₂×C₈₉	semidirect
608. #3220	C₂×C₈₉	semidirect
609. #3205	C₂×C₈₉	semidirect
610. #3176	C₂×C₈₉	semidirect
611. #3171	C₂×C₈₉	semidirect
612. #3138	C₂×C₈₉	semidirect
613. #3136	C₂×C₈₉	semidirect
614. #2969	C₂×C₈₉	semidirect
615. C₈₉	#62610	direct (N × H)
619. #555	C₂²×C₈₉	semidirect
620. #555	C₂²×C₈₉	semidirect
621. #554	C₂²×C₈₉	semidirect
622. #553	C₂²×C₈₉	semidirect
626. D₄×Q₈	C₂²×C₈₉	semidirect
628. #547	C₂²×C₈₉	semidirect
634. #544	C₂²×C₈₉	semidirect
638. #540	C₂²×C₈₉	semidirect
644. #533	C₂²×C₈₉	semidirect
645. #532	C₂²×C₈₉	semidirect
649. #501	C₂²×C₈₉	semidirect
650. #499	C₂²×C₈₉	semidirect
651. #496	C₂²×C₈₉	semidirect
652. #493	C₂²×C₈₉	semidirect
653. #490	C₂²×C₈₉	semidirect
654. #490	C₂²×C₈₉	semidirect
655. #490	C₂²×C₈₉	semidirect
656. #490	C₂²×C₈₉	semidirect
657. #489	C₂²×C₈₉	semidirect
658. #489	C₂²×C₈₉	semidirect
659. #488	C₂²×C₈₉	semidirect
660. #488	C₂²×C₈₉	semidirect
663. #486	C₂²×C₈₉	semidirect
664. #486	C₂²×C₈₉	semidirect
665. #486	C₂²×C₈₉	semidirect
666. #486	C₂²×C₈₉	semidirect
667. #485	C₂²×C₈₉	semidirect
669. #482	C₂²×C₈₉	semidirect
670. #482	C₂²×C₈₉	semidirect
671. #481	C₂²×C₈₉	semidirect
672. #480	C₂²×C₈₉	semidirect
673. #478	C₂²×C₈₉	semidirect
674. #478	C₂²×C₈₉	semidirect
675. #477	C₂²×C₈₉	semidirect
676. #476	C₂²×C₈₉	semidirect
677. #476	C₂²×C₈₉	semidirect
678. #475	C₂²×C₈₉	semidirect
679. #474	C₂²×C₈₉	semidirect
680. #474	C₂²×C₈₉	semidirect
683. #469	C₂²×C₈₉	semidirect
684. #469	C₂²×C₈₉	semidirect
685. #468	C₂²×C₈₉	semidirect
686. #468	C₂²×C₈₉	semidirect
687. #466	C₂²×C₈₉	semidirect
688. #466	C₂²×C₈₉	semidirect
689. #463	C₂²×C₈₉	semidirect
690. #463	C₂²×C₈₉	semidirect
693. #459	C₂²×C₈₉	semidirect
694. #459	C₂²×C₈₉	semidirect
695. #459	C₂²×C₈₉	semidirect
696. #459	C₂²×C₈₉	semidirect
697. #449	C₂²×C₈₉	semidirect
698. #449	C₂²×C₈₉	semidirect
699. #447	C₂²×C₈₉	semidirect
700. #447	C₂²×C₈₉	semidirect
701. #447	C₂²×C₈₉	semidirect
702. #447	C₂²×C₈₉	semidirect
703. #446	C₂²×C₈₉	semidirect
704. C₈×Q₈	C₂²×C₈₉	semidirect
705. #442	C₂²×C₈₉	semidirect
706. #442	C₂²×C₈₉	semidirect
707. C₄×SD₁₆	C₂²×C₈₉	semidirect
708. C₄×SD₁₆	C₂²×C₈₉	semidirect
709. C₄×D₈	C₂²×C₈₉	semidirect
710. C₄×D₈	C₂²×C₈₉	semidirect
711. C₄×D₈	C₂²×C₈₉	semidirect
712. C₄×D₈	C₂²×C₈₉	semidirect
713. #436	C₂²×C₈₉	semidirect
714. #436	C₂²×C₈₉	semidirect
715. #435	C₂²×C₈₉	semidirect
716. C₈×D₄	C₂²×C₈₉	semidirect
717. #433	C₂²×C₈₉	semidirect
718. #431	C₂²×C₈₉	semidirect
719. #418	C₂²×C₈₉	semidirect
720. #418	C₂²×C₈₉	semidirect
721. #418	C₂²×C₈₉	semidirect
722. #417	C₂²×C₈₉	semidirect
723. #416	C₂²×C₈₉	semidirect
724. C₂×#102	C₂²×C₈₉	semidirect
725. #405	C₂²×C₈₉	semidirect
726. C₄×M₁₆	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3547	2
C₈₉×#3543	2
C₈₉×#3373	2
C₈₉×#3366	2
C₈₉×#3361	2
C₈₉×#3358	2
C₈₉×#3332	2
C₈₉×#3325	2
C₈₉×#3322	2
C₈₉×#3319	2
C₈₉×#3318	2
C₈₉×#3305	2
C₈₉×#3294	2
C₈₉×#3241	2
C₈₉×#3233	2
C₈₉×#3220	2
C₈₉×#3205	2
C₈₉×#3176	2
C₈₉×#3171	2
C₈₉×#3138	2
C₈₉×#3136	2
C₈₉×#2969	2
#62610	89

Subgroups — C89×#62610 #36440458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62610 #36440458