Subgroups — C₈₉×#62570 #36440418

Order 22784.

1776 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3558	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3373	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3370	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3326	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3325	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3321	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3319	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3318	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3306	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3244	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3235	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3220	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3213	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3184	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#3179	C₂	1	2	yes	maximal, complemented
17	C₈₉×#3140	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#3136	C₂	1	2	yes	maximal, complemented
19	C₈₉×#2967	C₂	1	1	yes	maximal, characteristic, complemented
20	#562×C₈₉	—	2	1	no	—
21	#562×C₈₉	—	2	2	no	—
22	H(3,𝔽₄)×C₈₉	—	2	1	no	—
23	#559×C₈₉	C₂²	1	2	yes	—
24	#555×C₈₉	C₂²	1	1	yes	characteristic, complemented
25	#555×C₈₉	C₂²	1	2	yes	complemented
26	#554×C₈₉	C₂²	1	1	yes	characteristic, complemented
27	#553×C₈₉	C₂²	1	2	yes	complemented
28	#552×C₈₉	—	2	1	no	—
29	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
30	#548×C₈₉	—	2	1	no	—
31	#548×C₈₉	C₂²	1	2	yes	—
32	#547×C₈₉	C₂²	1	1	yes	characteristic, complemented
33	#546×C₈₉	—	2	2	no	—
34	#546×C₈₉	C₂²	1	2	yes	—
35	D₄²×C₈₉	C₂²	1	2	yes	—
36	#544×C₈₉	C₂²	1	2	yes	complemented
37	#542×C₈₉	—	2	2	no	—
38	#542×C₈₉	C₂²	1	2	yes	—
39	#540×C₈₉	C₂²	1	2	yes	complemented
40	#538×C₈₉	—	2	2	no	—
41	#538×C₈₉	—	2	1	no	—
42	#537×C₈₉	—	2	1	no	—
43	#536×C₈₉	—	2	1	no	—
44	#535×C₈₉	C₂²	1	2	yes	—
45	#534×C₈₉	—	2	1	no	—
46	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
47	#532×C₈₉	C₂²	1	1	yes	characteristic
48	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
49	#529×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
51	#501×C₈₉	C₂²	1	2	yes	complemented
52	#498×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	#496×C₈₉	C₂²	1	2	yes	complemented
54	#493×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	#490×C₈₉	C₂²	1	2	yes	—
56	#490×C₈₉	C₂²	1	2	yes	complemented
57	#489×C₈₉	C₂²	1	2	yes	complemented
58	#489×C₈₉	C₂²	1	2	yes	complemented
59	#489×C₈₉	C₂²	1	2	yes	complemented
60	#489×C₈₉	C₂²	1	2	yes	complemented
61	#488×C₈₉	C₂²	1	2	yes	complemented
62	#488×C₈₉	C₂²	1	2	yes	complemented
63	#488×C₈₉	C₂²	1	2	yes	complemented
64	#486×C₈₉	C₂²	1	2	yes	—
65	#486×C₈₉	C₂²	1	1	yes	characteristic, complemented
66	#486×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#485×C₈₉	C₂²	1	2	yes	complemented
68	#483×C₈₉	C₂²	1	2	yes	complemented
69	#482×C₈₉	C₂²	1	2	yes	—
70	#482×C₈₉	C₂²	1	2	yes	complemented
71	#482×C₈₉	C₂²	1	2	yes	complemented
72	#481×C₈₉	C₂²	1	2	yes	—
73	#479×C₈₉	C₂²	1	2	yes	complemented
74	#478×C₈₉	C₂²	1	2	yes	complemented
75	#476×C₈₉	C₂²	1	2	yes	complemented
76	#476×C₈₉	C₂²	1	2	yes	complemented
77	#475×C₈₉	C₂²	1	2	yes	complemented
78	#474×C₈₉	C₂²	1	2	yes	complemented
79	#469×C₈₉	C₂²	1	2	yes	—
80	#469×C₈₉	C₂²	1	2	yes	complemented
81	#469×C₈₉	C₂²	1	2	yes	complemented
82	#468×C₈₉	C₂²	1	2	yes	complemented
83	#466×C₈₉	C₂²	1	2	yes	—
84	#465×C₈₉	C₂²	1	2	yes	complemented
85	#463×C₈₉	C₂²	1	2	yes	complemented
86	#463×C₈₉	C₂²	1	2	yes	complemented
87	#463×C₈₉	C₂²	1	2	yes	complemented
88	#463×C₈₉	C₂²	1	2	yes	complemented
89	#459×C₈₉	C₂²	1	2	yes	—
90	#459×C₈₉	C₂²	1	2	yes	—
91	#449×C₈₉	C₂²	1	2	yes	complemented
92	#449×C₈₉	C₂²	1	2	yes	complemented
93	#448×C₈₉	C₂²	1	1	yes	characteristic, complemented
94	#448×C₈₉	C₂²	1	1	yes	characteristic, complemented
95	#447×C₈₉	C₂²	1	1	yes	characteristic
96	#447×C₈₉	C₂²	1	1	yes	characteristic
97	#447×C₈₉	C₂²	1	2	yes	complemented
98	#447×C₈₉	C₂²	1	2	yes	complemented
99	#446×C₈₉	C₂²	1	2	yes	complemented
100	#442×C₈₉	C₂²	1	2	yes	complemented
101	#442×C₈₉	C₂²	1	2	yes	complemented
102	#442×C₈₉	C₂²	1	2	yes	complemented
103	#440×C₈₉	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
105	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
106	#436×C₈₉	C₂²	1	2	yes	complemented
107	#435×C₈₉	C₂²	1	2	yes	complemented
108	#435×C₈₉	C₂²	1	2	yes	complemented
109	#433×C₈₉	C₂²	1	2	yes	complemented
110	#432×C₈₉	C₂²	1	1	yes	characteristic, complemented
111	#419×C₈₉	C₂²	1	2	yes	complemented
112	#418×C₈₉	C₂²	1	2	yes	—
113	#418×C₈₉	C₂²	1	2	yes	complemented
114	#417×C₈₉	C₂²	1	2	yes	complemented
115	#416×C₈₉	C₂²	1	2	yes	complemented
116	C₂×#102×C₈₉	C₂²	1	2	yes	complemented
117	#405×C₈₉	C₂²	1	2	yes	complemented
118	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	C₂×#41×C₈₉	—	2	1	no	—
120	C₂×#41×C₈₉	—	2	1	no	—
121	C₂×#41×C₈₉	—	2	1	no	—
122	C₂×#41×C₈₉	C₂³	1	2	yes	—
123	C₂²×Q₈×C₈₉	—	2	1	no	—
124	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₈₉	—	2	2	no	—
126	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
127	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
128	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
130	C₂×D₈×C₈₉	C₂³	1	2	yes	—
131	C₂×D₈×C₈₉	C₂³	1	2	yes	—
132	C₂×D₈×C₈₉	C₂³	1	2	yes	—
133	C₂×D₈×C₈₉	C₂³	1	2	yes	—
134	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
135	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
136	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₈₉	—	2	2	no	—
138	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
139	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
140	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
141	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
142	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
143	#127×C₈₉	C₂³	1	2	yes	—
144	#127×C₈₉	C₂³	1	1	yes	characteristic
145	#127×C₈₉	C₂³	1	1	yes	characteristic
146	#126×C₈₉	—	2	2	no	—
147	#126×C₈₉	—	2	2	no	—
148	#126×C₈₉	D₄	1	2	yes	—
149	#125×C₈₉	—	2	2	no	—
150	#125×C₈₉	D₄	1	1	yes	characteristic
151	#125×C₈₉	C₂³	1	2	yes	—
152	#125×C₈₉	C₂³	1	2	yes	—
153	#124×C₈₉	—	2	2	no	—
154	#124×C₈₉	—	2	2	no	—
155	#124×C₈₉	—	2	2	no	—
156	#124×C₈₉	—	2	2	no	—
157	#124×C₈₉	—	2	2	no	—
158	#124×C₈₉	—	2	2	no	—
159	#124×C₈₉	—	2	1	no	—
160	#124×C₈₉	—	2	1	no	—
161	#124×C₈₉	—	2	1	no	—
162	#124×C₈₉	—	2	1	no	—
163	#124×C₈₉	D₄	1	1	yes	characteristic
164	#124×C₈₉	C₂³	1	2	yes	—
165	#124×C₈₉	C₂³	1	2	yes	—
166	#124×C₈₉	C₂³	1	2	yes	—
167	#123×C₈₉	—	2	2	no	—
168	#123×C₈₉	—	2	2	no	—
169	#123×C₈₉	—	2	2	no	—
170	#123×C₈₉	—	2	2	no	—
171	#123×C₈₉	—	2	2	no	—
172	#123×C₈₉	—	2	2	no	—
173	#123×C₈₉	—	2	2	no	—
174	#123×C₈₉	—	2	2	no	—
175	#123×C₈₉	D₄	1	2	yes	—
176	C₂²⋊Q₈×C₈₉	—	2	1	no	—
177	C₂²⋊Q₈×C₈₉	—	2	1	no	—
178	C₂²⋊Q₈×C₈₉	—	2	1	no	—
179	C₂²⋊Q₈×C₈₉	—	2	1	no	—
180	C₂²⋊Q₈×C₈₉	—	2	1	no	—
181	C₂²⋊Q₈×C₈₉	—	2	2	no	—
182	C₂²⋊Q₈×C₈₉	—	2	2	no	—
183	C₂²⋊Q₈×C₈₉	—	2	2	no	—
184	C₂²⋊Q₈×C₈₉	—	2	2	no	—
185	C₂²⋊Q₈×C₈₉	—	2	2	no	—
186	C₂²⋊Q₈×C₈₉	—	2	2	no	—
187	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
188	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
189	#121×C₈₉	—	2	2	no	—
190	#121×C₈₉	—	2	1	no	—
191	#121×C₈₉	—	2	2	no	—
192	#121×C₈₉	—	2	2	no	—
193	#121×C₈₉	—	2	1	no	—
194	#121×C₈₉	—	2	1	no	—
195	#121×C₈₉	—	2	2	no	—
196	#121×C₈₉	—	2	2	no	—
197	#121×C₈₉	—	2	2	no	—
198	#121×C₈₉	—	2	2	no	—
199	#121×C₈₉	—	2	2	no	—
200	#121×C₈₉	—	2	2	no	—
201	#121×C₈₉	D₄	1	1	yes	characteristic
202	#121×C₈₉	C₂³	1	1	yes	characteristic
203	#121×C₈₉	C₂³	1	1	yes	characteristic
204	#121×C₈₉	C₂³	1	2	yes	—
205	#121×C₈₉	C₂³	1	2	yes	—
206	#121×C₈₉	C₂³	1	2	yes	—
207	#121×C₈₉	C₂³	1	2	yes	—
208	#120×C₈₉	—	2	2	no	—
209	#120×C₈₉	—	2	2	no	—
210	#120×C₈₉	—	2	2	no	—
211	#120×C₈₉	—	2	2	no	—
212	#120×C₈₉	—	2	2	no	—
213	C₄×Q₈×C₈₉	—	2	1	no	—
214	C₄×Q₈×C₈₉	—	2	1	no	—
215	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
216	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₈₉	—	2	2	no	—
218	C₄×D₄×C₈₉	—	2	2	no	—
219	C₄×D₄×C₈₉	—	2	2	no	—
220	C₄×D₄×C₈₉	—	2	1	no	—
221	C₄×D₄×C₈₉	—	2	1	no	—
222	C₄×D₄×C₈₉	C₂³	1	2	yes	—
223	C₄×D₄×C₈₉	C₂³	1	2	yes	—
224	C₄×D₄×C₈₉	C₂³	1	2	yes	—
225	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
226	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₈₉	C₂³	1	2	yes	—
228	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
229	C₄×D₄×C₈₉	C₂³	1	2	yes	—
230	#117×C₈₉	—	2	1	no	—
231	#117×C₈₉	—	2	2	no	—
232	#117×C₈₉	C₂³	1	2	yes	—
233	#117×C₈₉	C₂³	1	2	yes	—
234	#117×C₈₉	C₂³	1	2	yes	—
235	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
236	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
239	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
240	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
241	#107×C₈₉	C₂³	1	2	yes	—
242	#107×C₈₉	C₂³	1	2	yes	—
243	#106×C₈₉	C₂³	1	2	yes	—
244	#106×C₈₉	C₂³	1	2	yes	—
245	#106×C₈₉	C₂³	1	2	yes	—
246	#106×C₈₉	C₂³	1	2	yes	—
247	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
248	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
249	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
250	#103×C₈₉	C₂³	1	2	yes	—
251	#103×C₈₉	C₂³	1	2	yes	—
252	#103×C₈₉	C₂³	1	2	yes	—
253	#103×C₈₉	C₂³	1	2	yes	—
254	#103×C₈₉	C₂³	1	2	yes	—
255	#103×C₈₉	C₂³	1	2	yes	—
256	#102×C₈₉	C₂³	1	2	yes	—
257	#102×C₈₉	C₂³	1	2	yes	—
258	#102×C₈₉	C₂³	1	2	yes	—
259	#102×C₈₉	C₂³	1	2	yes	—
260	#102×C₈₉	C₂³	1	2	yes	—
261	#102×C₈₉	C₂³	1	2	yes	—
262	#102×C₈₉	C₂³	1	2	yes	—
263	#102×C₈₉	C₂³	1	2	yes	—
264	#102×C₈₉	C₂³	1	2	yes	—
265	#102×C₈₉	C₂³	1	2	yes	—
266	#102×C₈₉	C₂³	1	2	yes	—
267	#102×C₈₉	C₂³	1	2	yes	—
268	#102×C₈₉	C₂³	1	2	yes	—
269	#102×C₈₉	C₂³	1	2	yes	—
270	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
271	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
272	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
273	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
274	#97×C₈₉	C₂³	1	2	yes	—
275	#97×C₈₉	C₂³	1	2	yes	—
276	#97×C₈₉	C₂³	1	2	yes	—
277	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
278	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
279	C₄×C₈×C₈₉	C₂³	1	2	yes	—
280	C₂⁴×C₈₉	—	2	1	no	—
281	C₂⁴×C₈₉	—	2	2	no	—
282	#41×C₈₉	—	4	2	no	—
283	#41×C₈₉	—	4	2	no	—
284	#41×C₈₉	—	8	2	no	—
285	#41×C₈₉	—	8	2	no	—
286	#41×C₈₉	—	8	2	no	—
287	C₂×Q₈×C₈₉	—	2	1	no	—
288	C₂×Q₈×C₈₉	—	2	1	no	—
289	C₂×Q₈×C₈₉	—	2	1	no	—
290	C₂×Q₈×C₈₉	—	2	1	no	—
291	C₂×Q₈×C₈₉	—	2	2	no	—
292	C₂×Q₈×C₈₉	—	2	1	no	—
293	C₂×Q₈×C₈₉	—	4	2	no	—
294	C₂×Q₈×C₈₉	—	8	2	no	—
295	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
296	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
297	C₂×D₄×C₈₉	—	2	2	no	—
298	C₂×D₄×C₈₉	—	2	2	no	—
299	C₂×D₄×C₈₉	—	2	2	no	—
300	C₂×D₄×C₈₉	—	2	2	no	—
301	C₂×D₄×C₈₉	—	2	1	no	—
302	C₂×D₄×C₈₉	—	2	2	no	—
303	C₂×D₄×C₈₉	—	2	1	no	—
304	C₂×D₄×C₈₉	—	2	2	no	—
305	C₂×D₄×C₈₉	—	2	1	no	—
306	C₂×D₄×C₈₉	—	2	1	no	—
307	C₂×D₄×C₈₉	—	2	1	no	—
308	C₂×D₄×C₈₉	—	2	1	no	—
309	C₂×D₄×C₈₉	—	2	2	no	—
310	C₂×D₄×C₈₉	—	2	2	no	—
311	C₂×D₄×C₈₉	—	2	1	no	—
312	C₂×D₄×C₈₉	—	4	2	no	—
313	C₂×D₄×C₈₉	—	4	2	no	—
314	C₂×D₄×C₈₉	—	4	2	no	—
315	C₂×D₄×C₈₉	—	8	4	no	—
316	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
317	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
318	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
319	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
320	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
321	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₈₉	—	2	1	no	—
323	C₂²×C₄×C₈₉	—	2	2	no	—
324	C₂²×C₄×C₈₉	—	2	1	no	—
325	C₂²×C₄×C₈₉	—	2	1	no	—
326	C₂²×C₄×C₈₉	—	2	2	no	—
327	C₂²×C₄×C₈₉	—	2	2	no	—
328	C₂²×C₄×C₈₉	—	2	2	no	—
329	C₂²×C₄×C₈₉	—	2	2	no	—
330	C₂²×C₄×C₈₉	—	2	2	no	—
331	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
335	SD₁₆×C₈₉	—	4	2	no	—
336	SD₁₆×C₈₉	—	4	2	no	—
337	D₈×C₈₉	—	4	2	no	—
338	D₈×C₈₉	—	4	2	no	—
339	D₈×C₈₉	—	4	2	no	—
340	D₈×C₈₉	—	4	2	no	—
341	M₁₆×C₈₉	—	4	2	no	—
342	M₁₆×C₈₉	—	4	2	no	—
343	C₂×C₈×C₈₉	—	4	2	no	—
344	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
345	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
346	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
347	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
348	C₄⋊C₄×C₈₉	—	2	1	no	—
349	C₄⋊C₄×C₈₉	—	2	2	no	—
350	C₄⋊C₄×C₈₉	—	2	2	no	—
351	C₄⋊C₄×C₈₉	—	2	2	no	—
352	C₄⋊C₄×C₈₉	—	2	2	no	—
353	C₄⋊C₄×C₈₉	—	2	1	no	—
354	C₄⋊C₄×C₈₉	—	2	1	no	—
355	C₄⋊C₄×C₈₉	—	2	2	no	—
356	C₄⋊C₄×C₈₉	—	2	2	no	—
357	C₄⋊C₄×C₈₉	—	2	2	no	—
358	C₄⋊C₄×C₈₉	—	2	1	no	—
359	C₄⋊C₄×C₈₉	—	2	2	no	—
360	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
362	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
363	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
364	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
365	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
366	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
367	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
368	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
369	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
370	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
371	C₂²⋊C₄×C₈₉	—	2	2	no	—
372	C₂²⋊C₄×C₈₉	—	2	2	no	—
373	C₂²⋊C₄×C₈₉	—	2	2	no	—
374	C₂²⋊C₄×C₈₉	—	2	2	no	—
375	C₂²⋊C₄×C₈₉	—	2	2	no	—
376	C₂²⋊C₄×C₈₉	—	2	2	no	—
377	C₂²⋊C₄×C₈₉	—	2	2	no	—
378	C₂²⋊C₄×C₈₉	—	2	2	no	—
379	C₂²⋊C₄×C₈₉	—	2	1	no	—
380	C₂²⋊C₄×C₈₉	—	2	2	no	—
381	C₂²⋊C₄×C₈₉	—	2	2	no	—
382	C₂²⋊C₄×C₈₉	—	2	1	no	—
383	C₂²⋊C₄×C₈₉	—	2	2	no	—
384	C₂²⋊C₄×C₈₉	—	2	2	no	—
385	C₂²⋊C₄×C₈₉	—	2	2	no	—
386	C₂²⋊C₄×C₈₉	—	2	2	no	—
387	C₂²⋊C₄×C₈₉	—	2	2	no	—
388	C₂²⋊C₄×C₈₉	—	2	2	no	—
389	C₂²⋊C₄×C₈₉	—	2	1	no	—
390	C₂²⋊C₄×C₈₉	—	2	2	no	—
391	C₂²⋊C₄×C₈₉	—	2	1	no	—
392	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
393	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
394	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
395	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
396	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
397	C₄²×C₈₉	—	2	2	no	—
398	C₄²×C₈₉	—	2	2	no	—
399	C₄²×C₈₉	—	2	2	no	—
400	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
402	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
403	C₄²×C₈₉	C₂⁴	1	2	yes	—
404	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
405	C₂³×C₈₉	—	2	1	no	—
406	C₂³×C₈₉	—	2	1	no	—
407	C₂³×C₈₉	—	2	2	no	—
408	C₂³×C₈₉	—	2	2	no	—
409	C₂³×C₈₉	—	4	2	no	—
410	C₂³×C₈₉	—	8	1	no	—
411	C₂³×C₈₉	—	8	2	no	—
412	C₂³×C₈₉	—	8	2	no	—
413	C₂³×C₈₉	—	8	1	no	—
414	C₂³×C₈₉	—	8	2	no	—
415	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
416	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
417	Q₈×C₈₉	—	2	2	no	—
418	Q₈×C₈₉	—	2	2	no	—
419	Q₈×C₈₉	—	4	1	no	—
420	Q₈×C₈₉	—	4	2	no	—
421	Q₈×C₈₉	—	8	1	no	—
422	Q₈×C₈₉	—	8	1	no	—
423	Q₈×C₈₉	—	8	2	no	—
424	Q₈×C₈₉	—	8	1	no	—
425	Q₈×C₈₉	—	8	1	no	—
426	D₄×C₈₉	—	2	2	no	—
427	D₄×C₈₉	—	2	2	no	—
428	D₄×C₈₉	—	2	2	no	—
429	D₄×C₈₉	—	2	2	no	—
430	D₄×C₈₉	—	2	2	no	—
431	D₄×C₈₉	—	2	2	no	—
432	D₄×C₈₉	—	4	2	no	—
433	D₄×C₈₉	—	4	1	no	—
434	D₄×C₈₉	—	4	4	no	—
435	D₄×C₈₉	—	8	1	no	—
436	D₄×C₈₉	—	8	1	no	—
437	D₄×C₈₉	—	8	2	no	—
438	D₄×C₈₉	—	8	2	no	—
439	D₄×C₈₉	—	8	1	no	—
440	D₄×C₈₉	—	8	2	no	—
441	D₄×C₈₉	—	8	1	no	—
442	D₄×C₈₉	—	8	1	no	—
443	D₄×C₈₉	—	8	2	no	—
444	D₄×C₈₉	—	8	2	no	—
445	D₄×C₈₉	—	8	2	no	—
446	D₄×C₈₉	—	8	1	no	—
447	D₄×C₈₉	—	8	1	no	—
448	D₄×C₈₉	—	8	2	no	—
449	C₂×C₄×C₈₉	—	2	2	no	—
450	C₂×C₄×C₈₉	—	2	2	no	—
451	C₂×C₄×C₈₉	—	2	2	no	—
452	C₂×C₄×C₈₉	—	2	2	no	—
453	C₂×C₄×C₈₉	—	2	1	no	—
454	C₂×C₄×C₈₉	—	2	2	no	—
455	C₂×C₄×C₈₉	—	2	2	no	—
456	C₂×C₄×C₈₉	—	2	2	no	—
457	C₂×C₄×C₈₉	—	2	1	no	—
458	C₂×C₄×C₈₉	—	4	1	no	—
459	C₂×C₄×C₈₉	—	4	1	no	—
460	C₂×C₄×C₈₉	—	4	2	no	—
461	C₂×C₄×C₈₉	—	4	2	no	—
462	C₂×C₄×C₈₉	—	8	2	no	—
463	C₂×C₄×C₈₉	—	8	2	no	—
464	C₂×C₄×C₈₉	—	8	2	no	—
465	C₂×C₄×C₈₉	—	8	2	no	—
466	C₂×C₄×C₈₉	—	8	2	no	—
467	C₂×C₄×C₈₉	—	8	1	no	—
468	C₂×C₄×C₈₉	—	8	2	no	—
469	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
471	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
472	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
477	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
478	C₈×C₈₉	—	2	2	no	—
479	C₈×C₈₉	—	2	2	no	—
480	C₈×C₈₉	—	2	2	no	—
481	C₈×C₈₉	—	2	2	no	—
482	C₂²×C₈₉	—	2	1	no	—
483	C₂²×C₈₉	—	2	1	no	—
484	C₂²×C₈₉	—	2	2	no	—
485	C₂²×C₈₉	—	2	2	no	—
486	C₂²×C₈₉	—	2	1	no	—
487	C₂²×C₈₉	—	2	2	no	—
488	C₂²×C₈₉	—	4	1	no	—
489	C₂²×C₈₉	—	4	1	no	—
490	C₂²×C₈₉	—	4	1	no	—
491	C₂²×C₈₉	—	4	2	no	—
492	C₂²×C₈₉	—	4	2	no	—
493	C₂²×C₈₉	—	4	1	no	—
494	C₂²×C₈₉	—	4	2	no	—
495	C₂²×C₈₉	—	4	2	no	—
496	C₂²×C₈₉	—	4	2	no	—
497	C₂²×C₈₉	—	4	2	no	—
498	C₂²×C₈₉	—	4	1	no	—
499	C₂²×C₈₉	—	4	1	no	—
500	C₂²×C₈₉	—	16	2	no	—
501	C₂²×C₈₉	—	16	4	no	—
502	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
503	C₄×C₈₉	—	2	1	no	—
504	C₄×C₈₉	—	2	1	no	—
505	C₄×C₈₉	—	2	1	no	—
506	C₄×C₈₉	—	2	1	no	—
507	C₄×C₈₉	—	2	2	no	—
508	C₄×C₈₉	—	2	2	no	—
509	C₄×C₈₉	—	2	2	no	—
510	C₄×C₈₉	—	2	1	no	—
511	C₄×C₈₉	—	4	1	no	—
512	C₄×C₈₉	—	4	1	no	—
513	C₄×C₈₉	—	4	2	no	—
514	C₄×C₈₉	—	4	2	no	—
515	C₄×C₈₉	—	4	2	no	—
516	C₄×C₈₉	—	4	2	no	—
517	C₄×C₈₉	#585	1	2	yes	—
518	#62570	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
519	C₂×C₈₉	—	4	1	no	—
520	C₂×C₈₉	—	4	2	no	—
521	C₂×C₈₉	—	8	1	no	—
522	C₂×C₈₉	—	8	1	no	—
523	C₂×C₈₉	—	8	2	no	—
524	C₂×C₈₉	—	8	2	no	—
525	C₂×C₈₉	#3500	1	1	yes	characteristic
526	C₂×C₈₉	#3585	1	1	yes	characteristic
527	C₂×C₈₉	#3585	1	1	yes	characteristic
528	#3558	C₂×C₈₉	1	1	yes	characteristic, complemented
529	#3547	C₂×C₈₉	1	1	yes	characteristic, complemented
530	#3373	C₂×C₈₉	1	2	yes	complemented
531	#3370	C₂×C₈₉	1	2	yes	complemented
532	#3326	C₂×C₈₉	1	2	yes	complemented
533	#3325	C₂×C₈₉	1	2	yes	complemented
534	#3321	C₂×C₈₉	1	2	yes	complemented
535	#3319	C₂×C₈₉	1	2	yes	complemented
536	#3318	C₂×C₈₉	1	2	yes	complemented
537	#3306	C₂×C₈₉	1	2	yes	complemented
538	#3244	C₂×C₈₉	1	2	yes	complemented
539	#3235	C₂×C₈₉	1	1	yes	characteristic, complemented
540	#3220	C₂×C₈₉	1	2	yes	complemented
541	#3213	C₂×C₈₉	1	1	yes	characteristic, complemented
542	#3184	C₂×C₈₉	1	1	yes	characteristic, complemented
543	#3179	C₂×C₈₉	1	2	yes	complemented
544	#3140	C₂×C₈₉	1	1	yes	characteristic, complemented
545	#3136	C₂×C₈₉	1	2	yes	complemented
546	#2967	C₂×C₈₉	1	1	yes	characteristic, complemented
547	C₈₉	#62570	1	1	yes	characteristic, direct product factor, Sylow
548	#562	—	2	1	no	—
549	#562	—	2	2	no	—
550	H(3,𝔽₄)	—	2	1	no	—
551	#559	C₂²×C₈₉	1	2	yes	—
552	#555	C₂²×C₈₉	1	1	yes	characteristic, complemented
553	#555	C₂²×C₈₉	1	2	yes	complemented
554	#554	C₂²×C₈₉	1	1	yes	characteristic, complemented
555	#553	C₂²×C₈₉	1	2	yes	complemented
556	#552	—	2	1	no	—
557	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
558	#548	—	2	1	no	—
559	#548	C₂²×C₈₉	1	2	yes	—
560	#547	C₂²×C₈₉	1	1	yes	characteristic, complemented
561	#546	—	2	2	no	—
562	#546	C₂²×C₈₉	1	2	yes	—
563	D₄²	C₂²×C₈₉	1	2	yes	—
564	#544	C₂²×C₈₉	1	2	yes	complemented
565	#542	—	2	2	no	—
566	#542	C₂²×C₈₉	1	2	yes	—
567	#540	C₂²×C₈₉	1	2	yes	complemented
568	#538	—	2	2	no	—
569	#538	—	2	1	no	—
570	#537	—	2	1	no	—
571	#536	—	2	1	no	—
572	#535	C₂²×C₈₉	1	2	yes	—
573	#534	—	2	1	no	—
574	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
575	#532	C₂²×C₈₉	1	1	yes	characteristic
576	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
577	#529	C₂²×C₈₉	1	1	yes	characteristic
578	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
579	#501	C₂²×C₈₉	1	2	yes	complemented
580	#498	C₂²×C₈₉	1	1	yes	characteristic, complemented
581	#496	C₂²×C₈₉	1	2	yes	complemented
582	#493	C₂²×C₈₉	1	1	yes	characteristic, complemented
583	#490	C₂²×C₈₉	1	2	yes	—
584	#490	C₂²×C₈₉	1	2	yes	complemented
585	#489	C₂²×C₈₉	1	2	yes	complemented
586	#489	C₂²×C₈₉	1	2	yes	complemented
587	#489	C₂²×C₈₉	1	2	yes	complemented
588	#489	C₂²×C₈₉	1	2	yes	complemented
589	#488	C₂²×C₈₉	1	2	yes	complemented
590	#488	C₂²×C₈₉	1	2	yes	complemented
591	#488	C₂²×C₈₉	1	2	yes	complemented
592	#486	C₂²×C₈₉	1	2	yes	—
593	#486	C₂²×C₈₉	1	1	yes	characteristic, complemented
594	#486	C₂²×C₈₉	1	1	yes	characteristic, complemented
595	#485	C₂²×C₈₉	1	2	yes	complemented
596	#483	C₂²×C₈₉	1	2	yes	complemented
597	#482	C₂²×C₈₉	1	2	yes	—
598	#482	C₂²×C₈₉	1	2	yes	complemented
599	#482	C₂²×C₈₉	1	2	yes	complemented
600	#481	C₂²×C₈₉	1	2	yes	—
601	#479	C₂²×C₈₉	1	2	yes	complemented
602	#478	C₂²×C₈₉	1	2	yes	complemented
603	#476	C₂²×C₈₉	1	2	yes	complemented
604	#476	C₂²×C₈₉	1	2	yes	complemented
605	#475	C₂²×C₈₉	1	2	yes	complemented
606	#474	C₂²×C₈₉	1	2	yes	complemented
607	#469	C₂²×C₈₉	1	2	yes	—
608	#469	C₂²×C₈₉	1	2	yes	complemented
609	#469	C₂²×C₈₉	1	2	yes	complemented
610	#468	C₂²×C₈₉	1	2	yes	complemented
611	#466	C₂²×C₈₉	1	2	yes	—
612	#465	C₂²×C₈₉	1	2	yes	complemented
613	#463	C₂²×C₈₉	1	2	yes	complemented
614	#463	C₂²×C₈₉	1	2	yes	complemented
615	#463	C₂²×C₈₉	1	2	yes	complemented
616	#463	C₂²×C₈₉	1	2	yes	complemented
617	#459	C₂²×C₈₉	1	2	yes	—
618	#459	C₂²×C₈₉	1	2	yes	—
619	#449	C₂²×C₈₉	1	2	yes	complemented
620	#449	C₂²×C₈₉	1	2	yes	complemented
621	#448	C₂²×C₈₉	1	1	yes	characteristic, complemented
622	#448	C₂²×C₈₉	1	1	yes	characteristic, complemented
623	#447	C₂²×C₈₉	1	1	yes	characteristic
624	#447	C₂²×C₈₉	1	1	yes	characteristic
625	#447	C₂²×C₈₉	1	2	yes	complemented
626	#447	C₂²×C₈₉	1	2	yes	complemented
627	#446	C₂²×C₈₉	1	2	yes	complemented
628	#442	C₂²×C₈₉	1	2	yes	complemented
629	#442	C₂²×C₈₉	1	2	yes	complemented
630	#442	C₂²×C₈₉	1	2	yes	complemented
631	#440	C₂²×C₈₉	1	2	yes	complemented
632	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
633	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
634	#436	C₂²×C₈₉	1	2	yes	complemented
635	#435	C₂²×C₈₉	1	2	yes	complemented
636	#435	C₂²×C₈₉	1	2	yes	complemented
637	#433	C₂²×C₈₉	1	2	yes	complemented
638	#432	C₂²×C₈₉	1	1	yes	characteristic, complemented
639	#419	C₂²×C₈₉	1	2	yes	complemented
640	#418	C₂²×C₈₉	1	2	yes	—
641	#418	C₂²×C₈₉	1	2	yes	complemented
642	#417	C₂²×C₈₉	1	2	yes	complemented
643	#416	C₂²×C₈₉	1	2	yes	complemented
644	C₂×#102	C₂²×C₈₉	1	2	yes	complemented
645	#405	C₂²×C₈₉	1	2	yes	complemented
646	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
647	C₂×#41	—	2	1	no	—
648	C₂×#41	—	2	1	no	—
649	C₂×#41	—	2	1	no	—
650	C₂×#41	C₂³×C₈₉	1	2	yes	—
651	C₂²×Q₈	—	2	1	no	—
652	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
653	C₂²×D₄	—	2	2	no	—
654	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
655	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
656	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
657	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
658	C₂×D₈	C₂³×C₈₉	1	2	yes	—
659	C₂×D₈	C₂³×C₈₉	1	2	yes	—
660	C₂×D₈	C₂³×C₈₉	1	2	yes	—
661	C₂×D₈	C₂³×C₈₉	1	2	yes	—
662	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
663	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
664	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
665	C₄⋊Q₈	—	2	2	no	—
666	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
667	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
668	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
669	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
670	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
671	#127	C₂³×C₈₉	1	1	yes	characteristic
672	#127	C₂³×C₈₉	1	1	yes	characteristic
673	#127	C₂³×C₈₉	1	2	yes	—
674	#126	—	2	2	no	—
675	#126	—	2	2	no	—
676	#126	D₄×C₈₉	1	2	yes	—
677	#125	—	2	2	no	—
678	#125	D₄×C₈₉	1	1	yes	characteristic
679	#125	C₂³×C₈₉	1	2	yes	—
680	#125	C₂³×C₈₉	1	2	yes	—
681	#124	—	2	2	no	—
682	#124	—	2	2	no	—
683	#124	—	2	2	no	—
684	#124	—	2	2	no	—
685	#124	—	2	2	no	—
686	#124	—	2	2	no	—
687	#124	—	2	1	no	—
688	#124	—	2	1	no	—
689	#124	—	2	1	no	—
690	#124	—	2	1	no	—
691	#124	D₄×C₈₉	1	1	yes	characteristic
692	#124	C₂³×C₈₉	1	2	yes	—
693	#124	C₂³×C₈₉	1	2	yes	—
694	#124	C₂³×C₈₉	1	2	yes	—
695	#123	—	2	2	no	—
696	#123	—	2	2	no	—
697	#123	—	2	2	no	—
698	#123	—	2	2	no	—
699	#123	—	2	2	no	—
700	#123	—	2	2	no	—
701	#123	—	2	2	no	—
702	#123	—	2	2	no	—
703	#123	D₄×C₈₉	1	2	yes	—
704	C₂²⋊Q₈	—	2	1	no	—
705	C₂²⋊Q₈	—	2	1	no	—
706	C₂²⋊Q₈	—	2	1	no	—
707	C₂²⋊Q₈	—	2	1	no	—
708	C₂²⋊Q₈	—	2	1	no	—
709	C₂²⋊Q₈	—	2	2	no	—
710	C₂²⋊Q₈	—	2	2	no	—
711	C₂²⋊Q₈	—	2	2	no	—
712	C₂²⋊Q₈	—	2	2	no	—
713	C₂²⋊Q₈	—	2	2	no	—
714	C₂²⋊Q₈	—	2	2	no	—
715	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
716	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
717	#121	—	2	2	no	—
718	#121	—	2	1	no	—
719	#121	—	2	2	no	—
720	#121	—	2	2	no	—
721	#121	—	2	1	no	—
722	#121	—	2	1	no	—
723	#121	—	2	2	no	—
724	#121	—	2	2	no	—
725	#121	—	2	2	no	—
726	#121	—	2	2	no	—
727	#121	—	2	2	no	—
728	#121	—	2	2	no	—
729	#121	D₄×C₈₉	1	1	yes	characteristic
730	#121	C₂³×C₈₉	1	2	yes	—
731	#121	C₂³×C₈₉	1	1	yes	characteristic
732	#121	C₂³×C₈₉	1	1	yes	characteristic
733	#121	C₂³×C₈₉	1	2	yes	—
734	#121	C₂³×C₈₉	1	2	yes	—
735	#121	C₂³×C₈₉	1	2	yes	—
736	#120	—	2	2	no	—
737	#120	—	2	2	no	—
738	#120	—	2	2	no	—
739	#120	—	2	2	no	—
740	#120	—	2	2	no	—
741	C₄×Q₈	—	2	1	no	—
742	C₄×Q₈	—	2	1	no	—
743	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
744	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
745	C₄×D₄	—	2	2	no	—
746	C₄×D₄	—	2	2	no	—
747	C₄×D₄	—	2	2	no	—
748	C₄×D₄	—	2	1	no	—
749	C₄×D₄	—	2	1	no	—
750	C₄×D₄	C₂³×C₈₉	1	2	yes	—
751	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
752	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
753	C₄×D₄	C₂³×C₈₉	1	2	yes	—
754	C₄×D₄	C₂³×C₈₉	1	2	yes	—
755	C₄×D₄	C₂³×C₈₉	1	2	yes	—
756	C₄×D₄	C₂³×C₈₉	1	2	yes	—
757	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
758	#117	—	2	1	no	—
759	#117	—	2	2	no	—
760	#117	C₂³×C₈₉	1	2	yes	—
761	#117	C₂³×C₈₉	1	2	yes	—
762	#117	C₂³×C₈₉	1	2	yes	—
763	C₂×C₄⋊C₄	—	2	1	no	—
764	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
765	C₂×C₂²⋊C₄	—	2	1	no	—
766	C₂×C₂²⋊C₄	—	2	1	no	—
767	C₂×C₂²⋊C₄	—	2	2	no	—
768	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
769	#107	C₂³×C₈₉	1	2	yes	—
770	#107	C₂³×C₈₉	1	2	yes	—
771	#106	C₂³×C₈₉	1	2	yes	—
772	#106	C₂³×C₈₉	1	2	yes	—
773	#106	C₂³×C₈₉	1	2	yes	—
774	#106	C₂³×C₈₉	1	2	yes	—
775	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
776	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
777	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
778	#103	C₂³×C₈₉	1	2	yes	—
779	#103	C₂³×C₈₉	1	2	yes	—
780	#103	C₂³×C₈₉	1	2	yes	—
781	#103	C₂³×C₈₉	1	2	yes	—
782	#103	C₂³×C₈₉	1	2	yes	—
783	#103	C₂³×C₈₉	1	2	yes	—
784	#102	C₂³×C₈₉	1	2	yes	—
785	#102	C₂³×C₈₉	1	2	yes	—
786	#102	C₂³×C₈₉	1	2	yes	—
787	#102	C₂³×C₈₉	1	2	yes	—
788	#102	C₂³×C₈₉	1	2	yes	—
789	#102	C₂³×C₈₉	1	2	yes	—
790	#102	C₂³×C₈₉	1	2	yes	—
791	#102	C₂³×C₈₉	1	2	yes	—
792	#102	C₂³×C₈₉	1	2	yes	—
793	#102	C₂³×C₈₉	1	2	yes	—
794	#102	C₂³×C₈₉	1	2	yes	—
795	#102	C₂³×C₈₉	1	2	yes	—
796	#102	C₂³×C₈₉	1	2	yes	—
797	#102	C₂³×C₈₉	1	2	yes	—
798	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
799	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
800	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
801	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
802	#97	C₂³×C₈₉	1	2	yes	—
803	#97	C₂³×C₈₉	1	2	yes	—
804	#97	C₂³×C₈₉	1	2	yes	—
805	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
806	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
807	C₄×C₈	C₂³×C₈₉	1	2	yes	—
808	C₂⁴	—	2	1	no	—
809	C₂⁴	—	2	2	no	—
810	#41	—	4	2	no	—
811	#41	—	4	2	no	—
812	#41	—	8	2	no	—
813	#41	—	8	2	no	—
814	#41	—	8	2	no	—
815	C₂×Q₈	—	2	1	no	—
816	C₂×Q₈	—	2	1	no	—
817	C₂×Q₈	—	2	1	no	—
818	C₂×Q₈	—	2	1	no	—
819	C₂×Q₈	—	2	2	no	—
820	C₂×Q₈	—	2	1	no	—
821	C₂×Q₈	—	4	2	no	—
822	C₂×Q₈	—	8	2	no	—
823	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
824	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	2	no	—
829	C₂×D₄	—	2	1	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	1	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	1	no	—
834	C₂×D₄	—	2	1	no	—
835	C₂×D₄	—	2	1	no	—
836	C₂×D₄	—	2	1	no	—
837	C₂×D₄	—	2	2	no	—
838	C₂×D₄	—	2	2	no	—
839	C₂×D₄	—	2	1	no	—
840	C₂×D₄	—	4	2	no	—
841	C₂×D₄	—	4	2	no	—
842	C₂×D₄	—	4	2	no	—
843	C₂×D₄	—	8	4	no	—
844	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
845	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
846	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
847	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
848	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
849	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
850	C₂²×C₄	—	2	1	no	—
851	C₂²×C₄	—	2	2	no	—
852	C₂²×C₄	—	2	1	no	—
853	C₂²×C₄	—	2	1	no	—
854	C₂²×C₄	—	2	2	no	—
855	C₂²×C₄	—	2	2	no	—
856	C₂²×C₄	—	2	2	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
860	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
861	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
862	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
863	SD₁₆	—	4	2	no	—
864	SD₁₆	—	4	2	no	—
865	D₈	—	4	2	no	—
866	D₈	—	4	2	no	—
867	D₈	—	4	2	no	—
868	D₈	—	4	2	no	—
869	M₁₆	—	4	2	no	—
870	M₁₆	—	4	2	no	—
871	C₂×C₈	—	4	2	no	—
872	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
873	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
874	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
875	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
876	C₄⋊C₄	—	2	1	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	1	no	—
882	C₄⋊C₄	—	2	1	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	1	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
889	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
890	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
891	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
892	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
893	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
894	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
895	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
896	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
897	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
898	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	1	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	1	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	2	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	1	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	2	1	no	—
920	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
921	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
922	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
923	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
924	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
925	C₄²	—	2	2	no	—
926	C₄²	—	2	2	no	—
927	C₄²	—	2	2	no	—
928	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
929	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
930	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
931	C₄²	C₂⁴×C₈₉	1	2	yes	—
932	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
933	C₂³	—	2	1	no	—
934	C₂³	—	2	1	no	—
935	C₂³	—	2	2	no	—
936	C₂³	—	2	2	no	—
937	C₂³	—	4	2	no	—
938	C₂³	—	8	1	no	—
939	C₂³	—	8	2	no	—
940	C₂³	—	8	2	no	—
941	C₂³	—	8	1	no	—
942	C₂³	—	8	2	no	—
943	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
944	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
945	Q₈	—	2	2	no	—
946	Q₈	—	2	2	no	—
947	Q₈	—	4	1	no	—
948	Q₈	—	4	2	no	—
949	Q₈	—	8	1	no	—
950	Q₈	—	8	1	no	—
951	Q₈	—	8	2	no	—
952	Q₈	—	8	1	no	—
953	Q₈	—	8	1	no	—
954	D₄	—	2	2	no	—
955	D₄	—	2	2	no	—
956	D₄	—	2	2	no	—
957	D₄	—	2	2	no	—
958	D₄	—	2	2	no	—
959	D₄	—	2	2	no	—
960	D₄	—	4	2	no	—
961	D₄	—	4	1	no	—
962	D₄	—	4	4	no	—
963	D₄	—	8	1	no	—
964	D₄	—	8	1	no	—
965	D₄	—	8	2	no	—
966	D₄	—	8	2	no	—
967	D₄	—	8	1	no	—
968	D₄	—	8	2	no	—
969	D₄	—	8	1	no	—
970	D₄	—	8	1	no	—
971	D₄	—	8	2	no	—
972	D₄	—	8	2	no	—
973	D₄	—	8	2	no	—
974	D₄	—	8	1	no	—
975	D₄	—	8	1	no	—
976	D₄	—	8	2	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	4	1	no	—
987	C₂×C₄	—	4	1	no	—
988	C₂×C₄	—	4	2	no	—
989	C₂×C₄	—	4	2	no	—
990	C₂×C₄	—	8	2	no	—
991	C₂×C₄	—	8	2	no	—
992	C₂×C₄	—	8	2	no	—
993	C₂×C₄	—	8	2	no	—
994	C₂×C₄	—	8	2	no	—
995	C₂×C₄	—	8	1	no	—
996	C₂×C₄	—	8	2	no	—
997	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
998	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
999	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1000	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1001	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1002	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1003	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1004	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1005	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1006	C₈	—	2	2	no	—
1007	C₈	—	2	2	no	—
1008	C₈	—	2	2	no	—
1009	C₈	—	2	2	no	—
1010	C₂²	—	2	1	no	—
1011	C₂²	—	2	1	no	—
1012	C₂²	—	2	2	no	—
1013	C₂²	—	2	2	no	—
1014	C₂²	—	2	1	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	4	1	no	—
1017	C₂²	—	4	1	no	—
1018	C₂²	—	4	1	no	—
1019	C₂²	—	4	2	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	4	1	no	—
1022	C₂²	—	4	2	no	—
1023	C₂²	—	4	2	no	—
1024	C₂²	—	4	2	no	—
1025	C₂²	—	4	2	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	—	4	1	no	—
1028	C₂²	—	16	2	no	—
1029	C₂²	—	16	4	no	—
1030	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1031	C₄	—	2	1	no	—
1032	C₄	—	2	1	no	—
1033	C₄	—	2	1	no	—
1034	C₄	—	2	1	no	—
1035	C₄	—	2	2	no	—
1036	C₄	—	2	2	no	—
1037	C₄	—	2	2	no	—
1038	C₄	—	2	1	no	—
1039	C₄	—	4	1	no	—
1040	C₄	—	4	1	no	—
1041	C₄	—	4	2	no	—
1042	C₄	—	4	2	no	—
1043	C₄	—	4	2	no	—
1044	C₄	—	4	2	no	—
1045	C₄	#585×C₈₉	1	2	yes	—
1046	C₂	—	4	1	no	—
1047	C₂	—	4	2	no	—
1048	C₂	—	8	1	no	—
1049	C₂	—	8	1	no	—
1050	C₂	—	8	2	no	—
1051	C₂	—	8	2	no	—
1052	C₂	C₈₉×#3500	1	1	yes	characteristic
1053	C₂	C₈₉×#3585	1	1	yes	characteristic
1054	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×#3558	C₂	semidirect
2. C₈₉×#3547	C₂	semidirect
3. C₈₉×#3373	C₂	semidirect
4. C₈₉×#3370	C₂	semidirect
5. C₈₉×#3326	C₂	semidirect
6. C₈₉×#3325	C₂	semidirect
7. C₈₉×#3321	C₂	semidirect
8. C₈₉×#3319	C₂	semidirect
9. C₈₉×#3318	C₂	semidirect
10. C₈₉×#3306	C₂	semidirect
11. C₈₉×#3244	C₂	semidirect
12. C₈₉×#3235	C₂	semidirect
13. C₈₉×#3220	C₂	semidirect
14. C₈₉×#3213	C₂	semidirect
15. C₈₉×#3184	C₂	semidirect
16. C₈₉×#3179	C₂	semidirect
17. C₈₉×#3140	C₂	semidirect
18. C₈₉×#3136	C₂	semidirect
19. C₈₉×#2967	C₂	semidirect
24. #555×C₈₉	C₂²	semidirect
25. #555×C₈₉	C₂²	semidirect
26. #554×C₈₉	C₂²	semidirect
27. #553×C₈₉	C₂²	semidirect
29. D₄×Q₈×C₈₉	C₂²	semidirect
32. #547×C₈₉	C₂²	semidirect
36. #544×C₈₉	C₂²	semidirect
39. #540×C₈₉	C₂²	semidirect
46. #533×C₈₉	C₂²	semidirect
48. #532×C₈₉	C₂²	semidirect
51. #501×C₈₉	C₂²	semidirect
52. #498×C₈₉	C₂²	semidirect
53. #496×C₈₉	C₂²	semidirect
54. #493×C₈₉	C₂²	semidirect
56. #490×C₈₉	C₂²	semidirect
57. #489×C₈₉	C₂²	semidirect
58. #489×C₈₉	C₂²	semidirect
59. #489×C₈₉	C₂²	semidirect
60. #489×C₈₉	C₂²	semidirect
61. #488×C₈₉	C₂²	semidirect
62. #488×C₈₉	C₂²	semidirect
63. #488×C₈₉	C₂²	semidirect
65. #486×C₈₉	C₂²	semidirect
66. #486×C₈₉	C₂²	semidirect
67. #485×C₈₉	C₂²	semidirect
68. #483×C₈₉	C₂²	semidirect
70. #482×C₈₉	C₂²	semidirect
71. #482×C₈₉	C₂²	semidirect
73. #479×C₈₉	C₂²	semidirect
74. #478×C₈₉	C₂²	semidirect
75. #476×C₈₉	C₂²	semidirect
76. #476×C₈₉	C₂²	semidirect
77. #475×C₈₉	C₂²	semidirect
78. #474×C₈₉	C₂²	semidirect
80. #469×C₈₉	C₂²	semidirect
81. #469×C₈₉	C₂²	semidirect
82. #468×C₈₉	C₂²	semidirect
84. #465×C₈₉	C₂²	semidirect
85. #463×C₈₉	C₂²	semidirect
86. #463×C₈₉	C₂²	semidirect
87. #463×C₈₉	C₂²	semidirect
88. #463×C₈₉	C₂²	semidirect
91. #449×C₈₉	C₂²	semidirect
92. #449×C₈₉	C₂²	semidirect
93. #448×C₈₉	C₂²	semidirect
94. #448×C₈₉	C₂²	semidirect
97. #447×C₈₉	C₂²	semidirect
98. #447×C₈₉	C₂²	semidirect
99. #446×C₈₉	C₂²	semidirect
100. #442×C₈₉	C₂²	semidirect
101. #442×C₈₉	C₂²	semidirect
102. #442×C₈₉	C₂²	semidirect
103. #440×C₈₉	C₂²	semidirect
104. C₄×SD₁₆×C₈₉	C₂²	semidirect
105. C₄×D₈×C₈₉	C₂²	semidirect
106. #436×C₈₉	C₂²	semidirect
107. #435×C₈₉	C₂²	semidirect
108. #435×C₈₉	C₂²	semidirect
109. #433×C₈₉	C₂²	semidirect
110. #432×C₈₉	C₂²	semidirect
111. #419×C₈₉	C₂²	semidirect
113. #418×C₈₉	C₂²	semidirect
114. #417×C₈₉	C₂²	semidirect
115. #416×C₈₉	C₂²	semidirect
116. C₂×#102×C₈₉	C₂²	semidirect
117. #405×C₈₉	C₂²	semidirect
118. C₄×M₁₆×C₈₉	C₂²	semidirect
518. #62570	C₈₉	direct (N × H)
528. #3558	C₂×C₈₉	semidirect
529. #3547	C₂×C₈₉	semidirect
530. #3373	C₂×C₈₉	semidirect
531. #3370	C₂×C₈₉	semidirect
532. #3326	C₂×C₈₉	semidirect
533. #3325	C₂×C₈₉	semidirect
534. #3321	C₂×C₈₉	semidirect
535. #3319	C₂×C₈₉	semidirect
536. #3318	C₂×C₈₉	semidirect
537. #3306	C₂×C₈₉	semidirect
538. #3244	C₂×C₈₉	semidirect
539. #3235	C₂×C₈₉	semidirect
540. #3220	C₂×C₈₉	semidirect
541. #3213	C₂×C₈₉	semidirect
542. #3184	C₂×C₈₉	semidirect
543. #3179	C₂×C₈₉	semidirect
544. #3140	C₂×C₈₉	semidirect
545. #3136	C₂×C₈₉	semidirect
546. #2967	C₂×C₈₉	semidirect
547. C₈₉	#62570	direct (N × H)
552. #555	C₂²×C₈₉	semidirect
553. #555	C₂²×C₈₉	semidirect
554. #554	C₂²×C₈₉	semidirect
555. #553	C₂²×C₈₉	semidirect
557. D₄×Q₈	C₂²×C₈₉	semidirect
560. #547	C₂²×C₈₉	semidirect
564. #544	C₂²×C₈₉	semidirect
567. #540	C₂²×C₈₉	semidirect
574. #533	C₂²×C₈₉	semidirect
576. #532	C₂²×C₈₉	semidirect
579. #501	C₂²×C₈₉	semidirect
580. #498	C₂²×C₈₉	semidirect
581. #496	C₂²×C₈₉	semidirect
582. #493	C₂²×C₈₉	semidirect
584. #490	C₂²×C₈₉	semidirect
585. #489	C₂²×C₈₉	semidirect
586. #489	C₂²×C₈₉	semidirect
587. #489	C₂²×C₈₉	semidirect
588. #489	C₂²×C₈₉	semidirect
589. #488	C₂²×C₈₉	semidirect
590. #488	C₂²×C₈₉	semidirect
591. #488	C₂²×C₈₉	semidirect
593. #486	C₂²×C₈₉	semidirect
594. #486	C₂²×C₈₉	semidirect
595. #485	C₂²×C₈₉	semidirect
596. #483	C₂²×C₈₉	semidirect
598. #482	C₂²×C₈₉	semidirect
599. #482	C₂²×C₈₉	semidirect
601. #479	C₂²×C₈₉	semidirect
602. #478	C₂²×C₈₉	semidirect
603. #476	C₂²×C₈₉	semidirect
604. #476	C₂²×C₈₉	semidirect
605. #475	C₂²×C₈₉	semidirect
606. #474	C₂²×C₈₉	semidirect
608. #469	C₂²×C₈₉	semidirect
609. #469	C₂²×C₈₉	semidirect
610. #468	C₂²×C₈₉	semidirect
612. #465	C₂²×C₈₉	semidirect
613. #463	C₂²×C₈₉	semidirect
614. #463	C₂²×C₈₉	semidirect
615. #463	C₂²×C₈₉	semidirect
616. #463	C₂²×C₈₉	semidirect
619. #449	C₂²×C₈₉	semidirect
620. #449	C₂²×C₈₉	semidirect
621. #448	C₂²×C₈₉	semidirect
622. #448	C₂²×C₈₉	semidirect
625. #447	C₂²×C₈₉	semidirect
626. #447	C₂²×C₈₉	semidirect
627. #446	C₂²×C₈₉	semidirect
628. #442	C₂²×C₈₉	semidirect
629. #442	C₂²×C₈₉	semidirect
630. #442	C₂²×C₈₉	semidirect
631. #440	C₂²×C₈₉	semidirect
632. C₄×SD₁₆	C₂²×C₈₉	semidirect
633. C₄×D₈	C₂²×C₈₉	semidirect
634. #436	C₂²×C₈₉	semidirect
635. #435	C₂²×C₈₉	semidirect
636. #435	C₂²×C₈₉	semidirect
637. #433	C₂²×C₈₉	semidirect
638. #432	C₂²×C₈₉	semidirect
639. #419	C₂²×C₈₉	semidirect
641. #418	C₂²×C₈₉	semidirect
642. #417	C₂²×C₈₉	semidirect
643. #416	C₂²×C₈₉	semidirect
644. C₂×#102	C₂²×C₈₉	semidirect
645. #405	C₂²×C₈₉	semidirect
646. 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×#3558	2
C₈₉×#3547	2
C₈₉×#3373	2
C₈₉×#3370	2
C₈₉×#3326	2
C₈₉×#3325	2
C₈₉×#3321	2
C₈₉×#3319	2
C₈₉×#3318	2
C₈₉×#3306	2
C₈₉×#3244	2
C₈₉×#3235	2
C₈₉×#3220	2
C₈₉×#3213	2
C₈₉×#3184	2
C₈₉×#3179	2
C₈₉×#3140	2
C₈₉×#3136	2
C₈₉×#2967	2
#62570	89

Subgroups — C89×#62570 #36440418

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62570 #36440418