Subgroups — C₈₉×#62847 #36440695

Order 22784.

7106 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3521	C₂	1	8	yes	maximal, complemented
2	C₈₉×#3520	C₂	1	8	yes	maximal, complemented
3	C₈₉×#3515	C₂	1	8	yes	maximal, complemented
4	C₈₉×#3513	C₂	1	8	yes	maximal, complemented
5	C₈₉×#3507	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3505	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3501	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3496	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3492	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3491	C₂	1	4	yes	maximal, complemented
11	C₈₉×#3485	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3461	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3459	C₂	1	4	yes	maximal, complemented
14	C₈₉×#3455	C₂	1	2	yes	maximal, complemented
15	C₂×#539×C₈₉	C₂	1	4	yes	maximal, complemented
16	C₄×H(5,𝔽₂)×C₈₉	C₂	1	2	yes	maximal, complemented
17	C₂×#520×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	2	yes	—
19	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
20	#559×C₈₉	C₂²	1	4	yes	complemented
21	#557×C₈₉	C₂²	1	4	yes	complemented
22	#556×C₈₉	C₂²	1	8	yes	complemented
23	#556×C₈₉	C₂²	1	4	yes	complemented
24	#554×C₈₉	C₂²	1	8	yes	complemented
25	#554×C₈₉	C₂²	1	8	yes	complemented
26	#554×C₈₉	C₂²	1	4	yes	complemented
27	#554×C₈₉	C₂²	1	4	yes	complemented
28	#553×C₈₉	C₂²	1	8	yes	complemented
29	#553×C₈₉	C₂²	1	16	yes	complemented
30	#553×C₈₉	C₂²	1	8	yes	complemented
31	#552×C₈₉	C₂²	1	16	yes	complemented
32	#552×C₈₉	C₂²	1	16	yes	complemented
33	#552×C₈₉	C₂²	1	8	yes	complemented
34	#552×C₈₉	C₂²	1	8	yes	complemented
35	#552×C₈₉	C₂²	1	8	yes	complemented
36	#551×C₈₉	C₂²	1	16	yes	complemented
37	#551×C₈₉	C₂²	1	16	yes	complemented
38	#551×C₈₉	C₂²	1	16	yes	complemented
39	D₄×Q₈×C₈₉	C₂²	1	4	yes	complemented
40	#548×C₈₉	C₂²	1	8	yes	complemented
41	#547×C₈₉	C₂²	1	8	yes	complemented
42	#547×C₈₉	C₂²	1	8	yes	complemented
43	#547×C₈₉	C₂²	1	8	yes	complemented
44	#547×C₈₉	C₂²	1	4	yes	complemented
45	#546×C₈₉	C₂²	1	8	yes	complemented
46	#546×C₈₉	C₂²	1	8	yes	complemented
47	#546×C₈₉	C₂²	1	8	yes	complemented
48	#546×C₈₉	C₂²	1	8	yes	complemented
49	D₄²×C₈₉	C₂²	1	4	yes	complemented
50	#544×C₈₉	C₂²	1	2	yes	complemented
51	#543×C₈₉	C₂²	1	4	yes	complemented
52	#542×C₈₉	C₂²	1	4	yes	complemented
53	#542×C₈₉	C₂²	1	4	yes	complemented
54	#542×C₈₉	C₂²	1	8	yes	complemented
55	#541×C₈₉	C₂²	1	4	yes	complemented
56	#541×C₈₉	C₂²	1	8	yes	complemented
57	#540×C₈₉	C₂²	1	4	yes	complemented
58	#539×C₈₉	C₂²	1	4	yes	complemented
59	#539×C₈₉	C₂²	1	8	yes	complemented
60	#539×C₈₉	C₂²	1	8	yes	complemented
61	#539×C₈₉	C₂²	1	8	yes	complemented
62	#539×C₈₉	C₂²	1	16	yes	complemented
63	#539×C₈₉	C₂²	1	16	yes	complemented
64	#539×C₈₉	C₂²	1	4	yes	complemented
65	#539×C₈₉	C₂²	1	16	yes	complemented
66	#538×C₈₉	C₂²	1	4	yes	complemented
67	#538×C₈₉	C₂²	1	4	yes	complemented
68	#538×C₈₉	C₂²	1	16	yes	complemented
69	#537×C₈₉	C₂²	1	2	yes	—
70	#536×C₈₉	C₂²	1	4	yes	complemented
71	#534×C₈₉	C₂²	1	4	yes	—
72	#534×C₈₉	C₂²	1	8	yes	complemented
73	#533×C₈₉	C₂²	1	2	yes	complemented
74	#533×C₈₉	C₂²	1	8	yes	complemented
75	#532×C₈₉	C₂²	1	2	yes	—
76	#529×C₈₉	C₂²	1	8	yes	complemented
77	#529×C₈₉	C₂²	1	8	yes	complemented
78	#529×C₈₉	C₂²	1	8	yes	complemented
79	#529×C₈₉	C₂²	1	16	yes	complemented
80	#529×C₈₉	C₂²	1	8	yes	complemented
81	#529×C₈₉	C₂²	1	8	yes	complemented
82	C₂×#126×C₈₉	C₂²	1	8	yes	complemented
83	C₂×#125×C₈₉	C₂²	1	8	yes	complemented
84	#525×C₈₉	C₂²	1	4	yes	complemented
85	#525×C₈₉	C₂²	1	8	yes	complemented
86	#525×C₈₉	C₂²	1	16	yes	complemented
87	C₂×#123×C₈₉	C₂²	1	8	yes	complemented
88	C₂×#123×C₈₉	C₂²	1	8	yes	complemented
89	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
90	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	8	yes	complemented
91	C₂×#121×C₈₉	C₂²	1	4	yes	—
92	#520×C₈₉	C₂²	1	8	yes	complemented
93	#520×C₈₉	C₂²	1	8	yes	complemented
94	#520×C₈₉	C₂²	1	4	yes	complemented
95	#520×C₈₉	C₂²	1	8	yes	complemented
96	#518×C₈₉	C₂²	1	2	yes	—
97	#518×C₈₉	C₂²	1	8	yes	complemented
98	#518×C₈₉	C₂²	1	8	yes	complemented
99	C₄×#41×C₈₉	C₂²	1	4	yes	complemented
100	C₄×#41×C₈₉	C₂²	1	8	yes	complemented
101	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
102	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
103	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
104	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
105	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
106	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
107	C₂×C₄×D₄×C₈₉	C₂²	1	8	yes	complemented
108	C₂×C₄×D₄×C₈₉	C₂²	1	8	yes	complemented
109	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
110	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
111	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
112	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
113	H(5,𝔽₂)×C₈₉	—	2	16	no	—
114	C₂×#41×C₈₉	—	2	8	no	—
115	C₂×#41×C₈₉	C₂³	1	4	yes	—
116	C₂×#41×C₈₉	C₂³	1	8	yes	—
117	C₂×#41×C₈₉	C₂³	1	8	yes	—
118	C₂×#41×C₈₉	C₂³	1	8	yes	—
119	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
120	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
121	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
122	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
123	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
124	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
125	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
127	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
129	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
130	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
131	C₂³×C₄×C₈₉	C₂³	1	8	yes	—
132	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
133	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
134	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
135	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
136	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
137	#127×C₈₉	C₂³	1	2	yes	—
138	#126×C₈₉	C₂³	1	8	yes	—
139	#126×C₈₉	C₂³	1	16	yes	—
140	#126×C₈₉	C₂³	1	16	yes	—
141	#126×C₈₉	C₂³	1	16	yes	—
142	#126×C₈₉	C₂³	1	8	yes	—
143	#126×C₈₉	C₂³	1	16	yes	—
144	#126×C₈₉	C₂³	1	8	yes	—
145	#126×C₈₉	C₂³	1	8	yes	—
146	#126×C₈₉	C₂³	1	16	yes	—
147	#125×C₈₉	C₂³	1	8	yes	—
148	#125×C₈₉	C₂³	1	16	yes	—
149	#125×C₈₉	C₂³	1	16	yes	—
150	#125×C₈₉	C₂³	1	16	yes	—
151	#125×C₈₉	C₂³	1	8	yes	—
152	#125×C₈₉	C₂³	1	8	yes	—
153	#125×C₈₉	C₂³	1	8	yes	—
154	#125×C₈₉	C₂³	1	8	yes	—
155	#125×C₈₉	C₂³	1	4	yes	—
156	#124×C₈₉	C₂³	1	8	yes	—
157	#124×C₈₉	C₂³	1	8	yes	—
158	#124×C₈₉	C₂³	1	8	yes	—
159	#124×C₈₉	C₂³	1	8	yes	—
160	#124×C₈₉	C₂³	1	8	yes	—
161	#124×C₈₉	C₂³	1	4	yes	—
162	#123×C₈₉	C₂³	1	8	yes	—
163	#123×C₈₉	C₂³	1	8	yes	—
164	#123×C₈₉	C₂³	1	16	yes	—
165	#123×C₈₉	C₂³	1	16	yes	—
166	#123×C₈₉	C₂³	1	16	yes	—
167	#123×C₈₉	C₂³	1	16	yes	—
168	#123×C₈₉	C₂³	1	16	yes	—
169	#123×C₈₉	C₂³	1	16	yes	—
170	#123×C₈₉	C₂³	1	8	yes	—
171	#123×C₈₉	C₂³	1	16	yes	—
172	#123×C₈₉	C₂³	1	16	yes	—
173	#123×C₈₉	C₂³	1	16	yes	—
174	#123×C₈₉	C₂³	1	8	yes	—
175	#123×C₈₉	C₂³	1	8	yes	—
176	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
177	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
178	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
179	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
180	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
181	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
182	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
183	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
184	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
185	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
186	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
187	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
188	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
189	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
190	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
191	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
192	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
193	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
194	#121×C₈₉	C₂³	1	4	yes	—
195	#121×C₈₉	C₂³	1	8	yes	—
196	#121×C₈₉	C₂³	1	8	yes	—
197	#121×C₈₉	C₂³	1	8	yes	—
198	#121×C₈₉	C₂³	1	8	yes	—
199	#121×C₈₉	C₂³	1	16	yes	—
200	#121×C₈₉	C₂³	1	8	yes	—
201	#121×C₈₉	C₂³	1	4	yes	—
202	#121×C₈₉	C₂³	1	4	yes	—
203	#121×C₈₉	C₂³	1	4	yes	—
204	#121×C₈₉	C₂³	1	16	yes	—
205	#121×C₈₉	C₂³	1	8	yes	—
206	#121×C₈₉	C₂³	1	8	yes	—
207	#120×C₈₉	C₂³	1	8	yes	—
208	#120×C₈₉	C₂³	1	16	yes	—
209	#120×C₈₉	C₂³	1	16	yes	—
210	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
211	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
212	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
213	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
214	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
215	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
216	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
217	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
218	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
219	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
220	C₄×D₄×C₈₉	C₂³	1	8	yes	—
221	C₄×D₄×C₈₉	C₂³	1	4	yes	—
222	C₄×D₄×C₈₉	C₂³	1	4	yes	—
223	C₄×D₄×C₈₉	C₂³	1	8	yes	—
224	C₄×D₄×C₈₉	C₂³	1	16	yes	—
225	C₄×D₄×C₈₉	C₂³	1	4	yes	—
226	C₄×D₄×C₈₉	C₂³	1	8	yes	—
227	C₄×D₄×C₈₉	C₂³	1	16	yes	—
228	C₄×D₄×C₈₉	C₂³	1	16	yes	—
229	C₄×D₄×C₈₉	C₂³	1	8	yes	—
230	C₄×D₄×C₈₉	C₂³	1	16	yes	—
231	C₄×D₄×C₈₉	C₂³	1	16	yes	—
232	C₄×D₄×C₈₉	C₂³	1	8	yes	—
233	C₄×D₄×C₈₉	C₂³	1	8	yes	—
234	C₄×D₄×C₈₉	C₂³	1	8	yes	—
235	C₄×D₄×C₈₉	C₂³	1	8	yes	—
236	C₄×D₄×C₈₉	C₂³	1	4	yes	—
237	C₄×D₄×C₈₉	C₂³	1	16	yes	—
238	C₄×D₄×C₈₉	C₂³	1	8	yes	—
239	C₄×D₄×C₈₉	C₂³	1	16	yes	—
240	C₄×D₄×C₈₉	C₂³	1	8	yes	—
241	C₄×D₄×C₈₉	C₂³	1	8	yes	—
242	C₄×D₄×C₈₉	C₂³	1	8	yes	—
243	C₄×D₄×C₈₉	C₂³	1	4	yes	—
244	C₄×D₄×C₈₉	C₂³	1	4	yes	—
245	#117×C₈₉	C₂³	1	4	yes	—
246	#117×C₈₉	C₂³	1	4	yes	—
247	#117×C₈₉	C₂³	1	16	yes	—
248	#117×C₈₉	C₂³	1	4	yes	—
249	#117×C₈₉	C₂³	1	8	yes	—
250	#117×C₈₉	C₂³	1	16	yes	—
251	#117×C₈₉	C₂³	1	8	yes	—
252	#117×C₈₉	C₂³	1	16	yes	—
253	#117×C₈₉	C₂³	1	8	yes	—
254	#117×C₈₉	C₂³	1	16	yes	—
255	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
262	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
263	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
264	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
266	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
267	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
268	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
269	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
270	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
271	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
272	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
273	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
274	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
277	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
278	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
279	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
280	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
281	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
282	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
283	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
284	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
285	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
286	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
287	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
288	C₂⁴×C₈₉	C₂⁴	1	8	yes	—
289	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
290	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
291	#41×C₈₉	—	2	32	no	—
292	#41×C₈₉	—	2	32	no	—
293	#41×C₈₉	—	2	16	no	—
294	#41×C₈₉	—	8	8	no	—
295	C₂×Q₈×C₈₉	—	2	4	no	—
296	C₂×Q₈×C₈₉	—	8	4	no	—
297	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
298	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
299	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
300	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
301	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
302	C₂×D₄×C₈₉	—	2	8	no	—
303	C₂×D₄×C₈₉	—	2	32	no	—
304	C₂×D₄×C₈₉	—	2	32	no	—
305	C₂×D₄×C₈₉	—	8	4	no	—
306	C₂×D₄×C₈₉	#41	1	8	yes	complemented
307	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
308	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
309	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
310	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
311	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
312	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
313	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
314	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
315	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
316	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
317	C₂²×C₄×C₈₉	—	2	8	no	—
318	C₂²×C₄×C₈₉	—	2	4	no	—
319	C₂²×C₄×C₈₉	—	8	2	no	—
320	C₂²×C₄×C₈₉	—	8	8	no	—
321	C₂²×C₄×C₈₉	—	8	2	no	—
322	C₂²×C₄×C₈₉	—	8	2	no	—
323	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
325	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
326	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
327	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
329	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
332	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
333	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
336	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
339	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
340	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
341	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
342	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
343	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
344	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
345	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
346	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
347	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
348	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
349	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
350	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
351	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
352	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
353	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
354	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
355	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
356	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
357	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
358	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
359	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
360	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
361	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
362	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
363	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
364	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
365	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
366	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
367	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
368	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
369	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
370	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
371	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
372	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
373	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
374	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
375	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
376	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
377	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
378	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
379	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
380	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
381	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
382	C₂²⋊C₄×C₈₉	C₂⁴	1	2	yes	—
383	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
384	C₂²⋊C₄×C₈₉	C₂⁴	1	2	yes	—
385	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
386	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
387	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
388	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
389	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
390	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
391	C₄²×C₈₉	C₂⁴	1	4	yes	—
392	C₄²×C₈₉	C₂⁴	1	8	yes	—
393	C₄²×C₈₉	C₂⁴	1	16	yes	—
394	C₄²×C₈₉	C₂⁴	1	8	yes	—
395	C₄²×C₈₉	C₂⁴	1	8	yes	—
396	C₄²×C₈₉	C₂⁴	1	8	yes	—
397	C₄²×C₈₉	C₂⁴	1	8	yes	—
398	C₄²×C₈₉	C₂⁴	1	2	yes	—
399	C₄²×C₈₉	C₂⁴	1	2	yes	—
400	C₂³×C₈₉	—	2	2	no	—
401	C₂³×C₈₉	—	2	16	no	—
402	C₂³×C₈₉	—	4	2	no	—
403	C₂³×C₈₉	—	4	1	no	—
404	C₂³×C₈₉	—	4	2	no	—
405	C₂³×C₈₉	—	4	1	no	—
406	C₂³×C₈₉	—	4	8	no	—
407	C₂³×C₈₉	—	4	8	no	—
408	C₂³×C₈₉	C₂×#41	1	8	yes	—
409	C₂³×C₈₉	C₂⁵	1	8	yes	—
410	C₂³×C₈₉	C₂⁵	1	2	yes	—
411	C₂³×C₈₉	C₂⁵	1	4	yes	—
412	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
413	Q₈×C₈₉	—	2	8	no	—
414	Q₈×C₈₉	—	2	8	no	—
415	Q₈×C₈₉	—	4	4	no	—
416	Q₈×C₈₉	—	4	8	no	—
417	Q₈×C₈₉	—	4	4	no	—
418	D₄×C₈₉	—	2	32	no	—
419	D₄×C₈₉	—	2	16	no	—
420	D₄×C₈₉	—	2	16	no	—
421	D₄×C₈₉	—	2	8	no	—
422	D₄×C₈₉	—	4	4	no	—
423	D₄×C₈₉	—	4	8	no	—
424	D₄×C₈₉	—	4	8	no	—
425	D₄×C₈₉	—	4	4	no	—
426	D₄×C₈₉	—	4	8	no	—
427	D₄×C₈₉	C₂×#41	1	16	yes	—
428	C₂×C₄×C₈₉	—	2	2	no	—
429	C₂×C₄×C₈₉	—	2	4	no	—
430	C₂×C₄×C₈₉	—	2	16	no	—
431	C₂×C₄×C₈₉	—	2	16	no	—
432	C₂×C₄×C₈₉	—	2	8	no	—
433	C₂×C₄×C₈₉	—	2	16	no	—
434	C₂×C₄×C₈₉	—	4	1	no	—
435	C₂×C₄×C₈₉	—	4	8	no	—
436	C₂×C₄×C₈₉	—	4	2	no	—
437	C₂×C₄×C₈₉	—	4	8	no	—
438	C₂×C₄×C₈₉	—	4	1	no	—
439	C₂×C₄×C₈₉	—	4	2	no	—
440	C₂×C₄×C₈₉	—	4	4	no	—
441	C₂×C₄×C₈₉	—	4	4	no	—
442	C₂×C₄×C₈₉	—	4	8	no	—
443	C₂×C₄×C₈₉	—	4	8	no	—
444	C₂×C₄×C₈₉	—	4	16	no	—
445	C₂×C₄×C₈₉	—	4	1	no	—
446	C₂×C₄×C₈₉	—	4	8	no	—
447	C₂×C₄×C₈₉	—	4	8	no	—
448	C₂×C₄×C₈₉	—	4	1	no	—
449	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
450	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
451	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
452	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
453	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
454	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
455	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
456	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
457	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
458	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
459	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
460	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
461	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
462	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
463	C₂²×C₈₉	—	2	1	no	—
464	C₂²×C₈₉	—	2	4	no	—
465	C₂²×C₈₉	—	2	1	no	—
466	C₂²×C₈₉	—	2	4	no	—
467	C₂²×C₈₉	—	2	2	no	—
468	C₂²×C₈₉	—	2	8	no	—
469	C₂²×C₈₉	—	2	2	no	—
470	C₂²×C₈₉	—	2	8	no	—
471	C₂²×C₈₉	—	2	8	no	—
472	C₂²×C₈₉	—	2	2	no	—
473	C₂²×C₈₉	—	4	8	no	—
474	C₂²×C₈₉	—	4	4	no	—
475	C₂²×C₈₉	—	8	16	no	—
476	C₂²×C₈₉	C₂²×#41	1	8	yes	—
477	C₂²×C₈₉	C₂²×#41	1	2	yes	—
478	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
479	C₄×C₈₉	—	2	2	no	—
480	C₄×C₈₉	—	2	8	no	—
481	C₄×C₈₉	—	2	4	no	—
482	C₄×C₈₉	—	2	2	no	—
483	C₄×C₈₉	—	2	4	no	—
484	C₄×C₈₉	—	2	1	no	—
485	C₄×C₈₉	—	2	4	no	—
486	C₄×C₈₉	—	2	8	no	—
487	C₄×C₈₉	—	2	1	no	—
488	C₄×C₈₉	—	2	2	no	—
489	C₄×C₈₉	—	2	8	no	—
490	C₄×C₈₉	—	2	2	no	—
491	C₄×C₈₉	C₂²×#41	1	4	yes	—
492	#62847	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
493	C₂×C₈₉	—	2	2	no	—
494	C₂×C₈₉	—	2	8	no	—
495	C₂×C₈₉	—	4	2	no	—
496	C₂×C₈₉	—	4	8	no	—
497	C₂×C₈₉	C₂³×#41	1	1	yes	characteristic
498	C₂×C₈₉	H(7,𝔽₂)	1	1	yes	characteristic
499	C₂×C₈₉	2₋¹⁺⁶	1	1	yes	characteristic
500	#3521	C₂×C₈₉	1	8	yes	complemented
501	#3520	C₂×C₈₉	1	8	yes	complemented
502	#3515	C₂×C₈₉	1	8	yes	complemented
503	#3513	C₂×C₈₉	1	8	yes	complemented
504	#3507	C₂×C₈₉	1	2	yes	complemented
505	#3505	C₂×C₈₉	1	4	yes	complemented
506	#3501	C₂×C₈₉	1	1	yes	characteristic, complemented
507	#3496	C₂×C₈₉	1	1	yes	characteristic, complemented
508	#3492	C₂×C₈₉	1	2	yes	complemented
509	#3491	C₂×C₈₉	1	4	yes	complemented
510	#3485	C₂×C₈₉	1	2	yes	complemented
511	#3461	C₂×C₈₉	1	2	yes	complemented
512	#3459	C₂×C₈₉	1	4	yes	complemented
513	#3455	C₂×C₈₉	1	2	yes	complemented
514	C₂×#539	C₂×C₈₉	1	4	yes	complemented
515	C₄×H(5,𝔽₂)	C₂×C₈₉	1	2	yes	complemented
516	C₂×#520	C₂×C₈₉	1	1	yes	characteristic, complemented
517	C₈₉	#62847	1	1	yes	characteristic, direct product factor, Sylow
518	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	2	yes	—
519	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
520	#559	C₂²×C₈₉	1	4	yes	complemented
521	#557	C₂²×C₈₉	1	4	yes	complemented
522	#556	C₂²×C₈₉	1	8	yes	complemented
523	#556	C₂²×C₈₉	1	4	yes	complemented
524	#554	C₂²×C₈₉	1	8	yes	complemented
525	#554	C₂²×C₈₉	1	8	yes	complemented
526	#554	C₂²×C₈₉	1	4	yes	complemented
527	#554	C₂²×C₈₉	1	4	yes	complemented
528	#553	C₂²×C₈₉	1	8	yes	complemented
529	#553	C₂²×C₈₉	1	16	yes	complemented
530	#553	C₂²×C₈₉	1	8	yes	complemented
531	#552	C₂²×C₈₉	1	16	yes	complemented
532	#552	C₂²×C₈₉	1	16	yes	complemented
533	#552	C₂²×C₈₉	1	8	yes	complemented
534	#552	C₂²×C₈₉	1	8	yes	complemented
535	#552	C₂²×C₈₉	1	8	yes	complemented
536	#551	C₂²×C₈₉	1	16	yes	complemented
537	#551	C₂²×C₈₉	1	16	yes	complemented
538	#551	C₂²×C₈₉	1	16	yes	complemented
539	D₄×Q₈	C₂²×C₈₉	1	4	yes	complemented
540	#548	C₂²×C₈₉	1	8	yes	complemented
541	#547	C₂²×C₈₉	1	8	yes	complemented
542	#547	C₂²×C₈₉	1	8	yes	complemented
543	#547	C₂²×C₈₉	1	8	yes	complemented
544	#547	C₂²×C₈₉	1	4	yes	complemented
545	#546	C₂²×C₈₉	1	8	yes	complemented
546	#546	C₂²×C₈₉	1	8	yes	complemented
547	#546	C₂²×C₈₉	1	8	yes	complemented
548	#546	C₂²×C₈₉	1	8	yes	complemented
549	D₄²	C₂²×C₈₉	1	4	yes	complemented
550	#544	C₂²×C₈₉	1	2	yes	complemented
551	#543	C₂²×C₈₉	1	4	yes	complemented
552	#542	C₂²×C₈₉	1	4	yes	complemented
553	#542	C₂²×C₈₉	1	4	yes	complemented
554	#542	C₂²×C₈₉	1	8	yes	complemented
555	#541	C₂²×C₈₉	1	4	yes	complemented
556	#541	C₂²×C₈₉	1	8	yes	complemented
557	#540	C₂²×C₈₉	1	4	yes	complemented
558	#539	C₂²×C₈₉	1	4	yes	complemented
559	#539	C₂²×C₈₉	1	8	yes	complemented
560	#539	C₂²×C₈₉	1	8	yes	complemented
561	#539	C₂²×C₈₉	1	8	yes	complemented
562	#539	C₂²×C₈₉	1	16	yes	complemented
563	#539	C₂²×C₈₉	1	16	yes	complemented
564	#539	C₂²×C₈₉	1	4	yes	complemented
565	#539	C₂²×C₈₉	1	16	yes	complemented
566	#538	C₂²×C₈₉	1	4	yes	complemented
567	#538	C₂²×C₈₉	1	4	yes	complemented
568	#538	C₂²×C₈₉	1	16	yes	complemented
569	#537	C₂²×C₈₉	1	2	yes	—
570	#536	C₂²×C₈₉	1	4	yes	complemented
571	#534	C₂²×C₈₉	1	4	yes	—
572	#534	C₂²×C₈₉	1	8	yes	complemented
573	#533	C₂²×C₈₉	1	2	yes	complemented
574	#533	C₂²×C₈₉	1	8	yes	complemented
575	#532	C₂²×C₈₉	1	2	yes	—
576	#529	C₂²×C₈₉	1	8	yes	complemented
577	#529	C₂²×C₈₉	1	8	yes	complemented
578	#529	C₂²×C₈₉	1	8	yes	complemented
579	#529	C₂²×C₈₉	1	16	yes	complemented
580	#529	C₂²×C₈₉	1	8	yes	complemented
581	#529	C₂²×C₈₉	1	8	yes	complemented
582	C₂×#126	C₂²×C₈₉	1	8	yes	complemented
583	C₂×#125	C₂²×C₈₉	1	8	yes	complemented
584	#525	C₂²×C₈₉	1	4	yes	complemented
585	#525	C₂²×C₈₉	1	8	yes	complemented
586	#525	C₂²×C₈₉	1	16	yes	complemented
587	C₂×#123	C₂²×C₈₉	1	8	yes	complemented
588	C₂×#123	C₂²×C₈₉	1	8	yes	complemented
589	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
590	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	8	yes	complemented
591	C₂×#121	C₂²×C₈₉	1	4	yes	—
592	#520	C₂²×C₈₉	1	8	yes	complemented
593	#520	C₂²×C₈₉	1	8	yes	complemented
594	#520	C₂²×C₈₉	1	4	yes	complemented
595	#520	C₂²×C₈₉	1	8	yes	complemented
596	#518	C₂²×C₈₉	1	2	yes	—
597	#518	C₂²×C₈₉	1	8	yes	complemented
598	#518	C₂²×C₈₉	1	8	yes	complemented
599	C₄×#41	C₂²×C₈₉	1	4	yes	complemented
600	C₄×#41	C₂²×C₈₉	1	8	yes	complemented
601	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
602	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
603	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
604	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
605	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
606	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
607	C₂×C₄×D₄	C₂²×C₈₉	1	8	yes	complemented
608	C₂×C₄×D₄	C₂²×C₈₉	1	8	yes	complemented
609	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic, complemented
610	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
611	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
612	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
613	H(5,𝔽₂)	—	2	16	no	—
614	C₂×#41	—	2	8	no	—
615	C₂×#41	C₂³×C₈₉	1	4	yes	—
616	C₂×#41	C₂³×C₈₉	1	8	yes	—
617	C₂×#41	C₂³×C₈₉	1	8	yes	—
618	C₂×#41	C₂³×C₈₉	1	8	yes	—
619	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
620	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
621	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
622	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
623	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
624	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
625	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
626	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
627	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
628	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
629	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
630	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
631	C₂³×C₄	C₂³×C₈₉	1	8	yes	—
632	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
633	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
634	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
635	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
636	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
637	#127	C₂³×C₈₉	1	2	yes	—
638	#126	C₂³×C₈₉	1	8	yes	—
639	#126	C₂³×C₈₉	1	16	yes	—
640	#126	C₂³×C₈₉	1	16	yes	—
641	#126	C₂³×C₈₉	1	16	yes	—
642	#126	C₂³×C₈₉	1	8	yes	—
643	#126	C₂³×C₈₉	1	16	yes	—
644	#126	C₂³×C₈₉	1	8	yes	—
645	#126	C₂³×C₈₉	1	8	yes	—
646	#126	C₂³×C₈₉	1	16	yes	—
647	#125	C₂³×C₈₉	1	8	yes	—
648	#125	C₂³×C₈₉	1	16	yes	—
649	#125	C₂³×C₈₉	1	16	yes	—
650	#125	C₂³×C₈₉	1	16	yes	—
651	#125	C₂³×C₈₉	1	8	yes	—
652	#125	C₂³×C₈₉	1	8	yes	—
653	#125	C₂³×C₈₉	1	8	yes	—
654	#125	C₂³×C₈₉	1	8	yes	—
655	#125	C₂³×C₈₉	1	4	yes	—
656	#124	C₂³×C₈₉	1	8	yes	—
657	#124	C₂³×C₈₉	1	8	yes	—
658	#124	C₂³×C₈₉	1	8	yes	—
659	#124	C₂³×C₈₉	1	8	yes	—
660	#124	C₂³×C₈₉	1	8	yes	—
661	#124	C₂³×C₈₉	1	4	yes	—
662	#123	C₂³×C₈₉	1	8	yes	—
663	#123	C₂³×C₈₉	1	8	yes	—
664	#123	C₂³×C₈₉	1	16	yes	—
665	#123	C₂³×C₈₉	1	16	yes	—
666	#123	C₂³×C₈₉	1	16	yes	—
667	#123	C₂³×C₈₉	1	16	yes	—
668	#123	C₂³×C₈₉	1	16	yes	—
669	#123	C₂³×C₈₉	1	16	yes	—
670	#123	C₂³×C₈₉	1	8	yes	—
671	#123	C₂³×C₈₉	1	16	yes	—
672	#123	C₂³×C₈₉	1	16	yes	—
673	#123	C₂³×C₈₉	1	16	yes	—
674	#123	C₂³×C₈₉	1	8	yes	—
675	#123	C₂³×C₈₉	1	8	yes	—
676	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
677	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
678	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
679	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
680	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
681	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
682	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
683	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
684	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
685	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
686	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
687	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
688	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
689	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
690	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
691	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
692	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
693	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
694	#121	C₂³×C₈₉	1	4	yes	—
695	#121	C₂³×C₈₉	1	8	yes	—
696	#121	C₂³×C₈₉	1	8	yes	—
697	#121	C₂³×C₈₉	1	8	yes	—
698	#121	C₂³×C₈₉	1	8	yes	—
699	#121	C₂³×C₈₉	1	16	yes	—
700	#121	C₂³×C₈₉	1	8	yes	—
701	#121	C₂³×C₈₉	1	4	yes	—
702	#121	C₂³×C₈₉	1	4	yes	—
703	#121	C₂³×C₈₉	1	4	yes	—
704	#121	C₂³×C₈₉	1	16	yes	—
705	#121	C₂³×C₈₉	1	8	yes	—
706	#121	C₂³×C₈₉	1	8	yes	—
707	#120	C₂³×C₈₉	1	8	yes	—
708	#120	C₂³×C₈₉	1	16	yes	—
709	#120	C₂³×C₈₉	1	16	yes	—
710	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
711	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
712	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
713	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
714	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
715	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
716	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
717	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
718	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
719	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
720	C₄×D₄	C₂³×C₈₉	1	8	yes	—
721	C₄×D₄	C₂³×C₈₉	1	4	yes	—
722	C₄×D₄	C₂³×C₈₉	1	4	yes	—
723	C₄×D₄	C₂³×C₈₉	1	8	yes	—
724	C₄×D₄	C₂³×C₈₉	1	16	yes	—
725	C₄×D₄	C₂³×C₈₉	1	4	yes	—
726	C₄×D₄	C₂³×C₈₉	1	8	yes	—
727	C₄×D₄	C₂³×C₈₉	1	16	yes	—
728	C₄×D₄	C₂³×C₈₉	1	16	yes	—
729	C₄×D₄	C₂³×C₈₉	1	8	yes	—
730	C₄×D₄	C₂³×C₈₉	1	16	yes	—
731	C₄×D₄	C₂³×C₈₉	1	16	yes	—
732	C₄×D₄	C₂³×C₈₉	1	8	yes	—
733	C₄×D₄	C₂³×C₈₉	1	8	yes	—
734	C₄×D₄	C₂³×C₈₉	1	8	yes	—
735	C₄×D₄	C₂³×C₈₉	1	8	yes	—
736	C₄×D₄	C₂³×C₈₉	1	4	yes	—
737	C₄×D₄	C₂³×C₈₉	1	16	yes	—
738	C₄×D₄	C₂³×C₈₉	1	8	yes	—
739	C₄×D₄	C₂³×C₈₉	1	16	yes	—
740	C₄×D₄	C₂³×C₈₉	1	8	yes	—
741	C₄×D₄	C₂³×C₈₉	1	8	yes	—
742	C₄×D₄	C₂³×C₈₉	1	8	yes	—
743	C₄×D₄	C₂³×C₈₉	1	4	yes	—
744	C₄×D₄	C₂³×C₈₉	1	4	yes	—
745	#117	C₂³×C₈₉	1	4	yes	—
746	#117	C₂³×C₈₉	1	4	yes	—
747	#117	C₂³×C₈₉	1	16	yes	—
748	#117	C₂³×C₈₉	1	4	yes	—
749	#117	C₂³×C₈₉	1	8	yes	—
750	#117	C₂³×C₈₉	1	16	yes	—
751	#117	C₂³×C₈₉	1	8	yes	—
752	#117	C₂³×C₈₉	1	16	yes	—
753	#117	C₂³×C₈₉	1	8	yes	—
754	#117	C₂³×C₈₉	1	16	yes	—
755	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
756	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
757	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
758	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
759	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
760	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
761	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
762	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
763	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
764	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
765	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
766	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
767	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
768	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
769	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
770	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
771	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
775	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
776	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
777	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
780	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
781	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
782	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
783	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
784	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
785	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
786	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
787	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
788	C₂⁴	C₂⁴×C₈₉	1	8	yes	—
789	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
790	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
791	#41	—	2	32	no	—
792	#41	—	2	32	no	—
793	#41	—	2	16	no	—
794	#41	—	8	8	no	—
795	C₂×Q₈	—	2	4	no	—
796	C₂×Q₈	—	8	4	no	—
797	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
798	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
799	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
800	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
801	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
802	C₂×D₄	—	2	8	no	—
803	C₂×D₄	—	2	32	no	—
804	C₂×D₄	—	2	32	no	—
805	C₂×D₄	—	8	4	no	—
806	C₂×D₄	#41×C₈₉	1	8	yes	complemented
807	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
808	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
809	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
810	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
811	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
812	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
813	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
814	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
815	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
816	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
817	C₂²×C₄	—	2	8	no	—
818	C₂²×C₄	—	2	4	no	—
819	C₂²×C₄	—	8	2	no	—
820	C₂²×C₄	—	8	8	no	—
821	C₂²×C₄	—	8	2	no	—
822	C₂²×C₄	—	8	2	no	—
823	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
824	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
825	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
826	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
827	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
829	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
832	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
833	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
835	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
836	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
838	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
839	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
840	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
841	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
842	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
843	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
844	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
845	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
846	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
847	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
848	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
849	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
850	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
851	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
852	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
853	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
854	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
855	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
856	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
857	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
858	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
859	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
860	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
861	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
862	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
863	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
864	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
865	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
866	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
867	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
868	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
869	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
870	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
871	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
872	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
873	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
874	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
875	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
876	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
877	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
878	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
879	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
880	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
881	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
882	C₂²⋊C₄	C₂⁴×C₈₉	1	2	yes	—
883	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
884	C₂²⋊C₄	C₂⁴×C₈₉	1	2	yes	—
885	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
886	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
887	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
888	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
889	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
890	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
891	C₄²	C₂⁴×C₈₉	1	4	yes	—
892	C₄²	C₂⁴×C₈₉	1	8	yes	—
893	C₄²	C₂⁴×C₈₉	1	16	yes	—
894	C₄²	C₂⁴×C₈₉	1	8	yes	—
895	C₄²	C₂⁴×C₈₉	1	8	yes	—
896	C₄²	C₂⁴×C₈₉	1	8	yes	—
897	C₄²	C₂⁴×C₈₉	1	8	yes	—
898	C₄²	C₂⁴×C₈₉	1	2	yes	—
899	C₄²	C₂⁴×C₈₉	1	2	yes	—
900	C₂³	—	2	2	no	—
901	C₂³	—	2	16	no	—
902	C₂³	—	4	2	no	—
903	C₂³	—	4	1	no	—
904	C₂³	—	4	2	no	—
905	C₂³	—	4	1	no	—
906	C₂³	—	4	8	no	—
907	C₂³	—	4	8	no	—
908	C₂³	C₂×#41×C₈₉	1	8	yes	—
909	C₂³	C₂⁵×C₈₉	1	8	yes	—
910	C₂³	C₂⁵×C₈₉	1	2	yes	—
911	C₂³	C₂⁵×C₈₉	1	4	yes	—
912	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
913	Q₈	—	2	8	no	—
914	Q₈	—	2	8	no	—
915	Q₈	—	4	4	no	—
916	Q₈	—	4	8	no	—
917	Q₈	—	4	4	no	—
918	D₄	—	2	32	no	—
919	D₄	—	2	16	no	—
920	D₄	—	2	16	no	—
921	D₄	—	2	8	no	—
922	D₄	—	4	4	no	—
923	D₄	—	4	8	no	—
924	D₄	—	4	8	no	—
925	D₄	—	4	4	no	—
926	D₄	—	4	8	no	—
927	D₄	C₂×#41×C₈₉	1	16	yes	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	4	no	—
930	C₂×C₄	—	2	16	no	—
931	C₂×C₄	—	2	16	no	—
932	C₂×C₄	—	2	8	no	—
933	C₂×C₄	—	2	16	no	—
934	C₂×C₄	—	4	1	no	—
935	C₂×C₄	—	4	8	no	—
936	C₂×C₄	—	4	2	no	—
937	C₂×C₄	—	4	8	no	—
938	C₂×C₄	—	4	1	no	—
939	C₂×C₄	—	4	2	no	—
940	C₂×C₄	—	4	4	no	—
941	C₂×C₄	—	4	4	no	—
942	C₂×C₄	—	4	8	no	—
943	C₂×C₄	—	4	8	no	—
944	C₂×C₄	—	4	16	no	—
945	C₂×C₄	—	4	1	no	—
946	C₂×C₄	—	4	8	no	—
947	C₂×C₄	—	4	8	no	—
948	C₂×C₄	—	4	1	no	—
949	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
950	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
951	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
952	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
953	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
954	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
955	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
956	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
957	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
958	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
959	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
960	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
961	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
962	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
963	C₂²	—	2	1	no	—
964	C₂²	—	2	4	no	—
965	C₂²	—	2	1	no	—
966	C₂²	—	2	4	no	—
967	C₂²	—	2	2	no	—
968	C₂²	—	2	8	no	—
969	C₂²	—	2	2	no	—
970	C₂²	—	2	8	no	—
971	C₂²	—	2	8	no	—
972	C₂²	—	2	2	no	—
973	C₂²	—	4	8	no	—
974	C₂²	—	4	4	no	—
975	C₂²	—	8	16	no	—
976	C₂²	C₂²×#41×C₈₉	1	8	yes	—
977	C₂²	C₂²×#41×C₈₉	1	2	yes	—
978	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
979	C₄	—	2	2	no	—
980	C₄	—	2	8	no	—
981	C₄	—	2	4	no	—
982	C₄	—	2	2	no	—
983	C₄	—	2	4	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	4	no	—
986	C₄	—	2	8	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	2	no	—
989	C₄	—	2	8	no	—
990	C₄	—	2	2	no	—
991	C₄	C₂²×#41×C₈₉	1	4	yes	—
992	C₂	—	2	2	no	—
993	C₂	—	2	8	no	—
994	C₂	—	4	2	no	—
995	C₂	—	4	8	no	—
996	C₂	C₂³×#41×C₈₉	1	1	yes	characteristic
997	C₂	C₈₉×H(7,𝔽₂)	1	1	yes	characteristic
998	C₂	C₈₉×2₋¹⁺⁶	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₈₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3521	C₂	semidirect
2. C₈₉×#3520	C₂	semidirect
3. C₈₉×#3515	C₂	semidirect
4. C₈₉×#3513	C₂	semidirect
5. C₈₉×#3507	C₂	semidirect
6. C₈₉×#3505	C₂	semidirect
7. C₈₉×#3501	C₂	semidirect
8. C₈₉×#3496	C₂	semidirect
9. C₈₉×#3492	C₂	semidirect
10. C₈₉×#3491	C₂	semidirect
11. C₈₉×#3485	C₂	semidirect
12. C₈₉×#3461	C₂	semidirect
13. C₈₉×#3459	C₂	semidirect
14. C₈₉×#3455	C₂	semidirect
15. C₂×#539×C₈₉	C₂	semidirect
16. C₄×H(5,𝔽₂)×C₈₉	C₂	semidirect
17. C₂×#520×C₈₉	C₂	semidirect
20. #559×C₈₉	C₂²	semidirect
21. #557×C₈₉	C₂²	semidirect
22. #556×C₈₉	C₂²	semidirect
23. #556×C₈₉	C₂²	semidirect
24. #554×C₈₉	C₂²	semidirect
25. #554×C₈₉	C₂²	semidirect
26. #554×C₈₉	C₂²	semidirect
27. #554×C₈₉	C₂²	semidirect
28. #553×C₈₉	C₂²	semidirect
29. #553×C₈₉	C₂²	semidirect
30. #553×C₈₉	C₂²	semidirect
31. #552×C₈₉	C₂²	semidirect
32. #552×C₈₉	C₂²	semidirect
33. #552×C₈₉	C₂²	semidirect
34. #552×C₈₉	C₂²	semidirect
35. #552×C₈₉	C₂²	semidirect
36. #551×C₈₉	C₂²	semidirect
37. #551×C₈₉	C₂²	semidirect
38. #551×C₈₉	C₂²	semidirect
39. D₄×Q₈×C₈₉	C₂²	semidirect
40. #548×C₈₉	C₂²	semidirect
41. #547×C₈₉	C₂²	semidirect
42. #547×C₈₉	C₂²	semidirect
43. #547×C₈₉	C₂²	semidirect
44. #547×C₈₉	C₂²	semidirect
45. #546×C₈₉	C₂²	semidirect
46. #546×C₈₉	C₂²	semidirect
47. #546×C₈₉	C₂²	semidirect
48. #546×C₈₉	C₂²	semidirect
49. D₄²×C₈₉	C₂²	semidirect
50. #544×C₈₉	C₂²	semidirect
51. #543×C₈₉	C₂²	semidirect
52. #542×C₈₉	C₂²	semidirect
53. #542×C₈₉	C₂²	semidirect
54. #542×C₈₉	C₂²	semidirect
55. #541×C₈₉	C₂²	semidirect
56. #541×C₈₉	C₂²	semidirect
57. #540×C₈₉	C₂²	semidirect
58. #539×C₈₉	C₂²	semidirect
59. #539×C₈₉	C₂²	semidirect
60. #539×C₈₉	C₂²	semidirect
61. #539×C₈₉	C₂²	semidirect
62. #539×C₈₉	C₂²	semidirect
63. #539×C₈₉	C₂²	semidirect
64. #539×C₈₉	C₂²	semidirect
65. #539×C₈₉	C₂²	semidirect
66. #538×C₈₉	C₂²	semidirect
67. #538×C₈₉	C₂²	semidirect
68. #538×C₈₉	C₂²	semidirect
70. #536×C₈₉	C₂²	semidirect
72. #534×C₈₉	C₂²	semidirect
73. #533×C₈₉	C₂²	semidirect
74. #533×C₈₉	C₂²	semidirect
76. #529×C₈₉	C₂²	semidirect
77. #529×C₈₉	C₂²	semidirect
78. #529×C₈₉	C₂²	semidirect
79. #529×C₈₉	C₂²	semidirect
80. #529×C₈₉	C₂²	semidirect
81. #529×C₈₉	C₂²	semidirect
82. C₂×#126×C₈₉	C₂²	semidirect
83. C₂×#125×C₈₉	C₂²	semidirect
84. #525×C₈₉	C₂²	semidirect
85. #525×C₈₉	C₂²	semidirect
86. #525×C₈₉	C₂²	semidirect
87. C₂×#123×C₈₉	C₂²	semidirect
88. C₂×#123×C₈₉	C₂²	semidirect
89. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
90. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
92. #520×C₈₉	C₂²	semidirect
93. #520×C₈₉	C₂²	semidirect
94. #520×C₈₉	C₂²	semidirect
95. #520×C₈₉	C₂²	semidirect
97. #518×C₈₉	C₂²	semidirect
98. #518×C₈₉	C₂²	semidirect
99. C₄×#41×C₈₉	C₂²	semidirect
100. C₄×#41×C₈₉	C₂²	semidirect
101. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
102. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
105. C₂×C₄×D₄×C₈₉	C₂²	semidirect
106. C₂×C₄×D₄×C₈₉	C₂²	semidirect
107. C₂×C₄×D₄×C₈₉	C₂²	semidirect
108. C₂×C₄×D₄×C₈₉	C₂²	semidirect
109. C₂×#117×C₈₉	C₂²	semidirect
110. C₂×#117×C₈₉	C₂²	semidirect
111. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
112. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
306. C₂×D₄×C₈₉	#41	semidirect
492. #62847	C₈₉	direct (N × H)
500. #3521	C₂×C₈₉	semidirect
501. #3520	C₂×C₈₉	semidirect
502. #3515	C₂×C₈₉	semidirect
503. #3513	C₂×C₈₉	semidirect
504. #3507	C₂×C₈₉	semidirect
505. #3505	C₂×C₈₉	semidirect
506. #3501	C₂×C₈₉	semidirect
507. #3496	C₂×C₈₉	semidirect
508. #3492	C₂×C₈₉	semidirect
509. #3491	C₂×C₈₉	semidirect
510. #3485	C₂×C₈₉	semidirect
511. #3461	C₂×C₈₉	semidirect
512. #3459	C₂×C₈₉	semidirect
513. #3455	C₂×C₈₉	semidirect
514. C₂×#539	C₂×C₈₉	semidirect
515. C₄×H(5,𝔽₂)	C₂×C₈₉	semidirect
516. C₂×#520	C₂×C₈₉	semidirect
517. C₈₉	#62847	direct (N × H)
520. #559	C₂²×C₈₉	semidirect
521. #557	C₂²×C₈₉	semidirect
522. #556	C₂²×C₈₉	semidirect
523. #556	C₂²×C₈₉	semidirect
524. #554	C₂²×C₈₉	semidirect
525. #554	C₂²×C₈₉	semidirect
526. #554	C₂²×C₈₉	semidirect
527. #554	C₂²×C₈₉	semidirect
528. #553	C₂²×C₈₉	semidirect
529. #553	C₂²×C₈₉	semidirect
530. #553	C₂²×C₈₉	semidirect
531. #552	C₂²×C₈₉	semidirect
532. #552	C₂²×C₈₉	semidirect
533. #552	C₂²×C₈₉	semidirect
534. #552	C₂²×C₈₉	semidirect
535. #552	C₂²×C₈₉	semidirect
536. #551	C₂²×C₈₉	semidirect
537. #551	C₂²×C₈₉	semidirect
538. #551	C₂²×C₈₉	semidirect
539. D₄×Q₈	C₂²×C₈₉	semidirect
540. #548	C₂²×C₈₉	semidirect
541. #547	C₂²×C₈₉	semidirect
542. #547	C₂²×C₈₉	semidirect
543. #547	C₂²×C₈₉	semidirect
544. #547	C₂²×C₈₉	semidirect
545. #546	C₂²×C₈₉	semidirect
546. #546	C₂²×C₈₉	semidirect
547. #546	C₂²×C₈₉	semidirect
548. #546	C₂²×C₈₉	semidirect
549. D₄²	C₂²×C₈₉	semidirect
550. #544	C₂²×C₈₉	semidirect
551. #543	C₂²×C₈₉	semidirect
552. #542	C₂²×C₈₉	semidirect
553. #542	C₂²×C₈₉	semidirect
554. #542	C₂²×C₈₉	semidirect
555. #541	C₂²×C₈₉	semidirect
556. #541	C₂²×C₈₉	semidirect
557. #540	C₂²×C₈₉	semidirect
558. #539	C₂²×C₈₉	semidirect
559. #539	C₂²×C₈₉	semidirect
560. #539	C₂²×C₈₉	semidirect
561. #539	C₂²×C₈₉	semidirect
562. #539	C₂²×C₈₉	semidirect
563. #539	C₂²×C₈₉	semidirect
564. #539	C₂²×C₈₉	semidirect
565. #539	C₂²×C₈₉	semidirect
566. #538	C₂²×C₈₉	semidirect
567. #538	C₂²×C₈₉	semidirect
568. #538	C₂²×C₈₉	semidirect
570. #536	C₂²×C₈₉	semidirect
572. #534	C₂²×C₈₉	semidirect
573. #533	C₂²×C₈₉	semidirect
574. #533	C₂²×C₈₉	semidirect
576. #529	C₂²×C₈₉	semidirect
577. #529	C₂²×C₈₉	semidirect
578. #529	C₂²×C₈₉	semidirect
579. #529	C₂²×C₈₉	semidirect
580. #529	C₂²×C₈₉	semidirect
581. #529	C₂²×C₈₉	semidirect
582. C₂×#126	C₂²×C₈₉	semidirect
583. C₂×#125	C₂²×C₈₉	semidirect
584. #525	C₂²×C₈₉	semidirect
585. #525	C₂²×C₈₉	semidirect
586. #525	C₂²×C₈₉	semidirect
587. C₂×#123	C₂²×C₈₉	semidirect
588. C₂×#123	C₂²×C₈₉	semidirect
589. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
590. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
592. #520	C₂²×C₈₉	semidirect
593. #520	C₂²×C₈₉	semidirect
594. #520	C₂²×C₈₉	semidirect
595. #520	C₂²×C₈₉	semidirect
597. #518	C₂²×C₈₉	semidirect
598. #518	C₂²×C₈₉	semidirect
599. C₄×#41	C₂²×C₈₉	semidirect
600. C₄×#41	C₂²×C₈₉	semidirect
601. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
602. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
605. C₂×C₄×D₄	C₂²×C₈₉	semidirect
606. C₂×C₄×D₄	C₂²×C₈₉	semidirect
607. C₂×C₄×D₄	C₂²×C₈₉	semidirect
608. C₂×C₄×D₄	C₂²×C₈₉	semidirect
609. C₂×#117	C₂²×C₈₉	semidirect
610. C₂×#117	C₂²×C₈₉	semidirect
611. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
612. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
806. C₂×D₄	#41×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3521	2
C₈₉×#3520	2
C₈₉×#3515	2
C₈₉×#3513	2
C₈₉×#3507	2
C₈₉×#3505	2
C₈₉×#3501	2
C₈₉×#3496	2
C₈₉×#3492	2
C₈₉×#3491	2
C₈₉×#3485	2
C₈₉×#3461	2
C₈₉×#3459	2
C₈₉×#3455	2
C₂×#539×C₈₉	2
C₄×H(5,𝔽₂)×C₈₉	2
C₂×#520×C₈₉	2
#62847	89

Subgroups — C89×#62847 #36440695

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62847 #36440695