Subgroups — C₈₉×#62874 #36440722

Order 22784.

7422 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3551	C₂	1	4	yes	maximal, complemented
2	C₈₉×#3549	C₂	1	4	yes	maximal, complemented
3	C₈₉×#3546	C₂	1	8	yes	maximal, complemented
4	C₈₉×#3545	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3543	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3542	C₂	1	8	yes	maximal, complemented
7	C₈₉×#3540	C₂	1	4	yes	maximal, complemented
8	C₈₉×#3537	C₂	1	4	yes	maximal, complemented
9	C₈₉×#3532	C₂	1	8	yes	maximal, complemented
10	C₈₉×#3494	C₂	1	4	yes	maximal, complemented
11	C₈₉×#3493	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3488	C₂	1	4	yes	maximal, complemented
13	C₈₉×#3484	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3449	C₂	1	2	yes	maximal, complemented
15	C₂×#535×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	2	yes	complemented
17	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
18	C₂²×#41×C₈₉	C₂²	1	2	yes	complemented
19	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
20	#563×C₈₉	C₂²	1	4	yes	complemented
21	#562×C₈₉	C₂²	1	8	yes	complemented
22	H(3,𝔽₄)×C₈₉	C₂²	1	8	yes	complemented
23	H(3,𝔽₄)×C₈₉	C₂²	1	4	yes	complemented
24	#560×C₈₉	C₂²	1	16	yes	complemented
25	#560×C₈₉	C₂²	1	8	yes	complemented
26	#560×C₈₉	C₂²	1	8	yes	complemented
27	#560×C₈₉	C₂²	1	8	yes	complemented
28	#559×C₈₉	C₂²	1	4	yes	complemented
29	#556×C₈₉	C₂²	1	8	yes	complemented
30	#555×C₈₉	C₂²	1	8	yes	complemented
31	#555×C₈₉	C₂²	1	8	yes	complemented
32	#555×C₈₉	C₂²	1	8	yes	complemented
33	#553×C₈₉	C₂²	1	8	yes	complemented
34	#553×C₈₉	C₂²	1	8	yes	complemented
35	#553×C₈₉	C₂²	1	8	yes	complemented
36	#552×C₈₉	C₂²	1	8	yes	complemented
37	#551×C₈₉	C₂²	1	16	yes	complemented
38	#551×C₈₉	C₂²	1	8	yes	complemented
39	#551×C₈₉	C₂²	1	8	yes	complemented
40	#550×C₈₉	C₂²	1	8	yes	complemented
41	#550×C₈₉	C₂²	1	8	yes	complemented
42	#548×C₈₉	C₂²	1	8	yes	complemented
43	#547×C₈₉	C₂²	1	8	yes	complemented
44	#546×C₈₉	C₂²	1	8	yes	complemented
45	#546×C₈₉	C₂²	1	8	yes	complemented
46	#546×C₈₉	C₂²	1	16	yes	complemented
47	#546×C₈₉	C₂²	1	16	yes	complemented
48	#546×C₈₉	C₂²	1	16	yes	complemented
49	#546×C₈₉	C₂²	1	8	yes	complemented
50	D₄²×C₈₉	C₂²	1	8	yes	complemented
51	D₄²×C₈₉	C₂²	1	8	yes	complemented
52	D₄²×C₈₉	C₂²	1	16	yes	complemented
53	D₄²×C₈₉	C₂²	1	8	yes	complemented
54	D₄²×C₈₉	C₂²	1	4	yes	complemented
55	D₄²×C₈₉	C₂²	1	8	yes	complemented
56	#544×C₈₉	C₂²	1	2	yes	complemented
57	#542×C₈₉	C₂²	1	8	yes	complemented
58	#542×C₈₉	C₂²	1	16	yes	complemented
59	#540×C₈₉	C₂²	1	8	yes	complemented
60	#540×C₈₉	C₂²	1	16	yes	complemented
61	#538×C₈₉	C₂²	1	8	yes	complemented
62	#538×C₈₉	C₂²	1	16	yes	complemented
63	#538×C₈₉	C₂²	1	16	yes	complemented
64	#538×C₈₉	C₂²	1	16	yes	complemented
65	#537×C₈₉	C₂²	1	2	yes	complemented
66	#537×C₈₉	C₂²	1	4	yes	complemented
67	#537×C₈₉	C₂²	1	4	yes	complemented
68	#537×C₈₉	C₂²	1	8	yes	complemented
69	#536×C₈₉	C₂²	1	4	yes	complemented
70	#536×C₈₉	C₂²	1	2	yes	complemented
71	#536×C₈₉	C₂²	1	2	yes	complemented
72	#535×C₈₉	C₂²	1	4	yes	complemented
73	#535×C₈₉	C₂²	1	4	yes	complemented
74	#535×C₈₉	C₂²	1	4	yes	complemented
75	#535×C₈₉	C₂²	1	4	yes	complemented
76	#535×C₈₉	C₂²	1	4	yes	complemented
77	#535×C₈₉	C₂²	1	4	yes	complemented
78	#535×C₈₉	C₂²	1	16	yes	complemented
79	#535×C₈₉	C₂²	1	2	yes	complemented
80	#535×C₈₉	C₂²	1	2	yes	complemented
81	#535×C₈₉	C₂²	1	16	yes	complemented
82	#535×C₈₉	C₂²	1	8	yes	complemented
83	#534×C₈₉	C₂²	1	4	yes	complemented
84	#534×C₈₉	C₂²	1	8	yes	complemented
85	#534×C₈₉	C₂²	1	4	yes	complemented
86	#534×C₈₉	C₂²	1	16	yes	complemented
87	#532×C₈₉	C₂²	1	4	yes	complemented
88	#532×C₈₉	C₂²	1	4	yes	complemented
89	#532×C₈₉	C₂²	1	8	yes	complemented
90	C₂×#127×C₈₉	C₂²	1	2	yes	complemented
91	#529×C₈₉	C₂²	1	8	yes	complemented
92	#529×C₈₉	C₂²	1	8	yes	complemented
93	C₂×#124×C₈₉	C₂²	1	2	yes	complemented
94	#525×C₈₉	C₂²	1	4	yes	complemented
95	#525×C₈₉	C₂²	1	4	yes	complemented
96	#525×C₈₉	C₂²	1	4	yes	complemented
97	#525×C₈₉	C₂²	1	4	yes	complemented
98	#525×C₈₉	C₂²	1	8	yes	complemented
99	C₂×#121×C₈₉	C₂²	1	4	yes	complemented
100	C₂×#121×C₈₉	C₂²	1	8	yes	complemented
101	C₂×#120×C₈₉	C₂²	1	4	yes	complemented
102	C₂×#120×C₈₉	C₂²	1	8	yes	complemented
103	#520×C₈₉	C₂²	1	4	yes	complemented
104	#518×C₈₉	C₂²	1	2	yes	complemented
105	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
106	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
107	C₂⁵×C₈₉	C₂³	1	2	yes	—
108	H(5,𝔽₂)×C₈₉	—	4	8	no	—
109	C₂×#41×C₈₉	—	4	4	no	—
110	C₂×#41×C₈₉	—	4	8	no	—
111	C₂×#41×C₈₉	C₂³	1	4	yes	—
112	C₂×#41×C₈₉	C₂³	1	2	yes	—
113	C₂×#41×C₈₉	C₂³	1	2	yes	—
114	C₂×#41×C₈₉	C₂³	1	8	yes	—
115	C₂×#41×C₈₉	C₂³	1	2	yes	—
116	C₂×#41×C₈₉	C₂³	1	2	yes	—
117	C₂×#41×C₈₉	C₂³	1	4	yes	—
118	C₂×#41×C₈₉	C₂³	1	4	yes	complemented
119	C₂×#41×C₈₉	C₂³	1	4	yes	complemented
120	C₂×#41×C₈₉	C₂³	1	16	yes	complemented
121	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
122	C₂²×Q₈×C₈₉	C₂³	1	2	yes	complemented
123	C₂²×D₄×C₈₉	—	4	4	no	—
124	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
125	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
126	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
127	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
128	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
129	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
131	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
132	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
133	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
134	C₂²×D₄×C₈₉	C₂³	1	16	yes	—
135	C₂²×D₄×C₈₉	C₂³	1	2	yes	complemented
136	C₂²×D₄×C₈₉	C₂³	1	16	yes	complemented
137	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
138	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₈₉	C₂³	1	4	yes	complemented
140	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	complemented
141	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	complemented
142	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	complemented
143	#127×C₈₉	C₂³	1	8	yes	—
144	#127×C₈₉	C₂³	1	4	yes	—
145	#127×C₈₉	C₂³	1	4	yes	—
146	#127×C₈₉	C₂³	1	4	yes	—
147	#127×C₈₉	C₂³	1	4	yes	—
148	#127×C₈₉	C₂³	1	8	yes	—
149	#127×C₈₉	C₂³	1	16	yes	complemented
150	#126×C₈₉	C₂³	1	16	yes	—
151	#126×C₈₉	C₂³	1	16	yes	complemented
152	#126×C₈₉	C₂³	1	16	yes	complemented
153	#126×C₈₉	C₂³	1	16	yes	complemented
154	#125×C₈₉	C₂³	1	8	yes	complemented
155	#125×C₈₉	C₂³	1	8	yes	complemented
156	#124×C₈₉	C₂³	1	8	yes	—
157	#124×C₈₉	C₂³	1	4	yes	—
158	#124×C₈₉	C₂³	1	4	yes	—
159	#124×C₈₉	C₂³	1	8	yes	—
160	#124×C₈₉	C₂³	1	4	yes	—
161	#124×C₈₉	C₂³	1	4	yes	—
162	#124×C₈₉	C₂³	1	16	yes	—
163	#124×C₈₉	C₂³	1	8	yes	complemented
164	#124×C₈₉	C₂³	1	4	yes	complemented
165	#124×C₈₉	C₂³	1	4	yes	complemented
166	#124×C₈₉	C₂³	1	16	yes	complemented
167	#124×C₈₉	C₂³	1	16	yes	complemented
168	#124×C₈₉	C₂³	1	16	yes	complemented
169	#123×C₈₉	C₂³	1	8	yes	—
170	#123×C₈₉	C₂³	1	4	yes	—
171	#123×C₈₉	C₂³	1	8	yes	—
172	#123×C₈₉	C₂³	1	4	yes	—
173	#123×C₈₉	C₂³	1	16	yes	—
174	#123×C₈₉	C₂³	1	8	yes	—
175	#123×C₈₉	C₂³	1	8	yes	—
176	#123×C₈₉	C₂³	1	4	yes	complemented
177	#123×C₈₉	C₂³	1	4	yes	complemented
178	#123×C₈₉	C₂³	1	16	yes	complemented
179	#123×C₈₉	C₂³	1	16	yes	complemented
180	#123×C₈₉	C₂³	1	16	yes	complemented
181	#123×C₈₉	C₂³	1	16	yes	complemented
182	#123×C₈₉	C₂³	1	16	yes	complemented
183	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
184	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
185	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
186	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	complemented
187	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	complemented
188	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	complemented
189	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	complemented
190	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	complemented
191	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	complemented
192	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	complemented
193	#121×C₈₉	C₂³	1	8	yes	—
194	#121×C₈₉	C₂³	1	8	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	8	yes	—
200	#121×C₈₉	C₂³	1	4	yes	—
201	#121×C₈₉	C₂³	1	4	yes	—
202	#121×C₈₉	C₂³	1	8	yes	—
203	#121×C₈₉	C₂³	1	8	yes	—
204	#121×C₈₉	C₂³	1	8	yes	—
205	#121×C₈₉	C₂³	1	8	yes	—
206	#121×C₈₉	C₂³	1	16	yes	—
207	#121×C₈₉	C₂³	1	16	yes	—
208	#121×C₈₉	C₂³	1	16	yes	—
209	#121×C₈₉	C₂³	1	4	yes	complemented
210	#121×C₈₉	C₂³	1	16	yes	complemented
211	#121×C₈₉	C₂³	1	8	yes	complemented
212	#121×C₈₉	C₂³	1	16	yes	complemented
213	#121×C₈₉	C₂³	1	4	yes	complemented
214	#121×C₈₉	C₂³	1	8	yes	complemented
215	#121×C₈₉	C₂³	1	8	yes	complemented
216	#121×C₈₉	C₂³	1	16	yes	complemented
217	#121×C₈₉	C₂³	1	16	yes	complemented
218	#121×C₈₉	C₂³	1	16	yes	complemented
219	#121×C₈₉	C₂³	1	16	yes	complemented
220	#121×C₈₉	C₂³	1	16	yes	complemented
221	#121×C₈₉	C₂³	1	16	yes	complemented
222	#120×C₈₉	C₂³	1	8	yes	—
223	#120×C₈₉	C₂³	1	8	yes	—
224	#120×C₈₉	C₂³	1	16	yes	—
225	#120×C₈₉	C₂³	1	16	yes	—
226	#120×C₈₉	C₂³	1	8	yes	—
227	#120×C₈₉	C₂³	1	8	yes	—
228	#120×C₈₉	C₂³	1	8	yes	—
229	#120×C₈₉	C₂³	1	16	yes	—
230	#120×C₈₉	C₂³	1	4	yes	—
231	#120×C₈₉	C₂³	1	8	yes	—
232	#120×C₈₉	C₂³	1	4	yes	—
233	#120×C₈₉	C₂³	1	8	yes	—
234	#120×C₈₉	C₂³	1	8	yes	—
235	#120×C₈₉	C₂³	1	4	yes	complemented
236	#120×C₈₉	C₂³	1	4	yes	complemented
237	#120×C₈₉	C₂³	1	16	yes	complemented
238	#120×C₈₉	C₂³	1	16	yes	complemented
239	#120×C₈₉	C₂³	1	16	yes	complemented
240	C₄×Q₈×C₈₉	C₂³	1	8	yes	complemented
241	C₄×Q₈×C₈₉	C₂³	1	8	yes	complemented
242	C₄×D₄×C₈₉	C₂³	1	8	yes	—
243	C₄×D₄×C₈₉	C₂³	1	8	yes	—
244	C₄×D₄×C₈₉	C₂³	1	16	yes	—
245	C₄×D₄×C₈₉	C₂³	1	8	yes	—
246	C₄×D₄×C₈₉	C₂³	1	8	yes	—
247	C₄×D₄×C₈₉	C₂³	1	8	yes	complemented
248	C₄×D₄×C₈₉	C₂³	1	8	yes	complemented
249	C₄×D₄×C₈₉	C₂³	1	8	yes	complemented
250	C₄×D₄×C₈₉	C₂³	1	16	yes	complemented
251	C₄×D₄×C₈₉	C₂³	1	16	yes	complemented
252	C₄×D₄×C₈₉	C₂³	1	8	yes	complemented
253	C₄×D₄×C₈₉	C₂³	1	16	yes	complemented
254	C₄×D₄×C₈₉	C₂³	1	16	yes	complemented
255	#117×C₈₉	C₂³	1	4	yes	—
256	#117×C₈₉	C₂³	1	4	yes	—
257	#117×C₈₉	C₂³	1	4	yes	—
258	#117×C₈₉	C₂³	1	4	yes	—
259	#117×C₈₉	C₂³	1	4	yes	complemented
260	#117×C₈₉	C₂³	1	2	yes	complemented
261	#117×C₈₉	C₂³	1	2	yes	complemented
262	#117×C₈₉	C₂³	1	8	yes	complemented
263	#117×C₈₉	C₂³	1	16	yes	complemented
264	#117×C₈₉	C₂³	1	16	yes	complemented
265	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	complemented
267	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	complemented
268	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
269	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
270	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
271	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
272	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
273	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	complemented
274	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
275	C₂×C₄²×C₈₉	C₂³	1	4	yes	complemented
276	C₂⁴×C₈₉	—	4	4	no	—
277	C₂⁴×C₈₉	—	8	4	no	—
278	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
279	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
280	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
281	C₂⁴×C₈₉	C₂⁴	1	8	yes	—
282	C₂⁴×C₈₉	C₂⁴	1	8	yes	—
283	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
284	#41×C₈₉	—	2	16	no	—
285	#41×C₈₉	—	4	4	no	—
286	#41×C₈₉	—	4	4	no	—
287	#41×C₈₉	—	4	4	no	—
288	#41×C₈₉	—	4	4	no	—
289	#41×C₈₉	—	4	8	no	—
290	#41×C₈₉	—	4	8	no	—
291	#41×C₈₉	—	4	8	no	—
292	#41×C₈₉	—	4	16	no	—
293	#41×C₈₉	—	8	16	no	—
294	C₂×Q₈×C₈₉	—	4	2	no	—
295	C₂×Q₈×C₈₉	—	4	4	no	—
296	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
297	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
298	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
299	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
300	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
301	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
302	C₂×D₄×C₈₉	—	2	8	no	—
303	C₂×D₄×C₈₉	—	4	8	no	—
304	C₂×D₄×C₈₉	—	4	8	no	—
305	C₂×D₄×C₈₉	—	4	16	no	—
306	C₂×D₄×C₈₉	—	4	4	no	—
307	C₂×D₄×C₈₉	—	4	4	no	—
308	C₂×D₄×C₈₉	—	4	2	no	—
309	C₂×D₄×C₈₉	—	4	4	no	—
310	C₂×D₄×C₈₉	—	4	8	no	—
311	C₂×D₄×C₈₉	—	4	16	no	—
312	C₂×D₄×C₈₉	—	8	8	no	—
313	C₂×D₄×C₈₉	—	8	16	no	—
314	C₂×D₄×C₈₉	—	8	16	no	—
315	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
316	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
317	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
318	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
319	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
320	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
321	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
322	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
323	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
324	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
325	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
326	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
327	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
328	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
329	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
330	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
331	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
332	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
333	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
334	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
335	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
337	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
338	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₈₉	—	2	4	no	—
340	C₂²×C₄×C₈₉	—	2	8	no	—
341	C₂²×C₄×C₈₉	—	4	8	no	—
342	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
346	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
347	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
348	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
350	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
352	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
353	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
354	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
355	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
356	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
357	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
358	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	8	yes	—
367	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
368	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
369	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
370	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
371	C₂²⋊C₄×C₈₉	C₂⁴	1	8	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	16	yes	—
376	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
377	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
378	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
379	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
380	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
381	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
382	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
383	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
384	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
385	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
386	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
387	C₂²⋊C₄×C₈₉	C₂⁴	1	8	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	4	yes	—
393	C₄²×C₈₉	C₂⁴	1	4	yes	—
394	C₄²×C₈₉	C₂⁴	1	8	yes	—
395	C₄²×C₈₉	C₂⁴	1	4	yes	—
396	C₄²×C₈₉	C₂⁴	1	16	yes	—
397	C₂³×C₈₉	—	2	2	no	—
398	C₂³×C₈₉	—	2	4	no	—
399	C₂³×C₈₉	—	2	8	no	—
400	C₂³×C₈₉	—	4	2	no	—
401	C₂³×C₈₉	—	4	4	no	—
402	C₂³×C₈₉	—	4	8	no	—
403	C₂³×C₈₉	—	4	4	no	—
404	C₂³×C₈₉	—	4	8	no	—
405	C₂³×C₈₉	—	4	8	no	—
406	C₂³×C₈₉	—	4	16	no	—
407	C₂³×C₈₉	—	4	8	no	—
408	C₂³×C₈₉	—	4	16	no	—
409	C₂³×C₈₉	—	8	16	no	—
410	C₂³×C₈₉	C₂⁵	1	2	yes	—
411	C₂³×C₈₉	C₂⁵	1	8	yes	—
412	C₂³×C₈₉	C₂⁵	1	2	yes	—
413	C₂³×C₈₉	C₂⁵	1	8	yes	—
414	C₂³×C₈₉	C₂⁵	1	2	yes	—
415	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
416	Q₈×C₈₉	—	2	8	no	—
417	Q₈×C₈₉	—	4	1	no	—
418	Q₈×C₈₉	—	4	2	no	—
419	Q₈×C₈₉	—	4	1	no	—
420	Q₈×C₈₉	—	4	4	no	—
421	Q₈×C₈₉	—	4	8	no	—
422	D₄×C₈₉	—	2	16	no	—
423	D₄×C₈₉	—	2	16	no	—
424	D₄×C₈₉	—	2	8	no	—
425	D₄×C₈₉	—	4	4	no	—
426	D₄×C₈₉	—	4	4	no	—
427	D₄×C₈₉	—	4	16	no	—
428	D₄×C₈₉	—	4	2	no	—
429	D₄×C₈₉	—	4	2	no	—
430	D₄×C₈₉	—	4	1	no	—
431	D₄×C₈₉	—	4	2	no	—
432	D₄×C₈₉	—	4	1	no	—
433	D₄×C₈₉	—	4	2	no	—
434	D₄×C₈₉	—	4	2	no	—
435	D₄×C₈₉	—	4	4	no	—
436	D₄×C₈₉	—	4	8	no	—
437	D₄×C₈₉	—	4	8	no	—
438	D₄×C₈₉	—	4	16	no	—
439	D₄×C₈₉	—	4	8	no	—
440	D₄×C₈₉	—	4	16	no	—
441	D₄×C₈₉	—	4	8	no	—
442	D₄×C₈₉	—	4	8	no	—
443	D₄×C₈₉	—	4	16	no	—
444	D₄×C₈₉	—	4	16	no	—
445	D₄×C₈₉	—	4	8	no	—
446	C₂×C₄×C₈₉	—	2	2	no	—
447	C₂×C₄×C₈₉	—	2	4	no	—
448	C₂×C₄×C₈₉	—	2	4	no	—
449	C₂×C₄×C₈₉	—	2	4	no	—
450	C₂×C₄×C₈₉	—	2	4	no	—
451	C₂×C₄×C₈₉	—	2	4	no	—
452	C₂×C₄×C₈₉	—	2	4	no	—
453	C₂×C₄×C₈₉	—	2	4	no	—
454	C₂×C₄×C₈₉	—	2	16	no	—
455	C₂×C₄×C₈₉	—	4	4	no	—
456	C₂×C₄×C₈₉	—	4	8	no	—
457	C₂×C₄×C₈₉	—	4	8	no	—
458	C₂×C₄×C₈₉	—	4	4	no	—
459	C₂×C₄×C₈₉	—	4	16	no	—
460	C₂×C₄×C₈₉	—	4	16	no	—
461	C₂×C₄×C₈₉	—	4	8	no	—
462	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
463	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
464	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
465	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
466	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
467	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
468	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
469	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
470	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
471	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
472	C₂²×C₈₉	—	2	2	no	—
473	C₂²×C₈₉	—	2	2	no	—
474	C₂²×C₈₉	—	2	2	no	—
475	C₂²×C₈₉	—	2	2	no	—
476	C₂²×C₈₉	—	2	8	no	—
477	C₂²×C₈₉	—	2	8	no	—
478	C₂²×C₈₉	—	2	4	no	—
479	C₂²×C₈₉	—	2	8	no	—
480	C₂²×C₈₉	—	2	16	no	—
481	C₂²×C₈₉	—	2	4	no	—
482	C₂²×C₈₉	—	2	8	no	—
483	C₂²×C₈₉	—	2	4	no	—
484	C₂²×C₈₉	—	4	4	no	—
485	C₂²×C₈₉	—	8	4	no	—
486	C₂²×C₈₉	—	8	8	no	—
487	C₂²×C₈₉	—	8	8	no	—
488	C₂²×C₈₉	—	8	16	no	—
489	C₂²×C₈₉	—	16	8	no	—
490	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
491	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
492	C₄×C₈₉	—	2	2	no	—
493	C₄×C₈₉	—	2	1	no	—
494	C₄×C₈₉	—	2	1	no	—
495	C₄×C₈₉	—	2	2	no	—
496	C₄×C₈₉	—	2	8	no	—
497	C₄×C₈₉	—	2	8	no	—
498	C₄×C₈₉	—	2	8	no	—
499	C₄×C₈₉	—	2	8	no	—
500	C₄×C₈₉	C₂×H(5,𝔽₂)	1	4	yes	—
501	#62874	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
502	C₂×C₈₉	—	2	2	no	—
503	C₂×C₈₉	—	4	2	no	—
504	C₂×C₈₉	—	4	2	no	—
505	C₂×C₈₉	—	4	2	no	—
506	C₂×C₈₉	—	4	8	no	—
507	C₂×C₈₉	—	4	8	no	—
508	C₂×C₈₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
509	C₂×C₈₉	H(7,𝔽₂)	1	2	yes	—
510	#3551	C₂×C₈₉	1	4	yes	complemented
511	#3549	C₂×C₈₉	1	4	yes	complemented
512	#3546	C₂×C₈₉	1	8	yes	complemented
513	#3545	C₂×C₈₉	1	4	yes	complemented
514	#3543	C₂×C₈₉	1	4	yes	complemented
515	#3542	C₂×C₈₉	1	8	yes	complemented
516	#3540	C₂×C₈₉	1	4	yes	complemented
517	#3537	C₂×C₈₉	1	4	yes	complemented
518	#3532	C₂×C₈₉	1	8	yes	complemented
519	#3494	C₂×C₈₉	1	4	yes	complemented
520	#3493	C₂×C₈₉	1	2	yes	complemented
521	#3488	C₂×C₈₉	1	4	yes	complemented
522	#3484	C₂×C₈₉	1	2	yes	complemented
523	#3449	C₂×C₈₉	1	2	yes	complemented
524	C₂×#535	C₂×C₈₉	1	1	yes	characteristic, complemented
525	C₈₉	#62874	1	1	yes	characteristic, direct product factor, Sylow
526	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	2	yes	complemented
527	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic, complemented
528	C₂²×#41	C₂²×C₈₉	1	2	yes	complemented
529	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
530	#563	C₂²×C₈₉	1	4	yes	complemented
531	#562	C₂²×C₈₉	1	8	yes	complemented
532	H(3,𝔽₄)	C₂²×C₈₉	1	8	yes	complemented
533	H(3,𝔽₄)	C₂²×C₈₉	1	4	yes	complemented
534	#560	C₂²×C₈₉	1	16	yes	complemented
535	#560	C₂²×C₈₉	1	8	yes	complemented
536	#560	C₂²×C₈₉	1	8	yes	complemented
537	#560	C₂²×C₈₉	1	8	yes	complemented
538	#559	C₂²×C₈₉	1	4	yes	complemented
539	#556	C₂²×C₈₉	1	8	yes	complemented
540	#555	C₂²×C₈₉	1	8	yes	complemented
541	#555	C₂²×C₈₉	1	8	yes	complemented
542	#555	C₂²×C₈₉	1	8	yes	complemented
543	#553	C₂²×C₈₉	1	8	yes	complemented
544	#553	C₂²×C₈₉	1	8	yes	complemented
545	#553	C₂²×C₈₉	1	8	yes	complemented
546	#552	C₂²×C₈₉	1	8	yes	complemented
547	#551	C₂²×C₈₉	1	16	yes	complemented
548	#551	C₂²×C₈₉	1	8	yes	complemented
549	#551	C₂²×C₈₉	1	8	yes	complemented
550	#550	C₂²×C₈₉	1	8	yes	complemented
551	#550	C₂²×C₈₉	1	8	yes	complemented
552	#548	C₂²×C₈₉	1	8	yes	complemented
553	#547	C₂²×C₈₉	1	8	yes	complemented
554	#546	C₂²×C₈₉	1	8	yes	complemented
555	#546	C₂²×C₈₉	1	8	yes	complemented
556	#546	C₂²×C₈₉	1	16	yes	complemented
557	#546	C₂²×C₈₉	1	16	yes	complemented
558	#546	C₂²×C₈₉	1	16	yes	complemented
559	#546	C₂²×C₈₉	1	8	yes	complemented
560	D₄²	C₂²×C₈₉	1	8	yes	complemented
561	D₄²	C₂²×C₈₉	1	8	yes	complemented
562	D₄²	C₂²×C₈₉	1	16	yes	complemented
563	D₄²	C₂²×C₈₉	1	8	yes	complemented
564	D₄²	C₂²×C₈₉	1	4	yes	complemented
565	D₄²	C₂²×C₈₉	1	8	yes	complemented
566	#544	C₂²×C₈₉	1	2	yes	complemented
567	#542	C₂²×C₈₉	1	8	yes	complemented
568	#542	C₂²×C₈₉	1	16	yes	complemented
569	#540	C₂²×C₈₉	1	8	yes	complemented
570	#540	C₂²×C₈₉	1	16	yes	complemented
571	#538	C₂²×C₈₉	1	8	yes	complemented
572	#538	C₂²×C₈₉	1	16	yes	complemented
573	#538	C₂²×C₈₉	1	16	yes	complemented
574	#538	C₂²×C₈₉	1	16	yes	complemented
575	#537	C₂²×C₈₉	1	2	yes	complemented
576	#537	C₂²×C₈₉	1	4	yes	complemented
577	#537	C₂²×C₈₉	1	4	yes	complemented
578	#537	C₂²×C₈₉	1	8	yes	complemented
579	#536	C₂²×C₈₉	1	4	yes	complemented
580	#536	C₂²×C₈₉	1	2	yes	complemented
581	#536	C₂²×C₈₉	1	2	yes	complemented
582	#535	C₂²×C₈₉	1	4	yes	complemented
583	#535	C₂²×C₈₉	1	4	yes	complemented
584	#535	C₂²×C₈₉	1	4	yes	complemented
585	#535	C₂²×C₈₉	1	4	yes	complemented
586	#535	C₂²×C₈₉	1	4	yes	complemented
587	#535	C₂²×C₈₉	1	4	yes	complemented
588	#535	C₂²×C₈₉	1	16	yes	complemented
589	#535	C₂²×C₈₉	1	2	yes	complemented
590	#535	C₂²×C₈₉	1	2	yes	complemented
591	#535	C₂²×C₈₉	1	16	yes	complemented
592	#535	C₂²×C₈₉	1	8	yes	complemented
593	#534	C₂²×C₈₉	1	4	yes	complemented
594	#534	C₂²×C₈₉	1	8	yes	complemented
595	#534	C₂²×C₈₉	1	4	yes	complemented
596	#534	C₂²×C₈₉	1	16	yes	complemented
597	#532	C₂²×C₈₉	1	4	yes	complemented
598	#532	C₂²×C₈₉	1	4	yes	complemented
599	#532	C₂²×C₈₉	1	8	yes	complemented
600	C₂×#127	C₂²×C₈₉	1	2	yes	complemented
601	#529	C₂²×C₈₉	1	8	yes	complemented
602	#529	C₂²×C₈₉	1	8	yes	complemented
603	C₂×#124	C₂²×C₈₉	1	2	yes	complemented
604	#525	C₂²×C₈₉	1	4	yes	complemented
605	#525	C₂²×C₈₉	1	4	yes	complemented
606	#525	C₂²×C₈₉	1	4	yes	complemented
607	#525	C₂²×C₈₉	1	4	yes	complemented
608	#525	C₂²×C₈₉	1	8	yes	complemented
609	C₂×#121	C₂²×C₈₉	1	4	yes	complemented
610	C₂×#121	C₂²×C₈₉	1	8	yes	complemented
611	C₂×#120	C₂²×C₈₉	1	4	yes	complemented
612	C₂×#120	C₂²×C₈₉	1	8	yes	complemented
613	#520	C₂²×C₈₉	1	4	yes	complemented
614	#518	C₂²×C₈₉	1	2	yes	complemented
615	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic, complemented
616	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
617	C₂⁵	C₂³×C₈₉	1	2	yes	—
618	H(5,𝔽₂)	—	4	8	no	—
619	C₂×#41	—	4	4	no	—
620	C₂×#41	—	4	8	no	—
621	C₂×#41	C₂³×C₈₉	1	4	yes	—
622	C₂×#41	C₂³×C₈₉	1	2	yes	—
623	C₂×#41	C₂³×C₈₉	1	2	yes	—
624	C₂×#41	C₂³×C₈₉	1	8	yes	—
625	C₂×#41	C₂³×C₈₉	1	2	yes	—
626	C₂×#41	C₂³×C₈₉	1	2	yes	—
627	C₂×#41	C₂³×C₈₉	1	4	yes	—
628	C₂×#41	C₂³×C₈₉	1	4	yes	complemented
629	C₂×#41	C₂³×C₈₉	1	4	yes	complemented
630	C₂×#41	C₂³×C₈₉	1	16	yes	complemented
631	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
632	C₂²×Q₈	C₂³×C₈₉	1	2	yes	complemented
633	C₂²×D₄	—	4	4	no	—
634	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
635	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
636	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
637	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
638	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
639	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
640	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
641	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
642	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
643	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
644	C₂²×D₄	C₂³×C₈₉	1	16	yes	—
645	C₂²×D₄	C₂³×C₈₉	1	2	yes	complemented
646	C₂²×D₄	C₂³×C₈₉	1	16	yes	complemented
647	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
648	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
649	C₂³×C₄	C₂³×C₈₉	1	4	yes	complemented
650	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	complemented
651	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	complemented
652	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	complemented
653	#127	C₂³×C₈₉	1	8	yes	—
654	#127	C₂³×C₈₉	1	4	yes	—
655	#127	C₂³×C₈₉	1	4	yes	—
656	#127	C₂³×C₈₉	1	4	yes	—
657	#127	C₂³×C₈₉	1	4	yes	—
658	#127	C₂³×C₈₉	1	8	yes	—
659	#127	C₂³×C₈₉	1	16	yes	complemented
660	#126	C₂³×C₈₉	1	16	yes	—
661	#126	C₂³×C₈₉	1	16	yes	complemented
662	#126	C₂³×C₈₉	1	16	yes	complemented
663	#126	C₂³×C₈₉	1	16	yes	complemented
664	#125	C₂³×C₈₉	1	8	yes	complemented
665	#125	C₂³×C₈₉	1	8	yes	complemented
666	#124	C₂³×C₈₉	1	8	yes	—
667	#124	C₂³×C₈₉	1	4	yes	—
668	#124	C₂³×C₈₉	1	4	yes	—
669	#124	C₂³×C₈₉	1	8	yes	—
670	#124	C₂³×C₈₉	1	4	yes	—
671	#124	C₂³×C₈₉	1	4	yes	—
672	#124	C₂³×C₈₉	1	16	yes	—
673	#124	C₂³×C₈₉	1	8	yes	complemented
674	#124	C₂³×C₈₉	1	4	yes	complemented
675	#124	C₂³×C₈₉	1	4	yes	complemented
676	#124	C₂³×C₈₉	1	16	yes	complemented
677	#124	C₂³×C₈₉	1	16	yes	complemented
678	#124	C₂³×C₈₉	1	16	yes	complemented
679	#123	C₂³×C₈₉	1	8	yes	—
680	#123	C₂³×C₈₉	1	4	yes	—
681	#123	C₂³×C₈₉	1	8	yes	—
682	#123	C₂³×C₈₉	1	4	yes	—
683	#123	C₂³×C₈₉	1	16	yes	—
684	#123	C₂³×C₈₉	1	8	yes	—
685	#123	C₂³×C₈₉	1	8	yes	—
686	#123	C₂³×C₈₉	1	4	yes	complemented
687	#123	C₂³×C₈₉	1	4	yes	complemented
688	#123	C₂³×C₈₉	1	16	yes	complemented
689	#123	C₂³×C₈₉	1	16	yes	complemented
690	#123	C₂³×C₈₉	1	16	yes	complemented
691	#123	C₂³×C₈₉	1	16	yes	complemented
692	#123	C₂³×C₈₉	1	16	yes	complemented
693	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
694	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
695	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
696	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	complemented
697	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	complemented
698	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	complemented
699	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	complemented
700	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	complemented
701	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	complemented
702	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	complemented
703	#121	C₂³×C₈₉	1	8	yes	—
704	#121	C₂³×C₈₉	1	8	yes	—
705	#121	C₂³×C₈₉	1	8	yes	—
706	#121	C₂³×C₈₉	1	8	yes	—
707	#121	C₂³×C₈₉	1	8	yes	—
708	#121	C₂³×C₈₉	1	8	yes	—
709	#121	C₂³×C₈₉	1	8	yes	—
710	#121	C₂³×C₈₉	1	4	yes	—
711	#121	C₂³×C₈₉	1	4	yes	—
712	#121	C₂³×C₈₉	1	8	yes	—
713	#121	C₂³×C₈₉	1	8	yes	—
714	#121	C₂³×C₈₉	1	8	yes	—
715	#121	C₂³×C₈₉	1	8	yes	—
716	#121	C₂³×C₈₉	1	16	yes	—
717	#121	C₂³×C₈₉	1	16	yes	—
718	#121	C₂³×C₈₉	1	16	yes	—
719	#121	C₂³×C₈₉	1	4	yes	complemented
720	#121	C₂³×C₈₉	1	16	yes	complemented
721	#121	C₂³×C₈₉	1	8	yes	complemented
722	#121	C₂³×C₈₉	1	16	yes	complemented
723	#121	C₂³×C₈₉	1	4	yes	complemented
724	#121	C₂³×C₈₉	1	8	yes	complemented
725	#121	C₂³×C₈₉	1	8	yes	complemented
726	#121	C₂³×C₈₉	1	16	yes	complemented
727	#121	C₂³×C₈₉	1	16	yes	complemented
728	#121	C₂³×C₈₉	1	16	yes	complemented
729	#121	C₂³×C₈₉	1	16	yes	complemented
730	#121	C₂³×C₈₉	1	16	yes	complemented
731	#121	C₂³×C₈₉	1	16	yes	complemented
732	#120	C₂³×C₈₉	1	8	yes	—
733	#120	C₂³×C₈₉	1	8	yes	—
734	#120	C₂³×C₈₉	1	16	yes	—
735	#120	C₂³×C₈₉	1	16	yes	—
736	#120	C₂³×C₈₉	1	8	yes	—
737	#120	C₂³×C₈₉	1	8	yes	—
738	#120	C₂³×C₈₉	1	8	yes	—
739	#120	C₂³×C₈₉	1	16	yes	—
740	#120	C₂³×C₈₉	1	4	yes	—
741	#120	C₂³×C₈₉	1	8	yes	—
742	#120	C₂³×C₈₉	1	4	yes	—
743	#120	C₂³×C₈₉	1	8	yes	—
744	#120	C₂³×C₈₉	1	8	yes	—
745	#120	C₂³×C₈₉	1	4	yes	complemented
746	#120	C₂³×C₈₉	1	4	yes	complemented
747	#120	C₂³×C₈₉	1	16	yes	complemented
748	#120	C₂³×C₈₉	1	16	yes	complemented
749	#120	C₂³×C₈₉	1	16	yes	complemented
750	C₄×Q₈	C₂³×C₈₉	1	8	yes	complemented
751	C₄×Q₈	C₂³×C₈₉	1	8	yes	complemented
752	C₄×D₄	C₂³×C₈₉	1	8	yes	—
753	C₄×D₄	C₂³×C₈₉	1	8	yes	—
754	C₄×D₄	C₂³×C₈₉	1	16	yes	—
755	C₄×D₄	C₂³×C₈₉	1	8	yes	—
756	C₄×D₄	C₂³×C₈₉	1	8	yes	—
757	C₄×D₄	C₂³×C₈₉	1	8	yes	complemented
758	C₄×D₄	C₂³×C₈₉	1	8	yes	complemented
759	C₄×D₄	C₂³×C₈₉	1	8	yes	complemented
760	C₄×D₄	C₂³×C₈₉	1	16	yes	complemented
761	C₄×D₄	C₂³×C₈₉	1	16	yes	complemented
762	C₄×D₄	C₂³×C₈₉	1	8	yes	complemented
763	C₄×D₄	C₂³×C₈₉	1	16	yes	complemented
764	C₄×D₄	C₂³×C₈₉	1	16	yes	complemented
765	#117	C₂³×C₈₉	1	4	yes	—
766	#117	C₂³×C₈₉	1	4	yes	—
767	#117	C₂³×C₈₉	1	4	yes	—
768	#117	C₂³×C₈₉	1	4	yes	—
769	#117	C₂³×C₈₉	1	4	yes	complemented
770	#117	C₂³×C₈₉	1	2	yes	complemented
771	#117	C₂³×C₈₉	1	2	yes	complemented
772	#117	C₂³×C₈₉	1	8	yes	complemented
773	#117	C₂³×C₈₉	1	16	yes	complemented
774	#117	C₂³×C₈₉	1	16	yes	complemented
775	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
776	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	complemented
777	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	complemented
778	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
780	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
781	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
782	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
783	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	complemented
784	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
785	C₂×C₄²	C₂³×C₈₉	1	4	yes	complemented
786	C₂⁴	—	4	4	no	—
787	C₂⁴	—	8	4	no	—
788	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
789	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
790	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
791	C₂⁴	C₂⁴×C₈₉	1	8	yes	—
792	C₂⁴	C₂⁴×C₈₉	1	8	yes	—
793	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
794	#41	—	2	16	no	—
795	#41	—	4	4	no	—
796	#41	—	4	4	no	—
797	#41	—	4	4	no	—
798	#41	—	4	4	no	—
799	#41	—	4	8	no	—
800	#41	—	4	8	no	—
801	#41	—	4	8	no	—
802	#41	—	4	16	no	—
803	#41	—	8	16	no	—
804	C₂×Q₈	—	4	2	no	—
805	C₂×Q₈	—	4	4	no	—
806	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
807	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
808	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
809	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
810	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
811	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
812	C₂×D₄	—	2	8	no	—
813	C₂×D₄	—	4	8	no	—
814	C₂×D₄	—	4	8	no	—
815	C₂×D₄	—	4	16	no	—
816	C₂×D₄	—	4	4	no	—
817	C₂×D₄	—	4	4	no	—
818	C₂×D₄	—	4	2	no	—
819	C₂×D₄	—	4	4	no	—
820	C₂×D₄	—	4	8	no	—
821	C₂×D₄	—	4	16	no	—
822	C₂×D₄	—	8	8	no	—
823	C₂×D₄	—	8	16	no	—
824	C₂×D₄	—	8	16	no	—
825	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
826	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
827	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
828	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
829	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
830	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
831	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
832	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
833	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
834	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
835	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
836	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
837	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
838	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
839	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
840	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
841	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
842	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
843	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
844	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
845	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
846	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
847	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
848	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
849	C₂²×C₄	—	2	4	no	—
850	C₂²×C₄	—	2	8	no	—
851	C₂²×C₄	—	4	8	no	—
852	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
853	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
854	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
855	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
856	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
857	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
858	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
859	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
860	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
861	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
862	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
863	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
864	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
865	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
866	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
867	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
868	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
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	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
873	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
874	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
875	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
876	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
877	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
878	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
879	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
880	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
881	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
882	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
883	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
884	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
885	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
886	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
887	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
888	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
889	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
890	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
891	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
892	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
893	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
894	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
895	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
896	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
897	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
898	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
899	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
900	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
901	C₄²	C₂⁴×C₈₉	1	4	yes	—
902	C₄²	C₂⁴×C₈₉	1	4	yes	—
903	C₄²	C₂⁴×C₈₉	1	4	yes	—
904	C₄²	C₂⁴×C₈₉	1	8	yes	—
905	C₄²	C₂⁴×C₈₉	1	4	yes	—
906	C₄²	C₂⁴×C₈₉	1	16	yes	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	4	no	—
909	C₂³	—	2	8	no	—
910	C₂³	—	4	2	no	—
911	C₂³	—	4	4	no	—
912	C₂³	—	4	8	no	—
913	C₂³	—	4	4	no	—
914	C₂³	—	4	8	no	—
915	C₂³	—	4	8	no	—
916	C₂³	—	4	16	no	—
917	C₂³	—	4	8	no	—
918	C₂³	—	4	16	no	—
919	C₂³	—	8	16	no	—
920	C₂³	C₂⁵×C₈₉	1	2	yes	—
921	C₂³	C₂⁵×C₈₉	1	8	yes	—
922	C₂³	C₂⁵×C₈₉	1	2	yes	—
923	C₂³	C₂⁵×C₈₉	1	8	yes	—
924	C₂³	C₂⁵×C₈₉	1	2	yes	—
925	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
926	Q₈	—	2	8	no	—
927	Q₈	—	4	1	no	—
928	Q₈	—	4	2	no	—
929	Q₈	—	4	1	no	—
930	Q₈	—	4	4	no	—
931	Q₈	—	4	8	no	—
932	D₄	—	2	16	no	—
933	D₄	—	2	16	no	—
934	D₄	—	2	8	no	—
935	D₄	—	4	4	no	—
936	D₄	—	4	4	no	—
937	D₄	—	4	16	no	—
938	D₄	—	4	2	no	—
939	D₄	—	4	2	no	—
940	D₄	—	4	1	no	—
941	D₄	—	4	2	no	—
942	D₄	—	4	1	no	—
943	D₄	—	4	2	no	—
944	D₄	—	4	2	no	—
945	D₄	—	4	4	no	—
946	D₄	—	4	8	no	—
947	D₄	—	4	8	no	—
948	D₄	—	4	16	no	—
949	D₄	—	4	8	no	—
950	D₄	—	4	16	no	—
951	D₄	—	4	8	no	—
952	D₄	—	4	8	no	—
953	D₄	—	4	16	no	—
954	D₄	—	4	16	no	—
955	D₄	—	4	8	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	4	no	—
958	C₂×C₄	—	2	4	no	—
959	C₂×C₄	—	2	4	no	—
960	C₂×C₄	—	2	4	no	—
961	C₂×C₄	—	2	4	no	—
962	C₂×C₄	—	2	4	no	—
963	C₂×C₄	—	2	4	no	—
964	C₂×C₄	—	2	16	no	—
965	C₂×C₄	—	4	4	no	—
966	C₂×C₄	—	4	8	no	—
967	C₂×C₄	—	4	8	no	—
968	C₂×C₄	—	4	4	no	—
969	C₂×C₄	—	4	16	no	—
970	C₂×C₄	—	4	16	no	—
971	C₂×C₄	—	4	8	no	—
972	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
973	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
974	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
975	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
976	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
977	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
978	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
979	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
980	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
981	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
982	C₂²	—	2	2	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	2	2	no	—
985	C₂²	—	2	2	no	—
986	C₂²	—	2	8	no	—
987	C₂²	—	2	8	no	—
988	C₂²	—	2	4	no	—
989	C₂²	—	2	8	no	—
990	C₂²	—	2	16	no	—
991	C₂²	—	2	4	no	—
992	C₂²	—	2	8	no	—
993	C₂²	—	2	4	no	—
994	C₂²	—	4	4	no	—
995	C₂²	—	8	8	no	—
996	C₂²	—	8	4	no	—
997	C₂²	—	8	16	no	—
998	C₂²	—	8	8	no	—
999	C₂²	—	16	8	no	—
1000	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
1001	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
1002	C₄	—	2	2	no	—
1003	C₄	—	2	1	no	—
1004	C₄	—	2	1	no	—
1005	C₄	—	2	2	no	—
1006	C₄	—	2	8	no	—
1007	C₄	—	2	8	no	—
1008	C₄	—	2	8	no	—
1009	C₄	—	2	8	no	—
1010	C₄	C₂×H(5,𝔽₂)×C₈₉	1	4	yes	—
1011	C₂	—	2	2	no	—
1012	C₂	—	4	2	no	—
1013	C₂	—	4	2	no	—
1014	C₂	—	4	2	no	—
1015	C₂	—	4	8	no	—
1016	C₂	—	4	8	no	—
1017	C₂	C₂²×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1018	C₂	C₈₉×H(7,𝔽₂)	1	2	yes	—

	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×#3551	C₂	semidirect
2. C₈₉×#3549	C₂	semidirect
3. C₈₉×#3546	C₂	semidirect
4. C₈₉×#3545	C₂	semidirect
5. C₈₉×#3543	C₂	semidirect
6. C₈₉×#3542	C₂	semidirect
7. C₈₉×#3540	C₂	semidirect
8. C₈₉×#3537	C₂	semidirect
9. C₈₉×#3532	C₂	semidirect
10. C₈₉×#3494	C₂	semidirect
11. C₈₉×#3493	C₂	semidirect
12. C₈₉×#3488	C₂	semidirect
13. C₈₉×#3484	C₂	semidirect
14. C₈₉×#3449	C₂	semidirect
15. C₂×#535×C₈₉	C₂	semidirect
16. C₂×H(5,𝔽₂)×C₈₉	C₂²	semidirect
17. C₂²×#41×C₈₉	C₂²	semidirect
18. C₂²×#41×C₈₉	C₂²	semidirect
19. C₂³×D₄×C₈₉	C₂²	semidirect
20. #563×C₈₉	C₂²	semidirect
21. #562×C₈₉	C₂²	semidirect
22. H(3,𝔽₄)×C₈₉	C₂²	semidirect
23. H(3,𝔽₄)×C₈₉	C₂²	semidirect
24. #560×C₈₉	C₂²	semidirect
25. #560×C₈₉	C₂²	semidirect
26. #560×C₈₉	C₂²	semidirect
27. #560×C₈₉	C₂²	semidirect
28. #559×C₈₉	C₂²	semidirect
29. #556×C₈₉	C₂²	semidirect
30. #555×C₈₉	C₂²	semidirect
31. #555×C₈₉	C₂²	semidirect
32. #555×C₈₉	C₂²	semidirect
33. #553×C₈₉	C₂²	semidirect
34. #553×C₈₉	C₂²	semidirect
35. #553×C₈₉	C₂²	semidirect
36. #552×C₈₉	C₂²	semidirect
37. #551×C₈₉	C₂²	semidirect
38. #551×C₈₉	C₂²	semidirect
39. #551×C₈₉	C₂²	semidirect
40. #550×C₈₉	C₂²	semidirect
41. #550×C₈₉	C₂²	semidirect
42. #548×C₈₉	C₂²	semidirect
43. #547×C₈₉	C₂²	semidirect
44. #546×C₈₉	C₂²	semidirect
45. #546×C₈₉	C₂²	semidirect
46. #546×C₈₉	C₂²	semidirect
47. #546×C₈₉	C₂²	semidirect
48. #546×C₈₉	C₂²	semidirect
49. #546×C₈₉	C₂²	semidirect
50. D₄²×C₈₉	C₂²	semidirect
51. D₄²×C₈₉	C₂²	semidirect
52. D₄²×C₈₉	C₂²	semidirect
53. D₄²×C₈₉	C₂²	semidirect
54. D₄²×C₈₉	C₂²	semidirect
55. D₄²×C₈₉	C₂²	semidirect
56. #544×C₈₉	C₂²	semidirect
57. #542×C₈₉	C₂²	semidirect
58. #542×C₈₉	C₂²	semidirect
59. #540×C₈₉	C₂²	semidirect
60. #540×C₈₉	C₂²	semidirect
61. #538×C₈₉	C₂²	semidirect
62. #538×C₈₉	C₂²	semidirect
63. #538×C₈₉	C₂²	semidirect
64. #538×C₈₉	C₂²	semidirect
65. #537×C₈₉	C₂²	semidirect
66. #537×C₈₉	C₂²	semidirect
67. #537×C₈₉	C₂²	semidirect
68. #537×C₈₉	C₂²	semidirect
69. #536×C₈₉	C₂²	semidirect
70. #536×C₈₉	C₂²	semidirect
71. #536×C₈₉	C₂²	semidirect
72. #535×C₈₉	C₂²	semidirect
73. #535×C₈₉	C₂²	semidirect
74. #535×C₈₉	C₂²	semidirect
75. #535×C₈₉	C₂²	semidirect
76. #535×C₈₉	C₂²	semidirect
77. #535×C₈₉	C₂²	semidirect
78. #535×C₈₉	C₂²	semidirect
79. #535×C₈₉	C₂²	semidirect
80. #535×C₈₉	C₂²	semidirect
81. #535×C₈₉	C₂²	semidirect
82. #535×C₈₉	C₂²	semidirect
83. #534×C₈₉	C₂²	semidirect
84. #534×C₈₉	C₂²	semidirect
85. #534×C₈₉	C₂²	semidirect
86. #534×C₈₉	C₂²	semidirect
87. #532×C₈₉	C₂²	semidirect
88. #532×C₈₉	C₂²	semidirect
89. #532×C₈₉	C₂²	semidirect
90. C₂×#127×C₈₉	C₂²	semidirect
91. #529×C₈₉	C₂²	semidirect
92. #529×C₈₉	C₂²	semidirect
93. C₂×#124×C₈₉	C₂²	semidirect
94. #525×C₈₉	C₂²	semidirect
95. #525×C₈₉	C₂²	semidirect
96. #525×C₈₉	C₂²	semidirect
97. #525×C₈₉	C₂²	semidirect
98. #525×C₈₉	C₂²	semidirect
99. C₂×#121×C₈₉	C₂²	semidirect
100. C₂×#121×C₈₉	C₂²	semidirect
101. C₂×#120×C₈₉	C₂²	semidirect
102. C₂×#120×C₈₉	C₂²	semidirect
103. #520×C₈₉	C₂²	semidirect
104. #518×C₈₉	C₂²	semidirect
105. C₂×#117×C₈₉	C₂²	semidirect
106. C₂×#117×C₈₉	C₂²	semidirect
118. C₂×#41×C₈₉	C₂³	semidirect
119. C₂×#41×C₈₉	C₂³	semidirect
120. C₂×#41×C₈₉	C₂³	semidirect
122. C₂²×Q₈×C₈₉	C₂³	semidirect
135. C₂²×D₄×C₈₉	C₂³	semidirect
136. C₂²×D₄×C₈₉	C₂³	semidirect
139. C₂³×C₄×C₈₉	C₂³	semidirect
140. C₄⋊Q₈×C₈₉	C₂³	semidirect
141. C₄⋊Q₈×C₈₉	C₂³	semidirect
142. C₄⋊Q₈×C₈₉	C₂³	semidirect
149. #127×C₈₉	C₂³	semidirect
151. #126×C₈₉	C₂³	semidirect
152. #126×C₈₉	C₂³	semidirect
153. #126×C₈₉	C₂³	semidirect
154. #125×C₈₉	C₂³	semidirect
155. #125×C₈₉	C₂³	semidirect
163. #124×C₈₉	C₂³	semidirect
164. #124×C₈₉	C₂³	semidirect
165. #124×C₈₉	C₂³	semidirect
166. #124×C₈₉	C₂³	semidirect
167. #124×C₈₉	C₂³	semidirect
168. #124×C₈₉	C₂³	semidirect
176. #123×C₈₉	C₂³	semidirect
177. #123×C₈₉	C₂³	semidirect
178. #123×C₈₉	C₂³	semidirect
179. #123×C₈₉	C₂³	semidirect
180. #123×C₈₉	C₂³	semidirect
181. #123×C₈₉	C₂³	semidirect
182. #123×C₈₉	C₂³	semidirect
186. C₂²⋊Q₈×C₈₉	C₂³	semidirect
187. C₂²⋊Q₈×C₈₉	C₂³	semidirect
188. C₂²⋊Q₈×C₈₉	C₂³	semidirect
189. C₂²⋊Q₈×C₈₉	C₂³	semidirect
190. C₂²⋊Q₈×C₈₉	C₂³	semidirect
191. C₂²⋊Q₈×C₈₉	C₂³	semidirect
192. C₂²⋊Q₈×C₈₉	C₂³	semidirect
209. #121×C₈₉	C₂³	semidirect
210. #121×C₈₉	C₂³	semidirect
211. #121×C₈₉	C₂³	semidirect
212. #121×C₈₉	C₂³	semidirect
213. #121×C₈₉	C₂³	semidirect
214. #121×C₈₉	C₂³	semidirect
215. #121×C₈₉	C₂³	semidirect
216. #121×C₈₉	C₂³	semidirect
217. #121×C₈₉	C₂³	semidirect
218. #121×C₈₉	C₂³	semidirect
219. #121×C₈₉	C₂³	semidirect
220. #121×C₈₉	C₂³	semidirect
221. #121×C₈₉	C₂³	semidirect
235. #120×C₈₉	C₂³	semidirect
236. #120×C₈₉	C₂³	semidirect
237. #120×C₈₉	C₂³	semidirect
238. #120×C₈₉	C₂³	semidirect
239. #120×C₈₉	C₂³	semidirect
240. C₄×Q₈×C₈₉	C₂³	semidirect
241. C₄×Q₈×C₈₉	C₂³	semidirect
247. C₄×D₄×C₈₉	C₂³	semidirect
248. C₄×D₄×C₈₉	C₂³	semidirect
249. C₄×D₄×C₈₉	C₂³	semidirect
250. C₄×D₄×C₈₉	C₂³	semidirect
251. C₄×D₄×C₈₉	C₂³	semidirect
252. C₄×D₄×C₈₉	C₂³	semidirect
253. C₄×D₄×C₈₉	C₂³	semidirect
254. C₄×D₄×C₈₉	C₂³	semidirect
259. #117×C₈₉	C₂³	semidirect
260. #117×C₈₉	C₂³	semidirect
261. #117×C₈₉	C₂³	semidirect
262. #117×C₈₉	C₂³	semidirect
263. #117×C₈₉	C₂³	semidirect
264. #117×C₈₉	C₂³	semidirect
266. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
267. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
273. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
275. C₂×C₄²×C₈₉	C₂³	semidirect
501. #62874	C₈₉	direct (N × H)
510. #3551	C₂×C₈₉	semidirect
511. #3549	C₂×C₈₉	semidirect
512. #3546	C₂×C₈₉	semidirect
513. #3545	C₂×C₈₉	semidirect
514. #3543	C₂×C₈₉	semidirect
515. #3542	C₂×C₈₉	semidirect
516. #3540	C₂×C₈₉	semidirect
517. #3537	C₂×C₈₉	semidirect
518. #3532	C₂×C₈₉	semidirect
519. #3494	C₂×C₈₉	semidirect
520. #3493	C₂×C₈₉	semidirect
521. #3488	C₂×C₈₉	semidirect
522. #3484	C₂×C₈₉	semidirect
523. #3449	C₂×C₈₉	semidirect
524. C₂×#535	C₂×C₈₉	semidirect
525. C₈₉	#62874	direct (N × H)
526. C₂×H(5,𝔽₂)	C₂²×C₈₉	semidirect
527. C₂²×#41	C₂²×C₈₉	semidirect
528. C₂²×#41	C₂²×C₈₉	semidirect
529. C₂³×D₄	C₂²×C₈₉	semidirect
530. #563	C₂²×C₈₉	semidirect
531. #562	C₂²×C₈₉	semidirect
532. H(3,𝔽₄)	C₂²×C₈₉	semidirect
533. H(3,𝔽₄)	C₂²×C₈₉	semidirect
534. #560	C₂²×C₈₉	semidirect
535. #560	C₂²×C₈₉	semidirect
536. #560	C₂²×C₈₉	semidirect
537. #560	C₂²×C₈₉	semidirect
538. #559	C₂²×C₈₉	semidirect
539. #556	C₂²×C₈₉	semidirect
540. #555	C₂²×C₈₉	semidirect
541. #555	C₂²×C₈₉	semidirect
542. #555	C₂²×C₈₉	semidirect
543. #553	C₂²×C₈₉	semidirect
544. #553	C₂²×C₈₉	semidirect
545. #553	C₂²×C₈₉	semidirect
546. #552	C₂²×C₈₉	semidirect
547. #551	C₂²×C₈₉	semidirect
548. #551	C₂²×C₈₉	semidirect
549. #551	C₂²×C₈₉	semidirect
550. #550	C₂²×C₈₉	semidirect
551. #550	C₂²×C₈₉	semidirect
552. #548	C₂²×C₈₉	semidirect
553. #547	C₂²×C₈₉	semidirect
554. #546	C₂²×C₈₉	semidirect
555. #546	C₂²×C₈₉	semidirect
556. #546	C₂²×C₈₉	semidirect
557. #546	C₂²×C₈₉	semidirect
558. #546	C₂²×C₈₉	semidirect
559. #546	C₂²×C₈₉	semidirect
560. D₄²	C₂²×C₈₉	semidirect
561. D₄²	C₂²×C₈₉	semidirect
562. D₄²	C₂²×C₈₉	semidirect
563. D₄²	C₂²×C₈₉	semidirect
564. D₄²	C₂²×C₈₉	semidirect
565. D₄²	C₂²×C₈₉	semidirect
566. #544	C₂²×C₈₉	semidirect
567. #542	C₂²×C₈₉	semidirect
568. #542	C₂²×C₈₉	semidirect
569. #540	C₂²×C₈₉	semidirect
570. #540	C₂²×C₈₉	semidirect
571. #538	C₂²×C₈₉	semidirect
572. #538	C₂²×C₈₉	semidirect
573. #538	C₂²×C₈₉	semidirect
574. #538	C₂²×C₈₉	semidirect
575. #537	C₂²×C₈₉	semidirect
576. #537	C₂²×C₈₉	semidirect
577. #537	C₂²×C₈₉	semidirect
578. #537	C₂²×C₈₉	semidirect
579. #536	C₂²×C₈₉	semidirect
580. #536	C₂²×C₈₉	semidirect
581. #536	C₂²×C₈₉	semidirect
582. #535	C₂²×C₈₉	semidirect
583. #535	C₂²×C₈₉	semidirect
584. #535	C₂²×C₈₉	semidirect
585. #535	C₂²×C₈₉	semidirect
586. #535	C₂²×C₈₉	semidirect
587. #535	C₂²×C₈₉	semidirect
588. #535	C₂²×C₈₉	semidirect
589. #535	C₂²×C₈₉	semidirect
590. #535	C₂²×C₈₉	semidirect
591. #535	C₂²×C₈₉	semidirect
592. #535	C₂²×C₈₉	semidirect
593. #534	C₂²×C₈₉	semidirect
594. #534	C₂²×C₈₉	semidirect
595. #534	C₂²×C₈₉	semidirect
596. #534	C₂²×C₈₉	semidirect
597. #532	C₂²×C₈₉	semidirect
598. #532	C₂²×C₈₉	semidirect
599. #532	C₂²×C₈₉	semidirect
600. C₂×#127	C₂²×C₈₉	semidirect
601. #529	C₂²×C₈₉	semidirect
602. #529	C₂²×C₈₉	semidirect
603. C₂×#124	C₂²×C₈₉	semidirect
604. #525	C₂²×C₈₉	semidirect
605. #525	C₂²×C₈₉	semidirect
606. #525	C₂²×C₈₉	semidirect
607. #525	C₂²×C₈₉	semidirect
608. #525	C₂²×C₈₉	semidirect
609. C₂×#121	C₂²×C₈₉	semidirect
610. C₂×#121	C₂²×C₈₉	semidirect
611. C₂×#120	C₂²×C₈₉	semidirect
612. C₂×#120	C₂²×C₈₉	semidirect
613. #520	C₂²×C₈₉	semidirect
614. #518	C₂²×C₈₉	semidirect
615. C₂×#117	C₂²×C₈₉	semidirect
616. C₂×#117	C₂²×C₈₉	semidirect
628. C₂×#41	C₂³×C₈₉	semidirect
629. C₂×#41	C₂³×C₈₉	semidirect
630. C₂×#41	C₂³×C₈₉	semidirect
632. C₂²×Q₈	C₂³×C₈₉	semidirect
645. C₂²×D₄	C₂³×C₈₉	semidirect
646. C₂²×D₄	C₂³×C₈₉	semidirect
649. C₂³×C₄	C₂³×C₈₉	semidirect
650. C₄⋊Q₈	C₂³×C₈₉	semidirect
651. C₄⋊Q₈	C₂³×C₈₉	semidirect
652. C₄⋊Q₈	C₂³×C₈₉	semidirect
659. #127	C₂³×C₈₉	semidirect
661. #126	C₂³×C₈₉	semidirect
662. #126	C₂³×C₈₉	semidirect
663. #126	C₂³×C₈₉	semidirect
664. #125	C₂³×C₈₉	semidirect
665. #125	C₂³×C₈₉	semidirect
673. #124	C₂³×C₈₉	semidirect
674. #124	C₂³×C₈₉	semidirect
675. #124	C₂³×C₈₉	semidirect
676. #124	C₂³×C₈₉	semidirect
677. #124	C₂³×C₈₉	semidirect
678. #124	C₂³×C₈₉	semidirect
686. #123	C₂³×C₈₉	semidirect
687. #123	C₂³×C₈₉	semidirect
688. #123	C₂³×C₈₉	semidirect
689. #123	C₂³×C₈₉	semidirect
690. #123	C₂³×C₈₉	semidirect
691. #123	C₂³×C₈₉	semidirect
692. #123	C₂³×C₈₉	semidirect
696. C₂²⋊Q₈	C₂³×C₈₉	semidirect
697. C₂²⋊Q₈	C₂³×C₈₉	semidirect
698. C₂²⋊Q₈	C₂³×C₈₉	semidirect
699. C₂²⋊Q₈	C₂³×C₈₉	semidirect
700. C₂²⋊Q₈	C₂³×C₈₉	semidirect
701. C₂²⋊Q₈	C₂³×C₈₉	semidirect
702. C₂²⋊Q₈	C₂³×C₈₉	semidirect
719. #121	C₂³×C₈₉	semidirect
720. #121	C₂³×C₈₉	semidirect
721. #121	C₂³×C₈₉	semidirect
722. #121	C₂³×C₈₉	semidirect
723. #121	C₂³×C₈₉	semidirect
724. #121	C₂³×C₈₉	semidirect
725. #121	C₂³×C₈₉	semidirect
726. #121	C₂³×C₈₉	semidirect
727. #121	C₂³×C₈₉	semidirect
728. #121	C₂³×C₈₉	semidirect
729. #121	C₂³×C₈₉	semidirect
730. #121	C₂³×C₈₉	semidirect
731. #121	C₂³×C₈₉	semidirect
745. #120	C₂³×C₈₉	semidirect
746. #120	C₂³×C₈₉	semidirect
747. #120	C₂³×C₈₉	semidirect
748. #120	C₂³×C₈₉	semidirect
749. #120	C₂³×C₈₉	semidirect
750. C₄×Q₈	C₂³×C₈₉	semidirect
751. C₄×Q₈	C₂³×C₈₉	semidirect
757. C₄×D₄	C₂³×C₈₉	semidirect
758. C₄×D₄	C₂³×C₈₉	semidirect
759. C₄×D₄	C₂³×C₈₉	semidirect
760. C₄×D₄	C₂³×C₈₉	semidirect
761. C₄×D₄	C₂³×C₈₉	semidirect
762. C₄×D₄	C₂³×C₈₉	semidirect
763. C₄×D₄	C₂³×C₈₉	semidirect
764. C₄×D₄	C₂³×C₈₉	semidirect
769. #117	C₂³×C₈₉	semidirect
770. #117	C₂³×C₈₉	semidirect
771. #117	C₂³×C₈₉	semidirect
772. #117	C₂³×C₈₉	semidirect
773. #117	C₂³×C₈₉	semidirect
774. #117	C₂³×C₈₉	semidirect
776. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
777. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
783. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
785. C₂×C₄²	C₂³×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3551	2
C₈₉×#3549	2
C₈₉×#3546	2
C₈₉×#3545	2
C₈₉×#3543	2
C₈₉×#3542	2
C₈₉×#3540	2
C₈₉×#3537	2
C₈₉×#3532	2
C₈₉×#3494	2
C₈₉×#3493	2
C₈₉×#3488	2
C₈₉×#3484	2
C₈₉×#3449	2
C₂×#535×C₈₉	2
#62874	89

Subgroups — C89×#62874 #36440722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62874 #36440722