Subgroups — C₈₉×#61165 #36439013

Order 22784.

2118 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#556×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3328	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3324	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3313	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3311	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3304	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3302	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3093	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3079	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3056	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3037	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3007	C₂	1	2	yes	maximal, complemented
15	C₄×#137×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×M₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2896	C₂	1	2	yes	maximal, complemented
18	C₂²×#41×C₈₉	C₂²	1	2	yes	—
19	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#137×C₈₉	C₂²	1	2	yes	complemented
21	C₂²×M₁₆×C₈₉	C₂²	1	2	yes	complemented
22	#556×C₈₉	—	2	1	no	—
23	#556×C₈₉	—	2	2	no	—
24	#556×C₈₉	—	2	1	no	—
25	#556×C₈₉	C₂²	1	2	yes	—
26	#556×C₈₉	C₂²	1	2	yes	complemented
27	#556×C₈₉	C₂²	1	4	yes	complemented
28	#550×C₈₉	C₂²	1	1	yes	characteristic
29	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
30	#548×C₈₉	C₂²	1	2	yes	—
31	#547×C₈₉	—	2	1	no	—
32	#547×C₈₉	C₂²	1	1	yes	characteristic
33	#546×C₈₉	—	2	2	no	—
34	#546×C₈₉	C₂²	1	2	yes	—
35	D₄²×C₈₉	—	2	1	no	—
36	D₄²×C₈₉	C₂²	1	1	yes	characteristic
37	#532×C₈₉	—	2	1	no	—
38	#532×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×#126×C₈₉	—	2	2	no	—
41	C₂×#124×C₈₉	—	2	1	no	—
42	#525×C₈₉	—	2	2	no	—
43	#525×C₈₉	C₂²	1	2	yes	—
44	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
45	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
47	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₄×D₄×C₈₉	—	2	1	no	—
49	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
51	#489×C₈₉	C₂²	1	4	yes	complemented
52	#487×C₈₉	C₂²	1	2	yes	complemented
53	#486×C₈₉	C₂²	1	2	yes	complemented
54	#485×C₈₉	C₂²	1	4	yes	complemented
55	#485×C₈₉	C₂²	1	4	yes	complemented
56	#482×C₈₉	C₂²	1	4	yes	complemented
57	#482×C₈₉	C₂²	1	4	yes	complemented
58	#477×C₈₉	C₂²	1	2	yes	complemented
59	#476×C₈₉	C₂²	1	2	yes	complemented
60	#475×C₈₉	C₂²	1	2	yes	complemented
61	#474×C₈₉	C₂²	1	2	yes	complemented
62	#470×C₈₉	C₂²	1	4	yes	complemented
63	#468×C₈₉	C₂²	1	4	yes	complemented
64	#467×C₈₉	C₂²	1	4	yes	complemented
65	#465×C₈₉	C₂²	1	4	yes	complemented
66	#464×C₈₉	C₂²	1	4	yes	complemented
67	#462×C₈₉	C₂²	1	2	yes	complemented
68	#460×C₈₉	C₂²	1	2	yes	complemented
69	#452×C₈₉	C₂²	1	4	yes	complemented
70	#452×C₈₉	C₂²	1	4	yes	complemented
71	#451×C₈₉	C₂²	1	4	yes	complemented
72	#450×C₈₉	C₂²	1	4	yes	complemented
73	#441×C₈₉	C₂²	1	2	yes	complemented
74	#440×C₈₉	C₂²	1	2	yes	complemented
75	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
76	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
77	#436×C₈₉	C₂²	1	2	yes	—
78	#435×C₈₉	C₂²	1	4	yes	complemented
79	C₈×D₄×C₈₉	C₂²	1	2	yes	complemented
80	#428×C₈₉	C₂²	1	2	yes	complemented
81	#428×C₈₉	C₂²	1	1	yes	characteristic, complemented
82	#423×C₈₉	C₂²	1	1	yes	characteristic, complemented
83	#419×C₈₉	C₂²	1	4	yes	complemented
84	#419×C₈₉	C₂²	1	1	yes	characteristic, complemented
85	#418×C₈₉	C₂²	1	4	yes	complemented
86	#417×C₈₉	C₂²	1	2	yes	—
87	#417×C₈₉	C₂²	1	1	yes	characteristic
88	#417×C₈₉	C₂²	1	2	yes	complemented
89	#417×C₈₉	C₂²	1	2	yes	complemented
90	#417×C₈₉	C₂²	1	2	yes	complemented
91	#416×C₈₉	C₂²	1	4	yes	complemented
92	#416×C₈₉	C₂²	1	4	yes	complemented
93	#407×C₈₉	C₂²	1	2	yes	complemented
94	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
95	C₂×#41×C₈₉	—	2	2	no	—
96	C₂×#41×C₈₉	—	2	2	no	—
97	C₂×#41×C₈₉	—	2	8	no	—
98	C₂×#41×C₈₉	—	4	4	no	—
99	C₂×#41×C₈₉	C₂³	1	2	yes	—
100	C₂×#41×C₈₉	C₂³	1	2	yes	—
101	C₂×#41×C₈₉	C₂³	1	2	yes	—
102	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₈₉	—	2	1	no	—
104	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
105	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
106	C₂²×D₄×C₈₉	—	2	2	no	—
107	C₂²×D₄×C₈₉	—	2	1	no	—
108	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
109	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
110	C₂³×C₄×C₈₉	—	2	2	no	—
111	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
112	#137×C₈₉	—	2	4	no	—
113	#137×C₈₉	—	4	4	no	—
114	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
115	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
116	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
117	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
118	C₂×M₁₆×C₈₉	—	4	4	no	—
119	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
120	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
121	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
122	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
123	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
124	C₄⋊Q₈×C₈₉	—	2	1	no	—
125	C₄⋊Q₈×C₈₉	—	2	1	no	—
126	C₄⋊Q₈×C₈₉	—	2	1	no	—
127	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
128	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
129	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
130	#127×C₈₉	—	2	1	no	—
131	#127×C₈₉	C₂³	1	1	yes	characteristic
132	#126×C₈₉	—	2	4	no	—
133	#126×C₈₉	—	2	4	no	—
134	#126×C₈₉	—	2	4	no	—
135	#126×C₈₉	—	2	4	no	—
136	#124×C₈₉	—	2	2	no	—
137	#124×C₈₉	—	2	2	no	—
138	#124×C₈₉	—	2	4	no	—
139	#124×C₈₉	—	2	2	no	—
140	#124×C₈₉	C₂³	1	2	yes	—
141	#123×C₈₉	—	2	2	no	—
142	#123×C₈₉	—	2	2	no	—
143	#123×C₈₉	—	2	2	no	—
144	C₂²⋊Q₈×C₈₉	—	2	2	no	—
145	C₂²⋊Q₈×C₈₉	—	2	2	no	—
146	C₂²⋊Q₈×C₈₉	—	2	2	no	—
147	C₂²⋊Q₈×C₈₉	—	2	2	no	—
148	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
149	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
150	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
151	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
152	#121×C₈₉	—	2	2	no	—
153	#121×C₈₉	—	2	1	no	—
154	#121×C₈₉	—	2	1	no	—
155	#121×C₈₉	—	2	1	no	—
156	#121×C₈₉	—	2	1	no	—
157	#121×C₈₉	—	2	2	no	—
158	#121×C₈₉	—	2	2	no	—
159	#121×C₈₉	C₂³	1	2	yes	—
160	#121×C₈₉	C₂³	1	2	yes	—
161	#120×C₈₉	—	2	2	no	—
162	#120×C₈₉	—	2	2	no	—
163	#120×C₈₉	—	2	2	no	—
164	C₄×Q₈×C₈₉	—	2	2	no	—
165	C₄×Q₈×C₈₉	—	2	2	no	—
166	C₄×Q₈×C₈₉	—	2	4	no	—
167	C₄×Q₈×C₈₉	—	2	1	no	—
168	C₄×Q₈×C₈₉	—	2	1	no	—
169	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
170	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
172	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₈₉	—	2	1	no	—
174	C₄×D₄×C₈₉	—	2	2	no	—
175	C₄×D₄×C₈₉	—	2	1	no	—
176	C₄×D₄×C₈₉	—	2	1	no	—
177	C₄×D₄×C₈₉	—	2	2	no	—
178	C₄×D₄×C₈₉	—	2	1	no	—
179	C₄×D₄×C₈₉	—	2	2	no	—
180	C₄×D₄×C₈₉	—	2	1	no	—
181	C₄×D₄×C₈₉	—	2	1	no	—
182	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
183	C₄×D₄×C₈₉	D₄	1	2	yes	—
184	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
185	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₈₉	C₂³	1	2	yes	—
189	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
190	#117×C₈₉	—	2	2	no	—
191	#117×C₈₉	—	2	2	no	—
192	#117×C₈₉	—	2	1	no	—
193	#117×C₈₉	C₂³	1	4	yes	—
194	#117×C₈₉	C₂³	1	4	yes	—
195	#117×C₈₉	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
197	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
198	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
199	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
200	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
204	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
205	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
206	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
207	C₂×C₄²×C₈₉	—	2	2	no	—
208	C₂×C₄²×C₈₉	—	2	1	no	—
209	C₂×C₄²×C₈₉	—	2	1	no	—
210	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
211	#107×C₈₉	C₂³	1	2	yes	—
212	#107×C₈₉	C₂³	1	4	yes	—
213	#106×C₈₉	C₂³	1	2	yes	—
214	#106×C₈₉	C₂³	1	4	yes	—
215	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
216	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
217	#103×C₈₉	C₂³	1	2	yes	—
218	#103×C₈₉	C₂³	1	4	yes	—
219	#103×C₈₉	C₂³	1	4	yes	—
220	#103×C₈₉	C₂³	1	4	yes	—
221	#103×C₈₉	C₂³	1	4	yes	—
222	#103×C₈₉	C₂³	1	2	yes	—
223	#103×C₈₉	C₂³	1	2	yes	—
224	#102×C₈₉	C₂³	1	2	yes	—
225	#102×C₈₉	C₂³	1	4	yes	—
226	#102×C₈₉	C₂³	1	4	yes	—
227	#102×C₈₉	C₂³	1	4	yes	—
228	#102×C₈₉	C₂³	1	4	yes	—
229	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
230	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
231	#97×C₈₉	C₂³	1	2	yes	—
232	C₄×C₈×C₈₉	C₂³	1	2	yes	—
233	C₂⁴×C₈₉	—	2	2	no	—
234	C₂⁴×C₈₉	C₂×D₄	1	2	yes	—
235	#41×C₈₉	—	2	2	no	—
236	#41×C₈₉	—	2	4	no	—
237	#41×C₈₉	—	2	4	no	—
238	#41×C₈₉	—	2	4	no	—
239	#41×C₈₉	—	2	4	no	—
240	#41×C₈₉	—	4	8	no	—
241	#41×C₈₉	—	4	2	no	—
242	#41×C₈₉	—	4	2	no	—
243	#41×C₈₉	—	4	8	no	—
244	#41×C₈₉	#41	1	4	yes	—
245	C₂×Q₈×C₈₉	—	2	1	no	—
246	C₂×Q₈×C₈₉	—	2	2	no	—
247	C₂×Q₈×C₈₉	—	2	2	no	—
248	C₂×Q₈×C₈₉	—	2	2	no	—
249	C₂×Q₈×C₈₉	—	2	4	no	—
250	C₂×Q₈×C₈₉	—	2	2	no	—
251	C₂×Q₈×C₈₉	—	2	2	no	—
252	C₂×Q₈×C₈₉	—	4	2	no	—
253	C₂×Q₈×C₈₉	—	4	4	no	—
254	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
255	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
256	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
257	C₂×D₄×C₈₉	—	2	1	no	—
258	C₂×D₄×C₈₉	—	2	4	no	—
259	C₂×D₄×C₈₉	—	2	2	no	—
260	C₂×D₄×C₈₉	—	2	2	no	—
261	C₂×D₄×C₈₉	—	2	2	no	—
262	C₂×D₄×C₈₉	—	2	2	no	—
263	C₂×D₄×C₈₉	—	2	2	no	—
264	C₂×D₄×C₈₉	—	2	1	no	—
265	C₂×D₄×C₈₉	—	2	2	no	—
266	C₂×D₄×C₈₉	—	2	1	no	—
267	C₂×D₄×C₈₉	—	4	2	no	—
268	C₂×D₄×C₈₉	—	4	2	no	—
269	C₂×D₄×C₈₉	—	4	8	no	—
270	C₂×D₄×C₈₉	—	4	4	no	—
271	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
272	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
273	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
274	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
275	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₈₉	—	2	1	no	—
277	C₂²×C₄×C₈₉	—	2	4	no	—
278	C₂²×C₄×C₈₉	—	2	4	no	—
279	C₂²×C₄×C₈₉	—	2	1	no	—
280	C₂²×C₄×C₈₉	—	2	1	no	—
281	C₂²×C₄×C₈₉	—	2	2	no	—
282	C₂²×C₄×C₈₉	—	2	2	no	—
283	C₂²×C₄×C₈₉	—	2	1	no	—
284	C₂²×C₄×C₈₉	—	2	2	no	—
285	C₂²×C₄×C₈₉	—	2	2	no	—
286	C₂²×C₄×C₈₉	—	2	2	no	—
287	C₂²×C₄×C₈₉	—	2	1	no	—
288	C₂²×C₄×C₈₉	—	4	8	no	—
289	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
291	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
292	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
293	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
294	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
297	Q₁₆×C₈₉	—	2	4	no	—
298	Q₁₆×C₈₉	—	4	4	no	—
299	SD₁₆×C₈₉	—	2	4	no	—
300	SD₁₆×C₈₉	—	4	4	no	—
301	M₁₆×C₈₉	—	2	2	no	—
302	M₁₆×C₈₉	—	2	2	no	—
303	M₁₆×C₈₉	—	2	4	no	—
304	M₁₆×C₈₉	—	4	4	no	—
305	C₂×C₈×C₈₉	—	4	4	no	—
306	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
307	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
308	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
309	C₄⋊C₄×C₈₉	—	2	1	no	—
310	C₄⋊C₄×C₈₉	—	2	2	no	—
311	C₄⋊C₄×C₈₉	—	2	4	no	—
312	C₄⋊C₄×C₈₉	—	2	4	no	—
313	C₄⋊C₄×C₈₉	—	2	2	no	—
314	C₄⋊C₄×C₈₉	—	2	2	no	—
315	C₄⋊C₄×C₈₉	—	2	2	no	—
316	C₄⋊C₄×C₈₉	—	2	2	no	—
317	C₄⋊C₄×C₈₉	—	2	1	no	—
318	C₄⋊C₄×C₈₉	—	2	2	no	—
319	C₄⋊C₄×C₈₉	—	2	1	no	—
320	C₄⋊C₄×C₈₉	—	2	1	no	—
321	C₄⋊C₄×C₈₉	—	2	1	no	—
322	C₄⋊C₄×C₈₉	—	2	2	no	—
323	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
324	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
325	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
326	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
327	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
328	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
329	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
330	C₂²⋊C₄×C₈₉	—	2	4	no	—
331	C₂²⋊C₄×C₈₉	—	2	4	no	—
332	C₂²⋊C₄×C₈₉	—	2	2	no	—
333	C₂²⋊C₄×C₈₉	—	2	4	no	—
334	C₂²⋊C₄×C₈₉	—	2	4	no	—
335	C₂²⋊C₄×C₈₉	—	2	1	no	—
336	C₂²⋊C₄×C₈₉	—	2	2	no	—
337	C₂²⋊C₄×C₈₉	—	2	2	no	—
338	C₂²⋊C₄×C₈₉	—	2	2	no	—
339	C₂²⋊C₄×C₈₉	—	2	1	no	—
340	C₂²⋊C₄×C₈₉	—	2	1	no	—
341	C₂²⋊C₄×C₈₉	—	2	2	no	—
342	C₂²⋊C₄×C₈₉	—	2	2	no	—
343	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
344	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
345	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
346	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
347	C₄²×C₈₉	—	2	1	no	—
348	C₄²×C₈₉	—	2	4	no	—
349	C₄²×C₈₉	—	2	4	no	—
350	C₄²×C₈₉	—	2	1	no	—
351	C₄²×C₈₉	—	2	1	no	—
352	C₄²×C₈₉	—	2	2	no	—
353	C₄²×C₈₉	—	2	2	no	—
354	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
355	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
356	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
357	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
358	C₂³×C₈₉	—	2	1	no	—
359	C₂³×C₈₉	—	2	4	no	—
360	C₂³×C₈₉	—	2	2	no	—
361	C₂³×C₈₉	—	4	2	no	—
362	C₂³×C₈₉	—	4	2	no	—
363	C₂³×C₈₉	—	4	4	no	—
364	C₂³×C₈₉	—	4	4	no	—
365	C₂³×C₈₉	—	8	2	no	—
366	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
367	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
368	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
369	Q₈×C₈₉	—	2	1	no	—
370	Q₈×C₈₉	—	2	2	no	—
371	Q₈×C₈₉	—	2	2	no	—
372	Q₈×C₈₉	—	2	2	no	—
373	Q₈×C₈₉	—	2	2	no	—
374	Q₈×C₈₉	—	4	4	no	—
375	Q₈×C₈₉	—	4	4	no	—
376	Q₈×C₈₉	—	4	2	no	—
377	Q₈×C₈₉	—	4	4	no	—
378	Q₈×C₈₉	C₂×#41	1	2	yes	—
379	D₄×C₈₉	—	2	4	no	—
380	D₄×C₈₉	—	2	2	no	—
381	D₄×C₈₉	—	2	2	no	—
382	D₄×C₈₉	—	2	2	no	—
383	D₄×C₈₉	—	2	1	no	—
384	D₄×C₈₉	—	2	2	no	—
385	D₄×C₈₉	—	4	2	no	—
386	D₄×C₈₉	—	4	4	no	—
387	D₄×C₈₉	—	4	4	no	—
388	D₄×C₈₉	—	4	4	no	—
389	D₄×C₈₉	—	4	4	no	—
390	D₄×C₈₉	—	4	4	no	—
391	D₄×C₈₉	—	4	2	no	—
392	D₄×C₈₉	—	8	1	no	—
393	D₄×C₈₉	—	8	2	no	—
394	D₄×C₈₉	C₂×#41	1	2	yes	—
395	C₂×C₄×C₈₉	—	2	4	no	—
396	C₂×C₄×C₈₉	—	2	1	no	—
397	C₂×C₄×C₈₉	—	2	4	no	—
398	C₂×C₄×C₈₉	—	2	4	no	—
399	C₂×C₄×C₈₉	—	2	4	no	—
400	C₂×C₄×C₈₉	—	2	2	no	—
401	C₂×C₄×C₈₉	—	2	2	no	—
402	C₂×C₄×C₈₉	—	2	2	no	—
403	C₂×C₄×C₈₉	—	2	2	no	—
404	C₂×C₄×C₈₉	—	2	2	no	—
405	C₂×C₄×C₈₉	—	2	2	no	—
406	C₂×C₄×C₈₉	—	2	1	no	—
407	C₂×C₄×C₈₉	—	2	1	no	—
408	C₂×C₄×C₈₉	—	2	2	no	—
409	C₂×C₄×C₈₉	—	2	4	no	—
410	C₂×C₄×C₈₉	—	2	2	no	—
411	C₂×C₄×C₈₉	—	4	1	no	—
412	C₂×C₄×C₈₉	—	4	4	no	—
413	C₂×C₄×C₈₉	—	4	4	no	—
414	C₂×C₄×C₈₉	—	4	4	no	—
415	C₂×C₄×C₈₉	—	4	2	no	—
416	C₂×C₄×C₈₉	—	4	4	no	—
417	C₂×C₄×C₈₉	—	4	2	no	—
418	C₂×C₄×C₈₉	—	4	4	no	—
419	C₂×C₄×C₈₉	—	4	2	no	—
420	C₂×C₄×C₈₉	—	8	1	no	—
421	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
423	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
424	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
429	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
430	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
431	C₈×C₈₉	—	2	2	no	—
432	C₈×C₈₉	—	2	2	no	—
433	C₈×C₈₉	—	2	4	no	—
434	C₂²×C₈₉	—	2	1	no	—
435	C₂²×C₈₉	—	2	1	no	—
436	C₂²×C₈₉	—	2	2	no	—
437	C₂²×C₈₉	—	2	2	no	—
438	C₂²×C₈₉	—	2	2	no	—
439	C₂²×C₈₉	—	2	2	no	—
440	C₂²×C₈₉	—	2	2	no	—
441	C₂²×C₈₉	—	2	2	no	—
442	C₂²×C₈₉	—	2	2	no	—
443	C₂²×C₈₉	—	4	1	no	—
444	C₂²×C₈₉	—	4	1	no	—
445	C₂²×C₈₉	—	4	2	no	—
446	C₂²×C₈₉	—	4	2	no	—
447	C₂²×C₈₉	—	4	2	no	—
448	C₂²×C₈₉	—	8	4	no	—
449	C₂²×C₈₉	—	8	8	no	—
450	C₂²×C₈₉	#546	1	2	yes	—
451	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
452	C₄×C₈₉	—	2	1	no	—
453	C₄×C₈₉	—	2	1	no	—
454	C₄×C₈₉	—	2	2	no	—
455	C₄×C₈₉	—	2	2	no	—
456	C₄×C₈₉	—	2	2	no	—
457	C₄×C₈₉	—	2	1	no	—
458	C₄×C₈₉	—	4	2	no	—
459	C₄×C₈₉	—	4	1	no	—
460	C₄×C₈₉	—	4	2	no	—
461	C₄×C₈₉	—	4	2	no	—
462	C₄×C₈₉	—	4	1	no	—
463	C₄×C₈₉	—	4	4	no	—
464	C₄×C₈₉	#546	1	2	yes	—
465	C₄×C₈₉	#575	1	2	yes	—
466	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
467	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
468	#61165	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
469	C₂×C₈₉	—	2	2	no	—
470	C₂×C₈₉	—	4	2	no	—
471	C₂×C₈₉	—	4	2	no	—
472	C₂×C₈₉	—	4	2	no	—
473	C₂×C₈₉	—	8	2	no	—
474	C₂×C₈₉	C₂×#546	1	1	yes	characteristic
475	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
476	C₂×C₈₉	#3586	1	1	yes	characteristic
477	C₂×#556	C₂×C₈₉	1	1	yes	characteristic, complemented
478	D₄×#41	C₂×C₈₉	1	1	yes	characteristic
479	#3328	C₂×C₈₉	1	2	yes	complemented
480	#3324	C₂×C₈₉	1	2	yes	complemented
481	#3313	C₂×C₈₉	1	4	yes	complemented
482	#3311	C₂×C₈₉	1	4	yes	complemented
483	#3304	C₂×C₈₉	1	2	yes	complemented
484	#3302	C₂×C₈₉	1	2	yes	complemented
485	#3141	C₂×C₈₉	1	1	yes	characteristic, complemented
486	#3093	C₂×C₈₉	1	2	yes	complemented
487	#3079	C₂×C₈₉	1	1	yes	characteristic, complemented
488	#3056	C₂×C₈₉	1	2	yes	complemented
489	#3037	C₂×C₈₉	1	1	yes	characteristic, complemented
490	#3007	C₂×C₈₉	1	2	yes	complemented
491	C₄×#137	C₂×C₈₉	1	1	yes	characteristic, complemented
492	D₄×M₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
493	#2896	C₂×C₈₉	1	2	yes	complemented
494	C₈₉	#61165	1	1	yes	characteristic, direct product factor, Sylow
495	C₂²×#41	C₂²×C₈₉	1	2	yes	—
496	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
497	C₂×#137	C₂²×C₈₉	1	2	yes	complemented
498	C₂²×M₁₆	C₂²×C₈₉	1	2	yes	complemented
499	#556	—	2	1	no	—
500	#556	—	2	2	no	—
501	#556	—	2	1	no	—
502	#556	C₂²×C₈₉	1	2	yes	—
503	#556	C₂²×C₈₉	1	2	yes	complemented
504	#556	C₂²×C₈₉	1	4	yes	complemented
505	#550	C₂²×C₈₉	1	1	yes	characteristic
506	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
507	#548	C₂²×C₈₉	1	2	yes	—
508	#547	—	2	1	no	—
509	#547	C₂²×C₈₉	1	1	yes	characteristic
510	#546	—	2	2	no	—
511	#546	C₂²×C₈₉	1	2	yes	—
512	D₄²	—	2	1	no	—
513	D₄²	C₂²×C₈₉	1	1	yes	characteristic
514	#532	—	2	1	no	—
515	#532	C₂²×C₈₉	1	1	yes	characteristic
516	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
517	C₂×#126	—	2	2	no	—
518	C₂×#124	—	2	1	no	—
519	#525	—	2	2	no	—
520	#525	C₂²×C₈₉	1	2	yes	—
521	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
522	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
523	C₂×C₄×Q₈	—	2	1	no	—
524	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
525	C₂×C₄×D₄	—	2	1	no	—
526	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
527	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
528	#489	C₂²×C₈₉	1	4	yes	complemented
529	#487	C₂²×C₈₉	1	2	yes	complemented
530	#486	C₂²×C₈₉	1	2	yes	complemented
531	#485	C₂²×C₈₉	1	4	yes	complemented
532	#485	C₂²×C₈₉	1	4	yes	complemented
533	#482	C₂²×C₈₉	1	4	yes	complemented
534	#482	C₂²×C₈₉	1	4	yes	complemented
535	#477	C₂²×C₈₉	1	2	yes	complemented
536	#476	C₂²×C₈₉	1	2	yes	complemented
537	#475	C₂²×C₈₉	1	2	yes	complemented
538	#474	C₂²×C₈₉	1	2	yes	complemented
539	#470	C₂²×C₈₉	1	4	yes	complemented
540	#468	C₂²×C₈₉	1	4	yes	complemented
541	#467	C₂²×C₈₉	1	4	yes	complemented
542	#465	C₂²×C₈₉	1	4	yes	complemented
543	#464	C₂²×C₈₉	1	4	yes	complemented
544	#462	C₂²×C₈₉	1	2	yes	complemented
545	#460	C₂²×C₈₉	1	2	yes	complemented
546	#452	C₂²×C₈₉	1	4	yes	complemented
547	#452	C₂²×C₈₉	1	4	yes	complemented
548	#451	C₂²×C₈₉	1	4	yes	complemented
549	#450	C₂²×C₈₉	1	4	yes	complemented
550	#441	C₂²×C₈₉	1	2	yes	complemented
551	#440	C₂²×C₈₉	1	2	yes	complemented
552	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
553	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
554	#436	C₂²×C₈₉	1	2	yes	—
555	#435	C₂²×C₈₉	1	4	yes	complemented
556	C₈×D₄	C₂²×C₈₉	1	2	yes	complemented
557	#428	C₂²×C₈₉	1	2	yes	complemented
558	#428	C₂²×C₈₉	1	1	yes	characteristic, complemented
559	#423	C₂²×C₈₉	1	1	yes	characteristic, complemented
560	#419	C₂²×C₈₉	1	4	yes	complemented
561	#419	C₂²×C₈₉	1	1	yes	characteristic, complemented
562	#418	C₂²×C₈₉	1	4	yes	complemented
563	#417	C₂²×C₈₉	1	2	yes	—
564	#417	C₂²×C₈₉	1	1	yes	characteristic
565	#417	C₂²×C₈₉	1	2	yes	complemented
566	#417	C₂²×C₈₉	1	2	yes	complemented
567	#417	C₂²×C₈₉	1	2	yes	complemented
568	#416	C₂²×C₈₉	1	4	yes	complemented
569	#416	C₂²×C₈₉	1	4	yes	complemented
570	#407	C₂²×C₈₉	1	2	yes	complemented
571	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
572	C₂×#41	—	2	2	no	—
573	C₂×#41	—	2	2	no	—
574	C₂×#41	—	2	8	no	—
575	C₂×#41	—	4	4	no	—
576	C₂×#41	C₂³×C₈₉	1	2	yes	—
577	C₂×#41	C₂³×C₈₉	1	2	yes	—
578	C₂×#41	C₂³×C₈₉	1	2	yes	—
579	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
580	C₂²×Q₈	—	2	1	no	—
581	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
582	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
583	C₂²×D₄	—	2	2	no	—
584	C₂²×D₄	—	2	1	no	—
585	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
586	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
587	C₂³×C₄	—	2	2	no	—
588	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
589	#137	—	2	4	no	—
590	#137	—	4	4	no	—
591	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
592	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
593	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
594	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
595	C₂×M₁₆	—	4	4	no	—
596	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
597	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
598	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
599	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
600	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
601	C₄⋊Q₈	—	2	1	no	—
602	C₄⋊Q₈	—	2	1	no	—
603	C₄⋊Q₈	—	2	1	no	—
604	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
605	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
606	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
607	#127	—	2	1	no	—
608	#127	C₂³×C₈₉	1	1	yes	characteristic
609	#126	—	2	4	no	—
610	#126	—	2	4	no	—
611	#126	—	2	4	no	—
612	#126	—	2	4	no	—
613	#124	—	2	2	no	—
614	#124	—	2	2	no	—
615	#124	—	2	4	no	—
616	#124	—	2	2	no	—
617	#124	C₂³×C₈₉	1	2	yes	—
618	#123	—	2	2	no	—
619	#123	—	2	2	no	—
620	#123	—	2	2	no	—
621	C₂²⋊Q₈	—	2	2	no	—
622	C₂²⋊Q₈	—	2	2	no	—
623	C₂²⋊Q₈	—	2	2	no	—
624	C₂²⋊Q₈	—	2	2	no	—
625	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
626	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
627	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
628	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
629	#121	—	2	2	no	—
630	#121	—	2	1	no	—
631	#121	—	2	1	no	—
632	#121	—	2	1	no	—
633	#121	—	2	1	no	—
634	#121	—	2	2	no	—
635	#121	—	2	2	no	—
636	#121	C₂³×C₈₉	1	2	yes	—
637	#121	C₂³×C₈₉	1	2	yes	—
638	#120	—	2	2	no	—
639	#120	—	2	2	no	—
640	#120	—	2	2	no	—
641	C₄×Q₈	—	2	2	no	—
642	C₄×Q₈	—	2	2	no	—
643	C₄×Q₈	—	2	4	no	—
644	C₄×Q₈	—	2	1	no	—
645	C₄×Q₈	—	2	1	no	—
646	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
647	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
648	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
649	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
650	C₄×D₄	—	2	1	no	—
651	C₄×D₄	—	2	2	no	—
652	C₄×D₄	—	2	1	no	—
653	C₄×D₄	—	2	1	no	—
654	C₄×D₄	—	2	2	no	—
655	C₄×D₄	—	2	1	no	—
656	C₄×D₄	—	2	2	no	—
657	C₄×D₄	—	2	1	no	—
658	C₄×D₄	—	2	1	no	—
659	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
660	C₄×D₄	D₄×C₈₉	1	2	yes	—
661	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
662	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
663	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
664	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
665	C₄×D₄	C₂³×C₈₉	1	2	yes	—
666	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
667	#117	—	2	2	no	—
668	#117	—	2	2	no	—
669	#117	—	2	1	no	—
670	#117	C₂³×C₈₉	1	4	yes	—
671	#117	C₂³×C₈₉	1	4	yes	—
672	#117	C₂³×C₈₉	1	1	yes	characteristic
673	C₂×C₄⋊C₄	—	2	2	no	—
674	C₂×C₄⋊C₄	—	2	1	no	—
675	C₂×C₄⋊C₄	—	2	1	no	—
676	C₂×C₄⋊C₄	—	2	1	no	—
677	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
678	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
679	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
680	C₂×C₂²⋊C₄	—	2	2	no	—
681	C₂×C₂²⋊C₄	—	2	2	no	—
682	C₂×C₂²⋊C₄	—	2	2	no	—
683	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
684	C₂×C₄²	—	2	2	no	—
685	C₂×C₄²	—	2	1	no	—
686	C₂×C₄²	—	2	1	no	—
687	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
688	#107	C₂³×C₈₉	1	2	yes	—
689	#107	C₂³×C₈₉	1	4	yes	—
690	#106	C₂³×C₈₉	1	2	yes	—
691	#106	C₂³×C₈₉	1	4	yes	—
692	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
693	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
694	#103	C₂³×C₈₉	1	2	yes	—
695	#103	C₂³×C₈₉	1	4	yes	—
696	#103	C₂³×C₈₉	1	4	yes	—
697	#103	C₂³×C₈₉	1	4	yes	—
698	#103	C₂³×C₈₉	1	4	yes	—
699	#103	C₂³×C₈₉	1	2	yes	—
700	#103	C₂³×C₈₉	1	2	yes	—
701	#102	C₂³×C₈₉	1	2	yes	—
702	#102	C₂³×C₈₉	1	4	yes	—
703	#102	C₂³×C₈₉	1	4	yes	—
704	#102	C₂³×C₈₉	1	4	yes	—
705	#102	C₂³×C₈₉	1	4	yes	—
706	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
707	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
708	#97	C₂³×C₈₉	1	2	yes	—
709	C₄×C₈	C₂³×C₈₉	1	2	yes	—
710	C₂⁴	—	2	2	no	—
711	C₂⁴	C₂×D₄×C₈₉	1	2	yes	—
712	#41	—	2	2	no	—
713	#41	—	2	4	no	—
714	#41	—	2	4	no	—
715	#41	—	2	4	no	—
716	#41	—	2	4	no	—
717	#41	—	4	8	no	—
718	#41	—	4	2	no	—
719	#41	—	4	2	no	—
720	#41	—	4	8	no	—
721	#41	#41×C₈₉	1	4	yes	—
722	C₂×Q₈	—	2	1	no	—
723	C₂×Q₈	—	2	2	no	—
724	C₂×Q₈	—	2	2	no	—
725	C₂×Q₈	—	2	2	no	—
726	C₂×Q₈	—	2	4	no	—
727	C₂×Q₈	—	2	2	no	—
728	C₂×Q₈	—	2	2	no	—
729	C₂×Q₈	—	4	2	no	—
730	C₂×Q₈	—	4	4	no	—
731	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
732	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
733	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
734	C₂×D₄	—	2	1	no	—
735	C₂×D₄	—	2	4	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	2	no	—
739	C₂×D₄	—	2	2	no	—
740	C₂×D₄	—	2	2	no	—
741	C₂×D₄	—	2	1	no	—
742	C₂×D₄	—	2	2	no	—
743	C₂×D₄	—	2	1	no	—
744	C₂×D₄	—	4	2	no	—
745	C₂×D₄	—	4	2	no	—
746	C₂×D₄	—	4	8	no	—
747	C₂×D₄	—	4	4	no	—
748	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
749	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
750	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
751	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
752	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
753	C₂²×C₄	—	2	1	no	—
754	C₂²×C₄	—	2	4	no	—
755	C₂²×C₄	—	2	4	no	—
756	C₂²×C₄	—	2	1	no	—
757	C₂²×C₄	—	2	1	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	1	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	1	no	—
765	C₂²×C₄	—	4	8	no	—
766	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
767	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
768	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
769	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
770	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
774	Q₁₆	—	2	4	no	—
775	Q₁₆	—	4	4	no	—
776	SD₁₆	—	2	4	no	—
777	SD₁₆	—	4	4	no	—
778	M₁₆	—	2	2	no	—
779	M₁₆	—	2	2	no	—
780	M₁₆	—	2	4	no	—
781	M₁₆	—	4	4	no	—
782	C₂×C₈	—	4	4	no	—
783	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
784	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
785	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
786	C₄⋊C₄	—	2	1	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	4	no	—
789	C₄⋊C₄	—	2	4	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	1	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	1	no	—
797	C₄⋊C₄	—	2	1	no	—
798	C₄⋊C₄	—	2	1	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
801	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
802	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
803	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
804	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
805	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
806	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
807	C₂²⋊C₄	—	2	4	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	4	no	—
812	C₂²⋊C₄	—	2	1	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	1	no	—
817	C₂²⋊C₄	—	2	1	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
821	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
822	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
823	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
824	C₄²	—	2	1	no	—
825	C₄²	—	2	4	no	—
826	C₄²	—	2	4	no	—
827	C₄²	—	2	1	no	—
828	C₄²	—	2	1	no	—
829	C₄²	—	2	2	no	—
830	C₄²	—	2	2	no	—
831	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
832	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
833	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
834	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
835	C₂³	—	2	1	no	—
836	C₂³	—	2	4	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	4	2	no	—
839	C₂³	—	4	2	no	—
840	C₂³	—	4	4	no	—
841	C₂³	—	4	4	no	—
842	C₂³	—	8	2	no	—
843	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
844	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
845	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
846	Q₈	—	2	1	no	—
847	Q₈	—	2	2	no	—
848	Q₈	—	2	2	no	—
849	Q₈	—	2	2	no	—
850	Q₈	—	2	2	no	—
851	Q₈	—	4	4	no	—
852	Q₈	—	4	4	no	—
853	Q₈	—	4	2	no	—
854	Q₈	—	4	4	no	—
855	Q₈	C₂×#41×C₈₉	1	2	yes	—
856	D₄	—	2	4	no	—
857	D₄	—	2	2	no	—
858	D₄	—	2	2	no	—
859	D₄	—	2	2	no	—
860	D₄	—	2	1	no	—
861	D₄	—	2	2	no	—
862	D₄	—	4	2	no	—
863	D₄	—	4	4	no	—
864	D₄	—	4	4	no	—
865	D₄	—	4	4	no	—
866	D₄	—	4	4	no	—
867	D₄	—	4	4	no	—
868	D₄	—	4	2	no	—
869	D₄	—	8	1	no	—
870	D₄	—	8	2	no	—
871	D₄	C₂×#41×C₈₉	1	2	yes	—
872	C₂×C₄	—	2	4	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	4	no	—
875	C₂×C₄	—	2	4	no	—
876	C₂×C₄	—	2	4	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	4	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	4	1	no	—
889	C₂×C₄	—	4	4	no	—
890	C₂×C₄	—	4	4	no	—
891	C₂×C₄	—	4	4	no	—
892	C₂×C₄	—	4	2	no	—
893	C₂×C₄	—	4	4	no	—
894	C₂×C₄	—	4	2	no	—
895	C₂×C₄	—	4	4	no	—
896	C₂×C₄	—	4	2	no	—
897	C₂×C₄	—	8	1	no	—
898	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
899	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
900	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
901	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
902	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
903	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
904	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
905	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
906	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
907	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
908	C₈	—	2	2	no	—
909	C₈	—	2	2	no	—
910	C₈	—	2	4	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	4	1	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	8	4	no	—
926	C₂²	—	8	8	no	—
927	C₂²	#546×C₈₉	1	2	yes	—
928	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
929	C₄	—	2	1	no	—
930	C₄	—	2	1	no	—
931	C₄	—	2	1	no	—
932	C₄	—	2	2	no	—
933	C₄	—	2	2	no	—
934	C₄	—	2	2	no	—
935	C₄	—	4	1	no	—
936	C₄	—	4	4	no	—
937	C₄	—	4	2	no	—
938	C₄	—	4	1	no	—
939	C₄	—	4	2	no	—
940	C₄	—	4	2	no	—
941	C₄	#546×C₈₉	1	2	yes	—
942	C₄	#575×C₈₉	1	2	yes	—
943	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
944	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
945	C₂	—	2	2	no	—
946	C₂	—	4	2	no	—
947	C₂	—	4	2	no	—
948	C₂	—	4	2	no	—
949	C₂	—	8	2	no	—
950	C₂	C₂×#546×C₈₉	1	1	yes	characteristic
951	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
952	C₂	C₈₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	D₄×#41×C₈₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×C₄×D₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#556×C₈₉	C₂	semidirect
3. C₈₉×#3328	C₂	semidirect
4. C₈₉×#3324	C₂	semidirect
5. C₈₉×#3313	C₂	semidirect
6. C₈₉×#3311	C₂	semidirect
7. C₈₉×#3304	C₂	semidirect
8. C₈₉×#3302	C₂	semidirect
9. C₈₉×#3141	C₂	semidirect
10. C₈₉×#3093	C₂	semidirect
11. C₈₉×#3079	C₂	semidirect
12. C₈₉×#3056	C₂	semidirect
13. C₈₉×#3037	C₂	semidirect
14. C₈₉×#3007	C₂	semidirect
15. C₄×#137×C₈₉	C₂	semidirect
16. D₄×M₁₆×C₈₉	C₂	semidirect
17. C₈₉×#2896	C₂	semidirect
20. C₂×#137×C₈₉	C₂²	semidirect
21. C₂²×M₁₆×C₈₉	C₂²	semidirect
26. #556×C₈₉	C₂²	semidirect
27. #556×C₈₉	C₂²	semidirect
39. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
44. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
47. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
50. C₂×#117×C₈₉	C₂²	semidirect
51. #489×C₈₉	C₂²	semidirect
52. #487×C₈₉	C₂²	semidirect
53. #486×C₈₉	C₂²	semidirect
54. #485×C₈₉	C₂²	semidirect
55. #485×C₈₉	C₂²	semidirect
56. #482×C₈₉	C₂²	semidirect
57. #482×C₈₉	C₂²	semidirect
58. #477×C₈₉	C₂²	semidirect
59. #476×C₈₉	C₂²	semidirect
60. #475×C₈₉	C₂²	semidirect
61. #474×C₈₉	C₂²	semidirect
62. #470×C₈₉	C₂²	semidirect
63. #468×C₈₉	C₂²	semidirect
64. #467×C₈₉	C₂²	semidirect
65. #465×C₈₉	C₂²	semidirect
66. #464×C₈₉	C₂²	semidirect
67. #462×C₈₉	C₂²	semidirect
68. #460×C₈₉	C₂²	semidirect
69. #452×C₈₉	C₂²	semidirect
70. #452×C₈₉	C₂²	semidirect
71. #451×C₈₉	C₂²	semidirect
72. #450×C₈₉	C₂²	semidirect
73. #441×C₈₉	C₂²	semidirect
74. #440×C₈₉	C₂²	semidirect
75. C₄×Q₁₆×C₈₉	C₂²	semidirect
76. C₄×SD₁₆×C₈₉	C₂²	semidirect
78. #435×C₈₉	C₂²	semidirect
79. C₈×D₄×C₈₉	C₂²	semidirect
80. #428×C₈₉	C₂²	semidirect
81. #428×C₈₉	C₂²	semidirect
82. #423×C₈₉	C₂²	semidirect
83. #419×C₈₉	C₂²	semidirect
84. #419×C₈₉	C₂²	semidirect
85. #418×C₈₉	C₂²	semidirect
88. #417×C₈₉	C₂²	semidirect
89. #417×C₈₉	C₂²	semidirect
90. #417×C₈₉	C₂²	semidirect
91. #416×C₈₉	C₂²	semidirect
92. #416×C₈₉	C₂²	semidirect
93. #407×C₈₉	C₂²	semidirect
94. C₄×M₁₆×C₈₉	C₂²	semidirect
468. #61165	C₈₉	direct (N × H)
477. C₂×#556	C₂×C₈₉	semidirect
479. #3328	C₂×C₈₉	semidirect
480. #3324	C₂×C₈₉	semidirect
481. #3313	C₂×C₈₉	semidirect
482. #3311	C₂×C₈₉	semidirect
483. #3304	C₂×C₈₉	semidirect
484. #3302	C₂×C₈₉	semidirect
485. #3141	C₂×C₈₉	semidirect
486. #3093	C₂×C₈₉	semidirect
487. #3079	C₂×C₈₉	semidirect
488. #3056	C₂×C₈₉	semidirect
489. #3037	C₂×C₈₉	semidirect
490. #3007	C₂×C₈₉	semidirect
491. C₄×#137	C₂×C₈₉	semidirect
492. D₄×M₁₆	C₂×C₈₉	semidirect
493. #2896	C₂×C₈₉	semidirect
494. C₈₉	#61165	direct (N × H)
497. C₂×#137	C₂²×C₈₉	semidirect
498. C₂²×M₁₆	C₂²×C₈₉	semidirect
503. #556	C₂²×C₈₉	semidirect
504. #556	C₂²×C₈₉	semidirect
516. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
521. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
524. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
527. C₂×#117	C₂²×C₈₉	semidirect
528. #489	C₂²×C₈₉	semidirect
529. #487	C₂²×C₈₉	semidirect
530. #486	C₂²×C₈₉	semidirect
531. #485	C₂²×C₈₉	semidirect
532. #485	C₂²×C₈₉	semidirect
533. #482	C₂²×C₈₉	semidirect
534. #482	C₂²×C₈₉	semidirect
535. #477	C₂²×C₈₉	semidirect
536. #476	C₂²×C₈₉	semidirect
537. #475	C₂²×C₈₉	semidirect
538. #474	C₂²×C₈₉	semidirect
539. #470	C₂²×C₈₉	semidirect
540. #468	C₂²×C₈₉	semidirect
541. #467	C₂²×C₈₉	semidirect
542. #465	C₂²×C₈₉	semidirect
543. #464	C₂²×C₈₉	semidirect
544. #462	C₂²×C₈₉	semidirect
545. #460	C₂²×C₈₉	semidirect
546. #452	C₂²×C₈₉	semidirect
547. #452	C₂²×C₈₉	semidirect
548. #451	C₂²×C₈₉	semidirect
549. #450	C₂²×C₈₉	semidirect
550. #441	C₂²×C₈₉	semidirect
551. #440	C₂²×C₈₉	semidirect
552. C₄×Q₁₆	C₂²×C₈₉	semidirect
553. C₄×SD₁₆	C₂²×C₈₉	semidirect
555. #435	C₂²×C₈₉	semidirect
556. C₈×D₄	C₂²×C₈₉	semidirect
557. #428	C₂²×C₈₉	semidirect
558. #428	C₂²×C₈₉	semidirect
559. #423	C₂²×C₈₉	semidirect
560. #419	C₂²×C₈₉	semidirect
561. #419	C₂²×C₈₉	semidirect
562. #418	C₂²×C₈₉	semidirect
565. #417	C₂²×C₈₉	semidirect
566. #417	C₂²×C₈₉	semidirect
567. #417	C₂²×C₈₉	semidirect
568. #416	C₂²×C₈₉	semidirect
569. #416	C₂²×C₈₉	semidirect
570. #407	C₂²×C₈₉	semidirect
571. 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
C₂×#556×C₈₉	2
D₄×#41×C₈₉	2
C₈₉×#3328	2
C₈₉×#3324	2
C₈₉×#3313	2
C₈₉×#3311	2
C₈₉×#3304	2
C₈₉×#3302	2
C₈₉×#3141	2
C₈₉×#3093	2
C₈₉×#3079	2
C₈₉×#3056	2
C₈₉×#3037	2
C₈₉×#3007	2
C₄×#137×C₈₉	2
D₄×M₁₆×C₈₉	2
C₈₉×#2896	2
#61165	89

Subgroups — C89×#61165 #36439013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61165 #36439013