Subgroups — C₈₉×#60923 #36438771

Order 22784.

1812 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3460	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3260	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3258	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3254	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3252	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3248	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3246	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3082	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3077	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3063	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3057	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3043	C₂	1	2	yes	maximal, complemented
15	C₈₉×#3039	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#461×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2906	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#137×C₈₉	C₂²	1	2	yes	—
19	C₂²×SD₁₆×C₈₉	C₂²	1	2	yes	—
20	C₂×#131×C₈₉	C₂²	1	2	yes	—
21	#557×C₈₉	—	2	1	no	—
22	#557×C₈₉	—	2	1	no	—
23	#556×C₈₉	—	2	1	no	—
24	#556×C₈₉	—	2	1	no	—
25	#552×C₈₉	—	2	2	no	—
26	#552×C₈₉	—	2	2	no	—
27	#544×C₈₉	C₂²	1	1	yes	characteristic
28	#542×C₈₉	—	2	1	no	—
29	#542×C₈₉	C₂²	1	2	yes	—
30	#541×C₈₉	C₂²	1	4	yes	complemented
31	#540×C₈₉	—	2	1	no	—
32	#540×C₈₉	C₂²	1	2	yes	—
33	#538×C₈₉	—	2	2	no	—
34	#537×C₈₉	C₂²	1	1	yes	characteristic
35	#536×C₈₉	C₂²	1	2	yes	—
36	#535×C₈₉	C₂²	1	1	yes	characteristic
37	#535×C₈₉	C₂²	1	1	yes	characteristic
38	#533×C₈₉	C₂²	1	1	yes	characteristic
39	#533×C₈₉	C₂²	1	2	yes	complemented
40	#533×C₈₉	C₂²	1	2	yes	complemented
41	#532×C₈₉	—	2	1	no	—
42	#532×C₈₉	C₂²	1	2	yes	—
43	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
44	#529×C₈₉	—	2	1	no	—
45	#529×C₈₉	C₂²	1	2	yes	—
46	#525×C₈₉	—	2	2	no	—
47	#519×C₈₉	C₂²	1	2	yes	—
48	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
49	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
51	#479×C₈₉	C₂²	1	2	yes	complemented
52	#479×C₈₉	C₂²	1	4	yes	complemented
53	#479×C₈₉	C₂²	1	4	yes	complemented
54	#478×C₈₉	C₂²	1	4	yes	—
55	#478×C₈₉	C₂²	1	2	yes	complemented
56	#477×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	#477×C₈₉	C₂²	1	4	yes	complemented
58	#476×C₈₉	C₂²	1	2	yes	—
59	#476×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#475×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	#475×C₈₉	C₂²	1	4	yes	complemented
62	#474×C₈₉	C₂²	1	2	yes	—
63	#474×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	#470×C₈₉	C₂²	1	4	yes	complemented
65	#468×C₈₉	C₂²	1	4	yes	—
66	#468×C₈₉	C₂²	1	4	yes	—
67	#468×C₈₉	C₂²	1	4	yes	complemented
68	#467×C₈₉	C₂²	1	4	yes	complemented
69	#465×C₈₉	C₂²	1	4	yes	—
70	#465×C₈₉	C₂²	1	4	yes	—
71	#465×C₈₉	C₂²	1	4	yes	complemented
72	#464×C₈₉	C₂²	1	4	yes	—
73	#464×C₈₉	C₂²	1	4	yes	—
74	#462×C₈₉	C₂²	1	2	yes	complemented
75	#462×C₈₉	C₂²	1	2	yes	complemented
76	#461×C₈₉	C₂²	1	2	yes	—
77	#461×C₈₉	C₂²	1	2	yes	—
78	#461×C₈₉	C₂²	1	4	yes	—
79	#461×C₈₉	C₂²	1	2	yes	complemented
80	#461×C₈₉	C₂²	1	2	yes	complemented
81	#460×C₈₉	C₂²	1	4	yes	—
82	#460×C₈₉	C₂²	1	4	yes	—
83	#428×C₈₉	C₂²	1	2	yes	—
84	#427×C₈₉	C₂²	1	2	yes	—
85	#424×C₈₉	C₂²	1	2	yes	—
86	#424×C₈₉	C₂²	1	4	yes	complemented
87	#423×C₈₉	C₂²	1	1	yes	characteristic
88	#423×C₈₉	C₂²	1	2	yes	complemented
89	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
90	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	complemented
91	#419×C₈₉	C₂²	1	2	yes	—
92	#418×C₈₉	C₂²	1	2	yes	—
93	#416×C₈₉	C₂²	1	2	yes	—
94	C₂×#103×C₈₉	C₂²	1	2	yes	—
95	C₂×#41×C₈₉	—	2	2	no	—
96	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
97	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
99	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₈₉	—	2	1	no	—
101	#137×C₈₉	—	4	4	no	—
102	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
103	C₂×SD₁₆×C₈₉	—	4	4	no	—
104	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
106	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
107	#131×C₈₉	—	4	4	no	—
108	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
109	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
110	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
111	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
112	C₄⋊Q₈×C₈₉	—	2	2	no	—
113	C₄⋊Q₈×C₈₉	—	2	1	no	—
114	C₄⋊Q₈×C₈₉	—	2	1	no	—
115	C₄⋊Q₈×C₈₉	—	2	1	no	—
116	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
117	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
118	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
119	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
120	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
121	#127×C₈₉	—	2	1	no	—
122	#127×C₈₉	C₂³	1	2	yes	—
123	#126×C₈₉	—	2	2	no	—
124	#126×C₈₉	—	2	4	no	—
125	#126×C₈₉	—	2	4	no	—
126	#126×C₈₉	—	2	2	no	—
127	#125×C₈₉	—	2	1	no	—
128	#125×C₈₉	—	2	4	no	—
129	#125×C₈₉	—	2	4	no	—
130	#125×C₈₉	—	2	2	no	—
131	#125×C₈₉	—	2	2	no	—
132	#125×C₈₉	C₂³	1	2	yes	—
133	#125×C₈₉	C₂³	1	2	yes	—
134	#124×C₈₉	—	2	1	no	—
135	#124×C₈₉	—	2	2	no	—
136	#124×C₈₉	—	2	2	no	—
137	#124×C₈₉	—	2	2	no	—
138	#124×C₈₉	C₂³	1	2	yes	—
139	#123×C₈₉	—	2	4	no	—
140	#123×C₈₉	—	2	2	no	—
141	#123×C₈₉	—	2	2	no	—
142	#123×C₈₉	—	2	2	no	—
143	#123×C₈₉	—	2	2	no	—
144	C₂²⋊Q₈×C₈₉	—	2	1	no	—
145	C₂²⋊Q₈×C₈₉	—	2	1	no	—
146	C₂²⋊Q₈×C₈₉	—	2	1	no	—
147	C₂²⋊Q₈×C₈₉	—	2	2	no	—
148	C₂²⋊Q₈×C₈₉	—	2	2	no	—
149	C₂²⋊Q₈×C₈₉	—	2	2	no	—
150	C₂²⋊Q₈×C₈₉	—	2	2	no	—
151	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
152	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
153	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
154	#121×C₈₉	—	2	2	no	—
155	#121×C₈₉	—	2	1	no	—
156	#121×C₈₉	—	2	2	no	—
157	#121×C₈₉	—	2	1	no	—
158	#121×C₈₉	—	2	1	no	—
159	#121×C₈₉	—	2	2	no	—
160	#121×C₈₉	—	2	2	no	—
161	#121×C₈₉	C₂³	1	2	yes	—
162	#121×C₈₉	C₂³	1	2	yes	—
163	#121×C₈₉	C₂³	1	2	yes	—
164	#120×C₈₉	—	2	2	no	—
165	#120×C₈₉	—	2	2	no	—
166	C₄×Q₈×C₈₉	—	2	2	no	—
167	C₄×Q₈×C₈₉	—	2	2	no	—
168	C₄×Q₈×C₈₉	—	2	1	no	—
169	C₄×Q₈×C₈₉	—	2	1	no	—
170	C₄×Q₈×C₈₉	—	2	2	no	—
171	C₄×Q₈×C₈₉	—	2	2	no	—
172	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
173	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
174	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
175	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
176	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
177	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₈₉	—	2	1	no	—
179	C₄×D₄×C₈₉	—	2	1	no	—
180	C₄×D₄×C₈₉	—	2	2	no	—
181	C₄×D₄×C₈₉	—	2	1	no	—
182	C₄×D₄×C₈₉	—	2	1	no	—
183	C₄×D₄×C₈₉	—	2	2	no	—
184	C₄×D₄×C₈₉	D₄	1	2	yes	—
185	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
186	C₄×D₄×C₈₉	D₄	1	2	yes	—
187	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
188	C₄×D₄×C₈₉	C₂³	1	2	yes	—
189	C₄×D₄×C₈₉	C₂³	1	2	yes	—
190	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
192	#117×C₈₉	—	2	2	no	—
193	#117×C₈₉	—	2	2	no	—
194	#117×C₈₉	—	2	4	no	—
195	#117×C₈₉	—	2	1	no	—
196	#117×C₈₉	—	2	2	no	—
197	#117×C₈₉	C₂³	1	2	yes	—
198	#117×C₈₉	C₂³	1	1	yes	characteristic
199	#117×C₈₉	C₂³	1	1	yes	characteristic
200	#117×C₈₉	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
202	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
203	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
205	C₂×C₄²×C₈₉	—	2	1	no	—
206	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
208	#107×C₈₉	C₂³	1	2	yes	—
209	#107×C₈₉	C₂³	1	2	yes	—
210	#107×C₈₉	C₂³	1	4	yes	—
211	#106×C₈₉	C₂³	1	2	yes	—
212	#106×C₈₉	C₂³	1	2	yes	—
213	#106×C₈₉	C₂³	1	4	yes	—
214	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
215	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
216	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
217	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
218	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
219	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
220	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
221	#103×C₈₉	C₂³	1	4	yes	—
222	#103×C₈₉	C₂³	1	4	yes	—
223	#103×C₈₉	C₂³	1	2	yes	—
224	#103×C₈₉	C₂³	1	2	yes	—
225	#103×C₈₉	C₂³	1	4	yes	—
226	#103×C₈₉	C₂³	1	4	yes	—
227	#102×C₈₉	C₂³	1	2	yes	—
228	#102×C₈₉	C₂³	1	2	yes	—
229	#102×C₈₉	C₂³	1	4	yes	—
230	#102×C₈₉	C₂³	1	4	yes	—
231	C₂⁴×C₈₉	—	2	1	no	—
232	#41×C₈₉	—	2	2	no	—
233	#41×C₈₉	—	2	2	no	—
234	#41×C₈₉	—	2	2	no	—
235	#41×C₈₉	—	2	2	no	—
236	#41×C₈₉	—	8	4	no	—
237	C₂×Q₈×C₈₉	—	2	1	no	—
238	C₂×Q₈×C₈₉	—	2	1	no	—
239	C₂×Q₈×C₈₉	—	2	2	no	—
240	C₂×Q₈×C₈₉	—	2	2	no	—
241	C₂×Q₈×C₈₉	—	2	4	no	—
242	C₂×Q₈×C₈₉	—	2	4	no	—
243	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
245	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
246	C₂×D₄×C₈₉	—	2	1	no	—
247	C₂×D₄×C₈₉	—	2	2	no	—
248	C₂×D₄×C₈₉	—	2	2	no	—
249	C₂×D₄×C₈₉	—	2	2	no	—
250	C₂×D₄×C₈₉	—	2	1	no	—
251	C₂×D₄×C₈₉	—	2	2	no	—
252	C₂×D₄×C₈₉	—	2	2	no	—
253	C₂×D₄×C₈₉	—	2	2	no	—
254	C₂×D₄×C₈₉	—	2	2	no	—
255	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
256	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
257	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
258	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₈₉	—	2	2	no	—
260	C₂²×C₄×C₈₉	—	2	1	no	—
261	C₂²×C₄×C₈₉	—	2	1	no	—
262	C₂²×C₄×C₈₉	—	2	1	no	—
263	C₂²×C₄×C₈₉	—	2	2	no	—
264	C₂²×C₄×C₈₉	—	2	1	no	—
265	C₂²×C₄×C₈₉	—	2	2	no	—
266	C₂²×C₄×C₈₉	—	8	2	no	—
267	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
271	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
273	Q₁₆×C₈₉	—	4	4	no	—
274	SD₁₆×C₈₉	—	4	4	no	—
275	SD₁₆×C₈₉	—	4	4	no	—
276	SD₁₆×C₈₉	—	4	4	no	—
277	M₁₆×C₈₉	—	2	4	no	—
278	M₁₆×C₈₉	—	4	4	no	—
279	C₂×C₈×C₈₉	—	2	4	no	—
280	C₂×C₈×C₈₉	—	4	4	no	—
281	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
282	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
283	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₈₉	—	2	2	no	—
285	C₄⋊C₄×C₈₉	—	2	2	no	—
286	C₄⋊C₄×C₈₉	—	2	2	no	—
287	C₄⋊C₄×C₈₉	—	2	2	no	—
288	C₄⋊C₄×C₈₉	—	2	1	no	—
289	C₄⋊C₄×C₈₉	—	2	1	no	—
290	C₄⋊C₄×C₈₉	—	2	1	no	—
291	C₄⋊C₄×C₈₉	—	2	1	no	—
292	C₄⋊C₄×C₈₉	—	2	1	no	—
293	C₄⋊C₄×C₈₉	—	2	4	no	—
294	C₄⋊C₄×C₈₉	—	2	4	no	—
295	C₄⋊C₄×C₈₉	—	2	2	no	—
296	C₄⋊C₄×C₈₉	—	2	2	no	—
297	C₄⋊C₄×C₈₉	—	2	2	no	—
298	C₄⋊C₄×C₈₉	—	2	2	no	—
299	C₄⋊C₄×C₈₉	—	2	2	no	—
300	C₄⋊C₄×C₈₉	—	2	2	no	—
301	C₄⋊C₄×C₈₉	—	2	4	no	—
302	C₄⋊C₄×C₈₉	—	2	4	no	—
303	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
304	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
305	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
306	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
307	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
308	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
309	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
310	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
311	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
312	C₂²⋊C₄×C₈₉	—	2	2	no	—
313	C₂²⋊C₄×C₈₉	—	2	4	no	—
314	C₂²⋊C₄×C₈₉	—	2	4	no	—
315	C₂²⋊C₄×C₈₉	—	2	1	no	—
316	C₂²⋊C₄×C₈₉	—	2	2	no	—
317	C₂²⋊C₄×C₈₉	—	2	2	no	—
318	C₂²⋊C₄×C₈₉	—	2	2	no	—
319	C₂²⋊C₄×C₈₉	—	2	1	no	—
320	C₂²⋊C₄×C₈₉	—	2	1	no	—
321	C₂²⋊C₄×C₈₉	—	2	2	no	—
322	C₂²⋊C₄×C₈₉	—	2	2	no	—
323	C₂²⋊C₄×C₈₉	—	2	2	no	—
324	C₂²⋊C₄×C₈₉	—	2	2	no	—
325	C₂²⋊C₄×C₈₉	—	2	2	no	—
326	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
327	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
328	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
329	C₄²×C₈₉	—	2	1	no	—
330	C₄²×C₈₉	—	2	1	no	—
331	C₄²×C₈₉	—	2	1	no	—
332	C₄²×C₈₉	—	2	4	no	—
333	C₄²×C₈₉	—	2	4	no	—
334	C₄²×C₈₉	—	2	2	no	—
335	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
336	C₄²×C₈₉	C₂×D₄	1	2	yes	—
337	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₈₉	C₂×D₄	1	2	yes	—
339	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
340	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
341	C₄²×C₈₉	C₂⁴	1	2	yes	—
342	C₂³×C₈₉	—	2	2	no	—
343	C₂³×C₈₉	—	2	1	no	—
344	C₂³×C₈₉	—	4	2	no	—
345	C₂³×C₈₉	—	8	1	no	—
346	C₂³×C₈₉	—	8	1	no	—
347	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
348	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
349	Q₈×C₈₉	—	2	2	no	—
350	Q₈×C₈₉	—	2	4	no	—
351	Q₈×C₈₉	—	2	1	no	—
352	Q₈×C₈₉	—	2	4	no	—
353	Q₈×C₈₉	—	2	1	no	—
354	Q₈×C₈₉	—	4	2	no	—
355	Q₈×C₈₉	—	4	4	no	—
356	Q₈×C₈₉	—	4	2	no	—
357	Q₈×C₈₉	—	8	2	no	—
358	D₄×C₈₉	—	2	4	no	—
359	D₄×C₈₉	—	2	2	no	—
360	D₄×C₈₉	—	2	2	no	—
361	D₄×C₈₉	—	2	1	no	—
362	D₄×C₈₉	—	2	2	no	—
363	D₄×C₈₉	—	2	1	no	—
364	D₄×C₈₉	—	4	2	no	—
365	D₄×C₈₉	—	4	2	no	—
366	D₄×C₈₉	—	8	2	no	—
367	D₄×C₈₉	—	8	2	no	—
368	D₄×C₈₉	—	8	2	no	—
369	D₄×C₈₉	—	8	2	no	—
370	D₄×C₈₉	—	8	2	no	—
371	C₂×C₄×C₈₉	—	2	2	no	—
372	C₂×C₄×C₈₉	—	2	4	no	—
373	C₂×C₄×C₈₉	—	2	2	no	—
374	C₂×C₄×C₈₉	—	2	2	no	—
375	C₂×C₄×C₈₉	—	2	2	no	—
376	C₂×C₄×C₈₉	—	2	2	no	—
377	C₂×C₄×C₈₉	—	2	1	no	—
378	C₂×C₄×C₈₉	—	2	1	no	—
379	C₂×C₄×C₈₉	—	2	1	no	—
380	C₂×C₄×C₈₉	—	2	4	no	—
381	C₂×C₄×C₈₉	—	2	2	no	—
382	C₂×C₄×C₈₉	—	4	1	no	—
383	C₂×C₄×C₈₉	—	4	2	no	—
384	C₂×C₄×C₈₉	—	4	4	no	—
385	C₂×C₄×C₈₉	—	4	2	no	—
386	C₂×C₄×C₈₉	—	4	4	no	—
387	C₂×C₄×C₈₉	—	4	2	no	—
388	C₂×C₄×C₈₉	—	8	1	no	—
389	C₂×C₄×C₈₉	—	8	2	no	—
390	C₂×C₄×C₈₉	—	8	1	no	—
391	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
393	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
400	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
401	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
402	C₈×C₈₉	—	2	2	no	—
403	C₈×C₈₉	—	2	2	no	—
404	C₈×C₈₉	—	2	4	no	—
405	C₂²×C₈₉	—	2	1	no	—
406	C₂²×C₈₉	—	2	1	no	—
407	C₂²×C₈₉	—	2	2	no	—
408	C₂²×C₈₉	—	2	2	no	—
409	C₂²×C₈₉	—	2	2	no	—
410	C₂²×C₈₉	—	4	1	no	—
411	C₂²×C₈₉	—	4	2	no	—
412	C₂²×C₈₉	—	4	1	no	—
413	C₂²×C₈₉	—	4	2	no	—
414	C₂²×C₈₉	—	4	2	no	—
415	C₂²×C₈₉	—	4	1	no	—
416	C₂²×C₈₉	—	8	4	no	—
417	C₂²×C₈₉	#537	1	2	yes	—
418	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
419	C₄×C₈₉	—	2	1	no	—
420	C₄×C₈₉	—	2	1	no	—
421	C₄×C₈₉	—	2	2	no	—
422	C₄×C₈₉	—	2	2	no	—
423	C₄×C₈₉	—	2	1	no	—
424	C₄×C₈₉	—	2	2	no	—
425	C₄×C₈₉	—	4	1	no	—
426	C₄×C₈₉	—	4	2	no	—
427	C₄×C₈₉	—	4	1	no	—
428	C₄×C₈₉	—	4	4	no	—
429	C₄×C₈₉	—	4	2	no	—
430	C₄×C₈₉	—	4	1	no	—
431	C₄×C₈₉	—	4	2	no	—
432	C₄×C₈₉	#537	1	2	yes	—
433	C₄×C₈₉	#577	1	2	yes	—
434	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
435	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
436	#60923	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
437	C₂×C₈₉	—	2	2	no	—
438	C₂×C₈₉	—	4	2	no	—
439	C₂×C₈₉	—	8	1	no	—
440	C₂×C₈₉	—	8	2	no	—
441	C₂×C₈₉	C₂×#537	1	1	yes	characteristic
442	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
443	C₂×C₈₉	#3586	1	1	yes	characteristic
444	#3509	C₂×C₈₉	1	1	yes	characteristic, complemented
445	#3460	C₂×C₈₉	1	1	yes	characteristic
446	#3260	C₂×C₈₉	1	4	yes	complemented
447	#3258	C₂×C₈₉	1	4	yes	complemented
448	#3254	C₂×C₈₉	1	2	yes	complemented
449	#3252	C₂×C₈₉	1	2	yes	complemented
450	#3248	C₂×C₈₉	1	2	yes	complemented
451	#3246	C₂×C₈₉	1	2	yes	complemented
452	#3082	C₂×C₈₉	1	2	yes	complemented
453	#3077	C₂×C₈₉	1	1	yes	characteristic, complemented
454	#3076	C₂×C₈₉	1	1	yes	characteristic, complemented
455	#3063	C₂×C₈₉	1	2	yes	complemented
456	#3057	C₂×C₈₉	1	2	yes	complemented
457	#3043	C₂×C₈₉	1	2	yes	complemented
458	#3039	C₂×C₈₉	1	1	yes	characteristic, complemented
459	C₂×#461	C₂×C₈₉	1	1	yes	characteristic, complemented
460	#2906	C₂×C₈₉	1	1	yes	characteristic, complemented
461	C₈₉	#60923	1	1	yes	characteristic, direct product factor, Sylow
462	C₂×#137	C₂²×C₈₉	1	2	yes	—
463	C₂²×SD₁₆	C₂²×C₈₉	1	2	yes	—
464	C₂×#131	C₂²×C₈₉	1	2	yes	—
465	#557	—	2	1	no	—
466	#557	—	2	1	no	—
467	#556	—	2	1	no	—
468	#556	—	2	1	no	—
469	#552	—	2	2	no	—
470	#552	—	2	2	no	—
471	#544	C₂²×C₈₉	1	1	yes	characteristic
472	#542	—	2	1	no	—
473	#542	C₂²×C₈₉	1	2	yes	—
474	#541	C₂²×C₈₉	1	4	yes	complemented
475	#540	—	2	1	no	—
476	#540	C₂²×C₈₉	1	2	yes	—
477	#538	—	2	2	no	—
478	#537	C₂²×C₈₉	1	1	yes	characteristic
479	#536	C₂²×C₈₉	1	2	yes	—
480	#535	C₂²×C₈₉	1	1	yes	characteristic
481	#535	C₂²×C₈₉	1	1	yes	characteristic
482	#533	C₂²×C₈₉	1	1	yes	characteristic
483	#533	C₂²×C₈₉	1	2	yes	complemented
484	#533	C₂²×C₈₉	1	2	yes	complemented
485	#532	—	2	1	no	—
486	#532	C₂²×C₈₉	1	2	yes	—
487	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
488	#529	—	2	1	no	—
489	#529	C₂²×C₈₉	1	2	yes	—
490	#525	—	2	2	no	—
491	#519	C₂²×C₈₉	1	2	yes	—
492	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
493	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
494	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
495	#479	C₂²×C₈₉	1	2	yes	complemented
496	#479	C₂²×C₈₉	1	4	yes	complemented
497	#479	C₂²×C₈₉	1	4	yes	complemented
498	#478	C₂²×C₈₉	1	4	yes	—
499	#478	C₂²×C₈₉	1	2	yes	complemented
500	#477	C₂²×C₈₉	1	1	yes	characteristic, complemented
501	#477	C₂²×C₈₉	1	4	yes	complemented
502	#476	C₂²×C₈₉	1	2	yes	—
503	#476	C₂²×C₈₉	1	1	yes	characteristic, complemented
504	#475	C₂²×C₈₉	1	1	yes	characteristic, complemented
505	#475	C₂²×C₈₉	1	4	yes	complemented
506	#474	C₂²×C₈₉	1	2	yes	—
507	#474	C₂²×C₈₉	1	1	yes	characteristic, complemented
508	#470	C₂²×C₈₉	1	4	yes	complemented
509	#468	C₂²×C₈₉	1	4	yes	—
510	#468	C₂²×C₈₉	1	4	yes	—
511	#468	C₂²×C₈₉	1	4	yes	complemented
512	#467	C₂²×C₈₉	1	4	yes	complemented
513	#465	C₂²×C₈₉	1	4	yes	—
514	#465	C₂²×C₈₉	1	4	yes	—
515	#465	C₂²×C₈₉	1	4	yes	complemented
516	#464	C₂²×C₈₉	1	4	yes	—
517	#464	C₂²×C₈₉	1	4	yes	—
518	#462	C₂²×C₈₉	1	2	yes	complemented
519	#462	C₂²×C₈₉	1	2	yes	complemented
520	#461	C₂²×C₈₉	1	2	yes	—
521	#461	C₂²×C₈₉	1	2	yes	—
522	#461	C₂²×C₈₉	1	4	yes	—
523	#461	C₂²×C₈₉	1	2	yes	complemented
524	#461	C₂²×C₈₉	1	2	yes	complemented
525	#460	C₂²×C₈₉	1	4	yes	—
526	#460	C₂²×C₈₉	1	4	yes	—
527	#428	C₂²×C₈₉	1	2	yes	—
528	#427	C₂²×C₈₉	1	2	yes	—
529	#424	C₂²×C₈₉	1	2	yes	—
530	#424	C₂²×C₈₉	1	4	yes	complemented
531	#423	C₂²×C₈₉	1	1	yes	characteristic
532	#423	C₂²×C₈₉	1	2	yes	complemented
533	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
534	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	complemented
535	#419	C₂²×C₈₉	1	2	yes	—
536	#418	C₂²×C₈₉	1	2	yes	—
537	#416	C₂²×C₈₉	1	2	yes	—
538	C₂×#103	C₂²×C₈₉	1	2	yes	—
539	C₂×#41	—	2	2	no	—
540	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
541	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
542	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
543	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
544	C₂³×C₄	—	2	1	no	—
545	#137	—	4	4	no	—
546	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
547	C₂×SD₁₆	—	4	4	no	—
548	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
549	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
550	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
551	#131	—	4	4	no	—
552	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
553	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
554	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
555	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
556	C₄⋊Q₈	—	2	2	no	—
557	C₄⋊Q₈	—	2	1	no	—
558	C₄⋊Q₈	—	2	1	no	—
559	C₄⋊Q₈	—	2	1	no	—
560	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
561	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
562	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
563	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
564	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
565	#127	—	2	1	no	—
566	#127	C₂³×C₈₉	1	2	yes	—
567	#126	—	2	2	no	—
568	#126	—	2	4	no	—
569	#126	—	2	4	no	—
570	#126	—	2	2	no	—
571	#125	—	2	1	no	—
572	#125	—	2	4	no	—
573	#125	—	2	4	no	—
574	#125	—	2	2	no	—
575	#125	—	2	2	no	—
576	#125	C₂³×C₈₉	1	2	yes	—
577	#125	C₂³×C₈₉	1	2	yes	—
578	#124	—	2	1	no	—
579	#124	—	2	2	no	—
580	#124	—	2	2	no	—
581	#124	—	2	2	no	—
582	#124	C₂³×C₈₉	1	2	yes	—
583	#123	—	2	4	no	—
584	#123	—	2	2	no	—
585	#123	—	2	2	no	—
586	#123	—	2	2	no	—
587	#123	—	2	2	no	—
588	C₂²⋊Q₈	—	2	1	no	—
589	C₂²⋊Q₈	—	2	1	no	—
590	C₂²⋊Q₈	—	2	1	no	—
591	C₂²⋊Q₈	—	2	2	no	—
592	C₂²⋊Q₈	—	2	2	no	—
593	C₂²⋊Q₈	—	2	2	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
596	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
597	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
598	#121	—	2	2	no	—
599	#121	—	2	1	no	—
600	#121	—	2	2	no	—
601	#121	—	2	1	no	—
602	#121	—	2	1	no	—
603	#121	—	2	2	no	—
604	#121	—	2	2	no	—
605	#121	C₂³×C₈₉	1	2	yes	—
606	#121	C₂³×C₈₉	1	2	yes	—
607	#121	C₂³×C₈₉	1	2	yes	—
608	#120	—	2	2	no	—
609	#120	—	2	2	no	—
610	C₄×Q₈	—	2	2	no	—
611	C₄×Q₈	—	2	2	no	—
612	C₄×Q₈	—	2	1	no	—
613	C₄×Q₈	—	2	1	no	—
614	C₄×Q₈	—	2	2	no	—
615	C₄×Q₈	—	2	2	no	—
616	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
617	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
618	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
619	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
620	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
621	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	—	2	1	no	—
624	C₄×D₄	—	2	2	no	—
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	D₄×C₈₉	1	2	yes	—
629	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
630	C₄×D₄	D₄×C₈₉	1	2	yes	—
631	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
632	C₄×D₄	C₂³×C₈₉	1	2	yes	—
633	C₄×D₄	C₂³×C₈₉	1	2	yes	—
634	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
635	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
636	#117	—	2	2	no	—
637	#117	—	2	2	no	—
638	#117	—	2	4	no	—
639	#117	—	2	1	no	—
640	#117	—	2	2	no	—
641	#117	C₂³×C₈₉	1	1	yes	characteristic
642	#117	C₂³×C₈₉	1	2	yes	—
643	#117	C₂³×C₈₉	1	1	yes	characteristic
644	#117	C₂³×C₈₉	1	2	yes	—
645	C₂×C₄⋊C₄	—	2	1	no	—
646	C₂×C₄⋊C₄	—	2	1	no	—
647	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	—	2	1	no	—
649	C₂×C₄²	—	2	1	no	—
650	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
652	#107	C₂³×C₈₉	1	2	yes	—
653	#107	C₂³×C₈₉	1	2	yes	—
654	#107	C₂³×C₈₉	1	4	yes	—
655	#106	C₂³×C₈₉	1	2	yes	—
656	#106	C₂³×C₈₉	1	2	yes	—
657	#106	C₂³×C₈₉	1	4	yes	—
658	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
659	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
660	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
661	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
662	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
663	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
664	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
665	#103	C₂³×C₈₉	1	4	yes	—
666	#103	C₂³×C₈₉	1	4	yes	—
667	#103	C₂³×C₈₉	1	2	yes	—
668	#103	C₂³×C₈₉	1	2	yes	—
669	#103	C₂³×C₈₉	1	4	yes	—
670	#103	C₂³×C₈₉	1	4	yes	—
671	#102	C₂³×C₈₉	1	2	yes	—
672	#102	C₂³×C₈₉	1	2	yes	—
673	#102	C₂³×C₈₉	1	4	yes	—
674	#102	C₂³×C₈₉	1	4	yes	—
675	C₂⁴	—	2	1	no	—
676	#41	—	2	2	no	—
677	#41	—	2	2	no	—
678	#41	—	2	2	no	—
679	#41	—	2	2	no	—
680	#41	—	8	4	no	—
681	C₂×Q₈	—	2	1	no	—
682	C₂×Q₈	—	2	1	no	—
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	—	2	2	no	—
685	C₂×Q₈	—	2	4	no	—
686	C₂×Q₈	—	2	4	no	—
687	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
688	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
689	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
700	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
701	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
702	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	8	2	no	—
711	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
712	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
713	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
714	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
717	Q₁₆	—	4	4	no	—
718	SD₁₆	—	4	4	no	—
719	SD₁₆	—	4	4	no	—
720	SD₁₆	—	4	4	no	—
721	M₁₆	—	2	4	no	—
722	M₁₆	—	4	4	no	—
723	C₂×C₈	—	2	4	no	—
724	C₂×C₈	—	4	4	no	—
725	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
726	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
727	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
748	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
749	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
750	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
751	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
752	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
753	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
754	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
755	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	1	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	1	no	—
764	C₂²⋊C₄	—	2	1	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
771	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
772	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
773	C₄²	—	2	1	no	—
774	C₄²	—	2	1	no	—
775	C₄²	—	2	1	no	—
776	C₄²	—	2	4	no	—
777	C₄²	—	2	4	no	—
778	C₄²	—	2	2	no	—
779	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
780	C₄²	C₂×D₄×C₈₉	1	2	yes	—
781	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
782	C₄²	C₂×D₄×C₈₉	1	2	yes	—
783	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
784	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
785	C₄²	C₂⁴×C₈₉	1	2	yes	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	1	no	—
788	C₂³	—	4	2	no	—
789	C₂³	—	8	1	no	—
790	C₂³	—	8	1	no	—
791	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
792	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
793	Q₈	—	2	2	no	—
794	Q₈	—	2	4	no	—
795	Q₈	—	2	1	no	—
796	Q₈	—	2	4	no	—
797	Q₈	—	2	1	no	—
798	Q₈	—	4	2	no	—
799	Q₈	—	4	4	no	—
800	Q₈	—	4	2	no	—
801	Q₈	—	8	2	no	—
802	D₄	—	2	4	no	—
803	D₄	—	2	2	no	—
804	D₄	—	2	2	no	—
805	D₄	—	2	1	no	—
806	D₄	—	2	2	no	—
807	D₄	—	2	1	no	—
808	D₄	—	4	2	no	—
809	D₄	—	4	2	no	—
810	D₄	—	8	2	no	—
811	D₄	—	8	2	no	—
812	D₄	—	8	2	no	—
813	D₄	—	8	2	no	—
814	D₄	—	8	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	4	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	4	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	4	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	8	1	no	—
833	C₂×C₄	—	8	2	no	—
834	C₂×C₄	—	8	1	no	—
835	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
836	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
837	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
838	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
840	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
843	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
844	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
845	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
846	C₈	—	2	2	no	—
847	C₈	—	2	2	no	—
848	C₈	—	2	4	no	—
849	C₂²	—	2	1	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	8	4	no	—
861	C₂²	#537×C₈₉	1	2	yes	—
862	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
863	C₄	—	2	1	no	—
864	C₄	—	2	2	no	—
865	C₄	—	2	1	no	—
866	C₄	—	2	1	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	2	no	—
869	C₄	—	4	2	no	—
870	C₄	—	4	1	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	4	no	—
876	C₄	#537×C₈₉	1	2	yes	—
877	C₄	#577×C₈₉	1	2	yes	—
878	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
879	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
880	C₂	—	2	2	no	—
881	C₂	—	4	2	no	—
882	C₂	—	8	1	no	—
883	C₂	—	8	2	no	—
884	C₂	C₂×#537×C₈₉	1	1	yes	characteristic
885	C₂	C₂×#577×C₈₉	1	1	yes	characteristic
886	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	C₈₉×#3460	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3509	C₂	semidirect
3. C₈₉×#3260	C₂	semidirect
4. C₈₉×#3258	C₂	semidirect
5. C₈₉×#3254	C₂	semidirect
6. C₈₉×#3252	C₂	semidirect
7. C₈₉×#3248	C₂	semidirect
8. C₈₉×#3246	C₂	semidirect
9. C₈₉×#3082	C₂	semidirect
10. C₈₉×#3077	C₂	semidirect
11. C₈₉×#3076	C₂	semidirect
12. C₈₉×#3063	C₂	semidirect
13. C₈₉×#3057	C₂	semidirect
14. C₈₉×#3043	C₂	semidirect
15. C₈₉×#3039	C₂	semidirect
16. C₂×#461×C₈₉	C₂	semidirect
17. C₈₉×#2906	C₂	semidirect
30. #541×C₈₉	C₂²	semidirect
39. #533×C₈₉	C₂²	semidirect
40. #533×C₈₉	C₂²	semidirect
51. #479×C₈₉	C₂²	semidirect
52. #479×C₈₉	C₂²	semidirect
53. #479×C₈₉	C₂²	semidirect
55. #478×C₈₉	C₂²	semidirect
56. #477×C₈₉	C₂²	semidirect
57. #477×C₈₉	C₂²	semidirect
59. #476×C₈₉	C₂²	semidirect
60. #475×C₈₉	C₂²	semidirect
61. #475×C₈₉	C₂²	semidirect
63. #474×C₈₉	C₂²	semidirect
64. #470×C₈₉	C₂²	semidirect
67. #468×C₈₉	C₂²	semidirect
68. #467×C₈₉	C₂²	semidirect
71. #465×C₈₉	C₂²	semidirect
74. #462×C₈₉	C₂²	semidirect
75. #462×C₈₉	C₂²	semidirect
79. #461×C₈₉	C₂²	semidirect
80. #461×C₈₉	C₂²	semidirect
86. #424×C₈₉	C₂²	semidirect
88. #423×C₈₉	C₂²	semidirect
90. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
436. #60923	C₈₉	direct (N × H)
444. #3509	C₂×C₈₉	semidirect
446. #3260	C₂×C₈₉	semidirect
447. #3258	C₂×C₈₉	semidirect
448. #3254	C₂×C₈₉	semidirect
449. #3252	C₂×C₈₉	semidirect
450. #3248	C₂×C₈₉	semidirect
451. #3246	C₂×C₈₉	semidirect
452. #3082	C₂×C₈₉	semidirect
453. #3077	C₂×C₈₉	semidirect
454. #3076	C₂×C₈₉	semidirect
455. #3063	C₂×C₈₉	semidirect
456. #3057	C₂×C₈₉	semidirect
457. #3043	C₂×C₈₉	semidirect
458. #3039	C₂×C₈₉	semidirect
459. C₂×#461	C₂×C₈₉	semidirect
460. #2906	C₂×C₈₉	semidirect
461. C₈₉	#60923	direct (N × H)
474. #541	C₂²×C₈₉	semidirect
483. #533	C₂²×C₈₉	semidirect
484. #533	C₂²×C₈₉	semidirect
495. #479	C₂²×C₈₉	semidirect
496. #479	C₂²×C₈₉	semidirect
497. #479	C₂²×C₈₉	semidirect
499. #478	C₂²×C₈₉	semidirect
500. #477	C₂²×C₈₉	semidirect
501. #477	C₂²×C₈₉	semidirect
503. #476	C₂²×C₈₉	semidirect
504. #475	C₂²×C₈₉	semidirect
505. #475	C₂²×C₈₉	semidirect
507. #474	C₂²×C₈₉	semidirect
508. #470	C₂²×C₈₉	semidirect
511. #468	C₂²×C₈₉	semidirect
512. #467	C₂²×C₈₉	semidirect
515. #465	C₂²×C₈₉	semidirect
518. #462	C₂²×C₈₉	semidirect
519. #462	C₂²×C₈₉	semidirect
523. #461	C₂²×C₈₉	semidirect
524. #461	C₂²×C₈₉	semidirect
530. #424	C₂²×C₈₉	semidirect
532. #423	C₂²×C₈₉	semidirect
534. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3509	2
C₈₉×#3460	2
C₈₉×#3260	2
C₈₉×#3258	2
C₈₉×#3254	2
C₈₉×#3252	2
C₈₉×#3248	2
C₈₉×#3246	2
C₈₉×#3082	2
C₈₉×#3077	2
C₈₉×#3076	2
C₈₉×#3063	2
C₈₉×#3057	2
C₈₉×#3043	2
C₈₉×#3039	2
C₂×#461×C₈₉	2
C₈₉×#2906	2
#60923	89

Subgroups — C89×#60923 #36438771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60923 #36438771