Subgroups — C₈₉×#60925 #36438773

Order 22784.

1748 conjugacy classes of subgroups.

The subgroup lattice has 860 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×#3461	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3261	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3258	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3255	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3252	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3249	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3248	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3082	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3078	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
13	C₈₉×#3059	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3044	C₂	1	2	yes	maximal, complemented
15	C₈₉×#3039	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#462×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×Q₁₆×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	—	2	1	no	—
31	#541×C₈₉	C₂²	1	2	yes	—
32	#541×C₈₉	C₂²	1	4	yes	—
33	#539×C₈₉	—	2	2	no	—
34	#537×C₈₉	C₂²	1	1	yes	characteristic
35	#536×C₈₉	C₂²	1	1	yes	characteristic
36	#536×C₈₉	C₂²	1	2	yes	—
37	#536×C₈₉	C₂²	1	1	yes	characteristic
38	#533×C₈₉	—	2	1	no	—
39	#533×C₈₉	C₂²	1	2	yes	—
40	#533×C₈₉	C₂²	1	2	yes	—
41	#533×C₈₉	C₂²	1	2	yes	—
42	#533×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
44	#529×C₈₉	—	2	2	no	—
45	#529×C₈₉	—	2	1	no	—
46	#529×C₈₉	C₂²	1	2	yes	—
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×Q₈×C₈₉	C₂²	1	1	yes	characteristic
51	#479×C₈₉	C₂²	1	2	yes	—
52	#479×C₈₉	C₂²	1	4	yes	—
53	#479×C₈₉	C₂²	1	4	yes	—
54	#479×C₈₉	C₂²	1	4	yes	—
55	#478×C₈₉	C₂²	1	2	yes	—
56	#477×C₈₉	C₂²	1	1	yes	characteristic
57	#477×C₈₉	C₂²	1	2	yes	—
58	#477×C₈₉	C₂²	1	4	yes	—
59	#476×C₈₉	C₂²	1	1	yes	characteristic
60	#475×C₈₉	C₂²	1	1	yes	characteristic
61	#475×C₈₉	C₂²	1	2	yes	—
62	#475×C₈₉	C₂²	1	4	yes	—
63	#474×C₈₉	C₂²	1	1	yes	characteristic
64	#470×C₈₉	C₂²	1	4	yes	—
65	#470×C₈₉	C₂²	1	4	yes	—
66	#470×C₈₉	C₂²	1	4	yes	—
67	#468×C₈₉	C₂²	1	4	yes	—
68	#467×C₈₉	C₂²	1	4	yes	—
69	#467×C₈₉	C₂²	1	4	yes	—
70	#467×C₈₉	C₂²	1	4	yes	—
71	#465×C₈₉	C₂²	1	4	yes	—
72	#464×C₈₉	C₂²	1	4	yes	—
73	#464×C₈₉	C₂²	1	4	yes	—
74	#462×C₈₉	C₂²	1	2	yes	—
75	#462×C₈₉	C₂²	1	2	yes	—
76	#462×C₈₉	C₂²	1	4	yes	—
77	#462×C₈₉	C₂²	1	2	yes	—
78	#462×C₈₉	C₂²	1	4	yes	—
79	#462×C₈₉	C₂²	1	4	yes	—
80	#462×C₈₉	C₂²	1	2	yes	—
81	#461×C₈₉	C₂²	1	2	yes	—
82	#461×C₈₉	C₂²	1	2	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	—
87	#423×C₈₉	C₂²	1	1	yes	characteristic
88	#423×C₈₉	C₂²	1	2	yes	—
89	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
90	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
91	#419×C₈₉	C₂²	1	2	yes	—
92	#419×C₈₉	C₂²	1	2	yes	—
93	#416×C₈₉	C₂²	1	2	yes	—
94	C₂×#103×C₈₉	C₂²	1	2	yes	—
95	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
96	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
98	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
99	#137×C₈₉	—	4	4	no	—
100	C₂×Q₁₆×C₈₉	—	4	4	no	—
101	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
102	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
103	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
105	#131×C₈₉	—	4	4	no	—
106	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
107	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
108	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
109	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
110	C₄⋊Q₈×C₈₉	—	2	1	no	—
111	C₄⋊Q₈×C₈₉	—	2	2	no	—
112	C₄⋊Q₈×C₈₉	—	2	1	no	—
113	C₄⋊Q₈×C₈₉	—	2	1	no	—
114	C₄⋊Q₈×C₈₉	—	2	1	no	—
115	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
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	#126×C₈₉	—	2	2	no	—
122	#126×C₈₉	—	2	2	no	—
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	2	no	—
128	#125×C₈₉	—	2	1	no	—
129	#125×C₈₉	—	2	2	no	—
130	#125×C₈₉	—	2	4	no	—
131	#125×C₈₉	—	2	4	no	—
132	#125×C₈₉	—	2	2	no	—
133	#125×C₈₉	—	2	2	no	—
134	#125×C₈₉	—	2	2	no	—
135	#125×C₈₉	C₂³	1	2	yes	—
136	#125×C₈₉	C₂³	1	2	yes	—
137	#124×C₈₉	—	2	1	no	—
138	#124×C₈₉	—	2	2	no	—
139	#124×C₈₉	—	2	2	no	—
140	#124×C₈₉	C₂³	1	2	yes	—
141	#123×C₈₉	—	2	2	no	—
142	#123×C₈₉	—	2	4	no	—
143	#123×C₈₉	—	2	2	no	—
144	#123×C₈₉	—	2	2	no	—
145	#123×C₈₉	—	2	2	no	—
146	C₂²⋊Q₈×C₈₉	—	2	1	no	—
147	C₂²⋊Q₈×C₈₉	—	2	2	no	—
148	C₂²⋊Q₈×C₈₉	—	2	1	no	—
149	C₂²⋊Q₈×C₈₉	—	2	1	no	—
150	C₂²⋊Q₈×C₈₉	—	2	2	no	—
151	C₂²⋊Q₈×C₈₉	—	2	2	no	—
152	C₂²⋊Q₈×C₈₉	—	2	1	no	—
153	C₂²⋊Q₈×C₈₉	—	2	1	no	—
154	C₂²⋊Q₈×C₈₉	—	2	2	no	—
155	C₂²⋊Q₈×C₈₉	—	2	2	no	—
156	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
157	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
158	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
159	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
160	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
161	#121×C₈₉	—	2	2	no	—
162	#121×C₈₉	—	2	1	no	—
163	#121×C₈₉	C₂³	1	2	yes	—
164	C₄×Q₈×C₈₉	—	2	2	no	—
165	C₄×Q₈×C₈₉	—	2	2	no	—
166	C₄×Q₈×C₈₉	—	2	1	no	—
167	C₄×Q₈×C₈₉	—	2	1	no	—
168	C₄×Q₈×C₈₉	—	2	2	no	—
169	C₄×Q₈×C₈₉	—	2	2	no	—
170	C₄×Q₈×C₈₉	—	2	2	no	—
171	C₄×Q₈×C₈₉	—	2	1	no	—
172	C₄×Q₈×C₈₉	—	2	1	no	—
173	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
174	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
175	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
176	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
177	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
178	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
179	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
180	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
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	1	yes	characteristic
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	2	no	—
193	#117×C₈₉	—	2	4	no	—
194	#117×C₈₉	—	2	1	no	—
195	#117×C₈₉	—	2	2	no	—
196	#117×C₈₉	C₂³	1	2	yes	—
197	#117×C₈₉	C₂³	1	1	yes	characteristic
198	#117×C₈₉	C₂³	1	1	yes	characteristic
199	#117×C₈₉	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
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×C₄²×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	2	yes	—
216	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
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	#103×C₈₉	C₂³	1	4	yes	—
228	#103×C₈₉	C₂³	1	4	yes	—
229	#102×C₈₉	C₂³	1	2	yes	—
230	#102×C₈₉	C₂³	1	2	yes	—
231	#41×C₈₉	—	2	2	no	—
232	#41×C₈₉	—	2	2	no	—
233	#41×C₈₉	—	2	2	no	—
234	#41×C₈₉	—	2	2	no	—
235	C₂×Q₈×C₈₉	—	2	1	no	—
236	C₂×Q₈×C₈₉	—	2	1	no	—
237	C₂×Q₈×C₈₉	—	2	1	no	—
238	C₂×Q₈×C₈₉	—	2	2	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	—	2	2	no	—
244	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
245	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
246	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
247	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
248	C₂×D₄×C₈₉	—	2	1	no	—
249	C₂×D₄×C₈₉	—	2	2	no	—
250	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
251	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
252	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₈₉	—	2	1	no	—
254	C₂²×C₄×C₈₉	—	2	2	no	—
255	C₂²×C₄×C₈₉	—	2	1	no	—
256	C₂²×C₄×C₈₉	—	2	1	no	—
257	C₂²×C₄×C₈₉	—	2	1	no	—
258	C₂²×C₄×C₈₉	—	2	1	no	—
259	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
265	Q₁₆×C₈₉	—	4	4	no	—
266	Q₁₆×C₈₉	—	4	4	no	—
267	Q₁₆×C₈₉	—	4	4	no	—
268	SD₁₆×C₈₉	—	4	4	no	—
269	M₁₆×C₈₉	—	2	4	no	—
270	M₁₆×C₈₉	—	4	4	no	—
271	C₂×C₈×C₈₉	—	2	4	no	—
272	C₂×C₈×C₈₉	—	4	4	no	—
273	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
274	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
275	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
276	C₄⋊C₄×C₈₉	—	2	2	no	—
277	C₄⋊C₄×C₈₉	—	2	2	no	—
278	C₄⋊C₄×C₈₉	—	2	2	no	—
279	C₄⋊C₄×C₈₉	—	2	2	no	—
280	C₄⋊C₄×C₈₉	—	2	2	no	—
281	C₄⋊C₄×C₈₉	—	2	2	no	—
282	C₄⋊C₄×C₈₉	—	2	1	no	—
283	C₄⋊C₄×C₈₉	—	2	1	no	—
284	C₄⋊C₄×C₈₉	—	2	1	no	—
285	C₄⋊C₄×C₈₉	—	2	1	no	—
286	C₄⋊C₄×C₈₉	—	2	1	no	—
287	C₄⋊C₄×C₈₉	—	2	4	no	—
288	C₄⋊C₄×C₈₉	—	2	4	no	—
289	C₄⋊C₄×C₈₉	—	2	2	no	—
290	C₄⋊C₄×C₈₉	—	2	2	no	—
291	C₄⋊C₄×C₈₉	—	2	2	no	—
292	C₄⋊C₄×C₈₉	—	2	2	no	—
293	C₄⋊C₄×C₈₉	—	2	2	no	—
294	C₄⋊C₄×C₈₉	—	2	2	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	4	no	—
300	C₄⋊C₄×C₈₉	—	2	4	no	—
301	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
302	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
303	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
304	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
305	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
306	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
307	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
308	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
309	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
310	C₂²⋊C₄×C₈₉	—	2	2	no	—
311	C₂²⋊C₄×C₈₉	—	2	2	no	—
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	1	no	—
318	C₂²⋊C₄×C₈₉	—	2	1	no	—
319	C₂²⋊C₄×C₈₉	—	2	2	no	—
320	C₂²⋊C₄×C₈₉	—	2	2	no	—
321	C₂²⋊C₄×C₈₉	—	2	2	no	—
322	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
323	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
324	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
325	C₄²×C₈₉	—	2	2	no	—
326	C₄²×C₈₉	—	2	1	no	—
327	C₄²×C₈₉	—	2	1	no	—
328	C₄²×C₈₉	—	2	1	no	—
329	C₄²×C₈₉	—	2	2	no	—
330	C₄²×C₈₉	—	2	4	no	—
331	C₄²×C₈₉	—	2	4	no	—
332	C₄²×C₈₉	—	2	2	no	—
333	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₈₉	C₂×D₄	1	2	yes	—
335	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
336	C₄²×C₈₉	C₂×D₄	1	2	yes	—
337	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
338	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
339	C₄²×C₈₉	C₂⁴	1	2	yes	—
340	C₂³×C₈₉	—	2	1	no	—
341	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
342	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
343	Q₈×C₈₉	—	2	2	no	—
344	Q₈×C₈₉	—	2	4	no	—
345	Q₈×C₈₉	—	2	2	no	—
346	Q₈×C₈₉	—	2	1	no	—
347	Q₈×C₈₉	—	2	2	no	—
348	Q₈×C₈₉	—	2	4	no	—
349	Q₈×C₈₉	—	2	1	no	—
350	Q₈×C₈₉	—	4	2	no	—
351	Q₈×C₈₉	—	4	2	no	—
352	Q₈×C₈₉	—	4	4	no	—
353	Q₈×C₈₉	—	4	2	no	—
354	Q₈×C₈₉	—	8	2	no	—
355	D₄×C₈₉	—	2	4	no	—
356	D₄×C₈₉	—	2	2	no	—
357	D₄×C₈₉	—	2	1	no	—
358	D₄×C₈₉	—	2	1	no	—
359	D₄×C₈₉	—	4	2	no	—
360	D₄×C₈₉	—	8	2	no	—
361	C₂×C₄×C₈₉	—	2	2	no	—
362	C₂×C₄×C₈₉	—	2	4	no	—
363	C₂×C₄×C₈₉	—	2	2	no	—
364	C₂×C₄×C₈₉	—	2	2	no	—
365	C₂×C₄×C₈₉	—	2	2	no	—
366	C₂×C₄×C₈₉	—	2	2	no	—
367	C₂×C₄×C₈₉	—	2	1	no	—
368	C₂×C₄×C₈₉	—	2	2	no	—
369	C₂×C₄×C₈₉	—	2	1	no	—
370	C₂×C₄×C₈₉	—	2	1	no	—
371	C₂×C₄×C₈₉	—	2	4	no	—
372	C₂×C₄×C₈₉	—	2	2	no	—
373	C₂×C₄×C₈₉	—	4	1	no	—
374	C₂×C₄×C₈₉	—	4	2	no	—
375	C₂×C₄×C₈₉	—	4	2	no	—
376	C₂×C₄×C₈₉	—	4	4	no	—
377	C₂×C₄×C₈₉	—	4	2	no	—
378	C₂×C₄×C₈₉	—	4	2	no	—
379	C₂×C₄×C₈₉	—	8	1	no	—
380	C₂×C₄×C₈₉	—	8	1	no	—
381	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
387	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
390	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
391	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
392	C₈×C₈₉	—	2	2	no	—
393	C₈×C₈₉	—	2	2	no	—
394	C₈×C₈₉	—	2	4	no	—
395	C₂²×C₈₉	—	2	1	no	—
396	C₂²×C₈₉	—	2	1	no	—
397	C₂²×C₈₉	—	2	2	no	—
398	C₂²×C₈₉	—	2	2	no	—
399	C₂²×C₈₉	—	2	2	no	—
400	C₂²×C₈₉	—	4	1	no	—
401	C₂²×C₈₉	—	4	1	no	—
402	C₂²×C₈₉	—	4	1	no	—
403	C₂²×C₈₉	#537	1	2	yes	—
404	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
405	C₄×C₈₉	—	2	1	no	—
406	C₄×C₈₉	—	2	1	no	—
407	C₄×C₈₉	—	2	2	no	—
408	C₄×C₈₉	—	2	2	no	—
409	C₄×C₈₉	—	2	1	no	—
410	C₄×C₈₉	—	2	2	no	—
411	C₄×C₈₉	—	4	2	no	—
412	C₄×C₈₉	—	4	1	no	—
413	C₄×C₈₉	—	4	2	no	—
414	C₄×C₈₉	—	4	1	no	—
415	C₄×C₈₉	—	4	2	no	—
416	C₄×C₈₉	—	4	4	no	—
417	C₄×C₈₉	—	4	1	no	—
418	C₄×C₈₉	—	4	2	no	—
419	C₄×C₈₉	#537	1	2	yes	—
420	C₄×C₈₉	#578	1	2	yes	—
421	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
422	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
423	#60925	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
424	C₂×C₈₉	—	2	2	no	—
425	C₂×C₈₉	—	4	2	no	—
426	C₂×C₈₉	—	8	1	no	—
427	C₂×C₈₉	C₂×#537	1	1	yes	characteristic
428	C₂×C₈₉	C₂×#578	1	1	yes	characteristic
429	C₂×C₈₉	#3586	1	1	yes	characteristic
430	#3509	C₂×C₈₉	1	1	yes	characteristic, complemented
431	#3461	C₂×C₈₉	1	1	yes	characteristic
432	#3261	C₂×C₈₉	1	4	yes	complemented
433	#3258	C₂×C₈₉	1	4	yes	complemented
434	#3255	C₂×C₈₉	1	2	yes	complemented
435	#3252	C₂×C₈₉	1	2	yes	complemented
436	#3249	C₂×C₈₉	1	2	yes	complemented
437	#3248	C₂×C₈₉	1	2	yes	complemented
438	#3082	C₂×C₈₉	1	2	yes	complemented
439	#3078	C₂×C₈₉	1	1	yes	characteristic, complemented
440	#3076	C₂×C₈₉	1	1	yes	characteristic, complemented
441	#3063	C₂×C₈₉	1	2	yes	—
442	#3059	C₂×C₈₉	1	2	yes	complemented
443	#3044	C₂×C₈₉	1	2	yes	complemented
444	#3039	C₂×C₈₉	1	1	yes	characteristic, complemented
445	C₂×#462	C₂×C₈₉	1	1	yes	characteristic, complemented
446	#2906	C₂×C₈₉	1	1	yes	characteristic, complemented
447	C₈₉	#60925	1	1	yes	characteristic, direct product factor, Sylow
448	C₂×#137	C₂²×C₈₉	1	2	yes	—
449	C₂²×Q₁₆	C₂²×C₈₉	1	2	yes	—
450	C₂×#131	C₂²×C₈₉	1	2	yes	—
451	#557	—	2	1	no	—
452	#557	—	2	1	no	—
453	#556	—	2	1	no	—
454	#556	—	2	1	no	—
455	#552	—	2	2	no	—
456	#552	—	2	2	no	—
457	#544	C₂²×C₈₉	1	1	yes	characteristic
458	#542	—	2	1	no	—
459	#542	C₂²×C₈₉	1	2	yes	—
460	#541	—	2	1	no	—
461	#541	C₂²×C₈₉	1	2	yes	—
462	#541	C₂²×C₈₉	1	4	yes	—
463	#539	—	2	2	no	—
464	#537	C₂²×C₈₉	1	1	yes	characteristic
465	#536	C₂²×C₈₉	1	1	yes	characteristic
466	#536	C₂²×C₈₉	1	1	yes	characteristic
467	#536	C₂²×C₈₉	1	2	yes	—
468	#533	—	2	1	no	—
469	#533	C₂²×C₈₉	1	2	yes	—
470	#533	C₂²×C₈₉	1	2	yes	—
471	#533	C₂²×C₈₉	1	2	yes	—
472	#533	C₂²×C₈₉	1	1	yes	characteristic
473	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
474	#529	—	2	2	no	—
475	#529	—	2	1	no	—
476	#529	C₂²×C₈₉	1	2	yes	—
477	#519	C₂²×C₈₉	1	2	yes	—
478	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
479	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
480	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
481	#479	C₂²×C₈₉	1	2	yes	—
482	#479	C₂²×C₈₉	1	4	yes	—
483	#479	C₂²×C₈₉	1	4	yes	—
484	#479	C₂²×C₈₉	1	4	yes	—
485	#478	C₂²×C₈₉	1	2	yes	—
486	#477	C₂²×C₈₉	1	1	yes	characteristic
487	#477	C₂²×C₈₉	1	2	yes	—
488	#477	C₂²×C₈₉	1	4	yes	—
489	#476	C₂²×C₈₉	1	1	yes	characteristic
490	#475	C₂²×C₈₉	1	1	yes	characteristic
491	#475	C₂²×C₈₉	1	2	yes	—
492	#475	C₂²×C₈₉	1	4	yes	—
493	#474	C₂²×C₈₉	1	1	yes	characteristic
494	#470	C₂²×C₈₉	1	4	yes	—
495	#470	C₂²×C₈₉	1	4	yes	—
496	#470	C₂²×C₈₉	1	4	yes	—
497	#468	C₂²×C₈₉	1	4	yes	—
498	#467	C₂²×C₈₉	1	4	yes	—
499	#467	C₂²×C₈₉	1	4	yes	—
500	#467	C₂²×C₈₉	1	4	yes	—
501	#465	C₂²×C₈₉	1	4	yes	—
502	#464	C₂²×C₈₉	1	4	yes	—
503	#464	C₂²×C₈₉	1	4	yes	—
504	#462	C₂²×C₈₉	1	2	yes	—
505	#462	C₂²×C₈₉	1	2	yes	—
506	#462	C₂²×C₈₉	1	4	yes	—
507	#462	C₂²×C₈₉	1	2	yes	—
508	#462	C₂²×C₈₉	1	4	yes	—
509	#462	C₂²×C₈₉	1	4	yes	—
510	#462	C₂²×C₈₉	1	2	yes	—
511	#461	C₂²×C₈₉	1	2	yes	—
512	#461	C₂²×C₈₉	1	2	yes	—
513	#428	C₂²×C₈₉	1	2	yes	—
514	#427	C₂²×C₈₉	1	2	yes	—
515	#424	C₂²×C₈₉	1	2	yes	—
516	#424	C₂²×C₈₉	1	4	yes	—
517	#423	C₂²×C₈₉	1	1	yes	characteristic
518	#423	C₂²×C₈₉	1	2	yes	—
519	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
520	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
521	#419	C₂²×C₈₉	1	2	yes	—
522	#419	C₂²×C₈₉	1	2	yes	—
523	#416	C₂²×C₈₉	1	2	yes	—
524	C₂×#103	C₂²×C₈₉	1	2	yes	—
525	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
526	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
527	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
528	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
529	#137	—	4	4	no	—
530	C₂×Q₁₆	—	4	4	no	—
531	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
532	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
533	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
534	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
535	#131	—	4	4	no	—
536	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
537	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
538	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
539	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
540	C₄⋊Q₈	—	2	1	no	—
541	C₄⋊Q₈	—	2	2	no	—
542	C₄⋊Q₈	—	2	1	no	—
543	C₄⋊Q₈	—	2	1	no	—
544	C₄⋊Q₈	—	2	1	no	—
545	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
546	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
547	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
548	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
549	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
550	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
551	#126	—	2	2	no	—
552	#126	—	2	2	no	—
553	#126	—	2	2	no	—
554	#126	—	2	4	no	—
555	#126	—	2	4	no	—
556	#126	—	2	2	no	—
557	#125	—	2	2	no	—
558	#125	—	2	1	no	—
559	#125	—	2	2	no	—
560	#125	—	2	4	no	—
561	#125	—	2	4	no	—
562	#125	—	2	2	no	—
563	#125	—	2	2	no	—
564	#125	—	2	2	no	—
565	#125	C₂³×C₈₉	1	2	yes	—
566	#125	C₂³×C₈₉	1	2	yes	—
567	#124	—	2	1	no	—
568	#124	—	2	2	no	—
569	#124	—	2	2	no	—
570	#124	C₂³×C₈₉	1	2	yes	—
571	#123	—	2	2	no	—
572	#123	—	2	4	no	—
573	#123	—	2	2	no	—
574	#123	—	2	2	no	—
575	#123	—	2	2	no	—
576	C₂²⋊Q₈	—	2	1	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	1	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	—	2	2	no	—
582	C₂²⋊Q₈	—	2	1	no	—
583	C₂²⋊Q₈	—	2	1	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
587	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
588	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
589	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
590	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
591	#121	—	2	2	no	—
592	#121	—	2	1	no	—
593	#121	C₂³×C₈₉	1	2	yes	—
594	C₄×Q₈	—	2	2	no	—
595	C₄×Q₈	—	2	2	no	—
596	C₄×Q₈	—	2	1	no	—
597	C₄×Q₈	—	2	1	no	—
598	C₄×Q₈	—	2	2	no	—
599	C₄×Q₈	—	2	2	no	—
600	C₄×Q₈	—	2	2	no	—
601	C₄×Q₈	—	2	1	no	—
602	C₄×Q₈	—	2	1	no	—
603	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
604	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
605	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
606	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
607	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
608	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
609	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
610	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	D₄×C₈₉	1	2	yes	—
615	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
616	C₄×D₄	D₄×C₈₉	1	2	yes	—
617	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
618	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
619	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
620	#117	—	2	2	no	—
621	#117	—	2	2	no	—
622	#117	—	2	2	no	—
623	#117	—	2	4	no	—
624	#117	—	2	1	no	—
625	#117	—	2	2	no	—
626	#117	C₂³×C₈₉	1	1	yes	characteristic
627	#117	C₂³×C₈₉	1	2	yes	—
628	#117	C₂³×C₈₉	1	1	yes	characteristic
629	#117	C₂³×C₈₉	1	2	yes	—
630	C₂×C₄⋊C₄	—	2	1	no	—
631	C₂×C₄⋊C₄	—	2	1	no	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
634	C₂×C₄²	—	2	1	no	—
635	C₂×C₄²	—	2	1	no	—
636	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
637	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
638	#107	C₂³×C₈₉	1	2	yes	—
639	#107	C₂³×C₈₉	1	2	yes	—
640	#107	C₂³×C₈₉	1	4	yes	—
641	#106	C₂³×C₈₉	1	2	yes	—
642	#106	C₂³×C₈₉	1	2	yes	—
643	#106	C₂³×C₈₉	1	4	yes	—
644	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
645	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
646	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
647	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
648	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
649	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
650	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
651	#103	C₂³×C₈₉	1	4	yes	—
652	#103	C₂³×C₈₉	1	4	yes	—
653	#103	C₂³×C₈₉	1	2	yes	—
654	#103	C₂³×C₈₉	1	2	yes	—
655	#103	C₂³×C₈₉	1	4	yes	—
656	#103	C₂³×C₈₉	1	4	yes	—
657	#103	C₂³×C₈₉	1	4	yes	—
658	#103	C₂³×C₈₉	1	4	yes	—
659	#102	C₂³×C₈₉	1	2	yes	—
660	#102	C₂³×C₈₉	1	2	yes	—
661	#41	—	2	2	no	—
662	#41	—	2	2	no	—
663	#41	—	2	2	no	—
664	#41	—	2	2	no	—
665	C₂×Q₈	—	2	1	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	2	2	no	—
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	—	2	2	no	—
671	C₂×Q₈	—	2	4	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	4	no	—
674	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
675	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
676	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
677	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
681	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
682	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
690	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
691	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
692	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
695	Q₁₆	—	4	4	no	—
696	Q₁₆	—	4	4	no	—
697	Q₁₆	—	4	4	no	—
698	SD₁₆	—	4	4	no	—
699	M₁₆	—	2	4	no	—
700	M₁₆	—	4	4	no	—
701	C₂×C₈	—	2	4	no	—
702	C₂×C₈	—	4	4	no	—
703	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
704	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
705	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
732	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
733	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
734	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
735	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
736	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
738	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
739	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
753	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
754	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	1	no	—
757	C₄²	—	2	1	no	—
758	C₄²	—	2	1	no	—
759	C₄²	—	2	2	no	—
760	C₄²	—	2	4	no	—
761	C₄²	—	2	4	no	—
762	C₄²	—	2	2	no	—
763	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
764	C₄²	C₂×D₄×C₈₉	1	2	yes	—
765	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
766	C₄²	C₂×D₄×C₈₉	1	2	yes	—
767	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
768	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
769	C₄²	C₂⁴×C₈₉	1	2	yes	—
770	C₂³	—	2	1	no	—
771	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
772	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
773	Q₈	—	2	2	no	—
774	Q₈	—	2	4	no	—
775	Q₈	—	2	2	no	—
776	Q₈	—	2	1	no	—
777	Q₈	—	2	2	no	—
778	Q₈	—	2	4	no	—
779	Q₈	—	2	1	no	—
780	Q₈	—	4	2	no	—
781	Q₈	—	4	2	no	—
782	Q₈	—	4	4	no	—
783	Q₈	—	4	2	no	—
784	Q₈	—	8	2	no	—
785	D₄	—	2	4	no	—
786	D₄	—	2	2	no	—
787	D₄	—	2	1	no	—
788	D₄	—	2	1	no	—
789	D₄	—	4	2	no	—
790	D₄	—	8	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	4	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	2	no	—
808	C₂×C₄	—	4	2	no	—
809	C₂×C₄	—	8	1	no	—
810	C₂×C₄	—	8	1	no	—
811	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
812	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
813	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
814	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
816	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
817	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
819	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
820	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
821	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
822	C₈	—	2	2	no	—
823	C₈	—	2	2	no	—
824	C₈	—	2	4	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	2	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	#537×C₈₉	1	2	yes	—
834	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
835	C₄	—	2	1	no	—
836	C₄	—	2	2	no	—
837	C₄	—	2	1	no	—
838	C₄	—	2	1	no	—
839	C₄	—	2	2	no	—
840	C₄	—	2	2	no	—
841	C₄	—	4	1	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	4	no	—
849	C₄	#537×C₈₉	1	2	yes	—
850	C₄	#578×C₈₉	1	2	yes	—
851	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
852	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
853	C₂	—	2	2	no	—
854	C₂	—	4	2	no	—
855	C₂	—	8	1	no	—
856	C₂	C₂×#537×C₈₉	1	1	yes	characteristic
857	C₂	C₂×#578×C₈₉	1	1	yes	characteristic
858	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	#537×C₈₉	C₂²
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×#3261	C₂	semidirect
4. C₈₉×#3258	C₂	semidirect
5. C₈₉×#3255	C₂	semidirect
6. C₈₉×#3252	C₂	semidirect
7. C₈₉×#3249	C₂	semidirect
8. C₈₉×#3248	C₂	semidirect
9. C₈₉×#3082	C₂	semidirect
10. C₈₉×#3078	C₂	semidirect
11. C₈₉×#3076	C₂	semidirect
13. C₈₉×#3059	C₂	semidirect
14. C₈₉×#3044	C₂	semidirect
15. C₈₉×#3039	C₂	semidirect
16. C₂×#462×C₈₉	C₂	semidirect
17. C₈₉×#2906	C₂	semidirect
423. #60925	C₈₉	direct (N × H)
430. #3509	C₂×C₈₉	semidirect
432. #3261	C₂×C₈₉	semidirect
433. #3258	C₂×C₈₉	semidirect
434. #3255	C₂×C₈₉	semidirect
435. #3252	C₂×C₈₉	semidirect
436. #3249	C₂×C₈₉	semidirect
437. #3248	C₂×C₈₉	semidirect
438. #3082	C₂×C₈₉	semidirect
439. #3078	C₂×C₈₉	semidirect
440. #3076	C₂×C₈₉	semidirect
442. #3059	C₂×C₈₉	semidirect
443. #3044	C₂×C₈₉	semidirect
444. #3039	C₂×C₈₉	semidirect
445. C₂×#462	C₂×C₈₉	semidirect
446. #2906	C₂×C₈₉	semidirect
447. C₈₉	#60925	direct (N × H)

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×#3461	2
C₈₉×#3261	2
C₈₉×#3258	2
C₈₉×#3255	2
C₈₉×#3252	2
C₈₉×#3249	2
C₈₉×#3248	2
C₈₉×#3082	2
C₈₉×#3078	2
C₈₉×#3076	2
C₈₉×#3063	2
C₈₉×#3059	2
C₈₉×#3044	2
C₈₉×#3039	2
C₂×#462×C₈₉	2
C₈₉×#2906	2
#60925	89

Subgroups — C89×#60925 #36438773

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60925 #36438773