Subgroups — C₈₉×#60854 #36438702

Order 22784.

1780 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×#533×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3240	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3239	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3238	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3237	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3236	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3235	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3234	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3162	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3135	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3091	C₂	1	4	yes	maximal, complemented
13	C₈₉×#3076	C₂	1	4	yes	maximal, complemented
14	C₂×#432×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#533×C₈₉	—	2	1	no	—
16	#533×C₈₉	—	2	1	no	—
17	#533×C₈₉	—	2	1	no	—
18	#533×C₈₉	—	2	1	no	—
19	#533×C₈₉	C₂²	1	1	yes	characteristic
20	#533×C₈₉	C₂²	1	1	yes	characteristic
21	#533×C₈₉	C₂²	1	2	yes	—
22	#533×C₈₉	C₂²	1	2	yes	—
23	#533×C₈₉	C₂²	1	1	yes	characteristic
24	#533×C₈₉	C₂²	1	2	yes	—
25	#533×C₈₉	C₂²	1	2	yes	—
26	#532×C₈₉	C₂²	1	1	yes	characteristic
27	#532×C₈₉	C₂²	1	1	yes	characteristic
28	#532×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
31	#529×C₈₉	—	2	1	no	—
32	#529×C₈₉	—	2	1	no	—
33	#529×C₈₉	—	2	1	no	—
34	#529×C₈₉	—	2	1	no	—
35	#529×C₈₉	C₂²	1	2	yes	—
36	#529×C₈₉	C₂²	1	2	yes	—
37	C₂×#125×C₈₉	C₂²	1	2	yes	—
38	#525×C₈₉	—	2	1	no	—
39	#525×C₈₉	—	2	1	no	—
40	#525×C₈₉	C₂²	1	2	yes	—
41	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
42	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
43	C₄×#41×C₈₉	—	2	1	no	—
44	C₄×#41×C₈₉	—	2	1	no	—
45	C₄×#41×C₈₉	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
47	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
48	C₂×#117×C₈₉	C₂²	1	2	yes	—
49	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
50	#501×C₈₉	C₂²	1	4	yes	complemented
51	#501×C₈₉	C₂²	1	4	yes	complemented
52	#501×C₈₉	C₂²	1	4	yes	complemented
53	#501×C₈₉	C₂²	1	4	yes	complemented
54	#491×C₈₉	C₂²	1	4	yes	complemented
55	#490×C₈₉	C₂²	1	4	yes	complemented
56	#489×C₈₉	C₂²	1	4	yes	complemented
57	#489×C₈₉	C₂²	1	4	yes	complemented
58	#485×C₈₉	C₂²	1	8	yes	—
59	#484×C₈₉	C₂²	1	4	yes	—
60	#483×C₈₉	C₂²	1	4	yes	—
61	#482×C₈₉	C₂²	1	8	yes	—
62	#481×C₈₉	C₂²	1	4	yes	—
63	#480×C₈₉	C₂²	1	4	yes	—
64	#479×C₈₉	C₂²	1	8	yes	complemented
65	#478×C₈₉	C₂²	1	8	yes	complemented
66	#477×C₈₉	C₂²	1	4	yes	complemented
67	#476×C₈₉	C₂²	1	4	yes	complemented
68	#475×C₈₉	C₂²	1	4	yes	complemented
69	#474×C₈₉	C₂²	1	4	yes	complemented
70	#432×C₈₉	C₂²	1	2	yes	—
71	#432×C₈₉	C₂²	1	2	yes	—
72	#432×C₈₉	C₂²	1	2	yes	—
73	#432×C₈₉	C₂²	1	2	yes	—
74	#427×C₈₉	C₂²	1	8	yes	—
75	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
76	#416×C₈₉	C₂²	1	8	yes	—
77	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
78	C₂×#97×C₈₉	C₂²	1	2	yes	—
79	C₂×#41×C₈₉	—	2	1	no	—
80	C₂×#41×C₈₉	—	2	1	no	—
81	C₂×#41×C₈₉	C₂³	1	2	yes	—
82	C₂²×Q₈×C₈₉	—	2	1	no	—
83	C₂²×Q₈×C₈₉	—	2	1	no	—
84	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
85	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
86	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
88	C₄⋊Q₈×C₈₉	—	2	1	no	—
89	C₄⋊Q₈×C₈₉	—	2	1	no	—
90	C₄⋊Q₈×C₈₉	—	2	1	no	—
91	C₄⋊Q₈×C₈₉	—	2	1	no	—
92	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
94	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
95	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
96	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
97	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
99	#127×C₈₉	C₂³	1	1	yes	characteristic
100	#126×C₈₉	—	2	2	no	—
101	#126×C₈₉	—	2	2	no	—
102	#125×C₈₉	—	2	2	no	—
103	#125×C₈₉	—	2	2	no	—
104	#125×C₈₉	—	2	1	no	—
105	#125×C₈₉	—	2	1	no	—
106	#125×C₈₉	C₂³	1	4	yes	—
107	#125×C₈₉	C₂³	1	4	yes	—
108	#125×C₈₉	C₂³	1	2	yes	—
109	#124×C₈₉	—	2	1	no	—
110	#124×C₈₉	—	2	1	no	—
111	#124×C₈₉	C₂³	1	2	yes	—
112	#123×C₈₉	—	2	2	no	—
113	#123×C₈₉	—	2	2	no	—
114	#123×C₈₉	—	2	2	no	—
115	C₂²⋊Q₈×C₈₉	—	2	2	no	—
116	C₂²⋊Q₈×C₈₉	—	2	2	no	—
117	C₂²⋊Q₈×C₈₉	—	2	2	no	—
118	C₂²⋊Q₈×C₈₉	—	2	2	no	—
119	C₂²⋊Q₈×C₈₉	—	2	2	no	—
120	C₂²⋊Q₈×C₈₉	—	2	2	no	—
121	C₂²⋊Q₈×C₈₉	—	2	2	no	—
122	C₂²⋊Q₈×C₈₉	—	2	2	no	—
123	C₂²⋊Q₈×C₈₉	—	2	1	no	—
124	C₂²⋊Q₈×C₈₉	—	2	1	no	—
125	C₂²⋊Q₈×C₈₉	—	2	1	no	—
126	C₂²⋊Q₈×C₈₉	—	2	1	no	—
127	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
128	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
129	#121×C₈₉	—	2	1	no	—
130	#121×C₈₉	—	2	1	no	—
131	#121×C₈₉	—	2	1	no	—
132	#121×C₈₉	—	2	1	no	—
133	#121×C₈₉	C₂³	1	2	yes	—
134	#121×C₈₉	C₂³	1	2	yes	—
135	#120×C₈₉	—	2	2	no	—
136	C₄×Q₈×C₈₉	—	2	2	no	—
137	C₄×Q₈×C₈₉	—	2	2	no	—
138	C₄×Q₈×C₈₉	—	2	2	no	—
139	C₄×Q₈×C₈₉	—	2	2	no	—
140	C₄×Q₈×C₈₉	—	2	2	no	—
141	C₄×Q₈×C₈₉	—	2	2	no	—
142	C₄×Q₈×C₈₉	—	2	2	no	—
143	C₄×Q₈×C₈₉	—	2	2	no	—
144	C₄×Q₈×C₈₉	—	2	1	no	—
145	C₄×Q₈×C₈₉	—	2	1	no	—
146	C₄×Q₈×C₈₉	—	2	1	no	—
147	C₄×Q₈×C₈₉	—	2	1	no	—
148	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
149	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
150	C₄×D₄×C₈₉	—	2	2	no	—
151	C₄×D₄×C₈₉	—	2	2	no	—
152	C₄×D₄×C₈₉	—	2	2	no	—
153	C₄×D₄×C₈₉	—	2	2	no	—
154	C₄×D₄×C₈₉	—	2	2	no	—
155	C₄×D₄×C₈₉	—	2	2	no	—
156	C₄×D₄×C₈₉	—	2	1	no	—
157	C₄×D₄×C₈₉	—	2	1	no	—
158	C₄×D₄×C₈₉	—	2	1	no	—
159	C₄×D₄×C₈₉	—	2	1	no	—
160	C₄×D₄×C₈₉	C₂³	1	2	yes	—
161	C₄×D₄×C₈₉	C₂³	1	2	yes	—
162	#117×C₈₉	—	2	2	no	—
163	#117×C₈₉	—	2	2	no	—
164	#117×C₈₉	—	2	1	no	—
165	#117×C₈₉	—	2	1	no	—
166	#117×C₈₉	—	2	2	no	—
167	#117×C₈₉	—	2	2	no	—
168	#117×C₈₉	—	2	2	no	—
169	#117×C₈₉	C₂³	1	4	yes	—
170	#117×C₈₉	C₂³	1	2	yes	—
171	#117×C₈₉	C₂³	1	4	yes	—
172	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
173	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
174	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
175	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
176	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
179	C₂×C₄²×C₈₉	—	2	2	no	—
180	C₂×C₄²×C₈₉	—	2	2	no	—
181	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
182	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
183	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
184	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
185	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
186	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
193	#107×C₈₉	C₂³	1	8	yes	—
194	#107×C₈₉	C₂³	1	8	yes	—
195	#106×C₈₉	C₂³	1	8	yes	—
196	#106×C₈₉	C₂³	1	8	yes	—
197	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
198	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
199	#103×C₈₉	C₂³	1	8	yes	—
200	#103×C₈₉	C₂³	1	8	yes	—
201	#102×C₈₉	C₂³	1	8	yes	—
202	#102×C₈₉	C₂³	1	8	yes	—
203	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
204	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
205	#97×C₈₉	C₂³	1	4	yes	—
206	#97×C₈₉	C₂³	1	4	yes	—
207	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
208	#41×C₈₉	—	2	8	no	—
209	#41×C₈₉	—	4	4	no	—
210	#41×C₈₉	—	4	4	no	—
211	C₂×Q₈×C₈₉	—	2	1	no	—
212	C₂×Q₈×C₈₉	—	2	1	no	—
213	C₂×Q₈×C₈₉	—	2	2	no	—
214	C₂×Q₈×C₈₉	—	2	2	no	—
215	C₂×Q₈×C₈₉	—	2	2	no	—
216	C₂×Q₈×C₈₉	—	2	2	no	—
217	C₂×Q₈×C₈₉	—	4	4	no	—
218	C₂×Q₈×C₈₉	—	4	4	no	—
219	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
220	C₂×D₄×C₈₉	—	2	2	no	—
221	C₂×D₄×C₈₉	—	2	2	no	—
222	C₂×D₄×C₈₉	—	2	2	no	—
223	C₂×D₄×C₈₉	—	2	1	no	—
224	C₂×D₄×C₈₉	—	2	1	no	—
225	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₈₉	—	2	4	no	—
227	C₂²×C₄×C₈₉	—	2	2	no	—
228	C₂²×C₄×C₈₉	—	2	2	no	—
229	C₂²×C₄×C₈₉	—	2	2	no	—
230	C₂²×C₄×C₈₉	—	2	2	no	—
231	C₂²×C₄×C₈₉	—	2	2	no	—
232	C₂²×C₄×C₈₉	—	4	2	no	—
233	C₂²×C₄×C₈₉	—	4	2	no	—
234	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
252	C₂×C₈×C₈₉	—	2	8	no	—
253	C₂×C₈×C₈₉	C₂⁴	1	8	yes	—
254	C₄⋊C₄×C₈₉	—	2	4	no	—
255	C₄⋊C₄×C₈₉	—	2	4	no	—
256	C₄⋊C₄×C₈₉	—	2	4	no	—
257	C₄⋊C₄×C₈₉	—	2	4	no	—
258	C₄⋊C₄×C₈₉	—	2	2	no	—
259	C₄⋊C₄×C₈₉	—	2	2	no	—
260	C₄⋊C₄×C₈₉	—	2	2	no	—
261	C₄⋊C₄×C₈₉	—	2	2	no	—
262	C₄⋊C₄×C₈₉	—	2	2	no	—
263	C₄⋊C₄×C₈₉	—	2	2	no	—
264	C₄⋊C₄×C₈₉	—	2	1	no	—
265	C₄⋊C₄×C₈₉	—	2	1	no	—
266	C₄⋊C₄×C₈₉	—	2	1	no	—
267	C₄⋊C₄×C₈₉	—	2	1	no	—
268	C₄⋊C₄×C₈₉	—	2	2	no	—
269	C₄⋊C₄×C₈₉	—	2	2	no	—
270	C₄⋊C₄×C₈₉	—	2	2	no	—
271	C₄⋊C₄×C₈₉	—	2	2	no	—
272	C₄⋊C₄×C₈₉	—	2	2	no	—
273	C₄⋊C₄×C₈₉	—	2	2	no	—
274	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
275	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
276	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
278	C₂²⋊C₄×C₈₉	—	2	4	no	—
279	C₂²⋊C₄×C₈₉	—	2	4	no	—
280	C₂²⋊C₄×C₈₉	—	2	2	no	—
281	C₂²⋊C₄×C₈₉	—	2	2	no	—
282	C₂²⋊C₄×C₈₉	—	2	2	no	—
283	C₂²⋊C₄×C₈₉	—	2	2	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	2	no	—
288	C₂²⋊C₄×C₈₉	—	2	2	no	—
289	C₄²×C₈₉	—	2	2	no	—
290	C₄²×C₈₉	—	2	2	no	—
291	C₄²×C₈₉	—	2	4	no	—
292	C₄²×C₈₉	—	2	2	no	—
293	C₄²×C₈₉	—	2	4	no	—
294	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
295	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
296	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
297	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
307	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
308	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
309	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
310	C₂³×C₈₉	—	2	2	no	—
311	C₂³×C₈₉	—	2	2	no	—
312	C₂³×C₈₉	—	2	2	no	—
313	C₂³×C₈₉	—	4	1	no	—
314	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
315	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
316	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
317	Q₈×C₈₉	—	2	4	no	—
318	Q₈×C₈₉	—	4	4	no	—
319	Q₈×C₈₉	—	4	4	no	—
320	Q₈×C₈₉	—	4	4	no	—
321	Q₈×C₈₉	—	4	2	no	—
322	Q₈×C₈₉	—	4	2	no	—
323	Q₈×C₈₉	—	4	4	no	—
324	D₄×C₈₉	—	2	4	no	—
325	D₄×C₈₉	—	4	2	no	—
326	D₄×C₈₉	—	4	2	no	—
327	D₄×C₈₉	—	4	4	no	—
328	D₄×C₈₉	—	4	4	no	—
329	D₄×C₈₉	—	4	4	no	—
330	C₂×C₄×C₈₉	—	2	2	no	—
331	C₂×C₄×C₈₉	—	2	2	no	—
332	C₂×C₄×C₈₉	—	2	2	no	—
333	C₂×C₄×C₈₉	—	2	2	no	—
334	C₂×C₄×C₈₉	—	2	2	no	—
335	C₂×C₄×C₈₉	—	2	2	no	—
336	C₂×C₄×C₈₉	—	2	2	no	—
337	C₂×C₄×C₈₉	—	2	2	no	—
338	C₂×C₄×C₈₉	—	2	2	no	—
339	C₂×C₄×C₈₉	—	2	2	no	—
340	C₂×C₄×C₈₉	—	2	2	no	—
341	C₂×C₄×C₈₉	—	2	2	no	—
342	C₂×C₄×C₈₉	—	2	2	no	—
343	C₂×C₄×C₈₉	—	2	4	no	—
344	C₂×C₄×C₈₉	—	2	4	no	—
345	C₂×C₄×C₈₉	—	4	1	no	—
346	C₂×C₄×C₈₉	—	4	1	no	—
347	C₂×C₄×C₈₉	—	4	1	no	—
348	C₂×C₄×C₈₉	—	4	1	no	—
349	C₂×C₄×C₈₉	—	4	1	no	—
350	C₂×C₄×C₈₉	—	4	1	no	—
351	C₂×C₄×C₈₉	—	4	1	no	—
352	C₂×C₄×C₈₉	—	4	4	no	—
353	C₂×C₄×C₈₉	—	4	4	no	—
354	C₂×C₄×C₈₉	—	4	4	no	—
355	C₂×C₄×C₈₉	—	4	4	no	—
356	C₂×C₄×C₈₉	—	4	4	no	—
357	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
369	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
370	C₈×C₈₉	—	2	8	no	—
371	C₂²×C₈₉	—	2	1	no	—
372	C₂²×C₈₉	—	2	1	no	—
373	C₂²×C₈₉	—	2	1	no	—
374	C₂²×C₈₉	—	2	1	no	—
375	C₂²×C₈₉	—	2	1	no	—
376	C₂²×C₈₉	—	2	1	no	—
377	C₂²×C₈₉	—	2	1	no	—
378	C₂²×C₈₉	—	4	4	no	—
379	C₂²×C₈₉	—	4	2	no	—
380	C₂²×C₈₉	—	4	2	no	—
381	C₂²×C₈₉	—	4	2	no	—
382	C₂²×C₈₉	#536	1	2	yes	—
383	C₂²×C₈₉	#575	1	2	yes	—
384	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
385	C₄×C₈₉	—	2	1	no	—
386	C₄×C₈₉	—	2	1	no	—
387	C₄×C₈₉	—	2	1	no	—
388	C₄×C₈₉	—	2	1	no	—
389	C₄×C₈₉	—	2	1	no	—
390	C₄×C₈₉	—	2	1	no	—
391	C₄×C₈₉	—	2	1	no	—
392	C₄×C₈₉	—	2	1	no	—
393	C₄×C₈₉	—	2	1	no	—
394	C₄×C₈₉	—	4	2	no	—
395	C₄×C₈₉	—	4	2	no	—
396	C₄×C₈₉	—	4	2	no	—
397	C₄×C₈₉	—	4	4	no	—
398	C₄×C₈₉	—	4	4	no	—
399	C₄×C₈₉	#536	1	2	yes	—
400	C₄×C₈₉	#575	1	2	yes	—
401	C₄×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
402	#60854	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
403	C₂×C₈₉	—	2	2	no	—
404	C₂×C₈₉	—	2	2	no	—
405	C₂×C₈₉	—	4	1	no	—
406	C₂×C₈₉	—	8	2	no	—
407	C₂×C₈₉	C₂×#536	1	1	yes	characteristic
408	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
409	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
410	#3444	C₂×C₈₉	1	1	yes	characteristic
411	C₂×#533	C₂×C₈₉	1	1	yes	characteristic, complemented
412	#3240	C₂×C₈₉	1	4	yes	complemented
413	#3239	C₂×C₈₉	1	2	yes	complemented
414	#3238	C₂×C₈₉	1	2	yes	complemented
415	#3237	C₂×C₈₉	1	2	yes	complemented
416	#3236	C₂×C₈₉	1	2	yes	complemented
417	#3235	C₂×C₈₉	1	2	yes	complemented
418	#3234	C₂×C₈₉	1	2	yes	complemented
419	#3162	C₂×C₈₉	1	2	yes	complemented
420	#3135	C₂×C₈₉	1	2	yes	complemented
421	#3091	C₂×C₈₉	1	4	yes	complemented
422	#3076	C₂×C₈₉	1	4	yes	complemented
423	C₂×#432	C₂×C₈₉	1	1	yes	characteristic, complemented
424	C₈₉	#60854	1	1	yes	characteristic, direct product factor, Sylow
425	#533	—	2	1	no	—
426	#533	—	2	1	no	—
427	#533	—	2	1	no	—
428	#533	—	2	1	no	—
429	#533	C₂²×C₈₉	1	1	yes	characteristic
430	#533	C₂²×C₈₉	1	1	yes	characteristic
431	#533	C₂²×C₈₉	1	2	yes	—
432	#533	C₂²×C₈₉	1	2	yes	—
433	#533	C₂²×C₈₉	1	1	yes	characteristic
434	#533	C₂²×C₈₉	1	2	yes	—
435	#533	C₂²×C₈₉	1	2	yes	—
436	#532	C₂²×C₈₉	1	1	yes	characteristic
437	#532	C₂²×C₈₉	1	1	yes	characteristic
438	#532	C₂²×C₈₉	1	1	yes	characteristic
439	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
440	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
441	#529	—	2	1	no	—
442	#529	—	2	1	no	—
443	#529	—	2	1	no	—
444	#529	—	2	1	no	—
445	#529	C₂²×C₈₉	1	2	yes	—
446	#529	C₂²×C₈₉	1	2	yes	—
447	C₂×#125	C₂²×C₈₉	1	2	yes	—
448	#525	—	2	1	no	—
449	#525	—	2	1	no	—
450	#525	C₂²×C₈₉	1	2	yes	—
451	C₂×C₂²⋊Q₈	—	2	1	no	—
452	C₂×C₂²⋊Q₈	—	2	1	no	—
453	C₄×#41	—	2	1	no	—
454	C₄×#41	—	2	1	no	—
455	C₄×#41	C₂²×C₈₉	1	2	yes	—
456	C₂×C₄×Q₈	—	2	1	no	—
457	C₂×C₄×Q₈	—	2	1	no	—
458	C₂×#117	C₂²×C₈₉	1	2	yes	—
459	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
460	#501	C₂²×C₈₉	1	4	yes	complemented
461	#501	C₂²×C₈₉	1	4	yes	complemented
462	#501	C₂²×C₈₉	1	4	yes	complemented
463	#501	C₂²×C₈₉	1	4	yes	complemented
464	#491	C₂²×C₈₉	1	4	yes	complemented
465	#490	C₂²×C₈₉	1	4	yes	complemented
466	#489	C₂²×C₈₉	1	4	yes	complemented
467	#489	C₂²×C₈₉	1	4	yes	complemented
468	#485	C₂²×C₈₉	1	8	yes	—
469	#484	C₂²×C₈₉	1	4	yes	—
470	#483	C₂²×C₈₉	1	4	yes	—
471	#482	C₂²×C₈₉	1	8	yes	—
472	#481	C₂²×C₈₉	1	4	yes	—
473	#480	C₂²×C₈₉	1	4	yes	—
474	#479	C₂²×C₈₉	1	8	yes	complemented
475	#478	C₂²×C₈₉	1	8	yes	complemented
476	#477	C₂²×C₈₉	1	4	yes	complemented
477	#476	C₂²×C₈₉	1	4	yes	complemented
478	#475	C₂²×C₈₉	1	4	yes	complemented
479	#474	C₂²×C₈₉	1	4	yes	complemented
480	#432	C₂²×C₈₉	1	2	yes	—
481	#432	C₂²×C₈₉	1	2	yes	—
482	#432	C₂²×C₈₉	1	2	yes	—
483	#432	C₂²×C₈₉	1	2	yes	—
484	#427	C₂²×C₈₉	1	8	yes	—
485	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
486	#416	C₂²×C₈₉	1	8	yes	—
487	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
488	C₂×#97	C₂²×C₈₉	1	2	yes	—
489	C₂×#41	—	2	1	no	—
490	C₂×#41	—	2	1	no	—
491	C₂×#41	C₂³×C₈₉	1	2	yes	—
492	C₂²×Q₈	—	2	1	no	—
493	C₂²×Q₈	—	2	1	no	—
494	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
495	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
496	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
497	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
498	C₄⋊Q₈	—	2	1	no	—
499	C₄⋊Q₈	—	2	1	no	—
500	C₄⋊Q₈	—	2	1	no	—
501	C₄⋊Q₈	—	2	1	no	—
502	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
503	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
504	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
505	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
506	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
507	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
508	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
509	#127	C₂³×C₈₉	1	1	yes	characteristic
510	#126	—	2	2	no	—
511	#126	—	2	2	no	—
512	#125	—	2	2	no	—
513	#125	—	2	2	no	—
514	#125	—	2	1	no	—
515	#125	—	2	1	no	—
516	#125	C₂³×C₈₉	1	4	yes	—
517	#125	C₂³×C₈₉	1	4	yes	—
518	#125	C₂³×C₈₉	1	2	yes	—
519	#124	—	2	1	no	—
520	#124	—	2	1	no	—
521	#124	C₂³×C₈₉	1	2	yes	—
522	#123	—	2	2	no	—
523	#123	—	2	2	no	—
524	#123	—	2	2	no	—
525	C₂²⋊Q₈	—	2	2	no	—
526	C₂²⋊Q₈	—	2	2	no	—
527	C₂²⋊Q₈	—	2	2	no	—
528	C₂²⋊Q₈	—	2	2	no	—
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₂²⋊Q₈	—	2	2	no	—
532	C₂²⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	1	no	—
534	C₂²⋊Q₈	—	2	1	no	—
535	C₂²⋊Q₈	—	2	1	no	—
536	C₂²⋊Q₈	—	2	1	no	—
537	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
538	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
539	#121	—	2	1	no	—
540	#121	—	2	1	no	—
541	#121	—	2	1	no	—
542	#121	—	2	1	no	—
543	#121	C₂³×C₈₉	1	2	yes	—
544	#121	C₂³×C₈₉	1	2	yes	—
545	#120	—	2	2	no	—
546	C₄×Q₈	—	2	2	no	—
547	C₄×Q₈	—	2	2	no	—
548	C₄×Q₈	—	2	2	no	—
549	C₄×Q₈	—	2	2	no	—
550	C₄×Q₈	—	2	2	no	—
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	—	2	1	no	—
555	C₄×Q₈	—	2	1	no	—
556	C₄×Q₈	—	2	1	no	—
557	C₄×Q₈	—	2	1	no	—
558	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
559	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	2	2	no	—
562	C₄×D₄	—	2	2	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	2	2	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	—	2	1	no	—
568	C₄×D₄	—	2	1	no	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	C₂³×C₈₉	1	2	yes	—
571	C₄×D₄	C₂³×C₈₉	1	2	yes	—
572	#117	—	2	2	no	—
573	#117	—	2	2	no	—
574	#117	—	2	1	no	—
575	#117	—	2	1	no	—
576	#117	—	2	2	no	—
577	#117	—	2	2	no	—
578	#117	—	2	2	no	—
579	#117	C₂³×C₈₉	1	4	yes	—
580	#117	C₂³×C₈₉	1	4	yes	—
581	#117	C₂³×C₈₉	1	2	yes	—
582	C₂×C₄⋊C₄	—	2	2	no	—
583	C₂×C₄⋊C₄	—	2	2	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
588	C₂×C₂²⋊C₄	—	2	2	no	—
589	C₂×C₄²	—	2	2	no	—
590	C₂×C₄²	—	2	2	no	—
591	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
592	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
593	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
594	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
595	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
596	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
597	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
598	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
599	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
603	#107	C₂³×C₈₉	1	8	yes	—
604	#107	C₂³×C₈₉	1	8	yes	—
605	#106	C₂³×C₈₉	1	8	yes	—
606	#106	C₂³×C₈₉	1	8	yes	—
607	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
608	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
609	#103	C₂³×C₈₉	1	8	yes	—
610	#103	C₂³×C₈₉	1	8	yes	—
611	#102	C₂³×C₈₉	1	8	yes	—
612	#102	C₂³×C₈₉	1	8	yes	—
613	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
614	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
615	#97	C₂³×C₈₉	1	4	yes	—
616	#97	C₂³×C₈₉	1	4	yes	—
617	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
618	#41	—	2	8	no	—
619	#41	—	4	4	no	—
620	#41	—	4	4	no	—
621	C₂×Q₈	—	2	1	no	—
622	C₂×Q₈	—	2	1	no	—
623	C₂×Q₈	—	2	2	no	—
624	C₂×Q₈	—	2	2	no	—
625	C₂×Q₈	—	2	2	no	—
626	C₂×Q₈	—	2	2	no	—
627	C₂×Q₈	—	4	4	no	—
628	C₂×Q₈	—	4	4	no	—
629	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	2	2	no	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	4	2	no	—
643	C₂²×C₄	—	4	2	no	—
644	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
645	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
646	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
647	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
648	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
649	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
650	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
651	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
652	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
653	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
654	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
655	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
659	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
661	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
662	C₂×C₈	—	2	8	no	—
663	C₂×C₈	C₂⁴×C₈₉	1	8	yes	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	2	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	1	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
685	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
686	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
687	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₄²	—	2	2	no	—
700	C₄²	—	2	2	no	—
701	C₄²	—	2	2	no	—
702	C₄²	—	2	4	no	—
703	C₄²	—	2	4	no	—
704	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
705	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
706	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
707	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
708	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
709	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
710	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
711	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
712	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
713	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
714	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
715	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
716	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
717	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
718	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
719	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	4	1	no	—
724	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
725	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
726	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
727	Q₈	—	2	4	no	—
728	Q₈	—	4	4	no	—
729	Q₈	—	4	4	no	—
730	Q₈	—	4	4	no	—
731	Q₈	—	4	2	no	—
732	Q₈	—	4	2	no	—
733	Q₈	—	4	4	no	—
734	D₄	—	2	4	no	—
735	D₄	—	4	2	no	—
736	D₄	—	4	2	no	—
737	D₄	—	4	4	no	—
738	D₄	—	4	4	no	—
739	D₄	—	4	4	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	4	no	—
755	C₂×C₄	—	4	1	no	—
756	C₂×C₄	—	4	1	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	4	no	—
763	C₂×C₄	—	4	4	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	—	4	4	no	—
767	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
768	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
769	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
770	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
771	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
772	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
773	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
774	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
775	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
776	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
777	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
778	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
779	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
780	C₈	—	2	8	no	—
781	C₂²	—	2	1	no	—
782	C₂²	—	2	1	no	—
783	C₂²	—	2	1	no	—
784	C₂²	—	2	1	no	—
785	C₂²	—	2	1	no	—
786	C₂²	—	2	1	no	—
787	C₂²	—	2	1	no	—
788	C₂²	—	4	4	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	#536×C₈₉	1	2	yes	—
793	C₂²	#575×C₈₉	1	2	yes	—
794	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
795	C₄	—	2	1	no	—
796	C₄	—	2	1	no	—
797	C₄	—	2	1	no	—
798	C₄	—	2	1	no	—
799	C₄	—	2	1	no	—
800	C₄	—	2	1	no	—
801	C₄	—	2	1	no	—
802	C₄	—	2	1	no	—
803	C₄	—	2	1	no	—
804	C₄	—	4	2	no	—
805	C₄	—	4	2	no	—
806	C₄	—	4	4	no	—
807	C₄	—	4	4	no	—
808	C₄	—	4	2	no	—
809	C₄	#536×C₈₉	1	2	yes	—
810	C₄	#575×C₈₉	1	2	yes	—
811	C₄	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
812	C₂	—	2	2	no	—
813	C₂	—	2	2	no	—
814	C₂	—	4	1	no	—
815	C₂	—	8	2	no	—
816	C₂	C₂×#536×C₈₉	1	1	yes	characteristic
817	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
818	C₂	C₂×#575×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
socle	C₂²×C₈₉	C₂³×D₄
prime radical	C₈₉×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₉ ◁ C₂²×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#533×C₈₉	C₂	semidirect
3. C₈₉×#3240	C₂	semidirect
4. C₈₉×#3239	C₂	semidirect
5. C₈₉×#3238	C₂	semidirect
6. C₈₉×#3237	C₂	semidirect
7. C₈₉×#3236	C₂	semidirect
8. C₈₉×#3235	C₂	semidirect
9. C₈₉×#3234	C₂	semidirect
10. C₈₉×#3162	C₂	semidirect
11. C₈₉×#3135	C₂	semidirect
12. C₈₉×#3091	C₂	semidirect
13. C₈₉×#3076	C₂	semidirect
14. C₂×#432×C₈₉	C₂	semidirect
50. #501×C₈₉	C₂²	semidirect
51. #501×C₈₉	C₂²	semidirect
52. #501×C₈₉	C₂²	semidirect
53. #501×C₈₉	C₂²	semidirect
54. #491×C₈₉	C₂²	semidirect
55. #490×C₈₉	C₂²	semidirect
56. #489×C₈₉	C₂²	semidirect
57. #489×C₈₉	C₂²	semidirect
64. #479×C₈₉	C₂²	semidirect
65. #478×C₈₉	C₂²	semidirect
66. #477×C₈₉	C₂²	semidirect
67. #476×C₈₉	C₂²	semidirect
68. #475×C₈₉	C₂²	semidirect
69. #474×C₈₉	C₂²	semidirect
402. #60854	C₈₉	direct (N × H)
411. C₂×#533	C₂×C₈₉	semidirect
412. #3240	C₂×C₈₉	semidirect
413. #3239	C₂×C₈₉	semidirect
414. #3238	C₂×C₈₉	semidirect
415. #3237	C₂×C₈₉	semidirect
416. #3236	C₂×C₈₉	semidirect
417. #3235	C₂×C₈₉	semidirect
418. #3234	C₂×C₈₉	semidirect
419. #3162	C₂×C₈₉	semidirect
420. #3135	C₂×C₈₉	semidirect
421. #3091	C₂×C₈₉	semidirect
422. #3076	C₂×C₈₉	semidirect
423. C₂×#432	C₂×C₈₉	semidirect
424. C₈₉	#60854	direct (N × H)
460. #501	C₂²×C₈₉	semidirect
461. #501	C₂²×C₈₉	semidirect
462. #501	C₂²×C₈₉	semidirect
463. #501	C₂²×C₈₉	semidirect
464. #491	C₂²×C₈₉	semidirect
465. #490	C₂²×C₈₉	semidirect
466. #489	C₂²×C₈₉	semidirect
467. #489	C₂²×C₈₉	semidirect
474. #479	C₂²×C₈₉	semidirect
475. #478	C₂²×C₈₉	semidirect
476. #477	C₂²×C₈₉	semidirect
477. #476	C₂²×C₈₉	semidirect
478. #475	C₂²×C₈₉	semidirect
479. #474	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×#3444	2
C₂×#533×C₈₉	2
C₈₉×#3240	2
C₈₉×#3239	2
C₈₉×#3238	2
C₈₉×#3237	2
C₈₉×#3236	2
C₈₉×#3235	2
C₈₉×#3234	2
C₈₉×#3162	2
C₈₉×#3135	2
C₈₉×#3091	2
C₈₉×#3076	2
C₂×#432×C₈₉	2
#60854	89

Subgroups — C89×#60854 #36438702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60854 #36438702