Subgroups — C₈₉×#60146 #36437994

Order 22784.

2756 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#568×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#131×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×#41×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#2935	C₂	1	3	yes	maximal, complemented
5	D₄×M₁₆×C₈₉	C₂	1	3	yes	maximal, complemented
6	C₈₉×#2933	C₂	1	3	yes	maximal, complemented
7	C₈₉×#2933	C₂	1	3	yes	maximal, complemented
8	C₈₉×#2932	C₂	1	3	yes	maximal, complemented
9	C₈₉×#2930	C₂	1	3	yes	maximal, complemented
10	C₈₉×#2929	C₂	1	3	yes	maximal, complemented
11	C₂×#435×C₈₉	C₂	1	3	yes	maximal, complemented
12	C₈₉×#2906	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#2880	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2880	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2875	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
18	#568×C₈₉	—	2	8	no	—
19	C₂×#131×C₈₉	—	2	8	no	—
20	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#131×C₈₉	C₂²	1	3	yes	complemented
25	C₂×#131×C₈₉	C₂²	1	3	yes	complemented
26	C₂×#131×C₈₉	C₂²	1	3	yes	complemented
27	C₂×#131×C₈₉	C₂²	1	3	yes	complemented
28	C₂²×M₁₆×C₈₉	C₂²	1	3	yes	complemented
29	C₂²×M₁₆×C₈₉	C₂²	1	3	yes	complemented
30	C₂²×M₁₆×C₈₉	C₂²	1	3	yes	complemented
31	C₂³×C₈×C₈₉	C₂²	1	3	yes	complemented
32	#550×C₈₉	C₄	1	1	yes	characteristic
33	D₄×Q₈×C₈₉	C₄	1	1	yes	characteristic
34	#548×C₈₉	C₄	1	1	yes	characteristic
35	#548×C₈₉	C₄	1	1	yes	characteristic
36	#547×C₈₉	C₄	1	3	yes	—
37	#546×C₈₉	C₄	1	3	yes	—
38	#546×C₈₉	C₄	1	3	yes	—
39	D₄²×C₈₉	C₄	1	3	yes	—
40	#532×C₈₉	C₂²	1	3	yes	—
41	#525×C₈₉	C₂²	1	3	yes	—
42	#525×C₈₉	C₂²	1	3	yes	—
43	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₈₉	C₂²	1	3	yes	—
45	#436×C₈₉	C₂²	1	6	yes	complemented
46	#436×C₈₉	C₂²	1	6	yes	complemented
47	#435×C₈₉	C₂²	1	1	yes	characteristic
48	#435×C₈₉	C₂²	1	3	yes	—
49	#435×C₈₉	C₂²	1	3	yes	complemented
50	#435×C₈₉	C₂²	1	3	yes	complemented
51	#435×C₈₉	C₂²	1	3	yes	complemented
52	#435×C₈₉	C₂²	1	3	yes	complemented
53	#435×C₈₉	C₂²	1	3	yes	complemented
54	#435×C₈₉	C₂²	1	3	yes	complemented
55	#435×C₈₉	C₂²	1	6	yes	complemented
56	#435×C₈₉	C₂²	1	6	yes	complemented
57	#435×C₈₉	C₂²	1	6	yes	complemented
58	C₈×D₄×C₈₉	C₂²	1	6	yes	complemented
59	C₈×D₄×C₈₉	C₂²	1	6	yes	complemented
60	#424×C₈₉	C₂²	1	3	yes	complemented
61	#424×C₈₉	C₂²	1	3	yes	complemented
62	#423×C₈₉	C₂²	1	3	yes	complemented
63	C₂×C₄⋊C₈×C₈₉	C₂²	1	3	yes	complemented
64	#408×C₈₉	C₂²	1	3	yes	complemented
65	#408×C₈₉	C₂²	1	3	yes	complemented
66	#408×C₈₉	C₂²	1	3	yes	complemented
67	#408×C₈₉	C₂²	1	3	yes	complemented
68	#407×C₈₉	C₂²	1	3	yes	complemented
69	#407×C₈₉	C₂²	1	3	yes	complemented
70	C₂×C₂²⋊C₈×C₈₉	C₂²	1	3	yes	complemented
71	C₂×C₂²⋊C₈×C₈₉	C₂²	1	3	yes	complemented
72	#405×C₈₉	C₂²	1	3	yes	complemented
73	#405×C₈₉	C₂²	1	3	yes	complemented
74	C₄×M₁₆×C₈₉	C₂²	1	3	yes	complemented
75	C₂×#97×C₈₉	C₂²	1	3	yes	complemented
76	C₂×#41×C₈₉	—	2	4	no	—
77	C₂×#41×C₈₉	—	2	4	no	—
78	C₂×#41×C₈₉	—	2	4	no	—
79	C₂×#41×C₈₉	—	2	4	no	—
80	C₂×#41×C₈₉	C₂×C₄	1	3	yes	—
81	C₂×#41×C₈₉	C₂×C₄	1	3	yes	—
82	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
83	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
84	C₂×#41×C₈₉	C₂³	1	3	yes	—
85	C₂×#41×C₈₉	C₂³	1	3	yes	—
86	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
88	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
89	C₂²×D₄×C₈₉	C₂×C₄	1	3	yes	—
90	C₂²×D₄×C₈₉	C₂×C₄	1	3	yes	—
91	C₂²×D₄×C₈₉	C₂×C₄	1	3	yes	—
92	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
93	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
94	#131×C₈₉	—	2	4	no	—
95	#131×C₈₉	—	2	4	no	—
96	#131×C₈₉	—	2	4	no	—
97	#131×C₈₉	—	2	12	no	—
98	#131×C₈₉	—	2	12	no	—
99	#131×C₈₉	—	2	12	no	—
100	#131×C₈₉	—	2	12	no	—
101	#131×C₈₉	D₄	1	8	yes	complemented
102	C₂×M₁₆×C₈₉	—	2	12	no	—
103	C₂×M₁₆×C₈₉	—	2	12	no	—
104	C₂×M₁₆×C₈₉	—	2	12	no	—
105	C₂×M₁₆×C₈₉	C₂³	1	3	yes	—
106	C₂×M₁₆×C₈₉	C₂³	1	3	yes	—
107	C₂×M₁₆×C₈₉	C₂³	1	3	yes	—
108	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×M₁₆×C₈₉	C₂³	1	3	yes	—
110	C₂×M₁₆×C₈₉	C₂³	1	3	yes	—
111	C₂×M₁₆×C₈₉	C₂³	1	3	yes	—
112	C₂×M₁₆×C₈₉	C₂³	1	6	yes	—
113	C₂×M₁₆×C₈₉	C₂³	1	3	yes	—
114	C₂²×C₈×C₈₉	—	2	12	no	—
115	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
116	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
117	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
118	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
119	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
120	C₂²×C₈×C₈₉	C₂³	1	6	yes	—
121	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
123	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
124	C₄⋊Q₈×C₈₉	C₂×C₄	1	3	yes	—
125	#127×C₈₉	C₂×C₄	1	3	yes	—
126	#124×C₈₉	C₂×C₄	1	3	yes	—
127	#124×C₈₉	C₂×C₄	1	3	yes	—
128	#123×C₈₉	C₂×C₄	1	6	yes	—
129	#123×C₈₉	C₂×C₄	1	6	yes	—
130	C₂²⋊Q₈×C₈₉	C₂×C₄	1	3	yes	—
131	C₂²⋊Q₈×C₈₉	C₂×C₄	1	3	yes	—
132	C₂²⋊Q₈×C₈₉	C₂×C₄	1	3	yes	—
133	C₂²⋊Q₈×C₈₉	C₂×C₄	1	3	yes	—
134	#121×C₈₉	C₂×C₄	1	3	yes	—
135	#121×C₈₉	C₂×C₄	1	3	yes	—
136	#121×C₈₉	C₂×C₄	1	3	yes	—
137	#121×C₈₉	C₂×C₄	1	3	yes	—
138	#121×C₈₉	C₂×C₄	1	6	yes	—
139	#121×C₈₉	C₂×C₄	1	6	yes	—
140	#120×C₈₉	C₂×C₄	1	6	yes	—
141	#120×C₈₉	C₂×C₄	1	6	yes	—
142	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
143	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
144	C₄×D₄×C₈₉	C₂×C₄	1	3	yes	—
145	C₄×D₄×C₈₉	C₂×C₄	1	3	yes	—
146	C₄×D₄×C₈₉	C₂×C₄	1	3	yes	—
147	C₄×D₄×C₈₉	C₂×C₄	1	3	yes	—
148	C₄×D₄×C₈₉	C₂×C₄	1	3	yes	—
149	C₄×D₄×C₈₉	C₂×C₄	1	3	yes	—
150	C₄×D₄×C₈₉	C₂³	1	3	yes	—
151	C₄×D₄×C₈₉	C₂³	1	6	yes	—
152	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
153	C₄×D₄×C₈₉	C₂³	1	3	yes	—
154	C₄×D₄×C₈₉	C₂³	1	3	yes	—
155	#117×C₈₉	C₂³	1	3	yes	—
156	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	3	yes	—
157	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	3	yes	—
158	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	3	yes	—
159	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
160	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
161	C₄⋊C₈×C₈₉	C₂³	1	3	yes	—
162	C₄⋊C₈×C₈₉	C₂³	1	3	yes	—
163	C₄⋊C₈×C₈₉	C₂³	1	3	yes	—
164	C₄⋊C₈×C₈₉	C₂³	1	6	yes	—
165	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
166	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
167	C₂²⋊C₈×C₈₉	C₂³	1	3	yes	—
168	C₂²⋊C₈×C₈₉	C₂³	1	3	yes	—
169	C₂²⋊C₈×C₈₉	C₂³	1	3	yes	—
170	C₂²⋊C₈×C₈₉	C₂³	1	3	yes	—
171	C₂²⋊C₈×C₈₉	C₂³	1	3	yes	—
172	C₂²⋊C₈×C₈₉	C₂³	1	3	yes	—
173	C₂²⋊C₈×C₈₉	C₂³	1	6	yes	—
174	C₂²⋊C₈×C₈₉	C₂³	1	6	yes	—
175	#97×C₈₉	C₂³	1	1	yes	characteristic
176	#97×C₈₉	C₂³	1	3	yes	—
177	#97×C₈₉	C₂³	1	3	yes	—
178	#97×C₈₉	C₂³	1	3	yes	—
179	C₄×C₈×C₈₉	C₂³	1	6	yes	—
180	C₂⁴×C₈₉	C₂²×C₄	1	3	yes	—
181	C₂⁴×C₈₉	C₂²×C₄	1	3	yes	—
182	#41×C₈₉	—	2	4	no	—
183	#41×C₈₉	—	2	4	no	—
184	#41×C₈₉	—	2	12	no	—
185	#41×C₈₉	—	2	12	no	—
186	#41×C₈₉	—	2	6	no	—
187	#41×C₈₉	—	2	6	no	—
188	#41×C₈₉	—	2	6	no	—
189	#41×C₈₉	—	2	6	no	—
190	#41×C₈₉	C₂×D₄	1	4	yes	—
191	#41×C₈₉	#41	1	4	yes	—
192	C₂×Q₈×C₈₉	—	2	4	no	—
193	C₂×Q₈×C₈₉	—	2	4	no	—
194	C₂×Q₈×C₈₉	C₂²×C₄	1	3	yes	—
195	C₂×Q₈×C₈₉	C₂²×C₄	1	3	yes	—
196	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
197	C₂×D₄×C₈₉	—	2	12	no	—
198	C₂×D₄×C₈₉	—	2	12	no	—
199	C₂×D₄×C₈₉	—	4	6	no	—
200	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
201	C₂×D₄×C₈₉	C₂²×C₄	1	3	yes	—
202	C₂×D₄×C₈₉	C₂²×C₄	1	6	yes	—
203	C₂×D₄×C₈₉	C₂²×C₄	1	6	yes	—
204	C₂×D₄×C₈₉	C₂²×C₄	1	3	yes	—
205	C₂×D₄×C₈₉	C₂²×C₄	1	3	yes	—
206	C₂×D₄×C₈₉	C₂²×C₄	1	3	yes	—
207	C₂×D₄×C₈₉	C₂²×C₄	1	3	yes	—
208	C₂×D₄×C₈₉	C₂²×C₄	1	6	yes	—
209	C₂×D₄×C₈₉	C₂²×C₄	1	3	yes	—
210	C₂²×C₄×C₈₉	—	2	6	no	—
211	C₂²×C₄×C₈₉	—	2	6	no	—
212	C₂²×C₄×C₈₉	—	2	6	no	—
213	C₂²×C₄×C₈₉	—	2	6	no	—
214	C₂²×C₄×C₈₉	C₂²×C₄	1	3	yes	—
215	C₂²×C₄×C₈₉	C₂²×C₄	1	3	yes	—
216	C₂²×C₄×C₈₉	C₂²×C₄	1	3	yes	—
217	C₂²×C₄×C₈₉	C₂²×C₄	1	3	yes	—
218	C₂²×C₄×C₈₉	C₂²×C₄	1	3	yes	—
219	C₂²×C₄×C₈₉	C₂²×C₄	1	3	yes	—
220	C₂²×C₄×C₈₉	C₂²×C₄	1	3	yes	—
221	C₂²×C₄×C₈₉	C₂²×C₄	1	3	yes	—
222	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
224	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
225	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
227	M₁₆×C₈₉	—	2	6	no	—
228	M₁₆×C₈₉	—	2	6	no	—
229	M₁₆×C₈₉	—	2	6	no	—
230	M₁₆×C₈₉	—	2	2	no	—
231	M₁₆×C₈₉	—	2	6	no	—
232	M₁₆×C₈₉	—	2	6	no	—
233	M₁₆×C₈₉	—	2	12	no	—
234	M₁₆×C₈₉	—	2	6	no	—
235	M₁₆×C₈₉	C₂×D₄	1	12	yes	complemented
236	C₂×C₈×C₈₉	—	2	6	no	—
237	C₂×C₈×C₈₉	—	2	6	no	—
238	C₂×C₈×C₈₉	—	2	6	no	—
239	C₂×C₈×C₈₉	—	2	2	no	—
240	C₂×C₈×C₈₉	—	2	6	no	—
241	C₂×C₈×C₈₉	—	2	6	no	—
242	C₂×C₈×C₈₉	—	2	6	no	—
243	C₂×C₈×C₈₉	—	2	12	no	—
244	C₂×C₈×C₈₉	C₂×D₄	1	12	yes	complemented
245	C₂×C₈×C₈₉	C₂⁴	1	3	yes	—
246	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
247	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₈×C₈₉	C₂⁴	1	3	yes	—
250	C₂×C₈×C₈₉	C₂⁴	1	3	yes	—
251	C₂×C₈×C₈₉	C₂⁴	1	3	yes	—
252	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
253	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
254	C₄⋊C₄×C₈₉	C₂²×C₄	1	3	yes	—
255	C₄⋊C₄×C₈₉	C₂²×C₄	1	3	yes	—
256	C₄⋊C₄×C₈₉	C₂²×C₄	1	3	yes	—
257	C₄⋊C₄×C₈₉	C₂²×C₄	1	3	yes	—
258	C₄⋊C₄×C₈₉	C₂²×C₄	1	3	yes	—
259	C₄⋊C₄×C₈₉	C₂²×C₄	1	6	yes	—
260	C₂²⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
261	C₂²⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
262	C₂²⋊C₄×C₈₉	C₂²×C₄	1	3	yes	—
263	C₂²⋊C₄×C₈₉	C₂²×C₄	1	3	yes	—
264	C₂²⋊C₄×C₈₉	C₂²×C₄	1	3	yes	—
265	C₂²⋊C₄×C₈₉	C₂²×C₄	1	3	yes	—
266	C₂²⋊C₄×C₈₉	C₂²×C₄	1	3	yes	—
267	C₂²⋊C₄×C₈₉	C₂²×C₄	1	3	yes	—
268	C₂²⋊C₄×C₈₉	C₂²×C₄	1	6	yes	—
269	C₂²⋊C₄×C₈₉	C₂²×C₄	1	6	yes	—
270	C₂²⋊C₄×C₈₉	C₂²×C₄	1	6	yes	—
271	C₄²×C₈₉	C₂²×C₄	1	3	yes	—
272	C₄²×C₈₉	C₂²×C₄	1	3	yes	—
273	C₄²×C₈₉	C₂⁴	1	3	yes	—
274	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
275	C₂³×C₈₉	—	2	6	no	—
276	C₂³×C₈₉	—	2	6	no	—
277	C₂³×C₈₉	—	2	6	no	—
278	C₂³×C₈₉	—	4	3	no	—
279	C₂³×C₈₉	—	4	3	no	—
280	C₂³×C₈₉	—	4	3	no	—
281	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
282	C₂³×C₈₉	C₂³×C₄	1	3	yes	—
283	C₂³×C₈₉	C₂³×C₄	1	3	yes	—
284	C₂³×C₈₉	C₂³×C₄	1	3	yes	—
285	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
286	Q₈×C₈₉	—	2	6	no	—
287	Q₈×C₈₉	—	2	6	no	—
288	Q₈×C₈₉	C₄×D₄	1	4	yes	—
289	D₄×C₈₉	—	2	12	no	—
290	D₄×C₈₉	—	2	12	no	—
291	D₄×C₈₉	—	2	2	no	—
292	D₄×C₈₉	—	2	6	no	—
293	D₄×C₈₉	—	2	6	no	—
294	D₄×C₈₉	—	2	6	no	—
295	D₄×C₈₉	—	4	3	no	—
296	D₄×C₈₉	—	4	3	no	—
297	D₄×C₈₉	—	4	6	no	—
298	D₄×C₈₉	C₄×D₄	1	12	yes	—
299	C₂×C₄×C₈₉	—	2	6	no	—
300	C₂×C₄×C₈₉	—	2	6	no	—
301	C₂×C₄×C₈₉	—	2	6	no	—
302	C₂×C₄×C₈₉	—	2	6	no	—
303	C₂×C₄×C₈₉	—	2	6	no	—
304	C₂×C₄×C₈₉	—	2	6	no	—
305	C₂×C₄×C₈₉	—	2	1	no	—
306	C₂×C₄×C₈₉	—	2	3	no	—
307	C₂×C₄×C₈₉	—	2	3	no	—
308	C₂×C₄×C₈₉	—	2	1	no	—
309	C₂×C₄×C₈₉	—	2	1	no	—
310	C₂×C₄×C₈₉	—	2	1	no	—
311	C₂×C₄×C₈₉	—	2	3	no	—
312	C₂×C₄×C₈₉	—	2	3	no	—
313	C₂×C₄×C₈₉	—	4	3	no	—
314	C₂×C₄×C₈₉	—	4	3	no	—
315	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
316	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
317	C₂×C₄×C₈₉	C₂³×C₄	1	3	yes	—
318	C₂×C₄×C₈₉	C₂³×C₄	1	3	yes	—
319	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
320	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
321	C₂×C₄×C₈₉	C₂³×C₄	1	3	yes	—
322	C₂×C₄×C₈₉	C₂³×C₄	1	3	yes	—
323	C₂×C₄×C₈₉	C₂³×C₄	1	3	yes	—
324	C₂×C₄×C₈₉	C₂²×D₄	1	6	yes	—
325	C₂×C₄×C₈₉	C₂×#41	1	6	yes	—
326	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
327	C₈×C₈₉	—	2	1	no	—
328	C₈×C₈₉	—	2	3	no	—
329	C₈×C₈₉	—	2	1	no	—
330	C₈×C₈₉	—	2	3	no	—
331	C₈×C₈₉	—	2	1	no	—
332	C₈×C₈₉	—	2	3	no	—
333	C₈×C₈₉	C₂²×D₄	1	2	yes	—
334	C₈×C₈₉	C₂²×D₄	1	6	yes	—
335	C₂²×C₈₉	—	2	1	no	—
336	C₂²×C₈₉	—	2	3	no	—
337	C₂²×C₈₉	—	2	3	no	—
338	C₂²×C₈₉	—	2	1	no	—
339	C₂²×C₈₉	—	2	1	no	—
340	C₂²×C₈₉	—	2	3	no	—
341	C₂²×C₈₉	—	2	3	no	—
342	C₂²×C₈₉	—	2	1	no	—
343	C₂²×C₈₉	—	2	3	no	—
344	C₂²×C₈₉	—	2	3	no	—
345	C₂²×C₈₉	—	2	3	no	—
346	C₂²×C₈₉	—	2	3	no	—
347	C₂²×C₈₉	—	2	1	no	—
348	C₂²×C₈₉	—	4	12	no	—
349	C₂²×C₈₉	—	8	6	no	—
350	C₂²×C₈₉	C₂×C₄×D₄	1	6	yes	—
351	C₂²×C₈₉	#568	1	2	yes	complemented
352	C₂²×C₈₉	C₂⁴×C₄	1	1	yes	characteristic
353	C₄×C₈₉	—	2	1	no	—
354	C₄×C₈₉	—	2	1	no	—
355	C₄×C₈₉	—	2	3	no	—
356	C₄×C₈₉	—	2	3	no	—
357	C₄×C₈₉	—	2	1	no	—
358	C₄×C₈₉	—	2	3	no	—
359	C₄×C₈₉	—	2	1	no	—
360	C₄×C₈₉	—	2	3	no	—
361	C₄×C₈₉	C₂×C₄×D₄	1	6	yes	—
362	C₄×C₈₉	C₂³×D₄	1	1	yes	characteristic
363	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
364	#60146	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
365	C₂×C₈₉	—	2	2	no	—
366	C₂×C₈₉	—	2	6	no	—
367	C₂×C₈₉	—	4	3	no	—
368	C₂×C₈₉	—	4	3	no	—
369	C₂×C₈₉	—	4	1	no	—
370	C₂×C₈₉	C₂²×C₄×D₄	1	1	yes	characteristic
371	C₂×C₈₉	C₂×#568	1	1	yes	characteristic
372	C₂×C₈₉	#3573	1	1	yes	characteristic
373	C₂×#568	C₂×C₈₉	1	1	yes	characteristic, complemented
374	C₂²×#131	C₂×C₈₉	1	1	yes	characteristic, complemented
375	D₄×#41	C₂×C₈₉	1	1	yes	characteristic
376	#2935	C₂×C₈₉	1	3	yes	complemented
377	D₄×M₁₆	C₂×C₈₉	1	3	yes	complemented
378	#2933	C₂×C₈₉	1	3	yes	complemented
379	#2933	C₂×C₈₉	1	3	yes	complemented
380	#2932	C₂×C₈₉	1	3	yes	complemented
381	#2930	C₂×C₈₉	1	3	yes	complemented
382	#2929	C₂×C₈₉	1	3	yes	complemented
383	C₂×#435	C₂×C₈₉	1	3	yes	complemented
384	#2906	C₂×C₈₉	1	1	yes	characteristic, complemented
385	#2880	C₂×C₈₉	1	1	yes	characteristic, complemented
386	#2880	C₂×C₈₉	1	1	yes	characteristic, complemented
387	#2875	C₂×C₈₉	1	1	yes	characteristic, complemented
388	C₈₉	#60146	1	1	yes	characteristic, direct product factor, Sylow
389	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
390	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
391	#568	—	2	8	no	—
392	C₂×#131	—	2	8	no	—
393	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
394	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
395	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
396	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
397	C₂×#131	C₂²×C₈₉	1	3	yes	complemented
398	C₂×#131	C₂²×C₈₉	1	3	yes	complemented
399	C₂×#131	C₂²×C₈₉	1	3	yes	complemented
400	C₂×#131	C₂²×C₈₉	1	3	yes	complemented
401	C₂²×M₁₆	C₂²×C₈₉	1	3	yes	complemented
402	C₂²×M₁₆	C₂²×C₈₉	1	3	yes	complemented
403	C₂²×M₁₆	C₂²×C₈₉	1	3	yes	complemented
404	C₂³×C₈	C₂²×C₈₉	1	3	yes	complemented
405	#550	C₄×C₈₉	1	1	yes	characteristic
406	D₄×Q₈	C₄×C₈₉	1	1	yes	characteristic
407	#548	C₄×C₈₉	1	1	yes	characteristic
408	#548	C₄×C₈₉	1	1	yes	characteristic
409	#547	C₄×C₈₉	1	3	yes	—
410	#546	C₄×C₈₉	1	3	yes	—
411	#546	C₄×C₈₉	1	3	yes	—
412	D₄²	C₄×C₈₉	1	3	yes	—
413	#532	C₂²×C₈₉	1	3	yes	—
414	#525	C₂²×C₈₉	1	3	yes	—
415	#525	C₂²×C₈₉	1	3	yes	—
416	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
417	C₂×C₄×D₄	C₂²×C₈₉	1	3	yes	—
418	#436	C₂²×C₈₉	1	6	yes	complemented
419	#436	C₂²×C₈₉	1	6	yes	complemented
420	#435	C₂²×C₈₉	1	1	yes	characteristic
421	#435	C₂²×C₈₉	1	3	yes	—
422	#435	C₂²×C₈₉	1	3	yes	complemented
423	#435	C₂²×C₈₉	1	3	yes	complemented
424	#435	C₂²×C₈₉	1	3	yes	complemented
425	#435	C₂²×C₈₉	1	3	yes	complemented
426	#435	C₂²×C₈₉	1	3	yes	complemented
427	#435	C₂²×C₈₉	1	3	yes	complemented
428	#435	C₂²×C₈₉	1	6	yes	complemented
429	#435	C₂²×C₈₉	1	6	yes	complemented
430	#435	C₂²×C₈₉	1	6	yes	complemented
431	C₈×D₄	C₂²×C₈₉	1	6	yes	complemented
432	C₈×D₄	C₂²×C₈₉	1	6	yes	complemented
433	#424	C₂²×C₈₉	1	3	yes	complemented
434	#424	C₂²×C₈₉	1	3	yes	complemented
435	#423	C₂²×C₈₉	1	3	yes	complemented
436	C₂×C₄⋊C₈	C₂²×C₈₉	1	3	yes	complemented
437	#408	C₂²×C₈₉	1	3	yes	complemented
438	#408	C₂²×C₈₉	1	3	yes	complemented
439	#408	C₂²×C₈₉	1	3	yes	complemented
440	#408	C₂²×C₈₉	1	3	yes	complemented
441	#407	C₂²×C₈₉	1	3	yes	complemented
442	#407	C₂²×C₈₉	1	3	yes	complemented
443	C₂×C₂²⋊C₈	C₂²×C₈₉	1	3	yes	complemented
444	C₂×C₂²⋊C₈	C₂²×C₈₉	1	3	yes	complemented
445	#405	C₂²×C₈₉	1	3	yes	complemented
446	#405	C₂²×C₈₉	1	3	yes	complemented
447	C₄×M₁₆	C₂²×C₈₉	1	3	yes	complemented
448	C₂×#97	C₂²×C₈₉	1	3	yes	complemented
449	C₂×#41	—	2	4	no	—
450	C₂×#41	—	2	4	no	—
451	C₂×#41	—	2	4	no	—
452	C₂×#41	—	2	4	no	—
453	C₂×#41	C₂×C₄×C₈₉	1	3	yes	—
454	C₂×#41	C₂×C₄×C₈₉	1	3	yes	—
455	C₂×#41	C₂×C₄×C₈₉	1	1	yes	characteristic
456	C₂×#41	C₂×C₄×C₈₉	1	1	yes	characteristic
457	C₂×#41	C₂³×C₈₉	1	3	yes	—
458	C₂×#41	C₂³×C₈₉	1	3	yes	—
459	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
460	C₂²×Q₈	C₂×C₄×C₈₉	1	1	yes	characteristic
461	C₂²×Q₈	C₂×C₄×C₈₉	1	1	yes	characteristic
462	C₂²×D₄	C₂×C₄×C₈₉	1	3	yes	—
463	C₂²×D₄	C₂×C₄×C₈₉	1	3	yes	—
464	C₂²×D₄	C₂×C₄×C₈₉	1	3	yes	—
465	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
466	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
467	#131	—	2	4	no	—
468	#131	—	2	4	no	—
469	#131	—	2	4	no	—
470	#131	—	2	12	no	—
471	#131	—	2	12	no	—
472	#131	—	2	12	no	—
473	#131	—	2	12	no	—
474	#131	D₄×C₈₉	1	8	yes	complemented
475	C₂×M₁₆	—	2	12	no	—
476	C₂×M₁₆	—	2	12	no	—
477	C₂×M₁₆	—	2	12	no	—
478	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
479	C₂×M₁₆	C₂³×C₈₉	1	3	yes	—
480	C₂×M₁₆	C₂³×C₈₉	1	3	yes	—
481	C₂×M₁₆	C₂³×C₈₉	1	3	yes	—
482	C₂×M₁₆	C₂³×C₈₉	1	3	yes	—
483	C₂×M₁₆	C₂³×C₈₉	1	3	yes	—
484	C₂×M₁₆	C₂³×C₈₉	1	6	yes	—
485	C₂×M₁₆	C₂³×C₈₉	1	3	yes	—
486	C₂×M₁₆	C₂³×C₈₉	1	3	yes	—
487	C₂²×C₈	—	2	12	no	—
488	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
489	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
490	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
491	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
492	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
493	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
494	C₂²×C₈	C₂³×C₈₉	1	6	yes	—
495	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
496	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
497	C₄⋊Q₈	C₂×C₄×C₈₉	1	3	yes	—
498	#127	C₂×C₄×C₈₉	1	3	yes	—
499	#124	C₂×C₄×C₈₉	1	3	yes	—
500	#124	C₂×C₄×C₈₉	1	3	yes	—
501	#123	C₂×C₄×C₈₉	1	6	yes	—
502	#123	C₂×C₄×C₈₉	1	6	yes	—
503	C₂²⋊Q₈	C₂×C₄×C₈₉	1	3	yes	—
504	C₂²⋊Q₈	C₂×C₄×C₈₉	1	3	yes	—
505	C₂²⋊Q₈	C₂×C₄×C₈₉	1	3	yes	—
506	C₂²⋊Q₈	C₂×C₄×C₈₉	1	3	yes	—
507	#121	C₂×C₄×C₈₉	1	3	yes	—
508	#121	C₂×C₄×C₈₉	1	3	yes	—
509	#121	C₂×C₄×C₈₉	1	3	yes	—
510	#121	C₂×C₄×C₈₉	1	3	yes	—
511	#121	C₂×C₄×C₈₉	1	6	yes	—
512	#121	C₂×C₄×C₈₉	1	6	yes	—
513	#120	C₂×C₄×C₈₉	1	6	yes	—
514	#120	C₂×C₄×C₈₉	1	6	yes	—
515	C₄×Q₈	C₂×C₄×C₈₉	1	1	yes	characteristic
516	C₄×Q₈	C₂×C₄×C₈₉	1	1	yes	characteristic
517	C₄×D₄	C₂×C₄×C₈₉	1	3	yes	—
518	C₄×D₄	C₂×C₄×C₈₉	1	3	yes	—
519	C₄×D₄	C₂×C₄×C₈₉	1	3	yes	—
520	C₄×D₄	C₂×C₄×C₈₉	1	3	yes	—
521	C₄×D₄	C₂×C₄×C₈₉	1	3	yes	—
522	C₄×D₄	C₂×C₄×C₈₉	1	3	yes	—
523	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
524	C₄×D₄	C₂³×C₈₉	1	3	yes	—
525	C₄×D₄	C₂³×C₈₉	1	3	yes	—
526	C₄×D₄	C₂³×C₈₉	1	3	yes	—
527	C₄×D₄	C₂³×C₈₉	1	6	yes	—
528	#117	C₂³×C₈₉	1	3	yes	—
529	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	3	yes	—
530	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	3	yes	—
531	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	3	yes	—
532	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
533	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
534	C₄⋊C₈	C₂³×C₈₉	1	3	yes	—
535	C₄⋊C₈	C₂³×C₈₉	1	3	yes	—
536	C₄⋊C₈	C₂³×C₈₉	1	3	yes	—
537	C₄⋊C₈	C₂³×C₈₉	1	6	yes	—
538	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
539	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
540	C₂²⋊C₈	C₂³×C₈₉	1	3	yes	—
541	C₂²⋊C₈	C₂³×C₈₉	1	3	yes	—
542	C₂²⋊C₈	C₂³×C₈₉	1	3	yes	—
543	C₂²⋊C₈	C₂³×C₈₉	1	3	yes	—
544	C₂²⋊C₈	C₂³×C₈₉	1	3	yes	—
545	C₂²⋊C₈	C₂³×C₈₉	1	3	yes	—
546	C₂²⋊C₈	C₂³×C₈₉	1	6	yes	—
547	C₂²⋊C₈	C₂³×C₈₉	1	6	yes	—
548	#97	C₂³×C₈₉	1	1	yes	characteristic
549	#97	C₂³×C₈₉	1	3	yes	—
550	#97	C₂³×C₈₉	1	3	yes	—
551	#97	C₂³×C₈₉	1	3	yes	—
552	C₄×C₈	C₂³×C₈₉	1	6	yes	—
553	C₂⁴	C₂²×C₄×C₈₉	1	3	yes	—
554	C₂⁴	C₂²×C₄×C₈₉	1	3	yes	—
555	#41	—	2	4	no	—
556	#41	—	2	4	no	—
557	#41	—	2	12	no	—
558	#41	—	2	12	no	—
559	#41	—	2	6	no	—
560	#41	—	2	6	no	—
561	#41	—	2	6	no	—
562	#41	—	2	6	no	—
563	#41	C₂×D₄×C₈₉	1	4	yes	—
564	#41	#41×C₈₉	1	4	yes	—
565	C₂×Q₈	—	2	4	no	—
566	C₂×Q₈	—	2	4	no	—
567	C₂×Q₈	C₂²×C₄×C₈₉	1	3	yes	—
568	C₂×Q₈	C₂²×C₄×C₈₉	1	3	yes	—
569	C₂×Q₈	C₂²×C₄×C₈₉	1	1	yes	characteristic
570	C₂×D₄	—	2	12	no	—
571	C₂×D₄	—	2	12	no	—
572	C₂×D₄	—	4	6	no	—
573	C₂×D₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
574	C₂×D₄	C₂²×C₄×C₈₉	1	3	yes	—
575	C₂×D₄	C₂²×C₄×C₈₉	1	6	yes	—
576	C₂×D₄	C₂²×C₄×C₈₉	1	6	yes	—
577	C₂×D₄	C₂²×C₄×C₈₉	1	3	yes	—
578	C₂×D₄	C₂²×C₄×C₈₉	1	3	yes	—
579	C₂×D₄	C₂²×C₄×C₈₉	1	3	yes	—
580	C₂×D₄	C₂²×C₄×C₈₉	1	3	yes	—
581	C₂×D₄	C₂²×C₄×C₈₉	1	6	yes	—
582	C₂×D₄	C₂²×C₄×C₈₉	1	3	yes	—
583	C₂²×C₄	—	2	6	no	—
584	C₂²×C₄	—	2	6	no	—
585	C₂²×C₄	—	2	6	no	—
586	C₂²×C₄	—	2	6	no	—
587	C₂²×C₄	C₂²×C₄×C₈₉	1	3	yes	—
588	C₂²×C₄	C₂²×C₄×C₈₉	1	3	yes	—
589	C₂²×C₄	C₂²×C₄×C₈₉	1	3	yes	—
590	C₂²×C₄	C₂²×C₄×C₈₉	1	3	yes	—
591	C₂²×C₄	C₂²×C₄×C₈₉	1	3	yes	—
592	C₂²×C₄	C₂²×C₄×C₈₉	1	3	yes	—
593	C₂²×C₄	C₂²×C₄×C₈₉	1	3	yes	—
594	C₂²×C₄	C₂²×C₄×C₈₉	1	3	yes	—
595	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
597	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
598	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
599	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
600	M₁₆	—	2	6	no	—
601	M₁₆	—	2	6	no	—
602	M₁₆	—	2	6	no	—
603	M₁₆	—	2	2	no	—
604	M₁₆	—	2	6	no	—
605	M₁₆	—	2	6	no	—
606	M₁₆	—	2	12	no	—
607	M₁₆	—	2	6	no	—
608	M₁₆	C₂×D₄×C₈₉	1	12	yes	complemented
609	C₂×C₈	—	2	6	no	—
610	C₂×C₈	—	2	6	no	—
611	C₂×C₈	—	2	6	no	—
612	C₂×C₈	—	2	2	no	—
613	C₂×C₈	—	2	6	no	—
614	C₂×C₈	—	2	6	no	—
615	C₂×C₈	—	2	6	no	—
616	C₂×C₈	—	2	12	no	—
617	C₂×C₈	C₂×D₄×C₈₉	1	12	yes	complemented
618	C₂×C₈	C₂⁴×C₈₉	1	3	yes	—
619	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
620	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
621	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
622	C₂×C₈	C₂⁴×C₈₉	1	3	yes	—
623	C₂×C₈	C₂⁴×C₈₉	1	3	yes	—
624	C₂×C₈	C₂⁴×C₈₉	1	3	yes	—
625	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
626	C₄⋊C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
627	C₄⋊C₄	C₂²×C₄×C₈₉	1	3	yes	—
628	C₄⋊C₄	C₂²×C₄×C₈₉	1	3	yes	—
629	C₄⋊C₄	C₂²×C₄×C₈₉	1	3	yes	—
630	C₄⋊C₄	C₂²×C₄×C₈₉	1	3	yes	—
631	C₄⋊C₄	C₂²×C₄×C₈₉	1	3	yes	—
632	C₄⋊C₄	C₂²×C₄×C₈₉	1	6	yes	—
633	C₂²⋊C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
634	C₂²⋊C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
635	C₂²⋊C₄	C₂²×C₄×C₈₉	1	3	yes	—
636	C₂²⋊C₄	C₂²×C₄×C₈₉	1	3	yes	—
637	C₂²⋊C₄	C₂²×C₄×C₈₉	1	3	yes	—
638	C₂²⋊C₄	C₂²×C₄×C₈₉	1	3	yes	—
639	C₂²⋊C₄	C₂²×C₄×C₈₉	1	3	yes	—
640	C₂²⋊C₄	C₂²×C₄×C₈₉	1	3	yes	—
641	C₂²⋊C₄	C₂²×C₄×C₈₉	1	6	yes	—
642	C₂²⋊C₄	C₂²×C₄×C₈₉	1	6	yes	—
643	C₂²⋊C₄	C₂²×C₄×C₈₉	1	6	yes	—
644	C₄²	C₂²×C₄×C₈₉	1	3	yes	—
645	C₄²	C₂²×C₄×C₈₉	1	3	yes	—
646	C₄²	C₂⁴×C₈₉	1	3	yes	—
647	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
648	C₂³	—	2	6	no	—
649	C₂³	—	2	6	no	—
650	C₂³	—	2	6	no	—
651	C₂³	—	4	3	no	—
652	C₂³	—	4	3	no	—
653	C₂³	—	4	3	no	—
654	C₂³	C₂³×C₄×C₈₉	1	1	yes	characteristic
655	C₂³	C₂³×C₄×C₈₉	1	3	yes	—
656	C₂³	C₂³×C₄×C₈₉	1	3	yes	—
657	C₂³	C₂³×C₄×C₈₉	1	3	yes	—
658	C₂³	C₂³×C₄×C₈₉	1	1	yes	characteristic
659	Q₈	—	2	6	no	—
660	Q₈	—	2	6	no	—
661	Q₈	C₄×D₄×C₈₉	1	4	yes	—
662	D₄	—	2	12	no	—
663	D₄	—	2	12	no	—
664	D₄	—	2	2	no	—
665	D₄	—	2	6	no	—
666	D₄	—	2	6	no	—
667	D₄	—	2	6	no	—
668	D₄	—	4	3	no	—
669	D₄	—	4	3	no	—
670	D₄	—	4	6	no	—
671	D₄	C₄×D₄×C₈₉	1	12	yes	—
672	C₂×C₄	—	2	6	no	—
673	C₂×C₄	—	2	6	no	—
674	C₂×C₄	—	2	6	no	—
675	C₂×C₄	—	2	6	no	—
676	C₂×C₄	—	2	6	no	—
677	C₂×C₄	—	2	6	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	3	no	—
680	C₂×C₄	—	2	3	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	3	no	—
685	C₂×C₄	—	2	3	no	—
686	C₂×C₄	—	4	3	no	—
687	C₂×C₄	—	4	3	no	—
688	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
689	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
690	C₂×C₄	C₂³×C₄×C₈₉	1	3	yes	—
691	C₂×C₄	C₂³×C₄×C₈₉	1	3	yes	—
692	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
693	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
694	C₂×C₄	C₂³×C₄×C₈₉	1	3	yes	—
695	C₂×C₄	C₂³×C₄×C₈₉	1	3	yes	—
696	C₂×C₄	C₂³×C₄×C₈₉	1	3	yes	—
697	C₂×C₄	C₂²×D₄×C₈₉	1	6	yes	—
698	C₂×C₄	C₂×#41×C₈₉	1	6	yes	—
699	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
700	C₈	—	2	1	no	—
701	C₈	—	2	3	no	—
702	C₈	—	2	1	no	—
703	C₈	—	2	3	no	—
704	C₈	—	2	1	no	—
705	C₈	—	2	3	no	—
706	C₈	C₂²×D₄×C₈₉	1	2	yes	—
707	C₈	C₂²×D₄×C₈₉	1	6	yes	—
708	C₂²	—	2	1	no	—
709	C₂²	—	2	3	no	—
710	C₂²	—	2	3	no	—
711	C₂²	—	2	1	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	2	3	no	—
714	C₂²	—	2	3	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	3	no	—
717	C₂²	—	2	3	no	—
718	C₂²	—	2	3	no	—
719	C₂²	—	2	3	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	4	12	no	—
722	C₂²	—	8	6	no	—
723	C₂²	C₂×C₄×D₄×C₈₉	1	6	yes	—
724	C₂²	#568×C₈₉	1	2	yes	complemented
725	C₂²	C₂⁴×C₄×C₈₉	1	1	yes	characteristic
726	C₄	—	2	1	no	—
727	C₄	—	2	1	no	—
728	C₄	—	2	3	no	—
729	C₄	—	2	3	no	—
730	C₄	—	2	1	no	—
731	C₄	—	2	3	no	—
732	C₄	—	2	1	no	—
733	C₄	—	2	3	no	—
734	C₄	C₂×C₄×D₄×C₈₉	1	6	yes	—
735	C₄	C₂³×D₄×C₈₉	1	1	yes	characteristic
736	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
737	C₂	—	2	2	no	—
738	C₂	—	2	6	no	—
739	C₂	—	4	3	no	—
740	C₂	—	4	3	no	—
741	C₂	—	4	1	no	—
742	C₂	C₂²×C₄×D₄×C₈₉	1	1	yes	characteristic
743	C₂	C₂×#568×C₈₉	1	1	yes	characteristic
744	C₂	C₈₉×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₈₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
socle	C₂²×C₈₉	C₂⁴×C₄
prime radical	D₄×#41×C₈₉	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#568×C₈₉	C₂	semidirect
2. C₂²×#131×C₈₉	C₂	semidirect
4. C₈₉×#2935	C₂	semidirect
5. D₄×M₁₆×C₈₉	C₂	semidirect
6. C₈₉×#2933	C₂	semidirect
7. C₈₉×#2933	C₂	semidirect
8. C₈₉×#2932	C₂	semidirect
9. C₈₉×#2930	C₂	semidirect
10. C₈₉×#2929	C₂	semidirect
11. C₂×#435×C₈₉	C₂	semidirect
12. C₈₉×#2906	C₂	semidirect
13. C₈₉×#2880	C₂	semidirect
14. C₈₉×#2880	C₂	semidirect
15. C₈₉×#2875	C₂	semidirect
24. C₂×#131×C₈₉	C₂²	semidirect
25. C₂×#131×C₈₉	C₂²	semidirect
26. C₂×#131×C₈₉	C₂²	semidirect
27. C₂×#131×C₈₉	C₂²	semidirect
28. C₂²×M₁₆×C₈₉	C₂²	semidirect
29. C₂²×M₁₆×C₈₉	C₂²	semidirect
30. C₂²×M₁₆×C₈₉	C₂²	semidirect
31. C₂³×C₈×C₈₉	C₂²	semidirect
45. #436×C₈₉	C₂²	semidirect
46. #436×C₈₉	C₂²	semidirect
49. #435×C₈₉	C₂²	semidirect
50. #435×C₈₉	C₂²	semidirect
51. #435×C₈₉	C₂²	semidirect
52. #435×C₈₉	C₂²	semidirect
53. #435×C₈₉	C₂²	semidirect
54. #435×C₈₉	C₂²	semidirect
55. #435×C₈₉	C₂²	semidirect
56. #435×C₈₉	C₂²	semidirect
57. #435×C₈₉	C₂²	semidirect
58. C₈×D₄×C₈₉	C₂²	semidirect
59. C₈×D₄×C₈₉	C₂²	semidirect
60. #424×C₈₉	C₂²	semidirect
61. #424×C₈₉	C₂²	semidirect
62. #423×C₈₉	C₂²	semidirect
63. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
64. #408×C₈₉	C₂²	semidirect
65. #408×C₈₉	C₂²	semidirect
66. #408×C₈₉	C₂²	semidirect
67. #408×C₈₉	C₂²	semidirect
68. #407×C₈₉	C₂²	semidirect
69. #407×C₈₉	C₂²	semidirect
70. C₂×C₂²⋊C₈×C₈₉	C₂²	semidirect
71. C₂×C₂²⋊C₈×C₈₉	C₂²	semidirect
72. #405×C₈₉	C₂²	semidirect
73. #405×C₈₉	C₂²	semidirect
74. C₄×M₁₆×C₈₉	C₂²	semidirect
75. C₂×#97×C₈₉	C₂²	semidirect
101. #131×C₈₉	D₄	semidirect
235. M₁₆×C₈₉	C₂×D₄	semidirect
244. C₂×C₈×C₈₉	C₂×D₄	semidirect
351. C₂²×C₈₉	#568	semidirect
364. #60146	C₈₉	direct (N × H)
373. C₂×#568	C₂×C₈₉	semidirect
374. C₂²×#131	C₂×C₈₉	semidirect
376. #2935	C₂×C₈₉	semidirect
377. D₄×M₁₆	C₂×C₈₉	semidirect
378. #2933	C₂×C₈₉	semidirect
379. #2933	C₂×C₈₉	semidirect
380. #2932	C₂×C₈₉	semidirect
381. #2930	C₂×C₈₉	semidirect
382. #2929	C₂×C₈₉	semidirect
383. C₂×#435	C₂×C₈₉	semidirect
384. #2906	C₂×C₈₉	semidirect
385. #2880	C₂×C₈₉	semidirect
386. #2880	C₂×C₈₉	semidirect
387. #2875	C₂×C₈₉	semidirect
388. C₈₉	#60146	direct (N × H)
397. C₂×#131	C₂²×C₈₉	semidirect
398. C₂×#131	C₂²×C₈₉	semidirect
399. C₂×#131	C₂²×C₈₉	semidirect
400. C₂×#131	C₂²×C₈₉	semidirect
401. C₂²×M₁₆	C₂²×C₈₉	semidirect
402. C₂²×M₁₆	C₂²×C₈₉	semidirect
403. C₂²×M₁₆	C₂²×C₈₉	semidirect
404. C₂³×C₈	C₂²×C₈₉	semidirect
418. #436	C₂²×C₈₉	semidirect
419. #436	C₂²×C₈₉	semidirect
422. #435	C₂²×C₈₉	semidirect
423. #435	C₂²×C₈₉	semidirect
424. #435	C₂²×C₈₉	semidirect
425. #435	C₂²×C₈₉	semidirect
426. #435	C₂²×C₈₉	semidirect
427. #435	C₂²×C₈₉	semidirect
428. #435	C₂²×C₈₉	semidirect
429. #435	C₂²×C₈₉	semidirect
430. #435	C₂²×C₈₉	semidirect
431. C₈×D₄	C₂²×C₈₉	semidirect
432. C₈×D₄	C₂²×C₈₉	semidirect
433. #424	C₂²×C₈₉	semidirect
434. #424	C₂²×C₈₉	semidirect
435. #423	C₂²×C₈₉	semidirect
436. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
437. #408	C₂²×C₈₉	semidirect
438. #408	C₂²×C₈₉	semidirect
439. #408	C₂²×C₈₉	semidirect
440. #408	C₂²×C₈₉	semidirect
441. #407	C₂²×C₈₉	semidirect
442. #407	C₂²×C₈₉	semidirect
443. C₂×C₂²⋊C₈	C₂²×C₈₉	semidirect
444. C₂×C₂²⋊C₈	C₂²×C₈₉	semidirect
445. #405	C₂²×C₈₉	semidirect
446. #405	C₂²×C₈₉	semidirect
447. C₄×M₁₆	C₂²×C₈₉	semidirect
448. C₂×#97	C₂²×C₈₉	semidirect
474. #131	D₄×C₈₉	semidirect
608. M₁₆	C₂×D₄×C₈₉	semidirect
617. C₂×C₈	C₂×D₄×C₈₉	semidirect
724. C₂²	#568×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#568×C₈₉	2
C₂²×#131×C₈₉	2
D₄×#41×C₈₉	2
C₈₉×#2935	2
D₄×M₁₆×C₈₉	2
C₈₉×#2933	2
C₈₉×#2932	2
C₈₉×#2930	2
C₈₉×#2929	2
C₂×#435×C₈₉	2
C₈₉×#2906	2
C₈₉×#2880	2
C₈₉×#2875	2
#60146	89

Subgroups — C89×#60146 #36437994

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60146 #36437994