Subgroups — C₈₉×#35318 #36413166

Order 22784.

2106 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#542×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#541×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2862	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2861	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2857	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2850	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#2660	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2658	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2621	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2620	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#2556	C₂	1	4	yes	maximal, complemented
12	C₈₉×#2553	C₂	1	4	yes	maximal, complemented
13	C₈₉×#2521	C₂	1	4	yes	maximal, complemented
14	C₈₉×#2519	C₂	1	4	yes	maximal, complemented
15	C₈₉×#2327	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2326	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₄⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#124×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#117×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#542×C₈₉	—	2	8	no	—
21	#541×C₈₉	—	2	8	no	—
22	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#126×C₈₉	C₂²	1	2	yes	—
27	C₂×#126×C₈₉	C₂²	1	2	yes	—
28	C₂×#126×C₈₉	C₂²	1	2	yes	—
29	C₂×#125×C₈₉	C₂²	1	2	yes	—
30	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#125×C₈₉	C₂²	1	2	yes	—
32	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#124×C₈₉	C₂²	1	2	yes	—
36	C₂×#123×C₈₉	C₂²	1	2	yes	—
37	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
38	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
48	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
49	#399×C₈₉	C₂²	1	4	yes	—
50	#399×C₈₉	C₂²	1	4	yes	—
51	#398×C₈₉	C₂²	1	4	yes	—
52	#398×C₈₉	C₂²	1	4	yes	—
53	#397×C₈₉	C₂²	1	4	yes	—
54	#396×C₈₉	C₂²	1	4	yes	—
55	#395×C₈₉	C₂²	1	4	yes	—
56	#394×C₈₉	C₂²	1	4	yes	—
57	#391×C₈₉	C₂²	1	4	yes	—
58	#391×C₈₉	C₂²	1	1	yes	characteristic
59	#391×C₈₉	C₂²	1	1	yes	characteristic
60	#391×C₈₉	C₂²	1	1	yes	characteristic
61	#391×C₈₉	C₂²	1	1	yes	characteristic
62	#391×C₈₉	C₂²	1	1	yes	characteristic
63	#391×C₈₉	C₂²	1	1	yes	characteristic
64	#390×C₈₉	C₂²	1	1	yes	characteristic
65	#390×C₈₉	C₂²	1	1	yes	characteristic
66	#389×C₈₉	C₂²	1	4	yes	—
67	#389×C₈₉	C₂²	1	4	yes	—
68	#388×C₈₉	C₂²	1	4	yes	—
69	#388×C₈₉	C₂²	1	4	yes	—
70	#388×C₈₉	C₂²	1	4	yes	—
71	#388×C₈₉	C₂²	1	4	yes	—
72	#388×C₈₉	C₂²	1	4	yes	—
73	#387×C₈₉	C₂²	1	4	yes	—
74	#387×C₈₉	C₂²	1	4	yes	—
75	#386×C₈₉	C₂²	1	4	yes	—
76	#385×C₈₉	C₂²	1	4	yes	—
77	#384×C₈₉	C₂²	1	1	yes	characteristic
78	#384×C₈₉	C₂²	1	1	yes	characteristic
79	#382×C₈₉	C₂²	1	4	yes	—
80	#382×C₈₉	C₂²	1	1	yes	characteristic
81	#382×C₈₉	C₂²	1	1	yes	characteristic
82	#380×C₈₉	C₂²	1	4	yes	—
83	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
84	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
85	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
86	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
87	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
88	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
89	#376×C₈₉	C₂²	1	1	yes	characteristic
90	#376×C₈₉	C₂²	1	1	yes	characteristic
91	C₄³×C₈₉	C₂²	1	1	yes	characteristic
92	C₄³×C₈₉	C₂²	1	1	yes	characteristic
93	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
97	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
99	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
100	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
102	C₄⋊Q₈×C₈₉	—	2	4	no	—
103	C₄⋊Q₈×C₈₉	—	2	4	no	—
104	C₄⋊Q₈×C₈₉	—	2	4	no	—
105	C₄⋊Q₈×C₈₉	—	2	4	no	—
106	#126×C₈₉	—	2	8	no	—
107	#126×C₈₉	—	2	8	no	—
108	#126×C₈₉	—	2	8	no	—
109	#125×C₈₉	—	2	8	no	—
110	#125×C₈₉	—	2	8	no	—
111	#125×C₈₉	—	2	4	no	—
112	#124×C₈₉	—	2	8	no	—
113	#124×C₈₉	—	2	4	no	—
114	#124×C₈₉	—	2	4	no	—
115	#124×C₈₉	—	2	4	no	—
116	#123×C₈₉	—	2	8	no	—
117	C₂²⋊Q₈×C₈₉	—	2	4	no	—
118	C₂²⋊Q₈×C₈₉	—	2	4	no	—
119	C₂²⋊Q₈×C₈₉	—	2	4	no	—
120	C₂²⋊Q₈×C₈₉	—	2	8	no	—
121	#121×C₈₉	—	2	4	no	—
122	C₄×Q₈×C₈₉	—	2	4	no	—
123	C₄×Q₈×C₈₉	—	2	4	no	—
124	C₄×Q₈×C₈₉	—	2	4	no	—
125	C₄×D₄×C₈₉	—	2	4	no	—
126	#117×C₈₉	—	2	4	no	—
127	#117×C₈₉	D₄	1	8	yes	—
128	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
147	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
148	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
156	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
162	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
163	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₈₉	—	2	4	no	—
165	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
168	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
169	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
170	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
171	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
172	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
173	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
174	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
175	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
179	#95×C₈₉	C₂³	1	2	yes	—
180	#95×C₈₉	C₂³	1	2	yes	—
181	#95×C₈₉	C₂³	1	2	yes	—
182	#95×C₈₉	C₂³	1	2	yes	—
183	#95×C₈₉	C₂³	1	4	yes	—
184	#95×C₈₉	C₂³	1	4	yes	—
185	#95×C₈₉	C₂³	1	4	yes	—
186	#95×C₈₉	C₂³	1	4	yes	—
187	#95×C₈₉	C₂³	1	4	yes	—
188	#95×C₈₉	C₂³	1	4	yes	—
189	#95×C₈₉	C₂³	1	4	yes	—
190	#95×C₈₉	C₂³	1	4	yes	—
191	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
192	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
193	C₂×Q₈×C₈₉	—	2	2	no	—
194	C₂×Q₈×C₈₉	—	2	2	no	—
195	C₂×Q₈×C₈₉	—	2	2	no	—
196	C₂×Q₈×C₈₉	—	2	4	no	—
197	C₂×Q₈×C₈₉	—	2	2	no	—
198	C₂×Q₈×C₈₉	—	2	2	no	—
199	C₂×Q₈×C₈₉	—	2	2	no	—
200	C₂×Q₈×C₈₉	—	2	2	no	—
201	C₂×Q₈×C₈₉	—	2	2	no	—
202	C₂×Q₈×C₈₉	—	2	2	no	—
203	C₂×Q₈×C₈₉	—	4	4	no	—
204	C₂×D₄×C₈₉	—	2	4	no	—
205	C₂×D₄×C₈₉	—	2	2	no	—
206	C₂×D₄×C₈₉	—	2	2	no	—
207	C₂×D₄×C₈₉	—	2	2	no	—
208	C₂×D₄×C₈₉	—	4	4	no	—
209	C₂²×C₄×C₈₉	—	2	2	no	—
210	C₂²×C₄×C₈₉	—	2	2	no	—
211	C₂²×C₄×C₈₉	—	2	4	no	—
212	C₂²×C₄×C₈₉	—	2	4	no	—
213	C₂²×C₄×C₈₉	—	2	4	no	—
214	C₂²×C₄×C₈₉	—	4	2	no	—
215	C₂²×C₄×C₈₉	—	4	4	no	—
216	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
217	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
234	C₄⋊C₄×C₈₉	—	2	2	no	—
235	C₄⋊C₄×C₈₉	—	2	2	no	—
236	C₄⋊C₄×C₈₉	—	2	4	no	—
237	C₄⋊C₄×C₈₉	—	2	2	no	—
238	C₄⋊C₄×C₈₉	—	2	2	no	—
239	C₄⋊C₄×C₈₉	—	2	4	no	—
240	C₄⋊C₄×C₈₉	—	2	4	no	—
241	C₄⋊C₄×C₈₉	—	2	4	no	—
242	C₄⋊C₄×C₈₉	—	2	4	no	—
243	C₄⋊C₄×C₈₉	—	2	4	no	—
244	C₄⋊C₄×C₈₉	—	2	4	no	—
245	C₄⋊C₄×C₈₉	—	2	4	no	—
246	C₄⋊C₄×C₈₉	—	2	4	no	—
247	C₄⋊C₄×C₈₉	—	2	4	no	—
248	C₄⋊C₄×C₈₉	—	2	4	no	—
249	C₄⋊C₄×C₈₉	—	2	4	no	—
250	C₄⋊C₄×C₈₉	—	2	8	no	—
251	C₄⋊C₄×C₈₉	—	2	8	no	—
252	C₄⋊C₄×C₈₉	—	4	4	no	—
253	C₄⋊C₄×C₈₉	—	4	4	no	—
254	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
255	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
256	C₂²⋊C₄×C₈₉	—	2	4	no	—
257	C₂²⋊C₄×C₈₉	—	2	4	no	—
258	C₂²⋊C₄×C₈₉	—	2	4	no	—
259	C₂²⋊C₄×C₈₉	—	2	4	no	—
260	C₂²⋊C₄×C₈₉	—	2	4	no	—
261	C₂²⋊C₄×C₈₉	—	2	4	no	—
262	C₂²⋊C₄×C₈₉	—	2	4	no	—
263	C₂²⋊C₄×C₈₉	—	2	4	no	—
264	C₂²⋊C₄×C₈₉	—	2	8	no	—
265	C₂²⋊C₄×C₈₉	—	2	8	no	—
266	C₂²⋊C₄×C₈₉	—	2	8	no	—
267	C₂²⋊C₄×C₈₉	—	4	4	no	—
268	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
269	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
270	C₄²×C₈₉	—	2	4	no	—
271	C₄²×C₈₉	—	2	4	no	—
272	C₄²×C₈₉	—	2	4	no	—
273	C₄²×C₈₉	—	2	4	no	—
274	C₄²×C₈₉	—	2	2	no	—
275	C₄²×C₈₉	—	2	2	no	—
276	C₄²×C₈₉	—	2	4	no	—
277	C₄²×C₈₉	—	2	4	no	—
278	C₄²×C₈₉	—	4	2	no	—
279	C₄²×C₈₉	—	4	2	no	—
280	C₄²×C₈₉	C₂×D₄	1	4	yes	—
281	C₄²×C₈₉	C₂×D₄	1	4	yes	—
282	C₄²×C₈₉	#41	1	4	yes	—
283	C₄²×C₈₉	#41	1	4	yes	—
284	C₂³×C₈₉	—	2	1	no	—
285	C₂³×C₈₉	—	2	1	no	—
286	C₂³×C₈₉	—	2	2	no	—
287	C₂³×C₈₉	—	2	2	no	—
288	C₂³×C₈₉	—	2	2	no	—
289	C₂³×C₈₉	—	2	2	no	—
290	C₂³×C₈₉	—	2	2	no	—
291	C₂³×C₈₉	—	2	4	no	—
292	C₂³×C₈₉	—	2	4	no	—
293	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
294	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
295	Q₈×C₈₉	—	4	4	no	—
296	Q₈×C₈₉	—	4	4	no	—
297	Q₈×C₈₉	—	4	4	no	—
298	Q₈×C₈₉	—	8	4	no	—
299	D₄×C₈₉	—	4	4	no	—
300	D₄×C₈₉	—	8	4	no	—
301	C₂×C₄×C₈₉	—	2	1	no	—
302	C₂×C₄×C₈₉	—	2	2	no	—
303	C₂×C₄×C₈₉	—	2	1	no	—
304	C₂×C₄×C₈₉	—	2	2	no	—
305	C₂×C₄×C₈₉	—	2	2	no	—
306	C₂×C₄×C₈₉	—	2	2	no	—
307	C₂×C₄×C₈₉	—	2	2	no	—
308	C₂×C₄×C₈₉	—	2	2	no	—
309	C₂×C₄×C₈₉	—	2	2	no	—
310	C₂×C₄×C₈₉	—	2	2	no	—
311	C₂×C₄×C₈₉	—	2	2	no	—
312	C₂×C₄×C₈₉	—	2	2	no	—
313	C₂×C₄×C₈₉	—	2	8	no	—
314	C₂×C₄×C₈₉	—	2	2	no	—
315	C₂×C₄×C₈₉	—	2	2	no	—
316	C₂×C₄×C₈₉	—	2	2	no	—
317	C₂×C₄×C₈₉	—	2	2	no	—
318	C₂×C₄×C₈₉	—	2	2	no	—
319	C₂×C₄×C₈₉	—	2	2	no	—
320	C₂×C₄×C₈₉	—	2	2	no	—
321	C₂×C₄×C₈₉	—	2	2	no	—
322	C₂×C₄×C₈₉	—	2	2	no	—
323	C₂×C₄×C₈₉	—	2	2	no	—
324	C₂×C₄×C₈₉	—	2	2	no	—
325	C₂×C₄×C₈₉	—	2	2	no	—
326	C₂×C₄×C₈₉	—	2	2	no	—
327	C₂×C₄×C₈₉	—	2	2	no	—
328	C₂×C₄×C₈₉	—	2	2	no	—
329	C₂×C₄×C₈₉	—	2	4	no	—
330	C₂×C₄×C₈₉	—	2	2	no	—
331	C₂×C₄×C₈₉	—	2	4	no	—
332	C₂×C₄×C₈₉	—	2	4	no	—
333	C₂×C₄×C₈₉	—	2	4	no	—
334	C₂×C₄×C₈₉	—	4	8	no	—
335	C₂×C₄×C₈₉	—	8	4	no	—
336	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
340	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
341	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
343	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
344	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
345	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
346	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
347	C₂²×C₈₉	—	2	2	no	—
348	C₂²×C₈₉	—	2	2	no	—
349	C₂²×C₈₉	—	2	2	no	—
350	C₂²×C₈₉	—	4	2	no	—
351	C₂²×C₈₉	—	4	2	no	—
352	C₂²×C₈₉	—	4	2	no	—
353	C₂²×C₈₉	—	4	4	no	—
354	C₂²×C₈₉	—	4	4	no	—
355	C₂²×C₈₉	—	4	2	no	—
356	C₂²×C₈₉	—	4	2	no	—
357	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
358	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
359	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
360	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
361	C₂²×C₈₉	#585	1	2	yes	—
362	C₄×C₈₉	—	2	2	no	—
363	C₄×C₈₉	—	2	4	no	—
364	C₄×C₈₉	—	2	4	no	—
365	C₄×C₈₉	—	2	4	no	—
366	C₄×C₈₉	—	2	2	no	—
367	C₄×C₈₉	—	2	2	no	—
368	C₄×C₈₉	—	2	2	no	—
369	C₄×C₈₉	—	2	2	no	—
370	C₄×C₈₉	—	4	2	no	—
371	C₄×C₈₉	—	4	2	no	—
372	C₄×C₈₉	—	4	2	no	—
373	C₄×C₈₉	—	4	2	no	—
374	C₄×C₈₉	—	4	2	no	—
375	C₄×C₈₉	—	4	2	no	—
376	C₄×C₈₉	—	4	2	no	—
377	C₄×C₈₉	—	4	2	no	—
378	C₄×C₈₉	#532	1	4	yes	—
379	#35318	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
380	C₂×C₈₉	—	4	2	no	—
381	C₂×C₈₉	—	8	2	no	—
382	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
383	C₂×C₈₉	#3461	1	2	yes	—
384	C₂×C₈₉	#3495	1	2	yes	—
385	C₂×C₈₉	#3499	1	1	yes	characteristic
386	C₂×C₈₉	#3500	1	1	yes	characteristic
387	C₂×#542	C₂×C₈₉	1	1	yes	characteristic
388	C₂×#541	C₂×C₈₉	1	1	yes	characteristic, complemented
389	#2862	C₂×C₈₉	1	1	yes	characteristic, complemented
390	#2861	C₂×C₈₉	1	1	yes	characteristic, complemented
391	#2857	C₂×C₈₉	1	1	yes	characteristic, complemented
392	#2850	C₂×C₈₉	1	1	yes	characteristic
393	#2660	C₂×C₈₉	1	1	yes	characteristic, complemented
394	#2658	C₂×C₈₉	1	1	yes	characteristic, complemented
395	#2621	C₂×C₈₉	1	1	yes	characteristic, complemented
396	#2620	C₂×C₈₉	1	1	yes	characteristic
397	#2556	C₂×C₈₉	1	4	yes	complemented
398	#2553	C₂×C₈₉	1	4	yes	complemented
399	#2521	C₂×C₈₉	1	4	yes	complemented
400	#2519	C₂×C₈₉	1	4	yes	complemented
401	#2327	C₂×C₈₉	1	1	yes	characteristic, complemented
402	#2326	C₂×C₈₉	1	1	yes	characteristic, complemented
403	C₄×C₄⋊Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
404	C₄×#124	C₂×C₈₉	1	1	yes	characteristic, complemented
405	C₄×#117	C₂×C₈₉	1	1	yes	characteristic, complemented
406	C₈₉	#35318	1	1	yes	characteristic, direct product factor, Sylow
407	#542	—	2	8	no	—
408	#541	—	2	8	no	—
409	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
410	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
411	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
412	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
413	C₂×#126	C₂²×C₈₉	1	2	yes	—
414	C₂×#126	C₂²×C₈₉	1	2	yes	—
415	C₂×#126	C₂²×C₈₉	1	2	yes	—
416	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
417	C₂×#125	C₂²×C₈₉	1	2	yes	—
418	C₂×#125	C₂²×C₈₉	1	2	yes	—
419	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
420	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
421	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
422	C₂×#124	C₂²×C₈₉	1	2	yes	—
423	C₂×#123	C₂²×C₈₉	1	2	yes	—
424	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
425	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
426	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
427	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
428	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
429	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
430	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
431	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
432	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
433	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
434	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
435	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
436	#399	C₂²×C₈₉	1	4	yes	—
437	#399	C₂²×C₈₉	1	4	yes	—
438	#398	C₂²×C₈₉	1	4	yes	—
439	#398	C₂²×C₈₉	1	4	yes	—
440	#397	C₂²×C₈₉	1	4	yes	—
441	#396	C₂²×C₈₉	1	4	yes	—
442	#395	C₂²×C₈₉	1	4	yes	—
443	#394	C₂²×C₈₉	1	4	yes	—
444	#391	C₂²×C₈₉	1	1	yes	characteristic
445	#391	C₂²×C₈₉	1	1	yes	characteristic
446	#391	C₂²×C₈₉	1	1	yes	characteristic
447	#391	C₂²×C₈₉	1	1	yes	characteristic
448	#391	C₂²×C₈₉	1	1	yes	characteristic
449	#391	C₂²×C₈₉	1	1	yes	characteristic
450	#391	C₂²×C₈₉	1	4	yes	—
451	#390	C₂²×C₈₉	1	1	yes	characteristic
452	#390	C₂²×C₈₉	1	1	yes	characteristic
453	#389	C₂²×C₈₉	1	4	yes	—
454	#389	C₂²×C₈₉	1	4	yes	—
455	#388	C₂²×C₈₉	1	4	yes	—
456	#388	C₂²×C₈₉	1	4	yes	—
457	#388	C₂²×C₈₉	1	4	yes	—
458	#388	C₂²×C₈₉	1	4	yes	—
459	#388	C₂²×C₈₉	1	4	yes	—
460	#387	C₂²×C₈₉	1	4	yes	—
461	#387	C₂²×C₈₉	1	4	yes	—
462	#386	C₂²×C₈₉	1	4	yes	—
463	#385	C₂²×C₈₉	1	4	yes	—
464	#384	C₂²×C₈₉	1	1	yes	characteristic
465	#384	C₂²×C₈₉	1	1	yes	characteristic
466	#382	C₂²×C₈₉	1	1	yes	characteristic
467	#382	C₂²×C₈₉	1	4	yes	—
468	#382	C₂²×C₈₉	1	1	yes	characteristic
469	#380	C₂²×C₈₉	1	4	yes	—
470	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
471	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
472	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
473	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
474	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
475	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
476	#376	C₂²×C₈₉	1	1	yes	characteristic
477	#376	C₂²×C₈₉	1	1	yes	characteristic
478	C₄³	C₂²×C₈₉	1	1	yes	characteristic
479	C₄³	C₂²×C₈₉	1	1	yes	characteristic
480	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
481	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
482	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
483	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
484	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
485	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
486	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
487	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
488	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
489	C₄⋊Q₈	—	2	4	no	—
490	C₄⋊Q₈	—	2	4	no	—
491	C₄⋊Q₈	—	2	4	no	—
492	C₄⋊Q₈	—	2	4	no	—
493	#126	—	2	8	no	—
494	#126	—	2	8	no	—
495	#126	—	2	8	no	—
496	#125	—	2	8	no	—
497	#125	—	2	8	no	—
498	#125	—	2	4	no	—
499	#124	—	2	8	no	—
500	#124	—	2	4	no	—
501	#124	—	2	4	no	—
502	#124	—	2	4	no	—
503	#123	—	2	8	no	—
504	C₂²⋊Q₈	—	2	4	no	—
505	C₂²⋊Q₈	—	2	4	no	—
506	C₂²⋊Q₈	—	2	4	no	—
507	C₂²⋊Q₈	—	2	8	no	—
508	#121	—	2	4	no	—
509	C₄×Q₈	—	2	4	no	—
510	C₄×Q₈	—	2	4	no	—
511	C₄×Q₈	—	2	4	no	—
512	C₄×D₄	—	2	4	no	—
513	#117	—	2	4	no	—
514	#117	D₄×C₈₉	1	8	yes	—
515	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
532	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
533	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
534	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
535	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
537	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
550	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
551	C₂×C₄²	—	2	4	no	—
552	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
554	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
555	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
556	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
557	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
558	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
559	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
560	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
561	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
562	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
564	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
565	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
566	#95	C₂³×C₈₉	1	2	yes	—
567	#95	C₂³×C₈₉	1	2	yes	—
568	#95	C₂³×C₈₉	1	2	yes	—
569	#95	C₂³×C₈₉	1	2	yes	—
570	#95	C₂³×C₈₉	1	4	yes	—
571	#95	C₂³×C₈₉	1	4	yes	—
572	#95	C₂³×C₈₉	1	4	yes	—
573	#95	C₂³×C₈₉	1	4	yes	—
574	#95	C₂³×C₈₉	1	4	yes	—
575	#95	C₂³×C₈₉	1	4	yes	—
576	#95	C₂³×C₈₉	1	4	yes	—
577	#95	C₂³×C₈₉	1	4	yes	—
578	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
579	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
580	C₂×Q₈	—	2	2	no	—
581	C₂×Q₈	—	2	2	no	—
582	C₂×Q₈	—	2	2	no	—
583	C₂×Q₈	—	2	4	no	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×Q₈	—	2	2	no	—
586	C₂×Q₈	—	2	2	no	—
587	C₂×Q₈	—	2	2	no	—
588	C₂×Q₈	—	2	2	no	—
589	C₂×Q₈	—	2	2	no	—
590	C₂×Q₈	—	4	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	—	4	4	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	2	4	no	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	4	2	no	—
602	C₂²×C₄	—	4	4	no	—
603	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
604	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
615	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	8	no	—
638	C₄⋊C₄	—	2	8	no	—
639	C₄⋊C₄	—	4	4	no	—
640	C₄⋊C₄	—	4	4	no	—
641	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
642	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	8	no	—
652	C₂²⋊C₄	—	2	8	no	—
653	C₂²⋊C₄	—	2	8	no	—
654	C₂²⋊C₄	—	4	4	no	—
655	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
656	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	4	no	—
659	C₄²	—	2	4	no	—
660	C₄²	—	2	4	no	—
661	C₄²	—	2	2	no	—
662	C₄²	—	2	2	no	—
663	C₄²	—	2	4	no	—
664	C₄²	—	2	4	no	—
665	C₄²	—	4	2	no	—
666	C₄²	—	4	2	no	—
667	C₄²	C₂×D₄×C₈₉	1	4	yes	—
668	C₄²	C₂×D₄×C₈₉	1	4	yes	—
669	C₄²	#41×C₈₉	1	4	yes	—
670	C₄²	#41×C₈₉	1	4	yes	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	2	4	no	—
679	C₂³	—	2	4	no	—
680	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
681	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
682	Q₈	—	4	4	no	—
683	Q₈	—	4	4	no	—
684	Q₈	—	4	4	no	—
685	Q₈	—	8	4	no	—
686	D₄	—	4	4	no	—
687	D₄	—	8	4	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	8	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	4	no	—
719	C₂×C₄	—	2	4	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	4	8	no	—
722	C₂×C₄	—	8	4	no	—
723	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
724	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
725	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
726	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
728	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
729	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
730	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
731	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
732	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
733	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	4	no	—
741	C₂²	—	4	4	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
745	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
746	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
747	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
748	C₂²	#585×C₈₉	1	2	yes	—
749	C₄	—	2	2	no	—
750	C₄	—	2	4	no	—
751	C₄	—	2	4	no	—
752	C₄	—	2	4	no	—
753	C₄	—	2	2	no	—
754	C₄	—	2	2	no	—
755	C₄	—	2	2	no	—
756	C₄	—	2	2	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	#532×C₈₉	1	4	yes	—
766	C₂	—	4	2	no	—
767	C₂	—	8	2	no	—
768	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
769	C₂	C₈₉×#3461	1	2	yes	—
770	C₂	C₈₉×#3495	1	2	yes	—
771	C₂	C₈₉×#3499	1	1	yes	characteristic
772	C₂	C₈₉×#3500	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂×#121×C₈₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#541×C₈₉	C₂	semidirect
3. C₈₉×#2862	C₂	semidirect
4. C₈₉×#2861	C₂	semidirect
5. C₈₉×#2857	C₂	semidirect
7. C₈₉×#2660	C₂	semidirect
8. C₈₉×#2658	C₂	semidirect
9. C₈₉×#2621	C₂	semidirect
11. C₈₉×#2556	C₂	semidirect
12. C₈₉×#2553	C₂	semidirect
13. C₈₉×#2521	C₂	semidirect
14. C₈₉×#2519	C₂	semidirect
15. C₈₉×#2327	C₂	semidirect
16. C₈₉×#2326	C₂	semidirect
17. C₄×C₄⋊Q₈×C₈₉	C₂	semidirect
18. C₄×#124×C₈₉	C₂	semidirect
19. C₄×#117×C₈₉	C₂	semidirect
379. #35318	C₈₉	direct (N × H)
388. C₂×#541	C₂×C₈₉	semidirect
389. #2862	C₂×C₈₉	semidirect
390. #2861	C₂×C₈₉	semidirect
391. #2857	C₂×C₈₉	semidirect
393. #2660	C₂×C₈₉	semidirect
394. #2658	C₂×C₈₉	semidirect
395. #2621	C₂×C₈₉	semidirect
397. #2556	C₂×C₈₉	semidirect
398. #2553	C₂×C₈₉	semidirect
399. #2521	C₂×C₈₉	semidirect
400. #2519	C₂×C₈₉	semidirect
401. #2327	C₂×C₈₉	semidirect
402. #2326	C₂×C₈₉	semidirect
403. C₄×C₄⋊Q₈	C₂×C₈₉	semidirect
404. C₄×#124	C₂×C₈₉	semidirect
405. C₄×#117	C₂×C₈₉	semidirect
406. C₈₉	#35318	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#542×C₈₉	2
C₂×#541×C₈₉	2
C₈₉×#2862	2
C₈₉×#2861	2
C₈₉×#2857	2
C₈₉×#2850	2
C₈₉×#2660	2
C₈₉×#2658	2
C₈₉×#2621	2
C₈₉×#2620	2
C₈₉×#2556	2
C₈₉×#2553	2
C₈₉×#2521	2
C₈₉×#2519	2
C₈₉×#2327	2
C₈₉×#2326	2
C₄×C₄⋊Q₈×C₈₉	2
C₄×#124×C₈₉	2
C₄×#117×C₈₉	2
#35318	89

Subgroups — C89×#35318 #36413166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35318 #36413166