Subgroups — C₈₉×#36561 #36414409

Order 22784.

2384 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₈₉	C₂	1	2	yes	maximal, complemented
2	C₈₉×#2857	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2857	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2564	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2556	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2551	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2542	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2506	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2492	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2452	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2417	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2365	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#2360	C₂	1	2	yes	maximal, complemented
14	D₄×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#121×C₈₉	C₂	1	2	yes	maximal
16	C₄×#121×C₈₉	C₂	1	1	yes	maximal, characteristic
17	C₂×C₄×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#554×C₈₉	—	2	16	no	—
19	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
20	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
22	C₂×#125×C₈₉	C₂²	1	4	yes	—
23	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
24	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
25	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
28	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
31	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
34	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
35	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
39	#400×C₈₉	C₂²	1	4	yes	—
40	#399×C₈₉	C₂²	1	4	yes	—
41	#398×C₈₉	C₂²	1	4	yes	—
42	#396×C₈₉	C₂²	1	4	yes	—
43	#395×C₈₉	C₂²	1	4	yes	—
44	#393×C₈₉	C₂²	1	4	yes	—
45	#391×C₈₉	C₂²	1	4	yes	—
46	#391×C₈₉	C₂²	1	2	yes	—
47	#391×C₈₉	C₂²	1	2	yes	—
48	#390×C₈₉	C₂²	1	1	yes	characteristic
49	#390×C₈₉	C₂²	1	2	yes	—
50	#389×C₈₉	C₂²	1	2	yes	—
51	#389×C₈₉	C₂²	1	2	yes	—
52	#389×C₈₉	C₂²	1	1	yes	characteristic
53	#389×C₈₉	C₂²	1	2	yes	—
54	#389×C₈₉	C₂²	1	4	yes	—
55	#389×C₈₉	C₂²	1	2	yes	—
56	#389×C₈₉	C₂²	1	2	yes	—
57	#389×C₈₉	C₂²	1	2	yes	—
58	#388×C₈₉	C₂²	1	2	yes	—
59	#388×C₈₉	C₂²	1	4	yes	—
60	#387×C₈₉	C₂²	1	4	yes	—
61	#387×C₈₉	C₂²	1	4	yes	—
62	#386×C₈₉	C₂²	1	2	yes	—
63	#386×C₈₉	C₂²	1	4	yes	—
64	#385×C₈₉	C₂²	1	4	yes	—
65	#385×C₈₉	C₂²	1	4	yes	—
66	#384×C₈₉	C₂²	1	1	yes	characteristic
67	#384×C₈₉	C₂²	1	2	yes	—
68	#380×C₈₉	C₂²	1	2	yes	—
69	#380×C₈₉	C₂²	1	1	yes	characteristic
70	#380×C₈₉	C₂²	1	2	yes	—
71	#380×C₈₉	C₂²	1	4	yes	—
72	#380×C₈₉	C₂²	1	2	yes	—
73	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
74	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
75	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
76	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
77	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
78	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
79	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
81	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
82	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
83	C₂×#95×C₈₉	C₂²	1	2	yes	—
84	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
85	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
86	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
87	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
89	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
91	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
94	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
95	C₄⋊Q₈×C₈₉	—	2	8	no	—
96	C₄⋊Q₈×C₈₉	—	2	4	no	—
97	C₄⋊Q₈×C₈₉	—	4	4	no	—
98	#125×C₈₉	—	2	16	no	—
99	C₂²⋊Q₈×C₈₉	—	2	16	no	—
100	C₂²⋊Q₈×C₈₉	—	2	8	no	—
101	C₂²⋊Q₈×C₈₉	—	2	16	no	—
102	C₂²⋊Q₈×C₈₉	—	2	8	no	—
103	C₂²⋊Q₈×C₈₉	—	2	8	no	—
104	#121×C₈₉	Q₈	1	8	yes	complemented
105	C₄×Q₈×C₈₉	—	2	8	no	—
106	C₄×D₄×C₈₉	—	2	16	no	—
107	C₄×D₄×C₈₉	—	2	8	no	—
108	C₄×D₄×C₈₉	—	2	4	no	—
109	C₄×D₄×C₈₉	—	4	4	no	—
110	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
111	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
112	C₂×C₄⋊C₄×C₈₉	D₄	1	8	yes	complemented
113	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	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	1	yes	characteristic
131	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
144	C₂×C₄²×C₈₉	—	2	4	no	—
145	C₂×C₄²×C₈₉	—	4	4	no	—
146	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
148	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
149	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
150	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
151	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
154	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
156	#95×C₈₉	C₂³	1	2	yes	—
157	#95×C₈₉	C₂³	1	2	yes	—
158	#95×C₈₉	C₂³	1	2	yes	—
159	#95×C₈₉	C₂³	1	2	yes	—
160	#95×C₈₉	C₂³	1	4	yes	—
161	#95×C₈₉	C₂³	1	2	yes	—
162	#95×C₈₉	C₂³	1	2	yes	—
163	#95×C₈₉	C₂³	1	4	yes	—
164	#95×C₈₉	C₂³	1	2	yes	—
165	#95×C₈₉	C₂³	1	4	yes	—
166	#95×C₈₉	C₂³	1	4	yes	—
167	#95×C₈₉	C₂³	1	4	yes	—
168	#95×C₈₉	C₂³	1	4	yes	—
169	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
170	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
171	C₂×Q₈×C₈₉	—	2	4	no	—
172	C₂×Q₈×C₈₉	—	2	8	no	—
173	C₂×Q₈×C₈₉	—	2	4	no	—
174	C₂×Q₈×C₈₉	—	2	4	no	—
175	C₂×Q₈×C₈₉	—	4	4	no	—
176	C₂×Q₈×C₈₉	—	4	4	no	—
177	C₂×D₄×C₈₉	—	2	4	no	—
178	C₂×D₄×C₈₉	—	2	4	no	—
179	C₂×D₄×C₈₉	—	2	2	no	—
180	C₂×D₄×C₈₉	—	2	2	no	—
181	C₂×D₄×C₈₉	C₂×Q₈	1	8	yes	—
182	C₂×D₄×C₈₉	C₂×Q₈	1	4	yes	—
183	C₂²×C₄×C₈₉	—	2	2	no	—
184	C₂²×C₄×C₈₉	—	2	2	no	—
185	C₂²×C₄×C₈₉	—	2	2	no	—
186	C₂²×C₄×C₈₉	—	2	2	no	—
187	C₂²×C₄×C₈₉	—	2	2	no	—
188	C₂²×C₄×C₈₉	—	2	4	no	—
189	C₂²×C₄×C₈₉	—	2	4	no	—
190	C₂²×C₄×C₈₉	—	2	2	no	—
191	C₂²×C₄×C₈₉	—	2	4	no	—
192	C₂²×C₄×C₈₉	—	2	4	no	—
193	C₂²×C₄×C₈₉	—	2	4	no	—
194	C₂²×C₄×C₈₉	—	2	8	no	—
195	C₂²×C₄×C₈₉	—	4	2	no	—
196	C₂²×C₄×C₈₉	—	4	2	no	—
197	C₂²×C₄×C₈₉	—	4	1	no	—
198	C₂²×C₄×C₈₉	—	4	2	no	—
199	C₂²×C₄×C₈₉	—	4	4	no	—
200	C₂²×C₄×C₈₉	—	4	4	no	—
201	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
202	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
203	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
204	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
207	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
219	C₄⋊C₄×C₈₉	—	2	8	no	—
220	C₄⋊C₄×C₈₉	—	2	4	no	—
221	C₄⋊C₄×C₈₉	—	2	4	no	—
222	C₄⋊C₄×C₈₉	—	2	8	no	—
223	C₄⋊C₄×C₈₉	—	2	8	no	—
224	C₄⋊C₄×C₈₉	—	2	8	no	—
225	C₄⋊C₄×C₈₉	—	2	8	no	—
226	C₄⋊C₄×C₈₉	—	2	4	no	—
227	C₄⋊C₄×C₈₉	—	2	2	no	—
228	C₄⋊C₄×C₈₉	—	2	2	no	—
229	C₄⋊C₄×C₈₉	—	2	8	no	—
230	C₄⋊C₄×C₈₉	—	2	4	no	—
231	C₄⋊C₄×C₈₉	—	2	4	no	—
232	C₄⋊C₄×C₈₉	—	2	4	no	—
233	C₄⋊C₄×C₈₉	—	2	2	no	—
234	C₄⋊C₄×C₈₉	—	4	2	no	—
235	C₄⋊C₄×C₈₉	—	4	4	no	—
236	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
237	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
238	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
239	C₄⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
240	C₄⋊C₄×C₈₉	#41	1	4	yes	—
241	C₂²⋊C₄×C₈₉	—	2	8	no	—
242	C₂²⋊C₄×C₈₉	—	2	4	no	—
243	C₂²⋊C₄×C₈₉	—	2	8	no	—
244	C₂²⋊C₄×C₈₉	—	2	4	no	—
245	C₂²⋊C₄×C₈₉	—	2	4	no	—
246	C₂²⋊C₄×C₈₉	—	2	8	no	—
247	C₂²⋊C₄×C₈₉	—	4	2	no	—
248	C₂²⋊C₄×C₈₉	—	4	4	no	—
249	C₂²⋊C₄×C₈₉	C₂×Q₈	1	8	yes	—
250	C₄²×C₈₉	—	2	8	no	—
251	C₄²×C₈₉	—	2	4	no	—
252	C₄²×C₈₉	—	2	2	no	—
253	C₄²×C₈₉	—	2	2	no	—
254	C₄²×C₈₉	—	2	2	no	—
255	C₄²×C₈₉	—	2	4	no	—
256	C₄²×C₈₉	—	2	4	no	—
257	C₄²×C₈₉	—	4	2	no	—
258	C₄²×C₈₉	—	4	2	no	—
259	C₄²×C₈₉	#41	1	4	yes	—
260	C₂³×C₈₉	—	2	1	no	—
261	C₂³×C₈₉	—	2	1	no	—
262	C₂³×C₈₉	—	2	1	no	—
263	C₂³×C₈₉	—	2	1	no	—
264	C₂³×C₈₉	—	2	2	no	—
265	C₂³×C₈₉	—	2	2	no	—
266	C₂³×C₈₉	—	2	2	no	—
267	C₂³×C₈₉	—	2	2	no	—
268	C₂³×C₈₉	—	2	2	no	—
269	C₂³×C₈₉	—	2	2	no	—
270	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
271	C₂³×C₈₉	C₂²×Q₈	1	4	yes	—
272	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
273	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
274	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
275	Q₈×C₈₉	—	4	8	no	—
276	Q₈×C₈₉	—	8	8	no	—
277	D₄×C₈₉	—	2	16	no	—
278	D₄×C₈₉	—	2	8	no	—
279	C₂×C₄×C₈₉	—	2	2	no	—
280	C₂×C₄×C₈₉	—	2	1	no	—
281	C₂×C₄×C₈₉	—	2	1	no	—
282	C₂×C₄×C₈₉	—	2	1	no	—
283	C₂×C₄×C₈₉	—	2	2	no	—
284	C₂×C₄×C₈₉	—	2	2	no	—
285	C₂×C₄×C₈₉	—	2	2	no	—
286	C₂×C₄×C₈₉	—	2	1	no	—
287	C₂×C₄×C₈₉	—	2	1	no	—
288	C₂×C₄×C₈₉	—	2	2	no	—
289	C₂×C₄×C₈₉	—	2	2	no	—
290	C₂×C₄×C₈₉	—	2	1	no	—
291	C₂×C₄×C₈₉	—	2	2	no	—
292	C₂×C₄×C₈₉	—	2	2	no	—
293	C₂×C₄×C₈₉	—	2	8	no	—
294	C₂×C₄×C₈₉	—	2	8	no	—
295	C₂×C₄×C₈₉	—	2	4	no	—
296	C₂×C₄×C₈₉	—	2	2	no	—
297	C₂×C₄×C₈₉	—	2	2	no	—
298	C₂×C₄×C₈₉	—	2	4	no	—
299	C₂×C₄×C₈₉	—	2	1	no	—
300	C₂×C₄×C₈₉	—	2	2	no	—
301	C₂×C₄×C₈₉	—	2	4	no	—
302	C₂×C₄×C₈₉	—	2	2	no	—
303	C₂×C₄×C₈₉	—	2	2	no	—
304	C₂×C₄×C₈₉	—	2	4	no	—
305	C₂×C₄×C₈₉	—	2	2	no	—
306	C₂×C₄×C₈₉	—	2	4	no	—
307	C₂×C₄×C₈₉	—	2	2	no	—
308	C₂×C₄×C₈₉	—	2	1	no	—
309	C₂×C₄×C₈₉	—	2	2	no	—
310	C₂×C₄×C₈₉	—	2	1	no	—
311	C₂×C₄×C₈₉	—	2	2	no	—
312	C₂×C₄×C₈₉	—	2	4	no	—
313	C₂×C₄×C₈₉	—	4	8	no	—
314	C₂×C₄×C₈₉	—	4	4	no	—
315	C₂×C₄×C₈₉	—	4	8	no	—
316	C₂×C₄×C₈₉	—	4	8	no	—
317	C₂×C₄×C₈₉	—	8	8	no	—
318	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
319	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
321	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
323	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
324	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
325	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
326	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
327	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
328	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
329	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
330	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
331	C₂²×C₈₉	—	2	2	no	—
332	C₂²×C₈₉	—	2	2	no	—
333	C₂²×C₈₉	—	2	2	no	—
334	C₂²×C₈₉	—	2	2	no	—
335	C₂²×C₈₉	—	2	2	no	—
336	C₂²×C₈₉	—	2	2	no	—
337	C₂²×C₈₉	—	2	4	no	—
338	C₂²×C₈₉	—	2	4	no	—
339	C₂²×C₈₉	—	2	4	no	—
340	C₂²×C₈₉	—	4	2	no	—
341	C₂²×C₈₉	—	4	2	no	—
342	C₂²×C₈₉	—	4	2	no	—
343	C₂²×C₈₉	—	4	2	no	—
344	C₂²×C₈₉	D₄×Q₈	1	4	yes	—
345	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
346	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
347	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
348	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
349	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
350	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
351	C₂²×C₈₉	#585	1	1	yes	characteristic
352	C₄×C₈₉	—	2	2	no	—
353	C₄×C₈₉	—	2	4	no	—
354	C₄×C₈₉	—	2	2	no	—
355	C₄×C₈₉	—	2	2	no	—
356	C₄×C₈₉	—	2	4	no	—
357	C₄×C₈₉	—	2	4	no	—
358	C₄×C₈₉	—	2	4	no	—
359	C₄×C₈₉	—	4	2	no	—
360	C₄×C₈₉	—	4	4	no	—
361	C₄×C₈₉	—	4	1	no	—
362	C₄×C₈₉	—	4	4	no	—
363	C₄×C₈₉	—	4	2	no	—
364	C₄×C₈₉	—	4	2	no	—
365	C₄×C₈₉	#532	1	4	yes	—
366	C₄×C₈₉	#554	1	4	yes	complemented
367	#36561	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
368	C₂×C₈₉	—	2	4	no	—
369	C₂×C₈₉	—	4	4	no	—
370	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
371	C₂×C₈₉	C₂×D₄×Q₈	1	1	yes	characteristic
372	C₂×C₈₉	C₂×#554	1	1	yes	characteristic
373	C₂×C₈₉	Q₈×#41	1	1	yes	characteristic
374	C₂×C₈₉	#3495	1	1	yes	characteristic
375	C₂×C₈₉	#3496	1	1	yes	characteristic
376	C₂×C₈₉	#3520	1	1	yes	characteristic
377	C₂×#554	C₂×C₈₉	1	2	yes	complemented
378	#2857	C₂×C₈₉	1	2	yes	complemented
379	#2857	C₂×C₈₉	1	1	yes	characteristic, complemented
380	#2564	C₂×C₈₉	1	4	yes	complemented
381	#2556	C₂×C₈₉	1	4	yes	complemented
382	#2551	C₂×C₈₉	1	1	yes	characteristic, complemented
383	#2542	C₂×C₈₉	1	1	yes	characteristic, complemented
384	#2506	C₂×C₈₉	1	2	yes	complemented
385	#2492	C₂×C₈₉	1	2	yes	complemented
386	#2452	C₂×C₈₉	1	2	yes	complemented
387	#2417	C₂×C₈₉	1	2	yes	complemented
388	#2365	C₂×C₈₉	1	1	yes	characteristic, complemented
389	#2360	C₂×C₈₉	1	2	yes	complemented
390	D₄×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
391	C₄×#121	C₂×C₈₉	1	2	yes	—
392	C₄×#121	C₂×C₈₉	1	1	yes	characteristic
393	C₂×C₄×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
394	C₈₉	#36561	1	1	yes	characteristic, direct product factor, Sylow
395	#554	—	2	16	no	—
396	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
397	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
398	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
399	C₂×#125	C₂²×C₈₉	1	4	yes	—
400	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
401	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
402	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
403	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
404	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
405	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
406	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
407	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
408	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
409	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
410	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
411	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
412	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
413	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
414	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
415	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
416	#400	C₂²×C₈₉	1	4	yes	—
417	#399	C₂²×C₈₉	1	4	yes	—
418	#398	C₂²×C₈₉	1	4	yes	—
419	#396	C₂²×C₈₉	1	4	yes	—
420	#395	C₂²×C₈₉	1	4	yes	—
421	#393	C₂²×C₈₉	1	4	yes	—
422	#391	C₂²×C₈₉	1	2	yes	—
423	#391	C₂²×C₈₉	1	4	yes	—
424	#391	C₂²×C₈₉	1	2	yes	—
425	#390	C₂²×C₈₉	1	1	yes	characteristic
426	#390	C₂²×C₈₉	1	2	yes	—
427	#389	C₂²×C₈₉	1	2	yes	—
428	#389	C₂²×C₈₉	1	4	yes	—
429	#389	C₂²×C₈₉	1	2	yes	—
430	#389	C₂²×C₈₉	1	2	yes	—
431	#389	C₂²×C₈₉	1	2	yes	—
432	#389	C₂²×C₈₉	1	2	yes	—
433	#389	C₂²×C₈₉	1	1	yes	characteristic
434	#389	C₂²×C₈₉	1	2	yes	—
435	#388	C₂²×C₈₉	1	4	yes	—
436	#388	C₂²×C₈₉	1	2	yes	—
437	#387	C₂²×C₈₉	1	4	yes	—
438	#387	C₂²×C₈₉	1	4	yes	—
439	#386	C₂²×C₈₉	1	2	yes	—
440	#386	C₂²×C₈₉	1	4	yes	—
441	#385	C₂²×C₈₉	1	4	yes	—
442	#385	C₂²×C₈₉	1	4	yes	—
443	#384	C₂²×C₈₉	1	1	yes	characteristic
444	#384	C₂²×C₈₉	1	2	yes	—
445	#380	C₂²×C₈₉	1	2	yes	—
446	#380	C₂²×C₈₉	1	4	yes	—
447	#380	C₂²×C₈₉	1	2	yes	—
448	#380	C₂²×C₈₉	1	1	yes	characteristic
449	#380	C₂²×C₈₉	1	2	yes	—
450	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
451	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
452	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
453	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
454	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
455	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
456	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
457	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
458	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
459	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
460	C₂×#95	C₂²×C₈₉	1	2	yes	—
461	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
462	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
463	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
464	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
465	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
466	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
467	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
468	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
469	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
470	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
471	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
472	C₄⋊Q₈	—	2	8	no	—
473	C₄⋊Q₈	—	2	4	no	—
474	C₄⋊Q₈	—	4	4	no	—
475	#125	—	2	16	no	—
476	C₂²⋊Q₈	—	2	16	no	—
477	C₂²⋊Q₈	—	2	8	no	—
478	C₂²⋊Q₈	—	2	16	no	—
479	C₂²⋊Q₈	—	2	8	no	—
480	C₂²⋊Q₈	—	2	8	no	—
481	#121	Q₈×C₈₉	1	8	yes	complemented
482	C₄×Q₈	—	2	8	no	—
483	C₄×D₄	—	2	16	no	—
484	C₄×D₄	—	2	8	no	—
485	C₄×D₄	—	2	4	no	—
486	C₄×D₄	—	4	4	no	—
487	C₂×C₄⋊C₄	—	2	8	no	—
488	C₂×C₄⋊C₄	—	2	4	no	—
489	C₂×C₄⋊C₄	D₄×C₈₉	1	8	yes	complemented
490	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
491	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
496	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
499	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
500	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
501	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
502	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
506	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
512	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
521	C₂×C₄²	—	2	4	no	—
522	C₂×C₄²	—	4	4	no	—
523	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
524	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
525	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
526	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
527	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
528	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
531	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
532	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
533	#95	C₂³×C₈₉	1	2	yes	—
534	#95	C₂³×C₈₉	1	2	yes	—
535	#95	C₂³×C₈₉	1	2	yes	—
536	#95	C₂³×C₈₉	1	2	yes	—
537	#95	C₂³×C₈₉	1	4	yes	—
538	#95	C₂³×C₈₉	1	2	yes	—
539	#95	C₂³×C₈₉	1	2	yes	—
540	#95	C₂³×C₈₉	1	4	yes	—
541	#95	C₂³×C₈₉	1	2	yes	—
542	#95	C₂³×C₈₉	1	4	yes	—
543	#95	C₂³×C₈₉	1	4	yes	—
544	#95	C₂³×C₈₉	1	4	yes	—
545	#95	C₂³×C₈₉	1	4	yes	—
546	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
547	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
548	C₂×Q₈	—	2	4	no	—
549	C₂×Q₈	—	2	8	no	—
550	C₂×Q₈	—	2	4	no	—
551	C₂×Q₈	—	2	4	no	—
552	C₂×Q₈	—	4	4	no	—
553	C₂×Q₈	—	4	4	no	—
554	C₂×D₄	—	2	4	no	—
555	C₂×D₄	—	2	4	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	C₂×Q₈×C₈₉	1	8	yes	—
559	C₂×D₄	C₂×Q₈×C₈₉	1	4	yes	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	4	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	8	no	—
572	C₂²×C₄	—	4	2	no	—
573	C₂²×C₄	—	4	2	no	—
574	C₂²×C₄	—	4	1	no	—
575	C₂²×C₄	—	4	2	no	—
576	C₂²×C₄	—	4	4	no	—
577	C₂²×C₄	—	4	4	no	—
578	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
579	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
580	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
581	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
584	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
587	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
590	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
591	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
593	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
596	C₄⋊C₄	—	2	8	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	8	no	—
600	C₄⋊C₄	—	2	8	no	—
601	C₄⋊C₄	—	2	8	no	—
602	C₄⋊C₄	—	2	8	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	2	no	—
606	C₄⋊C₄	—	2	8	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	4	4	no	—
612	C₄⋊C₄	—	4	2	no	—
613	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
614	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
615	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
616	C₄⋊C₄	C₂×Q₈×C₈₉	1	4	yes	—
617	C₄⋊C₄	#41×C₈₉	1	4	yes	—
618	C₂²⋊C₄	—	2	8	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	8	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	8	no	—
624	C₂²⋊C₄	—	4	4	no	—
625	C₂²⋊C₄	—	4	2	no	—
626	C₂²⋊C₄	C₂×Q₈×C₈₉	1	8	yes	—
627	C₄²	—	2	8	no	—
628	C₄²	—	2	4	no	—
629	C₄²	—	2	2	no	—
630	C₄²	—	2	2	no	—
631	C₄²	—	2	2	no	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	4	no	—
634	C₄²	—	4	2	no	—
635	C₄²	—	4	2	no	—
636	C₄²	#41×C₈₉	1	4	yes	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	2	no	—
647	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
648	C₂³	C₂²×Q₈×C₈₉	1	4	yes	—
649	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
650	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
651	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
652	Q₈	—	4	8	no	—
653	Q₈	—	8	8	no	—
654	D₄	—	2	16	no	—
655	D₄	—	2	8	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	8	no	—
671	C₂×C₄	—	2	8	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	4	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	4	8	no	—
691	C₂×C₄	—	4	4	no	—
692	C₂×C₄	—	4	8	no	—
693	C₂×C₄	—	4	8	no	—
694	C₂×C₄	—	8	8	no	—
695	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
696	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
697	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
698	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
699	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
700	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
701	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
702	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
703	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
704	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
705	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
706	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
707	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
708	C₂²	—	2	2	no	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	4	no	—
715	C₂²	—	2	4	no	—
716	C₂²	—	2	4	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	D₄×Q₈×C₈₉	1	4	yes	—
722	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
723	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
724	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
725	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
726	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
727	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
728	C₂²	#585×C₈₉	1	1	yes	characteristic
729	C₄	—	2	2	no	—
730	C₄	—	2	4	no	—
731	C₄	—	2	2	no	—
732	C₄	—	2	2	no	—
733	C₄	—	2	4	no	—
734	C₄	—	2	4	no	—
735	C₄	—	2	4	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	4	no	—
738	C₄	—	4	1	no	—
739	C₄	—	4	4	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₄	#532×C₈₉	1	4	yes	—
743	C₄	#554×C₈₉	1	4	yes	complemented
744	C₂	—	2	4	no	—
745	C₂	—	4	4	no	—
746	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
747	C₂	C₂×D₄×Q₈×C₈₉	1	1	yes	characteristic
748	C₂	C₂×#554×C₈₉	1	1	yes	characteristic
749	C₂	Q₈×#41×C₈₉	1	1	yes	characteristic
750	C₂	C₈₉×#3495	1	1	yes	characteristic
751	C₂	C₈₉×#3496	1	1	yes	characteristic
752	C₂	C₈₉×#3520	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
1. C₂×#554×C₈₉	C₂	semidirect
2. C₈₉×#2857	C₂	semidirect
3. C₈₉×#2857	C₂	semidirect
4. C₈₉×#2564	C₂	semidirect
5. C₈₉×#2556	C₂	semidirect
6. C₈₉×#2551	C₂	semidirect
7. C₈₉×#2542	C₂	semidirect
8. C₈₉×#2506	C₂	semidirect
9. C₈₉×#2492	C₂	semidirect
10. C₈₉×#2452	C₂	semidirect
11. C₈₉×#2417	C₂	semidirect
12. C₈₉×#2365	C₂	semidirect
13. C₈₉×#2360	C₂	semidirect
14. D₄×C₄⋊C₄×C₈₉	C₂	semidirect
17. C₂×C₄×C₄⋊C₄×C₈₉	C₂	semidirect
104. #121×C₈₉	Q₈	semidirect
112. C₂×C₄⋊C₄×C₈₉	D₄	semidirect
366. C₄×C₈₉	#554	semidirect
367. #36561	C₈₉	direct (N × H)
377. C₂×#554	C₂×C₈₉	semidirect
378. #2857	C₂×C₈₉	semidirect
379. #2857	C₂×C₈₉	semidirect
380. #2564	C₂×C₈₉	semidirect
381. #2556	C₂×C₈₉	semidirect
382. #2551	C₂×C₈₉	semidirect
383. #2542	C₂×C₈₉	semidirect
384. #2506	C₂×C₈₉	semidirect
385. #2492	C₂×C₈₉	semidirect
386. #2452	C₂×C₈₉	semidirect
387. #2417	C₂×C₈₉	semidirect
388. #2365	C₂×C₈₉	semidirect
389. #2360	C₂×C₈₉	semidirect
390. D₄×C₄⋊C₄	C₂×C₈₉	semidirect
393. C₂×C₄×C₄⋊C₄	C₂×C₈₉	semidirect
394. C₈₉	#36561	direct (N × H)
481. #121	Q₈×C₈₉	semidirect
489. C₂×C₄⋊C₄	D₄×C₈₉	semidirect
743. C₄	#554×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#554×C₈₉	2
C₈₉×#2857	2
C₈₉×#2564	2
C₈₉×#2556	2
C₈₉×#2551	2
C₈₉×#2542	2
C₈₉×#2506	2
C₈₉×#2492	2
C₈₉×#2452	2
C₈₉×#2417	2
C₈₉×#2365	2
C₈₉×#2360	2
D₄×C₄⋊C₄×C₈₉	2
C₄×#121×C₈₉	2
C₂×C₄×C₄⋊C₄×C₈₉	2
#36561	89

Subgroups — C89×#36561 #36414409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#36561 #36414409