Subgroups — C₈₉×#35302 #36413150

Order 22784.

2534 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#117×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2854	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2848	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2847	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#2629	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2620	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2609	C₂	1	4	yes	maximal, complemented
10	C₈₉×#2601	C₂	1	4	yes	maximal, complemented
11	C₈₉×#2579	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2534	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2413	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2411	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2324	C₂	1	2	yes	maximal, complemented
16	C₈₉×#2323	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2285	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
19	#529×C₈₉	—	2	8	no	—
20	C₂×#126×C₈₉	C₂²	1	2	yes	complemented
21	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×#123×C₈₉	C₂²	1	2	yes	—
24	C₂×#123×C₈₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#121×C₈₉	C₂²	1	2	yes	—
28	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#120×C₈₉	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
33	C₂×#117×C₈₉	—	2	8	no	—
34	C₂×#117×C₈₉	C₂²	1	2	yes	—
35	C₂×#117×C₈₉	C₂²	1	2	yes	—
36	C₂×#117×C₈₉	C₂²	1	2	yes	—
37	C₂×#117×C₈₉	C₂²	1	2	yes	—
38	C₂×#117×C₈₉	C₂²	1	2	yes	—
39	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
40	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
41	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
42	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
43	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
45	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
46	#398×C₈₉	C₂²	1	4	yes	complemented
47	#398×C₈₉	C₂²	1	4	yes	complemented
48	#396×C₈₉	C₂²	1	4	yes	—
49	#396×C₈₉	C₂²	1	4	yes	—
50	#396×C₈₉	C₂²	1	4	yes	complemented
51	#396×C₈₉	C₂²	1	4	yes	complemented
52	#394×C₈₉	C₂²	1	4	yes	—
53	#394×C₈₉	C₂²	1	4	yes	—
54	#391×C₈₉	C₂²	1	2	yes	complemented
55	#390×C₈₉	C₂²	1	4	yes	—
56	#390×C₈₉	C₂²	1	2	yes	complemented
57	#389×C₈₉	C₂²	1	2	yes	complemented
58	#389×C₈₉	C₂²	1	4	yes	complemented
59	#389×C₈₉	C₂²	1	2	yes	complemented
60	#388×C₈₉	C₂²	1	4	yes	—
61	#388×C₈₉	C₂²	1	4	yes	—
62	#388×C₈₉	C₂²	1	4	yes	complemented
63	#388×C₈₉	C₂²	1	4	yes	complemented
64	#387×C₈₉	C₂²	1	4	yes	complemented
65	#387×C₈₉	C₂²	1	4	yes	complemented
66	#386×C₈₉	C₂²	1	2	yes	—
67	#386×C₈₉	C₂²	1	2	yes	—
68	#386×C₈₉	C₂²	1	4	yes	—
69	#386×C₈₉	C₂²	1	4	yes	—
70	#385×C₈₉	C₂²	1	2	yes	—
71	#385×C₈₉	C₂²	1	2	yes	—
72	#385×C₈₉	C₂²	1	4	yes	—
73	#385×C₈₉	C₂²	1	4	yes	complemented
74	#384×C₈₉	C₂²	1	2	yes	complemented
75	#382×C₈₉	C₂²	1	2	yes	complemented
76	#381×C₈₉	C₂²	1	2	yes	—
77	#380×C₈₉	C₂²	1	2	yes	—
78	#380×C₈₉	C₂²	1	2	yes	—
79	#380×C₈₉	C₂²	1	2	yes	—
80	#380×C₈₉	C₂²	1	1	yes	characteristic
81	#380×C₈₉	C₂²	1	1	yes	characteristic
82	#379×C₈₉	C₂²	1	2	yes	—
83	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
84	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
85	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
90	C₂³×C₄×C₈₉	—	2	4	no	—
91	C₂³×C₄×C₈₉	—	2	8	no	—
92	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
95	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
98	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
100	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
101	#126×C₈₉	—	2	8	no	—
102	#125×C₈₉	—	2	4	no	—
103	#124×C₈₉	—	2	4	no	—
104	#123×C₈₉	—	2	8	no	—
105	#123×C₈₉	—	4	4	no	—
106	C₂²⋊Q₈×C₈₉	—	2	4	no	—
107	C₂²⋊Q₈×C₈₉	—	2	8	no	—
108	#121×C₈₉	—	2	4	no	—
109	#121×C₈₉	—	2	8	no	—
110	#120×C₈₉	—	4	4	no	—
111	C₄×Q₈×C₈₉	—	2	4	no	—
112	C₄×D₄×C₈₉	—	2	8	no	—
113	C₄×D₄×C₈₉	—	2	4	no	—
114	#117×C₈₉	—	2	8	no	—
115	#117×C₈₉	—	2	8	no	—
116	#117×C₈₉	—	2	8	no	—
117	#117×C₈₉	—	2	8	no	—
118	#117×C₈₉	—	2	8	no	—
119	#117×C₈₉	—	4	4	no	—
120	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
121	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
122	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
130	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
135	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
136	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
138	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
140	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
141	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
155	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
156	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
157	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
158	C₂×C₄²×C₈₉	—	2	4	no	—
159	C₂×C₄²×C₈₉	D₄	1	8	yes	complemented
160	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
163	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
164	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
168	#95×C₈₉	C₂³	1	2	yes	—
169	#95×C₈₉	C₂³	1	4	yes	—
170	#95×C₈₉	C₂³	1	2	yes	—
171	#95×C₈₉	C₂³	1	4	yes	—
172	#95×C₈₉	C₂³	1	4	yes	—
173	#95×C₈₉	C₂³	1	4	yes	—
174	#95×C₈₉	C₂³	1	4	yes	—
175	#95×C₈₉	C₂³	1	4	yes	—
176	#95×C₈₉	C₂³	1	4	yes	—
177	C₂⁴×C₈₉	—	2	2	no	—
178	C₂⁴×C₈₉	—	2	4	no	—
179	C₂⁴×C₈₉	—	2	2	no	—
180	C₂⁴×C₈₉	—	2	2	no	—
181	C₂⁴×C₈₉	—	4	2	no	—
182	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
183	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
184	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
185	C₂×Q₈×C₈₉	—	2	2	no	—
186	C₂×Q₈×C₈₉	—	2	4	no	—
187	C₂×D₄×C₈₉	—	2	4	no	—
188	C₂×D₄×C₈₉	—	2	4	no	—
189	C₂×D₄×C₈₉	—	2	4	no	—
190	C₂×D₄×C₈₉	—	2	8	no	—
191	C₂×D₄×C₈₉	—	2	2	no	—
192	C₂×D₄×C₈₉	—	2	4	no	—
193	C₂×D₄×C₈₉	—	4	4	no	—
194	C₂×D₄×C₈₉	—	4	4	no	—
195	C₂²×C₄×C₈₉	—	2	32	no	—
196	C₂²×C₄×C₈₉	—	2	2	no	—
197	C₂²×C₄×C₈₉	—	2	4	no	—
198	C₂²×C₄×C₈₉	—	2	2	no	—
199	C₂²×C₄×C₈₉	—	2	2	no	—
200	C₂²×C₄×C₈₉	—	2	4	no	—
201	C₂²×C₄×C₈₉	—	2	4	no	—
202	C₂²×C₄×C₈₉	—	2	4	no	—
203	C₂²×C₄×C₈₉	—	2	4	no	—
204	C₂²×C₄×C₈₉	—	2	4	no	—
205	C₂²×C₄×C₈₉	—	2	4	no	—
206	C₂²×C₄×C₈₉	—	2	2	no	—
207	C₂²×C₄×C₈₉	—	2	2	no	—
208	C₂²×C₄×C₈₉	—	2	2	no	—
209	C₂²×C₄×C₈₉	—	2	2	no	—
210	C₂²×C₄×C₈₉	—	2	4	no	—
211	C₂²×C₄×C₈₉	—	4	2	no	—
212	C₂²×C₄×C₈₉	—	4	4	no	—
213	C₂²×C₄×C₈₉	—	4	2	no	—
214	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
215	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
216	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
217	C₂²×C₄×C₈₉	#41	1	8	yes	—
218	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₈₉	C₂⁴	1	4	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	1	yes	characteristic
232	C₄⋊C₄×C₈₉	—	2	4	no	—
233	C₄⋊C₄×C₈₉	—	2	4	no	—
234	C₄⋊C₄×C₈₉	—	2	4	no	—
235	C₄⋊C₄×C₈₉	—	2	4	no	—
236	C₄⋊C₄×C₈₉	—	2	4	no	—
237	C₄⋊C₄×C₈₉	—	2	4	no	—
238	C₄⋊C₄×C₈₉	—	2	2	no	—
239	C₄⋊C₄×C₈₉	—	2	4	no	—
240	C₄⋊C₄×C₈₉	—	2	2	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	8	no	—
245	C₄⋊C₄×C₈₉	—	4	4	no	—
246	C₄⋊C₄×C₈₉	—	4	4	no	—
247	C₄⋊C₄×C₈₉	—	4	4	no	—
248	C₄⋊C₄×C₈₉	—	4	4	no	—
249	C₂²⋊C₄×C₈₉	—	2	4	no	—
250	C₂²⋊C₄×C₈₉	—	2	8	no	—
251	C₂²⋊C₄×C₈₉	—	2	4	no	—
252	C₂²⋊C₄×C₈₉	—	2	4	no	—
253	C₂²⋊C₄×C₈₉	—	2	4	no	—
254	C₂²⋊C₄×C₈₉	—	2	4	no	—
255	C₂²⋊C₄×C₈₉	—	2	4	no	—
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	8	no	—
262	C₂²⋊C₄×C₈₉	—	4	4	no	—
263	C₂²⋊C₄×C₈₉	—	4	4	no	—
264	C₂²⋊C₄×C₈₉	—	4	4	no	—
265	C₂²⋊C₄×C₈₉	—	4	4	no	—
266	C₄²×C₈₉	—	2	4	no	—
267	C₄²×C₈₉	—	2	4	no	—
268	C₄²×C₈₉	—	2	4	no	—
269	C₄²×C₈₉	—	4	4	no	—
270	C₄²×C₈₉	C₂×D₄	1	4	yes	—
271	C₄²×C₈₉	C₂×D₄	1	4	yes	—
272	C₄²×C₈₉	C₂×D₄	1	4	yes	—
273	C₄²×C₈₉	C₂×D₄	1	4	yes	—
274	C₂³×C₈₉	—	2	2	no	—
275	C₂³×C₈₉	—	2	2	no	—
276	C₂³×C₈₉	—	2	8	no	—
277	C₂³×C₈₉	—	2	2	no	—
278	C₂³×C₈₉	—	2	2	no	—
279	C₂³×C₈₉	—	2	2	no	—
280	C₂³×C₈₉	—	2	2	no	—
281	C₂³×C₈₉	—	2	2	no	—
282	C₂³×C₈₉	—	2	2	no	—
283	C₂³×C₈₉	—	2	2	no	—
284	C₂³×C₈₉	—	2	4	no	—
285	C₂³×C₈₉	—	2	2	no	—
286	C₂³×C₈₉	—	2	2	no	—
287	C₂³×C₈₉	—	2	4	no	—
288	C₂³×C₈₉	—	4	8	no	—
289	C₂³×C₈₉	—	4	8	no	—
290	C₂³×C₈₉	—	4	4	no	—
291	C₂³×C₈₉	—	4	4	no	—
292	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
293	C₂³×C₈₉	C₂×#41	1	4	yes	—
294	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
295	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
296	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
297	Q₈×C₈₉	—	4	4	no	—
298	D₄×C₈₉	—	4	8	no	—
299	D₄×C₈₉	—	4	4	no	—
300	D₄×C₈₉	—	8	8	no	—
301	C₂×C₄×C₈₉	—	2	16	no	—
302	C₂×C₄×C₈₉	—	2	8	no	—
303	C₂×C₄×C₈₉	—	2	8	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	1	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	2	no	—
312	C₂×C₄×C₈₉	—	2	2	no	—
313	C₂×C₄×C₈₉	—	2	8	no	—
314	C₂×C₄×C₈₉	—	2	16	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	4	no	—
321	C₂×C₄×C₈₉	—	2	4	no	—
322	C₂×C₄×C₈₉	—	2	4	no	—
323	C₂×C₄×C₈₉	—	2	4	no	—
324	C₂×C₄×C₈₉	—	2	4	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	2	no	—
333	C₂×C₄×C₈₉	—	2	4	no	—
334	C₂×C₄×C₈₉	—	4	4	no	—
335	C₂×C₄×C₈₉	—	4	8	no	—
336	C₂×C₄×C₈₉	—	4	4	no	—
337	C₂×C₄×C₈₉	—	4	4	no	—
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	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
345	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
346	C₂²×C₈₉	—	2	2	no	—
347	C₂²×C₈₉	—	2	2	no	—
348	C₂²×C₈₉	—	2	4	no	—
349	C₂²×C₈₉	—	2	4	no	—
350	C₂²×C₈₉	—	2	4	no	—
351	C₂²×C₈₉	—	2	4	no	—
352	C₂²×C₈₉	—	2	4	no	—
353	C₂²×C₈₉	—	4	16	no	—
354	C₂²×C₈₉	—	4	2	no	—
355	C₂²×C₈₉	—	4	2	no	—
356	C₂²×C₈₉	—	4	2	no	—
357	C₂²×C₈₉	—	4	2	no	—
358	C₂²×C₈₉	—	4	2	no	—
359	C₂²×C₈₉	—	4	2	no	—
360	C₂²×C₈₉	—	4	2	no	—
361	C₂²×C₈₉	—	4	4	no	—
362	C₂²×C₈₉	—	4	4	no	—
363	C₂²×C₈₉	#537	1	4	yes	—
364	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
365	C₂²×C₈₉	C₂²×#41	1	2	yes	—
366	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
367	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
368	C₂²×C₈₉	#585	1	2	yes	—
369	C₄×C₈₉	—	2	2	no	—
370	C₄×C₈₉	—	2	4	no	—
371	C₄×C₈₉	—	2	2	no	—
372	C₄×C₈₉	—	2	2	no	—
373	C₄×C₈₉	—	2	2	no	—
374	C₄×C₈₉	—	2	2	no	—
375	C₄×C₈₉	—	4	2	no	—
376	C₄×C₈₉	—	4	2	no	—
377	C₄×C₈₉	—	4	2	no	—
378	C₄×C₈₉	—	4	2	no	—
379	C₄×C₈₉	—	4	2	no	—
380	C₄×C₈₉	—	4	4	no	—
381	C₄×C₈₉	—	4	4	no	—
382	C₄×C₈₉	#525	1	4	yes	—
383	#35302	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
384	C₂×C₈₉	—	2	4	no	—
385	C₂×C₈₉	—	4	4	no	—
386	C₂×C₈₉	—	8	2	no	—
387	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
388	C₂×C₈₉	C₂×#537	1	1	yes	characteristic
389	C₂×C₈₉	#3449	1	1	yes	characteristic
390	C₂×C₈₉	#3494	1	2	yes	—
391	C₂×C₈₉	#3495	1	2	yes	—
392	C₂×#529	C₂×C₈₉	1	1	yes	characteristic, complemented
393	C₂²×#117	C₂×C₈₉	1	1	yes	characteristic, complemented
394	#2855	C₂×C₈₉	1	1	yes	characteristic, complemented
395	#2854	C₂×C₈₉	1	1	yes	characteristic, complemented
396	#2848	C₂×C₈₉	1	1	yes	characteristic, complemented
397	#2847	C₂×C₈₉	1	1	yes	characteristic
398	#2629	C₂×C₈₉	1	2	yes	complemented
399	#2620	C₂×C₈₉	1	2	yes	complemented
400	#2609	C₂×C₈₉	1	4	yes	complemented
401	#2601	C₂×C₈₉	1	4	yes	complemented
402	#2579	C₂×C₈₉	1	2	yes	complemented
403	#2534	C₂×C₈₉	1	2	yes	complemented
404	#2413	C₂×C₈₉	1	2	yes	complemented
405	#2411	C₂×C₈₉	1	2	yes	complemented
406	#2324	C₂×C₈₉	1	2	yes	complemented
407	#2323	C₂×C₈₉	1	2	yes	complemented
408	#2285	C₂×C₈₉	1	1	yes	characteristic, complemented
409	C₈₉	#35302	1	1	yes	characteristic, direct product factor, Sylow
410	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
411	#529	—	2	8	no	—
412	C₂×#126	C₂²×C₈₉	1	2	yes	complemented
413	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic, complemented
414	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic, complemented
415	C₂×#123	C₂²×C₈₉	1	2	yes	—
416	C₂×#123	C₂²×C₈₉	1	2	yes	—
417	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
418	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
419	C₂×#121	C₂²×C₈₉	1	2	yes	—
420	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
421	C₂×#120	C₂²×C₈₉	1	2	yes	—
422	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
423	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
424	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
425	C₂×#117	—	2	8	no	—
426	C₂×#117	C₂²×C₈₉	1	2	yes	—
427	C₂×#117	C₂²×C₈₉	1	2	yes	—
428	C₂×#117	C₂²×C₈₉	1	2	yes	—
429	C₂×#117	C₂²×C₈₉	1	2	yes	—
430	C₂×#117	C₂²×C₈₉	1	2	yes	—
431	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
432	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
433	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
434	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
435	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
436	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
437	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
438	#398	C₂²×C₈₉	1	4	yes	complemented
439	#398	C₂²×C₈₉	1	4	yes	complemented
440	#396	C₂²×C₈₉	1	4	yes	—
441	#396	C₂²×C₈₉	1	4	yes	—
442	#396	C₂²×C₈₉	1	4	yes	complemented
443	#396	C₂²×C₈₉	1	4	yes	complemented
444	#394	C₂²×C₈₉	1	4	yes	—
445	#394	C₂²×C₈₉	1	4	yes	—
446	#391	C₂²×C₈₉	1	2	yes	complemented
447	#390	C₂²×C₈₉	1	4	yes	—
448	#390	C₂²×C₈₉	1	2	yes	complemented
449	#389	C₂²×C₈₉	1	2	yes	complemented
450	#389	C₂²×C₈₉	1	4	yes	complemented
451	#389	C₂²×C₈₉	1	2	yes	complemented
452	#388	C₂²×C₈₉	1	4	yes	—
453	#388	C₂²×C₈₉	1	4	yes	—
454	#388	C₂²×C₈₉	1	4	yes	complemented
455	#388	C₂²×C₈₉	1	4	yes	complemented
456	#387	C₂²×C₈₉	1	4	yes	complemented
457	#387	C₂²×C₈₉	1	4	yes	complemented
458	#386	C₂²×C₈₉	1	2	yes	—
459	#386	C₂²×C₈₉	1	2	yes	—
460	#386	C₂²×C₈₉	1	4	yes	—
461	#386	C₂²×C₈₉	1	4	yes	—
462	#385	C₂²×C₈₉	1	2	yes	—
463	#385	C₂²×C₈₉	1	2	yes	—
464	#385	C₂²×C₈₉	1	4	yes	—
465	#385	C₂²×C₈₉	1	4	yes	complemented
466	#384	C₂²×C₈₉	1	2	yes	complemented
467	#382	C₂²×C₈₉	1	2	yes	complemented
468	#381	C₂²×C₈₉	1	2	yes	—
469	#380	C₂²×C₈₉	1	2	yes	—
470	#380	C₂²×C₈₉	1	2	yes	—
471	#380	C₂²×C₈₉	1	2	yes	—
472	#380	C₂²×C₈₉	1	1	yes	characteristic
473	#380	C₂²×C₈₉	1	1	yes	characteristic
474	#379	C₂²×C₈₉	1	2	yes	—
475	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
476	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
477	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
478	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
479	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
480	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
481	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
482	C₂³×C₄	—	2	4	no	—
483	C₂³×C₄	—	2	8	no	—
484	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
487	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
488	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
490	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
492	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
493	#126	—	2	8	no	—
494	#125	—	2	4	no	—
495	#124	—	2	4	no	—
496	#123	—	2	8	no	—
497	#123	—	4	4	no	—
498	C₂²⋊Q₈	—	2	4	no	—
499	C₂²⋊Q₈	—	2	8	no	—
500	#121	—	2	4	no	—
501	#121	—	2	8	no	—
502	#120	—	4	4	no	—
503	C₄×Q₈	—	2	4	no	—
504	C₄×D₄	—	2	8	no	—
505	C₄×D₄	—	2	4	no	—
506	#117	—	2	8	no	—
507	#117	—	2	8	no	—
508	#117	—	2	8	no	—
509	#117	—	2	8	no	—
510	#117	—	2	8	no	—
511	#117	—	4	4	no	—
512	C₂×C₄⋊C₄	—	2	4	no	—
513	C₂×C₄⋊C₄	—	2	4	no	—
514	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	4	yes	—
527	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
528	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
529	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
530	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
531	C₂×C₂²⋊C₄	—	2	4	no	—
532	C₂×C₂²⋊C₄	—	2	4	no	—
533	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
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	4	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	4	yes	—
550	C₂×C₄²	—	2	4	no	—
551	C₂×C₄²	D₄×C₈₉	1	8	yes	complemented
552	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
553	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
554	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
555	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
556	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
557	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
558	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
559	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
560	#95	C₂³×C₈₉	1	2	yes	—
561	#95	C₂³×C₈₉	1	4	yes	—
562	#95	C₂³×C₈₉	1	2	yes	—
563	#95	C₂³×C₈₉	1	4	yes	—
564	#95	C₂³×C₈₉	1	4	yes	—
565	#95	C₂³×C₈₉	1	4	yes	—
566	#95	C₂³×C₈₉	1	4	yes	—
567	#95	C₂³×C₈₉	1	4	yes	—
568	#95	C₂³×C₈₉	1	4	yes	—
569	C₂⁴	—	2	2	no	—
570	C₂⁴	—	2	4	no	—
571	C₂⁴	—	2	2	no	—
572	C₂⁴	—	2	2	no	—
573	C₂⁴	—	4	2	no	—
574	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
575	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
576	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
577	C₂×Q₈	—	2	2	no	—
578	C₂×Q₈	—	2	4	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	8	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	4	4	no	—
586	C₂×D₄	—	4	4	no	—
587	C₂²×C₄	—	2	32	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	—	2	4	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	4	2	no	—
604	C₂²×C₄	—	4	4	no	—
605	C₂²×C₄	—	4	2	no	—
606	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
607	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
608	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
609	C₂²×C₄	#41×C₈₉	1	8	yes	—
610	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
611	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
614	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
621	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	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	2	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	8	no	—
637	C₄⋊C₄	—	4	4	no	—
638	C₄⋊C₄	—	4	4	no	—
639	C₄⋊C₄	—	4	4	no	—
640	C₄⋊C₄	—	4	4	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	8	no	—
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	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	8	no	—
654	C₂²⋊C₄	—	4	4	no	—
655	C₂²⋊C₄	—	4	4	no	—
656	C₂²⋊C₄	—	4	4	no	—
657	C₂²⋊C₄	—	4	4	no	—
658	C₄²	—	2	4	no	—
659	C₄²	—	2	4	no	—
660	C₄²	—	2	4	no	—
661	C₄²	—	4	4	no	—
662	C₄²	C₂×D₄×C₈₉	1	4	yes	—
663	C₄²	C₂×D₄×C₈₉	1	4	yes	—
664	C₄²	C₂×D₄×C₈₉	1	4	yes	—
665	C₄²	C₂×D₄×C₈₉	1	4	yes	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	8	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	4	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	4	no	—
680	C₂³	—	4	8	no	—
681	C₂³	—	4	8	no	—
682	C₂³	—	4	4	no	—
683	C₂³	—	4	4	no	—
684	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
685	C₂³	C₂×#41×C₈₉	1	4	yes	—
686	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
687	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
688	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
689	Q₈	—	4	4	no	—
690	D₄	—	4	8	no	—
691	D₄	—	4	4	no	—
692	D₄	—	8	8	no	—
693	C₂×C₄	—	2	16	no	—
694	C₂×C₄	—	2	8	no	—
695	C₂×C₄	—	2	8	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	8	no	—
706	C₂×C₄	—	2	16	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	4	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	4	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	4	no	—
726	C₂×C₄	—	4	4	no	—
727	C₂×C₄	—	4	8	no	—
728	C₂×C₄	—	4	4	no	—
729	C₂×C₄	—	4	4	no	—
730	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
731	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
732	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
733	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
734	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
735	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
736	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
737	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	4	no	—
741	C₂²	—	2	4	no	—
742	C₂²	—	2	4	no	—
743	C₂²	—	2	4	no	—
744	C₂²	—	2	4	no	—
745	C₂²	—	4	16	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	4	no	—
754	C₂²	—	4	4	no	—
755	C₂²	#537×C₈₉	1	4	yes	—
756	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
757	C₂²	C₂²×#41×C₈₉	1	2	yes	—
758	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
759	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
760	C₂²	#585×C₈₉	1	2	yes	—
761	C₄	—	2	2	no	—
762	C₄	—	2	4	no	—
763	C₄	—	2	2	no	—
764	C₄	—	2	2	no	—
765	C₄	—	2	2	no	—
766	C₄	—	2	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	4	no	—
773	C₄	—	4	4	no	—
774	C₄	#525×C₈₉	1	4	yes	—
775	C₂	—	2	4	no	—
776	C₂	—	4	4	no	—
777	C₂	—	8	2	no	—
778	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
779	C₂	C₂×#537×C₈₉	1	1	yes	characteristic
780	C₂	C₈₉×#3449	1	1	yes	characteristic
781	C₂	C₈₉×#3494	1	2	yes	—
782	C₂	C₈₉×#3495	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₈₉×#2847	C₂
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×#529×C₈₉	C₂	semidirect
2. C₂²×#117×C₈₉	C₂	semidirect
3. C₈₉×#2855	C₂	semidirect
4. C₈₉×#2854	C₂	semidirect
5. C₈₉×#2848	C₂	semidirect
7. C₈₉×#2629	C₂	semidirect
8. C₈₉×#2620	C₂	semidirect
9. C₈₉×#2609	C₂	semidirect
10. C₈₉×#2601	C₂	semidirect
11. C₈₉×#2579	C₂	semidirect
12. C₈₉×#2534	C₂	semidirect
13. C₈₉×#2413	C₂	semidirect
14. C₈₉×#2411	C₂	semidirect
15. C₈₉×#2324	C₂	semidirect
16. C₈₉×#2323	C₂	semidirect
17. C₈₉×#2285	C₂	semidirect
20. C₂×#126×C₈₉	C₂²	semidirect
21. C₂×#125×C₈₉	C₂²	semidirect
22. C₂×#124×C₈₉	C₂²	semidirect
30. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
32. C₂×C₄×D₄×C₈₉	C₂²	semidirect
39. C₂×#117×C₈₉	C₂²	semidirect
46. #398×C₈₉	C₂²	semidirect
47. #398×C₈₉	C₂²	semidirect
50. #396×C₈₉	C₂²	semidirect
51. #396×C₈₉	C₂²	semidirect
54. #391×C₈₉	C₂²	semidirect
56. #390×C₈₉	C₂²	semidirect
57. #389×C₈₉	C₂²	semidirect
58. #389×C₈₉	C₂²	semidirect
59. #389×C₈₉	C₂²	semidirect
62. #388×C₈₉	C₂²	semidirect
63. #388×C₈₉	C₂²	semidirect
64. #387×C₈₉	C₂²	semidirect
65. #387×C₈₉	C₂²	semidirect
73. #385×C₈₉	C₂²	semidirect
74. #384×C₈₉	C₂²	semidirect
75. #382×C₈₉	C₂²	semidirect
83. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
84. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
159. C₂×C₄²×C₈₉	D₄	semidirect
383. #35302	C₈₉	direct (N × H)
392. C₂×#529	C₂×C₈₉	semidirect
393. C₂²×#117	C₂×C₈₉	semidirect
394. #2855	C₂×C₈₉	semidirect
395. #2854	C₂×C₈₉	semidirect
396. #2848	C₂×C₈₉	semidirect
398. #2629	C₂×C₈₉	semidirect
399. #2620	C₂×C₈₉	semidirect
400. #2609	C₂×C₈₉	semidirect
401. #2601	C₂×C₈₉	semidirect
402. #2579	C₂×C₈₉	semidirect
403. #2534	C₂×C₈₉	semidirect
404. #2413	C₂×C₈₉	semidirect
405. #2411	C₂×C₈₉	semidirect
406. #2324	C₂×C₈₉	semidirect
407. #2323	C₂×C₈₉	semidirect
408. #2285	C₂×C₈₉	semidirect
409. C₈₉	#35302	direct (N × H)
412. C₂×#126	C₂²×C₈₉	semidirect
413. C₂×#125	C₂²×C₈₉	semidirect
414. C₂×#124	C₂²×C₈₉	semidirect
422. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
424. C₂×C₄×D₄	C₂²×C₈₉	semidirect
431. C₂×#117	C₂²×C₈₉	semidirect
438. #398	C₂²×C₈₉	semidirect
439. #398	C₂²×C₈₉	semidirect
442. #396	C₂²×C₈₉	semidirect
443. #396	C₂²×C₈₉	semidirect
446. #391	C₂²×C₈₉	semidirect
448. #390	C₂²×C₈₉	semidirect
449. #389	C₂²×C₈₉	semidirect
450. #389	C₂²×C₈₉	semidirect
451. #389	C₂²×C₈₉	semidirect
454. #388	C₂²×C₈₉	semidirect
455. #388	C₂²×C₈₉	semidirect
456. #387	C₂²×C₈₉	semidirect
457. #387	C₂²×C₈₉	semidirect
465. #385	C₂²×C₈₉	semidirect
466. #384	C₂²×C₈₉	semidirect
467. #382	C₂²×C₈₉	semidirect
475. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
476. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
551. C₂×C₄²	D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#529×C₈₉	2
C₂²×#117×C₈₉	2
C₈₉×#2855	2
C₈₉×#2854	2
C₈₉×#2848	2
C₈₉×#2847	2
C₈₉×#2629	2
C₈₉×#2620	2
C₈₉×#2609	2
C₈₉×#2601	2
C₈₉×#2579	2
C₈₉×#2534	2
C₈₉×#2413	2
C₈₉×#2411	2
C₈₉×#2324	2
C₈₉×#2323	2
C₈₉×#2285	2
#35302	89

Subgroups — C89×#35302 #36413150

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35302 #36413150