Subgroups — C₈₉×#35253 #36413101

Order 22784.

2470 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#544×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#117×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2857	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2851	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2629	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2628	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2442	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2441	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2440	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2439	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2438	C₂	1	4	yes	maximal, complemented
12	C₈₉×#2437	C₂	1	4	yes	maximal
13	C₈₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2316	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2280	C₂	1	1	yes	maximal, characteristic
17	C₂×#380×C₈₉	C₂	1	1	yes	maximal, characteristic
18	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
19	#544×C₈₉	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
21	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
22	C₂×#125×C₈₉	C₂²	1	2	yes	complemented
23	C₂×#125×C₈₉	C₂²	1	2	yes	complemented
24	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
25	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
26	C₂×#117×C₈₉	—	2	8	no	—
27	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#117×C₈₉	C₂²	1	2	yes	—
31	C₂×#117×C₈₉	C₂²	1	2	yes	—
32	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
40	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
41	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
42	#400×C₈₉	C₂²	1	4	yes	complemented
43	#399×C₈₉	C₂²	1	4	yes	—
44	#398×C₈₉	C₂²	1	4	yes	complemented
45	#398×C₈₉	C₂²	1	4	yes	complemented
46	#396×C₈₉	C₂²	1	4	yes	—
47	#396×C₈₉	C₂²	1	4	yes	—
48	#395×C₈₉	C₂²	1	4	yes	complemented
49	#393×C₈₉	C₂²	1	4	yes	—
50	#391×C₈₉	C₂²	1	4	yes	complemented
51	#389×C₈₉	C₂²	1	2	yes	complemented
52	#389×C₈₉	C₂²	1	2	yes	complemented
53	#389×C₈₉	C₂²	1	2	yes	complemented
54	#389×C₈₉	C₂²	1	2	yes	complemented
55	#389×C₈₉	C₂²	1	2	yes	complemented
56	#389×C₈₉	C₂²	1	2	yes	complemented
57	#389×C₈₉	C₂²	1	2	yes	complemented
58	#389×C₈₉	C₂²	1	2	yes	complemented
59	#389×C₈₉	C₂²	1	4	yes	complemented
60	#387×C₈₉	C₂²	1	4	yes	complemented
61	#387×C₈₉	C₂²	1	4	yes	complemented
62	#385×C₈₉	C₂²	1	4	yes	—
63	#385×C₈₉	C₂²	1	4	yes	—
64	#385×C₈₉	C₂²	1	4	yes	—
65	#385×C₈₉	C₂²	1	4	yes	—
66	#384×C₈₉	C₂²	1	2	yes	complemented
67	#384×C₈₉	C₂²	1	2	yes	complemented
68	#382×C₈₉	C₂²	1	2	yes	complemented
69	#382×C₈₉	C₂²	1	2	yes	complemented
70	#381×C₈₉	C₂²	1	2	yes	—
71	#380×C₈₉	C₂²	1	4	yes	—
72	#380×C₈₉	C₂²	1	1	yes	characteristic
73	#380×C₈₉	C₂²	1	2	yes	—
74	#380×C₈₉	C₂²	1	1	yes	characteristic
75	#380×C₈₉	C₂²	1	4	yes	—
76	#380×C₈₉	C₂²	1	1	yes	characteristic
77	#380×C₈₉	C₂²	1	2	yes	—
78	#380×C₈₉	C₂²	1	1	yes	characteristic
79	#380×C₈₉	C₂²	1	2	yes	—
80	#380×C₈₉	C₂²	1	2	yes	—
81	#379×C₈₉	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
84	C₂×#95×C₈₉	C₂²	1	2	yes	—
85	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
87	C₂³×C₄×C₈₉	—	2	4	no	—
88	C₂³×C₄×C₈₉	—	2	4	no	—
89	C₂³×C₄×C₈₉	Q₈	1	8	yes	complemented
90	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
91	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
92	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
99	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
100	C₄⋊Q₈×C₈₉	—	2	8	no	—
101	C₄⋊Q₈×C₈₉	—	2	8	no	—
102	#125×C₈₉	—	2	8	no	—
103	#125×C₈₉	—	2	8	no	—
104	C₂²⋊Q₈×C₈₉	—	2	16	no	—
105	C₂²⋊Q₈×C₈₉	—	4	8	no	—
106	#117×C₈₉	—	2	4	no	—
107	#117×C₈₉	—	2	4	no	—
108	#117×C₈₉	—	2	4	no	—
109	#117×C₈₉	—	2	4	no	—
110	#117×C₈₉	—	2	4	no	—
111	#117×C₈₉	—	2	8	no	—
112	#117×C₈₉	—	2	8	no	—
113	#117×C₈₉	D₄	1	8	yes	—
114	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
115	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
116	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
117	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
118	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	4	yes	—
127	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
132	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
134	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	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×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
142	C₂×C₂²⋊C₄×C₈₉	—	4	4	no	—
143	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	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	4	yes	—
154	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₈₉	—	2	8	no	—
156	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
162	#95×C₈₉	C₂³	1	4	yes	—
163	#95×C₈₉	C₂³	1	4	yes	—
164	#95×C₈₉	C₂³	1	2	yes	—
165	#95×C₈₉	C₂³	1	2	yes	—
166	#95×C₈₉	C₂³	1	2	yes	—
167	#95×C₈₉	C₂³	1	2	yes	—
168	#95×C₈₉	C₂³	1	4	yes	—
169	#95×C₈₉	C₂³	1	4	yes	—
170	#95×C₈₉	C₂³	1	4	yes	—
171	#95×C₈₉	C₂³	1	4	yes	—
172	#95×C₈₉	C₂³	1	4	yes	—
173	#95×C₈₉	C₂³	1	4	yes	—
174	C₂⁴×C₈₉	—	2	2	no	—
175	C₂⁴×C₈₉	—	2	2	no	—
176	C₂⁴×C₈₉	—	2	2	no	—
177	C₂⁴×C₈₉	—	2	2	no	—
178	C₂⁴×C₈₉	—	4	1	no	—
179	C₂⁴×C₈₉	—	4	1	no	—
180	C₂⁴×C₈₉	C₂×Q₈	1	4	yes	—
181	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
182	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
183	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
184	C₂×Q₈×C₈₉	—	2	8	no	—
185	C₂×Q₈×C₈₉	—	4	4	no	—
186	C₂×Q₈×C₈₉	—	4	4	no	—
187	C₂²×C₄×C₈₉	—	2	2	no	—
188	C₂²×C₄×C₈₉	—	2	2	no	—
189	C₂²×C₄×C₈₉	—	2	32	no	—
190	C₂²×C₄×C₈₉	—	2	2	no	—
191	C₂²×C₄×C₈₉	—	2	2	no	—
192	C₂²×C₄×C₈₉	—	2	2	no	—
193	C₂²×C₄×C₈₉	—	2	2	no	—
194	C₂²×C₄×C₈₉	—	2	2	no	—
195	C₂²×C₄×C₈₉	—	2	2	no	—
196	C₂²×C₄×C₈₉	—	2	2	no	—
197	C₂²×C₄×C₈₉	—	2	2	no	—
198	C₂²×C₄×C₈₉	—	2	4	no	—
199	C₂²×C₄×C₈₉	—	2	4	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	—	4	2	no	—
205	C₂²×C₄×C₈₉	—	4	2	no	—
206	C₂²×C₄×C₈₉	—	4	2	no	—
207	C₂²×C₄×C₈₉	—	4	2	no	—
208	C₂²×C₄×C₈₉	—	4	2	no	—
209	C₂²×C₄×C₈₉	—	4	2	no	—
210	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
211	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
212	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
213	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
214	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
215	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
216	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
217	C₂²×C₄×C₈₉	#41	1	4	yes	—
218	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₈₉	C₂⁴	1	4	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	4	yes	—
225	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	2	no	—
235	C₄⋊C₄×C₈₉	—	2	2	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	2	no	—
240	C₄⋊C₄×C₈₉	—	2	8	no	—
241	C₄⋊C₄×C₈₉	—	2	8	no	—
242	C₄⋊C₄×C₈₉	—	2	8	no	—
243	C₄⋊C₄×C₈₉	—	2	4	no	—
244	C₄⋊C₄×C₈₉	—	2	4	no	—
245	C₄⋊C₄×C₈₉	—	2	2	no	—
246	C₄⋊C₄×C₈₉	—	2	2	no	—
247	C₄⋊C₄×C₈₉	—	4	4	no	—
248	C₄⋊C₄×C₈₉	—	4	4	no	—
249	C₄⋊C₄×C₈₉	—	4	4	no	—
250	C₄⋊C₄×C₈₉	—	4	4	no	—
251	C₄⋊C₄×C₈₉	—	4	4	no	—
252	C₄⋊C₄×C₈₉	—	4	4	no	—
253	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
254	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
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	8	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	—	4	4	no	—
264	C₂²⋊C₄×C₈₉	—	4	2	no	—
265	C₂²⋊C₄×C₈₉	—	4	2	no	—
266	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
267	C₄²×C₈₉	—	2	4	no	—
268	C₄²×C₈₉	—	2	4	no	—
269	C₄²×C₈₉	—	2	4	no	—
270	C₄²×C₈₉	—	2	4	no	—
271	C₄²×C₈₉	—	2	4	no	—
272	C₄²×C₈₉	C₂×D₄	1	8	yes	—
273	C₂³×C₈₉	—	2	1	no	—
274	C₂³×C₈₉	—	2	1	no	—
275	C₂³×C₈₉	—	2	1	no	—
276	C₂³×C₈₉	—	2	1	no	—
277	C₂³×C₈₉	—	2	1	no	—
278	C₂³×C₈₉	—	2	1	no	—
279	C₂³×C₈₉	—	2	1	no	—
280	C₂³×C₈₉	—	2	1	no	—
281	C₂³×C₈₉	—	2	8	no	—
282	C₂³×C₈₉	—	2	8	no	—
283	C₂³×C₈₉	—	2	1	no	—
284	C₂³×C₈₉	—	2	1	no	—
285	C₂³×C₈₉	—	2	1	no	—
286	C₂³×C₈₉	—	2	1	no	—
287	C₂³×C₈₉	—	2	1	no	—
288	C₂³×C₈₉	—	2	1	no	—
289	C₂³×C₈₉	—	4	4	no	—
290	C₂³×C₈₉	—	4	4	no	—
291	C₂³×C₈₉	—	4	4	no	—
292	C₂³×C₈₉	—	4	4	no	—
293	C₂³×C₈₉	—	4	4	no	—
294	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
295	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
296	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
297	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
298	C₂³×C₈₉	C₂×#41	1	2	yes	—
299	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
300	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
301	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
302	Q₈×C₈₉	—	8	8	no	—
303	C₂×C₄×C₈₉	—	2	8	no	—
304	C₂×C₄×C₈₉	—	2	1	no	—
305	C₂×C₄×C₈₉	—	2	1	no	—
306	C₂×C₄×C₈₉	—	2	1	no	—
307	C₂×C₄×C₈₉	—	2	1	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	8	no	—
313	C₂×C₄×C₈₉	—	2	8	no	—
314	C₂×C₄×C₈₉	—	2	8	no	—
315	C₂×C₄×C₈₉	—	2	8	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	2	no	—
322	C₂×C₄×C₈₉	—	2	2	no	—
323	C₂×C₄×C₈₉	—	2	4	no	—
324	C₂×C₄×C₈₉	—	2	4	no	—
325	C₂×C₄×C₈₉	—	2	4	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	2	no	—
330	C₂×C₄×C₈₉	—	2	2	no	—
331	C₂×C₄×C₈₉	—	2	2	no	—
332	C₂×C₄×C₈₉	—	2	2	no	—
333	C₂×C₄×C₈₉	—	2	2	no	—
334	C₂×C₄×C₈₉	—	2	2	no	—
335	C₂×C₄×C₈₉	—	2	2	no	—
336	C₂×C₄×C₈₉	—	2	2	no	—
337	C₂×C₄×C₈₉	—	2	2	no	—
338	C₂×C₄×C₈₉	—	2	4	no	—
339	C₂×C₄×C₈₉	—	2	4	no	—
340	C₂×C₄×C₈₉	—	4	8	no	—
341	C₂×C₄×C₈₉	—	4	8	no	—
342	C₂×C₄×C₈₉	—	8	4	no	—
343	C₂×C₄×C₈₉	—	8	4	no	—
344	C₂×C₄×C₈₉	C₂²⋊Q₈	1	16	yes	complemented
345	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
346	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
347	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
348	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
349	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
350	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
351	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
352	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
353	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
354	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
355	C₂²×C₈₉	—	2	2	no	—
356	C₂²×C₈₉	—	2	2	no	—
357	C₂²×C₈₉	—	2	2	no	—
358	C₂²×C₈₉	—	2	2	no	—
359	C₂²×C₈₉	—	2	2	no	—
360	C₂²×C₈₉	—	2	2	no	—
361	C₂²×C₈₉	—	2	2	no	—
362	C₂²×C₈₉	—	2	2	no	—
363	C₂²×C₈₉	—	2	2	no	—
364	C₂²×C₈₉	—	2	2	no	—
365	C₂²×C₈₉	—	2	2	no	—
366	C₂²×C₈₉	—	2	2	no	—
367	C₂²×C₈₉	—	2	2	no	—
368	C₂²×C₈₉	—	2	2	no	—
369	C₂²×C₈₉	—	2	2	no	—
370	C₂²×C₈₉	—	4	16	no	—
371	C₂²×C₈₉	—	4	1	no	—
372	C₂²×C₈₉	—	4	1	no	—
373	C₂²×C₈₉	—	4	1	no	—
374	C₂²×C₈₉	—	4	1	no	—
375	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
376	C₂²×C₈₉	#544	1	4	yes	complemented
377	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
378	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
379	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
380	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
381	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
382	C₂²×C₈₉	#585	1	1	yes	characteristic
383	C₂²×C₈₉	#585	1	1	yes	characteristic
384	C₄×C₈₉	—	2	2	no	—
385	C₄×C₈₉	—	2	2	no	—
386	C₄×C₈₉	—	2	4	no	—
387	C₄×C₈₉	—	2	4	no	—
388	C₄×C₈₉	—	4	2	no	—
389	C₄×C₈₉	—	4	4	no	—
390	C₄×C₈₉	—	4	2	no	—
391	C₄×C₈₉	—	4	2	no	—
392	C₄×C₈₉	—	4	2	no	—
393	C₄×C₈₉	—	4	2	no	—
394	C₄×C₈₉	—	4	4	no	—
395	C₄×C₈₉	—	4	2	no	—
396	C₄×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
397	C₄×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
398	#35253	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
399	C₂×C₈₉	—	2	4	no	—
400	C₂×C₈₉	—	2	4	no	—
401	C₂×C₈₉	—	4	2	no	—
402	C₂×C₈₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
403	C₂×C₈₉	C₂×#544	1	1	yes	characteristic
404	C₂×C₈₉	#3458	1	1	yes	characteristic
405	C₂×C₈₉	#3488	1	1	yes	characteristic
406	C₂×C₈₉	#3489	1	1	yes	characteristic
407	C₂×C₈₉	#3494	1	1	yes	characteristic
408	C₂×C₈₉	#3495	1	1	yes	characteristic
409	C₂×#544	C₂×C₈₉	1	1	yes	characteristic, complemented
410	C₂²×#117	C₂×C₈₉	1	1	yes	characteristic
411	#2857	C₂×C₈₉	1	2	yes	complemented
412	#2851	C₂×C₈₉	1	2	yes	complemented
413	#2629	C₂×C₈₉	1	2	yes	complemented
414	#2628	C₂×C₈₉	1	2	yes	complemented
415	#2442	C₂×C₈₉	1	2	yes	complemented
416	#2441	C₂×C₈₉	1	2	yes	complemented
417	#2440	C₂×C₈₉	1	2	yes	complemented
418	#2439	C₂×C₈₉	1	2	yes	complemented
419	#2438	C₂×C₈₉	1	4	yes	complemented
420	#2437	C₂×C₈₉	1	4	yes	—
421	#2317	C₂×C₈₉	1	1	yes	characteristic, complemented
422	#2317	C₂×C₈₉	1	1	yes	characteristic, complemented
423	#2316	C₂×C₈₉	1	1	yes	characteristic, complemented
424	#2280	C₂×C₈₉	1	1	yes	characteristic
425	C₂×#380	C₂×C₈₉	1	1	yes	characteristic
426	C₈₉	#35253	1	1	yes	characteristic, direct product factor, Sylow
427	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
428	#544	—	2	8	no	—
429	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
430	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
431	C₂×#125	C₂²×C₈₉	1	2	yes	complemented
432	C₂×#125	C₂²×C₈₉	1	2	yes	complemented
433	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
434	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
435	C₂×#117	—	2	8	no	—
436	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
437	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
438	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
439	C₂×#117	C₂²×C₈₉	1	2	yes	—
440	C₂×#117	C₂²×C₈₉	1	2	yes	—
441	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
442	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
443	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
444	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
445	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
446	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
447	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
448	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
449	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
450	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
451	#400	C₂²×C₈₉	1	4	yes	complemented
452	#399	C₂²×C₈₉	1	4	yes	—
453	#398	C₂²×C₈₉	1	4	yes	complemented
454	#398	C₂²×C₈₉	1	4	yes	complemented
455	#396	C₂²×C₈₉	1	4	yes	—
456	#396	C₂²×C₈₉	1	4	yes	—
457	#395	C₂²×C₈₉	1	4	yes	complemented
458	#393	C₂²×C₈₉	1	4	yes	—
459	#391	C₂²×C₈₉	1	4	yes	complemented
460	#389	C₂²×C₈₉	1	2	yes	complemented
461	#389	C₂²×C₈₉	1	2	yes	complemented
462	#389	C₂²×C₈₉	1	2	yes	complemented
463	#389	C₂²×C₈₉	1	2	yes	complemented
464	#389	C₂²×C₈₉	1	2	yes	complemented
465	#389	C₂²×C₈₉	1	2	yes	complemented
466	#389	C₂²×C₈₉	1	2	yes	complemented
467	#389	C₂²×C₈₉	1	2	yes	complemented
468	#389	C₂²×C₈₉	1	4	yes	complemented
469	#387	C₂²×C₈₉	1	4	yes	complemented
470	#387	C₂²×C₈₉	1	4	yes	complemented
471	#385	C₂²×C₈₉	1	4	yes	—
472	#385	C₂²×C₈₉	1	4	yes	—
473	#385	C₂²×C₈₉	1	4	yes	—
474	#385	C₂²×C₈₉	1	4	yes	—
475	#384	C₂²×C₈₉	1	2	yes	complemented
476	#384	C₂²×C₈₉	1	2	yes	complemented
477	#382	C₂²×C₈₉	1	2	yes	complemented
478	#382	C₂²×C₈₉	1	2	yes	complemented
479	#381	C₂²×C₈₉	1	2	yes	—
480	#380	C₂²×C₈₉	1	4	yes	—
481	#380	C₂²×C₈₉	1	1	yes	characteristic
482	#380	C₂²×C₈₉	1	2	yes	—
483	#380	C₂²×C₈₉	1	1	yes	characteristic
484	#380	C₂²×C₈₉	1	4	yes	—
485	#380	C₂²×C₈₉	1	1	yes	characteristic
486	#380	C₂²×C₈₉	1	2	yes	—
487	#380	C₂²×C₈₉	1	1	yes	characteristic
488	#380	C₂²×C₈₉	1	2	yes	—
489	#380	C₂²×C₈₉	1	2	yes	—
490	#379	C₂²×C₈₉	1	2	yes	—
491	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
492	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
493	C₂×#95	C₂²×C₈₉	1	2	yes	—
494	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
495	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
496	C₂³×C₄	—	2	4	no	—
497	C₂³×C₄	—	2	4	no	—
498	C₂³×C₄	Q₈×C₈₉	1	8	yes	complemented
499	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
500	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
501	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
502	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
503	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
504	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
505	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
506	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
507	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
508	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
509	C₄⋊Q₈	—	2	8	no	—
510	C₄⋊Q₈	—	2	8	no	—
511	#125	—	2	8	no	—
512	#125	—	2	8	no	—
513	C₂²⋊Q₈	—	2	16	no	—
514	C₂²⋊Q₈	—	4	8	no	—
515	#117	—	2	4	no	—
516	#117	—	2	4	no	—
517	#117	—	2	4	no	—
518	#117	—	2	4	no	—
519	#117	—	2	4	no	—
520	#117	—	2	8	no	—
521	#117	—	2	8	no	—
522	#117	D₄×C₈₉	1	8	yes	—
523	C₂×C₄⋊C₄	—	2	4	no	—
524	C₂×C₄⋊C₄	—	2	4	no	—
525	C₂×C₄⋊C₄	—	2	4	no	—
526	C₂×C₄⋊C₄	—	2	4	no	—
527	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
540	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
541	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
542	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
543	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
544	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
545	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
546	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
547	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
548	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
550	C₂×C₂²⋊C₄	—	2	8	no	—
551	C₂×C₂²⋊C₄	—	4	4	no	—
552	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
564	C₂×C₄²	—	2	8	no	—
565	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
566	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
567	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
568	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
569	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
570	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
571	#95	C₂³×C₈₉	1	4	yes	—
572	#95	C₂³×C₈₉	1	4	yes	—
573	#95	C₂³×C₈₉	1	2	yes	—
574	#95	C₂³×C₈₉	1	2	yes	—
575	#95	C₂³×C₈₉	1	2	yes	—
576	#95	C₂³×C₈₉	1	2	yes	—
577	#95	C₂³×C₈₉	1	4	yes	—
578	#95	C₂³×C₈₉	1	4	yes	—
579	#95	C₂³×C₈₉	1	4	yes	—
580	#95	C₂³×C₈₉	1	4	yes	—
581	#95	C₂³×C₈₉	1	4	yes	—
582	#95	C₂³×C₈₉	1	4	yes	—
583	C₂⁴	—	2	2	no	—
584	C₂⁴	—	2	2	no	—
585	C₂⁴	—	2	2	no	—
586	C₂⁴	—	2	2	no	—
587	C₂⁴	—	4	1	no	—
588	C₂⁴	—	4	1	no	—
589	C₂⁴	C₂×Q₈×C₈₉	1	4	yes	—
590	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
591	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
592	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
593	C₂×Q₈	—	2	8	no	—
594	C₂×Q₈	—	4	4	no	—
595	C₂×Q₈	—	4	4	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	32	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	4	2	no	—
614	C₂²×C₄	—	4	2	no	—
615	C₂²×C₄	—	4	2	no	—
616	C₂²×C₄	—	4	2	no	—
617	C₂²×C₄	—	4	2	no	—
618	C₂²×C₄	—	4	2	no	—
619	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
620	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
621	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
622	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
623	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
624	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
625	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
626	C₂²×C₄	#41×C₈₉	1	4	yes	—
627	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
630	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
634	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	8	no	—
650	C₄⋊C₄	—	2	8	no	—
651	C₄⋊C₄	—	2	8	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	4	4	no	—
657	C₄⋊C₄	—	4	4	no	—
658	C₄⋊C₄	—	4	4	no	—
659	C₄⋊C₄	—	4	4	no	—
660	C₄⋊C₄	—	4	4	no	—
661	C₄⋊C₄	—	4	4	no	—
662	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
663	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	8	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	4	4	no	—
673	C₂²⋊C₄	—	4	2	no	—
674	C₂²⋊C₄	—	4	2	no	—
675	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
676	C₄²	—	2	4	no	—
677	C₄²	—	2	4	no	—
678	C₄²	—	2	4	no	—
679	C₄²	—	2	4	no	—
680	C₄²	—	2	4	no	—
681	C₄²	C₂×D₄×C₈₉	1	8	yes	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	1	no	—
684	C₂³	—	2	1	no	—
685	C₂³	—	2	1	no	—
686	C₂³	—	2	1	no	—
687	C₂³	—	2	1	no	—
688	C₂³	—	2	1	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	2	8	no	—
691	C₂³	—	2	8	no	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	4	4	no	—
699	C₂³	—	4	4	no	—
700	C₂³	—	4	4	no	—
701	C₂³	—	4	4	no	—
702	C₂³	—	4	4	no	—
703	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
704	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
705	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
706	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
707	C₂³	C₂×#41×C₈₉	1	2	yes	—
708	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
709	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
710	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
711	Q₈	—	8	8	no	—
712	C₂×C₄	—	2	8	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	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	8	no	—
722	C₂×C₄	—	2	8	no	—
723	C₂×C₄	—	2	8	no	—
724	C₂×C₄	—	2	8	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	4	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	4	no	—
733	C₂×C₄	—	2	4	no	—
734	C₂×C₄	—	2	4	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	4	no	—
749	C₂×C₄	—	4	8	no	—
750	C₂×C₄	—	4	8	no	—
751	C₂×C₄	—	8	4	no	—
752	C₂×C₄	—	8	4	no	—
753	C₂×C₄	C₂²⋊Q₈×C₈₉	1	16	yes	complemented
754	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
755	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
756	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
757	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
758	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
759	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
760	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
761	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
762	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
763	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	2	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	4	16	no	—
780	C₂²	—	4	1	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	1	no	—
784	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
785	C₂²	#544×C₈₉	1	4	yes	complemented
786	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
787	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
788	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
789	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
790	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
791	C₂²	#585×C₈₉	1	1	yes	characteristic
792	C₂²	#585×C₈₉	1	1	yes	characteristic
793	C₄	—	2	2	no	—
794	C₄	—	2	2	no	—
795	C₄	—	2	4	no	—
796	C₄	—	2	4	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	4	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	2	no	—
802	C₄	—	4	4	no	—
803	C₄	—	4	2	no	—
804	C₄	—	4	2	no	—
805	C₄	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
806	C₄	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
807	C₂	—	2	4	no	—
808	C₂	—	2	4	no	—
809	C₂	—	4	2	no	—
810	C₂	C₂²×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
811	C₂	C₂×#544×C₈₉	1	1	yes	characteristic
812	C₂	C₈₉×#3458	1	1	yes	characteristic
813	C₂	C₈₉×#3488	1	1	yes	characteristic
814	C₂	C₈₉×#3489	1	1	yes	characteristic
815	C₂	C₈₉×#3494	1	1	yes	characteristic
816	C₂	C₈₉×#3495	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂⁵×C₈₉	C₂³
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×#544×C₈₉	C₂	semidirect
3. C₈₉×#2857	C₂	semidirect
4. C₈₉×#2851	C₂	semidirect
5. C₈₉×#2629	C₂	semidirect
6. C₈₉×#2628	C₂	semidirect
7. C₈₉×#2442	C₂	semidirect
8. C₈₉×#2441	C₂	semidirect
9. C₈₉×#2440	C₂	semidirect
10. C₈₉×#2439	C₂	semidirect
11. C₈₉×#2438	C₂	semidirect
13. C₈₉×#2317	C₂	semidirect
14. C₈₉×#2317	C₂	semidirect
15. C₈₉×#2316	C₂	semidirect
20. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
21. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
22. C₂×#125×C₈₉	C₂²	semidirect
23. C₂×#125×C₈₉	C₂²	semidirect
42. #400×C₈₉	C₂²	semidirect
44. #398×C₈₉	C₂²	semidirect
45. #398×C₈₉	C₂²	semidirect
48. #395×C₈₉	C₂²	semidirect
50. #391×C₈₉	C₂²	semidirect
51. #389×C₈₉	C₂²	semidirect
52. #389×C₈₉	C₂²	semidirect
53. #389×C₈₉	C₂²	semidirect
54. #389×C₈₉	C₂²	semidirect
55. #389×C₈₉	C₂²	semidirect
56. #389×C₈₉	C₂²	semidirect
57. #389×C₈₉	C₂²	semidirect
58. #389×C₈₉	C₂²	semidirect
59. #389×C₈₉	C₂²	semidirect
60. #387×C₈₉	C₂²	semidirect
61. #387×C₈₉	C₂²	semidirect
66. #384×C₈₉	C₂²	semidirect
67. #384×C₈₉	C₂²	semidirect
68. #382×C₈₉	C₂²	semidirect
69. #382×C₈₉	C₂²	semidirect
89. C₂³×C₄×C₈₉	Q₈	semidirect
344. C₂×C₄×C₈₉	C₂²⋊Q₈	semidirect
376. C₂²×C₈₉	#544	semidirect
398. #35253	C₈₉	direct (N × H)
409. C₂×#544	C₂×C₈₉	semidirect
411. #2857	C₂×C₈₉	semidirect
412. #2851	C₂×C₈₉	semidirect
413. #2629	C₂×C₈₉	semidirect
414. #2628	C₂×C₈₉	semidirect
415. #2442	C₂×C₈₉	semidirect
416. #2441	C₂×C₈₉	semidirect
417. #2440	C₂×C₈₉	semidirect
418. #2439	C₂×C₈₉	semidirect
419. #2438	C₂×C₈₉	semidirect
421. #2317	C₂×C₈₉	semidirect
422. #2317	C₂×C₈₉	semidirect
423. #2316	C₂×C₈₉	semidirect
426. C₈₉	#35253	direct (N × H)
429. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
430. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
431. C₂×#125	C₂²×C₈₉	semidirect
432. C₂×#125	C₂²×C₈₉	semidirect
451. #400	C₂²×C₈₉	semidirect
453. #398	C₂²×C₈₉	semidirect
454. #398	C₂²×C₈₉	semidirect
457. #395	C₂²×C₈₉	semidirect
459. #391	C₂²×C₈₉	semidirect
460. #389	C₂²×C₈₉	semidirect
461. #389	C₂²×C₈₉	semidirect
462. #389	C₂²×C₈₉	semidirect
463. #389	C₂²×C₈₉	semidirect
464. #389	C₂²×C₈₉	semidirect
465. #389	C₂²×C₈₉	semidirect
466. #389	C₂²×C₈₉	semidirect
467. #389	C₂²×C₈₉	semidirect
468. #389	C₂²×C₈₉	semidirect
469. #387	C₂²×C₈₉	semidirect
470. #387	C₂²×C₈₉	semidirect
475. #384	C₂²×C₈₉	semidirect
476. #384	C₂²×C₈₉	semidirect
477. #382	C₂²×C₈₉	semidirect
478. #382	C₂²×C₈₉	semidirect
498. C₂³×C₄	Q₈×C₈₉	semidirect
753. C₂×C₄	C₂²⋊Q₈×C₈₉	semidirect
785. C₂²	#544×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#544×C₈₉	2
C₂²×#117×C₈₉	2
C₈₉×#2857	2
C₈₉×#2851	2
C₈₉×#2629	2
C₈₉×#2628	2
C₈₉×#2442	2
C₈₉×#2441	2
C₈₉×#2440	2
C₈₉×#2439	2
C₈₉×#2438	2
C₈₉×#2437	2
C₈₉×#2317	2
C₈₉×#2316	2
C₈₉×#2280	2
C₂×#380×C₈₉	2
#35253	89

Subgroups — C89×#35253 #36413101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35253 #36413101