Subgroups — C₈₉×#35355 #36413203

Order 22784.

3322 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#518×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2579	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2476	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2464	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2456	C₂	1	4	yes	maximal, complemented
7	C₈₉×#2424	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2408	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2405	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2405	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2403	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2403	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#2321	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2312	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#120×C₈₉	C₂	1	2	yes	maximal, complemented
16	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
20	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
21	C₂×#123×C₈₉	C₂²	1	2	yes	complemented
22	C₂×#123×C₈₉	C₂²	1	2	yes	complemented
23	C₂×#121×C₈₉	—	2	8	no	—
24	C₂×#121×C₈₉	C₂²	1	4	yes	—
25	C₂×#121×C₈₉	C₂²	1	4	yes	complemented
26	C₂×#121×C₈₉	C₂²	1	4	yes	complemented
27	C₂×#120×C₈₉	C₂²	1	2	yes	—
28	C₂×#120×C₈₉	C₂²	1	2	yes	—
29	C₂×#120×C₈₉	C₂²	1	2	yes	complemented
30	C₂×#120×C₈₉	C₂²	1	2	yes	complemented
31	#518×C₈₉	—	2	8	no	—
32	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
35	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
36	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
37	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
38	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
43	#398×C₈₉	C₂²	1	4	yes	complemented
44	#396×C₈₉	C₂²	1	4	yes	complemented
45	#394×C₈₉	C₂²	1	4	yes	complemented
46	#394×C₈₉	C₂²	1	4	yes	complemented
47	#394×C₈₉	C₂²	1	4	yes	complemented
48	#392×C₈₉	C₂²	1	4	yes	complemented
49	#392×C₈₉	C₂²	1	4	yes	complemented
50	#392×C₈₉	C₂²	1	4	yes	complemented
51	#390×C₈₉	C₂²	1	4	yes	complemented
52	#390×C₈₉	C₂²	1	4	yes	complemented
53	#388×C₈₉	C₂²	1	4	yes	complemented
54	#388×C₈₉	C₂²	1	4	yes	complemented
55	#388×C₈₉	C₂²	1	4	yes	complemented
56	#388×C₈₉	C₂²	1	4	yes	complemented
57	#387×C₈₉	C₂²	1	4	yes	complemented
58	#386×C₈₉	C₂²	1	2	yes	—
59	#386×C₈₉	C₂²	1	2	yes	—
60	#386×C₈₉	C₂²	1	4	yes	complemented
61	#386×C₈₉	C₂²	1	4	yes	complemented
62	#386×C₈₉	C₂²	1	2	yes	complemented
63	#386×C₈₉	C₂²	1	2	yes	complemented
64	#386×C₈₉	C₂²	1	2	yes	complemented
65	#386×C₈₉	C₂²	1	2	yes	complemented
66	#385×C₈₉	C₂²	1	2	yes	complemented
67	#385×C₈₉	C₂²	1	4	yes	complemented
68	#385×C₈₉	C₂²	1	2	yes	complemented
69	#385×C₈₉	C₂²	1	4	yes	complemented
70	#380×C₈₉	C₂²	1	2	yes	complemented
71	#379×C₈₉	C₂²	1	1	yes	characteristic
72	#379×C₈₉	C₂²	1	1	yes	characteristic
73	#379×C₈₉	C₂²	1	2	yes	complemented
74	#379×C₈₉	C₂²	1	2	yes	complemented
75	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
76	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	complemented
77	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
78	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
79	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
80	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₈₉	—	2	4	no	—
82	C₂²×D₄×C₈₉	—	2	8	no	—
83	C₂²×D₄×C₈₉	—	2	4	no	—
84	C₂²×D₄×C₈₉	—	2	4	no	—
85	C₂²×D₄×C₈₉	—	2	4	no	—
86	C₂²×D₄×C₈₉	—	4	4	no	—
87	C₂²×D₄×C₈₉	—	4	4	no	—
88	C₂²×D₄×C₈₉	—	4	4	no	—
89	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
90	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
91	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
93	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
94	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
95	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
96	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
97	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
98	C₂³×C₄×C₈₉	—	2	4	no	—
99	C₂³×C₄×C₈₉	—	4	4	no	—
100	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
103	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
105	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
108	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
110	#123×C₈₉	—	4	4	no	—
111	#123×C₈₉	—	4	4	no	—
112	#121×C₈₉	—	2	16	no	—
113	#121×C₈₉	—	2	16	no	—
114	#121×C₈₉	—	4	8	no	—
115	#120×C₈₉	—	2	8	no	—
116	#120×C₈₉	—	2	8	no	—
117	#120×C₈₉	—	4	4	no	—
118	#120×C₈₉	—	4	4	no	—
119	C₄×D₄×C₈₉	—	2	8	no	—
120	C₄×D₄×C₈₉	—	2	8	no	—
121	C₄×D₄×C₈₉	—	2	8	no	—
122	C₄×D₄×C₈₉	—	2	8	no	—
123	C₄×D₄×C₈₉	—	4	8	no	—
124	#117×C₈₉	—	2	8	no	—
125	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
126	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
129	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
133	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
134	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
135	C₂×C₂²⋊C₄×C₈₉	D₄	1	8	yes	complemented
136	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	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	4	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	4	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	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	4	yes	—
152	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
155	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×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	4	yes	—
160	#95×C₈₉	C₂³	1	4	yes	—
161	#95×C₈₉	C₂³	1	4	yes	—
162	#95×C₈₉	C₂³	1	4	yes	—
163	#95×C₈₉	C₂³	1	4	yes	—
164	#95×C₈₉	C₂³	1	4	yes	—
165	#95×C₈₉	C₂³	1	4	yes	—
166	C₂⁴×C₈₉	—	2	2	no	—
167	C₂⁴×C₈₉	—	2	4	no	—
168	C₂⁴×C₈₉	—	2	2	no	—
169	C₂⁴×C₈₉	—	2	4	no	—
170	C₂⁴×C₈₉	—	2	4	no	—
171	C₂⁴×C₈₉	—	2	2	no	—
172	C₂⁴×C₈₉	—	2	4	no	—
173	C₂⁴×C₈₉	—	2	4	no	—
174	C₂⁴×C₈₉	—	4	2	no	—
175	C₂⁴×C₈₉	—	4	2	no	—
176	C₂⁴×C₈₉	—	4	2	no	—
177	C₂⁴×C₈₉	—	4	2	no	—
178	C₂⁴×C₈₉	—	4	2	no	—
179	C₂⁴×C₈₉	—	4	2	no	—
180	C₂⁴×C₈₉	—	4	2	no	—
181	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
182	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
183	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
184	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
185	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
186	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
187	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
188	C₂×D₄×C₈₉	—	2	32	no	—
189	C₂×D₄×C₈₉	—	2	4	no	—
190	C₂×D₄×C₈₉	—	2	4	no	—
191	C₂×D₄×C₈₉	—	2	4	no	—
192	C₂×D₄×C₈₉	—	2	4	no	—
193	C₂×D₄×C₈₉	—	2	4	no	—
194	C₂×D₄×C₈₉	—	2	4	no	—
195	C₂×D₄×C₈₉	—	2	4	no	—
196	C₂×D₄×C₈₉	—	2	4	no	—
197	C₂×D₄×C₈₉	—	2	8	no	—
198	C₂×D₄×C₈₉	—	2	8	no	—
199	C₂×D₄×C₈₉	—	2	4	no	—
200	C₂×D₄×C₈₉	—	2	8	no	—
201	C₂×D₄×C₈₉	—	2	4	no	—
202	C₂×D₄×C₈₉	—	2	8	no	—
203	C₂×D₄×C₈₉	—	2	8	no	—
204	C₂×D₄×C₈₉	—	2	4	no	—
205	C₂×D₄×C₈₉	—	2	4	no	—
206	C₂×D₄×C₈₉	—	2	4	no	—
207	C₂×D₄×C₈₉	—	4	4	no	—
208	C₂×D₄×C₈₉	—	4	4	no	—
209	C₂×D₄×C₈₉	—	4	2	no	—
210	C₂×D₄×C₈₉	—	4	2	no	—
211	C₂×D₄×C₈₉	—	4	2	no	—
212	C₂×D₄×C₈₉	—	4	2	no	—
213	C₂×D₄×C₈₉	—	4	16	no	—
214	C₂×D₄×C₈₉	—	4	4	no	—
215	C₂×D₄×C₈₉	—	4	4	no	—
216	C₂×D₄×C₈₉	—	4	16	no	—
217	C₂×D₄×C₈₉	—	4	16	no	—
218	C₂×D₄×C₈₉	#41	1	8	yes	—
219	C₂²×C₄×C₈₉	—	2	2	no	—
220	C₂²×C₄×C₈₉	—	2	2	no	—
221	C₂²×C₄×C₈₉	—	2	4	no	—
222	C₂²×C₄×C₈₉	—	2	4	no	—
223	C₂²×C₄×C₈₉	—	2	2	no	—
224	C₂²×C₄×C₈₉	—	2	2	no	—
225	C₂²×C₄×C₈₉	—	2	2	no	—
226	C₂²×C₄×C₈₉	—	2	8	no	—
227	C₂²×C₄×C₈₉	—	2	8	no	—
228	C₂²×C₄×C₈₉	—	2	4	no	—
229	C₂²×C₄×C₈₉	—	2	4	no	—
230	C₂²×C₄×C₈₉	—	4	2	no	—
231	C₂²×C₄×C₈₉	—	4	4	no	—
232	C₂²×C₄×C₈₉	—	4	2	no	—
233	C₂²×C₄×C₈₉	—	4	2	no	—
234	C₂²×C₄×C₈₉	—	4	4	no	—
235	C₂²×C₄×C₈₉	—	4	4	no	—
236	C₂²×C₄×C₈₉	—	4	2	no	—
237	C₂²×C₄×C₈₉	—	4	2	no	—
238	C₂²×C₄×C₈₉	—	4	16	no	—
239	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
240	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
241	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
242	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
243	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
250	C₄⋊C₄×C₈₉	—	2	8	no	—
251	C₄⋊C₄×C₈₉	—	2	4	no	—
252	C₄⋊C₄×C₈₉	—	2	4	no	—
253	C₄⋊C₄×C₈₉	—	2	8	no	—
254	C₄⋊C₄×C₈₉	—	4	4	no	—
255	C₄⋊C₄×C₈₉	—	4	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	8	no	—
261	C₂²⋊C₄×C₈₉	—	2	4	no	—
262	C₂²⋊C₄×C₈₉	—	2	4	no	—
263	C₂²⋊C₄×C₈₉	—	2	8	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	—	4	2	no	—
269	C₂²⋊C₄×C₈₉	—	4	2	no	—
270	C₂²⋊C₄×C₈₉	—	4	4	no	—
271	C₂²⋊C₄×C₈₉	—	4	4	no	—
272	C₂²⋊C₄×C₈₉	—	4	2	no	—
273	C₂²⋊C₄×C₈₉	—	4	4	no	—
274	C₂²⋊C₄×C₈₉	—	4	2	no	—
275	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
276	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
277	C₄²×C₈₉	—	2	4	no	—
278	C₄²×C₈₉	—	2	4	no	—
279	C₄²×C₈₉	—	4	4	no	—
280	C₂³×C₈₉	—	2	2	no	—
281	C₂³×C₈₉	—	2	2	no	—
282	C₂³×C₈₉	—	2	8	no	—
283	C₂³×C₈₉	—	2	8	no	—
284	C₂³×C₈₉	—	2	2	no	—
285	C₂³×C₈₉	—	2	2	no	—
286	C₂³×C₈₉	—	2	4	no	—
287	C₂³×C₈₉	—	2	2	no	—
288	C₂³×C₈₉	—	2	2	no	—
289	C₂³×C₈₉	—	2	2	no	—
290	C₂³×C₈₉	—	2	4	no	—
291	C₂³×C₈₉	—	2	4	no	—
292	C₂³×C₈₉	—	2	2	no	—
293	C₂³×C₈₉	—	2	2	no	—
294	C₂³×C₈₉	—	2	4	no	—
295	C₂³×C₈₉	—	2	2	no	—
296	C₂³×C₈₉	—	2	2	no	—
297	C₂³×C₈₉	—	2	2	no	—
298	C₂³×C₈₉	—	2	8	no	—
299	C₂³×C₈₉	—	2	2	no	—
300	C₂³×C₈₉	—	2	4	no	—
301	C₂³×C₈₉	—	2	2	no	—
302	C₂³×C₈₉	—	2	4	no	—
303	C₂³×C₈₉	—	2	2	no	—
304	C₂³×C₈₉	—	4	4	no	—
305	C₂³×C₈₉	—	4	4	no	—
306	C₂³×C₈₉	—	4	16	no	—
307	C₂³×C₈₉	—	4	4	no	—
308	C₂³×C₈₉	—	4	4	no	—
309	C₂³×C₈₉	—	4	4	no	—
310	C₂³×C₈₉	—	4	4	no	—
311	C₂³×C₈₉	—	4	4	no	—
312	C₂³×C₈₉	—	8	8	no	—
313	C₂³×C₈₉	—	8	8	no	—
314	C₂³×C₈₉	—	8	2	no	—
315	C₂³×C₈₉	—	8	2	no	—
316	C₂³×C₈₉	—	8	8	no	—
317	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
318	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
319	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
320	C₂³×C₈₉	C₂×#41	1	4	yes	—
321	C₂³×C₈₉	C₂×#41	1	4	yes	—
322	C₂³×C₈₉	H(5,𝔽₂)	1	4	yes	—
323	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
324	D₄×C₈₉	—	2	16	no	—
325	D₄×C₈₉	—	2	16	no	—
326	D₄×C₈₉	—	4	8	no	—
327	D₄×C₈₉	—	4	8	no	—
328	D₄×C₈₉	—	4	16	no	—
329	D₄×C₈₉	—	4	16	no	—
330	D₄×C₈₉	—	4	8	no	—
331	D₄×C₈₉	—	4	8	no	—
332	D₄×C₈₉	—	8	8	no	—
333	C₂×C₄×C₈₉	—	2	8	no	—
334	C₂×C₄×C₈₉	—	2	8	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	—	2	2	no	—
341	C₂×C₄×C₈₉	—	2	2	no	—
342	C₂×C₄×C₈₉	—	2	2	no	—
343	C₂×C₄×C₈₉	—	2	2	no	—
344	C₂×C₄×C₈₉	—	2	4	no	—
345	C₂×C₄×C₈₉	—	2	4	no	—
346	C₂×C₄×C₈₉	—	2	4	no	—
347	C₂×C₄×C₈₉	—	2	4	no	—
348	C₂×C₄×C₈₉	—	2	4	no	—
349	C₂×C₄×C₈₉	—	2	4	no	—
350	C₂×C₄×C₈₉	—	2	4	no	—
351	C₂×C₄×C₈₉	—	2	4	no	—
352	C₂×C₄×C₈₉	—	2	2	no	—
353	C₂×C₄×C₈₉	—	2	2	no	—
354	C₂×C₄×C₈₉	—	4	4	no	—
355	C₂×C₄×C₈₉	—	4	4	no	—
356	C₂×C₄×C₈₉	—	4	16	no	—
357	C₂×C₄×C₈₉	—	4	4	no	—
358	C₂×C₄×C₈₉	—	8	4	no	—
359	C₂×C₄×C₈₉	—	8	4	no	—
360	C₂×C₄×C₈₉	—	8	2	no	—
361	C₂×C₄×C₈₉	—	8	2	no	—
362	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
363	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
364	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
365	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
366	C₂²×C₈₉	—	2	2	no	—
367	C₂²×C₈₉	—	2	2	no	—
368	C₂²×C₈₉	—	2	8	no	—
369	C₂²×C₈₉	—	2	2	no	—
370	C₂²×C₈₉	—	2	2	no	—
371	C₂²×C₈₉	—	2	4	no	—
372	C₂²×C₈₉	—	2	2	no	—
373	C₂²×C₈₉	—	2	2	no	—
374	C₂²×C₈₉	—	2	4	no	—
375	C₂²×C₈₉	—	2	2	no	—
376	C₂²×C₈₉	—	2	2	no	—
377	C₂²×C₈₉	—	2	8	no	—
378	C₂²×C₈₉	—	2	8	no	—
379	C₂²×C₈₉	—	4	16	no	—
380	C₂²×C₈₉	—	4	2	no	—
381	C₂²×C₈₉	—	4	2	no	—
382	C₂²×C₈₉	—	4	2	no	—
383	C₂²×C₈₉	—	4	2	no	—
384	C₂²×C₈₉	—	4	4	no	—
385	C₂²×C₈₉	—	4	4	no	—
386	C₂²×C₈₉	—	4	4	no	—
387	C₂²×C₈₉	—	4	4	no	—
388	C₂²×C₈₉	—	4	2	no	—
389	C₂²×C₈₉	—	4	2	no	—
390	C₂²×C₈₉	—	4	2	no	—
391	C₂²×C₈₉	—	4	4	no	—
392	C₂²×C₈₉	—	4	4	no	—
393	C₂²×C₈₉	—	8	8	no	—
394	C₂²×C₈₉	—	8	8	no	—
395	C₂²×C₈₉	—	8	8	no	—
396	C₂²×C₈₉	#525	1	4	yes	—
397	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
398	C₂²×C₈₉	C₂²×#41	1	2	yes	—
399	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
400	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
401	C₄×C₈₉	—	2	4	no	—
402	C₄×C₈₉	—	2	4	no	—
403	C₄×C₈₉	—	2	4	no	—
404	C₄×C₈₉	—	2	4	no	—
405	C₄×C₈₉	—	4	2	no	—
406	C₄×C₈₉	—	4	2	no	—
407	C₄×C₈₉	—	4	2	no	—
408	C₄×C₈₉	—	4	4	no	—
409	C₄×C₈₉	—	4	4	no	—
410	#35355	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
411	C₂×C₈₉	—	2	4	no	—
412	C₂×C₈₉	—	4	4	no	—
413	C₂×C₈₉	—	4	2	no	—
414	C₂×C₈₉	—	4	4	no	—
415	C₂×C₈₉	—	4	2	no	—
416	C₂×C₈₉	—	8	2	no	—
417	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
418	C₂×C₈₉	#3484	1	1	yes	characteristic
419	C₂×C₈₉	#3484	1	1	yes	characteristic
420	C₂×C₈₉	#3519	1	4	yes	—
421	C₂²×#121	C₂×C₈₉	1	1	yes	characteristic, complemented
422	C₂×#518	C₂×C₈₉	1	1	yes	characteristic, complemented
423	#2579	C₂×C₈₉	1	2	yes	complemented
424	#2476	C₂×C₈₉	1	4	yes	complemented
425	#2464	C₂×C₈₉	1	4	yes	complemented
426	#2456	C₂×C₈₉	1	4	yes	complemented
427	#2424	C₂×C₈₉	1	4	yes	complemented
428	#2408	C₂×C₈₉	1	2	yes	complemented
429	#2405	C₂×C₈₉	1	1	yes	characteristic, complemented
430	#2405	C₂×C₈₉	1	1	yes	characteristic, complemented
431	#2403	C₂×C₈₉	1	1	yes	characteristic, complemented
432	#2403	C₂×C₈₉	1	1	yes	characteristic, complemented
433	#2321	C₂×C₈₉	1	2	yes	complemented
434	#2312	C₂×C₈₉	1	1	yes	characteristic, complemented
435	C₄×#120	C₂×C₈₉	1	2	yes	complemented
436	C₈₉	#35355	1	1	yes	characteristic, direct product factor, Sylow
437	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
438	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
439	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
440	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
441	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
442	C₂×#123	C₂²×C₈₉	1	2	yes	complemented
443	C₂×#123	C₂²×C₈₉	1	2	yes	complemented
444	C₂×#121	—	2	8	no	—
445	C₂×#121	C₂²×C₈₉	1	4	yes	—
446	C₂×#121	C₂²×C₈₉	1	4	yes	complemented
447	C₂×#121	C₂²×C₈₉	1	4	yes	complemented
448	C₂×#120	C₂²×C₈₉	1	2	yes	—
449	C₂×#120	C₂²×C₈₉	1	2	yes	—
450	C₂×#120	C₂²×C₈₉	1	2	yes	complemented
451	C₂×#120	C₂²×C₈₉	1	2	yes	complemented
452	#518	—	2	8	no	—
453	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
454	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
455	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
456	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
457	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
458	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
459	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
460	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
461	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
462	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
463	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
464	#398	C₂²×C₈₉	1	4	yes	complemented
465	#396	C₂²×C₈₉	1	4	yes	complemented
466	#394	C₂²×C₈₉	1	4	yes	complemented
467	#394	C₂²×C₈₉	1	4	yes	complemented
468	#394	C₂²×C₈₉	1	4	yes	complemented
469	#392	C₂²×C₈₉	1	4	yes	complemented
470	#392	C₂²×C₈₉	1	4	yes	complemented
471	#392	C₂²×C₈₉	1	4	yes	complemented
472	#390	C₂²×C₈₉	1	4	yes	complemented
473	#390	C₂²×C₈₉	1	4	yes	complemented
474	#388	C₂²×C₈₉	1	4	yes	complemented
475	#388	C₂²×C₈₉	1	4	yes	complemented
476	#388	C₂²×C₈₉	1	4	yes	complemented
477	#388	C₂²×C₈₉	1	4	yes	complemented
478	#387	C₂²×C₈₉	1	4	yes	complemented
479	#386	C₂²×C₈₉	1	2	yes	—
480	#386	C₂²×C₈₉	1	2	yes	—
481	#386	C₂²×C₈₉	1	4	yes	complemented
482	#386	C₂²×C₈₉	1	2	yes	complemented
483	#386	C₂²×C₈₉	1	2	yes	complemented
484	#386	C₂²×C₈₉	1	2	yes	complemented
485	#386	C₂²×C₈₉	1	2	yes	complemented
486	#386	C₂²×C₈₉	1	4	yes	complemented
487	#385	C₂²×C₈₉	1	2	yes	complemented
488	#385	C₂²×C₈₉	1	2	yes	complemented
489	#385	C₂²×C₈₉	1	4	yes	complemented
490	#385	C₂²×C₈₉	1	4	yes	complemented
491	#380	C₂²×C₈₉	1	2	yes	complemented
492	#379	C₂²×C₈₉	1	1	yes	characteristic
493	#379	C₂²×C₈₉	1	1	yes	characteristic
494	#379	C₂²×C₈₉	1	2	yes	complemented
495	#379	C₂²×C₈₉	1	2	yes	complemented
496	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
497	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	complemented
498	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
499	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
500	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
501	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
502	C₂²×D₄	—	2	4	no	—
503	C₂²×D₄	—	2	8	no	—
504	C₂²×D₄	—	2	4	no	—
505	C₂²×D₄	—	2	4	no	—
506	C₂²×D₄	—	2	4	no	—
507	C₂²×D₄	—	4	4	no	—
508	C₂²×D₄	—	4	4	no	—
509	C₂²×D₄	—	4	4	no	—
510	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
511	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
512	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
513	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
514	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
515	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
516	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
517	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
518	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
519	C₂³×C₄	—	2	4	no	—
520	C₂³×C₄	—	4	4	no	—
521	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
522	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
523	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
524	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
525	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
526	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
527	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
528	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
529	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
530	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
531	#123	—	4	4	no	—
532	#123	—	4	4	no	—
533	#121	—	2	16	no	—
534	#121	—	2	16	no	—
535	#121	—	4	8	no	—
536	#120	—	2	8	no	—
537	#120	—	2	8	no	—
538	#120	—	4	4	no	—
539	#120	—	4	4	no	—
540	C₄×D₄	—	2	8	no	—
541	C₄×D₄	—	2	8	no	—
542	C₄×D₄	—	2	8	no	—
543	C₄×D₄	—	2	8	no	—
544	C₄×D₄	—	4	8	no	—
545	#117	—	2	8	no	—
546	C₂×C₄⋊C₄	—	2	4	no	—
547	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
548	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
551	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
552	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
553	C₂×C₂²⋊C₄	—	2	4	no	—
554	C₂×C₂²⋊C₄	—	2	4	no	—
555	C₂×C₂²⋊C₄	—	2	8	no	—
556	C₂×C₂²⋊C₄	D₄×C₈₉	1	8	yes	complemented
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	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
578	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
579	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
580	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
581	#95	C₂³×C₈₉	1	4	yes	—
582	#95	C₂³×C₈₉	1	4	yes	—
583	#95	C₂³×C₈₉	1	4	yes	—
584	#95	C₂³×C₈₉	1	4	yes	—
585	#95	C₂³×C₈₉	1	4	yes	—
586	#95	C₂³×C₈₉	1	4	yes	—
587	C₂⁴	—	2	2	no	—
588	C₂⁴	—	2	4	no	—
589	C₂⁴	—	2	2	no	—
590	C₂⁴	—	2	4	no	—
591	C₂⁴	—	2	4	no	—
592	C₂⁴	—	2	2	no	—
593	C₂⁴	—	2	4	no	—
594	C₂⁴	—	2	4	no	—
595	C₂⁴	—	4	2	no	—
596	C₂⁴	—	4	2	no	—
597	C₂⁴	—	4	2	no	—
598	C₂⁴	—	4	2	no	—
599	C₂⁴	—	4	2	no	—
600	C₂⁴	—	4	2	no	—
601	C₂⁴	—	4	2	no	—
602	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
603	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
604	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
605	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
606	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
607	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
608	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
609	C₂×D₄	—	2	32	no	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	8	no	—
619	C₂×D₄	—	2	8	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	8	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	8	no	—
624	C₂×D₄	—	2	8	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	2	4	no	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	4	4	no	—
629	C₂×D₄	—	4	4	no	—
630	C₂×D₄	—	4	2	no	—
631	C₂×D₄	—	4	2	no	—
632	C₂×D₄	—	4	2	no	—
633	C₂×D₄	—	4	2	no	—
634	C₂×D₄	—	4	16	no	—
635	C₂×D₄	—	4	4	no	—
636	C₂×D₄	—	4	4	no	—
637	C₂×D₄	—	4	16	no	—
638	C₂×D₄	—	4	16	no	—
639	C₂×D₄	#41×C₈₉	1	8	yes	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	4	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	8	no	—
648	C₂²×C₄	—	2	8	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	4	2	no	—
652	C₂²×C₄	—	4	4	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	—	4	4	no	—
656	C₂²×C₄	—	4	4	no	—
657	C₂²×C₄	—	4	2	no	—
658	C₂²×C₄	—	4	2	no	—
659	C₂²×C₄	—	4	16	no	—
660	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
661	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
662	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
663	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
664	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
671	C₄⋊C₄	—	2	8	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	8	no	—
675	C₄⋊C₄	—	4	4	no	—
676	C₄⋊C₄	—	4	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	8	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	8	no	—
685	C₂²⋊C₄	—	2	8	no	—
686	C₂²⋊C₄	—	2	8	no	—
687	C₂²⋊C₄	—	2	8	no	—
688	C₂²⋊C₄	—	4	4	no	—
689	C₂²⋊C₄	—	4	2	no	—
690	C₂²⋊C₄	—	4	2	no	—
691	C₂²⋊C₄	—	4	4	no	—
692	C₂²⋊C₄	—	4	4	no	—
693	C₂²⋊C₄	—	4	2	no	—
694	C₂²⋊C₄	—	4	4	no	—
695	C₂²⋊C₄	—	4	2	no	—
696	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
697	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
698	C₄²	—	2	4	no	—
699	C₄²	—	2	4	no	—
700	C₄²	—	4	4	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	8	no	—
704	C₂³	—	2	8	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	4	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	4	no	—
712	C₂³	—	2	4	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	4	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	8	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	4	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	4	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	4	4	no	—
726	C₂³	—	4	4	no	—
727	C₂³	—	4	16	no	—
728	C₂³	—	4	4	no	—
729	C₂³	—	4	4	no	—
730	C₂³	—	4	4	no	—
731	C₂³	—	4	4	no	—
732	C₂³	—	4	4	no	—
733	C₂³	—	8	8	no	—
734	C₂³	—	8	8	no	—
735	C₂³	—	8	2	no	—
736	C₂³	—	8	2	no	—
737	C₂³	—	8	8	no	—
738	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
739	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
740	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
741	C₂³	C₂×#41×C₈₉	1	4	yes	—
742	C₂³	C₂×#41×C₈₉	1	4	yes	—
743	C₂³	H(5,𝔽₂)×C₈₉	1	4	yes	—
744	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
745	D₄	—	2	16	no	—
746	D₄	—	2	16	no	—
747	D₄	—	4	8	no	—
748	D₄	—	4	8	no	—
749	D₄	—	4	16	no	—
750	D₄	—	4	16	no	—
751	D₄	—	4	8	no	—
752	D₄	—	4	8	no	—
753	D₄	—	8	8	no	—
754	C₂×C₄	—	2	8	no	—
755	C₂×C₄	—	2	8	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	4	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	4	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	4	no	—
768	C₂×C₄	—	2	4	no	—
769	C₂×C₄	—	2	4	no	—
770	C₂×C₄	—	2	4	no	—
771	C₂×C₄	—	2	4	no	—
772	C₂×C₄	—	2	4	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	4	4	no	—
776	C₂×C₄	—	4	4	no	—
777	C₂×C₄	—	4	16	no	—
778	C₂×C₄	—	4	4	no	—
779	C₂×C₄	—	8	4	no	—
780	C₂×C₄	—	8	4	no	—
781	C₂×C₄	—	8	2	no	—
782	C₂×C₄	—	8	2	no	—
783	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
784	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
785	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
786	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
787	C₂²	—	2	2	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	8	no	—
790	C₂²	—	2	2	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	2	4	no	—
793	C₂²	—	2	2	no	—
794	C₂²	—	2	2	no	—
795	C₂²	—	2	4	no	—
796	C₂²	—	2	2	no	—
797	C₂²	—	2	2	no	—
798	C₂²	—	2	8	no	—
799	C₂²	—	2	8	no	—
800	C₂²	—	4	16	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	4	no	—
806	C₂²	—	4	4	no	—
807	C₂²	—	4	4	no	—
808	C₂²	—	4	4	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	4	no	—
813	C₂²	—	4	4	no	—
814	C₂²	—	8	8	no	—
815	C₂²	—	8	8	no	—
816	C₂²	—	8	8	no	—
817	C₂²	#525×C₈₉	1	4	yes	—
818	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
819	C₂²	C₂²×#41×C₈₉	1	2	yes	—
820	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
821	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
822	C₄	—	2	4	no	—
823	C₄	—	2	4	no	—
824	C₄	—	2	4	no	—
825	C₄	—	2	4	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	4	no	—
830	C₄	—	4	4	no	—
831	C₂	—	2	4	no	—
832	C₂	—	4	4	no	—
833	C₂	—	4	2	no	—
834	C₂	—	4	4	no	—
835	C₂	—	4	2	no	—
836	C₂	—	8	2	no	—
837	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
838	C₂	C₈₉×#3484	1	1	yes	characteristic
839	C₂	C₈₉×#3484	1	1	yes	characteristic
840	C₂	C₈₉×#3519	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
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. C₂²×#121×C₈₉	C₂	semidirect
2. C₂×#518×C₈₉	C₂	semidirect
3. C₈₉×#2579	C₂	semidirect
4. C₈₉×#2476	C₂	semidirect
5. C₈₉×#2464	C₂	semidirect
6. C₈₉×#2456	C₂	semidirect
7. C₈₉×#2424	C₂	semidirect
8. C₈₉×#2408	C₂	semidirect
9. C₈₉×#2405	C₂	semidirect
10. C₈₉×#2405	C₂	semidirect
11. C₈₉×#2403	C₂	semidirect
12. C₈₉×#2403	C₂	semidirect
13. C₈₉×#2321	C₂	semidirect
14. C₈₉×#2312	C₂	semidirect
15. C₄×#120×C₈₉	C₂	semidirect
19. C₂³×D₄×C₈₉	C₂²	semidirect
20. C₂⁴×C₄×C₈₉	C₂²	semidirect
21. C₂×#123×C₈₉	C₂²	semidirect
22. C₂×#123×C₈₉	C₂²	semidirect
25. C₂×#121×C₈₉	C₂²	semidirect
26. C₂×#121×C₈₉	C₂²	semidirect
29. C₂×#120×C₈₉	C₂²	semidirect
30. C₂×#120×C₈₉	C₂²	semidirect
34. C₂×C₄×D₄×C₈₉	C₂²	semidirect
35. C₂×C₄×D₄×C₈₉	C₂²	semidirect
36. C₂×C₄×D₄×C₈₉	C₂²	semidirect
37. C₂×#117×C₈₉	C₂²	semidirect
38. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
41. C₂²×C₂²⋊C₄×C₈₉	C₂²	semidirect
42. C₂²×C₂²⋊C₄×C₈₉	C₂²	semidirect
43. #398×C₈₉	C₂²	semidirect
44. #396×C₈₉	C₂²	semidirect
45. #394×C₈₉	C₂²	semidirect
46. #394×C₈₉	C₂²	semidirect
47. #394×C₈₉	C₂²	semidirect
48. #392×C₈₉	C₂²	semidirect
49. #392×C₈₉	C₂²	semidirect
50. #392×C₈₉	C₂²	semidirect
51. #390×C₈₉	C₂²	semidirect
52. #390×C₈₉	C₂²	semidirect
53. #388×C₈₉	C₂²	semidirect
54. #388×C₈₉	C₂²	semidirect
55. #388×C₈₉	C₂²	semidirect
56. #388×C₈₉	C₂²	semidirect
57. #387×C₈₉	C₂²	semidirect
60. #386×C₈₉	C₂²	semidirect
61. #386×C₈₉	C₂²	semidirect
62. #386×C₈₉	C₂²	semidirect
63. #386×C₈₉	C₂²	semidirect
64. #386×C₈₉	C₂²	semidirect
65. #386×C₈₉	C₂²	semidirect
66. #385×C₈₉	C₂²	semidirect
67. #385×C₈₉	C₂²	semidirect
68. #385×C₈₉	C₂²	semidirect
69. #385×C₈₉	C₂²	semidirect
70. #380×C₈₉	C₂²	semidirect
73. #379×C₈₉	C₂²	semidirect
74. #379×C₈₉	C₂²	semidirect
75. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
76. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
135. C₂×C₂²⋊C₄×C₈₉	D₄	semidirect
410. #35355	C₈₉	direct (N × H)
421. C₂²×#121	C₂×C₈₉	semidirect
422. C₂×#518	C₂×C₈₉	semidirect
423. #2579	C₂×C₈₉	semidirect
424. #2476	C₂×C₈₉	semidirect
425. #2464	C₂×C₈₉	semidirect
426. #2456	C₂×C₈₉	semidirect
427. #2424	C₂×C₈₉	semidirect
428. #2408	C₂×C₈₉	semidirect
429. #2405	C₂×C₈₉	semidirect
430. #2405	C₂×C₈₉	semidirect
431. #2403	C₂×C₈₉	semidirect
432. #2403	C₂×C₈₉	semidirect
433. #2321	C₂×C₈₉	semidirect
434. #2312	C₂×C₈₉	semidirect
435. C₄×#120	C₂×C₈₉	semidirect
436. C₈₉	#35355	direct (N × H)
440. C₂³×D₄	C₂²×C₈₉	semidirect
441. C₂⁴×C₄	C₂²×C₈₉	semidirect
442. C₂×#123	C₂²×C₈₉	semidirect
443. C₂×#123	C₂²×C₈₉	semidirect
446. C₂×#121	C₂²×C₈₉	semidirect
447. C₂×#121	C₂²×C₈₉	semidirect
450. C₂×#120	C₂²×C₈₉	semidirect
451. C₂×#120	C₂²×C₈₉	semidirect
455. C₂×C₄×D₄	C₂²×C₈₉	semidirect
456. C₂×C₄×D₄	C₂²×C₈₉	semidirect
457. C₂×C₄×D₄	C₂²×C₈₉	semidirect
458. C₂×#117	C₂²×C₈₉	semidirect
459. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
462. C₂²×C₂²⋊C₄	C₂²×C₈₉	semidirect
463. C₂²×C₂²⋊C₄	C₂²×C₈₉	semidirect
464. #398	C₂²×C₈₉	semidirect
465. #396	C₂²×C₈₉	semidirect
466. #394	C₂²×C₈₉	semidirect
467. #394	C₂²×C₈₉	semidirect
468. #394	C₂²×C₈₉	semidirect
469. #392	C₂²×C₈₉	semidirect
470. #392	C₂²×C₈₉	semidirect
471. #392	C₂²×C₈₉	semidirect
472. #390	C₂²×C₈₉	semidirect
473. #390	C₂²×C₈₉	semidirect
474. #388	C₂²×C₈₉	semidirect
475. #388	C₂²×C₈₉	semidirect
476. #388	C₂²×C₈₉	semidirect
477. #388	C₂²×C₈₉	semidirect
478. #387	C₂²×C₈₉	semidirect
481. #386	C₂²×C₈₉	semidirect
482. #386	C₂²×C₈₉	semidirect
483. #386	C₂²×C₈₉	semidirect
484. #386	C₂²×C₈₉	semidirect
485. #386	C₂²×C₈₉	semidirect
486. #386	C₂²×C₈₉	semidirect
487. #385	C₂²×C₈₉	semidirect
488. #385	C₂²×C₈₉	semidirect
489. #385	C₂²×C₈₉	semidirect
490. #385	C₂²×C₈₉	semidirect
491. #380	C₂²×C₈₉	semidirect
494. #379	C₂²×C₈₉	semidirect
495. #379	C₂²×C₈₉	semidirect
496. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
497. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
556. C₂×C₂²⋊C₄	D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#121×C₈₉	2
C₂×#518×C₈₉	2
C₈₉×#2579	2
C₈₉×#2476	2
C₈₉×#2464	2
C₈₉×#2456	2
C₈₉×#2424	2
C₈₉×#2408	2
C₈₉×#2405	2
C₈₉×#2403	2
C₈₉×#2321	2
C₈₉×#2312	2
C₄×#120×C₈₉	2
#35355	89

Subgroups — C89×#35355 #36413203

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35355 #36413203