Subgroups — C₈₉×#24034 #36401882

Order 22784.

1380 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#550×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#482×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#416×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2041	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2041	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2034	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1869	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1865	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1788	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1788	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1788	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
19	#550×C₈₉	—	2	4	no	—
20	#550×C₈₉	—	2	4	no	—
21	C₂×#127×C₈₉	—	2	1	no	—
22	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#121×C₈₉	—	2	1	no	—
24	C₂×#121×C₈₉	—	2	1	no	—
25	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₈₉	—	2	1	no	—
29	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
31	#482×C₈₉	—	2	4	no	—
32	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
34	#416×C₈₉	—	2	4	no	—
35	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
50	#397×C₈₉	—	2	1	no	—
51	#394×C₈₉	—	2	1	no	—
52	#389×C₈₉	C₂²	1	1	yes	characteristic
53	#389×C₈₉	C₂²	1	1	yes	characteristic
54	#388×C₈₉	—	2	1	no	—
55	#387×C₈₉	—	2	1	no	—
56	#380×C₈₉	C₂²	1	1	yes	characteristic
57	#380×C₈₉	C₂²	1	1	yes	characteristic
58	#380×C₈₉	C₂²	1	1	yes	characteristic
59	#340×C₈₉	C₂²	1	1	yes	characteristic
60	#340×C₈₉	C₂²	1	1	yes	characteristic
61	#336×C₈₉	C₂²	1	1	yes	characteristic
62	#336×C₈₉	C₂²	1	1	yes	characteristic
63	C₂×#41×C₈₉	—	2	2	no	—
64	C₂×#41×C₈₉	—	2	2	no	—
65	C₂×#41×C₈₉	—	2	2	no	—
66	C₂×#41×C₈₉	—	2	2	no	—
67	C₂×#41×C₈₉	—	2	2	no	—
68	C₂×#41×C₈₉	—	2	2	no	—
69	C₂×#41×C₈₉	—	2	2	no	—
70	C₂×#41×C₈₉	—	4	1	no	—
71	C₂×#41×C₈₉	—	4	1	no	—
72	C₂×#41×C₈₉	—	4	1	no	—
73	C₂×#41×C₈₉	—	4	1	no	—
74	C₂×#41×C₈₉	D₄	1	4	yes	—
75	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₈₉	—	2	1	no	—
77	C₂²×D₄×C₈₉	—	2	1	no	—
78	C₂²×D₄×C₈₉	—	2	1	no	—
79	C₂²×D₄×C₈₉	—	2	1	no	—
80	C₂²×D₄×C₈₉	—	2	1	no	—
81	C₂²×D₄×C₈₉	—	2	1	no	—
82	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
83	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₈₉	—	2	1	no	—
86	C₂³×C₄×C₈₉	—	2	1	no	—
87	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₈₉	—	2	2	no	—
90	C₂²×C₈×C₈₉	—	4	1	no	—
91	C₂²×C₈×C₈₉	—	4	1	no	—
92	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
96	#127×C₈₉	—	2	8	no	—
97	#127×C₈₉	—	2	2	no	—
98	#127×C₈₉	—	2	2	no	—
99	#121×C₈₉	—	2	8	no	—
100	#121×C₈₉	—	2	8	no	—
101	#121×C₈₉	—	2	2	no	—
102	#121×C₈₉	—	2	2	no	—
103	#121×C₈₉	—	2	2	no	—
104	#121×C₈₉	D₄	1	4	yes	—
105	C₄×Q₈×C₈₉	—	2	2	no	—
106	C₄×Q₈×C₈₉	—	2	2	no	—
107	C₄×D₄×C₈₉	—	2	8	no	—
108	C₄×D₄×C₈₉	—	2	2	no	—
109	C₄×D₄×C₈₉	—	2	2	no	—
110	#117×C₈₉	—	2	2	no	—
111	#117×C₈₉	—	2	2	no	—
112	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
113	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
114	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
115	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
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	1	yes	characteristic
119	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
121	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
128	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
129	C₂×C₄²×C₈₉	—	2	1	no	—
130	C₂×C₄²×C₈₉	—	2	1	no	—
131	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
132	#107×C₈₉	—	2	2	no	—
133	#106×C₈₉	—	2	2	no	—
134	#103×C₈₉	—	2	2	no	—
135	#103×C₈₉	—	2	2	no	—
136	#103×C₈₉	—	2	2	no	—
137	#103×C₈₉	—	2	2	no	—
138	#102×C₈₉	—	2	2	no	—
139	#102×C₈₉	—	2	2	no	—
140	#102×C₈₉	—	2	2	no	—
141	#102×C₈₉	—	2	2	no	—
142	#102×C₈₉	—	4	1	no	—
143	#102×C₈₉	—	4	1	no	—
144	#102×C₈₉	—	4	1	no	—
145	#102×C₈₉	—	4	1	no	—
146	C₂²⋊C₈×C₈₉	—	2	2	no	—
147	C₂²⋊C₈×C₈₉	—	4	1	no	—
148	C₂²⋊C₈×C₈₉	—	4	1	no	—
149	#95×C₈₉	—	2	1	no	—
150	#95×C₈₉	—	2	1	no	—
151	#95×C₈₉	—	2	1	no	—
152	#95×C₈₉	—	2	1	no	—
153	#95×C₈₉	—	2	1	no	—
154	C₂⁴×C₈₉	—	2	1	no	—
155	C₂⁴×C₈₉	—	2	1	no	—
156	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
158	#41×C₈₉	—	2	8	no	—
159	#41×C₈₉	—	4	4	no	—
160	#41×C₈₉	—	4	4	no	—
161	#41×C₈₉	—	4	4	no	—
162	#41×C₈₉	—	4	4	no	—
163	#41×C₈₉	—	4	4	no	—
164	#41×C₈₉	—	4	4	no	—
165	#41×C₈₉	—	4	4	no	—
166	C₂×Q₈×C₈₉	—	2	1	no	—
167	C₂×Q₈×C₈₉	—	2	1	no	—
168	C₂×Q₈×C₈₉	—	2	1	no	—
169	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
170	C₂×Q₈×C₈₉	#41	1	2	yes	—
171	C₂×Q₈×C₈₉	#41	1	2	yes	—
172	C₂×D₄×C₈₉	—	2	4	no	—
173	C₂×D₄×C₈₉	—	2	4	no	—
174	C₂×D₄×C₈₉	—	2	2	no	—
175	C₂×D₄×C₈₉	—	2	4	no	—
176	C₂×D₄×C₈₉	—	2	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	1	no	—
181	C₂×D₄×C₈₉	—	2	1	no	—
182	C₂×D₄×C₈₉	—	2	1	no	—
183	C₂×D₄×C₈₉	—	2	1	no	—
184	C₂×D₄×C₈₉	—	2	1	no	—
185	C₂×D₄×C₈₉	—	2	1	no	—
186	C₂×D₄×C₈₉	—	2	1	no	—
187	C₂×D₄×C₈₉	—	2	1	no	—
188	C₂×D₄×C₈₉	—	2	1	no	—
189	C₂×D₄×C₈₉	—	2	1	no	—
190	C₂×D₄×C₈₉	—	4	1	no	—
191	C₂×D₄×C₈₉	—	4	2	no	—
192	C₂×D₄×C₈₉	—	4	2	no	—
193	C₂×D₄×C₈₉	—	4	2	no	—
194	C₂×D₄×C₈₉	—	4	2	no	—
195	C₂×D₄×C₈₉	—	4	2	no	—
196	C₂×D₄×C₈₉	—	4	2	no	—
197	C₂×D₄×C₈₉	—	8	1	no	—
198	C₂×D₄×C₈₉	—	8	1	no	—
199	C₂×D₄×C₈₉	—	8	1	no	—
200	C₂×D₄×C₈₉	—	8	1	no	—
201	C₂×D₄×C₈₉	—	8	1	no	—
202	C₂×D₄×C₈₉	—	8	1	no	—
203	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
204	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₈₉	—	2	1	no	—
206	C₂²×C₄×C₈₉	—	2	1	no	—
207	C₂²×C₄×C₈₉	—	2	1	no	—
208	C₂²×C₄×C₈₉	—	2	1	no	—
209	C₂²×C₄×C₈₉	—	2	1	no	—
210	C₂²×C₄×C₈₉	—	2	4	no	—
211	C₂²×C₄×C₈₉	—	2	1	no	—
212	C₂²×C₄×C₈₉	—	2	4	no	—
213	C₂²×C₄×C₈₉	—	2	1	no	—
214	C₂²×C₄×C₈₉	—	2	1	no	—
215	C₂²×C₄×C₈₉	—	2	1	no	—
216	C₂²×C₄×C₈₉	—	2	1	no	—
217	C₂²×C₄×C₈₉	—	2	1	no	—
218	C₂²×C₄×C₈₉	—	2	1	no	—
219	C₂²×C₄×C₈₉	—	2	1	no	—
220	C₂²×C₄×C₈₉	—	2	1	no	—
221	C₂²×C₄×C₈₉	—	2	1	no	—
222	C₂²×C₄×C₈₉	—	2	1	no	—
223	C₂²×C₄×C₈₉	—	4	2	no	—
224	C₂²×C₄×C₈₉	—	4	2	no	—
225	C₂²×C₄×C₈₉	—	4	2	no	—
226	C₂²×C₄×C₈₉	—	4	2	no	—
227	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
231	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
232	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
234	C₂×C₈×C₈₉	—	2	1	no	—
235	C₂×C₈×C₈₉	—	2	1	no	—
236	C₂×C₈×C₈₉	—	2	1	no	—
237	C₂×C₈×C₈₉	—	2	1	no	—
238	C₂×C₈×C₈₉	—	2	1	no	—
239	C₂×C₈×C₈₉	—	2	1	no	—
240	C₂×C₈×C₈₉	—	2	1	no	—
241	C₂×C₈×C₈₉	—	2	1	no	—
242	C₂×C₈×C₈₉	—	2	1	no	—
243	C₂×C₈×C₈₉	—	2	1	no	—
244	C₂×C₈×C₈₉	—	2	1	no	—
245	C₂×C₈×C₈₉	—	2	1	no	—
246	C₂×C₈×C₈₉	—	4	4	no	—
247	C₄⋊C₄×C₈₉	—	2	4	no	—
248	C₄⋊C₄×C₈₉	—	2	2	no	—
249	C₄⋊C₄×C₈₉	—	2	1	no	—
250	C₄⋊C₄×C₈₉	—	2	1	no	—
251	C₄⋊C₄×C₈₉	—	2	1	no	—
252	C₄⋊C₄×C₈₉	—	2	1	no	—
253	C₄⋊C₄×C₈₉	—	2	1	no	—
254	C₄⋊C₄×C₈₉	—	2	1	no	—
255	C₄⋊C₄×C₈₉	—	2	1	no	—
256	C₄⋊C₄×C₈₉	—	2	1	no	—
257	C₄⋊C₄×C₈₉	—	2	1	no	—
258	C₄⋊C₄×C₈₉	—	4	2	no	—
259	C₄⋊C₄×C₈₉	—	8	1	no	—
260	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
261	C₂²⋊C₄×C₈₉	—	2	4	no	—
262	C₂²⋊C₄×C₈₉	—	2	2	no	—
263	C₂²⋊C₄×C₈₉	—	2	4	no	—
264	C₂²⋊C₄×C₈₉	—	2	2	no	—
265	C₂²⋊C₄×C₈₉	—	4	2	no	—
266	C₂²⋊C₄×C₈₉	—	4	2	no	—
267	C₂²⋊C₄×C₈₉	—	8	1	no	—
268	C₂²⋊C₄×C₈₉	—	8	1	no	—
269	C₄²×C₈₉	—	2	4	no	—
270	C₄²×C₈₉	—	2	1	no	—
271	C₄²×C₈₉	—	2	1	no	—
272	C₄²×C₈₉	—	4	2	no	—
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	2	no	—
281	C₂³×C₈₉	—	2	2	no	—
282	C₂³×C₈₉	—	2	1	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	—	4	1	no	—
289	C₂³×C₈₉	—	4	1	no	—
290	C₂³×C₈₉	—	4	1	no	—
291	C₂³×C₈₉	—	4	1	no	—
292	C₂³×C₈₉	—	4	1	no	—
293	C₂³×C₈₉	—	4	1	no	—
294	C₂³×C₈₉	—	4	1	no	—
295	C₂³×C₈₉	—	4	1	no	—
296	C₂³×C₈₉	—	4	1	no	—
297	C₂³×C₈₉	—	4	1	no	—
298	C₂³×C₈₉	—	4	1	no	—
299	C₂³×C₈₉	—	4	1	no	—
300	C₂³×C₈₉	#120	1	2	yes	—
301	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
302	Q₈×C₈₉	—	2	2	no	—
303	Q₈×C₈₉	—	2	2	no	—
304	Q₈×C₈₉	—	2	2	no	—
305	Q₈×C₈₉	#123	1	4	yes	—
306	D₄×C₈₉	—	2	2	no	—
307	D₄×C₈₉	—	2	2	no	—
308	D₄×C₈₉	—	2	2	no	—
309	D₄×C₈₉	—	2	2	no	—
310	D₄×C₈₉	—	4	4	no	—
311	D₄×C₈₉	—	4	8	no	—
312	D₄×C₈₉	—	4	8	no	—
313	D₄×C₈₉	—	4	8	no	—
314	D₄×C₈₉	—	4	1	no	—
315	D₄×C₈₉	—	4	1	no	—
316	D₄×C₈₉	—	4	1	no	—
317	D₄×C₈₉	—	4	1	no	—
318	D₄×C₈₉	—	8	4	no	—
319	D₄×C₈₉	—	8	4	no	—
320	D₄×C₈₉	—	8	4	no	—
321	C₂×C₄×C₈₉	—	2	1	no	—
322	C₂×C₄×C₈₉	—	2	2	no	—
323	C₂×C₄×C₈₉	—	2	1	no	—
324	C₂×C₄×C₈₉	—	2	1	no	—
325	C₂×C₄×C₈₉	—	2	2	no	—
326	C₂×C₄×C₈₉	—	2	2	no	—
327	C₂×C₄×C₈₉	—	2	1	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	1	no	—
333	C₂×C₄×C₈₉	—	2	2	no	—
334	C₂×C₄×C₈₉	—	2	1	no	—
335	C₂×C₄×C₈₉	—	2	1	no	—
336	C₂×C₄×C₈₉	—	2	1	no	—
337	C₂×C₄×C₈₉	—	2	1	no	—
338	C₂×C₄×C₈₉	—	2	1	no	—
339	C₂×C₄×C₈₉	—	4	8	no	—
340	C₂×C₄×C₈₉	—	4	8	no	—
341	C₂×C₄×C₈₉	—	4	1	no	—
342	C₂×C₄×C₈₉	—	4	1	no	—
343	C₂×C₄×C₈₉	—	4	1	no	—
344	C₂×C₄×C₈₉	—	4	1	no	—
345	C₂×C₄×C₈₉	—	4	1	no	—
346	C₂×C₄×C₈₉	—	4	1	no	—
347	C₂×C₄×C₈₉	—	4	1	no	—
348	C₂×C₄×C₈₉	—	4	1	no	—
349	C₂×C₄×C₈₉	—	4	1	no	—
350	C₂×C₄×C₈₉	—	4	1	no	—
351	C₂×C₄×C₈₉	—	4	1	no	—
352	C₂×C₄×C₈₉	—	4	1	no	—
353	C₂×C₄×C₈₉	—	4	1	no	—
354	C₂×C₄×C₈₉	—	4	1	no	—
355	C₂×C₄×C₈₉	—	4	1	no	—
356	C₂×C₄×C₈₉	—	4	1	no	—
357	C₂×C₄×C₈₉	—	4	1	no	—
358	C₂×C₄×C₈₉	—	4	1	no	—
359	C₂×C₄×C₈₉	#120	1	2	yes	—
360	C₂×C₄×C₈₉	#135	1	2	yes	—
361	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
364	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
365	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
366	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
367	C₈×C₈₉	—	4	1	no	—
368	C₈×C₈₉	—	4	1	no	—
369	C₈×C₈₉	—	4	1	no	—
370	C₈×C₈₉	—	4	1	no	—
371	C₂²×C₈₉	—	2	2	no	—
372	C₂²×C₈₉	—	2	2	no	—
373	C₂²×C₈₉	—	2	2	no	—
374	C₂²×C₈₉	—	4	1	no	—
375	C₂²×C₈₉	—	4	1	no	—
376	C₂²×C₈₉	—	4	1	no	—
377	C₂²×C₈₉	—	4	1	no	—
378	C₂²×C₈₉	—	4	2	no	—
379	C₂²×C₈₉	—	4	2	no	—
380	C₂²×C₈₉	—	4	1	no	—
381	C₂²×C₈₉	—	4	1	no	—
382	C₂²×C₈₉	—	4	2	no	—
383	C₂²×C₈₉	—	4	2	no	—
384	C₂²×C₈₉	—	4	1	no	—
385	C₂²×C₈₉	—	4	2	no	—
386	C₂²×C₈₉	—	4	2	no	—
387	C₂²×C₈₉	—	4	1	no	—
388	C₂²×C₈₉	—	4	1	no	—
389	C₂²×C₈₉	—	4	1	no	—
390	C₂²×C₈₉	—	4	1	no	—
391	C₂²×C₈₉	—	8	1	no	—
392	C₂²×C₈₉	—	8	1	no	—
393	C₂²×C₈₉	—	8	1	no	—
394	C₂²×C₈₉	—	8	1	no	—
395	C₂²×C₈₉	—	8	1	no	—
396	C₂²×C₈₉	—	8	1	no	—
397	C₂²×C₈₉	—	8	1	no	—
398	C₂²×C₈₉	—	8	1	no	—
399	C₂²×C₈₉	C₂×#120	1	1	yes	characteristic
400	C₂²×C₈₉	#546	1	1	yes	characteristic
401	C₂²×C₈₉	#546	1	1	yes	characteristic
402	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
403	C₂²×C₈₉	#575	1	1	yes	characteristic
404	C₂²×C₈₉	#576	1	1	yes	characteristic
405	C₂²×C₈₉	#577	1	1	yes	characteristic
406	C₄×C₈₉	—	2	2	no	—
407	C₄×C₈₉	—	2	4	no	—
408	C₄×C₈₉	—	2	2	no	—
409	C₄×C₈₉	—	4	1	no	—
410	C₄×C₈₉	—	4	1	no	—
411	C₄×C₈₉	—	4	2	no	—
412	C₄×C₈₉	—	8	1	no	—
413	C₄×C₈₉	—	8	1	no	—
414	C₄×C₈₉	—	8	1	no	—
415	C₄×C₈₉	—	8	1	no	—
416	C₄×C₈₉	C₂×#123	1	1	yes	characteristic
417	C₄×C₈₉	#534	1	1	yes	characteristic
418	C₄×C₈₉	#546	1	1	yes	characteristic
419	C₄×C₈₉	#546	1	1	yes	characteristic
420	#24034	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
421	C₂×C₈₉	—	4	2	no	—
422	C₂×C₈₉	—	8	1	no	—
423	C₂×C₈₉	—	8	2	no	—
424	C₂×C₈₉	—	8	2	no	—
425	C₂×C₈₉	#2405	1	1	yes	characteristic
426	C₂×C₈₉	#3002	1	1	yes	characteristic
427	C₂×C₈₉	#3012	1	1	yes	characteristic
428	C₂×C₈₉	#3304	1	1	yes	characteristic
429	C₂×C₈₉	#3305	1	1	yes	characteristic
430	C₂×C₈₉	#3309	1	1	yes	characteristic
431	C₂×C₈₉	#3317	1	1	yes	characteristic
432	C₂×#550	C₂×C₈₉	1	1	yes	characteristic
433	C₂×#482	C₂×C₈₉	1	1	yes	characteristic, complemented
434	C₂×#416	C₂×C₈₉	1	1	yes	characteristic, complemented
435	#2485	C₂×C₈₉	1	1	yes	characteristic, complemented
436	#2041	C₂×C₈₉	1	1	yes	characteristic, complemented
437	#2041	C₂×C₈₉	1	1	yes	characteristic, complemented
438	#2034	C₂×C₈₉	1	1	yes	characteristic, complemented
439	#2033	C₂×C₈₉	1	1	yes	characteristic, complemented
440	#1893	C₂×C₈₉	1	1	yes	characteristic, complemented
441	#1869	C₂×C₈₉	1	1	yes	characteristic, complemented
442	#1865	C₂×C₈₉	1	1	yes	characteristic, complemented
443	#1863	C₂×C₈₉	1	1	yes	characteristic, complemented
444	#1788	C₂×C₈₉	1	1	yes	characteristic, complemented
445	#1788	C₂×C₈₉	1	1	yes	characteristic, complemented
446	#1788	C₂×C₈₉	1	1	yes	characteristic, complemented
447	C₈₉	#24034	1	1	yes	characteristic, direct product factor, Sylow
448	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
449	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
450	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
451	#550	—	2	4	no	—
452	#550	—	2	4	no	—
453	C₂×#127	—	2	1	no	—
454	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
455	C₂×#121	—	2	1	no	—
456	C₂×#121	—	2	1	no	—
457	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
458	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
459	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
460	C₂×C₄×D₄	—	2	1	no	—
461	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
462	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
463	#482	—	2	4	no	—
464	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
465	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
466	#416	—	2	4	no	—
467	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
468	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
469	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
470	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
471	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
472	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
473	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
474	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
475	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
476	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
477	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
478	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
479	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
480	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
481	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
482	#397	—	2	1	no	—
483	#394	—	2	1	no	—
484	#389	C₂²×C₈₉	1	1	yes	characteristic
485	#389	C₂²×C₈₉	1	1	yes	characteristic
486	#388	—	2	1	no	—
487	#387	—	2	1	no	—
488	#380	C₂²×C₈₉	1	1	yes	characteristic
489	#380	C₂²×C₈₉	1	1	yes	characteristic
490	#380	C₂²×C₈₉	1	1	yes	characteristic
491	#340	C₂²×C₈₉	1	1	yes	characteristic
492	#340	C₂²×C₈₉	1	1	yes	characteristic
493	#336	C₂²×C₈₉	1	1	yes	characteristic
494	#336	C₂²×C₈₉	1	1	yes	characteristic
495	C₂×#41	—	2	2	no	—
496	C₂×#41	—	2	2	no	—
497	C₂×#41	—	2	2	no	—
498	C₂×#41	—	2	2	no	—
499	C₂×#41	—	2	2	no	—
500	C₂×#41	—	2	2	no	—
501	C₂×#41	—	2	2	no	—
502	C₂×#41	—	4	1	no	—
503	C₂×#41	—	4	1	no	—
504	C₂×#41	—	4	1	no	—
505	C₂×#41	—	4	1	no	—
506	C₂×#41	D₄×C₈₉	1	4	yes	—
507	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
508	C₂²×D₄	—	2	1	no	—
509	C₂²×D₄	—	2	1	no	—
510	C₂²×D₄	—	2	1	no	—
511	C₂²×D₄	—	2	1	no	—
512	C₂²×D₄	—	2	1	no	—
513	C₂²×D₄	—	2	1	no	—
514	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
515	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
516	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
517	C₂³×C₄	—	2	1	no	—
518	C₂³×C₄	—	2	1	no	—
519	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
521	C₂²×C₈	—	2	2	no	—
522	C₂²×C₈	—	4	1	no	—
523	C₂²×C₈	—	4	1	no	—
524	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
525	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
526	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
527	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
528	#127	—	2	8	no	—
529	#127	—	2	2	no	—
530	#127	—	2	2	no	—
531	#121	—	2	8	no	—
532	#121	—	2	8	no	—
533	#121	—	2	2	no	—
534	#121	—	2	2	no	—
535	#121	—	2	2	no	—
536	#121	D₄×C₈₉	1	4	yes	—
537	C₄×Q₈	—	2	2	no	—
538	C₄×Q₈	—	2	2	no	—
539	C₄×D₄	—	2	8	no	—
540	C₄×D₄	—	2	2	no	—
541	C₄×D₄	—	2	2	no	—
542	#117	—	2	2	no	—
543	#117	—	2	2	no	—
544	C₂×C₄⋊C₄	—	2	1	no	—
545	C₂×C₄⋊C₄	—	2	1	no	—
546	C₂×C₄⋊C₄	—	2	1	no	—
547	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
551	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	C₂×C₂²⋊C₄	—	2	1	no	—
555	C₂×C₂²⋊C₄	—	2	1	no	—
556	C₂×C₂²⋊C₄	—	2	1	no	—
557	C₂×C₂²⋊C₄	—	2	1	no	—
558	C₂×C₂²⋊C₄	—	2	1	no	—
559	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
560	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
561	C₂×C₄²	—	2	1	no	—
562	C₂×C₄²	—	2	1	no	—
563	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
564	#107	—	2	2	no	—
565	#106	—	2	2	no	—
566	#103	—	2	2	no	—
567	#103	—	2	2	no	—
568	#103	—	2	2	no	—
569	#103	—	2	2	no	—
570	#102	—	2	2	no	—
571	#102	—	2	2	no	—
572	#102	—	2	2	no	—
573	#102	—	2	2	no	—
574	#102	—	4	1	no	—
575	#102	—	4	1	no	—
576	#102	—	4	1	no	—
577	#102	—	4	1	no	—
578	C₂²⋊C₈	—	2	2	no	—
579	C₂²⋊C₈	—	4	1	no	—
580	C₂²⋊C₈	—	4	1	no	—
581	#95	—	2	1	no	—
582	#95	—	2	1	no	—
583	#95	—	2	1	no	—
584	#95	—	2	1	no	—
585	#95	—	2	1	no	—
586	C₂⁴	—	2	1	no	—
587	C₂⁴	—	2	1	no	—
588	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
589	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
590	#41	—	2	8	no	—
591	#41	—	4	4	no	—
592	#41	—	4	4	no	—
593	#41	—	4	4	no	—
594	#41	—	4	4	no	—
595	#41	—	4	4	no	—
596	#41	—	4	4	no	—
597	#41	—	4	4	no	—
598	C₂×Q₈	—	2	1	no	—
599	C₂×Q₈	—	2	1	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
602	C₂×Q₈	#41×C₈₉	1	2	yes	—
603	C₂×Q₈	#41×C₈₉	1	2	yes	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	2	no	—
607	C₂×D₄	—	2	4	no	—
608	C₂×D₄	—	2	4	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	2	no	—
612	C₂×D₄	—	2	1	no	—
613	C₂×D₄	—	2	1	no	—
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	4	1	no	—
623	C₂×D₄	—	4	2	no	—
624	C₂×D₄	—	4	2	no	—
625	C₂×D₄	—	4	2	no	—
626	C₂×D₄	—	4	2	no	—
627	C₂×D₄	—	4	2	no	—
628	C₂×D₄	—	4	2	no	—
629	C₂×D₄	—	8	1	no	—
630	C₂×D₄	—	8	1	no	—
631	C₂×D₄	—	8	1	no	—
632	C₂×D₄	—	8	1	no	—
633	C₂×D₄	—	8	1	no	—
634	C₂×D₄	—	8	1	no	—
635	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
636	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	4	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	4	2	no	—
656	C₂²×C₄	—	4	2	no	—
657	C₂²×C₄	—	4	2	no	—
658	C₂²×C₄	—	4	2	no	—
659	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
660	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
661	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
662	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
663	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
664	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
665	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
666	C₂×C₈	—	2	1	no	—
667	C₂×C₈	—	2	1	no	—
668	C₂×C₈	—	2	1	no	—
669	C₂×C₈	—	2	1	no	—
670	C₂×C₈	—	2	1	no	—
671	C₂×C₈	—	2	1	no	—
672	C₂×C₈	—	2	1	no	—
673	C₂×C₈	—	2	1	no	—
674	C₂×C₈	—	2	1	no	—
675	C₂×C₈	—	2	1	no	—
676	C₂×C₈	—	2	1	no	—
677	C₂×C₈	—	2	1	no	—
678	C₂×C₈	—	4	4	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	4	2	no	—
691	C₄⋊C₄	—	8	1	no	—
692	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₂²⋊C₄	—	4	2	no	—
698	C₂²⋊C₄	—	4	2	no	—
699	C₂²⋊C₄	—	8	1	no	—
700	C₂²⋊C₄	—	8	1	no	—
701	C₄²	—	2	4	no	—
702	C₄²	—	2	1	no	—
703	C₄²	—	2	1	no	—
704	C₄²	—	4	2	no	—
705	C₂³	—	2	1	no	—
706	C₂³	—	2	1	no	—
707	C₂³	—	2	1	no	—
708	C₂³	—	2	1	no	—
709	C₂³	—	2	1	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	1	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	1	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	4	1	no	—
721	C₂³	—	4	1	no	—
722	C₂³	—	4	1	no	—
723	C₂³	—	4	1	no	—
724	C₂³	—	4	1	no	—
725	C₂³	—	4	1	no	—
726	C₂³	—	4	1	no	—
727	C₂³	—	4	1	no	—
728	C₂³	—	4	1	no	—
729	C₂³	—	4	1	no	—
730	C₂³	—	4	1	no	—
731	C₂³	—	4	1	no	—
732	C₂³	#120×C₈₉	1	2	yes	—
733	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
734	Q₈	—	2	2	no	—
735	Q₈	—	2	2	no	—
736	Q₈	—	2	2	no	—
737	Q₈	#123×C₈₉	1	4	yes	—
738	D₄	—	2	2	no	—
739	D₄	—	2	2	no	—
740	D₄	—	2	2	no	—
741	D₄	—	2	2	no	—
742	D₄	—	4	4	no	—
743	D₄	—	4	8	no	—
744	D₄	—	4	8	no	—
745	D₄	—	4	8	no	—
746	D₄	—	4	1	no	—
747	D₄	—	4	1	no	—
748	D₄	—	4	1	no	—
749	D₄	—	4	1	no	—
750	D₄	—	8	4	no	—
751	D₄	—	8	4	no	—
752	D₄	—	8	4	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	4	8	no	—
772	C₂×C₄	—	4	8	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	#120×C₈₉	1	2	yes	—
792	C₂×C₄	#135×C₈₉	1	2	yes	—
793	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
794	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
795	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
796	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
797	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
798	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
799	C₈	—	4	1	no	—
800	C₈	—	4	1	no	—
801	C₈	—	4	1	no	—
802	C₈	—	4	1	no	—
803	C₂²	—	2	2	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	2	2	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	1	no	—
813	C₂²	—	4	1	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	1	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	1	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	1	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	8	1	no	—
824	C₂²	—	8	1	no	—
825	C₂²	—	8	1	no	—
826	C₂²	—	8	1	no	—
827	C₂²	—	8	1	no	—
828	C₂²	—	8	1	no	—
829	C₂²	—	8	1	no	—
830	C₂²	—	8	1	no	—
831	C₂²	C₂×#120×C₈₉	1	1	yes	characteristic
832	C₂²	#546×C₈₉	1	1	yes	characteristic
833	C₂²	#546×C₈₉	1	1	yes	characteristic
834	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
835	C₂²	#575×C₈₉	1	1	yes	characteristic
836	C₂²	#576×C₈₉	1	1	yes	characteristic
837	C₂²	#577×C₈₉	1	1	yes	characteristic
838	C₄	—	2	2	no	—
839	C₄	—	2	4	no	—
840	C₄	—	2	2	no	—
841	C₄	—	4	1	no	—
842	C₄	—	4	1	no	—
843	C₄	—	4	2	no	—
844	C₄	—	8	1	no	—
845	C₄	—	8	1	no	—
846	C₄	—	8	1	no	—
847	C₄	—	8	1	no	—
848	C₄	C₂×#123×C₈₉	1	1	yes	characteristic
849	C₄	#534×C₈₉	1	1	yes	characteristic
850	C₄	#546×C₈₉	1	1	yes	characteristic
851	C₄	#546×C₈₉	1	1	yes	characteristic
852	C₂	—	4	2	no	—
853	C₂	—	8	1	no	—
854	C₂	—	8	2	no	—
855	C₂	—	8	2	no	—
856	C₂	C₈₉×#2405	1	1	yes	characteristic
857	C₂	C₈₉×#3002	1	1	yes	characteristic
858	C₂	C₈₉×#3012	1	1	yes	characteristic
859	C₂	C₈₉×#3304	1	1	yes	characteristic
860	C₂	C₈₉×#3305	1	1	yes	characteristic
861	C₂	C₈₉×#3309	1	1	yes	characteristic
862	C₂	C₈₉×#3317	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂×#550×C₈₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×C₄×D₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#482×C₈₉	C₂	semidirect
3. C₂×#416×C₈₉	C₂	semidirect
4. C₈₉×#2485	C₂	semidirect
5. C₈₉×#2041	C₂	semidirect
6. C₈₉×#2041	C₂	semidirect
7. C₈₉×#2034	C₂	semidirect
8. C₈₉×#2033	C₂	semidirect
9. C₈₉×#1893	C₂	semidirect
10. C₈₉×#1869	C₂	semidirect
11. C₈₉×#1865	C₂	semidirect
12. C₈₉×#1863	C₂	semidirect
13. C₈₉×#1788	C₂	semidirect
14. C₈₉×#1788	C₂	semidirect
15. C₈₉×#1788	C₂	semidirect
420. #24034	C₈₉	direct (N × H)
433. C₂×#482	C₂×C₈₉	semidirect
434. C₂×#416	C₂×C₈₉	semidirect
435. #2485	C₂×C₈₉	semidirect
436. #2041	C₂×C₈₉	semidirect
437. #2041	C₂×C₈₉	semidirect
438. #2034	C₂×C₈₉	semidirect
439. #2033	C₂×C₈₉	semidirect
440. #1893	C₂×C₈₉	semidirect
441. #1869	C₂×C₈₉	semidirect
442. #1865	C₂×C₈₉	semidirect
443. #1863	C₂×C₈₉	semidirect
444. #1788	C₂×C₈₉	semidirect
445. #1788	C₂×C₈₉	semidirect
446. #1788	C₂×C₈₉	semidirect
447. C₈₉	#24034	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#550×C₈₉	2
C₂×#482×C₈₉	2
C₂×#416×C₈₉	2
C₈₉×#2485	2
C₈₉×#2041	2
C₈₉×#2034	2
C₈₉×#2033	2
C₈₉×#1893	2
C₈₉×#1869	2
C₈₉×#1865	2
C₈₉×#1863	2
C₈₉×#1788	2
#24034	89

Subgroups — C89×#24034 #36401882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#24034 #36401882