Subgroups — C₂×C₈₉×#1881 #36398786

Order 22784.

1682 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#568×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#421×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#416×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#408×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#1881	C₂	1	8	yes	maximal, direct product factor
7	C₂×#344×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#341×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
10	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
11	#575×C₈₉	—	2	2	no	—
12	#575×C₈₉	—	2	2	no	—
13	#575×C₈₉	C₄	1	4	yes	complemented
14	#575×C₈₉	C₂²	1	4	yes	—
15	C₂×#137×C₈₉	—	2	1	no	—
16	C₂×#137×C₈₉	C₄	1	2	yes	complemented
17	C₂×AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
18	C₂×AGL(1,ℤ/8)×C₈₉	C₄	1	2	yes	complemented
19	C₂×#135×C₈₉	—	2	2	no	—
20	#568×C₈₉	—	2	2	no	—
21	#568×C₈₉	—	2	2	no	—
22	#568×C₈₉	—	2	2	no	—
23	#568×C₈₉	C₂²	1	4	yes	complemented
24	C₂×#131×C₈₉	—	2	2	no	—
25	C₂×#131×C₈₉	—	2	2	no	—
26	C₂²×M₁₆×C₈₉	—	2	2	no	—
27	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
28	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
29	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
30	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
32	#421×C₈₉	—	2	2	no	—
33	#421×C₈₉	C₂²	1	4	yes	complemented
34	C₂×#104×C₈₉	—	2	2	no	—
35	#416×C₈₉	—	2	2	no	—
36	#416×C₈₉	C₂²	1	4	yes	complemented
37	C₂×#103×C₈₉	—	2	1	no	—
38	C₂×#102×C₈₉	—	2	1	no	—
39	#408×C₈₉	—	2	2	no	—
40	#408×C₈₉	C₂²	1	4	yes	complemented
41	C₂×C₂²⋊C₈×C₈₉	—	2	2	no	—
42	#344×C₈₉	C₂²	1	4	yes	complemented
43	#341×C₈₉	C₂²	1	4	yes	complemented
44	C₂×#41×C₈₉	—	2	1	no	—
45	C₂×#41×C₈₉	—	2	1	no	—
46	C₂×#41×C₈₉	—	2	1	no	—
47	C₂×#41×C₈₉	—	2	1	no	—
48	C₂×#41×C₈₉	—	2	1	no	—
49	C₂×#41×C₈₉	—	2	1	no	—
50	C₂×#41×C₈₉	—	2	1	no	—
51	C₂×#41×C₈₉	—	2	1	no	—
52	C₂×#41×C₈₉	—	2	1	no	—
53	C₂×#41×C₈₉	—	2	1	no	—
54	C₂×#41×C₈₉	—	2	1	no	—
55	C₂×#41×C₈₉	—	2	1	no	—
56	C₂×#41×C₈₉	—	2	1	no	—
57	C₂×#41×C₈₉	—	2	1	no	—
58	C₂×#41×C₈₉	—	2	1	no	—
59	C₂×#41×C₈₉	—	2	1	no	—
60	C₂×#41×C₈₉	C₂×C₄	1	2	yes	—
61	C₂×#41×C₈₉	C₂×C₄	1	2	yes	—
62	C₂×#41×C₈₉	C₂×C₄	1	2	yes	—
63	C₂×#41×C₈₉	D₄	1	2	yes	—
64	C₂×#41×C₈₉	D₄	1	2	yes	—
65	C₂×#41×C₈₉	D₄	1	2	yes	—
66	C₂×#41×C₈₉	C₂³	1	2	yes	—
67	C₂×#41×C₈₉	C₂³	1	2	yes	—
68	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
69	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
70	C₂²×D₄×C₈₉	—	2	1	no	—
71	C₂²×D₄×C₈₉	—	2	1	no	—
72	C₂²×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
73	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
74	C₂³×C₄×C₈₉	—	2	1	no	—
75	C₂³×C₄×C₈₉	—	2	1	no	—
76	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
77	#137×C₈₉	—	2	4	no	—
78	#137×C₈₉	—	2	4	no	—
79	#137×C₈₉	—	2	4	no	—
80	#137×C₈₉	C₂×C₄	1	8	yes	complemented
81	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
82	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
83	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
84	AGL(1,ℤ/8)×C₈₉	C₂×C₄	1	8	yes	complemented
85	#135×C₈₉	—	2	8	no	—
86	#135×C₈₉	—	2	8	no	—
87	C₂×Q₁₆×C₈₉	—	2	2	no	—
88	C₂×SD₁₆×C₈₉	—	2	2	no	—
89	C₂×SD₁₆×C₈₉	—	2	2	no	—
90	C₂×D₈×C₈₉	—	2	2	no	—
91	#131×C₈₉	—	2	8	no	—
92	#131×C₈₉	—	2	8	no	—
93	#131×C₈₉	—	2	8	no	—
94	#131×C₈₉	—	2	8	no	—
95	C₂×M₁₆×C₈₉	—	2	4	no	—
96	C₂×M₁₆×C₈₉	—	2	8	no	—
97	C₂×M₁₆×C₈₉	—	2	1	no	—
98	C₂×M₁₆×C₈₉	—	2	1	no	—
99	C₂×M₁₆×C₈₉	—	2	1	no	—
100	C₂×M₁₆×C₈₉	—	2	1	no	—
101	C₂×M₁₆×C₈₉	—	2	1	no	—
102	C₂×M₁₆×C₈₉	—	2	1	no	—
103	C₂×M₁₆×C₈₉	—	2	1	no	—
104	C₂×M₁₆×C₈₉	—	2	1	no	—
105	C₂×M₁₆×C₈₉	—	2	1	no	—
106	C₂×M₁₆×C₈₉	—	2	1	no	—
107	C₂×M₁₆×C₈₉	—	2	8	no	—
108	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
109	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
110	C₂×M₁₆×C₈₉	D₄	1	2	yes	—
111	C₂×M₁₆×C₈₉	D₄	1	2	yes	—
112	C₂×M₁₆×C₈₉	D₄	1	2	yes	—
113	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
114	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
115	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
116	C₂²×C₈×C₈₉	—	2	4	no	—
117	C₂²×C₈×C₈₉	—	2	1	no	—
118	C₂²×C₈×C₈₉	—	2	1	no	—
119	C₂²×C₈×C₈₉	—	2	1	no	—
120	C₂²×C₈×C₈₉	—	2	1	no	—
121	C₂²×C₈×C₈₉	—	2	1	no	—
122	C₂²×C₈×C₈₉	—	2	1	no	—
123	C₂²×C₈×C₈₉	—	2	1	no	—
124	C₂²×C₈×C₈₉	—	2	1	no	—
125	C₂²×C₈×C₈₉	D₄	1	2	yes	—
126	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
127	#117×C₈₉	—	2	1	no	—
128	#117×C₈₉	—	2	1	no	—
129	#117×C₈₉	—	2	1	no	—
130	#117×C₈₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
133	C₂×C₄²×C₈₉	—	2	1	no	—
134	#104×C₈₉	—	2	8	no	—
135	#103×C₈₉	—	2	4	no	—
136	#102×C₈₉	—	2	4	no	—
137	C₂²⋊C₈×C₈₉	—	2	8	no	—
138	C₂⁴×C₈₉	—	2	1	no	—
139	C₂⁴×C₈₉	—	2	1	no	—
140	C₂⁴×C₈₉	#41	1	1	yes	characteristic
141	#41×C₈₉	—	2	2	no	—
142	#41×C₈₉	—	2	2	no	—
143	#41×C₈₉	—	2	2	no	—
144	#41×C₈₉	—	2	2	no	—
145	#41×C₈₉	—	2	2	no	—
146	#41×C₈₉	—	2	2	no	—
147	#41×C₈₉	—	2	2	no	—
148	#41×C₈₉	—	2	2	no	—
149	#41×C₈₉	—	2	2	no	—
150	#41×C₈₉	—	2	2	no	—
151	#41×C₈₉	—	2	2	no	—
152	#41×C₈₉	—	2	2	no	—
153	#41×C₈₉	—	2	2	no	—
154	#41×C₈₉	—	2	2	no	—
155	#41×C₈₉	—	2	2	no	—
156	#41×C₈₉	—	2	2	no	—
157	#41×C₈₉	—	2	2	no	—
158	#41×C₈₉	—	2	2	no	—
159	#41×C₈₉	—	2	2	no	—
160	#41×C₈₉	—	2	2	no	—
161	#41×C₈₉	—	4	1	no	—
162	#41×C₈₉	—	4	1	no	—
163	#41×C₈₉	—	4	1	no	—
164	#41×C₈₉	—	4	1	no	—
165	#41×C₈₉	—	4	1	no	—
166	#41×C₈₉	—	4	1	no	—
167	#41×C₈₉	—	4	1	no	—
168	#41×C₈₉	—	4	1	no	—
169	#41×C₈₉	C₂²⋊C₄	1	4	yes	—
170	#41×C₈₉	C₂²⋊C₄	1	4	yes	—
171	#41×C₈₉	C₂²×C₄	1	4	yes	—
172	#41×C₈₉	C₂×D₄	1	4	yes	—
173	C₂×Q₈×C₈₉	—	2	1	no	—
174	C₂×Q₈×C₈₉	—	2	1	no	—
175	C₂×Q₈×C₈₉	—	2	1	no	—
176	C₂×Q₈×C₈₉	—	2	1	no	—
177	C₂×Q₈×C₈₉	—	2	1	no	—
178	C₂×Q₈×C₈₉	—	2	1	no	—
179	C₂×Q₈×C₈₉	—	2	1	no	—
180	C₂×Q₈×C₈₉	—	2	1	no	—
181	C₂×Q₈×C₈₉	C₂²⋊C₄	1	2	yes	—
182	C₂×Q₈×C₈₉	C₂²⋊C₄	1	2	yes	—
183	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
184	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
185	C₂×D₄×C₈₉	—	2	2	no	—
186	C₂×D₄×C₈₉	—	2	2	no	—
187	C₂×D₄×C₈₉	—	2	2	no	—
188	C₂×D₄×C₈₉	—	2	2	no	—
189	C₂×D₄×C₈₉	—	2	2	no	—
190	C₂×D₄×C₈₉	—	2	2	no	—
191	C₂×D₄×C₈₉	—	2	2	no	—
192	C₂×D₄×C₈₉	—	2	2	no	—
193	C₂×D₄×C₈₉	—	2	1	no	—
194	C₂×D₄×C₈₉	—	2	1	no	—
195	C₂×D₄×C₈₉	—	2	1	no	—
196	C₂×D₄×C₈₉	—	2	1	no	—
197	C₂×D₄×C₈₉	—	2	1	no	—
198	C₂×D₄×C₈₉	—	2	1	no	—
199	C₂×D₄×C₈₉	—	2	1	no	—
200	C₂×D₄×C₈₉	—	2	1	no	—
201	C₂×D₄×C₈₉	—	4	1	no	—
202	C₂×D₄×C₈₉	—	4	1	no	—
203	C₂×D₄×C₈₉	—	4	1	no	—
204	C₂×D₄×C₈₉	—	4	1	no	—
205	C₂×D₄×C₈₉	C₂²⋊C₄	1	2	yes	—
206	C₂×D₄×C₈₉	C₂²⋊C₄	1	2	yes	—
207	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
208	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
209	C₂²×C₄×C₈₉	—	2	1	no	—
210	C₂²×C₄×C₈₉	—	2	2	no	—
211	C₂²×C₄×C₈₉	—	2	2	no	—
212	C₂²×C₄×C₈₉	—	2	2	no	—
213	C₂²×C₄×C₈₉	—	2	2	no	—
214	C₂²×C₄×C₈₉	—	2	2	no	—
215	C₂²×C₄×C₈₉	—	2	2	no	—
216	C₂²×C₄×C₈₉	—	2	1	no	—
217	C₂²×C₄×C₈₉	—	2	2	no	—
218	C₂²×C₄×C₈₉	—	2	2	no	—
219	C₂²×C₄×C₈₉	—	4	1	no	—
220	C₂²×C₄×C₈₉	—	4	1	no	—
221	C₂²×C₄×C₈₉	—	4	1	no	—
222	C₂²×C₄×C₈₉	—	4	1	no	—
223	C₂²×C₄×C₈₉	—	4	1	no	—
224	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
225	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
226	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
231	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
235	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
236	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
237	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
238	Q₁₆×C₈₉	—	2	8	no	—
239	SD₁₆×C₈₉	—	2	8	no	—
240	SD₁₆×C₈₉	—	2	8	no	—
241	D₈×C₈₉	—	2	8	no	—
242	M₁₆×C₈₉	—	2	16	no	—
243	M₁₆×C₈₉	—	2	2	no	—
244	M₁₆×C₈₉	—	2	2	no	—
245	M₁₆×C₈₉	—	2	2	no	—
246	M₁₆×C₈₉	—	2	2	no	—
247	M₁₆×C₈₉	—	2	2	no	—
248	M₁₆×C₈₉	—	2	2	no	—
249	M₁₆×C₈₉	—	2	2	no	—
250	M₁₆×C₈₉	—	2	2	no	—
251	M₁₆×C₈₉	—	2	2	no	—
252	M₁₆×C₈₉	—	2	2	no	—
253	M₁₆×C₈₉	C₂²×C₄	1	4	yes	—
254	M₁₆×C₈₉	C₂×D₄	1	4	yes	—
255	C₂×C₈×C₈₉	—	2	16	no	—
256	C₂×C₈×C₈₉	—	2	2	no	—
257	C₂×C₈×C₈₉	—	2	2	no	—
258	C₂×C₈×C₈₉	—	2	2	no	—
259	C₂×C₈×C₈₉	—	2	2	no	—
260	C₂×C₈×C₈₉	—	2	2	no	—
261	C₂×C₈×C₈₉	—	2	2	no	—
262	C₂×C₈×C₈₉	—	2	2	no	—
263	C₂×C₈×C₈₉	—	2	2	no	—
264	C₂×C₈×C₈₉	—	2	2	no	—
265	C₂×C₈×C₈₉	—	2	2	no	—
266	C₂×C₈×C₈₉	—	2	2	no	—
267	C₂×C₈×C₈₉	—	4	1	no	—
268	C₂×C₈×C₈₉	—	4	1	no	—
269	C₂×C₈×C₈₉	—	4	1	no	—
270	C₂×C₈×C₈₉	—	4	1	no	—
271	C₂×C₈×C₈₉	C₂×D₄	1	4	yes	—
272	C₄⋊C₄×C₈₉	—	2	2	no	—
273	C₄⋊C₄×C₈₉	—	4	1	no	—
274	C₂²⋊C₄×C₈₉	—	2	2	no	—
275	C₂²⋊C₄×C₈₉	—	4	1	no	—
276	C₄²×C₈₉	—	2	2	no	—
277	C₄²×C₈₉	—	4	1	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	—	4	2	no	—
283	C₂³×C₈₉	—	4	4	no	—
284	C₂³×C₈₉	—	4	1	no	—
285	C₂³×C₈₉	—	4	1	no	—
286	C₂³×C₈₉	—	8	2	no	—
287	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
288	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
289	C₂³×C₈₉	#121	1	1	yes	characteristic
290	C₂³×C₈₉	#121	1	1	yes	characteristic
291	C₂³×C₈₉	#123	1	1	yes	characteristic
292	C₂³×C₈₉	#123	1	1	yes	characteristic
293	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
294	Q₈×C₈₉	—	2	2	no	—
295	Q₈×C₈₉	—	2	2	no	—
296	Q₈×C₈₉	—	2	2	no	—
297	Q₈×C₈₉	—	2	2	no	—
298	Q₈×C₈₉	—	2	2	no	—
299	Q₈×C₈₉	—	4	1	no	—
300	Q₈×C₈₉	—	4	1	no	—
301	Q₈×C₈₉	C₂×C₂²⋊C₄	1	4	yes	—
302	D₄×C₈₉	—	2	4	no	—
303	D₄×C₈₉	—	2	4	no	—
304	D₄×C₈₉	—	2	4	no	—
305	D₄×C₈₉	—	2	4	no	—
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	—	2	2	no	—
311	D₄×C₈₉	—	4	2	no	—
312	D₄×C₈₉	—	4	2	no	—
313	D₄×C₈₉	—	4	2	no	—
314	D₄×C₈₉	—	4	2	no	—
315	D₄×C₈₉	—	4	1	no	—
316	D₄×C₈₉	—	4	1	no	—
317	D₄×C₈₉	C₂×C₂²⋊C₄	1	4	yes	—
318	C₂×C₄×C₈₉	—	2	2	no	—
319	C₂×C₄×C₈₉	—	2	2	no	—
320	C₂×C₄×C₈₉	—	2	2	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	—	4	1	no	—
327	C₂×C₄×C₈₉	—	4	1	no	—
328	C₂×C₄×C₈₉	—	4	2	no	—
329	C₂×C₄×C₈₉	—	4	2	no	—
330	C₂×C₄×C₈₉	—	4	2	no	—
331	C₂×C₄×C₈₉	—	4	2	no	—
332	C₂×C₄×C₈₉	—	4	2	no	—
333	C₂×C₄×C₈₉	—	8	2	no	—
334	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
335	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
336	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
337	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
338	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
339	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
340	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
341	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
342	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
343	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
344	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
345	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
346	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
347	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
348	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
349	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
350	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
351	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
352	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
353	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
354	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
355	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
356	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
357	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
362	C₈×C₈₉	—	2	4	no	—
363	C₈×C₈₉	—	2	4	no	—
364	C₈×C₈₉	—	2	4	no	—
365	C₈×C₈₉	—	4	2	no	—
366	C₂²×C₈₉	—	2	2	no	—
367	C₂²×C₈₉	—	2	2	no	—
368	C₂²×C₈₉	—	2	2	no	—
369	C₂²×C₈₉	—	2	4	no	—
370	C₂²×C₈₉	—	4	1	no	—
371	C₂²×C₈₉	—	4	1	no	—
372	C₂²×C₈₉	—	4	1	no	—
373	C₂²×C₈₉	—	4	1	no	—
374	C₂²×C₈₉	—	4	4	no	—
375	C₂²×C₈₉	—	4	4	no	—
376	C₂²×C₈₉	—	4	2	no	—
377	C₂²×C₈₉	—	8	2	no	—
378	C₂²×C₈₉	—	8	2	no	—
379	C₂²×C₈₉	—	8	2	no	—
380	C₂²×C₈₉	—	8	2	no	—
381	C₂²×C₈₉	#386	1	1	yes	characteristic
382	C₂²×C₈₉	#386	1	1	yes	characteristic
383	C₂²×C₈₉	#386	1	1	yes	characteristic
384	C₂²×C₈₉	#386	1	1	yes	characteristic
385	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
386	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
387	C₂²×C₈₉	C₂×#123	1	1	yes	characteristic
388	C₄×C₈₉	—	2	4	no	—
389	C₄×C₈₉	—	4	2	no	—
390	C₄×C₈₉	—	8	2	no	—
391	C₄×C₈₉	#386	1	1	yes	characteristic
392	C₄×C₈₉	#386	1	1	yes	characteristic
393	C₄×C₈₉	#386	1	1	yes	characteristic
394	C₄×C₈₉	#386	1	1	yes	characteristic
395	C₄×C₈₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
396	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
397	C₄×C₈₉	C₂×#120	1	1	yes	characteristic
398	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
399	C₂×#1881	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
400	C₂×C₈₉	—	2	1	no	—
401	C₂×C₈₉	—	2	1	no	—
402	C₂×C₈₉	—	2	1	no	—
403	C₂×C₈₉	—	2	1	no	—
404	C₂×C₈₉	—	2	1	no	—
405	C₂×C₈₉	—	2	1	no	—
406	C₂×C₈₉	—	4	4	no	—
407	C₂×C₈₉	—	8	2	no	—
408	C₂×C₈₉	#1881	1	2	yes	direct product factor
409	C₂×C₈₉	C₂×#386	1	1	yes	characteristic
410	C₂×#575	C₂×C₈₉	1	1	yes	characteristic
411	C₂×#568	C₂×C₈₉	1	1	yes	characteristic, complemented
412	C₂×#421	C₂×C₈₉	1	1	yes	characteristic, complemented
413	C₂×#416	C₂×C₈₉	1	1	yes	characteristic, complemented
414	C₂×#408	C₂×C₈₉	1	1	yes	characteristic, complemented
415	#1881	C₂×C₈₉	1	8	yes	direct product factor
416	C₂×#344	C₂×C₈₉	1	1	yes	characteristic, complemented
417	C₂×#341	C₂×C₈₉	1	1	yes	characteristic, complemented
418	C₈₉	C₂×#1881	1	1	yes	characteristic, direct product factor, Sylow
419	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
420	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
421	#575	—	2	2	no	—
422	#575	—	2	2	no	—
423	#575	C₄×C₈₉	1	4	yes	complemented
424	#575	C₂²×C₈₉	1	4	yes	—
425	C₂×#137	—	2	1	no	—
426	C₂×#137	C₄×C₈₉	1	2	yes	complemented
427	C₂×AGL(1,ℤ/8)	—	2	1	no	—
428	C₂×AGL(1,ℤ/8)	C₄×C₈₉	1	2	yes	complemented
429	C₂×#135	—	2	2	no	—
430	#568	—	2	2	no	—
431	#568	—	2	2	no	—
432	#568	—	2	2	no	—
433	#568	C₂²×C₈₉	1	4	yes	complemented
434	C₂×#131	—	2	2	no	—
435	C₂×#131	—	2	2	no	—
436	C₂²×M₁₆	—	2	2	no	—
437	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
438	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
439	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
440	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
441	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
442	#421	—	2	2	no	—
443	#421	C₂²×C₈₉	1	4	yes	complemented
444	C₂×#104	—	2	2	no	—
445	#416	—	2	2	no	—
446	#416	C₂²×C₈₉	1	4	yes	complemented
447	C₂×#103	—	2	1	no	—
448	C₂×#102	—	2	1	no	—
449	#408	—	2	2	no	—
450	#408	C₂²×C₈₉	1	4	yes	complemented
451	C₂×C₂²⋊C₈	—	2	2	no	—
452	#344	C₂²×C₈₉	1	4	yes	complemented
453	#341	C₂²×C₈₉	1	4	yes	complemented
454	C₂×#41	—	2	1	no	—
455	C₂×#41	—	2	1	no	—
456	C₂×#41	—	2	1	no	—
457	C₂×#41	—	2	1	no	—
458	C₂×#41	—	2	1	no	—
459	C₂×#41	—	2	1	no	—
460	C₂×#41	—	2	1	no	—
461	C₂×#41	—	2	1	no	—
462	C₂×#41	—	2	1	no	—
463	C₂×#41	—	2	1	no	—
464	C₂×#41	—	2	1	no	—
465	C₂×#41	—	2	1	no	—
466	C₂×#41	—	2	1	no	—
467	C₂×#41	—	2	1	no	—
468	C₂×#41	—	2	1	no	—
469	C₂×#41	—	2	1	no	—
470	C₂×#41	C₂×C₄×C₈₉	1	2	yes	—
471	C₂×#41	C₂×C₄×C₈₉	1	2	yes	—
472	C₂×#41	C₂×C₄×C₈₉	1	2	yes	—
473	C₂×#41	D₄×C₈₉	1	2	yes	—
474	C₂×#41	D₄×C₈₉	1	2	yes	—
475	C₂×#41	D₄×C₈₉	1	2	yes	—
476	C₂×#41	C₂³×C₈₉	1	2	yes	—
477	C₂×#41	C₂³×C₈₉	1	2	yes	—
478	C₂²×Q₈	C₂×C₄×C₈₉	1	1	yes	characteristic
479	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
480	C₂²×D₄	—	2	1	no	—
481	C₂²×D₄	—	2	1	no	—
482	C₂²×D₄	C₂×C₄×C₈₉	1	1	yes	characteristic
483	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
484	C₂³×C₄	—	2	1	no	—
485	C₂³×C₄	—	2	1	no	—
486	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
487	#137	—	2	4	no	—
488	#137	—	2	4	no	—
489	#137	—	2	4	no	—
490	#137	C₂×C₄×C₈₉	1	8	yes	complemented
491	AGL(1,ℤ/8)	—	2	4	no	—
492	AGL(1,ℤ/8)	—	2	4	no	—
493	AGL(1,ℤ/8)	—	2	4	no	—
494	AGL(1,ℤ/8)	C₂×C₄×C₈₉	1	8	yes	complemented
495	#135	—	2	8	no	—
496	#135	—	2	8	no	—
497	C₂×Q₁₆	—	2	2	no	—
498	C₂×SD₁₆	—	2	2	no	—
499	C₂×SD₁₆	—	2	2	no	—
500	C₂×D₈	—	2	2	no	—
501	#131	—	2	8	no	—
502	#131	—	2	8	no	—
503	#131	—	2	8	no	—
504	#131	—	2	8	no	—
505	C₂×M₁₆	—	2	4	no	—
506	C₂×M₁₆	—	2	8	no	—
507	C₂×M₁₆	—	2	1	no	—
508	C₂×M₁₆	—	2	1	no	—
509	C₂×M₁₆	—	2	1	no	—
510	C₂×M₁₆	—	2	1	no	—
511	C₂×M₁₆	—	2	1	no	—
512	C₂×M₁₆	—	2	1	no	—
513	C₂×M₁₆	—	2	1	no	—
514	C₂×M₁₆	—	2	1	no	—
515	C₂×M₁₆	—	2	1	no	—
516	C₂×M₁₆	—	2	1	no	—
517	C₂×M₁₆	—	2	8	no	—
518	C₂×M₁₆	C₂×C₄×C₈₉	1	2	yes	—
519	C₂×M₁₆	C₂×C₄×C₈₉	1	2	yes	—
520	C₂×M₁₆	D₄×C₈₉	1	2	yes	—
521	C₂×M₁₆	D₄×C₈₉	1	2	yes	—
522	C₂×M₁₆	D₄×C₈₉	1	2	yes	—
523	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
524	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
525	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
526	C₂²×C₈	—	2	4	no	—
527	C₂²×C₈	—	2	1	no	—
528	C₂²×C₈	—	2	1	no	—
529	C₂²×C₈	—	2	1	no	—
530	C₂²×C₈	—	2	1	no	—
531	C₂²×C₈	—	2	1	no	—
532	C₂²×C₈	—	2	1	no	—
533	C₂²×C₈	—	2	1	no	—
534	C₂²×C₈	—	2	1	no	—
535	C₂²×C₈	D₄×C₈₉	1	2	yes	—
536	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
537	#117	—	2	1	no	—
538	#117	—	2	1	no	—
539	#117	—	2	1	no	—
540	#117	C₂³×C₈₉	1	2	yes	—
541	C₂×C₄⋊C₄	—	2	1	no	—
542	C₂×C₂²⋊C₄	—	2	1	no	—
543	C₂×C₄²	—	2	1	no	—
544	#104	—	2	8	no	—
545	#103	—	2	4	no	—
546	#102	—	2	4	no	—
547	C₂²⋊C₈	—	2	8	no	—
548	C₂⁴	—	2	1	no	—
549	C₂⁴	—	2	1	no	—
550	C₂⁴	#41×C₈₉	1	1	yes	characteristic
551	#41	—	2	2	no	—
552	#41	—	2	2	no	—
553	#41	—	2	2	no	—
554	#41	—	2	2	no	—
555	#41	—	2	2	no	—
556	#41	—	2	2	no	—
557	#41	—	2	2	no	—
558	#41	—	2	2	no	—
559	#41	—	2	2	no	—
560	#41	—	2	2	no	—
561	#41	—	2	2	no	—
562	#41	—	2	2	no	—
563	#41	—	2	2	no	—
564	#41	—	2	2	no	—
565	#41	—	2	2	no	—
566	#41	—	2	2	no	—
567	#41	—	2	2	no	—
568	#41	—	2	2	no	—
569	#41	—	2	2	no	—
570	#41	—	2	2	no	—
571	#41	—	4	1	no	—
572	#41	—	4	1	no	—
573	#41	—	4	1	no	—
574	#41	—	4	1	no	—
575	#41	—	4	1	no	—
576	#41	—	4	1	no	—
577	#41	—	4	1	no	—
578	#41	—	4	1	no	—
579	#41	C₂²⋊C₄×C₈₉	1	4	yes	—
580	#41	C₂²⋊C₄×C₈₉	1	4	yes	—
581	#41	C₂²×C₄×C₈₉	1	4	yes	—
582	#41	C₂×D₄×C₈₉	1	4	yes	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	—	2	1	no	—
585	C₂×Q₈	—	2	1	no	—
586	C₂×Q₈	—	2	1	no	—
587	C₂×Q₈	—	2	1	no	—
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	—	2	1	no	—
590	C₂×Q₈	—	2	1	no	—
591	C₂×Q₈	C₂²⋊C₄×C₈₉	1	2	yes	—
592	C₂×Q₈	C₂²⋊C₄×C₈₉	1	2	yes	—
593	C₂×Q₈	C₂²×C₄×C₈₉	1	2	yes	—
594	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	1	no	—
604	C₂×D₄	—	2	1	no	—
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	—	2	1	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	2	1	no	—
609	C₂×D₄	—	2	1	no	—
610	C₂×D₄	—	2	1	no	—
611	C₂×D₄	—	4	1	no	—
612	C₂×D₄	—	4	1	no	—
613	C₂×D₄	—	4	1	no	—
614	C₂×D₄	—	4	1	no	—
615	C₂×D₄	C₂²⋊C₄×C₈₉	1	2	yes	—
616	C₂×D₄	C₂²⋊C₄×C₈₉	1	2	yes	—
617	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
618	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	4	1	no	—
630	C₂²×C₄	—	4	1	no	—
631	C₂²×C₄	—	4	1	no	—
632	C₂²×C₄	—	4	1	no	—
633	C₂²×C₄	—	4	1	no	—
634	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
635	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
636	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
637	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
638	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
639	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
640	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
641	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
642	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
643	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
644	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
645	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
646	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
647	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
648	Q₁₆	—	2	8	no	—
649	SD₁₆	—	2	8	no	—
650	SD₁₆	—	2	8	no	—
651	D₈	—	2	8	no	—
652	M₁₆	—	2	16	no	—
653	M₁₆	—	2	2	no	—
654	M₁₆	—	2	2	no	—
655	M₁₆	—	2	2	no	—
656	M₁₆	—	2	2	no	—
657	M₁₆	—	2	2	no	—
658	M₁₆	—	2	2	no	—
659	M₁₆	—	2	2	no	—
660	M₁₆	—	2	2	no	—
661	M₁₆	—	2	2	no	—
662	M₁₆	—	2	2	no	—
663	M₁₆	C₂²×C₄×C₈₉	1	4	yes	—
664	M₁₆	C₂×D₄×C₈₉	1	4	yes	—
665	C₂×C₈	—	2	16	no	—
666	C₂×C₈	—	2	2	no	—
667	C₂×C₈	—	2	2	no	—
668	C₂×C₈	—	2	2	no	—
669	C₂×C₈	—	2	2	no	—
670	C₂×C₈	—	2	2	no	—
671	C₂×C₈	—	2	2	no	—
672	C₂×C₈	—	2	2	no	—
673	C₂×C₈	—	2	2	no	—
674	C₂×C₈	—	2	2	no	—
675	C₂×C₈	—	2	2	no	—
676	C₂×C₈	—	2	2	no	—
677	C₂×C₈	—	4	1	no	—
678	C₂×C₈	—	4	1	no	—
679	C₂×C₈	—	4	1	no	—
680	C₂×C₈	—	4	1	no	—
681	C₂×C₈	C₂×D₄×C₈₉	1	4	yes	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	4	1	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	4	1	no	—
686	C₄²	—	2	2	no	—
687	C₄²	—	4	1	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	4	2	no	—
693	C₂³	—	4	4	no	—
694	C₂³	—	4	1	no	—
695	C₂³	—	4	1	no	—
696	C₂³	—	8	2	no	—
697	C₂³	C₄×D₄×C₈₉	1	1	yes	characteristic
698	C₂³	C₄×D₄×C₈₉	1	1	yes	characteristic
699	C₂³	#121×C₈₉	1	1	yes	characteristic
700	C₂³	#121×C₈₉	1	1	yes	characteristic
701	C₂³	#123×C₈₉	1	1	yes	characteristic
702	C₂³	#123×C₈₉	1	1	yes	characteristic
703	C₂³	C₂×#41×C₈₉	1	1	yes	characteristic
704	Q₈	—	2	2	no	—
705	Q₈	—	2	2	no	—
706	Q₈	—	2	2	no	—
707	Q₈	—	2	2	no	—
708	Q₈	—	2	2	no	—
709	Q₈	—	4	1	no	—
710	Q₈	—	4	1	no	—
711	Q₈	C₂×C₂²⋊C₄×C₈₉	1	4	yes	—
712	D₄	—	2	4	no	—
713	D₄	—	2	4	no	—
714	D₄	—	2	4	no	—
715	D₄	—	2	4	no	—
716	D₄	—	2	2	no	—
717	D₄	—	2	2	no	—
718	D₄	—	2	2	no	—
719	D₄	—	2	2	no	—
720	D₄	—	2	2	no	—
721	D₄	—	4	2	no	—
722	D₄	—	4	2	no	—
723	D₄	—	4	2	no	—
724	D₄	—	4	2	no	—
725	D₄	—	4	1	no	—
726	D₄	—	4	1	no	—
727	D₄	C₂×C₂²⋊C₄×C₈₉	1	4	yes	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	4	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	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	2	no	—
739	C₂×C₄	—	4	2	no	—
740	C₂×C₄	—	4	2	no	—
741	C₂×C₄	—	4	2	no	—
742	C₂×C₄	—	4	2	no	—
743	C₂×C₄	—	8	2	no	—
744	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
745	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
746	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
747	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
748	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
749	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
750	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
751	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
752	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
753	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
754	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
755	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
756	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
757	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
758	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
759	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
760	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
761	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
762	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
763	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
764	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
765	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
766	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
767	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
768	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
769	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
770	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
771	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
772	C₈	—	2	4	no	—
773	C₈	—	2	4	no	—
774	C₈	—	2	4	no	—
775	C₈	—	4	2	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	2	4	no	—
780	C₂²	—	4	1	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	4	no	—
785	C₂²	—	4	4	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	8	2	no	—
788	C₂²	—	8	2	no	—
789	C₂²	—	8	2	no	—
790	C₂²	—	8	2	no	—
791	C₂²	#386×C₈₉	1	1	yes	characteristic
792	C₂²	#386×C₈₉	1	1	yes	characteristic
793	C₂²	#386×C₈₉	1	1	yes	characteristic
794	C₂²	#386×C₈₉	1	1	yes	characteristic
795	C₂²	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
796	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
797	C₂²	C₂×#123×C₈₉	1	1	yes	characteristic
798	C₄	—	2	4	no	—
799	C₄	—	4	2	no	—
800	C₄	—	8	2	no	—
801	C₄	#386×C₈₉	1	1	yes	characteristic
802	C₄	#386×C₈₉	1	1	yes	characteristic
803	C₄	#386×C₈₉	1	1	yes	characteristic
804	C₄	#386×C₈₉	1	1	yes	characteristic
805	C₄	C₂²×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
806	C₄	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
807	C₄	C₂×#120×C₈₉	1	1	yes	characteristic
808	C₄	C₂×#121×C₈₉	1	1	yes	characteristic
809	C₂	—	2	1	no	—
810	C₂	—	2	1	no	—
811	C₂	—	2	1	no	—
812	C₂	—	2	1	no	—
813	C₂	—	2	1	no	—
814	C₂	—	2	1	no	—
815	C₂	—	4	4	no	—
816	C₂	—	8	2	no	—
817	C₂	C₈₉×#1881	1	2	yes	direct product factor
818	C₂	C₂×#386×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈₉	#120
commutator	C₂×C₄	C₂³×C₄×C₈₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
socle	C₂²×C₈₉	#386
prime radical	C₂×#575×C₈₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₉ ◁ C₂³×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#568×C₈₉	C₂	semidirect
3. C₂×#421×C₈₉	C₂	semidirect
4. C₂×#416×C₈₉	C₂	semidirect
5. C₂×#408×C₈₉	C₂	semidirect
6. C₈₉×#1881	C₂	direct (N × H)
7. C₂×#344×C₈₉	C₂	semidirect
8. C₂×#341×C₈₉	C₂	semidirect
13. #575×C₈₉	C₄	semidirect
16. C₂×#137×C₈₉	C₄	semidirect
18. C₂×AGL(1,ℤ/8)×C₈₉	C₄	semidirect
23. #568×C₈₉	C₂²	semidirect
33. #421×C₈₉	C₂²	semidirect
36. #416×C₈₉	C₂²	semidirect
40. #408×C₈₉	C₂²	semidirect
42. #344×C₈₉	C₂²	semidirect
43. #341×C₈₉	C₂²	semidirect
80. #137×C₈₉	C₂×C₄	semidirect
84. AGL(1,ℤ/8)×C₈₉	C₂×C₄	semidirect
399. C₂×#1881	C₈₉	direct (N × H)
408. C₂×C₈₉	#1881	direct (N × H)
411. C₂×#568	C₂×C₈₉	semidirect
412. C₂×#421	C₂×C₈₉	semidirect
413. C₂×#416	C₂×C₈₉	semidirect
414. C₂×#408	C₂×C₈₉	semidirect
415. #1881	C₂×C₈₉	direct (N × H)
416. C₂×#344	C₂×C₈₉	semidirect
417. C₂×#341	C₂×C₈₉	semidirect
418. C₈₉	C₂×#1881	direct (N × H)
423. #575	C₄×C₈₉	semidirect
426. C₂×#137	C₄×C₈₉	semidirect
428. C₂×AGL(1,ℤ/8)	C₄×C₈₉	semidirect
433. #568	C₂²×C₈₉	semidirect
443. #421	C₂²×C₈₉	semidirect
446. #416	C₂²×C₈₉	semidirect
450. #408	C₂²×C₈₉	semidirect
452. #344	C₂²×C₈₉	semidirect
453. #341	C₂²×C₈₉	semidirect
490. #137	C₂×C₄×C₈₉	semidirect
494. AGL(1,ℤ/8)	C₂×C₄×C₈₉	semidirect
817. C₂	C₈₉×#1881	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×#575×C₈₉	2
C₂×#568×C₈₉	2
C₂×#421×C₈₉	2
C₂×#416×C₈₉	2
C₂×#408×C₈₉	2
C₈₉×#1881	2
C₂×#344×C₈₉	2
C₂×#341×C₈₉	2
C₂×#1881	89

Subgroups — C2×C89×#1881 #36398786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#1881 #36398786