Subgroups — C₈₉×#25155 #36403003

Order 22784.

1126 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#464×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#452×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#449×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2427	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2341	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2065	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2034	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1968	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1923	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1878	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1865	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
27	#464×C₈₉	—	2	4	no	—
28	#452×C₈₉	—	2	4	no	—
29	#449×C₈₉	—	2	4	no	—
30	C₄×SD₁₆×C₈₉	—	2	4	no	—
31	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
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×#102×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×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
45	#397×C₈₉	—	2	1	no	—
46	#394×C₈₉	—	2	1	no	—
47	#391×C₈₉	C₂²	1	1	yes	characteristic
48	#390×C₈₉	—	2	1	no	—
49	#390×C₈₉	—	2	1	no	—
50	#390×C₈₉	C₂²	1	1	yes	characteristic
51	#390×C₈₉	C₂²	1	1	yes	characteristic
52	#389×C₈₉	C₂²	1	1	yes	characteristic
53	#386×C₈₉	—	2	1	no	—
54	#380×C₈₉	—	2	1	no	—
55	#380×C₈₉	—	2	1	no	—
56	#380×C₈₉	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
58	C₄×C₂²⋊C₄×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	—	4	1	no	—
68	C₂×#41×C₈₉	—	4	1	no	—
69	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₈₉	—	2	1	no	—
72	C₂²×D₄×C₈₉	—	2	1	no	—
73	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₈₉	—	2	1	no	—
76	C₂³×C₄×C₈₉	—	2	1	no	—
77	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
78	C₂×Q₁₆×C₈₉	—	2	2	no	—
79	C₂×Q₁₆×C₈₉	—	2	2	no	—
80	C₂×Q₁₆×C₈₉	—	2	2	no	—
81	C₂×SD₁₆×C₈₉	—	2	2	no	—
82	C₂×SD₁₆×C₈₉	—	2	2	no	—
83	C₂×SD₁₆×C₈₉	—	2	2	no	—
84	C₂×SD₁₆×C₈₉	—	2	2	no	—
85	C₂×SD₁₆×C₈₉	—	4	1	no	—
86	C₂×SD₁₆×C₈₉	D₄	1	4	yes	—
87	C₂×D₈×C₈₉	—	2	2	no	—
88	C₂×D₈×C₈₉	—	2	2	no	—
89	C₂×D₈×C₈₉	—	4	1	no	—
90	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	#124×C₈₉	—	2	2	no	—
95	#124×C₈₉	—	4	1	no	—
96	C₂²⋊Q₈×C₈₉	—	2	2	no	—
97	C₂²⋊Q₈×C₈₉	—	4	1	no	—
98	#121×C₈₉	—	2	2	no	—
99	#121×C₈₉	—	4	1	no	—
100	C₄×Q₈×C₈₉	—	2	2	no	—
101	C₄×Q₈×C₈₉	—	2	2	no	—
102	C₄×Q₈×C₈₉	—	4	1	no	—
103	C₄×Q₈×C₈₉	—	4	1	no	—
104	C₄×D₄×C₈₉	—	2	2	no	—
105	C₄×D₄×C₈₉	—	4	1	no	—
106	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
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	D₄	1	1	yes	characteristic
125	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
126	C₂×C₄²×C₈₉	—	2	1	no	—
127	C₂×C₄²×C₈₉	—	2	1	no	—
128	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
130	#106×C₈₉	—	2	2	no	—
131	#106×C₈₉	—	4	1	no	—
132	C₄⋊C₈×C₈₉	—	2	2	no	—
133	#103×C₈₉	—	2	2	no	—
134	#103×C₈₉	—	2	2	no	—
135	#103×C₈₉	—	4	1	no	—
136	#103×C₈₉	D₄	1	4	yes	complemented
137	#102×C₈₉	—	2	2	no	—
138	#102×C₈₉	—	2	2	no	—
139	#102×C₈₉	—	2	2	no	—
140	#102×C₈₉	—	2	2	no	—
141	C₂²⋊C₈×C₈₉	—	2	2	no	—
142	C₂²⋊C₈×C₈₉	—	2	2	no	—
143	C₄×C₈×C₈₉	—	2	2	no	—
144	#95×C₈₉	—	2	1	no	—
145	#95×C₈₉	—	2	1	no	—
146	#95×C₈₉	—	2	1	no	—
147	#95×C₈₉	—	2	1	no	—
148	#95×C₈₉	D₄	1	1	yes	characteristic
149	#95×C₈₉	D₄	1	1	yes	characteristic
150	C₂⁴×C₈₉	—	2	1	no	—
151	C₂⁴×C₈₉	—	2	1	no	—
152	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
153	#41×C₈₉	—	4	4	no	—
154	#41×C₈₉	—	4	4	no	—
155	#41×C₈₉	—	4	4	no	—
156	#41×C₈₉	—	4	4	no	—
157	C₂×Q₈×C₈₉	—	2	1	no	—
158	C₂×Q₈×C₈₉	—	2	1	no	—
159	C₂×Q₈×C₈₉	—	2	1	no	—
160	C₂×Q₈×C₈₉	—	2	1	no	—
161	C₂×Q₈×C₈₉	—	2	1	no	—
162	C₂×Q₈×C₈₉	—	2	1	no	—
163	C₂×Q₈×C₈₉	—	2	1	no	—
164	C₂×Q₈×C₈₉	—	2	1	no	—
165	C₂×Q₈×C₈₉	—	2	1	no	—
166	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
167	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
168	C₂×Q₈×C₈₉	#41	1	2	yes	—
169	C₂×D₄×C₈₉	—	2	4	no	—
170	C₂×D₄×C₈₉	—	2	1	no	—
171	C₂×D₄×C₈₉	—	2	1	no	—
172	C₂×D₄×C₈₉	—	2	1	no	—
173	C₂×D₄×C₈₉	—	2	1	no	—
174	C₂×D₄×C₈₉	—	2	1	no	—
175	C₂×D₄×C₈₉	—	2	1	no	—
176	C₂×D₄×C₈₉	—	2	1	no	—
177	C₂×D₄×C₈₉	—	2	1	no	—
178	C₂×D₄×C₈₉	—	2	1	no	—
179	C₂×D₄×C₈₉	—	2	1	no	—
180	C₂×D₄×C₈₉	—	4	2	no	—
181	C₂×D₄×C₈₉	—	4	2	no	—
182	C₂×D₄×C₈₉	—	4	2	no	—
183	C₂×D₄×C₈₉	—	4	2	no	—
184	C₂×D₄×C₈₉	—	8	1	no	—
185	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
186	C₂×D₄×C₈₉	#41	1	2	yes	—
187	C₂²×C₄×C₈₉	—	2	1	no	—
188	C₂²×C₄×C₈₉	—	2	4	no	—
189	C₂²×C₄×C₈₉	—	2	1	no	—
190	C₂²×C₄×C₈₉	—	2	1	no	—
191	C₂²×C₄×C₈₉	—	2	1	no	—
192	C₂²×C₄×C₈₉	—	2	1	no	—
193	C₂²×C₄×C₈₉	—	2	1	no	—
194	C₂²×C₄×C₈₉	—	2	1	no	—
195	C₂²×C₄×C₈₉	—	2	1	no	—
196	C₂²×C₄×C₈₉	—	2	1	no	—
197	C₂²×C₄×C₈₉	—	2	1	no	—
198	C₂²×C₄×C₈₉	—	2	1	no	—
199	C₂²×C₄×C₈₉	—	2	1	no	—
200	C₂²×C₄×C₈₉	—	4	2	no	—
201	C₂²×C₄×C₈₉	—	4	2	no	—
202	C₂²×C₄×C₈₉	—	4	2	no	—
203	C₂²×C₄×C₈₉	—	4	2	no	—
204	C₂²×C₄×C₈₉	—	8	1	no	—
205	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
211	Q₁₆×C₈₉	—	4	4	no	—
212	SD₁₆×C₈₉	—	2	8	no	—
213	SD₁₆×C₈₉	—	4	4	no	—
214	D₈×C₈₉	—	4	4	no	—
215	C₂×C₈×C₈₉	—	2	1	no	—
216	C₂×C₈×C₈₉	—	2	1	no	—
217	C₂×C₈×C₈₉	—	2	1	no	—
218	C₂×C₈×C₈₉	—	2	1	no	—
219	C₂×C₈×C₈₉	—	2	1	no	—
220	C₂×C₈×C₈₉	—	2	1	no	—
221	C₂×C₈×C₈₉	—	2	1	no	—
222	C₂×C₈×C₈₉	—	2	1	no	—
223	C₂×C₈×C₈₉	—	2	1	no	—
224	C₂×C₈×C₈₉	—	2	1	no	—
225	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
226	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
227	C₄⋊C₄×C₈₉	—	2	1	no	—
228	C₄⋊C₄×C₈₉	—	2	1	no	—
229	C₄⋊C₄×C₈₉	—	2	1	no	—
230	C₄⋊C₄×C₈₉	—	2	1	no	—
231	C₄⋊C₄×C₈₉	—	2	1	no	—
232	C₄⋊C₄×C₈₉	—	2	1	no	—
233	C₄⋊C₄×C₈₉	—	2	1	no	—
234	C₄⋊C₄×C₈₉	—	4	2	no	—
235	C₄⋊C₄×C₈₉	—	4	2	no	—
236	C₄⋊C₄×C₈₉	—	4	2	no	—
237	C₄⋊C₄×C₈₉	—	8	1	no	—
238	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
239	C₂²⋊C₄×C₈₉	—	2	2	no	—
240	C₂²⋊C₄×C₈₉	—	4	1	no	—
241	C₂²⋊C₄×C₈₉	—	4	2	no	—
242	C₂²⋊C₄×C₈₉	—	4	2	no	—
243	C₂²⋊C₄×C₈₉	—	4	2	no	—
244	C₂²⋊C₄×C₈₉	—	4	2	no	—
245	C₂²⋊C₄×C₈₉	—	4	2	no	—
246	C₂²⋊C₄×C₈₉	—	4	2	no	—
247	C₂²⋊C₄×C₈₉	—	4	2	no	—
248	C₂²⋊C₄×C₈₉	—	8	1	no	—
249	C₂²⋊C₄×C₈₉	—	8	1	no	—
250	C₂²⋊C₄×C₈₉	—	8	1	no	—
251	C₄²×C₈₉	—	2	1	no	—
252	C₄²×C₈₉	—	2	1	no	—
253	C₄²×C₈₉	—	2	1	no	—
254	C₄²×C₈₉	—	2	1	no	—
255	C₄²×C₈₉	—	4	2	no	—
256	C₄²×C₈₉	—	4	2	no	—
257	C₂³×C₈₉	—	2	1	no	—
258	C₂³×C₈₉	—	2	2	no	—
259	C₂³×C₈₉	—	2	2	no	—
260	C₂³×C₈₉	—	2	1	no	—
261	C₂³×C₈₉	—	2	1	no	—
262	C₂³×C₈₉	—	2	1	no	—
263	C₂³×C₈₉	—	2	1	no	—
264	C₂³×C₈₉	—	2	1	no	—
265	C₂³×C₈₉	—	2	1	no	—
266	C₂³×C₈₉	—	4	1	no	—
267	C₂³×C₈₉	—	4	1	no	—
268	C₂³×C₈₉	—	4	1	no	—
269	C₂³×C₈₉	—	4	1	no	—
270	C₂³×C₈₉	—	4	1	no	—
271	C₂³×C₈₉	—	4	1	no	—
272	C₂³×C₈₉	—	4	1	no	—
273	C₂³×C₈₉	—	4	1	no	—
274	C₂³×C₈₉	—	4	1	no	—
275	C₂³×C₈₉	—	4	1	no	—
276	C₂³×C₈₉	—	4	1	no	—
277	C₂³×C₈₉	—	4	1	no	—
278	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
279	Q₈×C₈₉	—	2	2	no	—
280	Q₈×C₈₉	—	2	2	no	—
281	Q₈×C₈₉	—	2	2	no	—
282	Q₈×C₈₉	—	4	1	no	—
283	Q₈×C₈₉	—	4	1	no	—
284	Q₈×C₈₉	—	4	1	no	—
285	Q₈×C₈₉	—	4	1	no	—
286	Q₈×C₈₉	#121	1	4	yes	—
287	D₄×C₈₉	—	2	2	no	—
288	D₄×C₈₉	—	2	2	no	—
289	D₄×C₈₉	—	2	2	no	—
290	D₄×C₈₉	—	2	2	no	—
291	D₄×C₈₉	—	4	8	no	—
292	D₄×C₈₉	—	4	1	no	—
293	D₄×C₈₉	—	4	1	no	—
294	D₄×C₈₉	—	4	1	no	—
295	D₄×C₈₉	—	4	1	no	—
296	D₄×C₈₉	—	8	4	no	—
297	C₂×C₄×C₈₉	—	2	2	no	—
298	C₂×C₄×C₈₉	—	2	1	no	—
299	C₂×C₄×C₈₉	—	2	2	no	—
300	C₂×C₄×C₈₉	—	2	2	no	—
301	C₂×C₄×C₈₉	—	2	1	no	—
302	C₂×C₄×C₈₉	—	2	1	no	—
303	C₂×C₄×C₈₉	—	2	1	no	—
304	C₂×C₄×C₈₉	—	2	1	no	—
305	C₂×C₄×C₈₉	—	2	1	no	—
306	C₂×C₄×C₈₉	—	2	2	no	—
307	C₂×C₄×C₈₉	—	2	1	no	—
308	C₂×C₄×C₈₉	—	2	1	no	—
309	C₂×C₄×C₈₉	—	2	1	no	—
310	C₂×C₄×C₈₉	—	2	1	no	—
311	C₂×C₄×C₈₉	—	2	1	no	—
312	C₂×C₄×C₈₉	—	2	1	no	—
313	C₂×C₄×C₈₉	—	2	1	no	—
314	C₂×C₄×C₈₉	—	2	1	no	—
315	C₂×C₄×C₈₉	—	4	8	no	—
316	C₂×C₄×C₈₉	—	4	1	no	—
317	C₂×C₄×C₈₉	—	4	1	no	—
318	C₂×C₄×C₈₉	—	4	1	no	—
319	C₂×C₄×C₈₉	—	4	1	no	—
320	C₂×C₄×C₈₉	—	4	1	no	—
321	C₂×C₄×C₈₉	—	4	1	no	—
322	C₂×C₄×C₈₉	—	4	1	no	—
323	C₂×C₄×C₈₉	—	4	1	no	—
324	C₂×C₄×C₈₉	—	4	1	no	—
325	C₂×C₄×C₈₉	—	4	1	no	—
326	C₂×C₄×C₈₉	—	4	1	no	—
327	C₂×C₄×C₈₉	—	4	1	no	—
328	C₂×C₄×C₈₉	—	4	1	no	—
329	C₂×C₄×C₈₉	—	4	1	no	—
330	C₂×C₄×C₈₉	—	4	1	no	—
331	C₂×C₄×C₈₉	—	4	1	no	—
332	C₂×C₄×C₈₉	—	4	1	no	—
333	C₂×C₄×C₈₉	—	4	1	no	—
334	C₂×C₄×C₈₉	—	8	4	no	—
335	C₂×C₄×C₈₉	#135	1	2	yes	—
336	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
339	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
340	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
341	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
342	C₈×C₈₉	—	2	2	no	—
343	C₈×C₈₉	—	2	2	no	—
344	C₈×C₈₉	—	4	1	no	—
345	C₈×C₈₉	—	4	1	no	—
346	C₂²×C₈₉	—	4	1	no	—
347	C₂²×C₈₉	—	4	2	no	—
348	C₂²×C₈₉	—	4	1	no	—
349	C₂²×C₈₉	—	4	2	no	—
350	C₂²×C₈₉	—	4	2	no	—
351	C₂²×C₈₉	—	4	1	no	—
352	C₂²×C₈₉	—	4	2	no	—
353	C₂²×C₈₉	—	4	1	no	—
354	C₂²×C₈₉	—	4	1	no	—
355	C₂²×C₈₉	—	4	2	no	—
356	C₂²×C₈₉	—	4	1	no	—
357	C₂²×C₈₉	—	4	1	no	—
358	C₂²×C₈₉	—	4	2	no	—
359	C₂²×C₈₉	—	8	1	no	—
360	C₂²×C₈₉	—	8	1	no	—
361	C₂²×C₈₉	—	8	1	no	—
362	C₂²×C₈₉	—	8	1	no	—
363	C₂²×C₈₉	—	8	1	no	—
364	C₂²×C₈₉	—	8	1	no	—
365	C₂²×C₈₉	—	8	1	no	—
366	C₂²×C₈₉	—	8	1	no	—
367	C₂²×C₈₉	#525	1	1	yes	characteristic
368	C₂²×C₈₉	D₄²	1	1	yes	characteristic
369	C₂²×C₈₉	D₄²	1	1	yes	characteristic
370	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
371	C₂²×C₈₉	#575	1	1	yes	characteristic
372	C₂²×C₈₉	#577	1	1	yes	characteristic
373	C₂²×C₈₉	#577	1	1	yes	characteristic
374	C₄×C₈₉	—	2	4	no	—
375	C₄×C₈₉	—	2	2	no	—
376	C₄×C₈₉	—	4	1	no	—
377	C₄×C₈₉	—	4	1	no	—
378	C₄×C₈₉	—	4	1	no	—
379	C₄×C₈₉	—	4	2	no	—
380	C₄×C₈₉	—	4	1	no	—
381	C₄×C₈₉	—	8	1	no	—
382	C₄×C₈₉	—	8	1	no	—
383	C₄×C₈₉	—	8	1	no	—
384	C₄×C₈₉	—	8	1	no	—
385	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
386	C₄×C₈₉	#538	1	1	yes	characteristic
387	C₄×C₈₉	#546	1	1	yes	characteristic
388	C₄×C₈₉	#546	1	1	yes	characteristic
389	#25155	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
390	C₂×C₈₉	—	8	1	no	—
391	C₂×C₈₉	—	8	2	no	—
392	C₂×C₈₉	—	8	2	no	—
393	C₂×C₈₉	#2424	1	1	yes	characteristic
394	C₂×C₈₉	#3102	1	1	yes	characteristic
395	C₂×C₈₉	#3125	1	1	yes	characteristic
396	C₂×C₈₉	#3271	1	1	yes	characteristic
397	C₂×C₈₉	#3275	1	1	yes	characteristic
398	C₂×C₈₉	#3282	1	1	yes	characteristic
399	C₂×C₈₉	#3284	1	1	yes	characteristic
400	C₂×#464	C₂×C₈₉	1	1	yes	characteristic, complemented
401	C₂×#452	C₂×C₈₉	1	1	yes	characteristic, complemented
402	C₂×#449	C₂×C₈₉	1	1	yes	characteristic
403	C₂×C₄×SD₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
404	#2427	C₂×C₈₉	1	1	yes	characteristic, complemented
405	#2341	C₂×C₈₉	1	1	yes	characteristic, complemented
406	#2065	C₂×C₈₉	1	1	yes	characteristic, complemented
407	#2035	C₂×C₈₉	1	1	yes	characteristic, complemented
408	#2034	C₂×C₈₉	1	1	yes	characteristic, complemented
409	#2012	C₂×C₈₉	1	1	yes	characteristic, complemented
410	#1968	C₂×C₈₉	1	1	yes	characteristic, complemented
411	#1923	C₂×C₈₉	1	1	yes	characteristic, complemented
412	#1879	C₂×C₈₉	1	1	yes	characteristic, complemented
413	#1878	C₂×C₈₉	1	1	yes	characteristic, complemented
414	#1865	C₂×C₈₉	1	1	yes	characteristic, complemented
415	C₈₉	#25155	1	1	yes	characteristic, direct product factor, Sylow
416	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
417	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
418	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
419	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
420	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
421	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
422	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
423	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
424	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
425	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
426	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
427	#464	—	2	4	no	—
428	#452	—	2	4	no	—
429	#449	—	2	4	no	—
430	C₄×SD₁₆	—	2	4	no	—
431	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
432	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
433	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
434	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
435	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
436	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
437	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
438	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
439	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
440	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
441	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
442	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
443	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
444	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
445	#397	—	2	1	no	—
446	#394	—	2	1	no	—
447	#391	C₂²×C₈₉	1	1	yes	characteristic
448	#390	—	2	1	no	—
449	#390	—	2	1	no	—
450	#390	C₂²×C₈₉	1	1	yes	characteristic
451	#390	C₂²×C₈₉	1	1	yes	characteristic
452	#389	C₂²×C₈₉	1	1	yes	characteristic
453	#386	—	2	1	no	—
454	#380	—	2	1	no	—
455	#380	—	2	1	no	—
456	#380	C₂²×C₈₉	1	1	yes	characteristic
457	C₄×C₂²⋊C₄	—	2	1	no	—
458	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
459	#340	C₂²×C₈₉	1	1	yes	characteristic
460	#340	C₂²×C₈₉	1	1	yes	characteristic
461	#336	C₂²×C₈₉	1	1	yes	characteristic
462	#336	C₂²×C₈₉	1	1	yes	characteristic
463	C₂×#41	—	2	2	no	—
464	C₂×#41	—	2	2	no	—
465	C₂×#41	—	2	2	no	—
466	C₂×#41	—	2	2	no	—
467	C₂×#41	—	4	1	no	—
468	C₂×#41	—	4	1	no	—
469	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
470	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
471	C₂²×D₄	—	2	1	no	—
472	C₂²×D₄	—	2	1	no	—
473	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
474	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
475	C₂³×C₄	—	2	1	no	—
476	C₂³×C₄	—	2	1	no	—
477	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
478	C₂×Q₁₆	—	2	2	no	—
479	C₂×Q₁₆	—	2	2	no	—
480	C₂×Q₁₆	—	2	2	no	—
481	C₂×SD₁₆	—	2	2	no	—
482	C₂×SD₁₆	—	2	2	no	—
483	C₂×SD₁₆	—	2	2	no	—
484	C₂×SD₁₆	—	2	2	no	—
485	C₂×SD₁₆	—	4	1	no	—
486	C₂×SD₁₆	D₄×C₈₉	1	4	yes	—
487	C₂×D₈	—	2	2	no	—
488	C₂×D₈	—	2	2	no	—
489	C₂×D₈	—	4	1	no	—
490	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
491	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
492	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
494	#124	—	2	2	no	—
495	#124	—	4	1	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	—	4	1	no	—
498	#121	—	2	2	no	—
499	#121	—	4	1	no	—
500	C₄×Q₈	—	2	2	no	—
501	C₄×Q₈	—	2	2	no	—
502	C₄×Q₈	—	4	1	no	—
503	C₄×Q₈	—	4	1	no	—
504	C₄×D₄	—	2	2	no	—
505	C₄×D₄	—	4	1	no	—
506	C₂×C₄⋊C₄	—	2	1	no	—
507	C₂×C₄⋊C₄	—	2	1	no	—
508	C₂×C₄⋊C₄	—	2	1	no	—
509	C₂×C₄⋊C₄	—	2	1	no	—
510	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
525	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
526	C₂×C₄²	—	2	1	no	—
527	C₂×C₄²	—	2	1	no	—
528	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
530	#106	—	2	2	no	—
531	#106	—	4	1	no	—
532	C₄⋊C₈	—	2	2	no	—
533	#103	—	2	2	no	—
534	#103	—	2	2	no	—
535	#103	—	4	1	no	—
536	#103	D₄×C₈₉	1	4	yes	complemented
537	#102	—	2	2	no	—
538	#102	—	2	2	no	—
539	#102	—	2	2	no	—
540	#102	—	2	2	no	—
541	C₂²⋊C₈	—	2	2	no	—
542	C₂²⋊C₈	—	2	2	no	—
543	C₄×C₈	—	2	2	no	—
544	#95	—	2	1	no	—
545	#95	—	2	1	no	—
546	#95	—	2	1	no	—
547	#95	—	2	1	no	—
548	#95	D₄×C₈₉	1	1	yes	characteristic
549	#95	D₄×C₈₉	1	1	yes	characteristic
550	C₂⁴	—	2	1	no	—
551	C₂⁴	—	2	1	no	—
552	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
553	#41	—	4	4	no	—
554	#41	—	4	4	no	—
555	#41	—	4	4	no	—
556	#41	—	4	4	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
567	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
568	C₂×Q₈	#41×C₈₉	1	2	yes	—
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	4	2	no	—
581	C₂×D₄	—	4	2	no	—
582	C₂×D₄	—	4	2	no	—
583	C₂×D₄	—	4	2	no	—
584	C₂×D₄	—	8	1	no	—
585	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
586	C₂×D₄	#41×C₈₉	1	2	yes	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	4	2	no	—
601	C₂²×C₄	—	4	2	no	—
602	C₂²×C₄	—	4	2	no	—
603	C₂²×C₄	—	4	2	no	—
604	C₂²×C₄	—	8	1	no	—
605	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
606	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
607	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
609	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
611	Q₁₆	—	4	4	no	—
612	SD₁₆	—	2	8	no	—
613	SD₁₆	—	4	4	no	—
614	D₈	—	4	4	no	—
615	C₂×C₈	—	2	1	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
626	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	4	2	no	—
635	C₄⋊C₄	—	4	2	no	—
636	C₄⋊C₄	—	4	2	no	—
637	C₄⋊C₄	—	8	1	no	—
638	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	4	1	no	—
641	C₂²⋊C₄	—	4	2	no	—
642	C₂²⋊C₄	—	4	2	no	—
643	C₂²⋊C₄	—	4	2	no	—
644	C₂²⋊C₄	—	4	2	no	—
645	C₂²⋊C₄	—	4	2	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₂²⋊C₄	—	8	1	no	—
649	C₂²⋊C₄	—	8	1	no	—
650	C₂²⋊C₄	—	8	1	no	—
651	C₄²	—	2	1	no	—
652	C₄²	—	2	1	no	—
653	C₄²	—	2	1	no	—
654	C₄²	—	2	1	no	—
655	C₄²	—	4	2	no	—
656	C₄²	—	4	2	no	—
657	C₂³	—	2	1	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	1	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	1	no	—
673	C₂³	—	4	1	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	—	4	1	no	—
678	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
679	Q₈	—	2	2	no	—
680	Q₈	—	2	2	no	—
681	Q₈	—	2	2	no	—
682	Q₈	—	4	1	no	—
683	Q₈	—	4	1	no	—
684	Q₈	—	4	1	no	—
685	Q₈	—	4	1	no	—
686	Q₈	#121×C₈₉	1	4	yes	—
687	D₄	—	2	2	no	—
688	D₄	—	2	2	no	—
689	D₄	—	2	2	no	—
690	D₄	—	2	2	no	—
691	D₄	—	4	8	no	—
692	D₄	—	4	1	no	—
693	D₄	—	4	1	no	—
694	D₄	—	4	1	no	—
695	D₄	—	4	1	no	—
696	D₄	—	8	4	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	4	8	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	8	4	no	—
735	C₂×C₄	#135×C₈₉	1	2	yes	—
736	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
737	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
738	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
739	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
740	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
741	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
742	C₈	—	2	2	no	—
743	C₈	—	2	2	no	—
744	C₈	—	4	1	no	—
745	C₈	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	1	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	1	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	1	no	—
754	C₂²	—	4	1	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	8	1	no	—
760	C₂²	—	8	1	no	—
761	C₂²	—	8	1	no	—
762	C₂²	—	8	1	no	—
763	C₂²	—	8	1	no	—
764	C₂²	—	8	1	no	—
765	C₂²	—	8	1	no	—
766	C₂²	—	8	1	no	—
767	C₂²	#525×C₈₉	1	1	yes	characteristic
768	C₂²	D₄²×C₈₉	1	1	yes	characteristic
769	C₂²	D₄²×C₈₉	1	1	yes	characteristic
770	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
771	C₂²	#575×C₈₉	1	1	yes	characteristic
772	C₂²	#577×C₈₉	1	1	yes	characteristic
773	C₂²	#577×C₈₉	1	1	yes	characteristic
774	C₄	—	2	4	no	—
775	C₄	—	2	2	no	—
776	C₄	—	4	1	no	—
777	C₄	—	4	1	no	—
778	C₄	—	4	1	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	1	no	—
781	C₄	—	8	1	no	—
782	C₄	—	8	1	no	—
783	C₄	—	8	1	no	—
784	C₄	—	8	1	no	—
785	C₄	C₂×#121×C₈₉	1	1	yes	characteristic
786	C₄	#538×C₈₉	1	1	yes	characteristic
787	C₄	#546×C₈₉	1	1	yes	characteristic
788	C₄	#546×C₈₉	1	1	yes	characteristic
789	C₂	—	8	1	no	—
790	C₂	—	8	2	no	—
791	C₂	—	8	2	no	—
792	C₂	C₈₉×#2424	1	1	yes	characteristic
793	C₂	C₈₉×#3102	1	1	yes	characteristic
794	C₂	C₈₉×#3125	1	1	yes	characteristic
795	C₂	C₈₉×#3271	1	1	yes	characteristic
796	C₂	C₈₉×#3275	1	1	yes	characteristic
797	C₂	C₈₉×#3282	1	1	yes	characteristic
798	C₂	C₈₉×#3284	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂×#449×C₈₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₄×C₂²⋊C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#464×C₈₉	C₂	semidirect
2. C₂×#452×C₈₉	C₂	semidirect
4. C₂×C₄×SD₁₆×C₈₉	C₂	semidirect
5. C₈₉×#2427	C₂	semidirect
6. C₈₉×#2341	C₂	semidirect
7. C₈₉×#2065	C₂	semidirect
8. C₈₉×#2035	C₂	semidirect
9. C₈₉×#2034	C₂	semidirect
10. C₈₉×#2012	C₂	semidirect
11. C₈₉×#1968	C₂	semidirect
12. C₈₉×#1923	C₂	semidirect
13. C₈₉×#1879	C₂	semidirect
14. C₈₉×#1878	C₂	semidirect
15. C₈₉×#1865	C₂	semidirect
136. #103×C₈₉	D₄	semidirect
389. #25155	C₈₉	direct (N × H)
400. C₂×#464	C₂×C₈₉	semidirect
401. C₂×#452	C₂×C₈₉	semidirect
403. C₂×C₄×SD₁₆	C₂×C₈₉	semidirect
404. #2427	C₂×C₈₉	semidirect
405. #2341	C₂×C₈₉	semidirect
406. #2065	C₂×C₈₉	semidirect
407. #2035	C₂×C₈₉	semidirect
408. #2034	C₂×C₈₉	semidirect
409. #2012	C₂×C₈₉	semidirect
410. #1968	C₂×C₈₉	semidirect
411. #1923	C₂×C₈₉	semidirect
412. #1879	C₂×C₈₉	semidirect
413. #1878	C₂×C₈₉	semidirect
414. #1865	C₂×C₈₉	semidirect
415. C₈₉	#25155	direct (N × H)
536. #103	D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#464×C₈₉	2
C₂×#452×C₈₉	2
C₂×#449×C₈₉	2
C₂×C₄×SD₁₆×C₈₉	2
C₈₉×#2427	2
C₈₉×#2341	2
C₈₉×#2065	2
C₈₉×#2035	2
C₈₉×#2034	2
C₈₉×#2012	2
C₈₉×#1968	2
C₈₉×#1923	2
C₈₉×#1879	2
C₈₉×#1878	2
C₈₉×#1865	2
#25155	89

Subgroups — C89×#25155 #36403003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25155 #36403003