Subgroups — C₈₉×#24403 #36402251

Order 22784.

1332 conjugacy classes of subgroups.

The subgroup lattice has 948 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×#473×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#471×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3007	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#452×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2880	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2052	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2051	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2020	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2019	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1908	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1907	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1901	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1855	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1785	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	#575×C₈₉	—	2	4	no	—
19	#575×C₈₉	—	2	4	no	—
20	C₂×#137×C₈₉	—	2	1	no	—
21	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
26	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#135×C₈₉	—	2	1	no	—
29	C₂×#135×C₈₉	—	2	1	no	—
30	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
31	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
32	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
34	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
36	#473×C₈₉	—	2	4	no	—
37	#471×C₈₉	—	2	4	no	—
38	#452×C₈₉	—	2	1	no	—
39	#452×C₈₉	—	2	1	no	—
40	#452×C₈₉	—	2	1	no	—
41	#452×C₈₉	—	2	1	no	—
42	#452×C₈₉	—	2	1	no	—
43	#452×C₈₉	—	2	1	no	—
44	#451×C₈₉	—	2	1	no	—
45	#450×C₈₉	—	2	1	no	—
46	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic, complemented
47	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic, complemented
48	#417×C₈₉	C₂²	1	1	yes	characteristic
49	#417×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
51	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
52	C₂×#101×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	C₂×#101×C₈₉	C₂²	1	1	yes	characteristic, complemented
54	C₂×#101×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×#101×C₈₉	C₂²	1	1	yes	characteristic, complemented
56	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#408×C₈₉	—	2	1	no	—
59	#408×C₈₉	—	2	1	no	—
60	#408×C₈₉	C₂²	1	1	yes	characteristic
61	#408×C₈₉	C₂²	1	1	yes	characteristic
62	#407×C₈₉	—	2	1	no	—
63	#407×C₈₉	C₂²	1	1	yes	characteristic
64	#407×C₈₉	C₂²	1	1	yes	characteristic
65	C₂×C₂²⋊C₈×C₈₉	—	2	1	no	—
66	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
67	#343×C₈₉	C₂²	1	1	yes	characteristic, complemented
68	#343×C₈₉	C₂²	1	1	yes	characteristic, complemented
69	#341×C₈₉	C₂²	1	1	yes	characteristic, complemented
70	#341×C₈₉	C₂²	1	1	yes	characteristic, complemented
71	C₂×#41×C₈₉	—	2	1	no	—
72	C₂×#41×C₈₉	—	2	1	no	—
73	C₂×#41×C₈₉	—	2	2	no	—
74	C₂×#41×C₈₉	—	2	2	no	—
75	C₂×#41×C₈₉	—	2	2	no	—
76	C₂×#41×C₈₉	—	2	2	no	—
77	C₂×#41×C₈₉	—	2	1	no	—
78	C₂×#41×C₈₉	—	2	1	no	—
79	C₂×#41×C₈₉	—	2	1	no	—
80	C₂×#41×C₈₉	—	2	1	no	—
81	C₂×#41×C₈₉	—	4	1	no	—
82	C₂×#41×C₈₉	—	4	1	no	—
83	C₂×#41×C₈₉	—	4	1	no	—
84	C₂×#41×C₈₉	—	4	1	no	—
85	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
86	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
87	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
88	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
90	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₈₉	—	2	1	no	—
93	C₂²×D₄×C₈₉	—	2	1	no	—
94	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
95	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₈₉	—	2	1	no	—
97	C₂³×C₄×C₈₉	—	2	1	no	—
98	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
99	#137×C₈₉	—	2	8	no	—
100	#137×C₈₉	—	2	2	no	—
101	#137×C₈₉	—	2	2	no	—
102	#137×C₈₉	—	2	2	no	—
103	#137×C₈₉	—	2	2	no	—
104	#137×C₈₉	—	2	2	no	—
105	#137×C₈₉	—	4	1	no	—
106	#137×C₈₉	—	4	1	no	—
107	#137×C₈₉	D₄	1	4	yes	—
108	AGL(1,ℤ/8)×C₈₉	—	2	8	no	—
109	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
110	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
111	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
112	AGL(1,ℤ/8)×C₈₉	D₄	1	4	yes	—
113	#135×C₈₉	—	2	8	no	—
114	#135×C₈₉	—	2	8	no	—
115	C₂×Q₁₆×C₈₉	—	2	1	no	—
116	C₂×Q₁₆×C₈₉	—	2	1	no	—
117	C₂×Q₁₆×C₈₉	—	2	1	no	—
118	C₂×Q₁₆×C₈₉	—	2	1	no	—
119	C₂×Q₁₆×C₈₉	—	2	2	no	—
120	C₂×Q₁₆×C₈₉	—	2	1	no	—
121	C₂×Q₁₆×C₈₉	—	2	1	no	—
122	C₂×Q₁₆×C₈₉	—	4	1	no	—
123	C₂×SD₁₆×C₈₉	—	2	1	no	—
124	C₂×SD₁₆×C₈₉	—	2	1	no	—
125	C₂×SD₁₆×C₈₉	—	2	1	no	—
126	C₂×SD₁₆×C₈₉	—	2	1	no	—
127	C₂×SD₁₆×C₈₉	—	2	1	no	—
128	C₂×SD₁₆×C₈₉	—	2	1	no	—
129	C₂×SD₁₆×C₈₉	—	2	2	no	—
130	C₂×SD₁₆×C₈₉	—	2	1	no	—
131	C₂×SD₁₆×C₈₉	—	2	1	no	—
132	C₂×SD₁₆×C₈₉	—	4	1	no	—
133	C₂×D₈×C₈₉	—	2	1	no	—
134	C₂×D₈×C₈₉	—	2	1	no	—
135	#131×C₈₉	—	2	2	no	—
136	#131×C₈₉	—	2	2	no	—
137	#131×C₈₉	—	4	1	no	—
138	#131×C₈₉	—	4	1	no	—
139	C₂×M₁₆×C₈₉	—	2	1	no	—
140	C₂×M₁₆×C₈₉	—	2	2	no	—
141	C₂×M₁₆×C₈₉	—	2	2	no	—
142	C₂×M₁₆×C₈₉	—	2	1	no	—
143	C₂×M₁₆×C₈₉	—	2	1	no	—
144	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
149	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₈₉	—	2	1	no	—
151	C₂²×C₈×C₈₉	—	2	1	no	—
152	C₂²×C₈×C₈₉	—	2	1	no	—
153	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
154	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
155	C₂²⋊Q₈×C₈₉	—	2	1	no	—
156	C₂²⋊Q₈×C₈₉	—	2	1	no	—
157	C₂²⋊Q₈×C₈₉	—	2	1	no	—
158	C₂²⋊Q₈×C₈₉	—	2	1	no	—
159	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
160	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
161	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
162	#108×C₈₉	—	2	2	no	—
163	#108×C₈₉	—	2	2	no	—
164	#103×C₈₉	—	2	1	no	—
165	#103×C₈₉	—	2	1	no	—
166	#103×C₈₉	—	2	1	no	—
167	#103×C₈₉	—	2	1	no	—
168	#102×C₈₉	—	2	1	no	—
169	#102×C₈₉	—	2	1	no	—
170	#102×C₈₉	—	2	1	no	—
171	#102×C₈₉	—	2	1	no	—
172	#101×C₈₉	—	2	2	no	—
173	#101×C₈₉	—	2	2	no	—
174	#101×C₈₉	—	2	2	no	—
175	#101×C₈₉	—	4	1	no	—
176	#100×C₈₉	—	2	2	no	—
177	#100×C₈₉	—	4	1	no	—
178	C₂²⋊C₈×C₈₉	—	2	1	no	—
179	C₂²⋊C₈×C₈₉	—	2	1	no	—
180	C₂²⋊C₈×C₈₉	—	2	1	no	—
181	C₂²⋊C₈×C₈₉	—	2	1	no	—
182	C₂²⋊C₈×C₈₉	—	2	1	no	—
183	C₂²⋊C₈×C₈₉	—	2	1	no	—
184	C₂²⋊C₈×C₈₉	—	2	1	no	—
185	C₂²⋊C₈×C₈₉	—	2	1	no	—
186	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
187	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
188	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
189	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
190	C₂⁴×C₈₉	—	2	1	no	—
191	C₂⁴×C₈₉	—	2	1	no	—
192	C₂⁴×C₈₉	#41	1	1	yes	characteristic
193	#41×C₈₉	—	2	1	no	—
194	#41×C₈₉	—	2	1	no	—
195	#41×C₈₉	—	2	4	no	—
196	#41×C₈₉	—	2	4	no	—
197	#41×C₈₉	—	2	2	no	—
198	#41×C₈₉	—	2	2	no	—
199	#41×C₈₉	—	2	1	no	—
200	#41×C₈₉	—	2	1	no	—
201	#41×C₈₉	—	2	1	no	—
202	#41×C₈₉	—	2	1	no	—
203	#41×C₈₉	—	4	2	no	—
204	#41×C₈₉	—	4	2	no	—
205	#41×C₈₉	—	4	1	no	—
206	#41×C₈₉	—	4	1	no	—
207	#41×C₈₉	—	4	2	no	—
208	#41×C₈₉	—	4	2	no	—
209	#41×C₈₉	—	4	2	no	—
210	#41×C₈₉	—	4	2	no	—
211	#41×C₈₉	—	4	2	no	—
212	#41×C₈₉	—	4	2	no	—
213	#41×C₈₉	—	4	2	no	—
214	#41×C₈₉	—	4	2	no	—
215	#41×C₈₉	C₂×D₄	1	2	yes	—
216	#41×C₈₉	C₂×D₄	1	2	yes	—
217	C₂×Q₈×C₈₉	—	2	1	no	—
218	C₂×Q₈×C₈₉	—	2	1	no	—
219	C₂×Q₈×C₈₉	—	2	2	no	—
220	C₂×Q₈×C₈₉	—	2	1	no	—
221	C₂×Q₈×C₈₉	—	2	1	no	—
222	C₂×Q₈×C₈₉	—	2	1	no	—
223	C₂×Q₈×C₈₉	—	2	1	no	—
224	C₂×Q₈×C₈₉	—	2	1	no	—
225	C₂×Q₈×C₈₉	—	2	1	no	—
226	C₂×Q₈×C₈₉	—	2	1	no	—
227	C₂×Q₈×C₈₉	—	2	1	no	—
228	C₂×Q₈×C₈₉	—	2	1	no	—
229	C₂×Q₈×C₈₉	—	2	1	no	—
230	C₂×Q₈×C₈₉	—	4	1	no	—
231	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
232	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
233	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
234	C₂×D₄×C₈₉	—	2	1	no	—
235	C₂×D₄×C₈₉	—	2	2	no	—
236	C₂×D₄×C₈₉	—	2	1	no	—
237	C₂×D₄×C₈₉	—	2	1	no	—
238	C₂×D₄×C₈₉	—	2	1	no	—
239	C₂×D₄×C₈₉	—	2	1	no	—
240	C₂×D₄×C₈₉	—	2	1	no	—
241	C₂×D₄×C₈₉	—	2	1	no	—
242	C₂×D₄×C₈₉	—	2	1	no	—
243	C₂×D₄×C₈₉	—	2	1	no	—
244	C₂×D₄×C₈₉	—	2	1	no	—
245	C₂×D₄×C₈₉	—	4	1	no	—
246	C₂×D₄×C₈₉	—	4	2	no	—
247	C₂×D₄×C₈₉	—	4	2	no	—
248	C₂×D₄×C₈₉	—	4	2	no	—
249	C₂×D₄×C₈₉	—	4	2	no	—
250	C₂×D₄×C₈₉	—	4	1	no	—
251	C₂×D₄×C₈₉	—	4	1	no	—
252	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
253	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
254	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₈₉	—	2	1	no	—
256	C₂²×C₄×C₈₉	—	2	1	no	—
257	C₂²×C₄×C₈₉	—	2	1	no	—
258	C₂²×C₄×C₈₉	—	2	1	no	—
259	C₂²×C₄×C₈₉	—	2	1	no	—
260	C₂²×C₄×C₈₉	—	2	1	no	—
261	C₂²×C₄×C₈₉	—	2	1	no	—
262	C₂²×C₄×C₈₉	—	2	1	no	—
263	C₂²×C₄×C₈₉	—	2	1	no	—
264	C₂²×C₄×C₈₉	—	2	1	no	—
265	C₂²×C₄×C₈₉	—	2	1	no	—
266	C₂²×C₄×C₈₉	—	2	1	no	—
267	C₂²×C₄×C₈₉	—	4	2	no	—
268	C₂²×C₄×C₈₉	—	4	2	no	—
269	C₂²×C₄×C₈₉	—	4	2	no	—
270	C₂²×C₄×C₈₉	—	4	2	no	—
271	C₂²×C₄×C₈₉	—	4	1	no	—
272	C₂²×C₄×C₈₉	—	4	1	no	—
273	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
278	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
279	Q₁₆×C₈₉	—	2	4	no	—
280	Q₁₆×C₈₉	—	2	4	no	—
281	Q₁₆×C₈₉	—	4	2	no	—
282	Q₁₆×C₈₉	—	4	2	no	—
283	Q₁₆×C₈₉	—	4	2	no	—
284	Q₁₆×C₈₉	—	4	2	no	—
285	SD₁₆×C₈₉	—	2	4	no	—
286	SD₁₆×C₈₉	—	2	4	no	—
287	SD₁₆×C₈₉	—	2	4	no	—
288	SD₁₆×C₈₉	—	2	4	no	—
289	SD₁₆×C₈₉	—	4	2	no	—
290	SD₁₆×C₈₉	—	4	2	no	—
291	SD₁₆×C₈₉	—	4	2	no	—
292	SD₁₆×C₈₉	—	4	2	no	—
293	D₈×C₈₉	—	2	4	no	—
294	D₈×C₈₉	—	2	4	no	—
295	M₁₆×C₈₉	—	2	4	no	—
296	M₁₆×C₈₉	—	2	1	no	—
297	M₁₆×C₈₉	—	2	1	no	—
298	M₁₆×C₈₉	—	2	1	no	—
299	M₁₆×C₈₉	—	2	1	no	—
300	M₁₆×C₈₉	—	2	1	no	—
301	M₁₆×C₈₉	—	2	1	no	—
302	M₁₆×C₈₉	—	2	1	no	—
303	M₁₆×C₈₉	—	2	1	no	—
304	M₁₆×C₈₉	—	2	1	no	—
305	M₁₆×C₈₉	—	2	1	no	—
306	M₁₆×C₈₉	—	4	2	no	—
307	M₁₆×C₈₉	—	4	2	no	—
308	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
309	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
310	C₂×C₈×C₈₉	—	2	4	no	—
311	C₂×C₈×C₈₉	—	2	1	no	—
312	C₂×C₈×C₈₉	—	2	1	no	—
313	C₂×C₈×C₈₉	—	2	1	no	—
314	C₂×C₈×C₈₉	—	2	1	no	—
315	C₂×C₈×C₈₉	—	2	1	no	—
316	C₂×C₈×C₈₉	—	2	1	no	—
317	C₂×C₈×C₈₉	—	2	1	no	—
318	C₂×C₈×C₈₉	—	2	1	no	—
319	C₂×C₈×C₈₉	—	2	1	no	—
320	C₂×C₈×C₈₉	—	2	1	no	—
321	C₂×C₈×C₈₉	—	4	2	no	—
322	C₂×C₈×C₈₉	—	4	2	no	—
323	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
324	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
325	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
326	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
327	C₄⋊C₄×C₈₉	—	2	1	no	—
328	C₄⋊C₄×C₈₉	—	2	1	no	—
329	C₄⋊C₄×C₈₉	—	4	1	no	—
330	C₄⋊C₄×C₈₉	—	4	1	no	—
331	C₂²⋊C₄×C₈₉	—	4	1	no	—
332	C₂²⋊C₄×C₈₉	—	4	1	no	—
333	C₂³×C₈₉	—	2	1	no	—
334	C₂³×C₈₉	—	2	1	no	—
335	C₂³×C₈₉	—	2	1	no	—
336	C₂³×C₈₉	—	2	1	no	—
337	C₂³×C₈₉	—	2	2	no	—
338	C₂³×C₈₉	—	4	1	no	—
339	C₂³×C₈₉	—	4	1	no	—
340	C₂³×C₈₉	—	4	2	no	—
341	C₂³×C₈₉	—	4	2	no	—
342	C₂³×C₈₉	—	4	1	no	—
343	C₂³×C₈₉	—	4	1	no	—
344	C₂³×C₈₉	—	8	1	no	—
345	C₂³×C₈₉	—	8	1	no	—
346	C₂³×C₈₉	—	8	1	no	—
347	C₂³×C₈₉	#121	1	1	yes	characteristic
348	C₂³×C₈₉	#121	1	1	yes	characteristic
349	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
350	Q₈×C₈₉	—	2	1	no	—
351	Q₈×C₈₉	—	2	1	no	—
352	Q₈×C₈₉	—	2	2	no	—
353	Q₈×C₈₉	—	2	1	no	—
354	Q₈×C₈₉	—	2	2	no	—
355	Q₈×C₈₉	—	4	2	no	—
356	Q₈×C₈₉	—	4	1	no	—
357	Q₈×C₈₉	—	4	1	no	—
358	Q₈×C₈₉	—	4	1	no	—
359	Q₈×C₈₉	—	4	1	no	—
360	Q₈×C₈₉	—	4	1	no	—
361	Q₈×C₈₉	—	4	1	no	—
362	Q₈×C₈₉	#120	1	2	yes	—
363	D₄×C₈₉	—	2	2	no	—
364	D₄×C₈₉	—	2	2	no	—
365	D₄×C₈₉	—	2	1	no	—
366	D₄×C₈₉	—	2	2	no	—
367	D₄×C₈₉	—	2	1	no	—
368	D₄×C₈₉	—	2	1	no	—
369	D₄×C₈₉	—	2	2	no	—
370	D₄×C₈₉	—	4	2	no	—
371	D₄×C₈₉	—	4	2	no	—
372	D₄×C₈₉	—	4	2	no	—
373	D₄×C₈₉	—	4	4	no	—
374	D₄×C₈₉	—	4	4	no	—
375	D₄×C₈₉	—	4	1	no	—
376	D₄×C₈₉	—	4	1	no	—
377	D₄×C₈₉	—	4	1	no	—
378	D₄×C₈₉	—	4	1	no	—
379	D₄×C₈₉	#120	1	2	yes	—
380	C₂×C₄×C₈₉	—	2	1	no	—
381	C₂×C₄×C₈₉	—	2	1	no	—
382	C₂×C₄×C₈₉	—	2	1	no	—
383	C₂×C₄×C₈₉	—	2	1	no	—
384	C₂×C₄×C₈₉	—	2	1	no	—
385	C₂×C₄×C₈₉	—	2	1	no	—
386	C₂×C₄×C₈₉	—	2	1	no	—
387	C₂×C₄×C₈₉	—	2	2	no	—
388	C₂×C₄×C₈₉	—	2	2	no	—
389	C₂×C₄×C₈₉	—	2	1	no	—
390	C₂×C₄×C₈₉	—	2	1	no	—
391	C₂×C₄×C₈₉	—	2	1	no	—
392	C₂×C₄×C₈₉	—	2	1	no	—
393	C₂×C₄×C₈₉	—	2	1	no	—
394	C₂×C₄×C₈₉	—	2	2	no	—
395	C₂×C₄×C₈₉	—	4	2	no	—
396	C₂×C₄×C₈₉	—	4	2	no	—
397	C₂×C₄×C₈₉	—	4	2	no	—
398	C₂×C₄×C₈₉	—	4	4	no	—
399	C₂×C₄×C₈₉	—	4	4	no	—
400	C₂×C₄×C₈₉	—	4	1	no	—
401	C₂×C₄×C₈₉	—	4	1	no	—
402	C₂×C₄×C₈₉	—	4	1	no	—
403	C₂×C₄×C₈₉	—	4	1	no	—
404	C₂×C₄×C₈₉	—	4	1	no	—
405	C₂×C₄×C₈₉	—	4	1	no	—
406	C₂×C₄×C₈₉	—	4	1	no	—
407	C₂×C₄×C₈₉	—	4	1	no	—
408	C₂×C₄×C₈₉	—	8	1	no	—
409	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
410	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
411	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
416	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
417	C₈×C₈₉	—	2	2	no	—
418	C₈×C₈₉	—	2	2	no	—
419	C₈×C₈₉	—	2	1	no	—
420	C₈×C₈₉	—	2	1	no	—
421	C₈×C₈₉	—	2	1	no	—
422	C₈×C₈₉	—	2	1	no	—
423	C₈×C₈₉	—	4	1	no	—
424	C₈×C₈₉	—	4	1	no	—
425	C₈×C₈₉	—	4	1	no	—
426	C₈×C₈₉	—	4	1	no	—
427	C₂²×C₈₉	—	2	1	no	—
428	C₂²×C₈₉	—	2	1	no	—
429	C₂²×C₈₉	—	2	1	no	—
430	C₂²×C₈₉	—	2	1	no	—
431	C₂²×C₈₉	—	2	2	no	—
432	C₂²×C₈₉	—	2	1	no	—
433	C₂²×C₈₉	—	2	1	no	—
434	C₂²×C₈₉	—	2	1	no	—
435	C₂²×C₈₉	—	2	1	no	—
436	C₂²×C₈₉	—	4	1	no	—
437	C₂²×C₈₉	—	4	1	no	—
438	C₂²×C₈₉	—	4	1	no	—
439	C₂²×C₈₉	—	4	2	no	—
440	C₂²×C₈₉	—	4	1	no	—
441	C₂²×C₈₉	—	4	1	no	—
442	C₂²×C₈₉	—	8	1	no	—
443	C₂²×C₈₉	—	8	1	no	—
444	C₂²×C₈₉	—	8	2	no	—
445	C₂²×C₈₉	—	8	2	no	—
446	C₂²×C₈₉	—	8	4	no	—
447	C₂²×C₈₉	—	8	1	no	—
448	C₂²×C₈₉	—	8	1	no	—
449	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
450	C₂²×C₈₉	#546	1	1	yes	characteristic
451	C₂²×C₈₉	#546	1	1	yes	characteristic
452	C₄×C₈₉	—	2	1	no	—
453	C₄×C₈₉	—	2	1	no	—
454	C₄×C₈₉	—	2	2	no	—
455	C₄×C₈₉	—	4	1	no	—
456	C₄×C₈₉	—	4	2	no	—
457	C₄×C₈₉	—	8	1	no	—
458	C₄×C₈₉	—	8	1	no	—
459	C₄×C₈₉	C₂×#120	1	1	yes	characteristic
460	C₄×C₈₉	#534	1	1	yes	characteristic
461	C₄×C₈₉	D₄²	1	1	yes	characteristic
462	C₄×C₈₉	D₄²	1	1	yes	characteristic
463	#24403	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
464	C₂×C₈₉	—	2	1	no	—
465	C₂×C₈₉	—	2	1	no	—
466	C₂×C₈₉	—	4	1	no	—
467	C₂×C₈₉	—	4	1	no	—
468	C₂×C₈₉	—	4	2	no	—
469	C₂×C₈₉	—	8	1	no	—
470	C₂×C₈₉	—	8	2	no	—
471	C₂×C₈₉	#2410	1	1	yes	characteristic
472	C₂×C₈₉	#3067	1	1	yes	characteristic
473	C₂×C₈₉	#3069	1	1	yes	characteristic
474	C₂×#575	C₂×C₈₉	1	1	yes	characteristic
475	C₂×#473	C₂×C₈₉	1	1	yes	characteristic, complemented
476	C₂×#471	C₂×C₈₉	1	1	yes	characteristic, complemented
477	#3007	C₂×C₈₉	1	1	yes	characteristic, complemented
478	C₂×#452	C₂×C₈₉	1	1	yes	characteristic, complemented
479	#2880	C₂×C₈₉	1	1	yes	characteristic, complemented
480	#2052	C₂×C₈₉	1	1	yes	characteristic, complemented
481	#2051	C₂×C₈₉	1	1	yes	characteristic, complemented
482	#2020	C₂×C₈₉	1	1	yes	characteristic, complemented
483	#2019	C₂×C₈₉	1	1	yes	characteristic, complemented
484	#1908	C₂×C₈₉	1	1	yes	characteristic, complemented
485	#1907	C₂×C₈₉	1	1	yes	characteristic, complemented
486	#1901	C₂×C₈₉	1	1	yes	characteristic, complemented
487	#1855	C₂×C₈₉	1	1	yes	characteristic, complemented
488	#1785	C₂×C₈₉	1	1	yes	characteristic, complemented
489	C₈₉	#24403	1	1	yes	characteristic, direct product factor, Sylow
490	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
491	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
492	#575	—	2	4	no	—
493	#575	—	2	4	no	—
494	C₂×#137	—	2	1	no	—
495	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
496	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
497	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
498	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
499	C₂×AGL(1,ℤ/8)	—	2	1	no	—
500	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
501	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
502	C₂×#135	—	2	1	no	—
503	C₂×#135	—	2	1	no	—
504	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
505	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
506	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
507	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
508	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
509	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
510	#473	—	2	4	no	—
511	#471	—	2	4	no	—
512	#452	—	2	1	no	—
513	#452	—	2	1	no	—
514	#452	—	2	1	no	—
515	#452	—	2	1	no	—
516	#452	—	2	1	no	—
517	#452	—	2	1	no	—
518	#451	—	2	1	no	—
519	#450	—	2	1	no	—
520	C₂×#108	C₂²×C₈₉	1	1	yes	characteristic, complemented
521	C₂×#108	C₂²×C₈₉	1	1	yes	characteristic, complemented
522	#417	C₂²×C₈₉	1	1	yes	characteristic
523	#417	C₂²×C₈₉	1	1	yes	characteristic
524	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
525	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
526	C₂×#101	C₂²×C₈₉	1	1	yes	characteristic, complemented
527	C₂×#101	C₂²×C₈₉	1	1	yes	characteristic, complemented
528	C₂×#101	C₂²×C₈₉	1	1	yes	characteristic, complemented
529	C₂×#101	C₂²×C₈₉	1	1	yes	characteristic, complemented
530	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic, complemented
531	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic, complemented
532	#408	—	2	1	no	—
533	#408	—	2	1	no	—
534	#408	C₂²×C₈₉	1	1	yes	characteristic
535	#408	C₂²×C₈₉	1	1	yes	characteristic
536	#407	—	2	1	no	—
537	#407	C₂²×C₈₉	1	1	yes	characteristic
538	#407	C₂²×C₈₉	1	1	yes	characteristic
539	C₂×C₂²⋊C₈	—	2	1	no	—
540	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
541	#343	C₂²×C₈₉	1	1	yes	characteristic, complemented
542	#343	C₂²×C₈₉	1	1	yes	characteristic, complemented
543	#341	C₂²×C₈₉	1	1	yes	characteristic, complemented
544	#341	C₂²×C₈₉	1	1	yes	characteristic, complemented
545	C₂×#41	—	2	1	no	—
546	C₂×#41	—	2	1	no	—
547	C₂×#41	—	2	2	no	—
548	C₂×#41	—	2	2	no	—
549	C₂×#41	—	2	2	no	—
550	C₂×#41	—	2	2	no	—
551	C₂×#41	—	2	1	no	—
552	C₂×#41	—	2	1	no	—
553	C₂×#41	—	2	1	no	—
554	C₂×#41	—	2	1	no	—
555	C₂×#41	—	4	1	no	—
556	C₂×#41	—	4	1	no	—
557	C₂×#41	—	4	1	no	—
558	C₂×#41	—	4	1	no	—
559	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
560	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
561	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
562	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
563	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
564	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
565	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
566	C₂²×D₄	—	2	1	no	—
567	C₂²×D₄	—	2	1	no	—
568	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
569	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
570	C₂³×C₄	—	2	1	no	—
571	C₂³×C₄	—	2	1	no	—
572	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
573	#137	—	2	8	no	—
574	#137	—	2	2	no	—
575	#137	—	2	2	no	—
576	#137	—	2	2	no	—
577	#137	—	2	2	no	—
578	#137	—	2	2	no	—
579	#137	—	4	1	no	—
580	#137	—	4	1	no	—
581	#137	D₄×C₈₉	1	4	yes	—
582	AGL(1,ℤ/8)	—	2	8	no	—
583	AGL(1,ℤ/8)	—	2	2	no	—
584	AGL(1,ℤ/8)	—	2	2	no	—
585	AGL(1,ℤ/8)	—	2	2	no	—
586	AGL(1,ℤ/8)	D₄×C₈₉	1	4	yes	—
587	#135	—	2	8	no	—
588	#135	—	2	8	no	—
589	C₂×Q₁₆	—	2	1	no	—
590	C₂×Q₁₆	—	2	1	no	—
591	C₂×Q₁₆	—	2	2	no	—
592	C₂×Q₁₆	—	2	1	no	—
593	C₂×Q₁₆	—	2	1	no	—
594	C₂×Q₁₆	—	2	1	no	—
595	C₂×Q₁₆	—	2	1	no	—
596	C₂×Q₁₆	—	4	1	no	—
597	C₂×SD₁₆	—	2	1	no	—
598	C₂×SD₁₆	—	2	1	no	—
599	C₂×SD₁₆	—	2	1	no	—
600	C₂×SD₁₆	—	2	1	no	—
601	C₂×SD₁₆	—	2	2	no	—
602	C₂×SD₁₆	—	2	1	no	—
603	C₂×SD₁₆	—	2	1	no	—
604	C₂×SD₁₆	—	2	1	no	—
605	C₂×SD₁₆	—	2	1	no	—
606	C₂×SD₁₆	—	4	1	no	—
607	C₂×D₈	—	2	1	no	—
608	C₂×D₈	—	2	1	no	—
609	#131	—	2	2	no	—
610	#131	—	2	2	no	—
611	#131	—	4	1	no	—
612	#131	—	4	1	no	—
613	C₂×M₁₆	—	2	1	no	—
614	C₂×M₁₆	—	2	2	no	—
615	C₂×M₁₆	—	2	2	no	—
616	C₂×M₁₆	—	2	1	no	—
617	C₂×M₁₆	—	2	1	no	—
618	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
619	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
620	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
621	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
622	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
623	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
624	C₂²×C₈	—	2	1	no	—
625	C₂²×C₈	—	2	1	no	—
626	C₂²×C₈	—	2	1	no	—
627	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
628	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
629	C₂²⋊Q₈	—	2	1	no	—
630	C₂²⋊Q₈	—	2	1	no	—
631	C₂²⋊Q₈	—	2	1	no	—
632	C₂²⋊Q₈	—	2	1	no	—
633	C₂×C₄⋊C₄	—	2	1	no	—
634	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	—	2	1	no	—
636	#108	—	2	2	no	—
637	#108	—	2	2	no	—
638	#103	—	2	1	no	—
639	#103	—	2	1	no	—
640	#103	—	2	1	no	—
641	#103	—	2	1	no	—
642	#102	—	2	1	no	—
643	#102	—	2	1	no	—
644	#102	—	2	1	no	—
645	#102	—	2	1	no	—
646	#101	—	2	2	no	—
647	#101	—	2	2	no	—
648	#101	—	2	2	no	—
649	#101	—	4	1	no	—
650	#100	—	2	2	no	—
651	#100	—	4	1	no	—
652	C₂²⋊C₈	—	2	1	no	—
653	C₂²⋊C₈	—	2	1	no	—
654	C₂²⋊C₈	—	2	1	no	—
655	C₂²⋊C₈	—	2	1	no	—
656	C₂²⋊C₈	—	2	1	no	—
657	C₂²⋊C₈	—	2	1	no	—
658	C₂²⋊C₈	—	2	1	no	—
659	C₂²⋊C₈	—	2	1	no	—
660	C₂²⋊C₈	D₄×C₈₉	1	1	yes	characteristic
661	C₂²⋊C₈	D₄×C₈₉	1	1	yes	characteristic
662	C₂²⋊C₈	D₄×C₈₉	1	1	yes	characteristic
663	C₂²⋊C₈	D₄×C₈₉	1	1	yes	characteristic
664	C₂⁴	—	2	1	no	—
665	C₂⁴	—	2	1	no	—
666	C₂⁴	#41×C₈₉	1	1	yes	characteristic
667	#41	—	2	1	no	—
668	#41	—	2	1	no	—
669	#41	—	2	4	no	—
670	#41	—	2	4	no	—
671	#41	—	2	2	no	—
672	#41	—	2	2	no	—
673	#41	—	2	1	no	—
674	#41	—	2	1	no	—
675	#41	—	2	1	no	—
676	#41	—	2	1	no	—
677	#41	—	4	2	no	—
678	#41	—	4	2	no	—
679	#41	—	4	1	no	—
680	#41	—	4	1	no	—
681	#41	—	4	2	no	—
682	#41	—	4	2	no	—
683	#41	—	4	2	no	—
684	#41	—	4	2	no	—
685	#41	—	4	2	no	—
686	#41	—	4	2	no	—
687	#41	—	4	2	no	—
688	#41	—	4	2	no	—
689	#41	C₂×D₄×C₈₉	1	2	yes	—
690	#41	C₂×D₄×C₈₉	1	2	yes	—
691	C₂×Q₈	—	2	1	no	—
692	C₂×Q₈	—	2	1	no	—
693	C₂×Q₈	—	2	2	no	—
694	C₂×Q₈	—	2	1	no	—
695	C₂×Q₈	—	2	1	no	—
696	C₂×Q₈	—	2	1	no	—
697	C₂×Q₈	—	2	1	no	—
698	C₂×Q₈	—	2	1	no	—
699	C₂×Q₈	—	2	1	no	—
700	C₂×Q₈	—	2	1	no	—
701	C₂×Q₈	—	2	1	no	—
702	C₂×Q₈	—	2	1	no	—
703	C₂×Q₈	—	2	1	no	—
704	C₂×Q₈	—	4	1	no	—
705	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
706	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
707	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
708	C₂×D₄	—	2	1	no	—
709	C₂×D₄	—	2	2	no	—
710	C₂×D₄	—	2	1	no	—
711	C₂×D₄	—	2	1	no	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	2	1	no	—
714	C₂×D₄	—	2	1	no	—
715	C₂×D₄	—	2	1	no	—
716	C₂×D₄	—	2	1	no	—
717	C₂×D₄	—	2	1	no	—
718	C₂×D₄	—	2	1	no	—
719	C₂×D₄	—	4	1	no	—
720	C₂×D₄	—	4	2	no	—
721	C₂×D₄	—	4	2	no	—
722	C₂×D₄	—	4	2	no	—
723	C₂×D₄	—	4	2	no	—
724	C₂×D₄	—	4	1	no	—
725	C₂×D₄	—	4	1	no	—
726	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
727	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
728	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
729	C₂²×C₄	—	2	1	no	—
730	C₂²×C₄	—	2	1	no	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	2	1	no	—
736	C₂²×C₄	—	2	1	no	—
737	C₂²×C₄	—	2	1	no	—
738	C₂²×C₄	—	2	1	no	—
739	C₂²×C₄	—	2	1	no	—
740	C₂²×C₄	—	2	1	no	—
741	C₂²×C₄	—	4	2	no	—
742	C₂²×C₄	—	4	2	no	—
743	C₂²×C₄	—	4	2	no	—
744	C₂²×C₄	—	4	2	no	—
745	C₂²×C₄	—	4	1	no	—
746	C₂²×C₄	—	4	1	no	—
747	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
748	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
749	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
750	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
751	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
753	Q₁₆	—	2	4	no	—
754	Q₁₆	—	2	4	no	—
755	Q₁₆	—	4	2	no	—
756	Q₁₆	—	4	2	no	—
757	Q₁₆	—	4	2	no	—
758	Q₁₆	—	4	2	no	—
759	SD₁₆	—	2	4	no	—
760	SD₁₆	—	2	4	no	—
761	SD₁₆	—	2	4	no	—
762	SD₁₆	—	2	4	no	—
763	SD₁₆	—	4	2	no	—
764	SD₁₆	—	4	2	no	—
765	SD₁₆	—	4	2	no	—
766	SD₁₆	—	4	2	no	—
767	D₈	—	2	4	no	—
768	D₈	—	2	4	no	—
769	M₁₆	—	2	4	no	—
770	M₁₆	—	2	1	no	—
771	M₁₆	—	2	1	no	—
772	M₁₆	—	2	1	no	—
773	M₁₆	—	2	1	no	—
774	M₁₆	—	2	1	no	—
775	M₁₆	—	2	1	no	—
776	M₁₆	—	2	1	no	—
777	M₁₆	—	2	1	no	—
778	M₁₆	—	2	1	no	—
779	M₁₆	—	2	1	no	—
780	M₁₆	—	4	2	no	—
781	M₁₆	—	4	2	no	—
782	M₁₆	C₂×D₄×C₈₉	1	2	yes	—
783	M₁₆	C₂×D₄×C₈₉	1	2	yes	—
784	C₂×C₈	—	2	4	no	—
785	C₂×C₈	—	2	1	no	—
786	C₂×C₈	—	2	1	no	—
787	C₂×C₈	—	2	1	no	—
788	C₂×C₈	—	2	1	no	—
789	C₂×C₈	—	2	1	no	—
790	C₂×C₈	—	2	1	no	—
791	C₂×C₈	—	2	1	no	—
792	C₂×C₈	—	2	1	no	—
793	C₂×C₈	—	2	1	no	—
794	C₂×C₈	—	2	1	no	—
795	C₂×C₈	—	4	2	no	—
796	C₂×C₈	—	4	2	no	—
797	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
798	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
799	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
800	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
801	C₄⋊C₄	—	2	1	no	—
802	C₄⋊C₄	—	2	1	no	—
803	C₄⋊C₄	—	4	1	no	—
804	C₄⋊C₄	—	4	1	no	—
805	C₂²⋊C₄	—	4	1	no	—
806	C₂²⋊C₄	—	4	1	no	—
807	C₂³	—	2	1	no	—
808	C₂³	—	2	1	no	—
809	C₂³	—	2	1	no	—
810	C₂³	—	2	1	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	4	1	no	—
813	C₂³	—	4	1	no	—
814	C₂³	—	4	2	no	—
815	C₂³	—	4	2	no	—
816	C₂³	—	4	1	no	—
817	C₂³	—	4	1	no	—
818	C₂³	—	8	1	no	—
819	C₂³	—	8	1	no	—
820	C₂³	—	8	1	no	—
821	C₂³	#121×C₈₉	1	1	yes	characteristic
822	C₂³	#121×C₈₉	1	1	yes	characteristic
823	C₂³	C₂×#41×C₈₉	1	1	yes	characteristic
824	Q₈	—	2	1	no	—
825	Q₈	—	2	1	no	—
826	Q₈	—	2	2	no	—
827	Q₈	—	2	1	no	—
828	Q₈	—	2	2	no	—
829	Q₈	—	4	2	no	—
830	Q₈	—	4	1	no	—
831	Q₈	—	4	1	no	—
832	Q₈	—	4	1	no	—
833	Q₈	—	4	1	no	—
834	Q₈	—	4	1	no	—
835	Q₈	—	4	1	no	—
836	Q₈	#120×C₈₉	1	2	yes	—
837	D₄	—	2	2	no	—
838	D₄	—	2	2	no	—
839	D₄	—	2	1	no	—
840	D₄	—	2	2	no	—
841	D₄	—	2	1	no	—
842	D₄	—	2	1	no	—
843	D₄	—	2	2	no	—
844	D₄	—	4	2	no	—
845	D₄	—	4	2	no	—
846	D₄	—	4	2	no	—
847	D₄	—	4	4	no	—
848	D₄	—	4	4	no	—
849	D₄	—	4	1	no	—
850	D₄	—	4	1	no	—
851	D₄	—	4	1	no	—
852	D₄	—	4	1	no	—
853	D₄	#120×C₈₉	1	2	yes	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	4	2	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	4	2	no	—
872	C₂×C₄	—	4	4	no	—
873	C₂×C₄	—	4	4	no	—
874	C₂×C₄	—	4	1	no	—
875	C₂×C₄	—	4	1	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	1	no	—
882	C₂×C₄	—	8	1	no	—
883	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
884	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
885	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
886	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
887	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
888	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
889	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
890	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
891	C₈	—	2	2	no	—
892	C₈	—	2	2	no	—
893	C₈	—	2	1	no	—
894	C₈	—	2	1	no	—
895	C₈	—	2	1	no	—
896	C₈	—	2	1	no	—
897	C₈	—	4	1	no	—
898	C₈	—	4	1	no	—
899	C₈	—	4	1	no	—
900	C₈	—	4	1	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	1	no	—
908	C₂²	—	2	1	no	—
909	C₂²	—	2	2	no	—
910	C₂²	—	4	1	no	—
911	C₂²	—	4	1	no	—
912	C₂²	—	4	1	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	4	1	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	8	1	no	—
917	C₂²	—	8	1	no	—
918	C₂²	—	8	2	no	—
919	C₂²	—	8	2	no	—
920	C₂²	—	8	4	no	—
921	C₂²	—	8	1	no	—
922	C₂²	—	8	1	no	—
923	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
924	C₂²	#546×C₈₉	1	1	yes	characteristic
925	C₂²	#546×C₈₉	1	1	yes	characteristic
926	C₄	—	2	1	no	—
927	C₄	—	2	1	no	—
928	C₄	—	2	2	no	—
929	C₄	—	4	1	no	—
930	C₄	—	4	2	no	—
931	C₄	—	8	1	no	—
932	C₄	—	8	1	no	—
933	C₄	C₂×#120×C₈₉	1	1	yes	characteristic
934	C₄	#534×C₈₉	1	1	yes	characteristic
935	C₄	D₄²×C₈₉	1	1	yes	characteristic
936	C₄	D₄²×C₈₉	1	1	yes	characteristic
937	C₂	—	2	1	no	—
938	C₂	—	2	1	no	—
939	C₂	—	4	1	no	—
940	C₂	—	4	1	no	—
941	C₂	—	4	2	no	—
942	C₂	—	8	1	no	—
943	C₂	—	8	2	no	—
944	C₂	C₈₉×#2410	1	1	yes	characteristic
945	C₂	C₈₉×#3067	1	1	yes	characteristic
946	C₂	C₈₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂×#575×C₈₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂³×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#473×C₈₉	C₂	semidirect
3. C₂×#471×C₈₉	C₂	semidirect
4. C₈₉×#3007	C₂	semidirect
5. C₂×#452×C₈₉	C₂	semidirect
6. C₈₉×#2880	C₂	semidirect
7. C₈₉×#2052	C₂	semidirect
8. C₈₉×#2051	C₂	semidirect
9. C₈₉×#2020	C₂	semidirect
10. C₈₉×#2019	C₂	semidirect
11. C₈₉×#1908	C₂	semidirect
12. C₈₉×#1907	C₂	semidirect
13. C₈₉×#1901	C₂	semidirect
14. C₈₉×#1855	C₂	semidirect
15. C₈₉×#1785	C₂	semidirect
30. C₂²×Q₁₆×C₈₉	C₂²	semidirect
31. C₂²×SD₁₆×C₈₉	C₂²	semidirect
46. C₂×#108×C₈₉	C₂²	semidirect
47. C₂×#108×C₈₉	C₂²	semidirect
50. C₂×#103×C₈₉	C₂²	semidirect
51. C₂×#102×C₈₉	C₂²	semidirect
52. C₂×#101×C₈₉	C₂²	semidirect
53. C₂×#101×C₈₉	C₂²	semidirect
54. C₂×#101×C₈₉	C₂²	semidirect
55. C₂×#101×C₈₉	C₂²	semidirect
56. C₂×#100×C₈₉	C₂²	semidirect
57. C₂×#100×C₈₉	C₂²	semidirect
67. #343×C₈₉	C₂²	semidirect
68. #343×C₈₉	C₂²	semidirect
69. #341×C₈₉	C₂²	semidirect
70. #341×C₈₉	C₂²	semidirect
463. #24403	C₈₉	direct (N × H)
475. C₂×#473	C₂×C₈₉	semidirect
476. C₂×#471	C₂×C₈₉	semidirect
477. #3007	C₂×C₈₉	semidirect
478. C₂×#452	C₂×C₈₉	semidirect
479. #2880	C₂×C₈₉	semidirect
480. #2052	C₂×C₈₉	semidirect
481. #2051	C₂×C₈₉	semidirect
482. #2020	C₂×C₈₉	semidirect
483. #2019	C₂×C₈₉	semidirect
484. #1908	C₂×C₈₉	semidirect
485. #1907	C₂×C₈₉	semidirect
486. #1901	C₂×C₈₉	semidirect
487. #1855	C₂×C₈₉	semidirect
488. #1785	C₂×C₈₉	semidirect
489. C₈₉	#24403	direct (N × H)
504. C₂²×Q₁₆	C₂²×C₈₉	semidirect
505. C₂²×SD₁₆	C₂²×C₈₉	semidirect
520. C₂×#108	C₂²×C₈₉	semidirect
521. C₂×#108	C₂²×C₈₉	semidirect
524. C₂×#103	C₂²×C₈₉	semidirect
525. C₂×#102	C₂²×C₈₉	semidirect
526. C₂×#101	C₂²×C₈₉	semidirect
527. C₂×#101	C₂²×C₈₉	semidirect
528. C₂×#101	C₂²×C₈₉	semidirect
529. C₂×#101	C₂²×C₈₉	semidirect
530. C₂×#100	C₂²×C₈₉	semidirect
531. C₂×#100	C₂²×C₈₉	semidirect
541. #343	C₂²×C₈₉	semidirect
542. #343	C₂²×C₈₉	semidirect
543. #341	C₂²×C₈₉	semidirect
544. #341	C₂²×C₈₉	semidirect

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×#473×C₈₉	2
C₂×#471×C₈₉	2
C₈₉×#3007	2
C₂×#452×C₈₉	2
C₈₉×#2880	2
C₈₉×#2052	2
C₈₉×#2051	2
C₈₉×#2020	2
C₈₉×#2019	2
C₈₉×#1908	2
C₈₉×#1907	2
C₈₉×#1901	2
C₈₉×#1855	2
C₈₉×#1785	2
#24403	89

Subgroups — C89×#24403 #36402251

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#24403 #36402251