Subgroups — C₈₉×#60387 #36438235

Order 22784.

4764 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#585×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#575×C₈₉	C₂	1	2	yes	maximal, complemented
3	C₈₉×#3449	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3022	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3021	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3020	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3019	C₂	1	4	yes	maximal, complemented
8	C₈₉×#3018	C₂	1	8	yes	maximal, complemented
9	C₂×#421×C₈₉	C₂	1	2	yes	maximal, complemented
10	C₂×#413×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#585×C₈₉	—	2	2	no	—
12	#585×C₈₉	—	2	2	no	—
13	#585×C₈₉	—	2	4	no	—
14	#585×C₈₉	—	2	4	no	—
15	#585×C₈₉	C₂²	1	4	yes	—
16	#585×C₈₉	C₂²	1	4	yes	complemented
17	C₂×2₋¹⁺⁴×C₈₉	—	2	2	no	—
18	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	2	yes	complemented
19	C₂×H(5,𝔽₂)×C₈₉	—	2	2	no	—
20	C₂×H(5,𝔽₂)×C₈₉	—	2	2	no	—
21	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	2	yes	complemented
22	C₂²×#41×C₈₉	—	2	4	no	—
23	C₂²×#41×C₈₉	—	2	2	no	—
24	C₂²×#41×C₈₉	C₂²	1	2	yes	—
25	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
26	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
27	#575×C₈₉	—	2	4	no	—
28	#575×C₈₉	—	2	4	no	—
29	#575×C₈₉	C₂²	1	8	yes	complemented
30	#575×C₈₉	C₂²	1	8	yes	complemented
31	C₂×#137×C₈₉	—	2	2	no	—
32	C₂×#137×C₈₉	C₂²	1	4	yes	complemented
33	C₂×AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
34	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	4	yes	complemented
35	C₂×#135×C₈₉	—	2	4	no	—
36	C₂²×M₁₆×C₈₉	C₂²	1	2	yes	complemented
37	#537×C₈₉	—	2	2	no	—
38	#536×C₈₉	C₂²	1	2	yes	complemented
39	#536×C₈₉	C₂²	1	2	yes	complemented
40	#535×C₈₉	C₂²	1	2	yes	complemented
41	#535×C₈₉	C₂²	1	2	yes	complemented
42	#534×C₈₉	—	2	2	no	—
43	#532×C₈₉	C₂²	1	4	yes	complemented
44	#525×C₈₉	—	2	2	no	—
45	#525×C₈₉	—	2	2	no	—
46	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
47	#456×C₈₉	C₂²	1	16	yes	complemented
48	#455×C₈₉	C₂²	1	16	yes	complemented
49	#454×C₈₉	C₂²	1	16	yes	complemented
50	#453×C₈₉	C₂²	1	16	yes	complemented
51	#421×C₈₉	C₂²	1	8	yes	complemented
52	#421×C₈₉	C₂²	1	8	yes	complemented
53	C₂×#104×C₈₉	C₂²	1	8	yes	complemented
54	#413×C₈₉	C₂²	1	4	yes	complemented
55	#413×C₈₉	C₂²	1	4	yes	complemented
56	C₂×#101×C₈₉	C₂²	1	2	yes	complemented
57	C₂×#100×C₈₉	C₂²	1	2	yes	complemented
58	2₋¹⁺⁴×C₈₉	—	2	8	no	—
59	2₋¹⁺⁴×C₈₉	—	2	8	no	—
60	2₋¹⁺⁴×C₈₉	—	2	8	no	—
61	2₋¹⁺⁴×C₈₉	—	2	8	no	—
62	2₋¹⁺⁴×C₈₉	—	2	8	no	—
63	2₋¹⁺⁴×C₈₉	—	2	4	no	—
64	2₋¹⁺⁴×C₈₉	C₂³	1	8	yes	—
65	H(5,𝔽₂)×C₈₉	—	2	8	no	—
66	H(5,𝔽₂)×C₈₉	—	2	8	no	—
67	H(5,𝔽₂)×C₈₉	—	2	16	no	—
68	H(5,𝔽₂)×C₈₉	—	2	8	no	—
69	H(5,𝔽₂)×C₈₉	—	2	8	no	—
70	H(5,𝔽₂)×C₈₉	—	2	8	no	—
71	H(5,𝔽₂)×C₈₉	—	2	8	no	—
72	H(5,𝔽₂)×C₈₉	—	2	8	no	—
73	H(5,𝔽₂)×C₈₉	—	2	4	no	—
74	H(5,𝔽₂)×C₈₉	C₂³	1	8	yes	—
75	C₂×#41×C₈₉	—	2	4	no	—
76	C₂×#41×C₈₉	—	2	8	no	—
77	C₂×#41×C₈₉	—	2	4	no	—
78	C₂×#41×C₈₉	—	2	16	no	—
79	C₂×#41×C₈₉	—	2	16	no	—
80	C₂×#41×C₈₉	—	2	8	no	—
81	C₂×#41×C₈₉	—	2	8	no	—
82	C₂×#41×C₈₉	—	2	16	no	—
83	C₂×#41×C₈₉	—	2	16	no	—
84	C₂×#41×C₈₉	—	2	4	no	—
85	C₂×#41×C₈₉	—	2	4	no	—
86	C₂×#41×C₈₉	—	2	2	no	—
87	C₂×#41×C₈₉	—	2	2	no	—
88	C₂×#41×C₈₉	—	2	4	no	—
89	C₂×#41×C₈₉	—	2	8	no	—
90	C₂×#41×C₈₉	—	2	8	no	—
91	C₂×#41×C₈₉	—	2	2	no	—
92	C₂×#41×C₈₉	—	2	2	no	—
93	C₂×#41×C₈₉	—	2	2	no	—
94	C₂×#41×C₈₉	—	2	2	no	—
95	C₂×#41×C₈₉	—	2	2	no	—
96	C₂×#41×C₈₉	—	2	2	no	—
97	C₂×#41×C₈₉	—	2	2	no	—
98	C₂×#41×C₈₉	—	2	2	no	—
99	C₂×#41×C₈₉	—	2	1	no	—
100	C₂×#41×C₈₉	—	2	1	no	—
101	C₂×#41×C₈₉	—	2	2	no	—
102	C₂×#41×C₈₉	—	2	2	no	—
103	C₂×#41×C₈₉	—	2	2	no	—
104	C₂×#41×C₈₉	—	2	2	no	—
105	C₂×#41×C₈₉	D₄	1	2	yes	—
106	C₂×#41×C₈₉	D₄	1	2	yes	—
107	C₂×#41×C₈₉	D₄	1	4	yes	complemented
108	C₂×#41×C₈₉	D₄	1	4	yes	complemented
109	C₂×#41×C₈₉	D₄	1	4	yes	complemented
110	C₂×#41×C₈₉	C₂³	1	4	yes	—
111	C₂×#41×C₈₉	C₂³	1	4	yes	—
112	C₂×#41×C₈₉	C₂³	1	4	yes	—
113	C₂×#41×C₈₉	C₂³	1	2	yes	—
114	C₂×#41×C₈₉	C₂³	1	2	yes	—
115	C₂×#41×C₈₉	C₂³	1	2	yes	—
116	C₂×#41×C₈₉	C₂³	1	2	yes	complemented
117	C₂²×Q₈×C₈₉	—	2	2	no	—
118	C₂²×Q₈×C₈₉	—	2	4	no	—
119	C₂²×Q₈×C₈₉	D₄	1	2	yes	complemented
120	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
121	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic, complemented
122	C₂²×D₄×C₈₉	—	2	8	no	—
123	C₂²×D₄×C₈₉	—	2	2	no	—
124	C₂²×D₄×C₈₉	—	2	4	no	—
125	C₂²×D₄×C₈₉	—	2	2	no	—
126	C₂²×D₄×C₈₉	—	2	4	no	—
127	C₂²×D₄×C₈₉	—	2	1	no	—
128	C₂²×D₄×C₈₉	D₄	1	2	yes	—
129	C₂²×D₄×C₈₉	D₄	1	2	yes	complemented
130	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic, complemented
132	C₂³×C₄×C₈₉	—	2	4	no	—
133	C₂³×C₄×C₈₉	—	2	2	no	—
134	C₂³×C₄×C₈₉	—	2	1	no	—
135	C₂³×C₄×C₈₉	D₄	1	2	yes	—
136	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
137	#137×C₈₉	—	2	8	no	—
138	#137×C₈₉	—	2	8	no	—
139	#137×C₈₉	—	2	8	no	—
140	#137×C₈₉	C₂³	1	16	yes	complemented
141	AGL(1,ℤ/8)×C₈₉	—	2	8	no	—
142	AGL(1,ℤ/8)×C₈₉	—	2	8	no	—
143	AGL(1,ℤ/8)×C₈₉	—	2	8	no	—
144	AGL(1,ℤ/8)×C₈₉	C₂³	1	16	yes	complemented
145	#135×C₈₉	—	2	16	no	—
146	#135×C₈₉	—	2	16	no	—
147	C₂×Q₁₆×C₈₉	—	2	4	no	—
148	C₂×SD₁₆×C₈₉	—	2	4	no	—
149	C₂×SD₁₆×C₈₉	—	2	4	no	—
150	C₂×D₈×C₈₉	—	2	4	no	—
151	C₂×M₁₆×C₈₉	—	2	2	no	—
152	C₂×M₁₆×C₈₉	—	2	2	no	—
153	C₂×M₁₆×C₈₉	—	2	2	no	—
154	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
155	C₂×M₁₆×C₈₉	C₂³	1	4	yes	complemented
156	C₂×M₁₆×C₈₉	C₂³	1	4	yes	complemented
157	C₂²×C₈×C₈₉	—	2	2	no	—
158	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	complemented
159	#127×C₈₉	C₂³	1	4	yes	complemented
160	#124×C₈₉	C₂³	1	4	yes	complemented
161	#124×C₈₉	C₂³	1	4	yes	complemented
162	#123×C₈₉	—	2	4	no	—
163	#123×C₈₉	—	2	4	no	—
164	C₂²⋊Q₈×C₈₉	—	2	4	no	—
165	C₂²⋊Q₈×C₈₉	—	2	4	no	—
166	#121×C₈₉	—	2	4	no	—
167	#121×C₈₉	—	2	8	no	—
168	#121×C₈₉	—	2	4	no	—
169	#120×C₈₉	—	2	4	no	—
170	#120×C₈₉	—	2	4	no	—
171	C₄×D₄×C₈₉	—	2	8	no	—
172	#117×C₈₉	—	2	1	no	—
173	#117×C₈₉	—	2	1	no	—
174	#117×C₈₉	C₂³	1	2	yes	—
175	#117×C₈₉	C₂³	1	2	yes	complemented
176	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
177	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
178	C₂×C₄²×C₈₉	C₂³	1	2	yes	complemented
179	#104×C₈₉	C₂³	1	32	yes	complemented
180	#101×C₈₉	C₂³	1	8	yes	complemented
181	#100×C₈₉	C₂³	1	8	yes	complemented
182	C₂⁴×C₈₉	—	2	4	no	—
183	C₂⁴×C₈₉	—	2	2	no	—
184	C₂⁴×C₈₉	—	2	1	no	—
185	C₂⁴×C₈₉	C₂×D₄	1	2	yes	—
186	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
187	#41×C₈₉	—	2	16	no	—
188	#41×C₈₉	—	2	16	no	—
189	#41×C₈₉	—	2	32	no	—
190	#41×C₈₉	—	2	32	no	—
191	#41×C₈₉	—	2	16	no	—
192	#41×C₈₉	—	2	16	no	—
193	#41×C₈₉	—	2	16	no	—
194	#41×C₈₉	—	2	16	no	—
195	#41×C₈₉	—	2	16	no	—
196	#41×C₈₉	—	2	16	no	—
197	#41×C₈₉	—	2	16	no	—
198	#41×C₈₉	—	2	4	no	—
199	#41×C₈₉	—	2	4	no	—
200	#41×C₈₉	—	2	4	no	—
201	#41×C₈₉	—	2	4	no	—
202	#41×C₈₉	—	2	4	no	—
203	#41×C₈₉	—	2	4	no	—
204	#41×C₈₉	—	2	4	no	—
205	#41×C₈₉	—	2	4	no	—
206	#41×C₈₉	—	2	4	no	—
207	#41×C₈₉	—	2	4	no	—
208	#41×C₈₉	—	2	4	no	—
209	#41×C₈₉	—	2	4	no	—
210	#41×C₈₉	—	2	4	no	—
211	#41×C₈₉	—	2	4	no	—
212	#41×C₈₉	—	2	16	no	—
213	#41×C₈₉	—	2	4	no	—
214	#41×C₈₉	—	2	4	no	—
215	#41×C₈₉	—	2	4	no	—
216	#41×C₈₉	—	2	4	no	—
217	#41×C₈₉	—	2	4	no	—
218	#41×C₈₉	—	2	4	no	—
219	#41×C₈₉	—	2	4	no	—
220	#41×C₈₉	—	2	4	no	—
221	#41×C₈₉	—	2	4	no	—
222	#41×C₈₉	—	2	4	no	—
223	#41×C₈₉	—	4	1	no	—
224	#41×C₈₉	—	4	1	no	—
225	#41×C₈₉	—	4	2	no	—
226	#41×C₈₉	—	4	2	no	—
227	#41×C₈₉	—	4	1	no	—
228	#41×C₈₉	—	4	1	no	—
229	#41×C₈₉	C₂×D₄	1	8	yes	—
230	#41×C₈₉	C₂×D₄	1	8	yes	—
231	#41×C₈₉	C₂×D₄	1	8	yes	—
232	#41×C₈₉	C₂⁴	1	8	yes	—
233	C₂×Q₈×C₈₉	—	2	4	no	—
234	C₂×Q₈×C₈₉	—	2	16	no	—
235	C₂×Q₈×C₈₉	—	2	8	no	—
236	C₂×Q₈×C₈₉	—	2	8	no	—
237	C₂×Q₈×C₈₉	—	2	16	no	—
238	C₂×Q₈×C₈₉	—	2	2	no	—
239	C₂×Q₈×C₈₉	—	2	2	no	—
240	C₂×Q₈×C₈₉	—	2	2	no	—
241	C₂×Q₈×C₈₉	—	2	2	no	—
242	C₂×Q₈×C₈₉	—	2	2	no	—
243	C₂×Q₈×C₈₉	—	2	1	no	—
244	C₂×Q₈×C₈₉	—	2	2	no	—
245	C₂×Q₈×C₈₉	—	2	2	no	—
246	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
247	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
248	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
249	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
250	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
251	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
252	C₂×D₄×C₈₉	—	2	8	no	—
253	C₂×D₄×C₈₉	—	2	4	no	—
254	C₂×D₄×C₈₉	—	2	16	no	—
255	C₂×D₄×C₈₉	—	2	32	no	—
256	C₂×D₄×C₈₉	—	2	32	no	—
257	C₂×D₄×C₈₉	—	2	16	no	—
258	C₂×D₄×C₈₉	—	2	8	no	—
259	C₂×D₄×C₈₉	—	2	8	no	—
260	C₂×D₄×C₈₉	—	2	4	no	—
261	C₂×D₄×C₈₉	—	2	4	no	—
262	C₂×D₄×C₈₉	—	2	4	no	—
263	C₂×D₄×C₈₉	—	2	4	no	—
264	C₂×D₄×C₈₉	—	2	4	no	—
265	C₂×D₄×C₈₉	—	2	4	no	—
266	C₂×D₄×C₈₉	—	2	16	no	—
267	C₂×D₄×C₈₉	—	2	4	no	—
268	C₂×D₄×C₈₉	—	2	4	no	—
269	C₂×D₄×C₈₉	—	2	16	no	—
270	C₂×D₄×C₈₉	—	2	2	no	—
271	C₂×D₄×C₈₉	—	2	2	no	—
272	C₂×D₄×C₈₉	—	2	8	no	—
273	C₂×D₄×C₈₉	—	2	2	no	—
274	C₂×D₄×C₈₉	—	2	2	no	—
275	C₂×D₄×C₈₉	—	2	2	no	—
276	C₂×D₄×C₈₉	—	2	2	no	—
277	C₂×D₄×C₈₉	—	2	2	no	—
278	C₂×D₄×C₈₉	—	2	2	no	—
279	C₂×D₄×C₈₉	—	2	2	no	—
280	C₂×D₄×C₈₉	—	2	1	no	—
281	C₂×D₄×C₈₉	—	4	2	no	—
282	C₂×D₄×C₈₉	—	4	2	no	—
283	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
284	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
285	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
286	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
287	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
288	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
289	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
290	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₈₉	—	2	4	no	—
292	C₂²×C₄×C₈₉	—	2	8	no	—
293	C₂²×C₄×C₈₉	—	2	16	no	—
294	C₂²×C₄×C₈₉	—	2	16	no	—
295	C₂²×C₄×C₈₉	—	2	2	no	—
296	C₂²×C₄×C₈₉	—	2	4	no	—
297	C₂²×C₄×C₈₉	—	2	2	no	—
298	C₂²×C₄×C₈₉	—	2	4	no	—
299	C₂²×C₄×C₈₉	—	2	4	no	—
300	C₂²×C₄×C₈₉	—	2	2	no	—
301	C₂²×C₄×C₈₉	—	2	2	no	—
302	C₂²×C₄×C₈₉	—	2	2	no	—
303	C₂²×C₄×C₈₉	—	2	4	no	—
304	C₂²×C₄×C₈₉	—	2	4	no	—
305	C₂²×C₄×C₈₉	—	2	4	no	—
306	C₂²×C₄×C₈₉	—	2	1	no	—
307	C₂²×C₄×C₈₉	—	2	2	no	—
308	C₂²×C₄×C₈₉	—	2	2	no	—
309	C₂²×C₄×C₈₉	—	2	2	no	—
310	C₂²×C₄×C₈₉	—	4	2	no	—
311	C₂²×C₄×C₈₉	—	4	2	no	—
312	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
313	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
314	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
315	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
316	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
317	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
318	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
319	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
320	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
321	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
322	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
325	Q₁₆×C₈₉	—	2	16	no	—
326	SD₁₆×C₈₉	—	2	16	no	—
327	SD₁₆×C₈₉	—	2	16	no	—
328	D₈×C₈₉	—	2	16	no	—
329	M₁₆×C₈₉	—	2	4	no	—
330	M₁₆×C₈₉	—	2	4	no	—
331	M₁₆×C₈₉	—	2	4	no	—
332	M₁₆×C₈₉	C₂⁴	1	8	yes	—
333	C₂×C₈×C₈₉	—	2	4	no	—
334	C₂×C₈×C₈₉	—	2	4	no	—
335	C₂×C₈×C₈₉	—	2	4	no	—
336	C₄⋊C₄×C₈₉	—	2	2	no	—
337	C₄⋊C₄×C₈₉	—	2	2	no	—
338	C₄⋊C₄×C₈₉	—	2	8	no	—
339	C₂²⋊C₄×C₈₉	—	2	2	no	—
340	C₂²⋊C₄×C₈₉	—	2	2	no	—
341	C₂²⋊C₄×C₈₉	—	2	8	no	—
342	C₂²⋊C₄×C₈₉	—	2	8	no	—
343	C₄²×C₈₉	—	2	2	no	—
344	C₄²×C₈₉	C₂⁴	1	4	yes	—
345	C₂³×C₈₉	—	2	16	no	—
346	C₂³×C₈₉	—	2	2	no	—
347	C₂³×C₈₉	—	2	4	no	—
348	C₂³×C₈₉	—	2	2	no	—
349	C₂³×C₈₉	—	2	4	no	—
350	C₂³×C₈₉	—	2	4	no	—
351	C₂³×C₈₉	—	2	2	no	—
352	C₂³×C₈₉	—	4	2	no	—
353	C₂³×C₈₉	—	8	1	no	—
354	C₂³×C₈₉	—	8	2	no	—
355	C₂³×C₈₉	—	8	4	no	—
356	C₂³×C₈₉	—	8	2	no	—
357	C₂³×C₈₉	—	8	8	no	—
358	C₂³×C₈₉	#120	1	2	yes	—
359	C₂³×C₈₉	#120	1	2	yes	—
360	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
361	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
362	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
363	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
364	Q₈×C₈₉	—	2	16	no	—
365	Q₈×C₈₉	—	2	4	no	—
366	Q₈×C₈₉	—	2	4	no	—
367	Q₈×C₈₉	—	2	4	no	—
368	Q₈×C₈₉	—	2	4	no	—
369	Q₈×C₈₉	—	2	4	no	—
370	Q₈×C₈₉	—	2	4	no	—
371	Q₈×C₈₉	—	4	1	no	—
372	Q₈×C₈₉	—	4	1	no	—
373	Q₈×C₈₉	C₂²×D₄	1	8	yes	—
374	D₄×C₈₉	—	2	32	no	—
375	D₄×C₈₉	—	2	16	no	—
376	D₄×C₈₉	—	2	8	no	—
377	D₄×C₈₉	—	2	8	no	—
378	D₄×C₈₉	—	2	8	no	—
379	D₄×C₈₉	—	2	8	no	—
380	D₄×C₈₉	—	2	8	no	—
381	D₄×C₈₉	—	2	8	no	—
382	D₄×C₈₉	—	2	4	no	—
383	D₄×C₈₉	—	2	4	no	—
384	D₄×C₈₉	—	2	4	no	—
385	D₄×C₈₉	—	2	4	no	—
386	D₄×C₈₉	—	2	4	no	—
387	D₄×C₈₉	—	2	4	no	—
388	D₄×C₈₉	—	4	2	no	—
389	D₄×C₈₉	—	4	2	no	—
390	D₄×C₈₉	—	4	4	no	—
391	D₄×C₈₉	—	4	1	no	—
392	D₄×C₈₉	—	4	1	no	—
393	D₄×C₈₉	—	8	8	no	—
394	D₄×C₈₉	C₂²×D₄	1	8	yes	—
395	C₂×C₄×C₈₉	—	2	16	no	—
396	C₂×C₄×C₈₉	—	2	32	no	—
397	C₂×C₄×C₈₉	—	2	4	no	—
398	C₂×C₄×C₈₉	—	2	2	no	—
399	C₂×C₄×C₈₉	—	2	4	no	—
400	C₂×C₄×C₈₉	—	2	4	no	—
401	C₂×C₄×C₈₉	—	2	2	no	—
402	C₂×C₄×C₈₉	—	2	8	no	—
403	C₂×C₄×C₈₉	—	2	4	no	—
404	C₂×C₄×C₈₉	—	2	8	no	—
405	C₂×C₄×C₈₉	—	2	4	no	—
406	C₂×C₄×C₈₉	—	2	4	no	—
407	C₂×C₄×C₈₉	—	2	8	no	—
408	C₂×C₄×C₈₉	—	2	4	no	—
409	C₂×C₄×C₈₉	—	2	8	no	—
410	C₂×C₄×C₈₉	—	2	4	no	—
411	C₂×C₄×C₈₉	—	2	2	no	—
412	C₂×C₄×C₈₉	—	4	2	no	—
413	C₂×C₄×C₈₉	—	4	2	no	—
414	C₂×C₄×C₈₉	—	4	4	no	—
415	C₂×C₄×C₈₉	—	4	2	no	—
416	C₂×C₄×C₈₉	—	8	2	no	—
417	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
418	C₂×C₄×C₈₉	#120	1	2	yes	—
419	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
420	C₂×C₄×C₈₉	#120	1	2	yes	—
421	C₂×C₄×C₈₉	#120	1	2	yes	—
422	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
423	C₂×C₄×C₈₉	#120	1	2	yes	—
424	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
425	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
426	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
433	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
434	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
435	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
436	C₈×C₈₉	—	2	8	no	—
437	C₂²×C₈₉	—	2	4	no	—
438	C₂²×C₈₉	—	2	8	no	—
439	C₂²×C₈₉	—	4	1	no	—
440	C₂²×C₈₉	—	4	2	no	—
441	C₂²×C₈₉	—	4	1	no	—
442	C₂²×C₈₉	—	4	1	no	—
443	C₂²×C₈₉	—	4	2	no	—
444	C₂²×C₈₉	—	4	4	no	—
445	C₂²×C₈₉	—	4	8	no	—
446	C₂²×C₈₉	—	4	4	no	—
447	C₂²×C₈₉	—	4	4	no	—
448	C₂²×C₈₉	—	4	2	no	—
449	C₂²×C₈₉	—	8	2	no	—
450	C₂²×C₈₉	—	8	4	no	—
451	C₂²×C₈₉	—	8	4	no	—
452	C₂²×C₈₉	—	8	4	no	—
453	C₂²×C₈₉	—	8	16	no	—
454	C₂²×C₈₉	C₂×#120	1	1	yes	characteristic
455	C₂²×C₈₉	C₂×#120	1	2	yes	—
456	C₂²×C₈₉	C₂×#120	1	2	yes	—
457	C₂²×C₈₉	C₂×#120	1	1	yes	characteristic
458	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
459	C₄×C₈₉	—	2	8	no	—
460	C₄×C₈₉	—	2	4	no	—
461	C₄×C₈₉	—	4	4	no	—
462	C₄×C₈₉	—	4	2	no	—
463	C₄×C₈₉	C₂×#120	1	1	yes	characteristic
464	C₄×C₈₉	C₂×#120	1	2	yes	—
465	C₄×C₈₉	C₂×#120	1	1	yes	characteristic
466	C₄×C₈₉	C₂×#120	1	1	yes	characteristic
467	C₄×C₈₉	C₂×#120	1	1	yes	characteristic
468	C₄×C₈₉	C₂³×D₄	1	2	yes	—
469	#60387	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
470	C₂×C₈₉	—	2	1	no	—
471	C₂×C₈₉	—	2	1	no	—
472	C₂×C₈₉	—	2	2	no	—
473	C₂×C₈₉	—	2	2	no	—
474	C₂×C₈₉	—	2	1	no	—
475	C₂×C₈₉	—	4	4	no	—
476	C₂×C₈₉	—	4	8	no	—
477	C₂×C₈₉	—	8	2	no	—
478	C₂×C₈₉	C₂²×#120	1	1	yes	characteristic
479	C₂×#585	C₂×C₈₉	1	1	yes	characteristic, complemented
480	C₂×#575	C₂×C₈₉	1	2	yes	complemented
481	#3449	C₂×C₈₉	1	1	yes	characteristic, complemented
482	#3022	C₂×C₈₉	1	4	yes	complemented
483	#3021	C₂×C₈₉	1	4	yes	complemented
484	#3020	C₂×C₈₉	1	4	yes	complemented
485	#3019	C₂×C₈₉	1	4	yes	complemented
486	#3018	C₂×C₈₉	1	8	yes	complemented
487	C₂×#421	C₂×C₈₉	1	2	yes	complemented
488	C₂×#413	C₂×C₈₉	1	1	yes	characteristic, complemented
489	C₈₉	#60387	1	1	yes	characteristic, direct product factor, Sylow
490	#585	—	2	2	no	—
491	#585	—	2	2	no	—
492	#585	—	2	4	no	—
493	#585	—	2	4	no	—
494	#585	C₂²×C₈₉	1	4	yes	—
495	#585	C₂²×C₈₉	1	4	yes	complemented
496	C₂×2₋¹⁺⁴	—	2	2	no	—
497	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	2	yes	complemented
498	C₂×H(5,𝔽₂)	—	2	2	no	—
499	C₂×H(5,𝔽₂)	—	2	2	no	—
500	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	2	yes	complemented
501	C₂²×#41	—	2	4	no	—
502	C₂²×#41	—	2	2	no	—
503	C₂²×#41	C₂²×C₈₉	1	2	yes	—
504	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
505	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic, complemented
506	#575	—	2	4	no	—
507	#575	—	2	4	no	—
508	#575	C₂²×C₈₉	1	8	yes	complemented
509	#575	C₂²×C₈₉	1	8	yes	complemented
510	C₂×#137	—	2	2	no	—
511	C₂×#137	C₂²×C₈₉	1	4	yes	complemented
512	C₂×AGL(1,ℤ/8)	—	2	2	no	—
513	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	4	yes	complemented
514	C₂×#135	—	2	4	no	—
515	C₂²×M₁₆	C₂²×C₈₉	1	2	yes	complemented
516	#537	—	2	2	no	—
517	#536	C₂²×C₈₉	1	2	yes	complemented
518	#536	C₂²×C₈₉	1	2	yes	complemented
519	#535	C₂²×C₈₉	1	2	yes	complemented
520	#535	C₂²×C₈₉	1	2	yes	complemented
521	#534	—	2	2	no	—
522	#532	C₂²×C₈₉	1	4	yes	complemented
523	#525	—	2	2	no	—
524	#525	—	2	2	no	—
525	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic, complemented
526	#456	C₂²×C₈₉	1	16	yes	complemented
527	#455	C₂²×C₈₉	1	16	yes	complemented
528	#454	C₂²×C₈₉	1	16	yes	complemented
529	#453	C₂²×C₈₉	1	16	yes	complemented
530	#421	C₂²×C₈₉	1	8	yes	complemented
531	#421	C₂²×C₈₉	1	8	yes	complemented
532	C₂×#104	C₂²×C₈₉	1	8	yes	complemented
533	#413	C₂²×C₈₉	1	4	yes	complemented
534	#413	C₂²×C₈₉	1	4	yes	complemented
535	C₂×#101	C₂²×C₈₉	1	2	yes	complemented
536	C₂×#100	C₂²×C₈₉	1	2	yes	complemented
537	2₋¹⁺⁴	—	2	8	no	—
538	2₋¹⁺⁴	—	2	8	no	—
539	2₋¹⁺⁴	—	2	8	no	—
540	2₋¹⁺⁴	—	2	8	no	—
541	2₋¹⁺⁴	—	2	8	no	—
542	2₋¹⁺⁴	—	2	4	no	—
543	2₋¹⁺⁴	C₂³×C₈₉	1	8	yes	—
544	H(5,𝔽₂)	—	2	8	no	—
545	H(5,𝔽₂)	—	2	8	no	—
546	H(5,𝔽₂)	—	2	16	no	—
547	H(5,𝔽₂)	—	2	8	no	—
548	H(5,𝔽₂)	—	2	8	no	—
549	H(5,𝔽₂)	—	2	8	no	—
550	H(5,𝔽₂)	—	2	8	no	—
551	H(5,𝔽₂)	—	2	8	no	—
552	H(5,𝔽₂)	—	2	4	no	—
553	H(5,𝔽₂)	C₂³×C₈₉	1	8	yes	—
554	C₂×#41	—	2	4	no	—
555	C₂×#41	—	2	8	no	—
556	C₂×#41	—	2	4	no	—
557	C₂×#41	—	2	16	no	—
558	C₂×#41	—	2	16	no	—
559	C₂×#41	—	2	8	no	—
560	C₂×#41	—	2	8	no	—
561	C₂×#41	—	2	16	no	—
562	C₂×#41	—	2	16	no	—
563	C₂×#41	—	2	4	no	—
564	C₂×#41	—	2	4	no	—
565	C₂×#41	—	2	2	no	—
566	C₂×#41	—	2	2	no	—
567	C₂×#41	—	2	4	no	—
568	C₂×#41	—	2	8	no	—
569	C₂×#41	—	2	8	no	—
570	C₂×#41	—	2	2	no	—
571	C₂×#41	—	2	2	no	—
572	C₂×#41	—	2	2	no	—
573	C₂×#41	—	2	2	no	—
574	C₂×#41	—	2	2	no	—
575	C₂×#41	—	2	2	no	—
576	C₂×#41	—	2	2	no	—
577	C₂×#41	—	2	2	no	—
578	C₂×#41	—	2	1	no	—
579	C₂×#41	—	2	1	no	—
580	C₂×#41	—	2	2	no	—
581	C₂×#41	—	2	2	no	—
582	C₂×#41	—	2	2	no	—
583	C₂×#41	—	2	2	no	—
584	C₂×#41	D₄×C₈₉	1	2	yes	—
585	C₂×#41	D₄×C₈₉	1	2	yes	—
586	C₂×#41	D₄×C₈₉	1	4	yes	complemented
587	C₂×#41	D₄×C₈₉	1	4	yes	complemented
588	C₂×#41	D₄×C₈₉	1	4	yes	complemented
589	C₂×#41	C₂³×C₈₉	1	4	yes	—
590	C₂×#41	C₂³×C₈₉	1	4	yes	—
591	C₂×#41	C₂³×C₈₉	1	4	yes	—
592	C₂×#41	C₂³×C₈₉	1	2	yes	—
593	C₂×#41	C₂³×C₈₉	1	2	yes	—
594	C₂×#41	C₂³×C₈₉	1	2	yes	—
595	C₂×#41	C₂³×C₈₉	1	2	yes	complemented
596	C₂²×Q₈	—	2	2	no	—
597	C₂²×Q₈	—	2	4	no	—
598	C₂²×Q₈	D₄×C₈₉	1	2	yes	complemented
599	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
600	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic, complemented
601	C₂²×D₄	—	2	8	no	—
602	C₂²×D₄	—	2	2	no	—
603	C₂²×D₄	—	2	4	no	—
604	C₂²×D₄	—	2	2	no	—
605	C₂²×D₄	—	2	4	no	—
606	C₂²×D₄	—	2	1	no	—
607	C₂²×D₄	D₄×C₈₉	1	2	yes	—
608	C₂²×D₄	D₄×C₈₉	1	2	yes	complemented
609	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
610	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic, complemented
611	C₂³×C₄	—	2	4	no	—
612	C₂³×C₄	—	2	2	no	—
613	C₂³×C₄	—	2	1	no	—
614	C₂³×C₄	D₄×C₈₉	1	2	yes	—
615	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
616	#137	—	2	8	no	—
617	#137	—	2	8	no	—
618	#137	—	2	8	no	—
619	#137	C₂³×C₈₉	1	16	yes	complemented
620	AGL(1,ℤ/8)	—	2	8	no	—
621	AGL(1,ℤ/8)	—	2	8	no	—
622	AGL(1,ℤ/8)	—	2	8	no	—
623	AGL(1,ℤ/8)	C₂³×C₈₉	1	16	yes	complemented
624	#135	—	2	16	no	—
625	#135	—	2	16	no	—
626	C₂×Q₁₆	—	2	4	no	—
627	C₂×SD₁₆	—	2	4	no	—
628	C₂×SD₁₆	—	2	4	no	—
629	C₂×D₈	—	2	4	no	—
630	C₂×M₁₆	—	2	2	no	—
631	C₂×M₁₆	—	2	2	no	—
632	C₂×M₁₆	—	2	2	no	—
633	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
634	C₂×M₁₆	C₂³×C₈₉	1	4	yes	complemented
635	C₂×M₁₆	C₂³×C₈₉	1	4	yes	complemented
636	C₂²×C₈	—	2	2	no	—
637	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	complemented
638	#127	C₂³×C₈₉	1	4	yes	complemented
639	#124	C₂³×C₈₉	1	4	yes	complemented
640	#124	C₂³×C₈₉	1	4	yes	complemented
641	#123	—	2	4	no	—
642	#123	—	2	4	no	—
643	C₂²⋊Q₈	—	2	4	no	—
644	C₂²⋊Q₈	—	2	4	no	—
645	#121	—	2	4	no	—
646	#121	—	2	8	no	—
647	#121	—	2	4	no	—
648	#120	—	2	4	no	—
649	#120	—	2	4	no	—
650	C₄×D₄	—	2	8	no	—
651	#117	—	2	1	no	—
652	#117	—	2	1	no	—
653	#117	C₂³×C₈₉	1	2	yes	—
654	#117	C₂³×C₈₉	1	2	yes	complemented
655	C₂×C₄⋊C₄	—	2	1	no	—
656	C₂×C₂²⋊C₄	—	2	1	no	—
657	C₂×C₄²	C₂³×C₈₉	1	2	yes	complemented
658	#104	C₂³×C₈₉	1	32	yes	complemented
659	#101	C₂³×C₈₉	1	8	yes	complemented
660	#100	C₂³×C₈₉	1	8	yes	complemented
661	C₂⁴	—	2	4	no	—
662	C₂⁴	—	2	2	no	—
663	C₂⁴	—	2	1	no	—
664	C₂⁴	C₂×D₄×C₈₉	1	2	yes	—
665	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
666	#41	—	2	16	no	—
667	#41	—	2	16	no	—
668	#41	—	2	32	no	—
669	#41	—	2	32	no	—
670	#41	—	2	16	no	—
671	#41	—	2	16	no	—
672	#41	—	2	16	no	—
673	#41	—	2	16	no	—
674	#41	—	2	16	no	—
675	#41	—	2	16	no	—
676	#41	—	2	16	no	—
677	#41	—	2	4	no	—
678	#41	—	2	4	no	—
679	#41	—	2	4	no	—
680	#41	—	2	4	no	—
681	#41	—	2	4	no	—
682	#41	—	2	4	no	—
683	#41	—	2	4	no	—
684	#41	—	2	4	no	—
685	#41	—	2	4	no	—
686	#41	—	2	4	no	—
687	#41	—	2	4	no	—
688	#41	—	2	4	no	—
689	#41	—	2	4	no	—
690	#41	—	2	4	no	—
691	#41	—	2	16	no	—
692	#41	—	2	4	no	—
693	#41	—	2	4	no	—
694	#41	—	2	4	no	—
695	#41	—	2	4	no	—
696	#41	—	2	4	no	—
697	#41	—	2	4	no	—
698	#41	—	2	4	no	—
699	#41	—	2	4	no	—
700	#41	—	2	4	no	—
701	#41	—	2	4	no	—
702	#41	—	4	1	no	—
703	#41	—	4	1	no	—
704	#41	—	4	1	no	—
705	#41	—	4	1	no	—
706	#41	—	4	2	no	—
707	#41	—	4	2	no	—
708	#41	C₂×D₄×C₈₉	1	8	yes	—
709	#41	C₂×D₄×C₈₉	1	8	yes	—
710	#41	C₂×D₄×C₈₉	1	8	yes	—
711	#41	C₂⁴×C₈₉	1	8	yes	—
712	C₂×Q₈	—	2	4	no	—
713	C₂×Q₈	—	2	16	no	—
714	C₂×Q₈	—	2	8	no	—
715	C₂×Q₈	—	2	8	no	—
716	C₂×Q₈	—	2	16	no	—
717	C₂×Q₈	—	2	2	no	—
718	C₂×Q₈	—	2	2	no	—
719	C₂×Q₈	—	2	2	no	—
720	C₂×Q₈	—	2	2	no	—
721	C₂×Q₈	—	2	2	no	—
722	C₂×Q₈	—	2	1	no	—
723	C₂×Q₈	—	2	2	no	—
724	C₂×Q₈	—	2	2	no	—
725	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
726	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
727	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
728	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
729	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
730	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
731	C₂×D₄	—	2	8	no	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	2	16	no	—
734	C₂×D₄	—	2	32	no	—
735	C₂×D₄	—	2	32	no	—
736	C₂×D₄	—	2	16	no	—
737	C₂×D₄	—	2	8	no	—
738	C₂×D₄	—	2	8	no	—
739	C₂×D₄	—	2	4	no	—
740	C₂×D₄	—	2	4	no	—
741	C₂×D₄	—	2	4	no	—
742	C₂×D₄	—	2	4	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	2	4	no	—
745	C₂×D₄	—	2	16	no	—
746	C₂×D₄	—	2	4	no	—
747	C₂×D₄	—	2	4	no	—
748	C₂×D₄	—	2	16	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	8	no	—
752	C₂×D₄	—	2	2	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	2	no	—
758	C₂×D₄	—	2	2	no	—
759	C₂×D₄	—	2	1	no	—
760	C₂×D₄	—	4	2	no	—
761	C₂×D₄	—	4	2	no	—
762	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
763	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
764	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
765	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
766	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
767	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
768	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
769	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
770	C₂²×C₄	—	2	4	no	—
771	C₂²×C₄	—	2	8	no	—
772	C₂²×C₄	—	2	16	no	—
773	C₂²×C₄	—	2	16	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	4	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	4	no	—
778	C₂²×C₄	—	2	4	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	2	4	no	—
783	C₂²×C₄	—	2	4	no	—
784	C₂²×C₄	—	2	4	no	—
785	C₂²×C₄	—	2	1	no	—
786	C₂²×C₄	—	2	2	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	4	2	no	—
790	C₂²×C₄	—	4	2	no	—
791	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
792	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
793	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
794	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
795	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
796	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
797	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
798	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
799	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
800	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
801	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
802	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
803	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
804	Q₁₆	—	2	16	no	—
805	SD₁₆	—	2	16	no	—
806	SD₁₆	—	2	16	no	—
807	D₈	—	2	16	no	—
808	M₁₆	—	2	4	no	—
809	M₁₆	—	2	4	no	—
810	M₁₆	—	2	4	no	—
811	M₁₆	C₂⁴×C₈₉	1	8	yes	—
812	C₂×C₈	—	2	4	no	—
813	C₂×C₈	—	2	4	no	—
814	C₂×C₈	—	2	4	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	8	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	8	no	—
821	C₂²⋊C₄	—	2	8	no	—
822	C₄²	—	2	2	no	—
823	C₄²	C₂⁴×C₈₉	1	4	yes	—
824	C₂³	—	2	16	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	2	4	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	4	no	—
829	C₂³	—	2	4	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	4	2	no	—
832	C₂³	—	8	1	no	—
833	C₂³	—	8	2	no	—
834	C₂³	—	8	4	no	—
835	C₂³	—	8	2	no	—
836	C₂³	—	8	8	no	—
837	C₂³	#120×C₈₉	1	2	yes	—
838	C₂³	#120×C₈₉	1	2	yes	—
839	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
840	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
841	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
842	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
843	Q₈	—	2	16	no	—
844	Q₈	—	2	4	no	—
845	Q₈	—	2	4	no	—
846	Q₈	—	2	4	no	—
847	Q₈	—	2	4	no	—
848	Q₈	—	2	4	no	—
849	Q₈	—	2	4	no	—
850	Q₈	—	4	1	no	—
851	Q₈	—	4	1	no	—
852	Q₈	C₂²×D₄×C₈₉	1	8	yes	—
853	D₄	—	2	32	no	—
854	D₄	—	2	16	no	—
855	D₄	—	2	8	no	—
856	D₄	—	2	8	no	—
857	D₄	—	2	8	no	—
858	D₄	—	2	8	no	—
859	D₄	—	2	8	no	—
860	D₄	—	2	8	no	—
861	D₄	—	2	4	no	—
862	D₄	—	2	4	no	—
863	D₄	—	2	4	no	—
864	D₄	—	2	4	no	—
865	D₄	—	2	4	no	—
866	D₄	—	2	4	no	—
867	D₄	—	4	2	no	—
868	D₄	—	4	2	no	—
869	D₄	—	4	4	no	—
870	D₄	—	4	1	no	—
871	D₄	—	4	1	no	—
872	D₄	—	8	8	no	—
873	D₄	C₂²×D₄×C₈₉	1	8	yes	—
874	C₂×C₄	—	2	16	no	—
875	C₂×C₄	—	2	32	no	—
876	C₂×C₄	—	2	4	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	4	no	—
879	C₂×C₄	—	2	4	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	8	no	—
882	C₂×C₄	—	2	8	no	—
883	C₂×C₄	—	2	4	no	—
884	C₂×C₄	—	2	4	no	—
885	C₂×C₄	—	2	8	no	—
886	C₂×C₄	—	2	4	no	—
887	C₂×C₄	—	2	4	no	—
888	C₂×C₄	—	2	8	no	—
889	C₂×C₄	—	2	4	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	4	2	no	—
892	C₂×C₄	—	4	2	no	—
893	C₂×C₄	—	4	2	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	—	8	2	no	—
896	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
897	C₂×C₄	#120×C₈₉	1	2	yes	—
898	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
899	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
900	C₂×C₄	#120×C₈₉	1	2	yes	—
901	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
902	C₂×C₄	#120×C₈₉	1	2	yes	—
903	C₂×C₄	#120×C₈₉	1	2	yes	—
904	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
905	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
906	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
907	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
908	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
909	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
910	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
911	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
912	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
913	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
914	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
915	C₈	—	2	8	no	—
916	C₂²	—	2	4	no	—
917	C₂²	—	2	8	no	—
918	C₂²	—	4	1	no	—
919	C₂²	—	4	2	no	—
920	C₂²	—	4	1	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	4	no	—
924	C₂²	—	4	4	no	—
925	C₂²	—	4	8	no	—
926	C₂²	—	4	4	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	8	4	no	—
929	C₂²	—	8	4	no	—
930	C₂²	—	8	2	no	—
931	C₂²	—	8	4	no	—
932	C₂²	—	8	16	no	—
933	C₂²	C₂×#120×C₈₉	1	1	yes	characteristic
934	C₂²	C₂×#120×C₈₉	1	2	yes	—
935	C₂²	C₂×#120×C₈₉	1	2	yes	—
936	C₂²	C₂×#120×C₈₉	1	1	yes	characteristic
937	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
938	C₄	—	2	8	no	—
939	C₄	—	2	4	no	—
940	C₄	—	4	4	no	—
941	C₄	—	4	2	no	—
942	C₄	C₂×#120×C₈₉	1	1	yes	characteristic
943	C₄	C₂×#120×C₈₉	1	1	yes	characteristic
944	C₄	C₂×#120×C₈₉	1	2	yes	—
945	C₄	C₂×#120×C₈₉	1	1	yes	characteristic
946	C₄	C₂×#120×C₈₉	1	1	yes	characteristic
947	C₄	C₂³×D₄×C₈₉	1	2	yes	—
948	C₂	—	2	1	no	—
949	C₂	—	2	1	no	—
950	C₂	—	2	2	no	—
951	C₂	—	2	2	no	—
952	C₂	—	2	1	no	—
953	C₂	—	4	4	no	—
954	C₂	—	4	8	no	—
955	C₂	—	8	2	no	—
956	C₂	C₂²×#120×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈₉	C₂×#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
socle	C₂×C₈₉	C₂²×#120
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈₉ ◁ C₂³×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#585×C₈₉	C₂	semidirect
2. C₂×#575×C₈₉	C₂	semidirect
3. C₈₉×#3449	C₂	semidirect
4. C₈₉×#3022	C₂	semidirect
5. C₈₉×#3021	C₂	semidirect
6. C₈₉×#3020	C₂	semidirect
7. C₈₉×#3019	C₂	semidirect
8. C₈₉×#3018	C₂	semidirect
9. C₂×#421×C₈₉	C₂	semidirect
10. C₂×#413×C₈₉	C₂	semidirect
16. #585×C₈₉	C₂²	semidirect
18. C₂×2₋¹⁺⁴×C₈₉	C₂²	semidirect
21. C₂×H(5,𝔽₂)×C₈₉	C₂²	semidirect
26. C₂²×#41×C₈₉	C₂²	semidirect
29. #575×C₈₉	C₂²	semidirect
30. #575×C₈₉	C₂²	semidirect
32. C₂×#137×C₈₉	C₂²	semidirect
34. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
36. C₂²×M₁₆×C₈₉	C₂²	semidirect
38. #536×C₈₉	C₂²	semidirect
39. #536×C₈₉	C₂²	semidirect
40. #535×C₈₉	C₂²	semidirect
41. #535×C₈₉	C₂²	semidirect
43. #532×C₈₉	C₂²	semidirect
46. C₂×#117×C₈₉	C₂²	semidirect
47. #456×C₈₉	C₂²	semidirect
48. #455×C₈₉	C₂²	semidirect
49. #454×C₈₉	C₂²	semidirect
50. #453×C₈₉	C₂²	semidirect
51. #421×C₈₉	C₂²	semidirect
52. #421×C₈₉	C₂²	semidirect
53. C₂×#104×C₈₉	C₂²	semidirect
54. #413×C₈₉	C₂²	semidirect
55. #413×C₈₉	C₂²	semidirect
56. C₂×#101×C₈₉	C₂²	semidirect
57. C₂×#100×C₈₉	C₂²	semidirect
107. C₂×#41×C₈₉	D₄	semidirect
108. C₂×#41×C₈₉	D₄	semidirect
109. C₂×#41×C₈₉	D₄	semidirect
116. C₂×#41×C₈₉	C₂³	semidirect
119. C₂²×Q₈×C₈₉	D₄	semidirect
121. C₂²×Q₈×C₈₉	C₂³	semidirect
129. C₂²×D₄×C₈₉	D₄	semidirect
131. C₂²×D₄×C₈₉	C₂³	semidirect
140. #137×C₈₉	C₂³	semidirect
144. AGL(1,ℤ/8)×C₈₉	C₂³	semidirect
155. C₂×M₁₆×C₈₉	C₂³	semidirect
156. C₂×M₁₆×C₈₉	C₂³	semidirect
158. C₄⋊Q₈×C₈₉	C₂³	semidirect
159. #127×C₈₉	C₂³	semidirect
160. #124×C₈₉	C₂³	semidirect
161. #124×C₈₉	C₂³	semidirect
175. #117×C₈₉	C₂³	semidirect
178. C₂×C₄²×C₈₉	C₂³	semidirect
179. #104×C₈₉	C₂³	semidirect
180. #101×C₈₉	C₂³	semidirect
181. #100×C₈₉	C₂³	semidirect
469. #60387	C₈₉	direct (N × H)
479. C₂×#585	C₂×C₈₉	semidirect
480. C₂×#575	C₂×C₈₉	semidirect
481. #3449	C₂×C₈₉	semidirect
482. #3022	C₂×C₈₉	semidirect
483. #3021	C₂×C₈₉	semidirect
484. #3020	C₂×C₈₉	semidirect
485. #3019	C₂×C₈₉	semidirect
486. #3018	C₂×C₈₉	semidirect
487. C₂×#421	C₂×C₈₉	semidirect
488. C₂×#413	C₂×C₈₉	semidirect
489. C₈₉	#60387	direct (N × H)
495. #585	C₂²×C₈₉	semidirect
497. C₂×2₋¹⁺⁴	C₂²×C₈₉	semidirect
500. C₂×H(5,𝔽₂)	C₂²×C₈₉	semidirect
505. C₂²×#41	C₂²×C₈₉	semidirect
508. #575	C₂²×C₈₉	semidirect
509. #575	C₂²×C₈₉	semidirect
511. C₂×#137	C₂²×C₈₉	semidirect
513. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
515. C₂²×M₁₆	C₂²×C₈₉	semidirect
517. #536	C₂²×C₈₉	semidirect
518. #536	C₂²×C₈₉	semidirect
519. #535	C₂²×C₈₉	semidirect
520. #535	C₂²×C₈₉	semidirect
522. #532	C₂²×C₈₉	semidirect
525. C₂×#117	C₂²×C₈₉	semidirect
526. #456	C₂²×C₈₉	semidirect
527. #455	C₂²×C₈₉	semidirect
528. #454	C₂²×C₈₉	semidirect
529. #453	C₂²×C₈₉	semidirect
530. #421	C₂²×C₈₉	semidirect
531. #421	C₂²×C₈₉	semidirect
532. C₂×#104	C₂²×C₈₉	semidirect
533. #413	C₂²×C₈₉	semidirect
534. #413	C₂²×C₈₉	semidirect
535. C₂×#101	C₂²×C₈₉	semidirect
536. C₂×#100	C₂²×C₈₉	semidirect
586. C₂×#41	D₄×C₈₉	semidirect
587. C₂×#41	D₄×C₈₉	semidirect
588. C₂×#41	D₄×C₈₉	semidirect
595. C₂×#41	C₂³×C₈₉	semidirect
598. C₂²×Q₈	D₄×C₈₉	semidirect
600. C₂²×Q₈	C₂³×C₈₉	semidirect
608. C₂²×D₄	D₄×C₈₉	semidirect
610. C₂²×D₄	C₂³×C₈₉	semidirect
619. #137	C₂³×C₈₉	semidirect
623. AGL(1,ℤ/8)	C₂³×C₈₉	semidirect
634. C₂×M₁₆	C₂³×C₈₉	semidirect
635. C₂×M₁₆	C₂³×C₈₉	semidirect
637. C₄⋊Q₈	C₂³×C₈₉	semidirect
638. #127	C₂³×C₈₉	semidirect
639. #124	C₂³×C₈₉	semidirect
640. #124	C₂³×C₈₉	semidirect
654. #117	C₂³×C₈₉	semidirect
657. C₂×C₄²	C₂³×C₈₉	semidirect
658. #104	C₂³×C₈₉	semidirect
659. #101	C₂³×C₈₉	semidirect
660. #100	C₂³×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#585×C₈₉	2
C₂×#575×C₈₉	2
C₈₉×#3449	2
C₈₉×#3022	2
C₈₉×#3021	2
C₈₉×#3020	2
C₈₉×#3019	2
C₈₉×#3018	2
C₂×#421×C₈₉	2
C₂×#413×C₈₉	2
#60387	89

Subgroups — C89×#60387 #36438235

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60387 #36438235