Subgroups — C₈₉×#23894 #36401742

Order 22784.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3586	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3585	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3020	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3019	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3010	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3009	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2019	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2017	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2009	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2008	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1903	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1902	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1881	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1881	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1794	C₂	1	1	yes	maximal, characteristic, complemented
16	#585×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	1	yes	characteristic, complemented
18	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	1	yes	characteristic
19	#578×C₈₉	—	2	2	no	—
20	#578×C₈₉	—	2	2	no	—
21	#577×C₈₉	—	2	2	no	—
22	#577×C₈₉	—	2	2	no	—
23	#577×C₈₉	—	2	2	no	—
24	#577×C₈₉	—	2	2	no	—
25	#576×C₈₉	—	2	2	no	—
26	#576×C₈₉	—	2	2	no	—
27	#575×C₈₉	—	2	2	no	—
28	#575×C₈₉	—	2	2	no	—
29	#575×C₈₉	C₂²	1	1	yes	characteristic
30	#575×C₈₉	C₂²	1	1	yes	characteristic
31	#575×C₈₉	C₂²	1	1	yes	characteristic
32	#575×C₈₉	C₂²	1	1	yes	characteristic, complemented
33	#575×C₈₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×#137×C₈₉	—	2	2	no	—
35	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic, complemented
37	C₂×AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
38	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
40	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
41	#568×C₈₉	C₂²	1	1	yes	characteristic
42	#568×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	#536×C₈₉	C₂²	1	1	yes	characteristic, complemented
44	#535×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	#456×C₈₉	—	2	2	no	—
46	#455×C₈₉	—	2	2	no	—
47	#454×C₈₉	—	2	2	no	—
48	#453×C₈₉	—	2	2	no	—
49	#452×C₈₉	—	2	2	no	—
50	#450×C₈₉	—	2	2	no	—
51	#449×C₈₉	—	2	2	no	—
52	#448×C₈₉	—	2	2	no	—
53	#421×C₈₉	C₂²	1	1	yes	characteristic
54	#421×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	#421×C₈₉	C₂²	1	1	yes	characteristic, complemented
56	#421×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	#419×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#418×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#416×C₈₉	C₂²	1	1	yes	characteristic
60	#416×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	C₂×#101×C₈₉	C₂²	1	1	yes	characteristic, complemented
62	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	#410×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	#408×C₈₉	C₂²	1	1	yes	characteristic, complemented
65	#408×C₈₉	C₂²	1	1	yes	characteristic, complemented
66	#408×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#344×C₈₉	C₂²	1	1	yes	characteristic, complemented
68	#344×C₈₉	C₂²	1	1	yes	characteristic, complemented
69	#341×C₈₉	C₂²	1	1	yes	characteristic, complemented
70	#338×C₈₉	C₂²	1	1	yes	characteristic, complemented
71	2₋¹⁺⁴×C₈₉	—	2	2	no	—
72	2₋¹⁺⁴×C₈₉	—	2	1	no	—
73	2₋¹⁺⁴×C₈₉	—	2	2	no	—
74	2₋¹⁺⁴×C₈₉	—	2	1	no	—
75	2₋¹⁺⁴×C₈₉	—	2	2	no	—
76	2₋¹⁺⁴×C₈₉	—	4	1	no	—
77	2₋¹⁺⁴×C₈₉	D₄	1	2	yes	complemented
78	H(5,𝔽₂)×C₈₉	—	2	2	no	—
79	H(5,𝔽₂)×C₈₉	—	2	1	no	—
80	H(5,𝔽₂)×C₈₉	—	2	2	no	—
81	H(5,𝔽₂)×C₈₉	—	2	1	no	—
82	H(5,𝔽₂)×C₈₉	—	2	2	no	—
83	H(5,𝔽₂)×C₈₉	—	4	1	no	—
84	H(5,𝔽₂)×C₈₉	—	4	1	no	—
85	H(5,𝔽₂)×C₈₉	D₄	1	2	yes	complemented
86	C₂×#41×C₈₉	—	2	2	no	—
87	C₂×#41×C₈₉	—	2	2	no	—
88	C₂×#41×C₈₉	—	2	1	no	—
89	C₂×#41×C₈₉	—	2	1	no	—
90	C₂×#41×C₈₉	—	2	1	no	—
91	C₂×#41×C₈₉	—	2	1	no	—
92	C₂×#41×C₈₉	—	4	1	no	—
93	C₂×#41×C₈₉	—	4	1	no	—
94	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
95	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
96	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
97	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
98	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
99	C₂²×Q₈×C₈₉	—	2	1	no	—
100	C₂²×Q₈×C₈₉	—	2	1	no	—
101	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₈₉	—	2	1	no	—
103	C₂²×D₄×C₈₉	—	2	1	no	—
104	C₂²×D₄×C₈₉	—	4	1	no	—
105	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
106	#137×C₈₉	—	2	4	no	—
107	#137×C₈₉	—	2	4	no	—
108	#137×C₈₉	—	2	4	no	—
109	#137×C₈₉	—	2	4	no	—
110	#137×C₈₉	—	2	2	no	—
111	#137×C₈₉	—	2	2	no	—
112	#137×C₈₉	—	2	1	no	—
113	#137×C₈₉	—	2	2	no	—
114	#137×C₈₉	—	2	1	no	—
115	#137×C₈₉	—	2	1	no	—
116	#137×C₈₉	—	2	1	no	—
117	#137×C₈₉	—	2	1	no	—
118	#137×C₈₉	—	2	1	no	—
119	#137×C₈₉	—	2	1	no	—
120	#137×C₈₉	—	2	1	no	—
121	#137×C₈₉	—	2	2	no	—
122	#137×C₈₉	D₄	1	2	yes	—
123	#137×C₈₉	D₄	1	2	yes	complemented
124	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
125	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
126	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
127	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
128	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
129	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
130	AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
131	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
132	AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
133	AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
134	AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
135	AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
136	AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
137	AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
138	AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
139	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
140	AGL(1,ℤ/8)×C₈₉	D₄	1	2	yes	—
141	AGL(1,ℤ/8)×C₈₉	D₄	1	2	yes	complemented
142	#135×C₈₉	—	2	4	no	—
143	#135×C₈₉	—	2	4	no	—
144	#135×C₈₉	—	2	4	no	—
145	#135×C₈₉	—	2	4	no	—
146	#135×C₈₉	—	2	2	no	—
147	#135×C₈₉	—	2	2	no	—
148	#135×C₈₉	—	2	2	no	—
149	#135×C₈₉	—	2	2	no	—
150	#135×C₈₉	—	4	1	no	—
151	C₂×Q₁₆×C₈₉	—	2	4	no	—
152	C₂×Q₁₆×C₈₉	—	2	1	no	—
153	C₂×Q₁₆×C₈₉	D₄	1	2	yes	complemented
154	C₂×SD₁₆×C₈₉	—	2	4	no	—
155	C₂×SD₁₆×C₈₉	—	2	4	no	—
156	C₂×SD₁₆×C₈₉	—	2	1	no	—
157	C₂×SD₁₆×C₈₉	—	2	1	no	—
158	C₂×SD₁₆×C₈₉	—	2	2	no	—
159	C₂×SD₁₆×C₈₉	—	2	2	no	—
160	C₂×SD₁₆×C₈₉	—	4	1	no	—
161	C₂×SD₁₆×C₈₉	D₄	1	2	yes	—
162	C₂×SD₁₆×C₈₉	D₄	1	2	yes	complemented
163	C₂×D₈×C₈₉	—	2	4	no	—
164	C₂×D₈×C₈₉	—	2	1	no	—
165	C₂×D₈×C₈₉	D₄	1	2	yes	—
166	#131×C₈₉	—	2	2	no	—
167	#131×C₈₉	—	2	2	no	—
168	#131×C₈₉	—	2	2	no	—
169	#131×C₈₉	—	2	2	no	—
170	C₂×M₁₆×C₈₉	—	2	2	no	—
171	C₂×M₁₆×C₈₉	—	2	2	no	—
172	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
173	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
174	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
175	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
176	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
178	C₄⋊Q₈×C₈₉	—	2	1	no	—
179	#127×C₈₉	—	2	1	no	—
180	#124×C₈₉	—	2	1	no	—
181	#124×C₈₉	—	2	1	no	—
182	#123×C₈₉	—	4	1	no	—
183	C₂²⋊Q₈×C₈₉	—	2	2	no	—
184	#121×C₈₉	—	2	2	no	—
185	#120×C₈₉	—	4	1	no	—
186	#117×C₈₉	C₂³	1	1	yes	characteristic
187	#117×C₈₉	C₂³	1	1	yes	characteristic
188	#104×C₈₉	—	2	2	no	—
189	#104×C₈₉	—	2	2	no	—
190	#104×C₈₉	—	2	2	no	—
191	#104×C₈₉	—	2	2	no	—
192	#103×C₈₉	—	2	1	no	—
193	#103×C₈₉	—	2	1	no	—
194	#103×C₈₉	—	2	2	no	—
195	#102×C₈₉	—	2	1	no	—
196	#102×C₈₉	—	2	1	no	—
197	#102×C₈₉	—	2	2	no	—
198	#101×C₈₉	—	2	2	no	—
199	#100×C₈₉	—	2	2	no	—
200	#99×C₈₉	—	4	1	no	—
201	C₂²⋊C₈×C₈₉	—	2	2	no	—
202	C₂²⋊C₈×C₈₉	—	2	2	no	—
203	C₂²⋊C₈×C₈₉	—	4	1	no	—
204	C₂⁴×C₈₉	—	2	1	no	—
205	C₂⁴×C₈₉	—	4	1	no	—
206	#41×C₈₉	—	2	1	no	—
207	#41×C₈₉	—	2	1	no	—
208	#41×C₈₉	—	2	1	no	—
209	#41×C₈₉	—	2	1	no	—
210	#41×C₈₉	—	2	4	no	—
211	#41×C₈₉	—	2	4	no	—
212	#41×C₈₉	—	2	2	no	—
213	#41×C₈₉	—	2	2	no	—
214	#41×C₈₉	—	2	2	no	—
215	#41×C₈₉	—	2	2	no	—
216	#41×C₈₉	—	2	1	no	—
217	#41×C₈₉	—	2	1	no	—
218	#41×C₈₉	—	2	1	no	—
219	#41×C₈₉	—	2	1	no	—
220	#41×C₈₉	—	2	1	no	—
221	#41×C₈₉	—	2	1	no	—
222	#41×C₈₉	—	2	1	no	—
223	#41×C₈₉	—	2	1	no	—
224	#41×C₈₉	—	2	1	no	—
225	#41×C₈₉	—	2	1	no	—
226	#41×C₈₉	—	2	1	no	—
227	#41×C₈₉	—	2	1	no	—
228	#41×C₈₉	—	4	2	no	—
229	#41×C₈₉	—	4	2	no	—
230	#41×C₈₉	—	4	2	no	—
231	#41×C₈₉	—	4	2	no	—
232	#41×C₈₉	—	4	2	no	—
233	#41×C₈₉	—	4	4	no	—
234	#41×C₈₉	—	4	2	no	—
235	#41×C₈₉	—	4	2	no	—
236	#41×C₈₉	—	4	2	no	—
237	#41×C₈₉	—	4	1	no	—
238	#41×C₈₉	—	4	1	no	—
239	#41×C₈₉	—	4	4	no	—
240	#41×C₈₉	—	4	2	no	—
241	#41×C₈₉	—	4	2	no	—
242	#41×C₈₉	C₂×D₄	1	2	yes	—
243	#41×C₈₉	C₂×D₄	1	2	yes	—
244	#41×C₈₉	C₂×D₄	1	2	yes	—
245	#41×C₈₉	C₂×D₄	1	2	yes	—
246	C₂×Q₈×C₈₉	—	2	1	no	—
247	C₂×Q₈×C₈₉	—	2	4	no	—
248	C₂×Q₈×C₈₉	—	2	2	no	—
249	C₂×Q₈×C₈₉	—	2	2	no	—
250	C₂×Q₈×C₈₉	—	2	1	no	—
251	C₂×Q₈×C₈₉	—	2	1	no	—
252	C₂×Q₈×C₈₉	—	2	1	no	—
253	C₂×Q₈×C₈₉	—	2	1	no	—
254	C₂×Q₈×C₈₉	—	4	1	no	—
255	C₂×Q₈×C₈₉	—	4	2	no	—
256	C₂×Q₈×C₈₉	—	4	2	no	—
257	C₂×Q₈×C₈₉	—	4	1	no	—
258	C₂×Q₈×C₈₉	—	4	2	no	—
259	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
260	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
261	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
262	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
263	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
264	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
265	C₂×D₄×C₈₉	—	2	1	no	—
266	C₂×D₄×C₈₉	—	2	1	no	—
267	C₂×D₄×C₈₉	—	2	4	no	—
268	C₂×D₄×C₈₉	—	2	2	no	—
269	C₂×D₄×C₈₉	—	2	2	no	—
270	C₂×D₄×C₈₉	—	2	1	no	—
271	C₂×D₄×C₈₉	—	2	1	no	—
272	C₂×D₄×C₈₉	—	2	1	no	—
273	C₂×D₄×C₈₉	—	2	1	no	—
274	C₂×D₄×C₈₉	—	2	1	no	—
275	C₂×D₄×C₈₉	—	2	1	no	—
276	C₂×D₄×C₈₉	—	2	1	no	—
277	C₂×D₄×C₈₉	—	2	1	no	—
278	C₂×D₄×C₈₉	—	4	2	no	—
279	C₂×D₄×C₈₉	—	4	1	no	—
280	C₂×D₄×C₈₉	—	4	1	no	—
281	C₂×D₄×C₈₉	—	4	2	no	—
282	C₂×D₄×C₈₉	—	4	2	no	—
283	C₂×D₄×C₈₉	—	4	1	no	—
284	C₂×D₄×C₈₉	—	4	4	no	—
285	C₂×D₄×C₈₉	—	4	2	no	—
286	C₂×D₄×C₈₉	—	4	2	no	—
287	C₂×D₄×C₈₉	—	4	4	no	—
288	C₂×D₄×C₈₉	—	4	1	no	—
289	C₂×D₄×C₈₉	—	4	2	no	—
290	C₂×D₄×C₈₉	—	4	2	no	—
291	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
292	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
293	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
294	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
295	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
296	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₈₉	—	2	1	no	—
298	C₂²×C₄×C₈₉	—	2	1	no	—
299	C₂²×C₄×C₈₉	—	2	1	no	—
300	C₂²×C₄×C₈₉	—	2	1	no	—
301	C₂²×C₄×C₈₉	—	2	1	no	—
302	C₂²×C₄×C₈₉	—	2	1	no	—
303	C₂²×C₄×C₈₉	—	4	1	no	—
304	C₂²×C₄×C₈₉	—	4	2	no	—
305	C₂²×C₄×C₈₉	—	4	1	no	—
306	C₂²×C₄×C₈₉	—	4	1	no	—
307	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
308	Q₁₆×C₈₉	—	2	4	no	—
309	Q₁₆×C₈₉	—	2	2	no	—
310	Q₁₆×C₈₉	—	2	2	no	—
311	Q₁₆×C₈₉	—	2	2	no	—
312	Q₁₆×C₈₉	—	2	4	no	—
313	Q₁₆×C₈₉	—	2	2	no	—
314	Q₁₆×C₈₉	—	4	1	no	—
315	SD₁₆×C₈₉	—	2	4	no	—
316	SD₁₆×C₈₉	—	2	2	no	—
317	SD₁₆×C₈₉	—	2	4	no	—
318	SD₁₆×C₈₉	—	2	2	no	—
319	SD₁₆×C₈₉	—	2	2	no	—
320	SD₁₆×C₈₉	—	2	2	no	—
321	SD₁₆×C₈₉	—	2	2	no	—
322	SD₁₆×C₈₉	—	2	4	no	—
323	SD₁₆×C₈₉	—	2	2	no	—
324	SD₁₆×C₈₉	—	2	2	no	—
325	SD₁₆×C₈₉	—	2	4	no	—
326	SD₁₆×C₈₉	—	2	2	no	—
327	SD₁₆×C₈₉	—	4	4	no	—
328	SD₁₆×C₈₉	—	4	1	no	—
329	SD₁₆×C₈₉	—	4	1	no	—
330	D₈×C₈₉	—	2	4	no	—
331	D₈×C₈₉	—	2	2	no	—
332	D₈×C₈₉	—	2	2	no	—
333	D₈×C₈₉	—	2	2	no	—
334	D₈×C₈₉	—	2	4	no	—
335	D₈×C₈₉	—	2	2	no	—
336	D₈×C₈₉	—	4	1	no	—
337	M₁₆×C₈₉	—	2	4	no	—
338	M₁₆×C₈₉	—	2	4	no	—
339	M₁₆×C₈₉	—	2	1	no	—
340	M₁₆×C₈₉	—	2	1	no	—
341	M₁₆×C₈₉	—	2	1	no	—
342	M₁₆×C₈₉	—	2	1	no	—
343	M₁₆×C₈₉	—	2	1	no	—
344	M₁₆×C₈₉	—	2	1	no	—
345	M₁₆×C₈₉	—	2	1	no	—
346	M₁₆×C₈₉	—	2	1	no	—
347	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
348	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
349	C₂×C₈×C₈₉	—	2	4	no	—
350	C₂×C₈×C₈₉	—	2	4	no	—
351	C₂×C₈×C₈₉	—	2	1	no	—
352	C₂×C₈×C₈₉	—	2	1	no	—
353	C₂×C₈×C₈₉	—	2	1	no	—
354	C₂×C₈×C₈₉	—	2	1	no	—
355	C₂×C₈×C₈₉	—	2	1	no	—
356	C₂×C₈×C₈₉	—	2	1	no	—
357	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
358	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
359	C₄⋊C₄×C₈₉	—	2	1	no	—
360	C₄⋊C₄×C₈₉	—	2	1	no	—
361	C₄⋊C₄×C₈₉	—	4	2	no	—
362	C₂²⋊C₄×C₈₉	—	2	1	no	—
363	C₂²⋊C₄×C₈₉	—	2	1	no	—
364	C₂²⋊C₄×C₈₉	—	4	2	no	—
365	C₂²⋊C₄×C₈₉	—	4	2	no	—
366	C₄²×C₈₉	—	2	1	no	—
367	C₄²×C₈₉	—	2	1	no	—
368	C₂³×C₈₉	—	2	1	no	—
369	C₂³×C₈₉	—	2	1	no	—
370	C₂³×C₈₉	—	2	1	no	—
371	C₂³×C₈₉	—	2	1	no	—
372	C₂³×C₈₉	—	2	1	no	—
373	C₂³×C₈₉	—	2	2	no	—
374	C₂³×C₈₉	—	4	2	no	—
375	C₂³×C₈₉	—	4	4	no	—
376	C₂³×C₈₉	—	4	1	no	—
377	C₂³×C₈₉	—	4	1	no	—
378	C₂³×C₈₉	—	16	1	no	—
379	C₂³×C₈₉	—	16	2	no	—
380	C₂³×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
381	Q₈×C₈₉	—	2	1	no	—
382	Q₈×C₈₉	—	2	1	no	—
383	Q₈×C₈₉	—	2	1	no	—
384	Q₈×C₈₉	—	2	1	no	—
385	Q₈×C₈₉	—	2	2	no	—
386	Q₈×C₈₉	—	2	1	no	—
387	Q₈×C₈₉	—	2	1	no	—
388	Q₈×C₈₉	—	2	2	no	—
389	Q₈×C₈₉	—	2	1	no	—
390	Q₈×C₈₉	—	2	1	no	—
391	Q₈×C₈₉	—	4	2	no	—
392	Q₈×C₈₉	—	4	4	no	—
393	Q₈×C₈₉	—	4	1	no	—
394	Q₈×C₈₉	—	4	1	no	—
395	Q₈×C₈₉	#120	1	2	yes	—
396	Q₈×C₈₉	#120	1	2	yes	—
397	D₄×C₈₉	—	2	2	no	—
398	D₄×C₈₉	—	2	2	no	—
399	D₄×C₈₉	—	2	2	no	—
400	D₄×C₈₉	—	2	2	no	—
401	D₄×C₈₉	—	2	1	no	—
402	D₄×C₈₉	—	2	1	no	—
403	D₄×C₈₉	—	2	2	no	—
404	D₄×C₈₉	—	2	1	no	—
405	D₄×C₈₉	—	2	1	no	—
406	D₄×C₈₉	—	2	1	no	—
407	D₄×C₈₉	—	2	1	no	—
408	D₄×C₈₉	—	2	1	no	—
409	D₄×C₈₉	—	2	1	no	—
410	D₄×C₈₉	—	2	2	no	—
411	D₄×C₈₉	—	4	2	no	—
412	D₄×C₈₉	—	4	2	no	—
413	D₄×C₈₉	—	4	4	no	—
414	D₄×C₈₉	—	4	2	no	—
415	D₄×C₈₉	—	4	4	no	—
416	D₄×C₈₉	—	4	4	no	—
417	D₄×C₈₉	—	4	1	no	—
418	D₄×C₈₉	—	4	1	no	—
419	D₄×C₈₉	—	4	1	no	—
420	D₄×C₈₉	—	4	1	no	—
421	D₄×C₈₉	—	4	1	no	—
422	D₄×C₈₉	—	4	1	no	—
423	D₄×C₈₉	—	4	1	no	—
424	D₄×C₈₉	—	4	1	no	—
425	D₄×C₈₉	—	16	2	no	—
426	D₄×C₈₉	#120	1	2	yes	—
427	D₄×C₈₉	#120	1	2	yes	—
428	C₂×C₄×C₈₉	—	2	1	no	—
429	C₂×C₄×C₈₉	—	2	1	no	—
430	C₂×C₄×C₈₉	—	2	2	no	—
431	C₂×C₄×C₈₉	—	2	2	no	—
432	C₂×C₄×C₈₉	—	2	2	no	—
433	C₂×C₄×C₈₉	—	2	2	no	—
434	C₂×C₄×C₈₉	—	2	1	no	—
435	C₂×C₄×C₈₉	—	2	1	no	—
436	C₂×C₄×C₈₉	—	2	2	no	—
437	C₂×C₄×C₈₉	—	2	1	no	—
438	C₂×C₄×C₈₉	—	4	2	no	—
439	C₂×C₄×C₈₉	—	4	2	no	—
440	C₂×C₄×C₈₉	—	4	2	no	—
441	C₂×C₄×C₈₉	—	4	4	no	—
442	C₂×C₄×C₈₉	—	4	4	no	—
443	C₂×C₄×C₈₉	—	4	4	no	—
444	C₂×C₄×C₈₉	—	4	1	no	—
445	C₂×C₄×C₈₉	—	4	1	no	—
446	C₂×C₄×C₈₉	—	4	1	no	—
447	C₂×C₄×C₈₉	—	4	1	no	—
448	C₂×C₄×C₈₉	—	4	1	no	—
449	C₂×C₄×C₈₉	—	4	1	no	—
450	C₂×C₄×C₈₉	—	4	1	no	—
451	C₂×C₄×C₈₉	—	4	1	no	—
452	C₂×C₄×C₈₉	—	4	1	no	—
453	C₂×C₄×C₈₉	—	4	1	no	—
454	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
460	C₈×C₈₉	—	2	2	no	—
461	C₈×C₈₉	—	2	2	no	—
462	C₈×C₈₉	—	2	2	no	—
463	C₈×C₈₉	—	2	2	no	—
464	C₈×C₈₉	—	4	1	no	—
465	C₈×C₈₉	—	4	1	no	—
466	C₂²×C₈₉	—	2	2	no	—
467	C₂²×C₈₉	—	2	2	no	—
468	C₂²×C₈₉	—	4	1	no	—
469	C₂²×C₈₉	—	4	2	no	—
470	C₂²×C₈₉	—	4	2	no	—
471	C₂²×C₈₉	—	4	1	no	—
472	C₂²×C₈₉	—	4	1	no	—
473	C₂²×C₈₉	—	4	1	no	—
474	C₂²×C₈₉	—	4	2	no	—
475	C₂²×C₈₉	—	8	1	no	—
476	C₂²×C₈₉	—	8	1	no	—
477	C₂²×C₈₉	—	8	2	no	—
478	C₂²×C₈₉	—	8	2	no	—
479	C₂²×C₈₉	—	8	1	no	—
480	C₂²×C₈₉	—	16	1	no	—
481	C₂²×C₈₉	—	16	2	no	—
482	C₂²×C₈₉	—	16	4	no	—
483	C₂²×C₈₉	#534	1	1	yes	characteristic
484	C₂²×C₈₉	D₄²	1	1	yes	characteristic
485	C₂²×C₈₉	D₄²	1	1	yes	characteristic
486	C₄×C₈₉	—	2	2	no	—
487	C₄×C₈₉	—	2	2	no	—
488	C₄×C₈₉	—	4	1	no	—
489	C₄×C₈₉	—	4	1	no	—
490	C₄×C₈₉	—	4	1	no	—
491	C₄×C₈₉	—	4	2	no	—
492	C₄×C₈₉	—	8	1	no	—
493	C₄×C₈₉	—	8	1	no	—
494	C₄×C₈₉	C₂×#120	1	1	yes	characteristic
495	C₄×C₈₉	C₂×#120	1	1	yes	characteristic
496	C₄×C₈₉	D₄²	1	1	yes	characteristic
497	C₄×C₈₉	D₄²	1	1	yes	characteristic
498	#23894	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
499	C₂×C₈₉	—	2	1	no	—
500	C₂×C₈₉	—	2	1	no	—
501	C₂×C₈₉	—	2	1	no	—
502	C₂×C₈₉	—	4	2	no	—
503	C₂×C₈₉	—	4	2	no	—
504	C₂×C₈₉	—	8	1	no	—
505	C₂×C₈₉	—	8	1	no	—
506	C₂×C₈₉	—	8	2	no	—
507	C₂×C₈₉	—	8	1	no	—
508	C₂×C₈₉	#2403	1	1	yes	characteristic
509	#3586	C₂×C₈₉	1	1	yes	characteristic, complemented
510	#3585	C₂×C₈₉	1	1	yes	characteristic, complemented
511	#3020	C₂×C₈₉	1	1	yes	characteristic, complemented
512	#3019	C₂×C₈₉	1	1	yes	characteristic, complemented
513	#3010	C₂×C₈₉	1	1	yes	characteristic, complemented
514	#3009	C₂×C₈₉	1	1	yes	characteristic, complemented
515	#2019	C₂×C₈₉	1	1	yes	characteristic, complemented
516	#2017	C₂×C₈₉	1	1	yes	characteristic, complemented
517	#2009	C₂×C₈₉	1	1	yes	characteristic, complemented
518	#2008	C₂×C₈₉	1	1	yes	characteristic, complemented
519	#1903	C₂×C₈₉	1	1	yes	characteristic, complemented
520	#1902	C₂×C₈₉	1	1	yes	characteristic, complemented
521	#1881	C₂×C₈₉	1	1	yes	characteristic, complemented
522	#1881	C₂×C₈₉	1	1	yes	characteristic, complemented
523	#1794	C₂×C₈₉	1	1	yes	characteristic, complemented
524	C₈₉	#23894	1	1	yes	characteristic, direct product factor, Sylow
525	#585	C₂²×C₈₉	1	1	yes	characteristic
526	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	1	yes	characteristic, complemented
527	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	1	yes	characteristic
528	#578	—	2	2	no	—
529	#578	—	2	2	no	—
530	#577	—	2	2	no	—
531	#577	—	2	2	no	—
532	#577	—	2	2	no	—
533	#577	—	2	2	no	—
534	#576	—	2	2	no	—
535	#576	—	2	2	no	—
536	#575	—	2	2	no	—
537	#575	—	2	2	no	—
538	#575	C₂²×C₈₉	1	1	yes	characteristic
539	#575	C₂²×C₈₉	1	1	yes	characteristic
540	#575	C₂²×C₈₉	1	1	yes	characteristic
541	#575	C₂²×C₈₉	1	1	yes	characteristic, complemented
542	#575	C₂²×C₈₉	1	1	yes	characteristic, complemented
543	C₂×#137	—	2	2	no	—
544	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
545	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic, complemented
546	C₂×AGL(1,ℤ/8)	—	2	2	no	—
547	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
548	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
549	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
550	#568	C₂²×C₈₉	1	1	yes	characteristic
551	#568	C₂²×C₈₉	1	1	yes	characteristic, complemented
552	#536	C₂²×C₈₉	1	1	yes	characteristic, complemented
553	#535	C₂²×C₈₉	1	1	yes	characteristic, complemented
554	#456	—	2	2	no	—
555	#455	—	2	2	no	—
556	#454	—	2	2	no	—
557	#453	—	2	2	no	—
558	#452	—	2	2	no	—
559	#450	—	2	2	no	—
560	#449	—	2	2	no	—
561	#448	—	2	2	no	—
562	#421	C₂²×C₈₉	1	1	yes	characteristic
563	#421	C₂²×C₈₉	1	1	yes	characteristic, complemented
564	#421	C₂²×C₈₉	1	1	yes	characteristic, complemented
565	#421	C₂²×C₈₉	1	1	yes	characteristic, complemented
566	#419	C₂²×C₈₉	1	1	yes	characteristic, complemented
567	#418	C₂²×C₈₉	1	1	yes	characteristic, complemented
568	#416	C₂²×C₈₉	1	1	yes	characteristic
569	#416	C₂²×C₈₉	1	1	yes	characteristic, complemented
570	C₂×#101	C₂²×C₈₉	1	1	yes	characteristic, complemented
571	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic, complemented
572	#410	C₂²×C₈₉	1	1	yes	characteristic, complemented
573	#408	C₂²×C₈₉	1	1	yes	characteristic, complemented
574	#408	C₂²×C₈₉	1	1	yes	characteristic, complemented
575	#408	C₂²×C₈₉	1	1	yes	characteristic, complemented
576	#344	C₂²×C₈₉	1	1	yes	characteristic, complemented
577	#344	C₂²×C₈₉	1	1	yes	characteristic, complemented
578	#341	C₂²×C₈₉	1	1	yes	characteristic, complemented
579	#338	C₂²×C₈₉	1	1	yes	characteristic, complemented
580	2₋¹⁺⁴	—	2	2	no	—
581	2₋¹⁺⁴	—	2	1	no	—
582	2₋¹⁺⁴	—	2	2	no	—
583	2₋¹⁺⁴	—	2	1	no	—
584	2₋¹⁺⁴	—	2	2	no	—
585	2₋¹⁺⁴	—	4	1	no	—
586	2₋¹⁺⁴	D₄×C₈₉	1	2	yes	complemented
587	H(5,𝔽₂)	—	2	2	no	—
588	H(5,𝔽₂)	—	2	1	no	—
589	H(5,𝔽₂)	—	2	2	no	—
590	H(5,𝔽₂)	—	2	1	no	—
591	H(5,𝔽₂)	—	2	2	no	—
592	H(5,𝔽₂)	—	4	1	no	—
593	H(5,𝔽₂)	—	4	1	no	—
594	H(5,𝔽₂)	D₄×C₈₉	1	2	yes	complemented
595	C₂×#41	—	2	2	no	—
596	C₂×#41	—	2	2	no	—
597	C₂×#41	—	2	1	no	—
598	C₂×#41	—	2	1	no	—
599	C₂×#41	—	2	1	no	—
600	C₂×#41	—	2	1	no	—
601	C₂×#41	—	4	1	no	—
602	C₂×#41	—	4	1	no	—
603	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
604	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
605	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
606	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
607	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
608	C₂²×Q₈	—	2	1	no	—
609	C₂²×Q₈	—	2	1	no	—
610	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
611	C₂²×D₄	—	2	1	no	—
612	C₂²×D₄	—	2	1	no	—
613	C₂²×D₄	—	4	1	no	—
614	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
615	#137	—	2	4	no	—
616	#137	—	2	4	no	—
617	#137	—	2	4	no	—
618	#137	—	2	4	no	—
619	#137	—	2	2	no	—
620	#137	—	2	2	no	—
621	#137	—	2	1	no	—
622	#137	—	2	2	no	—
623	#137	—	2	1	no	—
624	#137	—	2	1	no	—
625	#137	—	2	1	no	—
626	#137	—	2	1	no	—
627	#137	—	2	1	no	—
628	#137	—	2	1	no	—
629	#137	—	2	1	no	—
630	#137	—	2	2	no	—
631	#137	D₄×C₈₉	1	2	yes	—
632	#137	D₄×C₈₉	1	2	yes	complemented
633	AGL(1,ℤ/8)	—	2	4	no	—
634	AGL(1,ℤ/8)	—	2	4	no	—
635	AGL(1,ℤ/8)	—	2	4	no	—
636	AGL(1,ℤ/8)	—	2	4	no	—
637	AGL(1,ℤ/8)	—	2	2	no	—
638	AGL(1,ℤ/8)	—	2	2	no	—
639	AGL(1,ℤ/8)	—	2	1	no	—
640	AGL(1,ℤ/8)	—	2	2	no	—
641	AGL(1,ℤ/8)	—	2	1	no	—
642	AGL(1,ℤ/8)	—	2	1	no	—
643	AGL(1,ℤ/8)	—	2	1	no	—
644	AGL(1,ℤ/8)	—	2	1	no	—
645	AGL(1,ℤ/8)	—	2	1	no	—
646	AGL(1,ℤ/8)	—	2	1	no	—
647	AGL(1,ℤ/8)	—	2	1	no	—
648	AGL(1,ℤ/8)	—	2	2	no	—
649	AGL(1,ℤ/8)	D₄×C₈₉	1	2	yes	—
650	AGL(1,ℤ/8)	D₄×C₈₉	1	2	yes	complemented
651	#135	—	2	4	no	—
652	#135	—	2	4	no	—
653	#135	—	2	4	no	—
654	#135	—	2	4	no	—
655	#135	—	2	2	no	—
656	#135	—	2	2	no	—
657	#135	—	2	2	no	—
658	#135	—	2	2	no	—
659	#135	—	4	1	no	—
660	C₂×Q₁₆	—	2	4	no	—
661	C₂×Q₁₆	—	2	1	no	—
662	C₂×Q₁₆	D₄×C₈₉	1	2	yes	complemented
663	C₂×SD₁₆	—	2	4	no	—
664	C₂×SD₁₆	—	2	4	no	—
665	C₂×SD₁₆	—	2	1	no	—
666	C₂×SD₁₆	—	2	1	no	—
667	C₂×SD₁₆	—	2	2	no	—
668	C₂×SD₁₆	—	2	2	no	—
669	C₂×SD₁₆	—	4	1	no	—
670	C₂×SD₁₆	D₄×C₈₉	1	2	yes	—
671	C₂×SD₁₆	D₄×C₈₉	1	2	yes	complemented
672	C₂×D₈	—	2	4	no	—
673	C₂×D₈	—	2	1	no	—
674	C₂×D₈	D₄×C₈₉	1	2	yes	—
675	#131	—	2	2	no	—
676	#131	—	2	2	no	—
677	#131	—	2	2	no	—
678	#131	—	2	2	no	—
679	C₂×M₁₆	—	2	2	no	—
680	C₂×M₁₆	—	2	2	no	—
681	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
682	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
683	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
684	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
685	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
686	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
687	C₄⋊Q₈	—	2	1	no	—
688	#127	—	2	1	no	—
689	#124	—	2	1	no	—
690	#124	—	2	1	no	—
691	#123	—	4	1	no	—
692	C₂²⋊Q₈	—	2	2	no	—
693	#121	—	2	2	no	—
694	#120	—	4	1	no	—
695	#117	C₂³×C₈₉	1	1	yes	characteristic
696	#117	C₂³×C₈₉	1	1	yes	characteristic
697	#104	—	2	2	no	—
698	#104	—	2	2	no	—
699	#104	—	2	2	no	—
700	#104	—	2	2	no	—
701	#103	—	2	1	no	—
702	#103	—	2	1	no	—
703	#103	—	2	2	no	—
704	#102	—	2	1	no	—
705	#102	—	2	1	no	—
706	#102	—	2	2	no	—
707	#101	—	2	2	no	—
708	#100	—	2	2	no	—
709	#99	—	4	1	no	—
710	C₂²⋊C₈	—	2	2	no	—
711	C₂²⋊C₈	—	2	2	no	—
712	C₂²⋊C₈	—	4	1	no	—
713	C₂⁴	—	2	1	no	—
714	C₂⁴	—	4	1	no	—
715	#41	—	2	1	no	—
716	#41	—	2	1	no	—
717	#41	—	2	1	no	—
718	#41	—	2	1	no	—
719	#41	—	2	4	no	—
720	#41	—	2	4	no	—
721	#41	—	2	2	no	—
722	#41	—	2	2	no	—
723	#41	—	2	2	no	—
724	#41	—	2	2	no	—
725	#41	—	2	1	no	—
726	#41	—	2	1	no	—
727	#41	—	2	1	no	—
728	#41	—	2	1	no	—
729	#41	—	2	1	no	—
730	#41	—	2	1	no	—
731	#41	—	2	1	no	—
732	#41	—	2	1	no	—
733	#41	—	2	1	no	—
734	#41	—	2	1	no	—
735	#41	—	2	1	no	—
736	#41	—	2	1	no	—
737	#41	—	4	2	no	—
738	#41	—	4	2	no	—
739	#41	—	4	2	no	—
740	#41	—	4	2	no	—
741	#41	—	4	2	no	—
742	#41	—	4	4	no	—
743	#41	—	4	2	no	—
744	#41	—	4	2	no	—
745	#41	—	4	2	no	—
746	#41	—	4	1	no	—
747	#41	—	4	1	no	—
748	#41	—	4	4	no	—
749	#41	—	4	2	no	—
750	#41	—	4	2	no	—
751	#41	C₂×D₄×C₈₉	1	2	yes	—
752	#41	C₂×D₄×C₈₉	1	2	yes	—
753	#41	C₂×D₄×C₈₉	1	2	yes	—
754	#41	C₂×D₄×C₈₉	1	2	yes	—
755	C₂×Q₈	—	2	1	no	—
756	C₂×Q₈	—	2	4	no	—
757	C₂×Q₈	—	2	2	no	—
758	C₂×Q₈	—	2	2	no	—
759	C₂×Q₈	—	2	1	no	—
760	C₂×Q₈	—	2	1	no	—
761	C₂×Q₈	—	2	1	no	—
762	C₂×Q₈	—	2	1	no	—
763	C₂×Q₈	—	4	1	no	—
764	C₂×Q₈	—	4	2	no	—
765	C₂×Q₈	—	4	2	no	—
766	C₂×Q₈	—	4	1	no	—
767	C₂×Q₈	—	4	2	no	—
768	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
769	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
770	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
771	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
772	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
773	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
774	C₂×D₄	—	2	1	no	—
775	C₂×D₄	—	2	1	no	—
776	C₂×D₄	—	2	4	no	—
777	C₂×D₄	—	2	2	no	—
778	C₂×D₄	—	2	2	no	—
779	C₂×D₄	—	2	1	no	—
780	C₂×D₄	—	2	1	no	—
781	C₂×D₄	—	2	1	no	—
782	C₂×D₄	—	2	1	no	—
783	C₂×D₄	—	2	1	no	—
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	2	1	no	—
786	C₂×D₄	—	2	1	no	—
787	C₂×D₄	—	4	2	no	—
788	C₂×D₄	—	4	1	no	—
789	C₂×D₄	—	4	1	no	—
790	C₂×D₄	—	4	2	no	—
791	C₂×D₄	—	4	2	no	—
792	C₂×D₄	—	4	1	no	—
793	C₂×D₄	—	4	4	no	—
794	C₂×D₄	—	4	2	no	—
795	C₂×D₄	—	4	2	no	—
796	C₂×D₄	—	4	4	no	—
797	C₂×D₄	—	4	1	no	—
798	C₂×D₄	—	4	2	no	—
799	C₂×D₄	—	4	2	no	—
800	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
801	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
802	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
803	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
804	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
805	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
806	C₂²×C₄	—	2	1	no	—
807	C₂²×C₄	—	2	1	no	—
808	C₂²×C₄	—	2	1	no	—
809	C₂²×C₄	—	2	1	no	—
810	C₂²×C₄	—	2	1	no	—
811	C₂²×C₄	—	2	1	no	—
812	C₂²×C₄	—	4	1	no	—
813	C₂²×C₄	—	4	2	no	—
814	C₂²×C₄	—	4	1	no	—
815	C₂²×C₄	—	4	1	no	—
816	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
817	Q₁₆	—	2	4	no	—
818	Q₁₆	—	2	2	no	—
819	Q₁₆	—	2	2	no	—
820	Q₁₆	—	2	2	no	—
821	Q₁₆	—	2	4	no	—
822	Q₁₆	—	2	2	no	—
823	Q₁₆	—	4	1	no	—
824	SD₁₆	—	2	4	no	—
825	SD₁₆	—	2	2	no	—
826	SD₁₆	—	2	4	no	—
827	SD₁₆	—	2	2	no	—
828	SD₁₆	—	2	2	no	—
829	SD₁₆	—	2	2	no	—
830	SD₁₆	—	2	2	no	—
831	SD₁₆	—	2	4	no	—
832	SD₁₆	—	2	2	no	—
833	SD₁₆	—	2	2	no	—
834	SD₁₆	—	2	4	no	—
835	SD₁₆	—	2	2	no	—
836	SD₁₆	—	4	4	no	—
837	SD₁₆	—	4	1	no	—
838	SD₁₆	—	4	1	no	—
839	D₈	—	2	4	no	—
840	D₈	—	2	2	no	—
841	D₈	—	2	2	no	—
842	D₈	—	2	2	no	—
843	D₈	—	2	4	no	—
844	D₈	—	2	2	no	—
845	D₈	—	4	1	no	—
846	M₁₆	—	2	4	no	—
847	M₁₆	—	2	4	no	—
848	M₁₆	—	2	1	no	—
849	M₁₆	—	2	1	no	—
850	M₁₆	—	2	1	no	—
851	M₁₆	—	2	1	no	—
852	M₁₆	—	2	1	no	—
853	M₁₆	—	2	1	no	—
854	M₁₆	—	2	1	no	—
855	M₁₆	—	2	1	no	—
856	M₁₆	C₂×D₄×C₈₉	1	2	yes	—
857	M₁₆	C₂×D₄×C₈₉	1	2	yes	—
858	C₂×C₈	—	2	4	no	—
859	C₂×C₈	—	2	4	no	—
860	C₂×C₈	—	2	1	no	—
861	C₂×C₈	—	2	1	no	—
862	C₂×C₈	—	2	1	no	—
863	C₂×C₈	—	2	1	no	—
864	C₂×C₈	—	2	1	no	—
865	C₂×C₈	—	2	1	no	—
866	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
867	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
868	C₄⋊C₄	—	2	1	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	4	2	no	—
871	C₂²⋊C₄	—	2	1	no	—
872	C₂²⋊C₄	—	2	1	no	—
873	C₂²⋊C₄	—	4	2	no	—
874	C₂²⋊C₄	—	4	2	no	—
875	C₄²	—	2	1	no	—
876	C₄²	—	2	1	no	—
877	C₂³	—	2	1	no	—
878	C₂³	—	2	1	no	—
879	C₂³	—	2	1	no	—
880	C₂³	—	2	1	no	—
881	C₂³	—	2	1	no	—
882	C₂³	—	2	2	no	—
883	C₂³	—	4	2	no	—
884	C₂³	—	4	4	no	—
885	C₂³	—	4	1	no	—
886	C₂³	—	4	1	no	—
887	C₂³	—	16	1	no	—
888	C₂³	—	16	2	no	—
889	C₂³	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
890	Q₈	—	2	1	no	—
891	Q₈	—	2	1	no	—
892	Q₈	—	2	1	no	—
893	Q₈	—	2	1	no	—
894	Q₈	—	2	2	no	—
895	Q₈	—	2	1	no	—
896	Q₈	—	2	1	no	—
897	Q₈	—	2	2	no	—
898	Q₈	—	2	1	no	—
899	Q₈	—	2	1	no	—
900	Q₈	—	4	2	no	—
901	Q₈	—	4	4	no	—
902	Q₈	—	4	1	no	—
903	Q₈	—	4	1	no	—
904	Q₈	#120×C₈₉	1	2	yes	—
905	Q₈	#120×C₈₉	1	2	yes	—
906	D₄	—	2	2	no	—
907	D₄	—	2	2	no	—
908	D₄	—	2	2	no	—
909	D₄	—	2	2	no	—
910	D₄	—	2	1	no	—
911	D₄	—	2	1	no	—
912	D₄	—	2	2	no	—
913	D₄	—	2	1	no	—
914	D₄	—	2	1	no	—
915	D₄	—	2	1	no	—
916	D₄	—	2	1	no	—
917	D₄	—	2	1	no	—
918	D₄	—	2	1	no	—
919	D₄	—	2	2	no	—
920	D₄	—	4	2	no	—
921	D₄	—	4	2	no	—
922	D₄	—	4	4	no	—
923	D₄	—	4	2	no	—
924	D₄	—	4	4	no	—
925	D₄	—	4	4	no	—
926	D₄	—	4	1	no	—
927	D₄	—	4	1	no	—
928	D₄	—	4	1	no	—
929	D₄	—	4	1	no	—
930	D₄	—	4	1	no	—
931	D₄	—	4	1	no	—
932	D₄	—	4	1	no	—
933	D₄	—	4	1	no	—
934	D₄	—	16	2	no	—
935	D₄	#120×C₈₉	1	2	yes	—
936	D₄	#120×C₈₉	1	2	yes	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	4	2	no	—
948	C₂×C₄	—	4	2	no	—
949	C₂×C₄	—	4	2	no	—
950	C₂×C₄	—	4	4	no	—
951	C₂×C₄	—	4	4	no	—
952	C₂×C₄	—	4	4	no	—
953	C₂×C₄	—	4	1	no	—
954	C₂×C₄	—	4	1	no	—
955	C₂×C₄	—	4	1	no	—
956	C₂×C₄	—	4	1	no	—
957	C₂×C₄	—	4	1	no	—
958	C₂×C₄	—	4	1	no	—
959	C₂×C₄	—	4	1	no	—
960	C₂×C₄	—	4	1	no	—
961	C₂×C₄	—	4	1	no	—
962	C₂×C₄	—	4	1	no	—
963	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
964	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
965	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
966	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
967	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
968	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
969	C₈	—	2	2	no	—
970	C₈	—	2	2	no	—
971	C₈	—	2	2	no	—
972	C₈	—	2	2	no	—
973	C₈	—	4	1	no	—
974	C₈	—	4	1	no	—
975	C₂²	—	2	2	no	—
976	C₂²	—	2	2	no	—
977	C₂²	—	4	1	no	—
978	C₂²	—	4	2	no	—
979	C₂²	—	4	2	no	—
980	C₂²	—	4	1	no	—
981	C₂²	—	4	1	no	—
982	C₂²	—	4	1	no	—
983	C₂²	—	4	2	no	—
984	C₂²	—	8	1	no	—
985	C₂²	—	8	1	no	—
986	C₂²	—	8	2	no	—
987	C₂²	—	8	1	no	—
988	C₂²	—	8	2	no	—
989	C₂²	—	16	1	no	—
990	C₂²	—	16	2	no	—
991	C₂²	—	16	4	no	—
992	C₂²	#534×C₈₉	1	1	yes	characteristic
993	C₂²	D₄²×C₈₉	1	1	yes	characteristic
994	C₂²	D₄²×C₈₉	1	1	yes	characteristic
995	C₄	—	2	2	no	—
996	C₄	—	2	2	no	—
997	C₄	—	4	1	no	—
998	C₄	—	4	1	no	—
999	C₄	—	4	1	no	—
1000	C₄	—	4	2	no	—
1001	C₄	—	8	1	no	—
1002	C₄	—	8	1	no	—
1003	C₄	C₂×#120×C₈₉	1	1	yes	characteristic
1004	C₄	C₂×#120×C₈₉	1	1	yes	characteristic
1005	C₄	D₄²×C₈₉	1	1	yes	characteristic
1006	C₄	D₄²×C₈₉	1	1	yes	characteristic
1007	C₂	—	2	1	no	—
1008	C₂	—	2	1	no	—
1009	C₂	—	2	1	no	—
1010	C₂	—	4	2	no	—
1011	C₂	—	4	2	no	—
1012	C₂	—	8	1	no	—
1013	C₂	—	8	1	no	—
1014	C₂	—	8	2	no	—
1015	C₂	—	8	1	no	—
1016	C₂	C₈₉×#2403	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₈₉	#2403
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈₉ ◁ C₂²×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3586	C₂	semidirect
2. C₈₉×#3585	C₂	semidirect
3. C₈₉×#3020	C₂	semidirect
4. C₈₉×#3019	C₂	semidirect
5. C₈₉×#3010	C₂	semidirect
6. C₈₉×#3009	C₂	semidirect
7. C₈₉×#2019	C₂	semidirect
8. C₈₉×#2017	C₂	semidirect
9. C₈₉×#2009	C₂	semidirect
10. C₈₉×#2008	C₂	semidirect
11. C₈₉×#1903	C₂	semidirect
12. C₈₉×#1902	C₂	semidirect
13. C₈₉×#1881	C₂	semidirect
14. C₈₉×#1881	C₂	semidirect
15. C₈₉×#1794	C₂	semidirect
17. C₂×2₋¹⁺⁴×C₈₉	C₂²	semidirect
32. #575×C₈₉	C₂²	semidirect
33. #575×C₈₉	C₂²	semidirect
36. C₂×#137×C₈₉	C₂²	semidirect
40. C₂²×SD₁₆×C₈₉	C₂²	semidirect
42. #568×C₈₉	C₂²	semidirect
43. #536×C₈₉	C₂²	semidirect
44. #535×C₈₉	C₂²	semidirect
54. #421×C₈₉	C₂²	semidirect
55. #421×C₈₉	C₂²	semidirect
56. #421×C₈₉	C₂²	semidirect
57. #419×C₈₉	C₂²	semidirect
58. #418×C₈₉	C₂²	semidirect
60. #416×C₈₉	C₂²	semidirect
61. C₂×#101×C₈₉	C₂²	semidirect
62. C₂×#100×C₈₉	C₂²	semidirect
63. #410×C₈₉	C₂²	semidirect
64. #408×C₈₉	C₂²	semidirect
65. #408×C₈₉	C₂²	semidirect
66. #408×C₈₉	C₂²	semidirect
67. #344×C₈₉	C₂²	semidirect
68. #344×C₈₉	C₂²	semidirect
69. #341×C₈₉	C₂²	semidirect
70. #338×C₈₉	C₂²	semidirect
77. 2₋¹⁺⁴×C₈₉	D₄	semidirect
85. H(5,𝔽₂)×C₈₉	D₄	semidirect
123. #137×C₈₉	D₄	semidirect
141. AGL(1,ℤ/8)×C₈₉	D₄	semidirect
153. C₂×Q₁₆×C₈₉	D₄	semidirect
162. C₂×SD₁₆×C₈₉	D₄	semidirect
498. #23894	C₈₉	direct (N × H)
509. #3586	C₂×C₈₉	semidirect
510. #3585	C₂×C₈₉	semidirect
511. #3020	C₂×C₈₉	semidirect
512. #3019	C₂×C₈₉	semidirect
513. #3010	C₂×C₈₉	semidirect
514. #3009	C₂×C₈₉	semidirect
515. #2019	C₂×C₈₉	semidirect
516. #2017	C₂×C₈₉	semidirect
517. #2009	C₂×C₈₉	semidirect
518. #2008	C₂×C₈₉	semidirect
519. #1903	C₂×C₈₉	semidirect
520. #1902	C₂×C₈₉	semidirect
521. #1881	C₂×C₈₉	semidirect
522. #1881	C₂×C₈₉	semidirect
523. #1794	C₂×C₈₉	semidirect
524. C₈₉	#23894	direct (N × H)
526. C₂×2₋¹⁺⁴	C₂²×C₈₉	semidirect
541. #575	C₂²×C₈₉	semidirect
542. #575	C₂²×C₈₉	semidirect
545. C₂×#137	C₂²×C₈₉	semidirect
549. C₂²×SD₁₆	C₂²×C₈₉	semidirect
551. #568	C₂²×C₈₉	semidirect
552. #536	C₂²×C₈₉	semidirect
553. #535	C₂²×C₈₉	semidirect
563. #421	C₂²×C₈₉	semidirect
564. #421	C₂²×C₈₉	semidirect
565. #421	C₂²×C₈₉	semidirect
566. #419	C₂²×C₈₉	semidirect
567. #418	C₂²×C₈₉	semidirect
569. #416	C₂²×C₈₉	semidirect
570. C₂×#101	C₂²×C₈₉	semidirect
571. C₂×#100	C₂²×C₈₉	semidirect
572. #410	C₂²×C₈₉	semidirect
573. #408	C₂²×C₈₉	semidirect
574. #408	C₂²×C₈₉	semidirect
575. #408	C₂²×C₈₉	semidirect
576. #344	C₂²×C₈₉	semidirect
577. #344	C₂²×C₈₉	semidirect
578. #341	C₂²×C₈₉	semidirect
579. #338	C₂²×C₈₉	semidirect
586. 2₋¹⁺⁴	D₄×C₈₉	semidirect
594. H(5,𝔽₂)	D₄×C₈₉	semidirect
632. #137	D₄×C₈₉	semidirect
650. AGL(1,ℤ/8)	D₄×C₈₉	semidirect
662. C₂×Q₁₆	D₄×C₈₉	semidirect
671. C₂×SD₁₆	D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3586	2
C₈₉×#3585	2
C₈₉×#3020	2
C₈₉×#3019	2
C₈₉×#3010	2
C₈₉×#3009	2
C₈₉×#2019	2
C₈₉×#2017	2
C₈₉×#2009	2
C₈₉×#2008	2
C₈₉×#1903	2
C₈₉×#1902	2
C₈₉×#1881	2
C₈₉×#1794	2
#23894	89

Subgroups — C89×#23894 #36401742

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#23894 #36401742