Subgroups — C₈₉×#24473 #36402321

Order 22784.

1314 conjugacy classes of subgroups.

The subgroup lattice has 892 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×#3068	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3040	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3021	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#454×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2901	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2050	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2049	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2008	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2004	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1906	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1903	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1902	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1861	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1796	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
18	#578×C₈₉	—	2	2	no	—
19	#578×C₈₉	—	2	2	no	—
20	#577×C₈₉	—	2	2	no	—
21	#577×C₈₉	—	2	2	no	—
22	#575×C₈₉	—	2	2	no	—
23	#575×C₈₉	C₂²	1	1	yes	characteristic
24	#575×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#137×C₈₉	—	2	2	no	—
26	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic, complemented
31	#568×C₈₉	C₂²	1	1	yes	characteristic
32	#568×C₈₉	C₂²	1	1	yes	characteristic
33	#535×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
35	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
36	#472×C₈₉	—	2	2	no	—
37	#471×C₈₉	—	2	2	no	—
38	#464×C₈₉	—	2	2	no	—
39	#463×C₈₉	—	2	2	no	—
40	#454×C₈₉	—	2	2	no	—
41	#454×C₈₉	—	2	2	no	—
42	#454×C₈₉	—	2	2	no	—
43	#453×C₈₉	—	2	2	no	—
44	#430×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	#423×C₈₉	C₂²	1	1	yes	characteristic, complemented
46	#421×C₈₉	—	2	2	no	—
47	#421×C₈₉	C₂²	1	1	yes	characteristic
48	#421×C₈₉	C₂²	1	1	yes	characteristic
49	#421×C₈₉	C₂²	1	1	yes	characteristic
50	#421×C₈₉	C₂²	1	1	yes	characteristic
51	C₂×#104×C₈₉	—	2	2	no	—
52	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic
54	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	#419×C₈₉	C₂²	1	1	yes	characteristic, complemented
56	#419×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	#418×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#413×C₈₉	C₂²	1	1	yes	characteristic
59	#413×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	C₂×#101×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic, complemented
62	#410×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	#344×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	#344×C₈₉	C₂²	1	1	yes	characteristic, complemented
65	#339×C₈₉	C₂²	1	1	yes	characteristic, complemented
66	#338×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	2₋¹⁺⁴×C₈₉	—	2	2	no	—
68	2₋¹⁺⁴×C₈₉	—	2	2	no	—
69	2₋¹⁺⁴×C₈₉	—	2	1	no	—
70	2₋¹⁺⁴×C₈₉	—	2	1	no	—
71	2₋¹⁺⁴×C₈₉	—	2	2	no	—
72	2₋¹⁺⁴×C₈₉	—	4	1	no	—
73	2₋¹⁺⁴×C₈₉	D₄	1	2	yes	—
74	H(5,𝔽₂)×C₈₉	—	2	1	no	—
75	H(5,𝔽₂)×C₈₉	—	2	1	no	—
76	H(5,𝔽₂)×C₈₉	—	4	1	no	—
77	H(5,𝔽₂)×C₈₉	D₄	1	2	yes	—
78	C₂×#41×C₈₉	—	2	2	no	—
79	C₂×#41×C₈₉	—	2	2	no	—
80	C₂×#41×C₈₉	—	2	1	no	—
81	C₂×#41×C₈₉	—	2	1	no	—
82	C₂×#41×C₈₉	—	4	1	no	—
83	C₂×#41×C₈₉	—	4	1	no	—
84	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
85	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
86	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
87	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₈₉	—	2	1	no	—
89	C₂²×Q₈×C₈₉	—	2	1	no	—
90	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
92	#137×C₈₉	—	2	4	no	—
93	#137×C₈₉	—	2	4	no	—
94	#137×C₈₉	—	2	4	no	—
95	#137×C₈₉	—	2	2	no	—
96	#137×C₈₉	—	2	2	no	—
97	#137×C₈₉	—	2	1	no	—
98	#137×C₈₉	—	2	2	no	—
99	#137×C₈₉	—	2	1	no	—
100	#137×C₈₉	—	2	1	no	—
101	#137×C₈₉	—	2	2	no	—
102	#137×C₈₉	D₄	1	2	yes	complemented
103	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
104	AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
105	AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
106	AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
107	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
108	AGL(1,ℤ/8)×C₈₉	—	2	2	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	—	4	1	no	—
113	AGL(1,ℤ/8)×C₈₉	D₄	1	2	yes	complemented
114	#135×C₈₉	—	2	4	no	—
115	#135×C₈₉	—	2	4	no	—
116	#135×C₈₉	—	2	2	no	—
117	#135×C₈₉	—	2	2	no	—
118	C₂×Q₁₆×C₈₉	—	2	4	no	—
119	C₂×Q₁₆×C₈₉	—	2	1	no	—
120	C₂×Q₁₆×C₈₉	D₄	1	2	yes	complemented
121	C₂×SD₁₆×C₈₉	—	2	4	no	—
122	C₂×SD₁₆×C₈₉	—	2	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	D₄	1	2	yes	complemented
127	C₂×D₈×C₈₉	—	2	1	no	—
128	C₂×D₈×C₈₉	—	2	1	no	—
129	C₂×D₈×C₈₉	—	2	1	no	—
130	#131×C₈₉	—	2	2	no	—
131	#131×C₈₉	—	2	2	no	—
132	#131×C₈₉	—	2	2	no	—
133	#131×C₈₉	—	4	1	no	—
134	C₂×M₁₆×C₈₉	—	2	2	no	—
135	C₂×M₁₆×C₈₉	—	2	2	no	—
136	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
137	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
138	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
139	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
140	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
141	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
142	#127×C₈₉	—	2	1	no	—
143	#124×C₈₉	—	2	1	no	—
144	#124×C₈₉	—	2	2	no	—
145	#124×C₈₉	—	2	1	no	—
146	#124×C₈₉	—	2	1	no	—
147	#121×C₈₉	—	4	1	no	—
148	#120×C₈₉	—	4	1	no	—
149	C₄×Q₈×C₈₉	—	2	1	no	—
150	C₄×D₄×C₈₉	—	2	1	no	—
151	C₄×D₄×C₈₉	—	4	1	no	—
152	#117×C₈₉	—	2	1	no	—
153	#117×C₈₉	C₂³	1	1	yes	characteristic
154	#117×C₈₉	C₂³	1	1	yes	characteristic
155	C₂×C₂²⋊C₄×C₈₉	—	4	1	no	—
156	C₂×C₄²×C₈₉	—	2	1	no	—
157	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
158	#108×C₈₉	—	2	2	no	—
159	C₄⋊C₈×C₈₉	—	2	2	no	—
160	#104×C₈₉	—	2	2	no	—
161	#104×C₈₉	—	2	2	no	—
162	#104×C₈₉	—	2	2	no	—
163	#104×C₈₉	—	2	2	no	—
164	#104×C₈₉	—	2	1	no	—
165	#104×C₈₉	—	2	1	no	—
166	#104×C₈₉	—	2	1	no	—
167	#104×C₈₉	—	2	1	no	—
168	#104×C₈₉	D₄	1	2	yes	complemented
169	#104×C₈₉	D₄	1	2	yes	complemented
170	#103×C₈₉	—	2	2	no	—
171	#103×C₈₉	—	4	1	no	—
172	#102×C₈₉	—	2	2	no	—
173	#101×C₈₉	—	2	1	no	—
174	#101×C₈₉	—	2	1	no	—
175	#101×C₈₉	—	2	2	no	—
176	#100×C₈₉	—	2	1	no	—
177	#100×C₈₉	—	2	1	no	—
178	#100×C₈₉	—	2	2	no	—
179	#99×C₈₉	—	4	1	no	—
180	C₂⁴×C₈₉	—	2	1	no	—
181	#41×C₈₉	—	2	1	no	—
182	#41×C₈₉	—	2	1	no	—
183	#41×C₈₉	—	2	1	no	—
184	#41×C₈₉	—	2	1	no	—
185	#41×C₈₉	—	2	4	no	—
186	#41×C₈₉	—	2	2	no	—
187	#41×C₈₉	—	2	2	no	—
188	#41×C₈₉	—	2	2	no	—
189	#41×C₈₉	—	2	2	no	—
190	#41×C₈₉	—	2	1	no	—
191	#41×C₈₉	—	2	1	no	—
192	#41×C₈₉	—	2	1	no	—
193	#41×C₈₉	—	2	1	no	—
194	#41×C₈₉	—	2	1	no	—
195	#41×C₈₉	—	2	1	no	—
196	#41×C₈₉	—	2	1	no	—
197	#41×C₈₉	—	2	1	no	—
198	#41×C₈₉	—	4	2	no	—
199	#41×C₈₉	—	4	2	no	—
200	#41×C₈₉	—	4	2	no	—
201	#41×C₈₉	—	4	2	no	—
202	#41×C₈₉	—	4	2	no	—
203	#41×C₈₉	—	4	4	no	—
204	#41×C₈₉	—	4	2	no	—
205	#41×C₈₉	—	4	1	no	—
206	#41×C₈₉	—	4	1	no	—
207	#41×C₈₉	—	4	4	no	—
208	#41×C₈₉	—	4	2	no	—
209	#41×C₈₉	C₂×D₄	1	2	yes	—
210	#41×C₈₉	C₂×D₄	1	2	yes	—
211	#41×C₈₉	C₂×D₄	1	2	yes	—
212	#41×C₈₉	C₂×D₄	1	2	yes	—
213	C₂×Q₈×C₈₉	—	2	1	no	—
214	C₂×Q₈×C₈₉	—	2	4	no	—
215	C₂×Q₈×C₈₉	—	2	2	no	—
216	C₂×Q₈×C₈₉	—	2	2	no	—
217	C₂×Q₈×C₈₉	—	2	1	no	—
218	C₂×Q₈×C₈₉	—	2	1	no	—
219	C₂×Q₈×C₈₉	—	2	1	no	—
220	C₂×Q₈×C₈₉	—	2	1	no	—
221	C₂×Q₈×C₈₉	—	4	1	no	—
222	C₂×Q₈×C₈₉	—	4	2	no	—
223	C₂×Q₈×C₈₉	—	4	2	no	—
224	C₂×Q₈×C₈₉	—	4	1	no	—
225	C₂×Q₈×C₈₉	—	4	2	no	—
226	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
227	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
228	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
229	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
230	C₂×Q₈×C₈₉	#41	1	1	yes	characteristic
231	C₂×D₄×C₈₉	—	2	1	no	—
232	C₂×D₄×C₈₉	—	2	1	no	—
233	C₂×D₄×C₈₉	—	2	2	no	—
234	C₂×D₄×C₈₉	—	2	2	no	—
235	C₂×D₄×C₈₉	—	2	1	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	—	4	2	no	—
244	C₂×D₄×C₈₉	—	4	1	no	—
245	C₂×D₄×C₈₉	—	4	2	no	—
246	C₂×D₄×C₈₉	—	4	2	no	—
247	C₂×D₄×C₈₉	—	4	1	no	—
248	C₂×D₄×C₈₉	—	4	2	no	—
249	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
250	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
251	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
252	C₂×D₄×C₈₉	#41	1	1	yes	characteristic
253	C₂²×C₄×C₈₉	—	2	1	no	—
254	C₂²×C₄×C₈₉	—	2	1	no	—
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	—	4	2	no	—
260	C₂²×C₄×C₈₉	—	4	1	no	—
261	C₂²×C₄×C₈₉	—	4	1	no	—
262	C₂²×C₄×C₈₉	—	4	1	no	—
263	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
264	Q₁₆×C₈₉	—	2	4	no	—
265	Q₁₆×C₈₉	—	2	2	no	—
266	Q₁₆×C₈₉	—	2	2	no	—
267	Q₁₆×C₈₉	—	2	4	no	—
268	SD₁₆×C₈₉	—	2	4	no	—
269	SD₁₆×C₈₉	—	2	2	no	—
270	SD₁₆×C₈₉	—	2	2	no	—
271	SD₁₆×C₈₉	—	2	2	no	—
272	SD₁₆×C₈₉	—	2	2	no	—
273	SD₁₆×C₈₉	—	2	4	no	—
274	SD₁₆×C₈₉	—	4	2	no	—
275	SD₁₆×C₈₉	—	4	2	no	—
276	SD₁₆×C₈₉	—	4	2	no	—
277	D₈×C₈₉	—	2	2	no	—
278	D₈×C₈₉	—	2	2	no	—
279	D₈×C₈₉	—	4	2	no	—
280	D₈×C₈₉	—	4	2	no	—
281	D₈×C₈₉	—	4	2	no	—
282	M₁₆×C₈₉	—	2	4	no	—
283	M₁₆×C₈₉	—	2	1	no	—
284	M₁₆×C₈₉	—	2	1	no	—
285	M₁₆×C₈₉	—	2	1	no	—
286	M₁₆×C₈₉	—	2	1	no	—
287	M₁₆×C₈₉	—	2	1	no	—
288	M₁₆×C₈₉	—	2	1	no	—
289	M₁₆×C₈₉	—	2	1	no	—
290	M₁₆×C₈₉	—	2	1	no	—
291	M₁₆×C₈₉	—	2	1	no	—
292	M₁₆×C₈₉	—	2	1	no	—
293	M₁₆×C₈₉	—	4	2	no	—
294	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
295	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
296	C₂×C₈×C₈₉	—	2	4	no	—
297	C₂×C₈×C₈₉	—	2	1	no	—
298	C₂×C₈×C₈₉	—	2	1	no	—
299	C₂×C₈×C₈₉	—	2	1	no	—
300	C₂×C₈×C₈₉	—	2	1	no	—
301	C₂×C₈×C₈₉	—	2	1	no	—
302	C₂×C₈×C₈₉	—	4	2	no	—
303	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
304	C₄⋊C₄×C₈₉	—	2	1	no	—
305	C₄⋊C₄×C₈₉	—	2	1	no	—
306	C₄⋊C₄×C₈₉	—	4	1	no	—
307	C₂²⋊C₄×C₈₉	—	2	1	no	—
308	C₂²⋊C₄×C₈₉	—	2	1	no	—
309	C₂²⋊C₄×C₈₉	—	4	2	no	—
310	C₂²⋊C₄×C₈₉	—	4	2	no	—
311	C₂²⋊C₄×C₈₉	—	4	1	no	—
312	C₂²⋊C₄×C₈₉	—	4	2	no	—
313	C₄²×C₈₉	—	2	1	no	—
314	C₄²×C₈₉	—	2	1	no	—
315	C₄²×C₈₉	—	2	1	no	—
316	C₄²×C₈₉	—	4	1	no	—
317	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
319	C₂³×C₈₉	—	2	1	no	—
320	C₂³×C₈₉	—	2	1	no	—
321	C₂³×C₈₉	—	2	1	no	—
322	C₂³×C₈₉	—	2	1	no	—
323	C₂³×C₈₉	—	4	2	no	—
324	C₂³×C₈₉	—	4	1	no	—
325	C₂³×C₈₉	—	4	1	no	—
326	C₂³×C₈₉	—	4	1	no	—
327	C₂³×C₈₉	—	8	2	no	—
328	C₂³×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
329	Q₈×C₈₉	—	2	1	no	—
330	Q₈×C₈₉	—	2	1	no	—
331	Q₈×C₈₉	—	2	1	no	—
332	Q₈×C₈₉	—	2	2	no	—
333	Q₈×C₈₉	—	2	1	no	—
334	Q₈×C₈₉	—	2	1	no	—
335	Q₈×C₈₉	—	2	1	no	—
336	Q₈×C₈₉	—	2	2	no	—
337	Q₈×C₈₉	—	4	2	no	—
338	Q₈×C₈₉	—	4	4	no	—
339	Q₈×C₈₉	—	4	1	no	—
340	Q₈×C₈₉	—	4	1	no	—
341	Q₈×C₈₉	#120	1	2	yes	—
342	Q₈×C₈₉	#121	1	2	yes	—
343	D₄×C₈₉	—	2	2	no	—
344	D₄×C₈₉	—	2	2	no	—
345	D₄×C₈₉	—	2	2	no	—
346	D₄×C₈₉	—	2	2	no	—
347	D₄×C₈₉	—	2	1	no	—
348	D₄×C₈₉	—	2	1	no	—
349	D₄×C₈₉	—	2	1	no	—
350	D₄×C₈₉	—	2	1	no	—
351	D₄×C₈₉	—	2	1	no	—
352	D₄×C₈₉	—	2	1	no	—
353	D₄×C₈₉	—	4	2	no	—
354	D₄×C₈₉	—	4	2	no	—
355	D₄×C₈₉	—	4	2	no	—
356	D₄×C₈₉	—	4	4	no	—
357	D₄×C₈₉	—	4	1	no	—
358	D₄×C₈₉	—	4	1	no	—
359	D₄×C₈₉	—	4	1	no	—
360	D₄×C₈₉	—	4	1	no	—
361	D₄×C₈₉	—	4	1	no	—
362	D₄×C₈₉	—	4	1	no	—
363	D₄×C₈₉	—	4	1	no	—
364	D₄×C₈₉	—	4	1	no	—
365	D₄×C₈₉	—	16	2	no	—
366	D₄×C₈₉	#120	1	2	yes	—
367	D₄×C₈₉	#121	1	2	yes	—
368	C₂×C₄×C₈₉	—	2	1	no	—
369	C₂×C₄×C₈₉	—	2	1	no	—
370	C₂×C₄×C₈₉	—	2	2	no	—
371	C₂×C₄×C₈₉	—	2	2	no	—
372	C₂×C₄×C₈₉	—	2	2	no	—
373	C₂×C₄×C₈₉	—	2	2	no	—
374	C₂×C₄×C₈₉	—	2	1	no	—
375	C₂×C₄×C₈₉	—	2	1	no	—
376	C₂×C₄×C₈₉	—	2	1	no	—
377	C₂×C₄×C₈₉	—	2	2	no	—
378	C₂×C₄×C₈₉	—	2	1	no	—
379	C₂×C₄×C₈₉	—	4	2	no	—
380	C₂×C₄×C₈₉	—	4	2	no	—
381	C₂×C₄×C₈₉	—	4	2	no	—
382	C₂×C₄×C₈₉	—	4	4	no	—
383	C₂×C₄×C₈₉	—	4	4	no	—
384	C₂×C₄×C₈₉	—	4	1	no	—
385	C₂×C₄×C₈₉	—	4	1	no	—
386	C₂×C₄×C₈₉	—	4	1	no	—
387	C₂×C₄×C₈₉	—	4	1	no	—
388	C₂×C₄×C₈₉	—	4	1	no	—
389	C₂×C₄×C₈₉	—	4	1	no	—
390	C₂×C₄×C₈₉	—	4	1	no	—
391	C₂×C₄×C₈₉	—	4	1	no	—
392	C₂×C₄×C₈₉	—	8	1	no	—
393	C₂×C₄×C₈₉	—	8	2	no	—
394	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
399	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
400	C₈×C₈₉	—	2	2	no	—
401	C₈×C₈₉	—	2	2	no	—
402	C₈×C₈₉	—	2	2	no	—
403	C₈×C₈₉	—	4	1	no	—
404	C₈×C₈₉	—	4	1	no	—
405	C₈×C₈₉	—	4	1	no	—
406	C₂²×C₈₉	—	2	2	no	—
407	C₂²×C₈₉	—	2	2	no	—
408	C₂²×C₈₉	—	4	1	no	—
409	C₂²×C₈₉	—	4	1	no	—
410	C₂²×C₈₉	—	4	1	no	—
411	C₂²×C₈₉	—	8	1	no	—
412	C₂²×C₈₉	—	8	1	no	—
413	C₂²×C₈₉	—	8	1	no	—
414	C₂²×C₈₉	—	8	1	no	—
415	C₂²×C₈₉	—	8	2	no	—
416	C₂²×C₈₉	—	8	2	no	—
417	C₂²×C₈₉	—	8	1	no	—
418	C₂²×C₈₉	—	16	1	no	—
419	C₂²×C₈₉	—	16	2	no	—
420	C₂²×C₈₉	#534	1	1	yes	characteristic
421	C₂²×C₈₉	D₄²	1	1	yes	characteristic
422	C₂²×C₈₉	#546	1	1	yes	characteristic
423	C₄×C₈₉	—	2	2	no	—
424	C₄×C₈₉	—	2	2	no	—
425	C₄×C₈₉	—	4	1	no	—
426	C₄×C₈₉	—	4	1	no	—
427	C₄×C₈₉	—	4	1	no	—
428	C₄×C₈₉	—	4	2	no	—
429	C₄×C₈₉	—	4	1	no	—
430	C₄×C₈₉	—	8	1	no	—
431	C₄×C₈₉	—	8	1	no	—
432	C₄×C₈₉	C₂×#120	1	1	yes	characteristic
433	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
434	C₄×C₈₉	D₄²	1	1	yes	characteristic
435	C₄×C₈₉	#546	1	1	yes	characteristic
436	#24473	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
437	C₂×C₈₉	—	2	1	no	—
438	C₂×C₈₉	—	2	1	no	—
439	C₂×C₈₉	—	2	1	no	—
440	C₂×C₈₉	—	4	2	no	—
441	C₂×C₈₉	—	4	2	no	—
442	C₂×C₈₉	—	8	1	no	—
443	C₂×C₈₉	—	8	1	no	—
444	C₂×C₈₉	—	16	1	no	—
445	C₂×C₈₉	#2410	1	1	yes	characteristic
446	#3586	C₂×C₈₉	1	1	yes	characteristic, complemented
447	#3068	C₂×C₈₉	1	1	yes	characteristic, complemented
448	#3040	C₂×C₈₉	1	1	yes	characteristic, complemented
449	#3021	C₂×C₈₉	1	1	yes	characteristic, complemented
450	C₂×#454	C₂×C₈₉	1	1	yes	characteristic, complemented
451	#2901	C₂×C₈₉	1	1	yes	characteristic, complemented
452	#2050	C₂×C₈₉	1	1	yes	characteristic, complemented
453	#2049	C₂×C₈₉	1	1	yes	characteristic, complemented
454	#2008	C₂×C₈₉	1	1	yes	characteristic, complemented
455	#2004	C₂×C₈₉	1	1	yes	characteristic, complemented
456	#1906	C₂×C₈₉	1	1	yes	characteristic, complemented
457	#1903	C₂×C₈₉	1	1	yes	characteristic, complemented
458	#1902	C₂×C₈₉	1	1	yes	characteristic, complemented
459	#1861	C₂×C₈₉	1	1	yes	characteristic, complemented
460	#1796	C₂×C₈₉	1	1	yes	characteristic, complemented
461	C₈₉	#24473	1	1	yes	characteristic, direct product factor, Sylow
462	#585	C₂²×C₈₉	1	1	yes	characteristic
463	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	1	yes	characteristic
464	#578	—	2	2	no	—
465	#578	—	2	2	no	—
466	#577	—	2	2	no	—
467	#577	—	2	2	no	—
468	#575	—	2	2	no	—
469	#575	C₂²×C₈₉	1	1	yes	characteristic
470	#575	C₂²×C₈₉	1	1	yes	characteristic
471	C₂×#137	—	2	2	no	—
472	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
473	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
474	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
475	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
476	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic, complemented
477	#568	C₂²×C₈₉	1	1	yes	characteristic
478	#568	C₂²×C₈₉	1	1	yes	characteristic
479	#535	C₂²×C₈₉	1	1	yes	characteristic
480	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic, complemented
481	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
482	#472	—	2	2	no	—
483	#471	—	2	2	no	—
484	#464	—	2	2	no	—
485	#463	—	2	2	no	—
486	#454	—	2	2	no	—
487	#454	—	2	2	no	—
488	#454	—	2	2	no	—
489	#453	—	2	2	no	—
490	#430	C₂²×C₈₉	1	1	yes	characteristic, complemented
491	#423	C₂²×C₈₉	1	1	yes	characteristic, complemented
492	#421	—	2	2	no	—
493	#421	C₂²×C₈₉	1	1	yes	characteristic
494	#421	C₂²×C₈₉	1	1	yes	characteristic
495	#421	C₂²×C₈₉	1	1	yes	characteristic
496	#421	C₂²×C₈₉	1	1	yes	characteristic
497	C₂×#104	—	2	2	no	—
498	C₂×#104	C₂²×C₈₉	1	1	yes	characteristic
499	C₂×#104	C₂²×C₈₉	1	1	yes	characteristic
500	C₂×#104	C₂²×C₈₉	1	1	yes	characteristic, complemented
501	#419	C₂²×C₈₉	1	1	yes	characteristic, complemented
502	#419	C₂²×C₈₉	1	1	yes	characteristic, complemented
503	#418	C₂²×C₈₉	1	1	yes	characteristic, complemented
504	#413	C₂²×C₈₉	1	1	yes	characteristic
505	#413	C₂²×C₈₉	1	1	yes	characteristic, complemented
506	C₂×#101	C₂²×C₈₉	1	1	yes	characteristic, complemented
507	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic, complemented
508	#410	C₂²×C₈₉	1	1	yes	characteristic, complemented
509	#344	C₂²×C₈₉	1	1	yes	characteristic, complemented
510	#344	C₂²×C₈₉	1	1	yes	characteristic, complemented
511	#339	C₂²×C₈₉	1	1	yes	characteristic, complemented
512	#338	C₂²×C₈₉	1	1	yes	characteristic, complemented
513	2₋¹⁺⁴	—	2	2	no	—
514	2₋¹⁺⁴	—	2	2	no	—
515	2₋¹⁺⁴	—	2	1	no	—
516	2₋¹⁺⁴	—	2	1	no	—
517	2₋¹⁺⁴	—	2	2	no	—
518	2₋¹⁺⁴	—	4	1	no	—
519	2₋¹⁺⁴	D₄×C₈₉	1	2	yes	—
520	H(5,𝔽₂)	—	2	1	no	—
521	H(5,𝔽₂)	—	2	1	no	—
522	H(5,𝔽₂)	—	4	1	no	—
523	H(5,𝔽₂)	D₄×C₈₉	1	2	yes	—
524	C₂×#41	—	2	2	no	—
525	C₂×#41	—	2	2	no	—
526	C₂×#41	—	2	1	no	—
527	C₂×#41	—	2	1	no	—
528	C₂×#41	—	4	1	no	—
529	C₂×#41	—	4	1	no	—
530	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
531	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
532	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
533	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
534	C₂²×Q₈	—	2	1	no	—
535	C₂²×Q₈	—	2	1	no	—
536	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
537	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
538	#137	—	2	4	no	—
539	#137	—	2	4	no	—
540	#137	—	2	4	no	—
541	#137	—	2	2	no	—
542	#137	—	2	2	no	—
543	#137	—	2	1	no	—
544	#137	—	2	2	no	—
545	#137	—	2	1	no	—
546	#137	—	2	1	no	—
547	#137	—	2	2	no	—
548	#137	D₄×C₈₉	1	2	yes	complemented
549	AGL(1,ℤ/8)	—	2	4	no	—
550	AGL(1,ℤ/8)	—	2	1	no	—
551	AGL(1,ℤ/8)	—	2	1	no	—
552	AGL(1,ℤ/8)	—	2	1	no	—
553	AGL(1,ℤ/8)	—	2	2	no	—
554	AGL(1,ℤ/8)	—	2	2	no	—
555	AGL(1,ℤ/8)	—	2	2	no	—
556	AGL(1,ℤ/8)	—	2	2	no	—
557	AGL(1,ℤ/8)	—	2	2	no	—
558	AGL(1,ℤ/8)	—	4	1	no	—
559	AGL(1,ℤ/8)	D₄×C₈₉	1	2	yes	complemented
560	#135	—	2	4	no	—
561	#135	—	2	4	no	—
562	#135	—	2	2	no	—
563	#135	—	2	2	no	—
564	C₂×Q₁₆	—	2	4	no	—
565	C₂×Q₁₆	—	2	1	no	—
566	C₂×Q₁₆	D₄×C₈₉	1	2	yes	complemented
567	C₂×SD₁₆	—	2	4	no	—
568	C₂×SD₁₆	—	2	1	no	—
569	C₂×SD₁₆	—	2	1	no	—
570	C₂×SD₁₆	—	2	1	no	—
571	C₂×SD₁₆	—	2	1	no	—
572	C₂×SD₁₆	D₄×C₈₉	1	2	yes	complemented
573	C₂×D₈	—	2	1	no	—
574	C₂×D₈	—	2	1	no	—
575	C₂×D₈	—	2	1	no	—
576	#131	—	2	2	no	—
577	#131	—	2	2	no	—
578	#131	—	2	2	no	—
579	#131	—	4	1	no	—
580	C₂×M₁₆	—	2	2	no	—
581	C₂×M₁₆	—	2	2	no	—
582	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
583	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
584	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
585	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
586	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
587	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
588	#127	—	2	1	no	—
589	#124	—	2	2	no	—
590	#124	—	2	1	no	—
591	#124	—	2	1	no	—
592	#124	—	2	1	no	—
593	#121	—	4	1	no	—
594	#120	—	4	1	no	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	4	1	no	—
598	#117	—	2	1	no	—
599	#117	C₂³×C₈₉	1	1	yes	characteristic
600	#117	C₂³×C₈₉	1	1	yes	characteristic
601	C₂×C₂²⋊C₄	—	4	1	no	—
602	C₂×C₄²	—	2	1	no	—
603	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
604	#108	—	2	2	no	—
605	C₄⋊C₈	—	2	2	no	—
606	#104	—	2	2	no	—
607	#104	—	2	2	no	—
608	#104	—	2	2	no	—
609	#104	—	2	2	no	—
610	#104	—	2	1	no	—
611	#104	—	2	1	no	—
612	#104	—	2	1	no	—
613	#104	—	2	1	no	—
614	#104	D₄×C₈₉	1	2	yes	complemented
615	#104	D₄×C₈₉	1	2	yes	complemented
616	#103	—	2	2	no	—
617	#103	—	4	1	no	—
618	#102	—	2	2	no	—
619	#101	—	2	1	no	—
620	#101	—	2	1	no	—
621	#101	—	2	2	no	—
622	#100	—	2	1	no	—
623	#100	—	2	1	no	—
624	#100	—	2	2	no	—
625	#99	—	4	1	no	—
626	C₂⁴	—	2	1	no	—
627	#41	—	2	1	no	—
628	#41	—	2	1	no	—
629	#41	—	2	1	no	—
630	#41	—	2	1	no	—
631	#41	—	2	4	no	—
632	#41	—	2	2	no	—
633	#41	—	2	2	no	—
634	#41	—	2	2	no	—
635	#41	—	2	2	no	—
636	#41	—	2	1	no	—
637	#41	—	2	1	no	—
638	#41	—	2	1	no	—
639	#41	—	2	1	no	—
640	#41	—	2	1	no	—
641	#41	—	2	1	no	—
642	#41	—	2	1	no	—
643	#41	—	2	1	no	—
644	#41	—	4	2	no	—
645	#41	—	4	2	no	—
646	#41	—	4	2	no	—
647	#41	—	4	2	no	—
648	#41	—	4	2	no	—
649	#41	—	4	4	no	—
650	#41	—	4	2	no	—
651	#41	—	4	1	no	—
652	#41	—	4	1	no	—
653	#41	—	4	4	no	—
654	#41	—	4	2	no	—
655	#41	C₂×D₄×C₈₉	1	2	yes	—
656	#41	C₂×D₄×C₈₉	1	2	yes	—
657	#41	C₂×D₄×C₈₉	1	2	yes	—
658	#41	C₂×D₄×C₈₉	1	2	yes	—
659	C₂×Q₈	—	2	1	no	—
660	C₂×Q₈	—	2	4	no	—
661	C₂×Q₈	—	2	2	no	—
662	C₂×Q₈	—	2	2	no	—
663	C₂×Q₈	—	2	1	no	—
664	C₂×Q₈	—	2	1	no	—
665	C₂×Q₈	—	2	1	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	4	1	no	—
668	C₂×Q₈	—	4	2	no	—
669	C₂×Q₈	—	4	2	no	—
670	C₂×Q₈	—	4	1	no	—
671	C₂×Q₈	—	4	2	no	—
672	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
673	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
674	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
675	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
676	C₂×Q₈	#41×C₈₉	1	1	yes	characteristic
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	4	2	no	—
690	C₂×D₄	—	4	1	no	—
691	C₂×D₄	—	4	2	no	—
692	C₂×D₄	—	4	2	no	—
693	C₂×D₄	—	4	1	no	—
694	C₂×D₄	—	4	2	no	—
695	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
696	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
697	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
698	C₂×D₄	#41×C₈₉	1	1	yes	characteristic
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	4	2	no	—
706	C₂²×C₄	—	4	1	no	—
707	C₂²×C₄	—	4	1	no	—
708	C₂²×C₄	—	4	1	no	—
709	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
710	Q₁₆	—	2	4	no	—
711	Q₁₆	—	2	2	no	—
712	Q₁₆	—	2	2	no	—
713	Q₁₆	—	2	4	no	—
714	SD₁₆	—	2	4	no	—
715	SD₁₆	—	2	2	no	—
716	SD₁₆	—	2	2	no	—
717	SD₁₆	—	2	2	no	—
718	SD₁₆	—	2	2	no	—
719	SD₁₆	—	2	4	no	—
720	SD₁₆	—	4	2	no	—
721	SD₁₆	—	4	2	no	—
722	SD₁₆	—	4	2	no	—
723	D₈	—	2	2	no	—
724	D₈	—	2	2	no	—
725	D₈	—	4	2	no	—
726	D₈	—	4	2	no	—
727	D₈	—	4	2	no	—
728	M₁₆	—	2	4	no	—
729	M₁₆	—	2	1	no	—
730	M₁₆	—	2	1	no	—
731	M₁₆	—	2	1	no	—
732	M₁₆	—	2	1	no	—
733	M₁₆	—	2	1	no	—
734	M₁₆	—	2	1	no	—
735	M₁₆	—	2	1	no	—
736	M₁₆	—	2	1	no	—
737	M₁₆	—	2	1	no	—
738	M₁₆	—	2	1	no	—
739	M₁₆	—	4	2	no	—
740	M₁₆	C₂×D₄×C₈₉	1	2	yes	—
741	M₁₆	C₂×D₄×C₈₉	1	2	yes	—
742	C₂×C₈	—	2	4	no	—
743	C₂×C₈	—	2	1	no	—
744	C₂×C₈	—	2	1	no	—
745	C₂×C₈	—	2	1	no	—
746	C₂×C₈	—	2	1	no	—
747	C₂×C₈	—	2	1	no	—
748	C₂×C₈	—	4	2	no	—
749	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	1	no	—
752	C₄⋊C₄	—	4	1	no	—
753	C₂²⋊C₄	—	2	1	no	—
754	C₂²⋊C₄	—	2	1	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	—	4	2	no	—
757	C₂²⋊C₄	—	4	1	no	—
758	C₂²⋊C₄	—	4	2	no	—
759	C₄²	—	2	1	no	—
760	C₄²	—	2	1	no	—
761	C₄²	—	2	1	no	—
762	C₄²	—	4	1	no	—
763	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
764	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
765	C₂³	—	2	1	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	2	1	no	—
768	C₂³	—	2	1	no	—
769	C₂³	—	4	2	no	—
770	C₂³	—	4	1	no	—
771	C₂³	—	4	1	no	—
772	C₂³	—	4	1	no	—
773	C₂³	—	8	2	no	—
774	C₂³	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
775	Q₈	—	2	1	no	—
776	Q₈	—	2	1	no	—
777	Q₈	—	2	1	no	—
778	Q₈	—	2	2	no	—
779	Q₈	—	2	1	no	—
780	Q₈	—	2	1	no	—
781	Q₈	—	2	1	no	—
782	Q₈	—	2	2	no	—
783	Q₈	—	4	2	no	—
784	Q₈	—	4	4	no	—
785	Q₈	—	4	1	no	—
786	Q₈	—	4	1	no	—
787	Q₈	#120×C₈₉	1	2	yes	—
788	Q₈	#121×C₈₉	1	2	yes	—
789	D₄	—	2	2	no	—
790	D₄	—	2	2	no	—
791	D₄	—	2	2	no	—
792	D₄	—	2	2	no	—
793	D₄	—	2	1	no	—
794	D₄	—	2	1	no	—
795	D₄	—	2	1	no	—
796	D₄	—	2	1	no	—
797	D₄	—	2	1	no	—
798	D₄	—	2	1	no	—
799	D₄	—	4	2	no	—
800	D₄	—	4	2	no	—
801	D₄	—	4	2	no	—
802	D₄	—	4	4	no	—
803	D₄	—	4	1	no	—
804	D₄	—	4	1	no	—
805	D₄	—	4	1	no	—
806	D₄	—	4	1	no	—
807	D₄	—	4	1	no	—
808	D₄	—	4	1	no	—
809	D₄	—	4	1	no	—
810	D₄	—	4	1	no	—
811	D₄	—	16	2	no	—
812	D₄	#120×C₈₉	1	2	yes	—
813	D₄	#121×C₈₉	1	2	yes	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	4	2	no	—
826	C₂×C₄	—	4	2	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	4	no	—
829	C₂×C₄	—	4	4	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	1	no	—
834	C₂×C₄	—	4	1	no	—
835	C₂×C₄	—	4	1	no	—
836	C₂×C₄	—	4	1	no	—
837	C₂×C₄	—	4	1	no	—
838	C₂×C₄	—	8	1	no	—
839	C₂×C₄	—	8	2	no	—
840	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
844	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
845	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
846	C₈	—	2	2	no	—
847	C₈	—	2	2	no	—
848	C₈	—	2	2	no	—
849	C₈	—	4	1	no	—
850	C₈	—	4	1	no	—
851	C₈	—	4	1	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	4	1	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	8	1	no	—
858	C₂²	—	8	1	no	—
859	C₂²	—	8	1	no	—
860	C₂²	—	8	1	no	—
861	C₂²	—	8	2	no	—
862	C₂²	—	8	2	no	—
863	C₂²	—	8	1	no	—
864	C₂²	—	16	1	no	—
865	C₂²	—	16	2	no	—
866	C₂²	#534×C₈₉	1	1	yes	characteristic
867	C₂²	D₄²×C₈₉	1	1	yes	characteristic
868	C₂²	#546×C₈₉	1	1	yes	characteristic
869	C₄	—	2	2	no	—
870	C₄	—	2	2	no	—
871	C₄	—	4	1	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	1	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	1	no	—
876	C₄	—	8	1	no	—
877	C₄	—	8	1	no	—
878	C₄	C₂×#120×C₈₉	1	1	yes	characteristic
879	C₄	C₂×#121×C₈₉	1	1	yes	characteristic
880	C₄	D₄²×C₈₉	1	1	yes	characteristic
881	C₄	#546×C₈₉	1	1	yes	characteristic
882	C₂	—	2	1	no	—
883	C₂	—	2	1	no	—
884	C₂	—	2	1	no	—
885	C₂	—	4	2	no	—
886	C₂	—	4	2	no	—
887	C₂	—	8	1	no	—
888	C₂	—	8	1	no	—
889	C₂	—	16	1	no	—
890	C₂	C₈₉×#2410	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₈₉	#2410
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×#3068	C₂	semidirect
3. C₈₉×#3040	C₂	semidirect
4. C₈₉×#3021	C₂	semidirect
5. C₂×#454×C₈₉	C₂	semidirect
6. C₈₉×#2901	C₂	semidirect
7. C₈₉×#2050	C₂	semidirect
8. C₈₉×#2049	C₂	semidirect
9. C₈₉×#2008	C₂	semidirect
10. C₈₉×#2004	C₂	semidirect
11. C₈₉×#1906	C₂	semidirect
12. C₈₉×#1903	C₂	semidirect
13. C₈₉×#1902	C₂	semidirect
14. C₈₉×#1861	C₂	semidirect
15. C₈₉×#1796	C₂	semidirect
30. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
34. C₂×#124×C₈₉	C₂²	semidirect
44. #430×C₈₉	C₂²	semidirect
45. #423×C₈₉	C₂²	semidirect
54. C₂×#104×C₈₉	C₂²	semidirect
55. #419×C₈₉	C₂²	semidirect
56. #419×C₈₉	C₂²	semidirect
57. #418×C₈₉	C₂²	semidirect
59. #413×C₈₉	C₂²	semidirect
60. C₂×#101×C₈₉	C₂²	semidirect
61. C₂×#100×C₈₉	C₂²	semidirect
62. #410×C₈₉	C₂²	semidirect
63. #344×C₈₉	C₂²	semidirect
64. #344×C₈₉	C₂²	semidirect
65. #339×C₈₉	C₂²	semidirect
66. #338×C₈₉	C₂²	semidirect
102. #137×C₈₉	D₄	semidirect
113. AGL(1,ℤ/8)×C₈₉	D₄	semidirect
120. C₂×Q₁₆×C₈₉	D₄	semidirect
126. C₂×SD₁₆×C₈₉	D₄	semidirect
168. #104×C₈₉	D₄	semidirect
169. #104×C₈₉	D₄	semidirect
436. #24473	C₈₉	direct (N × H)
446. #3586	C₂×C₈₉	semidirect
447. #3068	C₂×C₈₉	semidirect
448. #3040	C₂×C₈₉	semidirect
449. #3021	C₂×C₈₉	semidirect
450. C₂×#454	C₂×C₈₉	semidirect
451. #2901	C₂×C₈₉	semidirect
452. #2050	C₂×C₈₉	semidirect
453. #2049	C₂×C₈₉	semidirect
454. #2008	C₂×C₈₉	semidirect
455. #2004	C₂×C₈₉	semidirect
456. #1906	C₂×C₈₉	semidirect
457. #1903	C₂×C₈₉	semidirect
458. #1902	C₂×C₈₉	semidirect
459. #1861	C₂×C₈₉	semidirect
460. #1796	C₂×C₈₉	semidirect
461. C₈₉	#24473	direct (N × H)
476. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
480. C₂×#124	C₂²×C₈₉	semidirect
490. #430	C₂²×C₈₉	semidirect
491. #423	C₂²×C₈₉	semidirect
500. C₂×#104	C₂²×C₈₉	semidirect
501. #419	C₂²×C₈₉	semidirect
502. #419	C₂²×C₈₉	semidirect
503. #418	C₂²×C₈₉	semidirect
505. #413	C₂²×C₈₉	semidirect
506. C₂×#101	C₂²×C₈₉	semidirect
507. C₂×#100	C₂²×C₈₉	semidirect
508. #410	C₂²×C₈₉	semidirect
509. #344	C₂²×C₈₉	semidirect
510. #344	C₂²×C₈₉	semidirect
511. #339	C₂²×C₈₉	semidirect
512. #338	C₂²×C₈₉	semidirect
548. #137	D₄×C₈₉	semidirect
559. AGL(1,ℤ/8)	D₄×C₈₉	semidirect
566. C₂×Q₁₆	D₄×C₈₉	semidirect
572. C₂×SD₁₆	D₄×C₈₉	semidirect
614. #104	D₄×C₈₉	semidirect
615. #104	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×#3068	2
C₈₉×#3040	2
C₈₉×#3021	2
C₂×#454×C₈₉	2
C₈₉×#2901	2
C₈₉×#2050	2
C₈₉×#2049	2
C₈₉×#2008	2
C₈₉×#2004	2
C₈₉×#1906	2
C₈₉×#1903	2
C₈₉×#1902	2
C₈₉×#1861	2
C₈₉×#1796	2
#24473	89

Subgroups — C89×#24473 #36402321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#24473 #36402321