Subgroups — C₈₉×#23889 #36401737

Order 22784.

1648 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#578×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#577×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#454×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#455×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3013	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3012	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2020	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2019	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2015	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2007	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×#1876	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1876	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1793	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×2₋¹⁺⁴×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	4	no	—
20	#578×C₈₉	—	2	4	no	—
21	#577×C₈₉	—	2	4	no	—
22	#577×C₈₉	—	2	4	no	—
23	C₂×#137×C₈₉	—	2	1	no	—
24	C₂×#137×C₈₉	—	2	1	no	—
25	C₂×#137×C₈₉	—	2	1	no	—
26	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
31	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#135×C₈₉	—	2	1	no	—
34	C₂×#135×C₈₉	—	2	1	no	—
35	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
37	C₂²×Q₁₆×C₈₉	—	2	1	no	—
38	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	C₂²×SD₁₆×C₈₉	—	2	1	no	—
40	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	#537×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
45	#455×C₈₉	—	2	4	no	—
46	#454×C₈₉	—	2	4	no	—
47	#452×C₈₉	—	2	1	no	—
48	#452×C₈₉	—	2	1	no	—
49	#451×C₈₉	—	2	1	no	—
50	#450×C₈₉	—	2	1	no	—
51	#449×C₈₉	—	2	1	no	—
52	#449×C₈₉	—	2	1	no	—
53	#448×C₈₉	—	2	1	no	—
54	#447×C₈₉	—	2	1	no	—
55	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic
56	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic
57	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#417×C₈₉	C₂²	1	1	yes	characteristic
60	#417×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
62	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
63	C₂×#101×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	C₂×#101×C₈₉	C₂²	1	1	yes	characteristic, complemented
65	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic
66	#408×C₈₉	C₂²	1	1	yes	characteristic
67	#408×C₈₉	C₂²	1	1	yes	characteristic, complemented
68	#391×C₈₉	C₂²	1	1	yes	characteristic, complemented
69	#343×C₈₉	C₂²	1	1	yes	characteristic, complemented
70	#341×C₈₉	C₂²	1	1	yes	characteristic, complemented
71	#341×C₈₉	C₂²	1	1	yes	characteristic, complemented
72	#336×C₈₉	C₂²	1	1	yes	characteristic, complemented
73	2₋¹⁺⁴×C₈₉	—	2	2	no	—
74	2₋¹⁺⁴×C₈₉	—	2	2	no	—
75	2₋¹⁺⁴×C₈₉	—	2	2	no	—
76	2₋¹⁺⁴×C₈₉	—	2	2	no	—
77	2₋¹⁺⁴×C₈₉	—	2	2	no	—
78	2₋¹⁺⁴×C₈₉	—	4	1	no	—
79	2₋¹⁺⁴×C₈₉	—	4	1	no	—
80	2₋¹⁺⁴×C₈₉	D₄	1	4	yes	complemented
81	H(5,𝔽₂)×C₈₉	—	2	2	no	—
82	H(5,𝔽₂)×C₈₉	—	2	2	no	—
83	H(5,𝔽₂)×C₈₉	—	2	2	no	—
84	H(5,𝔽₂)×C₈₉	—	4	1	no	—
85	C₂×#41×C₈₉	—	2	1	no	—
86	C₂×#41×C₈₉	—	2	1	no	—
87	C₂×#41×C₈₉	—	2	1	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	—	4	1	no	—
92	C₂×#41×C₈₉	—	4	1	no	—
93	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
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	C₂²×Q₈×C₈₉	—	2	1	no	—
98	C₂²×Q₈×C₈₉	—	2	1	no	—
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×Q₈×C₈₉	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₈₉	—	2	1	no	—
104	C₂²×D₄×C₈₉	—	2	1	no	—
105	C₂²×D₄×C₈₉	—	4	1	no	—
106	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
107	#137×C₈₉	—	2	8	no	—
108	#137×C₈₉	—	2	8	no	—
109	#137×C₈₉	—	2	8	no	—
110	#137×C₈₉	—	2	2	no	—
111	#137×C₈₉	—	2	2	no	—
112	#137×C₈₉	—	2	2	no	—
113	#137×C₈₉	—	2	2	no	—
114	#137×C₈₉	—	2	2	no	—
115	#137×C₈₉	—	2	2	no	—
116	#137×C₈₉	—	4	1	no	—
117	#137×C₈₉	D₄	1	4	yes	complemented
118	AGL(1,ℤ/8)×C₈₉	—	2	8	no	—
119	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
120	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
121	AGL(1,ℤ/8)×C₈₉	—	4	1	no	—
122	AGL(1,ℤ/8)×C₈₉	D₄	1	4	yes	complemented
123	#135×C₈₉	—	2	8	no	—
124	#135×C₈₉	—	2	8	no	—
125	#135×C₈₉	—	2	2	no	—
126	#135×C₈₉	—	2	2	no	—
127	#135×C₈₉	—	2	2	no	—
128	#135×C₈₉	—	2	2	no	—
129	C₂×Q₁₆×C₈₉	—	2	8	no	—
130	C₂×Q₁₆×C₈₉	—	2	1	no	—
131	C₂×Q₁₆×C₈₉	—	2	1	no	—
132	C₂×Q₁₆×C₈₉	—	2	2	no	—
133	C₂×Q₁₆×C₈₉	—	2	2	no	—
134	C₂×Q₁₆×C₈₉	—	2	1	no	—
135	C₂×Q₁₆×C₈₉	—	2	1	no	—
136	C₂×Q₁₆×C₈₉	—	2	1	no	—
137	C₂×Q₁₆×C₈₉	—	2	1	no	—
138	C₂×Q₁₆×C₈₉	D₄	1	1	yes	characteristic
139	C₂×Q₁₆×C₈₉	D₄	1	1	yes	characteristic
140	C₂×SD₁₆×C₈₉	—	2	8	no	—
141	C₂×SD₁₆×C₈₉	—	2	1	no	—
142	C₂×SD₁₆×C₈₉	—	2	2	no	—
143	C₂×SD₁₆×C₈₉	—	2	1	no	—
144	C₂×SD₁₆×C₈₉	—	2	2	no	—
145	C₂×SD₁₆×C₈₉	—	2	1	no	—
146	C₂×SD₁₆×C₈₉	—	2	1	no	—
147	C₂×SD₁₆×C₈₉	—	2	1	no	—
148	C₂×SD₁₆×C₈₉	—	2	1	no	—
149	C₂×SD₁₆×C₈₉	—	2	1	no	—
150	C₂×SD₁₆×C₈₉	—	2	1	no	—
151	C₂×SD₁₆×C₈₉	D₄	1	1	yes	characteristic
152	C₂×SD₁₆×C₈₉	D₄	1	1	yes	characteristic
153	C₂×SD₁₆×C₈₉	D₄	1	1	yes	characteristic
154	C₂×SD₁₆×C₈₉	D₄	1	1	yes	characteristic
155	C₂×D₈×C₈₉	—	2	1	no	—
156	C₂×D₈×C₈₉	—	2	1	no	—
157	C₂×D₈×C₈₉	D₄	1	1	yes	characteristic
158	C₂×D₈×C₈₉	D₄	1	1	yes	characteristic
159	#131×C₈₉	—	2	2	no	—
160	#131×C₈₉	—	2	2	no	—
161	#131×C₈₉	—	2	2	no	—
162	#131×C₈₉	—	2	2	no	—
163	C₂×M₁₆×C₈₉	—	2	1	no	—
164	C₂×M₁₆×C₈₉	—	2	1	no	—
165	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
166	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
167	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
168	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
169	C₂²×C₈×C₈₉	—	2	1	no	—
170	C₂²×C₈×C₈₉	—	2	1	no	—
171	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
172	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
173	#124×C₈₉	—	2	2	no	—
174	#124×C₈₉	—	2	2	no	—
175	C₂²⋊Q₈×C₈₉	—	2	1	no	—
176	C₂²⋊Q₈×C₈₉	—	2	1	no	—
177	#121×C₈₉	—	2	1	no	—
178	#121×C₈₉	—	2	1	no	—
179	#121×C₈₉	—	4	1	no	—
180	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₈₉	—	4	1	no	—
182	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
183	#104×C₈₉	—	2	2	no	—
184	#104×C₈₉	—	2	2	no	—
185	#104×C₈₉	—	2	2	no	—
186	#104×C₈₉	—	2	2	no	—
187	#103×C₈₉	—	2	1	no	—
188	#103×C₈₉	—	2	1	no	—
189	#103×C₈₉	—	2	1	no	—
190	#103×C₈₉	—	2	1	no	—
191	#102×C₈₉	—	2	1	no	—
192	#102×C₈₉	—	2	1	no	—
193	#102×C₈₉	—	2	1	no	—
194	#102×C₈₉	—	2	1	no	—
195	#101×C₈₉	—	2	2	no	—
196	#101×C₈₉	—	4	1	no	—
197	#100×C₈₉	—	2	2	no	—
198	C₂²⋊C₈×C₈₉	—	2	1	no	—
199	C₂²⋊C₈×C₈₉	—	2	1	no	—
200	C₂²⋊C₈×C₈₉	—	2	1	no	—
201	C₂²⋊C₈×C₈₉	—	2	1	no	—
202	#95×C₈₉	—	4	1	no	—
203	C₂⁴×C₈₉	—	2	1	no	—
204	C₂⁴×C₈₉	—	4	1	no	—
205	#41×C₈₉	—	2	1	no	—
206	#41×C₈₉	—	2	1	no	—
207	#41×C₈₉	—	2	1	no	—
208	#41×C₈₉	—	2	1	no	—
209	#41×C₈₉	—	2	4	no	—
210	#41×C₈₉	—	2	4	no	—
211	#41×C₈₉	—	2	4	no	—
212	#41×C₈₉	—	2	4	no	—
213	#41×C₈₉	—	2	1	no	—
214	#41×C₈₉	—	2	1	no	—
215	#41×C₈₉	—	2	1	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	—	4	4	no	—
222	#41×C₈₉	—	4	2	no	—
223	#41×C₈₉	—	4	2	no	—
224	#41×C₈₉	—	4	2	no	—
225	#41×C₈₉	—	4	4	no	—
226	#41×C₈₉	—	4	2	no	—
227	#41×C₈₉	—	4	4	no	—
228	#41×C₈₉	—	4	2	no	—
229	#41×C₈₉	—	4	2	no	—
230	#41×C₈₉	—	4	4	no	—
231	#41×C₈₉	—	4	2	no	—
232	#41×C₈₉	—	4	2	no	—
233	#41×C₈₉	C₂×D₄	1	2	yes	—
234	#41×C₈₉	C₂×D₄	1	2	yes	—
235	#41×C₈₉	C₂×D₄	1	2	yes	—
236	#41×C₈₉	C₂×D₄	1	2	yes	—
237	C₂×Q₈×C₈₉	—	2	1	no	—
238	C₂×Q₈×C₈₉	—	2	1	no	—
239	C₂×Q₈×C₈₉	—	2	4	no	—
240	C₂×Q₈×C₈₉	—	2	4	no	—
241	C₂×Q₈×C₈₉	—	2	4	no	—
242	C₂×Q₈×C₈₉	—	2	1	no	—
243	C₂×Q₈×C₈₉	—	2	1	no	—
244	C₂×Q₈×C₈₉	—	2	1	no	—
245	C₂×Q₈×C₈₉	—	2	1	no	—
246	C₂×Q₈×C₈₉	—	2	1	no	—
247	C₂×Q₈×C₈₉	—	2	1	no	—
248	C₂×Q₈×C₈₉	—	2	1	no	—
249	C₂×Q₈×C₈₉	—	2	1	no	—
250	C₂×Q₈×C₈₉	—	4	1	no	—
251	C₂×Q₈×C₈₉	—	4	1	no	—
252	C₂×Q₈×C₈₉	—	4	2	no	—
253	C₂×Q₈×C₈₉	—	4	2	no	—
254	C₂×Q₈×C₈₉	—	4	2	no	—
255	C₂×Q₈×C₈₉	—	4	2	no	—
256	C₂×Q₈×C₈₉	—	4	2	no	—
257	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
258	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
259	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
260	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
261	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
262	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
263	C₂×D₄×C₈₉	—	2	1	no	—
264	C₂×D₄×C₈₉	—	2	1	no	—
265	C₂×D₄×C₈₉	—	2	4	no	—
266	C₂×D₄×C₈₉	—	2	1	no	—
267	C₂×D₄×C₈₉	—	2	1	no	—
268	C₂×D₄×C₈₉	—	2	1	no	—
269	C₂×D₄×C₈₉	—	2	1	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	—	4	2	no	—
274	C₂×D₄×C₈₉	—	4	1	no	—
275	C₂×D₄×C₈₉	—	4	1	no	—
276	C₂×D₄×C₈₉	—	4	2	no	—
277	C₂×D₄×C₈₉	—	4	4	no	—
278	C₂×D₄×C₈₉	—	4	4	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	1	no	—
283	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
284	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
285	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
286	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
287	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₈₉	—	2	1	no	—
289	C₂²×C₄×C₈₉	—	2	1	no	—
290	C₂²×C₄×C₈₉	—	2	1	no	—
291	C₂²×C₄×C₈₉	—	2	1	no	—
292	C₂²×C₄×C₈₉	—	2	1	no	—
293	C₂²×C₄×C₈₉	—	2	1	no	—
294	C₂²×C₄×C₈₉	—	2	1	no	—
295	C₂²×C₄×C₈₉	—	2	1	no	—
296	C₂²×C₄×C₈₉	—	4	1	no	—
297	C₂²×C₄×C₈₉	—	4	1	no	—
298	C₂²×C₄×C₈₉	—	4	1	no	—
299	C₂²×C₄×C₈₉	—	4	1	no	—
300	C₂²×C₄×C₈₉	—	4	1	no	—
301	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
302	Q₁₆×C₈₉	—	2	4	no	—
303	Q₁₆×C₈₉	—	2	4	no	—
304	Q₁₆×C₈₉	—	2	4	no	—
305	Q₁₆×C₈₉	—	2	4	no	—
306	Q₁₆×C₈₉	—	2	2	no	—
307	Q₁₆×C₈₉	—	2	4	no	—
308	Q₁₆×C₈₉	—	2	2	no	—
309	Q₁₆×C₈₉	—	4	2	no	—
310	SD₁₆×C₈₉	—	2	4	no	—
311	SD₁₆×C₈₉	—	2	4	no	—
312	SD₁₆×C₈₉	—	2	4	no	—
313	SD₁₆×C₈₉	—	2	4	no	—
314	SD₁₆×C₈₉	—	2	2	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	—	4	2	no	—
321	SD₁₆×C₈₉	—	4	2	no	—
322	D₈×C₈₉	—	2	4	no	—
323	D₈×C₈₉	—	2	2	no	—
324	D₈×C₈₉	—	2	2	no	—
325	D₈×C₈₉	—	4	2	no	—
326	M₁₆×C₈₉	—	2	4	no	—
327	M₁₆×C₈₉	—	2	4	no	—
328	M₁₆×C₈₉	—	2	1	no	—
329	M₁₆×C₈₉	—	2	1	no	—
330	M₁₆×C₈₉	—	2	1	no	—
331	M₁₆×C₈₉	—	2	1	no	—
332	M₁₆×C₈₉	—	2	1	no	—
333	M₁₆×C₈₉	—	2	1	no	—
334	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
335	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
336	C₂×C₈×C₈₉	—	2	4	no	—
337	C₂×C₈×C₈₉	—	2	4	no	—
338	C₂×C₈×C₈₉	—	2	1	no	—
339	C₂×C₈×C₈₉	—	2	1	no	—
340	C₂×C₈×C₈₉	—	2	1	no	—
341	C₂×C₈×C₈₉	—	2	1	no	—
342	C₂×C₈×C₈₉	—	2	1	no	—
343	C₂×C₈×C₈₉	—	2	1	no	—
344	C₂×C₈×C₈₉	—	2	1	no	—
345	C₂×C₈×C₈₉	—	2	1	no	—
346	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
347	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
348	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
349	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
350	C₄⋊C₄×C₈₉	—	2	1	no	—
351	C₄⋊C₄×C₈₉	—	2	1	no	—
352	C₄⋊C₄×C₈₉	—	4	1	no	—
353	C₂²⋊C₄×C₈₉	—	4	4	no	—
354	C₂²⋊C₄×C₈₉	—	4	1	no	—
355	C₂²⋊C₄×C₈₉	—	4	1	no	—
356	C₄²×C₈₉	—	2	1	no	—
357	C₄²×C₈₉	—	2	1	no	—
358	C₂³×C₈₉	—	2	1	no	—
359	C₂³×C₈₉	—	2	1	no	—
360	C₂³×C₈₉	—	2	1	no	—
361	C₂³×C₈₉	—	2	1	no	—
362	C₂³×C₈₉	—	2	2	no	—
363	C₂³×C₈₉	—	4	4	no	—
364	C₂³×C₈₉	—	4	1	no	—
365	C₂³×C₈₉	—	4	1	no	—
366	C₂³×C₈₉	—	8	1	no	—
367	C₂³×C₈₉	—	8	1	no	—
368	C₂³×C₈₉	—	16	1	no	—
369	C₂³×C₈₉	—	16	1	no	—
370	C₂³×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
371	Q₈×C₈₉	—	2	1	no	—
372	Q₈×C₈₉	—	2	1	no	—
373	Q₈×C₈₉	—	2	2	no	—
374	Q₈×C₈₉	—	2	2	no	—
375	Q₈×C₈₉	—	2	2	no	—
376	Q₈×C₈₉	—	2	1	no	—
377	Q₈×C₈₉	—	2	1	no	—
378	Q₈×C₈₉	—	2	1	no	—
379	Q₈×C₈₉	—	2	2	no	—
380	Q₈×C₈₉	—	2	1	no	—
381	Q₈×C₈₉	—	4	4	no	—
382	Q₈×C₈₉	—	4	4	no	—
383	Q₈×C₈₉	—	4	1	no	—
384	Q₈×C₈₉	—	4	1	no	—
385	Q₈×C₈₉	—	4	1	no	—
386	Q₈×C₈₉	—	4	1	no	—
387	Q₈×C₈₉	#120	1	2	yes	—
388	Q₈×C₈₉	#120	1	2	yes	—
389	D₄×C₈₉	—	2	2	no	—
390	D₄×C₈₉	—	2	2	no	—
391	D₄×C₈₉	—	2	2	no	—
392	D₄×C₈₉	—	2	2	no	—
393	D₄×C₈₉	—	2	2	no	—
394	D₄×C₈₉	—	2	1	no	—
395	D₄×C₈₉	—	2	1	no	—
396	D₄×C₈₉	—	2	1	no	—
397	D₄×C₈₉	—	2	1	no	—
398	D₄×C₈₉	—	2	1	no	—
399	D₄×C₈₉	—	2	2	no	—
400	D₄×C₈₉	—	2	1	no	—
401	D₄×C₈₉	—	4	4	no	—
402	D₄×C₈₉	—	4	4	no	—
403	D₄×C₈₉	—	4	4	no	—
404	D₄×C₈₉	—	4	4	no	—
405	D₄×C₈₉	—	4	1	no	—
406	D₄×C₈₉	—	4	1	no	—
407	D₄×C₈₉	—	4	1	no	—
408	D₄×C₈₉	—	4	1	no	—
409	D₄×C₈₉	—	4	1	no	—
410	D₄×C₈₉	—	4	1	no	—
411	D₄×C₈₉	—	16	1	no	—
412	D₄×C₈₉	#120	1	2	yes	—
413	D₄×C₈₉	#120	1	2	yes	—
414	C₂×C₄×C₈₉	—	2	1	no	—
415	C₂×C₄×C₈₉	—	2	1	no	—
416	C₂×C₄×C₈₉	—	2	2	no	—
417	C₂×C₄×C₈₉	—	2	2	no	—
418	C₂×C₄×C₈₉	—	2	2	no	—
419	C₂×C₄×C₈₉	—	2	2	no	—
420	C₂×C₄×C₈₉	—	2	2	no	—
421	C₂×C₄×C₈₉	—	2	2	no	—
422	C₂×C₄×C₈₉	—	2	1	no	—
423	C₂×C₄×C₈₉	—	2	1	no	—
424	C₂×C₄×C₈₉	—	4	4	no	—
425	C₂×C₄×C₈₉	—	4	4	no	—
426	C₂×C₄×C₈₉	—	4	4	no	—
427	C₂×C₄×C₈₉	—	4	4	no	—
428	C₂×C₄×C₈₉	—	4	4	no	—
429	C₂×C₄×C₈₉	—	4	1	no	—
430	C₂×C₄×C₈₉	—	4	1	no	—
431	C₂×C₄×C₈₉	—	4	1	no	—
432	C₂×C₄×C₈₉	—	4	1	no	—
433	C₂×C₄×C₈₉	—	4	1	no	—
434	C₂×C₄×C₈₉	—	4	1	no	—
435	C₂×C₄×C₈₉	—	4	1	no	—
436	C₂×C₄×C₈₉	—	4	1	no	—
437	C₂×C₄×C₈₉	—	4	1	no	—
438	C₂×C₄×C₈₉	—	4	1	no	—
439	C₂×C₄×C₈₉	—	4	1	no	—
440	C₂×C₄×C₈₉	—	4	1	no	—
441	C₂×C₄×C₈₉	—	8	1	no	—
442	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
448	C₈×C₈₉	—	2	1	no	—
449	C₈×C₈₉	—	2	1	no	—
450	C₈×C₈₉	—	2	2	no	—
451	C₈×C₈₉	—	2	2	no	—
452	C₈×C₈₉	—	2	1	no	—
453	C₈×C₈₉	—	2	1	no	—
454	C₈×C₈₉	—	4	1	no	—
455	C₈×C₈₉	—	4	1	no	—
456	C₂²×C₈₉	—	2	1	no	—
457	C₂²×C₈₉	—	2	1	no	—
458	C₂²×C₈₉	—	2	2	no	—
459	C₂²×C₈₉	—	2	2	no	—
460	C₂²×C₈₉	—	4	1	no	—
461	C₂²×C₈₉	—	4	1	no	—
462	C₂²×C₈₉	—	4	1	no	—
463	C₂²×C₈₉	—	4	1	no	—
464	C₂²×C₈₉	—	4	1	no	—
465	C₂²×C₈₉	—	4	1	no	—
466	C₂²×C₈₉	—	4	2	no	—
467	C₂²×C₈₉	—	4	1	no	—
468	C₂²×C₈₉	—	4	1	no	—
469	C₂²×C₈₉	—	4	1	no	—
470	C₂²×C₈₉	—	4	1	no	—
471	C₂²×C₈₉	—	8	2	no	—
472	C₂²×C₈₉	—	8	1	no	—
473	C₂²×C₈₉	—	8	1	no	—
474	C₂²×C₈₉	—	16	1	no	—
475	C₂²×C₈₉	—	16	4	no	—
476	C₂²×C₈₉	#534	1	1	yes	characteristic
477	C₂²×C₈₉	D₄²	1	1	yes	characteristic
478	C₂²×C₈₉	D₄²	1	1	yes	characteristic
479	C₄×C₈₉	—	2	2	no	—
480	C₄×C₈₉	—	2	2	no	—
481	C₄×C₈₉	—	4	1	no	—
482	C₄×C₈₉	—	4	2	no	—
483	C₄×C₈₉	—	4	2	no	—
484	C₄×C₈₉	—	4	1	no	—
485	C₄×C₈₉	—	8	1	no	—
486	C₄×C₈₉	—	8	1	no	—
487	C₄×C₈₉	C₂×#120	1	1	yes	characteristic
488	C₄×C₈₉	C₂×#120	1	1	yes	characteristic
489	C₄×C₈₉	D₄²	1	1	yes	characteristic
490	C₄×C₈₉	D₄²	1	1	yes	characteristic
491	#23889	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
492	C₂×C₈₉	—	2	1	no	—
493	C₂×C₈₉	—	2	1	no	—
494	C₂×C₈₉	—	4	2	no	—
495	C₂×C₈₉	—	4	2	no	—
496	C₂×C₈₉	—	8	1	no	—
497	C₂×C₈₉	—	8	1	no	—
498	C₂×C₈₉	—	8	2	no	—
499	C₂×C₈₉	#2403	1	1	yes	characteristic
500	C₂×C₈₉	#3289	1	1	yes	characteristic
501	C₂×C₈₉	#3290	1	1	yes	characteristic
502	C₂×#578	C₂×C₈₉	1	1	yes	characteristic, complemented
503	C₂×#577	C₂×C₈₉	1	1	yes	characteristic, complemented
504	C₂×#454	C₂×C₈₉	1	1	yes	characteristic, complemented
505	C₂×#455	C₂×C₈₉	1	1	yes	characteristic, complemented
506	#3013	C₂×C₈₉	1	1	yes	characteristic, complemented
507	#3012	C₂×C₈₉	1	1	yes	characteristic, complemented
508	#2020	C₂×C₈₉	1	1	yes	characteristic, complemented
509	#2019	C₂×C₈₉	1	1	yes	characteristic, complemented
510	#2015	C₂×C₈₉	1	1	yes	characteristic, complemented
511	#2007	C₂×C₈₉	1	1	yes	characteristic, complemented
512	#1908	C₂×C₈₉	1	1	yes	characteristic, complemented
513	#1907	C₂×C₈₉	1	1	yes	characteristic, complemented
514	#1876	C₂×C₈₉	1	1	yes	characteristic, complemented
515	#1876	C₂×C₈₉	1	1	yes	characteristic, complemented
516	#1793	C₂×C₈₉	1	1	yes	characteristic, complemented
517	C₈₉	#23889	1	1	yes	characteristic, direct product factor, Sylow
518	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	1	yes	characteristic
519	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	1	yes	characteristic, complemented
520	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	1	yes	characteristic
521	#578	—	2	4	no	—
522	#578	—	2	4	no	—
523	#577	—	2	4	no	—
524	#577	—	2	4	no	—
525	C₂×#137	—	2	1	no	—
526	C₂×#137	—	2	1	no	—
527	C₂×#137	—	2	1	no	—
528	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
529	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
530	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
531	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic, complemented
532	C₂×AGL(1,ℤ/8)	—	2	1	no	—
533	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
534	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
535	C₂×#135	—	2	1	no	—
536	C₂×#135	—	2	1	no	—
537	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
538	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
539	C₂²×Q₁₆	—	2	1	no	—
540	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
541	C₂²×SD₁₆	—	2	1	no	—
542	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
543	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
544	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic, complemented
545	#537	C₂²×C₈₉	1	1	yes	characteristic
546	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
547	#455	—	2	4	no	—
548	#454	—	2	4	no	—
549	#452	—	2	1	no	—
550	#452	—	2	1	no	—
551	#451	—	2	1	no	—
552	#450	—	2	1	no	—
553	#449	—	2	1	no	—
554	#449	—	2	1	no	—
555	#448	—	2	1	no	—
556	#447	—	2	1	no	—
557	C₂×#104	C₂²×C₈₉	1	1	yes	characteristic
558	C₂×#104	C₂²×C₈₉	1	1	yes	characteristic
559	C₂×#104	C₂²×C₈₉	1	1	yes	characteristic, complemented
560	C₂×#104	C₂²×C₈₉	1	1	yes	characteristic, complemented
561	#417	C₂²×C₈₉	1	1	yes	characteristic
562	#417	C₂²×C₈₉	1	1	yes	characteristic, complemented
563	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
564	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
565	C₂×#101	C₂²×C₈₉	1	1	yes	characteristic, complemented
566	C₂×#101	C₂²×C₈₉	1	1	yes	characteristic, complemented
567	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic
568	#408	C₂²×C₈₉	1	1	yes	characteristic
569	#408	C₂²×C₈₉	1	1	yes	characteristic, complemented
570	#391	C₂²×C₈₉	1	1	yes	characteristic, complemented
571	#343	C₂²×C₈₉	1	1	yes	characteristic, complemented
572	#341	C₂²×C₈₉	1	1	yes	characteristic, complemented
573	#341	C₂²×C₈₉	1	1	yes	characteristic, complemented
574	#336	C₂²×C₈₉	1	1	yes	characteristic, complemented
575	2₋¹⁺⁴	—	2	2	no	—
576	2₋¹⁺⁴	—	2	2	no	—
577	2₋¹⁺⁴	—	2	2	no	—
578	2₋¹⁺⁴	—	2	2	no	—
579	2₋¹⁺⁴	—	2	2	no	—
580	2₋¹⁺⁴	—	4	1	no	—
581	2₋¹⁺⁴	—	4	1	no	—
582	2₋¹⁺⁴	D₄×C₈₉	1	4	yes	complemented
583	H(5,𝔽₂)	—	2	2	no	—
584	H(5,𝔽₂)	—	2	2	no	—
585	H(5,𝔽₂)	—	2	2	no	—
586	H(5,𝔽₂)	—	4	1	no	—
587	C₂×#41	—	2	1	no	—
588	C₂×#41	—	2	1	no	—
589	C₂×#41	—	2	1	no	—
590	C₂×#41	—	2	1	no	—
591	C₂×#41	—	2	1	no	—
592	C₂×#41	—	2	1	no	—
593	C₂×#41	—	4	1	no	—
594	C₂×#41	—	4	1	no	—
595	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
596	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
597	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
598	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
599	C₂²×Q₈	—	2	1	no	—
600	C₂²×Q₈	—	2	1	no	—
601	C₂²×Q₈	—	2	1	no	—
602	C₂²×Q₈	—	2	1	no	—
603	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
604	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
605	C₂²×D₄	—	2	1	no	—
606	C₂²×D₄	—	2	1	no	—
607	C₂²×D₄	—	4	1	no	—
608	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
609	#137	—	2	8	no	—
610	#137	—	2	8	no	—
611	#137	—	2	8	no	—
612	#137	—	2	2	no	—
613	#137	—	2	2	no	—
614	#137	—	2	2	no	—
615	#137	—	2	2	no	—
616	#137	—	2	2	no	—
617	#137	—	2	2	no	—
618	#137	—	4	1	no	—
619	#137	D₄×C₈₉	1	4	yes	complemented
620	AGL(1,ℤ/8)	—	2	8	no	—
621	AGL(1,ℤ/8)	—	2	2	no	—
622	AGL(1,ℤ/8)	—	2	2	no	—
623	AGL(1,ℤ/8)	—	4	1	no	—
624	AGL(1,ℤ/8)	D₄×C₈₉	1	4	yes	complemented
625	#135	—	2	8	no	—
626	#135	—	2	8	no	—
627	#135	—	2	2	no	—
628	#135	—	2	2	no	—
629	#135	—	2	2	no	—
630	#135	—	2	2	no	—
631	C₂×Q₁₆	—	2	8	no	—
632	C₂×Q₁₆	—	2	1	no	—
633	C₂×Q₁₆	—	2	1	no	—
634	C₂×Q₁₆	—	2	2	no	—
635	C₂×Q₁₆	—	2	2	no	—
636	C₂×Q₁₆	—	2	1	no	—
637	C₂×Q₁₆	—	2	1	no	—
638	C₂×Q₁₆	—	2	1	no	—
639	C₂×Q₁₆	—	2	1	no	—
640	C₂×Q₁₆	D₄×C₈₉	1	1	yes	characteristic
641	C₂×Q₁₆	D₄×C₈₉	1	1	yes	characteristic
642	C₂×SD₁₆	—	2	8	no	—
643	C₂×SD₁₆	—	2	1	no	—
644	C₂×SD₁₆	—	2	2	no	—
645	C₂×SD₁₆	—	2	1	no	—
646	C₂×SD₁₆	—	2	2	no	—
647	C₂×SD₁₆	—	2	1	no	—
648	C₂×SD₁₆	—	2	1	no	—
649	C₂×SD₁₆	—	2	1	no	—
650	C₂×SD₁₆	—	2	1	no	—
651	C₂×SD₁₆	—	2	1	no	—
652	C₂×SD₁₆	—	2	1	no	—
653	C₂×SD₁₆	D₄×C₈₉	1	1	yes	characteristic
654	C₂×SD₁₆	D₄×C₈₉	1	1	yes	characteristic
655	C₂×SD₁₆	D₄×C₈₉	1	1	yes	characteristic
656	C₂×SD₁₆	D₄×C₈₉	1	1	yes	characteristic
657	C₂×D₈	—	2	1	no	—
658	C₂×D₈	—	2	1	no	—
659	C₂×D₈	D₄×C₈₉	1	1	yes	characteristic
660	C₂×D₈	D₄×C₈₉	1	1	yes	characteristic
661	#131	—	2	2	no	—
662	#131	—	2	2	no	—
663	#131	—	2	2	no	—
664	#131	—	2	2	no	—
665	C₂×M₁₆	—	2	1	no	—
666	C₂×M₁₆	—	2	1	no	—
667	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
668	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
669	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
670	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
671	C₂²×C₈	—	2	1	no	—
672	C₂²×C₈	—	2	1	no	—
673	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
674	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
675	#124	—	2	2	no	—
676	#124	—	2	2	no	—
677	C₂²⋊Q₈	—	2	1	no	—
678	C₂²⋊Q₈	—	2	1	no	—
679	#121	—	2	1	no	—
680	#121	—	2	1	no	—
681	#121	—	4	1	no	—
682	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	—	4	1	no	—
684	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
685	#104	—	2	2	no	—
686	#104	—	2	2	no	—
687	#104	—	2	2	no	—
688	#104	—	2	2	no	—
689	#103	—	2	1	no	—
690	#103	—	2	1	no	—
691	#103	—	2	1	no	—
692	#103	—	2	1	no	—
693	#102	—	2	1	no	—
694	#102	—	2	1	no	—
695	#102	—	2	1	no	—
696	#102	—	2	1	no	—
697	#101	—	2	2	no	—
698	#101	—	4	1	no	—
699	#100	—	2	2	no	—
700	C₂²⋊C₈	—	2	1	no	—
701	C₂²⋊C₈	—	2	1	no	—
702	C₂²⋊C₈	—	2	1	no	—
703	C₂²⋊C₈	—	2	1	no	—
704	#95	—	4	1	no	—
705	C₂⁴	—	2	1	no	—
706	C₂⁴	—	4	1	no	—
707	#41	—	2	1	no	—
708	#41	—	2	1	no	—
709	#41	—	2	1	no	—
710	#41	—	2	1	no	—
711	#41	—	2	4	no	—
712	#41	—	2	4	no	—
713	#41	—	2	4	no	—
714	#41	—	2	4	no	—
715	#41	—	2	1	no	—
716	#41	—	2	1	no	—
717	#41	—	2	1	no	—
718	#41	—	2	1	no	—
719	#41	—	2	1	no	—
720	#41	—	2	1	no	—
721	#41	—	2	1	no	—
722	#41	—	2	1	no	—
723	#41	—	4	4	no	—
724	#41	—	4	2	no	—
725	#41	—	4	2	no	—
726	#41	—	4	2	no	—
727	#41	—	4	4	no	—
728	#41	—	4	2	no	—
729	#41	—	4	4	no	—
730	#41	—	4	2	no	—
731	#41	—	4	2	no	—
732	#41	—	4	4	no	—
733	#41	—	4	2	no	—
734	#41	—	4	2	no	—
735	#41	C₂×D₄×C₈₉	1	2	yes	—
736	#41	C₂×D₄×C₈₉	1	2	yes	—
737	#41	C₂×D₄×C₈₉	1	2	yes	—
738	#41	C₂×D₄×C₈₉	1	2	yes	—
739	C₂×Q₈	—	2	1	no	—
740	C₂×Q₈	—	2	1	no	—
741	C₂×Q₈	—	2	4	no	—
742	C₂×Q₈	—	2	4	no	—
743	C₂×Q₈	—	2	4	no	—
744	C₂×Q₈	—	2	1	no	—
745	C₂×Q₈	—	2	1	no	—
746	C₂×Q₈	—	2	1	no	—
747	C₂×Q₈	—	2	1	no	—
748	C₂×Q₈	—	2	1	no	—
749	C₂×Q₈	—	2	1	no	—
750	C₂×Q₈	—	2	1	no	—
751	C₂×Q₈	—	2	1	no	—
752	C₂×Q₈	—	4	1	no	—
753	C₂×Q₈	—	4	1	no	—
754	C₂×Q₈	—	4	2	no	—
755	C₂×Q₈	—	4	2	no	—
756	C₂×Q₈	—	4	2	no	—
757	C₂×Q₈	—	4	2	no	—
758	C₂×Q₈	—	4	2	no	—
759	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
760	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
761	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
762	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
763	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
764	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
765	C₂×D₄	—	2	1	no	—
766	C₂×D₄	—	2	1	no	—
767	C₂×D₄	—	2	4	no	—
768	C₂×D₄	—	2	1	no	—
769	C₂×D₄	—	2	1	no	—
770	C₂×D₄	—	2	1	no	—
771	C₂×D₄	—	2	1	no	—
772	C₂×D₄	—	2	1	no	—
773	C₂×D₄	—	2	1	no	—
774	C₂×D₄	—	2	1	no	—
775	C₂×D₄	—	4	2	no	—
776	C₂×D₄	—	4	1	no	—
777	C₂×D₄	—	4	1	no	—
778	C₂×D₄	—	4	2	no	—
779	C₂×D₄	—	4	4	no	—
780	C₂×D₄	—	4	4	no	—
781	C₂×D₄	—	4	1	no	—
782	C₂×D₄	—	4	1	no	—
783	C₂×D₄	—	4	2	no	—
784	C₂×D₄	—	4	1	no	—
785	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
786	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
787	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
788	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
789	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
790	C₂²×C₄	—	2	1	no	—
791	C₂²×C₄	—	2	1	no	—
792	C₂²×C₄	—	2	1	no	—
793	C₂²×C₄	—	2	1	no	—
794	C₂²×C₄	—	2	1	no	—
795	C₂²×C₄	—	2	1	no	—
796	C₂²×C₄	—	2	1	no	—
797	C₂²×C₄	—	2	1	no	—
798	C₂²×C₄	—	4	1	no	—
799	C₂²×C₄	—	4	1	no	—
800	C₂²×C₄	—	4	1	no	—
801	C₂²×C₄	—	4	1	no	—
802	C₂²×C₄	—	4	1	no	—
803	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
804	Q₁₆	—	2	4	no	—
805	Q₁₆	—	2	4	no	—
806	Q₁₆	—	2	4	no	—
807	Q₁₆	—	2	4	no	—
808	Q₁₆	—	2	2	no	—
809	Q₁₆	—	2	4	no	—
810	Q₁₆	—	2	2	no	—
811	Q₁₆	—	4	2	no	—
812	SD₁₆	—	2	4	no	—
813	SD₁₆	—	2	4	no	—
814	SD₁₆	—	2	4	no	—
815	SD₁₆	—	2	4	no	—
816	SD₁₆	—	2	2	no	—
817	SD₁₆	—	2	4	no	—
818	SD₁₆	—	2	2	no	—
819	SD₁₆	—	2	4	no	—
820	SD₁₆	—	2	2	no	—
821	SD₁₆	—	2	2	no	—
822	SD₁₆	—	4	2	no	—
823	SD₁₆	—	4	2	no	—
824	D₈	—	2	4	no	—
825	D₈	—	2	2	no	—
826	D₈	—	2	2	no	—
827	D₈	—	4	2	no	—
828	M₁₆	—	2	4	no	—
829	M₁₆	—	2	4	no	—
830	M₁₆	—	2	1	no	—
831	M₁₆	—	2	1	no	—
832	M₁₆	—	2	1	no	—
833	M₁₆	—	2	1	no	—
834	M₁₆	—	2	1	no	—
835	M₁₆	—	2	1	no	—
836	M₁₆	C₂×D₄×C₈₉	1	2	yes	—
837	M₁₆	C₂×D₄×C₈₉	1	2	yes	—
838	C₂×C₈	—	2	4	no	—
839	C₂×C₈	—	2	4	no	—
840	C₂×C₈	—	2	1	no	—
841	C₂×C₈	—	2	1	no	—
842	C₂×C₈	—	2	1	no	—
843	C₂×C₈	—	2	1	no	—
844	C₂×C₈	—	2	1	no	—
845	C₂×C₈	—	2	1	no	—
846	C₂×C₈	—	2	1	no	—
847	C₂×C₈	—	2	1	no	—
848	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
849	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
850	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
851	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
852	C₄⋊C₄	—	2	1	no	—
853	C₄⋊C₄	—	2	1	no	—
854	C₄⋊C₄	—	4	1	no	—
855	C₂²⋊C₄	—	4	4	no	—
856	C₂²⋊C₄	—	4	1	no	—
857	C₂²⋊C₄	—	4	1	no	—
858	C₄²	—	2	1	no	—
859	C₄²	—	2	1	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	1	no	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	4	4	no	—
866	C₂³	—	4	1	no	—
867	C₂³	—	4	1	no	—
868	C₂³	—	8	1	no	—
869	C₂³	—	8	1	no	—
870	C₂³	—	16	1	no	—
871	C₂³	—	16	1	no	—
872	C₂³	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
873	Q₈	—	2	1	no	—
874	Q₈	—	2	1	no	—
875	Q₈	—	2	2	no	—
876	Q₈	—	2	2	no	—
877	Q₈	—	2	2	no	—
878	Q₈	—	2	1	no	—
879	Q₈	—	2	1	no	—
880	Q₈	—	2	1	no	—
881	Q₈	—	2	2	no	—
882	Q₈	—	2	1	no	—
883	Q₈	—	4	4	no	—
884	Q₈	—	4	4	no	—
885	Q₈	—	4	1	no	—
886	Q₈	—	4	1	no	—
887	Q₈	—	4	1	no	—
888	Q₈	—	4	1	no	—
889	Q₈	#120×C₈₉	1	2	yes	—
890	Q₈	#120×C₈₉	1	2	yes	—
891	D₄	—	2	2	no	—
892	D₄	—	2	2	no	—
893	D₄	—	2	2	no	—
894	D₄	—	2	2	no	—
895	D₄	—	2	2	no	—
896	D₄	—	2	1	no	—
897	D₄	—	2	1	no	—
898	D₄	—	2	1	no	—
899	D₄	—	2	1	no	—
900	D₄	—	2	1	no	—
901	D₄	—	2	2	no	—
902	D₄	—	2	1	no	—
903	D₄	—	4	4	no	—
904	D₄	—	4	4	no	—
905	D₄	—	4	4	no	—
906	D₄	—	4	4	no	—
907	D₄	—	4	1	no	—
908	D₄	—	4	1	no	—
909	D₄	—	4	1	no	—
910	D₄	—	4	1	no	—
911	D₄	—	4	1	no	—
912	D₄	—	4	1	no	—
913	D₄	—	16	1	no	—
914	D₄	#120×C₈₉	1	2	yes	—
915	D₄	#120×C₈₉	1	2	yes	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	4	4	no	—
927	C₂×C₄	—	4	4	no	—
928	C₂×C₄	—	4	4	no	—
929	C₂×C₄	—	4	4	no	—
930	C₂×C₄	—	4	4	no	—
931	C₂×C₄	—	4	1	no	—
932	C₂×C₄	—	4	1	no	—
933	C₂×C₄	—	4	1	no	—
934	C₂×C₄	—	4	1	no	—
935	C₂×C₄	—	4	1	no	—
936	C₂×C₄	—	4	1	no	—
937	C₂×C₄	—	4	1	no	—
938	C₂×C₄	—	4	1	no	—
939	C₂×C₄	—	4	1	no	—
940	C₂×C₄	—	4	1	no	—
941	C₂×C₄	—	4	1	no	—
942	C₂×C₄	—	4	1	no	—
943	C₂×C₄	—	8	1	no	—
944	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
945	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
946	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
947	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
948	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
949	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
950	C₈	—	2	1	no	—
951	C₈	—	2	1	no	—
952	C₈	—	2	2	no	—
953	C₈	—	2	2	no	—
954	C₈	—	2	1	no	—
955	C₈	—	2	1	no	—
956	C₈	—	4	1	no	—
957	C₈	—	4	1	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	2	1	no	—
960	C₂²	—	2	2	no	—
961	C₂²	—	2	2	no	—
962	C₂²	—	4	1	no	—
963	C₂²	—	4	1	no	—
964	C₂²	—	4	1	no	—
965	C₂²	—	4	1	no	—
966	C₂²	—	4	1	no	—
967	C₂²	—	4	1	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	4	1	no	—
970	C₂²	—	4	1	no	—
971	C₂²	—	4	1	no	—
972	C₂²	—	4	1	no	—
973	C₂²	—	8	2	no	—
974	C₂²	—	8	1	no	—
975	C₂²	—	8	1	no	—
976	C₂²	—	16	1	no	—
977	C₂²	—	16	4	no	—
978	C₂²	#534×C₈₉	1	1	yes	characteristic
979	C₂²	D₄²×C₈₉	1	1	yes	characteristic
980	C₂²	D₄²×C₈₉	1	1	yes	characteristic
981	C₄	—	2	2	no	—
982	C₄	—	2	2	no	—
983	C₄	—	4	1	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	1	no	—
987	C₄	—	8	1	no	—
988	C₄	—	8	1	no	—
989	C₄	C₂×#120×C₈₉	1	1	yes	characteristic
990	C₄	C₂×#120×C₈₉	1	1	yes	characteristic
991	C₄	D₄²×C₈₉	1	1	yes	characteristic
992	C₄	D₄²×C₈₉	1	1	yes	characteristic
993	C₂	—	2	1	no	—
994	C₂	—	2	1	no	—
995	C₂	—	4	2	no	—
996	C₂	—	4	2	no	—
997	C₂	—	8	1	no	—
998	C₂	—	8	1	no	—
999	C₂	—	8	2	no	—
1000	C₂	C₈₉×#2403	1	1	yes	characteristic
1001	C₂	C₈₉×#3289	1	1	yes	characteristic
1002	C₂	C₈₉×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂²×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#578×C₈₉	C₂	semidirect
2. C₂×#577×C₈₉	C₂	semidirect
3. C₂×#454×C₈₉	C₂	semidirect
4. C₂×#455×C₈₉	C₂	semidirect
5. C₈₉×#3013	C₂	semidirect
6. C₈₉×#3012	C₂	semidirect
7. C₈₉×#2020	C₂	semidirect
8. C₈₉×#2019	C₂	semidirect
9. C₈₉×#2015	C₂	semidirect
10. C₈₉×#2007	C₂	semidirect
11. C₈₉×#1908	C₂	semidirect
12. C₈₉×#1907	C₂	semidirect
13. C₈₉×#1876	C₂	semidirect
14. C₈₉×#1876	C₂	semidirect
15. C₈₉×#1793	C₂	semidirect
17. C₂×2₋¹⁺⁴×C₈₉	C₂²	semidirect
29. C₂×#137×C₈₉	C₂²	semidirect
38. C₂²×Q₁₆×C₈₉	C₂²	semidirect
42. C₂×#131×C₈₉	C₂²	semidirect
57. C₂×#104×C₈₉	C₂²	semidirect
58. C₂×#104×C₈₉	C₂²	semidirect
60. #417×C₈₉	C₂²	semidirect
61. C₂×#103×C₈₉	C₂²	semidirect
63. C₂×#101×C₈₉	C₂²	semidirect
64. C₂×#101×C₈₉	C₂²	semidirect
67. #408×C₈₉	C₂²	semidirect
68. #391×C₈₉	C₂²	semidirect
69. #343×C₈₉	C₂²	semidirect
70. #341×C₈₉	C₂²	semidirect
71. #341×C₈₉	C₂²	semidirect
72. #336×C₈₉	C₂²	semidirect
80. 2₋¹⁺⁴×C₈₉	D₄	semidirect
117. #137×C₈₉	D₄	semidirect
122. AGL(1,ℤ/8)×C₈₉	D₄	semidirect
491. #23889	C₈₉	direct (N × H)
502. C₂×#578	C₂×C₈₉	semidirect
503. C₂×#577	C₂×C₈₉	semidirect
504. C₂×#454	C₂×C₈₉	semidirect
505. C₂×#455	C₂×C₈₉	semidirect
506. #3013	C₂×C₈₉	semidirect
507. #3012	C₂×C₈₉	semidirect
508. #2020	C₂×C₈₉	semidirect
509. #2019	C₂×C₈₉	semidirect
510. #2015	C₂×C₈₉	semidirect
511. #2007	C₂×C₈₉	semidirect
512. #1908	C₂×C₈₉	semidirect
513. #1907	C₂×C₈₉	semidirect
514. #1876	C₂×C₈₉	semidirect
515. #1876	C₂×C₈₉	semidirect
516. #1793	C₂×C₈₉	semidirect
517. C₈₉	#23889	direct (N × H)
519. C₂×2₋¹⁺⁴	C₂²×C₈₉	semidirect
531. C₂×#137	C₂²×C₈₉	semidirect
540. C₂²×Q₁₆	C₂²×C₈₉	semidirect
544. C₂×#131	C₂²×C₈₉	semidirect
559. C₂×#104	C₂²×C₈₉	semidirect
560. C₂×#104	C₂²×C₈₉	semidirect
562. #417	C₂²×C₈₉	semidirect
563. C₂×#103	C₂²×C₈₉	semidirect
565. C₂×#101	C₂²×C₈₉	semidirect
566. C₂×#101	C₂²×C₈₉	semidirect
569. #408	C₂²×C₈₉	semidirect
570. #391	C₂²×C₈₉	semidirect
571. #343	C₂²×C₈₉	semidirect
572. #341	C₂²×C₈₉	semidirect
573. #341	C₂²×C₈₉	semidirect
574. #336	C₂²×C₈₉	semidirect
582. 2₋¹⁺⁴	D₄×C₈₉	semidirect
619. #137	D₄×C₈₉	semidirect
624. AGL(1,ℤ/8)	D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#578×C₈₉	2
C₂×#577×C₈₉	2
C₂×#454×C₈₉	2
C₂×#455×C₈₉	2
C₈₉×#3013	2
C₈₉×#3012	2
C₈₉×#2020	2
C₈₉×#2019	2
C₈₉×#2015	2
C₈₉×#2007	2
C₈₉×#1908	2
C₈₉×#1907	2
C₈₉×#1876	2
C₈₉×#1793	2
#23889	89

Subgroups — C89×#23889 #36401737

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#23889 #36401737