Subgroups — C₈₉×#23888 #36401736

Order 22784.

1682 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#577×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#576×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×#2019	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2018	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2012	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2006	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×#1792	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	1	yes	characteristic, complemented
17	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	1	yes	characteristic
19	#577×C₈₉	—	2	4	no	—
20	#577×C₈₉	—	2	4	no	—
21	#576×C₈₉	—	2	4	no	—
22	#576×C₈₉	—	2	4	no	—
23	C₂×#137×C₈₉	—	2	1	no	—
24	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic, complemented
26	C₂×AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
27	C₂×AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
28	C₂×AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
29	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic, complemented
32	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic, complemented
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×SD₁₆×C₈₉	—	2	1	no	—
38	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	C₂²×D₈×C₈₉	—	2	1	no	—
40	C₂²×D₈×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, complemented
44	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
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, complemented
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, complemented
63	C₂×#101×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic, complemented
65	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic, complemented
66	#408×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#408×C₈₉	C₂²	1	1	yes	characteristic, complemented
68	#390×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	—	4	1	no	—
77	H(5,𝔽₂)×C₈₉	—	2	2	no	—
78	H(5,𝔽₂)×C₈₉	—	2	2	no	—
79	H(5,𝔽₂)×C₈₉	—	2	2	no	—
80	H(5,𝔽₂)×C₈₉	—	2	2	no	—
81	H(5,𝔽₂)×C₈₉	—	2	2	no	—
82	H(5,𝔽₂)×C₈₉	—	4	1	no	—
83	H(5,𝔽₂)×C₈₉	—	4	1	no	—
84	H(5,𝔽₂)×C₈₉	D₄	1	4	yes	complemented
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	C₂³	1	1	yes	characteristic
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	C₂²×Q₈×C₈₉	—	2	1	no	—
97	C₂²×Q₈×C₈₉	—	2	1	no	—
98	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₈₉	—	2	1	no	—
100	C₂²×D₄×C₈₉	—	2	1	no	—
101	C₂²×D₄×C₈₉	—	2	1	no	—
102	C₂²×D₄×C₈₉	—	2	1	no	—
103	C₂²×D₄×C₈₉	—	4	1	no	—
104	C₂²×D₄×C₈₉	—	4	1	no	—
105	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
107	#137×C₈₉	—	2	8	no	—
108	#137×C₈₉	—	2	2	no	—
109	#137×C₈₉	—	2	2	no	—
110	#137×C₈₉	—	4	1	no	—
111	#137×C₈₉	D₄	1	4	yes	complemented
112	AGL(1,ℤ/8)×C₈₉	—	2	8	no	—
113	AGL(1,ℤ/8)×C₈₉	—	2	8	no	—
114	AGL(1,ℤ/8)×C₈₉	—	2	8	no	—
115	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
116	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
117	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
118	AGL(1,ℤ/8)×C₈₉	—	2	2	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	1	no	—
130	C₂×Q₁₆×C₈₉	—	2	1	no	—
131	C₂×Q₁₆×C₈₉	D₄	1	1	yes	characteristic
132	C₂×Q₁₆×C₈₉	D₄	1	1	yes	characteristic
133	C₂×SD₁₆×C₈₉	—	2	8	no	—
134	C₂×SD₁₆×C₈₉	—	2	1	no	—
135	C₂×SD₁₆×C₈₉	—	2	2	no	—
136	C₂×SD₁₆×C₈₉	—	2	1	no	—
137	C₂×SD₁₆×C₈₉	—	2	1	no	—
138	C₂×SD₁₆×C₈₉	—	2	1	no	—
139	C₂×SD₁₆×C₈₉	—	2	2	no	—
140	C₂×SD₁₆×C₈₉	—	2	1	no	—
141	C₂×SD₁₆×C₈₉	—	2	1	no	—
142	C₂×SD₁₆×C₈₉	—	2	1	no	—
143	C₂×SD₁₆×C₈₉	—	2	1	no	—
144	C₂×SD₁₆×C₈₉	D₄	1	1	yes	characteristic
145	C₂×SD₁₆×C₈₉	D₄	1	1	yes	characteristic
146	C₂×SD₁₆×C₈₉	D₄	1	1	yes	characteristic
147	C₂×SD₁₆×C₈₉	D₄	1	1	yes	characteristic
148	C₂×D₈×C₈₉	—	2	8	no	—
149	C₂×D₈×C₈₉	—	2	1	no	—
150	C₂×D₈×C₈₉	—	2	1	no	—
151	C₂×D₈×C₈₉	—	2	2	no	—
152	C₂×D₈×C₈₉	—	2	2	no	—
153	C₂×D₈×C₈₉	—	2	1	no	—
154	C₂×D₈×C₈₉	—	2	1	no	—
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×C₂²⋊C₄×C₈₉	—	4	1	no	—
183	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
184	#104×C₈₉	—	2	2	no	—
185	#104×C₈₉	—	2	2	no	—
186	#104×C₈₉	—	2	2	no	—
187	#104×C₈₉	—	2	2	no	—
188	#103×C₈₉	—	2	1	no	—
189	#103×C₈₉	—	2	1	no	—
190	#103×C₈₉	—	2	1	no	—
191	#103×C₈₉	—	2	1	no	—
192	#102×C₈₉	—	2	1	no	—
193	#102×C₈₉	—	2	1	no	—
194	#102×C₈₉	—	2	1	no	—
195	#102×C₈₉	—	2	1	no	—
196	#101×C₈₉	—	2	2	no	—
197	#100×C₈₉	—	2	2	no	—
198	#100×C₈₉	—	4	1	no	—
199	C₂²⋊C₈×C₈₉	—	2	1	no	—
200	C₂²⋊C₈×C₈₉	—	2	1	no	—
201	C₂²⋊C₈×C₈₉	—	2	1	no	—
202	C₂²⋊C₈×C₈₉	—	2	1	no	—
203	C₂⁴×C₈₉	—	2	1	no	—
204	C₂⁴×C₈₉	—	2	1	no	—
205	C₂⁴×C₈₉	—	4	1	no	—
206	C₂⁴×C₈₉	—	4	1	no	—
207	#41×C₈₉	—	2	1	no	—
208	#41×C₈₉	—	2	1	no	—
209	#41×C₈₉	—	2	1	no	—
210	#41×C₈₉	—	2	1	no	—
211	#41×C₈₉	—	2	4	no	—
212	#41×C₈₉	—	2	4	no	—
213	#41×C₈₉	—	2	4	no	—
214	#41×C₈₉	—	2	4	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	—	2	1	no	—
222	#41×C₈₉	—	2	1	no	—
223	#41×C₈₉	—	4	2	no	—
224	#41×C₈₉	—	4	4	no	—
225	#41×C₈₉	—	4	2	no	—
226	#41×C₈₉	—	4	2	no	—
227	#41×C₈₉	—	4	2	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	4	no	—
239	C₂×Q₈×C₈₉	—	2	1	no	—
240	C₂×Q₈×C₈₉	—	2	1	no	—
241	C₂×Q₈×C₈₉	—	2	1	no	—
242	C₂×Q₈×C₈₉	—	2	1	no	—
243	C₂×Q₈×C₈₉	—	4	1	no	—
244	C₂×Q₈×C₈₉	—	4	2	no	—
245	C₂×Q₈×C₈₉	—	4	2	no	—
246	C₂×Q₈×C₈₉	—	4	2	no	—
247	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
248	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
249	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
250	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
251	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
252	C₂×D₄×C₈₉	—	2	1	no	—
253	C₂×D₄×C₈₉	—	2	1	no	—
254	C₂×D₄×C₈₉	—	2	4	no	—
255	C₂×D₄×C₈₉	—	2	4	no	—
256	C₂×D₄×C₈₉	—	2	4	no	—
257	C₂×D₄×C₈₉	—	2	1	no	—
258	C₂×D₄×C₈₉	—	2	1	no	—
259	C₂×D₄×C₈₉	—	2	1	no	—
260	C₂×D₄×C₈₉	—	2	1	no	—
261	C₂×D₄×C₈₉	—	2	1	no	—
262	C₂×D₄×C₈₉	—	2	1	no	—
263	C₂×D₄×C₈₉	—	2	1	no	—
264	C₂×D₄×C₈₉	—	2	1	no	—
265	C₂×D₄×C₈₉	—	2	1	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	—	4	2	no	—
270	C₂×D₄×C₈₉	—	4	2	no	—
271	C₂×D₄×C₈₉	—	4	2	no	—
272	C₂×D₄×C₈₉	—	4	1	no	—
273	C₂×D₄×C₈₉	—	4	1	no	—
274	C₂×D₄×C₈₉	—	4	1	no	—
275	C₂×D₄×C₈₉	—	4	1	no	—
276	C₂×D₄×C₈₉	—	4	4	no	—
277	C₂×D₄×C₈₉	—	4	2	no	—
278	C₂×D₄×C₈₉	—	4	4	no	—
279	C₂×D₄×C₈₉	—	4	4	no	—
280	C₂×D₄×C₈₉	—	4	4	no	—
281	C₂×D₄×C₈₉	—	4	1	no	—
282	C₂×D₄×C₈₉	—	4	2	no	—
283	C₂×D₄×C₈₉	—	4	1	no	—
284	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
285	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
286	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
287	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
288	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
289	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
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	—	2	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	2	no	—
304	Q₁₆×C₈₉	—	2	2	no	—
305	Q₁₆×C₈₉	—	4	2	no	—
306	SD₁₆×C₈₉	—	2	4	no	—
307	SD₁₆×C₈₉	—	2	4	no	—
308	SD₁₆×C₈₉	—	2	4	no	—
309	SD₁₆×C₈₉	—	2	4	no	—
310	SD₁₆×C₈₉	—	2	4	no	—
311	SD₁₆×C₈₉	—	2	2	no	—
312	SD₁₆×C₈₉	—	2	2	no	—
313	SD₁₆×C₈₉	—	2	2	no	—
314	SD₁₆×C₈₉	—	2	4	no	—
315	SD₁₆×C₈₉	—	2	2	no	—
316	SD₁₆×C₈₉	—	4	2	no	—
317	SD₁₆×C₈₉	—	4	2	no	—
318	D₈×C₈₉	—	2	4	no	—
319	D₈×C₈₉	—	2	4	no	—
320	D₈×C₈₉	—	2	4	no	—
321	D₈×C₈₉	—	2	4	no	—
322	D₈×C₈₉	—	2	2	no	—
323	D₈×C₈₉	—	2	4	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	C₂²⋊C₄×C₈₉	—	8	2	no	—
357	C₄²×C₈₉	—	2	1	no	—
358	C₄²×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	1	no	—
363	C₂³×C₈₉	—	2	2	no	—
364	C₂³×C₈₉	—	2	2	no	—
365	C₂³×C₈₉	—	4	4	no	—
366	C₂³×C₈₉	—	4	4	no	—
367	C₂³×C₈₉	—	4	1	no	—
368	C₂³×C₈₉	—	4	1	no	—
369	C₂³×C₈₉	—	4	1	no	—
370	C₂³×C₈₉	—	4	1	no	—
371	C₂³×C₈₉	—	8	1	no	—
372	C₂³×C₈₉	—	8	1	no	—
373	C₂³×C₈₉	—	8	1	no	—
374	C₂³×C₈₉	—	8	1	no	—
375	C₂³×C₈₉	—	16	1	no	—
376	C₂³×C₈₉	—	16	1	no	—
377	C₂³×C₈₉	—	16	1	no	—
378	C₂³×C₈₉	—	16	1	no	—
379	C₂³×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
380	Q₈×C₈₉	—	2	1	no	—
381	Q₈×C₈₉	—	2	1	no	—
382	Q₈×C₈₉	—	2	2	no	—
383	Q₈×C₈₉	—	2	1	no	—
384	Q₈×C₈₉	—	2	1	no	—
385	Q₈×C₈₉	—	2	1	no	—
386	Q₈×C₈₉	—	2	2	no	—
387	Q₈×C₈₉	—	2	1	no	—
388	Q₈×C₈₉	—	4	4	no	—
389	Q₈×C₈₉	—	4	1	no	—
390	Q₈×C₈₉	—	4	1	no	—
391	Q₈×C₈₉	#120	1	2	yes	—
392	Q₈×C₈₉	#120	1	2	yes	—
393	D₄×C₈₉	—	2	2	no	—
394	D₄×C₈₉	—	2	2	no	—
395	D₄×C₈₉	—	2	2	no	—
396	D₄×C₈₉	—	2	2	no	—
397	D₄×C₈₉	—	2	2	no	—
398	D₄×C₈₉	—	2	2	no	—
399	D₄×C₈₉	—	2	1	no	—
400	D₄×C₈₉	—	2	1	no	—
401	D₄×C₈₉	—	2	2	no	—
402	D₄×C₈₉	—	2	1	no	—
403	D₄×C₈₉	—	2	1	no	—
404	D₄×C₈₉	—	2	1	no	—
405	D₄×C₈₉	—	2	2	no	—
406	D₄×C₈₉	—	2	1	no	—
407	D₄×C₈₉	—	4	4	no	—
408	D₄×C₈₉	—	4	4	no	—
409	D₄×C₈₉	—	4	4	no	—
410	D₄×C₈₉	—	4	4	no	—
411	D₄×C₈₉	—	4	4	no	—
412	D₄×C₈₉	—	4	1	no	—
413	D₄×C₈₉	—	4	1	no	—
414	D₄×C₈₉	—	4	1	no	—
415	D₄×C₈₉	—	4	1	no	—
416	D₄×C₈₉	—	4	1	no	—
417	D₄×C₈₉	—	4	1	no	—
418	D₄×C₈₉	—	4	1	no	—
419	D₄×C₈₉	—	4	1	no	—
420	D₄×C₈₉	—	16	1	no	—
421	D₄×C₈₉	#120	1	2	yes	—
422	D₄×C₈₉	#120	1	2	yes	—
423	C₂×C₄×C₈₉	—	2	1	no	—
424	C₂×C₄×C₈₉	—	2	1	no	—
425	C₂×C₄×C₈₉	—	2	2	no	—
426	C₂×C₄×C₈₉	—	2	2	no	—
427	C₂×C₄×C₈₉	—	2	2	no	—
428	C₂×C₄×C₈₉	—	2	2	no	—
429	C₂×C₄×C₈₉	—	2	2	no	—
430	C₂×C₄×C₈₉	—	2	1	no	—
431	C₂×C₄×C₈₉	—	2	1	no	—
432	C₂×C₄×C₈₉	—	4	4	no	—
433	C₂×C₄×C₈₉	—	4	4	no	—
434	C₂×C₄×C₈₉	—	4	4	no	—
435	C₂×C₄×C₈₉	—	4	4	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	—	4	1	no	—
442	C₂×C₄×C₈₉	—	4	1	no	—
443	C₂×C₄×C₈₉	—	4	1	no	—
444	C₂×C₄×C₈₉	—	4	1	no	—
445	C₂×C₄×C₈₉	—	4	1	no	—
446	C₂×C₄×C₈₉	—	8	1	no	—
447	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
453	C₈×C₈₉	—	2	1	no	—
454	C₈×C₈₉	—	2	1	no	—
455	C₈×C₈₉	—	2	2	no	—
456	C₈×C₈₉	—	2	2	no	—
457	C₈×C₈₉	—	2	1	no	—
458	C₈×C₈₉	—	2	1	no	—
459	C₈×C₈₉	—	4	1	no	—
460	C₈×C₈₉	—	4	1	no	—
461	C₂²×C₈₉	—	2	1	no	—
462	C₂²×C₈₉	—	2	1	no	—
463	C₂²×C₈₉	—	2	2	no	—
464	C₂²×C₈₉	—	2	2	no	—
465	C₂²×C₈₉	—	4	1	no	—
466	C₂²×C₈₉	—	4	1	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	—	4	2	no	—
472	C₂²×C₈₉	—	4	2	no	—
473	C₂²×C₈₉	—	4	1	no	—
474	C₂²×C₈₉	—	4	1	no	—
475	C₂²×C₈₉	—	4	1	no	—
476	C₂²×C₈₉	—	4	1	no	—
477	C₂²×C₈₉	—	8	2	no	—
478	C₂²×C₈₉	—	8	2	no	—
479	C₂²×C₈₉	—	8	1	no	—
480	C₂²×C₈₉	—	8	1	no	—
481	C₂²×C₈₉	—	8	1	no	—
482	C₂²×C₈₉	—	8	1	no	—
483	C₂²×C₈₉	—	16	1	no	—
484	C₂²×C₈₉	—	16	1	no	—
485	C₂²×C₈₉	—	16	4	no	—
486	C₂²×C₈₉	—	16	4	no	—
487	C₂²×C₈₉	#534	1	1	yes	characteristic
488	C₂²×C₈₉	D₄²	1	1	yes	characteristic
489	C₂²×C₈₉	D₄²	1	1	yes	characteristic
490	C₄×C₈₉	—	2	2	no	—
491	C₄×C₈₉	—	2	2	no	—
492	C₄×C₈₉	—	4	1	no	—
493	C₄×C₈₉	—	4	2	no	—
494	C₄×C₈₉	—	4	1	no	—
495	C₄×C₈₉	—	8	1	no	—
496	C₄×C₈₉	—	8	1	no	—
497	C₄×C₈₉	C₂×#120	1	1	yes	characteristic
498	C₄×C₈₉	C₂×#120	1	1	yes	characteristic
499	C₄×C₈₉	D₄²	1	1	yes	characteristic
500	C₄×C₈₉	D₄²	1	1	yes	characteristic
501	#23888	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
502	C₂×C₈₉	—	2	1	no	—
503	C₂×C₈₉	—	2	1	no	—
504	C₂×C₈₉	—	4	2	no	—
505	C₂×C₈₉	—	4	2	no	—
506	C₂×C₈₉	—	8	1	no	—
507	C₂×C₈₉	—	8	1	no	—
508	C₂×C₈₉	—	8	2	no	—
509	C₂×C₈₉	—	8	2	no	—
510	C₂×C₈₉	#2403	1	1	yes	characteristic
511	C₂×C₈₉	#3288	1	1	yes	characteristic
512	C₂×C₈₉	#3290	1	1	yes	characteristic
513	C₂×#577	C₂×C₈₉	1	1	yes	characteristic, complemented
514	C₂×#576	C₂×C₈₉	1	1	yes	characteristic, complemented
515	C₂×#454	C₂×C₈₉	1	1	yes	characteristic, complemented
516	C₂×#455	C₂×C₈₉	1	1	yes	characteristic, complemented
517	#3013	C₂×C₈₉	1	1	yes	characteristic, complemented
518	#3012	C₂×C₈₉	1	1	yes	characteristic, complemented
519	#2019	C₂×C₈₉	1	1	yes	characteristic, complemented
520	#2018	C₂×C₈₉	1	1	yes	characteristic, complemented
521	#2012	C₂×C₈₉	1	1	yes	characteristic, complemented
522	#2006	C₂×C₈₉	1	1	yes	characteristic, complemented
523	#1908	C₂×C₈₉	1	1	yes	characteristic, complemented
524	#1907	C₂×C₈₉	1	1	yes	characteristic, complemented
525	#1876	C₂×C₈₉	1	1	yes	characteristic, complemented
526	#1876	C₂×C₈₉	1	1	yes	characteristic, complemented
527	#1792	C₂×C₈₉	1	1	yes	characteristic, complemented
528	C₈₉	#23888	1	1	yes	characteristic, direct product factor, Sylow
529	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	1	yes	characteristic, complemented
530	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	1	yes	characteristic
531	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	1	yes	characteristic
532	#577	—	2	4	no	—
533	#577	—	2	4	no	—
534	#576	—	2	4	no	—
535	#576	—	2	4	no	—
536	C₂×#137	—	2	1	no	—
537	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
538	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic, complemented
539	C₂×AGL(1,ℤ/8)	—	2	1	no	—
540	C₂×AGL(1,ℤ/8)	—	2	1	no	—
541	C₂×AGL(1,ℤ/8)	—	2	1	no	—
542	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
543	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
544	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic, complemented
545	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic, complemented
546	C₂×#135	—	2	1	no	—
547	C₂×#135	—	2	1	no	—
548	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
549	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
550	C₂²×SD₁₆	—	2	1	no	—
551	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
552	C₂²×D₈	—	2	1	no	—
553	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
554	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
555	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic, complemented
556	#537	C₂²×C₈₉	1	1	yes	characteristic, complemented
557	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic, complemented
558	#455	—	2	4	no	—
559	#454	—	2	4	no	—
560	#452	—	2	1	no	—
561	#452	—	2	1	no	—
562	#451	—	2	1	no	—
563	#450	—	2	1	no	—
564	#449	—	2	1	no	—
565	#449	—	2	1	no	—
566	#448	—	2	1	no	—
567	#447	—	2	1	no	—
568	C₂×#104	C₂²×C₈₉	1	1	yes	characteristic
569	C₂×#104	C₂²×C₈₉	1	1	yes	characteristic, complemented
570	C₂×#104	C₂²×C₈₉	1	1	yes	characteristic, complemented
571	C₂×#104	C₂²×C₈₉	1	1	yes	characteristic, complemented
572	#417	C₂²×C₈₉	1	1	yes	characteristic
573	#417	C₂²×C₈₉	1	1	yes	characteristic, complemented
574	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
575	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
576	C₂×#101	C₂²×C₈₉	1	1	yes	characteristic, complemented
577	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic, complemented
578	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic, complemented
579	#408	C₂²×C₈₉	1	1	yes	characteristic, complemented
580	#408	C₂²×C₈₉	1	1	yes	characteristic, complemented
581	#390	C₂²×C₈₉	1	1	yes	characteristic, complemented
582	#343	C₂²×C₈₉	1	1	yes	characteristic, complemented
583	#341	C₂²×C₈₉	1	1	yes	characteristic, complemented
584	#341	C₂²×C₈₉	1	1	yes	characteristic, complemented
585	#336	C₂²×C₈₉	1	1	yes	characteristic, complemented
586	2₋¹⁺⁴	—	2	2	no	—
587	2₋¹⁺⁴	—	2	2	no	—
588	2₋¹⁺⁴	—	2	2	no	—
589	2₋¹⁺⁴	—	4	1	no	—
590	H(5,𝔽₂)	—	2	2	no	—
591	H(5,𝔽₂)	—	2	2	no	—
592	H(5,𝔽₂)	—	2	2	no	—
593	H(5,𝔽₂)	—	2	2	no	—
594	H(5,𝔽₂)	—	2	2	no	—
595	H(5,𝔽₂)	—	4	1	no	—
596	H(5,𝔽₂)	—	4	1	no	—
597	H(5,𝔽₂)	D₄×C₈₉	1	4	yes	complemented
598	C₂×#41	—	2	1	no	—
599	C₂×#41	—	2	1	no	—
600	C₂×#41	—	2	1	no	—
601	C₂×#41	—	2	1	no	—
602	C₂×#41	—	2	1	no	—
603	C₂×#41	—	2	1	no	—
604	C₂×#41	—	4	1	no	—
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	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
609	C₂²×Q₈	—	2	1	no	—
610	C₂²×Q₈	—	2	1	no	—
611	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
612	C₂²×D₄	—	2	1	no	—
613	C₂²×D₄	—	2	1	no	—
614	C₂²×D₄	—	2	1	no	—
615	C₂²×D₄	—	2	1	no	—
616	C₂²×D₄	—	4	1	no	—
617	C₂²×D₄	—	4	1	no	—
618	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
619	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
620	#137	—	2	8	no	—
621	#137	—	2	2	no	—
622	#137	—	2	2	no	—
623	#137	—	4	1	no	—
624	#137	D₄×C₈₉	1	4	yes	complemented
625	AGL(1,ℤ/8)	—	2	8	no	—
626	AGL(1,ℤ/8)	—	2	8	no	—
627	AGL(1,ℤ/8)	—	2	8	no	—
628	AGL(1,ℤ/8)	—	2	2	no	—
629	AGL(1,ℤ/8)	—	2	2	no	—
630	AGL(1,ℤ/8)	—	2	2	no	—
631	AGL(1,ℤ/8)	—	2	2	no	—
632	AGL(1,ℤ/8)	—	2	2	no	—
633	AGL(1,ℤ/8)	—	2	2	no	—
634	AGL(1,ℤ/8)	—	4	1	no	—
635	AGL(1,ℤ/8)	D₄×C₈₉	1	4	yes	complemented
636	#135	—	2	8	no	—
637	#135	—	2	8	no	—
638	#135	—	2	2	no	—
639	#135	—	2	2	no	—
640	#135	—	2	2	no	—
641	#135	—	2	2	no	—
642	C₂×Q₁₆	—	2	1	no	—
643	C₂×Q₁₆	—	2	1	no	—
644	C₂×Q₁₆	D₄×C₈₉	1	1	yes	characteristic
645	C₂×Q₁₆	D₄×C₈₉	1	1	yes	characteristic
646	C₂×SD₁₆	—	2	8	no	—
647	C₂×SD₁₆	—	2	1	no	—
648	C₂×SD₁₆	—	2	2	no	—
649	C₂×SD₁₆	—	2	1	no	—
650	C₂×SD₁₆	—	2	1	no	—
651	C₂×SD₁₆	—	2	1	no	—
652	C₂×SD₁₆	—	2	2	no	—
653	C₂×SD₁₆	—	2	1	no	—
654	C₂×SD₁₆	—	2	1	no	—
655	C₂×SD₁₆	—	2	1	no	—
656	C₂×SD₁₆	—	2	1	no	—
657	C₂×SD₁₆	D₄×C₈₉	1	1	yes	characteristic
658	C₂×SD₁₆	D₄×C₈₉	1	1	yes	characteristic
659	C₂×SD₁₆	D₄×C₈₉	1	1	yes	characteristic
660	C₂×SD₁₆	D₄×C₈₉	1	1	yes	characteristic
661	C₂×D₈	—	2	8	no	—
662	C₂×D₈	—	2	1	no	—
663	C₂×D₈	—	2	1	no	—
664	C₂×D₈	—	2	2	no	—
665	C₂×D₈	—	2	2	no	—
666	C₂×D₈	—	2	1	no	—
667	C₂×D₈	—	2	1	no	—
668	C₂×D₈	—	2	1	no	—
669	C₂×D₈	—	2	1	no	—
670	C₂×D₈	D₄×C₈₉	1	1	yes	characteristic
671	C₂×D₈	D₄×C₈₉	1	1	yes	characteristic
672	#131	—	2	2	no	—
673	#131	—	2	2	no	—
674	#131	—	2	2	no	—
675	#131	—	2	2	no	—
676	C₂×M₁₆	—	2	1	no	—
677	C₂×M₁₆	—	2	1	no	—
678	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
679	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
680	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
681	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
682	C₂²×C₈	—	2	1	no	—
683	C₂²×C₈	—	2	1	no	—
684	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
685	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
686	#124	—	2	2	no	—
687	#124	—	2	2	no	—
688	C₂²⋊Q₈	—	2	1	no	—
689	C₂²⋊Q₈	—	2	1	no	—
690	#121	—	2	1	no	—
691	#121	—	2	1	no	—
692	#121	—	4	1	no	—
693	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
694	C₂×C₂²⋊C₄	—	4	1	no	—
695	C₂×C₂²⋊C₄	—	4	1	no	—
696	C₂×C₄²	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	1	no	—
704	#103	—	2	1	no	—
705	#102	—	2	1	no	—
706	#102	—	2	1	no	—
707	#102	—	2	1	no	—
708	#102	—	2	1	no	—
709	#101	—	2	2	no	—
710	#100	—	2	2	no	—
711	#100	—	4	1	no	—
712	C₂²⋊C₈	—	2	1	no	—
713	C₂²⋊C₈	—	2	1	no	—
714	C₂²⋊C₈	—	2	1	no	—
715	C₂²⋊C₈	—	2	1	no	—
716	C₂⁴	—	2	1	no	—
717	C₂⁴	—	2	1	no	—
718	C₂⁴	—	4	1	no	—
719	C₂⁴	—	4	1	no	—
720	#41	—	2	1	no	—
721	#41	—	2	1	no	—
722	#41	—	2	1	no	—
723	#41	—	2	1	no	—
724	#41	—	2	4	no	—
725	#41	—	2	4	no	—
726	#41	—	2	4	no	—
727	#41	—	2	4	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	—	4	2	no	—
737	#41	—	4	4	no	—
738	#41	—	4	2	no	—
739	#41	—	4	2	no	—
740	#41	—	4	2	no	—
741	#41	—	4	2	no	—
742	#41	—	4	2	no	—
743	#41	—	4	4	no	—
744	#41	—	4	2	no	—
745	#41	—	4	2	no	—
746	#41	C₂×D₄×C₈₉	1	2	yes	—
747	#41	C₂×D₄×C₈₉	1	2	yes	—
748	#41	C₂×D₄×C₈₉	1	2	yes	—
749	#41	C₂×D₄×C₈₉	1	2	yes	—
750	C₂×Q₈	—	2	1	no	—
751	C₂×Q₈	—	2	4	no	—
752	C₂×Q₈	—	2	1	no	—
753	C₂×Q₈	—	2	1	no	—
754	C₂×Q₈	—	2	1	no	—
755	C₂×Q₈	—	2	1	no	—
756	C₂×Q₈	—	4	1	no	—
757	C₂×Q₈	—	4	2	no	—
758	C₂×Q₈	—	4	2	no	—
759	C₂×Q₈	—	4	2	no	—
760	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
761	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
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	4	no	—
769	C₂×D₄	—	2	4	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	—	2	1	no	—
776	C₂×D₄	—	2	1	no	—
777	C₂×D₄	—	2	1	no	—
778	C₂×D₄	—	2	1	no	—
779	C₂×D₄	—	2	1	no	—
780	C₂×D₄	—	2	1	no	—
781	C₂×D₄	—	2	1	no	—
782	C₂×D₄	—	4	2	no	—
783	C₂×D₄	—	4	2	no	—
784	C₂×D₄	—	4	2	no	—
785	C₂×D₄	—	4	1	no	—
786	C₂×D₄	—	4	1	no	—
787	C₂×D₄	—	4	1	no	—
788	C₂×D₄	—	4	1	no	—
789	C₂×D₄	—	4	4	no	—
790	C₂×D₄	—	4	2	no	—
791	C₂×D₄	—	4	4	no	—
792	C₂×D₄	—	4	4	no	—
793	C₂×D₄	—	4	4	no	—
794	C₂×D₄	—	4	1	no	—
795	C₂×D₄	—	4	2	no	—
796	C₂×D₄	—	4	1	no	—
797	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
798	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
799	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
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	C₂²×C₄	—	2	1	no	—
804	C₂²×C₄	—	2	1	no	—
805	C₂²×C₄	—	2	1	no	—
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	—	4	1	no	—
811	C₂²×C₄	—	4	1	no	—
812	C₂²×C₄	—	4	1	no	—
813	C₂²×C₄	—	4	1	no	—
814	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
815	Q₁₆	—	2	4	no	—
816	Q₁₆	—	2	2	no	—
817	Q₁₆	—	2	2	no	—
818	Q₁₆	—	4	2	no	—
819	SD₁₆	—	2	4	no	—
820	SD₁₆	—	2	4	no	—
821	SD₁₆	—	2	4	no	—
822	SD₁₆	—	2	4	no	—
823	SD₁₆	—	2	4	no	—
824	SD₁₆	—	2	2	no	—
825	SD₁₆	—	2	2	no	—
826	SD₁₆	—	2	2	no	—
827	SD₁₆	—	2	4	no	—
828	SD₁₆	—	2	2	no	—
829	SD₁₆	—	4	2	no	—
830	SD₁₆	—	4	2	no	—
831	D₈	—	2	4	no	—
832	D₈	—	2	4	no	—
833	D₈	—	2	4	no	—
834	D₈	—	2	4	no	—
835	D₈	—	2	2	no	—
836	D₈	—	2	4	no	—
837	D₈	—	2	2	no	—
838	D₈	—	4	2	no	—
839	M₁₆	—	2	4	no	—
840	M₁₆	—	2	4	no	—
841	M₁₆	—	2	1	no	—
842	M₁₆	—	2	1	no	—
843	M₁₆	—	2	1	no	—
844	M₁₆	—	2	1	no	—
845	M₁₆	—	2	1	no	—
846	M₁₆	—	2	1	no	—
847	M₁₆	C₂×D₄×C₈₉	1	2	yes	—
848	M₁₆	C₂×D₄×C₈₉	1	2	yes	—
849	C₂×C₈	—	2	4	no	—
850	C₂×C₈	—	2	4	no	—
851	C₂×C₈	—	2	1	no	—
852	C₂×C₈	—	2	1	no	—
853	C₂×C₈	—	2	1	no	—
854	C₂×C₈	—	2	1	no	—
855	C₂×C₈	—	2	1	no	—
856	C₂×C₈	—	2	1	no	—
857	C₂×C₈	—	2	1	no	—
858	C₂×C₈	—	2	1	no	—
859	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
860	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
861	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
862	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
863	C₄⋊C₄	—	2	1	no	—
864	C₄⋊C₄	—	2	1	no	—
865	C₄⋊C₄	—	4	1	no	—
866	C₂²⋊C₄	—	4	4	no	—
867	C₂²⋊C₄	—	4	1	no	—
868	C₂²⋊C₄	—	4	1	no	—
869	C₂²⋊C₄	—	8	2	no	—
870	C₄²	—	2	1	no	—
871	C₄²	—	2	1	no	—
872	C₂³	—	2	1	no	—
873	C₂³	—	2	1	no	—
874	C₂³	—	2	1	no	—
875	C₂³	—	2	1	no	—
876	C₂³	—	2	2	no	—
877	C₂³	—	2	2	no	—
878	C₂³	—	4	4	no	—
879	C₂³	—	4	4	no	—
880	C₂³	—	4	1	no	—
881	C₂³	—	4	1	no	—
882	C₂³	—	4	1	no	—
883	C₂³	—	4	1	no	—
884	C₂³	—	8	1	no	—
885	C₂³	—	8	1	no	—
886	C₂³	—	8	1	no	—
887	C₂³	—	8	1	no	—
888	C₂³	—	16	1	no	—
889	C₂³	—	16	1	no	—
890	C₂³	—	16	1	no	—
891	C₂³	—	16	1	no	—
892	C₂³	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
893	Q₈	—	2	1	no	—
894	Q₈	—	2	1	no	—
895	Q₈	—	2	2	no	—
896	Q₈	—	2	1	no	—
897	Q₈	—	2	1	no	—
898	Q₈	—	2	1	no	—
899	Q₈	—	2	2	no	—
900	Q₈	—	2	1	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	2	no	—
911	D₄	—	2	2	no	—
912	D₄	—	2	1	no	—
913	D₄	—	2	1	no	—
914	D₄	—	2	2	no	—
915	D₄	—	2	1	no	—
916	D₄	—	2	1	no	—
917	D₄	—	2	1	no	—
918	D₄	—	2	2	no	—
919	D₄	—	2	1	no	—
920	D₄	—	4	4	no	—
921	D₄	—	4	4	no	—
922	D₄	—	4	4	no	—
923	D₄	—	4	4	no	—
924	D₄	—	4	4	no	—
925	D₄	—	4	1	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	—	16	1	no	—
934	D₄	#120×C₈₉	1	2	yes	—
935	D₄	#120×C₈₉	1	2	yes	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	2	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	—	4	4	no	—
946	C₂×C₄	—	4	4	no	—
947	C₂×C₄	—	4	4	no	—
948	C₂×C₄	—	4	4	no	—
949	C₂×C₄	—	4	1	no	—
950	C₂×C₄	—	4	1	no	—
951	C₂×C₄	—	4	1	no	—
952	C₂×C₄	—	4	1	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	—	8	1	no	—
960	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
961	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
962	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
963	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
964	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
965	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
966	C₈	—	2	1	no	—
967	C₈	—	2	1	no	—
968	C₈	—	2	2	no	—
969	C₈	—	2	2	no	—
970	C₈	—	2	1	no	—
971	C₈	—	2	1	no	—
972	C₈	—	4	1	no	—
973	C₈	—	4	1	no	—
974	C₂²	—	2	1	no	—
975	C₂²	—	2	1	no	—
976	C₂²	—	2	2	no	—
977	C₂²	—	2	2	no	—
978	C₂²	—	4	1	no	—
979	C₂²	—	4	1	no	—
980	C₂²	—	4	1	no	—
981	C₂²	—	4	1	no	—
982	C₂²	—	4	1	no	—
983	C₂²	—	4	1	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	4	2	no	—
986	C₂²	—	4	1	no	—
987	C₂²	—	4	1	no	—
988	C₂²	—	4	1	no	—
989	C₂²	—	4	1	no	—
990	C₂²	—	8	2	no	—
991	C₂²	—	8	2	no	—
992	C₂²	—	8	1	no	—
993	C₂²	—	8	1	no	—
994	C₂²	—	8	1	no	—
995	C₂²	—	8	1	no	—
996	C₂²	—	16	1	no	—
997	C₂²	—	16	1	no	—
998	C₂²	—	16	4	no	—
999	C₂²	—	16	4	no	—
1000	C₂²	#534×C₈₉	1	1	yes	characteristic
1001	C₂²	D₄²×C₈₉	1	1	yes	characteristic
1002	C₂²	D₄²×C₈₉	1	1	yes	characteristic
1003	C₄	—	2	2	no	—
1004	C₄	—	2	2	no	—
1005	C₄	—	4	1	no	—
1006	C₄	—	4	2	no	—
1007	C₄	—	4	1	no	—
1008	C₄	—	8	1	no	—
1009	C₄	—	8	1	no	—
1010	C₄	C₂×#120×C₈₉	1	1	yes	characteristic
1011	C₄	C₂×#120×C₈₉	1	1	yes	characteristic
1012	C₄	D₄²×C₈₉	1	1	yes	characteristic
1013	C₄	D₄²×C₈₉	1	1	yes	characteristic
1014	C₂	—	2	1	no	—
1015	C₂	—	2	1	no	—
1016	C₂	—	4	2	no	—
1017	C₂	—	4	2	no	—
1018	C₂	—	8	1	no	—
1019	C₂	—	8	1	no	—
1020	C₂	—	8	2	no	—
1021	C₂	—	8	2	no	—
1022	C₂	C₈₉×#2403	1	1	yes	characteristic
1023	C₂	C₈₉×#3288	1	1	yes	characteristic
1024	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×#577×C₈₉	C₂	semidirect
2. C₂×#576×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×#2019	C₂	semidirect
8. C₈₉×#2018	C₂	semidirect
9. C₈₉×#2012	C₂	semidirect
10. C₈₉×#2006	C₂	semidirect
11. C₈₉×#1908	C₂	semidirect
12. C₈₉×#1907	C₂	semidirect
13. C₈₉×#1876	C₂	semidirect
14. C₈₉×#1876	C₂	semidirect
15. C₈₉×#1792	C₂	semidirect
16. C₂×2₋¹⁺⁴×C₈₉	C₂²	semidirect
25. C₂×#137×C₈₉	C₂²	semidirect
31. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
32. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
38. C₂²×SD₁₆×C₈₉	C₂²	semidirect
42. C₂×#131×C₈₉	C₂²	semidirect
43. #537×C₈₉	C₂²	semidirect
44. C₂×#124×C₈₉	C₂²	semidirect
56. C₂×#104×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
62. C₂×#102×C₈₉	C₂²	semidirect
63. C₂×#101×C₈₉	C₂²	semidirect
64. C₂×#100×C₈₉	C₂²	semidirect
65. C₂×#100×C₈₉	C₂²	semidirect
66. #408×C₈₉	C₂²	semidirect
67. #408×C₈₉	C₂²	semidirect
68. #390×C₈₉	C₂²	semidirect
69. #343×C₈₉	C₂²	semidirect
70. #341×C₈₉	C₂²	semidirect
71. #341×C₈₉	C₂²	semidirect
72. #336×C₈₉	C₂²	semidirect
84. H(5,𝔽₂)×C₈₉	D₄	semidirect
111. #137×C₈₉	D₄	semidirect
122. AGL(1,ℤ/8)×C₈₉	D₄	semidirect
501. #23888	C₈₉	direct (N × H)
513. C₂×#577	C₂×C₈₉	semidirect
514. C₂×#576	C₂×C₈₉	semidirect
515. C₂×#454	C₂×C₈₉	semidirect
516. C₂×#455	C₂×C₈₉	semidirect
517. #3013	C₂×C₈₉	semidirect
518. #3012	C₂×C₈₉	semidirect
519. #2019	C₂×C₈₉	semidirect
520. #2018	C₂×C₈₉	semidirect
521. #2012	C₂×C₈₉	semidirect
522. #2006	C₂×C₈₉	semidirect
523. #1908	C₂×C₈₉	semidirect
524. #1907	C₂×C₈₉	semidirect
525. #1876	C₂×C₈₉	semidirect
526. #1876	C₂×C₈₉	semidirect
527. #1792	C₂×C₈₉	semidirect
528. C₈₉	#23888	direct (N × H)
529. C₂×2₋¹⁺⁴	C₂²×C₈₉	semidirect
538. C₂×#137	C₂²×C₈₉	semidirect
544. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
545. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
551. C₂²×SD₁₆	C₂²×C₈₉	semidirect
555. C₂×#131	C₂²×C₈₉	semidirect
556. #537	C₂²×C₈₉	semidirect
557. C₂×#124	C₂²×C₈₉	semidirect
569. C₂×#104	C₂²×C₈₉	semidirect
570. C₂×#104	C₂²×C₈₉	semidirect
571. C₂×#104	C₂²×C₈₉	semidirect
573. #417	C₂²×C₈₉	semidirect
574. C₂×#103	C₂²×C₈₉	semidirect
575. C₂×#102	C₂²×C₈₉	semidirect
576. C₂×#101	C₂²×C₈₉	semidirect
577. C₂×#100	C₂²×C₈₉	semidirect
578. C₂×#100	C₂²×C₈₉	semidirect
579. #408	C₂²×C₈₉	semidirect
580. #408	C₂²×C₈₉	semidirect
581. #390	C₂²×C₈₉	semidirect
582. #343	C₂²×C₈₉	semidirect
583. #341	C₂²×C₈₉	semidirect
584. #341	C₂²×C₈₉	semidirect
585. #336	C₂²×C₈₉	semidirect
597. H(5,𝔽₂)	D₄×C₈₉	semidirect
624. #137	D₄×C₈₉	semidirect
635. 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×#577×C₈₉	2
C₂×#576×C₈₉	2
C₂×#454×C₈₉	2
C₂×#455×C₈₉	2
C₈₉×#3013	2
C₈₉×#3012	2
C₈₉×#2019	2
C₈₉×#2018	2
C₈₉×#2012	2
C₈₉×#2006	2
C₈₉×#1908	2
C₈₉×#1907	2
C₈₉×#1876	2
C₈₉×#1792	2
#23888	89

Subgroups — C89×#23888 #36401736

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#23888 #36401736