Subgroups — C₈₉×#23412 #36401260

Order 22784.

1948 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#575×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3449	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#421×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2896	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#410×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2009	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2008	C₂	1	4	yes	maximal, complemented
9	C₂×#344×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
11	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
12	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
13	#575×C₈₉	—	2	2	no	—
14	#575×C₈₉	—	2	2	no	—
15	#575×C₈₉	—	2	2	no	—
16	#575×C₈₉	—	2	2	no	—
17	#575×C₈₉	—	2	2	no	—
18	#575×C₈₉	—	2	2	no	—
19	#575×C₈₉	—	2	2	no	—
20	#575×C₈₉	C₂²	1	4	yes	—
21	C₂×#137×C₈₉	—	2	1	no	—
22	C₂×#137×C₈₉	—	2	1	no	—
23	C₂×#137×C₈₉	—	2	1	no	—
24	C₂×#137×C₈₉	C₂²	1	2	yes	complemented
25	C₂×AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
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	C₂²	1	2	yes	complemented
29	C₂×#135×C₈₉	—	2	2	no	—
30	C₂×#135×C₈₉	—	2	2	no	—
31	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
32	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
33	#537×C₈₉	—	2	2	no	—
34	#536×C₈₉	—	2	1	no	—
35	#536×C₈₉	C₂²	1	2	yes	complemented
36	#535×C₈₉	—	2	1	no	—
37	#535×C₈₉	C₂²	1	2	yes	complemented
38	#534×C₈₉	—	2	2	no	—
39	#532×C₈₉	—	2	2	no	—
40	#525×C₈₉	—	2	2	no	—
41	#525×C₈₉	—	2	2	no	—
42	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
44	#421×C₈₉	—	2	2	no	—
45	#421×C₈₉	C₂²	1	4	yes	complemented
46	C₂×#104×C₈₉	—	2	2	no	—
47	#419×C₈₉	C₂²	1	2	yes	complemented
48	#418×C₈₉	C₂²	1	2	yes	complemented
49	#417×C₈₉	—	2	2	no	—
50	#416×C₈₉	—	2	2	no	—
51	#410×C₈₉	—	2	2	no	—
52	#410×C₈₉	C₂²	1	4	yes	complemented
53	C₂×#99×C₈₉	—	2	2	no	—
54	#344×C₈₉	C₂²	1	4	yes	complemented
55	C₂×#41×C₈₉	—	2	1	no	—
56	C₂×#41×C₈₉	—	2	1	no	—
57	C₂×#41×C₈₉	—	2	1	no	—
58	C₂×#41×C₈₉	—	2	1	no	—
59	C₂×#41×C₈₉	—	2	1	no	—
60	C₂×#41×C₈₉	—	2	1	no	—
61	C₂×#41×C₈₉	—	2	1	no	—
62	C₂×#41×C₈₉	—	2	1	no	—
63	C₂×#41×C₈₉	—	2	1	no	—
64	C₂×#41×C₈₉	—	2	1	no	—
65	C₂×#41×C₈₉	—	2	1	no	—
66	C₂×#41×C₈₉	—	2	1	no	—
67	C₂×#41×C₈₉	—	2	1	no	—
68	C₂×#41×C₈₉	—	2	1	no	—
69	C₂×#41×C₈₉	—	2	1	no	—
70	C₂×#41×C₈₉	—	2	1	no	—
71	C₂×#41×C₈₉	—	2	1	no	—
72	C₂×#41×C₈₉	—	2	1	no	—
73	C₂×#41×C₈₉	—	2	1	no	—
74	C₂×#41×C₈₉	—	2	1	no	—
75	C₂×#41×C₈₉	—	2	1	no	—
76	C₂×#41×C₈₉	—	2	1	no	—
77	C₂×#41×C₈₉	—	2	1	no	—
78	C₂×#41×C₈₉	—	2	1	no	—
79	C₂×#41×C₈₉	—	2	1	no	—
80	C₂×#41×C₈₉	—	2	1	no	—
81	C₂×#41×C₈₉	—	2	1	no	—
82	C₂×#41×C₈₉	—	2	1	no	—
83	C₂×#41×C₈₉	—	2	1	no	—
84	C₂×#41×C₈₉	—	2	1	no	—
85	C₂×#41×C₈₉	D₄	1	2	yes	—
86	C₂×#41×C₈₉	D₄	1	2	yes	—
87	C₂×#41×C₈₉	D₄	1	2	yes	—
88	C₂×#41×C₈₉	D₄	1	2	yes	complemented
89	C₂×#41×C₈₉	C₂³	1	2	yes	—
90	C₂×#41×C₈₉	C₂³	1	2	yes	—
91	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
92	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic, complemented
93	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₈₉	—	2	1	no	—
95	C₂²×D₄×C₈₉	—	2	1	no	—
96	C₂²×D₄×C₈₉	—	2	1	no	—
97	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
98	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic, complemented
99	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₈₉	—	2	1	no	—
101	C₂³×C₄×C₈₉	—	2	1	no	—
102	C₂³×C₄×C₈₉	—	2	1	no	—
103	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
104	#137×C₈₉	—	2	4	no	—
105	#137×C₈₉	—	2	4	no	—
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	4	no	—
111	#137×C₈₉	—	2	4	no	—
112	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
113	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
114	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
115	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
116	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
117	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
118	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
119	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
120	#135×C₈₉	—	2	8	no	—
121	#135×C₈₉	—	2	8	no	—
122	#135×C₈₉	—	2	8	no	—
123	#135×C₈₉	—	2	8	no	—
124	C₂×Q₁₆×C₈₉	—	2	2	no	—
125	C₂×Q₁₆×C₈₉	—	2	2	no	—
126	C₂×SD₁₆×C₈₉	—	2	2	no	—
127	C₂×SD₁₆×C₈₉	—	2	2	no	—
128	C₂×SD₁₆×C₈₉	—	2	2	no	—
129	C₂×SD₁₆×C₈₉	—	2	2	no	—
130	C₂×D₈×C₈₉	—	2	2	no	—
131	C₂×D₈×C₈₉	—	2	2	no	—
132	C₂×M₁₆×C₈₉	—	2	1	no	—
133	C₂×M₁₆×C₈₉	—	2	1	no	—
134	C₂×M₁₆×C₈₉	—	2	1	no	—
135	C₂×M₁₆×C₈₉	—	2	1	no	—
136	C₂×M₁₆×C₈₉	—	2	1	no	—
137	C₂×M₁₆×C₈₉	—	2	1	no	—
138	C₂×M₁₆×C₈₉	—	2	1	no	—
139	C₂×M₁₆×C₈₉	D₄	1	2	yes	complemented
140	C₂×M₁₆×C₈₉	D₄	1	2	yes	complemented
141	C₂×M₁₆×C₈₉	D₄	1	2	yes	complemented
142	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
143	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
144	C₂²×C₈×C₈₉	—	2	1	no	—
145	C₂²×C₈×C₈₉	D₄	1	2	yes	complemented
146	C₄⋊Q₈×C₈₉	—	2	2	no	—
147	#127×C₈₉	—	2	2	no	—
148	#124×C₈₉	—	2	2	no	—
149	#124×C₈₉	—	2	2	no	—
150	#123×C₈₉	—	2	4	no	—
151	#123×C₈₉	—	2	4	no	—
152	C₂²⋊Q₈×C₈₉	—	2	4	no	—
153	C₂²⋊Q₈×C₈₉	—	2	4	no	—
154	#121×C₈₉	—	2	4	no	—
155	#121×C₈₉	—	2	8	no	—
156	#121×C₈₉	—	2	4	no	—
157	#120×C₈₉	—	2	4	no	—
158	#120×C₈₉	—	2	4	no	—
159	C₄×D₄×C₈₉	—	2	8	no	—
160	#117×C₈₉	—	2	1	no	—
161	#117×C₈₉	—	2	1	no	—
162	#117×C₈₉	—	2	1	no	—
163	#117×C₈₉	—	2	1	no	—
164	#117×C₈₉	—	2	1	no	—
165	#117×C₈₉	D₄	1	2	yes	—
166	#117×C₈₉	C₂³	1	2	yes	—
167	#117×C₈₉	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
169	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
170	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
171	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
172	C₂×C₄²×C₈₉	—	2	1	no	—
173	C₂×C₄²×C₈₉	—	2	1	no	—
174	#104×C₈₉	—	2	8	no	—
175	#103×C₈₉	—	2	4	no	—
176	#102×C₈₉	—	2	4	no	—
177	#99×C₈₉	—	2	8	no	—
178	C₂⁴×C₈₉	—	2	1	no	—
179	C₂⁴×C₈₉	—	2	1	no	—
180	C₂⁴×C₈₉	—	2	1	no	—
181	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
182	#41×C₈₉	—	2	2	no	—
183	#41×C₈₉	—	2	2	no	—
184	#41×C₈₉	—	2	2	no	—
185	#41×C₈₉	—	2	2	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	2	no	—
191	#41×C₈₉	—	2	2	no	—
192	#41×C₈₉	—	2	2	no	—
193	#41×C₈₉	—	2	2	no	—
194	#41×C₈₉	—	2	2	no	—
195	#41×C₈₉	—	2	2	no	—
196	#41×C₈₉	—	2	2	no	—
197	#41×C₈₉	—	2	2	no	—
198	#41×C₈₉	—	2	2	no	—
199	#41×C₈₉	—	2	2	no	—
200	#41×C₈₉	—	2	2	no	—
201	#41×C₈₉	—	2	2	no	—
202	#41×C₈₉	—	2	2	no	—
203	#41×C₈₉	—	2	2	no	—
204	#41×C₈₉	—	2	2	no	—
205	#41×C₈₉	—	2	2	no	—
206	#41×C₈₉	—	4	1	no	—
207	#41×C₈₉	—	4	1	no	—
208	#41×C₈₉	—	4	1	no	—
209	#41×C₈₉	—	4	1	no	—
210	#41×C₈₉	—	4	1	no	—
211	#41×C₈₉	—	4	1	no	—
212	#41×C₈₉	—	4	1	no	—
213	#41×C₈₉	—	4	1	no	—
214	#41×C₈₉	—	4	1	no	—
215	#41×C₈₉	—	4	1	no	—
216	#41×C₈₉	—	4	1	no	—
217	#41×C₈₉	—	4	1	no	—
218	#41×C₈₉	—	4	1	no	—
219	#41×C₈₉	—	4	1	no	—
220	#41×C₈₉	—	4	1	no	—
221	#41×C₈₉	—	4	1	no	—
222	#41×C₈₉	—	4	1	no	—
223	#41×C₈₉	—	4	1	no	—
224	#41×C₈₉	—	4	1	no	—
225	#41×C₈₉	—	4	1	no	—
226	#41×C₈₉	—	4	1	no	—
227	#41×C₈₉	—	4	1	no	—
228	#41×C₈₉	—	4	1	no	—
229	#41×C₈₉	—	4	1	no	—
230	C₂×Q₈×C₈₉	—	2	1	no	—
231	C₂×Q₈×C₈₉	—	2	1	no	—
232	C₂×Q₈×C₈₉	—	2	1	no	—
233	C₂×Q₈×C₈₉	—	2	1	no	—
234	C₂×Q₈×C₈₉	—	2	1	no	—
235	C₂×Q₈×C₈₉	—	2	1	no	—
236	C₂×Q₈×C₈₉	—	2	1	no	—
237	C₂×Q₈×C₈₉	—	2	1	no	—
238	C₂×Q₈×C₈₉	—	2	1	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	—	2	1	no	—
244	C₂×Q₈×C₈₉	—	2	1	no	—
245	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
246	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
247	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
248	C₂×D₄×C₈₉	—	2	2	no	—
249	C₂×D₄×C₈₉	—	2	2	no	—
250	C₂×D₄×C₈₉	—	2	2	no	—
251	C₂×D₄×C₈₉	—	2	2	no	—
252	C₂×D₄×C₈₉	—	2	2	no	—
253	C₂×D₄×C₈₉	—	2	2	no	—
254	C₂×D₄×C₈₉	—	2	8	no	—
255	C₂×D₄×C₈₉	—	2	1	no	—
256	C₂×D₄×C₈₉	—	2	1	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	—	2	1	no	—
270	C₂×D₄×C₈₉	—	4	1	no	—
271	C₂×D₄×C₈₉	—	4	1	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	1	no	—
277	C₂×D₄×C₈₉	—	4	1	no	—
278	C₂×D₄×C₈₉	—	4	1	no	—
279	C₂×D₄×C₈₉	—	4	1	no	—
280	C₂×D₄×C₈₉	—	4	1	no	—
281	C₂×D₄×C₈₉	—	4	1	no	—
282	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
283	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
284	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
285	C₂²×C₄×C₈₉	—	2	1	no	—
286	C₂²×C₄×C₈₉	—	2	1	no	—
287	C₂²×C₄×C₈₉	—	2	1	no	—
288	C₂²×C₄×C₈₉	—	2	2	no	—
289	C₂²×C₄×C₈₉	—	2	2	no	—
290	C₂²×C₄×C₈₉	—	2	2	no	—
291	C₂²×C₄×C₈₉	—	2	2	no	—
292	C₂²×C₄×C₈₉	—	2	2	no	—
293	C₂²×C₄×C₈₉	—	2	2	no	—
294	C₂²×C₄×C₈₉	—	2	2	no	—
295	C₂²×C₄×C₈₉	—	4	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	—	4	1	no	—
302	C₂²×C₄×C₈₉	—	4	1	no	—
303	C₂²×C₄×C₈₉	—	4	1	no	—
304	C₂²×C₄×C₈₉	—	4	1	no	—
305	C₂²×C₄×C₈₉	—	4	1	no	—
306	C₂²×C₄×C₈₉	—	4	1	no	—
307	C₂²×C₄×C₈₉	—	4	1	no	—
308	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
310	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
314	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
315	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
316	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
317	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
318	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
320	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
321	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
322	Q₁₆×C₈₉	—	2	8	no	—
323	Q₁₆×C₈₉	—	2	8	no	—
324	SD₁₆×C₈₉	—	2	8	no	—
325	SD₁₆×C₈₉	—	2	8	no	—
326	SD₁₆×C₈₉	—	2	8	no	—
327	SD₁₆×C₈₉	—	2	8	no	—
328	D₈×C₈₉	—	2	8	no	—
329	D₈×C₈₉	—	2	8	no	—
330	M₁₆×C₈₉	—	2	2	no	—
331	M₁₆×C₈₉	—	2	2	no	—
332	M₁₆×C₈₉	—	2	2	no	—
333	M₁₆×C₈₉	—	2	2	no	—
334	M₁₆×C₈₉	—	2	2	no	—
335	M₁₆×C₈₉	—	2	2	no	—
336	M₁₆×C₈₉	—	2	2	no	—
337	M₁₆×C₈₉	C₂×D₄	1	4	yes	—
338	C₂×C₈×C₈₉	—	2	2	no	—
339	C₂×C₈×C₈₉	—	2	2	no	—
340	C₂×C₈×C₈₉	—	2	2	no	—
341	C₂×C₈×C₈₉	—	2	2	no	—
342	C₂×C₈×C₈₉	—	2	2	no	—
343	C₂×C₈×C₈₉	C₂×D₄	1	4	yes	—
344	C₄⋊C₄×C₈₉	—	2	8	no	—
345	C₄⋊C₄×C₈₉	—	2	2	no	—
346	C₄⋊C₄×C₈₉	—	2	2	no	—
347	C₄⋊C₄×C₈₉	—	2	2	no	—
348	C₄⋊C₄×C₈₉	—	4	1	no	—
349	C₂²⋊C₄×C₈₉	—	2	8	no	—
350	C₂²⋊C₄×C₈₉	—	2	8	no	—
351	C₂²⋊C₄×C₈₉	—	2	2	no	—
352	C₂²⋊C₄×C₈₉	—	2	2	no	—
353	C₂²⋊C₄×C₈₉	—	4	1	no	—
354	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
355	C₄²×C₈₉	—	2	2	no	—
356	C₄²×C₈₉	—	2	2	no	—
357	C₄²×C₈₉	—	2	2	no	—
358	C₄²×C₈₉	—	4	1	no	—
359	C₂³×C₈₉	—	2	2	no	—
360	C₂³×C₈₉	—	2	2	no	—
361	C₂³×C₈₉	—	2	2	no	—
362	C₂³×C₈₉	—	4	1	no	—
363	C₂³×C₈₉	—	4	1	no	—
364	C₂³×C₈₉	—	4	1	no	—
365	C₂³×C₈₉	—	4	1	no	—
366	C₂³×C₈₉	—	4	1	no	—
367	C₂³×C₈₉	—	4	1	no	—
368	C₂³×C₈₉	—	8	1	no	—
369	C₂³×C₈₉	—	8	2	no	—
370	C₂³×C₈₉	—	8	2	no	—
371	C₂³×C₈₉	—	8	2	no	—
372	C₂³×C₈₉	#120	1	1	yes	characteristic
373	C₂³×C₈₉	#120	1	1	yes	characteristic
374	C₂³×C₈₉	#121	1	1	yes	characteristic
375	C₂³×C₈₉	#121	1	1	yes	characteristic
376	C₂³×C₈₉	#127	1	1	yes	characteristic
377	C₂³×C₈₉	#127	1	1	yes	characteristic
378	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
379	Q₈×C₈₉	—	2	2	no	—
380	Q₈×C₈₉	—	2	2	no	—
381	Q₈×C₈₉	—	2	2	no	—
382	Q₈×C₈₉	—	2	2	no	—
383	Q₈×C₈₉	—	2	2	no	—
384	Q₈×C₈₉	—	2	2	no	—
385	Q₈×C₈₉	—	4	1	no	—
386	Q₈×C₈₉	—	4	1	no	—
387	Q₈×C₈₉	—	4	1	no	—
388	Q₈×C₈₉	—	4	1	no	—
389	Q₈×C₈₉	—	4	1	no	—
390	Q₈×C₈₉	—	4	1	no	—
391	D₄×C₈₉	—	2	2	no	—
392	D₄×C₈₉	—	2	2	no	—
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	—	4	2	no	—
398	D₄×C₈₉	—	4	2	no	—
399	D₄×C₈₉	—	4	2	no	—
400	D₄×C₈₉	—	4	2	no	—
401	D₄×C₈₉	—	4	2	no	—
402	D₄×C₈₉	—	4	2	no	—
403	D₄×C₈₉	—	4	2	no	—
404	D₄×C₈₉	—	4	2	no	—
405	D₄×C₈₉	—	4	2	no	—
406	D₄×C₈₉	—	4	2	no	—
407	D₄×C₈₉	—	4	2	no	—
408	D₄×C₈₉	—	4	2	no	—
409	D₄×C₈₉	—	4	1	no	—
410	D₄×C₈₉	—	4	1	no	—
411	D₄×C₈₉	—	4	1	no	—
412	D₄×C₈₉	—	4	1	no	—
413	D₄×C₈₉	—	4	1	no	—
414	D₄×C₈₉	—	4	1	no	—
415	D₄×C₈₉	—	8	8	no	—
416	C₂×C₄×C₈₉	—	2	4	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	—	4	1	no	—
421	C₂×C₄×C₈₉	—	4	1	no	—
422	C₂×C₄×C₈₉	—	4	1	no	—
423	C₂×C₄×C₈₉	—	4	1	no	—
424	C₂×C₄×C₈₉	—	4	1	no	—
425	C₂×C₄×C₈₉	—	4	1	no	—
426	C₂×C₄×C₈₉	—	4	2	no	—
427	C₂×C₄×C₈₉	—	4	2	no	—
428	C₂×C₄×C₈₉	—	4	2	no	—
429	C₂×C₄×C₈₉	—	4	2	no	—
430	C₂×C₄×C₈₉	—	4	2	no	—
431	C₂×C₄×C₈₉	—	4	2	no	—
432	C₂×C₄×C₈₉	—	4	2	no	—
433	C₂×C₄×C₈₉	—	4	2	no	—
434	C₂×C₄×C₈₉	—	4	2	no	—
435	C₂×C₄×C₈₉	—	4	2	no	—
436	C₂×C₄×C₈₉	—	4	2	no	—
437	C₂×C₄×C₈₉	—	4	2	no	—
438	C₂×C₄×C₈₉	—	4	2	no	—
439	C₂×C₄×C₈₉	—	8	2	no	—
440	C₂×C₄×C₈₉	—	8	2	no	—
441	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
442	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
443	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
444	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
445	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
446	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
447	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
448	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
449	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
450	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
451	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
452	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
453	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
454	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
455	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
456	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
457	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
458	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
459	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
460	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
461	C₂×C₄×C₈₉	#127	1	1	yes	characteristic
462	C₂×C₄×C₈₉	#127	1	1	yes	characteristic
463	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
469	C₈×C₈₉	—	2	4	no	—
470	C₈×C₈₉	—	2	4	no	—
471	C₂²×C₈₉	—	4	1	no	—
472	C₂²×C₈₉	—	4	1	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	—	4	1	no	—
478	C₂²×C₈₉	—	4	4	no	—
479	C₂²×C₈₉	—	4	4	no	—
480	C₂²×C₈₉	—	4	2	no	—
481	C₂²×C₈₉	—	4	2	no	—
482	C₂²×C₈₉	—	4	2	no	—
483	C₂²×C₈₉	—	8	2	no	—
484	C₂²×C₈₉	—	8	2	no	—
485	C₂²×C₈₉	—	8	2	no	—
486	C₂²×C₈₉	—	8	2	no	—
487	C₂²×C₈₉	—	8	2	no	—
488	C₂²×C₈₉	—	8	2	no	—
489	C₂²×C₈₉	—	8	2	no	—
490	C₂²×C₈₉	#392	1	1	yes	characteristic
491	C₂²×C₈₉	#392	1	1	yes	characteristic
492	C₂²×C₈₉	#392	1	1	yes	characteristic
493	C₂²×C₈₉	#392	1	1	yes	characteristic
494	C₂²×C₈₉	C₂×#120	1	1	yes	characteristic
495	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
496	C₂²×C₈₉	C₂×#127	1	1	yes	characteristic
497	C₄×C₈₉	—	4	4	no	—
498	C₄×C₈₉	—	4	2	no	—
499	C₄×C₈₉	—	4	2	no	—
500	C₄×C₈₉	—	4	2	no	—
501	C₄×C₈₉	—	8	2	no	—
502	C₄×C₈₉	#392	1	1	yes	characteristic
503	C₄×C₈₉	#392	1	1	yes	characteristic
504	C₄×C₈₉	#392	1	1	yes	characteristic
505	C₄×C₈₉	#392	1	1	yes	characteristic
506	C₄×C₈₉	C₂×#120	1	1	yes	characteristic
507	C₄×C₈₉	C₂×#120	1	1	yes	characteristic
508	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
509	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
510	#23412	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
511	C₂×C₈₉	—	2	1	no	—
512	C₂×C₈₉	—	2	1	no	—
513	C₂×C₈₉	—	2	1	no	—
514	C₂×C₈₉	—	2	1	no	—
515	C₂×C₈₉	—	2	1	no	—
516	C₂×C₈₉	—	2	1	no	—
517	C₂×C₈₉	—	2	1	no	—
518	C₂×C₈₉	—	8	2	no	—
519	C₂×C₈₉	—	8	2	no	—
520	C₂×C₈₉	—	8	2	no	—
521	C₂×C₈₉	C₂×#392	1	1	yes	characteristic
522	C₂×#575	C₂×C₈₉	1	1	yes	characteristic, complemented
523	C₂×#575	C₂×C₈₉	1	1	yes	characteristic, complemented
524	#3449	C₂×C₈₉	1	1	yes	characteristic, complemented
525	C₂×#421	C₂×C₈₉	1	1	yes	characteristic, complemented
526	#2896	C₂×C₈₉	1	1	yes	characteristic, complemented
527	C₂×#410	C₂×C₈₉	1	1	yes	characteristic, complemented
528	#2009	C₂×C₈₉	1	4	yes	complemented
529	#2008	C₂×C₈₉	1	4	yes	complemented
530	C₂×#344	C₂×C₈₉	1	1	yes	characteristic, complemented
531	C₈₉	#23412	1	1	yes	characteristic, direct product factor, Sylow
532	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
533	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
534	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
535	#575	—	2	2	no	—
536	#575	—	2	2	no	—
537	#575	—	2	2	no	—
538	#575	—	2	2	no	—
539	#575	—	2	2	no	—
540	#575	—	2	2	no	—
541	#575	—	2	2	no	—
542	#575	C₂²×C₈₉	1	4	yes	—
543	C₂×#137	—	2	1	no	—
544	C₂×#137	—	2	1	no	—
545	C₂×#137	—	2	1	no	—
546	C₂×#137	C₂²×C₈₉	1	2	yes	complemented
547	C₂×AGL(1,ℤ/8)	—	2	1	no	—
548	C₂×AGL(1,ℤ/8)	—	2	1	no	—
549	C₂×AGL(1,ℤ/8)	—	2	1	no	—
550	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	complemented
551	C₂×#135	—	2	2	no	—
552	C₂×#135	—	2	2	no	—
553	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
554	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
555	#537	—	2	2	no	—
556	#536	—	2	1	no	—
557	#536	C₂²×C₈₉	1	2	yes	complemented
558	#535	—	2	1	no	—
559	#535	C₂²×C₈₉	1	2	yes	complemented
560	#534	—	2	2	no	—
561	#532	—	2	2	no	—
562	#525	—	2	2	no	—
563	#525	—	2	2	no	—
564	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
565	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
566	#421	—	2	2	no	—
567	#421	C₂²×C₈₉	1	4	yes	complemented
568	C₂×#104	—	2	2	no	—
569	#419	C₂²×C₈₉	1	2	yes	complemented
570	#418	C₂²×C₈₉	1	2	yes	complemented
571	#417	—	2	2	no	—
572	#416	—	2	2	no	—
573	#410	—	2	2	no	—
574	#410	C₂²×C₈₉	1	4	yes	complemented
575	C₂×#99	—	2	2	no	—
576	#344	C₂²×C₈₉	1	4	yes	complemented
577	C₂×#41	—	2	1	no	—
578	C₂×#41	—	2	1	no	—
579	C₂×#41	—	2	1	no	—
580	C₂×#41	—	2	1	no	—
581	C₂×#41	—	2	1	no	—
582	C₂×#41	—	2	1	no	—
583	C₂×#41	—	2	1	no	—
584	C₂×#41	—	2	1	no	—
585	C₂×#41	—	2	1	no	—
586	C₂×#41	—	2	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	—	2	1	no	—
594	C₂×#41	—	2	1	no	—
595	C₂×#41	—	2	1	no	—
596	C₂×#41	—	2	1	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	—	2	1	no	—
602	C₂×#41	—	2	1	no	—
603	C₂×#41	—	2	1	no	—
604	C₂×#41	—	2	1	no	—
605	C₂×#41	—	2	1	no	—
606	C₂×#41	—	2	1	no	—
607	C₂×#41	D₄×C₈₉	1	2	yes	—
608	C₂×#41	D₄×C₈₉	1	2	yes	—
609	C₂×#41	D₄×C₈₉	1	2	yes	—
610	C₂×#41	D₄×C₈₉	1	2	yes	complemented
611	C₂×#41	C₂³×C₈₉	1	2	yes	—
612	C₂×#41	C₂³×C₈₉	1	2	yes	—
613	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
614	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic, complemented
615	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
616	C₂²×D₄	—	2	1	no	—
617	C₂²×D₄	—	2	1	no	—
618	C₂²×D₄	—	2	1	no	—
619	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
620	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic, complemented
621	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
622	C₂³×C₄	—	2	1	no	—
623	C₂³×C₄	—	2	1	no	—
624	C₂³×C₄	—	2	1	no	—
625	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
626	#137	—	2	4	no	—
627	#137	—	2	4	no	—
628	#137	—	2	4	no	—
629	#137	—	2	4	no	—
630	#137	—	2	4	no	—
631	#137	—	2	4	no	—
632	#137	—	2	4	no	—
633	#137	—	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	4	no	—
638	AGL(1,ℤ/8)	—	2	4	no	—
639	AGL(1,ℤ/8)	—	2	4	no	—
640	AGL(1,ℤ/8)	—	2	4	no	—
641	AGL(1,ℤ/8)	—	2	4	no	—
642	#135	—	2	8	no	—
643	#135	—	2	8	no	—
644	#135	—	2	8	no	—
645	#135	—	2	8	no	—
646	C₂×Q₁₆	—	2	2	no	—
647	C₂×Q₁₆	—	2	2	no	—
648	C₂×SD₁₆	—	2	2	no	—
649	C₂×SD₁₆	—	2	2	no	—
650	C₂×SD₁₆	—	2	2	no	—
651	C₂×SD₁₆	—	2	2	no	—
652	C₂×D₈	—	2	2	no	—
653	C₂×D₈	—	2	2	no	—
654	C₂×M₁₆	—	2	1	no	—
655	C₂×M₁₆	—	2	1	no	—
656	C₂×M₁₆	—	2	1	no	—
657	C₂×M₁₆	—	2	1	no	—
658	C₂×M₁₆	—	2	1	no	—
659	C₂×M₁₆	—	2	1	no	—
660	C₂×M₁₆	—	2	1	no	—
661	C₂×M₁₆	D₄×C₈₉	1	2	yes	complemented
662	C₂×M₁₆	D₄×C₈₉	1	2	yes	complemented
663	C₂×M₁₆	D₄×C₈₉	1	2	yes	complemented
664	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
665	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
666	C₂²×C₈	—	2	1	no	—
667	C₂²×C₈	D₄×C₈₉	1	2	yes	complemented
668	C₄⋊Q₈	—	2	2	no	—
669	#127	—	2	2	no	—
670	#124	—	2	2	no	—
671	#124	—	2	2	no	—
672	#123	—	2	4	no	—
673	#123	—	2	4	no	—
674	C₂²⋊Q₈	—	2	4	no	—
675	C₂²⋊Q₈	—	2	4	no	—
676	#121	—	2	4	no	—
677	#121	—	2	8	no	—
678	#121	—	2	4	no	—
679	#120	—	2	4	no	—
680	#120	—	2	4	no	—
681	C₄×D₄	—	2	8	no	—
682	#117	—	2	1	no	—
683	#117	—	2	1	no	—
684	#117	—	2	1	no	—
685	#117	—	2	1	no	—
686	#117	—	2	1	no	—
687	#117	D₄×C₈₉	1	2	yes	—
688	#117	C₂³×C₈₉	1	2	yes	—
689	#117	C₂³×C₈₉	1	2	yes	—
690	C₂×C₄⋊C₄	—	2	1	no	—
691	C₂×C₄⋊C₄	—	2	1	no	—
692	C₂×C₂²⋊C₄	—	2	1	no	—
693	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
694	C₂×C₄²	—	2	1	no	—
695	C₂×C₄²	—	2	1	no	—
696	#104	—	2	8	no	—
697	#103	—	2	4	no	—
698	#102	—	2	4	no	—
699	#99	—	2	8	no	—
700	C₂⁴	—	2	1	no	—
701	C₂⁴	—	2	1	no	—
702	C₂⁴	—	2	1	no	—
703	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
704	#41	—	2	2	no	—
705	#41	—	2	2	no	—
706	#41	—	2	2	no	—
707	#41	—	2	2	no	—
708	#41	—	2	2	no	—
709	#41	—	2	2	no	—
710	#41	—	2	2	no	—
711	#41	—	2	2	no	—
712	#41	—	2	2	no	—
713	#41	—	2	2	no	—
714	#41	—	2	2	no	—
715	#41	—	2	2	no	—
716	#41	—	2	2	no	—
717	#41	—	2	2	no	—
718	#41	—	2	2	no	—
719	#41	—	2	2	no	—
720	#41	—	2	2	no	—
721	#41	—	2	2	no	—
722	#41	—	2	2	no	—
723	#41	—	2	2	no	—
724	#41	—	2	2	no	—
725	#41	—	2	2	no	—
726	#41	—	2	2	no	—
727	#41	—	2	2	no	—
728	#41	—	4	1	no	—
729	#41	—	4	1	no	—
730	#41	—	4	1	no	—
731	#41	—	4	1	no	—
732	#41	—	4	1	no	—
733	#41	—	4	1	no	—
734	#41	—	4	1	no	—
735	#41	—	4	1	no	—
736	#41	—	4	1	no	—
737	#41	—	4	1	no	—
738	#41	—	4	1	no	—
739	#41	—	4	1	no	—
740	#41	—	4	1	no	—
741	#41	—	4	1	no	—
742	#41	—	4	1	no	—
743	#41	—	4	1	no	—
744	#41	—	4	1	no	—
745	#41	—	4	1	no	—
746	#41	—	4	1	no	—
747	#41	—	4	1	no	—
748	#41	—	4	1	no	—
749	#41	—	4	1	no	—
750	#41	—	4	1	no	—
751	#41	—	4	1	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	—	2	1	no	—
757	C₂×Q₈	—	2	1	no	—
758	C₂×Q₈	—	2	1	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	—	2	1	no	—
764	C₂×Q₈	—	2	1	no	—
765	C₂×Q₈	—	2	1	no	—
766	C₂×Q₈	—	2	1	no	—
767	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
768	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
769	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	2	no	—
774	C₂×D₄	—	2	2	no	—
775	C₂×D₄	—	2	2	no	—
776	C₂×D₄	—	2	8	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	—	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	—	2	1	no	—
788	C₂×D₄	—	2	1	no	—
789	C₂×D₄	—	2	1	no	—
790	C₂×D₄	—	2	1	no	—
791	C₂×D₄	—	2	1	no	—
792	C₂×D₄	—	4	1	no	—
793	C₂×D₄	—	4	1	no	—
794	C₂×D₄	—	4	1	no	—
795	C₂×D₄	—	4	1	no	—
796	C₂×D₄	—	4	1	no	—
797	C₂×D₄	—	4	1	no	—
798	C₂×D₄	—	4	1	no	—
799	C₂×D₄	—	4	1	no	—
800	C₂×D₄	—	4	1	no	—
801	C₂×D₄	—	4	1	no	—
802	C₂×D₄	—	4	1	no	—
803	C₂×D₄	—	4	1	no	—
804	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
805	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
806	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
807	C₂²×C₄	—	2	1	no	—
808	C₂²×C₄	—	2	1	no	—
809	C₂²×C₄	—	2	1	no	—
810	C₂²×C₄	—	2	2	no	—
811	C₂²×C₄	—	2	2	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	4	1	no	—
818	C₂²×C₄	—	4	1	no	—
819	C₂²×C₄	—	4	1	no	—
820	C₂²×C₄	—	4	1	no	—
821	C₂²×C₄	—	4	1	no	—
822	C₂²×C₄	—	4	1	no	—
823	C₂²×C₄	—	4	1	no	—
824	C₂²×C₄	—	4	1	no	—
825	C₂²×C₄	—	4	1	no	—
826	C₂²×C₄	—	4	1	no	—
827	C₂²×C₄	—	4	1	no	—
828	C₂²×C₄	—	4	1	no	—
829	C₂²×C₄	—	4	1	no	—
830	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
831	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
832	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
833	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
834	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
835	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
836	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
837	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
838	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
839	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
840	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
841	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
842	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
843	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
844	Q₁₆	—	2	8	no	—
845	Q₁₆	—	2	8	no	—
846	SD₁₆	—	2	8	no	—
847	SD₁₆	—	2	8	no	—
848	SD₁₆	—	2	8	no	—
849	SD₁₆	—	2	8	no	—
850	D₈	—	2	8	no	—
851	D₈	—	2	8	no	—
852	M₁₆	—	2	2	no	—
853	M₁₆	—	2	2	no	—
854	M₁₆	—	2	2	no	—
855	M₁₆	—	2	2	no	—
856	M₁₆	—	2	2	no	—
857	M₁₆	—	2	2	no	—
858	M₁₆	—	2	2	no	—
859	M₁₆	C₂×D₄×C₈₉	1	4	yes	—
860	C₂×C₈	—	2	2	no	—
861	C₂×C₈	—	2	2	no	—
862	C₂×C₈	—	2	2	no	—
863	C₂×C₈	—	2	2	no	—
864	C₂×C₈	—	2	2	no	—
865	C₂×C₈	C₂×D₄×C₈₉	1	4	yes	—
866	C₄⋊C₄	—	2	8	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	—	4	1	no	—
871	C₂²⋊C₄	—	2	8	no	—
872	C₂²⋊C₄	—	2	8	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	4	1	no	—
876	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	2	no	—
879	C₄²	—	2	2	no	—
880	C₄²	—	4	1	no	—
881	C₂³	—	2	2	no	—
882	C₂³	—	2	2	no	—
883	C₂³	—	2	2	no	—
884	C₂³	—	4	1	no	—
885	C₂³	—	4	1	no	—
886	C₂³	—	4	1	no	—
887	C₂³	—	4	1	no	—
888	C₂³	—	4	1	no	—
889	C₂³	—	4	1	no	—
890	C₂³	—	8	1	no	—
891	C₂³	—	8	2	no	—
892	C₂³	—	8	2	no	—
893	C₂³	—	8	2	no	—
894	C₂³	#120×C₈₉	1	1	yes	characteristic
895	C₂³	#120×C₈₉	1	1	yes	characteristic
896	C₂³	#121×C₈₉	1	1	yes	characteristic
897	C₂³	#121×C₈₉	1	1	yes	characteristic
898	C₂³	#127×C₈₉	1	1	yes	characteristic
899	C₂³	#127×C₈₉	1	1	yes	characteristic
900	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
901	Q₈	—	2	2	no	—
902	Q₈	—	2	2	no	—
903	Q₈	—	2	2	no	—
904	Q₈	—	2	2	no	—
905	Q₈	—	2	2	no	—
906	Q₈	—	2	2	no	—
907	Q₈	—	4	1	no	—
908	Q₈	—	4	1	no	—
909	Q₈	—	4	1	no	—
910	Q₈	—	4	1	no	—
911	Q₈	—	4	1	no	—
912	Q₈	—	4	1	no	—
913	D₄	—	2	2	no	—
914	D₄	—	2	2	no	—
915	D₄	—	2	2	no	—
916	D₄	—	2	2	no	—
917	D₄	—	2	2	no	—
918	D₄	—	2	2	no	—
919	D₄	—	4	2	no	—
920	D₄	—	4	2	no	—
921	D₄	—	4	2	no	—
922	D₄	—	4	2	no	—
923	D₄	—	4	2	no	—
924	D₄	—	4	2	no	—
925	D₄	—	4	2	no	—
926	D₄	—	4	2	no	—
927	D₄	—	4	2	no	—
928	D₄	—	4	2	no	—
929	D₄	—	4	2	no	—
930	D₄	—	4	2	no	—
931	D₄	—	4	1	no	—
932	D₄	—	4	1	no	—
933	D₄	—	4	1	no	—
934	D₄	—	4	1	no	—
935	D₄	—	4	1	no	—
936	D₄	—	4	1	no	—
937	D₄	—	8	8	no	—
938	C₂×C₄	—	2	4	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	4	1	no	—
943	C₂×C₄	—	4	1	no	—
944	C₂×C₄	—	4	1	no	—
945	C₂×C₄	—	4	1	no	—
946	C₂×C₄	—	4	1	no	—
947	C₂×C₄	—	4	1	no	—
948	C₂×C₄	—	4	2	no	—
949	C₂×C₄	—	4	2	no	—
950	C₂×C₄	—	4	2	no	—
951	C₂×C₄	—	4	2	no	—
952	C₂×C₄	—	4	2	no	—
953	C₂×C₄	—	4	2	no	—
954	C₂×C₄	—	4	2	no	—
955	C₂×C₄	—	4	2	no	—
956	C₂×C₄	—	4	2	no	—
957	C₂×C₄	—	4	2	no	—
958	C₂×C₄	—	4	2	no	—
959	C₂×C₄	—	4	2	no	—
960	C₂×C₄	—	4	2	no	—
961	C₂×C₄	—	8	2	no	—
962	C₂×C₄	—	8	2	no	—
963	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
964	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
965	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
966	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
967	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
968	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
969	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
970	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
971	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
972	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
973	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
974	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
975	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
976	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
977	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
978	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
979	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
980	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
981	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
982	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
983	C₂×C₄	#127×C₈₉	1	1	yes	characteristic
984	C₂×C₄	#127×C₈₉	1	1	yes	characteristic
985	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
986	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
987	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
988	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
989	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
990	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
991	C₈	—	2	4	no	—
992	C₈	—	2	4	no	—
993	C₂²	—	4	1	no	—
994	C₂²	—	4	1	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	1	no	—
997	C₂²	—	4	1	no	—
998	C₂²	—	4	1	no	—
999	C₂²	—	4	1	no	—
1000	C₂²	—	4	4	no	—
1001	C₂²	—	4	4	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	8	2	no	—
1006	C₂²	—	8	2	no	—
1007	C₂²	—	8	2	no	—
1008	C₂²	—	8	2	no	—
1009	C₂²	—	8	2	no	—
1010	C₂²	—	8	2	no	—
1011	C₂²	—	8	2	no	—
1012	C₂²	#392×C₈₉	1	1	yes	characteristic
1013	C₂²	#392×C₈₉	1	1	yes	characteristic
1014	C₂²	#392×C₈₉	1	1	yes	characteristic
1015	C₂²	#392×C₈₉	1	1	yes	characteristic
1016	C₂²	C₂×#120×C₈₉	1	1	yes	characteristic
1017	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
1018	C₂²	C₂×#127×C₈₉	1	1	yes	characteristic
1019	C₄	—	4	4	no	—
1020	C₄	—	4	2	no	—
1021	C₄	—	4	2	no	—
1022	C₄	—	4	2	no	—
1023	C₄	—	8	2	no	—
1024	C₄	#392×C₈₉	1	1	yes	characteristic
1025	C₄	#392×C₈₉	1	1	yes	characteristic
1026	C₄	#392×C₈₉	1	1	yes	characteristic
1027	C₄	#392×C₈₉	1	1	yes	characteristic
1028	C₄	C₂×#120×C₈₉	1	1	yes	characteristic
1029	C₄	C₂×#120×C₈₉	1	1	yes	characteristic
1030	C₄	C₂×#121×C₈₉	1	1	yes	characteristic
1031	C₄	C₂×#121×C₈₉	1	1	yes	characteristic
1032	C₂	—	2	1	no	—
1033	C₂	—	2	1	no	—
1034	C₂	—	2	1	no	—
1035	C₂	—	2	1	no	—
1036	C₂	—	2	1	no	—
1037	C₂	—	2	1	no	—
1038	C₂	—	2	1	no	—
1039	C₂	—	8	2	no	—
1040	C₂	—	8	2	no	—
1041	C₂	—	8	2	no	—
1042	C₂	C₂×#392×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈₉	#392
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
socle	C₂×C₈₉	C₂×#392
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈₉ ◁ C₂³×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#575×C₈₉	C₂	semidirect
2. C₂×#575×C₈₉	C₂	semidirect
3. C₈₉×#3449	C₂	semidirect
4. C₂×#421×C₈₉	C₂	semidirect
5. C₈₉×#2896	C₂	semidirect
6. C₂×#410×C₈₉	C₂	semidirect
7. C₈₉×#2009	C₂	semidirect
8. C₈₉×#2008	C₂	semidirect
9. C₂×#344×C₈₉	C₂	semidirect
24. C₂×#137×C₈₉	C₂²	semidirect
28. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
35. #536×C₈₉	C₂²	semidirect
37. #535×C₈₉	C₂²	semidirect
45. #421×C₈₉	C₂²	semidirect
47. #419×C₈₉	C₂²	semidirect
48. #418×C₈₉	C₂²	semidirect
52. #410×C₈₉	C₂²	semidirect
54. #344×C₈₉	C₂²	semidirect
88. C₂×#41×C₈₉	D₄	semidirect
92. C₂²×Q₈×C₈₉	D₄	semidirect
98. C₂²×D₄×C₈₉	D₄	semidirect
139. C₂×M₁₆×C₈₉	D₄	semidirect
140. C₂×M₁₆×C₈₉	D₄	semidirect
141. C₂×M₁₆×C₈₉	D₄	semidirect
145. C₂²×C₈×C₈₉	D₄	semidirect
510. #23412	C₈₉	direct (N × H)
522. C₂×#575	C₂×C₈₉	semidirect
523. C₂×#575	C₂×C₈₉	semidirect
524. #3449	C₂×C₈₉	semidirect
525. C₂×#421	C₂×C₈₉	semidirect
526. #2896	C₂×C₈₉	semidirect
527. C₂×#410	C₂×C₈₉	semidirect
528. #2009	C₂×C₈₉	semidirect
529. #2008	C₂×C₈₉	semidirect
530. C₂×#344	C₂×C₈₉	semidirect
531. C₈₉	#23412	direct (N × H)
546. C₂×#137	C₂²×C₈₉	semidirect
550. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
557. #536	C₂²×C₈₉	semidirect
559. #535	C₂²×C₈₉	semidirect
567. #421	C₂²×C₈₉	semidirect
569. #419	C₂²×C₈₉	semidirect
570. #418	C₂²×C₈₉	semidirect
574. #410	C₂²×C₈₉	semidirect
576. #344	C₂²×C₈₉	semidirect
610. C₂×#41	D₄×C₈₉	semidirect
614. C₂²×Q₈	D₄×C₈₉	semidirect
620. C₂²×D₄	D₄×C₈₉	semidirect
661. C₂×M₁₆	D₄×C₈₉	semidirect
662. C₂×M₁₆	D₄×C₈₉	semidirect
663. C₂×M₁₆	D₄×C₈₉	semidirect
667. C₂²×C₈	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×#575×C₈₉	2
C₈₉×#3449	2
C₂×#421×C₈₉	2
C₈₉×#2896	2
C₂×#410×C₈₉	2
C₈₉×#2009	2
C₈₉×#2008	2
C₂×#344×C₈₉	2
#23412	89

Subgroups — C89×#23412 #36401260

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#23412 #36401260