Subgroups — C₈₉×#60768 #36438616

Order 22784.

2268 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3488	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3203	C₂	1	2	yes	maximal, complemented
3	C₈₉×#3199	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3198	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3191	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3188	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3186	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3098	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3096	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3055	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3050	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#466×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3012	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3008	C₂	1	2	yes	maximal, complemented
15	C₂×#408×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	2	yes	complemented
17	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	complemented
19	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic, complemented
20	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
21	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
22	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
23	#550×C₈₉	—	2	2	no	—
24	#548×C₈₉	—	2	2	no	—
25	#546×C₈₉	—	2	4	no	—
26	#546×C₈₉	—	2	2	no	—
27	D₄²×C₈₉	—	2	4	no	—
28	D₄²×C₈₉	—	2	2	no	—
29	#537×C₈₉	C₂²	1	2	yes	—
30	#537×C₈₉	C₂²	1	4	yes	complemented
31	#535×C₈₉	C₂²	1	2	yes	—
32	#535×C₈₉	C₂²	1	4	yes	complemented
33	#525×C₈₉	C₂²	1	4	yes	complemented
34	#525×C₈₉	C₂²	1	2	yes	complemented
35	C₂×#121×C₈₉	C₂²	1	4	yes	complemented
36	C₂×#121×C₈₉	C₂²	1	2	yes	complemented
37	#520×C₈₉	C₂²	1	2	yes	complemented
38	#485×C₈₉	C₂²	1	4	yes	complemented
39	#484×C₈₉	C₂²	1	4	yes	complemented
40	#482×C₈₉	C₂²	1	4	yes	complemented
41	#482×C₈₉	C₂²	1	4	yes	complemented
42	#482×C₈₉	C₂²	1	4	yes	complemented
43	#481×C₈₉	C₂²	1	4	yes	complemented
44	#480×C₈₉	C₂²	1	4	yes	complemented
45	#480×C₈₉	C₂²	1	4	yes	complemented
46	#469×C₈₉	C₂²	1	4	yes	complemented
47	#468×C₈₉	C₂²	1	4	yes	complemented
48	#467×C₈₉	C₂²	1	1	yes	characteristic, complemented
49	#467×C₈₉	C₂²	1	1	yes	characteristic, complemented
50	#466×C₈₉	C₂²	1	1	yes	characteristic, complemented
51	#466×C₈₉	C₂²	1	4	yes	complemented
52	#466×C₈₉	C₂²	1	2	yes	complemented
53	#466×C₈₉	C₂²	1	2	yes	complemented
54	#466×C₈₉	C₂²	1	2	yes	complemented
55	#466×C₈₉	C₂²	1	1	yes	characteristic, complemented
56	#466×C₈₉	C₂²	1	2	yes	complemented
57	#465×C₈₉	C₂²	1	2	yes	complemented
58	#465×C₈₉	C₂²	1	4	yes	complemented
59	#465×C₈₉	C₂²	1	2	yes	complemented
60	#452×C₈₉	C₂²	1	4	yes	complemented
61	#450×C₈₉	C₂²	1	4	yes	complemented
62	#449×C₈₉	C₂²	1	4	yes	complemented
63	#449×C₈₉	C₂²	1	4	yes	complemented
64	#449×C₈₉	C₂²	1	4	yes	complemented
65	#447×C₈₉	C₂²	1	4	yes	complemented
66	#447×C₈₉	C₂²	1	4	yes	complemented
67	#447×C₈₉	C₂²	1	4	yes	complemented
68	#428×C₈₉	C₂²	1	2	yes	complemented
69	#427×C₈₉	C₂²	1	1	yes	characteristic, complemented
70	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic, complemented
71	#418×C₈₉	C₂²	1	2	yes	complemented
72	#417×C₈₉	C₂²	1	2	yes	complemented
73	#416×C₈₉	C₂²	1	2	yes	complemented
74	C₂×#102×C₈₉	C₂²	1	2	yes	complemented
75	#408×C₈₉	C₂²	1	2	yes	complemented
76	#408×C₈₉	C₂²	1	2	yes	complemented
77	#408×C₈₉	C₂²	1	2	yes	complemented
78	#408×C₈₉	C₂²	1	2	yes	complemented
79	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	complemented
80	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	complemented
81	H(5,𝔽₂)×C₈₉	—	4	4	no	—
82	H(5,𝔽₂)×C₈₉	—	4	4	no	—
83	C₂×#41×C₈₉	—	2	2	no	—
84	C₂×#41×C₈₉	—	4	2	no	—
85	C₂×#41×C₈₉	—	4	2	no	—
86	C₂×#41×C₈₉	D₄	1	2	yes	—
87	C₂×#41×C₈₉	D₄	1	2	yes	—
88	C₂×#41×C₈₉	C₂³	1	2	yes	—
89	C₂×#41×C₈₉	C₂³	1	4	yes	—
90	C₂×#41×C₈₉	C₂³	1	2	yes	—
91	C₂×#41×C₈₉	C₂³	1	2	yes	—
92	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
93	C₂²×D₄×C₈₉	—	2	2	no	—
94	C₂²×D₄×C₈₉	—	2	4	no	—
95	C₂²×D₄×C₈₉	—	2	4	no	—
96	C₂²×D₄×C₈₉	—	2	2	no	—
97	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
98	C₂²×D₄×C₈₉	D₄	1	2	yes	—
99	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
100	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
101	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
103	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
104	#135×C₈₉	—	4	2	no	—
105	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
106	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
107	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
108	C₂×D₈×C₈₉	—	4	2	no	—
109	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×D₈×C₈₉	C₂³	1	4	yes	—
111	C₂×D₈×C₈₉	C₂³	1	2	yes	—
112	C₂×D₈×C₈₉	C₂³	1	2	yes	—
113	C₂×M₁₆×C₈₉	—	4	2	no	—
114	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
115	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
116	C₂²×C₈×C₈₉	—	4	2	no	—
117	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
121	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
123	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
124	#127×C₈₉	—	2	2	no	—
125	#127×C₈₉	—	2	4	no	—
126	#124×C₈₉	—	2	2	no	—
127	#124×C₈₉	—	2	4	no	—
128	#123×C₈₉	—	2	2	no	—
129	#123×C₈₉	—	2	4	no	—
130	C₂²⋊Q₈×C₈₉	—	2	2	no	—
131	C₂²⋊Q₈×C₈₉	—	2	4	no	—
132	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
133	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
134	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
135	#121×C₈₉	—	2	4	no	—
136	#121×C₈₉	—	2	2	no	—
137	#121×C₈₉	—	2	4	no	—
138	#121×C₈₉	—	2	4	no	—
139	#121×C₈₉	—	2	4	no	—
140	#121×C₈₉	—	2	2	no	—
141	#121×C₈₉	—	2	4	no	—
142	#121×C₈₉	—	2	2	no	—
143	#121×C₈₉	—	2	4	no	—
144	#121×C₈₉	C₂³	1	4	yes	—
145	#121×C₈₉	C₂³	1	4	yes	—
146	#121×C₈₉	C₂³	1	4	yes	—
147	#121×C₈₉	C₂³	1	2	yes	—
148	#121×C₈₉	C₂³	1	4	yes	—
149	#121×C₈₉	C₂³	1	2	yes	—
150	#121×C₈₉	C₂³	1	4	yes	—
151	#120×C₈₉	—	2	2	no	—
152	#120×C₈₉	—	2	4	no	—
153	#120×C₈₉	—	2	4	no	—
154	#120×C₈₉	—	2	4	no	—
155	#120×C₈₉	—	2	4	no	—
156	C₄×Q₈×C₈₉	—	2	2	no	—
157	C₄×D₄×C₈₉	—	2	4	no	—
158	C₄×D₄×C₈₉	—	2	2	no	—
159	C₄×D₄×C₈₉	—	2	2	no	—
160	C₄×D₄×C₈₉	—	2	4	no	—
161	C₄×D₄×C₈₉	—	2	2	no	—
162	C₄×D₄×C₈₉	—	2	4	no	—
163	#117×C₈₉	C₂³	1	2	yes	—
164	#117×C₈₉	C₂³	1	4	yes	—
165	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
167	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
168	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
169	#107×C₈₉	C₂³	1	2	yes	—
170	#107×C₈₉	C₂³	1	2	yes	—
171	#107×C₈₉	C₂³	1	1	yes	characteristic
172	#107×C₈₉	C₂³	1	1	yes	characteristic
173	#107×C₈₉	C₂³	1	4	yes	—
174	#106×C₈₉	C₂³	1	2	yes	—
175	#106×C₈₉	C₂³	1	4	yes	—
176	#103×C₈₉	C₂³	1	2	yes	—
177	#103×C₈₉	C₂³	1	2	yes	—
178	#103×C₈₉	C₂³	1	4	yes	—
179	#102×C₈₉	C₂³	1	4	yes	—
180	#102×C₈₉	C₂³	1	4	yes	—
181	#102×C₈₉	C₂³	1	2	yes	—
182	#102×C₈₉	C₂³	1	2	yes	—
183	#102×C₈₉	C₂³	1	4	yes	—
184	#102×C₈₉	C₂³	1	4	yes	—
185	#102×C₈₉	C₂³	1	4	yes	—
186	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
187	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
188	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
189	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
190	C₂⁴×C₈₉	—	2	4	no	—
191	C₂⁴×C₈₉	—	2	2	no	—
192	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
193	C₂⁴×C₈₉	C₂×D₄	1	2	yes	—
194	#41×C₈₉	—	2	4	no	—
195	#41×C₈₉	—	2	4	no	—
196	#41×C₈₉	—	2	4	no	—
197	#41×C₈₉	—	2	4	no	—
198	#41×C₈₉	—	4	2	no	—
199	#41×C₈₉	—	4	2	no	—
200	#41×C₈₉	—	4	4	no	—
201	#41×C₈₉	—	4	4	no	—
202	#41×C₈₉	—	4	4	no	—
203	#41×C₈₉	—	4	4	no	—
204	#41×C₈₉	—	4	8	no	—
205	C₂×Q₈×C₈₉	—	4	2	no	—
206	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
207	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
208	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
209	C₂×D₄×C₈₉	—	2	2	no	—
210	C₂×D₄×C₈₉	—	2	4	no	—
211	C₂×D₄×C₈₉	—	2	4	no	—
212	C₂×D₄×C₈₉	—	2	2	no	—
213	C₂×D₄×C₈₉	—	2	4	no	—
214	C₂×D₄×C₈₉	—	2	2	no	—
215	C₂×D₄×C₈₉	—	2	4	no	—
216	C₂×D₄×C₈₉	—	2	4	no	—
217	C₂×D₄×C₈₉	—	2	4	no	—
218	C₂×D₄×C₈₉	—	2	4	no	—
219	C₂×D₄×C₈₉	—	2	2	no	—
220	C₂×D₄×C₈₉	—	2	4	no	—
221	C₂×D₄×C₈₉	—	2	4	no	—
222	C₂×D₄×C₈₉	—	4	2	no	—
223	C₂×D₄×C₈₉	—	4	4	no	—
224	C₂×D₄×C₈₉	—	4	4	no	—
225	C₂×D₄×C₈₉	—	4	4	no	—
226	C₂×D₄×C₈₉	—	4	16	no	—
227	C₂×D₄×C₈₉	—	4	8	no	—
228	C₂×D₄×C₈₉	—	8	4	no	—
229	C₂×D₄×C₈₉	—	8	8	no	—
230	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
231	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
232	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
233	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
234	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
235	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₈₉	—	2	2	no	—
237	C₂²×C₄×C₈₉	—	2	2	no	—
238	C₂²×C₄×C₈₉	—	2	4	no	—
239	C₂²×C₄×C₈₉	—	2	2	no	—
240	C₂²×C₄×C₈₉	—	2	4	no	—
241	C₂²×C₄×C₈₉	—	2	2	no	—
242	C₂²×C₄×C₈₉	—	4	2	no	—
243	C₂²×C₄×C₈₉	—	4	2	no	—
244	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
248	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
249	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
250	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
253	Q₁₆×C₈₉	—	4	1	no	—
254	SD₁₆×C₈₉	—	4	2	no	—
255	SD₁₆×C₈₉	—	4	4	no	—
256	D₈×C₈₉	—	4	2	no	—
257	D₈×C₈₉	—	4	2	no	—
258	D₈×C₈₉	—	4	1	no	—
259	D₈×C₈₉	—	4	4	no	—
260	M₁₆×C₈₉	—	2	4	no	—
261	M₁₆×C₈₉	—	4	2	no	—
262	C₂×C₈×C₈₉	—	2	2	no	—
263	C₂×C₈×C₈₉	—	2	2	no	—
264	C₂×C₈×C₈₉	—	4	1	no	—
265	C₂×C₈×C₈₉	—	4	1	no	—
266	C₂×C₈×C₈₉	—	4	1	no	—
267	C₂×C₈×C₈₉	—	4	1	no	—
268	C₂×C₈×C₈₉	—	4	2	no	—
269	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
270	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
271	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
272	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
273	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
274	C₄⋊C₄×C₈₉	—	2	4	no	—
275	C₄⋊C₄×C₈₉	—	2	2	no	—
276	C₄⋊C₄×C₈₉	—	2	2	no	—
277	C₄⋊C₄×C₈₉	—	2	4	no	—
278	C₄⋊C₄×C₈₉	—	2	2	no	—
279	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
281	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
282	C₂²⋊C₄×C₈₉	—	2	4	no	—
283	C₂²⋊C₄×C₈₉	—	2	2	no	—
284	C₂²⋊C₄×C₈₉	—	2	2	no	—
285	C₂²⋊C₄×C₈₉	—	2	4	no	—
286	C₂²⋊C₄×C₈₉	—	2	2	no	—
287	C₂²⋊C₄×C₈₉	—	2	4	no	—
288	C₂²⋊C₄×C₈₉	—	2	2	no	—
289	C₂²⋊C₄×C₈₉	—	2	4	no	—
290	C₂²⋊C₄×C₈₉	—	2	4	no	—
291	C₂²⋊C₄×C₈₉	—	2	4	no	—
292	C₂²⋊C₄×C₈₉	—	2	4	no	—
293	C₂²⋊C₄×C₈₉	—	2	2	no	—
294	C₄²×C₈₉	—	2	4	no	—
295	C₄²×C₈₉	—	2	2	no	—
296	C₂³×C₈₉	—	2	2	no	—
297	C₂³×C₈₉	—	2	2	no	—
298	C₂³×C₈₉	—	2	4	no	—
299	C₂³×C₈₉	—	2	4	no	—
300	C₂³×C₈₉	—	2	2	no	—
301	C₂³×C₈₉	—	4	1	no	—
302	C₂³×C₈₉	—	4	2	no	—
303	C₂³×C₈₉	—	4	2	no	—
304	C₂³×C₈₉	—	4	8	no	—
305	C₂³×C₈₉	—	4	4	no	—
306	C₂³×C₈₉	—	8	2	no	—
307	C₂³×C₈₉	—	8	4	no	—
308	C₂³×C₈₉	—	8	2	no	—
309	C₂³×C₈₉	—	8	4	no	—
310	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
311	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
312	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
313	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
314	Q₈×C₈₉	—	2	4	no	—
315	Q₈×C₈₉	—	2	2	no	—
316	Q₈×C₈₉	—	2	2	no	—
317	Q₈×C₈₉	—	4	2	no	—
318	D₄×C₈₉	—	2	8	no	—
319	D₄×C₈₉	—	2	4	no	—
320	D₄×C₈₉	—	2	4	no	—
321	D₄×C₈₉	—	2	2	no	—
322	D₄×C₈₉	—	2	4	no	—
323	D₄×C₈₉	—	2	2	no	—
324	D₄×C₈₉	—	4	2	no	—
325	D₄×C₈₉	—	4	4	no	—
326	D₄×C₈₉	—	4	8	no	—
327	D₄×C₈₉	—	4	8	no	—
328	D₄×C₈₉	—	4	4	no	—
329	D₄×C₈₉	—	4	8	no	—
330	D₄×C₈₉	—	4	4	no	—
331	D₄×C₈₉	—	4	4	no	—
332	D₄×C₈₉	—	8	2	no	—
333	D₄×C₈₉	—	8	4	no	—
334	D₄×C₈₉	—	8	4	no	—
335	D₄×C₈₉	—	8	4	no	—
336	D₄×C₈₉	—	8	4	no	—
337	C₂×C₄×C₈₉	—	2	2	no	—
338	C₂×C₄×C₈₉	—	2	2	no	—
339	C₂×C₄×C₈₉	—	2	2	no	—
340	C₂×C₄×C₈₉	—	2	1	no	—
341	C₂×C₄×C₈₉	—	2	1	no	—
342	C₂×C₄×C₈₉	—	2	1	no	—
343	C₂×C₄×C₈₉	—	2	1	no	—
344	C₂×C₄×C₈₉	—	2	4	no	—
345	C₂×C₄×C₈₉	—	2	4	no	—
346	C₂×C₄×C₈₉	—	2	2	no	—
347	C₂×C₄×C₈₉	—	2	4	no	—
348	C₂×C₄×C₈₉	—	2	2	no	—
349	C₂×C₄×C₈₉	—	2	2	no	—
350	C₂×C₄×C₈₉	—	4	2	no	—
351	C₂×C₄×C₈₉	—	4	4	no	—
352	C₂×C₄×C₈₉	—	4	8	no	—
353	C₂×C₄×C₈₉	—	4	4	no	—
354	C₂×C₄×C₈₉	—	8	2	no	—
355	C₂×C₄×C₈₉	—	8	4	no	—
356	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
357	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
361	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
362	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
363	C₈×C₈₉	—	2	1	no	—
364	C₈×C₈₉	—	2	1	no	—
365	C₈×C₈₉	—	2	1	no	—
366	C₈×C₈₉	—	2	1	no	—
367	C₈×C₈₉	—	2	4	no	—
368	C₂²×C₈₉	—	2	1	no	—
369	C₂²×C₈₉	—	2	1	no	—
370	C₂²×C₈₉	—	2	1	no	—
371	C₂²×C₈₉	—	2	1	no	—
372	C₂²×C₈₉	—	2	1	no	—
373	C₂²×C₈₉	—	2	4	no	—
374	C₂²×C₈₉	—	2	1	no	—
375	C₂²×C₈₉	—	2	4	no	—
376	C₂²×C₈₉	—	2	4	no	—
377	C₂²×C₈₉	—	2	1	no	—
378	C₂²×C₈₉	—	4	4	no	—
379	C₂²×C₈₉	—	4	4	no	—
380	C₂²×C₈₉	—	4	2	no	—
381	C₂²×C₈₉	—	4	4	no	—
382	C₂²×C₈₉	—	4	2	no	—
383	C₂²×C₈₉	—	4	4	no	—
384	C₂²×C₈₉	—	4	2	no	—
385	C₂²×C₈₉	—	8	4	no	—
386	C₂²×C₈₉	—	16	4	no	—
387	C₂²×C₈₉	—	16	8	no	—
388	C₂²×C₈₉	#534	1	2	yes	—
389	C₂²×C₈₉	#576	1	2	yes	—
390	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
391	C₄×C₈₉	—	2	1	no	—
392	C₄×C₈₉	—	2	1	no	—
393	C₄×C₈₉	—	2	4	no	—
394	C₄×C₈₉	—	4	2	no	—
395	C₄×C₈₉	—	4	2	no	—
396	C₄×C₈₉	—	4	4	no	—
397	C₄×C₈₉	—	4	2	no	—
398	C₄×C₈₉	#534	1	2	yes	—
399	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
400	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
401	#60768	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
402	C₂×C₈₉	—	2	2	no	—
403	C₂×C₈₉	—	2	2	no	—
404	C₂×C₈₉	—	4	1	no	—
405	C₂×C₈₉	—	4	4	no	—
406	C₂×C₈₉	—	8	4	no	—
407	C₂×C₈₉	—	8	2	no	—
408	C₂×C₈₉	C₂×#534	1	1	yes	characteristic
409	C₂×C₈₉	C₂×#576	1	1	yes	characteristic
410	C₂×C₈₉	#3584	1	1	yes	characteristic
411	#3488	C₂×C₈₉	1	2	yes	complemented
412	#3203	C₂×C₈₉	1	2	yes	complemented
413	#3199	C₂×C₈₉	1	2	yes	complemented
414	#3198	C₂×C₈₉	1	4	yes	complemented
415	#3191	C₂×C₈₉	1	2	yes	complemented
416	#3188	C₂×C₈₉	1	4	yes	complemented
417	#3186	C₂×C₈₉	1	2	yes	complemented
418	#3098	C₂×C₈₉	1	2	yes	complemented
419	#3096	C₂×C₈₉	1	2	yes	complemented
420	#3055	C₂×C₈₉	1	2	yes	complemented
421	#3050	C₂×C₈₉	1	1	yes	characteristic, complemented
422	C₂×#466	C₂×C₈₉	1	1	yes	characteristic, complemented
423	#3012	C₂×C₈₉	1	2	yes	complemented
424	#3008	C₂×C₈₉	1	2	yes	complemented
425	C₂×#408	C₂×C₈₉	1	1	yes	characteristic, complemented
426	C₈₉	#60768	1	1	yes	characteristic, direct product factor, Sylow
427	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	2	yes	complemented
428	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
429	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	complemented
430	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic, complemented
431	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
432	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
433	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
434	#550	—	2	2	no	—
435	#548	—	2	2	no	—
436	#546	—	2	4	no	—
437	#546	—	2	2	no	—
438	D₄²	—	2	4	no	—
439	D₄²	—	2	2	no	—
440	#537	C₂²×C₈₉	1	2	yes	—
441	#537	C₂²×C₈₉	1	4	yes	complemented
442	#535	C₂²×C₈₉	1	2	yes	—
443	#535	C₂²×C₈₉	1	4	yes	complemented
444	#525	C₂²×C₈₉	1	4	yes	complemented
445	#525	C₂²×C₈₉	1	2	yes	complemented
446	C₂×#121	C₂²×C₈₉	1	4	yes	complemented
447	C₂×#121	C₂²×C₈₉	1	2	yes	complemented
448	#520	C₂²×C₈₉	1	2	yes	complemented
449	#485	C₂²×C₈₉	1	4	yes	complemented
450	#484	C₂²×C₈₉	1	4	yes	complemented
451	#482	C₂²×C₈₉	1	4	yes	complemented
452	#482	C₂²×C₈₉	1	4	yes	complemented
453	#482	C₂²×C₈₉	1	4	yes	complemented
454	#481	C₂²×C₈₉	1	4	yes	complemented
455	#480	C₂²×C₈₉	1	4	yes	complemented
456	#480	C₂²×C₈₉	1	4	yes	complemented
457	#469	C₂²×C₈₉	1	4	yes	complemented
458	#468	C₂²×C₈₉	1	4	yes	complemented
459	#467	C₂²×C₈₉	1	1	yes	characteristic, complemented
460	#467	C₂²×C₈₉	1	1	yes	characteristic, complemented
461	#466	C₂²×C₈₉	1	1	yes	characteristic, complemented
462	#466	C₂²×C₈₉	1	4	yes	complemented
463	#466	C₂²×C₈₉	1	2	yes	complemented
464	#466	C₂²×C₈₉	1	2	yes	complemented
465	#466	C₂²×C₈₉	1	2	yes	complemented
466	#466	C₂²×C₈₉	1	1	yes	characteristic, complemented
467	#466	C₂²×C₈₉	1	2	yes	complemented
468	#465	C₂²×C₈₉	1	2	yes	complemented
469	#465	C₂²×C₈₉	1	4	yes	complemented
470	#465	C₂²×C₈₉	1	2	yes	complemented
471	#452	C₂²×C₈₉	1	4	yes	complemented
472	#450	C₂²×C₈₉	1	4	yes	complemented
473	#449	C₂²×C₈₉	1	4	yes	complemented
474	#449	C₂²×C₈₉	1	4	yes	complemented
475	#449	C₂²×C₈₉	1	4	yes	complemented
476	#447	C₂²×C₈₉	1	4	yes	complemented
477	#447	C₂²×C₈₉	1	4	yes	complemented
478	#447	C₂²×C₈₉	1	4	yes	complemented
479	#428	C₂²×C₈₉	1	2	yes	complemented
480	#427	C₂²×C₈₉	1	1	yes	characteristic, complemented
481	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic, complemented
482	#418	C₂²×C₈₉	1	2	yes	complemented
483	#417	C₂²×C₈₉	1	2	yes	complemented
484	#416	C₂²×C₈₉	1	2	yes	complemented
485	C₂×#102	C₂²×C₈₉	1	2	yes	complemented
486	#408	C₂²×C₈₉	1	2	yes	complemented
487	#408	C₂²×C₈₉	1	2	yes	complemented
488	#408	C₂²×C₈₉	1	2	yes	complemented
489	#408	C₂²×C₈₉	1	2	yes	complemented
490	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	complemented
491	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	complemented
492	H(5,𝔽₂)	—	4	4	no	—
493	H(5,𝔽₂)	—	4	4	no	—
494	C₂×#41	—	2	2	no	—
495	C₂×#41	—	4	2	no	—
496	C₂×#41	—	4	2	no	—
497	C₂×#41	D₄×C₈₉	1	2	yes	—
498	C₂×#41	D₄×C₈₉	1	2	yes	—
499	C₂×#41	C₂³×C₈₉	1	2	yes	—
500	C₂×#41	C₂³×C₈₉	1	4	yes	—
501	C₂×#41	C₂³×C₈₉	1	2	yes	—
502	C₂×#41	C₂³×C₈₉	1	2	yes	—
503	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
504	C₂²×D₄	—	2	2	no	—
505	C₂²×D₄	—	2	4	no	—
506	C₂²×D₄	—	2	4	no	—
507	C₂²×D₄	—	2	2	no	—
508	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
509	C₂²×D₄	D₄×C₈₉	1	2	yes	—
510	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
511	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
512	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
514	AGL(1,ℤ/8)	—	4	4	no	—
515	#135	—	4	2	no	—
516	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
517	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
518	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
519	C₂×D₈	—	4	2	no	—
520	C₂×D₈	C₂³×C₈₉	1	2	yes	—
521	C₂×D₈	C₂³×C₈₉	1	2	yes	—
522	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
523	C₂×D₈	C₂³×C₈₉	1	4	yes	—
524	C₂×M₁₆	—	4	2	no	—
525	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
526	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
527	C₂²×C₈	—	4	2	no	—
528	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
529	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
530	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
531	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
532	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
533	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
534	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
535	#127	—	2	2	no	—
536	#127	—	2	4	no	—
537	#124	—	2	2	no	—
538	#124	—	2	4	no	—
539	#123	—	2	2	no	—
540	#123	—	2	4	no	—
541	C₂²⋊Q₈	—	2	2	no	—
542	C₂²⋊Q₈	—	2	4	no	—
543	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
544	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
545	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
546	#121	—	2	4	no	—
547	#121	—	2	2	no	—
548	#121	—	2	4	no	—
549	#121	—	2	4	no	—
550	#121	—	2	4	no	—
551	#121	—	2	2	no	—
552	#121	—	2	4	no	—
553	#121	—	2	2	no	—
554	#121	—	2	4	no	—
555	#121	C₂³×C₈₉	1	2	yes	—
556	#121	C₂³×C₈₉	1	4	yes	—
557	#121	C₂³×C₈₉	1	4	yes	—
558	#121	C₂³×C₈₉	1	4	yes	—
559	#121	C₂³×C₈₉	1	4	yes	—
560	#121	C₂³×C₈₉	1	4	yes	—
561	#121	C₂³×C₈₉	1	2	yes	—
562	#120	—	2	2	no	—
563	#120	—	2	4	no	—
564	#120	—	2	4	no	—
565	#120	—	2	4	no	—
566	#120	—	2	4	no	—
567	C₄×Q₈	—	2	2	no	—
568	C₄×D₄	—	2	4	no	—
569	C₄×D₄	—	2	2	no	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	—	2	4	no	—
572	C₄×D₄	—	2	2	no	—
573	C₄×D₄	—	2	4	no	—
574	#117	C₂³×C₈₉	1	2	yes	—
575	#117	C₂³×C₈₉	1	4	yes	—
576	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
578	C₂×C₂²⋊C₄	—	2	2	no	—
579	C₂×C₂²⋊C₄	—	2	4	no	—
580	#107	C₂³×C₈₉	1	2	yes	—
581	#107	C₂³×C₈₉	1	2	yes	—
582	#107	C₂³×C₈₉	1	1	yes	characteristic
583	#107	C₂³×C₈₉	1	1	yes	characteristic
584	#107	C₂³×C₈₉	1	4	yes	—
585	#106	C₂³×C₈₉	1	2	yes	—
586	#106	C₂³×C₈₉	1	4	yes	—
587	#103	C₂³×C₈₉	1	2	yes	—
588	#103	C₂³×C₈₉	1	2	yes	—
589	#103	C₂³×C₈₉	1	4	yes	—
590	#102	C₂³×C₈₉	1	4	yes	—
591	#102	C₂³×C₈₉	1	4	yes	—
592	#102	C₂³×C₈₉	1	2	yes	—
593	#102	C₂³×C₈₉	1	2	yes	—
594	#102	C₂³×C₈₉	1	4	yes	—
595	#102	C₂³×C₈₉	1	4	yes	—
596	#102	C₂³×C₈₉	1	4	yes	—
597	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
598	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
599	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
600	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
601	C₂⁴	—	2	4	no	—
602	C₂⁴	—	2	2	no	—
603	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
604	C₂⁴	C₂×D₄×C₈₉	1	2	yes	—
605	#41	—	2	4	no	—
606	#41	—	2	4	no	—
607	#41	—	2	4	no	—
608	#41	—	2	4	no	—
609	#41	—	4	2	no	—
610	#41	—	4	2	no	—
611	#41	—	4	4	no	—
612	#41	—	4	4	no	—
613	#41	—	4	4	no	—
614	#41	—	4	4	no	—
615	#41	—	4	8	no	—
616	C₂×Q₈	—	4	2	no	—
617	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
618	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
619	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
620	C₂×D₄	—	2	2	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	2	4	no	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	4	2	no	—
634	C₂×D₄	—	4	4	no	—
635	C₂×D₄	—	4	4	no	—
636	C₂×D₄	—	4	4	no	—
637	C₂×D₄	—	4	16	no	—
638	C₂×D₄	—	4	8	no	—
639	C₂×D₄	—	8	4	no	—
640	C₂×D₄	—	8	8	no	—
641	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
642	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
643	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
644	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
645	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
646	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	4	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
659	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
661	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
662	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
664	Q₁₆	—	4	1	no	—
665	SD₁₆	—	4	2	no	—
666	SD₁₆	—	4	4	no	—
667	D₈	—	4	2	no	—
668	D₈	—	4	2	no	—
669	D₈	—	4	1	no	—
670	D₈	—	4	4	no	—
671	M₁₆	—	2	4	no	—
672	M₁₆	—	4	2	no	—
673	C₂×C₈	—	2	2	no	—
674	C₂×C₈	—	2	2	no	—
675	C₂×C₈	—	4	1	no	—
676	C₂×C₈	—	4	1	no	—
677	C₂×C₈	—	4	1	no	—
678	C₂×C₈	—	4	1	no	—
679	C₂×C₈	—	4	2	no	—
680	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
681	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
682	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
683	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
684	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
691	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
692	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₄²	—	2	4	no	—
706	C₄²	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	4	no	—
710	C₂³	—	2	4	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	4	1	no	—
713	C₂³	—	4	2	no	—
714	C₂³	—	4	2	no	—
715	C₂³	—	4	8	no	—
716	C₂³	—	4	4	no	—
717	C₂³	—	8	2	no	—
718	C₂³	—	8	4	no	—
719	C₂³	—	8	2	no	—
720	C₂³	—	8	4	no	—
721	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
722	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
723	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
724	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
725	Q₈	—	2	4	no	—
726	Q₈	—	2	2	no	—
727	Q₈	—	2	2	no	—
728	Q₈	—	4	2	no	—
729	D₄	—	2	8	no	—
730	D₄	—	2	4	no	—
731	D₄	—	2	4	no	—
732	D₄	—	2	2	no	—
733	D₄	—	2	4	no	—
734	D₄	—	2	2	no	—
735	D₄	—	4	2	no	—
736	D₄	—	4	4	no	—
737	D₄	—	4	8	no	—
738	D₄	—	4	8	no	—
739	D₄	—	4	4	no	—
740	D₄	—	4	8	no	—
741	D₄	—	4	4	no	—
742	D₄	—	4	4	no	—
743	D₄	—	8	2	no	—
744	D₄	—	8	4	no	—
745	D₄	—	8	4	no	—
746	D₄	—	8	4	no	—
747	D₄	—	8	4	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	4	no	—
756	C₂×C₄	—	2	4	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	4	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	4	2	no	—
762	C₂×C₄	—	4	4	no	—
763	C₂×C₄	—	4	8	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	8	2	no	—
766	C₂×C₄	—	8	4	no	—
767	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
768	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
769	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
770	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
771	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
772	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
773	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
774	C₈	—	2	1	no	—
775	C₈	—	2	1	no	—
776	C₈	—	2	1	no	—
777	C₈	—	2	1	no	—
778	C₈	—	2	4	no	—
779	C₂²	—	2	1	no	—
780	C₂²	—	2	1	no	—
781	C₂²	—	2	1	no	—
782	C₂²	—	2	1	no	—
783	C₂²	—	2	4	no	—
784	C₂²	—	2	1	no	—
785	C₂²	—	2	1	no	—
786	C₂²	—	2	4	no	—
787	C₂²	—	2	1	no	—
788	C₂²	—	2	4	no	—
789	C₂²	—	4	4	no	—
790	C₂²	—	4	4	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	4	4	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	4	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	8	4	no	—
797	C₂²	—	16	4	no	—
798	C₂²	—	16	8	no	—
799	C₂²	#534×C₈₉	1	2	yes	—
800	C₂²	#576×C₈₉	1	2	yes	—
801	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
802	C₄	—	2	1	no	—
803	C₄	—	2	1	no	—
804	C₄	—	2	4	no	—
805	C₄	—	4	4	no	—
806	C₄	—	4	2	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	#534×C₈₉	1	2	yes	—
810	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
811	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
812	C₂	—	2	2	no	—
813	C₂	—	2	2	no	—
814	C₂	—	4	1	no	—
815	C₂	—	4	4	no	—
816	C₂	—	8	4	no	—
817	C₂	—	8	2	no	—
818	C₂	C₂×#534×C₈₉	1	1	yes	characteristic
819	C₂	C₂×#576×C₈₉	1	1	yes	characteristic
820	C₂	C₈₉×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂²×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3488	C₂	semidirect
2. C₈₉×#3203	C₂	semidirect
3. C₈₉×#3199	C₂	semidirect
4. C₈₉×#3198	C₂	semidirect
5. C₈₉×#3191	C₂	semidirect
6. C₈₉×#3188	C₂	semidirect
7. C₈₉×#3186	C₂	semidirect
8. C₈₉×#3098	C₂	semidirect
9. C₈₉×#3096	C₂	semidirect
10. C₈₉×#3055	C₂	semidirect
11. C₈₉×#3050	C₂	semidirect
12. C₂×#466×C₈₉	C₂	semidirect
13. C₈₉×#3012	C₂	semidirect
14. C₈₉×#3008	C₂	semidirect
15. C₂×#408×C₈₉	C₂	semidirect
16. C₂×H(5,𝔽₂)×C₈₉	C₂²	semidirect
18. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
19. C₂×#135×C₈₉	C₂²	semidirect
20. C₂²×D₈×C₈₉	C₂²	semidirect
21. C₂²×M₁₆×C₈₉	C₂²	semidirect
22. C₂³×C₈×C₈₉	C₂²	semidirect
30. #537×C₈₉	C₂²	semidirect
32. #535×C₈₉	C₂²	semidirect
33. #525×C₈₉	C₂²	semidirect
34. #525×C₈₉	C₂²	semidirect
35. C₂×#121×C₈₉	C₂²	semidirect
36. C₂×#121×C₈₉	C₂²	semidirect
37. #520×C₈₉	C₂²	semidirect
38. #485×C₈₉	C₂²	semidirect
39. #484×C₈₉	C₂²	semidirect
40. #482×C₈₉	C₂²	semidirect
41. #482×C₈₉	C₂²	semidirect
42. #482×C₈₉	C₂²	semidirect
43. #481×C₈₉	C₂²	semidirect
44. #480×C₈₉	C₂²	semidirect
45. #480×C₈₉	C₂²	semidirect
46. #469×C₈₉	C₂²	semidirect
47. #468×C₈₉	C₂²	semidirect
48. #467×C₈₉	C₂²	semidirect
49. #467×C₈₉	C₂²	semidirect
50. #466×C₈₉	C₂²	semidirect
51. #466×C₈₉	C₂²	semidirect
52. #466×C₈₉	C₂²	semidirect
53. #466×C₈₉	C₂²	semidirect
54. #466×C₈₉	C₂²	semidirect
55. #466×C₈₉	C₂²	semidirect
56. #466×C₈₉	C₂²	semidirect
57. #465×C₈₉	C₂²	semidirect
58. #465×C₈₉	C₂²	semidirect
59. #465×C₈₉	C₂²	semidirect
60. #452×C₈₉	C₂²	semidirect
61. #450×C₈₉	C₂²	semidirect
62. #449×C₈₉	C₂²	semidirect
63. #449×C₈₉	C₂²	semidirect
64. #449×C₈₉	C₂²	semidirect
65. #447×C₈₉	C₂²	semidirect
66. #447×C₈₉	C₂²	semidirect
67. #447×C₈₉	C₂²	semidirect
68. #428×C₈₉	C₂²	semidirect
69. #427×C₈₉	C₂²	semidirect
70. C₂×#107×C₈₉	C₂²	semidirect
71. #418×C₈₉	C₂²	semidirect
72. #417×C₈₉	C₂²	semidirect
73. #416×C₈₉	C₂²	semidirect
74. C₂×#102×C₈₉	C₂²	semidirect
75. #408×C₈₉	C₂²	semidirect
76. #408×C₈₉	C₂²	semidirect
77. #408×C₈₉	C₂²	semidirect
78. #408×C₈₉	C₂²	semidirect
79. C₂×C₂²⋊C₈×C₈₉	C₂²	semidirect
80. C₂×C₂²⋊C₈×C₈₉	C₂²	semidirect
401. #60768	C₈₉	direct (N × H)
411. #3488	C₂×C₈₉	semidirect
412. #3203	C₂×C₈₉	semidirect
413. #3199	C₂×C₈₉	semidirect
414. #3198	C₂×C₈₉	semidirect
415. #3191	C₂×C₈₉	semidirect
416. #3188	C₂×C₈₉	semidirect
417. #3186	C₂×C₈₉	semidirect
418. #3098	C₂×C₈₉	semidirect
419. #3096	C₂×C₈₉	semidirect
420. #3055	C₂×C₈₉	semidirect
421. #3050	C₂×C₈₉	semidirect
422. C₂×#466	C₂×C₈₉	semidirect
423. #3012	C₂×C₈₉	semidirect
424. #3008	C₂×C₈₉	semidirect
425. C₂×#408	C₂×C₈₉	semidirect
426. C₈₉	#60768	direct (N × H)
427. C₂×H(5,𝔽₂)	C₂²×C₈₉	semidirect
429. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
430. C₂×#135	C₂²×C₈₉	semidirect
431. C₂²×D₈	C₂²×C₈₉	semidirect
432. C₂²×M₁₆	C₂²×C₈₉	semidirect
433. C₂³×C₈	C₂²×C₈₉	semidirect
441. #537	C₂²×C₈₉	semidirect
443. #535	C₂²×C₈₉	semidirect
444. #525	C₂²×C₈₉	semidirect
445. #525	C₂²×C₈₉	semidirect
446. C₂×#121	C₂²×C₈₉	semidirect
447. C₂×#121	C₂²×C₈₉	semidirect
448. #520	C₂²×C₈₉	semidirect
449. #485	C₂²×C₈₉	semidirect
450. #484	C₂²×C₈₉	semidirect
451. #482	C₂²×C₈₉	semidirect
452. #482	C₂²×C₈₉	semidirect
453. #482	C₂²×C₈₉	semidirect
454. #481	C₂²×C₈₉	semidirect
455. #480	C₂²×C₈₉	semidirect
456. #480	C₂²×C₈₉	semidirect
457. #469	C₂²×C₈₉	semidirect
458. #468	C₂²×C₈₉	semidirect
459. #467	C₂²×C₈₉	semidirect
460. #467	C₂²×C₈₉	semidirect
461. #466	C₂²×C₈₉	semidirect
462. #466	C₂²×C₈₉	semidirect
463. #466	C₂²×C₈₉	semidirect
464. #466	C₂²×C₈₉	semidirect
465. #466	C₂²×C₈₉	semidirect
466. #466	C₂²×C₈₉	semidirect
467. #466	C₂²×C₈₉	semidirect
468. #465	C₂²×C₈₉	semidirect
469. #465	C₂²×C₈₉	semidirect
470. #465	C₂²×C₈₉	semidirect
471. #452	C₂²×C₈₉	semidirect
472. #450	C₂²×C₈₉	semidirect
473. #449	C₂²×C₈₉	semidirect
474. #449	C₂²×C₈₉	semidirect
475. #449	C₂²×C₈₉	semidirect
476. #447	C₂²×C₈₉	semidirect
477. #447	C₂²×C₈₉	semidirect
478. #447	C₂²×C₈₉	semidirect
479. #428	C₂²×C₈₉	semidirect
480. #427	C₂²×C₈₉	semidirect
481. C₂×#107	C₂²×C₈₉	semidirect
482. #418	C₂²×C₈₉	semidirect
483. #417	C₂²×C₈₉	semidirect
484. #416	C₂²×C₈₉	semidirect
485. C₂×#102	C₂²×C₈₉	semidirect
486. #408	C₂²×C₈₉	semidirect
487. #408	C₂²×C₈₉	semidirect
488. #408	C₂²×C₈₉	semidirect
489. #408	C₂²×C₈₉	semidirect
490. C₂×C₂²⋊C₈	C₂²×C₈₉	semidirect
491. C₂×C₂²⋊C₈	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3488	2
C₈₉×#3203	2
C₈₉×#3199	2
C₈₉×#3198	2
C₈₉×#3191	2
C₈₉×#3188	2
C₈₉×#3186	2
C₈₉×#3098	2
C₈₉×#3096	2
C₈₉×#3055	2
C₈₉×#3050	2
C₂×#466×C₈₉	2
C₈₉×#3012	2
C₈₉×#3008	2
C₂×#408×C₈₉	2
#60768	89

Subgroups — C89×#60768 #36438616

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60768 #36438616