Subgroups — C₈₉×#36704 #36414552

Order 22784.

3018 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#535×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#121×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2849	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2688	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2686	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2673	C₂	1	4	yes	maximal, complemented
7	C₈₉×#2671	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2613	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2484	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2482	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2412	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2410	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2406	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2404	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2308	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
21	#535×C₈₉	—	2	8	no	—
22	C₂×#127×C₈₉	C₂²	1	2	yes	complemented
23	C₂×#124×C₈₉	C₂²	1	2	yes	complemented
24	C₂×#123×C₈₉	C₂²	1	2	yes	—
25	C₂×#123×C₈₉	C₂²	1	4	yes	complemented
26	C₂×#121×C₈₉	—	2	8	no	—
27	C₂×#121×C₈₉	C₂²	1	4	yes	—
28	C₂×#121×C₈₉	C₂²	1	4	yes	—
29	C₂×#121×C₈₉	C₂²	1	2	yes	complemented
30	C₂×#121×C₈₉	C₂²	1	2	yes	complemented
31	C₂×#121×C₈₉	C₂²	1	4	yes	complemented
32	C₂×#120×C₈₉	C₂²	1	2	yes	—
33	C₂×#120×C₈₉	C₂²	1	2	yes	—
34	C₂×#120×C₈₉	C₂²	1	2	yes	—
35	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
40	#400×C₈₉	C₂²	1	2	yes	complemented
41	#399×C₈₉	C₂²	1	2	yes	complemented
42	#398×C₈₉	C₂²	1	2	yes	complemented
43	#397×C₈₉	C₂²	1	4	yes	complemented
44	#397×C₈₉	C₂²	1	2	yes	complemented
45	#395×C₈₉	C₂²	1	2	yes	complemented
46	#394×C₈₉	C₂²	1	4	yes	complemented
47	#394×C₈₉	C₂²	1	4	yes	complemented
48	#394×C₈₉	C₂²	1	2	yes	complemented
49	#394×C₈₉	C₂²	1	4	yes	complemented
50	#394×C₈₉	C₂²	1	4	yes	complemented
51	#393×C₈₉	C₂²	1	2	yes	complemented
52	#392×C₈₉	C₂²	1	4	yes	complemented
53	#392×C₈₉	C₂²	1	4	yes	complemented
54	#392×C₈₉	C₂²	1	2	yes	complemented
55	#392×C₈₉	C₂²	1	4	yes	complemented
56	#388×C₈₉	C₂²	1	4	yes	complemented
57	#387×C₈₉	C₂²	1	4	yes	complemented
58	#386×C₈₉	C₂²	1	2	yes	—
59	#386×C₈₉	C₂²	1	2	yes	—
60	#386×C₈₉	C₂²	1	4	yes	complemented
61	#386×C₈₉	C₂²	1	4	yes	complemented
62	#386×C₈₉	C₂²	1	4	yes	complemented
63	#386×C₈₉	C₂²	1	4	yes	complemented
64	#386×C₈₉	C₂²	1	4	yes	complemented
65	#386×C₈₉	C₂²	1	4	yes	complemented
66	#385×C₈₉	C₂²	1	2	yes	—
67	#385×C₈₉	C₂²	1	2	yes	—
68	#385×C₈₉	C₂²	1	4	yes	complemented
69	#385×C₈₉	C₂²	1	4	yes	complemented
70	#381×C₈₉	C₂²	1	1	yes	characteristic
71	#381×C₈₉	C₂²	1	1	yes	characteristic
72	#381×C₈₉	C₂²	1	2	yes	—
73	#381×C₈₉	C₂²	1	4	yes	complemented
74	#380×C₈₉	C₂²	1	4	yes	complemented
75	#379×C₈₉	C₂²	1	2	yes	—
76	#379×C₈₉	C₂²	1	2	yes	—
77	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
78	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
79	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
80	C₂×#41×C₈₉	—	2	4	no	—
81	C₂×#41×C₈₉	—	4	4	no	—
82	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₈₉	—	2	4	no	—
84	C₂²×D₄×C₈₉	—	2	4	no	—
85	C₂²×D₄×C₈₉	—	4	4	no	—
86	C₂²×D₄×C₈₉	—	4	4	no	—
87	C₂²×D₄×C₈₉	—	4	4	no	—
88	C₂²×D₄×C₈₉	D₄	1	8	yes	complemented
89	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
90	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
91	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
93	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
94	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
96	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
97	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
98	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
99	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
100	C₂³×C₄×C₈₉	—	2	4	no	—
101	C₂³×C₄×C₈₉	—	4	4	no	—
102	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
105	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
108	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
109	#127×C₈₉	—	2	8	no	—
110	#124×C₈₉	—	2	8	no	—
111	#123×C₈₉	—	4	8	no	—
112	#123×C₈₉	—	4	4	no	—
113	#121×C₈₉	—	2	16	no	—
114	#121×C₈₉	—	2	16	no	—
115	#121×C₈₉	—	2	8	no	—
116	#121×C₈₉	—	2	8	no	—
117	#121×C₈₉	—	4	8	no	—
118	#120×C₈₉	—	2	8	no	—
119	#120×C₈₉	—	2	8	no	—
120	#120×C₈₉	—	4	4	no	—
121	#117×C₈₉	—	2	4	no	—
122	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
123	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
129	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
131	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
132	C₂×C₂²⋊C₄×C₈₉	—	4	4	no	—
133	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
152	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
153	#95×C₈₉	C₂³	1	4	yes	—
154	#95×C₈₉	C₂³	1	4	yes	—
155	#95×C₈₉	C₂³	1	2	yes	—
156	#95×C₈₉	C₂³	1	2	yes	—
157	#95×C₈₉	C₂³	1	2	yes	—
158	#95×C₈₉	C₂³	1	2	yes	—
159	#95×C₈₉	C₂³	1	4	yes	—
160	#95×C₈₉	C₂³	1	4	yes	—
161	#95×C₈₉	C₂³	1	4	yes	—
162	#95×C₈₉	C₂³	1	4	yes	—
163	C₂⁴×C₈₉	—	2	4	no	—
164	C₂⁴×C₈₉	—	2	4	no	—
165	C₂⁴×C₈₉	—	2	2	no	—
166	C₂⁴×C₈₉	—	2	4	no	—
167	C₂⁴×C₈₉	—	4	2	no	—
168	C₂⁴×C₈₉	—	4	2	no	—
169	C₂⁴×C₈₉	—	4	2	no	—
170	C₂⁴×C₈₉	—	4	2	no	—
171	C₂⁴×C₈₉	—	4	2	no	—
172	C₂⁴×C₈₉	—	4	2	no	—
173	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
174	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
175	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
176	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
177	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
178	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
179	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
180	#41×C₈₉	—	4	16	no	—
181	C₂×Q₈×C₈₉	—	2	2	no	—
182	C₂×Q₈×C₈₉	—	4	2	no	—
183	C₂×D₄×C₈₉	—	2	4	no	—
184	C₂×D₄×C₈₉	—	2	8	no	—
185	C₂×D₄×C₈₉	—	2	8	no	—
186	C₂×D₄×C₈₉	—	2	4	no	—
187	C₂×D₄×C₈₉	—	2	4	no	—
188	C₂×D₄×C₈₉	—	2	4	no	—
189	C₂×D₄×C₈₉	—	2	4	no	—
190	C₂×D₄×C₈₉	—	2	4	no	—
191	C₂×D₄×C₈₉	—	2	4	no	—
192	C₂×D₄×C₈₉	—	2	2	no	—
193	C₂×D₄×C₈₉	—	2	8	no	—
194	C₂×D₄×C₈₉	—	4	16	no	—
195	C₂×D₄×C₈₉	—	4	2	no	—
196	C₂×D₄×C₈₉	—	4	2	no	—
197	C₂×D₄×C₈₉	—	4	4	no	—
198	C₂×D₄×C₈₉	—	4	2	no	—
199	C₂×D₄×C₈₉	—	4	2	no	—
200	C₂×D₄×C₈₉	—	4	4	no	—
201	C₂×D₄×C₈₉	—	4	4	no	—
202	C₂×D₄×C₈₉	—	4	2	no	—
203	C₂×D₄×C₈₉	—	4	16	no	—
204	C₂×D₄×C₈₉	—	4	4	no	—
205	C₂×D₄×C₈₉	—	4	4	no	—
206	C₂×D₄×C₈₉	—	4	4	no	—
207	C₂×D₄×C₈₉	—	4	4	no	—
208	C₂×D₄×C₈₉	—	4	4	no	—
209	C₂×D₄×C₈₉	—	4	4	no	—
210	C₂×D₄×C₈₉	—	4	4	no	—
211	C₂×D₄×C₈₉	—	4	16	no	—
212	C₂×D₄×C₈₉	C₂×D₄	1	8	yes	—
213	C₂×D₄×C₈₉	C₂×D₄	1	8	yes	—
214	C₂²×C₄×C₈₉	—	2	2	no	—
215	C₂²×C₄×C₈₉	—	2	4	no	—
216	C₂²×C₄×C₈₉	—	2	4	no	—
217	C₂²×C₄×C₈₉	—	2	2	no	—
218	C₂²×C₄×C₈₉	—	2	2	no	—
219	C₂²×C₄×C₈₉	—	2	8	no	—
220	C₂²×C₄×C₈₉	—	2	4	no	—
221	C₂²×C₄×C₈₉	—	2	4	no	—
222	C₂²×C₄×C₈₉	—	2	8	no	—
223	C₂²×C₄×C₈₉	—	4	4	no	—
224	C₂²×C₄×C₈₉	—	4	2	no	—
225	C₂²×C₄×C₈₉	—	4	2	no	—
226	C₂²×C₄×C₈₉	—	4	2	no	—
227	C₂²×C₄×C₈₉	—	4	4	no	—
228	C₂²×C₄×C₈₉	—	4	4	no	—
229	C₂²×C₄×C₈₉	—	4	4	no	—
230	C₂²×C₄×C₈₉	—	4	16	no	—
231	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
232	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
234	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
235	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
242	C₄⋊C₄×C₈₉	—	2	4	no	—
243	C₄⋊C₄×C₈₉	—	2	4	no	—
244	C₄⋊C₄×C₈₉	—	2	2	no	—
245	C₄⋊C₄×C₈₉	—	2	2	no	—
246	C₄⋊C₄×C₈₉	—	2	8	no	—
247	C₄⋊C₄×C₈₉	—	4	4	no	—
248	C₄⋊C₄×C₈₉	—	4	4	no	—
249	C₂²⋊C₄×C₈₉	—	2	8	no	—
250	C₂²⋊C₄×C₈₉	—	2	4	no	—
251	C₂²⋊C₄×C₈₉	—	2	4	no	—
252	C₂²⋊C₄×C₈₉	—	2	4	no	—
253	C₂²⋊C₄×C₈₉	—	2	4	no	—
254	C₂²⋊C₄×C₈₉	—	2	4	no	—
255	C₂²⋊C₄×C₈₉	—	2	4	no	—
256	C₂²⋊C₄×C₈₉	—	2	4	no	—
257	C₂²⋊C₄×C₈₉	—	2	4	no	—
258	C₂²⋊C₄×C₈₉	—	2	4	no	—
259	C₂²⋊C₄×C₈₉	—	2	8	no	—
260	C₂²⋊C₄×C₈₉	—	4	4	no	—
261	C₂²⋊C₄×C₈₉	—	4	4	no	—
262	C₂²⋊C₄×C₈₉	—	4	4	no	—
263	C₂²⋊C₄×C₈₉	—	4	4	no	—
264	C₂²⋊C₄×C₈₉	—	4	4	no	—
265	C₂²⋊C₄×C₈₉	—	4	4	no	—
266	C₂²⋊C₄×C₈₉	—	4	4	no	—
267	C₂²⋊C₄×C₈₉	—	4	4	no	—
268	C₄²×C₈₉	—	2	4	no	—
269	C₂³×C₈₉	—	2	2	no	—
270	C₂³×C₈₉	—	2	2	no	—
271	C₂³×C₈₉	—	2	8	no	—
272	C₂³×C₈₉	—	2	2	no	—
273	C₂³×C₈₉	—	2	4	no	—
274	C₂³×C₈₉	—	2	2	no	—
275	C₂³×C₈₉	—	2	4	no	—
276	C₂³×C₈₉	—	2	2	no	—
277	C₂³×C₈₉	—	2	2	no	—
278	C₂³×C₈₉	—	2	4	no	—
279	C₂³×C₈₉	—	2	4	no	—
280	C₂³×C₈₉	—	2	8	no	—
281	C₂³×C₈₉	—	2	2	no	—
282	C₂³×C₈₉	—	2	2	no	—
283	C₂³×C₈₉	—	2	4	no	—
284	C₂³×C₈₉	—	2	2	no	—
285	C₂³×C₈₉	—	2	4	no	—
286	C₂³×C₈₉	—	2	4	no	—
287	C₂³×C₈₉	—	2	2	no	—
288	C₂³×C₈₉	—	2	2	no	—
289	C₂³×C₈₉	—	2	4	no	—
290	C₂³×C₈₉	—	2	2	no	—
291	C₂³×C₈₉	—	4	4	no	—
292	C₂³×C₈₉	—	4	4	no	—
293	C₂³×C₈₉	—	4	4	no	—
294	C₂³×C₈₉	—	4	4	no	—
295	C₂³×C₈₉	—	4	16	no	—
296	C₂³×C₈₉	—	4	4	no	—
297	C₂³×C₈₉	—	4	4	no	—
298	C₂³×C₈₉	—	4	4	no	—
299	C₂³×C₈₉	—	8	8	no	—
300	C₂³×C₈₉	—	8	8	no	—
301	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
302	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
303	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
304	C₂³×C₈₉	H(5,𝔽₂)	1	4	yes	—
305	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
306	Q₈×C₈₉	—	4	4	no	—
307	D₄×C₈₉	—	4	8	no	—
308	D₄×C₈₉	—	4	8	no	—
309	D₄×C₈₉	—	4	16	no	—
310	D₄×C₈₉	—	4	4	no	—
311	D₄×C₈₉	—	4	16	no	—
312	D₄×C₈₉	—	4	8	no	—
313	D₄×C₈₉	—	8	4	no	—
314	D₄×C₈₉	—	8	4	no	—
315	D₄×C₈₉	—	8	4	no	—
316	D₄×C₈₉	—	8	4	no	—
317	D₄×C₈₉	—	8	8	no	—
318	C₂×C₄×C₈₉	—	2	8	no	—
319	C₂×C₄×C₈₉	—	2	8	no	—
320	C₂×C₄×C₈₉	—	2	2	no	—
321	C₂×C₄×C₈₉	—	2	2	no	—
322	C₂×C₄×C₈₉	—	2	2	no	—
323	C₂×C₄×C₈₉	—	2	2	no	—
324	C₂×C₄×C₈₉	—	2	2	no	—
325	C₂×C₄×C₈₉	—	2	2	no	—
326	C₂×C₄×C₈₉	—	2	2	no	—
327	C₂×C₄×C₈₉	—	2	2	no	—
328	C₂×C₄×C₈₉	—	2	2	no	—
329	C₂×C₄×C₈₉	—	2	4	no	—
330	C₂×C₄×C₈₉	—	2	4	no	—
331	C₂×C₄×C₈₉	—	2	4	no	—
332	C₂×C₄×C₈₉	—	2	4	no	—
333	C₂×C₄×C₈₉	—	2	2	no	—
334	C₂×C₄×C₈₉	—	2	4	no	—
335	C₂×C₄×C₈₉	—	2	4	no	—
336	C₂×C₄×C₈₉	—	2	4	no	—
337	C₂×C₄×C₈₉	—	2	2	no	—
338	C₂×C₄×C₈₉	—	2	4	no	—
339	C₂×C₄×C₈₉	—	2	4	no	—
340	C₂×C₄×C₈₉	—	2	4	no	—
341	C₂×C₄×C₈₉	—	4	16	no	—
342	C₂×C₄×C₈₉	—	4	8	no	—
343	C₂×C₄×C₈₉	—	4	4	no	—
344	C₂×C₄×C₈₉	—	4	4	no	—
345	C₂×C₄×C₈₉	—	8	8	no	—
346	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
347	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
348	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
349	C₂²×C₈₉	—	2	2	no	—
350	C₂²×C₈₉	—	2	2	no	—
351	C₂²×C₈₉	—	2	8	no	—
352	C₂²×C₈₉	—	2	4	no	—
353	C₂²×C₈₉	—	2	4	no	—
354	C₂²×C₈₉	—	2	4	no	—
355	C₂²×C₈₉	—	2	4	no	—
356	C₂²×C₈₉	—	2	4	no	—
357	C₂²×C₈₉	—	2	4	no	—
358	C₂²×C₈₉	—	4	16	no	—
359	C₂²×C₈₉	—	4	4	no	—
360	C₂²×C₈₉	—	4	4	no	—
361	C₂²×C₈₉	—	4	4	no	—
362	C₂²×C₈₉	—	4	4	no	—
363	C₂²×C₈₉	—	4	2	no	—
364	C₂²×C₈₉	—	4	2	no	—
365	C₂²×C₈₉	—	4	2	no	—
366	C₂²×C₈₉	—	4	2	no	—
367	C₂²×C₈₉	—	4	2	no	—
368	C₂²×C₈₉	—	4	2	no	—
369	C₂²×C₈₉	—	4	4	no	—
370	C₂²×C₈₉	—	4	4	no	—
371	C₂²×C₈₉	—	4	4	no	—
372	C₂²×C₈₉	—	4	4	no	—
373	C₂²×C₈₉	—	8	8	no	—
374	C₂²×C₈₉	—	8	8	no	—
375	C₂²×C₈₉	#534	1	4	yes	—
376	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
377	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
378	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
379	C₂²×C₈₉	#585	1	2	yes	—
380	C₄×C₈₉	—	2	2	no	—
381	C₄×C₈₉	—	2	2	no	—
382	C₄×C₈₉	—	2	4	no	—
383	C₄×C₈₉	—	4	2	no	—
384	C₄×C₈₉	—	4	2	no	—
385	C₄×C₈₉	—	4	2	no	—
386	C₄×C₈₉	—	4	2	no	—
387	C₄×C₈₉	—	4	2	no	—
388	C₄×C₈₉	—	4	4	no	—
389	C₄×C₈₉	—	4	4	no	—
390	#36704	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
391	C₂×C₈₉	—	2	4	no	—
392	C₂×C₈₉	—	4	4	no	—
393	C₂×C₈₉	—	4	4	no	—
394	C₂×C₈₉	—	8	2	no	—
395	C₂×C₈₉	—	8	2	no	—
396	C₂×C₈₉	C₂×#534	1	1	yes	characteristic
397	C₂×C₈₉	#3484	1	1	yes	characteristic
398	C₂×C₈₉	#3485	1	1	yes	characteristic
399	C₂×C₈₉	#3542	1	4	yes	—
400	C₂×#535	C₂×C₈₉	1	1	yes	characteristic, complemented
401	C₂²×#121	C₂×C₈₉	1	1	yes	characteristic, complemented
402	#2849	C₂×C₈₉	1	2	yes	complemented
403	#2688	C₂×C₈₉	1	4	yes	complemented
404	#2686	C₂×C₈₉	1	4	yes	complemented
405	#2673	C₂×C₈₉	1	4	yes	complemented
406	#2671	C₂×C₈₉	1	4	yes	complemented
407	#2613	C₂×C₈₉	1	2	yes	complemented
408	#2484	C₂×C₈₉	1	1	yes	characteristic, complemented
409	#2482	C₂×C₈₉	1	1	yes	characteristic, complemented
410	#2412	C₂×C₈₉	1	2	yes	complemented
411	#2410	C₂×C₈₉	1	2	yes	complemented
412	#2406	C₂×C₈₉	1	1	yes	characteristic, complemented
413	#2404	C₂×C₈₉	1	1	yes	characteristic, complemented
414	#2308	C₂×C₈₉	1	1	yes	characteristic, complemented
415	C₈₉	#36704	1	1	yes	characteristic, direct product factor, Sylow
416	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
417	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
418	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
419	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
420	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
421	#535	—	2	8	no	—
422	C₂×#127	C₂²×C₈₉	1	2	yes	complemented
423	C₂×#124	C₂²×C₈₉	1	2	yes	complemented
424	C₂×#123	C₂²×C₈₉	1	2	yes	—
425	C₂×#123	C₂²×C₈₉	1	4	yes	complemented
426	C₂×#121	—	2	8	no	—
427	C₂×#121	C₂²×C₈₉	1	4	yes	—
428	C₂×#121	C₂²×C₈₉	1	4	yes	—
429	C₂×#121	C₂²×C₈₉	1	2	yes	complemented
430	C₂×#121	C₂²×C₈₉	1	2	yes	complemented
431	C₂×#121	C₂²×C₈₉	1	4	yes	complemented
432	C₂×#120	C₂²×C₈₉	1	2	yes	—
433	C₂×#120	C₂²×C₈₉	1	2	yes	—
434	C₂×#120	C₂²×C₈₉	1	2	yes	—
435	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
436	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
437	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
438	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
439	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
440	#400	C₂²×C₈₉	1	2	yes	complemented
441	#399	C₂²×C₈₉	1	2	yes	complemented
442	#398	C₂²×C₈₉	1	2	yes	complemented
443	#397	C₂²×C₈₉	1	4	yes	complemented
444	#397	C₂²×C₈₉	1	2	yes	complemented
445	#395	C₂²×C₈₉	1	2	yes	complemented
446	#394	C₂²×C₈₉	1	4	yes	complemented
447	#394	C₂²×C₈₉	1	4	yes	complemented
448	#394	C₂²×C₈₉	1	2	yes	complemented
449	#394	C₂²×C₈₉	1	4	yes	complemented
450	#394	C₂²×C₈₉	1	4	yes	complemented
451	#393	C₂²×C₈₉	1	2	yes	complemented
452	#392	C₂²×C₈₉	1	4	yes	complemented
453	#392	C₂²×C₈₉	1	4	yes	complemented
454	#392	C₂²×C₈₉	1	2	yes	complemented
455	#392	C₂²×C₈₉	1	4	yes	complemented
456	#388	C₂²×C₈₉	1	4	yes	complemented
457	#387	C₂²×C₈₉	1	4	yes	complemented
458	#386	C₂²×C₈₉	1	2	yes	—
459	#386	C₂²×C₈₉	1	2	yes	—
460	#386	C₂²×C₈₉	1	4	yes	complemented
461	#386	C₂²×C₈₉	1	4	yes	complemented
462	#386	C₂²×C₈₉	1	4	yes	complemented
463	#386	C₂²×C₈₉	1	4	yes	complemented
464	#386	C₂²×C₈₉	1	4	yes	complemented
465	#386	C₂²×C₈₉	1	4	yes	complemented
466	#385	C₂²×C₈₉	1	2	yes	—
467	#385	C₂²×C₈₉	1	2	yes	—
468	#385	C₂²×C₈₉	1	4	yes	complemented
469	#385	C₂²×C₈₉	1	4	yes	complemented
470	#381	C₂²×C₈₉	1	1	yes	characteristic
471	#381	C₂²×C₈₉	1	1	yes	characteristic
472	#381	C₂²×C₈₉	1	2	yes	—
473	#381	C₂²×C₈₉	1	4	yes	complemented
474	#380	C₂²×C₈₉	1	4	yes	complemented
475	#379	C₂²×C₈₉	1	2	yes	—
476	#379	C₂²×C₈₉	1	2	yes	—
477	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
478	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
479	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
480	C₂×#41	—	2	4	no	—
481	C₂×#41	—	4	4	no	—
482	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
483	C₂²×D₄	—	2	4	no	—
484	C₂²×D₄	—	2	4	no	—
485	C₂²×D₄	—	4	4	no	—
486	C₂²×D₄	—	4	4	no	—
487	C₂²×D₄	—	4	4	no	—
488	C₂²×D₄	D₄×C₈₉	1	8	yes	complemented
489	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
490	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
491	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
492	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
493	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
494	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
495	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
496	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
497	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
498	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
499	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
500	C₂³×C₄	—	2	4	no	—
501	C₂³×C₄	—	4	4	no	—
502	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
503	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
504	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
505	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
506	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
507	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
508	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
509	#127	—	2	8	no	—
510	#124	—	2	8	no	—
511	#123	—	4	8	no	—
512	#123	—	4	4	no	—
513	#121	—	2	16	no	—
514	#121	—	2	16	no	—
515	#121	—	2	8	no	—
516	#121	—	2	8	no	—
517	#121	—	4	8	no	—
518	#120	—	2	8	no	—
519	#120	—	2	8	no	—
520	#120	—	4	4	no	—
521	#117	—	2	4	no	—
522	C₂×C₄⋊C₄	—	2	4	no	—
523	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
528	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
529	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
530	C₂×C₂²⋊C₄	—	2	4	no	—
531	C₂×C₂²⋊C₄	—	2	4	no	—
532	C₂×C₂²⋊C₄	—	4	4	no	—
533	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
552	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
553	#95	C₂³×C₈₉	1	4	yes	—
554	#95	C₂³×C₈₉	1	4	yes	—
555	#95	C₂³×C₈₉	1	2	yes	—
556	#95	C₂³×C₈₉	1	2	yes	—
557	#95	C₂³×C₈₉	1	2	yes	—
558	#95	C₂³×C₈₉	1	2	yes	—
559	#95	C₂³×C₈₉	1	4	yes	—
560	#95	C₂³×C₈₉	1	4	yes	—
561	#95	C₂³×C₈₉	1	4	yes	—
562	#95	C₂³×C₈₉	1	4	yes	—
563	C₂⁴	—	2	4	no	—
564	C₂⁴	—	2	4	no	—
565	C₂⁴	—	2	2	no	—
566	C₂⁴	—	2	4	no	—
567	C₂⁴	—	4	2	no	—
568	C₂⁴	—	4	2	no	—
569	C₂⁴	—	4	2	no	—
570	C₂⁴	—	4	2	no	—
571	C₂⁴	—	4	2	no	—
572	C₂⁴	—	4	2	no	—
573	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
574	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
575	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
576	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
577	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
578	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
579	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
580	#41	—	4	16	no	—
581	C₂×Q₈	—	2	2	no	—
582	C₂×Q₈	—	4	2	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	8	no	—
585	C₂×D₄	—	2	8	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	8	no	—
594	C₂×D₄	—	4	16	no	—
595	C₂×D₄	—	4	2	no	—
596	C₂×D₄	—	4	2	no	—
597	C₂×D₄	—	4	4	no	—
598	C₂×D₄	—	4	2	no	—
599	C₂×D₄	—	4	2	no	—
600	C₂×D₄	—	4	4	no	—
601	C₂×D₄	—	4	4	no	—
602	C₂×D₄	—	4	2	no	—
603	C₂×D₄	—	4	16	no	—
604	C₂×D₄	—	4	4	no	—
605	C₂×D₄	—	4	4	no	—
606	C₂×D₄	—	4	4	no	—
607	C₂×D₄	—	4	4	no	—
608	C₂×D₄	—	4	4	no	—
609	C₂×D₄	—	4	4	no	—
610	C₂×D₄	—	4	4	no	—
611	C₂×D₄	—	4	16	no	—
612	C₂×D₄	C₂×D₄×C₈₉	1	8	yes	—
613	C₂×D₄	C₂×D₄×C₈₉	1	8	yes	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	8	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	8	no	—
623	C₂²×C₄	—	4	4	no	—
624	C₂²×C₄	—	4	2	no	—
625	C₂²×C₄	—	4	2	no	—
626	C₂²×C₄	—	4	2	no	—
627	C₂²×C₄	—	4	4	no	—
628	C₂²×C₄	—	4	4	no	—
629	C₂²×C₄	—	4	4	no	—
630	C₂²×C₄	—	4	16	no	—
631	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
632	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
634	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
635	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
641	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	8	no	—
647	C₄⋊C₄	—	4	4	no	—
648	C₄⋊C₄	—	4	4	no	—
649	C₂²⋊C₄	—	2	8	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	8	no	—
660	C₂²⋊C₄	—	4	4	no	—
661	C₂²⋊C₄	—	4	4	no	—
662	C₂²⋊C₄	—	4	4	no	—
663	C₂²⋊C₄	—	4	4	no	—
664	C₂²⋊C₄	—	4	4	no	—
665	C₂²⋊C₄	—	4	4	no	—
666	C₂²⋊C₄	—	4	4	no	—
667	C₂²⋊C₄	—	4	4	no	—
668	C₄²	—	2	4	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	8	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	4	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	4	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	2	4	no	—
679	C₂³	—	2	4	no	—
680	C₂³	—	2	8	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	4	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	4	no	—
686	C₂³	—	2	4	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	4	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	4	4	no	—
692	C₂³	—	4	4	no	—
693	C₂³	—	4	4	no	—
694	C₂³	—	4	4	no	—
695	C₂³	—	4	16	no	—
696	C₂³	—	4	4	no	—
697	C₂³	—	4	4	no	—
698	C₂³	—	4	4	no	—
699	C₂³	—	8	8	no	—
700	C₂³	—	8	8	no	—
701	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
702	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
703	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
704	C₂³	H(5,𝔽₂)×C₈₉	1	4	yes	—
705	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
706	Q₈	—	4	4	no	—
707	D₄	—	4	8	no	—
708	D₄	—	4	8	no	—
709	D₄	—	4	16	no	—
710	D₄	—	4	4	no	—
711	D₄	—	4	16	no	—
712	D₄	—	4	8	no	—
713	D₄	—	8	4	no	—
714	D₄	—	8	4	no	—
715	D₄	—	8	4	no	—
716	D₄	—	8	4	no	—
717	D₄	—	8	8	no	—
718	C₂×C₄	—	2	8	no	—
719	C₂×C₄	—	2	8	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	4	no	—
730	C₂×C₄	—	2	4	no	—
731	C₂×C₄	—	2	4	no	—
732	C₂×C₄	—	2	4	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	4	no	—
735	C₂×C₄	—	2	4	no	—
736	C₂×C₄	—	2	4	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	4	no	—
739	C₂×C₄	—	2	4	no	—
740	C₂×C₄	—	2	4	no	—
741	C₂×C₄	—	4	16	no	—
742	C₂×C₄	—	4	8	no	—
743	C₂×C₄	—	4	4	no	—
744	C₂×C₄	—	4	4	no	—
745	C₂×C₄	—	8	8	no	—
746	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
747	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
748	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
749	C₂²	—	2	2	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	8	no	—
752	C₂²	—	2	4	no	—
753	C₂²	—	2	4	no	—
754	C₂²	—	2	4	no	—
755	C₂²	—	2	4	no	—
756	C₂²	—	2	4	no	—
757	C₂²	—	2	4	no	—
758	C₂²	—	4	16	no	—
759	C₂²	—	4	4	no	—
760	C₂²	—	4	4	no	—
761	C₂²	—	4	4	no	—
762	C₂²	—	4	4	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	4	no	—
770	C₂²	—	4	4	no	—
771	C₂²	—	4	4	no	—
772	C₂²	—	4	4	no	—
773	C₂²	—	8	8	no	—
774	C₂²	—	8	8	no	—
775	C₂²	#534×C₈₉	1	4	yes	—
776	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
777	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
778	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
779	C₂²	#585×C₈₉	1	2	yes	—
780	C₄	—	2	2	no	—
781	C₄	—	2	2	no	—
782	C₄	—	2	4	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	2	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	4	no	—
789	C₄	—	4	4	no	—
790	C₂	—	2	4	no	—
791	C₂	—	4	4	no	—
792	C₂	—	4	4	no	—
793	C₂	—	8	2	no	—
794	C₂	—	8	2	no	—
795	C₂	C₂×#534×C₈₉	1	1	yes	characteristic
796	C₂	C₈₉×#3484	1	1	yes	characteristic
797	C₂	C₈₉×#3485	1	1	yes	characteristic
798	C₂	C₈₉×#3542	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#535×C₈₉	C₂	semidirect
2. C₂²×#121×C₈₉	C₂	semidirect
3. C₈₉×#2849	C₂	semidirect
4. C₈₉×#2688	C₂	semidirect
5. C₈₉×#2686	C₂	semidirect
6. C₈₉×#2673	C₂	semidirect
7. C₈₉×#2671	C₂	semidirect
8. C₈₉×#2613	C₂	semidirect
9. C₈₉×#2484	C₂	semidirect
10. C₈₉×#2482	C₂	semidirect
11. C₈₉×#2412	C₂	semidirect
12. C₈₉×#2410	C₂	semidirect
13. C₈₉×#2406	C₂	semidirect
14. C₈₉×#2404	C₂	semidirect
15. C₈₉×#2308	C₂	semidirect
22. C₂×#127×C₈₉	C₂²	semidirect
23. C₂×#124×C₈₉	C₂²	semidirect
25. C₂×#123×C₈₉	C₂²	semidirect
29. C₂×#121×C₈₉	C₂²	semidirect
30. C₂×#121×C₈₉	C₂²	semidirect
31. C₂×#121×C₈₉	C₂²	semidirect
40. #400×C₈₉	C₂²	semidirect
41. #399×C₈₉	C₂²	semidirect
42. #398×C₈₉	C₂²	semidirect
43. #397×C₈₉	C₂²	semidirect
44. #397×C₈₉	C₂²	semidirect
45. #395×C₈₉	C₂²	semidirect
46. #394×C₈₉	C₂²	semidirect
47. #394×C₈₉	C₂²	semidirect
48. #394×C₈₉	C₂²	semidirect
49. #394×C₈₉	C₂²	semidirect
50. #394×C₈₉	C₂²	semidirect
51. #393×C₈₉	C₂²	semidirect
52. #392×C₈₉	C₂²	semidirect
53. #392×C₈₉	C₂²	semidirect
54. #392×C₈₉	C₂²	semidirect
55. #392×C₈₉	C₂²	semidirect
56. #388×C₈₉	C₂²	semidirect
57. #387×C₈₉	C₂²	semidirect
60. #386×C₈₉	C₂²	semidirect
61. #386×C₈₉	C₂²	semidirect
62. #386×C₈₉	C₂²	semidirect
63. #386×C₈₉	C₂²	semidirect
64. #386×C₈₉	C₂²	semidirect
65. #386×C₈₉	C₂²	semidirect
68. #385×C₈₉	C₂²	semidirect
69. #385×C₈₉	C₂²	semidirect
73. #381×C₈₉	C₂²	semidirect
74. #380×C₈₉	C₂²	semidirect
88. C₂²×D₄×C₈₉	D₄	semidirect
390. #36704	C₈₉	direct (N × H)
400. C₂×#535	C₂×C₈₉	semidirect
401. C₂²×#121	C₂×C₈₉	semidirect
402. #2849	C₂×C₈₉	semidirect
403. #2688	C₂×C₈₉	semidirect
404. #2686	C₂×C₈₉	semidirect
405. #2673	C₂×C₈₉	semidirect
406. #2671	C₂×C₈₉	semidirect
407. #2613	C₂×C₈₉	semidirect
408. #2484	C₂×C₈₉	semidirect
409. #2482	C₂×C₈₉	semidirect
410. #2412	C₂×C₈₉	semidirect
411. #2410	C₂×C₈₉	semidirect
412. #2406	C₂×C₈₉	semidirect
413. #2404	C₂×C₈₉	semidirect
414. #2308	C₂×C₈₉	semidirect
415. C₈₉	#36704	direct (N × H)
422. C₂×#127	C₂²×C₈₉	semidirect
423. C₂×#124	C₂²×C₈₉	semidirect
425. C₂×#123	C₂²×C₈₉	semidirect
429. C₂×#121	C₂²×C₈₉	semidirect
430. C₂×#121	C₂²×C₈₉	semidirect
431. C₂×#121	C₂²×C₈₉	semidirect
440. #400	C₂²×C₈₉	semidirect
441. #399	C₂²×C₈₉	semidirect
442. #398	C₂²×C₈₉	semidirect
443. #397	C₂²×C₈₉	semidirect
444. #397	C₂²×C₈₉	semidirect
445. #395	C₂²×C₈₉	semidirect
446. #394	C₂²×C₈₉	semidirect
447. #394	C₂²×C₈₉	semidirect
448. #394	C₂²×C₈₉	semidirect
449. #394	C₂²×C₈₉	semidirect
450. #394	C₂²×C₈₉	semidirect
451. #393	C₂²×C₈₉	semidirect
452. #392	C₂²×C₈₉	semidirect
453. #392	C₂²×C₈₉	semidirect
454. #392	C₂²×C₈₉	semidirect
455. #392	C₂²×C₈₉	semidirect
456. #388	C₂²×C₈₉	semidirect
457. #387	C₂²×C₈₉	semidirect
460. #386	C₂²×C₈₉	semidirect
461. #386	C₂²×C₈₉	semidirect
462. #386	C₂²×C₈₉	semidirect
463. #386	C₂²×C₈₉	semidirect
464. #386	C₂²×C₈₉	semidirect
465. #386	C₂²×C₈₉	semidirect
468. #385	C₂²×C₈₉	semidirect
469. #385	C₂²×C₈₉	semidirect
473. #381	C₂²×C₈₉	semidirect
474. #380	C₂²×C₈₉	semidirect
488. C₂²×D₄	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×#535×C₈₉	2
C₂²×#121×C₈₉	2
C₈₉×#2849	2
C₈₉×#2688	2
C₈₉×#2686	2
C₈₉×#2673	2
C₈₉×#2671	2
C₈₉×#2613	2
C₈₉×#2484	2
C₈₉×#2482	2
C₈₉×#2412	2
C₈₉×#2410	2
C₈₉×#2406	2
C₈₉×#2404	2
C₈₉×#2308	2
#36704	89

Subgroups — C89×#36704 #36414552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#36704 #36414552