Subgroups — C₈₉×#35351 #36413199

Order 22784.

3006 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#518×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2484	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2483	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2482	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2444	C₂	1	8	yes	maximal, complemented
7	C₈₉×#2443	C₂	1	8	yes	maximal, complemented
8	C₈₉×#2405	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2308	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2308	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#385×C₈₉	C₂	1	2	yes	maximal, complemented
12	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×#123×C₈₉	C₂²	1	4	yes	complemented
17	C₂×#121×C₈₉	—	2	8	no	—
18	C₂×#121×C₈₉	C₂²	1	8	yes	—
19	#518×C₈₉	—	2	8	no	—
20	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
21	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
22	C₂×#117×C₈₉	C₂²	1	2	yes	—
23	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₈₉	C₂²	1	4	yes	complemented
25	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
28	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
30	#400×C₈₉	C₂²	1	4	yes	complemented
31	#399×C₈₉	C₂²	1	4	yes	complemented
32	#398×C₈₉	C₂²	1	4	yes	complemented
33	#397×C₈₉	C₂²	1	8	yes	complemented
34	#397×C₈₉	C₂²	1	4	yes	complemented
35	#394×C₈₉	C₂²	1	8	yes	complemented
36	#388×C₈₉	C₂²	1	8	yes	complemented
37	#387×C₈₉	C₂²	1	8	yes	complemented
38	#386×C₈₉	C₂²	1	4	yes	complemented
39	#386×C₈₉	C₂²	1	8	yes	complemented
40	#386×C₈₉	C₂²	1	8	yes	complemented
41	#386×C₈₉	C₂²	1	4	yes	complemented
42	#386×C₈₉	C₂²	1	4	yes	complemented
43	#385×C₈₉	C₂²	1	4	yes	—
44	#385×C₈₉	C₂²	1	4	yes	—
45	#385×C₈₉	C₂²	1	4	yes	complemented
46	#385×C₈₉	C₂²	1	8	yes	complemented
47	#381×C₈₉	C₂²	1	2	yes	—
48	#381×C₈₉	C₂²	1	4	yes	—
49	#381×C₈₉	C₂²	1	4	yes	complemented
50	#379×C₈₉	C₂²	1	4	yes	—
51	#379×C₈₉	C₂²	1	2	yes	—
52	C₂×#95×C₈₉	C₂²	1	4	yes	complemented
53	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
54	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
55	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₈₉	—	2	8	no	—
57	C₂²×D₄×C₈₉	—	2	4	no	—
58	C₂²×D₄×C₈₉	—	2	4	no	—
59	C₂²×D₄×C₈₉	—	2	8	no	—
60	C₂²×D₄×C₈₉	—	4	4	no	—
61	C₂²×D₄×C₈₉	D₄	1	8	yes	—
62	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
63	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
64	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
65	C₂³×C₄×C₈₉	—	2	4	no	—
66	C₂³×C₄×C₈₉	—	4	4	no	—
67	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
70	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
72	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
73	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
74	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
76	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
77	#123×C₈₉	—	4	8	no	—
78	#121×C₈₉	—	2	32	no	—
79	C₄×D₄×C₈₉	—	2	16	no	—
80	C₄×D₄×C₈₉	—	2	16	no	—
81	#117×C₈₉	—	2	8	no	—
82	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
83	C₂×C₄⋊C₄×C₈₉	—	4	8	no	—
84	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
85	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
86	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
89	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
90	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
91	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
92	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
93	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
94	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
98	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
99	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
101	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
102	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
103	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
105	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
106	#95×C₈₉	C₂³	1	8	yes	—
107	#95×C₈₉	C₂³	1	8	yes	—
108	#95×C₈₉	C₂³	1	8	yes	—
109	#95×C₈₉	C₂³	1	8	yes	—
110	#95×C₈₉	C₂³	1	4	yes	—
111	#95×C₈₉	C₂³	1	4	yes	—
112	C₂⁴×C₈₉	—	2	4	no	—
113	C₂⁴×C₈₉	—	2	2	no	—
114	C₂⁴×C₈₉	—	2	4	no	—
115	C₂⁴×C₈₉	—	4	2	no	—
116	C₂⁴×C₈₉	—	4	2	no	—
117	C₂⁴×C₈₉	—	4	2	no	—
118	C₂⁴×C₈₉	—	4	2	no	—
119	C₂⁴×C₈₉	—	4	2	no	—
120	C₂⁴×C₈₉	—	4	2	no	—
121	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
122	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
123	C₂⁴×C₈₉	#41	1	8	yes	—
124	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
125	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
126	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
127	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
128	C₂×D₄×C₈₉	—	2	32	no	—
129	C₂×D₄×C₈₉	—	2	8	no	—
130	C₂×D₄×C₈₉	—	2	8	no	—
131	C₂×D₄×C₈₉	—	2	8	no	—
132	C₂×D₄×C₈₉	—	2	8	no	—
133	C₂×D₄×C₈₉	—	2	8	no	—
134	C₂×D₄×C₈₉	—	2	8	no	—
135	C₂×D₄×C₈₉	—	2	8	no	—
136	C₂×D₄×C₈₉	—	4	4	no	—
137	C₂×D₄×C₈₉	—	4	16	no	—
138	C₂×D₄×C₈₉	—	4	16	no	—
139	C₂×D₄×C₈₉	C₂×D₄	1	16	yes	—
140	C₂²×C₄×C₈₉	—	2	2	no	—
141	C₂²×C₄×C₈₉	—	2	4	no	—
142	C₂²×C₄×C₈₉	—	2	4	no	—
143	C₂²×C₄×C₈₉	—	2	2	no	—
144	C₂²×C₄×C₈₉	—	2	2	no	—
145	C₂²×C₄×C₈₉	—	2	8	no	—
146	C₂²×C₄×C₈₉	—	2	8	no	—
147	C₂²×C₄×C₈₉	—	2	4	no	—
148	C₂²×C₄×C₈₉	—	2	4	no	—
149	C₂²×C₄×C₈₉	—	2	4	no	—
150	C₂²×C₄×C₈₉	—	2	4	no	—
151	C₂²×C₄×C₈₉	—	2	4	no	—
152	C₂²×C₄×C₈₉	—	2	8	no	—
153	C₂²×C₄×C₈₉	—	4	4	no	—
154	C₂²×C₄×C₈₉	—	4	4	no	—
155	C₂²×C₄×C₈₉	—	4	2	no	—
156	C₂²×C₄×C₈₉	—	4	4	no	—
157	C₂²×C₄×C₈₉	—	4	4	no	—
158	C₂²×C₄×C₈₉	—	4	4	no	—
159	C₂²×C₄×C₈₉	—	4	4	no	—
160	C₂²×C₄×C₈₉	—	4	4	no	—
161	C₂²×C₄×C₈₉	—	4	16	no	—
162	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
163	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
166	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
170	C₄⋊C₄×C₈₉	—	2	8	no	—
171	C₄⋊C₄×C₈₉	—	2	4	no	—
172	C₄⋊C₄×C₈₉	—	2	4	no	—
173	C₄⋊C₄×C₈₉	—	2	16	no	—
174	C₄⋊C₄×C₈₉	—	4	8	no	—
175	C₂²⋊C₄×C₈₉	—	2	8	no	—
176	C₂²⋊C₄×C₈₉	—	2	8	no	—
177	C₂²⋊C₄×C₈₉	—	2	8	no	—
178	C₂²⋊C₄×C₈₉	—	2	8	no	—
179	C₂²⋊C₄×C₈₉	—	2	8	no	—
180	C₂²⋊C₄×C₈₉	—	2	8	no	—
181	C₂²⋊C₄×C₈₉	—	2	8	no	—
182	C₂²⋊C₄×C₈₉	—	4	4	no	—
183	C₂²⋊C₄×C₈₉	—	4	8	no	—
184	C₂²⋊C₄×C₈₉	—	4	4	no	—
185	C₂²⋊C₄×C₈₉	—	4	8	no	—
186	C₄²×C₈₉	—	2	8	no	—
187	C₂³×C₈₉	—	2	4	no	—
188	C₂³×C₈₉	—	2	2	no	—
189	C₂³×C₈₉	—	2	4	no	—
190	C₂³×C₈₉	—	2	2	no	—
191	C₂³×C₈₉	—	2	4	no	—
192	C₂³×C₈₉	—	2	4	no	—
193	C₂³×C₈₉	—	2	4	no	—
194	C₂³×C₈₉	—	2	8	no	—
195	C₂³×C₈₉	—	2	2	no	—
196	C₂³×C₈₉	—	2	4	no	—
197	C₂³×C₈₉	—	2	4	no	—
198	C₂³×C₈₉	—	2	4	no	—
199	C₂³×C₈₉	—	4	4	no	—
200	C₂³×C₈₉	—	4	4	no	—
201	C₂³×C₈₉	—	4	16	no	—
202	C₂³×C₈₉	—	4	4	no	—
203	C₂³×C₈₉	—	4	4	no	—
204	C₂³×C₈₉	—	4	4	no	—
205	C₂³×C₈₉	—	4	4	no	—
206	C₂³×C₈₉	—	4	4	no	—
207	C₂³×C₈₉	—	8	8	no	—
208	C₂³×C₈₉	—	8	8	no	—
209	C₂³×C₈₉	#123	1	16	yes	complemented
210	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
211	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
212	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
213	C₂³×C₈₉	C₂×#41	1	4	yes	—
214	C₂³×C₈₉	C₂×#41	1	4	yes	—
215	C₂³×C₈₉	C₂×#41	1	4	yes	—
216	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
217	D₄×C₈₉	—	2	32	no	—
218	D₄×C₈₉	—	4	16	no	—
219	D₄×C₈₉	—	4	16	no	—
220	C₂×C₄×C₈₉	—	2	8	no	—
221	C₂×C₄×C₈₉	—	2	8	no	—
222	C₂×C₄×C₈₉	—	2	2	no	—
223	C₂×C₄×C₈₉	—	2	4	no	—
224	C₂×C₄×C₈₉	—	2	2	no	—
225	C₂×C₄×C₈₉	—	2	4	no	—
226	C₂×C₄×C₈₉	—	2	4	no	—
227	C₂×C₄×C₈₉	—	2	2	no	—
228	C₂×C₄×C₈₉	—	2	2	no	—
229	C₂×C₄×C₈₉	—	2	8	no	—
230	C₂×C₄×C₈₉	—	2	4	no	—
231	C₂×C₄×C₈₉	—	2	8	no	—
232	C₂×C₄×C₈₉	—	2	8	no	—
233	C₂×C₄×C₈₉	—	2	4	no	—
234	C₂×C₄×C₈₉	—	2	8	no	—
235	C₂×C₄×C₈₉	—	2	8	no	—
236	C₂×C₄×C₈₉	—	4	16	no	—
237	C₂×C₄×C₈₉	—	4	16	no	—
238	C₂×C₄×C₈₉	—	4	4	no	—
239	C₂×C₄×C₈₉	—	4	4	no	—
240	C₂×C₄×C₈₉	—	8	4	no	—
241	C₂×C₄×C₈₉	—	8	4	no	—
242	C₂×C₄×C₈₉	—	8	4	no	—
243	C₂×C₄×C₈₉	—	8	4	no	—
244	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
245	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
246	C₂²×C₈₉	—	2	2	no	—
247	C₂²×C₈₉	—	2	4	no	—
248	C₂²×C₈₉	—	2	4	no	—
249	C₂²×C₈₉	—	2	2	no	—
250	C₂²×C₈₉	—	2	8	no	—
251	C₂²×C₈₉	—	2	8	no	—
252	C₂²×C₈₉	—	2	8	no	—
253	C₂²×C₈₉	—	2	4	no	—
254	C₂²×C₈₉	—	2	4	no	—
255	C₂²×C₈₉	—	2	4	no	—
256	C₂²×C₈₉	—	4	16	no	—
257	C₂²×C₈₉	—	4	8	no	—
258	C₂²×C₈₉	—	4	2	no	—
259	C₂²×C₈₉	—	4	2	no	—
260	C₂²×C₈₉	—	4	2	no	—
261	C₂²×C₈₉	—	4	8	no	—
262	C₂²×C₈₉	—	8	8	no	—
263	C₂²×C₈₉	—	8	8	no	—
264	C₂²×C₈₉	C₂×#123	1	4	yes	—
265	C₂²×C₈₉	C₂×#123	1	8	yes	—
266	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
267	C₂²×C₈₉	C₂²×#41	1	2	yes	—
268	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
269	C₂²×C₈₉	#585	1	2	yes	—
270	C₄×C₈₉	—	2	4	no	—
271	C₄×C₈₉	—	2	4	no	—
272	C₄×C₈₉	—	4	2	no	—
273	C₄×C₈₉	—	4	2	no	—
274	C₄×C₈₉	—	4	4	no	—
275	C₄×C₈₉	—	4	4	no	—
276	C₄×C₈₉	—	4	8	no	—
277	#35351	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
278	C₂×C₈₉	—	2	4	no	—
279	C₂×C₈₉	—	2	8	no	—
280	C₂×C₈₉	—	4	4	no	—
281	C₂×C₈₉	—	8	2	no	—
282	C₂×C₈₉	C₂²×#123	1	1	yes	characteristic
283	C₂×C₈₉	#3484	1	1	yes	characteristic
284	C₂×C₈₉	#3485	1	1	yes	characteristic
285	C₂×C₈₉	#3505	1	4	yes	—
286	C₂²×#121	C₂×C₈₉	1	1	yes	characteristic
287	C₂×#518	C₂×C₈₉	1	1	yes	characteristic, complemented
288	#2484	C₂×C₈₉	1	2	yes	complemented
289	#2483	C₂×C₈₉	1	2	yes	complemented
290	#2482	C₂×C₈₉	1	2	yes	complemented
291	#2444	C₂×C₈₉	1	8	yes	complemented
292	#2443	C₂×C₈₉	1	8	yes	complemented
293	#2405	C₂×C₈₉	1	2	yes	complemented
294	#2308	C₂×C₈₉	1	1	yes	characteristic, complemented
295	#2308	C₂×C₈₉	1	2	yes	complemented
296	C₂×#385	C₂×C₈₉	1	2	yes	complemented
297	C₈₉	#35351	1	1	yes	characteristic, direct product factor, Sylow
298	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
299	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
300	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
301	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
302	C₂×#123	C₂²×C₈₉	1	4	yes	complemented
303	C₂×#121	—	2	8	no	—
304	C₂×#121	C₂²×C₈₉	1	8	yes	—
305	#518	—	2	8	no	—
306	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
307	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
308	C₂×#117	C₂²×C₈₉	1	2	yes	—
309	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
310	C₂²×C₄⋊C₄	C₂²×C₈₉	1	4	yes	complemented
311	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
312	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
313	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
314	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
315	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
316	#400	C₂²×C₈₉	1	4	yes	complemented
317	#399	C₂²×C₈₉	1	4	yes	complemented
318	#398	C₂²×C₈₉	1	4	yes	complemented
319	#397	C₂²×C₈₉	1	8	yes	complemented
320	#397	C₂²×C₈₉	1	4	yes	complemented
321	#394	C₂²×C₈₉	1	8	yes	complemented
322	#388	C₂²×C₈₉	1	8	yes	complemented
323	#387	C₂²×C₈₉	1	8	yes	complemented
324	#386	C₂²×C₈₉	1	4	yes	complemented
325	#386	C₂²×C₈₉	1	8	yes	complemented
326	#386	C₂²×C₈₉	1	8	yes	complemented
327	#386	C₂²×C₈₉	1	4	yes	complemented
328	#386	C₂²×C₈₉	1	4	yes	complemented
329	#385	C₂²×C₈₉	1	4	yes	—
330	#385	C₂²×C₈₉	1	4	yes	—
331	#385	C₂²×C₈₉	1	4	yes	complemented
332	#385	C₂²×C₈₉	1	8	yes	complemented
333	#381	C₂²×C₈₉	1	2	yes	—
334	#381	C₂²×C₈₉	1	4	yes	—
335	#381	C₂²×C₈₉	1	4	yes	complemented
336	#379	C₂²×C₈₉	1	4	yes	—
337	#379	C₂²×C₈₉	1	2	yes	—
338	C₂×#95	C₂²×C₈₉	1	4	yes	complemented
339	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
340	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
341	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
342	C₂²×D₄	—	2	8	no	—
343	C₂²×D₄	—	2	4	no	—
344	C₂²×D₄	—	2	4	no	—
345	C₂²×D₄	—	2	8	no	—
346	C₂²×D₄	—	4	4	no	—
347	C₂²×D₄	D₄×C₈₉	1	8	yes	—
348	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
349	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
350	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
351	C₂³×C₄	—	2	4	no	—
352	C₂³×C₄	—	4	4	no	—
353	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
354	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
355	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
356	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
357	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
359	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
360	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
361	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
362	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
363	#123	—	4	8	no	—
364	#121	—	2	32	no	—
365	C₄×D₄	—	2	16	no	—
366	C₄×D₄	—	2	16	no	—
367	#117	—	2	8	no	—
368	C₂×C₄⋊C₄	—	2	4	no	—
369	C₂×C₄⋊C₄	—	4	8	no	—
370	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
371	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
372	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
373	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
374	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
375	C₂×C₂²⋊C₄	—	2	8	no	—
376	C₂×C₂²⋊C₄	—	2	8	no	—
377	C₂×C₂²⋊C₄	—	2	4	no	—
378	C₂×C₂²⋊C₄	—	2	8	no	—
379	C₂×C₂²⋊C₄	—	2	4	no	—
380	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
382	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
391	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
392	#95	C₂³×C₈₉	1	8	yes	—
393	#95	C₂³×C₈₉	1	8	yes	—
394	#95	C₂³×C₈₉	1	8	yes	—
395	#95	C₂³×C₈₉	1	8	yes	—
396	#95	C₂³×C₈₉	1	4	yes	—
397	#95	C₂³×C₈₉	1	4	yes	—
398	C₂⁴	—	2	4	no	—
399	C₂⁴	—	2	2	no	—
400	C₂⁴	—	2	4	no	—
401	C₂⁴	—	4	2	no	—
402	C₂⁴	—	4	2	no	—
403	C₂⁴	—	4	2	no	—
404	C₂⁴	—	4	2	no	—
405	C₂⁴	—	4	2	no	—
406	C₂⁴	—	4	2	no	—
407	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
408	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
409	C₂⁴	#41×C₈₉	1	8	yes	—
410	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
411	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
412	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
413	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
414	C₂×D₄	—	2	32	no	—
415	C₂×D₄	—	2	8	no	—
416	C₂×D₄	—	2	8	no	—
417	C₂×D₄	—	2	8	no	—
418	C₂×D₄	—	2	8	no	—
419	C₂×D₄	—	2	8	no	—
420	C₂×D₄	—	2	8	no	—
421	C₂×D₄	—	2	8	no	—
422	C₂×D₄	—	4	4	no	—
423	C₂×D₄	—	4	16	no	—
424	C₂×D₄	—	4	16	no	—
425	C₂×D₄	C₂×D₄×C₈₉	1	16	yes	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	8	no	—
432	C₂²×C₄	—	2	8	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	8	no	—
439	C₂²×C₄	—	4	4	no	—
440	C₂²×C₄	—	4	4	no	—
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	—	4	4	no	—
443	C₂²×C₄	—	4	4	no	—
444	C₂²×C₄	—	4	4	no	—
445	C₂²×C₄	—	4	4	no	—
446	C₂²×C₄	—	4	4	no	—
447	C₂²×C₄	—	4	16	no	—
448	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
449	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
450	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
451	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
452	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
453	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
454	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
455	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
456	C₄⋊C₄	—	2	8	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	16	no	—
460	C₄⋊C₄	—	4	8	no	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	2	8	no	—
463	C₂²⋊C₄	—	2	8	no	—
464	C₂²⋊C₄	—	2	8	no	—
465	C₂²⋊C₄	—	2	8	no	—
466	C₂²⋊C₄	—	2	8	no	—
467	C₂²⋊C₄	—	2	8	no	—
468	C₂²⋊C₄	—	4	4	no	—
469	C₂²⋊C₄	—	4	8	no	—
470	C₂²⋊C₄	—	4	4	no	—
471	C₂²⋊C₄	—	4	8	no	—
472	C₄²	—	2	8	no	—
473	C₂³	—	2	4	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	4	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	4	no	—
478	C₂³	—	2	4	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	2	8	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	4	no	—
485	C₂³	—	4	4	no	—
486	C₂³	—	4	4	no	—
487	C₂³	—	4	16	no	—
488	C₂³	—	4	4	no	—
489	C₂³	—	4	4	no	—
490	C₂³	—	4	4	no	—
491	C₂³	—	4	4	no	—
492	C₂³	—	4	4	no	—
493	C₂³	—	8	8	no	—
494	C₂³	—	8	8	no	—
495	C₂³	#123×C₈₉	1	16	yes	complemented
496	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
497	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
498	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
499	C₂³	C₂×#41×C₈₉	1	4	yes	—
500	C₂³	C₂×#41×C₈₉	1	4	yes	—
501	C₂³	C₂×#41×C₈₉	1	4	yes	—
502	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
503	D₄	—	2	32	no	—
504	D₄	—	4	16	no	—
505	D₄	—	4	16	no	—
506	C₂×C₄	—	2	8	no	—
507	C₂×C₄	—	2	8	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	8	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	8	no	—
518	C₂×C₄	—	2	8	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	8	no	—
521	C₂×C₄	—	2	8	no	—
522	C₂×C₄	—	4	16	no	—
523	C₂×C₄	—	4	16	no	—
524	C₂×C₄	—	4	4	no	—
525	C₂×C₄	—	4	4	no	—
526	C₂×C₄	—	8	4	no	—
527	C₂×C₄	—	8	4	no	—
528	C₂×C₄	—	8	4	no	—
529	C₂×C₄	—	8	4	no	—
530	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
531	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	4	no	—
534	C₂²	—	2	4	no	—
535	C₂²	—	2	2	no	—
536	C₂²	—	2	8	no	—
537	C₂²	—	2	8	no	—
538	C₂²	—	2	8	no	—
539	C₂²	—	2	4	no	—
540	C₂²	—	2	4	no	—
541	C₂²	—	2	4	no	—
542	C₂²	—	4	16	no	—
543	C₂²	—	4	8	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	8	no	—
548	C₂²	—	8	8	no	—
549	C₂²	—	8	8	no	—
550	C₂²	C₂×#123×C₈₉	1	4	yes	—
551	C₂²	C₂×#123×C₈₉	1	8	yes	—
552	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
553	C₂²	C₂²×#41×C₈₉	1	2	yes	—
554	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
555	C₂²	#585×C₈₉	1	2	yes	—
556	C₄	—	2	4	no	—
557	C₄	—	2	4	no	—
558	C₄	—	4	2	no	—
559	C₄	—	4	2	no	—
560	C₄	—	4	4	no	—
561	C₄	—	4	4	no	—
562	C₄	—	4	8	no	—
563	C₂	—	2	4	no	—
564	C₂	—	2	8	no	—
565	C₂	—	4	4	no	—
566	C₂	—	8	2	no	—
567	C₂	C₂²×#123×C₈₉	1	1	yes	characteristic
568	C₂	C₈₉×#3484	1	1	yes	characteristic
569	C₂	C₈₉×#3485	1	1	yes	characteristic
570	C₂	C₈₉×#3505	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂²×#121×C₈₉	C₂
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
2. C₂×#518×C₈₉	C₂	semidirect
3. C₈₉×#2484	C₂	semidirect
4. C₈₉×#2483	C₂	semidirect
5. C₈₉×#2482	C₂	semidirect
6. C₈₉×#2444	C₂	semidirect
7. C₈₉×#2443	C₂	semidirect
8. C₈₉×#2405	C₂	semidirect
9. C₈₉×#2308	C₂	semidirect
10. C₈₉×#2308	C₂	semidirect
11. C₂×#385×C₈₉	C₂	semidirect
16. C₂×#123×C₈₉	C₂²	semidirect
20. C₂×C₄×D₄×C₈₉	C₂²	semidirect
21. C₂×C₄×D₄×C₈₉	C₂²	semidirect
24. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
30. #400×C₈₉	C₂²	semidirect
31. #399×C₈₉	C₂²	semidirect
32. #398×C₈₉	C₂²	semidirect
33. #397×C₈₉	C₂²	semidirect
34. #397×C₈₉	C₂²	semidirect
35. #394×C₈₉	C₂²	semidirect
36. #388×C₈₉	C₂²	semidirect
37. #387×C₈₉	C₂²	semidirect
38. #386×C₈₉	C₂²	semidirect
39. #386×C₈₉	C₂²	semidirect
40. #386×C₈₉	C₂²	semidirect
41. #386×C₈₉	C₂²	semidirect
42. #386×C₈₉	C₂²	semidirect
45. #385×C₈₉	C₂²	semidirect
46. #385×C₈₉	C₂²	semidirect
49. #381×C₈₉	C₂²	semidirect
52. C₂×#95×C₈₉	C₂²	semidirect
209. C₂³×C₈₉	#123	semidirect
277. #35351	C₈₉	direct (N × H)
287. C₂×#518	C₂×C₈₉	semidirect
288. #2484	C₂×C₈₉	semidirect
289. #2483	C₂×C₈₉	semidirect
290. #2482	C₂×C₈₉	semidirect
291. #2444	C₂×C₈₉	semidirect
292. #2443	C₂×C₈₉	semidirect
293. #2405	C₂×C₈₉	semidirect
294. #2308	C₂×C₈₉	semidirect
295. #2308	C₂×C₈₉	semidirect
296. C₂×#385	C₂×C₈₉	semidirect
297. C₈₉	#35351	direct (N × H)
302. C₂×#123	C₂²×C₈₉	semidirect
306. C₂×C₄×D₄	C₂²×C₈₉	semidirect
307. C₂×C₄×D₄	C₂²×C₈₉	semidirect
310. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
316. #400	C₂²×C₈₉	semidirect
317. #399	C₂²×C₈₉	semidirect
318. #398	C₂²×C₈₉	semidirect
319. #397	C₂²×C₈₉	semidirect
320. #397	C₂²×C₈₉	semidirect
321. #394	C₂²×C₈₉	semidirect
322. #388	C₂²×C₈₉	semidirect
323. #387	C₂²×C₈₉	semidirect
324. #386	C₂²×C₈₉	semidirect
325. #386	C₂²×C₈₉	semidirect
326. #386	C₂²×C₈₉	semidirect
327. #386	C₂²×C₈₉	semidirect
328. #386	C₂²×C₈₉	semidirect
331. #385	C₂²×C₈₉	semidirect
332. #385	C₂²×C₈₉	semidirect
335. #381	C₂²×C₈₉	semidirect
338. C₂×#95	C₂²×C₈₉	semidirect
495. C₂³	#123×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#121×C₈₉	2
C₂×#518×C₈₉	2
C₈₉×#2484	2
C₈₉×#2483	2
C₈₉×#2482	2
C₈₉×#2444	2
C₈₉×#2443	2
C₈₉×#2405	2
C₈₉×#2308	2
C₂×#385×C₈₉	2
#35351	89

Subgroups — C89×#35351 #36413199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35351 #36413199