Subgroups — C₈₉×#35266 #36413114

Order 22784.

2018 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2860	C₂	1	4	yes	maximal, complemented
2	C₈₉×#2644	C₂	1	4	yes	maximal, complemented
3	C₈₉×#2513	C₂	1	4	yes	maximal, complemented
4	C₈₉×#2512	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2480	C₂	1	8	yes	maximal, complemented
6	C₈₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2316	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2309	C₂	1	1	yes	maximal, characteristic
9	C₈₉×#2309	C₂	1	1	yes	maximal, characteristic
10	C₈₉×#2296	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#390×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₄×#117×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×#126×C₈₉	C₂²	1	8	yes	complemented
15	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
21	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
22	#397×C₈₉	C₂²	1	8	yes	complemented
23	#397×C₈₉	C₂²	1	8	yes	complemented
24	#397×C₈₉	C₂²	1	8	yes	complemented
25	#396×C₈₉	C₂²	1	8	yes	complemented
26	#390×C₈₉	C₂²	1	4	yes	—
27	#390×C₈₉	C₂²	1	4	yes	—
28	#390×C₈₉	C₂²	1	2	yes	—
29	#390×C₈₉	C₂²	1	4	yes	—
30	#390×C₈₉	C₂²	1	2	yes	—
31	#390×C₈₉	C₂²	1	2	yes	—
32	#390×C₈₉	C₂²	1	2	yes	—
33	#390×C₈₉	C₂²	1	4	yes	—
34	#389×C₈₉	C₂²	1	2	yes	complemented
35	#389×C₈₉	C₂²	1	2	yes	complemented
36	#389×C₈₉	C₂²	1	4	yes	complemented
37	#389×C₈₉	C₂²	1	4	yes	complemented
38	#389×C₈₉	C₂²	1	4	yes	complemented
39	#388×C₈₉	C₂²	1	8	yes	complemented
40	#388×C₈₉	C₂²	1	8	yes	complemented
41	#388×C₈₉	C₂²	1	8	yes	complemented
42	#385×C₈₉	C₂²	1	4	yes	—
43	#385×C₈₉	C₂²	1	4	yes	—
44	#384×C₈₉	C₂²	1	2	yes	complemented
45	#382×C₈₉	C₂²	1	2	yes	complemented
46	#380×C₈₉	C₂²	1	4	yes	—
47	#379×C₈₉	C₂²	1	4	yes	—
48	#379×C₈₉	C₂²	1	4	yes	—
49	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	complemented
50	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
51	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
52	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
53	#376×C₈₉	C₂²	1	2	yes	complemented
54	C₄³×C₈₉	C₂²	1	2	yes	complemented
55	C₂⁵×C₈₉	C₂³	1	2	yes	—
56	C₂²×D₄×C₈₉	—	2	4	no	—
57	C₂²×D₄×C₈₉	—	2	4	no	—
58	C₂²×D₄×C₈₉	—	2	4	no	—
59	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
60	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
61	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
62	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
63	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
64	#126×C₈₉	—	4	16	no	—
65	#117×C₈₉	—	2	4	no	—
66	#117×C₈₉	—	2	4	no	—
67	#117×C₈₉	—	2	4	no	—
68	#117×C₈₉	—	2	4	no	—
69	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
70	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
74	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
79	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
80	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
81	C₂×C₂²⋊C₄×C₈₉	—	4	8	no	—
82	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
83	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
84	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
85	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
86	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
87	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
88	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
89	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
90	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
91	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
92	C₂×C₄²×C₈₉	—	2	4	no	—
93	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
95	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
96	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
97	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
99	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
100	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
101	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
102	#95×C₈₉	C₂³	1	4	yes	—
103	#95×C₈₉	C₂³	1	4	yes	—
104	#95×C₈₉	C₂³	1	4	yes	—
105	#95×C₈₉	C₂³	1	4	yes	—
106	#95×C₈₉	C₂³	1	8	yes	—
107	#95×C₈₉	C₂³	1	8	yes	—
108	C₂⁴×C₈₉	—	2	4	no	—
109	C₂⁴×C₈₉	—	2	4	no	—
110	C₂⁴×C₈₉	—	2	4	no	—
111	C₂⁴×C₈₉	—	4	4	no	—
112	C₂⁴×C₈₉	—	4	4	no	—
113	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
114	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
115	C₂×D₄×C₈₉	—	2	4	no	—
116	C₂×D₄×C₈₉	—	2	4	no	—
117	C₂×D₄×C₈₉	—	2	4	no	—
118	C₂×D₄×C₈₉	—	2	4	no	—
119	C₂×D₄×C₈₉	—	2	4	no	—
120	C₂×D₄×C₈₉	—	2	4	no	—
121	C₂×D₄×C₈₉	—	4	16	no	—
122	C₂²×C₄×C₈₉	—	2	4	no	—
123	C₂²×C₄×C₈₉	—	2	4	no	—
124	C₂²×C₄×C₈₉	—	2	4	no	—
125	C₂²×C₄×C₈₉	—	4	2	no	—
126	C₂²×C₄×C₈₉	—	4	4	no	—
127	C₂²×C₄×C₈₉	#41	1	4	yes	—
128	C₂²×C₄×C₈₉	#41	1	4	yes	—
129	C₂²×C₄×C₈₉	#41	1	4	yes	—
130	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
131	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
132	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
139	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
140	C₄⋊C₄×C₈₉	—	2	4	no	—
141	C₄⋊C₄×C₈₉	—	2	4	no	—
142	C₄⋊C₄×C₈₉	—	2	4	no	—
143	C₄⋊C₄×C₈₉	—	2	4	no	—
144	C₄⋊C₄×C₈₉	—	2	4	no	—
145	C₄⋊C₄×C₈₉	—	2	2	no	—
146	C₄⋊C₄×C₈₉	—	2	2	no	—
147	C₄⋊C₄×C₈₉	—	2	8	no	—
148	C₄⋊C₄×C₈₉	—	4	4	no	—
149	C₄⋊C₄×C₈₉	—	4	8	no	—
150	C₄⋊C₄×C₈₉	—	4	8	no	—
151	C₂²⋊C₄×C₈₉	—	2	4	no	—
152	C₂²⋊C₄×C₈₉	—	2	4	no	—
153	C₂²⋊C₄×C₈₉	—	2	4	no	—
154	C₂²⋊C₄×C₈₉	—	2	4	no	—
155	C₂²⋊C₄×C₈₉	—	2	16	no	—
156	C₂²⋊C₄×C₈₉	—	4	8	no	—
157	C₂²⋊C₄×C₈₉	—	4	8	no	—
158	C₂²⋊C₄×C₈₉	—	4	8	no	—
159	C₂²⋊C₄×C₈₉	—	4	8	no	—
160	C₂²⋊C₄×C₈₉	—	4	8	no	—
161	C₄²×C₈₉	—	2	2	no	—
162	C₄²×C₈₉	—	2	4	no	—
163	C₄²×C₈₉	—	2	2	no	—
164	C₄²×C₈₉	—	2	4	no	—
165	C₄²×C₈₉	—	2	4	no	—
166	C₄²×C₈₉	—	2	4	no	—
167	C₄²×C₈₉	—	2	4	no	—
168	C₄²×C₈₉	—	2	8	no	—
169	C₄²×C₈₉	—	4	4	no	—
170	C₂³×C₈₉	—	2	2	no	—
171	C₂³×C₈₉	—	2	2	no	—
172	C₂³×C₈₉	—	2	4	no	—
173	C₂³×C₈₉	—	2	4	no	—
174	C₂³×C₈₉	—	2	4	no	—
175	C₂³×C₈₉	—	2	8	no	—
176	C₂³×C₈₉	—	2	8	no	—
177	C₂³×C₈₉	—	4	16	no	—
178	C₂³×C₈₉	—	4	8	no	—
179	C₂³×C₈₉	—	8	8	no	—
180	C₂³×C₈₉	—	8	4	no	—
181	C₂³×C₈₉	—	8	4	no	—
182	C₂³×C₈₉	C₂×#41	1	2	yes	—
183	C₂³×C₈₉	C₂×#41	1	2	yes	—
184	C₂³×C₈₉	C₂×#41	1	2	yes	—
185	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
186	D₄×C₈₉	—	4	8	no	—
187	D₄×C₈₉	—	4	8	no	—
188	C₂×C₄×C₈₉	—	2	2	no	—
189	C₂×C₄×C₈₉	—	2	2	no	—
190	C₂×C₄×C₈₉	—	2	2	no	—
191	C₂×C₄×C₈₉	—	2	4	no	—
192	C₂×C₄×C₈₉	—	2	4	no	—
193	C₂×C₄×C₈₉	—	2	4	no	—
194	C₂×C₄×C₈₉	—	2	2	no	—
195	C₂×C₄×C₈₉	—	2	2	no	—
196	C₂×C₄×C₈₉	—	2	4	no	—
197	C₂×C₄×C₈₉	—	2	4	no	—
198	C₂×C₄×C₈₉	—	2	4	no	—
199	C₂×C₄×C₈₉	—	2	8	no	—
200	C₂×C₄×C₈₉	—	2	2	no	—
201	C₂×C₄×C₈₉	—	2	4	no	—
202	C₂×C₄×C₈₉	—	2	4	no	—
203	C₂×C₄×C₈₉	—	2	4	no	—
204	C₂×C₄×C₈₉	—	2	4	no	—
205	C₂×C₄×C₈₉	—	2	4	no	—
206	C₂×C₄×C₈₉	—	2	4	no	—
207	C₂×C₄×C₈₉	—	2	2	no	—
208	C₂×C₄×C₈₉	—	4	8	no	—
209	C₂×C₄×C₈₉	—	8	4	no	—
210	C₂×C₄×C₈₉	#126	1	16	yes	complemented
211	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
212	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
213	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
214	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
215	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
216	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
217	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
218	C₂²×C₈₉	—	2	4	no	—
219	C₂²×C₈₉	—	2	4	no	—
220	C₂²×C₈₉	—	2	2	no	—
221	C₂²×C₈₉	—	2	2	no	—
222	C₂²×C₈₉	—	4	4	no	—
223	C₂²×C₈₉	—	4	8	no	—
224	C₂²×C₈₉	—	4	8	no	—
225	C₂²×C₈₉	—	4	4	no	—
226	C₂²×C₈₉	—	4	4	no	—
227	C₂²×C₈₉	—	8	16	no	—
228	C₂²×C₈₉	C₂×#126	1	4	yes	—
229	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
230	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
231	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
232	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
233	C₂²×C₈₉	#585	1	2	yes	—
234	C₄×C₈₉	—	2	4	no	—
235	C₄×C₈₉	—	4	4	no	—
236	C₄×C₈₉	—	4	4	no	—
237	C₄×C₈₉	—	4	4	no	—
238	C₄×C₈₉	—	4	2	no	—
239	C₄×C₈₉	—	4	2	no	—
240	C₄×C₈₉	—	4	4	no	—
241	C₄×C₈₉	—	4	2	no	—
242	C₄×C₈₉	C₂×#126	1	4	yes	—
243	C₄×C₈₉	C₂×#126	1	4	yes	—
244	#35266	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
245	C₂×C₈₉	—	2	4	no	—
246	C₂×C₈₉	—	8	4	no	—
247	C₂×C₈₉	C₂²×#126	1	1	yes	characteristic
248	C₂×C₈₉	#3460	1	2	yes	—
249	C₂×C₈₉	#3494	1	2	yes	—
250	C₂×C₈₉	#3508	1	1	yes	characteristic
251	C₂×C₈₉	#3510	1	1	yes	characteristic
252	#2860	C₂×C₈₉	1	4	yes	complemented
253	#2644	C₂×C₈₉	1	4	yes	complemented
254	#2513	C₂×C₈₉	1	4	yes	complemented
255	#2512	C₂×C₈₉	1	4	yes	complemented
256	#2480	C₂×C₈₉	1	8	yes	complemented
257	#2317	C₂×C₈₉	1	1	yes	characteristic, complemented
258	#2316	C₂×C₈₉	1	1	yes	characteristic, complemented
259	#2309	C₂×C₈₉	1	1	yes	characteristic
260	#2309	C₂×C₈₉	1	1	yes	characteristic
261	#2296	C₂×C₈₉	1	1	yes	characteristic, complemented
262	C₂×#390	C₂×C₈₉	1	1	yes	characteristic
263	C₄×#117	C₂×C₈₉	1	1	yes	characteristic, complemented
264	C₈₉	#35266	1	1	yes	characteristic, direct product factor, Sylow
265	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
266	C₂×#126	C₂²×C₈₉	1	8	yes	complemented
267	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
268	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
269	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
270	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
271	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
272	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
273	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
274	#397	C₂²×C₈₉	1	8	yes	complemented
275	#397	C₂²×C₈₉	1	8	yes	complemented
276	#397	C₂²×C₈₉	1	8	yes	complemented
277	#396	C₂²×C₈₉	1	8	yes	complemented
278	#390	C₂²×C₈₉	1	4	yes	—
279	#390	C₂²×C₈₉	1	4	yes	—
280	#390	C₂²×C₈₉	1	2	yes	—
281	#390	C₂²×C₈₉	1	4	yes	—
282	#390	C₂²×C₈₉	1	2	yes	—
283	#390	C₂²×C₈₉	1	2	yes	—
284	#390	C₂²×C₈₉	1	2	yes	—
285	#390	C₂²×C₈₉	1	4	yes	—
286	#389	C₂²×C₈₉	1	4	yes	complemented
287	#389	C₂²×C₈₉	1	4	yes	complemented
288	#389	C₂²×C₈₉	1	4	yes	complemented
289	#389	C₂²×C₈₉	1	2	yes	complemented
290	#389	C₂²×C₈₉	1	2	yes	complemented
291	#388	C₂²×C₈₉	1	8	yes	complemented
292	#388	C₂²×C₈₉	1	8	yes	complemented
293	#388	C₂²×C₈₉	1	8	yes	complemented
294	#385	C₂²×C₈₉	1	4	yes	—
295	#385	C₂²×C₈₉	1	4	yes	—
296	#384	C₂²×C₈₉	1	2	yes	complemented
297	#382	C₂²×C₈₉	1	2	yes	complemented
298	#380	C₂²×C₈₉	1	4	yes	—
299	#379	C₂²×C₈₉	1	4	yes	—
300	#379	C₂²×C₈₉	1	4	yes	—
301	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
302	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	complemented
303	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
304	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
305	#376	C₂²×C₈₉	1	2	yes	complemented
306	C₄³	C₂²×C₈₉	1	2	yes	complemented
307	C₂⁵	C₂³×C₈₉	1	2	yes	—
308	C₂²×D₄	—	2	4	no	—
309	C₂²×D₄	—	2	4	no	—
310	C₂²×D₄	—	2	4	no	—
311	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
312	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
313	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
314	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
315	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
316	#126	—	4	16	no	—
317	#117	—	2	4	no	—
318	#117	—	2	4	no	—
319	#117	—	2	4	no	—
320	#117	—	2	4	no	—
321	C₂×C₄⋊C₄	—	2	4	no	—
322	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
323	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
324	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
330	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
331	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
332	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
333	C₂×C₂²⋊C₄	—	4	8	no	—
334	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
335	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
336	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
337	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
338	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
339	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
340	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
341	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
342	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
343	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
344	C₂×C₄²	—	2	4	no	—
345	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
346	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
347	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
348	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
349	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
350	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
351	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
352	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
353	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
354	#95	C₂³×C₈₉	1	4	yes	—
355	#95	C₂³×C₈₉	1	4	yes	—
356	#95	C₂³×C₈₉	1	4	yes	—
357	#95	C₂³×C₈₉	1	4	yes	—
358	#95	C₂³×C₈₉	1	8	yes	—
359	#95	C₂³×C₈₉	1	8	yes	—
360	C₂⁴	—	2	4	no	—
361	C₂⁴	—	2	4	no	—
362	C₂⁴	—	2	4	no	—
363	C₂⁴	—	4	4	no	—
364	C₂⁴	—	4	4	no	—
365	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
366	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	2	4	no	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	—	4	16	no	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	4	no	—
379	C₂²×C₄	#41×C₈₉	1	4	yes	—
380	C₂²×C₄	#41×C₈₉	1	4	yes	—
381	C₂²×C₄	#41×C₈₉	1	4	yes	—
382	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
383	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
384	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
385	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
386	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
387	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
388	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
389	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
390	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
391	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	8	no	—
400	C₄⋊C₄	—	4	8	no	—
401	C₄⋊C₄	—	4	8	no	—
402	C₄⋊C₄	—	4	4	no	—
403	C₂²⋊C₄	—	2	4	no	—
404	C₂²⋊C₄	—	2	4	no	—
405	C₂²⋊C₄	—	2	4	no	—
406	C₂²⋊C₄	—	2	4	no	—
407	C₂²⋊C₄	—	2	16	no	—
408	C₂²⋊C₄	—	4	8	no	—
409	C₂²⋊C₄	—	4	8	no	—
410	C₂²⋊C₄	—	4	8	no	—
411	C₂²⋊C₄	—	4	8	no	—
412	C₂²⋊C₄	—	4	8	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	4	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	2	4	no	—
417	C₄²	—	2	4	no	—
418	C₄²	—	2	4	no	—
419	C₄²	—	2	4	no	—
420	C₄²	—	2	8	no	—
421	C₄²	—	4	4	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	4	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	2	8	no	—
428	C₂³	—	2	8	no	—
429	C₂³	—	4	16	no	—
430	C₂³	—	4	8	no	—
431	C₂³	—	8	8	no	—
432	C₂³	—	8	4	no	—
433	C₂³	—	8	4	no	—
434	C₂³	C₂×#41×C₈₉	1	2	yes	—
435	C₂³	C₂×#41×C₈₉	1	2	yes	—
436	C₂³	C₂×#41×C₈₉	1	2	yes	—
437	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
438	D₄	—	4	8	no	—
439	D₄	—	4	8	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	8	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	4	8	no	—
461	C₂×C₄	—	8	4	no	—
462	C₂×C₄	#126×C₈₉	1	16	yes	complemented
463	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
464	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
465	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
466	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
467	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
468	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
469	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
470	C₂²	—	2	4	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	8	no	—
476	C₂²	—	4	8	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	8	16	no	—
480	C₂²	C₂×#126×C₈₉	1	4	yes	—
481	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
482	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
483	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
484	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
485	C₂²	#585×C₈₉	1	2	yes	—
486	C₄	—	2	4	no	—
487	C₄	—	4	4	no	—
488	C₄	—	4	4	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	4	no	—
491	C₄	—	4	4	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	2	no	—
494	C₄	C₂×#126×C₈₉	1	4	yes	—
495	C₄	C₂×#126×C₈₉	1	4	yes	—
496	C₂	—	2	4	no	—
497	C₂	—	8	4	no	—
498	C₂	C₂²×#126×C₈₉	1	1	yes	characteristic
499	C₂	C₈₉×#3460	1	2	yes	—
500	C₂	C₈₉×#3494	1	2	yes	—
501	C₂	C₈₉×#3508	1	1	yes	characteristic
502	C₂	C₈₉×#3510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂³×D₄×C₈₉	C₂²
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. C₈₉×#2860	C₂	semidirect
2. C₈₉×#2644	C₂	semidirect
3. C₈₉×#2513	C₂	semidirect
4. C₈₉×#2512	C₂	semidirect
5. C₈₉×#2480	C₂	semidirect
6. C₈₉×#2317	C₂	semidirect
7. C₈₉×#2316	C₂	semidirect
10. C₈₉×#2296	C₂	semidirect
12. C₄×#117×C₈₉	C₂	semidirect
14. C₂×#126×C₈₉	C₂²	semidirect
22. #397×C₈₉	C₂²	semidirect
23. #397×C₈₉	C₂²	semidirect
24. #397×C₈₉	C₂²	semidirect
25. #396×C₈₉	C₂²	semidirect
34. #389×C₈₉	C₂²	semidirect
35. #389×C₈₉	C₂²	semidirect
36. #389×C₈₉	C₂²	semidirect
37. #389×C₈₉	C₂²	semidirect
38. #389×C₈₉	C₂²	semidirect
39. #388×C₈₉	C₂²	semidirect
40. #388×C₈₉	C₂²	semidirect
41. #388×C₈₉	C₂²	semidirect
44. #384×C₈₉	C₂²	semidirect
45. #382×C₈₉	C₂²	semidirect
49. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
50. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
51. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
53. #376×C₈₉	C₂²	semidirect
54. C₄³×C₈₉	C₂²	semidirect
210. C₂×C₄×C₈₉	#126	semidirect
244. #35266	C₈₉	direct (N × H)
252. #2860	C₂×C₈₉	semidirect
253. #2644	C₂×C₈₉	semidirect
254. #2513	C₂×C₈₉	semidirect
255. #2512	C₂×C₈₉	semidirect
256. #2480	C₂×C₈₉	semidirect
257. #2317	C₂×C₈₉	semidirect
258. #2316	C₂×C₈₉	semidirect
261. #2296	C₂×C₈₉	semidirect
263. C₄×#117	C₂×C₈₉	semidirect
264. C₈₉	#35266	direct (N × H)
266. C₂×#126	C₂²×C₈₉	semidirect
274. #397	C₂²×C₈₉	semidirect
275. #397	C₂²×C₈₉	semidirect
276. #397	C₂²×C₈₉	semidirect
277. #396	C₂²×C₈₉	semidirect
286. #389	C₂²×C₈₉	semidirect
287. #389	C₂²×C₈₉	semidirect
288. #389	C₂²×C₈₉	semidirect
289. #389	C₂²×C₈₉	semidirect
290. #389	C₂²×C₈₉	semidirect
291. #388	C₂²×C₈₉	semidirect
292. #388	C₂²×C₈₉	semidirect
293. #388	C₂²×C₈₉	semidirect
296. #384	C₂²×C₈₉	semidirect
297. #382	C₂²×C₈₉	semidirect
301. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
302. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
303. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
305. #376	C₂²×C₈₉	semidirect
306. C₄³	C₂²×C₈₉	semidirect
462. C₂×C₄	#126×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#2860	2
C₈₉×#2644	2
C₈₉×#2513	2
C₈₉×#2512	2
C₈₉×#2480	2
C₈₉×#2317	2
C₈₉×#2316	2
C₈₉×#2309	2
C₈₉×#2296	2
C₂×#390×C₈₉	2
C₄×#117×C₈₉	2
#35266	89

Subgroups — C89×#35266 #36413114

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35266 #36413114