Subgroups — C₄×#560×C₈₉ #36412199

Order 22784.

2568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#560×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2383	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2377	C₂	1	6	yes	maximal, complemented
5	C₈₉×#2376	C₂	1	3	yes	maximal, complemented
6	C₈₉×#2375	C₂	1	3	yes	maximal, complemented
7	C₄×#127×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#126×C₈₉	C₂	1	2	yes	maximal, complemented
9	C₄×#123×C₈₉	C₂	1	3	yes	maximal, complemented
10	C₄×#121×C₈₉	C₂	1	6	yes	maximal, complemented
11	C₄×#120×C₈₉	C₂	1	3	yes	maximal, complemented
12	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
13	#560×C₈₉	C₄	1	16	yes	direct product factor
14	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×#126×C₈₉	C₂²	1	2	yes	—
16	C₂×#123×C₈₉	C₂²	1	3	yes	—
17	C₂×#121×C₈₉	C₂²	1	6	yes	—
18	C₂×#120×C₈₉	C₂²	1	3	yes	—
19	C₂×C₄×D₄×C₈₉	C₂²	1	6	yes	—
20	C₂×C₄×D₄×C₈₉	C₂²	1	3	yes	—
21	C₂×C₄×D₄×C₈₉	C₂²	1	3	yes	complemented
22	C₂²×C₄²×C₈₉	C₂²	1	3	yes	complemented
23	#390×C₈₉	C₂²	1	6	yes	—
24	#390×C₈₉	C₂²	1	3	yes	—
25	#390×C₈₉	C₂²	1	3	yes	complemented
26	#389×C₈₉	C₂²	1	6	yes	complemented
27	#388×C₈₉	C₂²	1	6	yes	—
28	#388×C₈₉	C₂²	1	6	yes	—
29	#388×C₈₉	C₂²	1	6	yes	—
30	#388×C₈₉	C₂²	1	6	yes	complemented
31	#387×C₈₉	C₂²	1	6	yes	complemented
32	#387×C₈₉	C₂²	1	6	yes	complemented
33	#386×C₈₉	C₂²	1	3	yes	—
34	#386×C₈₉	C₂²	1	6	yes	—
35	#386×C₈₉	C₂²	1	6	yes	—
36	#386×C₈₉	C₂²	1	3	yes	—
37	#386×C₈₉	C₂²	1	6	yes	complemented
38	#385×C₈₉	C₂²	1	3	yes	—
39	#385×C₈₉	C₂²	1	6	yes	—
40	#385×C₈₉	C₂²	1	3	yes	complemented
41	#384×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	#383×C₈₉	C₂²	1	2	yes	complemented
43	#381×C₈₉	C₂²	1	3	yes	complemented
44	#380×C₈₉	C₂²	1	6	yes	complemented
45	#379×C₈₉	C₂²	1	3	yes	—
46	C₄×C₄⋊C₄×C₈₉	C₂²	1	6	yes	complemented
47	C₄×C₂²⋊C₄×C₈₉	C₂²	1	6	yes	—
48	C₄×C₂²⋊C₄×C₈₉	C₂²	1	3	yes	—
49	C₄×C₂²⋊C₄×C₈₉	C₂²	1	3	yes	complemented
50	C₄³×C₈₉	C₂²	1	1	yes	characteristic, complemented
51	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
53	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
54	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
55	C₂³×C₄×C₈₉	—	4	6	no	—
56	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
57	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
59	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
61	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
62	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
63	#127×C₈₉	C₂×C₄	1	8	yes	complemented
64	#126×C₈₉	C₂×C₄	1	16	yes	complemented
65	#123×C₈₉	C₂×C₄	1	24	yes	complemented
66	#121×C₈₉	C₂×C₄	1	48	yes	complemented
67	#120×C₈₉	C₂×C₄	1	24	yes	complemented
68	C₄×D₄×C₈₉	—	4	12	no	—
69	C₄×D₄×C₈₉	—	4	6	no	—
70	C₄×D₄×C₈₉	—	4	6	no	—
71	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
72	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
73	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
74	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
75	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
76	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
77	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
78	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
79	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
80	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
81	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
82	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
83	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
84	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
85	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
86	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
87	C₂×C₄²×C₈₉	—	4	6	no	—
88	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
89	C₂×C₄²×C₈₉	C₂³	1	6	yes	—
90	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
91	C₂×C₄²×C₈₉	C₂³	1	6	yes	—
92	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
93	#95×C₈₉	C₂³	1	6	yes	—
94	#95×C₈₉	C₂³	1	6	yes	—
95	#95×C₈₉	C₂³	1	6	yes	—
96	#95×C₈₉	C₂³	1	6	yes	—
97	#95×C₈₉	C₂³	1	6	yes	—
98	#95×C₈₉	C₂³	1	6	yes	—
99	C₂⁴×C₈₉	—	4	3	no	—
100	C₂⁴×C₈₉	—	4	3	no	—
101	C₂⁴×C₈₉	C₂²×C₄	1	4	yes	—
102	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
103	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
104	C₂⁴×C₈₉	C₂⁴	1	3	yes	—
105	C₂×D₄×C₈₉	—	4	6	no	—
106	C₂×D₄×C₈₉	—	4	3	no	—
107	C₂×D₄×C₈₉	—	4	3	no	—
108	C₂×D₄×C₈₉	—	4	3	no	—
109	C₂×D₄×C₈₉	—	4	3	no	—
110	C₂×D₄×C₈₉	—	4	6	no	—
111	C₂×D₄×C₈₉	C₂²×C₄	1	24	yes	—
112	C₂×D₄×C₈₉	C₂²×C₄	1	12	yes	—
113	C₂×D₄×C₈₉	C₂²×C₄	1	12	yes	complemented
114	C₂²×C₄×C₈₉	—	2	6	no	—
115	C₂²×C₄×C₈₉	—	2	12	no	—
116	C₂²×C₄×C₈₉	—	2	12	no	—
117	C₂²×C₄×C₈₉	—	2	6	no	—
118	C₂²×C₄×C₈₉	—	4	3	no	—
119	C₂²×C₄×C₈₉	—	4	3	no	—
120	C₂²×C₄×C₈₉	—	4	3	no	—
121	C₂²×C₄×C₈₉	—	4	6	no	—
122	C₂²×C₄×C₈₉	—	4	3	no	—
123	C₂²×C₄×C₈₉	—	4	6	no	—
124	C₂²×C₄×C₈₉	—	4	16	no	—
125	C₂²×C₄×C₈₉	C₂²×C₄	1	12	yes	complemented
126	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
127	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
128	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
130	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
131	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
132	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
133	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
134	C₄⋊C₄×C₈₉	—	4	6	no	—
135	C₄⋊C₄×C₈₉	—	4	6	no	—
136	C₄⋊C₄×C₈₉	—	4	3	no	—
137	C₄⋊C₄×C₈₉	—	4	3	no	—
138	C₄⋊C₄×C₈₉	C₂²×C₄	1	24	yes	complemented
139	C₂²⋊C₄×C₈₉	—	4	6	no	—
140	C₂²⋊C₄×C₈₉	—	4	3	no	—
141	C₂²⋊C₄×C₈₉	—	4	3	no	—
142	C₂²⋊C₄×C₈₉	—	4	6	no	—
143	C₂²⋊C₄×C₈₉	—	4	6	no	—
144	C₂²⋊C₄×C₈₉	—	4	3	no	—
145	C₂²⋊C₄×C₈₉	—	4	6	no	—
146	C₂²⋊C₄×C₈₉	—	4	3	no	—
147	C₂²⋊C₄×C₈₉	C₂²×C₄	1	24	yes	—
148	C₂²⋊C₄×C₈₉	C₂²×C₄	1	12	yes	—
149	C₂²⋊C₄×C₈₉	C₂²×C₄	1	12	yes	complemented
150	C₄²×C₈₉	—	2	12	no	—
151	C₄²×C₈₉	—	2	6	no	—
152	C₄²×C₈₉	—	4	6	no	—
153	C₄²×C₈₉	—	4	3	no	—
154	C₄²×C₈₉	C₂²×C₄	1	4	yes	complemented
155	C₂³×C₈₉	—	2	6	no	—
156	C₂³×C₈₉	—	2	3	no	—
157	C₂³×C₈₉	—	2	6	no	—
158	C₂³×C₈₉	—	2	3	no	—
159	C₂³×C₈₉	—	2	3	no	—
160	C₂³×C₈₉	—	2	6	no	—
161	C₂³×C₈₉	—	2	3	no	—
162	C₂³×C₈₉	—	2	6	no	—
163	C₂³×C₈₉	—	4	12	no	—
164	C₂³×C₈₉	—	4	4	no	—
165	C₂³×C₈₉	—	4	12	no	—
166	C₂³×C₈₉	C₂³×C₄	1	4	yes	—
167	C₂³×C₈₉	C₂³×C₄	1	2	yes	—
168	C₂³×C₈₉	C₂³×C₄	1	6	yes	—
169	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
170	D₄×C₈₉	—	4	24	no	—
171	D₄×C₈₉	—	4	12	no	—
172	D₄×C₈₉	—	4	12	no	—
173	C₂×C₄×C₈₉	—	2	6	no	—
174	C₂×C₄×C₈₉	—	2	3	no	—
175	C₂×C₄×C₈₉	—	2	3	no	—
176	C₂×C₄×C₈₉	—	2	6	no	—
177	C₂×C₄×C₈₉	—	2	6	no	—
178	C₂×C₄×C₈₉	—	2	3	no	—
179	C₂×C₄×C₈₉	—	2	3	no	—
180	C₂×C₄×C₈₉	—	2	6	no	—
181	C₂×C₄×C₈₉	—	2	6	no	—
182	C₂×C₄×C₈₉	—	2	3	no	—
183	C₂×C₄×C₈₉	—	2	6	no	—
184	C₂×C₄×C₈₉	—	2	6	no	—
185	C₂×C₄×C₈₉	—	2	6	no	—
186	C₂×C₄×C₈₉	—	4	12	no	—
187	C₂×C₄×C₈₉	—	4	12	no	—
188	C₂×C₄×C₈₉	—	4	4	no	—
189	C₂×C₄×C₈₉	—	4	8	no	—
190	C₂×C₄×C₈₉	—	4	12	no	—
191	C₂×C₄×C₈₉	—	4	8	no	—
192	C₂×C₄×C₈₉	—	4	4	no	—
193	C₂×C₄×C₈₉	C₂³×C₄	1	6	yes	—
194	C₂×C₄×C₈₉	C₂³×C₄	1	12	yes	—
195	C₂×C₄×C₈₉	H(5,𝔽₂)	1	6	yes	—
196	C₂²×C₈₉	—	2	6	no	—
197	C₂²×C₈₉	—	2	12	no	—
198	C₂²×C₈₉	—	2	12	no	—
199	C₂²×C₈₉	—	2	6	no	—
200	C₂²×C₈₉	—	4	16	no	—
201	C₂²×C₈₉	—	4	2	no	—
202	C₂²×C₈₉	—	4	1	no	—
203	C₂²×C₈₉	—	4	3	no	—
204	C₂²×C₈₉	—	4	3	no	—
205	C₂²×C₈₉	—	4	6	no	—
206	C₂²×C₈₉	—	4	6	no	—
207	C₂²×C₈₉	—	4	3	no	—
208	C₂²×C₈₉	C₂⁴×C₄	1	1	yes	characteristic
209	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	3	yes	—
210	C₂²×C₈₉	#585	1	3	yes	—
211	C₄×C₈₉	—	2	12	no	—
212	C₄×C₈₉	—	2	6	no	—
213	C₄×C₈₉	—	4	3	no	—
214	C₄×C₈₉	—	4	2	no	—
215	C₄×C₈₉	—	4	1	no	—
216	C₄×C₈₉	—	4	3	no	—
217	C₄×C₈₉	—	4	6	no	—
218	C₄×C₈₉	#560	1	4	yes	direct product factor
219	C₄×#560	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂×C₈₉	—	4	6	no	—
221	C₂×C₈₉	—	4	4	no	—
222	C₂×C₈₉	—	4	2	no	—
223	C₂×C₈₉	C₄×H(5,𝔽₂)	1	3	yes	—
224	C₂×C₈₉	C₂×#560	1	1	yes	characteristic
225	C₂×C₈₉	#3529	1	3	yes	—
226	C₂×#560	C₂×C₈₉	1	1	yes	characteristic
227	#2383	C₂×C₈₉	1	2	yes	complemented
228	#2380	C₂×C₈₉	1	1	yes	characteristic, complemented
229	#2377	C₂×C₈₉	1	6	yes	complemented
230	#2376	C₂×C₈₉	1	3	yes	complemented
231	#2375	C₂×C₈₉	1	3	yes	complemented
232	C₄×#127	C₂×C₈₉	1	1	yes	characteristic, complemented
233	C₄×#126	C₂×C₈₉	1	2	yes	complemented
234	C₄×#123	C₂×C₈₉	1	3	yes	complemented
235	C₄×#121	C₂×C₈₉	1	6	yes	complemented
236	C₄×#120	C₂×C₈₉	1	3	yes	complemented
237	C₈₉	C₄×#560	1	1	yes	characteristic, direct product factor, Sylow
238	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
239	#560	C₄×C₈₉	1	16	yes	direct product factor
240	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
241	C₂×#126	C₂²×C₈₉	1	2	yes	—
242	C₂×#123	C₂²×C₈₉	1	3	yes	—
243	C₂×#121	C₂²×C₈₉	1	6	yes	—
244	C₂×#120	C₂²×C₈₉	1	3	yes	—
245	C₂×C₄×D₄	C₂²×C₈₉	1	3	yes	—
246	C₂×C₄×D₄	C₂²×C₈₉	1	6	yes	—
247	C₂×C₄×D₄	C₂²×C₈₉	1	3	yes	complemented
248	C₂²×C₄²	C₂²×C₈₉	1	3	yes	complemented
249	#390	C₂²×C₈₉	1	3	yes	—
250	#390	C₂²×C₈₉	1	6	yes	—
251	#390	C₂²×C₈₉	1	3	yes	complemented
252	#389	C₂²×C₈₉	1	6	yes	complemented
253	#388	C₂²×C₈₉	1	6	yes	—
254	#388	C₂²×C₈₉	1	6	yes	—
255	#388	C₂²×C₈₉	1	6	yes	—
256	#388	C₂²×C₈₉	1	6	yes	complemented
257	#387	C₂²×C₈₉	1	6	yes	complemented
258	#387	C₂²×C₈₉	1	6	yes	complemented
259	#386	C₂²×C₈₉	1	6	yes	—
260	#386	C₂²×C₈₉	1	3	yes	—
261	#386	C₂²×C₈₉	1	3	yes	—
262	#386	C₂²×C₈₉	1	6	yes	—
263	#386	C₂²×C₈₉	1	6	yes	complemented
264	#385	C₂²×C₈₉	1	3	yes	—
265	#385	C₂²×C₈₉	1	6	yes	—
266	#385	C₂²×C₈₉	1	3	yes	complemented
267	#384	C₂²×C₈₉	1	1	yes	characteristic, complemented
268	#383	C₂²×C₈₉	1	2	yes	complemented
269	#381	C₂²×C₈₉	1	3	yes	complemented
270	#380	C₂²×C₈₉	1	6	yes	complemented
271	#379	C₂²×C₈₉	1	3	yes	—
272	C₄×C₄⋊C₄	C₂²×C₈₉	1	6	yes	complemented
273	C₄×C₂²⋊C₄	C₂²×C₈₉	1	6	yes	—
274	C₄×C₂²⋊C₄	C₂²×C₈₉	1	3	yes	—
275	C₄×C₂²⋊C₄	C₂²×C₈₉	1	3	yes	complemented
276	C₄³	C₂²×C₈₉	1	1	yes	characteristic, complemented
277	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
278	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
279	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
280	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
281	C₂³×C₄	—	4	6	no	—
282	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
283	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
284	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
285	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
287	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
288	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
289	#127	C₂×C₄×C₈₉	1	8	yes	complemented
290	#126	C₂×C₄×C₈₉	1	16	yes	complemented
291	#123	C₂×C₄×C₈₉	1	24	yes	complemented
292	#121	C₂×C₄×C₈₉	1	48	yes	complemented
293	#120	C₂×C₄×C₈₉	1	24	yes	complemented
294	C₄×D₄	—	4	12	no	—
295	C₄×D₄	—	4	6	no	—
296	C₄×D₄	—	4	6	no	—
297	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
298	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
299	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
300	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
301	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
302	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
303	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
304	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
305	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
306	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
307	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
308	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
309	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
310	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
311	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
312	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
313	C₂×C₄²	—	4	6	no	—
314	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
315	C₂×C₄²	C₂³×C₈₉	1	6	yes	—
316	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
317	C₂×C₄²	C₂³×C₈₉	1	6	yes	—
318	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
319	#95	C₂³×C₈₉	1	6	yes	—
320	#95	C₂³×C₈₉	1	6	yes	—
321	#95	C₂³×C₈₉	1	6	yes	—
322	#95	C₂³×C₈₉	1	6	yes	—
323	#95	C₂³×C₈₉	1	6	yes	—
324	#95	C₂³×C₈₉	1	6	yes	—
325	C₂⁴	—	4	3	no	—
326	C₂⁴	—	4	3	no	—
327	C₂⁴	C₂²×C₄×C₈₉	1	4	yes	—
328	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
329	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
330	C₂⁴	C₂⁴×C₈₉	1	3	yes	—
331	C₂×D₄	—	4	6	no	—
332	C₂×D₄	—	4	3	no	—
333	C₂×D₄	—	4	3	no	—
334	C₂×D₄	—	4	3	no	—
335	C₂×D₄	—	4	3	no	—
336	C₂×D₄	—	4	6	no	—
337	C₂×D₄	C₂²×C₄×C₈₉	1	24	yes	—
338	C₂×D₄	C₂²×C₄×C₈₉	1	12	yes	—
339	C₂×D₄	C₂²×C₄×C₈₉	1	12	yes	complemented
340	C₂²×C₄	—	2	6	no	—
341	C₂²×C₄	—	2	12	no	—
342	C₂²×C₄	—	2	12	no	—
343	C₂²×C₄	—	2	6	no	—
344	C₂²×C₄	—	4	3	no	—
345	C₂²×C₄	—	4	3	no	—
346	C₂²×C₄	—	4	3	no	—
347	C₂²×C₄	—	4	6	no	—
348	C₂²×C₄	—	4	3	no	—
349	C₂²×C₄	—	4	6	no	—
350	C₂²×C₄	—	4	16	no	—
351	C₂²×C₄	C₂²×C₄×C₈₉	1	12	yes	complemented
352	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
353	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
354	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
355	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
356	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
357	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
358	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
359	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
360	C₄⋊C₄	—	4	6	no	—
361	C₄⋊C₄	—	4	3	no	—
362	C₄⋊C₄	—	4	3	no	—
363	C₄⋊C₄	—	4	6	no	—
364	C₄⋊C₄	C₂²×C₄×C₈₉	1	24	yes	complemented
365	C₂²⋊C₄	—	4	6	no	—
366	C₂²⋊C₄	—	4	6	no	—
367	C₂²⋊C₄	—	4	3	no	—
368	C₂²⋊C₄	—	4	6	no	—
369	C₂²⋊C₄	—	4	3	no	—
370	C₂²⋊C₄	—	4	6	no	—
371	C₂²⋊C₄	—	4	3	no	—
372	C₂²⋊C₄	—	4	3	no	—
373	C₂²⋊C₄	C₂²×C₄×C₈₉	1	24	yes	—
374	C₂²⋊C₄	C₂²×C₄×C₈₉	1	12	yes	—
375	C₂²⋊C₄	C₂²×C₄×C₈₉	1	12	yes	complemented
376	C₄²	—	2	12	no	—
377	C₄²	—	2	6	no	—
378	C₄²	—	4	6	no	—
379	C₄²	—	4	3	no	—
380	C₄²	C₂²×C₄×C₈₉	1	4	yes	complemented
381	C₂³	—	2	6	no	—
382	C₂³	—	2	3	no	—
383	C₂³	—	2	6	no	—
384	C₂³	—	2	3	no	—
385	C₂³	—	2	3	no	—
386	C₂³	—	2	6	no	—
387	C₂³	—	2	3	no	—
388	C₂³	—	2	6	no	—
389	C₂³	—	4	12	no	—
390	C₂³	—	4	4	no	—
391	C₂³	—	4	12	no	—
392	C₂³	C₂³×C₄×C₈₉	1	4	yes	—
393	C₂³	C₂³×C₄×C₈₉	1	2	yes	—
394	C₂³	C₂³×C₄×C₈₉	1	6	yes	—
395	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
396	D₄	—	4	24	no	—
397	D₄	—	4	12	no	—
398	D₄	—	4	12	no	—
399	C₂×C₄	—	2	6	no	—
400	C₂×C₄	—	2	3	no	—
401	C₂×C₄	—	2	3	no	—
402	C₂×C₄	—	2	6	no	—
403	C₂×C₄	—	2	6	no	—
404	C₂×C₄	—	2	3	no	—
405	C₂×C₄	—	2	3	no	—
406	C₂×C₄	—	2	6	no	—
407	C₂×C₄	—	2	6	no	—
408	C₂×C₄	—	2	3	no	—
409	C₂×C₄	—	2	6	no	—
410	C₂×C₄	—	2	6	no	—
411	C₂×C₄	—	2	6	no	—
412	C₂×C₄	—	4	12	no	—
413	C₂×C₄	—	4	12	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	8	no	—
416	C₂×C₄	—	4	12	no	—
417	C₂×C₄	—	4	8	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	C₂³×C₄×C₈₉	1	6	yes	—
420	C₂×C₄	C₂³×C₄×C₈₉	1	12	yes	—
421	C₂×C₄	H(5,𝔽₂)×C₈₉	1	6	yes	—
422	C₂²	—	2	6	no	—
423	C₂²	—	2	12	no	—
424	C₂²	—	2	12	no	—
425	C₂²	—	2	6	no	—
426	C₂²	—	4	16	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	4	3	no	—
430	C₂²	—	4	3	no	—
431	C₂²	—	4	6	no	—
432	C₂²	—	4	3	no	—
433	C₂²	—	4	6	no	—
434	C₂²	C₂⁴×C₄×C₈₉	1	1	yes	characteristic
435	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	3	yes	—
436	C₂²	#585×C₈₉	1	3	yes	—
437	C₄	—	2	12	no	—
438	C₄	—	2	6	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	3	no	—
442	C₄	—	4	6	no	—
443	C₄	—	4	3	no	—
444	C₄	#560×C₈₉	1	4	yes	direct product factor
445	C₂	—	4	6	no	—
446	C₂	—	4	4	no	—
447	C₂	—	4	2	no	—
448	C₂	C₄×H(5,𝔽₂)×C₈₉	1	3	yes	—
449	C₂	C₂×#560×C₈₉	1	1	yes	characteristic
450	C₂	C₈₉×#3529	1	3	yes	—

	subgroup	G/H
center	C₂²×C₄×C₈₉	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₈₉
Frattini, cosocle	C₂³	C₂⁵×C₈₉
socle	C₂³×C₈₉	C₂⁵
prime radical	C₂×#560×C₈₉	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₉×#2383	C₂	semidirect
3. C₈₉×#2380	C₂	semidirect
4. C₈₉×#2377	C₂	semidirect
5. C₈₉×#2376	C₂	semidirect
6. C₈₉×#2375	C₂	semidirect
7. C₄×#127×C₈₉	C₂	semidirect
8. C₄×#126×C₈₉	C₂	semidirect
9. C₄×#123×C₈₉	C₂	semidirect
10. C₄×#121×C₈₉	C₂	semidirect
11. C₄×#120×C₈₉	C₂	semidirect
13. #560×C₈₉	C₄	direct (N × H)
21. C₂×C₄×D₄×C₈₉	C₂²	semidirect
22. C₂²×C₄²×C₈₉	C₂²	semidirect
25. #390×C₈₉	C₂²	semidirect
26. #389×C₈₉	C₂²	semidirect
30. #388×C₈₉	C₂²	semidirect
31. #387×C₈₉	C₂²	semidirect
32. #387×C₈₉	C₂²	semidirect
37. #386×C₈₉	C₂²	semidirect
40. #385×C₈₉	C₂²	semidirect
41. #384×C₈₉	C₂²	semidirect
42. #383×C₈₉	C₂²	semidirect
43. #381×C₈₉	C₂²	semidirect
44. #380×C₈₉	C₂²	semidirect
46. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
49. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
50. C₄³×C₈₉	C₂²	semidirect
63. #127×C₈₉	C₂×C₄	semidirect
64. #126×C₈₉	C₂×C₄	semidirect
65. #123×C₈₉	C₂×C₄	semidirect
66. #121×C₈₉	C₂×C₄	semidirect
67. #120×C₈₉	C₂×C₄	semidirect
113. C₂×D₄×C₈₉	C₂²×C₄	semidirect
125. C₂²×C₄×C₈₉	C₂²×C₄	semidirect
138. C₄⋊C₄×C₈₉	C₂²×C₄	semidirect
149. C₂²⋊C₄×C₈₉	C₂²×C₄	semidirect
154. C₄²×C₈₉	C₂²×C₄	semidirect
218. C₄×C₈₉	#560	direct (N × H)
219. C₄×#560	C₈₉	direct (N × H)
227. #2383	C₂×C₈₉	semidirect
228. #2380	C₂×C₈₉	semidirect
229. #2377	C₂×C₈₉	semidirect
230. #2376	C₂×C₈₉	semidirect
231. #2375	C₂×C₈₉	semidirect
232. C₄×#127	C₂×C₈₉	semidirect
233. C₄×#126	C₂×C₈₉	semidirect
234. C₄×#123	C₂×C₈₉	semidirect
235. C₄×#121	C₂×C₈₉	semidirect
236. C₄×#120	C₂×C₈₉	semidirect
237. C₈₉	C₄×#560	direct (N × H)
239. #560	C₄×C₈₉	direct (N × H)
247. C₂×C₄×D₄	C₂²×C₈₉	semidirect
248. C₂²×C₄²	C₂²×C₈₉	semidirect
251. #390	C₂²×C₈₉	semidirect
252. #389	C₂²×C₈₉	semidirect
256. #388	C₂²×C₈₉	semidirect
257. #387	C₂²×C₈₉	semidirect
258. #387	C₂²×C₈₉	semidirect
263. #386	C₂²×C₈₉	semidirect
266. #385	C₂²×C₈₉	semidirect
267. #384	C₂²×C₈₉	semidirect
268. #383	C₂²×C₈₉	semidirect
269. #381	C₂²×C₈₉	semidirect
270. #380	C₂²×C₈₉	semidirect
272. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
275. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
276. C₄³	C₂²×C₈₉	semidirect
289. #127	C₂×C₄×C₈₉	semidirect
290. #126	C₂×C₄×C₈₉	semidirect
291. #123	C₂×C₄×C₈₉	semidirect
292. #121	C₂×C₄×C₈₉	semidirect
293. #120	C₂×C₄×C₈₉	semidirect
339. C₂×D₄	C₂²×C₄×C₈₉	semidirect
351. C₂²×C₄	C₂²×C₄×C₈₉	semidirect
364. C₄⋊C₄	C₂²×C₄×C₈₉	semidirect
375. C₂²⋊C₄	C₂²×C₄×C₈₉	semidirect
380. C₄²	C₂²×C₄×C₈₉	semidirect
444. C₄	#560×C₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#560×C₈₉	2
C₈₉×#2383	2
C₈₉×#2380	2
C₈₉×#2377	2
C₈₉×#2376	2
C₈₉×#2375	2
C₄×#127×C₈₉	2
C₄×#126×C₈₉	2
C₄×#123×C₈₉	2
C₄×#121×C₈₉	2
C₄×#120×C₈₉	2
C₄×#560	89

Subgroups — C4×#560×C89 #36412199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#560×C₈₉ #36412199