Subgroups — C₈₉×#35537 #36413385

Order 22784.

2962 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#540×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#518×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2566	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2541	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2500	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2456	C₂	1	8	yes	maximal, complemented
7	C₈₉×#2433	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2424	C₂	1	8	yes	maximal, complemented
9	C₈₉×#2328	C₂	1	2	yes	maximal, complemented
10	C₄×#127×C₈₉	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2298	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
13	#540×C₈₉	—	2	8	no	—
14	C₂×#127×C₈₉	C₂²	1	2	yes	—
15	C₂×#127×C₈₉	C₂²	1	2	yes	—
16	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic, complemented
17	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic, complemented
18	C₂×#123×C₈₉	C₂²	1	4	yes	complemented
19	C₂×#121×C₈₉	C₂²	1	4	yes	—
20	C₂×#121×C₈₉	C₂²	1	2	yes	—
21	C₂×#121×C₈₉	C₂²	1	8	yes	complemented
22	C₂×#120×C₈₉	C₂²	1	8	yes	—
23	#518×C₈₉	—	2	8	no	—
24	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
28	C₂×C₄×D₄×C₈₉	C₂²	1	8	yes	complemented
29	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
32	#396×C₈₉	C₂²	1	8	yes	complemented
33	#394×C₈₉	C₂²	1	8	yes	—
34	#392×C₈₉	C₂²	1	8	yes	—
35	#392×C₈₉	C₂²	1	8	yes	complemented
36	#390×C₈₉	C₂²	1	2	yes	—
37	#390×C₈₉	C₂²	1	2	yes	—
38	#390×C₈₉	C₂²	1	8	yes	complemented
39	#390×C₈₉	C₂²	1	2	yes	complemented
40	#390×C₈₉	C₂²	1	2	yes	complemented
41	#388×C₈₉	C₂²	1	4	yes	—
42	#388×C₈₉	C₂²	1	8	yes	complemented
43	#387×C₈₉	C₂²	1	4	yes	complemented
44	#386×C₈₉	C₂²	1	8	yes	complemented
45	#386×C₈₉	C₂²	1	8	yes	complemented
46	#385×C₈₉	C₂²	1	8	yes	complemented
47	#384×C₈₉	C₂²	1	2	yes	complemented
48	#382×C₈₉	C₂²	1	2	yes	complemented
49	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
50	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
51	#376×C₈₉	C₂²	1	1	yes	characteristic, complemented
52	C₄³×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	C₂⁵×C₈₉	C₂³	1	2	yes	—
54	C₂²×D₄×C₈₉	—	2	8	no	—
55	C₂²×D₄×C₈₉	—	2	4	no	—
56	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
57	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
58	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
59	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
60	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
61	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
62	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
63	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
65	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
66	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
67	#127×C₈₉	—	2	8	no	—
68	#127×C₈₉	—	2	8	no	—
69	#127×C₈₉	—	2	4	no	—
70	#125×C₈₉	—	2	4	no	—
71	#123×C₈₉	—	2	16	no	—
72	#121×C₈₉	—	2	8	no	—
73	#121×C₈₉	—	2	16	no	—
74	#121×C₈₉	—	4	16	no	—
75	#120×C₈₉	—	4	16	no	—
76	C₄×D₄×C₈₉	—	2	16	no	—
77	C₄×D₄×C₈₉	—	2	8	no	—
78	C₄×D₄×C₈₉	—	2	8	no	—
79	C₄×D₄×C₈₉	—	2	8	no	—
80	C₄×D₄×C₈₉	—	4	16	no	—
81	#117×C₈₉	—	2	4	no	—
82	#117×C₈₉	D₄	1	8	yes	complemented
83	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
88	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
89	C₂×C₂²⋊C₄×C₈₉	—	2	16	no	—
90	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
91	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
92	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
93	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
96	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
98	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
99	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
100	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
101	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
102	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
103	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
104	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
105	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
107	#95×C₈₉	C₂³	1	4	yes	—
108	#95×C₈₉	C₂³	1	4	yes	—
109	#95×C₈₉	C₂³	1	4	yes	—
110	#95×C₈₉	C₂³	1	8	yes	—
111	C₂⁴×C₈₉	—	2	4	no	—
112	C₂⁴×C₈₉	—	2	8	no	—
113	C₂⁴×C₈₉	—	4	8	no	—
114	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
115	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
116	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
117	C₂×D₄×C₈₉	—	2	32	no	—
118	C₂×D₄×C₈₉	—	2	8	no	—
119	C₂×D₄×C₈₉	—	2	16	no	—
120	C₂×D₄×C₈₉	—	2	8	no	—
121	C₂×D₄×C₈₉	—	2	16	no	—
122	C₂×D₄×C₈₉	—	2	4	no	—
123	C₂×D₄×C₈₉	—	2	4	no	—
124	C₂×D₄×C₈₉	—	2	4	no	—
125	C₂×D₄×C₈₉	—	2	8	no	—
126	C₂×D₄×C₈₉	—	2	4	no	—
127	C₂×D₄×C₈₉	—	2	4	no	—
128	C₂×D₄×C₈₉	—	2	4	no	—
129	C₂×D₄×C₈₉	—	2	16	no	—
130	C₂×D₄×C₈₉	—	4	8	no	—
131	C₂×D₄×C₈₉	—	4	8	no	—
132	C₂×D₄×C₈₉	—	4	8	no	—
133	C₂×D₄×C₈₉	—	4	8	no	—
134	C₂×D₄×C₈₉	—	4	8	no	—
135	C₂×D₄×C₈₉	#41	1	8	yes	—
136	C₂²×C₄×C₈₉	—	2	4	no	—
137	C₂²×C₄×C₈₉	—	2	8	no	—
138	C₂²×C₄×C₈₉	—	2	8	no	—
139	C₂²×C₄×C₈₉	—	2	8	no	—
140	C₂²×C₄×C₈₉	—	4	8	no	—
141	C₂²×C₄×C₈₉	—	4	8	no	—
142	C₂²×C₄×C₈₉	—	4	8	no	—
143	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
148	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
152	C₄⋊C₄×C₈₉	—	2	4	no	—
153	C₄⋊C₄×C₈₉	—	2	4	no	—
154	C₄⋊C₄×C₈₉	—	2	8	no	—
155	C₄⋊C₄×C₈₉	—	2	8	no	—
156	C₄⋊C₄×C₈₉	—	4	8	no	—
157	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
158	C₂²⋊C₄×C₈₉	—	2	4	no	—
159	C₂²⋊C₄×C₈₉	—	2	8	no	—
160	C₂²⋊C₄×C₈₉	—	2	8	no	—
161	C₂²⋊C₄×C₈₉	—	2	8	no	—
162	C₂²⋊C₄×C₈₉	—	2	8	no	—
163	C₂²⋊C₄×C₈₉	—	2	16	no	—
164	C₂²⋊C₄×C₈₉	—	2	16	no	—
165	C₂²⋊C₄×C₈₉	—	2	8	no	—
166	C₂²⋊C₄×C₈₉	—	4	8	no	—
167	C₂²⋊C₄×C₈₉	—	4	8	no	—
168	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
169	C₄²×C₈₉	—	2	4	no	—
170	C₄²×C₈₉	—	2	4	no	—
171	C₄²×C₈₉	—	2	4	no	—
172	C₄²×C₈₉	—	2	8	no	—
173	C₄²×C₈₉	C₂×D₄	1	4	yes	—
174	C₄²×C₈₉	C₂×D₄	1	4	yes	—
175	C₂³×C₈₉	—	2	16	no	—
176	C₂³×C₈₉	—	2	4	no	—
177	C₂³×C₈₉	—	2	2	no	—
178	C₂³×C₈₉	—	2	4	no	—
179	C₂³×C₈₉	—	2	8	no	—
180	C₂³×C₈₉	—	2	4	no	—
181	C₂³×C₈₉	—	2	8	no	—
182	C₂³×C₈₉	—	2	4	no	—
183	C₂³×C₈₉	—	2	4	no	—
184	C₂³×C₈₉	—	2	4	no	—
185	C₂³×C₈₉	—	2	8	no	—
186	C₂³×C₈₉	—	2	8	no	—
187	C₂³×C₈₉	—	8	8	no	—
188	C₂³×C₈₉	—	8	16	no	—
189	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
190	C₂³×C₈₉	C₂×#41	1	8	yes	—
191	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
192	D₄×C₈₉	—	2	16	no	—
193	D₄×C₈₉	—	2	16	no	—
194	D₄×C₈₉	—	4	32	no	—
195	D₄×C₈₉	—	4	8	no	—
196	D₄×C₈₉	—	8	8	no	—
197	D₄×C₈₉	—	8	8	no	—
198	D₄×C₈₉	—	8	16	no	—
199	C₂×C₄×C₈₉	—	2	4	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	8	no	—
205	C₂×C₄×C₈₉	—	2	4	no	—
206	C₂×C₄×C₈₉	—	2	4	no	—
207	C₂×C₄×C₈₉	—	2	4	no	—
208	C₂×C₄×C₈₉	—	2	4	no	—
209	C₂×C₄×C₈₉	—	2	8	no	—
210	C₂×C₄×C₈₉	—	2	8	no	—
211	C₂×C₄×C₈₉	—	2	4	no	—
212	C₂×C₄×C₈₉	—	8	8	no	—
213	C₂×C₄×C₈₉	—	8	8	no	—
214	C₂×C₄×C₈₉	—	8	8	no	—
215	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
217	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
218	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
219	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
220	C₂×C₄×C₈₉	H(5,𝔽₂)	1	8	yes	—
221	C₂²×C₈₉	—	2	2	no	—
222	C₂²×C₈₉	—	2	8	no	—
223	C₂²×C₈₉	—	2	4	no	—
224	C₂²×C₈₉	—	2	16	no	—
225	C₂²×C₈₉	—	4	4	no	—
226	C₂²×C₈₉	—	4	4	no	—
227	C₂²×C₈₉	—	4	8	no	—
228	C₂²×C₈₉	—	4	4	no	—
229	C₂²×C₈₉	—	4	4	no	—
230	C₂²×C₈₉	—	4	4	no	—
231	C₂²×C₈₉	—	4	4	no	—
232	C₂²×C₈₉	—	4	8	no	—
233	C₂²×C₈₉	—	4	8	no	—
234	C₂²×C₈₉	—	8	16	no	—
235	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
236	C₂²×C₈₉	C₂²×#41	1	2	yes	—
237	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	4	yes	—
238	C₄×C₈₉	—	2	2	no	—
239	C₄×C₈₉	—	2	4	no	—
240	C₄×C₈₉	—	2	4	no	—
241	C₄×C₈₉	—	2	8	no	—
242	C₄×C₈₉	—	4	4	no	—
243	C₄×C₈₉	—	4	4	no	—
244	C₄×C₈₉	—	4	4	no	—
245	C₄×C₈₉	#525	1	4	yes	—
246	#35537	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₂×C₈₉	—	4	8	no	—
248	C₂×C₈₉	—	4	2	no	—
249	C₂×C₈₉	—	8	4	no	—
250	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
251	C₂×C₈₉	#3498	1	2	yes	—
252	C₂×C₈₉	#3519	1	4	yes	—
253	C₂×#540	C₂×C₈₉	1	1	yes	characteristic, complemented
254	C₂×#518	C₂×C₈₉	1	1	yes	characteristic, complemented
255	#2566	C₂×C₈₉	1	2	yes	complemented
256	#2541	C₂×C₈₉	1	2	yes	complemented
257	#2500	C₂×C₈₉	1	2	yes	complemented
258	#2456	C₂×C₈₉	1	8	yes	complemented
259	#2433	C₂×C₈₉	1	2	yes	complemented
260	#2424	C₂×C₈₉	1	8	yes	complemented
261	#2328	C₂×C₈₉	1	2	yes	complemented
262	C₄×#127	C₂×C₈₉	1	2	yes	complemented
263	#2298	C₂×C₈₉	1	1	yes	characteristic, complemented
264	C₈₉	#35537	1	1	yes	characteristic, direct product factor, Sylow
265	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
266	#540	—	2	8	no	—
267	C₂×#127	C₂²×C₈₉	1	2	yes	—
268	C₂×#127	C₂²×C₈₉	1	2	yes	—
269	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic, complemented
270	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic, complemented
271	C₂×#123	C₂²×C₈₉	1	4	yes	complemented
272	C₂×#121	C₂²×C₈₉	1	4	yes	—
273	C₂×#121	C₂²×C₈₉	1	2	yes	—
274	C₂×#121	C₂²×C₈₉	1	8	yes	complemented
275	C₂×#120	C₂²×C₈₉	1	8	yes	—
276	#518	—	2	8	no	—
277	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
278	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
279	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
280	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
281	C₂×C₄×D₄	C₂²×C₈₉	1	8	yes	complemented
282	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
283	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
284	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
285	#396	C₂²×C₈₉	1	8	yes	complemented
286	#394	C₂²×C₈₉	1	8	yes	—
287	#392	C₂²×C₈₉	1	8	yes	—
288	#392	C₂²×C₈₉	1	8	yes	complemented
289	#390	C₂²×C₈₉	1	2	yes	—
290	#390	C₂²×C₈₉	1	2	yes	—
291	#390	C₂²×C₈₉	1	8	yes	complemented
292	#390	C₂²×C₈₉	1	2	yes	complemented
293	#390	C₂²×C₈₉	1	2	yes	complemented
294	#388	C₂²×C₈₉	1	4	yes	—
295	#388	C₂²×C₈₉	1	8	yes	complemented
296	#387	C₂²×C₈₉	1	4	yes	complemented
297	#386	C₂²×C₈₉	1	8	yes	complemented
298	#386	C₂²×C₈₉	1	8	yes	complemented
299	#385	C₂²×C₈₉	1	8	yes	complemented
300	#384	C₂²×C₈₉	1	2	yes	complemented
301	#382	C₂²×C₈₉	1	2	yes	complemented
302	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
303	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
304	#376	C₂²×C₈₉	1	1	yes	characteristic, complemented
305	C₄³	C₂²×C₈₉	1	1	yes	characteristic, complemented
306	C₂⁵	C₂³×C₈₉	1	2	yes	—
307	C₂²×D₄	—	2	8	no	—
308	C₂²×D₄	—	2	4	no	—
309	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
310	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
311	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
312	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
313	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
314	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
315	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
316	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
317	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
318	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
319	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
320	#127	—	2	8	no	—
321	#127	—	2	8	no	—
322	#127	—	2	4	no	—
323	#125	—	2	4	no	—
324	#123	—	2	16	no	—
325	#121	—	2	8	no	—
326	#121	—	2	16	no	—
327	#121	—	4	16	no	—
328	#120	—	4	16	no	—
329	C₄×D₄	—	2	16	no	—
330	C₄×D₄	—	2	8	no	—
331	C₄×D₄	—	2	8	no	—
332	C₄×D₄	—	2	8	no	—
333	C₄×D₄	—	4	16	no	—
334	#117	—	2	4	no	—
335	#117	D₄×C₈₉	1	8	yes	complemented
336	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
337	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
338	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
339	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
340	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
341	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
342	C₂×C₂²⋊C₄	—	2	16	no	—
343	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
344	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
354	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
355	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
356	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
357	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
358	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
359	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
360	#95	C₂³×C₈₉	1	4	yes	—
361	#95	C₂³×C₈₉	1	4	yes	—
362	#95	C₂³×C₈₉	1	4	yes	—
363	#95	C₂³×C₈₉	1	8	yes	—
364	C₂⁴	—	2	4	no	—
365	C₂⁴	—	2	8	no	—
366	C₂⁴	—	4	8	no	—
367	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
368	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
369	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
370	C₂×D₄	—	2	32	no	—
371	C₂×D₄	—	2	8	no	—
372	C₂×D₄	—	2	16	no	—
373	C₂×D₄	—	2	8	no	—
374	C₂×D₄	—	2	16	no	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	8	no	—
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	—	2	16	no	—
383	C₂×D₄	—	4	8	no	—
384	C₂×D₄	—	4	8	no	—
385	C₂×D₄	—	4	8	no	—
386	C₂×D₄	—	4	8	no	—
387	C₂×D₄	—	4	8	no	—
388	C₂×D₄	#41×C₈₉	1	8	yes	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	8	no	—
391	C₂²×C₄	—	2	8	no	—
392	C₂²×C₄	—	2	8	no	—
393	C₂²×C₄	—	4	8	no	—
394	C₂²×C₄	—	4	8	no	—
395	C₂²×C₄	—	4	8	no	—
396	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
397	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
398	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
399	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
400	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
401	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
402	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
403	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
404	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	8	no	—
408	C₄⋊C₄	—	2	8	no	—
409	C₄⋊C₄	—	4	8	no	—
410	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
411	C₂²⋊C₄	—	2	4	no	—
412	C₂²⋊C₄	—	2	8	no	—
413	C₂²⋊C₄	—	2	8	no	—
414	C₂²⋊C₄	—	2	8	no	—
415	C₂²⋊C₄	—	2	8	no	—
416	C₂²⋊C₄	—	2	16	no	—
417	C₂²⋊C₄	—	2	16	no	—
418	C₂²⋊C₄	—	2	8	no	—
419	C₂²⋊C₄	—	4	8	no	—
420	C₂²⋊C₄	—	4	8	no	—
421	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
422	C₄²	—	2	4	no	—
423	C₄²	—	2	4	no	—
424	C₄²	—	2	4	no	—
425	C₄²	—	2	8	no	—
426	C₄²	C₂×D₄×C₈₉	1	4	yes	—
427	C₄²	C₂×D₄×C₈₉	1	4	yes	—
428	C₂³	—	2	16	no	—
429	C₂³	—	2	4	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	4	no	—
432	C₂³	—	2	8	no	—
433	C₂³	—	2	4	no	—
434	C₂³	—	2	8	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	2	4	no	—
437	C₂³	—	2	4	no	—
438	C₂³	—	2	8	no	—
439	C₂³	—	2	8	no	—
440	C₂³	—	8	8	no	—
441	C₂³	—	8	16	no	—
442	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
443	C₂³	C₂×#41×C₈₉	1	8	yes	—
444	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
445	D₄	—	2	16	no	—
446	D₄	—	2	16	no	—
447	D₄	—	4	32	no	—
448	D₄	—	4	8	no	—
449	D₄	—	8	8	no	—
450	D₄	—	8	8	no	—
451	D₄	—	8	16	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	8	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	8	no	—
463	C₂×C₄	—	2	8	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	8	8	no	—
466	C₂×C₄	—	8	8	no	—
467	C₂×C₄	—	8	8	no	—
468	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
469	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
470	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
471	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
472	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
473	C₂×C₄	H(5,𝔽₂)×C₈₉	1	8	yes	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	8	no	—
476	C₂²	—	2	4	no	—
477	C₂²	—	2	16	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	4	4	no	—
480	C₂²	—	4	4	no	—
481	C₂²	—	4	8	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	4	8	no	—
486	C₂²	—	4	8	no	—
487	C₂²	—	8	16	no	—
488	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
489	C₂²	C₂²×#41×C₈₉	1	2	yes	—
490	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	4	yes	—
491	C₄	—	2	2	no	—
492	C₄	—	2	4	no	—
493	C₄	—	2	4	no	—
494	C₄	—	2	8	no	—
495	C₄	—	4	4	no	—
496	C₄	—	4	4	no	—
497	C₄	—	4	4	no	—
498	C₄	#525×C₈₉	1	4	yes	—
499	C₂	—	4	8	no	—
500	C₂	—	4	2	no	—
501	C₂	—	8	4	no	—
502	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
503	C₂	C₈₉×#3498	1	2	yes	—
504	C₂	C₈₉×#3519	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×#540×C₈₉	C₂	semidirect
2. C₂×#518×C₈₉	C₂	semidirect
3. C₈₉×#2566	C₂	semidirect
4. C₈₉×#2541	C₂	semidirect
5. C₈₉×#2500	C₂	semidirect
6. C₈₉×#2456	C₂	semidirect
7. C₈₉×#2433	C₂	semidirect
8. C₈₉×#2424	C₂	semidirect
9. C₈₉×#2328	C₂	semidirect
10. C₄×#127×C₈₉	C₂	semidirect
11. C₈₉×#2298	C₂	semidirect
16. C₂×#127×C₈₉	C₂²	semidirect
17. C₂×#125×C₈₉	C₂²	semidirect
18. C₂×#123×C₈₉	C₂²	semidirect
21. C₂×#121×C₈₉	C₂²	semidirect
27. C₂×C₄×D₄×C₈₉	C₂²	semidirect
28. C₂×C₄×D₄×C₈₉	C₂²	semidirect
32. #396×C₈₉	C₂²	semidirect
35. #392×C₈₉	C₂²	semidirect
38. #390×C₈₉	C₂²	semidirect
39. #390×C₈₉	C₂²	semidirect
40. #390×C₈₉	C₂²	semidirect
42. #388×C₈₉	C₂²	semidirect
43. #387×C₈₉	C₂²	semidirect
44. #386×C₈₉	C₂²	semidirect
45. #386×C₈₉	C₂²	semidirect
46. #385×C₈₉	C₂²	semidirect
47. #384×C₈₉	C₂²	semidirect
48. #382×C₈₉	C₂²	semidirect
49. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
51. #376×C₈₉	C₂²	semidirect
52. C₄³×C₈₉	C₂²	semidirect
82. #117×C₈₉	D₄	semidirect
246. #35537	C₈₉	direct (N × H)
253. C₂×#540	C₂×C₈₉	semidirect
254. C₂×#518	C₂×C₈₉	semidirect
255. #2566	C₂×C₈₉	semidirect
256. #2541	C₂×C₈₉	semidirect
257. #2500	C₂×C₈₉	semidirect
258. #2456	C₂×C₈₉	semidirect
259. #2433	C₂×C₈₉	semidirect
260. #2424	C₂×C₈₉	semidirect
261. #2328	C₂×C₈₉	semidirect
262. C₄×#127	C₂×C₈₉	semidirect
263. #2298	C₂×C₈₉	semidirect
264. C₈₉	#35537	direct (N × H)
269. C₂×#127	C₂²×C₈₉	semidirect
270. C₂×#125	C₂²×C₈₉	semidirect
271. C₂×#123	C₂²×C₈₉	semidirect
274. C₂×#121	C₂²×C₈₉	semidirect
280. C₂×C₄×D₄	C₂²×C₈₉	semidirect
281. C₂×C₄×D₄	C₂²×C₈₉	semidirect
285. #396	C₂²×C₈₉	semidirect
288. #392	C₂²×C₈₉	semidirect
291. #390	C₂²×C₈₉	semidirect
292. #390	C₂²×C₈₉	semidirect
293. #390	C₂²×C₈₉	semidirect
295. #388	C₂²×C₈₉	semidirect
296. #387	C₂²×C₈₉	semidirect
297. #386	C₂²×C₈₉	semidirect
298. #386	C₂²×C₈₉	semidirect
299. #385	C₂²×C₈₉	semidirect
300. #384	C₂²×C₈₉	semidirect
301. #382	C₂²×C₈₉	semidirect
302. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
304. #376	C₂²×C₈₉	semidirect
305. C₄³	C₂²×C₈₉	semidirect
335. #117	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×#540×C₈₉	2
C₂×#518×C₈₉	2
C₈₉×#2566	2
C₈₉×#2541	2
C₈₉×#2500	2
C₈₉×#2456	2
C₈₉×#2433	2
C₈₉×#2424	2
C₈₉×#2328	2
C₄×#127×C₈₉	2
C₈₉×#2298	2
#35537	89

Subgroups — C89×#35537 #36413385

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35537 #36413385