Subgroups — #36707540

Order 22784.

590 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028674	C₂	1	1	yes	maximal, characteristic
2	#26022059	C₂	1	1	yes	maximal, characteristic, complemented
3	#26022058	C₂	1	1	yes	maximal, characteristic, complemented
4	#26022058	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022053	C₂	1	1	yes	maximal, characteristic, complemented
6	#26022052	C₂	1	1	yes	maximal, characteristic, complemented
7	#26022049	C₂	1	1	yes	maximal, characteristic, complemented
8	#26022048	C₂	1	1	yes	maximal, characteristic, complemented
9	#26022006	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄⋊C₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#26021864	C₂	1	1	yes	maximal, characteristic
12	#26021864	C₂	1	1	yes	maximal, characteristic
13	#26021850	C₂	1	1	yes	maximal, characteristic, complemented
14	#26021847	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2164	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668020	C₄	1	1	yes	characteristic
17	C₂×#15668018	C₂²	1	1	yes	characteristic
18	#19152066	C₄	1	1	yes	characteristic
19	C₂×#15667951	C₂²	1	1	yes	characteristic
20	C₂×#15667951	C₂²	1	1	yes	characteristic
21	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
23	#19151555	C₄	1	1	yes	characteristic
24	#19151555	C₄	1	1	yes	characteristic
25	#19151554	C₄	1	1	yes	characteristic
26	#19151552	C₂²	1	1	yes	characteristic
27	#19151552	C₂²	1	1	yes	characteristic
28	#19151550	C₄	1	1	yes	characteristic
29	#19151550	C₄	1	1	yes	characteristic
30	M₁₆×Dic₈₉	C₄	1	1	yes	characteristic
31	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
32	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
34	C₄⋊#13083549	C₂²	1	1	yes	characteristic
35	C₄⋊#13083549	C₂²	1	1	yes	characteristic
36	#19151416	C₂²	1	1	yes	characteristic
37	#19151416	C₂²	1	1	yes	characteristic
38	#19151416	C₂²	1	1	yes	characteristic
39	#19151416	C₂²	1	1	yes	characteristic
40	C₂²⋊#13083549	C₂²	1	1	yes	characteristic
41	C₂²⋊#13083549	C₂²	1	1	yes	characteristic
42	#19151377	C₂²	1	1	yes	characteristic
43	#19151377	C₂²	1	1	yes	characteristic
44	#19151377	C₂²	1	1	yes	characteristic
45	#19151377	C₂²	1	1	yes	characteristic
46	#19151374	C₂²	1	1	yes	characteristic
47	#19151373	C₂²	1	1	yes	characteristic
48	#19151373	C₂²	1	1	yes	characteristic
49	C₄×#13083549	C₂²	1	1	yes	characteristic
50	C₁₆×Dic₈₉	C₂²	1	1	yes	characteristic
51	C₁₆×Dic₈₉	C₂²	1	1	yes	characteristic
52	#405×C₈₉	C₂²	1	1	yes	characteristic
53	C₄⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic
54	C₄⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic
55	C₂²⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic
56	C₂²⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic
57	#346×C₈₉	C₂²	1	1	yes	characteristic
58	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
59	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
60	#15668020	—	2	4	no	—
61	#15668018	—	2	2	no	—
62	#15668018	—	2	2	no	—
63	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
64	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
65	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
66	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
67	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
68	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
69	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
72	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
73	#15667977	C₈	1	1	yes	characteristic
74	#15667977	C₈	1	1	yes	characteristic
75	#15667974	C₈	1	1	yes	characteristic
76	#15667974	C₈	1	1	yes	characteristic
77	#15667972	C₈	1	1	yes	characteristic
78	#15667972	C₈	1	1	yes	characteristic
79	#15667972	C₈	1	1	yes	characteristic
80	#15667972	C₈	1	1	yes	characteristic
81	#15667969	C₂×C₄	1	1	yes	characteristic
82	#15667969	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
84	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
85	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
86	#15667951	—	2	2	no	—
87	#15667951	—	2	2	no	—
88	C₂×#13083549	C₂³	1	1	yes	characteristic
89	C₂×#13083549	C₂³	1	1	yes	characteristic
90	C₂×#13083549	C₂³	1	1	yes	characteristic
91	C₂×#13083549	C₂³	1	1	yes	characteristic
92	C₁₆×D₈₉	—	2	2	no	—
93	C₁₆×D₈₉	—	2	2	no	—
94	#15667923	C₂×C₄	1	1	yes	characteristic
95	#15667923	C₂×C₄	1	1	yes	characteristic
96	#15667922	C₂×C₄	1	1	yes	characteristic
97	#15667922	C₂×C₄	1	1	yes	characteristic
98	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
99	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
100	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
101	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
102	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
103	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
104	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
105	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
106	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
107	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
108	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
109	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
111	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
112	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
113	#97×C₈₉	C₂×C₄	1	1	yes	characteristic
114	#97×C₈₉	C₂×C₄	1	1	yes	characteristic
115	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
116	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
117	#13083574	—	2	2	no	—
118	#13083574	—	2	2	no	—
119	C₂×Dic₁₇₈	C₂×C₈	1	1	yes	characteristic
120	C₂×D₃₅₆	C₂×C₈	1	1	yes	characteristic
121	C₂×C₂²⋊D₈₉	C₂×C₈	1	1	yes	characteristic
122	C₂×C₂²⋊D₈₉	C₂×C₈	1	1	yes	characteristic
123	C₂²×Dic₈₉	C₂×C₈	1	1	yes	characteristic
124	C₂²×Dic₈₉	C₂×C₈	1	1	yes	characteristic
125	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
126	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
127	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
128	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
129	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
131	#13083558	—	2	2	no	—
132	#13083557	—	2	2	no	—
133	#13083557	—	2	2	no	—
134	#13083557	—	2	2	no	—
135	#13083557	M₁₆	1	4	yes	—
136	C₂×#10623494	—	2	2	no	—
137	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
138	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
139	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
140	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
141	C₈×D₈₉	—	2	2	no	—
142	C₈×D₈₉	—	2	2	no	—
143	C₈×D₈₉	—	2	1	no	—
144	C₈×D₈₉	—	2	1	no	—
145	C₈×D₈₉	#41	1	2	yes	—
146	C₈×D₈₉	#41	1	2	yes	—
147	#13083553	C₂×C₈	1	1	yes	characteristic
148	#13083553	C₂×C₈	1	1	yes	characteristic
149	#13083553	C₂×C₈	1	1	yes	characteristic
150	#13083553	C₂×C₈	1	1	yes	characteristic
151	#13083551	C₂×C₈	1	1	yes	characteristic
152	#13083551	C₂×C₈	1	1	yes	characteristic
153	#13083551	C₂×C₈	1	1	yes	characteristic
154	#13083551	C₂×C₈	1	1	yes	characteristic
155	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
156	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
157	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
158	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
159	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
160	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
161	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
162	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
163	#13083549	—	2	1	no	—
164	#13083549	—	2	1	no	—
165	#13083549	—	2	1	no	—
166	#13083549	—	2	1	no	—
167	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
168	M₁₆×C₈₉	—	2	2	no	—
169	C₂×C₈×C₈₉	—	2	1	no	—
170	C₂×C₈×C₈₉	—	2	1	no	—
171	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
175	C₄⋊C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
176	C₄⋊C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
177	C₂²⋊C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
178	C₂²⋊C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
179	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
180	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
181	C₁₆×C₈₉	—	2	1	no	—
182	C₁₆×C₈₉	—	2	1	no	—
183	C₁₆×C₈₉	—	2	1	no	—
184	C₁₆×C₈₉	—	2	1	no	—
185	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
186	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
187	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
188	C₂×C₄×C₈₉	—	2	1	no	—
189	C₂×C₄×C₈₉	—	2	1	no	—
190	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
191	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
192	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
193	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
194	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
195	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
196	C₂²⋊D₈₉	—	2	2	no	—
197	C₂²⋊D₈₉	—	2	2	no	—
198	C₂×Dic₈₉	—	2	2	no	—
199	C₂×Dic₈₉	—	4	1	no	—
200	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
201	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
202	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
203	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
204	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
205	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
206	D₃₅₆	—	2	2	no	—
207	C₄×D₈₉	—	2	1	no	—
208	C₄×D₈₉	—	2	1	no	—
209	C₄×D₈₉	—	2	2	no	—
210	C₄×D₈₉	—	2	2	no	—
211	C₄×D₈₉	—	4	1	no	—
212	C₄×D₈₉	—	4	1	no	—
213	C₄×D₈₉	#117	1	2	yes	—
214	C₄×D₈₉	C₂×M₁₆	1	2	yes	—
215	Dic₁₇₈	—	2	2	no	—
216	C₈×C₈₉	—	2	1	no	—
217	C₈×C₈₉	—	2	1	no	—
218	C₈×C₈₉	C₂×M₁₆	1	2	yes	—
219	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
220	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
221	#10623494	—	2	1	no	—
222	#10623494	—	2	1	no	—
223	#10623494	#117	1	2	yes	—
224	#10623494	C₂×M₁₆	1	2	yes	—
225	C₂²×C₈₉	—	2	1	no	—
226	C₂²×C₈₉	—	2	1	no	—
227	C₂²×C₈₉	—	2	1	no	—
228	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
229	C₂×D₈₉	—	2	1	no	—
230	C₂×D₈₉	—	2	1	no	—
231	C₂×D₈₉	—	2	1	no	—
232	C₂×D₈₉	—	2	1	no	—
233	C₂×D₈₉	—	2	1	no	—
234	C₂×D₈₉	#431	1	2	yes	—
235	C₄×C₈₉	—	2	1	no	—
236	C₄×C₈₉	—	2	1	no	—
237	C₄×C₈₉	—	2	1	no	—
238	C₄×C₈₉	—	2	1	no	—
239	C₄×C₈₉	—	2	1	no	—
240	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
241	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
242	Dic₈₉	—	2	1	no	—
243	Dic₈₉	—	2	1	no	—
244	Dic₈₉	—	2	1	no	—
245	Dic₈₉	—	2	1	no	—
246	Dic₈₉	#431	1	2	yes	—
247	Dic₈₉	#504	1	2	yes	—
248	#33423	—	89	1	no	maximal, Sylow
249	C₂×C₈₉	—	4	1	no	—
250	C₂×C₈₉	C₂×#431	1	1	yes	characteristic
251	C₂×C₈₉	C₂×#504	1	1	yes	characteristic
252	C₂×C₈₉	#3407	1	1	yes	characteristic
253	D₈₉	—	2	2	no	—
254	D₈₉	—	4	1	no	—
255	C₄×#131	—	89	1	no	—
256	#2164	—	89	1	no	—
257	#2164	—	89	1	no	—
258	#2164	—	89	1	no	—
259	#2164	D₈₉	1	1	yes	characteristic, complemented
260	#2163	—	89	1	no	—
261	#2163	—	89	1	no	—
262	#2162	—	89	1	no	—
263	#2162	—	89	1	no	—
264	#2150	—	89	1	no	—
265	C₂×C₄⋊C₁₆	—	89	1	no	—
266	#2113	—	89	1	no	—
267	#2113	—	89	1	no	—
268	#2108	—	89	1	no	—
269	#2108	—	89	1	no	—
270	C₈₉	#33423	1	1	yes	characteristic, complemented, Sylow
271	C₂×#131	—	89	1	no	—
272	C₂×#131	—	89	1	no	—
273	C₄×#41	—	89	1	no	—
274	C₂×M₃₂	—	89	1	no	—
275	C₂×M₃₂	—	89	1	no	—
276	C₂²×C₁₆	—	89	1	no	—
277	C₂²×C₁₆	—	89	1	no	—
278	#405	—	89	1	no	—
279	#405	—	89	1	no	—
280	#405	—	89	1	no	—
281	#405	—	89	1	no	—
282	#405	—	89	1	no	—
283	#405	C₂×D₈₉	1	1	yes	characteristic
284	C₄×M₁₆	—	89	1	no	—
285	C₄×M₁₆	—	89	1	no	—
286	C₄×M₁₆	—	89	1	no	—
287	C₂×C₄×C₈	—	89	1	no	—
288	C₂×C₄×C₈	—	89	1	no	—
289	C₂×C₄×C₈	—	89	1	no	—
290	C₄⋊C₁₆	—	89	1	no	—
291	C₄⋊C₁₆	—	89	1	no	—
292	C₄⋊C₁₆	—	89	1	no	—
293	C₄⋊C₁₆	—	89	1	no	—
294	C₄⋊C₁₆	—	89	1	no	—
295	C₄⋊C₁₆	—	89	1	no	—
296	C₄⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic
297	C₄⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic
298	C₂²⋊C₁₆	—	89	1	no	—
299	C₂²⋊C₁₆	—	89	1	no	—
300	C₂²⋊C₁₆	—	89	1	no	—
301	C₂²⋊C₁₆	—	89	1	no	—
302	C₂²⋊C₁₆	—	89	1	no	—
303	C₂²⋊C₁₆	—	89	1	no	—
304	C₂²⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic
305	C₂²⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic
306	#346	—	89	1	no	—
307	#346	—	89	1	no	—
308	#346	—	89	1	no	—
309	#346	C₂×D₈₉	1	1	yes	characteristic
310	C₄×C₁₆	—	89	1	no	—
311	C₄×C₁₆	—	89	1	no	—
312	C₄×C₁₆	—	89	1	no	—
313	C₄×C₁₆	C₂×D₈₉	1	1	yes	characteristic
314	C₂×#41	—	89	1	no	—
315	#131	—	178	2	no	—
316	#131	—	178	2	no	—
317	#131	—	178	4	no	—
318	C₂×M₁₆	—	89	1	no	—
319	C₂×M₁₆	—	89	1	no	—
320	C₂×M₁₆	—	89	1	no	—
321	C₂×M₁₆	—	89	1	no	—
322	C₂×M₁₆	—	89	1	no	—
323	C₂×M₁₆	C₄×D₈₉	1	1	yes	characteristic
324	C₂²×C₈	—	89	1	no	—
325	C₂²×C₈	—	89	1	no	—
326	C₂²×C₈	—	89	1	no	—
327	C₂²×C₈	—	89	1	no	—
328	C₂²×C₈	—	89	1	no	—
329	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
330	C₄×Q₈	—	89	1	no	—
331	C₄×Q₈	—	89	1	no	—
332	C₄×D₄	—	89	1	no	—
333	C₄×D₄	—	89	1	no	—
334	C₄×D₄	—	89	1	no	—
335	C₄×D₄	—	89	1	no	—
336	C₄×D₄	—	89	1	no	—
337	C₄×D₄	—	89	1	no	—
338	#117	—	89	1	no	—
339	#117	—	89	1	no	—
340	#117	C₄×D₈₉	1	1	yes	characteristic
341	C₂×C₄²	—	89	1	no	—
342	C₂×C₄²	—	89	1	no	—
343	C₂×C₄²	—	89	1	no	—
344	M₃₂	—	178	2	no	—
345	M₃₂	—	178	2	no	—
346	C₂×C₁₆	—	89	1	no	—
347	C₂×C₁₆	—	89	1	no	—
348	C₂×C₁₆	—	89	1	no	—
349	C₂×C₁₆	—	89	1	no	—
350	C₂×C₁₆	—	178	2	no	—
351	C₂×C₁₆	—	178	2	no	—
352	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
353	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
354	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
355	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
356	#97	—	89	1	no	—
357	#97	—	89	1	no	—
358	#97	—	89	1	no	—
359	#97	—	89	1	no	—
360	#97	C₄×D₈₉	1	1	yes	characteristic
361	#97	C₄×D₈₉	1	1	yes	characteristic
362	C₄×C₈	—	89	1	no	—
363	C₄×C₈	—	89	1	no	—
364	C₄×C₈	—	89	1	no	—
365	C₄×C₈	—	89	1	no	—
366	C₄×C₈	—	89	1	no	—
367	C₄×C₈	—	89	1	no	—
368	C₄×C₈	—	89	1	no	—
369	C₄×C₈	—	89	1	no	—
370	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
371	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
372	#41	—	178	2	no	—
373	#41	—	178	2	no	—
374	C₂×Q₈	—	89	1	no	—
375	C₂×D₄	—	89	1	no	—
376	C₂×D₄	—	89	1	no	—
377	C₂×D₄	—	89	1	no	—
378	C₂²×C₄	—	89	1	no	—
379	C₂²×C₄	—	89	1	no	—
380	C₂²×C₄	—	89	1	no	—
381	C₂²×C₄	—	89	1	no	—
382	C₂²×C₄	—	89	1	no	—
383	C₂²×C₄	—	89	1	no	—
384	C₂²×C₄	—	89	1	no	—
385	C₂²×C₄	—	89	1	no	—
386	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
387	M₁₆	—	2	2	no	—
388	M₁₆	—	89	4	no	—
389	M₁₆	—	178	2	no	—
390	M₁₆	—	178	2	no	—
391	M₁₆	—	178	2	no	—
392	M₁₆	—	178	2	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	89	1	no	—
396	C₂×C₈	—	89	1	no	—
397	C₂×C₈	—	89	2	no	—
398	C₂×C₈	—	89	2	no	—
399	C₂×C₈	—	89	1	no	—
400	C₂×C₈	—	89	1	no	—
401	C₂×C₈	—	178	2	no	—
402	C₂×C₈	—	178	2	no	—
403	C₂×C₈	—	178	2	no	—
404	C₂×C₈	—	178	1	no	—
405	C₂×C₈	—	178	1	no	—
406	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
407	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
408	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
409	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
410	C₄⋊C₄	—	89	1	no	—
411	C₄⋊C₄	—	89	1	no	—
412	C₄⋊C₄	—	89	1	no	—
413	C₄⋊C₄	—	89	1	no	—
414	C₄⋊C₄	C₈×D₈₉	1	1	yes	characteristic
415	C₄⋊C₄	C₈×D₈₉	1	1	yes	characteristic
416	C₂²⋊C₄	—	89	1	no	—
417	C₂²⋊C₄	—	89	1	no	—
418	C₂²⋊C₄	—	89	1	no	—
419	C₂²⋊C₄	—	89	1	no	—
420	C₂²⋊C₄	C₈×D₈₉	1	1	yes	characteristic
421	C₂²⋊C₄	C₈×D₈₉	1	1	yes	characteristic
422	C₄²	—	89	1	no	—
423	C₄²	—	89	1	no	—
424	C₄²	—	89	1	no	—
425	C₄²	—	89	1	no	—
426	C₄²	—	89	1	no	—
427	C₄²	—	89	1	no	—
428	C₄²	—	89	1	no	—
429	C₄²	—	89	1	no	—
430	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
431	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
432	C₁₆	—	2	1	no	—
433	C₁₆	—	2	1	no	—
434	C₁₆	—	2	1	no	—
435	C₁₆	—	2	1	no	—
436	C₁₆	—	178	1	no	—
437	C₁₆	—	178	1	no	—
438	C₁₆	—	178	1	no	—
439	C₁₆	—	178	1	no	—
440	C₂³	—	89	1	no	—
441	C₂³	—	89	1	no	—
442	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
443	Q₈	—	178	2	no	—
444	D₄	—	178	2	no	—
445	D₄	—	178	2	no	—
446	D₄	—	178	2	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	89	1	no	—
450	C₂×C₄	—	89	1	no	—
451	C₂×C₄	—	89	2	no	—
452	C₂×C₄	—	89	2	no	—
453	C₂×C₄	—	89	1	no	—
454	C₂×C₄	—	89	1	no	—
455	C₂×C₄	—	89	1	no	—
456	C₂×C₄	—	89	1	no	—
457	C₂×C₄	—	356	1	no	—
458	C₂×C₄	—	356	1	no	—
459	C₂×C₄	—	356	1	no	—
460	C₂×C₄	—	178	2	no	—
461	C₂×C₄	—	178	2	no	—
462	C₂×C₄	—	178	2	no	—
463	C₂×C₄	—	178	1	no	—
464	C₂×C₄	—	178	1	no	—
465	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
466	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
467	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
468	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
469	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
470	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
471	C₈	—	2	1	no	—
472	C₈	—	2	1	no	—
473	C₈	—	89	2	no	—
474	C₈	—	89	2	no	—
475	C₈	—	178	1	no	—
476	C₈	—	178	1	no	—
477	C₈	M₁₆×D₈₉	1	2	yes	—
478	C₈	#41×D₈₉	1	1	yes	characteristic
479	C₈	#41×D₈₉	1	1	yes	characteristic
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	89	2	no	—
484	C₂²	—	178	1	no	—
485	C₂²	—	178	1	no	—
486	C₂²	—	178	1	no	—
487	C₂²	—	178	1	no	—
488	C₂²	—	178	1	no	—
489	C₂²	C₂²×C₈×D₈₉	1	1	yes	characteristic
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	89	2	no	—
496	C₄	—	89	2	no	—
497	C₄	—	178	1	no	—
498	C₄	—	178	1	no	—
499	C₄	—	178	1	no	—
500	C₄	—	178	1	no	—
501	C₄	#117×D₈₉	1	1	yes	characteristic
502	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
503	C₂	—	4	1	no	—
504	C₂	—	356	1	no	—
505	C₂	—	178	2	no	—
506	C₂	#431×D₈₉	1	1	yes	characteristic
507	C₂	#504×D₈₉	1	1	yes	characteristic
508	C₂	#26033353	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₈₉
commutator, socle	C₂²×C₈₉	C₂³×C₈
Fitting	C₈₉×#2164	C₂
prime radical	C₂×#13083574	C₂×C₄
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	#2164	D₈₉
hypocenter	C₈₉	#33423
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ #2164

Complements

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

N	H ≅ G/N	type
2. #26022059	C₂	semidirect
3. #26022058	C₂	semidirect
4. #26022058	C₂	semidirect
5. #26022053	C₂	semidirect
6. #26022052	C₂	semidirect
7. #26022049	C₂	semidirect
8. #26022048	C₂	semidirect
9. #26022006	C₂	semidirect
10. C₄⋊C₁₆×D₈₉	C₂	semidirect
13. #26021850	C₂	semidirect
14. #26021847	C₂	semidirect
15. C₈₉×#2164	C₂	semidirect
259. #2164	D₈₉	semidirect
270. C₈₉	#33423	semidirect

Maximal subgroups

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

subgroup	index
#26028674	2
#26022059	2
#26022058	2
#26022053	2
#26022052	2
#26022049	2
#26022048	2
#26022006	2
C₄⋊C₁₆×D₈₉	2
#26021864	2
#26021850	2
#26021847	2
C₈₉×#2164	2
#33423	89