Subgroups — #36561804

Order 22784.

794 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028947	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151554	C₂	1	1	yes	maximal, characteristic, complemented
3	#26020902	C₂	1	2	yes	maximal, complemented
4	#26020853	C₂	1	2	yes	maximal, complemented
5	#26020555	C₂	1	1	yes	maximal, characteristic
6	#26020459	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020351	C₂	1	1	yes	maximal, characteristic, complemented
8	#26020133	C₂	1	2	yes	maximal, complemented
9	#26020092	C₂	1	2	yes	maximal, complemented
10	#26020026	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3091	C₂	1	1	yes	maximal, characteristic
12	C₂×#15668019	C₂²	1	1	yes	characteristic
13	C₂²×#13083558	C₂²	1	1	yes	characteristic
14	C₂³×#10623494	C₂²	1	1	yes	characteristic
15	#19151670	—	2	1	no	—
16	#19151670	—	2	1	no	—
17	D₄×#10623494	—	2	1	no	—
18	D₄×#10623494	—	2	1	no	—
19	C₂×#15667948	C₂²	1	2	yes	—
20	#19151625	C₂²	1	1	yes	characteristic
21	C₂×#15667939	C₂²	1	2	yes	—
22	#19151565	C₂²	1	1	yes	characteristic
23	#19151562	C₂²	1	1	yes	characteristic
24	#19151554	—	2	1	no	—
25	#19151554	—	2	1	no	—
26	#19151554	C₂²	1	1	yes	characteristic
27	#19151554	C₂²	1	2	yes	—
28	#19151554	C₂²	1	2	yes	—
29	C₂×#15667923	—	2	1	no	—
30	C₂×C₄×#10623494	—	2	1	no	—
31	C₂×C₈×Dic₈₉	C₂²	1	2	yes	—
32	C₄×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
33	#19151363	C₂²	1	2	yes	—
34	#19151357	C₂²	1	2	yes	—
35	#19151357	C₂²	1	2	yes	—
36	#19151357	C₂²	1	2	yes	—
37	#19151352	C₂²	1	2	yes	—
38	#525×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
40	#485×C₈₉	C₄	1	2	yes	complemented
41	#484×C₈₉	C₄	1	1	yes	characteristic, complemented
42	#483×C₈₉	C₄	1	1	yes	characteristic, complemented
43	#482×C₈₉	C₄	1	2	yes	complemented
44	#481×C₈₉	C₄	1	1	yes	characteristic, complemented
45	#480×C₈₉	C₄	1	1	yes	characteristic, complemented
46	#427×C₈₉	C₂²	1	2	yes	—
47	#416×C₈₉	C₂²	1	2	yes	—
48	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
49	#15668019	—	2	4	no	—
50	C₂×#13083558	—	2	4	no	—
51	C₂×#13083558	—	2	1	no	—
52	C₂×#13083558	—	2	1	no	—
53	C₂×#13083558	C₂³	1	1	yes	characteristic
54	C₂×#13083558	C₂³	1	1	yes	characteristic
55	C₂×#13083558	C₂³	1	2	yes	—
56	C₂²×#10623494	—	2	4	no	—
57	C₂²×#10623494	—	2	1	no	—
58	C₂²×#10623494	—	2	1	no	—
59	C₂²×#10623494	D₄	1	1	yes	characteristic
60	C₂²×#10623494	D₄	1	1	yes	characteristic
61	C₂²×#10623494	D₄	1	1	yes	characteristic
62	C₂²×#10623494	D₄	1	1	yes	characteristic
63	C₂²×#10623494	C₂³	1	1	yes	characteristic
64	C₂²×#10623494	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊Dic₈₉	—	2	1	no	—
66	C₂×C₄×Dic₈₉	C₂³	1	2	yes	—
67	#15667948	—	2	4	no	—
68	C₄⋊#10623494	—	2	1	no	—
69	C₄⋊#10623494	—	2	1	no	—
70	#15667939	—	2	4	no	—
71	C₂²⋊#10623494	—	2	1	no	—
72	C₂²⋊#10623494	—	2	1	no	—
73	C₂²⋊#10623494	—	2	1	no	—
74	C₂²⋊#10623494	—	2	1	no	—
75	#15667923	—	2	1	no	—
76	#15667923	—	2	2	no	—
77	#15667923	—	2	2	no	—
78	C₄×#10623494	—	2	1	no	—
79	C₄×#10623494	—	2	2	no	—
80	C₄×#10623494	—	2	2	no	—
81	C₈×Dic₈₉	—	2	4	no	—
82	#15667919	—	2	1	no	—
83	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
86	#123×C₈₉	—	2	1	no	—
87	C₂²⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
88	C₂²⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
89	#121×C₈₉	C₂×C₄	1	1	yes	characteristic
90	#121×C₈₉	C₂×C₄	1	1	yes	characteristic
91	#120×C₈₉	—	2	1	no	—
92	C₄×D₄×C₈₉	—	2	1	no	—
93	C₄×D₄×C₈₉	—	2	1	no	—
94	#117×C₈₉	—	2	1	no	—
95	#117×C₈₉	—	2	1	no	—
96	#117×C₈₉	C₂×C₄	1	2	yes	—
97	#117×C₈₉	C₂³	1	1	yes	characteristic
98	#117×C₈₉	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
102	C₂×C₄²×C₈₉	—	2	1	no	—
103	#107×C₈₉	C₂×C₄	1	2	yes	—
104	#107×C₈₉	C₂×C₄	1	2	yes	—
105	#106×C₈₉	C₂×C₄	1	2	yes	—
106	#106×C₈₉	C₂×C₄	1	2	yes	—
107	#103×C₈₉	C₂×C₄	1	2	yes	—
108	#103×C₈₉	C₂×C₄	1	2	yes	—
109	#102×C₈₉	C₂×C₄	1	2	yes	—
110	#102×C₈₉	C₂×C₄	1	2	yes	—
111	C₂²⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
112	C₂²⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
114	C₂²×Dic₈₉	—	2	2	no	—
115	#13083558	—	2	4	no	—
116	#13083558	—	2	2	no	—
117	#13083558	—	2	2	no	—
118	#13083558	—	2	2	no	—
119	#13083558	—	4	2	no	—
120	#13083558	#41	1	4	yes	—
121	C₂×#10623494	—	2	4	no	—
122	C₂×#10623494	—	2	2	no	—
123	C₂×#10623494	—	2	2	no	—
124	C₂×#10623494	—	2	2	no	—
125	C₂×#10623494	—	2	2	no	—
126	C₂×#10623494	—	2	2	no	—
127	C₂×#10623494	—	2	2	no	—
128	C₂×#10623494	—	2	1	no	—
129	C₂×#10623494	—	2	1	no	—
130	C₂×#10623494	—	4	2	no	—
131	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
132	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
133	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
134	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
135	C₂×#10623494	#41	1	4	yes	—
136	C₂²⋊Dic₈₉	—	2	4	no	—
137	C₄×Dic₈₉	—	2	2	no	—
138	C₄×Dic₈₉	—	2	2	no	—
139	C₂⁴×C₈₉	#41	1	1	yes	characteristic
140	#41×C₈₉	—	2	2	no	—
141	#41×C₈₉	—	2	2	no	—
142	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
143	C₂×D₄×C₈₉	—	2	1	no	—
144	C₂×D₄×C₈₉	—	2	1	no	—
145	C₂×D₄×C₈₉	—	2	1	no	—
146	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₈₉	—	2	2	no	—
148	C₂²×C₄×C₈₉	—	2	2	no	—
149	C₂²×C₄×C₈₉	—	2	1	no	—
150	C₂²×C₄×C₈₉	—	2	1	no	—
151	C₂²×C₄×C₈₉	—	2	1	no	—
152	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
157	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
158	C₂×C₈×C₈₉	—	2	2	no	—
159	C₂×C₈×C₈₉	—	2	2	no	—
160	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
161	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
162	C₄⋊C₄×C₈₉	—	2	1	no	—
163	C₄⋊C₄×C₈₉	—	2	1	no	—
164	C₄⋊C₄×C₈₉	—	2	1	no	—
165	C₄⋊C₄×C₈₉	—	2	1	no	—
166	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
167	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
168	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
169	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
170	C₂²⋊C₄×C₈₉	—	2	2	no	—
171	C₂²⋊C₄×C₈₉	—	2	1	no	—
172	C₂²⋊C₄×C₈₉	—	2	1	no	—
173	C₂²⋊C₄×C₈₉	—	2	2	no	—
174	C₂²⋊C₄×C₈₉	—	2	1	no	—
175	C₂²⋊C₄×C₈₉	—	2	1	no	—
176	C₂²⋊C₄×C₈₉	—	2	1	no	—
177	C₄²×C₈₉	—	2	2	no	—
178	C₄²×C₈₉	—	2	2	no	—
179	C₄²×C₈₉	—	2	1	no	—
180	C₂³×C₈₉	—	2	2	no	—
181	C₂³×C₈₉	—	2	2	no	—
182	C₂³×C₈₉	—	2	1	no	—
183	C₂³×C₈₉	—	4	1	no	—
184	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
185	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
186	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
187	Q₈×C₈₉	—	2	2	no	—
188	D₄×C₈₉	—	2	2	no	—
189	D₄×C₈₉	—	4	2	no	—
190	D₄×C₈₉	—	4	2	no	—
191	D₄×C₈₉	—	4	2	no	—
192	C₂×C₄×C₈₉	—	2	2	no	—
193	C₂×C₄×C₈₉	—	2	2	no	—
194	C₂×C₄×C₈₉	—	2	2	no	—
195	C₂×C₄×C₈₉	—	2	1	no	—
196	C₂×C₄×C₈₉	—	2	1	no	—
197	C₂×C₄×C₈₉	—	2	1	no	—
198	C₂×C₄×C₈₉	—	2	1	no	—
199	C₂×C₄×C₈₉	—	2	2	no	—
200	C₂×C₄×C₈₉	—	2	2	no	—
201	C₂×C₄×C₈₉	—	2	1	no	—
202	C₂×C₄×C₈₉	—	2	1	no	—
203	C₂×C₄×C₈₉	—	2	1	no	—
204	C₂×C₄×C₈₉	—	4	2	no	—
205	C₂×C₄×C₈₉	—	4	2	no	—
206	C₂×C₄×C₈₉	—	4	1	no	—
207	C₂×C₄×C₈₉	—	4	1	no	—
208	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
209	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
213	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
214	C₂×Dic₈₉	—	2	4	no	—
215	C₂×Dic₈₉	—	4	2	no	—
216	C₂×Dic₈₉	—	4	2	no	—
217	C₈×C₈₉	—	2	2	no	—
218	C₈×C₈₉	—	2	2	no	—
219	#10623494	—	2	1	no	—
220	#10623494	—	2	1	no	—
221	#10623494	—	2	4	no	—
222	#10623494	—	4	1	no	—
223	#10623494	—	4	1	no	—
224	#10623494	#123	1	2	yes	—
225	#10623494	#123	1	2	yes	—
226	C₂²×C₈₉	—	2	1	no	—
227	C₂²×C₈₉	—	2	1	no	—
228	C₂²×C₈₉	—	2	1	no	—
229	C₂²×C₈₉	—	2	1	no	—
230	C₂²×C₈₉	—	2	1	no	—
231	C₂²×C₈₉	—	2	1	no	—
232	C₂²×C₈₉	—	2	1	no	—
233	C₂²×C₈₉	—	4	4	no	—
234	C₂²×C₈₉	—	4	1	no	—
235	C₂²×C₈₉	—	4	1	no	—
236	C₂²×C₈₉	—	4	1	no	—
237	C₂²×C₈₉	#443	1	2	yes	—
238	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
239	C₂²×C₈₉	#529	1	2	yes	—
240	C₄×C₈₉	—	2	1	no	—
241	C₄×C₈₉	—	2	1	no	—
242	C₄×C₈₉	—	4	2	no	—
243	C₄×C₈₉	—	4	1	no	—
244	C₄×C₈₉	—	4	2	no	—
245	C₄×C₈₉	—	4	1	no	—
246	C₄×C₈₉	—	4	1	no	—
247	C₄×C₈₉	C₄×#41	1	2	yes	—
248	C₄×C₈₉	C₂×#123	1	1	yes	characteristic
249	C₄×C₈₉	#525	1	1	yes	characteristic
250	Dic₈₉	—	4	4	no	—
251	#21592	—	89	1	no	maximal, Sylow
252	C₂×C₈₉	—	2	2	no	—
253	C₂×C₈₉	—	2	2	no	—
254	C₂×C₈₉	—	4	1	no	—
255	C₂×C₈₉	—	8	1	no	—
256	C₂×C₈₉	C₄×#123	1	1	yes	characteristic
257	C₂×C₈₉	C₂×#443	1	1	yes	characteristic
258	C₂×C₈₉	#2955	1	1	yes	characteristic
259	#3091	D₈₉	1	1	yes	characteristic
260	#2929	—	89	1	no	—
261	C₂×#405	—	89	1	no	—
262	#1929	—	89	2	no	—
263	#1922	—	89	2	no	—
264	#1871	—	89	1	no	—
265	#1855	—	89	1	no	—
266	#1826	—	89	1	no	—
267	#1772	—	89	2	no	—
268	#1764	—	89	2	no	—
269	C₈×C₂²⋊C₄	—	89	1	no	—
270	C₈₉	#21592	1	1	yes	characteristic, complemented, Sylow
271	C₂×#131	—	89	1	no	—
272	C₂²×M₁₆	—	89	1	no	—
273	C₂³×C₈	—	89	1	no	—
274	#525	C₂×D₈₉	1	1	yes	characteristic
275	C₂×#117	C₂×D₈₉	1	1	yes	characteristic
276	#485	Dic₈₉	1	2	yes	complemented
277	#484	Dic₈₉	1	1	yes	characteristic, complemented
278	#483	Dic₈₉	1	1	yes	characteristic, complemented
279	#482	Dic₈₉	1	2	yes	complemented
280	#481	Dic₈₉	1	1	yes	characteristic, complemented
281	#480	Dic₈₉	1	1	yes	characteristic, complemented
282	#435	—	178	1	no	—
283	#435	—	178	1	no	—
284	C₈×D₄	—	178	1	no	—
285	C₈×D₄	—	178	1	no	—
286	C₂×#108	—	89	2	no	—
287	#427	C₂×D₈₉	1	2	yes	—
288	#424	—	89	1	no	—
289	C₂×#104	—	89	2	no	—
290	#416	C₂×D₈₉	1	2	yes	—
291	#408	—	89	1	no	—
292	#407	—	89	1	no	—
293	C₂×C₂²⋊C₈	C₂×D₈₉	1	1	yes	characteristic
294	#405	—	89	2	no	—
295	#405	—	89	2	no	—
296	#405	—	89	1	no	—
297	#405	—	178	1	no	—
298	#405	—	178	1	no	—
299	C₂×#97	—	178	1	no	—
300	C₂×C₄×C₈	—	89	2	no	—
301	C₂×C₄×C₈	—	178	1	no	—
302	C₄×C₂²⋊C₄	—	89	1	no	—
303	#341	—	89	2	no	—
304	#339	—	89	2	no	—
305	#339	—	89	2	no	—
306	#339	—	89	2	no	—
307	#336	—	89	2	no	—
308	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
309	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
310	#131	—	178	4	no	—
311	C₂×M₁₆	—	89	2	no	—
312	C₂×M₁₆	—	89	1	no	—
313	C₂×M₁₆	—	89	1	no	—
314	C₂×M₁₆	—	178	1	no	—
315	C₂×M₁₆	—	178	4	no	—
316	C₂×M₁₆	—	178	1	no	—
317	C₂²×C₈	—	89	1	no	—
318	C₂²×C₈	—	89	1	no	—
319	C₂²×C₈	—	89	1	no	—
320	C₂²×C₈	—	89	1	no	—
321	C₂²×C₈	—	89	1	no	—
322	C₂²×C₈	—	89	1	no	—
323	C₂²×C₈	—	178	1	no	—
324	C₂²×C₈	—	178	4	no	—
325	C₂²×C₈	—	178	1	no	—
326	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
327	#123	—	2	1	no	—
328	C₂²⋊Q₈	C₂×Dic₈₉	1	1	yes	characteristic
329	C₂²⋊Q₈	C₂×Dic₈₉	1	1	yes	characteristic
330	#121	C₂×Dic₈₉	1	1	yes	characteristic
331	#121	C₂×Dic₈₉	1	1	yes	characteristic
332	#120	—	2	1	no	—
333	C₄×D₄	—	2	1	no	—
334	C₄×D₄	—	2	1	no	—
335	#117	—	2	1	no	—
336	#117	—	2	1	no	—
337	#117	C₂×Dic₈₉	1	2	yes	—
338	#117	C₂²×D₈₉	1	2	yes	—
339	#117	C₂²×D₈₉	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₂²⋊C₄	—	178	1	no	—
344	C₂×C₄²	—	2	1	no	—
345	C₂×C₄²	—	89	2	no	—
346	#108	—	178	4	no	—
347	#107	C₂×Dic₈₉	1	2	yes	—
348	#107	C₂×Dic₈₉	1	2	yes	—
349	#106	C₂×Dic₈₉	1	2	yes	—
350	#106	C₂×Dic₈₉	1	2	yes	—
351	C₄⋊C₈	—	178	1	no	—
352	C₄⋊C₈	—	178	1	no	—
353	#104	—	178	4	no	—
354	#103	C₂×Dic₈₉	1	2	yes	—
355	#103	C₂×Dic₈₉	1	2	yes	—
356	#102	C₂×Dic₈₉	1	2	yes	—
357	#102	C₂×Dic₈₉	1	2	yes	—
358	C₂²⋊C₈	—	178	1	no	—
359	C₂²⋊C₈	—	178	1	no	—
360	C₂²⋊C₈	—	178	1	no	—
361	C₂²⋊C₈	—	178	1	no	—
362	C₂²⋊C₈	C₂×Dic₈₉	1	1	yes	characteristic
363	C₂²⋊C₈	C₂×Dic₈₉	1	1	yes	characteristic
364	C₂²⋊C₈	C₂×Dic₈₉	1	2	yes	—
365	#97	—	178	2	no	—
366	#97	—	178	2	no	—
367	#97	—	178	1	no	—
368	C₄×C₈	—	178	2	no	—
369	C₄×C₈	—	178	2	no	—
370	C₄×C₈	—	178	1	no	—
371	C₄×C₈	—	178	4	no	—
372	#95	—	178	1	no	—
373	C₂⁴	#13083573	1	1	yes	characteristic
374	#41	—	2	2	no	—
375	#41	—	2	2	no	—
376	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	178	2	no	—
387	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
388	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
389	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
390	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
391	C₂²×C₄	#13083573	1	1	yes	characteristic
392	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
393	M₁₆	—	89	4	no	—
394	M₁₆	—	356	2	no	—
395	M₁₆	—	178	2	no	—
396	M₁₆	—	178	2	no	—
397	M₁₆	—	178	4	no	—
398	M₁₆	—	178	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	89	1	no	—
402	C₂×C₈	—	89	1	no	—
403	C₂×C₈	—	89	4	no	—
404	C₂×C₈	—	89	1	no	—
405	C₂×C₈	—	89	1	no	—
406	C₂×C₈	—	356	2	no	—
407	C₂×C₈	—	178	2	no	—
408	C₂×C₈	—	178	2	no	—
409	C₂×C₈	—	178	2	no	—
410	C₂×C₈	—	178	2	no	—
411	C₂×C₈	—	178	1	no	—
412	C₂×C₈	—	178	1	no	—
413	C₂×C₈	—	178	4	no	—
414	C₂×C₈	—	178	2	no	—
415	C₂×C₈	—	178	2	no	—
416	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
417	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
423	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
424	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
425	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	1	no	—
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	1	no	—
431	C₂²⋊C₄	—	2	1	no	—
432	C₂²⋊C₄	—	2	1	no	—
433	C₂²⋊C₄	—	178	4	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	2	no	—
436	C₄²	—	2	1	no	—
437	C₄²	—	178	2	no	—
438	C₄²	—	178	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
444	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
445	C₂³	C₂×#13083573	1	1	yes	characteristic
446	Q₈	—	2	2	no	—
447	D₄	—	2	2	no	—
448	D₄	—	4	2	no	—
449	D₄	—	4	2	no	—
450	D₄	—	4	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	356	2	no	—
468	C₂×C₄	—	356	2	no	—
469	C₂×C₄	—	178	4	no	—
470	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
471	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
472	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
473	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
474	C₂×C₄	#41×D₈₉	1	2	yes	—
475	C₂×C₄	#41×D₈₉	1	2	yes	—
476	C₈	—	2	2	no	—
477	C₈	—	2	2	no	—
478	C₈	—	89	2	no	—
479	C₈	—	89	2	no	—
480	C₈	—	356	1	no	—
481	C₈	—	356	1	no	—
482	C₈	—	178	1	no	—
483	C₈	—	178	1	no	—
484	C₈	—	178	4	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	1	no	—
496	C₂²	#19151715	1	2	yes	—
497	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
498	C₂²	#19152125	1	2	yes	—
499	C₄	—	2	1	no	—
500	C₄	—	2	1	no	—
501	C₄	—	4	2	no	—
502	C₄	—	4	1	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	1	no	—
505	C₄	—	4	1	no	—
506	C₄	—	356	4	no	—
507	C₄	#41×Dic₈₉	1	2	yes	—
508	C₄	#123×D₈₉	1	1	yes	characteristic
509	C₄	#19152106	1	1	yes	characteristic
510	C₂	—	2	2	no	—
511	C₂	—	2	2	no	—
512	C₂	—	4	1	no	—
513	C₂	—	8	1	no	—
514	C₂	#123×Dic₈₉	1	1	yes	characteristic
515	C₂	C₂×#19151715	1	1	yes	characteristic
516	C₂	#26029155	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#3091	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#525×C₈₉	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#3091	D₈₉
hypocenter	C₈₉	#21592
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #3091

Complements

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

N	H ≅ G/N	type
2. C₂×#19151554	C₂	semidirect
3. #26020902	C₂	semidirect
4. #26020853	C₂	semidirect
6. #26020459	C₂	semidirect
7. #26020351	C₂	semidirect
8. #26020133	C₂	semidirect
9. #26020092	C₂	semidirect
10. #26020026	C₂	semidirect
40. #485×C₈₉	C₄	semidirect
41. #484×C₈₉	C₄	semidirect
42. #483×C₈₉	C₄	semidirect
43. #482×C₈₉	C₄	semidirect
44. #481×C₈₉	C₄	semidirect
45. #480×C₈₉	C₄	semidirect
270. C₈₉	#21592	semidirect
276. #485	Dic₈₉	semidirect
277. #484	Dic₈₉	semidirect
278. #483	Dic₈₉	semidirect
279. #482	Dic₈₉	semidirect
280. #481	Dic₈₉	semidirect
281. #480	Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26028947	2
C₂×#19151554	2
#26020902	2
#26020853	2
#26020555	2
#26020459	2
#26020351	2
#26020133	2
#26020092	2
#26020026	2
C₈₉×#3091	2
#21592	89