Subgroups — #36576986

Order 22784.

880 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151720	C₂	1	1	yes	maximal, characteristic, complemented
2	#26028979	C₂	1	2	yes	maximal, complemented
3	C₂²×#15667948	C₂	1	1	yes	maximal, characteristic, complemented
4	#26021146	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021006	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020902	C₂	1	2	yes	maximal, complemented
7	#26020555	C₂	1	2	yes	maximal, complemented
8	#26020529	C₂	1	2	yes	maximal, complemented
9	#26020138	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020028	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3050	C₂	1	1	yes	maximal, characteristic
12	C₂×#15668019	C₂²	1	2	yes	—
13	C₂²×#13083558	C₂²	1	2	yes	—
14	#19151720	—	2	4	no	—
15	#19151676	—	2	2	no	—
16	#19151670	—	2	2	no	—
17	#19151670	—	2	2	no	—
18	D₄×#10623494	—	2	2	no	—
19	C₂×#15667948	—	2	4	no	—
20	C₂×#15667948	C₂²	1	1	yes	characteristic
21	C₂×#15667948	C₂²	1	2	yes	—
22	C₂×#15667948	C₂²	1	1	yes	characteristic
23	#19151625	C₂²	1	2	yes	—
24	C₂×#15667939	C₂²	1	2	yes	—
25	C₂×#15667939	C₂²	1	2	yes	—
26	#19151565	C₂²	1	2	yes	—
27	C₂×C₂²⋊#10623494	C₂²	1	1	yes	characteristic
28	#19151554	C₂²	1	2	yes	—
29	C₂×#15667922	C₂²	1	1	yes	characteristic
30	C₂×#15667922	C₂²	1	1	yes	characteristic
31	C₄×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
32	#19151357	C₂²	1	2	yes	—
33	#19151357	C₂²	1	2	yes	—
34	#19151352	C₂²	1	1	yes	characteristic
35	#19151352	C₂²	1	1	yes	characteristic
36	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
37	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
38	#525×C₈₉	C₂²	1	2	yes	—
39	#467×C₈₉	C₄	1	1	yes	characteristic, complemented
40	#467×C₈₉	C₄	1	1	yes	characteristic, complemented
41	#466×C₈₉	C₄	1	1	yes	characteristic, complemented
42	#466×C₈₉	C₄	1	1	yes	characteristic, complemented
43	#465×C₈₉	C₄	1	2	yes	complemented
44	#465×C₈₉	C₄	1	2	yes	complemented
45	#427×C₈₉	C₂²	1	1	yes	characteristic
46	#416×C₈₉	C₂²	1	2	yes	—
47	#15668019	—	2	4	no	—
48	#15668019	—	4	2	no	—
49	C₂×#13083558	—	2	2	no	—
50	C₂×#13083558	—	2	4	no	—
51	C₂×#13083558	—	2	2	no	—
52	C₂×#13083558	—	4	2	no	—
53	C₂×#13083558	C₂³	1	2	yes	—
54	C₂×#13083558	C₂³	1	2	yes	—
55	C₂²×#10623494	—	2	2	no	—
56	C₂²×#10623494	—	2	2	no	—
57	C₂²×#10623494	C₂³	1	1	yes	characteristic
58	C₂²×#10623494	C₂³	1	1	yes	characteristic
59	C₂×C₂²⋊Dic₈₉	—	2	1	no	—
60	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
61	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
62	#15667948	—	2	4	no	—
63	#15667948	—	2	2	no	—
64	#15667948	D₄	1	4	yes	complemented
65	C₄⋊#10623494	—	2	2	no	—
66	C₄⋊#10623494	—	2	2	no	—
67	#15667939	—	2	4	no	—
68	#15667939	—	4	2	no	—
69	C₂²⋊#10623494	—	2	2	no	—
70	C₂²⋊#10623494	—	2	2	no	—
71	C₂²⋊#10623494	D₄	1	2	yes	—
72	C₂²⋊#10623494	D₄	1	2	yes	—
73	#15667923	—	2	2	no	—
74	#15667922	—	2	2	no	—
75	#15667922	—	2	2	no	—
76	C₄×#10623494	—	2	2	no	—
77	#15667919	—	2	1	no	—
78	C₂×#41×C₈₉	C₂³	1	2	yes	—
79	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
80	#135×C₈₉	—	2	2	no	—
81	#135×C₈₉	—	2	2	no	—
82	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
83	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
84	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
85	C₂²×C₈×C₈₉	—	2	2	no	—
86	C₂²×C₈×C₈₉	—	2	2	no	—
87	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
88	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
89	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
90	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
91	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	#123×C₈₉	—	2	2	no	—
94	C₂²⋊Q₈×C₈₉	C₂×C₄	1	2	yes	—
95	C₂²⋊Q₈×C₈₉	C₂×C₄	1	2	yes	—
96	#121×C₈₉	C₂×C₄	1	2	yes	—
97	#121×C₈₉	C₂×C₄	1	2	yes	—
98	#120×C₈₉	—	2	2	no	—
99	C₄×D₄×C₈₉	—	2	2	no	—
100	C₄×D₄×C₈₉	—	2	2	no	—
101	#117×C₈₉	C₂³	1	2	yes	—
102	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
103	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
104	#106×C₈₉	C₂×C₄	1	2	yes	—
105	#103×C₈₉	C₂×C₄	1	2	yes	—
106	#103×C₈₉	C₂×C₄	1	2	yes	—
107	#102×C₈₉	C₂×C₄	1	2	yes	—
108	#102×C₈₉	C₂×C₄	1	2	yes	—
109	C₂²×Dic₈₉	—	2	1	no	—
110	C₂²×Dic₈₉	—	2	1	no	—
111	#13083558	—	2	2	no	—
112	#13083558	—	2	2	no	—
113	#13083558	—	2	2	no	—
114	#13083558	—	4	4	no	—
115	#13083558	—	4	4	no	—
116	#13083558	C₂×D₄	1	4	yes	—
117	C₂×#10623494	—	2	2	no	—
118	C₂×#10623494	—	2	1	no	—
119	C₂×#10623494	—	2	1	no	—
120	C₂×#10623494	—	2	1	no	—
121	C₂×#10623494	—	2	1	no	—
122	C₂×#10623494	—	2	2	no	—
123	C₂×#10623494	—	4	4	no	—
124	C₂×#10623494	—	4	4	no	—
125	C₂×#10623494	C₂×D₄	1	2	yes	—
126	C₂×#10623494	C₂×D₄	1	2	yes	—
127	C₂²⋊Dic₈₉	—	4	2	no	—
128	C₄×Dic₈₉	—	2	1	no	—
129	C₄×Dic₈₉	—	2	1	no	—
130	C₄×Dic₈₉	—	2	1	no	—
131	C₄×Dic₈₉	—	2	1	no	—
132	C₂⁴×C₈₉	#41	1	1	yes	characteristic
133	#41×C₈₉	—	2	2	no	—
134	#41×C₈₉	—	2	2	no	—
135	#41×C₈₉	—	2	2	no	—
136	#41×C₈₉	—	2	2	no	—
137	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
138	C₂×D₄×C₈₉	—	2	2	no	—
139	C₂×D₄×C₈₉	—	2	2	no	—
140	C₂×D₄×C₈₉	—	2	2	no	—
141	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₈₉	—	2	1	no	—
143	C₂²×C₄×C₈₉	—	2	1	no	—
144	C₂²×C₄×C₈₉	—	2	1	no	—
145	C₂²×C₄×C₈₉	—	2	1	no	—
146	C₂²×C₄×C₈₉	—	2	2	no	—
147	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
152	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
153	Q₁₆×C₈₉	—	2	2	no	—
154	SD₁₆×C₈₉	—	2	4	no	—
155	D₈×C₈₉	—	2	2	no	—
156	C₂×C₈×C₈₉	—	2	1	no	—
157	C₂×C₈×C₈₉	—	2	1	no	—
158	C₂×C₈×C₈₉	—	2	2	no	—
159	C₂×C₈×C₈₉	—	2	2	no	—
160	C₂×C₈×C₈₉	—	2	2	no	—
161	C₂×C₈×C₈₉	—	2	2	no	—
162	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
167	C₂×C₈×C₈₉	#41	1	2	yes	—
168	C₄⋊C₄×C₈₉	—	2	2	no	—
169	C₄⋊C₄×C₈₉	—	2	2	no	—
170	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
171	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
172	C₂²⋊C₄×C₈₉	—	2	2	no	—
173	C₂²⋊C₄×C₈₉	—	2	2	no	—
174	C₂²⋊C₄×C₈₉	—	2	2	no	—
175	C₂²⋊C₄×C₈₉	—	2	2	no	—
176	C₂²⋊C₄×C₈₉	—	2	2	no	—
177	C₄²×C₈₉	—	2	2	no	—
178	C₂³×C₈₉	—	2	1	no	—
179	C₂³×C₈₉	—	2	1	no	—
180	C₂³×C₈₉	—	2	2	no	—
181	C₂³×C₈₉	—	2	2	no	—
182	C₂³×C₈₉	—	4	1	no	—
183	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
184	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
185	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
186	Q₈×C₈₉	—	2	2	no	—
187	Q₈×C₈₉	—	2	2	no	—
188	D₄×C₈₉	—	2	2	no	—
189	D₄×C₈₉	—	2	2	no	—
190	D₄×C₈₉	—	4	2	no	—
191	D₄×C₈₉	—	4	2	no	—
192	D₄×C₈₉	—	4	4	no	—
193	D₄×C₈₉	—	8	2	no	—
194	C₂×C₄×C₈₉	—	2	1	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	1	no	—
200	C₂×C₄×C₈₉	—	2	1	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	—	2	2	no	—
205	C₂×C₄×C₈₉	—	2	2	no	—
206	C₂×C₄×C₈₉	—	2	2	no	—
207	C₂×C₄×C₈₉	—	4	2	no	—
208	C₂×C₄×C₈₉	—	4	2	no	—
209	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
217	C₂×Dic₈₉	—	4	1	no	—
218	C₂×Dic₈₉	—	4	1	no	—
219	C₂×Dic₈₉	—	4	1	no	—
220	C₂×Dic₈₉	—	4	1	no	—
221	C₂×Dic₈₉	—	4	1	no	—
222	C₂×Dic₈₉	—	4	1	no	—
223	C₈×C₈₉	—	2	1	no	—
224	C₈×C₈₉	—	2	1	no	—
225	C₈×C₈₉	C₄×D₄	1	2	yes	—
226	C₈×C₈₉	C₄×D₄	1	2	yes	—
227	#10623494	—	2	2	no	—
228	#10623494	—	2	4	no	—
229	#10623494	—	2	2	no	—
230	#10623494	—	4	2	no	—
231	C₂²×C₈₉	—	2	1	no	—
232	C₂²×C₈₉	—	2	1	no	—
233	C₂²×C₈₉	—	2	1	no	—
234	C₂²×C₈₉	—	2	1	no	—
235	C₂²×C₈₉	—	2	1	no	—
236	C₂²×C₈₉	—	2	1	no	—
237	C₂²×C₈₉	—	2	1	no	—
238	C₂²×C₈₉	—	4	2	no	—
239	C₂²×C₈₉	—	4	2	no	—
240	C₂²×C₈₉	—	4	2	no	—
241	C₂²×C₈₉	—	4	2	no	—
242	C₂²×C₈₉	—	4	2	no	—
243	C₂²×C₈₉	#444	1	2	yes	complemented
244	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
245	C₂²×C₈₉	#548	1	1	yes	characteristic
246	C₂²×C₈₉	#553	1	1	yes	characteristic
247	C₄×C₈₉	—	2	1	no	—
248	C₄×C₈₉	—	2	1	no	—
249	C₄×C₈₉	—	4	2	no	—
250	C₄×C₈₉	—	4	2	no	—
251	C₄×C₈₉	—	4	2	no	—
252	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
253	C₄×C₈₉	#520	1	1	yes	characteristic
254	C₄×C₈₉	D₄²	1	1	yes	characteristic
255	C₄×C₈₉	#547	1	1	yes	characteristic
256	Dic₈₉	—	8	1	no	—
257	Dic₈₉	—	8	1	no	—
258	#23019	—	89	1	no	maximal, Sylow
259	C₂×C₈₉	—	2	1	no	—
260	C₂×C₈₉	—	2	1	no	—
261	C₂×C₈₉	—	2	2	no	—
262	C₂×C₈₉	—	4	1	no	—
263	C₂×C₈₉	—	8	2	no	—
264	C₂×C₈₉	#2361	1	1	yes	characteristic
265	C₂×C₈₉	C₂×#444	1	1	yes	characteristic
266	C₂×C₈₉	#2957	1	1	yes	characteristic
267	#3050	D₈₉	1	1	yes	characteristic
268	C₂×#444	—	89	1	no	—
269	#2933	—	89	2	no	—
270	C₂²×#108	—	89	1	no	—
271	#1975	—	89	1	no	—
272	#1946	—	89	1	no	—
273	#1929	—	89	2	no	—
274	#1871	—	89	2	no	—
275	#1866	—	89	2	no	—
276	#1773	—	89	1	no	—
277	#1752	—	89	1	no	—
278	C₈₉	#23019	1	1	yes	characteristic, complemented, Sylow
279	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
280	C₂×#131	—	89	2	no	—
281	C₂²×M₁₆	—	89	2	no	—
282	C₂³×C₈	C₂×D₈₉	1	1	yes	characteristic
283	#525	C₂×D₈₉	1	2	yes	—
284	#467	Dic₈₉	1	1	yes	characteristic, complemented
285	#467	Dic₈₉	1	1	yes	characteristic, complemented
286	#466	Dic₈₉	1	1	yes	characteristic, complemented
287	#466	Dic₈₉	1	1	yes	characteristic, complemented
288	#465	Dic₈₉	1	2	yes	complemented
289	#465	Dic₈₉	1	2	yes	complemented
290	#444	—	178	4	no	—
291	#436	—	178	2	no	—
292	#435	—	178	2	no	—
293	#435	—	178	2	no	—
294	C₈×D₄	—	178	2	no	—
295	C₂×#108	—	89	1	no	—
296	C₂×#108	—	89	2	no	—
297	C₂×#108	—	89	1	no	—
298	C₂×#108	—	178	4	no	—
299	#427	C₂×D₈₉	1	1	yes	characteristic
300	#424	—	89	2	no	—
301	C₂×#104	—	89	2	no	—
302	C₂×#104	—	89	2	no	—
303	#416	C₂×D₈₉	1	2	yes	—
304	#408	—	89	2	no	—
305	C₂×C₂²⋊C₈	—	89	1	no	—
306	#405	—	89	2	no	—
307	C₂×#97	—	89	1	no	—
308	C₂×#97	—	89	1	no	—
309	C₄×C₂²⋊C₄	—	89	1	no	—
310	#339	—	89	2	no	—
311	#339	—	89	2	no	—
312	#336	—	89	1	no	—
313	#336	—	89	1	no	—
314	C₂×#41	C₂²×D₈₉	1	2	yes	—
315	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
316	#135	—	2	2	no	—
317	#135	—	2	2	no	—
318	C₂×Q₁₆	C₂×Dic₈₉	1	1	yes	characteristic
319	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	—
320	C₂×D₈	C₂×Dic₈₉	1	1	yes	characteristic
321	#131	—	356	2	no	—
322	#131	—	178	4	no	—
323	C₂×M₁₆	—	89	2	no	—
324	C₂×M₁₆	—	89	2	no	—
325	C₂×M₁₆	—	356	2	no	—
326	C₂×M₁₆	—	178	2	no	—
327	C₂×M₁₆	—	178	4	no	—
328	C₂×M₁₆	—	178	2	no	—
329	C₂²×C₈	—	2	2	no	—
330	C₂²×C₈	—	2	2	no	—
331	C₂²×C₈	—	89	1	no	—
332	C₂²×C₈	—	89	1	no	—
333	C₂²×C₈	—	178	2	no	—
334	C₂²×C₈	—	178	2	no	—
335	C₂²×C₈	C₂×Dic₈₉	1	1	yes	characteristic
336	C₂²×C₈	C₂×Dic₈₉	1	1	yes	characteristic
337	C₂²×C₈	C₂×Dic₈₉	1	1	yes	characteristic
338	C₂²×C₈	C₂×Dic₈₉	1	1	yes	characteristic
339	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
340	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
341	#123	—	2	2	no	—
342	C₂²⋊Q₈	C₂×Dic₈₉	1	2	yes	—
343	C₂²⋊Q₈	C₂×Dic₈₉	1	2	yes	—
344	#121	C₂×Dic₈₉	1	2	yes	—
345	#121	C₂×Dic₈₉	1	2	yes	—
346	#120	—	2	2	no	—
347	C₄×D₄	—	2	2	no	—
348	C₄×D₄	—	2	2	no	—
349	#117	C₂²×D₈₉	1	2	yes	—
350	C₂×C₂²⋊C₄	—	178	1	no	—
351	C₂×C₄²	—	89	1	no	—
352	C₂×C₄²	—	89	1	no	—
353	#108	—	89	4	no	—
354	#108	—	178	4	no	—
355	#108	—	178	2	no	—
356	#107	C₂×Dic₈₉	1	1	yes	characteristic
357	#107	C₂×Dic₈₉	1	1	yes	characteristic
358	#106	C₂×Dic₈₉	1	2	yes	—
359	C₄⋊C₈	—	178	2	no	—
360	C₄⋊C₈	—	178	2	no	—
361	#104	—	356	2	no	—
362	#104	—	178	4	no	—
363	#103	C₂×Dic₈₉	1	2	yes	—
364	#103	C₂×Dic₈₉	1	2	yes	—
365	#102	C₂×Dic₈₉	1	2	yes	—
366	#102	C₂×Dic₈₉	1	2	yes	—
367	C₂²⋊C₈	—	89	2	no	—
368	C₂²⋊C₈	—	89	2	no	—
369	C₂²⋊C₈	—	178	2	no	—
370	C₂²⋊C₈	—	178	2	no	—
371	#97	—	178	2	no	—
372	#97	—	178	2	no	—
373	#97	—	178	2	no	—
374	C₄×C₈	—	178	2	no	—
375	#95	—	178	1	no	—
376	C₂⁴	#13083573	1	1	yes	characteristic
377	#41	—	2	2	no	—
378	#41	—	2	2	no	—
379	#41	—	2	2	no	—
380	#41	—	2	2	no	—
381	C₂×Q₈	C₂²×Dic₈₉	1	2	yes	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	C₂²×Dic₈₉	1	2	yes	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	178	1	no	—
392	C₂²×C₄	—	178	1	no	—
393	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
394	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
395	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
396	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
397	C₂²×C₄	#13083573	1	1	yes	characteristic
398	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
399	Q₁₆	—	2	2	no	—
400	SD₁₆	—	2	4	no	—
401	D₈	—	2	2	no	—
402	M₁₆	—	89	4	no	—
403	M₁₆	—	356	4	no	—
404	M₁₆	—	356	4	no	—
405	M₁₆	—	178	2	no	—
406	M₁₆	—	178	2	no	—
407	M₁₆	—	178	2	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	89	2	no	—
415	C₂×C₈	—	89	2	no	—
416	C₂×C₈	—	356	4	no	—
417	C₂×C₈	—	356	4	no	—
418	C₂×C₈	—	178	2	no	—
419	C₂×C₈	—	178	1	no	—
420	C₂×C₈	—	178	2	no	—
421	C₂×C₈	—	178	1	no	—
422	C₂×C₈	—	178	1	no	—
423	C₂×C₈	—	178	1	no	—
424	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
425	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
426	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
427	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
428	C₂×C₈	D₄×D₈₉	1	2	yes	—
429	C₂×C₈	#13083573	1	2	yes	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
433	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	356	2	no	—
440	C₄²	—	2	2	no	—
441	C₄²	—	178	1	no	—
442	C₄²	—	178	1	no	—
443	C₄²	—	178	1	no	—
444	C₄²	—	178	1	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	2	1	no	—
447	C₂³	—	2	1	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	4	1	no	—
450	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
451	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
452	C₂³	C₂×#13083573	1	1	yes	characteristic
453	Q₈	—	2	2	no	—
454	Q₈	—	2	2	no	—
455	D₄	—	2	2	no	—
456	D₄	—	2	2	no	—
457	D₄	—	4	4	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	8	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	356	1	no	—
477	C₂×C₄	—	356	1	no	—
478	C₂×C₄	—	356	1	no	—
479	C₂×C₄	—	356	1	no	—
480	C₂×C₄	—	356	1	no	—
481	C₂×C₄	—	356	1	no	—
482	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
483	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
484	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
485	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
486	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
487	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
488	C₂×C₄	#15668058	1	1	yes	characteristic
489	C₂×C₄	#15668059	1	1	yes	characteristic
490	C₈	—	2	1	no	—
491	C₈	—	2	1	no	—
492	C₈	—	356	2	no	—
493	C₈	—	178	2	no	—
494	C₈	—	178	4	no	—
495	C₈	—	178	2	no	—
496	C₈	D₄×Dic₈₉	1	2	yes	—
497	C₈	D₄×Dic₈₉	1	2	yes	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	#19151720	1	2	yes	complemented
511	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
512	C₂²	#19152254	1	1	yes	characteristic
513	C₂²	#19152300	1	1	yes	characteristic
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	712	1	no	—
520	C₄	—	712	1	no	—
521	C₄	C₂×D₄×Dic₈₉	1	1	yes	characteristic
522	C₄	#19152081	1	1	yes	characteristic
523	C₄	#19152232	1	1	yes	characteristic
524	C₄	#19152248	1	1	yes	characteristic
525	C₂	—	2	1	no	—
526	C₂	—	2	1	no	—
527	C₂	—	2	2	no	—
528	C₂	—	4	1	no	—
529	C₂	—	8	2	no	—
530	C₂	#26023272	1	1	yes	characteristic
531	C₂	C₂×#19151720	1	1	yes	characteristic
532	C₂	#26029169	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, prime radical	C₈₉×#3050	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#3050	D₈₉
hypocenter	C₈₉	#23019
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #3050

Complements

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

N	H ≅ G/N	type
1. C₂×#19151720	C₂	semidirect
2. #26028979	C₂	semidirect
3. C₂²×#15667948	C₂	semidirect
4. #26021146	C₂	semidirect
5. #26021006	C₂	semidirect
6. #26020902	C₂	semidirect
7. #26020555	C₂	semidirect
8. #26020529	C₂	semidirect
9. #26020138	C₂	semidirect
10. #26020028	C₂	semidirect
39. #467×C₈₉	C₄	semidirect
40. #467×C₈₉	C₄	semidirect
41. #466×C₈₉	C₄	semidirect
42. #466×C₈₉	C₄	semidirect
43. #465×C₈₉	C₄	semidirect
44. #465×C₈₉	C₄	semidirect
64. #15667948	D₄	semidirect
243. C₂²×C₈₉	#444	semidirect
278. C₈₉	#23019	semidirect
284. #467	Dic₈₉	semidirect
285. #467	Dic₈₉	semidirect
286. #466	Dic₈₉	semidirect
287. #466	Dic₈₉	semidirect
288. #465	Dic₈₉	semidirect
289. #465	Dic₈₉	semidirect
510. C₂²	#19151720	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151720	2
#26028979	2
C₂²×#15667948	2
#26021146	2
#26021006	2
#26020902	2
#26020555	2
#26020529	2
#26020138	2
#26020028	2
C₈₉×#3050	2
#23019	89