Subgroups — #36612494

Order 22784.

696 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26023976	C₂	1	1	yes	maximal, characteristic
2	#26023135	C₂	1	1	yes	maximal, characteristic
3	#26021821	C₂	1	1	yes	maximal, characteristic, complemented
4	#26021750	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021750	C₂	1	1	yes	maximal, characteristic, complemented
6	#26021591	C₂	1	1	yes	maximal, characteristic, complemented
7	#26021207	C₂	1	1	yes	maximal, characteristic, complemented
8	#26021022	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020831	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020831	C₂	1	1	yes	maximal, characteristic, complemented
11	#26020447	C₂	1	1	yes	maximal, characteristic
12	#26020348	C₂	1	1	yes	maximal, characteristic
13	#26020285	C₂	1	1	yes	maximal, characteristic
14	#26019972	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#1851	C₂	1	1	yes	maximal, characteristic
16	C₂×#15668004	C₂²	1	1	yes	characteristic
17	C₂×#15667971	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
19	C₂×#15667946	C₂²	1	1	yes	characteristic
20	C₂×#15667944	C₂²	1	1	yes	characteristic
21	C₂×#15667944	C₂²	1	1	yes	characteristic
22	C₂×#15667944	C₂²	1	1	yes	characteristic
23	#19151540	—	2	1	no	—
24	#19151532	—	2	1	no	—
25	#19151496	C₂²	1	1	yes	characteristic
26	#19151496	C₂²	1	1	yes	characteristic
27	#19151496	C₂²	1	1	yes	characteristic
28	#19151496	C₂²	1	1	yes	characteristic
29	#19151486	—	2	1	no	—
30	#19151486	—	2	1	no	—
31	#19151470	—	2	1	no	—
32	#19151464	C₂²	1	1	yes	characteristic
33	#19151462	—	2	1	no	—
34	#19151458	C₂²	1	1	yes	characteristic
35	#19151458	C₂²	1	1	yes	characteristic
36	#19151456	—	2	1	no	—
37	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
39	#19151443	—	2	1	no	—
40	#19151361	C₂²	1	1	yes	characteristic
41	#19151361	C₂²	1	1	yes	characteristic
42	#19151361	C₂²	1	1	yes	characteristic
43	#19151361	C₂²	1	1	yes	characteristic
44	#19151361	C₂²	1	1	yes	characteristic
45	#19151361	C₂²	1	1	yes	characteristic
46	#19151361	C₂²	1	1	yes	characteristic
47	#19151361	C₂²	1	1	yes	characteristic
48	#19151361	C₂²	1	1	yes	characteristic
49	#19151361	C₂²	1	1	yes	characteristic
50	#19151361	C₂²	1	1	yes	characteristic
51	#19151361	C₂²	1	1	yes	characteristic
52	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
54	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
55	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
57	#336×C₈₉	C₂²	1	1	yes	characteristic
58	#336×C₈₉	C₂²	1	1	yes	characteristic
59	C₂³×Dic₈₉	—	2	1	no	—
60	#15668004	—	2	2	no	—
61	#15668004	—	4	1	no	—
62	#15667971	—	2	2	no	—
63	#15667971	Q₈	1	4	yes	—
64	C₂×C₄⋊Dic₈₉	—	2	2	no	—
65	C₂×C₄⋊Dic₈₉	—	2	1	no	—
66	C₂×C₄⋊Dic₈₉	—	4	1	no	—
67	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
75	C₂×#13083553	—	2	1	no	—
76	C₂×#13083553	—	2	1	no	—
77	C₂×#13083553	—	2	1	no	—
78	C₂×#13083553	—	2	1	no	—
79	C₂×#13083553	—	2	1	no	—
80	C₂×#13083553	—	2	1	no	—
81	C₂×C₂²⋊Dic₈₉	—	2	1	no	—
82	C₂×C₂²⋊Dic₈₉	—	2	1	no	—
83	C₂×C₂²⋊Dic₈₉	—	2	1	no	—
84	C₂×C₄×Dic₈₉	—	2	1	no	—
85	C₂×C₄×Dic₈₉	—	2	1	no	—
86	C₂×C₄×Dic₈₉	—	2	1	no	—
87	#15667946	—	4	1	no	—
88	#15667944	—	2	2	no	—
89	#15667944	—	2	2	no	—
90	#15667944	—	4	1	no	—
91	#15667919	—	2	1	no	—
92	#15667919	—	2	1	no	—
93	#15667919	—	2	1	no	—
94	#15667919	—	2	1	no	—
95	#15667919	—	2	1	no	—
96	#15667919	—	2	1	no	—
97	#15667919	—	2	1	no	—
98	#15667919	—	2	1	no	—
99	#15667919	—	2	1	no	—
100	#15667919	—	2	1	no	—
101	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
102	C₂×M₁₆×C₈₉	—	2	2	no	—
103	C₂×M₁₆×C₈₉	—	2	2	no	—
104	C₂×M₁₆×C₈₉	—	4	1	no	—
105	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
111	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
113	C₄⋊C₈×C₈₉	—	2	2	no	—
114	C₄⋊C₈×C₈₉	—	4	1	no	—
115	C₂²⋊C₈×C₈₉	—	2	2	no	—
116	#95×C₈₉	D₄	1	1	yes	characteristic
117	#95×C₈₉	D₄	1	1	yes	characteristic
118	C₂²×Dic₈₉	—	2	1	no	—
119	C₂²×Dic₈₉	—	2	1	no	—
120	C₂²×Dic₈₉	—	2	1	no	—
121	C₂²×Dic₈₉	—	2	1	no	—
122	C₂²×Dic₈₉	—	2	1	no	—
123	C₂²×Dic₈₉	—	2	1	no	—
124	C₂²×Dic₈₉	—	2	1	no	—
125	C₂²×Dic₈₉	—	2	1	no	—
126	C₂²×Dic₈₉	—	4	2	no	—
127	C₂²×Dic₈₉	—	4	2	no	—
128	C₂²×Dic₈₉	—	8	1	no	—
129	C₄⋊Dic₈₉	—	2	1	no	—
130	C₄⋊Dic₈₉	—	2	1	no	—
131	C₄⋊Dic₈₉	—	2	1	no	—
132	C₄⋊Dic₈₉	—	2	1	no	—
133	C₄⋊Dic₈₉	—	2	1	no	—
134	C₄⋊Dic₈₉	—	2	1	no	—
135	C₄⋊Dic₈₉	—	2	1	no	—
136	C₄⋊Dic₈₉	—	2	1	no	—
137	C₄⋊Dic₈₉	—	2	1	no	—
138	C₄⋊Dic₈₉	—	2	1	no	—
139	C₄⋊Dic₈₉	—	2	1	no	—
140	C₄⋊Dic₈₉	—	2	1	no	—
141	C₄⋊Dic₈₉	—	2	1	no	—
142	C₄⋊Dic₈₉	—	4	2	no	—
143	C₄⋊Dic₈₉	C₂×Q₈	1	2	yes	—
144	C₄⋊Dic₈₉	C₂×Q₈	1	2	yes	—
145	C₄⋊Dic₈₉	#41	1	2	yes	—
146	#13083553	—	4	2	no	—
147	#13083553	—	4	2	no	—
148	#13083553	—	8	1	no	—
149	#13083553	—	8	1	no	—
150	#13083553	—	8	1	no	—
151	#13083553	—	8	1	no	—
152	C₂²⋊Dic₈₉	—	2	4	no	—
153	C₂²⋊Dic₈₉	—	4	2	no	—
154	C₂²⋊Dic₈₉	—	8	1	no	—
155	C₄×Dic₈₉	—	2	4	no	—
156	C₄×Dic₈₉	—	4	2	no	—
157	C₄×Dic₈₉	—	4	2	no	—
158	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₈₉	—	2	1	no	—
160	C₂²×C₄×C₈₉	—	2	1	no	—
161	C₂²×C₄×C₈₉	—	2	1	no	—
162	C₂²×C₄×C₈₉	—	2	1	no	—
163	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₈₉	C₂×Q₈	1	2	yes	—
169	C₂²×C₄×C₈₉	#41	1	2	yes	—
170	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
171	M₁₆×C₈₉	—	4	4	no	—
172	C₂×C₈×C₈₉	—	2	1	no	—
173	C₂×C₈×C₈₉	—	2	1	no	—
174	C₂×C₈×C₈₉	—	2	1	no	—
175	C₂×C₈×C₈₉	—	2	1	no	—
176	C₂×C₈×C₈₉	—	2	1	no	—
177	C₂×C₈×C₈₉	—	2	1	no	—
178	C₂×C₈×C₈₉	—	2	1	no	—
179	C₂×C₈×C₈₉	—	2	1	no	—
180	C₂×C₈×C₈₉	—	2	1	no	—
181	C₂×C₈×C₈₉	—	2	1	no	—
182	C₂×C₈×C₈₉	—	2	1	no	—
183	C₂×C₈×C₈₉	#41	1	2	yes	—
184	C₂²⋊C₄×C₈₉	—	4	1	no	—
185	C₂²⋊C₄×C₈₉	—	4	1	no	—
186	C₄²×C₈₉	—	2	1	no	—
187	C₄²×C₈₉	—	2	1	no	—
188	C₄²×C₈₉	—	2	1	no	—
189	C₄²×C₈₉	—	2	1	no	—
190	C₂³×C₈₉	—	2	1	no	—
191	C₂³×C₈₉	—	2	1	no	—
192	C₂³×C₈₉	—	2	1	no	—
193	C₂³×C₈₉	—	2	1	no	—
194	C₂³×C₈₉	—	2	1	no	—
195	C₂³×C₈₉	—	2	1	no	—
196	C₂³×C₈₉	C₂²⋊Q₈	1	2	yes	—
197	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₈₉	—	2	1	no	—
199	C₂×C₄×C₈₉	—	2	1	no	—
200	C₂×C₄×C₈₉	—	2	2	no	—
201	C₂×C₄×C₈₉	—	2	2	no	—
202	C₂×C₄×C₈₉	—	2	2	no	—
203	C₂×C₄×C₈₉	—	2	2	no	—
204	C₂×C₄×C₈₉	—	2	1	no	—
205	C₂×C₄×C₈₉	—	2	1	no	—
206	C₂×C₄×C₈₉	—	2	1	no	—
207	C₂×C₄×C₈₉	—	2	1	no	—
208	C₂×C₄×C₈₉	—	2	1	no	—
209	C₂×C₄×C₈₉	—	2	1	no	—
210	C₂×C₄×C₈₉	—	2	1	no	—
211	C₂×C₄×C₈₉	—	2	1	no	—
212	C₂×C₄×C₈₉	—	2	1	no	—
213	C₂×C₄×C₈₉	—	2	1	no	—
214	C₂×C₄×C₈₉	—	2	1	no	—
215	C₂×C₄×C₈₉	—	2	1	no	—
216	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
217	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
218	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
222	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
223	C₂×Dic₈₉	—	2	2	no	—
224	C₂×Dic₈₉	—	2	2	no	—
225	C₂×Dic₈₉	—	2	2	no	—
226	C₂×Dic₈₉	—	4	1	no	—
227	C₂×Dic₈₉	—	4	1	no	—
228	C₂×Dic₈₉	—	4	1	no	—
229	C₂×Dic₈₉	—	4	1	no	—
230	C₂×Dic₈₉	—	4	1	no	—
231	C₂×Dic₈₉	—	4	1	no	—
232	C₂×Dic₈₉	—	4	1	no	—
233	C₂×Dic₈₉	—	4	1	no	—
234	C₂×Dic₈₉	—	4	1	no	—
235	C₂×Dic₈₉	—	4	1	no	—
236	C₂×Dic₈₉	—	4	1	no	—
237	C₂×Dic₈₉	—	4	1	no	—
238	C₂×Dic₈₉	—	4	1	no	—
239	C₂×Dic₈₉	—	4	1	no	—
240	C₂×Dic₈₉	—	4	1	no	—
241	C₂×Dic₈₉	—	4	1	no	—
242	C₂×Dic₈₉	—	4	1	no	—
243	C₂×Dic₈₉	—	4	1	no	—
244	C₂×Dic₈₉	—	4	1	no	—
245	C₂×Dic₈₉	—	4	1	no	—
246	C₂×Dic₈₉	—	4	1	no	—
247	C₂×Dic₈₉	—	8	4	no	—
248	C₈×C₈₉	—	2	2	no	—
249	C₈×C₈₉	—	4	1	no	—
250	C₈×C₈₉	—	4	1	no	—
251	C₈×C₈₉	—	4	1	no	—
252	C₂²×C₈₉	—	2	2	no	—
253	C₂²×C₈₉	—	2	2	no	—
254	C₂²×C₈₉	—	2	2	no	—
255	C₂²×C₈₉	—	4	1	no	—
256	C₂²×C₈₉	—	4	1	no	—
257	C₂²×C₈₉	—	4	1	no	—
258	C₂²×C₈₉	—	4	1	no	—
259	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
260	C₂²×C₈₉	#546	1	1	yes	characteristic
261	C₂²×C₈₉	#547	1	1	yes	characteristic
262	C₂²×C₈₉	#575	1	1	yes	characteristic
263	C₂²×C₈₉	#575	1	1	yes	characteristic
264	C₂²×C₈₉	#577	1	1	yes	characteristic
265	C₂²×C₈₉	#577	1	1	yes	characteristic
266	C₄×C₈₉	—	2	2	no	—
267	C₄×C₈₉	—	4	1	no	—
268	C₄×C₈₉	—	4	1	no	—
269	C₄×C₈₉	—	4	1	no	—
270	C₄×C₈₉	—	4	1	no	—
271	C₄×C₈₉	#533	1	1	yes	characteristic
272	C₄×C₈₉	#544	1	1	yes	characteristic
273	C₄×C₈₉	#551	1	1	yes	characteristic
274	C₄×C₈₉	#552	1	1	yes	characteristic
275	Dic₈₉	—	4	2	no	—
276	Dic₈₉	—	4	2	no	—
277	Dic₈₉	—	4	2	no	—
278	Dic₈₉	—	8	1	no	—
279	Dic₈₉	—	8	1	no	—
280	Dic₈₉	—	8	1	no	—
281	Dic₈₉	—	8	1	no	—
282	Dic₈₉	—	8	1	no	—
283	#26019	—	89	1	no	maximal, Sylow
284	C₂×C₈₉	—	4	2	no	—
285	C₂×C₈₉	#2438	1	1	yes	characteristic
286	C₂×C₈₉	#3080	1	1	yes	characteristic
287	C₂×C₈₉	#3084	1	1	yes	characteristic
288	C₂×C₈₉	#3321	1	1	yes	characteristic
289	C₂×C₈₉	#3323	1	1	yes	characteristic
290	C₂×C₈₉	#3348	1	1	yes	characteristic
291	C₂×C₈₉	#3351	1	1	yes	characteristic
292	#2442	—	89	1	no	—
293	#2346	—	89	1	no	—
294	#2101	—	89	1	no	—
295	#2088	—	89	1	no	—
296	#2088	—	89	1	no	—
297	#2059	—	89	1	no	—
298	#1989	—	89	1	no	—
299	#1949	—	89	1	no	—
300	#1919	—	89	1	no	—
301	#1919	—	89	1	no	—
302	#1853	—	89	1	no	—
303	#1851	D₈₉	1	1	yes	characteristic
304	#1825	—	89	1	no	—
305	#1809	—	89	1	no	—
306	#1736	—	89	1	no	—
307	C₈₉	#26019	1	1	yes	characteristic, complemented, Sylow
308	C₂²×M₁₆	C₂×D₈₉	1	1	yes	characteristic
309	C₂×#125	—	89	1	no	—
310	C₂×#117	—	89	1	no	—
311	C₂²×C₄⋊C₄	—	89	1	no	—
312	C₂×#107	—	89	1	no	—
313	C₂×#106	—	89	1	no	—
314	C₂×#106	—	89	1	no	—
315	C₂×#106	—	89	1	no	—
316	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
317	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
318	C₂×C₂²⋊C₈	C₂×D₈₉	1	1	yes	characteristic
319	#400	—	178	1	no	—
320	#398	—	178	1	no	—
321	#389	—	89	1	no	—
322	#389	—	89	1	no	—
323	#389	—	89	1	no	—
324	#389	—	89	1	no	—
325	#388	—	178	1	no	—
326	#388	—	178	1	no	—
327	#385	—	178	1	no	—
328	#382	—	89	1	no	—
329	#382	—	178	1	no	—
330	#380	—	89	1	no	—
331	#380	—	89	1	no	—
332	#380	—	178	1	no	—
333	C₄×C₄⋊C₄	—	89	1	no	—
334	C₄×C₄⋊C₄	—	89	1	no	—
335	C₄×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
336	#376	—	178	1	no	—
337	#340	—	89	1	no	—
338	#340	—	89	1	no	—
339	#340	—	89	1	no	—
340	#340	—	89	1	no	—
341	#340	—	89	1	no	—
342	#340	—	89	1	no	—
343	#340	—	89	1	no	—
344	#340	—	89	1	no	—
345	#340	—	89	1	no	—
346	#340	—	89	1	no	—
347	#340	—	89	1	no	—
348	#340	—	89	1	no	—
349	#336	C₂×D₈₉	1	1	yes	characteristic
350	#336	C₂×D₈₉	1	1	yes	characteristic
351	C₂³×C₄	—	178	1	no	—
352	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
353	C₂×M₁₆	—	2	2	no	—
354	C₂×M₁₆	—	2	2	no	—
355	C₂×M₁₆	—	4	1	no	—
356	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
357	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
358	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
359	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
360	#125	—	356	1	no	—
361	#125	—	178	2	no	—
362	#117	—	89	4	no	—
363	#117	—	178	2	no	—
364	C₂×C₄⋊C₄	—	89	1	no	—
365	C₂×C₄⋊C₄	—	89	1	no	—
366	C₂×C₄⋊C₄	—	89	1	no	—
367	C₂×C₄⋊C₄	—	89	1	no	—
368	C₂×C₄⋊C₄	—	89	1	no	—
369	C₂×C₄⋊C₄	—	89	1	no	—
370	C₂×C₄⋊C₄	—	89	1	no	—
371	C₂×C₄⋊C₄	—	89	1	no	—
372	C₂×C₄⋊C₄	—	356	1	no	—
373	C₂×C₄⋊C₄	—	178	2	no	—
374	C₂×C₄⋊C₄	—	178	1	no	—
375	C₂×C₄⋊C₄	—	178	1	no	—
376	C₂×C₄⋊C₄	—	178	1	no	—
377	C₂×C₄⋊C₄	—	178	1	no	—
378	C₂×C₄⋊C₄	—	178	1	no	—
379	C₂×C₄⋊C₄	—	178	1	no	—
380	C₂×C₄⋊C₄	—	178	1	no	—
381	C₂×C₂²⋊C₄	—	178	1	no	—
382	C₂×C₂²⋊C₄	—	178	1	no	—
383	C₂×C₂²⋊C₄	—	178	1	no	—
384	C₂×C₂²⋊C₄	D₃₅₆	1	1	yes	characteristic
385	C₂×C₂²⋊C₄	D₃₅₆	1	1	yes	characteristic
386	C₂×C₄²	—	178	1	no	—
387	C₂×C₄²	—	178	1	no	—
388	C₂×C₄²	—	178	1	no	—
389	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
390	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
391	#107	—	356	1	no	—
392	#106	—	356	1	no	—
393	#106	—	178	2	no	—
394	#106	—	178	2	no	—
395	C₄⋊C₈	—	2	2	no	—
396	C₄⋊C₈	—	4	1	no	—
397	C₂²⋊C₈	—	2	2	no	—
398	#95	—	178	1	no	—
399	#95	—	178	1	no	—
400	#95	—	178	1	no	—
401	#95	—	178	1	no	—
402	#95	—	178	1	no	—
403	#95	—	178	1	no	—
404	#95	—	178	1	no	—
405	#95	—	178	1	no	—
406	#95	—	178	1	no	—
407	#95	—	178	1	no	—
408	#95	D₃₅₆	1	1	yes	characteristic
409	#95	D₃₅₆	1	1	yes	characteristic
410	C₂⁴	C₂×D₃₅₆	1	1	yes	characteristic
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	356	2	no	—
416	C₂²×C₄	—	356	2	no	—
417	C₂²×C₄	—	178	1	no	—
418	C₂²×C₄	—	178	1	no	—
419	C₂²×C₄	—	178	1	no	—
420	C₂²×C₄	—	178	1	no	—
421	C₂²×C₄	—	178	1	no	—
422	C₂²×C₄	—	178	1	no	—
423	C₂²×C₄	—	178	1	no	—
424	C₂²×C₄	—	178	1	no	—
425	C₂²×C₄	—	712	1	no	—
426	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
431	C₂²×C₄	Q₈×D₈₉	1	2	yes	—
432	C₂²×C₄	#13083573	1	2	yes	—
433	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
434	M₁₆	—	4	4	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	#13083573	1	2	yes	—
447	C₄⋊C₄	—	89	2	no	—
448	C₄⋊C₄	—	89	2	no	—
449	C₄⋊C₄	—	89	2	no	—
450	C₄⋊C₄	—	356	2	no	—
451	C₄⋊C₄	—	356	2	no	—
452	C₄⋊C₄	—	356	2	no	—
453	C₄⋊C₄	—	178	1	no	—
454	C₄⋊C₄	—	178	1	no	—
455	C₄⋊C₄	—	178	1	no	—
456	C₄⋊C₄	—	178	1	no	—
457	C₄⋊C₄	—	178	1	no	—
458	C₄⋊C₄	—	178	1	no	—
459	C₄⋊C₄	—	178	1	no	—
460	C₄⋊C₄	—	178	1	no	—
461	C₄⋊C₄	—	178	1	no	—
462	C₄⋊C₄	—	178	1	no	—
463	C₄⋊C₄	—	178	1	no	—
464	C₄⋊C₄	—	178	1	no	—
465	C₄⋊C₄	—	178	1	no	—
466	C₄⋊C₄	—	712	1	no	—
467	C₄⋊C₄	—	712	1	no	—
468	C₄⋊C₄	—	712	1	no	—
469	C₄⋊C₄	—	712	1	no	—
470	C₂²⋊C₄	—	4	1	no	—
471	C₂²⋊C₄	—	4	1	no	—
472	C₂²⋊C₄	—	356	2	no	—
473	C₂²⋊C₄	—	178	4	no	—
474	C₂²⋊C₄	—	712	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	356	2	no	—
480	C₄²	—	356	2	no	—
481	C₄²	—	178	4	no	—
482	C₂³	—	2	1	no	—
483	C₂³	—	2	1	no	—
484	C₂³	—	2	1	no	—
485	C₂³	—	2	1	no	—
486	C₂³	—	2	1	no	—
487	C₂³	—	2	1	no	—
488	C₂³	#15667992	1	2	yes	—
489	C₂³	C₂²×D₃₅₆	1	1	yes	characteristic
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	356	1	no	—
509	C₂×C₄	—	356	1	no	—
510	C₂×C₄	—	356	1	no	—
511	C₂×C₄	—	356	1	no	—
512	C₂×C₄	—	356	1	no	—
513	C₂×C₄	—	356	1	no	—
514	C₂×C₄	—	356	1	no	—
515	C₂×C₄	—	356	1	no	—
516	C₂×C₄	—	356	1	no	—
517	C₂×C₄	—	356	1	no	—
518	C₂×C₄	—	356	1	no	—
519	C₂×C₄	—	356	1	no	—
520	C₂×C₄	—	356	1	no	—
521	C₂×C₄	—	356	1	no	—
522	C₂×C₄	—	356	1	no	—
523	C₂×C₄	—	356	1	no	—
524	C₂×C₄	—	356	1	no	—
525	C₂×C₄	—	356	1	no	—
526	C₂×C₄	—	356	1	no	—
527	C₂×C₄	—	356	1	no	—
528	C₂×C₄	—	356	1	no	—
529	C₂×C₄	—	178	2	no	—
530	C₂×C₄	—	178	2	no	—
531	C₂×C₄	—	178	2	no	—
532	C₂×C₄	—	712	4	no	—
533	C₂×C₄	#15667992	1	2	yes	—
534	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
535	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
536	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
537	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
538	C₂×C₄	#15668057	1	1	yes	characteristic
539	C₂×C₄	#15668059	1	1	yes	characteristic
540	C₈	—	2	2	no	—
541	C₈	—	4	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	C₂×#15667992	1	1	yes	characteristic
552	C₂²	#19152243	1	1	yes	characteristic
553	C₂²	#19152252	1	1	yes	characteristic
554	C₂²	#19152398	1	1	yes	characteristic
555	C₂²	#19152398	1	1	yes	characteristic
556	C₂²	#19152410	1	1	yes	characteristic
557	C₂²	#19152410	1	1	yes	characteristic
558	C₄	—	2	2	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	356	2	no	—
564	C₄	—	356	2	no	—
565	C₄	—	356	2	no	—
566	C₄	—	712	1	no	—
567	C₄	—	712	1	no	—
568	C₄	—	712	1	no	—
569	C₄	—	712	1	no	—
570	C₄	—	712	1	no	—
571	C₄	#19152150	1	1	yes	characteristic
572	C₄	#19152227	1	1	yes	characteristic
573	C₄	#19152279	1	1	yes	characteristic
574	C₄	#19152285	1	1	yes	characteristic
575	C₂	—	4	2	no	—
576	C₂	#26023926	1	1	yes	characteristic
577	C₂	#26030075	1	1	yes	characteristic
578	C₂	#26030116	1	1	yes	characteristic
579	C₂	#26032440	1	1	yes	characteristic
580	C₂	#26032470	1	1	yes	characteristic
581	C₂	#26032769	1	1	yes	characteristic
582	C₂	#26032814	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₃₅₆
commutator, cosocle	C₂²×C₄×C₈₉	C₂⁴
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1851	C₂
socle	C₂³×C₈₉	C₂²×D₄
prime radical	C₂⁴×C₈₉	C₂×D₄
hypercenter	#1851	D₈₉
hypocenter	C₈₉	#26019
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₄×C₂²⋊C₄ ◁ #1851

Complements

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

N	H ≅ G/N	type
3. #26021821	C₂	semidirect
4. #26021750	C₂	semidirect
5. #26021750	C₂	semidirect
6. #26021591	C₂	semidirect
7. #26021207	C₂	semidirect
8. #26021022	C₂	semidirect
9. #26020831	C₂	semidirect
10. #26020831	C₂	semidirect
307. C₈₉	#26019	semidirect

Maximal subgroups

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

subgroup	index
#26023976	2
#26023135	2
#26021821	2
#26021750	2
#26021591	2
#26021207	2
#26021022	2
#26020831	2
#26020447	2
#26020348	2
#26020285	2
#26019972	2
C₈₉×#1851	2
#26019	89