Subgroups — #36571851

Order 22784.

708 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26022749	C₂	1	1	yes	maximal, characteristic
2	#26020813	C₂	1	1	yes	maximal, characteristic, complemented
3	#26020807	C₂	1	1	yes	maximal, characteristic, complemented
4	#26020807	C₂	1	1	yes	maximal, characteristic, complemented
5	#26020806	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020433	C₂	1	1	yes	maximal, characteristic
7	#26020428	C₂	1	1	yes	maximal, characteristic
8	#26020396	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020322	C₂	1	1	yes	maximal, characteristic
10	#26020108	C₂	1	1	yes	maximal, characteristic, complemented
11	#26020032	C₂	1	1	yes	maximal, characteristic
12	#26020022	C₂	1	1	yes	maximal, characteristic
13	#26019998	C₂	1	1	yes	maximal, characteristic, complemented
14	#26019947	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#1831	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#13083557	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₈₉	C₂²	1	1	yes	characteristic
18	C₂×#15667969	C₂²	1	1	yes	characteristic
19	C₂×#15667941	C₂²	1	1	yes	characteristic
20	C₂×#15667941	C₂²	1	1	yes	characteristic
21	C₂×#15667924	C₂²	1	1	yes	characteristic
22	C₂×#15667924	C₂²	1	1	yes	characteristic
23	C₂×#15667922	C₂²	1	1	yes	characteristic
24	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
25	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
26	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
27	#19151489	C₄	1	1	yes	characteristic
28	#19151489	C₄	1	1	yes	characteristic
29	#19151489	C₄	1	1	yes	characteristic
30	#19151489	C₄	1	1	yes	characteristic
31	#19151482	C₄	1	1	yes	characteristic
32	#19151482	C₄	1	1	yes	characteristic
33	#19151482	C₄	1	1	yes	characteristic
34	#19151482	C₄	1	1	yes	characteristic
35	C₄×#13083553	C₂²	1	1	yes	characteristic
36	C₄×#13083553	C₂²	1	1	yes	characteristic
37	C₄×#13083551	C₂²	1	1	yes	characteristic
38	C₄×#13083551	C₂²	1	1	yes	characteristic
39	#19151444	C₂²	1	1	yes	characteristic
40	#19151353	C₂²	1	1	yes	characteristic
41	#19151353	C₂²	1	1	yes	characteristic
42	#19151353	C₂²	1	1	yes	characteristic
43	#19151353	C₂²	1	1	yes	characteristic
44	#19151352	C₂²	1	1	yes	characteristic
45	#19151352	C₂²	1	1	yes	characteristic
46	#19151352	C₂²	1	1	yes	characteristic
47	#19151352	C₂²	1	1	yes	characteristic
48	#19151352	C₂²	1	1	yes	characteristic
49	#19151352	C₂²	1	1	yes	characteristic
50	#19151352	C₂²	1	1	yes	characteristic
51	#19151352	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
54	C₄³×C₈₉	C₂²	1	1	yes	characteristic
55	#336×C₈₉	C₂²	1	1	yes	characteristic
56	#336×C₈₉	C₂²	1	1	yes	characteristic
57	#336×C₈₉	C₂²	1	1	yes	characteristic
58	#336×C₈₉	C₂²	1	1	yes	characteristic
59	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
60	C₂×#13083557	—	2	2	no	—
61	C₂×#13083557	—	2	2	no	—
62	C₂×#13083557	—	4	1	no	—
63	C₂²×#10623494	C₂³	1	1	yes	characteristic
64	C₂²×#10623494	C₂³	1	1	yes	characteristic
65	C₂²×#10623494	C₂³	1	1	yes	characteristic
66	C₂²×#10623494	C₂³	1	1	yes	characteristic
67	C₂×C₈×D₈₉	—	2	2	no	—
68	C₂×C₈×D₈₉	—	2	2	no	—
69	C₂×C₈×D₈₉	—	4	1	no	—
70	#15667969	—	2	2	no	—
71	#15667969	—	2	2	no	—
72	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
73	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
74	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
75	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
76	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
77	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
78	C₂×#13083551	C₂×C₄	1	1	yes	characteristic
79	C₂×#13083551	C₂×C₄	1	1	yes	characteristic
80	C₂×#13083551	C₂×C₄	1	1	yes	characteristic
81	C₂×#13083551	C₂×C₄	1	1	yes	characteristic
82	C₂×#13083551	C₂×C₄	1	1	yes	characteristic
83	C₂×#13083551	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
85	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
86	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
87	#15667941	—	2	2	no	—
88	#15667941	—	2	2	no	—
89	#15667924	—	2	2	no	—
90	#15667924	—	2	2	no	—
91	#15667922	—	4	1	no	—
92	C₄×#10623494	—	2	2	no	—
93	C₄×#10623494	—	2	2	no	—
94	C₈×Dic₈₉	—	4	1	no	—
95	#15667919	C₂×C₄	1	1	yes	characteristic
96	#15667919	C₂×C₄	1	1	yes	characteristic
97	#15667919	C₂×C₄	1	1	yes	characteristic
98	#15667919	C₂×C₄	1	1	yes	characteristic
99	#15667919	C₂×C₄	1	1	yes	characteristic
100	#15667919	C₂×C₄	1	1	yes	characteristic
101	#15667919	C₂×C₄	1	1	yes	characteristic
102	#15667919	C₂×C₄	1	1	yes	characteristic
103	#15667919	C₂×C₄	1	1	yes	characteristic
104	#15667919	C₂×C₄	1	1	yes	characteristic
105	#15667919	C₂×C₄	1	1	yes	characteristic
106	#15667919	C₂×C₄	1	1	yes	characteristic
107	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
118	C₄⋊C₈×C₈₉	—	4	1	no	—
119	C₄⋊C₈×C₈₉	—	4	1	no	—
120	C₂³×D₈₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₄×D₈₉	—	2	1	no	—
129	C₂×C₄×D₈₉	—	2	1	no	—
130	C₂×C₄×D₈₉	—	2	1	no	—
131	C₂×C₄×D₈₉	—	2	1	no	—
132	C₂×C₄×D₈₉	#41	1	2	yes	—
133	C₂×C₄×D₈₉	#41	1	2	yes	—
134	#13083557	—	4	4	no	—
135	C₂×#10623494	—	2	1	no	—
136	C₂×#10623494	—	2	1	no	—
137	C₂×#10623494	—	2	1	no	—
138	C₂×#10623494	—	2	1	no	—
139	C₂×#10623494	—	2	1	no	—
140	C₂×#10623494	—	2	1	no	—
141	C₂×#10623494	—	2	1	no	—
142	C₂×#10623494	—	2	1	no	—
143	C₂×#10623494	—	2	1	no	—
144	C₂×#10623494	—	2	1	no	—
145	C₂×#10623494	#41	1	2	yes	—
146	C₂×#10623494	#41	1	2	yes	—
147	C₈×D₈₉	—	4	4	no	—
148	#13083553	—	2	2	no	—
149	#13083553	—	2	2	no	—
150	#13083553	—	2	2	no	—
151	#13083553	—	2	2	no	—
152	#13083553	—	2	2	no	—
153	#13083553	—	4	1	no	—
154	#13083551	—	2	2	no	—
155	#13083551	—	2	2	no	—
156	#13083551	—	2	2	no	—
157	#13083551	—	2	2	no	—
158	#13083551	—	2	2	no	—
159	#13083551	—	4	1	no	—
160	C₄×Dic₈₉	—	2	1	no	—
161	C₄×Dic₈₉	—	2	1	no	—
162	C₄×Dic₈₉	—	2	1	no	—
163	C₄×Dic₈₉	—	2	1	no	—
164	C₄×Dic₈₉	—	2	1	no	—
165	C₄×Dic₈₉	—	2	1	no	—
166	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
184	C₂×C₈×C₈₉	—	2	1	no	—
185	C₄²×C₈₉	—	2	2	no	—
186	C₄²×C₈₉	—	2	2	no	—
187	C₄²×C₈₉	—	2	2	no	—
188	C₄²×C₈₉	—	2	1	no	—
189	C₄²×C₈₉	—	2	1	no	—
190	C₄²×C₈₉	—	2	1	no	—
191	C₄²×C₈₉	—	2	1	no	—
192	C₄²×C₈₉	—	2	1	no	—
193	C₄²×C₈₉	—	2	1	no	—
194	C₄²×C₈₉	—	4	1	no	—
195	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
196	C₂²×D₈₉	—	2	1	no	—
197	C₂²×D₈₉	—	2	1	no	—
198	C₂²×D₈₉	—	2	1	no	—
199	C₂²×D₈₉	—	2	1	no	—
200	C₂²×D₈₉	—	2	1	no	—
201	C₂²×D₈₉	—	2	1	no	—
202	C₂²×D₈₉	#117	1	2	yes	—
203	C₂×C₄×C₈₉	—	2	1	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	—	2	1	no	—
217	C₂×C₄×C₈₉	—	2	1	no	—
218	C₂×C₄×C₈₉	#131	1	2	yes	—
219	C₂×C₄×C₈₉	#131	1	2	yes	—
220	C₂×C₄×C₈₉	#131	1	2	yes	—
221	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
226	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
227	C₂×Dic₈₉	—	2	1	no	—
228	C₂×Dic₈₉	—	2	1	no	—
229	C₂×Dic₈₉	—	2	1	no	—
230	C₂×Dic₈₉	—	2	1	no	—
231	C₂×Dic₈₉	—	2	1	no	—
232	C₂×Dic₈₉	—	2	1	no	—
233	C₂×Dic₈₉	—	2	1	no	—
234	C₂×Dic₈₉	—	2	1	no	—
235	C₂×Dic₈₉	—	2	1	no	—
236	C₂×Dic₈₉	—	2	1	no	—
237	C₂×Dic₈₉	—	2	1	no	—
238	C₂×Dic₈₉	—	2	1	no	—
239	C₂×Dic₈₉	—	2	1	no	—
240	C₂×Dic₈₉	—	2	1	no	—
241	C₂×Dic₈₉	—	2	1	no	—
242	C₂×Dic₈₉	—	2	1	no	—
243	C₂×Dic₈₉	—	2	1	no	—
244	C₂×Dic₈₉	—	2	1	no	—
245	C₂×Dic₈₉	—	2	1	no	—
246	C₂×Dic₈₉	—	2	1	no	—
247	C₂×Dic₈₉	#117	1	2	yes	—
248	C₄×D₈₉	—	2	2	no	—
249	C₄×D₈₉	—	2	2	no	—
250	C₄×D₈₉	—	2	2	no	—
251	C₄×D₈₉	—	2	2	no	—
252	C₈×C₈₉	—	4	1	no	—
253	C₈×C₈₉	—	4	1	no	—
254	C₈×C₈₉	—	4	1	no	—
255	C₈×C₈₉	—	4	1	no	—
256	#10623494	—	2	2	no	—
257	#10623494	—	2	2	no	—
258	#10623494	—	4	1	no	—
259	#10623494	—	4	1	no	—
260	C₂²×C₈₉	C₂×#117	1	1	yes	characteristic
261	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
262	C₂²×C₈₉	#520	1	1	yes	characteristic
263	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
264	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
265	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
266	C₂²×C₈₉	#568	1	1	yes	characteristic
267	C₂×D₈₉	—	2	2	no	—
268	C₂×D₈₉	—	2	2	no	—
269	C₂×D₈₉	—	2	2	no	—
270	C₂×D₈₉	—	4	1	no	—
271	C₂×D₈₉	—	4	1	no	—
272	C₂×D₈₉	—	4	1	no	—
273	C₂×D₈₉	—	4	1	no	—
274	C₄×C₈₉	—	2	2	no	—
275	C₄×C₈₉	—	2	2	no	—
276	C₄×C₈₉	—	2	2	no	—
277	C₄×C₈₉	—	4	1	no	—
278	C₄×C₈₉	—	4	1	no	—
279	C₄×C₈₉	—	4	1	no	—
280	C₄×C₈₉	#551	1	1	yes	characteristic
281	C₄×C₈₉	#551	1	1	yes	characteristic
282	C₄×C₈₉	#552	1	1	yes	characteristic
283	C₄×C₈₉	#552	1	1	yes	characteristic
284	Dic₈₉	—	2	2	no	—
285	Dic₈₉	—	4	1	no	—
286	Dic₈₉	—	4	1	no	—
287	Dic₈₉	—	4	1	no	—
288	Dic₈₉	—	4	1	no	—
289	Dic₈₉	—	4	1	no	—
290	Dic₈₉	—	4	1	no	—
291	#22593	—	89	1	no	maximal, Sylow
292	C₂×C₈₉	#2343	1	1	yes	characteristic
293	C₂×C₈₉	#2922	1	1	yes	characteristic
294	C₂×C₈₉	#2925	1	1	yes	characteristic
295	C₂×C₈₉	#2966	1	1	yes	characteristic
296	C₂×C₈₉	#2968	1	1	yes	characteristic
297	C₂×C₈₉	#2993	1	1	yes	characteristic
298	C₂×C₈₉	#2994	1	1	yes	characteristic
299	D₈₉	—	4	2	no	—
300	#2298	—	89	1	no	—
301	#1917	—	89	1	no	—
302	#1916	—	89	1	no	—
303	#1916	—	89	1	no	—
304	#1916	—	89	1	no	—
305	#1851	—	89	1	no	—
306	#1850	—	89	1	no	—
307	#1840	—	89	1	no	—
308	#1831	D₈₉	1	1	yes	characteristic, complemented
309	#1818	—	89	1	no	—
310	#1768	—	89	1	no	—
311	#1753	—	89	1	no	—
312	C₈×C₂²⋊C₄	—	89	1	no	—
313	#1744	—	89	1	no	—
314	#1729	—	89	1	no	—
315	C₈₉	#22593	1	1	yes	characteristic, complemented, Sylow
316	C₂²×M₁₆	—	89	1	no	—
317	C₂³×C₈	—	89	1	no	—
318	C₂×#117	—	89	1	no	—
319	C₂×C₄⋊C₈	—	89	1	no	—
320	C₂×C₄⋊C₈	—	89	1	no	—
321	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
322	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
323	C₂×C₂²⋊C₈	—	89	1	no	—
324	C₂×C₂²⋊C₈	—	89	1	no	—
325	C₂×#97	—	89	1	no	—
326	C₂×C₄×C₈	—	89	1	no	—
327	C₂×C₄×C₈	—	89	1	no	—
328	C₂×C₄×C₈	—	89	1	no	—
329	#388	—	89	1	no	—
330	#388	—	89	1	no	—
331	#388	—	89	1	no	—
332	#388	—	89	1	no	—
333	#387	—	89	1	no	—
334	#387	—	89	1	no	—
335	#387	—	89	1	no	—
336	#387	—	89	1	no	—
337	C₄×C₄⋊C₄	—	89	1	no	—
338	C₄×C₄⋊C₄	—	89	1	no	—
339	C₄×C₂²⋊C₄	—	89	1	no	—
340	C₄×C₂²⋊C₄	—	89	1	no	—
341	#376	—	89	1	no	—
342	C₄³	C₂×D₈₉	1	1	yes	characteristic
343	#336	—	89	1	no	—
344	#336	—	89	1	no	—
345	#336	—	89	1	no	—
346	#336	—	89	1	no	—
347	#336	—	89	1	no	—
348	#336	—	89	1	no	—
349	#336	—	89	1	no	—
350	#336	—	89	1	no	—
351	#336	—	89	1	no	—
352	#336	—	89	1	no	—
353	#336	—	89	1	no	—
354	#336	—	89	1	no	—
355	#336	C₂×D₈₉	1	1	yes	characteristic
356	#336	C₂×D₈₉	1	1	yes	characteristic
357	#336	C₂×D₈₉	1	1	yes	characteristic
358	#336	C₂×D₈₉	1	1	yes	characteristic
359	C₂³×C₄	—	89	1	no	—
360	C₂×M₁₆	—	356	1	no	—
361	C₂×M₁₆	—	178	2	no	—
362	C₂×M₁₆	—	178	2	no	—
363	C₂²×C₈	—	89	1	no	—
364	C₂²×C₈	—	89	1	no	—
365	C₂²×C₈	—	89	1	no	—
366	C₂²×C₈	—	89	1	no	—
367	C₂²×C₈	—	356	1	no	—
368	C₂²×C₈	—	178	2	no	—
369	C₂²×C₈	—	178	2	no	—
370	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
371	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
372	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
373	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
374	#117	—	178	2	no	—
375	#117	—	178	2	no	—
376	C₂×C₄⋊C₄	—	89	1	no	—
377	C₂×C₄⋊C₄	—	89	1	no	—
378	C₂×C₄⋊C₄	—	89	1	no	—
379	C₂×C₄⋊C₄	—	89	1	no	—
380	C₂×C₄⋊C₄	—	89	1	no	—
381	C₂×C₄⋊C₄	—	89	1	no	—
382	C₂×C₂²⋊C₄	—	89	1	no	—
383	C₂×C₂²⋊C₄	—	89	1	no	—
384	C₂×C₂²⋊C₄	—	89	1	no	—
385	C₂×C₂²⋊C₄	—	89	1	no	—
386	C₂×C₂²⋊C₄	—	89	1	no	—
387	C₂×C₂²⋊C₄	—	89	1	no	—
388	C₂×C₄²	—	89	1	no	—
389	C₂×C₄²	—	89	1	no	—
390	C₂×C₄²	—	89	1	no	—
391	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
392	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
393	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
394	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
395	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
396	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
397	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
398	C₄⋊C₈	—	4	1	no	—
399	C₄⋊C₈	—	4	1	no	—
400	C₄⋊C₈	—	178	2	no	—
401	C₄⋊C₈	—	178	2	no	—
402	C₂²⋊C₈	—	178	2	no	—
403	C₂²⋊C₈	—	178	2	no	—
404	#97	—	356	1	no	—
405	C₄×C₈	—	356	1	no	—
406	C₄×C₈	—	178	2	no	—
407	C₄×C₈	—	178	2	no	—
408	#95	—	89	1	no	—
409	#95	—	89	1	no	—
410	#95	—	89	1	no	—
411	#95	—	89	1	no	—
412	#95	—	89	1	no	—
413	#95	—	89	1	no	—
414	#95	—	89	1	no	—
415	#95	—	89	1	no	—
416	#95	—	89	1	no	—
417	#95	—	89	1	no	—
418	#95	—	89	1	no	—
419	#95	—	89	1	no	—
420	C₂⁴	—	89	1	no	—
421	C₂²×C₄	—	89	1	no	—
422	C₂²×C₄	—	89	2	no	—
423	C₂²×C₄	—	89	2	no	—
424	C₂²×C₄	—	89	1	no	—
425	C₂²×C₄	—	89	1	no	—
426	C₂²×C₄	—	89	1	no	—
427	C₂²×C₄	—	89	1	no	—
428	C₂²×C₄	—	89	1	no	—
429	C₂²×C₄	—	89	1	no	—
430	C₂²×C₄	—	178	1	no	—
431	C₂²×C₄	—	178	1	no	—
432	C₂²×C₄	—	178	1	no	—
433	C₂²×C₄	—	178	1	no	—
434	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
435	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
436	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
437	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
439	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
440	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
441	M₁₆	—	356	4	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	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	89	2	no	—
455	C₂×C₈	—	89	2	no	—
456	C₂×C₈	—	356	4	no	—
457	C₂×C₈	—	178	1	no	—
458	C₂×C₈	—	178	1	no	—
459	C₂×C₈	—	178	1	no	—
460	C₂×C₈	—	178	1	no	—
461	C₂×C₈	—	178	1	no	—
462	C₂×C₈	—	178	1	no	—
463	C₂×C₈	—	178	1	no	—
464	C₂×C₈	—	178	1	no	—
465	C₂×C₈	—	178	1	no	—
466	C₂×C₈	—	178	1	no	—
467	C₄⋊C₄	—	356	1	no	—
468	C₄⋊C₄	—	178	2	no	—
469	C₄⋊C₄	—	178	2	no	—
470	C₄⋊C₄	—	178	2	no	—
471	C₄⋊C₄	—	178	2	no	—
472	C₄⋊C₄	—	178	2	no	—
473	C₂²⋊C₄	—	356	1	no	—
474	C₂²⋊C₄	—	178	2	no	—
475	C₂²⋊C₄	—	178	2	no	—
476	C₂²⋊C₄	—	178	2	no	—
477	C₂²⋊C₄	—	178	2	no	—
478	C₂²⋊C₄	—	178	2	no	—
479	C₄²	—	2	2	no	—
480	C₄²	—	2	2	no	—
481	C₄²	—	2	2	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	4	1	no	—
489	C₄²	—	178	1	no	—
490	C₄²	—	178	1	no	—
491	C₄²	—	178	1	no	—
492	C₄²	—	178	1	no	—
493	C₄²	—	178	1	no	—
494	C₄²	—	178	1	no	—
495	C₂³	—	89	2	no	—
496	C₂³	—	178	1	no	—
497	C₂³	—	178	1	no	—
498	C₂³	—	178	1	no	—
499	C₂³	—	178	1	no	—
500	C₂³	—	178	1	no	—
501	C₂³	—	178	1	no	—
502	C₂³	C₂²×C₄×D₈₉	1	1	yes	characteristic
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	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	89	2	no	—
519	C₂×C₄	—	178	1	no	—
520	C₂×C₄	—	178	1	no	—
521	C₂×C₄	—	178	1	no	—
522	C₂×C₄	—	178	1	no	—
523	C₂×C₄	—	178	1	no	—
524	C₂×C₄	—	178	1	no	—
525	C₂×C₄	—	178	1	no	—
526	C₂×C₄	—	178	1	no	—
527	C₂×C₄	—	178	1	no	—
528	C₂×C₄	—	178	1	no	—
529	C₂×C₄	—	178	1	no	—
530	C₂×C₄	—	178	1	no	—
531	C₂×C₄	—	178	1	no	—
532	C₂×C₄	—	178	1	no	—
533	C₂×C₄	—	178	1	no	—
534	C₂×C₄	—	178	1	no	—
535	C₂×C₄	—	178	1	no	—
536	C₂×C₄	—	178	1	no	—
537	C₂×C₄	—	178	1	no	—
538	C₂×C₄	—	178	1	no	—
539	C₂×C₄	—	178	2	no	—
540	C₂×C₄	—	178	2	no	—
541	C₂×C₄	—	178	2	no	—
542	C₂×C₄	—	178	2	no	—
543	C₂×C₄	#15668018	1	2	yes	—
544	C₂×C₄	#15668020	1	2	yes	—
545	C₂×C₄	#15668020	1	2	yes	—
546	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
547	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
548	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
549	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
550	C₂×C₄	#15668057	1	1	yes	characteristic
551	C₂×C₄	#15668060	1	1	yes	characteristic
552	C₈	—	4	1	no	—
553	C₈	—	4	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	4	1	no	—
556	C₈	—	356	1	no	—
557	C₈	—	356	1	no	—
558	C₈	—	178	2	no	—
559	C₈	—	178	2	no	—
560	C₂²	—	356	1	no	—
561	C₂²	—	356	1	no	—
562	C₂²	—	356	1	no	—
563	C₂²	—	356	1	no	—
564	C₂²	—	178	2	no	—
565	C₂²	—	178	2	no	—
566	C₂²	—	178	2	no	—
567	C₂²	#117×D₈₉	1	1	yes	characteristic
568	C₂²	#19152066	1	1	yes	characteristic
569	C₂²	#19152079	1	1	yes	characteristic
570	C₂²	C₂×#15668018	1	1	yes	characteristic
571	C₂²	C₂×#15668020	1	1	yes	characteristic
572	C₂²	C₂×#15668020	1	1	yes	characteristic
573	C₂²	#19152364	1	1	yes	characteristic
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	356	1	no	—
581	C₄	—	356	1	no	—
582	C₄	—	356	1	no	—
583	C₄	—	356	1	no	—
584	C₄	—	356	1	no	—
585	C₄	—	356	1	no	—
586	C₄	—	178	2	no	—
587	C₄	#19152278	1	1	yes	characteristic
588	C₄	#19152278	1	1	yes	characteristic
589	C₄	#19152280	1	1	yes	characteristic
590	C₄	#19152280	1	1	yes	characteristic
591	C₂	—	356	2	no	—
592	C₂	#26023105	1	1	yes	characteristic
593	C₂	#26028891	1	1	yes	characteristic
594	C₂	#26028919	1	1	yes	characteristic
595	C₂	#26029221	1	1	yes	characteristic
596	C₂	#26029241	1	1	yes	characteristic
597	C₂	#26029397	1	1	yes	characteristic
598	C₂	#26029408	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₉
commutator, socle	C₂³×C₈₉	C₂³×C₄
Fitting	C₈₉×#1831	C₂
prime radical	C₂³×D₈₉	C₂²×C₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1831	D₈₉
hypocenter	C₈₉	#22593
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1831

Complements

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

N	H ≅ G/N	type
2. #26020813	C₂	semidirect
3. #26020807	C₂	semidirect
4. #26020807	C₂	semidirect
5. #26020806	C₂	semidirect
8. #26020396	C₂	semidirect
10. #26020108	C₂	semidirect
13. #26019998	C₂	semidirect
15. C₈₉×#1831	C₂	semidirect
308. #1831	D₈₉	semidirect
315. C₈₉	#22593	semidirect

Maximal subgroups

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

subgroup	index
#26022749	2
#26020813	2
#26020807	2
#26020806	2
#26020433	2
#26020428	2
#26020396	2
#26020322	2
#26020108	2
#26020032	2
#26020022	2
#26019998	2
#26019947	2
C₈₉×#1831	2
#22593	89