Subgroups — C₄₁×#25381 #23801582

Order 10496.

1012 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#497	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#464	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#463	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₁×#463	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#2547	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#2015	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#2012	C₂	1	1	yes	maximal, characteristic
11	C₄₁×#1981	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#1940	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#1878	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#1877	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#1762	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
29	C₄₁×#497	—	2	4	no	—
30	C₄₁×#464	—	2	4	no	—
31	C₄₁×#463	—	2	4	no	—
32	C₄₁×#463	—	2	4	no	—
33	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
36	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
37	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
38	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
40	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
41	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
42	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
43	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
44	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
45	C₄₁×#397	—	2	1	no	—
46	C₄₁×#397	—	2	1	no	—
47	C₄₁×#391	C₂²	1	1	yes	characteristic
48	C₄₁×#391	C₂²	1	1	yes	characteristic
49	C₄₁×#391	C₂²	1	1	yes	characteristic
50	C₄₁×#390	C₂²	1	1	yes	characteristic
51	C₄₁×#388	—	2	1	no	—
52	C₄₁×#388	—	2	1	no	—
53	C₄₁×#385	—	2	1	no	—
54	C₄₁×#380	—	2	1	no	—
55	C₄₁×#380	—	2	1	no	—
56	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
57	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
58	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
59	C₄₁×#340	C₂²	1	1	yes	characteristic
60	C₄₁×#340	C₂²	1	1	yes	characteristic
61	C₄₁×#336	C₂²	1	1	yes	characteristic
62	C₄₁×#336	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
65	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₄₁	—	2	1	no	—
69	C₂³×C₄×C₄₁	—	2	1	no	—
70	C₂×Q₁₆×C₄₁	—	2	2	no	—
71	C₂×Q₁₆×C₄₁	—	2	2	no	—
72	C₂×Q₁₆×C₄₁	—	2	2	no	—
73	C₂×Q₁₆×C₄₁	—	2	2	no	—
74	C₂×Q₁₆×C₄₁	—	4	1	no	—
75	C₂×Q₁₆×C₄₁	—	4	1	no	—
76	C₂×SD₁₆×C₄₁	—	2	2	no	—
77	C₂×SD₁₆×C₄₁	—	2	2	no	—
78	C₂×SD₁₆×C₄₁	—	2	2	no	—
79	C₂×SD₁₆×C₄₁	—	2	2	no	—
80	C₂×SD₁₆×C₄₁	—	2	2	no	—
81	C₂×SD₁₆×C₄₁	—	2	2	no	—
82	C₂×SD₁₆×C₄₁	—	4	1	no	—
83	C₂×SD₁₆×C₄₁	—	4	1	no	—
84	C₂×SD₁₆×C₄₁	—	4	1	no	—
85	C₂×D₈×C₄₁	—	2	2	no	—
86	C₂×D₈×C₄₁	—	2	2	no	—
87	C₂×D₈×C₄₁	—	4	1	no	—
88	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
92	C₄⋊Q₈×C₄₁	—	2	2	no	—
93	C₄⋊Q₈×C₄₁	—	2	2	no	—
94	#124×C₄₁	—	2	2	no	—
95	#124×C₄₁	—	2	2	no	—
96	#124×C₄₁	—	2	2	no	—
97	#124×C₄₁	—	4	1	no	—
98	#124×C₄₁	—	4	1	no	—
99	#124×C₄₁	D₄	1	4	yes	—
100	C₄×Q₈×C₄₁	—	2	2	no	—
101	C₄×Q₈×C₄₁	—	4	1	no	—
102	C₄×D₄×C₄₁	—	2	2	no	—
103	C₄×D₄×C₄₁	—	2	2	no	—
104	C₄×D₄×C₄₁	—	2	2	no	—
105	C₄×D₄×C₄₁	—	4	1	no	—
106	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
107	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
108	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
109	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
124	C₂×C₄²×C₄₁	—	2	1	no	—
125	C₂×C₄²×C₄₁	—	2	1	no	—
126	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
129	C₄⋊C₈×C₄₁	—	2	2	no	—
130	C₄⋊C₈×C₄₁	—	2	2	no	—
131	C₄⋊C₈×C₄₁	—	2	2	no	—
132	#103×C₄₁	—	2	2	no	—
133	#103×C₄₁	—	2	2	no	—
134	#103×C₄₁	—	2	2	no	—
135	#103×C₄₁	—	4	1	no	—
136	#103×C₄₁	—	4	1	no	—
137	#102×C₄₁	—	2	2	no	—
138	#102×C₄₁	—	2	2	no	—
139	#102×C₄₁	D₄	1	4	yes	—
140	#97×C₄₁	—	2	2	no	—
141	#95×C₄₁	—	2	1	no	—
142	#95×C₄₁	—	2	1	no	—
143	#95×C₄₁	—	2	1	no	—
144	#95×C₄₁	—	2	1	no	—
145	#95×C₄₁	—	2	1	no	—
146	#95×C₄₁	—	2	1	no	—
147	#95×C₄₁	—	2	1	no	—
148	#95×C₄₁	D₄	1	1	yes	characteristic
149	#95×C₄₁	D₄	1	1	yes	characteristic
150	C₂⁴×C₄₁	—	2	1	no	—
151	C₂⁴×C₄₁	—	2	1	no	—
152	C₂×Q₈×C₄₁	—	2	1	no	—
153	C₂×Q₈×C₄₁	—	2	1	no	—
154	C₂×Q₈×C₄₁	—	2	1	no	—
155	C₂×Q₈×C₄₁	—	2	1	no	—
156	C₂×Q₈×C₄₁	—	2	1	no	—
157	C₂×Q₈×C₄₁	—	2	1	no	—
158	C₂×Q₈×C₄₁	—	2	1	no	—
159	C₂×Q₈×C₄₁	—	2	1	no	—
160	C₂×Q₈×C₄₁	—	2	1	no	—
161	C₂×Q₈×C₄₁	—	2	1	no	—
162	C₂×Q₈×C₄₁	—	2	1	no	—
163	C₂×Q₈×C₄₁	—	2	1	no	—
164	C₂×Q₈×C₄₁	—	2	1	no	—
165	C₂×Q₈×C₄₁	—	2	1	no	—
166	C₂×Q₈×C₄₁	—	2	1	no	—
167	C₂×Q₈×C₄₁	—	2	1	no	—
168	C₂×Q₈×C₄₁	—	2	1	no	—
169	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
170	C₂×D₄×C₄₁	—	2	1	no	—
171	C₂×D₄×C₄₁	—	2	1	no	—
172	C₂×D₄×C₄₁	—	2	1	no	—
173	C₂×D₄×C₄₁	—	2	1	no	—
174	C₂×D₄×C₄₁	—	2	1	no	—
175	C₂×D₄×C₄₁	—	2	1	no	—
176	C₂×D₄×C₄₁	—	2	1	no	—
177	C₂×D₄×C₄₁	—	2	1	no	—
178	C₂×D₄×C₄₁	—	2	1	no	—
179	C₂×D₄×C₄₁	—	2	1	no	—
180	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
181	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
182	C₂²×C₄×C₄₁	—	2	1	no	—
183	C₂²×C₄×C₄₁	—	2	1	no	—
184	C₂²×C₄×C₄₁	—	2	1	no	—
185	C₂²×C₄×C₄₁	—	2	1	no	—
186	C₂²×C₄×C₄₁	—	2	1	no	—
187	C₂²×C₄×C₄₁	—	2	1	no	—
188	C₂²×C₄×C₄₁	—	4	2	no	—
189	C₂²×C₄×C₄₁	—	4	2	no	—
190	C₂²×C₄×C₄₁	—	4	2	no	—
191	C₂²×C₄×C₄₁	—	4	2	no	—
192	C₂²×C₄×C₄₁	—	4	2	no	—
193	C₂²×C₄×C₄₁	—	8	1	no	—
194	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
201	Q₁₆×C₄₁	—	4	4	no	—
202	Q₁₆×C₄₁	—	4	4	no	—
203	SD₁₆×C₄₁	—	4	4	no	—
204	SD₁₆×C₄₁	—	4	4	no	—
205	SD₁₆×C₄₁	—	4	4	no	—
206	D₈×C₄₁	—	4	4	no	—
207	C₂×C₈×C₄₁	—	2	1	no	—
208	C₂×C₈×C₄₁	—	2	1	no	—
209	C₂×C₈×C₄₁	—	2	1	no	—
210	C₂×C₈×C₄₁	—	2	1	no	—
211	C₂×C₈×C₄₁	—	2	1	no	—
212	C₂×C₈×C₄₁	—	2	1	no	—
213	C₂×C₈×C₄₁	—	2	1	no	—
214	C₂×C₈×C₄₁	—	2	1	no	—
215	C₂×C₈×C₄₁	—	2	1	no	—
216	C₂×C₈×C₄₁	—	2	1	no	—
217	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
218	C₂×C₈×C₄₁	#41	1	2	yes	—
219	C₄⋊C₄×C₄₁	—	2	1	no	—
220	C₄⋊C₄×C₄₁	—	2	1	no	—
221	C₄⋊C₄×C₄₁	—	2	1	no	—
222	C₄⋊C₄×C₄₁	—	2	1	no	—
223	C₄⋊C₄×C₄₁	—	2	1	no	—
224	C₄⋊C₄×C₄₁	—	4	1	no	—
225	C₄⋊C₄×C₄₁	—	4	1	no	—
226	C₄⋊C₄×C₄₁	—	4	2	no	—
227	C₄⋊C₄×C₄₁	—	4	2	no	—
228	C₄⋊C₄×C₄₁	—	4	2	no	—
229	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
230	C₂²⋊C₄×C₄₁	—	2	4	no	—
231	C₂²⋊C₄×C₄₁	—	2	4	no	—
232	C₂²⋊C₄×C₄₁	—	4	2	no	—
233	C₂²⋊C₄×C₄₁	—	4	2	no	—
234	C₂²⋊C₄×C₄₁	—	4	2	no	—
235	C₂²⋊C₄×C₄₁	—	4	2	no	—
236	C₂²⋊C₄×C₄₁	—	4	2	no	—
237	C₂²⋊C₄×C₄₁	—	4	2	no	—
238	C₂²⋊C₄×C₄₁	—	4	2	no	—
239	C₂²⋊C₄×C₄₁	—	8	1	no	—
240	C₄²×C₄₁	—	2	1	no	—
241	C₄²×C₄₁	—	2	1	no	—
242	C₄²×C₄₁	—	2	1	no	—
243	C₄²×C₄₁	—	2	1	no	—
244	C₄²×C₄₁	—	4	2	no	—
245	C₄²×C₄₁	—	8	1	no	—
246	C₄²×C₄₁	C₂×D₄	1	2	yes	—
247	C₄²×C₄₁	#41	1	2	yes	—
248	C₂³×C₄₁	—	2	2	no	—
249	C₂³×C₄₁	—	2	2	no	—
250	C₂³×C₄₁	—	4	1	no	—
251	C₂³×C₄₁	—	4	1	no	—
252	C₂³×C₄₁	—	4	1	no	—
253	C₂³×C₄₁	—	4	1	no	—
254	C₂³×C₄₁	—	4	1	no	—
255	C₂³×C₄₁	—	4	1	no	—
256	C₂³×C₄₁	—	4	1	no	—
257	C₂³×C₄₁	—	4	1	no	—
258	C₂³×C₄₁	—	4	1	no	—
259	C₂³×C₄₁	—	4	1	no	—
260	C₂³×C₄₁	—	4	1	no	—
261	C₂³×C₄₁	—	4	1	no	—
262	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
263	Q₈×C₄₁	—	2	2	no	—
264	Q₈×C₄₁	—	2	2	no	—
265	Q₈×C₄₁	—	4	1	no	—
266	Q₈×C₄₁	—	4	1	no	—
267	Q₈×C₄₁	—	4	1	no	—
268	Q₈×C₄₁	—	4	1	no	—
269	Q₈×C₄₁	—	4	1	no	—
270	Q₈×C₄₁	—	4	1	no	—
271	Q₈×C₄₁	—	4	1	no	—
272	Q₈×C₄₁	—	4	1	no	—
273	Q₈×C₄₁	—	4	1	no	—
274	Q₈×C₄₁	—	4	1	no	—
275	D₄×C₄₁	—	2	2	no	—
276	D₄×C₄₁	—	2	2	no	—
277	D₄×C₄₁	—	2	2	no	—
278	D₄×C₄₁	—	2	2	no	—
279	D₄×C₄₁	—	4	1	no	—
280	D₄×C₄₁	—	4	1	no	—
281	D₄×C₄₁	—	4	1	no	—
282	D₄×C₄₁	—	4	1	no	—
283	C₂×C₄×C₄₁	—	2	1	no	—
284	C₂×C₄×C₄₁	—	2	1	no	—
285	C₂×C₄×C₄₁	—	2	1	no	—
286	C₂×C₄×C₄₁	—	2	1	no	—
287	C₂×C₄×C₄₁	—	2	2	no	—
288	C₂×C₄×C₄₁	—	2	1	no	—
289	C₂×C₄×C₄₁	—	2	1	no	—
290	C₂×C₄×C₄₁	—	2	1	no	—
291	C₂×C₄×C₄₁	—	2	1	no	—
292	C₂×C₄×C₄₁	—	2	2	no	—
293	C₂×C₄×C₄₁	—	2	1	no	—
294	C₂×C₄×C₄₁	—	2	1	no	—
295	C₂×C₄×C₄₁	—	2	1	no	—
296	C₂×C₄×C₄₁	—	2	1	no	—
297	C₂×C₄×C₄₁	—	2	1	no	—
298	C₂×C₄×C₄₁	—	2	1	no	—
299	C₂×C₄×C₄₁	—	2	1	no	—
300	C₂×C₄×C₄₁	—	2	1	no	—
301	C₂×C₄×C₄₁	—	4	1	no	—
302	C₂×C₄×C₄₁	—	4	1	no	—
303	C₂×C₄×C₄₁	—	4	1	no	—
304	C₂×C₄×C₄₁	—	4	1	no	—
305	C₂×C₄×C₄₁	—	4	1	no	—
306	C₂×C₄×C₄₁	—	4	1	no	—
307	C₂×C₄×C₄₁	—	4	1	no	—
308	C₂×C₄×C₄₁	—	4	1	no	—
309	C₂×C₄×C₄₁	—	4	1	no	—
310	C₂×C₄×C₄₁	—	4	1	no	—
311	C₂×C₄×C₄₁	—	4	1	no	—
312	C₂×C₄×C₄₁	—	4	1	no	—
313	C₂×C₄×C₄₁	—	4	1	no	—
314	C₂×C₄×C₄₁	—	4	1	no	—
315	C₂×C₄×C₄₁	—	4	1	no	—
316	C₂×C₄×C₄₁	—	4	1	no	—
317	C₂×C₄×C₄₁	—	8	4	no	—
318	C₂×C₄×C₄₁	—	8	4	no	—
319	C₂×C₄×C₄₁	#121	1	2	yes	—
320	C₂×C₄×C₄₁	#121	1	2	yes	—
321	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
324	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
325	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
326	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
327	C₈×C₄₁	—	2	2	no	—
328	C₈×C₄₁	—	2	2	no	—
329	C₈×C₄₁	—	4	1	no	—
330	C₈×C₄₁	—	4	1	no	—
331	#25381	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
332	C₂²×C₄₁	—	4	2	no	—
333	C₂²×C₄₁	—	4	2	no	—
334	C₂²×C₄₁	—	4	2	no	—
335	C₂²×C₄₁	—	4	2	no	—
336	C₂²×C₄₁	—	4	2	no	—
337	C₂²×C₄₁	—	4	2	no	—
338	C₂²×C₄₁	—	8	1	no	—
339	C₂²×C₄₁	—	8	1	no	—
340	C₂²×C₄₁	—	8	1	no	—
341	C₂²×C₄₁	—	8	1	no	—
342	C₂²×C₄₁	—	8	1	no	—
343	C₂²×C₄₁	—	8	1	no	—
344	C₂²×C₄₁	—	8	1	no	—
345	C₂²×C₄₁	—	8	1	no	—
346	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
347	C₂²×C₄₁	D₄²	1	1	yes	characteristic
348	C₂²×C₄₁	#550	1	1	yes	characteristic
349	C₂²×C₄₁	#575	1	1	yes	characteristic
350	C₂²×C₄₁	#575	1	1	yes	characteristic
351	C₂²×C₄₁	#577	1	1	yes	characteristic
352	C₂²×C₄₁	#578	1	1	yes	characteristic
353	C₄×C₄₁	—	2	2	no	—
354	C₄×C₄₁	—	2	2	no	—
355	C₄×C₄₁	—	4	2	no	—
356	C₄×C₄₁	—	4	1	no	—
357	C₄×C₄₁	—	4	1	no	—
358	C₄×C₄₁	—	4	2	no	—
359	C₄×C₄₁	—	4	1	no	—
360	C₄×C₄₁	—	4	1	no	—
361	C₄×C₄₁	—	8	1	no	—
362	C₄×C₄₁	—	8	1	no	—
363	C₄×C₄₁	—	8	1	no	—
364	C₄×C₄₁	—	8	1	no	—
365	C₄×C₄₁	#532	1	1	yes	characteristic
366	C₄×C₄₁	#540	1	1	yes	characteristic
367	C₄×C₄₁	D₄²	1	1	yes	characteristic
368	C₄×C₄₁	#546	1	1	yes	characteristic
369	C₂×#497	C₂×C₄₁	1	1	yes	characteristic, complemented
370	C₂×#464	C₂×C₄₁	1	1	yes	characteristic, complemented
371	C₂×#463	C₂×C₄₁	1	1	yes	characteristic
372	C₂×#463	C₂×C₄₁	1	1	yes	characteristic
373	#2547	C₂×C₄₁	1	1	yes	characteristic, complemented
374	#2367	C₂×C₄₁	1	1	yes	characteristic, complemented
375	#2056	C₂×C₄₁	1	1	yes	characteristic, complemented
376	#2055	C₂×C₄₁	1	1	yes	characteristic, complemented
377	#2015	C₂×C₄₁	1	1	yes	characteristic, complemented
378	#2012	C₂×C₄₁	1	1	yes	characteristic
379	#1981	C₂×C₄₁	1	1	yes	characteristic, complemented
380	#1940	C₂×C₄₁	1	1	yes	characteristic, complemented
381	#1878	C₂×C₄₁	1	1	yes	characteristic, complemented
382	#1877	C₂×C₄₁	1	1	yes	characteristic, complemented
383	#1762	C₂×C₄₁	1	1	yes	characteristic, complemented
384	C₂×C₄₁	—	8	2	no	—
385	C₂×C₄₁	—	8	2	no	—
386	C₂×C₄₁	#2428	1	1	yes	characteristic
387	C₂×C₄₁	#3040	1	1	yes	characteristic
388	C₂×C₄₁	#3046	1	1	yes	characteristic
389	C₂×C₄₁	#3267	1	1	yes	characteristic
390	C₂×C₄₁	#3269	1	1	yes	characteristic
391	C₂×C₄₁	#3401	1	1	yes	characteristic
392	C₂×C₄₁	#3402	1	1	yes	characteristic
393	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
394	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
395	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
396	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
397	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
398	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
399	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
400	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
401	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
402	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
403	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
404	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
405	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
406	#497	—	2	4	no	—
407	#464	—	2	4	no	—
408	#463	—	2	4	no	—
409	#463	—	2	4	no	—
410	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
411	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
412	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
413	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
414	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
415	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
416	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
417	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
418	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
419	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
420	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
421	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
422	#397	—	2	1	no	—
423	#397	—	2	1	no	—
424	#391	C₂²×C₄₁	1	1	yes	characteristic
425	#391	C₂²×C₄₁	1	1	yes	characteristic
426	#391	C₂²×C₄₁	1	1	yes	characteristic
427	#390	C₂²×C₄₁	1	1	yes	characteristic
428	#388	—	2	1	no	—
429	#388	—	2	1	no	—
430	#385	—	2	1	no	—
431	#380	—	2	1	no	—
432	#380	—	2	1	no	—
433	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
434	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
435	C₄×C₂²⋊C₄	—	2	1	no	—
436	#340	C₂²×C₄₁	1	1	yes	characteristic
437	#340	C₂²×C₄₁	1	1	yes	characteristic
438	#336	C₂²×C₄₁	1	1	yes	characteristic
439	#336	C₂²×C₄₁	1	1	yes	characteristic
440	C₄₁	#25381	1	1	yes	characteristic, direct product factor, Sylow
441	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
442	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
443	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
444	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
445	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
446	C₂³×C₄	—	2	1	no	—
447	C₂³×C₄	—	2	1	no	—
448	C₂×Q₁₆	—	2	2	no	—
449	C₂×Q₁₆	—	2	2	no	—
450	C₂×Q₁₆	—	2	2	no	—
451	C₂×Q₁₆	—	2	2	no	—
452	C₂×Q₁₆	—	4	1	no	—
453	C₂×Q₁₆	—	4	1	no	—
454	C₂×SD₁₆	—	2	2	no	—
455	C₂×SD₁₆	—	2	2	no	—
456	C₂×SD₁₆	—	2	2	no	—
457	C₂×SD₁₆	—	2	2	no	—
458	C₂×SD₁₆	—	2	2	no	—
459	C₂×SD₁₆	—	2	2	no	—
460	C₂×SD₁₆	—	4	1	no	—
461	C₂×SD₁₆	—	4	1	no	—
462	C₂×SD₁₆	—	4	1	no	—
463	C₂×D₈	—	2	2	no	—
464	C₂×D₈	—	2	2	no	—
465	C₂×D₈	—	4	1	no	—
466	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
467	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
468	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
469	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
470	C₄⋊Q₈	—	2	2	no	—
471	C₄⋊Q₈	—	2	2	no	—
472	#124	—	2	2	no	—
473	#124	—	2	2	no	—
474	#124	—	2	2	no	—
475	#124	—	4	1	no	—
476	#124	—	4	1	no	—
477	#124	D₄×C₄₁	1	4	yes	—
478	C₄×Q₈	—	2	2	no	—
479	C₄×Q₈	—	4	1	no	—
480	C₄×D₄	—	2	2	no	—
481	C₄×D₄	—	2	2	no	—
482	C₄×D₄	—	2	2	no	—
483	C₄×D₄	—	4	1	no	—
484	C₂×C₄⋊C₄	—	2	1	no	—
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄⋊C₄	—	2	1	no	—
487	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
488	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	—	2	1	no	—
493	C₂×C₂²⋊C₄	—	2	1	no	—
494	C₂×C₂²⋊C₄	—	2	1	no	—
495	C₂×C₂²⋊C₄	—	2	1	no	—
496	C₂×C₂²⋊C₄	—	2	1	no	—
497	C₂×C₂²⋊C₄	—	2	1	no	—
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	—	2	1	no	—
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₄²	—	2	1	no	—
503	C₂×C₄²	—	2	1	no	—
504	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
506	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
507	C₄⋊C₈	—	2	2	no	—
508	C₄⋊C₈	—	2	2	no	—
509	C₄⋊C₈	—	2	2	no	—
510	#103	—	2	2	no	—
511	#103	—	2	2	no	—
512	#103	—	2	2	no	—
513	#103	—	4	1	no	—
514	#103	—	4	1	no	—
515	#102	—	2	2	no	—
516	#102	—	2	2	no	—
517	#102	D₄×C₄₁	1	4	yes	—
518	#97	—	2	2	no	—
519	#95	—	2	1	no	—
520	#95	—	2	1	no	—
521	#95	—	2	1	no	—
522	#95	—	2	1	no	—
523	#95	—	2	1	no	—
524	#95	—	2	1	no	—
525	#95	—	2	1	no	—
526	#95	D₄×C₄₁	1	1	yes	characteristic
527	#95	D₄×C₄₁	1	1	yes	characteristic
528	C₂⁴	—	2	1	no	—
529	C₂⁴	—	2	1	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	1	no	—
533	C₂×Q₈	—	2	1	no	—
534	C₂×Q₈	—	2	1	no	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	—	2	1	no	—
542	C₂×Q₈	—	2	1	no	—
543	C₂×Q₈	—	2	1	no	—
544	C₂×Q₈	—	2	1	no	—
545	C₂×Q₈	—	2	1	no	—
546	C₂×Q₈	—	2	1	no	—
547	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
559	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	4	2	no	—
567	C₂²×C₄	—	4	2	no	—
568	C₂²×C₄	—	4	2	no	—
569	C₂²×C₄	—	4	2	no	—
570	C₂²×C₄	—	4	2	no	—
571	C₂²×C₄	—	8	1	no	—
572	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
573	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
574	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
575	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
576	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
577	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
578	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
579	Q₁₆	—	4	4	no	—
580	Q₁₆	—	4	4	no	—
581	SD₁₆	—	4	4	no	—
582	SD₁₆	—	4	4	no	—
583	SD₁₆	—	4	4	no	—
584	D₈	—	4	4	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
596	C₂×C₈	#41×C₄₁	1	2	yes	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	4	1	no	—
603	C₄⋊C₄	—	4	1	no	—
604	C₄⋊C₄	—	4	2	no	—
605	C₄⋊C₄	—	4	2	no	—
606	C₄⋊C₄	—	4	2	no	—
607	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	4	2	no	—
611	C₂²⋊C₄	—	4	2	no	—
612	C₂²⋊C₄	—	4	2	no	—
613	C₂²⋊C₄	—	4	2	no	—
614	C₂²⋊C₄	—	4	2	no	—
615	C₂²⋊C₄	—	4	2	no	—
616	C₂²⋊C₄	—	4	2	no	—
617	C₂²⋊C₄	—	8	1	no	—
618	C₄²	—	2	1	no	—
619	C₄²	—	2	1	no	—
620	C₄²	—	2	1	no	—
621	C₄²	—	2	1	no	—
622	C₄²	—	4	2	no	—
623	C₄²	—	8	1	no	—
624	C₄²	C₂×D₄×C₄₁	1	2	yes	—
625	C₄²	#41×C₄₁	1	2	yes	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	4	1	no	—
629	C₂³	—	4	1	no	—
630	C₂³	—	4	1	no	—
631	C₂³	—	4	1	no	—
632	C₂³	—	4	1	no	—
633	C₂³	—	4	1	no	—
634	C₂³	—	4	1	no	—
635	C₂³	—	4	1	no	—
636	C₂³	—	4	1	no	—
637	C₂³	—	4	1	no	—
638	C₂³	—	4	1	no	—
639	C₂³	—	4	1	no	—
640	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
641	Q₈	—	2	2	no	—
642	Q₈	—	2	2	no	—
643	Q₈	—	4	1	no	—
644	Q₈	—	4	1	no	—
645	Q₈	—	4	1	no	—
646	Q₈	—	4	1	no	—
647	Q₈	—	4	1	no	—
648	Q₈	—	4	1	no	—
649	Q₈	—	4	1	no	—
650	Q₈	—	4	1	no	—
651	Q₈	—	4	1	no	—
652	Q₈	—	4	1	no	—
653	D₄	—	2	2	no	—
654	D₄	—	2	2	no	—
655	D₄	—	2	2	no	—
656	D₄	—	2	2	no	—
657	D₄	—	4	1	no	—
658	D₄	—	4	1	no	—
659	D₄	—	4	1	no	—
660	D₄	—	4	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	8	4	no	—
696	C₂×C₄	—	8	4	no	—
697	C₂×C₄	#121×C₄₁	1	2	yes	—
698	C₂×C₄	#121×C₄₁	1	2	yes	—
699	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
700	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
701	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
702	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
703	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
704	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
705	C₈	—	2	2	no	—
706	C₈	—	2	2	no	—
707	C₈	—	4	1	no	—
708	C₈	—	4	1	no	—
709	C₂²	—	4	2	no	—
710	C₂²	—	4	2	no	—
711	C₂²	—	4	2	no	—
712	C₂²	—	4	2	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	8	1	no	—
716	C₂²	—	8	1	no	—
717	C₂²	—	8	1	no	—
718	C₂²	—	8	1	no	—
719	C₂²	—	8	1	no	—
720	C₂²	—	8	1	no	—
721	C₂²	—	8	1	no	—
722	C₂²	—	8	1	no	—
723	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
724	C₂²	D₄²×C₄₁	1	1	yes	characteristic
725	C₂²	C₄₁×#550	1	1	yes	characteristic
726	C₂²	C₄₁×#575	1	1	yes	characteristic
727	C₂²	C₄₁×#575	1	1	yes	characteristic
728	C₂²	C₄₁×#577	1	1	yes	characteristic
729	C₂²	C₄₁×#578	1	1	yes	characteristic
730	C₄	—	2	2	no	—
731	C₄	—	2	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	1	no	—
734	C₄	—	4	1	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	1	no	—
737	C₄	—	4	1	no	—
738	C₄	—	8	1	no	—
739	C₄	—	8	1	no	—
740	C₄	—	8	1	no	—
741	C₄	—	8	1	no	—
742	C₄	C₄₁×#532	1	1	yes	characteristic
743	C₄	C₄₁×#540	1	1	yes	characteristic
744	C₄	D₄²×C₄₁	1	1	yes	characteristic
745	C₄	C₄₁×#546	1	1	yes	characteristic
746	C₂	—	8	2	no	—
747	C₂	—	8	2	no	—
748	C₂	C₄₁×#2428	1	1	yes	characteristic
749	C₂	C₄₁×#3040	1	1	yes	characteristic
750	C₂	C₄₁×#3046	1	1	yes	characteristic
751	C₂	C₄₁×#3267	1	1	yes	characteristic
752	C₂	C₄₁×#3269	1	1	yes	characteristic
753	C₂	C₄₁×#3401	1	1	yes	characteristic
754	C₂	C₄₁×#3402	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×D₈×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄×C₄⋊C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#497	C₂	semidirect
2. C₂×C₄₁×#464	C₂	semidirect
5. C₄₁×#2547	C₂	semidirect
6. C₄₁×#2367	C₂	semidirect
7. C₄₁×#2056	C₂	semidirect
8. C₄₁×#2055	C₂	semidirect
9. C₄₁×#2015	C₂	semidirect
11. C₄₁×#1981	C₂	semidirect
12. C₄₁×#1940	C₂	semidirect
13. C₄₁×#1878	C₂	semidirect
14. C₄₁×#1877	C₂	semidirect
15. C₄₁×#1762	C₂	semidirect
331. #25381	C₄₁	direct (N × H)
369. C₂×#497	C₂×C₄₁	semidirect
370. C₂×#464	C₂×C₄₁	semidirect
373. #2547	C₂×C₄₁	semidirect
374. #2367	C₂×C₄₁	semidirect
375. #2056	C₂×C₄₁	semidirect
376. #2055	C₂×C₄₁	semidirect
377. #2015	C₂×C₄₁	semidirect
379. #1981	C₂×C₄₁	semidirect
380. #1940	C₂×C₄₁	semidirect
381. #1878	C₂×C₄₁	semidirect
382. #1877	C₂×C₄₁	semidirect
383. #1762	C₂×C₄₁	semidirect
440. C₄₁	#25381	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#497	2
C₂×C₄₁×#464	2
C₂×C₄₁×#463	2
C₄₁×#2547	2
C₄₁×#2367	2
C₄₁×#2056	2
C₄₁×#2055	2
C₄₁×#2015	2
C₄₁×#2012	2
C₄₁×#1981	2
C₄₁×#1940	2
C₄₁×#1878	2
C₄₁×#1877	2
C₄₁×#1762	2
#25381	41

Subgroups — C41×#25381 #23801582

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25381 #23801582