Subgroups — C₄₁×#25382 #23801583

Order 10496.

980 conjugacy classes of subgroups.

The subgroup lattice has 728 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
2	C₂×C₄₁×#464	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#462	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#461	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#2546	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2367	C₂	1	1	yes	maximal, characteristic
7	C₄₁×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#2055	C₂	1	1	yes	maximal, characteristic
9	C₄₁×#2016	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#2013	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
15	C₄₁×#1763	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×Q₁₆×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×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×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×Q₈×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×#462	—	2	4	no	—
32	C₄₁×#461	—	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×#103×C₄₁	C₂²	1	1	yes	characteristic
42	C₂×#103×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×#398	—	2	1	no	—
46	C₄₁×#398	—	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×#389	—	2	1	no	—
52	C₄₁×#389	—	2	1	no	—
53	C₄₁×#388	—	2	1	no	—
54	C₄₁×#388	—	2	1	no	—
55	C₄₁×#385	—	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×Q₈×C₄₁	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₄₁	—	2	1	no	—
69	C₂×Q₁₆×C₄₁	—	2	2	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	—	2	2	no	—
75	C₂×Q₁₆×C₄₁	—	4	1	no	—
76	C₂×Q₁₆×C₄₁	—	4	1	no	—
77	C₂×Q₁₆×C₄₁	—	4	1	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	—	2	2	no	—
83	C₂×SD₁₆×C₄₁	—	2	2	no	—
84	C₂×SD₁₆×C₄₁	—	4	1	no	—
85	C₂×SD₁₆×C₄₁	—	4	1	no	—
86	C₂×SD₁₆×C₄₁	—	4	1	no	—
87	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
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	C₄⋊Q₈×C₄₁	—	2	2	no	—
92	C₄⋊Q₈×C₄₁	—	2	2	no	—
93	C₄⋊Q₈×C₄₁	—	2	2	no	—
94	C₄⋊Q₈×C₄₁	—	2	2	no	—
95	C₄⋊Q₈×C₄₁	—	4	1	no	—
96	C₄⋊Q₈×C₄₁	—	4	1	no	—
97	#124×C₄₁	—	2	2	no	—
98	#124×C₄₁	D₄	1	4	yes	—
99	C₄×Q₈×C₄₁	—	2	2	no	—
100	C₄×Q₈×C₄₁	—	2	2	no	—
101	C₄×Q₈×C₄₁	—	2	2	no	—
102	C₄×Q₈×C₄₁	—	4	1	no	—
103	C₄×D₄×C₄₁	—	2	2	no	—
104	C₄×D₄×C₄₁	—	4	1	no	—
105	C₂×C₄⋊C₄×C₄₁	—	2	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	—	2	1	no	—
110	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
111	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
112	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
113	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
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×C₄²×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	—	2	2	no	—
136	#103×C₄₁	—	4	1	no	—
137	#103×C₄₁	—	4	1	no	—
138	#103×C₄₁	D₄	1	4	yes	—
139	#102×C₄₁	—	2	2	no	—
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	C₂×Q₈×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	—	2	1	no	—
170	C₂×Q₈×C₄₁	—	2	1	no	—
171	C₂×Q₈×C₄₁	—	2	1	no	—
172	C₂×Q₈×C₄₁	—	2	1	no	—
173	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
174	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
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	C₂²×C₄×C₄₁	—	2	1	no	—
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	—	8	1	no	—
191	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
198	Q₁₆×C₄₁	—	4	4	no	—
199	Q₁₆×C₄₁	—	4	4	no	—
200	Q₁₆×C₄₁	—	4	4	no	—
201	SD₁₆×C₄₁	—	4	4	no	—
202	SD₁₆×C₄₁	—	4	4	no	—
203	SD₁₆×C₄₁	—	4	4	no	—
204	C₂×C₈×C₄₁	—	2	1	no	—
205	C₂×C₈×C₄₁	—	2	1	no	—
206	C₂×C₈×C₄₁	—	2	1	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	C₂×D₄	1	2	yes	—
215	C₂×C₈×C₄₁	#41	1	2	yes	—
216	C₄⋊C₄×C₄₁	—	2	2	no	—
217	C₄⋊C₄×C₄₁	—	2	2	no	—
218	C₄⋊C₄×C₄₁	—	2	1	no	—
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	—	4	2	no	—
224	C₄⋊C₄×C₄₁	—	4	2	no	—
225	C₄⋊C₄×C₄₁	—	4	2	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	—	4	2	no	—
230	C₄⋊C₄×C₄₁	—	4	2	no	—
231	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
232	C₂²⋊C₄×C₄₁	—	2	4	no	—
233	C₂²⋊C₄×C₄₁	—	2	4	no	—
234	C₂²⋊C₄×C₄₁	—	4	2	no	—
235	C₂²⋊C₄×C₄₁	—	4	2	no	—
236	C₂²⋊C₄×C₄₁	—	8	1	no	—
237	C₄²×C₄₁	—	2	1	no	—
238	C₄²×C₄₁	—	2	1	no	—
239	C₄²×C₄₁	—	2	1	no	—
240	C₄²×C₄₁	—	2	1	no	—
241	C₄²×C₄₁	—	4	2	no	—
242	C₄²×C₄₁	—	4	2	no	—
243	C₄²×C₄₁	—	8	1	no	—
244	C₄²×C₄₁	C₂×D₄	1	2	yes	—
245	C₄²×C₄₁	#41	1	2	yes	—
246	C₂³×C₄₁	—	2	2	no	—
247	C₂³×C₄₁	—	4	1	no	—
248	C₂³×C₄₁	—	4	1	no	—
249	C₂³×C₄₁	—	4	1	no	—
250	C₂³×C₄₁	—	4	1	no	—
251	C₂³×C₄₁	—	4	1	no	—
252	C₂³×C₄₁	—	4	1	no	—
253	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
254	Q₈×C₄₁	—	2	2	no	—
255	Q₈×C₄₁	—	2	2	no	—
256	Q₈×C₄₁	—	2	2	no	—
257	Q₈×C₄₁	—	2	2	no	—
258	Q₈×C₄₁	—	4	1	no	—
259	Q₈×C₄₁	—	4	1	no	—
260	Q₈×C₄₁	—	4	1	no	—
261	Q₈×C₄₁	—	4	1	no	—
262	Q₈×C₄₁	—	4	1	no	—
263	Q₈×C₄₁	—	4	1	no	—
264	Q₈×C₄₁	—	4	1	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	D₄×C₄₁	—	2	2	no	—
271	D₄×C₄₁	—	2	2	no	—
272	D₄×C₄₁	—	4	1	no	—
273	D₄×C₄₁	—	4	1	no	—
274	C₂×C₄×C₄₁	—	2	1	no	—
275	C₂×C₄×C₄₁	—	2	1	no	—
276	C₂×C₄×C₄₁	—	2	1	no	—
277	C₂×C₄×C₄₁	—	2	1	no	—
278	C₂×C₄×C₄₁	—	2	1	no	—
279	C₂×C₄×C₄₁	—	2	1	no	—
280	C₂×C₄×C₄₁	—	2	1	no	—
281	C₂×C₄×C₄₁	—	2	1	no	—
282	C₂×C₄×C₄₁	—	2	2	no	—
283	C₂×C₄×C₄₁	—	2	1	no	—
284	C₂×C₄×C₄₁	—	2	1	no	—
285	C₂×C₄×C₄₁	—	2	2	no	—
286	C₂×C₄×C₄₁	—	2	2	no	—
287	C₂×C₄×C₄₁	—	2	1	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	—	4	1	no	—
292	C₂×C₄×C₄₁	—	4	1	no	—
293	C₂×C₄×C₄₁	—	4	1	no	—
294	C₂×C₄×C₄₁	—	4	1	no	—
295	C₂×C₄×C₄₁	—	4	1	no	—
296	C₂×C₄×C₄₁	—	4	1	no	—
297	C₂×C₄×C₄₁	—	4	1	no	—
298	C₂×C₄×C₄₁	—	4	1	no	—
299	C₂×C₄×C₄₁	—	4	1	no	—
300	C₂×C₄×C₄₁	—	4	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	—	8	4	no	—
310	C₂×C₄×C₄₁	#121	1	2	yes	—
311	C₂×C₄×C₄₁	#121	1	2	yes	—
312	C₂×C₄×C₄₁	#137	1	2	yes	—
313	C₂×C₄×C₄₁	#137	1	2	yes	—
314	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
317	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
318	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
319	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
320	C₈×C₄₁	—	2	2	no	—
321	C₈×C₄₁	—	2	2	no	—
322	C₈×C₄₁	—	4	1	no	—
323	C₈×C₄₁	—	4	1	no	—
324	#25382	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
325	C₂²×C₄₁	—	4	2	no	—
326	C₂²×C₄₁	—	4	2	no	—
327	C₂²×C₄₁	—	4	2	no	—
328	C₂²×C₄₁	—	8	1	no	—
329	C₂²×C₄₁	—	8	1	no	—
330	C₂²×C₄₁	—	8	1	no	—
331	C₂²×C₄₁	—	8	1	no	—
332	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
333	C₂²×C₄₁	D₄²	1	1	yes	characteristic
334	C₂²×C₄₁	#550	1	1	yes	characteristic
335	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
336	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
337	C₂²×C₄₁	#577	1	1	yes	characteristic
338	C₂²×C₄₁	#578	1	1	yes	characteristic
339	C₄×C₄₁	—	2	2	no	—
340	C₄×C₄₁	—	2	2	no	—
341	C₄×C₄₁	—	2	2	no	—
342	C₄×C₄₁	—	2	2	no	—
343	C₄×C₄₁	—	4	2	no	—
344	C₄×C₄₁	—	4	2	no	—
345	C₄×C₄₁	—	4	1	no	—
346	C₄×C₄₁	—	4	2	no	—
347	C₄×C₄₁	—	4	1	no	—
348	C₄×C₄₁	—	8	1	no	—
349	C₄×C₄₁	—	8	1	no	—
350	C₄×C₄₁	—	8	1	no	—
351	C₄×C₄₁	—	8	1	no	—
352	C₄×C₄₁	#532	1	1	yes	characteristic
353	C₄×C₄₁	#540	1	1	yes	characteristic
354	C₄×C₄₁	D₄²	1	1	yes	characteristic
355	C₄×C₄₁	#546	1	1	yes	characteristic
356	C₂×#497	C₂×C₄₁	1	1	yes	characteristic
357	C₂×#464	C₂×C₄₁	1	1	yes	characteristic
358	C₂×#462	C₂×C₄₁	1	1	yes	characteristic, complemented
359	C₂×#461	C₂×C₄₁	1	1	yes	characteristic
360	#2546	C₂×C₄₁	1	1	yes	characteristic, complemented
361	#2367	C₂×C₄₁	1	1	yes	characteristic
362	#2056	C₂×C₄₁	1	1	yes	characteristic, complemented
363	#2055	C₂×C₄₁	1	1	yes	characteristic
364	#2016	C₂×C₄₁	1	1	yes	characteristic, complemented
365	#2013	C₂×C₄₁	1	1	yes	characteristic
366	#1981	C₂×C₄₁	1	1	yes	characteristic, complemented
367	#1940	C₂×C₄₁	1	1	yes	characteristic, complemented
368	#1878	C₂×C₄₁	1	1	yes	characteristic, complemented
369	#1877	C₂×C₄₁	1	1	yes	characteristic
370	#1763	C₂×C₄₁	1	1	yes	characteristic, complemented
371	C₂×C₄₁	—	8	2	no	—
372	C₂×C₄₁	#2428	1	1	yes	characteristic
373	C₂×C₄₁	#3039	1	1	yes	characteristic
374	C₂×C₄₁	#3046	1	1	yes	characteristic
375	C₂×C₄₁	#3266	1	1	yes	characteristic
376	C₂×C₄₁	#3270	1	1	yes	characteristic
377	C₂×C₄₁	#3398	1	1	yes	characteristic
378	C₂×C₄₁	#3400	1	1	yes	characteristic
379	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
380	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
381	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
382	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
383	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
384	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
385	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
386	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
387	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
388	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
389	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
390	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
391	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
392	#497	—	2	4	no	—
393	#464	—	2	4	no	—
394	#462	—	2	4	no	—
395	#461	—	2	4	no	—
396	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
397	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
398	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
399	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
400	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
401	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
402	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
403	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
404	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
405	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
406	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
407	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
408	#398	—	2	1	no	—
409	#398	—	2	1	no	—
410	#391	C₂²×C₄₁	1	1	yes	characteristic
411	#391	C₂²×C₄₁	1	1	yes	characteristic
412	#391	C₂²×C₄₁	1	1	yes	characteristic
413	#390	C₂²×C₄₁	1	1	yes	characteristic
414	#389	—	2	1	no	—
415	#389	—	2	1	no	—
416	#388	—	2	1	no	—
417	#388	—	2	1	no	—
418	#385	—	2	1	no	—
419	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
420	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
421	C₄×C₂²⋊C₄	—	2	1	no	—
422	#340	C₂²×C₄₁	1	1	yes	characteristic
423	#340	C₂²×C₄₁	1	1	yes	characteristic
424	#336	C₂²×C₄₁	1	1	yes	characteristic
425	#336	C₂²×C₄₁	1	1	yes	characteristic
426	C₄₁	#25382	1	1	yes	characteristic, direct product factor, Sylow
427	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
428	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
429	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
430	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
431	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
432	C₂³×C₄	—	2	1	no	—
433	C₂×Q₁₆	—	2	2	no	—
434	C₂×Q₁₆	—	2	2	no	—
435	C₂×Q₁₆	—	2	2	no	—
436	C₂×Q₁₆	—	2	2	no	—
437	C₂×Q₁₆	—	2	2	no	—
438	C₂×Q₁₆	—	2	2	no	—
439	C₂×Q₁₆	—	4	1	no	—
440	C₂×Q₁₆	—	4	1	no	—
441	C₂×Q₁₆	—	4	1	no	—
442	C₂×SD₁₆	—	2	2	no	—
443	C₂×SD₁₆	—	2	2	no	—
444	C₂×SD₁₆	—	2	2	no	—
445	C₂×SD₁₆	—	2	2	no	—
446	C₂×SD₁₆	—	2	2	no	—
447	C₂×SD₁₆	—	2	2	no	—
448	C₂×SD₁₆	—	4	1	no	—
449	C₂×SD₁₆	—	4	1	no	—
450	C₂×SD₁₆	—	4	1	no	—
451	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
452	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
453	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
454	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
455	C₄⋊Q₈	—	2	2	no	—
456	C₄⋊Q₈	—	2	2	no	—
457	C₄⋊Q₈	—	2	2	no	—
458	C₄⋊Q₈	—	2	2	no	—
459	C₄⋊Q₈	—	4	1	no	—
460	C₄⋊Q₈	—	4	1	no	—
461	#124	—	2	2	no	—
462	#124	D₄×C₄₁	1	4	yes	—
463	C₄×Q₈	—	2	2	no	—
464	C₄×Q₈	—	2	2	no	—
465	C₄×Q₈	—	2	2	no	—
466	C₄×Q₈	—	4	1	no	—
467	C₄×D₄	—	2	2	no	—
468	C₄×D₄	—	4	1	no	—
469	C₂×C₄⋊C₄	—	2	1	no	—
470	C₂×C₄⋊C₄	—	2	1	no	—
471	C₂×C₄⋊C₄	—	2	1	no	—
472	C₂×C₄⋊C₄	—	2	1	no	—
473	C₂×C₄⋊C₄	—	2	1	no	—
474	C₂×C₄⋊C₄	—	2	1	no	—
475	C₂×C₄⋊C₄	—	2	1	no	—
476	C₂×C₄⋊C₄	—	2	1	no	—
477	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
478	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
479	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
480	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
482	C₂×C₂²⋊C₄	—	2	1	no	—
483	C₂×C₂²⋊C₄	—	2	1	no	—
484	C₂×C₂²⋊C₄	—	2	1	no	—
485	C₂×C₂²⋊C₄	—	2	1	no	—
486	C₂×C₂²⋊C₄	—	2	1	no	—
487	C₂×C₄²	—	2	1	no	—
488	C₂×C₄²	—	2	1	no	—
489	C₂×C₄²	—	2	1	no	—
490	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
491	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
492	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
493	C₄⋊C₈	—	2	2	no	—
494	C₄⋊C₈	—	2	2	no	—
495	C₄⋊C₈	—	2	2	no	—
496	#103	—	2	2	no	—
497	#103	—	2	2	no	—
498	#103	—	2	2	no	—
499	#103	—	2	2	no	—
500	#103	—	4	1	no	—
501	#103	—	4	1	no	—
502	#103	D₄×C₄₁	1	4	yes	—
503	#102	—	2	2	no	—
504	#97	—	2	2	no	—
505	#95	—	2	1	no	—
506	#95	—	2	1	no	—
507	#95	—	2	1	no	—
508	#95	—	2	1	no	—
509	#95	—	2	1	no	—
510	#95	—	2	1	no	—
511	#95	—	2	1	no	—
512	#95	D₄×C₄₁	1	1	yes	characteristic
513	#95	D₄×C₄₁	1	1	yes	characteristic
514	C₂⁴	—	2	1	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	—	2	1	no	—
520	C₂×Q₈	—	2	1	no	—
521	C₂×Q₈	—	2	1	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	—	2	1	no	—
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	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	C₂×D₄×C₄₁	1	2	yes	—
538	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	4	2	no	—
553	C₂²×C₄	—	4	2	no	—
554	C₂²×C₄	—	8	1	no	—
555	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
556	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
557	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
558	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
559	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
560	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
561	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
562	Q₁₆	—	4	4	no	—
563	Q₁₆	—	4	4	no	—
564	Q₁₆	—	4	4	no	—
565	SD₁₆	—	4	4	no	—
566	SD₁₆	—	4	4	no	—
567	SD₁₆	—	4	4	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
579	C₂×C₈	#41×C₄₁	1	2	yes	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	—	2	2	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	4	2	no	—
588	C₄⋊C₄	—	4	2	no	—
589	C₄⋊C₄	—	4	2	no	—
590	C₄⋊C₄	—	4	2	no	—
591	C₄⋊C₄	—	4	2	no	—
592	C₄⋊C₄	—	4	2	no	—
593	C₄⋊C₄	—	4	2	no	—
594	C₄⋊C₄	—	4	2	no	—
595	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
596	C₂²⋊C₄	—	2	4	no	—
597	C₂²⋊C₄	—	2	4	no	—
598	C₂²⋊C₄	—	4	2	no	—
599	C₂²⋊C₄	—	4	2	no	—
600	C₂²⋊C₄	—	8	1	no	—
601	C₄²	—	2	1	no	—
602	C₄²	—	2	1	no	—
603	C₄²	—	2	1	no	—
604	C₄²	—	2	1	no	—
605	C₄²	—	4	2	no	—
606	C₄²	—	4	2	no	—
607	C₄²	—	8	1	no	—
608	C₄²	C₂×D₄×C₄₁	1	2	yes	—
609	C₄²	#41×C₄₁	1	2	yes	—
610	C₂³	—	2	2	no	—
611	C₂³	—	4	1	no	—
612	C₂³	—	4	1	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	4	1	no	—
616	C₂³	—	4	1	no	—
617	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
618	Q₈	—	2	2	no	—
619	Q₈	—	2	2	no	—
620	Q₈	—	2	2	no	—
621	Q₈	—	2	2	no	—
622	Q₈	—	4	1	no	—
623	Q₈	—	4	1	no	—
624	Q₈	—	4	1	no	—
625	Q₈	—	4	1	no	—
626	Q₈	—	4	1	no	—
627	Q₈	—	4	1	no	—
628	Q₈	—	4	1	no	—
629	Q₈	—	4	1	no	—
630	Q₈	—	4	1	no	—
631	Q₈	—	4	1	no	—
632	Q₈	—	4	1	no	—
633	Q₈	—	4	1	no	—
634	D₄	—	2	2	no	—
635	D₄	—	2	2	no	—
636	D₄	—	4	1	no	—
637	D₄	—	4	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	8	4	no	—
674	C₂×C₄	#121×C₄₁	1	2	yes	—
675	C₂×C₄	#121×C₄₁	1	2	yes	—
676	C₂×C₄	#137×C₄₁	1	2	yes	—
677	C₂×C₄	#137×C₄₁	1	2	yes	—
678	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
679	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
680	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
681	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
682	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
683	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
684	C₈	—	2	2	no	—
685	C₈	—	2	2	no	—
686	C₈	—	4	1	no	—
687	C₈	—	4	1	no	—
688	C₂²	—	4	2	no	—
689	C₂²	—	4	2	no	—
690	C₂²	—	4	2	no	—
691	C₂²	—	8	1	no	—
692	C₂²	—	8	1	no	—
693	C₂²	—	8	1	no	—
694	C₂²	—	8	1	no	—
695	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
696	C₂²	D₄²×C₄₁	1	1	yes	characteristic
697	C₂²	C₄₁×#550	1	1	yes	characteristic
698	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
699	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
700	C₂²	C₄₁×#577	1	1	yes	characteristic
701	C₂²	C₄₁×#578	1	1	yes	characteristic
702	C₄	—	2	2	no	—
703	C₄	—	2	2	no	—
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	4	2	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	1	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	1	no	—
711	C₄	—	8	1	no	—
712	C₄	—	8	1	no	—
713	C₄	—	8	1	no	—
714	C₄	—	8	1	no	—
715	C₄	C₄₁×#532	1	1	yes	characteristic
716	C₄	C₄₁×#540	1	1	yes	characteristic
717	C₄	D₄²×C₄₁	1	1	yes	characteristic
718	C₄	C₄₁×#546	1	1	yes	characteristic
719	C₂	—	8	2	no	—
720	C₂	C₄₁×#2428	1	1	yes	characteristic
721	C₂	C₄₁×#3039	1	1	yes	characteristic
722	C₂	C₄₁×#3046	1	1	yes	characteristic
723	C₂	C₄₁×#3266	1	1	yes	characteristic
724	C₂	C₄₁×#3270	1	1	yes	characteristic
725	C₂	C₄₁×#3398	1	1	yes	characteristic
726	C₂	C₄₁×#3400	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×D₄×C₄₁	C₂³
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
3. C₂×C₄₁×#462	C₂	semidirect
5. C₄₁×#2546	C₂	semidirect
7. C₄₁×#2056	C₂	semidirect
9. C₄₁×#2016	C₂	semidirect
11. C₄₁×#1981	C₂	semidirect
12. C₄₁×#1940	C₂	semidirect
13. C₄₁×#1878	C₂	semidirect
15. C₄₁×#1763	C₂	semidirect
324. #25382	C₄₁	direct (N × H)
358. C₂×#462	C₂×C₄₁	semidirect
360. #2546	C₂×C₄₁	semidirect
362. #2056	C₂×C₄₁	semidirect
364. #2016	C₂×C₄₁	semidirect
366. #1981	C₂×C₄₁	semidirect
367. #1940	C₂×C₄₁	semidirect
368. #1878	C₂×C₄₁	semidirect
370. #1763	C₂×C₄₁	semidirect
426. C₄₁	#25382	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×#462	2
C₂×C₄₁×#461	2
C₄₁×#2546	2
C₄₁×#2367	2
C₄₁×#2056	2
C₄₁×#2055	2
C₄₁×#2016	2
C₄₁×#2013	2
C₄₁×#1981	2
C₄₁×#1940	2
C₄₁×#1878	2
C₄₁×#1877	2
C₄₁×#1763	2
#25382	41

Subgroups — C41×#25382 #23801583

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25382 #23801583