Subgroups — C₄₁×#24203 #23800404

Order 10496.

1036 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#557	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#462	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#441	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2581	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#2043	C₂	1	2	yes	maximal
6	C₄₁×#2016	C₂	1	2	yes	maximal
7	C₄₁×#1985	C₂	1	1	yes	maximal, characteristic
8	C₄₁×#1960	C₂	1	1	yes	maximal, characteristic
9	C₄₁×#1878	C₂	1	2	yes	maximal
10	C₄₁×#1865	C₂	1	2	yes	maximal
11	C₄₁×#1805	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₄₁	C₂²	1	2	yes	—
14	C₄₁×#557	—	2	4	no	—
15	C₄₁×#557	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₄₁	C₂²	1	2	yes	—
17	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#125×C₄₁	—	2	2	no	—
19	C₂×#125×C₄₁	—	2	1	no	—
20	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
21	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₄₁×#462	—	2	4	no	—
26	C₄₁×#441	—	2	4	no	—
27	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×#103×C₄₁	C₂²	1	2	yes	—
30	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×#103×C₄₁	C₂²	1	2	yes	—
32	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×#103×C₄₁	C₂²	1	2	yes	—
34	C₂×#103×C₄₁	C₂²	1	2	yes	—
35	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
36	C₄₁×#400	—	2	1	no	—
37	C₄₁×#395	—	2	1	no	—
38	C₄₁×#391	C₂²	1	2	yes	—
39	C₄₁×#389	C₂²	1	2	yes	—
40	C₄₁×#387	—	2	2	no	—
41	C₄₁×#382	C₂²	1	1	yes	characteristic
42	C₄₁×#340	C₂²	1	2	yes	—
43	C₄₁×#336	C₂²	1	2	yes	—
44	C₄₁×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
47	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
49	C₂×Q₁₆×C₄₁	—	2	2	no	—
50	C₂×Q₁₆×C₄₁	—	2	2	no	—
51	C₂×Q₁₆×C₄₁	—	2	4	no	—
52	C₂×Q₁₆×C₄₁	—	2	4	no	—
53	C₂×Q₁₆×C₄₁	—	2	2	no	—
54	C₂×Q₁₆×C₄₁	—	4	2	no	—
55	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
56	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
58	C₄⋊Q₈×C₄₁	—	2	4	no	—
59	C₄⋊Q₈×C₄₁	—	2	4	no	—
60	C₄⋊Q₈×C₄₁	—	2	2	no	—
61	C₄⋊Q₈×C₄₁	D₄	1	4	yes	—
62	#125×C₄₁	—	2	16	no	—
63	#125×C₄₁	—	2	8	no	—
64	C₄×Q₈×C₄₁	—	2	8	no	—
65	C₄×Q₈×C₄₁	—	2	4	no	—
66	C₄×Q₈×C₄₁	—	2	4	no	—
67	C₄×Q₈×C₄₁	—	2	2	no	—
68	C₄×Q₈×C₄₁	—	2	2	no	—
69	C₄×Q₈×C₄₁	—	2	2	no	—
70	C₄×Q₈×C₄₁	—	2	2	no	—
71	C₄×Q₈×C₄₁	—	2	2	no	—
72	C₄×Q₈×C₄₁	D₄	1	4	yes	—
73	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
74	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
76	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
78	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
79	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
81	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
82	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₄₁	—	2	2	no	—
87	C₂×C₄²×C₄₁	—	2	1	no	—
88	C₂×C₄²×C₄₁	—	2	1	no	—
89	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
90	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
91	#106×C₄₁	—	2	2	no	—
92	C₄⋊C₈×C₄₁	—	2	2	no	—
93	#103×C₄₁	—	2	2	no	—
94	#103×C₄₁	—	2	4	no	—
95	#103×C₄₁	—	2	4	no	—
96	#103×C₄₁	—	2	2	no	—
97	#103×C₄₁	—	4	2	no	—
98	#103×C₄₁	—	4	2	no	—
99	#97×C₄₁	—	2	2	no	—
100	#95×C₄₁	—	2	1	no	—
101	#95×C₄₁	—	2	1	no	—
102	#95×C₄₁	—	2	2	no	—
103	#95×C₄₁	—	2	2	no	—
104	#95×C₄₁	—	2	2	no	—
105	C₂×Q₈×C₄₁	—	2	2	no	—
106	C₂×Q₈×C₄₁	—	2	4	no	—
107	C₂×Q₈×C₄₁	—	2	2	no	—
108	C₂×Q₈×C₄₁	—	2	1	no	—
109	C₂×Q₈×C₄₁	—	2	1	no	—
110	C₂×Q₈×C₄₁	—	2	1	no	—
111	C₂×Q₈×C₄₁	—	2	1	no	—
112	C₂×Q₈×C₄₁	—	2	2	no	—
113	C₂×Q₈×C₄₁	—	2	1	no	—
114	C₂×Q₈×C₄₁	—	2	2	no	—
115	C₂×Q₈×C₄₁	—	2	1	no	—
116	C₂×Q₈×C₄₁	—	2	1	no	—
117	C₂×Q₈×C₄₁	—	2	1	no	—
118	C₂×Q₈×C₄₁	—	2	2	no	—
119	C₂×Q₈×C₄₁	—	2	1	no	—
120	C₂×Q₈×C₄₁	—	2	1	no	—
121	C₂×Q₈×C₄₁	—	2	2	no	—
122	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
123	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
124	C₂×Q₈×C₄₁	#41	1	2	yes	—
125	C₂²×C₄×C₄₁	—	2	1	no	—
126	C₂²×C₄×C₄₁	—	2	1	no	—
127	C₂²×C₄×C₄₁	—	2	2	no	—
128	C₂²×C₄×C₄₁	—	2	1	no	—
129	C₂²×C₄×C₄₁	—	2	2	no	—
130	C₂²×C₄×C₄₁	—	2	1	no	—
131	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
136	Q₁₆×C₄₁	—	2	8	no	—
137	Q₁₆×C₄₁	—	4	8	no	—
138	C₂×C₈×C₄₁	—	2	1	no	—
139	C₂×C₈×C₄₁	—	2	1	no	—
140	C₂×C₈×C₄₁	—	2	1	no	—
141	C₂×C₈×C₄₁	—	2	2	no	—
142	C₂×C₈×C₄₁	—	2	2	no	—
143	C₂×C₈×C₄₁	—	2	1	no	—
144	C₂×C₈×C₄₁	—	2	2	no	—
145	C₂×C₈×C₄₁	—	2	1	no	—
146	C₂×C₈×C₄₁	#41	1	2	yes	—
147	C₄⋊C₄×C₄₁	—	2	8	no	—
148	C₄⋊C₄×C₄₁	—	2	8	no	—
149	C₄⋊C₄×C₄₁	—	2	8	no	—
150	C₄⋊C₄×C₄₁	—	2	4	no	—
151	C₄⋊C₄×C₄₁	—	2	4	no	—
152	C₄⋊C₄×C₄₁	—	2	4	no	—
153	C₄⋊C₄×C₄₁	—	2	4	no	—
154	C₄⋊C₄×C₄₁	—	2	2	no	—
155	C₄⋊C₄×C₄₁	—	2	1	no	—
156	C₄⋊C₄×C₄₁	—	2	1	no	—
157	C₄⋊C₄×C₄₁	—	2	1	no	—
158	C₄⋊C₄×C₄₁	—	2	2	no	—
159	C₄⋊C₄×C₄₁	—	2	2	no	—
160	C₄⋊C₄×C₄₁	—	4	2	no	—
161	C₄⋊C₄×C₄₁	—	4	4	no	—
162	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
163	C₄²×C₄₁	—	2	8	no	—
164	C₄²×C₄₁	—	2	4	no	—
165	C₄²×C₄₁	—	2	2	no	—
166	C₄²×C₄₁	—	2	2	no	—
167	C₄²×C₄₁	—	4	2	no	—
168	C₄²×C₄₁	C₂×D₄	1	2	yes	—
169	C₄²×C₄₁	C₂×D₄	1	2	yes	—
170	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₄₁	—	2	8	no	—
172	Q₈×C₄₁	—	2	2	no	—
173	Q₈×C₄₁	—	2	2	no	—
174	Q₈×C₄₁	—	2	2	no	—
175	Q₈×C₄₁	—	2	2	no	—
176	Q₈×C₄₁	—	2	4	no	—
177	Q₈×C₄₁	—	2	4	no	—
178	Q₈×C₄₁	—	4	2	no	—
179	Q₈×C₄₁	—	4	2	no	—
180	Q₈×C₄₁	—	4	1	no	—
181	Q₈×C₄₁	—	4	1	no	—
182	Q₈×C₄₁	—	4	1	no	—
183	Q₈×C₄₁	—	4	1	no	—
184	C₂×C₄×C₄₁	—	2	2	no	—
185	C₂×C₄×C₄₁	—	2	2	no	—
186	C₂×C₄×C₄₁	—	2	2	no	—
187	C₂×C₄×C₄₁	—	2	2	no	—
188	C₂×C₄×C₄₁	—	2	2	no	—
189	C₂×C₄×C₄₁	—	2	2	no	—
190	C₂×C₄×C₄₁	—	2	4	no	—
191	C₂×C₄×C₄₁	—	2	2	no	—
192	C₂×C₄×C₄₁	—	2	2	no	—
193	C₂×C₄×C₄₁	—	2	4	no	—
194	C₂×C₄×C₄₁	—	4	1	no	—
195	C₂×C₄×C₄₁	—	4	1	no	—
196	C₂×C₄×C₄₁	—	4	2	no	—
197	C₂×C₄×C₄₁	—	4	1	no	—
198	C₂×C₄×C₄₁	—	4	2	no	—
199	C₂×C₄×C₄₁	—	4	1	no	—
200	C₂×C₄×C₄₁	—	4	2	no	—
201	C₂×C₄×C₄₁	—	4	1	no	—
202	C₂×C₄×C₄₁	—	4	2	no	—
203	C₂×C₄×C₄₁	—	4	2	no	—
204	C₂×C₄×C₄₁	—	4	2	no	—
205	C₂×C₄×C₄₁	—	4	2	no	—
206	C₂×C₄×C₄₁	#120	1	2	yes	—
207	C₂×C₄×C₄₁	#120	1	2	yes	—
208	C₂×C₄×C₄₁	#137	1	4	yes	—
209	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
214	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
215	C₈×C₄₁	—	2	2	no	—
216	C₈×C₄₁	—	4	1	no	—
217	C₈×C₄₁	—	4	2	no	—
218	#24203	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
220	C₂²×C₄₁	#548	1	1	yes	characteristic
221	C₂²×C₄₁	#550	1	1	yes	characteristic
222	C₂²×C₄₁	C₂×#137	1	2	yes	—
223	C₂²×C₄₁	#578	1	2	yes	—
224	C₄×C₄₁	—	2	2	no	—
225	C₄×C₄₁	—	2	4	no	—
226	C₄×C₄₁	—	2	2	no	—
227	C₄×C₄₁	—	4	2	no	—
228	C₄×C₄₁	—	4	4	no	—
229	C₄×C₄₁	—	4	2	no	—
230	C₄×C₄₁	—	4	2	no	—
231	C₄×C₄₁	—	4	2	no	—
232	C₄×C₄₁	—	8	2	no	—
233	C₄×C₄₁	—	8	1	no	—
234	C₄×C₄₁	#525	1	1	yes	characteristic
235	C₄×C₄₁	#537	1	1	yes	characteristic
236	C₄×C₄₁	#546	1	1	yes	characteristic
237	C₄×C₄₁	#547	1	1	yes	characteristic
238	C₂×#557	C₂×C₄₁	1	1	yes	characteristic
239	C₂×#462	C₂×C₄₁	1	1	yes	characteristic
240	C₂×#441	C₂×C₄₁	1	1	yes	characteristic
241	#2581	C₂×C₄₁	1	1	yes	characteristic
242	#2043	C₂×C₄₁	1	2	yes	—
243	#2016	C₂×C₄₁	1	2	yes	—
244	#1985	C₂×C₄₁	1	1	yes	characteristic
245	#1960	C₂×C₄₁	1	1	yes	characteristic
246	#1878	C₂×C₄₁	1	2	yes	—
247	#1865	C₂×C₄₁	1	2	yes	—
248	#1805	C₂×C₄₁	1	1	yes	characteristic
249	C₂×C₄₁	#2407	1	1	yes	characteristic
250	C₂×C₄₁	#3004	1	1	yes	characteristic
251	C₂×C₄₁	#3011	1	1	yes	characteristic
252	C₂×C₄₁	#3374	1	2	yes	—
253	C₂×C₄₁	#3398	1	2	yes	—
254	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
255	C₂²×Q₁₆	C₂²×C₄₁	1	2	yes	—
256	#557	—	2	4	no	—
257	#557	—	2	4	no	—
258	C₂×C₄⋊Q₈	C₂²×C₄₁	1	2	yes	—
259	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
260	C₂×#125	—	2	2	no	—
261	C₂×#125	—	2	1	no	—
262	C₂×C₄×Q₈	—	2	1	no	—
263	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
264	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
265	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
266	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
267	#462	—	2	4	no	—
268	#441	—	2	4	no	—
269	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
270	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
271	C₂×#103	C₂²×C₄₁	1	2	yes	—
272	C₂×#103	C₂²×C₄₁	1	2	yes	—
273	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
274	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
275	C₂×#103	C₂²×C₄₁	1	2	yes	—
276	C₂×#103	C₂²×C₄₁	1	2	yes	—
277	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
278	#400	—	2	1	no	—
279	#395	—	2	1	no	—
280	#391	C₂²×C₄₁	1	2	yes	—
281	#389	C₂²×C₄₁	1	2	yes	—
282	#387	—	2	2	no	—
283	#382	C₂²×C₄₁	1	1	yes	characteristic
284	#340	C₂²×C₄₁	1	2	yes	—
285	#336	C₂²×C₄₁	1	2	yes	—
286	#336	C₂²×C₄₁	1	2	yes	—
287	C₄₁	#24203	1	1	yes	characteristic, direct product factor, Sylow
288	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
289	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
290	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
291	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
292	C₂×Q₁₆	—	2	2	no	—
293	C₂×Q₁₆	—	2	2	no	—
294	C₂×Q₁₆	—	2	4	no	—
295	C₂×Q₁₆	—	2	4	no	—
296	C₂×Q₁₆	—	2	2	no	—
297	C₂×Q₁₆	—	4	2	no	—
298	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
299	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
301	C₄⋊Q₈	—	2	4	no	—
302	C₄⋊Q₈	—	2	4	no	—
303	C₄⋊Q₈	—	2	2	no	—
304	C₄⋊Q₈	D₄×C₄₁	1	4	yes	—
305	#125	—	2	16	no	—
306	#125	—	2	8	no	—
307	C₄×Q₈	—	2	8	no	—
308	C₄×Q₈	—	2	4	no	—
309	C₄×Q₈	—	2	4	no	—
310	C₄×Q₈	—	2	2	no	—
311	C₄×Q₈	—	2	2	no	—
312	C₄×Q₈	—	2	2	no	—
313	C₄×Q₈	—	2	2	no	—
314	C₄×Q₈	—	2	2	no	—
315	C₄×Q₈	D₄×C₄₁	1	4	yes	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
325	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
329	C₂×C₄²	—	2	2	no	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	—	2	1	no	—
332	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
333	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
334	#106	—	2	2	no	—
335	C₄⋊C₈	—	2	2	no	—
336	#103	—	2	2	no	—
337	#103	—	2	4	no	—
338	#103	—	2	4	no	—
339	#103	—	2	2	no	—
340	#103	—	4	2	no	—
341	#103	—	4	2	no	—
342	#97	—	2	2	no	—
343	#95	—	2	1	no	—
344	#95	—	2	1	no	—
345	#95	—	2	2	no	—
346	#95	—	2	2	no	—
347	#95	—	2	2	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	4	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
366	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
367	C₂×Q₈	#41×C₄₁	1	2	yes	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
375	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
378	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
379	Q₁₆	—	2	8	no	—
380	Q₁₆	—	4	8	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	#41×C₄₁	1	2	yes	—
390	C₄⋊C₄	—	2	8	no	—
391	C₄⋊C₄	—	2	8	no	—
392	C₄⋊C₄	—	2	8	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	4	2	no	—
404	C₄⋊C₄	—	4	4	no	—
405	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
406	C₄²	—	2	8	no	—
407	C₄²	—	2	4	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	4	2	no	—
411	C₄²	C₂×D₄×C₄₁	1	2	yes	—
412	C₄²	C₂×D₄×C₄₁	1	2	yes	—
413	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
414	Q₈	—	2	8	no	—
415	Q₈	—	2	2	no	—
416	Q₈	—	2	2	no	—
417	Q₈	—	2	2	no	—
418	Q₈	—	2	2	no	—
419	Q₈	—	2	4	no	—
420	Q₈	—	2	4	no	—
421	Q₈	—	4	2	no	—
422	Q₈	—	4	2	no	—
423	Q₈	—	4	1	no	—
424	Q₈	—	4	1	no	—
425	Q₈	—	4	1	no	—
426	Q₈	—	4	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	#120×C₄₁	1	2	yes	—
450	C₂×C₄	#120×C₄₁	1	2	yes	—
451	C₂×C₄	#137×C₄₁	1	4	yes	—
452	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
454	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
455	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
456	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
457	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
458	C₈	—	2	2	no	—
459	C₈	—	4	1	no	—
460	C₈	—	4	2	no	—
461	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
462	C₂²	C₄₁×#548	1	1	yes	characteristic
463	C₂²	C₄₁×#550	1	1	yes	characteristic
464	C₂²	C₂×#137×C₄₁	1	2	yes	—
465	C₂²	C₄₁×#578	1	2	yes	—
466	C₄	—	2	2	no	—
467	C₄	—	2	4	no	—
468	C₄	—	2	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	4	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	8	2	no	—
475	C₄	—	8	1	no	—
476	C₄	C₄₁×#525	1	1	yes	characteristic
477	C₄	C₄₁×#537	1	1	yes	characteristic
478	C₄	C₄₁×#546	1	1	yes	characteristic
479	C₄	C₄₁×#547	1	1	yes	characteristic
480	C₂	C₄₁×#2407	1	1	yes	characteristic
481	C₂	C₄₁×#3004	1	1	yes	characteristic
482	C₂	C₄₁×#3011	1	1	yes	characteristic
483	C₂	C₄₁×#3374	1	2	yes	—
484	C₂	C₄₁×#3398	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×C₄×Q₈×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
218. #24203	C₄₁	direct (N × H)
287. C₄₁	#24203	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×#557	2
C₂×C₄₁×#462	2
C₂×C₄₁×#441	2
C₄₁×#2581	2
C₄₁×#2043	2
C₄₁×#2016	2
C₄₁×#1985	2
C₄₁×#1960	2
C₄₁×#1878	2
C₄₁×#1865	2
C₄₁×#1805	2
#24203	41

Subgroups — C41×#24203 #23800404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24203 #23800404