Subgroups — C₄₁×#24810 #23801011

Order 10496.

810 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3069	C₂	1	2	yes	maximal
2	C₂×C₄₁×#473	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#473	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2955	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#2916	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2070	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2049	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1979	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1953	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1902	C₂	1	2	yes	maximal, complemented
11	C₄₁×#1813	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#575	C₂²	1	1	yes	characteristic
13	C₂×#137×C₄₁	C₂²	1	2	yes	—
14	C₂×#137×C₄₁	C₂²	1	2	yes	—
15	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
16	C₄₁×#568	C₂²	1	2	yes	—
17	C₂×#131×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#131×C₄₁	C₂²	1	1	yes	characteristic
19	C₄₁×#473	—	2	4	no	—
20	C₄₁×#473	—	2	2	no	—
21	C₄₁×#473	—	2	2	no	—
22	C₄₁×#473	—	2	2	no	—
23	C₄₁×#473	—	2	2	no	—
24	C₄₁×#471	—	2	4	no	—
25	C₄₁×#444	—	2	2	no	—
26	C₄₁×#443	—	2	2	no	—
27	C₄₁×#430	—	2	2	no	—
28	C₄₁×#430	C₂²	1	2	yes	—
29	C₄₁×#430	C₂²	1	2	yes	—
30	C₄₁×#430	C₂²	1	1	yes	characteristic
31	C₂×#108×C₄₁	—	2	2	no	—
32	C₂×#108×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×#108×C₄₁	C₂²	1	1	yes	characteristic
34	C₂×#108×C₄₁	C₂²	1	1	yes	characteristic
35	C₄₁×#421	C₂²	1	1	yes	characteristic
36	C₄₁×#421	C₂²	1	1	yes	characteristic
37	C₄₁×#419	C₂²	1	2	yes	—
38	C₄₁×#413	C₂²	1	2	yes	—
39	C₂×#101×C₄₁	C₂²	1	2	yes	—
40	C₂×#101×C₄₁	C₂²	1	2	yes	—
41	C₂×#101×C₄₁	C₂²	1	2	yes	—
42	C₄₁×#405	C₂²	1	1	yes	characteristic
43	C₄₁×#344	C₂²	1	2	yes	—
44	C₄₁×#338	C₂²	1	2	yes	—
45	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
46	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
47	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
48	#137×C₄₁	—	2	1	no	—
49	#137×C₄₁	—	2	4	no	—
50	#137×C₄₁	—	2	4	no	—
51	#137×C₄₁	—	2	4	no	—
52	#137×C₄₁	—	4	2	no	—
53	#137×C₄₁	D₄	1	2	yes	—
54	AGL(1,ℤ/8)×C₄₁	—	2	1	no	—
55	AGL(1,ℤ/8)×C₄₁	D₄	1	2	yes	—
56	#135×C₄₁	—	2	2	no	—
57	C₂×Q₁₆×C₄₁	—	2	2	no	—
58	C₂×Q₁₆×C₄₁	—	2	2	no	—
59	C₂×Q₁₆×C₄₁	—	2	1	no	—
60	C₂×Q₁₆×C₄₁	—	2	1	no	—
61	C₂×Q₁₆×C₄₁	—	2	1	no	—
62	C₂×Q₁₆×C₄₁	—	2	1	no	—
63	C₂×Q₁₆×C₄₁	—	2	1	no	—
64	C₂×Q₁₆×C₄₁	—	2	1	no	—
65	C₂×SD₁₆×C₄₁	—	2	2	no	—
66	C₂×SD₁₆×C₄₁	—	2	2	no	—
67	#131×C₄₁	—	2	1	no	—
68	#131×C₄₁	—	2	1	no	—
69	#131×C₄₁	—	2	4	no	—
70	#131×C₄₁	—	2	1	no	—
71	#131×C₄₁	—	2	1	no	—
72	#131×C₄₁	—	2	1	no	—
73	#131×C₄₁	—	2	1	no	—
74	#131×C₄₁	—	4	2	no	—
75	#131×C₄₁	D₄	1	2	yes	—
76	#131×C₄₁	D₄	1	2	yes	—
77	C₂×M₁₆×C₄₁	—	2	1	no	—
78	C₂×M₁₆×C₄₁	—	2	1	no	—
79	C₂×M₁₆×C₄₁	—	2	4	no	—
80	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
81	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
82	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
83	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
85	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₄₁	—	2	1	no	—
87	C₂²×C₈×C₄₁	—	2	1	no	—
88	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
89	#117×C₄₁	C₂³	1	1	yes	characteristic
90	#108×C₄₁	—	2	4	no	—
91	#108×C₄₁	—	2	2	no	—
92	#108×C₄₁	—	2	4	no	—
93	#108×C₄₁	—	2	1	no	—
94	#108×C₄₁	—	2	1	no	—
95	#108×C₄₁	—	2	1	no	—
96	#108×C₄₁	—	2	1	no	—
97	#108×C₄₁	D₄	1	2	yes	—
98	#108×C₄₁	D₄	1	2	yes	—
99	#104×C₄₁	—	2	2	no	—
100	#104×C₄₁	—	2	2	no	—
101	#103×C₄₁	—	4	2	no	—
102	#101×C₄₁	—	2	2	no	—
103	#101×C₄₁	—	2	4	no	—
104	#101×C₄₁	—	2	4	no	—
105	#101×C₄₁	—	2	4	no	—
106	#100×C₄₁	—	2	2	no	—
107	#97×C₄₁	—	2	1	no	—
108	C₄×C₈×C₄₁	—	2	1	no	—
109	#41×C₄₁	—	2	1	no	—
110	#41×C₄₁	—	2	1	no	—
111	#41×C₄₁	—	2	1	no	—
112	#41×C₄₁	—	2	1	no	—
113	#41×C₄₁	—	2	1	no	—
114	#41×C₄₁	—	2	1	no	—
115	#41×C₄₁	C₂×D₄	1	2	yes	—
116	#41×C₄₁	C₂×D₄	1	2	yes	—
117	C₂×Q₈×C₄₁	—	2	2	no	—
118	C₂×Q₈×C₄₁	—	2	2	no	—
119	C₂×Q₈×C₄₁	—	2	2	no	—
120	C₂×Q₈×C₄₁	—	2	2	no	—
121	C₂×Q₈×C₄₁	—	2	2	no	—
122	C₂×Q₈×C₄₁	—	2	2	no	—
123	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
124	C₂×Q₈×C₄₁	#41	1	1	yes	characteristic
125	C₂×D₄×C₄₁	—	2	1	no	—
126	C₂×D₄×C₄₁	—	2	1	no	—
127	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
128	C₂×D₄×C₄₁	#41	1	1	yes	characteristic
129	C₂²×C₄×C₄₁	—	2	1	no	—
130	C₂²×C₄×C₄₁	—	2	1	no	—
131	C₂²×C₄×C₄₁	—	2	2	no	—
132	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
133	Q₁₆×C₄₁	—	2	2	no	—
134	Q₁₆×C₄₁	—	4	4	no	—
135	Q₁₆×C₄₁	—	4	4	no	—
136	Q₁₆×C₄₁	—	4	1	no	—
137	Q₁₆×C₄₁	—	4	1	no	—
138	Q₁₆×C₄₁	—	4	1	no	—
139	Q₁₆×C₄₁	—	4	1	no	—
140	SD₁₆×C₄₁	—	2	2	no	—
141	SD₁₆×C₄₁	—	2	2	no	—
142	SD₁₆×C₄₁	—	4	4	no	—
143	SD₁₆×C₄₁	—	4	4	no	—
144	D₈×C₄₁	—	2	2	no	—
145	M₁₆×C₄₁	—	2	1	no	—
146	M₁₆×C₄₁	—	2	1	no	—
147	M₁₆×C₄₁	—	2	2	no	—
148	M₁₆×C₄₁	—	2	2	no	—
149	M₁₆×C₄₁	—	2	2	no	—
150	M₁₆×C₄₁	—	2	2	no	—
151	M₁₆×C₄₁	—	2	2	no	—
152	M₁₆×C₄₁	—	2	1	no	—
153	M₁₆×C₄₁	—	2	2	no	—
154	M₁₆×C₄₁	—	2	1	no	—
155	M₁₆×C₄₁	—	2	2	no	—
156	M₁₆×C₄₁	—	4	4	no	—
157	M₁₆×C₄₁	—	4	1	no	—
158	M₁₆×C₄₁	—	4	1	no	—
159	M₁₆×C₄₁	C₂×D₄	1	2	yes	—
160	M₁₆×C₄₁	C₂×D₄	1	2	yes	—
161	M₁₆×C₄₁	C₂×D₄	1	4	yes	—
162	C₂×C₈×C₄₁	—	2	1	no	—
163	C₂×C₈×C₄₁	—	2	1	no	—
164	C₂×C₈×C₄₁	—	2	2	no	—
165	C₂×C₈×C₄₁	—	2	2	no	—
166	C₂×C₈×C₄₁	—	2	2	no	—
167	C₂×C₈×C₄₁	—	2	1	no	—
168	C₂×C₈×C₄₁	—	2	2	no	—
169	C₂×C₈×C₄₁	—	2	2	no	—
170	C₂×C₈×C₄₁	—	4	4	no	—
171	C₂×C₈×C₄₁	—	4	1	no	—
172	C₂×C₈×C₄₁	—	4	1	no	—
173	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
175	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₄₁	#41	1	1	yes	characteristic
178	C₂×C₈×C₄₁	#41	1	1	yes	characteristic
179	C₄⋊C₄×C₄₁	—	2	1	no	—
180	C₂²⋊C₄×C₄₁	—	2	1	no	—
181	C₄²×C₄₁	—	2	1	no	—
182	C₂³×C₄₁	—	2	1	no	—
183	C₂³×C₄₁	—	2	1	no	—
184	C₂³×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
185	Q₈×C₄₁	—	2	1	no	—
186	Q₈×C₄₁	—	2	1	no	—
187	Q₈×C₄₁	—	2	1	no	—
188	Q₈×C₄₁	—	4	2	no	—
189	Q₈×C₄₁	—	4	2	no	—
190	Q₈×C₄₁	—	4	2	no	—
191	Q₈×C₄₁	—	4	2	no	—
192	Q₈×C₄₁	#121	1	2	yes	—
193	D₄×C₄₁	—	2	2	no	—
194	D₄×C₄₁	—	2	2	no	—
195	D₄×C₄₁	—	2	1	no	—
196	D₄×C₄₁	—	2	1	no	—
197	D₄×C₄₁	—	2	1	no	—
198	D₄×C₄₁	—	4	1	no	—
199	D₄×C₄₁	—	4	1	no	—
200	D₄×C₄₁	#121	1	2	yes	—
201	C₂×C₄×C₄₁	—	2	1	no	—
202	C₂×C₄×C₄₁	—	2	2	no	—
203	C₂×C₄×C₄₁	—	2	2	no	—
204	C₂×C₄×C₄₁	—	2	1	no	—
205	C₂×C₄×C₄₁	—	4	1	no	—
206	C₂×C₄×C₄₁	—	4	1	no	—
207	C₂×C₄×C₄₁	—	4	1	no	—
208	C₂×C₄×C₄₁	—	4	2	no	—
209	C₂×C₄×C₄₁	—	4	2	no	—
210	C₂×C₄×C₄₁	—	4	2	no	—
211	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
217	C₈×C₄₁	—	2	2	no	—
218	C₈×C₄₁	—	2	2	no	—
219	C₈×C₄₁	—	2	4	no	—
220	C₈×C₄₁	—	4	1	no	—
221	C₈×C₄₁	—	4	2	no	—
222	C₈×C₄₁	—	4	2	no	—
223	C₈×C₄₁	#121	1	1	yes	characteristic
224	C₈×C₄₁	#121	1	1	yes	characteristic
225	C₈×C₄₁	#121	1	1	yes	characteristic
226	C₈×C₄₁	#121	1	1	yes	characteristic
227	#24810	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂²×C₄₁	—	2	2	no	—
229	C₂²×C₄₁	—	4	1	no	—
230	C₂²×C₄₁	—	4	1	no	—
231	C₂²×C₄₁	—	8	1	no	—
232	C₂²×C₄₁	—	8	1	no	—
233	C₂²×C₄₁	#537	1	1	yes	characteristic
234	C₂²×C₄₁	#547	1	1	yes	characteristic
235	C₂²×C₄₁	#548	1	1	yes	characteristic
236	C₄×C₄₁	—	2	2	no	—
237	C₄×C₄₁	—	4	1	no	—
238	C₄×C₄₁	—	8	1	no	—
239	C₄×C₄₁	—	8	2	no	—
240	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
241	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
242	C₄×C₄₁	D₄²	1	1	yes	characteristic
243	C₄×C₄₁	#553	1	1	yes	characteristic
244	#3069	C₂×C₄₁	1	2	yes	—
245	C₂×#473	C₂×C₄₁	1	1	yes	characteristic, complemented
246	C₂×#473	C₂×C₄₁	1	1	yes	characteristic, complemented
247	#2955	C₂×C₄₁	1	1	yes	characteristic
248	#2916	C₂×C₄₁	1	1	yes	characteristic, complemented
249	#2070	C₂×C₄₁	1	2	yes	complemented
250	#2049	C₂×C₄₁	1	2	yes	complemented
251	#1979	C₂×C₄₁	1	1	yes	characteristic, complemented
252	#1953	C₂×C₄₁	1	1	yes	characteristic, complemented
253	#1902	C₂×C₄₁	1	2	yes	complemented
254	#1813	C₂×C₄₁	1	1	yes	characteristic, complemented
255	C₂×C₄₁	—	2	1	no	—
256	C₂×C₄₁	—	2	1	no	—
257	C₂×C₄₁	—	2	1	no	—
258	C₂×C₄₁	—	4	2	no	—
259	C₂×C₄₁	—	8	1	no	—
260	C₂×C₄₁	#2416	1	1	yes	characteristic
261	#575	C₂²×C₄₁	1	1	yes	characteristic
262	C₂×#137	C₂²×C₄₁	1	2	yes	—
263	C₂×#137	C₂²×C₄₁	1	2	yes	—
264	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
265	#568	C₂²×C₄₁	1	2	yes	—
266	C₂×#131	C₂²×C₄₁	1	1	yes	characteristic
267	C₂×#131	C₂²×C₄₁	1	1	yes	characteristic
268	#473	—	2	4	no	—
269	#473	—	2	2	no	—
270	#473	—	2	2	no	—
271	#473	—	2	2	no	—
272	#473	—	2	2	no	—
273	#471	—	2	4	no	—
274	#444	—	2	2	no	—
275	#443	—	2	2	no	—
276	#430	—	2	2	no	—
277	#430	C₂²×C₄₁	1	2	yes	—
278	#430	C₂²×C₄₁	1	1	yes	characteristic
279	#430	C₂²×C₄₁	1	2	yes	—
280	C₂×#108	—	2	2	no	—
281	C₂×#108	C₂²×C₄₁	1	1	yes	characteristic
282	C₂×#108	C₂²×C₄₁	1	1	yes	characteristic
283	C₂×#108	C₂²×C₄₁	1	1	yes	characteristic
284	#421	C₂²×C₄₁	1	1	yes	characteristic
285	#421	C₂²×C₄₁	1	1	yes	characteristic
286	#419	C₂²×C₄₁	1	2	yes	—
287	#413	C₂²×C₄₁	1	2	yes	—
288	C₂×#101	C₂²×C₄₁	1	2	yes	—
289	C₂×#101	C₂²×C₄₁	1	2	yes	—
290	C₂×#101	C₂²×C₄₁	1	2	yes	—
291	#405	C₂²×C₄₁	1	1	yes	characteristic
292	#344	C₂²×C₄₁	1	2	yes	—
293	#338	C₂²×C₄₁	1	2	yes	—
294	C₄₁	#24810	1	1	yes	characteristic, direct product factor, Sylow
295	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
296	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
297	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
298	#137	—	2	1	no	—
299	#137	—	2	4	no	—
300	#137	—	2	4	no	—
301	#137	—	2	4	no	—
302	#137	—	4	2	no	—
303	#137	D₄×C₄₁	1	2	yes	—
304	AGL(1,ℤ/8)	—	2	1	no	—
305	AGL(1,ℤ/8)	D₄×C₄₁	1	2	yes	—
306	#135	—	2	2	no	—
307	C₂×Q₁₆	—	2	2	no	—
308	C₂×Q₁₆	—	2	2	no	—
309	C₂×Q₁₆	—	2	1	no	—
310	C₂×Q₁₆	—	2	1	no	—
311	C₂×Q₁₆	—	2	1	no	—
312	C₂×Q₁₆	—	2	1	no	—
313	C₂×Q₁₆	—	2	1	no	—
314	C₂×Q₁₆	—	2	1	no	—
315	C₂×SD₁₆	—	2	2	no	—
316	C₂×SD₁₆	—	2	2	no	—
317	#131	—	2	1	no	—
318	#131	—	2	1	no	—
319	#131	—	2	4	no	—
320	#131	—	2	1	no	—
321	#131	—	2	1	no	—
322	#131	—	2	1	no	—
323	#131	—	2	1	no	—
324	#131	—	4	2	no	—
325	#131	D₄×C₄₁	1	2	yes	—
326	#131	D₄×C₄₁	1	2	yes	—
327	C₂×M₁₆	—	2	1	no	—
328	C₂×M₁₆	—	2	1	no	—
329	C₂×M₁₆	—	2	4	no	—
330	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
331	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
332	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
333	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
334	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
335	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
336	C₂²×C₈	—	2	1	no	—
337	C₂²×C₈	—	2	1	no	—
338	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
339	#117	C₂³×C₄₁	1	1	yes	characteristic
340	#108	—	2	4	no	—
341	#108	—	2	2	no	—
342	#108	—	2	4	no	—
343	#108	—	2	1	no	—
344	#108	—	2	1	no	—
345	#108	—	2	1	no	—
346	#108	—	2	1	no	—
347	#108	D₄×C₄₁	1	2	yes	—
348	#108	D₄×C₄₁	1	2	yes	—
349	#104	—	2	2	no	—
350	#104	—	2	2	no	—
351	#103	—	4	2	no	—
352	#101	—	2	2	no	—
353	#101	—	2	4	no	—
354	#101	—	2	4	no	—
355	#101	—	2	4	no	—
356	#100	—	2	2	no	—
357	#97	—	2	1	no	—
358	C₄×C₈	—	2	1	no	—
359	#41	—	2	1	no	—
360	#41	—	2	1	no	—
361	#41	—	2	1	no	—
362	#41	—	2	1	no	—
363	#41	—	2	1	no	—
364	#41	—	2	1	no	—
365	#41	C₂×D₄×C₄₁	1	2	yes	—
366	#41	C₂×D₄×C₄₁	1	2	yes	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
374	C₂×Q₈	#41×C₄₁	1	1	yes	characteristic
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
378	C₂×D₄	#41×C₄₁	1	1	yes	characteristic
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
383	Q₁₆	—	2	2	no	—
384	Q₁₆	—	4	4	no	—
385	Q₁₆	—	4	4	no	—
386	Q₁₆	—	4	1	no	—
387	Q₁₆	—	4	1	no	—
388	Q₁₆	—	4	1	no	—
389	Q₁₆	—	4	1	no	—
390	SD₁₆	—	2	2	no	—
391	SD₁₆	—	2	2	no	—
392	SD₁₆	—	4	4	no	—
393	SD₁₆	—	4	4	no	—
394	D₈	—	2	2	no	—
395	M₁₆	—	2	1	no	—
396	M₁₆	—	2	1	no	—
397	M₁₆	—	2	2	no	—
398	M₁₆	—	2	2	no	—
399	M₁₆	—	2	2	no	—
400	M₁₆	—	2	2	no	—
401	M₁₆	—	2	2	no	—
402	M₁₆	—	2	1	no	—
403	M₁₆	—	2	2	no	—
404	M₁₆	—	2	1	no	—
405	M₁₆	—	2	2	no	—
406	M₁₆	—	4	4	no	—
407	M₁₆	—	4	1	no	—
408	M₁₆	—	4	1	no	—
409	M₁₆	C₂×D₄×C₄₁	1	2	yes	—
410	M₁₆	C₂×D₄×C₄₁	1	2	yes	—
411	M₁₆	C₂×D₄×C₄₁	1	4	yes	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	4	4	no	—
421	C₂×C₈	—	4	1	no	—
422	C₂×C₈	—	4	1	no	—
423	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
424	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
425	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
426	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
427	C₂×C₈	#41×C₄₁	1	1	yes	characteristic
428	C₂×C₈	#41×C₄₁	1	1	yes	characteristic
429	C₄⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	2	1	no	—
431	C₄²	—	2	1	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
435	Q₈	—	2	1	no	—
436	Q₈	—	2	1	no	—
437	Q₈	—	2	1	no	—
438	Q₈	—	4	2	no	—
439	Q₈	—	4	2	no	—
440	Q₈	—	4	2	no	—
441	Q₈	—	4	2	no	—
442	Q₈	#121×C₄₁	1	2	yes	—
443	D₄	—	2	2	no	—
444	D₄	—	2	2	no	—
445	D₄	—	2	1	no	—
446	D₄	—	2	1	no	—
447	D₄	—	2	1	no	—
448	D₄	—	4	1	no	—
449	D₄	—	4	1	no	—
450	D₄	#121×C₄₁	1	2	yes	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
464	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
465	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
466	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
467	C₈	—	2	2	no	—
468	C₈	—	2	2	no	—
469	C₈	—	2	4	no	—
470	C₈	—	4	1	no	—
471	C₈	—	4	2	no	—
472	C₈	—	4	2	no	—
473	C₈	#121×C₄₁	1	1	yes	characteristic
474	C₈	#121×C₄₁	1	1	yes	characteristic
475	C₈	#121×C₄₁	1	1	yes	characteristic
476	C₈	#121×C₄₁	1	1	yes	characteristic
477	C₂²	—	2	2	no	—
478	C₂²	—	4	1	no	—
479	C₂²	—	4	1	no	—
480	C₂²	—	8	1	no	—
481	C₂²	—	8	1	no	—
482	C₂²	C₄₁×#537	1	1	yes	characteristic
483	C₂²	C₄₁×#547	1	1	yes	characteristic
484	C₂²	C₄₁×#548	1	1	yes	characteristic
485	C₄	—	2	2	no	—
486	C₄	—	4	1	no	—
487	C₄	—	8	1	no	—
488	C₄	—	8	2	no	—
489	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
490	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
491	C₄	D₄²×C₄₁	1	1	yes	characteristic
492	C₄	C₄₁×#553	1	1	yes	characteristic
493	C₂	—	2	1	no	—
494	C₂	—	2	1	no	—
495	C₂	—	2	1	no	—
496	C₂	—	4	2	no	—
497	C₂	—	8	1	no	—
498	C₂	C₄₁×#2416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₄₁	#2416
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₄₁×#575	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄₁ ◁ C₂²×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#473	C₂	semidirect
3. C₂×C₄₁×#473	C₂	semidirect
5. C₄₁×#2916	C₂	semidirect
6. C₄₁×#2070	C₂	semidirect
7. C₄₁×#2049	C₂	semidirect
8. C₄₁×#1979	C₂	semidirect
9. C₄₁×#1953	C₂	semidirect
10. C₄₁×#1902	C₂	semidirect
11. C₄₁×#1813	C₂	semidirect
227. #24810	C₄₁	direct (N × H)
245. C₂×#473	C₂×C₄₁	semidirect
246. C₂×#473	C₂×C₄₁	semidirect
248. #2916	C₂×C₄₁	semidirect
249. #2070	C₂×C₄₁	semidirect
250. #2049	C₂×C₄₁	semidirect
251. #1979	C₂×C₄₁	semidirect
252. #1953	C₂×C₄₁	semidirect
253. #1902	C₂×C₄₁	semidirect
254. #1813	C₂×C₄₁	semidirect
294. C₄₁	#24810	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#3069	2
C₂×C₄₁×#473	2
C₄₁×#2955	2
C₄₁×#2916	2
C₄₁×#2070	2
C₄₁×#2049	2
C₄₁×#1979	2
C₄₁×#1953	2
C₄₁×#1902	2
C₄₁×#1813	2
#24810	41

Subgroups — C41×#24810 #23801011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24810 #23801011