Subgroups — C₄₁×#24227 #23800428

Order 10496.

1378 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3497	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3036	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₁×#454	C₂	1	2	yes	maximal, complemented
4	C₄₁×#2326	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2039	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2006	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1963	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1801	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1793	C₂	1	2	yes	maximal, complemented
10	C₂×2₋¹⁺⁴×C₄₁	C₂²	1	2	yes	—
11	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	4	yes	—
12	C₄₁×#550	—	2	2	no	—
13	D₄×Q₈×C₄₁	—	2	2	no	—
14	C₄₁×#548	—	2	4	no	—
15	C₄₁×#537	—	2	2	no	—
16	C₄₁×#537	C₂²	1	2	yes	—
17	C₄₁×#532	—	2	2	no	—
18	C₄₁×#532	C₂²	1	2	yes	—
19	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
22	C₄₁×#463	—	2	4	no	—
23	C₄₁×#461	—	2	2	no	—
24	C₄₁×#459	—	2	2	no	—
25	C₄₁×#454	—	2	8	no	—
26	C₄₁×#423	C₂²	1	2	yes	—
27	C₂×#104×C₄₁	C₂²	1	4	yes	—
28	C₂×#104×C₄₁	C₂²	1	4	yes	—
29	C₄₁×#417	C₂²	1	4	yes	—
30	C₂×#101×C₄₁	C₂²	1	2	yes	—
31	C₄₁×#391	C₂²	1	1	yes	characteristic
32	C₄₁×#390	C₂²	1	1	yes	characteristic
33	C₄₁×#388	—	2	2	no	—
34	C₄₁×#385	—	2	2	no	—
35	C₄₁×#384	C₂²	1	1	yes	characteristic
36	C₄₁×#376	C₂²	1	1	yes	characteristic
37	C₄₁×#343	C₂²	1	2	yes	—
38	2₋¹⁺⁴×C₄₁	—	2	4	no	—
39	2₋¹⁺⁴×C₄₁	—	2	4	no	—
40	2₋¹⁺⁴×C₄₁	—	4	4	no	—
41	C₂×#41×C₄₁	—	2	4	no	—
42	C₂×#41×C₄₁	—	2	4	no	—
43	C₂×#41×C₄₁	C₂³	1	4	yes	—
44	C₂²×Q₈×C₄₁	—	2	4	no	—
45	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₄₁	—	2	1	no	—
48	AGL(1,ℤ/8)×C₄₁	—	2	8	no	—
49	AGL(1,ℤ/8)×C₄₁	—	4	4	no	—
50	C₂×SD₁₆×C₄₁	—	2	4	no	—
51	C₂×D₈×C₄₁	—	2	4	no	—
52	C₂×M₁₆×C₄₁	C₂³	1	4	yes	—
53	C₄⋊Q₈×C₄₁	—	2	2	no	—
54	C₄⋊Q₈×C₄₁	D₄	1	2	yes	—
55	#127×C₄₁	—	2	2	no	—
56	#127×C₄₁	D₄	1	2	yes	—
57	#124×C₄₁	—	2	4	no	—
58	#124×C₄₁	—	2	2	no	—
59	#124×C₄₁	D₄	1	4	yes	—
60	#124×C₄₁	D₄	1	4	yes	complemented
61	C₂²⋊Q₈×C₄₁	—	2	8	no	—
62	C₂²⋊Q₈×C₄₁	—	2	4	no	—
63	#121×C₄₁	—	2	8	no	—
64	#121×C₄₁	—	2	4	no	—
65	#121×C₄₁	—	2	2	no	—
66	#121×C₄₁	—	2	4	no	—
67	#121×C₄₁	—	2	2	no	—
68	C₄×Q₈×C₄₁	—	2	2	no	—
69	C₄×Q₈×C₄₁	—	2	2	no	—
70	C₄×D₄×C₄₁	—	2	4	no	—
71	C₄×D₄×C₄₁	—	2	4	no	—
72	C₄×D₄×C₄₁	—	2	2	no	—
73	C₄×D₄×C₄₁	—	2	2	no	—
74	C₄×D₄×C₄₁	—	2	2	no	—
75	C₄×D₄×C₄₁	—	2	2	no	—
76	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
77	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
78	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
80	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
83	C₂×C₄²×C₄₁	D₄	1	2	yes	—
84	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₄₁	—	2	2	no	—
88	C₄⋊C₈×C₄₁	—	2	2	no	—
89	#104×C₄₁	—	2	8	no	—
90	#104×C₄₁	—	4	4	no	—
91	#103×C₄₁	—	2	4	no	—
92	#102×C₄₁	—	2	4	no	—
93	#101×C₄₁	—	2	4	no	—
94	#95×C₄₁	—	2	1	no	—
95	#95×C₄₁	—	2	1	no	—
96	#95×C₄₁	—	2	2	no	—
97	C₂⁴×C₄₁	—	2	1	no	—
98	#41×C₄₁	—	2	4	no	—
99	#41×C₄₁	—	2	4	no	—
100	#41×C₄₁	—	2	4	no	—
101	#41×C₄₁	—	2	4	no	—
102	#41×C₄₁	—	4	8	no	—
103	#41×C₄₁	—	4	8	no	—
104	#41×C₄₁	—	4	8	no	—
105	#41×C₄₁	—	4	8	no	—
106	C₂×Q₈×C₄₁	—	2	4	no	—
107	C₂×Q₈×C₄₁	—	2	2	no	—
108	C₂×Q₈×C₄₁	—	2	2	no	—
109	C₂×Q₈×C₄₁	—	4	8	no	—
110	C₂×Q₈×C₄₁	—	4	8	no	—
111	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
112	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
113	C₂×Q₈×C₄₁	#41	1	2	yes	—
114	C₂×D₄×C₄₁	—	2	4	no	—
115	C₂×D₄×C₄₁	—	2	4	no	—
116	C₂×D₄×C₄₁	—	2	4	no	—
117	C₂×D₄×C₄₁	—	2	2	no	—
118	C₂×D₄×C₄₁	—	2	2	no	—
119	C₂×D₄×C₄₁	—	2	2	no	—
120	C₂×D₄×C₄₁	—	2	1	no	—
121	C₂×D₄×C₄₁	—	2	2	no	—
122	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
123	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₄₁	—	2	8	no	—
125	C₂²×C₄×C₄₁	—	2	1	no	—
126	C₂²×C₄×C₄₁	—	2	4	no	—
127	C₂²×C₄×C₄₁	—	2	1	no	—
128	C₂²×C₄×C₄₁	—	2	1	no	—
129	C₂²×C₄×C₄₁	—	4	2	no	—
130	C₂²×C₄×C₄₁	—	8	2	no	—
131	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
136	SD₁₆×C₄₁	—	4	8	no	—
137	D₈×C₄₁	—	4	8	no	—
138	M₁₆×C₄₁	—	2	4	no	—
139	M₁₆×C₄₁	—	2	4	no	—
140	C₂×C₈×C₄₁	—	2	4	no	—
141	C₄⋊C₄×C₄₁	—	2	4	no	—
142	C₄⋊C₄×C₄₁	—	2	4	no	—
143	C₄⋊C₄×C₄₁	—	2	2	no	—
144	C₄⋊C₄×C₄₁	—	2	2	no	—
145	C₄⋊C₄×C₄₁	—	2	2	no	—
146	C₄⋊C₄×C₄₁	—	2	2	no	—
147	C₄⋊C₄×C₄₁	—	8	2	no	—
148	C₂²⋊C₄×C₄₁	—	2	8	no	—
149	C₂²⋊C₄×C₄₁	—	2	4	no	—
150	C₂²⋊C₄×C₄₁	—	2	4	no	—
151	C₂²⋊C₄×C₄₁	—	2	8	no	—
152	C₂²⋊C₄×C₄₁	—	4	1	no	—
153	C₂²⋊C₄×C₄₁	—	4	1	no	—
154	C₂²⋊C₄×C₄₁	—	8	2	no	—
155	C₄²×C₄₁	—	2	2	no	—
156	C₄²×C₄₁	—	2	2	no	—
157	C₄²×C₄₁	—	2	1	no	—
158	C₄²×C₄₁	—	2	2	no	—
159	C₄²×C₄₁	C₂×D₄	1	2	yes	—
160	C₄²×C₄₁	C₂×D₄	1	2	yes	—
161	C₄²×C₄₁	C₂×D₄	1	2	yes	—
162	C₂³×C₄₁	—	2	4	no	—
163	C₂³×C₄₁	—	2	2	no	—
164	C₂³×C₄₁	—	4	2	no	—
165	C₂³×C₄₁	—	4	2	no	—
166	C₂³×C₄₁	—	4	1	no	—
167	C₂³×C₄₁	—	4	1	no	—
168	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
169	Q₈×C₄₁	—	2	4	no	—
170	Q₈×C₄₁	—	2	4	no	—
171	Q₈×C₄₁	—	2	4	no	—
172	Q₈×C₄₁	—	2	4	no	—
173	Q₈×C₄₁	—	4	8	no	—
174	D₄×C₄₁	—	2	4	no	—
175	D₄×C₄₁	—	2	4	no	—
176	D₄×C₄₁	—	2	4	no	—
177	D₄×C₄₁	—	4	4	no	—
178	D₄×C₄₁	—	4	8	no	—
179	D₄×C₄₁	—	4	4	no	—
180	D₄×C₄₁	—	4	4	no	—
181	D₄×C₄₁	—	4	2	no	—
182	D₄×C₄₁	—	8	2	no	—
183	D₄×C₄₁	—	8	4	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	4	no	—
188	C₂×C₄×C₄₁	—	2	2	no	—
189	C₂×C₄×C₄₁	—	4	1	no	—
190	C₂×C₄×C₄₁	—	4	1	no	—
191	C₂×C₄×C₄₁	—	4	16	no	—
192	C₂×C₄×C₄₁	—	4	1	no	—
193	C₂×C₄×C₄₁	—	4	1	no	—
194	C₂×C₄×C₄₁	—	4	4	no	—
195	C₂×C₄×C₄₁	—	4	4	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	1	no	—
201	C₂×C₄×C₄₁	—	4	1	no	—
202	C₂×C₄×C₄₁	—	8	4	no	—
203	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
204	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
205	C₂×C₄×C₄₁	#120	1	2	yes	—
206	C₂×C₄×C₄₁	#121	1	4	yes	—
207	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
209	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
211	C₈×C₄₁	—	4	4	no	—
212	#24227	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂²×C₄₁	—	2	1	no	—
214	C₂²×C₄₁	—	2	1	no	—
215	C₂²×C₄₁	—	4	4	no	—
216	C₂²×C₄₁	—	4	4	no	—
217	C₂²×C₄₁	—	4	2	no	—
218	C₂²×C₄₁	—	4	4	no	—
219	C₂²×C₄₁	—	4	4	no	—
220	C₂²×C₄₁	—	8	2	no	—
221	C₂²×C₄₁	—	8	1	no	—
222	C₂²×C₄₁	—	8	1	no	—
223	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
224	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
225	C₂²×C₄₁	#535	1	1	yes	characteristic
226	C₄×C₄₁	—	2	4	no	—
227	C₄×C₄₁	—	2	1	no	—
228	C₄×C₄₁	—	2	1	no	—
229	C₄×C₄₁	—	2	2	no	—
230	C₄×C₄₁	—	4	2	no	—
231	C₄×C₄₁	—	4	4	no	—
232	C₄×C₄₁	—	4	2	no	—
233	C₄×C₄₁	—	8	1	no	—
234	C₄×C₄₁	—	8	1	no	—
235	C₄×C₄₁	D₄²	1	2	yes	—
236	C₄×C₄₁	#546	1	2	yes	—
237	#3497	C₂×C₄₁	1	1	yes	characteristic, complemented
238	#3036	C₂×C₄₁	1	2	yes	complemented
239	C₂×#454	C₂×C₄₁	1	2	yes	complemented
240	#2326	C₂×C₄₁	1	1	yes	characteristic, complemented
241	#2039	C₂×C₄₁	1	2	yes	complemented
242	#2006	C₂×C₄₁	1	2	yes	complemented
243	#1963	C₂×C₄₁	1	2	yes	complemented
244	#1801	C₂×C₄₁	1	1	yes	characteristic, complemented
245	#1793	C₂×C₄₁	1	2	yes	complemented
246	C₂×C₄₁	—	2	1	no	—
247	C₂×C₄₁	—	2	1	no	—
248	C₂×C₄₁	—	8	4	no	—
249	C₂×C₄₁	—	8	2	no	—
250	C₂×C₄₁	#2408	1	1	yes	characteristic
251	C₂×C₄₁	#3020	1	1	yes	characteristic
252	C₂×C₄₁	#3021	1	1	yes	characteristic
253	C₂×2₋¹⁺⁴	C₂²×C₄₁	1	2	yes	—
254	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	4	yes	—
255	#550	—	2	2	no	—
256	D₄×Q₈	—	2	2	no	—
257	#548	—	2	4	no	—
258	#537	—	2	2	no	—
259	#537	C₂²×C₄₁	1	2	yes	—
260	#532	—	2	2	no	—
261	#532	C₂²×C₄₁	1	2	yes	—
262	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
263	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
264	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
265	#463	—	2	4	no	—
266	#461	—	2	2	no	—
267	#459	—	2	2	no	—
268	#454	—	2	8	no	—
269	#423	C₂²×C₄₁	1	2	yes	—
270	C₂×#104	C₂²×C₄₁	1	4	yes	—
271	C₂×#104	C₂²×C₄₁	1	4	yes	—
272	#417	C₂²×C₄₁	1	4	yes	—
273	C₂×#101	C₂²×C₄₁	1	2	yes	—
274	#391	C₂²×C₄₁	1	1	yes	characteristic
275	#390	C₂²×C₄₁	1	1	yes	characteristic
276	#388	—	2	2	no	—
277	#385	—	2	2	no	—
278	#384	C₂²×C₄₁	1	1	yes	characteristic
279	#376	C₂²×C₄₁	1	1	yes	characteristic
280	#343	C₂²×C₄₁	1	2	yes	—
281	C₄₁	#24227	1	1	yes	characteristic, direct product factor, Sylow
282	2₋¹⁺⁴	—	2	4	no	—
283	2₋¹⁺⁴	—	2	4	no	—
284	2₋¹⁺⁴	—	4	4	no	—
285	C₂×#41	—	2	4	no	—
286	C₂×#41	—	2	4	no	—
287	C₂×#41	C₂³×C₄₁	1	4	yes	—
288	C₂²×Q₈	—	2	4	no	—
289	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
290	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
291	C₂³×C₄	—	2	1	no	—
292	AGL(1,ℤ/8)	—	2	8	no	—
293	AGL(1,ℤ/8)	—	4	4	no	—
294	C₂×SD₁₆	—	2	4	no	—
295	C₂×D₈	—	2	4	no	—
296	C₂×M₁₆	C₂³×C₄₁	1	4	yes	—
297	C₄⋊Q₈	—	2	2	no	—
298	C₄⋊Q₈	D₄×C₄₁	1	2	yes	—
299	#127	—	2	2	no	—
300	#127	D₄×C₄₁	1	2	yes	—
301	#124	—	2	4	no	—
302	#124	—	2	2	no	—
303	#124	D₄×C₄₁	1	4	yes	—
304	#124	D₄×C₄₁	1	4	yes	complemented
305	C₂²⋊Q₈	—	2	8	no	—
306	C₂²⋊Q₈	—	2	4	no	—
307	#121	—	2	8	no	—
308	#121	—	2	4	no	—
309	#121	—	2	2	no	—
310	#121	—	2	4	no	—
311	#121	—	2	2	no	—
312	C₄×Q₈	—	2	2	no	—
313	C₄×Q₈	—	2	2	no	—
314	C₄×D₄	—	2	4	no	—
315	C₄×D₄	—	2	4	no	—
316	C₄×D₄	—	2	2	no	—
317	C₄×D₄	—	2	2	no	—
318	C₄×D₄	—	2	2	no	—
319	C₄×D₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₄²	D₄×C₄₁	1	2	yes	—
328	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
330	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
331	C₄⋊C₈	—	2	2	no	—
332	C₄⋊C₈	—	2	2	no	—
333	#104	—	2	8	no	—
334	#104	—	4	4	no	—
335	#103	—	2	4	no	—
336	#102	—	2	4	no	—
337	#101	—	2	4	no	—
338	#95	—	2	1	no	—
339	#95	—	2	1	no	—
340	#95	—	2	2	no	—
341	C₂⁴	—	2	1	no	—
342	#41	—	2	4	no	—
343	#41	—	2	4	no	—
344	#41	—	2	4	no	—
345	#41	—	2	4	no	—
346	#41	—	4	8	no	—
347	#41	—	4	8	no	—
348	#41	—	4	8	no	—
349	#41	—	4	8	no	—
350	C₂×Q₈	—	2	4	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	4	8	no	—
354	C₂×Q₈	—	4	8	no	—
355	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
356	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
357	C₂×Q₈	#41×C₄₁	1	2	yes	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
367	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
368	C₂²×C₄	—	2	8	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	8	2	no	—
375	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
376	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
377	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
379	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
380	SD₁₆	—	4	8	no	—
381	D₈	—	4	8	no	—
382	M₁₆	—	2	4	no	—
383	M₁₆	—	2	4	no	—
384	C₂×C₈	—	2	4	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	8	2	no	—
392	C₂²⋊C₄	—	2	8	no	—
393	C₂²⋊C₄	—	2	4	no	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	2	8	no	—
396	C₂²⋊C₄	—	4	1	no	—
397	C₂²⋊C₄	—	4	1	no	—
398	C₂²⋊C₄	—	8	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	1	no	—
402	C₄²	—	2	2	no	—
403	C₄²	C₂×D₄×C₄₁	1	2	yes	—
404	C₄²	C₂×D₄×C₄₁	1	2	yes	—
405	C₄²	C₂×D₄×C₄₁	1	2	yes	—
406	C₂³	—	2	4	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	1	no	—
411	C₂³	—	4	1	no	—
412	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
413	Q₈	—	2	4	no	—
414	Q₈	—	2	4	no	—
415	Q₈	—	2	4	no	—
416	Q₈	—	2	4	no	—
417	Q₈	—	4	8	no	—
418	D₄	—	2	4	no	—
419	D₄	—	2	4	no	—
420	D₄	—	2	4	no	—
421	D₄	—	4	8	no	—
422	D₄	—	4	4	no	—
423	D₄	—	4	4	no	—
424	D₄	—	4	4	no	—
425	D₄	—	4	2	no	—
426	D₄	—	8	2	no	—
427	D₄	—	8	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	16	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	4	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	8	4	no	—
447	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
448	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
449	C₂×C₄	#120×C₄₁	1	2	yes	—
450	C₂×C₄	#121×C₄₁	1	4	yes	—
451	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
452	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
453	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
454	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
455	C₈	—	4	4	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	8	2	no	—
464	C₂²	—	8	1	no	—
465	C₂²	—	8	1	no	—
466	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
467	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
468	C₂²	C₄₁×#535	1	1	yes	characteristic
469	C₄	—	2	4	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	4	no	—
475	C₄	—	4	2	no	—
476	C₄	—	8	1	no	—
477	C₄	—	8	1	no	—
478	C₄	D₄²×C₄₁	1	2	yes	—
479	C₄	C₄₁×#546	1	2	yes	—
480	C₂	—	2	1	no	—
481	C₂	—	2	1	no	—
482	C₂	—	8	2	no	—
483	C₂	—	8	4	no	—
484	C₂	C₄₁×#2408	1	1	yes	characteristic
485	C₂	C₄₁×#3020	1	1	yes	characteristic
486	C₂	C₄₁×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3497	C₂	semidirect
2. C₄₁×#3036	C₂	semidirect
3. C₂×C₄₁×#454	C₂	semidirect
4. C₄₁×#2326	C₂	semidirect
5. C₄₁×#2039	C₂	semidirect
6. C₄₁×#2006	C₂	semidirect
7. C₄₁×#1963	C₂	semidirect
8. C₄₁×#1801	C₂	semidirect
9. C₄₁×#1793	C₂	semidirect
60. #124×C₄₁	D₄	semidirect
212. #24227	C₄₁	direct (N × H)
237. #3497	C₂×C₄₁	semidirect
238. #3036	C₂×C₄₁	semidirect
239. C₂×#454	C₂×C₄₁	semidirect
240. #2326	C₂×C₄₁	semidirect
241. #2039	C₂×C₄₁	semidirect
242. #2006	C₂×C₄₁	semidirect
243. #1963	C₂×C₄₁	semidirect
244. #1801	C₂×C₄₁	semidirect
245. #1793	C₂×C₄₁	semidirect
281. C₄₁	#24227	direct (N × H)
304. #124	D₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3497	2
C₄₁×#3036	2
C₂×C₄₁×#454	2
C₄₁×#2326	2
C₄₁×#2039	2
C₄₁×#2006	2
C₄₁×#1963	2
C₄₁×#1801	2
C₄₁×#1793	2
#24227	41

Subgroups — C41×#24227 #23800428

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24227 #23800428