Subgroups — C₄₁×#25676 #23801877

Order 10496.

1318 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#490	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2851	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2034	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2033	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1961	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1864	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1862	C₂	1	2	yes	maximal, complemented
11	C₄₁×#1749	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₁	—	2	1	no	—
13	C₄₁×#532	—	2	4	no	—
14	C₄₁×#532	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#124×C₄₁	—	2	1	no	—
19	C₂×#121×C₄₁	—	2	1	no	—
20	C₂×#121×C₄₁	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₄₁	—	2	1	no	—
22	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
23	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
24	C₄₁×#501	—	2	4	no	—
25	C₄₁×#490	—	2	4	no	—
26	C₂×#107×C₄₁	C₂²	1	2	yes	—
27	C₂×#106×C₄₁	C₂²	1	2	yes	—
28	C₂×#102×C₄₁	C₂²	1	2	yes	—
29	C₂×#102×C₄₁	C₂²	1	2	yes	—
30	C₂×#102×C₄₁	C₂²	1	2	yes	—
31	C₂×#102×C₄₁	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
33	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
34	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
35	C₄₁×#389	C₂²	1	1	yes	characteristic
36	C₄₁×#389	C₂²	1	1	yes	characteristic
37	C₄₁×#387	—	2	1	no	—
38	C₄₁×#387	—	2	1	no	—
39	C₄₁×#385	—	2	1	no	—
40	C₄₁×#385	—	2	1	no	—
41	C₄₁×#382	C₂²	1	1	yes	characteristic
42	C₄₁×#380	C₂²	1	1	yes	characteristic
43	C₄₁×#380	C₂²	1	1	yes	characteristic
44	C₄₁×#340	C₂²	1	2	yes	—
45	C₄₁×#340	C₂²	1	2	yes	—
46	C₄₁×#336	C₂²	1	2	yes	—
47	C₂×#41×C₄₁	—	2	8	no	—
48	C₂×#41×C₄₁	—	4	4	no	—
49	C₂×#41×C₄₁	—	4	4	no	—
50	C₂²×Q₈×C₄₁	—	2	1	no	—
51	C₂²×D₄×C₄₁	—	2	2	no	—
52	C₂²×D₄×C₄₁	—	2	1	no	—
53	C₂²×D₄×C₄₁	—	2	1	no	—
54	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
55	C₂³×C₄×C₄₁	—	2	2	no	—
56	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
60	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
61	C₄⋊Q₈×C₄₁	—	2	2	no	—
62	C₄⋊Q₈×C₄₁	D₄	1	4	yes	—
63	#127×C₄₁	—	2	2	no	—
64	#127×C₄₁	D₄	1	4	yes	—
65	#125×C₄₁	—	2	2	no	—
66	#125×C₄₁	—	2	2	no	—
67	#124×C₄₁	—	2	8	no	—
68	#121×C₄₁	—	2	8	no	—
69	#121×C₄₁	—	2	4	no	—
70	#121×C₄₁	—	2	4	no	—
71	C₄×D₄×C₄₁	—	2	8	no	—
72	C₄×D₄×C₄₁	—	2	4	no	—
73	C₄×D₄×C₄₁	—	2	4	no	—
74	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
76	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
78	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
79	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
84	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
88	C₂×C₄²×C₄₁	—	2	2	no	—
89	C₂×C₄²×C₄₁	—	2	2	no	—
90	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
94	#107×C₄₁	—	2	4	no	—
95	#106×C₄₁	—	2	4	no	—
96	#102×C₄₁	—	2	4	no	—
97	#102×C₄₁	—	2	4	no	—
98	#102×C₄₁	—	2	4	no	—
99	#102×C₄₁	—	2	4	no	—
100	C₂²⋊C₈×C₄₁	—	2	4	no	—
101	#97×C₄₁	—	2	2	no	—
102	#97×C₄₁	—	2	2	no	—
103	#95×C₄₁	—	2	1	no	—
104	#95×C₄₁	—	2	1	no	—
105	#95×C₄₁	—	2	1	no	—
106	#95×C₄₁	—	2	1	no	—
107	#95×C₄₁	—	2	1	no	—
108	#95×C₄₁	—	2	1	no	—
109	C₂⁴×C₄₁	—	2	2	no	—
110	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
111	#41×C₄₁	—	4	32	no	—
112	C₂×Q₈×C₄₁	—	2	4	no	—
113	C₂×Q₈×C₄₁	—	4	2	no	—
114	C₂×Q₈×C₄₁	—	4	2	no	—
115	C₂×D₄×C₄₁	—	2	8	no	—
116	C₂×D₄×C₄₁	—	2	4	no	—
117	C₂×D₄×C₄₁	—	2	4	no	—
118	C₂×D₄×C₄₁	—	2	2	no	—
119	C₂×D₄×C₄₁	—	2	2	no	—
120	C₂×D₄×C₄₁	—	2	2	no	—
121	C₂×D₄×C₄₁	—	2	2	no	—
122	C₂×D₄×C₄₁	—	2	2	no	—
123	C₂×D₄×C₄₁	—	4	2	no	—
124	C₂×D₄×C₄₁	—	4	2	no	—
125	C₂×D₄×C₄₁	—	4	2	no	—
126	C₂×D₄×C₄₁	—	4	2	no	—
127	C₂×D₄×C₄₁	—	4	4	no	—
128	C₂×D₄×C₄₁	—	4	4	no	—
129	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₄₁	—	2	2	no	—
131	C₂²×C₄×C₄₁	—	2	2	no	—
132	C₂²×C₄×C₄₁	—	2	2	no	—
133	C₂²×C₄×C₄₁	—	2	8	no	—
134	C₂²×C₄×C₄₁	—	2	2	no	—
135	C₂²×C₄×C₄₁	—	2	2	no	—
136	C₂²×C₄×C₄₁	—	2	1	no	—
137	C₂²×C₄×C₄₁	—	2	1	no	—
138	C₂²×C₄×C₄₁	—	2	2	no	—
139	C₂²×C₄×C₄₁	—	2	2	no	—
140	C₂²×C₄×C₄₁	—	2	1	no	—
141	C₂²×C₄×C₄₁	—	2	1	no	—
142	C₂²×C₄×C₄₁	—	2	1	no	—
143	C₂²×C₄×C₄₁	—	2	1	no	—
144	C₂²×C₄×C₄₁	—	4	1	no	—
145	C₂²×C₄×C₄₁	—	4	1	no	—
146	C₂²×C₄×C₄₁	—	4	4	no	—
147	C₂²×C₄×C₄₁	—	4	4	no	—
148	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
154	C₂×C₈×C₄₁	—	2	2	no	—
155	C₂×C₈×C₄₁	—	2	2	no	—
156	C₂×C₈×C₄₁	—	2	2	no	—
157	C₂×C₈×C₄₁	—	2	2	no	—
158	C₂×C₈×C₄₁	—	2	2	no	—
159	C₂×C₈×C₄₁	#41	1	4	yes	complemented
160	C₄⋊C₄×C₄₁	—	2	4	no	—
161	C₄⋊C₄×C₄₁	—	2	2	no	—
162	C₄⋊C₄×C₄₁	—	2	1	no	—
163	C₄⋊C₄×C₄₁	—	2	1	no	—
164	C₄⋊C₄×C₄₁	—	2	1	no	—
165	C₄⋊C₄×C₄₁	—	2	1	no	—
166	C₄⋊C₄×C₄₁	—	2	2	no	—
167	C₄⋊C₄×C₄₁	—	2	2	no	—
168	C₄⋊C₄×C₄₁	—	4	2	no	—
169	C₄⋊C₄×C₄₁	—	4	2	no	—
170	C₄⋊C₄×C₄₁	—	4	2	no	—
171	C₄⋊C₄×C₄₁	—	4	2	no	—
172	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
173	C₂²⋊C₄×C₄₁	—	2	8	no	—
174	C₂²⋊C₄×C₄₁	—	2	8	no	—
175	C₂²⋊C₄×C₄₁	—	4	2	no	—
176	C₂²⋊C₄×C₄₁	—	4	2	no	—
177	C₄²×C₄₁	—	2	2	no	—
178	C₄²×C₄₁	—	2	2	no	—
179	C₄²×C₄₁	—	2	1	no	—
180	C₄²×C₄₁	—	2	1	no	—
181	C₄²×C₄₁	C₂×D₄	1	2	yes	—
182	C₄²×C₄₁	C₂×D₄	1	2	yes	—
183	C₂³×C₄₁	—	2	1	no	—
184	C₂³×C₄₁	—	2	1	no	—
185	C₂³×C₄₁	—	2	1	no	—
186	C₂³×C₄₁	—	2	1	no	—
187	C₂³×C₄₁	—	2	1	no	—
188	C₂³×C₄₁	—	2	1	no	—
189	C₂³×C₄₁	—	2	4	no	—
190	C₂³×C₄₁	—	4	2	no	—
191	C₂³×C₄₁	—	4	2	no	—
192	C₂³×C₄₁	—	4	2	no	—
193	C₂³×C₄₁	—	4	2	no	—
194	C₂³×C₄₁	—	4	2	no	—
195	C₂³×C₄₁	—	4	2	no	—
196	C₂³×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
197	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
198	Q₈×C₄₁	—	4	8	no	—
199	D₄×C₄₁	—	2	4	no	—
200	D₄×C₄₁	—	2	4	no	—
201	D₄×C₄₁	—	4	8	no	—
202	D₄×C₄₁	—	4	8	no	—
203	D₄×C₄₁	—	4	16	no	—
204	D₄×C₄₁	—	4	2	no	—
205	D₄×C₄₁	—	4	2	no	—
206	C₂×C₄×C₄₁	—	2	8	no	—
207	C₂×C₄×C₄₁	—	2	1	no	—
208	C₂×C₄×C₄₁	—	2	1	no	—
209	C₂×C₄×C₄₁	—	2	1	no	—
210	C₂×C₄×C₄₁	—	2	1	no	—
211	C₂×C₄×C₄₁	—	2	1	no	—
212	C₂×C₄×C₄₁	—	2	1	no	—
213	C₂×C₄×C₄₁	—	2	1	no	—
214	C₂×C₄×C₄₁	—	2	1	no	—
215	C₂×C₄×C₄₁	—	2	4	no	—
216	C₂×C₄×C₄₁	—	2	1	no	—
217	C₂×C₄×C₄₁	—	2	1	no	—
218	C₂×C₄×C₄₁	—	2	1	no	—
219	C₂×C₄×C₄₁	—	2	1	no	—
220	C₂×C₄×C₄₁	—	4	4	no	—
221	C₂×C₄×C₄₁	—	4	16	no	—
222	C₂×C₄×C₄₁	—	4	2	no	—
223	C₂×C₄×C₄₁	—	4	2	no	—
224	C₂×C₄×C₄₁	—	4	2	no	—
225	C₂×C₄×C₄₁	—	4	2	no	—
226	C₂×C₄×C₄₁	—	4	1	no	—
227	C₂×C₄×C₄₁	—	4	1	no	—
228	C₂×C₄×C₄₁	—	4	1	no	—
229	C₂×C₄×C₄₁	—	4	1	no	—
230	C₂×C₄×C₄₁	—	4	1	no	—
231	C₂×C₄×C₄₁	—	4	1	no	—
232	C₂×C₄×C₄₁	—	4	1	no	—
233	C₂×C₄×C₄₁	—	4	1	no	—
234	C₂×C₄×C₄₁	—	4	1	no	—
235	C₂×C₄×C₄₁	—	4	1	no	—
236	C₂×C₄×C₄₁	—	4	1	no	—
237	C₂×C₄×C₄₁	—	4	1	no	—
238	C₂×C₄×C₄₁	#120	1	2	yes	—
239	C₂×C₄×C₄₁	#120	1	2	yes	—
240	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
241	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
244	C₂×C₄×C₄₁	2₋¹⁺⁴	1	2	yes	—
245	C₈×C₄₁	—	2	4	no	—
246	C₈×C₄₁	—	4	2	no	—
247	#25676	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
248	C₂²×C₄₁	—	2	2	no	—
249	C₂²×C₄₁	—	2	2	no	—
250	C₂²×C₄₁	—	2	2	no	—
251	C₂²×C₄₁	—	4	1	no	—
252	C₂²×C₄₁	—	4	1	no	—
253	C₂²×C₄₁	—	4	1	no	—
254	C₂²×C₄₁	—	4	1	no	—
255	C₂²×C₄₁	—	4	4	no	—
256	C₂²×C₄₁	—	4	4	no	—
257	C₂²×C₄₁	—	4	4	no	—
258	C₂²×C₄₁	—	8	2	no	—
259	C₂²×C₄₁	—	8	2	no	—
260	C₂²×C₄₁	—	8	2	no	—
261	C₂²×C₄₁	—	8	2	no	—
262	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
263	C₂²×C₄₁	#532	1	1	yes	characteristic
264	C₂²×C₄₁	#536	1	1	yes	characteristic
265	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
266	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
267	C₂²×C₄₁	#575	1	1	yes	characteristic
268	C₂²×C₄₁	#575	1	1	yes	characteristic
269	C₄×C₄₁	—	2	2	no	—
270	C₄×C₄₁	—	2	2	no	—
271	C₄×C₄₁	—	2	2	no	—
272	C₄×C₄₁	—	4	1	no	—
273	C₄×C₄₁	—	4	4	no	—
274	C₄×C₄₁	—	4	1	no	—
275	C₄×C₄₁	—	8	1	no	—
276	C₄×C₄₁	—	8	1	no	—
277	C₄×C₄₁	—	8	1	no	—
278	C₄×C₄₁	—	8	1	no	—
279	C₄×C₄₁	#547	1	2	yes	—
280	C₄×C₄₁	#548	1	2	yes	—
281	C₂×#532	C₂×C₄₁	1	1	yes	characteristic
282	C₂×#501	C₂×C₄₁	1	1	yes	characteristic, complemented
283	C₂×#490	C₂×C₄₁	1	1	yes	characteristic, complemented
284	#2851	C₂×C₄₁	1	1	yes	characteristic, complemented
285	#2034	C₂×C₄₁	1	2	yes	complemented
286	#2033	C₂×C₄₁	1	2	yes	complemented
287	#1993	C₂×C₄₁	1	1	yes	characteristic, complemented
288	#1961	C₂×C₄₁	1	1	yes	characteristic, complemented
289	#1864	C₂×C₄₁	1	2	yes	complemented
290	#1862	C₂×C₄₁	1	2	yes	complemented
291	#1749	C₂×C₄₁	1	1	yes	characteristic, complemented
292	C₂×C₄₁	—	4	2	no	—
293	C₂×C₄₁	—	8	4	no	—
294	C₂×C₄₁	#2432	1	1	yes	characteristic
295	C₂×C₄₁	#3003	1	1	yes	characteristic
296	C₂×C₄₁	#3005	1	1	yes	characteristic
297	C₂×C₄₁	#3171	1	1	yes	characteristic
298	C₂×C₄₁	#3180	1	1	yes	characteristic
299	C₂×C₄₁	#3234	1	1	yes	characteristic
300	C₂×C₄₁	#3235	1	1	yes	characteristic
301	C₂²×#41	—	2	1	no	—
302	#532	—	2	4	no	—
303	#532	—	2	4	no	—
304	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
305	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
306	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic
307	C₂×#124	—	2	1	no	—
308	C₂×#121	—	2	1	no	—
309	C₂×#121	C₂²×C₄₁	1	2	yes	—
310	C₂×C₄×D₄	—	2	1	no	—
311	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
312	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
313	#501	—	2	4	no	—
314	#490	—	2	4	no	—
315	C₂×#107	C₂²×C₄₁	1	2	yes	—
316	C₂×#106	C₂²×C₄₁	1	2	yes	—
317	C₂×#102	C₂²×C₄₁	1	2	yes	—
318	C₂×#102	C₂²×C₄₁	1	2	yes	—
319	C₂×#102	C₂²×C₄₁	1	2	yes	—
320	C₂×#102	C₂²×C₄₁	1	2	yes	—
321	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
322	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
323	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
324	#389	C₂²×C₄₁	1	1	yes	characteristic
325	#389	C₂²×C₄₁	1	1	yes	characteristic
326	#387	—	2	1	no	—
327	#387	—	2	1	no	—
328	#385	—	2	1	no	—
329	#385	—	2	1	no	—
330	#382	C₂²×C₄₁	1	1	yes	characteristic
331	#380	C₂²×C₄₁	1	1	yes	characteristic
332	#380	C₂²×C₄₁	1	1	yes	characteristic
333	#340	C₂²×C₄₁	1	2	yes	—
334	#340	C₂²×C₄₁	1	2	yes	—
335	#336	C₂²×C₄₁	1	2	yes	—
336	C₄₁	#25676	1	1	yes	characteristic, direct product factor, Sylow
337	C₂×#41	—	2	8	no	—
338	C₂×#41	—	4	4	no	—
339	C₂×#41	—	4	4	no	—
340	C₂²×Q₈	—	2	1	no	—
341	C₂²×D₄	—	2	2	no	—
342	C₂²×D₄	—	2	1	no	—
343	C₂²×D₄	—	2	1	no	—
344	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
345	C₂³×C₄	—	2	2	no	—
346	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
347	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
348	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
349	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
350	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
351	C₄⋊Q₈	—	2	2	no	—
352	C₄⋊Q₈	D₄×C₄₁	1	4	yes	—
353	#127	—	2	2	no	—
354	#127	D₄×C₄₁	1	4	yes	—
355	#125	—	2	2	no	—
356	#125	—	2	2	no	—
357	#124	—	2	8	no	—
358	#121	—	2	8	no	—
359	#121	—	2	4	no	—
360	#121	—	2	4	no	—
361	C₄×D₄	—	2	8	no	—
362	C₄×D₄	—	2	4	no	—
363	C₄×D₄	—	2	4	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
374	C₂×C₂²⋊C₄	—	2	2	no	—
375	C₂×C₂²⋊C₄	—	2	2	no	—
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₄²	—	2	2	no	—
379	C₂×C₄²	—	2	2	no	—
380	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
381	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
382	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
383	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
384	#107	—	2	4	no	—
385	#106	—	2	4	no	—
386	#102	—	2	4	no	—
387	#102	—	2	4	no	—
388	#102	—	2	4	no	—
389	#102	—	2	4	no	—
390	C₂²⋊C₈	—	2	4	no	—
391	#97	—	2	2	no	—
392	#97	—	2	2	no	—
393	#95	—	2	1	no	—
394	#95	—	2	1	no	—
395	#95	—	2	1	no	—
396	#95	—	2	1	no	—
397	#95	—	2	1	no	—
398	#95	—	2	1	no	—
399	C₂⁴	—	2	2	no	—
400	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
401	#41	—	4	32	no	—
402	C₂×Q₈	—	2	4	no	—
403	C₂×Q₈	—	4	2	no	—
404	C₂×Q₈	—	4	2	no	—
405	C₂×D₄	—	2	8	no	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	4	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	4	2	no	—
414	C₂×D₄	—	4	2	no	—
415	C₂×D₄	—	4	2	no	—
416	C₂×D₄	—	4	2	no	—
417	C₂×D₄	—	4	4	no	—
418	C₂×D₄	—	4	4	no	—
419	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	8	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	4	1	no	—
435	C₂²×C₄	—	4	1	no	—
436	C₂²×C₄	—	4	4	no	—
437	C₂²×C₄	—	4	4	no	—
438	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
443	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	#41×C₄₁	1	4	yes	complemented
450	C₄⋊C₄	—	2	4	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	4	2	no	—
459	C₄⋊C₄	—	4	2	no	—
460	C₄⋊C₄	—	4	2	no	—
461	C₄⋊C₄	—	4	2	no	—
462	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
463	C₂²⋊C₄	—	2	8	no	—
464	C₂²⋊C₄	—	2	8	no	—
465	C₂²⋊C₄	—	4	2	no	—
466	C₂²⋊C₄	—	4	2	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	C₂×D₄×C₄₁	1	2	yes	—
472	C₄²	C₂×D₄×C₄₁	1	2	yes	—
473	C₂³	—	2	1	no	—
474	C₂³	—	2	1	no	—
475	C₂³	—	2	1	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	2	1	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
487	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
488	Q₈	—	4	8	no	—
489	D₄	—	2	4	no	—
490	D₄	—	2	4	no	—
491	D₄	—	4	8	no	—
492	D₄	—	4	8	no	—
493	D₄	—	4	16	no	—
494	D₄	—	4	2	no	—
495	D₄	—	4	2	no	—
496	C₂×C₄	—	2	8	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	4	16	no	—
511	C₂×C₄	—	4	4	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	#120×C₄₁	1	2	yes	—
529	C₂×C₄	#120×C₄₁	1	2	yes	—
530	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
531	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
532	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
533	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
534	C₂×C₄	2₋¹⁺⁴×C₄₁	1	2	yes	—
535	C₈	—	2	4	no	—
536	C₈	—	4	2	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	4	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	4	4	no	—
547	C₂²	—	8	2	no	—
548	C₂²	—	8	2	no	—
549	C₂²	—	8	2	no	—
550	C₂²	—	8	2	no	—
551	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
552	C₂²	C₄₁×#532	1	1	yes	characteristic
553	C₂²	C₄₁×#536	1	1	yes	characteristic
554	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
555	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
556	C₂²	C₄₁×#575	1	1	yes	characteristic
557	C₂²	C₄₁×#575	1	1	yes	characteristic
558	C₄	—	2	2	no	—
559	C₄	—	2	2	no	—
560	C₄	—	2	2	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	4	no	—
563	C₄	—	4	1	no	—
564	C₄	—	8	1	no	—
565	C₄	—	8	1	no	—
566	C₄	—	8	1	no	—
567	C₄	—	8	1	no	—
568	C₄	C₄₁×#547	1	2	yes	—
569	C₄	C₄₁×#548	1	2	yes	—
570	C₂	—	4	2	no	—
571	C₂	—	8	4	no	—
572	C₂	C₄₁×#2432	1	1	yes	characteristic
573	C₂	C₄₁×#3003	1	1	yes	characteristic
574	C₂	C₄₁×#3005	1	1	yes	characteristic
575	C₂	C₄₁×#3171	1	1	yes	characteristic
576	C₂	C₄₁×#3180	1	1	yes	characteristic
577	C₂	C₄₁×#3234	1	1	yes	characteristic
578	C₂	C₄₁×#3235	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#532	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#501	C₂	semidirect
3. C₂×C₄₁×#490	C₂	semidirect
4. C₄₁×#2851	C₂	semidirect
5. C₄₁×#2034	C₂	semidirect
6. C₄₁×#2033	C₂	semidirect
7. C₄₁×#1993	C₂	semidirect
8. C₄₁×#1961	C₂	semidirect
9. C₄₁×#1864	C₂	semidirect
10. C₄₁×#1862	C₂	semidirect
11. C₄₁×#1749	C₂	semidirect
159. C₂×C₈×C₄₁	#41	semidirect
247. #25676	C₄₁	direct (N × H)
282. C₂×#501	C₂×C₄₁	semidirect
283. C₂×#490	C₂×C₄₁	semidirect
284. #2851	C₂×C₄₁	semidirect
285. #2034	C₂×C₄₁	semidirect
286. #2033	C₂×C₄₁	semidirect
287. #1993	C₂×C₄₁	semidirect
288. #1961	C₂×C₄₁	semidirect
289. #1864	C₂×C₄₁	semidirect
290. #1862	C₂×C₄₁	semidirect
291. #1749	C₂×C₄₁	semidirect
336. C₄₁	#25676	direct (N × H)
449. C₂×C₈	#41×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#532	2
C₂×C₄₁×#501	2
C₂×C₄₁×#490	2
C₄₁×#2851	2
C₄₁×#2034	2
C₄₁×#2033	2
C₄₁×#1993	2
C₄₁×#1961	2
C₄₁×#1864	2
C₄₁×#1862	2
C₄₁×#1749	2
#25676	41

Subgroups — C41×#25676 #23801877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25676 #23801877