Subgroups — C₄₁×#24477 #23800678

Order 10496.

1130 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#483	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#102×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2435	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2344	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2065	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2042	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1983	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1926	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1892	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1850	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1786	C₂	1	1	yes	maximal, characteristic
12	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#124×C₄₁	C₂²	1	2	yes	—
15	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×#117×C₄₁	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
18	C₄₁×#483	—	2	4	no	—
19	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic, complemented
20	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	complemented
22	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic, complemented
23	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic, complemented
24	C₂×#103×C₄₁	C₂²	1	2	yes	complemented
25	C₂×#102×C₄₁	—	2	4	no	—
26	C₂×#102×C₄₁	C₂²	1	2	yes	—
27	C₂×#102×C₄₁	C₂²	1	2	yes	—
28	C₂×#102×C₄₁	C₂²	1	2	yes	—
29	C₂×#102×C₄₁	C₂²	1	2	yes	—
30	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₄₁×#394	—	2	2	no	—
32	C₄₁×#390	C₂²	1	2	yes	—
33	C₄₁×#389	C₂²	1	2	yes	complemented
34	C₄₁×#387	—	2	2	no	—
35	C₄₁×#381	—	2	1	no	—
36	C₄₁×#380	C₂²	1	1	yes	characteristic
37	C₄₁×#379	—	2	1	no	—
38	C₄₁×#379	—	2	1	no	—
39	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	complemented
40	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
41	C₄₁×#340	C₂²	1	2	yes	complemented
42	C₄₁×#336	C₂²	1	2	yes	complemented
43	C₂⁵×C₄₁	—	2	1	no	—
44	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₄₁	—	2	4	no	—
46	C₂²×D₄×C₄₁	—	2	2	no	—
47	C₂²×D₄×C₄₁	—	2	1	no	—
48	C₂²×D₄×C₄₁	—	2	2	no	—
49	C₂²×D₄×C₄₁	—	4	2	no	—
50	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
51	C₂³×C₄×C₄₁	—	2	1	no	—
52	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₄₁	—	2	2	no	—
54	C₂²×C₈×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	#124×C₄₁	—	2	4	no	—
59	#124×C₄₁	—	4	2	no	—
60	C₂²⋊Q₈×C₄₁	—	2	2	no	—
61	C₂²⋊Q₈×C₄₁	—	2	2	no	—
62	#117×C₄₁	—	4	4	no	—
63	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₁	D₄	1	4	yes	—
68	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₄₁	—	2	2	no	—
81	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
82	#106×C₄₁	—	2	2	no	—
83	#106×C₄₁	—	2	2	no	—
84	C₄⋊C₈×C₄₁	—	4	2	no	—
85	#103×C₄₁	—	2	2	no	—
86	#103×C₄₁	—	2	2	no	—
87	#103×C₄₁	—	4	2	no	—
88	#102×C₄₁	—	2	4	no	—
89	#102×C₄₁	—	2	4	no	—
90	#102×C₄₁	—	2	4	no	—
91	#102×C₄₁	—	4	2	no	—
92	C₂²⋊C₈×C₄₁	—	2	2	no	—
93	#95×C₄₁	—	2	2	no	—
94	#95×C₄₁	—	2	1	no	—
95	#95×C₄₁	—	2	2	no	—
96	#95×C₄₁	D₄	1	2	yes	—
97	C₂⁴×C₄₁	—	2	2	no	—
98	C₂⁴×C₄₁	—	4	4	no	—
99	C₂⁴×C₄₁	—	4	2	no	—
100	C₂⁴×C₄₁	—	4	2	no	—
101	C₂⁴×C₄₁	—	4	2	no	—
102	C₂⁴×C₄₁	—	8	2	no	—
103	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
104	C₂×Q₈×C₄₁	—	2	1	no	—
105	C₂×Q₈×C₄₁	—	2	1	no	—
106	C₂×Q₈×C₄₁	—	2	2	no	—
107	C₂×Q₈×C₄₁	—	2	2	no	—
108	C₂×D₄×C₄₁	—	2	8	no	—
109	C₂×D₄×C₄₁	—	2	2	no	—
110	C₂×D₄×C₄₁	—	2	2	no	—
111	C₂×D₄×C₄₁	—	2	2	no	—
112	C₂×D₄×C₄₁	—	2	2	no	—
113	C₂×D₄×C₄₁	—	2	2	no	—
114	C₂×D₄×C₄₁	—	4	8	no	—
115	C₂×D₄×C₄₁	—	4	4	no	—
116	C₂×D₄×C₄₁	—	4	4	no	—
117	C₂×D₄×C₄₁	—	4	2	no	—
118	C₂×D₄×C₄₁	#41	1	4	yes	—
119	C₂²×C₄×C₄₁	—	2	2	no	—
120	C₂²×C₄×C₄₁	—	2	2	no	—
121	C₂²×C₄×C₄₁	—	2	4	no	—
122	C₂²×C₄×C₄₁	—	2	1	no	—
123	C₂²×C₄×C₄₁	—	2	1	no	—
124	C₂²×C₄×C₄₁	—	2	2	no	—
125	C₂²×C₄×C₄₁	—	2	1	no	—
126	C₂²×C₄×C₄₁	—	2	1	no	—
127	C₂²×C₄×C₄₁	—	4	2	no	—
128	C₂²×C₄×C₄₁	—	4	2	no	—
129	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₄₁	#41	1	2	yes	—
134	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
135	C₂×C₈×C₄₁	—	2	1	no	—
136	C₂×C₈×C₄₁	—	2	1	no	—
137	C₂×C₈×C₄₁	—	2	2	no	—
138	C₂×C₈×C₄₁	—	2	2	no	—
139	C₂×C₈×C₄₁	—	2	2	no	—
140	C₂×C₈×C₄₁	—	2	2	no	—
141	C₂×C₈×C₄₁	—	2	2	no	—
142	C₂×C₈×C₄₁	—	4	4	no	—
143	C₄⋊C₄×C₄₁	—	2	4	no	—
144	C₄⋊C₄×C₄₁	—	2	1	no	—
145	C₄⋊C₄×C₄₁	—	2	1	no	—
146	C₄⋊C₄×C₄₁	—	2	1	no	—
147	C₄⋊C₄×C₄₁	—	2	2	no	—
148	C₄⋊C₄×C₄₁	—	2	1	no	—
149	C₄⋊C₄×C₄₁	—	2	2	no	—
150	C₄⋊C₄×C₄₁	—	4	4	no	—
151	C₄⋊C₄×C₄₁	—	4	2	no	—
152	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
153	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
154	C₂²⋊C₄×C₄₁	—	2	2	no	—
155	C₂²⋊C₄×C₄₁	—	2	2	no	—
156	C₂²⋊C₄×C₄₁	—	4	4	no	—
157	C₂²⋊C₄×C₄₁	—	4	4	no	—
158	C₂²⋊C₄×C₄₁	—	4	2	no	—
159	C₂²⋊C₄×C₄₁	—	4	2	no	—
160	C₂²⋊C₄×C₄₁	—	8	2	no	—
161	C₂²⋊C₄×C₄₁	—	8	2	no	—
162	C₄²×C₄₁	—	2	2	no	—
163	C₄²×C₄₁	—	2	2	no	—
164	C₄²×C₄₁	—	4	4	no	—
165	C₂³×C₄₁	—	2	2	no	—
166	C₂³×C₄₁	—	2	2	no	—
167	C₂³×C₄₁	—	2	4	no	—
168	C₂³×C₄₁	—	4	8	no	—
169	C₂³×C₄₁	—	4	2	no	—
170	C₂³×C₄₁	—	4	2	no	—
171	C₂³×C₄₁	—	4	2	no	—
172	C₂³×C₄₁	—	4	2	no	—
173	C₂³×C₄₁	—	4	2	no	—
174	C₂³×C₄₁	—	4	2	no	—
175	C₂³×C₄₁	—	8	8	no	—
176	C₂³×C₄₁	—	8	8	no	—
177	C₂³×C₄₁	—	8	4	no	—
178	C₂³×C₄₁	—	8	4	no	—
179	C₂³×C₄₁	#121	1	2	yes	—
180	C₂³×C₄₁	#135	1	2	yes	—
181	C₂³×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
182	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
183	Q₈×C₄₁	—	4	1	no	—
184	Q₈×C₄₁	—	4	1	no	—
185	Q₈×C₄₁	—	4	2	no	—
186	D₄×C₄₁	—	2	4	no	—
187	D₄×C₄₁	—	2	4	no	—
188	D₄×C₄₁	—	4	8	no	—
189	D₄×C₄₁	—	4	2	no	—
190	D₄×C₄₁	—	4	2	no	—
191	C₂×C₄×C₄₁	—	2	2	no	—
192	C₂×C₄×C₄₁	—	2	2	no	—
193	C₂×C₄×C₄₁	—	2	2	no	—
194	C₂×C₄×C₄₁	—	2	4	no	—
195	C₂×C₄×C₄₁	—	2	2	no	—
196	C₂×C₄×C₄₁	—	2	2	no	—
197	C₂×C₄×C₄₁	—	2	2	no	—
198	C₂×C₄×C₄₁	—	2	2	no	—
199	C₂×C₄×C₄₁	—	2	2	no	—
200	C₂×C₄×C₄₁	—	2	2	no	—
201	C₂×C₄×C₄₁	—	2	2	no	—
202	C₂×C₄×C₄₁	—	2	2	no	—
203	C₂×C₄×C₄₁	—	4	1	no	—
204	C₂×C₄×C₄₁	—	4	1	no	—
205	C₂×C₄×C₄₁	—	4	1	no	—
206	C₂×C₄×C₄₁	—	4	1	no	—
207	C₂×C₄×C₄₁	—	4	8	no	—
208	C₂×C₄×C₄₁	—	4	1	no	—
209	C₂×C₄×C₄₁	—	4	1	no	—
210	C₂×C₄×C₄₁	—	4	2	no	—
211	C₂×C₄×C₄₁	—	4	2	no	—
212	C₂×C₄×C₄₁	—	4	2	no	—
213	C₂×C₄×C₄₁	—	4	2	no	—
214	C₂×C₄×C₄₁	—	4	2	no	—
215	C₂×C₄×C₄₁	#121	1	2	yes	—
216	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
218	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
220	C₈×C₄₁	—	4	1	no	—
221	C₈×C₄₁	—	4	1	no	—
222	C₈×C₄₁	—	4	2	no	—
223	#24477	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₂²×C₄₁	—	2	2	no	—
225	C₂²×C₄₁	—	2	4	no	—
226	C₂²×C₄₁	—	2	2	no	—
227	C₂²×C₄₁	—	2	4	no	—
228	C₂²×C₄₁	—	4	4	no	—
229	C₂²×C₄₁	—	4	4	no	—
230	C₂²×C₄₁	—	4	4	no	—
231	C₂²×C₄₁	—	8	16	no	—
232	C₂²×C₄₁	—	8	2	no	—
233	C₂²×C₄₁	—	8	2	no	—
234	C₂²×C₄₁	—	8	2	no	—
235	C₂²×C₄₁	—	8	2	no	—
236	C₂²×C₄₁	#463	1	4	yes	—
237	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
238	C₂²×C₄₁	#546	1	2	yes	—
239	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
240	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
241	C₂²×C₄₁	#577	1	2	yes	—
242	C₄×C₄₁	—	2	2	no	—
243	C₄×C₄₁	—	4	2	no	—
244	C₄×C₄₁	—	4	2	no	—
245	C₄×C₄₁	—	4	2	no	—
246	C₄×C₄₁	—	4	2	no	—
247	C₄×C₄₁	—	8	1	no	—
248	C₄×C₄₁	—	8	1	no	—
249	C₄×C₄₁	—	8	2	no	—
250	C₄×C₄₁	#525	1	1	yes	characteristic
251	C₄×C₄₁	#535	1	1	yes	characteristic
252	C₄×C₄₁	#551	1	2	yes	—
253	C₂×#483	C₂×C₄₁	1	1	yes	characteristic, complemented
254	C₂²×#102	C₂×C₄₁	1	1	yes	characteristic
255	#2435	C₂×C₄₁	1	1	yes	characteristic
256	#2344	C₂×C₄₁	1	1	yes	characteristic, complemented
257	#2065	C₂×C₄₁	1	2	yes	complemented
258	#2042	C₂×C₄₁	1	2	yes	complemented
259	#1983	C₂×C₄₁	1	2	yes	complemented
260	#1926	C₂×C₄₁	1	2	yes	complemented
261	#1892	C₂×C₄₁	1	1	yes	characteristic, complemented
262	#1850	C₂×C₄₁	1	1	yes	characteristic, complemented
263	#1786	C₂×C₄₁	1	1	yes	characteristic
264	C₂×C₄₁	—	2	4	no	—
265	C₂×C₄₁	—	8	4	no	—
266	C₂×C₄₁	#2411	1	1	yes	characteristic
267	C₂×C₄₁	C₂×#463	1	1	yes	characteristic
268	C₂×C₄₁	#3043	1	1	yes	characteristic
269	C₂×C₄₁	#3296	1	2	yes	—
270	C₂×C₄₁	#3306	1	2	yes	—
271	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
272	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
273	C₂×#124	C₂²×C₄₁	1	2	yes	—
274	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
275	C₂×#117	—	2	1	no	—
276	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
277	#483	—	2	4	no	—
278	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic, complemented
279	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic, complemented
280	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	complemented
281	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic, complemented
282	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic, complemented
283	C₂×#103	C₂²×C₄₁	1	2	yes	complemented
284	C₂×#102	—	2	4	no	—
285	C₂×#102	C₂²×C₄₁	1	2	yes	—
286	C₂×#102	C₂²×C₄₁	1	2	yes	—
287	C₂×#102	C₂²×C₄₁	1	2	yes	—
288	C₂×#102	C₂²×C₄₁	1	2	yes	—
289	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
290	#394	—	2	2	no	—
291	#390	C₂²×C₄₁	1	2	yes	—
292	#389	C₂²×C₄₁	1	2	yes	complemented
293	#387	—	2	2	no	—
294	#381	—	2	1	no	—
295	#380	C₂²×C₄₁	1	1	yes	characteristic
296	#379	—	2	1	no	—
297	#379	—	2	1	no	—
298	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	complemented
299	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
300	#340	C₂²×C₄₁	1	2	yes	complemented
301	#336	C₂²×C₄₁	1	2	yes	complemented
302	C₄₁	#24477	1	1	yes	characteristic, direct product factor, Sylow
303	C₂⁵	—	2	1	no	—
304	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
305	C₂²×D₄	—	2	4	no	—
306	C₂²×D₄	—	2	2	no	—
307	C₂²×D₄	—	2	1	no	—
308	C₂²×D₄	—	2	2	no	—
309	C₂²×D₄	—	4	2	no	—
310	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
311	C₂³×C₄	—	2	1	no	—
312	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
313	C₂²×C₈	—	2	2	no	—
314	C₂²×C₈	—	4	2	no	—
315	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
316	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
318	#124	—	2	4	no	—
319	#124	—	4	2	no	—
320	C₂²⋊Q₈	—	2	2	no	—
321	C₂²⋊Q₈	—	2	2	no	—
322	#117	—	4	4	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	2	no	—
325	C₂×C₄⋊C₄	—	2	2	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	D₄×C₄₁	1	4	yes	—
328	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
330	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
339	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
340	C₂×C₄²	—	2	2	no	—
341	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
342	#106	—	2	2	no	—
343	#106	—	2	2	no	—
344	C₄⋊C₈	—	4	2	no	—
345	#103	—	2	2	no	—
346	#103	—	2	2	no	—
347	#103	—	4	2	no	—
348	#102	—	2	4	no	—
349	#102	—	2	4	no	—
350	#102	—	2	4	no	—
351	#102	—	4	2	no	—
352	C₂²⋊C₈	—	2	2	no	—
353	#95	—	2	2	no	—
354	#95	—	2	1	no	—
355	#95	—	2	2	no	—
356	#95	D₄×C₄₁	1	2	yes	—
357	C₂⁴	—	2	2	no	—
358	C₂⁴	—	4	4	no	—
359	C₂⁴	—	4	2	no	—
360	C₂⁴	—	4	2	no	—
361	C₂⁴	—	4	2	no	—
362	C₂⁴	—	8	2	no	—
363	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×D₄	—	2	8	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	4	8	no	—
375	C₂×D₄	—	4	4	no	—
376	C₂×D₄	—	4	4	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	#41×C₄₁	1	4	yes	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	—	4	2	no	—
389	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
390	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
391	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
393	C₂²×C₄	#41×C₄₁	1	2	yes	—
394	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	4	4	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	4	4	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
413	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	4	4	no	—
417	C₂²⋊C₄	—	4	4	no	—
418	C₂²⋊C₄	—	4	2	no	—
419	C₂²⋊C₄	—	4	2	no	—
420	C₂²⋊C₄	—	8	2	no	—
421	C₂²⋊C₄	—	8	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	4	4	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	2	4	no	—
428	C₂³	—	4	8	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	8	8	no	—
436	C₂³	—	8	8	no	—
437	C₂³	—	8	4	no	—
438	C₂³	—	8	4	no	—
439	C₂³	#121×C₄₁	1	2	yes	—
440	C₂³	#135×C₄₁	1	2	yes	—
441	C₂³	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
442	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
443	Q₈	—	4	1	no	—
444	Q₈	—	4	1	no	—
445	Q₈	—	4	2	no	—
446	D₄	—	2	4	no	—
447	D₄	—	2	4	no	—
448	D₄	—	4	8	no	—
449	D₄	—	4	2	no	—
450	D₄	—	4	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	8	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	#121×C₄₁	1	2	yes	—
476	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
477	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
478	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
479	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
480	C₈	—	4	1	no	—
481	C₈	—	4	2	no	—
482	C₈	—	4	1	no	—
483	C₂²	—	2	4	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	4	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	8	16	no	—
491	C₂²	—	8	2	no	—
492	C₂²	—	8	2	no	—
493	C₂²	—	8	2	no	—
494	C₂²	—	8	2	no	—
495	C₂²	C₄₁×#463	1	4	yes	—
496	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
497	C₂²	C₄₁×#546	1	2	yes	—
498	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
499	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
500	C₂²	C₄₁×#577	1	2	yes	—
501	C₄	—	2	2	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	2	no	—
506	C₄	—	8	1	no	—
507	C₄	—	8	2	no	—
508	C₄	—	8	1	no	—
509	C₄	C₄₁×#525	1	1	yes	characteristic
510	C₄	C₄₁×#535	1	1	yes	characteristic
511	C₄	C₄₁×#551	1	2	yes	—
512	C₂	—	2	4	no	—
513	C₂	—	8	4	no	—
514	C₂	C₄₁×#2411	1	1	yes	characteristic
515	C₂	C₂×C₄₁×#463	1	1	yes	characteristic
516	C₂	C₄₁×#3043	1	1	yes	characteristic
517	C₂	C₄₁×#3296	1	2	yes	—
518	C₂	C₄₁×#3306	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#483	C₂	semidirect
4. C₄₁×#2344	C₂	semidirect
5. C₄₁×#2065	C₂	semidirect
6. C₄₁×#2042	C₂	semidirect
7. C₄₁×#1983	C₂	semidirect
8. C₄₁×#1926	C₂	semidirect
9. C₄₁×#1892	C₂	semidirect
10. C₄₁×#1850	C₂	semidirect
19. C₂×#106×C₄₁	C₂²	semidirect
20. C₂×#106×C₄₁	C₂²	semidirect
21. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
22. C₂×#103×C₄₁	C₂²	semidirect
23. C₂×#103×C₄₁	C₂²	semidirect
24. C₂×#103×C₄₁	C₂²	semidirect
33. C₄₁×#389	C₂²	semidirect
39. C₄×C₄⋊C₄×C₄₁	C₂²	semidirect
41. C₄₁×#340	C₂²	semidirect
42. C₄₁×#336	C₂²	semidirect
223. #24477	C₄₁	direct (N × H)
253. C₂×#483	C₂×C₄₁	semidirect
256. #2344	C₂×C₄₁	semidirect
257. #2065	C₂×C₄₁	semidirect
258. #2042	C₂×C₄₁	semidirect
259. #1983	C₂×C₄₁	semidirect
260. #1926	C₂×C₄₁	semidirect
261. #1892	C₂×C₄₁	semidirect
262. #1850	C₂×C₄₁	semidirect
278. C₂×#106	C₂²×C₄₁	semidirect
279. C₂×#106	C₂²×C₄₁	semidirect
280. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
281. C₂×#103	C₂²×C₄₁	semidirect
282. C₂×#103	C₂²×C₄₁	semidirect
283. C₂×#103	C₂²×C₄₁	semidirect
292. #389	C₂²×C₄₁	semidirect
298. C₄×C₄⋊C₄	C₂²×C₄₁	semidirect
300. #340	C₂²×C₄₁	semidirect
301. #336	C₂²×C₄₁	semidirect
302. C₄₁	#24477	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×#483	2
C₂²×#102×C₄₁	2
C₄₁×#2435	2
C₄₁×#2344	2
C₄₁×#2065	2
C₄₁×#2042	2
C₄₁×#1983	2
C₄₁×#1926	2
C₄₁×#1892	2
C₄₁×#1850	2
C₄₁×#1786	2
#24477	41

Subgroups — C41×#24477 #23800678

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24477 #23800678