Subgroups — C₂×C₄₁×#2065 #23799806

Order 10496.

1422 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	C₂²×#106×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#102×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×#102×C₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₁×#390	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄₁×#389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2065	C₂	1	8	yes	maximal, direct product factor
8	C₂×C₄₁×#340	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₄₁	—	2	1	no	—
13	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₄₁	—	2	1	no	—
17	C₂²×C₂²⋊C₄×C₄₁	—	2	1	no	—
18	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×#106×C₄₁	—	2	4	no	—
20	C₂×#106×C₄₁	C₂²	1	4	yes	complemented
21	C₂×C₄⋊C₈×C₄₁	—	2	4	no	—
22	C₂×C₄⋊C₈×C₄₁	C₂²	1	4	yes	complemented
23	C₂×#102×C₄₁	—	2	4	no	—
24	C₂×#102×C₄₁	—	2	4	no	—
25	C₂×#102×C₄₁	C₂²	1	4	yes	—
26	C₂×#102×C₄₁	C₂²	1	4	yes	—
27	C₄₁×#390	—	2	2	no	—
28	C₄₁×#390	C₂²	1	4	yes	—
29	C₄₁×#389	—	2	2	no	—
30	C₄₁×#389	C₂²	1	4	yes	complemented
31	C₂×#95×C₄₁	—	2	1	no	—
32	C₄₁×#340	C₂²	1	4	yes	complemented
33	C₂⁵×C₄₁	—	2	1	no	—
34	C₂²×D₄×C₄₁	—	2	2	no	—
35	C₂²×D₄×C₄₁	—	2	2	no	—
36	C₂²×D₄×C₄₁	—	2	1	no	—
37	C₂²×D₄×C₄₁	—	2	2	no	—
38	C₂²×D₄×C₄₁	—	2	2	no	—
39	C₂²×D₄×C₄₁	—	2	2	no	—
40	C₂²×D₄×C₄₁	Q₈	1	4	yes	—
41	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
42	C₂³×C₄×C₄₁	—	2	1	no	—
43	C₂³×C₄×C₄₁	—	2	1	no	—
44	C₂³×C₄×C₄₁	—	2	1	no	—
45	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₄₁	—	2	2	no	—
49	C₂²×C₈×C₄₁	—	2	2	no	—
50	C₂²×C₈×C₄₁	—	2	2	no	—
51	C₂²×C₈×C₄₁	—	2	2	no	—
52	C₂²×C₈×C₄₁	—	2	2	no	—
53	C₂²×C₈×C₄₁	D₄	1	4	yes	—
54	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
55	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
63	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₁	—	4	4	no	—
66	C₂×C₄⋊C₄×C₄₁	D₄	1	4	yes	—
67	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
71	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
73	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
74	C₂×C₄²×C₄₁	—	2	2	no	—
75	C₂×C₄²×C₄₁	—	2	2	no	—
76	C₂×C₄²×C₄₁	D₄	1	2	yes	—
77	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
78	#106×C₄₁	—	2	8	no	—
79	C₄⋊C₈×C₄₁	—	2	8	no	—
80	#102×C₄₁	—	2	8	no	—
81	#102×C₄₁	—	2	8	no	—
82	#95×C₄₁	—	2	4	no	—
83	C₂⁴×C₄₁	—	2	4	no	—
84	C₂⁴×C₄₁	—	2	2	no	—
85	C₂⁴×C₄₁	—	4	2	no	—
86	C₂⁴×C₄₁	—	4	2	no	—
87	C₂⁴×C₄₁	—	4	2	no	—
88	C₂⁴×C₄₁	—	4	2	no	—
89	C₂⁴×C₄₁	—	4	2	no	—
90	C₂⁴×C₄₁	—	4	2	no	—
91	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
92	C₂×D₄×C₄₁	—	2	8	no	—
93	C₂×D₄×C₄₁	—	2	8	no	—
94	C₂×D₄×C₄₁	—	2	4	no	—
95	C₂×D₄×C₄₁	—	2	2	no	—
96	C₂×D₄×C₄₁	—	2	2	no	—
97	C₂×D₄×C₄₁	—	2	2	no	—
98	C₂×D₄×C₄₁	—	2	2	no	—
99	C₂×D₄×C₄₁	—	2	2	no	—
100	C₂×D₄×C₄₁	—	4	4	no	—
101	C₂×D₄×C₄₁	—	4	2	no	—
102	C₂×D₄×C₄₁	—	4	2	no	—
103	C₂×D₄×C₄₁	—	4	4	no	—
104	C₂×D₄×C₄₁	C₂×Q₈	1	4	yes	—
105	C₂²×C₄×C₄₁	—	2	2	no	—
106	C₂²×C₄×C₄₁	—	2	2	no	—
107	C₂²×C₄×C₄₁	—	2	2	no	—
108	C₂²×C₄×C₄₁	—	2	4	no	—
109	C₂²×C₄×C₄₁	—	2	2	no	—
110	C₂²×C₄×C₄₁	—	2	2	no	—
111	C₂²×C₄×C₄₁	—	2	2	no	—
112	C₂²×C₄×C₄₁	—	2	2	no	—
113	C₂²×C₄×C₄₁	—	2	2	no	—
114	C₂²×C₄×C₄₁	—	4	2	no	—
115	C₂²×C₄×C₄₁	—	4	2	no	—
116	C₂²×C₄×C₄₁	—	4	2	no	—
117	C₂²×C₄×C₄₁	—	4	2	no	—
118	C₂²×C₄×C₄₁	—	4	2	no	—
119	C₂²×C₄×C₄₁	—	4	2	no	—
120	C₂²×C₄×C₄₁	—	4	2	no	—
121	C₂²×C₄×C₄₁	—	4	2	no	—
122	C₂²×C₄×C₄₁	SD₁₆	1	4	yes	—
123	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
129	C₂²×C₄×C₄₁	#41	1	2	yes	—
130	C₂²×C₄×C₄₁	#41	1	2	yes	—
131	C₂²×C₄×C₄₁	#41	1	2	yes	—
132	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
133	C₂×C₈×C₄₁	—	2	8	no	—
134	C₂×C₈×C₄₁	—	2	2	no	—
135	C₂×C₈×C₄₁	—	2	2	no	—
136	C₂×C₈×C₄₁	—	2	2	no	—
137	C₂×C₈×C₄₁	—	2	2	no	—
138	C₂×C₈×C₄₁	—	2	2	no	—
139	C₂×C₈×C₄₁	—	4	4	no	—
140	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
141	C₄⋊C₄×C₄₁	—	2	4	no	—
142	C₄⋊C₄×C₄₁	—	2	2	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	—	4	8	no	—
148	C₄⋊C₄×C₄₁	—	4	2	no	—
149	C₄⋊C₄×C₄₁	—	4	2	no	—
150	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
151	C₂²⋊C₄×C₄₁	—	4	8	no	—
152	C₂²⋊C₄×C₄₁	—	4	8	no	—
153	C₄²×C₄₁	—	2	4	no	—
154	C₄²×C₄₁	—	2	2	no	—
155	C₄²×C₄₁	—	2	2	no	—
156	C₂³×C₄₁	—	2	4	no	—
157	C₂³×C₄₁	—	4	2	no	—
158	C₂³×C₄₁	—	4	2	no	—
159	C₂³×C₄₁	—	4	2	no	—
160	C₂³×C₄₁	—	4	2	no	—
161	C₂³×C₄₁	—	4	2	no	—
162	C₂³×C₄₁	—	4	2	no	—
163	C₂³×C₄₁	—	4	8	no	—
164	C₂³×C₄₁	—	4	8	no	—
165	C₂³×C₄₁	—	4	8	no	—
166	C₂³×C₄₁	—	8	4	no	—
167	C₂³×C₄₁	—	8	4	no	—
168	C₂³×C₄₁	—	8	4	no	—
169	C₂³×C₄₁	—	8	4	no	—
170	C₂³×C₄₁	#121	1	2	yes	—
171	C₂³×C₄₁	#121	1	2	yes	—
172	C₂³×C₄₁	C₂²⋊Q₈	1	2	yes	—
173	C₂³×C₄₁	C₂×SD₁₆	1	2	yes	—
174	C₂³×C₄₁	#135	1	2	yes	—
175	C₂³×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
176	C₂³×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
177	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
178	D₄×C₄₁	—	2	4	no	—
179	D₄×C₄₁	—	2	4	no	—
180	D₄×C₄₁	—	4	2	no	—
181	D₄×C₄₁	—	4	2	no	—
182	D₄×C₄₁	—	4	8	no	—
183	C₂×C₄×C₄₁	—	2	2	no	—
184	C₂×C₄×C₄₁	—	2	2	no	—
185	C₂×C₄×C₄₁	—	2	8	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	—	2	2	no	—
190	C₂×C₄×C₄₁	—	4	2	no	—
191	C₂×C₄×C₄₁	—	4	2	no	—
192	C₂×C₄×C₄₁	—	4	8	no	—
193	C₂×C₄×C₄₁	—	4	4	no	—
194	C₂×C₄×C₄₁	—	4	2	no	—
195	C₂×C₄×C₄₁	—	4	2	no	—
196	C₂×C₄×C₄₁	—	4	2	no	—
197	C₂×C₄×C₄₁	—	4	2	no	—
198	C₂×C₄×C₄₁	—	4	2	no	—
199	C₂×C₄×C₄₁	—	4	2	no	—
200	C₂×C₄×C₄₁	—	8	4	no	—
201	C₂×C₄×C₄₁	—	8	4	no	—
202	C₂×C₄×C₄₁	#121	1	4	yes	—
203	C₂×C₄×C₄₁	#121	1	2	yes	—
204	C₂×C₄×C₄₁	#121	1	2	yes	—
205	C₂×C₄×C₄₁	C₂²⋊Q₈	1	4	yes	—
206	C₂×C₄×C₄₁	C₂²⋊Q₈	1	4	yes	—
207	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
208	C₂×C₄×C₄₁	#126	1	4	yes	—
209	C₂×C₄×C₄₁	C₂×SD₁₆	1	4	yes	—
210	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
213	C₂×C₄×C₄₁	C₂×#41	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	C₈×C₄₁	—	2	4	no	—
217	C₈×C₄₁	—	4	2	no	—
218	C₂×#2065	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂²×C₄₁	—	4	4	no	—
220	C₂²×C₄₁	—	4	4	no	—
221	C₂²×C₄₁	—	4	4	no	—
222	C₂²×C₄₁	—	8	16	no	—
223	C₂²×C₄₁	—	8	2	no	—
224	C₂²×C₄₁	—	8	2	no	—
225	C₂²×C₄₁	—	8	2	no	—
226	C₂²×C₄₁	—	8	2	no	—
227	C₂²×C₄₁	#396	1	4	yes	—
228	C₂²×C₄₁	#460	1	4	yes	—
229	C₂²×C₄₁	#463	1	4	yes	—
230	C₂²×C₄₁	#465	1	4	yes	—
231	C₂²×C₄₁	#469	1	4	yes	—
232	C₂²×C₄₁	#476	1	4	yes	—
233	C₂²×C₄₁	#478	1	4	yes	—
234	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
235	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
236	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
237	C₂²×C₄₁	C₂²×SD₁₆	1	1	yes	characteristic
238	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
239	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
240	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
241	C₄×C₄₁	—	2	4	no	—
242	C₄×C₄₁	—	4	4	no	—
243	C₄×C₄₁	—	4	2	no	—
244	C₄×C₄₁	—	8	2	no	—
245	C₄×C₄₁	—	8	2	no	—
246	C₄×C₄₁	#396	1	4	yes	—
247	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
248	C₄×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
249	C₄×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
250	C₄×C₄₁	C₂×#126	1	1	yes	characteristic
251	C₂²×#106	C₂×C₄₁	1	1	yes	characteristic, complemented
252	C₂²×C₄⋊C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
253	C₂²×#102	C₂×C₄₁	1	1	yes	characteristic
254	C₂²×#102	C₂×C₄₁	1	1	yes	characteristic
255	C₂×#390	C₂×C₄₁	1	1	yes	characteristic
256	C₂×#389	C₂×C₄₁	1	1	yes	characteristic, complemented
257	#2065	C₂×C₄₁	1	8	yes	direct product factor
258	C₂×#340	C₂×C₄₁	1	1	yes	characteristic, complemented
259	C₂×C₄₁	—	8	4	no	—
260	C₂×C₄₁	#2065	1	8	yes	direct product factor
261	C₂×C₄₁	C₂×#396	1	1	yes	characteristic
262	C₂×C₄₁	C₂×#463	1	1	yes	characteristic
263	C₂×C₄₁	C₂×#460	1	1	yes	characteristic
264	C₂×C₄₁	C₂×#465	1	1	yes	characteristic
265	C₂×C₄₁	C₂×#469	1	1	yes	characteristic
266	C₂×C₄₁	C₂×#476	1	1	yes	characteristic
267	C₂×C₄₁	C₂×#478	1	1	yes	characteristic
268	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
269	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
270	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
271	C₂²×C₄⋊C₄	—	2	1	no	—
272	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
273	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
274	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
275	C₂²×C₂²⋊C₄	—	2	1	no	—
276	C₂²×C₂²⋊C₄	—	2	1	no	—
277	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
278	C₂×#106	—	2	4	no	—
279	C₂×#106	C₂²×C₄₁	1	4	yes	complemented
280	C₂×C₄⋊C₈	—	2	4	no	—
281	C₂×C₄⋊C₈	C₂²×C₄₁	1	4	yes	complemented
282	C₂×#102	—	2	4	no	—
283	C₂×#102	—	2	4	no	—
284	C₂×#102	C₂²×C₄₁	1	4	yes	—
285	C₂×#102	C₂²×C₄₁	1	4	yes	—
286	#390	—	2	2	no	—
287	#390	C₂²×C₄₁	1	4	yes	—
288	#389	—	2	2	no	—
289	#389	C₂²×C₄₁	1	4	yes	complemented
290	C₂×#95	—	2	1	no	—
291	#340	C₂²×C₄₁	1	4	yes	complemented
292	C₄₁	C₂×#2065	1	1	yes	characteristic, direct product factor, Sylow
293	C₂⁵	—	2	1	no	—
294	C₂²×D₄	—	2	2	no	—
295	C₂²×D₄	—	2	2	no	—
296	C₂²×D₄	—	2	1	no	—
297	C₂²×D₄	—	2	2	no	—
298	C₂²×D₄	—	2	2	no	—
299	C₂²×D₄	—	2	2	no	—
300	C₂²×D₄	Q₈×C₄₁	1	4	yes	—
301	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
302	C₂³×C₄	—	2	1	no	—
303	C₂³×C₄	—	2	1	no	—
304	C₂³×C₄	—	2	1	no	—
305	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
306	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
307	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
308	C₂²×C₈	—	2	2	no	—
309	C₂²×C₈	—	2	2	no	—
310	C₂²×C₈	—	2	2	no	—
311	C₂²×C₈	—	2	2	no	—
312	C₂²×C₈	—	2	2	no	—
313	C₂²×C₈	D₄×C₄₁	1	4	yes	—
314	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
315	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	—	2	4	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	4	4	no	—
326	C₂×C₄⋊C₄	D₄×C₄₁	1	4	yes	—
327	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
330	C₂×C₂²⋊C₄	—	2	4	no	—
331	C₂×C₂²⋊C₄	—	2	4	no	—
332	C₂×C₂²⋊C₄	—	4	4	no	—
333	C₂×C₂²⋊C₄	—	4	4	no	—
334	C₂×C₄²	—	2	2	no	—
335	C₂×C₄²	—	2	2	no	—
336	C₂×C₄²	D₄×C₄₁	1	2	yes	—
337	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
338	#106	—	2	8	no	—
339	C₄⋊C₈	—	2	8	no	—
340	#102	—	2	8	no	—
341	#102	—	2	8	no	—
342	#95	—	2	4	no	—
343	C₂⁴	—	2	4	no	—
344	C₂⁴	—	2	2	no	—
345	C₂⁴	—	4	2	no	—
346	C₂⁴	—	4	2	no	—
347	C₂⁴	—	4	2	no	—
348	C₂⁴	—	4	2	no	—
349	C₂⁴	—	4	2	no	—
350	C₂⁴	—	4	2	no	—
351	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
352	C₂×D₄	—	2	8	no	—
353	C₂×D₄	—	2	8	no	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	4	4	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	—	4	4	no	—
364	C₂×D₄	C₂×Q₈×C₄₁	1	4	yes	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	—	4	2	no	—
380	C₂²×C₄	—	4	2	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	SD₁₆×C₄₁	1	4	yes	—
383	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
384	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
385	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
388	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
389	C₂²×C₄	#41×C₄₁	1	2	yes	—
390	C₂²×C₄	#41×C₄₁	1	2	yes	—
391	C₂²×C₄	#41×C₄₁	1	2	yes	—
392	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
393	C₂×C₈	—	2	8	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	4	4	no	—
400	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	4	8	no	—
408	C₄⋊C₄	—	4	2	no	—
409	C₄⋊C₄	—	4	2	no	—
410	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
411	C₂²⋊C₄	—	4	8	no	—
412	C₂²⋊C₄	—	4	8	no	—
413	C₄²	—	2	4	no	—
414	C₄²	—	2	2	no	—
415	C₄²	—	2	2	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	8	no	—
424	C₂³	—	4	8	no	—
425	C₂³	—	4	8	no	—
426	C₂³	—	8	4	no	—
427	C₂³	—	8	4	no	—
428	C₂³	—	8	4	no	—
429	C₂³	—	8	4	no	—
430	C₂³	#121×C₄₁	1	2	yes	—
431	C₂³	#121×C₄₁	1	2	yes	—
432	C₂³	C₂²⋊Q₈×C₄₁	1	2	yes	—
433	C₂³	C₂×SD₁₆×C₄₁	1	2	yes	—
434	C₂³	#135×C₄₁	1	2	yes	—
435	C₂³	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
436	C₂³	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
437	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
438	D₄	—	2	4	no	—
439	D₄	—	2	4	no	—
440	D₄	—	4	2	no	—
441	D₄	—	4	2	no	—
442	D₄	—	4	8	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	8	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	8	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	8	4	no	—
461	C₂×C₄	—	8	4	no	—
462	C₂×C₄	#121×C₄₁	1	4	yes	—
463	C₂×C₄	#121×C₄₁	1	2	yes	—
464	C₂×C₄	#121×C₄₁	1	2	yes	—
465	C₂×C₄	C₂²⋊Q₈×C₄₁	1	4	yes	—
466	C₂×C₄	C₂²⋊Q₈×C₄₁	1	4	yes	—
467	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
468	C₂×C₄	#126×C₄₁	1	4	yes	—
469	C₂×C₄	C₂×SD₁₆×C₄₁	1	4	yes	—
470	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
471	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
472	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
473	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
474	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
475	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
476	C₈	—	2	4	no	—
477	C₈	—	4	2	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	4	4	no	—
480	C₂²	—	4	4	no	—
481	C₂²	—	8	2	no	—
482	C₂²	—	8	2	no	—
483	C₂²	—	8	16	no	—
484	C₂²	—	8	2	no	—
485	C₂²	—	8	2	no	—
486	C₂²	C₄₁×#396	1	4	yes	—
487	C₂²	C₄₁×#460	1	4	yes	—
488	C₂²	C₄₁×#463	1	4	yes	—
489	C₂²	C₄₁×#465	1	4	yes	—
490	C₂²	C₄₁×#469	1	4	yes	—
491	C₂²	C₄₁×#476	1	4	yes	—
492	C₂²	C₄₁×#478	1	4	yes	—
493	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
494	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
495	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
496	C₂²	C₂²×SD₁₆×C₄₁	1	1	yes	characteristic
497	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
498	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
499	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
500	C₄	—	2	4	no	—
501	C₄	—	4	2	no	—
502	C₄	—	4	4	no	—
503	C₄	—	8	2	no	—
504	C₄	—	8	2	no	—
505	C₄	C₄₁×#396	1	4	yes	—
506	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
507	C₄	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
508	C₄	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
509	C₄	C₂×#126×C₄₁	1	1	yes	characteristic
510	C₂	—	8	4	no	—
511	C₂	C₄₁×#2065	1	8	yes	direct product factor
512	C₂	C₂×C₄₁×#396	1	1	yes	characteristic
513	C₂	C₂×C₄₁×#463	1	1	yes	characteristic
514	C₂	C₂×C₄₁×#460	1	1	yes	characteristic
515	C₂	C₂×C₄₁×#465	1	1	yes	characteristic
516	C₂	C₂×C₄₁×#469	1	1	yes	characteristic
517	C₂	C₂×C₄₁×#476	1	1	yes	characteristic
518	C₂	C₂×C₄₁×#478	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×#106×C₄₁	C₂	semidirect
2. C₂²×C₄⋊C₈×C₄₁	C₂	semidirect
6. C₂×C₄₁×#389	C₂	semidirect
7. C₄₁×#2065	C₂	direct (N × H)
8. C₂×C₄₁×#340	C₂	semidirect
20. C₂×#106×C₄₁	C₂²	semidirect
22. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
30. C₄₁×#389	C₂²	semidirect
32. C₄₁×#340	C₂²	semidirect
218. C₂×#2065	C₄₁	direct (N × H)
251. C₂²×#106	C₂×C₄₁	semidirect
252. C₂²×C₄⋊C₈	C₂×C₄₁	semidirect
256. C₂×#389	C₂×C₄₁	semidirect
257. #2065	C₂×C₄₁	direct (N × H)
258. C₂×#340	C₂×C₄₁	semidirect
260. C₂×C₄₁	#2065	direct (N × H)
279. C₂×#106	C₂²×C₄₁	semidirect
281. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
289. #389	C₂²×C₄₁	semidirect
291. #340	C₂²×C₄₁	semidirect
292. C₄₁	C₂×#2065	direct (N × H)
511. C₂	C₄₁×#2065	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#106×C₄₁	2
C₂²×C₄⋊C₈×C₄₁	2
C₂²×#102×C₄₁	2
C₂×C₄₁×#390	2
C₂×C₄₁×#389	2
C₄₁×#2065	2
C₂×C₄₁×#340	2
C₂×#2065	41

Subgroups — C2×C41×#2065 #23799806

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#2065 #23799806