Subgroups — C₂×C₄₁×#1441 #23790039

Order 10496.

3246 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×#95×C₄₁	C₂	1	2	yes	maximal
4	C₂²×#95×C₄₁	C₂	1	2	yes	maximal
5	C₂²×#95×C₄₁	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#1441	C₂	1	8	yes	maximal, direct product factor
7	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₄₁	C₂²	1	2	yes	—
9	C₂⁴×C₄×C₄₁	C₂²	1	2	yes	—
10	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₄₁	—	2	8	no	—
13	C₂²×C₄⋊C₄×C₄₁	—	2	4	no	—
14	C₂²×C₄⋊C₄×C₄₁	—	2	4	no	—
15	C₂²×C₄⋊C₄×C₄₁	—	2	4	no	—
16	C₂²×C₄⋊C₄×C₄₁	C₄	1	8	yes	complemented
17	C₂²×C₄⋊C₄×C₄₁	C₂²	1	4	yes	—
18	C₂²×C₄⋊C₄×C₄₁	C₂²	1	4	yes	—
19	C₂×#95×C₄₁	—	2	8	no	—
20	C₂×#95×C₄₁	—	2	4	no	—
21	C₂×#95×C₄₁	—	2	8	no	—
22	C₂×#95×C₄₁	C₂²	1	8	yes	—
23	C₂×#95×C₄₁	C₂²	1	8	yes	—
24	C₂×#95×C₄₁	C₂²	1	4	yes	—
25	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
26	C₂³×C₄×C₄₁	—	2	2	no	—
27	C₂³×C₄×C₄₁	—	2	2	no	—
28	C₂³×C₄×C₄₁	—	2	4	no	—
29	C₂³×C₄×C₄₁	—	2	2	no	—
30	C₂³×C₄×C₄₁	—	2	2	no	—
31	C₂³×C₄×C₄₁	—	2	4	no	—
32	C₂³×C₄×C₄₁	—	2	2	no	—
33	C₂³×C₄×C₄₁	—	2	2	no	—
34	C₂³×C₄×C₄₁	—	2	4	no	—
35	C₂³×C₄×C₄₁	—	2	4	no	—
36	C₂³×C₄×C₄₁	—	2	4	no	—
37	C₂³×C₄×C₄₁	—	2	4	no	—
38	C₂³×C₄×C₄₁	—	2	4	no	—
39	C₂³×C₄×C₄₁	—	2	4	no	—
40	C₂³×C₄×C₄₁	—	2	4	no	—
41	C₂³×C₄×C₄₁	—	2	4	no	—
42	C₂³×C₄×C₄₁	—	2	4	no	—
43	C₂³×C₄×C₄₁	—	2	4	no	—
44	C₂³×C₄×C₄₁	—	2	4	no	—
45	C₂³×C₄×C₄₁	—	2	4	no	—
46	C₂³×C₄×C₄₁	—	2	4	no	—
47	C₂³×C₄×C₄₁	—	2	4	no	—
48	C₂³×C₄×C₄₁	C₂×C₄	1	4	yes	—
49	C₂³×C₄×C₄₁	C₂×C₄	1	4	yes	—
50	C₂³×C₄×C₄₁	C₂×C₄	1	4	yes	—
51	C₂³×C₄×C₄₁	D₄	1	8	yes	—
52	C₂³×C₄×C₄₁	D₄	1	4	yes	—
53	C₂³×C₄×C₄₁	D₄	1	4	yes	—
54	C₂³×C₄×C₄₁	D₄	1	4	yes	—
55	C₂³×C₄×C₄₁	Q₈	1	8	yes	—
56	C₂³×C₄×C₄₁	Q₈	1	4	yes	—
57	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
58	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
59	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
60	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
61	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₄₁	—	2	32	no	—
63	C₂×C₄⋊C₄×C₄₁	—	2	32	no	—
64	C₂×C₄⋊C₄×C₄₁	—	2	16	no	—
65	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
66	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
67	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
68	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	16	yes	complemented
69	#95×C₄₁	—	2	16	no	—
70	#95×C₄₁	—	2	8	no	—
71	#95×C₄₁	—	2	16	no	—
72	C₂⁴×C₄₁	C₂²×C₄	1	2	yes	—
73	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
74	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
75	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
76	C₂⁴×C₄₁	C₂×D₄	1	4	yes	—
77	C₂⁴×C₄₁	C₂×Q₈	1	2	yes	—
78	C₂⁴×C₄₁	C₂×Q₈	1	4	yes	—
79	C₂⁴×C₄₁	#41	1	2	yes	—
80	C₂⁴×C₄₁	#41	1	2	yes	—
81	C₂⁴×C₄₁	#41	1	4	yes	—
82	C₂⁴×C₄₁	#41	1	4	yes	—
83	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
84	C₂²×C₄×C₄₁	—	2	8	no	—
85	C₂²×C₄×C₄₁	—	2	8	no	—
86	C₂²×C₄×C₄₁	—	2	16	no	—
87	C₂²×C₄×C₄₁	—	2	8	no	—
88	C₂²×C₄×C₄₁	—	2	8	no	—
89	C₂²×C₄×C₄₁	—	2	8	no	—
90	C₂²×C₄×C₄₁	—	2	16	no	—
91	C₂²×C₄×C₄₁	—	2	8	no	—
92	C₂²×C₄×C₄₁	—	2	8	no	—
93	C₂²×C₄×C₄₁	—	2	8	no	—
94	C₂²×C₄×C₄₁	—	2	2	no	—
95	C₂²×C₄×C₄₁	—	2	2	no	—
96	C₂²×C₄×C₄₁	—	2	4	no	—
97	C₂²×C₄×C₄₁	—	2	2	no	—
98	C₂²×C₄×C₄₁	—	2	2	no	—
99	C₂²×C₄×C₄₁	—	2	4	no	—
100	C₂²×C₄×C₄₁	—	2	8	no	—
101	C₂²×C₄×C₄₁	—	2	16	no	—
102	C₂²×C₄×C₄₁	—	2	16	no	—
103	C₂²×C₄×C₄₁	—	2	16	no	—
104	C₂²×C₄×C₄₁	—	2	16	no	—
105	C₂²×C₄×C₄₁	—	2	16	no	—
106	C₂²×C₄×C₄₁	—	2	16	no	—
107	C₂²×C₄×C₄₁	—	2	16	no	—
108	C₂²×C₄×C₄₁	—	2	4	no	—
109	C₂²×C₄×C₄₁	—	2	4	no	—
110	C₂²×C₄×C₄₁	—	2	4	no	—
111	C₂²×C₄×C₄₁	—	2	4	no	—
112	C₂²×C₄×C₄₁	—	2	4	no	—
113	C₂²×C₄×C₄₁	—	2	2	no	—
114	C₂²×C₄×C₄₁	—	2	2	no	—
115	C₂²×C₄×C₄₁	—	2	4	no	—
116	C₂²×C₄×C₄₁	—	2	4	no	—
117	C₂²×C₄×C₄₁	—	2	4	no	—
118	C₂²×C₄×C₄₁	—	2	4	no	—
119	C₂²×C₄×C₄₁	—	2	4	no	—
120	C₂²×C₄×C₄₁	—	2	4	no	—
121	C₂²×C₄×C₄₁	—	2	4	no	—
122	C₂²×C₄×C₄₁	—	2	4	no	—
123	C₂²×C₄×C₄₁	—	2	4	no	—
124	C₂²×C₄×C₄₁	—	4	4	no	—
125	C₂²×C₄×C₄₁	—	4	8	no	—
126	C₂²×C₄×C₄₁	—	4	8	no	—
127	C₂²×C₄×C₄₁	—	4	8	no	—
128	C₂²×C₄×C₄₁	—	4	8	no	—
129	C₂²×C₄×C₄₁	—	4	8	no	—
130	C₂²×C₄×C₄₁	—	4	8	no	—
131	C₂²×C₄×C₄₁	—	4	4	no	—
132	C₂²×C₄×C₄₁	—	4	8	no	—
133	C₂²×C₄×C₄₁	—	4	8	no	—
134	C₂²×C₄×C₄₁	—	4	8	no	—
135	C₂²×C₄×C₄₁	C₂²⋊C₄	1	16	yes	—
136	C₂²×C₄×C₄₁	C₄⋊C₄	1	16	yes	complemented
137	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
138	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
139	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
140	C₂²×C₄×C₄₁	C₂×D₄	1	8	yes	—
141	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₄₁	C₂×Q₈	1	8	yes	—
145	C₂²×C₄×C₄₁	C₂×Q₈	1	4	yes	—
146	C₄⋊C₄×C₄₁	—	2	32	no	—
147	C₄⋊C₄×C₄₁	—	2	32	no	—
148	C₂³×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
149	C₂³×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
150	C₂³×C₄₁	#117	1	4	yes	—
151	C₂³×C₄₁	C₄×D₄	1	8	yes	—
152	C₂³×C₄₁	C₄×Q₈	1	8	yes	—
153	C₂³×C₄₁	#120	1	4	yes	—
154	C₂³×C₄₁	#121	1	4	yes	—
155	C₂³×C₄₁	#121	1	4	yes	—
156	C₂³×C₄₁	#121	1	8	yes	—
157	C₂³×C₄₁	#121	1	8	yes	—
158	C₂³×C₄₁	C₂²⋊Q₈	1	4	yes	—
159	C₂³×C₄₁	C₂²⋊Q₈	1	4	yes	—
160	C₂³×C₄₁	C₂²⋊Q₈	1	8	yes	—
161	C₂³×C₄₁	C₂²⋊Q₈	1	8	yes	—
162	C₂³×C₄₁	C₂²⋊Q₈	1	8	yes	—
163	C₂³×C₄₁	#123	1	4	yes	—
164	C₂³×C₄₁	#123	1	8	yes	—
165	C₂³×C₄₁	#124	1	4	yes	—
166	C₂³×C₄₁	#125	1	8	yes	—
167	C₂³×C₄₁	#125	1	8	yes	—
168	C₂³×C₄₁	#126	1	8	yes	—
169	C₂³×C₄₁	C₄⋊Q₈	1	8	yes	—
170	C₂³×C₄₁	C₄⋊Q₈	1	4	yes	—
171	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
172	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
173	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
174	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
175	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
176	C₂³×C₄₁	C₂²×Q₈	1	1	yes	characteristic
177	C₂³×C₄₁	C₂²×Q₈	1	2	yes	—
178	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
179	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
180	C₂³×C₄₁	C₂×#41	1	2	yes	—
181	C₂³×C₄₁	C₂×#41	1	2	yes	—
182	C₂×C₄×C₄₁	—	2	4	no	—
183	C₂×C₄×C₄₁	—	2	4	no	—
184	C₂×C₄×C₄₁	—	2	8	no	—
185	C₂×C₄×C₄₁	—	2	4	no	—
186	C₂×C₄×C₄₁	—	2	4	no	—
187	C₂×C₄×C₄₁	—	2	4	no	—
188	C₂×C₄×C₄₁	—	2	8	no	—
189	C₂×C₄×C₄₁	—	2	4	no	—
190	C₂×C₄×C₄₁	—	2	4	no	—
191	C₂×C₄×C₄₁	—	2	4	no	—
192	C₂×C₄×C₄₁	—	2	32	no	—
193	C₂×C₄×C₄₁	—	2	32	no	—
194	C₂×C₄×C₄₁	—	2	4	no	—
195	C₂×C₄×C₄₁	—	2	8	no	—
196	C₂×C₄×C₄₁	—	2	8	no	—
197	C₂×C₄×C₄₁	—	2	8	no	—
198	C₂×C₄×C₄₁	—	2	8	no	—
199	C₂×C₄×C₄₁	—	2	8	no	—
200	C₂×C₄×C₄₁	—	2	8	no	—
201	C₂×C₄×C₄₁	—	2	8	no	—
202	C₂×C₄×C₄₁	—	4	2	no	—
203	C₂×C₄×C₄₁	—	4	4	no	—
204	C₂×C₄×C₄₁	—	4	4	no	—
205	C₂×C₄×C₄₁	—	4	4	no	—
206	C₂×C₄×C₄₁	—	4	4	no	—
207	C₂×C₄×C₄₁	—	4	4	no	—
208	C₂×C₄×C₄₁	—	4	4	no	—
209	C₂×C₄×C₄₁	—	4	4	no	—
210	C₂×C₄×C₄₁	—	4	2	no	—
211	C₂×C₄×C₄₁	—	4	4	no	—
212	C₂×C₄×C₄₁	—	4	4	no	—
213	C₂×C₄×C₄₁	—	4	16	no	—
214	C₂×C₄×C₄₁	—	4	32	no	—
215	C₂×C₄×C₄₁	—	4	32	no	—
216	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	8	yes	—
217	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	8	yes	complemented
218	C₂×#1441	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂²×C₄₁	#380	1	8	yes	—
220	C₂²×C₄₁	#386	1	8	yes	—
221	C₂²×C₄₁	#387	1	16	yes	—
222	C₂²×C₄₁	#389	1	16	yes	—
223	C₂²×C₄₁	#391	1	8	yes	—
224	C₂²×C₄₁	#394	1	8	yes	—
225	C₂²×C₄₁	#395	1	8	yes	—
226	C₂²×C₄₁	#396	1	16	yes	—
227	C₂²×C₄₁	#398	1	8	yes	—
228	C₂²×C₄₁	#398	1	16	yes	—
229	C₂²×C₄₁	#400	1	8	yes	—
230	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
231	C₂²×C₄₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
232	C₂²×C₄₁	C₂×#117	1	1	yes	characteristic
233	C₂²×C₄₁	C₂×C₄×D₄	1	2	yes	—
234	C₂²×C₄₁	C₂×C₄×Q₈	1	2	yes	—
235	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
236	C₂²×C₄₁	C₂×#121	1	2	yes	—
237	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
238	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
239	C₂²×C₄₁	C₂×#121	1	2	yes	—
240	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	2	yes	—
241	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
242	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	2	yes	—
243	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	2	yes	—
244	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
245	C₂²×C₄₁	C₂×#123	1	2	yes	—
246	C₂²×C₄₁	C₂×#123	1	1	yes	characteristic
247	C₂²×C₄₁	C₂×#124	1	1	yes	characteristic
248	C₂²×C₄₁	C₂×#125	1	2	yes	—
249	C₂²×C₄₁	C₂×#125	1	2	yes	—
250	C₂²×C₄₁	C₂×#126	1	2	yes	—
251	C₂²×C₄₁	C₂×C₄⋊Q₈	1	2	yes	—
252	C₂²×C₄₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
253	C₄×C₄₁	—	2	8	no	—
254	C₄×C₄₁	—	2	8	no	—
255	C₄×C₄₁	—	4	8	no	—
256	C₄×C₄₁	—	4	8	no	—
257	C₄×C₄₁	—	4	4	no	—
258	C₂³×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic
259	C₂³×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic
260	C₂²×#95	C₂×C₄₁	1	2	yes	—
261	C₂²×#95	C₂×C₄₁	1	2	yes	—
262	C₂²×#95	C₂×C₄₁	1	1	yes	characteristic
263	#1441	C₂×C₄₁	1	8	yes	direct product factor
264	C₂×C₄₁	#1441	1	16	yes	direct product factor
265	C₂×C₄₁	C₂×#380	1	1	yes	characteristic
266	C₂×C₄₁	C₂×#386	1	1	yes	characteristic
267	C₂×C₄₁	C₂×#387	1	2	yes	—
268	C₂×C₄₁	C₂×#389	1	2	yes	—
269	C₂×C₄₁	C₂×#391	1	1	yes	characteristic
270	C₂×C₄₁	C₂×#394	1	1	yes	characteristic
271	C₂×C₄₁	C₂×#395	1	1	yes	characteristic
272	C₂×C₄₁	C₂×#396	1	2	yes	—
273	C₂×C₄₁	C₂×#398	1	1	yes	characteristic
274	C₂×C₄₁	C₂×#398	1	2	yes	—
275	C₂×C₄₁	C₂×#400	1	1	yes	characteristic
276	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
277	C₂⁴×C₄	C₂²×C₄₁	1	2	yes	—
278	C₂⁴×C₄	C₂²×C₄₁	1	2	yes	—
279	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
280	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
281	C₂²×C₄⋊C₄	—	2	8	no	—
282	C₂²×C₄⋊C₄	—	2	4	no	—
283	C₂²×C₄⋊C₄	—	2	4	no	—
284	C₂²×C₄⋊C₄	—	2	4	no	—
285	C₂²×C₄⋊C₄	C₄×C₄₁	1	8	yes	complemented
286	C₂²×C₄⋊C₄	C₂²×C₄₁	1	4	yes	—
287	C₂²×C₄⋊C₄	C₂²×C₄₁	1	4	yes	—
288	C₂×#95	—	2	8	no	—
289	C₂×#95	—	2	4	no	—
290	C₂×#95	—	2	8	no	—
291	C₂×#95	C₂²×C₄₁	1	8	yes	—
292	C₂×#95	C₂²×C₄₁	1	8	yes	—
293	C₂×#95	C₂²×C₄₁	1	4	yes	—
294	C₄₁	C₂×#1441	1	1	yes	characteristic, direct product factor, Sylow
295	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
296	C₂³×C₄	—	2	2	no	—
297	C₂³×C₄	—	2	2	no	—
298	C₂³×C₄	—	2	4	no	—
299	C₂³×C₄	—	2	2	no	—
300	C₂³×C₄	—	2	2	no	—
301	C₂³×C₄	—	2	4	no	—
302	C₂³×C₄	—	2	2	no	—
303	C₂³×C₄	—	2	2	no	—
304	C₂³×C₄	—	2	4	no	—
305	C₂³×C₄	—	2	4	no	—
306	C₂³×C₄	—	2	4	no	—
307	C₂³×C₄	—	2	4	no	—
308	C₂³×C₄	—	2	4	no	—
309	C₂³×C₄	—	2	4	no	—
310	C₂³×C₄	—	2	4	no	—
311	C₂³×C₄	—	2	4	no	—
312	C₂³×C₄	—	2	4	no	—
313	C₂³×C₄	—	2	4	no	—
314	C₂³×C₄	—	2	4	no	—
315	C₂³×C₄	—	2	4	no	—
316	C₂³×C₄	—	2	4	no	—
317	C₂³×C₄	—	2	4	no	—
318	C₂³×C₄	C₂×C₄×C₄₁	1	4	yes	—
319	C₂³×C₄	C₂×C₄×C₄₁	1	4	yes	—
320	C₂³×C₄	C₂×C₄×C₄₁	1	4	yes	—
321	C₂³×C₄	D₄×C₄₁	1	8	yes	—
322	C₂³×C₄	D₄×C₄₁	1	4	yes	—
323	C₂³×C₄	D₄×C₄₁	1	4	yes	—
324	C₂³×C₄	D₄×C₄₁	1	4	yes	—
325	C₂³×C₄	Q₈×C₄₁	1	8	yes	—
326	C₂³×C₄	Q₈×C₄₁	1	4	yes	—
327	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
328	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
329	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
330	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
331	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
332	C₂×C₄⋊C₄	—	2	32	no	—
333	C₂×C₄⋊C₄	—	2	32	no	—
334	C₂×C₄⋊C₄	—	2	16	no	—
335	C₂×C₄⋊C₄	—	2	8	no	—
336	C₂×C₄⋊C₄	—	2	8	no	—
337	C₂×C₄⋊C₄	—	2	8	no	—
338	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	16	yes	complemented
339	#95	—	2	16	no	—
340	#95	—	2	8	no	—
341	#95	—	2	16	no	—
342	C₂⁴	C₂²×C₄×C₄₁	1	2	yes	—
343	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
344	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
345	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
346	C₂⁴	C₂×D₄×C₄₁	1	4	yes	—
347	C₂⁴	C₂×Q₈×C₄₁	1	2	yes	—
348	C₂⁴	C₂×Q₈×C₄₁	1	4	yes	—
349	C₂⁴	#41×C₄₁	1	2	yes	—
350	C₂⁴	#41×C₄₁	1	2	yes	—
351	C₂⁴	#41×C₄₁	1	4	yes	—
352	C₂⁴	#41×C₄₁	1	4	yes	—
353	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
354	C₂²×C₄	—	2	8	no	—
355	C₂²×C₄	—	2	8	no	—
356	C₂²×C₄	—	2	16	no	—
357	C₂²×C₄	—	2	8	no	—
358	C₂²×C₄	—	2	8	no	—
359	C₂²×C₄	—	2	8	no	—
360	C₂²×C₄	—	2	16	no	—
361	C₂²×C₄	—	2	8	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	2	8	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	8	no	—
371	C₂²×C₄	—	2	16	no	—
372	C₂²×C₄	—	2	16	no	—
373	C₂²×C₄	—	2	16	no	—
374	C₂²×C₄	—	2	16	no	—
375	C₂²×C₄	—	2	16	no	—
376	C₂²×C₄	—	2	16	no	—
377	C₂²×C₄	—	2	16	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	4	4	no	—
395	C₂²×C₄	—	4	8	no	—
396	C₂²×C₄	—	4	8	no	—
397	C₂²×C₄	—	4	8	no	—
398	C₂²×C₄	—	4	8	no	—
399	C₂²×C₄	—	4	8	no	—
400	C₂²×C₄	—	4	8	no	—
401	C₂²×C₄	—	4	4	no	—
402	C₂²×C₄	—	4	8	no	—
403	C₂²×C₄	—	4	8	no	—
404	C₂²×C₄	—	4	8	no	—
405	C₂²×C₄	C₂²⋊C₄×C₄₁	1	16	yes	—
406	C₂²×C₄	C₄⋊C₄×C₄₁	1	16	yes	complemented
407	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
408	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
409	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
410	C₂²×C₄	C₂×D₄×C₄₁	1	8	yes	—
411	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
412	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
413	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
414	C₂²×C₄	C₂×Q₈×C₄₁	1	8	yes	—
415	C₂²×C₄	C₂×Q₈×C₄₁	1	4	yes	—
416	C₄⋊C₄	—	2	32	no	—
417	C₄⋊C₄	—	2	32	no	—
418	C₂³	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
419	C₂³	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
420	C₂³	#117×C₄₁	1	4	yes	—
421	C₂³	C₄×D₄×C₄₁	1	8	yes	—
422	C₂³	C₄×Q₈×C₄₁	1	8	yes	—
423	C₂³	#120×C₄₁	1	4	yes	—
424	C₂³	#121×C₄₁	1	4	yes	—
425	C₂³	#121×C₄₁	1	4	yes	—
426	C₂³	#121×C₄₁	1	8	yes	—
427	C₂³	#121×C₄₁	1	8	yes	—
428	C₂³	C₂²⋊Q₈×C₄₁	1	4	yes	—
429	C₂³	C₂²⋊Q₈×C₄₁	1	4	yes	—
430	C₂³	C₂²⋊Q₈×C₄₁	1	8	yes	—
431	C₂³	C₂²⋊Q₈×C₄₁	1	8	yes	—
432	C₂³	C₂²⋊Q₈×C₄₁	1	8	yes	—
433	C₂³	#123×C₄₁	1	4	yes	—
434	C₂³	#123×C₄₁	1	8	yes	—
435	C₂³	#124×C₄₁	1	4	yes	—
436	C₂³	#125×C₄₁	1	8	yes	—
437	C₂³	#125×C₄₁	1	8	yes	—
438	C₂³	#126×C₄₁	1	8	yes	—
439	C₂³	C₄⋊Q₈×C₄₁	1	8	yes	—
440	C₂³	C₄⋊Q₈×C₄₁	1	4	yes	—
441	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
442	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
443	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
444	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
445	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
446	C₂³	C₂²×Q₈×C₄₁	1	1	yes	characteristic
447	C₂³	C₂²×Q₈×C₄₁	1	2	yes	—
448	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
449	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
450	C₂³	C₂×#41×C₄₁	1	2	yes	—
451	C₂³	C₂×#41×C₄₁	1	2	yes	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	8	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	32	no	—
463	C₂×C₄	—	2	32	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	8	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	8	no	—
468	C₂×C₄	—	2	8	no	—
469	C₂×C₄	—	2	8	no	—
470	C₂×C₄	—	2	8	no	—
471	C₂×C₄	—	2	8	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	—	4	4	no	—
482	C₂×C₄	—	4	4	no	—
483	C₂×C₄	—	4	16	no	—
484	C₂×C₄	—	4	32	no	—
485	C₂×C₄	—	4	32	no	—
486	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	8	yes	—
487	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	8	yes	complemented
488	C₂²	C₄₁×#380	1	8	yes	—
489	C₂²	C₄₁×#386	1	8	yes	—
490	C₂²	C₄₁×#387	1	16	yes	—
491	C₂²	C₄₁×#389	1	16	yes	—
492	C₂²	C₄₁×#391	1	8	yes	—
493	C₂²	C₄₁×#394	1	8	yes	—
494	C₂²	C₄₁×#395	1	8	yes	—
495	C₂²	C₄₁×#396	1	16	yes	—
496	C₂²	C₄₁×#398	1	8	yes	—
497	C₂²	C₄₁×#398	1	16	yes	—
498	C₂²	C₄₁×#400	1	8	yes	—
499	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
500	C₂²	C₂²×C₄⋊C₄×C₄₁	1	1	yes	characteristic
501	C₂²	C₂×#117×C₄₁	1	1	yes	characteristic
502	C₂²	C₂×C₄×D₄×C₄₁	1	2	yes	—
503	C₂²	C₂×C₄×Q₈×C₄₁	1	2	yes	—
504	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
505	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
506	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
507	C₂²	C₂×#121×C₄₁	1	2	yes	—
508	C₂²	C₂×#121×C₄₁	1	2	yes	—
509	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
510	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
511	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	2	yes	—
512	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	2	yes	—
513	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	2	yes	—
514	C₂²	C₂×#123×C₄₁	1	1	yes	characteristic
515	C₂²	C₂×#123×C₄₁	1	2	yes	—
516	C₂²	C₂×#124×C₄₁	1	1	yes	characteristic
517	C₂²	C₂×#125×C₄₁	1	2	yes	—
518	C₂²	C₂×#125×C₄₁	1	2	yes	—
519	C₂²	C₂×#126×C₄₁	1	2	yes	—
520	C₂²	C₂×C₄⋊Q₈×C₄₁	1	2	yes	—
521	C₂²	C₂×C₄⋊Q₈×C₄₁	1	1	yes	characteristic
522	C₄	—	2	8	no	—
523	C₄	—	2	8	no	—
524	C₄	—	4	4	no	—
525	C₄	—	4	8	no	—
526	C₄	—	4	8	no	—
527	C₂	C₄₁×#1441	1	16	yes	direct product factor
528	C₂	C₂×C₄₁×#380	1	1	yes	characteristic
529	C₂	C₂×C₄₁×#386	1	1	yes	characteristic
530	C₂	C₂×C₄₁×#387	1	2	yes	—
531	C₂	C₂×C₄₁×#389	1	2	yes	—
532	C₂	C₂×C₄₁×#391	1	1	yes	characteristic
533	C₂	C₂×C₄₁×#394	1	1	yes	characteristic
534	C₂	C₂×C₄₁×#395	1	1	yes	characteristic
535	C₂	C₂×C₄₁×#396	1	2	yes	—
536	C₂	C₂×C₄₁×#398	1	1	yes	characteristic
537	C₂	C₂×C₄₁×#398	1	2	yes	—
538	C₂	C₂×C₄₁×#400	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁵×C₄₁	C₂³
commutator	C₂³	C₂³×C₄×C₄₁
Frattini, cosocle	C₂⁴	C₂⁴×C₄₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁵×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₄₁×#1441	C₂	direct (N × H)
16. C₂²×C₄⋊C₄×C₄₁	C₄	semidirect
68. C₂×C₄⋊C₄×C₄₁	C₂×C₄	semidirect
136. C₂²×C₄×C₄₁	C₄⋊C₄	semidirect
217. C₂×C₄×C₄₁	C₂×C₄⋊C₄	semidirect
218. C₂×#1441	C₄₁	direct (N × H)
263. #1441	C₂×C₄₁	direct (N × H)
264. C₂×C₄₁	#1441	direct (N × H)
285. C₂²×C₄⋊C₄	C₄×C₄₁	semidirect
294. C₄₁	C₂×#1441	direct (N × H)
338. C₂×C₄⋊C₄	C₂×C₄×C₄₁	semidirect
406. C₂²×C₄	C₄⋊C₄×C₄₁	semidirect
487. C₂×C₄	C₂×C₄⋊C₄×C₄₁	semidirect
527. C₂	C₄₁×#1441	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊C₄×C₄₁	2
C₂²×#95×C₄₁	2
C₄₁×#1441	2
C₂×#1441	41

Subgroups — C2×C41×#1441 #23790039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#1441 #23790039