Subgroups — C₄₁×#22334 #23798535

Order 10496.

806 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2392	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#1955	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#1954	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1924	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1917	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1916	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1870	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1870	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1869	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1869	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#1818	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#1753	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×C₂²⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
34	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
35	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
38	C₄₁×#398	C₄	1	1	yes	characteristic
39	C₄₁×#397	C₄	1	1	yes	characteristic
40	C₄₁×#396	C₄	1	1	yes	characteristic
41	C₄₁×#396	C₄	1	1	yes	characteristic
42	C₄₁×#394	C₄	1	1	yes	characteristic
43	C₄₁×#394	C₄	1	1	yes	characteristic
44	C₄₁×#394	C₄	1	1	yes	characteristic
45	C₄₁×#392	C₄	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
47	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
48	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
49	C₄₁×#336	C₂²	1	1	yes	characteristic
50	C₄₁×#336	C₂²	1	1	yes	characteristic
51	C₄₁×#336	C₂²	1	1	yes	characteristic
52	C₄₁×#336	C₂²	1	1	yes	characteristic
53	C₄₁×#336	C₂²	1	1	yes	characteristic
54	C₄₁×#336	C₂²	1	1	yes	characteristic
55	C₄₁×#336	C₂²	1	1	yes	characteristic
56	C₄₁×#336	C₂²	1	1	yes	characteristic
57	C₄₁×#336	C₂²	1	1	yes	characteristic
58	C₄₁×#336	C₂²	1	1	yes	characteristic
59	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
60	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
61	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
65	C₂×M₁₆×C₄₁	—	2	2	no	—
66	C₂×M₁₆×C₄₁	—	4	1	no	—
67	C₂×M₁₆×C₄₁	—	4	1	no	—
68	C₂²×C₈×C₄₁	—	2	2	no	—
69	C₂²×C₈×C₄₁	—	4	1	no	—
70	C₂²×C₈×C₄₁	—	4	1	no	—
71	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
79	C₄×D₄×C₄₁	—	4	1	no	—
80	C₄×D₄×C₄₁	—	4	1	no	—
81	C₄×D₄×C₄₁	—	4	1	no	—
82	C₄×D₄×C₄₁	—	4	1	no	—
83	C₄×D₄×C₄₁	—	4	1	no	—
84	C₄×D₄×C₄₁	—	4	1	no	—
85	#117×C₄₁	—	4	1	no	—
86	#117×C₄₁	—	4	1	no	—
87	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
110	C₄⋊C₈×C₄₁	—	4	1	no	—
111	C₄⋊C₈×C₄₁	—	4	1	no	—
112	C₂²⋊C₈×C₄₁	—	2	2	no	—
113	C₂²⋊C₈×C₄₁	—	2	2	no	—
114	C₂²⋊C₈×C₄₁	—	2	2	no	—
115	C₂²⋊C₈×C₄₁	—	2	2	no	—
116	C₂²⋊C₈×C₄₁	—	4	1	no	—
117	C₂²⋊C₈×C₄₁	—	4	1	no	—
118	C₂²⋊C₈×C₄₁	—	4	1	no	—
119	C₂²⋊C₈×C₄₁	—	4	1	no	—
120	C₂²⋊C₈×C₄₁	—	4	1	no	—
121	C₂²⋊C₈×C₄₁	—	4	1	no	—
122	#97×C₄₁	—	4	1	no	—
123	#97×C₄₁	—	4	1	no	—
124	C₄×C₈×C₄₁	—	4	1	no	—
125	C₄×C₈×C₄₁	—	4	1	no	—
126	#95×C₄₁	C₂×C₄	1	1	yes	characteristic
127	#95×C₄₁	C₂×C₄	1	1	yes	characteristic
128	#95×C₄₁	C₂×C₄	1	1	yes	characteristic
129	#95×C₄₁	C₂×C₄	1	1	yes	characteristic
130	#95×C₄₁	C₂×C₄	1	1	yes	characteristic
131	#95×C₄₁	C₂×C₄	1	1	yes	characteristic
132	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
133	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
134	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
135	C₂×D₄×C₄₁	—	2	2	no	—
136	C₂×D₄×C₄₁	—	2	2	no	—
137	C₂×D₄×C₄₁	—	2	2	no	—
138	C₂×D₄×C₄₁	—	4	1	no	—
139	C₂×D₄×C₄₁	—	4	1	no	—
140	C₂×D₄×C₄₁	—	4	1	no	—
141	C₂×D₄×C₄₁	—	4	1	no	—
142	C₂×D₄×C₄₁	—	4	1	no	—
143	C₂×D₄×C₄₁	—	4	1	no	—
144	C₂²×C₄×C₄₁	—	2	1	no	—
145	C₂²×C₄×C₄₁	—	2	1	no	—
146	C₂²×C₄×C₄₁	—	2	1	no	—
147	C₂²×C₄×C₄₁	—	2	1	no	—
148	C₂²×C₄×C₄₁	—	2	1	no	—
149	C₂²×C₄×C₄₁	—	2	1	no	—
150	C₂²×C₄×C₄₁	—	2	1	no	—
151	C₂²×C₄×C₄₁	—	2	1	no	—
152	C₂²×C₄×C₄₁	—	2	1	no	—
153	C₂²×C₄×C₄₁	—	2	1	no	—
154	C₂²×C₄×C₄₁	—	2	1	no	—
155	C₂²×C₄×C₄₁	—	2	1	no	—
156	C₂²×C₄×C₄₁	—	2	1	no	—
157	C₂²×C₄×C₄₁	—	2	1	no	—
158	C₂²×C₄×C₄₁	—	2	1	no	—
159	C₂²×C₄×C₄₁	—	2	1	no	—
160	C₂²×C₄×C₄₁	—	2	1	no	—
161	C₂²×C₄×C₄₁	—	2	1	no	—
162	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
174	M₁₆×C₄₁	—	4	4	no	—
175	C₂×C₈×C₄₁	—	2	1	no	—
176	C₂×C₈×C₄₁	—	2	1	no	—
177	C₂×C₈×C₄₁	—	2	1	no	—
178	C₂×C₈×C₄₁	—	2	1	no	—
179	C₂×C₈×C₄₁	—	2	1	no	—
180	C₂×C₈×C₄₁	—	2	1	no	—
181	C₂×C₈×C₄₁	—	2	1	no	—
182	C₂×C₈×C₄₁	—	2	1	no	—
183	C₂×C₈×C₄₁	—	2	1	no	—
184	C₂×C₈×C₄₁	—	2	1	no	—
185	C₂×C₈×C₄₁	—	2	1	no	—
186	C₂×C₈×C₄₁	—	2	1	no	—
187	C₂×C₈×C₄₁	—	2	1	no	—
188	C₂×C₈×C₄₁	—	2	1	no	—
189	C₂×C₈×C₄₁	—	2	1	no	—
190	C₂×C₈×C₄₁	—	2	1	no	—
191	C₂×C₈×C₄₁	—	2	1	no	—
192	C₂×C₈×C₄₁	—	2	1	no	—
193	C₂×C₈×C₄₁	—	2	1	no	—
194	C₂×C₈×C₄₁	—	2	1	no	—
195	C₂×C₈×C₄₁	—	2	1	no	—
196	C₂×C₈×C₄₁	—	2	1	no	—
197	C₂×C₈×C₄₁	—	4	4	no	—
198	C₂×C₈×C₄₁	#41	1	2	yes	—
199	C₂×C₈×C₄₁	#41	1	2	yes	—
200	C₄⋊C₄×C₄₁	—	2	2	no	—
201	C₄⋊C₄×C₄₁	—	4	1	no	—
202	C₄⋊C₄×C₄₁	—	4	1	no	—
203	C₄⋊C₄×C₄₁	—	4	1	no	—
204	C₄⋊C₄×C₄₁	—	4	1	no	—
205	C₄⋊C₄×C₄₁	—	4	1	no	—
206	C₄⋊C₄×C₄₁	—	4	1	no	—
207	C₂²⋊C₄×C₄₁	—	2	2	no	—
208	C₂²⋊C₄×C₄₁	—	2	2	no	—
209	C₂²⋊C₄×C₄₁	—	4	1	no	—
210	C₂²⋊C₄×C₄₁	—	4	1	no	—
211	C₂²⋊C₄×C₄₁	—	4	1	no	—
212	C₂²⋊C₄×C₄₁	—	4	1	no	—
213	C₂²⋊C₄×C₄₁	—	4	1	no	—
214	C₂²⋊C₄×C₄₁	—	4	1	no	—
215	C₂²⋊C₄×C₄₁	—	4	1	no	—
216	C₂²⋊C₄×C₄₁	—	4	1	no	—
217	C₂²⋊C₄×C₄₁	—	4	1	no	—
218	C₂²⋊C₄×C₄₁	—	4	1	no	—
219	C₄²×C₄₁	—	2	1	no	—
220	C₄²×C₄₁	—	2	1	no	—
221	C₄²×C₄₁	—	2	1	no	—
222	C₄²×C₄₁	—	2	1	no	—
223	C₄²×C₄₁	—	2	1	no	—
224	C₄²×C₄₁	—	2	1	no	—
225	C₄²×C₄₁	—	2	1	no	—
226	C₄²×C₄₁	—	2	1	no	—
227	C₂³×C₄₁	—	2	1	no	—
228	C₂³×C₄₁	—	2	1	no	—
229	C₂³×C₄₁	—	2	1	no	—
230	C₂³×C₄₁	—	2	1	no	—
231	C₂³×C₄₁	—	2	1	no	—
232	C₂³×C₄₁	—	2	1	no	—
233	C₂³×C₄₁	—	2	1	no	—
234	C₂³×C₄₁	—	2	1	no	—
235	C₂³×C₄₁	—	2	1	no	—
236	C₂³×C₄₁	—	2	1	no	—
237	C₂³×C₄₁	—	2	1	no	—
238	C₂³×C₄₁	—	2	1	no	—
239	C₂³×C₄₁	—	2	1	no	—
240	C₂³×C₄₁	—	2	1	no	—
241	C₂³×C₄₁	—	2	1	no	—
242	C₂³×C₄₁	—	2	1	no	—
243	C₂³×C₄₁	—	2	1	no	—
244	C₂³×C₄₁	—	2	1	no	—
245	C₂³×C₄₁	—	2	1	no	—
246	C₂³×C₄₁	—	2	1	no	—
247	C₂³×C₄₁	#131	1	2	yes	—
248	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
249	D₄×C₄₁	—	4	4	no	—
250	D₄×C₄₁	—	4	4	no	—
251	D₄×C₄₁	—	4	4	no	—
252	C₂×C₄×C₄₁	—	2	1	no	—
253	C₂×C₄×C₄₁	—	2	1	no	—
254	C₂×C₄×C₄₁	—	2	1	no	—
255	C₂×C₄×C₄₁	—	2	1	no	—
256	C₂×C₄×C₄₁	—	2	1	no	—
257	C₂×C₄×C₄₁	—	2	1	no	—
258	C₂×C₄×C₄₁	—	2	1	no	—
259	C₂×C₄×C₄₁	—	2	1	no	—
260	C₂×C₄×C₄₁	—	2	1	no	—
261	C₂×C₄×C₄₁	—	2	1	no	—
262	C₂×C₄×C₄₁	—	2	1	no	—
263	C₂×C₄×C₄₁	—	2	1	no	—
264	C₂×C₄×C₄₁	—	2	1	no	—
265	C₂×C₄×C₄₁	—	2	1	no	—
266	C₂×C₄×C₄₁	—	2	1	no	—
267	C₂×C₄×C₄₁	—	2	1	no	—
268	C₂×C₄×C₄₁	—	2	1	no	—
269	C₂×C₄×C₄₁	—	2	1	no	—
270	C₂×C₄×C₄₁	—	2	1	no	—
271	C₂×C₄×C₄₁	—	2	1	no	—
272	C₂×C₄×C₄₁	—	2	1	no	—
273	C₂×C₄×C₄₁	—	2	1	no	—
274	C₂×C₄×C₄₁	—	2	1	no	—
275	C₂×C₄×C₄₁	—	2	1	no	—
276	C₂×C₄×C₄₁	—	2	1	no	—
277	C₂×C₄×C₄₁	—	2	1	no	—
278	C₂×C₄×C₄₁	—	2	1	no	—
279	C₂×C₄×C₄₁	—	2	1	no	—
280	C₂×C₄×C₄₁	—	2	1	no	—
281	C₂×C₄×C₄₁	—	2	1	no	—
282	C₂×C₄×C₄₁	—	2	1	no	—
283	C₂×C₄×C₄₁	—	2	1	no	—
284	C₂×C₄×C₄₁	—	4	1	no	—
285	C₂×C₄×C₄₁	—	4	1	no	—
286	C₂×C₄×C₄₁	—	4	1	no	—
287	C₂×C₄×C₄₁	—	4	1	no	—
288	C₂×C₄×C₄₁	—	4	1	no	—
289	C₂×C₄×C₄₁	—	4	1	no	—
290	C₂×C₄×C₄₁	—	4	1	no	—
291	C₂×C₄×C₄₁	—	4	1	no	—
292	C₂×C₄×C₄₁	—	4	1	no	—
293	C₂×C₄×C₄₁	—	4	1	no	—
294	C₂×C₄×C₄₁	—	4	1	no	—
295	C₂×C₄×C₄₁	—	4	1	no	—
296	C₂×C₄×C₄₁	#131	1	2	yes	—
297	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
299	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
300	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
301	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
302	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
303	C₈×C₄₁	—	2	2	no	—
304	C₈×C₄₁	—	2	2	no	—
305	C₈×C₄₁	—	4	1	no	—
306	C₈×C₄₁	—	4	1	no	—
307	C₈×C₄₁	—	4	1	no	—
308	C₈×C₄₁	—	4	1	no	—
309	C₈×C₄₁	—	4	1	no	—
310	C₈×C₄₁	—	4	1	no	—
311	#22334	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
312	C₂²×C₄₁	—	2	2	no	—
313	C₂²×C₄₁	—	2	2	no	—
314	C₂²×C₄₁	—	2	2	no	—
315	C₂²×C₄₁	—	4	1	no	—
316	C₂²×C₄₁	—	4	1	no	—
317	C₂²×C₄₁	—	4	1	no	—
318	C₂²×C₄₁	—	4	1	no	—
319	C₂²×C₄₁	—	4	1	no	—
320	C₂²×C₄₁	—	4	1	no	—
321	C₂²×C₄₁	—	4	1	no	—
322	C₂²×C₄₁	—	4	1	no	—
323	C₂²×C₄₁	—	4	1	no	—
324	C₂²×C₄₁	—	4	1	no	—
325	C₂²×C₄₁	—	4	1	no	—
326	C₂²×C₄₁	—	4	1	no	—
327	C₂²×C₄₁	—	4	1	no	—
328	C₂²×C₄₁	—	4	1	no	—
329	C₂²×C₄₁	—	4	1	no	—
330	C₂²×C₄₁	—	4	1	no	—
331	C₂²×C₄₁	—	4	1	no	—
332	C₂²×C₄₁	—	4	1	no	—
333	C₂²×C₄₁	C₄×#41	1	1	yes	characteristic
334	C₂²×C₄₁	#518	1	1	yes	characteristic
335	C₂²×C₄₁	#518	1	1	yes	characteristic
336	C₂²×C₄₁	C₂×#131	1	1	yes	characteristic
337	C₂²×C₄₁	C₂×#131	1	1	yes	characteristic
338	C₂²×C₄₁	#568	1	1	yes	characteristic
339	C₂²×C₄₁	#568	1	1	yes	characteristic
340	C₄×C₄₁	—	2	2	no	—
341	C₄×C₄₁	—	4	1	no	—
342	C₄×C₄₁	—	4	1	no	—
343	C₄×C₄₁	—	4	1	no	—
344	C₄×C₄₁	—	4	1	no	—
345	C₄×C₄₁	—	4	1	no	—
346	C₄×C₄₁	—	4	1	no	—
347	C₄×C₄₁	—	4	1	no	—
348	C₄×C₄₁	—	4	1	no	—
349	C₄×C₄₁	—	4	1	no	—
350	C₄×C₄₁	—	4	1	no	—
351	C₄×C₄₁	#538	1	1	yes	characteristic
352	C₄×C₄₁	#538	1	1	yes	characteristic
353	C₄×C₄₁	#540	1	1	yes	characteristic
354	C₄×C₄₁	#540	1	1	yes	characteristic
355	#2392	C₂×C₄₁	1	1	yes	characteristic
356	#1955	C₂×C₄₁	1	1	yes	characteristic, complemented
357	#1954	C₂×C₄₁	1	1	yes	characteristic, complemented
358	#1924	C₂×C₄₁	1	1	yes	characteristic, complemented
359	#1924	C₂×C₄₁	1	1	yes	characteristic, complemented
360	#1917	C₂×C₄₁	1	1	yes	characteristic, complemented
361	#1916	C₂×C₄₁	1	1	yes	characteristic, complemented
362	#1870	C₂×C₄₁	1	1	yes	characteristic, complemented
363	#1870	C₂×C₄₁	1	1	yes	characteristic, complemented
364	#1869	C₂×C₄₁	1	1	yes	characteristic, complemented
365	#1869	C₂×C₄₁	1	1	yes	characteristic, complemented
366	#1818	C₂×C₄₁	1	1	yes	characteristic, complemented
367	#1753	C₂×C₄₁	1	1	yes	characteristic, complemented
368	C₈×C₂²⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
369	#1750	C₂×C₄₁	1	1	yes	characteristic, complemented
370	C₂×C₄₁	—	4	2	no	—
371	C₂×C₄₁	—	8	1	no	—
372	C₂×C₄₁	—	8	1	no	—
373	C₂×C₄₁	#2333	1	1	yes	characteristic
374	C₂×C₄₁	#2966	1	1	yes	characteristic
375	C₂×C₄₁	#2967	1	1	yes	characteristic
376	C₂×C₄₁	#2976	1	1	yes	characteristic
377	C₂×C₄₁	#2976	1	1	yes	characteristic
378	C₂×C₄₁	#2976	1	1	yes	characteristic
379	C₂×C₄₁	#2981	1	1	yes	characteristic
380	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
381	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
382	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
383	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
384	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
385	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
386	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
387	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
388	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
389	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
390	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
391	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
392	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
393	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
394	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
395	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
396	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
397	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
398	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
399	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
400	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
401	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
402	#398	C₄×C₄₁	1	1	yes	characteristic
403	#397	C₄×C₄₁	1	1	yes	characteristic
404	#396	C₄×C₄₁	1	1	yes	characteristic
405	#396	C₄×C₄₁	1	1	yes	characteristic
406	#394	C₄×C₄₁	1	1	yes	characteristic
407	#394	C₄×C₄₁	1	1	yes	characteristic
408	#394	C₄×C₄₁	1	1	yes	characteristic
409	#392	C₄×C₄₁	1	1	yes	characteristic
410	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
411	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
412	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
413	#336	C₂²×C₄₁	1	1	yes	characteristic
414	#336	C₂²×C₄₁	1	1	yes	characteristic
415	#336	C₂²×C₄₁	1	1	yes	characteristic
416	#336	C₂²×C₄₁	1	1	yes	characteristic
417	#336	C₂²×C₄₁	1	1	yes	characteristic
418	#336	C₂²×C₄₁	1	1	yes	characteristic
419	#336	C₂²×C₄₁	1	1	yes	characteristic
420	#336	C₂²×C₄₁	1	1	yes	characteristic
421	#336	C₂²×C₄₁	1	1	yes	characteristic
422	#336	C₂²×C₄₁	1	1	yes	characteristic
423	C₄₁	#22334	1	1	yes	characteristic, direct product factor, Sylow
424	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
425	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
426	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
427	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
429	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
430	C₂×M₁₆	—	2	2	no	—
431	C₂×M₁₆	—	4	1	no	—
432	C₂×M₁₆	—	4	1	no	—
433	C₂²×C₈	—	2	2	no	—
434	C₂²×C₈	—	4	1	no	—
435	C₂²×C₈	—	4	1	no	—
436	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
437	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
438	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
439	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
440	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
441	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
442	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
443	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
444	C₄×D₄	—	4	1	no	—
445	C₄×D₄	—	4	1	no	—
446	C₄×D₄	—	4	1	no	—
447	C₄×D₄	—	4	1	no	—
448	C₄×D₄	—	4	1	no	—
449	C₄×D₄	—	4	1	no	—
450	#117	—	4	1	no	—
451	#117	—	4	1	no	—
452	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
459	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
460	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
461	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
462	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
464	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
465	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
466	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
467	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
468	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
469	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
470	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
471	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
472	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
473	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
474	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
475	C₄⋊C₈	—	4	1	no	—
476	C₄⋊C₈	—	4	1	no	—
477	C₂²⋊C₈	—	2	2	no	—
478	C₂²⋊C₈	—	2	2	no	—
479	C₂²⋊C₈	—	2	2	no	—
480	C₂²⋊C₈	—	2	2	no	—
481	C₂²⋊C₈	—	4	1	no	—
482	C₂²⋊C₈	—	4	1	no	—
483	C₂²⋊C₈	—	4	1	no	—
484	C₂²⋊C₈	—	4	1	no	—
485	C₂²⋊C₈	—	4	1	no	—
486	C₂²⋊C₈	—	4	1	no	—
487	#97	—	4	1	no	—
488	#97	—	4	1	no	—
489	C₄×C₈	—	4	1	no	—
490	C₄×C₈	—	4	1	no	—
491	#95	C₂×C₄×C₄₁	1	1	yes	characteristic
492	#95	C₂×C₄×C₄₁	1	1	yes	characteristic
493	#95	C₂×C₄×C₄₁	1	1	yes	characteristic
494	#95	C₂×C₄×C₄₁	1	1	yes	characteristic
495	#95	C₂×C₄×C₄₁	1	1	yes	characteristic
496	#95	C₂×C₄×C₄₁	1	1	yes	characteristic
497	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
498	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
499	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
500	C₂×D₄	—	2	2	no	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	—	2	2	no	—
503	C₂×D₄	—	4	1	no	—
504	C₂×D₄	—	4	1	no	—
505	C₂×D₄	—	4	1	no	—
506	C₂×D₄	—	4	1	no	—
507	C₂×D₄	—	4	1	no	—
508	C₂×D₄	—	4	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
528	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
529	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
530	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
531	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
532	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
533	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
534	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
535	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
536	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
537	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
538	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
539	M₁₆	—	4	4	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	4	4	no	—
563	C₂×C₈	#41×C₄₁	1	2	yes	—
564	C₂×C₈	#41×C₄₁	1	2	yes	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	4	1	no	—
567	C₄⋊C₄	—	4	1	no	—
568	C₄⋊C₄	—	4	1	no	—
569	C₄⋊C₄	—	4	1	no	—
570	C₄⋊C₄	—	4	1	no	—
571	C₄⋊C₄	—	4	1	no	—
572	C₂²⋊C₄	—	2	2	no	—
573	C₂²⋊C₄	—	2	2	no	—
574	C₂²⋊C₄	—	4	1	no	—
575	C₂²⋊C₄	—	4	1	no	—
576	C₂²⋊C₄	—	4	1	no	—
577	C₂²⋊C₄	—	4	1	no	—
578	C₂²⋊C₄	—	4	1	no	—
579	C₂²⋊C₄	—	4	1	no	—
580	C₂²⋊C₄	—	4	1	no	—
581	C₂²⋊C₄	—	4	1	no	—
582	C₂²⋊C₄	—	4	1	no	—
583	C₂²⋊C₄	—	4	1	no	—
584	C₄²	—	2	1	no	—
585	C₄²	—	2	1	no	—
586	C₄²	—	2	1	no	—
587	C₄²	—	2	1	no	—
588	C₄²	—	2	1	no	—
589	C₄²	—	2	1	no	—
590	C₄²	—	2	1	no	—
591	C₄²	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	2	1	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	1	no	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	1	no	—
612	C₂³	#131×C₄₁	1	2	yes	—
613	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
614	D₄	—	4	4	no	—
615	D₄	—	4	4	no	—
616	D₄	—	4	4	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	#131×C₄₁	1	2	yes	—
662	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
663	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
664	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
665	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
666	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
667	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
668	C₈	—	2	2	no	—
669	C₈	—	2	2	no	—
670	C₈	—	4	1	no	—
671	C₈	—	4	1	no	—
672	C₈	—	4	1	no	—
673	C₈	—	4	1	no	—
674	C₈	—	4	1	no	—
675	C₈	—	4	1	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	4	1	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	1	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	1	no	—
689	C₂²	—	4	1	no	—
690	C₂²	—	4	1	no	—
691	C₂²	—	4	1	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	1	no	—
697	C₂²	C₄×#41×C₄₁	1	1	yes	characteristic
698	C₂²	C₄₁×#518	1	1	yes	characteristic
699	C₂²	C₄₁×#518	1	1	yes	characteristic
700	C₂²	C₂×#131×C₄₁	1	1	yes	characteristic
701	C₂²	C₂×#131×C₄₁	1	1	yes	characteristic
702	C₂²	C₄₁×#568	1	1	yes	characteristic
703	C₂²	C₄₁×#568	1	1	yes	characteristic
704	C₄	—	2	2	no	—
705	C₄	—	4	1	no	—
706	C₄	—	4	1	no	—
707	C₄	—	4	1	no	—
708	C₄	—	4	1	no	—
709	C₄	—	4	1	no	—
710	C₄	—	4	1	no	—
711	C₄	—	4	1	no	—
712	C₄	—	4	1	no	—
713	C₄	—	4	1	no	—
714	C₄	—	4	1	no	—
715	C₄	C₄₁×#538	1	1	yes	characteristic
716	C₄	C₄₁×#538	1	1	yes	characteristic
717	C₄	C₄₁×#540	1	1	yes	characteristic
718	C₄	C₄₁×#540	1	1	yes	characteristic
719	C₂	—	4	2	no	—
720	C₂	—	8	1	no	—
721	C₂	—	8	1	no	—
722	C₂	C₄₁×#2333	1	1	yes	characteristic
723	C₂	C₄₁×#2966	1	1	yes	characteristic
724	C₂	C₄₁×#2967	1	1	yes	characteristic
725	C₂	C₄₁×#2976	1	1	yes	characteristic
726	C₂	C₄₁×#2976	1	1	yes	characteristic
727	C₂	C₄₁×#2976	1	1	yes	characteristic
728	C₂	C₄₁×#2981	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₄₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂³×C₄₁	C₂³×C₄
prime radical	C₄₁×#392	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#1955	C₂	semidirect
3. C₄₁×#1954	C₂	semidirect
4. C₄₁×#1924	C₂	semidirect
5. C₄₁×#1924	C₂	semidirect
6. C₄₁×#1917	C₂	semidirect
7. C₄₁×#1916	C₂	semidirect
8. C₄₁×#1870	C₂	semidirect
9. C₄₁×#1870	C₂	semidirect
10. C₄₁×#1869	C₂	semidirect
11. C₄₁×#1869	C₂	semidirect
12. C₄₁×#1818	C₂	semidirect
13. C₄₁×#1753	C₂	semidirect
14. C₈×C₂²⋊C₄×C₄₁	C₂	semidirect
15. C₄₁×#1750	C₂	semidirect
311. #22334	C₄₁	direct (N × H)
356. #1955	C₂×C₄₁	semidirect
357. #1954	C₂×C₄₁	semidirect
358. #1924	C₂×C₄₁	semidirect
359. #1924	C₂×C₄₁	semidirect
360. #1917	C₂×C₄₁	semidirect
361. #1916	C₂×C₄₁	semidirect
362. #1870	C₂×C₄₁	semidirect
363. #1870	C₂×C₄₁	semidirect
364. #1869	C₂×C₄₁	semidirect
365. #1869	C₂×C₄₁	semidirect
366. #1818	C₂×C₄₁	semidirect
367. #1753	C₂×C₄₁	semidirect
368. C₈×C₂²⋊C₄	C₂×C₄₁	semidirect
369. #1750	C₂×C₄₁	semidirect
423. C₄₁	#22334	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#2392	2
C₄₁×#1955	2
C₄₁×#1954	2
C₄₁×#1924	2
C₄₁×#1917	2
C₄₁×#1916	2
C₄₁×#1870	2
C₄₁×#1869	2
C₄₁×#1818	2
C₄₁×#1753	2
C₈×C₂²⋊C₄×C₄₁	2
C₄₁×#1750	2
#22334	41

Subgroups — C41×#22334 #23798535

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#22334 #23798535