Subgroups — C₄₁×#25373 #23801574

Order 10496.

1068 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#464	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#463	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#459	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#2544	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#2054	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#2014	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#2012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1983	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#1939	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#1880	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#1877	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#102×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
29	C₄₁×#495	—	2	4	no	—
30	C₄₁×#464	—	2	4	no	—
31	C₄₁×#463	—	2	4	no	—
32	C₄₁×#459	—	2	4	no	—
33	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
36	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
37	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
38	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
40	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
41	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
42	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
43	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
45	C₄₁×#394	—	2	1	no	—
46	C₄₁×#394	—	2	1	no	—
47	C₄₁×#391	C₂²	1	1	yes	characteristic
48	C₄₁×#391	C₂²	1	1	yes	characteristic
49	C₄₁×#390	C₂²	1	1	yes	characteristic
50	C₄₁×#390	C₂²	1	1	yes	characteristic
51	C₄₁×#388	—	2	1	no	—
52	C₄₁×#388	—	2	1	no	—
53	C₄₁×#386	—	2	1	no	—
54	C₄₁×#386	—	2	1	no	—
55	C₄₁×#385	—	2	1	no	—
56	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
57	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
58	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
59	C₄₁×#340	C₂²	1	1	yes	characteristic
60	C₄₁×#340	C₂²	1	1	yes	characteristic
61	C₄₁×#336	C₂²	1	1	yes	characteristic
62	C₄₁×#336	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₄₁	—	2	1	no	—
66	C₂²×D₄×C₄₁	—	2	1	no	—
67	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₄₁	—	2	1	no	—
71	C₂³×C₄×C₄₁	—	2	1	no	—
72	C₂×Q₁₆×C₄₁	—	2	2	no	—
73	C₂×Q₁₆×C₄₁	—	2	2	no	—
74	C₂×Q₁₆×C₄₁	—	4	1	no	—
75	C₂×SD₁₆×C₄₁	—	2	2	no	—
76	C₂×SD₁₆×C₄₁	—	2	2	no	—
77	C₂×SD₁₆×C₄₁	—	2	2	no	—
78	C₂×SD₁₆×C₄₁	—	2	2	no	—
79	C₂×SD₁₆×C₄₁	—	2	2	no	—
80	C₂×SD₁₆×C₄₁	—	2	2	no	—
81	C₂×SD₁₆×C₄₁	—	4	1	no	—
82	C₂×SD₁₆×C₄₁	—	4	1	no	—
83	C₂×SD₁₆×C₄₁	—	4	1	no	—
84	C₂×D₈×C₄₁	—	2	2	no	—
85	C₂×D₈×C₄₁	—	2	2	no	—
86	C₂×D₈×C₄₁	—	2	2	no	—
87	C₂×D₈×C₄₁	—	2	2	no	—
88	C₂×D₈×C₄₁	—	4	1	no	—
89	C₂×D₈×C₄₁	—	4	1	no	—
90	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
94	#127×C₄₁	—	2	2	no	—
95	#127×C₄₁	—	4	1	no	—
96	#124×C₄₁	—	2	2	no	—
97	#124×C₄₁	—	2	2	no	—
98	#124×C₄₁	—	2	2	no	—
99	#124×C₄₁	—	2	2	no	—
100	#124×C₄₁	—	4	1	no	—
101	#124×C₄₁	D₄	1	4	yes	complemented
102	C₄×Q₈×C₄₁	—	2	2	no	—
103	C₄×Q₈×C₄₁	—	4	1	no	—
104	C₄×D₄×C₄₁	—	2	2	no	—
105	C₄×D₄×C₄₁	—	2	2	no	—
106	C₄×D₄×C₄₁	—	2	2	no	—
107	C₄×D₄×C₄₁	—	4	1	no	—
108	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
109	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
126	C₂×C₄²×C₄₁	—	2	1	no	—
127	C₂×C₄²×C₄₁	—	2	1	no	—
128	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
131	C₄⋊C₈×C₄₁	—	2	2	no	—
132	C₄⋊C₈×C₄₁	—	2	2	no	—
133	C₄⋊C₈×C₄₁	—	2	2	no	—
134	#103×C₄₁	—	2	2	no	—
135	#103×C₄₁	—	2	2	no	—
136	#103×C₄₁	—	4	1	no	—
137	#102×C₄₁	—	2	2	no	—
138	#102×C₄₁	—	2	2	no	—
139	#102×C₄₁	—	2	2	no	—
140	#102×C₄₁	—	4	1	no	—
141	#102×C₄₁	D₄	1	4	yes	—
142	C₄×C₈×C₄₁	—	2	2	no	—
143	#95×C₄₁	—	2	1	no	—
144	#95×C₄₁	—	2	1	no	—
145	#95×C₄₁	—	2	1	no	—
146	#95×C₄₁	—	2	1	no	—
147	#95×C₄₁	—	2	1	no	—
148	#95×C₄₁	D₄	1	1	yes	characteristic
149	#95×C₄₁	D₄	1	1	yes	characteristic
150	C₂⁴×C₄₁	—	2	1	no	—
151	C₂⁴×C₄₁	—	2	1	no	—
152	C₂⁴×C₄₁	—	2	1	no	—
153	C₂×Q₈×C₄₁	—	2	1	no	—
154	C₂×Q₈×C₄₁	—	2	1	no	—
155	C₂×Q₈×C₄₁	—	2	1	no	—
156	C₂×Q₈×C₄₁	—	2	1	no	—
157	C₂×Q₈×C₄₁	—	2	1	no	—
158	C₂×Q₈×C₄₁	—	2	1	no	—
159	C₂×Q₈×C₄₁	—	2	1	no	—
160	C₂×Q₈×C₄₁	—	2	1	no	—
161	C₂×Q₈×C₄₁	—	2	1	no	—
162	C₂×Q₈×C₄₁	—	2	1	no	—
163	C₂×Q₈×C₄₁	—	2	1	no	—
164	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
165	C₂×D₄×C₄₁	—	2	1	no	—
166	C₂×D₄×C₄₁	—	2	1	no	—
167	C₂×D₄×C₄₁	—	2	1	no	—
168	C₂×D₄×C₄₁	—	2	1	no	—
169	C₂×D₄×C₄₁	—	2	1	no	—
170	C₂×D₄×C₄₁	—	2	1	no	—
171	C₂×D₄×C₄₁	—	2	1	no	—
172	C₂×D₄×C₄₁	—	2	1	no	—
173	C₂×D₄×C₄₁	—	2	1	no	—
174	C₂×D₄×C₄₁	—	2	1	no	—
175	C₂×D₄×C₄₁	—	2	1	no	—
176	C₂×D₄×C₄₁	—	2	1	no	—
177	C₂×D₄×C₄₁	—	2	1	no	—
178	C₂×D₄×C₄₁	—	2	1	no	—
179	C₂×D₄×C₄₁	—	2	1	no	—
180	C₂×D₄×C₄₁	—	2	1	no	—
181	C₂×D₄×C₄₁	—	4	2	no	—
182	C₂×D₄×C₄₁	—	4	2	no	—
183	C₂×D₄×C₄₁	—	4	2	no	—
184	C₂×D₄×C₄₁	—	4	2	no	—
185	C₂×D₄×C₄₁	—	8	1	no	—
186	C₂×D₄×C₄₁	—	8	1	no	—
187	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
188	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
189	C₂²×C₄×C₄₁	—	2	1	no	—
190	C₂²×C₄×C₄₁	—	2	1	no	—
191	C₂²×C₄×C₄₁	—	2	1	no	—
192	C₂²×C₄×C₄₁	—	2	1	no	—
193	C₂²×C₄×C₄₁	—	2	1	no	—
194	C₂²×C₄×C₄₁	—	4	2	no	—
195	C₂²×C₄×C₄₁	—	4	2	no	—
196	C₂²×C₄×C₄₁	—	4	2	no	—
197	C₂²×C₄×C₄₁	—	8	1	no	—
198	C₂²×C₄×C₄₁	—	8	1	no	—
199	C₂²×C₄×C₄₁	—	8	1	no	—
200	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
207	Q₁₆×C₄₁	—	4	4	no	—
208	SD₁₆×C₄₁	—	4	4	no	—
209	SD₁₆×C₄₁	—	4	4	no	—
210	SD₁₆×C₄₁	—	4	4	no	—
211	D₈×C₄₁	—	4	4	no	—
212	D₈×C₄₁	—	4	4	no	—
213	C₂×C₈×C₄₁	—	2	1	no	—
214	C₂×C₈×C₄₁	—	2	1	no	—
215	C₂×C₈×C₄₁	—	2	1	no	—
216	C₂×C₈×C₄₁	—	2	1	no	—
217	C₂×C₈×C₄₁	—	2	1	no	—
218	C₂×C₈×C₄₁	—	2	1	no	—
219	C₂×C₈×C₄₁	—	2	1	no	—
220	C₂×C₈×C₄₁	—	2	1	no	—
221	C₂×C₈×C₄₁	—	2	1	no	—
222	C₂×C₈×C₄₁	—	2	1	no	—
223	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
224	C₂×C₈×C₄₁	#41	1	2	yes	—
225	C₄⋊C₄×C₄₁	—	2	2	no	—
226	C₄⋊C₄×C₄₁	—	2	1	no	—
227	C₄⋊C₄×C₄₁	—	2	1	no	—
228	C₄⋊C₄×C₄₁	—	2	1	no	—
229	C₄⋊C₄×C₄₁	—	2	1	no	—
230	C₄⋊C₄×C₄₁	—	2	1	no	—
231	C₄⋊C₄×C₄₁	—	4	1	no	—
232	C₄⋊C₄×C₄₁	—	4	2	no	—
233	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
234	C₂²⋊C₄×C₄₁	—	2	4	no	—
235	C₂²⋊C₄×C₄₁	—	2	4	no	—
236	C₂²⋊C₄×C₄₁	—	4	2	no	—
237	C₂²⋊C₄×C₄₁	—	4	2	no	—
238	C₂²⋊C₄×C₄₁	—	4	2	no	—
239	C₂²⋊C₄×C₄₁	—	4	2	no	—
240	C₂²⋊C₄×C₄₁	—	4	2	no	—
241	C₂²⋊C₄×C₄₁	—	4	2	no	—
242	C₂²⋊C₄×C₄₁	—	4	2	no	—
243	C₂²⋊C₄×C₄₁	—	8	1	no	—
244	C₂²⋊C₄×C₄₁	—	8	1	no	—
245	C₂²⋊C₄×C₄₁	—	8	1	no	—
246	C₄²×C₄₁	—	2	1	no	—
247	C₄²×C₄₁	—	2	1	no	—
248	C₄²×C₄₁	—	2	1	no	—
249	C₄²×C₄₁	—	2	1	no	—
250	C₄²×C₄₁	—	4	2	no	—
251	C₄²×C₄₁	—	8	1	no	—
252	C₄²×C₄₁	C₂×D₄	1	2	yes	—
253	C₄²×C₄₁	#41	1	2	yes	—
254	C₂³×C₄₁	—	2	2	no	—
255	C₂³×C₄₁	—	2	2	no	—
256	C₂³×C₄₁	—	4	1	no	—
257	C₂³×C₄₁	—	4	1	no	—
258	C₂³×C₄₁	—	4	1	no	—
259	C₂³×C₄₁	—	4	1	no	—
260	C₂³×C₄₁	—	4	1	no	—
261	C₂³×C₄₁	—	4	1	no	—
262	C₂³×C₄₁	—	4	1	no	—
263	C₂³×C₄₁	—	4	1	no	—
264	C₂³×C₄₁	—	4	1	no	—
265	C₂³×C₄₁	—	4	1	no	—
266	C₂³×C₄₁	—	4	1	no	—
267	C₂³×C₄₁	—	4	1	no	—
268	C₂³×C₄₁	—	4	1	no	—
269	C₂³×C₄₁	—	4	1	no	—
270	C₂³×C₄₁	—	4	1	no	—
271	C₂³×C₄₁	—	4	1	no	—
272	C₂³×C₄₁	—	4	1	no	—
273	C₂³×C₄₁	—	4	1	no	—
274	C₂³×C₄₁	—	4	1	no	—
275	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
276	Q₈×C₄₁	—	2	2	no	—
277	Q₈×C₄₁	—	2	2	no	—
278	Q₈×C₄₁	—	4	1	no	—
279	Q₈×C₄₁	—	4	1	no	—
280	Q₈×C₄₁	—	4	1	no	—
281	Q₈×C₄₁	—	4	1	no	—
282	Q₈×C₄₁	—	4	1	no	—
283	Q₈×C₄₁	—	4	1	no	—
284	D₄×C₄₁	—	2	2	no	—
285	D₄×C₄₁	—	2	2	no	—
286	D₄×C₄₁	—	2	2	no	—
287	D₄×C₄₁	—	2	2	no	—
288	D₄×C₄₁	—	4	1	no	—
289	D₄×C₄₁	—	4	1	no	—
290	D₄×C₄₁	—	4	1	no	—
291	D₄×C₄₁	—	4	1	no	—
292	D₄×C₄₁	—	4	1	no	—
293	D₄×C₄₁	—	4	1	no	—
294	D₄×C₄₁	—	4	1	no	—
295	D₄×C₄₁	—	4	1	no	—
296	D₄×C₄₁	—	8	4	no	—
297	D₄×C₄₁	—	8	4	no	—
298	C₂×C₄×C₄₁	—	2	1	no	—
299	C₂×C₄×C₄₁	—	2	1	no	—
300	C₂×C₄×C₄₁	—	2	1	no	—
301	C₂×C₄×C₄₁	—	2	1	no	—
302	C₂×C₄×C₄₁	—	2	1	no	—
303	C₂×C₄×C₄₁	—	2	1	no	—
304	C₂×C₄×C₄₁	—	2	2	no	—
305	C₂×C₄×C₄₁	—	2	1	no	—
306	C₂×C₄×C₄₁	—	2	1	no	—
307	C₂×C₄×C₄₁	—	2	1	no	—
308	C₂×C₄×C₄₁	—	2	2	no	—
309	C₂×C₄×C₄₁	—	2	1	no	—
310	C₂×C₄×C₄₁	—	2	1	no	—
311	C₂×C₄×C₄₁	—	2	1	no	—
312	C₂×C₄×C₄₁	—	2	1	no	—
313	C₂×C₄×C₄₁	—	2	1	no	—
314	C₂×C₄×C₄₁	—	2	1	no	—
315	C₂×C₄×C₄₁	—	4	1	no	—
316	C₂×C₄×C₄₁	—	4	1	no	—
317	C₂×C₄×C₄₁	—	4	1	no	—
318	C₂×C₄×C₄₁	—	4	1	no	—
319	C₂×C₄×C₄₁	—	4	1	no	—
320	C₂×C₄×C₄₁	—	4	1	no	—
321	C₂×C₄×C₄₁	—	4	1	no	—
322	C₂×C₄×C₄₁	—	4	1	no	—
323	C₂×C₄×C₄₁	—	4	1	no	—
324	C₂×C₄×C₄₁	—	4	1	no	—
325	C₂×C₄×C₄₁	—	4	1	no	—
326	C₂×C₄×C₄₁	—	4	1	no	—
327	C₂×C₄×C₄₁	—	4	1	no	—
328	C₂×C₄×C₄₁	—	8	4	no	—
329	C₂×C₄×C₄₁	—	8	4	no	—
330	C₂×C₄×C₄₁	#121	1	2	yes	—
331	C₂×C₄×C₄₁	#121	1	2	yes	—
332	C₂×C₄×C₄₁	#135	1	2	yes	—
333	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
336	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
337	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
339	C₈×C₄₁	—	2	2	no	—
340	C₈×C₄₁	—	2	2	no	—
341	C₈×C₄₁	—	4	1	no	—
342	C₈×C₄₁	—	4	1	no	—
343	#25373	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
344	C₂²×C₄₁	—	4	2	no	—
345	C₂²×C₄₁	—	4	2	no	—
346	C₂²×C₄₁	—	4	2	no	—
347	C₂²×C₄₁	—	4	2	no	—
348	C₂²×C₄₁	—	4	2	no	—
349	C₂²×C₄₁	—	4	2	no	—
350	C₂²×C₄₁	—	8	1	no	—
351	C₂²×C₄₁	—	8	1	no	—
352	C₂²×C₄₁	—	8	1	no	—
353	C₂²×C₄₁	—	8	1	no	—
354	C₂²×C₄₁	—	8	1	no	—
355	C₂²×C₄₁	—	8	1	no	—
356	C₂²×C₄₁	—	8	1	no	—
357	C₂²×C₄₁	—	8	1	no	—
358	C₂²×C₄₁	—	8	1	no	—
359	C₂²×C₄₁	—	8	1	no	—
360	C₂²×C₄₁	—	8	1	no	—
361	C₂²×C₄₁	—	8	1	no	—
362	C₂²×C₄₁	—	8	1	no	—
363	C₂²×C₄₁	—	8	1	no	—
364	C₂²×C₄₁	—	8	1	no	—
365	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
366	C₂²×C₄₁	D₄²	1	1	yes	characteristic
367	C₂²×C₄₁	#550	1	1	yes	characteristic
368	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
369	C₂²×C₄₁	#575	1	1	yes	characteristic
370	C₂²×C₄₁	#576	1	1	yes	characteristic
371	C₂²×C₄₁	#577	1	1	yes	characteristic
372	C₄×C₄₁	—	2	2	no	—
373	C₄×C₄₁	—	2	2	no	—
374	C₄×C₄₁	—	2	2	no	—
375	C₄×C₄₁	—	4	2	no	—
376	C₄×C₄₁	—	4	1	no	—
377	C₄×C₄₁	—	4	1	no	—
378	C₄×C₄₁	—	4	1	no	—
379	C₄×C₄₁	—	4	2	no	—
380	C₄×C₄₁	—	8	1	no	—
381	C₄×C₄₁	—	8	1	no	—
382	C₄×C₄₁	—	8	1	no	—
383	C₄×C₄₁	#532	1	1	yes	characteristic
384	C₄×C₄₁	#540	1	1	yes	characteristic
385	C₄×C₄₁	D₄²	1	1	yes	characteristic
386	C₄×C₄₁	#546	1	1	yes	characteristic
387	C₂×#495	C₂×C₄₁	1	1	yes	characteristic, complemented
388	C₂×#464	C₂×C₄₁	1	1	yes	characteristic, complemented
389	C₂×#463	C₂×C₄₁	1	1	yes	characteristic, complemented
390	C₂×#459	C₂×C₄₁	1	1	yes	characteristic
391	#2544	C₂×C₄₁	1	1	yes	characteristic, complemented
392	#2367	C₂×C₄₁	1	1	yes	characteristic, complemented
393	#2056	C₂×C₄₁	1	1	yes	characteristic, complemented
394	#2054	C₂×C₄₁	1	1	yes	characteristic, complemented
395	#2014	C₂×C₄₁	1	1	yes	characteristic, complemented
396	#2012	C₂×C₄₁	1	1	yes	characteristic, complemented
397	#1983	C₂×C₄₁	1	1	yes	characteristic, complemented
398	#1939	C₂×C₄₁	1	1	yes	characteristic, complemented
399	#1880	C₂×C₄₁	1	1	yes	characteristic, complemented
400	#1877	C₂×C₄₁	1	1	yes	characteristic, complemented
401	C₄×#102	C₂×C₄₁	1	1	yes	characteristic, complemented
402	C₂×C₄₁	—	8	2	no	—
403	C₂×C₄₁	—	8	2	no	—
404	C₂×C₄₁	—	16	1	no	—
405	C₂×C₄₁	#2428	1	1	yes	characteristic
406	C₂×C₄₁	#3035	1	1	yes	characteristic
407	C₂×C₄₁	#3045	1	1	yes	characteristic
408	C₂×C₄₁	#3275	1	1	yes	characteristic
409	C₂×C₄₁	#3280	1	1	yes	characteristic
410	C₂×C₄₁	#3394	1	1	yes	characteristic
411	C₂×C₄₁	#3403	1	1	yes	characteristic
412	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
413	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
414	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
415	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
416	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
417	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
418	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
419	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
420	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
421	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
422	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
423	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
424	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
425	#495	—	2	4	no	—
426	#464	—	2	4	no	—
427	#463	—	2	4	no	—
428	#459	—	2	4	no	—
429	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
430	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
431	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
432	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
433	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
434	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
435	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
436	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
437	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
438	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
439	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
440	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
441	#394	—	2	1	no	—
442	#394	—	2	1	no	—
443	#391	C₂²×C₄₁	1	1	yes	characteristic
444	#391	C₂²×C₄₁	1	1	yes	characteristic
445	#390	C₂²×C₄₁	1	1	yes	characteristic
446	#390	C₂²×C₄₁	1	1	yes	characteristic
447	#388	—	2	1	no	—
448	#388	—	2	1	no	—
449	#386	—	2	1	no	—
450	#386	—	2	1	no	—
451	#385	—	2	1	no	—
452	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
453	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
454	C₄×C₂²⋊C₄	—	2	1	no	—
455	#340	C₂²×C₄₁	1	1	yes	characteristic
456	#340	C₂²×C₄₁	1	1	yes	characteristic
457	#336	C₂²×C₄₁	1	1	yes	characteristic
458	#336	C₂²×C₄₁	1	1	yes	characteristic
459	C₄₁	#25373	1	1	yes	characteristic, direct product factor, Sylow
460	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
461	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
462	C₂²×D₄	—	2	1	no	—
463	C₂²×D₄	—	2	1	no	—
464	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
465	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
466	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
467	C₂³×C₄	—	2	1	no	—
468	C₂³×C₄	—	2	1	no	—
469	C₂×Q₁₆	—	2	2	no	—
470	C₂×Q₁₆	—	2	2	no	—
471	C₂×Q₁₆	—	4	1	no	—
472	C₂×SD₁₆	—	2	2	no	—
473	C₂×SD₁₆	—	2	2	no	—
474	C₂×SD₁₆	—	2	2	no	—
475	C₂×SD₁₆	—	2	2	no	—
476	C₂×SD₁₆	—	2	2	no	—
477	C₂×SD₁₆	—	2	2	no	—
478	C₂×SD₁₆	—	4	1	no	—
479	C₂×SD₁₆	—	4	1	no	—
480	C₂×SD₁₆	—	4	1	no	—
481	C₂×D₈	—	2	2	no	—
482	C₂×D₈	—	2	2	no	—
483	C₂×D₈	—	2	2	no	—
484	C₂×D₈	—	2	2	no	—
485	C₂×D₈	—	4	1	no	—
486	C₂×D₈	—	4	1	no	—
487	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
488	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
489	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
490	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
491	#127	—	2	2	no	—
492	#127	—	4	1	no	—
493	#124	—	2	2	no	—
494	#124	—	2	2	no	—
495	#124	—	2	2	no	—
496	#124	—	2	2	no	—
497	#124	—	4	1	no	—
498	#124	D₄×C₄₁	1	4	yes	complemented
499	C₄×Q₈	—	2	2	no	—
500	C₄×Q₈	—	4	1	no	—
501	C₄×D₄	—	2	2	no	—
502	C₄×D₄	—	2	2	no	—
503	C₄×D₄	—	2	2	no	—
504	C₄×D₄	—	4	1	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
507	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₄²	—	2	1	no	—
524	C₂×C₄²	—	2	1	no	—
525	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
526	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
527	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
528	C₄⋊C₈	—	2	2	no	—
529	C₄⋊C₈	—	2	2	no	—
530	C₄⋊C₈	—	2	2	no	—
531	#103	—	2	2	no	—
532	#103	—	2	2	no	—
533	#103	—	4	1	no	—
534	#102	—	2	2	no	—
535	#102	—	2	2	no	—
536	#102	—	2	2	no	—
537	#102	—	4	1	no	—
538	#102	D₄×C₄₁	1	4	yes	—
539	C₄×C₈	—	2	2	no	—
540	#95	—	2	1	no	—
541	#95	—	2	1	no	—
542	#95	—	2	1	no	—
543	#95	—	2	1	no	—
544	#95	—	2	1	no	—
545	#95	D₄×C₄₁	1	1	yes	characteristic
546	#95	D₄×C₄₁	1	1	yes	characteristic
547	C₂⁴	—	2	1	no	—
548	C₂⁴	—	2	1	no	—
549	C₂⁴	—	2	1	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	4	2	no	—
579	C₂×D₄	—	4	2	no	—
580	C₂×D₄	—	4	2	no	—
581	C₂×D₄	—	4	2	no	—
582	C₂×D₄	—	8	1	no	—
583	C₂×D₄	—	8	1	no	—
584	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
585	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	—	8	1	no	—
595	C₂²×C₄	—	8	1	no	—
596	C₂²×C₄	—	8	1	no	—
597	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
601	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
602	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
604	Q₁₆	—	4	4	no	—
605	SD₁₆	—	4	4	no	—
606	SD₁₆	—	4	4	no	—
607	SD₁₆	—	4	4	no	—
608	D₈	—	4	4	no	—
609	D₈	—	4	4	no	—
610	C₂×C₈	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	—	2	1	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
621	C₂×C₈	#41×C₄₁	1	2	yes	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	4	1	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	4	2	no	—
634	C₂²⋊C₄	—	4	2	no	—
635	C₂²⋊C₄	—	4	2	no	—
636	C₂²⋊C₄	—	4	2	no	—
637	C₂²⋊C₄	—	4	2	no	—
638	C₂²⋊C₄	—	4	2	no	—
639	C₂²⋊C₄	—	4	2	no	—
640	C₂²⋊C₄	—	8	1	no	—
641	C₂²⋊C₄	—	8	1	no	—
642	C₂²⋊C₄	—	8	1	no	—
643	C₄²	—	2	1	no	—
644	C₄²	—	2	1	no	—
645	C₄²	—	2	1	no	—
646	C₄²	—	2	1	no	—
647	C₄²	—	4	2	no	—
648	C₄²	—	8	1	no	—
649	C₄²	C₂×D₄×C₄₁	1	2	yes	—
650	C₄²	#41×C₄₁	1	2	yes	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	4	1	no	—
654	C₂³	—	4	1	no	—
655	C₂³	—	4	1	no	—
656	C₂³	—	4	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	1	no	—
661	C₂³	—	4	1	no	—
662	C₂³	—	4	1	no	—
663	C₂³	—	4	1	no	—
664	C₂³	—	4	1	no	—
665	C₂³	—	4	1	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	—	4	1	no	—
672	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
673	Q₈	—	2	2	no	—
674	Q₈	—	2	2	no	—
675	Q₈	—	4	1	no	—
676	Q₈	—	4	1	no	—
677	Q₈	—	4	1	no	—
678	Q₈	—	4	1	no	—
679	Q₈	—	4	1	no	—
680	Q₈	—	4	1	no	—
681	D₄	—	2	2	no	—
682	D₄	—	2	2	no	—
683	D₄	—	2	2	no	—
684	D₄	—	2	2	no	—
685	D₄	—	4	1	no	—
686	D₄	—	4	1	no	—
687	D₄	—	4	1	no	—
688	D₄	—	4	1	no	—
689	D₄	—	4	1	no	—
690	D₄	—	4	1	no	—
691	D₄	—	4	1	no	—
692	D₄	—	4	1	no	—
693	D₄	—	8	4	no	—
694	D₄	—	8	4	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	8	4	no	—
726	C₂×C₄	—	8	4	no	—
727	C₂×C₄	#121×C₄₁	1	2	yes	—
728	C₂×C₄	#121×C₄₁	1	2	yes	—
729	C₂×C₄	#135×C₄₁	1	2	yes	—
730	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
731	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
732	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
733	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
734	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
735	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
736	C₈	—	2	2	no	—
737	C₈	—	2	2	no	—
738	C₈	—	4	1	no	—
739	C₈	—	4	1	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	8	1	no	—
747	C₂²	—	8	1	no	—
748	C₂²	—	8	1	no	—
749	C₂²	—	8	1	no	—
750	C₂²	—	8	1	no	—
751	C₂²	—	8	1	no	—
752	C₂²	—	8	1	no	—
753	C₂²	—	8	1	no	—
754	C₂²	—	8	1	no	—
755	C₂²	—	8	1	no	—
756	C₂²	—	8	1	no	—
757	C₂²	—	8	1	no	—
758	C₂²	—	8	1	no	—
759	C₂²	—	8	1	no	—
760	C₂²	—	8	1	no	—
761	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
762	C₂²	D₄²×C₄₁	1	1	yes	characteristic
763	C₂²	C₄₁×#550	1	1	yes	characteristic
764	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
765	C₂²	C₄₁×#575	1	1	yes	characteristic
766	C₂²	C₄₁×#576	1	1	yes	characteristic
767	C₂²	C₄₁×#577	1	1	yes	characteristic
768	C₄	—	2	2	no	—
769	C₄	—	2	2	no	—
770	C₄	—	2	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	1	no	—
773	C₄	—	4	1	no	—
774	C₄	—	4	1	no	—
775	C₄	—	4	2	no	—
776	C₄	—	8	1	no	—
777	C₄	—	8	1	no	—
778	C₄	—	8	1	no	—
779	C₄	C₄₁×#532	1	1	yes	characteristic
780	C₄	C₄₁×#540	1	1	yes	characteristic
781	C₄	D₄²×C₄₁	1	1	yes	characteristic
782	C₄	C₄₁×#546	1	1	yes	characteristic
783	C₂	—	8	2	no	—
784	C₂	—	8	2	no	—
785	C₂	—	16	1	no	—
786	C₂	C₄₁×#2428	1	1	yes	characteristic
787	C₂	C₄₁×#3035	1	1	yes	characteristic
788	C₂	C₄₁×#3045	1	1	yes	characteristic
789	C₂	C₄₁×#3275	1	1	yes	characteristic
790	C₂	C₄₁×#3280	1	1	yes	characteristic
791	C₂	C₄₁×#3394	1	1	yes	characteristic
792	C₂	C₄₁×#3403	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#459	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄×C₄⋊C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#495	C₂	semidirect
2. C₂×C₄₁×#464	C₂	semidirect
3. C₂×C₄₁×#463	C₂	semidirect
5. C₄₁×#2544	C₂	semidirect
6. C₄₁×#2367	C₂	semidirect
7. C₄₁×#2056	C₂	semidirect
8. C₄₁×#2054	C₂	semidirect
9. C₄₁×#2014	C₂	semidirect
10. C₄₁×#2012	C₂	semidirect
11. C₄₁×#1983	C₂	semidirect
12. C₄₁×#1939	C₂	semidirect
13. C₄₁×#1880	C₂	semidirect
14. C₄₁×#1877	C₂	semidirect
15. C₄×#102×C₄₁	C₂	semidirect
101. #124×C₄₁	D₄	semidirect
343. #25373	C₄₁	direct (N × H)
387. C₂×#495	C₂×C₄₁	semidirect
388. C₂×#464	C₂×C₄₁	semidirect
389. C₂×#463	C₂×C₄₁	semidirect
391. #2544	C₂×C₄₁	semidirect
392. #2367	C₂×C₄₁	semidirect
393. #2056	C₂×C₄₁	semidirect
394. #2054	C₂×C₄₁	semidirect
395. #2014	C₂×C₄₁	semidirect
396. #2012	C₂×C₄₁	semidirect
397. #1983	C₂×C₄₁	semidirect
398. #1939	C₂×C₄₁	semidirect
399. #1880	C₂×C₄₁	semidirect
400. #1877	C₂×C₄₁	semidirect
401. C₄×#102	C₂×C₄₁	semidirect
459. C₄₁	#25373	direct (N × H)
498. #124	D₄×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×#495	2
C₂×C₄₁×#464	2
C₂×C₄₁×#463	2
C₂×C₄₁×#459	2
C₄₁×#2544	2
C₄₁×#2367	2
C₄₁×#2056	2
C₄₁×#2054	2
C₄₁×#2014	2
C₄₁×#2012	2
C₄₁×#1983	2
C₄₁×#1939	2
C₄₁×#1880	2
C₄₁×#1877	2
C₄×#102×C₄₁	2
#25373	41

Subgroups — C41×#25373 #23801574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25373 #23801574