Subgroups — C₄₁×#25346 #23801547

Order 10496.

926 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#476	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#436	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2563	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2537	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#2077	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2033	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1947	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1895	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1809	C₂	1	2	yes	maximal, complemented
11	C₄×#102×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
13	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#121×C₄₁	—	2	1	no	—
15	C₂×#121×C₄₁	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
18	C₄₁×#476	—	2	4	no	—
19	C₄₁×#436	—	2	4	no	—
20	C₂×#107×C₄₁	C₂²	1	2	yes	—
21	C₂×#106×C₄₁	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#102×C₄₁	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
28	C₄₁×#394	—	2	2	no	—
29	C₄₁×#393	—	2	2	no	—
30	C₄₁×#390	—	2	1	no	—
31	C₄₁×#384	C₂²	1	1	yes	characteristic
32	C₄₁×#382	—	2	1	no	—
33	C₄₁×#380	—	2	1	no	—
34	C₄₁×#380	C₂²	1	2	yes	—
35	C₄₁×#380	C₂²	1	2	yes	—
36	C₄₁×#380	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
38	C₄₁×#340	C₂²	1	1	yes	characteristic
39	C₄₁×#340	C₂²	1	1	yes	characteristic
40	C₄₁×#340	C₂²	1	2	yes	—
41	C₄₁×#340	C₂²	1	2	yes	—
42	C₄₁×#340	C₂²	1	2	yes	—
43	C₂²×Q₈×C₄₁	—	2	1	no	—
44	C₂²×D₄×C₄₁	—	2	2	no	—
45	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₄₁	—	2	1	no	—
48	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
49	C₂×M₁₆×C₄₁	—	2	4	no	—
50	C₂×M₁₆×C₄₁	—	2	4	no	—
51	C₂×M₁₆×C₄₁	—	4	2	no	—
52	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
54	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
55	C₄⋊Q₈×C₄₁	—	2	2	no	—
56	C₄⋊Q₈×C₄₁	—	2	2	no	—
57	#121×C₄₁	—	2	4	no	—
58	#121×C₄₁	—	4	2	no	—
59	#121×C₄₁	—	4	4	no	—
60	C₄×D₄×C₄₁	—	2	2	no	—
61	C₄×D₄×C₄₁	—	2	2	no	—
62	C₄×D₄×C₄₁	—	2	2	no	—
63	C₄×D₄×C₄₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
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	2	yes	—
71	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₄₁	—	2	1	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	2	yes	—
79	C₂×C₄²×C₄₁	—	2	1	no	—
80	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
81	#107×C₄₁	—	4	2	no	—
82	#106×C₄₁	—	2	4	no	—
83	C₄⋊C₈×C₄₁	D₄	1	4	yes	complemented
84	#102×C₄₁	—	2	2	no	—
85	#102×C₄₁	—	2	4	no	—
86	#102×C₄₁	—	2	2	no	—
87	C₂²⋊C₈×C₄₁	—	2	4	no	—
88	C₄×C₈×C₄₁	—	2	2	no	—
89	#95×C₄₁	—	2	1	no	—
90	#95×C₄₁	—	2	2	no	—
91	#95×C₄₁	—	2	2	no	—
92	#95×C₄₁	—	2	2	no	—
93	C₂⁴×C₄₁	—	2	1	no	—
94	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
95	C₂×Q₈×C₄₁	—	4	2	no	—
96	C₂×Q₈×C₄₁	—	8	1	no	—
97	C₂×Q₈×C₄₁	—	8	1	no	—
98	C₂×D₄×C₄₁	—	2	2	no	—
99	C₂×D₄×C₄₁	—	2	2	no	—
100	C₂×D₄×C₄₁	—	2	2	no	—
101	C₂×D₄×C₄₁	—	2	1	no	—
102	C₂×D₄×C₄₁	—	2	1	no	—
103	C₂×D₄×C₄₁	—	2	1	no	—
104	C₂×D₄×C₄₁	—	2	1	no	—
105	C₂×D₄×C₄₁	—	2	1	no	—
106	C₂×D₄×C₄₁	—	4	4	no	—
107	C₂×D₄×C₄₁	—	4	4	no	—
108	C₂×D₄×C₄₁	—	8	2	no	—
109	C₂×D₄×C₄₁	#41	1	2	yes	—
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	—	2	2	no	—
115	C₂²×C₄×C₄₁	—	2	2	no	—
116	C₂²×C₄×C₄₁	—	2	1	no	—
117	C₂²×C₄×C₄₁	—	2	1	no	—
118	C₂²×C₄×C₄₁	—	2	1	no	—
119	C₂²×C₄×C₄₁	—	2	2	no	—
120	C₂²×C₄×C₄₁	—	2	2	no	—
121	C₂²×C₄×C₄₁	—	4	2	no	—
122	C₂²×C₄×C₄₁	—	4	2	no	—
123	C₂²×C₄×C₄₁	—	4	2	no	—
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	1	yes	characteristic
127	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
128	M₁₆×C₄₁	—	4	8	no	—
129	C₂×C₈×C₄₁	—	2	1	no	—
130	C₂×C₈×C₄₁	—	2	2	no	—
131	C₂×C₈×C₄₁	—	2	2	no	—
132	C₂×C₈×C₄₁	—	2	1	no	—
133	C₂×C₈×C₄₁	—	2	1	no	—
134	C₂×C₈×C₄₁	—	2	1	no	—
135	C₂×C₈×C₄₁	—	2	1	no	—
136	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
137	C₂×C₈×C₄₁	#41	1	2	yes	—
138	C₄⋊C₄×C₄₁	—	2	2	no	—
139	C₄⋊C₄×C₄₁	—	2	2	no	—
140	C₄⋊C₄×C₄₁	—	2	1	no	—
141	C₄⋊C₄×C₄₁	—	2	1	no	—
142	C₄⋊C₄×C₄₁	—	2	1	no	—
143	C₄⋊C₄×C₄₁	—	2	1	no	—
144	C₄⋊C₄×C₄₁	—	2	2	no	—
145	C₄⋊C₄×C₄₁	—	2	2	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	—	4	2	no	—
150	C₄⋊C₄×C₄₁	—	4	2	no	—
151	C₄⋊C₄×C₄₁	—	8	1	no	—
152	C₂²⋊C₄×C₄₁	—	2	4	no	—
153	C₂²⋊C₄×C₄₁	—	4	4	no	—
154	C₂²⋊C₄×C₄₁	—	4	4	no	—
155	C₂²⋊C₄×C₄₁	—	4	2	no	—
156	C₂²⋊C₄×C₄₁	—	8	2	no	—
157	C₂²⋊C₄×C₄₁	—	8	2	no	—
158	C₄²×C₄₁	—	4	2	no	—
159	C₄²×C₄₁	C₂×D₄	1	2	yes	—
160	C₄²×C₄₁	#41	1	2	yes	—
161	C₂³×C₄₁	—	2	2	no	—
162	C₂³×C₄₁	—	2	2	no	—
163	C₂³×C₄₁	—	2	2	no	—
164	C₂³×C₄₁	—	2	2	no	—
165	C₂³×C₄₁	—	2	2	no	—
166	C₂³×C₄₁	—	2	2	no	—
167	C₂³×C₄₁	—	2	2	no	—
168	C₂³×C₄₁	—	2	2	no	—
169	C₂³×C₄₁	—	4	1	no	—
170	C₂³×C₄₁	—	4	1	no	—
171	C₂³×C₄₁	—	4	1	no	—
172	C₂³×C₄₁	—	4	1	no	—
173	C₂³×C₄₁	—	4	1	no	—
174	C₂³×C₄₁	—	4	1	no	—
175	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
176	Q₈×C₄₁	—	8	4	no	—
177	D₄×C₄₁	—	2	2	no	—
178	D₄×C₄₁	—	2	2	no	—
179	D₄×C₄₁	—	4	1	no	—
180	D₄×C₄₁	—	4	1	no	—
181	D₄×C₄₁	—	4	4	no	—
182	D₄×C₄₁	—	8	8	no	—
183	C₂×C₄×C₄₁	—	2	1	no	—
184	C₂×C₄×C₄₁	—	2	1	no	—
185	C₂×C₄×C₄₁	—	2	2	no	—
186	C₂×C₄×C₄₁	—	2	2	no	—
187	C₂×C₄×C₄₁	—	2	2	no	—
188	C₂×C₄×C₄₁	—	4	2	no	—
189	C₂×C₄×C₄₁	—	4	2	no	—
190	C₂×C₄×C₄₁	—	4	2	no	—
191	C₂×C₄×C₄₁	—	4	2	no	—
192	C₂×C₄×C₄₁	—	4	1	no	—
193	C₂×C₄×C₄₁	—	4	2	no	—
194	C₂×C₄×C₄₁	—	4	2	no	—
195	C₂×C₄×C₄₁	—	4	1	no	—
196	C₂×C₄×C₄₁	—	4	1	no	—
197	C₂×C₄×C₄₁	—	4	1	no	—
198	C₂×C₄×C₄₁	—	4	1	no	—
199	C₂×C₄×C₄₁	—	4	1	no	—
200	C₂×C₄×C₄₁	—	4	2	no	—
201	C₂×C₄×C₄₁	—	4	1	no	—
202	C₂×C₄×C₄₁	—	4	1	no	—
203	C₂×C₄×C₄₁	—	4	2	no	—
204	C₂×C₄×C₄₁	—	4	2	no	—
205	C₂×C₄×C₄₁	—	4	1	no	—
206	C₂×C₄×C₄₁	—	4	2	no	—
207	C₂×C₄×C₄₁	—	8	4	no	—
208	C₂×C₄×C₄₁	#121	1	2	yes	—
209	C₂×C₄×C₄₁	#121	1	2	yes	—
210	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
211	C₂×C₄×C₄₁	#137	1	2	yes	—
212	C₂×C₄×C₄₁	C₂²×D₄	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	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
217	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
218	C₈×C₄₁	—	2	4	no	—
219	C₈×C₄₁	—	2	2	no	—
220	C₈×C₄₁	—	4	1	no	—
221	#25346	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂²×C₄₁	—	4	2	no	—
223	C₂²×C₄₁	—	4	2	no	—
224	C₂²×C₄₁	—	4	2	no	—
225	C₂²×C₄₁	—	4	2	no	—
226	C₂²×C₄₁	—	4	2	no	—
227	C₂²×C₄₁	—	4	2	no	—
228	C₂²×C₄₁	—	4	2	no	—
229	C₂²×C₄₁	—	4	2	no	—
230	C₂²×C₄₁	—	4	2	no	—
231	C₂²×C₄₁	—	4	2	no	—
232	C₂²×C₄₁	—	8	1	no	—
233	C₂²×C₄₁	—	8	1	no	—
234	C₂²×C₄₁	—	8	1	no	—
235	C₂²×C₄₁	—	8	1	no	—
236	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
237	C₂²×C₄₁	#546	1	1	yes	characteristic
238	C₂²×C₄₁	#547	1	1	yes	characteristic
239	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
240	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
241	C₂²×C₄₁	#576	1	1	yes	characteristic
242	C₂²×C₄₁	#577	1	1	yes	characteristic
243	C₄×C₄₁	—	2	2	no	—
244	C₄×C₄₁	—	4	2	no	—
245	C₄×C₄₁	—	8	1	no	—
246	C₄×C₄₁	—	8	1	no	—
247	C₄×C₄₁	—	8	2	no	—
248	C₄×C₄₁	—	8	1	no	—
249	C₄×C₄₁	—	8	2	no	—
250	C₄×C₄₁	#468	1	4	yes	—
251	C₄×C₄₁	#529	1	1	yes	characteristic
252	C₄×C₄₁	#542	1	1	yes	characteristic
253	C₄×C₄₁	#546	1	1	yes	characteristic
254	C₄×C₄₁	#548	1	1	yes	characteristic
255	C₂×#476	C₂×C₄₁	1	1	yes	characteristic, complemented
256	C₂×#436	C₂×C₄₁	1	1	yes	characteristic, complemented
257	#2563	C₂×C₄₁	1	1	yes	characteristic, complemented
258	#2537	C₂×C₄₁	1	1	yes	characteristic
259	#2077	C₂×C₄₁	1	2	yes	complemented
260	#2033	C₂×C₄₁	1	2	yes	complemented
261	#1990	C₂×C₄₁	1	1	yes	characteristic, complemented
262	#1947	C₂×C₄₁	1	1	yes	characteristic, complemented
263	#1895	C₂×C₄₁	1	2	yes	complemented
264	#1809	C₂×C₄₁	1	2	yes	complemented
265	C₄×#102	C₂×C₄₁	1	1	yes	characteristic, complemented
266	C₂×C₄₁	—	8	2	no	—
267	C₂×C₄₁	—	8	2	no	—
268	C₂×C₄₁	#2427	1	1	yes	characteristic
269	C₂×C₄₁	C₂×#468	1	1	yes	characteristic
270	C₂×C₄₁	#3062	1	1	yes	characteristic
271	C₂×C₄₁	#3325	1	1	yes	characteristic
272	C₂×C₄₁	#3331	1	1	yes	characteristic
273	C₂×C₄₁	#3354	1	1	yes	characteristic
274	C₂×C₄₁	#3357	1	1	yes	characteristic
275	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
276	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
277	C₂×#121	—	2	1	no	—
278	C₂×#121	C₂²×C₄₁	1	2	yes	—
279	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
280	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
281	#476	—	2	4	no	—
282	#436	—	2	4	no	—
283	C₂×#107	C₂²×C₄₁	1	2	yes	—
284	C₂×#106	C₂²×C₄₁	1	2	yes	—
285	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
286	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
287	C₂×#102	C₂²×C₄₁	1	2	yes	—
288	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
289	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
290	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
291	#394	—	2	2	no	—
292	#393	—	2	2	no	—
293	#390	—	2	1	no	—
294	#384	C₂²×C₄₁	1	1	yes	characteristic
295	#382	—	2	1	no	—
296	#380	—	2	1	no	—
297	#380	C₂²×C₄₁	1	2	yes	—
298	#380	C₂²×C₄₁	1	2	yes	—
299	#380	C₂²×C₄₁	1	2	yes	—
300	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
301	#340	C₂²×C₄₁	1	1	yes	characteristic
302	#340	C₂²×C₄₁	1	2	yes	—
303	#340	C₂²×C₄₁	1	1	yes	characteristic
304	#340	C₂²×C₄₁	1	2	yes	—
305	#340	C₂²×C₄₁	1	2	yes	—
306	C₄₁	#25346	1	1	yes	characteristic, direct product factor, Sylow
307	C₂²×Q₈	—	2	1	no	—
308	C₂²×D₄	—	2	2	no	—
309	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
310	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
311	C₂³×C₄	—	2	1	no	—
312	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
313	C₂×M₁₆	—	2	4	no	—
314	C₂×M₁₆	—	2	4	no	—
315	C₂×M₁₆	—	4	2	no	—
316	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
318	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
319	C₄⋊Q₈	—	2	2	no	—
320	C₄⋊Q₈	—	2	2	no	—
321	#121	—	2	4	no	—
322	#121	—	4	2	no	—
323	#121	—	4	4	no	—
324	C₄×D₄	—	2	2	no	—
325	C₄×D₄	—	2	2	no	—
326	C₄×D₄	—	2	2	no	—
327	C₄×D₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	—	2	2	no	—
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
343	C₂×C₄²	—	2	1	no	—
344	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
345	#107	—	4	2	no	—
346	#106	—	2	4	no	—
347	C₄⋊C₈	D₄×C₄₁	1	4	yes	complemented
348	#102	—	2	2	no	—
349	#102	—	2	4	no	—
350	#102	—	2	2	no	—
351	C₂²⋊C₈	—	2	4	no	—
352	C₄×C₈	—	2	2	no	—
353	#95	—	2	1	no	—
354	#95	—	2	2	no	—
355	#95	—	2	2	no	—
356	#95	—	2	2	no	—
357	C₂⁴	—	2	1	no	—
358	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
359	C₂×Q₈	—	4	2	no	—
360	C₂×Q₈	—	8	1	no	—
361	C₂×Q₈	—	8	1	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	4	4	no	—
371	C₂×D₄	—	4	4	no	—
372	C₂×D₄	—	8	2	no	—
373	C₂×D₄	#41×C₄₁	1	2	yes	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	4	2	no	—
386	C₂²×C₄	—	4	2	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
389	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
391	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
392	M₁₆	—	4	8	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
401	C₂×C₈	#41×C₄₁	1	2	yes	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	4	2	no	—
414	C₄⋊C₄	—	4	2	no	—
415	C₄⋊C₄	—	8	1	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	4	4	no	—
418	C₂²⋊C₄	—	4	4	no	—
419	C₂²⋊C₄	—	4	2	no	—
420	C₂²⋊C₄	—	8	2	no	—
421	C₂²⋊C₄	—	8	2	no	—
422	C₄²	—	4	2	no	—
423	C₄²	C₂×D₄×C₄₁	1	2	yes	—
424	C₄²	#41×C₄₁	1	2	yes	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	1	no	—
437	C₂³	—	4	1	no	—
438	C₂³	—	4	1	no	—
439	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
440	Q₈	—	8	4	no	—
441	D₄	—	2	2	no	—
442	D₄	—	2	2	no	—
443	D₄	—	4	1	no	—
444	D₄	—	4	1	no	—
445	D₄	—	4	4	no	—
446	D₄	—	8	8	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	8	4	no	—
472	C₂×C₄	#121×C₄₁	1	2	yes	—
473	C₂×C₄	#121×C₄₁	1	2	yes	—
474	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
475	C₂×C₄	#137×C₄₁	1	2	yes	—
476	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
477	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
478	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
479	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
480	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
481	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
482	C₈	—	2	4	no	—
483	C₈	—	2	2	no	—
484	C₈	—	4	1	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	8	1	no	—
496	C₂²	—	8	1	no	—
497	C₂²	—	8	1	no	—
498	C₂²	—	8	1	no	—
499	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
500	C₂²	C₄₁×#546	1	1	yes	characteristic
501	C₂²	C₄₁×#547	1	1	yes	characteristic
502	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
503	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
504	C₂²	C₄₁×#576	1	1	yes	characteristic
505	C₂²	C₄₁×#577	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	4	2	no	—
508	C₄	—	8	1	no	—
509	C₄	—	8	2	no	—
510	C₄	—	8	2	no	—
511	C₄	—	8	1	no	—
512	C₄	—	8	1	no	—
513	C₄	C₄₁×#468	1	4	yes	—
514	C₄	C₄₁×#529	1	1	yes	characteristic
515	C₄	C₄₁×#542	1	1	yes	characteristic
516	C₄	C₄₁×#546	1	1	yes	characteristic
517	C₄	C₄₁×#548	1	1	yes	characteristic
518	C₂	—	8	2	no	—
519	C₂	—	8	2	no	—
520	C₂	C₄₁×#2427	1	1	yes	characteristic
521	C₂	C₂×C₄₁×#468	1	1	yes	characteristic
522	C₂	C₄₁×#3062	1	1	yes	characteristic
523	C₂	C₄₁×#3325	1	1	yes	characteristic
524	C₂	C₄₁×#3331	1	1	yes	characteristic
525	C₂	C₄₁×#3354	1	1	yes	characteristic
526	C₂	C₄₁×#3357	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₄₁×#2537	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×C₄×D₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#476	C₂	semidirect
2. C₂×C₄₁×#436	C₂	semidirect
3. C₄₁×#2563	C₂	semidirect
5. C₄₁×#2077	C₂	semidirect
6. C₄₁×#2033	C₂	semidirect
7. C₄₁×#1990	C₂	semidirect
8. C₄₁×#1947	C₂	semidirect
9. C₄₁×#1895	C₂	semidirect
10. C₄₁×#1809	C₂	semidirect
11. C₄×#102×C₄₁	C₂	semidirect
83. C₄⋊C₈×C₄₁	D₄	semidirect
221. #25346	C₄₁	direct (N × H)
255. C₂×#476	C₂×C₄₁	semidirect
256. C₂×#436	C₂×C₄₁	semidirect
257. #2563	C₂×C₄₁	semidirect
259. #2077	C₂×C₄₁	semidirect
260. #2033	C₂×C₄₁	semidirect
261. #1990	C₂×C₄₁	semidirect
262. #1947	C₂×C₄₁	semidirect
263. #1895	C₂×C₄₁	semidirect
264. #1809	C₂×C₄₁	semidirect
265. C₄×#102	C₂×C₄₁	semidirect
306. C₄₁	#25346	direct (N × H)
347. C₄⋊C₈	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×#476	2
C₂×C₄₁×#436	2
C₄₁×#2563	2
C₄₁×#2537	2
C₄₁×#2077	2
C₄₁×#2033	2
C₄₁×#1990	2
C₄₁×#1947	2
C₄₁×#1895	2
C₄₁×#1809	2
C₄×#102×C₄₁	2
#25346	41

Subgroups — C41×#25346 #23801547

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25346 #23801547