Subgroups — C₄₁×#25415 #23801616

Order 10496.

970 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#467	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#467	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×Q₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2429	C₂	1	2	yes	maximal
6	C₄₁×#2043	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2001	C₂	1	2	yes	maximal
8	C₄₁×#1969	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1942	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1878	C₂	1	2	yes	maximal, complemented
11	C₈×C₂²⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₄₁	C₂²	1	2	yes	—
14	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₄₁	C₂²	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
18	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
20	C₄₁×#494	—	2	4	no	—
21	C₄₁×#467	—	2	4	no	—
22	C₄₁×#467	—	2	4	no	—
23	C₄×Q₁₆×C₄₁	—	2	4	no	—
24	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#103×C₄₁	C₂²	1	2	yes	—
27	C₂×#103×C₄₁	C₂²	1	2	yes	—
28	C₂×#103×C₄₁	C₂²	1	2	yes	—
29	C₂×#103×C₄₁	C₂²	1	2	yes	—
30	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
33	C₄₁×#398	—	2	2	no	—
34	C₄₁×#396	—	2	2	no	—
35	C₄₁×#391	C₂²	1	2	yes	—
36	C₄₁×#389	—	2	2	no	—
37	C₄₁×#389	C₂²	1	2	yes	—
38	C₄₁×#388	—	2	2	no	—
39	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
40	C₄₁×#340	C₂²	1	2	yes	—
41	C₄₁×#336	C₂²	1	1	yes	characteristic
42	C₄₁×#336	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
44	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
45	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
46	C₂×Q₁₆×C₄₁	—	2	4	no	—
47	C₂×Q₁₆×C₄₁	—	2	2	no	—
48	C₂×Q₁₆×C₄₁	—	2	2	no	—
49	C₂×Q₁₆×C₄₁	—	2	2	no	—
50	C₂×Q₁₆×C₄₁	—	2	2	no	—
51	C₂×Q₁₆×C₄₁	—	2	4	no	—
52	C₂×Q₁₆×C₄₁	—	2	2	no	—
53	C₂×Q₁₆×C₄₁	—	4	2	no	—
54	C₂×Q₁₆×C₄₁	D₄	1	4	yes	—
55	C₂²×C₈×C₄₁	—	2	2	no	—
56	C₂²×C₈×C₄₁	—	2	2	no	—
57	C₂²×C₈×C₄₁	—	2	2	no	—
58	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
62	C₄⋊Q₈×C₄₁	—	2	4	no	—
63	C₄⋊Q₈×C₄₁	—	4	2	no	—
64	C₂²⋊Q₈×C₄₁	—	2	4	no	—
65	C₂²⋊Q₈×C₄₁	—	2	4	no	—
66	C₂²⋊Q₈×C₄₁	—	4	2	no	—
67	C₂²⋊Q₈×C₄₁	—	4	2	no	—
68	C₄×Q₈×C₄₁	—	2	4	no	—
69	C₄×Q₈×C₄₁	—	4	2	no	—
70	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
72	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
73	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
74	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
75	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
76	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
78	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₄₁	—	2	2	no	—
83	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
85	#107×C₄₁	—	2	2	no	—
86	#107×C₄₁	D₄	1	4	yes	—
87	#103×C₄₁	—	2	4	no	—
88	#103×C₄₁	—	2	4	no	—
89	#103×C₄₁	—	2	4	no	—
90	#103×C₄₁	—	4	2	no	—
91	C₂²⋊C₈×C₄₁	—	2	2	no	—
92	C₄×C₈×C₄₁	—	2	2	no	—
93	C₄×C₈×C₄₁	—	2	2	no	—
94	#95×C₄₁	—	2	2	no	—
95	#95×C₄₁	—	2	2	no	—
96	#95×C₄₁	—	2	2	no	—
97	#95×C₄₁	D₄	1	1	yes	characteristic
98	#95×C₄₁	D₄	1	1	yes	characteristic
99	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
100	C₂×Q₈×C₄₁	—	2	2	no	—
101	C₂×Q₈×C₄₁	—	2	2	no	—
102	C₂×Q₈×C₄₁	—	2	2	no	—
103	C₂×Q₈×C₄₁	—	2	2	no	—
104	C₂×Q₈×C₄₁	—	2	2	no	—
105	C₂×Q₈×C₄₁	—	2	2	no	—
106	C₂×Q₈×C₄₁	—	2	2	no	—
107	C₂×Q₈×C₄₁	—	2	2	no	—
108	C₂×Q₈×C₄₁	—	2	2	no	—
109	C₂×Q₈×C₄₁	—	2	2	no	—
110	C₂×Q₈×C₄₁	—	2	2	no	—
111	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
112	C₂²×C₄×C₄₁	—	2	2	no	—
113	C₂²×C₄×C₄₁	—	2	2	no	—
114	C₂²×C₄×C₄₁	—	2	1	no	—
115	C₂²×C₄×C₄₁	—	2	1	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	1	no	—
120	C₂²×C₄×C₄₁	—	2	2	no	—
121	C₂²×C₄×C₄₁	—	2	2	no	—
122	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
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	Q₁₆×C₄₁	—	2	8	no	—
129	Q₁₆×C₄₁	—	4	8	no	—
130	Q₁₆×C₄₁	—	4	4	no	—
131	C₂×C₈×C₄₁	—	2	1	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	—	2	1	no	—
137	C₂×C₈×C₄₁	—	2	1	no	—
138	C₂×C₈×C₄₁	—	2	1	no	—
139	C₂×C₈×C₄₁	—	4	4	no	—
140	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₄₁	#41	1	2	yes	—
143	C₂×C₈×C₄₁	#41	1	2	yes	—
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	4	no	—
148	C₄⋊C₄×C₄₁	—	4	4	no	—
149	C₄⋊C₄×C₄₁	—	4	4	no	—
150	C₄⋊C₄×C₄₁	—	4	4	no	—
151	C₄⋊C₄×C₄₁	—	4	4	no	—
152	C₄⋊C₄×C₄₁	—	4	4	no	—
153	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
154	C₂²⋊C₄×C₄₁	—	2	2	no	—
155	C₂²⋊C₄×C₄₁	—	4	4	no	—
156	C₂²⋊C₄×C₄₁	—	4	4	no	—
157	C₂²⋊C₄×C₄₁	Q₁₆	1	4	yes	complemented
158	C₄²×C₄₁	—	2	1	no	—
159	C₄²×C₄₁	—	2	1	no	—
160	C₄²×C₄₁	—	2	1	no	—
161	C₄²×C₄₁	—	2	1	no	—
162	C₄²×C₄₁	—	4	4	no	—
163	C₂³×C₄₁	—	2	1	no	—
164	C₂³×C₄₁	—	2	1	no	—
165	C₂³×C₄₁	—	2	1	no	—
166	C₂³×C₄₁	—	2	1	no	—
167	C₂³×C₄₁	—	2	1	no	—
168	C₂³×C₄₁	—	2	1	no	—
169	C₂³×C₄₁	C₂×Q₁₆	1	2	yes	—
170	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₄₁	—	2	4	no	—
172	Q₈×C₄₁	—	2	4	no	—
173	Q₈×C₄₁	—	4	2	no	—
174	Q₈×C₄₁	—	4	2	no	—
175	Q₈×C₄₁	—	4	2	no	—
176	Q₈×C₄₁	—	4	2	no	—
177	Q₈×C₄₁	—	4	2	no	—
178	Q₈×C₄₁	—	4	2	no	—
179	C₂×C₄×C₄₁	—	2	1	no	—
180	C₂×C₄×C₄₁	—	2	1	no	—
181	C₂×C₄×C₄₁	—	2	1	no	—
182	C₂×C₄×C₄₁	—	2	1	no	—
183	C₂×C₄×C₄₁	—	2	1	no	—
184	C₂×C₄×C₄₁	—	2	1	no	—
185	C₂×C₄×C₄₁	—	2	1	no	—
186	C₂×C₄×C₄₁	—	2	1	no	—
187	C₂×C₄×C₄₁	—	2	4	no	—
188	C₂×C₄×C₄₁	—	2	4	no	—
189	C₂×C₄×C₄₁	—	2	1	no	—
190	C₂×C₄×C₄₁	—	2	1	no	—
191	C₂×C₄×C₄₁	—	2	1	no	—
192	C₂×C₄×C₄₁	—	2	1	no	—
193	C₂×C₄×C₄₁	—	4	2	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	1	no	—
198	C₂×C₄×C₄₁	—	4	1	no	—
199	C₂×C₄×C₄₁	—	4	1	no	—
200	C₂×C₄×C₄₁	—	4	1	no	—
201	C₂×C₄×C₄₁	—	4	2	no	—
202	C₂×C₄×C₄₁	—	4	2	no	—
203	C₂×C₄×C₄₁	—	4	2	no	—
204	C₂×C₄×C₄₁	—	4	2	no	—
205	C₂×C₄×C₄₁	—	4	2	no	—
206	C₂×C₄×C₄₁	—	4	2	no	—
207	C₂×C₄×C₄₁	C₂×Q₁₆	1	2	yes	—
208	C₂×C₄×C₄₁	C₂×Q₁₆	1	2	yes	—
209	C₂×C₄×C₄₁	#135	1	2	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	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
215	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
216	C₈×C₄₁	—	2	2	no	—
217	C₈×C₄₁	—	4	1	no	—
218	C₈×C₄₁	—	4	1	no	—
219	C₈×C₄₁	#121	1	4	yes	—
220	#25415	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂²×C₄₁	—	2	2	no	—
222	C₂²×C₄₁	—	2	2	no	—
223	C₂²×C₄₁	—	2	2	no	—
224	C₂²×C₄₁	—	4	1	no	—
225	C₂²×C₄₁	—	4	1	no	—
226	C₂²×C₄₁	—	4	1	no	—
227	C₂²×C₄₁	—	4	1	no	—
228	C₂²×C₄₁	#532	1	1	yes	characteristic
229	C₂²×C₄₁	D₄²	1	1	yes	characteristic
230	C₂²×C₄₁	D₄²	1	1	yes	characteristic
231	C₂²×C₄₁	C₂²×Q₁₆	1	1	yes	characteristic
232	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
233	C₂²×C₄₁	#578	1	1	yes	characteristic
234	C₂²×C₄₁	#578	1	1	yes	characteristic
235	C₄×C₄₁	—	2	2	no	—
236	C₄×C₄₁	—	2	2	no	—
237	C₄×C₄₁	—	2	2	no	—
238	C₄×C₄₁	—	4	1	no	—
239	C₄×C₄₁	—	4	4	no	—
240	C₄×C₄₁	—	4	1	no	—
241	C₄×C₄₁	—	4	4	no	—
242	C₄×C₄₁	—	8	2	no	—
243	C₄×C₄₁	—	8	2	no	—
244	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
245	C₄×C₄₁	#540	1	1	yes	characteristic
246	C₄×C₄₁	#546	1	1	yes	characteristic
247	C₄×C₄₁	#550	1	1	yes	characteristic
248	C₂×#494	C₂×C₄₁	1	1	yes	characteristic, complemented
249	C₂×#467	C₂×C₄₁	1	1	yes	characteristic
250	C₂×#467	C₂×C₄₁	1	1	yes	characteristic
251	C₂×C₄×Q₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
252	#2429	C₂×C₄₁	1	2	yes	—
253	#2043	C₂×C₄₁	1	2	yes	complemented
254	#2001	C₂×C₄₁	1	2	yes	—
255	#1969	C₂×C₄₁	1	1	yes	characteristic, complemented
256	#1942	C₂×C₄₁	1	1	yes	characteristic, complemented
257	#1878	C₂×C₄₁	1	2	yes	complemented
258	C₈×C₂²⋊C₄	C₂×C₄₁	1	1	yes	characteristic
259	C₂×C₄₁	—	4	2	no	—
260	C₂×C₄₁	#2428	1	1	yes	characteristic
261	C₂×C₄₁	#3170	1	1	yes	characteristic
262	C₂×C₄₁	#3177	1	1	yes	characteristic
263	C₂×C₄₁	#3283	1	1	yes	characteristic
264	C₂×C₄₁	#3285	1	1	yes	characteristic
265	C₂×C₄₁	D₄×Q₁₆	1	1	yes	characteristic
266	C₂×C₄₁	D₄×Q₁₆	1	1	yes	characteristic
267	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
268	C₂²×Q₁₆	C₂²×C₄₁	1	2	yes	—
269	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
270	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
271	C₂×C₄⋊Q₈	C₂²×C₄₁	1	2	yes	—
272	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
273	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
274	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
275	#494	—	2	4	no	—
276	#467	—	2	4	no	—
277	#467	—	2	4	no	—
278	C₄×Q₁₆	—	2	4	no	—
279	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
280	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
281	C₂×#103	C₂²×C₄₁	1	2	yes	—
282	C₂×#103	C₂²×C₄₁	1	2	yes	—
283	C₂×#103	C₂²×C₄₁	1	2	yes	—
284	C₂×#103	C₂²×C₄₁	1	2	yes	—
285	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
286	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
287	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
288	#398	—	2	2	no	—
289	#396	—	2	2	no	—
290	#391	C₂²×C₄₁	1	2	yes	—
291	#389	—	2	2	no	—
292	#389	C₂²×C₄₁	1	2	yes	—
293	#388	—	2	2	no	—
294	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
295	#340	C₂²×C₄₁	1	2	yes	—
296	#336	C₂²×C₄₁	1	1	yes	characteristic
297	#336	C₂²×C₄₁	1	1	yes	characteristic
298	C₄₁	#25415	1	1	yes	characteristic, direct product factor, Sylow
299	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
300	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
301	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
302	C₂×Q₁₆	—	2	4	no	—
303	C₂×Q₁₆	—	2	2	no	—
304	C₂×Q₁₆	—	2	2	no	—
305	C₂×Q₁₆	—	2	2	no	—
306	C₂×Q₁₆	—	2	2	no	—
307	C₂×Q₁₆	—	2	4	no	—
308	C₂×Q₁₆	—	2	2	no	—
309	C₂×Q₁₆	—	4	2	no	—
310	C₂×Q₁₆	D₄×C₄₁	1	4	yes	—
311	C₂²×C₈	—	2	2	no	—
312	C₂²×C₈	—	2	2	no	—
313	C₂²×C₈	—	2	2	no	—
314	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
315	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
316	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
318	C₄⋊Q₈	—	2	4	no	—
319	C₄⋊Q₈	—	4	2	no	—
320	C₂²⋊Q₈	—	2	4	no	—
321	C₂²⋊Q₈	—	2	4	no	—
322	C₂²⋊Q₈	—	4	2	no	—
323	C₂²⋊Q₈	—	4	2	no	—
324	C₄×Q₈	—	2	4	no	—
325	C₄×Q₈	—	4	2	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
338	C₂×C₄²	—	2	2	no	—
339	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
340	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
341	#107	—	2	2	no	—
342	#107	D₄×C₄₁	1	4	yes	—
343	#103	—	2	4	no	—
344	#103	—	2	4	no	—
345	#103	—	2	4	no	—
346	#103	—	4	2	no	—
347	C₂²⋊C₈	—	2	2	no	—
348	C₄×C₈	—	2	2	no	—
349	C₄×C₈	—	2	2	no	—
350	#95	—	2	2	no	—
351	#95	—	2	2	no	—
352	#95	—	2	2	no	—
353	#95	D₄×C₄₁	1	1	yes	characteristic
354	#95	D₄×C₄₁	1	1	yes	characteristic
355	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
383	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
384	Q₁₆	—	2	8	no	—
385	Q₁₆	—	4	8	no	—
386	Q₁₆	—	4	4	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	4	4	no	—
396	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
397	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
398	C₂×C₈	#41×C₄₁	1	2	yes	—
399	C₂×C₈	#41×C₄₁	1	2	yes	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	4	4	no	—
404	C₄⋊C₄	—	4	4	no	—
405	C₄⋊C₄	—	4	4	no	—
406	C₄⋊C₄	—	4	4	no	—
407	C₄⋊C₄	—	4	4	no	—
408	C₄⋊C₄	—	4	4	no	—
409	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	4	4	no	—
412	C₂²⋊C₄	—	4	4	no	—
413	C₂²⋊C₄	Q₁₆×C₄₁	1	4	yes	complemented
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	4	4	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	1	no	—
422	C₂³	—	2	1	no	—
423	C₂³	—	2	1	no	—
424	C₂³	—	2	1	no	—
425	C₂³	C₂×Q₁₆×C₄₁	1	2	yes	—
426	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
427	Q₈	—	2	4	no	—
428	Q₈	—	2	4	no	—
429	Q₈	—	4	2	no	—
430	Q₈	—	4	2	no	—
431	Q₈	—	4	2	no	—
432	Q₈	—	4	2	no	—
433	Q₈	—	4	2	no	—
434	Q₈	—	4	2	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	C₂×Q₁₆×C₄₁	1	2	yes	—
464	C₂×C₄	C₂×Q₁₆×C₄₁	1	2	yes	—
465	C₂×C₄	#135×C₄₁	1	2	yes	—
466	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
467	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
468	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
469	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
470	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
471	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
472	C₈	—	2	2	no	—
473	C₈	—	4	1	no	—
474	C₈	—	4	1	no	—
475	C₈	#121×C₄₁	1	4	yes	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	4	1	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	1	no	—
482	C₂²	—	4	1	no	—
483	C₂²	C₄₁×#532	1	1	yes	characteristic
484	C₂²	D₄²×C₄₁	1	1	yes	characteristic
485	C₂²	D₄²×C₄₁	1	1	yes	characteristic
486	C₂²	C₂²×Q₁₆×C₄₁	1	1	yes	characteristic
487	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
488	C₂²	C₄₁×#578	1	1	yes	characteristic
489	C₂²	C₄₁×#578	1	1	yes	characteristic
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	4	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	4	no	—
497	C₄	—	8	2	no	—
498	C₄	—	8	2	no	—
499	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
500	C₄	C₄₁×#540	1	1	yes	characteristic
501	C₄	C₄₁×#546	1	1	yes	characteristic
502	C₄	C₄₁×#550	1	1	yes	characteristic
503	C₂	—	4	2	no	—
504	C₂	C₄₁×#2428	1	1	yes	characteristic
505	C₂	C₄₁×#3170	1	1	yes	characteristic
506	C₂	C₄₁×#3177	1	1	yes	characteristic
507	C₂	C₄₁×#3283	1	1	yes	characteristic
508	C₂	C₄₁×#3285	1	1	yes	characteristic
509	C₂	D₄×Q₁₆×C₄₁	1	1	yes	characteristic
510	C₂	D₄×Q₁₆×C₄₁	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#494	C₂	semidirect
4. C₂×C₄×Q₁₆×C₄₁	C₂	semidirect
6. C₄₁×#2043	C₂	semidirect
8. C₄₁×#1969	C₂	semidirect
9. C₄₁×#1942	C₂	semidirect
10. C₄₁×#1878	C₂	semidirect
157. C₂²⋊C₄×C₄₁	Q₁₆	semidirect
220. #25415	C₄₁	direct (N × H)
248. C₂×#494	C₂×C₄₁	semidirect
251. C₂×C₄×Q₁₆	C₂×C₄₁	semidirect
253. #2043	C₂×C₄₁	semidirect
255. #1969	C₂×C₄₁	semidirect
256. #1942	C₂×C₄₁	semidirect
257. #1878	C₂×C₄₁	semidirect
298. C₄₁	#25415	direct (N × H)
413. C₂²⋊C₄	Q₁₆×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×#494	2
C₂×C₄₁×#467	2
C₂×C₄×Q₁₆×C₄₁	2
C₄₁×#2429	2
C₄₁×#2043	2
C₄₁×#2001	2
C₄₁×#1969	2
C₄₁×#1942	2
C₄₁×#1878	2
C₈×C₂²⋊C₄×C₄₁	2
#25415	41

Subgroups — C41×#25415 #23801616

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25415 #23801616