Subgroups — C₄₁×#24360 #23800561

Order 10496.

1382 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#462	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₁×#451	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2434	C₂	1	1	yes	maximal, characteristic
5	Q₈×C₂²⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#2056	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2016	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1892	C₂	1	1	yes	maximal, characteristic
9	C₄₁×#1878	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1850	C₂	1	1	yes	maximal, characteristic
11	C₄₁×#1787	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₄₁	—	2	4	no	—
15	C₂²×Q₁₆×C₄₁	—	2	8	no	—
16	C₂²×Q₁₆×C₄₁	C₂²	1	2	yes	—
17	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₄₁	C₂²	1	2	yes	—
19	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₄₁	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
24	C₄₁×#462	—	2	8	no	—
25	C₄₁×#451	—	2	4	no	—
26	C₂×C₄⋊C₈×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	1	yes	characteristic
30	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×#103×C₄₁	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
33	C₄₁×#395	—	2	2	no	—
34	C₄₁×#391	—	2	2	no	—
35	C₄₁×#391	C₂²	1	2	yes	—
36	C₄₁×#391	C₂²	1	2	yes	—
37	C₄₁×#385	—	2	1	no	—
38	C₄₁×#385	—	2	1	no	—
39	C₄₁×#380	—	2	1	no	—
40	C₄₁×#380	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
42	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
43	C₄₁×#340	C₂²	1	2	yes	—
44	C₄₁×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₄₁	—	2	1	no	—
46	C₂²×Q₈×C₄₁	—	2	1	no	—
47	C₂²×Q₈×C₄₁	—	2	2	no	—
48	C₂²×Q₈×C₄₁	—	2	4	no	—
49	C₂²×Q₈×C₄₁	—	2	4	no	—
50	C₂²×Q₈×C₄₁	—	2	2	no	—
51	C₂²×Q₈×C₄₁	—	2	2	no	—
52	C₂²×Q₈×C₄₁	—	4	2	no	—
53	C₂²×Q₈×C₄₁	—	4	2	no	—
54	C₂²×Q₈×C₄₁	D₄	1	4	yes	—
55	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
56	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
57	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
58	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₄₁	—	2	1	no	—
60	C₂³×C₄×C₄₁	—	2	1	no	—
61	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
62	C₂×Q₁₆×C₄₁	—	2	32	no	—
63	C₂×Q₁₆×C₄₁	—	2	4	no	—
64	C₂×Q₁₆×C₄₁	—	2	4	no	—
65	C₂×Q₁₆×C₄₁	—	2	4	no	—
66	C₂×Q₁₆×C₄₁	—	2	4	no	—
67	C₂×Q₁₆×C₄₁	—	2	2	no	—
68	C₂×Q₁₆×C₄₁	—	2	2	no	—
69	C₂×Q₁₆×C₄₁	—	2	4	no	—
70	C₂×Q₁₆×C₄₁	—	2	4	no	—
71	C₂×Q₁₆×C₄₁	—	4	2	no	—
72	C₂×Q₁₆×C₄₁	D₄	1	8	yes	—
73	C₂²×C₈×C₄₁	—	2	2	no	—
74	C₂²×C₈×C₄₁	—	2	4	no	—
75	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
78	C₄⋊Q₈×C₄₁	—	2	4	no	—
79	C₄⋊Q₈×C₄₁	—	4	2	no	—
80	C₂²⋊Q₈×C₄₁	—	2	2	no	—
81	C₂²⋊Q₈×C₄₁	—	2	2	no	—
82	C₄×Q₈×C₄₁	—	2	4	no	—
83	C₄×Q₈×C₄₁	—	4	2	no	—
84	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
85	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
86	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
87	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
88	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₁	—	2	2	no	—
95	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
96	C₄⋊C₈×C₄₁	—	2	4	no	—
97	#103×C₄₁	—	2	2	no	—
98	#103×C₄₁	—	2	2	no	—
99	#103×C₄₁	—	2	4	no	—
100	#103×C₄₁	—	2	4	no	—
101	#103×C₄₁	—	4	2	no	—
102	C₂²⋊C₈×C₄₁	—	2	2	no	—
103	#95×C₄₁	—	2	2	no	—
104	#95×C₄₁	—	2	2	no	—
105	#95×C₄₁	—	2	1	no	—
106	#95×C₄₁	—	2	2	no	—
107	#95×C₄₁	—	2	2	no	—
108	#95×C₄₁	D₄	1	2	yes	—
109	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
110	C₂×Q₈×C₄₁	—	2	4	no	—
111	C₂×Q₈×C₄₁	—	2	1	no	—
112	C₂×Q₈×C₄₁	—	2	1	no	—
113	C₂×Q₈×C₄₁	—	2	2	no	—
114	C₂×Q₈×C₄₁	—	2	2	no	—
115	C₂×Q₈×C₄₁	—	2	8	no	—
116	C₂×Q₈×C₄₁	—	2	8	no	—
117	C₂×Q₈×C₄₁	—	2	2	no	—
118	C₂×Q₈×C₄₁	—	2	2	no	—
119	C₂×Q₈×C₄₁	—	2	2	no	—
120	C₂×Q₈×C₄₁	—	2	2	no	—
121	C₂×Q₈×C₄₁	—	2	1	no	—
122	C₂×Q₈×C₄₁	—	2	2	no	—
123	C₂×Q₈×C₄₁	—	2	1	no	—
124	C₂×Q₈×C₄₁	—	2	2	no	—
125	C₂×Q₈×C₄₁	—	2	2	no	—
126	C₂×Q₈×C₄₁	—	2	2	no	—
127	C₂×Q₈×C₄₁	—	4	4	no	—
128	C₂×Q₈×C₄₁	—	4	4	no	—
129	C₂×Q₈×C₄₁	—	4	4	no	—
130	C₂×Q₈×C₄₁	—	4	8	no	—
131	C₂×Q₈×C₄₁	—	4	8	no	—
132	C₂×Q₈×C₄₁	—	4	4	no	—
133	C₂×Q₈×C₄₁	—	4	2	no	—
134	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
135	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
136	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
137	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₄₁	—	2	1	no	—
139	C₂²×C₄×C₄₁	—	2	2	no	—
140	C₂²×C₄×C₄₁	—	2	2	no	—
141	C₂²×C₄×C₄₁	—	2	4	no	—
142	C₂²×C₄×C₄₁	—	2	1	no	—
143	C₂²×C₄×C₄₁	—	2	2	no	—
144	C₂²×C₄×C₄₁	—	2	1	no	—
145	C₂²×C₄×C₄₁	—	2	2	no	—
146	C₂²×C₄×C₄₁	—	2	1	no	—
147	C₂²×C₄×C₄₁	—	4	4	no	—
148	C₂²×C₄×C₄₁	—	4	4	no	—
149	C₂²×C₄×C₄₁	—	4	2	no	—
150	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₄₁	#41	1	2	yes	—
155	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
156	Q₁₆×C₄₁	—	2	16	no	—
157	Q₁₆×C₄₁	—	2	16	no	—
158	Q₁₆×C₄₁	—	4	4	no	—
159	Q₁₆×C₄₁	—	4	4	no	—
160	C₂×C₈×C₄₁	—	2	8	no	—
161	C₂×C₈×C₄₁	—	2	2	no	—
162	C₂×C₈×C₄₁	—	2	2	no	—
163	C₂×C₈×C₄₁	—	2	1	no	—
164	C₂×C₈×C₄₁	—	2	1	no	—
165	C₂×C₈×C₄₁	—	2	2	no	—
166	C₂×C₈×C₄₁	—	2	2	no	—
167	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
168	C₄⋊C₄×C₄₁	—	2	2	no	—
169	C₄⋊C₄×C₄₁	—	2	1	no	—
170	C₄⋊C₄×C₄₁	—	2	1	no	—
171	C₄⋊C₄×C₄₁	—	2	2	no	—
172	C₄⋊C₄×C₄₁	—	4	4	no	—
173	C₄⋊C₄×C₄₁	—	4	4	no	—
174	C₄⋊C₄×C₄₁	—	4	4	no	—
175	C₄⋊C₄×C₄₁	—	4	2	no	—
176	C₂²⋊C₄×C₄₁	—	2	2	no	—
177	C₂²⋊C₄×C₄₁	—	4	2	no	—
178	C₂²⋊C₄×C₄₁	—	4	2	no	—
179	C₂²⋊C₄×C₄₁	Q₁₆	1	4	yes	complemented
180	C₄²×C₄₁	—	2	2	no	—
181	C₄²×C₄₁	—	2	2	no	—
182	C₄²×C₄₁	—	4	4	no	—
183	C₂³×C₄₁	—	2	2	no	—
184	C₂³×C₄₁	—	2	2	no	—
185	C₂³×C₄₁	#121	1	2	yes	—
186	C₂³×C₄₁	C₂×Q₁₆	1	2	yes	—
187	C₂³×C₄₁	#137	1	2	yes	—
188	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
189	Q₈×C₄₁	—	2	2	no	—
190	Q₈×C₄₁	—	2	4	no	—
191	Q₈×C₄₁	—	2	2	no	—
192	Q₈×C₄₁	—	2	4	no	—
193	Q₈×C₄₁	—	2	2	no	—
194	Q₈×C₄₁	—	2	4	no	—
195	Q₈×C₄₁	—	4	8	no	—
196	Q₈×C₄₁	—	4	8	no	—
197	Q₈×C₄₁	—	4	2	no	—
198	Q₈×C₄₁	—	4	2	no	—
199	Q₈×C₄₁	—	4	2	no	—
200	Q₈×C₄₁	—	4	1	no	—
201	Q₈×C₄₁	—	4	1	no	—
202	Q₈×C₄₁	—	4	2	no	—
203	Q₈×C₄₁	#120	1	4	yes	—
204	C₂×C₄×C₄₁	—	2	2	no	—
205	C₂×C₄×C₄₁	—	2	2	no	—
206	C₂×C₄×C₄₁	—	2	4	no	—
207	C₂×C₄×C₄₁	—	2	2	no	—
208	C₂×C₄×C₄₁	—	2	2	no	—
209	C₂×C₄×C₄₁	—	2	2	no	—
210	C₂×C₄×C₄₁	—	2	2	no	—
211	C₂×C₄×C₄₁	—	2	4	no	—
212	C₂×C₄×C₄₁	—	2	2	no	—
213	C₂×C₄×C₄₁	—	2	2	no	—
214	C₂×C₄×C₄₁	—	2	4	no	—
215	C₂×C₄×C₄₁	—	2	2	no	—
216	C₂×C₄×C₄₁	—	2	2	no	—
217	C₂×C₄×C₄₁	—	4	8	no	—
218	C₂×C₄×C₄₁	—	4	8	no	—
219	C₂×C₄×C₄₁	—	4	2	no	—
220	C₂×C₄×C₄₁	—	4	2	no	—
221	C₂×C₄×C₄₁	—	4	2	no	—
222	C₂×C₄×C₄₁	—	4	1	no	—
223	C₂×C₄×C₄₁	—	4	1	no	—
224	C₂×C₄×C₄₁	—	4	2	no	—
225	C₂×C₄×C₄₁	—	4	2	no	—
226	C₂×C₄×C₄₁	—	4	2	no	—
227	C₂×C₄×C₄₁	—	4	2	no	—
228	C₂×C₄×C₄₁	—	4	2	no	—
229	C₂×C₄×C₄₁	#121	1	2	yes	—
230	C₂×C₄×C₄₁	C₂×Q₁₆	1	4	yes	complemented
231	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
233	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
235	C₈×C₄₁	—	2	4	no	—
236	C₈×C₄₁	—	4	1	no	—
237	C₈×C₄₁	—	4	1	no	—
238	#24360	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂²×C₄₁	—	2	2	no	—
240	C₂²×C₄₁	—	2	4	no	—
241	C₂²×C₄₁	—	2	4	no	—
242	C₂²×C₄₁	—	2	2	no	—
243	C₂²×C₄₁	#462	1	4	yes	complemented
244	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
245	C₂²×C₄₁	D₄²	1	2	yes	—
246	C₂²×C₄₁	C₂²×Q₁₆	1	1	yes	characteristic
247	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
248	C₂²×C₄₁	#578	1	2	yes	—
249	C₄×C₄₁	—	2	2	no	—
250	C₄×C₄₁	—	2	4	no	—
251	C₄×C₄₁	—	2	4	no	—
252	C₄×C₄₁	—	4	2	no	—
253	C₄×C₄₁	—	4	4	no	—
254	C₄×C₄₁	—	4	2	no	—
255	C₄×C₄₁	—	8	1	no	—
256	C₄×C₄₁	—	8	2	no	—
257	C₄×C₄₁	—	8	1	no	—
258	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
259	C₄×C₄₁	#534	1	1	yes	characteristic
260	C₄×C₄₁	#546	1	2	yes	—
261	C₂³×Q₁₆	C₂×C₄₁	1	1	yes	characteristic
262	C₂×#462	C₂×C₄₁	1	2	yes	complemented
263	C₂×#451	C₂×C₄₁	1	1	yes	characteristic
264	#2434	C₂×C₄₁	1	1	yes	characteristic
265	Q₈×C₂²⋊C₄	C₂×C₄₁	1	1	yes	characteristic
266	#2056	C₂×C₄₁	1	2	yes	complemented
267	#2016	C₂×C₄₁	1	2	yes	complemented
268	#1892	C₂×C₄₁	1	1	yes	characteristic
269	#1878	C₂×C₄₁	1	2	yes	complemented
270	#1850	C₂×C₄₁	1	1	yes	characteristic
271	#1787	C₂×C₄₁	1	1	yes	characteristic
272	C₂×C₄₁	—	2	4	no	—
273	C₂×C₄₁	#2410	1	1	yes	characteristic
274	C₂×C₄₁	C₂×#462	1	1	yes	characteristic
275	C₂×C₄₁	#3044	1	1	yes	characteristic
276	C₂×C₄₁	#3270	1	2	yes	—
277	C₂×C₄₁	D₄×Q₁₆	1	2	yes	—
278	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
279	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
280	C₂²×Q₁₆	—	2	4	no	—
281	C₂²×Q₁₆	—	2	8	no	—
282	C₂²×Q₁₆	C₂²×C₄₁	1	2	yes	—
283	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
284	C₂²×Q₁₆	C₂²×C₄₁	1	2	yes	—
285	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
286	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
287	C₂×C₄⋊Q₈	C₂²×C₄₁	1	2	yes	—
288	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
289	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
290	#462	—	2	8	no	—
291	#451	—	2	4	no	—
292	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
293	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
294	C₂×#103	C₂²×C₄₁	1	2	yes	—
295	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
296	C₂×#103	C₂²×C₄₁	1	2	yes	—
297	C₂×#103	C₂²×C₄₁	1	2	yes	—
298	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
299	#395	—	2	2	no	—
300	#391	—	2	2	no	—
301	#391	C₂²×C₄₁	1	2	yes	—
302	#391	C₂²×C₄₁	1	2	yes	—
303	#385	—	2	1	no	—
304	#385	—	2	1	no	—
305	#380	—	2	1	no	—
306	#380	C₂²×C₄₁	1	1	yes	characteristic
307	C₄×C₂²⋊C₄	—	2	1	no	—
308	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
309	#340	C₂²×C₄₁	1	2	yes	—
310	#336	C₂²×C₄₁	1	2	yes	—
311	C₄₁	#24360	1	1	yes	characteristic, direct product factor, Sylow
312	C₂²×Q₈	—	2	1	no	—
313	C₂²×Q₈	—	2	1	no	—
314	C₂²×Q₈	—	2	2	no	—
315	C₂²×Q₈	—	2	4	no	—
316	C₂²×Q₈	—	2	4	no	—
317	C₂²×Q₈	—	2	2	no	—
318	C₂²×Q₈	—	2	2	no	—
319	C₂²×Q₈	—	4	2	no	—
320	C₂²×Q₈	—	4	2	no	—
321	C₂²×Q₈	D₄×C₄₁	1	4	yes	—
322	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
323	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
324	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
325	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
326	C₂³×C₄	—	2	1	no	—
327	C₂³×C₄	—	2	1	no	—
328	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
329	C₂×Q₁₆	—	2	32	no	—
330	C₂×Q₁₆	—	2	4	no	—
331	C₂×Q₁₆	—	2	4	no	—
332	C₂×Q₁₆	—	2	4	no	—
333	C₂×Q₁₆	—	2	4	no	—
334	C₂×Q₁₆	—	2	2	no	—
335	C₂×Q₁₆	—	2	2	no	—
336	C₂×Q₁₆	—	2	4	no	—
337	C₂×Q₁₆	—	2	4	no	—
338	C₂×Q₁₆	—	4	2	no	—
339	C₂×Q₁₆	D₄×C₄₁	1	8	yes	—
340	C₂²×C₈	—	2	2	no	—
341	C₂²×C₈	—	2	4	no	—
342	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
343	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
344	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
345	C₄⋊Q₈	—	2	4	no	—
346	C₄⋊Q₈	—	4	2	no	—
347	C₂²⋊Q₈	—	2	2	no	—
348	C₂²⋊Q₈	—	2	2	no	—
349	C₄×Q₈	—	2	4	no	—
350	C₄×Q₈	—	4	2	no	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	2	no	—
354	C₂×C₄⋊C₄	—	2	2	no	—
355	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
356	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
360	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
361	C₂×C₄²	—	2	2	no	—
362	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
363	C₄⋊C₈	—	2	4	no	—
364	#103	—	2	2	no	—
365	#103	—	2	2	no	—
366	#103	—	2	4	no	—
367	#103	—	2	4	no	—
368	#103	—	4	2	no	—
369	C₂²⋊C₈	—	2	2	no	—
370	#95	—	2	2	no	—
371	#95	—	2	2	no	—
372	#95	—	2	1	no	—
373	#95	—	2	2	no	—
374	#95	—	2	2	no	—
375	#95	D₄×C₄₁	1	2	yes	—
376	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
377	C₂×Q₈	—	2	4	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	8	no	—
383	C₂×Q₈	—	2	8	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	4	4	no	—
395	C₂×Q₈	—	4	4	no	—
396	C₂×Q₈	—	4	4	no	—
397	C₂×Q₈	—	4	8	no	—
398	C₂×Q₈	—	4	8	no	—
399	C₂×Q₈	—	4	4	no	—
400	C₂×Q₈	—	4	2	no	—
401	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
402	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
403	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
404	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	4	4	no	—
415	C₂²×C₄	—	4	4	no	—
416	C₂²×C₄	—	4	2	no	—
417	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
418	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
420	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
421	C₂²×C₄	#41×C₄₁	1	2	yes	—
422	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
423	Q₁₆	—	2	16	no	—
424	Q₁₆	—	2	16	no	—
425	Q₁₆	—	4	4	no	—
426	Q₁₆	—	4	4	no	—
427	C₂×C₈	—	2	8	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	4	4	no	—
440	C₄⋊C₄	—	4	4	no	—
441	C₄⋊C₄	—	4	4	no	—
442	C₄⋊C₄	—	4	2	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	4	2	no	—
445	C₂²⋊C₄	—	4	2	no	—
446	C₂²⋊C₄	Q₁₆×C₄₁	1	4	yes	complemented
447	C₄²	—	2	2	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	4	4	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	#121×C₄₁	1	2	yes	—
453	C₂³	C₂×Q₁₆×C₄₁	1	2	yes	—
454	C₂³	#137×C₄₁	1	2	yes	—
455	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
456	Q₈	—	2	2	no	—
457	Q₈	—	2	4	no	—
458	Q₈	—	2	2	no	—
459	Q₈	—	2	4	no	—
460	Q₈	—	2	2	no	—
461	Q₈	—	2	4	no	—
462	Q₈	—	4	8	no	—
463	Q₈	—	4	8	no	—
464	Q₈	—	4	2	no	—
465	Q₈	—	4	2	no	—
466	Q₈	—	4	2	no	—
467	Q₈	—	4	1	no	—
468	Q₈	—	4	1	no	—
469	Q₈	—	4	2	no	—
470	Q₈	#120×C₄₁	1	4	yes	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	4	8	no	—
485	C₂×C₄	—	4	8	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	#121×C₄₁	1	2	yes	—
497	C₂×C₄	C₂×Q₁₆×C₄₁	1	4	yes	complemented
498	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
499	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
500	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
501	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
502	C₈	—	2	4	no	—
503	C₈	—	4	1	no	—
504	C₈	—	4	1	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	4	no	—
508	C₂²	—	2	4	no	—
509	C₂²	C₄₁×#462	1	4	yes	complemented
510	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
511	C₂²	D₄²×C₄₁	1	2	yes	—
512	C₂²	C₂²×Q₁₆×C₄₁	1	1	yes	characteristic
513	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
514	C₂²	C₄₁×#578	1	2	yes	—
515	C₄	—	2	2	no	—
516	C₄	—	2	4	no	—
517	C₄	—	2	4	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	4	no	—
520	C₄	—	4	2	no	—
521	C₄	—	8	1	no	—
522	C₄	—	8	1	no	—
523	C₄	—	8	2	no	—
524	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
525	C₄	C₄₁×#534	1	1	yes	characteristic
526	C₄	C₄₁×#546	1	2	yes	—
527	C₂	—	2	4	no	—
528	C₂	C₄₁×#2410	1	1	yes	characteristic
529	C₂	C₂×C₄₁×#462	1	1	yes	characteristic
530	C₂	C₄₁×#3044	1	1	yes	characteristic
531	C₂	C₄₁×#3270	1	2	yes	—
532	C₂	D₄×Q₁₆×C₄₁	1	2	yes	—

	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
2. C₂×C₄₁×#462	C₂	semidirect
6. C₄₁×#2056	C₂	semidirect
7. C₄₁×#2016	C₂	semidirect
9. C₄₁×#1878	C₂	semidirect
179. C₂²⋊C₄×C₄₁	Q₁₆	semidirect
230. C₂×C₄×C₄₁	C₂×Q₁₆	semidirect
238. #24360	C₄₁	direct (N × H)
243. C₂²×C₄₁	#462	semidirect
262. C₂×#462	C₂×C₄₁	semidirect
266. #2056	C₂×C₄₁	semidirect
267. #2016	C₂×C₄₁	semidirect
269. #1878	C₂×C₄₁	semidirect
311. C₄₁	#24360	direct (N × H)
446. C₂²⋊C₄	Q₁₆×C₄₁	semidirect
497. C₂×C₄	C₂×Q₁₆×C₄₁	semidirect
509. C₂²	C₄₁×#462	semidirect

Maximal subgroups

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

subgroup	index
C₂³×Q₁₆×C₄₁	2
C₂×C₄₁×#462	2
C₂×C₄₁×#451	2
C₄₁×#2434	2
Q₈×C₂²⋊C₄×C₄₁	2
C₄₁×#2056	2
C₄₁×#2016	2
C₄₁×#1892	2
C₄₁×#1878	2
C₄₁×#1850	2
C₄₁×#1787	2
#24360	41

Subgroups — C41×#24360 #23800561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24360 #23800561