Subgroups — C₄₁×#25369 #23801570

Order 10496.

1014 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#492	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#464	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₁×#462	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2548	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#2365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2055	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2015	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1982	C₂	1	1	yes	maximal, characteristic
9	C₄₁×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1880	C₂	1	2	yes	maximal, complemented
11	C₄×#103×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₄₁	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
15	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×#124×C₄₁	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
20	C₄₁×#492	—	2	4	no	—
21	C₄₁×#464	—	2	8	no	—
22	C₄₁×#462	—	2	4	no	—
23	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#103×C₄₁	C₂²	1	2	yes	—
27	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×#102×C₄₁	C₂²	1	2	yes	—
29	C₂×#102×C₄₁	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₄₁×#394	—	2	2	no	—
32	C₄₁×#391	C₂²	1	2	yes	—
33	C₄₁×#390	—	2	1	no	—
34	C₄₁×#390	—	2	1	no	—
35	C₄₁×#390	C₂²	1	2	yes	—
36	C₄₁×#389	—	2	1	no	—
37	C₄₁×#387	—	2	2	no	—
38	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
39	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
41	C₄₁×#340	C₂²	1	1	yes	characteristic
42	C₄₁×#340	C₂²	1	1	yes	characteristic
43	C₄₁×#336	C₂²	1	2	yes	—
44	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
46	C₂²×D₄×C₄₁	—	2	1	no	—
47	C₂²×D₄×C₄₁	—	2	1	no	—
48	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
49	C₂×Q₁₆×C₄₁	—	2	4	no	—
50	C₂×Q₁₆×C₄₁	—	2	4	no	—
51	C₂×Q₁₆×C₄₁	—	4	2	no	—
52	C₂×SD₁₆×C₄₁	—	2	4	no	—
53	C₂×SD₁₆×C₄₁	—	2	4	no	—
54	C₂×SD₁₆×C₄₁	—	2	4	no	—
55	C₂×SD₁₆×C₄₁	—	2	4	no	—
56	C₂×SD₁₆×C₄₁	—	4	2	no	—
57	C₂×SD₁₆×C₄₁	—	4	2	no	—
58	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
59	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
61	C₄⋊Q₈×C₄₁	—	2	2	no	—
62	C₄⋊Q₈×C₄₁	D₄	1	4	yes	—
63	#127×C₄₁	—	2	2	no	—
64	#127×C₄₁	—	2	2	no	—
65	#124×C₄₁	—	2	4	no	—
66	#124×C₄₁	—	4	2	no	—
67	C₄×Q₈×C₄₁	—	2	4	no	—
68	C₄×Q₈×C₄₁	—	2	2	no	—
69	C₄×Q₈×C₄₁	—	2	2	no	—
70	C₄×Q₈×C₄₁	—	4	2	no	—
71	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
73	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
74	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
80	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
84	C₂×C₄²×C₄₁	—	2	2	no	—
85	C₂×C₄²×C₄₁	—	2	1	no	—
86	C₂×C₄²×C₄₁	—	2	1	no	—
87	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
88	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₄₁	—	2	4	no	—
90	C₄⋊C₈×C₄₁	—	2	2	no	—
91	#103×C₄₁	—	2	4	no	—
92	#103×C₄₁	—	2	2	no	—
93	#103×C₄₁	D₄	1	4	yes	complemented
94	#102×C₄₁	—	2	4	no	—
95	#102×C₄₁	—	4	2	no	—
96	C₄×C₈×C₄₁	—	2	2	no	—
97	#95×C₄₁	—	2	2	no	—
98	#95×C₄₁	—	2	1	no	—
99	#95×C₄₁	—	2	2	no	—
100	#95×C₄₁	D₄	1	2	yes	—
101	C₂⁴×C₄₁	—	2	2	no	—
102	C₂×Q₈×C₄₁	—	2	2	no	—
103	C₂×Q₈×C₄₁	—	2	1	no	—
104	C₂×Q₈×C₄₁	—	2	2	no	—
105	C₂×Q₈×C₄₁	—	2	1	no	—
106	C₂×Q₈×C₄₁	—	2	1	no	—
107	C₂×Q₈×C₄₁	—	2	1	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	—	2	1	no	—
112	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
113	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
114	C₂×D₄×C₄₁	—	2	2	no	—
115	C₂×D₄×C₄₁	—	2	2	no	—
116	C₂×D₄×C₄₁	—	2	2	no	—
117	C₂×D₄×C₄₁	—	2	2	no	—
118	C₂×D₄×C₄₁	—	2	2	no	—
119	C₂×D₄×C₄₁	—	2	2	no	—
120	C₂×D₄×C₄₁	—	4	2	no	—
121	C₂×D₄×C₄₁	—	4	2	no	—
122	C₂×D₄×C₄₁	—	4	2	no	—
123	C₂×D₄×C₄₁	—	4	2	no	—
124	C₂×D₄×C₄₁	—	8	1	no	—
125	C₂×D₄×C₄₁	—	8	1	no	—
126	C₂²×C₄×C₄₁	—	2	2	no	—
127	C₂²×C₄×C₄₁	—	2	1	no	—
128	C₂²×C₄×C₄₁	—	2	1	no	—
129	C₂²×C₄×C₄₁	—	2	1	no	—
130	C₂²×C₄×C₄₁	—	2	1	no	—
131	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
136	Q₁₆×C₄₁	—	4	8	no	—
137	SD₁₆×C₄₁	—	4	8	no	—
138	SD₁₆×C₄₁	—	4	8	no	—
139	C₂×C₈×C₄₁	—	2	1	no	—
140	C₂×C₈×C₄₁	—	2	1	no	—
141	C₂×C₈×C₄₁	—	2	1	no	—
142	C₂×C₈×C₄₁	—	2	1	no	—
143	C₂×C₈×C₄₁	—	2	2	no	—
144	C₂×C₈×C₄₁	—	2	2	no	—
145	C₂×C₈×C₄₁	—	2	2	no	—
146	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₄₁	#41	1	2	yes	—
148	C₄⋊C₄×C₄₁	—	2	4	no	—
149	C₄⋊C₄×C₄₁	—	2	4	no	—
150	C₄⋊C₄×C₄₁	—	2	2	no	—
151	C₄⋊C₄×C₄₁	—	2	2	no	—
152	C₄⋊C₄×C₄₁	—	2	1	no	—
153	C₄⋊C₄×C₄₁	—	2	1	no	—
154	C₄⋊C₄×C₄₁	—	2	1	no	—
155	C₄⋊C₄×C₄₁	—	2	1	no	—
156	C₄⋊C₄×C₄₁	—	2	1	no	—
157	C₄⋊C₄×C₄₁	—	4	4	no	—
158	C₄⋊C₄×C₄₁	—	4	2	no	—
159	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
160	C₂²⋊C₄×C₄₁	—	4	4	no	—
161	C₂²⋊C₄×C₄₁	—	4	4	no	—
162	C₂²⋊C₄×C₄₁	—	8	2	no	—
163	C₂²⋊C₄×C₄₁	—	8	2	no	—
164	C₄²×C₄₁	—	2	2	no	—
165	C₄²×C₄₁	—	2	2	no	—
166	C₄²×C₄₁	—	4	4	no	—
167	C₄²×C₄₁	—	4	2	no	—
168	C₄²×C₄₁	—	4	2	no	—
169	C₄²×C₄₁	C₂×D₄	1	2	yes	—
170	C₄²×C₄₁	#41	1	2	yes	—
171	C₂³×C₄₁	—	4	2	no	—
172	C₂³×C₄₁	—	4	2	no	—
173	C₂³×C₄₁	—	4	2	no	—
174	C₂³×C₄₁	—	4	2	no	—
175	C₂³×C₄₁	—	4	2	no	—
176	C₂³×C₄₁	—	4	2	no	—
177	C₂³×C₄₁	—	4	2	no	—
178	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
179	Q₈×C₄₁	—	2	2	no	—
180	Q₈×C₄₁	—	2	4	no	—
181	Q₈×C₄₁	—	2	2	no	—
182	Q₈×C₄₁	—	2	4	no	—
183	Q₈×C₄₁	—	4	2	no	—
184	Q₈×C₄₁	—	4	2	no	—
185	Q₈×C₄₁	—	4	1	no	—
186	Q₈×C₄₁	—	4	1	no	—
187	D₄×C₄₁	—	4	2	no	—
188	D₄×C₄₁	—	4	2	no	—
189	D₄×C₄₁	—	4	2	no	—
190	D₄×C₄₁	—	4	2	no	—
191	D₄×C₄₁	—	8	4	no	—
192	D₄×C₄₁	—	8	4	no	—
193	C₂×C₄×C₄₁	—	2	1	no	—
194	C₂×C₄×C₄₁	—	2	1	no	—
195	C₂×C₄×C₄₁	—	2	4	no	—
196	C₂×C₄×C₄₁	—	2	2	no	—
197	C₂×C₄×C₄₁	—	2	2	no	—
198	C₂×C₄×C₄₁	—	2	2	no	—
199	C₂×C₄×C₄₁	—	2	2	no	—
200	C₂×C₄×C₄₁	—	2	2	no	—
201	C₂×C₄×C₄₁	—	2	2	no	—
202	C₂×C₄×C₄₁	—	2	2	no	—
203	C₂×C₄×C₄₁	—	2	2	no	—
204	C₂×C₄×C₄₁	—	4	1	no	—
205	C₂×C₄×C₄₁	—	4	2	no	—
206	C₂×C₄×C₄₁	—	4	2	no	—
207	C₂×C₄×C₄₁	—	4	1	no	—
208	C₂×C₄×C₄₁	—	4	1	no	—
209	C₂×C₄×C₄₁	—	4	1	no	—
210	C₂×C₄×C₄₁	—	4	1	no	—
211	C₂×C₄×C₄₁	—	4	1	no	—
212	C₂×C₄×C₄₁	—	4	1	no	—
213	C₂×C₄×C₄₁	—	4	1	no	—
214	C₂×C₄×C₄₁	—	4	1	no	—
215	C₂×C₄×C₄₁	—	4	1	no	—
216	C₂×C₄×C₄₁	#121	1	2	yes	—
217	C₂×C₄×C₄₁	#121	1	2	yes	—
218	C₂×C₄×C₄₁	#135	1	2	yes	—
219	C₂×C₄×C₄₁	#137	1	2	yes	—
220	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
225	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
226	C₈×C₄₁	—	2	2	no	—
227	C₈×C₄₁	—	2	2	no	—
228	C₈×C₄₁	—	4	2	no	—
229	#25369	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂²×C₄₁	—	8	2	no	—
231	C₂²×C₄₁	—	8	2	no	—
232	C₂²×C₄₁	—	8	2	no	—
233	C₂²×C₄₁	—	8	2	no	—
234	C₂²×C₄₁	—	8	2	no	—
235	C₂²×C₄₁	—	8	2	no	—
236	C₂²×C₄₁	—	8	2	no	—
237	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
238	C₂²×C₄₁	D₄²	1	1	yes	characteristic
239	C₂²×C₄₁	#550	1	1	yes	characteristic
240	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
241	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
242	C₂²×C₄₁	#577	1	1	yes	characteristic
243	C₂²×C₄₁	#577	1	1	yes	characteristic
244	C₄×C₄₁	—	2	2	no	—
245	C₄×C₄₁	—	4	4	no	—
246	C₄×C₄₁	—	4	2	no	—
247	C₄×C₄₁	—	4	2	no	—
248	C₄×C₄₁	—	4	2	no	—
249	C₄×C₄₁	—	4	2	no	—
250	C₄×C₄₁	—	8	1	no	—
251	C₄×C₄₁	—	8	1	no	—
252	C₄×C₄₁	#464	1	4	yes	complemented
253	C₄×C₄₁	#532	1	1	yes	characteristic
254	C₄×C₄₁	#540	1	1	yes	characteristic
255	C₄×C₄₁	D₄²	1	1	yes	characteristic
256	C₄×C₄₁	#546	1	1	yes	characteristic
257	C₂×#492	C₂×C₄₁	1	1	yes	characteristic
258	C₂×#464	C₂×C₄₁	1	2	yes	complemented
259	C₂×#462	C₂×C₄₁	1	1	yes	characteristic, complemented
260	#2548	C₂×C₄₁	1	1	yes	characteristic
261	#2365	C₂×C₄₁	1	1	yes	characteristic, complemented
262	#2055	C₂×C₄₁	1	2	yes	complemented
263	#2015	C₂×C₄₁	1	2	yes	complemented
264	#1982	C₂×C₄₁	1	1	yes	characteristic
265	#1939	C₂×C₄₁	1	1	yes	characteristic, complemented
266	#1880	C₂×C₄₁	1	2	yes	complemented
267	C₄×#103	C₂×C₄₁	1	1	yes	characteristic, complemented
268	C₂×C₄₁	—	16	2	no	—
269	C₂×C₄₁	#2428	1	1	yes	characteristic
270	C₂×C₄₁	C₂×#464	1	1	yes	characteristic
271	C₂×C₄₁	#3043	1	1	yes	characteristic
272	C₂×C₄₁	#3278	1	1	yes	characteristic
273	C₂×C₄₁	#3284	1	1	yes	characteristic
274	C₂×C₄₁	#3394	1	1	yes	characteristic
275	C₂×C₄₁	#3400	1	1	yes	characteristic
276	C₂²×Q₁₆	C₂²×C₄₁	1	2	yes	—
277	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
278	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
279	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
280	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
281	C₂×#124	C₂²×C₄₁	1	2	yes	—
282	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
283	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
284	#492	—	2	4	no	—
285	#464	—	2	8	no	—
286	#462	—	2	4	no	—
287	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
288	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
289	C₂×#103	C₂²×C₄₁	1	2	yes	—
290	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
291	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
292	C₂×#102	C₂²×C₄₁	1	2	yes	—
293	C₂×#102	C₂²×C₄₁	1	2	yes	—
294	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
295	#394	—	2	2	no	—
296	#391	C₂²×C₄₁	1	2	yes	—
297	#390	—	2	1	no	—
298	#390	—	2	1	no	—
299	#390	C₂²×C₄₁	1	2	yes	—
300	#389	—	2	1	no	—
301	#387	—	2	2	no	—
302	C₄×C₄⋊C₄	—	2	1	no	—
303	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
304	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
305	#340	C₂²×C₄₁	1	1	yes	characteristic
306	#340	C₂²×C₄₁	1	1	yes	characteristic
307	#336	C₂²×C₄₁	1	2	yes	—
308	C₄₁	#25369	1	1	yes	characteristic, direct product factor, Sylow
309	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
310	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
311	C₂²×D₄	—	2	1	no	—
312	C₂²×D₄	—	2	1	no	—
313	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
314	C₂×Q₁₆	—	2	4	no	—
315	C₂×Q₁₆	—	2	4	no	—
316	C₂×Q₁₆	—	4	2	no	—
317	C₂×SD₁₆	—	2	4	no	—
318	C₂×SD₁₆	—	2	4	no	—
319	C₂×SD₁₆	—	2	4	no	—
320	C₂×SD₁₆	—	2	4	no	—
321	C₂×SD₁₆	—	4	2	no	—
322	C₂×SD₁₆	—	4	2	no	—
323	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
324	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
325	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
326	C₄⋊Q₈	—	2	2	no	—
327	C₄⋊Q₈	D₄×C₄₁	1	4	yes	—
328	#127	—	2	2	no	—
329	#127	—	2	2	no	—
330	#124	—	2	4	no	—
331	#124	—	4	2	no	—
332	C₄×Q₈	—	2	4	no	—
333	C₄×Q₈	—	2	2	no	—
334	C₄×Q₈	—	2	2	no	—
335	C₄×Q₈	—	4	2	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
341	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
345	C₂×C₂²⋊C₄	—	2	2	no	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₄²	—	2	2	no	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	—	2	1	no	—
352	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
353	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
354	C₄⋊C₈	—	2	4	no	—
355	C₄⋊C₈	—	2	2	no	—
356	#103	—	2	4	no	—
357	#103	—	2	2	no	—
358	#103	D₄×C₄₁	1	4	yes	complemented
359	#102	—	2	4	no	—
360	#102	—	4	2	no	—
361	C₄×C₈	—	2	2	no	—
362	#95	—	2	2	no	—
363	#95	—	2	1	no	—
364	#95	—	2	2	no	—
365	#95	D₄×C₄₁	1	2	yes	—
366	C₂⁴	—	2	2	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	1	no	—
377	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
378	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	4	2	no	—
386	C₂×D₄	—	4	2	no	—
387	C₂×D₄	—	4	2	no	—
388	C₂×D₄	—	4	2	no	—
389	C₂×D₄	—	8	1	no	—
390	C₂×D₄	—	8	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
397	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
398	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
400	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
401	Q₁₆	—	4	8	no	—
402	SD₁₆	—	4	8	no	—
403	SD₁₆	—	4	8	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
412	C₂×C₈	#41×C₄₁	1	2	yes	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	4	4	no	—
423	C₄⋊C₄	—	4	2	no	—
424	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
425	C₂²⋊C₄	—	4	4	no	—
426	C₂²⋊C₄	—	4	4	no	—
427	C₂²⋊C₄	—	8	2	no	—
428	C₂²⋊C₄	—	8	2	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	4	4	no	—
432	C₄²	—	4	2	no	—
433	C₄²	—	4	2	no	—
434	C₄²	C₂×D₄×C₄₁	1	2	yes	—
435	C₄²	#41×C₄₁	1	2	yes	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	2	no	—
443	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
444	Q₈	—	2	2	no	—
445	Q₈	—	2	4	no	—
446	Q₈	—	2	2	no	—
447	Q₈	—	2	4	no	—
448	Q₈	—	4	2	no	—
449	Q₈	—	4	2	no	—
450	Q₈	—	4	1	no	—
451	Q₈	—	4	1	no	—
452	D₄	—	4	2	no	—
453	D₄	—	4	2	no	—
454	D₄	—	4	2	no	—
455	D₄	—	4	2	no	—
456	D₄	—	8	4	no	—
457	D₄	—	8	4	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	#121×C₄₁	1	2	yes	—
482	C₂×C₄	#121×C₄₁	1	2	yes	—
483	C₂×C₄	#135×C₄₁	1	2	yes	—
484	C₂×C₄	#137×C₄₁	1	2	yes	—
485	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
486	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
487	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
488	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
489	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
490	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
491	C₈	—	2	2	no	—
492	C₈	—	2	2	no	—
493	C₈	—	4	2	no	—
494	C₂²	—	8	2	no	—
495	C₂²	—	8	2	no	—
496	C₂²	—	8	2	no	—
497	C₂²	—	8	2	no	—
498	C₂²	—	8	2	no	—
499	C₂²	—	8	2	no	—
500	C₂²	—	8	2	no	—
501	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
502	C₂²	D₄²×C₄₁	1	1	yes	characteristic
503	C₂²	C₄₁×#550	1	1	yes	characteristic
504	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
505	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
506	C₂²	C₄₁×#577	1	1	yes	characteristic
507	C₂²	C₄₁×#577	1	1	yes	characteristic
508	C₄	—	2	2	no	—
509	C₄	—	4	4	no	—
510	C₄	—	4	2	no	—
511	C₄	—	4	2	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	2	no	—
514	C₄	—	8	1	no	—
515	C₄	—	8	1	no	—
516	C₄	C₄₁×#464	1	4	yes	complemented
517	C₄	C₄₁×#532	1	1	yes	characteristic
518	C₄	C₄₁×#540	1	1	yes	characteristic
519	C₄	D₄²×C₄₁	1	1	yes	characteristic
520	C₄	C₄₁×#546	1	1	yes	characteristic
521	C₂	—	16	2	no	—
522	C₂	C₄₁×#2428	1	1	yes	characteristic
523	C₂	C₂×C₄₁×#464	1	1	yes	characteristic
524	C₂	C₄₁×#3043	1	1	yes	characteristic
525	C₂	C₄₁×#3278	1	1	yes	characteristic
526	C₂	C₄₁×#3284	1	1	yes	characteristic
527	C₂	C₄₁×#3394	1	1	yes	characteristic
528	C₂	C₄₁×#3400	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×#127×C₄₁	C₂²
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
2. C₂×C₄₁×#464	C₂	semidirect
3. C₂×C₄₁×#462	C₂	semidirect
5. C₄₁×#2365	C₂	semidirect
6. C₄₁×#2055	C₂	semidirect
7. C₄₁×#2015	C₂	semidirect
9. C₄₁×#1939	C₂	semidirect
10. C₄₁×#1880	C₂	semidirect
11. C₄×#103×C₄₁	C₂	semidirect
93. #103×C₄₁	D₄	semidirect
229. #25369	C₄₁	direct (N × H)
252. C₄×C₄₁	#464	semidirect
258. C₂×#464	C₂×C₄₁	semidirect
259. C₂×#462	C₂×C₄₁	semidirect
261. #2365	C₂×C₄₁	semidirect
262. #2055	C₂×C₄₁	semidirect
263. #2015	C₂×C₄₁	semidirect
265. #1939	C₂×C₄₁	semidirect
266. #1880	C₂×C₄₁	semidirect
267. C₄×#103	C₂×C₄₁	semidirect
308. C₄₁	#25369	direct (N × H)
358. #103	D₄×C₄₁	semidirect
516. C₄	C₄₁×#464	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#492	2
C₂×C₄₁×#464	2
C₂×C₄₁×#462	2
C₄₁×#2548	2
C₄₁×#2365	2
C₄₁×#2055	2
C₄₁×#2015	2
C₄₁×#1982	2
C₄₁×#1939	2
C₄₁×#1880	2
C₄×#103×C₄₁	2
#25369	41

Subgroups — C41×#25369 #23801570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25369 #23801570