Subgroups — C₄₁×#25406 #23801607

Order 10496.

884 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3152	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#473	C₂	1	2	yes	maximal, complemented
3	C₄₁×#3037	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₁×#462	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2935	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#2052	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2020	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1966	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1950	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1908	C₂	1	2	yes	maximal, complemented
11	C₄×#101×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₄₁	C₂²	1	2	yes	—
13	C₂×#137×C₄₁	C₂²	1	2	yes	—
14	C₂×#137×C₄₁	C₂²	1	2	yes	—
15	C₂²×Q₁₆×C₄₁	C₂²	1	2	yes	—
16	C₂×#131×C₄₁	C₂²	1	2	yes	—
17	C₄₁×#532	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
20	C₄₁×#497	—	2	2	no	—
21	C₄₁×#494	—	2	1	no	—
22	C₄₁×#492	—	2	1	no	—
23	C₄₁×#473	—	2	8	no	—
24	C₄₁×#464	—	2	2	no	—
25	C₄₁×#462	—	2	1	no	—
26	C₄₁×#462	—	2	1	no	—
27	C₄₁×#462	—	2	2	no	—
28	C₄₁×#462	—	2	1	no	—
29	C₄₁×#460	—	2	1	no	—
30	C₄₁×#436	—	2	1	no	—
31	C₄₁×#435	—	2	2	no	—
32	C₈×D₄×C₄₁	—	2	1	no	—
33	C₂×#108×C₄₁	C₂²	1	2	yes	—
34	C₄₁×#423	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
36	C₄₁×#417	C₂²	1	2	yes	—
37	C₂×#103×C₄₁	C₂²	1	2	yes	—
38	C₂×#101×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×#101×C₄₁	C₂²	1	2	yes	—
40	C₂×#101×C₄₁	C₂²	1	2	yes	—
41	C₂×#101×C₄₁	C₂²	1	1	yes	characteristic
42	C₄₁×#408	C₂²	1	2	yes	—
43	C₄×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
45	C₄₁×#343	C₂²	1	1	yes	characteristic
46	C₄₁×#343	C₂²	1	1	yes	characteristic
47	C₄₁×#341	C₂²	1	2	yes	—
48	C₂×#41×C₄₁	C₂³	1	2	yes	—
49	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
50	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
51	#137×C₄₁	—	2	4	no	—
52	#137×C₄₁	—	2	4	no	—
53	#137×C₄₁	—	2	4	no	—
54	#137×C₄₁	—	4	2	no	—
55	#137×C₄₁	—	4	2	no	—
56	#137×C₄₁	—	4	2	no	—
57	C₂×Q₁₆×C₄₁	—	2	4	no	—
58	C₂×Q₁₆×C₄₁	—	2	2	no	—
59	C₂×Q₁₆×C₄₁	—	2	2	no	—
60	C₂×Q₁₆×C₄₁	—	2	2	no	—
61	C₂×Q₁₆×C₄₁	—	2	2	no	—
62	C₂×Q₁₆×C₄₁	—	2	2	no	—
63	C₂×Q₁₆×C₄₁	—	4	2	no	—
64	C₂×SD₁₆×C₄₁	—	2	2	no	—
65	C₂×SD₁₆×C₄₁	—	2	2	no	—
66	C₂×SD₁₆×C₄₁	—	2	2	no	—
67	#131×C₄₁	—	2	4	no	—
68	#131×C₄₁	—	4	2	no	—
69	C₂×M₁₆×C₄₁	—	2	2	no	—
70	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
71	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
72	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
73	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
74	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₄₁	—	2	2	no	—
76	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
77	C₄⋊Q₈×C₄₁	—	2	1	no	—
78	C₄⋊Q₈×C₄₁	—	2	1	no	—
79	C₄⋊Q₈×C₄₁	—	2	1	no	—
80	C₄⋊Q₈×C₄₁	—	2	1	no	—
81	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
82	#127×C₄₁	D₄	1	1	yes	characteristic
83	#124×C₄₁	D₄	1	2	yes	—
84	#121×C₄₁	—	2	1	no	—
85	#121×C₄₁	—	2	1	no	—
86	C₄×Q₈×C₄₁	—	2	1	no	—
87	C₄×Q₈×C₄₁	—	2	1	no	—
88	C₄×Q₈×C₄₁	—	2	1	no	—
89	C₄×Q₈×C₄₁	—	2	1	no	—
90	C₄×D₄×C₄₁	—	2	1	no	—
91	C₄×D₄×C₄₁	—	2	1	no	—
92	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
93	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
94	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
95	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₄₁	—	2	1	no	—
97	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
98	#108×C₄₁	—	2	4	no	—
99	C₄⋊C₈×C₄₁	—	2	1	no	—
100	C₄⋊C₈×C₄₁	—	2	1	no	—
101	C₄⋊C₈×C₄₁	D₄	1	1	yes	characteristic
102	C₄⋊C₈×C₄₁	D₄	1	2	yes	—
103	C₄⋊C₈×C₄₁	D₄	1	1	yes	characteristic
104	#103×C₄₁	—	2	2	no	—
105	#103×C₄₁	—	2	2	no	—
106	#103×C₄₁	—	2	2	no	—
107	#102×C₄₁	—	2	2	no	—
108	#101×C₄₁	—	2	4	no	—
109	#101×C₄₁	—	2	2	no	—
110	#101×C₄₁	—	4	2	no	—
111	#101×C₄₁	D₄	1	4	yes	complemented
112	C₂²⋊C₈×C₄₁	—	2	2	no	—
113	C₂²⋊C₈×C₄₁	—	2	2	no	—
114	#97×C₄₁	—	2	1	no	—
115	#97×C₄₁	—	2	1	no	—
116	C₄×C₈×C₄₁	—	2	1	no	—
117	C₄×C₈×C₄₁	—	2	1	no	—
118	#41×C₄₁	—	2	2	no	—
119	#41×C₄₁	—	2	2	no	—
120	#41×C₄₁	—	2	2	no	—
121	#41×C₄₁	—	2	2	no	—
122	C₂×Q₈×C₄₁	—	2	1	no	—
123	C₂×Q₈×C₄₁	—	2	1	no	—
124	C₂×Q₈×C₄₁	—	2	1	no	—
125	C₂×Q₈×C₄₁	—	2	2	no	—
126	C₂×Q₈×C₄₁	—	2	2	no	—
127	C₂×Q₈×C₄₁	—	2	2	no	—
128	C₂×Q₈×C₄₁	—	2	2	no	—
129	C₂×Q₈×C₄₁	—	2	1	no	—
130	C₂×Q₈×C₄₁	—	2	1	no	—
131	C₂×Q₈×C₄₁	—	2	2	no	—
132	C₂×Q₈×C₄₁	—	2	2	no	—
133	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
134	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
135	C₂×D₄×C₄₁	—	2	2	no	—
136	C₂×D₄×C₄₁	—	2	1	no	—
137	C₂×D₄×C₄₁	—	2	1	no	—
138	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₄₁	—	2	1	no	—
140	C₂²×C₄×C₄₁	—	2	2	no	—
141	C₂²×C₄×C₄₁	—	2	2	no	—
142	C₂²×C₄×C₄₁	—	2	1	no	—
143	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
144	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
145	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
146	Q₁₆×C₄₁	—	4	4	no	—
147	Q₁₆×C₄₁	—	4	4	no	—
148	Q₁₆×C₄₁	—	4	4	no	—
149	Q₁₆×C₄₁	—	4	4	no	—
150	Q₁₆×C₄₁	—	4	4	no	—
151	SD₁₆×C₄₁	—	4	4	no	—
152	SD₁₆×C₄₁	—	4	4	no	—
153	SD₁₆×C₄₁	—	4	4	no	—
154	M₁₆×C₄₁	—	2	1	no	—
155	M₁₆×C₄₁	—	2	1	no	—
156	M₁₆×C₄₁	—	2	1	no	—
157	M₁₆×C₄₁	—	2	2	no	—
158	M₁₆×C₄₁	—	2	1	no	—
159	M₁₆×C₄₁	—	2	1	no	—
160	M₁₆×C₄₁	—	2	2	no	—
161	M₁₆×C₄₁	—	4	4	no	—
162	M₁₆×C₄₁	C₂×D₄	1	2	yes	—
163	M₁₆×C₄₁	C₂×D₄	1	2	yes	—
164	M₁₆×C₄₁	#41	1	2	yes	—
165	C₂×C₈×C₄₁	—	2	1	no	—
166	C₂×C₈×C₄₁	—	2	1	no	—
167	C₂×C₈×C₄₁	—	2	1	no	—
168	C₂×C₈×C₄₁	—	2	2	no	—
169	C₂×C₈×C₄₁	—	2	2	no	—
170	C₂×C₈×C₄₁	—	2	1	no	—
171	C₂×C₈×C₄₁	—	2	2	no	—
172	C₂×C₈×C₄₁	—	4	4	no	—
173	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
174	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
175	C₄⋊C₄×C₄₁	—	2	1	no	—
176	C₄⋊C₄×C₄₁	—	2	1	no	—
177	C₄⋊C₄×C₄₁	—	2	1	no	—
178	C₄⋊C₄×C₄₁	—	2	1	no	—
179	C₄⋊C₄×C₄₁	—	4	1	no	—
180	C₄⋊C₄×C₄₁	—	4	1	no	—
181	C₄⋊C₄×C₄₁	—	4	1	no	—
182	C₄⋊C₄×C₄₁	—	4	1	no	—
183	C₄⋊C₄×C₄₁	—	4	1	no	—
184	C₄⋊C₄×C₄₁	—	4	1	no	—
185	C₂²⋊C₄×C₄₁	—	2	2	no	—
186	C₂²⋊C₄×C₄₁	—	2	2	no	—
187	C₄²×C₄₁	—	4	1	no	—
188	C₄²×C₄₁	—	4	1	no	—
189	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
193	C₂³×C₄₁	—	2	2	no	—
194	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
195	Q₈×C₄₁	—	2	2	no	—
196	Q₈×C₄₁	—	2	2	no	—
197	Q₈×C₄₁	—	2	2	no	—
198	Q₈×C₄₁	—	2	2	no	—
199	Q₈×C₄₁	—	4	1	no	—
200	Q₈×C₄₁	—	4	1	no	—
201	Q₈×C₄₁	—	4	2	no	—
202	Q₈×C₄₁	—	4	2	no	—
203	Q₈×C₄₁	—	4	2	no	—
204	Q₈×C₄₁	—	4	2	no	—
205	D₄×C₄₁	—	2	2	no	—
206	D₄×C₄₁	—	2	2	no	—
207	D₄×C₄₁	—	4	2	no	—
208	D₄×C₄₁	—	4	2	no	—
209	D₄×C₄₁	—	4	2	no	—
210	D₄×C₄₁	—	8	1	no	—
211	C₂×C₄×C₄₁	—	2	2	no	—
212	C₂×C₄×C₄₁	—	2	2	no	—
213	C₂×C₄×C₄₁	—	2	2	no	—
214	C₂×C₄×C₄₁	—	4	1	no	—
215	C₂×C₄×C₄₁	—	4	1	no	—
216	C₂×C₄×C₄₁	—	4	1	no	—
217	C₂×C₄×C₄₁	—	4	2	no	—
218	C₂×C₄×C₄₁	—	4	2	no	—
219	C₂×C₄×C₄₁	—	4	1	no	—
220	C₂×C₄×C₄₁	—	4	2	no	—
221	C₂×C₄×C₄₁	—	4	2	no	—
222	C₂×C₄×C₄₁	—	4	2	no	—
223	C₂×C₄×C₄₁	—	8	1	no	—
224	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
225	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
226	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
227	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
228	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
234	C₈×C₄₁	—	2	2	no	—
235	C₈×C₄₁	—	2	2	no	—
236	C₈×C₄₁	—	2	2	no	—
237	C₈×C₄₁	—	2	2	no	—
238	C₈×C₄₁	—	2	2	no	—
239	C₈×C₄₁	—	4	2	no	—
240	C₈×C₄₁	—	4	1	no	—
241	#25406	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
242	C₂²×C₄₁	—	2	1	no	—
243	C₂²×C₄₁	—	2	1	no	—
244	C₂²×C₄₁	—	4	2	no	—
245	C₂²×C₄₁	—	4	2	no	—
246	C₂²×C₄₁	—	4	2	no	—
247	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
248	C₂²×C₄₁	#532	1	1	yes	characteristic
249	C₂²×C₄₁	#540	1	1	yes	characteristic
250	C₄×C₄₁	—	2	1	no	—
251	C₄×C₄₁	—	2	1	no	—
252	C₄×C₄₁	—	2	1	no	—
253	C₄×C₄₁	—	4	2	no	—
254	C₄×C₄₁	—	4	2	no	—
255	C₄×C₄₁	—	8	2	no	—
256	C₄×C₄₁	—	8	1	no	—
257	C₄×C₄₁	#473	1	2	yes	complemented
258	C₄×C₄₁	D₄²	1	1	yes	characteristic
259	C₄×C₄₁	D₄²	1	1	yes	characteristic
260	C₄×C₄₁	#546	1	1	yes	characteristic
261	C₄×C₄₁	#550	1	1	yes	characteristic
262	#3152	C₂×C₄₁	1	1	yes	characteristic
263	C₂×#473	C₂×C₄₁	1	2	yes	complemented
264	#3037	C₂×C₄₁	1	1	yes	characteristic
265	C₂×#462	C₂×C₄₁	1	1	yes	characteristic, complemented
266	#2935	C₂×C₄₁	1	1	yes	characteristic
267	#2052	C₂×C₄₁	1	2	yes	complemented
268	#2020	C₂×C₄₁	1	2	yes	complemented
269	#1966	C₂×C₄₁	1	1	yes	characteristic, complemented
270	#1950	C₂×C₄₁	1	1	yes	characteristic, complemented
271	#1908	C₂×C₄₁	1	2	yes	complemented
272	C₄×#101	C₂×C₄₁	1	1	yes	characteristic, complemented
273	C₂×C₄₁	—	2	1	no	—
274	C₂×C₄₁	—	2	1	no	—
275	C₂×C₄₁	—	8	2	no	—
276	C₂×C₄₁	#2428	1	1	yes	characteristic
277	C₂×C₄₁	C₂×#473	1	1	yes	characteristic
278	C₂×C₄₁	#3069	1	1	yes	characteristic
279	C₂×#137	C₂²×C₄₁	1	2	yes	—
280	C₂×#137	C₂²×C₄₁	1	2	yes	—
281	C₂×#137	C₂²×C₄₁	1	2	yes	—
282	C₂²×Q₁₆	C₂²×C₄₁	1	2	yes	—
283	C₂×#131	C₂²×C₄₁	1	2	yes	—
284	#532	C₂²×C₄₁	1	1	yes	characteristic
285	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
286	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
287	#497	—	2	2	no	—
288	#494	—	2	1	no	—
289	#492	—	2	1	no	—
290	#473	—	2	8	no	—
291	#464	—	2	2	no	—
292	#462	—	2	1	no	—
293	#462	—	2	1	no	—
294	#462	—	2	2	no	—
295	#462	—	2	1	no	—
296	#460	—	2	1	no	—
297	#436	—	2	1	no	—
298	#435	—	2	2	no	—
299	C₈×D₄	—	2	1	no	—
300	C₂×#108	C₂²×C₄₁	1	2	yes	—
301	#423	C₂²×C₄₁	1	1	yes	characteristic
302	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
303	#417	C₂²×C₄₁	1	2	yes	—
304	C₂×#103	C₂²×C₄₁	1	2	yes	—
305	C₂×#101	C₂²×C₄₁	1	2	yes	—
306	C₂×#101	C₂²×C₄₁	1	1	yes	characteristic
307	C₂×#101	C₂²×C₄₁	1	2	yes	—
308	C₂×#101	C₂²×C₄₁	1	1	yes	characteristic
309	#408	C₂²×C₄₁	1	2	yes	—
310	C₄×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
311	C₄×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
312	#343	C₂²×C₄₁	1	1	yes	characteristic
313	#343	C₂²×C₄₁	1	1	yes	characteristic
314	#341	C₂²×C₄₁	1	2	yes	—
315	C₄₁	#25406	1	1	yes	characteristic, direct product factor, Sylow
316	C₂×#41	C₂³×C₄₁	1	2	yes	—
317	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
318	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
319	#137	—	2	4	no	—
320	#137	—	2	4	no	—
321	#137	—	2	4	no	—
322	#137	—	4	2	no	—
323	#137	—	4	2	no	—
324	#137	—	4	2	no	—
325	C₂×Q₁₆	—	2	4	no	—
326	C₂×Q₁₆	—	2	2	no	—
327	C₂×Q₁₆	—	2	2	no	—
328	C₂×Q₁₆	—	2	2	no	—
329	C₂×Q₁₆	—	2	2	no	—
330	C₂×Q₁₆	—	2	2	no	—
331	C₂×Q₁₆	—	4	2	no	—
332	C₂×SD₁₆	—	2	2	no	—
333	C₂×SD₁₆	—	2	2	no	—
334	C₂×SD₁₆	—	2	2	no	—
335	#131	—	2	4	no	—
336	#131	—	4	2	no	—
337	C₂×M₁₆	—	2	2	no	—
338	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
339	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
340	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
341	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
342	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
343	C₂²×C₈	—	2	2	no	—
344	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
345	C₄⋊Q₈	—	2	1	no	—
346	C₄⋊Q₈	—	2	1	no	—
347	C₄⋊Q₈	—	2	1	no	—
348	C₄⋊Q₈	—	2	1	no	—
349	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
350	#127	D₄×C₄₁	1	1	yes	characteristic
351	#124	D₄×C₄₁	1	2	yes	—
352	#121	—	2	1	no	—
353	#121	—	2	1	no	—
354	C₄×Q₈	—	2	1	no	—
355	C₄×Q₈	—	2	1	no	—
356	C₄×Q₈	—	2	1	no	—
357	C₄×Q₈	—	2	1	no	—
358	C₄×D₄	—	2	1	no	—
359	C₄×D₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
366	#108	—	2	4	no	—
367	C₄⋊C₈	—	2	1	no	—
368	C₄⋊C₈	—	2	1	no	—
369	C₄⋊C₈	D₄×C₄₁	1	1	yes	characteristic
370	C₄⋊C₈	D₄×C₄₁	1	2	yes	—
371	C₄⋊C₈	D₄×C₄₁	1	1	yes	characteristic
372	#103	—	2	2	no	—
373	#103	—	2	2	no	—
374	#103	—	2	2	no	—
375	#102	—	2	2	no	—
376	#101	—	2	4	no	—
377	#101	—	2	2	no	—
378	#101	—	4	2	no	—
379	#101	D₄×C₄₁	1	4	yes	complemented
380	C₂²⋊C₈	—	2	2	no	—
381	C₂²⋊C₈	—	2	2	no	—
382	#97	—	2	1	no	—
383	#97	—	2	1	no	—
384	C₄×C₈	—	2	1	no	—
385	C₄×C₈	—	2	1	no	—
386	#41	—	2	2	no	—
387	#41	—	2	2	no	—
388	#41	—	2	2	no	—
389	#41	—	2	2	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
402	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
412	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
413	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
414	Q₁₆	—	4	4	no	—
415	Q₁₆	—	4	4	no	—
416	Q₁₆	—	4	4	no	—
417	Q₁₆	—	4	4	no	—
418	Q₁₆	—	4	4	no	—
419	SD₁₆	—	4	4	no	—
420	SD₁₆	—	4	4	no	—
421	SD₁₆	—	4	4	no	—
422	M₁₆	—	2	1	no	—
423	M₁₆	—	2	1	no	—
424	M₁₆	—	2	1	no	—
425	M₁₆	—	2	2	no	—
426	M₁₆	—	2	1	no	—
427	M₁₆	—	2	1	no	—
428	M₁₆	—	2	2	no	—
429	M₁₆	—	4	4	no	—
430	M₁₆	C₂×D₄×C₄₁	1	2	yes	—
431	M₁₆	C₂×D₄×C₄₁	1	2	yes	—
432	M₁₆	#41×C₄₁	1	2	yes	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	4	4	no	—
441	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
442	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	4	1	no	—
448	C₄⋊C₄	—	4	1	no	—
449	C₄⋊C₄	—	4	1	no	—
450	C₄⋊C₄	—	4	1	no	—
451	C₄⋊C₄	—	4	1	no	—
452	C₄⋊C₄	—	4	1	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₄²	—	4	1	no	—
456	C₄²	—	4	1	no	—
457	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
458	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
459	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
460	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
461	C₂³	—	2	2	no	—
462	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
463	Q₈	—	2	2	no	—
464	Q₈	—	2	2	no	—
465	Q₈	—	2	2	no	—
466	Q₈	—	2	2	no	—
467	Q₈	—	4	1	no	—
468	Q₈	—	4	1	no	—
469	Q₈	—	4	2	no	—
470	Q₈	—	4	2	no	—
471	Q₈	—	4	2	no	—
472	Q₈	—	4	2	no	—
473	D₄	—	2	2	no	—
474	D₄	—	2	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	D₄	—	8	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	8	1	no	—
492	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
493	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
494	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
495	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
496	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
498	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
499	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
500	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
501	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
502	C₈	—	2	2	no	—
503	C₈	—	2	2	no	—
504	C₈	—	2	2	no	—
505	C₈	—	2	2	no	—
506	C₈	—	2	2	no	—
507	C₈	—	4	2	no	—
508	C₈	—	4	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	2	no	—
514	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
515	C₂²	C₄₁×#532	1	1	yes	characteristic
516	C₂²	C₄₁×#540	1	1	yes	characteristic
517	C₄	—	2	1	no	—
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	2	no	—
522	C₄	—	8	1	no	—
523	C₄	—	8	2	no	—
524	C₄	C₄₁×#473	1	2	yes	complemented
525	C₄	D₄²×C₄₁	1	1	yes	characteristic
526	C₄	D₄²×C₄₁	1	1	yes	characteristic
527	C₄	C₄₁×#546	1	1	yes	characteristic
528	C₄	C₄₁×#550	1	1	yes	characteristic
529	C₂	—	2	1	no	—
530	C₂	—	2	1	no	—
531	C₂	—	8	2	no	—
532	C₂	C₄₁×#2428	1	1	yes	characteristic
533	C₂	C₂×C₄₁×#473	1	1	yes	characteristic
534	C₂	C₄₁×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₄₁×#532	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#473	C₂	semidirect
4. C₂×C₄₁×#462	C₂	semidirect
6. C₄₁×#2052	C₂	semidirect
7. C₄₁×#2020	C₂	semidirect
8. C₄₁×#1966	C₂	semidirect
9. C₄₁×#1950	C₂	semidirect
10. C₄₁×#1908	C₂	semidirect
11. C₄×#101×C₄₁	C₂	semidirect
111. #101×C₄₁	D₄	semidirect
241. #25406	C₄₁	direct (N × H)
257. C₄×C₄₁	#473	semidirect
263. C₂×#473	C₂×C₄₁	semidirect
265. C₂×#462	C₂×C₄₁	semidirect
267. #2052	C₂×C₄₁	semidirect
268. #2020	C₂×C₄₁	semidirect
269. #1966	C₂×C₄₁	semidirect
270. #1950	C₂×C₄₁	semidirect
271. #1908	C₂×C₄₁	semidirect
272. C₄×#101	C₂×C₄₁	semidirect
315. C₄₁	#25406	direct (N × H)
379. #101	D₄×C₄₁	semidirect
524. C₄	C₄₁×#473	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3152	2
C₂×C₄₁×#473	2
C₄₁×#3037	2
C₂×C₄₁×#462	2
C₄₁×#2935	2
C₄₁×#2052	2
C₄₁×#2020	2
C₄₁×#1966	2
C₄₁×#1950	2
C₄₁×#1908	2
C₄×#101×C₄₁	2
#25406	41

Subgroups — C41×#25406 #23801607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25406 #23801607