Subgroups — C₄₁×#11159 #23787360

Order 10496.

804 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#421	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#421	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#413	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₁×#344	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1742	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1733	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₁×#338	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
15	C₄₁×#421	—	2	2	no	—
16	C₄₁×#421	—	2	2	no	—
17	C₄₁×#421	—	2	2	no	—
18	C₄₁×#421	—	2	2	no	—
19	C₂×#104×C₄₁	—	2	2	no	—
20	C₂×#104×C₄₁	—	2	2	no	—
21	C₄₁×#413	—	2	2	no	—
22	C₄₁×#413	—	2	2	no	—
23	C₂×#101×C₄₁	C₄	1	2	yes	complemented
24	C₂×#100×C₄₁	C₄	1	2	yes	complemented
25	C₄₁×#344	—	2	2	no	—
26	C₄₁×#343	—	2	2	no	—
27	C₄₁×#339	—	2	2	no	—
28	C₄₁×#338	—	2	2	no	—
29	C₂×#41×C₄₁	—	2	1	no	—
30	C₂×#41×C₄₁	—	2	1	no	—
31	C₂×#41×C₄₁	—	2	1	no	—
32	C₂×#41×C₄₁	—	2	1	no	—
33	C₂×#41×C₄₁	—	2	1	no	—
34	C₂×#41×C₄₁	—	2	1	no	—
35	C₂×#41×C₄₁	—	2	1	no	—
36	C₂×#41×C₄₁	—	2	1	no	—
37	C₂×#41×C₄₁	—	2	1	no	—
38	C₂×#41×C₄₁	—	2	1	no	—
39	C₂×#41×C₄₁	D₄	1	2	yes	—
40	C₂×#41×C₄₁	D₄	1	2	yes	—
41	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
42	C₂²×D₄×C₄₁	—	2	1	no	—
43	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₁	—	2	1	no	—
45	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₄₁	—	2	1	no	—
47	C₂×M₁₆×C₄₁	—	2	1	no	—
48	C₂×M₁₆×C₄₁	—	2	1	no	—
49	C₂×M₁₆×C₄₁	—	2	1	no	—
50	C₂×M₁₆×C₄₁	—	2	1	no	—
51	C₂×M₁₆×C₄₁	—	2	1	no	—
52	C₂×M₁₆×C₄₁	—	2	1	no	—
53	C₂×M₁₆×C₄₁	—	2	1	no	—
54	C₂×M₁₆×C₄₁	—	2	1	no	—
55	C₂×M₁₆×C₄₁	—	2	1	no	—
56	C₂×M₁₆×C₄₁	—	2	1	no	—
57	C₂×M₁₆×C₄₁	—	2	1	no	—
58	C₂×M₁₆×C₄₁	—	2	1	no	—
59	C₂×M₁₆×C₄₁	—	2	1	no	—
60	C₂×M₁₆×C₄₁	—	2	1	no	—
61	C₂×M₁₆×C₄₁	—	2	1	no	—
62	C₂×M₁₆×C₄₁	—	2	1	no	—
63	C₂×M₁₆×C₄₁	—	2	1	no	—
64	C₂×M₁₆×C₄₁	—	2	1	no	—
65	C₂×M₁₆×C₄₁	—	2	1	no	—
66	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	—
67	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	—
68	C₂×M₁₆×C₄₁	D₄	1	2	yes	—
69	C₂×M₁₆×C₄₁	D₄	1	2	yes	—
70	C₂²×C₈×C₄₁	—	2	1	no	—
71	C₂²×C₈×C₄₁	—	2	1	no	—
72	C₂²×C₈×C₄₁	—	2	1	no	—
73	C₂²×C₈×C₄₁	—	2	1	no	—
74	#117×C₄₁	—	2	1	no	—
75	#117×C₄₁	—	2	1	no	—
76	#117×C₄₁	—	2	1	no	—
77	#117×C₄₁	—	2	1	no	—
78	#117×C₄₁	—	2	1	no	—
79	#117×C₄₁	—	2	1	no	—
80	#117×C₄₁	—	2	1	no	—
81	#117×C₄₁	D₄	1	2	yes	—
82	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
83	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
86	C₂×C₄²×C₄₁	—	2	1	no	—
87	C₂×C₄²×C₄₁	D₄	1	2	yes	—
88	#104×C₄₁	—	2	8	no	—
89	#104×C₄₁	—	2	8	no	—
90	#101×C₄₁	—	2	4	no	—
91	#100×C₄₁	—	2	4	no	—
92	C₂⁴×C₄₁	—	2	1	no	—
93	C₂⁴×C₄₁	#41	1	1	yes	characteristic
94	#41×C₄₁	—	2	2	no	—
95	#41×C₄₁	—	2	2	no	—
96	#41×C₄₁	—	2	2	no	—
97	#41×C₄₁	—	2	2	no	—
98	#41×C₄₁	—	2	2	no	—
99	#41×C₄₁	—	2	2	no	—
100	#41×C₄₁	—	2	2	no	—
101	#41×C₄₁	—	2	2	no	—
102	#41×C₄₁	—	4	1	no	—
103	#41×C₄₁	—	4	1	no	—
104	#41×C₄₁	—	4	1	no	—
105	#41×C₄₁	—	4	1	no	—
106	#41×C₄₁	—	4	1	no	—
107	#41×C₄₁	—	4	1	no	—
108	#41×C₄₁	—	4	1	no	—
109	#41×C₄₁	—	4	1	no	—
110	C₂×Q₈×C₄₁	—	2	1	no	—
111	C₂×Q₈×C₄₁	—	2	1	no	—
112	C₂×Q₈×C₄₁	—	2	1	no	—
113	C₂×Q₈×C₄₁	—	2	1	no	—
114	C₂×Q₈×C₄₁	—	2	1	no	—
115	C₂×Q₈×C₄₁	C₂²⋊C₄	1	2	yes	—
116	C₂×D₄×C₄₁	—	2	2	no	—
117	C₂×D₄×C₄₁	—	2	2	no	—
118	C₂×D₄×C₄₁	—	2	1	no	—
119	C₂×D₄×C₄₁	—	2	1	no	—
120	C₂×D₄×C₄₁	—	2	1	no	—
121	C₂×D₄×C₄₁	—	2	1	no	—
122	C₂×D₄×C₄₁	—	2	1	no	—
123	C₂×D₄×C₄₁	—	4	1	no	—
124	C₂×D₄×C₄₁	—	4	1	no	—
125	C₂×D₄×C₄₁	—	4	1	no	—
126	C₂×D₄×C₄₁	—	4	1	no	—
127	C₂×D₄×C₄₁	C₂²⋊C₄	1	2	yes	—
128	C₂²×C₄×C₄₁	—	2	1	no	—
129	C₂²×C₄×C₄₁	—	2	2	no	—
130	C₂²×C₄×C₄₁	—	2	2	no	—
131	C₂²×C₄×C₄₁	—	2	2	no	—
132	C₂²×C₄×C₄₁	—	4	1	no	—
133	C₂²×C₄×C₄₁	—	4	1	no	—
134	C₂²×C₄×C₄₁	—	4	1	no	—
135	C₂²×C₄×C₄₁	—	4	1	no	—
136	C₂²×C₄×C₄₁	—	4	1	no	—
137	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
145	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
146	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
147	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
148	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
149	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
150	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
151	M₁₆×C₄₁	—	2	2	no	—
152	M₁₆×C₄₁	—	2	2	no	—
153	M₁₆×C₄₁	—	2	2	no	—
154	M₁₆×C₄₁	—	2	2	no	—
155	M₁₆×C₄₁	—	2	2	no	—
156	M₁₆×C₄₁	—	2	2	no	—
157	M₁₆×C₄₁	—	2	2	no	—
158	M₁₆×C₄₁	—	2	2	no	—
159	M₁₆×C₄₁	—	4	1	no	—
160	M₁₆×C₄₁	—	4	1	no	—
161	M₁₆×C₄₁	—	4	1	no	—
162	M₁₆×C₄₁	—	4	1	no	—
163	M₁₆×C₄₁	—	4	1	no	—
164	M₁₆×C₄₁	—	4	1	no	—
165	M₁₆×C₄₁	—	4	1	no	—
166	M₁₆×C₄₁	—	4	1	no	—
167	C₂×C₈×C₄₁	—	2	2	no	—
168	C₂×C₈×C₄₁	—	2	2	no	—
169	C₂×C₈×C₄₁	—	2	2	no	—
170	C₂×C₈×C₄₁	—	2	2	no	—
171	C₂×C₈×C₄₁	—	4	1	no	—
172	C₂×C₈×C₄₁	—	4	1	no	—
173	C₂×C₈×C₄₁	—	4	1	no	—
174	C₂×C₈×C₄₁	—	4	1	no	—
175	C₂×C₈×C₄₁	—	4	1	no	—
176	C₂×C₈×C₄₁	—	4	1	no	—
177	C₂×C₈×C₄₁	—	4	1	no	—
178	C₂×C₈×C₄₁	—	4	1	no	—
179	C₄⋊C₄×C₄₁	—	2	2	no	—
180	C₄⋊C₄×C₄₁	—	4	1	no	—
181	C₄⋊C₄×C₄₁	—	4	1	no	—
182	C₄⋊C₄×C₄₁	—	4	1	no	—
183	C₂²⋊C₄×C₄₁	—	2	2	no	—
184	C₂²⋊C₄×C₄₁	—	4	1	no	—
185	C₂²⋊C₄×C₄₁	—	4	1	no	—
186	C₂²⋊C₄×C₄₁	—	4	1	no	—
187	C₄²×C₄₁	—	2	2	no	—
188	C₄²×C₄₁	—	2	2	no	—
189	C₄²×C₄₁	—	2	2	no	—
190	C₄²×C₄₁	—	4	1	no	—
191	C₂³×C₄₁	—	2	2	no	—
192	C₂³×C₄₁	—	4	1	no	—
193	C₂³×C₄₁	—	4	1	no	—
194	C₂³×C₄₁	—	8	1	no	—
195	C₂³×C₄₁	—	8	2	no	—
196	C₂³×C₄₁	#117	1	1	yes	characteristic
197	C₂³×C₄₁	#121	1	1	yes	characteristic
198	C₂³×C₄₁	#123	1	1	yes	characteristic
199	C₂³×C₄₁	#123	1	1	yes	characteristic
200	C₂³×C₄₁	#123	1	1	yes	characteristic
201	C₂³×C₄₁	#124	1	1	yes	characteristic
202	C₂³×C₄₁	#126	1	1	yes	characteristic
203	Q₈×C₄₁	—	2	2	no	—
204	Q₈×C₄₁	—	2	2	no	—
205	Q₈×C₄₁	—	4	1	no	—
206	Q₈×C₄₁	—	4	1	no	—
207	D₄×C₄₁	—	2	2	no	—
208	D₄×C₄₁	—	2	2	no	—
209	D₄×C₄₁	—	4	2	no	—
210	D₄×C₄₁	—	4	2	no	—
211	D₄×C₄₁	—	4	2	no	—
212	D₄×C₄₁	—	4	2	no	—
213	D₄×C₄₁	—	4	1	no	—
214	D₄×C₄₁	—	4	1	no	—
215	C₂×C₄×C₄₁	—	2	2	no	—
216	C₂×C₄×C₄₁	—	4	1	no	—
217	C₂×C₄×C₄₁	—	4	1	no	—
218	C₂×C₄×C₄₁	—	4	2	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	2	no	—
223	C₂×C₄×C₄₁	—	4	2	no	—
224	C₂×C₄×C₄₁	—	8	2	no	—
225	C₂×C₄×C₄₁	—	8	2	no	—
226	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₄₁	#117	1	1	yes	characteristic
228	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
233	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
234	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
235	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
236	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
237	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
238	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
239	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
240	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
241	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
242	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
243	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
244	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
245	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
246	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
247	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
248	C₂×C₄×C₄₁	#124	1	1	yes	characteristic
249	C₂×C₄×C₄₁	#124	1	1	yes	characteristic
250	C₂×C₄×C₄₁	#124	1	1	yes	characteristic
251	C₂×C₄×C₄₁	#126	1	1	yes	characteristic
252	C₂×C₄×C₄₁	#126	1	1	yes	characteristic
253	C₂×C₄×C₄₁	#126	1	1	yes	characteristic
254	C₈×C₄₁	—	4	2	no	—
255	C₈×C₄₁	—	4	2	no	—
256	C₈×C₄₁	—	4	2	no	—
257	C₈×C₄₁	—	4	2	no	—
258	#11159	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
259	C₂²×C₄₁	—	4	1	no	—
260	C₂²×C₄₁	—	4	1	no	—
261	C₂²×C₄₁	—	4	1	no	—
262	C₂²×C₄₁	—	4	1	no	—
263	C₂²×C₄₁	—	4	1	no	—
264	C₂²×C₄₁	—	4	1	no	—
265	C₂²×C₄₁	—	4	1	no	—
266	C₂²×C₄₁	—	4	2	no	—
267	C₂²×C₄₁	—	8	2	no	—
268	C₂²×C₄₁	—	8	2	no	—
269	C₂²×C₄₁	—	8	2	no	—
270	C₂²×C₄₁	#381	1	1	yes	characteristic
271	C₂²×C₄₁	#388	1	1	yes	characteristic
272	C₂²×C₄₁	#388	1	1	yes	characteristic
273	C₂²×C₄₁	#394	1	1	yes	characteristic
274	C₂²×C₄₁	#394	1	1	yes	characteristic
275	C₂²×C₄₁	#397	1	1	yes	characteristic
276	C₂²×C₄₁	#397	1	1	yes	characteristic
277	C₄×C₄₁	—	4	2	no	—
278	C₄×C₄₁	—	8	2	no	—
279	C₄×C₄₁	—	8	2	no	—
280	C₄×C₄₁	#386	1	1	yes	characteristic
281	C₄×C₄₁	#386	1	1	yes	characteristic
282	C₄×C₄₁	#388	1	1	yes	characteristic
283	C₄×C₄₁	#388	1	1	yes	characteristic
284	C₄×C₄₁	#394	1	1	yes	characteristic
285	C₄×C₄₁	#394	1	1	yes	characteristic
286	C₄×C₄₁	#397	1	1	yes	characteristic
287	C₄×C₄₁	#397	1	1	yes	characteristic
288	C₂×#421	C₂×C₄₁	1	1	yes	characteristic
289	C₂×#421	C₂×C₄₁	1	1	yes	characteristic
290	C₂×#413	C₂×C₄₁	1	1	yes	characteristic
291	C₂×#344	C₂×C₄₁	1	1	yes	characteristic, complemented
292	#1742	C₂×C₄₁	1	1	yes	characteristic, complemented
293	#1733	C₂×C₄₁	1	1	yes	characteristic, complemented
294	C₂×#338	C₂×C₄₁	1	1	yes	characteristic, complemented
295	C₂×C₄₁	—	2	1	no	—
296	C₂×C₄₁	—	2	1	no	—
297	C₂×C₄₁	—	2	1	no	—
298	C₂×C₄₁	—	2	1	no	—
299	C₂×C₄₁	—	2	1	no	—
300	C₂×C₄₁	—	2	1	no	—
301	C₂×C₄₁	—	2	1	no	—
302	C₂×C₄₁	—	8	2	no	—
303	C₂×C₄₁	#1440	1	1	yes	characteristic
304	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
305	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
306	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
307	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
308	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
309	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
310	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
311	#421	—	2	2	no	—
312	#421	—	2	2	no	—
313	#421	—	2	2	no	—
314	#421	—	2	2	no	—
315	C₂×#104	—	2	2	no	—
316	C₂×#104	—	2	2	no	—
317	#413	—	2	2	no	—
318	#413	—	2	2	no	—
319	C₂×#101	C₄×C₄₁	1	2	yes	complemented
320	C₂×#100	C₄×C₄₁	1	2	yes	complemented
321	#344	—	2	2	no	—
322	#343	—	2	2	no	—
323	#339	—	2	2	no	—
324	#338	—	2	2	no	—
325	C₄₁	#11159	1	1	yes	characteristic, direct product factor, Sylow
326	C₂×#41	—	2	1	no	—
327	C₂×#41	—	2	1	no	—
328	C₂×#41	—	2	1	no	—
329	C₂×#41	—	2	1	no	—
330	C₂×#41	—	2	1	no	—
331	C₂×#41	—	2	1	no	—
332	C₂×#41	—	2	1	no	—
333	C₂×#41	—	2	1	no	—
334	C₂×#41	—	2	1	no	—
335	C₂×#41	—	2	1	no	—
336	C₂×#41	D₄×C₄₁	1	2	yes	—
337	C₂×#41	D₄×C₄₁	1	2	yes	—
338	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
339	C₂²×D₄	—	2	1	no	—
340	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
341	C₂³×C₄	—	2	1	no	—
342	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
343	C₂×M₁₆	—	2	1	no	—
344	C₂×M₁₆	—	2	1	no	—
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	—	2	1	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	—
364	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	—
365	C₂×M₁₆	D₄×C₄₁	1	2	yes	—
366	C₂×M₁₆	D₄×C₄₁	1	2	yes	—
367	C₂²×C₈	—	2	1	no	—
368	C₂²×C₈	—	2	1	no	—
369	C₂²×C₈	—	2	1	no	—
370	C₂²×C₈	—	2	1	no	—
371	#117	—	2	1	no	—
372	#117	—	2	1	no	—
373	#117	—	2	1	no	—
374	#117	—	2	1	no	—
375	#117	—	2	1	no	—
376	#117	—	2	1	no	—
377	#117	—	2	1	no	—
378	#117	D₄×C₄₁	1	2	yes	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	D₄×C₄₁	1	2	yes	—
385	#104	—	2	8	no	—
386	#104	—	2	8	no	—
387	#101	—	2	4	no	—
388	#100	—	2	4	no	—
389	C₂⁴	—	2	1	no	—
390	C₂⁴	#41×C₄₁	1	1	yes	characteristic
391	#41	—	2	2	no	—
392	#41	—	2	2	no	—
393	#41	—	2	2	no	—
394	#41	—	2	2	no	—
395	#41	—	2	2	no	—
396	#41	—	2	2	no	—
397	#41	—	2	2	no	—
398	#41	—	2	2	no	—
399	#41	—	4	1	no	—
400	#41	—	4	1	no	—
401	#41	—	4	1	no	—
402	#41	—	4	1	no	—
403	#41	—	4	1	no	—
404	#41	—	4	1	no	—
405	#41	—	4	1	no	—
406	#41	—	4	1	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	—	2	1	no	—
410	C₂×Q₈	—	2	1	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	C₂²⋊C₄×C₄₁	1	2	yes	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	4	1	no	—
421	C₂×D₄	—	4	1	no	—
422	C₂×D₄	—	4	1	no	—
423	C₂×D₄	—	4	1	no	—
424	C₂×D₄	C₂²⋊C₄×C₄₁	1	2	yes	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	4	1	no	—
430	C₂²×C₄	—	4	1	no	—
431	C₂²×C₄	—	4	1	no	—
432	C₂²×C₄	—	4	1	no	—
433	C₂²×C₄	—	4	1	no	—
434	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
441	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
442	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
443	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
444	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
445	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
446	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
447	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
448	M₁₆	—	2	2	no	—
449	M₁₆	—	2	2	no	—
450	M₁₆	—	2	2	no	—
451	M₁₆	—	2	2	no	—
452	M₁₆	—	2	2	no	—
453	M₁₆	—	2	2	no	—
454	M₁₆	—	2	2	no	—
455	M₁₆	—	2	2	no	—
456	M₁₆	—	4	1	no	—
457	M₁₆	—	4	1	no	—
458	M₁₆	—	4	1	no	—
459	M₁₆	—	4	1	no	—
460	M₁₆	—	4	1	no	—
461	M₁₆	—	4	1	no	—
462	M₁₆	—	4	1	no	—
463	M₁₆	—	4	1	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	2	no	—
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	4	1	no	—
469	C₂×C₈	—	4	1	no	—
470	C₂×C₈	—	4	1	no	—
471	C₂×C₈	—	4	1	no	—
472	C₂×C₈	—	4	1	no	—
473	C₂×C₈	—	4	1	no	—
474	C₂×C₈	—	4	1	no	—
475	C₂×C₈	—	4	1	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	—	4	1	no	—
479	C₄⋊C₄	—	4	1	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	4	1	no	—
483	C₂²⋊C₄	—	4	1	no	—
484	C₄²	—	2	2	no	—
485	C₄²	—	2	2	no	—
486	C₄²	—	2	2	no	—
487	C₄²	—	4	1	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	4	1	no	—
490	C₂³	—	4	1	no	—
491	C₂³	—	8	1	no	—
492	C₂³	—	8	2	no	—
493	C₂³	#117×C₄₁	1	1	yes	characteristic
494	C₂³	#121×C₄₁	1	1	yes	characteristic
495	C₂³	#123×C₄₁	1	1	yes	characteristic
496	C₂³	#123×C₄₁	1	1	yes	characteristic
497	C₂³	#123×C₄₁	1	1	yes	characteristic
498	C₂³	#124×C₄₁	1	1	yes	characteristic
499	C₂³	#126×C₄₁	1	1	yes	characteristic
500	Q₈	—	2	2	no	—
501	Q₈	—	2	2	no	—
502	Q₈	—	4	1	no	—
503	Q₈	—	4	1	no	—
504	D₄	—	2	2	no	—
505	D₄	—	2	2	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	2	no	—
508	D₄	—	4	2	no	—
509	D₄	—	4	2	no	—
510	D₄	—	4	1	no	—
511	D₄	—	4	1	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	8	2	no	—
522	C₂×C₄	—	8	2	no	—
523	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
524	C₂×C₄	#117×C₄₁	1	1	yes	characteristic
525	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
526	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
527	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
528	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
529	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
530	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
531	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
532	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
533	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
534	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
535	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
536	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
537	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
538	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
539	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
540	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
541	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
542	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
543	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
544	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
545	C₂×C₄	#124×C₄₁	1	1	yes	characteristic
546	C₂×C₄	#124×C₄₁	1	1	yes	characteristic
547	C₂×C₄	#124×C₄₁	1	1	yes	characteristic
548	C₂×C₄	#126×C₄₁	1	1	yes	characteristic
549	C₂×C₄	#126×C₄₁	1	1	yes	characteristic
550	C₂×C₄	#126×C₄₁	1	1	yes	characteristic
551	C₈	—	4	2	no	—
552	C₈	—	4	2	no	—
553	C₈	—	4	2	no	—
554	C₈	—	4	2	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	8	2	no	—
564	C₂²	—	8	2	no	—
565	C₂²	—	8	2	no	—
566	C₂²	C₄₁×#381	1	1	yes	characteristic
567	C₂²	C₄₁×#388	1	1	yes	characteristic
568	C₂²	C₄₁×#388	1	1	yes	characteristic
569	C₂²	C₄₁×#394	1	1	yes	characteristic
570	C₂²	C₄₁×#394	1	1	yes	characteristic
571	C₂²	C₄₁×#397	1	1	yes	characteristic
572	C₂²	C₄₁×#397	1	1	yes	characteristic
573	C₄	—	4	2	no	—
574	C₄	—	8	2	no	—
575	C₄	—	8	2	no	—
576	C₄	C₄₁×#386	1	1	yes	characteristic
577	C₄	C₄₁×#386	1	1	yes	characteristic
578	C₄	C₄₁×#388	1	1	yes	characteristic
579	C₄	C₄₁×#388	1	1	yes	characteristic
580	C₄	C₄₁×#394	1	1	yes	characteristic
581	C₄	C₄₁×#394	1	1	yes	characteristic
582	C₄	C₄₁×#397	1	1	yes	characteristic
583	C₄	C₄₁×#397	1	1	yes	characteristic
584	C₂	—	2	1	no	—
585	C₂	—	2	1	no	—
586	C₂	—	2	1	no	—
587	C₂	—	2	1	no	—
588	C₂	—	2	1	no	—
589	C₂	—	2	1	no	—
590	C₂	—	2	1	no	—
591	C₂	—	8	2	no	—
592	C₂	C₄₁×#1440	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₄₁	#397
commutator	C₂²×C₄	C₂²×C₄×C₄₁
Frattini, cosocle	C₂³×C₄	C₂³×C₄₁
socle	C₂×C₄₁	#1440
prime radical	C₂²×#41×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₄₁×#344	C₂	semidirect
5. C₄₁×#1742	C₂	semidirect
6. C₄₁×#1733	C₂	semidirect
7. C₂×C₄₁×#338	C₂	semidirect
23. C₂×#101×C₄₁	C₄	semidirect
24. C₂×#100×C₄₁	C₄	semidirect
258. #11159	C₄₁	direct (N × H)
291. C₂×#344	C₂×C₄₁	semidirect
292. #1742	C₂×C₄₁	semidirect
293. #1733	C₂×C₄₁	semidirect
294. C₂×#338	C₂×C₄₁	semidirect
319. C₂×#101	C₄×C₄₁	semidirect
320. C₂×#100	C₄×C₄₁	semidirect
325. C₄₁	#11159	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#421	2
C₂×C₄₁×#413	2
C₂×C₄₁×#344	2
C₄₁×#1742	2
C₄₁×#1733	2
C₂×C₄₁×#338	2
#11159	41

Subgroups — C41×#11159 #23787360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#11159 #23787360