Subgroups — C₄₁×#8409 #23784610

Order 10496.

972 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3449	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#1798	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#1540	C₂	1	2	yes	maximal, complemented
4	C₄₁×#1480	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1458	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#41×C₄₁	—	2	1	no	—
7	C₄₁×#537	—	2	1	no	—
8	C₄₁×#537	C₄	1	2	yes	—
9	C₄₁×#536	—	2	2	no	—
10	C₄₁×#535	—	2	2	no	—
11	C₄₁×#534	—	2	1	no	—
12	C₄₁×#534	C₄	1	2	yes	—
13	C₄₁×#532	—	2	1	no	—
14	C₄₁×#532	C₂²	1	2	yes	—
15	C₄₁×#525	—	2	4	no	—
16	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
17	C₄₁×#431	C₂²	1	2	yes	complemented
18	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₂²⋊C₈×C₄₁	—	2	1	no	—
21	C₄₁×#336	—	2	1	no	—
22	C₄₁×#332	—	2	2	no	—
23	C₄₁×#331	—	2	2	no	—
24	C₄₁×D₄⋊C₈	—	2	4	no	—
25	C₄₁×#324	—	2	1	no	—
26	C₄₁×#323	—	2	1	no	—
27	C₂×#41×C₄₁	—	2	2	no	—
28	C₂×#41×C₄₁	—	2	2	no	—
29	C₂×#41×C₄₁	—	2	2	no	—
30	C₂×#41×C₄₁	—	2	2	no	—
31	C₂×#41×C₄₁	—	4	2	no	—
32	C₂×#41×C₄₁	—	4	2	no	—
33	C₂×#41×C₄₁	—	4	2	no	—
34	C₂×#41×C₄₁	—	4	2	no	—
35	C₂²×Q₈×C₄₁	—	2	1	no	—
36	C₂²×D₄×C₄₁	—	2	1	no	—
37	C₂²×D₄×C₄₁	—	2	2	no	—
38	C₂³×C₄×C₄₁	—	2	2	no	—
39	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
40	C₂²×C₈×C₄₁	—	2	1	no	—
41	C₂²×C₈×C₄₁	—	2	1	no	—
42	C₄⋊Q₈×C₄₁	—	2	1	no	—
43	C₄⋊Q₈×C₄₁	D₄	1	2	yes	—
44	#127×C₄₁	—	2	1	no	—
45	#127×C₄₁	D₄	1	2	yes	—
46	#124×C₄₁	—	2	2	no	—
47	#124×C₄₁	—	2	2	no	—
48	#123×C₄₁	—	2	4	no	—
49	#123×C₄₁	—	2	4	no	—
50	C₂²⋊Q₈×C₄₁	—	2	4	no	—
51	C₂²⋊Q₈×C₄₁	—	2	4	no	—
52	#121×C₄₁	—	2	4	no	—
53	#121×C₄₁	—	2	4	no	—
54	#121×C₄₁	—	2	2	no	—
55	#121×C₄₁	—	2	2	no	—
56	#121×C₄₁	—	2	2	no	—
57	#121×C₄₁	C₂×C₄	1	4	yes	—
58	#120×C₄₁	—	2	4	no	—
59	#120×C₄₁	—	2	4	no	—
60	C₄×D₄×C₄₁	—	2	2	no	—
61	C₄×D₄×C₄₁	—	2	2	no	—
62	C₄×D₄×C₄₁	—	2	2	no	—
63	C₄×D₄×C₄₁	D₄	1	4	yes	—
64	#117×C₄₁	—	2	2	no	—
65	#117×C₄₁	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
72	C₄⋊C₈×C₄₁	—	2	2	no	—
73	C₄⋊C₈×C₄₁	—	2	2	no	—
74	C₄⋊C₈×C₄₁	—	2	2	no	—
75	C₂²⋊C₈×C₄₁	—	2	2	no	—
76	C₂²⋊C₈×C₄₁	—	4	2	no	—
77	C₄×C₈×C₄₁	—	2	2	no	—
78	C₂⁴×C₄₁	—	2	2	no	—
79	C₂⁴×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
80	#41×C₄₁	—	4	4	no	—
81	#41×C₄₁	—	4	4	no	—
82	#41×C₄₁	—	4	4	no	—
83	#41×C₄₁	—	4	4	no	—
84	#41×C₄₁	—	4	4	no	—
85	#41×C₄₁	—	4	4	no	—
86	#41×C₄₁	—	4	2	no	—
87	#41×C₄₁	—	4	2	no	—
88	#41×C₄₁	—	4	2	no	—
89	#41×C₄₁	—	4	2	no	—
90	C₂×Q₈×C₄₁	—	2	2	no	—
91	C₂×Q₈×C₄₁	—	2	2	no	—
92	C₂×Q₈×C₄₁	—	4	2	no	—
93	C₂×Q₈×C₄₁	—	4	2	no	—
94	C₂×D₄×C₄₁	—	2	4	no	—
95	C₂×D₄×C₄₁	—	2	2	no	—
96	C₂×D₄×C₄₁	—	2	4	no	—
97	C₂×D₄×C₄₁	—	2	2	no	—
98	C₂×D₄×C₄₁	—	2	2	no	—
99	C₂×D₄×C₄₁	—	2	2	no	—
100	C₂×D₄×C₄₁	—	2	2	no	—
101	C₂×D₄×C₄₁	—	4	2	no	—
102	C₂×D₄×C₄₁	—	4	2	no	—
103	C₂×D₄×C₄₁	—	4	4	no	—
104	C₂×D₄×C₄₁	—	4	4	no	—
105	C₂×D₄×C₄₁	C₂²⋊C₄	1	4	yes	—
106	C₂²×C₄×C₄₁	—	2	1	no	—
107	C₂²×C₄×C₄₁	—	2	1	no	—
108	C₂²×C₄×C₄₁	—	2	1	no	—
109	C₂²×C₄×C₄₁	—	2	1	no	—
110	C₂²×C₄×C₄₁	—	2	4	no	—
111	C₂²×C₄×C₄₁	—	2	2	no	—
112	C₂²×C₄×C₄₁	—	2	4	no	—
113	C₂²×C₄×C₄₁	—	4	4	no	—
114	C₂²×C₄×C₄₁	—	4	4	no	—
115	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₁	D₈	1	2	yes	—
119	C₂²×C₄×C₄₁	SD₁₆	1	2	yes	—
120	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₄₁	—	4	2	no	—
124	C₂×C₈×C₄₁	—	4	1	no	—
125	C₂×C₈×C₄₁	—	4	1	no	—
126	C₂×C₈×C₄₁	—	4	1	no	—
127	C₂×C₈×C₄₁	—	4	1	no	—
128	C₂×C₈×C₄₁	—	4	1	no	—
129	C₂×C₈×C₄₁	—	4	1	no	—
130	C₄⋊C₄×C₄₁	—	2	2	no	—
131	C₄⋊C₄×C₄₁	—	2	2	no	—
132	C₄⋊C₄×C₄₁	—	2	2	no	—
133	C₄⋊C₄×C₄₁	—	2	2	no	—
134	C₄⋊C₄×C₄₁	—	2	2	no	—
135	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
136	C₂²⋊C₄×C₄₁	—	2	4	no	—
137	C₂²⋊C₄×C₄₁	—	2	4	no	—
138	C₂²⋊C₄×C₄₁	—	2	2	no	—
139	C₂²⋊C₄×C₄₁	—	2	4	no	—
140	C₂²⋊C₄×C₄₁	—	2	2	no	—
141	C₂²⋊C₄×C₄₁	—	2	4	no	—
142	C₄²×C₄₁	—	2	1	no	—
143	C₄²×C₄₁	—	2	1	no	—
144	C₄²×C₄₁	C₂×D₄	1	2	yes	—
145	C₄²×C₄₁	C₂×D₄	1	2	yes	—
146	C₂³×C₄₁	—	2	1	no	—
147	C₂³×C₄₁	—	2	1	no	—
148	C₂³×C₄₁	—	2	4	no	—
149	C₂³×C₄₁	—	4	1	no	—
150	C₂³×C₄₁	—	4	1	no	—
151	C₂³×C₄₁	—	4	4	no	—
152	C₂³×C₄₁	—	8	2	no	—
153	C₂³×C₄₁	—	8	2	no	—
154	C₂³×C₄₁	#102	1	2	yes	—
155	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	Q₈×C₄₁	—	4	4	no	—
157	Q₈×C₄₁	—	4	2	no	—
158	Q₈×C₄₁	—	4	2	no	—
159	D₄×C₄₁	—	4	4	no	—
160	D₄×C₄₁	—	4	4	no	—
161	D₄×C₄₁	—	4	8	no	—
162	D₄×C₄₁	—	4	4	no	—
163	D₄×C₄₁	—	4	4	no	—
164	D₄×C₄₁	—	4	2	no	—
165	D₄×C₄₁	—	4	2	no	—
166	D₄×C₄₁	—	8	2	no	—
167	D₄×C₄₁	—	8	2	no	—
168	D₄×C₄₁	—	8	2	no	—
169	C₂×C₄×C₄₁	—	2	1	no	—
170	C₂×C₄×C₄₁	—	2	1	no	—
171	C₂×C₄×C₄₁	—	2	2	no	—
172	C₂×C₄×C₄₁	—	2	2	no	—
173	C₂×C₄×C₄₁	—	2	2	no	—
174	C₂×C₄×C₄₁	—	2	2	no	—
175	C₂×C₄×C₄₁	—	2	1	no	—
176	C₂×C₄×C₄₁	—	2	1	no	—
177	C₂×C₄×C₄₁	—	2	4	no	—
178	C₂×C₄×C₄₁	—	4	1	no	—
179	C₂×C₄×C₄₁	—	4	1	no	—
180	C₂×C₄×C₄₁	—	4	8	no	—
181	C₂×C₄×C₄₁	—	4	4	no	—
182	C₂×C₄×C₄₁	—	4	4	no	—
183	C₂×C₄×C₄₁	—	4	4	no	—
184	C₂×C₄×C₄₁	—	4	1	no	—
185	C₂×C₄×C₄₁	—	4	1	no	—
186	C₂×C₄×C₄₁	#102	1	2	yes	—
187	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
188	C₂×C₄×C₄₁	#120	1	2	yes	—
189	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
190	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
191	C₂×C₄×C₄₁	C₂×D₈	1	1	yes	characteristic
192	C₂×C₄×C₄₁	C₂×SD₁₆	1	1	yes	characteristic
193	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	1	yes	characteristic
194	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₈×C₄₁	—	8	2	no	—
196	C₈×C₄₁	—	8	1	no	—
197	C₈×C₄₁	—	8	1	no	—
198	#8409	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂²×C₄₁	—	2	1	no	—
200	C₂²×C₄₁	—	2	1	no	—
201	C₂²×C₄₁	—	2	2	no	—
202	C₂²×C₄₁	—	4	2	no	—
203	C₂²×C₄₁	—	4	1	no	—
204	C₂²×C₄₁	—	4	1	no	—
205	C₂²×C₄₁	—	4	4	no	—
206	C₂²×C₄₁	—	4	4	no	—
207	C₂²×C₄₁	—	4	4	no	—
208	C₂²×C₄₁	—	8	1	no	—
209	C₂²×C₄₁	—	8	8	no	—
210	C₂²×C₄₁	#379	1	1	yes	characteristic
211	C₂²×C₄₁	C₂×#102	1	1	yes	characteristic
212	C₂²×C₄₁	#418	1	1	yes	characteristic
213	C₄×C₄₁	—	2	2	no	—
214	C₄×C₄₁	—	2	2	no	—
215	C₄×C₄₁	—	2	2	no	—
216	C₄×C₄₁	—	4	1	no	—
217	C₄×C₄₁	—	4	4	no	—
218	C₄×C₄₁	—	4	1	no	—
219	C₄×C₄₁	#447	1	1	yes	characteristic
220	C₄×C₄₁	#447	1	1	yes	characteristic
221	C₄×C₄₁	#450	1	1	yes	characteristic
222	C₄×C₄₁	#450	1	1	yes	characteristic
223	#3449	C₂×C₄₁	1	1	yes	characteristic
224	#1798	C₂×C₄₁	1	1	yes	characteristic, complemented
225	#1540	C₂×C₄₁	1	2	yes	complemented
226	#1480	C₂×C₄₁	1	2	yes	complemented
227	#1458	C₂×C₄₁	1	1	yes	characteristic, complemented
228	C₂×C₄₁	—	2	1	no	—
229	C₂×C₄₁	—	2	1	no	—
230	C₂×C₄₁	—	4	2	no	—
231	C₂×C₄₁	—	8	4	no	—
232	C₂×C₄₁	#1786	1	1	yes	characteristic
233	C₂×C₄₁	#1791	1	1	yes	characteristic
234	C₂×C₄₁	#1794	1	1	yes	characteristic
235	C₂²×#41	—	2	1	no	—
236	#537	—	2	1	no	—
237	#537	C₄×C₄₁	1	2	yes	—
238	#536	—	2	2	no	—
239	#535	—	2	2	no	—
240	#534	—	2	1	no	—
241	#534	C₄×C₄₁	1	2	yes	—
242	#532	—	2	1	no	—
243	#532	C₂²×C₄₁	1	2	yes	—
244	#525	—	2	4	no	—
245	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
246	#431	C₂²×C₄₁	1	2	yes	complemented
247	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
248	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
249	C₂×C₂²⋊C₈	—	2	1	no	—
250	#336	—	2	1	no	—
251	#332	—	2	2	no	—
252	#331	—	2	2	no	—
253	D₄⋊C₈	—	2	4	no	—
254	#324	—	2	1	no	—
255	#323	—	2	1	no	—
256	C₄₁	#8409	1	1	yes	characteristic, direct product factor, Sylow
257	C₂×#41	—	2	2	no	—
258	C₂×#41	—	2	2	no	—
259	C₂×#41	—	2	2	no	—
260	C₂×#41	—	2	2	no	—
261	C₂×#41	—	4	2	no	—
262	C₂×#41	—	4	2	no	—
263	C₂×#41	—	4	2	no	—
264	C₂×#41	—	4	2	no	—
265	C₂²×Q₈	—	2	1	no	—
266	C₂²×D₄	—	2	1	no	—
267	C₂²×D₄	—	2	2	no	—
268	C₂³×C₄	—	2	2	no	—
269	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	—	2	1	no	—
272	C₄⋊Q₈	—	2	1	no	—
273	C₄⋊Q₈	D₄×C₄₁	1	2	yes	—
274	#127	—	2	1	no	—
275	#127	D₄×C₄₁	1	2	yes	—
276	#124	—	2	2	no	—
277	#124	—	2	2	no	—
278	#123	—	2	4	no	—
279	#123	—	2	4	no	—
280	C₂²⋊Q₈	—	2	4	no	—
281	C₂²⋊Q₈	—	2	4	no	—
282	#121	—	2	4	no	—
283	#121	—	2	4	no	—
284	#121	—	2	2	no	—
285	#121	—	2	2	no	—
286	#121	—	2	2	no	—
287	#121	C₂×C₄×C₄₁	1	4	yes	—
288	#120	—	2	4	no	—
289	#120	—	2	4	no	—
290	C₄×D₄	—	2	2	no	—
291	C₄×D₄	—	2	2	no	—
292	C₄×D₄	—	2	2	no	—
293	C₄×D₄	D₄×C₄₁	1	4	yes	—
294	#117	—	2	2	no	—
295	#117	—	2	2	no	—
296	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
297	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
300	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
302	C₄⋊C₈	—	2	2	no	—
303	C₄⋊C₈	—	2	2	no	—
304	C₄⋊C₈	—	2	2	no	—
305	C₂²⋊C₈	—	2	2	no	—
306	C₂²⋊C₈	—	4	2	no	—
307	C₄×C₈	—	2	2	no	—
308	C₂⁴	—	2	2	no	—
309	C₂⁴	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
310	#41	—	4	4	no	—
311	#41	—	4	4	no	—
312	#41	—	4	4	no	—
313	#41	—	4	4	no	—
314	#41	—	4	4	no	—
315	#41	—	4	4	no	—
316	#41	—	4	2	no	—
317	#41	—	4	2	no	—
318	#41	—	4	2	no	—
319	#41	—	4	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	4	2	no	—
323	C₂×Q₈	—	4	2	no	—
324	C₂×D₄	—	2	4	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	—	4	4	no	—
334	C₂×D₄	—	4	4	no	—
335	C₂×D₄	C₂²⋊C₄×C₄₁	1	4	yes	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	4	4	no	—
344	C₂²×C₄	—	4	4	no	—
345	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
346	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
347	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
348	C₂²×C₄	D₈×C₄₁	1	2	yes	—
349	C₂²×C₄	SD₁₆×C₄₁	1	2	yes	—
350	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
353	C₂×C₈	—	4	2	no	—
354	C₂×C₈	—	4	1	no	—
355	C₂×C₈	—	4	1	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	—	4	1	no	—
359	C₂×C₈	—	4	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
366	C₂²⋊C₄	—	2	4	no	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	1	no	—
374	C₄²	C₂×D₄×C₄₁	1	2	yes	—
375	C₄²	C₂×D₄×C₄₁	1	2	yes	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	4	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	4	no	—
382	C₂³	—	8	2	no	—
383	C₂³	—	8	2	no	—
384	C₂³	#102×C₄₁	1	2	yes	—
385	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
386	Q₈	—	4	4	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	4	2	no	—
389	D₄	—	4	4	no	—
390	D₄	—	4	4	no	—
391	D₄	—	4	8	no	—
392	D₄	—	4	4	no	—
393	D₄	—	4	4	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	8	2	no	—
397	D₄	—	8	2	no	—
398	D₄	—	8	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	8	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	#102×C₄₁	1	2	yes	—
417	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
418	C₂×C₄	#120×C₄₁	1	2	yes	—
419	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
420	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
421	C₂×C₄	C₂×D₈×C₄₁	1	1	yes	characteristic
422	C₂×C₄	C₂×SD₁₆×C₄₁	1	1	yes	characteristic
423	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
424	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
425	C₈	—	8	2	no	—
426	C₈	—	8	1	no	—
427	C₈	—	8	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	8	no	—
439	C₂²	C₄₁×#379	1	1	yes	characteristic
440	C₂²	C₂×#102×C₄₁	1	1	yes	characteristic
441	C₂²	C₄₁×#418	1	1	yes	characteristic
442	C₄	—	2	2	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	4	4	no	—
446	C₄	—	4	1	no	—
447	C₄	—	4	1	no	—
448	C₄	C₄₁×#447	1	1	yes	characteristic
449	C₄	C₄₁×#447	1	1	yes	characteristic
450	C₄	C₄₁×#450	1	1	yes	characteristic
451	C₄	C₄₁×#450	1	1	yes	characteristic
452	C₂	—	2	1	no	—
453	C₂	—	2	1	no	—
454	C₂	—	4	2	no	—
455	C₂	—	8	4	no	—
456	C₂	C₄₁×#1786	1	1	yes	characteristic
457	C₂	C₄₁×#1791	1	1	yes	characteristic
458	C₂	C₄₁×#1794	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₁	#120
commutator	C₂²×C₄	C₂²×C₄×C₄₁
Frattini, cosocle	C₂×C₄²	C₂³×C₄₁
socle	C₂²×C₄₁	#379
prime radical	C₄₁×#3449	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#1798	C₂	semidirect
3. C₄₁×#1540	C₂	semidirect
4. C₄₁×#1480	C₂	semidirect
5. C₄₁×#1458	C₂	semidirect
17. C₄₁×#431	C₂²	semidirect
18. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
19. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
198. #8409	C₄₁	direct (N × H)
224. #1798	C₂×C₄₁	semidirect
225. #1540	C₂×C₄₁	semidirect
226. #1480	C₂×C₄₁	semidirect
227. #1458	C₂×C₄₁	semidirect
246. #431	C₂²×C₄₁	semidirect
247. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
248. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
256. C₄₁	#8409	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#3449	2
C₄₁×#1798	2
C₄₁×#1540	2
C₄₁×#1480	2
C₄₁×#1458	2
#8409	41

Subgroups — C41×#8409 #23784610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#8409 #23784610