Subgroups — C₄₁×#18485 #23794686

Order 10496.

996 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3481	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#3131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3107	C₂	1	2	yes	maximal, complemented
4	C₄₁×#1644	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1643	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1640	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1639	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1543	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1476	C₂	1	2	yes	maximal, complemented
10	C₄₁×#559	C₂²	1	1	yes	characteristic
11	C₄₁×#554	C₂²	1	2	yes	—
12	C₄₁×#553	—	2	2	no	—
13	C₄₁×#551	—	2	2	no	—
14	C₄₁×#546	—	2	2	no	—
15	D₄²×C₄₁	C₂²	1	1	yes	characteristic
16	C₄₁×#533	C₂²	1	1	yes	characteristic, complemented
17	C₄₁×#532	C₂²	1	1	yes	characteristic
18	C₄₁×#529	—	2	2	no	—
19	C₄₁×#525	—	2	2	no	—
20	C₄×#41×C₄₁	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₄₁	—	2	2	no	—
22	C₄₁×#488	—	2	2	no	—
23	C₄₁×#487	C₂²	1	2	yes	complemented
24	C₄₁×#486	C₂²	1	2	yes	—
25	C₄₁×#485	—	2	2	no	—
26	C₄₁×#475	C₂²	1	2	yes	complemented
27	C₄₁×#474	C₂²	1	2	yes	—
28	C₄₁×#462	C₂²	1	2	yes	complemented
29	C₄₁×#461	C₂²	1	2	yes	—
30	C₄₁×#452	—	2	2	no	—
31	C₄×Q₁₆×C₄₁	—	2	2	no	—
32	C₄×SD₁₆×C₄₁	—	2	2	no	—
33	C₄₁×#431	C₂²	1	2	yes	complemented
34	C₄₁×#416	—	2	2	no	—
35	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
36	C₄₁×#333	C₂²	1	1	yes	characteristic, complemented
37	C₄₁×#333	C₂²	1	1	yes	characteristic, complemented
38	C₄₁×#331	C₂²	1	2	yes	—
39	C₄₁×Q₈⋊C₈	C₂²	1	2	yes	complemented
40	C₄₁×Q₈⋊C₈	C₂²	1	2	yes	complemented
41	C₄₁×D₄⋊C₈	C₂²	1	2	yes	—
42	C₄₁×D₄⋊C₈	C₂²	1	2	yes	—
43	C₂×#41×C₄₁	D₄	1	2	yes	—
44	C₂×#41×C₄₁	D₄	1	2	yes	—
45	C₂²×D₄×C₄₁	—	2	2	no	—
46	C₂³×C₄×C₄₁	—	2	2	no	—
47	C₂×Q₁₆×C₄₁	—	2	2	no	—
48	C₂×SD₁₆×C₄₁	—	2	2	no	—
49	C₂²×C₈×C₄₁	—	2	1	no	—
50	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
52	#127×C₄₁	C₂³	1	1	yes	characteristic
53	#126×C₄₁	—	2	4	no	—
54	#125×C₄₁	—	2	2	no	—
55	#125×C₄₁	—	2	1	no	—
56	#124×C₄₁	—	2	2	no	—
57	#124×C₄₁	D₄	1	2	yes	—
58	#123×C₄₁	—	2	2	no	—
59	#123×C₄₁	—	2	4	no	—
60	#123×C₄₁	—	2	2	no	—
61	C₂²⋊Q₈×C₄₁	—	2	4	no	—
62	C₂²⋊Q₈×C₄₁	—	2	2	no	—
63	C₂²⋊Q₈×C₄₁	—	2	2	no	—
64	#121×C₄₁	—	2	4	no	—
65	#121×C₄₁	—	2	2	no	—
66	#121×C₄₁	—	2	2	no	—
67	#120×C₄₁	—	2	2	no	—
68	#120×C₄₁	—	2	2	no	—
69	C₄×Q₈×C₄₁	—	2	2	no	—
70	C₄×Q₈×C₄₁	D₄	1	2	yes	—
71	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
72	C₄×D₄×C₄₁	—	2	4	no	—
73	C₄×D₄×C₄₁	—	2	4	no	—
74	C₄×D₄×C₄₁	—	2	2	no	—
75	C₄×D₄×C₄₁	—	2	2	no	—
76	C₄×D₄×C₄₁	—	2	2	no	—
77	C₄×D₄×C₄₁	—	2	2	no	—
78	C₄×D₄×C₄₁	—	2	2	no	—
79	C₄×D₄×C₄₁	D₄	1	2	yes	—
80	C₄×D₄×C₄₁	C₂³	1	2	yes	—
81	#117×C₄₁	—	2	2	no	—
82	#117×C₄₁	—	2	2	no	—
83	#117×C₄₁	—	2	1	no	—
84	#117×C₄₁	D₄	1	2	yes	—
85	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
87	C₂×C₄²×C₄₁	—	2	2	no	—
88	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
89	#107×C₄₁	—	2	2	no	—
90	#106×C₄₁	—	2	2	no	—
91	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
92	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
93	#103×C₄₁	—	2	4	no	—
94	#103×C₄₁	—	2	2	no	—
95	#103×C₄₁	—	2	2	no	—
96	#103×C₄₁	—	2	2	no	—
97	#102×C₄₁	—	2	4	no	—
98	#102×C₄₁	—	2	2	no	—
99	C₂²⋊C₈×C₄₁	—	2	2	no	—
100	C₄×C₈×C₄₁	—	2	1	no	—
101	C₄×C₈×C₄₁	—	2	2	no	—
102	C₄×C₈×C₄₁	C₂³	1	2	yes	—
103	C₂⁴×C₄₁	—	2	2	no	—
104	#41×C₄₁	—	2	4	no	—
105	#41×C₄₁	—	4	2	no	—
106	#41×C₄₁	—	4	4	no	—
107	C₂×Q₈×C₄₁	—	2	2	no	—
108	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
109	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
110	C₂×D₄×C₄₁	—	2	4	no	—
111	C₂×D₄×C₄₁	—	2	2	no	—
112	C₂×D₄×C₄₁	—	2	2	no	—
113	C₂×D₄×C₄₁	—	2	2	no	—
114	C₂×D₄×C₄₁	—	4	4	no	—
115	C₂×D₄×C₄₁	—	4	4	no	—
116	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
117	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₁	—	2	4	no	—
119	C₂²×C₄×C₄₁	—	2	2	no	—
120	C₂²×C₄×C₄₁	—	2	2	no	—
121	C₂²×C₄×C₄₁	—	2	2	no	—
122	C₂²×C₄×C₄₁	—	2	2	no	—
123	C₂²×C₄×C₄₁	—	2	2	no	—
124	C₂²×C₄×C₄₁	—	8	4	no	—
125	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
127	Q₁₆×C₄₁	—	4	4	no	—
128	SD₁₆×C₄₁	—	4	4	no	—
129	C₂×C₈×C₄₁	—	2	2	no	—
130	C₂×C₈×C₄₁	—	2	2	no	—
131	C₂×C₈×C₄₁	—	2	2	no	—
132	C₂×C₈×C₄₁	—	4	2	no	—
133	C₄⋊C₄×C₄₁	—	2	4	no	—
134	C₄⋊C₄×C₄₁	—	2	4	no	—
135	C₄⋊C₄×C₄₁	—	2	2	no	—
136	C₄⋊C₄×C₄₁	—	2	2	no	—
137	C₄⋊C₄×C₄₁	—	2	2	no	—
138	C₄⋊C₄×C₄₁	—	2	2	no	—
139	C₄⋊C₄×C₄₁	—	2	2	no	—
140	C₄⋊C₄×C₄₁	—	4	2	no	—
141	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
142	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
143	C₂²⋊C₄×C₄₁	—	2	4	no	—
144	C₂²⋊C₄×C₄₁	—	2	4	no	—
145	C₂²⋊C₄×C₄₁	—	2	2	no	—
146	C₂²⋊C₄×C₄₁	—	2	2	no	—
147	C₂²⋊C₄×C₄₁	—	2	2	no	—
148	C₂²⋊C₄×C₄₁	—	2	2	no	—
149	C₂²⋊C₄×C₄₁	—	2	4	no	—
150	C₂²⋊C₄×C₄₁	—	2	2	no	—
151	C₂²⋊C₄×C₄₁	—	4	1	no	—
152	C₄²×C₄₁	—	2	2	no	—
153	C₄²×C₄₁	—	2	2	no	—
154	C₄²×C₄₁	—	2	2	no	—
155	C₄²×C₄₁	—	4	1	no	—
156	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₄₁	C₂×D₄	1	2	yes	—
158	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
159	C₂³×C₄₁	—	2	2	no	—
160	C₂³×C₄₁	—	2	2	no	—
161	C₂³×C₄₁	—	4	8	no	—
162	C₂³×C₄₁	—	8	2	no	—
163	C₂³×C₄₁	#120	1	1	yes	characteristic
164	Q₈×C₄₁	—	2	2	no	—
165	Q₈×C₄₁	—	2	2	no	—
166	Q₈×C₄₁	—	4	2	no	—
167	Q₈×C₄₁	—	4	2	no	—
168	Q₈×C₄₁	—	4	2	no	—
169	D₄×C₄₁	—	2	2	no	—
170	D₄×C₄₁	—	4	2	no	—
171	D₄×C₄₁	—	4	4	no	—
172	D₄×C₄₁	—	4	8	no	—
173	D₄×C₄₁	—	4	2	no	—
174	D₄×C₄₁	—	4	2	no	—
175	D₄×C₄₁	—	8	2	no	—
176	D₄×C₄₁	#135	1	4	yes	—
177	C₂×C₄×C₄₁	—	2	2	no	—
178	C₂×C₄×C₄₁	—	2	2	no	—
179	C₂×C₄×C₄₁	—	2	2	no	—
180	C₂×C₄×C₄₁	—	2	2	no	—
181	C₂×C₄×C₄₁	—	2	2	no	—
182	C₂×C₄×C₄₁	—	2	2	no	—
183	C₂×C₄×C₄₁	—	2	2	no	—
184	C₂×C₄×C₄₁	—	4	4	no	—
185	C₂×C₄×C₄₁	—	4	2	no	—
186	C₂×C₄×C₄₁	—	4	2	no	—
187	C₂×C₄×C₄₁	—	4	4	no	—
188	C₂×C₄×C₄₁	—	4	4	no	—
189	C₂×C₄×C₄₁	—	4	2	no	—
190	C₂×C₄×C₄₁	—	8	2	no	—
191	C₂×C₄×C₄₁	—	8	4	no	—
192	C₂×C₄×C₄₁	#120	1	2	yes	—
193	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
194	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
196	C₈×C₄₁	—	4	2	no	—
197	C₈×C₄₁	—	4	2	no	—
198	C₈×C₄₁	—	4	2	no	—
199	#18485	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂²×C₄₁	—	2	2	no	—
201	C₂²×C₄₁	—	2	4	no	—
202	C₂²×C₄₁	—	2	1	no	—
203	C₂²×C₄₁	—	4	2	no	—
204	C₂²×C₄₁	—	4	2	no	—
205	C₂²×C₄₁	—	4	4	no	—
206	C₂²×C₄₁	—	4	2	no	—
207	C₂²×C₄₁	—	8	8	no	—
208	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
209	C₄×C₄₁	—	2	2	no	—
210	C₄×C₄₁	—	2	1	no	—
211	C₄×C₄₁	—	4	2	no	—
212	C₄×C₄₁	—	4	2	no	—
213	C₄×C₄₁	—	4	2	no	—
214	C₄×C₄₁	—	4	2	no	—
215	C₄×C₄₁	—	8	2	no	—
216	C₄×C₄₁	#455	1	2	yes	—
217	C₄×C₄₁	C₂×#135	1	2	yes	—
218	C₄×C₄₁	#575	1	2	yes	—
219	#3481	C₂×C₄₁	1	1	yes	characteristic
220	#3131	C₂×C₄₁	1	1	yes	characteristic, complemented
221	#3107	C₂×C₄₁	1	2	yes	complemented
222	#1644	C₂×C₄₁	1	2	yes	complemented
223	#1643	C₂×C₄₁	1	2	yes	complemented
224	#1640	C₂×C₄₁	1	2	yes	complemented
225	#1639	C₂×C₄₁	1	2	yes	complemented
226	#1543	C₂×C₄₁	1	1	yes	characteristic, complemented
227	#1476	C₂×C₄₁	1	2	yes	complemented
228	C₂×C₄₁	—	4	1	no	—
229	C₂×C₄₁	—	4	4	no	—
230	C₂×C₄₁	—	8	2	no	—
231	C₂×C₄₁	#3002	1	2	yes	—
232	C₂×C₄₁	C₂×#455	1	1	yes	characteristic
233	#559	C₂²×C₄₁	1	1	yes	characteristic
234	#554	C₂²×C₄₁	1	2	yes	—
235	#553	—	2	2	no	—
236	#551	—	2	2	no	—
237	#546	—	2	2	no	—
238	D₄²	C₂²×C₄₁	1	1	yes	characteristic
239	#533	C₂²×C₄₁	1	1	yes	characteristic, complemented
240	#532	C₂²×C₄₁	1	1	yes	characteristic
241	#529	—	2	2	no	—
242	#525	—	2	2	no	—
243	C₄×#41	C₂²×C₄₁	1	2	yes	—
244	C₂×C₄×D₄	—	2	2	no	—
245	#488	—	2	2	no	—
246	#487	C₂²×C₄₁	1	2	yes	complemented
247	#486	C₂²×C₄₁	1	2	yes	—
248	#485	—	2	2	no	—
249	#475	C₂²×C₄₁	1	2	yes	complemented
250	#474	C₂²×C₄₁	1	2	yes	—
251	#462	C₂²×C₄₁	1	2	yes	complemented
252	#461	C₂²×C₄₁	1	2	yes	—
253	#452	—	2	2	no	—
254	C₄×Q₁₆	—	2	2	no	—
255	C₄×SD₁₆	—	2	2	no	—
256	#431	C₂²×C₄₁	1	2	yes	complemented
257	#416	—	2	2	no	—
258	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
259	#333	C₂²×C₄₁	1	1	yes	characteristic, complemented
260	#333	C₂²×C₄₁	1	1	yes	characteristic, complemented
261	#331	C₂²×C₄₁	1	2	yes	—
262	Q₈⋊C₈	C₂²×C₄₁	1	2	yes	complemented
263	Q₈⋊C₈	C₂²×C₄₁	1	2	yes	complemented
264	D₄⋊C₈	C₂²×C₄₁	1	2	yes	—
265	D₄⋊C₈	C₂²×C₄₁	1	2	yes	—
266	C₄₁	#18485	1	1	yes	characteristic, direct product factor, Sylow
267	C₂×#41	D₄×C₄₁	1	2	yes	—
268	C₂×#41	D₄×C₄₁	1	2	yes	—
269	C₂²×D₄	—	2	2	no	—
270	C₂³×C₄	—	2	2	no	—
271	C₂×Q₁₆	—	2	2	no	—
272	C₂×SD₁₆	—	2	2	no	—
273	C₂²×C₈	—	2	1	no	—
274	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
275	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
276	#127	C₂³×C₄₁	1	1	yes	characteristic
277	#126	—	2	4	no	—
278	#125	—	2	2	no	—
279	#125	—	2	1	no	—
280	#124	—	2	2	no	—
281	#124	D₄×C₄₁	1	2	yes	—
282	#123	—	2	2	no	—
283	#123	—	2	4	no	—
284	#123	—	2	2	no	—
285	C₂²⋊Q₈	—	2	4	no	—
286	C₂²⋊Q₈	—	2	2	no	—
287	C₂²⋊Q₈	—	2	2	no	—
288	#121	—	2	4	no	—
289	#121	—	2	2	no	—
290	#121	—	2	2	no	—
291	#120	—	2	2	no	—
292	#120	—	2	2	no	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×Q₈	D₄×C₄₁	1	2	yes	—
295	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
296	C₄×D₄	—	2	4	no	—
297	C₄×D₄	—	2	4	no	—
298	C₄×D₄	—	2	2	no	—
299	C₄×D₄	—	2	2	no	—
300	C₄×D₄	—	2	2	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	—	2	2	no	—
303	C₄×D₄	D₄×C₄₁	1	2	yes	—
304	C₄×D₄	C₂³×C₄₁	1	2	yes	—
305	#117	—	2	2	no	—
306	#117	—	2	2	no	—
307	#117	—	2	1	no	—
308	#117	D₄×C₄₁	1	2	yes	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	4	no	—
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
313	#107	—	2	2	no	—
314	#106	—	2	2	no	—
315	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
316	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
317	#103	—	2	4	no	—
318	#103	—	2	2	no	—
319	#103	—	2	2	no	—
320	#103	—	2	2	no	—
321	#102	—	2	4	no	—
322	#102	—	2	2	no	—
323	C₂²⋊C₈	—	2	2	no	—
324	C₄×C₈	—	2	1	no	—
325	C₄×C₈	—	2	2	no	—
326	C₄×C₈	C₂³×C₄₁	1	2	yes	—
327	C₂⁴	—	2	2	no	—
328	#41	—	2	4	no	—
329	#41	—	4	2	no	—
330	#41	—	4	4	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
333	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	4	4	no	—
339	C₂×D₄	—	4	4	no	—
340	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
341	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	8	4	no	—
349	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
351	Q₁₆	—	4	4	no	—
352	SD₁₆	—	4	4	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	4	2	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	2	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	—	4	2	no	—
365	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
366	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	2	4	no	—
374	C₂²⋊C₄	—	2	2	no	—
375	C₂²⋊C₄	—	4	1	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	4	1	no	—
380	C₄²	C₂×D₄×C₄₁	1	2	yes	—
381	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
382	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
383	C₂³	—	2	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	4	8	no	—
386	C₂³	—	8	2	no	—
387	C₂³	#120×C₄₁	1	1	yes	characteristic
388	Q₈	—	2	2	no	—
389	Q₈	—	2	2	no	—
390	Q₈	—	4	2	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	4	2	no	—
393	D₄	—	2	2	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	4	no	—
396	D₄	—	4	8	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	8	2	no	—
400	D₄	#135×C₄₁	1	4	yes	—
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	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	8	2	no	—
415	C₂×C₄	—	8	4	no	—
416	C₂×C₄	#120×C₄₁	1	2	yes	—
417	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
418	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
419	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
420	C₈	—	4	2	no	—
421	C₈	—	4	2	no	—
422	C₈	—	4	2	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	4	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	8	8	no	—
431	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
432	C₄	—	2	2	no	—
433	C₄	—	2	1	no	—
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	8	2	no	—
439	C₄	C₄₁×#455	1	2	yes	—
440	C₄	C₂×#135×C₄₁	1	2	yes	—
441	C₄	C₄₁×#575	1	2	yes	—
442	C₂	—	4	1	no	—
443	C₂	—	4	4	no	—
444	C₂	—	8	2	no	—
445	C₂	C₄₁×#3002	1	2	yes	—
446	C₂	C₂×C₄₁×#455	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₁	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
socle	C₂²×C₄₁	C₂×#120
prime radical	C₄₁×#3481	C₂
LCS	G ▷ C₄² ▷ 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×#3131	C₂	semidirect
3. C₄₁×#3107	C₂	semidirect
4. C₄₁×#1644	C₂	semidirect
5. C₄₁×#1643	C₂	semidirect
6. C₄₁×#1640	C₂	semidirect
7. C₄₁×#1639	C₂	semidirect
8. C₄₁×#1543	C₂	semidirect
9. C₄₁×#1476	C₂	semidirect
16. C₄₁×#533	C₂²	semidirect
23. C₄₁×#487	C₂²	semidirect
26. C₄₁×#475	C₂²	semidirect
28. C₄₁×#462	C₂²	semidirect
33. C₄₁×#431	C₂²	semidirect
35. C₂×C₄×C₈×C₄₁	C₂²	semidirect
36. C₄₁×#333	C₂²	semidirect
37. C₄₁×#333	C₂²	semidirect
39. C₄₁×Q₈⋊C₈	C₂²	semidirect
40. C₄₁×Q₈⋊C₈	C₂²	semidirect
199. #18485	C₄₁	direct (N × H)
220. #3131	C₂×C₄₁	semidirect
221. #3107	C₂×C₄₁	semidirect
222. #1644	C₂×C₄₁	semidirect
223. #1643	C₂×C₄₁	semidirect
224. #1640	C₂×C₄₁	semidirect
225. #1639	C₂×C₄₁	semidirect
226. #1543	C₂×C₄₁	semidirect
227. #1476	C₂×C₄₁	semidirect
239. #533	C₂²×C₄₁	semidirect
246. #487	C₂²×C₄₁	semidirect
249. #475	C₂²×C₄₁	semidirect
251. #462	C₂²×C₄₁	semidirect
256. #431	C₂²×C₄₁	semidirect
258. C₂×C₄×C₈	C₂²×C₄₁	semidirect
259. #333	C₂²×C₄₁	semidirect
260. #333	C₂²×C₄₁	semidirect
262. Q₈⋊C₈	C₂²×C₄₁	semidirect
263. Q₈⋊C₈	C₂²×C₄₁	semidirect
266. C₄₁	#18485	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×#3481	2
C₄₁×#3131	2
C₄₁×#3107	2
C₄₁×#1644	2
C₄₁×#1643	2
C₄₁×#1640	2
C₄₁×#1639	2
C₄₁×#1543	2
C₄₁×#1476	2
#18485	41

Subgroups — C41×#18485 #23794686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#18485 #23794686