Subgroups — C₄₁×#19226 #23795427

Order 10496.

562 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3233	C₂	1	2	yes	maximal
2	C₄₁×#3170	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2966	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1696	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1695	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1690	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1689	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1684	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1683	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1564	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1554	C₂	1	2	yes	maximal, complemented
12	C₄₁×#533	C₂²	1	2	yes	—
13	C₄₁×#529	C₂²	1	1	yes	characteristic
14	C₄₁×#500	C₂²	1	1	yes	characteristic
15	C₄₁×#499	—	2	2	no	—
16	C₄₁×#494	C₂²	1	1	yes	characteristic
17	C₄₁×#488	—	2	2	no	—
18	C₄₁×#487	C₂²	1	2	yes	—
19	C₄₁×#485	—	2	2	no	—
20	C₄₁×#482	—	2	2	no	—
21	C₄₁×#477	C₂²	1	2	yes	—
22	C₄₁×#476	C₂²	1	2	yes	—
23	C₄₁×#475	C₂²	1	2	yes	—
24	C₄₁×#474	C₂²	1	2	yes	—
25	C₄₁×#467	—	2	1	no	—
26	C₄₁×#467	—	2	1	no	—
27	C₄₁×#446	C₂²	1	1	yes	characteristic
28	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic
29	C₄×Q₁₆×C₄₁	—	2	1	no	—
30	C₄×Q₁₆×C₄₁	—	2	1	no	—
31	C₄₁×#436	C₂²	1	1	yes	characteristic
32	C₄₁×#435	—	2	1	no	—
33	C₈×D₄×C₄₁	—	2	1	no	—
34	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
35	C₄₁×#433	—	2	1	no	—
36	C₄₁×#432	C₂²	1	1	yes	characteristic
37	C₄₁×#431	C₂²	1	2	yes	—
38	C₄₁×#405	—	2	1	no	—
39	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
40	C₄₁×#335	C₂²	1	2	yes	—
41	C₄₁×#334	C₂²	1	1	yes	characteristic
42	C₄₁×#334	C₂²	1	1	yes	characteristic
43	C₄₁×#333	C₂²	1	2	yes	—
44	C₄₁×#333	C₂²	1	2	yes	—
45	C₄₁×#332	C₂²	1	2	yes	—
46	C₄₁×#332	C₂²	1	2	yes	—
47	C₂×Q₁₆×C₄₁	—	2	1	no	—
48	C₂×Q₁₆×C₄₁	—	2	1	no	—
49	C₂×M₁₆×C₄₁	—	2	1	no	—
50	C₂²×C₈×C₄₁	—	2	1	no	—
51	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
53	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
54	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
55	#126×C₄₁	—	2	1	no	—
56	#125×C₄₁	—	2	2	no	—
57	#125×C₄₁	D₄	1	1	yes	characteristic
58	#124×C₄₁	D₄	1	1	yes	characteristic
59	#123×C₄₁	—	2	1	no	—
60	C₂²⋊Q₈×C₄₁	—	2	2	no	—
61	C₂²⋊Q₈×C₄₁	—	2	2	no	—
62	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
63	#121×C₄₁	D₄	1	1	yes	characteristic
64	C₄×Q₈×C₄₁	—	2	2	no	—
65	C₄×Q₈×C₄₁	—	2	2	no	—
66	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
67	C₄×D₄×C₄₁	—	2	1	no	—
68	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
69	#117×C₄₁	—	2	1	no	—
70	#117×C₄₁	—	2	2	no	—
71	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
72	#107×C₄₁	—	2	1	no	—
73	#107×C₄₁	—	2	1	no	—
74	#107×C₄₁	—	2	2	no	—
75	#107×C₄₁	—	2	2	no	—
76	#106×C₄₁	—	2	2	no	—
77	#106×C₄₁	—	2	2	no	—
78	C₄⋊C₈×C₄₁	—	2	1	no	—
79	C₄⋊C₈×C₄₁	—	2	1	no	—
80	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
81	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
82	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
83	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
84	#103×C₄₁	—	2	2	no	—
85	#103×C₄₁	—	2	2	no	—
86	#103×C₄₁	—	2	2	no	—
87	#103×C₄₁	—	2	2	no	—
88	#102×C₄₁	—	2	2	no	—
89	#102×C₄₁	—	2	2	no	—
90	C₂²⋊C₈×C₄₁	—	2	2	no	—
91	C₂²⋊C₈×C₄₁	—	2	1	no	—
92	C₂²⋊C₈×C₄₁	—	2	1	no	—
93	C₂²⋊C₈×C₄₁	—	2	1	no	—
94	#97×C₄₁	—	2	1	no	—
95	#97×C₄₁	—	2	1	no	—
96	C₄×C₈×C₄₁	—	2	1	no	—
97	C₄×C₈×C₄₁	—	2	2	no	—
98	C₄×C₈×C₄₁	D₄	1	1	yes	characteristic
99	C₄×C₈×C₄₁	D₄	1	1	yes	characteristic
100	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
102	C₂×Q₈×C₄₁	—	2	2	no	—
103	C₂×Q₈×C₄₁	—	2	2	no	—
104	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
105	C₂×D₄×C₄₁	—	2	1	no	—
106	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₁	—	2	1	no	—
108	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
111	Q₁₆×C₄₁	—	4	2	no	—
112	Q₁₆×C₄₁	—	4	2	no	—
113	M₁₆×C₄₁	—	4	2	no	—
114	C₂×C₈×C₄₁	—	2	2	no	—
115	C₂×C₈×C₄₁	—	2	1	no	—
116	C₂×C₈×C₄₁	—	2	2	no	—
117	C₂×C₈×C₄₁	—	2	2	no	—
118	C₂×C₈×C₄₁	—	2	1	no	—
119	C₂×C₈×C₄₁	—	4	1	no	—
120	C₂×C₈×C₄₁	—	4	2	no	—
121	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
125	C₄⋊C₄×C₄₁	—	2	1	no	—
126	C₄⋊C₄×C₄₁	—	2	1	no	—
127	C₄⋊C₄×C₄₁	—	2	1	no	—
128	C₄⋊C₄×C₄₁	—	2	1	no	—
129	C₄⋊C₄×C₄₁	—	2	2	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	—	4	2	no	—
134	C₄⋊C₄×C₄₁	—	4	2	no	—
135	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
136	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
137	C₂²⋊C₄×C₄₁	—	2	1	no	—
138	C₂²⋊C₄×C₄₁	—	2	1	no	—
139	C₂²⋊C₄×C₄₁	—	2	1	no	—
140	C₂²⋊C₄×C₄₁	—	2	1	no	—
141	C₂²⋊C₄×C₄₁	—	2	1	no	—
142	C₂²⋊C₄×C₄₁	—	4	2	no	—
143	C₄²×C₄₁	—	2	1	no	—
144	C₄²×C₄₁	—	4	2	no	—
145	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₄₁	#41	1	1	yes	characteristic
148	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
149	C₂³×C₄₁	—	2	1	no	—
150	C₂³×C₄₁	#121	1	1	yes	characteristic
151	Q₈×C₄₁	—	2	2	no	—
152	Q₈×C₄₁	—	4	2	no	—
153	Q₈×C₄₁	—	4	2	no	—
154	Q₈×C₄₁	—	8	2	no	—
155	D₄×C₄₁	—	2	2	no	—
156	D₄×C₄₁	—	4	2	no	—
157	C₂×C₄×C₄₁	—	2	1	no	—
158	C₂×C₄×C₄₁	—	2	1	no	—
159	C₂×C₄×C₄₁	—	2	2	no	—
160	C₂×C₄×C₄₁	—	2	1	no	—
161	C₂×C₄×C₄₁	—	2	1	no	—
162	C₂×C₄×C₄₁	—	2	1	no	—
163	C₂×C₄×C₄₁	—	4	1	no	—
164	C₂×C₄×C₄₁	—	4	1	no	—
165	C₂×C₄×C₄₁	—	4	1	no	—
166	C₂×C₄×C₄₁	—	4	2	no	—
167	C₂×C₄×C₄₁	—	4	2	no	—
168	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
169	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
170	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
171	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
174	C₈×C₄₁	—	2	1	no	—
175	C₈×C₄₁	—	2	1	no	—
176	C₈×C₄₁	—	2	1	no	—
177	C₈×C₄₁	—	4	1	no	—
178	C₈×C₄₁	—	4	1	no	—
179	C₈×C₄₁	—	4	2	no	—
180	C₈×C₄₁	—	4	2	no	—
181	C₈×C₄₁	#135	1	2	yes	—
182	#19226	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂²×C₄₁	—	2	1	no	—
184	C₂²×C₄₁	—	2	1	no	—
185	C₂²×C₄₁	—	2	1	no	—
186	C₂²×C₄₁	—	4	1	no	—
187	C₂²×C₄₁	—	4	1	no	—
188	C₂²×C₄₁	—	4	1	no	—
189	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
190	C₄×C₄₁	—	2	1	no	—
191	C₄×C₄₁	—	2	1	no	—
192	C₄×C₄₁	—	2	1	no	—
193	C₄×C₄₁	—	2	1	no	—
194	C₄×C₄₁	—	4	1	no	—
195	C₄×C₄₁	—	4	1	no	—
196	C₄×C₄₁	—	4	1	no	—
197	C₄×C₄₁	—	8	2	no	—
198	C₄×C₄₁	—	8	2	no	—
199	C₄×C₄₁	C₂×#135	1	1	yes	characteristic
200	C₄×C₄₁	#575	1	1	yes	characteristic
201	C₄×C₄₁	#578	1	2	yes	—
202	#3233	C₂×C₄₁	1	2	yes	—
203	#3170	C₂×C₄₁	1	1	yes	characteristic, complemented
204	#2966	C₂×C₄₁	1	1	yes	characteristic
205	#1696	C₂×C₄₁	1	1	yes	characteristic, complemented
206	#1695	C₂×C₄₁	1	1	yes	characteristic, complemented
207	#1690	C₂×C₄₁	1	1	yes	characteristic, complemented
208	#1689	C₂×C₄₁	1	1	yes	characteristic, complemented
209	#1684	C₂×C₄₁	1	2	yes	complemented
210	#1683	C₂×C₄₁	1	2	yes	complemented
211	#1564	C₂×C₄₁	1	1	yes	characteristic, complemented
212	#1554	C₂×C₄₁	1	2	yes	complemented
213	C₂×C₄₁	—	4	1	no	—
214	C₂×C₄₁	—	8	1	no	—
215	C₂×C₄₁	#3035	1	1	yes	characteristic
216	C₂×C₄₁	#3059	1	1	yes	characteristic
217	C₂×C₄₁	#3067	1	1	yes	characteristic
218	#533	C₂²×C₄₁	1	2	yes	—
219	#529	C₂²×C₄₁	1	1	yes	characteristic
220	#500	C₂²×C₄₁	1	1	yes	characteristic
221	#499	—	2	2	no	—
222	#494	C₂²×C₄₁	1	1	yes	characteristic
223	#488	—	2	2	no	—
224	#487	C₂²×C₄₁	1	2	yes	—
225	#485	—	2	2	no	—
226	#482	—	2	2	no	—
227	#477	C₂²×C₄₁	1	2	yes	—
228	#476	C₂²×C₄₁	1	2	yes	—
229	#475	C₂²×C₄₁	1	2	yes	—
230	#474	C₂²×C₄₁	1	2	yes	—
231	#467	—	2	1	no	—
232	#467	—	2	1	no	—
233	#446	C₂²×C₄₁	1	1	yes	characteristic
234	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic
235	C₄×Q₁₆	—	2	1	no	—
236	C₄×Q₁₆	—	2	1	no	—
237	#436	C₂²×C₄₁	1	1	yes	characteristic
238	#435	—	2	1	no	—
239	C₈×D₄	—	2	1	no	—
240	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
241	#433	—	2	1	no	—
242	#432	C₂²×C₄₁	1	1	yes	characteristic
243	#431	C₂²×C₄₁	1	2	yes	—
244	#405	—	2	1	no	—
245	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
246	#335	C₂²×C₄₁	1	2	yes	—
247	#334	C₂²×C₄₁	1	1	yes	characteristic
248	#334	C₂²×C₄₁	1	1	yes	characteristic
249	#333	C₂²×C₄₁	1	2	yes	—
250	#333	C₂²×C₄₁	1	2	yes	—
251	#332	C₂²×C₄₁	1	2	yes	—
252	#332	C₂²×C₄₁	1	2	yes	—
253	C₄₁	#19226	1	1	yes	characteristic, direct product factor, Sylow
254	C₂×Q₁₆	—	2	1	no	—
255	C₂×Q₁₆	—	2	1	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂²×C₈	—	2	1	no	—
258	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
259	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
260	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
261	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
262	#126	—	2	1	no	—
263	#125	—	2	2	no	—
264	#125	D₄×C₄₁	1	1	yes	characteristic
265	#124	D₄×C₄₁	1	1	yes	characteristic
266	#123	—	2	1	no	—
267	C₂²⋊Q₈	—	2	2	no	—
268	C₂²⋊Q₈	—	2	2	no	—
269	C₂²⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
270	#121	D₄×C₄₁	1	1	yes	characteristic
271	C₄×Q₈	—	2	2	no	—
272	C₄×Q₈	—	2	2	no	—
273	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
274	C₄×D₄	—	2	1	no	—
275	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
276	#117	—	2	1	no	—
277	#117	—	2	2	no	—
278	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
279	#107	—	2	1	no	—
280	#107	—	2	1	no	—
281	#107	—	2	2	no	—
282	#107	—	2	2	no	—
283	#106	—	2	2	no	—
284	#106	—	2	2	no	—
285	C₄⋊C₈	—	2	1	no	—
286	C₄⋊C₈	—	2	1	no	—
287	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
288	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
289	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
290	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
291	#103	—	2	2	no	—
292	#103	—	2	2	no	—
293	#103	—	2	2	no	—
294	#103	—	2	2	no	—
295	#102	—	2	2	no	—
296	#102	—	2	2	no	—
297	C₂²⋊C₈	—	2	2	no	—
298	C₂²⋊C₈	—	2	1	no	—
299	C₂²⋊C₈	—	2	1	no	—
300	C₂²⋊C₈	—	2	1	no	—
301	#97	—	2	1	no	—
302	#97	—	2	1	no	—
303	C₄×C₈	—	2	1	no	—
304	C₄×C₈	—	2	2	no	—
305	C₄×C₈	D₄×C₄₁	1	1	yes	characteristic
306	C₄×C₈	D₄×C₄₁	1	1	yes	characteristic
307	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
308	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
317	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
318	Q₁₆	—	4	2	no	—
319	Q₁₆	—	4	2	no	—
320	M₁₆	—	4	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	4	2	no	—
328	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
329	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
330	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
331	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
343	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
344	C₂²⋊C₄	—	2	1	no	—
345	C₂²⋊C₄	—	2	1	no	—
346	C₂²⋊C₄	—	2	1	no	—
347	C₂²⋊C₄	—	2	1	no	—
348	C₂²⋊C₄	—	2	1	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	4	2	no	—
352	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
353	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
354	C₄²	#41×C₄₁	1	1	yes	characteristic
355	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
356	C₂³	—	2	1	no	—
357	C₂³	#121×C₄₁	1	1	yes	characteristic
358	Q₈	—	2	2	no	—
359	Q₈	—	4	2	no	—
360	Q₈	—	4	2	no	—
361	Q₈	—	8	2	no	—
362	D₄	—	2	2	no	—
363	D₄	—	4	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
376	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
377	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
378	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
379	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
380	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
381	C₈	—	2	1	no	—
382	C₈	—	2	1	no	—
383	C₈	—	2	1	no	—
384	C₈	—	4	1	no	—
385	C₈	—	4	1	no	—
386	C₈	—	4	2	no	—
387	C₈	—	4	2	no	—
388	C₈	#135×C₄₁	1	2	yes	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	4	1	no	—
401	C₄	—	4	1	no	—
402	C₄	—	4	1	no	—
403	C₄	—	8	2	no	—
404	C₄	—	8	2	no	—
405	C₄	C₂×#135×C₄₁	1	1	yes	characteristic
406	C₄	C₄₁×#575	1	1	yes	characteristic
407	C₄	C₄₁×#578	1	2	yes	—
408	C₂	—	4	1	no	—
409	C₂	—	8	1	no	—
410	C₂	C₄₁×#3035	1	1	yes	characteristic
411	C₂	C₄₁×#3059	1	1	yes	characteristic
412	C₂	C₄₁×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
prime radical	#121×C₄₁	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ 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. C₄₁×#3170	C₂	semidirect
4. C₄₁×#1696	C₂	semidirect
5. C₄₁×#1695	C₂	semidirect
6. C₄₁×#1690	C₂	semidirect
7. C₄₁×#1689	C₂	semidirect
8. C₄₁×#1684	C₂	semidirect
9. C₄₁×#1683	C₂	semidirect
10. C₄₁×#1564	C₂	semidirect
11. C₄₁×#1554	C₂	semidirect
182. #19226	C₄₁	direct (N × H)
203. #3170	C₂×C₄₁	semidirect
205. #1696	C₂×C₄₁	semidirect
206. #1695	C₂×C₄₁	semidirect
207. #1690	C₂×C₄₁	semidirect
208. #1689	C₂×C₄₁	semidirect
209. #1684	C₂×C₄₁	semidirect
210. #1683	C₂×C₄₁	semidirect
211. #1564	C₂×C₄₁	semidirect
212. #1554	C₂×C₄₁	semidirect
253. C₄₁	#19226	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×#3233	2
C₄₁×#3170	2
C₄₁×#2966	2
C₄₁×#1696	2
C₄₁×#1695	2
C₄₁×#1690	2
C₄₁×#1689	2
C₄₁×#1684	2
C₄₁×#1683	2
C₄₁×#1564	2
C₄₁×#1554	2
#19226	41

Subgroups — C41×#19226 #23795427

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#19226 #23795427