Subgroups — C₄₁×#29114 #23805315

Order 10496.

866 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2851	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#2297	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2074	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2073	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2026	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2025	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1936	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1935	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1825	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1788	C₂	1	2	yes	maximal
11	C₄₁×#1749	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×#103×C₄₁	C₂²	1	2	yes	—
17	C₂×#103×C₄₁	C₂²	1	2	yes	—
18	C₂×#102×C₄₁	C₂²	1	2	yes	—
19	C₂×#102×C₄₁	C₂²	1	2	yes	—
20	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
21	C₂×#97×C₄₁	C₂²	1	2	yes	—
22	C₄₁×#391	C₂²	1	1	yes	characteristic
23	C₄₁×#391	C₂²	1	1	yes	characteristic
24	C₄₁×#390	C₂²	1	1	yes	characteristic
25	C₄₁×#390	C₂²	1	1	yes	characteristic
26	C₄₁×#389	C₂²	1	2	yes	—
27	C₄₁×#387	—	2	2	no	—
28	C₄₁×#386	—	2	2	no	—
29	C₄₁×#385	—	2	2	no	—
30	C₄₁×#382	C₂²	1	1	yes	characteristic
31	C₄₁×#380	C₂²	1	2	yes	—
32	C₄×C₂²⋊C₄×C₄₁	—	2	2	no	—
33	C₄₁×#340	C₂²	1	2	yes	—
34	C₄₁×#340	C₂²	1	2	yes	—
35	C₄₁×#340	C₂²	1	2	yes	—
36	C₄₁×#340	C₂²	1	2	yes	—
37	C₄₁×#336	C₂²	1	1	yes	characteristic
38	C₄₁×#336	C₂²	1	1	yes	characteristic
39	C₂×#41×C₄₁	—	2	2	no	—
40	C₂×#41×C₄₁	—	2	2	no	—
41	C₂×#41×C₄₁	—	2	4	no	—
42	C₂×#41×C₄₁	—	4	2	no	—
43	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₄₁	—	2	1	no	—
45	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₁	—	2	1	no	—
47	C₂³×C₄×C₄₁	D₄	1	2	yes	—
48	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
50	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
51	#125×C₄₁	—	4	2	no	—
52	#117×C₄₁	—	2	4	no	—
53	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
59	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
60	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
63	C₂×C₄²×C₄₁	—	2	1	no	—
64	C₂×C₄²×C₄₁	—	4	2	no	—
65	C₂×C₄²×C₄₁	D₄	1	2	yes	—
66	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
68	#103×C₄₁	—	2	4	no	—
69	#103×C₄₁	—	4	2	no	—
70	#102×C₄₁	—	2	4	no	—
71	#102×C₄₁	—	4	2	no	—
72	C₂²⋊C₈×C₄₁	—	2	4	no	—
73	#97×C₄₁	—	4	2	no	—
74	#95×C₄₁	—	2	2	no	—
75	#95×C₄₁	—	2	2	no	—
76	#95×C₄₁	—	2	2	no	—
77	#95×C₄₁	—	2	2	no	—
78	#95×C₄₁	—	2	2	no	—
79	C₂⁴×C₄₁	—	2	1	no	—
80	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
81	#41×C₄₁	—	4	8	no	—
82	#41×C₄₁	—	4	8	no	—
83	C₂×Q₈×C₄₁	—	2	1	no	—
84	C₂×Q₈×C₄₁	—	2	2	no	—
85	C₂×Q₈×C₄₁	—	2	2	no	—
86	C₂×Q₈×C₄₁	#41	1	2	yes	—
87	C₂×D₄×C₄₁	—	2	4	no	—
88	C₂×D₄×C₄₁	—	2	2	no	—
89	C₂×D₄×C₄₁	—	2	1	no	—
90	C₂×D₄×C₄₁	—	2	2	no	—
91	C₂×D₄×C₄₁	—	4	2	no	—
92	C₂×D₄×C₄₁	—	4	2	no	—
93	C₂×D₄×C₄₁	#41	1	2	yes	—
94	C₂²×C₄×C₄₁	—	2	1	no	—
95	C₂²×C₄×C₄₁	—	2	1	no	—
96	C₂²×C₄×C₄₁	—	2	2	no	—
97	C₂²×C₄×C₄₁	—	2	4	no	—
98	C₂²×C₄×C₄₁	—	2	1	no	—
99	C₂²×C₄×C₄₁	—	2	2	no	—
100	C₂²×C₄×C₄₁	—	2	1	no	—
101	C₂²×C₄×C₄₁	—	2	1	no	—
102	C₂²×C₄×C₄₁	—	2	2	no	—
103	C₂²×C₄×C₄₁	—	4	2	no	—
104	C₂²×C₄×C₄₁	—	4	2	no	—
105	C₂²×C₄×C₄₁	—	4	2	no	—
106	C₂²×C₄×C₄₁	—	4	2	no	—
107	C₂²×C₄×C₄₁	—	4	2	no	—
108	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₁	#41	1	4	yes	—
112	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
113	C₂×C₈×C₄₁	—	2	2	no	—
114	C₂×C₈×C₄₁	—	2	2	no	—
115	C₂×C₈×C₄₁	—	2	2	no	—
116	C₂×C₈×C₄₁	—	2	2	no	—
117	C₂×C₈×C₄₁	—	2	2	no	—
118	C₂×C₈×C₄₁	—	2	2	no	—
119	C₄⋊C₄×C₄₁	—	2	2	no	—
120	C₄⋊C₄×C₄₁	—	2	2	no	—
121	C₄⋊C₄×C₄₁	—	2	2	no	—
122	C₄⋊C₄×C₄₁	—	2	2	no	—
123	C₄⋊C₄×C₄₁	—	2	2	no	—
124	C₄⋊C₄×C₄₁	—	2	2	no	—
125	C₄⋊C₄×C₄₁	—	4	4	no	—
126	C₄⋊C₄×C₄₁	—	4	4	no	—
127	C₂²⋊C₄×C₄₁	—	4	4	no	—
128	C₂²⋊C₄×C₄₁	—	4	4	no	—
129	C₂²⋊C₄×C₄₁	—	4	4	no	—
130	C₂²⋊C₄×C₄₁	—	4	2	no	—
131	C₄²×C₄₁	—	2	2	no	—
132	C₄²×C₄₁	—	2	2	no	—
133	C₄²×C₄₁	—	4	2	no	—
134	C₄²×C₄₁	—	4	2	no	—
135	C₂³×C₄₁	—	2	1	no	—
136	C₂³×C₄₁	—	2	1	no	—
137	C₂³×C₄₁	—	2	2	no	—
138	C₂³×C₄₁	—	2	2	no	—
139	C₂³×C₄₁	—	2	2	no	—
140	C₂³×C₄₁	—	4	1	no	—
141	C₂³×C₄₁	—	4	1	no	—
142	C₂³×C₄₁	—	4	2	no	—
143	C₂³×C₄₁	—	4	2	no	—
144	C₂³×C₄₁	#124	1	2	yes	—
145	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₄₁	—	2	4	no	—
147	Q₈×C₄₁	—	4	2	no	—
148	D₄×C₄₁	—	2	4	no	—
149	D₄×C₄₁	—	4	8	no	—
150	D₄×C₄₁	—	4	2	no	—
151	C₂×C₄×C₄₁	—	2	1	no	—
152	C₂×C₄×C₄₁	—	2	1	no	—
153	C₂×C₄×C₄₁	—	2	4	no	—
154	C₂×C₄×C₄₁	—	2	4	no	—
155	C₂×C₄×C₄₁	—	2	2	no	—
156	C₂×C₄×C₄₁	—	2	2	no	—
157	C₂×C₄×C₄₁	—	2	2	no	—
158	C₂×C₄×C₄₁	—	2	2	no	—
159	C₂×C₄×C₄₁	—	2	2	no	—
160	C₂×C₄×C₄₁	—	2	2	no	—
161	C₂×C₄×C₄₁	—	2	2	no	—
162	C₂×C₄×C₄₁	—	4	8	no	—
163	C₂×C₄×C₄₁	—	4	8	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	1	no	—
168	C₂×C₄×C₄₁	—	4	1	no	—
169	C₂×C₄×C₄₁	—	4	2	no	—
170	C₂×C₄×C₄₁	—	4	2	no	—
171	C₂×C₄×C₄₁	—	4	2	no	—
172	C₂×C₄×C₄₁	—	4	2	no	—
173	C₂×C₄×C₄₁	—	4	2	no	—
174	C₂×C₄×C₄₁	—	4	2	no	—
175	C₂×C₄×C₄₁	—	4	2	no	—
176	C₂×C₄×C₄₁	#124	1	2	yes	—
177	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
180	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
181	C₈×C₄₁	—	4	2	no	—
182	C₈×C₄₁	—	4	2	no	—
183	#29114	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂²×C₄₁	—	2	2	no	—
185	C₂²×C₄₁	—	2	2	no	—
186	C₂²×C₄₁	—	2	2	no	—
187	C₂²×C₄₁	—	4	2	no	—
188	C₂²×C₄₁	—	4	2	no	—
189	C₂²×C₄₁	—	4	2	no	—
190	C₂²×C₄₁	—	4	4	no	—
191	C₂²×C₄₁	—	8	1	no	—
192	C₂²×C₄₁	—	8	1	no	—
193	C₂²×C₄₁	—	8	2	no	—
194	C₂²×C₄₁	#525	1	1	yes	characteristic
195	C₂²×C₄₁	C₂×#124	1	1	yes	characteristic
196	C₂²×C₄₁	#534	1	1	yes	characteristic
197	C₂²×C₄₁	#575	1	2	yes	—
198	C₂²×C₄₁	#575	1	2	yes	—
199	C₄×C₄₁	—	2	2	no	—
200	C₄×C₄₁	—	4	2	no	—
201	C₄×C₄₁	—	4	2	no	—
202	C₄×C₄₁	—	4	2	no	—
203	C₄×C₄₁	—	8	2	no	—
204	C₄×C₄₁	—	8	1	no	—
205	C₄×C₄₁	—	8	1	no	—
206	C₄×C₄₁	—	8	2	no	—
207	C₄×C₄₁	#551	1	2	yes	—
208	C₄×C₄₁	#551	1	2	yes	—
209	#2851	C₂×C₄₁	1	1	yes	characteristic, complemented
210	#2297	C₂×C₄₁	1	1	yes	characteristic
211	#2074	C₂×C₄₁	1	1	yes	characteristic, complemented
212	#2073	C₂×C₄₁	1	1	yes	characteristic, complemented
213	#2026	C₂×C₄₁	1	1	yes	characteristic, complemented
214	#2025	C₂×C₄₁	1	1	yes	characteristic, complemented
215	#1936	C₂×C₄₁	1	2	yes	complemented
216	#1935	C₂×C₄₁	1	2	yes	complemented
217	#1825	C₂×C₄₁	1	2	yes	complemented
218	#1788	C₂×C₄₁	1	2	yes	—
219	#1749	C₂×C₄₁	1	1	yes	characteristic, complemented
220	C₂×C₄₁	—	4	2	no	—
221	C₂×C₄₁	—	8	2	no	—
222	C₂×C₄₁	#2561	1	1	yes	characteristic
223	C₂×C₄₁	#3111	1	2	yes	—
224	C₂×C₄₁	#3135	1	1	yes	characteristic
225	C₂×C₄₁	#3142	1	1	yes	characteristic
226	C₂×C₄₁	#3197	1	2	yes	—
227	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
228	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic
229	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
230	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
231	C₂×#103	C₂²×C₄₁	1	2	yes	—
232	C₂×#103	C₂²×C₄₁	1	2	yes	—
233	C₂×#102	C₂²×C₄₁	1	2	yes	—
234	C₂×#102	C₂²×C₄₁	1	2	yes	—
235	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
236	C₂×#97	C₂²×C₄₁	1	2	yes	—
237	#391	C₂²×C₄₁	1	1	yes	characteristic
238	#391	C₂²×C₄₁	1	1	yes	characteristic
239	#390	C₂²×C₄₁	1	1	yes	characteristic
240	#390	C₂²×C₄₁	1	1	yes	characteristic
241	#389	C₂²×C₄₁	1	2	yes	—
242	#387	—	2	2	no	—
243	#386	—	2	2	no	—
244	#385	—	2	2	no	—
245	#382	C₂²×C₄₁	1	1	yes	characteristic
246	#380	C₂²×C₄₁	1	2	yes	—
247	C₄×C₂²⋊C₄	—	2	2	no	—
248	#340	C₂²×C₄₁	1	2	yes	—
249	#340	C₂²×C₄₁	1	2	yes	—
250	#340	C₂²×C₄₁	1	2	yes	—
251	#340	C₂²×C₄₁	1	2	yes	—
252	#336	C₂²×C₄₁	1	1	yes	characteristic
253	#336	C₂²×C₄₁	1	1	yes	characteristic
254	C₄₁	#29114	1	1	yes	characteristic, direct product factor, Sylow
255	C₂×#41	—	2	2	no	—
256	C₂×#41	—	2	2	no	—
257	C₂×#41	—	2	4	no	—
258	C₂×#41	—	4	2	no	—
259	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
260	C₂²×D₄	—	2	1	no	—
261	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
262	C₂³×C₄	—	2	1	no	—
263	C₂³×C₄	D₄×C₄₁	1	2	yes	—
264	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
266	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
267	#125	—	4	2	no	—
268	#117	—	2	4	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
274	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	—	4	2	no	—
281	C₂×C₄²	D₄×C₄₁	1	2	yes	—
282	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
283	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
284	#103	—	2	4	no	—
285	#103	—	4	2	no	—
286	#102	—	2	4	no	—
287	#102	—	4	2	no	—
288	C₂²⋊C₈	—	2	4	no	—
289	#97	—	4	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	#95	—	2	2	no	—
293	#95	—	2	2	no	—
294	#95	—	2	2	no	—
295	C₂⁴	—	2	1	no	—
296	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
297	#41	—	4	8	no	—
298	#41	—	4	8	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	#41×C₄₁	1	2	yes	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂×D₄	#41×C₄₁	1	2	yes	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	4	2	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
325	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
326	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
327	C₂²×C₄	#41×C₄₁	1	4	yes	—
328	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₄⋊C₄	—	2	2	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	—	2	2	no	—
341	C₄⋊C₄	—	4	4	no	—
342	C₄⋊C₄	—	4	4	no	—
343	C₂²⋊C₄	—	4	4	no	—
344	C₂²⋊C₄	—	4	4	no	—
345	C₂²⋊C₄	—	4	4	no	—
346	C₂²⋊C₄	—	4	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	4	2	no	—
350	C₄²	—	4	2	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	4	1	no	—
357	C₂³	—	4	1	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	#124×C₄₁	1	2	yes	—
361	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
362	Q₈	—	2	4	no	—
363	Q₈	—	4	2	no	—
364	D₄	—	2	4	no	—
365	D₄	—	4	8	no	—
366	D₄	—	4	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	8	no	—
379	C₂×C₄	—	4	8	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	#124×C₄₁	1	2	yes	—
393	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
394	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
395	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
396	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
397	C₈	—	4	2	no	—
398	C₈	—	4	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	4	2	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	8	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	2	no	—
409	C₂²	C₄₁×#525	1	1	yes	characteristic
410	C₂²	C₂×#124×C₄₁	1	1	yes	characteristic
411	C₂²	C₄₁×#534	1	1	yes	characteristic
412	C₂²	C₄₁×#575	1	2	yes	—
413	C₂²	C₄₁×#575	1	2	yes	—
414	C₄	—	2	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	2	no	—
418	C₄	—	8	2	no	—
419	C₄	—	8	1	no	—
420	C₄	—	8	1	no	—
421	C₄	—	8	2	no	—
422	C₄	C₄₁×#551	1	2	yes	—
423	C₄	C₄₁×#551	1	2	yes	—
424	C₂	—	4	2	no	—
425	C₂	—	8	2	no	—
426	C₂	C₄₁×#2561	1	1	yes	characteristic
427	C₂	C₄₁×#3111	1	2	yes	—
428	C₂	C₄₁×#3135	1	1	yes	characteristic
429	C₂	C₄₁×#3142	1	1	yes	characteristic
430	C₂	C₄₁×#3197	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×#41×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#2851	C₂	semidirect
3. C₄₁×#2074	C₂	semidirect
4. C₄₁×#2073	C₂	semidirect
5. C₄₁×#2026	C₂	semidirect
6. C₄₁×#2025	C₂	semidirect
7. C₄₁×#1936	C₂	semidirect
8. C₄₁×#1935	C₂	semidirect
9. C₄₁×#1825	C₂	semidirect
11. C₄₁×#1749	C₂	semidirect
183. #29114	C₄₁	direct (N × H)
209. #2851	C₂×C₄₁	semidirect
211. #2074	C₂×C₄₁	semidirect
212. #2073	C₂×C₄₁	semidirect
213. #2026	C₂×C₄₁	semidirect
214. #2025	C₂×C₄₁	semidirect
215. #1936	C₂×C₄₁	semidirect
216. #1935	C₂×C₄₁	semidirect
217. #1825	C₂×C₄₁	semidirect
219. #1749	C₂×C₄₁	semidirect
254. C₄₁	#29114	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×#2851	2
C₄₁×#2297	2
C₄₁×#2074	2
C₄₁×#2073	2
C₄₁×#2026	2
C₄₁×#2025	2
C₄₁×#1936	2
C₄₁×#1935	2
C₄₁×#1825	2
C₄₁×#1788	2
C₄₁×#1749	2
#29114	41

Subgroups — C41×#29114 #23805315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#29114 #23805315