Subgroups — C₄₁×#17389 #23793590

Order 10496.

1040 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#540	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2975	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2972	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1471	C₂	1	4	yes	maximal, complemented
5	C₄₁×#1468	C₂	1	4	yes	maximal, complemented
6	C₄₁×#1460	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1458	C₂	1	2	yes	maximal, complemented
8	C₄₁×#540	—	2	4	no	—
9	C₄₁×#540	—	2	4	no	—
10	C₂×#127×C₄₁	C₄	1	1	yes	characteristic
11	C₂×#125×C₄₁	C₄	1	1	yes	characteristic
12	C₂×#123×C₄₁	C₄	1	2	yes	—
13	C₂×#123×C₄₁	C₂²	1	2	yes	—
14	C₂×#121×C₄₁	C₄	1	2	yes	—
15	C₂×#121×C₄₁	C₄	1	1	yes	characteristic
16	C₂×#121×C₄₁	C₄	1	1	yes	characteristic
17	C₂×#121×C₄₁	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
21	C₄₁×#436	—	2	4	no	—
22	C₈×D₄×C₄₁	—	2	4	no	—
23	C₄₁×#431	C₂²	1	2	yes	—
24	C₄₁×#431	C₂²	1	2	yes	—
25	C₄₁×#407	C₂²	1	4	yes	—
26	C₂×C₂²⋊C₈×C₄₁	C₂²	1	4	yes	—
27	C₄₁×#324	C₂²	1	4	yes	—
28	C₄₁×#323	C₂²	1	4	yes	—
29	C₄₁×#323	C₂²	1	8	yes	—
30	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
31	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
32	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
33	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
34	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
35	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
36	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
39	C₂×M₁₆×C₄₁	—	2	4	no	—
40	C₂²×C₈×C₄₁	—	2	4	no	—
41	#127×C₄₁	—	2	4	no	—
42	#125×C₄₁	—	2	4	no	—
43	#123×C₄₁	—	2	4	no	—
44	#123×C₄₁	—	2	4	no	—
45	#123×C₄₁	—	2	8	no	—
46	#121×C₄₁	—	2	4	no	—
47	#121×C₄₁	—	2	4	no	—
48	#121×C₄₁	—	2	4	no	—
49	#121×C₄₁	—	2	4	no	—
50	#121×C₄₁	—	2	8	no	—
51	C₄×D₄×C₄₁	—	2	2	no	—
52	C₄×D₄×C₄₁	—	2	2	no	—
53	C₄×D₄×C₄₁	D₄	1	4	yes	—
54	C₄×D₄×C₄₁	D₄	1	4	yes	—
55	#117×C₄₁	—	2	2	no	—
56	#117×C₄₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
65	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
66	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
67	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
69	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₄₁	—	2	2	no	—
72	C₄⋊C₈×C₄₁	—	2	2	no	—
73	C₂²⋊C₈×C₄₁	—	2	4	no	—
74	C₂²⋊C₈×C₄₁	—	2	4	no	—
75	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
76	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
77	C₄×C₈×C₄₁	—	2	2	no	—
78	C₄×C₈×C₄₁	—	2	2	no	—
79	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
80	C₂⁴×C₄₁	C₂²×C₄	1	2	yes	—
81	C₂⁴×C₄₁	C₂²×C₄	1	2	yes	—
82	C₂×D₄×C₄₁	—	2	4	no	—
83	C₂×D₄×C₄₁	—	2	4	no	—
84	C₂×D₄×C₄₁	—	2	4	no	—
85	C₂×D₄×C₄₁	—	2	2	no	—
86	C₂×D₄×C₄₁	—	2	4	no	—
87	C₂×D₄×C₄₁	—	2	4	no	—
88	C₂×D₄×C₄₁	—	2	4	no	—
89	C₂×D₄×C₄₁	—	8	2	no	—
90	C₂×D₄×C₄₁	—	8	2	no	—
91	C₂×D₄×C₄₁	—	8	2	no	—
92	C₂×D₄×C₄₁	—	8	2	no	—
93	C₂×D₄×C₄₁	C₂²⋊C₄	1	4	yes	—
94	C₂²×C₄×C₄₁	—	2	2	no	—
95	C₂²×C₄×C₄₁	—	2	4	no	—
96	C₂²×C₄×C₄₁	—	2	4	no	—
97	C₂²×C₄×C₄₁	—	8	2	no	—
98	C₂²×C₄×C₄₁	—	8	2	no	—
99	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
109	M₁₆×C₄₁	—	8	4	no	—
110	C₂×C₈×C₄₁	—	2	4	no	—
111	C₂×C₈×C₄₁	—	2	4	no	—
112	C₂×C₈×C₄₁	—	8	4	no	—
113	C₄⋊C₄×C₄₁	—	2	2	no	—
114	C₄⋊C₄×C₄₁	—	2	2	no	—
115	C₄⋊C₄×C₄₁	—	2	4	no	—
116	C₄⋊C₄×C₄₁	—	2	4	no	—
117	C₄⋊C₄×C₄₁	—	2	1	no	—
118	C₄⋊C₄×C₄₁	—	2	1	no	—
119	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
120	C₂²⋊C₄×C₄₁	—	2	4	no	—
121	C₂²⋊C₄×C₄₁	—	2	2	no	—
122	C₂²⋊C₄×C₄₁	—	2	4	no	—
123	C₂²⋊C₄×C₄₁	—	2	1	no	—
124	C₂²⋊C₄×C₄₁	—	2	1	no	—
125	C₂²⋊C₄×C₄₁	—	2	2	no	—
126	C₂²⋊C₄×C₄₁	—	2	2	no	—
127	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	8	yes	—
128	C₄²×C₄₁	—	2	2	no	—
129	C₄²×C₄₁	C₂×D₄	1	2	yes	—
130	C₄²×C₄₁	C₂×D₄	1	2	yes	—
131	C₂³×C₄₁	—	2	4	no	—
132	C₂³×C₄₁	—	2	1	no	—
133	C₂³×C₄₁	—	2	2	no	—
134	C₂³×C₄₁	—	2	2	no	—
135	C₂³×C₄₁	—	2	4	no	—
136	C₂³×C₄₁	—	4	2	no	—
137	C₂³×C₄₁	—	4	2	no	—
138	C₂³×C₄₁	—	4	2	no	—
139	C₂³×C₄₁	—	4	1	no	—
140	C₂³×C₄₁	—	4	2	no	—
141	C₂³×C₄₁	—	4	1	no	—
142	C₂³×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
143	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
144	D₄×C₄₁	—	2	8	no	—
145	D₄×C₄₁	—	4	4	no	—
146	D₄×C₄₁	—	8	4	no	—
147	D₄×C₄₁	—	8	4	no	—
148	D₄×C₄₁	—	8	4	no	—
149	D₄×C₄₁	—	8	4	no	—
150	C₂×C₄×C₄₁	—	2	1	no	—
151	C₂×C₄×C₄₁	—	2	1	no	—
152	C₂×C₄×C₄₁	—	2	1	no	—
153	C₂×C₄×C₄₁	—	2	2	no	—
154	C₂×C₄×C₄₁	—	2	2	no	—
155	C₂×C₄×C₄₁	—	4	4	no	—
156	C₂×C₄×C₄₁	—	4	4	no	—
157	C₂×C₄×C₄₁	—	4	1	no	—
158	C₂×C₄×C₄₁	—	4	1	no	—
159	C₂×C₄×C₄₁	—	4	2	no	—
160	C₂×C₄×C₄₁	—	4	4	no	—
161	C₂×C₄×C₄₁	—	4	2	no	—
162	C₂×C₄×C₄₁	—	4	1	no	—
163	C₂×C₄×C₄₁	—	4	1	no	—
164	C₂×C₄×C₄₁	—	8	4	no	—
165	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
167	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₄₁	#131	1	4	yes	—
169	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
171	C₈×C₄₁	—	4	4	no	—
172	C₈×C₄₁	—	4	4	no	—
173	#17389	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂²×C₄₁	—	2	1	no	—
175	C₂²×C₄₁	—	2	1	no	—
176	C₂²×C₄₁	—	2	4	no	—
177	C₂²×C₄₁	—	2	4	no	—
178	C₂²×C₄₁	—	2	4	no	—
179	C₂²×C₄₁	—	4	1	no	—
180	C₂²×C₄₁	—	4	2	no	—
181	C₂²×C₄₁	—	4	1	no	—
182	C₂²×C₄₁	—	4	2	no	—
183	C₂²×C₄₁	—	4	2	no	—
184	C₂²×C₄₁	—	4	1	no	—
185	C₂²×C₄₁	—	8	4	no	—
186	C₂²×C₄₁	—	8	2	no	—
187	C₂²×C₄₁	—	8	4	no	—
188	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
189	C₂²×C₄₁	C₂×#131	1	2	yes	—
190	C₄×C₄₁	—	2	1	no	—
191	C₄×C₄₁	—	2	1	no	—
192	C₄×C₄₁	—	2	4	no	—
193	C₄×C₄₁	—	2	2	no	—
194	C₄×C₄₁	—	4	1	no	—
195	C₄×C₄₁	—	4	1	no	—
196	C₄×C₄₁	—	4	2	no	—
197	C₄×C₄₁	—	4	1	no	—
198	C₄×C₄₁	#408	1	4	yes	—
199	C₂×#540	C₂×C₄₁	1	1	yes	characteristic
200	#2975	C₂×C₄₁	1	1	yes	characteristic, complemented
201	#2972	C₂×C₄₁	1	1	yes	characteristic, complemented
202	#1471	C₂×C₄₁	1	4	yes	complemented
203	#1468	C₂×C₄₁	1	4	yes	complemented
204	#1460	C₂×C₄₁	1	2	yes	complemented
205	#1458	C₂×C₄₁	1	2	yes	complemented
206	C₂×C₄₁	—	2	2	no	—
207	C₂×C₄₁	—	4	4	no	—
208	C₂×C₄₁	—	8	1	no	—
209	C₂×C₄₁	—	8	2	no	—
210	C₂×C₄₁	C₂×#408	1	1	yes	characteristic
211	C₂×C₄₁	#2883	1	1	yes	characteristic
212	C₂×C₄₁	#2888	1	1	yes	characteristic
213	#540	—	2	4	no	—
214	#540	—	2	4	no	—
215	C₂×#127	C₄×C₄₁	1	1	yes	characteristic
216	C₂×#125	C₄×C₄₁	1	1	yes	characteristic
217	C₂×#123	C₄×C₄₁	1	2	yes	—
218	C₂×#123	C₂²×C₄₁	1	2	yes	—
219	C₂×#121	C₄×C₄₁	1	2	yes	—
220	C₂×#121	C₄×C₄₁	1	1	yes	characteristic
221	C₂×#121	C₄×C₄₁	1	1	yes	characteristic
222	C₂×#121	C₂²×C₄₁	1	2	yes	—
223	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
224	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
225	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
226	#436	—	2	4	no	—
227	C₈×D₄	—	2	4	no	—
228	#431	C₂²×C₄₁	1	2	yes	—
229	#431	C₂²×C₄₁	1	2	yes	—
230	#407	C₂²×C₄₁	1	4	yes	—
231	C₂×C₂²⋊C₈	C₂²×C₄₁	1	4	yes	—
232	#324	C₂²×C₄₁	1	4	yes	—
233	#323	C₂²×C₄₁	1	4	yes	—
234	#323	C₂²×C₄₁	1	8	yes	—
235	C₄₁	#17389	1	1	yes	characteristic, direct product factor, Sylow
236	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
237	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
238	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
239	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
240	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
241	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
242	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
243	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
244	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
245	C₂×M₁₆	—	2	4	no	—
246	C₂²×C₈	—	2	4	no	—
247	#127	—	2	4	no	—
248	#125	—	2	4	no	—
249	#123	—	2	4	no	—
250	#123	—	2	4	no	—
251	#123	—	2	8	no	—
252	#121	—	2	4	no	—
253	#121	—	2	4	no	—
254	#121	—	2	4	no	—
255	#121	—	2	4	no	—
256	#121	—	2	8	no	—
257	C₄×D₄	—	2	2	no	—
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	D₄×C₄₁	1	4	yes	—
260	C₄×D₄	D₄×C₄₁	1	4	yes	—
261	#117	—	2	2	no	—
262	#117	—	2	2	no	—
263	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
266	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
267	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
271	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
272	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
273	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
275	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
276	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	—	2	2	no	—
279	C₂²⋊C₈	—	2	4	no	—
280	C₂²⋊C₈	—	2	4	no	—
281	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
282	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
283	C₄×C₈	—	2	2	no	—
284	C₄×C₈	—	2	2	no	—
285	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
286	C₂⁴	C₂²×C₄×C₄₁	1	2	yes	—
287	C₂⁴	C₂²×C₄×C₄₁	1	2	yes	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	2	4	no	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	2	4	no	—
295	C₂×D₄	—	8	2	no	—
296	C₂×D₄	—	8	2	no	—
297	C₂×D₄	—	8	2	no	—
298	C₂×D₄	—	8	2	no	—
299	C₂×D₄	C₂²⋊C₄×C₄₁	1	4	yes	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	8	2	no	—
304	C₂²×C₄	—	8	2	no	—
305	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
306	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
307	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
308	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
309	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
310	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
311	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
313	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
314	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
315	M₁₆	—	8	4	no	—
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	2	4	no	—
318	C₂×C₈	—	8	4	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
326	C₂²⋊C₄	—	2	4	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	2	1	no	—
330	C₂²⋊C₄	—	2	1	no	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	2	2	no	—
333	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	8	yes	—
334	C₄²	—	2	2	no	—
335	C₄²	C₂×D₄×C₄₁	1	2	yes	—
336	C₄²	C₂×D₄×C₄₁	1	2	yes	—
337	C₂³	—	2	4	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	2	4	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	1	no	—
348	C₂³	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
349	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
350	D₄	—	2	8	no	—
351	D₄	—	4	4	no	—
352	D₄	—	8	4	no	—
353	D₄	—	8	4	no	—
354	D₄	—	8	4	no	—
355	D₄	—	8	4	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	8	4	no	—
371	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
372	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
373	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
374	C₂×C₄	#131×C₄₁	1	4	yes	—
375	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
376	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
377	C₈	—	4	4	no	—
378	C₈	—	4	4	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	2	4	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	8	4	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	4	no	—
393	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
394	C₂²	C₂×#131×C₄₁	1	2	yes	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	4	no	—
398	C₄	—	2	2	no	—
399	C₄	—	4	1	no	—
400	C₄	—	4	1	no	—
401	C₄	—	4	2	no	—
402	C₄	—	4	1	no	—
403	C₄	C₄₁×#408	1	4	yes	—
404	C₂	—	2	2	no	—
405	C₂	—	4	4	no	—
406	C₂	—	8	1	no	—
407	C₂	—	8	2	no	—
408	C₂	C₂×C₄₁×#408	1	1	yes	characteristic
409	C₂	C₄₁×#2883	1	1	yes	characteristic
410	C₂	C₄₁×#2888	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#540	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄×D₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2975	C₂	semidirect
3. C₄₁×#2972	C₂	semidirect
4. C₄₁×#1471	C₂	semidirect
5. C₄₁×#1468	C₂	semidirect
6. C₄₁×#1460	C₂	semidirect
7. C₄₁×#1458	C₂	semidirect
173. #17389	C₄₁	direct (N × H)
200. #2975	C₂×C₄₁	semidirect
201. #2972	C₂×C₄₁	semidirect
202. #1471	C₂×C₄₁	semidirect
203. #1468	C₂×C₄₁	semidirect
204. #1460	C₂×C₄₁	semidirect
205. #1458	C₂×C₄₁	semidirect
235. C₄₁	#17389	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×#540	2
C₄₁×#2975	2
C₄₁×#2972	2
C₄₁×#1471	2
C₄₁×#1468	2
C₄₁×#1460	2
C₄₁×#1458	2
#17389	41

Subgroups — C41×#17389 #23793590

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#17389 #23793590