Subgroups — C₄₁×#24134 #23800335

Order 10496.

1120 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#554	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#441	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2536	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#2035	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2001	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1955	C₂	1	1	yes	maximal, characteristic
9	C₄₁×#1872	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1853	C₂	1	2	yes	maximal, complemented
11	C₄₁×#1805	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
13	C₄₁×#554	—	2	4	no	—
14	C₄₁×#554	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×#125×C₄₁	—	2	1	no	—
17	C₂×C₂²⋊Q₈×C₄₁	—	2	2	no	—
18	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
19	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₄₁	—	2	1	no	—
23	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
25	C₄₁×#475	—	2	4	no	—
26	C₄₁×#441	—	2	4	no	—
27	C₂×#106×C₄₁	C₂²	1	2	yes	—
28	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×#103×C₄₁	C₂²	1	2	yes	—
32	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×#103×C₄₁	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
35	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
36	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
37	C₄₁×#398	—	2	1	no	—
38	C₄₁×#394	—	2	1	no	—
39	C₄₁×#388	—	2	2	no	—
40	C₄₁×#382	C₂²	1	1	yes	characteristic
41	C₄₁×#380	C₂²	1	2	yes	—
42	C₄₁×#340	C₂²	1	2	yes	—
43	C₄₁×#340	C₂²	1	2	yes	—
44	C₄₁×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₄₁	—	2	1	no	—
46	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
47	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₁	—	2	2	no	—
50	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
51	C₂×Q₁₆×C₄₁	—	2	2	no	—
52	C₂×Q₁₆×C₄₁	—	2	2	no	—
53	C₂×Q₁₆×C₄₁	—	2	2	no	—
54	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
56	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
57	C₄⋊Q₈×C₄₁	—	2	2	no	—
58	C₄⋊Q₈×C₄₁	D₄	1	4	yes	—
59	#125×C₄₁	—	2	8	no	—
60	C₂²⋊Q₈×C₄₁	—	2	16	no	—
61	C₂²⋊Q₈×C₄₁	—	2	4	no	—
62	C₂²⋊Q₈×C₄₁	—	2	4	no	—
63	C₂²⋊Q₈×C₄₁	—	2	4	no	—
64	C₂²⋊Q₈×C₄₁	—	4	2	no	—
65	C₄×Q₈×C₄₁	—	2	2	no	—
66	C₄×Q₈×C₄₁	—	2	2	no	—
67	C₄×Q₈×C₄₁	—	2	2	no	—
68	C₄×Q₈×C₄₁	D₄	1	4	yes	—
69	C₄×D₄×C₄₁	—	2	8	no	—
70	C₄×D₄×C₄₁	—	2	2	no	—
71	C₄×D₄×C₄₁	—	2	2	no	—
72	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
73	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
74	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
76	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
77	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
78	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
79	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
80	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
85	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
89	C₂×C₄²×C₄₁	—	2	1	no	—
90	C₂×C₄²×C₄₁	—	2	1	no	—
91	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
92	#106×C₄₁	—	2	2	no	—
93	#106×C₄₁	—	2	4	no	—
94	C₄⋊C₈×C₄₁	—	2	2	no	—
95	#103×C₄₁	—	2	2	no	—
96	#103×C₄₁	—	2	2	no	—
97	#103×C₄₁	—	2	4	no	—
98	#103×C₄₁	—	4	2	no	—
99	C₂²⋊C₈×C₄₁	—	2	4	no	—
100	C₂²⋊C₈×C₄₁	—	4	2	no	—
101	#97×C₄₁	—	2	2	no	—
102	#95×C₄₁	—	2	2	no	—
103	#95×C₄₁	—	2	1	no	—
104	#95×C₄₁	—	2	1	no	—
105	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
106	C₂×Q₈×C₄₁	—	2	4	no	—
107	C₂×Q₈×C₄₁	—	2	1	no	—
108	C₂×Q₈×C₄₁	—	2	1	no	—
109	C₂×Q₈×C₄₁	—	2	1	no	—
110	C₂×Q₈×C₄₁	—	2	1	no	—
111	C₂×Q₈×C₄₁	—	2	1	no	—
112	C₂×Q₈×C₄₁	—	2	1	no	—
113	C₂×Q₈×C₄₁	—	2	1	no	—
114	C₂×Q₈×C₄₁	—	2	1	no	—
115	C₂×Q₈×C₄₁	—	2	1	no	—
116	C₂×Q₈×C₄₁	—	2	1	no	—
117	C₂×Q₈×C₄₁	—	8	2	no	—
118	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
119	C₂×Q₈×C₄₁	#41	1	2	yes	—
120	C₂×D₄×C₄₁	—	2	4	no	—
121	C₂×D₄×C₄₁	—	2	2	no	—
122	C₂²×C₄×C₄₁	—	2	1	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	8	no	—
127	C₂²×C₄×C₄₁	—	2	2	no	—
128	C₂²×C₄×C₄₁	—	2	2	no	—
129	C₂²×C₄×C₄₁	—	2	2	no	—
130	C₂²×C₄×C₄₁	—	2	2	no	—
131	C₂²×C₄×C₄₁	—	2	2	no	—
132	C₂²×C₄×C₄₁	—	2	2	no	—
133	C₂²×C₄×C₄₁	—	2	2	no	—
134	C₂²×C₄×C₄₁	—	2	1	no	—
135	C₂²×C₄×C₄₁	—	8	2	no	—
136	C₂²×C₄×C₄₁	—	8	2	no	—
137	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
141	Q₁₆×C₄₁	—	2	8	no	—
142	C₂×C₈×C₄₁	—	2	1	no	—
143	C₂×C₈×C₄₁	—	2	1	no	—
144	C₂×C₈×C₄₁	—	2	1	no	—
145	C₂×C₈×C₄₁	—	2	2	no	—
146	C₂×C₈×C₄₁	—	2	2	no	—
147	C₂×C₈×C₄₁	—	2	1	no	—
148	C₂×C₈×C₄₁	—	2	2	no	—
149	C₂×C₈×C₄₁	—	2	1	no	—
150	C₂×C₈×C₄₁	#41	1	2	yes	—
151	C₄⋊C₄×C₄₁	—	2	8	no	—
152	C₄⋊C₄×C₄₁	—	2	8	no	—
153	C₄⋊C₄×C₄₁	—	2	4	no	—
154	C₄⋊C₄×C₄₁	—	2	4	no	—
155	C₄⋊C₄×C₄₁	—	2	2	no	—
156	C₄⋊C₄×C₄₁	—	2	1	no	—
157	C₄⋊C₄×C₄₁	—	2	2	no	—
158	C₄⋊C₄×C₄₁	—	2	1	no	—
159	C₄⋊C₄×C₄₁	—	2	1	no	—
160	C₄⋊C₄×C₄₁	—	2	2	no	—
161	C₄⋊C₄×C₄₁	—	2	2	no	—
162	C₄⋊C₄×C₄₁	—	4	4	no	—
163	C₄⋊C₄×C₄₁	—	4	2	no	—
164	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
165	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
166	C₂²⋊C₄×C₄₁	—	2	8	no	—
167	C₂²⋊C₄×C₄₁	—	2	4	no	—
168	C₂²⋊C₄×C₄₁	—	4	4	no	—
169	C₂²⋊C₄×C₄₁	—	4	4	no	—
170	C₄²×C₄₁	—	2	4	no	—
171	C₄²×C₄₁	—	4	2	no	—
172	C₄²×C₄₁	C₂×D₄	1	2	yes	—
173	C₄²×C₄₁	C₂×D₄	1	2	yes	—
174	C₂³×C₄₁	—	2	2	no	—
175	C₂³×C₄₁	—	2	2	no	—
176	C₂³×C₄₁	—	2	2	no	—
177	C₂³×C₄₁	—	2	2	no	—
178	C₂³×C₄₁	—	2	2	no	—
179	C₂³×C₄₁	—	2	2	no	—
180	C₂³×C₄₁	#137	1	4	yes	—
181	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₄₁	—	2	2	no	—
183	Q₈×C₄₁	—	2	2	no	—
184	Q₈×C₄₁	—	2	2	no	—
185	Q₈×C₄₁	—	2	2	no	—
186	Q₈×C₄₁	—	4	1	no	—
187	Q₈×C₄₁	—	4	1	no	—
188	Q₈×C₄₁	—	4	1	no	—
189	Q₈×C₄₁	—	4	1	no	—
190	Q₈×C₄₁	—	8	4	no	—
191	D₄×C₄₁	—	2	8	no	—
192	C₂×C₄×C₄₁	—	2	2	no	—
193	C₂×C₄×C₄₁	—	2	2	no	—
194	C₂×C₄×C₄₁	—	2	2	no	—
195	C₂×C₄×C₄₁	—	2	2	no	—
196	C₂×C₄×C₄₁	—	2	2	no	—
197	C₂×C₄×C₄₁	—	2	4	no	—
198	C₂×C₄×C₄₁	—	2	2	no	—
199	C₂×C₄×C₄₁	—	2	2	no	—
200	C₂×C₄×C₄₁	—	2	2	no	—
201	C₂×C₄×C₄₁	—	4	1	no	—
202	C₂×C₄×C₄₁	—	4	1	no	—
203	C₂×C₄×C₄₁	—	4	1	no	—
204	C₂×C₄×C₄₁	—	4	1	no	—
205	C₂×C₄×C₄₁	—	4	2	no	—
206	C₂×C₄×C₄₁	—	4	2	no	—
207	C₂×C₄×C₄₁	—	4	2	no	—
208	C₂×C₄×C₄₁	—	4	2	no	—
209	C₂×C₄×C₄₁	—	4	2	no	—
210	C₂×C₄×C₄₁	—	4	2	no	—
211	C₂×C₄×C₄₁	—	4	2	no	—
212	C₂×C₄×C₄₁	—	4	1	no	—
213	C₂×C₄×C₄₁	—	4	2	no	—
214	C₂×C₄×C₄₁	—	4	2	no	—
215	C₂×C₄×C₄₁	—	4	2	no	—
216	C₂×C₄×C₄₁	—	4	2	no	—
217	C₂×C₄×C₄₁	—	8	8	no	—
218	C₂×C₄×C₄₁	#120	1	2	yes	—
219	C₂×C₄×C₄₁	#120	1	2	yes	—
220	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
225	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
226	C₈×C₄₁	—	2	2	no	—
227	C₈×C₄₁	—	4	1	no	—
228	C₈×C₄₁	—	4	2	no	—
229	#24134	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂²×C₄₁	—	2	4	no	—
231	C₂²×C₄₁	—	2	4	no	—
232	C₂²×C₄₁	—	2	4	no	—
233	C₂²×C₄₁	—	4	2	no	—
234	C₂²×C₄₁	—	4	2	no	—
235	C₂²×C₄₁	—	4	2	no	—
236	C₂²×C₄₁	—	4	2	no	—
237	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
238	C₂²×C₄₁	#546	1	1	yes	characteristic
239	C₂²×C₄₁	#547	1	1	yes	characteristic
240	C₂²×C₄₁	C₂×#137	1	2	yes	—
241	C₂²×C₄₁	#577	1	2	yes	—
242	C₄×C₄₁	—	2	2	no	—
243	C₄×C₄₁	—	2	2	no	—
244	C₄×C₄₁	—	4	2	no	—
245	C₄×C₄₁	—	4	2	no	—
246	C₄×C₄₁	—	4	2	no	—
247	C₄×C₄₁	—	4	2	no	—
248	C₄×C₄₁	—	4	4	no	—
249	C₄×C₄₁	—	8	1	no	—
250	C₄×C₄₁	—	8	2	no	—
251	C₄×C₄₁	#525	1	1	yes	characteristic
252	C₄×C₄₁	#537	1	1	yes	characteristic
253	C₄×C₄₁	#548	1	1	yes	characteristic
254	C₄×C₄₁	#550	1	1	yes	characteristic
255	C₂×#554	C₂×C₄₁	1	1	yes	characteristic
256	C₂×#475	C₂×C₄₁	1	1	yes	characteristic, complemented
257	C₂×#441	C₂×C₄₁	1	1	yes	characteristic, complemented
258	#2536	C₂×C₄₁	1	1	yes	characteristic
259	#2035	C₂×C₄₁	1	2	yes	complemented
260	#2001	C₂×C₄₁	1	2	yes	complemented
261	#1993	C₂×C₄₁	1	1	yes	characteristic, complemented
262	#1955	C₂×C₄₁	1	1	yes	characteristic
263	#1872	C₂×C₄₁	1	2	yes	complemented
264	#1853	C₂×C₄₁	1	2	yes	complemented
265	#1805	C₂×C₄₁	1	1	yes	characteristic, complemented
266	C₂×C₄₁	—	4	4	no	—
267	C₂×C₄₁	#2407	1	1	yes	characteristic
268	C₂×C₄₁	#3004	1	1	yes	characteristic
269	C₂×C₄₁	#3009	1	1	yes	characteristic
270	C₂×C₄₁	#3316	1	2	yes	—
271	C₂×C₄₁	#3344	1	2	yes	—
272	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
273	#554	—	2	4	no	—
274	#554	—	2	4	no	—
275	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
276	C₂×#125	—	2	1	no	—
277	C₂×C₂²⋊Q₈	—	2	2	no	—
278	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
279	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
280	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
281	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
282	C₂×C₄×D₄	—	2	1	no	—
283	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
284	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
285	#475	—	2	4	no	—
286	#441	—	2	4	no	—
287	C₂×#106	C₂²×C₄₁	1	2	yes	—
288	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
289	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
290	C₂×#103	C₂²×C₄₁	1	2	yes	—
291	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
292	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
293	C₂×#103	C₂²×C₄₁	1	2	yes	—
294	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
295	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
296	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
297	#398	—	2	1	no	—
298	#394	—	2	1	no	—
299	#388	—	2	2	no	—
300	#382	C₂²×C₄₁	1	1	yes	characteristic
301	#380	C₂²×C₄₁	1	2	yes	—
302	#340	C₂²×C₄₁	1	2	yes	—
303	#340	C₂²×C₄₁	1	2	yes	—
304	#340	C₂²×C₄₁	1	2	yes	—
305	C₄₁	#24134	1	1	yes	characteristic, direct product factor, Sylow
306	C₂²×Q₈	—	2	1	no	—
307	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
308	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
309	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
310	C₂³×C₄	—	2	2	no	—
311	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
312	C₂×Q₁₆	—	2	2	no	—
313	C₂×Q₁₆	—	2	2	no	—
314	C₂×Q₁₆	—	2	2	no	—
315	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
316	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
317	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
318	C₄⋊Q₈	—	2	2	no	—
319	C₄⋊Q₈	D₄×C₄₁	1	4	yes	—
320	#125	—	2	8	no	—
321	C₂²⋊Q₈	—	2	16	no	—
322	C₂²⋊Q₈	—	2	4	no	—
323	C₂²⋊Q₈	—	2	4	no	—
324	C₂²⋊Q₈	—	2	4	no	—
325	C₂²⋊Q₈	—	4	2	no	—
326	C₄×Q₈	—	2	2	no	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	D₄×C₄₁	1	4	yes	—
330	C₄×D₄	—	2	8	no	—
331	C₄×D₄	—	2	2	no	—
332	C₄×D₄	—	2	2	no	—
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	4	no	—
338	C₂×C₄⋊C₄	—	2	4	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
344	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	—	2	1	no	—
352	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
353	#106	—	2	2	no	—
354	#106	—	2	4	no	—
355	C₄⋊C₈	—	2	2	no	—
356	#103	—	2	2	no	—
357	#103	—	2	2	no	—
358	#103	—	2	4	no	—
359	#103	—	4	2	no	—
360	C₂²⋊C₈	—	2	4	no	—
361	C₂²⋊C₈	—	4	2	no	—
362	#97	—	2	2	no	—
363	#95	—	2	2	no	—
364	#95	—	2	1	no	—
365	#95	—	2	1	no	—
366	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
367	C₂×Q₈	—	2	4	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	2	1	no	—
375	C₂×Q₈	—	2	1	no	—
376	C₂×Q₈	—	2	1	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	8	2	no	—
379	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
380	C₂×Q₈	#41×C₄₁	1	2	yes	—
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	8	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	8	2	no	—
397	C₂²×C₄	—	8	2	no	—
398	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
399	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
401	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
402	Q₁₆	—	2	8	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	#41×C₄₁	1	2	yes	—
412	C₄⋊C₄	—	2	8	no	—
413	C₄⋊C₄	—	2	8	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	4	4	no	—
424	C₄⋊C₄	—	4	2	no	—
425	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
426	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
427	C₂²⋊C₄	—	2	8	no	—
428	C₂²⋊C₄	—	2	4	no	—
429	C₂²⋊C₄	—	4	4	no	—
430	C₂²⋊C₄	—	4	4	no	—
431	C₄²	—	2	4	no	—
432	C₄²	—	4	2	no	—
433	C₄²	C₂×D₄×C₄₁	1	2	yes	—
434	C₄²	C₂×D₄×C₄₁	1	2	yes	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	#137×C₄₁	1	4	yes	—
442	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
443	Q₈	—	2	2	no	—
444	Q₈	—	2	2	no	—
445	Q₈	—	2	2	no	—
446	Q₈	—	2	2	no	—
447	Q₈	—	4	1	no	—
448	Q₈	—	4	1	no	—
449	Q₈	—	4	1	no	—
450	Q₈	—	4	1	no	—
451	Q₈	—	8	4	no	—
452	D₄	—	2	8	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	8	8	no	—
479	C₂×C₄	#120×C₄₁	1	2	yes	—
480	C₂×C₄	#120×C₄₁	1	2	yes	—
481	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
482	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
483	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
484	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
485	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
486	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
487	C₈	—	2	2	no	—
488	C₈	—	4	1	no	—
489	C₈	—	4	2	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	2	4	no	—
492	C₂²	—	2	4	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
498	C₂²	C₄₁×#546	1	1	yes	characteristic
499	C₂²	C₄₁×#547	1	1	yes	characteristic
500	C₂²	C₂×#137×C₄₁	1	2	yes	—
501	C₂²	C₄₁×#577	1	2	yes	—
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	2	no	—
506	C₄	—	4	2	no	—
507	C₄	—	4	2	no	—
508	C₄	—	4	4	no	—
509	C₄	—	8	2	no	—
510	C₄	—	8	1	no	—
511	C₄	C₄₁×#525	1	1	yes	characteristic
512	C₄	C₄₁×#537	1	1	yes	characteristic
513	C₄	C₄₁×#548	1	1	yes	characteristic
514	C₄	C₄₁×#550	1	1	yes	characteristic
515	C₂	—	4	4	no	—
516	C₂	C₄₁×#2407	1	1	yes	characteristic
517	C₂	C₄₁×#3004	1	1	yes	characteristic
518	C₂	C₄₁×#3009	1	1	yes	characteristic
519	C₂	C₄₁×#3316	1	2	yes	—
520	C₂	C₄₁×#3344	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#475	C₂	semidirect
3. C₂×C₄₁×#441	C₂	semidirect
5. C₄₁×#2035	C₂	semidirect
6. C₄₁×#2001	C₂	semidirect
7. C₄₁×#1993	C₂	semidirect
9. C₄₁×#1872	C₂	semidirect
10. C₄₁×#1853	C₂	semidirect
11. C₄₁×#1805	C₂	semidirect
229. #24134	C₄₁	direct (N × H)
256. C₂×#475	C₂×C₄₁	semidirect
257. C₂×#441	C₂×C₄₁	semidirect
259. #2035	C₂×C₄₁	semidirect
260. #2001	C₂×C₄₁	semidirect
261. #1993	C₂×C₄₁	semidirect
263. #1872	C₂×C₄₁	semidirect
264. #1853	C₂×C₄₁	semidirect
265. #1805	C₂×C₄₁	semidirect
305. C₄₁	#24134	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×#554	2
C₂×C₄₁×#475	2
C₂×C₄₁×#441	2
C₄₁×#2536	2
C₄₁×#2035	2
C₄₁×#2001	2
C₄₁×#1993	2
C₄₁×#1955	2
C₄₁×#1872	2
C₄₁×#1853	2
C₄₁×#1805	2
#24134	41

Subgroups — C41×#24134 #23800335

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24134 #23800335