Subgroups — C₄₁×#24269 #23800470

Order 10496.

1580 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×SD₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#468	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₁×#435	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2409	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2408	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#2055	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2000	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1973	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1808	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1787	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1786	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₄₁	—	2	8	no	—
15	C₂²×SD₁₆×C₄₁	—	2	4	no	—
16	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
17	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
18	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	complemented
21	C₂×#121×C₄₁	C₂²	1	2	yes	—
22	C₂×#120×C₄₁	—	2	1	no	—
23	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
24	C₄₁×#468	—	2	8	no	—
25	C₄₁×#435	—	2	4	no	—
26	C₂×#107×C₄₁	C₂²	1	2	yes	complemented
27	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
28	C₂×#103×C₄₁	C₂²	1	2	yes	complemented
29	C₂×#103×C₄₁	C₂²	1	2	yes	complemented
30	C₂×#102×C₄₁	C₂²	1	2	yes	—
31	C₂×#102×C₄₁	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
34	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic, complemented
35	C₄₁×#395	—	2	1	no	—
36	C₄₁×#394	—	2	1	no	—
37	C₄₁×#393	—	2	1	no	—
38	C₄₁×#392	—	2	1	no	—
39	C₄₁×#391	C₂²	1	2	yes	complemented
40	C₄₁×#390	C₂²	1	2	yes	—
41	C₄₁×#386	—	2	1	no	—
42	C₄₁×#385	—	2	1	no	—
43	C₄₁×#380	C₂²	1	1	yes	characteristic
44	C₄₁×#380	C₂²	1	1	yes	characteristic
45	C₄₁×#379	—	2	1	no	—
46	C₄₁×#340	C₂²	1	2	yes	complemented
47	C₂⁵×C₄₁	—	2	1	no	—
48	C₂²×Q₈×C₄₁	—	2	1	no	—
49	C₂²×Q₈×C₄₁	—	2	4	no	—
50	C₂²×Q₈×C₄₁	—	2	2	no	—
51	C₂²×Q₈×C₄₁	—	2	2	no	—
52	C₂²×Q₈×C₄₁	—	4	2	no	—
53	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
54	C₂²×D₄×C₄₁	—	2	4	no	—
55	C₂²×D₄×C₄₁	—	2	2	no	—
56	C₂²×D₄×C₄₁	—	2	2	no	—
57	C₂²×D₄×C₄₁	—	2	1	no	—
58	C₂²×D₄×C₄₁	—	2	2	no	—
59	C₂²×D₄×C₄₁	—	4	2	no	—
60	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
62	C₂³×C₄×C₄₁	—	2	1	no	—
63	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
65	C₂×SD₁₆×C₄₁	—	2	32	no	—
66	C₂×SD₁₆×C₄₁	—	2	4	no	—
67	C₂×SD₁₆×C₄₁	—	2	4	no	—
68	C₂×SD₁₆×C₄₁	—	2	4	no	—
69	C₂×SD₁₆×C₄₁	—	2	4	no	—
70	C₂×SD₁₆×C₄₁	—	2	4	no	—
71	C₂×SD₁₆×C₄₁	D₄	1	8	yes	complemented
72	C₂×M₁₆×C₄₁	—	2	2	no	—
73	C₂×M₁₆×C₄₁	—	2	4	no	—
74	C₂²×C₈×C₄₁	—	2	4	no	—
75	C₂²×C₈×C₄₁	D₄	1	4	yes	complemented
76	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
80	C₂²⋊Q₈×C₄₁	—	2	4	no	—
81	C₂²⋊Q₈×C₄₁	—	4	2	no	—
82	#121×C₄₁	—	2	4	no	—
83	#121×C₄₁	—	4	2	no	—
84	#120×C₄₁	—	4	4	no	—
85	C₄×D₄×C₄₁	—	2	2	no	—
86	C₄×D₄×C₄₁	—	2	2	no	—
87	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
88	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
91	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
100	#107×C₄₁	—	2	4	no	—
101	C₄⋊C₈×C₄₁	—	2	2	no	—
102	#103×C₄₁	—	2	4	no	—
103	#103×C₄₁	—	4	2	no	—
104	#102×C₄₁	—	2	4	no	—
105	#102×C₄₁	—	4	2	no	—
106	C₂²⋊C₈×C₄₁	—	2	2	no	—
107	C₂²⋊C₈×C₄₁	—	2	2	no	—
108	#97×C₄₁	—	2	2	no	—
109	#95×C₄₁	—	2	1	no	—
110	#95×C₄₁	—	2	1	no	—
111	#95×C₄₁	—	2	2	no	—
112	#95×C₄₁	—	2	2	no	—
113	C₂⁴×C₄₁	—	2	2	no	—
114	C₂⁴×C₄₁	—	4	4	no	—
115	C₂⁴×C₄₁	—	4	2	no	—
116	C₂⁴×C₄₁	—	4	2	no	—
117	C₂⁴×C₄₁	—	4	2	no	—
118	C₂⁴×C₄₁	—	8	2	no	—
119	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
120	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
121	C₂×Q₈×C₄₁	—	2	2	no	—
122	C₂×Q₈×C₄₁	—	2	8	no	—
123	C₂×Q₈×C₄₁	—	2	2	no	—
124	C₂×Q₈×C₄₁	—	2	2	no	—
125	C₂×Q₈×C₄₁	—	2	2	no	—
126	C₂×Q₈×C₄₁	—	2	2	no	—
127	C₂×Q₈×C₄₁	—	4	4	no	—
128	C₂×Q₈×C₄₁	—	4	8	no	—
129	C₂×Q₈×C₄₁	—	4	4	no	—
130	C₂×Q₈×C₄₁	—	4	2	no	—
131	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
132	C₂×D₄×C₄₁	—	2	8	no	—
133	C₂×D₄×C₄₁	—	2	2	no	—
134	C₂×D₄×C₄₁	—	2	2	no	—
135	C₂×D₄×C₄₁	—	2	2	no	—
136	C₂×D₄×C₄₁	—	2	2	no	—
137	C₂×D₄×C₄₁	—	2	2	no	—
138	C₂×D₄×C₄₁	—	2	2	no	—
139	C₂×D₄×C₄₁	—	2	2	no	—
140	C₂×D₄×C₄₁	—	2	2	no	—
141	C₂×D₄×C₄₁	—	4	8	no	—
142	C₂×D₄×C₄₁	—	4	4	no	—
143	C₂×D₄×C₄₁	—	4	4	no	—
144	C₂×D₄×C₄₁	—	4	4	no	—
145	C₂×D₄×C₄₁	—	4	4	no	—
146	C₂×D₄×C₄₁	—	4	2	no	—
147	C₂×D₄×C₄₁	—	8	2	no	—
148	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
149	C₂²×C₄×C₄₁	—	2	2	no	—
150	C₂²×C₄×C₄₁	—	2	2	no	—
151	C₂²×C₄×C₄₁	—	2	2	no	—
152	C₂²×C₄×C₄₁	—	2	1	no	—
153	C₂²×C₄×C₄₁	—	2	2	no	—
154	C₂²×C₄×C₄₁	—	2	1	no	—
155	C₂²×C₄×C₄₁	—	2	2	no	—
156	C₂²×C₄×C₄₁	—	2	2	no	—
157	C₂²×C₄×C₄₁	—	2	2	no	—
158	C₂²×C₄×C₄₁	—	4	4	no	—
159	C₂²×C₄×C₄₁	—	4	2	no	—
160	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₄₁	#41	1	2	yes	—
166	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
167	SD₁₆×C₄₁	—	2	16	no	—
168	SD₁₆×C₄₁	—	2	16	no	—
169	M₁₆×C₄₁	—	4	4	no	—
170	C₂×C₈×C₄₁	—	2	2	no	—
171	C₂×C₈×C₄₁	—	2	8	no	—
172	C₂×C₈×C₄₁	—	2	1	no	—
173	C₂×C₈×C₄₁	—	2	1	no	—
174	C₂×C₈×C₄₁	—	2	2	no	—
175	C₂×C₈×C₄₁	—	2	2	no	—
176	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
177	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
178	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
179	C₄⋊C₄×C₄₁	—	2	2	no	—
180	C₄⋊C₄×C₄₁	—	2	2	no	—
181	C₄⋊C₄×C₄₁	—	2	2	no	—
182	C₄⋊C₄×C₄₁	—	2	2	no	—
183	C₄⋊C₄×C₄₁	—	2	2	no	—
184	C₄⋊C₄×C₄₁	—	4	4	no	—
185	C₂²⋊C₄×C₄₁	—	2	2	no	—
186	C₂²⋊C₄×C₄₁	—	2	2	no	—
187	C₂²⋊C₄×C₄₁	—	4	4	no	—
188	C₂²⋊C₄×C₄₁	—	4	4	no	—
189	C₂²⋊C₄×C₄₁	—	4	4	no	—
190	C₂²⋊C₄×C₄₁	—	4	2	no	—
191	C₂²⋊C₄×C₄₁	—	4	2	no	—
192	C₂²⋊C₄×C₄₁	—	8	2	no	—
193	C₄²×C₄₁	—	2	1	no	—
194	C₄²×C₄₁	—	2	1	no	—
195	C₂³×C₄₁	—	2	2	no	—
196	C₂³×C₄₁	—	2	2	no	—
197	C₂³×C₄₁	—	2	1	no	—
198	C₂³×C₄₁	—	2	2	no	—
199	C₂³×C₄₁	—	2	4	no	—
200	C₂³×C₄₁	—	2	1	no	—
201	C₂³×C₄₁	—	2	1	no	—
202	C₂³×C₄₁	—	2	2	no	—
203	C₂³×C₄₁	—	4	8	no	—
204	C₂³×C₄₁	—	4	2	no	—
205	C₂³×C₄₁	—	4	2	no	—
206	C₂³×C₄₁	—	4	2	no	—
207	C₂³×C₄₁	—	4	2	no	—
208	C₂³×C₄₁	—	4	2	no	—
209	C₂³×C₄₁	—	4	2	no	—
210	C₂³×C₄₁	—	8	8	no	—
211	C₂³×C₄₁	—	8	8	no	—
212	C₂³×C₄₁	—	8	4	no	—
213	C₂³×C₄₁	—	8	4	no	—
214	C₂³×C₄₁	#121	1	2	yes	—
215	C₂³×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
216	C₂³×C₄₁	#137	1	2	yes	—
217	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
218	Q₈×C₄₁	—	2	4	no	—
219	Q₈×C₄₁	—	2	4	no	—
220	Q₈×C₄₁	—	4	8	no	—
221	Q₈×C₄₁	—	4	2	no	—
222	Q₈×C₄₁	—	4	2	no	—
223	D₄×C₄₁	—	2	4	no	—
224	D₄×C₄₁	—	2	4	no	—
225	D₄×C₄₁	—	4	8	no	—
226	D₄×C₄₁	—	4	4	no	—
227	D₄×C₄₁	—	4	2	no	—
228	D₄×C₄₁	—	4	2	no	—
229	D₄×C₄₁	—	8	8	no	—
230	C₂×C₄×C₄₁	—	2	2	no	—
231	C₂×C₄×C₄₁	—	2	2	no	—
232	C₂×C₄×C₄₁	—	2	2	no	—
233	C₂×C₄×C₄₁	—	2	4	no	—
234	C₂×C₄×C₄₁	—	2	1	no	—
235	C₂×C₄×C₄₁	—	2	1	no	—
236	C₂×C₄×C₄₁	—	2	1	no	—
237	C₂×C₄×C₄₁	—	2	2	no	—
238	C₂×C₄×C₄₁	—	2	4	no	—
239	C₂×C₄×C₄₁	—	2	1	no	—
240	C₂×C₄×C₄₁	—	2	1	no	—
241	C₂×C₄×C₄₁	—	2	2	no	—
242	C₂×C₄×C₄₁	—	4	8	no	—
243	C₂×C₄×C₄₁	—	4	2	no	—
244	C₂×C₄×C₄₁	—	4	2	no	—
245	C₂×C₄×C₄₁	—	4	1	no	—
246	C₂×C₄×C₄₁	—	4	1	no	—
247	C₂×C₄×C₄₁	—	4	2	no	—
248	C₂×C₄×C₄₁	—	4	2	no	—
249	C₂×C₄×C₄₁	—	4	2	no	—
250	C₂×C₄×C₄₁	—	4	2	no	—
251	C₂×C₄×C₄₁	—	4	2	no	—
252	C₂×C₄×C₄₁	—	4	2	no	—
253	C₂×C₄×C₄₁	—	4	2	no	—
254	C₂×C₄×C₄₁	#121	1	2	yes	—
255	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
259	C₈×C₄₁	—	2	2	no	—
260	C₈×C₄₁	—	4	1	no	—
261	C₈×C₄₁	—	4	1	no	—
262	C₈×C₄₁	#120	1	4	yes	complemented
263	#24269	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
264	C₂²×C₄₁	—	2	2	no	—
265	C₂²×C₄₁	—	2	4	no	—
266	C₂²×C₄₁	—	2	4	no	—
267	C₂²×C₄₁	—	2	2	no	—
268	C₂²×C₄₁	—	4	1	no	—
269	C₂²×C₄₁	—	4	4	no	—
270	C₂²×C₄₁	—	4	2	no	—
271	C₂²×C₄₁	—	4	4	no	—
272	C₂²×C₄₁	—	4	2	no	—
273	C₂²×C₄₁	—	4	4	no	—
274	C₂²×C₄₁	—	4	1	no	—
275	C₂²×C₄₁	—	4	1	no	—
276	C₂²×C₄₁	—	8	16	no	—
277	C₂²×C₄₁	—	8	2	no	—
278	C₂²×C₄₁	—	8	2	no	—
279	C₂²×C₄₁	—	8	2	no	—
280	C₂²×C₄₁	—	8	2	no	—
281	C₂²×C₄₁	#468	1	4	yes	complemented
282	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
283	C₂²×C₄₁	D₄²	1	2	yes	—
284	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
285	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
286	C₂²×C₄₁	#577	1	2	yes	—
287	C₄×C₄₁	—	2	2	no	—
288	C₄×C₄₁	—	4	1	no	—
289	C₄×C₄₁	—	4	4	no	—
290	C₄×C₄₁	—	4	1	no	—
291	C₄×C₄₁	—	4	1	no	—
292	C₄×C₄₁	—	8	2	no	—
293	C₄×C₄₁	—	8	2	no	—
294	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
295	C₄×C₄₁	#535	1	1	yes	characteristic
296	C₄×C₄₁	#546	1	2	yes	—
297	C₂³×SD₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
298	C₂×#468	C₂×C₄₁	1	2	yes	complemented
299	C₂×#435	C₂×C₄₁	1	1	yes	characteristic, complemented
300	#2409	C₂×C₄₁	1	1	yes	characteristic, complemented
301	#2408	C₂×C₄₁	1	1	yes	characteristic
302	#2055	C₂×C₄₁	1	2	yes	complemented
303	#2000	C₂×C₄₁	1	2	yes	complemented
304	#1973	C₂×C₄₁	1	2	yes	complemented
305	#1808	C₂×C₄₁	1	1	yes	characteristic, complemented
306	#1787	C₂×C₄₁	1	1	yes	characteristic, complemented
307	#1786	C₂×C₄₁	1	1	yes	characteristic, complemented
308	C₂×C₄₁	—	2	4	no	—
309	C₂×C₄₁	—	8	1	no	—
310	C₂×C₄₁	—	8	4	no	—
311	C₂×C₄₁	#2408	1	1	yes	characteristic
312	C₂×C₄₁	C₂×#468	1	1	yes	characteristic
313	C₂×C₄₁	#3057	1	1	yes	characteristic
314	C₂×C₄₁	#3265	1	2	yes	—
315	C₂×C₄₁	#3266	1	2	yes	—
316	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
317	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
318	C₂²×SD₁₆	—	2	8	no	—
319	C₂²×SD₁₆	—	2	4	no	—
320	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
321	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
322	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
323	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
324	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	complemented
325	C₂×#121	C₂²×C₄₁	1	2	yes	—
326	C₂×#120	—	2	1	no	—
327	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
328	#468	—	2	8	no	—
329	#435	—	2	4	no	—
330	C₂×#107	C₂²×C₄₁	1	2	yes	complemented
331	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
332	C₂×#103	C₂²×C₄₁	1	2	yes	complemented
333	C₂×#103	C₂²×C₄₁	1	2	yes	complemented
334	C₂×#102	C₂²×C₄₁	1	2	yes	—
335	C₂×#102	C₂²×C₄₁	1	2	yes	—
336	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
337	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
338	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic, complemented
339	#395	—	2	1	no	—
340	#394	—	2	1	no	—
341	#393	—	2	1	no	—
342	#392	—	2	1	no	—
343	#391	C₂²×C₄₁	1	2	yes	complemented
344	#390	C₂²×C₄₁	1	2	yes	—
345	#386	—	2	1	no	—
346	#385	—	2	1	no	—
347	#380	C₂²×C₄₁	1	1	yes	characteristic
348	#380	C₂²×C₄₁	1	1	yes	characteristic
349	#379	—	2	1	no	—
350	#340	C₂²×C₄₁	1	2	yes	complemented
351	C₄₁	#24269	1	1	yes	characteristic, direct product factor, Sylow
352	C₂⁵	—	2	1	no	—
353	C₂²×Q₈	—	2	1	no	—
354	C₂²×Q₈	—	2	4	no	—
355	C₂²×Q₈	—	2	2	no	—
356	C₂²×Q₈	—	2	2	no	—
357	C₂²×Q₈	—	4	2	no	—
358	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
359	C₂²×D₄	—	2	4	no	—
360	C₂²×D₄	—	2	2	no	—
361	C₂²×D₄	—	2	2	no	—
362	C₂²×D₄	—	2	1	no	—
363	C₂²×D₄	—	2	2	no	—
364	C₂²×D₄	—	4	2	no	—
365	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
366	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
367	C₂³×C₄	—	2	1	no	—
368	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
369	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
370	C₂×SD₁₆	—	2	32	no	—
371	C₂×SD₁₆	—	2	4	no	—
372	C₂×SD₁₆	—	2	4	no	—
373	C₂×SD₁₆	—	2	4	no	—
374	C₂×SD₁₆	—	2	4	no	—
375	C₂×SD₁₆	—	2	4	no	—
376	C₂×SD₁₆	D₄×C₄₁	1	8	yes	complemented
377	C₂×M₁₆	—	2	2	no	—
378	C₂×M₁₆	—	2	4	no	—
379	C₂²×C₈	—	2	4	no	—
380	C₂²×C₈	D₄×C₄₁	1	4	yes	complemented
381	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
382	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
383	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
384	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
385	C₂²⋊Q₈	—	2	4	no	—
386	C₂²⋊Q₈	—	4	2	no	—
387	#121	—	2	4	no	—
388	#121	—	4	2	no	—
389	#120	—	4	4	no	—
390	C₄×D₄	—	2	2	no	—
391	C₄×D₄	—	2	2	no	—
392	C₂×C₄⋊C₄	—	2	2	no	—
393	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
395	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
396	C₂×C₂²⋊C₄	—	2	1	no	—
397	C₂×C₂²⋊C₄	—	2	2	no	—
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₂²⋊C₄	—	2	2	no	—
400	C₂×C₂²⋊C₄	—	2	2	no	—
401	C₂×C₂²⋊C₄	—	2	2	no	—
402	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
403	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
404	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
405	#107	—	2	4	no	—
406	C₄⋊C₈	—	2	2	no	—
407	#103	—	2	4	no	—
408	#103	—	4	2	no	—
409	#102	—	2	4	no	—
410	#102	—	4	2	no	—
411	C₂²⋊C₈	—	2	2	no	—
412	C₂²⋊C₈	—	2	2	no	—
413	#97	—	2	2	no	—
414	#95	—	2	1	no	—
415	#95	—	2	1	no	—
416	#95	—	2	2	no	—
417	#95	—	2	2	no	—
418	C₂⁴	—	2	2	no	—
419	C₂⁴	—	4	4	no	—
420	C₂⁴	—	4	2	no	—
421	C₂⁴	—	4	2	no	—
422	C₂⁴	—	4	2	no	—
423	C₂⁴	—	8	2	no	—
424	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
425	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	—	2	8	no	—
428	C₂×Q₈	—	2	2	no	—
429	C₂×Q₈	—	2	2	no	—
430	C₂×Q₈	—	2	2	no	—
431	C₂×Q₈	—	2	2	no	—
432	C₂×Q₈	—	4	4	no	—
433	C₂×Q₈	—	4	8	no	—
434	C₂×Q₈	—	4	4	no	—
435	C₂×Q₈	—	4	2	no	—
436	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
437	C₂×D₄	—	2	8	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	4	8	no	—
447	C₂×D₄	—	4	4	no	—
448	C₂×D₄	—	4	4	no	—
449	C₂×D₄	—	4	4	no	—
450	C₂×D₄	—	4	4	no	—
451	C₂×D₄	—	4	2	no	—
452	C₂×D₄	—	8	2	no	—
453	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	4	4	no	—
464	C₂²×C₄	—	4	2	no	—
465	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
470	C₂²×C₄	#41×C₄₁	1	2	yes	—
471	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
472	SD₁₆	—	2	16	no	—
473	SD₁₆	—	2	16	no	—
474	M₁₆	—	4	4	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	8	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
482	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
483	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	4	4	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	4	4	no	—
493	C₂²⋊C₄	—	4	4	no	—
494	C₂²⋊C₄	—	4	4	no	—
495	C₂²⋊C₄	—	4	2	no	—
496	C₂²⋊C₄	—	4	2	no	—
497	C₂²⋊C₄	—	8	2	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	2	no	—
502	C₂³	—	2	1	no	—
503	C₂³	—	2	2	no	—
504	C₂³	—	2	4	no	—
505	C₂³	—	2	1	no	—
506	C₂³	—	2	1	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	4	8	no	—
509	C₂³	—	4	2	no	—
510	C₂³	—	4	2	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	4	2	no	—
514	C₂³	—	4	2	no	—
515	C₂³	—	8	8	no	—
516	C₂³	—	8	8	no	—
517	C₂³	—	8	4	no	—
518	C₂³	—	8	4	no	—
519	C₂³	#121×C₄₁	1	2	yes	—
520	C₂³	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
521	C₂³	#137×C₄₁	1	2	yes	—
522	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
523	Q₈	—	2	4	no	—
524	Q₈	—	2	4	no	—
525	Q₈	—	4	8	no	—
526	Q₈	—	4	2	no	—
527	Q₈	—	4	2	no	—
528	D₄	—	2	4	no	—
529	D₄	—	2	4	no	—
530	D₄	—	4	8	no	—
531	D₄	—	4	4	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	8	8	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	4	8	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	#121×C₄₁	1	2	yes	—
560	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
561	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
562	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
563	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
564	C₈	—	2	2	no	—
565	C₈	—	4	1	no	—
566	C₈	—	4	1	no	—
567	C₈	#120×C₄₁	1	4	yes	complemented
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	4	no	—
571	C₂²	—	2	4	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	4	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	4	4	no	—
580	C₂²	—	8	16	no	—
581	C₂²	—	8	2	no	—
582	C₂²	—	8	2	no	—
583	C₂²	—	8	2	no	—
584	C₂²	—	8	2	no	—
585	C₂²	C₄₁×#468	1	4	yes	complemented
586	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
587	C₂²	D₄²×C₄₁	1	2	yes	—
588	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
589	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
590	C₂²	C₄₁×#577	1	2	yes	—
591	C₄	—	2	2	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	1	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	4	no	—
596	C₄	—	8	2	no	—
597	C₄	—	8	2	no	—
598	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
599	C₄	C₄₁×#535	1	1	yes	characteristic
600	C₄	C₄₁×#546	1	2	yes	—
601	C₂	—	2	4	no	—
602	C₂	—	8	1	no	—
603	C₂	—	8	4	no	—
604	C₂	C₄₁×#2408	1	1	yes	characteristic
605	C₂	C₂×C₄₁×#468	1	1	yes	characteristic
606	C₂	C₄₁×#3057	1	1	yes	characteristic
607	C₂	C₄₁×#3265	1	2	yes	—
608	C₂	C₄₁×#3266	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₄₁×#2408	C₂
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
1. C₂³×SD₁₆×C₄₁	C₂	semidirect
2. C₂×C₄₁×#468	C₂	semidirect
3. C₂×C₄₁×#435	C₂	semidirect
4. C₄₁×#2409	C₂	semidirect
6. C₄₁×#2055	C₂	semidirect
7. C₄₁×#2000	C₂	semidirect
8. C₄₁×#1973	C₂	semidirect
9. C₄₁×#1808	C₂	semidirect
10. C₄₁×#1787	C₂	semidirect
11. C₄₁×#1786	C₂	semidirect
18. C₂²×M₁₆×C₄₁	C₂²	semidirect
20. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
26. C₂×#107×C₄₁	C₂²	semidirect
27. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
28. C₂×#103×C₄₁	C₂²	semidirect
29. C₂×#103×C₄₁	C₂²	semidirect
33. C₂×C₂²⋊C₈×C₄₁	C₂²	semidirect
34. C₂×#97×C₄₁	C₂²	semidirect
39. C₄₁×#391	C₂²	semidirect
46. C₄₁×#340	C₂²	semidirect
71. C₂×SD₁₆×C₄₁	D₄	semidirect
75. C₂²×C₈×C₄₁	D₄	semidirect
262. C₈×C₄₁	#120	semidirect
263. #24269	C₄₁	direct (N × H)
281. C₂²×C₄₁	#468	semidirect
297. C₂³×SD₁₆	C₂×C₄₁	semidirect
298. C₂×#468	C₂×C₄₁	semidirect
299. C₂×#435	C₂×C₄₁	semidirect
300. #2409	C₂×C₄₁	semidirect
302. #2055	C₂×C₄₁	semidirect
303. #2000	C₂×C₄₁	semidirect
304. #1973	C₂×C₄₁	semidirect
305. #1808	C₂×C₄₁	semidirect
306. #1787	C₂×C₄₁	semidirect
307. #1786	C₂×C₄₁	semidirect
322. C₂²×M₁₆	C₂²×C₄₁	semidirect
324. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
330. C₂×#107	C₂²×C₄₁	semidirect
331. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
332. C₂×#103	C₂²×C₄₁	semidirect
333. C₂×#103	C₂²×C₄₁	semidirect
337. C₂×C₂²⋊C₈	C₂²×C₄₁	semidirect
338. C₂×#97	C₂²×C₄₁	semidirect
343. #391	C₂²×C₄₁	semidirect
350. #340	C₂²×C₄₁	semidirect
351. C₄₁	#24269	direct (N × H)
376. C₂×SD₁₆	D₄×C₄₁	semidirect
380. C₂²×C₈	D₄×C₄₁	semidirect
567. C₈	#120×C₄₁	semidirect
585. C₂²	C₄₁×#468	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×SD₁₆×C₄₁	2
C₂×C₄₁×#468	2
C₂×C₄₁×#435	2
C₄₁×#2409	2
C₄₁×#2408	2
C₄₁×#2055	2
C₄₁×#2000	2
C₄₁×#1973	2
C₄₁×#1808	2
C₄₁×#1787	2
C₄₁×#1786	2
#24269	41

Subgroups — C41×#24269 #23800470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24269 #23800470