Subgroups — C₄₁×#24375 #23800576

Order 10496.

1422 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#464	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₁×#449	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2436	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2055	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2012	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1895	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1878	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1851	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1787	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#137×C₄₁	—	2	4	no	—
15	C₂×#137×C₄₁	—	2	8	no	—
16	C₂²×Q₁₆×C₄₁	C₂²	1	2	yes	—
17	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
18	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#124×C₄₁	C₂²	1	2	yes	—
22	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
24	C₄₁×#464	—	2	8	no	—
25	C₄₁×#449	—	2	4	no	—
26	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
27	C₂×#103×C₄₁	C₂²	1	2	yes	—
28	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×#103×C₄₁	C₂²	1	2	yes	—
30	C₂×#102×C₄₁	C₂²	1	2	yes	—
31	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
33	C₄₁×#393	—	2	1	no	—
34	C₄₁×#393	—	2	1	no	—
35	C₄₁×#391	C₂²	1	2	yes	—
36	C₄₁×#390	—	2	2	no	—
37	C₄₁×#390	C₂²	1	2	yes	—
38	C₄₁×#386	—	2	2	no	—
39	C₄₁×#380	—	2	1	no	—
40	C₄₁×#380	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
42	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
43	C₄₁×#340	C₂²	1	2	yes	—
44	C₄₁×#336	C₂²	1	2	yes	—
45	C₂×#41×C₄₁	—	2	2	no	—
46	C₂×#41×C₄₁	—	2	4	no	—
47	C₂×#41×C₄₁	—	4	2	no	—
48	C₂×#41×C₄₁	D₄	1	4	yes	—
49	C₂²×Q₈×C₄₁	—	2	1	no	—
50	C₂²×Q₈×C₄₁	—	2	4	no	—
51	C₂²×Q₈×C₄₁	—	2	2	no	—
52	C₂²×Q₈×C₄₁	—	2	2	no	—
53	C₂²×Q₈×C₄₁	—	4	2	no	—
54	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
55	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₄₁	—	2	1	no	—
57	C₂²×D₄×C₄₁	—	2	1	no	—
58	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₄₁	—	2	1	no	—
61	C₂³×C₄×C₄₁	—	2	1	no	—
62	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
63	#137×C₄₁	—	2	32	no	—
64	C₂×Q₁₆×C₄₁	—	2	4	no	—
65	C₂×Q₁₆×C₄₁	—	2	4	no	—
66	C₂×Q₁₆×C₄₁	D₄	1	8	yes	complemented
67	C₂×SD₁₆×C₄₁	—	2	4	no	—
68	C₂×SD₁₆×C₄₁	—	2	4	no	—
69	C₂×SD₁₆×C₄₁	—	2	2	no	—
70	C₂×SD₁₆×C₄₁	—	2	4	no	—
71	C₂×SD₁₆×C₄₁	—	2	4	no	—
72	C₂×D₈×C₄₁	—	2	2	no	—
73	C₂×D₈×C₄₁	—	4	2	no	—
74	C₂×M₁₆×C₄₁	—	2	2	no	—
75	C₂×M₁₆×C₄₁	—	2	4	no	—
76	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
79	#124×C₄₁	—	2	4	no	—
80	#124×C₄₁	—	4	2	no	—
81	#121×C₄₁	—	2	2	no	—
82	#121×C₄₁	—	2	2	no	—
83	C₄×Q₈×C₄₁	—	2	4	no	—
84	C₄×Q₈×C₄₁	—	4	2	no	—
85	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
86	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
88	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
95	C₂×C₄²×C₄₁	—	2	2	no	—
96	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
97	C₄⋊C₈×C₄₁	—	2	4	no	—
98	#103×C₄₁	—	2	2	no	—
99	#103×C₄₁	—	2	4	no	—
100	#103×C₄₁	—	4	2	no	—
101	#102×C₄₁	—	2	2	no	—
102	#102×C₄₁	—	2	4	no	—
103	C₂²⋊C₈×C₄₁	—	2	2	no	—
104	#95×C₄₁	—	2	1	no	—
105	#95×C₄₁	—	2	2	no	—
106	#95×C₄₁	—	2	2	no	—
107	#95×C₄₁	D₄	1	1	yes	characteristic
108	#95×C₄₁	D₄	1	1	yes	characteristic
109	C₂⁴×C₄₁	—	2	1	no	—
110	C₂⁴×C₄₁	—	2	1	no	—
111	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
112	#41×C₄₁	—	2	8	no	—
113	#41×C₄₁	—	4	4	no	—
114	#41×C₄₁	—	4	8	no	—
115	C₂×Q₈×C₄₁	—	2	1	no	—
116	C₂×Q₈×C₄₁	—	2	2	no	—
117	C₂×Q₈×C₄₁	—	2	2	no	—
118	C₂×Q₈×C₄₁	—	2	8	no	—
119	C₂×Q₈×C₄₁	—	2	2	no	—
120	C₂×Q₈×C₄₁	—	2	2	no	—
121	C₂×Q₈×C₄₁	—	2	2	no	—
122	C₂×Q₈×C₄₁	—	2	2	no	—
123	C₂×Q₈×C₄₁	—	4	4	no	—
124	C₂×Q₈×C₄₁	—	4	8	no	—
125	C₂×Q₈×C₄₁	—	4	4	no	—
126	C₂×Q₈×C₄₁	—	4	2	no	—
127	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
128	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
129	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
130	C₂×D₄×C₄₁	—	2	4	no	—
131	C₂×D₄×C₄₁	—	2	2	no	—
132	C₂×D₄×C₄₁	—	2	2	no	—
133	C₂×D₄×C₄₁	—	2	1	no	—
134	C₂×D₄×C₄₁	—	2	1	no	—
135	C₂×D₄×C₄₁	—	2	1	no	—
136	C₂×D₄×C₄₁	—	2	2	no	—
137	C₂×D₄×C₄₁	—	2	2	no	—
138	C₂×D₄×C₄₁	—	4	4	no	—
139	C₂×D₄×C₄₁	—	4	4	no	—
140	C₂×D₄×C₄₁	—	4	2	no	—
141	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₄₁	—	2	1	no	—
143	C₂²×C₄×C₄₁	—	2	2	no	—
144	C₂²×C₄×C₄₁	—	2	2	no	—
145	C₂²×C₄×C₄₁	—	2	2	no	—
146	C₂²×C₄×C₄₁	—	2	4	no	—
147	C₂²×C₄×C₄₁	—	2	1	no	—
148	C₂²×C₄×C₄₁	—	2	2	no	—
149	C₂²×C₄×C₄₁	—	4	4	no	—
150	C₂²×C₄×C₄₁	—	4	4	no	—
151	C₂²×C₄×C₄₁	—	4	2	no	—
152	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₄₁	#41	1	2	yes	—
157	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
158	Q₁₆×C₄₁	—	2	16	no	—
159	SD₁₆×C₄₁	—	2	16	no	—
160	SD₁₆×C₄₁	—	4	4	no	—
161	D₈×C₄₁	—	4	4	no	—
162	M₁₆×C₄₁	—	2	8	no	—
163	C₂×C₈×C₄₁	—	2	2	no	—
164	C₂×C₈×C₄₁	—	2	2	no	—
165	C₂×C₈×C₄₁	—	2	1	no	—
166	C₂×C₈×C₄₁	—	2	1	no	—
167	C₂×C₈×C₄₁	—	2	2	no	—
168	C₂×C₈×C₄₁	—	2	2	no	—
169	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
170	C₄⋊C₄×C₄₁	—	2	2	no	—
171	C₄⋊C₄×C₄₁	—	2	1	no	—
172	C₄⋊C₄×C₄₁	—	2	1	no	—
173	C₄⋊C₄×C₄₁	—	2	2	no	—
174	C₄⋊C₄×C₄₁	—	4	4	no	—
175	C₂²⋊C₄×C₄₁	—	4	2	no	—
176	C₂²⋊C₄×C₄₁	—	4	4	no	—
177	C₂²⋊C₄×C₄₁	—	4	4	no	—
178	C₂²⋊C₄×C₄₁	—	4	4	no	—
179	C₂²⋊C₄×C₄₁	—	4	2	no	—
180	C₂²⋊C₄×C₄₁	—	8	2	no	—
181	C₂²⋊C₄×C₄₁	—	8	1	no	—
182	C₄²×C₄₁	—	2	2	no	—
183	C₄²×C₄₁	—	2	2	no	—
184	C₄²×C₄₁	—	4	4	no	—
185	C₂³×C₄₁	—	2	2	no	—
186	C₂³×C₄₁	—	2	2	no	—
187	C₂³×C₄₁	—	2	1	no	—
188	C₂³×C₄₁	—	2	1	no	—
189	C₂³×C₄₁	—	2	2	no	—
190	C₂³×C₄₁	—	4	2	no	—
191	C₂³×C₄₁	—	4	2	no	—
192	C₂³×C₄₁	—	4	1	no	—
193	C₂³×C₄₁	—	4	1	no	—
194	C₂³×C₄₁	—	4	1	no	—
195	C₂³×C₄₁	—	4	2	no	—
196	C₂³×C₄₁	—	4	2	no	—
197	C₂³×C₄₁	—	4	1	no	—
198	C₂³×C₄₁	—	4	1	no	—
199	C₂³×C₄₁	#121	1	2	yes	—
200	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
201	Q₈×C₄₁	—	2	2	no	—
202	Q₈×C₄₁	—	2	4	no	—
203	Q₈×C₄₁	—	2	4	no	—
204	Q₈×C₄₁	—	2	4	no	—
205	Q₈×C₄₁	—	4	8	no	—
206	Q₈×C₄₁	—	4	2	no	—
207	Q₈×C₄₁	—	4	2	no	—
208	Q₈×C₄₁	#120	1	4	yes	—
209	D₄×C₄₁	—	2	2	no	—
210	D₄×C₄₁	—	2	2	no	—
211	D₄×C₄₁	—	4	8	no	—
212	D₄×C₄₁	—	4	1	no	—
213	D₄×C₄₁	—	4	1	no	—
214	D₄×C₄₁	—	4	2	no	—
215	D₄×C₄₁	—	4	2	no	—
216	D₄×C₄₁	—	8	4	no	—
217	C₂×C₄×C₄₁	—	2	2	no	—
218	C₂×C₄×C₄₁	—	2	4	no	—
219	C₂×C₄×C₄₁	—	2	2	no	—
220	C₂×C₄×C₄₁	—	2	2	no	—
221	C₂×C₄×C₄₁	—	2	2	no	—
222	C₂×C₄×C₄₁	—	2	4	no	—
223	C₂×C₄×C₄₁	—	2	2	no	—
224	C₂×C₄×C₄₁	—	2	2	no	—
225	C₂×C₄×C₄₁	—	2	4	no	—
226	C₂×C₄×C₄₁	—	2	2	no	—
227	C₂×C₄×C₄₁	—	2	2	no	—
228	C₂×C₄×C₄₁	—	2	2	no	—
229	C₂×C₄×C₄₁	—	2	2	no	—
230	C₂×C₄×C₄₁	—	4	8	no	—
231	C₂×C₄×C₄₁	—	4	8	no	—
232	C₂×C₄×C₄₁	—	4	2	no	—
233	C₂×C₄×C₄₁	—	4	2	no	—
234	C₂×C₄×C₄₁	—	4	1	no	—
235	C₂×C₄×C₄₁	—	4	2	no	—
236	C₂×C₄×C₄₁	—	4	2	no	—
237	C₂×C₄×C₄₁	—	4	2	no	—
238	C₂×C₄×C₄₁	—	4	2	no	—
239	C₂×C₄×C₄₁	#121	1	2	yes	—
240	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
242	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
243	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
244	C₈×C₄₁	—	2	4	no	—
245	C₈×C₄₁	—	4	1	no	—
246	C₈×C₄₁	—	4	1	no	—
247	#24375	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
248	C₂²×C₄₁	—	2	2	no	—
249	C₂²×C₄₁	—	2	2	no	—
250	C₂²×C₄₁	—	2	2	no	—
251	C₂²×C₄₁	—	4	2	no	—
252	C₂²×C₄₁	—	4	2	no	—
253	C₂²×C₄₁	—	4	2	no	—
254	C₂²×C₄₁	—	4	2	no	—
255	C₂²×C₄₁	—	4	2	no	—
256	C₂²×C₄₁	—	8	2	no	—
257	C₂²×C₄₁	—	8	2	no	—
258	C₂²×C₄₁	—	8	1	no	—
259	C₂²×C₄₁	—	8	2	no	—
260	C₂²×C₄₁	—	8	2	no	—
261	C₂²×C₄₁	—	8	1	no	—
262	C₂²×C₄₁	—	8	1	no	—
263	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
264	C₂²×C₄₁	D₄²	1	2	yes	—
265	C₂²×C₄₁	#575	1	2	yes	—
266	C₂²×C₄₁	#577	1	1	yes	characteristic
267	C₂²×C₄₁	#578	1	1	yes	characteristic
268	C₄×C₄₁	—	2	2	no	—
269	C₄×C₄₁	—	2	4	no	—
270	C₄×C₄₁	—	4	4	no	—
271	C₄×C₄₁	—	4	2	no	—
272	C₄×C₄₁	—	4	2	no	—
273	C₄×C₄₁	—	8	2	no	—
274	C₄×C₄₁	—	8	1	no	—
275	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
276	C₄×C₄₁	#534	1	1	yes	characteristic
277	C₄×C₄₁	#546	1	2	yes	—
278	C₂²×#137	C₂×C₄₁	1	1	yes	characteristic, complemented
279	C₂×#464	C₂×C₄₁	1	2	yes	complemented
280	C₂×#449	C₂×C₄₁	1	1	yes	characteristic
281	#2436	C₂×C₄₁	1	1	yes	characteristic, complemented
282	#2341	C₂×C₄₁	1	1	yes	characteristic, complemented
283	#2055	C₂×C₄₁	1	2	yes	complemented
284	#2012	C₂×C₄₁	1	2	yes	complemented
285	#1895	C₂×C₄₁	1	1	yes	characteristic, complemented
286	#1878	C₂×C₄₁	1	2	yes	complemented
287	#1851	C₂×C₄₁	1	1	yes	characteristic, complemented
288	#1787	C₂×C₄₁	1	1	yes	characteristic, complemented
289	C₂×C₄₁	—	4	2	no	—
290	C₂×C₄₁	—	8	2	no	—
291	C₂×C₄₁	—	16	1	no	—
292	C₂×C₄₁	#2410	1	1	yes	characteristic
293	C₂×C₄₁	#3040	1	1	yes	characteristic
294	C₂×C₄₁	#3046	1	1	yes	characteristic
295	C₂×C₄₁	#3271	1	2	yes	—
296	C₂×C₄₁	#3277	1	2	yes	—
297	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
298	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
299	C₂×#137	—	2	4	no	—
300	C₂×#137	—	2	8	no	—
301	C₂²×Q₁₆	C₂²×C₄₁	1	2	yes	—
302	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
303	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
304	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
305	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
306	C₂×#124	C₂²×C₄₁	1	2	yes	—
307	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
308	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
309	#464	—	2	8	no	—
310	#449	—	2	4	no	—
311	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
312	C₂×#103	C₂²×C₄₁	1	2	yes	—
313	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
314	C₂×#103	C₂²×C₄₁	1	2	yes	—
315	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
316	C₂×#102	C₂²×C₄₁	1	2	yes	—
317	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
318	#393	—	2	1	no	—
319	#393	—	2	1	no	—
320	#391	C₂²×C₄₁	1	2	yes	—
321	#390	—	2	2	no	—
322	#390	C₂²×C₄₁	1	2	yes	—
323	#386	—	2	2	no	—
324	#380	—	2	1	no	—
325	#380	C₂²×C₄₁	1	1	yes	characteristic
326	C₄×C₂²⋊C₄	—	2	1	no	—
327	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
328	#340	C₂²×C₄₁	1	2	yes	—
329	#336	C₂²×C₄₁	1	2	yes	—
330	C₄₁	#24375	1	1	yes	characteristic, direct product factor, Sylow
331	C₂×#41	—	2	2	no	—
332	C₂×#41	—	2	4	no	—
333	C₂×#41	—	4	2	no	—
334	C₂×#41	D₄×C₄₁	1	4	yes	—
335	C₂²×Q₈	—	2	1	no	—
336	C₂²×Q₈	—	2	4	no	—
337	C₂²×Q₈	—	2	2	no	—
338	C₂²×Q₈	—	2	2	no	—
339	C₂²×Q₈	—	4	2	no	—
340	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
341	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
342	C₂²×D₄	—	2	1	no	—
343	C₂²×D₄	—	2	1	no	—
344	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
345	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
346	C₂³×C₄	—	2	1	no	—
347	C₂³×C₄	—	2	1	no	—
348	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
349	#137	—	2	32	no	—
350	C₂×Q₁₆	—	2	4	no	—
351	C₂×Q₁₆	—	2	4	no	—
352	C₂×Q₁₆	D₄×C₄₁	1	8	yes	complemented
353	C₂×SD₁₆	—	2	4	no	—
354	C₂×SD₁₆	—	2	4	no	—
355	C₂×SD₁₆	—	2	2	no	—
356	C₂×SD₁₆	—	2	4	no	—
357	C₂×SD₁₆	—	2	4	no	—
358	C₂×D₈	—	2	2	no	—
359	C₂×D₈	—	4	2	no	—
360	C₂×M₁₆	—	2	2	no	—
361	C₂×M₁₆	—	2	4	no	—
362	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
363	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
365	#124	—	2	4	no	—
366	#124	—	4	2	no	—
367	#121	—	2	2	no	—
368	#121	—	2	2	no	—
369	C₄×Q₈	—	2	4	no	—
370	C₄×Q₈	—	4	2	no	—
371	C₂×C₄⋊C₄	—	2	2	no	—
372	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
373	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
374	C₂×C₂²⋊C₄	—	2	1	no	—
375	C₂×C₂²⋊C₄	—	2	2	no	—
376	C₂×C₂²⋊C₄	—	2	2	no	—
377	C₂×C₂²⋊C₄	—	2	2	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
381	C₂×C₄²	—	2	2	no	—
382	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
383	C₄⋊C₈	—	2	4	no	—
384	#103	—	2	2	no	—
385	#103	—	2	4	no	—
386	#103	—	4	2	no	—
387	#102	—	2	2	no	—
388	#102	—	2	4	no	—
389	C₂²⋊C₈	—	2	2	no	—
390	#95	—	2	1	no	—
391	#95	—	2	2	no	—
392	#95	—	2	2	no	—
393	#95	D₄×C₄₁	1	1	yes	characteristic
394	#95	D₄×C₄₁	1	1	yes	characteristic
395	C₂⁴	—	2	1	no	—
396	C₂⁴	—	2	1	no	—
397	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
398	#41	—	2	8	no	—
399	#41	—	4	4	no	—
400	#41	—	4	8	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	8	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	4	4	no	—
410	C₂×Q₈	—	4	8	no	—
411	C₂×Q₈	—	4	4	no	—
412	C₂×Q₈	—	4	2	no	—
413	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
414	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
415	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
416	C₂×D₄	—	2	4	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	4	4	no	—
425	C₂×D₄	—	4	4	no	—
426	C₂×D₄	—	4	2	no	—
427	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	4	4	no	—
436	C₂²×C₄	—	4	4	no	—
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
439	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
440	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
442	C₂²×C₄	#41×C₄₁	1	2	yes	—
443	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
444	Q₁₆	—	2	16	no	—
445	SD₁₆	—	2	16	no	—
446	SD₁₆	—	4	4	no	—
447	D₈	—	4	4	no	—
448	M₁₆	—	2	8	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	4	4	no	—
461	C₂²⋊C₄	—	4	2	no	—
462	C₂²⋊C₄	—	4	4	no	—
463	C₂²⋊C₄	—	4	4	no	—
464	C₂²⋊C₄	—	4	4	no	—
465	C₂²⋊C₄	—	4	2	no	—
466	C₂²⋊C₄	—	8	2	no	—
467	C₂²⋊C₄	—	8	1	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	2	no	—
470	C₄²	—	4	4	no	—
471	C₂³	—	2	2	no	—
472	C₂³	—	2	2	no	—
473	C₂³	—	2	1	no	—
474	C₂³	—	2	1	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	4	2	no	—
477	C₂³	—	4	2	no	—
478	C₂³	—	4	1	no	—
479	C₂³	—	4	1	no	—
480	C₂³	—	4	1	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	1	no	—
485	C₂³	#121×C₄₁	1	2	yes	—
486	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
487	Q₈	—	2	2	no	—
488	Q₈	—	2	4	no	—
489	Q₈	—	2	4	no	—
490	Q₈	—	2	4	no	—
491	Q₈	—	4	8	no	—
492	Q₈	—	4	2	no	—
493	Q₈	—	4	2	no	—
494	Q₈	#120×C₄₁	1	4	yes	—
495	D₄	—	2	2	no	—
496	D₄	—	2	2	no	—
497	D₄	—	4	8	no	—
498	D₄	—	4	1	no	—
499	D₄	—	4	1	no	—
500	D₄	—	4	2	no	—
501	D₄	—	4	2	no	—
502	D₄	—	8	4	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	4	8	no	—
517	C₂×C₄	—	4	8	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	#121×C₄₁	1	2	yes	—
526	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
528	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
529	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
530	C₈	—	2	4	no	—
531	C₈	—	4	1	no	—
532	C₈	—	4	1	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	2	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	8	2	no	—
542	C₂²	—	8	2	no	—
543	C₂²	—	8	1	no	—
544	C₂²	—	8	1	no	—
545	C₂²	—	8	1	no	—
546	C₂²	—	8	2	no	—
547	C₂²	—	8	2	no	—
548	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
549	C₂²	D₄²×C₄₁	1	2	yes	—
550	C₂²	C₄₁×#575	1	2	yes	—
551	C₂²	C₄₁×#577	1	1	yes	characteristic
552	C₂²	C₄₁×#578	1	1	yes	characteristic
553	C₄	—	2	2	no	—
554	C₄	—	2	4	no	—
555	C₄	—	4	4	no	—
556	C₄	—	4	2	no	—
557	C₄	—	4	2	no	—
558	C₄	—	8	1	no	—
559	C₄	—	8	2	no	—
560	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
561	C₄	C₄₁×#534	1	1	yes	characteristic
562	C₄	C₄₁×#546	1	2	yes	—
563	C₂	—	4	2	no	—
564	C₂	—	8	2	no	—
565	C₂	—	16	1	no	—
566	C₂	C₄₁×#2410	1	1	yes	characteristic
567	C₂	C₄₁×#3040	1	1	yes	characteristic
568	C₂	C₄₁×#3046	1	1	yes	characteristic
569	C₂	C₄₁×#3271	1	2	yes	—
570	C₂	C₄₁×#3277	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#449	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄×C₂²⋊C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#137×C₄₁	C₂	semidirect
2. C₂×C₄₁×#464	C₂	semidirect
4. C₄₁×#2436	C₂	semidirect
5. C₄₁×#2341	C₂	semidirect
6. C₄₁×#2055	C₂	semidirect
7. C₄₁×#2012	C₂	semidirect
8. C₄₁×#1895	C₂	semidirect
9. C₄₁×#1878	C₂	semidirect
10. C₄₁×#1851	C₂	semidirect
11. C₄₁×#1787	C₂	semidirect
66. C₂×Q₁₆×C₄₁	D₄	semidirect
247. #24375	C₄₁	direct (N × H)
278. C₂²×#137	C₂×C₄₁	semidirect
279. C₂×#464	C₂×C₄₁	semidirect
281. #2436	C₂×C₄₁	semidirect
282. #2341	C₂×C₄₁	semidirect
283. #2055	C₂×C₄₁	semidirect
284. #2012	C₂×C₄₁	semidirect
285. #1895	C₂×C₄₁	semidirect
286. #1878	C₂×C₄₁	semidirect
287. #1851	C₂×C₄₁	semidirect
288. #1787	C₂×C₄₁	semidirect
330. C₄₁	#24375	direct (N × H)
352. C₂×Q₁₆	D₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#137×C₄₁	2
C₂×C₄₁×#464	2
C₂×C₄₁×#449	2
C₄₁×#2436	2
C₄₁×#2341	2
C₄₁×#2055	2
C₄₁×#2012	2
C₄₁×#1895	2
C₄₁×#1878	2
C₄₁×#1851	2
C₄₁×#1787	2
#24375	41

Subgroups — C41×#24375 #23800576

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24375 #23800576