Subgroups — C₄₁×#25426 #23801627

Order 10496.

1220 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#493	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#469	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#469	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#442	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2428	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2041	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1999	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1972	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1941	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1879	C₂	1	2	yes	maximal, complemented
11	C₄₁×#1753	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂²×D₈×C₄₁	C₂²	1	2	yes	—
14	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×#127×C₄₁	C₂²	1	2	yes	—
17	C₂×#121×C₄₁	—	2	2	no	—
18	C₂×#121×C₄₁	C₂²	1	2	yes	—
19	C₂×#121×C₄₁	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
21	C₄₁×#493	—	2	4	no	—
22	C₄₁×#469	—	2	4	no	—
23	C₄₁×#469	—	2	4	no	—
24	C₄₁×#442	—	2	4	no	—
25	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×#102×C₄₁	C₂²	1	2	yes	—
28	C₂×#102×C₄₁	C₂²	1	2	yes	—
29	C₂×#102×C₄₁	C₂²	1	2	yes	—
30	C₂×#102×C₄₁	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
34	C₄₁×#394	—	2	2	no	—
35	C₄₁×#392	—	2	2	no	—
36	C₄₁×#390	C₂²	1	2	yes	—
37	C₄₁×#389	C₂²	1	2	yes	—
38	C₄₁×#386	—	2	2	no	—
39	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
40	C₄₁×#340	C₂²	1	2	yes	—
41	C₄₁×#336	C₂²	1	1	yes	characteristic
42	C₄₁×#336	C₂²	1	1	yes	characteristic
43	C₂²×D₄×C₄₁	—	2	2	no	—
44	C₂²×D₄×C₄₁	—	2	2	no	—
45	C₂²×D₄×C₄₁	—	2	2	no	—
46	C₂²×D₄×C₄₁	—	2	2	no	—
47	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
48	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
49	C₂³×C₄×C₄₁	—	2	2	no	—
50	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
51	C₂×D₈×C₄₁	—	2	4	no	—
52	C₂×D₈×C₄₁	—	2	2	no	—
53	C₂×D₈×C₄₁	—	2	2	no	—
54	C₂×D₈×C₄₁	—	2	2	no	—
55	C₂×D₈×C₄₁	—	2	2	no	—
56	C₂×D₈×C₄₁	—	2	4	no	—
57	C₂×D₈×C₄₁	—	2	2	no	—
58	C₂×D₈×C₄₁	—	4	2	no	—
59	C₂×D₈×C₄₁	D₄	1	4	yes	complemented
60	C₂×M₁₆×C₄₁	—	2	2	no	—
61	C₂×M₁₆×C₄₁	—	2	2	no	—
62	C₂×M₁₆×C₄₁	—	2	2	no	—
63	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
67	#127×C₄₁	—	2	4	no	—
68	#127×C₄₁	—	4	2	no	—
69	#121×C₄₁	—	2	4	no	—
70	#121×C₄₁	—	2	4	no	—
71	#121×C₄₁	—	4	8	no	—
72	#121×C₄₁	—	4	2	no	—
73	#121×C₄₁	—	4	2	no	—
74	C₄×D₄×C₄₁	—	2	4	no	—
75	C₄×D₄×C₄₁	—	4	2	no	—
76	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
77	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
85	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
87	#106×C₄₁	—	2	2	no	—
88	#106×C₄₁	D₄	1	4	yes	complemented
89	#102×C₄₁	—	2	4	no	—
90	#102×C₄₁	—	2	4	no	—
91	#102×C₄₁	—	2	4	no	—
92	#102×C₄₁	—	4	2	no	—
93	C₂²⋊C₈×C₄₁	—	2	2	no	—
94	#97×C₄₁	—	2	2	no	—
95	C₄×C₈×C₄₁	—	2	2	no	—
96	#95×C₄₁	—	2	2	no	—
97	#95×C₄₁	D₄	1	2	yes	—
98	C₂⁴×C₄₁	—	2	2	no	—
99	C₂⁴×C₄₁	—	2	2	no	—
100	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
101	C₂×D₄×C₄₁	—	2	2	no	—
102	C₂×D₄×C₄₁	—	2	2	no	—
103	C₂×D₄×C₄₁	—	2	2	no	—
104	C₂×D₄×C₄₁	—	2	2	no	—
105	C₂×D₄×C₄₁	—	2	2	no	—
106	C₂×D₄×C₄₁	—	2	2	no	—
107	C₂×D₄×C₄₁	—	2	2	no	—
108	C₂×D₄×C₄₁	—	2	2	no	—
109	C₂×D₄×C₄₁	—	2	2	no	—
110	C₂×D₄×C₄₁	—	2	2	no	—
111	C₂×D₄×C₄₁	—	2	2	no	—
112	C₂×D₄×C₄₁	—	4	4	no	—
113	C₂×D₄×C₄₁	—	4	4	no	—
114	C₂×D₄×C₄₁	—	4	4	no	—
115	C₂×D₄×C₄₁	—	4	4	no	—
116	C₂×D₄×C₄₁	—	4	4	no	—
117	C₂×D₄×C₄₁	—	4	4	no	—
118	C₂×D₄×C₄₁	—	4	4	no	—
119	C₂×D₄×C₄₁	—	4	4	no	—
120	C₂×D₄×C₄₁	—	8	2	no	—
121	C₂×D₄×C₄₁	—	8	2	no	—
122	C₂×D₄×C₄₁	—	8	2	no	—
123	C₂×D₄×C₄₁	—	8	2	no	—
124	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
125	C₂²×C₄×C₄₁	—	2	2	no	—
126	C₂²×C₄×C₄₁	—	2	1	no	—
127	C₂²×C₄×C₄₁	—	2	1	no	—
128	C₂²×C₄×C₄₁	—	2	1	no	—
129	C₂²×C₄×C₄₁	—	2	1	no	—
130	C₂²×C₄×C₄₁	—	2	1	no	—
131	C₂²×C₄×C₄₁	—	2	1	no	—
132	C₂²×C₄×C₄₁	—	2	2	no	—
133	C₂²×C₄×C₄₁	—	4	4	no	—
134	C₂²×C₄×C₄₁	—	4	4	no	—
135	C₂²×C₄×C₄₁	—	8	2	no	—
136	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
140	D₈×C₄₁	—	2	8	no	—
141	D₈×C₄₁	—	4	8	no	—
142	D₈×C₄₁	—	4	4	no	—
143	M₁₆×C₄₁	—	4	4	no	—
144	C₂×C₈×C₄₁	—	2	1	no	—
145	C₂×C₈×C₄₁	—	2	1	no	—
146	C₂×C₈×C₄₁	—	2	1	no	—
147	C₂×C₈×C₄₁	—	2	1	no	—
148	C₂×C₈×C₄₁	—	2	1	no	—
149	C₂×C₈×C₄₁	—	2	1	no	—
150	C₂×C₈×C₄₁	—	2	1	no	—
151	C₂×C₈×C₄₁	—	2	1	no	—
152	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
154	C₂×C₈×C₄₁	#41	1	2	yes	—
155	C₂×C₈×C₄₁	#41	1	2	yes	—
156	C₄⋊C₄×C₄₁	—	2	2	no	—
157	C₄⋊C₄×C₄₁	—	2	2	no	—
158	C₄⋊C₄×C₄₁	—	2	2	no	—
159	C₄⋊C₄×C₄₁	—	4	4	no	—
160	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
161	C₂²⋊C₄×C₄₁	—	2	4	no	—
162	C₂²⋊C₄×C₄₁	—	4	4	no	—
163	C₂²⋊C₄×C₄₁	—	4	4	no	—
164	C₂²⋊C₄×C₄₁	—	4	4	no	—
165	C₂²⋊C₄×C₄₁	—	4	4	no	—
166	C₂²⋊C₄×C₄₁	—	8	2	no	—
167	C₄²×C₄₁	—	2	1	no	—
168	C₄²×C₄₁	—	2	1	no	—
169	C₄²×C₄₁	—	2	1	no	—
170	C₄²×C₄₁	—	2	1	no	—
171	C₂³×C₄₁	—	2	1	no	—
172	C₂³×C₄₁	—	2	4	no	—
173	C₂³×C₄₁	—	2	1	no	—
174	C₂³×C₄₁	—	2	1	no	—
175	C₂³×C₄₁	—	2	2	no	—
176	C₂³×C₄₁	—	2	2	no	—
177	C₂³×C₄₁	—	4	2	no	—
178	C₂³×C₄₁	—	4	2	no	—
179	C₂³×C₄₁	—	4	2	no	—
180	C₂³×C₄₁	—	4	2	no	—
181	C₂³×C₄₁	—	4	2	no	—
182	C₂³×C₄₁	—	4	2	no	—
183	C₂³×C₄₁	—	4	2	no	—
184	C₂³×C₄₁	—	4	2	no	—
185	C₂³×C₄₁	—	4	2	no	—
186	C₂³×C₄₁	—	4	2	no	—
187	C₂³×C₄₁	—	4	2	no	—
188	C₂³×C₄₁	—	4	2	no	—
189	C₂³×C₄₁	—	4	2	no	—
190	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
191	D₄×C₄₁	—	2	4	no	—
192	D₄×C₄₁	—	2	4	no	—
193	D₄×C₄₁	—	4	2	no	—
194	D₄×C₄₁	—	4	2	no	—
195	D₄×C₄₁	—	4	2	no	—
196	D₄×C₄₁	—	4	2	no	—
197	D₄×C₄₁	—	4	2	no	—
198	D₄×C₄₁	—	4	2	no	—
199	D₄×C₄₁	—	8	8	no	—
200	D₄×C₄₁	—	8	8	no	—
201	D₄×C₄₁	—	8	8	no	—
202	D₄×C₄₁	—	8	8	no	—
203	C₂×C₄×C₄₁	—	2	2	no	—
204	C₂×C₄×C₄₁	—	2	2	no	—
205	C₂×C₄×C₄₁	—	2	1	no	—
206	C₂×C₄×C₄₁	—	2	2	no	—
207	C₂×C₄×C₄₁	—	2	1	no	—
208	C₂×C₄×C₄₁	—	2	1	no	—
209	C₂×C₄×C₄₁	—	2	4	no	—
210	C₂×C₄×C₄₁	—	2	2	no	—
211	C₂×C₄×C₄₁	—	2	2	no	—
212	C₂×C₄×C₄₁	—	4	2	no	—
213	C₂×C₄×C₄₁	—	4	2	no	—
214	C₂×C₄×C₄₁	—	4	1	no	—
215	C₂×C₄×C₄₁	—	4	1	no	—
216	C₂×C₄×C₄₁	—	4	1	no	—
217	C₂×C₄×C₄₁	—	4	1	no	—
218	C₂×C₄×C₄₁	—	4	2	no	—
219	C₂×C₄×C₄₁	—	4	2	no	—
220	C₂×C₄×C₄₁	—	4	2	no	—
221	C₂×C₄×C₄₁	—	8	8	no	—
222	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	4	yes	—
223	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
228	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
229	C₈×C₄₁	—	2	2	no	—
230	C₈×C₄₁	—	4	1	no	—
231	C₈×C₄₁	—	4	1	no	—
232	C₈×C₄₁	#121	1	4	yes	complemented
233	#25426	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂²×C₄₁	—	4	1	no	—
235	C₂²×C₄₁	—	4	1	no	—
236	C₂²×C₄₁	—	4	1	no	—
237	C₂²×C₄₁	—	4	4	no	—
238	C₂²×C₄₁	—	4	2	no	—
239	C₂²×C₄₁	—	4	4	no	—
240	C₂²×C₄₁	—	4	4	no	—
241	C₂²×C₄₁	—	4	2	no	—
242	C₂²×C₄₁	—	8	2	no	—
243	C₂²×C₄₁	—	8	2	no	—
244	C₂²×C₄₁	—	8	2	no	—
245	C₂²×C₄₁	—	8	2	no	—
246	C₂²×C₄₁	—	8	2	no	—
247	C₂²×C₄₁	—	8	2	no	—
248	C₂²×C₄₁	—	8	2	no	—
249	C₂²×C₄₁	—	8	2	no	—
250	C₂²×C₄₁	—	8	2	no	—
251	C₂²×C₄₁	—	8	2	no	—
252	C₂²×C₄₁	—	8	2	no	—
253	C₂²×C₄₁	#532	1	1	yes	characteristic
254	C₂²×C₄₁	D₄²	1	1	yes	characteristic
255	C₂²×C₄₁	D₄²	1	1	yes	characteristic
256	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
257	C₂²×C₄₁	#576	1	2	yes	—
258	C₄×C₄₁	—	2	4	no	—
259	C₄×C₄₁	—	4	1	no	—
260	C₄×C₄₁	—	4	2	no	—
261	C₄×C₄₁	—	4	4	no	—
262	C₄×C₄₁	—	8	2	no	—
263	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
264	C₄×C₄₁	#540	1	1	yes	characteristic
265	C₄×C₄₁	#546	1	1	yes	characteristic
266	C₄×C₄₁	#550	1	1	yes	characteristic
267	C₂×#493	C₂×C₄₁	1	1	yes	characteristic, complemented
268	C₂×#469	C₂×C₄₁	1	1	yes	characteristic, complemented
269	C₂×#469	C₂×C₄₁	1	1	yes	characteristic, complemented
270	C₂×#442	C₂×C₄₁	1	1	yes	characteristic, complemented
271	#2428	C₂×C₄₁	1	2	yes	complemented
272	#2041	C₂×C₄₁	1	2	yes	complemented
273	#1999	C₂×C₄₁	1	2	yes	complemented
274	#1972	C₂×C₄₁	1	1	yes	characteristic, complemented
275	#1941	C₂×C₄₁	1	1	yes	characteristic, complemented
276	#1879	C₂×C₄₁	1	2	yes	complemented
277	#1753	C₂×C₄₁	1	1	yes	characteristic, complemented
278	C₂×C₄₁	—	8	1	no	—
279	C₂×C₄₁	—	8	4	no	—
280	C₂×C₄₁	—	16	2	no	—
281	C₂×C₄₁	#2428	1	1	yes	characteristic
282	C₂×C₄₁	#3176	1	1	yes	characteristic
283	C₂×C₄₁	#3184	1	1	yes	characteristic
284	C₂×C₄₁	#3264	1	2	yes	—
285	C₂×C₄₁	#3274	1	2	yes	—
286	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
287	C₂²×D₈	C₂²×C₄₁	1	2	yes	—
288	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
289	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
290	C₂×#127	C₂²×C₄₁	1	2	yes	—
291	C₂×#121	—	2	2	no	—
292	C₂×#121	C₂²×C₄₁	1	2	yes	—
293	C₂×#121	C₂²×C₄₁	1	2	yes	—
294	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
295	#493	—	2	4	no	—
296	#469	—	2	4	no	—
297	#469	—	2	4	no	—
298	#442	—	2	4	no	—
299	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
300	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
301	C₂×#102	C₂²×C₄₁	1	2	yes	—
302	C₂×#102	C₂²×C₄₁	1	2	yes	—
303	C₂×#102	C₂²×C₄₁	1	2	yes	—
304	C₂×#102	C₂²×C₄₁	1	2	yes	—
305	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
306	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
307	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
308	#394	—	2	2	no	—
309	#392	—	2	2	no	—
310	#390	C₂²×C₄₁	1	2	yes	—
311	#389	C₂²×C₄₁	1	2	yes	—
312	#386	—	2	2	no	—
313	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
314	#340	C₂²×C₄₁	1	2	yes	—
315	#336	C₂²×C₄₁	1	1	yes	characteristic
316	#336	C₂²×C₄₁	1	1	yes	characteristic
317	C₄₁	#25426	1	1	yes	characteristic, direct product factor, Sylow
318	C₂²×D₄	—	2	2	no	—
319	C₂²×D₄	—	2	2	no	—
320	C₂²×D₄	—	2	2	no	—
321	C₂²×D₄	—	2	2	no	—
322	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
323	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
324	C₂³×C₄	—	2	2	no	—
325	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
326	C₂×D₈	—	2	4	no	—
327	C₂×D₈	—	2	2	no	—
328	C₂×D₈	—	2	2	no	—
329	C₂×D₈	—	2	2	no	—
330	C₂×D₈	—	2	2	no	—
331	C₂×D₈	—	2	4	no	—
332	C₂×D₈	—	2	2	no	—
333	C₂×D₈	—	4	2	no	—
334	C₂×D₈	D₄×C₄₁	1	4	yes	complemented
335	C₂×M₁₆	—	2	2	no	—
336	C₂×M₁₆	—	2	2	no	—
337	C₂×M₁₆	—	2	2	no	—
338	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
342	#127	—	2	4	no	—
343	#127	—	4	2	no	—
344	#121	—	2	4	no	—
345	#121	—	2	4	no	—
346	#121	—	4	8	no	—
347	#121	—	4	2	no	—
348	#121	—	4	2	no	—
349	C₄×D₄	—	2	4	no	—
350	C₄×D₄	—	4	2	no	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
353	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
360	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
361	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
362	#106	—	2	2	no	—
363	#106	D₄×C₄₁	1	4	yes	complemented
364	#102	—	2	4	no	—
365	#102	—	2	4	no	—
366	#102	—	2	4	no	—
367	#102	—	4	2	no	—
368	C₂²⋊C₈	—	2	2	no	—
369	#97	—	2	2	no	—
370	C₄×C₈	—	2	2	no	—
371	#95	—	2	2	no	—
372	#95	D₄×C₄₁	1	2	yes	—
373	C₂⁴	—	2	2	no	—
374	C₂⁴	—	2	2	no	—
375	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	4	4	no	—
388	C₂×D₄	—	4	4	no	—
389	C₂×D₄	—	4	4	no	—
390	C₂×D₄	—	4	4	no	—
391	C₂×D₄	—	4	4	no	—
392	C₂×D₄	—	4	4	no	—
393	C₂×D₄	—	4	4	no	—
394	C₂×D₄	—	4	4	no	—
395	C₂×D₄	—	8	2	no	—
396	C₂×D₄	—	8	2	no	—
397	C₂×D₄	—	8	2	no	—
398	C₂×D₄	—	8	2	no	—
399	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	4	4	no	—
409	C₂²×C₄	—	4	4	no	—
410	C₂²×C₄	—	8	2	no	—
411	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
413	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
414	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
415	D₈	—	2	8	no	—
416	D₈	—	4	8	no	—
417	D₈	—	4	4	no	—
418	M₁₆	—	4	4	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
428	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
429	C₂×C₈	#41×C₄₁	1	2	yes	—
430	C₂×C₈	#41×C₄₁	1	2	yes	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	4	4	no	—
435	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
436	C₂²⋊C₄	—	2	4	no	—
437	C₂²⋊C₄	—	4	4	no	—
438	C₂²⋊C₄	—	4	4	no	—
439	C₂²⋊C₄	—	4	4	no	—
440	C₂²⋊C₄	—	4	4	no	—
441	C₂²⋊C₄	—	8	2	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	2	1	no	—
446	C₂³	—	2	1	no	—
447	C₂³	—	2	4	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	2	no	—
465	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
466	D₄	—	2	4	no	—
467	D₄	—	2	4	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	2	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	8	8	no	—
475	D₄	—	8	8	no	—
476	D₄	—	8	8	no	—
477	D₄	—	8	8	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	8	8	no	—
497	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	4	yes	—
498	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
499	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
500	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
501	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
502	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
503	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
504	C₈	—	2	2	no	—
505	C₈	—	4	1	no	—
506	C₈	—	4	1	no	—
507	C₈	#121×C₄₁	1	4	yes	complemented
508	C₂²	—	4	1	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	4	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	4	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	8	2	no	—
517	C₂²	—	8	2	no	—
518	C₂²	—	8	2	no	—
519	C₂²	—	8	2	no	—
520	C₂²	—	8	2	no	—
521	C₂²	—	8	2	no	—
522	C₂²	—	8	2	no	—
523	C₂²	—	8	2	no	—
524	C₂²	—	8	2	no	—
525	C₂²	—	8	2	no	—
526	C₂²	—	8	2	no	—
527	C₂²	C₄₁×#532	1	1	yes	characteristic
528	C₂²	D₄²×C₄₁	1	1	yes	characteristic
529	C₂²	D₄²×C₄₁	1	1	yes	characteristic
530	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
531	C₂²	C₄₁×#576	1	2	yes	—
532	C₄	—	2	4	no	—
533	C₄	—	4	1	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	4	no	—
536	C₄	—	8	2	no	—
537	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
538	C₄	C₄₁×#540	1	1	yes	characteristic
539	C₄	C₄₁×#546	1	1	yes	characteristic
540	C₄	C₄₁×#550	1	1	yes	characteristic
541	C₂	—	8	1	no	—
542	C₂	—	8	4	no	—
543	C₂	—	16	2	no	—
544	C₂	C₄₁×#2428	1	1	yes	characteristic
545	C₂	C₄₁×#3176	1	1	yes	characteristic
546	C₂	C₄₁×#3184	1	1	yes	characteristic
547	C₂	C₄₁×#3264	1	2	yes	—
548	C₂	C₄₁×#3274	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
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. C₂×C₄₁×#493	C₂	semidirect
2. C₂×C₄₁×#469	C₂	semidirect
3. C₂×C₄₁×#469	C₂	semidirect
4. C₂×C₄₁×#442	C₂	semidirect
5. C₄₁×#2428	C₂	semidirect
6. C₄₁×#2041	C₂	semidirect
7. C₄₁×#1999	C₂	semidirect
8. C₄₁×#1972	C₂	semidirect
9. C₄₁×#1941	C₂	semidirect
10. C₄₁×#1879	C₂	semidirect
11. C₄₁×#1753	C₂	semidirect
59. C₂×D₈×C₄₁	D₄	semidirect
88. #106×C₄₁	D₄	semidirect
232. C₈×C₄₁	#121	semidirect
233. #25426	C₄₁	direct (N × H)
267. C₂×#493	C₂×C₄₁	semidirect
268. C₂×#469	C₂×C₄₁	semidirect
269. C₂×#469	C₂×C₄₁	semidirect
270. C₂×#442	C₂×C₄₁	semidirect
271. #2428	C₂×C₄₁	semidirect
272. #2041	C₂×C₄₁	semidirect
273. #1999	C₂×C₄₁	semidirect
274. #1972	C₂×C₄₁	semidirect
275. #1941	C₂×C₄₁	semidirect
276. #1879	C₂×C₄₁	semidirect
277. #1753	C₂×C₄₁	semidirect
317. C₄₁	#25426	direct (N × H)
334. C₂×D₈	D₄×C₄₁	semidirect
363. #106	D₄×C₄₁	semidirect
507. C₈	#121×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#493	2
C₂×C₄₁×#469	2
C₂×C₄₁×#442	2
C₄₁×#2428	2
C₄₁×#2041	2
C₄₁×#1999	2
C₄₁×#1972	2
C₄₁×#1941	2
C₄₁×#1879	2
C₄₁×#1753	2
#25426	41

Subgroups — C41×#25426 #23801627

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25426 #23801627