Subgroups — C₄₁×#24642 #23800843

Order 10496.

1068 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#459	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2541	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2357	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2054	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2011	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1982	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1961	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1940	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1926	C₂	1	2	yes	maximal, complemented
11	C₄₁×#1804	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	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×#127×C₄₁	C₂²	1	2	yes	—
16	C₂×#121×C₄₁	—	2	2	no	—
17	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
19	C₄₁×#459	—	2	4	no	—
20	C₄₁×#442	—	2	4	no	—
21	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
24	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#102×C₄₁	C₂²	1	2	yes	—
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×#97×C₄₁	C₂²	1	1	yes	characteristic
31	C₄₁×#392	—	2	1	no	—
32	C₄₁×#392	—	2	1	no	—
33	C₄₁×#390	C₂²	1	2	yes	—
34	C₄₁×#390	C₂²	1	2	yes	—
35	C₄₁×#388	—	2	2	no	—
36	C₄₁×#382	C₂²	1	1	yes	characteristic
37	C₄₁×#381	—	2	1	no	—
38	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
39	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
41	C₄₁×#340	C₂²	1	2	yes	—
42	C₄₁×#336	C₂²	1	2	yes	—
43	C₂²×D₄×C₄₁	—	2	1	no	—
44	C₂²×D₄×C₄₁	—	2	2	no	—
45	C₂²×D₄×C₄₁	—	2	2	no	—
46	C₂²×D₄×C₄₁	—	2	1	no	—
47	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
48	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₄₁	—	2	1	no	—
51	C₂³×C₄×C₄₁	—	2	1	no	—
52	C₂×D₈×C₄₁	—	2	2	no	—
53	C₂×D₈×C₄₁	—	2	2	no	—
54	C₂×D₈×C₄₁	—	2	4	no	—
55	C₂×D₈×C₄₁	—	2	2	no	—
56	C₂×D₈×C₄₁	—	4	2	no	—
57	C₂×D₈×C₄₁	—	4	2	no	—
58	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
59	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
61	#127×C₄₁	—	2	4	no	—
62	#127×C₄₁	—	2	2	no	—
63	#127×C₄₁	—	2	2	no	—
64	#127×C₄₁	—	4	2	no	—
65	#121×C₄₁	—	4	8	no	—
66	C₄×D₄×C₄₁	—	2	2	no	—
67	C₄×D₄×C₄₁	—	2	2	no	—
68	C₄×D₄×C₄₁	—	2	2	no	—
69	C₄×D₄×C₄₁	D₄	1	4	yes	complemented
70	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
80	C₂×C₄²×C₄₁	—	2	2	no	—
81	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
82	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
83	#106×C₄₁	—	2	2	no	—
84	C₄⋊C₈×C₄₁	—	2	2	no	—
85	C₄⋊C₈×C₄₁	—	4	2	no	—
86	#102×C₄₁	—	2	2	no	—
87	#102×C₄₁	—	2	4	no	—
88	#102×C₄₁	—	2	2	no	—
89	#102×C₄₁	—	2	4	no	—
90	#102×C₄₁	—	4	2	no	—
91	#102×C₄₁	—	4	2	no	—
92	#97×C₄₁	—	2	2	no	—
93	#95×C₄₁	—	2	1	no	—
94	#95×C₄₁	—	2	2	no	—
95	#95×C₄₁	—	2	1	no	—
96	#95×C₄₁	D₄	1	1	yes	characteristic
97	#95×C₄₁	D₄	1	1	yes	characteristic
98	C₂⁴×C₄₁	—	2	1	no	—
99	C₂⁴×C₄₁	—	2	1	no	—
100	C₂⁴×C₄₁	—	2	2	no	—
101	C₂×D₄×C₄₁	—	2	1	no	—
102	C₂×D₄×C₄₁	—	2	2	no	—
103	C₂×D₄×C₄₁	—	2	1	no	—
104	C₂×D₄×C₄₁	—	2	1	no	—
105	C₂×D₄×C₄₁	—	2	1	no	—
106	C₂×D₄×C₄₁	—	2	1	no	—
107	C₂×D₄×C₄₁	—	2	1	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	1	no	—
112	C₂×D₄×C₄₁	—	2	1	no	—
113	C₂×D₄×C₄₁	—	2	1	no	—
114	C₂×D₄×C₄₁	—	2	1	no	—
115	C₂×D₄×C₄₁	—	2	2	no	—
116	C₂×D₄×C₄₁	—	2	2	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	—	4	4	no	—
121	C₂×D₄×C₄₁	—	4	2	no	—
122	C₂×D₄×C₄₁	—	4	2	no	—
123	C₂×D₄×C₄₁	—	4	4	no	—
124	C₂×D₄×C₄₁	—	8	2	no	—
125	C₂×D₄×C₄₁	—	8	2	no	—
126	C₂×D₄×C₄₁	—	8	2	no	—
127	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
128	C₂×D₄×C₄₁	#41	1	2	yes	—
129	C₂²×C₄×C₄₁	—	2	1	no	—
130	C₂²×C₄×C₄₁	—	2	4	no	—
131	C₂²×C₄×C₄₁	—	2	2	no	—
132	C₂²×C₄×C₄₁	—	2	1	no	—
133	C₂²×C₄×C₄₁	—	4	4	no	—
134	C₂²×C₄×C₄₁	—	4	2	no	—
135	C₂²×C₄×C₄₁	—	8	2	no	—
136	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
141	D₈×C₄₁	—	2	8	no	—
142	D₈×C₄₁	—	4	8	no	—
143	C₂×C₈×C₄₁	—	2	1	no	—
144	C₂×C₈×C₄₁	—	2	1	no	—
145	C₂×C₈×C₄₁	—	2	1	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	—	2	2	no	—
151	C₂×C₈×C₄₁	#41	1	2	yes	—
152	C₄⋊C₄×C₄₁	—	2	4	no	—
153	C₄⋊C₄×C₄₁	—	2	1	no	—
154	C₄⋊C₄×C₄₁	—	2	1	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	C₂×D₄	1	2	yes	—
159	C₂²⋊C₄×C₄₁	—	2	4	no	—
160	C₂²⋊C₄×C₄₁	—	4	4	no	—
161	C₂²⋊C₄×C₄₁	—	4	2	no	—
162	C₂²⋊C₄×C₄₁	—	4	4	no	—
163	C₂²⋊C₄×C₄₁	—	4	4	no	—
164	C₂²⋊C₄×C₄₁	—	8	2	no	—
165	C₄²×C₄₁	—	2	2	no	—
166	C₄²×C₄₁	—	2	2	no	—
167	C₄²×C₄₁	—	8	2	no	—
168	C₄²×C₄₁	C₂×D₄	1	2	yes	—
169	C₄²×C₄₁	#41	1	2	yes	—
170	C₂³×C₄₁	—	2	2	no	—
171	C₂³×C₄₁	—	2	2	no	—
172	C₂³×C₄₁	—	4	1	no	—
173	C₂³×C₄₁	—	4	1	no	—
174	C₂³×C₄₁	—	4	1	no	—
175	C₂³×C₄₁	—	4	1	no	—
176	C₂³×C₄₁	—	4	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	C₂²×D₄	1	1	yes	characteristic
188	D₄×C₄₁	—	2	2	no	—
189	D₄×C₄₁	—	2	2	no	—
190	D₄×C₄₁	—	2	2	no	—
191	D₄×C₄₁	—	2	2	no	—
192	D₄×C₄₁	—	4	2	no	—
193	D₄×C₄₁	—	4	1	no	—
194	D₄×C₄₁	—	4	2	no	—
195	D₄×C₄₁	—	4	1	no	—
196	D₄×C₄₁	—	4	2	no	—
197	D₄×C₄₁	—	4	1	no	—
198	D₄×C₄₁	—	4	1	no	—
199	D₄×C₄₁	—	4	2	no	—
200	D₄×C₄₁	—	8	8	no	—
201	D₄×C₄₁	—	8	4	no	—
202	D₄×C₄₁	—	8	4	no	—
203	D₄×C₄₁	—	8	8	no	—
204	C₂×C₄×C₄₁	—	2	2	no	—
205	C₂×C₄×C₄₁	—	2	2	no	—
206	C₂×C₄×C₄₁	—	2	2	no	—
207	C₂×C₄×C₄₁	—	2	2	no	—
208	C₂×C₄×C₄₁	—	2	2	no	—
209	C₂×C₄×C₄₁	—	2	2	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	1	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	—	4	2	no	—
218	C₂×C₄×C₄₁	—	8	4	no	—
219	C₂×C₄×C₄₁	—	8	4	no	—
220	C₂×C₄×C₄₁	#121	1	2	yes	—
221	C₂×C₄×C₄₁	#121	1	2	yes	—
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	C₂×#41	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	2	no	—
232	#24642	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	4	4	no	—
238	C₂²×C₄₁	—	8	2	no	—
239	C₂²×C₄₁	—	8	2	no	—
240	C₂²×C₄₁	—	8	1	no	—
241	C₂²×C₄₁	—	8	1	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	C₂×#121	1	1	yes	characteristic
251	C₂²×C₄₁	#546	1	1	yes	characteristic
252	C₂²×C₄₁	#550	1	1	yes	characteristic
253	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
254	C₂²×C₄₁	#576	1	2	yes	—
255	C₄×C₄₁	—	2	2	no	—
256	C₄×C₄₁	—	2	2	no	—
257	C₄×C₄₁	—	2	4	no	—
258	C₄×C₄₁	—	4	2	no	—
259	C₄×C₄₁	—	4	2	no	—
260	C₄×C₄₁	—	8	2	no	—
261	C₄×C₄₁	—	8	1	no	—
262	C₄×C₄₁	#525	1	1	yes	characteristic
263	C₄×C₄₁	#535	1	1	yes	characteristic
264	C₄×C₄₁	#553	1	1	yes	characteristic
265	C₄×C₄₁	#555	1	1	yes	characteristic
266	C₂×#459	C₂×C₄₁	1	1	yes	characteristic, complemented
267	C₂×#442	C₂×C₄₁	1	1	yes	characteristic, complemented
268	#2541	C₂×C₄₁	1	1	yes	characteristic, complemented
269	#2357	C₂×C₄₁	1	1	yes	characteristic, complemented
270	#2054	C₂×C₄₁	1	2	yes	complemented
271	#2011	C₂×C₄₁	1	2	yes	complemented
272	#1982	C₂×C₄₁	1	2	yes	complemented
273	#1961	C₂×C₄₁	1	1	yes	characteristic, complemented
274	#1940	C₂×C₄₁	1	1	yes	characteristic, complemented
275	#1926	C₂×C₄₁	1	2	yes	complemented
276	#1804	C₂×C₄₁	1	1	yes	characteristic, complemented
277	C₂×C₄₁	—	8	2	no	—
278	C₂×C₄₁	—	8	2	no	—
279	C₂×C₄₁	—	16	2	no	—
280	C₂×C₄₁	#2414	1	1	yes	characteristic
281	C₂×C₄₁	#3038	1	1	yes	characteristic
282	C₂×C₄₁	#3041	1	1	yes	characteristic
283	C₂×C₄₁	#3318	1	2	yes	—
284	C₂×C₄₁	#3399	1	2	yes	—
285	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
286	C₂²×D₈	C₂²×C₄₁	1	2	yes	—
287	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
288	C₂×#127	C₂²×C₄₁	1	2	yes	—
289	C₂×#121	—	2	2	no	—
290	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
291	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
292	#459	—	2	4	no	—
293	#442	—	2	4	no	—
294	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
295	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
296	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
297	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
298	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
299	C₂×#102	C₂²×C₄₁	1	2	yes	—
300	C₂×#102	C₂²×C₄₁	1	2	yes	—
301	C₂×#102	C₂²×C₄₁	1	2	yes	—
302	C₂×#102	C₂²×C₄₁	1	2	yes	—
303	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
304	#392	—	2	1	no	—
305	#392	—	2	1	no	—
306	#390	C₂²×C₄₁	1	2	yes	—
307	#390	C₂²×C₄₁	1	2	yes	—
308	#388	—	2	2	no	—
309	#382	C₂²×C₄₁	1	1	yes	characteristic
310	#381	—	2	1	no	—
311	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
312	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
313	C₄×C₂²⋊C₄	—	2	1	no	—
314	#340	C₂²×C₄₁	1	2	yes	—
315	#336	C₂²×C₄₁	1	2	yes	—
316	C₄₁	#24642	1	1	yes	characteristic, direct product factor, Sylow
317	C₂²×D₄	—	2	1	no	—
318	C₂²×D₄	—	2	2	no	—
319	C₂²×D₄	—	2	2	no	—
320	C₂²×D₄	—	2	1	no	—
321	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
322	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
323	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
324	C₂³×C₄	—	2	1	no	—
325	C₂³×C₄	—	2	1	no	—
326	C₂×D₈	—	2	2	no	—
327	C₂×D₈	—	2	2	no	—
328	C₂×D₈	—	2	4	no	—
329	C₂×D₈	—	2	2	no	—
330	C₂×D₈	—	4	2	no	—
331	C₂×D₈	—	4	2	no	—
332	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
333	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
334	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
335	#127	—	2	4	no	—
336	#127	—	2	2	no	—
337	#127	—	2	2	no	—
338	#127	—	4	2	no	—
339	#121	—	4	8	no	—
340	C₄×D₄	—	2	2	no	—
341	C₄×D₄	—	2	2	no	—
342	C₄×D₄	—	2	2	no	—
343	C₄×D₄	D₄×C₄₁	1	4	yes	complemented
344	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
345	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
347	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₂²⋊C₄	—	2	1	no	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₂²⋊C₄	—	2	2	no	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₄²	—	2	2	no	—
355	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
356	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
357	#106	—	2	2	no	—
358	C₄⋊C₈	—	2	2	no	—
359	C₄⋊C₈	—	4	2	no	—
360	#102	—	2	2	no	—
361	#102	—	2	4	no	—
362	#102	—	2	2	no	—
363	#102	—	2	4	no	—
364	#102	—	4	2	no	—
365	#102	—	4	2	no	—
366	#97	—	2	2	no	—
367	#95	—	2	1	no	—
368	#95	—	2	2	no	—
369	#95	—	2	1	no	—
370	#95	D₄×C₄₁	1	1	yes	characteristic
371	#95	D₄×C₄₁	1	1	yes	characteristic
372	C₂⁴	—	2	1	no	—
373	C₂⁴	—	2	1	no	—
374	C₂⁴	—	2	2	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	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	—	4	2	no	—
396	C₂×D₄	—	4	2	no	—
397	C₂×D₄	—	4	4	no	—
398	C₂×D₄	—	8	2	no	—
399	C₂×D₄	—	8	2	no	—
400	C₂×D₄	—	8	2	no	—
401	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
402	C₂×D₄	#41×C₄₁	1	2	yes	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	4	4	no	—
408	C₂²×C₄	—	4	2	no	—
409	C₂²×C₄	—	8	2	no	—
410	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
411	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
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	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	#41×C₄₁	1	2	yes	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
433	C₂²⋊C₄	—	2	4	no	—
434	C₂²⋊C₄	—	4	4	no	—
435	C₂²⋊C₄	—	4	2	no	—
436	C₂²⋊C₄	—	4	4	no	—
437	C₂²⋊C₄	—	4	4	no	—
438	C₂²⋊C₄	—	8	2	no	—
439	C₄²	—	2	2	no	—
440	C₄²	—	2	2	no	—
441	C₄²	—	8	2	no	—
442	C₄²	C₂×D₄×C₄₁	1	2	yes	—
443	C₄²	#41×C₄₁	1	2	yes	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	4	1	no	—
447	C₂³	—	4	1	no	—
448	C₂³	—	4	1	no	—
449	C₂³	—	4	1	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	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	C₂²×D₄×C₄₁	1	1	yes	characteristic
462	D₄	—	2	2	no	—
463	D₄	—	2	2	no	—
464	D₄	—	2	2	no	—
465	D₄	—	2	2	no	—
466	D₄	—	4	2	no	—
467	D₄	—	4	1	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	1	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	1	no	—
472	D₄	—	4	1	no	—
473	D₄	—	4	2	no	—
474	D₄	—	8	8	no	—
475	D₄	—	8	4	no	—
476	D₄	—	8	4	no	—
477	D₄	—	8	8	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	8	4	no	—
493	C₂×C₄	—	8	4	no	—
494	C₂×C₄	#121×C₄₁	1	2	yes	—
495	C₂×C₄	#121×C₄₁	1	2	yes	—
496	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	4	yes	—
497	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
498	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
499	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
500	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
501	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
502	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
503	C₈	—	2	2	no	—
504	C₈	—	4	2	no	—
505	C₈	—	4	1	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	8	1	no	—
512	C₂²	—	8	1	no	—
513	C₂²	—	8	2	no	—
514	C₂²	—	8	2	no	—
515	C₂²	—	8	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	C₂×#121×C₄₁	1	1	yes	characteristic
524	C₂²	C₄₁×#546	1	1	yes	characteristic
525	C₂²	C₄₁×#550	1	1	yes	characteristic
526	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
527	C₂²	C₄₁×#576	1	2	yes	—
528	C₄	—	2	2	no	—
529	C₄	—	2	2	no	—
530	C₄	—	2	4	no	—
531	C₄	—	4	2	no	—
532	C₄	—	4	2	no	—
533	C₄	—	8	1	no	—
534	C₄	—	8	2	no	—
535	C₄	C₄₁×#525	1	1	yes	characteristic
536	C₄	C₄₁×#535	1	1	yes	characteristic
537	C₄	C₄₁×#553	1	1	yes	characteristic
538	C₄	C₄₁×#555	1	1	yes	characteristic
539	C₂	—	8	2	no	—
540	C₂	—	8	2	no	—
541	C₂	—	16	2	no	—
542	C₂	C₄₁×#2414	1	1	yes	characteristic
543	C₂	C₄₁×#3038	1	1	yes	characteristic
544	C₂	C₄₁×#3041	1	1	yes	characteristic
545	C₂	C₄₁×#3318	1	2	yes	—
546	C₂	C₄₁×#3399	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×C₄⋊C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#459	C₂	semidirect
2. C₂×C₄₁×#442	C₂	semidirect
3. C₄₁×#2541	C₂	semidirect
4. C₄₁×#2357	C₂	semidirect
5. C₄₁×#2054	C₂	semidirect
6. C₄₁×#2011	C₂	semidirect
7. C₄₁×#1982	C₂	semidirect
8. C₄₁×#1961	C₂	semidirect
9. C₄₁×#1940	C₂	semidirect
10. C₄₁×#1926	C₂	semidirect
11. C₄₁×#1804	C₂	semidirect
69. C₄×D₄×C₄₁	D₄	semidirect
232. #24642	C₄₁	direct (N × H)
266. C₂×#459	C₂×C₄₁	semidirect
267. C₂×#442	C₂×C₄₁	semidirect
268. #2541	C₂×C₄₁	semidirect
269. #2357	C₂×C₄₁	semidirect
270. #2054	C₂×C₄₁	semidirect
271. #2011	C₂×C₄₁	semidirect
272. #1982	C₂×C₄₁	semidirect
273. #1961	C₂×C₄₁	semidirect
274. #1940	C₂×C₄₁	semidirect
275. #1926	C₂×C₄₁	semidirect
276. #1804	C₂×C₄₁	semidirect
316. C₄₁	#24642	direct (N × H)
343. C₄×D₄	D₄×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×#459	2
C₂×C₄₁×#442	2
C₄₁×#2541	2
C₄₁×#2357	2
C₄₁×#2054	2
C₄₁×#2011	2
C₄₁×#1982	2
C₄₁×#1961	2
C₄₁×#1940	2
C₄₁×#1926	2
C₄₁×#1804	2
#24642	41

Subgroups — C41×#24642 #23800843

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24642 #23800843