Subgroups — C₄₁×#25364 #23801565

Order 10496.

1290 conjugacy classes of subgroups.

The subgroup lattice has 620 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×#459	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#459	C₂	1	2	yes	maximal, complemented
4	C₄₁×#2541	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2366	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2054	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2011	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1982	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1879	C₂	1	2	yes	maximal, complemented
11	C₄×#102×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₄₁	C₂²	1	2	yes	—
13	C₂²×D₈×C₄₁	C₂²	1	2	yes	—
14	C₂²×D₈×C₄₁	C₂²	1	2	yes	—
15	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×#127×C₄₁	C₂²	1	2	yes	—
17	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#121×C₄₁	—	2	1	no	—
19	C₂×#121×C₄₁	—	2	1	no	—
20	C₂×C₄×D₄×C₄₁	—	2	1	no	—
21	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
23	C₄₁×#493	—	2	4	no	—
24	C₄₁×#459	—	2	4	no	—
25	C₄₁×#459	—	2	8	no	—
26	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
27	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×#102×C₄₁	C₂²	1	2	yes	—
30	C₂×#102×C₄₁	C₂²	1	2	yes	—
31	C₂×#102×C₄₁	C₂²	1	2	yes	—
32	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
34	C₄₁×#392	—	2	2	no	—
35	C₄₁×#390	—	2	1	no	—
36	C₄₁×#390	C₂²	1	2	yes	—
37	C₄₁×#390	C₂²	1	2	yes	—
38	C₄₁×#386	—	2	2	no	—
39	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
41	C₄₁×#340	C₂²	1	1	yes	characteristic
42	C₄₁×#340	C₂²	1	1	yes	characteristic
43	C₄₁×#336	C₂²	1	2	yes	—
44	C₂²×D₄×C₄₁	—	2	1	no	—
45	C₂²×D₄×C₄₁	—	2	1	no	—
46	C₂²×D₄×C₄₁	—	2	1	no	—
47	C₂²×D₄×C₄₁	—	2	2	no	—
48	C₂²×D₄×C₄₁	—	2	2	no	—
49	C₂²×D₄×C₄₁	—	2	1	no	—
50	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
51	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
53	C₂³×C₄×C₄₁	—	2	1	no	—
54	C₂³×C₄×C₄₁	—	2	2	no	—
55	C₂×D₈×C₄₁	—	2	4	no	—
56	C₂×D₈×C₄₁	—	2	4	no	—
57	C₂×D₈×C₄₁	—	2	4	no	—
58	C₂×D₈×C₄₁	—	2	4	no	—
59	C₂×D₈×C₄₁	—	2	4	no	—
60	C₂×D₈×C₄₁	—	2	4	no	—
61	C₂×D₈×C₄₁	—	4	2	no	—
62	C₂×D₈×C₄₁	—	4	2	no	—
63	C₂×D₈×C₄₁	—	4	2	no	—
64	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
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	—	2	2	no	—
69	#127×C₄₁	—	2	2	no	—
70	#127×C₄₁	—	2	2	no	—
71	#127×C₄₁	—	4	2	no	—
72	#127×C₄₁	D₄	1	4	yes	complemented
73	#121×C₄₁	—	4	4	no	—
74	#121×C₄₁	—	4	4	no	—
75	C₄×D₄×C₄₁	—	2	4	no	—
76	C₄×D₄×C₄₁	—	2	2	no	—
77	C₄×D₄×C₄₁	—	2	2	no	—
78	C₄×D₄×C₄₁	—	4	2	no	—
79	C₄×D₄×C₄₁	—	4	4	no	—
80	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
85	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
91	C₂×C₄²×C₄₁	—	2	1	no	—
92	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
93	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₄₁	—	2	4	no	—
95	C₄⋊C₈×C₄₁	—	2	2	no	—
96	#102×C₄₁	—	2	4	no	—
97	#102×C₄₁	—	2	2	no	—
98	#102×C₄₁	—	2	4	no	—
99	#102×C₄₁	—	4	2	no	—
100	#102×C₄₁	D₄	1	4	yes	complemented
101	C₄×C₈×C₄₁	—	2	2	no	—
102	#95×C₄₁	—	2	1	no	—
103	#95×C₄₁	D₄	1	2	yes	—
104	C₂⁴×C₄₁	—	2	2	no	—
105	C₂⁴×C₄₁	—	2	1	no	—
106	C₂⁴×C₄₁	—	2	2	no	—
107	C₂×D₄×C₄₁	—	2	4	no	—
108	C₂×D₄×C₄₁	—	2	4	no	—
109	C₂×D₄×C₄₁	—	2	2	no	—
110	C₂×D₄×C₄₁	—	2	1	no	—
111	C₂×D₄×C₄₁	—	2	2	no	—
112	C₂×D₄×C₄₁	—	2	2	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	—	2	2	no	—
118	C₂×D₄×C₄₁	—	2	2	no	—
119	C₂×D₄×C₄₁	—	2	2	no	—
120	C₂×D₄×C₄₁	—	2	1	no	—
121	C₂×D₄×C₄₁	—	2	2	no	—
122	C₂×D₄×C₄₁	—	2	1	no	—
123	C₂×D₄×C₄₁	—	2	2	no	—
124	C₂×D₄×C₄₁	—	2	2	no	—
125	C₂×D₄×C₄₁	—	4	4	no	—
126	C₂×D₄×C₄₁	—	4	4	no	—
127	C₂×D₄×C₄₁	—	4	4	no	—
128	C₂×D₄×C₄₁	—	4	2	no	—
129	C₂×D₄×C₄₁	—	4	2	no	—
130	C₂×D₄×C₄₁	—	4	2	no	—
131	C₂×D₄×C₄₁	—	4	4	no	—
132	C₂×D₄×C₄₁	—	4	2	no	—
133	C₂×D₄×C₄₁	—	4	2	no	—
134	C₂×D₄×C₄₁	—	4	2	no	—
135	C₂×D₄×C₄₁	—	8	2	no	—
136	C₂×D₄×C₄₁	—	8	1	no	—
137	C₂×D₄×C₄₁	—	8	1	no	—
138	C₂×D₄×C₄₁	—	8	1	no	—
139	C₂×D₄×C₄₁	—	8	1	no	—
140	C₂×D₄×C₄₁	—	8	2	no	—
141	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
142	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₄₁	—	2	1	no	—
144	C₂²×C₄×C₄₁	—	2	1	no	—
145	C₂²×C₄×C₄₁	—	2	1	no	—
146	C₂²×C₄×C₄₁	—	4	4	no	—
147	C₂²×C₄×C₄₁	—	4	2	no	—
148	C₂²×C₄×C₄₁	—	4	4	no	—
149	C₂²×C₄×C₄₁	—	4	2	no	—
150	C₂²×C₄×C₄₁	—	4	2	no	—
151	C₂²×C₄×C₄₁	—	8	2	no	—
152	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
157	D₈×C₄₁	—	4	8	no	—
158	D₈×C₄₁	—	4	8	no	—
159	D₈×C₄₁	—	4	8	no	—
160	C₂×C₈×C₄₁	—	2	1	no	—
161	C₂×C₈×C₄₁	—	2	1	no	—
162	C₂×C₈×C₄₁	—	2	1	no	—
163	C₂×C₈×C₄₁	—	2	1	no	—
164	C₂×C₈×C₄₁	—	2	2	no	—
165	C₂×C₈×C₄₁	—	2	2	no	—
166	C₂×C₈×C₄₁	—	2	2	no	—
167	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
168	C₂×C₈×C₄₁	#41	1	2	yes	—
169	C₄⋊C₄×C₄₁	—	2	2	no	—
170	C₄⋊C₄×C₄₁	—	2	1	no	—
171	C₄⋊C₄×C₄₁	—	2	1	no	—
172	C₄⋊C₄×C₄₁	—	2	1	no	—
173	C₄⋊C₄×C₄₁	—	2	1	no	—
174	C₄⋊C₄×C₄₁	—	2	1	no	—
175	C₄⋊C₄×C₄₁	D₈	1	4	yes	complemented
176	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
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	—	4	4	no	—
181	C₂²⋊C₄×C₄₁	—	4	4	no	—
182	C₂²⋊C₄×C₄₁	—	8	2	no	—
183	C₄²×C₄₁	—	2	2	no	—
184	C₄²×C₄₁	—	2	2	no	—
185	C₄²×C₄₁	—	4	2	no	—
186	C₄²×C₄₁	C₂×D₄	1	2	yes	—
187	C₄²×C₄₁	#41	1	2	yes	—
188	C₂³×C₄₁	—	2	4	no	—
189	C₂³×C₄₁	—	2	2	no	—
190	C₂³×C₄₁	—	4	1	no	—
191	C₂³×C₄₁	—	4	2	no	—
192	C₂³×C₄₁	—	4	1	no	—
193	C₂³×C₄₁	—	4	2	no	—
194	C₂³×C₄₁	—	4	2	no	—
195	C₂³×C₄₁	—	4	1	no	—
196	C₂³×C₄₁	—	4	1	no	—
197	C₂³×C₄₁	—	4	2	no	—
198	C₂³×C₄₁	—	4	2	no	—
199	C₂³×C₄₁	—	4	2	no	—
200	C₂³×C₄₁	—	4	1	no	—
201	C₂³×C₄₁	—	4	1	no	—
202	C₂³×C₄₁	—	4	2	no	—
203	C₂³×C₄₁	—	4	2	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	C₂²×D₄	1	1	yes	characteristic
210	D₄×C₄₁	—	2	2	no	—
211	D₄×C₄₁	—	2	4	no	—
212	D₄×C₄₁	—	2	2	no	—
213	D₄×C₄₁	—	2	4	no	—
214	D₄×C₄₁	—	4	2	no	—
215	D₄×C₄₁	—	4	2	no	—
216	D₄×C₄₁	—	4	1	no	—
217	D₄×C₄₁	—	4	2	no	—
218	D₄×C₄₁	—	4	2	no	—
219	D₄×C₄₁	—	4	2	no	—
220	D₄×C₄₁	—	4	1	no	—
221	D₄×C₄₁	—	4	2	no	—
222	D₄×C₄₁	—	4	8	no	—
223	D₄×C₄₁	—	8	4	no	—
224	D₄×C₄₁	—	8	8	no	—
225	D₄×C₄₁	—	8	4	no	—
226	D₄×C₄₁	—	8	8	no	—
227	D₄×C₄₁	—	8	4	no	—
228	C₂×C₄×C₄₁	—	2	2	no	—
229	C₂×C₄×C₄₁	—	2	2	no	—
230	C₂×C₄×C₄₁	—	2	1	no	—
231	C₂×C₄×C₄₁	—	2	1	no	—
232	C₂×C₄×C₄₁	—	2	2	no	—
233	C₂×C₄×C₄₁	—	2	2	no	—
234	C₂×C₄×C₄₁	—	2	2	no	—
235	C₂×C₄×C₄₁	—	2	2	no	—
236	C₂×C₄×C₄₁	—	4	1	no	—
237	C₂×C₄×C₄₁	—	4	1	no	—
238	C₂×C₄×C₄₁	—	4	1	no	—
239	C₂×C₄×C₄₁	—	4	1	no	—
240	C₂×C₄×C₄₁	—	4	1	no	—
241	C₂×C₄×C₄₁	—	4	1	no	—
242	C₂×C₄×C₄₁	—	4	1	no	—
243	C₂×C₄×C₄₁	—	4	1	no	—
244	C₂×C₄×C₄₁	—	8	8	no	—
245	C₂×C₄×C₄₁	—	8	4	no	—
246	C₂×C₄×C₄₁	#121	1	2	yes	—
247	C₂×C₄×C₄₁	#121	1	2	yes	—
248	C₂×C₄×C₄₁	C₂×D₈	1	4	yes	—
249	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
250	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
251	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
255	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
256	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
257	C₈×C₄₁	—	2	2	no	—
258	C₈×C₄₁	—	2	2	no	—
259	C₈×C₄₁	—	4	2	no	—
260	#25364	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
261	C₂²×C₄₁	—	4	2	no	—
262	C₂²×C₄₁	—	4	4	no	—
263	C₂²×C₄₁	—	4	2	no	—
264	C₂²×C₄₁	—	4	2	no	—
265	C₂²×C₄₁	—	4	4	no	—
266	C₂²×C₄₁	—	4	4	no	—
267	C₂²×C₄₁	—	8	2	no	—
268	C₂²×C₄₁	—	8	1	no	—
269	C₂²×C₄₁	—	8	1	no	—
270	C₂²×C₄₁	—	8	2	no	—
271	C₂²×C₄₁	—	8	2	no	—
272	C₂²×C₄₁	—	8	2	no	—
273	C₂²×C₄₁	—	8	1	no	—
274	C₂²×C₄₁	—	8	1	no	—
275	C₂²×C₄₁	—	8	2	no	—
276	C₂²×C₄₁	—	8	2	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	—	8	2	no	—
282	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
283	C₂²×C₄₁	D₄²	1	1	yes	characteristic
284	C₂²×C₄₁	#550	1	1	yes	characteristic
285	C₂²×C₄₁	C₂²×D₈	1	1	yes	characteristic
286	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
287	C₂²×C₄₁	#576	1	1	yes	characteristic
288	C₂²×C₄₁	#576	1	1	yes	characteristic
289	C₄×C₄₁	—	2	4	no	—
290	C₄×C₄₁	—	2	2	no	—
291	C₄×C₄₁	—	4	2	no	—
292	C₄×C₄₁	—	4	2	no	—
293	C₄×C₄₁	—	8	1	no	—
294	C₄×C₄₁	—	8	1	no	—
295	C₄×C₄₁	#459	1	4	yes	complemented
296	C₄×C₄₁	#532	1	1	yes	characteristic
297	C₄×C₄₁	#540	1	1	yes	characteristic
298	C₄×C₄₁	D₄²	1	1	yes	characteristic
299	C₄×C₄₁	#546	1	1	yes	characteristic
300	C₂×#493	C₂×C₄₁	1	1	yes	characteristic, complemented
301	C₂×#459	C₂×C₄₁	1	1	yes	characteristic, complemented
302	C₂×#459	C₂×C₄₁	1	2	yes	complemented
303	#2541	C₂×C₄₁	1	1	yes	characteristic, complemented
304	#2366	C₂×C₄₁	1	1	yes	characteristic, complemented
305	#2054	C₂×C₄₁	1	2	yes	complemented
306	#2011	C₂×C₄₁	1	2	yes	complemented
307	#1982	C₂×C₄₁	1	1	yes	characteristic, complemented
308	#1939	C₂×C₄₁	1	1	yes	characteristic, complemented
309	#1879	C₂×C₄₁	1	2	yes	complemented
310	C₄×#102	C₂×C₄₁	1	1	yes	characteristic, complemented
311	C₂×C₄₁	—	8	2	no	—
312	C₂×C₄₁	—	8	4	no	—
313	C₂×C₄₁	—	16	2	no	—
314	C₂×C₄₁	#2428	1	1	yes	characteristic
315	C₂×C₄₁	C₂×#459	1	1	yes	characteristic
316	C₂×C₄₁	#3041	1	1	yes	characteristic
317	C₂×C₄₁	#3274	1	1	yes	characteristic
318	C₂×C₄₁	D₄×D₈	1	1	yes	characteristic
319	C₂×C₄₁	#3391	1	1	yes	characteristic
320	C₂×C₄₁	#3399	1	1	yes	characteristic
321	C₂²×D₈	C₂²×C₄₁	1	2	yes	—
322	C₂²×D₈	C₂²×C₄₁	1	2	yes	—
323	C₂²×D₈	C₂²×C₄₁	1	2	yes	—
324	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
325	C₂×#127	C₂²×C₄₁	1	2	yes	—
326	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
327	C₂×#121	—	2	1	no	—
328	C₂×#121	—	2	1	no	—
329	C₂×C₄×D₄	—	2	1	no	—
330	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
331	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
332	#493	—	2	4	no	—
333	#459	—	2	4	no	—
334	#459	—	2	8	no	—
335	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
336	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
337	C₂×#102	C₂²×C₄₁	1	2	yes	—
338	C₂×#102	C₂²×C₄₁	1	2	yes	—
339	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
340	C₂×#102	C₂²×C₄₁	1	2	yes	—
341	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
342	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
343	#392	—	2	2	no	—
344	#390	—	2	1	no	—
345	#390	C₂²×C₄₁	1	2	yes	—
346	#390	C₂²×C₄₁	1	2	yes	—
347	#386	—	2	2	no	—
348	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
349	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
350	#340	C₂²×C₄₁	1	1	yes	characteristic
351	#340	C₂²×C₄₁	1	1	yes	characteristic
352	#336	C₂²×C₄₁	1	2	yes	—
353	C₄₁	#25364	1	1	yes	characteristic, direct product factor, Sylow
354	C₂²×D₄	—	2	1	no	—
355	C₂²×D₄	—	2	1	no	—
356	C₂²×D₄	—	2	1	no	—
357	C₂²×D₄	—	2	2	no	—
358	C₂²×D₄	—	2	2	no	—
359	C₂²×D₄	—	2	1	no	—
360	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
361	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
362	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
363	C₂³×C₄	—	2	1	no	—
364	C₂³×C₄	—	2	2	no	—
365	C₂×D₈	—	2	4	no	—
366	C₂×D₈	—	2	4	no	—
367	C₂×D₈	—	2	4	no	—
368	C₂×D₈	—	2	4	no	—
369	C₂×D₈	—	2	4	no	—
370	C₂×D₈	—	2	4	no	—
371	C₂×D₈	—	4	2	no	—
372	C₂×D₈	—	4	2	no	—
373	C₂×D₈	—	4	2	no	—
374	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
375	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
376	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
377	#127	—	2	4	no	—
378	#127	—	2	2	no	—
379	#127	—	2	2	no	—
380	#127	—	2	2	no	—
381	#127	—	4	2	no	—
382	#127	D₄×C₄₁	1	4	yes	complemented
383	#121	—	4	4	no	—
384	#121	—	4	4	no	—
385	C₄×D₄	—	2	4	no	—
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	—	4	2	no	—
389	C₄×D₄	—	4	4	no	—
390	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
391	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
395	C₂×C₂²⋊C₄	—	2	2	no	—
396	C₂×C₂²⋊C₄	—	2	2	no	—
397	C₂×C₂²⋊C₄	—	2	1	no	—
398	C₂×C₂²⋊C₄	—	2	2	no	—
399	C₂×C₂²⋊C₄	—	2	2	no	—
400	C₂×C₂²⋊C₄	—	2	2	no	—
401	C₂×C₄²	—	2	1	no	—
402	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
403	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
404	C₄⋊C₈	—	2	4	no	—
405	C₄⋊C₈	—	2	2	no	—
406	#102	—	2	4	no	—
407	#102	—	2	2	no	—
408	#102	—	2	4	no	—
409	#102	—	4	2	no	—
410	#102	D₄×C₄₁	1	4	yes	complemented
411	C₄×C₈	—	2	2	no	—
412	#95	—	2	1	no	—
413	#95	D₄×C₄₁	1	2	yes	—
414	C₂⁴	—	2	2	no	—
415	C₂⁴	—	2	1	no	—
416	C₂⁴	—	2	2	no	—
417	C₂×D₄	—	2	4	no	—
418	C₂×D₄	—	2	4	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	4	4	no	—
436	C₂×D₄	—	4	4	no	—
437	C₂×D₄	—	4	4	no	—
438	C₂×D₄	—	4	2	no	—
439	C₂×D₄	—	4	2	no	—
440	C₂×D₄	—	4	2	no	—
441	C₂×D₄	—	4	4	no	—
442	C₂×D₄	—	4	2	no	—
443	C₂×D₄	—	4	2	no	—
444	C₂×D₄	—	4	2	no	—
445	C₂×D₄	—	8	2	no	—
446	C₂×D₄	—	8	1	no	—
447	C₂×D₄	—	8	1	no	—
448	C₂×D₄	—	8	1	no	—
449	C₂×D₄	—	8	1	no	—
450	C₂×D₄	—	8	2	no	—
451	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
452	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	4	4	no	—
457	C₂²×C₄	—	4	2	no	—
458	C₂²×C₄	—	4	4	no	—
459	C₂²×C₄	—	4	2	no	—
460	C₂²×C₄	—	4	2	no	—
461	C₂²×C₄	—	8	2	no	—
462	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
463	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
465	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
466	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
467	D₈	—	4	8	no	—
468	D₈	—	4	8	no	—
469	D₈	—	4	8	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
478	C₂×C₈	#41×C₄₁	1	2	yes	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	D₈×C₄₁	1	4	yes	complemented
486	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
487	C₂²⋊C₄	—	4	4	no	—
488	C₂²⋊C₄	—	4	4	no	—
489	C₂²⋊C₄	—	4	2	no	—
490	C₂²⋊C₄	—	4	4	no	—
491	C₂²⋊C₄	—	4	4	no	—
492	C₂²⋊C₄	—	8	2	no	—
493	C₄²	—	2	2	no	—
494	C₄²	—	2	2	no	—
495	C₄²	—	4	2	no	—
496	C₄²	C₂×D₄×C₄₁	1	2	yes	—
497	C₄²	#41×C₄₁	1	2	yes	—
498	C₂³	—	2	4	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	1	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	4	2	no	—
505	C₂³	—	4	1	no	—
506	C₂³	—	4	1	no	—
507	C₂³	—	4	2	no	—
508	C₂³	—	4	2	no	—
509	C₂³	—	4	2	no	—
510	C₂³	—	4	1	no	—
511	C₂³	—	4	1	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	4	2	no	—
514	C₂³	—	4	2	no	—
515	C₂³	—	4	2	no	—
516	C₂³	—	4	2	no	—
517	C₂³	—	4	2	no	—
518	C₂³	—	4	2	no	—
519	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
520	D₄	—	2	2	no	—
521	D₄	—	2	4	no	—
522	D₄	—	2	2	no	—
523	D₄	—	2	4	no	—
524	D₄	—	4	2	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	1	no	—
527	D₄	—	4	2	no	—
528	D₄	—	4	2	no	—
529	D₄	—	4	2	no	—
530	D₄	—	4	1	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	8	no	—
533	D₄	—	8	4	no	—
534	D₄	—	8	8	no	—
535	D₄	—	8	4	no	—
536	D₄	—	8	8	no	—
537	D₄	—	8	4	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	8	8	no	—
555	C₂×C₄	—	8	4	no	—
556	C₂×C₄	#121×C₄₁	1	2	yes	—
557	C₂×C₄	#121×C₄₁	1	2	yes	—
558	C₂×C₄	C₂×D₈×C₄₁	1	4	yes	—
559	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
560	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
561	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
562	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
563	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
564	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
565	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
566	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
567	C₈	—	2	2	no	—
568	C₈	—	2	2	no	—
569	C₈	—	4	2	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	4	4	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	4	2	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	8	1	no	—
577	C₂²	—	8	2	no	—
578	C₂²	—	8	1	no	—
579	C₂²	—	8	1	no	—
580	C₂²	—	8	2	no	—
581	C₂²	—	8	2	no	—
582	C₂²	—	8	2	no	—
583	C₂²	—	8	1	no	—
584	C₂²	—	8	2	no	—
585	C₂²	—	8	2	no	—
586	C₂²	—	8	2	no	—
587	C₂²	—	8	2	no	—
588	C₂²	—	8	2	no	—
589	C₂²	—	8	2	no	—
590	C₂²	—	8	2	no	—
591	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
592	C₂²	D₄²×C₄₁	1	1	yes	characteristic
593	C₂²	C₄₁×#550	1	1	yes	characteristic
594	C₂²	C₂²×D₈×C₄₁	1	1	yes	characteristic
595	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
596	C₂²	C₄₁×#576	1	1	yes	characteristic
597	C₂²	C₄₁×#576	1	1	yes	characteristic
598	C₄	—	2	2	no	—
599	C₄	—	2	4	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	2	no	—
602	C₄	—	8	1	no	—
603	C₄	—	8	1	no	—
604	C₄	C₄₁×#459	1	4	yes	complemented
605	C₄	C₄₁×#532	1	1	yes	characteristic
606	C₄	C₄₁×#540	1	1	yes	characteristic
607	C₄	D₄²×C₄₁	1	1	yes	characteristic
608	C₄	C₄₁×#546	1	1	yes	characteristic
609	C₂	—	8	4	no	—
610	C₂	—	8	2	no	—
611	C₂	—	16	2	no	—
612	C₂	C₄₁×#2428	1	1	yes	characteristic
613	C₂	C₂×C₄₁×#459	1	1	yes	characteristic
614	C₂	C₄₁×#3041	1	1	yes	characteristic
615	C₂	C₄₁×#3274	1	1	yes	characteristic
616	C₂	D₄×D₈×C₄₁	1	1	yes	characteristic
617	C₂	C₄₁×#3391	1	1	yes	characteristic
618	C₂	C₄₁×#3399	1	1	yes	characteristic

	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×#493	C₂	semidirect
2. C₂×C₄₁×#459	C₂	semidirect
3. C₂×C₄₁×#459	C₂	semidirect
4. C₄₁×#2541	C₂	semidirect
5. C₄₁×#2366	C₂	semidirect
6. C₄₁×#2054	C₂	semidirect
7. C₄₁×#2011	C₂	semidirect
8. C₄₁×#1982	C₂	semidirect
9. C₄₁×#1939	C₂	semidirect
10. C₄₁×#1879	C₂	semidirect
11. C₄×#102×C₄₁	C₂	semidirect
72. #127×C₄₁	D₄	semidirect
100. #102×C₄₁	D₄	semidirect
175. C₄⋊C₄×C₄₁	D₈	semidirect
260. #25364	C₄₁	direct (N × H)
295. C₄×C₄₁	#459	semidirect
300. C₂×#493	C₂×C₄₁	semidirect
301. C₂×#459	C₂×C₄₁	semidirect
302. C₂×#459	C₂×C₄₁	semidirect
303. #2541	C₂×C₄₁	semidirect
304. #2366	C₂×C₄₁	semidirect
305. #2054	C₂×C₄₁	semidirect
306. #2011	C₂×C₄₁	semidirect
307. #1982	C₂×C₄₁	semidirect
308. #1939	C₂×C₄₁	semidirect
309. #1879	C₂×C₄₁	semidirect
310. C₄×#102	C₂×C₄₁	semidirect
353. C₄₁	#25364	direct (N × H)
382. #127	D₄×C₄₁	semidirect
410. #102	D₄×C₄₁	semidirect
485. C₄⋊C₄	D₈×C₄₁	semidirect
604. C₄	C₄₁×#459	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×#459	2
C₄₁×#2541	2
C₄₁×#2366	2
C₄₁×#2054	2
C₄₁×#2011	2
C₄₁×#1982	2
C₄₁×#1939	2
C₄₁×#1879	2
C₄×#102×C₄₁	2
#25364	41

Subgroups — C41×#25364 #23801565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25364 #23801565