Subgroups — C₄₁×#21445 #23797646

Order 10496.

1456 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#131×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#436	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₁×#435	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2388	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1870	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1869	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1851	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1850	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1780	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1753	C₂	1	2	yes	maximal, complemented
11	C₈×C₂²⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#131×C₄₁	—	2	8	no	—
14	C₂×#131×C₄₁	—	2	4	no	—
15	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
16	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
18	C₂³×C₈×C₄₁	C₂²	1	2	yes	—
19	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
22	C₄₁×#436	—	2	8	no	—
23	C₄₁×#435	—	2	4	no	—
24	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
32	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
34	C₄₁×#395	C₄	1	1	yes	characteristic
35	C₄₁×#394	C₄	1	2	yes	—
36	C₄₁×#394	C₄	1	1	yes	characteristic
37	C₄₁×#393	C₄	1	1	yes	characteristic
38	C₄₁×#392	C₄	1	1	yes	characteristic
39	C₄₁×#392	C₄	1	2	yes	—
40	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
41	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
42	C₄₁×#336	C₂²	1	2	yes	—
43	C₄₁×#336	C₂²	1	2	yes	—
44	C₄₁×#336	C₂²	1	2	yes	—
45	C₂×#41×C₄₁	—	2	4	no	—
46	C₂×#41×C₄₁	—	2	2	no	—
47	C₂×#41×C₄₁	—	2	2	no	—
48	C₂×#41×C₄₁	—	2	4	no	—
49	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
50	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
51	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
52	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
53	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
56	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
57	#131×C₄₁	—	2	32	no	—
58	C₂×M₁₆×C₄₁	—	2	2	no	—
59	C₂×M₁₆×C₄₁	—	2	4	no	—
60	C₂×M₁₆×C₄₁	—	2	4	no	—
61	C₂×M₁₆×C₄₁	—	2	4	no	—
62	C₂×M₁₆×C₄₁	—	2	2	no	—
63	C₂×M₁₆×C₄₁	—	2	4	no	—
64	C₂×M₁₆×C₄₁	D₄	1	8	yes	complemented
65	C₂²×C₈×C₄₁	—	2	4	no	—
66	C₂²×C₈×C₄₁	—	2	4	no	—
67	C₂²×C₈×C₄₁	—	2	4	no	—
68	C₂²×C₈×C₄₁	—	2	4	no	—
69	C₂²×C₈×C₄₁	D₄	1	4	yes	complemented
70	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
72	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
75	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
76	C₄×D₄×C₄₁	—	2	2	no	—
77	C₄×D₄×C₄₁	—	2	4	no	—
78	C₄×D₄×C₄₁	—	2	4	no	—
79	C₄×D₄×C₄₁	—	2	2	no	—
80	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
83	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
85	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
87	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
88	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
89	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
90	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₄₁	—	2	2	no	—
92	C₄⋊C₈×C₄₁	—	2	4	no	—
93	C₂²⋊C₈×C₄₁	—	2	2	no	—
94	C₂²⋊C₈×C₄₁	—	2	4	no	—
95	C₂²⋊C₈×C₄₁	—	2	4	no	—
96	C₂²⋊C₈×C₄₁	—	2	2	no	—
97	C₂²⋊C₈×C₄₁	—	2	2	no	—
98	C₂²⋊C₈×C₄₁	—	2	4	no	—
99	#97×C₄₁	—	2	2	no	—
100	C₄×C₈×C₄₁	—	2	4	no	—
101	#95×C₄₁	C₂×C₄	1	2	yes	—
102	#95×C₄₁	C₂×C₄	1	1	yes	characteristic
103	#95×C₄₁	C₂×C₄	1	2	yes	—
104	#95×C₄₁	C₂×C₄	1	1	yes	characteristic
105	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
106	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
107	C₂⁴×C₄₁	C₂²×C₄	1	2	yes	—
108	#41×C₄₁	—	2	8	no	—
109	#41×C₄₁	—	2	16	no	—
110	#41×C₄₁	—	2	8	no	—
111	C₂×Q₈×C₄₁	—	2	2	no	—
112	C₂×Q₈×C₄₁	—	2	4	no	—
113	C₂×D₄×C₄₁	—	2	4	no	—
114	C₂×D₄×C₄₁	—	2	4	no	—
115	C₂×D₄×C₄₁	—	2	4	no	—
116	C₂×D₄×C₄₁	—	2	4	no	—
117	C₂×D₄×C₄₁	—	2	2	no	—
118	C₂×D₄×C₄₁	—	2	2	no	—
119	C₂×D₄×C₄₁	—	2	4	no	—
120	C₂×D₄×C₄₁	—	2	4	no	—
121	C₂×D₄×C₄₁	—	4	2	no	—
122	C₂×D₄×C₄₁	—	4	1	no	—
123	C₂×D₄×C₄₁	—	4	1	no	—
124	C₂²×C₄×C₄₁	—	2	2	no	—
125	C₂²×C₄×C₄₁	—	2	2	no	—
126	C₂²×C₄×C₄₁	—	2	2	no	—
127	C₂²×C₄×C₄₁	—	2	2	no	—
128	C₂²×C₄×C₄₁	—	2	2	no	—
129	C₂²×C₄×C₄₁	—	2	2	no	—
130	C₂²×C₄×C₄₁	—	2	1	no	—
131	C₂²×C₄×C₄₁	—	2	2	no	—
132	C₂²×C₄×C₄₁	—	2	1	no	—
133	C₂²×C₄×C₄₁	—	2	2	no	—
134	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₄₁	#41	1	2	yes	—
144	C₂²×C₄×C₄₁	#41	1	4	yes	—
145	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
146	M₁₆×C₄₁	—	2	8	no	—
147	M₁₆×C₄₁	—	2	16	no	—
148	M₁₆×C₄₁	—	4	4	no	—
149	C₂×C₈×C₄₁	—	2	16	no	—
150	C₂×C₈×C₄₁	—	2	2	no	—
151	C₂×C₈×C₄₁	—	2	2	no	—
152	C₂×C₈×C₄₁	—	2	2	no	—
153	C₂×C₈×C₄₁	—	2	8	no	—
154	C₂×C₈×C₄₁	—	2	2	no	—
155	C₂×C₈×C₄₁	—	2	1	no	—
156	C₂×C₈×C₄₁	—	2	1	no	—
157	C₂×C₈×C₄₁	—	2	2	no	—
158	C₂×C₈×C₄₁	—	2	2	no	—
159	C₂×C₈×C₄₁	—	2	2	no	—
160	C₂×C₈×C₄₁	—	2	2	no	—
161	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
162	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
163	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
164	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
165	C₄⋊C₄×C₄₁	—	2	4	no	—
166	C₄⋊C₄×C₄₁	—	2	2	no	—
167	C₂²⋊C₄×C₄₁	—	2	2	no	—
168	C₂²⋊C₄×C₄₁	—	2	4	no	—
169	C₂²⋊C₄×C₄₁	—	2	2	no	—
170	C₂²⋊C₄×C₄₁	—	2	4	no	—
171	C₂²⋊C₄×C₄₁	—	2	4	no	—
172	C₂²⋊C₄×C₄₁	—	2	4	no	—
173	C₂²⋊C₄×C₄₁	—	4	2	no	—
174	C₄²×C₄₁	—	2	2	no	—
175	C₄²×C₄₁	—	2	1	no	—
176	C₄²×C₄₁	—	2	2	no	—
177	C₄²×C₄₁	—	2	1	no	—
178	C₂³×C₄₁	—	2	2	no	—
179	C₂³×C₄₁	—	2	2	no	—
180	C₂³×C₄₁	—	2	2	no	—
181	C₂³×C₄₁	—	2	2	no	—
182	C₂³×C₄₁	—	2	2	no	—
183	C₂³×C₄₁	—	2	2	no	—
184	C₂³×C₄₁	—	2	2	no	—
185	C₂³×C₄₁	—	2	1	no	—
186	C₂³×C₄₁	—	2	1	no	—
187	C₂³×C₄₁	—	2	2	no	—
188	C₂³×C₄₁	—	2	1	no	—
189	C₂³×C₄₁	—	2	2	no	—
190	C₂³×C₄₁	—	2	2	no	—
191	C₂³×C₄₁	—	2	1	no	—
192	C₂³×C₄₁	—	2	1	no	—
193	C₂³×C₄₁	C₄×D₄	1	2	yes	—
194	C₂³×C₄₁	C₄×D₄	1	4	yes	—
195	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
196	Q₈×C₄₁	—	2	8	no	—
197	D₄×C₄₁	—	2	16	no	—
198	D₄×C₄₁	—	2	8	no	—
199	D₄×C₄₁	—	4	8	no	—
200	D₄×C₄₁	—	4	4	no	—
201	C₂×C₄×C₄₁	—	2	2	no	—
202	C₂×C₄×C₄₁	—	2	2	no	—
203	C₂×C₄×C₄₁	—	2	2	no	—
204	C₂×C₄×C₄₁	—	2	2	no	—
205	C₂×C₄×C₄₁	—	2	2	no	—
206	C₂×C₄×C₄₁	—	2	4	no	—
207	C₂×C₄×C₄₁	—	2	2	no	—
208	C₂×C₄×C₄₁	—	2	4	no	—
209	C₂×C₄×C₄₁	—	2	2	no	—
210	C₂×C₄×C₄₁	—	2	4	no	—
211	C₂×C₄×C₄₁	—	2	4	no	—
212	C₂×C₄×C₄₁	—	2	4	no	—
213	C₂×C₄×C₄₁	—	2	1	no	—
214	C₂×C₄×C₄₁	—	2	2	no	—
215	C₂×C₄×C₄₁	—	2	1	no	—
216	C₂×C₄×C₄₁	—	2	1	no	—
217	C₂×C₄×C₄₁	—	2	2	no	—
218	C₂×C₄×C₄₁	—	2	2	no	—
219	C₂×C₄×C₄₁	—	2	2	no	—
220	C₂×C₄×C₄₁	—	2	1	no	—
221	C₂×C₄×C₄₁	—	2	2	no	—
222	C₂×C₄×C₄₁	—	2	1	no	—
223	C₂×C₄×C₄₁	—	4	1	no	—
224	C₂×C₄×C₄₁	—	4	1	no	—
225	C₂×C₄×C₄₁	—	4	2	no	—
226	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
227	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
228	C₂×C₄×C₄₁	#131	1	4	yes	complemented
229	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
231	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
233	C₈×C₄₁	—	2	2	no	—
234	C₈×C₄₁	—	2	4	no	—
235	C₈×C₄₁	—	4	1	no	—
236	C₈×C₄₁	—	4	2	no	—
237	C₈×C₄₁	—	4	1	no	—
238	C₈×C₄₁	#120	1	4	yes	—
239	#21445	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂²×C₄₁	—	2	2	no	—
241	C₂²×C₄₁	—	2	2	no	—
242	C₂²×C₄₁	—	2	4	no	—
243	C₂²×C₄₁	—	2	4	no	—
244	C₂²×C₄₁	—	2	2	no	—
245	C₂²×C₄₁	—	2	4	no	—
246	C₂²×C₄₁	—	4	2	no	—
247	C₂²×C₄₁	—	4	2	no	—
248	C₂²×C₄₁	—	4	2	no	—
249	C₂²×C₄₁	—	4	2	no	—
250	C₂²×C₄₁	—	4	2	no	—
251	C₂²×C₄₁	—	4	2	no	—
252	C₂²×C₄₁	—	4	1	no	—
253	C₂²×C₄₁	—	4	1	no	—
254	C₂²×C₄₁	—	4	2	no	—
255	C₂²×C₄₁	—	4	2	no	—
256	C₂²×C₄₁	—	4	1	no	—
257	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
258	C₂²×C₄₁	C₂×C₄×D₄	1	2	yes	—
259	C₂²×C₄₁	C₂×#131	1	2	yes	—
260	C₂²×C₄₁	#568	1	1	yes	characteristic
261	C₂²×C₄₁	#568	1	1	yes	characteristic
262	C₄×C₄₁	—	2	4	no	—
263	C₄×C₄₁	—	2	4	no	—
264	C₄×C₄₁	—	2	2	no	—
265	C₄×C₄₁	—	4	1	no	—
266	C₄×C₄₁	—	4	1	no	—
267	C₄×C₄₁	—	4	2	no	—
268	C₄×C₄₁	—	4	1	no	—
269	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
270	C₄×C₄₁	#525	1	2	yes	—
271	C₄×C₄₁	#525	1	1	yes	characteristic
272	C₂²×#131	C₂×C₄₁	1	1	yes	characteristic, complemented
273	C₂×#436	C₂×C₄₁	1	2	yes	complemented
274	C₂×#435	C₂×C₄₁	1	1	yes	characteristic, complemented
275	#2388	C₂×C₄₁	1	1	yes	characteristic
276	#1870	C₂×C₄₁	1	1	yes	characteristic, complemented
277	#1869	C₂×C₄₁	1	2	yes	complemented
278	#1851	C₂×C₄₁	1	1	yes	characteristic, complemented
279	#1850	C₂×C₄₁	1	2	yes	complemented
280	#1780	C₂×C₄₁	1	1	yes	characteristic, complemented
281	#1753	C₂×C₄₁	1	2	yes	complemented
282	C₈×C₂²⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
283	C₂×C₄₁	—	4	2	no	—
284	C₂×C₄₁	—	4	4	no	—
285	C₂×C₄₁	—	8	1	no	—
286	C₂×C₄₁	C₄×#120	1	1	yes	characteristic
287	C₂×C₄₁	#2930	1	1	yes	characteristic
288	C₂×C₄₁	#2931	1	1	yes	characteristic
289	C₂×C₄₁	#2933	1	2	yes	—
290	C₂×C₄₁	#2935	1	2	yes	—
291	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
292	C₂×#131	—	2	8	no	—
293	C₂×#131	—	2	4	no	—
294	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
295	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
296	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
297	C₂³×C₈	C₂²×C₄₁	1	2	yes	—
298	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
299	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
300	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
301	#436	—	2	8	no	—
302	#435	—	2	4	no	—
303	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
304	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
305	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
306	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
307	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
308	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
309	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
310	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
311	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
312	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
313	#395	C₄×C₄₁	1	1	yes	characteristic
314	#394	C₄×C₄₁	1	2	yes	—
315	#394	C₄×C₄₁	1	1	yes	characteristic
316	#393	C₄×C₄₁	1	1	yes	characteristic
317	#392	C₄×C₄₁	1	1	yes	characteristic
318	#392	C₄×C₄₁	1	2	yes	—
319	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
320	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
321	#336	C₂²×C₄₁	1	2	yes	—
322	#336	C₂²×C₄₁	1	2	yes	—
323	#336	C₂²×C₄₁	1	2	yes	—
324	C₄₁	#21445	1	1	yes	characteristic, direct product factor, Sylow
325	C₂×#41	—	2	4	no	—
326	C₂×#41	—	2	2	no	—
327	C₂×#41	—	2	2	no	—
328	C₂×#41	—	2	4	no	—
329	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
330	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
331	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
332	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
333	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
334	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
335	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
336	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
337	#131	—	2	32	no	—
338	C₂×M₁₆	—	2	2	no	—
339	C₂×M₁₆	—	2	4	no	—
340	C₂×M₁₆	—	2	4	no	—
341	C₂×M₁₆	—	2	4	no	—
342	C₂×M₁₆	—	2	2	no	—
343	C₂×M₁₆	—	2	4	no	—
344	C₂×M₁₆	D₄×C₄₁	1	8	yes	complemented
345	C₂²×C₈	—	2	4	no	—
346	C₂²×C₈	—	2	4	no	—
347	C₂²×C₈	—	2	4	no	—
348	C₂²×C₈	—	2	4	no	—
349	C₂²×C₈	D₄×C₄₁	1	4	yes	complemented
350	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
351	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
352	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
353	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
354	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
355	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
356	C₄×D₄	—	2	2	no	—
357	C₄×D₄	—	2	4	no	—
358	C₄×D₄	—	2	4	no	—
359	C₄×D₄	—	2	2	no	—
360	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
362	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
363	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
365	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
366	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
367	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
368	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
369	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
370	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
371	C₄⋊C₈	—	2	2	no	—
372	C₄⋊C₈	—	2	4	no	—
373	C₂²⋊C₈	—	2	2	no	—
374	C₂²⋊C₈	—	2	4	no	—
375	C₂²⋊C₈	—	2	4	no	—
376	C₂²⋊C₈	—	2	2	no	—
377	C₂²⋊C₈	—	2	2	no	—
378	C₂²⋊C₈	—	2	4	no	—
379	#97	—	2	2	no	—
380	C₄×C₈	—	2	4	no	—
381	#95	C₂×C₄×C₄₁	1	2	yes	—
382	#95	C₂×C₄×C₄₁	1	1	yes	characteristic
383	#95	C₂×C₄×C₄₁	1	2	yes	—
384	#95	C₂×C₄×C₄₁	1	1	yes	characteristic
385	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
386	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
387	C₂⁴	C₂²×C₄×C₄₁	1	2	yes	—
388	#41	—	2	8	no	—
389	#41	—	2	16	no	—
390	#41	—	2	8	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	4	no	—
393	C₂×D₄	—	2	4	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	4	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	—	4	1	no	—
403	C₂×D₄	—	4	1	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
415	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
416	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
417	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
418	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
419	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
420	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
421	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
422	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
423	C₂²×C₄	#41×C₄₁	1	2	yes	—
424	C₂²×C₄	#41×C₄₁	1	4	yes	—
425	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
426	M₁₆	—	2	8	no	—
427	M₁₆	—	2	16	no	—
428	M₁₆	—	4	4	no	—
429	C₂×C₈	—	2	16	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	8	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
442	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
443	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
444	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	4	no	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	—	4	2	no	—
454	C₄²	—	2	2	no	—
455	C₄²	—	2	1	no	—
456	C₄²	—	2	2	no	—
457	C₄²	—	2	1	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	1	no	—
466	C₂³	—	2	1	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	1	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	2	1	no	—
472	C₂³	—	2	1	no	—
473	C₂³	C₄×D₄×C₄₁	1	2	yes	—
474	C₂³	C₄×D₄×C₄₁	1	4	yes	—
475	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
476	Q₈	—	2	8	no	—
477	D₄	—	2	16	no	—
478	D₄	—	2	8	no	—
479	D₄	—	4	8	no	—
480	D₄	—	4	4	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	—	2	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
507	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
508	C₂×C₄	#131×C₄₁	1	4	yes	complemented
509	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
510	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
511	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
512	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
513	C₈	—	2	2	no	—
514	C₈	—	2	4	no	—
515	C₈	—	4	1	no	—
516	C₈	—	4	2	no	—
517	C₈	—	4	1	no	—
518	C₈	#120×C₄₁	1	4	yes	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	4	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	4	no	—
524	C₂²	—	2	4	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
537	C₂²	C₂×C₄×D₄×C₄₁	1	2	yes	—
538	C₂²	C₂×#131×C₄₁	1	2	yes	—
539	C₂²	C₄₁×#568	1	1	yes	characteristic
540	C₂²	C₄₁×#568	1	1	yes	characteristic
541	C₄	—	2	4	no	—
542	C₄	—	2	2	no	—
543	C₄	—	2	4	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	2	no	—
548	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
549	C₄	C₄₁×#525	1	2	yes	—
550	C₄	C₄₁×#525	1	1	yes	characteristic
551	C₂	—	4	2	no	—
552	C₂	—	4	4	no	—
553	C₂	—	8	1	no	—
554	C₂	C₄×#120×C₄₁	1	1	yes	characteristic
555	C₂	C₄₁×#2930	1	1	yes	characteristic
556	C₂	C₄₁×#2931	1	1	yes	characteristic
557	C₂	C₄₁×#2933	1	2	yes	—
558	C₂	C₄₁×#2935	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂³×C₄₁	C₂³×C₄
prime radical	C₄₁×#2388	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#131×C₄₁	C₂	semidirect
2. C₂×C₄₁×#436	C₂	semidirect
3. C₂×C₄₁×#435	C₂	semidirect
5. C₄₁×#1870	C₂	semidirect
6. C₄₁×#1869	C₂	semidirect
7. C₄₁×#1851	C₂	semidirect
8. C₄₁×#1850	C₂	semidirect
9. C₄₁×#1780	C₂	semidirect
10. C₄₁×#1753	C₂	semidirect
11. C₈×C₂²⋊C₄×C₄₁	C₂	semidirect
64. C₂×M₁₆×C₄₁	D₄	semidirect
69. C₂²×C₈×C₄₁	D₄	semidirect
228. C₂×C₄×C₄₁	#131	semidirect
239. #21445	C₄₁	direct (N × H)
272. C₂²×#131	C₂×C₄₁	semidirect
273. C₂×#436	C₂×C₄₁	semidirect
274. C₂×#435	C₂×C₄₁	semidirect
276. #1870	C₂×C₄₁	semidirect
277. #1869	C₂×C₄₁	semidirect
278. #1851	C₂×C₄₁	semidirect
279. #1850	C₂×C₄₁	semidirect
280. #1780	C₂×C₄₁	semidirect
281. #1753	C₂×C₄₁	semidirect
282. C₈×C₂²⋊C₄	C₂×C₄₁	semidirect
324. C₄₁	#21445	direct (N × H)
344. C₂×M₁₆	D₄×C₄₁	semidirect
349. C₂²×C₈	D₄×C₄₁	semidirect
508. C₂×C₄	#131×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#131×C₄₁	2
C₂×C₄₁×#436	2
C₂×C₄₁×#435	2
C₄₁×#2388	2
C₄₁×#1870	2
C₄₁×#1869	2
C₄₁×#1851	2
C₄₁×#1850	2
C₄₁×#1780	2
C₄₁×#1753	2
C₈×C₂²⋊C₄×C₄₁	2
#21445	41

Subgroups — C41×#21445 #23797646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21445 #23797646