Subgroups — C₄₁×#18566 #23794767

Order 10496.

1324 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3253	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3151	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1631	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1629	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1621	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1619	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1545	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1489	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1484	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×H(5,𝔽₂)×C₄₁	—	2	1	no	—
13	C₂×AGL(1,ℤ/8)×C₄₁	—	2	2	no	—
14	C₄₁×#550	—	2	1	no	—
15	C₄₁×#550	C₂²	1	2	yes	—
16	D₄²×C₄₁	—	2	2	no	—
17	D₄²×C₄₁	—	2	2	no	—
18	D₄²×C₄₁	—	2	1	no	—
19	D₄²×C₄₁	C₂²	1	2	yes	—
20	C₄₁×#535	—	2	2	no	—
21	C₄₁×#535	—	2	1	no	—
22	C₄₁×#532	—	2	1	no	—
23	C₄₁×#532	C₂²	1	1	yes	characteristic
24	C₄₁×#532	C₂²	1	1	yes	characteristic, complemented
25	C₂×#127×C₄₁	—	2	1	no	—
26	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
27	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
28	C₄₁×#496	—	2	2	no	—
29	C₄₁×#493	C₂²	1	2	yes	complemented
30	C₄₁×#492	C₂²	1	2	yes	complemented
31	C₄₁×#482	—	2	1	no	—
32	C₄₁×#477	C₂²	1	1	yes	characteristic, complemented
33	C₄₁×#476	—	2	1	no	—
34	C₄₁×#476	C₂²	1	1	yes	characteristic, complemented
35	C₄₁×#476	C₂²	1	2	yes	complemented
36	C₄₁×#469	—	2	2	no	—
37	C₄₁×#460	C₂²	1	1	yes	characteristic, complemented
38	C₄₁×#459	—	2	1	no	—
39	C₄₁×#459	C₂²	1	1	yes	characteristic, complemented
40	C₄₁×#459	C₂²	1	2	yes	complemented
41	C₄₁×#449	—	2	1	no	—
42	C₄×SD₁₆×C₄₁	—	2	1	no	—
43	C₄×D₈×C₄₁	—	2	1	no	—
44	C₄₁×#431	C₂²	1	1	yes	characteristic, complemented
45	C₄₁×#423	C₂²	1	1	yes	characteristic, complemented
46	C₄×M₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
47	C₄₁×#331	C₂²	1	2	yes	complemented
48	C₄₁×#331	C₂²	1	2	yes	complemented
49	C₄₁×Q₈⋊C₈	C₂²	1	2	yes	complemented
50	C₄₁×D₄⋊C₈	C₂²	1	2	yes	complemented
51	C₄₁×D₄⋊C₈	C₂²	1	2	yes	complemented
52	C₄₁×D₄⋊C₈	C₂²	1	2	yes	complemented
53	H(5,𝔽₂)×C₄₁	—	4	4	no	—
54	H(5,𝔽₂)×C₄₁	—	4	4	no	—
55	C₂×#41×C₄₁	—	2	2	no	—
56	C₂×#41×C₄₁	—	2	2	no	—
57	C₂×#41×C₄₁	—	2	1	no	—
58	C₂×#41×C₄₁	—	2	1	no	—
59	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
60	C₂²×D₄×C₄₁	—	2	2	no	—
61	C₂²×D₄×C₄₁	—	2	4	no	—
62	C₂²×D₄×C₄₁	—	2	2	no	—
63	C₂²×D₄×C₄₁	—	2	2	no	—
64	C₂²×D₄×C₄₁	—	2	2	no	—
65	C₂²×D₄×C₄₁	—	2	1	no	—
66	C₂²×D₄×C₄₁	—	2	1	no	—
67	C₂²×D₄×C₄₁	D₄	1	2	yes	—
68	AGL(1,ℤ/8)×C₄₁	—	4	8	no	—
69	C₂×SD₁₆×C₄₁	—	2	1	no	—
70	C₂×SD₁₆×C₄₁	—	2	4	no	—
71	C₂×D₈×C₄₁	—	2	4	no	—
72	C₂×D₈×C₄₁	—	2	1	no	—
73	C₂×D₈×C₄₁	—	2	2	no	—
74	C₂×M₁₆×C₄₁	—	2	1	no	—
75	C₂×M₁₆×C₄₁	—	2	1	no	—
76	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
77	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
78	#127×C₄₁	—	2	2	no	—
79	#127×C₄₁	—	2	2	no	—
80	#127×C₄₁	—	2	2	no	—
81	#127×C₄₁	—	2	1	no	—
82	#127×C₄₁	—	2	1	no	—
83	#127×C₄₁	D₄	1	1	yes	characteristic
84	#127×C₄₁	D₄	1	2	yes	—
85	#127×C₄₁	C₂³	1	1	yes	characteristic
86	#127×C₄₁	C₂³	1	2	yes	—
87	#124×C₄₁	—	2	2	no	—
88	#124×C₄₁	—	2	1	no	—
89	#124×C₄₁	—	2	1	no	—
90	#121×C₄₁	—	2	2	no	—
91	#121×C₄₁	—	2	4	no	—
92	#121×C₄₁	—	2	4	no	—
93	#121×C₄₁	—	2	1	no	—
94	#121×C₄₁	—	2	2	no	—
95	#121×C₄₁	—	2	2	no	—
96	#121×C₄₁	—	2	2	no	—
97	#121×C₄₁	—	2	1	no	—
98	#121×C₄₁	—	2	1	no	—
99	#121×C₄₁	D₄	1	2	yes	—
100	#120×C₄₁	—	2	4	no	—
101	#120×C₄₁	—	2	4	no	—
102	#120×C₄₁	—	2	4	no	—
103	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
104	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
105	C₄×D₄×C₄₁	—	2	2	no	—
106	C₄×D₄×C₄₁	—	2	1	no	—
107	C₄×D₄×C₄₁	—	2	1	no	—
108	C₄×D₄×C₄₁	—	2	2	no	—
109	C₄×D₄×C₄₁	—	2	1	no	—
110	C₄×D₄×C₄₁	—	2	1	no	—
111	C₄×D₄×C₄₁	—	2	1	no	—
112	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
113	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
114	C₄×D₄×C₄₁	C₂³	1	2	yes	—
115	#117×C₄₁	—	2	1	no	—
116	#117×C₄₁	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₄₁	—	2	1	no	—
118	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
119	#107×C₄₁	—	2	1	no	—
120	#106×C₄₁	—	2	1	no	—
121	#106×C₄₁	—	2	2	no	—
122	C₄⋊C₈×C₄₁	—	2	1	no	—
123	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
124	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
125	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
126	#103×C₄₁	—	2	1	no	—
127	#102×C₄₁	—	2	1	no	—
128	#102×C₄₁	—	2	2	no	—
129	#102×C₄₁	—	2	1	no	—
130	#102×C₄₁	—	2	1	no	—
131	#102×C₄₁	—	2	2	no	—
132	C₂²⋊C₈×C₄₁	—	2	1	no	—
133	#97×C₄₁	—	2	1	no	—
134	C₄×C₈×C₄₁	—	2	1	no	—
135	C₄×C₈×C₄₁	C₂³	1	2	yes	—
136	C₂⁴×C₄₁	—	2	4	no	—
137	C₂⁴×C₄₁	—	2	2	no	—
138	#41×C₄₁	—	2	2	no	—
139	#41×C₄₁	—	2	2	no	—
140	#41×C₄₁	—	4	8	no	—
141	#41×C₄₁	—	4	2	no	—
142	#41×C₄₁	—	4	2	no	—
143	#41×C₄₁	—	4	4	no	—
144	#41×C₄₁	—	4	4	no	—
145	#41×C₄₁	—	4	4	no	—
146	C₂×Q₈×C₄₁	—	2	1	no	—
147	C₂×Q₈×C₄₁	—	2	1	no	—
148	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
149	C₂×D₄×C₄₁	—	2	1	no	—
150	C₂×D₄×C₄₁	—	2	4	no	—
151	C₂×D₄×C₄₁	—	2	4	no	—
152	C₂×D₄×C₄₁	—	2	2	no	—
153	C₂×D₄×C₄₁	—	2	4	no	—
154	C₂×D₄×C₄₁	—	2	4	no	—
155	C₂×D₄×C₄₁	—	2	2	no	—
156	C₂×D₄×C₄₁	—	2	1	no	—
157	C₂×D₄×C₄₁	—	2	2	no	—
158	C₂×D₄×C₄₁	—	2	1	no	—
159	C₂×D₄×C₄₁	—	2	2	no	—
160	C₂×D₄×C₄₁	—	2	2	no	—
161	C₂×D₄×C₄₁	—	2	2	no	—
162	C₂×D₄×C₄₁	—	2	1	no	—
163	C₂×D₄×C₄₁	—	2	1	no	—
164	C₂×D₄×C₄₁	—	2	1	no	—
165	C₂×D₄×C₄₁	—	4	8	no	—
166	C₂×D₄×C₄₁	—	4	2	no	—
167	C₂×D₄×C₄₁	—	4	2	no	—
168	C₂×D₄×C₄₁	—	4	4	no	—
169	C₂×D₄×C₄₁	—	4	16	no	—
170	C₂×D₄×C₄₁	—	4	4	no	—
171	C₂×D₄×C₄₁	—	4	4	no	—
172	C₂×D₄×C₄₁	—	4	1	no	—
173	C₂×D₄×C₄₁	—	8	1	no	—
174	C₂×D₄×C₄₁	—	8	1	no	—
175	C₂×D₄×C₄₁	—	8	2	no	—
176	C₂×D₄×C₄₁	—	8	2	no	—
177	C₂×D₄×C₄₁	—	8	4	no	—
178	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
179	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
180	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
181	C₂²×C₄×C₄₁	—	2	1	no	—
182	C₂²×C₄×C₄₁	—	2	4	no	—
183	C₂²×C₄×C₄₁	—	2	1	no	—
184	C₂²×C₄×C₄₁	—	2	1	no	—
185	C₂²×C₄×C₄₁	—	2	2	no	—
186	C₂²×C₄×C₄₁	—	4	1	no	—
187	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
190	SD₁₆×C₄₁	—	4	8	no	—
191	SD₁₆×C₄₁	—	4	2	no	—
192	D₈×C₄₁	—	4	8	no	—
193	D₈×C₄₁	—	4	2	no	—
194	D₈×C₄₁	—	8	2	no	—
195	M₁₆×C₄₁	—	2	4	no	—
196	M₁₆×C₄₁	—	8	1	no	—
197	C₂×C₈×C₄₁	—	2	2	no	—
198	C₂×C₈×C₄₁	—	2	1	no	—
199	C₂×C₈×C₄₁	—	2	1	no	—
200	C₂×C₈×C₄₁	—	2	2	no	—
201	C₄⋊C₄×C₄₁	—	2	1	no	—
202	C₄⋊C₄×C₄₁	—	2	1	no	—
203	C₄⋊C₄×C₄₁	—	2	1	no	—
204	C₄⋊C₄×C₄₁	—	2	1	no	—
205	C₄⋊C₄×C₄₁	—	2	1	no	—
206	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
207	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
208	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
209	C₂²⋊C₄×C₄₁	—	2	4	no	—
210	C₂²⋊C₄×C₄₁	—	2	4	no	—
211	C₂²⋊C₄×C₄₁	—	2	1	no	—
212	C₂²⋊C₄×C₄₁	—	2	1	no	—
213	C₂²⋊C₄×C₄₁	—	2	2	no	—
214	C₂²⋊C₄×C₄₁	—	2	1	no	—
215	C₂²⋊C₄×C₄₁	—	2	2	no	—
216	C₂²⋊C₄×C₄₁	—	4	1	no	—
217	C₂²⋊C₄×C₄₁	—	4	1	no	—
218	C₄²×C₄₁	—	2	1	no	—
219	C₄²×C₄₁	—	2	1	no	—
220	C₄²×C₄₁	—	2	1	no	—
221	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
222	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
223	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
224	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
225	C₂³×C₄₁	—	2	1	no	—
226	C₂³×C₄₁	—	2	2	no	—
227	C₂³×C₄₁	—	2	4	no	—
228	C₂³×C₄₁	—	4	4	no	—
229	C₂³×C₄₁	—	4	8	no	—
230	C₂³×C₄₁	—	4	1	no	—
231	C₂³×C₄₁	—	8	2	no	—
232	C₂³×C₄₁	—	8	2	no	—
233	C₂³×C₄₁	—	8	4	no	—
234	C₂³×C₄₁	—	8	4	no	—
235	C₂³×C₄₁	#120	1	1	yes	characteristic
236	Q₈×C₄₁	—	2	1	no	—
237	Q₈×C₄₁	—	4	2	no	—
238	Q₈×C₄₁	—	4	2	no	—
239	Q₈×C₄₁	AGL(1,ℤ/8)	1	2	yes	complemented
240	D₄×C₄₁	—	2	4	no	—
241	D₄×C₄₁	—	2	1	no	—
242	D₄×C₄₁	—	2	2	no	—
243	D₄×C₄₁	—	2	2	no	—
244	D₄×C₄₁	—	4	4	no	—
245	D₄×C₄₁	—	4	4	no	—
246	D₄×C₄₁	—	4	2	no	—
247	D₄×C₄₁	—	4	8	no	—
248	D₄×C₄₁	—	4	2	no	—
249	D₄×C₄₁	—	4	4	no	—
250	D₄×C₄₁	—	4	8	no	—
251	D₄×C₄₁	—	4	2	no	—
252	D₄×C₄₁	—	4	2	no	—
253	D₄×C₄₁	—	4	1	no	—
254	D₄×C₄₁	—	4	1	no	—
255	D₄×C₄₁	—	4	2	no	—
256	D₄×C₄₁	—	4	1	no	—
257	D₄×C₄₁	—	4	2	no	—
258	D₄×C₄₁	—	4	1	no	—
259	D₄×C₄₁	—	4	4	no	—
260	D₄×C₄₁	—	4	2	no	—
261	D₄×C₄₁	—	8	2	no	—
262	D₄×C₄₁	—	8	4	no	—
263	D₄×C₄₁	—	8	4	no	—
264	D₄×C₄₁	—	8	2	no	—
265	D₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	complemented
266	C₂×C₄×C₄₁	—	2	4	no	—
267	C₂×C₄×C₄₁	—	2	1	no	—
268	C₂×C₄×C₄₁	—	2	1	no	—
269	C₂×C₄×C₄₁	—	2	1	no	—
270	C₂×C₄×C₄₁	—	2	1	no	—
271	C₂×C₄×C₄₁	—	2	1	no	—
272	C₂×C₄×C₄₁	—	2	2	no	—
273	C₂×C₄×C₄₁	—	2	1	no	—
274	C₂×C₄×C₄₁	—	2	1	no	—
275	C₂×C₄×C₄₁	—	2	2	no	—
276	C₂×C₄×C₄₁	—	4	8	no	—
277	C₂×C₄×C₄₁	—	4	2	no	—
278	C₂×C₄×C₄₁	—	4	2	no	—
279	C₂×C₄×C₄₁	—	4	1	no	—
280	C₂×C₄×C₄₁	—	4	1	no	—
281	C₂×C₄×C₄₁	—	4	2	no	—
282	C₂×C₄×C₄₁	—	4	1	no	—
283	C₂×C₄×C₄₁	—	8	2	no	—
284	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
285	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
286	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
287	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
290	C₈×C₄₁	—	2	4	no	—
291	C₈×C₄₁	—	4	1	no	—
292	C₈×C₄₁	—	4	1	no	—
293	C₈×C₄₁	—	4	2	no	—
294	#18566	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
295	C₂²×C₄₁	—	2	1	no	—
296	C₂²×C₄₁	—	2	2	no	—
297	C₂²×C₄₁	—	2	1	no	—
298	C₂²×C₄₁	—	2	1	no	—
299	C₂²×C₄₁	—	4	1	no	—
300	C₂²×C₄₁	—	4	1	no	—
301	C₂²×C₄₁	—	4	4	no	—
302	C₂²×C₄₁	—	4	2	no	—
303	C₂²×C₄₁	—	4	2	no	—
304	C₂²×C₄₁	—	4	4	no	—
305	C₂²×C₄₁	—	4	4	no	—
306	C₂²×C₄₁	—	4	2	no	—
307	C₂²×C₄₁	—	8	1	no	—
308	C₂²×C₄₁	—	8	1	no	—
309	C₂²×C₄₁	—	8	1	no	—
310	C₂²×C₄₁	—	16	4	no	—
311	C₂²×C₄₁	—	16	8	no	—
312	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
313	C₄×C₄₁	—	2	1	no	—
314	C₄×C₄₁	—	2	2	no	—
315	C₄×C₄₁	—	2	1	no	—
316	C₄×C₄₁	—	2	1	no	—
317	C₄×C₄₁	—	4	2	no	—
318	C₄×C₄₁	—	4	1	no	—
319	C₄×C₄₁	—	4	1	no	—
320	C₄×C₄₁	—	8	1	no	—
321	C₄×C₄₁	#453	1	2	yes	—
322	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
323	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
324	C₄×C₄₁	#576	1	1	yes	characteristic
325	C₄×C₄₁	#577	1	1	yes	characteristic
326	#3498	C₂×C₄₁	1	1	yes	characteristic, complemented
327	#3253	C₂×C₄₁	1	1	yes	characteristic, complemented
328	#3151	C₂×C₄₁	1	1	yes	characteristic, complemented
329	#3106	C₂×C₄₁	1	1	yes	characteristic, complemented
330	#1631	C₂×C₄₁	1	2	yes	complemented
331	#1629	C₂×C₄₁	1	2	yes	complemented
332	#1621	C₂×C₄₁	1	2	yes	complemented
333	#1619	C₂×C₄₁	1	2	yes	complemented
334	#1545	C₂×C₄₁	1	1	yes	characteristic, complemented
335	#1489	C₂×C₄₁	1	1	yes	characteristic, complemented
336	#1484	C₂×C₄₁	1	1	yes	characteristic, complemented
337	C₂×C₄₁	—	4	1	no	—
338	C₂×C₄₁	—	4	2	no	—
339	C₂×C₄₁	—	8	2	no	—
340	C₂×C₄₁	—	8	4	no	—
341	C₂×C₄₁	—	16	1	no	—
342	C₂×C₄₁	#3003	1	1	yes	characteristic
343	C₂×C₄₁	#3012	1	1	yes	characteristic
344	C₂×C₄₁	C₂×#453	1	1	yes	characteristic
345	C₂×H(5,𝔽₂)	—	2	1	no	—
346	C₂×AGL(1,ℤ/8)	—	2	2	no	—
347	#550	—	2	1	no	—
348	#550	C₂²×C₄₁	1	2	yes	—
349	D₄²	—	2	2	no	—
350	D₄²	—	2	2	no	—
351	D₄²	—	2	1	no	—
352	D₄²	C₂²×C₄₁	1	2	yes	—
353	#535	—	2	2	no	—
354	#535	—	2	1	no	—
355	#532	—	2	1	no	—
356	#532	C₂²×C₄₁	1	1	yes	characteristic
357	#532	C₂²×C₄₁	1	1	yes	characteristic, complemented
358	C₂×#127	—	2	1	no	—
359	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
360	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
361	#496	—	2	2	no	—
362	#493	C₂²×C₄₁	1	2	yes	complemented
363	#492	C₂²×C₄₁	1	2	yes	complemented
364	#482	—	2	1	no	—
365	#477	C₂²×C₄₁	1	1	yes	characteristic, complemented
366	#476	—	2	1	no	—
367	#476	C₂²×C₄₁	1	1	yes	characteristic, complemented
368	#476	C₂²×C₄₁	1	2	yes	complemented
369	#469	—	2	2	no	—
370	#460	C₂²×C₄₁	1	1	yes	characteristic, complemented
371	#459	—	2	1	no	—
372	#459	C₂²×C₄₁	1	1	yes	characteristic, complemented
373	#459	C₂²×C₄₁	1	2	yes	complemented
374	#449	—	2	1	no	—
375	C₄×SD₁₆	—	2	1	no	—
376	C₄×D₈	—	2	1	no	—
377	#431	C₂²×C₄₁	1	1	yes	characteristic, complemented
378	#423	C₂²×C₄₁	1	1	yes	characteristic, complemented
379	C₄×M₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
380	#331	C₂²×C₄₁	1	2	yes	complemented
381	#331	C₂²×C₄₁	1	2	yes	complemented
382	Q₈⋊C₈	C₂²×C₄₁	1	2	yes	complemented
383	D₄⋊C₈	C₂²×C₄₁	1	2	yes	complemented
384	D₄⋊C₈	C₂²×C₄₁	1	2	yes	complemented
385	D₄⋊C₈	C₂²×C₄₁	1	2	yes	complemented
386	C₄₁	#18566	1	1	yes	characteristic, direct product factor, Sylow
387	H(5,𝔽₂)	—	4	4	no	—
388	H(5,𝔽₂)	—	4	4	no	—
389	C₂×#41	—	2	2	no	—
390	C₂×#41	—	2	2	no	—
391	C₂×#41	—	2	1	no	—
392	C₂×#41	—	2	1	no	—
393	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
394	C₂²×D₄	—	2	2	no	—
395	C₂²×D₄	—	2	4	no	—
396	C₂²×D₄	—	2	2	no	—
397	C₂²×D₄	—	2	2	no	—
398	C₂²×D₄	—	2	2	no	—
399	C₂²×D₄	—	2	1	no	—
400	C₂²×D₄	—	2	1	no	—
401	C₂²×D₄	D₄×C₄₁	1	2	yes	—
402	AGL(1,ℤ/8)	—	4	8	no	—
403	C₂×SD₁₆	—	2	1	no	—
404	C₂×SD₁₆	—	2	4	no	—
405	C₂×D₈	—	2	4	no	—
406	C₂×D₈	—	2	1	no	—
407	C₂×D₈	—	2	2	no	—
408	C₂×M₁₆	—	2	1	no	—
409	C₂×M₁₆	—	2	1	no	—
410	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
411	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
412	#127	—	2	2	no	—
413	#127	—	2	2	no	—
414	#127	—	2	2	no	—
415	#127	—	2	1	no	—
416	#127	—	2	1	no	—
417	#127	D₄×C₄₁	1	1	yes	characteristic
418	#127	D₄×C₄₁	1	2	yes	—
419	#127	C₂³×C₄₁	1	1	yes	characteristic
420	#127	C₂³×C₄₁	1	2	yes	—
421	#124	—	2	2	no	—
422	#124	—	2	1	no	—
423	#124	—	2	1	no	—
424	#121	—	2	2	no	—
425	#121	—	2	4	no	—
426	#121	—	2	4	no	—
427	#121	—	2	1	no	—
428	#121	—	2	2	no	—
429	#121	—	2	2	no	—
430	#121	—	2	2	no	—
431	#121	—	2	1	no	—
432	#121	—	2	1	no	—
433	#121	D₄×C₄₁	1	2	yes	—
434	#120	—	2	4	no	—
435	#120	—	2	4	no	—
436	#120	—	2	4	no	—
437	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
438	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
439	C₄×D₄	—	2	2	no	—
440	C₄×D₄	—	2	1	no	—
441	C₄×D₄	—	2	1	no	—
442	C₄×D₄	—	2	2	no	—
443	C₄×D₄	—	2	1	no	—
444	C₄×D₄	—	2	1	no	—
445	C₄×D₄	—	2	1	no	—
446	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
447	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
448	C₄×D₄	C₂³×C₄₁	1	2	yes	—
449	#117	—	2	1	no	—
450	#117	D₄×C₄₁	1	1	yes	characteristic
451	C₂×C₄²	—	2	1	no	—
452	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
453	#107	—	2	1	no	—
454	#106	—	2	1	no	—
455	#106	—	2	2	no	—
456	C₄⋊C₈	—	2	1	no	—
457	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
458	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
459	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
460	#103	—	2	1	no	—
461	#102	—	2	1	no	—
462	#102	—	2	2	no	—
463	#102	—	2	1	no	—
464	#102	—	2	1	no	—
465	#102	—	2	2	no	—
466	C₂²⋊C₈	—	2	1	no	—
467	#97	—	2	1	no	—
468	C₄×C₈	—	2	1	no	—
469	C₄×C₈	C₂³×C₄₁	1	2	yes	—
470	C₂⁴	—	2	4	no	—
471	C₂⁴	—	2	2	no	—
472	#41	—	2	2	no	—
473	#41	—	2	2	no	—
474	#41	—	4	8	no	—
475	#41	—	4	2	no	—
476	#41	—	4	2	no	—
477	#41	—	4	4	no	—
478	#41	—	4	4	no	—
479	#41	—	4	4	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	4	no	—
485	C₂×D₄	—	2	4	no	—
486	C₂×D₄	—	2	2	no	—
487	C₂×D₄	—	2	4	no	—
488	C₂×D₄	—	2	4	no	—
489	C₂×D₄	—	2	2	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	2	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	2	no	—
494	C₂×D₄	—	2	2	no	—
495	C₂×D₄	—	2	2	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	4	8	no	—
500	C₂×D₄	—	4	2	no	—
501	C₂×D₄	—	4	2	no	—
502	C₂×D₄	—	4	4	no	—
503	C₂×D₄	—	4	16	no	—
504	C₂×D₄	—	4	4	no	—
505	C₂×D₄	—	4	4	no	—
506	C₂×D₄	—	4	1	no	—
507	C₂×D₄	—	8	1	no	—
508	C₂×D₄	—	8	1	no	—
509	C₂×D₄	—	8	2	no	—
510	C₂×D₄	—	8	2	no	—
511	C₂×D₄	—	8	4	no	—
512	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
513	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
514	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	4	1	no	—
521	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
522	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
523	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
524	SD₁₆	—	4	8	no	—
525	SD₁₆	—	4	2	no	—
526	D₈	—	4	8	no	—
527	D₈	—	4	2	no	—
528	D₈	—	8	2	no	—
529	M₁₆	—	2	4	no	—
530	M₁₆	—	8	1	no	—
531	C₂×C₈	—	2	2	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	2	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
541	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
542	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
543	C₂²⋊C₄	—	2	4	no	—
544	C₂²⋊C₄	—	2	4	no	—
545	C₂²⋊C₄	—	2	1	no	—
546	C₂²⋊C₄	—	2	1	no	—
547	C₂²⋊C₄	—	2	2	no	—
548	C₂²⋊C₄	—	2	1	no	—
549	C₂²⋊C₄	—	2	2	no	—
550	C₂²⋊C₄	—	4	1	no	—
551	C₂²⋊C₄	—	4	1	no	—
552	C₄²	—	2	1	no	—
553	C₄²	—	2	1	no	—
554	C₄²	—	2	1	no	—
555	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
556	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
557	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
558	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
559	C₂³	—	2	1	no	—
560	C₂³	—	2	2	no	—
561	C₂³	—	2	4	no	—
562	C₂³	—	4	4	no	—
563	C₂³	—	4	8	no	—
564	C₂³	—	4	1	no	—
565	C₂³	—	8	2	no	—
566	C₂³	—	8	2	no	—
567	C₂³	—	8	4	no	—
568	C₂³	—	8	4	no	—
569	C₂³	#120×C₄₁	1	1	yes	characteristic
570	Q₈	—	2	1	no	—
571	Q₈	—	4	2	no	—
572	Q₈	—	4	2	no	—
573	Q₈	AGL(1,ℤ/8)×C₄₁	1	2	yes	complemented
574	D₄	—	2	4	no	—
575	D₄	—	2	1	no	—
576	D₄	—	2	2	no	—
577	D₄	—	2	2	no	—
578	D₄	—	4	4	no	—
579	D₄	—	4	4	no	—
580	D₄	—	4	2	no	—
581	D₄	—	4	8	no	—
582	D₄	—	4	2	no	—
583	D₄	—	4	4	no	—
584	D₄	—	4	8	no	—
585	D₄	—	4	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	4	1	no	—
588	D₄	—	4	1	no	—
589	D₄	—	4	2	no	—
590	D₄	—	4	1	no	—
591	D₄	—	4	2	no	—
592	D₄	—	4	1	no	—
593	D₄	—	4	4	no	—
594	D₄	—	4	2	no	—
595	D₄	—	8	2	no	—
596	D₄	—	8	4	no	—
597	D₄	—	8	4	no	—
598	D₄	—	8	2	no	—
599	D₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	complemented
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	4	8	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	2	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	8	2	no	—
618	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
619	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
620	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
621	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
622	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
623	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
624	C₈	—	2	4	no	—
625	C₈	—	4	1	no	—
626	C₈	—	4	1	no	—
627	C₈	—	4	2	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	4	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	4	2	no	—
637	C₂²	—	4	4	no	—
638	C₂²	—	4	4	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	8	1	no	—
641	C₂²	—	8	1	no	—
642	C₂²	—	8	1	no	—
643	C₂²	—	16	4	no	—
644	C₂²	—	16	8	no	—
645	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
646	C₄	—	2	1	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	4	2	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	8	1	no	—
654	C₄	C₄₁×#453	1	2	yes	—
655	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
656	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
657	C₄	C₄₁×#576	1	1	yes	characteristic
658	C₄	C₄₁×#577	1	1	yes	characteristic
659	C₂	—	4	1	no	—
660	C₂	—	4	2	no	—
661	C₂	—	8	2	no	—
662	C₂	—	8	4	no	—
663	C₂	—	16	1	no	—
664	C₂	C₄₁×#3003	1	1	yes	characteristic
665	C₂	C₄₁×#3012	1	1	yes	characteristic
666	C₂	C₂×C₄₁×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3498	C₂	semidirect
2. C₄₁×#3253	C₂	semidirect
3. C₄₁×#3151	C₂	semidirect
4. C₄₁×#3106	C₂	semidirect
5. C₄₁×#1631	C₂	semidirect
6. C₄₁×#1629	C₂	semidirect
7. C₄₁×#1621	C₂	semidirect
8. C₄₁×#1619	C₂	semidirect
9. C₄₁×#1545	C₂	semidirect
10. C₄₁×#1489	C₂	semidirect
11. C₄₁×#1484	C₂	semidirect
24. C₄₁×#532	C₂²	semidirect
29. C₄₁×#493	C₂²	semidirect
30. C₄₁×#492	C₂²	semidirect
32. C₄₁×#477	C₂²	semidirect
34. C₄₁×#476	C₂²	semidirect
35. C₄₁×#476	C₂²	semidirect
37. C₄₁×#460	C₂²	semidirect
39. C₄₁×#459	C₂²	semidirect
40. C₄₁×#459	C₂²	semidirect
44. C₄₁×#431	C₂²	semidirect
45. C₄₁×#423	C₂²	semidirect
46. C₄×M₁₆×C₄₁	C₂²	semidirect
47. C₄₁×#331	C₂²	semidirect
48. C₄₁×#331	C₂²	semidirect
49. C₄₁×Q₈⋊C₈	C₂²	semidirect
50. C₄₁×D₄⋊C₈	C₂²	semidirect
51. C₄₁×D₄⋊C₈	C₂²	semidirect
52. C₄₁×D₄⋊C₈	C₂²	semidirect
239. Q₈×C₄₁	AGL(1,ℤ/8)	semidirect
265. D₄×C₄₁	AGL(1,ℤ/8)	semidirect
294. #18566	C₄₁	direct (N × H)
326. #3498	C₂×C₄₁	semidirect
327. #3253	C₂×C₄₁	semidirect
328. #3151	C₂×C₄₁	semidirect
329. #3106	C₂×C₄₁	semidirect
330. #1631	C₂×C₄₁	semidirect
331. #1629	C₂×C₄₁	semidirect
332. #1621	C₂×C₄₁	semidirect
333. #1619	C₂×C₄₁	semidirect
334. #1545	C₂×C₄₁	semidirect
335. #1489	C₂×C₄₁	semidirect
336. #1484	C₂×C₄₁	semidirect
357. #532	C₂²×C₄₁	semidirect
362. #493	C₂²×C₄₁	semidirect
363. #492	C₂²×C₄₁	semidirect
365. #477	C₂²×C₄₁	semidirect
367. #476	C₂²×C₄₁	semidirect
368. #476	C₂²×C₄₁	semidirect
370. #460	C₂²×C₄₁	semidirect
372. #459	C₂²×C₄₁	semidirect
373. #459	C₂²×C₄₁	semidirect
377. #431	C₂²×C₄₁	semidirect
378. #423	C₂²×C₄₁	semidirect
379. C₄×M₁₆	C₂²×C₄₁	semidirect
380. #331	C₂²×C₄₁	semidirect
381. #331	C₂²×C₄₁	semidirect
382. Q₈⋊C₈	C₂²×C₄₁	semidirect
383. D₄⋊C₈	C₂²×C₄₁	semidirect
384. D₄⋊C₈	C₂²×C₄₁	semidirect
385. D₄⋊C₈	C₂²×C₄₁	semidirect
386. C₄₁	#18566	direct (N × H)
573. Q₈	AGL(1,ℤ/8)×C₄₁	semidirect
599. D₄	AGL(1,ℤ/8)×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3498	2
C₄₁×#3253	2
C₄₁×#3151	2
C₄₁×#3106	2
C₄₁×#1631	2
C₄₁×#1629	2
C₄₁×#1621	2
C₄₁×#1619	2
C₄₁×#1545	2
C₄₁×#1489	2
C₄₁×#1484	2
#18566	41

Subgroups — C41×#18566 #23794767

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#18566 #23794767