Subgroups — C₄₁×#25669 #23801870

Order 10496.

992 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3511	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#3142	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3080	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2660	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2040	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2039	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1997	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1963	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1860	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1859	C₂	1	2	yes	maximal, complemented
11	C₄₁×#1759	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#556	—	2	1	no	—
13	C₄₁×#555	—	2	1	no	—
14	C₄₁×#554	—	2	1	no	—
15	C₄₁×#553	—	2	2	no	—
16	C₄₁×#548	—	2	2	no	—
17	C₄₁×#547	—	2	1	no	—
18	C₄₁×#542	—	2	2	no	—
19	C₄₁×#537	C₂²	1	2	yes	—
20	C₄₁×#533	—	2	1	no	—
21	C₄₁×#532	—	2	1	no	—
22	C₄₁×#532	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic
25	C₄₁×#520	C₂²	1	2	yes	—
26	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
27	C₄₁×#491	—	2	1	no	—
28	C₄₁×#490	—	2	1	no	—
29	C₄₁×#488	—	2	2	no	—
30	C₄₁×#479	—	2	1	no	—
31	C₄₁×#479	—	2	1	no	—
32	C₄₁×#478	—	2	1	no	—
33	C₄₁×#478	—	2	1	no	—
34	C₄₁×#428	C₂²	1	1	yes	characteristic
35	C₄₁×#428	C₂²	1	1	yes	characteristic
36	C₄₁×#423	C₂²	1	1	yes	characteristic
37	C₂×#104×C₄₁	C₂²	1	2	yes	—
38	C₂×#104×C₄₁	C₂²	1	2	yes	—
39	C₂×#104×C₄₁	C₂²	1	2	yes	—
40	C₄₁×#417	C₂²	1	1	yes	characteristic
41	C₄₁×#417	C₂²	1	2	yes	—
42	C₄₁×#417	C₂²	1	1	yes	characteristic
43	C₄₁×#417	C₂²	1	2	yes	—
44	C₄×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
45	C₄₁×#398	—	2	2	no	—
46	C₄₁×#395	—	2	2	no	—
47	C₄₁×#384	C₂²	1	2	yes	—
48	C₄₁×#382	C₂²	1	2	yes	—
49	C₄₁×#376	C₂²	1	1	yes	characteristic
50	C₄₁×#343	C₂²	1	2	yes	—
51	C₄₁×#343	C₂²	1	2	yes	—
52	C₄₁×#339	C₂²	1	2	yes	—
53	C₂×#41×C₄₁	—	2	2	no	—
54	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
55	C₂×#41×C₄₁	C₂³	1	2	yes	—
56	C₂²×Q₈×C₄₁	D₄	1	2	yes	—
57	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
58	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
59	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
60	C₄⋊Q₈×C₄₁	—	2	1	no	—
61	C₄⋊Q₈×C₄₁	—	2	1	no	—
62	C₄⋊Q₈×C₄₁	—	2	1	no	—
63	C₄⋊Q₈×C₄₁	—	2	1	no	—
64	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
65	#127×C₄₁	D₄	1	1	yes	characteristic
66	#126×C₄₁	—	2	4	no	—
67	#125×C₄₁	—	2	2	no	—
68	#125×C₄₁	—	2	1	no	—
69	#125×C₄₁	—	2	1	no	—
70	#125×C₄₁	—	2	1	no	—
71	#125×C₄₁	—	2	1	no	—
72	#124×C₄₁	—	2	2	no	—
73	#124×C₄₁	—	2	4	no	—
74	#124×C₄₁	D₄	1	2	yes	—
75	#123×C₄₁	—	2	4	no	—
76	C₂²⋊Q₈×C₄₁	—	2	2	no	—
77	C₂²⋊Q₈×C₄₁	—	2	4	no	—
78	C₂²⋊Q₈×C₄₁	—	2	2	no	—
79	C₂²⋊Q₈×C₄₁	—	2	2	no	—
80	#121×C₄₁	—	2	2	no	—
81	#121×C₄₁	—	2	2	no	—
82	#121×C₄₁	—	2	2	no	—
83	#121×C₄₁	—	2	1	no	—
84	#121×C₄₁	—	2	1	no	—
85	#121×C₄₁	—	2	4	no	—
86	C₄×Q₈×C₄₁	—	2	2	no	—
87	C₄×Q₈×C₄₁	—	2	2	no	—
88	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
89	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
90	C₄×D₄×C₄₁	—	2	2	no	—
91	C₄×D₄×C₄₁	—	2	2	no	—
92	C₄×D₄×C₄₁	—	2	1	no	—
93	C₄×D₄×C₄₁	—	2	1	no	—
94	C₄×D₄×C₄₁	—	2	4	no	—
95	C₄×D₄×C₄₁	—	2	1	no	—
96	C₄×D₄×C₄₁	—	2	1	no	—
97	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
98	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
99	#117×C₄₁	—	2	2	no	—
100	#117×C₄₁	—	2	2	no	—
101	#117×C₄₁	—	2	1	no	—
102	#117×C₄₁	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
104	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
105	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
106	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
107	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
108	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
111	C₂×C₄²×C₄₁	—	2	1	no	—
112	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
113	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
114	#107×C₄₁	—	2	1	no	—
115	#107×C₄₁	—	2	1	no	—
116	#106×C₄₁	—	2	1	no	—
117	#106×C₄₁	—	2	1	no	—
118	C₄⋊C₈×C₄₁	—	2	1	no	—
119	C₄⋊C₈×C₄₁	—	2	1	no	—
120	#104×C₄₁	—	2	4	no	—
121	#104×C₄₁	—	2	4	no	—
122	#104×C₄₁	—	2	4	no	—
123	#103×C₄₁	—	2	1	no	—
124	#103×C₄₁	—	2	1	no	—
125	#103×C₄₁	—	2	2	no	—
126	#103×C₄₁	—	2	2	no	—
127	#102×C₄₁	—	2	1	no	—
128	#102×C₄₁	—	2	1	no	—
129	#102×C₄₁	—	2	2	no	—
130	#102×C₄₁	—	2	2	no	—
131	#97×C₄₁	—	2	1	no	—
132	C₄×C₈×C₄₁	—	2	1	no	—
133	#95×C₄₁	—	2	1	no	—
134	#95×C₄₁	—	2	1	no	—
135	#95×C₄₁	—	2	4	no	—
136	#41×C₄₁	—	2	2	no	—
137	#41×C₄₁	—	2	2	no	—
138	#41×C₄₁	—	2	2	no	—
139	#41×C₄₁	—	2	2	no	—
140	#41×C₄₁	—	2	2	no	—
141	#41×C₄₁	—	2	2	no	—
142	#41×C₄₁	—	8	4	no	—
143	C₂×Q₈×C₄₁	—	2	2	no	—
144	C₂×Q₈×C₄₁	—	2	2	no	—
145	C₂×Q₈×C₄₁	—	8	2	no	—
146	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
147	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
148	C₂×D₄×C₄₁	—	2	1	no	—
149	C₂×D₄×C₄₁	—	2	2	no	—
150	C₂×D₄×C₄₁	—	2	4	no	—
151	C₂×D₄×C₄₁	—	2	1	no	—
152	C₂×D₄×C₄₁	—	2	1	no	—
153	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
154	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₄₁	—	2	2	no	—
156	C₂²×C₄×C₄₁	—	2	4	no	—
157	C₂²×C₄×C₄₁	—	2	1	no	—
158	C₂²×C₄×C₄₁	—	2	1	no	—
159	C₂²×C₄×C₄₁	—	2	1	no	—
160	C₂²×C₄×C₄₁	—	2	2	no	—
161	C₂²×C₄×C₄₁	—	2	1	no	—
162	C₂²×C₄×C₄₁	—	2	1	no	—
163	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
164	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
167	M₁₆×C₄₁	—	2	2	no	—
168	M₁₆×C₄₁	—	2	2	no	—
169	M₁₆×C₄₁	—	2	2	no	—
170	M₁₆×C₄₁	—	2	2	no	—
171	C₂×C₈×C₄₁	—	2	2	no	—
172	C₂×C₈×C₄₁	—	2	1	no	—
173	C₂×C₈×C₄₁	—	2	1	no	—
174	C₄⋊C₄×C₄₁	—	2	4	no	—
175	C₄⋊C₄×C₄₁	—	2	4	no	—
176	C₄⋊C₄×C₄₁	—	2	2	no	—
177	C₄⋊C₄×C₄₁	—	2	2	no	—
178	C₄⋊C₄×C₄₁	—	2	1	no	—
179	C₄⋊C₄×C₄₁	—	2	1	no	—
180	C₄⋊C₄×C₄₁	—	2	1	no	—
181	C₄⋊C₄×C₄₁	—	2	1	no	—
182	C₄⋊C₄×C₄₁	—	2	2	no	—
183	C₄⋊C₄×C₄₁	—	2	2	no	—
184	C₄⋊C₄×C₄₁	—	2	1	no	—
185	C₄⋊C₄×C₄₁	—	2	1	no	—
186	C₄⋊C₄×C₄₁	—	2	1	no	—
187	C₄⋊C₄×C₄₁	—	2	1	no	—
188	C₄⋊C₄×C₄₁	—	4	1	no	—
189	C₄⋊C₄×C₄₁	—	4	1	no	—
190	C₄⋊C₄×C₄₁	—	4	1	no	—
191	C₄⋊C₄×C₄₁	—	4	1	no	—
192	C₄⋊C₄×C₄₁	—	8	4	no	—
193	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
194	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
195	C₂²⋊C₄×C₄₁	—	2	4	no	—
196	C₂²⋊C₄×C₄₁	—	2	4	no	—
197	C₂²⋊C₄×C₄₁	—	2	4	no	—
198	C₂²⋊C₄×C₄₁	—	2	1	no	—
199	C₂²⋊C₄×C₄₁	—	2	1	no	—
200	C₂²⋊C₄×C₄₁	—	2	1	no	—
201	C₂²⋊C₄×C₄₁	—	2	2	no	—
202	C₂²⋊C₄×C₄₁	—	2	2	no	—
203	C₄²×C₄₁	—	2	4	no	—
204	C₄²×C₄₁	—	2	1	no	—
205	C₄²×C₄₁	—	2	1	no	—
206	C₄²×C₄₁	—	2	1	no	—
207	C₄²×C₄₁	—	2	2	no	—
208	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₄₁	#41	1	4	yes	complemented
213	C₂³×C₄₁	—	2	1	no	—
214	C₂³×C₄₁	—	2	2	no	—
215	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
216	Q₈×C₄₁	—	2	1	no	—
217	Q₈×C₄₁	—	2	1	no	—
218	Q₈×C₄₁	—	2	2	no	—
219	Q₈×C₄₁	—	2	2	no	—
220	Q₈×C₄₁	—	4	4	no	—
221	Q₈×C₄₁	—	8	2	no	—
222	D₄×C₄₁	—	2	1	no	—
223	D₄×C₄₁	—	2	1	no	—
224	D₄×C₄₁	—	2	2	no	—
225	D₄×C₄₁	—	2	2	no	—
226	D₄×C₄₁	—	4	2	no	—
227	D₄×C₄₁	—	4	2	no	—
228	D₄×C₄₁	—	4	2	no	—
229	D₄×C₄₁	—	4	2	no	—
230	D₄×C₄₁	—	4	2	no	—
231	D₄×C₄₁	—	8	4	no	—
232	C₂×C₄×C₄₁	—	2	1	no	—
233	C₂×C₄×C₄₁	—	2	2	no	—
234	C₂×C₄×C₄₁	—	2	1	no	—
235	C₂×C₄×C₄₁	—	2	1	no	—
236	C₂×C₄×C₄₁	—	2	4	no	—
237	C₂×C₄×C₄₁	—	2	4	no	—
238	C₂×C₄×C₄₁	—	4	1	no	—
239	C₂×C₄×C₄₁	—	4	1	no	—
240	C₂×C₄×C₄₁	—	4	2	no	—
241	C₂×C₄×C₄₁	—	4	2	no	—
242	C₂×C₄×C₄₁	—	4	2	no	—
243	C₂×C₄×C₄₁	—	4	2	no	—
244	C₂×C₄×C₄₁	—	4	2	no	—
245	C₂×C₄×C₄₁	—	4	2	no	—
246	C₂×C₄×C₄₁	—	4	2	no	—
247	C₂×C₄×C₄₁	—	4	4	no	—
248	C₂×C₄×C₄₁	—	4	2	no	—
249	C₂×C₄×C₄₁	—	4	2	no	—
250	C₂×C₄×C₄₁	—	4	1	no	—
251	C₂×C₄×C₄₁	—	4	1	no	—
252	C₂×C₄×C₄₁	—	8	4	no	—
253	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
254	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
255	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
256	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
257	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
260	C₂×C₄×C₄₁	2₋¹⁺⁴	1	2	yes	—
261	C₈×C₄₁	—	4	1	no	—
262	C₈×C₄₁	—	4	1	no	—
263	C₈×C₄₁	—	4	2	no	—
264	#25669	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₂²×C₄₁	—	2	1	no	—
266	C₂²×C₄₁	—	2	1	no	—
267	C₂²×C₄₁	—	4	2	no	—
268	C₂²×C₄₁	—	4	1	no	—
269	C₂²×C₄₁	—	4	1	no	—
270	C₂²×C₄₁	—	4	2	no	—
271	C₂²×C₄₁	—	4	1	no	—
272	C₂²×C₄₁	—	4	2	no	—
273	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
274	C₂²×C₄₁	#548	1	2	yes	—
275	C₄×C₄₁	—	2	1	no	—
276	C₄×C₄₁	—	2	1	no	—
277	C₄×C₄₁	—	2	1	no	—
278	C₄×C₄₁	—	2	1	no	—
279	C₄×C₄₁	—	4	4	no	—
280	C₄×C₄₁	—	4	2	no	—
281	C₄×C₄₁	—	4	1	no	—
282	C₄×C₄₁	—	4	1	no	—
283	C₄×C₄₁	—	4	4	no	—
284	C₄×C₄₁	—	4	1	no	—
285	C₄×C₄₁	—	8	1	no	—
286	C₄×C₄₁	—	8	1	no	—
287	C₄×C₄₁	#532	1	1	yes	characteristic
288	C₄×C₄₁	#536	1	1	yes	characteristic
289	C₄×C₄₁	#547	1	2	yes	—
290	#3511	C₂×C₄₁	1	1	yes	characteristic
291	#3142	C₂×C₄₁	1	1	yes	characteristic, complemented
292	#3080	C₂×C₄₁	1	1	yes	characteristic, complemented
293	#2660	C₂×C₄₁	1	1	yes	characteristic, complemented
294	#2040	C₂×C₄₁	1	2	yes	complemented
295	#2039	C₂×C₄₁	1	2	yes	complemented
296	#1997	C₂×C₄₁	1	1	yes	characteristic, complemented
297	#1963	C₂×C₄₁	1	1	yes	characteristic, complemented
298	#1860	C₂×C₄₁	1	2	yes	complemented
299	#1859	C₂×C₄₁	1	2	yes	complemented
300	#1759	C₂×C₄₁	1	1	yes	characteristic, complemented
301	C₂×C₄₁	—	2	2	no	—
302	C₂×C₄₁	—	8	1	no	—
303	C₂×C₄₁	—	8	2	no	—
304	C₂×C₄₁	#2432	1	1	yes	characteristic
305	C₂×C₄₁	#3019	1	1	yes	characteristic
306	C₂×C₄₁	#3020	1	1	yes	characteristic
307	#556	—	2	1	no	—
308	#555	—	2	1	no	—
309	#554	—	2	1	no	—
310	#553	—	2	2	no	—
311	#548	—	2	2	no	—
312	#547	—	2	1	no	—
313	#542	—	2	2	no	—
314	#537	C₂²×C₄₁	1	2	yes	—
315	#533	—	2	1	no	—
316	#532	—	2	1	no	—
317	#532	C₂²×C₄₁	1	1	yes	characteristic
318	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
319	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic
320	#520	C₂²×C₄₁	1	2	yes	—
321	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
322	#491	—	2	1	no	—
323	#490	—	2	1	no	—
324	#488	—	2	2	no	—
325	#479	—	2	1	no	—
326	#479	—	2	1	no	—
327	#478	—	2	1	no	—
328	#478	—	2	1	no	—
329	#428	C₂²×C₄₁	1	1	yes	characteristic
330	#428	C₂²×C₄₁	1	1	yes	characteristic
331	#423	C₂²×C₄₁	1	1	yes	characteristic
332	C₂×#104	C₂²×C₄₁	1	2	yes	—
333	C₂×#104	C₂²×C₄₁	1	2	yes	—
334	C₂×#104	C₂²×C₄₁	1	2	yes	—
335	#417	C₂²×C₄₁	1	1	yes	characteristic
336	#417	C₂²×C₄₁	1	1	yes	characteristic
337	#417	C₂²×C₄₁	1	2	yes	—
338	#417	C₂²×C₄₁	1	2	yes	—
339	C₄×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
340	#398	—	2	2	no	—
341	#395	—	2	2	no	—
342	#384	C₂²×C₄₁	1	2	yes	—
343	#382	C₂²×C₄₁	1	2	yes	—
344	#376	C₂²×C₄₁	1	1	yes	characteristic
345	#343	C₂²×C₄₁	1	2	yes	—
346	#343	C₂²×C₄₁	1	2	yes	—
347	#339	C₂²×C₄₁	1	2	yes	—
348	C₄₁	#25669	1	1	yes	characteristic, direct product factor, Sylow
349	C₂×#41	—	2	2	no	—
350	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
351	C₂×#41	C₂³×C₄₁	1	2	yes	—
352	C₂²×Q₈	D₄×C₄₁	1	2	yes	—
353	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
354	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
355	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
356	C₄⋊Q₈	—	2	1	no	—
357	C₄⋊Q₈	—	2	1	no	—
358	C₄⋊Q₈	—	2	1	no	—
359	C₄⋊Q₈	—	2	1	no	—
360	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
361	#127	D₄×C₄₁	1	1	yes	characteristic
362	#126	—	2	4	no	—
363	#125	—	2	2	no	—
364	#125	—	2	1	no	—
365	#125	—	2	1	no	—
366	#125	—	2	1	no	—
367	#125	—	2	1	no	—
368	#124	—	2	2	no	—
369	#124	—	2	4	no	—
370	#124	D₄×C₄₁	1	2	yes	—
371	#123	—	2	4	no	—
372	C₂²⋊Q₈	—	2	2	no	—
373	C₂²⋊Q₈	—	2	4	no	—
374	C₂²⋊Q₈	—	2	2	no	—
375	C₂²⋊Q₈	—	2	2	no	—
376	#121	—	2	2	no	—
377	#121	—	2	2	no	—
378	#121	—	2	2	no	—
379	#121	—	2	1	no	—
380	#121	—	2	1	no	—
381	#121	—	2	4	no	—
382	C₄×Q₈	—	2	2	no	—
383	C₄×Q₈	—	2	2	no	—
384	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
385	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	—	2	4	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
394	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
395	#117	—	2	2	no	—
396	#117	—	2	2	no	—
397	#117	—	2	1	no	—
398	#117	C₂³×C₄₁	1	1	yes	characteristic
399	C₂×C₄⋊C₄	—	2	2	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	4	no	—
403	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
404	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
407	C₂×C₄²	—	2	1	no	—
408	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
409	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
410	#107	—	2	1	no	—
411	#107	—	2	1	no	—
412	#106	—	2	1	no	—
413	#106	—	2	1	no	—
414	C₄⋊C₈	—	2	1	no	—
415	C₄⋊C₈	—	2	1	no	—
416	#104	—	2	4	no	—
417	#104	—	2	4	no	—
418	#104	—	2	4	no	—
419	#103	—	2	1	no	—
420	#103	—	2	1	no	—
421	#103	—	2	2	no	—
422	#103	—	2	2	no	—
423	#102	—	2	1	no	—
424	#102	—	2	1	no	—
425	#102	—	2	2	no	—
426	#102	—	2	2	no	—
427	#97	—	2	1	no	—
428	C₄×C₈	—	2	1	no	—
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	#95	—	2	4	no	—
432	#41	—	2	2	no	—
433	#41	—	2	2	no	—
434	#41	—	2	2	no	—
435	#41	—	2	2	no	—
436	#41	—	2	2	no	—
437	#41	—	2	2	no	—
438	#41	—	8	4	no	—
439	C₂×Q₈	—	2	2	no	—
440	C₂×Q₈	—	2	2	no	—
441	C₂×Q₈	—	8	2	no	—
442	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
443	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	4	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
450	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
460	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
462	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
463	M₁₆	—	2	2	no	—
464	M₁₆	—	2	2	no	—
465	M₁₆	—	2	2	no	—
466	M₁₆	—	2	2	no	—
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	4	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	2	no	—
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	—	4	1	no	—
485	C₄⋊C₄	—	4	1	no	—
486	C₄⋊C₄	—	4	1	no	—
487	C₄⋊C₄	—	4	1	no	—
488	C₄⋊C₄	—	8	4	no	—
489	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
490	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	4	no	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	2	1	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₄²	—	2	4	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	2	no	—
504	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
505	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
506	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
507	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
508	C₄²	#41×C₄₁	1	4	yes	complemented
509	C₂³	—	2	1	no	—
510	C₂³	—	2	2	no	—
511	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
512	Q₈	—	2	1	no	—
513	Q₈	—	2	1	no	—
514	Q₈	—	2	2	no	—
515	Q₈	—	2	2	no	—
516	Q₈	—	4	4	no	—
517	Q₈	—	8	2	no	—
518	D₄	—	2	1	no	—
519	D₄	—	2	1	no	—
520	D₄	—	2	2	no	—
521	D₄	—	2	2	no	—
522	D₄	—	4	2	no	—
523	D₄	—	4	2	no	—
524	D₄	—	4	2	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	8	4	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	4	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	8	4	no	—
549	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
550	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
551	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
552	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
553	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
554	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
555	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
556	C₂×C₄	2₋¹⁺⁴×C₄₁	1	2	yes	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	2	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	2	1	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	2	no	—
568	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
569	C₂²	C₄₁×#548	1	2	yes	—
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	4	4	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	4	no	—
579	C₄	—	4	1	no	—
580	C₄	—	8	1	no	—
581	C₄	—	8	1	no	—
582	C₄	C₄₁×#532	1	1	yes	characteristic
583	C₄	C₄₁×#536	1	1	yes	characteristic
584	C₄	C₄₁×#547	1	2	yes	—
585	C₂	—	2	2	no	—
586	C₂	—	8	1	no	—
587	C₂	—	8	2	no	—
588	C₂	C₄₁×#2432	1	1	yes	characteristic
589	C₂	C₄₁×#3019	1	1	yes	characteristic
590	C₂	C₄₁×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₄₁×#3511	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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
2. C₄₁×#3142	C₂	semidirect
3. C₄₁×#3080	C₂	semidirect
4. C₄₁×#2660	C₂	semidirect
5. C₄₁×#2040	C₂	semidirect
6. C₄₁×#2039	C₂	semidirect
7. C₄₁×#1997	C₂	semidirect
8. C₄₁×#1963	C₂	semidirect
9. C₄₁×#1860	C₂	semidirect
10. C₄₁×#1859	C₂	semidirect
11. C₄₁×#1759	C₂	semidirect
212. C₄²×C₄₁	#41	semidirect
264. #25669	C₄₁	direct (N × H)
291. #3142	C₂×C₄₁	semidirect
292. #3080	C₂×C₄₁	semidirect
293. #2660	C₂×C₄₁	semidirect
294. #2040	C₂×C₄₁	semidirect
295. #2039	C₂×C₄₁	semidirect
296. #1997	C₂×C₄₁	semidirect
297. #1963	C₂×C₄₁	semidirect
298. #1860	C₂×C₄₁	semidirect
299. #1859	C₂×C₄₁	semidirect
300. #1759	C₂×C₄₁	semidirect
348. C₄₁	#25669	direct (N × H)
508. C₄²	#41×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3511	2
C₄₁×#3142	2
C₄₁×#3080	2
C₄₁×#2660	2
C₄₁×#2040	2
C₄₁×#2039	2
C₄₁×#1997	2
C₄₁×#1963	2
C₄₁×#1860	2
C₄₁×#1859	2
C₄₁×#1759	2
#25669	41

Subgroups — C41×#25669 #23801870

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25669 #23801870