Subgroups — C₄₁×#23495 #23799696

Order 10496.

1422 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3449	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#421	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#417	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₁×#413	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2311	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2038	C₂	1	4	yes	maximal, complemented
8	C₄₁×#2037	C₂	1	4	yes	maximal, complemented
9	C₄₁×#1733	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
11	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
14	C₄₁×#537	—	2	1	no	—
15	C₄₁×#537	—	2	1	no	—
16	C₄₁×#536	—	2	1	no	—
17	C₄₁×#536	C₂²	1	2	yes	—
18	C₄₁×#535	—	2	1	no	—
19	C₄₁×#535	C₂²	1	2	yes	—
20	C₄₁×#534	—	2	2	no	—
21	C₄₁×#532	—	2	2	no	—
22	C₄₁×#525	—	2	2	no	—
23	C₄₁×#525	—	2	2	no	—
24	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
27	C₄₁×#428	—	2	2	no	—
28	C₄₁×#428	C₂²	1	4	yes	complemented
29	C₂×#107×C₄₁	—	2	1	no	—
30	C₂×#106×C₄₁	—	2	1	no	—
31	C₄₁×#421	—	2	4	no	—
32	C₂×#104×C₄₁	C₂²	1	4	yes	—
33	C₄₁×#417	—	2	2	no	—
34	C₄₁×#417	C₂²	1	4	yes	—
35	C₂×#103×C₄₁	—	2	1	no	—
36	C₂×#102×C₄₁	—	2	1	no	—
37	C₄₁×#413	—	2	4	no	—
38	C₂×#101×C₄₁	C₂²	1	2	yes	complemented
39	C₂×#100×C₄₁	C₂²	1	2	yes	complemented
40	C₄₁×#391	C₂²	1	2	yes	complemented
41	C₄₁×#390	C₂²	1	2	yes	complemented
42	C₄₁×#386	—	2	2	no	—
43	C₄₁×#380	—	2	2	no	—
44	C₄₁×#339	C₂²	1	4	yes	complemented
45	C₂×#41×C₄₁	—	2	1	no	—
46	C₂×#41×C₄₁	—	2	1	no	—
47	C₂×#41×C₄₁	—	2	1	no	—
48	C₂×#41×C₄₁	—	2	1	no	—
49	C₂×#41×C₄₁	—	2	1	no	—
50	C₂×#41×C₄₁	—	2	1	no	—
51	C₂×#41×C₄₁	—	2	2	no	—
52	C₂×#41×C₄₁	—	2	2	no	—
53	C₂×#41×C₄₁	—	2	2	no	—
54	C₂×#41×C₄₁	—	2	2	no	—
55	C₂×#41×C₄₁	—	2	2	no	—
56	C₂×#41×C₄₁	—	2	2	no	—
57	C₂×#41×C₄₁	—	2	2	no	—
58	C₂×#41×C₄₁	—	2	2	no	—
59	C₂×#41×C₄₁	D₄	1	2	yes	—
60	C₂×#41×C₄₁	C₂³	1	2	yes	—
61	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
62	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₄₁	—	2	1	no	—
64	C₂²×D₄×C₄₁	D₄	1	2	yes	—
65	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
66	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₄₁	—	2	1	no	—
68	C₂³×C₄×C₄₁	—	2	1	no	—
69	C₂³×C₄×C₄₁	D₄	1	2	yes	—
70	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
71	C₂×M₁₆×C₄₁	—	2	1	no	—
72	C₂×M₁₆×C₄₁	—	2	2	no	—
73	C₂×M₁₆×C₄₁	—	2	1	no	—
74	C₂×M₁₆×C₄₁	—	2	2	no	—
75	C₂×M₁₆×C₄₁	—	2	2	no	—
76	C₂×M₁₆×C₄₁	D₄	1	4	yes	complemented
77	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
78	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
79	C₂²×C₈×C₄₁	—	2	1	no	—
80	C₂²×C₈×C₄₁	—	2	1	no	—
81	C₄⋊Q₈×C₄₁	—	2	2	no	—
82	#127×C₄₁	—	2	2	no	—
83	#124×C₄₁	—	2	2	no	—
84	#124×C₄₁	—	2	2	no	—
85	#123×C₄₁	—	2	4	no	—
86	#123×C₄₁	—	2	4	no	—
87	C₂²⋊Q₈×C₄₁	—	2	2	no	—
88	C₂²⋊Q₈×C₄₁	—	2	2	no	—
89	C₂²⋊Q₈×C₄₁	—	2	2	no	—
90	C₂²⋊Q₈×C₄₁	—	2	2	no	—
91	#121×C₄₁	—	2	2	no	—
92	#121×C₄₁	—	2	2	no	—
93	#121×C₄₁	—	2	4	no	—
94	#121×C₄₁	—	2	4	no	—
95	#121×C₄₁	—	2	2	no	—
96	#121×C₄₁	—	2	2	no	—
97	#120×C₄₁	—	2	4	no	—
98	#120×C₄₁	—	2	4	no	—
99	C₄×D₄×C₄₁	—	2	4	no	—
100	C₄×D₄×C₄₁	—	2	4	no	—
101	#117×C₄₁	—	2	1	no	—
102	#117×C₄₁	—	2	1	no	—
103	#117×C₄₁	—	2	2	no	—
104	#117×C₄₁	—	2	2	no	—
105	#117×C₄₁	D₄	1	2	yes	—
106	#117×C₄₁	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
108	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
109	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
110	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
111	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
112	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
113	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
119	C₂×C₄²×C₄₁	—	2	1	no	—
120	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
121	#107×C₄₁	—	2	4	no	—
122	#106×C₄₁	—	2	4	no	—
123	#104×C₄₁	—	2	8	no	—
124	#103×C₄₁	—	2	4	no	—
125	#102×C₄₁	—	2	4	no	—
126	#101×C₄₁	—	2	4	no	—
127	#100×C₄₁	—	2	4	no	—
128	#95×C₄₁	—	2	4	no	—
129	C₂⁴×C₄₁	—	2	1	no	—
130	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
131	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
132	#41×C₄₁	—	2	4	no	—
133	#41×C₄₁	—	2	4	no	—
134	#41×C₄₁	—	2	2	no	—
135	#41×C₄₁	—	2	2	no	—
136	#41×C₄₁	—	2	2	no	—
137	#41×C₄₁	—	2	2	no	—
138	#41×C₄₁	—	4	2	no	—
139	#41×C₄₁	—	4	2	no	—
140	#41×C₄₁	—	4	2	no	—
141	#41×C₄₁	—	4	2	no	—
142	#41×C₄₁	—	4	2	no	—
143	#41×C₄₁	—	4	2	no	—
144	#41×C₄₁	—	4	2	no	—
145	#41×C₄₁	—	4	2	no	—
146	#41×C₄₁	—	4	2	no	—
147	#41×C₄₁	—	4	2	no	—
148	#41×C₄₁	—	4	2	no	—
149	#41×C₄₁	—	4	2	no	—
150	C₂×Q₈×C₄₁	—	2	1	no	—
151	C₂×Q₈×C₄₁	—	2	1	no	—
152	C₂×Q₈×C₄₁	—	2	1	no	—
153	C₂×Q₈×C₄₁	—	2	1	no	—
154	C₂×Q₈×C₄₁	—	2	1	no	—
155	C₂×Q₈×C₄₁	—	2	1	no	—
156	C₂×Q₈×C₄₁	—	2	1	no	—
157	C₂×Q₈×C₄₁	—	2	2	no	—
158	C₂×Q₈×C₄₁	—	2	2	no	—
159	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
160	C₂×D₄×C₄₁	—	2	2	no	—
161	C₂×D₄×C₄₁	—	2	2	no	—
162	C₂×D₄×C₄₁	—	2	2	no	—
163	C₂×D₄×C₄₁	—	2	4	no	—
164	C₂×D₄×C₄₁	—	2	4	no	—
165	C₂×D₄×C₄₁	—	2	2	no	—
166	C₂×D₄×C₄₁	—	2	4	no	—
167	C₂×D₄×C₄₁	—	2	4	no	—
168	C₂×D₄×C₄₁	—	2	1	no	—
169	C₂×D₄×C₄₁	—	2	2	no	—
170	C₂×D₄×C₄₁	—	2	2	no	—
171	C₂×D₄×C₄₁	—	2	1	no	—
172	C₂×D₄×C₄₁	—	2	1	no	—
173	C₂×D₄×C₄₁	—	2	1	no	—
174	C₂×D₄×C₄₁	—	2	1	no	—
175	C₂×D₄×C₄₁	—	2	1	no	—
176	C₂×D₄×C₄₁	—	2	1	no	—
177	C₂×D₄×C₄₁	—	4	2	no	—
178	C₂×D₄×C₄₁	—	4	2	no	—
179	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₄₁	—	2	1	no	—
181	C₂²×C₄×C₄₁	—	2	1	no	—
182	C₂²×C₄×C₄₁	—	2	1	no	—
183	C₂²×C₄×C₄₁	—	2	2	no	—
184	C₂²×C₄×C₄₁	—	2	2	no	—
185	C₂²×C₄×C₄₁	—	2	2	no	—
186	C₂²×C₄×C₄₁	—	2	4	no	—
187	C₂²×C₄×C₄₁	—	2	4	no	—
188	C₂²×C₄×C₄₁	—	2	2	no	—
189	C₂²×C₄×C₄₁	—	2	2	no	—
190	C₂²×C₄×C₄₁	—	2	2	no	—
191	C₂²×C₄×C₄₁	—	4	2	no	—
192	C₂²×C₄×C₄₁	—	4	2	no	—
193	C₂²×C₄×C₄₁	—	4	1	no	—
194	C₂²×C₄×C₄₁	—	4	1	no	—
195	C₂²×C₄×C₄₁	—	8	2	no	—
196	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
197	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
203	C₂²×C₄×C₄₁	#41	1	2	yes	—
204	C₂²×C₄×C₄₁	#41	1	2	yes	—
205	C₂²×C₄×C₄₁	#41	1	2	yes	—
206	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
207	M₁₆×C₄₁	—	2	4	no	—
208	M₁₆×C₄₁	—	2	2	no	—
209	M₁₆×C₄₁	—	2	2	no	—
210	M₁₆×C₄₁	—	2	2	no	—
211	M₁₆×C₄₁	—	4	2	no	—
212	M₁₆×C₄₁	C₂×D₄	1	4	yes	—
213	C₂×C₈×C₄₁	—	2	4	no	—
214	C₂×C₈×C₄₁	—	2	2	no	—
215	C₂×C₈×C₄₁	—	2	2	no	—
216	C₂×C₈×C₄₁	—	4	2	no	—
217	C₄⋊C₄×C₄₁	—	2	4	no	—
218	C₄⋊C₄×C₄₁	—	2	4	no	—
219	C₄⋊C₄×C₄₁	—	2	1	no	—
220	C₄⋊C₄×C₄₁	—	2	1	no	—
221	C₄⋊C₄×C₄₁	—	2	2	no	—
222	C₄⋊C₄×C₄₁	—	2	2	no	—
223	C₄⋊C₄×C₄₁	—	4	1	no	—
224	C₄⋊C₄×C₄₁	—	4	1	no	—
225	C₄⋊C₄×C₄₁	—	4	2	no	—
226	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
227	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
228	C₂²⋊C₄×C₄₁	—	2	4	no	—
229	C₂²⋊C₄×C₄₁	—	2	4	no	—
230	C₂²⋊C₄×C₄₁	—	2	4	no	—
231	C₂²⋊C₄×C₄₁	—	2	4	no	—
232	C₂²⋊C₄×C₄₁	—	2	2	no	—
233	C₂²⋊C₄×C₄₁	—	2	2	no	—
234	C₂²⋊C₄×C₄₁	—	4	2	no	—
235	C₂²⋊C₄×C₄₁	—	8	4	no	—
236	C₄²×C₄₁	—	2	2	no	—
237	C₄²×C₄₁	—	2	2	no	—
238	C₄²×C₄₁	—	2	2	no	—
239	C₄²×C₄₁	—	2	2	no	—
240	C₂³×C₄₁	—	2	2	no	—
241	C₂³×C₄₁	—	2	2	no	—
242	C₂³×C₄₁	—	2	2	no	—
243	C₂³×C₄₁	—	2	2	no	—
244	C₂³×C₄₁	—	4	1	no	—
245	C₂³×C₄₁	—	4	1	no	—
246	C₂³×C₄₁	—	4	2	no	—
247	C₂³×C₄₁	—	4	2	no	—
248	C₂³×C₄₁	—	4	2	no	—
249	C₂³×C₄₁	—	8	1	no	—
250	C₂³×C₄₁	—	8	1	no	—
251	C₂³×C₄₁	#120	1	1	yes	characteristic
252	C₂³×C₄₁	#120	1	1	yes	characteristic
253	C₂³×C₄₁	#121	1	2	yes	—
254	C₂³×C₄₁	#123	1	2	yes	—
255	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
256	Q₈×C₄₁	—	2	2	no	—
257	Q₈×C₄₁	—	2	2	no	—
258	Q₈×C₄₁	—	4	1	no	—
259	Q₈×C₄₁	—	4	1	no	—
260	Q₈×C₄₁	—	4	1	no	—
261	Q₈×C₄₁	—	4	1	no	—
262	Q₈×C₄₁	—	4	2	no	—
263	D₄×C₄₁	—	2	2	no	—
264	D₄×C₄₁	—	2	2	no	—
265	D₄×C₄₁	—	4	2	no	—
266	D₄×C₄₁	—	4	2	no	—
267	D₄×C₄₁	—	4	4	no	—
268	D₄×C₄₁	—	4	4	no	—
269	D₄×C₄₁	—	4	4	no	—
270	D₄×C₄₁	—	4	1	no	—
271	D₄×C₄₁	—	4	1	no	—
272	D₄×C₄₁	—	4	1	no	—
273	D₄×C₄₁	—	4	1	no	—
274	D₄×C₄₁	—	4	2	no	—
275	D₄×C₄₁	—	8	4	no	—
276	D₄×C₄₁	—	8	4	no	—
277	C₂×C₄×C₄₁	—	2	2	no	—
278	C₂×C₄×C₄₁	—	2	2	no	—
279	C₂×C₄×C₄₁	—	2	2	no	—
280	C₂×C₄×C₄₁	—	2	2	no	—
281	C₂×C₄×C₄₁	—	2	2	no	—
282	C₂×C₄×C₄₁	—	2	2	no	—
283	C₂×C₄×C₄₁	—	4	2	no	—
284	C₂×C₄×C₄₁	—	4	2	no	—
285	C₂×C₄×C₄₁	—	4	2	no	—
286	C₂×C₄×C₄₁	—	4	4	no	—
287	C₂×C₄×C₄₁	—	4	4	no	—
288	C₂×C₄×C₄₁	—	4	4	no	—
289	C₂×C₄×C₄₁	—	4	2	no	—
290	C₂×C₄×C₄₁	—	4	4	no	—
291	C₂×C₄×C₄₁	—	4	2	no	—
292	C₂×C₄×C₄₁	—	4	2	no	—
293	C₂×C₄×C₄₁	—	4	2	no	—
294	C₂×C₄×C₄₁	—	8	1	no	—
295	C₂×C₄×C₄₁	—	8	1	no	—
296	C₂×C₄×C₄₁	—	8	2	no	—
297	C₂×C₄×C₄₁	—	8	2	no	—
298	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
299	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
300	C₂×C₄×C₄₁	#121	1	2	yes	—
301	C₂×C₄×C₄₁	#121	1	2	yes	—
302	C₂×C₄×C₄₁	#121	1	2	yes	—
303	C₂×C₄×C₄₁	#121	1	2	yes	—
304	C₂×C₄×C₄₁	#121	1	2	yes	—
305	C₂×C₄×C₄₁	#123	1	2	yes	—
306	C₂×C₄×C₄₁	#123	1	2	yes	—
307	C₂×C₄×C₄₁	#123	1	2	yes	—
308	C₂×C₄×C₄₁	#124	1	2	yes	—
309	C₂×C₄×C₄₁	#124	1	2	yes	—
310	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
312	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
314	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
315	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
316	C₈×C₄₁	—	2	4	no	—
317	C₈×C₄₁	—	4	2	no	—
318	#23495	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
319	C₂²×C₄₁	—	2	1	no	—
320	C₂²×C₄₁	—	2	1	no	—
321	C₂²×C₄₁	—	2	1	no	—
322	C₂²×C₄₁	—	2	1	no	—
323	C₂²×C₄₁	—	2	1	no	—
324	C₂²×C₄₁	—	2	1	no	—
325	C₂²×C₄₁	—	4	2	no	—
326	C₂²×C₄₁	—	4	2	no	—
327	C₂²×C₄₁	—	4	4	no	—
328	C₂²×C₄₁	—	4	2	no	—
329	C₂²×C₄₁	—	4	2	no	—
330	C₂²×C₄₁	—	4	2	no	—
331	C₂²×C₄₁	—	4	2	no	—
332	C₂²×C₄₁	—	4	2	no	—
333	C₂²×C₄₁	—	4	2	no	—
334	C₂²×C₄₁	—	8	2	no	—
335	C₂²×C₄₁	—	8	4	no	—
336	C₂²×C₄₁	#394	1	2	yes	—
337	C₂²×C₄₁	#394	1	2	yes	—
338	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
339	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
340	C₂²×C₄₁	C₂×#123	1	1	yes	characteristic
341	C₄×C₄₁	—	4	2	no	—
342	C₄×C₄₁	—	4	2	no	—
343	C₄×C₄₁	—	4	2	no	—
344	C₄×C₄₁	—	4	2	no	—
345	C₄×C₄₁	—	8	2	no	—
346	C₄×C₄₁	—	8	2	no	—
347	C₄×C₄₁	#394	1	2	yes	—
348	C₄×C₄₁	#394	1	2	yes	—
349	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
350	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
351	C₄×C₄₁	C₂×#123	1	1	yes	characteristic
352	C₄×C₄₁	C₂×#124	1	1	yes	characteristic
353	#3449	C₂×C₄₁	1	1	yes	characteristic
354	C₂×#428	C₂×C₄₁	1	1	yes	characteristic, complemented
355	C₂×#421	C₂×C₄₁	1	1	yes	characteristic, complemented
356	C₂×#417	C₂×C₄₁	1	1	yes	characteristic, complemented
357	C₂×#413	C₂×C₄₁	1	1	yes	characteristic, complemented
358	#2311	C₂×C₄₁	1	1	yes	characteristic, complemented
359	#2038	C₂×C₄₁	1	4	yes	complemented
360	#2037	C₂×C₄₁	1	4	yes	complemented
361	#1733	C₂×C₄₁	1	1	yes	characteristic, complemented
362	C₂×C₄₁	—	2	1	no	—
363	C₂×C₄₁	—	2	1	no	—
364	C₂×C₄₁	—	2	2	no	—
365	C₂×C₄₁	—	2	2	no	—
366	C₂×C₄₁	—	8	2	no	—
367	C₂×C₄₁	—	8	2	no	—
368	C₂×C₄₁	C₂×#394	1	1	yes	characteristic
369	C₂×C₄₁	#3021	1	1	yes	characteristic
370	C₂×C₄₁	#3022	1	1	yes	characteristic
371	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
372	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
373	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
374	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
375	#537	—	2	1	no	—
376	#537	—	2	1	no	—
377	#536	—	2	1	no	—
378	#536	C₂²×C₄₁	1	2	yes	—
379	#535	—	2	1	no	—
380	#535	C₂²×C₄₁	1	2	yes	—
381	#534	—	2	2	no	—
382	#532	—	2	2	no	—
383	#525	—	2	2	no	—
384	#525	—	2	2	no	—
385	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
386	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
387	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
388	#428	—	2	2	no	—
389	#428	C₂²×C₄₁	1	4	yes	complemented
390	C₂×#107	—	2	1	no	—
391	C₂×#106	—	2	1	no	—
392	#421	—	2	4	no	—
393	C₂×#104	C₂²×C₄₁	1	4	yes	—
394	#417	—	2	2	no	—
395	#417	C₂²×C₄₁	1	4	yes	—
396	C₂×#103	—	2	1	no	—
397	C₂×#102	—	2	1	no	—
398	#413	—	2	4	no	—
399	C₂×#101	C₂²×C₄₁	1	2	yes	complemented
400	C₂×#100	C₂²×C₄₁	1	2	yes	complemented
401	#391	C₂²×C₄₁	1	2	yes	complemented
402	#390	C₂²×C₄₁	1	2	yes	complemented
403	#386	—	2	2	no	—
404	#380	—	2	2	no	—
405	#339	C₂²×C₄₁	1	4	yes	complemented
406	C₄₁	#23495	1	1	yes	characteristic, direct product factor, Sylow
407	C₂×#41	—	2	1	no	—
408	C₂×#41	—	2	1	no	—
409	C₂×#41	—	2	1	no	—
410	C₂×#41	—	2	1	no	—
411	C₂×#41	—	2	1	no	—
412	C₂×#41	—	2	1	no	—
413	C₂×#41	—	2	2	no	—
414	C₂×#41	—	2	2	no	—
415	C₂×#41	—	2	2	no	—
416	C₂×#41	—	2	2	no	—
417	C₂×#41	—	2	2	no	—
418	C₂×#41	—	2	2	no	—
419	C₂×#41	—	2	2	no	—
420	C₂×#41	—	2	2	no	—
421	C₂×#41	D₄×C₄₁	1	2	yes	—
422	C₂×#41	C₂³×C₄₁	1	2	yes	—
423	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
424	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
425	C₂²×D₄	—	2	1	no	—
426	C₂²×D₄	D₄×C₄₁	1	2	yes	—
427	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
428	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
429	C₂³×C₄	—	2	1	no	—
430	C₂³×C₄	—	2	1	no	—
431	C₂³×C₄	D₄×C₄₁	1	2	yes	—
432	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
433	C₂×M₁₆	—	2	1	no	—
434	C₂×M₁₆	—	2	2	no	—
435	C₂×M₁₆	—	2	1	no	—
436	C₂×M₁₆	—	2	2	no	—
437	C₂×M₁₆	—	2	2	no	—
438	C₂×M₁₆	D₄×C₄₁	1	4	yes	complemented
439	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
440	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
441	C₂²×C₈	—	2	1	no	—
442	C₂²×C₈	—	2	1	no	—
443	C₄⋊Q₈	—	2	2	no	—
444	#127	—	2	2	no	—
445	#124	—	2	2	no	—
446	#124	—	2	2	no	—
447	#123	—	2	4	no	—
448	#123	—	2	4	no	—
449	C₂²⋊Q₈	—	2	2	no	—
450	C₂²⋊Q₈	—	2	2	no	—
451	C₂²⋊Q₈	—	2	2	no	—
452	C₂²⋊Q₈	—	2	2	no	—
453	#121	—	2	2	no	—
454	#121	—	2	2	no	—
455	#121	—	2	4	no	—
456	#121	—	2	4	no	—
457	#121	—	2	2	no	—
458	#121	—	2	2	no	—
459	#120	—	2	4	no	—
460	#120	—	2	4	no	—
461	C₄×D₄	—	2	4	no	—
462	C₄×D₄	—	2	4	no	—
463	#117	—	2	1	no	—
464	#117	—	2	1	no	—
465	#117	—	2	2	no	—
466	#117	—	2	2	no	—
467	#117	D₄×C₄₁	1	2	yes	—
468	#117	C₂³×C₄₁	1	2	yes	—
469	C₂×C₄⋊C₄	—	2	1	no	—
470	C₂×C₄⋊C₄	—	2	1	no	—
471	C₂×C₄⋊C₄	—	2	1	no	—
472	C₂×C₄⋊C₄	—	2	1	no	—
473	C₂×C₄⋊C₄	—	2	1	no	—
474	C₂×C₄⋊C₄	—	2	1	no	—
475	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
476	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
477	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
478	C₂×C₂²⋊C₄	—	2	1	no	—
479	C₂×C₂²⋊C₄	—	2	1	no	—
480	C₂×C₂²⋊C₄	—	2	4	no	—
481	C₂×C₄²	—	2	1	no	—
482	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
483	#107	—	2	4	no	—
484	#106	—	2	4	no	—
485	#104	—	2	8	no	—
486	#103	—	2	4	no	—
487	#102	—	2	4	no	—
488	#101	—	2	4	no	—
489	#100	—	2	4	no	—
490	#95	—	2	4	no	—
491	C₂⁴	—	2	1	no	—
492	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
493	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
494	#41	—	2	4	no	—
495	#41	—	2	4	no	—
496	#41	—	2	2	no	—
497	#41	—	2	2	no	—
498	#41	—	2	2	no	—
499	#41	—	2	2	no	—
500	#41	—	4	2	no	—
501	#41	—	4	2	no	—
502	#41	—	4	2	no	—
503	#41	—	4	2	no	—
504	#41	—	4	2	no	—
505	#41	—	4	2	no	—
506	#41	—	4	2	no	—
507	#41	—	4	2	no	—
508	#41	—	4	2	no	—
509	#41	—	4	2	no	—
510	#41	—	4	2	no	—
511	#41	—	4	2	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	2	1	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	—	2	2	no	—
520	C₂×Q₈	—	2	2	no	—
521	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
522	C₂×D₄	—	2	2	no	—
523	C₂×D₄	—	2	2	no	—
524	C₂×D₄	—	2	2	no	—
525	C₂×D₄	—	2	4	no	—
526	C₂×D₄	—	2	4	no	—
527	C₂×D₄	—	2	2	no	—
528	C₂×D₄	—	2	4	no	—
529	C₂×D₄	—	2	4	no	—
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	—	2	1	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	2	1	no	—
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	4	2	no	—
540	C₂×D₄	—	4	2	no	—
541	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	4	no	—
549	C₂²×C₄	—	2	4	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	4	2	no	—
554	C₂²×C₄	—	4	2	no	—
555	C₂²×C₄	—	4	1	no	—
556	C₂²×C₄	—	4	1	no	—
557	C₂²×C₄	—	8	2	no	—
558	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
559	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
560	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
561	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
562	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
564	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
565	C₂²×C₄	#41×C₄₁	1	2	yes	—
566	C₂²×C₄	#41×C₄₁	1	2	yes	—
567	C₂²×C₄	#41×C₄₁	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
569	M₁₆	—	2	4	no	—
570	M₁₆	—	2	2	no	—
571	M₁₆	—	2	2	no	—
572	M₁₆	—	2	2	no	—
573	M₁₆	—	4	2	no	—
574	M₁₆	C₂×D₄×C₄₁	1	4	yes	—
575	C₂×C₈	—	2	4	no	—
576	C₂×C₈	—	2	2	no	—
577	C₂×C₈	—	2	2	no	—
578	C₂×C₈	—	4	2	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	2	no	—
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	4	1	no	—
586	C₄⋊C₄	—	4	1	no	—
587	C₄⋊C₄	—	4	2	no	—
588	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
589	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
590	C₂²⋊C₄	—	2	4	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	—	2	4	no	—
594	C₂²⋊C₄	—	2	2	no	—
595	C₂²⋊C₄	—	2	2	no	—
596	C₂²⋊C₄	—	4	2	no	—
597	C₂²⋊C₄	—	8	4	no	—
598	C₄²	—	2	2	no	—
599	C₄²	—	2	2	no	—
600	C₄²	—	2	2	no	—
601	C₄²	—	2	2	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	2	no	—
609	C₂³	—	4	2	no	—
610	C₂³	—	4	2	no	—
611	C₂³	—	8	1	no	—
612	C₂³	—	8	1	no	—
613	C₂³	#120×C₄₁	1	1	yes	characteristic
614	C₂³	#120×C₄₁	1	1	yes	characteristic
615	C₂³	#121×C₄₁	1	2	yes	—
616	C₂³	#123×C₄₁	1	2	yes	—
617	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
618	Q₈	—	2	2	no	—
619	Q₈	—	2	2	no	—
620	Q₈	—	4	1	no	—
621	Q₈	—	4	1	no	—
622	Q₈	—	4	1	no	—
623	Q₈	—	4	1	no	—
624	Q₈	—	4	2	no	—
625	D₄	—	2	2	no	—
626	D₄	—	2	2	no	—
627	D₄	—	4	2	no	—
628	D₄	—	4	2	no	—
629	D₄	—	4	4	no	—
630	D₄	—	4	4	no	—
631	D₄	—	4	4	no	—
632	D₄	—	4	1	no	—
633	D₄	—	4	1	no	—
634	D₄	—	4	1	no	—
635	D₄	—	4	1	no	—
636	D₄	—	4	2	no	—
637	D₄	—	8	4	no	—
638	D₄	—	8	4	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	4	2	no	—
646	C₂×C₄	—	4	2	no	—
647	C₂×C₄	—	4	2	no	—
648	C₂×C₄	—	4	4	no	—
649	C₂×C₄	—	4	4	no	—
650	C₂×C₄	—	4	4	no	—
651	C₂×C₄	—	4	2	no	—
652	C₂×C₄	—	4	4	no	—
653	C₂×C₄	—	4	2	no	—
654	C₂×C₄	—	4	2	no	—
655	C₂×C₄	—	4	2	no	—
656	C₂×C₄	—	8	1	no	—
657	C₂×C₄	—	8	1	no	—
658	C₂×C₄	—	8	2	no	—
659	C₂×C₄	—	8	2	no	—
660	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
661	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
662	C₂×C₄	#121×C₄₁	1	2	yes	—
663	C₂×C₄	#121×C₄₁	1	2	yes	—
664	C₂×C₄	#121×C₄₁	1	2	yes	—
665	C₂×C₄	#121×C₄₁	1	2	yes	—
666	C₂×C₄	#121×C₄₁	1	2	yes	—
667	C₂×C₄	#123×C₄₁	1	2	yes	—
668	C₂×C₄	#123×C₄₁	1	2	yes	—
669	C₂×C₄	#123×C₄₁	1	2	yes	—
670	C₂×C₄	#124×C₄₁	1	2	yes	—
671	C₂×C₄	#124×C₄₁	1	2	yes	—
672	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
673	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
674	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
675	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
676	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
677	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
678	C₈	—	2	4	no	—
679	C₈	—	4	2	no	—
680	C₂²	—	2	1	no	—
681	C₂²	—	2	1	no	—
682	C₂²	—	2	1	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	2	1	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	4	2	no	—
687	C₂²	—	4	2	no	—
688	C₂²	—	4	4	no	—
689	C₂²	—	4	2	no	—
690	C₂²	—	4	2	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	8	2	no	—
696	C₂²	—	8	4	no	—
697	C₂²	C₄₁×#394	1	2	yes	—
698	C₂²	C₄₁×#394	1	2	yes	—
699	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
700	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
701	C₂²	C₂×#123×C₄₁	1	1	yes	characteristic
702	C₄	—	4	2	no	—
703	C₄	—	4	2	no	—
704	C₄	—	4	2	no	—
705	C₄	—	4	2	no	—
706	C₄	—	8	2	no	—
707	C₄	—	8	2	no	—
708	C₄	C₄₁×#394	1	2	yes	—
709	C₄	C₄₁×#394	1	2	yes	—
710	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
711	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
712	C₄	C₂×#123×C₄₁	1	1	yes	characteristic
713	C₄	C₂×#124×C₄₁	1	1	yes	characteristic
714	C₂	—	2	1	no	—
715	C₂	—	2	1	no	—
716	C₂	—	2	2	no	—
717	C₂	—	2	2	no	—
718	C₂	—	8	2	no	—
719	C₂	—	8	2	no	—
720	C₂	C₂×C₄₁×#394	1	1	yes	characteristic
721	C₂	C₄₁×#3021	1	1	yes	characteristic
722	C₂	C₄₁×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₄₁×#3449	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#428	C₂	semidirect
3. C₂×C₄₁×#421	C₂	semidirect
4. C₂×C₄₁×#417	C₂	semidirect
5. C₂×C₄₁×#413	C₂	semidirect
6. C₄₁×#2311	C₂	semidirect
7. C₄₁×#2038	C₂	semidirect
8. C₄₁×#2037	C₂	semidirect
9. C₄₁×#1733	C₂	semidirect
28. C₄₁×#428	C₂²	semidirect
38. C₂×#101×C₄₁	C₂²	semidirect
39. C₂×#100×C₄₁	C₂²	semidirect
40. C₄₁×#391	C₂²	semidirect
41. C₄₁×#390	C₂²	semidirect
44. C₄₁×#339	C₂²	semidirect
76. C₂×M₁₆×C₄₁	D₄	semidirect
318. #23495	C₄₁	direct (N × H)
354. C₂×#428	C₂×C₄₁	semidirect
355. C₂×#421	C₂×C₄₁	semidirect
356. C₂×#417	C₂×C₄₁	semidirect
357. C₂×#413	C₂×C₄₁	semidirect
358. #2311	C₂×C₄₁	semidirect
359. #2038	C₂×C₄₁	semidirect
360. #2037	C₂×C₄₁	semidirect
361. #1733	C₂×C₄₁	semidirect
389. #428	C₂²×C₄₁	semidirect
399. C₂×#101	C₂²×C₄₁	semidirect
400. C₂×#100	C₂²×C₄₁	semidirect
401. #391	C₂²×C₄₁	semidirect
402. #390	C₂²×C₄₁	semidirect
405. #339	C₂²×C₄₁	semidirect
406. C₄₁	#23495	direct (N × H)
438. C₂×M₁₆	D₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3449	2
C₂×C₄₁×#428	2
C₂×C₄₁×#421	2
C₂×C₄₁×#417	2
C₂×C₄₁×#413	2
C₄₁×#2311	2
C₄₁×#2038	2
C₄₁×#2037	2
C₄₁×#1733	2
#23495	41

Subgroups — C41×#23495 #23799696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23495 #23799696