Subgroups — C₄₁×#25394 #23801595

Order 10496.

986 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#470	C₂	1	2	yes	maximal, complemented
2	C₂×C₄₁×#462	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#436	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2542	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#2538	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#2035	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2001	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1956	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1948	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1894	C₂	1	2	yes	maximal, complemented
11	C₄×#103×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₄₁	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
20	C₄₁×#470	—	2	8	no	—
21	C₄₁×#462	—	2	4	no	—
22	C₄₁×#436	—	2	4	no	—
23	C₂×#106×C₄₁	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#103×C₄₁	C₂²	1	2	yes	—
27	C₂×#103×C₄₁	C₂²	1	2	yes	—
28	C₂×#103×C₄₁	C₂²	1	2	yes	—
29	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
32	C₄₁×#399	—	2	2	no	—
33	C₄₁×#396	—	2	2	no	—
34	C₄₁×#390	—	2	1	no	—
35	C₄₁×#390	—	2	1	no	—
36	C₄₁×#389	—	2	1	no	—
37	C₄₁×#384	—	2	1	no	—
38	C₄₁×#384	C₂²	1	1	yes	characteristic
39	C₄₁×#380	C₂²	1	2	yes	—
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×#340	C₂²	1	2	yes	—
44	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
45	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
48	C₂×Q₁₆×C₄₁	—	2	4	no	—
49	C₂×Q₁₆×C₄₁	—	2	4	no	—
50	C₂×Q₁₆×C₄₁	—	4	2	no	—
51	C₂×M₁₆×C₄₁	—	2	4	no	—
52	C₂×M₁₆×C₄₁	—	2	4	no	—
53	C₂×M₁₆×C₄₁	—	4	2	no	—
54	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₄₁	—	2	2	no	—
58	C₄⋊Q₈×C₄₁	—	2	2	no	—
59	C₂²⋊Q₈×C₄₁	—	2	4	no	—
60	C₂²⋊Q₈×C₄₁	—	2	4	no	—
61	C₂²⋊Q₈×C₄₁	—	2	4	no	—
62	C₂²⋊Q₈×C₄₁	—	4	2	no	—
63	C₂²⋊Q₈×C₄₁	—	4	2	no	—
64	C₂²⋊Q₈×C₄₁	—	4	2	no	—
65	C₄×Q₈×C₄₁	—	2	2	no	—
66	C₄×Q₈×C₄₁	—	2	2	no	—
67	C₄×D₄×C₄₁	—	2	2	no	—
68	C₄×D₄×C₄₁	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
72	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
73	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
74	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
76	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
87	C₂×C₄²×C₄₁	—	2	1	no	—
88	C₂×C₄²×C₄₁	—	2	1	no	—
89	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
90	#106×C₄₁	—	2	4	no	—
91	C₄⋊C₈×C₄₁	D₄	1	4	yes	—
92	#103×C₄₁	—	2	4	no	—
93	#103×C₄₁	—	2	4	no	—
94	#103×C₄₁	—	2	2	no	—
95	#103×C₄₁	—	4	2	no	—
96	#103×C₄₁	D₄	1	4	yes	complemented
97	C₂²⋊C₈×C₄₁	—	2	4	no	—
98	C₄×C₈×C₄₁	—	2	2	no	—
99	#95×C₄₁	—	2	1	no	—
100	#95×C₄₁	—	2	2	no	—
101	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
102	C₂×Q₈×C₄₁	—	2	1	no	—
103	C₂×Q₈×C₄₁	—	2	1	no	—
104	C₂×Q₈×C₄₁	—	2	2	no	—
105	C₂×Q₈×C₄₁	—	2	2	no	—
106	C₂×Q₈×C₄₁	—	2	1	no	—
107	C₂×Q₈×C₄₁	—	2	1	no	—
108	C₂×Q₈×C₄₁	—	2	2	no	—
109	C₂×Q₈×C₄₁	—	2	2	no	—
110	C₂×Q₈×C₄₁	—	2	1	no	—
111	C₂×Q₈×C₄₁	—	2	2	no	—
112	C₂×Q₈×C₄₁	—	2	2	no	—
113	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
114	C₂×D₄×C₄₁	—	2	2	no	—
115	C₂×D₄×C₄₁	—	2	2	no	—
116	C₂×D₄×C₄₁	—	2	2	no	—
117	C₂²×C₄×C₄₁	—	2	1	no	—
118	C₂²×C₄×C₄₁	—	2	1	no	—
119	C₂²×C₄×C₄₁	—	2	1	no	—
120	C₂²×C₄×C₄₁	—	2	2	no	—
121	C₂²×C₄×C₄₁	—	2	2	no	—
122	C₂²×C₄×C₄₁	—	2	2	no	—
123	C₂²×C₄×C₄₁	—	2	2	no	—
124	C₂²×C₄×C₄₁	—	2	2	no	—
125	C₂²×C₄×C₄₁	—	2	2	no	—
126	C₂²×C₄×C₄₁	—	2	1	no	—
127	C₂²×C₄×C₄₁	—	2	2	no	—
128	C₂²×C₄×C₄₁	—	2	2	no	—
129	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
133	Q₁₆×C₄₁	—	4	8	no	—
134	M₁₆×C₄₁	—	4	8	no	—
135	C₂×C₈×C₄₁	—	2	1	no	—
136	C₂×C₈×C₄₁	—	2	2	no	—
137	C₂×C₈×C₄₁	—	2	1	no	—
138	C₂×C₈×C₄₁	—	2	2	no	—
139	C₂×C₈×C₄₁	—	2	1	no	—
140	C₂×C₈×C₄₁	—	2	1	no	—
141	C₂×C₈×C₄₁	—	2	1	no	—
142	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
143	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
144	C₄⋊C₄×C₄₁	—	2	2	no	—
145	C₄⋊C₄×C₄₁	—	2	1	no	—
146	C₄⋊C₄×C₄₁	—	2	1	no	—
147	C₄⋊C₄×C₄₁	—	2	1	no	—
148	C₄⋊C₄×C₄₁	—	2	2	no	—
149	C₄⋊C₄×C₄₁	—	2	1	no	—
150	C₄⋊C₄×C₄₁	—	2	2	no	—
151	C₄⋊C₄×C₄₁	—	4	4	no	—
152	C₄⋊C₄×C₄₁	—	4	4	no	—
153	C₄⋊C₄×C₄₁	—	4	4	no	—
154	C₄⋊C₄×C₄₁	—	4	2	no	—
155	C₄⋊C₄×C₄₁	—	4	2	no	—
156	C₄⋊C₄×C₄₁	—	4	2	no	—
157	C₄⋊C₄×C₄₁	—	4	2	no	—
158	C₄⋊C₄×C₄₁	—	8	1	no	—
159	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
160	C₄⋊C₄×C₄₁	#41	1	2	yes	—
161	C₂²⋊C₄×C₄₁	—	2	4	no	—
162	C₂²⋊C₄×C₄₁	—	4	4	no	—
163	C₂²⋊C₄×C₄₁	—	4	4	no	—
164	C₂²⋊C₄×C₄₁	—	4	4	no	—
165	C₂²⋊C₄×C₄₁	—	8	2	no	—
166	C₄²×C₄₁	—	4	2	no	—
167	C₄²×C₄₁	—	4	2	no	—
168	C₄²×C₄₁	C₂×D₄	1	2	yes	—
169	C₄²×C₄₁	#41	1	2	yes	—
170	C₂³×C₄₁	—	2	2	no	—
171	C₂³×C₄₁	—	2	2	no	—
172	C₂³×C₄₁	—	2	2	no	—
173	C₂³×C₄₁	—	2	2	no	—
174	C₂³×C₄₁	—	2	2	no	—
175	C₂³×C₄₁	—	2	2	no	—
176	C₂³×C₄₁	—	2	2	no	—
177	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
178	Q₈×C₄₁	—	2	2	no	—
179	Q₈×C₄₁	—	2	2	no	—
180	Q₈×C₄₁	—	4	1	no	—
181	Q₈×C₄₁	—	4	1	no	—
182	Q₈×C₄₁	—	4	2	no	—
183	Q₈×C₄₁	—	4	2	no	—
184	Q₈×C₄₁	—	4	2	no	—
185	Q₈×C₄₁	—	4	2	no	—
186	D₄×C₄₁	—	4	4	no	—
187	C₂×C₄×C₄₁	—	2	1	no	—
188	C₂×C₄×C₄₁	—	2	1	no	—
189	C₂×C₄×C₄₁	—	2	2	no	—
190	C₂×C₄×C₄₁	—	2	2	no	—
191	C₂×C₄×C₄₁	—	2	2	no	—
192	C₂×C₄×C₄₁	—	2	2	no	—
193	C₂×C₄×C₄₁	—	2	2	no	—
194	C₂×C₄×C₄₁	—	2	2	no	—
195	C₂×C₄×C₄₁	—	4	1	no	—
196	C₂×C₄×C₄₁	—	4	1	no	—
197	C₂×C₄×C₄₁	—	4	1	no	—
198	C₂×C₄×C₄₁	—	4	1	no	—
199	C₂×C₄×C₄₁	—	4	1	no	—
200	C₂×C₄×C₄₁	—	4	1	no	—
201	C₂×C₄×C₄₁	—	4	2	no	—
202	C₂×C₄×C₄₁	—	4	2	no	—
203	C₂×C₄×C₄₁	—	4	2	no	—
204	C₂×C₄×C₄₁	—	4	2	no	—
205	C₂×C₄×C₄₁	—	4	1	no	—
206	C₂×C₄×C₄₁	—	4	2	no	—
207	C₂×C₄×C₄₁	—	4	2	no	—
208	C₂×C₄×C₄₁	—	4	2	no	—
209	C₂×C₄×C₄₁	—	4	2	no	—
210	C₂×C₄×C₄₁	—	4	2	no	—
211	C₂×C₄×C₄₁	—	4	1	no	—
212	C₂×C₄×C₄₁	—	4	2	no	—
213	C₂×C₄×C₄₁	—	4	1	no	—
214	C₂×C₄×C₄₁	#121	1	2	yes	—
215	C₂×C₄×C₄₁	#121	1	2	yes	—
216	C₂×C₄×C₄₁	#137	1	2	yes	—
217	C₂×C₄×C₄₁	#137	1	2	yes	—
218	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
224	C₈×C₄₁	—	2	2	no	—
225	C₈×C₄₁	—	2	4	no	—
226	C₈×C₄₁	—	4	1	no	—
227	#25394	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂²×C₄₁	—	4	2	no	—
229	C₂²×C₄₁	—	4	2	no	—
230	C₂²×C₄₁	—	4	2	no	—
231	C₂²×C₄₁	—	4	2	no	—
232	C₂²×C₄₁	—	4	2	no	—
233	C₂²×C₄₁	—	4	2	no	—
234	C₂²×C₄₁	—	4	2	no	—
235	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
236	C₂²×C₄₁	D₄²	1	1	yes	characteristic
237	C₂²×C₄₁	#546	1	1	yes	characteristic
238	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
239	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
240	C₂²×C₄₁	#577	1	1	yes	characteristic
241	C₂²×C₄₁	#578	1	1	yes	characteristic
242	C₄×C₄₁	—	2	2	no	—
243	C₄×C₄₁	—	4	2	no	—
244	C₄×C₄₁	—	4	2	no	—
245	C₄×C₄₁	—	4	2	no	—
246	C₄×C₄₁	—	4	2	no	—
247	C₄×C₄₁	—	8	2	no	—
248	C₄×C₄₁	—	8	2	no	—
249	C₄×C₄₁	—	8	1	no	—
250	C₄×C₄₁	#470	1	4	yes	complemented
251	C₄×C₄₁	#532	1	1	yes	characteristic
252	C₄×C₄₁	#540	1	1	yes	characteristic
253	C₄×C₄₁	D₄²	1	1	yes	characteristic
254	C₄×C₄₁	#550	1	1	yes	characteristic
255	C₂×#470	C₂×C₄₁	1	2	yes	complemented
256	C₂×#462	C₂×C₄₁	1	1	yes	characteristic, complemented
257	C₂×#436	C₂×C₄₁	1	1	yes	characteristic
258	#2542	C₂×C₄₁	1	1	yes	characteristic
259	#2538	C₂×C₄₁	1	1	yes	characteristic
260	#2035	C₂×C₄₁	1	2	yes	complemented
261	#2001	C₂×C₄₁	1	2	yes	complemented
262	#1956	C₂×C₄₁	1	1	yes	characteristic, complemented
263	#1948	C₂×C₄₁	1	1	yes	characteristic, complemented
264	#1894	C₂×C₄₁	1	2	yes	complemented
265	C₄×#103	C₂×C₄₁	1	1	yes	characteristic, complemented
266	C₂×C₄₁	—	8	2	no	—
267	C₂×C₄₁	#2428	1	1	yes	characteristic
268	C₂×C₄₁	C₂×#470	1	1	yes	characteristic
269	C₂×C₄₁	#3063	1	1	yes	characteristic
270	C₂×C₄₁	#3276	1	1	yes	characteristic
271	C₂×C₄₁	#3278	1	1	yes	characteristic
272	C₂×C₄₁	#3328	1	1	yes	characteristic
273	C₂×C₄₁	#3331	1	1	yes	characteristic
274	C₂²×Q₁₆	C₂²×C₄₁	1	2	yes	—
275	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
276	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
277	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
278	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
279	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
280	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
281	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
282	#470	—	2	8	no	—
283	#462	—	2	4	no	—
284	#436	—	2	4	no	—
285	C₂×#106	C₂²×C₄₁	1	2	yes	—
286	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
287	C₂×#103	C₂²×C₄₁	1	2	yes	—
288	C₂×#103	C₂²×C₄₁	1	2	yes	—
289	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
290	C₂×#103	C₂²×C₄₁	1	2	yes	—
291	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
292	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
293	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
294	#399	—	2	2	no	—
295	#396	—	2	2	no	—
296	#390	—	2	1	no	—
297	#390	—	2	1	no	—
298	#389	—	2	1	no	—
299	#384	—	2	1	no	—
300	#384	C₂²×C₄₁	1	1	yes	characteristic
301	#380	C₂²×C₄₁	1	2	yes	—
302	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
303	#340	C₂²×C₄₁	1	1	yes	characteristic
304	#340	C₂²×C₄₁	1	2	yes	—
305	#340	C₂²×C₄₁	1	1	yes	characteristic
306	C₄₁	#25394	1	1	yes	characteristic, direct product factor, Sylow
307	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
308	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
309	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
310	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
311	C₂×Q₁₆	—	2	4	no	—
312	C₂×Q₁₆	—	2	4	no	—
313	C₂×Q₁₆	—	4	2	no	—
314	C₂×M₁₆	—	2	4	no	—
315	C₂×M₁₆	—	2	4	no	—
316	C₂×M₁₆	—	4	2	no	—
317	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
318	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
319	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
320	C₄⋊Q₈	—	2	2	no	—
321	C₄⋊Q₈	—	2	2	no	—
322	C₂²⋊Q₈	—	2	4	no	—
323	C₂²⋊Q₈	—	2	4	no	—
324	C₂²⋊Q₈	—	2	4	no	—
325	C₂²⋊Q₈	—	4	2	no	—
326	C₂²⋊Q₈	—	4	2	no	—
327	C₂²⋊Q₈	—	4	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×D₄	—	2	2	no	—
331	C₄×D₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
343	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
345	C₂×C₂²⋊C₄	—	2	2	no	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	—	2	1	no	—
352	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
353	#106	—	2	4	no	—
354	C₄⋊C₈	D₄×C₄₁	1	4	yes	—
355	#103	—	2	4	no	—
356	#103	—	2	4	no	—
357	#103	—	2	2	no	—
358	#103	—	4	2	no	—
359	#103	D₄×C₄₁	1	4	yes	complemented
360	C₂²⋊C₈	—	2	4	no	—
361	C₄×C₈	—	2	2	no	—
362	#95	—	2	1	no	—
363	#95	—	2	2	no	—
364	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
393	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
396	Q₁₆	—	4	8	no	—
397	M₁₆	—	4	8	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
406	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	4	4	no	—
415	C₄⋊C₄	—	4	4	no	—
416	C₄⋊C₄	—	4	4	no	—
417	C₄⋊C₄	—	4	2	no	—
418	C₄⋊C₄	—	4	2	no	—
419	C₄⋊C₄	—	4	2	no	—
420	C₄⋊C₄	—	4	2	no	—
421	C₄⋊C₄	—	8	1	no	—
422	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
423	C₄⋊C₄	#41×C₄₁	1	2	yes	—
424	C₂²⋊C₄	—	2	4	no	—
425	C₂²⋊C₄	—	4	4	no	—
426	C₂²⋊C₄	—	4	4	no	—
427	C₂²⋊C₄	—	4	4	no	—
428	C₂²⋊C₄	—	8	2	no	—
429	C₄²	—	4	2	no	—
430	C₄²	—	4	2	no	—
431	C₄²	C₂×D₄×C₄₁	1	2	yes	—
432	C₄²	#41×C₄₁	1	2	yes	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
441	Q₈	—	2	2	no	—
442	Q₈	—	2	2	no	—
443	Q₈	—	4	1	no	—
444	Q₈	—	4	1	no	—
445	Q₈	—	4	2	no	—
446	Q₈	—	4	2	no	—
447	Q₈	—	4	2	no	—
448	Q₈	—	4	2	no	—
449	D₄	—	4	4	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	#121×C₄₁	1	2	yes	—
478	C₂×C₄	#121×C₄₁	1	2	yes	—
479	C₂×C₄	#137×C₄₁	1	2	yes	—
480	C₂×C₄	#137×C₄₁	1	2	yes	—
481	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
482	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
483	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
484	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
485	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
486	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
487	C₈	—	2	2	no	—
488	C₈	—	2	4	no	—
489	C₈	—	4	1	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
498	C₂²	D₄²×C₄₁	1	1	yes	characteristic
499	C₂²	C₄₁×#546	1	1	yes	characteristic
500	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
501	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
502	C₂²	C₄₁×#577	1	1	yes	characteristic
503	C₂²	C₄₁×#578	1	1	yes	characteristic
504	C₄	—	2	2	no	—
505	C₄	—	4	2	no	—
506	C₄	—	4	2	no	—
507	C₄	—	4	2	no	—
508	C₄	—	4	2	no	—
509	C₄	—	8	1	no	—
510	C₄	—	8	2	no	—
511	C₄	—	8	2	no	—
512	C₄	C₄₁×#470	1	4	yes	complemented
513	C₄	C₄₁×#532	1	1	yes	characteristic
514	C₄	C₄₁×#540	1	1	yes	characteristic
515	C₄	D₄²×C₄₁	1	1	yes	characteristic
516	C₄	C₄₁×#550	1	1	yes	characteristic
517	C₂	—	8	2	no	—
518	C₂	C₄₁×#2428	1	1	yes	characteristic
519	C₂	C₂×C₄₁×#470	1	1	yes	characteristic
520	C₂	C₄₁×#3063	1	1	yes	characteristic
521	C₂	C₄₁×#3276	1	1	yes	characteristic
522	C₂	C₄₁×#3278	1	1	yes	characteristic
523	C₂	C₄₁×#3328	1	1	yes	characteristic
524	C₂	C₄₁×#3331	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×D₄×C₄₁	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×C₄×D₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#470	C₂	semidirect
2. C₂×C₄₁×#462	C₂	semidirect
6. C₄₁×#2035	C₂	semidirect
7. C₄₁×#2001	C₂	semidirect
8. C₄₁×#1956	C₂	semidirect
9. C₄₁×#1948	C₂	semidirect
10. C₄₁×#1894	C₂	semidirect
11. C₄×#103×C₄₁	C₂	semidirect
96. #103×C₄₁	D₄	semidirect
227. #25394	C₄₁	direct (N × H)
250. C₄×C₄₁	#470	semidirect
255. C₂×#470	C₂×C₄₁	semidirect
256. C₂×#462	C₂×C₄₁	semidirect
260. #2035	C₂×C₄₁	semidirect
261. #2001	C₂×C₄₁	semidirect
262. #1956	C₂×C₄₁	semidirect
263. #1948	C₂×C₄₁	semidirect
264. #1894	C₂×C₄₁	semidirect
265. C₄×#103	C₂×C₄₁	semidirect
306. C₄₁	#25394	direct (N × H)
359. #103	D₄×C₄₁	semidirect
512. C₄	C₄₁×#470	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#470	2
C₂×C₄₁×#462	2
C₂×C₄₁×#436	2
C₄₁×#2542	2
C₄₁×#2538	2
C₄₁×#2035	2
C₄₁×#2001	2
C₄₁×#1956	2
C₄₁×#1948	2
C₄₁×#1894	2
C₄×#103×C₄₁	2
#25394	41

Subgroups — C41×#25394 #23801595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25394 #23801595