Subgroups — C₄₁×#25385 #23801586

Order 10496.

1102 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#465	C₂	1	2	yes	maximal, complemented
2	C₂×C₄₁×#461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2542	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2537	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#2035	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2000	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×#1892	C₂	1	2	yes	maximal, complemented
11	C₄×#102×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
13	C₂³×C₈×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×#121×C₄₁	—	2	1	no	—
18	C₂×#121×C₄₁	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
21	C₄₁×#465	—	2	8	no	—
22	C₄₁×#461	—	2	4	no	—
23	C₈×D₄×C₄₁	—	2	4	no	—
24	C₂×#106×C₄₁	C₂²	1	2	yes	—
25	C₂×C₄⋊C₈×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×#102×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
33	C₄₁×#399	—	2	2	no	—
34	C₄₁×#394	—	2	2	no	—
35	C₄₁×#390	—	2	1	no	—
36	C₄₁×#384	—	2	1	no	—
37	C₄₁×#384	C₂²	1	1	yes	characteristic
38	C₄₁×#380	—	2	1	no	—
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×D₄×C₄₁	—	2	2	no	—
46	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₄₁	—	2	1	no	—
49	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
50	C₂×SD₁₆×C₄₁	—	2	4	no	—
51	C₂×SD₁₆×C₄₁	—	2	4	no	—
52	C₂×SD₁₆×C₄₁	—	4	2	no	—
53	C₂²×C₈×C₄₁	—	2	4	no	—
54	C₂²×C₈×C₄₁	—	2	4	no	—
55	C₂²×C₈×C₄₁	—	4	2	no	—
56	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
59	C₄⋊Q₈×C₄₁	—	2	2	no	—
60	C₄⋊Q₈×C₄₁	—	2	2	no	—
61	C₂²⋊Q₈×C₄₁	—	2	4	no	—
62	C₂²⋊Q₈×C₄₁	—	2	4	no	—
63	C₂²⋊Q₈×C₄₁	—	4	2	no	—
64	C₂²⋊Q₈×C₄₁	—	4	2	no	—
65	#121×C₄₁	—	2	4	no	—
66	#121×C₄₁	—	4	2	no	—
67	#121×C₄₁	—	4	4	no	—
68	C₄×D₄×C₄₁	—	2	2	no	—
69	C₄×D₄×C₄₁	—	2	2	no	—
70	C₄×D₄×C₄₁	—	2	2	no	—
71	C₄×D₄×C₄₁	—	2	2	no	—
72	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
73	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
74	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
75	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
76	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
78	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
89	C₂×C₄²×C₄₁	—	2	1	no	—
90	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
91	#106×C₄₁	—	2	4	no	—
92	C₄⋊C₈×C₄₁	D₄	1	4	yes	complemented
93	#103×C₄₁	—	2	4	no	—
94	#103×C₄₁	—	2	4	no	—
95	#103×C₄₁	—	4	2	no	—
96	#102×C₄₁	—	2	2	no	—
97	#102×C₄₁	D₄	1	4	yes	complemented
98	C₂²⋊C₈×C₄₁	—	2	4	no	—
99	C₄×C₈×C₄₁	—	2	2	no	—
100	#95×C₄₁	—	2	1	no	—
101	#95×C₄₁	—	2	2	no	—
102	C₂⁴×C₄₁	—	2	1	no	—
103	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
104	C₂×Q₈×C₄₁	—	2	2	no	—
105	C₂×Q₈×C₄₁	—	2	2	no	—
106	C₂×Q₈×C₄₁	—	2	2	no	—
107	C₂×Q₈×C₄₁	—	2	2	no	—
108	C₂×Q₈×C₄₁	—	2	2	no	—
109	C₂×Q₈×C₄₁	—	2	2	no	—
110	C₂×D₄×C₄₁	—	2	2	no	—
111	C₂×D₄×C₄₁	—	2	2	no	—
112	C₂×D₄×C₄₁	—	2	1	no	—
113	C₂×D₄×C₄₁	—	2	1	no	—
114	C₂×D₄×C₄₁	—	2	1	no	—
115	C₂×D₄×C₄₁	—	2	1	no	—
116	C₂×D₄×C₄₁	—	2	1	no	—
117	C₂×D₄×C₄₁	—	4	4	no	—
118	C₂×D₄×C₄₁	—	4	4	no	—
119	C₂×D₄×C₄₁	—	8	2	no	—
120	C₂×D₄×C₄₁	SD₁₆	1	4	yes	complemented
121	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₄₁	—	2	1	no	—
123	C₂²×C₄×C₄₁	—	2	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	2	no	—
133	C₂²×C₄×C₄₁	—	4	2	no	—
134	C₂²×C₄×C₄₁	—	4	2	no	—
135	C₂²×C₄×C₄₁	—	4	2	no	—
136	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
140	SD₁₆×C₄₁	—	4	8	no	—
141	C₂×C₈×C₄₁	—	2	1	no	—
142	C₂×C₈×C₄₁	—	2	2	no	—
143	C₂×C₈×C₄₁	—	2	1	no	—
144	C₂×C₈×C₄₁	—	2	2	no	—
145	C₂×C₈×C₄₁	—	2	1	no	—
146	C₂×C₈×C₄₁	—	2	1	no	—
147	C₂×C₈×C₄₁	—	2	1	no	—
148	C₂×C₈×C₄₁	—	4	8	no	—
149	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
150	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
151	C₄⋊C₄×C₄₁	—	2	2	no	—
152	C₄⋊C₄×C₄₁	—	2	1	no	—
153	C₄⋊C₄×C₄₁	—	2	1	no	—
154	C₄⋊C₄×C₄₁	—	2	1	no	—
155	C₄⋊C₄×C₄₁	—	2	2	no	—
156	C₄⋊C₄×C₄₁	—	2	1	no	—
157	C₄⋊C₄×C₄₁	—	2	2	no	—
158	C₄⋊C₄×C₄₁	—	4	4	no	—
159	C₄⋊C₄×C₄₁	—	4	4	no	—
160	C₄⋊C₄×C₄₁	—	4	2	no	—
161	C₄⋊C₄×C₄₁	—	4	2	no	—
162	C₄⋊C₄×C₄₁	—	4	2	no	—
163	C₄⋊C₄×C₄₁	—	8	1	no	—
164	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
165	C₄⋊C₄×C₄₁	#41	1	2	yes	—
166	C₂²⋊C₄×C₄₁	—	2	4	no	—
167	C₂²⋊C₄×C₄₁	—	4	4	no	—
168	C₂²⋊C₄×C₄₁	—	4	4	no	—
169	C₂²⋊C₄×C₄₁	—	4	4	no	—
170	C₂²⋊C₄×C₄₁	—	4	4	no	—
171	C₂²⋊C₄×C₄₁	—	4	2	no	—
172	C₄²×C₄₁	—	4	2	no	—
173	C₄²×C₄₁	C₂×D₄	1	2	yes	—
174	C₄²×C₄₁	#41	1	2	yes	—
175	C₂³×C₄₁	—	2	2	no	—
176	C₂³×C₄₁	—	2	2	no	—
177	C₂³×C₄₁	—	2	2	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	—	4	1	no	—
183	C₂³×C₄₁	—	4	1	no	—
184	C₂³×C₄₁	—	4	1	no	—
185	C₂³×C₄₁	—	4	1	no	—
186	C₂³×C₄₁	—	4	1	no	—
187	C₂³×C₄₁	—	4	1	no	—
188	C₂³×C₄₁	C₂×SD₁₆	1	4	yes	—
189	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₄₁	—	4	2	no	—
191	Q₈×C₄₁	—	4	2	no	—
192	Q₈×C₄₁	—	4	2	no	—
193	Q₈×C₄₁	—	4	2	no	—
194	D₄×C₄₁	—	2	2	no	—
195	D₄×C₄₁	—	2	2	no	—
196	D₄×C₄₁	—	2	8	no	—
197	D₄×C₄₁	—	4	1	no	—
198	D₄×C₄₁	—	4	1	no	—
199	D₄×C₄₁	—	8	8	no	—
200	C₂×C₄×C₄₁	—	2	1	no	—
201	C₂×C₄×C₄₁	—	2	1	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	2	no	—
207	C₂×C₄×C₄₁	—	4	1	no	—
208	C₂×C₄×C₄₁	—	4	1	no	—
209	C₂×C₄×C₄₁	—	4	1	no	—
210	C₂×C₄×C₄₁	—	4	1	no	—
211	C₂×C₄×C₄₁	—	4	2	no	—
212	C₂×C₄×C₄₁	—	4	2	no	—
213	C₂×C₄×C₄₁	—	4	2	no	—
214	C₂×C₄×C₄₁	—	4	2	no	—
215	C₂×C₄×C₄₁	—	4	1	no	—
216	C₂×C₄×C₄₁	—	4	2	no	—
217	C₂×C₄×C₄₁	—	4	2	no	—
218	C₂×C₄×C₄₁	—	4	2	no	—
219	C₂×C₄×C₄₁	—	4	2	no	—
220	C₂×C₄×C₄₁	—	4	1	no	—
221	C₂×C₄×C₄₁	—	4	2	no	—
222	C₂×C₄×C₄₁	—	4	1	no	—
223	C₂×C₄×C₄₁	—	4	2	no	—
224	C₂×C₄×C₄₁	—	8	4	no	—
225	C₂×C₄×C₄₁	#121	1	2	yes	—
226	C₂×C₄×C₄₁	#121	1	2	yes	—
227	C₂×C₄×C₄₁	C₂×SD₁₆	1	2	yes	—
228	C₂×C₄×C₄₁	#135	1	2	yes	—
229	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
235	C₈×C₄₁	—	2	2	no	—
236	C₈×C₄₁	—	2	4	no	—
237	C₈×C₄₁	—	4	1	no	—
238	#25385	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂²×C₄₁	—	2	4	no	—
240	C₂²×C₄₁	—	2	4	no	—
241	C₂²×C₄₁	—	2	4	no	—
242	C₂²×C₄₁	—	4	2	no	—
243	C₂²×C₄₁	—	4	2	no	—
244	C₂²×C₄₁	—	4	2	no	—
245	C₂²×C₄₁	—	4	2	no	—
246	C₂²×C₄₁	—	4	2	no	—
247	C₂²×C₄₁	—	4	2	no	—
248	C₂²×C₄₁	—	4	2	no	—
249	C₂²×C₄₁	—	8	1	no	—
250	C₂²×C₄₁	—	8	1	no	—
251	C₂²×C₄₁	—	8	1	no	—
252	C₂²×C₄₁	—	8	1	no	—
253	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
254	C₂²×C₄₁	D₄²	1	1	yes	characteristic
255	C₂²×C₄₁	#546	1	1	yes	characteristic
256	C₂²×C₄₁	C₂²×SD₁₆	1	1	yes	characteristic
257	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
258	C₂²×C₄₁	#577	1	1	yes	characteristic
259	C₂²×C₄₁	#578	1	1	yes	characteristic
260	C₄×C₄₁	—	2	2	no	—
261	C₄×C₄₁	—	4	2	no	—
262	C₄×C₄₁	—	4	2	no	—
263	C₄×C₄₁	—	4	2	no	—
264	C₄×C₄₁	—	8	2	no	—
265	C₄×C₄₁	—	8	2	no	—
266	C₄×C₄₁	—	8	1	no	—
267	C₄×C₄₁	#465	1	4	yes	complemented
268	C₄×C₄₁	#532	1	1	yes	characteristic
269	C₄×C₄₁	#540	1	1	yes	characteristic
270	C₄×C₄₁	D₄²	1	1	yes	characteristic
271	C₄×C₄₁	#550	1	1	yes	characteristic
272	C₂×#465	C₂×C₄₁	1	2	yes	complemented
273	C₂×#461	C₂×C₄₁	1	1	yes	characteristic, complemented
274	C₂×C₈×D₄	C₂×C₄₁	1	1	yes	characteristic, complemented
275	#2542	C₂×C₄₁	1	1	yes	characteristic, complemented
276	#2537	C₂×C₄₁	1	1	yes	characteristic
277	#2035	C₂×C₄₁	1	2	yes	complemented
278	#2000	C₂×C₄₁	1	2	yes	complemented
279	#1956	C₂×C₄₁	1	1	yes	characteristic, complemented
280	#1948	C₂×C₄₁	1	1	yes	characteristic, complemented
281	#1892	C₂×C₄₁	1	2	yes	complemented
282	C₄×#102	C₂×C₄₁	1	1	yes	characteristic, complemented
283	C₂×C₄₁	—	4	4	no	—
284	C₂×C₄₁	—	8	2	no	—
285	C₂×C₄₁	#2428	1	1	yes	characteristic
286	C₂×C₄₁	C₂×#465	1	1	yes	characteristic
287	C₂×C₄₁	#3063	1	1	yes	characteristic
288	C₂×C₄₁	D₄×SD₁₆	1	1	yes	characteristic
289	C₂×C₄₁	#3283	1	1	yes	characteristic
290	C₂×C₄₁	#3298	1	1	yes	characteristic
291	C₂×C₄₁	#3303	1	1	yes	characteristic
292	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
293	C₂³×C₈	C₂²×C₄₁	1	2	yes	—
294	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
295	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
296	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
297	C₂×#121	—	2	1	no	—
298	C₂×#121	C₂²×C₄₁	1	2	yes	—
299	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
300	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
301	#465	—	2	8	no	—
302	#461	—	2	4	no	—
303	C₈×D₄	—	2	4	no	—
304	C₂×#106	C₂²×C₄₁	1	2	yes	—
305	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
306	C₂×#103	C₂²×C₄₁	1	2	yes	—
307	C₂×#103	C₂²×C₄₁	1	2	yes	—
308	C₂×#103	C₂²×C₄₁	1	2	yes	—
309	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
310	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
311	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
312	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
313	#399	—	2	2	no	—
314	#394	—	2	2	no	—
315	#390	—	2	1	no	—
316	#384	—	2	1	no	—
317	#384	C₂²×C₄₁	1	1	yes	characteristic
318	#380	—	2	1	no	—
319	#380	C₂²×C₄₁	1	2	yes	—
320	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
321	#340	C₂²×C₄₁	1	1	yes	characteristic
322	#340	C₂²×C₄₁	1	2	yes	—
323	#340	C₂²×C₄₁	1	1	yes	characteristic
324	C₄₁	#25385	1	1	yes	characteristic, direct product factor, Sylow
325	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
326	C₂²×D₄	—	2	2	no	—
327	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
328	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
329	C₂³×C₄	—	2	1	no	—
330	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
331	C₂×SD₁₆	—	2	4	no	—
332	C₂×SD₁₆	—	2	4	no	—
333	C₂×SD₁₆	—	4	2	no	—
334	C₂²×C₈	—	2	4	no	—
335	C₂²×C₈	—	2	4	no	—
336	C₂²×C₈	—	4	2	no	—
337	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
340	C₄⋊Q₈	—	2	2	no	—
341	C₄⋊Q₈	—	2	2	no	—
342	C₂²⋊Q₈	—	2	4	no	—
343	C₂²⋊Q₈	—	2	4	no	—
344	C₂²⋊Q₈	—	4	2	no	—
345	C₂²⋊Q₈	—	4	2	no	—
346	#121	—	2	4	no	—
347	#121	—	4	2	no	—
348	#121	—	4	4	no	—
349	C₄×D₄	—	2	2	no	—
350	C₄×D₄	—	2	2	no	—
351	C₄×D₄	—	2	2	no	—
352	C₄×D₄	—	2	2	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	2	no	—
355	C₂×C₄⋊C₄	—	2	2	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
362	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	—	2	2	no	—
365	C₂×C₂²⋊C₄	—	2	2	no	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
370	C₂×C₄²	—	2	1	no	—
371	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
372	#106	—	2	4	no	—
373	C₄⋊C₈	D₄×C₄₁	1	4	yes	complemented
374	#103	—	2	4	no	—
375	#103	—	2	4	no	—
376	#103	—	4	2	no	—
377	#102	—	2	2	no	—
378	#102	D₄×C₄₁	1	4	yes	complemented
379	C₂²⋊C₈	—	2	4	no	—
380	C₄×C₈	—	2	2	no	—
381	#95	—	2	1	no	—
382	#95	—	2	2	no	—
383	C₂⁴	—	2	1	no	—
384	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	4	4	no	—
399	C₂×D₄	—	4	4	no	—
400	C₂×D₄	—	8	2	no	—
401	C₂×D₄	SD₁₆×C₄₁	1	4	yes	complemented
402	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	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	2	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	4	2	no	—
415	C₂²×C₄	—	4	2	no	—
416	C₂²×C₄	—	4	2	no	—
417	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
418	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
420	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
421	SD₁₆	—	4	8	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	4	8	no	—
430	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
431	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	4	4	no	—
440	C₄⋊C₄	—	4	4	no	—
441	C₄⋊C₄	—	4	2	no	—
442	C₄⋊C₄	—	4	2	no	—
443	C₄⋊C₄	—	4	2	no	—
444	C₄⋊C₄	—	8	1	no	—
445	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
446	C₄⋊C₄	#41×C₄₁	1	2	yes	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	4	4	no	—
449	C₂²⋊C₄	—	4	4	no	—
450	C₂²⋊C₄	—	4	4	no	—
451	C₂²⋊C₄	—	4	4	no	—
452	C₂²⋊C₄	—	4	2	no	—
453	C₄²	—	4	2	no	—
454	C₄²	C₂×D₄×C₄₁	1	2	yes	—
455	C₄²	#41×C₄₁	1	2	yes	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	2	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	—	4	1	no	—
464	C₂³	—	4	1	no	—
465	C₂³	—	4	1	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	1	no	—
468	C₂³	—	4	1	no	—
469	C₂³	C₂×SD₁₆×C₄₁	1	4	yes	—
470	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
471	Q₈	—	4	2	no	—
472	Q₈	—	4	2	no	—
473	Q₈	—	4	2	no	—
474	Q₈	—	4	2	no	—
475	D₄	—	2	2	no	—
476	D₄	—	2	2	no	—
477	D₄	—	2	8	no	—
478	D₄	—	4	1	no	—
479	D₄	—	4	1	no	—
480	D₄	—	8	8	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	8	4	no	—
506	C₂×C₄	#121×C₄₁	1	2	yes	—
507	C₂×C₄	#121×C₄₁	1	2	yes	—
508	C₂×C₄	C₂×SD₁₆×C₄₁	1	2	yes	—
509	C₂×C₄	#135×C₄₁	1	2	yes	—
510	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
512	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
513	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
514	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
515	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
516	C₈	—	2	2	no	—
517	C₈	—	2	4	no	—
518	C₈	—	4	1	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	2	4	no	—
521	C₂²	—	2	4	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	8	1	no	—
530	C₂²	—	8	1	no	—
531	C₂²	—	8	1	no	—
532	C₂²	—	8	1	no	—
533	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
534	C₂²	D₄²×C₄₁	1	1	yes	characteristic
535	C₂²	C₄₁×#546	1	1	yes	characteristic
536	C₂²	C₂²×SD₁₆×C₄₁	1	1	yes	characteristic
537	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
538	C₂²	C₄₁×#577	1	1	yes	characteristic
539	C₂²	C₄₁×#578	1	1	yes	characteristic
540	C₄	—	2	2	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	2	no	—
543	C₄	—	4	2	no	—
544	C₄	—	8	1	no	—
545	C₄	—	8	2	no	—
546	C₄	—	8	2	no	—
547	C₄	C₄₁×#465	1	4	yes	complemented
548	C₄	C₄₁×#532	1	1	yes	characteristic
549	C₄	C₄₁×#540	1	1	yes	characteristic
550	C₄	D₄²×C₄₁	1	1	yes	characteristic
551	C₄	C₄₁×#550	1	1	yes	characteristic
552	C₂	—	4	4	no	—
553	C₂	—	8	2	no	—
554	C₂	C₄₁×#2428	1	1	yes	characteristic
555	C₂	C₂×C₄₁×#465	1	1	yes	characteristic
556	C₂	C₄₁×#3063	1	1	yes	characteristic
557	C₂	D₄×SD₁₆×C₄₁	1	1	yes	characteristic
558	C₂	C₄₁×#3283	1	1	yes	characteristic
559	C₂	C₄₁×#3298	1	1	yes	characteristic
560	C₂	C₄₁×#3303	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₄₁×#2537	C₂
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×#465	C₂	semidirect
2. C₂×C₄₁×#461	C₂	semidirect
3. C₂×C₈×D₄×C₄₁	C₂	semidirect
4. C₄₁×#2542	C₂	semidirect
6. C₄₁×#2035	C₂	semidirect
7. C₄₁×#2000	C₂	semidirect
8. C₄₁×#1956	C₂	semidirect
9. C₄₁×#1948	C₂	semidirect
10. C₄₁×#1892	C₂	semidirect
11. C₄×#102×C₄₁	C₂	semidirect
92. C₄⋊C₈×C₄₁	D₄	semidirect
97. #102×C₄₁	D₄	semidirect
120. C₂×D₄×C₄₁	SD₁₆	semidirect
238. #25385	C₄₁	direct (N × H)
267. C₄×C₄₁	#465	semidirect
272. C₂×#465	C₂×C₄₁	semidirect
273. C₂×#461	C₂×C₄₁	semidirect
274. C₂×C₈×D₄	C₂×C₄₁	semidirect
275. #2542	C₂×C₄₁	semidirect
277. #2035	C₂×C₄₁	semidirect
278. #2000	C₂×C₄₁	semidirect
279. #1956	C₂×C₄₁	semidirect
280. #1948	C₂×C₄₁	semidirect
281. #1892	C₂×C₄₁	semidirect
282. C₄×#102	C₂×C₄₁	semidirect
324. C₄₁	#25385	direct (N × H)
373. C₄⋊C₈	D₄×C₄₁	semidirect
378. #102	D₄×C₄₁	semidirect
401. C₂×D₄	SD₁₆×C₄₁	semidirect
547. C₄	C₄₁×#465	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#465	2
C₂×C₄₁×#461	2
C₂×C₈×D₄×C₄₁	2
C₄₁×#2542	2
C₄₁×#2537	2
C₄₁×#2035	2
C₄₁×#2000	2
C₄₁×#1956	2
C₄₁×#1948	2
C₄₁×#1892	2
C₄×#102×C₄₁	2
#25385	41

Subgroups — C41×#25385 #23801586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25385 #23801586