Subgroups — C₄₁×#24374 #23800575

Order 10496.

1396 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#462	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₁×#452	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2434	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2341	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#2055	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2013	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1894	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1878	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1851	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1787	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#137×C₄₁	—	2	4	no	—
15	C₂×#137×C₄₁	—	2	8	no	—
16	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₄₁	C₂²	1	2	yes	—
18	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
19	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₄₁	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
24	C₄₁×#462	—	2	8	no	—
25	C₄₁×#452	—	2	4	no	—
26	C₂×C₄⋊C₈×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×#103×C₄₁	C₂²	1	2	yes	—
31	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
33	C₄₁×#395	—	2	1	no	—
34	C₄₁×#395	—	2	1	no	—
35	C₄₁×#391	C₂²	1	2	yes	—
36	C₄₁×#390	—	2	2	no	—
37	C₄₁×#390	C₂²	1	2	yes	—
38	C₄₁×#385	—	2	2	no	—
39	C₄₁×#380	—	2	1	no	—
40	C₄₁×#380	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
42	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
43	C₄₁×#340	C₂²	1	2	yes	—
44	C₄₁×#336	C₂²	1	2	yes	—
45	C₂×#41×C₄₁	—	2	2	no	—
46	C₂×#41×C₄₁	—	2	4	no	—
47	C₂×#41×C₄₁	—	4	2	no	—
48	C₂×#41×C₄₁	D₄	1	4	yes	—
49	C₂²×Q₈×C₄₁	—	2	1	no	—
50	C₂²×Q₈×C₄₁	—	2	4	no	—
51	C₂²×Q₈×C₄₁	—	2	2	no	—
52	C₂²×Q₈×C₄₁	—	2	2	no	—
53	C₂²×Q₈×C₄₁	—	4	2	no	—
54	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
56	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
57	C₂²×D₄×C₄₁	—	2	1	no	—
58	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₄₁	—	2	1	no	—
60	C₂³×C₄×C₄₁	—	2	1	no	—
61	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
62	#137×C₄₁	—	2	32	no	—
63	C₂×Q₁₆×C₄₁	—	2	4	no	—
64	C₂×Q₁₆×C₄₁	—	2	4	no	—
65	C₂×Q₁₆×C₄₁	—	2	2	no	—
66	C₂×Q₁₆×C₄₁	—	2	4	no	—
67	C₂×Q₁₆×C₄₁	D₄	1	8	yes	—
68	C₂×SD₁₆×C₄₁	—	2	4	no	—
69	C₂×SD₁₆×C₄₁	—	2	4	no	—
70	C₂×SD₁₆×C₄₁	—	2	2	no	—
71	C₂×SD₁₆×C₄₁	—	2	4	no	—
72	C₂×SD₁₆×C₄₁	—	4	2	no	—
73	C₂×M₁₆×C₄₁	—	2	2	no	—
74	C₂×M₁₆×C₄₁	—	2	4	no	—
75	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
78	C₄⋊Q₈×C₄₁	—	2	4	no	—
79	C₄⋊Q₈×C₄₁	—	4	2	no	—
80	C₂²⋊Q₈×C₄₁	—	2	2	no	—
81	C₂²⋊Q₈×C₄₁	—	2	2	no	—
82	C₄×Q₈×C₄₁	—	2	4	no	—
83	C₄×Q₈×C₄₁	—	4	2	no	—
84	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
85	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
86	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
87	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
88	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
95	C₂×C₄²×C₄₁	—	2	2	no	—
96	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
97	C₄⋊C₈×C₄₁	—	2	4	no	—
98	#103×C₄₁	—	2	2	no	—
99	#103×C₄₁	—	2	4	no	—
100	#103×C₄₁	—	2	4	no	—
101	#103×C₄₁	—	4	2	no	—
102	#102×C₄₁	—	2	2	no	—
103	C₂²⋊C₈×C₄₁	—	2	2	no	—
104	#95×C₄₁	—	2	1	no	—
105	#95×C₄₁	—	2	2	no	—
106	#95×C₄₁	—	2	2	no	—
107	#95×C₄₁	D₄	1	1	yes	characteristic
108	#95×C₄₁	D₄	1	1	yes	characteristic
109	C₂⁴×C₄₁	—	2	1	no	—
110	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
111	#41×C₄₁	—	2	8	no	—
112	#41×C₄₁	—	4	4	no	—
113	#41×C₄₁	—	4	8	no	—
114	C₂×Q₈×C₄₁	—	2	1	no	—
115	C₂×Q₈×C₄₁	—	2	2	no	—
116	C₂×Q₈×C₄₁	—	2	2	no	—
117	C₂×Q₈×C₄₁	—	2	8	no	—
118	C₂×Q₈×C₄₁	—	2	2	no	—
119	C₂×Q₈×C₄₁	—	2	2	no	—
120	C₂×Q₈×C₄₁	—	2	2	no	—
121	C₂×Q₈×C₄₁	—	2	1	no	—
122	C₂×Q₈×C₄₁	—	2	2	no	—
123	C₂×Q₈×C₄₁	—	2	1	no	—
124	C₂×Q₈×C₄₁	—	2	2	no	—
125	C₂×Q₈×C₄₁	—	2	2	no	—
126	C₂×Q₈×C₄₁	—	4	4	no	—
127	C₂×Q₈×C₄₁	—	4	8	no	—
128	C₂×Q₈×C₄₁	—	4	4	no	—
129	C₂×Q₈×C₄₁	—	4	2	no	—
130	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
131	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
132	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
133	C₂×D₄×C₄₁	—	2	4	no	—
134	C₂×D₄×C₄₁	—	2	2	no	—
135	C₂×D₄×C₄₁	—	2	1	no	—
136	C₂×D₄×C₄₁	—	2	2	no	—
137	C₂×D₄×C₄₁	—	4	4	no	—
138	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₄₁	—	2	1	no	—
140	C₂²×C₄×C₄₁	—	2	2	no	—
141	C₂²×C₄×C₄₁	—	2	2	no	—
142	C₂²×C₄×C₄₁	—	2	2	no	—
143	C₂²×C₄×C₄₁	—	2	4	no	—
144	C₂²×C₄×C₄₁	—	2	1	no	—
145	C₂²×C₄×C₄₁	—	2	2	no	—
146	C₂²×C₄×C₄₁	—	2	1	no	—
147	C₂²×C₄×C₄₁	—	4	4	no	—
148	C₂²×C₄×C₄₁	—	4	4	no	—
149	C₂²×C₄×C₄₁	—	4	2	no	—
150	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₄₁	#41	1	2	yes	—
155	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
156	Q₁₆×C₄₁	—	2	16	no	—
157	Q₁₆×C₄₁	—	4	4	no	—
158	SD₁₆×C₄₁	—	2	16	no	—
159	SD₁₆×C₄₁	—	4	4	no	—
160	M₁₆×C₄₁	—	2	8	no	—
161	C₂×C₈×C₄₁	—	2	2	no	—
162	C₂×C₈×C₄₁	—	2	2	no	—
163	C₂×C₈×C₄₁	—	2	1	no	—
164	C₂×C₈×C₄₁	—	2	1	no	—
165	C₂×C₈×C₄₁	—	2	2	no	—
166	C₂×C₈×C₄₁	—	2	2	no	—
167	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
168	C₄⋊C₄×C₄₁	—	2	1	no	—
169	C₄⋊C₄×C₄₁	—	2	2	no	—
170	C₄⋊C₄×C₄₁	—	2	1	no	—
171	C₄⋊C₄×C₄₁	—	2	2	no	—
172	C₄⋊C₄×C₄₁	—	4	4	no	—
173	C₄⋊C₄×C₄₁	—	4	4	no	—
174	C₄⋊C₄×C₄₁	—	4	4	no	—
175	C₄⋊C₄×C₄₁	—	4	2	no	—
176	C₂²⋊C₄×C₄₁	—	2	4	no	—
177	C₂²⋊C₄×C₄₁	—	4	2	no	—
178	C₂²⋊C₄×C₄₁	—	4	4	no	—
179	C₂²⋊C₄×C₄₁	—	8	2	no	—
180	C₂²⋊C₄×C₄₁	—	8	1	no	—
181	C₄²×C₄₁	—	2	2	no	—
182	C₄²×C₄₁	—	2	2	no	—
183	C₄²×C₄₁	—	4	4	no	—
184	C₂³×C₄₁	—	2	2	no	—
185	C₂³×C₄₁	—	2	2	no	—
186	C₂³×C₄₁	—	2	1	no	—
187	C₂³×C₄₁	—	2	1	no	—
188	C₂³×C₄₁	—	2	2	no	—
189	C₂³×C₄₁	—	4	2	no	—
190	C₂³×C₄₁	—	4	2	no	—
191	C₂³×C₄₁	—	4	1	no	—
192	C₂³×C₄₁	—	4	1	no	—
193	C₂³×C₄₁	#121	1	2	yes	—
194	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
195	Q₈×C₄₁	—	2	2	no	—
196	Q₈×C₄₁	—	2	4	no	—
197	Q₈×C₄₁	—	2	4	no	—
198	Q₈×C₄₁	—	2	4	no	—
199	Q₈×C₄₁	—	4	8	no	—
200	Q₈×C₄₁	—	4	2	no	—
201	Q₈×C₄₁	—	4	2	no	—
202	Q₈×C₄₁	—	4	1	no	—
203	Q₈×C₄₁	—	4	1	no	—
204	Q₈×C₄₁	—	4	2	no	—
205	Q₈×C₄₁	#120	1	4	yes	—
206	D₄×C₄₁	—	2	2	no	—
207	D₄×C₄₁	—	2	2	no	—
208	D₄×C₄₁	—	4	8	no	—
209	D₄×C₄₁	—	4	2	no	—
210	C₂×C₄×C₄₁	—	2	2	no	—
211	C₂×C₄×C₄₁	—	2	2	no	—
212	C₂×C₄×C₄₁	—	2	4	no	—
213	C₂×C₄×C₄₁	—	2	2	no	—
214	C₂×C₄×C₄₁	—	2	2	no	—
215	C₂×C₄×C₄₁	—	2	2	no	—
216	C₂×C₄×C₄₁	—	2	2	no	—
217	C₂×C₄×C₄₁	—	2	4	no	—
218	C₂×C₄×C₄₁	—	2	2	no	—
219	C₂×C₄×C₄₁	—	2	4	no	—
220	C₂×C₄×C₄₁	—	2	2	no	—
221	C₂×C₄×C₄₁	—	2	2	no	—
222	C₂×C₄×C₄₁	—	4	8	no	—
223	C₂×C₄×C₄₁	—	4	8	no	—
224	C₂×C₄×C₄₁	—	4	2	no	—
225	C₂×C₄×C₄₁	—	4	2	no	—
226	C₂×C₄×C₄₁	—	4	1	no	—
227	C₂×C₄×C₄₁	—	4	1	no	—
228	C₂×C₄×C₄₁	—	4	2	no	—
229	C₂×C₄×C₄₁	—	4	2	no	—
230	C₂×C₄×C₄₁	—	4	2	no	—
231	C₂×C₄×C₄₁	—	4	2	no	—
232	C₂×C₄×C₄₁	—	4	1	no	—
233	C₂×C₄×C₄₁	—	4	1	no	—
234	C₂×C₄×C₄₁	#121	1	2	yes	—
235	C₂×C₄×C₄₁	#137	1	4	yes	complemented
236	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
238	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
240	C₈×C₄₁	—	2	4	no	—
241	C₈×C₄₁	—	4	1	no	—
242	C₈×C₄₁	—	4	1	no	—
243	#24374	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₂²×C₄₁	—	2	2	no	—
245	C₂²×C₄₁	—	2	2	no	—
246	C₂²×C₄₁	—	2	2	no	—
247	C₂²×C₄₁	—	4	2	no	—
248	C₂²×C₄₁	—	4	2	no	—
249	C₂²×C₄₁	—	4	2	no	—
250	C₂²×C₄₁	—	4	2	no	—
251	C₂²×C₄₁	—	4	2	no	—
252	C₂²×C₄₁	—	8	2	no	—
253	C₂²×C₄₁	—	8	2	no	—
254	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
255	C₂²×C₄₁	D₄²	1	2	yes	—
256	C₂²×C₄₁	C₂×#137	1	2	yes	—
257	C₂²×C₄₁	#577	1	1	yes	characteristic
258	C₂²×C₄₁	#578	1	1	yes	characteristic
259	C₄×C₄₁	—	2	2	no	—
260	C₄×C₄₁	—	2	4	no	—
261	C₄×C₄₁	—	2	4	no	—
262	C₄×C₄₁	—	4	4	no	—
263	C₄×C₄₁	—	4	2	no	—
264	C₄×C₄₁	—	8	1	no	—
265	C₄×C₄₁	—	8	2	no	—
266	C₄×C₄₁	—	8	1	no	—
267	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
268	C₄×C₄₁	#534	1	1	yes	characteristic
269	C₄×C₄₁	#546	1	2	yes	—
270	C₂²×#137	C₂×C₄₁	1	1	yes	characteristic
271	C₂×#462	C₂×C₄₁	1	2	yes	complemented
272	C₂×#452	C₂×C₄₁	1	1	yes	characteristic
273	#2434	C₂×C₄₁	1	1	yes	characteristic, complemented
274	#2341	C₂×C₄₁	1	1	yes	characteristic
275	#2055	C₂×C₄₁	1	2	yes	complemented
276	#2013	C₂×C₄₁	1	2	yes	complemented
277	#1894	C₂×C₄₁	1	1	yes	characteristic, complemented
278	#1878	C₂×C₄₁	1	2	yes	complemented
279	#1851	C₂×C₄₁	1	1	yes	characteristic, complemented
280	#1787	C₂×C₄₁	1	1	yes	characteristic, complemented
281	C₂×C₄₁	—	4	2	no	—
282	C₂×C₄₁	—	8	2	no	—
283	C₂×C₄₁	#2410	1	1	yes	characteristic
284	C₂×C₄₁	#3039	1	1	yes	characteristic
285	C₂×C₄₁	#3046	1	1	yes	characteristic
286	C₂×C₄₁	#3270	1	2	yes	—
287	C₂×C₄₁	#3278	1	2	yes	—
288	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
289	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
290	C₂×#137	—	2	4	no	—
291	C₂×#137	—	2	8	no	—
292	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
293	C₂²×Q₁₆	C₂²×C₄₁	1	2	yes	—
294	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
295	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
296	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
297	C₂×C₄⋊Q₈	C₂²×C₄₁	1	2	yes	—
298	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
299	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
300	#462	—	2	8	no	—
301	#452	—	2	4	no	—
302	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
303	C₂×#103	C₂²×C₄₁	1	2	yes	—
304	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
305	C₂×#103	C₂²×C₄₁	1	2	yes	—
306	C₂×#103	C₂²×C₄₁	1	2	yes	—
307	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
308	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
309	#395	—	2	1	no	—
310	#395	—	2	1	no	—
311	#391	C₂²×C₄₁	1	2	yes	—
312	#390	—	2	2	no	—
313	#390	C₂²×C₄₁	1	2	yes	—
314	#385	—	2	2	no	—
315	#380	—	2	1	no	—
316	#380	C₂²×C₄₁	1	1	yes	characteristic
317	C₄×C₂²⋊C₄	—	2	1	no	—
318	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
319	#340	C₂²×C₄₁	1	2	yes	—
320	#336	C₂²×C₄₁	1	2	yes	—
321	C₄₁	#24374	1	1	yes	characteristic, direct product factor, Sylow
322	C₂×#41	—	2	2	no	—
323	C₂×#41	—	2	4	no	—
324	C₂×#41	—	4	2	no	—
325	C₂×#41	D₄×C₄₁	1	4	yes	—
326	C₂²×Q₈	—	2	1	no	—
327	C₂²×Q₈	—	2	4	no	—
328	C₂²×Q₈	—	2	2	no	—
329	C₂²×Q₈	—	2	2	no	—
330	C₂²×Q₈	—	4	2	no	—
331	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
332	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
333	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
334	C₂²×D₄	—	2	1	no	—
335	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
336	C₂³×C₄	—	2	1	no	—
337	C₂³×C₄	—	2	1	no	—
338	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
339	#137	—	2	32	no	—
340	C₂×Q₁₆	—	2	4	no	—
341	C₂×Q₁₆	—	2	4	no	—
342	C₂×Q₁₆	—	2	2	no	—
343	C₂×Q₁₆	—	2	4	no	—
344	C₂×Q₁₆	D₄×C₄₁	1	8	yes	—
345	C₂×SD₁₆	—	2	4	no	—
346	C₂×SD₁₆	—	2	4	no	—
347	C₂×SD₁₆	—	2	2	no	—
348	C₂×SD₁₆	—	2	4	no	—
349	C₂×SD₁₆	—	4	2	no	—
350	C₂×M₁₆	—	2	2	no	—
351	C₂×M₁₆	—	2	4	no	—
352	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
353	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
354	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
355	C₄⋊Q₈	—	2	4	no	—
356	C₄⋊Q₈	—	4	2	no	—
357	C₂²⋊Q₈	—	2	2	no	—
358	C₂²⋊Q₈	—	2	2	no	—
359	C₄×Q₈	—	2	4	no	—
360	C₄×Q₈	—	4	2	no	—
361	C₂×C₄⋊C₄	—	2	2	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	2	no	—
364	C₂×C₄⋊C₄	—	2	2	no	—
365	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₂²⋊C₄	—	2	2	no	—
371	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
372	C₂×C₄²	—	2	2	no	—
373	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
374	C₄⋊C₈	—	2	4	no	—
375	#103	—	2	2	no	—
376	#103	—	2	4	no	—
377	#103	—	2	4	no	—
378	#103	—	4	2	no	—
379	#102	—	2	2	no	—
380	C₂²⋊C₈	—	2	2	no	—
381	#95	—	2	1	no	—
382	#95	—	2	2	no	—
383	#95	—	2	2	no	—
384	#95	D₄×C₄₁	1	1	yes	characteristic
385	#95	D₄×C₄₁	1	1	yes	characteristic
386	C₂⁴	—	2	1	no	—
387	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
388	#41	—	2	8	no	—
389	#41	—	4	4	no	—
390	#41	—	4	8	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	8	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	4	4	no	—
404	C₂×Q₈	—	4	8	no	—
405	C₂×Q₈	—	4	4	no	—
406	C₂×Q₈	—	4	2	no	—
407	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
408	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
409	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	4	4	no	—
415	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	4	4	no	—
425	C₂²×C₄	—	4	4	no	—
426	C₂²×C₄	—	4	2	no	—
427	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
428	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
430	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
431	C₂²×C₄	#41×C₄₁	1	2	yes	—
432	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
433	Q₁₆	—	2	16	no	—
434	Q₁₆	—	4	4	no	—
435	SD₁₆	—	2	16	no	—
436	SD₁₆	—	4	4	no	—
437	M₁₆	—	2	8	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	4	4	no	—
450	C₄⋊C₄	—	4	4	no	—
451	C₄⋊C₄	—	4	4	no	—
452	C₄⋊C₄	—	4	2	no	—
453	C₂²⋊C₄	—	2	4	no	—
454	C₂²⋊C₄	—	4	2	no	—
455	C₂²⋊C₄	—	4	4	no	—
456	C₂²⋊C₄	—	8	2	no	—
457	C₂²⋊C₄	—	8	1	no	—
458	C₄²	—	2	2	no	—
459	C₄²	—	2	2	no	—
460	C₄²	—	4	4	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	1	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	4	2	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	4	1	no	—
470	C₂³	#121×C₄₁	1	2	yes	—
471	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
472	Q₈	—	2	2	no	—
473	Q₈	—	2	4	no	—
474	Q₈	—	2	4	no	—
475	Q₈	—	2	4	no	—
476	Q₈	—	4	8	no	—
477	Q₈	—	4	2	no	—
478	Q₈	—	4	2	no	—
479	Q₈	—	4	1	no	—
480	Q₈	—	4	1	no	—
481	Q₈	—	4	2	no	—
482	Q₈	#120×C₄₁	1	4	yes	—
483	D₄	—	2	2	no	—
484	D₄	—	2	2	no	—
485	D₄	—	4	8	no	—
486	D₄	—	4	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	4	8	no	—
500	C₂×C₄	—	4	8	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	#121×C₄₁	1	2	yes	—
512	C₂×C₄	#137×C₄₁	1	4	yes	complemented
513	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
515	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
516	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
517	C₈	—	2	4	no	—
518	C₈	—	4	1	no	—
519	C₈	—	4	1	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	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	—	8	2	no	—
529	C₂²	—	8	2	no	—
530	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
531	C₂²	D₄²×C₄₁	1	2	yes	—
532	C₂²	C₂×#137×C₄₁	1	2	yes	—
533	C₂²	C₄₁×#577	1	1	yes	characteristic
534	C₂²	C₄₁×#578	1	1	yes	characteristic
535	C₄	—	2	2	no	—
536	C₄	—	2	4	no	—
537	C₄	—	2	4	no	—
538	C₄	—	4	4	no	—
539	C₄	—	4	2	no	—
540	C₄	—	8	1	no	—
541	C₄	—	8	1	no	—
542	C₄	—	8	2	no	—
543	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
544	C₄	C₄₁×#534	1	1	yes	characteristic
545	C₄	C₄₁×#546	1	2	yes	—
546	C₂	—	4	2	no	—
547	C₂	—	8	2	no	—
548	C₂	C₄₁×#2410	1	1	yes	characteristic
549	C₂	C₄₁×#3039	1	1	yes	characteristic
550	C₂	C₄₁×#3046	1	1	yes	characteristic
551	C₂	C₄₁×#3270	1	2	yes	—
552	C₂	C₄₁×#3278	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×#41×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄×C₂²⋊C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#462	C₂	semidirect
4. C₄₁×#2434	C₂	semidirect
6. C₄₁×#2055	C₂	semidirect
7. C₄₁×#2013	C₂	semidirect
8. C₄₁×#1894	C₂	semidirect
9. C₄₁×#1878	C₂	semidirect
10. C₄₁×#1851	C₂	semidirect
11. C₄₁×#1787	C₂	semidirect
235. C₂×C₄×C₄₁	#137	semidirect
243. #24374	C₄₁	direct (N × H)
271. C₂×#462	C₂×C₄₁	semidirect
273. #2434	C₂×C₄₁	semidirect
275. #2055	C₂×C₄₁	semidirect
276. #2013	C₂×C₄₁	semidirect
277. #1894	C₂×C₄₁	semidirect
278. #1878	C₂×C₄₁	semidirect
279. #1851	C₂×C₄₁	semidirect
280. #1787	C₂×C₄₁	semidirect
321. C₄₁	#24374	direct (N × H)
512. C₂×C₄	#137×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#137×C₄₁	2
C₂×C₄₁×#462	2
C₂×C₄₁×#452	2
C₄₁×#2434	2
C₄₁×#2341	2
C₄₁×#2055	2
C₄₁×#2013	2
C₄₁×#1894	2
C₄₁×#1878	2
C₄₁×#1851	2
C₄₁×#1787	2
#24374	41

Subgroups — C41×#24374 #23800575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24374 #23800575