Subgroups — C₄₁×#23147 #23799348

Order 10496.

808 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3050	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2933	C₂	1	2	yes	maximal, complemented
3	C₄₁×#1938	C₂	1	2	yes	maximal, complemented
4	C₄₁×#1922	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1876	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1871	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1765	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1752	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₁×#341	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#135×C₄₁	C₂²	1	1	yes	characteristic
11	C₂×#131×C₄₁	C₂²	1	2	yes	—
12	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
13	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₄₁×#525	C₂²	1	2	yes	—
15	C₄₁×#467	C₄	1	1	yes	characteristic, complemented
16	C₄₁×#467	C₄	1	1	yes	characteristic, complemented
17	C₄₁×#466	C₄	1	1	yes	characteristic, complemented
18	C₄₁×#466	C₄	1	1	yes	characteristic, complemented
19	C₄₁×#465	C₄	1	2	yes	complemented
20	C₄₁×#465	C₄	1	2	yes	complemented
21	C₄₁×#436	—	2	2	no	—
22	C₄₁×#435	—	2	2	no	—
23	C₄₁×#435	—	2	2	no	—
24	C₈×D₄×C₄₁	—	2	2	no	—
25	C₄₁×#427	C₂²	1	1	yes	characteristic
26	C₄₁×#424	C₂²	1	2	yes	—
27	C₂×#104×C₄₁	C₂²	1	2	yes	—
28	C₂×#104×C₄₁	C₂²	1	2	yes	—
29	C₄₁×#416	C₂²	1	2	yes	—
30	C₄₁×#408	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
32	C₄₁×#405	C₂²	1	2	yes	—
33	C₂×#97×C₄₁	C₂²	1	2	yes	—
34	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
35	C₄₁×#341	C₂²	1	1	yes	characteristic
36	C₄₁×#341	C₂²	1	2	yes	—
37	C₄₁×#341	C₂²	1	1	yes	characteristic
38	C₄₁×#339	C₂²	1	2	yes	—
39	C₄₁×#339	C₂²	1	2	yes	—
40	C₄₁×#336	C₂²	1	2	yes	—
41	C₂×#41×C₄₁	C₂³	1	2	yes	—
42	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
43	#135×C₄₁	—	4	2	no	—
44	C₂×Q₁₆×C₄₁	C₂×C₄	1	1	yes	characteristic
45	C₂×SD₁₆×C₄₁	C₂×C₄	1	2	yes	—
46	C₂×D₈×C₄₁	C₂×C₄	1	1	yes	characteristic
47	#131×C₄₁	—	2	4	no	—
48	#131×C₄₁	—	4	2	no	—
49	C₂×M₁₆×C₄₁	—	2	2	no	—
50	C₂×M₁₆×C₄₁	—	2	2	no	—
51	C₂×M₁₆×C₄₁	—	2	4	no	—
52	C₂×M₁₆×C₄₁	—	4	2	no	—
53	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
54	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
55	C₂²×C₈×C₄₁	—	2	2	no	—
56	C₂²×C₈×C₄₁	—	2	2	no	—
57	C₂²×C₈×C₄₁	—	4	2	no	—
58	C₂²×C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
65	#123×C₄₁	—	2	2	no	—
66	C₂²⋊Q₈×C₄₁	C₂×C₄	1	2	yes	—
67	C₂²⋊Q₈×C₄₁	C₂×C₄	1	2	yes	—
68	#121×C₄₁	C₂×C₄	1	2	yes	—
69	#121×C₄₁	C₂×C₄	1	2	yes	—
70	#120×C₄₁	—	2	2	no	—
71	C₄×D₄×C₄₁	—	2	2	no	—
72	C₄×D₄×C₄₁	—	2	2	no	—
73	#117×C₄₁	C₂³	1	2	yes	—
74	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
75	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
76	#107×C₄₁	C₂×C₄	1	1	yes	characteristic
77	#107×C₄₁	C₂×C₄	1	1	yes	characteristic
78	#106×C₄₁	C₂×C₄	1	2	yes	—
79	C₄⋊C₈×C₄₁	—	2	2	no	—
80	C₄⋊C₈×C₄₁	—	2	2	no	—
81	#104×C₄₁	—	2	4	no	—
82	#104×C₄₁	—	4	2	no	—
83	#103×C₄₁	C₂×C₄	1	2	yes	—
84	#103×C₄₁	C₂×C₄	1	2	yes	—
85	#102×C₄₁	C₂×C₄	1	2	yes	—
86	#102×C₄₁	C₂×C₄	1	2	yes	—
87	C₂²⋊C₈×C₄₁	—	2	2	no	—
88	C₂²⋊C₈×C₄₁	—	2	2	no	—
89	C₂²⋊C₈×C₄₁	D₄	1	2	yes	—
90	C₂²⋊C₈×C₄₁	D₄	1	1	yes	characteristic
91	C₂²⋊C₈×C₄₁	D₄	1	1	yes	characteristic
92	#97×C₄₁	—	2	2	no	—
93	#97×C₄₁	—	4	2	no	—
94	C₄×C₈×C₄₁	—	2	2	no	—
95	#95×C₄₁	—	2	1	no	—
96	C₂⁴×C₄₁	#41	1	1	yes	characteristic
97	#41×C₄₁	—	2	2	no	—
98	#41×C₄₁	—	2	2	no	—
99	#41×C₄₁	—	2	2	no	—
100	#41×C₄₁	—	2	2	no	—
101	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₄₁	—	2	2	no	—
103	C₂×D₄×C₄₁	—	2	2	no	—
104	C₂×D₄×C₄₁	—	2	2	no	—
105	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₄₁	—	2	2	no	—
107	C₂²×C₄×C₄₁	—	2	2	no	—
108	C₂²×C₄×C₄₁	—	2	2	no	—
109	C₂²×C₄×C₄₁	—	2	2	no	—
110	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
115	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
116	Q₁₆×C₄₁	—	4	1	no	—
117	SD₁₆×C₄₁	—	4	2	no	—
118	D₈×C₄₁	—	4	1	no	—
119	M₁₆×C₄₁	—	2	2	no	—
120	M₁₆×C₄₁	—	2	2	no	—
121	M₁₆×C₄₁	—	2	2	no	—
122	M₁₆×C₄₁	—	4	4	no	—
123	M₁₆×C₄₁	—	4	4	no	—
124	M₁₆×C₄₁	#41	1	4	yes	—
125	C₂×C₈×C₄₁	—	2	2	no	—
126	C₂×C₈×C₄₁	—	2	2	no	—
127	C₂×C₈×C₄₁	—	2	2	no	—
128	C₂×C₈×C₄₁	—	2	2	no	—
129	C₂×C₈×C₄₁	—	2	2	no	—
130	C₂×C₈×C₄₁	—	2	2	no	—
131	C₂×C₈×C₄₁	—	4	1	no	—
132	C₂×C₈×C₄₁	—	4	1	no	—
133	C₂×C₈×C₄₁	—	4	1	no	—
134	C₂×C₈×C₄₁	—	4	1	no	—
135	C₂×C₈×C₄₁	—	4	4	no	—
136	C₂×C₈×C₄₁	—	4	4	no	—
137	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
143	C₄⋊C₄×C₄₁	—	2	2	no	—
144	C₄⋊C₄×C₄₁	—	2	2	no	—
145	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
146	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
147	C₂²⋊C₄×C₄₁	—	2	2	no	—
148	C₂²⋊C₄×C₄₁	—	2	2	no	—
149	C₂²⋊C₄×C₄₁	—	2	2	no	—
150	C₂²⋊C₄×C₄₁	—	2	2	no	—
151	C₂²⋊C₄×C₄₁	—	2	2	no	—
152	C₂²⋊C₄×C₄₁	—	4	2	no	—
153	C₄²×C₄₁	—	2	2	no	—
154	C₄²×C₄₁	—	2	2	no	—
155	C₄²×C₄₁	—	2	2	no	—
156	C₂³×C₄₁	—	2	2	no	—
157	C₂³×C₄₁	—	2	2	no	—
158	C₂³×C₄₁	—	2	2	no	—
159	C₂³×C₄₁	—	4	1	no	—
160	C₂³×C₄₁	C₄×D₄	1	1	yes	characteristic
161	C₂³×C₄₁	C₄×D₄	1	1	yes	characteristic
162	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
163	Q₈×C₄₁	—	2	2	no	—
164	Q₈×C₄₁	—	2	2	no	—
165	D₄×C₄₁	—	2	2	no	—
166	D₄×C₄₁	—	2	2	no	—
167	D₄×C₄₁	—	4	2	no	—
168	D₄×C₄₁	—	4	2	no	—
169	D₄×C₄₁	—	4	4	no	—
170	D₄×C₄₁	—	8	2	no	—
171	C₂×C₄×C₄₁	—	2	2	no	—
172	C₂×C₄×C₄₁	—	2	1	no	—
173	C₂×C₄×C₄₁	—	2	1	no	—
174	C₂×C₄×C₄₁	—	2	1	no	—
175	C₂×C₄×C₄₁	—	2	1	no	—
176	C₂×C₄×C₄₁	—	2	2	no	—
177	C₂×C₄×C₄₁	—	2	2	no	—
178	C₂×C₄×C₄₁	—	2	2	no	—
179	C₂×C₄×C₄₁	—	2	2	no	—
180	C₂×C₄×C₄₁	—	2	2	no	—
181	C₂×C₄×C₄₁	—	4	2	no	—
182	C₂×C₄×C₄₁	—	4	2	no	—
183	C₂×C₄×C₄₁	—	4	2	no	—
184	C₂×C₄×C₄₁	—	4	2	no	—
185	C₂×C₄×C₄₁	—	4	2	no	—
186	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
191	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
192	C₈×C₄₁	—	2	1	no	—
193	C₈×C₄₁	—	2	1	no	—
194	C₈×C₄₁	—	2	1	no	—
195	C₈×C₄₁	—	2	1	no	—
196	C₈×C₄₁	—	2	2	no	—
197	C₈×C₄₁	—	2	2	no	—
198	C₈×C₄₁	—	2	4	no	—
199	C₈×C₄₁	—	4	2	no	—
200	#23147	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂²×C₄₁	—	2	1	no	—
202	C₂²×C₄₁	—	2	1	no	—
203	C₂²×C₄₁	—	2	1	no	—
204	C₂²×C₄₁	—	2	1	no	—
205	C₂²×C₄₁	—	2	1	no	—
206	C₂²×C₄₁	—	2	1	no	—
207	C₂²×C₄₁	—	2	1	no	—
208	C₂²×C₄₁	—	4	4	no	—
209	C₂²×C₄₁	—	4	2	no	—
210	C₂²×C₄₁	—	4	2	no	—
211	C₂²×C₄₁	—	4	2	no	—
212	C₂²×C₄₁	#444	1	2	yes	—
213	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
214	C₂²×C₄₁	#553	1	2	yes	—
215	C₄×C₄₁	—	2	1	no	—
216	C₄×C₄₁	—	2	1	no	—
217	C₄×C₄₁	—	4	2	no	—
218	C₄×C₄₁	—	4	2	no	—
219	C₄×C₄₁	—	4	2	no	—
220	C₄×C₄₁	—	8	2	no	—
221	C₄×C₄₁	C₄×#41	1	1	yes	characteristic
222	C₄×C₄₁	#518	1	1	yes	characteristic
223	C₄×C₄₁	#546	1	2	yes	—
224	#3050	C₂×C₄₁	1	1	yes	characteristic
225	#2933	C₂×C₄₁	1	2	yes	complemented
226	#1938	C₂×C₄₁	1	2	yes	complemented
227	#1922	C₂×C₄₁	1	2	yes	complemented
228	#1876	C₂×C₄₁	1	2	yes	complemented
229	#1871	C₂×C₄₁	1	2	yes	complemented
230	#1765	C₂×C₄₁	1	2	yes	complemented
231	#1752	C₂×C₄₁	1	1	yes	characteristic, complemented
232	C₂×#341	C₂×C₄₁	1	1	yes	characteristic, complemented
233	C₂×C₄₁	—	2	2	no	—
234	C₂×C₄₁	—	2	2	no	—
235	C₂×C₄₁	—	4	1	no	—
236	C₂×C₄₁	—	8	2	no	—
237	C₂×C₄₁	#2364	1	1	yes	characteristic
238	C₂×C₄₁	C₂×#444	1	1	yes	characteristic
239	C₂×C₄₁	#2957	1	1	yes	characteristic
240	C₂×#135	C₂²×C₄₁	1	1	yes	characteristic
241	C₂×#131	C₂²×C₄₁	1	2	yes	—
242	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
243	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
244	#525	C₂²×C₄₁	1	2	yes	—
245	#467	C₄×C₄₁	1	1	yes	characteristic, complemented
246	#467	C₄×C₄₁	1	1	yes	characteristic, complemented
247	#466	C₄×C₄₁	1	1	yes	characteristic, complemented
248	#466	C₄×C₄₁	1	1	yes	characteristic, complemented
249	#465	C₄×C₄₁	1	2	yes	complemented
250	#465	C₄×C₄₁	1	2	yes	complemented
251	#436	—	2	2	no	—
252	#435	—	2	2	no	—
253	#435	—	2	2	no	—
254	C₈×D₄	—	2	2	no	—
255	#427	C₂²×C₄₁	1	1	yes	characteristic
256	#424	C₂²×C₄₁	1	2	yes	—
257	C₂×#104	C₂²×C₄₁	1	2	yes	—
258	C₂×#104	C₂²×C₄₁	1	2	yes	—
259	#416	C₂²×C₄₁	1	2	yes	—
260	#408	C₂²×C₄₁	1	2	yes	—
261	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
262	#405	C₂²×C₄₁	1	2	yes	—
263	C₂×#97	C₂²×C₄₁	1	2	yes	—
264	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
265	#341	C₂²×C₄₁	1	2	yes	—
266	#341	C₂²×C₄₁	1	1	yes	characteristic
267	#341	C₂²×C₄₁	1	1	yes	characteristic
268	#339	C₂²×C₄₁	1	2	yes	—
269	#339	C₂²×C₄₁	1	2	yes	—
270	#336	C₂²×C₄₁	1	2	yes	—
271	C₄₁	#23147	1	1	yes	characteristic, direct product factor, Sylow
272	C₂×#41	C₂³×C₄₁	1	2	yes	—
273	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
274	#135	—	4	2	no	—
275	C₂×Q₁₆	C₂×C₄×C₄₁	1	1	yes	characteristic
276	C₂×SD₁₆	C₂×C₄×C₄₁	1	2	yes	—
277	C₂×D₈	C₂×C₄×C₄₁	1	1	yes	characteristic
278	#131	—	2	4	no	—
279	#131	—	4	2	no	—
280	C₂×M₁₆	—	2	2	no	—
281	C₂×M₁₆	—	2	2	no	—
282	C₂×M₁₆	—	2	4	no	—
283	C₂×M₁₆	—	4	2	no	—
284	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
285	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
286	C₂²×C₈	—	2	2	no	—
287	C₂²×C₈	—	2	2	no	—
288	C₂²×C₈	—	4	2	no	—
289	C₂²×C₈	C₂×C₄×C₄₁	1	1	yes	characteristic
290	C₂²×C₈	C₂×C₄×C₄₁	1	1	yes	characteristic
291	C₂²×C₈	C₂×C₄×C₄₁	1	1	yes	characteristic
292	C₂²×C₈	C₂×C₄×C₄₁	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
294	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
295	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
296	#123	—	2	2	no	—
297	C₂²⋊Q₈	C₂×C₄×C₄₁	1	2	yes	—
298	C₂²⋊Q₈	C₂×C₄×C₄₁	1	2	yes	—
299	#121	C₂×C₄×C₄₁	1	2	yes	—
300	#121	C₂×C₄×C₄₁	1	2	yes	—
301	#120	—	2	2	no	—
302	C₄×D₄	—	2	2	no	—
303	C₄×D₄	—	2	2	no	—
304	#117	C₂³×C₄₁	1	2	yes	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
307	#107	C₂×C₄×C₄₁	1	1	yes	characteristic
308	#107	C₂×C₄×C₄₁	1	1	yes	characteristic
309	#106	C₂×C₄×C₄₁	1	2	yes	—
310	C₄⋊C₈	—	2	2	no	—
311	C₄⋊C₈	—	2	2	no	—
312	#104	—	2	4	no	—
313	#104	—	4	2	no	—
314	#103	C₂×C₄×C₄₁	1	2	yes	—
315	#103	C₂×C₄×C₄₁	1	2	yes	—
316	#102	C₂×C₄×C₄₁	1	2	yes	—
317	#102	C₂×C₄×C₄₁	1	2	yes	—
318	C₂²⋊C₈	—	2	2	no	—
319	C₂²⋊C₈	—	2	2	no	—
320	C₂²⋊C₈	D₄×C₄₁	1	2	yes	—
321	C₂²⋊C₈	D₄×C₄₁	1	1	yes	characteristic
322	C₂²⋊C₈	D₄×C₄₁	1	1	yes	characteristic
323	#97	—	2	2	no	—
324	#97	—	4	2	no	—
325	C₄×C₈	—	2	2	no	—
326	#95	—	2	1	no	—
327	C₂⁴	#41×C₄₁	1	1	yes	characteristic
328	#41	—	2	2	no	—
329	#41	—	2	2	no	—
330	#41	—	2	2	no	—
331	#41	—	2	2	no	—
332	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
342	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
345	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
346	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
347	Q₁₆	—	4	1	no	—
348	SD₁₆	—	4	2	no	—
349	D₈	—	4	1	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	2	2	no	—
353	M₁₆	—	4	4	no	—
354	M₁₆	—	4	4	no	—
355	M₁₆	#41×C₄₁	1	4	yes	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	4	1	no	—
363	C₂×C₈	—	4	1	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	—	4	1	no	—
366	C₂×C₈	—	4	4	no	—
367	C₂×C₈	—	4	4	no	—
368	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
369	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
370	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
371	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
372	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
373	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
377	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	4	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	4	1	no	—
391	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
392	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
393	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
394	Q₈	—	2	2	no	—
395	Q₈	—	2	2	no	—
396	D₄	—	2	2	no	—
397	D₄	—	2	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	4	no	—
401	D₄	—	8	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
418	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
419	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
420	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
421	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
422	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
423	C₈	—	2	1	no	—
424	C₈	—	2	1	no	—
425	C₈	—	2	1	no	—
426	C₈	—	2	1	no	—
427	C₈	—	2	2	no	—
428	C₈	—	2	2	no	—
429	C₈	—	2	4	no	—
430	C₈	—	4	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	C₄₁×#444	1	2	yes	—
443	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
444	C₂²	C₄₁×#553	1	2	yes	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	8	2	no	—
451	C₄	C₄×#41×C₄₁	1	1	yes	characteristic
452	C₄	C₄₁×#518	1	1	yes	characteristic
453	C₄	C₄₁×#546	1	2	yes	—
454	C₂	—	2	2	no	—
455	C₂	—	2	2	no	—
456	C₂	—	4	1	no	—
457	C₂	—	8	2	no	—
458	C₂	C₄₁×#2364	1	1	yes	characteristic
459	C₂	C₂×C₄₁×#444	1	1	yes	characteristic
460	C₂	C₄₁×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂²×C₄₁	C₂×C₄×D₄
prime radical	C₄₁×#3050	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂×C₂²⋊C₈×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2933	C₂	semidirect
3. C₄₁×#1938	C₂	semidirect
4. C₄₁×#1922	C₂	semidirect
5. C₄₁×#1876	C₂	semidirect
6. C₄₁×#1871	C₂	semidirect
7. C₄₁×#1765	C₂	semidirect
8. C₄₁×#1752	C₂	semidirect
9. C₂×C₄₁×#341	C₂	semidirect
15. C₄₁×#467	C₄	semidirect
16. C₄₁×#467	C₄	semidirect
17. C₄₁×#466	C₄	semidirect
18. C₄₁×#466	C₄	semidirect
19. C₄₁×#465	C₄	semidirect
20. C₄₁×#465	C₄	semidirect
200. #23147	C₄₁	direct (N × H)
225. #2933	C₂×C₄₁	semidirect
226. #1938	C₂×C₄₁	semidirect
227. #1922	C₂×C₄₁	semidirect
228. #1876	C₂×C₄₁	semidirect
229. #1871	C₂×C₄₁	semidirect
230. #1765	C₂×C₄₁	semidirect
231. #1752	C₂×C₄₁	semidirect
232. C₂×#341	C₂×C₄₁	semidirect
245. #467	C₄×C₄₁	semidirect
246. #467	C₄×C₄₁	semidirect
247. #466	C₄×C₄₁	semidirect
248. #466	C₄×C₄₁	semidirect
249. #465	C₄×C₄₁	semidirect
250. #465	C₄×C₄₁	semidirect
271. C₄₁	#23147	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#3050	2
C₄₁×#2933	2
C₄₁×#1938	2
C₄₁×#1922	2
C₄₁×#1876	2
C₄₁×#1871	2
C₄₁×#1765	2
C₄₁×#1752	2
C₂×C₄₁×#341	2
#23147	41

Subgroups — C41×#23147 #23799348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23147 #23799348