Subgroups — C₄₁×#25643 #23801844

Order 10496.

1108 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#556	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#497	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#462	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2568	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2016	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2015	C₂	1	2	yes	maximal
7	C₄₁×#1985	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1983	C₂	1	1	yes	maximal, characteristic
9	C₄₁×#1878	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1877	C₂	1	2	yes	maximal
11	C₄₁×#1763	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₄₁	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₄₁	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
15	C₄₁×#556	—	2	4	no	—
16	C₄₁×#556	—	2	4	no	—
17	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×#126×C₄₁	—	2	1	no	—
20	C₂×#126×C₄₁	—	2	1	no	—
21	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
24	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×#117×C₄₁	—	2	1	no	—
29	C₄₁×#497	—	2	4	no	—
30	C₄₁×#462	—	2	4	no	—
31	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×#103×C₄₁	C₂²	1	2	yes	—
33	C₂×#103×C₄₁	C₂²	1	2	yes	—
34	C₂×#103×C₄₁	C₂²	1	2	yes	—
35	C₂×#102×C₄₁	C₂²	1	2	yes	—
36	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
37	C₄₁×#400	—	2	1	no	—
38	C₄₁×#400	—	2	1	no	—
39	C₄₁×#391	—	2	1	no	—
40	C₄₁×#391	C₂²	1	2	yes	—
41	C₄₁×#391	C₂²	1	2	yes	—
42	C₄₁×#382	—	2	1	no	—
43	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
44	C₄₁×#340	C₂²	1	2	yes	—
45	C₄₁×#336	C₂²	1	2	yes	—
46	C₄₁×#336	C₂²	1	2	yes	—
47	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
48	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
49	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
50	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₄₁	—	2	1	no	—
53	C₂×Q₁₆×C₄₁	—	2	4	no	—
54	C₂×Q₁₆×C₄₁	—	2	4	no	—
55	C₂×Q₁₆×C₄₁	—	2	4	no	—
56	C₂×Q₁₆×C₄₁	—	4	2	no	—
57	C₂×Q₁₆×C₄₁	—	4	2	no	—
58	C₂×Q₁₆×C₄₁	—	4	2	no	—
59	C₂×SD₁₆×C₄₁	—	2	4	no	—
60	C₂×SD₁₆×C₄₁	—	2	4	no	—
61	C₂×SD₁₆×C₄₁	—	4	2	no	—
62	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
63	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
64	C₄⋊Q₈×C₄₁	—	2	2	no	—
65	C₄⋊Q₈×C₄₁	—	2	2	no	—
66	C₄⋊Q₈×C₄₁	—	2	2	no	—
67	C₄⋊Q₈×C₄₁	—	2	2	no	—
68	#126×C₄₁	—	2	8	no	—
69	#126×C₄₁	—	2	8	no	—
70	#124×C₄₁	—	2	2	no	—
71	#124×C₄₁	—	2	2	no	—
72	#124×C₄₁	—	2	2	no	—
73	#124×C₄₁	D₄	1	4	yes	—
74	C₂²⋊Q₈×C₄₁	—	2	8	no	—
75	C₄×Q₈×C₄₁	—	2	2	no	—
76	C₄×Q₈×C₄₁	—	2	2	no	—
77	C₄×Q₈×C₄₁	—	2	2	no	—
78	C₄×Q₈×C₄₁	—	2	2	no	—
79	C₄×Q₈×C₄₁	—	2	2	no	—
80	C₄×Q₈×C₄₁	D₄	1	4	yes	—
81	C₄×D₄×C₄₁	—	2	2	no	—
82	C₄×D₄×C₄₁	—	2	2	no	—
83	#117×C₄₁	—	2	8	no	—
84	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
85	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
86	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
87	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
88	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
89	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
90	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
100	C₂×C₄²×C₄₁	—	2	1	no	—
101	C₂×C₄²×C₄₁	—	2	1	no	—
102	C₂×C₄²×C₄₁	—	2	1	no	—
103	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
106	C₄⋊C₈×C₄₁	—	2	2	no	—
107	#103×C₄₁	—	2	4	no	—
108	#103×C₄₁	—	2	4	no	—
109	#103×C₄₁	—	4	2	no	—
110	#102×C₄₁	—	4	2	no	—
111	#97×C₄₁	—	2	2	no	—
112	#95×C₄₁	—	2	1	no	—
113	#95×C₄₁	—	2	2	no	—
114	#95×C₄₁	—	2	2	no	—
115	#95×C₄₁	—	2	2	no	—
116	#95×C₄₁	—	2	2	no	—
117	C₂⁴×C₄₁	—	2	1	no	—
118	C₂×Q₈×C₄₁	—	2	2	no	—
119	C₂×Q₈×C₄₁	—	2	2	no	—
120	C₂×Q₈×C₄₁	—	2	1	no	—
121	C₂×Q₈×C₄₁	—	2	1	no	—
122	C₂×Q₈×C₄₁	—	2	2	no	—
123	C₂×Q₈×C₄₁	—	2	2	no	—
124	C₂×Q₈×C₄₁	—	2	2	no	—
125	C₂×Q₈×C₄₁	—	2	2	no	—
126	C₂×Q₈×C₄₁	—	2	2	no	—
127	C₂×Q₈×C₄₁	—	2	2	no	—
128	C₂×Q₈×C₄₁	—	2	2	no	—
129	C₂×Q₈×C₄₁	—	2	2	no	—
130	C₂×Q₈×C₄₁	—	2	2	no	—
131	C₂×Q₈×C₄₁	—	2	2	no	—
132	C₂×Q₈×C₄₁	—	4	1	no	—
133	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
134	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
135	C₂×D₄×C₄₁	—	2	1	no	—
136	C₂×D₄×C₄₁	—	2	2	no	—
137	C₂×D₄×C₄₁	—	2	2	no	—
138	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₄₁	—	2	4	no	—
140	C₂²×C₄×C₄₁	—	2	1	no	—
141	C₂²×C₄×C₄₁	—	2	1	no	—
142	C₂²×C₄×C₄₁	—	2	1	no	—
143	C₂²×C₄×C₄₁	—	2	2	no	—
144	C₂²×C₄×C₄₁	—	2	2	no	—
145	C₂²×C₄×C₄₁	—	4	2	no	—
146	C₂²×C₄×C₄₁	—	4	2	no	—
147	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
154	Q₁₆×C₄₁	—	4	8	no	—
155	Q₁₆×C₄₁	—	4	8	no	—
156	SD₁₆×C₄₁	—	4	8	no	—
157	C₂×C₈×C₄₁	—	2	2	no	—
158	C₂×C₈×C₄₁	—	2	2	no	—
159	C₂×C₈×C₄₁	—	2	2	no	—
160	C₂×C₈×C₄₁	—	2	2	no	—
161	C₂×C₈×C₄₁	—	2	2	no	—
162	C₂×C₈×C₄₁	#41	1	4	yes	—
163	C₄⋊C₄×C₄₁	—	2	4	no	—
164	C₄⋊C₄×C₄₁	—	2	4	no	—
165	C₄⋊C₄×C₄₁	—	2	4	no	—
166	C₄⋊C₄×C₄₁	—	2	4	no	—
167	C₄⋊C₄×C₄₁	—	2	2	no	—
168	C₄⋊C₄×C₄₁	—	2	2	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	—	2	2	no	—
173	C₄⋊C₄×C₄₁	—	4	2	no	—
174	C₄⋊C₄×C₄₁	—	4	2	no	—
175	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
176	C₂²⋊C₄×C₄₁	—	2	4	no	—
177	C₂²⋊C₄×C₄₁	—	2	4	no	—
178	C₂²⋊C₄×C₄₁	—	2	4	no	—
179	C₂²⋊C₄×C₄₁	—	2	4	no	—
180	C₂²⋊C₄×C₄₁	—	2	4	no	—
181	C₄²×C₄₁	—	2	4	no	—
182	C₄²×C₄₁	—	2	4	no	—
183	C₄²×C₄₁	—	2	1	no	—
184	C₄²×C₄₁	—	2	1	no	—
185	C₄²×C₄₁	—	2	1	no	—
186	C₄²×C₄₁	—	2	1	no	—
187	C₄²×C₄₁	—	4	2	no	—
188	C₄²×C₄₁	C₂×D₄	1	2	yes	—
189	C₄²×C₄₁	C₂×D₄	1	2	yes	—
190	C₂³×C₄₁	—	2	2	no	—
191	C₂³×C₄₁	—	4	2	no	—
192	C₂³×C₄₁	—	4	1	no	—
193	C₂³×C₄₁	—	4	1	no	—
194	C₂³×C₄₁	—	4	2	no	—
195	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
196	Q₈×C₄₁	—	2	2	no	—
197	Q₈×C₄₁	—	2	2	no	—
198	Q₈×C₄₁	—	2	4	no	—
199	Q₈×C₄₁	—	4	4	no	—
200	Q₈×C₄₁	—	4	1	no	—
201	Q₈×C₄₁	—	4	1	no	—
202	Q₈×C₄₁	—	4	2	no	—
203	Q₈×C₄₁	—	4	2	no	—
204	Q₈×C₄₁	—	4	2	no	—
205	Q₈×C₄₁	—	4	2	no	—
206	Q₈×C₄₁	—	4	2	no	—
207	D₄×C₄₁	—	2	4	no	—
208	D₄×C₄₁	—	4	1	no	—
209	D₄×C₄₁	—	4	1	no	—
210	C₂×C₄×C₄₁	—	2	1	no	—
211	C₂×C₄×C₄₁	—	2	1	no	—
212	C₂×C₄×C₄₁	—	2	1	no	—
213	C₂×C₄×C₄₁	—	2	1	no	—
214	C₂×C₄×C₄₁	—	2	2	no	—
215	C₂×C₄×C₄₁	—	2	1	no	—
216	C₂×C₄×C₄₁	—	2	2	no	—
217	C₂×C₄×C₄₁	—	2	1	no	—
218	C₂×C₄×C₄₁	—	2	2	no	—
219	C₂×C₄×C₄₁	—	2	2	no	—
220	C₂×C₄×C₄₁	—	2	1	no	—
221	C₂×C₄×C₄₁	—	2	1	no	—
222	C₂×C₄×C₄₁	—	2	1	no	—
223	C₂×C₄×C₄₁	—	2	2	no	—
224	C₂×C₄×C₄₁	—	2	2	no	—
225	C₂×C₄×C₄₁	—	4	8	no	—
226	C₂×C₄×C₄₁	—	4	2	no	—
227	C₂×C₄×C₄₁	—	4	2	no	—
228	C₂×C₄×C₄₁	—	4	1	no	—
229	C₂×C₄×C₄₁	—	4	1	no	—
230	C₂×C₄×C₄₁	—	4	2	no	—
231	C₂×C₄×C₄₁	—	4	2	no	—
232	C₂×C₄×C₄₁	—	4	2	no	—
233	C₂×C₄×C₄₁	—	4	2	no	—
234	C₂×C₄×C₄₁	—	4	2	no	—
235	C₂×C₄×C₄₁	—	4	2	no	—
236	C₂×C₄×C₄₁	#120	1	2	yes	—
237	C₂×C₄×C₄₁	#120	1	2	yes	—
238	C₂×C₄×C₄₁	#137	1	2	yes	—
239	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
242	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
243	C₈×C₄₁	—	2	4	no	—
244	C₈×C₄₁	—	4	2	no	—
245	#25643	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
246	C₂²×C₄₁	—	4	2	no	—
247	C₂²×C₄₁	—	4	2	no	—
248	C₂²×C₄₁	—	4	2	no	—
249	C₂²×C₄₁	—	8	2	no	—
250	C₂²×C₄₁	—	8	2	no	—
251	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
252	C₂²×C₄₁	#550	1	2	yes	—
253	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
254	C₂²×C₄₁	#575	1	1	yes	characteristic
255	C₂²×C₄₁	#578	1	2	yes	—
256	C₄×C₄₁	—	2	2	no	—
257	C₄×C₄₁	—	2	2	no	—
258	C₄×C₄₁	—	2	2	no	—
259	C₄×C₄₁	—	4	2	no	—
260	C₄×C₄₁	—	4	2	no	—
261	C₄×C₄₁	—	4	1	no	—
262	C₄×C₄₁	—	4	2	no	—
263	C₄×C₄₁	—	4	1	no	—
264	C₄×C₄₁	—	4	1	no	—
265	C₄×C₄₁	—	8	2	no	—
266	C₄×C₄₁	—	8	2	no	—
267	C₄×C₄₁	#532	1	1	yes	characteristic
268	C₄×C₄₁	#535	1	1	yes	characteristic
269	C₄×C₄₁	#546	1	2	yes	—
270	C₂×#556	C₂×C₄₁	1	1	yes	characteristic
271	C₂×#497	C₂×C₄₁	1	1	yes	characteristic
272	C₂×#462	C₂×C₄₁	1	1	yes	characteristic, complemented
273	#2568	C₂×C₄₁	1	1	yes	characteristic, complemented
274	#2016	C₂×C₄₁	1	2	yes	complemented
275	#2015	C₂×C₄₁	1	2	yes	—
276	#1985	C₂×C₄₁	1	1	yes	characteristic, complemented
277	#1983	C₂×C₄₁	1	1	yes	characteristic
278	#1878	C₂×C₄₁	1	2	yes	complemented
279	#1877	C₂×C₄₁	1	2	yes	—
280	#1763	C₂×C₄₁	1	1	yes	characteristic, complemented
281	C₂×C₄₁	—	8	2	no	—
282	C₂×C₄₁	#2431	1	1	yes	characteristic
283	C₂×C₄₁	#3007	1	1	yes	characteristic
284	C₂×C₄₁	#3011	1	1	yes	characteristic
285	C₂×C₄₁	#3398	1	2	yes	—
286	C₂×C₄₁	#3402	1	2	yes	—
287	C₂²×Q₁₆	C₂²×C₄₁	1	2	yes	—
288	C₂²×Q₁₆	C₂²×C₄₁	1	2	yes	—
289	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
290	#556	—	2	4	no	—
291	#556	—	2	4	no	—
292	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
293	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
294	C₂×#126	—	2	1	no	—
295	C₂×#126	—	2	1	no	—
296	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
297	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
298	C₂×C₂²⋊Q₈	—	2	1	no	—
299	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
300	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
301	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
302	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
303	C₂×#117	—	2	1	no	—
304	#497	—	2	4	no	—
305	#462	—	2	4	no	—
306	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
307	C₂×#103	C₂²×C₄₁	1	2	yes	—
308	C₂×#103	C₂²×C₄₁	1	2	yes	—
309	C₂×#103	C₂²×C₄₁	1	2	yes	—
310	C₂×#102	C₂²×C₄₁	1	2	yes	—
311	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
312	#400	—	2	1	no	—
313	#400	—	2	1	no	—
314	#391	—	2	1	no	—
315	#391	C₂²×C₄₁	1	2	yes	—
316	#391	C₂²×C₄₁	1	2	yes	—
317	#382	—	2	1	no	—
318	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
319	#340	C₂²×C₄₁	1	2	yes	—
320	#336	C₂²×C₄₁	1	2	yes	—
321	#336	C₂²×C₄₁	1	2	yes	—
322	C₄₁	#25643	1	1	yes	characteristic, direct product factor, Sylow
323	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
324	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
325	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
326	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
327	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
328	C₂³×C₄	—	2	1	no	—
329	C₂×Q₁₆	—	2	4	no	—
330	C₂×Q₁₆	—	2	4	no	—
331	C₂×Q₁₆	—	2	4	no	—
332	C₂×Q₁₆	—	4	2	no	—
333	C₂×Q₁₆	—	4	2	no	—
334	C₂×Q₁₆	—	4	2	no	—
335	C₂×SD₁₆	—	2	4	no	—
336	C₂×SD₁₆	—	2	4	no	—
337	C₂×SD₁₆	—	4	2	no	—
338	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
339	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
340	C₄⋊Q₈	—	2	2	no	—
341	C₄⋊Q₈	—	2	2	no	—
342	C₄⋊Q₈	—	2	2	no	—
343	C₄⋊Q₈	—	2	2	no	—
344	#126	—	2	8	no	—
345	#126	—	2	8	no	—
346	#124	—	2	2	no	—
347	#124	—	2	2	no	—
348	#124	—	2	2	no	—
349	#124	D₄×C₄₁	1	4	yes	—
350	C₂²⋊Q₈	—	2	8	no	—
351	C₄×Q₈	—	2	2	no	—
352	C₄×Q₈	—	2	2	no	—
353	C₄×Q₈	—	2	2	no	—
354	C₄×Q₈	—	2	2	no	—
355	C₄×Q₈	—	2	2	no	—
356	C₄×Q₈	D₄×C₄₁	1	4	yes	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	#117	—	2	8	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
367	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
368	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	1	no	—
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₂²⋊C₄	—	2	1	no	—
375	C₂×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₄²	—	2	1	no	—
377	C₂×C₄²	—	2	1	no	—
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
382	C₄⋊C₈	—	2	2	no	—
383	#103	—	2	4	no	—
384	#103	—	2	4	no	—
385	#103	—	4	2	no	—
386	#102	—	4	2	no	—
387	#97	—	2	2	no	—
388	#95	—	2	1	no	—
389	#95	—	2	2	no	—
390	#95	—	2	2	no	—
391	#95	—	2	2	no	—
392	#95	—	2	2	no	—
393	C₂⁴	—	2	1	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	1	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	4	1	no	—
409	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
410	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	4	2	no	—
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
429	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
430	Q₁₆	—	4	8	no	—
431	Q₁₆	—	4	8	no	—
432	SD₁₆	—	4	8	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	#41×C₄₁	1	4	yes	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	4	2	no	—
450	C₄⋊C₄	—	4	2	no	—
451	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	—	2	4	no	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₄²	—	2	4	no	—
458	C₄²	—	2	4	no	—
459	C₄²	—	2	1	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	1	no	—
462	C₄²	—	2	1	no	—
463	C₄²	—	4	2	no	—
464	C₄²	C₂×D₄×C₄₁	1	2	yes	—
465	C₄²	C₂×D₄×C₄₁	1	2	yes	—
466	C₂³	—	2	2	no	—
467	C₂³	—	4	2	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	4	1	no	—
470	C₂³	—	4	2	no	—
471	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
472	Q₈	—	2	2	no	—
473	Q₈	—	2	2	no	—
474	Q₈	—	2	4	no	—
475	Q₈	—	4	4	no	—
476	Q₈	—	4	1	no	—
477	Q₈	—	4	1	no	—
478	Q₈	—	4	2	no	—
479	Q₈	—	4	2	no	—
480	Q₈	—	4	2	no	—
481	Q₈	—	4	2	no	—
482	Q₈	—	4	2	no	—
483	D₄	—	2	4	no	—
484	D₄	—	4	1	no	—
485	D₄	—	4	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	4	8	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	#120×C₄₁	1	2	yes	—
513	C₂×C₄	#120×C₄₁	1	2	yes	—
514	C₂×C₄	#137×C₄₁	1	2	yes	—
515	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
516	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
517	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
518	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
519	C₈	—	2	4	no	—
520	C₈	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	8	2	no	—
525	C₂²	—	8	2	no	—
526	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
527	C₂²	C₄₁×#550	1	2	yes	—
528	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
529	C₂²	C₄₁×#575	1	1	yes	characteristic
530	C₂²	C₄₁×#578	1	2	yes	—
531	C₄	—	2	2	no	—
532	C₄	—	2	2	no	—
533	C₄	—	2	2	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	2	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	1	no	—
540	C₄	—	8	2	no	—
541	C₄	—	8	2	no	—
542	C₄	C₄₁×#532	1	1	yes	characteristic
543	C₄	C₄₁×#535	1	1	yes	characteristic
544	C₄	C₄₁×#546	1	2	yes	—
545	C₂	—	8	2	no	—
546	C₂	C₄₁×#2431	1	1	yes	characteristic
547	C₂	C₄₁×#3007	1	1	yes	characteristic
548	C₂	C₄₁×#3011	1	1	yes	characteristic
549	C₂	C₄₁×#3398	1	2	yes	—
550	C₂	C₄₁×#3402	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×D₄×C₄₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×C₄×Q₈×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄₁×#462	C₂	semidirect
4. C₄₁×#2568	C₂	semidirect
5. C₄₁×#2016	C₂	semidirect
7. C₄₁×#1985	C₂	semidirect
9. C₄₁×#1878	C₂	semidirect
11. C₄₁×#1763	C₂	semidirect
245. #25643	C₄₁	direct (N × H)
272. C₂×#462	C₂×C₄₁	semidirect
273. #2568	C₂×C₄₁	semidirect
274. #2016	C₂×C₄₁	semidirect
276. #1985	C₂×C₄₁	semidirect
278. #1878	C₂×C₄₁	semidirect
280. #1763	C₂×C₄₁	semidirect
322. C₄₁	#25643	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#556	2
C₂×C₄₁×#497	2
C₂×C₄₁×#462	2
C₄₁×#2568	2
C₄₁×#2016	2
C₄₁×#2015	2
C₄₁×#1985	2
C₄₁×#1983	2
C₄₁×#1878	2
C₄₁×#1877	2
C₄₁×#1763	2
#25643	41

Subgroups — C41×#25643 #23801844

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25643 #23801844