Subgroups — C₄₁×#25671 #23801872

Order 10496.

1374 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2857	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2034	C₂	1	4	yes	maximal, complemented
6	C₄₁×#1990	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1957	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1864	C₂	1	4	yes	maximal, complemented
9	C₄×C₂²⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₁	—	2	1	no	—
11	C₄₁×#532	—	2	4	no	—
12	C₄₁×#532	—	2	4	no	—
13	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×#124×C₄₁	—	2	1	no	—
17	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
18	C₂×#121×C₄₁	—	2	1	no	—
19	C₂×#121×C₄₁	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₄₁	—	2	1	no	—
21	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
22	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
23	C₄₁×#498	—	2	4	no	—
24	C₄₁×#486	—	2	4	no	—
25	C₂×#106×C₄₁	C₂²	1	4	yes	—
26	C₂×#102×C₄₁	C₂²	1	4	yes	—
27	C₂×#102×C₄₁	C₂²	1	4	yes	—
28	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₄₁×#391	—	2	1	no	—
32	C₄₁×#389	—	2	1	no	—
33	C₄₁×#389	C₂²	1	2	yes	—
34	C₄₁×#384	C₂²	1	1	yes	characteristic
35	C₄₁×#380	—	2	1	no	—
36	C₄₁×#380	C₂²	1	2	yes	—
37	C₄₁×#340	C₂²	1	4	yes	—
38	C₄₁×#336	C₂²	1	2	yes	—
39	C₂×#41×C₄₁	—	2	8	no	—
40	C₂×#41×C₄₁	—	4	4	no	—
41	C₂×#41×C₄₁	—	4	4	no	—
42	C₂²×Q₈×C₄₁	—	2	1	no	—
43	C₂²×Q₈×C₄₁	—	2	1	no	—
44	C₂²×D₄×C₄₁	—	2	2	no	—
45	C₂²×D₄×C₄₁	—	2	1	no	—
46	C₂²×D₄×C₄₁	—	2	1	no	—
47	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
48	C₂³×C₄×C₄₁	—	2	2	no	—
49	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
53	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
54	C₄⋊Q₈×C₄₁	—	2	2	no	—
55	C₄⋊Q₈×C₄₁	—	2	2	no	—
56	C₄⋊Q₈×C₄₁	—	2	2	no	—
57	C₄⋊Q₈×C₄₁	D₄	1	4	yes	—
58	#127×C₄₁	—	2	2	no	—
59	#127×C₄₁	D₄	1	4	yes	—
60	#124×C₄₁	—	2	8	no	—
61	C₂²⋊Q₈×C₄₁	—	4	4	no	—
62	#121×C₄₁	—	2	8	no	—
63	#121×C₄₁	—	2	4	no	—
64	#121×C₄₁	—	2	4	no	—
65	C₄×D₄×C₄₁	—	2	8	no	—
66	C₄×D₄×C₄₁	—	2	4	no	—
67	C₄×D₄×C₄₁	—	2	4	no	—
68	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
73	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
76	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
79	C₂×C₄²×C₄₁	—	2	2	no	—
80	C₂×C₄²×C₄₁	—	2	2	no	—
81	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
85	#106×C₄₁	—	2	8	no	—
86	#102×C₄₁	—	2	8	no	—
87	#102×C₄₁	—	2	8	no	—
88	C₂²⋊C₈×C₄₁	—	2	4	no	—
89	C₄×C₈×C₄₁	—	2	2	no	—
90	C₄×C₈×C₄₁	—	2	2	no	—
91	#95×C₄₁	—	2	2	no	—
92	#95×C₄₁	—	2	2	no	—
93	C₂⁴×C₄₁	—	2	2	no	—
94	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
95	#41×C₄₁	—	4	32	no	—
96	C₂×Q₈×C₄₁	—	2	4	no	—
97	C₂×Q₈×C₄₁	—	4	2	no	—
98	C₂×Q₈×C₄₁	—	4	2	no	—
99	C₂×Q₈×C₄₁	—	4	2	no	—
100	C₂×Q₈×C₄₁	—	4	2	no	—
101	C₂×Q₈×C₄₁	—	4	2	no	—
102	C₂×D₄×C₄₁	—	2	8	no	—
103	C₂×D₄×C₄₁	—	2	4	no	—
104	C₂×D₄×C₄₁	—	2	4	no	—
105	C₂×D₄×C₄₁	—	2	2	no	—
106	C₂×D₄×C₄₁	—	2	4	no	—
107	C₂×D₄×C₄₁	—	2	4	no	—
108	C₂×D₄×C₄₁	—	4	4	no	—
109	C₂×D₄×C₄₁	—	4	4	no	—
110	C₂×D₄×C₄₁	—	4	2	no	—
111	C₂×D₄×C₄₁	—	4	2	no	—
112	C₂×D₄×C₄₁	—	4	2	no	—
113	C₂×D₄×C₄₁	—	4	2	no	—
114	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₄₁	—	2	2	no	—
116	C₂²×C₄×C₄₁	—	2	2	no	—
117	C₂²×C₄×C₄₁	—	2	8	no	—
118	C₂²×C₄×C₄₁	—	2	2	no	—
119	C₂²×C₄×C₄₁	—	2	2	no	—
120	C₂²×C₄×C₄₁	—	2	2	no	—
121	C₂²×C₄×C₄₁	—	2	2	no	—
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	—	4	4	no	—
129	C₂²×C₄×C₄₁	—	4	4	no	—
130	C₂²×C₄×C₄₁	SD₁₆	1	4	yes	—
131	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
137	C₂×C₈×C₄₁	—	2	2	no	—
138	C₂×C₈×C₄₁	—	2	2	no	—
139	C₂×C₈×C₄₁	—	2	2	no	—
140	C₂×C₈×C₄₁	—	2	2	no	—
141	C₂×C₈×C₄₁	—	2	2	no	—
142	C₂×C₈×C₄₁	#41	1	4	yes	complemented
143	C₄⋊C₄×C₄₁	—	2	4	no	—
144	C₄⋊C₄×C₄₁	—	2	2	no	—
145	C₄⋊C₄×C₄₁	—	2	2	no	—
146	C₄⋊C₄×C₄₁	—	2	2	no	—
147	C₄⋊C₄×C₄₁	—	2	4	no	—
148	C₄⋊C₄×C₄₁	—	4	4	no	—
149	C₄⋊C₄×C₄₁	—	4	2	no	—
150	C₄⋊C₄×C₄₁	—	4	2	no	—
151	C₄⋊C₄×C₄₁	—	4	2	no	—
152	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
153	C₂²⋊C₄×C₄₁	—	2	8	no	—
154	C₂²⋊C₄×C₄₁	—	2	8	no	—
155	C₂²⋊C₄×C₄₁	—	4	4	no	—
156	C₄²×C₄₁	—	2	2	no	—
157	C₄²×C₄₁	—	2	2	no	—
158	C₄²×C₄₁	—	2	1	no	—
159	C₄²×C₄₁	—	2	1	no	—
160	C₄²×C₄₁	C₂×D₄	1	2	yes	—
161	C₄²×C₄₁	C₂×D₄	1	2	yes	—
162	C₂³×C₄₁	—	2	1	no	—
163	C₂³×C₄₁	—	2	1	no	—
164	C₂³×C₄₁	—	2	1	no	—
165	C₂³×C₄₁	—	2	1	no	—
166	C₂³×C₄₁	—	2	1	no	—
167	C₂³×C₄₁	—	2	1	no	—
168	C₂³×C₄₁	—	2	4	no	—
169	C₂³×C₄₁	—	4	2	no	—
170	C₂³×C₄₁	—	4	2	no	—
171	C₂³×C₄₁	—	4	2	no	—
172	C₂³×C₄₁	—	4	2	no	—
173	C₂³×C₄₁	—	4	2	no	—
174	C₂³×C₄₁	—	4	2	no	—
175	C₂³×C₄₁	C₂×SD₁₆	1	2	yes	—
176	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
177	Q₈×C₄₁	—	4	8	no	—
178	Q₈×C₄₁	—	8	4	no	—
179	D₄×C₄₁	—	2	8	no	—
180	D₄×C₄₁	—	4	16	no	—
181	D₄×C₄₁	—	4	4	no	—
182	D₄×C₄₁	—	4	8	no	—
183	D₄×C₄₁	—	4	8	no	—
184	C₂×C₄×C₄₁	—	2	1	no	—
185	C₂×C₄×C₄₁	—	2	1	no	—
186	C₂×C₄×C₄₁	—	2	8	no	—
187	C₂×C₄×C₄₁	—	2	1	no	—
188	C₂×C₄×C₄₁	—	2	1	no	—
189	C₂×C₄×C₄₁	—	2	4	no	—
190	C₂×C₄×C₄₁	—	2	1	no	—
191	C₂×C₄×C₄₁	—	2	1	no	—
192	C₂×C₄×C₄₁	—	2	1	no	—
193	C₂×C₄×C₄₁	—	2	1	no	—
194	C₂×C₄×C₄₁	—	4	16	no	—
195	C₂×C₄×C₄₁	—	4	2	no	—
196	C₂×C₄×C₄₁	—	4	2	no	—
197	C₂×C₄×C₄₁	—	4	2	no	—
198	C₂×C₄×C₄₁	—	4	2	no	—
199	C₂×C₄×C₄₁	—	4	4	no	—
200	C₂×C₄×C₄₁	—	4	2	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	2	no	—
206	C₂×C₄×C₄₁	#120	1	2	yes	—
207	C₂×C₄×C₄₁	#120	1	2	yes	—
208	C₂×C₄×C₄₁	C₂×SD₁₆	1	2	yes	—
209	C₂×C₄×C₄₁	C₂×SD₁₆	1	2	yes	—
210	C₂×C₄×C₄₁	#135	1	2	yes	—
211	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
212	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
213	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
216	C₂×C₄×C₄₁	2₋¹⁺⁴	1	2	yes	—
217	C₈×C₄₁	—	2	4	no	—
218	C₈×C₄₁	—	4	2	no	—
219	#25671	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂²×C₄₁	—	2	2	no	—
221	C₂²×C₄₁	—	2	2	no	—
222	C₂²×C₄₁	—	2	2	no	—
223	C₂²×C₄₁	—	4	1	no	—
224	C₂²×C₄₁	—	4	1	no	—
225	C₂²×C₄₁	—	4	1	no	—
226	C₂²×C₄₁	—	4	1	no	—
227	C₂²×C₄₁	—	4	4	no	—
228	C₂²×C₄₁	—	4	4	no	—
229	C₂²×C₄₁	—	4	4	no	—
230	C₂²×C₄₁	—	8	2	no	—
231	C₂²×C₄₁	—	8	2	no	—
232	C₂²×C₄₁	—	8	2	no	—
233	C₂²×C₄₁	—	8	2	no	—
234	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
235	C₂²×C₄₁	#532	1	1	yes	characteristic
236	C₂²×C₄₁	#536	1	1	yes	characteristic
237	C₂²×C₄₁	C₂²×SD₁₆	1	1	yes	characteristic
238	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
239	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
240	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
241	C₄×C₄₁	—	2	2	no	—
242	C₄×C₄₁	—	4	1	no	—
243	C₄×C₄₁	—	4	4	no	—
244	C₄×C₄₁	—	4	1	no	—
245	C₄×C₄₁	—	8	2	no	—
246	C₄×C₄₁	—	8	2	no	—
247	C₄×C₄₁	#449	1	4	yes	—
248	C₄×C₄₁	#450	1	4	yes	—
249	C₄×C₄₁	#547	1	2	yes	—
250	C₄×C₄₁	#548	1	2	yes	—
251	C₂×#532	C₂×C₄₁	1	1	yes	characteristic
252	C₂×#498	C₂×C₄₁	1	1	yes	characteristic, complemented
253	C₂×#486	C₂×C₄₁	1	1	yes	characteristic, complemented
254	#2857	C₂×C₄₁	1	1	yes	characteristic, complemented
255	#2034	C₂×C₄₁	1	4	yes	complemented
256	#1990	C₂×C₄₁	1	1	yes	characteristic, complemented
257	#1957	C₂×C₄₁	1	1	yes	characteristic, complemented
258	#1864	C₂×C₄₁	1	4	yes	complemented
259	C₄×C₂²⋊C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
260	C₂×C₄₁	—	4	2	no	—
261	C₂×C₄₁	—	8	4	no	—
262	C₂×C₄₁	#2432	1	1	yes	characteristic
263	C₂×C₄₁	C₂×#450	1	1	yes	characteristic
264	C₂×C₄₁	C₂×#449	1	1	yes	characteristic
265	C₂×C₄₁	#3167	1	1	yes	characteristic
266	C₂×C₄₁	#3184	1	1	yes	characteristic
267	C₂×C₄₁	#3227	1	1	yes	characteristic
268	C₂×C₄₁	#3228	1	1	yes	characteristic
269	C₂²×#41	—	2	1	no	—
270	#532	—	2	4	no	—
271	#532	—	2	4	no	—
272	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
273	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
274	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
275	C₂×#124	—	2	1	no	—
276	C₂×C₂²⋊Q₈	—	2	1	no	—
277	C₂×#121	—	2	1	no	—
278	C₂×#121	C₂²×C₄₁	1	2	yes	—
279	C₂×C₄×D₄	—	2	1	no	—
280	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
281	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
282	#498	—	2	4	no	—
283	#486	—	2	4	no	—
284	C₂×#106	C₂²×C₄₁	1	4	yes	—
285	C₂×#102	C₂²×C₄₁	1	4	yes	—
286	C₂×#102	C₂²×C₄₁	1	4	yes	—
287	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
288	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
289	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
290	#391	—	2	1	no	—
291	#389	—	2	1	no	—
292	#389	C₂²×C₄₁	1	2	yes	—
293	#384	C₂²×C₄₁	1	1	yes	characteristic
294	#380	—	2	1	no	—
295	#380	C₂²×C₄₁	1	2	yes	—
296	#340	C₂²×C₄₁	1	4	yes	—
297	#336	C₂²×C₄₁	1	2	yes	—
298	C₄₁	#25671	1	1	yes	characteristic, direct product factor, Sylow
299	C₂×#41	—	2	8	no	—
300	C₂×#41	—	4	4	no	—
301	C₂×#41	—	4	4	no	—
302	C₂²×Q₈	—	2	1	no	—
303	C₂²×Q₈	—	2	1	no	—
304	C₂²×D₄	—	2	2	no	—
305	C₂²×D₄	—	2	1	no	—
306	C₂²×D₄	—	2	1	no	—
307	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
308	C₂³×C₄	—	2	2	no	—
309	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
310	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
311	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
313	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
314	C₄⋊Q₈	—	2	2	no	—
315	C₄⋊Q₈	—	2	2	no	—
316	C₄⋊Q₈	—	2	2	no	—
317	C₄⋊Q₈	D₄×C₄₁	1	4	yes	—
318	#127	—	2	2	no	—
319	#127	D₄×C₄₁	1	4	yes	—
320	#124	—	2	8	no	—
321	C₂²⋊Q₈	—	4	4	no	—
322	#121	—	2	8	no	—
323	#121	—	2	4	no	—
324	#121	—	2	4	no	—
325	C₄×D₄	—	2	8	no	—
326	C₄×D₄	—	2	4	no	—
327	C₄×D₄	—	2	4	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₄²	—	2	2	no	—
340	C₂×C₄²	—	2	2	no	—
341	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
342	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
343	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
345	#106	—	2	8	no	—
346	#102	—	2	8	no	—
347	#102	—	2	8	no	—
348	C₂²⋊C₈	—	2	4	no	—
349	C₄×C₈	—	2	2	no	—
350	C₄×C₈	—	2	2	no	—
351	#95	—	2	2	no	—
352	#95	—	2	2	no	—
353	C₂⁴	—	2	2	no	—
354	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
355	#41	—	4	32	no	—
356	C₂×Q₈	—	2	4	no	—
357	C₂×Q₈	—	4	2	no	—
358	C₂×Q₈	—	4	2	no	—
359	C₂×Q₈	—	4	2	no	—
360	C₂×Q₈	—	4	2	no	—
361	C₂×Q₈	—	4	2	no	—
362	C₂×D₄	—	2	8	no	—
363	C₂×D₄	—	2	4	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	4	4	no	—
369	C₂×D₄	—	4	4	no	—
370	C₂×D₄	—	4	2	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	—	4	2	no	—
374	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	8	no	—
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	1	no	—
383	C₂²×C₄	—	2	1	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	—	4	4	no	—
389	C₂²×C₄	—	4	4	no	—
390	C₂²×C₄	SD₁₆×C₄₁	1	4	yes	—
391	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
396	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	#41×C₄₁	1	4	yes	complemented
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	4	4	no	—
409	C₄⋊C₄	—	4	2	no	—
410	C₄⋊C₄	—	4	2	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
413	C₂²⋊C₄	—	2	8	no	—
414	C₂²⋊C₄	—	2	8	no	—
415	C₂²⋊C₄	—	4	4	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	2	1	no	—
420	C₄²	C₂×D₄×C₄₁	1	2	yes	—
421	C₄²	C₂×D₄×C₄₁	1	2	yes	—
422	C₂³	—	2	1	no	—
423	C₂³	—	2	1	no	—
424	C₂³	—	2	1	no	—
425	C₂³	—	2	1	no	—
426	C₂³	—	2	1	no	—
427	C₂³	—	2	1	no	—
428	C₂³	—	2	4	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	C₂×SD₁₆×C₄₁	1	2	yes	—
436	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
437	Q₈	—	4	8	no	—
438	Q₈	—	8	4	no	—
439	D₄	—	2	8	no	—
440	D₄	—	4	16	no	—
441	D₄	—	4	4	no	—
442	D₄	—	4	8	no	—
443	D₄	—	4	8	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	8	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	4	16	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	#120×C₄₁	1	2	yes	—
467	C₂×C₄	#120×C₄₁	1	2	yes	—
468	C₂×C₄	C₂×SD₁₆×C₄₁	1	2	yes	—
469	C₂×C₄	C₂×SD₁₆×C₄₁	1	2	yes	—
470	C₂×C₄	#135×C₄₁	1	2	yes	—
471	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
472	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
473	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
474	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
475	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
476	C₂×C₄	2₋¹⁺⁴×C₄₁	1	2	yes	—
477	C₈	—	2	4	no	—
478	C₈	—	4	2	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	8	2	no	—
491	C₂²	—	8	2	no	—
492	C₂²	—	8	2	no	—
493	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
494	C₂²	C₄₁×#532	1	1	yes	characteristic
495	C₂²	C₄₁×#536	1	1	yes	characteristic
496	C₂²	C₂²×SD₁₆×C₄₁	1	1	yes	characteristic
497	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
498	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
499	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	4	1	no	—
502	C₄	—	4	4	no	—
503	C₄	—	4	1	no	—
504	C₄	—	8	2	no	—
505	C₄	—	8	2	no	—
506	C₄	C₄₁×#449	1	4	yes	—
507	C₄	C₄₁×#450	1	4	yes	—
508	C₄	C₄₁×#547	1	2	yes	—
509	C₄	C₄₁×#548	1	2	yes	—
510	C₂	—	4	2	no	—
511	C₂	—	8	4	no	—
512	C₂	C₄₁×#2432	1	1	yes	characteristic
513	C₂	C₂×C₄₁×#450	1	1	yes	characteristic
514	C₂	C₂×C₄₁×#449	1	1	yes	characteristic
515	C₂	C₄₁×#3167	1	1	yes	characteristic
516	C₂	C₄₁×#3184	1	1	yes	characteristic
517	C₂	C₄₁×#3227	1	1	yes	characteristic
518	C₂	C₄₁×#3228	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#532	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#498	C₂	semidirect
3. C₂×C₄₁×#486	C₂	semidirect
4. C₄₁×#2857	C₂	semidirect
5. C₄₁×#2034	C₂	semidirect
6. C₄₁×#1990	C₂	semidirect
7. C₄₁×#1957	C₂	semidirect
8. C₄₁×#1864	C₂	semidirect
9. C₄×C₂²⋊C₈×C₄₁	C₂	semidirect
142. C₂×C₈×C₄₁	#41	semidirect
219. #25671	C₄₁	direct (N × H)
252. C₂×#498	C₂×C₄₁	semidirect
253. C₂×#486	C₂×C₄₁	semidirect
254. #2857	C₂×C₄₁	semidirect
255. #2034	C₂×C₄₁	semidirect
256. #1990	C₂×C₄₁	semidirect
257. #1957	C₂×C₄₁	semidirect
258. #1864	C₂×C₄₁	semidirect
259. C₄×C₂²⋊C₈	C₂×C₄₁	semidirect
298. C₄₁	#25671	direct (N × H)
402. C₂×C₈	#41×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#532	2
C₂×C₄₁×#498	2
C₂×C₄₁×#486	2
C₄₁×#2857	2
C₄₁×#2034	2
C₄₁×#1990	2
C₄₁×#1957	2
C₄₁×#1864	2
C₄×C₂²⋊C₈×C₄₁	2
#25671	41

Subgroups — C41×#25671 #23801872

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25671 #23801872