Subgroups — C₂×C₄₁×#1641 #23794712

Order 10496.

1290 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#550	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#474	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#462	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1641	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₁×#331	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₁×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₁×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₄₁	—	2	1	no	—
10	C₂²×Q₁₆×C₄₁	—	2	1	no	—
11	C₄₁×#550	—	2	2	no	—
12	C₄₁×#550	—	2	2	no	—
13	C₄₁×#550	—	2	2	no	—
14	C₄₁×#550	C₂²	1	4	yes	—
15	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×#127×C₄₁	—	2	1	no	—
17	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#121×C₄₁	—	2	2	no	—
19	C₂×#121×C₄₁	—	2	1	no	—
20	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₄₁	—	2	1	no	—
22	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
23	C₄₁×#486	—	2	2	no	—
24	C₄₁×#486	C₂²	1	4	yes	complemented
25	C₄₁×#474	—	2	2	no	—
26	C₄₁×#474	C₂²	1	4	yes	complemented
27	C₄₁×#462	—	2	2	no	—
28	C₄₁×#462	C₂²	1	4	yes	complemented
29	C₂×#107×C₄₁	—	2	1	no	—
30	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×#103×C₄₁	—	2	1	no	—
33	C₂×#102×C₄₁	—	2	1	no	—
34	C₂×#102×C₄₁	—	2	2	no	—
35	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
36	C₄₁×#331	C₂²	1	4	yes	complemented
37	C₄₁×Q₈⋊C₈	C₂²	1	4	yes	complemented
38	C₄₁×D₄⋊C₈	C₂²	1	4	yes	complemented
39	C₂×#41×C₄₁	—	2	4	no	—
40	C₂×#41×C₄₁	—	2	4	no	—
41	C₂×#41×C₄₁	—	4	4	no	—
42	C₂×#41×C₄₁	—	4	4	no	—
43	C₂²×Q₈×C₄₁	—	2	1	no	—
44	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
45	C₂²×D₄×C₄₁	—	2	2	no	—
46	C₂²×D₄×C₄₁	—	2	2	no	—
47	C₂²×D₄×C₄₁	—	2	1	no	—
48	C₂²×D₄×C₄₁	—	2	1	no	—
49	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₄₁	D₄	1	2	yes	—
51	C₂³×C₄×C₄₁	—	2	2	no	—
52	C₂³×C₄×C₄₁	—	2	1	no	—
53	C₂×Q₁₆×C₄₁	—	2	4	no	—
54	C₂×Q₁₆×C₄₁	—	4	4	no	—
55	C₂²×C₈×C₄₁	—	2	1	no	—
56	C₂²×C₈×C₄₁	—	2	1	no	—
57	C₂²×C₈×C₄₁	—	2	1	no	—
58	C₄⋊Q₈×C₄₁	—	2	1	no	—
59	C₄⋊Q₈×C₄₁	—	2	1	no	—
60	C₄⋊Q₈×C₄₁	—	2	1	no	—
61	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
62	#127×C₄₁	—	2	4	no	—
63	#127×C₄₁	—	2	4	no	—
64	#127×C₄₁	—	2	1	no	—
65	#127×C₄₁	—	2	1	no	—
66	#127×C₄₁	D₄	1	2	yes	—
67	#127×C₄₁	C₂³	1	2	yes	—
68	#121×C₄₁	—	2	4	no	—
69	#121×C₄₁	—	2	8	no	—
70	#121×C₄₁	—	2	8	no	—
71	#121×C₄₁	—	2	4	no	—
72	C₄×Q₈×C₄₁	—	2	1	no	—
73	C₄×Q₈×C₄₁	—	2	1	no	—
74	C₄×Q₈×C₄₁	D₄	1	2	yes	—
75	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
76	C₄×D₄×C₄₁	—	2	4	no	—
77	C₄×D₄×C₄₁	—	2	4	no	—
78	C₄×D₄×C₄₁	—	2	1	no	—
79	C₄×D₄×C₄₁	—	2	1	no	—
80	C₄×D₄×C₄₁	D₄	1	2	yes	—
81	C₄×D₄×C₄₁	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
83	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
85	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
89	C₂×C₄²×C₄₁	—	2	1	no	—
90	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
91	#107×C₄₁	—	2	4	no	—
92	C₄⋊C₈×C₄₁	—	2	1	no	—
93	C₄⋊C₈×C₄₁	—	2	1	no	—
94	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
95	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
96	#103×C₄₁	—	2	4	no	—
97	#102×C₄₁	—	2	4	no	—
98	#102×C₄₁	—	2	8	no	—
99	C₄×C₈×C₄₁	—	2	1	no	—
100	C₄×C₈×C₄₁	C₂³	1	2	yes	—
101	C₂⁴×C₄₁	—	2	1	no	—
102	C₂⁴×C₄₁	—	2	2	no	—
103	#41×C₄₁	—	4	8	no	—
104	#41×C₄₁	—	4	16	no	—
105	#41×C₄₁	—	4	8	no	—
106	C₂×Q₈×C₄₁	—	2	1	no	—
107	C₂×Q₈×C₄₁	—	2	2	no	—
108	C₂×Q₈×C₄₁	—	2	2	no	—
109	C₂×Q₈×C₄₁	—	4	1	no	—
110	C₂×Q₈×C₄₁	—	4	2	no	—
111	C₂×Q₈×C₄₁	—	4	2	no	—
112	C₂×Q₈×C₄₁	D₈	1	4	yes	—
113	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
114	C₂×D₄×C₄₁	—	2	8	no	—
115	C₂×D₄×C₄₁	—	2	8	no	—
116	C₂×D₄×C₄₁	—	2	1	no	—
117	C₂×D₄×C₄₁	—	2	2	no	—
118	C₂×D₄×C₄₁	—	2	2	no	—
119	C₂×D₄×C₄₁	—	2	2	no	—
120	C₂×D₄×C₄₁	—	2	2	no	—
121	C₂×D₄×C₄₁	—	2	2	no	—
122	C₂×D₄×C₄₁	—	2	2	no	—
123	C₂×D₄×C₄₁	—	2	2	no	—
124	C₂×D₄×C₄₁	—	4	8	no	—
125	C₂×D₄×C₄₁	—	4	4	no	—
126	C₂×D₄×C₄₁	—	4	2	no	—
127	C₂×D₄×C₄₁	—	4	2	no	—
128	C₂×D₄×C₄₁	—	4	2	no	—
129	C₂×D₄×C₄₁	—	4	2	no	—
130	C₂×D₄×C₄₁	—	8	4	no	—
131	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
132	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
133	C₂²×C₄×C₄₁	—	2	1	no	—
134	C₂²×C₄×C₄₁	—	2	8	no	—
135	C₂²×C₄×C₄₁	—	2	1	no	—
136	C₂²×C₄×C₄₁	—	2	1	no	—
137	C₂²×C₄×C₄₁	—	2	2	no	—
138	C₂²×C₄×C₄₁	—	2	2	no	—
139	C₂²×C₄×C₄₁	—	4	8	no	—
140	C₂²×C₄×C₄₁	—	4	2	no	—
141	C₂²×C₄×C₄₁	—	4	2	no	—
142	C₂²×C₄×C₄₁	—	4	1	no	—
143	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
146	Q₁₆×C₄₁	—	4	8	no	—
147	C₂×C₈×C₄₁	—	2	2	no	—
148	C₂×C₈×C₄₁	—	2	2	no	—
149	C₂×C₈×C₄₁	—	2	2	no	—
150	C₂×C₈×C₄₁	—	4	2	no	—
151	C₂×C₈×C₄₁	—	4	2	no	—
152	C₂×C₈×C₄₁	—	4	2	no	—
153	C₄⋊C₄×C₄₁	—	2	2	no	—
154	C₄⋊C₄×C₄₁	—	2	1	no	—
155	C₄⋊C₄×C₄₁	—	2	1	no	—
156	C₄⋊C₄×C₄₁	—	2	2	no	—
157	C₄⋊C₄×C₄₁	—	2	2	no	—
158	C₄⋊C₄×C₄₁	—	2	2	no	—
159	C₄⋊C₄×C₄₁	—	4	1	no	—
160	C₄⋊C₄×C₄₁	—	4	1	no	—
161	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
162	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
163	C₂²⋊C₄×C₄₁	—	2	8	no	—
164	C₂²⋊C₄×C₄₁	—	2	2	no	—
165	C₂²⋊C₄×C₄₁	—	2	2	no	—
166	C₄²×C₄₁	—	2	2	no	—
167	C₄²×C₄₁	—	2	2	no	—
168	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
172	C₂³×C₄₁	—	2	2	no	—
173	C₂³×C₄₁	—	2	4	no	—
174	C₂³×C₄₁	—	4	4	no	—
175	C₂³×C₄₁	—	4	2	no	—
176	C₂³×C₄₁	—	4	2	no	—
177	C₂³×C₄₁	—	4	4	no	—
178	C₂³×C₄₁	—	4	4	no	—
179	C₂³×C₄₁	—	4	2	no	—
180	C₂³×C₄₁	#120	1	1	yes	characteristic
181	Q₈×C₄₁	—	2	2	no	—
182	Q₈×C₄₁	—	2	4	no	—
183	Q₈×C₄₁	—	4	2	no	—
184	Q₈×C₄₁	—	4	2	no	—
185	Q₈×C₄₁	—	8	2	no	—
186	Q₈×C₄₁	C₂×D₈	1	4	yes	—
187	D₄×C₄₁	—	2	2	no	—
188	D₄×C₄₁	—	2	2	no	—
189	D₄×C₄₁	—	4	4	no	—
190	D₄×C₄₁	—	4	16	no	—
191	D₄×C₄₁	—	4	2	no	—
192	D₄×C₄₁	—	4	2	no	—
193	D₄×C₄₁	—	4	2	no	—
194	D₄×C₄₁	—	4	2	no	—
195	D₄×C₄₁	—	4	4	no	—
196	D₄×C₄₁	—	4	2	no	—
197	D₄×C₄₁	—	4	4	no	—
198	D₄×C₄₁	—	8	2	no	—
199	D₄×C₄₁	—	8	8	no	—
200	C₂×C₄×C₄₁	—	2	2	no	—
201	C₂×C₄×C₄₁	—	2	4	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	—	4	16	no	—
206	C₂×C₄×C₄₁	—	4	2	no	—
207	C₂×C₄×C₄₁	—	4	2	no	—
208	C₂×C₄×C₄₁	—	4	2	no	—
209	C₂×C₄×C₄₁	—	4	2	no	—
210	C₂×C₄×C₄₁	—	4	4	no	—
211	C₂×C₄×C₄₁	—	4	2	no	—
212	C₂×C₄×C₄₁	—	8	2	no	—
213	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
214	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
215	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
216	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
217	C₂×C₄×C₄₁	#135	1	2	yes	—
218	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
219	C₂×C₄×C₄₁	#137	1	2	yes	—
220	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
223	C₈×C₄₁	—	4	2	no	—
224	C₈×C₄₁	—	4	2	no	—
225	C₈×C₄₁	—	4	2	no	—
226	C₂×#1641	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂²×C₄₁	—	4	4	no	—
228	C₂²×C₄₁	—	4	2	no	—
229	C₂²×C₄₁	—	4	2	no	—
230	C₂²×C₄₁	—	4	4	no	—
231	C₂²×C₄₁	—	4	4	no	—
232	C₂²×C₄₁	—	4	2	no	—
233	C₂²×C₄₁	—	8	4	no	—
234	C₂²×C₄₁	—	8	8	no	—
235	C₂²×C₄₁	#447	1	2	yes	—
236	C₂²×C₄₁	#452	1	2	yes	—
237	C₂²×C₄₁	#455	1	2	yes	—
238	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
239	C₄×C₄₁	—	2	4	no	—
240	C₄×C₄₁	—	2	1	no	—
241	C₄×C₄₁	—	2	1	no	—
242	C₄×C₄₁	—	4	2	no	—
243	C₄×C₄₁	—	4	2	no	—
244	C₄×C₄₁	—	8	2	no	—
245	C₄×C₄₁	#447	1	2	yes	—
246	C₄×C₄₁	#452	1	2	yes	—
247	C₄×C₄₁	C₂²×D₈	1	1	yes	characteristic
248	C₄×C₄₁	C₂×#135	1	1	yes	characteristic
249	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
250	C₄×C₄₁	C₂×#137	1	1	yes	characteristic
251	C₂×#550	C₂×C₄₁	1	1	yes	characteristic
252	C₂×#486	C₂×C₄₁	1	1	yes	characteristic, complemented
253	C₂×#474	C₂×C₄₁	1	1	yes	characteristic, complemented
254	C₂×#462	C₂×C₄₁	1	1	yes	characteristic, complemented
255	#1641	C₂×C₄₁	1	8	yes	direct product factor
256	C₂×#331	C₂×C₄₁	1	1	yes	characteristic, complemented
257	C₂×Q₈⋊C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
258	C₂×D₄⋊C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
259	C₂×C₄₁	—	8	2	no	—
260	C₂×C₄₁	—	8	4	no	—
261	C₂×C₄₁	#1641	1	4	yes	direct product factor
262	C₂×C₄₁	C₂×#447	1	1	yes	characteristic
263	C₂×C₄₁	C₂×#452	1	1	yes	characteristic
264	C₂×C₄₁	C₂×#455	1	1	yes	characteristic
265	C₂²×#41	—	2	1	no	—
266	C₂²×Q₁₆	—	2	1	no	—
267	#550	—	2	2	no	—
268	#550	—	2	2	no	—
269	#550	—	2	2	no	—
270	#550	C₂²×C₄₁	1	4	yes	—
271	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
272	C₂×#127	—	2	1	no	—
273	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
274	C₂×#121	—	2	2	no	—
275	C₂×#121	—	2	1	no	—
276	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
277	C₂×C₄×D₄	—	2	1	no	—
278	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
279	#486	—	2	2	no	—
280	#486	C₂²×C₄₁	1	4	yes	complemented
281	#474	—	2	2	no	—
282	#474	C₂²×C₄₁	1	4	yes	complemented
283	#462	—	2	2	no	—
284	#462	C₂²×C₄₁	1	4	yes	complemented
285	C₂×#107	—	2	1	no	—
286	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
287	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
288	C₂×#103	—	2	1	no	—
289	C₂×#102	—	2	2	no	—
290	C₂×#102	—	2	1	no	—
291	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
292	#331	C₂²×C₄₁	1	4	yes	complemented
293	Q₈⋊C₈	C₂²×C₄₁	1	4	yes	complemented
294	D₄⋊C₈	C₂²×C₄₁	1	4	yes	complemented
295	C₄₁	C₂×#1641	1	1	yes	characteristic, direct product factor, Sylow
296	C₂×#41	—	2	4	no	—
297	C₂×#41	—	2	4	no	—
298	C₂×#41	—	4	4	no	—
299	C₂×#41	—	4	4	no	—
300	C₂²×Q₈	—	2	1	no	—
301	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
302	C₂²×D₄	—	2	2	no	—
303	C₂²×D₄	—	2	2	no	—
304	C₂²×D₄	—	2	1	no	—
305	C₂²×D₄	—	2	1	no	—
306	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
307	C₂²×D₄	D₄×C₄₁	1	2	yes	—
308	C₂³×C₄	—	2	2	no	—
309	C₂³×C₄	—	2	1	no	—
310	C₂×Q₁₆	—	2	4	no	—
311	C₂×Q₁₆	—	4	4	no	—
312	C₂²×C₈	—	2	1	no	—
313	C₂²×C₈	—	2	1	no	—
314	C₂²×C₈	—	2	1	no	—
315	C₄⋊Q₈	—	2	1	no	—
316	C₄⋊Q₈	—	2	1	no	—
317	C₄⋊Q₈	—	2	1	no	—
318	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
319	#127	—	2	4	no	—
320	#127	—	2	4	no	—
321	#127	—	2	1	no	—
322	#127	—	2	1	no	—
323	#127	D₄×C₄₁	1	2	yes	—
324	#127	C₂³×C₄₁	1	2	yes	—
325	#121	—	2	4	no	—
326	#121	—	2	8	no	—
327	#121	—	2	8	no	—
328	#121	—	2	4	no	—
329	C₄×Q₈	—	2	1	no	—
330	C₄×Q₈	—	2	1	no	—
331	C₄×Q₈	D₄×C₄₁	1	2	yes	—
332	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
333	C₄×D₄	—	2	4	no	—
334	C₄×D₄	—	2	4	no	—
335	C₄×D₄	—	2	1	no	—
336	C₄×D₄	—	2	1	no	—
337	C₄×D₄	D₄×C₄₁	1	2	yes	—
338	C₄×D₄	C₂³×C₄₁	1	2	yes	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
343	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₄²	—	2	1	no	—
347	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
348	#107	—	2	4	no	—
349	C₄⋊C₈	—	2	1	no	—
350	C₄⋊C₈	—	2	1	no	—
351	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
352	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
353	#103	—	2	4	no	—
354	#102	—	2	4	no	—
355	#102	—	2	8	no	—
356	C₄×C₈	—	2	1	no	—
357	C₄×C₈	C₂³×C₄₁	1	2	yes	—
358	C₂⁴	—	2	1	no	—
359	C₂⁴	—	2	2	no	—
360	#41	—	4	8	no	—
361	#41	—	4	16	no	—
362	#41	—	4	8	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	4	1	no	—
367	C₂×Q₈	—	4	2	no	—
368	C₂×Q₈	—	4	2	no	—
369	C₂×Q₈	D₈×C₄₁	1	4	yes	—
370	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
371	C₂×D₄	—	2	8	no	—
372	C₂×D₄	—	2	8	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	4	8	no	—
382	C₂×D₄	—	4	4	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	—	4	2	no	—
386	C₂×D₄	—	4	2	no	—
387	C₂×D₄	—	8	4	no	—
388	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
389	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	8	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	4	8	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	—	4	1	no	—
400	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
403	Q₁₆	—	4	8	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	4	2	no	—
408	C₂×C₈	—	4	2	no	—
409	C₂×C₈	—	4	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	4	1	no	—
417	C₄⋊C₄	—	4	1	no	—
418	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
419	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
420	C₂²⋊C₄	—	2	8	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
426	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
427	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
428	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
429	C₂³	—	2	2	no	—
430	C₂³	—	2	4	no	—
431	C₂³	—	4	4	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	4	no	—
435	C₂³	—	4	4	no	—
436	C₂³	—	4	2	no	—
437	C₂³	#120×C₄₁	1	1	yes	characteristic
438	Q₈	—	2	2	no	—
439	Q₈	—	2	4	no	—
440	Q₈	—	4	2	no	—
441	Q₈	—	4	2	no	—
442	Q₈	—	8	2	no	—
443	Q₈	C₂×D₈×C₄₁	1	4	yes	—
444	D₄	—	2	2	no	—
445	D₄	—	2	2	no	—
446	D₄	—	4	4	no	—
447	D₄	—	4	16	no	—
448	D₄	—	4	2	no	—
449	D₄	—	4	2	no	—
450	D₄	—	4	2	no	—
451	D₄	—	4	2	no	—
452	D₄	—	4	4	no	—
453	D₄	—	4	2	no	—
454	D₄	—	4	4	no	—
455	D₄	—	8	2	no	—
456	D₄	—	8	8	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	4	16	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	8	2	no	—
470	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
471	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
472	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
473	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
474	C₂×C₄	#135×C₄₁	1	2	yes	—
475	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
476	C₂×C₄	#137×C₄₁	1	2	yes	—
477	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
478	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
479	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
480	C₈	—	4	2	no	—
481	C₈	—	4	2	no	—
482	C₈	—	4	2	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	8	4	no	—
490	C₂²	—	8	8	no	—
491	C₂²	C₄₁×#447	1	2	yes	—
492	C₂²	C₄₁×#452	1	2	yes	—
493	C₂²	C₄₁×#455	1	2	yes	—
494	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
495	C₄	—	2	4	no	—
496	C₄	—	2	1	no	—
497	C₄	—	2	1	no	—
498	C₄	—	4	2	no	—
499	C₄	—	4	2	no	—
500	C₄	—	8	2	no	—
501	C₄	C₄₁×#447	1	2	yes	—
502	C₄	C₄₁×#452	1	2	yes	—
503	C₄	C₂²×D₈×C₄₁	1	1	yes	characteristic
504	C₄	C₂×#135×C₄₁	1	1	yes	characteristic
505	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
506	C₄	C₂×#137×C₄₁	1	1	yes	characteristic
507	C₂	—	8	2	no	—
508	C₂	—	8	4	no	—
509	C₂	C₄₁×#1641	1	4	yes	direct product factor
510	C₂	C₂×C₄₁×#447	1	1	yes	characteristic
511	C₂	C₂×C₄₁×#452	1	1	yes	characteristic
512	C₂	C₂×C₄₁×#455	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#550	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#486	C₂	semidirect
3. C₂×C₄₁×#474	C₂	semidirect
4. C₂×C₄₁×#462	C₂	semidirect
5. C₄₁×#1641	C₂	direct (N × H)
6. C₂×C₄₁×#331	C₂	semidirect
7. C₂×C₄₁×Q₈⋊C₈	C₂	semidirect
8. C₂×C₄₁×D₄⋊C₈	C₂	semidirect
24. C₄₁×#486	C₂²	semidirect
26. C₄₁×#474	C₂²	semidirect
28. C₄₁×#462	C₂²	semidirect
36. C₄₁×#331	C₂²	semidirect
37. C₄₁×Q₈⋊C₈	C₂²	semidirect
38. C₄₁×D₄⋊C₈	C₂²	semidirect
226. C₂×#1641	C₄₁	direct (N × H)
252. C₂×#486	C₂×C₄₁	semidirect
253. C₂×#474	C₂×C₄₁	semidirect
254. C₂×#462	C₂×C₄₁	semidirect
255. #1641	C₂×C₄₁	direct (N × H)
256. C₂×#331	C₂×C₄₁	semidirect
257. C₂×Q₈⋊C₈	C₂×C₄₁	semidirect
258. C₂×D₄⋊C₈	C₂×C₄₁	semidirect
261. C₂×C₄₁	#1641	direct (N × H)
280. #486	C₂²×C₄₁	semidirect
282. #474	C₂²×C₄₁	semidirect
284. #462	C₂²×C₄₁	semidirect
292. #331	C₂²×C₄₁	semidirect
293. Q₈⋊C₈	C₂²×C₄₁	semidirect
294. D₄⋊C₈	C₂²×C₄₁	semidirect
295. C₄₁	C₂×#1641	direct (N × H)
509. C₂	C₄₁×#1641	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×#550	2
C₂×C₄₁×#486	2
C₂×C₄₁×#474	2
C₂×C₄₁×#462	2
C₄₁×#1641	2
C₂×C₄₁×#331	2
C₂×C₄₁×Q₈⋊C₈	2
C₂×C₄₁×D₄⋊C₈	2
C₂×#1641	41

Subgroups — C2×C41×#1641 #23794712

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#1641 #23794712