Subgroups — C₄₁×#18644 #23794845

Order 10496.

968 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3038	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1628	C₂	1	4	yes	maximal, complemented
6	C₄₁×#1626	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1546	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1493	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×AGL(1,ℤ/8)×C₄₁	—	2	1	no	—
11	C₄₁×#557	—	2	1	no	—
12	C₄₁×#557	C₂²	1	2	yes	complemented
13	C₄₁×#556	—	2	1	no	—
14	C₄₁×#556	C₂²	1	2	yes	complemented
15	C₄₁×#552	—	2	2	no	—
16	C₄₁×#552	—	2	2	no	—
17	C₄₁×#541	—	2	2	no	—
18	C₄₁×#536	—	2	1	no	—
19	C₄₁×#533	—	2	1	no	—
20	C₄₁×#533	—	2	1	no	—
21	C₄₁×#533	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
24	C₄₁×#519	—	2	1	no	—
25	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
26	C₄₁×#492	—	2	1	no	—
27	C₄₁×#486	—	2	2	no	—
28	C₄₁×#486	—	2	1	no	—
29	C₄₁×#486	C₂²	1	4	yes	—
30	C₄₁×#460	—	2	1	no	—
31	C₄₁×#460	C₂²	1	2	yes	—
32	C₄₁×#460	C₂²	1	4	yes	—
33	C₄₁×#459	—	2	1	no	—
34	C₄₁×#459	C₂²	1	2	yes	—
35	C₄₁×#450	—	2	2	no	—
36	C₄₁×#431	C₂²	1	1	yes	characteristic
37	C₄₁×#423	C₂²	1	1	yes	characteristic
38	C₄₁×#418	—	2	1	no	—
39	C₂×#102×C₄₁	—	2	2	no	—
40	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
41	C₄₁×#332	C₂²	1	4	yes	complemented
42	C₄₁×Q₈⋊C₈	C₂²	1	2	yes	complemented
43	C₄₁×Q₈⋊C₈	C₂²	1	4	yes	complemented
44	C₄₁×D₄⋊C₈	C₂²	1	2	yes	complemented
45	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₄₁	—	2	1	no	—
47	C₂²×D₄×C₄₁	—	2	1	no	—
48	C₂²×D₄×C₄₁	—	2	1	no	—
49	C₂²×D₄×C₄₁	—	2	1	no	—
50	AGL(1,ℤ/8)×C₄₁	—	4	4	no	—
51	C₂×SD₁₆×C₄₁	—	2	2	no	—
52	C₂×SD₁₆×C₄₁	—	2	4	no	—
53	C₂×D₈×C₄₁	—	2	2	no	—
54	C₂×M₁₆×C₄₁	—	2	1	no	—
55	C₂²×C₈×C₄₁	—	2	1	no	—
56	C₄⋊Q₈×C₄₁	—	2	2	no	—
57	C₄⋊Q₈×C₄₁	—	2	1	no	—
58	C₄⋊Q₈×C₄₁	—	2	1	no	—
59	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
60	C₄⋊Q₈×C₄₁	D₄	1	2	yes	—
61	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
62	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
63	#127×C₄₁	—	2	1	no	—
64	#127×C₄₁	—	2	1	no	—
65	#127×C₄₁	—	2	1	no	—
66	#127×C₄₁	C₂³	1	2	yes	—
67	#126×C₄₁	—	2	4	no	—
68	#126×C₄₁	—	2	4	no	—
69	#125×C₄₁	—	2	2	no	—
70	#125×C₄₁	—	2	4	no	—
71	#125×C₄₁	—	2	2	no	—
72	#125×C₄₁	—	2	4	no	—
73	#125×C₄₁	—	2	1	no	—
74	#124×C₄₁	—	2	2	no	—
75	#123×C₄₁	—	2	4	no	—
76	C₂²⋊Q₈×C₄₁	—	2	2	no	—
77	C₂²⋊Q₈×C₄₁	—	2	2	no	—
78	C₂²⋊Q₈×C₄₁	—	2	2	no	—
79	C₂²⋊Q₈×C₄₁	—	2	2	no	—
80	C₂²⋊Q₈×C₄₁	—	2	1	no	—
81	C₂²⋊Q₈×C₄₁	D₄	1	2	yes	—
82	C₄×Q₈×C₄₁	—	2	2	no	—
83	C₄×Q₈×C₄₁	—	2	2	no	—
84	C₄×Q₈×C₄₁	—	2	2	no	—
85	C₄×Q₈×C₄₁	—	2	2	no	—
86	C₄×Q₈×C₄₁	—	2	2	no	—
87	C₄×Q₈×C₄₁	—	2	2	no	—
88	C₄×Q₈×C₄₁	—	2	1	no	—
89	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
90	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
91	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
92	C₄×D₄×C₄₁	—	2	1	no	—
93	C₄×D₄×C₄₁	—	2	1	no	—
94	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
95	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
96	#117×C₄₁	—	2	4	no	—
97	#117×C₄₁	—	2	2	no	—
98	#117×C₄₁	—	2	1	no	—
99	#117×C₄₁	—	2	2	no	—
100	#117×C₄₁	—	2	1	no	—
101	#117×C₄₁	D₄	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
103	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
104	C₂×C₄²×C₄₁	—	2	1	no	—
105	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
106	C₄⋊C₈×C₄₁	—	2	1	no	—
107	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
108	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
109	#102×C₄₁	—	2	8	no	—
110	#102×C₄₁	—	2	2	no	—
111	#102×C₄₁	—	2	2	no	—
112	#102×C₄₁	—	2	4	no	—
113	C₂²⋊C₈×C₄₁	—	2	1	no	—
114	C₄×C₈×C₄₁	—	2	1	no	—
115	C₄×C₈×C₄₁	—	2	1	no	—
116	C₄×C₈×C₄₁	C₂³	1	2	yes	—
117	C₂⁴×C₄₁	—	4	1	no	—
118	#41×C₄₁	—	2	2	no	—
119	#41×C₄₁	—	2	2	no	—
120	C₂×Q₈×C₄₁	—	2	1	no	—
121	C₂×Q₈×C₄₁	—	2	2	no	—
122	C₂×Q₈×C₄₁	—	2	2	no	—
123	C₂×Q₈×C₄₁	—	4	2	no	—
124	C₂×Q₈×C₄₁	—	4	2	no	—
125	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
126	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
127	C₂×D₄×C₄₁	—	2	1	no	—
128	C₂×D₄×C₄₁	—	2	2	no	—
129	C₂×D₄×C₄₁	—	2	2	no	—
130	C₂×D₄×C₄₁	—	2	2	no	—
131	C₂×D₄×C₄₁	—	4	4	no	—
132	C₂×D₄×C₄₁	—	4	1	no	—
133	C₂×D₄×C₄₁	—	4	1	no	—
134	C₂×D₄×C₄₁	—	4	1	no	—
135	C₂×D₄×C₄₁	—	4	2	no	—
136	C₂×D₄×C₄₁	—	4	2	no	—
137	C₂×D₄×C₄₁	—	8	2	no	—
138	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₁	—	2	2	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	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	SD₁₆×C₄₁	—	4	4	no	—
147	SD₁₆×C₄₁	—	8	4	no	—
148	D₈×C₄₁	—	4	4	no	—
149	M₁₆×C₄₁	—	4	2	no	—
150	C₂×C₈×C₄₁	—	2	2	no	—
151	C₂×C₈×C₄₁	—	2	2	no	—
152	C₂×C₈×C₄₁	—	2	2	no	—
153	C₂×C₈×C₄₁	—	4	2	no	—
154	C₄⋊C₄×C₄₁	—	2	4	no	—
155	C₄⋊C₄×C₄₁	—	2	4	no	—
156	C₄⋊C₄×C₄₁	—	2	4	no	—
157	C₄⋊C₄×C₄₁	—	2	4	no	—
158	C₄⋊C₄×C₄₁	—	2	2	no	—
159	C₄⋊C₄×C₄₁	—	2	2	no	—
160	C₄⋊C₄×C₄₁	—	2	1	no	—
161	C₄⋊C₄×C₄₁	—	2	1	no	—
162	C₄⋊C₄×C₄₁	—	2	1	no	—
163	C₄⋊C₄×C₄₁	—	2	1	no	—
164	C₄⋊C₄×C₄₁	—	2	2	no	—
165	C₄⋊C₄×C₄₁	—	2	2	no	—
166	C₄⋊C₄×C₄₁	—	2	1	no	—
167	C₄⋊C₄×C₄₁	—	2	2	no	—
168	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
169	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
170	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
171	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
172	C₂²⋊C₄×C₄₁	—	2	4	no	—
173	C₂²⋊C₄×C₄₁	—	2	4	no	—
174	C₂²⋊C₄×C₄₁	—	2	1	no	—
175	C₂²⋊C₄×C₄₁	—	2	2	no	—
176	C₂²⋊C₄×C₄₁	—	2	1	no	—
177	C₂²⋊C₄×C₄₁	—	2	1	no	—
178	C₄²×C₄₁	—	2	4	no	—
179	C₄²×C₄₁	—	2	4	no	—
180	C₄²×C₄₁	—	2	1	no	—
181	C₄²×C₄₁	—	2	1	no	—
182	C₄²×C₄₁	—	2	1	no	—
183	C₄²×C₄₁	—	2	2	no	—
184	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
188	C₂³×C₄₁	—	2	1	no	—
189	C₂³×C₄₁	—	4	2	no	—
190	C₂³×C₄₁	—	8	2	no	—
191	C₂³×C₄₁	—	8	2	no	—
192	C₂³×C₄₁	—	8	2	no	—
193	C₂³×C₄₁	#120	1	1	yes	characteristic
194	Q₈×C₄₁	—	2	1	no	—
195	Q₈×C₄₁	—	2	1	no	—
196	Q₈×C₄₁	—	2	4	no	—
197	Q₈×C₄₁	—	4	2	no	—
198	Q₈×C₄₁	—	4	2	no	—
199	Q₈×C₄₁	—	4	4	no	—
200	Q₈×C₄₁	—	4	2	no	—
201	D₄×C₄₁	—	2	1	no	—
202	D₄×C₄₁	—	2	1	no	—
203	D₄×C₄₁	—	4	4	no	—
204	D₄×C₄₁	—	4	2	no	—
205	D₄×C₄₁	—	4	2	no	—
206	D₄×C₄₁	—	4	2	no	—
207	D₄×C₄₁	—	4	4	no	—
208	D₄×C₄₁	—	8	2	no	—
209	D₄×C₄₁	—	8	2	no	—
210	D₄×C₄₁	—	8	2	no	—
211	C₂×C₄×C₄₁	—	2	2	no	—
212	C₂×C₄×C₄₁	—	2	2	no	—
213	C₂×C₄×C₄₁	—	2	1	no	—
214	C₂×C₄×C₄₁	—	2	1	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	1	no	—
219	C₂×C₄×C₄₁	—	4	4	no	—
220	C₂×C₄×C₄₁	—	4	2	no	—
221	C₂×C₄×C₄₁	—	4	2	no	—
222	C₂×C₄×C₄₁	—	4	2	no	—
223	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
224	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
225	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
226	C₂×C₄×C₄₁	#135	1	2	yes	—
227	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
228	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
231	C₈×C₄₁	—	4	2	no	—
232	C₈×C₄₁	—	4	2	no	—
233	C₈×C₄₁	—	4	2	no	—
234	#18644	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂²×C₄₁	—	2	1	no	—
236	C₂²×C₄₁	—	2	1	no	—
237	C₂²×C₄₁	—	4	1	no	—
238	C₂²×C₄₁	—	4	1	no	—
239	C₂²×C₄₁	—	4	1	no	—
240	C₂²×C₄₁	—	8	2	no	—
241	C₂²×C₄₁	—	8	2	no	—
242	C₂²×C₄₁	—	8	2	no	—
243	C₂²×C₄₁	—	16	4	no	—
244	C₂²×C₄₁	#449	1	2	yes	—
245	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
246	C₄×C₄₁	—	2	1	no	—
247	C₄×C₄₁	—	2	1	no	—
248	C₄×C₄₁	—	4	1	no	—
249	C₄×C₄₁	—	4	4	no	—
250	C₄×C₄₁	—	4	1	no	—
251	C₄×C₄₁	—	4	2	no	—
252	C₄×C₄₁	—	4	1	no	—
253	C₄×C₄₁	—	4	2	no	—
254	C₄×C₄₁	#449	1	2	yes	—
255	C₄×C₄₁	#454	1	2	yes	—
256	C₄×C₄₁	C₂×#135	1	1	yes	characteristic
257	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
258	C₄×C₄₁	#577	1	2	yes	—
259	#3509	C₂×C₄₁	1	1	yes	characteristic, complemented
260	#3208	C₂×C₄₁	1	1	yes	characteristic, complemented
261	C₂×#486	C₂×C₄₁	1	1	yes	characteristic, complemented
262	#3038	C₂×C₄₁	1	1	yes	characteristic
263	#1628	C₂×C₄₁	1	4	yes	complemented
264	#1626	C₂×C₄₁	1	4	yes	complemented
265	#1546	C₂×C₄₁	1	1	yes	characteristic, complemented
266	#1493	C₂×C₄₁	1	1	yes	characteristic, complemented
267	#1476	C₂×C₄₁	1	1	yes	characteristic, complemented
268	C₂×C₄₁	—	2	2	no	—
269	C₂×C₄₁	—	8	1	no	—
270	C₂×C₄₁	—	16	2	no	—
271	C₂×C₄₁	C₂×#449	1	1	yes	characteristic
272	C₂×C₄₁	#3010	1	1	yes	characteristic
273	C₂×C₄₁	C₂×#454	1	1	yes	characteristic
274	C₂×AGL(1,ℤ/8)	—	2	1	no	—
275	#557	—	2	1	no	—
276	#557	C₂²×C₄₁	1	2	yes	complemented
277	#556	—	2	1	no	—
278	#556	C₂²×C₄₁	1	2	yes	complemented
279	#552	—	2	2	no	—
280	#552	—	2	2	no	—
281	#541	—	2	2	no	—
282	#536	—	2	1	no	—
283	#533	—	2	1	no	—
284	#533	—	2	1	no	—
285	#533	C₂²×C₄₁	1	1	yes	characteristic
286	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
287	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
288	#519	—	2	1	no	—
289	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
290	#492	—	2	1	no	—
291	#486	—	2	2	no	—
292	#486	—	2	1	no	—
293	#486	C₂²×C₄₁	1	4	yes	—
294	#460	—	2	1	no	—
295	#460	C₂²×C₄₁	1	2	yes	—
296	#460	C₂²×C₄₁	1	4	yes	—
297	#459	—	2	1	no	—
298	#459	C₂²×C₄₁	1	2	yes	—
299	#450	—	2	2	no	—
300	#431	C₂²×C₄₁	1	1	yes	characteristic
301	#423	C₂²×C₄₁	1	1	yes	characteristic
302	#418	—	2	1	no	—
303	C₂×#102	—	2	2	no	—
304	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
305	#332	C₂²×C₄₁	1	4	yes	complemented
306	Q₈⋊C₈	C₂²×C₄₁	1	2	yes	complemented
307	Q₈⋊C₈	C₂²×C₄₁	1	4	yes	complemented
308	D₄⋊C₈	C₂²×C₄₁	1	2	yes	complemented
309	C₄₁	#18644	1	1	yes	characteristic, direct product factor, Sylow
310	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
311	C₂²×Q₈	—	2	1	no	—
312	C₂²×D₄	—	2	1	no	—
313	C₂²×D₄	—	2	1	no	—
314	C₂²×D₄	—	2	1	no	—
315	AGL(1,ℤ/8)	—	4	4	no	—
316	C₂×SD₁₆	—	2	2	no	—
317	C₂×SD₁₆	—	2	4	no	—
318	C₂×D₈	—	2	2	no	—
319	C₂×M₁₆	—	2	1	no	—
320	C₂²×C₈	—	2	1	no	—
321	C₄⋊Q₈	—	2	2	no	—
322	C₄⋊Q₈	—	2	1	no	—
323	C₄⋊Q₈	—	2	1	no	—
324	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
325	C₄⋊Q₈	D₄×C₄₁	1	2	yes	—
326	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
327	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
328	#127	—	2	1	no	—
329	#127	—	2	1	no	—
330	#127	—	2	1	no	—
331	#127	C₂³×C₄₁	1	2	yes	—
332	#126	—	2	4	no	—
333	#126	—	2	4	no	—
334	#125	—	2	2	no	—
335	#125	—	2	4	no	—
336	#125	—	2	2	no	—
337	#125	—	2	4	no	—
338	#125	—	2	1	no	—
339	#124	—	2	2	no	—
340	#123	—	2	4	no	—
341	C₂²⋊Q₈	—	2	2	no	—
342	C₂²⋊Q₈	—	2	2	no	—
343	C₂²⋊Q₈	—	2	2	no	—
344	C₂²⋊Q₈	—	2	2	no	—
345	C₂²⋊Q₈	—	2	1	no	—
346	C₂²⋊Q₈	D₄×C₄₁	1	2	yes	—
347	C₄×Q₈	—	2	2	no	—
348	C₄×Q₈	—	2	2	no	—
349	C₄×Q₈	—	2	2	no	—
350	C₄×Q₈	—	2	2	no	—
351	C₄×Q₈	—	2	2	no	—
352	C₄×Q₈	—	2	2	no	—
353	C₄×Q₈	—	2	1	no	—
354	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
355	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
356	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
357	C₄×D₄	—	2	1	no	—
358	C₄×D₄	—	2	1	no	—
359	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
360	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
361	#117	—	2	4	no	—
362	#117	—	2	2	no	—
363	#117	—	2	1	no	—
364	#117	—	2	2	no	—
365	#117	—	2	1	no	—
366	#117	D₄×C₄₁	1	1	yes	characteristic
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
371	C₄⋊C₈	—	2	1	no	—
372	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
373	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
374	#102	—	2	8	no	—
375	#102	—	2	2	no	—
376	#102	—	2	2	no	—
377	#102	—	2	4	no	—
378	C₂²⋊C₈	—	2	1	no	—
379	C₄×C₈	—	2	1	no	—
380	C₄×C₈	—	2	1	no	—
381	C₄×C₈	C₂³×C₄₁	1	2	yes	—
382	C₂⁴	—	4	1	no	—
383	#41	—	2	2	no	—
384	#41	—	2	2	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	4	2	no	—
389	C₂×Q₈	—	4	2	no	—
390	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
391	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	4	4	no	—
397	C₂×D₄	—	4	1	no	—
398	C₂×D₄	—	4	1	no	—
399	C₂×D₄	—	4	1	no	—
400	C₂×D₄	—	4	2	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	—	8	2	no	—
403	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
411	SD₁₆	—	4	4	no	—
412	SD₁₆	—	8	4	no	—
413	D₈	—	4	4	no	—
414	M₁₆	—	4	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	4	2	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
434	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
435	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
436	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
437	C₂²⋊C₄	—	2	4	no	—
438	C₂²⋊C₄	—	2	4	no	—
439	C₂²⋊C₄	—	2	1	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	1	no	—
442	C₂²⋊C₄	—	2	1	no	—
443	C₄²	—	2	4	no	—
444	C₄²	—	2	4	no	—
445	C₄²	—	2	1	no	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	2	no	—
449	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
450	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
451	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
452	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
453	C₂³	—	2	1	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	8	2	no	—
456	C₂³	—	8	2	no	—
457	C₂³	—	8	2	no	—
458	C₂³	#120×C₄₁	1	1	yes	characteristic
459	Q₈	—	2	1	no	—
460	Q₈	—	2	1	no	—
461	Q₈	—	2	4	no	—
462	Q₈	—	4	2	no	—
463	Q₈	—	4	2	no	—
464	Q₈	—	4	4	no	—
465	Q₈	—	4	2	no	—
466	D₄	—	2	1	no	—
467	D₄	—	2	1	no	—
468	D₄	—	4	4	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	2	no	—
472	D₄	—	4	4	no	—
473	D₄	—	8	2	no	—
474	D₄	—	8	2	no	—
475	D₄	—	8	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
489	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
490	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
491	C₂×C₄	#135×C₄₁	1	2	yes	—
492	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
493	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
494	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
495	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
496	C₈	—	4	2	no	—
497	C₈	—	4	2	no	—
498	C₈	—	4	2	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	4	1	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	8	2	no	—
505	C₂²	—	8	2	no	—
506	C₂²	—	8	2	no	—
507	C₂²	—	16	4	no	—
508	C₂²	C₄₁×#449	1	2	yes	—
509	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
510	C₄	—	2	1	no	—
511	C₄	—	2	1	no	—
512	C₄	—	4	1	no	—
513	C₄	—	4	4	no	—
514	C₄	—	4	1	no	—
515	C₄	—	4	2	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	2	no	—
518	C₄	C₄₁×#449	1	2	yes	—
519	C₄	C₄₁×#454	1	2	yes	—
520	C₄	C₂×#135×C₄₁	1	1	yes	characteristic
521	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
522	C₄	C₄₁×#577	1	2	yes	—
523	C₂	—	2	2	no	—
524	C₂	—	8	1	no	—
525	C₂	—	16	2	no	—
526	C₂	C₂×C₄₁×#449	1	1	yes	characteristic
527	C₂	C₄₁×#3010	1	1	yes	characteristic
528	C₂	C₂×C₄₁×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
prime radical	C₄₁×#3038	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3509	C₂	semidirect
2. C₄₁×#3208	C₂	semidirect
3. C₂×C₄₁×#486	C₂	semidirect
5. C₄₁×#1628	C₂	semidirect
6. C₄₁×#1626	C₂	semidirect
7. C₄₁×#1546	C₂	semidirect
8. C₄₁×#1493	C₂	semidirect
9. C₄₁×#1476	C₂	semidirect
12. C₄₁×#557	C₂²	semidirect
14. C₄₁×#556	C₂²	semidirect
41. C₄₁×#332	C₂²	semidirect
42. C₄₁×Q₈⋊C₈	C₂²	semidirect
43. C₄₁×Q₈⋊C₈	C₂²	semidirect
44. C₄₁×D₄⋊C₈	C₂²	semidirect
234. #18644	C₄₁	direct (N × H)
259. #3509	C₂×C₄₁	semidirect
260. #3208	C₂×C₄₁	semidirect
261. C₂×#486	C₂×C₄₁	semidirect
263. #1628	C₂×C₄₁	semidirect
264. #1626	C₂×C₄₁	semidirect
265. #1546	C₂×C₄₁	semidirect
266. #1493	C₂×C₄₁	semidirect
267. #1476	C₂×C₄₁	semidirect
276. #557	C₂²×C₄₁	semidirect
278. #556	C₂²×C₄₁	semidirect
305. #332	C₂²×C₄₁	semidirect
306. Q₈⋊C₈	C₂²×C₄₁	semidirect
307. Q₈⋊C₈	C₂²×C₄₁	semidirect
308. D₄⋊C₈	C₂²×C₄₁	semidirect
309. C₄₁	#18644	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×#3509	2
C₄₁×#3208	2
C₂×C₄₁×#486	2
C₄₁×#3038	2
C₄₁×#1628	2
C₄₁×#1626	2
C₄₁×#1546	2
C₄₁×#1493	2
C₄₁×#1476	2
#18644	41

Subgroups — C41×#18644 #23794845

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#18644 #23794845