Subgroups — C₄₁×#18631 #23794832

Order 10496.

1262 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3498	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#3206	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3079	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1642	C₂	1	4	yes	maximal, complemented
6	C₄₁×#1639	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1545	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1492	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×H(5,𝔽₂)×C₄₁	—	2	1	no	—
11	C₄₁×#550	—	2	1	no	—
12	C₄₁×#550	C₂²	1	2	yes	—
13	D₄²×C₄₁	—	2	2	no	—
14	D₄²×C₄₁	—	2	2	no	—
15	D₄²×C₄₁	—	2	1	no	—
16	D₄²×C₄₁	C₂²	1	2	yes	—
17	C₄₁×#535	—	2	2	no	—
18	C₄₁×#535	—	2	1	no	—
19	C₄₁×#532	—	2	1	no	—
20	C₄₁×#532	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
22	C₂×#127×C₄₁	—	2	1	no	—
23	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
24	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
25	C₄₁×#492	—	2	1	no	—
26	C₄₁×#487	—	2	1	no	—
27	C₄₁×#486	—	2	2	no	—
28	C₄₁×#486	C₂²	1	4	yes	complemented
29	C₄₁×#477	—	2	1	no	—
30	C₄₁×#476	—	2	1	no	—
31	C₄₁×#475	C₂²	1	2	yes	complemented
32	C₄₁×#474	C₂²	1	2	yes	complemented
33	C₄₁×#461	C₂²	1	4	yes	complemented
34	C₄₁×#448	—	2	2	no	—
35	C₄₁×#431	C₂²	1	1	yes	characteristic, complemented
36	C₄₁×#428	—	2	1	no	—
37	C₄₁×#423	C₂²	1	1	yes	characteristic, complemented
38	C₄₁×#417	—	2	1	no	—
39	C₂×#102×C₄₁	—	2	2	no	—
40	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
41	C₄₁×#331	C₂²	1	4	yes	complemented
42	C₄₁×Q₈⋊C₈	C₂²	1	2	yes	complemented
43	C₄₁×D₄⋊C₈	C₂²	1	2	yes	complemented
44	C₄₁×D₄⋊C₈	C₂²	1	4	yes	complemented
45	H(5,𝔽₂)×C₄₁	—	4	4	no	—
46	H(5,𝔽₂)×C₄₁	—	4	4	no	—
47	C₂×#41×C₄₁	—	2	2	no	—
48	C₂×#41×C₄₁	—	2	2	no	—
49	C₂×#41×C₄₁	—	2	1	no	—
50	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
51	C₂²×Q₈×C₄₁	—	2	1	no	—
52	C₂²×D₄×C₄₁	—	2	2	no	—
53	C₂²×D₄×C₄₁	—	2	4	no	—
54	C₂²×D₄×C₄₁	—	2	2	no	—
55	C₂²×D₄×C₄₁	—	2	2	no	—
56	C₂²×D₄×C₄₁	—	2	2	no	—
57	C₂²×D₄×C₄₁	—	2	1	no	—
58	C₂²×D₄×C₄₁	—	2	1	no	—
59	C₂²×D₄×C₄₁	D₄	1	2	yes	—
60	C₂×SD₁₆×C₄₁	—	2	4	no	—
61	C₂×M₁₆×C₄₁	—	2	1	no	—
62	C₂²×C₈×C₄₁	—	2	1	no	—
63	C₄⋊Q₈×C₄₁	—	2	1	no	—
64	C₄⋊Q₈×C₄₁	—	2	1	no	—
65	C₄⋊Q₈×C₄₁	—	2	1	no	—
66	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
67	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
68	#127×C₄₁	—	2	2	no	—
69	#127×C₄₁	—	2	2	no	—
70	#127×C₄₁	—	2	2	no	—
71	#127×C₄₁	—	2	1	no	—
72	#127×C₄₁	—	2	1	no	—
73	#127×C₄₁	D₄	1	1	yes	characteristic
74	#127×C₄₁	D₄	1	2	yes	—
75	#127×C₄₁	C₂³	1	2	yes	—
76	#124×C₄₁	—	2	2	no	—
77	#124×C₄₁	—	2	1	no	—
78	#121×C₄₁	—	2	2	no	—
79	#121×C₄₁	—	2	4	no	—
80	#121×C₄₁	—	2	4	no	—
81	#121×C₄₁	—	2	1	no	—
82	#121×C₄₁	—	2	2	no	—
83	#121×C₄₁	—	2	2	no	—
84	#121×C₄₁	—	2	2	no	—
85	#121×C₄₁	D₄	1	2	yes	—
86	#120×C₄₁	—	2	4	no	—
87	#120×C₄₁	—	2	4	no	—
88	#120×C₄₁	—	2	4	no	—
89	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
90	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
91	C₄×D₄×C₄₁	—	2	2	no	—
92	C₄×D₄×C₄₁	—	2	1	no	—
93	C₄×D₄×C₄₁	—	2	1	no	—
94	C₄×D₄×C₄₁	—	2	2	no	—
95	C₄×D₄×C₄₁	—	2	1	no	—
96	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
97	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
98	C₄×D₄×C₄₁	C₂³	1	2	yes	—
99	#117×C₄₁	—	2	1	no	—
100	#117×C₄₁	D₄	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
102	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
103	C₂×C₄²×C₄₁	—	2	1	no	—
104	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
105	#107×C₄₁	—	2	2	no	—
106	#106×C₄₁	—	2	2	no	—
107	C₄⋊C₈×C₄₁	—	2	1	no	—
108	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
109	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
110	#103×C₄₁	—	2	2	no	—
111	#103×C₄₁	—	2	4	no	—
112	#102×C₄₁	—	2	8	no	—
113	#102×C₄₁	—	2	2	no	—
114	C₂²⋊C₈×C₄₁	—	2	1	no	—
115	C₄×C₈×C₄₁	—	2	1	no	—
116	C₄×C₈×C₄₁	—	2	1	no	—
117	C₄×C₈×C₄₁	C₂³	1	2	yes	—
118	C₂⁴×C₄₁	—	2	4	no	—
119	C₂⁴×C₄₁	—	2	2	no	—
120	#41×C₄₁	—	2	2	no	—
121	#41×C₄₁	—	4	8	no	—
122	#41×C₄₁	—	4	4	no	—
123	#41×C₄₁	—	4	4	no	—
124	#41×C₄₁	—	4	2	no	—
125	#41×C₄₁	—	4	2	no	—
126	#41×C₄₁	SD₁₆	1	4	yes	complemented
127	C₂×Q₈×C₄₁	—	2	1	no	—
128	C₂×Q₈×C₄₁	—	2	2	no	—
129	C₂×Q₈×C₄₁	—	4	1	no	—
130	C₂×Q₈×C₄₁	—	8	2	no	—
131	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
132	C₂×D₄×C₄₁	—	2	1	no	—
133	C₂×D₄×C₄₁	—	2	4	no	—
134	C₂×D₄×C₄₁	—	2	4	no	—
135	C₂×D₄×C₄₁	—	2	2	no	—
136	C₂×D₄×C₄₁	—	2	4	no	—
137	C₂×D₄×C₄₁	—	2	4	no	—
138	C₂×D₄×C₄₁	—	2	2	no	—
139	C₂×D₄×C₄₁	—	2	1	no	—
140	C₂×D₄×C₄₁	—	2	2	no	—
141	C₂×D₄×C₄₁	—	2	1	no	—
142	C₂×D₄×C₄₁	—	2	2	no	—
143	C₂×D₄×C₄₁	—	2	2	no	—
144	C₂×D₄×C₄₁	—	2	2	no	—
145	C₂×D₄×C₄₁	—	4	8	no	—
146	C₂×D₄×C₄₁	—	4	4	no	—
147	C₂×D₄×C₄₁	—	4	16	no	—
148	C₂×D₄×C₄₁	—	4	4	no	—
149	C₂×D₄×C₄₁	—	4	4	no	—
150	C₂×D₄×C₄₁	—	4	2	no	—
151	C₂×D₄×C₄₁	—	4	2	no	—
152	C₂×D₄×C₄₁	—	8	2	no	—
153	C₂×D₄×C₄₁	—	8	4	no	—
154	C₂×D₄×C₄₁	—	8	4	no	—
155	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
156	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
157	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₄₁	—	2	1	no	—
159	C₂²×C₄×C₄₁	—	2	4	no	—
160	C₂²×C₄×C₄₁	—	2	1	no	—
161	C₂²×C₄×C₄₁	—	2	1	no	—
162	C₂²×C₄×C₄₁	—	2	2	no	—
163	C₂²×C₄×C₄₁	—	4	1	no	—
164	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
167	SD₁₆×C₄₁	—	8	4	no	—
168	M₁₆×C₄₁	—	4	2	no	—
169	C₂×C₈×C₄₁	—	2	2	no	—
170	C₂×C₈×C₄₁	—	2	2	no	—
171	C₂×C₈×C₄₁	—	2	2	no	—
172	C₂×C₈×C₄₁	—	4	2	no	—
173	C₄⋊C₄×C₄₁	—	2	1	no	—
174	C₄⋊C₄×C₄₁	—	2	1	no	—
175	C₄⋊C₄×C₄₁	—	2	1	no	—
176	C₄⋊C₄×C₄₁	—	2	2	no	—
177	C₄⋊C₄×C₄₁	—	2	2	no	—
178	C₄⋊C₄×C₄₁	—	4	1	no	—
179	C₄⋊C₄×C₄₁	—	4	1	no	—
180	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
181	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
182	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
183	C₂²⋊C₄×C₄₁	—	2	4	no	—
184	C₂²⋊C₄×C₄₁	—	2	4	no	—
185	C₂²⋊C₄×C₄₁	—	2	1	no	—
186	C₂²⋊C₄×C₄₁	—	2	1	no	—
187	C₂²⋊C₄×C₄₁	—	2	2	no	—
188	C₂²⋊C₄×C₄₁	—	2	1	no	—
189	C₂²⋊C₄×C₄₁	—	2	2	no	—
190	C₄²×C₄₁	—	2	1	no	—
191	C₄²×C₄₁	—	2	1	no	—
192	C₄²×C₄₁	—	2	1	no	—
193	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
197	C₂³×C₄₁	—	2	1	no	—
198	C₂³×C₄₁	—	2	2	no	—
199	C₂³×C₄₁	—	2	4	no	—
200	C₂³×C₄₁	—	4	8	no	—
201	C₂³×C₄₁	—	4	4	no	—
202	C₂³×C₄₁	—	8	2	no	—
203	C₂³×C₄₁	—	8	2	no	—
204	C₂³×C₄₁	—	8	4	no	—
205	C₂³×C₄₁	—	8	4	no	—
206	C₂³×C₄₁	#120	1	1	yes	characteristic
207	Q₈×C₄₁	—	2	1	no	—
208	Q₈×C₄₁	—	4	2	no	—
209	Q₈×C₄₁	—	4	4	no	—
210	Q₈×C₄₁	—	8	2	no	—
211	Q₈×C₄₁	C₂×SD₁₆	1	2	yes	—
212	D₄×C₄₁	—	2	4	no	—
213	D₄×C₄₁	—	2	1	no	—
214	D₄×C₄₁	—	2	4	no	—
215	D₄×C₄₁	—	4	4	no	—
216	D₄×C₄₁	—	4	8	no	—
217	D₄×C₄₁	—	4	8	no	—
218	D₄×C₄₁	—	4	4	no	—
219	D₄×C₄₁	—	4	2	no	—
220	D₄×C₄₁	—	4	2	no	—
221	D₄×C₄₁	—	4	4	no	—
222	D₄×C₄₁	—	4	2	no	—
223	D₄×C₄₁	—	4	4	no	—
224	D₄×C₄₁	—	4	4	no	—
225	D₄×C₄₁	—	4	2	no	—
226	D₄×C₄₁	—	8	2	no	—
227	D₄×C₄₁	—	8	4	no	—
228	D₄×C₄₁	—	8	4	no	—
229	D₄×C₄₁	C₂×SD₁₆	1	2	yes	—
230	C₂×C₄×C₄₁	—	2	1	no	—
231	C₂×C₄×C₄₁	—	2	2	no	—
232	C₂×C₄×C₄₁	—	2	4	no	—
233	C₂×C₄×C₄₁	—	2	2	no	—
234	C₂×C₄×C₄₁	—	2	1	no	—
235	C₂×C₄×C₄₁	—	2	1	no	—
236	C₂×C₄×C₄₁	—	2	2	no	—
237	C₂×C₄×C₄₁	—	4	8	no	—
238	C₂×C₄×C₄₁	—	4	2	no	—
239	C₂×C₄×C₄₁	—	4	2	no	—
240	C₂×C₄×C₄₁	—	4	2	no	—
241	C₂×C₄×C₄₁	—	4	2	no	—
242	C₂×C₄×C₄₁	—	4	2	no	—
243	C₂×C₄×C₄₁	—	8	2	no	—
244	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
245	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
246	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
247	C₂×C₄×C₄₁	C₂×SD₁₆	1	2	yes	—
248	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
249	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
252	C₈×C₄₁	—	4	2	no	—
253	C₈×C₄₁	—	4	2	no	—
254	C₈×C₄₁	—	4	2	no	—
255	#18631	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂²×C₄₁	—	2	1	no	—
257	C₂²×C₄₁	—	2	1	no	—
258	C₂²×C₄₁	—	2	2	no	—
259	C₂²×C₄₁	—	4	1	no	—
260	C₂²×C₄₁	—	4	1	no	—
261	C₂²×C₄₁	—	4	4	no	—
262	C₂²×C₄₁	—	4	2	no	—
263	C₂²×C₄₁	—	4	2	no	—
264	C₂²×C₄₁	—	4	4	no	—
265	C₂²×C₄₁	—	4	4	no	—
266	C₂²×C₄₁	—	4	2	no	—
267	C₂²×C₄₁	—	16	4	no	—
268	C₂²×C₄₁	—	16	8	no	—
269	C₂²×C₄₁	#450	1	2	yes	—
270	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
271	C₄×C₄₁	—	2	2	no	—
272	C₄×C₄₁	—	2	1	no	—
273	C₄×C₄₁	—	2	1	no	—
274	C₄×C₄₁	—	4	2	no	—
275	C₄×C₄₁	—	4	1	no	—
276	C₄×C₄₁	—	4	1	no	—
277	C₄×C₄₁	—	8	2	no	—
278	C₄×C₄₁	#450	1	2	yes	—
279	C₄×C₄₁	#455	1	2	yes	—
280	C₄×C₄₁	C₂²×SD₁₆	1	1	yes	characteristic
281	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
282	C₄×C₄₁	#576	1	2	yes	—
283	#3498	C₂×C₄₁	1	1	yes	characteristic
284	#3206	C₂×C₄₁	1	1	yes	characteristic, complemented
285	C₂×#486	C₂×C₄₁	1	1	yes	characteristic, complemented
286	#3079	C₂×C₄₁	1	1	yes	characteristic, complemented
287	#1642	C₂×C₄₁	1	4	yes	complemented
288	#1639	C₂×C₄₁	1	4	yes	complemented
289	#1545	C₂×C₄₁	1	1	yes	characteristic, complemented
290	#1492	C₂×C₄₁	1	1	yes	characteristic, complemented
291	#1476	C₂×C₄₁	1	1	yes	characteristic, complemented
292	C₂×C₄₁	—	2	2	no	—
293	C₂×C₄₁	—	4	2	no	—
294	C₂×C₄₁	—	8	2	no	—
295	C₂×C₄₁	—	8	4	no	—
296	C₂×C₄₁	C₂×#450	1	1	yes	characteristic
297	C₂×C₄₁	#3008	1	1	yes	characteristic
298	C₂×C₄₁	C₂×#455	1	1	yes	characteristic
299	C₂×H(5,𝔽₂)	—	2	1	no	—
300	#550	—	2	1	no	—
301	#550	C₂²×C₄₁	1	2	yes	—
302	D₄²	—	2	2	no	—
303	D₄²	—	2	2	no	—
304	D₄²	—	2	1	no	—
305	D₄²	C₂²×C₄₁	1	2	yes	—
306	#535	—	2	2	no	—
307	#535	—	2	1	no	—
308	#532	—	2	1	no	—
309	#532	C₂²×C₄₁	1	1	yes	characteristic
310	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
311	C₂×#127	—	2	1	no	—
312	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
313	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
314	#492	—	2	1	no	—
315	#487	—	2	1	no	—
316	#486	—	2	2	no	—
317	#486	C₂²×C₄₁	1	4	yes	complemented
318	#477	—	2	1	no	—
319	#476	—	2	1	no	—
320	#475	C₂²×C₄₁	1	2	yes	complemented
321	#474	C₂²×C₄₁	1	2	yes	complemented
322	#461	C₂²×C₄₁	1	4	yes	complemented
323	#448	—	2	2	no	—
324	#431	C₂²×C₄₁	1	1	yes	characteristic, complemented
325	#428	—	2	1	no	—
326	#423	C₂²×C₄₁	1	1	yes	characteristic, complemented
327	#417	—	2	1	no	—
328	C₂×#102	—	2	2	no	—
329	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
330	#331	C₂²×C₄₁	1	4	yes	complemented
331	Q₈⋊C₈	C₂²×C₄₁	1	2	yes	complemented
332	D₄⋊C₈	C₂²×C₄₁	1	2	yes	complemented
333	D₄⋊C₈	C₂²×C₄₁	1	4	yes	complemented
334	C₄₁	#18631	1	1	yes	characteristic, direct product factor, Sylow
335	H(5,𝔽₂)	—	4	4	no	—
336	H(5,𝔽₂)	—	4	4	no	—
337	C₂×#41	—	2	2	no	—
338	C₂×#41	—	2	2	no	—
339	C₂×#41	—	2	1	no	—
340	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
341	C₂²×Q₈	—	2	1	no	—
342	C₂²×D₄	—	2	2	no	—
343	C₂²×D₄	—	2	4	no	—
344	C₂²×D₄	—	2	2	no	—
345	C₂²×D₄	—	2	2	no	—
346	C₂²×D₄	—	2	2	no	—
347	C₂²×D₄	—	2	1	no	—
348	C₂²×D₄	—	2	1	no	—
349	C₂²×D₄	D₄×C₄₁	1	2	yes	—
350	C₂×SD₁₆	—	2	4	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₂²×C₈	—	2	1	no	—
353	C₄⋊Q₈	—	2	1	no	—
354	C₄⋊Q₈	—	2	1	no	—
355	C₄⋊Q₈	—	2	1	no	—
356	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
357	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
358	#127	—	2	2	no	—
359	#127	—	2	2	no	—
360	#127	—	2	2	no	—
361	#127	—	2	1	no	—
362	#127	—	2	1	no	—
363	#127	D₄×C₄₁	1	1	yes	characteristic
364	#127	D₄×C₄₁	1	2	yes	—
365	#127	C₂³×C₄₁	1	2	yes	—
366	#124	—	2	2	no	—
367	#124	—	2	1	no	—
368	#121	—	2	2	no	—
369	#121	—	2	4	no	—
370	#121	—	2	4	no	—
371	#121	—	2	1	no	—
372	#121	—	2	2	no	—
373	#121	—	2	2	no	—
374	#121	—	2	2	no	—
375	#121	D₄×C₄₁	1	2	yes	—
376	#120	—	2	4	no	—
377	#120	—	2	4	no	—
378	#120	—	2	4	no	—
379	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
380	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
381	C₄×D₄	—	2	2	no	—
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	—	2	1	no	—
384	C₄×D₄	—	2	2	no	—
385	C₄×D₄	—	2	1	no	—
386	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
387	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
388	C₄×D₄	C₂³×C₄₁	1	2	yes	—
389	#117	—	2	1	no	—
390	#117	D₄×C₄₁	1	1	yes	characteristic
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄²	—	2	1	no	—
394	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
395	#107	—	2	2	no	—
396	#106	—	2	2	no	—
397	C₄⋊C₈	—	2	1	no	—
398	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
399	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
400	#103	—	2	2	no	—
401	#103	—	2	4	no	—
402	#102	—	2	8	no	—
403	#102	—	2	2	no	—
404	C₂²⋊C₈	—	2	1	no	—
405	C₄×C₈	—	2	1	no	—
406	C₄×C₈	—	2	1	no	—
407	C₄×C₈	C₂³×C₄₁	1	2	yes	—
408	C₂⁴	—	2	4	no	—
409	C₂⁴	—	2	2	no	—
410	#41	—	2	2	no	—
411	#41	—	4	8	no	—
412	#41	—	4	4	no	—
413	#41	—	4	4	no	—
414	#41	—	4	2	no	—
415	#41	—	4	2	no	—
416	#41	SD₁₆×C₄₁	1	4	yes	complemented
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	4	1	no	—
420	C₂×Q₈	—	8	2	no	—
421	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	4	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	4	8	no	—
436	C₂×D₄	—	4	4	no	—
437	C₂×D₄	—	4	16	no	—
438	C₂×D₄	—	4	4	no	—
439	C₂×D₄	—	4	4	no	—
440	C₂×D₄	—	4	2	no	—
441	C₂×D₄	—	4	2	no	—
442	C₂×D₄	—	8	2	no	—
443	C₂×D₄	—	8	4	no	—
444	C₂×D₄	—	8	4	no	—
445	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
446	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
447	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	4	1	no	—
454	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
457	SD₁₆	—	8	4	no	—
458	M₁₆	—	4	2	no	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	4	2	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	4	1	no	—
469	C₄⋊C₄	—	4	1	no	—
470	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
471	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
472	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
473	C₂²⋊C₄	—	2	4	no	—
474	C₂²⋊C₄	—	2	4	no	—
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	2	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	2	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
484	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
485	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
486	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
487	C₂³	—	2	1	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	4	8	no	—
491	C₂³	—	4	4	no	—
492	C₂³	—	8	2	no	—
493	C₂³	—	8	2	no	—
494	C₂³	—	8	4	no	—
495	C₂³	—	8	4	no	—
496	C₂³	#120×C₄₁	1	1	yes	characteristic
497	Q₈	—	2	1	no	—
498	Q₈	—	4	2	no	—
499	Q₈	—	4	4	no	—
500	Q₈	—	8	2	no	—
501	Q₈	C₂×SD₁₆×C₄₁	1	2	yes	—
502	D₄	—	2	4	no	—
503	D₄	—	2	1	no	—
504	D₄	—	2	4	no	—
505	D₄	—	4	4	no	—
506	D₄	—	4	8	no	—
507	D₄	—	4	8	no	—
508	D₄	—	4	4	no	—
509	D₄	—	4	2	no	—
510	D₄	—	4	2	no	—
511	D₄	—	4	4	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	4	no	—
514	D₄	—	4	4	no	—
515	D₄	—	4	2	no	—
516	D₄	—	8	2	no	—
517	D₄	—	8	4	no	—
518	D₄	—	8	4	no	—
519	D₄	C₂×SD₁₆×C₄₁	1	2	yes	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	4	8	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	8	2	no	—
534	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
535	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
536	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
537	C₂×C₄	C₂×SD₁₆×C₄₁	1	2	yes	—
538	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
539	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
540	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
541	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
542	C₈	—	4	2	no	—
543	C₈	—	4	2	no	—
544	C₈	—	4	2	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	4	no	—
554	C₂²	—	4	4	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	16	4	no	—
557	C₂²	—	16	8	no	—
558	C₂²	C₄₁×#450	1	2	yes	—
559	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
560	C₄	—	2	2	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	8	2	no	—
567	C₄	C₄₁×#450	1	2	yes	—
568	C₄	C₄₁×#455	1	2	yes	—
569	C₄	C₂²×SD₁₆×C₄₁	1	1	yes	characteristic
570	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
571	C₄	C₄₁×#576	1	2	yes	—
572	C₂	—	2	2	no	—
573	C₂	—	4	2	no	—
574	C₂	—	8	2	no	—
575	C₂	—	8	4	no	—
576	C₂	C₂×C₄₁×#450	1	1	yes	characteristic
577	C₂	C₄₁×#3008	1	1	yes	characteristic
578	C₂	C₂×C₄₁×#455	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
prime radical	C₄₁×#3498	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
2. C₄₁×#3206	C₂	semidirect
3. C₂×C₄₁×#486	C₂	semidirect
4. C₄₁×#3079	C₂	semidirect
5. C₄₁×#1642	C₂	semidirect
6. C₄₁×#1639	C₂	semidirect
7. C₄₁×#1545	C₂	semidirect
8. C₄₁×#1492	C₂	semidirect
9. C₄₁×#1476	C₂	semidirect
21. C₂×C₄⋊Q₈×C₄₁	C₂²	semidirect
28. C₄₁×#486	C₂²	semidirect
31. C₄₁×#475	C₂²	semidirect
32. C₄₁×#474	C₂²	semidirect
33. C₄₁×#461	C₂²	semidirect
35. C₄₁×#431	C₂²	semidirect
37. C₄₁×#423	C₂²	semidirect
40. C₂×C₄×C₈×C₄₁	C₂²	semidirect
41. C₄₁×#331	C₂²	semidirect
42. C₄₁×Q₈⋊C₈	C₂²	semidirect
43. C₄₁×D₄⋊C₈	C₂²	semidirect
44. C₄₁×D₄⋊C₈	C₂²	semidirect
126. #41×C₄₁	SD₁₆	semidirect
255. #18631	C₄₁	direct (N × H)
284. #3206	C₂×C₄₁	semidirect
285. C₂×#486	C₂×C₄₁	semidirect
286. #3079	C₂×C₄₁	semidirect
287. #1642	C₂×C₄₁	semidirect
288. #1639	C₂×C₄₁	semidirect
289. #1545	C₂×C₄₁	semidirect
290. #1492	C₂×C₄₁	semidirect
291. #1476	C₂×C₄₁	semidirect
310. C₂×C₄⋊Q₈	C₂²×C₄₁	semidirect
317. #486	C₂²×C₄₁	semidirect
320. #475	C₂²×C₄₁	semidirect
321. #474	C₂²×C₄₁	semidirect
322. #461	C₂²×C₄₁	semidirect
324. #431	C₂²×C₄₁	semidirect
326. #423	C₂²×C₄₁	semidirect
329. C₂×C₄×C₈	C₂²×C₄₁	semidirect
330. #331	C₂²×C₄₁	semidirect
331. Q₈⋊C₈	C₂²×C₄₁	semidirect
332. D₄⋊C₈	C₂²×C₄₁	semidirect
333. D₄⋊C₈	C₂²×C₄₁	semidirect
334. C₄₁	#18631	direct (N × H)
416. #41	SD₁₆×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3498	2
C₄₁×#3206	2
C₂×C₄₁×#486	2
C₄₁×#3079	2
C₄₁×#1642	2
C₄₁×#1639	2
C₄₁×#1545	2
C₄₁×#1492	2
C₄₁×#1476	2
#18631	41

Subgroups — C41×#18631 #23794832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#18631 #23794832