Subgroups — C₄₁×#33571 #23809772

Order 10496.

1084 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	C₄₁×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3022	C₂	1	2	yes	maximal, complemented
3	C₄₁×#3018	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2205	C₂	1	4	yes	maximal, complemented
5	C₄₁×#2203	C₂	1	4	yes	maximal, complemented
6	C₄₁×#2135	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2132	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#585	C₂²	1	1	yes	characteristic
9	C₄₁×#575	—	2	1	no	—
10	C₂×#137×C₄₁	—	2	2	no	—
11	C₄₁×#563	—	2	1	no	—
12	C₄₁×#563	C₂²	1	2	yes	complemented
13	C₄₁×#559	—	2	1	no	—
14	Q₈²×C₄₁	C₂²	1	2	yes	complemented
15	C₄₁×#556	—	2	2	no	—
16	D₄×Q₈×C₄₁	—	2	2	no	—
17	C₄₁×#542	—	2	4	no	—
18	C₄₁×#536	—	2	1	no	—
19	C₄₁×#536	C₂²	1	2	yes	—
20	C₄₁×#533	—	2	1	no	—
21	C₄₁×#532	C₂²	1	1	yes	characteristic
22	C₄₁×#456	C₂²	1	8	yes	—
23	C₄₁×#456	C₂²	1	2	yes	—
24	C₄₁×#455	—	2	1	no	—
25	C₄₁×#455	—	2	4	no	—
26	C₄₁×#454	C₂²	1	2	yes	—
27	C₄₁×#453	—	2	1	no	—
28	C₄₁×#421	—	2	2	no	—
29	C₂×#104×C₄₁	—	2	1	no	—
30	C₄₁×#413	C₂²	1	2	yes	—
31	C₄₁×#413	C₂²	1	1	yes	characteristic
32	C₄₁×#356	C₂²	1	2	yes	complemented
33	C₄₁×#356	C₂²	1	8	yes	complemented
34	C₄₁×#355	C₂²	1	2	yes	complemented
35	2₋¹⁺⁴×C₄₁	—	4	1	no	—
36	2₋¹⁺⁴×C₄₁	C₂³	1	2	yes	—
37	H(5,𝔽₂)×C₄₁	—	2	1	no	—
38	H(5,𝔽₂)×C₄₁	—	2	2	no	—
39	H(5,𝔽₂)×C₄₁	—	4	1	no	—
40	C₂×#41×C₄₁	—	2	2	no	—
41	C₂×#41×C₄₁	—	2	1	no	—
42	C₂×#41×C₄₁	—	4	2	no	—
43	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
44	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₄₁	—	2	1	no	—
46	C₂²×Q₈×C₄₁	D₄	1	2	yes	—
47	#137×C₄₁	—	2	8	no	—
48	#137×C₄₁	—	2	2	no	—
49	#137×C₄₁	—	4	1	no	—
50	#137×C₄₁	—	4	4	no	—
51	AGL(1,ℤ/8)×C₄₁	—	2	2	no	—
52	AGL(1,ℤ/8)×C₄₁	—	4	1	no	—
53	#135×C₄₁	—	4	2	no	—
54	C₂×Q₁₆×C₄₁	—	4	2	no	—
55	C₂×SD₁₆×C₄₁	—	4	2	no	—
56	C₂×M₁₆×C₄₁	—	2	2	no	—
57	C₂×M₁₆×C₄₁	—	2	1	no	—
58	C₄⋊Q₈×C₄₁	—	2	1	no	—
59	C₄⋊Q₈×C₄₁	—	2	1	no	—
60	C₄⋊Q₈×C₄₁	—	2	2	no	—
61	C₄⋊Q₈×C₄₁	—	2	4	no	—
62	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
63	C₄⋊Q₈×C₄₁	C₂³	1	4	yes	—
64	#127×C₄₁	D₄	1	1	yes	characteristic
65	#126×C₄₁	—	2	4	no	—
66	#126×C₄₁	—	2	4	no	—
67	#125×C₄₁	—	2	2	no	—
68	#124×C₄₁	—	2	2	no	—
69	#124×C₄₁	—	2	4	no	—
70	#124×C₄₁	D₄	1	1	yes	characteristic
71	#124×C₄₁	D₄	1	4	yes	—
72	#124×C₄₁	C₂³	1	1	yes	characteristic
73	#123×C₄₁	—	2	2	no	—
74	#123×C₄₁	—	2	2	no	—
75	#123×C₄₁	—	2	2	no	—
76	#123×C₄₁	—	2	2	no	—
77	C₂²⋊Q₈×C₄₁	—	2	2	no	—
78	C₂²⋊Q₈×C₄₁	—	2	2	no	—
79	C₂²⋊Q₈×C₄₁	—	2	4	no	—
80	C₂²⋊Q₈×C₄₁	—	2	4	no	—
81	C₂²⋊Q₈×C₄₁	—	2	2	no	—
82	C₂²⋊Q₈×C₄₁	—	2	2	no	—
83	#121×C₄₁	—	2	2	no	—
84	C₄×Q₈×C₄₁	—	2	2	no	—
85	C₄×Q₈×C₄₁	—	2	2	no	—
86	C₄×Q₈×C₄₁	—	2	4	no	—
87	C₄×D₄×C₄₁	—	2	4	no	—
88	C₄×D₄×C₄₁	—	2	2	no	—
89	#117×C₄₁	—	2	2	no	—
90	#117×C₄₁	—	2	1	no	—
91	#117×C₄₁	D₄	1	2	yes	—
92	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
93	#104×C₄₁	—	2	2	no	—
94	#104×C₄₁	—	2	2	no	—
95	#104×C₄₁	—	2	8	no	—
96	#101×C₄₁	C₂³	1	4	yes	—
97	#101×C₄₁	C₂³	1	2	yes	—
98	#100×C₄₁	—	2	1	no	—
99	#100×C₄₁	—	2	2	no	—
100	#41×C₄₁	—	2	2	no	—
101	#41×C₄₁	—	2	4	no	—
102	#41×C₄₁	—	2	2	no	—
103	#41×C₄₁	—	2	4	no	—
104	#41×C₄₁	—	4	1	no	—
105	#41×C₄₁	—	4	1	no	—
106	#41×C₄₁	—	4	2	no	—
107	#41×C₄₁	—	4	1	no	—
108	#41×C₄₁	—	4	1	no	—
109	#41×C₄₁	—	4	1	no	—
110	#41×C₄₁	—	4	2	no	—
111	#41×C₄₁	—	4	2	no	—
112	#41×C₄₁	—	4	4	no	—
113	#41×C₄₁	—	4	1	no	—
114	C₂×Q₈×C₄₁	—	2	2	no	—
115	C₂×Q₈×C₄₁	—	2	2	no	—
116	C₂×Q₈×C₄₁	—	2	2	no	—
117	C₂×Q₈×C₄₁	—	2	2	no	—
118	C₂×Q₈×C₄₁	—	2	1	no	—
119	C₂×Q₈×C₄₁	—	4	2	no	—
120	C₂×Q₈×C₄₁	—	4	2	no	—
121	C₂×Q₈×C₄₁	—	4	2	no	—
122	C₂×Q₈×C₄₁	—	8	1	no	—
123	C₂×Q₈×C₄₁	—	8	1	no	—
124	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
125	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
126	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
127	C₂×D₄×C₄₁	—	2	2	no	—
128	C₂×D₄×C₄₁	—	2	1	no	—
129	C₂×D₄×C₄₁	—	2	2	no	—
130	C₂×D₄×C₄₁	—	2	1	no	—
131	C₂×D₄×C₄₁	—	4	2	no	—
132	C₂×D₄×C₄₁	—	4	4	no	—
133	C₂×D₄×C₄₁	—	4	2	no	—
134	C₂×D₄×C₄₁	—	4	1	no	—
135	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
136	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
137	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₁	—	2	1	no	—
139	C₂²×C₄×C₄₁	—	2	2	no	—
140	C₂²×C₄×C₄₁	—	2	2	no	—
141	C₂²×C₄×C₄₁	—	2	1	no	—
142	C₂²×C₄×C₄₁	—	4	1	no	—
143	C₂²×C₄×C₄₁	—	4	2	no	—
144	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
146	Q₁₆×C₄₁	—	4	8	no	—
147	Q₁₆×C₄₁	—	4	2	no	—
148	SD₁₆×C₄₁	—	4	8	no	—
149	SD₁₆×C₄₁	—	4	2	no	—
150	SD₁₆×C₄₁	—	4	2	no	—
151	D₈×C₄₁	—	4	2	no	—
152	M₁₆×C₄₁	—	2	2	no	—
153	M₁₆×C₄₁	—	2	4	no	—
154	M₁₆×C₄₁	—	4	1	no	—
155	M₁₆×C₄₁	—	4	2	no	—
156	C₂×C₈×C₄₁	—	4	2	no	—
157	C₂×C₈×C₄₁	—	4	1	no	—
158	C₄⋊C₄×C₄₁	—	2	2	no	—
159	C₄⋊C₄×C₄₁	—	2	2	no	—
160	C₄⋊C₄×C₄₁	—	2	2	no	—
161	C₄⋊C₄×C₄₁	—	2	4	no	—
162	C₄⋊C₄×C₄₁	—	2	4	no	—
163	C₄⋊C₄×C₄₁	—	2	2	no	—
164	C₄⋊C₄×C₄₁	—	2	2	no	—
165	C₄⋊C₄×C₄₁	—	2	4	no	—
166	C₄⋊C₄×C₄₁	—	2	4	no	—
167	C₂²⋊C₄×C₄₁	—	2	2	no	—
168	C₂²⋊C₄×C₄₁	—	2	4	no	—
169	C₂²⋊C₄×C₄₁	—	2	4	no	—
170	C₂²⋊C₄×C₄₁	—	2	2	no	—
171	C₂²⋊C₄×C₄₁	—	2	2	no	—
172	C₂²⋊C₄×C₄₁	—	2	4	no	—
173	C₂²⋊C₄×C₄₁	—	2	2	no	—
174	C₄²×C₄₁	—	2	4	no	—
175	C₄²×C₄₁	—	2	2	no	—
176	C₄²×C₄₁	—	2	1	no	—
177	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₄₁	C₂×D₄	1	4	yes	—
180	C₂³×C₄₁	—	2	1	no	—
181	C₂³×C₄₁	—	4	2	no	—
182	C₂³×C₄₁	—	4	1	no	—
183	C₂³×C₄₁	#120	1	2	yes	—
184	C₂³×C₄₁	#120	1	1	yes	characteristic
185	Q₈×C₄₁	—	2	2	no	—
186	Q₈×C₄₁	—	2	4	no	—
187	Q₈×C₄₁	—	4	1	no	—
188	Q₈×C₄₁	—	4	4	no	—
189	Q₈×C₄₁	—	4	1	no	—
190	Q₈×C₄₁	—	4	4	no	—
191	Q₈×C₄₁	—	4	1	no	—
192	Q₈×C₄₁	—	4	2	no	—
193	Q₈×C₄₁	—	4	2	no	—
194	Q₈×C₄₁	—	8	2	no	—
195	D₄×C₄₁	—	2	2	no	—
196	D₄×C₄₁	—	2	4	no	—
197	D₄×C₄₁	—	4	1	no	—
198	D₄×C₄₁	—	4	2	no	—
199	D₄×C₄₁	—	4	1	no	—
200	D₄×C₄₁	—	4	4	no	—
201	D₄×C₄₁	—	4	4	no	—
202	D₄×C₄₁	—	4	2	no	—
203	D₄×C₄₁	—	4	2	no	—
204	D₄×C₄₁	—	4	1	no	—
205	D₄×C₄₁	—	8	1	no	—
206	C₂×C₄×C₄₁	—	2	1	no	—
207	C₂×C₄×C₄₁	—	2	1	no	—
208	C₂×C₄×C₄₁	—	2	2	no	—
209	C₂×C₄×C₄₁	—	2	2	no	—
210	C₂×C₄×C₄₁	—	2	1	no	—
211	C₂×C₄×C₄₁	—	2	4	no	—
212	C₂×C₄×C₄₁	—	2	1	no	—
213	C₂×C₄×C₄₁	—	2	1	no	—
214	C₂×C₄×C₄₁	—	2	4	no	—
215	C₂×C₄×C₄₁	—	4	2	no	—
216	C₂×C₄×C₄₁	—	4	2	no	—
217	C₂×C₄×C₄₁	—	4	4	no	—
218	C₂×C₄×C₄₁	—	4	2	no	—
219	C₂×C₄×C₄₁	—	4	1	no	—
220	C₂×C₄×C₄₁	—	4	1	no	—
221	C₂×C₄×C₄₁	—	4	1	no	—
222	C₂×C₄×C₄₁	—	4	2	no	—
223	C₂×C₄×C₄₁	—	8	2	no	—
224	C₂×C₄×C₄₁	—	8	2	no	—
225	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
226	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
227	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
228	C₈×C₄₁	—	4	2	no	—
229	C₈×C₄₁	—	4	4	no	—
230	#33571	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂²×C₄₁	—	2	2	no	—
232	C₂²×C₄₁	—	2	1	no	—
233	C₂²×C₄₁	—	4	1	no	—
234	C₂²×C₄₁	—	4	2	no	—
235	C₂²×C₄₁	—	4	2	no	—
236	C₂²×C₄₁	—	4	2	no	—
237	C₂²×C₄₁	—	4	1	no	—
238	C₂²×C₄₁	—	16	2	no	—
239	C₂²×C₄₁	—	16	1	no	—
240	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
241	C₄×C₄₁	—	2	2	no	—
242	C₄×C₄₁	—	2	1	no	—
243	C₄×C₄₁	—	2	2	no	—
244	C₄×C₄₁	—	4	1	no	—
245	C₄×C₄₁	—	4	4	no	—
246	C₄×C₄₁	—	4	1	no	—
247	C₄×C₄₁	—	4	4	no	—
248	C₄×C₄₁	—	4	2	no	—
249	C₄×C₄₁	B(4,𝔽₂)	1	1	yes	characteristic
250	C₄×C₄₁	B(4,𝔽₂)	1	1	yes	characteristic
251	#3550	C₂×C₄₁	1	1	yes	characteristic, complemented
252	#3022	C₂×C₄₁	1	2	yes	complemented
253	#3018	C₂×C₄₁	1	1	yes	characteristic
254	#2205	C₂×C₄₁	1	4	yes	complemented
255	#2203	C₂×C₄₁	1	4	yes	complemented
256	#2135	C₂×C₄₁	1	2	yes	complemented
257	#2132	C₂×C₄₁	1	1	yes	characteristic, complemented
258	C₂×C₄₁	—	2	1	no	—
259	C₂×C₄₁	—	4	2	no	—
260	C₂×C₄₁	—	4	1	no	—
261	C₂×C₄₁	—	8	1	no	—
262	C₂×C₄₁	—	8	2	no	—
263	C₂×C₄₁	C₂×B(4,𝔽₂)	1	1	yes	characteristic
264	#585	C₂²×C₄₁	1	1	yes	characteristic
265	#575	—	2	1	no	—
266	C₂×#137	—	2	2	no	—
267	#563	—	2	1	no	—
268	#563	C₂²×C₄₁	1	2	yes	complemented
269	#559	—	2	1	no	—
270	Q₈²	C₂²×C₄₁	1	2	yes	complemented
271	#556	—	2	2	no	—
272	D₄×Q₈	—	2	2	no	—
273	#542	—	2	4	no	—
274	#536	—	2	1	no	—
275	#536	C₂²×C₄₁	1	2	yes	—
276	#533	—	2	1	no	—
277	#532	C₂²×C₄₁	1	1	yes	characteristic
278	#456	C₂²×C₄₁	1	8	yes	—
279	#456	C₂²×C₄₁	1	2	yes	—
280	#455	—	2	1	no	—
281	#455	—	2	4	no	—
282	#454	C₂²×C₄₁	1	2	yes	—
283	#453	—	2	1	no	—
284	#421	—	2	2	no	—
285	C₂×#104	—	2	1	no	—
286	#413	C₂²×C₄₁	1	2	yes	—
287	#413	C₂²×C₄₁	1	1	yes	characteristic
288	#356	C₂²×C₄₁	1	2	yes	complemented
289	#356	C₂²×C₄₁	1	8	yes	complemented
290	#355	C₂²×C₄₁	1	2	yes	complemented
291	C₄₁	#33571	1	1	yes	characteristic, direct product factor, Sylow
292	2₋¹⁺⁴	—	4	1	no	—
293	2₋¹⁺⁴	C₂³×C₄₁	1	2	yes	—
294	H(5,𝔽₂)	—	2	1	no	—
295	H(5,𝔽₂)	—	2	2	no	—
296	H(5,𝔽₂)	—	4	1	no	—
297	C₂×#41	—	2	2	no	—
298	C₂×#41	—	2	1	no	—
299	C₂×#41	—	4	2	no	—
300	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
301	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
302	C₂²×Q₈	—	2	1	no	—
303	C₂²×Q₈	D₄×C₄₁	1	2	yes	—
304	#137	—	2	8	no	—
305	#137	—	2	2	no	—
306	#137	—	4	1	no	—
307	#137	—	4	4	no	—
308	AGL(1,ℤ/8)	—	2	2	no	—
309	AGL(1,ℤ/8)	—	4	1	no	—
310	#135	—	4	2	no	—
311	C₂×Q₁₆	—	4	2	no	—
312	C₂×SD₁₆	—	4	2	no	—
313	C₂×M₁₆	—	2	2	no	—
314	C₂×M₁₆	—	2	1	no	—
315	C₄⋊Q₈	—	2	1	no	—
316	C₄⋊Q₈	—	2	1	no	—
317	C₄⋊Q₈	—	2	2	no	—
318	C₄⋊Q₈	—	2	4	no	—
319	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
320	C₄⋊Q₈	C₂³×C₄₁	1	4	yes	—
321	#127	D₄×C₄₁	1	1	yes	characteristic
322	#126	—	2	4	no	—
323	#126	—	2	4	no	—
324	#125	—	2	2	no	—
325	#124	—	2	2	no	—
326	#124	—	2	4	no	—
327	#124	D₄×C₄₁	1	1	yes	characteristic
328	#124	D₄×C₄₁	1	4	yes	—
329	#124	C₂³×C₄₁	1	1	yes	characteristic
330	#123	—	2	2	no	—
331	#123	—	2	2	no	—
332	#123	—	2	2	no	—
333	#123	—	2	2	no	—
334	C₂²⋊Q₈	—	2	2	no	—
335	C₂²⋊Q₈	—	2	2	no	—
336	C₂²⋊Q₈	—	2	4	no	—
337	C₂²⋊Q₈	—	2	4	no	—
338	C₂²⋊Q₈	—	2	2	no	—
339	C₂²⋊Q₈	—	2	2	no	—
340	#121	—	2	2	no	—
341	C₄×Q₈	—	2	2	no	—
342	C₄×Q₈	—	2	2	no	—
343	C₄×Q₈	—	2	4	no	—
344	C₄×D₄	—	2	4	no	—
345	C₄×D₄	—	2	2	no	—
346	#117	—	2	2	no	—
347	#117	—	2	1	no	—
348	#117	D₄×C₄₁	1	2	yes	—
349	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
350	#104	—	2	2	no	—
351	#104	—	2	2	no	—
352	#104	—	2	8	no	—
353	#101	C₂³×C₄₁	1	4	yes	—
354	#101	C₂³×C₄₁	1	2	yes	—
355	#100	—	2	1	no	—
356	#100	—	2	2	no	—
357	#41	—	2	2	no	—
358	#41	—	2	4	no	—
359	#41	—	2	2	no	—
360	#41	—	2	4	no	—
361	#41	—	4	1	no	—
362	#41	—	4	1	no	—
363	#41	—	4	2	no	—
364	#41	—	4	1	no	—
365	#41	—	4	1	no	—
366	#41	—	4	1	no	—
367	#41	—	4	2	no	—
368	#41	—	4	2	no	—
369	#41	—	4	4	no	—
370	#41	—	4	1	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	1	no	—
376	C₂×Q₈	—	4	2	no	—
377	C₂×Q₈	—	4	2	no	—
378	C₂×Q₈	—	4	2	no	—
379	C₂×Q₈	—	8	1	no	—
380	C₂×Q₈	—	8	1	no	—
381	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
382	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
383	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	4	2	no	—
389	C₂×D₄	—	4	4	no	—
390	C₂×D₄	—	4	2	no	—
391	C₂×D₄	—	4	1	no	—
392	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
393	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
394	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	4	1	no	—
400	C₂²×C₄	—	4	2	no	—
401	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
403	Q₁₆	—	4	8	no	—
404	Q₁₆	—	4	2	no	—
405	SD₁₆	—	4	8	no	—
406	SD₁₆	—	4	2	no	—
407	SD₁₆	—	4	2	no	—
408	D₈	—	4	2	no	—
409	M₁₆	—	2	2	no	—
410	M₁₆	—	2	4	no	—
411	M₁₆	—	4	1	no	—
412	M₁₆	—	4	2	no	—
413	C₂×C₈	—	4	2	no	—
414	C₂×C₈	—	4	1	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	4	no	—
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	4	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₄²	—	2	4	no	—
432	C₄²	—	2	2	no	—
433	C₄²	—	2	1	no	—
434	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
435	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
436	C₄²	C₂×D₄×C₄₁	1	4	yes	—
437	C₂³	—	2	1	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	1	no	—
440	C₂³	#120×C₄₁	1	2	yes	—
441	C₂³	#120×C₄₁	1	1	yes	characteristic
442	Q₈	—	2	2	no	—
443	Q₈	—	2	4	no	—
444	Q₈	—	4	1	no	—
445	Q₈	—	4	4	no	—
446	Q₈	—	4	1	no	—
447	Q₈	—	4	4	no	—
448	Q₈	—	4	1	no	—
449	Q₈	—	4	2	no	—
450	Q₈	—	4	2	no	—
451	Q₈	—	8	2	no	—
452	D₄	—	2	2	no	—
453	D₄	—	2	4	no	—
454	D₄	—	4	1	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	1	no	—
457	D₄	—	4	4	no	—
458	D₄	—	4	4	no	—
459	D₄	—	4	2	no	—
460	D₄	—	4	2	no	—
461	D₄	—	4	1	no	—
462	D₄	—	8	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	8	2	no	—
481	C₂×C₄	—	8	2	no	—
482	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
483	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
484	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
485	C₈	—	4	2	no	—
486	C₈	—	4	4	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	4	1	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	16	2	no	—
495	C₂²	—	16	1	no	—
496	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
497	C₄	—	2	2	no	—
498	C₄	—	2	1	no	—
499	C₄	—	2	2	no	—
500	C₄	—	4	1	no	—
501	C₄	—	4	4	no	—
502	C₄	—	4	1	no	—
503	C₄	—	4	4	no	—
504	C₄	—	4	2	no	—
505	C₄	C₄₁×B(4,𝔽₂)	1	1	yes	characteristic
506	C₄	C₄₁×B(4,𝔽₂)	1	1	yes	characteristic
507	C₂	—	2	1	no	—
508	C₂	—	4	2	no	—
509	C₂	—	4	1	no	—
510	C₂	—	8	1	no	—
511	C₂	—	8	2	no	—
512	C₂	C₂×C₄₁×B(4,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₄₁	C₂×B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×Q₈	C₂⁴×C₄₁
prime radical	C₄₁×#3018	C₂
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄₁ ◁ C₂×C₄×C₄₁ ◁ C₂×#41×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3550	C₂	semidirect
2. C₄₁×#3022	C₂	semidirect
4. C₄₁×#2205	C₂	semidirect
5. C₄₁×#2203	C₂	semidirect
6. C₄₁×#2135	C₂	semidirect
7. C₄₁×#2132	C₂	semidirect
12. C₄₁×#563	C₂²	semidirect
14. Q₈²×C₄₁	C₂²	semidirect
32. C₄₁×#356	C₂²	semidirect
33. C₄₁×#356	C₂²	semidirect
34. C₄₁×#355	C₂²	semidirect
230. #33571	C₄₁	direct (N × H)
251. #3550	C₂×C₄₁	semidirect
252. #3022	C₂×C₄₁	semidirect
254. #2205	C₂×C₄₁	semidirect
255. #2203	C₂×C₄₁	semidirect
256. #2135	C₂×C₄₁	semidirect
257. #2132	C₂×C₄₁	semidirect
268. #563	C₂²×C₄₁	semidirect
270. Q₈²	C₂²×C₄₁	semidirect
288. #356	C₂²×C₄₁	semidirect
289. #356	C₂²×C₄₁	semidirect
290. #355	C₂²×C₄₁	semidirect
291. C₄₁	#33571	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×#3550	2
C₄₁×#3022	2
C₄₁×#3018	2
C₄₁×#2205	2
C₄₁×#2203	2
C₄₁×#2135	2
C₄₁×#2132	2
#33571	41

Subgroups — C41×#33571 #23809772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33571 #23809772