Subgroups — C₄₁×#61680 #23837881

Order 10496.

2096 conjugacy classes of subgroups.

The subgroup lattice has 788 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×#3496	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#3324	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3311	C₂	1	4	yes	maximal, complemented
5	C₄₁×#3302	C₂	1	2	yes	maximal, complemented
6	D₄×SD₁₆×C₄₁	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3276	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3266	C₂	1	4	yes	maximal, complemented
9	C₄₁×#3216	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#3210	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#3201	C₂	1	4	yes	maximal, complemented
12	C₄₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3101	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3009	C₂	1	4	yes	maximal, complemented
15	C₄₁×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×H(5,𝔽₂)×C₄₁	C₂²	1	2	yes	—
17	C₂×#137×C₄₁	C₂²	1	4	yes	complemented
18	C₂²×SD₁₆×C₄₁	C₂²	1	4	yes	complemented
19	C₄₁×#563	—	2	2	no	—
20	C₄₁×#559	—	2	1	no	—
21	Q₈²×C₄₁	—	2	1	no	—
22	C₄₁×#556	C₂²	1	2	yes	complemented
23	C₄₁×#556	C₂²	1	2	yes	complemented
24	D₄×Q₈×C₄₁	C₂²	1	2	yes	complemented
25	D₄×Q₈×C₄₁	C₂²	1	2	yes	complemented
26	C₄₁×#547	—	2	1	no	—
27	C₄₁×#547	C₂²	1	2	yes	—
28	C₄₁×#546	—	2	2	no	—
29	C₄₁×#546	C₂²	1	4	yes	—
30	D₄²×C₄₁	—	2	1	no	—
31	D₄²×C₄₁	C₂²	1	2	yes	—
32	C₄₁×#542	—	2	2	no	—
33	C₄₁×#542	—	2	2	no	—
34	C₄₁×#537	C₂²	1	2	yes	—
35	C₄₁×#536	C₂²	1	4	yes	complemented
36	C₄₁×#534	—	2	2	no	—
37	C₄₁×#533	C₂²	1	1	yes	characteristic, complemented
38	C₄₁×#533	C₂²	1	1	yes	characteristic, complemented
39	C₄₁×#532	C₂²	1	1	yes	characteristic
40	C₄₁×#532	C₂²	1	1	yes	characteristic
41	C₂×#121×C₄₁	—	2	2	no	—
42	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
43	C₄₁×#497	C₂²	1	2	yes	complemented
44	C₄₁×#494	C₂²	1	1	yes	characteristic, complemented
45	C₄₁×#492	C₂²	1	1	yes	characteristic, complemented
46	C₄₁×#489	C₂²	1	2	yes	complemented
47	C₄₁×#487	C₂²	1	1	yes	characteristic, complemented
48	C₄₁×#486	C₂²	1	1	yes	characteristic, complemented
49	C₄₁×#485	C₂²	1	4	yes	complemented
50	C₄₁×#484	C₂²	1	2	yes	complemented
51	C₄₁×#483	C₂²	1	2	yes	complemented
52	C₄₁×#482	C₂²	1	4	yes	complemented
53	C₄₁×#476	C₂²	1	2	yes	complemented
54	C₄₁×#474	C₂²	1	2	yes	complemented
55	C₄₁×#470	C₂²	1	4	yes	complemented
56	C₄₁×#468	C₂²	1	4	yes	complemented
57	C₄₁×#467	C₂²	1	4	yes	complemented
58	C₄₁×#465	C₂²	1	4	yes	complemented
59	C₄₁×#464	C₂²	1	4	yes	complemented
60	C₄₁×#462	C₂²	1	2	yes	complemented
61	C₄₁×#461	C₂²	1	2	yes	complemented
62	C₄₁×#461	C₂²	1	2	yes	complemented
63	C₄₁×#460	C₂²	1	2	yes	complemented
64	C₄₁×#452	C₂²	1	4	yes	complemented
65	C₄₁×#452	C₂²	1	4	yes	complemented
66	C₄₁×#452	C₂²	1	4	yes	complemented
67	C₄₁×#452	C₂²	1	4	yes	complemented
68	C₄₁×#451	C₂²	1	4	yes	complemented
69	C₄₁×#450	C₂²	1	2	yes	—
70	C₄₁×#450	C₂²	1	2	yes	—
71	C₄₁×#450	C₂²	1	4	yes	complemented
72	C₄₁×#450	C₂²	1	4	yes	complemented
73	C₄₁×#448	C₂²	1	4	yes	complemented
74	C₄₁×#440	C₂²	1	4	yes	complemented
75	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
76	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
77	C₄₁×#436	C₂²	1	2	yes	complemented
78	C₄₁×#435	C₂²	1	4	yes	complemented
79	C₈×D₄×C₄₁	C₂²	1	2	yes	complemented
80	C₄₁×#432	C₂²	1	1	yes	characteristic, complemented
81	C₄₁×#431	C₂²	1	1	yes	characteristic, complemented
82	C₄₁×#418	C₂²	1	4	yes	complemented
83	C₄₁×#416	C₂²	1	4	yes	complemented
84	C₄₁×#408	C₂²	1	4	yes	complemented
85	H(5,𝔽₂)×C₄₁	—	4	8	no	—
86	C₂×#41×C₄₁	—	2	2	no	—
87	C₂×#41×C₄₁	C₂³	1	4	yes	—
88	C₂×#41×C₄₁	C₂³	1	2	yes	—
89	C₂×#41×C₄₁	C₂³	1	2	yes	—
90	C₂²×Q₈×C₄₁	C₂³	1	4	yes	—
91	C₂²×D₄×C₄₁	—	2	4	no	—
92	C₂²×D₄×C₄₁	—	2	2	no	—
93	C₂²×D₄×C₄₁	—	2	2	no	—
94	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
96	C₂³×C₄×C₄₁	—	2	1	no	—
97	#137×C₄₁	—	4	8	no	—
98	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
99	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₄₁	—	4	8	no	—
101	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
103	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
106	C₂×M₁₆×C₄₁	C₂³	1	4	yes	—
107	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
108	C₄⋊Q₈×C₄₁	—	2	4	no	—
109	C₄⋊Q₈×C₄₁	—	2	2	no	—
110	C₄⋊Q₈×C₄₁	—	2	2	no	—
111	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
112	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
116	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
117	#127×C₄₁	D₄	1	1	yes	characteristic
118	#127×C₄₁	C₂³	1	1	yes	characteristic
119	#126×C₄₁	—	2	4	no	—
120	#126×C₄₁	—	2	4	no	—
121	#125×C₄₁	—	2	1	no	—
122	#125×C₄₁	—	2	1	no	—
123	#124×C₄₁	—	2	4	no	—
124	#124×C₄₁	—	2	2	no	—
125	#124×C₄₁	—	2	2	no	—
126	#124×C₄₁	D₄	1	2	yes	—
127	#124×C₄₁	C₂³	1	2	yes	—
128	#123×C₄₁	—	2	4	no	—
129	#123×C₄₁	—	2	4	no	—
130	#123×C₄₁	—	2	4	no	—
131	#123×C₄₁	—	2	4	no	—
132	C₂²⋊Q₈×C₄₁	—	2	2	no	—
133	C₂²⋊Q₈×C₄₁	—	2	1	no	—
134	C₂²⋊Q₈×C₄₁	—	2	1	no	—
135	C₂²⋊Q₈×C₄₁	—	2	4	no	—
136	C₂²⋊Q₈×C₄₁	—	2	4	no	—
137	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
138	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
139	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
140	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
141	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
142	#121×C₄₁	—	2	4	no	—
143	#121×C₄₁	—	2	2	no	—
144	#121×C₄₁	—	2	2	no	—
145	#121×C₄₁	—	2	1	no	—
146	#121×C₄₁	—	2	1	no	—
147	#121×C₄₁	—	2	2	no	—
148	#121×C₄₁	—	2	4	no	—
149	#121×C₄₁	D₄	1	2	yes	—
150	#121×C₄₁	D₄	1	2	yes	—
151	#121×C₄₁	C₂³	1	4	yes	—
152	#120×C₄₁	—	2	4	no	—
153	#120×C₄₁	—	2	4	no	—
154	C₄×Q₈×C₄₁	—	2	2	no	—
155	C₄×Q₈×C₄₁	—	2	2	no	—
156	C₄×Q₈×C₄₁	—	2	1	no	—
157	C₄×Q₈×C₄₁	—	2	1	no	—
158	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
159	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
160	C₄×D₄×C₄₁	—	2	2	no	—
161	C₄×D₄×C₄₁	—	2	2	no	—
162	C₄×D₄×C₄₁	—	2	1	no	—
163	C₄×D₄×C₄₁	—	2	1	no	—
164	C₄×D₄×C₄₁	—	2	1	no	—
165	C₄×D₄×C₄₁	—	2	1	no	—
166	C₄×D₄×C₄₁	C₂³	1	2	yes	—
167	C₄×D₄×C₄₁	C₂³	1	2	yes	—
168	C₄×D₄×C₄₁	C₂³	1	2	yes	—
169	C₄×D₄×C₄₁	C₂³	1	2	yes	—
170	#117×C₄₁	—	2	1	no	—
171	#117×C₄₁	—	2	1	no	—
172	#117×C₄₁	C₂³	1	4	yes	—
173	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
174	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
176	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
177	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
178	#107×C₄₁	C₂³	1	4	yes	—
179	#106×C₄₁	C₂³	1	2	yes	—
180	#106×C₄₁	C₂³	1	2	yes	—
181	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
182	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
183	#103×C₄₁	C₂³	1	4	yes	—
184	#103×C₄₁	C₂³	1	4	yes	—
185	#103×C₄₁	C₂³	1	2	yes	—
186	#103×C₄₁	C₂³	1	2	yes	—
187	#103×C₄₁	C₂³	1	4	yes	—
188	#102×C₄₁	C₂³	1	2	yes	—
189	#102×C₄₁	C₂³	1	4	yes	—
190	#102×C₄₁	C₂³	1	2	yes	—
191	#102×C₄₁	C₂³	1	4	yes	—
192	#102×C₄₁	C₂³	1	4	yes	—
193	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
194	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
195	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
196	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
197	#97×C₄₁	C₂³	1	2	yes	—
198	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
199	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
200	C₂⁴×C₄₁	—	2	1	no	—
201	C₂⁴×C₄₁	—	2	4	no	—
202	#41×C₄₁	—	2	8	no	—
203	#41×C₄₁	—	4	4	no	—
204	#41×C₄₁	—	4	4	no	—
205	#41×C₄₁	—	4	4	no	—
206	#41×C₄₁	—	4	8	no	—
207	C₂×Q₈×C₄₁	—	2	1	no	—
208	C₂×Q₈×C₄₁	—	2	1	no	—
209	C₂×Q₈×C₄₁	—	2	4	no	—
210	C₂×Q₈×C₄₁	—	4	4	no	—
211	C₂×Q₈×C₄₁	—	4	4	no	—
212	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
213	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
214	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
215	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
216	C₂×D₄×C₄₁	—	2	4	no	—
217	C₂×D₄×C₄₁	—	2	8	no	—
218	C₂×D₄×C₄₁	—	2	4	no	—
219	C₂×D₄×C₄₁	—	2	2	no	—
220	C₂×D₄×C₄₁	—	2	4	no	—
221	C₂×D₄×C₄₁	—	2	1	no	—
222	C₂×D₄×C₄₁	—	2	1	no	—
223	C₂×D₄×C₄₁	—	2	4	no	—
224	C₂×D₄×C₄₁	—	2	1	no	—
225	C₂×D₄×C₄₁	—	4	4	no	—
226	C₂×D₄×C₄₁	—	4	8	no	—
227	C₂×D₄×C₄₁	—	4	16	no	—
228	C₂×D₄×C₄₁	—	8	4	no	—
229	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
230	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
231	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
232	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
233	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
234	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₄₁	—	2	1	no	—
236	C₂²×C₄×C₄₁	—	2	4	no	—
237	C₂²×C₄×C₄₁	—	2	4	no	—
238	C₂²×C₄×C₄₁	—	2	2	no	—
239	C₂²×C₄×C₄₁	—	2	2	no	—
240	C₂²×C₄×C₄₁	—	2	2	no	—
241	C₂²×C₄×C₄₁	—	8	2	no	—
242	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
246	Q₁₆×C₄₁	—	4	4	no	—
247	Q₁₆×C₄₁	—	4	4	no	—
248	SD₁₆×C₄₁	—	2	4	no	—
249	SD₁₆×C₄₁	—	2	8	no	—
250	SD₁₆×C₄₁	—	2	4	no	—
251	SD₁₆×C₄₁	—	4	4	no	—
252	SD₁₆×C₄₁	—	4	4	no	—
253	M₁₆×C₄₁	—	4	4	no	—
254	C₂×C₈×C₄₁	—	4	4	no	—
255	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
256	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
257	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
258	C₄⋊C₄×C₄₁	—	2	1	no	—
259	C₄⋊C₄×C₄₁	—	2	4	no	—
260	C₄⋊C₄×C₄₁	—	2	1	no	—
261	C₄⋊C₄×C₄₁	—	2	1	no	—
262	C₄⋊C₄×C₄₁	—	2	1	no	—
263	C₄⋊C₄×C₄₁	—	2	1	no	—
264	C₄⋊C₄×C₄₁	—	2	1	no	—
265	C₄⋊C₄×C₄₁	—	2	1	no	—
266	C₄⋊C₄×C₄₁	—	2	1	no	—
267	C₄⋊C₄×C₄₁	—	2	1	no	—
268	C₄⋊C₄×C₄₁	—	2	4	no	—
269	C₄⋊C₄×C₄₁	—	2	4	no	—
270	C₄⋊C₄×C₄₁	—	2	2	no	—
271	C₄⋊C₄×C₄₁	—	2	2	no	—
272	C₄⋊C₄×C₄₁	—	2	2	no	—
273	C₄⋊C₄×C₄₁	—	2	2	no	—
274	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
275	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
278	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
279	C₂²⋊C₄×C₄₁	—	2	4	no	—
280	C₂²⋊C₄×C₄₁	—	2	2	no	—
281	C₂²⋊C₄×C₄₁	—	2	2	no	—
282	C₂²⋊C₄×C₄₁	—	2	4	no	—
283	C₂²⋊C₄×C₄₁	—	2	4	no	—
284	C₂²⋊C₄×C₄₁	—	2	4	no	—
285	C₂²⋊C₄×C₄₁	—	2	2	no	—
286	C₂²⋊C₄×C₄₁	—	2	2	no	—
287	C₂²⋊C₄×C₄₁	—	2	2	no	—
288	C₂²⋊C₄×C₄₁	—	2	4	no	—
289	C₂²⋊C₄×C₄₁	—	2	2	no	—
290	C₂²⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
291	C₂²⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
292	C₄²×C₄₁	—	2	2	no	—
293	C₄²×C₄₁	—	2	2	no	—
294	C₄²×C₄₁	—	2	4	no	—
295	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
296	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
297	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
298	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
299	C₂³×C₄₁	—	2	4	no	—
300	C₂³×C₄₁	—	2	2	no	—
301	C₂³×C₄₁	—	2	2	no	—
302	C₂³×C₄₁	—	4	8	no	—
303	C₂³×C₄₁	—	8	1	no	—
304	C₂³×C₄₁	—	8	1	no	—
305	C₂³×C₄₁	—	8	4	no	—
306	C₂³×C₄₁	—	8	4	no	—
307	C₂³×C₄₁	C₂²×D₄	1	4	yes	—
308	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
309	Q₈×C₄₁	—	2	2	no	—
310	Q₈×C₄₁	—	2	4	no	—
311	Q₈×C₄₁	—	2	2	no	—
312	Q₈×C₄₁	—	2	4	no	—
313	Q₈×C₄₁	—	4	2	no	—
314	Q₈×C₄₁	—	4	2	no	—
315	Q₈×C₄₁	—	4	2	no	—
316	Q₈×C₄₁	—	8	4	no	—
317	D₄×C₄₁	—	2	4	no	—
318	D₄×C₄₁	—	2	4	no	—
319	D₄×C₄₁	—	2	2	no	—
320	D₄×C₄₁	—	2	4	no	—
321	D₄×C₄₁	—	4	2	no	—
322	D₄×C₄₁	—	4	4	no	—
323	D₄×C₄₁	—	4	2	no	—
324	D₄×C₄₁	—	4	8	no	—
325	D₄×C₄₁	—	4	8	no	—
326	D₄×C₄₁	—	4	4	no	—
327	D₄×C₄₁	—	4	2	no	—
328	D₄×C₄₁	—	8	1	no	—
329	D₄×C₄₁	—	8	4	no	—
330	D₄×C₄₁	H(5,𝔽₂)	1	4	yes	—
331	C₂×C₄×C₄₁	—	2	2	no	—
332	C₂×C₄×C₄₁	—	2	4	no	—
333	C₂×C₄×C₄₁	—	2	4	no	—
334	C₂×C₄×C₄₁	—	2	2	no	—
335	C₂×C₄×C₄₁	—	2	2	no	—
336	C₂×C₄×C₄₁	—	2	2	no	—
337	C₂×C₄×C₄₁	—	2	2	no	—
338	C₂×C₄×C₄₁	—	2	2	no	—
339	C₂×C₄×C₄₁	—	2	2	no	—
340	C₂×C₄×C₄₁	—	2	2	no	—
341	C₂×C₄×C₄₁	—	4	1	no	—
342	C₂×C₄×C₄₁	—	4	8	no	—
343	C₂×C₄×C₄₁	—	4	4	no	—
344	C₂×C₄×C₄₁	—	4	4	no	—
345	C₂×C₄×C₄₁	—	8	2	no	—
346	C₂×C₄×C₄₁	—	8	1	no	—
347	C₂×C₄×C₄₁	—	8	4	no	—
348	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
350	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
355	C₈×C₄₁	—	2	2	no	—
356	C₈×C₄₁	—	2	4	no	—
357	C₈×C₄₁	—	2	2	no	—
358	#61680	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
359	C₂²×C₄₁	—	2	1	no	—
360	C₂²×C₄₁	—	2	4	no	—
361	C₂²×C₄₁	—	2	4	no	—
362	C₂²×C₄₁	—	2	1	no	—
363	C₂²×C₄₁	—	2	4	no	—
364	C₂²×C₄₁	—	2	1	no	—
365	C₂²×C₄₁	—	2	4	no	—
366	C₂²×C₄₁	—	4	2	no	—
367	C₂²×C₄₁	—	4	2	no	—
368	C₂²×C₄₁	—	4	2	no	—
369	C₂²×C₄₁	—	4	2	no	—
370	C₂²×C₄₁	—	4	2	no	—
371	C₂²×C₄₁	—	8	4	no	—
372	C₂²×C₄₁	—	16	8	no	—
373	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
374	C₄×C₄₁	—	2	1	no	—
375	C₄×C₄₁	—	2	1	no	—
376	C₄×C₄₁	—	2	1	no	—
377	C₄×C₄₁	—	2	4	no	—
378	C₄×C₄₁	—	2	1	no	—
379	C₄×C₄₁	—	4	2	no	—
380	C₄×C₄₁	—	4	2	no	—
381	C₄×C₄₁	—	4	2	no	—
382	C₄×C₄₁	—	4	2	no	—
383	C₄×C₄₁	—	4	2	no	—
384	C₄×C₄₁	—	4	2	no	—
385	C₄×C₄₁	#577	1	2	yes	—
386	C₄×C₄₁	C₂×H(5,𝔽₂)	1	2	yes	—
387	#3550	C₂×C₄₁	1	1	yes	characteristic, complemented
388	#3496	C₂×C₄₁	1	1	yes	characteristic
389	#3324	C₂×C₄₁	1	2	yes	complemented
390	#3311	C₂×C₄₁	1	4	yes	complemented
391	#3302	C₂×C₄₁	1	2	yes	complemented
392	D₄×SD₁₆	C₂×C₄₁	1	2	yes	complemented
393	#3276	C₂×C₄₁	1	2	yes	complemented
394	#3266	C₂×C₄₁	1	4	yes	complemented
395	#3216	C₂×C₄₁	1	1	yes	characteristic, complemented
396	#3210	C₂×C₄₁	1	1	yes	characteristic, complemented
397	#3201	C₂×C₄₁	1	4	yes	complemented
398	#3110	C₂×C₄₁	1	1	yes	characteristic, complemented
399	#3101	C₂×C₄₁	1	1	yes	characteristic, complemented
400	#3009	C₂×C₄₁	1	4	yes	complemented
401	#2981	C₂×C₄₁	1	1	yes	characteristic, complemented
402	C₂×C₄₁	—	4	1	no	—
403	C₂×C₄₁	—	4	4	no	—
404	C₂×C₄₁	—	4	4	no	—
405	C₂×C₄₁	—	8	2	no	—
406	C₂×C₄₁	#3484	1	1	yes	characteristic
407	C₂×C₄₁	C₂×#577	1	1	yes	characteristic
408	C₂×C₄₁	#3586	1	1	yes	characteristic
409	C₂×H(5,𝔽₂)	C₂²×C₄₁	1	2	yes	—
410	C₂×#137	C₂²×C₄₁	1	4	yes	complemented
411	C₂²×SD₁₆	C₂²×C₄₁	1	4	yes	complemented
412	#563	—	2	2	no	—
413	#559	—	2	1	no	—
414	Q₈²	—	2	1	no	—
415	#556	C₂²×C₄₁	1	2	yes	complemented
416	#556	C₂²×C₄₁	1	2	yes	complemented
417	D₄×Q₈	C₂²×C₄₁	1	2	yes	complemented
418	D₄×Q₈	C₂²×C₄₁	1	2	yes	complemented
419	#547	—	2	1	no	—
420	#547	C₂²×C₄₁	1	2	yes	—
421	#546	—	2	2	no	—
422	#546	C₂²×C₄₁	1	4	yes	—
423	D₄²	—	2	1	no	—
424	D₄²	C₂²×C₄₁	1	2	yes	—
425	#542	—	2	2	no	—
426	#542	—	2	2	no	—
427	#537	C₂²×C₄₁	1	2	yes	—
428	#536	C₂²×C₄₁	1	4	yes	complemented
429	#534	—	2	2	no	—
430	#533	C₂²×C₄₁	1	1	yes	characteristic, complemented
431	#533	C₂²×C₄₁	1	1	yes	characteristic, complemented
432	#532	C₂²×C₄₁	1	1	yes	characteristic
433	#532	C₂²×C₄₁	1	1	yes	characteristic
434	C₂×#121	—	2	2	no	—
435	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
436	#497	C₂²×C₄₁	1	2	yes	complemented
437	#494	C₂²×C₄₁	1	1	yes	characteristic, complemented
438	#492	C₂²×C₄₁	1	1	yes	characteristic, complemented
439	#489	C₂²×C₄₁	1	2	yes	complemented
440	#487	C₂²×C₄₁	1	1	yes	characteristic, complemented
441	#486	C₂²×C₄₁	1	1	yes	characteristic, complemented
442	#485	C₂²×C₄₁	1	4	yes	complemented
443	#484	C₂²×C₄₁	1	2	yes	complemented
444	#483	C₂²×C₄₁	1	2	yes	complemented
445	#482	C₂²×C₄₁	1	4	yes	complemented
446	#476	C₂²×C₄₁	1	2	yes	complemented
447	#474	C₂²×C₄₁	1	2	yes	complemented
448	#470	C₂²×C₄₁	1	4	yes	complemented
449	#468	C₂²×C₄₁	1	4	yes	complemented
450	#467	C₂²×C₄₁	1	4	yes	complemented
451	#465	C₂²×C₄₁	1	4	yes	complemented
452	#464	C₂²×C₄₁	1	4	yes	complemented
453	#462	C₂²×C₄₁	1	2	yes	complemented
454	#461	C₂²×C₄₁	1	2	yes	complemented
455	#461	C₂²×C₄₁	1	2	yes	complemented
456	#460	C₂²×C₄₁	1	2	yes	complemented
457	#452	C₂²×C₄₁	1	4	yes	complemented
458	#452	C₂²×C₄₁	1	4	yes	complemented
459	#452	C₂²×C₄₁	1	4	yes	complemented
460	#452	C₂²×C₄₁	1	4	yes	complemented
461	#451	C₂²×C₄₁	1	4	yes	complemented
462	#450	C₂²×C₄₁	1	2	yes	—
463	#450	C₂²×C₄₁	1	2	yes	—
464	#450	C₂²×C₄₁	1	4	yes	complemented
465	#450	C₂²×C₄₁	1	4	yes	complemented
466	#448	C₂²×C₄₁	1	4	yes	complemented
467	#440	C₂²×C₄₁	1	4	yes	complemented
468	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
469	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
470	#436	C₂²×C₄₁	1	2	yes	complemented
471	#435	C₂²×C₄₁	1	4	yes	complemented
472	C₈×D₄	C₂²×C₄₁	1	2	yes	complemented
473	#432	C₂²×C₄₁	1	1	yes	characteristic, complemented
474	#431	C₂²×C₄₁	1	1	yes	characteristic, complemented
475	#418	C₂²×C₄₁	1	4	yes	complemented
476	#416	C₂²×C₄₁	1	4	yes	complemented
477	#408	C₂²×C₄₁	1	4	yes	complemented
478	C₄₁	#61680	1	1	yes	characteristic, direct product factor, Sylow
479	H(5,𝔽₂)	—	4	8	no	—
480	C₂×#41	—	2	2	no	—
481	C₂×#41	C₂³×C₄₁	1	4	yes	—
482	C₂×#41	C₂³×C₄₁	1	2	yes	—
483	C₂×#41	C₂³×C₄₁	1	2	yes	—
484	C₂²×Q₈	C₂³×C₄₁	1	4	yes	—
485	C₂²×D₄	—	2	4	no	—
486	C₂²×D₄	—	2	2	no	—
487	C₂²×D₄	—	2	2	no	—
488	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
489	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
490	C₂³×C₄	—	2	1	no	—
491	#137	—	4	8	no	—
492	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
493	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
494	C₂×SD₁₆	—	4	8	no	—
495	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
496	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
497	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
498	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
499	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
500	C₂×M₁₆	C₂³×C₄₁	1	4	yes	—
501	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
502	C₄⋊Q₈	—	2	4	no	—
503	C₄⋊Q₈	—	2	2	no	—
504	C₄⋊Q₈	—	2	2	no	—
505	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
506	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
507	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
508	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
509	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
510	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
511	#127	D₄×C₄₁	1	1	yes	characteristic
512	#127	C₂³×C₄₁	1	1	yes	characteristic
513	#126	—	2	4	no	—
514	#126	—	2	4	no	—
515	#125	—	2	1	no	—
516	#125	—	2	1	no	—
517	#124	—	2	4	no	—
518	#124	—	2	2	no	—
519	#124	—	2	2	no	—
520	#124	D₄×C₄₁	1	2	yes	—
521	#124	C₂³×C₄₁	1	2	yes	—
522	#123	—	2	4	no	—
523	#123	—	2	4	no	—
524	#123	—	2	4	no	—
525	#123	—	2	4	no	—
526	C₂²⋊Q₈	—	2	2	no	—
527	C₂²⋊Q₈	—	2	1	no	—
528	C₂²⋊Q₈	—	2	1	no	—
529	C₂²⋊Q₈	—	2	4	no	—
530	C₂²⋊Q₈	—	2	4	no	—
531	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
532	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
533	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
534	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
535	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
536	#121	—	2	4	no	—
537	#121	—	2	2	no	—
538	#121	—	2	2	no	—
539	#121	—	2	1	no	—
540	#121	—	2	1	no	—
541	#121	—	2	2	no	—
542	#121	—	2	4	no	—
543	#121	D₄×C₄₁	1	2	yes	—
544	#121	D₄×C₄₁	1	2	yes	—
545	#121	C₂³×C₄₁	1	4	yes	—
546	#120	—	2	4	no	—
547	#120	—	2	4	no	—
548	C₄×Q₈	—	2	2	no	—
549	C₄×Q₈	—	2	2	no	—
550	C₄×Q₈	—	2	1	no	—
551	C₄×Q₈	—	2	1	no	—
552	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
553	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	2	2	no	—
556	C₄×D₄	—	2	1	no	—
557	C₄×D₄	—	2	1	no	—
558	C₄×D₄	—	2	1	no	—
559	C₄×D₄	—	2	1	no	—
560	C₄×D₄	C₂³×C₄₁	1	2	yes	—
561	C₄×D₄	C₂³×C₄₁	1	2	yes	—
562	C₄×D₄	C₂³×C₄₁	1	2	yes	—
563	C₄×D₄	C₂³×C₄₁	1	2	yes	—
564	#117	—	2	1	no	—
565	#117	—	2	1	no	—
566	#117	C₂³×C₄₁	1	4	yes	—
567	C₂×C₄⋊C₄	—	2	2	no	—
568	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
569	C₂×C₂²⋊C₄	—	2	1	no	—
570	C₂×C₂²⋊C₄	—	2	4	no	—
571	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
572	#107	C₂³×C₄₁	1	4	yes	—
573	#106	C₂³×C₄₁	1	2	yes	—
574	#106	C₂³×C₄₁	1	2	yes	—
575	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
576	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
577	#103	C₂³×C₄₁	1	4	yes	—
578	#103	C₂³×C₄₁	1	4	yes	—
579	#103	C₂³×C₄₁	1	2	yes	—
580	#103	C₂³×C₄₁	1	2	yes	—
581	#103	C₂³×C₄₁	1	4	yes	—
582	#102	C₂³×C₄₁	1	2	yes	—
583	#102	C₂³×C₄₁	1	4	yes	—
584	#102	C₂³×C₄₁	1	2	yes	—
585	#102	C₂³×C₄₁	1	4	yes	—
586	#102	C₂³×C₄₁	1	4	yes	—
587	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
588	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
589	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
590	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
591	#97	C₂³×C₄₁	1	2	yes	—
592	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
593	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
594	C₂⁴	—	2	1	no	—
595	C₂⁴	—	2	4	no	—
596	#41	—	2	8	no	—
597	#41	—	4	4	no	—
598	#41	—	4	4	no	—
599	#41	—	4	4	no	—
600	#41	—	4	8	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	2	4	no	—
604	C₂×Q₈	—	4	4	no	—
605	C₂×Q₈	—	4	4	no	—
606	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
607	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
608	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
609	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	8	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	2	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	4	4	no	—
620	C₂×D₄	—	4	8	no	—
621	C₂×D₄	—	4	16	no	—
622	C₂×D₄	—	8	4	no	—
623	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
624	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
625	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
626	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
627	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
628	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	8	2	no	—
636	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
637	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
640	Q₁₆	—	4	4	no	—
641	Q₁₆	—	4	4	no	—
642	SD₁₆	—	2	4	no	—
643	SD₁₆	—	2	8	no	—
644	SD₁₆	—	2	4	no	—
645	SD₁₆	—	4	4	no	—
646	SD₁₆	—	4	4	no	—
647	M₁₆	—	4	4	no	—
648	C₂×C₈	—	4	4	no	—
649	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
650	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
651	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
669	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
670	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
671	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
672	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	2	no	—
675	C₂²⋊C₄	—	2	2	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	2	no	—
681	C₂²⋊C₄	—	2	2	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
685	C₂²⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
686	C₄²	—	2	2	no	—
687	C₄²	—	2	2	no	—
688	C₄²	—	2	4	no	—
689	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
690	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
691	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
692	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
693	C₂³	—	2	4	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	4	8	no	—
697	C₂³	—	8	1	no	—
698	C₂³	—	8	1	no	—
699	C₂³	—	8	4	no	—
700	C₂³	—	8	4	no	—
701	C₂³	C₂²×D₄×C₄₁	1	4	yes	—
702	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
703	Q₈	—	2	2	no	—
704	Q₈	—	2	4	no	—
705	Q₈	—	2	2	no	—
706	Q₈	—	2	4	no	—
707	Q₈	—	4	2	no	—
708	Q₈	—	4	2	no	—
709	Q₈	—	4	2	no	—
710	Q₈	—	8	4	no	—
711	D₄	—	2	4	no	—
712	D₄	—	2	4	no	—
713	D₄	—	2	2	no	—
714	D₄	—	2	4	no	—
715	D₄	—	4	2	no	—
716	D₄	—	4	4	no	—
717	D₄	—	4	2	no	—
718	D₄	—	4	8	no	—
719	D₄	—	4	8	no	—
720	D₄	—	4	4	no	—
721	D₄	—	4	2	no	—
722	D₄	—	8	1	no	—
723	D₄	—	8	4	no	—
724	D₄	H(5,𝔽₂)×C₄₁	1	4	yes	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	2	4	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	8	no	—
737	C₂×C₄	—	4	4	no	—
738	C₂×C₄	—	4	4	no	—
739	C₂×C₄	—	8	2	no	—
740	C₂×C₄	—	8	1	no	—
741	C₂×C₄	—	8	4	no	—
742	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
743	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
744	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
745	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
746	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
747	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
748	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
749	C₈	—	2	2	no	—
750	C₈	—	2	4	no	—
751	C₈	—	2	2	no	—
752	C₂²	—	2	1	no	—
753	C₂²	—	2	4	no	—
754	C₂²	—	2	1	no	—
755	C₂²	—	2	4	no	—
756	C₂²	—	2	4	no	—
757	C₂²	—	2	1	no	—
758	C₂²	—	2	4	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	8	4	no	—
765	C₂²	—	16	8	no	—
766	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
767	C₄	—	2	1	no	—
768	C₄	—	2	1	no	—
769	C₄	—	2	1	no	—
770	C₄	—	2	1	no	—
771	C₄	—	2	4	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	C₄₁×#577	1	2	yes	—
779	C₄	C₂×H(5,𝔽₂)×C₄₁	1	2	yes	—
780	C₂	—	4	1	no	—
781	C₂	—	4	4	no	—
782	C₂	—	4	4	no	—
783	C₂	—	8	2	no	—
784	C₂	C₄₁×#3484	1	1	yes	characteristic
785	C₂	C₂×C₄₁×#577	1	1	yes	characteristic
786	C₂	C₄₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
prime radical	C₄₁×#3496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3550	C₂	semidirect
3. C₄₁×#3324	C₂	semidirect
4. C₄₁×#3311	C₂	semidirect
5. C₄₁×#3302	C₂	semidirect
6. D₄×SD₁₆×C₄₁	C₂	semidirect
7. C₄₁×#3276	C₂	semidirect
8. C₄₁×#3266	C₂	semidirect
9. C₄₁×#3216	C₂	semidirect
10. C₄₁×#3210	C₂	semidirect
11. C₄₁×#3201	C₂	semidirect
12. C₄₁×#3110	C₂	semidirect
13. C₄₁×#3101	C₂	semidirect
14. C₄₁×#3009	C₂	semidirect
15. C₄₁×#2981	C₂	semidirect
17. C₂×#137×C₄₁	C₂²	semidirect
18. C₂²×SD₁₆×C₄₁	C₂²	semidirect
22. C₄₁×#556	C₂²	semidirect
23. C₄₁×#556	C₂²	semidirect
24. D₄×Q₈×C₄₁	C₂²	semidirect
25. D₄×Q₈×C₄₁	C₂²	semidirect
35. C₄₁×#536	C₂²	semidirect
37. C₄₁×#533	C₂²	semidirect
38. C₄₁×#533	C₂²	semidirect
43. C₄₁×#497	C₂²	semidirect
44. C₄₁×#494	C₂²	semidirect
45. C₄₁×#492	C₂²	semidirect
46. C₄₁×#489	C₂²	semidirect
47. C₄₁×#487	C₂²	semidirect
48. C₄₁×#486	C₂²	semidirect
49. C₄₁×#485	C₂²	semidirect
50. C₄₁×#484	C₂²	semidirect
51. C₄₁×#483	C₂²	semidirect
52. C₄₁×#482	C₂²	semidirect
53. C₄₁×#476	C₂²	semidirect
54. C₄₁×#474	C₂²	semidirect
55. C₄₁×#470	C₂²	semidirect
56. C₄₁×#468	C₂²	semidirect
57. C₄₁×#467	C₂²	semidirect
58. C₄₁×#465	C₂²	semidirect
59. C₄₁×#464	C₂²	semidirect
60. C₄₁×#462	C₂²	semidirect
61. C₄₁×#461	C₂²	semidirect
62. C₄₁×#461	C₂²	semidirect
63. C₄₁×#460	C₂²	semidirect
64. C₄₁×#452	C₂²	semidirect
65. C₄₁×#452	C₂²	semidirect
66. C₄₁×#452	C₂²	semidirect
67. C₄₁×#452	C₂²	semidirect
68. C₄₁×#451	C₂²	semidirect
71. C₄₁×#450	C₂²	semidirect
72. C₄₁×#450	C₂²	semidirect
73. C₄₁×#448	C₂²	semidirect
74. C₄₁×#440	C₂²	semidirect
75. C₄×SD₁₆×C₄₁	C₂²	semidirect
76. C₄×SD₁₆×C₄₁	C₂²	semidirect
77. C₄₁×#436	C₂²	semidirect
78. C₄₁×#435	C₂²	semidirect
79. C₈×D₄×C₄₁	C₂²	semidirect
80. C₄₁×#432	C₂²	semidirect
81. C₄₁×#431	C₂²	semidirect
82. C₄₁×#418	C₂²	semidirect
83. C₄₁×#416	C₂²	semidirect
84. C₄₁×#408	C₂²	semidirect
358. #61680	C₄₁	direct (N × H)
387. #3550	C₂×C₄₁	semidirect
389. #3324	C₂×C₄₁	semidirect
390. #3311	C₂×C₄₁	semidirect
391. #3302	C₂×C₄₁	semidirect
392. D₄×SD₁₆	C₂×C₄₁	semidirect
393. #3276	C₂×C₄₁	semidirect
394. #3266	C₂×C₄₁	semidirect
395. #3216	C₂×C₄₁	semidirect
396. #3210	C₂×C₄₁	semidirect
397. #3201	C₂×C₄₁	semidirect
398. #3110	C₂×C₄₁	semidirect
399. #3101	C₂×C₄₁	semidirect
400. #3009	C₂×C₄₁	semidirect
401. #2981	C₂×C₄₁	semidirect
410. C₂×#137	C₂²×C₄₁	semidirect
411. C₂²×SD₁₆	C₂²×C₄₁	semidirect
415. #556	C₂²×C₄₁	semidirect
416. #556	C₂²×C₄₁	semidirect
417. D₄×Q₈	C₂²×C₄₁	semidirect
418. D₄×Q₈	C₂²×C₄₁	semidirect
428. #536	C₂²×C₄₁	semidirect
430. #533	C₂²×C₄₁	semidirect
431. #533	C₂²×C₄₁	semidirect
436. #497	C₂²×C₄₁	semidirect
437. #494	C₂²×C₄₁	semidirect
438. #492	C₂²×C₄₁	semidirect
439. #489	C₂²×C₄₁	semidirect
440. #487	C₂²×C₄₁	semidirect
441. #486	C₂²×C₄₁	semidirect
442. #485	C₂²×C₄₁	semidirect
443. #484	C₂²×C₄₁	semidirect
444. #483	C₂²×C₄₁	semidirect
445. #482	C₂²×C₄₁	semidirect
446. #476	C₂²×C₄₁	semidirect
447. #474	C₂²×C₄₁	semidirect
448. #470	C₂²×C₄₁	semidirect
449. #468	C₂²×C₄₁	semidirect
450. #467	C₂²×C₄₁	semidirect
451. #465	C₂²×C₄₁	semidirect
452. #464	C₂²×C₄₁	semidirect
453. #462	C₂²×C₄₁	semidirect
454. #461	C₂²×C₄₁	semidirect
455. #461	C₂²×C₄₁	semidirect
456. #460	C₂²×C₄₁	semidirect
457. #452	C₂²×C₄₁	semidirect
458. #452	C₂²×C₄₁	semidirect
459. #452	C₂²×C₄₁	semidirect
460. #452	C₂²×C₄₁	semidirect
461. #451	C₂²×C₄₁	semidirect
464. #450	C₂²×C₄₁	semidirect
465. #450	C₂²×C₄₁	semidirect
466. #448	C₂²×C₄₁	semidirect
467. #440	C₂²×C₄₁	semidirect
468. C₄×SD₁₆	C₂²×C₄₁	semidirect
469. C₄×SD₁₆	C₂²×C₄₁	semidirect
470. #436	C₂²×C₄₁	semidirect
471. #435	C₂²×C₄₁	semidirect
472. C₈×D₄	C₂²×C₄₁	semidirect
473. #432	C₂²×C₄₁	semidirect
474. #431	C₂²×C₄₁	semidirect
475. #418	C₂²×C₄₁	semidirect
476. #416	C₂²×C₄₁	semidirect
477. #408	C₂²×C₄₁	semidirect
478. C₄₁	#61680	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×#3496	2
C₄₁×#3324	2
C₄₁×#3311	2
C₄₁×#3302	2
D₄×SD₁₆×C₄₁	2
C₄₁×#3276	2
C₄₁×#3266	2
C₄₁×#3216	2
C₄₁×#3210	2
C₄₁×#3201	2
C₄₁×#3110	2
C₄₁×#3101	2
C₄₁×#3009	2
C₄₁×#2981	2
#61680	41

Subgroups — C41×#61680 #23837881

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61680 #23837881