Subgroups — C₄₁×#24277 #23800478

Order 10496.

1608 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,ℤ/8)×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#469	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#468	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#436	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2408	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2407	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2055	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#2054	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#2000	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1999	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1970	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#1968	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#1809	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#1788	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#1786	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×AGL(1,ℤ/8)×C₄₁	—	2	4	no	—
19	C₂×AGL(1,ℤ/8)×C₄₁	—	2	4	no	—
20	C₂×AGL(1,ℤ/8)×C₄₁	—	2	4	no	—
21	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
22	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
23	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
24	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
28	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic, complemented
31	C₂×#120×C₄₁	—	2	1	no	—
32	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
33	C₄₁×#469	—	2	4	no	—
34	C₄₁×#468	—	2	4	no	—
35	C₄₁×#436	—	2	4	no	—
36	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic, complemented
37	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
39	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic, complemented
40	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic, complemented
41	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
42	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
43	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
44	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
45	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic, complemented
46	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
50	C₄₁×#394	—	2	1	no	—
51	C₄₁×#394	—	2	1	no	—
52	C₄₁×#392	—	2	1	no	—
53	C₄₁×#392	—	2	1	no	—
54	C₄₁×#391	C₂²	1	1	yes	characteristic, complemented
55	C₄₁×#390	C₂²	1	1	yes	characteristic
56	C₄₁×#390	C₂²	1	1	yes	characteristic
57	C₄₁×#390	C₂²	1	1	yes	characteristic, complemented
58	C₄₁×#386	—	2	1	no	—
59	C₄₁×#385	—	2	1	no	—
60	C₄₁×#380	C₂²	1	1	yes	characteristic
61	C₄₁×#380	C₂²	1	1	yes	characteristic
62	C₄₁×#379	—	2	1	no	—
63	C₄₁×#340	C₂²	1	1	yes	characteristic, complemented
64	C₄₁×#340	C₂²	1	1	yes	characteristic, complemented
65	C₂⁵×C₄₁	—	2	1	no	—
66	C₂×#41×C₄₁	—	2	2	no	—
67	C₂×#41×C₄₁	—	2	2	no	—
68	C₂×#41×C₄₁	—	2	2	no	—
69	C₂×#41×C₄₁	—	2	2	no	—
70	C₂×#41×C₄₁	—	4	1	no	—
71	C₂×#41×C₄₁	—	4	1	no	—
72	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₄₁	—	2	2	no	—
74	C₂²×D₄×C₄₁	—	2	2	no	—
75	C₂²×D₄×C₄₁	—	2	1	no	—
76	C₂²×D₄×C₄₁	—	2	1	no	—
77	C₂²×D₄×C₄₁	—	2	1	no	—
78	C₂²×D₄×C₄₁	—	2	1	no	—
79	C₂²×D₄×C₄₁	—	2	2	no	—
80	C₂²×D₄×C₄₁	—	2	1	no	—
81	C₂²×D₄×C₄₁	—	2	2	no	—
82	C₂²×D₄×C₄₁	—	4	1	no	—
83	C₂²×D₄×C₄₁	—	4	1	no	—
84	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
85	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₄₁	—	2	1	no	—
89	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
91	AGL(1,ℤ/8)×C₄₁	—	2	32	no	—
92	C₂×SD₁₆×C₄₁	—	2	2	no	—
93	C₂×SD₁₆×C₄₁	—	2	2	no	—
94	C₂×SD₁₆×C₄₁	—	2	2	no	—
95	C₂×SD₁₆×C₄₁	—	2	2	no	—
96	C₂×SD₁₆×C₄₁	—	2	2	no	—
97	C₂×SD₁₆×C₄₁	D₄	1	4	yes	complemented
98	C₂×D₈×C₄₁	—	2	2	no	—
99	C₂×D₈×C₄₁	—	2	2	no	—
100	C₂×D₈×C₄₁	—	2	2	no	—
101	C₂×D₈×C₄₁	—	2	2	no	—
102	C₂×D₈×C₄₁	—	2	2	no	—
103	C₂×D₈×C₄₁	D₄	1	4	yes	complemented
104	C₂×M₁₆×C₄₁	—	2	2	no	—
105	C₂×M₁₆×C₄₁	—	2	2	no	—
106	C₂×M₁₆×C₄₁	—	2	2	no	—
107	C₂×M₁₆×C₄₁	—	2	2	no	—
108	C₂×M₁₆×C₄₁	—	2	2	no	—
109	C₂×M₁₆×C₄₁	D₄	1	4	yes	complemented
110	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
114	C₂²⋊Q₈×C₄₁	—	2	2	no	—
115	C₂²⋊Q₈×C₄₁	—	4	1	no	—
116	#121×C₄₁	—	2	2	no	—
117	#121×C₄₁	—	2	2	no	—
118	#121×C₄₁	—	2	2	no	—
119	#121×C₄₁	—	4	1	no	—
120	#121×C₄₁	—	4	1	no	—
121	#121×C₄₁	—	4	1	no	—
122	#120×C₄₁	—	4	4	no	—
123	C₄×D₄×C₄₁	—	2	2	no	—
124	C₄×D₄×C₄₁	—	2	2	no	—
125	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
126	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
133	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
134	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
135	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
136	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
137	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
138	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
139	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
140	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
141	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
142	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
143	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
144	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
145	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
146	#107×C₄₁	—	2	2	no	—
147	#106×C₄₁	—	2	2	no	—
148	C₄⋊C₈×C₄₁	—	2	2	no	—
149	#103×C₄₁	—	2	2	no	—
150	#103×C₄₁	—	4	1	no	—
151	#102×C₄₁	—	2	2	no	—
152	#102×C₄₁	—	2	2	no	—
153	#102×C₄₁	—	2	2	no	—
154	#102×C₄₁	—	4	1	no	—
155	#102×C₄₁	—	4	1	no	—
156	#102×C₄₁	—	4	1	no	—
157	C₂²⋊C₈×C₄₁	—	2	2	no	—
158	C₂²⋊C₈×C₄₁	—	2	2	no	—
159	C₄×C₈×C₄₁	—	2	2	no	—
160	#95×C₄₁	—	2	1	no	—
161	#95×C₄₁	—	2	1	no	—
162	#95×C₄₁	—	2	1	no	—
163	#95×C₄₁	—	2	1	no	—
164	C₂⁴×C₄₁	—	2	1	no	—
165	C₂⁴×C₄₁	—	2	1	no	—
166	C₂⁴×C₄₁	—	2	1	no	—
167	C₂⁴×C₄₁	—	4	2	no	—
168	C₂⁴×C₄₁	—	4	2	no	—
169	C₂⁴×C₄₁	—	4	2	no	—
170	C₂⁴×C₄₁	—	4	2	no	—
171	C₂⁴×C₄₁	—	4	2	no	—
172	C₂⁴×C₄₁	—	8	1	no	—
173	C₂⁴×C₄₁	—	8	1	no	—
174	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
175	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
176	#41×C₄₁	—	2	8	no	—
177	#41×C₄₁	—	4	4	no	—
178	#41×C₄₁	—	4	4	no	—
179	#41×C₄₁	—	4	4	no	—
180	C₂×Q₈×C₄₁	—	2	1	no	—
181	C₂×Q₈×C₄₁	—	2	1	no	—
182	C₂×Q₈×C₄₁	—	2	1	no	—
183	C₂×Q₈×C₄₁	—	2	1	no	—
184	C₂×Q₈×C₄₁	—	2	1	no	—
185	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
186	C₂×D₄×C₄₁	—	2	8	no	—
187	C₂×D₄×C₄₁	—	2	2	no	—
188	C₂×D₄×C₄₁	—	2	2	no	—
189	C₂×D₄×C₄₁	—	2	1	no	—
190	C₂×D₄×C₄₁	—	2	1	no	—
191	C₂×D₄×C₄₁	—	2	1	no	—
192	C₂×D₄×C₄₁	—	2	1	no	—
193	C₂×D₄×C₄₁	—	2	1	no	—
194	C₂×D₄×C₄₁	—	2	1	no	—
195	C₂×D₄×C₄₁	—	2	1	no	—
196	C₂×D₄×C₄₁	—	2	1	no	—
197	C₂×D₄×C₄₁	—	2	1	no	—
198	C₂×D₄×C₄₁	—	2	1	no	—
199	C₂×D₄×C₄₁	—	2	1	no	—
200	C₂×D₄×C₄₁	—	2	1	no	—
201	C₂×D₄×C₄₁	—	2	1	no	—
202	C₂×D₄×C₄₁	—	2	1	no	—
203	C₂×D₄×C₄₁	—	2	1	no	—
204	C₂×D₄×C₄₁	—	4	4	no	—
205	C₂×D₄×C₄₁	—	4	4	no	—
206	C₂×D₄×C₄₁	—	4	1	no	—
207	C₂×D₄×C₄₁	—	4	2	no	—
208	C₂×D₄×C₄₁	—	4	2	no	—
209	C₂×D₄×C₄₁	—	4	2	no	—
210	C₂×D₄×C₄₁	—	4	4	no	—
211	C₂×D₄×C₄₁	—	4	2	no	—
212	C₂×D₄×C₄₁	—	4	2	no	—
213	C₂×D₄×C₄₁	—	4	2	no	—
214	C₂×D₄×C₄₁	—	4	2	no	—
215	C₂×D₄×C₄₁	—	4	2	no	—
216	C₂×D₄×C₄₁	—	4	2	no	—
217	C₂×D₄×C₄₁	—	4	2	no	—
218	C₂×D₄×C₄₁	—	4	2	no	—
219	C₂×D₄×C₄₁	—	4	2	no	—
220	C₂×D₄×C₄₁	—	8	1	no	—
221	C₂×D₄×C₄₁	—	8	1	no	—
222	C₂×D₄×C₄₁	—	8	1	no	—
223	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
224	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
225	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₄₁	—	2	1	no	—
227	C₂²×C₄×C₄₁	—	2	1	no	—
228	C₂²×C₄×C₄₁	—	2	1	no	—
229	C₂²×C₄×C₄₁	—	2	1	no	—
230	C₂²×C₄×C₄₁	—	2	1	no	—
231	C₂²×C₄×C₄₁	—	2	1	no	—
232	C₂²×C₄×C₄₁	—	2	1	no	—
233	C₂²×C₄×C₄₁	—	2	1	no	—
234	C₂²×C₄×C₄₁	—	2	1	no	—
235	C₂²×C₄×C₄₁	—	2	1	no	—
236	C₂²×C₄×C₄₁	—	2	1	no	—
237	C₂²×C₄×C₄₁	—	2	1	no	—
238	C₂²×C₄×C₄₁	—	2	1	no	—
239	C₂²×C₄×C₄₁	—	2	1	no	—
240	C₂²×C₄×C₄₁	—	2	1	no	—
241	C₂²×C₄×C₄₁	—	4	2	no	—
242	C₂²×C₄×C₄₁	—	4	2	no	—
243	C₂²×C₄×C₄₁	—	4	2	no	—
244	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
248	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₄₁	#41	1	2	yes	—
250	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
251	SD₁₆×C₄₁	—	2	8	no	—
252	SD₁₆×C₄₁	—	2	8	no	—
253	D₈×C₄₁	—	2	8	no	—
254	D₈×C₄₁	—	2	8	no	—
255	M₁₆×C₄₁	—	2	8	no	—
256	M₁₆×C₄₁	—	4	4	no	—
257	C₂×C₈×C₄₁	—	2	1	no	—
258	C₂×C₈×C₄₁	—	2	1	no	—
259	C₂×C₈×C₄₁	—	2	1	no	—
260	C₂×C₈×C₄₁	—	2	1	no	—
261	C₂×C₈×C₄₁	—	2	1	no	—
262	C₂×C₈×C₄₁	—	2	1	no	—
263	C₂×C₈×C₄₁	—	2	1	no	—
264	C₂×C₈×C₄₁	—	2	1	no	—
265	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
266	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
267	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
268	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
269	C₄⋊C₄×C₄₁	—	2	2	no	—
270	C₄⋊C₄×C₄₁	—	2	1	no	—
271	C₄⋊C₄×C₄₁	—	2	1	no	—
272	C₄⋊C₄×C₄₁	—	2	1	no	—
273	C₄⋊C₄×C₄₁	—	2	1	no	—
274	C₄⋊C₄×C₄₁	—	2	1	no	—
275	C₄⋊C₄×C₄₁	—	2	1	no	—
276	C₄⋊C₄×C₄₁	—	2	1	no	—
277	C₄⋊C₄×C₄₁	—	2	1	no	—
278	C₄⋊C₄×C₄₁	—	4	2	no	—
279	C₂²⋊C₄×C₄₁	—	2	2	no	—
280	C₂²⋊C₄×C₄₁	—	2	2	no	—
281	C₂²⋊C₄×C₄₁	—	4	2	no	—
282	C₂²⋊C₄×C₄₁	—	4	2	no	—
283	C₂²⋊C₄×C₄₁	—	4	2	no	—
284	C₂²⋊C₄×C₄₁	—	4	2	no	—
285	C₂²⋊C₄×C₄₁	—	4	2	no	—
286	C₂²⋊C₄×C₄₁	—	4	2	no	—
287	C₂²⋊C₄×C₄₁	—	4	2	no	—
288	C₂²⋊C₄×C₄₁	—	4	2	no	—
289	C₂²⋊C₄×C₄₁	—	8	1	no	—
290	C₂²⋊C₄×C₄₁	—	8	1	no	—
291	C₂²⋊C₄×C₄₁	—	8	1	no	—
292	C₂²⋊C₄×C₄₁	—	8	1	no	—
293	C₄²×C₄₁	—	2	1	no	—
294	C₄²×C₄₁	—	2	1	no	—
295	C₂³×C₄₁	—	2	1	no	—
296	C₂³×C₄₁	—	2	1	no	—
297	C₂³×C₄₁	—	2	1	no	—
298	C₂³×C₄₁	—	2	1	no	—
299	C₂³×C₄₁	—	2	1	no	—
300	C₂³×C₄₁	—	2	1	no	—
301	C₂³×C₄₁	—	2	1	no	—
302	C₂³×C₄₁	—	2	1	no	—
303	C₂³×C₄₁	—	2	2	no	—
304	C₂³×C₄₁	—	2	2	no	—
305	C₂³×C₄₁	—	2	2	no	—
306	C₂³×C₄₁	—	2	1	no	—
307	C₂³×C₄₁	—	2	1	no	—
308	C₂³×C₄₁	—	2	1	no	—
309	C₂³×C₄₁	—	2	1	no	—
310	C₂³×C₄₁	—	2	1	no	—
311	C₂³×C₄₁	—	4	8	no	—
312	C₂³×C₄₁	—	4	1	no	—
313	C₂³×C₄₁	—	4	1	no	—
314	C₂³×C₄₁	—	4	1	no	—
315	C₂³×C₄₁	—	4	1	no	—
316	C₂³×C₄₁	—	4	1	no	—
317	C₂³×C₄₁	—	4	1	no	—
318	C₂³×C₄₁	—	4	1	no	—
319	C₂³×C₄₁	—	4	1	no	—
320	C₂³×C₄₁	—	4	1	no	—
321	C₂³×C₄₁	—	4	1	no	—
322	C₂³×C₄₁	—	4	1	no	—
323	C₂³×C₄₁	—	4	1	no	—
324	C₂³×C₄₁	—	4	1	no	—
325	C₂³×C₄₁	—	4	1	no	—
326	C₂³×C₄₁	—	4	1	no	—
327	C₂³×C₄₁	—	4	1	no	—
328	C₂³×C₄₁	—	4	1	no	—
329	C₂³×C₄₁	—	4	1	no	—
330	C₂³×C₄₁	—	8	4	no	—
331	C₂³×C₄₁	—	8	4	no	—
332	C₂³×C₄₁	—	8	4	no	—
333	C₂³×C₄₁	—	8	4	no	—
334	C₂³×C₄₁	—	8	4	no	—
335	C₂³×C₄₁	—	8	4	no	—
336	C₂³×C₄₁	#121	1	2	yes	—
337	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
338	Q₈×C₄₁	—	2	2	no	—
339	Q₈×C₄₁	—	2	2	no	—
340	Q₈×C₄₁	—	4	1	no	—
341	Q₈×C₄₁	—	4	1	no	—
342	D₄×C₄₁	—	2	2	no	—
343	D₄×C₄₁	—	2	2	no	—
344	D₄×C₄₁	—	2	2	no	—
345	D₄×C₄₁	—	2	2	no	—
346	D₄×C₄₁	—	2	2	no	—
347	D₄×C₄₁	—	2	2	no	—
348	D₄×C₄₁	—	4	4	no	—
349	D₄×C₄₁	—	4	8	no	—
350	D₄×C₄₁	—	4	8	no	—
351	D₄×C₄₁	—	4	1	no	—
352	D₄×C₄₁	—	4	1	no	—
353	D₄×C₄₁	—	4	1	no	—
354	D₄×C₄₁	—	4	1	no	—
355	D₄×C₄₁	—	4	1	no	—
356	D₄×C₄₁	—	4	1	no	—
357	D₄×C₄₁	—	8	4	no	—
358	D₄×C₄₁	—	8	4	no	—
359	D₄×C₄₁	—	8	4	no	—
360	C₂×C₄×C₄₁	—	2	1	no	—
361	C₂×C₄×C₄₁	—	2	1	no	—
362	C₂×C₄×C₄₁	—	2	1	no	—
363	C₂×C₄×C₄₁	—	2	1	no	—
364	C₂×C₄×C₄₁	—	2	2	no	—
365	C₂×C₄×C₄₁	—	2	2	no	—
366	C₂×C₄×C₄₁	—	2	2	no	—
367	C₂×C₄×C₄₁	—	2	2	no	—
368	C₂×C₄×C₄₁	—	2	1	no	—
369	C₂×C₄×C₄₁	—	2	1	no	—
370	C₂×C₄×C₄₁	—	2	1	no	—
371	C₂×C₄×C₄₁	—	2	1	no	—
372	C₂×C₄×C₄₁	—	2	2	no	—
373	C₂×C₄×C₄₁	—	2	1	no	—
374	C₂×C₄×C₄₁	—	2	1	no	—
375	C₂×C₄×C₄₁	—	4	8	no	—
376	C₂×C₄×C₄₁	—	4	1	no	—
377	C₂×C₄×C₄₁	—	4	1	no	—
378	C₂×C₄×C₄₁	—	4	1	no	—
379	C₂×C₄×C₄₁	—	4	1	no	—
380	C₂×C₄×C₄₁	—	4	1	no	—
381	C₂×C₄×C₄₁	—	4	1	no	—
382	C₂×C₄×C₄₁	—	4	1	no	—
383	C₂×C₄×C₄₁	—	4	1	no	—
384	C₂×C₄×C₄₁	—	4	1	no	—
385	C₂×C₄×C₄₁	—	4	1	no	—
386	C₂×C₄×C₄₁	—	4	1	no	—
387	C₂×C₄×C₄₁	—	4	1	no	—
388	C₂×C₄×C₄₁	—	4	1	no	—
389	C₂×C₄×C₄₁	—	4	1	no	—
390	C₂×C₄×C₄₁	—	4	1	no	—
391	C₂×C₄×C₄₁	—	4	1	no	—
392	C₂×C₄×C₄₁	—	4	1	no	—
393	C₂×C₄×C₄₁	—	4	1	no	—
394	C₂×C₄×C₄₁	#121	1	2	yes	—
395	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	complemented
396	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
400	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
401	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
402	C₈×C₄₁	—	2	2	no	—
403	C₈×C₄₁	—	4	1	no	—
404	C₈×C₄₁	—	4	1	no	—
405	C₈×C₄₁	#120	1	4	yes	complemented
406	#24277	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
407	C₂²×C₄₁	—	2	2	no	—
408	C₂²×C₄₁	—	2	2	no	—
409	C₂²×C₄₁	—	2	2	no	—
410	C₂²×C₄₁	—	4	1	no	—
411	C₂²×C₄₁	—	4	1	no	—
412	C₂²×C₄₁	—	4	1	no	—
413	C₂²×C₄₁	—	4	1	no	—
414	C₂²×C₄₁	—	4	2	no	—
415	C₂²×C₄₁	—	4	1	no	—
416	C₂²×C₄₁	—	4	2	no	—
417	C₂²×C₄₁	—	4	2	no	—
418	C₂²×C₄₁	—	4	1	no	—
419	C₂²×C₄₁	—	4	2	no	—
420	C₂²×C₄₁	—	4	2	no	—
421	C₂²×C₄₁	—	4	1	no	—
422	C₂²×C₄₁	—	4	2	no	—
423	C₂²×C₄₁	—	4	2	no	—
424	C₂²×C₄₁	—	4	1	no	—
425	C₂²×C₄₁	—	4	2	no	—
426	C₂²×C₄₁	—	4	1	no	—
427	C₂²×C₄₁	—	4	2	no	—
428	C₂²×C₄₁	—	4	1	no	—
429	C₂²×C₄₁	—	4	1	no	—
430	C₂²×C₄₁	—	8	16	no	—
431	C₂²×C₄₁	—	8	1	no	—
432	C₂²×C₄₁	—	8	1	no	—
433	C₂²×C₄₁	—	8	1	no	—
434	C₂²×C₄₁	—	8	1	no	—
435	C₂²×C₄₁	—	8	1	no	—
436	C₂²×C₄₁	—	8	1	no	—
437	C₂²×C₄₁	—	8	1	no	—
438	C₂²×C₄₁	—	8	1	no	—
439	C₂²×C₄₁	—	8	1	no	—
440	C₂²×C₄₁	—	8	1	no	—
441	C₂²×C₄₁	—	8	1	no	—
442	C₂²×C₄₁	—	8	1	no	—
443	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
444	C₂²×C₄₁	D₄²	1	1	yes	characteristic
445	C₂²×C₄₁	D₄²	1	1	yes	characteristic
446	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
447	C₂²×C₄₁	#575	1	1	yes	characteristic
448	C₂²×C₄₁	#576	1	1	yes	characteristic
449	C₂²×C₄₁	#577	1	1	yes	characteristic
450	C₄×C₄₁	—	2	2	no	—
451	C₄×C₄₁	—	2	2	no	—
452	C₄×C₄₁	—	4	1	no	—
453	C₄×C₄₁	—	4	2	no	—
454	C₄×C₄₁	—	4	1	no	—
455	C₄×C₄₁	—	8	1	no	—
456	C₄×C₄₁	—	8	1	no	—
457	C₄×C₄₁	—	8	1	no	—
458	C₄×C₄₁	—	8	1	no	—
459	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
460	C₄×C₄₁	#535	1	1	yes	characteristic
461	C₄×C₄₁	#546	1	1	yes	characteristic
462	C₄×C₄₁	#546	1	1	yes	characteristic
463	C₂²×AGL(1,ℤ/8)	C₂×C₄₁	1	1	yes	characteristic, complemented
464	C₂×#469	C₂×C₄₁	1	1	yes	characteristic, complemented
465	C₂×#468	C₂×C₄₁	1	1	yes	characteristic, complemented
466	C₂×#436	C₂×C₄₁	1	1	yes	characteristic, complemented
467	#2408	C₂×C₄₁	1	1	yes	characteristic, complemented
468	#2407	C₂×C₄₁	1	1	yes	characteristic, complemented
469	#2055	C₂×C₄₁	1	1	yes	characteristic, complemented
470	#2054	C₂×C₄₁	1	1	yes	characteristic, complemented
471	#2000	C₂×C₄₁	1	1	yes	characteristic, complemented
472	#1999	C₂×C₄₁	1	1	yes	characteristic, complemented
473	#1970	C₂×C₄₁	1	1	yes	characteristic, complemented
474	#1968	C₂×C₄₁	1	1	yes	characteristic, complemented
475	#1809	C₂×C₄₁	1	1	yes	characteristic, complemented
476	#1788	C₂×C₄₁	1	1	yes	characteristic, complemented
477	#1786	C₂×C₄₁	1	1	yes	characteristic, complemented
478	C₂×C₄₁	—	4	2	no	—
479	C₂×C₄₁	—	8	1	no	—
480	C₂×C₄₁	—	8	2	no	—
481	C₂×C₄₁	—	8	2	no	—
482	C₂×C₄₁	—	8	2	no	—
483	C₂×C₄₁	#2408	1	1	yes	characteristic
484	C₂×C₄₁	#3055	1	1	yes	characteristic
485	C₂×C₄₁	#3062	1	1	yes	characteristic
486	C₂×C₄₁	#3272	1	1	yes	characteristic
487	C₂×C₄₁	#3273	1	1	yes	characteristic
488	C₂×C₄₁	#3274	1	1	yes	characteristic
489	C₂×C₄₁	#3275	1	1	yes	characteristic
490	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
491	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
492	C₂×AGL(1,ℤ/8)	—	2	4	no	—
493	C₂×AGL(1,ℤ/8)	—	2	4	no	—
494	C₂×AGL(1,ℤ/8)	—	2	4	no	—
495	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
496	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
497	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
498	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
499	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
500	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
501	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
502	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
503	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
504	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic, complemented
505	C₂×#120	—	2	1	no	—
506	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
507	#469	—	2	4	no	—
508	#468	—	2	4	no	—
509	#436	—	2	4	no	—
510	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic, complemented
511	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic, complemented
512	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
513	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic, complemented
514	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic, complemented
515	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
516	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
517	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
518	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
519	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic, complemented
520	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic, complemented
521	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
522	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
523	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
524	#394	—	2	1	no	—
525	#394	—	2	1	no	—
526	#392	—	2	1	no	—
527	#392	—	2	1	no	—
528	#391	C₂²×C₄₁	1	1	yes	characteristic, complemented
529	#390	C₂²×C₄₁	1	1	yes	characteristic
530	#390	C₂²×C₄₁	1	1	yes	characteristic
531	#390	C₂²×C₄₁	1	1	yes	characteristic, complemented
532	#386	—	2	1	no	—
533	#385	—	2	1	no	—
534	#380	C₂²×C₄₁	1	1	yes	characteristic
535	#380	C₂²×C₄₁	1	1	yes	characteristic
536	#379	—	2	1	no	—
537	#340	C₂²×C₄₁	1	1	yes	characteristic, complemented
538	#340	C₂²×C₄₁	1	1	yes	characteristic, complemented
539	C₄₁	#24277	1	1	yes	characteristic, direct product factor, Sylow
540	C₂⁵	—	2	1	no	—
541	C₂×#41	—	2	2	no	—
542	C₂×#41	—	2	2	no	—
543	C₂×#41	—	2	2	no	—
544	C₂×#41	—	2	2	no	—
545	C₂×#41	—	4	1	no	—
546	C₂×#41	—	4	1	no	—
547	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
548	C₂²×D₄	—	2	2	no	—
549	C₂²×D₄	—	2	2	no	—
550	C₂²×D₄	—	2	1	no	—
551	C₂²×D₄	—	2	1	no	—
552	C₂²×D₄	—	2	1	no	—
553	C₂²×D₄	—	2	1	no	—
554	C₂²×D₄	—	2	2	no	—
555	C₂²×D₄	—	2	1	no	—
556	C₂²×D₄	—	2	2	no	—
557	C₂²×D₄	—	4	1	no	—
558	C₂²×D₄	—	4	1	no	—
559	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
560	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
561	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
562	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
563	C₂³×C₄	—	2	1	no	—
564	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
565	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
566	AGL(1,ℤ/8)	—	2	32	no	—
567	C₂×SD₁₆	—	2	2	no	—
568	C₂×SD₁₆	—	2	2	no	—
569	C₂×SD₁₆	—	2	2	no	—
570	C₂×SD₁₆	—	2	2	no	—
571	C₂×SD₁₆	—	2	2	no	—
572	C₂×SD₁₆	D₄×C₄₁	1	4	yes	complemented
573	C₂×D₈	—	2	2	no	—
574	C₂×D₈	—	2	2	no	—
575	C₂×D₈	—	2	2	no	—
576	C₂×D₈	—	2	2	no	—
577	C₂×D₈	—	2	2	no	—
578	C₂×D₈	D₄×C₄₁	1	4	yes	complemented
579	C₂×M₁₆	—	2	2	no	—
580	C₂×M₁₆	—	2	2	no	—
581	C₂×M₁₆	—	2	2	no	—
582	C₂×M₁₆	—	2	2	no	—
583	C₂×M₁₆	—	2	2	no	—
584	C₂×M₁₆	D₄×C₄₁	1	4	yes	complemented
585	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
586	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
587	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
588	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
589	C₂²⋊Q₈	—	2	2	no	—
590	C₂²⋊Q₈	—	4	1	no	—
591	#121	—	2	2	no	—
592	#121	—	2	2	no	—
593	#121	—	2	2	no	—
594	#121	—	4	1	no	—
595	#121	—	4	1	no	—
596	#121	—	4	1	no	—
597	#120	—	4	4	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	2	no	—
600	C₂×C₄⋊C₄	—	2	1	no	—
601	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
606	C₂×C₂²⋊C₄	—	2	1	no	—
607	C₂×C₂²⋊C₄	—	2	1	no	—
608	C₂×C₂²⋊C₄	—	2	1	no	—
609	C₂×C₂²⋊C₄	—	2	1	no	—
610	C₂×C₂²⋊C₄	—	2	1	no	—
611	C₂×C₂²⋊C₄	—	2	1	no	—
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
619	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
621	#107	—	2	2	no	—
622	#106	—	2	2	no	—
623	C₄⋊C₈	—	2	2	no	—
624	#103	—	2	2	no	—
625	#103	—	4	1	no	—
626	#102	—	2	2	no	—
627	#102	—	2	2	no	—
628	#102	—	2	2	no	—
629	#102	—	4	1	no	—
630	#102	—	4	1	no	—
631	#102	—	4	1	no	—
632	C₂²⋊C₈	—	2	2	no	—
633	C₂²⋊C₈	—	2	2	no	—
634	C₄×C₈	—	2	2	no	—
635	#95	—	2	1	no	—
636	#95	—	2	1	no	—
637	#95	—	2	1	no	—
638	#95	—	2	1	no	—
639	C₂⁴	—	2	1	no	—
640	C₂⁴	—	2	1	no	—
641	C₂⁴	—	2	1	no	—
642	C₂⁴	—	4	2	no	—
643	C₂⁴	—	4	2	no	—
644	C₂⁴	—	4	2	no	—
645	C₂⁴	—	4	2	no	—
646	C₂⁴	—	4	2	no	—
647	C₂⁴	—	8	1	no	—
648	C₂⁴	—	8	1	no	—
649	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
650	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
651	#41	—	2	8	no	—
652	#41	—	4	4	no	—
653	#41	—	4	4	no	—
654	#41	—	4	4	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	—	2	1	no	—
658	C₂×Q₈	—	2	1	no	—
659	C₂×Q₈	—	2	1	no	—
660	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
661	C₂×D₄	—	2	8	no	—
662	C₂×D₄	—	2	2	no	—
663	C₂×D₄	—	2	2	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	2	1	no	—
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	—	2	1	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	4	4	no	—
680	C₂×D₄	—	4	4	no	—
681	C₂×D₄	—	4	1	no	—
682	C₂×D₄	—	4	2	no	—
683	C₂×D₄	—	4	2	no	—
684	C₂×D₄	—	4	2	no	—
685	C₂×D₄	—	4	4	no	—
686	C₂×D₄	—	4	2	no	—
687	C₂×D₄	—	4	2	no	—
688	C₂×D₄	—	4	2	no	—
689	C₂×D₄	—	4	2	no	—
690	C₂×D₄	—	4	2	no	—
691	C₂×D₄	—	4	2	no	—
692	C₂×D₄	—	4	2	no	—
693	C₂×D₄	—	4	2	no	—
694	C₂×D₄	—	4	2	no	—
695	C₂×D₄	—	8	1	no	—
696	C₂×D₄	—	8	1	no	—
697	C₂×D₄	—	8	1	no	—
698	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
699	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
700	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	4	2	no	—
717	C₂²×C₄	—	4	2	no	—
718	C₂²×C₄	—	4	2	no	—
719	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
720	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
721	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
722	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
723	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
724	C₂²×C₄	#41×C₄₁	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
726	SD₁₆	—	2	8	no	—
727	SD₁₆	—	2	8	no	—
728	D₈	—	2	8	no	—
729	D₈	—	2	8	no	—
730	M₁₆	—	2	8	no	—
731	M₁₆	—	4	4	no	—
732	C₂×C₈	—	2	1	no	—
733	C₂×C₈	—	2	1	no	—
734	C₂×C₈	—	2	1	no	—
735	C₂×C₈	—	2	1	no	—
736	C₂×C₈	—	2	1	no	—
737	C₂×C₈	—	2	1	no	—
738	C₂×C₈	—	2	1	no	—
739	C₂×C₈	—	2	1	no	—
740	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
741	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
742	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
743	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	—	2	1	no	—
748	C₄⋊C₄	—	2	1	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	1	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	4	2	no	—
757	C₂²⋊C₄	—	4	2	no	—
758	C₂²⋊C₄	—	4	2	no	—
759	C₂²⋊C₄	—	4	2	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	—	4	2	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	8	1	no	—
765	C₂²⋊C₄	—	8	1	no	—
766	C₂²⋊C₄	—	8	1	no	—
767	C₂²⋊C₄	—	8	1	no	—
768	C₄²	—	2	1	no	—
769	C₄²	—	2	1	no	—
770	C₂³	—	2	1	no	—
771	C₂³	—	2	1	no	—
772	C₂³	—	2	1	no	—
773	C₂³	—	2	1	no	—
774	C₂³	—	2	1	no	—
775	C₂³	—	2	1	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	1	no	—
782	C₂³	—	2	1	no	—
783	C₂³	—	2	1	no	—
784	C₂³	—	2	1	no	—
785	C₂³	—	2	1	no	—
786	C₂³	—	4	8	no	—
787	C₂³	—	4	1	no	—
788	C₂³	—	4	1	no	—
789	C₂³	—	4	1	no	—
790	C₂³	—	4	1	no	—
791	C₂³	—	4	1	no	—
792	C₂³	—	4	1	no	—
793	C₂³	—	4	1	no	—
794	C₂³	—	4	1	no	—
795	C₂³	—	4	1	no	—
796	C₂³	—	4	1	no	—
797	C₂³	—	4	1	no	—
798	C₂³	—	4	1	no	—
799	C₂³	—	4	1	no	—
800	C₂³	—	4	1	no	—
801	C₂³	—	4	1	no	—
802	C₂³	—	4	1	no	—
803	C₂³	—	4	1	no	—
804	C₂³	—	4	1	no	—
805	C₂³	—	8	4	no	—
806	C₂³	—	8	4	no	—
807	C₂³	—	8	4	no	—
808	C₂³	—	8	4	no	—
809	C₂³	—	8	4	no	—
810	C₂³	—	8	4	no	—
811	C₂³	#121×C₄₁	1	2	yes	—
812	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
813	Q₈	—	2	2	no	—
814	Q₈	—	2	2	no	—
815	Q₈	—	4	1	no	—
816	Q₈	—	4	1	no	—
817	D₄	—	2	2	no	—
818	D₄	—	2	2	no	—
819	D₄	—	2	2	no	—
820	D₄	—	2	2	no	—
821	D₄	—	2	2	no	—
822	D₄	—	2	2	no	—
823	D₄	—	4	4	no	—
824	D₄	—	4	8	no	—
825	D₄	—	4	8	no	—
826	D₄	—	4	1	no	—
827	D₄	—	4	1	no	—
828	D₄	—	4	1	no	—
829	D₄	—	4	1	no	—
830	D₄	—	4	1	no	—
831	D₄	—	4	1	no	—
832	D₄	—	8	4	no	—
833	D₄	—	8	4	no	—
834	D₄	—	8	4	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	4	8	no	—
851	C₂×C₄	—	4	1	no	—
852	C₂×C₄	—	4	1	no	—
853	C₂×C₄	—	4	1	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	1	no	—
856	C₂×C₄	—	4	1	no	—
857	C₂×C₄	—	4	1	no	—
858	C₂×C₄	—	4	1	no	—
859	C₂×C₄	—	4	1	no	—
860	C₂×C₄	—	4	1	no	—
861	C₂×C₄	—	4	1	no	—
862	C₂×C₄	—	4	1	no	—
863	C₂×C₄	—	4	1	no	—
864	C₂×C₄	—	4	1	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	4	1	no	—
867	C₂×C₄	—	4	1	no	—
868	C₂×C₄	—	4	1	no	—
869	C₂×C₄	#121×C₄₁	1	2	yes	—
870	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	complemented
871	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
872	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
873	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
874	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
875	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
876	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
877	C₈	—	2	2	no	—
878	C₈	—	4	1	no	—
879	C₈	—	4	1	no	—
880	C₈	#120×C₄₁	1	4	yes	complemented
881	C₂²	—	2	2	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	2	2	no	—
884	C₂²	—	4	1	no	—
885	C₂²	—	4	1	no	—
886	C₂²	—	4	1	no	—
887	C₂²	—	4	1	no	—
888	C₂²	—	4	1	no	—
889	C₂²	—	4	1	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	1	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	1	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	1	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	4	1	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	1	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	8	16	no	—
905	C₂²	—	8	1	no	—
906	C₂²	—	8	1	no	—
907	C₂²	—	8	1	no	—
908	C₂²	—	8	1	no	—
909	C₂²	—	8	1	no	—
910	C₂²	—	8	1	no	—
911	C₂²	—	8	1	no	—
912	C₂²	—	8	1	no	—
913	C₂²	—	8	1	no	—
914	C₂²	—	8	1	no	—
915	C₂²	—	8	1	no	—
916	C₂²	—	8	1	no	—
917	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
918	C₂²	D₄²×C₄₁	1	1	yes	characteristic
919	C₂²	D₄²×C₄₁	1	1	yes	characteristic
920	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
921	C₂²	C₄₁×#575	1	1	yes	characteristic
922	C₂²	C₄₁×#576	1	1	yes	characteristic
923	C₂²	C₄₁×#577	1	1	yes	characteristic
924	C₄	—	2	2	no	—
925	C₄	—	2	2	no	—
926	C₄	—	4	1	no	—
927	C₄	—	4	1	no	—
928	C₄	—	4	2	no	—
929	C₄	—	8	1	no	—
930	C₄	—	8	1	no	—
931	C₄	—	8	1	no	—
932	C₄	—	8	1	no	—
933	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
934	C₄	C₄₁×#535	1	1	yes	characteristic
935	C₄	C₄₁×#546	1	1	yes	characteristic
936	C₄	C₄₁×#546	1	1	yes	characteristic
937	C₂	—	4	2	no	—
938	C₂	—	8	1	no	—
939	C₂	—	8	2	no	—
940	C₂	—	8	2	no	—
941	C₂	—	8	2	no	—
942	C₂	C₄₁×#2408	1	1	yes	characteristic
943	C₂	C₄₁×#3055	1	1	yes	characteristic
944	C₂	C₄₁×#3062	1	1	yes	characteristic
945	C₂	C₄₁×#3272	1	1	yes	characteristic
946	C₂	C₄₁×#3273	1	1	yes	characteristic
947	C₂	C₄₁×#3274	1	1	yes	characteristic
948	C₂	C₄₁×#3275	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×C₄×D₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×AGL(1,ℤ/8)×C₄₁	C₂	semidirect
2. C₂×C₄₁×#469	C₂	semidirect
3. C₂×C₄₁×#468	C₂	semidirect
4. C₂×C₄₁×#436	C₂	semidirect
5. C₄₁×#2408	C₂	semidirect
6. C₄₁×#2407	C₂	semidirect
7. C₄₁×#2055	C₂	semidirect
8. C₄₁×#2054	C₂	semidirect
9. C₄₁×#2000	C₂	semidirect
10. C₄₁×#1999	C₂	semidirect
11. C₄₁×#1970	C₂	semidirect
12. C₄₁×#1968	C₂	semidirect
13. C₄₁×#1809	C₂	semidirect
14. C₄₁×#1788	C₂	semidirect
15. C₄₁×#1786	C₂	semidirect
26. C₂²×M₁₆×C₄₁	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
30. C₂×#121×C₄₁	C₂²	semidirect
36. C₂×#107×C₄₁	C₂²	semidirect
37. C₂×#106×C₄₁	C₂²	semidirect
38. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
39. C₂×#103×C₄₁	C₂²	semidirect
40. C₂×#103×C₄₁	C₂²	semidirect
45. C₂×#102×C₄₁	C₂²	semidirect
46. C₂×#102×C₄₁	C₂²	semidirect
48. C₂×C₂²⋊C₈×C₄₁	C₂²	semidirect
49. C₂×C₄×C₈×C₄₁	C₂²	semidirect
54. C₄₁×#391	C₂²	semidirect
57. C₄₁×#390	C₂²	semidirect
63. C₄₁×#340	C₂²	semidirect
64. C₄₁×#340	C₂²	semidirect
97. C₂×SD₁₆×C₄₁	D₄	semidirect
103. C₂×D₈×C₄₁	D₄	semidirect
109. C₂×M₁₆×C₄₁	D₄	semidirect
395. C₂×C₄×C₄₁	AGL(1,ℤ/8)	semidirect
405. C₈×C₄₁	#120	semidirect
406. #24277	C₄₁	direct (N × H)
463. C₂²×AGL(1,ℤ/8)	C₂×C₄₁	semidirect
464. C₂×#469	C₂×C₄₁	semidirect
465. C₂×#468	C₂×C₄₁	semidirect
466. C₂×#436	C₂×C₄₁	semidirect
467. #2408	C₂×C₄₁	semidirect
468. #2407	C₂×C₄₁	semidirect
469. #2055	C₂×C₄₁	semidirect
470. #2054	C₂×C₄₁	semidirect
471. #2000	C₂×C₄₁	semidirect
472. #1999	C₂×C₄₁	semidirect
473. #1970	C₂×C₄₁	semidirect
474. #1968	C₂×C₄₁	semidirect
475. #1809	C₂×C₄₁	semidirect
476. #1788	C₂×C₄₁	semidirect
477. #1786	C₂×C₄₁	semidirect
500. C₂²×M₁₆	C₂²×C₄₁	semidirect
501. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
504. C₂×#121	C₂²×C₄₁	semidirect
510. C₂×#107	C₂²×C₄₁	semidirect
511. C₂×#106	C₂²×C₄₁	semidirect
512. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
513. C₂×#103	C₂²×C₄₁	semidirect
514. C₂×#103	C₂²×C₄₁	semidirect
519. C₂×#102	C₂²×C₄₁	semidirect
520. C₂×#102	C₂²×C₄₁	semidirect
522. C₂×C₂²⋊C₈	C₂²×C₄₁	semidirect
523. C₂×C₄×C₈	C₂²×C₄₁	semidirect
528. #391	C₂²×C₄₁	semidirect
531. #390	C₂²×C₄₁	semidirect
537. #340	C₂²×C₄₁	semidirect
538. #340	C₂²×C₄₁	semidirect
539. C₄₁	#24277	direct (N × H)
572. C₂×SD₁₆	D₄×C₄₁	semidirect
578. C₂×D₈	D₄×C₄₁	semidirect
584. C₂×M₁₆	D₄×C₄₁	semidirect
870. C₂×C₄	AGL(1,ℤ/8)×C₄₁	semidirect
880. C₈	#120×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×AGL(1,ℤ/8)×C₄₁	2
C₂×C₄₁×#469	2
C₂×C₄₁×#468	2
C₂×C₄₁×#436	2
C₄₁×#2408	2
C₄₁×#2407	2
C₄₁×#2055	2
C₄₁×#2054	2
C₄₁×#2000	2
C₄₁×#1999	2
C₄₁×#1970	2
C₄₁×#1968	2
C₄₁×#1809	2
C₄₁×#1788	2
C₄₁×#1786	2
#24277	41

Subgroups — C41×#24277 #23800478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24277 #23800478