Subgroups — C₄₁×#24247 #23800448

Order 10496.

1564 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#546	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#464	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#452	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#450	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×SD₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2536	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2035	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#2034	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#2001	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1958	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#1954	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#1804	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	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
19	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
21	C₄₁×#546	—	2	4	no	—
22	C₄₁×#546	—	2	4	no	—
23	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×#123×C₄₁	—	2	1	no	—
25	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
28	C₂×#121×C₄₁	—	2	1	no	—
29	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×#120×C₄₁	—	2	1	no	—
31	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₄₁	—	2	1	no	—
35	C₄₁×#464	—	2	4	no	—
36	C₄₁×#452	—	2	4	no	—
37	C₄₁×#450	—	2	4	no	—
38	C₄×SD₁₆×C₄₁	—	2	4	no	—
39	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
41	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic, complemented
42	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic, complemented
43	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic, complemented
44	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic, complemented
45	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
46	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
47	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
48	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
49	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
50	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
56	C₄₁×#398	—	2	1	no	—
57	C₄₁×#394	—	2	1	no	—
58	C₄₁×#388	—	2	1	no	—
59	C₄₁×#388	—	2	1	no	—
60	C₄₁×#382	C₂²	1	1	yes	characteristic, complemented
61	C₄₁×#380	C₂²	1	1	yes	characteristic
62	C₄₁×#380	C₂²	1	1	yes	characteristic, complemented
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×Q₈×C₄₁	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₄₁	—	2	1	no	—
75	C₂²×D₄×C₄₁	—	2	1	no	—
76	C₂²×D₄×C₄₁	—	2	2	no	—
77	C₂²×D₄×C₄₁	—	2	2	no	—
78	C₂²×D₄×C₄₁	—	2	2	no	—
79	C₂²×D₄×C₄₁	—	2	2	no	—
80	C₂²×D₄×C₄₁	—	2	1	no	—
81	C₂²×D₄×C₄₁	—	4	1	no	—
82	C₂²×D₄×C₄₁	—	4	1	no	—
83	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
84	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₄₁	—	2	1	no	—
87	C₂³×C₄×C₄₁	—	2	1	no	—
88	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
90	C₂×Q₁₆×C₄₁	—	2	2	no	—
91	C₂×Q₁₆×C₄₁	—	2	2	no	—
92	C₂×Q₁₆×C₄₁	—	4	1	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	—	4	1	no	—
98	C₂×SD₁₆×C₄₁	D₄	1	4	yes	complemented
99	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
103	#124×C₄₁	—	2	2	no	—
104	#124×C₄₁	D₄	1	4	yes	—
105	#123×C₄₁	—	2	8	no	—
106	C₂²⋊Q₈×C₄₁	—	2	2	no	—
107	C₂²⋊Q₈×C₄₁	—	2	2	no	—
108	C₂²⋊Q₈×C₄₁	—	2	2	no	—
109	C₂²⋊Q₈×C₄₁	—	2	2	no	—
110	C₂²⋊Q₈×C₄₁	—	4	1	no	—
111	C₂²⋊Q₈×C₄₁	—	4	1	no	—
112	#121×C₄₁	—	2	8	no	—
113	#121×C₄₁	—	2	2	no	—
114	#121×C₄₁	—	2	2	no	—
115	#120×C₄₁	—	2	8	no	—
116	C₄×Q₈×C₄₁	—	2	2	no	—
117	C₄×Q₈×C₄₁	—	2	2	no	—
118	C₄×D₄×C₄₁	—	2	2	no	—
119	C₄×D₄×C₄₁	—	2	2	no	—
120	C₄×D₄×C₄₁	—	2	2	no	—
121	C₄×D₄×C₄₁	D₄	1	4	yes	—
122	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
123	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
124	C₂×C₄⋊C₄×C₄₁	—	2	1	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	8	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	D₄	1	1	yes	characteristic
142	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
143	C₂×C₄²×C₄₁	—	2	1	no	—
144	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
145	#106×C₄₁	—	2	2	no	—
146	C₄⋊C₈×C₄₁	—	2	2	no	—
147	#103×C₄₁	—	2	2	no	—
148	#103×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	—	2	2	no	—
155	#102×C₄₁	—	2	2	no	—
156	#102×C₄₁	—	4	1	no	—
157	C₂²⋊C₈×C₄₁	—	2	2	no	—
158	C₂²⋊C₈×C₄₁	—	2	2	no	—
159	C₂²⋊C₈×C₄₁	—	4	1	no	—
160	C₂²⋊C₈×C₄₁	—	4	1	no	—
161	C₄×C₈×C₄₁	—	2	2	no	—
162	#95×C₄₁	—	2	1	no	—
163	#95×C₄₁	—	2	1	no	—
164	#95×C₄₁	—	2	1	no	—
165	#95×C₄₁	—	2	1	no	—
166	C₂⁴×C₄₁	—	2	1	no	—
167	C₂⁴×C₄₁	—	2	4	no	—
168	C₂⁴×C₄₁	—	2	1	no	—
169	C₂⁴×C₄₁	—	4	2	no	—
170	C₂⁴×C₄₁	—	4	2	no	—
171	C₂⁴×C₄₁	—	4	2	no	—
172	C₂⁴×C₄₁	—	4	2	no	—
173	C₂⁴×C₄₁	—	8	1	no	—
174	C₂⁴×C₄₁	—	8	1	no	—
175	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
176	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
177	#41×C₄₁	—	4	4	no	—
178	#41×C₄₁	—	4	4	no	—
179	#41×C₄₁	—	4	4	no	—
180	#41×C₄₁	—	4	4	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	—	2	1	no	—
186	C₂×Q₈×C₄₁	—	2	1	no	—
187	C₂×Q₈×C₄₁	—	2	1	no	—
188	C₂×Q₈×C₄₁	—	2	1	no	—
189	C₂×Q₈×C₄₁	—	2	1	no	—
190	C₂×Q₈×C₄₁	—	2	1	no	—
191	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
192	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
193	C₂×D₄×C₄₁	—	2	4	no	—
194	C₂×D₄×C₄₁	—	2	4	no	—
195	C₂×D₄×C₄₁	—	2	2	no	—
196	C₂×D₄×C₄₁	—	2	4	no	—
197	C₂×D₄×C₄₁	—	2	2	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	—	2	1	no	—
205	C₂×D₄×C₄₁	—	2	1	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	4	no	—
210	C₂×D₄×C₄₁	—	4	4	no	—
211	C₂×D₄×C₄₁	—	4	4	no	—
212	C₂×D₄×C₄₁	—	4	2	no	—
213	C₂×D₄×C₄₁	—	4	2	no	—
214	C₂×D₄×C₄₁	—	4	4	no	—
215	C₂×D₄×C₄₁	—	8	1	no	—
216	C₂×D₄×C₄₁	—	8	1	no	—
217	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
218	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
219	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
220	C₂×D₄×C₄₁	#41	1	2	yes	—
221	C₂²×C₄×C₄₁	—	2	4	no	—
222	C₂²×C₄×C₄₁	—	2	1	no	—
223	C₂²×C₄×C₄₁	—	2	1	no	—
224	C₂²×C₄×C₄₁	—	2	1	no	—
225	C₂²×C₄×C₄₁	—	2	1	no	—
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	4	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	—	8	1	no	—
244	C₂²×C₄×C₄₁	—	8	1	no	—
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	1	yes	characteristic
248	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
250	Q₁₆×C₄₁	—	4	4	no	—
251	SD₁₆×C₄₁	—	2	8	no	—
252	SD₁₆×C₄₁	—	4	4	no	—
253	C₂×C₈×C₄₁	—	2	1	no	—
254	C₂×C₈×C₄₁	—	2	1	no	—
255	C₂×C₈×C₄₁	—	2	1	no	—
256	C₂×C₈×C₄₁	—	2	1	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	C₂×D₄	1	2	yes	—
265	C₄⋊C₄×C₄₁	—	2	4	no	—
266	C₄⋊C₄×C₄₁	—	2	2	no	—
267	C₄⋊C₄×C₄₁	—	2	1	no	—
268	C₄⋊C₄×C₄₁	—	2	1	no	—
269	C₄⋊C₄×C₄₁	—	2	1	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	—	4	2	no	—
275	C₄⋊C₄×C₄₁	—	4	2	no	—
276	C₄⋊C₄×C₄₁	—	4	2	no	—
277	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
278	C₂²⋊C₄×C₄₁	—	2	4	no	—
279	C₂²⋊C₄×C₄₁	—	2	4	no	—
280	C₂²⋊C₄×C₄₁	—	2	2	no	—
281	C₂²⋊C₄×C₄₁	—	2	4	no	—
282	C₂²⋊C₄×C₄₁	—	2	4	no	—
283	C₂²⋊C₄×C₄₁	—	2	4	no	—
284	C₂²⋊C₄×C₄₁	—	2	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	C₄²×C₄₁	—	4	2	no	—
290	C₄²×C₄₁	C₂×D₄	1	2	yes	—
291	C₄²×C₄₁	C₂×D₄	1	2	yes	—
292	C₂³×C₄₁	—	2	1	no	—
293	C₂³×C₄₁	—	2	2	no	—
294	C₂³×C₄₁	—	2	1	no	—
295	C₂³×C₄₁	—	2	2	no	—
296	C₂³×C₄₁	—	2	1	no	—
297	C₂³×C₄₁	—	2	2	no	—
298	C₂³×C₄₁	—	2	1	no	—
299	C₂³×C₄₁	—	2	1	no	—
300	C₂³×C₄₁	—	2	1	no	—
301	C₂³×C₄₁	—	2	2	no	—
302	C₂³×C₄₁	—	2	1	no	—
303	C₂³×C₄₁	—	2	1	no	—
304	C₂³×C₄₁	—	2	1	no	—
305	C₂³×C₄₁	—	2	1	no	—
306	C₂³×C₄₁	—	2	1	no	—
307	C₂³×C₄₁	—	2	1	no	—
308	C₂³×C₄₁	—	2	1	no	—
309	C₂³×C₄₁	—	4	8	no	—
310	C₂³×C₄₁	—	4	8	no	—
311	C₂³×C₄₁	—	4	1	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	—	8	4	no	—
322	C₂³×C₄₁	—	8	4	no	—
323	C₂³×C₄₁	—	8	4	no	—
324	C₂³×C₄₁	—	8	4	no	—
325	C₂³×C₄₁	—	8	4	no	—
326	C₂³×C₄₁	#135	1	2	yes	—
327	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
328	Q₈×C₄₁	—	2	2	no	—
329	Q₈×C₄₁	—	2	2	no	—
330	Q₈×C₄₁	—	2	2	no	—
331	Q₈×C₄₁	—	2	2	no	—
332	Q₈×C₄₁	—	4	1	no	—
333	Q₈×C₄₁	—	4	1	no	—
334	Q₈×C₄₁	—	4	1	no	—
335	Q₈×C₄₁	—	4	1	no	—
336	D₄×C₄₁	—	2	2	no	—
337	D₄×C₄₁	—	2	2	no	—
338	D₄×C₄₁	—	2	2	no	—
339	D₄×C₄₁	—	2	2	no	—
340	D₄×C₄₁	—	2	2	no	—
341	D₄×C₄₁	—	4	4	no	—
342	D₄×C₄₁	—	4	8	no	—
343	D₄×C₄₁	—	4	8	no	—
344	D₄×C₄₁	—	4	1	no	—
345	D₄×C₄₁	—	4	1	no	—
346	D₄×C₄₁	—	8	4	no	—
347	D₄×C₄₁	#121	1	4	yes	—
348	C₂×C₄×C₄₁	—	2	1	no	—
349	C₂×C₄×C₄₁	—	2	1	no	—
350	C₂×C₄×C₄₁	—	2	1	no	—
351	C₂×C₄×C₄₁	—	2	1	no	—
352	C₂×C₄×C₄₁	—	2	2	no	—
353	C₂×C₄×C₄₁	—	2	1	no	—
354	C₂×C₄×C₄₁	—	2	2	no	—
355	C₂×C₄×C₄₁	—	2	1	no	—
356	C₂×C₄×C₄₁	—	2	2	no	—
357	C₂×C₄×C₄₁	—	2	1	no	—
358	C₂×C₄×C₄₁	—	2	1	no	—
359	C₂×C₄×C₄₁	—	2	1	no	—
360	C₂×C₄×C₄₁	—	2	1	no	—
361	C₂×C₄×C₄₁	—	4	8	no	—
362	C₂×C₄×C₄₁	—	4	1	no	—
363	C₂×C₄×C₄₁	—	4	1	no	—
364	C₂×C₄×C₄₁	—	4	1	no	—
365	C₂×C₄×C₄₁	—	4	1	no	—
366	C₂×C₄×C₄₁	—	4	1	no	—
367	C₂×C₄×C₄₁	—	4	1	no	—
368	C₂×C₄×C₄₁	—	4	1	no	—
369	C₂×C₄×C₄₁	—	4	1	no	—
370	C₂×C₄×C₄₁	—	4	1	no	—
371	C₂×C₄×C₄₁	—	4	1	no	—
372	C₂×C₄×C₄₁	—	4	1	no	—
373	C₂×C₄×C₄₁	—	4	1	no	—
374	C₂×C₄×C₄₁	—	4	1	no	—
375	C₂×C₄×C₄₁	—	4	1	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	—	8	4	no	—
386	C₂×C₄×C₄₁	#120	1	2	yes	—
387	C₂×C₄×C₄₁	#120	1	2	yes	—
388	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
392	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
393	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
394	C₈×C₄₁	—	2	2	no	—
395	C₈×C₄₁	—	4	1	no	—
396	C₈×C₄₁	—	4	1	no	—
397	C₈×C₄₁	—	4	1	no	—
398	#24247	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
399	C₂²×C₄₁	—	2	4	no	—
400	C₂²×C₄₁	—	2	2	no	—
401	C₂²×C₄₁	—	2	2	no	—
402	C₂²×C₄₁	—	2	2	no	—
403	C₂²×C₄₁	—	4	1	no	—
404	C₂²×C₄₁	—	4	2	no	—
405	C₂²×C₄₁	—	4	2	no	—
406	C₂²×C₄₁	—	4	1	no	—
407	C₂²×C₄₁	—	4	1	no	—
408	C₂²×C₄₁	—	4	2	no	—
409	C₂²×C₄₁	—	4	2	no	—
410	C₂²×C₄₁	—	4	2	no	—
411	C₂²×C₄₁	—	4	1	no	—
412	C₂²×C₄₁	—	4	2	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	1	no	—
418	C₂²×C₄₁	—	4	2	no	—
419	C₂²×C₄₁	—	4	1	no	—
420	C₂²×C₄₁	—	4	1	no	—
421	C₂²×C₄₁	—	4	1	no	—
422	C₂²×C₄₁	—	4	1	no	—
423	C₂²×C₄₁	—	8	16	no	—
424	C₂²×C₄₁	—	8	1	no	—
425	C₂²×C₄₁	—	8	1	no	—
426	C₂²×C₄₁	—	8	1	no	—
427	C₂²×C₄₁	—	8	1	no	—
428	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
429	C₂²×C₄₁	D₄²	1	1	yes	characteristic
430	C₂²×C₄₁	#546	1	1	yes	characteristic
431	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
432	C₂²×C₄₁	#575	1	1	yes	characteristic
433	C₂²×C₄₁	#577	1	1	yes	characteristic
434	C₂²×C₄₁	#577	1	1	yes	characteristic
435	C₄×C₄₁	—	2	2	no	—
436	C₄×C₄₁	—	2	2	no	—
437	C₄×C₄₁	—	4	1	no	—
438	C₄×C₄₁	—	4	1	no	—
439	C₄×C₄₁	—	4	2	no	—
440	C₄×C₄₁	—	4	2	no	—
441	C₄×C₄₁	—	4	2	no	—
442	C₄×C₄₁	—	8	1	no	—
443	C₄×C₄₁	—	8	1	no	—
444	C₄×C₄₁	—	8	1	no	—
445	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
446	C₄×C₄₁	#535	1	1	yes	characteristic
447	C₄×C₄₁	D₄²	1	1	yes	characteristic
448	C₄×C₄₁	#546	1	1	yes	characteristic
449	C₂×#546	C₂×C₄₁	1	1	yes	characteristic
450	C₂×#464	C₂×C₄₁	1	1	yes	characteristic, complemented
451	C₂×#452	C₂×C₄₁	1	1	yes	characteristic, complemented
452	C₂×#450	C₂×C₄₁	1	1	yes	characteristic, complemented
453	C₂×C₄×SD₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
454	#2536	C₂×C₄₁	1	1	yes	characteristic, complemented
455	#2035	C₂×C₄₁	1	1	yes	characteristic, complemented
456	#2034	C₂×C₄₁	1	1	yes	characteristic, complemented
457	#2001	C₂×C₄₁	1	1	yes	characteristic, complemented
458	#2000	C₂×C₄₁	1	1	yes	characteristic, complemented
459	#1958	C₂×C₄₁	1	1	yes	characteristic, complemented
460	#1954	C₂×C₄₁	1	1	yes	characteristic, complemented
461	#1804	C₂×C₄₁	1	1	yes	characteristic, complemented
462	#1788	C₂×C₄₁	1	1	yes	characteristic, complemented
463	#1786	C₂×C₄₁	1	1	yes	characteristic, complemented
464	C₂×C₄₁	—	4	2	no	—
465	C₂×C₄₁	—	4	4	no	—
466	C₂×C₄₁	—	8	1	no	—
467	C₂×C₄₁	—	8	2	no	—
468	C₂×C₄₁	#2408	1	1	yes	characteristic
469	C₂×C₄₁	#3002	1	1	yes	characteristic
470	C₂×C₄₁	#3009	1	1	yes	characteristic
471	C₂×C₄₁	#3275	1	1	yes	characteristic
472	C₂×C₄₁	#3282	1	1	yes	characteristic
473	C₂×C₄₁	#3296	1	1	yes	characteristic
474	C₂×C₄₁	#3323	1	1	yes	characteristic
475	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
476	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
477	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
478	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
479	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
480	#546	—	2	4	no	—
481	#546	—	2	4	no	—
482	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
483	C₂×#123	—	2	1	no	—
484	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
485	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
486	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
487	C₂×#121	—	2	1	no	—
488	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
489	C₂×#120	—	2	1	no	—
490	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
491	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
492	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
493	C₂²×C₂²⋊C₄	—	2	1	no	—
494	#464	—	2	4	no	—
495	#452	—	2	4	no	—
496	#450	—	2	4	no	—
497	C₄×SD₁₆	—	2	4	no	—
498	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic, complemented
499	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
500	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic, complemented
501	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic, complemented
502	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic, complemented
503	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic, complemented
504	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
505	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
506	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
507	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
508	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
509	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
510	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
511	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
512	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
513	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
514	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
515	#398	—	2	1	no	—
516	#394	—	2	1	no	—
517	#388	—	2	1	no	—
518	#388	—	2	1	no	—
519	#382	C₂²×C₄₁	1	1	yes	characteristic, complemented
520	#380	C₂²×C₄₁	1	1	yes	characteristic
521	#380	C₂²×C₄₁	1	1	yes	characteristic, complemented
522	#340	C₂²×C₄₁	1	1	yes	characteristic, complemented
523	#340	C₂²×C₄₁	1	1	yes	characteristic, complemented
524	C₄₁	#24247	1	1	yes	characteristic, direct product factor, Sylow
525	C₂⁵	—	2	1	no	—
526	C₂×#41	—	2	2	no	—
527	C₂×#41	—	2	2	no	—
528	C₂×#41	—	2	2	no	—
529	C₂×#41	—	2	2	no	—
530	C₂×#41	—	4	1	no	—
531	C₂×#41	—	4	1	no	—
532	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
533	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
534	C₂²×D₄	—	2	1	no	—
535	C₂²×D₄	—	2	1	no	—
536	C₂²×D₄	—	2	2	no	—
537	C₂²×D₄	—	2	2	no	—
538	C₂²×D₄	—	2	2	no	—
539	C₂²×D₄	—	2	2	no	—
540	C₂²×D₄	—	2	1	no	—
541	C₂²×D₄	—	4	1	no	—
542	C₂²×D₄	—	4	1	no	—
543	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
544	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
545	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
546	C₂³×C₄	—	2	1	no	—
547	C₂³×C₄	—	2	1	no	—
548	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
549	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
550	C₂×Q₁₆	—	2	2	no	—
551	C₂×Q₁₆	—	2	2	no	—
552	C₂×Q₁₆	—	4	1	no	—
553	C₂×SD₁₆	—	2	2	no	—
554	C₂×SD₁₆	—	2	2	no	—
555	C₂×SD₁₆	—	2	2	no	—
556	C₂×SD₁₆	—	2	2	no	—
557	C₂×SD₁₆	—	4	1	no	—
558	C₂×SD₁₆	D₄×C₄₁	1	4	yes	complemented
559	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
560	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
561	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
562	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
563	#124	—	2	2	no	—
564	#124	D₄×C₄₁	1	4	yes	—
565	#123	—	2	8	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	—	2	2	no	—
570	C₂²⋊Q₈	—	4	1	no	—
571	C₂²⋊Q₈	—	4	1	no	—
572	#121	—	2	8	no	—
573	#121	—	2	2	no	—
574	#121	—	2	2	no	—
575	#120	—	2	8	no	—
576	C₄×Q₈	—	2	2	no	—
577	C₄×Q₈	—	2	2	no	—
578	C₄×D₄	—	2	2	no	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	2	2	no	—
581	C₄×D₄	D₄×C₄₁	1	4	yes	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
591	C₂×C₂²⋊C₄	—	2	8	no	—
592	C₂×C₂²⋊C₄	—	2	1	no	—
593	C₂×C₂²⋊C₄	—	2	1	no	—
594	C₂×C₂²⋊C₄	—	2	1	no	—
595	C₂×C₂²⋊C₄	—	2	1	no	—
596	C₂×C₂²⋊C₄	—	2	1	no	—
597	C₂×C₂²⋊C₄	—	2	1	no	—
598	C₂×C₂²⋊C₄	—	2	1	no	—
599	C₂×C₂²⋊C₄	—	2	1	no	—
600	C₂×C₂²⋊C₄	—	2	1	no	—
601	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
602	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
603	C₂×C₄²	—	2	1	no	—
604	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
605	#106	—	2	2	no	—
606	C₄⋊C₈	—	2	2	no	—
607	#103	—	2	2	no	—
608	#103	—	2	2	no	—
609	#103	—	2	2	no	—
610	#103	—	4	1	no	—
611	#102	—	2	2	no	—
612	#102	—	2	2	no	—
613	#102	—	2	2	no	—
614	#102	—	2	2	no	—
615	#102	—	2	2	no	—
616	#102	—	4	1	no	—
617	C₂²⋊C₈	—	2	2	no	—
618	C₂²⋊C₈	—	2	2	no	—
619	C₂²⋊C₈	—	4	1	no	—
620	C₂²⋊C₈	—	4	1	no	—
621	C₄×C₈	—	2	2	no	—
622	#95	—	2	1	no	—
623	#95	—	2	1	no	—
624	#95	—	2	1	no	—
625	#95	—	2	1	no	—
626	C₂⁴	—	2	1	no	—
627	C₂⁴	—	2	4	no	—
628	C₂⁴	—	2	1	no	—
629	C₂⁴	—	4	2	no	—
630	C₂⁴	—	4	2	no	—
631	C₂⁴	—	4	2	no	—
632	C₂⁴	—	4	2	no	—
633	C₂⁴	—	8	1	no	—
634	C₂⁴	—	8	1	no	—
635	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
636	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
637	#41	—	4	4	no	—
638	#41	—	4	4	no	—
639	#41	—	4	4	no	—
640	#41	—	4	4	no	—
641	C₂×Q₈	—	2	1	no	—
642	C₂×Q₈	—	2	1	no	—
643	C₂×Q₈	—	2	1	no	—
644	C₂×Q₈	—	2	1	no	—
645	C₂×Q₈	—	2	1	no	—
646	C₂×Q₈	—	2	1	no	—
647	C₂×Q₈	—	2	1	no	—
648	C₂×Q₈	—	2	1	no	—
649	C₂×Q₈	—	2	1	no	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
652	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
653	C₂×D₄	—	2	4	no	—
654	C₂×D₄	—	2	4	no	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	4	no	—
657	C₂×D₄	—	2	2	no	—
658	C₂×D₄	—	2	1	no	—
659	C₂×D₄	—	2	1	no	—
660	C₂×D₄	—	2	1	no	—
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	4	1	no	—
667	C₂×D₄	—	4	2	no	—
668	C₂×D₄	—	4	2	no	—
669	C₂×D₄	—	4	4	no	—
670	C₂×D₄	—	4	4	no	—
671	C₂×D₄	—	4	4	no	—
672	C₂×D₄	—	4	2	no	—
673	C₂×D₄	—	4	2	no	—
674	C₂×D₄	—	4	4	no	—
675	C₂×D₄	—	8	1	no	—
676	C₂×D₄	—	8	1	no	—
677	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
678	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
679	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
680	C₂×D₄	#41×C₄₁	1	2	yes	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	1	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	4	2	no	—
702	C₂²×C₄	—	4	2	no	—
703	C₂²×C₄	—	8	1	no	—
704	C₂²×C₄	—	8	1	no	—
705	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
706	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
707	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
708	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
710	Q₁₆	—	4	4	no	—
711	SD₁₆	—	2	8	no	—
712	SD₁₆	—	4	4	no	—
713	C₂×C₈	—	2	1	no	—
714	C₂×C₈	—	2	1	no	—
715	C₂×C₈	—	2	1	no	—
716	C₂×C₈	—	2	1	no	—
717	C₂×C₈	—	2	1	no	—
718	C₂×C₈	—	2	1	no	—
719	C₂×C₈	—	2	1	no	—
720	C₂×C₈	—	2	1	no	—
721	C₂×C₈	—	2	1	no	—
722	C₂×C₈	—	2	1	no	—
723	C₂×C₈	—	2	1	no	—
724	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
725	C₄⋊C₄	—	2	4	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	4	2	no	—
746	C₂²⋊C₄	—	4	2	no	—
747	C₂²⋊C₄	—	4	2	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₄²	—	4	2	no	—
750	C₄²	C₂×D₄×C₄₁	1	2	yes	—
751	C₄²	C₂×D₄×C₄₁	1	2	yes	—
752	C₂³	—	2	1	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	1	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	1	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	1	no	—
759	C₂³	—	2	1	no	—
760	C₂³	—	2	1	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	1	no	—
763	C₂³	—	2	1	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	2	1	no	—
768	C₂³	—	2	1	no	—
769	C₂³	—	4	8	no	—
770	C₂³	—	4	8	no	—
771	C₂³	—	4	1	no	—
772	C₂³	—	4	1	no	—
773	C₂³	—	4	1	no	—
774	C₂³	—	4	1	no	—
775	C₂³	—	4	1	no	—
776	C₂³	—	4	1	no	—
777	C₂³	—	4	1	no	—
778	C₂³	—	4	1	no	—
779	C₂³	—	4	1	no	—
780	C₂³	—	4	1	no	—
781	C₂³	—	8	4	no	—
782	C₂³	—	8	4	no	—
783	C₂³	—	8	4	no	—
784	C₂³	—	8	4	no	—
785	C₂³	—	8	4	no	—
786	C₂³	#135×C₄₁	1	2	yes	—
787	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
788	Q₈	—	2	2	no	—
789	Q₈	—	2	2	no	—
790	Q₈	—	2	2	no	—
791	Q₈	—	2	2	no	—
792	Q₈	—	4	1	no	—
793	Q₈	—	4	1	no	—
794	Q₈	—	4	1	no	—
795	Q₈	—	4	1	no	—
796	D₄	—	2	2	no	—
797	D₄	—	2	2	no	—
798	D₄	—	2	2	no	—
799	D₄	—	2	2	no	—
800	D₄	—	2	2	no	—
801	D₄	—	4	4	no	—
802	D₄	—	4	8	no	—
803	D₄	—	4	8	no	—
804	D₄	—	4	1	no	—
805	D₄	—	4	1	no	—
806	D₄	—	8	4	no	—
807	D₄	#121×C₄₁	1	4	yes	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	4	8	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	1	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	1	no	—
834	C₂×C₄	—	4	1	no	—
835	C₂×C₄	—	4	1	no	—
836	C₂×C₄	—	4	1	no	—
837	C₂×C₄	—	4	1	no	—
838	C₂×C₄	—	4	1	no	—
839	C₂×C₄	—	4	1	no	—
840	C₂×C₄	—	4	1	no	—
841	C₂×C₄	—	4	1	no	—
842	C₂×C₄	—	4	1	no	—
843	C₂×C₄	—	4	1	no	—
844	C₂×C₄	—	4	1	no	—
845	C₂×C₄	—	8	4	no	—
846	C₂×C₄	#120×C₄₁	1	2	yes	—
847	C₂×C₄	#120×C₄₁	1	2	yes	—
848	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
850	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
851	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
852	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
853	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
854	C₈	—	2	2	no	—
855	C₈	—	4	1	no	—
856	C₈	—	4	1	no	—
857	C₈	—	4	1	no	—
858	C₂²	—	2	2	no	—
859	C₂²	—	2	4	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	1	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	4	2	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	1	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	1	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	1	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	8	16	no	—
883	C₂²	—	8	1	no	—
884	C₂²	—	8	1	no	—
885	C₂²	—	8	1	no	—
886	C₂²	—	8	1	no	—
887	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
888	C₂²	D₄²×C₄₁	1	1	yes	characteristic
889	C₂²	C₄₁×#546	1	1	yes	characteristic
890	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
891	C₂²	C₄₁×#575	1	1	yes	characteristic
892	C₂²	C₄₁×#577	1	1	yes	characteristic
893	C₂²	C₄₁×#577	1	1	yes	characteristic
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	4	1	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	8	1	no	—
902	C₄	—	8	1	no	—
903	C₄	—	8	1	no	—
904	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
905	C₄	C₄₁×#535	1	1	yes	characteristic
906	C₄	D₄²×C₄₁	1	1	yes	characteristic
907	C₄	C₄₁×#546	1	1	yes	characteristic
908	C₂	—	4	2	no	—
909	C₂	—	4	4	no	—
910	C₂	—	8	1	no	—
911	C₂	—	8	2	no	—
912	C₂	C₄₁×#2408	1	1	yes	characteristic
913	C₂	C₄₁×#3002	1	1	yes	characteristic
914	C₂	C₄₁×#3009	1	1	yes	characteristic
915	C₂	C₄₁×#3275	1	1	yes	characteristic
916	C₂	C₄₁×#3282	1	1	yes	characteristic
917	C₂	C₄₁×#3296	1	1	yes	characteristic
918	C₂	C₄₁×#3323	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#546	C₂
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
2. C₂×C₄₁×#464	C₂	semidirect
3. C₂×C₄₁×#452	C₂	semidirect
4. C₂×C₄₁×#450	C₂	semidirect
5. C₂×C₄×SD₁₆×C₄₁	C₂	semidirect
6. C₄₁×#2536	C₂	semidirect
7. C₄₁×#2035	C₂	semidirect
8. C₄₁×#2034	C₂	semidirect
9. C₄₁×#2001	C₂	semidirect
10. C₄₁×#2000	C₂	semidirect
11. C₄₁×#1958	C₂	semidirect
12. C₄₁×#1954	C₂	semidirect
13. C₄₁×#1804	C₂	semidirect
14. C₄₁×#1788	C₂	semidirect
15. C₄₁×#1786	C₂	semidirect
18. C₂²×Q₁₆×C₄₁	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
31. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
39. C₂×#106×C₄₁	C₂²	semidirect
40. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
41. C₂×#103×C₄₁	C₂²	semidirect
42. C₂×#103×C₄₁	C₂²	semidirect
43. C₂×#103×C₄₁	C₂²	semidirect
44. C₂×#103×C₄₁	C₂²	semidirect
53. C₂×C₂²⋊C₈×C₄₁	C₂²	semidirect
54. C₂×C₂²⋊C₈×C₄₁	C₂²	semidirect
55. C₂×C₄×C₈×C₄₁	C₂²	semidirect
60. C₄₁×#382	C₂²	semidirect
62. C₄₁×#380	C₂²	semidirect
63. C₄₁×#340	C₂²	semidirect
64. C₄₁×#340	C₂²	semidirect
98. C₂×SD₁₆×C₄₁	D₄	semidirect
398. #24247	C₄₁	direct (N × H)
450. C₂×#464	C₂×C₄₁	semidirect
451. C₂×#452	C₂×C₄₁	semidirect
452. C₂×#450	C₂×C₄₁	semidirect
453. C₂×C₄×SD₁₆	C₂×C₄₁	semidirect
454. #2536	C₂×C₄₁	semidirect
455. #2035	C₂×C₄₁	semidirect
456. #2034	C₂×C₄₁	semidirect
457. #2001	C₂×C₄₁	semidirect
458. #2000	C₂×C₄₁	semidirect
459. #1958	C₂×C₄₁	semidirect
460. #1954	C₂×C₄₁	semidirect
461. #1804	C₂×C₄₁	semidirect
462. #1788	C₂×C₄₁	semidirect
463. #1786	C₂×C₄₁	semidirect
477. C₂²×Q₁₆	C₂²×C₄₁	semidirect
486. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
490. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
498. C₂×#106	C₂²×C₄₁	semidirect
499. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
500. C₂×#103	C₂²×C₄₁	semidirect
501. C₂×#103	C₂²×C₄₁	semidirect
502. C₂×#103	C₂²×C₄₁	semidirect
503. C₂×#103	C₂²×C₄₁	semidirect
512. C₂×C₂²⋊C₈	C₂²×C₄₁	semidirect
513. C₂×C₂²⋊C₈	C₂²×C₄₁	semidirect
514. C₂×C₄×C₈	C₂²×C₄₁	semidirect
519. #382	C₂²×C₄₁	semidirect
521. #380	C₂²×C₄₁	semidirect
522. #340	C₂²×C₄₁	semidirect
523. #340	C₂²×C₄₁	semidirect
524. C₄₁	#24247	direct (N × H)
558. C₂×SD₁₆	D₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#546	2
C₂×C₄₁×#464	2
C₂×C₄₁×#452	2
C₂×C₄₁×#450	2
C₂×C₄×SD₁₆×C₄₁	2
C₄₁×#2536	2
C₄₁×#2035	2
C₄₁×#2034	2
C₄₁×#2001	2
C₄₁×#2000	2
C₄₁×#1958	2
C₄₁×#1954	2
C₄₁×#1804	2
C₄₁×#1788	2
C₄₁×#1786	2
#24247	41

Subgroups — C41×#24247 #23800448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24247 #23800448