Subgroups — C₄₁×#24366 #23800567

Order 10496.

1662 conjugacy classes of subgroups.

The subgroup lattice has 956 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×#463	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#459	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#447	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2431	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×C₂²⋊C₄×C₄₁	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×#2012	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#2011	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1895	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#1879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#1877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#1851	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#1788	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×D₈×C₄₁	C₂²	1	1	yes	characteristic
26	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic, complemented
29	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic, complemented
30	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₄₁	—	2	1	no	—
34	C₄₁×#463	—	2	4	no	—
35	C₄₁×#459	—	2	4	no	—
36	C₄₁×#447	—	2	4	no	—
37	C₂×C₄⋊C₈×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, complemented
44	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic, complemented
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	C₄₁×#392	—	2	1	no	—
49	C₄₁×#392	—	2	1	no	—
50	C₄₁×#391	C₂²	1	1	yes	characteristic, complemented
51	C₄₁×#390	C₂²	1	1	yes	characteristic
52	C₄₁×#390	C₂²	1	1	yes	characteristic
53	C₄₁×#390	C₂²	1	1	yes	characteristic, complemented
54	C₄₁×#386	—	2	1	no	—
55	C₄₁×#386	—	2	1	no	—
56	C₄₁×#386	—	2	1	no	—
57	C₄₁×#386	—	2	1	no	—
58	C₄₁×#380	C₂²	1	1	yes	characteristic
59	C₄₁×#379	—	2	1	no	—
60	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
61	C₄₁×#340	C₂²	1	1	yes	characteristic, complemented
62	C₄₁×#340	C₂²	1	1	yes	characteristic, complemented
63	C₄₁×#336	C₂²	1	1	yes	characteristic, complemented
64	C₄₁×#336	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	1	no	—
80	C₂²×D₄×C₄₁	—	2	2	no	—
81	C₂²×D₄×C₄₁	—	4	1	no	—
82	C₂²×D₄×C₄₁	—	4	1	no	—
83	C₂²×D₄×C₄₁	D₄	1	4	yes	complemented
84	C₂²×D₄×C₄₁	C₂³	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	—	2	1	no	—
90	C₂³×C₄×C₄₁	—	2	1	no	—
91	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
92	AGL(1,ℤ/8)×C₄₁	—	2	32	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	—	2	2	no	—
98	C₂×SD₁₆×C₄₁	D₄	1	4	yes	complemented
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	—	2	2	no	—
104	C₂×D₈×C₄₁	—	2	2	no	—
105	C₂×D₈×C₄₁	—	2	2	no	—
106	C₂×D₈×C₄₁	—	2	2	no	—
107	C₂×D₈×C₄₁	—	2	2	no	—
108	C₂×D₈×C₄₁	—	4	1	no	—
109	C₂×D₈×C₄₁	—	4	1	no	—
110	C₂×D₈×C₄₁	D₄	1	4	yes	complemented
111	C₂×M₁₆×C₄₁	—	2	2	no	—
112	C₂×M₁₆×C₄₁	—	2	2	no	—
113	C₂×M₁₆×C₄₁	—	2	2	no	—
114	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
118	#127×C₄₁	—	2	2	no	—
119	#127×C₄₁	—	4	1	no	—
120	#124×C₄₁	—	2	2	no	—
121	#124×C₄₁	—	4	1	no	—
122	#121×C₄₁	—	2	2	no	—
123	#121×C₄₁	—	2	2	no	—
124	C₄×D₄×C₄₁	—	2	2	no	—
125	C₄×D₄×C₄₁	—	2	2	no	—
126	C₄×D₄×C₄₁	—	4	1	no	—
127	C₄×D₄×C₄₁	—	4	1	no	—
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	—	4	4	no	—
144	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
145	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
146	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
148	C₄⋊C₈×C₄₁	—	2	2	no	—
149	C₄⋊C₈×C₄₁	—	2	2	no	—
150	#103×C₄₁	—	2	2	no	—
151	#103×C₄₁	—	4	1	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	—	2	2	no	—
157	#102×C₄₁	—	4	1	no	—
158	C₂²⋊C₈×C₄₁	—	2	2	no	—
159	#95×C₄₁	—	2	1	no	—
160	#95×C₄₁	—	2	1	no	—
161	#95×C₄₁	—	2	1	no	—
162	#95×C₄₁	D₄	1	1	yes	characteristic
163	#95×C₄₁	D₄	1	1	yes	characteristic
164	C₂⁴×C₄₁	—	2	1	no	—
165	C₂⁴×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	#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	4	no	—
188	C₂×D₄×C₄₁	—	2	1	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	—	2	1	no	—
205	C₂×D₄×C₄₁	—	2	1	no	—
206	C₂×D₄×C₄₁	—	2	1	no	—
207	C₂×D₄×C₄₁	—	4	4	no	—
208	C₂×D₄×C₄₁	—	4	4	no	—
209	C₂×D₄×C₄₁	—	4	4	no	—
210	C₂×D₄×C₄₁	—	4	2	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	—	8	1	no	—
224	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
225	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
226	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
227	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
228	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
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	—	4	2	no	—
238	C₂²×C₄×C₄₁	—	4	2	no	—
239	C₂²×C₄×C₄₁	—	4	2	no	—
240	C₂²×C₄×C₄₁	—	4	2	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	—	8	1	no	—
245	C₂²×C₄×C₄₁	—	8	1	no	—
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	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
251	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₄₁	#41	1	2	yes	—
253	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
254	SD₁₆×C₄₁	—	2	8	no	—
255	SD₁₆×C₄₁	—	2	8	no	—
256	D₈×C₄₁	—	2	8	no	—
257	D₈×C₄₁	—	2	8	no	—
258	D₈×C₄₁	—	4	4	no	—
259	D₈×C₄₁	—	4	4	no	—
260	M₁₆×C₄₁	—	2	8	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	—	2	1	no	—
266	C₂×C₈×C₄₁	—	2	1	no	—
267	C₂×C₈×C₄₁	—	2	1	no	—
268	C₂×C₈×C₄₁	—	2	1	no	—
269	C₂×C₈×C₄₁	—	2	1	no	—
270	C₂×C₈×C₄₁	—	2	1	no	—
271	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
272	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
279	C₂²⋊C₄×C₄₁	—	2	2	no	—
280	C₂²⋊C₄×C₄₁	—	4	1	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	C₄²×C₄₁	—	2	1	no	—
296	C₄²×C₄₁	—	2	1	no	—
297	C₂³×C₄₁	—	2	2	no	—
298	C₂³×C₄₁	—	2	2	no	—
299	C₂³×C₄₁	—	2	2	no	—
300	C₂³×C₄₁	—	2	1	no	—
301	C₂³×C₄₁	—	2	1	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	2	no	—
307	C₂³×C₄₁	—	2	2	no	—
308	C₂³×C₄₁	—	4	8	no	—
309	C₂³×C₄₁	—	4	8	no	—
310	C₂³×C₄₁	—	4	1	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	—	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	—	4	1	no	—
331	C₂³×C₄₁	—	4	1	no	—
332	C₂³×C₄₁	—	4	1	no	—
333	C₂³×C₄₁	—	8	4	no	—
334	C₂³×C₄₁	—	8	4	no	—
335	C₂³×C₄₁	—	8	4	no	—
336	C₂³×C₄₁	—	8	4	no	—
337	C₂³×C₄₁	—	8	4	no	—
338	C₂³×C₄₁	#121	1	2	yes	—
339	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
340	Q₈×C₄₁	—	2	2	no	—
341	Q₈×C₄₁	—	2	2	no	—
342	Q₈×C₄₁	—	4	1	no	—
343	Q₈×C₄₁	—	4	1	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	—	2	2	no	—
349	D₄×C₄₁	—	2	2	no	—
350	D₄×C₄₁	—	2	2	no	—
351	D₄×C₄₁	—	4	8	no	—
352	D₄×C₄₁	—	4	8	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	—	4	1	no	—
358	D₄×C₄₁	—	4	1	no	—
359	D₄×C₄₁	—	4	1	no	—
360	D₄×C₄₁	—	4	1	no	—
361	D₄×C₄₁	—	8	4	no	—
362	D₄×C₄₁	—	8	4	no	—
363	D₄×C₄₁	—	8	4	no	—
364	D₄×C₄₁	#120	1	4	yes	—
365	C₂×C₄×C₄₁	—	2	1	no	—
366	C₂×C₄×C₄₁	—	2	1	no	—
367	C₂×C₄×C₄₁	—	2	1	no	—
368	C₂×C₄×C₄₁	—	2	1	no	—
369	C₂×C₄×C₄₁	—	2	2	no	—
370	C₂×C₄×C₄₁	—	2	2	no	—
371	C₂×C₄×C₄₁	—	2	2	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	—	2	1	no	—
376	C₂×C₄×C₄₁	—	2	2	no	—
377	C₂×C₄×C₄₁	—	2	1	no	—
378	C₂×C₄×C₄₁	—	2	1	no	—
379	C₂×C₄×C₄₁	—	2	1	no	—
380	C₂×C₄×C₄₁	—	2	1	no	—
381	C₂×C₄×C₄₁	—	2	1	no	—
382	C₂×C₄×C₄₁	—	2	1	no	—
383	C₂×C₄×C₄₁	—	4	8	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	—	4	1	no	—
395	C₂×C₄×C₄₁	—	8	4	no	—
396	C₂×C₄×C₄₁	—	8	4	no	—
397	C₂×C₄×C₄₁	#121	1	2	yes	—
398	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	complemented
399	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
403	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
404	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
405	C₈×C₄₁	—	2	2	no	—
406	C₈×C₄₁	—	2	2	no	—
407	C₈×C₄₁	—	4	1	no	—
408	C₈×C₄₁	—	4	1	no	—
409	#24366	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
410	C₂²×C₄₁	—	2	2	no	—
411	C₂²×C₄₁	—	2	4	no	—
412	C₂²×C₄₁	—	2	2	no	—
413	C₂²×C₄₁	—	2	2	no	—
414	C₂²×C₄₁	—	4	2	no	—
415	C₂²×C₄₁	—	4	1	no	—
416	C₂²×C₄₁	—	4	1	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	2	no	—
425	C₂²×C₄₁	—	4	2	no	—
426	C₂²×C₄₁	—	4	2	no	—
427	C₂²×C₄₁	—	4	2	no	—
428	C₂²×C₄₁	—	4	2	no	—
429	C₂²×C₄₁	—	4	2	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	—	8	1	no	—
444	C₂²×C₄₁	—	8	1	no	—
445	C₂²×C₄₁	—	8	1	no	—
446	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
447	C₂²×C₄₁	D₄²	1	1	yes	characteristic
448	C₂²×C₄₁	D₄²	1	1	yes	characteristic
449	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
450	C₂²×C₄₁	#575	1	1	yes	characteristic
451	C₂²×C₄₁	#576	1	1	yes	characteristic
452	C₂²×C₄₁	#576	1	1	yes	characteristic
453	C₄×C₄₁	—	2	2	no	—
454	C₄×C₄₁	—	2	2	no	—
455	C₄×C₄₁	—	4	2	no	—
456	C₄×C₄₁	—	4	1	no	—
457	C₄×C₄₁	—	4	1	no	—
458	C₄×C₄₁	—	4	1	no	—
459	C₄×C₄₁	—	8	1	no	—
460	C₄×C₄₁	—	8	1	no	—
461	C₄×C₄₁	—	8	1	no	—
462	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
463	C₄×C₄₁	#534	1	1	yes	characteristic
464	C₄×C₄₁	#546	1	1	yes	characteristic
465	C₄×C₄₁	#546	1	1	yes	characteristic
466	C₂²×AGL(1,ℤ/8)	C₂×C₄₁	1	1	yes	characteristic, complemented
467	C₂×#463	C₂×C₄₁	1	1	yes	characteristic, complemented
468	C₂×#459	C₂×C₄₁	1	1	yes	characteristic, complemented
469	C₂×#447	C₂×C₄₁	1	1	yes	characteristic, complemented
470	#2431	C₂×C₄₁	1	1	yes	characteristic, complemented
471	D₄×C₂²⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
472	#2055	C₂×C₄₁	1	1	yes	characteristic, complemented
473	#2054	C₂×C₄₁	1	1	yes	characteristic, complemented
474	#2012	C₂×C₄₁	1	1	yes	characteristic, complemented
475	#2011	C₂×C₄₁	1	1	yes	characteristic, complemented
476	#1895	C₂×C₄₁	1	1	yes	characteristic, complemented
477	#1879	C₂×C₄₁	1	1	yes	characteristic, complemented
478	#1877	C₂×C₄₁	1	1	yes	characteristic, complemented
479	#1851	C₂×C₄₁	1	1	yes	characteristic, complemented
480	#1788	C₂×C₄₁	1	1	yes	characteristic, complemented
481	C₂×C₄₁	—	4	2	no	—
482	C₂×C₄₁	—	4	4	no	—
483	C₂×C₄₁	—	8	2	no	—
484	C₂×C₄₁	—	8	2	no	—
485	C₂×C₄₁	—	16	1	no	—
486	C₂×C₄₁	#2410	1	1	yes	characteristic
487	C₂×C₄₁	#3036	1	1	yes	characteristic
488	C₂×C₄₁	#3041	1	1	yes	characteristic
489	C₂×C₄₁	#3264	1	1	yes	characteristic
490	C₂×C₄₁	#3268	1	1	yes	characteristic
491	C₂×C₄₁	#3273	1	1	yes	characteristic
492	C₂×C₄₁	#3274	1	1	yes	characteristic
493	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
494	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
495	C₂×AGL(1,ℤ/8)	—	2	4	no	—
496	C₂×AGL(1,ℤ/8)	—	2	4	no	—
497	C₂×AGL(1,ℤ/8)	—	2	4	no	—
498	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
499	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
500	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
501	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
502	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
503	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
504	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
505	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic, complemented
506	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic, complemented
507	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
508	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
509	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
510	C₂²×C₂²⋊C₄	—	2	1	no	—
511	#463	—	2	4	no	—
512	#459	—	2	4	no	—
513	#447	—	2	4	no	—
514	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
515	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
516	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic, complemented
517	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic, complemented
518	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
519	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
520	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic, complemented
521	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic, complemented
522	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic, complemented
523	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic, complemented
524	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
525	#392	—	2	1	no	—
526	#392	—	2	1	no	—
527	#391	C₂²×C₄₁	1	1	yes	characteristic, complemented
528	#390	C₂²×C₄₁	1	1	yes	characteristic
529	#390	C₂²×C₄₁	1	1	yes	characteristic
530	#390	C₂²×C₄₁	1	1	yes	characteristic, complemented
531	#386	—	2	1	no	—
532	#386	—	2	1	no	—
533	#386	—	2	1	no	—
534	#386	—	2	1	no	—
535	#380	C₂²×C₄₁	1	1	yes	characteristic
536	#379	—	2	1	no	—
537	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
538	#340	C₂²×C₄₁	1	1	yes	characteristic, complemented
539	#340	C₂²×C₄₁	1	1	yes	characteristic, complemented
540	#336	C₂²×C₄₁	1	1	yes	characteristic, complemented
541	#336	C₂²×C₄₁	1	1	yes	characteristic, complemented
542	C₄₁	#24366	1	1	yes	characteristic, direct product factor, Sylow
543	C₂⁵	—	2	1	no	—
544	C₂×#41	—	2	2	no	—
545	C₂×#41	—	2	2	no	—
546	C₂×#41	—	2	2	no	—
547	C₂×#41	—	2	2	no	—
548	C₂×#41	—	4	1	no	—
549	C₂×#41	—	4	1	no	—
550	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
551	C₂²×D₄	—	2	2	no	—
552	C₂²×D₄	—	2	2	no	—
553	C₂²×D₄	—	2	1	no	—
554	C₂²×D₄	—	2	1	no	—
555	C₂²×D₄	—	2	1	no	—
556	C₂²×D₄	—	2	1	no	—
557	C₂²×D₄	—	2	1	no	—
558	C₂²×D₄	—	2	2	no	—
559	C₂²×D₄	—	4	1	no	—
560	C₂²×D₄	—	4	1	no	—
561	C₂²×D₄	D₄×C₄₁	1	4	yes	complemented
562	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
563	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
564	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
565	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
566	C₂³×C₄	—	2	1	no	—
567	C₂³×C₄	—	2	1	no	—
568	C₂³×C₄	—	2	1	no	—
569	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
570	AGL(1,ℤ/8)	—	2	32	no	—
571	C₂×SD₁₆	—	2	2	no	—
572	C₂×SD₁₆	—	2	2	no	—
573	C₂×SD₁₆	—	2	2	no	—
574	C₂×SD₁₆	—	2	2	no	—
575	C₂×SD₁₆	—	2	2	no	—
576	C₂×SD₁₆	D₄×C₄₁	1	4	yes	complemented
577	C₂×D₈	—	2	2	no	—
578	C₂×D₈	—	2	2	no	—
579	C₂×D₈	—	2	2	no	—
580	C₂×D₈	—	2	2	no	—
581	C₂×D₈	—	2	2	no	—
582	C₂×D₈	—	2	2	no	—
583	C₂×D₈	—	2	2	no	—
584	C₂×D₈	—	2	2	no	—
585	C₂×D₈	—	2	2	no	—
586	C₂×D₈	—	4	1	no	—
587	C₂×D₈	—	4	1	no	—
588	C₂×D₈	D₄×C₄₁	1	4	yes	complemented
589	C₂×M₁₆	—	2	2	no	—
590	C₂×M₁₆	—	2	2	no	—
591	C₂×M₁₆	—	2	2	no	—
592	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
593	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
594	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
595	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
596	#127	—	2	2	no	—
597	#127	—	4	1	no	—
598	#124	—	2	2	no	—
599	#124	—	4	1	no	—
600	#121	—	2	2	no	—
601	#121	—	2	2	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	4	1	no	—
605	C₄×D₄	—	4	1	no	—
606	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
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	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	—	2	1	no	—
621	C₂×C₂²⋊C₄	—	4	4	no	—
622	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
623	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
626	C₄⋊C₈	—	2	2	no	—
627	C₄⋊C₈	—	2	2	no	—
628	#103	—	2	2	no	—
629	#103	—	4	1	no	—
630	#102	—	2	2	no	—
631	#102	—	2	2	no	—
632	#102	—	2	2	no	—
633	#102	—	2	2	no	—
634	#102	—	2	2	no	—
635	#102	—	4	1	no	—
636	C₂²⋊C₈	—	2	2	no	—
637	#95	—	2	1	no	—
638	#95	—	2	1	no	—
639	#95	—	2	1	no	—
640	#95	D₄×C₄₁	1	1	yes	characteristic
641	#95	D₄×C₄₁	1	1	yes	characteristic
642	C₂⁴	—	2	1	no	—
643	C₂⁴	—	2	1	no	—
644	C₂⁴	—	2	1	no	—
645	C₂⁴	—	2	4	no	—
646	C₂⁴	—	2	1	no	—
647	C₂⁴	—	4	2	no	—
648	C₂⁴	—	4	2	no	—
649	C₂⁴	—	4	2	no	—
650	C₂⁴	—	4	2	no	—
651	C₂⁴	—	8	1	no	—
652	C₂⁴	—	8	1	no	—
653	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
654	#41	—	2	8	no	—
655	#41	—	4	4	no	—
656	#41	—	4	4	no	—
657	#41	—	4	4	no	—
658	C₂×Q₈	—	2	1	no	—
659	C₂×Q₈	—	2	1	no	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	1	no	—
662	C₂×Q₈	—	2	1	no	—
663	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
664	C₂×D₄	—	2	8	no	—
665	C₂×D₄	—	2	4	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	—	2	1	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	4	4	no	—
686	C₂×D₄	—	4	4	no	—
687	C₂×D₄	—	4	4	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	—	4	2	no	—
696	C₂×D₄	—	4	2	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂×D₄	—	8	1	no	—
699	C₂×D₄	—	8	1	no	—
700	C₂×D₄	—	8	1	no	—
701	C₂×D₄	—	8	1	no	—
702	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
703	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
704	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
705	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
706	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
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	—	4	2	no	—
716	C₂²×C₄	—	4	2	no	—
717	C₂²×C₄	—	4	2	no	—
718	C₂²×C₄	—	4	2	no	—
719	C₂²×C₄	—	4	2	no	—
720	C₂²×C₄	—	4	2	no	—
721	C₂²×C₄	—	4	2	no	—
722	C₂²×C₄	—	8	1	no	—
723	C₂²×C₄	—	8	1	no	—
724	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
725	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
726	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
727	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
728	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
729	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
730	C₂²×C₄	#41×C₄₁	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
732	SD₁₆	—	2	8	no	—
733	SD₁₆	—	2	8	no	—
734	D₈	—	2	8	no	—
735	D₈	—	2	8	no	—
736	D₈	—	4	4	no	—
737	D₈	—	4	4	no	—
738	M₁₆	—	2	8	no	—
739	C₂×C₈	—	2	1	no	—
740	C₂×C₈	—	2	1	no	—
741	C₂×C₈	—	2	1	no	—
742	C₂×C₈	—	2	1	no	—
743	C₂×C₈	—	2	1	no	—
744	C₂×C₈	—	2	1	no	—
745	C₂×C₈	—	2	1	no	—
746	C₂×C₈	—	2	1	no	—
747	C₂×C₈	—	2	1	no	—
748	C₂×C₈	—	2	1	no	—
749	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
750	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
751	C₄⋊C₄	—	2	1	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	—	2	1	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	2	1	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	4	1	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	—	4	2	no	—
765	C₂²⋊C₄	—	4	2	no	—
766	C₂²⋊C₄	—	4	2	no	—
767	C₂²⋊C₄	—	8	1	no	—
768	C₂²⋊C₄	—	8	1	no	—
769	C₂²⋊C₄	—	8	1	no	—
770	C₂²⋊C₄	—	8	1	no	—
771	C₄²	—	2	1	no	—
772	C₄²	—	2	1	no	—
773	C₄²	—	2	1	no	—
774	C₄²	—	2	1	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	2	1	no	—
779	C₂³	—	2	1	no	—
780	C₂³	—	2	1	no	—
781	C₂³	—	2	1	no	—
782	C₂³	—	2	1	no	—
783	C₂³	—	2	1	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	4	8	no	—
787	C₂³	—	4	8	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	—	4	1	no	—
806	C₂³	—	4	1	no	—
807	C₂³	—	4	1	no	—
808	C₂³	—	4	1	no	—
809	C₂³	—	4	1	no	—
810	C₂³	—	4	1	no	—
811	C₂³	—	8	4	no	—
812	C₂³	—	8	4	no	—
813	C₂³	—	8	4	no	—
814	C₂³	—	8	4	no	—
815	C₂³	—	8	4	no	—
816	C₂³	#121×C₄₁	1	2	yes	—
817	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
818	Q₈	—	2	2	no	—
819	Q₈	—	2	2	no	—
820	Q₈	—	4	1	no	—
821	Q₈	—	4	1	no	—
822	D₄	—	2	2	no	—
823	D₄	—	2	2	no	—
824	D₄	—	2	2	no	—
825	D₄	—	2	2	no	—
826	D₄	—	2	2	no	—
827	D₄	—	2	2	no	—
828	D₄	—	2	2	no	—
829	D₄	—	4	8	no	—
830	D₄	—	4	8	no	—
831	D₄	—	4	1	no	—
832	D₄	—	4	1	no	—
833	D₄	—	4	1	no	—
834	D₄	—	4	1	no	—
835	D₄	—	4	1	no	—
836	D₄	—	4	1	no	—
837	D₄	—	4	1	no	—
838	D₄	—	4	1	no	—
839	D₄	—	8	4	no	—
840	D₄	—	8	4	no	—
841	D₄	—	8	4	no	—
842	D₄	#120×C₄₁	1	4	yes	—
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	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	4	8	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	—	4	1	no	—
870	C₂×C₄	—	4	1	no	—
871	C₂×C₄	—	4	1	no	—
872	C₂×C₄	—	4	1	no	—
873	C₂×C₄	—	8	4	no	—
874	C₂×C₄	—	8	4	no	—
875	C₂×C₄	#121×C₄₁	1	2	yes	—
876	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	complemented
877	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
878	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
879	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
880	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
881	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
882	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
883	C₈	—	2	2	no	—
884	C₈	—	2	2	no	—
885	C₈	—	4	1	no	—
886	C₈	—	4	1	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	2	no	—
890	C₂²	—	2	4	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	1	no	—
895	C₂²	—	4	1	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	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	8	16	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	—	8	1	no	—
918	C₂²	—	8	1	no	—
919	C₂²	—	8	1	no	—
920	C₂²	—	8	1	no	—
921	C₂²	—	8	1	no	—
922	C₂²	—	8	1	no	—
923	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
924	C₂²	D₄²×C₄₁	1	1	yes	characteristic
925	C₂²	D₄²×C₄₁	1	1	yes	characteristic
926	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
927	C₂²	C₄₁×#575	1	1	yes	characteristic
928	C₂²	C₄₁×#576	1	1	yes	characteristic
929	C₂²	C₄₁×#576	1	1	yes	characteristic
930	C₄	—	2	2	no	—
931	C₄	—	2	2	no	—
932	C₄	—	4	2	no	—
933	C₄	—	4	1	no	—
934	C₄	—	4	1	no	—
935	C₄	—	4	1	no	—
936	C₄	—	8	1	no	—
937	C₄	—	8	1	no	—
938	C₄	—	8	1	no	—
939	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
940	C₄	C₄₁×#534	1	1	yes	characteristic
941	C₄	C₄₁×#546	1	1	yes	characteristic
942	C₄	C₄₁×#546	1	1	yes	characteristic
943	C₂	—	4	2	no	—
944	C₂	—	4	4	no	—
945	C₂	—	8	2	no	—
946	C₂	—	8	2	no	—
947	C₂	—	16	1	no	—
948	C₂	C₄₁×#2410	1	1	yes	characteristic
949	C₂	C₄₁×#3036	1	1	yes	characteristic
950	C₂	C₄₁×#3041	1	1	yes	characteristic
951	C₂	C₄₁×#3264	1	1	yes	characteristic
952	C₂	C₄₁×#3268	1	1	yes	characteristic
953	C₂	C₄₁×#3273	1	1	yes	characteristic
954	C₂	C₄₁×#3274	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 ◁ C₄×C₂²⋊C₄×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×#463	C₂	semidirect
3. C₂×C₄₁×#459	C₂	semidirect
4. C₂×C₄₁×#447	C₂	semidirect
5. C₄₁×#2431	C₂	semidirect
6. D₄×C₂²⋊C₄×C₄₁	C₂	semidirect
7. C₄₁×#2055	C₂	semidirect
8. C₄₁×#2054	C₂	semidirect
9. C₄₁×#2012	C₂	semidirect
10. C₄₁×#2011	C₂	semidirect
11. C₄₁×#1895	C₂	semidirect
12. C₄₁×#1879	C₂	semidirect
13. C₄₁×#1877	C₂	semidirect
14. C₄₁×#1851	C₂	semidirect
15. C₄₁×#1788	C₂	semidirect
28. C₂×#127×C₄₁	C₂²	semidirect
29. C₂×#124×C₄₁	C₂²	semidirect
37. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
38. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
39. C₂×#103×C₄₁	C₂²	semidirect
40. C₂×#103×C₄₁	C₂²	semidirect
43. C₂×#102×C₄₁	C₂²	semidirect
44. C₂×#102×C₄₁	C₂²	semidirect
45. C₂×#102×C₄₁	C₂²	semidirect
46. C₂×#102×C₄₁	C₂²	semidirect
50. C₄₁×#391	C₂²	semidirect
53. C₄₁×#390	C₂²	semidirect
61. C₄₁×#340	C₂²	semidirect
62. C₄₁×#340	C₂²	semidirect
63. C₄₁×#336	C₂²	semidirect
64. C₄₁×#336	C₂²	semidirect
83. C₂²×D₄×C₄₁	D₄	semidirect
98. C₂×SD₁₆×C₄₁	D₄	semidirect
110. C₂×D₈×C₄₁	D₄	semidirect
398. C₂×C₄×C₄₁	AGL(1,ℤ/8)	semidirect
409. #24366	C₄₁	direct (N × H)
466. C₂²×AGL(1,ℤ/8)	C₂×C₄₁	semidirect
467. C₂×#463	C₂×C₄₁	semidirect
468. C₂×#459	C₂×C₄₁	semidirect
469. C₂×#447	C₂×C₄₁	semidirect
470. #2431	C₂×C₄₁	semidirect
471. D₄×C₂²⋊C₄	C₂×C₄₁	semidirect
472. #2055	C₂×C₄₁	semidirect
473. #2054	C₂×C₄₁	semidirect
474. #2012	C₂×C₄₁	semidirect
475. #2011	C₂×C₄₁	semidirect
476. #1895	C₂×C₄₁	semidirect
477. #1879	C₂×C₄₁	semidirect
478. #1877	C₂×C₄₁	semidirect
479. #1851	C₂×C₄₁	semidirect
480. #1788	C₂×C₄₁	semidirect
505. C₂×#127	C₂²×C₄₁	semidirect
506. C₂×#124	C₂²×C₄₁	semidirect
514. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
515. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
516. C₂×#103	C₂²×C₄₁	semidirect
517. C₂×#103	C₂²×C₄₁	semidirect
520. C₂×#102	C₂²×C₄₁	semidirect
521. C₂×#102	C₂²×C₄₁	semidirect
522. C₂×#102	C₂²×C₄₁	semidirect
523. C₂×#102	C₂²×C₄₁	semidirect
527. #391	C₂²×C₄₁	semidirect
530. #390	C₂²×C₄₁	semidirect
538. #340	C₂²×C₄₁	semidirect
539. #340	C₂²×C₄₁	semidirect
540. #336	C₂²×C₄₁	semidirect
541. #336	C₂²×C₄₁	semidirect
542. C₄₁	#24366	direct (N × H)
561. C₂²×D₄	D₄×C₄₁	semidirect
576. C₂×SD₁₆	D₄×C₄₁	semidirect
588. C₂×D₈	D₄×C₄₁	semidirect
876. C₂×C₄	AGL(1,ℤ/8)×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×#463	2
C₂×C₄₁×#459	2
C₂×C₄₁×#447	2
C₄₁×#2431	2
D₄×C₂²⋊C₄×C₄₁	2
C₄₁×#2055	2
C₄₁×#2054	2
C₄₁×#2012	2
C₄₁×#2011	2
C₄₁×#1895	2
C₄₁×#1879	2
C₄₁×#1877	2
C₄₁×#1851	2
C₄₁×#1788	2
#24366	41

Subgroups — C41×#24366 #23800567

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24366 #23800567