Subgroups — C₄₁×#22863 #23799064

Order 10496.

1190 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#449	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#440	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#417	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2361	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1970	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1936	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1925	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1895	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1880	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#1863	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#1852	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#103×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₄₁	—	2	1	no	—
24	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
26	C₄₁×#449	C₄	1	8	yes	complemented
27	C₄₁×#440	—	2	4	no	—
28	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
30	C₄₁×#417	—	2	4	no	—
31	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
34	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
35	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
36	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
37	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
38	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
40	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
42	C₄₁×#390	—	2	1	no	—
43	C₄₁×#390	—	2	1	no	—
44	C₄₁×#390	C₂²	1	1	yes	characteristic
45	C₄₁×#390	C₂²	1	1	yes	characteristic
46	C₄₁×#390	C₂²	1	1	yes	characteristic
47	C₄₁×#389	C₂²	1	1	yes	characteristic
48	C₄₁×#388	—	2	1	no	—
49	C₄₁×#386	—	2	1	no	—
50	C₄₁×#385	—	2	1	no	—
51	C₄₁×#380	—	2	1	no	—
52	C₄₁×#380	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
55	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
56	C₄₁×#340	C₂²	1	1	yes	characteristic
57	C₄₁×#340	C₂²	1	1	yes	characteristic
58	C₄₁×#340	C₂²	1	1	yes	characteristic
59	C₄₁×#340	C₂²	1	1	yes	characteristic
60	C₄₁×#336	C₂²	1	1	yes	characteristic
61	C₄₁×#336	C₂²	1	1	yes	characteristic
62	C₂×#41×C₄₁	—	2	2	no	—
63	C₂×#41×C₄₁	—	2	2	no	—
64	C₂×#41×C₄₁	—	2	2	no	—
65	C₂×#41×C₄₁	—	4	1	no	—
66	C₂×#41×C₄₁	—	4	1	no	—
67	C₂×#41×C₄₁	C₂×C₄	1	4	yes	complemented
68	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₄₁	—	2	1	no	—
70	C₂²×D₄×C₄₁	—	2	1	no	—
71	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₄₁	—	2	1	no	—
74	C₂³×C₄×C₄₁	—	2	1	no	—
75	C₂³×C₄×C₄₁	—	2	1	no	—
76	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
77	C₂×SD₁₆×C₄₁	—	2	2	no	—
78	C₂×SD₁₆×C₄₁	—	2	2	no	—
79	C₂×SD₁₆×C₄₁	C₂×C₄	1	4	yes	complemented
80	C₂×D₈×C₄₁	—	4	1	no	—
81	C₂×D₈×C₄₁	—	4	1	no	—
82	C₂×D₈×C₄₁	C₂×C₄	1	4	yes	complemented
83	C₂×M₁₆×C₄₁	—	2	2	no	—
84	C₂×M₁₆×C₄₁	—	2	2	no	—
85	C₂×M₁₆×C₄₁	—	4	1	no	—
86	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
90	#121×C₄₁	—	2	2	no	—
91	#121×C₄₁	C₂×C₄	1	4	yes	—
92	C₄×Q₈×C₄₁	—	2	2	no	—
93	C₄×Q₈×C₄₁	—	2	2	no	—
94	C₄×Q₈×C₄₁	—	4	1	no	—
95	C₄×Q₈×C₄₁	—	4	1	no	—
96	C₄×D₄×C₄₁	—	2	2	no	—
97	C₄×D₄×C₄₁	—	4	1	no	—
98	C₄×D₄×C₄₁	—	4	4	no	—
99	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
100	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
101	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
102	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
103	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
104	C₂×C₄⋊C₄×C₄₁	—	4	1	no	—
105	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
121	C₂×C₄²×C₄₁	—	2	1	no	—
122	C₂×C₄²×C₄₁	—	2	1	no	—
123	C₂×C₄²×C₄₁	—	2	1	no	—
124	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
126	#107×C₄₁	—	2	2	no	—
127	#107×C₄₁	—	4	1	no	—
128	#103×C₄₁	—	2	2	no	—
129	#103×C₄₁	C₂×C₄	1	4	yes	complemented
130	#103×C₄₁	D₄	1	4	yes	complemented
131	#102×C₄₁	—	2	2	no	—
132	#102×C₄₁	—	2	2	no	—
133	#102×C₄₁	—	2	2	no	—
134	#102×C₄₁	—	4	1	no	—
135	#102×C₄₁	C₂×C₄	1	4	yes	complemented
136	C₂²⋊C₈×C₄₁	C₂×C₄	1	4	yes	complemented
137	#97×C₄₁	—	2	2	no	—
138	C₄×C₈×C₄₁	—	4	1	no	—
139	#95×C₄₁	—	2	1	no	—
140	#95×C₄₁	—	2	1	no	—
141	#95×C₄₁	—	2	1	no	—
142	#95×C₄₁	D₄	1	1	yes	characteristic
143	#95×C₄₁	D₄	1	1	yes	characteristic
144	C₂⁴×C₄₁	—	2	1	no	—
145	C₂⁴×C₄₁	—	2	1	no	—
146	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
147	#41×C₄₁	—	2	8	no	—
148	#41×C₄₁	—	4	4	no	—
149	#41×C₄₁	—	4	4	no	—
150	#41×C₄₁	—	4	4	no	—
151	C₂×Q₈×C₄₁	—	2	1	no	—
152	C₂×Q₈×C₄₁	—	2	1	no	—
153	C₂×Q₈×C₄₁	—	2	1	no	—
154	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
155	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
156	C₂×Q₈×C₄₁	#41	1	2	yes	—
157	C₂×D₄×C₄₁	—	2	4	no	—
158	C₂×D₄×C₄₁	—	2	4	no	—
159	C₂×D₄×C₄₁	—	2	1	no	—
160	C₂×D₄×C₄₁	—	2	1	no	—
161	C₂×D₄×C₄₁	—	2	1	no	—
162	C₂×D₄×C₄₁	—	2	1	no	—
163	C₂×D₄×C₄₁	—	2	1	no	—
164	C₂×D₄×C₄₁	—	2	1	no	—
165	C₂×D₄×C₄₁	—	2	1	no	—
166	C₂×D₄×C₄₁	—	2	1	no	—
167	C₂×D₄×C₄₁	—	2	1	no	—
168	C₂×D₄×C₄₁	—	2	1	no	—
169	C₂×D₄×C₄₁	—	4	2	no	—
170	C₂×D₄×C₄₁	—	4	2	no	—
171	C₂×D₄×C₄₁	—	4	2	no	—
172	C₂×D₄×C₄₁	—	4	2	no	—
173	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
174	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
175	C₂²×C₄×C₄₁	—	2	1	no	—
176	C₂²×C₄×C₄₁	—	2	1	no	—
177	C₂²×C₄×C₄₁	—	2	1	no	—
178	C₂²×C₄×C₄₁	—	2	1	no	—
179	C₂²×C₄×C₄₁	—	2	1	no	—
180	C₂²×C₄×C₄₁	—	2	1	no	—
181	C₂²×C₄×C₄₁	—	2	1	no	—
182	C₂²×C₄×C₄₁	—	2	4	no	—
183	C₂²×C₄×C₄₁	—	2	1	no	—
184	C₂²×C₄×C₄₁	—	2	1	no	—
185	C₂²×C₄×C₄₁	—	2	1	no	—
186	C₂²×C₄×C₄₁	—	4	2	no	—
187	C₂²×C₄×C₄₁	—	4	2	no	—
188	C₂²×C₄×C₄₁	—	4	2	no	—
189	C₂²×C₄×C₄₁	—	4	2	no	—
190	C₂²×C₄×C₄₁	—	4	2	no	—
191	C₂²×C₄×C₄₁	—	4	2	no	—
192	C₂²×C₄×C₄₁	—	8	1	no	—
193	C₂²×C₄×C₄₁	—	8	1	no	—
194	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
195	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₄₁	#41	1	2	yes	—
201	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
202	SD₁₆×C₄₁	—	2	8	no	—
203	D₈×C₄₁	—	4	4	no	—
204	M₁₆×C₄₁	—	4	4	no	—
205	C₂×C₈×C₄₁	—	2	1	no	—
206	C₂×C₈×C₄₁	—	2	1	no	—
207	C₂×C₈×C₄₁	—	2	1	no	—
208	C₂×C₈×C₄₁	—	2	1	no	—
209	C₂×C₈×C₄₁	—	2	1	no	—
210	C₂×C₈×C₄₁	—	2	1	no	—
211	C₂×C₈×C₄₁	—	2	1	no	—
212	C₂×C₈×C₄₁	—	2	1	no	—
213	C₂×C₈×C₄₁	—	2	1	no	—
214	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
215	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
216	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
217	C₄⋊C₄×C₄₁	—	2	1	no	—
218	C₄⋊C₄×C₄₁	—	2	1	no	—
219	C₄⋊C₄×C₄₁	—	2	1	no	—
220	C₄⋊C₄×C₄₁	—	2	1	no	—
221	C₄⋊C₄×C₄₁	—	2	1	no	—
222	C₄⋊C₄×C₄₁	—	2	1	no	—
223	C₄⋊C₄×C₄₁	—	2	1	no	—
224	C₄⋊C₄×C₄₁	—	2	1	no	—
225	C₄⋊C₄×C₄₁	—	4	2	no	—
226	C₄⋊C₄×C₄₁	—	4	2	no	—
227	C₄⋊C₄×C₄₁	—	4	2	no	—
228	C₄⋊C₄×C₄₁	—	4	2	no	—
229	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
230	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
231	C₂²⋊C₄×C₄₁	—	2	4	no	—
232	C₂²⋊C₄×C₄₁	—	2	2	no	—
233	C₂²⋊C₄×C₄₁	—	4	1	no	—
234	C₂²⋊C₄×C₄₁	—	4	2	no	—
235	C₂²⋊C₄×C₄₁	—	4	2	no	—
236	C₂²⋊C₄×C₄₁	—	4	2	no	—
237	C₂²⋊C₄×C₄₁	—	4	2	no	—
238	C₂²⋊C₄×C₄₁	—	8	1	no	—
239	C₂²⋊C₄×C₄₁	—	8	1	no	—
240	C₂²⋊C₄×C₄₁	—	8	1	no	—
241	C₂²⋊C₄×C₄₁	—	8	1	no	—
242	C₄²×C₄₁	—	2	1	no	—
243	C₄²×C₄₁	—	2	1	no	—
244	C₄²×C₄₁	—	2	1	no	—
245	C₄²×C₄₁	—	2	1	no	—
246	C₄²×C₄₁	—	4	2	no	—
247	C₄²×C₄₁	—	4	2	no	—
248	C₄²×C₄₁	—	4	2	no	—
249	C₂³×C₄₁	—	2	1	no	—
250	C₂³×C₄₁	—	2	1	no	—
251	C₂³×C₄₁	—	2	1	no	—
252	C₂³×C₄₁	—	2	1	no	—
253	C₂³×C₄₁	—	2	1	no	—
254	C₂³×C₄₁	—	2	1	no	—
255	C₂³×C₄₁	—	2	2	no	—
256	C₂³×C₄₁	—	2	2	no	—
257	C₂³×C₄₁	—	4	1	no	—
258	C₂³×C₄₁	—	4	1	no	—
259	C₂³×C₄₁	—	4	1	no	—
260	C₂³×C₄₁	—	4	1	no	—
261	C₂³×C₄₁	—	4	1	no	—
262	C₂³×C₄₁	—	4	1	no	—
263	C₂³×C₄₁	—	4	1	no	—
264	C₂³×C₄₁	—	4	1	no	—
265	C₂³×C₄₁	—	4	1	no	—
266	C₂³×C₄₁	—	4	1	no	—
267	C₂³×C₄₁	—	4	1	no	—
268	C₂³×C₄₁	—	4	1	no	—
269	C₂³×C₄₁	C₄×D₄	1	2	yes	—
270	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
271	Q₈×C₄₁	—	2	2	no	—
272	Q₈×C₄₁	—	2	2	no	—
273	Q₈×C₄₁	—	2	2	no	—
274	Q₈×C₄₁	C₄×D₄	1	4	yes	complemented
275	D₄×C₄₁	—	2	2	no	—
276	D₄×C₄₁	—	2	2	no	—
277	D₄×C₄₁	—	2	2	no	—
278	D₄×C₄₁	—	2	2	no	—
279	D₄×C₄₁	—	4	8	no	—
280	D₄×C₄₁	—	4	8	no	—
281	D₄×C₄₁	—	4	1	no	—
282	D₄×C₄₁	—	4	1	no	—
283	D₄×C₄₁	—	4	1	no	—
284	D₄×C₄₁	—	4	1	no	—
285	C₂×C₄×C₄₁	—	2	2	no	—
286	C₂×C₄×C₄₁	—	2	2	no	—
287	C₂×C₄×C₄₁	—	2	1	no	—
288	C₂×C₄×C₄₁	—	2	1	no	—
289	C₂×C₄×C₄₁	—	2	2	no	—
290	C₂×C₄×C₄₁	—	2	1	no	—
291	C₂×C₄×C₄₁	—	2	1	no	—
292	C₂×C₄×C₄₁	—	2	2	no	—
293	C₂×C₄×C₄₁	—	2	2	no	—
294	C₂×C₄×C₄₁	—	2	2	no	—
295	C₂×C₄×C₄₁	—	2	2	no	—
296	C₂×C₄×C₄₁	—	2	2	no	—
297	C₂×C₄×C₄₁	—	2	1	no	—
298	C₂×C₄×C₄₁	—	2	1	no	—
299	C₂×C₄×C₄₁	—	2	2	no	—
300	C₂×C₄×C₄₁	—	2	1	no	—
301	C₂×C₄×C₄₁	—	2	1	no	—
302	C₂×C₄×C₄₁	—	2	1	no	—
303	C₂×C₄×C₄₁	—	2	1	no	—
304	C₂×C₄×C₄₁	—	2	1	no	—
305	C₂×C₄×C₄₁	—	2	1	no	—
306	C₂×C₄×C₄₁	—	2	1	no	—
307	C₂×C₄×C₄₁	—	4	8	no	—
308	C₂×C₄×C₄₁	—	4	1	no	—
309	C₂×C₄×C₄₁	—	4	1	no	—
310	C₂×C₄×C₄₁	—	4	1	no	—
311	C₂×C₄×C₄₁	—	4	1	no	—
312	C₂×C₄×C₄₁	—	4	1	no	—
313	C₂×C₄×C₄₁	—	4	1	no	—
314	C₂×C₄×C₄₁	—	4	1	no	—
315	C₂×C₄×C₄₁	—	4	1	no	—
316	C₂×C₄×C₄₁	—	4	1	no	—
317	C₂×C₄×C₄₁	—	4	1	no	—
318	C₂×C₄×C₄₁	—	4	1	no	—
319	C₂×C₄×C₄₁	—	4	1	no	—
320	C₂×C₄×C₄₁	—	4	1	no	—
321	C₂×C₄×C₄₁	—	8	4	no	—
322	C₂×C₄×C₄₁	—	8	4	no	—
323	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
324	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
325	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
326	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
328	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
329	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
330	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
331	C₈×C₄₁	—	2	2	no	—
332	C₈×C₄₁	—	2	2	no	—
333	C₈×C₄₁	—	2	2	no	—
334	C₈×C₄₁	—	4	1	no	—
335	#22863	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
336	C₂²×C₄₁	—	2	2	no	—
337	C₂²×C₄₁	—	2	2	no	—
338	C₂²×C₄₁	—	2	2	no	—
339	C₂²×C₄₁	—	4	1	no	—
340	C₂²×C₄₁	—	4	1	no	—
341	C₂²×C₄₁	—	4	1	no	—
342	C₂²×C₄₁	—	4	1	no	—
343	C₂²×C₄₁	—	4	2	no	—
344	C₂²×C₄₁	—	4	2	no	—
345	C₂²×C₄₁	—	4	2	no	—
346	C₂²×C₄₁	—	4	2	no	—
347	C₂²×C₄₁	—	4	2	no	—
348	C₂²×C₄₁	—	4	2	no	—
349	C₂²×C₄₁	—	8	1	no	—
350	C₂²×C₄₁	—	8	1	no	—
351	C₂²×C₄₁	—	8	1	no	—
352	C₂²×C₄₁	—	8	1	no	—
353	C₂²×C₄₁	—	8	1	no	—
354	C₂²×C₄₁	—	8	1	no	—
355	C₂²×C₄₁	—	8	1	no	—
356	C₂²×C₄₁	—	8	1	no	—
357	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
358	C₂²×C₄₁	D₄²	1	1	yes	characteristic
359	C₂²×C₄₁	#546	1	1	yes	characteristic
360	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
361	C₂²×C₄₁	#575	1	1	yes	characteristic
362	C₂²×C₄₁	#576	1	1	yes	characteristic
363	C₂²×C₄₁	#578	1	1	yes	characteristic
364	C₄×C₄₁	—	2	2	no	—
365	C₄×C₄₁	—	2	4	no	—
366	C₄×C₄₁	—	2	2	no	—
367	C₄×C₄₁	—	4	2	no	—
368	C₄×C₄₁	—	4	1	no	—
369	C₄×C₄₁	—	4	2	no	—
370	C₄×C₄₁	—	4	1	no	—
371	C₄×C₄₁	—	4	1	no	—
372	C₄×C₄₁	—	8	1	no	—
373	C₄×C₄₁	—	8	1	no	—
374	C₄×C₄₁	—	8	1	no	—
375	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
376	C₄×C₄₁	#518	1	1	yes	characteristic
377	C₄×C₄₁	#546	1	1	yes	characteristic
378	C₄×C₄₁	#551	1	1	yes	characteristic
379	C₂×#449	C₂×C₄₁	1	1	yes	characteristic
380	C₂×#440	C₂×C₄₁	1	1	yes	characteristic, complemented
381	C₂×#417	C₂×C₄₁	1	1	yes	characteristic, complemented
382	#2361	C₂×C₄₁	1	1	yes	characteristic, complemented
383	#2341	C₂×C₄₁	1	1	yes	characteristic, complemented
384	#1970	C₂×C₄₁	1	1	yes	characteristic, complemented
385	#1936	C₂×C₄₁	1	1	yes	characteristic, complemented
386	#1925	C₂×C₄₁	1	1	yes	characteristic, complemented
387	#1895	C₂×C₄₁	1	1	yes	characteristic, complemented
388	#1880	C₂×C₄₁	1	1	yes	characteristic, complemented
389	#1879	C₂×C₄₁	1	1	yes	characteristic, complemented
390	#1863	C₂×C₄₁	1	1	yes	characteristic, complemented
391	#1852	C₂×C₄₁	1	1	yes	characteristic, complemented
392	C₄×#103	C₂×C₄₁	1	1	yes	characteristic, complemented
393	#1753	C₂×C₄₁	1	1	yes	characteristic, complemented
394	C₂×C₄₁	—	4	2	no	—
395	C₂×C₄₁	—	8	2	no	—
396	C₂×C₄₁	—	8	2	no	—
397	C₂×C₄₁	#2358	1	1	yes	characteristic
398	C₂×C₄₁	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
399	C₂×C₄₁	#2951	1	1	yes	characteristic
400	C₂×C₄₁	#3274	1	1	yes	characteristic
401	C₂×C₄₁	#3277	1	1	yes	characteristic
402	C₂×C₄₁	#3308	1	1	yes	characteristic
403	C₂×C₄₁	#3309	1	1	yes	characteristic
404	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
405	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
406	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
407	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
408	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
409	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
410	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
411	C₂×C₄×D₄	—	2	1	no	—
412	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
413	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
414	#449	C₄×C₄₁	1	8	yes	complemented
415	#440	—	2	4	no	—
416	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
417	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
418	#417	—	2	4	no	—
419	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
420	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
421	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
422	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
423	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
424	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
425	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
426	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
427	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
428	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
429	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
430	#390	—	2	1	no	—
431	#390	—	2	1	no	—
432	#390	C₂²×C₄₁	1	1	yes	characteristic
433	#390	C₂²×C₄₁	1	1	yes	characteristic
434	#390	C₂²×C₄₁	1	1	yes	characteristic
435	#389	C₂²×C₄₁	1	1	yes	characteristic
436	#388	—	2	1	no	—
437	#386	—	2	1	no	—
438	#385	—	2	1	no	—
439	#380	—	2	1	no	—
440	#380	C₂²×C₄₁	1	1	yes	characteristic
441	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
442	C₄×C₂²⋊C₄	—	2	1	no	—
443	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
444	#340	C₂²×C₄₁	1	1	yes	characteristic
445	#340	C₂²×C₄₁	1	1	yes	characteristic
446	#340	C₂²×C₄₁	1	1	yes	characteristic
447	#340	C₂²×C₄₁	1	1	yes	characteristic
448	#336	C₂²×C₄₁	1	1	yes	characteristic
449	#336	C₂²×C₄₁	1	1	yes	characteristic
450	C₄₁	#22863	1	1	yes	characteristic, direct product factor, Sylow
451	C₂×#41	—	2	2	no	—
452	C₂×#41	—	2	2	no	—
453	C₂×#41	—	2	2	no	—
454	C₂×#41	—	4	1	no	—
455	C₂×#41	—	4	1	no	—
456	C₂×#41	C₂×C₄×C₄₁	1	4	yes	complemented
457	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
458	C₂²×D₄	—	2	1	no	—
459	C₂²×D₄	—	2	1	no	—
460	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
461	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
462	C₂³×C₄	—	2	1	no	—
463	C₂³×C₄	—	2	1	no	—
464	C₂³×C₄	—	2	1	no	—
465	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
466	C₂×SD₁₆	—	2	2	no	—
467	C₂×SD₁₆	—	2	2	no	—
468	C₂×SD₁₆	C₂×C₄×C₄₁	1	4	yes	complemented
469	C₂×D₈	—	4	1	no	—
470	C₂×D₈	—	4	1	no	—
471	C₂×D₈	C₂×C₄×C₄₁	1	4	yes	complemented
472	C₂×M₁₆	—	2	2	no	—
473	C₂×M₁₆	—	2	2	no	—
474	C₂×M₁₆	—	4	1	no	—
475	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
476	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
477	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
478	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
479	#121	—	2	2	no	—
480	#121	C₂×C₄×C₄₁	1	4	yes	—
481	C₄×Q₈	—	2	2	no	—
482	C₄×Q₈	—	2	2	no	—
483	C₄×Q₈	—	4	1	no	—
484	C₄×Q₈	—	4	1	no	—
485	C₄×D₄	—	2	2	no	—
486	C₄×D₄	—	4	1	no	—
487	C₄×D₄	—	4	4	no	—
488	C₂×C₄⋊C₄	—	2	2	no	—
489	C₂×C₄⋊C₄	—	2	1	no	—
490	C₂×C₄⋊C₄	—	2	1	no	—
491	C₂×C₄⋊C₄	—	2	1	no	—
492	C₂×C₄⋊C₄	—	2	1	no	—
493	C₂×C₄⋊C₄	—	4	1	no	—
494	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
499	C₂×C₂²⋊C₄	—	2	1	no	—
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₂²⋊C₄	—	2	1	no	—
503	C₂×C₂²⋊C₄	—	2	1	no	—
504	C₂×C₂²⋊C₄	—	2	1	no	—
505	C₂×C₂²⋊C₄	—	2	1	no	—
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
509	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
510	C₂×C₄²	—	2	1	no	—
511	C₂×C₄²	—	2	1	no	—
512	C₂×C₄²	—	2	1	no	—
513	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
514	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
515	#107	—	2	2	no	—
516	#107	—	4	1	no	—
517	#103	—	2	2	no	—
518	#103	C₂×C₄×C₄₁	1	4	yes	complemented
519	#103	D₄×C₄₁	1	4	yes	complemented
520	#102	—	2	2	no	—
521	#102	—	2	2	no	—
522	#102	—	2	2	no	—
523	#102	—	4	1	no	—
524	#102	C₂×C₄×C₄₁	1	4	yes	complemented
525	C₂²⋊C₈	C₂×C₄×C₄₁	1	4	yes	complemented
526	#97	—	2	2	no	—
527	C₄×C₈	—	4	1	no	—
528	#95	—	2	1	no	—
529	#95	—	2	1	no	—
530	#95	—	2	1	no	—
531	#95	D₄×C₄₁	1	1	yes	characteristic
532	#95	D₄×C₄₁	1	1	yes	characteristic
533	C₂⁴	—	2	1	no	—
534	C₂⁴	—	2	1	no	—
535	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
536	#41	—	2	8	no	—
537	#41	—	4	4	no	—
538	#41	—	4	4	no	—
539	#41	—	4	4	no	—
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	—	2	1	no	—
542	C₂×Q₈	—	2	1	no	—
543	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
544	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
545	C₂×Q₈	#41×C₄₁	1	2	yes	—
546	C₂×D₄	—	2	4	no	—
547	C₂×D₄	—	2	4	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	4	2	no	—
559	C₂×D₄	—	4	2	no	—
560	C₂×D₄	—	4	2	no	—
561	C₂×D₄	—	4	2	no	—
562	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
563	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	4	2	no	—
576	C₂²×C₄	—	4	2	no	—
577	C₂²×C₄	—	4	2	no	—
578	C₂²×C₄	—	4	2	no	—
579	C₂²×C₄	—	4	2	no	—
580	C₂²×C₄	—	4	2	no	—
581	C₂²×C₄	—	8	1	no	—
582	C₂²×C₄	—	8	1	no	—
583	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
584	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
585	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
586	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
587	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
588	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
589	C₂²×C₄	#41×C₄₁	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
591	SD₁₆	—	2	8	no	—
592	D₈	—	4	4	no	—
593	M₁₆	—	4	4	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	—	2	1	no	—
601	C₂×C₈	—	2	1	no	—
602	C₂×C₈	—	2	1	no	—
603	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
604	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
605	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	4	2	no	—
615	C₄⋊C₄	—	4	2	no	—
616	C₄⋊C₄	—	4	2	no	—
617	C₄⋊C₄	—	4	2	no	—
618	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
619	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	2	no	—
622	C₂²⋊C₄	—	4	1	no	—
623	C₂²⋊C₄	—	4	2	no	—
624	C₂²⋊C₄	—	4	2	no	—
625	C₂²⋊C₄	—	4	2	no	—
626	C₂²⋊C₄	—	4	2	no	—
627	C₂²⋊C₄	—	8	1	no	—
628	C₂²⋊C₄	—	8	1	no	—
629	C₂²⋊C₄	—	8	1	no	—
630	C₂²⋊C₄	—	8	1	no	—
631	C₄²	—	2	1	no	—
632	C₄²	—	2	1	no	—
633	C₄²	—	2	1	no	—
634	C₄²	—	2	1	no	—
635	C₄²	—	4	2	no	—
636	C₄²	—	4	2	no	—
637	C₄²	—	4	2	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	4	1	no	—
649	C₂³	—	4	1	no	—
650	C₂³	—	4	1	no	—
651	C₂³	—	4	1	no	—
652	C₂³	—	4	1	no	—
653	C₂³	—	4	1	no	—
654	C₂³	—	4	1	no	—
655	C₂³	—	4	1	no	—
656	C₂³	—	4	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	C₄×D₄×C₄₁	1	2	yes	—
659	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
660	Q₈	—	2	2	no	—
661	Q₈	—	2	2	no	—
662	Q₈	—	2	2	no	—
663	Q₈	C₄×D₄×C₄₁	1	4	yes	complemented
664	D₄	—	2	2	no	—
665	D₄	—	2	2	no	—
666	D₄	—	2	2	no	—
667	D₄	—	2	2	no	—
668	D₄	—	4	8	no	—
669	D₄	—	4	8	no	—
670	D₄	—	4	1	no	—
671	D₄	—	4	1	no	—
672	D₄	—	4	1	no	—
673	D₄	—	4	1	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	4	8	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	1	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	8	4	no	—
711	C₂×C₄	—	8	4	no	—
712	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
713	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
714	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
715	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
716	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
717	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
718	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
719	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
720	C₈	—	2	2	no	—
721	C₈	—	2	2	no	—
722	C₈	—	2	2	no	—
723	C₈	—	4	1	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	2	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	8	1	no	—
738	C₂²	—	8	1	no	—
739	C₂²	—	8	1	no	—
740	C₂²	—	8	1	no	—
741	C₂²	—	8	1	no	—
742	C₂²	—	8	1	no	—
743	C₂²	—	8	1	no	—
744	C₂²	—	8	1	no	—
745	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
746	C₂²	D₄²×C₄₁	1	1	yes	characteristic
747	C₂²	C₄₁×#546	1	1	yes	characteristic
748	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
749	C₂²	C₄₁×#575	1	1	yes	characteristic
750	C₂²	C₄₁×#576	1	1	yes	characteristic
751	C₂²	C₄₁×#578	1	1	yes	characteristic
752	C₄	—	2	2	no	—
753	C₄	—	2	2	no	—
754	C₄	—	2	4	no	—
755	C₄	—	4	1	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	1	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	1	no	—
760	C₄	—	8	1	no	—
761	C₄	—	8	1	no	—
762	C₄	—	8	1	no	—
763	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
764	C₄	C₄₁×#518	1	1	yes	characteristic
765	C₄	C₄₁×#546	1	1	yes	characteristic
766	C₄	C₄₁×#551	1	1	yes	characteristic
767	C₂	—	4	2	no	—
768	C₂	—	8	2	no	—
769	C₂	—	8	2	no	—
770	C₂	C₄₁×#2358	1	1	yes	characteristic
771	C₂	C₄×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
772	C₂	C₄₁×#2951	1	1	yes	characteristic
773	C₂	C₄₁×#3274	1	1	yes	characteristic
774	C₂	C₄₁×#3277	1	1	yes	characteristic
775	C₂	C₄₁×#3308	1	1	yes	characteristic
776	C₂	C₄₁×#3309	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#449	C₂
LCS	G ▷ C₂×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
2. C₂×C₄₁×#440	C₂	semidirect
3. C₂×C₄₁×#417	C₂	semidirect
4. C₄₁×#2361	C₂	semidirect
5. C₄₁×#2341	C₂	semidirect
6. C₄₁×#1970	C₂	semidirect
7. C₄₁×#1936	C₂	semidirect
8. C₄₁×#1925	C₂	semidirect
9. C₄₁×#1895	C₂	semidirect
10. C₄₁×#1880	C₂	semidirect
11. C₄₁×#1879	C₂	semidirect
12. C₄₁×#1863	C₂	semidirect
13. C₄₁×#1852	C₂	semidirect
14. C₄×#103×C₄₁	C₂	semidirect
15. C₄₁×#1753	C₂	semidirect
26. C₄₁×#449	C₄	semidirect
67. C₂×#41×C₄₁	C₂×C₄	semidirect
79. C₂×SD₁₆×C₄₁	C₂×C₄	semidirect
82. C₂×D₈×C₄₁	C₂×C₄	semidirect
129. #103×C₄₁	C₂×C₄	semidirect
130. #103×C₄₁	D₄	semidirect
135. #102×C₄₁	C₂×C₄	semidirect
136. C₂²⋊C₈×C₄₁	C₂×C₄	semidirect
274. Q₈×C₄₁	C₄×D₄	semidirect
335. #22863	C₄₁	direct (N × H)
380. C₂×#440	C₂×C₄₁	semidirect
381. C₂×#417	C₂×C₄₁	semidirect
382. #2361	C₂×C₄₁	semidirect
383. #2341	C₂×C₄₁	semidirect
384. #1970	C₂×C₄₁	semidirect
385. #1936	C₂×C₄₁	semidirect
386. #1925	C₂×C₄₁	semidirect
387. #1895	C₂×C₄₁	semidirect
388. #1880	C₂×C₄₁	semidirect
389. #1879	C₂×C₄₁	semidirect
390. #1863	C₂×C₄₁	semidirect
391. #1852	C₂×C₄₁	semidirect
392. C₄×#103	C₂×C₄₁	semidirect
393. #1753	C₂×C₄₁	semidirect
414. #449	C₄×C₄₁	semidirect
450. C₄₁	#22863	direct (N × H)
456. C₂×#41	C₂×C₄×C₄₁	semidirect
468. C₂×SD₁₆	C₂×C₄×C₄₁	semidirect
471. C₂×D₈	C₂×C₄×C₄₁	semidirect
518. #103	C₂×C₄×C₄₁	semidirect
519. #103	D₄×C₄₁	semidirect
524. #102	C₂×C₄×C₄₁	semidirect
525. C₂²⋊C₈	C₂×C₄×C₄₁	semidirect
663. Q₈	C₄×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×#449	2
C₂×C₄₁×#440	2
C₂×C₄₁×#417	2
C₄₁×#2361	2
C₄₁×#2341	2
C₄₁×#1970	2
C₄₁×#1936	2
C₄₁×#1925	2
C₄₁×#1895	2
C₄₁×#1880	2
C₄₁×#1879	2
C₄₁×#1863	2
C₄₁×#1852	2
C₄×#103×C₄₁	2
C₄₁×#1753	2
#22863	41

Subgroups — C41×#22863 #23799064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#22863 #23799064