Subgroups — C₄₁×#24040 #23800241

Order 10496.

1322 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#548	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#485	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#416	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2042	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2042	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2034	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1892	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1869	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1865	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#1863	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#1788	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#1787	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#1787	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₄₁×#548	—	2	4	no	—
20	C₄₁×#548	—	2	4	no	—
21	C₂×#124×C₄₁	—	2	1	no	—
22	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
24	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#121×C₄₁	—	2	1	no	—
26	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₄₁	—	2	1	no	—
29	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
31	C₄₁×#485	—	2	4	no	—
32	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
34	C₄₁×#416	—	2	4	no	—
35	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
36	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
37	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
38	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
40	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
41	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
42	C₂×#103×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
46	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
50	C₄₁×#397	—	2	1	no	—
51	C₄₁×#394	—	2	1	no	—
52	C₄₁×#389	C₂²	1	1	yes	characteristic
53	C₄₁×#389	C₂²	1	1	yes	characteristic
54	C₄₁×#388	—	2	1	no	—
55	C₄₁×#387	—	2	1	no	—
56	C₄₁×#380	C₂²	1	1	yes	characteristic
57	C₄₁×#380	C₂²	1	1	yes	characteristic
58	C₄₁×#380	C₂²	1	1	yes	characteristic
59	C₄₁×#340	C₂²	1	1	yes	characteristic
60	C₄₁×#340	C₂²	1	1	yes	characteristic
61	C₄₁×#336	C₂²	1	1	yes	characteristic
62	C₄₁×#336	C₂²	1	1	yes	characteristic
63	C₂×#41×C₄₁	—	2	2	no	—
64	C₂×#41×C₄₁	—	2	2	no	—
65	C₂×#41×C₄₁	—	2	2	no	—
66	C₂×#41×C₄₁	—	4	1	no	—
67	C₂×#41×C₄₁	—	4	1	no	—
68	C₂×#41×C₄₁	D₄	1	4	yes	—
69	C₂²×Q₈×C₄₁	—	2	2	no	—
70	C₂²×Q₈×C₄₁	—	2	2	no	—
71	C₂²×Q₈×C₄₁	—	2	1	no	—
72	C₂²×Q₈×C₄₁	—	2	2	no	—
73	C₂²×Q₈×C₄₁	—	2	2	no	—
74	C₂²×Q₈×C₄₁	—	4	1	no	—
75	C₂²×Q₈×C₄₁	—	4	1	no	—
76	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
77	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₄₁	—	2	1	no	—
79	C₂²×D₄×C₄₁	—	2	1	no	—
80	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
81	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₄₁	—	2	1	no	—
83	C₂³×C₄×C₄₁	—	2	1	no	—
84	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₄₁	—	2	2	no	—
87	C₂²×C₈×C₄₁	—	4	1	no	—
88	C₂²×C₈×C₄₁	—	4	1	no	—
89	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
93	#124×C₄₁	—	2	8	no	—
94	#124×C₄₁	—	2	2	no	—
95	#124×C₄₁	—	2	2	no	—
96	C₂²⋊Q₈×C₄₁	—	2	8	no	—
97	C₂²⋊Q₈×C₄₁	—	2	2	no	—
98	C₂²⋊Q₈×C₄₁	D₄	1	4	yes	—
99	#121×C₄₁	—	2	8	no	—
100	#121×C₄₁	—	2	2	no	—
101	#121×C₄₁	—	2	2	no	—
102	C₄×Q₈×C₄₁	—	2	2	no	—
103	C₄×Q₈×C₄₁	—	2	2	no	—
104	C₄×D₄×C₄₁	—	2	8	no	—
105	C₄×D₄×C₄₁	—	2	2	no	—
106	C₄×D₄×C₄₁	—	2	2	no	—
107	#117×C₄₁	—	2	2	no	—
108	#117×C₄₁	—	2	2	no	—
109	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
110	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
111	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
112	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
113	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
128	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
129	C₂×C₄²×C₄₁	—	2	1	no	—
130	C₂×C₄²×C₄₁	—	2	1	no	—
131	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
132	#107×C₄₁	—	2	2	no	—
133	#106×C₄₁	—	2	2	no	—
134	#103×C₄₁	—	2	2	no	—
135	#103×C₄₁	—	2	2	no	—
136	#103×C₄₁	—	2	2	no	—
137	#103×C₄₁	—	2	2	no	—
138	#103×C₄₁	—	2	2	no	—
139	#103×C₄₁	—	2	2	no	—
140	#103×C₄₁	—	4	1	no	—
141	#103×C₄₁	—	4	1	no	—
142	#102×C₄₁	—	2	2	no	—
143	#102×C₄₁	—	2	2	no	—
144	#102×C₄₁	—	4	1	no	—
145	#102×C₄₁	—	4	1	no	—
146	C₂²⋊C₈×C₄₁	—	2	2	no	—
147	C₂²⋊C₈×C₄₁	—	4	1	no	—
148	C₂²⋊C₈×C₄₁	—	4	1	no	—
149	#95×C₄₁	—	2	1	no	—
150	#95×C₄₁	—	2	1	no	—
151	#95×C₄₁	—	2	1	no	—
152	#95×C₄₁	—	2	1	no	—
153	#95×C₄₁	—	2	1	no	—
154	C₂⁴×C₄₁	—	2	1	no	—
155	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
156	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
157	#41×C₄₁	—	2	8	no	—
158	#41×C₄₁	—	4	4	no	—
159	#41×C₄₁	—	4	4	no	—
160	#41×C₄₁	—	4	4	no	—
161	C₂×Q₈×C₄₁	—	2	4	no	—
162	C₂×Q₈×C₄₁	—	2	1	no	—
163	C₂×Q₈×C₄₁	—	2	1	no	—
164	C₂×Q₈×C₄₁	—	2	1	no	—
165	C₂×Q₈×C₄₁	—	2	1	no	—
166	C₂×Q₈×C₄₁	—	2	1	no	—
167	C₂×Q₈×C₄₁	—	2	1	no	—
168	C₂×Q₈×C₄₁	—	2	1	no	—
169	C₂×Q₈×C₄₁	—	2	1	no	—
170	C₂×Q₈×C₄₁	—	4	2	no	—
171	C₂×Q₈×C₄₁	—	4	2	no	—
172	C₂×Q₈×C₄₁	—	4	4	no	—
173	C₂×Q₈×C₄₁	—	4	4	no	—
174	C₂×Q₈×C₄₁	—	4	4	no	—
175	C₂×Q₈×C₄₁	—	4	4	no	—
176	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
177	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
178	C₂×Q₈×C₄₁	#41	1	2	yes	—
179	C₂×Q₈×C₄₁	#41	1	2	yes	—
180	C₂×D₄×C₄₁	—	2	4	no	—
181	C₂×D₄×C₄₁	—	2	2	no	—
182	C₂×D₄×C₄₁	—	2	4	no	—
183	C₂×D₄×C₄₁	—	2	2	no	—
184	C₂×D₄×C₄₁	—	2	1	no	—
185	C₂×D₄×C₄₁	—	2	1	no	—
186	C₂×D₄×C₄₁	—	2	1	no	—
187	C₂×D₄×C₄₁	—	2	1	no	—
188	C₂×D₄×C₄₁	—	2	1	no	—
189	C₂×D₄×C₄₁	—	4	1	no	—
190	C₂×D₄×C₄₁	—	4	2	no	—
191	C₂×D₄×C₄₁	—	4	2	no	—
192	C₂×D₄×C₄₁	—	4	2	no	—
193	C₂×D₄×C₄₁	—	4	2	no	—
194	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
195	C₂²×C₄×C₄₁	—	2	1	no	—
196	C₂²×C₄×C₄₁	—	2	1	no	—
197	C₂²×C₄×C₄₁	—	2	1	no	—
198	C₂²×C₄×C₄₁	—	2	1	no	—
199	C₂²×C₄×C₄₁	—	2	1	no	—
200	C₂²×C₄×C₄₁	—	2	4	no	—
201	C₂²×C₄×C₄₁	—	2	1	no	—
202	C₂²×C₄×C₄₁	—	2	1	no	—
203	C₂²×C₄×C₄₁	—	2	4	no	—
204	C₂²×C₄×C₄₁	—	2	1	no	—
205	C₂²×C₄×C₄₁	—	2	1	no	—
206	C₂²×C₄×C₄₁	—	2	1	no	—
207	C₂²×C₄×C₄₁	—	2	1	no	—
208	C₂²×C₄×C₄₁	—	2	1	no	—
209	C₂²×C₄×C₄₁	—	2	1	no	—
210	C₂²×C₄×C₄₁	—	2	1	no	—
211	C₂²×C₄×C₄₁	—	2	1	no	—
212	C₂²×C₄×C₄₁	—	2	1	no	—
213	C₂²×C₄×C₄₁	—	2	1	no	—
214	C₂²×C₄×C₄₁	—	4	2	no	—
215	C₂²×C₄×C₄₁	—	4	2	no	—
216	C₂²×C₄×C₄₁	—	4	2	no	—
217	C₂²×C₄×C₄₁	—	4	2	no	—
218	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
223	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
224	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
225	C₂×C₈×C₄₁	—	2	1	no	—
226	C₂×C₈×C₄₁	—	2	1	no	—
227	C₂×C₈×C₄₁	—	2	1	no	—
228	C₂×C₈×C₄₁	—	2	1	no	—
229	C₂×C₈×C₄₁	—	2	1	no	—
230	C₂×C₈×C₄₁	—	2	1	no	—
231	C₂×C₈×C₄₁	—	2	1	no	—
232	C₂×C₈×C₄₁	—	2	1	no	—
233	C₂×C₈×C₄₁	—	2	1	no	—
234	C₂×C₈×C₄₁	—	2	1	no	—
235	C₂×C₈×C₄₁	—	2	1	no	—
236	C₂×C₈×C₄₁	—	2	1	no	—
237	C₂×C₈×C₄₁	—	4	4	no	—
238	C₄⋊C₄×C₄₁	—	2	4	no	—
239	C₄⋊C₄×C₄₁	—	2	4	no	—
240	C₄⋊C₄×C₄₁	—	2	2	no	—
241	C₄⋊C₄×C₄₁	—	2	1	no	—
242	C₄⋊C₄×C₄₁	—	2	1	no	—
243	C₄⋊C₄×C₄₁	—	2	1	no	—
244	C₄⋊C₄×C₄₁	—	2	1	no	—
245	C₄⋊C₄×C₄₁	—	2	1	no	—
246	C₄⋊C₄×C₄₁	—	2	1	no	—
247	C₄⋊C₄×C₄₁	—	2	1	no	—
248	C₄⋊C₄×C₄₁	—	2	1	no	—
249	C₄⋊C₄×C₄₁	—	2	1	no	—
250	C₄⋊C₄×C₄₁	—	4	2	no	—
251	C₄⋊C₄×C₄₁	—	8	1	no	—
252	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
253	C₂²⋊C₄×C₄₁	—	2	4	no	—
254	C₂²⋊C₄×C₄₁	—	2	4	no	—
255	C₂²⋊C₄×C₄₁	—	2	4	no	—
256	C₂²⋊C₄×C₄₁	—	2	4	no	—
257	C₂²⋊C₄×C₄₁	—	2	2	no	—
258	C₂²⋊C₄×C₄₁	—	2	2	no	—
259	C₂²⋊C₄×C₄₁	—	4	2	no	—
260	C₂²⋊C₄×C₄₁	—	4	2	no	—
261	C₂²⋊C₄×C₄₁	—	8	1	no	—
262	C₂²⋊C₄×C₄₁	—	8	1	no	—
263	C₄²×C₄₁	—	2	4	no	—
264	C₄²×C₄₁	—	2	1	no	—
265	C₄²×C₄₁	—	2	1	no	—
266	C₄²×C₄₁	—	4	2	no	—
267	C₂³×C₄₁	—	2	1	no	—
268	C₂³×C₄₁	—	2	1	no	—
269	C₂³×C₄₁	—	2	1	no	—
270	C₂³×C₄₁	—	2	1	no	—
271	C₂³×C₄₁	—	2	1	no	—
272	C₂³×C₄₁	—	2	1	no	—
273	C₂³×C₄₁	—	2	1	no	—
274	C₂³×C₄₁	—	2	1	no	—
275	C₂³×C₄₁	—	2	1	no	—
276	C₂³×C₄₁	—	2	1	no	—
277	C₂³×C₄₁	—	2	1	no	—
278	C₂³×C₄₁	—	2	1	no	—
279	C₂³×C₄₁	—	2	2	no	—
280	C₂³×C₄₁	—	4	1	no	—
281	C₂³×C₄₁	—	4	1	no	—
282	C₂³×C₄₁	—	4	1	no	—
283	C₂³×C₄₁	—	4	1	no	—
284	C₂³×C₄₁	—	4	1	no	—
285	C₂³×C₄₁	—	4	1	no	—
286	C₂³×C₄₁	#120	1	2	yes	—
287	C₂³×C₄₁	#135	1	2	yes	—
288	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
289	Q₈×C₄₁	—	2	2	no	—
290	Q₈×C₄₁	—	2	2	no	—
291	Q₈×C₄₁	—	2	2	no	—
292	Q₈×C₄₁	—	2	2	no	—
293	Q₈×C₄₁	—	2	2	no	—
294	Q₈×C₄₁	—	4	8	no	—
295	Q₈×C₄₁	—	4	1	no	—
296	Q₈×C₄₁	—	4	1	no	—
297	Q₈×C₄₁	#123	1	4	yes	—
298	D₄×C₄₁	—	2	2	no	—
299	D₄×C₄₁	—	2	2	no	—
300	D₄×C₄₁	—	4	8	no	—
301	D₄×C₄₁	—	4	4	no	—
302	D₄×C₄₁	—	4	8	no	—
303	D₄×C₄₁	—	4	1	no	—
304	D₄×C₄₁	—	4	1	no	—
305	C₂×C₄×C₄₁	—	2	2	no	—
306	C₂×C₄×C₄₁	—	2	1	no	—
307	C₂×C₄×C₄₁	—	2	1	no	—
308	C₂×C₄×C₄₁	—	2	2	no	—
309	C₂×C₄×C₄₁	—	2	2	no	—
310	C₂×C₄×C₄₁	—	2	2	no	—
311	C₂×C₄×C₄₁	—	2	2	no	—
312	C₂×C₄×C₄₁	—	2	2	no	—
313	C₂×C₄×C₄₁	—	2	2	no	—
314	C₂×C₄×C₄₁	—	2	1	no	—
315	C₂×C₄×C₄₁	—	2	1	no	—
316	C₂×C₄×C₄₁	—	2	2	no	—
317	C₂×C₄×C₄₁	—	2	2	no	—
318	C₂×C₄×C₄₁	—	2	1	no	—
319	C₂×C₄×C₄₁	—	2	1	no	—
320	C₂×C₄×C₄₁	—	2	1	no	—
321	C₂×C₄×C₄₁	—	2	1	no	—
322	C₂×C₄×C₄₁	—	2	1	no	—
323	C₂×C₄×C₄₁	—	2	1	no	—
324	C₂×C₄×C₄₁	—	2	1	no	—
325	C₂×C₄×C₄₁	—	4	8	no	—
326	C₂×C₄×C₄₁	—	4	8	no	—
327	C₂×C₄×C₄₁	—	4	1	no	—
328	C₂×C₄×C₄₁	—	4	1	no	—
329	C₂×C₄×C₄₁	—	4	1	no	—
330	C₂×C₄×C₄₁	—	4	1	no	—
331	C₂×C₄×C₄₁	—	4	1	no	—
332	C₂×C₄×C₄₁	—	4	1	no	—
333	C₂×C₄×C₄₁	—	4	1	no	—
334	C₂×C₄×C₄₁	—	4	1	no	—
335	C₂×C₄×C₄₁	—	4	1	no	—
336	C₂×C₄×C₄₁	—	4	1	no	—
337	C₂×C₄×C₄₁	—	4	1	no	—
338	C₂×C₄×C₄₁	—	4	1	no	—
339	C₂×C₄×C₄₁	—	4	1	no	—
340	C₂×C₄×C₄₁	—	4	1	no	—
341	C₂×C₄×C₄₁	—	4	1	no	—
342	C₂×C₄×C₄₁	—	4	1	no	—
343	C₂×C₄×C₄₁	—	4	1	no	—
344	C₂×C₄×C₄₁	—	4	1	no	—
345	C₂×C₄×C₄₁	—	4	1	no	—
346	C₂×C₄×C₄₁	—	4	1	no	—
347	C₂×C₄×C₄₁	#120	1	2	yes	—
348	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
351	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
352	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
353	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
354	C₈×C₄₁	—	4	1	no	—
355	C₈×C₄₁	—	4	1	no	—
356	C₈×C₄₁	—	4	1	no	—
357	C₈×C₄₁	—	4	1	no	—
358	#24040	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
359	C₂²×C₄₁	—	2	2	no	—
360	C₂²×C₄₁	—	2	2	no	—
361	C₂²×C₄₁	—	2	2	no	—
362	C₂²×C₄₁	—	2	2	no	—
363	C₂²×C₄₁	—	2	2	no	—
364	C₂²×C₄₁	—	2	2	no	—
365	C₂²×C₄₁	—	4	1	no	—
366	C₂²×C₄₁	—	4	1	no	—
367	C₂²×C₄₁	—	4	1	no	—
368	C₂²×C₄₁	—	4	1	no	—
369	C₂²×C₄₁	—	4	1	no	—
370	C₂²×C₄₁	—	4	1	no	—
371	C₂²×C₄₁	—	4	1	no	—
372	C₂²×C₄₁	—	4	1	no	—
373	C₂²×C₄₁	—	4	2	no	—
374	C₂²×C₄₁	—	4	2	no	—
375	C₂²×C₄₁	—	4	2	no	—
376	C₂²×C₄₁	—	8	1	no	—
377	C₂²×C₄₁	—	8	1	no	—
378	C₂²×C₄₁	—	8	1	no	—
379	C₂²×C₄₁	—	8	1	no	—
380	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
381	C₂²×C₄₁	#546	1	1	yes	characteristic
382	C₂²×C₄₁	#546	1	1	yes	characteristic
383	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
384	C₂²×C₄₁	#575	1	1	yes	characteristic
385	C₂²×C₄₁	#577	1	1	yes	characteristic
386	C₂²×C₄₁	#578	1	1	yes	characteristic
387	C₄×C₄₁	—	2	2	no	—
388	C₄×C₄₁	—	2	4	no	—
389	C₄×C₄₁	—	4	1	no	—
390	C₄×C₄₁	—	4	2	no	—
391	C₄×C₄₁	—	4	1	no	—
392	C₄×C₄₁	—	4	2	no	—
393	C₄×C₄₁	—	4	1	no	—
394	C₄×C₄₁	—	8	1	no	—
395	C₄×C₄₁	—	8	1	no	—
396	C₄×C₄₁	—	8	1	no	—
397	C₄×C₄₁	—	8	1	no	—
398	C₄×C₄₁	C₂×#123	1	1	yes	characteristic
399	C₄×C₄₁	#534	1	1	yes	characteristic
400	C₄×C₄₁	#546	1	1	yes	characteristic
401	C₄×C₄₁	#546	1	1	yes	characteristic
402	C₂×#548	C₂×C₄₁	1	1	yes	characteristic
403	C₂×#485	C₂×C₄₁	1	1	yes	characteristic, complemented
404	C₂×#416	C₂×C₄₁	1	1	yes	characteristic, complemented
405	#2485	C₂×C₄₁	1	1	yes	characteristic, complemented
406	#2042	C₂×C₄₁	1	1	yes	characteristic, complemented
407	#2042	C₂×C₄₁	1	1	yes	characteristic, complemented
408	#2034	C₂×C₄₁	1	1	yes	characteristic, complemented
409	#2033	C₂×C₄₁	1	1	yes	characteristic, complemented
410	#1892	C₂×C₄₁	1	1	yes	characteristic, complemented
411	#1869	C₂×C₄₁	1	1	yes	characteristic, complemented
412	#1865	C₂×C₄₁	1	1	yes	characteristic, complemented
413	#1863	C₂×C₄₁	1	1	yes	characteristic, complemented
414	#1788	C₂×C₄₁	1	1	yes	characteristic, complemented
415	#1787	C₂×C₄₁	1	1	yes	characteristic, complemented
416	#1787	C₂×C₄₁	1	1	yes	characteristic, complemented
417	C₂×C₄₁	—	4	2	no	—
418	C₂×C₄₁	—	4	2	no	—
419	C₂×C₄₁	—	8	2	no	—
420	C₂×C₄₁	#2405	1	1	yes	characteristic
421	C₂×C₄₁	#3002	1	1	yes	characteristic
422	C₂×C₄₁	#3013	1	1	yes	characteristic
423	C₂×C₄₁	#3300	1	1	yes	characteristic
424	C₂×C₄₁	#3301	1	1	yes	characteristic
425	C₂×C₄₁	#3313	1	1	yes	characteristic
426	C₂×C₄₁	#3321	1	1	yes	characteristic
427	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
428	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
429	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
430	#548	—	2	4	no	—
431	#548	—	2	4	no	—
432	C₂×#124	—	2	1	no	—
433	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
434	C₂×C₂²⋊Q₈	—	2	1	no	—
435	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
436	C₂×#121	—	2	1	no	—
437	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
438	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
439	C₂×C₄×D₄	—	2	1	no	—
440	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
441	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
442	#485	—	2	4	no	—
443	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
444	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
445	#416	—	2	4	no	—
446	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
447	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
448	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
449	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
450	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
451	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
452	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
453	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
454	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
455	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
456	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
457	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
458	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
459	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
460	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
461	#397	—	2	1	no	—
462	#394	—	2	1	no	—
463	#389	C₂²×C₄₁	1	1	yes	characteristic
464	#389	C₂²×C₄₁	1	1	yes	characteristic
465	#388	—	2	1	no	—
466	#387	—	2	1	no	—
467	#380	C₂²×C₄₁	1	1	yes	characteristic
468	#380	C₂²×C₄₁	1	1	yes	characteristic
469	#380	C₂²×C₄₁	1	1	yes	characteristic
470	#340	C₂²×C₄₁	1	1	yes	characteristic
471	#340	C₂²×C₄₁	1	1	yes	characteristic
472	#336	C₂²×C₄₁	1	1	yes	characteristic
473	#336	C₂²×C₄₁	1	1	yes	characteristic
474	C₄₁	#24040	1	1	yes	characteristic, direct product factor, Sylow
475	C₂×#41	—	2	2	no	—
476	C₂×#41	—	2	2	no	—
477	C₂×#41	—	2	2	no	—
478	C₂×#41	—	4	1	no	—
479	C₂×#41	—	4	1	no	—
480	C₂×#41	D₄×C₄₁	1	4	yes	—
481	C₂²×Q₈	—	2	2	no	—
482	C₂²×Q₈	—	2	2	no	—
483	C₂²×Q₈	—	2	1	no	—
484	C₂²×Q₈	—	2	2	no	—
485	C₂²×Q₈	—	2	2	no	—
486	C₂²×Q₈	—	4	1	no	—
487	C₂²×Q₈	—	4	1	no	—
488	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
489	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
490	C₂²×D₄	—	2	1	no	—
491	C₂²×D₄	—	2	1	no	—
492	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
493	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
494	C₂³×C₄	—	2	1	no	—
495	C₂³×C₄	—	2	1	no	—
496	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
497	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
498	C₂²×C₈	—	2	2	no	—
499	C₂²×C₈	—	4	1	no	—
500	C₂²×C₈	—	4	1	no	—
501	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
502	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
503	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
504	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
505	#124	—	2	8	no	—
506	#124	—	2	2	no	—
507	#124	—	2	2	no	—
508	C₂²⋊Q₈	—	2	8	no	—
509	C₂²⋊Q₈	—	2	2	no	—
510	C₂²⋊Q₈	D₄×C₄₁	1	4	yes	—
511	#121	—	2	8	no	—
512	#121	—	2	2	no	—
513	#121	—	2	2	no	—
514	C₄×Q₈	—	2	2	no	—
515	C₄×Q₈	—	2	2	no	—
516	C₄×D₄	—	2	8	no	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	—	2	2	no	—
519	#117	—	2	2	no	—
520	#117	—	2	2	no	—
521	C₂×C₄⋊C₄	—	2	1	no	—
522	C₂×C₄⋊C₄	—	2	1	no	—
523	C₂×C₄⋊C₄	—	2	1	no	—
524	C₂×C₄⋊C₄	—	2	1	no	—
525	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
531	C₂×C₂²⋊C₄	—	2	1	no	—
532	C₂×C₂²⋊C₄	—	2	1	no	—
533	C₂×C₂²⋊C₄	—	2	1	no	—
534	C₂×C₂²⋊C₄	—	2	1	no	—
535	C₂×C₂²⋊C₄	—	2	1	no	—
536	C₂×C₂²⋊C₄	—	2	1	no	—
537	C₂×C₂²⋊C₄	—	2	1	no	—
538	C₂×C₂²⋊C₄	—	2	1	no	—
539	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
541	C₂×C₄²	—	2	1	no	—
542	C₂×C₄²	—	2	1	no	—
543	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
544	#107	—	2	2	no	—
545	#106	—	2	2	no	—
546	#103	—	2	2	no	—
547	#103	—	2	2	no	—
548	#103	—	2	2	no	—
549	#103	—	2	2	no	—
550	#103	—	2	2	no	—
551	#103	—	2	2	no	—
552	#103	—	4	1	no	—
553	#103	—	4	1	no	—
554	#102	—	2	2	no	—
555	#102	—	2	2	no	—
556	#102	—	4	1	no	—
557	#102	—	4	1	no	—
558	C₂²⋊C₈	—	2	2	no	—
559	C₂²⋊C₈	—	4	1	no	—
560	C₂²⋊C₈	—	4	1	no	—
561	#95	—	2	1	no	—
562	#95	—	2	1	no	—
563	#95	—	2	1	no	—
564	#95	—	2	1	no	—
565	#95	—	2	1	no	—
566	C₂⁴	—	2	1	no	—
567	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
568	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
569	#41	—	2	8	no	—
570	#41	—	4	4	no	—
571	#41	—	4	4	no	—
572	#41	—	4	4	no	—
573	C₂×Q₈	—	2	4	no	—
574	C₂×Q₈	—	2	1	no	—
575	C₂×Q₈	—	2	1	no	—
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	1	no	—
582	C₂×Q₈	—	4	2	no	—
583	C₂×Q₈	—	4	2	no	—
584	C₂×Q₈	—	4	4	no	—
585	C₂×Q₈	—	4	4	no	—
586	C₂×Q₈	—	4	4	no	—
587	C₂×Q₈	—	4	4	no	—
588	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
589	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
590	C₂×Q₈	#41×C₄₁	1	2	yes	—
591	C₂×Q₈	#41×C₄₁	1	2	yes	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	1	no	—
597	C₂×D₄	—	2	1	no	—
598	C₂×D₄	—	2	1	no	—
599	C₂×D₄	—	2	1	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	4	1	no	—
602	C₂×D₄	—	4	2	no	—
603	C₂×D₄	—	4	2	no	—
604	C₂×D₄	—	4	2	no	—
605	C₂×D₄	—	4	2	no	—
606	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	4	2	no	—
627	C₂²×C₄	—	4	2	no	—
628	C₂²×C₄	—	4	2	no	—
629	C₂²×C₄	—	4	2	no	—
630	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
631	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
632	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
633	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
634	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
635	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
637	C₂×C₈	—	2	1	no	—
638	C₂×C₈	—	2	1	no	—
639	C₂×C₈	—	2	1	no	—
640	C₂×C₈	—	2	1	no	—
641	C₂×C₈	—	2	1	no	—
642	C₂×C₈	—	2	1	no	—
643	C₂×C₈	—	2	1	no	—
644	C₂×C₈	—	2	1	no	—
645	C₂×C₈	—	2	1	no	—
646	C₂×C₈	—	2	1	no	—
647	C₂×C₈	—	2	1	no	—
648	C₂×C₈	—	2	1	no	—
649	C₂×C₈	—	4	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	4	2	no	—
663	C₄⋊C₄	—	8	1	no	—
664	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	—	2	2	no	—
671	C₂²⋊C₄	—	4	2	no	—
672	C₂²⋊C₄	—	4	2	no	—
673	C₂²⋊C₄	—	8	1	no	—
674	C₂²⋊C₄	—	8	1	no	—
675	C₄²	—	2	4	no	—
676	C₄²	—	2	1	no	—
677	C₄²	—	2	1	no	—
678	C₄²	—	4	2	no	—
679	C₂³	—	2	1	no	—
680	C₂³	—	2	1	no	—
681	C₂³	—	2	1	no	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	1	no	—
684	C₂³	—	2	1	no	—
685	C₂³	—	2	1	no	—
686	C₂³	—	2	1	no	—
687	C₂³	—	2	1	no	—
688	C₂³	—	2	1	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	2	1	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	4	1	no	—
693	C₂³	—	4	1	no	—
694	C₂³	—	4	1	no	—
695	C₂³	—	4	1	no	—
696	C₂³	—	4	1	no	—
697	C₂³	—	4	1	no	—
698	C₂³	#120×C₄₁	1	2	yes	—
699	C₂³	#135×C₄₁	1	2	yes	—
700	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
701	Q₈	—	2	2	no	—
702	Q₈	—	2	2	no	—
703	Q₈	—	2	2	no	—
704	Q₈	—	2	2	no	—
705	Q₈	—	2	2	no	—
706	Q₈	—	4	8	no	—
707	Q₈	—	4	1	no	—
708	Q₈	—	4	1	no	—
709	Q₈	#123×C₄₁	1	4	yes	—
710	D₄	—	2	2	no	—
711	D₄	—	2	2	no	—
712	D₄	—	4	8	no	—
713	D₄	—	4	4	no	—
714	D₄	—	4	8	no	—
715	D₄	—	4	1	no	—
716	D₄	—	4	1	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	4	8	no	—
738	C₂×C₄	—	4	8	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	1	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	1	no	—
756	C₂×C₄	—	4	1	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	#120×C₄₁	1	2	yes	—
760	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
761	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
762	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
763	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
764	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
765	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
766	C₈	—	4	1	no	—
767	C₈	—	4	1	no	—
768	C₈	—	4	1	no	—
769	C₈	—	4	1	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	2	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	4	1	no	—
778	C₂²	—	4	1	no	—
779	C₂²	—	4	1	no	—
780	C₂²	—	4	1	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	8	1	no	—
788	C₂²	—	8	1	no	—
789	C₂²	—	8	1	no	—
790	C₂²	—	8	1	no	—
791	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
792	C₂²	C₄₁×#546	1	1	yes	characteristic
793	C₂²	C₄₁×#546	1	1	yes	characteristic
794	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
795	C₂²	C₄₁×#575	1	1	yes	characteristic
796	C₂²	C₄₁×#577	1	1	yes	characteristic
797	C₂²	C₄₁×#578	1	1	yes	characteristic
798	C₄	—	2	2	no	—
799	C₄	—	2	4	no	—
800	C₄	—	4	1	no	—
801	C₄	—	4	2	no	—
802	C₄	—	4	1	no	—
803	C₄	—	4	2	no	—
804	C₄	—	4	1	no	—
805	C₄	—	8	1	no	—
806	C₄	—	8	1	no	—
807	C₄	—	8	1	no	—
808	C₄	—	8	1	no	—
809	C₄	C₂×#123×C₄₁	1	1	yes	characteristic
810	C₄	C₄₁×#534	1	1	yes	characteristic
811	C₄	C₄₁×#546	1	1	yes	characteristic
812	C₄	C₄₁×#546	1	1	yes	characteristic
813	C₂	—	4	2	no	—
814	C₂	—	4	2	no	—
815	C₂	—	8	2	no	—
816	C₂	C₄₁×#2405	1	1	yes	characteristic
817	C₂	C₄₁×#3002	1	1	yes	characteristic
818	C₂	C₄₁×#3013	1	1	yes	characteristic
819	C₂	C₄₁×#3300	1	1	yes	characteristic
820	C₂	C₄₁×#3301	1	1	yes	characteristic
821	C₂	C₄₁×#3313	1	1	yes	characteristic
822	C₂	C₄₁×#3321	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#548	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×#485	C₂	semidirect
3. C₂×C₄₁×#416	C₂	semidirect
4. C₄₁×#2485	C₂	semidirect
5. C₄₁×#2042	C₂	semidirect
6. C₄₁×#2042	C₂	semidirect
7. C₄₁×#2034	C₂	semidirect
8. C₄₁×#2033	C₂	semidirect
9. C₄₁×#1892	C₂	semidirect
10. C₄₁×#1869	C₂	semidirect
11. C₄₁×#1865	C₂	semidirect
12. C₄₁×#1863	C₂	semidirect
13. C₄₁×#1788	C₂	semidirect
14. C₄₁×#1787	C₂	semidirect
15. C₄₁×#1787	C₂	semidirect
358. #24040	C₄₁	direct (N × H)
403. C₂×#485	C₂×C₄₁	semidirect
404. C₂×#416	C₂×C₄₁	semidirect
405. #2485	C₂×C₄₁	semidirect
406. #2042	C₂×C₄₁	semidirect
407. #2042	C₂×C₄₁	semidirect
408. #2034	C₂×C₄₁	semidirect
409. #2033	C₂×C₄₁	semidirect
410. #1892	C₂×C₄₁	semidirect
411. #1869	C₂×C₄₁	semidirect
412. #1865	C₂×C₄₁	semidirect
413. #1863	C₂×C₄₁	semidirect
414. #1788	C₂×C₄₁	semidirect
415. #1787	C₂×C₄₁	semidirect
416. #1787	C₂×C₄₁	semidirect
474. C₄₁	#24040	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#548	2
C₂×C₄₁×#485	2
C₂×C₄₁×#416	2
C₄₁×#2485	2
C₄₁×#2042	2
C₄₁×#2034	2
C₄₁×#2033	2
C₄₁×#1892	2
C₄₁×#1869	2
C₄₁×#1865	2
C₄₁×#1863	2
C₄₁×#1788	2
C₄₁×#1787	2
#24040	41

Subgroups — C41×#24040 #23800241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24040 #23800241