Subgroups — C₄₁×#25380 #23801581

Order 10496.

1184 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#463	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#459	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2541	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2367	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×#2014	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#2011	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1982	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#1940	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#1880	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#1879	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#1762	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#121×C₄₁	—	2	1	no	—
27	C₂×#121×C₄₁	—	2	1	no	—
28	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
31	C₄₁×#496	—	2	4	no	—
32	C₄₁×#463	—	2	4	no	—
33	C₄₁×#460	—	2	4	no	—
34	C₄₁×#459	—	2	4	no	—
35	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
38	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
40	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
41	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
42	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
43	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
44	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
45	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
46	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
47	C₄₁×#392	—	2	1	no	—
48	C₄₁×#392	—	2	1	no	—
49	C₄₁×#391	C₂²	1	1	yes	characteristic
50	C₄₁×#390	C₂²	1	1	yes	characteristic
51	C₄₁×#390	C₂²	1	1	yes	characteristic
52	C₄₁×#390	C₂²	1	1	yes	characteristic
53	C₄₁×#388	—	2	1	no	—
54	C₄₁×#388	—	2	1	no	—
55	C₄₁×#385	—	2	1	no	—
56	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
57	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
58	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
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	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₄₁	—	2	1	no	—
65	C₂²×D₄×C₄₁	—	2	1	no	—
66	C₂²×D₄×C₄₁	—	2	1	no	—
67	C₂²×D₄×C₄₁	—	2	1	no	—
68	C₂²×D₄×C₄₁	—	2	1	no	—
69	C₂²×D₄×C₄₁	—	2	1	no	—
70	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₄₁	—	2	1	no	—
75	C₂³×C₄×C₄₁	—	2	1	no	—
76	C₂×SD₁₆×C₄₁	—	2	2	no	—
77	C₂×SD₁₆×C₄₁	—	2	2	no	—
78	C₂×SD₁₆×C₄₁	—	2	2	no	—
79	C₂×SD₁₆×C₄₁	—	2	2	no	—
80	C₂×SD₁₆×C₄₁	—	2	2	no	—
81	C₂×SD₁₆×C₄₁	—	2	2	no	—
82	C₂×SD₁₆×C₄₁	—	4	1	no	—
83	C₂×SD₁₆×C₄₁	—	4	1	no	—
84	C₂×SD₁₆×C₄₁	—	4	1	no	—
85	C₂×D₈×C₄₁	—	2	2	no	—
86	C₂×D₈×C₄₁	—	2	2	no	—
87	C₂×D₈×C₄₁	—	2	2	no	—
88	C₂×D₈×C₄₁	—	2	2	no	—
89	C₂×D₈×C₄₁	—	2	2	no	—
90	C₂×D₈×C₄₁	—	2	2	no	—
91	C₂×D₈×C₄₁	—	4	1	no	—
92	C₂×D₈×C₄₁	—	4	1	no	—
93	C₂×D₈×C₄₁	—	4	1	no	—
94	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
98	#127×C₄₁	—	2	2	no	—
99	#127×C₄₁	—	2	2	no	—
100	#127×C₄₁	—	2	2	no	—
101	#127×C₄₁	—	2	2	no	—
102	#127×C₄₁	—	4	1	no	—
103	#127×C₄₁	—	4	1	no	—
104	#124×C₄₁	—	2	2	no	—
105	#124×C₄₁	D₄	1	4	yes	complemented
106	#121×C₄₁	—	4	4	no	—
107	#121×C₄₁	—	4	4	no	—
108	C₄×Q₈×C₄₁	—	2	2	no	—
109	C₄×Q₈×C₄₁	—	4	1	no	—
110	C₄×D₄×C₄₁	—	2	2	no	—
111	C₄×D₄×C₄₁	—	2	2	no	—
112	C₄×D₄×C₄₁	—	2	2	no	—
113	C₄×D₄×C₄₁	—	4	1	no	—
114	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
115	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₄₁	D₄	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×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
130	C₂×C₄²×C₄₁	—	2	1	no	—
131	C₂×C₄²×C₄₁	—	2	1	no	—
132	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
135	C₄⋊C₈×C₄₁	—	2	2	no	—
136	C₄⋊C₈×C₄₁	—	2	2	no	—
137	C₄⋊C₈×C₄₁	—	2	2	no	—
138	#103×C₄₁	—	2	2	no	—
139	#102×C₄₁	—	2	2	no	—
140	#102×C₄₁	—	2	2	no	—
141	#102×C₄₁	—	2	2	no	—
142	#102×C₄₁	—	2	2	no	—
143	#102×C₄₁	—	4	1	no	—
144	#102×C₄₁	—	4	1	no	—
145	#102×C₄₁	D₄	1	4	yes	complemented
146	#97×C₄₁	—	2	2	no	—
147	#95×C₄₁	—	2	1	no	—
148	#95×C₄₁	—	2	1	no	—
149	#95×C₄₁	—	2	1	no	—
150	#95×C₄₁	D₄	1	1	yes	characteristic
151	#95×C₄₁	D₄	1	1	yes	characteristic
152	C₂⁴×C₄₁	—	2	1	no	—
153	C₂⁴×C₄₁	—	2	1	no	—
154	C₂⁴×C₄₁	—	2	1	no	—
155	C₂⁴×C₄₁	—	2	1	no	—
156	C₂×Q₈×C₄₁	—	2	1	no	—
157	C₂×Q₈×C₄₁	—	2	1	no	—
158	C₂×Q₈×C₄₁	—	2	1	no	—
159	C₂×Q₈×C₄₁	—	2	1	no	—
160	C₂×Q₈×C₄₁	—	2	1	no	—
161	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
170	C₂×D₄×C₄₁	—	2	1	no	—
171	C₂×D₄×C₄₁	—	2	1	no	—
172	C₂×D₄×C₄₁	—	2	1	no	—
173	C₂×D₄×C₄₁	—	2	1	no	—
174	C₂×D₄×C₄₁	—	2	1	no	—
175	C₂×D₄×C₄₁	—	2	1	no	—
176	C₂×D₄×C₄₁	—	2	1	no	—
177	C₂×D₄×C₄₁	—	2	1	no	—
178	C₂×D₄×C₄₁	—	2	1	no	—
179	C₂×D₄×C₄₁	—	2	1	no	—
180	C₂×D₄×C₄₁	—	2	1	no	—
181	C₂×D₄×C₄₁	—	2	1	no	—
182	C₂×D₄×C₄₁	—	2	1	no	—
183	C₂×D₄×C₄₁	—	2	1	no	—
184	C₂×D₄×C₄₁	—	4	2	no	—
185	C₂×D₄×C₄₁	—	4	2	no	—
186	C₂×D₄×C₄₁	—	4	2	no	—
187	C₂×D₄×C₄₁	—	4	2	no	—
188	C₂×D₄×C₄₁	—	4	2	no	—
189	C₂×D₄×C₄₁	—	4	2	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	—	4	2	no	—
195	C₂×D₄×C₄₁	—	4	2	no	—
196	C₂×D₄×C₄₁	—	8	1	no	—
197	C₂×D₄×C₄₁	—	8	1	no	—
198	C₂×D₄×C₄₁	—	8	1	no	—
199	C₂×D₄×C₄₁	—	8	1	no	—
200	C₂×D₄×C₄₁	—	8	1	no	—
201	C₂×D₄×C₄₁	—	8	1	no	—
202	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
203	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
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	—	4	2	no	—
209	C₂²×C₄×C₄₁	—	4	2	no	—
210	C₂²×C₄×C₄₁	—	4	2	no	—
211	C₂²×C₄×C₄₁	—	4	2	no	—
212	C₂²×C₄×C₄₁	—	4	2	no	—
213	C₂²×C₄×C₄₁	—	8	1	no	—
214	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
221	SD₁₆×C₄₁	—	4	4	no	—
222	SD₁₆×C₄₁	—	4	4	no	—
223	SD₁₆×C₄₁	—	4	4	no	—
224	D₈×C₄₁	—	4	4	no	—
225	D₈×C₄₁	—	4	4	no	—
226	D₈×C₄₁	—	4	4	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	C₂×D₄	1	2	yes	—
238	C₂×C₈×C₄₁	#41	1	2	yes	—
239	C₄⋊C₄×C₄₁	—	2	2	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	—	4	2	no	—
247	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
248	C₂²⋊C₄×C₄₁	—	2	4	no	—
249	C₂²⋊C₄×C₄₁	—	2	4	no	—
250	C₂²⋊C₄×C₄₁	—	4	2	no	—
251	C₂²⋊C₄×C₄₁	—	4	2	no	—
252	C₂²⋊C₄×C₄₁	—	4	2	no	—
253	C₂²⋊C₄×C₄₁	—	4	2	no	—
254	C₂²⋊C₄×C₄₁	—	4	2	no	—
255	C₂²⋊C₄×C₄₁	—	4	2	no	—
256	C₂²⋊C₄×C₄₁	—	4	2	no	—
257	C₂²⋊C₄×C₄₁	—	8	1	no	—
258	C₄²×C₄₁	—	2	1	no	—
259	C₄²×C₄₁	—	2	1	no	—
260	C₄²×C₄₁	—	2	1	no	—
261	C₄²×C₄₁	—	2	1	no	—
262	C₄²×C₄₁	—	4	2	no	—
263	C₄²×C₄₁	—	8	1	no	—
264	C₄²×C₄₁	C₂×D₄	1	2	yes	—
265	C₄²×C₄₁	#41	1	2	yes	—
266	C₂³×C₄₁	—	2	2	no	—
267	C₂³×C₄₁	—	2	2	no	—
268	C₂³×C₄₁	—	4	1	no	—
269	C₂³×C₄₁	—	4	1	no	—
270	C₂³×C₄₁	—	4	1	no	—
271	C₂³×C₄₁	—	4	1	no	—
272	C₂³×C₄₁	—	4	1	no	—
273	C₂³×C₄₁	—	4	1	no	—
274	C₂³×C₄₁	—	4	1	no	—
275	C₂³×C₄₁	—	4	1	no	—
276	C₂³×C₄₁	—	4	1	no	—
277	C₂³×C₄₁	—	4	1	no	—
278	C₂³×C₄₁	—	4	1	no	—
279	C₂³×C₄₁	—	4	1	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	—	4	1	no	—
287	C₂³×C₄₁	—	4	1	no	—
288	C₂³×C₄₁	—	4	1	no	—
289	C₂³×C₄₁	—	4	1	no	—
290	C₂³×C₄₁	—	4	1	no	—
291	C₂³×C₄₁	—	4	1	no	—
292	C₂³×C₄₁	—	4	1	no	—
293	C₂³×C₄₁	—	4	1	no	—
294	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
295	Q₈×C₄₁	—	2	2	no	—
296	Q₈×C₄₁	—	2	2	no	—
297	Q₈×C₄₁	—	4	1	no	—
298	Q₈×C₄₁	—	4	1	no	—
299	D₄×C₄₁	—	2	2	no	—
300	D₄×C₄₁	—	2	2	no	—
301	D₄×C₄₁	—	2	2	no	—
302	D₄×C₄₁	—	2	2	no	—
303	D₄×C₄₁	—	4	1	no	—
304	D₄×C₄₁	—	4	1	no	—
305	D₄×C₄₁	—	4	1	no	—
306	D₄×C₄₁	—	4	1	no	—
307	D₄×C₄₁	—	4	1	no	—
308	D₄×C₄₁	—	4	1	no	—
309	D₄×C₄₁	—	4	1	no	—
310	D₄×C₄₁	—	4	1	no	—
311	D₄×C₄₁	—	4	1	no	—
312	D₄×C₄₁	—	4	1	no	—
313	D₄×C₄₁	—	4	1	no	—
314	D₄×C₄₁	—	4	1	no	—
315	D₄×C₄₁	—	8	4	no	—
316	D₄×C₄₁	—	8	4	no	—
317	D₄×C₄₁	—	8	4	no	—
318	D₄×C₄₁	—	8	4	no	—
319	D₄×C₄₁	—	8	4	no	—
320	D₄×C₄₁	—	8	4	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	—	2	1	no	—
326	C₂×C₄×C₄₁	—	2	1	no	—
327	C₂×C₄×C₄₁	—	2	1	no	—
328	C₂×C₄×C₄₁	—	2	1	no	—
329	C₂×C₄×C₄₁	—	2	2	no	—
330	C₂×C₄×C₄₁	—	2	1	no	—
331	C₂×C₄×C₄₁	—	2	1	no	—
332	C₂×C₄×C₄₁	—	2	2	no	—
333	C₂×C₄×C₄₁	—	2	1	no	—
334	C₂×C₄×C₄₁	—	2	1	no	—
335	C₂×C₄×C₄₁	—	2	1	no	—
336	C₂×C₄×C₄₁	—	2	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	—	8	4	no	—
348	C₂×C₄×C₄₁	—	8	4	no	—
349	C₂×C₄×C₄₁	#121	1	2	yes	—
350	C₂×C₄×C₄₁	#121	1	2	yes	—
351	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
352	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
353	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
356	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
357	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
358	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
359	C₈×C₄₁	—	2	2	no	—
360	C₈×C₄₁	—	2	2	no	—
361	C₈×C₄₁	—	4	1	no	—
362	C₈×C₄₁	—	4	1	no	—
363	#25380	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
364	C₂²×C₄₁	—	4	2	no	—
365	C₂²×C₄₁	—	4	2	no	—
366	C₂²×C₄₁	—	4	2	no	—
367	C₂²×C₄₁	—	4	2	no	—
368	C₂²×C₄₁	—	4	2	no	—
369	C₂²×C₄₁	—	4	2	no	—
370	C₂²×C₄₁	—	8	1	no	—
371	C₂²×C₄₁	—	8	1	no	—
372	C₂²×C₄₁	—	8	1	no	—
373	C₂²×C₄₁	—	8	1	no	—
374	C₂²×C₄₁	—	8	1	no	—
375	C₂²×C₄₁	—	8	1	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	—	8	1	no	—
381	C₂²×C₄₁	—	8	1	no	—
382	C₂²×C₄₁	—	8	1	no	—
383	C₂²×C₄₁	—	8	1	no	—
384	C₂²×C₄₁	—	8	1	no	—
385	C₂²×C₄₁	—	8	1	no	—
386	C₂²×C₄₁	—	8	1	no	—
387	C₂²×C₄₁	—	8	1	no	—
388	C₂²×C₄₁	—	8	1	no	—
389	C₂²×C₄₁	—	8	1	no	—
390	C₂²×C₄₁	—	8	1	no	—
391	C₂²×C₄₁	—	8	1	no	—
392	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
393	C₂²×C₄₁	D₄²	1	1	yes	characteristic
394	C₂²×C₄₁	#550	1	1	yes	characteristic
395	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
396	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
397	C₂²×C₄₁	#576	1	1	yes	characteristic
398	C₂²×C₄₁	#577	1	1	yes	characteristic
399	C₄×C₄₁	—	2	2	no	—
400	C₄×C₄₁	—	2	2	no	—
401	C₄×C₄₁	—	2	2	no	—
402	C₄×C₄₁	—	2	2	no	—
403	C₄×C₄₁	—	4	2	no	—
404	C₄×C₄₁	—	4	1	no	—
405	C₄×C₄₁	—	4	2	no	—
406	C₄×C₄₁	—	4	1	no	—
407	C₄×C₄₁	—	8	1	no	—
408	C₄×C₄₁	—	8	1	no	—
409	C₄×C₄₁	#532	1	1	yes	characteristic
410	C₄×C₄₁	#540	1	1	yes	characteristic
411	C₄×C₄₁	D₄²	1	1	yes	characteristic
412	C₄×C₄₁	#546	1	1	yes	characteristic
413	C₂×#496	C₂×C₄₁	1	1	yes	characteristic, complemented
414	C₂×#460	C₂×C₄₁	1	1	yes	characteristic, complemented
415	C₂×#463	C₂×C₄₁	1	1	yes	characteristic, complemented
416	C₂×#459	C₂×C₄₁	1	1	yes	characteristic, complemented
417	#2541	C₂×C₄₁	1	1	yes	characteristic, complemented
418	#2367	C₂×C₄₁	1	1	yes	characteristic, complemented
419	#2055	C₂×C₄₁	1	1	yes	characteristic, complemented
420	#2054	C₂×C₄₁	1	1	yes	characteristic, complemented
421	#2014	C₂×C₄₁	1	1	yes	characteristic, complemented
422	#2011	C₂×C₄₁	1	1	yes	characteristic, complemented
423	#1982	C₂×C₄₁	1	1	yes	characteristic, complemented
424	#1940	C₂×C₄₁	1	1	yes	characteristic, complemented
425	#1880	C₂×C₄₁	1	1	yes	characteristic, complemented
426	#1879	C₂×C₄₁	1	1	yes	characteristic, complemented
427	#1762	C₂×C₄₁	1	1	yes	characteristic, complemented
428	C₂×C₄₁	—	8	2	no	—
429	C₂×C₄₁	—	8	2	no	—
430	C₂×C₄₁	—	16	1	no	—
431	C₂×C₄₁	—	16	1	no	—
432	C₂×C₄₁	#2428	1	1	yes	characteristic
433	C₂×C₄₁	#3038	1	1	yes	characteristic
434	C₂×C₄₁	#3045	1	1	yes	characteristic
435	C₂×C₄₁	#3264	1	1	yes	characteristic
436	C₂×C₄₁	#3265	1	1	yes	characteristic
437	C₂×C₄₁	#3397	1	1	yes	characteristic
438	C₂×C₄₁	#3399	1	1	yes	characteristic
439	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
440	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
441	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
442	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
443	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
444	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
445	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
446	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
447	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
448	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
449	C₂×#121	—	2	1	no	—
450	C₂×#121	—	2	1	no	—
451	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
452	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
453	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
454	#496	—	2	4	no	—
455	#463	—	2	4	no	—
456	#460	—	2	4	no	—
457	#459	—	2	4	no	—
458	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
459	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
460	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
461	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
462	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
463	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
464	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
465	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
466	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
467	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
468	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
469	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
470	#392	—	2	1	no	—
471	#392	—	2	1	no	—
472	#391	C₂²×C₄₁	1	1	yes	characteristic
473	#390	C₂²×C₄₁	1	1	yes	characteristic
474	#390	C₂²×C₄₁	1	1	yes	characteristic
475	#390	C₂²×C₄₁	1	1	yes	characteristic
476	#388	—	2	1	no	—
477	#388	—	2	1	no	—
478	#385	—	2	1	no	—
479	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
480	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
481	C₄×C₂²⋊C₄	—	2	1	no	—
482	#340	C₂²×C₄₁	1	1	yes	characteristic
483	#340	C₂²×C₄₁	1	1	yes	characteristic
484	#336	C₂²×C₄₁	1	1	yes	characteristic
485	#336	C₂²×C₄₁	1	1	yes	characteristic
486	C₄₁	#25380	1	1	yes	characteristic, direct product factor, Sylow
487	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
488	C₂²×D₄	—	2	1	no	—
489	C₂²×D₄	—	2	1	no	—
490	C₂²×D₄	—	2	1	no	—
491	C₂²×D₄	—	2	1	no	—
492	C₂²×D₄	—	2	1	no	—
493	C₂²×D₄	—	2	1	no	—
494	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
495	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
496	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
497	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
498	C₂³×C₄	—	2	1	no	—
499	C₂³×C₄	—	2	1	no	—
500	C₂×SD₁₆	—	2	2	no	—
501	C₂×SD₁₆	—	2	2	no	—
502	C₂×SD₁₆	—	2	2	no	—
503	C₂×SD₁₆	—	2	2	no	—
504	C₂×SD₁₆	—	2	2	no	—
505	C₂×SD₁₆	—	2	2	no	—
506	C₂×SD₁₆	—	4	1	no	—
507	C₂×SD₁₆	—	4	1	no	—
508	C₂×SD₁₆	—	4	1	no	—
509	C₂×D₈	—	2	2	no	—
510	C₂×D₈	—	2	2	no	—
511	C₂×D₈	—	2	2	no	—
512	C₂×D₈	—	2	2	no	—
513	C₂×D₈	—	2	2	no	—
514	C₂×D₈	—	2	2	no	—
515	C₂×D₈	—	4	1	no	—
516	C₂×D₈	—	4	1	no	—
517	C₂×D₈	—	4	1	no	—
518	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
519	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
520	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
521	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
522	#127	—	2	2	no	—
523	#127	—	2	2	no	—
524	#127	—	2	2	no	—
525	#127	—	2	2	no	—
526	#127	—	4	1	no	—
527	#127	—	4	1	no	—
528	#124	—	2	2	no	—
529	#124	D₄×C₄₁	1	4	yes	complemented
530	#121	—	4	4	no	—
531	#121	—	4	4	no	—
532	C₄×Q₈	—	2	2	no	—
533	C₄×Q₈	—	4	1	no	—
534	C₄×D₄	—	2	2	no	—
535	C₄×D₄	—	2	2	no	—
536	C₄×D₄	—	2	2	no	—
537	C₄×D₄	—	4	1	no	—
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
540	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
544	C₂×C₂²⋊C₄	—	2	1	no	—
545	C₂×C₂²⋊C₄	—	2	1	no	—
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	—	2	1	no	—
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	C₂×C₄²	—	2	1	no	—
555	C₂×C₄²	—	2	1	no	—
556	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
557	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
558	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
559	C₄⋊C₈	—	2	2	no	—
560	C₄⋊C₈	—	2	2	no	—
561	C₄⋊C₈	—	2	2	no	—
562	#103	—	2	2	no	—
563	#102	—	2	2	no	—
564	#102	—	2	2	no	—
565	#102	—	2	2	no	—
566	#102	—	2	2	no	—
567	#102	—	4	1	no	—
568	#102	—	4	1	no	—
569	#102	D₄×C₄₁	1	4	yes	complemented
570	#97	—	2	2	no	—
571	#95	—	2	1	no	—
572	#95	—	2	1	no	—
573	#95	—	2	1	no	—
574	#95	D₄×C₄₁	1	1	yes	characteristic
575	#95	D₄×C₄₁	1	1	yes	characteristic
576	C₂⁴	—	2	1	no	—
577	C₂⁴	—	2	1	no	—
578	C₂⁴	—	2	1	no	—
579	C₂⁴	—	2	1	no	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	1	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	—	2	1	no	—
585	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	1	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	—	2	1	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	2	1	no	—
604	C₂×D₄	—	2	1	no	—
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	—	2	1	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	4	2	no	—
609	C₂×D₄	—	4	2	no	—
610	C₂×D₄	—	4	2	no	—
611	C₂×D₄	—	4	2	no	—
612	C₂×D₄	—	4	2	no	—
613	C₂×D₄	—	4	2	no	—
614	C₂×D₄	—	4	2	no	—
615	C₂×D₄	—	4	2	no	—
616	C₂×D₄	—	4	2	no	—
617	C₂×D₄	—	4	2	no	—
618	C₂×D₄	—	4	2	no	—
619	C₂×D₄	—	4	2	no	—
620	C₂×D₄	—	8	1	no	—
621	C₂×D₄	—	8	1	no	—
622	C₂×D₄	—	8	1	no	—
623	C₂×D₄	—	8	1	no	—
624	C₂×D₄	—	8	1	no	—
625	C₂×D₄	—	8	1	no	—
626	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
627	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	4	2	no	—
633	C₂²×C₄	—	4	2	no	—
634	C₂²×C₄	—	4	2	no	—
635	C₂²×C₄	—	4	2	no	—
636	C₂²×C₄	—	4	2	no	—
637	C₂²×C₄	—	8	1	no	—
638	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
639	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
640	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
641	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
642	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
643	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
644	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
645	SD₁₆	—	4	4	no	—
646	SD₁₆	—	4	4	no	—
647	SD₁₆	—	4	4	no	—
648	D₈	—	4	4	no	—
649	D₈	—	4	4	no	—
650	D₈	—	4	4	no	—
651	C₂×C₈	—	2	1	no	—
652	C₂×C₈	—	2	1	no	—
653	C₂×C₈	—	2	1	no	—
654	C₂×C₈	—	2	1	no	—
655	C₂×C₈	—	2	1	no	—
656	C₂×C₈	—	2	1	no	—
657	C₂×C₈	—	2	1	no	—
658	C₂×C₈	—	2	1	no	—
659	C₂×C₈	—	2	1	no	—
660	C₂×C₈	—	2	1	no	—
661	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
662	C₂×C₈	#41×C₄₁	1	2	yes	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	4	2	no	—
671	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	4	2	no	—
675	C₂²⋊C₄	—	4	2	no	—
676	C₂²⋊C₄	—	4	2	no	—
677	C₂²⋊C₄	—	4	2	no	—
678	C₂²⋊C₄	—	4	2	no	—
679	C₂²⋊C₄	—	4	2	no	—
680	C₂²⋊C₄	—	4	2	no	—
681	C₂²⋊C₄	—	8	1	no	—
682	C₄²	—	2	1	no	—
683	C₄²	—	2	1	no	—
684	C₄²	—	2	1	no	—
685	C₄²	—	2	1	no	—
686	C₄²	—	4	2	no	—
687	C₄²	—	8	1	no	—
688	C₄²	C₂×D₄×C₄₁	1	2	yes	—
689	C₄²	#41×C₄₁	1	2	yes	—
690	C₂³	—	2	2	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	—	4	1	no	—
699	C₂³	—	4	1	no	—
700	C₂³	—	4	1	no	—
701	C₂³	—	4	1	no	—
702	C₂³	—	4	1	no	—
703	C₂³	—	4	1	no	—
704	C₂³	—	4	1	no	—
705	C₂³	—	4	1	no	—
706	C₂³	—	4	1	no	—
707	C₂³	—	4	1	no	—
708	C₂³	—	4	1	no	—
709	C₂³	—	4	1	no	—
710	C₂³	—	4	1	no	—
711	C₂³	—	4	1	no	—
712	C₂³	—	4	1	no	—
713	C₂³	—	4	1	no	—
714	C₂³	—	4	1	no	—
715	C₂³	—	4	1	no	—
716	C₂³	—	4	1	no	—
717	C₂³	—	4	1	no	—
718	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
719	Q₈	—	2	2	no	—
720	Q₈	—	2	2	no	—
721	Q₈	—	4	1	no	—
722	Q₈	—	4	1	no	—
723	D₄	—	2	2	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	2	no	—
726	D₄	—	2	2	no	—
727	D₄	—	4	1	no	—
728	D₄	—	4	1	no	—
729	D₄	—	4	1	no	—
730	D₄	—	4	1	no	—
731	D₄	—	4	1	no	—
732	D₄	—	4	1	no	—
733	D₄	—	4	1	no	—
734	D₄	—	4	1	no	—
735	D₄	—	4	1	no	—
736	D₄	—	4	1	no	—
737	D₄	—	4	1	no	—
738	D₄	—	4	1	no	—
739	D₄	—	8	4	no	—
740	D₄	—	8	4	no	—
741	D₄	—	8	4	no	—
742	D₄	—	8	4	no	—
743	D₄	—	8	4	no	—
744	D₄	—	8	4	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	8	4	no	—
772	C₂×C₄	—	8	4	no	—
773	C₂×C₄	#121×C₄₁	1	2	yes	—
774	C₂×C₄	#121×C₄₁	1	2	yes	—
775	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
776	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
777	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
778	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
779	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
780	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
781	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
782	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
783	C₈	—	2	2	no	—
784	C₈	—	2	2	no	—
785	C₈	—	4	1	no	—
786	C₈	—	4	1	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	8	1	no	—
794	C₂²	—	8	1	no	—
795	C₂²	—	8	1	no	—
796	C₂²	—	8	1	no	—
797	C₂²	—	8	1	no	—
798	C₂²	—	8	1	no	—
799	C₂²	—	8	1	no	—
800	C₂²	—	8	1	no	—
801	C₂²	—	8	1	no	—
802	C₂²	—	8	1	no	—
803	C₂²	—	8	1	no	—
804	C₂²	—	8	1	no	—
805	C₂²	—	8	1	no	—
806	C₂²	—	8	1	no	—
807	C₂²	—	8	1	no	—
808	C₂²	—	8	1	no	—
809	C₂²	—	8	1	no	—
810	C₂²	—	8	1	no	—
811	C₂²	—	8	1	no	—
812	C₂²	—	8	1	no	—
813	C₂²	—	8	1	no	—
814	C₂²	—	8	1	no	—
815	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
816	C₂²	D₄²×C₄₁	1	1	yes	characteristic
817	C₂²	C₄₁×#550	1	1	yes	characteristic
818	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
819	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
820	C₂²	C₄₁×#576	1	1	yes	characteristic
821	C₂²	C₄₁×#577	1	1	yes	characteristic
822	C₄	—	2	2	no	—
823	C₄	—	2	2	no	—
824	C₄	—	2	2	no	—
825	C₄	—	2	2	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	1	no	—
830	C₄	—	8	1	no	—
831	C₄	—	8	1	no	—
832	C₄	C₄₁×#532	1	1	yes	characteristic
833	C₄	C₄₁×#540	1	1	yes	characteristic
834	C₄	D₄²×C₄₁	1	1	yes	characteristic
835	C₄	C₄₁×#546	1	1	yes	characteristic
836	C₂	—	8	2	no	—
837	C₂	—	8	2	no	—
838	C₂	—	16	1	no	—
839	C₂	—	16	1	no	—
840	C₂	C₄₁×#2428	1	1	yes	characteristic
841	C₂	C₄₁×#3038	1	1	yes	characteristic
842	C₂	C₄₁×#3045	1	1	yes	characteristic
843	C₂	C₄₁×#3264	1	1	yes	characteristic
844	C₂	C₄₁×#3265	1	1	yes	characteristic
845	C₂	C₄₁×#3397	1	1	yes	characteristic
846	C₂	C₄₁×#3399	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×C₄⋊C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#496	C₂	semidirect
2. C₂×C₄₁×#460	C₂	semidirect
3. C₂×C₄₁×#463	C₂	semidirect
4. C₂×C₄₁×#459	C₂	semidirect
5. C₄₁×#2541	C₂	semidirect
6. C₄₁×#2367	C₂	semidirect
7. C₄₁×#2055	C₂	semidirect
8. C₄₁×#2054	C₂	semidirect
9. C₄₁×#2014	C₂	semidirect
10. C₄₁×#2011	C₂	semidirect
11. C₄₁×#1982	C₂	semidirect
12. C₄₁×#1940	C₂	semidirect
13. C₄₁×#1880	C₂	semidirect
14. C₄₁×#1879	C₂	semidirect
15. C₄₁×#1762	C₂	semidirect
105. #124×C₄₁	D₄	semidirect
145. #102×C₄₁	D₄	semidirect
363. #25380	C₄₁	direct (N × H)
413. C₂×#496	C₂×C₄₁	semidirect
414. C₂×#460	C₂×C₄₁	semidirect
415. C₂×#463	C₂×C₄₁	semidirect
416. C₂×#459	C₂×C₄₁	semidirect
417. #2541	C₂×C₄₁	semidirect
418. #2367	C₂×C₄₁	semidirect
419. #2055	C₂×C₄₁	semidirect
420. #2054	C₂×C₄₁	semidirect
421. #2014	C₂×C₄₁	semidirect
422. #2011	C₂×C₄₁	semidirect
423. #1982	C₂×C₄₁	semidirect
424. #1940	C₂×C₄₁	semidirect
425. #1880	C₂×C₄₁	semidirect
426. #1879	C₂×C₄₁	semidirect
427. #1762	C₂×C₄₁	semidirect
486. C₄₁	#25380	direct (N × H)
529. #124	D₄×C₄₁	semidirect
569. #102	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×#496	2
C₂×C₄₁×#460	2
C₂×C₄₁×#463	2
C₂×C₄₁×#459	2
C₄₁×#2541	2
C₄₁×#2367	2
C₄₁×#2055	2
C₄₁×#2054	2
C₄₁×#2014	2
C₄₁×#2011	2
C₄₁×#1982	2
C₄₁×#1940	2
C₄₁×#1880	2
C₄₁×#1879	2
C₄₁×#1762	2
#25380	41

Subgroups — C41×#25380 #23801581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25380 #23801581