Subgroups — C₄₁×#36764 #23812965

Order 10496.

1646 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#2850	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2796	C₂	1	2	yes	maximal, complemented
4	C₄₁×#2793	C₂	1	2	yes	maximal, complemented
5	C₄₁×#2777	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2765	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2762	C₂	1	2	yes	maximal, complemented
8	C₄₁×#2755	C₂	1	2	yes	maximal, complemented
9	C₄₁×#2729	C₂	1	2	yes	maximal, complemented
10	C₄₁×#2700	C₂	1	2	yes	maximal, complemented
11	C₄₁×#2627	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#2618	C₂	1	1	yes	maximal, characteristic
13	C₄₁×#2510	C₂	1	2	yes	maximal, complemented
14	C₄₁×#2488	C₂	1	2	yes	maximal, complemented
15	C₄₁×#2449	C₂	1	2	yes	maximal, complemented
16	C₄₁×#2419	C₂	1	2	yes	maximal, complemented
17	C₄₁×#2329	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄₁×#2325	C₂	1	1	yes	maximal, characteristic
19	C₂×C₄₁×#387	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×#123×C₄₁	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
26	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
28	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
31	C₄₁×#401	C₂²	1	2	yes	—
32	C₄₁×#400	C₂²	1	2	yes	—
33	C₄₁×#400	C₂²	1	2	yes	—
34	C₄₁×#400	C₂²	1	2	yes	—
35	C₄₁×#400	C₂²	1	2	yes	—
36	C₄₁×#400	C₂²	1	2	yes	—
37	C₄₁×#399	C₂²	1	2	yes	—
38	C₄₁×#398	C₂²	1	2	yes	—
39	C₄₁×#398	C₂²	1	2	yes	—
40	C₄₁×#398	C₂²	1	2	yes	—
41	C₄₁×#398	C₂²	1	2	yes	—
42	C₄₁×#398	C₂²	1	2	yes	—
43	C₄₁×#397	C₂²	1	2	yes	—
44	C₄₁×#397	C₂²	1	2	yes	—
45	C₄₁×#397	C₂²	1	2	yes	—
46	C₄₁×#397	C₂²	1	2	yes	—
47	C₄₁×#397	C₂²	1	2	yes	—
48	C₄₁×#396	C₂²	1	2	yes	—
49	C₄₁×#396	C₂²	1	2	yes	—
50	C₄₁×#396	C₂²	1	2	yes	—
51	C₄₁×#395	C₂²	1	2	yes	—
52	C₄₁×#395	C₂²	1	2	yes	—
53	C₄₁×#394	C₂²	1	2	yes	—
54	C₄₁×#393	C₂²	1	2	yes	—
55	C₄₁×#391	C₂²	1	2	yes	—
56	C₄₁×#391	C₂²	1	1	yes	characteristic
57	C₄₁×#391	C₂²	1	2	yes	—
58	C₄₁×#391	C₂²	1	2	yes	—
59	C₄₁×#390	C₂²	1	1	yes	characteristic
60	C₄₁×#389	C₂²	1	2	yes	—
61	C₄₁×#389	C₂²	1	2	yes	—
62	C₄₁×#389	C₂²	1	1	yes	characteristic
63	C₄₁×#389	C₂²	1	1	yes	characteristic
64	C₄₁×#389	C₂²	1	2	yes	—
65	C₄₁×#388	C₂²	1	2	yes	—
66	C₄₁×#388	C₂²	1	2	yes	—
67	C₄₁×#388	C₂²	1	2	yes	—
68	C₄₁×#388	C₂²	1	2	yes	—
69	C₄₁×#388	C₂²	1	2	yes	—
70	C₄₁×#388	C₂²	1	2	yes	—
71	C₄₁×#388	C₂²	1	2	yes	—
72	C₄₁×#387	C₂²	1	2	yes	—
73	C₄₁×#387	C₂²	1	2	yes	—
74	C₄₁×#387	C₂²	1	2	yes	—
75	C₄₁×#387	C₂²	1	2	yes	—
76	C₄₁×#387	C₂²	1	2	yes	—
77	C₄₁×#387	C₂²	1	2	yes	—
78	C₄₁×#387	C₂²	1	2	yes	—
79	C₄₁×#387	C₂²	1	2	yes	—
80	C₄₁×#387	C₂²	1	2	yes	—
81	C₄₁×#387	C₂²	1	2	yes	—
82	C₄₁×#387	C₂²	1	2	yes	—
83	C₄₁×#386	C₂²	1	2	yes	—
84	C₄₁×#386	C₂²	1	2	yes	—
85	C₄₁×#386	C₂²	1	2	yes	—
86	C₄₁×#386	C₂²	1	2	yes	—
87	C₄₁×#386	C₂²	1	2	yes	—
88	C₄₁×#385	C₂²	1	2	yes	—
89	C₄₁×#385	C₂²	1	2	yes	—
90	C₄₁×#385	C₂²	1	2	yes	—
91	C₄₁×#385	C₂²	1	2	yes	—
92	C₄₁×#385	C₂²	1	2	yes	—
93	C₄₁×#384	C₂²	1	1	yes	characteristic
94	C₄₁×#383	C₂²	1	2	yes	—
95	C₄₁×#382	C₂²	1	1	yes	characteristic
96	C₄₁×#382	C₂²	1	2	yes	—
97	C₄₁×#381	C₂²	1	2	yes	—
98	C₄₁×#381	C₂²	1	2	yes	—
99	C₄₁×#380	C₂²	1	1	yes	characteristic
100	C₄₁×#380	C₂²	1	1	yes	characteristic
101	C₄₁×#380	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
103	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
104	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
105	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
106	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
108	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
110	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
118	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
119	C₄⋊Q₈×C₄₁	—	4	2	no	—
120	#124×C₄₁	—	4	2	no	—
121	#123×C₄₁	—	4	4	no	—
122	C₂²⋊Q₈×C₄₁	—	2	4	no	—
123	C₂²⋊Q₈×C₄₁	—	4	4	no	—
124	C₂²⋊Q₈×C₄₁	—	4	4	no	—
125	#121×C₄₁	—	2	4	no	—
126	C₄×D₄×C₄₁	—	4	4	no	—
127	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
128	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
129	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
167	C₂×C₄²×C₄₁	—	4	2	no	—
168	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
173	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
174	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
175	#95×C₄₁	C₂³	1	2	yes	—
176	#95×C₄₁	C₂³	1	2	yes	—
177	#95×C₄₁	C₂³	1	2	yes	—
178	#95×C₄₁	C₂³	1	2	yes	—
179	#95×C₄₁	C₂³	1	2	yes	—
180	#95×C₄₁	C₂³	1	2	yes	—
181	#95×C₄₁	C₂³	1	2	yes	—
182	#95×C₄₁	C₂³	1	2	yes	—
183	#95×C₄₁	C₂³	1	2	yes	—
184	#95×C₄₁	C₂³	1	2	yes	—
185	#95×C₄₁	C₂³	1	2	yes	—
186	#95×C₄₁	C₂³	1	2	yes	—
187	#95×C₄₁	C₂³	1	2	yes	—
188	#95×C₄₁	C₂³	1	2	yes	—
189	#95×C₄₁	C₂³	1	2	yes	—
190	#95×C₄₁	C₂³	1	2	yes	—
191	#95×C₄₁	C₂³	1	2	yes	—
192	#95×C₄₁	C₂³	1	2	yes	—
193	#95×C₄₁	C₂³	1	2	yes	—
194	#95×C₄₁	C₂³	1	2	yes	—
195	#95×C₄₁	C₂³	1	2	yes	—
196	#95×C₄₁	C₂³	1	2	yes	—
197	#95×C₄₁	C₂³	1	2	yes	—
198	#95×C₄₁	C₂³	1	2	yes	—
199	#95×C₄₁	C₂³	1	2	yes	—
200	#95×C₄₁	C₂³	1	2	yes	—
201	#95×C₄₁	C₂³	1	2	yes	—
202	#95×C₄₁	C₂³	1	2	yes	—
203	#95×C₄₁	C₂³	1	2	yes	—
204	#95×C₄₁	C₂³	1	2	yes	—
205	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
206	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
207	C₂×Q₈×C₄₁	—	2	2	no	—
208	C₂×Q₈×C₄₁	—	2	4	no	—
209	C₂×Q₈×C₄₁	—	4	2	no	—
210	C₂×Q₈×C₄₁	—	4	1	no	—
211	C₂×Q₈×C₄₁	—	4	1	no	—
212	C₂×Q₈×C₄₁	—	4	2	no	—
213	C₂×D₄×C₄₁	—	2	4	no	—
214	C₂×D₄×C₄₁	—	2	4	no	—
215	C₂×D₄×C₄₁	—	2	4	no	—
216	C₂×D₄×C₄₁	—	2	2	no	—
217	C₂×D₄×C₄₁	—	4	1	no	—
218	C₂×D₄×C₄₁	—	4	1	no	—
219	C₂²×C₄×C₄₁	—	2	2	no	—
220	C₂²×C₄×C₄₁	—	2	2	no	—
221	C₂²×C₄×C₄₁	—	2	2	no	—
222	C₂²×C₄×C₄₁	—	2	2	no	—
223	C₂²×C₄×C₄₁	—	2	2	no	—
224	C₂²×C₄×C₄₁	—	2	2	no	—
225	C₂²×C₄×C₄₁	—	2	2	no	—
226	C₂²×C₄×C₄₁	—	2	2	no	—
227	C₂²×C₄×C₄₁	—	2	2	no	—
228	C₂²×C₄×C₄₁	—	2	2	no	—
229	C₂²×C₄×C₄₁	—	4	1	no	—
230	C₂²×C₄×C₄₁	—	4	1	no	—
231	C₂²×C₄×C₄₁	—	4	1	no	—
232	C₂²×C₄×C₄₁	—	4	1	no	—
233	C₂²×C₄×C₄₁	—	4	1	no	—
234	C₂²×C₄×C₄₁	—	4	1	no	—
235	C₂²×C₄×C₄₁	—	4	1	no	—
236	C₂²×C₄×C₄₁	—	4	2	no	—
237	C₂²×C₄×C₄₁	—	4	2	no	—
238	C₂²×C₄×C₄₁	—	4	1	no	—
239	C₂²×C₄×C₄₁	—	4	1	no	—
240	C₂²×C₄×C₄₁	—	4	2	no	—
241	C₂²×C₄×C₄₁	—	4	1	no	—
242	C₂²×C₄×C₄₁	#41	1	4	yes	—
243	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
260	C₄⋊C₄×C₄₁	—	2	4	no	—
261	C₄⋊C₄×C₄₁	—	2	4	no	—
262	C₄⋊C₄×C₄₁	—	2	2	no	—
263	C₄⋊C₄×C₄₁	—	2	2	no	—
264	C₄⋊C₄×C₄₁	—	2	4	no	—
265	C₄⋊C₄×C₄₁	—	2	4	no	—
266	C₄⋊C₄×C₄₁	—	2	4	no	—
267	C₄⋊C₄×C₄₁	—	4	2	no	—
268	C₄⋊C₄×C₄₁	—	4	1	no	—
269	C₄⋊C₄×C₄₁	—	4	1	no	—
270	C₄⋊C₄×C₄₁	—	4	2	no	—
271	C₄⋊C₄×C₄₁	—	4	2	no	—
272	C₄⋊C₄×C₄₁	—	4	2	no	—
273	C₄⋊C₄×C₄₁	—	4	2	no	—
274	C₄⋊C₄×C₄₁	—	4	2	no	—
275	C₄⋊C₄×C₄₁	—	4	2	no	—
276	C₄⋊C₄×C₄₁	—	4	2	no	—
277	C₄⋊C₄×C₄₁	—	4	2	no	—
278	C₄⋊C₄×C₄₁	—	4	2	no	—
279	C₄⋊C₄×C₄₁	—	4	2	no	—
280	C₄⋊C₄×C₄₁	—	4	1	no	—
281	C₄⋊C₄×C₄₁	—	4	2	no	—
282	C₄⋊C₄×C₄₁	—	4	1	no	—
283	C₂²⋊C₄×C₄₁	—	2	4	no	—
284	C₂²⋊C₄×C₄₁	—	2	4	no	—
285	C₂²⋊C₄×C₄₁	—	2	4	no	—
286	C₂²⋊C₄×C₄₁	—	2	4	no	—
287	C₂²⋊C₄×C₄₁	—	2	4	no	—
288	C₂²⋊C₄×C₄₁	—	2	4	no	—
289	C₂²⋊C₄×C₄₁	—	4	2	no	—
290	C₂²⋊C₄×C₄₁	—	4	2	no	—
291	C₂²⋊C₄×C₄₁	—	4	2	no	—
292	C₂²⋊C₄×C₄₁	—	4	2	no	—
293	C₂²⋊C₄×C₄₁	—	4	2	no	—
294	C₂²⋊C₄×C₄₁	—	4	2	no	—
295	C₂²⋊C₄×C₄₁	—	4	2	no	—
296	C₂²⋊C₄×C₄₁	—	4	2	no	—
297	C₂²⋊C₄×C₄₁	—	4	2	no	—
298	C₄²×C₄₁	—	2	2	no	—
299	C₄²×C₄₁	—	2	2	no	—
300	C₄²×C₄₁	—	4	1	no	—
301	C₄²×C₄₁	—	4	1	no	—
302	C₄²×C₄₁	—	4	2	no	—
303	C₄²×C₄₁	—	4	2	no	—
304	C₄²×C₄₁	—	4	2	no	—
305	C₂³×C₄₁	—	2	1	no	—
306	C₂³×C₄₁	—	2	1	no	—
307	C₂³×C₄₁	—	2	1	no	—
308	C₂³×C₄₁	—	2	1	no	—
309	C₂³×C₄₁	—	2	2	no	—
310	C₂³×C₄₁	—	2	2	no	—
311	C₂³×C₄₁	—	2	2	no	—
312	C₂³×C₄₁	—	2	2	no	—
313	C₂³×C₄₁	—	2	2	no	—
314	C₂³×C₄₁	—	2	2	no	—
315	C₂³×C₄₁	—	2	2	no	—
316	C₂³×C₄₁	C₂×#41	1	2	yes	—
317	C₂³×C₄₁	H(5,𝔽₂)	1	2	yes	—
318	C₂³×C₄₁	2₋¹⁺⁴	1	2	yes	—
319	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
320	Q₈×C₄₁	—	8	2	no	—
321	Q₈×C₄₁	—	8	4	no	—
322	D₄×C₄₁	—	4	8	no	—
323	D₄×C₄₁	—	8	2	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	1	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	2	no	—
334	C₂×C₄×C₄₁	—	2	2	no	—
335	C₂×C₄×C₄₁	—	2	2	no	—
336	C₂×C₄×C₄₁	—	2	2	no	—
337	C₂×C₄×C₄₁	—	2	1	no	—
338	C₂×C₄×C₄₁	—	2	1	no	—
339	C₂×C₄×C₄₁	—	2	2	no	—
340	C₂×C₄×C₄₁	—	2	2	no	—
341	C₂×C₄×C₄₁	—	2	2	no	—
342	C₂×C₄×C₄₁	—	2	2	no	—
343	C₂×C₄×C₄₁	—	2	2	no	—
344	C₂×C₄×C₄₁	—	2	2	no	—
345	C₂×C₄×C₄₁	—	2	2	no	—
346	C₂×C₄×C₄₁	—	2	2	no	—
347	C₂×C₄×C₄₁	—	2	2	no	—
348	C₂×C₄×C₄₁	—	2	2	no	—
349	C₂×C₄×C₄₁	—	2	2	no	—
350	C₂×C₄×C₄₁	—	2	1	no	—
351	C₂×C₄×C₄₁	—	2	2	no	—
352	C₂×C₄×C₄₁	—	2	2	no	—
353	C₂×C₄×C₄₁	—	2	2	no	—
354	C₂×C₄×C₄₁	—	2	2	no	—
355	C₂×C₄×C₄₁	—	2	2	no	—
356	C₂×C₄×C₄₁	—	2	1	no	—
357	C₂×C₄×C₄₁	—	2	1	no	—
358	C₂×C₄×C₄₁	—	2	2	no	—
359	C₂×C₄×C₄₁	—	2	2	no	—
360	C₂×C₄×C₄₁	—	2	2	no	—
361	C₂×C₄×C₄₁	—	2	2	no	—
362	C₂×C₄×C₄₁	—	2	2	no	—
363	C₂×C₄×C₄₁	—	2	2	no	—
364	C₂×C₄×C₄₁	—	2	2	no	—
365	C₂×C₄×C₄₁	—	2	2	no	—
366	C₂×C₄×C₄₁	—	2	1	no	—
367	C₂×C₄×C₄₁	—	2	2	no	—
368	C₂×C₄×C₄₁	—	2	2	no	—
369	C₂×C₄×C₄₁	—	2	2	no	—
370	C₂×C₄×C₄₁	—	2	2	no	—
371	C₂×C₄×C₄₁	—	4	4	no	—
372	C₂×C₄×C₄₁	—	4	4	no	—
373	C₂×C₄×C₄₁	—	4	4	no	—
374	C₂×C₄×C₄₁	—	4	4	no	—
375	C₂×C₄×C₄₁	—	4	4	no	—
376	C₂×C₄×C₄₁	—	8	2	no	—
377	C₂×C₄×C₄₁	—	8	2	no	—
378	C₂×C₄×C₄₁	—	8	4	no	—
379	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
380	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
381	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
382	C₂×C₄×C₄₁	2₋¹⁺⁴	1	2	yes	—
383	#36764	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
384	C₂²×C₄₁	—	2	2	no	—
385	C₂²×C₄₁	—	2	2	no	—
386	C₂²×C₄₁	—	2	2	no	—
387	C₂²×C₄₁	—	2	2	no	—
388	C₂²×C₄₁	—	2	2	no	—
389	C₂²×C₄₁	—	2	2	no	—
390	C₂²×C₄₁	—	4	2	no	—
391	C₂²×C₄₁	—	4	2	no	—
392	C₂²×C₄₁	—	4	2	no	—
393	C₂²×C₄₁	—	4	2	no	—
394	C₂²×C₄₁	—	4	2	no	—
395	C₂²×C₄₁	—	4	2	no	—
396	C₂²×C₄₁	—	4	2	no	—
397	C₂²×C₄₁	#542	1	4	yes	—
398	C₂²×C₄₁	C₂²×#41	1	1	yes	characteristic
399	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
400	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
401	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
402	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
403	C₂²×C₄₁	#585	1	1	yes	characteristic
404	C₂²×C₄₁	#585	1	1	yes	characteristic
405	C₄×C₄₁	—	2	2	no	—
406	C₄×C₄₁	—	2	2	no	—
407	C₄×C₄₁	—	2	2	no	—
408	C₄×C₄₁	—	2	2	no	—
409	C₄×C₄₁	—	4	2	no	—
410	C₄×C₄₁	—	4	2	no	—
411	C₄×C₄₁	—	4	2	no	—
412	C₄×C₄₁	—	4	2	no	—
413	C₄×C₄₁	—	4	2	no	—
414	C₄×C₄₁	—	4	1	no	—
415	C₄×C₄₁	—	4	2	no	—
416	C₄×C₄₁	—	4	2	no	—
417	C₄×C₄₁	—	4	2	no	—
418	C₄×C₄₁	—	4	1	no	—
419	C₄×C₄₁	—	4	2	no	—
420	C₄×C₄₁	—	4	2	no	—
421	C₄×C₄₁	—	4	2	no	—
422	#2857	C₂×C₄₁	1	1	yes	characteristic, complemented
423	#2850	C₂×C₄₁	1	1	yes	characteristic
424	#2796	C₂×C₄₁	1	2	yes	complemented
425	#2793	C₂×C₄₁	1	2	yes	complemented
426	#2777	C₂×C₄₁	1	2	yes	complemented
427	#2765	C₂×C₄₁	1	2	yes	complemented
428	#2762	C₂×C₄₁	1	2	yes	complemented
429	#2755	C₂×C₄₁	1	2	yes	complemented
430	#2729	C₂×C₄₁	1	2	yes	complemented
431	#2700	C₂×C₄₁	1	2	yes	complemented
432	#2627	C₂×C₄₁	1	1	yes	characteristic, complemented
433	#2618	C₂×C₄₁	1	1	yes	characteristic
434	#2510	C₂×C₄₁	1	2	yes	complemented
435	#2488	C₂×C₄₁	1	2	yes	complemented
436	#2449	C₂×C₄₁	1	2	yes	complemented
437	#2419	C₂×C₄₁	1	2	yes	complemented
438	#2329	C₂×C₄₁	1	1	yes	characteristic, complemented
439	#2325	C₂×C₄₁	1	1	yes	characteristic
440	C₂×#387	C₂×C₄₁	1	1	yes	characteristic, complemented
441	C₂×C₄₁	—	2	4	no	—
442	C₂×C₄₁	—	8	2	no	—
443	C₂×C₄₁	C₂×#542	1	1	yes	characteristic
444	C₂×C₄₁	#3505	1	1	yes	characteristic
445	C₂×C₄₁	#3507	1	1	yes	characteristic
446	C₂×C₄₁	#3534	1	1	yes	characteristic
447	C₂×C₄₁	#3538	1	1	yes	characteristic
448	C₂×C₄₁	#3559	1	1	yes	characteristic
449	C₂×C₄₁	#3564	1	1	yes	characteristic
450	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
451	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
452	C₂×#123	C₂²×C₄₁	1	2	yes	—
453	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
454	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
455	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
456	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
457	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
458	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
459	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
460	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
461	#401	C₂²×C₄₁	1	2	yes	—
462	#400	C₂²×C₄₁	1	2	yes	—
463	#400	C₂²×C₄₁	1	2	yes	—
464	#400	C₂²×C₄₁	1	2	yes	—
465	#400	C₂²×C₄₁	1	2	yes	—
466	#400	C₂²×C₄₁	1	2	yes	—
467	#399	C₂²×C₄₁	1	2	yes	—
468	#398	C₂²×C₄₁	1	2	yes	—
469	#398	C₂²×C₄₁	1	2	yes	—
470	#398	C₂²×C₄₁	1	2	yes	—
471	#398	C₂²×C₄₁	1	2	yes	—
472	#398	C₂²×C₄₁	1	2	yes	—
473	#397	C₂²×C₄₁	1	2	yes	—
474	#397	C₂²×C₄₁	1	2	yes	—
475	#397	C₂²×C₄₁	1	2	yes	—
476	#397	C₂²×C₄₁	1	2	yes	—
477	#397	C₂²×C₄₁	1	2	yes	—
478	#396	C₂²×C₄₁	1	2	yes	—
479	#396	C₂²×C₄₁	1	2	yes	—
480	#396	C₂²×C₄₁	1	2	yes	—
481	#395	C₂²×C₄₁	1	2	yes	—
482	#395	C₂²×C₄₁	1	2	yes	—
483	#394	C₂²×C₄₁	1	2	yes	—
484	#393	C₂²×C₄₁	1	2	yes	—
485	#391	C₂²×C₄₁	1	2	yes	—
486	#391	C₂²×C₄₁	1	1	yes	characteristic
487	#391	C₂²×C₄₁	1	2	yes	—
488	#391	C₂²×C₄₁	1	2	yes	—
489	#390	C₂²×C₄₁	1	1	yes	characteristic
490	#389	C₂²×C₄₁	1	2	yes	—
491	#389	C₂²×C₄₁	1	2	yes	—
492	#389	C₂²×C₄₁	1	1	yes	characteristic
493	#389	C₂²×C₄₁	1	1	yes	characteristic
494	#389	C₂²×C₄₁	1	2	yes	—
495	#388	C₂²×C₄₁	1	2	yes	—
496	#388	C₂²×C₄₁	1	2	yes	—
497	#388	C₂²×C₄₁	1	2	yes	—
498	#388	C₂²×C₄₁	1	2	yes	—
499	#388	C₂²×C₄₁	1	2	yes	—
500	#388	C₂²×C₄₁	1	2	yes	—
501	#388	C₂²×C₄₁	1	2	yes	—
502	#387	C₂²×C₄₁	1	2	yes	—
503	#387	C₂²×C₄₁	1	2	yes	—
504	#387	C₂²×C₄₁	1	2	yes	—
505	#387	C₂²×C₄₁	1	2	yes	—
506	#387	C₂²×C₄₁	1	2	yes	—
507	#387	C₂²×C₄₁	1	2	yes	—
508	#387	C₂²×C₄₁	1	2	yes	—
509	#387	C₂²×C₄₁	1	2	yes	—
510	#387	C₂²×C₄₁	1	2	yes	—
511	#387	C₂²×C₄₁	1	2	yes	—
512	#387	C₂²×C₄₁	1	2	yes	—
513	#386	C₂²×C₄₁	1	2	yes	—
514	#386	C₂²×C₄₁	1	2	yes	—
515	#386	C₂²×C₄₁	1	2	yes	—
516	#386	C₂²×C₄₁	1	2	yes	—
517	#386	C₂²×C₄₁	1	2	yes	—
518	#385	C₂²×C₄₁	1	2	yes	—
519	#385	C₂²×C₄₁	1	2	yes	—
520	#385	C₂²×C₄₁	1	2	yes	—
521	#385	C₂²×C₄₁	1	2	yes	—
522	#385	C₂²×C₄₁	1	2	yes	—
523	#384	C₂²×C₄₁	1	1	yes	characteristic
524	#383	C₂²×C₄₁	1	2	yes	—
525	#382	C₂²×C₄₁	1	1	yes	characteristic
526	#382	C₂²×C₄₁	1	2	yes	—
527	#381	C₂²×C₄₁	1	2	yes	—
528	#381	C₂²×C₄₁	1	2	yes	—
529	#380	C₂²×C₄₁	1	1	yes	characteristic
530	#380	C₂²×C₄₁	1	1	yes	characteristic
531	#380	C₂²×C₄₁	1	2	yes	—
532	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
533	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
534	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
535	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
536	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
537	C₄₁	#36764	1	1	yes	characteristic, direct product factor, Sylow
538	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
539	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
540	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
541	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
543	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
544	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
545	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
546	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
547	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
548	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
549	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
550	C₄⋊Q₈	—	4	2	no	—
551	#124	—	4	2	no	—
552	#123	—	4	4	no	—
553	C₂²⋊Q₈	—	2	4	no	—
554	C₂²⋊Q₈	—	4	4	no	—
555	C₂²⋊Q₈	—	4	4	no	—
556	#121	—	2	4	no	—
557	C₄×D₄	—	4	4	no	—
558	C₂×C₄⋊C₄	—	2	4	no	—
559	C₂×C₄⋊C₄	—	4	2	no	—
560	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
598	C₂×C₄²	—	4	2	no	—
599	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
602	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
603	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
604	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
606	#95	C₂³×C₄₁	1	2	yes	—
607	#95	C₂³×C₄₁	1	2	yes	—
608	#95	C₂³×C₄₁	1	2	yes	—
609	#95	C₂³×C₄₁	1	2	yes	—
610	#95	C₂³×C₄₁	1	2	yes	—
611	#95	C₂³×C₄₁	1	2	yes	—
612	#95	C₂³×C₄₁	1	2	yes	—
613	#95	C₂³×C₄₁	1	2	yes	—
614	#95	C₂³×C₄₁	1	2	yes	—
615	#95	C₂³×C₄₁	1	2	yes	—
616	#95	C₂³×C₄₁	1	2	yes	—
617	#95	C₂³×C₄₁	1	2	yes	—
618	#95	C₂³×C₄₁	1	2	yes	—
619	#95	C₂³×C₄₁	1	2	yes	—
620	#95	C₂³×C₄₁	1	2	yes	—
621	#95	C₂³×C₄₁	1	2	yes	—
622	#95	C₂³×C₄₁	1	2	yes	—
623	#95	C₂³×C₄₁	1	2	yes	—
624	#95	C₂³×C₄₁	1	2	yes	—
625	#95	C₂³×C₄₁	1	2	yes	—
626	#95	C₂³×C₄₁	1	2	yes	—
627	#95	C₂³×C₄₁	1	2	yes	—
628	#95	C₂³×C₄₁	1	2	yes	—
629	#95	C₂³×C₄₁	1	2	yes	—
630	#95	C₂³×C₄₁	1	2	yes	—
631	#95	C₂³×C₄₁	1	2	yes	—
632	#95	C₂³×C₄₁	1	2	yes	—
633	#95	C₂³×C₄₁	1	2	yes	—
634	#95	C₂³×C₄₁	1	2	yes	—
635	#95	C₂³×C₄₁	1	2	yes	—
636	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
637	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
638	C₂×Q₈	—	2	2	no	—
639	C₂×Q₈	—	2	4	no	—
640	C₂×Q₈	—	4	2	no	—
641	C₂×Q₈	—	4	1	no	—
642	C₂×Q₈	—	4	1	no	—
643	C₂×Q₈	—	4	2	no	—
644	C₂×D₄	—	2	4	no	—
645	C₂×D₄	—	2	4	no	—
646	C₂×D₄	—	2	4	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	4	1	no	—
649	C₂×D₄	—	4	1	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	4	1	no	—
661	C₂²×C₄	—	4	1	no	—
662	C₂²×C₄	—	4	1	no	—
663	C₂²×C₄	—	4	1	no	—
664	C₂²×C₄	—	4	1	no	—
665	C₂²×C₄	—	4	1	no	—
666	C₂²×C₄	—	4	1	no	—
667	C₂²×C₄	—	4	2	no	—
668	C₂²×C₄	—	4	2	no	—
669	C₂²×C₄	—	4	1	no	—
670	C₂²×C₄	—	4	1	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	—	4	1	no	—
673	C₂²×C₄	#41×C₄₁	1	4	yes	—
674	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₄⋊C₄	—	4	2	no	—
700	C₄⋊C₄	—	4	2	no	—
701	C₄⋊C₄	—	4	2	no	—
702	C₄⋊C₄	—	4	2	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	4	2	no	—
705	C₄⋊C₄	—	4	2	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₄⋊C₄	—	4	1	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	—	4	1	no	—
710	C₄⋊C₄	—	4	1	no	—
711	C₄⋊C₄	—	4	1	no	—
712	C₄⋊C₄	—	4	2	no	—
713	C₄⋊C₄	—	4	2	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	4	2	no	—
721	C₂²⋊C₄	—	4	2	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	—	4	2	no	—
724	C₂²⋊C₄	—	4	2	no	—
725	C₂²⋊C₄	—	4	2	no	—
726	C₂²⋊C₄	—	4	2	no	—
727	C₂²⋊C₄	—	4	2	no	—
728	C₂²⋊C₄	—	4	2	no	—
729	C₄²	—	2	2	no	—
730	C₄²	—	2	2	no	—
731	C₄²	—	4	1	no	—
732	C₄²	—	4	1	no	—
733	C₄²	—	4	2	no	—
734	C₄²	—	4	2	no	—
735	C₄²	—	4	2	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	1	no	—
739	C₂³	—	2	1	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	C₂×#41×C₄₁	1	2	yes	—
748	C₂³	H(5,𝔽₂)×C₄₁	1	2	yes	—
749	C₂³	2₋¹⁺⁴×C₄₁	1	2	yes	—
750	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
751	Q₈	—	8	2	no	—
752	Q₈	—	8	4	no	—
753	D₄	—	4	8	no	—
754	D₄	—	8	2	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	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	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	4	4	no	—
803	C₂×C₄	—	4	4	no	—
804	C₂×C₄	—	4	4	no	—
805	C₂×C₄	—	4	4	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	8	2	no	—
808	C₂×C₄	—	8	2	no	—
809	C₂×C₄	—	8	4	no	—
810	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
811	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
812	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
813	C₂×C₄	2₋¹⁺⁴×C₄₁	1	2	yes	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	2	no	—
827	C₂²	C₄₁×#542	1	4	yes	—
828	C₂²	C₂²×#41×C₄₁	1	1	yes	characteristic
829	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
830	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
831	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
832	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
833	C₂²	C₄₁×#585	1	1	yes	characteristic
834	C₂²	C₄₁×#585	1	1	yes	characteristic
835	C₄	—	2	2	no	—
836	C₄	—	2	2	no	—
837	C₄	—	2	2	no	—
838	C₄	—	2	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	2	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	1	no	—
852	C₂	—	2	4	no	—
853	C₂	—	8	2	no	—
854	C₂	C₂×C₄₁×#542	1	1	yes	characteristic
855	C₂	C₄₁×#3505	1	1	yes	characteristic
856	C₂	C₄₁×#3507	1	1	yes	characteristic
857	C₂	C₄₁×#3534	1	1	yes	characteristic
858	C₂	C₄₁×#3538	1	1	yes	characteristic
859	C₂	C₄₁×#3559	1	1	yes	characteristic
860	C₂	C₄₁×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₁
prime radical	C₂×#121×C₄₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#2857	C₂	semidirect
3. C₄₁×#2796	C₂	semidirect
4. C₄₁×#2793	C₂	semidirect
5. C₄₁×#2777	C₂	semidirect
6. C₄₁×#2765	C₂	semidirect
7. C₄₁×#2762	C₂	semidirect
8. C₄₁×#2755	C₂	semidirect
9. C₄₁×#2729	C₂	semidirect
10. C₄₁×#2700	C₂	semidirect
11. C₄₁×#2627	C₂	semidirect
13. C₄₁×#2510	C₂	semidirect
14. C₄₁×#2488	C₂	semidirect
15. C₄₁×#2449	C₂	semidirect
16. C₄₁×#2419	C₂	semidirect
17. C₄₁×#2329	C₂	semidirect
19. C₂×C₄₁×#387	C₂	semidirect
383. #36764	C₄₁	direct (N × H)
422. #2857	C₂×C₄₁	semidirect
424. #2796	C₂×C₄₁	semidirect
425. #2793	C₂×C₄₁	semidirect
426. #2777	C₂×C₄₁	semidirect
427. #2765	C₂×C₄₁	semidirect
428. #2762	C₂×C₄₁	semidirect
429. #2755	C₂×C₄₁	semidirect
430. #2729	C₂×C₄₁	semidirect
431. #2700	C₂×C₄₁	semidirect
432. #2627	C₂×C₄₁	semidirect
434. #2510	C₂×C₄₁	semidirect
435. #2488	C₂×C₄₁	semidirect
436. #2449	C₂×C₄₁	semidirect
437. #2419	C₂×C₄₁	semidirect
438. #2329	C₂×C₄₁	semidirect
440. C₂×#387	C₂×C₄₁	semidirect
537. C₄₁	#36764	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#2857	2
C₄₁×#2850	2
C₄₁×#2796	2
C₄₁×#2793	2
C₄₁×#2777	2
C₄₁×#2765	2
C₄₁×#2762	2
C₄₁×#2755	2
C₄₁×#2729	2
C₄₁×#2700	2
C₄₁×#2627	2
C₄₁×#2618	2
C₄₁×#2510	2
C₄₁×#2488	2
C₄₁×#2449	2
C₄₁×#2419	2
C₄₁×#2329	2
C₄₁×#2325	2
C₂×C₄₁×#387	2
#36764	41

Subgroups — C41×#36764 #23812965

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#36764 #23812965