Subgroups — C₄₁×#34597 #23810798

Order 10496.

1940 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2667	C₂	1	2	yes	maximal, complemented
2	C₄₁×#2661	C₂	1	2	yes	maximal, complemented
3	C₄₁×#2654	C₂	1	2	yes	maximal, complemented
4	C₄₁×#2651	C₂	1	2	yes	maximal, complemented
5	C₄₁×#2649	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2648	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2635	C₂	1	2	yes	maximal, complemented
8	C₄₁×#2630	C₂	1	2	yes	maximal, complemented
9	C₄₁×#2402	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#2397	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#2395	C₂	1	2	yes	maximal, complemented
12	C₄₁×#2392	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#2392	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#2392	C₂	1	2	yes	maximal, complemented
15	C₄×#123×C₄₁	C₂	1	2	yes	maximal, complemented
16	C₄×#121×C₄₁	C₂	1	2	yes	maximal, complemented
17	C₄₁×#2298	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄₁×#2293	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄²×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#123×C₄₁	C₂²	1	2	yes	—
21	C₂×#121×C₄₁	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
29	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×#117×C₄₁	C₂²	1	2	yes	—
31	C₂²×C₄²×C₄₁	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×#399	C₂²	1	2	yes	—
36	C₄₁×#399	C₂²	1	2	yes	—
37	C₄₁×#399	C₂²	1	2	yes	—
38	C₄₁×#398	C₂²	1	2	yes	—
39	C₄₁×#398	C₂²	1	1	yes	characteristic
40	C₄₁×#398	C₂²	1	2	yes	—
41	C₄₁×#398	C₂²	1	1	yes	characteristic
42	C₄₁×#398	C₂²	1	2	yes	—
43	C₄₁×#398	C₂²	1	2	yes	—
44	C₄₁×#397	C₂²	1	2	yes	—
45	C₄₁×#397	C₂²	1	2	yes	—
46	C₄₁×#397	C₂²	1	1	yes	characteristic
47	C₄₁×#397	C₂²	1	1	yes	characteristic
48	C₄₁×#397	C₂²	1	2	yes	—
49	C₄₁×#397	C₂²	1	2	yes	—
50	C₄₁×#396	C₂²	1	2	yes	—
51	C₄₁×#396	C₂²	1	2	yes	—
52	C₄₁×#396	C₂²	1	2	yes	—
53	C₄₁×#396	C₂²	1	2	yes	—
54	C₄₁×#394	C₂²	1	1	yes	characteristic
55	C₄₁×#394	C₂²	1	2	yes	—
56	C₄₁×#394	C₂²	1	2	yes	—
57	C₄₁×#394	C₂²	1	2	yes	—
58	C₄₁×#394	C₂²	1	2	yes	—
59	C₄₁×#394	C₂²	1	2	yes	—
60	C₄₁×#394	C₂²	1	1	yes	characteristic
61	C₄₁×#394	C₂²	1	2	yes	—
62	C₄₁×#394	C₂²	1	2	yes	—
63	C₄₁×#392	C₂²	1	2	yes	—
64	C₄₁×#392	C₂²	1	1	yes	characteristic
65	C₄₁×#392	C₂²	1	2	yes	—
66	C₄₁×#392	C₂²	1	1	yes	characteristic
67	C₄₁×#392	C₂²	1	2	yes	—
68	C₄₁×#390	C₂²	1	2	yes	—
69	C₄₁×#390	C₂²	1	2	yes	—
70	C₄₁×#389	C₂²	1	2	yes	—
71	C₄₁×#389	C₂²	1	2	yes	—
72	C₄₁×#388	C₂²	1	2	yes	—
73	C₄₁×#388	C₂²	1	2	yes	—
74	C₄₁×#388	C₂²	1	2	yes	—
75	C₄₁×#388	C₂²	1	2	yes	—
76	C₄₁×#388	C₂²	1	2	yes	—
77	C₄₁×#388	C₂²	1	2	yes	—
78	C₄₁×#388	C₂²	1	2	yes	—
79	C₄₁×#388	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×#387	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×#385	C₂²	1	2	yes	—
88	C₄₁×#381	C₂²	1	2	yes	—
89	C₄₁×#380	C₂²	1	2	yes	—
90	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
91	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
93	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
94	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
95	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
105	C₄₁×#376	C₂²	1	1	yes	characteristic
106	C₄³×C₄₁	C₂²	1	1	yes	characteristic
107	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
109	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
110	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
111	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
112	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
114	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
116	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
117	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
118	#123×C₄₁	—	2	8	no	—
119	#121×C₄₁	—	2	8	no	—
120	C₄×D₄×C₄₁	—	2	8	no	—
121	C₄×D₄×C₄₁	—	2	4	no	—
122	C₄×D₄×C₄₁	—	2	4	no	—
123	C₄×D₄×C₄₁	—	4	4	no	—
124	C₄×D₄×C₄₁	—	4	4	no	—
125	C₄×D₄×C₄₁	—	4	4	no	—
126	C₄×D₄×C₄₁	—	4	4	no	—
127	#117×C₄₁	—	2	4	no	—
128	#117×C₄₁	—	4	4	no	—
129	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
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	2	yes	—
146	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
151	C₂×C₂²⋊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×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
171	C₂×C₄²×C₄₁	—	4	4	no	—
172	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
173	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
175	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
177	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
181	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
182	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
183	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
184	#95×C₄₁	C₂³	1	2	yes	—
185	#95×C₄₁	C₂³	1	2	yes	—
186	#95×C₄₁	C₂³	1	1	yes	characteristic
187	#95×C₄₁	C₂³	1	2	yes	—
188	#95×C₄₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
205	#95×C₄₁	C₂³	1	1	yes	characteristic
206	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
207	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
208	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
209	C₂×D₄×C₄₁	—	2	4	no	—
210	C₂×D₄×C₄₁	—	2	4	no	—
211	C₂×D₄×C₄₁	—	2	4	no	—
212	C₂×D₄×C₄₁	—	2	4	no	—
213	C₂×D₄×C₄₁	—	2	2	no	—
214	C₂×D₄×C₄₁	—	2	2	no	—
215	C₂×D₄×C₄₁	—	2	4	no	—
216	C₂×D₄×C₄₁	—	4	2	no	—
217	C₂×D₄×C₄₁	—	4	2	no	—
218	C₂×D₄×C₄₁	—	4	2	no	—
219	C₂×D₄×C₄₁	—	4	2	no	—
220	C₂×D₄×C₄₁	—	4	2	no	—
221	C₂×D₄×C₄₁	—	4	2	no	—
222	C₂×D₄×C₄₁	—	4	2	no	—
223	C₂×D₄×C₄₁	—	4	2	no	—
224	C₂×D₄×C₄₁	—	4	2	no	—
225	C₂²×C₄×C₄₁	—	2	2	no	—
226	C₂²×C₄×C₄₁	—	2	4	no	—
227	C₂²×C₄×C₄₁	—	2	4	no	—
228	C₂²×C₄×C₄₁	—	2	4	no	—
229	C₂²×C₄×C₄₁	—	2	4	no	—
230	C₂²×C₄×C₄₁	—	2	4	no	—
231	C₂²×C₄×C₄₁	—	2	4	no	—
232	C₂²×C₄×C₄₁	—	2	2	no	—
233	C₂²×C₄×C₄₁	—	2	4	no	—
234	C₂²×C₄×C₄₁	—	2	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	—	4	2	no	—
239	C₂²×C₄×C₄₁	#41	1	8	yes	—
240	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
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	1	yes	characteristic
251	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
256	C₄⋊C₄×C₄₁	—	2	2	no	—
257	C₄⋊C₄×C₄₁	—	2	2	no	—
258	C₄⋊C₄×C₄₁	—	2	4	no	—
259	C₄⋊C₄×C₄₁	—	2	2	no	—
260	C₄⋊C₄×C₄₁	—	2	2	no	—
261	C₄⋊C₄×C₄₁	—	2	4	no	—
262	C₄⋊C₄×C₄₁	—	2	4	no	—
263	C₄⋊C₄×C₄₁	—	2	4	no	—
264	C₄⋊C₄×C₄₁	—	4	2	no	—
265	C₄⋊C₄×C₄₁	—	4	2	no	—
266	C₄⋊C₄×C₄₁	—	4	2	no	—
267	C₄⋊C₄×C₄₁	—	4	2	no	—
268	C₄⋊C₄×C₄₁	—	4	2	no	—
269	C₄⋊C₄×C₄₁	—	4	2	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	C₂²⋊C₄×C₄₁	—	2	4	no	—
275	C₂²⋊C₄×C₄₁	—	2	4	no	—
276	C₂²⋊C₄×C₄₁	—	2	2	no	—
277	C₂²⋊C₄×C₄₁	—	2	2	no	—
278	C₂²⋊C₄×C₄₁	—	2	4	no	—
279	C₂²⋊C₄×C₄₁	—	2	4	no	—
280	C₂²⋊C₄×C₄₁	—	2	4	no	—
281	C₂²⋊C₄×C₄₁	—	2	4	no	—
282	C₂²⋊C₄×C₄₁	—	2	4	no	—
283	C₂²⋊C₄×C₄₁	—	2	4	no	—
284	C₂²⋊C₄×C₄₁	—	2	4	no	—
285	C₂²⋊C₄×C₄₁	—	4	2	no	—
286	C₂²⋊C₄×C₄₁	—	4	2	no	—
287	C₂²⋊C₄×C₄₁	—	4	2	no	—
288	C₂²⋊C₄×C₄₁	—	4	2	no	—
289	C₂²⋊C₄×C₄₁	—	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	4	no	—
300	C₄²×C₄₁	—	2	2	no	—
301	C₄²×C₄₁	—	2	4	no	—
302	C₄²×C₄₁	—	2	2	no	—
303	C₄²×C₄₁	—	2	4	no	—
304	C₄²×C₄₁	—	2	2	no	—
305	C₄²×C₄₁	—	2	2	no	—
306	C₄²×C₄₁	—	4	2	no	—
307	C₄²×C₄₁	—	4	2	no	—
308	C₄²×C₄₁	—	4	2	no	—
309	C₄²×C₄₁	#41	1	4	yes	—
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	—	2	1	no	—
317	C₂³×C₄₁	—	2	2	no	—
318	C₂³×C₄₁	—	2	2	no	—
319	C₂³×C₄₁	—	2	2	no	—
320	C₂³×C₄₁	—	2	2	no	—
321	C₂³×C₄₁	—	2	2	no	—
322	C₂³×C₄₁	—	2	1	no	—
323	C₂³×C₄₁	—	2	2	no	—
324	C₂³×C₄₁	—	2	1	no	—
325	C₂³×C₄₁	—	2	2	no	—
326	C₂³×C₄₁	—	2	2	no	—
327	C₂³×C₄₁	—	2	2	no	—
328	C₂³×C₄₁	C₂×#41	1	4	yes	—
329	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
330	D₄×C₄₁	—	2	8	no	—
331	D₄×C₄₁	—	4	4	no	—
332	D₄×C₄₁	—	4	8	no	—
333	D₄×C₄₁	—	4	8	no	—
334	D₄×C₄₁	—	4	8	no	—
335	D₄×C₄₁	—	4	8	no	—
336	C₂×C₄×C₄₁	—	2	2	no	—
337	C₂×C₄×C₄₁	—	2	2	no	—
338	C₂×C₄×C₄₁	—	2	2	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	1	no	—
344	C₂×C₄×C₄₁	—	2	1	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	2	no	—
351	C₂×C₄×C₄₁	—	2	2	no	—
352	C₂×C₄×C₄₁	—	2	1	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	2	no	—
357	C₂×C₄×C₄₁	—	2	2	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	1	no	—
363	C₂×C₄×C₄₁	—	2	2	no	—
364	C₂×C₄×C₄₁	—	2	1	no	—
365	C₂×C₄×C₄₁	—	2	2	no	—
366	C₂×C₄×C₄₁	—	2	2	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	—	2	2	no	—
372	C₂×C₄×C₄₁	—	2	2	no	—
373	C₂×C₄×C₄₁	—	4	8	no	—
374	C₂×C₄×C₄₁	—	4	8	no	—
375	C₂×C₄×C₄₁	—	4	8	no	—
376	C₂×C₄×C₄₁	—	4	4	no	—
377	C₂×C₄×C₄₁	—	4	8	no	—
378	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
379	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
380	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
381	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
382	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
383	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
384	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
385	#34597	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
386	C₂²×C₄₁	—	2	4	no	—
387	C₂²×C₄₁	—	2	4	no	—
388	C₂²×C₄₁	—	2	4	no	—
389	C₂²×C₄₁	—	4	2	no	—
390	C₂²×C₄₁	—	4	2	no	—
391	C₂²×C₄₁	—	4	2	no	—
392	C₂²×C₄₁	—	4	2	no	—
393	C₂²×C₄₁	—	4	1	no	—
394	C₂²×C₄₁	—	4	2	no	—
395	C₂²×C₄₁	—	4	1	no	—
396	C₂²×C₄₁	—	4	2	no	—
397	C₂²×C₄₁	—	4	2	no	—
398	C₂²×C₄₁	—	4	1	no	—
399	C₂²×C₄₁	—	4	2	no	—
400	C₂²×C₄₁	—	4	2	no	—
401	C₂²×C₄₁	—	4	2	no	—
402	C₂²×C₄₁	—	4	2	no	—
403	C₂²×C₄₁	—	4	2	no	—
404	C₂²×C₄₁	—	4	2	no	—
405	C₂²×C₄₁	C₂²×#41	1	1	yes	characteristic
406	C₂²×C₄₁	C₂²×#41	1	2	yes	—
407	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
408	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
409	C₂²×C₄₁	#585	1	2	yes	—
410	C₄×C₄₁	—	2	2	no	—
411	C₄×C₄₁	—	2	2	no	—
412	C₄×C₄₁	—	2	4	no	—
413	C₄×C₄₁	—	2	4	no	—
414	C₄×C₄₁	—	4	1	no	—
415	C₄×C₄₁	—	4	2	no	—
416	C₄×C₄₁	—	4	2	no	—
417	C₄×C₄₁	—	4	1	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	C₄×C₄₁	—	4	2	no	—
423	C₄×C₄₁	—	4	2	no	—
424	C₄×C₄₁	—	4	2	no	—
425	C₄×C₄₁	#540	1	4	yes	—
426	#2667	C₂×C₄₁	1	2	yes	complemented
427	#2661	C₂×C₄₁	1	2	yes	complemented
428	#2654	C₂×C₄₁	1	2	yes	complemented
429	#2651	C₂×C₄₁	1	2	yes	complemented
430	#2649	C₂×C₄₁	1	2	yes	complemented
431	#2648	C₂×C₄₁	1	2	yes	complemented
432	#2635	C₂×C₄₁	1	2	yes	complemented
433	#2630	C₂×C₄₁	1	2	yes	complemented
434	#2402	C₂×C₄₁	1	1	yes	characteristic, complemented
435	#2397	C₂×C₄₁	1	1	yes	characteristic, complemented
436	#2395	C₂×C₄₁	1	2	yes	complemented
437	#2392	C₂×C₄₁	1	1	yes	characteristic, complemented
438	#2392	C₂×C₄₁	1	1	yes	characteristic, complemented
439	#2392	C₂×C₄₁	1	2	yes	complemented
440	C₄×#123	C₂×C₄₁	1	2	yes	complemented
441	C₄×#121	C₂×C₄₁	1	2	yes	complemented
442	#2298	C₂×C₄₁	1	1	yes	characteristic, complemented
443	#2293	C₂×C₄₁	1	1	yes	characteristic, complemented
444	C₄²×D₄	C₂×C₄₁	1	1	yes	characteristic, complemented
445	C₂×C₄₁	—	4	4	no	—
446	C₂×C₄₁	—	8	2	no	—
447	C₂×C₄₁	—	8	1	no	—
448	C₂×C₄₁	#3444	1	1	yes	characteristic
449	C₂×C₄₁	C₂×#540	1	1	yes	characteristic
450	C₂×C₄₁	#3455	1	1	yes	characteristic
451	C₂×C₄₁	#3459	1	2	yes	—
452	C₂×C₄₁	#3460	1	2	yes	—
453	C₂×#123	C₂²×C₄₁	1	2	yes	—
454	C₂×#121	C₂²×C₄₁	1	2	yes	—
455	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
456	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
457	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
458	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
459	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
460	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
461	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
462	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
463	C₂×#117	C₂²×C₄₁	1	2	yes	—
464	C₂²×C₄²	C₂²×C₄₁	1	2	yes	—
465	#400	C₂²×C₄₁	1	2	yes	—
466	#400	C₂²×C₄₁	1	2	yes	—
467	#400	C₂²×C₄₁	1	2	yes	—
468	#399	C₂²×C₄₁	1	2	yes	—
469	#399	C₂²×C₄₁	1	2	yes	—
470	#399	C₂²×C₄₁	1	2	yes	—
471	#398	C₂²×C₄₁	1	2	yes	—
472	#398	C₂²×C₄₁	1	1	yes	characteristic
473	#398	C₂²×C₄₁	1	2	yes	—
474	#398	C₂²×C₄₁	1	1	yes	characteristic
475	#398	C₂²×C₄₁	1	2	yes	—
476	#398	C₂²×C₄₁	1	2	yes	—
477	#397	C₂²×C₄₁	1	2	yes	—
478	#397	C₂²×C₄₁	1	2	yes	—
479	#397	C₂²×C₄₁	1	1	yes	characteristic
480	#397	C₂²×C₄₁	1	1	yes	characteristic
481	#397	C₂²×C₄₁	1	2	yes	—
482	#397	C₂²×C₄₁	1	2	yes	—
483	#396	C₂²×C₄₁	1	2	yes	—
484	#396	C₂²×C₄₁	1	2	yes	—
485	#396	C₂²×C₄₁	1	2	yes	—
486	#396	C₂²×C₄₁	1	2	yes	—
487	#394	C₂²×C₄₁	1	1	yes	characteristic
488	#394	C₂²×C₄₁	1	2	yes	—
489	#394	C₂²×C₄₁	1	2	yes	—
490	#394	C₂²×C₄₁	1	2	yes	—
491	#394	C₂²×C₄₁	1	2	yes	—
492	#394	C₂²×C₄₁	1	2	yes	—
493	#394	C₂²×C₄₁	1	1	yes	characteristic
494	#394	C₂²×C₄₁	1	2	yes	—
495	#394	C₂²×C₄₁	1	2	yes	—
496	#392	C₂²×C₄₁	1	2	yes	—
497	#392	C₂²×C₄₁	1	1	yes	characteristic
498	#392	C₂²×C₄₁	1	2	yes	—
499	#392	C₂²×C₄₁	1	1	yes	characteristic
500	#392	C₂²×C₄₁	1	2	yes	—
501	#390	C₂²×C₄₁	1	2	yes	—
502	#390	C₂²×C₄₁	1	2	yes	—
503	#389	C₂²×C₄₁	1	2	yes	—
504	#389	C₂²×C₄₁	1	2	yes	—
505	#388	C₂²×C₄₁	1	2	yes	—
506	#388	C₂²×C₄₁	1	2	yes	—
507	#388	C₂²×C₄₁	1	2	yes	—
508	#388	C₂²×C₄₁	1	2	yes	—
509	#388	C₂²×C₄₁	1	2	yes	—
510	#388	C₂²×C₄₁	1	2	yes	—
511	#388	C₂²×C₄₁	1	2	yes	—
512	#388	C₂²×C₄₁	1	2	yes	—
513	#387	C₂²×C₄₁	1	2	yes	—
514	#387	C₂²×C₄₁	1	2	yes	—
515	#387	C₂²×C₄₁	1	2	yes	—
516	#387	C₂²×C₄₁	1	2	yes	—
517	#386	C₂²×C₄₁	1	2	yes	—
518	#386	C₂²×C₄₁	1	2	yes	—
519	#386	C₂²×C₄₁	1	2	yes	—
520	#385	C₂²×C₄₁	1	2	yes	—
521	#381	C₂²×C₄₁	1	2	yes	—
522	#380	C₂²×C₄₁	1	2	yes	—
523	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
524	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
525	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
526	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
527	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
528	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
529	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
530	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
531	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
532	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
533	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
534	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
535	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
536	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
537	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
538	#376	C₂²×C₄₁	1	1	yes	characteristic
539	C₄³	C₂²×C₄₁	1	1	yes	characteristic
540	C₄₁	#34597	1	1	yes	characteristic, direct product factor, Sylow
541	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
542	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
543	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
544	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
545	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
546	C₂²×D₄	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	2	yes	—
550	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
551	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
552	#123	—	2	8	no	—
553	#121	—	2	8	no	—
554	C₄×D₄	—	2	8	no	—
555	C₄×D₄	—	2	4	no	—
556	C₄×D₄	—	2	4	no	—
557	C₄×D₄	—	4	4	no	—
558	C₄×D₄	—	4	4	no	—
559	C₄×D₄	—	4	4	no	—
560	C₄×D₄	—	4	4	no	—
561	#117	—	2	4	no	—
562	#117	—	4	4	no	—
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	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
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	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
582	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
605	C₂×C₄²	—	4	4	no	—
606	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
608	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
609	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
610	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
611	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
612	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
613	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
615	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
616	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
617	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
618	#95	C₂³×C₄₁	1	2	yes	—
619	#95	C₂³×C₄₁	1	2	yes	—
620	#95	C₂³×C₄₁	1	1	yes	characteristic
621	#95	C₂³×C₄₁	1	2	yes	—
622	#95	C₂³×C₄₁	1	1	yes	characteristic
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	#95	C₂³×C₄₁	1	2	yes	—
637	#95	C₂³×C₄₁	1	2	yes	—
638	#95	C₂³×C₄₁	1	1	yes	characteristic
639	#95	C₂³×C₄₁	1	1	yes	characteristic
640	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
641	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
642	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
643	C₂×D₄	—	2	4	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	—	2	2	no	—
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	4	2	no	—
651	C₂×D₄	—	4	2	no	—
652	C₂×D₄	—	4	2	no	—
653	C₂×D₄	—	4	2	no	—
654	C₂×D₄	—	4	2	no	—
655	C₂×D₄	—	4	2	no	—
656	C₂×D₄	—	4	2	no	—
657	C₂×D₄	—	4	2	no	—
658	C₂×D₄	—	4	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	2	4	no	—
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	4	2	no	—
670	C₂²×C₄	—	4	2	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	#41×C₄₁	1	8	yes	—
674	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
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	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	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	2	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	2	no	—
711	C₂²⋊C₄	—	2	2	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	4	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	—	4	2	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	C₂²⋊C₄	—	4	2	no	—
730	C₂²⋊C₄	—	4	2	no	—
731	C₂²⋊C₄	—	4	2	no	—
732	C₄²	—	2	2	no	—
733	C₄²	—	2	4	no	—
734	C₄²	—	2	2	no	—
735	C₄²	—	2	4	no	—
736	C₄²	—	2	2	no	—
737	C₄²	—	2	4	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	2	no	—
740	C₄²	—	4	2	no	—
741	C₄²	—	4	2	no	—
742	C₄²	—	4	2	no	—
743	C₄²	#41×C₄₁	1	4	yes	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	1	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	1	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	1	no	—
759	C₂³	—	2	2	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	C₂×#41×C₄₁	1	4	yes	—
763	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
764	D₄	—	2	8	no	—
765	D₄	—	4	4	no	—
766	D₄	—	4	8	no	—
767	D₄	—	4	8	no	—
768	D₄	—	4	8	no	—
769	D₄	—	4	8	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	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	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	1	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	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	1	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	4	8	no	—
808	C₂×C₄	—	4	8	no	—
809	C₂×C₄	—	4	8	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	4	8	no	—
812	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
813	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
814	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
815	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
816	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
817	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
818	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
819	C₂²	—	2	4	no	—
820	C₂²	—	2	4	no	—
821	C₂²	—	2	4	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	C₂²×#41×C₄₁	1	1	yes	characteristic
839	C₂²	C₂²×#41×C₄₁	1	2	yes	—
840	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
841	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
842	C₂²	C₄₁×#585	1	2	yes	—
843	C₄	—	2	2	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	4	no	—
846	C₄	—	2	4	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₄	C₄₁×#540	1	4	yes	—
859	C₂	—	4	4	no	—
860	C₂	—	8	2	no	—
861	C₂	—	8	1	no	—
862	C₂	C₄₁×#3444	1	1	yes	characteristic
863	C₂	C₂×C₄₁×#540	1	1	yes	characteristic
864	C₂	C₄₁×#3455	1	1	yes	characteristic
865	C₂	C₄₁×#3459	1	2	yes	—
866	C₂	C₄₁×#3460	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₁
socle	C₂³×C₄₁	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#2667	C₂	semidirect
2. C₄₁×#2661	C₂	semidirect
3. C₄₁×#2654	C₂	semidirect
4. C₄₁×#2651	C₂	semidirect
5. C₄₁×#2649	C₂	semidirect
6. C₄₁×#2648	C₂	semidirect
7. C₄₁×#2635	C₂	semidirect
8. C₄₁×#2630	C₂	semidirect
9. C₄₁×#2402	C₂	semidirect
10. C₄₁×#2397	C₂	semidirect
11. C₄₁×#2395	C₂	semidirect
12. C₄₁×#2392	C₂	semidirect
13. C₄₁×#2392	C₂	semidirect
14. C₄₁×#2392	C₂	semidirect
15. C₄×#123×C₄₁	C₂	semidirect
16. C₄×#121×C₄₁	C₂	semidirect
17. C₄₁×#2298	C₂	semidirect
18. C₄₁×#2293	C₂	semidirect
19. C₄²×D₄×C₄₁	C₂	semidirect
385. #34597	C₄₁	direct (N × H)
426. #2667	C₂×C₄₁	semidirect
427. #2661	C₂×C₄₁	semidirect
428. #2654	C₂×C₄₁	semidirect
429. #2651	C₂×C₄₁	semidirect
430. #2649	C₂×C₄₁	semidirect
431. #2648	C₂×C₄₁	semidirect
432. #2635	C₂×C₄₁	semidirect
433. #2630	C₂×C₄₁	semidirect
434. #2402	C₂×C₄₁	semidirect
435. #2397	C₂×C₄₁	semidirect
436. #2395	C₂×C₄₁	semidirect
437. #2392	C₂×C₄₁	semidirect
438. #2392	C₂×C₄₁	semidirect
439. #2392	C₂×C₄₁	semidirect
440. C₄×#123	C₂×C₄₁	semidirect
441. C₄×#121	C₂×C₄₁	semidirect
442. #2298	C₂×C₄₁	semidirect
443. #2293	C₂×C₄₁	semidirect
444. C₄²×D₄	C₂×C₄₁	semidirect
540. C₄₁	#34597	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×#2667	2
C₄₁×#2661	2
C₄₁×#2654	2
C₄₁×#2651	2
C₄₁×#2649	2
C₄₁×#2648	2
C₄₁×#2635	2
C₄₁×#2630	2
C₄₁×#2402	2
C₄₁×#2397	2
C₄₁×#2395	2
C₄₁×#2392	2
C₄×#123×C₄₁	2
C₄×#121×C₄₁	2
C₄₁×#2298	2
C₄₁×#2293	2
C₄²×D₄×C₄₁	2
#34597	41

Subgroups — C41×#34597 #23810798

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#34597 #23810798