Subgroups — C₄₁×#24365 #23800566

Order 10496.

1454 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	C₂²×#135×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#463	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#461	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#452	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2432	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2339	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#2016	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#2015	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1892	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#1879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#1877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#1850	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#1788	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#135×C₄₁	—	2	4	no	—
19	C₂×#135×C₄₁	—	2	4	no	—
20	C₂×#135×C₄₁	—	2	4	no	—
21	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
22	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
23	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
24	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
25	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
26	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
27	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
33	C₄₁×#463	—	2	4	no	—
34	C₄₁×#461	—	2	4	no	—
35	C₄₁×#452	—	2	4	no	—
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×#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×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
47	C₄₁×#394	—	2	1	no	—
48	C₄₁×#394	—	2	1	no	—
49	C₄₁×#391	C₂²	1	1	yes	characteristic
50	C₄₁×#391	C₂²	1	1	yes	characteristic
51	C₄₁×#391	C₂²	1	1	yes	characteristic
52	C₄₁×#390	C₂²	1	1	yes	characteristic
53	C₄₁×#386	—	2	1	no	—
54	C₄₁×#386	—	2	1	no	—
55	C₄₁×#385	—	2	1	no	—
56	C₄₁×#385	—	2	1	no	—
57	C₄₁×#381	—	2	1	no	—
58	C₄₁×#380	C₂²	1	1	yes	characteristic
59	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
60	C₂×#95×C₄₁	—	2	1	no	—
61	C₄₁×#340	C₂²	1	1	yes	characteristic
62	C₄₁×#340	C₂²	1	1	yes	characteristic
63	C₄₁×#336	C₂²	1	1	yes	characteristic
64	C₄₁×#336	C₂²	1	1	yes	characteristic
65	C₂×#41×C₄₁	—	2	2	no	—
66	C₂×#41×C₄₁	—	2	2	no	—
67	C₂×#41×C₄₁	—	2	2	no	—
68	C₂×#41×C₄₁	—	2	2	no	—
69	C₂×#41×C₄₁	—	2	2	no	—
70	C₂×#41×C₄₁	—	2	2	no	—
71	C₂×#41×C₄₁	—	2	2	no	—
72	C₂×#41×C₄₁	—	4	1	no	—
73	C₂×#41×C₄₁	—	4	1	no	—
74	C₂×#41×C₄₁	—	4	1	no	—
75	C₂×#41×C₄₁	—	4	1	no	—
76	C₂×#41×C₄₁	D₄	1	4	yes	—
77	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₄₁	—	2	1	no	—
81	C₂²×D₄×C₄₁	—	2	1	no	—
82	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₄₁	—	2	1	no	—
85	C₂³×C₄×C₄₁	—	2	1	no	—
86	C₂³×C₄×C₄₁	—	2	1	no	—
87	C₂³×C₄×C₄₁	—	2	1	no	—
88	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
89	#135×C₄₁	—	2	32	no	—
90	C₂×Q₁₆×C₄₁	—	2	2	no	—
91	C₂×Q₁₆×C₄₁	—	2	2	no	—
92	C₂×Q₁₆×C₄₁	—	2	2	no	—
93	C₂×Q₁₆×C₄₁	—	2	2	no	—
94	C₂×Q₁₆×C₄₁	—	4	1	no	—
95	C₂×Q₁₆×C₄₁	—	4	1	no	—
96	C₂×SD₁₆×C₄₁	—	2	2	no	—
97	C₂×SD₁₆×C₄₁	—	2	2	no	—
98	C₂×SD₁₆×C₄₁	—	2	2	no	—
99	C₂×SD₁₆×C₄₁	—	2	2	no	—
100	C₂×SD₁₆×C₄₁	—	2	2	no	—
101	C₂×SD₁₆×C₄₁	—	2	2	no	—
102	C₂×SD₁₆×C₄₁	—	2	2	no	—
103	C₂×SD₁₆×C₄₁	—	2	2	no	—
104	C₂×SD₁₆×C₄₁	D₄	1	4	yes	—
105	C₂×D₈×C₄₁	—	2	2	no	—
106	C₂×D₈×C₄₁	—	2	2	no	—
107	C₂×D₈×C₄₁	D₄	1	4	yes	—
108	C₂²×C₈×C₄₁	—	2	2	no	—
109	C₂²×C₈×C₄₁	—	2	2	no	—
110	C₂²×C₈×C₄₁	—	2	2	no	—
111	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₄₁	—	2	2	no	—
116	C₄⋊Q₈×C₄₁	—	4	1	no	—
117	#124×C₄₁	—	2	2	no	—
118	#124×C₄₁	—	4	1	no	—
119	C₂²⋊Q₈×C₄₁	—	2	2	no	—
120	C₂²⋊Q₈×C₄₁	—	2	2	no	—
121	C₄×D₄×C₄₁	—	2	2	no	—
122	C₄×D₄×C₄₁	—	2	2	no	—
123	C₄×D₄×C₄₁	—	4	1	no	—
124	C₄×D₄×C₄₁	—	4	1	no	—
125	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
126	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
127	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
128	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
133	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
134	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
135	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
136	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
137	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
138	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
139	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
140	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
141	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
143	C₄⋊C₈×C₄₁	—	2	2	no	—
144	C₄⋊C₈×C₄₁	—	2	2	no	—
145	#103×C₄₁	—	2	2	no	—
146	#103×C₄₁	—	2	2	no	—
147	#103×C₄₁	—	2	2	no	—
148	#103×C₄₁	—	2	2	no	—
149	#103×C₄₁	—	4	1	no	—
150	#102×C₄₁	—	2	2	no	—
151	#102×C₄₁	—	2	2	no	—
152	#102×C₄₁	—	4	1	no	—
153	C₂²⋊C₈×C₄₁	—	2	2	no	—
154	#95×C₄₁	—	2	1	no	—
155	#95×C₄₁	—	2	1	no	—
156	#95×C₄₁	—	2	1	no	—
157	#95×C₄₁	—	2	1	no	—
158	#95×C₄₁	—	2	1	no	—
159	#95×C₄₁	—	2	1	no	—
160	#95×C₄₁	—	2	1	no	—
161	#95×C₄₁	D₄	1	1	yes	characteristic
162	#95×C₄₁	D₄	1	1	yes	characteristic
163	C₂⁴×C₄₁	—	2	1	no	—
164	C₂⁴×C₄₁	—	2	1	no	—
165	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
166	#41×C₄₁	—	2	8	no	—
167	#41×C₄₁	—	2	8	no	—
168	#41×C₄₁	—	4	4	no	—
169	#41×C₄₁	—	4	4	no	—
170	#41×C₄₁	—	4	4	no	—
171	#41×C₄₁	—	4	4	no	—
172	#41×C₄₁	—	4	4	no	—
173	#41×C₄₁	—	4	4	no	—
174	C₂×Q₈×C₄₁	—	2	1	no	—
175	C₂×Q₈×C₄₁	—	2	1	no	—
176	C₂×Q₈×C₄₁	—	2	1	no	—
177	C₂×Q₈×C₄₁	—	2	1	no	—
178	C₂×Q₈×C₄₁	—	2	1	no	—
179	C₂×Q₈×C₄₁	—	2	1	no	—
180	C₂×Q₈×C₄₁	—	2	1	no	—
181	C₂×Q₈×C₄₁	—	2	1	no	—
182	C₂×Q₈×C₄₁	—	2	1	no	—
183	C₂×Q₈×C₄₁	—	2	1	no	—
184	C₂×Q₈×C₄₁	—	2	1	no	—
185	C₂×Q₈×C₄₁	—	2	1	no	—
186	C₂×Q₈×C₄₁	—	2	1	no	—
187	C₂×Q₈×C₄₁	—	2	1	no	—
188	C₂×Q₈×C₄₁	—	2	1	no	—
189	C₂×Q₈×C₄₁	—	2	1	no	—
190	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
191	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
192	C₂×D₄×C₄₁	—	2	4	no	—
193	C₂×D₄×C₄₁	—	2	1	no	—
194	C₂×D₄×C₄₁	—	2	1	no	—
195	C₂×D₄×C₄₁	—	2	1	no	—
196	C₂×D₄×C₄₁	—	2	1	no	—
197	C₂×D₄×C₄₁	—	2	1	no	—
198	C₂×D₄×C₄₁	—	2	1	no	—
199	C₂×D₄×C₄₁	—	2	1	no	—
200	C₂×D₄×C₄₁	—	2	1	no	—
201	C₂×D₄×C₄₁	—	4	2	no	—
202	C₂×D₄×C₄₁	—	4	2	no	—
203	C₂×D₄×C₄₁	—	4	2	no	—
204	C₂×D₄×C₄₁	—	4	2	no	—
205	C₂×D₄×C₄₁	—	4	2	no	—
206	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
207	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
208	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
209	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
215	C₂²×C₄×C₄₁	—	2	1	no	—
216	C₂²×C₄×C₄₁	—	2	4	no	—
217	C₂²×C₄×C₄₁	—	2	1	no	—
218	C₂²×C₄×C₄₁	—	2	1	no	—
219	C₂²×C₄×C₄₁	—	2	1	no	—
220	C₂²×C₄×C₄₁	—	2	1	no	—
221	C₂²×C₄×C₄₁	—	4	2	no	—
222	C₂²×C₄×C₄₁	—	4	2	no	—
223	C₂²×C₄×C₄₁	—	4	2	no	—
224	C₂²×C₄×C₄₁	—	4	2	no	—
225	C₂²×C₄×C₄₁	—	4	2	no	—
226	C₂²×C₄×C₄₁	—	4	2	no	—
227	C₂²×C₄×C₄₁	—	4	2	no	—
228	C₂²×C₄×C₄₁	—	4	2	no	—
229	C₂²×C₄×C₄₁	—	4	2	no	—
230	C₂²×C₄×C₄₁	—	8	1	no	—
231	C₂²×C₄×C₄₁	—	8	1	no	—
232	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
237	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₄₁	#41	1	2	yes	—
239	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
240	Q₁₆×C₄₁	—	2	8	no	—
241	Q₁₆×C₄₁	—	4	4	no	—
242	SD₁₆×C₄₁	—	2	8	no	—
243	SD₁₆×C₄₁	—	2	8	no	—
244	SD₁₆×C₄₁	—	4	4	no	—
245	D₈×C₄₁	—	2	8	no	—
246	C₂×C₈×C₄₁	—	2	8	no	—
247	C₂×C₈×C₄₁	—	2	1	no	—
248	C₂×C₈×C₄₁	—	2	1	no	—
249	C₂×C₈×C₄₁	—	2	1	no	—
250	C₂×C₈×C₄₁	—	2	1	no	—
251	C₂×C₈×C₄₁	—	2	1	no	—
252	C₂×C₈×C₄₁	—	2	1	no	—
253	C₂×C₈×C₄₁	—	2	1	no	—
254	C₂×C₈×C₄₁	—	2	1	no	—
255	C₂×C₈×C₄₁	—	2	1	no	—
256	C₂×C₈×C₄₁	—	2	1	no	—
257	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
258	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
259	C₄⋊C₄×C₄₁	—	2	1	no	—
260	C₄⋊C₄×C₄₁	—	2	1	no	—
261	C₄⋊C₄×C₄₁	—	2	1	no	—
262	C₄⋊C₄×C₄₁	—	2	1	no	—
263	C₄⋊C₄×C₄₁	—	2	1	no	—
264	C₄⋊C₄×C₄₁	—	2	1	no	—
265	C₄⋊C₄×C₄₁	—	4	2	no	—
266	C₄⋊C₄×C₄₁	—	4	2	no	—
267	C₄⋊C₄×C₄₁	—	4	2	no	—
268	C₂²⋊C₄×C₄₁	—	2	2	no	—
269	C₂²⋊C₄×C₄₁	—	4	1	no	—
270	C₂²⋊C₄×C₄₁	—	4	2	no	—
271	C₂²⋊C₄×C₄₁	—	4	2	no	—
272	C₂²⋊C₄×C₄₁	—	4	2	no	—
273	C₂²⋊C₄×C₄₁	—	4	2	no	—
274	C₂²⋊C₄×C₄₁	—	4	2	no	—
275	C₂²⋊C₄×C₄₁	—	4	2	no	—
276	C₂²⋊C₄×C₄₁	—	4	2	no	—
277	C₂²⋊C₄×C₄₁	—	8	1	no	—
278	C₄²×C₄₁	—	2	1	no	—
279	C₄²×C₄₁	—	2	1	no	—
280	C₄²×C₄₁	—	2	1	no	—
281	C₄²×C₄₁	—	2	1	no	—
282	C₂³×C₄₁	—	2	2	no	—
283	C₂³×C₄₁	—	2	2	no	—
284	C₂³×C₄₁	—	2	2	no	—
285	C₂³×C₄₁	—	2	1	no	—
286	C₂³×C₄₁	—	2	1	no	—
287	C₂³×C₄₁	—	2	1	no	—
288	C₂³×C₄₁	—	2	1	no	—
289	C₂³×C₄₁	—	2	1	no	—
290	C₂³×C₄₁	—	2	1	no	—
291	C₂³×C₄₁	—	2	2	no	—
292	C₂³×C₄₁	—	4	1	no	—
293	C₂³×C₄₁	—	4	1	no	—
294	C₂³×C₄₁	—	4	1	no	—
295	C₂³×C₄₁	—	4	1	no	—
296	C₂³×C₄₁	—	4	1	no	—
297	C₂³×C₄₁	—	4	1	no	—
298	C₂³×C₄₁	—	4	1	no	—
299	C₂³×C₄₁	—	4	1	no	—
300	C₂³×C₄₁	—	4	1	no	—
301	C₂³×C₄₁	—	4	1	no	—
302	C₂³×C₄₁	#121	1	2	yes	—
303	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
304	Q₈×C₄₁	—	2	2	no	—
305	Q₈×C₄₁	—	2	2	no	—
306	Q₈×C₄₁	—	2	2	no	—
307	Q₈×C₄₁	—	2	2	no	—
308	Q₈×C₄₁	—	4	1	no	—
309	Q₈×C₄₁	—	4	1	no	—
310	Q₈×C₄₁	—	4	1	no	—
311	Q₈×C₄₁	—	4	1	no	—
312	Q₈×C₄₁	—	4	1	no	—
313	Q₈×C₄₁	—	4	1	no	—
314	Q₈×C₄₁	—	4	1	no	—
315	Q₈×C₄₁	—	4	1	no	—
316	D₄×C₄₁	—	2	2	no	—
317	D₄×C₄₁	—	2	2	no	—
318	D₄×C₄₁	—	2	2	no	—
319	D₄×C₄₁	—	2	2	no	—
320	D₄×C₄₁	—	2	2	no	—
321	D₄×C₄₁	—	4	8	no	—
322	D₄×C₄₁	—	4	8	no	—
323	D₄×C₄₁	—	4	1	no	—
324	D₄×C₄₁	—	4	1	no	—
325	D₄×C₄₁	#120	1	4	yes	—
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	2	no	—
331	C₂×C₄×C₄₁	—	2	2	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	1	no	—
336	C₂×C₄×C₄₁	—	2	1	no	—
337	C₂×C₄×C₄₁	—	2	1	no	—
338	C₂×C₄×C₄₁	—	2	2	no	—
339	C₂×C₄×C₄₁	—	2	1	no	—
340	C₂×C₄×C₄₁	—	2	1	no	—
341	C₂×C₄×C₄₁	—	2	1	no	—
342	C₂×C₄×C₄₁	—	2	1	no	—
343	C₂×C₄×C₄₁	—	2	1	no	—
344	C₂×C₄×C₄₁	—	2	1	no	—
345	C₂×C₄×C₄₁	—	4	8	no	—
346	C₂×C₄×C₄₁	—	4	8	no	—
347	C₂×C₄×C₄₁	—	4	1	no	—
348	C₂×C₄×C₄₁	—	4	1	no	—
349	C₂×C₄×C₄₁	—	4	1	no	—
350	C₂×C₄×C₄₁	—	4	1	no	—
351	C₂×C₄×C₄₁	—	4	1	no	—
352	C₂×C₄×C₄₁	—	4	1	no	—
353	C₂×C₄×C₄₁	—	4	1	no	—
354	C₂×C₄×C₄₁	—	4	1	no	—
355	C₂×C₄×C₄₁	—	4	1	no	—
356	C₂×C₄×C₄₁	—	4	1	no	—
357	C₂×C₄×C₄₁	—	4	1	no	—
358	C₂×C₄×C₄₁	—	4	1	no	—
359	C₂×C₄×C₄₁	—	4	1	no	—
360	C₂×C₄×C₄₁	—	4	1	no	—
361	C₂×C₄×C₄₁	—	4	1	no	—
362	C₂×C₄×C₄₁	—	4	1	no	—
363	C₂×C₄×C₄₁	—	8	4	no	—
364	C₂×C₄×C₄₁	—	8	4	no	—
365	C₂×C₄×C₄₁	#121	1	2	yes	—
366	C₂×C₄×C₄₁	#135	1	2	yes	complemented
367	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
371	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
372	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
373	C₈×C₄₁	—	2	2	no	—
374	C₈×C₄₁	—	2	2	no	—
375	C₈×C₄₁	—	4	1	no	—
376	C₈×C₄₁	—	4	1	no	—
377	#24365	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
378	C₂²×C₄₁	—	2	2	no	—
379	C₂²×C₄₁	—	2	4	no	—
380	C₂²×C₄₁	—	2	2	no	—
381	C₂²×C₄₁	—	2	2	no	—
382	C₂²×C₄₁	—	4	2	no	—
383	C₂²×C₄₁	—	4	1	no	—
384	C₂²×C₄₁	—	4	1	no	—
385	C₂²×C₄₁	—	4	2	no	—
386	C₂²×C₄₁	—	4	2	no	—
387	C₂²×C₄₁	—	4	1	no	—
388	C₂²×C₄₁	—	4	1	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	2	no	—
394	C₂²×C₄₁	—	4	2	no	—
395	C₂²×C₄₁	—	8	1	no	—
396	C₂²×C₄₁	—	8	1	no	—
397	C₂²×C₄₁	—	8	1	no	—
398	C₂²×C₄₁	—	8	1	no	—
399	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
400	C₂²×C₄₁	D₄²	1	1	yes	characteristic
401	C₂²×C₄₁	D₄²	1	1	yes	characteristic
402	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
403	C₂²×C₄₁	#575	1	1	yes	characteristic
404	C₂²×C₄₁	#577	1	1	yes	characteristic
405	C₂²×C₄₁	#578	1	1	yes	characteristic
406	C₄×C₄₁	—	2	2	no	—
407	C₄×C₄₁	—	2	2	no	—
408	C₄×C₄₁	—	4	2	no	—
409	C₄×C₄₁	—	4	2	no	—
410	C₄×C₄₁	—	4	1	no	—
411	C₄×C₄₁	—	4	1	no	—
412	C₄×C₄₁	—	4	1	no	—
413	C₄×C₄₁	—	8	1	no	—
414	C₄×C₄₁	—	8	1	no	—
415	C₄×C₄₁	—	8	1	no	—
416	C₄×C₄₁	—	8	1	no	—
417	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
418	C₄×C₄₁	#534	1	1	yes	characteristic
419	C₄×C₄₁	#546	1	1	yes	characteristic
420	C₄×C₄₁	#546	1	1	yes	characteristic
421	C₂²×#135	C₂×C₄₁	1	1	yes	characteristic
422	C₂×#463	C₂×C₄₁	1	1	yes	characteristic, complemented
423	C₂×#461	C₂×C₄₁	1	1	yes	characteristic, complemented
424	C₂×#452	C₂×C₄₁	1	1	yes	characteristic, complemented
425	#2432	C₂×C₄₁	1	1	yes	characteristic, complemented
426	#2339	C₂×C₄₁	1	1	yes	characteristic, complemented
427	#2056	C₂×C₄₁	1	1	yes	characteristic, complemented
428	#2055	C₂×C₄₁	1	1	yes	characteristic, complemented
429	#2016	C₂×C₄₁	1	1	yes	characteristic, complemented
430	#2015	C₂×C₄₁	1	1	yes	characteristic, complemented
431	#1892	C₂×C₄₁	1	1	yes	characteristic, complemented
432	#1879	C₂×C₄₁	1	1	yes	characteristic, complemented
433	#1877	C₂×C₄₁	1	1	yes	characteristic, complemented
434	#1850	C₂×C₄₁	1	1	yes	characteristic, complemented
435	#1788	C₂×C₄₁	1	1	yes	characteristic, complemented
436	C₂×C₄₁	—	4	2	no	—
437	C₂×C₄₁	—	4	4	no	—
438	C₂×C₄₁	—	8	2	no	—
439	C₂×C₄₁	#2410	1	1	yes	characteristic
440	C₂×C₄₁	#3035	1	1	yes	characteristic
441	C₂×C₄₁	#3046	1	1	yes	characteristic
442	C₂×C₄₁	#3267	1	1	yes	characteristic
443	C₂×C₄₁	#3269	1	1	yes	characteristic
444	C₂×C₄₁	#3282	1	1	yes	characteristic
445	C₂×C₄₁	#3283	1	1	yes	characteristic
446	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
447	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
448	C₂×#135	—	2	4	no	—
449	C₂×#135	—	2	4	no	—
450	C₂×#135	—	2	4	no	—
451	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
452	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
453	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
454	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
455	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
456	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
457	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
458	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
459	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
460	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
461	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
462	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
463	#463	—	2	4	no	—
464	#461	—	2	4	no	—
465	#452	—	2	4	no	—
466	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
467	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
468	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
469	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
470	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
471	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
472	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
473	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
474	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
475	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
476	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
477	#394	—	2	1	no	—
478	#394	—	2	1	no	—
479	#391	C₂²×C₄₁	1	1	yes	characteristic
480	#391	C₂²×C₄₁	1	1	yes	characteristic
481	#391	C₂²×C₄₁	1	1	yes	characteristic
482	#390	C₂²×C₄₁	1	1	yes	characteristic
483	#386	—	2	1	no	—
484	#386	—	2	1	no	—
485	#385	—	2	1	no	—
486	#385	—	2	1	no	—
487	#381	—	2	1	no	—
488	#380	C₂²×C₄₁	1	1	yes	characteristic
489	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
490	C₂×#95	—	2	1	no	—
491	#340	C₂²×C₄₁	1	1	yes	characteristic
492	#340	C₂²×C₄₁	1	1	yes	characteristic
493	#336	C₂²×C₄₁	1	1	yes	characteristic
494	#336	C₂²×C₄₁	1	1	yes	characteristic
495	C₄₁	#24365	1	1	yes	characteristic, direct product factor, Sylow
496	C₂×#41	—	2	2	no	—
497	C₂×#41	—	2	2	no	—
498	C₂×#41	—	2	2	no	—
499	C₂×#41	—	2	2	no	—
500	C₂×#41	—	2	2	no	—
501	C₂×#41	—	2	2	no	—
502	C₂×#41	—	2	2	no	—
503	C₂×#41	—	4	1	no	—
504	C₂×#41	—	4	1	no	—
505	C₂×#41	—	4	1	no	—
506	C₂×#41	—	4	1	no	—
507	C₂×#41	D₄×C₄₁	1	4	yes	—
508	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
509	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
510	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
511	C₂²×D₄	—	2	1	no	—
512	C₂²×D₄	—	2	1	no	—
513	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
514	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
515	C₂³×C₄	—	2	1	no	—
516	C₂³×C₄	—	2	1	no	—
517	C₂³×C₄	—	2	1	no	—
518	C₂³×C₄	—	2	1	no	—
519	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
520	#135	—	2	32	no	—
521	C₂×Q₁₆	—	2	2	no	—
522	C₂×Q₁₆	—	2	2	no	—
523	C₂×Q₁₆	—	2	2	no	—
524	C₂×Q₁₆	—	2	2	no	—
525	C₂×Q₁₆	—	4	1	no	—
526	C₂×Q₁₆	—	4	1	no	—
527	C₂×SD₁₆	—	2	2	no	—
528	C₂×SD₁₆	—	2	2	no	—
529	C₂×SD₁₆	—	2	2	no	—
530	C₂×SD₁₆	—	2	2	no	—
531	C₂×SD₁₆	—	2	2	no	—
532	C₂×SD₁₆	—	2	2	no	—
533	C₂×SD₁₆	—	2	2	no	—
534	C₂×SD₁₆	—	2	2	no	—
535	C₂×SD₁₆	D₄×C₄₁	1	4	yes	—
536	C₂×D₈	—	2	2	no	—
537	C₂×D₈	—	2	2	no	—
538	C₂×D₈	D₄×C₄₁	1	4	yes	—
539	C₂²×C₈	—	2	2	no	—
540	C₂²×C₈	—	2	2	no	—
541	C₂²×C₈	—	2	2	no	—
542	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
543	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
544	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
545	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
546	C₄⋊Q₈	—	2	2	no	—
547	C₄⋊Q₈	—	4	1	no	—
548	#124	—	2	2	no	—
549	#124	—	4	1	no	—
550	C₂²⋊Q₈	—	2	2	no	—
551	C₂²⋊Q₈	—	2	2	no	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	4	1	no	—
555	C₄×D₄	—	4	1	no	—
556	C₂×C₄⋊C₄	—	2	1	no	—
557	C₂×C₄⋊C₄	—	2	1	no	—
558	C₂×C₄⋊C₄	—	2	1	no	—
559	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
562	C₂×C₂²⋊C₄	—	2	1	no	—
563	C₂×C₂²⋊C₄	—	2	1	no	—
564	C₂×C₂²⋊C₄	—	2	1	no	—
565	C₂×C₂²⋊C₄	—	2	1	no	—
566	C₂×C₂²⋊C₄	—	2	1	no	—
567	C₂×C₂²⋊C₄	—	2	1	no	—
568	C₂×C₂²⋊C₄	—	2	1	no	—
569	C₂×C₂²⋊C₄	—	2	1	no	—
570	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
571	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
572	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
573	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
574	C₄⋊C₈	—	2	2	no	—
575	C₄⋊C₈	—	2	2	no	—
576	#103	—	2	2	no	—
577	#103	—	2	2	no	—
578	#103	—	2	2	no	—
579	#103	—	2	2	no	—
580	#103	—	4	1	no	—
581	#102	—	2	2	no	—
582	#102	—	2	2	no	—
583	#102	—	4	1	no	—
584	C₂²⋊C₈	—	2	2	no	—
585	#95	—	2	1	no	—
586	#95	—	2	1	no	—
587	#95	—	2	1	no	—
588	#95	—	2	1	no	—
589	#95	—	2	1	no	—
590	#95	—	2	1	no	—
591	#95	—	2	1	no	—
592	#95	D₄×C₄₁	1	1	yes	characteristic
593	#95	D₄×C₄₁	1	1	yes	characteristic
594	C₂⁴	—	2	1	no	—
595	C₂⁴	—	2	1	no	—
596	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
597	#41	—	2	8	no	—
598	#41	—	2	8	no	—
599	#41	—	4	4	no	—
600	#41	—	4	4	no	—
601	#41	—	4	4	no	—
602	#41	—	4	4	no	—
603	#41	—	4	4	no	—
604	#41	—	4	4	no	—
605	C₂×Q₈	—	2	1	no	—
606	C₂×Q₈	—	2	1	no	—
607	C₂×Q₈	—	2	1	no	—
608	C₂×Q₈	—	2	1	no	—
609	C₂×Q₈	—	2	1	no	—
610	C₂×Q₈	—	2	1	no	—
611	C₂×Q₈	—	2	1	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	—	2	1	no	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
622	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	4	2	no	—
633	C₂×D₄	—	4	2	no	—
634	C₂×D₄	—	4	2	no	—
635	C₂×D₄	—	4	2	no	—
636	C₂×D₄	—	4	2	no	—
637	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
638	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
639	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
640	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	4	2	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	—	4	2	no	—
656	C₂²×C₄	—	4	2	no	—
657	C₂²×C₄	—	4	2	no	—
658	C₂²×C₄	—	4	2	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	—	8	1	no	—
662	C₂²×C₄	—	8	1	no	—
663	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
664	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
665	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
666	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
667	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
668	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
669	C₂²×C₄	#41×C₄₁	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
671	Q₁₆	—	2	8	no	—
672	Q₁₆	—	4	4	no	—
673	SD₁₆	—	2	8	no	—
674	SD₁₆	—	2	8	no	—
675	SD₁₆	—	4	4	no	—
676	D₈	—	2	8	no	—
677	C₂×C₈	—	2	8	no	—
678	C₂×C₈	—	2	1	no	—
679	C₂×C₈	—	2	1	no	—
680	C₂×C₈	—	2	1	no	—
681	C₂×C₈	—	2	1	no	—
682	C₂×C₈	—	2	1	no	—
683	C₂×C₈	—	2	1	no	—
684	C₂×C₈	—	2	1	no	—
685	C₂×C₈	—	2	1	no	—
686	C₂×C₈	—	2	1	no	—
687	C₂×C₈	—	2	1	no	—
688	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
689	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	4	2	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	4	1	no	—
701	C₂²⋊C₄	—	4	2	no	—
702	C₂²⋊C₄	—	4	2	no	—
703	C₂²⋊C₄	—	4	2	no	—
704	C₂²⋊C₄	—	4	2	no	—
705	C₂²⋊C₄	—	4	2	no	—
706	C₂²⋊C₄	—	4	2	no	—
707	C₂²⋊C₄	—	4	2	no	—
708	C₂²⋊C₄	—	8	1	no	—
709	C₄²	—	2	1	no	—
710	C₄²	—	2	1	no	—
711	C₄²	—	2	1	no	—
712	C₄²	—	2	1	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	1	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	4	1	no	—
724	C₂³	—	4	1	no	—
725	C₂³	—	4	1	no	—
726	C₂³	—	4	1	no	—
727	C₂³	—	4	1	no	—
728	C₂³	—	4	1	no	—
729	C₂³	—	4	1	no	—
730	C₂³	—	4	1	no	—
731	C₂³	—	4	1	no	—
732	C₂³	—	4	1	no	—
733	C₂³	#121×C₄₁	1	2	yes	—
734	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
735	Q₈	—	2	2	no	—
736	Q₈	—	2	2	no	—
737	Q₈	—	2	2	no	—
738	Q₈	—	2	2	no	—
739	Q₈	—	4	1	no	—
740	Q₈	—	4	1	no	—
741	Q₈	—	4	1	no	—
742	Q₈	—	4	1	no	—
743	Q₈	—	4	1	no	—
744	Q₈	—	4	1	no	—
745	Q₈	—	4	1	no	—
746	Q₈	—	4	1	no	—
747	D₄	—	2	2	no	—
748	D₄	—	2	2	no	—
749	D₄	—	2	2	no	—
750	D₄	—	2	2	no	—
751	D₄	—	2	2	no	—
752	D₄	—	4	8	no	—
753	D₄	—	4	8	no	—
754	D₄	—	4	1	no	—
755	D₄	—	4	1	no	—
756	D₄	#120×C₄₁	1	4	yes	—
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	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	4	8	no	—
777	C₂×C₄	—	4	8	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	1	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	—	8	4	no	—
795	C₂×C₄	—	8	4	no	—
796	C₂×C₄	#121×C₄₁	1	2	yes	—
797	C₂×C₄	#135×C₄₁	1	2	yes	complemented
798	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
799	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
800	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
801	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
802	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
803	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
804	C₈	—	2	2	no	—
805	C₈	—	2	2	no	—
806	C₈	—	4	1	no	—
807	C₈	—	4	1	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	2	no	—
810	C₂²	—	2	4	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	4	1	no	—
815	C₂²	—	4	1	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	1	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	—	8	1	no	—
826	C₂²	—	8	1	no	—
827	C₂²	—	8	1	no	—
828	C₂²	—	8	1	no	—
829	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
830	C₂²	D₄²×C₄₁	1	1	yes	characteristic
831	C₂²	D₄²×C₄₁	1	1	yes	characteristic
832	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
833	C₂²	C₄₁×#575	1	1	yes	characteristic
834	C₂²	C₄₁×#577	1	1	yes	characteristic
835	C₂²	C₄₁×#578	1	1	yes	characteristic
836	C₄	—	2	2	no	—
837	C₄	—	2	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	1	no	—
841	C₄	—	4	1	no	—
842	C₄	—	4	1	no	—
843	C₄	—	8	1	no	—
844	C₄	—	8	1	no	—
845	C₄	—	8	1	no	—
846	C₄	—	8	1	no	—
847	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
848	C₄	C₄₁×#534	1	1	yes	characteristic
849	C₄	C₄₁×#546	1	1	yes	characteristic
850	C₄	C₄₁×#546	1	1	yes	characteristic
851	C₂	—	4	2	no	—
852	C₂	—	4	4	no	—
853	C₂	—	8	2	no	—
854	C₂	C₄₁×#2410	1	1	yes	characteristic
855	C₂	C₄₁×#3035	1	1	yes	characteristic
856	C₂	C₄₁×#3046	1	1	yes	characteristic
857	C₂	C₄₁×#3267	1	1	yes	characteristic
858	C₂	C₄₁×#3269	1	1	yes	characteristic
859	C₂	C₄₁×#3282	1	1	yes	characteristic
860	C₂	C₄₁×#3283	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×#135×C₄₁	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄×C₂²⋊C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#463	C₂	semidirect
3. C₂×C₄₁×#461	C₂	semidirect
4. C₂×C₄₁×#452	C₂	semidirect
5. C₄₁×#2432	C₂	semidirect
6. C₄₁×#2339	C₂	semidirect
7. C₄₁×#2056	C₂	semidirect
8. C₄₁×#2055	C₂	semidirect
9. C₄₁×#2016	C₂	semidirect
10. C₄₁×#2015	C₂	semidirect
11. C₄₁×#1892	C₂	semidirect
12. C₄₁×#1879	C₂	semidirect
13. C₄₁×#1877	C₂	semidirect
14. C₄₁×#1850	C₂	semidirect
15. C₄₁×#1788	C₂	semidirect
366. C₂×C₄×C₄₁	#135	semidirect
377. #24365	C₄₁	direct (N × H)
422. C₂×#463	C₂×C₄₁	semidirect
423. C₂×#461	C₂×C₄₁	semidirect
424. C₂×#452	C₂×C₄₁	semidirect
425. #2432	C₂×C₄₁	semidirect
426. #2339	C₂×C₄₁	semidirect
427. #2056	C₂×C₄₁	semidirect
428. #2055	C₂×C₄₁	semidirect
429. #2016	C₂×C₄₁	semidirect
430. #2015	C₂×C₄₁	semidirect
431. #1892	C₂×C₄₁	semidirect
432. #1879	C₂×C₄₁	semidirect
433. #1877	C₂×C₄₁	semidirect
434. #1850	C₂×C₄₁	semidirect
435. #1788	C₂×C₄₁	semidirect
495. C₄₁	#24365	direct (N × H)
797. C₂×C₄	#135×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#135×C₄₁	2
C₂×C₄₁×#463	2
C₂×C₄₁×#461	2
C₂×C₄₁×#452	2
C₄₁×#2432	2
C₄₁×#2339	2
C₄₁×#2056	2
C₄₁×#2055	2
C₄₁×#2016	2
C₄₁×#2015	2
C₄₁×#1892	2
C₄₁×#1879	2
C₄₁×#1877	2
C₄₁×#1850	2
C₄₁×#1788	2
#24365	41

Subgroups — C41×#24365 #23800566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24365 #23800566