Subgroups — C₄₁×#61487 #23837688

Order 10496.

1800 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3521	C₂	1	2	yes	maximal, complemented
2	C₄₁×#3393	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3376	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3342	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#3339	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#3336	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#3323	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3311	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3307	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3283	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3280	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3280	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3177	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3175	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#3168	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#3125	C₂	1	2	yes	maximal, complemented
18	C₄₁×#3123	C₂	1	2	yes	maximal, complemented
19	C₄₁×#3111	C₂	1	2	yes	maximal, complemented
20	C₄₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄₁×#2951	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄₁×#2948	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#135×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#135×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#135×C₄₁	C₂²	1	1	yes	characteristic
26	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
27	C₄₁×#556	C₂²	1	2	yes	—
28	C₄₁×#556	C₂²	1	2	yes	complemented
29	C₄₁×#554	C₂²	1	2	yes	complemented
30	C₄₁×#553	—	2	2	no	—
31	C₄₁×#553	C₂²	1	2	yes	complemented
32	C₄₁×#552	—	2	2	no	—
33	C₄₁×#552	C₂²	1	2	yes	—
34	C₄₁×#551	—	2	2	no	—
35	C₄₁×#551	—	2	2	no	—
36	C₄₁×#547	C₂²	1	2	yes	complemented
37	C₄₁×#546	C₂²	1	2	yes	—
38	C₄₁×#546	C₂²	1	2	yes	—
39	C₄₁×#542	C₂²	1	2	yes	complemented
40	C₄₁×#541	C₂²	1	2	yes	—
41	C₄₁×#539	—	2	2	no	—
42	C₄₁×#538	—	2	2	no	—
43	C₄₁×#529	—	2	2	no	—
44	C₄₁×#529	C₂²	1	1	yes	characteristic
45	C₄₁×#529	C₂²	1	2	yes	complemented
46	C₂×#126×C₄₁	—	2	2	no	—
47	C₄₁×#520	C₂²	1	2	yes	complemented
48	C₄₁×#518	C₂²	1	2	yes	—
49	C₄×#41×C₄₁	C₂²	1	2	yes	complemented
50	C₄₁×#500	C₂²	1	1	yes	characteristic, complemented
51	C₄₁×#499	C₂²	1	1	yes	characteristic, complemented
52	C₄₁×#499	C₂²	1	1	yes	characteristic, complemented
53	C₄₁×#495	C₂²	1	1	yes	characteristic
54	C₄₁×#495	C₂²	1	1	yes	characteristic
55	C₄₁×#494	C₂²	1	1	yes	characteristic, complemented
56	C₄₁×#491	C₂²	1	2	yes	complemented
57	C₄₁×#489	C₂²	1	2	yes	complemented
58	C₄₁×#488	C₂²	1	2	yes	complemented
59	C₄₁×#485	C₂²	1	2	yes	—
60	C₄₁×#485	C₂²	1	2	yes	—
61	C₄₁×#485	C₂²	1	2	yes	complemented
62	C₄₁×#483	C₂²	1	2	yes	complemented
63	C₄₁×#482	C₂²	1	2	yes	complemented
64	C₄₁×#481	C₂²	1	2	yes	complemented
65	C₄₁×#479	C₂²	1	2	yes	complemented
66	C₄₁×#478	C₂²	1	2	yes	complemented
67	C₄₁×#478	C₂²	1	2	yes	complemented
68	C₄₁×#478	C₂²	1	2	yes	complemented
69	C₄₁×#476	C₂²	1	2	yes	complemented
70	C₄₁×#475	C₂²	1	2	yes	complemented
71	C₄₁×#470	C₂²	1	2	yes	—
72	C₄₁×#468	C₂²	1	2	yes	complemented
73	C₄₁×#467	C₂²	1	1	yes	characteristic
74	C₄₁×#467	C₂²	1	1	yes	characteristic
75	C₄₁×#467	C₂²	1	1	yes	characteristic, complemented
76	C₄₁×#467	C₂²	1	1	yes	characteristic, complemented
77	C₄₁×#466	C₂²	1	1	yes	characteristic
78	C₄₁×#466	C₂²	1	1	yes	characteristic
79	C₄₁×#465	C₂²	1	2	yes	complemented
80	C₄₁×#464	C₂²	1	2	yes	complemented
81	C₄₁×#464	C₂²	1	2	yes	complemented
82	C₄₁×#463	C₂²	1	2	yes	—
83	C₄₁×#463	C₂²	1	2	yes	—
84	C₄₁×#461	C₂²	1	2	yes	complemented
85	C₄₁×#461	C₂²	1	2	yes	complemented
86	C₄₁×#452	C₂²	1	2	yes	complemented
87	C₄₁×#452	C₂²	1	2	yes	complemented
88	C₄₁×#450	C₂²	1	2	yes	—
89	C₄₁×#450	C₂²	1	2	yes	—
90	C₄₁×#449	C₂²	1	2	yes	—
91	C₄₁×#449	C₂²	1	2	yes	—
92	C₄₁×#446	C₂²	1	1	yes	characteristic, complemented
93	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
94	C₄₁×#442	C₂²	1	2	yes	—
95	C₄₁×#442	C₂²	1	2	yes	—
96	C₄₁×#441	C₂²	1	2	yes	complemented
97	C₄₁×#440	C₂²	1	2	yes	complemented
98	C₄₁×#440	C₂²	1	2	yes	complemented
99	C₄₁×#440	C₂²	1	2	yes	complemented
100	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
101	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
102	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
103	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
104	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
106	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
107	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
108	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
109	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
110	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
111	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
112	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
113	C₄₁×#436	C₂²	1	1	yes	characteristic
114	C₄₁×#435	C₂²	1	1	yes	characteristic
115	C₄₁×#435	C₂²	1	1	yes	characteristic, complemented
116	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
117	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
118	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
119	C₄₁×#433	C₂²	1	1	yes	characteristic
120	C₄₁×#433	C₂²	1	1	yes	characteristic, complemented
121	C₄₁×#432	C₂²	1	1	yes	characteristic, complemented
122	C₄₁×#427	C₂²	1	1	yes	characteristic
123	C₄₁×#427	C₂²	1	1	yes	characteristic, complemented
124	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic, complemented
125	C₄₁×#418	C₂²	1	2	yes	—
126	C₄₁×#417	C₂²	1	2	yes	complemented
127	C₄₁×#416	C₂²	1	2	yes	complemented
128	C₄₁×#405	C₂²	1	1	yes	characteristic
129	C₄₁×#405	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
131	C₂×#41×C₄₁	C₂³	1	2	yes	—
132	C₂×#41×C₄₁	C₂³	1	2	yes	—
133	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
134	#135×C₄₁	—	2	4	no	—
135	#135×C₄₁	—	2	4	no	—
136	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
137	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
138	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
139	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
140	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
142	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
143	C₂×D₈×C₄₁	—	2	4	no	—
144	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
145	C₂×D₈×C₄₁	C₂³	1	2	yes	—
146	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
148	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
149	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
154	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
155	#126×C₄₁	—	2	2	no	—
156	#126×C₄₁	—	2	2	no	—
157	#126×C₄₁	—	2	2	no	—
158	#126×C₄₁	—	2	2	no	—
159	#126×C₄₁	—	2	2	no	—
160	#126×C₄₁	—	2	2	no	—
161	#126×C₄₁	—	2	2	no	—
162	#126×C₄₁	—	2	2	no	—
163	#126×C₄₁	—	2	2	no	—
164	#126×C₄₁	—	2	2	no	—
165	#126×C₄₁	D₄	1	1	yes	characteristic
166	#126×C₄₁	D₄	1	1	yes	characteristic
167	#125×C₄₁	—	2	2	no	—
168	#125×C₄₁	—	2	2	no	—
169	#125×C₄₁	—	2	2	no	—
170	#125×C₄₁	D₄	1	1	yes	characteristic
171	#125×C₄₁	C₂³	1	2	yes	—
172	#125×C₄₁	C₂³	1	2	yes	—
173	#124×C₄₁	—	2	2	no	—
174	#124×C₄₁	—	2	2	no	—
175	#124×C₄₁	D₄	1	1	yes	characteristic
176	#124×C₄₁	C₂³	1	2	yes	—
177	#124×C₄₁	C₂³	1	2	yes	—
178	#123×C₄₁	—	2	2	no	—
179	#123×C₄₁	—	2	2	no	—
180	#123×C₄₁	—	2	2	no	—
181	#123×C₄₁	—	2	2	no	—
182	#123×C₄₁	—	2	2	no	—
183	#123×C₄₁	—	2	2	no	—
184	#123×C₄₁	—	2	2	no	—
185	#123×C₄₁	—	2	2	no	—
186	#123×C₄₁	D₄	1	1	yes	characteristic
187	#123×C₄₁	D₄	1	1	yes	characteristic
188	C₂²⋊Q₈×C₄₁	—	2	2	no	—
189	C₂²⋊Q₈×C₄₁	—	2	2	no	—
190	C₂²⋊Q₈×C₄₁	—	2	2	no	—
191	C₂²⋊Q₈×C₄₁	—	2	2	no	—
192	C₂²⋊Q₈×C₄₁	—	2	2	no	—
193	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
194	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
195	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
197	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
198	#121×C₄₁	—	2	2	no	—
199	#121×C₄₁	—	2	2	no	—
200	#121×C₄₁	—	2	2	no	—
201	#121×C₄₁	—	2	2	no	—
202	#121×C₄₁	D₄	1	1	yes	characteristic
203	#121×C₄₁	C₂³	1	2	yes	—
204	#121×C₄₁	C₂³	1	2	yes	—
205	#120×C₄₁	—	2	2	no	—
206	#120×C₄₁	—	2	2	no	—
207	C₄×Q₈×C₄₁	—	2	2	no	—
208	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
209	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
210	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
211	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
212	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
213	C₄×D₄×C₄₁	—	2	2	no	—
214	C₄×D₄×C₄₁	—	2	2	no	—
215	C₄×D₄×C₄₁	—	2	2	no	—
216	C₄×D₄×C₄₁	—	2	2	no	—
217	C₄×D₄×C₄₁	—	2	2	no	—
218	C₄×D₄×C₄₁	—	2	2	no	—
219	C₄×D₄×C₄₁	—	2	2	no	—
220	C₄×D₄×C₄₁	—	2	2	no	—
221	C₄×D₄×C₄₁	C₂³	1	2	yes	—
222	C₄×D₄×C₄₁	C₂³	1	2	yes	—
223	C₄×D₄×C₄₁	C₂³	1	2	yes	—
224	C₄×D₄×C₄₁	C₂³	1	2	yes	—
225	C₄×D₄×C₄₁	C₂³	1	2	yes	—
226	C₄×D₄×C₄₁	C₂³	1	2	yes	—
227	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
229	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
230	#117×C₄₁	—	2	2	no	—
231	#117×C₄₁	—	2	2	no	—
232	#117×C₄₁	—	2	2	no	—
233	#117×C₄₁	—	2	2	no	—
234	#117×C₄₁	—	2	2	no	—
235	#117×C₄₁	C₂³	1	2	yes	—
236	#117×C₄₁	C₂³	1	2	yes	—
237	#117×C₄₁	C₂³	1	1	yes	characteristic
238	#117×C₄₁	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
240	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
241	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
242	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
243	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
244	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
245	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
246	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
247	C₂×C₄²×C₄₁	—	2	2	no	—
248	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
249	#107×C₄₁	C₂³	1	1	yes	characteristic
250	#107×C₄₁	C₂³	1	1	yes	characteristic
251	#107×C₄₁	C₂³	1	2	yes	—
252	#107×C₄₁	C₂³	1	1	yes	characteristic
253	#107×C₄₁	C₂³	1	1	yes	characteristic
254	#107×C₄₁	C₂³	1	2	yes	—
255	#106×C₄₁	C₂³	1	2	yes	—
256	#106×C₄₁	C₂³	1	2	yes	—
257	#106×C₄₁	C₂³	1	2	yes	—
258	#106×C₄₁	C₂³	1	2	yes	—
259	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
260	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
261	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
262	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
263	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
264	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
265	#103×C₄₁	C₂³	1	2	yes	—
266	#103×C₄₁	C₂³	1	2	yes	—
267	#103×C₄₁	C₂³	1	2	yes	—
268	#103×C₄₁	C₂³	1	2	yes	—
269	#103×C₄₁	C₂³	1	2	yes	—
270	#103×C₄₁	C₂³	1	2	yes	—
271	#103×C₄₁	C₂³	1	2	yes	—
272	#103×C₄₁	C₂³	1	2	yes	—
273	#102×C₄₁	C₂³	1	2	yes	—
274	#102×C₄₁	C₂³	1	2	yes	—
275	#102×C₄₁	C₂³	1	2	yes	—
276	#102×C₄₁	C₂³	1	2	yes	—
277	#102×C₄₁	C₂³	1	2	yes	—
278	#102×C₄₁	C₂³	1	2	yes	—
279	#102×C₄₁	C₂³	1	2	yes	—
280	#102×C₄₁	C₂³	1	2	yes	—
281	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
282	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
283	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
284	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
285	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
286	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
287	#97×C₄₁	C₂³	1	1	yes	characteristic
288	#97×C₄₁	C₂³	1	1	yes	characteristic
289	#97×C₄₁	C₂³	1	1	yes	characteristic
290	#97×C₄₁	C₂³	1	1	yes	characteristic
291	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
292	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
293	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
294	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
295	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
297	C₂⁴×C₄₁	—	2	2	no	—
298	#41×C₄₁	—	2	4	no	—
299	#41×C₄₁	—	2	4	no	—
300	#41×C₄₁	—	4	2	no	—
301	#41×C₄₁	—	4	2	no	—
302	C₂×Q₈×C₄₁	—	2	2	no	—
303	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
304	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
305	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
306	C₂×D₄×C₄₁	—	2	4	no	—
307	C₂×D₄×C₄₁	—	2	2	no	—
308	C₂×D₄×C₄₁	—	2	2	no	—
309	C₂×D₄×C₄₁	—	2	2	no	—
310	C₂×D₄×C₄₁	—	2	2	no	—
311	C₂×D₄×C₄₁	—	2	2	no	—
312	C₂×D₄×C₄₁	—	4	2	no	—
313	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
314	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
315	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
316	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
317	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₄₁	—	2	2	no	—
319	C₂²×C₄×C₄₁	—	2	2	no	—
320	C₂²×C₄×C₄₁	—	2	2	no	—
321	C₂²×C₄×C₄₁	—	2	2	no	—
322	C₂²×C₄×C₄₁	—	2	2	no	—
323	C₂²×C₄×C₄₁	—	2	2	no	—
324	C₂²×C₄×C₄₁	—	2	2	no	—
325	C₂²×C₄×C₄₁	—	2	2	no	—
326	C₂²×C₄×C₄₁	—	2	2	no	—
327	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
328	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
329	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
332	Q₁₆×C₄₁	—	2	2	no	—
333	Q₁₆×C₄₁	—	2	2	no	—
334	Q₁₆×C₄₁	—	4	2	no	—
335	SD₁₆×C₄₁	—	2	4	no	—
336	SD₁₆×C₄₁	—	2	4	no	—
337	SD₁₆×C₄₁	—	4	2	no	—
338	SD₁₆×C₄₁	—	4	2	no	—
339	D₈×C₄₁	—	2	4	no	—
340	D₈×C₄₁	—	2	2	no	—
341	D₈×C₄₁	#41	1	4	yes	—
342	M₁₆×C₄₁	—	4	1	no	—
343	M₁₆×C₄₁	—	4	1	no	—
344	C₂×C₈×C₄₁	—	2	2	no	—
345	C₂×C₈×C₄₁	—	2	2	no	—
346	C₂×C₈×C₄₁	—	2	2	no	—
347	C₂×C₈×C₄₁	—	4	1	no	—
348	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
349	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
350	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
351	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
352	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
354	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
356	C₄⋊C₄×C₄₁	—	2	2	no	—
357	C₄⋊C₄×C₄₁	—	2	2	no	—
358	C₄⋊C₄×C₄₁	—	2	2	no	—
359	C₄⋊C₄×C₄₁	—	2	2	no	—
360	C₄⋊C₄×C₄₁	—	2	2	no	—
361	C₄⋊C₄×C₄₁	—	2	2	no	—
362	C₄⋊C₄×C₄₁	—	2	2	no	—
363	C₄⋊C₄×C₄₁	—	2	2	no	—
364	C₄⋊C₄×C₄₁	—	2	2	no	—
365	C₄⋊C₄×C₄₁	—	2	2	no	—
366	C₄⋊C₄×C₄₁	—	2	2	no	—
367	C₄⋊C₄×C₄₁	—	2	2	no	—
368	C₄⋊C₄×C₄₁	—	2	2	no	—
369	C₄⋊C₄×C₄₁	—	2	2	no	—
370	C₄⋊C₄×C₄₁	—	2	2	no	—
371	C₄⋊C₄×C₄₁	—	2	2	no	—
372	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
373	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
374	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
375	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
376	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
377	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
378	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
379	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
380	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
381	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
382	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
383	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
384	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
385	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
386	C₂²⋊C₄×C₄₁	—	2	2	no	—
387	C₂²⋊C₄×C₄₁	—	2	2	no	—
388	C₂²⋊C₄×C₄₁	—	2	2	no	—
389	C₂²⋊C₄×C₄₁	—	2	2	no	—
390	C₂²⋊C₄×C₄₁	—	2	2	no	—
391	C₂²⋊C₄×C₄₁	—	2	2	no	—
392	C₂²⋊C₄×C₄₁	—	2	2	no	—
393	C₂²⋊C₄×C₄₁	—	2	2	no	—
394	C₂²⋊C₄×C₄₁	—	2	2	no	—
395	C₂²⋊C₄×C₄₁	—	2	2	no	—
396	C₂²⋊C₄×C₄₁	—	2	2	no	—
397	C₂²⋊C₄×C₄₁	—	2	2	no	—
398	C₂²⋊C₄×C₄₁	—	2	2	no	—
399	C₂²⋊C₄×C₄₁	—	2	2	no	—
400	C₂²⋊C₄×C₄₁	—	2	2	no	—
401	C₂²⋊C₄×C₄₁	—	2	2	no	—
402	C₂²⋊C₄×C₄₁	—	2	2	no	—
403	C₂²⋊C₄×C₄₁	—	2	2	no	—
404	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
405	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
406	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
407	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
408	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
409	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
410	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
411	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
412	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
413	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
414	C₄²×C₄₁	—	2	2	no	—
415	C₄²×C₄₁	—	2	2	no	—
416	C₄²×C₄₁	—	2	2	no	—
417	C₄²×C₄₁	—	2	2	no	—
418	C₄²×C₄₁	—	2	2	no	—
419	C₄²×C₄₁	—	2	2	no	—
420	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
421	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
422	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
423	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
424	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
425	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
426	C₂³×C₄₁	—	2	2	no	—
427	C₂³×C₄₁	—	2	2	no	—
428	C₂³×C₄₁	—	4	4	no	—
429	C₂³×C₄₁	—	8	2	no	—
430	C₂³×C₄₁	—	8	2	no	—
431	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
432	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
433	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
434	Q₈×C₄₁	—	2	2	no	—
435	Q₈×C₄₁	—	2	2	no	—
436	Q₈×C₄₁	—	2	2	no	—
437	Q₈×C₄₁	—	2	2	no	—
438	Q₈×C₄₁	—	4	1	no	—
439	Q₈×C₄₁	—	8	2	no	—
440	D₄×C₄₁	—	2	2	no	—
441	D₄×C₄₁	—	2	2	no	—
442	D₄×C₄₁	—	2	2	no	—
443	D₄×C₄₁	—	4	1	no	—
444	D₄×C₄₁	—	4	1	no	—
445	D₄×C₄₁	—	4	1	no	—
446	D₄×C₄₁	—	4	4	no	—
447	D₄×C₄₁	—	4	4	no	—
448	D₄×C₄₁	—	4	4	no	—
449	D₄×C₄₁	—	8	2	no	—
450	D₄×C₄₁	—	8	2	no	—
451	D₄×C₄₁	C₂×#41	1	4	yes	—
452	C₂×C₄×C₄₁	—	2	1	no	—
453	C₂×C₄×C₄₁	—	2	1	no	—
454	C₂×C₄×C₄₁	—	2	1	no	—
455	C₂×C₄×C₄₁	—	2	1	no	—
456	C₂×C₄×C₄₁	—	2	1	no	—
457	C₂×C₄×C₄₁	—	2	1	no	—
458	C₂×C₄×C₄₁	—	2	2	no	—
459	C₂×C₄×C₄₁	—	2	2	no	—
460	C₂×C₄×C₄₁	—	2	2	no	—
461	C₂×C₄×C₄₁	—	2	2	no	—
462	C₂×C₄×C₄₁	—	2	2	no	—
463	C₂×C₄×C₄₁	—	2	2	no	—
464	C₂×C₄×C₄₁	—	4	1	no	—
465	C₂×C₄×C₄₁	—	4	1	no	—
466	C₂×C₄×C₄₁	—	4	4	no	—
467	C₂×C₄×C₄₁	—	4	4	no	—
468	C₂×C₄×C₄₁	—	8	2	no	—
469	C₂×C₄×C₄₁	—	8	2	no	—
470	C₂×C₄×C₄₁	—	8	2	no	—
471	C₂×C₄×C₄₁	—	8	2	no	—
472	C₂×C₄×C₄₁	—	8	2	no	—
473	C₂×C₄×C₄₁	—	8	2	no	—
474	C₂×C₄×C₄₁	—	8	2	no	—
475	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
487	C₈×C₄₁	—	2	1	no	—
488	C₈×C₄₁	—	2	1	no	—
489	C₈×C₄₁	—	2	1	no	—
490	C₈×C₄₁	—	2	1	no	—
491	C₈×C₄₁	—	2	1	no	—
492	C₈×C₄₁	—	2	1	no	—
493	C₈×C₄₁	—	2	1	no	—
494	C₈×C₄₁	C₂×#41	1	2	yes	—
495	#61487	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
496	C₂²×C₄₁	—	2	1	no	—
497	C₂²×C₄₁	—	2	1	no	—
498	C₂²×C₄₁	—	2	1	no	—
499	C₂²×C₄₁	—	2	1	no	—
500	C₂²×C₄₁	—	2	1	no	—
501	C₂²×C₄₁	—	2	1	no	—
502	C₂²×C₄₁	—	2	1	no	—
503	C₂²×C₄₁	—	2	1	no	—
504	C₂²×C₄₁	—	2	1	no	—
505	C₂²×C₄₁	—	2	4	no	—
506	C₂²×C₄₁	—	4	2	no	—
507	C₂²×C₄₁	—	4	2	no	—
508	C₂²×C₄₁	—	4	2	no	—
509	C₂²×C₄₁	—	4	2	no	—
510	C₂²×C₄₁	—	4	2	no	—
511	C₂²×C₄₁	—	16	4	no	—
512	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
513	C₄×C₄₁	—	2	1	no	—
514	C₄×C₄₁	—	2	1	no	—
515	C₄×C₄₁	—	2	1	no	—
516	C₄×C₄₁	—	2	1	no	—
517	C₄×C₄₁	—	2	1	no	—
518	C₄×C₄₁	—	2	1	no	—
519	C₄×C₄₁	—	2	1	no	—
520	C₄×C₄₁	—	2	1	no	—
521	C₄×C₄₁	—	2	1	no	—
522	C₄×C₄₁	—	2	1	no	—
523	C₄×C₄₁	—	2	1	no	—
524	C₄×C₄₁	—	4	2	no	—
525	C₄×C₄₁	—	4	2	no	—
526	C₄×C₄₁	—	4	2	no	—
527	C₄×C₄₁	—	4	2	no	—
528	C₄×C₄₁	—	4	2	no	—
529	C₄×C₄₁	—	4	2	no	—
530	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
531	C₄×C₄₁	#585	1	1	yes	characteristic
532	#3521	C₂×C₄₁	1	2	yes	complemented
533	#3393	C₂×C₄₁	1	1	yes	characteristic, complemented
534	#3380	C₂×C₄₁	1	1	yes	characteristic, complemented
535	#3376	C₂×C₄₁	1	2	yes	complemented
536	#3342	C₂×C₄₁	1	1	yes	characteristic, complemented
537	#3339	C₂×C₄₁	1	1	yes	characteristic, complemented
538	#3336	C₂×C₄₁	1	1	yes	characteristic, complemented
539	#3323	C₂×C₄₁	1	2	yes	complemented
540	#3311	C₂×C₄₁	1	2	yes	complemented
541	#3307	C₂×C₄₁	1	2	yes	complemented
542	#3283	C₂×C₄₁	1	1	yes	characteristic, complemented
543	#3280	C₂×C₄₁	1	1	yes	characteristic, complemented
544	#3280	C₂×C₄₁	1	1	yes	characteristic, complemented
545	#3177	C₂×C₄₁	1	1	yes	characteristic, complemented
546	#3175	C₂×C₄₁	1	1	yes	characteristic, complemented
547	#3168	C₂×C₄₁	1	1	yes	characteristic, complemented
548	#3125	C₂×C₄₁	1	2	yes	complemented
549	#3123	C₂×C₄₁	1	2	yes	complemented
550	#3111	C₂×C₄₁	1	2	yes	complemented
551	#2966	C₂×C₄₁	1	1	yes	characteristic, complemented
552	#2951	C₂×C₄₁	1	1	yes	characteristic, complemented
553	#2948	C₂×C₄₁	1	1	yes	characteristic, complemented
554	C₄×#135	C₂×C₄₁	1	1	yes	characteristic, complemented
555	C₂×C₄₁	—	4	1	no	—
556	C₂×C₄₁	—	4	1	no	—
557	C₂×C₄₁	—	4	1	no	—
558	C₂×C₄₁	—	4	4	no	—
559	C₂×C₄₁	—	8	2	no	—
560	C₂×C₄₁	D₄×#41	1	1	yes	characteristic
561	C₂×C₄₁	#3584	1	1	yes	characteristic
562	C₂×C₄₁	#3584	1	1	yes	characteristic
563	C₂×#135	C₂²×C₄₁	1	1	yes	characteristic
564	C₂×#135	C₂²×C₄₁	1	1	yes	characteristic
565	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
566	#556	C₂²×C₄₁	1	2	yes	—
567	#556	C₂²×C₄₁	1	2	yes	complemented
568	#554	C₂²×C₄₁	1	2	yes	complemented
569	#553	—	2	2	no	—
570	#553	C₂²×C₄₁	1	2	yes	complemented
571	#552	—	2	2	no	—
572	#552	C₂²×C₄₁	1	2	yes	—
573	#551	—	2	2	no	—
574	#551	—	2	2	no	—
575	#547	C₂²×C₄₁	1	2	yes	complemented
576	#546	C₂²×C₄₁	1	2	yes	—
577	#546	C₂²×C₄₁	1	2	yes	—
578	#542	C₂²×C₄₁	1	2	yes	complemented
579	#541	C₂²×C₄₁	1	2	yes	—
580	#539	—	2	2	no	—
581	#538	—	2	2	no	—
582	#529	—	2	2	no	—
583	#529	C₂²×C₄₁	1	1	yes	characteristic
584	#529	C₂²×C₄₁	1	2	yes	complemented
585	C₂×#126	—	2	2	no	—
586	#520	C₂²×C₄₁	1	2	yes	complemented
587	#518	C₂²×C₄₁	1	2	yes	—
588	C₄×#41	C₂²×C₄₁	1	2	yes	complemented
589	#500	C₂²×C₄₁	1	1	yes	characteristic, complemented
590	#499	C₂²×C₄₁	1	1	yes	characteristic, complemented
591	#499	C₂²×C₄₁	1	1	yes	characteristic, complemented
592	#495	C₂²×C₄₁	1	1	yes	characteristic
593	#495	C₂²×C₄₁	1	1	yes	characteristic
594	#494	C₂²×C₄₁	1	1	yes	characteristic, complemented
595	#491	C₂²×C₄₁	1	2	yes	complemented
596	#489	C₂²×C₄₁	1	2	yes	complemented
597	#488	C₂²×C₄₁	1	2	yes	complemented
598	#485	C₂²×C₄₁	1	2	yes	—
599	#485	C₂²×C₄₁	1	2	yes	—
600	#485	C₂²×C₄₁	1	2	yes	complemented
601	#483	C₂²×C₄₁	1	2	yes	complemented
602	#482	C₂²×C₄₁	1	2	yes	complemented
603	#481	C₂²×C₄₁	1	2	yes	complemented
604	#479	C₂²×C₄₁	1	2	yes	complemented
605	#478	C₂²×C₄₁	1	2	yes	complemented
606	#478	C₂²×C₄₁	1	2	yes	complemented
607	#478	C₂²×C₄₁	1	2	yes	complemented
608	#476	C₂²×C₄₁	1	2	yes	complemented
609	#475	C₂²×C₄₁	1	2	yes	complemented
610	#470	C₂²×C₄₁	1	2	yes	—
611	#468	C₂²×C₄₁	1	2	yes	complemented
612	#467	C₂²×C₄₁	1	1	yes	characteristic
613	#467	C₂²×C₄₁	1	1	yes	characteristic
614	#467	C₂²×C₄₁	1	1	yes	characteristic, complemented
615	#467	C₂²×C₄₁	1	1	yes	characteristic, complemented
616	#466	C₂²×C₄₁	1	1	yes	characteristic
617	#466	C₂²×C₄₁	1	1	yes	characteristic
618	#465	C₂²×C₄₁	1	2	yes	complemented
619	#464	C₂²×C₄₁	1	2	yes	complemented
620	#464	C₂²×C₄₁	1	2	yes	complemented
621	#463	C₂²×C₄₁	1	2	yes	—
622	#463	C₂²×C₄₁	1	2	yes	—
623	#461	C₂²×C₄₁	1	2	yes	complemented
624	#461	C₂²×C₄₁	1	2	yes	complemented
625	#452	C₂²×C₄₁	1	2	yes	complemented
626	#452	C₂²×C₄₁	1	2	yes	complemented
627	#450	C₂²×C₄₁	1	2	yes	—
628	#450	C₂²×C₄₁	1	2	yes	—
629	#449	C₂²×C₄₁	1	2	yes	—
630	#449	C₂²×C₄₁	1	2	yes	—
631	#446	C₂²×C₄₁	1	1	yes	characteristic, complemented
632	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
633	#442	C₂²×C₄₁	1	2	yes	—
634	#442	C₂²×C₄₁	1	2	yes	—
635	#441	C₂²×C₄₁	1	2	yes	complemented
636	#440	C₂²×C₄₁	1	2	yes	complemented
637	#440	C₂²×C₄₁	1	2	yes	complemented
638	#440	C₂²×C₄₁	1	2	yes	complemented
639	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
640	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
641	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
642	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
643	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
644	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
645	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
646	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
647	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
648	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
649	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
650	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
651	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
652	#436	C₂²×C₄₁	1	1	yes	characteristic
653	#435	C₂²×C₄₁	1	1	yes	characteristic
654	#435	C₂²×C₄₁	1	1	yes	characteristic, complemented
655	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
656	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
657	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
658	#433	C₂²×C₄₁	1	1	yes	characteristic
659	#433	C₂²×C₄₁	1	1	yes	characteristic, complemented
660	#432	C₂²×C₄₁	1	1	yes	characteristic, complemented
661	#427	C₂²×C₄₁	1	1	yes	characteristic
662	#427	C₂²×C₄₁	1	1	yes	characteristic, complemented
663	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic, complemented
664	#418	C₂²×C₄₁	1	2	yes	—
665	#417	C₂²×C₄₁	1	2	yes	complemented
666	#416	C₂²×C₄₁	1	2	yes	complemented
667	#405	C₂²×C₄₁	1	1	yes	characteristic
668	#405	C₂²×C₄₁	1	1	yes	characteristic, complemented
669	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
670	C₄₁	#61487	1	1	yes	characteristic, direct product factor, Sylow
671	C₂×#41	C₂³×C₄₁	1	2	yes	—
672	C₂×#41	C₂³×C₄₁	1	2	yes	—
673	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
674	#135	—	2	4	no	—
675	#135	—	2	4	no	—
676	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
677	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
678	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
679	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
680	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
681	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
682	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
683	C₂×D₈	—	2	4	no	—
684	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
685	C₂×D₈	C₂³×C₄₁	1	2	yes	—
686	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
687	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
688	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
689	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
690	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
691	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
692	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
693	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
694	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
695	#126	—	2	2	no	—
696	#126	—	2	2	no	—
697	#126	—	2	2	no	—
698	#126	—	2	2	no	—
699	#126	—	2	2	no	—
700	#126	—	2	2	no	—
701	#126	—	2	2	no	—
702	#126	—	2	2	no	—
703	#126	—	2	2	no	—
704	#126	—	2	2	no	—
705	#126	D₄×C₄₁	1	1	yes	characteristic
706	#126	D₄×C₄₁	1	1	yes	characteristic
707	#125	—	2	2	no	—
708	#125	—	2	2	no	—
709	#125	—	2	2	no	—
710	#125	D₄×C₄₁	1	1	yes	characteristic
711	#125	C₂³×C₄₁	1	2	yes	—
712	#125	C₂³×C₄₁	1	2	yes	—
713	#124	—	2	2	no	—
714	#124	—	2	2	no	—
715	#124	D₄×C₄₁	1	1	yes	characteristic
716	#124	C₂³×C₄₁	1	2	yes	—
717	#124	C₂³×C₄₁	1	2	yes	—
718	#123	—	2	2	no	—
719	#123	—	2	2	no	—
720	#123	—	2	2	no	—
721	#123	—	2	2	no	—
722	#123	—	2	2	no	—
723	#123	—	2	2	no	—
724	#123	—	2	2	no	—
725	#123	—	2	2	no	—
726	#123	D₄×C₄₁	1	1	yes	characteristic
727	#123	D₄×C₄₁	1	1	yes	characteristic
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	—	2	2	no	—
732	C₂²⋊Q₈	—	2	2	no	—
733	C₂²⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
734	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
735	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
736	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
737	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
738	#121	—	2	2	no	—
739	#121	—	2	2	no	—
740	#121	—	2	2	no	—
741	#121	—	2	2	no	—
742	#121	D₄×C₄₁	1	1	yes	characteristic
743	#121	C₂³×C₄₁	1	2	yes	—
744	#121	C₂³×C₄₁	1	2	yes	—
745	#120	—	2	2	no	—
746	#120	—	2	2	no	—
747	C₄×Q₈	—	2	2	no	—
748	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
749	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
750	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
751	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
752	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
753	C₄×D₄	—	2	2	no	—
754	C₄×D₄	—	2	2	no	—
755	C₄×D₄	—	2	2	no	—
756	C₄×D₄	—	2	2	no	—
757	C₄×D₄	—	2	2	no	—
758	C₄×D₄	—	2	2	no	—
759	C₄×D₄	—	2	2	no	—
760	C₄×D₄	—	2	2	no	—
761	C₄×D₄	C₂³×C₄₁	1	2	yes	—
762	C₄×D₄	C₂³×C₄₁	1	2	yes	—
763	C₄×D₄	C₂³×C₄₁	1	2	yes	—
764	C₄×D₄	C₂³×C₄₁	1	2	yes	—
765	C₄×D₄	C₂³×C₄₁	1	2	yes	—
766	C₄×D₄	C₂³×C₄₁	1	2	yes	—
767	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
768	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
769	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
770	#117	—	2	2	no	—
771	#117	—	2	2	no	—
772	#117	—	2	2	no	—
773	#117	—	2	2	no	—
774	#117	—	2	2	no	—
775	#117	C₂³×C₄₁	1	2	yes	—
776	#117	C₂³×C₄₁	1	2	yes	—
777	#117	C₂³×C₄₁	1	1	yes	characteristic
778	#117	C₂³×C₄₁	1	1	yes	characteristic
779	C₂×C₄⋊C₄	—	2	2	no	—
780	C₂×C₄⋊C₄	—	2	2	no	—
781	C₂×C₄⋊C₄	—	2	2	no	—
782	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
783	C₂×C₂²⋊C₄	—	2	2	no	—
784	C₂×C₂²⋊C₄	—	2	2	no	—
785	C₂×C₂²⋊C₄	—	2	2	no	—
786	C₂×C₂²⋊C₄	—	2	2	no	—
787	C₂×C₄²	—	2	2	no	—
788	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
789	#107	C₂³×C₄₁	1	1	yes	characteristic
790	#107	C₂³×C₄₁	1	1	yes	characteristic
791	#107	C₂³×C₄₁	1	2	yes	—
792	#107	C₂³×C₄₁	1	1	yes	characteristic
793	#107	C₂³×C₄₁	1	1	yes	characteristic
794	#107	C₂³×C₄₁	1	2	yes	—
795	#106	C₂³×C₄₁	1	2	yes	—
796	#106	C₂³×C₄₁	1	2	yes	—
797	#106	C₂³×C₄₁	1	2	yes	—
798	#106	C₂³×C₄₁	1	2	yes	—
799	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
800	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
801	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
802	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
803	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
804	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
805	#103	C₂³×C₄₁	1	2	yes	—
806	#103	C₂³×C₄₁	1	2	yes	—
807	#103	C₂³×C₄₁	1	2	yes	—
808	#103	C₂³×C₄₁	1	2	yes	—
809	#103	C₂³×C₄₁	1	2	yes	—
810	#103	C₂³×C₄₁	1	2	yes	—
811	#103	C₂³×C₄₁	1	2	yes	—
812	#103	C₂³×C₄₁	1	2	yes	—
813	#102	C₂³×C₄₁	1	2	yes	—
814	#102	C₂³×C₄₁	1	2	yes	—
815	#102	C₂³×C₄₁	1	2	yes	—
816	#102	C₂³×C₄₁	1	2	yes	—
817	#102	C₂³×C₄₁	1	2	yes	—
818	#102	C₂³×C₄₁	1	2	yes	—
819	#102	C₂³×C₄₁	1	2	yes	—
820	#102	C₂³×C₄₁	1	2	yes	—
821	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
822	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
823	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
824	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
825	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
826	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
827	#97	C₂³×C₄₁	1	1	yes	characteristic
828	#97	C₂³×C₄₁	1	1	yes	characteristic
829	#97	C₂³×C₄₁	1	1	yes	characteristic
830	#97	C₂³×C₄₁	1	1	yes	characteristic
831	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
832	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
833	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
834	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
835	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
836	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
837	C₂⁴	—	2	2	no	—
838	#41	—	2	4	no	—
839	#41	—	2	4	no	—
840	#41	—	4	2	no	—
841	#41	—	4	2	no	—
842	C₂×Q₈	—	2	2	no	—
843	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
844	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
845	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
846	C₂×D₄	—	2	4	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	2	no	—
849	C₂×D₄	—	2	2	no	—
850	C₂×D₄	—	2	2	no	—
851	C₂×D₄	—	2	2	no	—
852	C₂×D₄	—	4	2	no	—
853	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
854	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
855	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
856	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
857	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	2	no	—
863	C₂²×C₄	—	2	2	no	—
864	C₂²×C₄	—	2	2	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
868	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
872	Q₁₆	—	2	2	no	—
873	Q₁₆	—	2	2	no	—
874	Q₁₆	—	4	2	no	—
875	SD₁₆	—	2	4	no	—
876	SD₁₆	—	2	4	no	—
877	SD₁₆	—	4	2	no	—
878	SD₁₆	—	4	2	no	—
879	D₈	—	2	4	no	—
880	D₈	—	2	2	no	—
881	D₈	#41×C₄₁	1	4	yes	—
882	M₁₆	—	4	1	no	—
883	M₁₆	—	4	1	no	—
884	C₂×C₈	—	2	2	no	—
885	C₂×C₈	—	2	2	no	—
886	C₂×C₈	—	2	2	no	—
887	C₂×C₈	—	4	1	no	—
888	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
889	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
890	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
891	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
892	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
893	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
894	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
895	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
913	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
914	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
915	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
916	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
917	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
918	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
919	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
920	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
921	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
922	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
923	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
924	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
925	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	2	no	—
932	C₂²⋊C₄	—	2	2	no	—
933	C₂²⋊C₄	—	2	2	no	—
934	C₂²⋊C₄	—	2	2	no	—
935	C₂²⋊C₄	—	2	2	no	—
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
945	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
946	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
947	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
948	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
949	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
950	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
951	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
952	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
953	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
954	C₄²	—	2	2	no	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	2	no	—
957	C₄²	—	2	2	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	2	2	no	—
960	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
961	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
962	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
963	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
964	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
965	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
966	C₂³	—	2	2	no	—
967	C₂³	—	2	2	no	—
968	C₂³	—	4	4	no	—
969	C₂³	—	8	2	no	—
970	C₂³	—	8	2	no	—
971	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
972	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
973	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
974	Q₈	—	2	2	no	—
975	Q₈	—	2	2	no	—
976	Q₈	—	2	2	no	—
977	Q₈	—	2	2	no	—
978	Q₈	—	4	1	no	—
979	Q₈	—	8	2	no	—
980	D₄	—	2	2	no	—
981	D₄	—	2	2	no	—
982	D₄	—	2	2	no	—
983	D₄	—	4	1	no	—
984	D₄	—	4	1	no	—
985	D₄	—	4	1	no	—
986	D₄	—	4	4	no	—
987	D₄	—	4	4	no	—
988	D₄	—	4	4	no	—
989	D₄	—	8	2	no	—
990	D₄	—	8	2	no	—
991	D₄	C₂×#41×C₄₁	1	4	yes	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	4	1	no	—
1005	C₂×C₄	—	4	1	no	—
1006	C₂×C₄	—	4	4	no	—
1007	C₂×C₄	—	4	4	no	—
1008	C₂×C₄	—	8	2	no	—
1009	C₂×C₄	—	8	2	no	—
1010	C₂×C₄	—	8	2	no	—
1011	C₂×C₄	—	8	2	no	—
1012	C₂×C₄	—	8	2	no	—
1013	C₂×C₄	—	8	2	no	—
1014	C₂×C₄	—	8	2	no	—
1015	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1016	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1017	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1018	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1019	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1020	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1021	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1022	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1023	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1024	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1025	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1026	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
1027	C₈	—	2	1	no	—
1028	C₈	—	2	1	no	—
1029	C₈	—	2	1	no	—
1030	C₈	—	2	1	no	—
1031	C₈	—	2	1	no	—
1032	C₈	—	2	1	no	—
1033	C₈	—	2	1	no	—
1034	C₈	C₂×#41×C₄₁	1	2	yes	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	2	1	no	—
1040	C₂²	—	2	1	no	—
1041	C₂²	—	2	1	no	—
1042	C₂²	—	2	1	no	—
1043	C₂²	—	2	1	no	—
1044	C₂²	—	2	4	no	—
1045	C₂²	—	4	2	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	4	2	no	—
1048	C₂²	—	4	2	no	—
1049	C₂²	—	4	2	no	—
1050	C₂²	—	16	4	no	—
1051	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	1	no	—
1057	C₄	—	2	1	no	—
1058	C₄	—	2	1	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	1	no	—
1061	C₄	—	2	1	no	—
1062	C₄	—	2	1	no	—
1063	C₄	—	4	2	no	—
1064	C₄	—	4	2	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	4	2	no	—
1067	C₄	—	4	2	no	—
1068	C₄	—	4	2	no	—
1069	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
1070	C₄	C₄₁×#585	1	1	yes	characteristic
1071	C₂	—	4	1	no	—
1072	C₂	—	4	1	no	—
1073	C₂	—	4	1	no	—
1074	C₂	—	4	4	no	—
1075	C₂	—	8	2	no	—
1076	C₂	D₄×#41×C₄₁	1	1	yes	characteristic
1077	C₂	C₄₁×#3584	1	1	yes	characteristic
1078	C₂	C₄₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3521	C₂	semidirect
2. C₄₁×#3393	C₂	semidirect
3. C₄₁×#3380	C₂	semidirect
4. C₄₁×#3376	C₂	semidirect
5. C₄₁×#3342	C₂	semidirect
6. C₄₁×#3339	C₂	semidirect
7. C₄₁×#3336	C₂	semidirect
8. C₄₁×#3323	C₂	semidirect
9. C₄₁×#3311	C₂	semidirect
10. C₄₁×#3307	C₂	semidirect
11. C₄₁×#3283	C₂	semidirect
12. C₄₁×#3280	C₂	semidirect
13. C₄₁×#3280	C₂	semidirect
14. C₄₁×#3177	C₂	semidirect
15. C₄₁×#3175	C₂	semidirect
16. C₄₁×#3168	C₂	semidirect
17. C₄₁×#3125	C₂	semidirect
18. C₄₁×#3123	C₂	semidirect
19. C₄₁×#3111	C₂	semidirect
20. C₄₁×#2966	C₂	semidirect
21. C₄₁×#2951	C₂	semidirect
22. C₄₁×#2948	C₂	semidirect
23. C₄×#135×C₄₁	C₂	semidirect
28. C₄₁×#556	C₂²	semidirect
29. C₄₁×#554	C₂²	semidirect
31. C₄₁×#553	C₂²	semidirect
36. C₄₁×#547	C₂²	semidirect
39. C₄₁×#542	C₂²	semidirect
45. C₄₁×#529	C₂²	semidirect
47. C₄₁×#520	C₂²	semidirect
49. C₄×#41×C₄₁	C₂²	semidirect
50. C₄₁×#500	C₂²	semidirect
51. C₄₁×#499	C₂²	semidirect
52. C₄₁×#499	C₂²	semidirect
55. C₄₁×#494	C₂²	semidirect
56. C₄₁×#491	C₂²	semidirect
57. C₄₁×#489	C₂²	semidirect
58. C₄₁×#488	C₂²	semidirect
61. C₄₁×#485	C₂²	semidirect
62. C₄₁×#483	C₂²	semidirect
63. C₄₁×#482	C₂²	semidirect
64. C₄₁×#481	C₂²	semidirect
65. C₄₁×#479	C₂²	semidirect
66. C₄₁×#478	C₂²	semidirect
67. C₄₁×#478	C₂²	semidirect
68. C₄₁×#478	C₂²	semidirect
69. C₄₁×#476	C₂²	semidirect
70. C₄₁×#475	C₂²	semidirect
72. C₄₁×#468	C₂²	semidirect
75. C₄₁×#467	C₂²	semidirect
76. C₄₁×#467	C₂²	semidirect
79. C₄₁×#465	C₂²	semidirect
80. C₄₁×#464	C₂²	semidirect
81. C₄₁×#464	C₂²	semidirect
84. C₄₁×#461	C₂²	semidirect
85. C₄₁×#461	C₂²	semidirect
86. C₄₁×#452	C₂²	semidirect
87. C₄₁×#452	C₂²	semidirect
92. C₄₁×#446	C₂²	semidirect
93. C₈×Q₈×C₄₁	C₂²	semidirect
96. C₄₁×#441	C₂²	semidirect
97. C₄₁×#440	C₂²	semidirect
98. C₄₁×#440	C₂²	semidirect
99. C₄₁×#440	C₂²	semidirect
100. C₄×Q₁₆×C₄₁	C₂²	semidirect
101. C₄×Q₁₆×C₄₁	C₂²	semidirect
102. C₄×Q₁₆×C₄₁	C₂²	semidirect
103. C₄×Q₁₆×C₄₁	C₂²	semidirect
104. C₄×SD₁₆×C₄₁	C₂²	semidirect
105. C₄×SD₁₆×C₄₁	C₂²	semidirect
106. C₄×SD₁₆×C₄₁	C₂²	semidirect
115. C₄₁×#435	C₂²	semidirect
118. C₈×D₄×C₄₁	C₂²	semidirect
120. C₄₁×#433	C₂²	semidirect
121. C₄₁×#432	C₂²	semidirect
123. C₄₁×#427	C₂²	semidirect
124. C₂×#107×C₄₁	C₂²	semidirect
126. C₄₁×#417	C₂²	semidirect
127. C₄₁×#416	C₂²	semidirect
129. C₄₁×#405	C₂²	semidirect
130. C₂×C₄×C₈×C₄₁	C₂²	semidirect
495. #61487	C₄₁	direct (N × H)
532. #3521	C₂×C₄₁	semidirect
533. #3393	C₂×C₄₁	semidirect
534. #3380	C₂×C₄₁	semidirect
535. #3376	C₂×C₄₁	semidirect
536. #3342	C₂×C₄₁	semidirect
537. #3339	C₂×C₄₁	semidirect
538. #3336	C₂×C₄₁	semidirect
539. #3323	C₂×C₄₁	semidirect
540. #3311	C₂×C₄₁	semidirect
541. #3307	C₂×C₄₁	semidirect
542. #3283	C₂×C₄₁	semidirect
543. #3280	C₂×C₄₁	semidirect
544. #3280	C₂×C₄₁	semidirect
545. #3177	C₂×C₄₁	semidirect
546. #3175	C₂×C₄₁	semidirect
547. #3168	C₂×C₄₁	semidirect
548. #3125	C₂×C₄₁	semidirect
549. #3123	C₂×C₄₁	semidirect
550. #3111	C₂×C₄₁	semidirect
551. #2966	C₂×C₄₁	semidirect
552. #2951	C₂×C₄₁	semidirect
553. #2948	C₂×C₄₁	semidirect
554. C₄×#135	C₂×C₄₁	semidirect
567. #556	C₂²×C₄₁	semidirect
568. #554	C₂²×C₄₁	semidirect
570. #553	C₂²×C₄₁	semidirect
575. #547	C₂²×C₄₁	semidirect
578. #542	C₂²×C₄₁	semidirect
584. #529	C₂²×C₄₁	semidirect
586. #520	C₂²×C₄₁	semidirect
588. C₄×#41	C₂²×C₄₁	semidirect
589. #500	C₂²×C₄₁	semidirect
590. #499	C₂²×C₄₁	semidirect
591. #499	C₂²×C₄₁	semidirect
594. #494	C₂²×C₄₁	semidirect
595. #491	C₂²×C₄₁	semidirect
596. #489	C₂²×C₄₁	semidirect
597. #488	C₂²×C₄₁	semidirect
600. #485	C₂²×C₄₁	semidirect
601. #483	C₂²×C₄₁	semidirect
602. #482	C₂²×C₄₁	semidirect
603. #481	C₂²×C₄₁	semidirect
604. #479	C₂²×C₄₁	semidirect
605. #478	C₂²×C₄₁	semidirect
606. #478	C₂²×C₄₁	semidirect
607. #478	C₂²×C₄₁	semidirect
608. #476	C₂²×C₄₁	semidirect
609. #475	C₂²×C₄₁	semidirect
611. #468	C₂²×C₄₁	semidirect
614. #467	C₂²×C₄₁	semidirect
615. #467	C₂²×C₄₁	semidirect
618. #465	C₂²×C₄₁	semidirect
619. #464	C₂²×C₄₁	semidirect
620. #464	C₂²×C₄₁	semidirect
623. #461	C₂²×C₄₁	semidirect
624. #461	C₂²×C₄₁	semidirect
625. #452	C₂²×C₄₁	semidirect
626. #452	C₂²×C₄₁	semidirect
631. #446	C₂²×C₄₁	semidirect
632. C₈×Q₈	C₂²×C₄₁	semidirect
635. #441	C₂²×C₄₁	semidirect
636. #440	C₂²×C₄₁	semidirect
637. #440	C₂²×C₄₁	semidirect
638. #440	C₂²×C₄₁	semidirect
639. C₄×Q₁₆	C₂²×C₄₁	semidirect
640. C₄×Q₁₆	C₂²×C₄₁	semidirect
641. C₄×Q₁₆	C₂²×C₄₁	semidirect
642. C₄×Q₁₆	C₂²×C₄₁	semidirect
643. C₄×SD₁₆	C₂²×C₄₁	semidirect
644. C₄×SD₁₆	C₂²×C₄₁	semidirect
645. C₄×SD₁₆	C₂²×C₄₁	semidirect
654. #435	C₂²×C₄₁	semidirect
657. C₈×D₄	C₂²×C₄₁	semidirect
659. #433	C₂²×C₄₁	semidirect
660. #432	C₂²×C₄₁	semidirect
662. #427	C₂²×C₄₁	semidirect
663. C₂×#107	C₂²×C₄₁	semidirect
665. #417	C₂²×C₄₁	semidirect
666. #416	C₂²×C₄₁	semidirect
668. #405	C₂²×C₄₁	semidirect
669. C₂×C₄×C₈	C₂²×C₄₁	semidirect
670. C₄₁	#61487	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×#3521	2
C₄₁×#3393	2
C₄₁×#3380	2
C₄₁×#3376	2
C₄₁×#3342	2
C₄₁×#3339	2
C₄₁×#3336	2
C₄₁×#3323	2
C₄₁×#3311	2
C₄₁×#3307	2
C₄₁×#3283	2
C₄₁×#3280	2
C₄₁×#3177	2
C₄₁×#3175	2
C₄₁×#3168	2
C₄₁×#3125	2
C₄₁×#3123	2
C₄₁×#3111	2
C₄₁×#2966	2
C₄₁×#2951	2
C₄₁×#2948	2
C₄×#135×C₄₁	2
#61487	41

Subgroups — C41×#61487 #23837688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61487 #23837688