Subgroups — C₄₁×#60871 #23837072

Order 10496.

1742 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3494	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#544	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3243	C₂	1	4	yes	maximal, complemented
4	C₄₁×#3241	C₂	1	4	yes	maximal, complemented
5	C₄₁×#3238	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3234	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3232	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3226	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3164	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3136	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3094	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3092	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3091	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄₁×#480	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3083	C₂	1	2	yes	maximal, complemented
16	C₄₁×#3081	C₂	1	2	yes	maximal, complemented
17	C₄₁×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄₁×#555	—	2	1	no	—
19	C₄₁×#553	—	2	1	no	—
20	C₄₁×#553	—	2	1	no	—
21	C₄₁×#551	—	2	2	no	—
22	C₄₁×#547	—	2	1	no	—
23	C₄₁×#546	—	2	2	no	—
24	C₄₁×#544	—	2	2	no	—
25	C₄₁×#544	—	2	1	no	—
26	C₄₁×#544	—	2	1	no	—
27	C₄₁×#544	C₂²	1	2	yes	—
28	C₄₁×#544	C₂²	1	2	yes	—
29	C₄₁×#544	C₂²	1	1	yes	characteristic
30	C₄₁×#544	C₂²	1	4	yes	complemented
31	C₄₁×#542	C₂²	1	2	yes	—
32	C₄₁×#540	C₂²	1	2	yes	—
33	C₄₁×#535	C₂²	1	1	yes	characteristic
34	C₄₁×#532	C₂²	1	2	yes	—
35	C₂×C₄⋊Q₈×C₄₁	—	2	1	no	—
36	C₂×C₄⋊Q₈×C₄₁	C₂²	1	2	yes	complemented
37	C₄₁×#529	C₂²	1	2	yes	—
38	C₂×#125×C₄₁	—	2	1	no	—
39	C₂×#125×C₄₁	C₂²	1	2	yes	complemented
40	C₄₁×#525	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊Q₈×C₄₁	—	2	2	no	—
42	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
43	C₄₁×#520	C₂²	1	1	yes	characteristic
44	C₄₁×#518	C₂²	1	1	yes	characteristic
45	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
46	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
47	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
48	C₄₁×#501	C₂²	1	4	yes	complemented
49	C₄₁×#501	C₂²	1	4	yes	complemented
50	C₄₁×#500	C₂²	1	4	yes	complemented
51	C₄₁×#499	C₂²	1	4	yes	complemented
52	C₄₁×#490	C₂²	1	4	yes	complemented
53	C₄₁×#489	C₂²	1	4	yes	complemented
54	C₄₁×#488	C₂²	1	4	yes	complemented
55	C₄₁×#486	C₂²	1	4	yes	complemented
56	C₄₁×#485	C₂²	1	2	yes	complemented
57	C₄₁×#484	C₂²	1	1	yes	characteristic, complemented
58	C₄₁×#484	C₂²	1	2	yes	complemented
59	C₄₁×#483	C₂²	1	1	yes	characteristic, complemented
60	C₄₁×#483	C₂²	1	2	yes	complemented
61	C₄₁×#482	C₂²	1	4	yes	—
62	C₄₁×#482	C₂²	1	2	yes	complemented
63	C₄₁×#481	C₂²	1	2	yes	—
64	C₄₁×#481	C₂²	1	1	yes	characteristic, complemented
65	C₄₁×#481	C₂²	1	2	yes	complemented
66	C₄₁×#480	C₂²	1	2	yes	—
67	C₄₁×#480	C₂²	1	2	yes	—
68	C₄₁×#480	C₂²	1	4	yes	—
69	C₄₁×#480	C₂²	1	2	yes	—
70	C₄₁×#480	C₂²	1	1	yes	characteristic, complemented
71	C₄₁×#480	C₂²	1	2	yes	complemented
72	C₄₁×#479	C₂²	1	4	yes	complemented
73	C₄₁×#478	C₂²	1	4	yes	complemented
74	C₄₁×#478	C₂²	1	4	yes	complemented
75	C₄₁×#478	C₂²	1	4	yes	complemented
76	C₄₁×#477	C₂²	1	4	yes	complemented
77	C₄₁×#476	C₂²	1	4	yes	complemented
78	C₄₁×#474	C₂²	1	4	yes	complemented
79	C₄₁×#474	C₂²	1	4	yes	complemented
80	C₄₁×#433	C₂²	1	4	yes	complemented
81	C₄₁×#432	C₂²	1	2	yes	complemented
82	C₄₁×#431	C₂²	1	2	yes	complemented
83	C₄₁×#428	C₂²	1	2	yes	—
84	C₄₁×#428	C₂²	1	2	yes	—
85	C₄₁×#427	C₂²	1	2	yes	—
86	C₂×#107×C₄₁	C₂²	1	2	yes	—
87	C₄₁×#424	C₂²	1	2	yes	—
88	C₄₁×#418	C₂²	1	2	yes	—
89	C₄₁×#417	C₂²	1	2	yes	—
90	C₄₁×#416	C₂²	1	2	yes	—
91	C₂×#102×C₄₁	C₂²	1	2	yes	—
92	C₄₁×#407	C₂²	1	1	yes	characteristic
93	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
94	C₄₁×#405	C₂²	1	2	yes	—
95	C₂×#41×C₄₁	—	2	2	no	—
96	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₄₁	—	2	2	no	—
98	C₂²×D₄×C₄₁	—	2	1	no	—
99	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₄₁	—	2	1	no	—
101	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
102	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
103	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
104	C₄⋊Q₈×C₄₁	—	2	2	no	—
105	C₄⋊Q₈×C₄₁	—	2	2	no	—
106	C₄⋊Q₈×C₄₁	—	2	4	no	—
107	C₄⋊Q₈×C₄₁	—	2	1	no	—
108	C₄⋊Q₈×C₄₁	—	2	2	no	—
109	C₄⋊Q₈×C₄₁	—	2	2	no	—
110	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
111	C₄⋊Q₈×C₄₁	C₂³	1	4	yes	—
112	C₄⋊Q₈×C₄₁	C₂³	1	4	yes	—
113	#127×C₄₁	C₂³	1	2	yes	—
114	#126×C₄₁	—	2	2	no	—
115	#126×C₄₁	—	2	2	no	—
116	#125×C₄₁	—	2	2	no	—
117	#125×C₄₁	—	2	2	no	—
118	#125×C₄₁	—	2	4	no	—
119	#125×C₄₁	—	2	1	no	—
120	#125×C₄₁	—	2	2	no	—
121	#125×C₄₁	—	2	2	no	—
122	#125×C₄₁	C₂³	1	2	yes	—
123	#125×C₄₁	C₂³	1	4	yes	—
124	#125×C₄₁	C₂³	1	4	yes	—
125	#124×C₄₁	—	2	2	no	—
126	#124×C₄₁	—	2	2	no	—
127	#124×C₄₁	C₂³	1	2	yes	—
128	#123×C₄₁	—	2	1	no	—
129	#123×C₄₁	—	2	2	no	—
130	#123×C₄₁	—	2	2	no	—
131	#123×C₄₁	—	2	2	no	—
132	#123×C₄₁	—	2	2	no	—
133	C₂²⋊Q₈×C₄₁	—	2	2	no	—
134	C₂²⋊Q₈×C₄₁	—	2	4	no	—
135	C₂²⋊Q₈×C₄₁	—	2	4	no	—
136	C₂²⋊Q₈×C₄₁	—	2	4	no	—
137	C₂²⋊Q₈×C₄₁	—	2	4	no	—
138	C₂²⋊Q₈×C₄₁	—	2	2	no	—
139	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
140	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
141	#121×C₄₁	—	2	1	no	—
142	#121×C₄₁	—	2	1	no	—
143	#121×C₄₁	—	2	2	no	—
144	#121×C₄₁	—	2	1	no	—
145	#121×C₄₁	—	2	1	no	—
146	#121×C₄₁	—	2	2	no	—
147	#121×C₄₁	—	2	2	no	—
148	#121×C₄₁	C₂³	1	2	yes	—
149	#121×C₄₁	C₂³	1	2	yes	—
150	#121×C₄₁	C₂³	1	1	yes	characteristic
151	#121×C₄₁	C₂³	1	1	yes	characteristic
152	#120×C₄₁	—	2	1	no	—
153	#120×C₄₁	—	2	2	no	—
154	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
155	C₄×D₄×C₄₁	—	2	1	no	—
156	C₄×D₄×C₄₁	—	2	1	no	—
157	C₄×D₄×C₄₁	—	2	2	no	—
158	C₄×D₄×C₄₁	—	2	1	no	—
159	C₄×D₄×C₄₁	—	2	1	no	—
160	C₄×D₄×C₄₁	—	2	2	no	—
161	C₄×D₄×C₄₁	—	2	2	no	—
162	C₄×D₄×C₄₁	C₂³	1	2	yes	—
163	C₄×D₄×C₄₁	C₂³	1	2	yes	—
164	C₄×D₄×C₄₁	C₂³	1	2	yes	—
165	#117×C₄₁	—	2	1	no	—
166	#117×C₄₁	—	2	1	no	—
167	#117×C₄₁	—	2	1	no	—
168	#117×C₄₁	—	2	2	no	—
169	#117×C₄₁	D₄	1	2	yes	—
170	#117×C₄₁	D₄	1	1	yes	characteristic
171	#117×C₄₁	D₄	1	1	yes	characteristic
172	#117×C₄₁	C₂³	1	2	yes	—
173	#117×C₄₁	C₂³	1	2	yes	—
174	#117×C₄₁	C₂³	1	1	yes	characteristic
175	#117×C₄₁	C₂³	1	1	yes	characteristic
176	#117×C₄₁	C₂³	1	1	yes	characteristic
177	#117×C₄₁	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
179	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
180	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
181	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
182	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
183	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
184	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
185	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
194	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
195	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
196	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
197	C₂×C₄²×C₄₁	—	2	1	no	—
198	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
199	#107×C₄₁	C₂³	1	2	yes	—
200	#107×C₄₁	C₂³	1	4	yes	—
201	#107×C₄₁	C₂³	1	4	yes	—
202	#107×C₄₁	C₂³	1	4	yes	—
203	#107×C₄₁	C₂³	1	4	yes	—
204	#107×C₄₁	C₂³	1	2	yes	—
205	#106×C₄₁	C₂³	1	2	yes	—
206	#106×C₄₁	C₂³	1	2	yes	—
207	#106×C₄₁	C₂³	1	4	yes	—
208	#106×C₄₁	C₂³	1	4	yes	—
209	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
210	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
211	#103×C₄₁	C₂³	1	2	yes	—
212	#103×C₄₁	C₂³	1	2	yes	—
213	#103×C₄₁	C₂³	1	4	yes	—
214	#102×C₄₁	C₂³	1	4	yes	—
215	#102×C₄₁	C₂³	1	4	yes	—
216	#102×C₄₁	C₂³	1	2	yes	—
217	#102×C₄₁	C₂³	1	2	yes	—
218	#102×C₄₁	C₂³	1	4	yes	—
219	#102×C₄₁	C₂³	1	4	yes	—
220	#102×C₄₁	C₂³	1	4	yes	—
221	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
222	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
223	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
224	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
225	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
226	#97×C₄₁	C₂³	1	4	yes	—
227	C₄×C₈×C₄₁	C₂³	1	4	yes	—
228	C₂⁴×C₄₁	—	2	1	no	—
229	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
230	#41×C₄₁	—	2	4	no	—
231	#41×C₄₁	—	8	4	no	—
232	C₂×Q₈×C₄₁	—	2	2	no	—
233	C₂×Q₈×C₄₁	—	2	4	no	—
234	C₂×Q₈×C₄₁	—	2	4	no	—
235	C₂×Q₈×C₄₁	—	8	4	no	—
236	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
237	C₂×D₄×C₄₁	—	2	1	no	—
238	C₂×D₄×C₄₁	—	2	1	no	—
239	C₂×D₄×C₄₁	—	2	2	no	—
240	C₂×D₄×C₄₁	—	2	1	no	—
241	C₂×D₄×C₄₁	—	2	2	no	—
242	C₂×D₄×C₄₁	—	2	1	no	—
243	C₂×D₄×C₄₁	—	2	2	no	—
244	C₂×D₄×C₄₁	—	2	2	no	—
245	C₂×D₄×C₄₁	—	2	4	no	—
246	C₂×D₄×C₄₁	—	8	2	no	—
247	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
248	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₄₁	—	2	4	no	—
250	C₂²×C₄×C₄₁	—	2	1	no	—
251	C₂²×C₄×C₄₁	—	2	1	no	—
252	C₂²×C₄×C₄₁	—	2	2	no	—
253	C₂²×C₄×C₄₁	—	2	1	no	—
254	C₂²×C₄×C₄₁	—	2	2	no	—
255	C₂²×C₄×C₄₁	—	2	2	no	—
256	C₂²×C₄×C₄₁	—	2	1	no	—
257	C₂²×C₄×C₄₁	—	2	2	no	—
258	C₂²×C₄×C₄₁	—	2	2	no	—
259	C₂²×C₄×C₄₁	—	2	2	no	—
260	C₂²×C₄×C₄₁	—	8	2	no	—
261	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
266	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
269	M₁₆×C₄₁	—	2	4	no	—
270	C₂×C₈×C₄₁	—	2	4	no	—
271	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
272	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
273	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
274	C₄⋊C₄×C₄₁	—	2	2	no	—
275	C₄⋊C₄×C₄₁	—	2	2	no	—
276	C₄⋊C₄×C₄₁	—	2	2	no	—
277	C₄⋊C₄×C₄₁	—	2	1	no	—
278	C₄⋊C₄×C₄₁	—	2	2	no	—
279	C₄⋊C₄×C₄₁	—	2	4	no	—
280	C₄⋊C₄×C₄₁	—	2	4	no	—
281	C₄⋊C₄×C₄₁	—	2	4	no	—
282	C₄⋊C₄×C₄₁	—	2	4	no	—
283	C₄⋊C₄×C₄₁	—	2	4	no	—
284	C₄⋊C₄×C₄₁	—	2	4	no	—
285	C₄⋊C₄×C₄₁	—	2	1	no	—
286	C₄⋊C₄×C₄₁	—	2	1	no	—
287	C₄⋊C₄×C₄₁	—	2	1	no	—
288	C₄⋊C₄×C₄₁	—	2	2	no	—
289	C₄⋊C₄×C₄₁	—	2	2	no	—
290	C₄⋊C₄×C₄₁	—	2	2	no	—
291	C₄⋊C₄×C₄₁	—	2	1	no	—
292	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
293	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
294	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
295	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
296	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
300	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
304	C₂²⋊C₄×C₄₁	—	2	1	no	—
305	C₂²⋊C₄×C₄₁	—	2	2	no	—
306	C₂²⋊C₄×C₄₁	—	2	2	no	—
307	C₂²⋊C₄×C₄₁	—	2	1	no	—
308	C₂²⋊C₄×C₄₁	—	2	1	no	—
309	C₂²⋊C₄×C₄₁	—	2	2	no	—
310	C₂²⋊C₄×C₄₁	—	2	2	no	—
311	C₂²⋊C₄×C₄₁	—	2	2	no	—
312	C₂²⋊C₄×C₄₁	—	2	2	no	—
313	C₂²⋊C₄×C₄₁	—	2	2	no	—
314	C₂²⋊C₄×C₄₁	—	2	2	no	—
315	C₂²⋊C₄×C₄₁	—	2	1	no	—
316	C₂²⋊C₄×C₄₁	—	2	2	no	—
317	C₂²⋊C₄×C₄₁	—	2	1	no	—
318	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
319	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
320	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
321	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
322	C₄²×C₄₁	—	2	2	no	—
323	C₄²×C₄₁	—	2	2	no	—
324	C₄²×C₄₁	—	2	2	no	—
325	C₄²×C₄₁	—	2	1	no	—
326	C₄²×C₄₁	C₂×D₄	1	2	yes	—
327	C₄²×C₄₁	C₂×D₄	1	2	yes	—
328	C₄²×C₄₁	C₂⁴	1	2	yes	—
329	C₄²×C₄₁	C₂⁴	1	2	yes	—
330	C₂³×C₄₁	—	2	2	no	—
331	C₂³×C₄₁	—	2	2	no	—
332	C₂³×C₄₁	—	2	2	no	—
333	C₂³×C₄₁	—	2	1	no	—
334	C₂³×C₄₁	—	4	1	no	—
335	C₂³×C₄₁	—	4	2	no	—
336	C₂³×C₄₁	—	8	1	no	—
337	C₂³×C₄₁	—	8	1	no	—
338	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
339	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
340	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
341	Q₈×C₄₁	—	2	2	no	—
342	Q₈×C₄₁	—	8	4	no	—
343	Q₈×C₄₁	—	8	4	no	—
344	Q₈×C₄₁	—	8	2	no	—
345	D₄×C₄₁	—	2	4	no	—
346	D₄×C₄₁	—	2	2	no	—
347	D₄×C₄₁	—	4	2	no	—
348	D₄×C₄₁	—	4	4	no	—
349	D₄×C₄₁	—	4	2	no	—
350	D₄×C₄₁	—	4	2	no	—
351	D₄×C₄₁	—	8	2	no	—
352	D₄×C₄₁	—	8	2	no	—
353	D₄×C₄₁	—	8	1	no	—
354	D₄×C₄₁	—	8	2	no	—
355	C₂×C₄×C₄₁	—	2	2	no	—
356	C₂×C₄×C₄₁	—	2	4	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	1	no	—
362	C₂×C₄×C₄₁	—	2	2	no	—
363	C₂×C₄×C₄₁	—	2	2	no	—
364	C₂×C₄×C₄₁	—	2	1	no	—
365	C₂×C₄×C₄₁	—	2	1	no	—
366	C₂×C₄×C₄₁	—	2	2	no	—
367	C₂×C₄×C₄₁	—	2	4	no	—
368	C₂×C₄×C₄₁	—	4	2	no	—
369	C₂×C₄×C₄₁	—	4	2	no	—
370	C₂×C₄×C₄₁	—	4	4	no	—
371	C₂×C₄×C₄₁	—	4	2	no	—
372	C₂×C₄×C₄₁	—	4	2	no	—
373	C₂×C₄×C₄₁	—	8	2	no	—
374	C₂×C₄×C₄₁	—	8	2	no	—
375	C₂×C₄×C₄₁	—	8	2	no	—
376	C₂×C₄×C₄₁	—	8	2	no	—
377	C₂×C₄×C₄₁	—	8	2	no	—
378	C₂×C₄×C₄₁	—	8	1	no	—
379	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
381	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₄₁	2₋¹⁺⁴	1	4	yes	—
387	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
388	C₈×C₄₁	—	2	2	no	—
389	C₈×C₄₁	—	2	2	no	—
390	C₈×C₄₁	—	2	4	no	—
391	#60871	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
392	C₂²×C₄₁	—	2	1	no	—
393	C₂²×C₄₁	—	2	1	no	—
394	C₂²×C₄₁	—	2	1	no	—
395	C₂²×C₄₁	—	2	1	no	—
396	C₂²×C₄₁	—	2	1	no	—
397	C₂²×C₄₁	—	2	1	no	—
398	C₂²×C₄₁	—	2	1	no	—
399	C₂²×C₄₁	—	4	4	no	—
400	C₂²×C₄₁	—	4	2	no	—
401	C₂²×C₄₁	—	4	1	no	—
402	C₂²×C₄₁	—	4	1	no	—
403	C₂²×C₄₁	—	4	2	no	—
404	C₂²×C₄₁	—	4	1	no	—
405	C₂²×C₄₁	—	4	2	no	—
406	C₂²×C₄₁	—	16	2	no	—
407	C₂²×C₄₁	#536	1	2	yes	—
408	C₂²×C₄₁	#576	1	2	yes	—
409	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
410	C₄×C₄₁	—	2	2	no	—
411	C₄×C₄₁	—	2	2	no	—
412	C₄×C₄₁	—	2	1	no	—
413	C₄×C₄₁	—	2	1	no	—
414	C₄×C₄₁	—	2	2	no	—
415	C₄×C₄₁	—	2	2	no	—
416	C₄×C₄₁	—	4	2	no	—
417	C₄×C₄₁	—	4	1	no	—
418	C₄×C₄₁	—	4	1	no	—
419	C₄×C₄₁	—	4	4	no	—
420	C₄×C₄₁	—	4	2	no	—
421	C₄×C₄₁	—	4	2	no	—
422	C₄×C₄₁	—	4	1	no	—
423	C₄×C₄₁	#536	1	2	yes	—
424	C₄×C₄₁	C₂×2₋¹⁺⁴	1	2	yes	—
425	#3494	C₂×C₄₁	1	1	yes	characteristic
426	C₂×#544	C₂×C₄₁	1	1	yes	characteristic, complemented
427	#3243	C₂×C₄₁	1	4	yes	complemented
428	#3241	C₂×C₄₁	1	4	yes	complemented
429	#3238	C₂×C₄₁	1	2	yes	complemented
430	#3234	C₂×C₄₁	1	2	yes	complemented
431	#3232	C₂×C₄₁	1	2	yes	complemented
432	#3226	C₂×C₄₁	1	2	yes	complemented
433	#3164	C₂×C₄₁	1	2	yes	complemented
434	#3136	C₂×C₄₁	1	2	yes	complemented
435	#3094	C₂×C₄₁	1	1	yes	characteristic, complemented
436	#3092	C₂×C₄₁	1	1	yes	characteristic, complemented
437	#3091	C₂×C₄₁	1	1	yes	characteristic, complemented
438	C₂×#480	C₂×C₄₁	1	1	yes	characteristic, complemented
439	#3083	C₂×C₄₁	1	2	yes	complemented
440	#3081	C₂×C₄₁	1	2	yes	complemented
441	#2924	C₂×C₄₁	1	1	yes	characteristic, complemented
442	C₂×C₄₁	—	2	2	no	—
443	C₂×C₄₁	—	2	2	no	—
444	C₂×C₄₁	—	4	1	no	—
445	C₂×C₄₁	—	8	1	no	—
446	C₂×C₄₁	—	8	2	no	—
447	C₂×C₄₁	C₂×#536	1	1	yes	characteristic
448	C₂×C₄₁	C₂×#576	1	1	yes	characteristic
449	C₂×C₄₁	#3586	1	1	yes	characteristic
450	#555	—	2	1	no	—
451	#553	—	2	1	no	—
452	#553	—	2	1	no	—
453	#551	—	2	2	no	—
454	#547	—	2	1	no	—
455	#546	—	2	2	no	—
456	#544	—	2	2	no	—
457	#544	—	2	1	no	—
458	#544	—	2	1	no	—
459	#544	C₂²×C₄₁	1	2	yes	—
460	#544	C₂²×C₄₁	1	2	yes	—
461	#544	C₂²×C₄₁	1	1	yes	characteristic
462	#544	C₂²×C₄₁	1	4	yes	complemented
463	#542	C₂²×C₄₁	1	2	yes	—
464	#540	C₂²×C₄₁	1	2	yes	—
465	#535	C₂²×C₄₁	1	1	yes	characteristic
466	#532	C₂²×C₄₁	1	2	yes	—
467	C₂×C₄⋊Q₈	—	2	1	no	—
468	C₂×C₄⋊Q₈	C₂²×C₄₁	1	2	yes	complemented
469	#529	C₂²×C₄₁	1	2	yes	—
470	C₂×#125	—	2	1	no	—
471	C₂×#125	C₂²×C₄₁	1	2	yes	complemented
472	#525	C₂²×C₄₁	1	1	yes	characteristic
473	C₂×C₂²⋊Q₈	—	2	2	no	—
474	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
475	#520	C₂²×C₄₁	1	1	yes	characteristic
476	#518	C₂²×C₄₁	1	1	yes	characteristic
477	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
478	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
479	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
480	#501	C₂²×C₄₁	1	4	yes	complemented
481	#501	C₂²×C₄₁	1	4	yes	complemented
482	#500	C₂²×C₄₁	1	4	yes	complemented
483	#499	C₂²×C₄₁	1	4	yes	complemented
484	#490	C₂²×C₄₁	1	4	yes	complemented
485	#489	C₂²×C₄₁	1	4	yes	complemented
486	#488	C₂²×C₄₁	1	4	yes	complemented
487	#486	C₂²×C₄₁	1	4	yes	complemented
488	#485	C₂²×C₄₁	1	2	yes	complemented
489	#484	C₂²×C₄₁	1	1	yes	characteristic, complemented
490	#484	C₂²×C₄₁	1	2	yes	complemented
491	#483	C₂²×C₄₁	1	1	yes	characteristic, complemented
492	#483	C₂²×C₄₁	1	2	yes	complemented
493	#482	C₂²×C₄₁	1	4	yes	—
494	#482	C₂²×C₄₁	1	2	yes	complemented
495	#481	C₂²×C₄₁	1	2	yes	—
496	#481	C₂²×C₄₁	1	1	yes	characteristic, complemented
497	#481	C₂²×C₄₁	1	2	yes	complemented
498	#480	C₂²×C₄₁	1	2	yes	—
499	#480	C₂²×C₄₁	1	2	yes	—
500	#480	C₂²×C₄₁	1	4	yes	—
501	#480	C₂²×C₄₁	1	2	yes	—
502	#480	C₂²×C₄₁	1	1	yes	characteristic, complemented
503	#480	C₂²×C₄₁	1	2	yes	complemented
504	#479	C₂²×C₄₁	1	4	yes	complemented
505	#478	C₂²×C₄₁	1	4	yes	complemented
506	#478	C₂²×C₄₁	1	4	yes	complemented
507	#478	C₂²×C₄₁	1	4	yes	complemented
508	#477	C₂²×C₄₁	1	4	yes	complemented
509	#476	C₂²×C₄₁	1	4	yes	complemented
510	#474	C₂²×C₄₁	1	4	yes	complemented
511	#474	C₂²×C₄₁	1	4	yes	complemented
512	#433	C₂²×C₄₁	1	4	yes	complemented
513	#432	C₂²×C₄₁	1	2	yes	complemented
514	#431	C₂²×C₄₁	1	2	yes	complemented
515	#428	C₂²×C₄₁	1	2	yes	—
516	#428	C₂²×C₄₁	1	2	yes	—
517	#427	C₂²×C₄₁	1	2	yes	—
518	C₂×#107	C₂²×C₄₁	1	2	yes	—
519	#424	C₂²×C₄₁	1	2	yes	—
520	#418	C₂²×C₄₁	1	2	yes	—
521	#417	C₂²×C₄₁	1	2	yes	—
522	#416	C₂²×C₄₁	1	2	yes	—
523	C₂×#102	C₂²×C₄₁	1	2	yes	—
524	#407	C₂²×C₄₁	1	1	yes	characteristic
525	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
526	#405	C₂²×C₄₁	1	2	yes	—
527	C₄₁	#60871	1	1	yes	characteristic, direct product factor, Sylow
528	C₂×#41	—	2	2	no	—
529	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
530	C₂²×Q₈	—	2	2	no	—
531	C₂²×D₄	—	2	1	no	—
532	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
533	C₂³×C₄	—	2	1	no	—
534	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
535	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
536	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
537	C₄⋊Q₈	—	2	2	no	—
538	C₄⋊Q₈	—	2	2	no	—
539	C₄⋊Q₈	—	2	4	no	—
540	C₄⋊Q₈	—	2	1	no	—
541	C₄⋊Q₈	—	2	2	no	—
542	C₄⋊Q₈	—	2	2	no	—
543	C₄⋊Q₈	C₂³×C₄₁	1	4	yes	—
544	C₄⋊Q₈	C₂³×C₄₁	1	4	yes	—
545	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
546	#127	C₂³×C₄₁	1	2	yes	—
547	#126	—	2	2	no	—
548	#126	—	2	2	no	—
549	#125	—	2	2	no	—
550	#125	—	2	2	no	—
551	#125	—	2	4	no	—
552	#125	—	2	1	no	—
553	#125	—	2	2	no	—
554	#125	—	2	2	no	—
555	#125	C₂³×C₄₁	1	4	yes	—
556	#125	C₂³×C₄₁	1	4	yes	—
557	#125	C₂³×C₄₁	1	2	yes	—
558	#124	—	2	2	no	—
559	#124	—	2	2	no	—
560	#124	C₂³×C₄₁	1	2	yes	—
561	#123	—	2	1	no	—
562	#123	—	2	2	no	—
563	#123	—	2	2	no	—
564	#123	—	2	2	no	—
565	#123	—	2	2	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	4	no	—
568	C₂²⋊Q₈	—	2	4	no	—
569	C₂²⋊Q₈	—	2	4	no	—
570	C₂²⋊Q₈	—	2	4	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
573	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
574	#121	—	2	1	no	—
575	#121	—	2	1	no	—
576	#121	—	2	2	no	—
577	#121	—	2	1	no	—
578	#121	—	2	1	no	—
579	#121	—	2	2	no	—
580	#121	—	2	2	no	—
581	#121	C₂³×C₄₁	1	2	yes	—
582	#121	C₂³×C₄₁	1	2	yes	—
583	#121	C₂³×C₄₁	1	1	yes	characteristic
584	#121	C₂³×C₄₁	1	1	yes	characteristic
585	#120	—	2	1	no	—
586	#120	—	2	2	no	—
587	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
588	C₄×D₄	—	2	1	no	—
589	C₄×D₄	—	2	1	no	—
590	C₄×D₄	—	2	2	no	—
591	C₄×D₄	—	2	1	no	—
592	C₄×D₄	—	2	1	no	—
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	C₂³×C₄₁	1	2	yes	—
596	C₄×D₄	C₂³×C₄₁	1	2	yes	—
597	C₄×D₄	C₂³×C₄₁	1	2	yes	—
598	#117	—	2	1	no	—
599	#117	—	2	1	no	—
600	#117	—	2	1	no	—
601	#117	—	2	2	no	—
602	#117	D₄×C₄₁	1	2	yes	—
603	#117	D₄×C₄₁	1	1	yes	characteristic
604	#117	D₄×C₄₁	1	1	yes	characteristic
605	#117	C₂³×C₄₁	1	2	yes	—
606	#117	C₂³×C₄₁	1	2	yes	—
607	#117	C₂³×C₄₁	1	1	yes	characteristic
608	#117	C₂³×C₄₁	1	1	yes	characteristic
609	#117	C₂³×C₄₁	1	1	yes	characteristic
610	#117	C₂³×C₄₁	1	2	yes	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	—	2	2	no	—
615	C₂×C₄⋊C₄	—	2	2	no	—
616	C₂×C₄⋊C₄	—	2	2	no	—
617	C₂×C₄⋊C₄	—	2	1	no	—
618	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
619	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	2	no	—
629	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
630	C₂×C₄²	—	2	1	no	—
631	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
632	#107	C₂³×C₄₁	1	4	yes	—
633	#107	C₂³×C₄₁	1	4	yes	—
634	#107	C₂³×C₄₁	1	2	yes	—
635	#107	C₂³×C₄₁	1	2	yes	—
636	#107	C₂³×C₄₁	1	4	yes	—
637	#107	C₂³×C₄₁	1	4	yes	—
638	#106	C₂³×C₄₁	1	2	yes	—
639	#106	C₂³×C₄₁	1	2	yes	—
640	#106	C₂³×C₄₁	1	4	yes	—
641	#106	C₂³×C₄₁	1	4	yes	—
642	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
643	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
644	#103	C₂³×C₄₁	1	2	yes	—
645	#103	C₂³×C₄₁	1	2	yes	—
646	#103	C₂³×C₄₁	1	4	yes	—
647	#102	C₂³×C₄₁	1	4	yes	—
648	#102	C₂³×C₄₁	1	4	yes	—
649	#102	C₂³×C₄₁	1	2	yes	—
650	#102	C₂³×C₄₁	1	2	yes	—
651	#102	C₂³×C₄₁	1	4	yes	—
652	#102	C₂³×C₄₁	1	4	yes	—
653	#102	C₂³×C₄₁	1	4	yes	—
654	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
655	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
656	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
657	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
658	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
659	#97	C₂³×C₄₁	1	4	yes	—
660	C₄×C₈	C₂³×C₄₁	1	4	yes	—
661	C₂⁴	—	2	1	no	—
662	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
663	#41	—	2	4	no	—
664	#41	—	8	4	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	4	no	—
667	C₂×Q₈	—	2	4	no	—
668	C₂×Q₈	—	8	4	no	—
669	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	8	2	no	—
680	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
681	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
682	C₂²×C₄	—	2	4	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	8	2	no	—
694	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
695	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
696	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
697	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
698	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
702	M₁₆	—	2	4	no	—
703	C₂×C₈	—	2	4	no	—
704	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
705	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
706	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
726	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
727	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
728	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
729	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
730	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
731	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
732	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
733	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
734	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
735	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
736	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
737	C₂²⋊C₄	—	2	1	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	1	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
752	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
753	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
754	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	1	no	—
759	C₄²	C₂×D₄×C₄₁	1	2	yes	—
760	C₄²	C₂×D₄×C₄₁	1	2	yes	—
761	C₄²	C₂⁴×C₄₁	1	2	yes	—
762	C₄²	C₂⁴×C₄₁	1	2	yes	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	4	1	no	—
768	C₂³	—	4	2	no	—
769	C₂³	—	8	1	no	—
770	C₂³	—	8	1	no	—
771	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
772	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
773	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
774	Q₈	—	2	2	no	—
775	Q₈	—	8	4	no	—
776	Q₈	—	8	4	no	—
777	Q₈	—	8	2	no	—
778	D₄	—	2	4	no	—
779	D₄	—	2	2	no	—
780	D₄	—	4	2	no	—
781	D₄	—	4	4	no	—
782	D₄	—	4	2	no	—
783	D₄	—	4	2	no	—
784	D₄	—	8	2	no	—
785	D₄	—	8	2	no	—
786	D₄	—	8	2	no	—
787	D₄	—	8	1	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	4	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	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	4	2	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	4	4	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	8	2	no	—
807	C₂×C₄	—	8	2	no	—
808	C₂×C₄	—	8	2	no	—
809	C₂×C₄	—	8	2	no	—
810	C₂×C₄	—	8	2	no	—
811	C₂×C₄	—	8	1	no	—
812	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
813	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
814	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
816	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
817	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
818	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
819	C₂×C₄	2₋¹⁺⁴×C₄₁	1	4	yes	—
820	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
821	C₈	—	2	2	no	—
822	C₈	—	2	2	no	—
823	C₈	—	2	4	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	2	1	no	—
830	C₂²	—	2	1	no	—
831	C₂²	—	4	4	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	16	2	no	—
839	C₂²	C₄₁×#536	1	2	yes	—
840	C₂²	C₄₁×#576	1	2	yes	—
841	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	1	no	—
847	C₄	—	2	1	no	—
848	C₄	—	4	4	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	1	no	—
855	C₄	C₄₁×#536	1	2	yes	—
856	C₄	C₂×2₋¹⁺⁴×C₄₁	1	2	yes	—
857	C₂	—	2	2	no	—
858	C₂	—	2	2	no	—
859	C₂	—	4	1	no	—
860	C₂	—	8	2	no	—
861	C₂	—	8	1	no	—
862	C₂	C₂×C₄₁×#536	1	1	yes	characteristic
863	C₂	C₂×C₄₁×#576	1	1	yes	characteristic
864	C₂	C₄₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
prime radical	C₄₁×#3494	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×#117×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#544	C₂	semidirect
3. C₄₁×#3243	C₂	semidirect
4. C₄₁×#3241	C₂	semidirect
5. C₄₁×#3238	C₂	semidirect
6. C₄₁×#3234	C₂	semidirect
7. C₄₁×#3232	C₂	semidirect
8. C₄₁×#3226	C₂	semidirect
9. C₄₁×#3164	C₂	semidirect
10. C₄₁×#3136	C₂	semidirect
11. C₄₁×#3094	C₂	semidirect
12. C₄₁×#3092	C₂	semidirect
13. C₄₁×#3091	C₂	semidirect
14. C₂×C₄₁×#480	C₂	semidirect
15. C₄₁×#3083	C₂	semidirect
16. C₄₁×#3081	C₂	semidirect
17. C₄₁×#2924	C₂	semidirect
30. C₄₁×#544	C₂²	semidirect
36. C₂×C₄⋊Q₈×C₄₁	C₂²	semidirect
39. C₂×#125×C₄₁	C₂²	semidirect
48. C₄₁×#501	C₂²	semidirect
49. C₄₁×#501	C₂²	semidirect
50. C₄₁×#500	C₂²	semidirect
51. C₄₁×#499	C₂²	semidirect
52. C₄₁×#490	C₂²	semidirect
53. C₄₁×#489	C₂²	semidirect
54. C₄₁×#488	C₂²	semidirect
55. C₄₁×#486	C₂²	semidirect
56. C₄₁×#485	C₂²	semidirect
57. C₄₁×#484	C₂²	semidirect
58. C₄₁×#484	C₂²	semidirect
59. C₄₁×#483	C₂²	semidirect
60. C₄₁×#483	C₂²	semidirect
62. C₄₁×#482	C₂²	semidirect
64. C₄₁×#481	C₂²	semidirect
65. C₄₁×#481	C₂²	semidirect
70. C₄₁×#480	C₂²	semidirect
71. C₄₁×#480	C₂²	semidirect
72. C₄₁×#479	C₂²	semidirect
73. C₄₁×#478	C₂²	semidirect
74. C₄₁×#478	C₂²	semidirect
75. C₄₁×#478	C₂²	semidirect
76. C₄₁×#477	C₂²	semidirect
77. C₄₁×#476	C₂²	semidirect
78. C₄₁×#474	C₂²	semidirect
79. C₄₁×#474	C₂²	semidirect
80. C₄₁×#433	C₂²	semidirect
81. C₄₁×#432	C₂²	semidirect
82. C₄₁×#431	C₂²	semidirect
391. #60871	C₄₁	direct (N × H)
426. C₂×#544	C₂×C₄₁	semidirect
427. #3243	C₂×C₄₁	semidirect
428. #3241	C₂×C₄₁	semidirect
429. #3238	C₂×C₄₁	semidirect
430. #3234	C₂×C₄₁	semidirect
431. #3232	C₂×C₄₁	semidirect
432. #3226	C₂×C₄₁	semidirect
433. #3164	C₂×C₄₁	semidirect
434. #3136	C₂×C₄₁	semidirect
435. #3094	C₂×C₄₁	semidirect
436. #3092	C₂×C₄₁	semidirect
437. #3091	C₂×C₄₁	semidirect
438. C₂×#480	C₂×C₄₁	semidirect
439. #3083	C₂×C₄₁	semidirect
440. #3081	C₂×C₄₁	semidirect
441. #2924	C₂×C₄₁	semidirect
462. #544	C₂²×C₄₁	semidirect
468. C₂×C₄⋊Q₈	C₂²×C₄₁	semidirect
471. C₂×#125	C₂²×C₄₁	semidirect
480. #501	C₂²×C₄₁	semidirect
481. #501	C₂²×C₄₁	semidirect
482. #500	C₂²×C₄₁	semidirect
483. #499	C₂²×C₄₁	semidirect
484. #490	C₂²×C₄₁	semidirect
485. #489	C₂²×C₄₁	semidirect
486. #488	C₂²×C₄₁	semidirect
487. #486	C₂²×C₄₁	semidirect
488. #485	C₂²×C₄₁	semidirect
489. #484	C₂²×C₄₁	semidirect
490. #484	C₂²×C₄₁	semidirect
491. #483	C₂²×C₄₁	semidirect
492. #483	C₂²×C₄₁	semidirect
494. #482	C₂²×C₄₁	semidirect
496. #481	C₂²×C₄₁	semidirect
497. #481	C₂²×C₄₁	semidirect
502. #480	C₂²×C₄₁	semidirect
503. #480	C₂²×C₄₁	semidirect
504. #479	C₂²×C₄₁	semidirect
505. #478	C₂²×C₄₁	semidirect
506. #478	C₂²×C₄₁	semidirect
507. #478	C₂²×C₄₁	semidirect
508. #477	C₂²×C₄₁	semidirect
509. #476	C₂²×C₄₁	semidirect
510. #474	C₂²×C₄₁	semidirect
511. #474	C₂²×C₄₁	semidirect
512. #433	C₂²×C₄₁	semidirect
513. #432	C₂²×C₄₁	semidirect
514. #431	C₂²×C₄₁	semidirect
527. C₄₁	#60871	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×#3494	2
C₂×C₄₁×#544	2
C₄₁×#3243	2
C₄₁×#3241	2
C₄₁×#3238	2
C₄₁×#3234	2
C₄₁×#3232	2
C₄₁×#3226	2
C₄₁×#3164	2
C₄₁×#3136	2
C₄₁×#3094	2
C₄₁×#3092	2
C₄₁×#3091	2
C₂×C₄₁×#480	2
C₄₁×#3083	2
C₄₁×#3081	2
C₄₁×#2924	2
#60871	41

Subgroups — C41×#60871 #23837072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#60871 #23837072