Subgroups — C₄₁×#60593 #23836794

Order 10496.

2110 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×2₋¹⁺⁴×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3126	C₂	1	4	yes	maximal, complemented
4	C₄₁×#3119	C₂	1	4	yes	maximal, complemented
5	C₄₁×#3115	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3112	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3106	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3103	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3096	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3038	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄₁×#460	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3010	C₂	1	2	yes	maximal, complemented
15	C₄₁×#2949	C₂	1	2	yes	maximal, complemented
16	C₄₁×#2946	C₂	1	2	yes	maximal, complemented
17	C₄₁×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×2₋¹⁺⁴×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	2	yes	—
20	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
21	C₄₁×#559	—	2	1	no	—
22	C₄₁×#559	—	2	1	no	—
23	C₄₁×#550	—	2	1	no	—
24	C₄₁×#550	—	2	1	no	—
25	C₄₁×#546	—	2	2	no	—
26	C₄₁×#546	—	2	2	no	—
27	C₄₁×#540	C₂²	1	4	yes	—
28	C₄₁×#535	C₂²	1	2	yes	—
29	C₄₁×#533	C₂²	1	1	yes	characteristic
30	C₄₁×#532	C₂²	1	2	yes	—
31	C₄₁×#532	C₂²	1	2	yes	—
32	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
33	C₄₁×#520	—	2	2	no	—
34	C₄₁×#520	—	2	1	no	—
35	C₄₁×#520	C₂²	1	1	yes	characteristic
36	C₄₁×#520	C₂²	1	1	yes	characteristic
37	C₄₁×#520	C₂²	1	2	yes	complemented
38	C₄₁×#519	—	2	1	no	—
39	C₄₁×#519	C₂²	1	1	yes	characteristic
40	C₄₁×#519	C₂²	1	2	yes	complemented
41	C₄₁×#518	C₂²	1	2	yes	—
42	C₄×#41×C₄₁	—	2	2	no	—
43	C₄×#41×C₄₁	—	2	1	no	—
44	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
45	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
46	C₄×#41×C₄₁	C₂²	1	2	yes	complemented
47	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
48	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	complemented
50	C₄₁×#482	C₂²	1	4	yes	complemented
51	C₄₁×#482	C₂²	1	4	yes	complemented
52	C₄₁×#481	C₂²	1	4	yes	complemented
53	C₄₁×#480	C₂²	1	4	yes	complemented
54	C₄₁×#479	C₂²	1	2	yes	complemented
55	C₄₁×#479	C₂²	1	4	yes	complemented
56	C₄₁×#478	C₂²	1	2	yes	complemented
57	C₄₁×#477	C₂²	1	1	yes	characteristic, complemented
58	C₄₁×#477	C₂²	1	2	yes	complemented
59	C₄₁×#476	C₂²	1	1	yes	characteristic, complemented
60	C₄₁×#475	C₂²	1	1	yes	characteristic, complemented
61	C₄₁×#475	C₂²	1	2	yes	complemented
62	C₄₁×#474	C₂²	1	1	yes	characteristic, complemented
63	C₄₁×#460	C₂²	1	2	yes	—
64	C₄₁×#460	C₂²	1	2	yes	—
65	C₄₁×#460	C₂²	1	2	yes	—
66	C₄₁×#460	C₂²	1	2	yes	—
67	C₄₁×#460	C₂²	1	4	yes	—
68	C₄₁×#459	C₂²	1	2	yes	—
69	C₄₁×#459	C₂²	1	2	yes	—
70	C₄₁×#449	C₂²	1	4	yes	complemented
71	C₄₁×#449	C₂²	1	4	yes	complemented
72	C₄₁×#448	C₂²	1	4	yes	complemented
73	C₄₁×#448	C₂²	1	4	yes	complemented
74	C₄₁×#442	C₂²	1	4	yes	complemented
75	C₄₁×#440	C₂²	1	4	yes	complemented
76	C₄₁×#440	C₂²	1	4	yes	complemented
77	C₄₁×#440	C₂²	1	4	yes	complemented
78	C₄×SD₁₆×C₄₁	C₂²	1	4	yes	complemented
79	C₄×SD₁₆×C₄₁	C₂²	1	4	yes	complemented
80	C₄×SD₁₆×C₄₁	C₂²	1	4	yes	complemented
81	C₄×D₈×C₄₁	C₂²	1	4	yes	complemented
82	C₄₁×#433	C₂²	1	4	yes	complemented
83	C₄₁×#432	C₂²	1	2	yes	complemented
84	C₄₁×#431	C₂²	1	2	yes	complemented
85	C₄₁×#428	C₂²	1	2	yes	—
86	C₄₁×#427	C₂²	1	2	yes	—
87	C₄₁×#423	C₂²	1	1	yes	characteristic
88	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
89	C₄₁×#419	C₂²	1	2	yes	—
90	C₄₁×#418	C₂²	1	2	yes	—
91	C₄₁×#416	C₂²	1	2	yes	—
92	C₂×#102×C₄₁	C₂²	1	2	yes	—
93	C₄₁×#408	C₂²	1	2	yes	—
94	C₄₁×#405	C₂²	1	2	yes	—
95	2₋¹⁺⁴×C₄₁	—	2	4	no	—
96	2₋¹⁺⁴×C₄₁	—	2	4	no	—
97	C₂×#41×C₄₁	—	2	2	no	—
98	C₂×#41×C₄₁	—	2	1	no	—
99	C₂×#41×C₄₁	—	2	2	no	—
100	C₂×#41×C₄₁	—	2	2	no	—
101	C₂×#41×C₄₁	C₂³	1	2	yes	—
102	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
103	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
104	C₂²×Q₈×C₄₁	—	2	1	no	—
105	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
106	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
107	C₂²×D₄×C₄₁	—	2	1	no	—
108	C₂²×D₄×C₄₁	—	2	1	no	—
109	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
110	AGL(1,ℤ/8)×C₄₁	—	2	8	no	—
111	C₂×SD₁₆×C₄₁	—	2	8	no	—
112	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
113	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
114	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
115	C₂×D₈×C₄₁	C₂³	1	4	yes	—
116	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
117	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
118	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
119	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
120	#127×C₄₁	—	2	2	no	—
121	#127×C₄₁	—	2	1	no	—
122	#127×C₄₁	—	2	1	no	—
123	#127×C₄₁	C₂³	1	2	yes	—
124	#127×C₄₁	C₂³	1	2	yes	—
125	#125×C₄₁	C₂³	1	2	yes	—
126	#124×C₄₁	—	2	2	no	—
127	#124×C₄₁	—	2	2	no	—
128	#124×C₄₁	—	2	2	no	—
129	#123×C₄₁	—	2	4	no	—
130	#123×C₄₁	—	2	4	no	—
131	C₂²⋊Q₈×C₄₁	—	2	1	no	—
132	C₂²⋊Q₈×C₄₁	—	2	1	no	—
133	#121×C₄₁	—	2	2	no	—
134	#121×C₄₁	—	2	2	no	—
135	#121×C₄₁	—	2	4	no	—
136	#121×C₄₁	—	2	4	no	—
137	#121×C₄₁	C₂³	1	4	yes	—
138	#121×C₄₁	C₂³	1	4	yes	—
139	#120×C₄₁	—	2	4	no	—
140	C₄×Q₈×C₄₁	—	2	1	no	—
141	C₄×Q₈×C₄₁	—	2	1	no	—
142	C₄×Q₈×C₄₁	—	2	2	no	—
143	C₄×Q₈×C₄₁	—	2	1	no	—
144	C₄×Q₈×C₄₁	—	2	2	no	—
145	C₄×Q₈×C₄₁	—	2	1	no	—
146	C₄×Q₈×C₄₁	—	2	2	no	—
147	C₄×Q₈×C₄₁	—	2	1	no	—
148	C₄×Q₈×C₄₁	—	2	2	no	—
149	C₄×Q₈×C₄₁	—	2	1	no	—
150	C₄×Q₈×C₄₁	—	2	1	no	—
151	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
152	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
153	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
154	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
155	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
156	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
157	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
158	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
159	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
160	C₄×D₄×C₄₁	—	2	2	no	—
161	C₄×D₄×C₄₁	—	2	1	no	—
162	C₄×D₄×C₄₁	—	2	1	no	—
163	C₄×D₄×C₄₁	—	2	2	no	—
164	C₄×D₄×C₄₁	—	2	1	no	—
165	C₄×D₄×C₄₁	—	2	2	no	—
166	C₄×D₄×C₄₁	—	2	2	no	—
167	C₄×D₄×C₄₁	—	2	2	no	—
168	C₄×D₄×C₄₁	—	2	2	no	—
169	C₄×D₄×C₄₁	—	2	2	no	—
170	C₄×D₄×C₄₁	—	2	2	no	—
171	C₄×D₄×C₄₁	—	2	2	no	—
172	C₄×D₄×C₄₁	—	2	2	no	—
173	C₄×D₄×C₄₁	D₄	1	2	yes	—
174	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
175	C₄×D₄×C₄₁	D₄	1	2	yes	—
176	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
177	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₄₁	C₂³	1	2	yes	—
180	C₄×D₄×C₄₁	C₂³	1	4	yes	—
181	C₄×D₄×C₄₁	C₂³	1	4	yes	—
182	#117×C₄₁	—	2	1	no	—
183	#117×C₄₁	—	2	2	no	—
184	#117×C₄₁	—	2	2	no	—
185	#117×C₄₁	—	2	2	no	—
186	#117×C₄₁	—	2	2	no	—
187	#117×C₄₁	—	2	1	no	—
188	#117×C₄₁	—	2	2	no	—
189	#117×C₄₁	C₂³	1	1	yes	characteristic
190	#117×C₄₁	C₂³	1	2	yes	—
191	#117×C₄₁	C₂³	1	2	yes	—
192	#117×C₄₁	C₂³	1	1	yes	characteristic
193	#117×C₄₁	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
195	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
196	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
197	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
198	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
201	C₂×C₄²×C₄₁	—	2	1	no	—
202	C₂×C₄²×C₄₁	—	2	2	no	—
203	C₂×C₄²×C₄₁	—	2	1	no	—
204	C₂×C₄²×C₄₁	—	2	2	no	—
205	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
207	#107×C₄₁	C₂³	1	2	yes	—
208	#107×C₄₁	C₂³	1	2	yes	—
209	#107×C₄₁	C₂³	1	4	yes	—
210	#106×C₄₁	C₂³	1	2	yes	—
211	#106×C₄₁	C₂³	1	2	yes	—
212	#106×C₄₁	C₂³	1	4	yes	—
213	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
214	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
215	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
216	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
217	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
218	#103×C₄₁	C₂³	1	2	yes	—
219	#103×C₄₁	C₂³	1	2	yes	—
220	#103×C₄₁	C₂³	1	4	yes	—
221	#103×C₄₁	C₂³	1	4	yes	—
222	#102×C₄₁	C₂³	1	4	yes	—
223	#102×C₄₁	C₂³	1	4	yes	—
224	#102×C₄₁	C₂³	1	2	yes	—
225	#102×C₄₁	C₂³	1	2	yes	—
226	#102×C₄₁	C₂³	1	4	yes	—
227	#102×C₄₁	C₂³	1	4	yes	—
228	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
229	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
230	#97×C₄₁	C₂³	1	4	yes	—
231	C₄×C₈×C₄₁	C₂³	1	4	yes	—
232	C₂⁴×C₄₁	—	2	2	no	—
233	#41×C₄₁	—	2	16	no	—
234	#41×C₄₁	—	2	8	no	—
235	#41×C₄₁	—	2	4	no	—
236	#41×C₄₁	—	2	4	no	—
237	#41×C₄₁	—	2	2	no	—
238	#41×C₄₁	—	2	2	no	—
239	#41×C₄₁	—	2	2	no	—
240	#41×C₄₁	—	8	4	no	—
241	#41×C₄₁	—	8	4	no	—
242	#41×C₄₁	#41	1	4	yes	complemented
243	C₂×Q₈×C₄₁	—	2	8	no	—
244	C₂×Q₈×C₄₁	—	2	4	no	—
245	C₂×Q₈×C₄₁	—	2	4	no	—
246	C₂×Q₈×C₄₁	—	2	2	no	—
247	C₂×Q₈×C₄₁	—	2	1	no	—
248	C₂×Q₈×C₄₁	—	2	1	no	—
249	C₂×Q₈×C₄₁	—	2	1	no	—
250	C₂×Q₈×C₄₁	—	2	2	no	—
251	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
252	C₂×Q₈×C₄₁	#41	1	4	yes	complemented
253	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
254	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
255	C₂×D₄×C₄₁	—	2	2	no	—
256	C₂×D₄×C₄₁	—	2	1	no	—
257	C₂×D₄×C₄₁	—	2	4	no	—
258	C₂×D₄×C₄₁	—	2	4	no	—
259	C₂×D₄×C₄₁	—	2	2	no	—
260	C₂×D₄×C₄₁	—	2	2	no	—
261	C₂×D₄×C₄₁	—	2	2	no	—
262	C₂×D₄×C₄₁	—	2	2	no	—
263	C₂×D₄×C₄₁	—	2	2	no	—
264	C₂×D₄×C₄₁	—	2	4	no	—
265	C₂×D₄×C₄₁	—	2	4	no	—
266	C₂×D₄×C₄₁	—	8	2	no	—
267	C₂×D₄×C₄₁	—	8	2	no	—
268	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
269	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
270	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
271	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₄₁	—	2	2	no	—
273	C₂²×C₄×C₄₁	—	2	1	no	—
274	C₂²×C₄×C₄₁	—	2	2	no	—
275	C₂²×C₄×C₄₁	—	2	1	no	—
276	C₂²×C₄×C₄₁	—	2	2	no	—
277	C₂²×C₄×C₄₁	—	2	1	no	—
278	C₂²×C₄×C₄₁	—	2	1	no	—
279	C₂²×C₄×C₄₁	—	2	2	no	—
280	C₂²×C₄×C₄₁	—	2	1	no	—
281	C₂²×C₄×C₄₁	—	2	4	no	—
282	C₂²×C₄×C₄₁	—	2	4	no	—
283	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
284	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
286	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
289	SD₁₆×C₄₁	—	2	8	no	—
290	SD₁₆×C₄₁	—	2	8	no	—
291	SD₁₆×C₄₁	—	2	8	no	—
292	D₈×C₄₁	—	2	8	no	—
293	M₁₆×C₄₁	—	2	4	no	—
294	C₂×C₈×C₄₁	—	2	4	no	—
295	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
296	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
297	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
298	C₄⋊C₄×C₄₁	—	2	2	no	—
299	C₄⋊C₄×C₄₁	—	2	2	no	—
300	C₄⋊C₄×C₄₁	—	2	2	no	—
301	C₄⋊C₄×C₄₁	—	2	2	no	—
302	C₄⋊C₄×C₄₁	—	2	1	no	—
303	C₄⋊C₄×C₄₁	—	2	2	no	—
304	C₄⋊C₄×C₄₁	—	2	1	no	—
305	C₄⋊C₄×C₄₁	—	2	2	no	—
306	C₄⋊C₄×C₄₁	—	2	1	no	—
307	C₄⋊C₄×C₄₁	—	2	1	no	—
308	C₄⋊C₄×C₄₁	—	2	1	no	—
309	C₄⋊C₄×C₄₁	—	2	2	no	—
310	C₄⋊C₄×C₄₁	—	2	2	no	—
311	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
312	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
313	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
314	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
315	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
316	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
317	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
318	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
319	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
320	C₂²⋊C₄×C₄₁	—	2	2	no	—
321	C₂²⋊C₄×C₄₁	—	2	2	no	—
322	C₂²⋊C₄×C₄₁	—	2	1	no	—
323	C₂²⋊C₄×C₄₁	—	2	4	no	—
324	C₂²⋊C₄×C₄₁	—	2	4	no	—
325	C₂²⋊C₄×C₄₁	—	2	1	no	—
326	C₂²⋊C₄×C₄₁	—	2	2	no	—
327	C₂²⋊C₄×C₄₁	—	2	1	no	—
328	C₂²⋊C₄×C₄₁	—	2	4	no	—
329	C₂²⋊C₄×C₄₁	—	2	4	no	—
330	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
331	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
332	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
333	C₄²×C₄₁	—	2	2	no	—
334	C₄²×C₄₁	—	2	1	no	—
335	C₄²×C₄₁	—	2	2	no	—
336	C₄²×C₄₁	—	2	1	no	—
337	C₄²×C₄₁	—	2	2	no	—
338	C₄²×C₄₁	—	2	2	no	—
339	C₄²×C₄₁	—	2	2	no	—
340	C₄²×C₄₁	—	2	2	no	—
341	C₄²×C₄₁	—	2	1	no	—
342	C₄²×C₄₁	—	2	2	no	—
343	C₄²×C₄₁	C₂×D₄	1	2	yes	—
344	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
345	C₄²×C₄₁	C₂×D₄	1	2	yes	—
346	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
347	C₄²×C₄₁	C₂⁴	1	2	yes	—
348	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
349	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
350	C₂³×C₄₁	—	2	1	no	—
351	C₂³×C₄₁	—	2	4	no	—
352	C₂³×C₄₁	—	4	4	no	—
353	C₂³×C₄₁	—	8	2	no	—
354	C₂³×C₄₁	—	8	2	no	—
355	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
356	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
357	Q₈×C₄₁	—	2	8	no	—
358	Q₈×C₄₁	—	2	2	no	—
359	Q₈×C₄₁	—	2	4	no	—
360	Q₈×C₄₁	—	2	1	no	—
361	Q₈×C₄₁	—	2	2	no	—
362	Q₈×C₄₁	—	4	2	no	—
363	Q₈×C₄₁	—	4	2	no	—
364	Q₈×C₄₁	C₂×#41	1	2	yes	—
365	Q₈×C₄₁	C₂×#41	1	4	yes	—
366	D₄×C₄₁	—	2	8	no	—
367	D₄×C₄₁	—	2	4	no	—
368	D₄×C₄₁	—	2	4	no	—
369	D₄×C₄₁	—	2	2	no	—
370	D₄×C₄₁	—	2	1	no	—
371	D₄×C₄₁	—	2	4	no	—
372	D₄×C₄₁	—	2	4	no	—
373	D₄×C₄₁	—	4	4	no	—
374	D₄×C₄₁	—	4	4	no	—
375	D₄×C₄₁	—	4	4	no	—
376	D₄×C₄₁	—	8	2	no	—
377	D₄×C₄₁	—	8	2	no	—
378	D₄×C₄₁	—	8	4	no	—
379	D₄×C₄₁	—	8	4	no	—
380	D₄×C₄₁	C₂×#41	1	2	yes	—
381	C₂×C₄×C₄₁	—	2	8	no	—
382	C₂×C₄×C₄₁	—	2	8	no	—
383	C₂×C₄×C₄₁	—	2	4	no	—
384	C₂×C₄×C₄₁	—	2	2	no	—
385	C₂×C₄×C₄₁	—	2	1	no	—
386	C₂×C₄×C₄₁	—	2	4	no	—
387	C₂×C₄×C₄₁	—	2	2	no	—
388	C₂×C₄×C₄₁	—	2	4	no	—
389	C₂×C₄×C₄₁	—	2	2	no	—
390	C₂×C₄×C₄₁	—	2	2	no	—
391	C₂×C₄×C₄₁	—	2	1	no	—
392	C₂×C₄×C₄₁	—	2	2	no	—
393	C₂×C₄×C₄₁	—	2	1	no	—
394	C₂×C₄×C₄₁	—	2	2	no	—
395	C₂×C₄×C₄₁	—	2	2	no	—
396	C₂×C₄×C₄₁	—	4	1	no	—
397	C₂×C₄×C₄₁	—	4	2	no	—
398	C₂×C₄×C₄₁	—	4	2	no	—
399	C₂×C₄×C₄₁	—	8	2	no	—
400	C₂×C₄×C₄₁	—	8	1	no	—
401	C₂×C₄×C₄₁	—	8	4	no	—
402	C₂×C₄×C₄₁	—	8	4	no	—
403	C₂×C₄×C₄₁	—	8	1	no	—
404	C₂×C₄×C₄₁	—	8	2	no	—
405	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
406	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
408	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
409	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
414	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
415	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
416	C₈×C₄₁	—	2	2	no	—
417	C₈×C₄₁	—	2	2	no	—
418	C₈×C₄₁	—	2	4	no	—
419	#60593	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
420	C₂²×C₄₁	—	2	1	no	—
421	C₂²×C₄₁	—	2	1	no	—
422	C₂²×C₄₁	—	2	2	no	—
423	C₂²×C₄₁	—	2	2	no	—
424	C₂²×C₄₁	—	2	2	no	—
425	C₂²×C₄₁	—	2	2	no	—
426	C₂²×C₄₁	—	4	1	no	—
427	C₂²×C₄₁	—	4	1	no	—
428	C₂²×C₄₁	—	4	4	no	—
429	C₂²×C₄₁	—	4	4	no	—
430	C₂²×C₄₁	—	4	4	no	—
431	C₂²×C₄₁	—	16	4	no	—
432	C₂²×C₄₁	#525	1	2	yes	—
433	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
434	C₄×C₄₁	—	2	1	no	—
435	C₄×C₄₁	—	2	2	no	—
436	C₄×C₄₁	—	2	1	no	—
437	C₄×C₄₁	—	2	4	no	—
438	C₄×C₄₁	—	2	2	no	—
439	C₄×C₄₁	—	2	2	no	—
440	C₄×C₄₁	—	2	2	no	—
441	C₄×C₄₁	—	2	1	no	—
442	C₄×C₄₁	—	4	2	no	—
443	C₄×C₄₁	—	4	1	no	—
444	C₄×C₄₁	—	4	2	no	—
445	C₄×C₄₁	—	4	1	no	—
446	C₄×C₄₁	—	4	2	no	—
447	C₄×C₄₁	#525	1	2	yes	—
448	C₄×C₄₁	#577	1	2	yes	—
449	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
450	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
451	#3508	C₂×C₄₁	1	1	yes	characteristic, complemented
452	C₄×2₋¹⁺⁴	C₂×C₄₁	1	1	yes	characteristic, complemented
453	#3126	C₂×C₄₁	1	4	yes	complemented
454	#3119	C₂×C₄₁	1	4	yes	complemented
455	#3115	C₂×C₄₁	1	2	yes	complemented
456	#3112	C₂×C₄₁	1	2	yes	complemented
457	#3106	C₂×C₄₁	1	2	yes	complemented
458	#3103	C₂×C₄₁	1	2	yes	complemented
459	#3096	C₂×C₄₁	1	2	yes	complemented
460	#3078	C₂×C₄₁	1	1	yes	characteristic, complemented
461	#3076	C₂×C₄₁	1	1	yes	characteristic, complemented
462	#3038	C₂×C₄₁	1	1	yes	characteristic, complemented
463	C₂×#460	C₂×C₄₁	1	1	yes	characteristic, complemented
464	#3010	C₂×C₄₁	1	2	yes	complemented
465	#2949	C₂×C₄₁	1	2	yes	complemented
466	#2946	C₂×C₄₁	1	2	yes	complemented
467	#2925	C₂×C₄₁	1	1	yes	characteristic, complemented
468	C₂×C₄₁	—	2	2	no	—
469	C₂×C₄₁	—	4	2	no	—
470	C₂×C₄₁	—	4	2	no	—
471	C₂×C₄₁	—	8	4	no	—
472	C₂×C₄₁	C₂×#525	1	1	yes	characteristic
473	C₂×C₄₁	C₂×#577	1	1	yes	characteristic
474	C₂×C₄₁	#3585	1	1	yes	characteristic
475	C₂×2₋¹⁺⁴	C₂²×C₄₁	1	1	yes	characteristic
476	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	2	yes	—
477	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
478	#559	—	2	1	no	—
479	#559	—	2	1	no	—
480	#550	—	2	1	no	—
481	#550	—	2	1	no	—
482	#546	—	2	2	no	—
483	#546	—	2	2	no	—
484	#540	C₂²×C₄₁	1	4	yes	—
485	#535	C₂²×C₄₁	1	2	yes	—
486	#533	C₂²×C₄₁	1	1	yes	characteristic
487	#532	C₂²×C₄₁	1	2	yes	—
488	#532	C₂²×C₄₁	1	2	yes	—
489	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
490	#520	—	2	2	no	—
491	#520	—	2	1	no	—
492	#520	C₂²×C₄₁	1	1	yes	characteristic
493	#520	C₂²×C₄₁	1	1	yes	characteristic
494	#520	C₂²×C₄₁	1	2	yes	complemented
495	#519	—	2	1	no	—
496	#519	C₂²×C₄₁	1	1	yes	characteristic
497	#519	C₂²×C₄₁	1	2	yes	complemented
498	#518	C₂²×C₄₁	1	2	yes	—
499	C₄×#41	—	2	2	no	—
500	C₄×#41	—	2	1	no	—
501	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
502	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
503	C₄×#41	C₂²×C₄₁	1	2	yes	complemented
504	C₂×C₄×Q₈	—	2	1	no	—
505	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
506	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	complemented
507	#482	C₂²×C₄₁	1	4	yes	complemented
508	#482	C₂²×C₄₁	1	4	yes	complemented
509	#481	C₂²×C₄₁	1	4	yes	complemented
510	#480	C₂²×C₄₁	1	4	yes	complemented
511	#479	C₂²×C₄₁	1	2	yes	complemented
512	#479	C₂²×C₄₁	1	4	yes	complemented
513	#478	C₂²×C₄₁	1	2	yes	complemented
514	#477	C₂²×C₄₁	1	1	yes	characteristic, complemented
515	#477	C₂²×C₄₁	1	2	yes	complemented
516	#476	C₂²×C₄₁	1	1	yes	characteristic, complemented
517	#475	C₂²×C₄₁	1	1	yes	characteristic, complemented
518	#475	C₂²×C₄₁	1	2	yes	complemented
519	#474	C₂²×C₄₁	1	1	yes	characteristic, complemented
520	#460	C₂²×C₄₁	1	2	yes	—
521	#460	C₂²×C₄₁	1	2	yes	—
522	#460	C₂²×C₄₁	1	2	yes	—
523	#460	C₂²×C₄₁	1	4	yes	—
524	#460	C₂²×C₄₁	1	2	yes	—
525	#459	C₂²×C₄₁	1	2	yes	—
526	#459	C₂²×C₄₁	1	2	yes	—
527	#449	C₂²×C₄₁	1	4	yes	complemented
528	#449	C₂²×C₄₁	1	4	yes	complemented
529	#448	C₂²×C₄₁	1	4	yes	complemented
530	#448	C₂²×C₄₁	1	4	yes	complemented
531	#442	C₂²×C₄₁	1	4	yes	complemented
532	#440	C₂²×C₄₁	1	4	yes	complemented
533	#440	C₂²×C₄₁	1	4	yes	complemented
534	#440	C₂²×C₄₁	1	4	yes	complemented
535	C₄×SD₁₆	C₂²×C₄₁	1	4	yes	complemented
536	C₄×SD₁₆	C₂²×C₄₁	1	4	yes	complemented
537	C₄×SD₁₆	C₂²×C₄₁	1	4	yes	complemented
538	C₄×D₈	C₂²×C₄₁	1	4	yes	complemented
539	#433	C₂²×C₄₁	1	4	yes	complemented
540	#432	C₂²×C₄₁	1	2	yes	complemented
541	#431	C₂²×C₄₁	1	2	yes	complemented
542	#428	C₂²×C₄₁	1	2	yes	—
543	#427	C₂²×C₄₁	1	2	yes	—
544	#423	C₂²×C₄₁	1	1	yes	characteristic
545	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
546	#419	C₂²×C₄₁	1	2	yes	—
547	#418	C₂²×C₄₁	1	2	yes	—
548	#416	C₂²×C₄₁	1	2	yes	—
549	C₂×#102	C₂²×C₄₁	1	2	yes	—
550	#408	C₂²×C₄₁	1	2	yes	—
551	#405	C₂²×C₄₁	1	2	yes	—
552	C₄₁	#60593	1	1	yes	characteristic, direct product factor, Sylow
553	2₋¹⁺⁴	—	2	4	no	—
554	2₋¹⁺⁴	—	2	4	no	—
555	C₂×#41	—	2	2	no	—
556	C₂×#41	—	2	1	no	—
557	C₂×#41	—	2	2	no	—
558	C₂×#41	—	2	2	no	—
559	C₂×#41	C₂³×C₄₁	1	2	yes	—
560	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
561	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
562	C₂²×Q₈	—	2	1	no	—
563	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
564	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
565	C₂²×D₄	—	2	1	no	—
566	C₂²×D₄	—	2	1	no	—
567	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
568	AGL(1,ℤ/8)	—	2	8	no	—
569	C₂×SD₁₆	—	2	8	no	—
570	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
571	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
572	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
573	C₂×D₈	C₂³×C₄₁	1	4	yes	—
574	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
575	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
576	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
577	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
578	#127	—	2	2	no	—
579	#127	—	2	1	no	—
580	#127	—	2	1	no	—
581	#127	C₂³×C₄₁	1	2	yes	—
582	#127	C₂³×C₄₁	1	2	yes	—
583	#125	C₂³×C₄₁	1	2	yes	—
584	#124	—	2	2	no	—
585	#124	—	2	2	no	—
586	#124	—	2	2	no	—
587	#123	—	2	4	no	—
588	#123	—	2	4	no	—
589	C₂²⋊Q₈	—	2	1	no	—
590	C₂²⋊Q₈	—	2	1	no	—
591	#121	—	2	2	no	—
592	#121	—	2	2	no	—
593	#121	—	2	4	no	—
594	#121	—	2	4	no	—
595	#121	C₂³×C₄₁	1	4	yes	—
596	#121	C₂³×C₄₁	1	4	yes	—
597	#120	—	2	4	no	—
598	C₄×Q₈	—	2	1	no	—
599	C₄×Q₈	—	2	1	no	—
600	C₄×Q₈	—	2	2	no	—
601	C₄×Q₈	—	2	1	no	—
602	C₄×Q₈	—	2	2	no	—
603	C₄×Q₈	—	2	1	no	—
604	C₄×Q₈	—	2	2	no	—
605	C₄×Q₈	—	2	1	no	—
606	C₄×Q₈	—	2	2	no	—
607	C₄×Q₈	—	2	1	no	—
608	C₄×Q₈	—	2	1	no	—
609	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
610	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
611	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
612	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
613	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
614	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
615	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
616	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
617	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	2	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	D₄×C₄₁	1	2	yes	—
632	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
633	C₄×D₄	D₄×C₄₁	1	2	yes	—
634	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
635	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
636	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
637	C₄×D₄	C₂³×C₄₁	1	2	yes	—
638	C₄×D₄	C₂³×C₄₁	1	4	yes	—
639	C₄×D₄	C₂³×C₄₁	1	4	yes	—
640	#117	—	2	1	no	—
641	#117	—	2	2	no	—
642	#117	—	2	2	no	—
643	#117	—	2	2	no	—
644	#117	—	2	2	no	—
645	#117	—	2	1	no	—
646	#117	—	2	2	no	—
647	#117	C₂³×C₄₁	1	1	yes	characteristic
648	#117	C₂³×C₄₁	1	2	yes	—
649	#117	C₂³×C₄₁	1	2	yes	—
650	#117	C₂³×C₄₁	1	1	yes	characteristic
651	#117	C₂³×C₄₁	1	2	yes	—
652	C₂×C₄⋊C₄	—	2	1	no	—
653	C₂×C₄⋊C₄	—	2	2	no	—
654	C₂×C₄⋊C₄	—	2	1	no	—
655	C₂×C₄⋊C₄	—	2	2	no	—
656	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
658	C₂×C₂²⋊C₄	—	2	4	no	—
659	C₂×C₄²	—	2	1	no	—
660	C₂×C₄²	—	2	2	no	—
661	C₂×C₄²	—	2	1	no	—
662	C₂×C₄²	—	2	2	no	—
663	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
664	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
665	#107	C₂³×C₄₁	1	2	yes	—
666	#107	C₂³×C₄₁	1	2	yes	—
667	#107	C₂³×C₄₁	1	4	yes	—
668	#106	C₂³×C₄₁	1	2	yes	—
669	#106	C₂³×C₄₁	1	2	yes	—
670	#106	C₂³×C₄₁	1	4	yes	—
671	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
672	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
673	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
674	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
675	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
676	#103	C₂³×C₄₁	1	2	yes	—
677	#103	C₂³×C₄₁	1	2	yes	—
678	#103	C₂³×C₄₁	1	4	yes	—
679	#103	C₂³×C₄₁	1	4	yes	—
680	#102	C₂³×C₄₁	1	4	yes	—
681	#102	C₂³×C₄₁	1	4	yes	—
682	#102	C₂³×C₄₁	1	2	yes	—
683	#102	C₂³×C₄₁	1	2	yes	—
684	#102	C₂³×C₄₁	1	4	yes	—
685	#102	C₂³×C₄₁	1	4	yes	—
686	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
687	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
688	#97	C₂³×C₄₁	1	4	yes	—
689	C₄×C₈	C₂³×C₄₁	1	4	yes	—
690	C₂⁴	—	2	2	no	—
691	#41	—	2	16	no	—
692	#41	—	2	8	no	—
693	#41	—	2	4	no	—
694	#41	—	2	4	no	—
695	#41	—	2	2	no	—
696	#41	—	2	2	no	—
697	#41	—	2	2	no	—
698	#41	—	8	4	no	—
699	#41	—	8	4	no	—
700	#41	#41×C₄₁	1	4	yes	complemented
701	C₂×Q₈	—	2	8	no	—
702	C₂×Q₈	—	2	4	no	—
703	C₂×Q₈	—	2	4	no	—
704	C₂×Q₈	—	2	2	no	—
705	C₂×Q₈	—	2	1	no	—
706	C₂×Q₈	—	2	1	no	—
707	C₂×Q₈	—	2	1	no	—
708	C₂×Q₈	—	2	2	no	—
709	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
710	C₂×Q₈	#41×C₄₁	1	4	yes	complemented
711	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
712	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	1	no	—
715	C₂×D₄	—	2	4	no	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	8	2	no	—
725	C₂×D₄	—	8	2	no	—
726	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
727	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
728	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
729	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	1	no	—
736	C₂²×C₄	—	2	1	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	1	no	—
739	C₂²×C₄	—	2	4	no	—
740	C₂²×C₄	—	2	4	no	—
741	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
742	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
743	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
744	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
747	SD₁₆	—	2	8	no	—
748	SD₁₆	—	2	8	no	—
749	SD₁₆	—	2	8	no	—
750	D₈	—	2	8	no	—
751	M₁₆	—	2	4	no	—
752	C₂×C₈	—	2	4	no	—
753	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
754	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
755	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	1	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	1	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	2	1	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
770	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
771	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
772	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
773	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
774	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
775	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
776	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
777	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	1	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	1	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	1	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
789	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
790	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
791	C₄²	—	2	2	no	—
792	C₄²	—	2	1	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	1	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	2	no	—
797	C₄²	—	2	2	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	2	1	no	—
800	C₄²	—	2	2	no	—
801	C₄²	C₂×D₄×C₄₁	1	2	yes	—
802	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
803	C₄²	C₂×D₄×C₄₁	1	2	yes	—
804	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
805	C₄²	C₂⁴×C₄₁	1	2	yes	—
806	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
807	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
808	C₂³	—	2	1	no	—
809	C₂³	—	2	4	no	—
810	C₂³	—	4	4	no	—
811	C₂³	—	8	2	no	—
812	C₂³	—	8	2	no	—
813	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
814	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
815	Q₈	—	2	8	no	—
816	Q₈	—	2	2	no	—
817	Q₈	—	2	4	no	—
818	Q₈	—	2	1	no	—
819	Q₈	—	2	2	no	—
820	Q₈	—	4	2	no	—
821	Q₈	—	4	2	no	—
822	Q₈	C₂×#41×C₄₁	1	2	yes	—
823	Q₈	C₂×#41×C₄₁	1	4	yes	—
824	D₄	—	2	8	no	—
825	D₄	—	2	4	no	—
826	D₄	—	2	4	no	—
827	D₄	—	2	2	no	—
828	D₄	—	2	1	no	—
829	D₄	—	2	4	no	—
830	D₄	—	2	4	no	—
831	D₄	—	4	4	no	—
832	D₄	—	4	4	no	—
833	D₄	—	4	4	no	—
834	D₄	—	8	2	no	—
835	D₄	—	8	2	no	—
836	D₄	—	8	4	no	—
837	D₄	—	8	4	no	—
838	D₄	C₂×#41×C₄₁	1	2	yes	—
839	C₂×C₄	—	2	8	no	—
840	C₂×C₄	—	2	8	no	—
841	C₂×C₄	—	2	4	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	4	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	4	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	2	no	—
856	C₂×C₄	—	4	2	no	—
857	C₂×C₄	—	8	4	no	—
858	C₂×C₄	—	8	4	no	—
859	C₂×C₄	—	8	2	no	—
860	C₂×C₄	—	8	1	no	—
861	C₂×C₄	—	8	1	no	—
862	C₂×C₄	—	8	2	no	—
863	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
864	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
865	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
866	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
867	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
868	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
869	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
870	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
871	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
872	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
873	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
874	C₈	—	2	2	no	—
875	C₈	—	2	2	no	—
876	C₈	—	2	4	no	—
877	C₂²	—	2	1	no	—
878	C₂²	—	2	1	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	2	2	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	4	1	no	—
884	C₂²	—	4	1	no	—
885	C₂²	—	4	4	no	—
886	C₂²	—	4	4	no	—
887	C₂²	—	4	4	no	—
888	C₂²	—	16	4	no	—
889	C₂²	C₄₁×#525	1	2	yes	—
890	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
891	C₄	—	2	2	no	—
892	C₄	—	2	1	no	—
893	C₄	—	2	1	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	1	no	—
896	C₄	—	2	4	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	2	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	2	no	—
904	C₄	C₄₁×#525	1	2	yes	—
905	C₄	C₄₁×#577	1	2	yes	—
906	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
907	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
908	C₂	—	2	2	no	—
909	C₂	—	4	2	no	—
910	C₂	—	4	2	no	—
911	C₂	—	8	4	no	—
912	C₂	C₂×C₄₁×#525	1	1	yes	characteristic
913	C₂	C₂×C₄₁×#577	1	1	yes	characteristic
914	C₂	C₄₁×#3585	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 ◁ C₄×#41×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3508	C₂	semidirect
2. C₄×2₋¹⁺⁴×C₄₁	C₂	semidirect
3. C₄₁×#3126	C₂	semidirect
4. C₄₁×#3119	C₂	semidirect
5. C₄₁×#3115	C₂	semidirect
6. C₄₁×#3112	C₂	semidirect
7. C₄₁×#3106	C₂	semidirect
8. C₄₁×#3103	C₂	semidirect
9. C₄₁×#3096	C₂	semidirect
10. C₄₁×#3078	C₂	semidirect
11. C₄₁×#3076	C₂	semidirect
12. C₄₁×#3038	C₂	semidirect
13. C₂×C₄₁×#460	C₂	semidirect
14. C₄₁×#3010	C₂	semidirect
15. C₄₁×#2949	C₂	semidirect
16. C₄₁×#2946	C₂	semidirect
17. C₄₁×#2925	C₂	semidirect
37. C₄₁×#520	C₂²	semidirect
40. C₄₁×#519	C₂²	semidirect
46. C₄×#41×C₄₁	C₂²	semidirect
49. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
50. C₄₁×#482	C₂²	semidirect
51. C₄₁×#482	C₂²	semidirect
52. C₄₁×#481	C₂²	semidirect
53. C₄₁×#480	C₂²	semidirect
54. C₄₁×#479	C₂²	semidirect
55. C₄₁×#479	C₂²	semidirect
56. C₄₁×#478	C₂²	semidirect
57. C₄₁×#477	C₂²	semidirect
58. C₄₁×#477	C₂²	semidirect
59. C₄₁×#476	C₂²	semidirect
60. C₄₁×#475	C₂²	semidirect
61. C₄₁×#475	C₂²	semidirect
62. C₄₁×#474	C₂²	semidirect
70. C₄₁×#449	C₂²	semidirect
71. C₄₁×#449	C₂²	semidirect
72. C₄₁×#448	C₂²	semidirect
73. C₄₁×#448	C₂²	semidirect
74. C₄₁×#442	C₂²	semidirect
75. C₄₁×#440	C₂²	semidirect
76. C₄₁×#440	C₂²	semidirect
77. C₄₁×#440	C₂²	semidirect
78. C₄×SD₁₆×C₄₁	C₂²	semidirect
79. C₄×SD₁₆×C₄₁	C₂²	semidirect
80. C₄×SD₁₆×C₄₁	C₂²	semidirect
81. C₄×D₈×C₄₁	C₂²	semidirect
82. C₄₁×#433	C₂²	semidirect
83. C₄₁×#432	C₂²	semidirect
84. C₄₁×#431	C₂²	semidirect
242. #41×C₄₁	#41	semidirect
252. C₂×Q₈×C₄₁	#41	semidirect
419. #60593	C₄₁	direct (N × H)
451. #3508	C₂×C₄₁	semidirect
452. C₄×2₋¹⁺⁴	C₂×C₄₁	semidirect
453. #3126	C₂×C₄₁	semidirect
454. #3119	C₂×C₄₁	semidirect
455. #3115	C₂×C₄₁	semidirect
456. #3112	C₂×C₄₁	semidirect
457. #3106	C₂×C₄₁	semidirect
458. #3103	C₂×C₄₁	semidirect
459. #3096	C₂×C₄₁	semidirect
460. #3078	C₂×C₄₁	semidirect
461. #3076	C₂×C₄₁	semidirect
462. #3038	C₂×C₄₁	semidirect
463. C₂×#460	C₂×C₄₁	semidirect
464. #3010	C₂×C₄₁	semidirect
465. #2949	C₂×C₄₁	semidirect
466. #2946	C₂×C₄₁	semidirect
467. #2925	C₂×C₄₁	semidirect
494. #520	C₂²×C₄₁	semidirect
497. #519	C₂²×C₄₁	semidirect
503. C₄×#41	C₂²×C₄₁	semidirect
506. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
507. #482	C₂²×C₄₁	semidirect
508. #482	C₂²×C₄₁	semidirect
509. #481	C₂²×C₄₁	semidirect
510. #480	C₂²×C₄₁	semidirect
511. #479	C₂²×C₄₁	semidirect
512. #479	C₂²×C₄₁	semidirect
513. #478	C₂²×C₄₁	semidirect
514. #477	C₂²×C₄₁	semidirect
515. #477	C₂²×C₄₁	semidirect
516. #476	C₂²×C₄₁	semidirect
517. #475	C₂²×C₄₁	semidirect
518. #475	C₂²×C₄₁	semidirect
519. #474	C₂²×C₄₁	semidirect
527. #449	C₂²×C₄₁	semidirect
528. #449	C₂²×C₄₁	semidirect
529. #448	C₂²×C₄₁	semidirect
530. #448	C₂²×C₄₁	semidirect
531. #442	C₂²×C₄₁	semidirect
532. #440	C₂²×C₄₁	semidirect
533. #440	C₂²×C₄₁	semidirect
534. #440	C₂²×C₄₁	semidirect
535. C₄×SD₁₆	C₂²×C₄₁	semidirect
536. C₄×SD₁₆	C₂²×C₄₁	semidirect
537. C₄×SD₁₆	C₂²×C₄₁	semidirect
538. C₄×D₈	C₂²×C₄₁	semidirect
539. #433	C₂²×C₄₁	semidirect
540. #432	C₂²×C₄₁	semidirect
541. #431	C₂²×C₄₁	semidirect
552. C₄₁	#60593	direct (N × H)
700. #41	#41×C₄₁	semidirect
710. C₂×Q₈	#41×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3508	2
C₄×2₋¹⁺⁴×C₄₁	2
C₄₁×#3126	2
C₄₁×#3119	2
C₄₁×#3115	2
C₄₁×#3112	2
C₄₁×#3106	2
C₄₁×#3103	2
C₄₁×#3096	2
C₄₁×#3078	2
C₄₁×#3076	2
C₄₁×#3038	2
C₂×C₄₁×#460	2
C₄₁×#3010	2
C₄₁×#2949	2
C₄₁×#2946	2
C₄₁×#2925	2
#60593	41

Subgroups — C41×#60593 #23836794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#60593 #23836794