Subgroups — C₄₁×#61206 #23837407

Order 10496.

2150 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3498	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#3333	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3324	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3317	C₂	1	4	yes	maximal, complemented
6	C₄₁×#3310	C₂	1	4	yes	maximal, complemented
7	C₄₁×#3304	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3295	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#3096	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3057	C₂	1	2	yes	maximal, complemented
13	C₂×C₄₁×#460	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3009	C₂	1	2	yes	maximal, complemented
15	C₄×#137×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#2935	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#2897	C₂	1	2	yes	maximal, complemented
18	C₂×H(5,𝔽₂)×C₄₁	C₂²	1	2	yes	—
19	C₂×#137×C₄₁	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
21	C₂×#131×C₄₁	C₂²	1	2	yes	complemented
22	C₄₁×#559	—	2	1	no	—
23	C₄₁×#557	—	2	1	no	—
24	C₄₁×#556	—	2	2	no	—
25	C₄₁×#556	C₂²	1	2	yes	complemented
26	C₄₁×#554	C₂²	1	2	yes	complemented
27	C₄₁×#552	C₂²	1	4	yes	complemented
28	C₄₁×#550	C₂²	1	2	yes	—
29	C₄₁×#550	C₂²	1	2	yes	—
30	D₄²×C₄₁	—	2	2	no	—
31	D₄²×C₄₁	—	2	2	no	—
32	D₄²×C₄₁	C₂²	1	2	yes	—
33	D₄²×C₄₁	C₂²	1	2	yes	—
34	C₄₁×#539	—	2	2	no	—
35	C₄₁×#536	C₂²	1	2	yes	complemented
36	C₄₁×#535	—	2	2	no	—
37	C₄₁×#535	C₂²	1	2	yes	—
38	C₄₁×#533	C₂²	1	1	yes	characteristic, complemented
39	C₄₁×#532	—	2	1	no	—
40	C₄₁×#532	C₂²	1	1	yes	characteristic
41	C₂×#127×C₄₁	—	2	1	no	—
42	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
43	C₄₁×#529	—	2	2	no	—
44	C₄₁×#520	C₂²	1	2	yes	complemented
45	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
47	C₄₁×#490	C₂²	1	4	yes	complemented
48	C₄₁×#486	C₂²	1	2	yes	complemented
49	C₄₁×#486	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×#478	C₂²	1	2	yes	complemented
56	C₄₁×#477	C₂²	1	1	yes	characteristic, complemented
57	C₄₁×#476	C₂²	1	1	yes	characteristic, complemented
58	C₄₁×#475	C₂²	1	1	yes	characteristic, complemented
59	C₄₁×#474	C₂²	1	1	yes	characteristic, complemented
60	C₄₁×#468	C₂²	1	4	yes	complemented
61	C₄₁×#468	C₂²	1	4	yes	complemented
62	C₄₁×#465	C₂²	1	4	yes	complemented
63	C₄₁×#465	C₂²	1	4	yes	complemented
64	C₄₁×#460	C₂²	1	2	yes	complemented
65	C₄₁×#460	C₂²	1	4	yes	complemented
66	C₄₁×#460	C₂²	1	2	yes	complemented
67	C₄₁×#452	C₂²	1	4	yes	complemented
68	C₄₁×#452	C₂²	1	4	yes	complemented
69	C₄₁×#450	C₂²	1	4	yes	complemented
70	C₄₁×#450	C₂²	1	4	yes	complemented
71	C₄₁×#441	C₂²	1	2	yes	complemented
72	C₄₁×#440	C₂²	1	2	yes	complemented
73	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	complemented
74	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
75	C₄₁×#436	C₂²	1	2	yes	complemented
76	C₄₁×#435	C₂²	1	4	yes	complemented
77	C₈×D₄×C₄₁	C₂²	1	2	yes	complemented
78	C₄₁×#428	C₂²	1	1	yes	characteristic, complemented
79	C₄₁×#427	C₂²	1	2	yes	complemented
80	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
81	C₄₁×#419	C₂²	1	1	yes	characteristic, complemented
82	C₄₁×#418	C₂²	1	4	yes	complemented
83	C₄₁×#418	C₂²	1	2	yes	complemented
84	C₄₁×#418	C₂²	1	2	yes	complemented
85	C₄₁×#417	C₂²	1	1	yes	characteristic
86	C₄₁×#417	C₂²	1	4	yes	complemented
87	C₄₁×#416	C₂²	1	2	yes	—
88	C₄₁×#416	C₂²	1	4	yes	complemented
89	C₂×#102×C₄₁	C₂²	1	4	yes	complemented
90	C₂×#102×C₄₁	C₂²	1	2	yes	complemented
91	C₄₁×#408	C₂²	1	2	yes	complemented
92	C₄×M₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
93	H(5,𝔽₂)×C₄₁	—	2	8	no	—
94	H(5,𝔽₂)×C₄₁	—	4	4	no	—
95	C₂×#41×C₄₁	—	2	2	no	—
96	C₂×#41×C₄₁	C₂³	1	4	yes	—
97	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
98	C₂×#41×C₄₁	C₂³	1	2	yes	—
99	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₄₁	—	2	2	no	—
101	C₂²×D₄×C₄₁	—	2	4	no	—
102	C₂²×D₄×C₄₁	—	2	2	no	—
103	C₂²×D₄×C₄₁	—	2	2	no	—
104	C₂²×D₄×C₄₁	—	2	1	no	—
105	C₂²×D₄×C₄₁	—	2	1	no	—
106	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
107	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
108	#137×C₄₁	—	2	4	no	—
109	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
110	C₂×SD₁₆×C₄₁	—	4	4	no	—
111	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
112	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
113	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
114	#131×C₄₁	—	4	4	no	—
115	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
116	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
117	C₂×M₁₆×C₄₁	C₂³	1	4	yes	—
118	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
119	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
120	C₄⋊Q₈×C₄₁	—	2	2	no	—
121	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
122	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
123	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
124	#127×C₄₁	—	2	2	no	—
125	#127×C₄₁	—	2	2	no	—
126	#127×C₄₁	—	2	2	no	—
127	#127×C₄₁	—	2	1	no	—
128	#127×C₄₁	—	2	1	no	—
129	#127×C₄₁	D₄	1	1	yes	characteristic
130	#127×C₄₁	C₂³	1	2	yes	—
131	#127×C₄₁	C₂³	1	2	yes	—
132	#126×C₄₁	—	2	4	no	—
133	#126×C₄₁	—	2	4	no	—
134	#125×C₄₁	—	2	2	no	—
135	#125×C₄₁	—	2	4	no	—
136	#125×C₄₁	C₂³	1	2	yes	—
137	#124×C₄₁	—	2	2	no	—
138	#124×C₄₁	—	2	2	no	—
139	#124×C₄₁	—	2	2	no	—
140	#124×C₄₁	D₄	1	2	yes	—
141	#123×C₄₁	—	2	4	no	—
142	#123×C₄₁	—	2	4	no	—
143	C₂²⋊Q₈×C₄₁	—	2	1	no	—
144	C₂²⋊Q₈×C₄₁	—	2	1	no	—
145	C₂²⋊Q₈×C₄₁	—	2	4	no	—
146	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
147	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
148	#121×C₄₁	—	2	2	no	—
149	#121×C₄₁	—	2	2	no	—
150	#121×C₄₁	—	2	4	no	—
151	#121×C₄₁	—	2	4	no	—
152	#121×C₄₁	D₄	1	2	yes	—
153	#121×C₄₁	D₄	1	2	yes	—
154	#121×C₄₁	C₂³	1	4	yes	—
155	#121×C₄₁	C₂³	1	4	yes	—
156	#120×C₄₁	—	2	4	no	—
157	#120×C₄₁	—	2	4	no	—
158	#120×C₄₁	—	2	4	no	—
159	C₄×Q₈×C₄₁	—	2	2	no	—
160	C₄×Q₈×C₄₁	—	2	2	no	—
161	C₄×Q₈×C₄₁	—	2	1	no	—
162	C₄×Q₈×C₄₁	—	2	1	no	—
163	C₄×Q₈×C₄₁	—	2	1	no	—
164	C₄×Q₈×C₄₁	—	2	1	no	—
165	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
166	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
167	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
169	C₄×D₄×C₄₁	—	2	4	no	—
170	C₄×D₄×C₄₁	—	2	2	no	—
171	C₄×D₄×C₄₁	—	2	2	no	—
172	C₄×D₄×C₄₁	—	2	1	no	—
173	C₄×D₄×C₄₁	—	2	1	no	—
174	C₄×D₄×C₄₁	—	2	2	no	—
175	C₄×D₄×C₄₁	—	2	2	no	—
176	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₄₁	C₂³	1	2	yes	—
179	C₄×D₄×C₄₁	C₂³	1	2	yes	—
180	#117×C₄₁	—	2	4	no	—
181	#117×C₄₁	—	2	1	no	—
182	#117×C₄₁	C₂³	1	1	yes	characteristic
183	#117×C₄₁	C₂³	1	2	yes	—
184	#117×C₄₁	C₂³	1	4	yes	—
185	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
186	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
188	C₂×C₄²×C₄₁	—	2	1	no	—
189	C₂×C₄²×C₄₁	—	2	1	no	—
190	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
191	#107×C₄₁	C₂³	1	2	yes	—
192	#107×C₄₁	C₂³	1	2	yes	—
193	#107×C₄₁	C₂³	1	2	yes	—
194	#106×C₄₁	C₂³	1	2	yes	—
195	#106×C₄₁	C₂³	1	2	yes	—
196	#106×C₄₁	C₂³	1	2	yes	—
197	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
198	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
199	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
200	#103×C₄₁	C₂³	1	2	yes	—
201	#103×C₄₁	C₂³	1	2	yes	—
202	#103×C₄₁	C₂³	1	2	yes	—
203	#103×C₄₁	C₂³	1	2	yes	—
204	#103×C₄₁	C₂³	1	2	yes	—
205	#102×C₄₁	C₂³	1	2	yes	—
206	#102×C₄₁	C₂³	1	4	yes	—
207	#102×C₄₁	C₂³	1	2	yes	—
208	#102×C₄₁	C₂³	1	4	yes	—
209	#102×C₄₁	C₂³	1	4	yes	—
210	#102×C₄₁	C₂³	1	2	yes	—
211	#102×C₄₁	C₂³	1	4	yes	—
212	#102×C₄₁	C₂³	1	4	yes	—
213	#102×C₄₁	C₂³	1	4	yes	—
214	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
215	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
216	#97×C₄₁	C₂³	1	2	yes	—
217	C₄×C₈×C₄₁	C₂³	1	2	yes	—
218	C₂⁴×C₄₁	—	2	4	no	—
219	C₂⁴×C₄₁	—	2	2	no	—
220	#41×C₄₁	—	2	4	no	—
221	#41×C₄₁	—	2	4	no	—
222	#41×C₄₁	—	2	2	no	—
223	#41×C₄₁	—	2	8	no	—
224	#41×C₄₁	—	4	4	no	—
225	#41×C₄₁	—	4	8	no	—
226	#41×C₄₁	#41	1	4	yes	—
227	C₂×Q₈×C₄₁	—	2	1	no	—
228	C₂×Q₈×C₄₁	—	2	1	no	—
229	C₂×Q₈×C₄₁	—	2	1	no	—
230	C₂×Q₈×C₄₁	—	2	2	no	—
231	C₂×Q₈×C₄₁	—	2	2	no	—
232	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
233	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
234	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
235	C₂×D₄×C₄₁	—	2	1	no	—
236	C₂×D₄×C₄₁	—	2	8	no	—
237	C₂×D₄×C₄₁	—	2	4	no	—
238	C₂×D₄×C₄₁	—	2	4	no	—
239	C₂×D₄×C₄₁	—	2	4	no	—
240	C₂×D₄×C₄₁	—	2	2	no	—
241	C₂×D₄×C₄₁	—	2	2	no	—
242	C₂×D₄×C₄₁	—	2	4	no	—
243	C₂×D₄×C₄₁	—	2	2	no	—
244	C₂×D₄×C₄₁	—	2	2	no	—
245	C₂×D₄×C₄₁	—	2	2	no	—
246	C₂×D₄×C₄₁	—	2	4	no	—
247	C₂×D₄×C₄₁	—	2	4	no	—
248	C₂×D₄×C₄₁	—	4	4	no	—
249	C₂×D₄×C₄₁	—	4	8	no	—
250	C₂×D₄×C₄₁	—	4	16	no	—
251	C₂×D₄×C₄₁	—	8	2	no	—
252	C₂×D₄×C₄₁	—	8	4	no	—
253	C₂×D₄×C₄₁	—	8	2	no	—
254	C₂×D₄×C₄₁	—	8	4	no	—
255	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
256	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
257	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
258	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
259	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
260	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₄₁	—	2	1	no	—
262	C₂²×C₄×C₄₁	—	2	1	no	—
263	C₂²×C₄×C₄₁	—	2	1	no	—
264	C₂²×C₄×C₄₁	—	2	4	no	—
265	C₂²×C₄×C₄₁	—	2	1	no	—
266	C₂²×C₄×C₄₁	—	2	1	no	—
267	C₂²×C₄×C₄₁	—	2	4	no	—
268	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
271	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
272	Q₁₆×C₄₁	—	2	4	no	—
273	SD₁₆×C₄₁	—	2	4	no	—
274	SD₁₆×C₄₁	—	4	4	no	—
275	SD₁₆×C₄₁	—	4	4	no	—
276	M₁₆×C₄₁	—	2	2	no	—
277	M₁₆×C₄₁	—	2	2	no	—
278	M₁₆×C₄₁	—	4	4	no	—
279	C₂×C₈×C₄₁	—	2	4	no	—
280	C₂×C₈×C₄₁	—	4	4	no	—
281	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
282	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
283	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
284	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
285	C₄⋊C₄×C₄₁	—	2	2	no	—
286	C₄⋊C₄×C₄₁	—	2	2	no	—
287	C₄⋊C₄×C₄₁	—	2	1	no	—
288	C₄⋊C₄×C₄₁	—	2	4	no	—
289	C₄⋊C₄×C₄₁	—	2	2	no	—
290	C₄⋊C₄×C₄₁	—	2	1	no	—
291	C₄⋊C₄×C₄₁	—	2	1	no	—
292	C₄⋊C₄×C₄₁	—	2	4	no	—
293	C₄⋊C₄×C₄₁	—	2	1	no	—
294	C₄⋊C₄×C₄₁	—	2	2	no	—
295	C₄⋊C₄×C₄₁	—	2	1	no	—
296	C₄⋊C₄×C₄₁	—	2	4	no	—
297	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
300	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
304	C₂²⋊C₄×C₄₁	—	2	4	no	—
305	C₂²⋊C₄×C₄₁	—	2	1	no	—
306	C₂²⋊C₄×C₄₁	—	2	2	no	—
307	C₂²⋊C₄×C₄₁	—	2	4	no	—
308	C₂²⋊C₄×C₄₁	—	2	4	no	—
309	C₂²⋊C₄×C₄₁	—	2	1	no	—
310	C₂²⋊C₄×C₄₁	—	2	1	no	—
311	C₂²⋊C₄×C₄₁	—	2	4	no	—
312	C₂²⋊C₄×C₄₁	—	2	4	no	—
313	C₂²⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
314	C₂²⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
315	C₄²×C₄₁	—	2	2	no	—
316	C₄²×C₄₁	—	2	1	no	—
317	C₄²×C₄₁	—	2	1	no	—
318	C₄²×C₄₁	—	2	1	no	—
319	C₄²×C₄₁	—	2	2	no	—
320	C₄²×C₄₁	—	2	4	no	—
321	C₄²×C₄₁	—	2	2	no	—
322	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
325	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
326	C₂³×C₄₁	—	2	1	no	—
327	C₂³×C₄₁	—	2	4	no	—
328	C₂³×C₄₁	—	4	8	no	—
329	C₂³×C₄₁	—	4	4	no	—
330	C₂³×C₄₁	—	8	2	no	—
331	C₂³×C₄₁	—	8	2	no	—
332	C₂³×C₄₁	—	8	4	no	—
333	C₂³×C₄₁	—	8	4	no	—
334	C₂³×C₄₁	C₂²×D₄	1	4	yes	—
335	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
336	Q₈×C₄₁	—	2	4	no	—
337	Q₈×C₄₁	—	2	1	no	—
338	Q₈×C₄₁	—	2	2	no	—
339	Q₈×C₄₁	—	2	2	no	—
340	Q₈×C₄₁	—	4	2	no	—
341	Q₈×C₄₁	—	4	2	no	—
342	Q₈×C₄₁	—	8	1	no	—
343	Q₈×C₄₁	C₂×#41	1	2	yes	—
344	D₄×C₄₁	—	2	4	no	—
345	D₄×C₄₁	—	2	8	no	—
346	D₄×C₄₁	—	2	4	no	—
347	D₄×C₄₁	—	2	4	no	—
348	D₄×C₄₁	—	2	4	no	—
349	D₄×C₄₁	—	2	1	no	—
350	D₄×C₄₁	—	2	4	no	—
351	D₄×C₄₁	—	4	2	no	—
352	D₄×C₄₁	—	4	8	no	—
353	D₄×C₄₁	—	4	8	no	—
354	D₄×C₄₁	—	4	4	no	—
355	D₄×C₄₁	—	4	4	no	—
356	D₄×C₄₁	—	4	4	no	—
357	D₄×C₄₁	—	8	2	no	—
358	D₄×C₄₁	—	8	2	no	—
359	D₄×C₄₁	—	8	4	no	—
360	D₄×C₄₁	—	8	4	no	—
361	D₄×C₄₁	C₂×#41	1	2	yes	—
362	C₂×C₄×C₄₁	—	2	1	no	—
363	C₂×C₄×C₄₁	—	2	4	no	—
364	C₂×C₄×C₄₁	—	2	2	no	—
365	C₂×C₄×C₄₁	—	2	4	no	—
366	C₂×C₄×C₄₁	—	2	4	no	—
367	C₂×C₄×C₄₁	—	2	2	no	—
368	C₂×C₄×C₄₁	—	2	2	no	—
369	C₂×C₄×C₄₁	—	2	1	no	—
370	C₂×C₄×C₄₁	—	2	1	no	—
371	C₂×C₄×C₄₁	—	2	2	no	—
372	C₂×C₄×C₄₁	—	2	2	no	—
373	C₂×C₄×C₄₁	—	4	1	no	—
374	C₂×C₄×C₄₁	—	4	8	no	—
375	C₂×C₄×C₄₁	—	4	2	no	—
376	C₂×C₄×C₄₁	—	4	2	no	—
377	C₂×C₄×C₄₁	—	4	2	no	—
378	C₂×C₄×C₄₁	—	8	1	no	—
379	C₂×C₄×C₄₁	—	8	4	no	—
380	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
383	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
387	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
388	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
389	C₈×C₄₁	—	2	2	no	—
390	C₈×C₄₁	—	2	2	no	—
391	C₈×C₄₁	—	2	2	no	—
392	C₈×C₄₁	—	2	2	no	—
393	#61206	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
394	C₂²×C₄₁	—	2	1	no	—
395	C₂²×C₄₁	—	2	1	no	—
396	C₂²×C₄₁	—	2	4	no	—
397	C₂²×C₄₁	—	2	4	no	—
398	C₂²×C₄₁	—	2	2	no	—
399	C₂²×C₄₁	—	2	4	no	—
400	C₂²×C₄₁	—	4	1	no	—
401	C₂²×C₄₁	—	4	1	no	—
402	C₂²×C₄₁	—	4	4	no	—
403	C₂²×C₄₁	—	4	4	no	—
404	C₂²×C₄₁	—	4	4	no	—
405	C₂²×C₄₁	—	16	4	no	—
406	C₂²×C₄₁	—	16	8	no	—
407	C₂²×C₄₁	#546	1	2	yes	—
408	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
409	C₄×C₄₁	—	2	1	no	—
410	C₄×C₄₁	—	2	1	no	—
411	C₄×C₄₁	—	2	2	no	—
412	C₄×C₄₁	—	2	4	no	—
413	C₄×C₄₁	—	2	1	no	—
414	C₄×C₄₁	—	4	1	no	—
415	C₄×C₄₁	—	4	2	no	—
416	C₄×C₄₁	—	4	2	no	—
417	C₄×C₄₁	—	4	2	no	—
418	C₄×C₄₁	—	4	1	no	—
419	C₄×C₄₁	—	4	2	no	—
420	C₄×C₄₁	#546	1	2	yes	—
421	C₄×C₄₁	#577	1	2	yes	—
422	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
423	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
424	#3507	C₂×C₄₁	1	1	yes	characteristic, complemented
425	#3498	C₂×C₄₁	1	1	yes	characteristic
426	#3333	C₂×C₄₁	1	2	yes	complemented
427	#3324	C₂×C₄₁	1	2	yes	complemented
428	#3317	C₂×C₄₁	1	4	yes	complemented
429	#3310	C₂×C₄₁	1	4	yes	complemented
430	#3304	C₂×C₄₁	1	2	yes	complemented
431	#3295	C₂×C₄₁	1	2	yes	complemented
432	#3138	C₂×C₄₁	1	1	yes	characteristic, complemented
433	#3096	C₂×C₄₁	1	2	yes	complemented
434	#3076	C₂×C₄₁	1	1	yes	characteristic, complemented
435	#3057	C₂×C₄₁	1	2	yes	complemented
436	C₂×#460	C₂×C₄₁	1	1	yes	characteristic, complemented
437	#3009	C₂×C₄₁	1	2	yes	complemented
438	C₄×#137	C₂×C₄₁	1	1	yes	characteristic, complemented
439	#2935	C₂×C₄₁	1	1	yes	characteristic, complemented
440	#2897	C₂×C₄₁	1	2	yes	complemented
441	C₂×C₄₁	—	2	2	no	—
442	C₂×C₄₁	—	4	4	no	—
443	C₂×C₄₁	—	4	2	no	—
444	C₂×C₄₁	—	8	4	no	—
445	C₂×C₄₁	C₂×#546	1	1	yes	characteristic
446	C₂×C₄₁	C₂×#577	1	1	yes	characteristic
447	C₂×C₄₁	#3585	1	1	yes	characteristic
448	C₂×H(5,𝔽₂)	C₂²×C₄₁	1	2	yes	—
449	C₂×#137	C₂²×C₄₁	1	1	yes	characteristic
450	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
451	C₂×#131	C₂²×C₄₁	1	2	yes	complemented
452	#559	—	2	1	no	—
453	#557	—	2	1	no	—
454	#556	—	2	2	no	—
455	#556	C₂²×C₄₁	1	2	yes	complemented
456	#554	C₂²×C₄₁	1	2	yes	complemented
457	#552	C₂²×C₄₁	1	4	yes	complemented
458	#550	C₂²×C₄₁	1	2	yes	—
459	#550	C₂²×C₄₁	1	2	yes	—
460	D₄²	—	2	2	no	—
461	D₄²	—	2	2	no	—
462	D₄²	C₂²×C₄₁	1	2	yes	—
463	D₄²	C₂²×C₄₁	1	2	yes	—
464	#539	—	2	2	no	—
465	#536	C₂²×C₄₁	1	2	yes	complemented
466	#535	—	2	2	no	—
467	#535	C₂²×C₄₁	1	2	yes	—
468	#533	C₂²×C₄₁	1	1	yes	characteristic, complemented
469	#532	—	2	1	no	—
470	#532	C₂²×C₄₁	1	1	yes	characteristic
471	C₂×#127	—	2	1	no	—
472	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
473	#529	—	2	2	no	—
474	#520	C₂²×C₄₁	1	2	yes	complemented
475	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
476	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
477	#490	C₂²×C₄₁	1	4	yes	complemented
478	#486	C₂²×C₄₁	1	2	yes	complemented
479	#486	C₂²×C₄₁	1	2	yes	complemented
480	#482	C₂²×C₄₁	1	4	yes	complemented
481	#482	C₂²×C₄₁	1	4	yes	complemented
482	#481	C₂²×C₄₁	1	4	yes	complemented
483	#480	C₂²×C₄₁	1	4	yes	complemented
484	#479	C₂²×C₄₁	1	2	yes	complemented
485	#478	C₂²×C₄₁	1	2	yes	complemented
486	#477	C₂²×C₄₁	1	1	yes	characteristic, complemented
487	#476	C₂²×C₄₁	1	1	yes	characteristic, complemented
488	#475	C₂²×C₄₁	1	1	yes	characteristic, complemented
489	#474	C₂²×C₄₁	1	1	yes	characteristic, complemented
490	#468	C₂²×C₄₁	1	4	yes	complemented
491	#468	C₂²×C₄₁	1	4	yes	complemented
492	#465	C₂²×C₄₁	1	4	yes	complemented
493	#465	C₂²×C₄₁	1	4	yes	complemented
494	#460	C₂²×C₄₁	1	2	yes	complemented
495	#460	C₂²×C₄₁	1	2	yes	complemented
496	#460	C₂²×C₄₁	1	4	yes	complemented
497	#452	C₂²×C₄₁	1	4	yes	complemented
498	#452	C₂²×C₄₁	1	4	yes	complemented
499	#450	C₂²×C₄₁	1	4	yes	complemented
500	#450	C₂²×C₄₁	1	4	yes	complemented
501	#441	C₂²×C₄₁	1	2	yes	complemented
502	#440	C₂²×C₄₁	1	2	yes	complemented
503	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	complemented
504	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
505	#436	C₂²×C₄₁	1	2	yes	complemented
506	#435	C₂²×C₄₁	1	4	yes	complemented
507	C₈×D₄	C₂²×C₄₁	1	2	yes	complemented
508	#428	C₂²×C₄₁	1	1	yes	characteristic, complemented
509	#427	C₂²×C₄₁	1	2	yes	complemented
510	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
511	#419	C₂²×C₄₁	1	1	yes	characteristic, complemented
512	#418	C₂²×C₄₁	1	2	yes	complemented
513	#418	C₂²×C₄₁	1	2	yes	complemented
514	#418	C₂²×C₄₁	1	4	yes	complemented
515	#417	C₂²×C₄₁	1	1	yes	characteristic
516	#417	C₂²×C₄₁	1	4	yes	complemented
517	#416	C₂²×C₄₁	1	2	yes	—
518	#416	C₂²×C₄₁	1	4	yes	complemented
519	C₂×#102	C₂²×C₄₁	1	2	yes	complemented
520	C₂×#102	C₂²×C₄₁	1	4	yes	complemented
521	#408	C₂²×C₄₁	1	2	yes	complemented
522	C₄×M₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
523	C₄₁	#61206	1	1	yes	characteristic, direct product factor, Sylow
524	H(5,𝔽₂)	—	2	8	no	—
525	H(5,𝔽₂)	—	4	4	no	—
526	C₂×#41	—	2	2	no	—
527	C₂×#41	C₂³×C₄₁	1	4	yes	—
528	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
529	C₂×#41	C₂³×C₄₁	1	2	yes	—
530	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
531	C₂²×D₄	—	2	2	no	—
532	C₂²×D₄	—	2	4	no	—
533	C₂²×D₄	—	2	2	no	—
534	C₂²×D₄	—	2	2	no	—
535	C₂²×D₄	—	2	1	no	—
536	C₂²×D₄	—	2	1	no	—
537	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
538	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
539	#137	—	2	4	no	—
540	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
541	C₂×SD₁₆	—	4	4	no	—
542	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
543	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
544	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
545	#131	—	4	4	no	—
546	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
547	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
548	C₂×M₁₆	C₂³×C₄₁	1	4	yes	—
549	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
550	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
551	C₄⋊Q₈	—	2	2	no	—
552	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
553	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
554	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
555	#127	—	2	2	no	—
556	#127	—	2	2	no	—
557	#127	—	2	2	no	—
558	#127	—	2	1	no	—
559	#127	—	2	1	no	—
560	#127	D₄×C₄₁	1	1	yes	characteristic
561	#127	C₂³×C₄₁	1	2	yes	—
562	#127	C₂³×C₄₁	1	2	yes	—
563	#126	—	2	4	no	—
564	#126	—	2	4	no	—
565	#125	—	2	2	no	—
566	#125	—	2	4	no	—
567	#125	C₂³×C₄₁	1	2	yes	—
568	#124	—	2	2	no	—
569	#124	—	2	2	no	—
570	#124	—	2	2	no	—
571	#124	D₄×C₄₁	1	2	yes	—
572	#123	—	2	4	no	—
573	#123	—	2	4	no	—
574	C₂²⋊Q₈	—	2	1	no	—
575	C₂²⋊Q₈	—	2	1	no	—
576	C₂²⋊Q₈	—	2	4	no	—
577	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
578	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
579	#121	—	2	2	no	—
580	#121	—	2	2	no	—
581	#121	—	2	4	no	—
582	#121	—	2	4	no	—
583	#121	D₄×C₄₁	1	2	yes	—
584	#121	D₄×C₄₁	1	2	yes	—
585	#121	C₂³×C₄₁	1	4	yes	—
586	#121	C₂³×C₄₁	1	4	yes	—
587	#120	—	2	4	no	—
588	#120	—	2	4	no	—
589	#120	—	2	4	no	—
590	C₄×Q₈	—	2	2	no	—
591	C₄×Q₈	—	2	2	no	—
592	C₄×Q₈	—	2	1	no	—
593	C₄×Q₈	—	2	1	no	—
594	C₄×Q₈	—	2	1	no	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
597	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
598	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
599	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
600	C₄×D₄	—	2	4	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
608	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
609	C₄×D₄	C₂³×C₄₁	1	2	yes	—
610	C₄×D₄	C₂³×C₄₁	1	2	yes	—
611	#117	—	2	4	no	—
612	#117	—	2	1	no	—
613	#117	C₂³×C₄₁	1	1	yes	characteristic
614	#117	C₂³×C₄₁	1	2	yes	—
615	#117	C₂³×C₄₁	1	4	yes	—
616	C₂×C₄⋊C₄	—	2	1	no	—
617	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
619	C₂×C₄²	—	2	1	no	—
620	C₂×C₄²	—	2	1	no	—
621	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
622	#107	C₂³×C₄₁	1	2	yes	—
623	#107	C₂³×C₄₁	1	2	yes	—
624	#107	C₂³×C₄₁	1	2	yes	—
625	#106	C₂³×C₄₁	1	2	yes	—
626	#106	C₂³×C₄₁	1	2	yes	—
627	#106	C₂³×C₄₁	1	2	yes	—
628	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
629	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
630	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
631	#103	C₂³×C₄₁	1	2	yes	—
632	#103	C₂³×C₄₁	1	2	yes	—
633	#103	C₂³×C₄₁	1	2	yes	—
634	#103	C₂³×C₄₁	1	2	yes	—
635	#103	C₂³×C₄₁	1	2	yes	—
636	#102	C₂³×C₄₁	1	2	yes	—
637	#102	C₂³×C₄₁	1	4	yes	—
638	#102	C₂³×C₄₁	1	2	yes	—
639	#102	C₂³×C₄₁	1	4	yes	—
640	#102	C₂³×C₄₁	1	4	yes	—
641	#102	C₂³×C₄₁	1	2	yes	—
642	#102	C₂³×C₄₁	1	4	yes	—
643	#102	C₂³×C₄₁	1	4	yes	—
644	#102	C₂³×C₄₁	1	4	yes	—
645	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
646	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
647	#97	C₂³×C₄₁	1	2	yes	—
648	C₄×C₈	C₂³×C₄₁	1	2	yes	—
649	C₂⁴	—	2	4	no	—
650	C₂⁴	—	2	2	no	—
651	#41	—	2	4	no	—
652	#41	—	2	4	no	—
653	#41	—	2	2	no	—
654	#41	—	2	8	no	—
655	#41	—	4	4	no	—
656	#41	—	4	8	no	—
657	#41	#41×C₄₁	1	4	yes	—
658	C₂×Q₈	—	2	1	no	—
659	C₂×Q₈	—	2	1	no	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	2	no	—
662	C₂×Q₈	—	2	2	no	—
663	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
664	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
665	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	—	2	8	no	—
668	C₂×D₄	—	2	4	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	2	4	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	4	4	no	—
680	C₂×D₄	—	4	8	no	—
681	C₂×D₄	—	4	16	no	—
682	C₂×D₄	—	8	2	no	—
683	C₂×D₄	—	8	4	no	—
684	C₂×D₄	—	8	2	no	—
685	C₂×D₄	—	8	4	no	—
686	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
687	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
688	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
689	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
690	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
691	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	4	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	1	no	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
700	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
702	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
703	Q₁₆	—	2	4	no	—
704	SD₁₆	—	2	4	no	—
705	SD₁₆	—	4	4	no	—
706	SD₁₆	—	4	4	no	—
707	M₁₆	—	2	2	no	—
708	M₁₆	—	2	2	no	—
709	M₁₆	—	4	4	no	—
710	C₂×C₈	—	2	4	no	—
711	C₂×C₈	—	4	4	no	—
712	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
713	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
714	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
715	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
729	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
730	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
731	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
732	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
733	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
734	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	1	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	1	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
745	C₂²⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
746	C₄²	—	2	2	no	—
747	C₄²	—	2	1	no	—
748	C₄²	—	2	1	no	—
749	C₄²	—	2	1	no	—
750	C₄²	—	2	2	no	—
751	C₄²	—	2	4	no	—
752	C₄²	—	2	2	no	—
753	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
754	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
755	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
756	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
757	C₂³	—	2	1	no	—
758	C₂³	—	2	4	no	—
759	C₂³	—	4	8	no	—
760	C₂³	—	4	4	no	—
761	C₂³	—	8	2	no	—
762	C₂³	—	8	2	no	—
763	C₂³	—	8	4	no	—
764	C₂³	—	8	4	no	—
765	C₂³	C₂²×D₄×C₄₁	1	4	yes	—
766	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
767	Q₈	—	2	4	no	—
768	Q₈	—	2	1	no	—
769	Q₈	—	2	2	no	—
770	Q₈	—	2	2	no	—
771	Q₈	—	4	2	no	—
772	Q₈	—	4	2	no	—
773	Q₈	—	8	1	no	—
774	Q₈	C₂×#41×C₄₁	1	2	yes	—
775	D₄	—	2	4	no	—
776	D₄	—	2	8	no	—
777	D₄	—	2	4	no	—
778	D₄	—	2	4	no	—
779	D₄	—	2	4	no	—
780	D₄	—	2	1	no	—
781	D₄	—	2	4	no	—
782	D₄	—	4	2	no	—
783	D₄	—	4	8	no	—
784	D₄	—	4	8	no	—
785	D₄	—	4	4	no	—
786	D₄	—	4	4	no	—
787	D₄	—	4	4	no	—
788	D₄	—	8	2	no	—
789	D₄	—	8	2	no	—
790	D₄	—	8	4	no	—
791	D₄	—	8	4	no	—
792	D₄	C₂×#41×C₄₁	1	2	yes	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	4	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	4	no	—
797	C₂×C₄	—	2	4	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	4	1	no	—
805	C₂×C₄	—	4	8	no	—
806	C₂×C₄	—	4	2	no	—
807	C₂×C₄	—	4	2	no	—
808	C₂×C₄	—	4	2	no	—
809	C₂×C₄	—	8	1	no	—
810	C₂×C₄	—	8	4	no	—
811	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
812	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
813	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
814	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
816	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
817	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
818	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
819	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
820	C₈	—	2	2	no	—
821	C₈	—	2	2	no	—
822	C₈	—	2	2	no	—
823	C₈	—	2	2	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	4	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	4	no	—
833	C₂²	—	4	4	no	—
834	C₂²	—	4	4	no	—
835	C₂²	—	16	4	no	—
836	C₂²	—	16	8	no	—
837	C₂²	C₄₁×#546	1	2	yes	—
838	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
839	C₄	—	2	1	no	—
840	C₄	—	2	1	no	—
841	C₄	—	2	1	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	4	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	2	no	—
850	C₄	C₄₁×#546	1	2	yes	—
851	C₄	C₄₁×#577	1	2	yes	—
852	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
853	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
854	C₂	—	2	2	no	—
855	C₂	—	4	4	no	—
856	C₂	—	4	2	no	—
857	C₂	—	8	4	no	—
858	C₂	C₂×C₄₁×#546	1	1	yes	characteristic
859	C₂	C₂×C₄₁×#577	1	1	yes	characteristic
860	C₂	C₄₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
prime radical	C₄₁×#3498	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3507	C₂	semidirect
3. C₄₁×#3333	C₂	semidirect
4. C₄₁×#3324	C₂	semidirect
5. C₄₁×#3317	C₂	semidirect
6. C₄₁×#3310	C₂	semidirect
7. C₄₁×#3304	C₂	semidirect
8. C₄₁×#3295	C₂	semidirect
9. C₄₁×#3138	C₂	semidirect
10. C₄₁×#3096	C₂	semidirect
11. C₄₁×#3076	C₂	semidirect
12. C₄₁×#3057	C₂	semidirect
13. C₂×C₄₁×#460	C₂	semidirect
14. C₄₁×#3009	C₂	semidirect
15. C₄×#137×C₄₁	C₂	semidirect
16. C₄₁×#2935	C₂	semidirect
17. C₄₁×#2897	C₂	semidirect
20. C₂²×SD₁₆×C₄₁	C₂²	semidirect
21. C₂×#131×C₄₁	C₂²	semidirect
25. C₄₁×#556	C₂²	semidirect
26. C₄₁×#554	C₂²	semidirect
27. C₄₁×#552	C₂²	semidirect
35. C₄₁×#536	C₂²	semidirect
38. C₄₁×#533	C₂²	semidirect
44. C₄₁×#520	C₂²	semidirect
46. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
47. C₄₁×#490	C₂²	semidirect
48. C₄₁×#486	C₂²	semidirect
49. C₄₁×#486	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×#478	C₂²	semidirect
56. C₄₁×#477	C₂²	semidirect
57. C₄₁×#476	C₂²	semidirect
58. C₄₁×#475	C₂²	semidirect
59. C₄₁×#474	C₂²	semidirect
60. C₄₁×#468	C₂²	semidirect
61. C₄₁×#468	C₂²	semidirect
62. C₄₁×#465	C₂²	semidirect
63. C₄₁×#465	C₂²	semidirect
64. C₄₁×#460	C₂²	semidirect
65. C₄₁×#460	C₂²	semidirect
66. C₄₁×#460	C₂²	semidirect
67. C₄₁×#452	C₂²	semidirect
68. C₄₁×#452	C₂²	semidirect
69. C₄₁×#450	C₂²	semidirect
70. C₄₁×#450	C₂²	semidirect
71. C₄₁×#441	C₂²	semidirect
72. C₄₁×#440	C₂²	semidirect
73. C₄×Q₁₆×C₄₁	C₂²	semidirect
74. C₄×SD₁₆×C₄₁	C₂²	semidirect
75. C₄₁×#436	C₂²	semidirect
76. C₄₁×#435	C₂²	semidirect
77. C₈×D₄×C₄₁	C₂²	semidirect
78. C₄₁×#428	C₂²	semidirect
79. C₄₁×#427	C₂²	semidirect
80. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
81. C₄₁×#419	C₂²	semidirect
82. C₄₁×#418	C₂²	semidirect
83. C₄₁×#418	C₂²	semidirect
84. C₄₁×#418	C₂²	semidirect
86. C₄₁×#417	C₂²	semidirect
88. C₄₁×#416	C₂²	semidirect
89. C₂×#102×C₄₁	C₂²	semidirect
90. C₂×#102×C₄₁	C₂²	semidirect
91. C₄₁×#408	C₂²	semidirect
92. C₄×M₁₆×C₄₁	C₂²	semidirect
393. #61206	C₄₁	direct (N × H)
424. #3507	C₂×C₄₁	semidirect
426. #3333	C₂×C₄₁	semidirect
427. #3324	C₂×C₄₁	semidirect
428. #3317	C₂×C₄₁	semidirect
429. #3310	C₂×C₄₁	semidirect
430. #3304	C₂×C₄₁	semidirect
431. #3295	C₂×C₄₁	semidirect
432. #3138	C₂×C₄₁	semidirect
433. #3096	C₂×C₄₁	semidirect
434. #3076	C₂×C₄₁	semidirect
435. #3057	C₂×C₄₁	semidirect
436. C₂×#460	C₂×C₄₁	semidirect
437. #3009	C₂×C₄₁	semidirect
438. C₄×#137	C₂×C₄₁	semidirect
439. #2935	C₂×C₄₁	semidirect
440. #2897	C₂×C₄₁	semidirect
450. C₂²×SD₁₆	C₂²×C₄₁	semidirect
451. C₂×#131	C₂²×C₄₁	semidirect
455. #556	C₂²×C₄₁	semidirect
456. #554	C₂²×C₄₁	semidirect
457. #552	C₂²×C₄₁	semidirect
465. #536	C₂²×C₄₁	semidirect
468. #533	C₂²×C₄₁	semidirect
474. #520	C₂²×C₄₁	semidirect
476. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
477. #490	C₂²×C₄₁	semidirect
478. #486	C₂²×C₄₁	semidirect
479. #486	C₂²×C₄₁	semidirect
480. #482	C₂²×C₄₁	semidirect
481. #482	C₂²×C₄₁	semidirect
482. #481	C₂²×C₄₁	semidirect
483. #480	C₂²×C₄₁	semidirect
484. #479	C₂²×C₄₁	semidirect
485. #478	C₂²×C₄₁	semidirect
486. #477	C₂²×C₄₁	semidirect
487. #476	C₂²×C₄₁	semidirect
488. #475	C₂²×C₄₁	semidirect
489. #474	C₂²×C₄₁	semidirect
490. #468	C₂²×C₄₁	semidirect
491. #468	C₂²×C₄₁	semidirect
492. #465	C₂²×C₄₁	semidirect
493. #465	C₂²×C₄₁	semidirect
494. #460	C₂²×C₄₁	semidirect
495. #460	C₂²×C₄₁	semidirect
496. #460	C₂²×C₄₁	semidirect
497. #452	C₂²×C₄₁	semidirect
498. #452	C₂²×C₄₁	semidirect
499. #450	C₂²×C₄₁	semidirect
500. #450	C₂²×C₄₁	semidirect
501. #441	C₂²×C₄₁	semidirect
502. #440	C₂²×C₄₁	semidirect
503. C₄×Q₁₆	C₂²×C₄₁	semidirect
504. C₄×SD₁₆	C₂²×C₄₁	semidirect
505. #436	C₂²×C₄₁	semidirect
506. #435	C₂²×C₄₁	semidirect
507. C₈×D₄	C₂²×C₄₁	semidirect
508. #428	C₂²×C₄₁	semidirect
509. #427	C₂²×C₄₁	semidirect
510. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
511. #419	C₂²×C₄₁	semidirect
512. #418	C₂²×C₄₁	semidirect
513. #418	C₂²×C₄₁	semidirect
514. #418	C₂²×C₄₁	semidirect
516. #417	C₂²×C₄₁	semidirect
518. #416	C₂²×C₄₁	semidirect
519. C₂×#102	C₂²×C₄₁	semidirect
520. C₂×#102	C₂²×C₄₁	semidirect
521. #408	C₂²×C₄₁	semidirect
522. C₄×M₁₆	C₂²×C₄₁	semidirect
523. C₄₁	#61206	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×#3507	2
C₄₁×#3498	2
C₄₁×#3333	2
C₄₁×#3324	2
C₄₁×#3317	2
C₄₁×#3310	2
C₄₁×#3304	2
C₄₁×#3295	2
C₄₁×#3138	2
C₄₁×#3096	2
C₄₁×#3076	2
C₄₁×#3057	2
C₂×C₄₁×#460	2
C₄₁×#3009	2
C₄×#137×C₄₁	2
C₄₁×#2935	2
C₄₁×#2897	2
#61206	41

Subgroups — C41×#61206 #23837407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61206 #23837407