Subgroups — C₄₁×#61207 #23837408

Order 10496.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1208 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×#3500	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#3327	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3323	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3316	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3314	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3313	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3311	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3300	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3296	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3140	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3096	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3059	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#3057	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₄₁×#464	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄₁×#3011	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#3009	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#137×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄₁×#2935	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄₁×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₁×#2897	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×H(5,𝔽₂)×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#137×C₄₁	C₂²	1	1	yes	characteristic
27	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
28	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×#131×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×#131×C₄₁	C₂²	1	1	yes	characteristic, complemented
31	C₄₁×#559	—	2	1	no	—
32	C₄₁×#557	—	2	1	no	—
33	C₄₁×#556	—	2	1	no	—
34	C₄₁×#556	—	2	1	no	—
35	C₄₁×#556	C₂²	1	2	yes	complemented
36	C₄₁×#554	C₂²	1	2	yes	complemented
37	C₄₁×#552	C₂²	1	2	yes	complemented
38	C₄₁×#552	C₂²	1	2	yes	complemented
39	C₄₁×#548	C₂²	1	2	yes	—
40	C₄₁×#548	C₂²	1	2	yes	—
41	C₄₁×#546	—	2	2	no	—
42	C₄₁×#546	—	2	2	no	—
43	C₄₁×#546	C₂²	1	2	yes	—
44	C₄₁×#546	C₂²	1	2	yes	—
45	C₄₁×#539	—	2	2	no	—
46	C₄₁×#536	—	2	1	no	—
47	C₄₁×#536	C₂²	1	1	yes	characteristic
48	C₄₁×#536	C₂²	1	1	yes	characteristic
49	C₄₁×#536	C₂²	1	1	yes	characteristic, complemented
50	C₄₁×#535	—	2	1	no	—
51	C₄₁×#535	C₂²	1	1	yes	characteristic
52	C₄₁×#533	C₂²	1	1	yes	characteristic, complemented
53	C₄₁×#532	—	2	1	no	—
54	C₄₁×#532	C₂²	1	1	yes	characteristic
55	C₄₁×#529	—	2	2	no	—
56	C₂×#124×C₄₁	—	2	1	no	—
57	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
58	C₄₁×#520	C₂²	1	1	yes	characteristic
59	C₄₁×#520	C₂²	1	1	yes	characteristic, complemented
60	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
61	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
62	C₄₁×#489	C₂²	1	2	yes	complemented
63	C₄₁×#489	C₂²	1	2	yes	complemented
64	C₄₁×#488	C₂²	1	2	yes	complemented
65	C₄₁×#488	C₂²	1	2	yes	complemented
66	C₄₁×#485	C₂²	1	2	yes	complemented
67	C₄₁×#485	C₂²	1	2	yes	complemented
68	C₄₁×#484	C₂²	1	2	yes	complemented
69	C₄₁×#483	C₂²	1	2	yes	complemented
70	C₄₁×#482	C₂²	1	2	yes	complemented
71	C₄₁×#482	C₂²	1	2	yes	complemented
72	C₄₁×#481	C₂²	1	2	yes	complemented
73	C₄₁×#480	C₂²	1	2	yes	complemented
74	C₄₁×#479	C₂²	1	1	yes	characteristic, complemented
75	C₄₁×#479	C₂²	1	1	yes	characteristic, complemented
76	C₄₁×#478	C₂²	1	1	yes	characteristic, complemented
77	C₄₁×#478	C₂²	1	1	yes	characteristic, complemented
78	C₄₁×#477	C₂²	1	1	yes	characteristic, complemented
79	C₄₁×#476	C₂²	1	1	yes	characteristic, complemented
80	C₄₁×#475	C₂²	1	1	yes	characteristic, complemented
81	C₄₁×#474	C₂²	1	1	yes	characteristic, complemented
82	C₄₁×#470	C₂²	1	2	yes	complemented
83	C₄₁×#470	C₂²	1	2	yes	complemented
84	C₄₁×#468	C₂²	1	2	yes	complemented
85	C₄₁×#468	C₂²	1	2	yes	complemented
86	C₄₁×#467	C₂²	1	2	yes	complemented
87	C₄₁×#467	C₂²	1	2	yes	complemented
88	C₄₁×#465	C₂²	1	2	yes	complemented
89	C₄₁×#465	C₂²	1	2	yes	complemented
90	C₄₁×#464	C₂²	1	2	yes	complemented
91	C₄₁×#464	C₂²	1	2	yes	complemented
92	C₄₁×#464	C₂²	1	2	yes	complemented
93	C₄₁×#464	C₂²	1	2	yes	complemented
94	C₄₁×#452	C₂²	1	2	yes	—
95	C₄₁×#452	C₂²	1	2	yes	—
96	C₄₁×#452	C₂²	1	2	yes	complemented
97	C₄₁×#452	C₂²	1	2	yes	complemented
98	C₄₁×#451	C₂²	1	2	yes	complemented
99	C₄₁×#451	C₂²	1	2	yes	complemented
100	C₄₁×#450	C₂²	1	2	yes	—
101	C₄₁×#450	C₂²	1	2	yes	—
102	C₄₁×#441	C₂²	1	2	yes	complemented
103	C₄₁×#440	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
106	C₄₁×#436	C₂²	1	2	yes	complemented
107	C₄₁×#435	C₂²	1	2	yes	complemented
108	C₄₁×#435	C₂²	1	2	yes	complemented
109	C₈×D₄×C₄₁	C₂²	1	2	yes	complemented
110	C₄₁×#428	C₂²	1	1	yes	characteristic, complemented
111	C₄₁×#427	C₂²	1	1	yes	characteristic, complemented
112	C₄₁×#427	C₂²	1	1	yes	characteristic, complemented
113	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
114	C₄₁×#419	C₂²	1	1	yes	characteristic, complemented
115	C₄₁×#419	C₂²	1	2	yes	complemented
116	C₄₁×#419	C₂²	1	1	yes	characteristic, complemented
117	C₄₁×#419	C₂²	1	1	yes	characteristic, complemented
118	C₄₁×#418	C₂²	1	2	yes	—
119	C₄₁×#418	C₂²	1	1	yes	characteristic
120	C₄₁×#418	C₂²	1	1	yes	characteristic
121	C₄₁×#417	C₂²	1	2	yes	—
122	C₄₁×#417	C₂²	1	1	yes	characteristic
123	C₄₁×#417	C₂²	1	2	yes	complemented
124	C₄₁×#416	C₂²	1	2	yes	—
125	C₄₁×#416	C₂²	1	1	yes	characteristic
126	C₄₁×#416	C₂²	1	1	yes	characteristic
127	C₄₁×#416	C₂²	1	2	yes	complemented
128	C₂×#103×C₄₁	C₂²	1	2	yes	complemented
129	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic, complemented
130	C₂×#102×C₄₁	C₂²	1	2	yes	—
131	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
132	C₄₁×#408	C₂²	1	1	yes	characteristic
133	C₄₁×#408	C₂²	1	1	yes	characteristic, complemented
134	C₄×M₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
135	2₋¹⁺⁴×C₄₁	—	2	4	no	—
136	2₋¹⁺⁴×C₄₁	—	4	2	no	—
137	H(5,𝔽₂)×C₄₁	—	2	4	no	—
138	H(5,𝔽₂)×C₄₁	—	4	2	no	—
139	C₂×#41×C₄₁	—	2	1	no	—
140	C₂×#41×C₄₁	—	2	1	no	—
141	C₂×#41×C₄₁	—	2	2	no	—
142	C₂×#41×C₄₁	C₂³	1	2	yes	—
143	C₂×#41×C₄₁	C₂³	1	2	yes	—
144	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
145	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
146	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
147	C₂²×Q₈×C₄₁	—	2	1	no	—
148	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
150	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
151	C₂²×D₄×C₄₁	—	2	1	no	—
152	C₂²×D₄×C₄₁	—	2	2	no	—
153	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
154	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
155	#137×C₄₁	—	2	4	no	—
156	C₂×Q₁₆×C₄₁	—	4	2	no	—
157	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
158	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
159	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₄₁	—	4	2	no	—
161	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
164	#131×C₄₁	—	4	2	no	—
165	#131×C₄₁	—	4	2	no	—
166	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
167	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
168	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
169	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
170	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
171	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
172	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
173	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
174	C₄⋊Q₈×C₄₁	—	2	1	no	—
175	C₄⋊Q₈×C₄₁	—	2	1	no	—
176	C₄⋊Q₈×C₄₁	—	2	1	no	—
177	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
178	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
179	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
180	#127×C₄₁	—	2	1	no	—
181	#127×C₄₁	D₄	1	1	yes	characteristic
182	#126×C₄₁	—	2	2	no	—
183	#126×C₄₁	—	2	2	no	—
184	#126×C₄₁	—	2	2	no	—
185	#126×C₄₁	—	2	2	no	—
186	#125×C₄₁	—	2	2	no	—
187	#125×C₄₁	—	2	2	no	—
188	#125×C₄₁	—	2	2	no	—
189	#125×C₄₁	C₂³	1	1	yes	characteristic
190	#125×C₄₁	C₂³	1	1	yes	characteristic
191	#124×C₄₁	—	2	1	no	—
192	#124×C₄₁	—	2	1	no	—
193	#124×C₄₁	—	2	2	no	—
194	#124×C₄₁	—	2	1	no	—
195	#124×C₄₁	—	2	1	no	—
196	#124×C₄₁	—	2	2	no	—
197	#124×C₄₁	—	2	2	no	—
198	#124×C₄₁	—	2	1	no	—
199	#124×C₄₁	—	2	1	no	—
200	#124×C₄₁	D₄	1	1	yes	characteristic
201	#124×C₄₁	D₄	1	1	yes	characteristic
202	#124×C₄₁	C₂³	1	2	yes	—
203	#124×C₄₁	C₂³	1	2	yes	—
204	#123×C₄₁	—	2	2	no	—
205	#123×C₄₁	—	2	2	no	—
206	#123×C₄₁	—	2	2	no	—
207	#123×C₄₁	—	2	2	no	—
208	#123×C₄₁	—	2	2	no	—
209	#123×C₄₁	—	2	2	no	—
210	#123×C₄₁	—	2	2	no	—
211	C₂²⋊Q₈×C₄₁	—	2	1	no	—
212	C₂²⋊Q₈×C₄₁	—	2	1	no	—
213	C₂²⋊Q₈×C₄₁	—	2	2	no	—
214	C₂²⋊Q₈×C₄₁	—	2	2	no	—
215	C₂²⋊Q₈×C₄₁	—	2	2	no	—
216	C₂²⋊Q₈×C₄₁	—	2	2	no	—
217	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
218	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
219	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
220	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
221	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
222	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
223	#121×C₄₁	—	2	2	no	—
224	#121×C₄₁	—	2	2	no	—
225	#121×C₄₁	—	2	2	no	—
226	#121×C₄₁	—	2	2	no	—
227	#121×C₄₁	D₄	1	2	yes	—
228	#121×C₄₁	D₄	1	2	yes	—
229	#121×C₄₁	C₂³	1	2	yes	—
230	#121×C₄₁	C₂³	1	2	yes	—
231	#120×C₄₁	—	2	2	no	—
232	#120×C₄₁	—	2	2	no	—
233	#120×C₄₁	—	2	2	no	—
234	C₄×Q₈×C₄₁	—	2	1	no	—
235	C₄×Q₈×C₄₁	—	2	1	no	—
236	C₄×Q₈×C₄₁	—	2	2	no	—
237	C₄×Q₈×C₄₁	—	2	1	no	—
238	C₄×Q₈×C₄₁	—	2	1	no	—
239	C₄×Q₈×C₄₁	—	2	1	no	—
240	C₄×Q₈×C₄₁	—	2	1	no	—
241	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
242	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
243	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₄₁	—	2	2	no	—
246	C₄×D₄×C₄₁	—	2	1	no	—
247	C₄×D₄×C₄₁	—	2	2	no	—
248	C₄×D₄×C₄₁	—	2	1	no	—
249	C₄×D₄×C₄₁	—	2	2	no	—
250	C₄×D₄×C₄₁	—	2	1	no	—
251	C₄×D₄×C₄₁	—	2	1	no	—
252	C₄×D₄×C₄₁	—	2	2	no	—
253	C₄×D₄×C₄₁	—	2	2	no	—
254	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₄₁	C₂³	1	2	yes	—
257	C₄×D₄×C₄₁	C₂³	1	2	yes	—
258	#117×C₄₁	—	2	2	no	—
259	#117×C₄₁	—	2	2	no	—
260	#117×C₄₁	—	2	1	no	—
261	#117×C₄₁	C₂³	1	1	yes	characteristic
262	#117×C₄₁	C₂³	1	1	yes	characteristic
263	#117×C₄₁	C₂³	1	2	yes	—
264	#117×C₄₁	C₂³	1	1	yes	characteristic
265	#117×C₄₁	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
267	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
270	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
271	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
272	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
273	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
274	C₂×C₄²×C₄₁	—	2	1	no	—
275	C₂×C₄²×C₄₁	—	2	1	no	—
276	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
277	#107×C₄₁	C₂³	1	1	yes	characteristic
278	#107×C₄₁	C₂³	1	1	yes	characteristic
279	#107×C₄₁	C₂³	1	1	yes	characteristic
280	#107×C₄₁	C₂³	1	1	yes	characteristic
281	#107×C₄₁	C₂³	1	2	yes	—
282	#106×C₄₁	C₂³	1	1	yes	characteristic
283	#106×C₄₁	C₂³	1	1	yes	characteristic
284	#106×C₄₁	C₂³	1	1	yes	characteristic
285	#106×C₄₁	C₂³	1	1	yes	characteristic
286	#106×C₄₁	C₂³	1	2	yes	—
287	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
288	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
289	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
290	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
291	#103×C₄₁	C₂³	1	1	yes	characteristic
292	#103×C₄₁	C₂³	1	2	yes	—
293	#103×C₄₁	C₂³	1	2	yes	—
294	#103×C₄₁	C₂³	1	2	yes	—
295	#103×C₄₁	C₂³	1	2	yes	—
296	#103×C₄₁	C₂³	1	1	yes	characteristic
297	#103×C₄₁	C₂³	1	1	yes	characteristic
298	#103×C₄₁	C₂³	1	1	yes	characteristic
299	#103×C₄₁	C₂³	1	2	yes	—
300	#103×C₄₁	C₂³	1	2	yes	—
301	#103×C₄₁	C₂³	1	2	yes	—
302	#103×C₄₁	C₂³	1	2	yes	—
303	#103×C₄₁	C₂³	1	2	yes	—
304	#102×C₄₁	C₂³	1	1	yes	characteristic
305	#102×C₄₁	C₂³	1	2	yes	—
306	#102×C₄₁	C₂³	1	2	yes	—
307	#102×C₄₁	C₂³	1	2	yes	—
308	#102×C₄₁	C₂³	1	2	yes	—
309	#102×C₄₁	C₂³	1	1	yes	characteristic
310	#102×C₄₁	C₂³	1	1	yes	characteristic
311	#102×C₄₁	C₂³	1	1	yes	characteristic
312	#102×C₄₁	C₂³	1	2	yes	—
313	#102×C₄₁	C₂³	1	2	yes	—
314	#102×C₄₁	C₂³	1	2	yes	—
315	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
316	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
317	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
318	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
319	#97×C₄₁	C₂³	1	2	yes	—
320	C₄×C₈×C₄₁	C₂³	1	2	yes	—
321	C₂⁴×C₄₁	—	2	2	no	—
322	C₂⁴×C₄₁	—	2	1	no	—
323	#41×C₄₁	—	2	2	no	—
324	#41×C₄₁	—	2	2	no	—
325	#41×C₄₁	—	2	2	no	—
326	#41×C₄₁	—	2	2	no	—
327	#41×C₄₁	—	2	2	no	—
328	#41×C₄₁	—	2	4	no	—
329	#41×C₄₁	—	2	4	no	—
330	#41×C₄₁	—	4	2	no	—
331	#41×C₄₁	—	4	2	no	—
332	#41×C₄₁	—	4	4	no	—
333	#41×C₄₁	—	4	4	no	—
334	#41×C₄₁	—	4	8	no	—
335	#41×C₄₁	#41	1	4	yes	—
336	C₂×Q₈×C₄₁	—	2	1	no	—
337	C₂×Q₈×C₄₁	—	2	1	no	—
338	C₂×Q₈×C₄₁	—	2	2	no	—
339	C₂×Q₈×C₄₁	—	2	1	no	—
340	C₂×Q₈×C₄₁	—	2	1	no	—
341	C₂×Q₈×C₄₁	—	2	4	no	—
342	C₂×Q₈×C₄₁	—	2	2	no	—
343	C₂×Q₈×C₄₁	—	2	2	no	—
344	C₂×Q₈×C₄₁	—	2	2	no	—
345	C₂×Q₈×C₄₁	—	2	2	no	—
346	C₂×Q₈×C₄₁	—	4	2	no	—
347	C₂×Q₈×C₄₁	—	4	4	no	—
348	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
349	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
350	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
351	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
352	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₄₁	—	2	1	no	—
354	C₂×D₄×C₄₁	—	2	4	no	—
355	C₂×D₄×C₄₁	—	2	2	no	—
356	C₂×D₄×C₄₁	—	2	2	no	—
357	C₂×D₄×C₄₁	—	2	2	no	—
358	C₂×D₄×C₄₁	—	2	2	no	—
359	C₂×D₄×C₄₁	—	2	2	no	—
360	C₂×D₄×C₄₁	—	2	1	no	—
361	C₂×D₄×C₄₁	—	2	2	no	—
362	C₂×D₄×C₄₁	—	2	2	no	—
363	C₂×D₄×C₄₁	—	4	2	no	—
364	C₂×D₄×C₄₁	—	4	4	no	—
365	C₂×D₄×C₄₁	—	4	8	no	—
366	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
367	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
368	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
369	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
370	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
371	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
372	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
373	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₄₁	—	2	1	no	—
375	C₂²×C₄×C₄₁	—	2	1	no	—
376	C₂²×C₄×C₄₁	—	2	1	no	—
377	C₂²×C₄×C₄₁	—	2	2	no	—
378	C₂²×C₄×C₄₁	—	2	1	no	—
379	C₂²×C₄×C₄₁	—	2	2	no	—
380	C₂²×C₄×C₄₁	—	2	2	no	—
381	C₂²×C₄×C₄₁	—	2	2	no	—
382	C₂²×C₄×C₄₁	—	2	2	no	—
383	C₂²×C₄×C₄₁	—	2	1	no	—
384	C₂²×C₄×C₄₁	—	2	1	no	—
385	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
388	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
389	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
390	Q₁₆×C₄₁	—	2	4	no	—
391	Q₁₆×C₄₁	—	4	2	no	—
392	Q₁₆×C₄₁	—	4	2	no	—
393	SD₁₆×C₄₁	—	2	4	no	—
394	SD₁₆×C₄₁	—	4	2	no	—
395	SD₁₆×C₄₁	—	4	2	no	—
396	M₁₆×C₄₁	—	2	2	no	—
397	M₁₆×C₄₁	—	2	2	no	—
398	M₁₆×C₄₁	—	4	2	no	—
399	M₁₆×C₄₁	—	4	2	no	—
400	C₂×C₈×C₄₁	—	2	2	no	—
401	C₂×C₈×C₄₁	—	2	2	no	—
402	C₂×C₈×C₄₁	—	4	2	no	—
403	C₂×C₈×C₄₁	—	4	2	no	—
404	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
405	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
406	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
407	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
408	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
409	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₄₁	—	2	2	no	—
411	C₄⋊C₄×C₄₁	—	2	2	no	—
412	C₄⋊C₄×C₄₁	—	2	1	no	—
413	C₄⋊C₄×C₄₁	—	2	2	no	—
414	C₄⋊C₄×C₄₁	—	2	2	no	—
415	C₄⋊C₄×C₄₁	—	2	1	no	—
416	C₄⋊C₄×C₄₁	—	2	1	no	—
417	C₄⋊C₄×C₄₁	—	2	1	no	—
418	C₄⋊C₄×C₄₁	—	2	1	no	—
419	C₄⋊C₄×C₄₁	—	2	2	no	—
420	C₄⋊C₄×C₄₁	—	2	2	no	—
421	C₄⋊C₄×C₄₁	—	2	1	no	—
422	C₄⋊C₄×C₄₁	—	2	2	no	—
423	C₄⋊C₄×C₄₁	—	2	2	no	—
424	C₄⋊C₄×C₄₁	—	2	1	no	—
425	C₄⋊C₄×C₄₁	—	2	1	no	—
426	C₄⋊C₄×C₄₁	—	2	1	no	—
427	C₄⋊C₄×C₄₁	—	2	2	no	—
428	C₄⋊C₄×C₄₁	—	2	2	no	—
429	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
430	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
431	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
432	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
433	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
434	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
435	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
436	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
438	C₂²⋊C₄×C₄₁	—	2	2	no	—
439	C₂²⋊C₄×C₄₁	—	2	2	no	—
440	C₂²⋊C₄×C₄₁	—	2	2	no	—
441	C₂²⋊C₄×C₄₁	—	2	2	no	—
442	C₂²⋊C₄×C₄₁	—	2	1	no	—
443	C₂²⋊C₄×C₄₁	—	2	1	no	—
444	C₂²⋊C₄×C₄₁	—	2	1	no	—
445	C₂²⋊C₄×C₄₁	—	2	2	no	—
446	C₂²⋊C₄×C₄₁	—	2	2	no	—
447	C₂²⋊C₄×C₄₁	—	2	2	no	—
448	C₂²⋊C₄×C₄₁	—	2	2	no	—
449	C₂²⋊C₄×C₄₁	—	2	2	no	—
450	C₂²⋊C₄×C₄₁	—	2	2	no	—
451	C₂²⋊C₄×C₄₁	—	2	2	no	—
452	C₂²⋊C₄×C₄₁	—	2	2	no	—
453	C₂²⋊C₄×C₄₁	—	2	2	no	—
454	C₂²⋊C₄×C₄₁	—	2	2	no	—
455	C₂²⋊C₄×C₄₁	—	2	1	no	—
456	C₂²⋊C₄×C₄₁	—	2	1	no	—
457	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
458	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
459	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
460	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
461	C₄²×C₄₁	—	2	2	no	—
462	C₄²×C₄₁	—	2	1	no	—
463	C₄²×C₄₁	—	2	1	no	—
464	C₄²×C₄₁	—	2	1	no	—
465	C₄²×C₄₁	—	2	2	no	—
466	C₄²×C₄₁	—	2	2	no	—
467	C₄²×C₄₁	—	2	2	no	—
468	C₄²×C₄₁	—	2	1	no	—
469	C₄²×C₄₁	—	2	1	no	—
470	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
471	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
472	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
473	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
474	C₂³×C₄₁	—	2	1	no	—
475	C₂³×C₄₁	—	2	2	no	—
476	C₂³×C₄₁	—	4	4	no	—
477	C₂³×C₄₁	—	4	2	no	—
478	C₂³×C₄₁	—	8	1	no	—
479	C₂³×C₄₁	—	8	1	no	—
480	C₂³×C₄₁	—	8	2	no	—
481	C₂³×C₄₁	—	8	2	no	—
482	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
483	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
484	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
485	Q₈×C₄₁	—	2	2	no	—
486	Q₈×C₄₁	—	2	2	no	—
487	Q₈×C₄₁	—	2	1	no	—
488	Q₈×C₄₁	—	2	2	no	—
489	Q₈×C₄₁	—	2	2	no	—
490	Q₈×C₄₁	—	2	2	no	—
491	Q₈×C₄₁	—	2	2	no	—
492	Q₈×C₄₁	—	4	4	no	—
493	Q₈×C₄₁	—	4	2	no	—
494	Q₈×C₄₁	—	4	2	no	—
495	Q₈×C₄₁	—	4	2	no	—
496	Q₈×C₄₁	—	8	1	no	—
497	Q₈×C₄₁	C₂×#41	1	2	yes	—
498	D₄×C₄₁	—	2	4	no	—
499	D₄×C₄₁	—	2	4	no	—
500	D₄×C₄₁	—	2	4	no	—
501	D₄×C₄₁	—	2	2	no	—
502	D₄×C₄₁	—	2	2	no	—
503	D₄×C₄₁	—	2	2	no	—
504	D₄×C₄₁	—	2	1	no	—
505	D₄×C₄₁	—	2	2	no	—
506	D₄×C₄₁	—	4	2	no	—
507	D₄×C₄₁	—	4	2	no	—
508	D₄×C₄₁	—	4	4	no	—
509	D₄×C₄₁	—	4	4	no	—
510	D₄×C₄₁	—	4	4	no	—
511	D₄×C₄₁	—	4	2	no	—
512	D₄×C₄₁	—	8	2	no	—
513	D₄×C₄₁	—	8	2	no	—
514	D₄×C₄₁	C₂×#41	1	2	yes	—
515	C₂×C₄×C₄₁	—	2	1	no	—
516	C₂×C₄×C₄₁	—	2	4	no	—
517	C₂×C₄×C₄₁	—	2	2	no	—
518	C₂×C₄×C₄₁	—	2	2	no	—
519	C₂×C₄×C₄₁	—	2	2	no	—
520	C₂×C₄×C₄₁	—	2	2	no	—
521	C₂×C₄×C₄₁	—	2	2	no	—
522	C₂×C₄×C₄₁	—	2	1	no	—
523	C₂×C₄×C₄₁	—	2	1	no	—
524	C₂×C₄×C₄₁	—	2	1	no	—
525	C₂×C₄×C₄₁	—	2	1	no	—
526	C₂×C₄×C₄₁	—	2	2	no	—
527	C₂×C₄×C₄₁	—	2	1	no	—
528	C₂×C₄×C₄₁	—	2	1	no	—
529	C₂×C₄×C₄₁	—	2	2	no	—
530	C₂×C₄×C₄₁	—	4	1	no	—
531	C₂×C₄×C₄₁	—	4	1	no	—
532	C₂×C₄×C₄₁	—	4	4	no	—
533	C₂×C₄×C₄₁	—	4	4	no	—
534	C₂×C₄×C₄₁	—	4	4	no	—
535	C₂×C₄×C₄₁	—	4	2	no	—
536	C₂×C₄×C₄₁	—	4	2	no	—
537	C₂×C₄×C₄₁	—	8	1	no	—
538	C₂×C₄×C₄₁	—	8	1	no	—
539	C₂×C₄×C₄₁	—	8	1	no	—
540	C₂×C₄×C₄₁	—	8	2	no	—
541	C₂×C₄×C₄₁	—	8	2	no	—
542	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
546	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
547	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
549	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
550	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
551	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
552	C₈×C₄₁	—	2	2	no	—
553	C₈×C₄₁	—	2	1	no	—
554	C₈×C₄₁	—	2	1	no	—
555	C₈×C₄₁	—	2	1	no	—
556	C₈×C₄₁	—	2	1	no	—
557	C₈×C₄₁	—	2	2	no	—
558	#61207	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
559	C₂²×C₄₁	—	2	1	no	—
560	C₂²×C₄₁	—	2	1	no	—
561	C₂²×C₄₁	—	2	2	no	—
562	C₂²×C₄₁	—	2	2	no	—
563	C₂²×C₄₁	—	2	2	no	—
564	C₂²×C₄₁	—	2	2	no	—
565	C₂²×C₄₁	—	2	2	no	—
566	C₂²×C₄₁	—	2	2	no	—
567	C₂²×C₄₁	—	2	2	no	—
568	C₂²×C₄₁	—	4	1	no	—
569	C₂²×C₄₁	—	4	1	no	—
570	C₂²×C₄₁	—	4	2	no	—
571	C₂²×C₄₁	—	4	2	no	—
572	C₂²×C₄₁	—	4	2	no	—
573	C₂²×C₄₁	—	16	2	no	—
574	C₂²×C₄₁	—	16	4	no	—
575	C₂²×C₄₁	#546	1	2	yes	—
576	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
577	C₄×C₄₁	—	2	1	no	—
578	C₄×C₄₁	—	2	1	no	—
579	C₄×C₄₁	—	2	1	no	—
580	C₄×C₄₁	—	2	1	no	—
581	C₄×C₄₁	—	2	2	no	—
582	C₄×C₄₁	—	2	2	no	—
583	C₄×C₄₁	—	2	2	no	—
584	C₄×C₄₁	—	4	2	no	—
585	C₄×C₄₁	—	4	1	no	—
586	C₄×C₄₁	—	4	1	no	—
587	C₄×C₄₁	—	4	1	no	—
588	C₄×C₄₁	—	4	1	no	—
589	C₄×C₄₁	—	4	1	no	—
590	C₄×C₄₁	—	4	1	no	—
591	C₄×C₄₁	—	4	2	no	—
592	C₄×C₄₁	—	4	2	no	—
593	C₄×C₄₁	#546	1	2	yes	—
594	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
595	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
596	#3507	C₂×C₄₁	1	1	yes	characteristic, complemented
597	#3500	C₂×C₄₁	1	1	yes	characteristic
598	#3327	C₂×C₄₁	1	2	yes	complemented
599	#3323	C₂×C₄₁	1	2	yes	complemented
600	#3316	C₂×C₄₁	1	2	yes	complemented
601	#3314	C₂×C₄₁	1	2	yes	complemented
602	#3313	C₂×C₄₁	1	2	yes	complemented
603	#3311	C₂×C₄₁	1	2	yes	complemented
604	#3300	C₂×C₄₁	1	2	yes	complemented
605	#3296	C₂×C₄₁	1	2	yes	complemented
606	#3140	C₂×C₄₁	1	1	yes	characteristic, complemented
607	#3097	C₂×C₄₁	1	1	yes	characteristic, complemented
608	#3096	C₂×C₄₁	1	1	yes	characteristic, complemented
609	#3076	C₂×C₄₁	1	1	yes	characteristic, complemented
610	#3059	C₂×C₄₁	1	1	yes	characteristic, complemented
611	#3057	C₂×C₄₁	1	1	yes	characteristic, complemented
612	C₂×#464	C₂×C₄₁	1	1	yes	characteristic, complemented
613	#3011	C₂×C₄₁	1	1	yes	characteristic, complemented
614	#3009	C₂×C₄₁	1	1	yes	characteristic, complemented
615	C₄×#137	C₂×C₄₁	1	1	yes	characteristic, complemented
616	#2935	C₂×C₄₁	1	1	yes	characteristic, complemented
617	#2898	C₂×C₄₁	1	1	yes	characteristic, complemented
618	#2897	C₂×C₄₁	1	1	yes	characteristic, complemented
619	C₂×C₄₁	—	2	2	no	—
620	C₂×C₄₁	—	4	2	no	—
621	C₂×C₄₁	—	4	2	no	—
622	C₂×C₄₁	—	4	2	no	—
623	C₂×C₄₁	—	8	2	no	—
624	C₂×C₄₁	C₂×#546	1	1	yes	characteristic
625	C₂×C₄₁	#3584	1	1	yes	characteristic
626	C₂×C₄₁	#3586	1	1	yes	characteristic
627	C₂×2₋¹⁺⁴	C₂²×C₄₁	1	1	yes	characteristic
628	C₂×H(5,𝔽₂)	C₂²×C₄₁	1	1	yes	characteristic
629	C₂×#137	C₂²×C₄₁	1	1	yes	characteristic
630	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
631	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
632	C₂×#131	C₂²×C₄₁	1	1	yes	characteristic
633	C₂×#131	C₂²×C₄₁	1	1	yes	characteristic, complemented
634	#559	—	2	1	no	—
635	#557	—	2	1	no	—
636	#556	—	2	1	no	—
637	#556	—	2	1	no	—
638	#556	C₂²×C₄₁	1	2	yes	complemented
639	#554	C₂²×C₄₁	1	2	yes	complemented
640	#552	C₂²×C₄₁	1	2	yes	complemented
641	#552	C₂²×C₄₁	1	2	yes	complemented
642	#548	C₂²×C₄₁	1	2	yes	—
643	#548	C₂²×C₄₁	1	2	yes	—
644	#546	—	2	2	no	—
645	#546	—	2	2	no	—
646	#546	C₂²×C₄₁	1	2	yes	—
647	#546	C₂²×C₄₁	1	2	yes	—
648	#539	—	2	2	no	—
649	#536	—	2	1	no	—
650	#536	C₂²×C₄₁	1	1	yes	characteristic
651	#536	C₂²×C₄₁	1	1	yes	characteristic
652	#536	C₂²×C₄₁	1	1	yes	characteristic, complemented
653	#535	—	2	1	no	—
654	#535	C₂²×C₄₁	1	1	yes	characteristic
655	#533	C₂²×C₄₁	1	1	yes	characteristic, complemented
656	#532	—	2	1	no	—
657	#532	C₂²×C₄₁	1	1	yes	characteristic
658	#529	—	2	2	no	—
659	C₂×#124	—	2	1	no	—
660	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
661	#520	C₂²×C₄₁	1	1	yes	characteristic
662	#520	C₂²×C₄₁	1	1	yes	characteristic, complemented
663	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
664	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
665	#489	C₂²×C₄₁	1	2	yes	complemented
666	#489	C₂²×C₄₁	1	2	yes	complemented
667	#488	C₂²×C₄₁	1	2	yes	complemented
668	#488	C₂²×C₄₁	1	2	yes	complemented
669	#485	C₂²×C₄₁	1	2	yes	complemented
670	#485	C₂²×C₄₁	1	2	yes	complemented
671	#484	C₂²×C₄₁	1	2	yes	complemented
672	#483	C₂²×C₄₁	1	2	yes	complemented
673	#482	C₂²×C₄₁	1	2	yes	complemented
674	#482	C₂²×C₄₁	1	2	yes	complemented
675	#481	C₂²×C₄₁	1	2	yes	complemented
676	#480	C₂²×C₄₁	1	2	yes	complemented
677	#479	C₂²×C₄₁	1	1	yes	characteristic, complemented
678	#479	C₂²×C₄₁	1	1	yes	characteristic, complemented
679	#478	C₂²×C₄₁	1	1	yes	characteristic, complemented
680	#478	C₂²×C₄₁	1	1	yes	characteristic, complemented
681	#477	C₂²×C₄₁	1	1	yes	characteristic, complemented
682	#476	C₂²×C₄₁	1	1	yes	characteristic, complemented
683	#475	C₂²×C₄₁	1	1	yes	characteristic, complemented
684	#474	C₂²×C₄₁	1	1	yes	characteristic, complemented
685	#470	C₂²×C₄₁	1	2	yes	complemented
686	#470	C₂²×C₄₁	1	2	yes	complemented
687	#468	C₂²×C₄₁	1	2	yes	complemented
688	#468	C₂²×C₄₁	1	2	yes	complemented
689	#467	C₂²×C₄₁	1	2	yes	complemented
690	#467	C₂²×C₄₁	1	2	yes	complemented
691	#465	C₂²×C₄₁	1	2	yes	complemented
692	#465	C₂²×C₄₁	1	2	yes	complemented
693	#464	C₂²×C₄₁	1	2	yes	complemented
694	#464	C₂²×C₄₁	1	2	yes	complemented
695	#464	C₂²×C₄₁	1	2	yes	complemented
696	#464	C₂²×C₄₁	1	2	yes	complemented
697	#452	C₂²×C₄₁	1	2	yes	—
698	#452	C₂²×C₄₁	1	2	yes	—
699	#452	C₂²×C₄₁	1	2	yes	complemented
700	#452	C₂²×C₄₁	1	2	yes	complemented
701	#451	C₂²×C₄₁	1	2	yes	complemented
702	#451	C₂²×C₄₁	1	2	yes	complemented
703	#450	C₂²×C₄₁	1	2	yes	—
704	#450	C₂²×C₄₁	1	2	yes	—
705	#441	C₂²×C₄₁	1	2	yes	complemented
706	#440	C₂²×C₄₁	1	2	yes	complemented
707	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	complemented
708	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
709	#436	C₂²×C₄₁	1	2	yes	complemented
710	#435	C₂²×C₄₁	1	2	yes	complemented
711	#435	C₂²×C₄₁	1	2	yes	complemented
712	C₈×D₄	C₂²×C₄₁	1	2	yes	complemented
713	#428	C₂²×C₄₁	1	1	yes	characteristic, complemented
714	#427	C₂²×C₄₁	1	1	yes	characteristic, complemented
715	#427	C₂²×C₄₁	1	1	yes	characteristic, complemented
716	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
717	#419	C₂²×C₄₁	1	1	yes	characteristic, complemented
718	#419	C₂²×C₄₁	1	1	yes	characteristic, complemented
719	#419	C₂²×C₄₁	1	2	yes	complemented
720	#419	C₂²×C₄₁	1	1	yes	characteristic, complemented
721	#418	C₂²×C₄₁	1	1	yes	characteristic
722	#418	C₂²×C₄₁	1	1	yes	characteristic
723	#418	C₂²×C₄₁	1	2	yes	—
724	#417	C₂²×C₄₁	1	1	yes	characteristic
725	#417	C₂²×C₄₁	1	2	yes	—
726	#417	C₂²×C₄₁	1	2	yes	complemented
727	#416	C₂²×C₄₁	1	1	yes	characteristic
728	#416	C₂²×C₄₁	1	1	yes	characteristic
729	#416	C₂²×C₄₁	1	2	yes	—
730	#416	C₂²×C₄₁	1	2	yes	complemented
731	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic, complemented
732	C₂×#103	C₂²×C₄₁	1	2	yes	complemented
733	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
734	C₂×#102	C₂²×C₄₁	1	2	yes	—
735	#408	C₂²×C₄₁	1	1	yes	characteristic
736	#408	C₂²×C₄₁	1	1	yes	characteristic, complemented
737	C₄×M₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
738	C₄₁	#61207	1	1	yes	characteristic, direct product factor, Sylow
739	2₋¹⁺⁴	—	2	4	no	—
740	2₋¹⁺⁴	—	4	2	no	—
741	H(5,𝔽₂)	—	2	4	no	—
742	H(5,𝔽₂)	—	4	2	no	—
743	C₂×#41	—	2	1	no	—
744	C₂×#41	—	2	1	no	—
745	C₂×#41	—	2	2	no	—
746	C₂×#41	C₂³×C₄₁	1	2	yes	—
747	C₂×#41	C₂³×C₄₁	1	2	yes	—
748	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
749	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
750	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
751	C₂²×Q₈	—	2	1	no	—
752	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
753	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
754	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
755	C₂²×D₄	—	2	1	no	—
756	C₂²×D₄	—	2	2	no	—
757	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
758	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
759	#137	—	2	4	no	—
760	C₂×Q₁₆	—	4	2	no	—
761	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
762	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
763	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
764	C₂×SD₁₆	—	4	2	no	—
765	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
766	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
767	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
768	#131	—	4	2	no	—
769	#131	—	4	2	no	—
770	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
771	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
772	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
773	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
774	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
775	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
776	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
777	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
778	C₄⋊Q₈	—	2	1	no	—
779	C₄⋊Q₈	—	2	1	no	—
780	C₄⋊Q₈	—	2	1	no	—
781	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
782	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
783	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
784	#127	—	2	1	no	—
785	#127	D₄×C₄₁	1	1	yes	characteristic
786	#126	—	2	2	no	—
787	#126	—	2	2	no	—
788	#126	—	2	2	no	—
789	#126	—	2	2	no	—
790	#125	—	2	2	no	—
791	#125	—	2	2	no	—
792	#125	—	2	2	no	—
793	#125	C₂³×C₄₁	1	1	yes	characteristic
794	#125	C₂³×C₄₁	1	1	yes	characteristic
795	#124	—	2	1	no	—
796	#124	—	2	1	no	—
797	#124	—	2	2	no	—
798	#124	—	2	1	no	—
799	#124	—	2	1	no	—
800	#124	—	2	2	no	—
801	#124	—	2	2	no	—
802	#124	—	2	1	no	—
803	#124	—	2	1	no	—
804	#124	D₄×C₄₁	1	1	yes	characteristic
805	#124	D₄×C₄₁	1	1	yes	characteristic
806	#124	C₂³×C₄₁	1	2	yes	—
807	#124	C₂³×C₄₁	1	2	yes	—
808	#123	—	2	2	no	—
809	#123	—	2	2	no	—
810	#123	—	2	2	no	—
811	#123	—	2	2	no	—
812	#123	—	2	2	no	—
813	#123	—	2	2	no	—
814	#123	—	2	2	no	—
815	C₂²⋊Q₈	—	2	1	no	—
816	C₂²⋊Q₈	—	2	1	no	—
817	C₂²⋊Q₈	—	2	2	no	—
818	C₂²⋊Q₈	—	2	2	no	—
819	C₂²⋊Q₈	—	2	2	no	—
820	C₂²⋊Q₈	—	2	2	no	—
821	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
822	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
823	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
824	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
825	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
826	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
827	#121	—	2	2	no	—
828	#121	—	2	2	no	—
829	#121	—	2	2	no	—
830	#121	—	2	2	no	—
831	#121	D₄×C₄₁	1	2	yes	—
832	#121	D₄×C₄₁	1	2	yes	—
833	#121	C₂³×C₄₁	1	2	yes	—
834	#121	C₂³×C₄₁	1	2	yes	—
835	#120	—	2	2	no	—
836	#120	—	2	2	no	—
837	#120	—	2	2	no	—
838	C₄×Q₈	—	2	1	no	—
839	C₄×Q₈	—	2	1	no	—
840	C₄×Q₈	—	2	2	no	—
841	C₄×Q₈	—	2	1	no	—
842	C₄×Q₈	—	2	1	no	—
843	C₄×Q₈	—	2	1	no	—
844	C₄×Q₈	—	2	1	no	—
845	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
846	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
847	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
848	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
849	C₄×D₄	—	2	2	no	—
850	C₄×D₄	—	2	1	no	—
851	C₄×D₄	—	2	2	no	—
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	—	2	2	no	—
854	C₄×D₄	—	2	1	no	—
855	C₄×D₄	—	2	1	no	—
856	C₄×D₄	—	2	2	no	—
857	C₄×D₄	—	2	2	no	—
858	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
859	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
860	C₄×D₄	C₂³×C₄₁	1	2	yes	—
861	C₄×D₄	C₂³×C₄₁	1	2	yes	—
862	#117	—	2	2	no	—
863	#117	—	2	2	no	—
864	#117	—	2	1	no	—
865	#117	C₂³×C₄₁	1	1	yes	characteristic
866	#117	C₂³×C₄₁	1	1	yes	characteristic
867	#117	C₂³×C₄₁	1	2	yes	—
868	#117	C₂³×C₄₁	1	1	yes	characteristic
869	#117	C₂³×C₄₁	1	2	yes	—
870	C₂×C₄⋊C₄	—	2	1	no	—
871	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
872	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
873	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
874	C₂×C₂²⋊C₄	—	2	1	no	—
875	C₂×C₂²⋊C₄	—	2	1	no	—
876	C₂×C₂²⋊C₄	—	2	2	no	—
877	C₂×C₂²⋊C₄	—	2	2	no	—
878	C₂×C₄²	—	2	1	no	—
879	C₂×C₄²	—	2	1	no	—
880	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
881	#107	C₂³×C₄₁	1	1	yes	characteristic
882	#107	C₂³×C₄₁	1	1	yes	characteristic
883	#107	C₂³×C₄₁	1	1	yes	characteristic
884	#107	C₂³×C₄₁	1	1	yes	characteristic
885	#107	C₂³×C₄₁	1	2	yes	—
886	#106	C₂³×C₄₁	1	1	yes	characteristic
887	#106	C₂³×C₄₁	1	1	yes	characteristic
888	#106	C₂³×C₄₁	1	1	yes	characteristic
889	#106	C₂³×C₄₁	1	1	yes	characteristic
890	#106	C₂³×C₄₁	1	2	yes	—
891	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
892	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
893	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
894	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
895	#103	C₂³×C₄₁	1	1	yes	characteristic
896	#103	C₂³×C₄₁	1	2	yes	—
897	#103	C₂³×C₄₁	1	2	yes	—
898	#103	C₂³×C₄₁	1	2	yes	—
899	#103	C₂³×C₄₁	1	2	yes	—
900	#103	C₂³×C₄₁	1	1	yes	characteristic
901	#103	C₂³×C₄₁	1	1	yes	characteristic
902	#103	C₂³×C₄₁	1	1	yes	characteristic
903	#103	C₂³×C₄₁	1	2	yes	—
904	#103	C₂³×C₄₁	1	2	yes	—
905	#103	C₂³×C₄₁	1	2	yes	—
906	#103	C₂³×C₄₁	1	2	yes	—
907	#103	C₂³×C₄₁	1	2	yes	—
908	#102	C₂³×C₄₁	1	1	yes	characteristic
909	#102	C₂³×C₄₁	1	2	yes	—
910	#102	C₂³×C₄₁	1	2	yes	—
911	#102	C₂³×C₄₁	1	2	yes	—
912	#102	C₂³×C₄₁	1	2	yes	—
913	#102	C₂³×C₄₁	1	1	yes	characteristic
914	#102	C₂³×C₄₁	1	1	yes	characteristic
915	#102	C₂³×C₄₁	1	1	yes	characteristic
916	#102	C₂³×C₄₁	1	2	yes	—
917	#102	C₂³×C₄₁	1	2	yes	—
918	#102	C₂³×C₄₁	1	2	yes	—
919	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
920	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
921	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
922	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
923	#97	C₂³×C₄₁	1	2	yes	—
924	C₄×C₈	C₂³×C₄₁	1	2	yes	—
925	C₂⁴	—	2	2	no	—
926	C₂⁴	—	2	1	no	—
927	#41	—	2	2	no	—
928	#41	—	2	2	no	—
929	#41	—	2	2	no	—
930	#41	—	2	2	no	—
931	#41	—	2	2	no	—
932	#41	—	2	4	no	—
933	#41	—	2	4	no	—
934	#41	—	4	2	no	—
935	#41	—	4	2	no	—
936	#41	—	4	4	no	—
937	#41	—	4	4	no	—
938	#41	—	4	8	no	—
939	#41	#41×C₄₁	1	4	yes	—
940	C₂×Q₈	—	2	1	no	—
941	C₂×Q₈	—	2	1	no	—
942	C₂×Q₈	—	2	2	no	—
943	C₂×Q₈	—	2	1	no	—
944	C₂×Q₈	—	2	1	no	—
945	C₂×Q₈	—	2	4	no	—
946	C₂×Q₈	—	2	2	no	—
947	C₂×Q₈	—	2	2	no	—
948	C₂×Q₈	—	2	2	no	—
949	C₂×Q₈	—	2	2	no	—
950	C₂×Q₈	—	4	2	no	—
951	C₂×Q₈	—	4	4	no	—
952	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
953	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
954	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
955	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
956	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
957	C₂×D₄	—	2	1	no	—
958	C₂×D₄	—	2	4	no	—
959	C₂×D₄	—	2	2	no	—
960	C₂×D₄	—	2	2	no	—
961	C₂×D₄	—	2	2	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	2	no	—
964	C₂×D₄	—	2	1	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	2	no	—
967	C₂×D₄	—	4	2	no	—
968	C₂×D₄	—	4	4	no	—
969	C₂×D₄	—	4	8	no	—
970	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
971	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
972	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
973	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
974	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
975	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
976	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
977	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	1	no	—
980	C₂²×C₄	—	2	1	no	—
981	C₂²×C₄	—	2	2	no	—
982	C₂²×C₄	—	2	1	no	—
983	C₂²×C₄	—	2	2	no	—
984	C₂²×C₄	—	2	2	no	—
985	C₂²×C₄	—	2	2	no	—
986	C₂²×C₄	—	2	2	no	—
987	C₂²×C₄	—	2	1	no	—
988	C₂²×C₄	—	2	1	no	—
989	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
990	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
991	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
992	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
993	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
994	Q₁₆	—	2	4	no	—
995	Q₁₆	—	4	2	no	—
996	Q₁₆	—	4	2	no	—
997	SD₁₆	—	2	4	no	—
998	SD₁₆	—	4	2	no	—
999	SD₁₆	—	4	2	no	—
1000	M₁₆	—	2	2	no	—
1001	M₁₆	—	2	2	no	—
1002	M₁₆	—	4	2	no	—
1003	M₁₆	—	4	2	no	—
1004	C₂×C₈	—	2	2	no	—
1005	C₂×C₈	—	2	2	no	—
1006	C₂×C₈	—	4	2	no	—
1007	C₂×C₈	—	4	2	no	—
1008	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1009	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1010	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1011	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1012	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1013	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	—	2	2	no	—
1019	C₄⋊C₄	—	2	1	no	—
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	1	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	1	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	2	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1034	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1035	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
1036	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1037	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1038	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1039	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1040	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1041	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	1	no	—
1047	C₂²⋊C₄	—	2	1	no	—
1048	C₂²⋊C₄	—	2	1	no	—
1049	C₂²⋊C₄	—	2	2	no	—
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	2	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	1	no	—
1060	C₂²⋊C₄	—	2	1	no	—
1061	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1062	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1063	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1064	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1065	C₄²	—	2	2	no	—
1066	C₄²	—	2	1	no	—
1067	C₄²	—	2	1	no	—
1068	C₄²	—	2	1	no	—
1069	C₄²	—	2	2	no	—
1070	C₄²	—	2	2	no	—
1071	C₄²	—	2	2	no	—
1072	C₄²	—	2	1	no	—
1073	C₄²	—	2	1	no	—
1074	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1075	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1076	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1077	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1078	C₂³	—	2	1	no	—
1079	C₂³	—	2	2	no	—
1080	C₂³	—	4	4	no	—
1081	C₂³	—	4	2	no	—
1082	C₂³	—	8	1	no	—
1083	C₂³	—	8	1	no	—
1084	C₂³	—	8	2	no	—
1085	C₂³	—	8	2	no	—
1086	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
1087	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
1088	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1089	Q₈	—	2	2	no	—
1090	Q₈	—	2	2	no	—
1091	Q₈	—	2	1	no	—
1092	Q₈	—	2	2	no	—
1093	Q₈	—	2	2	no	—
1094	Q₈	—	2	2	no	—
1095	Q₈	—	2	2	no	—
1096	Q₈	—	4	4	no	—
1097	Q₈	—	4	2	no	—
1098	Q₈	—	4	2	no	—
1099	Q₈	—	4	2	no	—
1100	Q₈	—	8	1	no	—
1101	Q₈	C₂×#41×C₄₁	1	2	yes	—
1102	D₄	—	2	4	no	—
1103	D₄	—	2	4	no	—
1104	D₄	—	2	4	no	—
1105	D₄	—	2	2	no	—
1106	D₄	—	2	2	no	—
1107	D₄	—	2	2	no	—
1108	D₄	—	2	1	no	—
1109	D₄	—	2	2	no	—
1110	D₄	—	4	2	no	—
1111	D₄	—	4	2	no	—
1112	D₄	—	4	4	no	—
1113	D₄	—	4	4	no	—
1114	D₄	—	4	4	no	—
1115	D₄	—	4	2	no	—
1116	D₄	—	8	2	no	—
1117	D₄	—	8	2	no	—
1118	D₄	C₂×#41×C₄₁	1	2	yes	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	4	no	—
1121	C₂×C₄	—	2	2	no	—
1122	C₂×C₄	—	2	2	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	2	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	2	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	2	no	—
1134	C₂×C₄	—	4	1	no	—
1135	C₂×C₄	—	4	1	no	—
1136	C₂×C₄	—	4	4	no	—
1137	C₂×C₄	—	4	4	no	—
1138	C₂×C₄	—	4	4	no	—
1139	C₂×C₄	—	4	2	no	—
1140	C₂×C₄	—	4	2	no	—
1141	C₂×C₄	—	8	1	no	—
1142	C₂×C₄	—	8	1	no	—
1143	C₂×C₄	—	8	1	no	—
1144	C₂×C₄	—	8	2	no	—
1145	C₂×C₄	—	8	2	no	—
1146	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1147	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1148	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1149	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1150	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1151	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1152	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1153	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
1154	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
1155	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
1156	C₈	—	2	2	no	—
1157	C₈	—	2	1	no	—
1158	C₈	—	2	1	no	—
1159	C₈	—	2	1	no	—
1160	C₈	—	2	1	no	—
1161	C₈	—	2	2	no	—
1162	C₂²	—	2	1	no	—
1163	C₂²	—	2	1	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	2	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	2	2	no	—
1168	C₂²	—	2	2	no	—
1169	C₂²	—	2	2	no	—
1170	C₂²	—	2	2	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	4	2	no	—
1174	C₂²	—	4	2	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	16	2	no	—
1177	C₂²	—	16	4	no	—
1178	C₂²	C₄₁×#546	1	2	yes	—
1179	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
1180	C₄	—	2	1	no	—
1181	C₄	—	2	1	no	—
1182	C₄	—	2	1	no	—
1183	C₄	—	2	1	no	—
1184	C₄	—	2	2	no	—
1185	C₄	—	2	2	no	—
1186	C₄	—	2	2	no	—
1187	C₄	—	4	2	no	—
1188	C₄	—	4	1	no	—
1189	C₄	—	4	1	no	—
1190	C₄	—	4	1	no	—
1191	C₄	—	4	1	no	—
1192	C₄	—	4	1	no	—
1193	C₄	—	4	1	no	—
1194	C₄	—	4	2	no	—
1195	C₄	—	4	2	no	—
1196	C₄	C₄₁×#546	1	2	yes	—
1197	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
1198	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1199	C₂	—	2	2	no	—
1200	C₂	—	4	2	no	—
1201	C₂	—	4	2	no	—
1202	C₂	—	4	2	no	—
1203	C₂	—	8	2	no	—
1204	C₂	C₂×C₄₁×#546	1	1	yes	characteristic
1205	C₂	C₄₁×#3584	1	1	yes	characteristic
1206	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×#3500	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×#3327	C₂	semidirect
4. C₄₁×#3323	C₂	semidirect
5. C₄₁×#3316	C₂	semidirect
6. C₄₁×#3314	C₂	semidirect
7. C₄₁×#3313	C₂	semidirect
8. C₄₁×#3311	C₂	semidirect
9. C₄₁×#3300	C₂	semidirect
10. C₄₁×#3296	C₂	semidirect
11. C₄₁×#3140	C₂	semidirect
12. C₄₁×#3097	C₂	semidirect
13. C₄₁×#3096	C₂	semidirect
14. C₄₁×#3076	C₂	semidirect
15. C₄₁×#3059	C₂	semidirect
16. C₄₁×#3057	C₂	semidirect
17. C₂×C₄₁×#464	C₂	semidirect
18. C₄₁×#3011	C₂	semidirect
19. C₄₁×#3009	C₂	semidirect
20. C₄×#137×C₄₁	C₂	semidirect
21. C₄₁×#2935	C₂	semidirect
22. C₄₁×#2898	C₂	semidirect
23. C₄₁×#2897	C₂	semidirect
27. C₂²×Q₁₆×C₄₁	C₂²	semidirect
30. C₂×#131×C₄₁	C₂²	semidirect
35. C₄₁×#556	C₂²	semidirect
36. C₄₁×#554	C₂²	semidirect
37. C₄₁×#552	C₂²	semidirect
38. C₄₁×#552	C₂²	semidirect
49. C₄₁×#536	C₂²	semidirect
52. C₄₁×#533	C₂²	semidirect
59. C₄₁×#520	C₂²	semidirect
61. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
62. C₄₁×#489	C₂²	semidirect
63. C₄₁×#489	C₂²	semidirect
64. C₄₁×#488	C₂²	semidirect
65. C₄₁×#488	C₂²	semidirect
66. C₄₁×#485	C₂²	semidirect
67. C₄₁×#485	C₂²	semidirect
68. C₄₁×#484	C₂²	semidirect
69. C₄₁×#483	C₂²	semidirect
70. C₄₁×#482	C₂²	semidirect
71. C₄₁×#482	C₂²	semidirect
72. C₄₁×#481	C₂²	semidirect
73. C₄₁×#480	C₂²	semidirect
74. C₄₁×#479	C₂²	semidirect
75. C₄₁×#479	C₂²	semidirect
76. C₄₁×#478	C₂²	semidirect
77. C₄₁×#478	C₂²	semidirect
78. C₄₁×#477	C₂²	semidirect
79. C₄₁×#476	C₂²	semidirect
80. C₄₁×#475	C₂²	semidirect
81. C₄₁×#474	C₂²	semidirect
82. C₄₁×#470	C₂²	semidirect
83. C₄₁×#470	C₂²	semidirect
84. C₄₁×#468	C₂²	semidirect
85. C₄₁×#468	C₂²	semidirect
86. C₄₁×#467	C₂²	semidirect
87. C₄₁×#467	C₂²	semidirect
88. C₄₁×#465	C₂²	semidirect
89. C₄₁×#465	C₂²	semidirect
90. C₄₁×#464	C₂²	semidirect
91. C₄₁×#464	C₂²	semidirect
92. C₄₁×#464	C₂²	semidirect
93. C₄₁×#464	C₂²	semidirect
96. C₄₁×#452	C₂²	semidirect
97. C₄₁×#452	C₂²	semidirect
98. C₄₁×#451	C₂²	semidirect
99. C₄₁×#451	C₂²	semidirect
102. C₄₁×#441	C₂²	semidirect
103. C₄₁×#440	C₂²	semidirect
104. C₄×Q₁₆×C₄₁	C₂²	semidirect
105. C₄×SD₁₆×C₄₁	C₂²	semidirect
106. C₄₁×#436	C₂²	semidirect
107. C₄₁×#435	C₂²	semidirect
108. C₄₁×#435	C₂²	semidirect
109. C₈×D₄×C₄₁	C₂²	semidirect
110. C₄₁×#428	C₂²	semidirect
111. C₄₁×#427	C₂²	semidirect
112. C₄₁×#427	C₂²	semidirect
113. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
114. C₄₁×#419	C₂²	semidirect
115. C₄₁×#419	C₂²	semidirect
116. C₄₁×#419	C₂²	semidirect
117. C₄₁×#419	C₂²	semidirect
123. C₄₁×#417	C₂²	semidirect
127. C₄₁×#416	C₂²	semidirect
128. C₂×#103×C₄₁	C₂²	semidirect
129. C₂×#103×C₄₁	C₂²	semidirect
133. C₄₁×#408	C₂²	semidirect
134. C₄×M₁₆×C₄₁	C₂²	semidirect
558. #61207	C₄₁	direct (N × H)
596. #3507	C₂×C₄₁	semidirect
598. #3327	C₂×C₄₁	semidirect
599. #3323	C₂×C₄₁	semidirect
600. #3316	C₂×C₄₁	semidirect
601. #3314	C₂×C₄₁	semidirect
602. #3313	C₂×C₄₁	semidirect
603. #3311	C₂×C₄₁	semidirect
604. #3300	C₂×C₄₁	semidirect
605. #3296	C₂×C₄₁	semidirect
606. #3140	C₂×C₄₁	semidirect
607. #3097	C₂×C₄₁	semidirect
608. #3096	C₂×C₄₁	semidirect
609. #3076	C₂×C₄₁	semidirect
610. #3059	C₂×C₄₁	semidirect
611. #3057	C₂×C₄₁	semidirect
612. C₂×#464	C₂×C₄₁	semidirect
613. #3011	C₂×C₄₁	semidirect
614. #3009	C₂×C₄₁	semidirect
615. C₄×#137	C₂×C₄₁	semidirect
616. #2935	C₂×C₄₁	semidirect
617. #2898	C₂×C₄₁	semidirect
618. #2897	C₂×C₄₁	semidirect
630. C₂²×Q₁₆	C₂²×C₄₁	semidirect
633. C₂×#131	C₂²×C₄₁	semidirect
638. #556	C₂²×C₄₁	semidirect
639. #554	C₂²×C₄₁	semidirect
640. #552	C₂²×C₄₁	semidirect
641. #552	C₂²×C₄₁	semidirect
652. #536	C₂²×C₄₁	semidirect
655. #533	C₂²×C₄₁	semidirect
662. #520	C₂²×C₄₁	semidirect
664. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
665. #489	C₂²×C₄₁	semidirect
666. #489	C₂²×C₄₁	semidirect
667. #488	C₂²×C₄₁	semidirect
668. #488	C₂²×C₄₁	semidirect
669. #485	C₂²×C₄₁	semidirect
670. #485	C₂²×C₄₁	semidirect
671. #484	C₂²×C₄₁	semidirect
672. #483	C₂²×C₄₁	semidirect
673. #482	C₂²×C₄₁	semidirect
674. #482	C₂²×C₄₁	semidirect
675. #481	C₂²×C₄₁	semidirect
676. #480	C₂²×C₄₁	semidirect
677. #479	C₂²×C₄₁	semidirect
678. #479	C₂²×C₄₁	semidirect
679. #478	C₂²×C₄₁	semidirect
680. #478	C₂²×C₄₁	semidirect
681. #477	C₂²×C₄₁	semidirect
682. #476	C₂²×C₄₁	semidirect
683. #475	C₂²×C₄₁	semidirect
684. #474	C₂²×C₄₁	semidirect
685. #470	C₂²×C₄₁	semidirect
686. #470	C₂²×C₄₁	semidirect
687. #468	C₂²×C₄₁	semidirect
688. #468	C₂²×C₄₁	semidirect
689. #467	C₂²×C₄₁	semidirect
690. #467	C₂²×C₄₁	semidirect
691. #465	C₂²×C₄₁	semidirect
692. #465	C₂²×C₄₁	semidirect
693. #464	C₂²×C₄₁	semidirect
694. #464	C₂²×C₄₁	semidirect
695. #464	C₂²×C₄₁	semidirect
696. #464	C₂²×C₄₁	semidirect
699. #452	C₂²×C₄₁	semidirect
700. #452	C₂²×C₄₁	semidirect
701. #451	C₂²×C₄₁	semidirect
702. #451	C₂²×C₄₁	semidirect
705. #441	C₂²×C₄₁	semidirect
706. #440	C₂²×C₄₁	semidirect
707. C₄×Q₁₆	C₂²×C₄₁	semidirect
708. C₄×SD₁₆	C₂²×C₄₁	semidirect
709. #436	C₂²×C₄₁	semidirect
710. #435	C₂²×C₄₁	semidirect
711. #435	C₂²×C₄₁	semidirect
712. C₈×D₄	C₂²×C₄₁	semidirect
713. #428	C₂²×C₄₁	semidirect
714. #427	C₂²×C₄₁	semidirect
715. #427	C₂²×C₄₁	semidirect
716. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
717. #419	C₂²×C₄₁	semidirect
718. #419	C₂²×C₄₁	semidirect
719. #419	C₂²×C₄₁	semidirect
720. #419	C₂²×C₄₁	semidirect
726. #417	C₂²×C₄₁	semidirect
730. #416	C₂²×C₄₁	semidirect
731. C₂×#103	C₂²×C₄₁	semidirect
732. C₂×#103	C₂²×C₄₁	semidirect
736. #408	C₂²×C₄₁	semidirect
737. C₄×M₁₆	C₂²×C₄₁	semidirect
738. C₄₁	#61207	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×#3500	2
C₄₁×#3327	2
C₄₁×#3323	2
C₄₁×#3316	2
C₄₁×#3314	2
C₄₁×#3313	2
C₄₁×#3311	2
C₄₁×#3300	2
C₄₁×#3296	2
C₄₁×#3140	2
C₄₁×#3097	2
C₄₁×#3096	2
C₄₁×#3076	2
C₄₁×#3059	2
C₄₁×#3057	2
C₂×C₄₁×#464	2
C₄₁×#3011	2
C₄₁×#3009	2
C₄×#137×C₄₁	2
C₄₁×#2935	2
C₄₁×#2898	2
C₄₁×#2897	2
#61207	41

Subgroups — C41×#61207 #23837408

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61207 #23837408