Subgroups — C₄₁×#62070 #23838271

Order 10496.

1846 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3515	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3392	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#3331	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#3317	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3296	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3295	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#3284	C₂	1	2	yes	maximal, complemented
12	C₄₁×#3283	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3267	C₂	1	2	yes	maximal, complemented
15	C₄₁×#3258	C₂	1	2	yes	maximal, complemented
16	C₄₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#3222	C₂	1	2	yes	maximal, complemented
18	C₄₁×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#3125	C₂	1	2	yes	maximal, complemented
20	C₄₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄₁×#3045	C₂	1	2	yes	maximal, complemented
22	C₄₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₁×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	2	yes	—
25	C₂×#135×C₄₁	C₂²	1	2	yes	complemented
26	C₂×#135×C₄₁	C₂²	1	2	yes	complemented
27	C₄₁×#560	—	2	2	no	—
28	C₄₁×#557	C₂²	1	1	yes	characteristic, complemented
29	C₄₁×#556	C₂²	1	1	yes	characteristic
30	C₄₁×#554	C₂²	1	1	yes	characteristic
31	C₄₁×#554	C₂²	1	1	yes	characteristic, complemented
32	C₄₁×#553	—	2	1	no	—
33	C₄₁×#553	—	2	1	no	—
34	C₄₁×#552	—	2	2	no	—
35	C₄₁×#552	—	2	1	no	—
36	C₄₁×#552	C₂²	1	2	yes	complemented
37	C₄₁×#550	C₂²	1	2	yes	—
38	C₄₁×#550	C₂²	1	1	yes	characteristic
39	C₄₁×#547	C₂²	1	1	yes	characteristic
40	C₄₁×#547	C₂²	1	1	yes	characteristic
41	C₄₁×#547	C₂²	1	2	yes	complemented
42	C₄₁×#546	—	2	1	no	—
43	C₄₁×#546	C₂²	1	2	yes	—
44	D₄²×C₄₁	C₂²	1	1	yes	characteristic
45	C₄₁×#542	C₂²	1	2	yes	—
46	C₄₁×#541	C₂²	1	2	yes	complemented
47	C₄₁×#539	—	2	2	no	—
48	C₄₁×#538	—	2	2	no	—
49	C₄₁×#537	—	2	1	no	—
50	C₄₁×#535	—	2	1	no	—
51	C₄₁×#535	C₂²	1	2	yes	—
52	C₄₁×#533	C₂²	1	1	yes	characteristic, complemented
53	C₄₁×#532	C₂²	1	1	yes	characteristic
54	C₄₁×#532	C₂²	1	1	yes	characteristic
55	C₄₁×#529	—	2	1	no	—
56	C₄₁×#529	C₂²	1	1	yes	characteristic
57	C₂×#125×C₄₁	—	2	1	no	—
58	C₄₁×#520	C₂²	1	2	yes	complemented
59	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic, complemented
60	C₄₁×#497	C₂²	1	2	yes	—
61	C₄₁×#494	C₂²	1	1	yes	characteristic, complemented
62	C₄₁×#492	C₂²	1	1	yes	characteristic
63	C₄₁×#492	C₂²	1	2	yes	complemented
64	C₄₁×#490	C₂²	1	2	yes	complemented
65	C₄₁×#488	C₂²	1	2	yes	—
66	C₄₁×#487	C₂²	1	1	yes	characteristic, complemented
67	C₄₁×#486	C₂²	1	1	yes	characteristic
68	C₄₁×#483	C₂²	1	2	yes	complemented
69	C₄₁×#482	C₂²	1	1	yes	characteristic
70	C₄₁×#482	C₂²	1	1	yes	characteristic, complemented
71	C₄₁×#481	C₂²	1	2	yes	—
72	C₄₁×#479	C₂²	1	2	yes	complemented
73	C₄₁×#478	C₂²	1	2	yes	complemented
74	C₄₁×#477	C₂²	1	1	yes	characteristic, complemented
75	C₄₁×#476	C₂²	1	1	yes	characteristic
76	C₄₁×#476	C₂²	1	1	yes	characteristic, complemented
77	C₄₁×#476	C₂²	1	1	yes	characteristic, complemented
78	C₄₁×#475	C₂²	1	2	yes	complemented
79	C₄₁×#470	C₂²	1	2	yes	complemented
80	C₄₁×#468	C₂²	1	2	yes	—
81	C₄₁×#467	C₂²	1	2	yes	complemented
82	C₄₁×#465	C₂²	1	2	yes	—
83	C₄₁×#465	C₂²	1	2	yes	—
84	C₄₁×#465	C₂²	1	2	yes	complemented
85	C₄₁×#464	C₂²	1	2	yes	—
86	C₄₁×#464	C₂²	1	2	yes	complemented
87	C₄₁×#464	C₂²	1	2	yes	complemented
88	C₄₁×#464	C₂²	1	2	yes	complemented
89	C₄₁×#463	C₂²	1	2	yes	—
90	C₄₁×#463	C₂²	1	2	yes	complemented
91	C₄₁×#462	C₂²	1	1	yes	characteristic, complemented
92	C₄₁×#462	C₂²	1	2	yes	complemented
93	C₄₁×#461	C₂²	1	1	yes	characteristic
94	C₄₁×#461	C₂²	1	1	yes	characteristic, complemented
95	C₄₁×#461	C₂²	1	1	yes	characteristic, complemented
96	C₄₁×#461	C₂²	1	2	yes	complemented
97	C₄₁×#460	C₂²	1	1	yes	characteristic
98	C₄₁×#460	C₂²	1	2	yes	—
99	C₄₁×#460	C₂²	1	1	yes	characteristic
100	C₄₁×#460	C₂²	1	2	yes	complemented
101	C₄₁×#459	C₂²	1	1	yes	characteristic
102	C₄₁×#459	C₂²	1	1	yes	characteristic
103	C₄₁×#459	C₂²	1	2	yes	complemented
104	C₄₁×#452	C₂²	1	2	yes	complemented
105	C₄₁×#452	C₂²	1	2	yes	complemented
106	C₄₁×#452	C₂²	1	2	yes	complemented
107	C₄₁×#452	C₂²	1	2	yes	complemented
108	C₄₁×#452	C₂²	1	2	yes	complemented
109	C₄₁×#450	C₂²	1	2	yes	—
110	C₄₁×#450	C₂²	1	2	yes	—
111	C₄₁×#449	C₂²	1	1	yes	characteristic
112	C₄₁×#449	C₂²	1	2	yes	—
113	C₄₁×#449	C₂²	1	1	yes	characteristic, complemented
114	C₄₁×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
116	C₄₁×#442	C₂²	1	2	yes	complemented
117	C₄₁×#441	C₂²	1	2	yes	complemented
118	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
121	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
122	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
123	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
124	C₄₁×#436	C₂²	1	1	yes	characteristic
125	C₄₁×#435	C₂²	1	2	yes	complemented
126	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
127	C₈×D₄×C₄₁	C₂²	1	2	yes	complemented
128	C₄₁×#433	C₂²	1	2	yes	complemented
129	C₄₁×#431	C₂²	1	1	yes	characteristic, complemented
130	C₄₁×#424	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
132	C₄₁×#417	C₂²	1	2	yes	complemented
133	C₄₁×#416	C₂²	1	2	yes	complemented
134	C₂×#102×C₄₁	C₂²	1	2	yes	—
135	C₂×#41×C₄₁	—	2	1	no	—
136	C₂×#41×C₄₁	—	2	1	no	—
137	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
138	C₂×#41×C₄₁	C₂³	1	2	yes	—
139	C₂×#41×C₄₁	C₂³	1	2	yes	—
140	C₂×#41×C₄₁	C₂³	1	2	yes	—
141	C₂²×D₄×C₄₁	—	2	1	no	—
142	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
143	AGL(1,ℤ/8)×C₄₁	—	4	4	no	—
144	#135×C₄₁	—	4	4	no	—
145	#135×C₄₁	—	4	4	no	—
146	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
155	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
157	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
158	C₂×D₈×C₄₁	C₂³	1	2	yes	—
159	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
160	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
161	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
162	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
166	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
168	#127×C₄₁	—	2	2	no	—
169	#127×C₄₁	C₂³	1	1	yes	characteristic
170	#127×C₄₁	C₂³	1	1	yes	characteristic
171	#127×C₄₁	C₂³	1	2	yes	—
172	#126×C₄₁	—	2	2	no	—
173	#126×C₄₁	—	2	2	no	—
174	#126×C₄₁	—	2	2	no	—
175	#126×C₄₁	—	2	2	no	—
176	#126×C₄₁	—	2	2	no	—
177	#126×C₄₁	D₄	1	2	yes	—
178	#125×C₄₁	—	2	2	no	—
179	#125×C₄₁	—	2	2	no	—
180	#125×C₄₁	—	2	1	no	—
181	#125×C₄₁	—	2	1	no	—
182	#125×C₄₁	—	2	2	no	—
183	#125×C₄₁	—	2	2	no	—
184	#125×C₄₁	—	2	1	no	—
185	#125×C₄₁	D₄	1	1	yes	characteristic
186	#125×C₄₁	C₂³	1	2	yes	—
187	#124×C₄₁	—	2	2	no	—
188	#124×C₄₁	—	2	1	no	—
189	#124×C₄₁	D₄	1	1	yes	characteristic
190	#124×C₄₁	C₂³	1	2	yes	—
191	#124×C₄₁	C₂³	1	2	yes	—
192	#123×C₄₁	—	2	2	no	—
193	#123×C₄₁	—	2	2	no	—
194	#123×C₄₁	—	2	2	no	—
195	#123×C₄₁	—	2	2	no	—
196	#123×C₄₁	—	2	2	no	—
197	#123×C₄₁	—	2	2	no	—
198	#123×C₄₁	—	2	2	no	—
199	#123×C₄₁	D₄	1	2	yes	—
200	C₂²⋊Q₈×C₄₁	—	2	1	no	—
201	C₂²⋊Q₈×C₄₁	—	2	1	no	—
202	C₂²⋊Q₈×C₄₁	—	2	1	no	—
203	C₂²⋊Q₈×C₄₁	—	2	2	no	—
204	C₂²⋊Q₈×C₄₁	—	2	2	no	—
205	C₂²⋊Q₈×C₄₁	—	2	2	no	—
206	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
207	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
208	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
209	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
211	#121×C₄₁	—	2	1	no	—
212	#121×C₄₁	—	2	1	no	—
213	#121×C₄₁	—	2	2	no	—
214	#121×C₄₁	—	2	1	no	—
215	#121×C₄₁	—	2	1	no	—
216	#121×C₄₁	—	2	1	no	—
217	#121×C₄₁	—	2	1	no	—
218	#121×C₄₁	—	2	2	no	—
219	#121×C₄₁	—	2	2	no	—
220	#121×C₄₁	—	2	1	no	—
221	#121×C₄₁	—	2	2	no	—
222	#121×C₄₁	—	2	2	no	—
223	#121×C₄₁	—	2	2	no	—
224	#121×C₄₁	—	2	2	no	—
225	#121×C₄₁	D₄	1	1	yes	characteristic
226	#121×C₄₁	C₂³	1	1	yes	characteristic
227	#121×C₄₁	C₂³	1	1	yes	characteristic
228	#121×C₄₁	C₂³	1	2	yes	—
229	#120×C₄₁	—	2	2	no	—
230	#120×C₄₁	—	2	2	no	—
231	#120×C₄₁	—	2	2	no	—
232	#120×C₄₁	—	2	2	no	—
233	C₄×Q₈×C₄₁	—	2	1	no	—
234	C₄×Q₈×C₄₁	—	2	1	no	—
235	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
238	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
239	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
240	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₄₁	—	2	1	no	—
242	C₄×D₄×C₄₁	—	2	1	no	—
243	C₄×D₄×C₄₁	—	2	1	no	—
244	C₄×D₄×C₄₁	—	2	2	no	—
245	C₄×D₄×C₄₁	—	2	2	no	—
246	C₄×D₄×C₄₁	—	2	2	no	—
247	C₄×D₄×C₄₁	—	2	1	no	—
248	C₄×D₄×C₄₁	—	2	1	no	—
249	C₄×D₄×C₄₁	—	2	1	no	—
250	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₄₁	C₂³	1	2	yes	—
253	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₄₁	C₂³	1	2	yes	—
256	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₄₁	C₂³	1	2	yes	—
258	#117×C₄₁	—	2	1	no	—
259	#117×C₄₁	—	2	2	no	—
260	#117×C₄₁	—	2	1	no	—
261	#117×C₄₁	—	2	2	no	—
262	#117×C₄₁	—	2	1	no	—
263	#117×C₄₁	C₂³	1	1	yes	characteristic
264	#117×C₄₁	C₂³	1	2	yes	—
265	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
266	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
267	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
268	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
269	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
270	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
271	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
272	C₂×C₄²×C₄₁	—	2	1	no	—
273	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
274	#107×C₄₁	C₂³	1	1	yes	characteristic
275	#107×C₄₁	C₂³	1	1	yes	characteristic
276	#106×C₄₁	C₂³	1	1	yes	characteristic
277	#106×C₄₁	C₂³	1	1	yes	characteristic
278	#106×C₄₁	C₂³	1	2	yes	—
279	#106×C₄₁	C₂³	1	2	yes	—
280	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
281	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
285	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
286	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
287	#103×C₄₁	C₂³	1	2	yes	—
288	#103×C₄₁	C₂³	1	2	yes	—
289	#103×C₄₁	C₂³	1	2	yes	—
290	#103×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	#102×C₄₁	C₂³	1	1	yes	characteristic
296	#102×C₄₁	C₂³	1	2	yes	—
297	#102×C₄₁	C₂³	1	2	yes	—
298	#102×C₄₁	C₂³	1	2	yes	—
299	#102×C₄₁	C₂³	1	2	yes	—
300	#102×C₄₁	C₂³	1	1	yes	characteristic
301	#102×C₄₁	C₂³	1	2	yes	—
302	#102×C₄₁	C₂³	1	1	yes	characteristic
303	#102×C₄₁	C₂³	1	1	yes	characteristic
304	#102×C₄₁	C₂³	1	1	yes	characteristic
305	#102×C₄₁	C₂³	1	1	yes	characteristic
306	#102×C₄₁	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
311	#97×C₄₁	C₂³	1	2	yes	—
312	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₄₁	C₂³	1	2	yes	—
315	C₂⁴×C₄₁	—	2	2	no	—
316	#41×C₄₁	—	2	2	no	—
317	#41×C₄₁	—	2	4	no	—
318	#41×C₄₁	—	4	2	no	—
319	#41×C₄₁	—	4	1	no	—
320	#41×C₄₁	—	4	2	no	—
321	#41×C₄₁	—	4	2	no	—
322	#41×C₄₁	—	4	2	no	—
323	#41×C₄₁	—	4	2	no	—
324	#41×C₄₁	—	8	2	no	—
325	#41×C₄₁	—	8	2	no	—
326	C₂×Q₈×C₄₁	—	2	1	no	—
327	C₂×Q₈×C₄₁	—	2	1	no	—
328	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₄₁	—	2	2	no	—
333	C₂×D₄×C₄₁	—	2	1	no	—
334	C₂×D₄×C₄₁	—	2	1	no	—
335	C₂×D₄×C₄₁	—	2	2	no	—
336	C₂×D₄×C₄₁	—	2	2	no	—
337	C₂×D₄×C₄₁	—	2	2	no	—
338	C₂×D₄×C₄₁	—	2	1	no	—
339	C₂×D₄×C₄₁	—	2	1	no	—
340	C₂×D₄×C₄₁	—	2	1	no	—
341	C₂×D₄×C₄₁	—	2	1	no	—
342	C₂×D₄×C₄₁	—	2	2	no	—
343	C₂×D₄×C₄₁	—	2	1	no	—
344	C₂×D₄×C₄₁	—	2	2	no	—
345	C₂×D₄×C₄₁	—	2	2	no	—
346	C₂×D₄×C₄₁	—	4	2	no	—
347	C₂×D₄×C₄₁	—	4	2	no	—
348	C₂×D₄×C₄₁	—	8	2	no	—
349	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
353	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
354	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₄₁	—	2	2	no	—
356	C₂²×C₄×C₄₁	—	2	1	no	—
357	C₂²×C₄×C₄₁	—	2	1	no	—
358	C₂²×C₄×C₄₁	—	2	2	no	—
359	C₂²×C₄×C₄₁	—	2	1	no	—
360	C₂²×C₄×C₄₁	—	2	1	no	—
361	C₂²×C₄×C₄₁	—	2	1	no	—
362	C₂²×C₄×C₄₁	—	2	2	no	—
363	C₂²×C₄×C₄₁	—	2	2	no	—
364	C₂²×C₄×C₄₁	—	2	2	no	—
365	C₂²×C₄×C₄₁	—	2	2	no	—
366	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
370	Q₁₆×C₄₁	—	4	2	no	—
371	Q₁₆×C₄₁	—	4	2	no	—
372	Q₁₆×C₄₁	—	4	2	no	—
373	SD₁₆×C₄₁	—	2	4	no	—
374	SD₁₆×C₄₁	—	4	2	no	—
375	SD₁₆×C₄₁	—	4	1	no	—
376	SD₁₆×C₄₁	—	4	1	no	—
377	SD₁₆×C₄₁	—	4	2	no	—
378	SD₁₆×C₄₁	—	4	2	no	—
379	SD₁₆×C₄₁	—	4	2	no	—
380	SD₁₆×C₄₁	—	4	2	no	—
381	D₈×C₄₁	—	2	2	no	—
382	D₈×C₄₁	—	2	4	no	—
383	D₈×C₄₁	—	2	2	no	—
384	M₁₆×C₄₁	—	4	2	no	—
385	C₂×C₈×C₄₁	—	4	2	no	—
386	C₂×C₈×C₄₁	—	4	2	no	—
387	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
391	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
393	C₄⋊C₄×C₄₁	—	2	2	no	—
394	C₄⋊C₄×C₄₁	—	2	1	no	—
395	C₄⋊C₄×C₄₁	—	2	1	no	—
396	C₄⋊C₄×C₄₁	—	2	1	no	—
397	C₄⋊C₄×C₄₁	—	2	2	no	—
398	C₄⋊C₄×C₄₁	—	2	2	no	—
399	C₄⋊C₄×C₄₁	—	2	2	no	—
400	C₄⋊C₄×C₄₁	—	2	2	no	—
401	C₄⋊C₄×C₄₁	—	2	2	no	—
402	C₄⋊C₄×C₄₁	—	2	2	no	—
403	C₄⋊C₄×C₄₁	—	2	2	no	—
404	C₄⋊C₄×C₄₁	—	2	2	no	—
405	C₄⋊C₄×C₄₁	—	2	1	no	—
406	C₄⋊C₄×C₄₁	—	2	1	no	—
407	C₄⋊C₄×C₄₁	—	2	2	no	—
408	C₄⋊C₄×C₄₁	—	2	1	no	—
409	C₄⋊C₄×C₄₁	—	2	1	no	—
410	C₄⋊C₄×C₄₁	—	2	1	no	—
411	C₄⋊C₄×C₄₁	—	2	2	no	—
412	C₄⋊C₄×C₄₁	—	2	2	no	—
413	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
415	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
416	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
418	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
421	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
424	C₂²⋊C₄×C₄₁	—	2	2	no	—
425	C₂²⋊C₄×C₄₁	—	2	2	no	—
426	C₂²⋊C₄×C₄₁	—	2	2	no	—
427	C₂²⋊C₄×C₄₁	—	2	1	no	—
428	C₂²⋊C₄×C₄₁	—	2	2	no	—
429	C₂²⋊C₄×C₄₁	—	2	1	no	—
430	C₂²⋊C₄×C₄₁	—	2	2	no	—
431	C₂²⋊C₄×C₄₁	—	2	1	no	—
432	C₂²⋊C₄×C₄₁	—	2	1	no	—
433	C₂²⋊C₄×C₄₁	—	2	2	no	—
434	C₂²⋊C₄×C₄₁	—	2	2	no	—
435	C₂²⋊C₄×C₄₁	—	2	1	no	—
436	C₂²⋊C₄×C₄₁	—	2	2	no	—
437	C₂²⋊C₄×C₄₁	—	2	2	no	—
438	C₂²⋊C₄×C₄₁	—	2	2	no	—
439	C₂²⋊C₄×C₄₁	—	2	1	no	—
440	C₂²⋊C₄×C₄₁	—	2	2	no	—
441	C₂²⋊C₄×C₄₁	—	2	1	no	—
442	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
447	C₄²×C₄₁	—	2	1	no	—
448	C₄²×C₄₁	—	2	1	no	—
449	C₄²×C₄₁	—	2	1	no	—
450	C₄²×C₄₁	—	2	2	no	—
451	C₄²×C₄₁	—	2	2	no	—
452	C₄²×C₄₁	—	2	2	no	—
453	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
456	C₄²×C₄₁	C₂⁴	1	2	yes	—
457	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
458	C₂³×C₄₁	—	2	1	no	—
459	C₂³×C₄₁	—	2	1	no	—
460	C₂³×C₄₁	—	2	2	no	—
461	C₂³×C₄₁	—	2	1	no	—
462	C₂³×C₄₁	—	8	2	no	—
463	C₂³×C₄₁	—	8	2	no	—
464	C₂³×C₄₁	—	8	2	no	—
465	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
466	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
467	Q₈×C₄₁	—	2	2	no	—
468	Q₈×C₄₁	—	2	2	no	—
469	Q₈×C₄₁	—	2	2	no	—
470	Q₈×C₄₁	—	2	1	no	—
471	Q₈×C₄₁	—	2	1	no	—
472	Q₈×C₄₁	—	2	2	no	—
473	Q₈×C₄₁	—	2	2	no	—
474	Q₈×C₄₁	—	8	1	no	—
475	Q₈×C₄₁	—	8	1	no	—
476	D₄×C₄₁	—	2	2	no	—
477	D₄×C₄₁	—	2	1	no	—
478	D₄×C₄₁	—	2	2	no	—
479	D₄×C₄₁	—	2	1	no	—
480	D₄×C₄₁	—	2	1	no	—
481	D₄×C₄₁	—	2	1	no	—
482	D₄×C₄₁	—	2	2	no	—
483	D₄×C₄₁	—	2	1	no	—
484	D₄×C₄₁	—	4	2	no	—
485	D₄×C₄₁	—	4	2	no	—
486	D₄×C₄₁	—	4	4	no	—
487	D₄×C₄₁	—	4	2	no	—
488	D₄×C₄₁	—	8	1	no	—
489	D₄×C₄₁	—	8	1	no	—
490	D₄×C₄₁	—	8	2	no	—
491	D₄×C₄₁	—	8	2	no	—
492	D₄×C₄₁	—	8	1	no	—
493	D₄×C₄₁	—	8	2	no	—
494	D₄×C₄₁	—	8	2	no	—
495	D₄×C₄₁	—	8	2	no	—
496	D₄×C₄₁	—	8	2	no	—
497	D₄×C₄₁	—	8	1	no	—
498	D₄×C₄₁	—	8	1	no	—
499	D₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
500	C₂×C₄×C₄₁	—	2	2	no	—
501	C₂×C₄×C₄₁	—	2	1	no	—
502	C₂×C₄×C₄₁	—	2	2	no	—
503	C₂×C₄×C₄₁	—	2	2	no	—
504	C₂×C₄×C₄₁	—	2	1	no	—
505	C₂×C₄×C₄₁	—	2	1	no	—
506	C₂×C₄×C₄₁	—	2	1	no	—
507	C₂×C₄×C₄₁	—	2	1	no	—
508	C₂×C₄×C₄₁	—	2	1	no	—
509	C₂×C₄×C₄₁	—	2	2	no	—
510	C₂×C₄×C₄₁	—	2	2	no	—
511	C₂×C₄×C₄₁	—	2	2	no	—
512	C₂×C₄×C₄₁	—	2	1	no	—
513	C₂×C₄×C₄₁	—	4	1	no	—
514	C₂×C₄×C₄₁	—	4	2	no	—
515	C₂×C₄×C₄₁	—	4	4	no	—
516	C₂×C₄×C₄₁	—	4	2	no	—
517	C₂×C₄×C₄₁	—	4	2	no	—
518	C₂×C₄×C₄₁	—	4	2	no	—
519	C₂×C₄×C₄₁	—	8	1	no	—
520	C₂×C₄×C₄₁	—	8	2	no	—
521	C₂×C₄×C₄₁	—	8	2	no	—
522	C₂×C₄×C₄₁	—	8	2	no	—
523	C₂×C₄×C₄₁	—	8	2	no	—
524	C₂×C₄×C₄₁	—	8	2	no	—
525	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
534	C₈×C₄₁	—	2	1	no	—
535	C₈×C₄₁	—	2	2	no	—
536	C₈×C₄₁	—	2	2	no	—
537	C₈×C₄₁	—	2	1	no	—
538	C₈×C₄₁	—	2	1	no	—
539	C₈×C₄₁	—	2	1	no	—
540	#62070	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
541	C₂²×C₄₁	—	2	1	no	—
542	C₂²×C₄₁	—	2	2	no	—
543	C₂²×C₄₁	—	2	1	no	—
544	C₂²×C₄₁	—	2	2	no	—
545	C₂²×C₄₁	—	2	2	no	—
546	C₂²×C₄₁	—	2	1	no	—
547	C₂²×C₄₁	—	2	2	no	—
548	C₂²×C₄₁	—	4	1	no	—
549	C₂²×C₄₁	—	4	1	no	—
550	C₂²×C₄₁	—	4	1	no	—
551	C₂²×C₄₁	—	4	2	no	—
552	C₂²×C₄₁	—	4	1	no	—
553	C₂²×C₄₁	—	4	1	no	—
554	C₂²×C₄₁	—	4	2	no	—
555	C₂²×C₄₁	—	4	1	no	—
556	C₂²×C₄₁	—	4	1	no	—
557	C₂²×C₄₁	—	4	1	no	—
558	C₂²×C₄₁	—	4	2	no	—
559	C₂²×C₄₁	—	16	4	no	—
560	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
561	C₄×C₄₁	—	2	1	no	—
562	C₄×C₄₁	—	2	1	no	—
563	C₄×C₄₁	—	2	2	no	—
564	C₄×C₄₁	—	2	1	no	—
565	C₄×C₄₁	—	2	2	no	—
566	C₄×C₄₁	—	2	1	no	—
567	C₄×C₄₁	—	2	2	no	—
568	C₄×C₄₁	—	4	1	no	—
569	C₄×C₄₁	—	4	2	no	—
570	C₄×C₄₁	—	4	2	no	—
571	C₄×C₄₁	—	4	1	no	—
572	C₄×C₄₁	—	4	2	no	—
573	C₄×C₄₁	—	4	1	no	—
574	C₄×C₄₁	—	4	1	no	—
575	C₄×C₄₁	—	4	1	no	—
576	C₄×C₄₁	#577	1	2	yes	—
577	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
578	C₄×C₄₁	#585	1	1	yes	characteristic
579	#3546	C₂×C₄₁	1	1	yes	characteristic, complemented
580	#3515	C₂×C₄₁	1	1	yes	characteristic, complemented
581	#3398	C₂×C₄₁	1	1	yes	characteristic, complemented
582	#3392	C₂×C₄₁	1	1	yes	characteristic, complemented
583	#3366	C₂×C₄₁	1	1	yes	characteristic, complemented
584	#3360	C₂×C₄₁	1	1	yes	characteristic, complemented
585	#3331	C₂×C₄₁	1	1	yes	characteristic, complemented
586	#3317	C₂×C₄₁	1	2	yes	complemented
587	#3296	C₂×C₄₁	1	2	yes	complemented
588	#3295	C₂×C₄₁	1	1	yes	characteristic, complemented
589	#3284	C₂×C₄₁	1	2	yes	complemented
590	#3283	C₂×C₄₁	1	1	yes	characteristic, complemented
591	#3272	C₂×C₄₁	1	1	yes	characteristic, complemented
592	#3267	C₂×C₄₁	1	2	yes	complemented
593	#3258	C₂×C₄₁	1	2	yes	complemented
594	#3246	C₂×C₄₁	1	1	yes	characteristic, complemented
595	#3222	C₂×C₄₁	1	2	yes	complemented
596	#3210	C₂×C₄₁	1	1	yes	characteristic, complemented
597	#3125	C₂×C₄₁	1	2	yes	complemented
598	#3106	C₂×C₄₁	1	1	yes	characteristic, complemented
599	#3045	C₂×C₄₁	1	2	yes	complemented
600	#3035	C₂×C₄₁	1	1	yes	characteristic, complemented
601	#2994	C₂×C₄₁	1	1	yes	characteristic, complemented
602	C₂×C₄₁	—	4	1	no	—
603	C₂×C₄₁	—	4	2	no	—
604	C₂×C₄₁	—	4	2	no	—
605	C₂×C₄₁	—	8	1	no	—
606	C₂×C₄₁	—	8	2	no	—
607	C₂×C₄₁	—	8	1	no	—
608	C₂×C₄₁	#3488	1	1	yes	characteristic
609	C₂×C₄₁	C₂×#577	1	1	yes	characteristic
610	C₂×C₄₁	#3584	1	1	yes	characteristic
611	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	2	yes	—
612	C₂×#135	C₂²×C₄₁	1	2	yes	complemented
613	C₂×#135	C₂²×C₄₁	1	2	yes	complemented
614	#560	—	2	2	no	—
615	#557	C₂²×C₄₁	1	1	yes	characteristic, complemented
616	#556	C₂²×C₄₁	1	1	yes	characteristic
617	#554	C₂²×C₄₁	1	1	yes	characteristic
618	#554	C₂²×C₄₁	1	1	yes	characteristic, complemented
619	#553	—	2	1	no	—
620	#553	—	2	1	no	—
621	#552	—	2	2	no	—
622	#552	—	2	1	no	—
623	#552	C₂²×C₄₁	1	2	yes	complemented
624	#550	C₂²×C₄₁	1	2	yes	—
625	#550	C₂²×C₄₁	1	1	yes	characteristic
626	#547	C₂²×C₄₁	1	1	yes	characteristic
627	#547	C₂²×C₄₁	1	1	yes	characteristic
628	#547	C₂²×C₄₁	1	2	yes	complemented
629	#546	—	2	1	no	—
630	#546	C₂²×C₄₁	1	2	yes	—
631	D₄²	C₂²×C₄₁	1	1	yes	characteristic
632	#542	C₂²×C₄₁	1	2	yes	—
633	#541	C₂²×C₄₁	1	2	yes	complemented
634	#539	—	2	2	no	—
635	#538	—	2	2	no	—
636	#537	—	2	1	no	—
637	#535	—	2	1	no	—
638	#535	C₂²×C₄₁	1	2	yes	—
639	#533	C₂²×C₄₁	1	1	yes	characteristic, complemented
640	#532	C₂²×C₄₁	1	1	yes	characteristic
641	#532	C₂²×C₄₁	1	1	yes	characteristic
642	#529	—	2	1	no	—
643	#529	C₂²×C₄₁	1	1	yes	characteristic
644	C₂×#125	—	2	1	no	—
645	#520	C₂²×C₄₁	1	2	yes	complemented
646	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic, complemented
647	#497	C₂²×C₄₁	1	2	yes	—
648	#494	C₂²×C₄₁	1	1	yes	characteristic, complemented
649	#492	C₂²×C₄₁	1	1	yes	characteristic
650	#492	C₂²×C₄₁	1	2	yes	complemented
651	#490	C₂²×C₄₁	1	2	yes	complemented
652	#488	C₂²×C₄₁	1	2	yes	—
653	#487	C₂²×C₄₁	1	1	yes	characteristic, complemented
654	#486	C₂²×C₄₁	1	1	yes	characteristic
655	#483	C₂²×C₄₁	1	2	yes	complemented
656	#482	C₂²×C₄₁	1	1	yes	characteristic
657	#482	C₂²×C₄₁	1	1	yes	characteristic, complemented
658	#481	C₂²×C₄₁	1	2	yes	—
659	#479	C₂²×C₄₁	1	2	yes	complemented
660	#478	C₂²×C₄₁	1	2	yes	complemented
661	#477	C₂²×C₄₁	1	1	yes	characteristic, complemented
662	#476	C₂²×C₄₁	1	1	yes	characteristic
663	#476	C₂²×C₄₁	1	1	yes	characteristic, complemented
664	#476	C₂²×C₄₁	1	1	yes	characteristic, complemented
665	#475	C₂²×C₄₁	1	2	yes	complemented
666	#470	C₂²×C₄₁	1	2	yes	complemented
667	#468	C₂²×C₄₁	1	2	yes	—
668	#467	C₂²×C₄₁	1	2	yes	complemented
669	#465	C₂²×C₄₁	1	2	yes	—
670	#465	C₂²×C₄₁	1	2	yes	—
671	#465	C₂²×C₄₁	1	2	yes	complemented
672	#464	C₂²×C₄₁	1	2	yes	—
673	#464	C₂²×C₄₁	1	2	yes	complemented
674	#464	C₂²×C₄₁	1	2	yes	complemented
675	#464	C₂²×C₄₁	1	2	yes	complemented
676	#463	C₂²×C₄₁	1	2	yes	—
677	#463	C₂²×C₄₁	1	2	yes	complemented
678	#462	C₂²×C₄₁	1	1	yes	characteristic, complemented
679	#462	C₂²×C₄₁	1	2	yes	complemented
680	#461	C₂²×C₄₁	1	1	yes	characteristic
681	#461	C₂²×C₄₁	1	1	yes	characteristic, complemented
682	#461	C₂²×C₄₁	1	1	yes	characteristic, complemented
683	#461	C₂²×C₄₁	1	2	yes	complemented
684	#460	C₂²×C₄₁	1	1	yes	characteristic
685	#460	C₂²×C₄₁	1	1	yes	characteristic
686	#460	C₂²×C₄₁	1	2	yes	—
687	#460	C₂²×C₄₁	1	2	yes	complemented
688	#459	C₂²×C₄₁	1	1	yes	characteristic
689	#459	C₂²×C₄₁	1	1	yes	characteristic
690	#459	C₂²×C₄₁	1	2	yes	complemented
691	#452	C₂²×C₄₁	1	2	yes	complemented
692	#452	C₂²×C₄₁	1	2	yes	complemented
693	#452	C₂²×C₄₁	1	2	yes	complemented
694	#452	C₂²×C₄₁	1	2	yes	complemented
695	#452	C₂²×C₄₁	1	2	yes	complemented
696	#450	C₂²×C₄₁	1	2	yes	—
697	#450	C₂²×C₄₁	1	2	yes	—
698	#449	C₂²×C₄₁	1	1	yes	characteristic
699	#449	C₂²×C₄₁	1	2	yes	—
700	#449	C₂²×C₄₁	1	1	yes	characteristic, complemented
701	#446	C₂²×C₄₁	1	1	yes	characteristic, complemented
702	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
703	#442	C₂²×C₄₁	1	2	yes	complemented
704	#441	C₂²×C₄₁	1	2	yes	complemented
705	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
706	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
707	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
708	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
709	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
710	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
711	#436	C₂²×C₄₁	1	1	yes	characteristic
712	#435	C₂²×C₄₁	1	2	yes	complemented
713	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
714	C₈×D₄	C₂²×C₄₁	1	2	yes	complemented
715	#433	C₂²×C₄₁	1	2	yes	complemented
716	#431	C₂²×C₄₁	1	1	yes	characteristic, complemented
717	#424	C₂²×C₄₁	1	2	yes	complemented
718	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
719	#417	C₂²×C₄₁	1	2	yes	complemented
720	#416	C₂²×C₄₁	1	2	yes	complemented
721	C₂×#102	C₂²×C₄₁	1	2	yes	—
722	C₄₁	#62070	1	1	yes	characteristic, direct product factor, Sylow
723	C₂×#41	—	2	1	no	—
724	C₂×#41	—	2	1	no	—
725	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
726	C₂×#41	C₂³×C₄₁	1	2	yes	—
727	C₂×#41	C₂³×C₄₁	1	2	yes	—
728	C₂×#41	C₂³×C₄₁	1	2	yes	—
729	C₂²×D₄	—	2	1	no	—
730	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
731	AGL(1,ℤ/8)	—	4	4	no	—
732	#135	—	4	4	no	—
733	#135	—	4	4	no	—
734	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
735	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
736	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
737	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
738	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
739	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
740	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
741	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
742	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
743	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
744	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
745	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
746	C₂×D₈	C₂³×C₄₁	1	2	yes	—
747	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
748	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
749	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
750	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
751	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
752	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
753	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
754	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
755	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
756	#127	—	2	2	no	—
757	#127	C₂³×C₄₁	1	1	yes	characteristic
758	#127	C₂³×C₄₁	1	1	yes	characteristic
759	#127	C₂³×C₄₁	1	2	yes	—
760	#126	—	2	2	no	—
761	#126	—	2	2	no	—
762	#126	—	2	2	no	—
763	#126	—	2	2	no	—
764	#126	—	2	2	no	—
765	#126	D₄×C₄₁	1	2	yes	—
766	#125	—	2	2	no	—
767	#125	—	2	2	no	—
768	#125	—	2	1	no	—
769	#125	—	2	1	no	—
770	#125	—	2	2	no	—
771	#125	—	2	2	no	—
772	#125	—	2	1	no	—
773	#125	D₄×C₄₁	1	1	yes	characteristic
774	#125	C₂³×C₄₁	1	2	yes	—
775	#124	—	2	2	no	—
776	#124	—	2	1	no	—
777	#124	D₄×C₄₁	1	1	yes	characteristic
778	#124	C₂³×C₄₁	1	2	yes	—
779	#124	C₂³×C₄₁	1	2	yes	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	#123	—	2	2	no	—
786	#123	—	2	2	no	—
787	#123	D₄×C₄₁	1	2	yes	—
788	C₂²⋊Q₈	—	2	1	no	—
789	C₂²⋊Q₈	—	2	1	no	—
790	C₂²⋊Q₈	—	2	1	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
795	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
796	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
797	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
798	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
799	#121	—	2	1	no	—
800	#121	—	2	1	no	—
801	#121	—	2	2	no	—
802	#121	—	2	1	no	—
803	#121	—	2	1	no	—
804	#121	—	2	1	no	—
805	#121	—	2	1	no	—
806	#121	—	2	2	no	—
807	#121	—	2	2	no	—
808	#121	—	2	1	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	—	2	2	no	—
812	#121	—	2	2	no	—
813	#121	D₄×C₄₁	1	1	yes	characteristic
814	#121	C₂³×C₄₁	1	1	yes	characteristic
815	#121	C₂³×C₄₁	1	1	yes	characteristic
816	#121	C₂³×C₄₁	1	2	yes	—
817	#120	—	2	2	no	—
818	#120	—	2	2	no	—
819	#120	—	2	2	no	—
820	#120	—	2	2	no	—
821	C₄×Q₈	—	2	1	no	—
822	C₄×Q₈	—	2	1	no	—
823	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
824	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
825	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
826	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
827	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
828	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	—	2	2	no	—
833	C₄×D₄	—	2	2	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
840	C₄×D₄	C₂³×C₄₁	1	2	yes	—
841	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
842	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
843	C₄×D₄	C₂³×C₄₁	1	2	yes	—
844	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
845	C₄×D₄	C₂³×C₄₁	1	2	yes	—
846	#117	—	2	1	no	—
847	#117	—	2	2	no	—
848	#117	—	2	1	no	—
849	#117	—	2	2	no	—
850	#117	—	2	1	no	—
851	#117	C₂³×C₄₁	1	1	yes	characteristic
852	#117	C₂³×C₄₁	1	2	yes	—
853	C₂×C₄⋊C₄	—	2	2	no	—
854	C₂×C₄⋊C₄	—	2	1	no	—
855	C₂×C₄⋊C₄	—	2	2	no	—
856	C₂×C₄⋊C₄	—	2	1	no	—
857	C₂×C₄⋊C₄	—	2	1	no	—
858	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
859	C₂×C₂²⋊C₄	—	2	2	no	—
860	C₂×C₄²	—	2	1	no	—
861	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
862	#107	C₂³×C₄₁	1	1	yes	characteristic
863	#107	C₂³×C₄₁	1	1	yes	characteristic
864	#106	C₂³×C₄₁	1	1	yes	characteristic
865	#106	C₂³×C₄₁	1	1	yes	characteristic
866	#106	C₂³×C₄₁	1	2	yes	—
867	#106	C₂³×C₄₁	1	2	yes	—
868	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
869	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
870	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
871	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
872	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
873	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
874	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
875	#103	C₂³×C₄₁	1	2	yes	—
876	#103	C₂³×C₄₁	1	2	yes	—
877	#103	C₂³×C₄₁	1	2	yes	—
878	#103	C₂³×C₄₁	1	1	yes	characteristic
879	#103	C₂³×C₄₁	1	1	yes	characteristic
880	#103	C₂³×C₄₁	1	2	yes	—
881	#103	C₂³×C₄₁	1	2	yes	—
882	#103	C₂³×C₄₁	1	2	yes	—
883	#102	C₂³×C₄₁	1	1	yes	characteristic
884	#102	C₂³×C₄₁	1	2	yes	—
885	#102	C₂³×C₄₁	1	2	yes	—
886	#102	C₂³×C₄₁	1	2	yes	—
887	#102	C₂³×C₄₁	1	2	yes	—
888	#102	C₂³×C₄₁	1	1	yes	characteristic
889	#102	C₂³×C₄₁	1	2	yes	—
890	#102	C₂³×C₄₁	1	1	yes	characteristic
891	#102	C₂³×C₄₁	1	1	yes	characteristic
892	#102	C₂³×C₄₁	1	1	yes	characteristic
893	#102	C₂³×C₄₁	1	1	yes	characteristic
894	#102	C₂³×C₄₁	1	2	yes	—
895	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
896	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
897	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
898	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
899	#97	C₂³×C₄₁	1	2	yes	—
900	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
901	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
902	C₄×C₈	C₂³×C₄₁	1	2	yes	—
903	C₂⁴	—	2	2	no	—
904	#41	—	2	2	no	—
905	#41	—	2	4	no	—
906	#41	—	4	2	no	—
907	#41	—	4	1	no	—
908	#41	—	4	2	no	—
909	#41	—	4	2	no	—
910	#41	—	4	2	no	—
911	#41	—	4	2	no	—
912	#41	—	8	2	no	—
913	#41	—	8	2	no	—
914	C₂×Q₈	—	2	1	no	—
915	C₂×Q₈	—	2	1	no	—
916	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
917	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
918	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
919	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	1	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	4	2	no	—
935	C₂×D₄	—	4	2	no	—
936	C₂×D₄	—	8	2	no	—
937	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
938	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
939	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
940	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
941	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
942	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	2	2	no	—
952	C₂²×C₄	—	2	2	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
955	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
956	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
957	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
958	Q₁₆	—	4	2	no	—
959	Q₁₆	—	4	2	no	—
960	Q₁₆	—	4	2	no	—
961	SD₁₆	—	2	4	no	—
962	SD₁₆	—	4	2	no	—
963	SD₁₆	—	4	1	no	—
964	SD₁₆	—	4	1	no	—
965	SD₁₆	—	4	2	no	—
966	SD₁₆	—	4	2	no	—
967	SD₁₆	—	4	2	no	—
968	SD₁₆	—	4	2	no	—
969	D₈	—	2	2	no	—
970	D₈	—	2	4	no	—
971	D₈	—	2	2	no	—
972	M₁₆	—	4	2	no	—
973	C₂×C₈	—	4	2	no	—
974	C₂×C₈	—	4	2	no	—
975	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
976	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
977	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
978	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
979	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
980	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	1	no	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1002	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1003	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1004	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1005	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1006	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1007	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1008	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
1009	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1010	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1011	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1031	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1032	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1033	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1034	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1035	C₄²	—	2	1	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	2	1	no	—
1038	C₄²	—	2	2	no	—
1039	C₄²	—	2	2	no	—
1040	C₄²	—	2	2	no	—
1041	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1042	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1043	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1044	C₄²	C₂⁴×C₄₁	1	2	yes	—
1045	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1046	C₂³	—	2	1	no	—
1047	C₂³	—	2	1	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	8	2	no	—
1051	C₂³	—	8	2	no	—
1052	C₂³	—	8	2	no	—
1053	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
1054	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1055	Q₈	—	2	2	no	—
1056	Q₈	—	2	2	no	—
1057	Q₈	—	2	2	no	—
1058	Q₈	—	2	1	no	—
1059	Q₈	—	2	1	no	—
1060	Q₈	—	2	2	no	—
1061	Q₈	—	2	2	no	—
1062	Q₈	—	8	1	no	—
1063	Q₈	—	8	1	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	1	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	2	1	no	—
1069	D₄	—	2	1	no	—
1070	D₄	—	2	2	no	—
1071	D₄	—	2	1	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	2	no	—
1074	D₄	—	4	4	no	—
1075	D₄	—	4	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	1	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	1	no	—
1080	D₄	—	8	1	no	—
1081	D₄	—	8	2	no	—
1082	D₄	—	8	2	no	—
1083	D₄	—	8	2	no	—
1084	D₄	—	8	2	no	—
1085	D₄	—	8	1	no	—
1086	D₄	—	8	1	no	—
1087	D₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	4	1	no	—
1102	C₂×C₄	—	4	2	no	—
1103	C₂×C₄	—	4	4	no	—
1104	C₂×C₄	—	4	2	no	—
1105	C₂×C₄	—	4	2	no	—
1106	C₂×C₄	—	4	2	no	—
1107	C₂×C₄	—	8	2	no	—
1108	C₂×C₄	—	8	2	no	—
1109	C₂×C₄	—	8	2	no	—
1110	C₂×C₄	—	8	1	no	—
1111	C₂×C₄	—	8	2	no	—
1112	C₂×C₄	—	8	2	no	—
1113	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1114	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1115	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1116	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1117	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1118	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1119	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1120	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1121	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
1122	C₈	—	2	1	no	—
1123	C₈	—	2	2	no	—
1124	C₈	—	2	2	no	—
1125	C₈	—	2	1	no	—
1126	C₈	—	2	1	no	—
1127	C₈	—	2	1	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	2	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	2	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	2	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	4	2	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	16	4	no	—
1147	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
1148	C₄	—	2	1	no	—
1149	C₄	—	2	2	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	2	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	2	no	—
1155	C₄	—	4	1	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	2	no	—
1160	C₄	—	4	2	no	—
1161	C₄	—	4	1	no	—
1162	C₄	—	4	2	no	—
1163	C₄	C₄₁×#577	1	2	yes	—
1164	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1165	C₄	C₄₁×#585	1	1	yes	characteristic
1166	C₂	—	4	2	no	—
1167	C₂	—	4	1	no	—
1168	C₂	—	4	2	no	—
1169	C₂	—	8	1	no	—
1170	C₂	—	8	2	no	—
1171	C₂	—	8	1	no	—
1172	C₂	C₄₁×#3488	1	1	yes	characteristic
1173	C₂	C₂×C₄₁×#577	1	1	yes	characteristic
1174	C₂	C₄₁×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3546	C₂	semidirect
2. C₄₁×#3515	C₂	semidirect
3. C₄₁×#3398	C₂	semidirect
4. C₄₁×#3392	C₂	semidirect
5. C₄₁×#3366	C₂	semidirect
6. C₄₁×#3360	C₂	semidirect
7. C₄₁×#3331	C₂	semidirect
8. C₄₁×#3317	C₂	semidirect
9. C₄₁×#3296	C₂	semidirect
10. C₄₁×#3295	C₂	semidirect
11. C₄₁×#3284	C₂	semidirect
12. C₄₁×#3283	C₂	semidirect
13. C₄₁×#3272	C₂	semidirect
14. C₄₁×#3267	C₂	semidirect
15. C₄₁×#3258	C₂	semidirect
16. C₄₁×#3246	C₂	semidirect
17. C₄₁×#3222	C₂	semidirect
18. C₄₁×#3210	C₂	semidirect
19. C₄₁×#3125	C₂	semidirect
20. C₄₁×#3106	C₂	semidirect
21. C₄₁×#3045	C₂	semidirect
22. C₄₁×#3035	C₂	semidirect
23. C₄₁×#2994	C₂	semidirect
25. C₂×#135×C₄₁	C₂²	semidirect
26. C₂×#135×C₄₁	C₂²	semidirect
28. C₄₁×#557	C₂²	semidirect
31. C₄₁×#554	C₂²	semidirect
36. C₄₁×#552	C₂²	semidirect
41. C₄₁×#547	C₂²	semidirect
46. C₄₁×#541	C₂²	semidirect
52. C₄₁×#533	C₂²	semidirect
58. C₄₁×#520	C₂²	semidirect
59. C₄×#41×C₄₁	C₂²	semidirect
61. C₄₁×#494	C₂²	semidirect
63. C₄₁×#492	C₂²	semidirect
64. C₄₁×#490	C₂²	semidirect
66. C₄₁×#487	C₂²	semidirect
68. C₄₁×#483	C₂²	semidirect
70. C₄₁×#482	C₂²	semidirect
72. C₄₁×#479	C₂²	semidirect
73. C₄₁×#478	C₂²	semidirect
74. C₄₁×#477	C₂²	semidirect
76. C₄₁×#476	C₂²	semidirect
77. C₄₁×#476	C₂²	semidirect
78. C₄₁×#475	C₂²	semidirect
79. C₄₁×#470	C₂²	semidirect
81. C₄₁×#467	C₂²	semidirect
84. C₄₁×#465	C₂²	semidirect
86. C₄₁×#464	C₂²	semidirect
87. C₄₁×#464	C₂²	semidirect
88. C₄₁×#464	C₂²	semidirect
90. C₄₁×#463	C₂²	semidirect
91. C₄₁×#462	C₂²	semidirect
92. C₄₁×#462	C₂²	semidirect
94. C₄₁×#461	C₂²	semidirect
95. C₄₁×#461	C₂²	semidirect
96. C₄₁×#461	C₂²	semidirect
100. C₄₁×#460	C₂²	semidirect
103. C₄₁×#459	C₂²	semidirect
104. C₄₁×#452	C₂²	semidirect
105. C₄₁×#452	C₂²	semidirect
106. C₄₁×#452	C₂²	semidirect
107. C₄₁×#452	C₂²	semidirect
108. C₄₁×#452	C₂²	semidirect
113. C₄₁×#449	C₂²	semidirect
114. C₄₁×#446	C₂²	semidirect
115. C₈×Q₈×C₄₁	C₂²	semidirect
116. C₄₁×#442	C₂²	semidirect
117. C₄₁×#441	C₂²	semidirect
119. C₄×SD₁₆×C₄₁	C₂²	semidirect
120. C₄×SD₁₆×C₄₁	C₂²	semidirect
121. C₄×SD₁₆×C₄₁	C₂²	semidirect
123. C₄×D₈×C₄₁	C₂²	semidirect
125. C₄₁×#435	C₂²	semidirect
127. C₈×D₄×C₄₁	C₂²	semidirect
128. C₄₁×#433	C₂²	semidirect
129. C₄₁×#431	C₂²	semidirect
130. C₄₁×#424	C₂²	semidirect
131. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
132. C₄₁×#417	C₂²	semidirect
133. C₄₁×#416	C₂²	semidirect
540. #62070	C₄₁	direct (N × H)
579. #3546	C₂×C₄₁	semidirect
580. #3515	C₂×C₄₁	semidirect
581. #3398	C₂×C₄₁	semidirect
582. #3392	C₂×C₄₁	semidirect
583. #3366	C₂×C₄₁	semidirect
584. #3360	C₂×C₄₁	semidirect
585. #3331	C₂×C₄₁	semidirect
586. #3317	C₂×C₄₁	semidirect
587. #3296	C₂×C₄₁	semidirect
588. #3295	C₂×C₄₁	semidirect
589. #3284	C₂×C₄₁	semidirect
590. #3283	C₂×C₄₁	semidirect
591. #3272	C₂×C₄₁	semidirect
592. #3267	C₂×C₄₁	semidirect
593. #3258	C₂×C₄₁	semidirect
594. #3246	C₂×C₄₁	semidirect
595. #3222	C₂×C₄₁	semidirect
596. #3210	C₂×C₄₁	semidirect
597. #3125	C₂×C₄₁	semidirect
598. #3106	C₂×C₄₁	semidirect
599. #3045	C₂×C₄₁	semidirect
600. #3035	C₂×C₄₁	semidirect
601. #2994	C₂×C₄₁	semidirect
612. C₂×#135	C₂²×C₄₁	semidirect
613. C₂×#135	C₂²×C₄₁	semidirect
615. #557	C₂²×C₄₁	semidirect
618. #554	C₂²×C₄₁	semidirect
623. #552	C₂²×C₄₁	semidirect
628. #547	C₂²×C₄₁	semidirect
633. #541	C₂²×C₄₁	semidirect
639. #533	C₂²×C₄₁	semidirect
645. #520	C₂²×C₄₁	semidirect
646. C₄×#41	C₂²×C₄₁	semidirect
648. #494	C₂²×C₄₁	semidirect
650. #492	C₂²×C₄₁	semidirect
651. #490	C₂²×C₄₁	semidirect
653. #487	C₂²×C₄₁	semidirect
655. #483	C₂²×C₄₁	semidirect
657. #482	C₂²×C₄₁	semidirect
659. #479	C₂²×C₄₁	semidirect
660. #478	C₂²×C₄₁	semidirect
661. #477	C₂²×C₄₁	semidirect
663. #476	C₂²×C₄₁	semidirect
664. #476	C₂²×C₄₁	semidirect
665. #475	C₂²×C₄₁	semidirect
666. #470	C₂²×C₄₁	semidirect
668. #467	C₂²×C₄₁	semidirect
671. #465	C₂²×C₄₁	semidirect
673. #464	C₂²×C₄₁	semidirect
674. #464	C₂²×C₄₁	semidirect
675. #464	C₂²×C₄₁	semidirect
677. #463	C₂²×C₄₁	semidirect
678. #462	C₂²×C₄₁	semidirect
679. #462	C₂²×C₄₁	semidirect
681. #461	C₂²×C₄₁	semidirect
682. #461	C₂²×C₄₁	semidirect
683. #461	C₂²×C₄₁	semidirect
687. #460	C₂²×C₄₁	semidirect
690. #459	C₂²×C₄₁	semidirect
691. #452	C₂²×C₄₁	semidirect
692. #452	C₂²×C₄₁	semidirect
693. #452	C₂²×C₄₁	semidirect
694. #452	C₂²×C₄₁	semidirect
695. #452	C₂²×C₄₁	semidirect
700. #449	C₂²×C₄₁	semidirect
701. #446	C₂²×C₄₁	semidirect
702. C₈×Q₈	C₂²×C₄₁	semidirect
703. #442	C₂²×C₄₁	semidirect
704. #441	C₂²×C₄₁	semidirect
706. C₄×SD₁₆	C₂²×C₄₁	semidirect
707. C₄×SD₁₆	C₂²×C₄₁	semidirect
708. C₄×SD₁₆	C₂²×C₄₁	semidirect
710. C₄×D₈	C₂²×C₄₁	semidirect
712. #435	C₂²×C₄₁	semidirect
714. C₈×D₄	C₂²×C₄₁	semidirect
715. #433	C₂²×C₄₁	semidirect
716. #431	C₂²×C₄₁	semidirect
717. #424	C₂²×C₄₁	semidirect
718. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
719. #417	C₂²×C₄₁	semidirect
720. #416	C₂²×C₄₁	semidirect
722. C₄₁	#62070	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×#3546	2
C₄₁×#3515	2
C₄₁×#3398	2
C₄₁×#3392	2
C₄₁×#3366	2
C₄₁×#3360	2
C₄₁×#3331	2
C₄₁×#3317	2
C₄₁×#3296	2
C₄₁×#3295	2
C₄₁×#3284	2
C₄₁×#3283	2
C₄₁×#3272	2
C₄₁×#3267	2
C₄₁×#3258	2
C₄₁×#3246	2
C₄₁×#3222	2
C₄₁×#3210	2
C₄₁×#3125	2
C₄₁×#3106	2
C₄₁×#3045	2
C₄₁×#3035	2
C₄₁×#2994	2
#62070	41

Subgroups — C41×#62070 #23838271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#62070 #23838271