Subgroups — C₄₁×#60766 #23836967

Order 10496.

2140 conjugacy classes of subgroups.

The subgroup lattice has 1328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3489	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3202	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3201	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3200	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3198	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3197	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3196	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3191	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3190	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3099	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3093	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄₁×#485	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#3063	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#3061	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄₁×#3060	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#3013	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄₁×#3013	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄₁×#3007	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄₁×#3002	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₁×#2880	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₄₁	C₂²	1	1	yes	characteristic, complemented
25	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
26	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×#137×C₄₁	C₂²	1	1	yes	characteristic, complemented
28	C₂×#137×C₄₁	C₂²	1	1	yes	characteristic, complemented
29	C₂×#135×C₄₁	C₂²	1	1	yes	characteristic, complemented
30	C₂×#135×C₄₁	C₂²	1	1	yes	characteristic, complemented
31	C₂×#131×C₄₁	C₂²	1	1	yes	characteristic, complemented
32	C₂×#131×C₄₁	C₂²	1	1	yes	characteristic, complemented
33	D₄×Q₈×C₄₁	—	2	1	no	—
34	C₄₁×#548	—	2	1	no	—
35	C₄₁×#547	—	2	2	no	—
36	C₄₁×#547	—	2	1	no	—
37	C₄₁×#546	—	2	2	no	—
38	C₄₁×#546	—	2	1	no	—
39	C₄₁×#537	C₂²	1	1	yes	characteristic
40	C₄₁×#537	C₂²	1	1	yes	characteristic
41	C₄₁×#537	C₂²	1	1	yes	characteristic
42	C₄₁×#537	C₂²	1	1	yes	characteristic
43	C₄₁×#537	C₂²	1	2	yes	—
44	C₄₁×#537	C₂²	1	1	yes	characteristic, complemented
45	C₄₁×#536	—	2	1	no	—
46	C₄₁×#536	C₂²	1	2	yes	—
47	C₄₁×#536	C₂²	1	2	yes	—
48	C₄₁×#536	C₂²	1	1	yes	characteristic, complemented
49	C₄₁×#535	—	2	1	no	—
50	C₄₁×#535	C₂²	1	2	yes	—
51	C₄₁×#534	—	2	2	no	—
52	C₄₁×#532	—	2	2	no	—
53	C₄₁×#525	—	2	1	no	—
54	C₄₁×#525	—	2	1	no	—
55	C₄₁×#525	C₂²	1	1	yes	characteristic
56	C₄₁×#525	C₂²	1	2	yes	—
57	C₄₁×#525	C₂²	1	2	yes	—
58	C₄₁×#525	C₂²	1	2	yes	complemented
59	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
60	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	complemented
61	C₄₁×#520	C₂²	1	1	yes	characteristic, complemented
62	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
63	C₄₁×#485	C₂²	1	2	yes	complemented
64	C₄₁×#485	C₂²	1	2	yes	complemented
65	C₄₁×#485	C₂²	1	2	yes	complemented
66	C₄₁×#485	C₂²	1	2	yes	complemented
67	C₄₁×#485	C₂²	1	2	yes	complemented
68	C₄₁×#485	C₂²	1	2	yes	complemented
69	C₄₁×#485	C₂²	1	2	yes	complemented
70	C₄₁×#485	C₂²	1	2	yes	complemented
71	C₄₁×#484	C₂²	1	2	yes	complemented
72	C₄₁×#483	C₂²	1	2	yes	complemented
73	C₄₁×#482	C₂²	1	2	yes	complemented
74	C₄₁×#482	C₂²	1	2	yes	complemented
75	C₄₁×#482	C₂²	1	2	yes	complemented
76	C₄₁×#482	C₂²	1	2	yes	complemented
77	C₄₁×#481	C₂²	1	2	yes	complemented
78	C₄₁×#480	C₂²	1	2	yes	complemented
79	C₄₁×#470	C₂²	1	2	yes	complemented
80	C₄₁×#470	C₂²	1	2	yes	complemented
81	C₄₁×#470	C₂²	1	2	yes	complemented
82	C₄₁×#469	C₂²	1	2	yes	complemented
83	C₄₁×#468	C₂²	1	2	yes	complemented
84	C₄₁×#468	C₂²	1	2	yes	complemented
85	C₄₁×#468	C₂²	1	2	yes	complemented
86	C₄₁×#468	C₂²	1	2	yes	complemented
87	C₄₁×#467	C₂²	1	2	yes	complemented
88	C₄₁×#467	C₂²	1	2	yes	complemented
89	C₄₁×#467	C₂²	1	2	yes	complemented
90	C₄₁×#466	C₂²	1	2	yes	complemented
91	C₄₁×#465	C₂²	1	2	yes	complemented
92	C₄₁×#465	C₂²	1	2	yes	complemented
93	C₄₁×#465	C₂²	1	2	yes	complemented
94	C₄₁×#465	C₂²	1	2	yes	complemented
95	C₄₁×#452	C₂²	1	1	yes	characteristic
96	C₄₁×#452	C₂²	1	2	yes	—
97	C₄₁×#452	C₂²	1	2	yes	—
98	C₄₁×#452	C₂²	1	1	yes	characteristic
99	C₄₁×#452	C₂²	1	2	yes	complemented
100	C₄₁×#452	C₂²	1	2	yes	complemented
101	C₄₁×#451	C₂²	1	2	yes	complemented
102	C₄₁×#451	C₂²	1	2	yes	complemented
103	C₄₁×#451	C₂²	1	2	yes	complemented
104	C₄₁×#451	C₂²	1	1	yes	characteristic, complemented
105	C₄₁×#450	C₂²	1	2	yes	complemented
106	C₄₁×#450	C₂²	1	1	yes	characteristic, complemented
107	C₄₁×#449	C₂²	1	1	yes	characteristic
108	C₄₁×#449	C₂²	1	1	yes	characteristic
109	C₄₁×#449	C₂²	1	2	yes	complemented
110	C₄₁×#449	C₂²	1	2	yes	complemented
111	C₄₁×#448	C₂²	1	2	yes	complemented
112	C₄₁×#448	C₂²	1	2	yes	complemented
113	C₄₁×#448	C₂²	1	1	yes	characteristic, complemented
114	C₄₁×#447	C₂²	1	1	yes	characteristic, complemented
115	C₄₁×#428	C₂²	1	1	yes	characteristic, complemented
116	C₄₁×#428	C₂²	1	1	yes	characteristic, complemented
117	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic, complemented
118	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic, complemented
119	C₄₁×#417	C₂²	1	1	yes	characteristic, complemented
120	C₄₁×#417	C₂²	1	1	yes	characteristic, complemented
121	C₄₁×#417	C₂²	1	1	yes	characteristic, complemented
122	C₄₁×#417	C₂²	1	1	yes	characteristic, complemented
123	C₄₁×#416	C₂²	1	1	yes	characteristic, complemented
124	C₄₁×#416	C₂²	1	1	yes	characteristic, complemented
125	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic, complemented
126	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic, complemented
127	C₄₁×#408	C₂²	1	2	yes	—
128	C₄₁×#408	C₂²	1	2	yes	—
129	C₄₁×#408	C₂²	1	1	yes	characteristic, complemented
130	C₄₁×#408	C₂²	1	1	yes	characteristic, complemented
131	C₄₁×#407	C₂²	1	1	yes	characteristic
132	C₄₁×#407	C₂²	1	2	yes	complemented
133	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
134	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	complemented
135	2₋¹⁺⁴×C₄₁	—	4	2	no	—
136	2₋¹⁺⁴×C₄₁	—	4	2	no	—
137	C₂×#41×C₄₁	—	2	1	no	—
138	C₂×#41×C₄₁	—	2	2	no	—
139	C₂×#41×C₄₁	—	2	1	no	—
140	C₂×#41×C₄₁	—	2	1	no	—
141	C₂×#41×C₄₁	—	4	2	no	—
142	C₂×#41×C₄₁	—	4	2	no	—
143	C₂×#41×C₄₁	—	4	2	no	—
144	C₂×#41×C₄₁	—	4	2	no	—
145	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
146	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
147	C₂×#41×C₄₁	D₄	1	2	yes	—
148	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
149	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
150	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
151	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
152	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
153	C₂×#41×C₄₁	C₂³	1	2	yes	—
154	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
155	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
156	C₂×#41×C₄₁	C₂³	1	2	yes	—
157	C₂²×Q₈×C₄₁	—	2	1	no	—
158	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
159	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
160	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
161	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
162	C₂²×D₄×C₄₁	—	2	1	no	—
163	C₂²×D₄×C₄₁	D₄	1	2	yes	—
164	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
165	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
166	C₂³×C₄×C₄₁	—	2	1	no	—
167	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
168	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
169	#137×C₄₁	—	4	2	no	—
170	#137×C₄₁	—	4	2	no	—
171	#135×C₄₁	—	4	2	no	—
172	#135×C₄₁	—	4	2	no	—
173	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
174	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
175	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
176	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
177	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
178	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
179	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
180	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
181	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
182	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
183	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
184	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
185	#131×C₄₁	—	4	2	no	—
186	#131×C₄₁	—	4	2	no	—
187	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
188	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
189	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
190	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
191	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
192	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
193	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
194	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
195	C₄⋊Q₈×C₄₁	—	2	2	no	—
196	C₄⋊Q₈×C₄₁	—	2	2	no	—
197	C₄⋊Q₈×C₄₁	—	2	1	no	—
198	#127×C₄₁	—	2	2	no	—
199	#124×C₄₁	—	2	2	no	—
200	#124×C₄₁	—	2	2	no	—
201	#124×C₄₁	—	2	2	no	—
202	#124×C₄₁	—	2	1	no	—
203	#123×C₄₁	—	2	2	no	—
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	1	no	—
211	#123×C₄₁	—	2	2	no	—
212	C₂²⋊Q₈×C₄₁	—	2	1	no	—
213	C₂²⋊Q₈×C₄₁	—	2	1	no	—
214	C₂²⋊Q₈×C₄₁	—	2	1	no	—
215	C₂²⋊Q₈×C₄₁	—	2	1	no	—
216	C₂²⋊Q₈×C₄₁	—	2	2	no	—
217	C₂²⋊Q₈×C₄₁	—	2	1	no	—
218	C₂²⋊Q₈×C₄₁	—	2	1	no	—
219	C₂²⋊Q₈×C₄₁	—	2	1	no	—
220	C₂²⋊Q₈×C₄₁	—	2	2	no	—
221	C₂²⋊Q₈×C₄₁	—	2	2	no	—
222	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
223	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
224	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
225	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
226	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
227	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
228	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
229	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
230	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
231	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
232	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
233	#121×C₄₁	—	2	1	no	—
234	#121×C₄₁	—	2	1	no	—
235	#121×C₄₁	—	2	1	no	—
236	#121×C₄₁	—	2	1	no	—
237	#121×C₄₁	—	2	2	no	—
238	#121×C₄₁	—	2	2	no	—
239	#121×C₄₁	—	2	2	no	—
240	#121×C₄₁	—	2	2	no	—
241	#121×C₄₁	—	2	2	no	—
242	#121×C₄₁	—	2	2	no	—
243	#121×C₄₁	—	2	2	no	—
244	#121×C₄₁	—	2	2	no	—
245	#121×C₄₁	—	2	1	no	—
246	#121×C₄₁	C₂³	1	1	yes	characteristic
247	#121×C₄₁	C₂³	1	2	yes	—
248	#121×C₄₁	C₂³	1	2	yes	—
249	#121×C₄₁	C₂³	1	2	yes	—
250	#121×C₄₁	C₂³	1	2	yes	—
251	#121×C₄₁	C₂³	1	1	yes	characteristic
252	#121×C₄₁	C₂³	1	2	yes	—
253	#120×C₄₁	—	2	2	no	—
254	#120×C₄₁	—	2	2	no	—
255	#120×C₄₁	—	2	1	no	—
256	#120×C₄₁	—	2	2	no	—
257	#120×C₄₁	—	2	2	no	—
258	#120×C₄₁	—	2	2	no	—
259	C₄×Q₈×C₄₁	—	2	1	no	—
260	C₄×D₄×C₄₁	—	2	2	no	—
261	C₄×D₄×C₄₁	—	2	1	no	—
262	C₄×D₄×C₄₁	—	2	2	no	—
263	C₄×D₄×C₄₁	—	2	2	no	—
264	C₄×D₄×C₄₁	—	2	2	no	—
265	C₄×D₄×C₄₁	—	2	2	no	—
266	C₄×D₄×C₄₁	—	2	1	no	—
267	C₄×D₄×C₄₁	—	2	1	no	—
268	C₄×D₄×C₄₁	—	2	2	no	—
269	C₄×D₄×C₄₁	—	2	2	no	—
270	#117×C₄₁	—	2	1	no	—
271	#117×C₄₁	—	2	1	no	—
272	#117×C₄₁	C₂³	1	2	yes	—
273	#117×C₄₁	C₂³	1	2	yes	—
274	#117×C₄₁	C₂³	1	1	yes	characteristic
275	#117×C₄₁	C₂³	1	2	yes	—
276	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
277	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
278	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
279	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
280	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
281	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
282	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
283	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
284	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
285	C₂×C₄²×C₄₁	—	2	1	no	—
286	#107×C₄₁	C₂³	1	2	yes	—
287	#107×C₄₁	C₂³	1	2	yes	—
288	#107×C₄₁	C₂³	1	2	yes	—
289	#107×C₄₁	C₂³	1	2	yes	—
290	#106×C₄₁	C₂³	1	2	yes	—
291	#106×C₄₁	C₂³	1	2	yes	—
292	#106×C₄₁	C₂³	1	2	yes	—
293	#106×C₄₁	C₂³	1	2	yes	—
294	#103×C₄₁	C₂³	1	2	yes	—
295	#103×C₄₁	C₂³	1	2	yes	—
296	#103×C₄₁	C₂³	1	2	yes	—
297	#103×C₄₁	C₂³	1	2	yes	—
298	#103×C₄₁	C₂³	1	1	yes	characteristic
299	#103×C₄₁	C₂³	1	1	yes	characteristic
300	#103×C₄₁	C₂³	1	1	yes	characteristic
301	#103×C₄₁	C₂³	1	1	yes	characteristic
302	#103×C₄₁	C₂³	1	2	yes	—
303	#103×C₄₁	C₂³	1	2	yes	—
304	#103×C₄₁	C₂³	1	2	yes	—
305	#103×C₄₁	C₂³	1	2	yes	—
306	#102×C₄₁	C₂³	1	1	yes	characteristic
307	#102×C₄₁	C₂³	1	1	yes	characteristic
308	#102×C₄₁	C₂³	1	1	yes	characteristic
309	#102×C₄₁	C₂³	1	1	yes	characteristic
310	#102×C₄₁	C₂³	1	2	yes	—
311	#102×C₄₁	C₂³	1	2	yes	—
312	#102×C₄₁	C₂³	1	2	yes	—
313	#102×C₄₁	C₂³	1	2	yes	—
314	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
315	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
316	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
317	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
318	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
319	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
320	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
321	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
322	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
323	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
324	C₂⁴×C₄₁	—	2	1	no	—
325	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
326	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
327	#41×C₄₁	—	2	2	no	—
328	#41×C₄₁	—	2	2	no	—
329	#41×C₄₁	—	2	2	no	—
330	#41×C₄₁	—	2	2	no	—
331	#41×C₄₁	—	2	2	no	—
332	#41×C₄₁	—	2	2	no	—
333	#41×C₄₁	—	2	2	no	—
334	#41×C₄₁	—	2	2	no	—
335	#41×C₄₁	—	2	2	no	—
336	#41×C₄₁	—	2	2	no	—
337	#41×C₄₁	—	4	2	no	—
338	#41×C₄₁	—	4	2	no	—
339	#41×C₄₁	—	4	4	no	—
340	#41×C₄₁	—	4	2	no	—
341	#41×C₄₁	—	4	2	no	—
342	#41×C₄₁	—	4	1	no	—
343	#41×C₄₁	—	4	1	no	—
344	#41×C₄₁	—	4	1	no	—
345	#41×C₄₁	—	4	1	no	—
346	#41×C₄₁	—	4	2	no	—
347	#41×C₄₁	—	4	2	no	—
348	#41×C₄₁	—	4	4	no	—
349	#41×C₄₁	—	4	4	no	—
350	#41×C₄₁	—	4	8	no	—
351	#41×C₄₁	—	4	4	no	—
352	C₂×Q₈×C₄₁	—	2	2	no	—
353	C₂×Q₈×C₄₁	—	2	1	no	—
354	C₂×Q₈×C₄₁	—	2	1	no	—
355	C₂×Q₈×C₄₁	—	2	2	no	—
356	C₂×Q₈×C₄₁	—	2	2	no	—
357	C₂×Q₈×C₄₁	—	4	2	no	—
358	C₂×Q₈×C₄₁	—	4	1	no	—
359	C₂×Q₈×C₄₁	—	4	1	no	—
360	C₂×Q₈×C₄₁	—	4	2	no	—
361	C₂×Q₈×C₄₁	—	4	2	no	—
362	C₂×Q₈×C₄₁	—	4	4	no	—
363	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
364	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
365	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
366	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
367	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
368	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
369	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
370	C₂×D₄×C₄₁	—	2	1	no	—
371	C₂×D₄×C₄₁	—	2	1	no	—
372	C₂×D₄×C₄₁	—	2	1	no	—
373	C₂×D₄×C₄₁	—	2	2	no	—
374	C₂×D₄×C₄₁	—	2	1	no	—
375	C₂×D₄×C₄₁	—	2	1	no	—
376	C₂×D₄×C₄₁	—	2	1	no	—
377	C₂×D₄×C₄₁	—	2	2	no	—
378	C₂×D₄×C₄₁	—	2	2	no	—
379	C₂×D₄×C₄₁	—	2	2	no	—
380	C₂×D₄×C₄₁	—	2	2	no	—
381	C₂×D₄×C₄₁	—	2	1	no	—
382	C₂×D₄×C₄₁	—	2	2	no	—
383	C₂×D₄×C₄₁	—	2	1	no	—
384	C₂×D₄×C₄₁	—	4	2	no	—
385	C₂×D₄×C₄₁	—	4	1	no	—
386	C₂×D₄×C₄₁	—	4	1	no	—
387	C₂×D₄×C₄₁	—	4	4	no	—
388	C₂×D₄×C₄₁	—	4	4	no	—
389	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
390	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
391	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
392	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
393	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
394	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
395	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
396	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
397	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
398	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄×C₄₁	—	2	2	no	—
400	C₂²×C₄×C₄₁	—	2	2	no	—
401	C₂²×C₄×C₄₁	—	2	2	no	—
402	C₂²×C₄×C₄₁	—	2	1	no	—
403	C₂²×C₄×C₄₁	—	2	1	no	—
404	C₂²×C₄×C₄₁	—	2	1	no	—
405	C₂²×C₄×C₄₁	—	2	1	no	—
406	C₂²×C₄×C₄₁	—	2	2	no	—
407	C₂²×C₄×C₄₁	—	2	1	no	—
408	C₂²×C₄×C₄₁	—	2	1	no	—
409	C₂²×C₄×C₄₁	—	2	1	no	—
410	C₂²×C₄×C₄₁	—	2	2	no	—
411	C₂²×C₄×C₄₁	—	2	1	no	—
412	C₂²×C₄×C₄₁	—	2	1	no	—
413	C₂²×C₄×C₄₁	—	2	1	no	—
414	C₂²×C₄×C₄₁	—	4	2	no	—
415	C₂²×C₄×C₄₁	—	4	2	no	—
416	C₂²×C₄×C₄₁	—	4	4	no	—
417	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
418	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
419	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
420	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
421	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
422	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
423	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
424	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
425	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
426	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
427	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
428	Q₁₆×C₄₁	—	4	1	no	—
429	Q₁₆×C₄₁	—	4	1	no	—
430	Q₁₆×C₄₁	—	4	2	no	—
431	Q₁₆×C₄₁	—	4	2	no	—
432	SD₁₆×C₄₁	—	4	1	no	—
433	SD₁₆×C₄₁	—	4	1	no	—
434	SD₁₆×C₄₁	—	4	1	no	—
435	SD₁₆×C₄₁	—	4	1	no	—
436	SD₁₆×C₄₁	—	4	2	no	—
437	SD₁₆×C₄₁	—	4	2	no	—
438	D₈×C₄₁	—	4	1	no	—
439	D₈×C₄₁	—	4	1	no	—
440	M₁₆×C₄₁	—	2	2	no	—
441	M₁₆×C₄₁	—	2	2	no	—
442	M₁₆×C₄₁	—	4	2	no	—
443	M₁₆×C₄₁	—	4	2	no	—
444	C₂×C₈×C₄₁	—	2	2	no	—
445	C₂×C₈×C₄₁	—	2	2	no	—
446	C₂×C₈×C₄₁	—	4	2	no	—
447	C₂×C₈×C₄₁	—	4	2	no	—
448	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
449	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
450	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
451	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
452	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
453	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄×C₄₁	—	2	2	no	—
455	C₄⋊C₄×C₄₁	—	2	1	no	—
456	C₄⋊C₄×C₄₁	—	2	2	no	—
457	C₄⋊C₄×C₄₁	—	2	2	no	—
458	C₄⋊C₄×C₄₁	—	2	2	no	—
459	C₄⋊C₄×C₄₁	—	2	1	no	—
460	C₄⋊C₄×C₄₁	—	2	1	no	—
461	C₄⋊C₄×C₄₁	—	2	2	no	—
462	C₄⋊C₄×C₄₁	—	2	1	no	—
463	C₄⋊C₄×C₄₁	—	2	2	no	—
464	C₄⋊C₄×C₄₁	—	2	2	no	—
465	C₄⋊C₄×C₄₁	—	2	2	no	—
466	C₄⋊C₄×C₄₁	—	2	2	no	—
467	C₄⋊C₄×C₄₁	—	2	1	no	—
468	C₄⋊C₄×C₄₁	—	2	2	no	—
469	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
470	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
471	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
472	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
473	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
474	C₂²⋊C₄×C₄₁	—	2	2	no	—
475	C₂²⋊C₄×C₄₁	—	2	1	no	—
476	C₂²⋊C₄×C₄₁	—	2	2	no	—
477	C₂²⋊C₄×C₄₁	—	2	2	no	—
478	C₂²⋊C₄×C₄₁	—	2	2	no	—
479	C₂²⋊C₄×C₄₁	—	2	2	no	—
480	C₂²⋊C₄×C₄₁	—	2	2	no	—
481	C₂²⋊C₄×C₄₁	—	2	2	no	—
482	C₂²⋊C₄×C₄₁	—	2	1	no	—
483	C₂²⋊C₄×C₄₁	—	2	2	no	—
484	C₂²⋊C₄×C₄₁	—	2	2	no	—
485	C₂²⋊C₄×C₄₁	—	2	2	no	—
486	C₂²⋊C₄×C₄₁	—	2	2	no	—
487	C₂²⋊C₄×C₄₁	—	2	1	no	—
488	C₂²⋊C₄×C₄₁	—	2	2	no	—
489	C₂²⋊C₄×C₄₁	—	2	1	no	—
490	C₂²⋊C₄×C₄₁	—	2	2	no	—
491	C₂²⋊C₄×C₄₁	—	2	2	no	—
492	C₂²⋊C₄×C₄₁	—	2	2	no	—
493	C₂²⋊C₄×C₄₁	—	2	2	no	—
494	C₂²⋊C₄×C₄₁	—	2	1	no	—
495	C₂²⋊C₄×C₄₁	—	2	2	no	—
496	C₄²×C₄₁	—	2	2	no	—
497	C₄²×C₄₁	—	2	2	no	—
498	C₄²×C₄₁	—	2	2	no	—
499	C₄²×C₄₁	—	2	1	no	—
500	C₂³×C₄₁	—	2	2	no	—
501	C₂³×C₄₁	—	2	1	no	—
502	C₂³×C₄₁	—	2	1	no	—
503	C₂³×C₄₁	—	2	1	no	—
504	C₂³×C₄₁	—	4	2	no	—
505	C₂³×C₄₁	—	4	1	no	—
506	C₂³×C₄₁	—	4	1	no	—
507	C₂³×C₄₁	—	4	2	no	—
508	C₂³×C₄₁	—	4	2	no	—
509	C₂³×C₄₁	—	4	2	no	—
510	C₂³×C₄₁	—	8	1	no	—
511	C₂³×C₄₁	—	8	1	no	—
512	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
513	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
514	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
515	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
516	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
517	Q₈×C₄₁	—	2	2	no	—
518	Q₈×C₄₁	—	2	2	no	—
519	Q₈×C₄₁	—	2	2	no	—
520	Q₈×C₄₁	—	2	2	no	—
521	Q₈×C₄₁	—	2	1	no	—
522	Q₈×C₄₁	—	2	1	no	—
523	Q₈×C₄₁	—	2	1	no	—
524	Q₈×C₄₁	—	2	1	no	—
525	Q₈×C₄₁	—	2	1	no	—
526	Q₈×C₄₁	—	2	1	no	—
527	Q₈×C₄₁	—	4	2	no	—
528	Q₈×C₄₁	—	4	4	no	—
529	Q₈×C₄₁	—	4	2	no	—
530	Q₈×C₄₁	—	4	2	no	—
531	D₄×C₄₁	—	2	4	no	—
532	D₄×C₄₁	—	2	4	no	—
533	D₄×C₄₁	—	2	2	no	—
534	D₄×C₄₁	—	2	2	no	—
535	D₄×C₄₁	—	2	1	no	—
536	D₄×C₄₁	—	2	1	no	—
537	D₄×C₄₁	—	2	1	no	—
538	D₄×C₄₁	—	2	1	no	—
539	D₄×C₄₁	—	2	1	no	—
540	D₄×C₄₁	—	2	1	no	—
541	D₄×C₄₁	—	4	2	no	—
542	D₄×C₄₁	—	4	2	no	—
543	D₄×C₄₁	—	4	2	no	—
544	D₄×C₄₁	—	4	2	no	—
545	D₄×C₄₁	—	4	2	no	—
546	D₄×C₄₁	—	4	2	no	—
547	D₄×C₄₁	—	4	2	no	—
548	D₄×C₄₁	—	4	4	no	—
549	D₄×C₄₁	—	4	2	no	—
550	D₄×C₄₁	—	4	2	no	—
551	D₄×C₄₁	—	4	2	no	—
552	D₄×C₄₁	—	8	2	no	—
553	D₄×C₄₁	—	8	1	no	—
554	D₄×C₄₁	—	8	2	no	—
555	D₄×C₄₁	—	8	2	no	—
556	D₄×C₄₁	—	8	2	no	—
557	D₄×C₄₁	—	8	2	no	—
558	C₂×C₄×C₄₁	—	2	2	no	—
559	C₂×C₄×C₄₁	—	2	2	no	—
560	C₂×C₄×C₄₁	—	2	2	no	—
561	C₂×C₄×C₄₁	—	2	2	no	—
562	C₂×C₄×C₄₁	—	2	2	no	—
563	C₂×C₄×C₄₁	—	2	1	no	—
564	C₂×C₄×C₄₁	—	2	1	no	—
565	C₂×C₄×C₄₁	—	2	1	no	—
566	C₂×C₄×C₄₁	—	2	1	no	—
567	C₂×C₄×C₄₁	—	2	2	no	—
568	C₂×C₄×C₄₁	—	2	2	no	—
569	C₂×C₄×C₄₁	—	2	1	no	—
570	C₂×C₄×C₄₁	—	2	2	no	—
571	C₂×C₄×C₄₁	—	2	2	no	—
572	C₂×C₄×C₄₁	—	2	2	no	—
573	C₂×C₄×C₄₁	—	2	1	no	—
574	C₂×C₄×C₄₁	—	2	1	no	—
575	C₂×C₄×C₄₁	—	2	1	no	—
576	C₂×C₄×C₄₁	—	2	2	no	—
577	C₂×C₄×C₄₁	—	2	1	no	—
578	C₂×C₄×C₄₁	—	4	2	no	—
579	C₂×C₄×C₄₁	—	4	2	no	—
580	C₂×C₄×C₄₁	—	4	2	no	—
581	C₂×C₄×C₄₁	—	4	2	no	—
582	C₂×C₄×C₄₁	—	4	2	no	—
583	C₂×C₄×C₄₁	—	4	4	no	—
584	C₂×C₄×C₄₁	—	4	2	no	—
585	C₂×C₄×C₄₁	—	4	4	no	—
586	C₂×C₄×C₄₁	—	4	2	no	—
587	C₂×C₄×C₄₁	—	4	2	no	—
588	C₂×C₄×C₄₁	—	4	2	no	—
589	C₂×C₄×C₄₁	—	4	2	no	—
590	C₂×C₄×C₄₁	—	8	1	no	—
591	C₂×C₄×C₄₁	—	8	2	no	—
592	C₂×C₄×C₄₁	—	8	1	no	—
593	C₂×C₄×C₄₁	—	8	1	no	—
594	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
595	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
596	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
597	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
598	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
599	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
600	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
601	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
602	C₈×C₄₁	—	2	1	no	—
603	C₈×C₄₁	—	2	1	no	—
604	C₈×C₄₁	—	2	1	no	—
605	C₈×C₄₁	—	2	1	no	—
606	C₈×C₄₁	—	2	2	no	—
607	C₈×C₄₁	—	2	2	no	—
608	#60766	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
609	C₂²×C₄₁	—	2	1	no	—
610	C₂²×C₄₁	—	2	1	no	—
611	C₂²×C₄₁	—	2	2	no	—
612	C₂²×C₄₁	—	2	2	no	—
613	C₂²×C₄₁	—	2	1	no	—
614	C₂²×C₄₁	—	2	1	no	—
615	C₂²×C₄₁	—	2	1	no	—
616	C₂²×C₄₁	—	2	2	no	—
617	C₂²×C₄₁	—	2	2	no	—
618	C₂²×C₄₁	—	2	1	no	—
619	C₂²×C₄₁	—	2	1	no	—
620	C₂²×C₄₁	—	2	1	no	—
621	C₂²×C₄₁	—	2	2	no	—
622	C₂²×C₄₁	—	2	2	no	—
623	C₂²×C₄₁	—	4	1	no	—
624	C₂²×C₄₁	—	4	1	no	—
625	C₂²×C₄₁	—	4	1	no	—
626	C₂²×C₄₁	—	4	1	no	—
627	C₂²×C₄₁	—	4	1	no	—
628	C₂²×C₄₁	—	4	1	no	—
629	C₂²×C₄₁	—	4	1	no	—
630	C₂²×C₄₁	—	4	1	no	—
631	C₂²×C₄₁	—	4	1	no	—
632	C₂²×C₄₁	—	8	2	no	—
633	C₂²×C₄₁	—	8	4	no	—
634	C₂²×C₄₁	—	8	4	no	—
635	C₂²×C₄₁	#534	1	2	yes	—
636	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
637	C₄×C₄₁	—	2	1	no	—
638	C₄×C₄₁	—	2	1	no	—
639	C₄×C₄₁	—	2	2	no	—
640	C₄×C₄₁	—	2	2	no	—
641	C₄×C₄₁	—	4	2	no	—
642	C₄×C₄₁	—	4	1	no	—
643	C₄×C₄₁	—	4	2	no	—
644	C₄×C₄₁	—	4	2	no	—
645	C₄×C₄₁	—	4	1	no	—
646	C₄×C₄₁	—	4	1	no	—
647	C₄×C₄₁	—	4	1	no	—
648	C₄×C₄₁	—	4	2	no	—
649	C₄×C₄₁	—	4	1	no	—
650	C₄×C₄₁	#534	1	2	yes	—
651	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
652	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
653	#3489	C₂×C₄₁	1	1	yes	characteristic, complemented
654	#3449	C₂×C₄₁	1	1	yes	characteristic, complemented
655	#3202	C₂×C₄₁	1	2	yes	complemented
656	#3201	C₂×C₄₁	1	2	yes	complemented
657	#3200	C₂×C₄₁	1	2	yes	complemented
658	#3198	C₂×C₄₁	1	2	yes	complemented
659	#3197	C₂×C₄₁	1	2	yes	complemented
660	#3196	C₂×C₄₁	1	2	yes	complemented
661	#3191	C₂×C₄₁	1	2	yes	complemented
662	#3190	C₂×C₄₁	1	2	yes	complemented
663	#3099	C₂×C₄₁	1	1	yes	characteristic, complemented
664	#3098	C₂×C₄₁	1	1	yes	characteristic, complemented
665	#3093	C₂×C₄₁	1	1	yes	characteristic, complemented
666	C₂×#485	C₂×C₄₁	1	1	yes	characteristic, complemented
667	#3063	C₂×C₄₁	1	1	yes	characteristic, complemented
668	#3063	C₂×C₄₁	1	1	yes	characteristic, complemented
669	#3061	C₂×C₄₁	1	1	yes	characteristic, complemented
670	#3060	C₂×C₄₁	1	1	yes	characteristic, complemented
671	#3013	C₂×C₄₁	1	1	yes	characteristic, complemented
672	#3013	C₂×C₄₁	1	1	yes	characteristic, complemented
673	#3007	C₂×C₄₁	1	1	yes	characteristic, complemented
674	#3002	C₂×C₄₁	1	1	yes	characteristic, complemented
675	#2880	C₂×C₄₁	1	1	yes	characteristic, complemented
676	C₂×C₄₁	—	2	2	no	—
677	C₂×C₄₁	—	4	2	no	—
678	C₂×C₄₁	—	4	2	no	—
679	C₂×C₄₁	—	4	1	no	—
680	C₂×C₄₁	—	4	1	no	—
681	C₂×C₄₁	—	8	1	no	—
682	C₂×C₄₁	—	8	1	no	—
683	C₂×C₄₁	—	8	1	no	—
684	C₂×C₄₁	C₂×#534	1	1	yes	characteristic
685	C₂×C₄₁	#3584	1	1	yes	characteristic
686	C₂×C₄₁	#3586	1	1	yes	characteristic
687	C₂×2₋¹⁺⁴	C₂²×C₄₁	1	1	yes	characteristic, complemented
688	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
689	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
690	C₂×#137	C₂²×C₄₁	1	1	yes	characteristic, complemented
691	C₂×#137	C₂²×C₄₁	1	1	yes	characteristic, complemented
692	C₂×#135	C₂²×C₄₁	1	1	yes	characteristic, complemented
693	C₂×#135	C₂²×C₄₁	1	1	yes	characteristic, complemented
694	C₂×#131	C₂²×C₄₁	1	1	yes	characteristic, complemented
695	C₂×#131	C₂²×C₄₁	1	1	yes	characteristic, complemented
696	D₄×Q₈	—	2	1	no	—
697	#548	—	2	1	no	—
698	#547	—	2	2	no	—
699	#547	—	2	1	no	—
700	#546	—	2	2	no	—
701	#546	—	2	1	no	—
702	#537	C₂²×C₄₁	1	1	yes	characteristic
703	#537	C₂²×C₄₁	1	1	yes	characteristic
704	#537	C₂²×C₄₁	1	1	yes	characteristic
705	#537	C₂²×C₄₁	1	1	yes	characteristic
706	#537	C₂²×C₄₁	1	2	yes	—
707	#537	C₂²×C₄₁	1	1	yes	characteristic, complemented
708	#536	—	2	1	no	—
709	#536	C₂²×C₄₁	1	2	yes	—
710	#536	C₂²×C₄₁	1	2	yes	—
711	#536	C₂²×C₄₁	1	1	yes	characteristic, complemented
712	#535	—	2	1	no	—
713	#535	C₂²×C₄₁	1	2	yes	—
714	#534	—	2	2	no	—
715	#532	—	2	2	no	—
716	#525	—	2	1	no	—
717	#525	—	2	1	no	—
718	#525	C₂²×C₄₁	1	1	yes	characteristic
719	#525	C₂²×C₄₁	1	2	yes	—
720	#525	C₂²×C₄₁	1	2	yes	—
721	#525	C₂²×C₄₁	1	2	yes	complemented
722	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
723	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	complemented
724	#520	C₂²×C₄₁	1	1	yes	characteristic, complemented
725	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
726	#485	C₂²×C₄₁	1	2	yes	complemented
727	#485	C₂²×C₄₁	1	2	yes	complemented
728	#485	C₂²×C₄₁	1	2	yes	complemented
729	#485	C₂²×C₄₁	1	2	yes	complemented
730	#485	C₂²×C₄₁	1	2	yes	complemented
731	#485	C₂²×C₄₁	1	2	yes	complemented
732	#485	C₂²×C₄₁	1	2	yes	complemented
733	#485	C₂²×C₄₁	1	2	yes	complemented
734	#484	C₂²×C₄₁	1	2	yes	complemented
735	#483	C₂²×C₄₁	1	2	yes	complemented
736	#482	C₂²×C₄₁	1	2	yes	complemented
737	#482	C₂²×C₄₁	1	2	yes	complemented
738	#482	C₂²×C₄₁	1	2	yes	complemented
739	#482	C₂²×C₄₁	1	2	yes	complemented
740	#481	C₂²×C₄₁	1	2	yes	complemented
741	#480	C₂²×C₄₁	1	2	yes	complemented
742	#470	C₂²×C₄₁	1	2	yes	complemented
743	#470	C₂²×C₄₁	1	2	yes	complemented
744	#470	C₂²×C₄₁	1	2	yes	complemented
745	#469	C₂²×C₄₁	1	2	yes	complemented
746	#468	C₂²×C₄₁	1	2	yes	complemented
747	#468	C₂²×C₄₁	1	2	yes	complemented
748	#468	C₂²×C₄₁	1	2	yes	complemented
749	#468	C₂²×C₄₁	1	2	yes	complemented
750	#467	C₂²×C₄₁	1	2	yes	complemented
751	#467	C₂²×C₄₁	1	2	yes	complemented
752	#467	C₂²×C₄₁	1	2	yes	complemented
753	#466	C₂²×C₄₁	1	2	yes	complemented
754	#465	C₂²×C₄₁	1	2	yes	complemented
755	#465	C₂²×C₄₁	1	2	yes	complemented
756	#465	C₂²×C₄₁	1	2	yes	complemented
757	#465	C₂²×C₄₁	1	2	yes	complemented
758	#452	C₂²×C₄₁	1	1	yes	characteristic
759	#452	C₂²×C₄₁	1	2	yes	—
760	#452	C₂²×C₄₁	1	2	yes	—
761	#452	C₂²×C₄₁	1	1	yes	characteristic
762	#452	C₂²×C₄₁	1	2	yes	complemented
763	#452	C₂²×C₄₁	1	2	yes	complemented
764	#451	C₂²×C₄₁	1	2	yes	complemented
765	#451	C₂²×C₄₁	1	2	yes	complemented
766	#451	C₂²×C₄₁	1	2	yes	complemented
767	#451	C₂²×C₄₁	1	1	yes	characteristic, complemented
768	#450	C₂²×C₄₁	1	2	yes	complemented
769	#450	C₂²×C₄₁	1	1	yes	characteristic, complemented
770	#449	C₂²×C₄₁	1	1	yes	characteristic
771	#449	C₂²×C₄₁	1	1	yes	characteristic
772	#449	C₂²×C₄₁	1	2	yes	complemented
773	#449	C₂²×C₄₁	1	2	yes	complemented
774	#448	C₂²×C₄₁	1	2	yes	complemented
775	#448	C₂²×C₄₁	1	2	yes	complemented
776	#448	C₂²×C₄₁	1	1	yes	characteristic, complemented
777	#447	C₂²×C₄₁	1	1	yes	characteristic, complemented
778	#428	C₂²×C₄₁	1	1	yes	characteristic, complemented
779	#428	C₂²×C₄₁	1	1	yes	characteristic, complemented
780	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic, complemented
781	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic, complemented
782	#417	C₂²×C₄₁	1	1	yes	characteristic, complemented
783	#417	C₂²×C₄₁	1	1	yes	characteristic, complemented
784	#417	C₂²×C₄₁	1	1	yes	characteristic, complemented
785	#417	C₂²×C₄₁	1	1	yes	characteristic, complemented
786	#416	C₂²×C₄₁	1	1	yes	characteristic, complemented
787	#416	C₂²×C₄₁	1	1	yes	characteristic, complemented
788	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic, complemented
789	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic, complemented
790	#408	C₂²×C₄₁	1	2	yes	—
791	#408	C₂²×C₄₁	1	2	yes	—
792	#408	C₂²×C₄₁	1	1	yes	characteristic, complemented
793	#408	C₂²×C₄₁	1	1	yes	characteristic, complemented
794	#407	C₂²×C₄₁	1	1	yes	characteristic
795	#407	C₂²×C₄₁	1	2	yes	complemented
796	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
797	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	complemented
798	C₄₁	#60766	1	1	yes	characteristic, direct product factor, Sylow
799	2₋¹⁺⁴	—	4	2	no	—
800	2₋¹⁺⁴	—	4	2	no	—
801	C₂×#41	—	2	1	no	—
802	C₂×#41	—	2	2	no	—
803	C₂×#41	—	2	1	no	—
804	C₂×#41	—	2	1	no	—
805	C₂×#41	—	4	2	no	—
806	C₂×#41	—	4	2	no	—
807	C₂×#41	—	4	2	no	—
808	C₂×#41	—	4	2	no	—
809	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
810	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
811	C₂×#41	D₄×C₄₁	1	2	yes	—
812	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
813	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
814	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
815	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
816	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
817	C₂×#41	C₂³×C₄₁	1	2	yes	—
818	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
819	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
820	C₂×#41	C₂³×C₄₁	1	2	yes	—
821	C₂²×Q₈	—	2	1	no	—
822	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
823	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
824	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
825	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
826	C₂²×D₄	—	2	1	no	—
827	C₂²×D₄	D₄×C₄₁	1	2	yes	—
828	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
829	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
830	C₂³×C₄	—	2	1	no	—
831	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
832	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
833	#137	—	4	2	no	—
834	#137	—	4	2	no	—
835	#135	—	4	2	no	—
836	#135	—	4	2	no	—
837	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
838	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
839	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
840	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
841	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
842	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
843	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
844	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
845	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
846	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
847	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
848	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
849	#131	—	4	2	no	—
850	#131	—	4	2	no	—
851	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
852	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
853	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
854	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
855	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
856	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
857	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
858	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
859	C₄⋊Q₈	—	2	2	no	—
860	C₄⋊Q₈	—	2	2	no	—
861	C₄⋊Q₈	—	2	1	no	—
862	#127	—	2	2	no	—
863	#124	—	2	2	no	—
864	#124	—	2	2	no	—
865	#124	—	2	2	no	—
866	#124	—	2	1	no	—
867	#123	—	2	2	no	—
868	#123	—	2	2	no	—
869	#123	—	2	2	no	—
870	#123	—	2	2	no	—
871	#123	—	2	2	no	—
872	#123	—	2	2	no	—
873	#123	—	2	2	no	—
874	#123	—	2	1	no	—
875	#123	—	2	2	no	—
876	C₂²⋊Q₈	—	2	1	no	—
877	C₂²⋊Q₈	—	2	1	no	—
878	C₂²⋊Q₈	—	2	1	no	—
879	C₂²⋊Q₈	—	2	1	no	—
880	C₂²⋊Q₈	—	2	2	no	—
881	C₂²⋊Q₈	—	2	1	no	—
882	C₂²⋊Q₈	—	2	1	no	—
883	C₂²⋊Q₈	—	2	1	no	—
884	C₂²⋊Q₈	—	2	2	no	—
885	C₂²⋊Q₈	—	2	2	no	—
886	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
887	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
888	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
889	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
890	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
891	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
892	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
893	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
894	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
895	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
896	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
897	#121	—	2	1	no	—
898	#121	—	2	1	no	—
899	#121	—	2	1	no	—
900	#121	—	2	1	no	—
901	#121	—	2	2	no	—
902	#121	—	2	2	no	—
903	#121	—	2	2	no	—
904	#121	—	2	2	no	—
905	#121	—	2	2	no	—
906	#121	—	2	2	no	—
907	#121	—	2	2	no	—
908	#121	—	2	2	no	—
909	#121	—	2	1	no	—
910	#121	C₂³×C₄₁	1	1	yes	characteristic
911	#121	C₂³×C₄₁	1	2	yes	—
912	#121	C₂³×C₄₁	1	2	yes	—
913	#121	C₂³×C₄₁	1	2	yes	—
914	#121	C₂³×C₄₁	1	2	yes	—
915	#121	C₂³×C₄₁	1	1	yes	characteristic
916	#121	C₂³×C₄₁	1	2	yes	—
917	#120	—	2	2	no	—
918	#120	—	2	2	no	—
919	#120	—	2	1	no	—
920	#120	—	2	2	no	—
921	#120	—	2	2	no	—
922	#120	—	2	2	no	—
923	C₄×Q₈	—	2	1	no	—
924	C₄×D₄	—	2	2	no	—
925	C₄×D₄	—	2	1	no	—
926	C₄×D₄	—	2	2	no	—
927	C₄×D₄	—	2	2	no	—
928	C₄×D₄	—	2	2	no	—
929	C₄×D₄	—	2	2	no	—
930	C₄×D₄	—	2	1	no	—
931	C₄×D₄	—	2	1	no	—
932	C₄×D₄	—	2	2	no	—
933	C₄×D₄	—	2	2	no	—
934	#117	—	2	1	no	—
935	#117	—	2	1	no	—
936	#117	C₂³×C₄₁	1	2	yes	—
937	#117	C₂³×C₄₁	1	2	yes	—
938	#117	C₂³×C₄₁	1	1	yes	characteristic
939	#117	C₂³×C₄₁	1	2	yes	—
940	C₂×C₄⋊C₄	—	2	1	no	—
941	C₂×C₄⋊C₄	—	2	2	no	—
942	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
943	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
944	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
945	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
946	C₂×C₂²⋊C₄	—	2	1	no	—
947	C₂×C₂²⋊C₄	—	2	1	no	—
948	C₂×C₂²⋊C₄	—	2	2	no	—
949	C₂×C₄²	—	2	1	no	—
950	#107	C₂³×C₄₁	1	2	yes	—
951	#107	C₂³×C₄₁	1	2	yes	—
952	#107	C₂³×C₄₁	1	2	yes	—
953	#107	C₂³×C₄₁	1	2	yes	—
954	#106	C₂³×C₄₁	1	2	yes	—
955	#106	C₂³×C₄₁	1	2	yes	—
956	#106	C₂³×C₄₁	1	2	yes	—
957	#106	C₂³×C₄₁	1	2	yes	—
958	#103	C₂³×C₄₁	1	2	yes	—
959	#103	C₂³×C₄₁	1	2	yes	—
960	#103	C₂³×C₄₁	1	2	yes	—
961	#103	C₂³×C₄₁	1	2	yes	—
962	#103	C₂³×C₄₁	1	1	yes	characteristic
963	#103	C₂³×C₄₁	1	1	yes	characteristic
964	#103	C₂³×C₄₁	1	1	yes	characteristic
965	#103	C₂³×C₄₁	1	1	yes	characteristic
966	#103	C₂³×C₄₁	1	2	yes	—
967	#103	C₂³×C₄₁	1	2	yes	—
968	#103	C₂³×C₄₁	1	2	yes	—
969	#103	C₂³×C₄₁	1	2	yes	—
970	#102	C₂³×C₄₁	1	1	yes	characteristic
971	#102	C₂³×C₄₁	1	1	yes	characteristic
972	#102	C₂³×C₄₁	1	1	yes	characteristic
973	#102	C₂³×C₄₁	1	1	yes	characteristic
974	#102	C₂³×C₄₁	1	2	yes	—
975	#102	C₂³×C₄₁	1	2	yes	—
976	#102	C₂³×C₄₁	1	2	yes	—
977	#102	C₂³×C₄₁	1	2	yes	—
978	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
979	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
980	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
981	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
982	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
983	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
984	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
985	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
986	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
987	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
988	C₂⁴	—	2	1	no	—
989	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
990	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
991	#41	—	2	2	no	—
992	#41	—	2	2	no	—
993	#41	—	2	2	no	—
994	#41	—	2	2	no	—
995	#41	—	2	2	no	—
996	#41	—	2	2	no	—
997	#41	—	2	2	no	—
998	#41	—	2	2	no	—
999	#41	—	2	2	no	—
1000	#41	—	2	2	no	—
1001	#41	—	4	2	no	—
1002	#41	—	4	2	no	—
1003	#41	—	4	4	no	—
1004	#41	—	4	2	no	—
1005	#41	—	4	2	no	—
1006	#41	—	4	1	no	—
1007	#41	—	4	1	no	—
1008	#41	—	4	1	no	—
1009	#41	—	4	1	no	—
1010	#41	—	4	2	no	—
1011	#41	—	4	2	no	—
1012	#41	—	4	4	no	—
1013	#41	—	4	4	no	—
1014	#41	—	4	8	no	—
1015	#41	—	4	4	no	—
1016	C₂×Q₈	—	2	2	no	—
1017	C₂×Q₈	—	2	1	no	—
1018	C₂×Q₈	—	2	1	no	—
1019	C₂×Q₈	—	2	2	no	—
1020	C₂×Q₈	—	2	2	no	—
1021	C₂×Q₈	—	4	2	no	—
1022	C₂×Q₈	—	4	1	no	—
1023	C₂×Q₈	—	4	1	no	—
1024	C₂×Q₈	—	4	2	no	—
1025	C₂×Q₈	—	4	2	no	—
1026	C₂×Q₈	—	4	4	no	—
1027	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
1028	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
1029	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
1030	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
1031	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
1032	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
1033	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
1034	C₂×D₄	—	2	1	no	—
1035	C₂×D₄	—	2	1	no	—
1036	C₂×D₄	—	2	1	no	—
1037	C₂×D₄	—	2	2	no	—
1038	C₂×D₄	—	2	1	no	—
1039	C₂×D₄	—	2	1	no	—
1040	C₂×D₄	—	2	1	no	—
1041	C₂×D₄	—	2	2	no	—
1042	C₂×D₄	—	2	2	no	—
1043	C₂×D₄	—	2	2	no	—
1044	C₂×D₄	—	2	2	no	—
1045	C₂×D₄	—	2	1	no	—
1046	C₂×D₄	—	2	2	no	—
1047	C₂×D₄	—	2	1	no	—
1048	C₂×D₄	—	4	2	no	—
1049	C₂×D₄	—	4	1	no	—
1050	C₂×D₄	—	4	1	no	—
1051	C₂×D₄	—	4	4	no	—
1052	C₂×D₄	—	4	4	no	—
1053	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
1054	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1055	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
1056	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1057	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
1058	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
1059	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
1060	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
1061	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
1062	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
1063	C₂²×C₄	—	2	2	no	—
1064	C₂²×C₄	—	2	2	no	—
1065	C₂²×C₄	—	2	2	no	—
1066	C₂²×C₄	—	2	1	no	—
1067	C₂²×C₄	—	2	1	no	—
1068	C₂²×C₄	—	2	1	no	—
1069	C₂²×C₄	—	2	1	no	—
1070	C₂²×C₄	—	2	2	no	—
1071	C₂²×C₄	—	2	1	no	—
1072	C₂²×C₄	—	2	1	no	—
1073	C₂²×C₄	—	2	1	no	—
1074	C₂²×C₄	—	2	2	no	—
1075	C₂²×C₄	—	2	1	no	—
1076	C₂²×C₄	—	2	1	no	—
1077	C₂²×C₄	—	2	1	no	—
1078	C₂²×C₄	—	4	2	no	—
1079	C₂²×C₄	—	4	2	no	—
1080	C₂²×C₄	—	4	4	no	—
1081	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1082	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1083	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1084	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
1085	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
1086	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
1087	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
1088	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1089	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1090	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
1091	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1092	Q₁₆	—	4	1	no	—
1093	Q₁₆	—	4	1	no	—
1094	Q₁₆	—	4	2	no	—
1095	Q₁₆	—	4	2	no	—
1096	SD₁₆	—	4	1	no	—
1097	SD₁₆	—	4	1	no	—
1098	SD₁₆	—	4	1	no	—
1099	SD₁₆	—	4	1	no	—
1100	SD₁₆	—	4	2	no	—
1101	SD₁₆	—	4	2	no	—
1102	D₈	—	4	1	no	—
1103	D₈	—	4	1	no	—
1104	M₁₆	—	2	2	no	—
1105	M₁₆	—	2	2	no	—
1106	M₁₆	—	4	2	no	—
1107	M₁₆	—	4	2	no	—
1108	C₂×C₈	—	2	2	no	—
1109	C₂×C₈	—	2	2	no	—
1110	C₂×C₈	—	4	2	no	—
1111	C₂×C₈	—	4	2	no	—
1112	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1113	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1114	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1115	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1116	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1117	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1118	C₄⋊C₄	—	2	2	no	—
1119	C₄⋊C₄	—	2	1	no	—
1120	C₄⋊C₄	—	2	2	no	—
1121	C₄⋊C₄	—	2	2	no	—
1122	C₄⋊C₄	—	2	2	no	—
1123	C₄⋊C₄	—	2	1	no	—
1124	C₄⋊C₄	—	2	1	no	—
1125	C₄⋊C₄	—	2	2	no	—
1126	C₄⋊C₄	—	2	1	no	—
1127	C₄⋊C₄	—	2	2	no	—
1128	C₄⋊C₄	—	2	2	no	—
1129	C₄⋊C₄	—	2	2	no	—
1130	C₄⋊C₄	—	2	2	no	—
1131	C₄⋊C₄	—	2	1	no	—
1132	C₄⋊C₄	—	2	2	no	—
1133	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1134	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
1135	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1136	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
1137	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
1138	C₂²⋊C₄	—	2	2	no	—
1139	C₂²⋊C₄	—	2	1	no	—
1140	C₂²⋊C₄	—	2	2	no	—
1141	C₂²⋊C₄	—	2	2	no	—
1142	C₂²⋊C₄	—	2	2	no	—
1143	C₂²⋊C₄	—	2	2	no	—
1144	C₂²⋊C₄	—	2	2	no	—
1145	C₂²⋊C₄	—	2	2	no	—
1146	C₂²⋊C₄	—	2	1	no	—
1147	C₂²⋊C₄	—	2	2	no	—
1148	C₂²⋊C₄	—	2	2	no	—
1149	C₂²⋊C₄	—	2	2	no	—
1150	C₂²⋊C₄	—	2	2	no	—
1151	C₂²⋊C₄	—	2	1	no	—
1152	C₂²⋊C₄	—	2	2	no	—
1153	C₂²⋊C₄	—	2	1	no	—
1154	C₂²⋊C₄	—	2	2	no	—
1155	C₂²⋊C₄	—	2	2	no	—
1156	C₂²⋊C₄	—	2	2	no	—
1157	C₂²⋊C₄	—	2	2	no	—
1158	C₂²⋊C₄	—	2	1	no	—
1159	C₂²⋊C₄	—	2	2	no	—
1160	C₄²	—	2	2	no	—
1161	C₄²	—	2	2	no	—
1162	C₄²	—	2	2	no	—
1163	C₄²	—	2	1	no	—
1164	C₂³	—	2	2	no	—
1165	C₂³	—	2	1	no	—
1166	C₂³	—	2	1	no	—
1167	C₂³	—	2	1	no	—
1168	C₂³	—	4	2	no	—
1169	C₂³	—	4	1	no	—
1170	C₂³	—	4	1	no	—
1171	C₂³	—	4	2	no	—
1172	C₂³	—	4	2	no	—
1173	C₂³	—	4	2	no	—
1174	C₂³	—	8	1	no	—
1175	C₂³	—	8	1	no	—
1176	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1177	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1178	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
1179	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
1180	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1181	Q₈	—	2	2	no	—
1182	Q₈	—	2	2	no	—
1183	Q₈	—	2	2	no	—
1184	Q₈	—	2	2	no	—
1185	Q₈	—	2	1	no	—
1186	Q₈	—	2	1	no	—
1187	Q₈	—	2	1	no	—
1188	Q₈	—	2	1	no	—
1189	Q₈	—	2	1	no	—
1190	Q₈	—	2	1	no	—
1191	Q₈	—	4	2	no	—
1192	Q₈	—	4	4	no	—
1193	Q₈	—	4	2	no	—
1194	Q₈	—	4	2	no	—
1195	D₄	—	2	4	no	—
1196	D₄	—	2	4	no	—
1197	D₄	—	2	2	no	—
1198	D₄	—	2	2	no	—
1199	D₄	—	2	1	no	—
1200	D₄	—	2	1	no	—
1201	D₄	—	2	1	no	—
1202	D₄	—	2	1	no	—
1203	D₄	—	2	1	no	—
1204	D₄	—	2	1	no	—
1205	D₄	—	4	2	no	—
1206	D₄	—	4	2	no	—
1207	D₄	—	4	2	no	—
1208	D₄	—	4	2	no	—
1209	D₄	—	4	2	no	—
1210	D₄	—	4	2	no	—
1211	D₄	—	4	4	no	—
1212	D₄	—	4	2	no	—
1213	D₄	—	4	2	no	—
1214	D₄	—	4	2	no	—
1215	D₄	—	4	2	no	—
1216	D₄	—	8	2	no	—
1217	D₄	—	8	1	no	—
1218	D₄	—	8	2	no	—
1219	D₄	—	8	2	no	—
1220	D₄	—	8	2	no	—
1221	D₄	—	8	2	no	—
1222	C₂×C₄	—	2	2	no	—
1223	C₂×C₄	—	2	2	no	—
1224	C₂×C₄	—	2	2	no	—
1225	C₂×C₄	—	2	2	no	—
1226	C₂×C₄	—	2	2	no	—
1227	C₂×C₄	—	2	1	no	—
1228	C₂×C₄	—	2	1	no	—
1229	C₂×C₄	—	2	1	no	—
1230	C₂×C₄	—	2	1	no	—
1231	C₂×C₄	—	2	2	no	—
1232	C₂×C₄	—	2	2	no	—
1233	C₂×C₄	—	2	1	no	—
1234	C₂×C₄	—	2	2	no	—
1235	C₂×C₄	—	2	2	no	—
1236	C₂×C₄	—	2	2	no	—
1237	C₂×C₄	—	2	1	no	—
1238	C₂×C₄	—	2	1	no	—
1239	C₂×C₄	—	2	1	no	—
1240	C₂×C₄	—	2	2	no	—
1241	C₂×C₄	—	2	1	no	—
1242	C₂×C₄	—	4	2	no	—
1243	C₂×C₄	—	4	2	no	—
1244	C₂×C₄	—	4	2	no	—
1245	C₂×C₄	—	4	2	no	—
1246	C₂×C₄	—	4	2	no	—
1247	C₂×C₄	—	4	4	no	—
1248	C₂×C₄	—	4	2	no	—
1249	C₂×C₄	—	4	4	no	—
1250	C₂×C₄	—	4	2	no	—
1251	C₂×C₄	—	4	2	no	—
1252	C₂×C₄	—	4	2	no	—
1253	C₂×C₄	—	4	2	no	—
1254	C₂×C₄	—	8	1	no	—
1255	C₂×C₄	—	8	2	no	—
1256	C₂×C₄	—	8	1	no	—
1257	C₂×C₄	—	8	1	no	—
1258	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1259	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1260	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1261	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1262	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1263	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
1264	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
1265	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
1266	C₈	—	2	1	no	—
1267	C₈	—	2	1	no	—
1268	C₈	—	2	1	no	—
1269	C₈	—	2	1	no	—
1270	C₈	—	2	2	no	—
1271	C₈	—	2	2	no	—
1272	C₂²	—	2	1	no	—
1273	C₂²	—	2	1	no	—
1274	C₂²	—	2	2	no	—
1275	C₂²	—	2	2	no	—
1276	C₂²	—	2	1	no	—
1277	C₂²	—	2	1	no	—
1278	C₂²	—	2	1	no	—
1279	C₂²	—	2	2	no	—
1280	C₂²	—	2	2	no	—
1281	C₂²	—	2	1	no	—
1282	C₂²	—	2	1	no	—
1283	C₂²	—	2	1	no	—
1284	C₂²	—	2	2	no	—
1285	C₂²	—	2	2	no	—
1286	C₂²	—	4	1	no	—
1287	C₂²	—	4	1	no	—
1288	C₂²	—	4	1	no	—
1289	C₂²	—	4	1	no	—
1290	C₂²	—	4	1	no	—
1291	C₂²	—	4	1	no	—
1292	C₂²	—	4	1	no	—
1293	C₂²	—	4	1	no	—
1294	C₂²	—	4	1	no	—
1295	C₂²	—	8	2	no	—
1296	C₂²	—	8	4	no	—
1297	C₂²	—	8	4	no	—
1298	C₂²	C₄₁×#534	1	2	yes	—
1299	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
1300	C₄	—	2	1	no	—
1301	C₄	—	2	1	no	—
1302	C₄	—	2	2	no	—
1303	C₄	—	2	2	no	—
1304	C₄	—	4	2	no	—
1305	C₄	—	4	1	no	—
1306	C₄	—	4	2	no	—
1307	C₄	—	4	2	no	—
1308	C₄	—	4	1	no	—
1309	C₄	—	4	1	no	—
1310	C₄	—	4	1	no	—
1311	C₄	—	4	2	no	—
1312	C₄	—	4	1	no	—
1313	C₄	C₄₁×#534	1	2	yes	—
1314	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1315	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1316	C₂	—	2	2	no	—
1317	C₂	—	4	1	no	—
1318	C₂	—	4	1	no	—
1319	C₂	—	4	2	no	—
1320	C₂	—	4	2	no	—
1321	C₂	—	8	1	no	—
1322	C₂	—	8	1	no	—
1323	C₂	—	8	1	no	—
1324	C₂	C₂×C₄₁×#534	1	1	yes	characteristic
1325	C₂	C₄₁×#3584	1	1	yes	characteristic
1326	C₂	C₄₁×#3586	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 ◁ C₂²×#41×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3489	C₂	semidirect
2. C₄₁×#3449	C₂	semidirect
3. C₄₁×#3202	C₂	semidirect
4. C₄₁×#3201	C₂	semidirect
5. C₄₁×#3200	C₂	semidirect
6. C₄₁×#3198	C₂	semidirect
7. C₄₁×#3197	C₂	semidirect
8. C₄₁×#3196	C₂	semidirect
9. C₄₁×#3191	C₂	semidirect
10. C₄₁×#3190	C₂	semidirect
11. C₄₁×#3099	C₂	semidirect
12. C₄₁×#3098	C₂	semidirect
13. C₄₁×#3093	C₂	semidirect
14. C₂×C₄₁×#485	C₂	semidirect
15. C₄₁×#3063	C₂	semidirect
16. C₄₁×#3063	C₂	semidirect
17. C₄₁×#3061	C₂	semidirect
18. C₄₁×#3060	C₂	semidirect
19. C₄₁×#3013	C₂	semidirect
20. C₄₁×#3013	C₂	semidirect
21. C₄₁×#3007	C₂	semidirect
22. C₄₁×#3002	C₂	semidirect
23. C₄₁×#2880	C₂	semidirect
24. C₂×2₋¹⁺⁴×C₄₁	C₂²	semidirect
27. C₂×#137×C₄₁	C₂²	semidirect
28. C₂×#137×C₄₁	C₂²	semidirect
29. C₂×#135×C₄₁	C₂²	semidirect
30. C₂×#135×C₄₁	C₂²	semidirect
31. C₂×#131×C₄₁	C₂²	semidirect
32. C₂×#131×C₄₁	C₂²	semidirect
44. C₄₁×#537	C₂²	semidirect
48. C₄₁×#536	C₂²	semidirect
58. C₄₁×#525	C₂²	semidirect
60. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
61. C₄₁×#520	C₂²	semidirect
63. C₄₁×#485	C₂²	semidirect
64. C₄₁×#485	C₂²	semidirect
65. C₄₁×#485	C₂²	semidirect
66. C₄₁×#485	C₂²	semidirect
67. C₄₁×#485	C₂²	semidirect
68. C₄₁×#485	C₂²	semidirect
69. C₄₁×#485	C₂²	semidirect
70. C₄₁×#485	C₂²	semidirect
71. C₄₁×#484	C₂²	semidirect
72. C₄₁×#483	C₂²	semidirect
73. C₄₁×#482	C₂²	semidirect
74. C₄₁×#482	C₂²	semidirect
75. C₄₁×#482	C₂²	semidirect
76. C₄₁×#482	C₂²	semidirect
77. C₄₁×#481	C₂²	semidirect
78. C₄₁×#480	C₂²	semidirect
79. C₄₁×#470	C₂²	semidirect
80. C₄₁×#470	C₂²	semidirect
81. C₄₁×#470	C₂²	semidirect
82. C₄₁×#469	C₂²	semidirect
83. C₄₁×#468	C₂²	semidirect
84. C₄₁×#468	C₂²	semidirect
85. C₄₁×#468	C₂²	semidirect
86. C₄₁×#468	C₂²	semidirect
87. C₄₁×#467	C₂²	semidirect
88. C₄₁×#467	C₂²	semidirect
89. C₄₁×#467	C₂²	semidirect
90. C₄₁×#466	C₂²	semidirect
91. C₄₁×#465	C₂²	semidirect
92. C₄₁×#465	C₂²	semidirect
93. C₄₁×#465	C₂²	semidirect
94. C₄₁×#465	C₂²	semidirect
99. C₄₁×#452	C₂²	semidirect
100. C₄₁×#452	C₂²	semidirect
101. C₄₁×#451	C₂²	semidirect
102. C₄₁×#451	C₂²	semidirect
103. C₄₁×#451	C₂²	semidirect
104. C₄₁×#451	C₂²	semidirect
105. C₄₁×#450	C₂²	semidirect
106. C₄₁×#450	C₂²	semidirect
109. C₄₁×#449	C₂²	semidirect
110. C₄₁×#449	C₂²	semidirect
111. C₄₁×#448	C₂²	semidirect
112. C₄₁×#448	C₂²	semidirect
113. C₄₁×#448	C₂²	semidirect
114. C₄₁×#447	C₂²	semidirect
115. C₄₁×#428	C₂²	semidirect
116. C₄₁×#428	C₂²	semidirect
117. C₂×#107×C₄₁	C₂²	semidirect
118. C₂×#106×C₄₁	C₂²	semidirect
119. C₄₁×#417	C₂²	semidirect
120. C₄₁×#417	C₂²	semidirect
121. C₄₁×#417	C₂²	semidirect
122. C₄₁×#417	C₂²	semidirect
123. C₄₁×#416	C₂²	semidirect
124. C₄₁×#416	C₂²	semidirect
125. C₂×#103×C₄₁	C₂²	semidirect
126. C₂×#103×C₄₁	C₂²	semidirect
129. C₄₁×#408	C₂²	semidirect
130. C₄₁×#408	C₂²	semidirect
132. C₄₁×#407	C₂²	semidirect
134. C₂×C₂²⋊C₈×C₄₁	C₂²	semidirect
608. #60766	C₄₁	direct (N × H)
653. #3489	C₂×C₄₁	semidirect
654. #3449	C₂×C₄₁	semidirect
655. #3202	C₂×C₄₁	semidirect
656. #3201	C₂×C₄₁	semidirect
657. #3200	C₂×C₄₁	semidirect
658. #3198	C₂×C₄₁	semidirect
659. #3197	C₂×C₄₁	semidirect
660. #3196	C₂×C₄₁	semidirect
661. #3191	C₂×C₄₁	semidirect
662. #3190	C₂×C₄₁	semidirect
663. #3099	C₂×C₄₁	semidirect
664. #3098	C₂×C₄₁	semidirect
665. #3093	C₂×C₄₁	semidirect
666. C₂×#485	C₂×C₄₁	semidirect
667. #3063	C₂×C₄₁	semidirect
668. #3063	C₂×C₄₁	semidirect
669. #3061	C₂×C₄₁	semidirect
670. #3060	C₂×C₄₁	semidirect
671. #3013	C₂×C₄₁	semidirect
672. #3013	C₂×C₄₁	semidirect
673. #3007	C₂×C₄₁	semidirect
674. #3002	C₂×C₄₁	semidirect
675. #2880	C₂×C₄₁	semidirect
687. C₂×2₋¹⁺⁴	C₂²×C₄₁	semidirect
690. C₂×#137	C₂²×C₄₁	semidirect
691. C₂×#137	C₂²×C₄₁	semidirect
692. C₂×#135	C₂²×C₄₁	semidirect
693. C₂×#135	C₂²×C₄₁	semidirect
694. C₂×#131	C₂²×C₄₁	semidirect
695. C₂×#131	C₂²×C₄₁	semidirect
707. #537	C₂²×C₄₁	semidirect
711. #536	C₂²×C₄₁	semidirect
721. #525	C₂²×C₄₁	semidirect
723. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
724. #520	C₂²×C₄₁	semidirect
726. #485	C₂²×C₄₁	semidirect
727. #485	C₂²×C₄₁	semidirect
728. #485	C₂²×C₄₁	semidirect
729. #485	C₂²×C₄₁	semidirect
730. #485	C₂²×C₄₁	semidirect
731. #485	C₂²×C₄₁	semidirect
732. #485	C₂²×C₄₁	semidirect
733. #485	C₂²×C₄₁	semidirect
734. #484	C₂²×C₄₁	semidirect
735. #483	C₂²×C₄₁	semidirect
736. #482	C₂²×C₄₁	semidirect
737. #482	C₂²×C₄₁	semidirect
738. #482	C₂²×C₄₁	semidirect
739. #482	C₂²×C₄₁	semidirect
740. #481	C₂²×C₄₁	semidirect
741. #480	C₂²×C₄₁	semidirect
742. #470	C₂²×C₄₁	semidirect
743. #470	C₂²×C₄₁	semidirect
744. #470	C₂²×C₄₁	semidirect
745. #469	C₂²×C₄₁	semidirect
746. #468	C₂²×C₄₁	semidirect
747. #468	C₂²×C₄₁	semidirect
748. #468	C₂²×C₄₁	semidirect
749. #468	C₂²×C₄₁	semidirect
750. #467	C₂²×C₄₁	semidirect
751. #467	C₂²×C₄₁	semidirect
752. #467	C₂²×C₄₁	semidirect
753. #466	C₂²×C₄₁	semidirect
754. #465	C₂²×C₄₁	semidirect
755. #465	C₂²×C₄₁	semidirect
756. #465	C₂²×C₄₁	semidirect
757. #465	C₂²×C₄₁	semidirect
762. #452	C₂²×C₄₁	semidirect
763. #452	C₂²×C₄₁	semidirect
764. #451	C₂²×C₄₁	semidirect
765. #451	C₂²×C₄₁	semidirect
766. #451	C₂²×C₄₁	semidirect
767. #451	C₂²×C₄₁	semidirect
768. #450	C₂²×C₄₁	semidirect
769. #450	C₂²×C₄₁	semidirect
772. #449	C₂²×C₄₁	semidirect
773. #449	C₂²×C₄₁	semidirect
774. #448	C₂²×C₄₁	semidirect
775. #448	C₂²×C₄₁	semidirect
776. #448	C₂²×C₄₁	semidirect
777. #447	C₂²×C₄₁	semidirect
778. #428	C₂²×C₄₁	semidirect
779. #428	C₂²×C₄₁	semidirect
780. C₂×#107	C₂²×C₄₁	semidirect
781. C₂×#106	C₂²×C₄₁	semidirect
782. #417	C₂²×C₄₁	semidirect
783. #417	C₂²×C₄₁	semidirect
784. #417	C₂²×C₄₁	semidirect
785. #417	C₂²×C₄₁	semidirect
786. #416	C₂²×C₄₁	semidirect
787. #416	C₂²×C₄₁	semidirect
788. C₂×#103	C₂²×C₄₁	semidirect
789. C₂×#103	C₂²×C₄₁	semidirect
792. #408	C₂²×C₄₁	semidirect
793. #408	C₂²×C₄₁	semidirect
795. #407	C₂²×C₄₁	semidirect
797. C₂×C₂²⋊C₈	C₂²×C₄₁	semidirect
798. C₄₁	#60766	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×#3489	2
C₄₁×#3449	2
C₄₁×#3202	2
C₄₁×#3201	2
C₄₁×#3200	2
C₄₁×#3198	2
C₄₁×#3197	2
C₄₁×#3196	2
C₄₁×#3191	2
C₄₁×#3190	2
C₄₁×#3099	2
C₄₁×#3098	2
C₄₁×#3093	2
C₂×C₄₁×#485	2
C₄₁×#3063	2
C₄₁×#3061	2
C₄₁×#3060	2
C₄₁×#3013	2
C₄₁×#3007	2
C₄₁×#3002	2
C₄₁×#2880	2
#60766	41

Subgroups — C41×#60766 #23836967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#60766 #23836967