Subgroups — C₄₁×#60816 #23837017

Order 10496.

2048 conjugacy classes of subgroups.

The subgroup lattice has 1292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3225	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3224	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3223	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3222	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3219	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3216	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3212	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3210	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3156	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3154	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3137	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3136	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3046	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#3045	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#3044	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄₁×#3043	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#3007	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄₁×#3005	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄₁×#3002	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄₁×#452	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₁×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#137×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×#137×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×#137×C₄₁	C₂²	1	1	yes	characteristic, complemented
29	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	1	yes	characteristic, complemented
30	C₂×#135×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×#135×C₄₁	C₂²	1	1	yes	characteristic
32	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
33	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
34	C₄₁×#556	—	2	1	no	—
35	C₄₁×#554	—	2	1	no	—
36	C₄₁×#552	—	2	2	no	—
37	C₄₁×#552	—	2	1	no	—
38	C₄₁×#552	—	2	1	no	—
39	C₄₁×#551	—	2	2	no	—
40	C₄₁×#544	C₂²	1	1	yes	characteristic, complemented
41	C₄₁×#542	C₂²	1	2	yes	complemented
42	C₄₁×#541	C₂²	1	2	yes	complemented
43	C₄₁×#537	—	2	1	no	—
44	C₄₁×#537	—	2	1	no	—
45	C₄₁×#536	C₂²	1	1	yes	characteristic
46	C₄₁×#536	C₂²	1	1	yes	characteristic
47	C₄₁×#536	C₂²	1	2	yes	—
48	C₄₁×#536	C₂²	1	1	yes	characteristic, complemented
49	C₄₁×#535	C₂²	1	1	yes	characteristic
50	C₄₁×#535	C₂²	1	1	yes	characteristic
51	C₄₁×#535	C₂²	1	2	yes	—
52	C₄₁×#534	—	2	2	no	—
53	C₄₁×#533	C₂²	1	2	yes	complemented
54	C₄₁×#532	C₂²	1	2	yes	—
55	C₄₁×#532	C₂²	1	2	yes	—
56	C₄₁×#529	C₂²	1	2	yes	complemented
57	C₄₁×#525	—	2	1	no	—
58	C₄₁×#525	—	2	2	no	—
59	C₄₁×#525	—	2	1	no	—
60	C₄₁×#525	C₂²	1	1	yes	characteristic
61	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
62	C₄₁×#520	C₂²	1	1	yes	characteristic, complemented
63	C₄₁×#519	C₂²	1	1	yes	characteristic, complemented
64	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
65	C₄₁×#497	C₂²	1	2	yes	complemented
66	C₄₁×#497	C₂²	1	2	yes	complemented
67	C₄₁×#497	C₂²	1	2	yes	complemented
68	C₄₁×#496	C₂²	1	2	yes	complemented
69	C₄₁×#495	C₂²	1	2	yes	complemented
70	C₄₁×#495	C₂²	1	2	yes	complemented
71	C₄₁×#494	C₂²	1	2	yes	complemented
72	C₄₁×#492	C₂²	1	2	yes	complemented
73	C₄₁×#491	C₂²	1	2	yes	complemented
74	C₄₁×#490	C₂²	1	2	yes	complemented
75	C₄₁×#489	C₂²	1	2	yes	complemented
76	C₄₁×#489	C₂²	1	2	yes	complemented
77	C₄₁×#488	C₂²	1	2	yes	complemented
78	C₄₁×#488	C₂²	1	2	yes	complemented
79	C₄₁×#487	C₂²	1	2	yes	complemented
80	C₄₁×#486	C₂²	1	2	yes	complemented
81	C₄₁×#464	C₂²	1	2	yes	complemented
82	C₄₁×#464	C₂²	1	2	yes	complemented
83	C₄₁×#464	C₂²	1	2	yes	complemented
84	C₄₁×#464	C₂²	1	2	yes	complemented
85	C₄₁×#464	C₂²	1	2	yes	complemented
86	C₄₁×#464	C₂²	1	2	yes	complemented
87	C₄₁×#463	C₂²	1	2	yes	complemented
88	C₄₁×#463	C₂²	1	2	yes	complemented
89	C₄₁×#462	C₂²	1	2	yes	complemented
90	C₄₁×#462	C₂²	1	2	yes	complemented
91	C₄₁×#462	C₂²	1	2	yes	complemented
92	C₄₁×#461	C₂²	1	2	yes	complemented
93	C₄₁×#460	C₂²	1	2	yes	complemented
94	C₄₁×#460	C₂²	1	2	yes	complemented
95	C₄₁×#460	C₂²	1	2	yes	complemented
96	C₄₁×#459	C₂²	1	2	yes	complemented
97	C₄₁×#452	C₂²	1	2	yes	—
98	C₄₁×#452	C₂²	1	2	yes	—
99	C₄₁×#452	C₂²	1	2	yes	—
100	C₄₁×#452	C₂²	1	1	yes	characteristic, complemented
101	C₄₁×#452	C₂²	1	2	yes	complemented
102	C₄₁×#452	C₂²	1	2	yes	complemented
103	C₄₁×#452	C₂²	1	2	yes	complemented
104	C₄₁×#452	C₂²	1	2	yes	complemented
105	C₄₁×#452	C₂²	1	1	yes	characteristic, complemented
106	C₄₁×#452	C₂²	1	2	yes	complemented
107	C₄₁×#451	C₂²	1	1	yes	characteristic, complemented
108	C₄₁×#451	C₂²	1	2	yes	complemented
109	C₄₁×#450	C₂²	1	1	yes	characteristic, complemented
110	C₄₁×#450	C₂²	1	2	yes	complemented
111	C₄₁×#449	C₂²	1	2	yes	—
112	C₄₁×#449	C₂²	1	1	yes	characteristic, complemented
113	C₄₁×#449	C₂²	1	2	yes	complemented
114	C₄₁×#449	C₂²	1	1	yes	characteristic, complemented
115	C₄₁×#448	C₂²	1	1	yes	characteristic, complemented
116	C₄₁×#447	C₂²	1	1	yes	characteristic, complemented
117	C₄₁×#433	C₂²	1	2	yes	complemented
118	C₄₁×#433	C₂²	1	2	yes	complemented
119	C₄₁×#432	C₂²	1	2	yes	complemented
120	C₄₁×#431	C₂²	1	2	yes	complemented
121	C₄₁×#424	C₂²	1	1	yes	characteristic, complemented
122	C₄₁×#424	C₂²	1	1	yes	characteristic, complemented
123	C₄₁×#419	C₂²	1	1	yes	characteristic, complemented
124	C₄₁×#418	C₂²	1	1	yes	characteristic, complemented
125	C₄₁×#417	C₂²	1	1	yes	characteristic
126	C₄₁×#417	C₂²	1	1	yes	characteristic
127	C₄₁×#416	C₂²	1	1	yes	characteristic
128	C₄₁×#416	C₂²	1	1	yes	characteristic
129	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic, complemented
130	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic, complemented
131	C₄₁×#407	C₂²	1	1	yes	characteristic
132	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
133	C₄₁×#405	C₂²	1	1	yes	characteristic, complemented
134	C₄₁×#405	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₄₁	—	2	1	no	—
136	C₂×#41×C₄₁	—	2	1	no	—
137	C₂×#41×C₄₁	—	2	1	no	—
138	C₂×#41×C₄₁	—	2	1	no	—
139	C₂×#41×C₄₁	—	4	2	no	—
140	C₂×#41×C₄₁	—	4	2	no	—
141	C₂×#41×C₄₁	—	4	2	no	—
142	C₂×#41×C₄₁	—	4	2	no	—
143	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
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	C₂×#41×C₄₁	C₂³	1	2	yes	—
148	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
149	C₂×#41×C₄₁	C₂³	1	2	yes	—
150	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
151	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
152	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
153	C₂²×D₄×C₄₁	—	2	1	no	—
154	C₂²×D₄×C₄₁	—	2	1	no	—
155	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
156	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
157	C₂³×C₄×C₄₁	—	2	1	no	—
158	C₂³×C₄×C₄₁	—	2	1	no	—
159	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
160	#137×C₄₁	—	4	2	no	—
161	#137×C₄₁	—	4	2	no	—
162	#137×C₄₁	—	4	2	no	—
163	AGL(1,ℤ/8)×C₄₁	—	4	2	no	—
164	#135×C₄₁	—	4	2	no	—
165	#135×C₄₁	—	4	2	no	—
166	C₂×Q₁₆×C₄₁	—	4	2	no	—
167	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
168	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
169	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
170	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
171	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
172	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
173	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
174	C₂×SD₁₆×C₄₁	—	4	2	no	—
175	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
176	C₂×SD₁₆×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×SD₁₆×C₄₁	C₂³	1	2	yes	—
184	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
185	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
186	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
187	C₂×D₈×C₄₁	C₂³	1	2	yes	—
188	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
189	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
190	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
191	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
192	C₄⋊Q₈×C₄₁	—	2	1	no	—
193	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
194	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
195	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
196	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
197	#127×C₄₁	C₂³	1	2	yes	—
198	#127×C₄₁	C₂³	1	2	yes	—
199	#126×C₄₁	—	2	2	no	—
200	#126×C₄₁	—	2	2	no	—
201	#126×C₄₁	—	2	2	no	—
202	#126×C₄₁	—	2	2	no	—
203	#125×C₄₁	—	2	2	no	—
204	#125×C₄₁	—	2	2	no	—
205	#125×C₄₁	—	2	1	no	—
206	#125×C₄₁	—	2	2	no	—
207	#125×C₄₁	C₂³	1	2	yes	—
208	#124×C₄₁	—	2	2	no	—
209	#124×C₄₁	C₂³	1	2	yes	—
210	#124×C₄₁	C₂³	1	2	yes	—
211	#124×C₄₁	C₂³	1	2	yes	—
212	#124×C₄₁	C₂³	1	2	yes	—
213	#124×C₄₁	C₂³	1	2	yes	—
214	#123×C₄₁	—	2	1	no	—
215	#123×C₄₁	—	2	2	no	—
216	#123×C₄₁	—	2	2	no	—
217	#123×C₄₁	—	2	2	no	—
218	#123×C₄₁	—	2	2	no	—
219	#123×C₄₁	—	2	2	no	—
220	#123×C₄₁	—	2	2	no	—
221	#123×C₄₁	—	2	2	no	—
222	C₂²⋊Q₈×C₄₁	—	2	1	no	—
223	C₂²⋊Q₈×C₄₁	—	2	1	no	—
224	C₂²⋊Q₈×C₄₁	—	2	2	no	—
225	C₂²⋊Q₈×C₄₁	—	2	1	no	—
226	C₂²⋊Q₈×C₄₁	—	2	1	no	—
227	C₂²⋊Q₈×C₄₁	—	2	1	no	—
228	C₂²⋊Q₈×C₄₁	—	2	2	no	—
229	C₂²⋊Q₈×C₄₁	—	2	1	no	—
230	C₂²⋊Q₈×C₄₁	—	2	2	no	—
231	C₂²⋊Q₈×C₄₁	—	2	1	no	—
232	C₂²⋊Q₈×C₄₁	—	2	1	no	—
233	C₂²⋊Q₈×C₄₁	—	2	2	no	—
234	C₂²⋊Q₈×C₄₁	—	2	2	no	—
235	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
236	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
237	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
238	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
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	1	no	—
244	#121×C₄₁	—	2	1	no	—
245	#121×C₄₁	—	2	1	no	—
246	#121×C₄₁	—	2	2	no	—
247	#121×C₄₁	—	2	1	no	—
248	#121×C₄₁	—	2	2	no	—
249	#121×C₄₁	C₂³	1	1	yes	characteristic
250	#121×C₄₁	C₂³	1	1	yes	characteristic
251	#120×C₄₁	—	2	1	no	—
252	#120×C₄₁	—	2	2	no	—
253	#120×C₄₁	—	2	2	no	—
254	#120×C₄₁	—	2	2	no	—
255	#120×C₄₁	—	2	2	no	—
256	C₄×Q₈×C₄₁	—	2	1	no	—
257	C₄×Q₈×C₄₁	—	2	1	no	—
258	C₄×Q₈×C₄₁	—	2	2	no	—
259	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
260	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
261	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
262	C₄×D₄×C₄₁	—	2	1	no	—
263	C₄×D₄×C₄₁	—	2	1	no	—
264	C₄×D₄×C₄₁	—	2	2	no	—
265	C₄×D₄×C₄₁	—	2	2	no	—
266	C₄×D₄×C₄₁	—	2	2	no	—
267	C₄×D₄×C₄₁	—	2	2	no	—
268	C₄×D₄×C₄₁	—	2	2	no	—
269	C₄×D₄×C₄₁	—	2	2	no	—
270	C₄×D₄×C₄₁	C₂³	1	2	yes	—
271	#117×C₄₁	—	2	2	no	—
272	#117×C₄₁	—	2	1	no	—
273	#117×C₄₁	—	2	2	no	—
274	#117×C₄₁	—	2	2	no	—
275	#117×C₄₁	D₄	1	1	yes	characteristic
276	#117×C₄₁	D₄	1	2	yes	—
277	#117×C₄₁	D₄	1	1	yes	characteristic
278	#117×C₄₁	C₂³	1	1	yes	characteristic
279	#117×C₄₁	C₂³	1	1	yes	characteristic
280	#117×C₄₁	C₂³	1	1	yes	characteristic
281	#117×C₄₁	C₂³	1	2	yes	—
282	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
283	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
284	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
285	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
286	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
288	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
289	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
290	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
291	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
292	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
293	C₄⋊C₈×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	1	yes	characteristic
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	2	yes	—
305	#102×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	#97×C₄₁	C₂³	1	2	yes	—
321	#97×C₄₁	C₂³	1	2	yes	—
322	C₄×C₈×C₄₁	C₂³	1	2	yes	—
323	C₄×C₈×C₄₁	C₂³	1	2	yes	—
324	C₂⁴×C₄₁	—	2	1	no	—
325	C₂⁴×C₄₁	—	2	1	no	—
326	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
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	—	4	2	no	—
334	#41×C₄₁	—	4	2	no	—
335	#41×C₄₁	—	4	2	no	—
336	#41×C₄₁	—	4	1	no	—
337	#41×C₄₁	—	4	1	no	—
338	#41×C₄₁	—	4	2	no	—
339	#41×C₄₁	—	4	1	no	—
340	#41×C₄₁	—	4	1	no	—
341	#41×C₄₁	—	4	4	no	—
342	#41×C₄₁	—	4	4	no	—
343	#41×C₄₁	—	4	4	no	—
344	#41×C₄₁	—	4	4	no	—
345	C₂×Q₈×C₄₁	—	2	1	no	—
346	C₂×Q₈×C₄₁	—	2	1	no	—
347	C₂×Q₈×C₄₁	—	2	1	no	—
348	C₂×Q₈×C₄₁	—	2	2	no	—
349	C₂×Q₈×C₄₁	—	2	2	no	—
350	C₂×Q₈×C₄₁	—	2	2	no	—
351	C₂×Q₈×C₄₁	—	2	2	no	—
352	C₂×Q₈×C₄₁	—	2	2	no	—
353	C₂×Q₈×C₄₁	—	4	1	no	—
354	C₂×Q₈×C₄₁	—	4	1	no	—
355	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
356	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
357	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
358	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
359	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
360	C₂×D₄×C₄₁	—	2	1	no	—
361	C₂×D₄×C₄₁	—	2	1	no	—
362	C₂×D₄×C₄₁	—	2	2	no	—
363	C₂×D₄×C₄₁	—	2	1	no	—
364	C₂×D₄×C₄₁	—	2	1	no	—
365	C₂×D₄×C₄₁	—	2	1	no	—
366	C₂×D₄×C₄₁	—	2	2	no	—
367	C₂×D₄×C₄₁	—	2	1	no	—
368	C₂×D₄×C₄₁	—	2	1	no	—
369	C₂×D₄×C₄₁	—	2	1	no	—
370	C₂×D₄×C₄₁	—	2	1	no	—
371	C₂×D₄×C₄₁	—	2	2	no	—
372	C₂×D₄×C₄₁	—	2	2	no	—
373	C₂×D₄×C₄₁	—	2	2	no	—
374	C₂×D₄×C₄₁	—	2	2	no	—
375	C₂×D₄×C₄₁	—	2	2	no	—
376	C₂×D₄×C₄₁	—	2	2	no	—
377	C₂×D₄×C₄₁	—	4	1	no	—
378	C₂×D₄×C₄₁	—	4	1	no	—
379	C₂×D₄×C₄₁	—	4	4	no	—
380	C₂×D₄×C₄₁	—	4	4	no	—
381	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
382	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
383	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
384	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₄₁	—	2	2	no	—
386	C₂²×C₄×C₄₁	—	2	2	no	—
387	C₂²×C₄×C₄₁	—	2	1	no	—
388	C₂²×C₄×C₄₁	—	2	1	no	—
389	C₂²×C₄×C₄₁	—	2	1	no	—
390	C₂²×C₄×C₄₁	—	2	1	no	—
391	C₂²×C₄×C₄₁	—	2	1	no	—
392	C₂²×C₄×C₄₁	—	2	1	no	—
393	C₂²×C₄×C₄₁	—	2	2	no	—
394	C₂²×C₄×C₄₁	—	2	1	no	—
395	C₂²×C₄×C₄₁	—	2	2	no	—
396	C₂²×C₄×C₄₁	—	2	1	no	—
397	C₂²×C₄×C₄₁	—	2	1	no	—
398	C₂²×C₄×C₄₁	—	2	2	no	—
399	C₂²×C₄×C₄₁	—	4	4	no	—
400	C₂²×C₄×C₄₁	—	4	4	no	—
401	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
404	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
405	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
406	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
409	Q₁₆×C₄₁	—	4	2	no	—
410	Q₁₆×C₄₁	—	4	2	no	—
411	Q₁₆×C₄₁	—	4	1	no	—
412	Q₁₆×C₄₁	—	4	1	no	—
413	Q₁₆×C₄₁	—	4	2	no	—
414	Q₁₆×C₄₁	—	4	2	no	—
415	Q₁₆×C₄₁	—	4	2	no	—
416	SD₁₆×C₄₁	—	4	2	no	—
417	SD₁₆×C₄₁	—	4	2	no	—
418	SD₁₆×C₄₁	—	4	1	no	—
419	SD₁₆×C₄₁	—	4	1	no	—
420	SD₁₆×C₄₁	—	4	1	no	—
421	SD₁₆×C₄₁	—	4	1	no	—
422	SD₁₆×C₄₁	—	4	2	no	—
423	SD₁₆×C₄₁	—	4	2	no	—
424	SD₁₆×C₄₁	—	4	2	no	—
425	SD₁₆×C₄₁	—	4	2	no	—
426	D₈×C₄₁	—	4	1	no	—
427	D₈×C₄₁	—	4	1	no	—
428	D₈×C₄₁	—	4	2	no	—
429	M₁₆×C₄₁	—	2	2	no	—
430	M₁₆×C₄₁	—	2	2	no	—
431	C₂×C₈×C₄₁	—	2	2	no	—
432	C₂×C₈×C₄₁	—	2	2	no	—
433	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
434	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
435	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
436	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
437	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
438	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₄₁	—	2	1	no	—
440	C₄⋊C₄×C₄₁	—	2	2	no	—
441	C₄⋊C₄×C₄₁	—	2	2	no	—
442	C₄⋊C₄×C₄₁	—	2	2	no	—
443	C₄⋊C₄×C₄₁	—	2	2	no	—
444	C₄⋊C₄×C₄₁	—	2	2	no	—
445	C₄⋊C₄×C₄₁	—	2	2	no	—
446	C₄⋊C₄×C₄₁	—	2	2	no	—
447	C₄⋊C₄×C₄₁	—	2	2	no	—
448	C₄⋊C₄×C₄₁	—	2	1	no	—
449	C₄⋊C₄×C₄₁	—	2	2	no	—
450	C₄⋊C₄×C₄₁	—	2	2	no	—
451	C₄⋊C₄×C₄₁	—	2	2	no	—
452	C₄⋊C₄×C₄₁	—	2	2	no	—
453	C₄⋊C₄×C₄₁	—	2	2	no	—
454	C₄⋊C₄×C₄₁	—	2	1	no	—
455	C₄⋊C₄×C₄₁	—	2	2	no	—
456	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
457	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
458	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
459	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
460	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
461	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
462	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
463	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
464	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
465	C₂²⋊C₄×C₄₁	—	2	2	no	—
466	C₂²⋊C₄×C₄₁	—	2	2	no	—
467	C₂²⋊C₄×C₄₁	—	2	1	no	—
468	C₂²⋊C₄×C₄₁	—	2	1	no	—
469	C₂²⋊C₄×C₄₁	—	2	1	no	—
470	C₂²⋊C₄×C₄₁	—	2	1	no	—
471	C₂²⋊C₄×C₄₁	—	2	2	no	—
472	C₂²⋊C₄×C₄₁	—	2	2	no	—
473	C₂²⋊C₄×C₄₁	—	2	2	no	—
474	C₂²⋊C₄×C₄₁	—	2	2	no	—
475	C₂²⋊C₄×C₄₁	—	2	2	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	1	no	—
482	C₂²⋊C₄×C₄₁	—	2	2	no	—
483	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
484	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
485	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
486	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
487	C₄²×C₄₁	—	2	2	no	—
488	C₄²×C₄₁	—	2	2	no	—
489	C₄²×C₄₁	—	2	2	no	—
490	C₄²×C₄₁	—	2	1	no	—
491	C₄²×C₄₁	C₂×D₄	1	2	yes	—
492	C₄²×C₄₁	C₂×D₄	1	2	yes	—
493	C₄²×C₄₁	C₂⁴	1	2	yes	—
494	C₄²×C₄₁	C₂⁴	1	2	yes	—
495	C₂³×C₄₁	—	2	2	no	—
496	C₂³×C₄₁	—	2	1	no	—
497	C₂³×C₄₁	—	2	2	no	—
498	C₂³×C₄₁	—	2	1	no	—
499	C₂³×C₄₁	—	2	1	no	—
500	C₂³×C₄₁	—	4	1	no	—
501	C₂³×C₄₁	—	4	1	no	—
502	C₂³×C₄₁	—	4	2	no	—
503	C₂³×C₄₁	—	4	2	no	—
504	C₂³×C₄₁	—	8	1	no	—
505	C₂³×C₄₁	—	8	1	no	—
506	C₂³×C₄₁	—	8	1	no	—
507	C₂³×C₄₁	—	8	1	no	—
508	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
509	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
510	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
511	Q₈×C₄₁	—	2	2	no	—
512	Q₈×C₄₁	—	2	1	no	—
513	Q₈×C₄₁	—	2	2	no	—
514	Q₈×C₄₁	—	2	1	no	—
515	Q₈×C₄₁	—	2	2	no	—
516	Q₈×C₄₁	—	2	1	no	—
517	Q₈×C₄₁	—	2	1	no	—
518	Q₈×C₄₁	—	2	2	no	—
519	Q₈×C₄₁	—	2	1	no	—
520	Q₈×C₄₁	—	2	1	no	—
521	Q₈×C₄₁	—	4	2	no	—
522	Q₈×C₄₁	—	4	2	no	—
523	Q₈×C₄₁	—	4	2	no	—
524	Q₈×C₄₁	—	8	2	no	—
525	D₄×C₄₁	—	2	1	no	—
526	D₄×C₄₁	—	2	1	no	—
527	D₄×C₄₁	—	2	2	no	—
528	D₄×C₄₁	—	2	1	no	—
529	D₄×C₄₁	—	2	1	no	—
530	D₄×C₄₁	—	2	2	no	—
531	D₄×C₄₁	—	2	1	no	—
532	D₄×C₄₁	—	2	1	no	—
533	D₄×C₄₁	—	4	2	no	—
534	D₄×C₄₁	—	4	2	no	—
535	D₄×C₄₁	—	4	4	no	—
536	D₄×C₄₁	—	4	4	no	—
537	D₄×C₄₁	—	4	2	no	—
538	D₄×C₄₁	—	4	2	no	—
539	D₄×C₄₁	—	4	2	no	—
540	D₄×C₄₁	—	4	2	no	—
541	D₄×C₄₁	—	4	2	no	—
542	D₄×C₄₁	—	4	2	no	—
543	D₄×C₄₁	—	8	2	no	—
544	D₄×C₄₁	—	8	2	no	—
545	D₄×C₄₁	—	8	2	no	—
546	D₄×C₄₁	—	8	2	no	—
547	D₄×C₄₁	—	8	1	no	—
548	C₂×C₄×C₄₁	—	2	2	no	—
549	C₂×C₄×C₄₁	—	2	2	no	—
550	C₂×C₄×C₄₁	—	2	2	no	—
551	C₂×C₄×C₄₁	—	2	1	no	—
552	C₂×C₄×C₄₁	—	2	1	no	—
553	C₂×C₄×C₄₁	—	2	1	no	—
554	C₂×C₄×C₄₁	—	2	1	no	—
555	C₂×C₄×C₄₁	—	2	1	no	—
556	C₂×C₄×C₄₁	—	2	1	no	—
557	C₂×C₄×C₄₁	—	2	2	no	—
558	C₂×C₄×C₄₁	—	2	1	no	—
559	C₂×C₄×C₄₁	—	2	2	no	—
560	C₂×C₄×C₄₁	—	2	2	no	—
561	C₂×C₄×C₄₁	—	2	1	no	—
562	C₂×C₄×C₄₁	—	2	1	no	—
563	C₂×C₄×C₄₁	—	4	2	no	—
564	C₂×C₄×C₄₁	—	4	2	no	—
565	C₂×C₄×C₄₁	—	4	4	no	—
566	C₂×C₄×C₄₁	—	4	2	no	—
567	C₂×C₄×C₄₁	—	4	2	no	—
568	C₂×C₄×C₄₁	—	4	4	no	—
569	C₂×C₄×C₄₁	—	4	2	no	—
570	C₂×C₄×C₄₁	—	4	2	no	—
571	C₂×C₄×C₄₁	—	4	2	no	—
572	C₂×C₄×C₄₁	—	4	2	no	—
573	C₂×C₄×C₄₁	—	4	2	no	—
574	C₂×C₄×C₄₁	—	4	2	no	—
575	C₂×C₄×C₄₁	—	8	2	no	—
576	C₂×C₄×C₄₁	—	8	1	no	—
577	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
578	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
579	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
581	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
582	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
583	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
584	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
585	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
586	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
587	C₈×C₄₁	—	2	1	no	—
588	C₈×C₄₁	—	2	1	no	—
589	C₈×C₄₁	—	2	1	no	—
590	C₈×C₄₁	—	2	1	no	—
591	C₈×C₄₁	—	2	2	no	—
592	C₈×C₄₁	—	2	2	no	—
593	#60816	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
594	C₂²×C₄₁	—	2	1	no	—
595	C₂²×C₄₁	—	2	1	no	—
596	C₂²×C₄₁	—	2	1	no	—
597	C₂²×C₄₁	—	2	1	no	—
598	C₂²×C₄₁	—	2	1	no	—
599	C₂²×C₄₁	—	2	1	no	—
600	C₂²×C₄₁	—	2	1	no	—
601	C₂²×C₄₁	—	2	1	no	—
602	C₂²×C₄₁	—	4	1	no	—
603	C₂²×C₄₁	—	4	2	no	—
604	C₂²×C₄₁	—	4	1	no	—
605	C₂²×C₄₁	—	4	1	no	—
606	C₂²×C₄₁	—	4	1	no	—
607	C₂²×C₄₁	—	4	2	no	—
608	C₂²×C₄₁	—	4	1	no	—
609	C₂²×C₄₁	—	4	1	no	—
610	C₂²×C₄₁	—	4	2	no	—
611	C₂²×C₄₁	—	4	1	no	—
612	C₂²×C₄₁	—	4	1	no	—
613	C₂²×C₄₁	—	4	1	no	—
614	C₂²×C₄₁	—	8	2	no	—
615	C₂²×C₄₁	—	8	4	no	—
616	C₂²×C₄₁	—	8	4	no	—
617	C₂²×C₄₁	#535	1	2	yes	—
618	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
619	C₄×C₄₁	—	2	2	no	—
620	C₄×C₄₁	—	2	2	no	—
621	C₄×C₄₁	—	2	2	no	—
622	C₄×C₄₁	—	2	2	no	—
623	C₄×C₄₁	—	2	1	no	—
624	C₄×C₄₁	—	2	1	no	—
625	C₄×C₄₁	—	4	2	no	—
626	C₄×C₄₁	—	4	1	no	—
627	C₄×C₄₁	—	4	1	no	—
628	C₄×C₄₁	—	4	2	no	—
629	C₄×C₄₁	—	4	1	no	—
630	C₄×C₄₁	—	4	1	no	—
631	C₄×C₄₁	—	4	1	no	—
632	C₄×C₄₁	—	4	2	no	—
633	C₄×C₄₁	#535	1	2	yes	—
634	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
635	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
636	#3495	C₂×C₄₁	1	1	yes	characteristic, complemented
637	#3449	C₂×C₄₁	1	1	yes	characteristic, complemented
638	#3225	C₂×C₄₁	1	2	yes	complemented
639	#3224	C₂×C₄₁	1	2	yes	complemented
640	#3223	C₂×C₄₁	1	2	yes	complemented
641	#3222	C₂×C₄₁	1	2	yes	complemented
642	#3219	C₂×C₄₁	1	2	yes	complemented
643	#3216	C₂×C₄₁	1	2	yes	complemented
644	#3212	C₂×C₄₁	1	2	yes	complemented
645	#3210	C₂×C₄₁	1	2	yes	complemented
646	#3156	C₂×C₄₁	1	1	yes	characteristic, complemented
647	#3154	C₂×C₄₁	1	1	yes	characteristic, complemented
648	#3137	C₂×C₄₁	1	1	yes	characteristic, complemented
649	#3136	C₂×C₄₁	1	1	yes	characteristic, complemented
650	#3046	C₂×C₄₁	1	1	yes	characteristic, complemented
651	#3045	C₂×C₄₁	1	1	yes	characteristic, complemented
652	#3044	C₂×C₄₁	1	1	yes	characteristic, complemented
653	#3043	C₂×C₄₁	1	1	yes	characteristic, complemented
654	#3007	C₂×C₄₁	1	1	yes	characteristic, complemented
655	#3005	C₂×C₄₁	1	1	yes	characteristic, complemented
656	#3002	C₂×C₄₁	1	1	yes	characteristic, complemented
657	C₂×#452	C₂×C₄₁	1	1	yes	characteristic, complemented
658	#2924	C₂×C₄₁	1	1	yes	characteristic, complemented
659	C₂×C₄₁	—	2	2	no	—
660	C₂×C₄₁	—	4	1	no	—
661	C₂×C₄₁	—	4	1	no	—
662	C₂×C₄₁	—	8	1	no	—
663	C₂×C₄₁	—	8	2	no	—
664	C₂×C₄₁	—	8	1	no	—
665	C₂×C₄₁	—	8	1	no	—
666	C₂×C₄₁	C₂×#535	1	1	yes	characteristic
667	C₂×C₄₁	#3584	1	1	yes	characteristic
668	C₂×C₄₁	#3586	1	1	yes	characteristic
669	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
670	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
671	C₂×#137	C₂²×C₄₁	1	1	yes	characteristic
672	C₂×#137	C₂²×C₄₁	1	1	yes	characteristic
673	C₂×#137	C₂²×C₄₁	1	1	yes	characteristic, complemented
674	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	1	yes	characteristic, complemented
675	C₂×#135	C₂²×C₄₁	1	1	yes	characteristic
676	C₂×#135	C₂²×C₄₁	1	1	yes	characteristic
677	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
678	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
679	#556	—	2	1	no	—
680	#554	—	2	1	no	—
681	#552	—	2	2	no	—
682	#552	—	2	1	no	—
683	#552	—	2	1	no	—
684	#551	—	2	2	no	—
685	#544	C₂²×C₄₁	1	1	yes	characteristic, complemented
686	#542	C₂²×C₄₁	1	2	yes	complemented
687	#541	C₂²×C₄₁	1	2	yes	complemented
688	#537	—	2	1	no	—
689	#537	—	2	1	no	—
690	#536	C₂²×C₄₁	1	1	yes	characteristic
691	#536	C₂²×C₄₁	1	2	yes	—
692	#536	C₂²×C₄₁	1	1	yes	characteristic
693	#536	C₂²×C₄₁	1	1	yes	characteristic, complemented
694	#535	C₂²×C₄₁	1	1	yes	characteristic
695	#535	C₂²×C₄₁	1	2	yes	—
696	#535	C₂²×C₄₁	1	1	yes	characteristic
697	#534	—	2	2	no	—
698	#533	C₂²×C₄₁	1	2	yes	complemented
699	#532	C₂²×C₄₁	1	2	yes	—
700	#532	C₂²×C₄₁	1	2	yes	—
701	#529	C₂²×C₄₁	1	2	yes	complemented
702	#525	—	2	1	no	—
703	#525	—	2	2	no	—
704	#525	—	2	1	no	—
705	#525	C₂²×C₄₁	1	1	yes	characteristic
706	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
707	#520	C₂²×C₄₁	1	1	yes	characteristic, complemented
708	#519	C₂²×C₄₁	1	1	yes	characteristic, complemented
709	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
710	#497	C₂²×C₄₁	1	2	yes	complemented
711	#497	C₂²×C₄₁	1	2	yes	complemented
712	#497	C₂²×C₄₁	1	2	yes	complemented
713	#496	C₂²×C₄₁	1	2	yes	complemented
714	#495	C₂²×C₄₁	1	2	yes	complemented
715	#495	C₂²×C₄₁	1	2	yes	complemented
716	#494	C₂²×C₄₁	1	2	yes	complemented
717	#492	C₂²×C₄₁	1	2	yes	complemented
718	#491	C₂²×C₄₁	1	2	yes	complemented
719	#490	C₂²×C₄₁	1	2	yes	complemented
720	#489	C₂²×C₄₁	1	2	yes	complemented
721	#489	C₂²×C₄₁	1	2	yes	complemented
722	#488	C₂²×C₄₁	1	2	yes	complemented
723	#488	C₂²×C₄₁	1	2	yes	complemented
724	#487	C₂²×C₄₁	1	2	yes	complemented
725	#486	C₂²×C₄₁	1	2	yes	complemented
726	#464	C₂²×C₄₁	1	2	yes	complemented
727	#464	C₂²×C₄₁	1	2	yes	complemented
728	#464	C₂²×C₄₁	1	2	yes	complemented
729	#464	C₂²×C₄₁	1	2	yes	complemented
730	#464	C₂²×C₄₁	1	2	yes	complemented
731	#464	C₂²×C₄₁	1	2	yes	complemented
732	#463	C₂²×C₄₁	1	2	yes	complemented
733	#463	C₂²×C₄₁	1	2	yes	complemented
734	#462	C₂²×C₄₁	1	2	yes	complemented
735	#462	C₂²×C₄₁	1	2	yes	complemented
736	#462	C₂²×C₄₁	1	2	yes	complemented
737	#461	C₂²×C₄₁	1	2	yes	complemented
738	#460	C₂²×C₄₁	1	2	yes	complemented
739	#460	C₂²×C₄₁	1	2	yes	complemented
740	#460	C₂²×C₄₁	1	2	yes	complemented
741	#459	C₂²×C₄₁	1	2	yes	complemented
742	#452	C₂²×C₄₁	1	2	yes	—
743	#452	C₂²×C₄₁	1	2	yes	—
744	#452	C₂²×C₄₁	1	2	yes	—
745	#452	C₂²×C₄₁	1	1	yes	characteristic, complemented
746	#452	C₂²×C₄₁	1	2	yes	complemented
747	#452	C₂²×C₄₁	1	2	yes	complemented
748	#452	C₂²×C₄₁	1	2	yes	complemented
749	#452	C₂²×C₄₁	1	2	yes	complemented
750	#452	C₂²×C₄₁	1	1	yes	characteristic, complemented
751	#452	C₂²×C₄₁	1	2	yes	complemented
752	#451	C₂²×C₄₁	1	1	yes	characteristic, complemented
753	#451	C₂²×C₄₁	1	2	yes	complemented
754	#450	C₂²×C₄₁	1	1	yes	characteristic, complemented
755	#450	C₂²×C₄₁	1	2	yes	complemented
756	#449	C₂²×C₄₁	1	2	yes	—
757	#449	C₂²×C₄₁	1	1	yes	characteristic, complemented
758	#449	C₂²×C₄₁	1	2	yes	complemented
759	#449	C₂²×C₄₁	1	1	yes	characteristic, complemented
760	#448	C₂²×C₄₁	1	1	yes	characteristic, complemented
761	#447	C₂²×C₄₁	1	1	yes	characteristic, complemented
762	#433	C₂²×C₄₁	1	2	yes	complemented
763	#433	C₂²×C₄₁	1	2	yes	complemented
764	#432	C₂²×C₄₁	1	2	yes	complemented
765	#431	C₂²×C₄₁	1	2	yes	complemented
766	#424	C₂²×C₄₁	1	1	yes	characteristic, complemented
767	#424	C₂²×C₄₁	1	1	yes	characteristic, complemented
768	#419	C₂²×C₄₁	1	1	yes	characteristic, complemented
769	#418	C₂²×C₄₁	1	1	yes	characteristic, complemented
770	#417	C₂²×C₄₁	1	1	yes	characteristic
771	#417	C₂²×C₄₁	1	1	yes	characteristic
772	#416	C₂²×C₄₁	1	1	yes	characteristic
773	#416	C₂²×C₄₁	1	1	yes	characteristic
774	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic, complemented
775	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic, complemented
776	#407	C₂²×C₄₁	1	1	yes	characteristic
777	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
778	#405	C₂²×C₄₁	1	1	yes	characteristic, complemented
779	#405	C₂²×C₄₁	1	1	yes	characteristic, complemented
780	C₄₁	#60816	1	1	yes	characteristic, direct product factor, Sylow
781	C₂×#41	—	2	1	no	—
782	C₂×#41	—	2	1	no	—
783	C₂×#41	—	2	1	no	—
784	C₂×#41	—	2	1	no	—
785	C₂×#41	—	4	2	no	—
786	C₂×#41	—	4	2	no	—
787	C₂×#41	—	4	2	no	—
788	C₂×#41	—	4	2	no	—
789	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
790	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
791	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
792	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
793	C₂×#41	C₂³×C₄₁	1	2	yes	—
794	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
795	C₂×#41	C₂³×C₄₁	1	2	yes	—
796	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
797	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
798	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
799	C₂²×D₄	—	2	1	no	—
800	C₂²×D₄	—	2	1	no	—
801	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
802	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
803	C₂³×C₄	—	2	1	no	—
804	C₂³×C₄	—	2	1	no	—
805	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
806	#137	—	4	2	no	—
807	#137	—	4	2	no	—
808	#137	—	4	2	no	—
809	AGL(1,ℤ/8)	—	4	2	no	—
810	#135	—	4	2	no	—
811	#135	—	4	2	no	—
812	C₂×Q₁₆	—	4	2	no	—
813	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
814	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
815	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
816	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
817	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
818	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
819	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
820	C₂×SD₁₆	—	4	2	no	—
821	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
822	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
823	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
824	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
825	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
826	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
827	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
828	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
829	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
830	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
831	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
832	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
833	C₂×D₈	C₂³×C₄₁	1	2	yes	—
834	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
835	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
836	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
837	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
838	C₄⋊Q₈	—	2	1	no	—
839	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
840	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
841	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
842	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
843	#127	C₂³×C₄₁	1	2	yes	—
844	#127	C₂³×C₄₁	1	2	yes	—
845	#126	—	2	2	no	—
846	#126	—	2	2	no	—
847	#126	—	2	2	no	—
848	#126	—	2	2	no	—
849	#125	—	2	2	no	—
850	#125	—	2	2	no	—
851	#125	—	2	1	no	—
852	#125	—	2	2	no	—
853	#125	C₂³×C₄₁	1	2	yes	—
854	#124	—	2	2	no	—
855	#124	C₂³×C₄₁	1	2	yes	—
856	#124	C₂³×C₄₁	1	2	yes	—
857	#124	C₂³×C₄₁	1	2	yes	—
858	#124	C₂³×C₄₁	1	2	yes	—
859	#124	C₂³×C₄₁	1	2	yes	—
860	#123	—	2	1	no	—
861	#123	—	2	2	no	—
862	#123	—	2	2	no	—
863	#123	—	2	2	no	—
864	#123	—	2	2	no	—
865	#123	—	2	2	no	—
866	#123	—	2	2	no	—
867	#123	—	2	2	no	—
868	C₂²⋊Q₈	—	2	1	no	—
869	C₂²⋊Q₈	—	2	1	no	—
870	C₂²⋊Q₈	—	2	2	no	—
871	C₂²⋊Q₈	—	2	1	no	—
872	C₂²⋊Q₈	—	2	1	no	—
873	C₂²⋊Q₈	—	2	1	no	—
874	C₂²⋊Q₈	—	2	2	no	—
875	C₂²⋊Q₈	—	2	1	no	—
876	C₂²⋊Q₈	—	2	2	no	—
877	C₂²⋊Q₈	—	2	1	no	—
878	C₂²⋊Q₈	—	2	1	no	—
879	C₂²⋊Q₈	—	2	2	no	—
880	C₂²⋊Q₈	—	2	2	no	—
881	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
882	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
883	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
884	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
885	#121	—	2	2	no	—
886	#121	—	2	2	no	—
887	#121	—	2	2	no	—
888	#121	—	2	2	no	—
889	#121	—	2	1	no	—
890	#121	—	2	1	no	—
891	#121	—	2	1	no	—
892	#121	—	2	2	no	—
893	#121	—	2	1	no	—
894	#121	—	2	2	no	—
895	#121	C₂³×C₄₁	1	1	yes	characteristic
896	#121	C₂³×C₄₁	1	1	yes	characteristic
897	#120	—	2	1	no	—
898	#120	—	2	2	no	—
899	#120	—	2	2	no	—
900	#120	—	2	2	no	—
901	#120	—	2	2	no	—
902	C₄×Q₈	—	2	1	no	—
903	C₄×Q₈	—	2	1	no	—
904	C₄×Q₈	—	2	2	no	—
905	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
906	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
907	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
908	C₄×D₄	—	2	1	no	—
909	C₄×D₄	—	2	1	no	—
910	C₄×D₄	—	2	2	no	—
911	C₄×D₄	—	2	2	no	—
912	C₄×D₄	—	2	2	no	—
913	C₄×D₄	—	2	2	no	—
914	C₄×D₄	—	2	2	no	—
915	C₄×D₄	—	2	2	no	—
916	C₄×D₄	C₂³×C₄₁	1	2	yes	—
917	#117	—	2	2	no	—
918	#117	—	2	1	no	—
919	#117	—	2	2	no	—
920	#117	—	2	2	no	—
921	#117	D₄×C₄₁	1	1	yes	characteristic
922	#117	D₄×C₄₁	1	2	yes	—
923	#117	D₄×C₄₁	1	1	yes	characteristic
924	#117	C₂³×C₄₁	1	1	yes	characteristic
925	#117	C₂³×C₄₁	1	1	yes	characteristic
926	#117	C₂³×C₄₁	1	1	yes	characteristic
927	#117	C₂³×C₄₁	1	2	yes	—
928	C₂×C₄⋊C₄	—	2	1	no	—
929	C₂×C₄⋊C₄	—	2	1	no	—
930	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
931	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
932	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
933	C₂×C₂²⋊C₄	—	2	1	no	—
934	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
935	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
936	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
937	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
938	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
939	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
940	#103	C₂³×C₄₁	1	2	yes	—
941	#103	C₂³×C₄₁	1	2	yes	—
942	#103	C₂³×C₄₁	1	1	yes	characteristic
943	#103	C₂³×C₄₁	1	1	yes	characteristic
944	#103	C₂³×C₄₁	1	1	yes	characteristic
945	#103	C₂³×C₄₁	1	1	yes	characteristic
946	#103	C₂³×C₄₁	1	2	yes	—
947	#103	C₂³×C₄₁	1	2	yes	—
948	#103	C₂³×C₄₁	1	2	yes	—
949	#103	C₂³×C₄₁	1	2	yes	—
950	#102	C₂³×C₄₁	1	2	yes	—
951	#102	C₂³×C₄₁	1	2	yes	—
952	#102	C₂³×C₄₁	1	1	yes	characteristic
953	#102	C₂³×C₄₁	1	1	yes	characteristic
954	#102	C₂³×C₄₁	1	1	yes	characteristic
955	#102	C₂³×C₄₁	1	1	yes	characteristic
956	#102	C₂³×C₄₁	1	2	yes	—
957	#102	C₂³×C₄₁	1	2	yes	—
958	#102	C₂³×C₄₁	1	2	yes	—
959	#102	C₂³×C₄₁	1	2	yes	—
960	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
961	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
962	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
963	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
964	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
965	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
966	#97	C₂³×C₄₁	1	2	yes	—
967	#97	C₂³×C₄₁	1	2	yes	—
968	C₄×C₈	C₂³×C₄₁	1	2	yes	—
969	C₄×C₈	C₂³×C₄₁	1	2	yes	—
970	C₂⁴	—	2	1	no	—
971	C₂⁴	—	2	1	no	—
972	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
973	#41	—	2	2	no	—
974	#41	—	2	2	no	—
975	#41	—	2	2	no	—
976	#41	—	2	2	no	—
977	#41	—	2	2	no	—
978	#41	—	2	2	no	—
979	#41	—	4	2	no	—
980	#41	—	4	2	no	—
981	#41	—	4	2	no	—
982	#41	—	4	1	no	—
983	#41	—	4	1	no	—
984	#41	—	4	2	no	—
985	#41	—	4	1	no	—
986	#41	—	4	1	no	—
987	#41	—	4	4	no	—
988	#41	—	4	4	no	—
989	#41	—	4	4	no	—
990	#41	—	4	4	no	—
991	C₂×Q₈	—	2	1	no	—
992	C₂×Q₈	—	2	1	no	—
993	C₂×Q₈	—	2	1	no	—
994	C₂×Q₈	—	2	2	no	—
995	C₂×Q₈	—	2	2	no	—
996	C₂×Q₈	—	2	2	no	—
997	C₂×Q₈	—	2	2	no	—
998	C₂×Q₈	—	2	2	no	—
999	C₂×Q₈	—	4	1	no	—
1000	C₂×Q₈	—	4	1	no	—
1001	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
1002	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
1003	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
1004	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
1005	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
1006	C₂×D₄	—	2	1	no	—
1007	C₂×D₄	—	2	1	no	—
1008	C₂×D₄	—	2	2	no	—
1009	C₂×D₄	—	2	1	no	—
1010	C₂×D₄	—	2	1	no	—
1011	C₂×D₄	—	2	1	no	—
1012	C₂×D₄	—	2	2	no	—
1013	C₂×D₄	—	2	1	no	—
1014	C₂×D₄	—	2	1	no	—
1015	C₂×D₄	—	2	1	no	—
1016	C₂×D₄	—	2	1	no	—
1017	C₂×D₄	—	2	2	no	—
1018	C₂×D₄	—	2	2	no	—
1019	C₂×D₄	—	2	2	no	—
1020	C₂×D₄	—	2	2	no	—
1021	C₂×D₄	—	2	2	no	—
1022	C₂×D₄	—	2	2	no	—
1023	C₂×D₄	—	4	1	no	—
1024	C₂×D₄	—	4	1	no	—
1025	C₂×D₄	—	4	4	no	—
1026	C₂×D₄	—	4	4	no	—
1027	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
1028	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
1029	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
1030	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
1031	C₂²×C₄	—	2	2	no	—
1032	C₂²×C₄	—	2	2	no	—
1033	C₂²×C₄	—	2	1	no	—
1034	C₂²×C₄	—	2	1	no	—
1035	C₂²×C₄	—	2	1	no	—
1036	C₂²×C₄	—	2	1	no	—
1037	C₂²×C₄	—	2	1	no	—
1038	C₂²×C₄	—	2	1	no	—
1039	C₂²×C₄	—	2	2	no	—
1040	C₂²×C₄	—	2	1	no	—
1041	C₂²×C₄	—	2	2	no	—
1042	C₂²×C₄	—	2	1	no	—
1043	C₂²×C₄	—	2	1	no	—
1044	C₂²×C₄	—	2	2	no	—
1045	C₂²×C₄	—	4	4	no	—
1046	C₂²×C₄	—	4	4	no	—
1047	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1048	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1049	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1050	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
1051	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
1052	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1053	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1054	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1055	Q₁₆	—	4	2	no	—
1056	Q₁₆	—	4	2	no	—
1057	Q₁₆	—	4	1	no	—
1058	Q₁₆	—	4	1	no	—
1059	Q₁₆	—	4	2	no	—
1060	Q₁₆	—	4	2	no	—
1061	Q₁₆	—	4	2	no	—
1062	SD₁₆	—	4	2	no	—
1063	SD₁₆	—	4	2	no	—
1064	SD₁₆	—	4	1	no	—
1065	SD₁₆	—	4	1	no	—
1066	SD₁₆	—	4	1	no	—
1067	SD₁₆	—	4	1	no	—
1068	SD₁₆	—	4	2	no	—
1069	SD₁₆	—	4	2	no	—
1070	SD₁₆	—	4	2	no	—
1071	SD₁₆	—	4	2	no	—
1072	D₈	—	4	1	no	—
1073	D₈	—	4	1	no	—
1074	D₈	—	4	2	no	—
1075	M₁₆	—	2	2	no	—
1076	M₁₆	—	2	2	no	—
1077	C₂×C₈	—	2	2	no	—
1078	C₂×C₈	—	2	2	no	—
1079	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1080	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1081	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1082	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1083	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1084	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1085	C₄⋊C₄	—	2	1	no	—
1086	C₄⋊C₄	—	2	2	no	—
1087	C₄⋊C₄	—	2	2	no	—
1088	C₄⋊C₄	—	2	2	no	—
1089	C₄⋊C₄	—	2	2	no	—
1090	C₄⋊C₄	—	2	2	no	—
1091	C₄⋊C₄	—	2	2	no	—
1092	C₄⋊C₄	—	2	2	no	—
1093	C₄⋊C₄	—	2	2	no	—
1094	C₄⋊C₄	—	2	1	no	—
1095	C₄⋊C₄	—	2	2	no	—
1096	C₄⋊C₄	—	2	2	no	—
1097	C₄⋊C₄	—	2	2	no	—
1098	C₄⋊C₄	—	2	2	no	—
1099	C₄⋊C₄	—	2	2	no	—
1100	C₄⋊C₄	—	2	1	no	—
1101	C₄⋊C₄	—	2	2	no	—
1102	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1103	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1104	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1105	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1106	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1107	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1108	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
1109	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1110	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1111	C₂²⋊C₄	—	2	2	no	—
1112	C₂²⋊C₄	—	2	2	no	—
1113	C₂²⋊C₄	—	2	1	no	—
1114	C₂²⋊C₄	—	2	1	no	—
1115	C₂²⋊C₄	—	2	1	no	—
1116	C₂²⋊C₄	—	2	1	no	—
1117	C₂²⋊C₄	—	2	2	no	—
1118	C₂²⋊C₄	—	2	2	no	—
1119	C₂²⋊C₄	—	2	2	no	—
1120	C₂²⋊C₄	—	2	2	no	—
1121	C₂²⋊C₄	—	2	2	no	—
1122	C₂²⋊C₄	—	2	2	no	—
1123	C₂²⋊C₄	—	2	2	no	—
1124	C₂²⋊C₄	—	2	2	no	—
1125	C₂²⋊C₄	—	2	2	no	—
1126	C₂²⋊C₄	—	2	2	no	—
1127	C₂²⋊C₄	—	2	1	no	—
1128	C₂²⋊C₄	—	2	2	no	—
1129	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1130	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1131	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1132	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1133	C₄²	—	2	2	no	—
1134	C₄²	—	2	2	no	—
1135	C₄²	—	2	2	no	—
1136	C₄²	—	2	1	no	—
1137	C₄²	C₂×D₄×C₄₁	1	2	yes	—
1138	C₄²	C₂×D₄×C₄₁	1	2	yes	—
1139	C₄²	C₂⁴×C₄₁	1	2	yes	—
1140	C₄²	C₂⁴×C₄₁	1	2	yes	—
1141	C₂³	—	2	2	no	—
1142	C₂³	—	2	1	no	—
1143	C₂³	—	2	2	no	—
1144	C₂³	—	2	1	no	—
1145	C₂³	—	2	1	no	—
1146	C₂³	—	4	1	no	—
1147	C₂³	—	4	1	no	—
1148	C₂³	—	4	2	no	—
1149	C₂³	—	4	2	no	—
1150	C₂³	—	8	1	no	—
1151	C₂³	—	8	1	no	—
1152	C₂³	—	8	1	no	—
1153	C₂³	—	8	1	no	—
1154	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1155	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1156	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1157	Q₈	—	2	2	no	—
1158	Q₈	—	2	1	no	—
1159	Q₈	—	2	2	no	—
1160	Q₈	—	2	1	no	—
1161	Q₈	—	2	2	no	—
1162	Q₈	—	2	1	no	—
1163	Q₈	—	2	1	no	—
1164	Q₈	—	2	2	no	—
1165	Q₈	—	2	1	no	—
1166	Q₈	—	2	1	no	—
1167	Q₈	—	4	2	no	—
1168	Q₈	—	4	2	no	—
1169	Q₈	—	4	2	no	—
1170	Q₈	—	8	2	no	—
1171	D₄	—	2	1	no	—
1172	D₄	—	2	1	no	—
1173	D₄	—	2	2	no	—
1174	D₄	—	2	1	no	—
1175	D₄	—	2	1	no	—
1176	D₄	—	2	2	no	—
1177	D₄	—	2	1	no	—
1178	D₄	—	2	1	no	—
1179	D₄	—	4	2	no	—
1180	D₄	—	4	4	no	—
1181	D₄	—	4	4	no	—
1182	D₄	—	4	2	no	—
1183	D₄	—	4	2	no	—
1184	D₄	—	4	2	no	—
1185	D₄	—	4	2	no	—
1186	D₄	—	4	2	no	—
1187	D₄	—	4	2	no	—
1188	D₄	—	4	2	no	—
1189	D₄	—	8	2	no	—
1190	D₄	—	8	2	no	—
1191	D₄	—	8	2	no	—
1192	D₄	—	8	2	no	—
1193	D₄	—	8	1	no	—
1194	C₂×C₄	—	2	2	no	—
1195	C₂×C₄	—	2	2	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	2	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	2	no	—
1206	C₂×C₄	—	2	2	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	4	2	no	—
1210	C₂×C₄	—	4	2	no	—
1211	C₂×C₄	—	4	4	no	—
1212	C₂×C₄	—	4	2	no	—
1213	C₂×C₄	—	4	2	no	—
1214	C₂×C₄	—	4	4	no	—
1215	C₂×C₄	—	4	2	no	—
1216	C₂×C₄	—	4	2	no	—
1217	C₂×C₄	—	4	2	no	—
1218	C₂×C₄	—	4	2	no	—
1219	C₂×C₄	—	4	2	no	—
1220	C₂×C₄	—	4	2	no	—
1221	C₂×C₄	—	8	2	no	—
1222	C₂×C₄	—	8	1	no	—
1223	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1224	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1225	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1226	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1227	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1228	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1229	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1230	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
1231	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
1232	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
1233	C₈	—	2	1	no	—
1234	C₈	—	2	1	no	—
1235	C₈	—	2	1	no	—
1236	C₈	—	2	1	no	—
1237	C₈	—	2	2	no	—
1238	C₈	—	2	2	no	—
1239	C₂²	—	2	1	no	—
1240	C₂²	—	2	1	no	—
1241	C₂²	—	2	1	no	—
1242	C₂²	—	2	1	no	—
1243	C₂²	—	2	1	no	—
1244	C₂²	—	2	1	no	—
1245	C₂²	—	2	1	no	—
1246	C₂²	—	2	1	no	—
1247	C₂²	—	4	1	no	—
1248	C₂²	—	4	2	no	—
1249	C₂²	—	4	1	no	—
1250	C₂²	—	4	1	no	—
1251	C₂²	—	4	1	no	—
1252	C₂²	—	4	2	no	—
1253	C₂²	—	4	1	no	—
1254	C₂²	—	4	1	no	—
1255	C₂²	—	4	2	no	—
1256	C₂²	—	4	1	no	—
1257	C₂²	—	4	1	no	—
1258	C₂²	—	4	1	no	—
1259	C₂²	—	8	2	no	—
1260	C₂²	—	8	4	no	—
1261	C₂²	—	8	4	no	—
1262	C₂²	C₄₁×#535	1	2	yes	—
1263	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
1264	C₄	—	2	2	no	—
1265	C₄	—	2	2	no	—
1266	C₄	—	2	2	no	—
1267	C₄	—	2	2	no	—
1268	C₄	—	2	1	no	—
1269	C₄	—	2	1	no	—
1270	C₄	—	4	2	no	—
1271	C₄	—	4	1	no	—
1272	C₄	—	4	1	no	—
1273	C₄	—	4	2	no	—
1274	C₄	—	4	1	no	—
1275	C₄	—	4	1	no	—
1276	C₄	—	4	1	no	—
1277	C₄	—	4	2	no	—
1278	C₄	C₄₁×#535	1	2	yes	—
1279	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1280	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1281	C₂	—	2	2	no	—
1282	C₂	—	4	1	no	—
1283	C₂	—	4	1	no	—
1284	C₂	—	8	2	no	—
1285	C₂	—	8	1	no	—
1286	C₂	—	8	1	no	—
1287	C₂	—	8	1	no	—
1288	C₂	C₂×C₄₁×#535	1	1	yes	characteristic
1289	C₂	C₄₁×#3584	1	1	yes	characteristic
1290	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 ◁ C₂×#117×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3495	C₂	semidirect
2. C₄₁×#3449	C₂	semidirect
3. C₄₁×#3225	C₂	semidirect
4. C₄₁×#3224	C₂	semidirect
5. C₄₁×#3223	C₂	semidirect
6. C₄₁×#3222	C₂	semidirect
7. C₄₁×#3219	C₂	semidirect
8. C₄₁×#3216	C₂	semidirect
9. C₄₁×#3212	C₂	semidirect
10. C₄₁×#3210	C₂	semidirect
11. C₄₁×#3156	C₂	semidirect
12. C₄₁×#3154	C₂	semidirect
13. C₄₁×#3137	C₂	semidirect
14. C₄₁×#3136	C₂	semidirect
15. C₄₁×#3046	C₂	semidirect
16. C₄₁×#3045	C₂	semidirect
17. C₄₁×#3044	C₂	semidirect
18. C₄₁×#3043	C₂	semidirect
19. C₄₁×#3007	C₂	semidirect
20. C₄₁×#3005	C₂	semidirect
21. C₄₁×#3002	C₂	semidirect
22. C₂×C₄₁×#452	C₂	semidirect
23. C₄₁×#2924	C₂	semidirect
28. C₂×#137×C₄₁	C₂²	semidirect
29. C₂×AGL(1,ℤ/8)×C₄₁	C₂²	semidirect
32. C₂²×Q₁₆×C₄₁	C₂²	semidirect
33. C₂²×SD₁₆×C₄₁	C₂²	semidirect
40. C₄₁×#544	C₂²	semidirect
41. C₄₁×#542	C₂²	semidirect
42. C₄₁×#541	C₂²	semidirect
48. C₄₁×#536	C₂²	semidirect
53. C₄₁×#533	C₂²	semidirect
56. C₄₁×#529	C₂²	semidirect
62. C₄₁×#520	C₂²	semidirect
63. C₄₁×#519	C₂²	semidirect
65. C₄₁×#497	C₂²	semidirect
66. C₄₁×#497	C₂²	semidirect
67. C₄₁×#497	C₂²	semidirect
68. C₄₁×#496	C₂²	semidirect
69. C₄₁×#495	C₂²	semidirect
70. C₄₁×#495	C₂²	semidirect
71. C₄₁×#494	C₂²	semidirect
72. C₄₁×#492	C₂²	semidirect
73. C₄₁×#491	C₂²	semidirect
74. C₄₁×#490	C₂²	semidirect
75. C₄₁×#489	C₂²	semidirect
76. C₄₁×#489	C₂²	semidirect
77. C₄₁×#488	C₂²	semidirect
78. C₄₁×#488	C₂²	semidirect
79. C₄₁×#487	C₂²	semidirect
80. C₄₁×#486	C₂²	semidirect
81. C₄₁×#464	C₂²	semidirect
82. C₄₁×#464	C₂²	semidirect
83. C₄₁×#464	C₂²	semidirect
84. C₄₁×#464	C₂²	semidirect
85. C₄₁×#464	C₂²	semidirect
86. C₄₁×#464	C₂²	semidirect
87. C₄₁×#463	C₂²	semidirect
88. C₄₁×#463	C₂²	semidirect
89. C₄₁×#462	C₂²	semidirect
90. C₄₁×#462	C₂²	semidirect
91. C₄₁×#462	C₂²	semidirect
92. C₄₁×#461	C₂²	semidirect
93. C₄₁×#460	C₂²	semidirect
94. C₄₁×#460	C₂²	semidirect
95. C₄₁×#460	C₂²	semidirect
96. C₄₁×#459	C₂²	semidirect
100. C₄₁×#452	C₂²	semidirect
101. C₄₁×#452	C₂²	semidirect
102. C₄₁×#452	C₂²	semidirect
103. C₄₁×#452	C₂²	semidirect
104. C₄₁×#452	C₂²	semidirect
105. C₄₁×#452	C₂²	semidirect
106. C₄₁×#452	C₂²	semidirect
107. C₄₁×#451	C₂²	semidirect
108. C₄₁×#451	C₂²	semidirect
109. C₄₁×#450	C₂²	semidirect
110. C₄₁×#450	C₂²	semidirect
112. C₄₁×#449	C₂²	semidirect
113. C₄₁×#449	C₂²	semidirect
114. C₄₁×#449	C₂²	semidirect
115. C₄₁×#448	C₂²	semidirect
116. C₄₁×#447	C₂²	semidirect
117. C₄₁×#433	C₂²	semidirect
118. C₄₁×#433	C₂²	semidirect
119. C₄₁×#432	C₂²	semidirect
120. C₄₁×#431	C₂²	semidirect
121. C₄₁×#424	C₂²	semidirect
122. C₄₁×#424	C₂²	semidirect
123. C₄₁×#419	C₂²	semidirect
124. C₄₁×#418	C₂²	semidirect
129. C₂×#103×C₄₁	C₂²	semidirect
130. C₂×#102×C₄₁	C₂²	semidirect
133. C₄₁×#405	C₂²	semidirect
134. C₄₁×#405	C₂²	semidirect
593. #60816	C₄₁	direct (N × H)
636. #3495	C₂×C₄₁	semidirect
637. #3449	C₂×C₄₁	semidirect
638. #3225	C₂×C₄₁	semidirect
639. #3224	C₂×C₄₁	semidirect
640. #3223	C₂×C₄₁	semidirect
641. #3222	C₂×C₄₁	semidirect
642. #3219	C₂×C₄₁	semidirect
643. #3216	C₂×C₄₁	semidirect
644. #3212	C₂×C₄₁	semidirect
645. #3210	C₂×C₄₁	semidirect
646. #3156	C₂×C₄₁	semidirect
647. #3154	C₂×C₄₁	semidirect
648. #3137	C₂×C₄₁	semidirect
649. #3136	C₂×C₄₁	semidirect
650. #3046	C₂×C₄₁	semidirect
651. #3045	C₂×C₄₁	semidirect
652. #3044	C₂×C₄₁	semidirect
653. #3043	C₂×C₄₁	semidirect
654. #3007	C₂×C₄₁	semidirect
655. #3005	C₂×C₄₁	semidirect
656. #3002	C₂×C₄₁	semidirect
657. C₂×#452	C₂×C₄₁	semidirect
658. #2924	C₂×C₄₁	semidirect
673. C₂×#137	C₂²×C₄₁	semidirect
674. C₂×AGL(1,ℤ/8)	C₂²×C₄₁	semidirect
677. C₂²×Q₁₆	C₂²×C₄₁	semidirect
678. C₂²×SD₁₆	C₂²×C₄₁	semidirect
685. #544	C₂²×C₄₁	semidirect
686. #542	C₂²×C₄₁	semidirect
687. #541	C₂²×C₄₁	semidirect
693. #536	C₂²×C₄₁	semidirect
698. #533	C₂²×C₄₁	semidirect
701. #529	C₂²×C₄₁	semidirect
707. #520	C₂²×C₄₁	semidirect
708. #519	C₂²×C₄₁	semidirect
710. #497	C₂²×C₄₁	semidirect
711. #497	C₂²×C₄₁	semidirect
712. #497	C₂²×C₄₁	semidirect
713. #496	C₂²×C₄₁	semidirect
714. #495	C₂²×C₄₁	semidirect
715. #495	C₂²×C₄₁	semidirect
716. #494	C₂²×C₄₁	semidirect
717. #492	C₂²×C₄₁	semidirect
718. #491	C₂²×C₄₁	semidirect
719. #490	C₂²×C₄₁	semidirect
720. #489	C₂²×C₄₁	semidirect
721. #489	C₂²×C₄₁	semidirect
722. #488	C₂²×C₄₁	semidirect
723. #488	C₂²×C₄₁	semidirect
724. #487	C₂²×C₄₁	semidirect
725. #486	C₂²×C₄₁	semidirect
726. #464	C₂²×C₄₁	semidirect
727. #464	C₂²×C₄₁	semidirect
728. #464	C₂²×C₄₁	semidirect
729. #464	C₂²×C₄₁	semidirect
730. #464	C₂²×C₄₁	semidirect
731. #464	C₂²×C₄₁	semidirect
732. #463	C₂²×C₄₁	semidirect
733. #463	C₂²×C₄₁	semidirect
734. #462	C₂²×C₄₁	semidirect
735. #462	C₂²×C₄₁	semidirect
736. #462	C₂²×C₄₁	semidirect
737. #461	C₂²×C₄₁	semidirect
738. #460	C₂²×C₄₁	semidirect
739. #460	C₂²×C₄₁	semidirect
740. #460	C₂²×C₄₁	semidirect
741. #459	C₂²×C₄₁	semidirect
745. #452	C₂²×C₄₁	semidirect
746. #452	C₂²×C₄₁	semidirect
747. #452	C₂²×C₄₁	semidirect
748. #452	C₂²×C₄₁	semidirect
749. #452	C₂²×C₄₁	semidirect
750. #452	C₂²×C₄₁	semidirect
751. #452	C₂²×C₄₁	semidirect
752. #451	C₂²×C₄₁	semidirect
753. #451	C₂²×C₄₁	semidirect
754. #450	C₂²×C₄₁	semidirect
755. #450	C₂²×C₄₁	semidirect
757. #449	C₂²×C₄₁	semidirect
758. #449	C₂²×C₄₁	semidirect
759. #449	C₂²×C₄₁	semidirect
760. #448	C₂²×C₄₁	semidirect
761. #447	C₂²×C₄₁	semidirect
762. #433	C₂²×C₄₁	semidirect
763. #433	C₂²×C₄₁	semidirect
764. #432	C₂²×C₄₁	semidirect
765. #431	C₂²×C₄₁	semidirect
766. #424	C₂²×C₄₁	semidirect
767. #424	C₂²×C₄₁	semidirect
768. #419	C₂²×C₄₁	semidirect
769. #418	C₂²×C₄₁	semidirect
774. C₂×#103	C₂²×C₄₁	semidirect
775. C₂×#102	C₂²×C₄₁	semidirect
778. #405	C₂²×C₄₁	semidirect
779. #405	C₂²×C₄₁	semidirect
780. C₄₁	#60816	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×#3495	2
C₄₁×#3449	2
C₄₁×#3225	2
C₄₁×#3224	2
C₄₁×#3223	2
C₄₁×#3222	2
C₄₁×#3219	2
C₄₁×#3216	2
C₄₁×#3212	2
C₄₁×#3210	2
C₄₁×#3156	2
C₄₁×#3154	2
C₄₁×#3137	2
C₄₁×#3136	2
C₄₁×#3046	2
C₄₁×#3045	2
C₄₁×#3044	2
C₄₁×#3043	2
C₄₁×#3007	2
C₄₁×#3005	2
C₄₁×#3002	2
C₂×C₄₁×#452	2
C₄₁×#2924	2
#60816	41

Subgroups — C41×#60816 #23837017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#60816 #23837017