Subgroups — C₄₁×#62041 #23838242

Order 10496.

1896 conjugacy classes of subgroups.

The subgroup lattice has 1204 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×#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3393	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#3333	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3330	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#3314	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#3283	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3273	C₂	1	2	yes	maximal, complemented
13	C₄₁×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3268	C₂	1	2	yes	maximal, complemented
15	C₄₁×#3262	C₂	1	2	yes	maximal, complemented
16	C₄₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#3224	C₂	1	2	yes	maximal, complemented
18	C₄₁×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#3124	C₂	1	2	yes	maximal, complemented
20	C₄₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄₁×#3045	C₂	1	2	yes	maximal, complemented
22	C₄₁×#3036	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₁×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	2	yes	—
25	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	2	yes	complemented
26	C₂×#135×C₄₁	C₂²	1	2	yes	complemented
27	C₄₁×#560	—	2	2	no	—
28	C₄₁×#556	C₂²	1	1	yes	characteristic, complemented
29	C₄₁×#556	C₂²	1	1	yes	characteristic, complemented
30	C₄₁×#554	C₂²	1	2	yes	complemented
31	C₄₁×#553	—	2	1	no	—
32	C₄₁×#552	—	2	1	no	—
33	C₄₁×#551	—	2	2	no	—
34	C₄₁×#550	C₂²	1	2	yes	—
35	C₄₁×#550	C₂²	1	1	yes	characteristic, complemented
36	D₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
37	C₄₁×#548	—	2	1	no	—
38	C₄₁×#547	C₂²	1	1	yes	characteristic
39	C₄₁×#547	C₂²	1	1	yes	characteristic
40	C₄₁×#547	C₂²	1	1	yes	characteristic, complemented
41	C₄₁×#546	—	2	1	no	—
42	C₄₁×#546	C₂²	1	2	yes	—
43	C₄₁×#546	C₂²	1	2	yes	complemented
44	D₄²×C₄₁	C₂²	1	1	yes	characteristic, complemented
45	C₄₁×#542	C₂²	1	2	yes	complemented
46	C₄₁×#542	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	complemented
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	C₂²	1	1	yes	characteristic
56	C₄₁×#525	—	2	1	no	—
57	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
58	C₄₁×#520	C₂²	1	2	yes	complemented
59	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
60	C₄₁×#496	C₂²	1	2	yes	complemented
61	C₄₁×#495	C₂²	1	2	yes	—
62	C₄₁×#494	C₂²	1	1	yes	characteristic, complemented
63	C₄₁×#492	C₂²	1	1	yes	characteristic, complemented
64	C₄₁×#489	C₂²	1	2	yes	complemented
65	C₄₁×#487	C₂²	1	1	yes	characteristic, complemented
66	C₄₁×#486	C₂²	1	1	yes	characteristic, complemented
67	C₄₁×#486	C₂²	1	2	yes	complemented
68	C₄₁×#484	C₂²	1	2	yes	complemented
69	C₄₁×#480	C₂²	1	1	yes	characteristic
70	C₄₁×#480	C₂²	1	2	yes	complemented
71	C₄₁×#480	C₂²	1	1	yes	characteristic, complemented
72	C₄₁×#477	C₂²	1	2	yes	complemented
73	C₄₁×#477	C₂²	1	2	yes	complemented
74	C₄₁×#474	C₂²	1	1	yes	characteristic, complemented
75	C₄₁×#474	C₂²	1	2	yes	complemented
76	C₄₁×#474	C₂²	1	1	yes	characteristic, complemented
77	C₄₁×#474	C₂²	1	1	yes	characteristic, complemented
78	C₄₁×#474	C₂²	1	1	yes	characteristic, complemented
79	C₄₁×#468	C₂²	1	2	yes	—
80	C₄₁×#468	C₂²	1	2	yes	complemented
81	C₄₁×#468	C₂²	1	2	yes	complemented
82	C₄₁×#468	C₂²	1	2	yes	complemented
83	C₄₁×#467	C₂²	1	2	yes	complemented
84	C₄₁×#466	C₂²	1	2	yes	—
85	C₄₁×#464	C₂²	1	2	yes	complemented
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×#463	C₂²	1	2	yes	complemented
92	C₄₁×#463	C₂²	1	2	yes	complemented
93	C₄₁×#461	C₂²	1	1	yes	characteristic, complemented
94	C₄₁×#461	C₂²	1	1	yes	characteristic, complemented
95	C₄₁×#461	C₂²	1	1	yes	characteristic, complemented
96	C₄₁×#461	C₂²	1	1	yes	characteristic, complemented
97	C₄₁×#460	C₂²	1	2	yes	complemented
98	C₄₁×#460	C₂²	1	2	yes	complemented
99	C₄₁×#459	C₂²	1	1	yes	characteristic
100	C₄₁×#459	C₂²	1	1	yes	characteristic
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×#450	C₂²	1	2	yes	complemented
109	C₄₁×#449	C₂²	1	2	yes	—
110	C₄₁×#449	C₂²	1	2	yes	complemented
111	C₄₁×#447	C₂²	1	2	yes	—
112	C₄₁×#447	C₂²	1	1	yes	characteristic
113	C₄₁×#447	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×#440	C₂²	1	2	yes	complemented
117	C₄₁×#440	C₂²	1	2	yes	complemented
118	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	complemented
119	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
121	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
124	C₄₁×#436	C₂²	1	1	yes	characteristic, complemented
125	C₄₁×#436	C₂²	1	2	yes	complemented
126	C₄₁×#435	C₂²	1	2	yes	complemented
127	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic, 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	C₄₁×#423	C₂²	1	1	yes	characteristic, complemented
132	C₄₁×#417	C₂²	1	2	yes	complemented
133	C₄₁×#417	C₂²	1	2	yes	complemented
134	C₂×#102×C₄₁	C₂²	1	2	yes	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	C₂³	1	2	yes	—
139	C₂×#41×C₄₁	C₂³	1	2	yes	—
140	C₂×#41×C₄₁	C₂³	1	2	yes	—
141	C₂²×Q₈×C₄₁	—	2	1	no	—
142	C₂²×D₄×C₄₁	—	2	1	no	—
143	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
144	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
145	C₂³×C₄×C₄₁	—	2	1	no	—
146	AGL(1,ℤ/8)×C₄₁	—	4	4	no	—
147	AGL(1,ℤ/8)×C₄₁	—	4	4	no	—
148	#135×C₄₁	—	4	4	no	—
149	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
150	C₂×Q₁₆×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	2	yes	—
155	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
157	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
158	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
159	C₂×D₈×C₄₁	C₂³	1	2	yes	—
160	C₂×D₈×C₄₁	C₂³	1	2	yes	—
161	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
162	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
163	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
164	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
165	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
166	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
171	#127×C₄₁	—	2	2	no	—
172	#127×C₄₁	C₂³	1	1	yes	characteristic
173	#127×C₄₁	C₂³	1	1	yes	characteristic
174	#127×C₄₁	C₂³	1	2	yes	—
175	#126×C₄₁	—	2	2	no	—
176	#126×C₄₁	—	2	2	no	—
177	#126×C₄₁	—	2	2	no	—
178	#126×C₄₁	—	2	2	no	—
179	#126×C₄₁	D₄	1	2	yes	—
180	#125×C₄₁	—	2	2	no	—
181	#125×C₄₁	—	2	1	no	—
182	#125×C₄₁	D₄	1	1	yes	characteristic
183	#124×C₄₁	—	2	2	no	—
184	#124×C₄₁	—	2	2	no	—
185	#124×C₄₁	—	2	1	no	—
186	#124×C₄₁	D₄	1	1	yes	characteristic
187	#124×C₄₁	C₂³	1	2	yes	—
188	#124×C₄₁	C₂³	1	2	yes	—
189	#124×C₄₁	C₂³	1	2	yes	—
190	#123×C₄₁	—	2	2	no	—
191	#123×C₄₁	—	2	2	no	—
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	D₄	1	2	yes	—
198	C₂²⋊Q₈×C₄₁	—	2	1	no	—
199	C₂²⋊Q₈×C₄₁	—	2	1	no	—
200	C₂²⋊Q₈×C₄₁	—	2	1	no	—
201	C₂²⋊Q₈×C₄₁	—	2	2	no	—
202	C₂²⋊Q₈×C₄₁	—	2	1	no	—
203	C₂²⋊Q₈×C₄₁	—	2	1	no	—
204	C₂²⋊Q₈×C₄₁	—	2	2	no	—
205	C₂²⋊Q₈×C₄₁	—	2	2	no	—
206	C₂²⋊Q₈×C₄₁	—	2	2	no	—
207	C₂²⋊Q₈×C₄₁	—	2	2	no	—
208	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
209	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
212	#121×C₄₁	—	2	1	no	—
213	#121×C₄₁	—	2	1	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	—	2	2	no	—
226	#121×C₄₁	D₄	1	1	yes	characteristic
227	#121×C₄₁	C₂³	1	1	yes	characteristic
228	#121×C₄₁	C₂³	1	1	yes	characteristic
229	#121×C₄₁	C₂³	1	2	yes	—
230	#121×C₄₁	C₂³	1	2	yes	—
231	#120×C₄₁	—	2	2	no	—
232	#120×C₄₁	—	2	2	no	—
233	#120×C₄₁	—	2	2	no	—
234	#120×C₄₁	—	2	2	no	—
235	#120×C₄₁	—	2	2	no	—
236	C₄×Q₈×C₄₁	—	2	1	no	—
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	2	no	—
242	C₄×D₄×C₄₁	—	2	2	no	—
243	C₄×D₄×C₄₁	—	2	2	no	—
244	C₄×D₄×C₄₁	—	2	2	no	—
245	C₄×D₄×C₄₁	—	2	1	no	—
246	C₄×D₄×C₄₁	—	2	1	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	1	yes	characteristic
253	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₄₁	C₂³	1	2	yes	—
255	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₄₁	C₂³	1	2	yes	—
258	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₄₁	C₂³	1	2	yes	—
260	#117×C₄₁	—	2	1	no	—
261	#117×C₄₁	—	2	2	no	—
262	#117×C₄₁	—	2	1	no	—
263	#117×C₄₁	—	2	1	no	—
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	1	no	—
268	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
270	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
271	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
272	C₂×C₂²⋊C₄×C₄₁	—	2	2	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	#107×C₄₁	C₂³	1	1	yes	characteristic
277	#107×C₄₁	C₂³	1	1	yes	characteristic
278	#107×C₄₁	C₂³	1	2	yes	—
279	#107×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	2	yes	—
291	#103×C₄₁	C₂³	1	2	yes	—
292	#103×C₄₁	C₂³	1	2	yes	—
293	#102×C₄₁	C₂³	1	1	yes	characteristic
294	#102×C₄₁	C₂³	1	2	yes	—
295	#102×C₄₁	C₂³	1	2	yes	—
296	#102×C₄₁	C₂³	1	2	yes	—
297	#102×C₄₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
302	#102×C₄₁	C₂³	1	1	yes	characteristic
303	#102×C₄₁	C₂³	1	1	yes	characteristic
304	#102×C₄₁	C₂³	1	2	yes	—
305	#102×C₄₁	C₂³	1	1	yes	characteristic
306	#102×C₄₁	C₂³	1	1	yes	characteristic
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	1	no	—
316	C₂⁴×C₄₁	—	2	2	no	—
317	#41×C₄₁	—	2	4	no	—
318	#41×C₄₁	—	4	2	no	—
319	#41×C₄₁	—	4	2	no	—
320	#41×C₄₁	—	4	2	no	—
321	#41×C₄₁	—	4	2	no	—
322	#41×C₄₁	—	4	2	no	—
323	#41×C₄₁	—	8	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	2	no	—
328	C₂×Q₈×C₄₁	—	2	1	no	—
329	C₂×Q₈×C₄₁	—	8	2	no	—
330	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
333	C₂×D₄×C₄₁	—	2	2	no	—
334	C₂×D₄×C₄₁	—	2	2	no	—
335	C₂×D₄×C₄₁	—	2	1	no	—
336	C₂×D₄×C₄₁	—	2	2	no	—
337	C₂×D₄×C₄₁	—	2	2	no	—
338	C₂×D₄×C₄₁	—	2	2	no	—
339	C₂×D₄×C₄₁	—	2	2	no	—
340	C₂×D₄×C₄₁	—	2	1	no	—
341	C₂×D₄×C₄₁	—	2	1	no	—
342	C₂×D₄×C₄₁	—	2	1	no	—
343	C₂×D₄×C₄₁	—	2	1	no	—
344	C₂×D₄×C₄₁	—	2	1	no	—
345	C₂×D₄×C₄₁	—	2	2	no	—
346	C₂×D₄×C₄₁	—	2	1	no	—
347	C₂×D₄×C₄₁	—	2	2	no	—
348	C₂×D₄×C₄₁	—	2	2	no	—
349	C₂×D₄×C₄₁	—	4	1	no	—
350	C₂×D₄×C₄₁	—	4	2	no	—
351	C₂×D₄×C₄₁	—	4	2	no	—
352	C₂×D₄×C₄₁	—	8	2	no	—
353	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
354	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
355	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
356	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
357	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
359	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₄₁	—	2	1	no	—
361	C₂²×C₄×C₄₁	—	2	2	no	—
362	C₂²×C₄×C₄₁	—	2	2	no	—
363	C₂²×C₄×C₄₁	—	2	1	no	—
364	C₂²×C₄×C₄₁	—	2	1	no	—
365	C₂²×C₄×C₄₁	—	2	1	no	—
366	C₂²×C₄×C₄₁	—	2	1	no	—
367	C₂²×C₄×C₄₁	—	2	2	no	—
368	C₂²×C₄×C₄₁	—	2	2	no	—
369	C₂²×C₄×C₄₁	—	2	2	no	—
370	C₂²×C₄×C₄₁	—	2	1	no	—
371	C₂²×C₄×C₄₁	—	2	2	no	—
372	C₂²×C₄×C₄₁	—	2	1	no	—
373	C₂²×C₄×C₄₁	—	8	2	no	—
374	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
376	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
378	Q₁₆×C₄₁	—	4	2	no	—
379	Q₁₆×C₄₁	—	4	2	no	—
380	SD₁₆×C₄₁	—	2	4	no	—
381	SD₁₆×C₄₁	—	4	2	no	—
382	SD₁₆×C₄₁	—	4	2	no	—
383	SD₁₆×C₄₁	—	4	2	no	—
384	SD₁₆×C₄₁	—	4	2	no	—
385	SD₁₆×C₄₁	—	4	2	no	—
386	D₈×C₄₁	—	2	2	no	—
387	D₈×C₄₁	—	2	4	no	—
388	D₈×C₄₁	—	2	2	no	—
389	D₈×C₄₁	—	4	1	no	—
390	D₈×C₄₁	—	4	1	no	—
391	D₈×C₄₁	—	4	2	no	—
392	M₁₆×C₄₁	—	4	2	no	—
393	M₁₆×C₄₁	—	4	2	no	—
394	C₂×C₈×C₄₁	—	4	2	no	—
395	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
397	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
398	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
399	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
400	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₄₁	—	2	2	no	—
402	C₄⋊C₄×C₄₁	—	2	1	no	—
403	C₄⋊C₄×C₄₁	—	2	1	no	—
404	C₄⋊C₄×C₄₁	—	2	2	no	—
405	C₄⋊C₄×C₄₁	—	2	2	no	—
406	C₄⋊C₄×C₄₁	—	2	2	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	1	no	—
412	C₄⋊C₄×C₄₁	—	2	1	no	—
413	C₄⋊C₄×C₄₁	—	2	2	no	—
414	C₄⋊C₄×C₄₁	—	2	2	no	—
415	C₄⋊C₄×C₄₁	—	2	2	no	—
416	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
417	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
418	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
420	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
422	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
425	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
427	C₂²⋊C₄×C₄₁	—	2	2	no	—
428	C₂²⋊C₄×C₄₁	—	2	2	no	—
429	C₂²⋊C₄×C₄₁	—	2	2	no	—
430	C₂²⋊C₄×C₄₁	—	2	1	no	—
431	C₂²⋊C₄×C₄₁	—	2	1	no	—
432	C₂²⋊C₄×C₄₁	—	2	1	no	—
433	C₂²⋊C₄×C₄₁	—	2	1	no	—
434	C₂²⋊C₄×C₄₁	—	2	1	no	—
435	C₂²⋊C₄×C₄₁	—	2	2	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	2	no	—
440	C₂²⋊C₄×C₄₁	—	2	2	no	—
441	C₂²⋊C₄×C₄₁	—	2	1	no	—
442	C₂²⋊C₄×C₄₁	—	2	2	no	—
443	C₂²⋊C₄×C₄₁	—	2	2	no	—
444	C₂²⋊C₄×C₄₁	—	2	2	no	—
445	C₂²⋊C₄×C₄₁	—	2	1	no	—
446	C₂²⋊C₄×C₄₁	—	2	2	no	—
447	C₂²⋊C₄×C₄₁	—	2	1	no	—
448	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
449	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
451	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
452	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
453	C₄²×C₄₁	—	2	2	no	—
454	C₄²×C₄₁	—	2	2	no	—
455	C₄²×C₄₁	—	2	2	no	—
456	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
458	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
459	C₄²×C₄₁	C₂⁴	1	2	yes	—
460	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
461	C₂³×C₄₁	—	2	1	no	—
462	C₂³×C₄₁	—	2	1	no	—
463	C₂³×C₄₁	—	2	1	no	—
464	C₂³×C₄₁	—	2	2	no	—
465	C₂³×C₄₁	—	2	1	no	—
466	C₂³×C₄₁	—	4	2	no	—
467	C₂³×C₄₁	—	4	2	no	—
468	C₂³×C₄₁	—	8	1	no	—
469	C₂³×C₄₁	—	8	2	no	—
470	C₂³×C₄₁	—	8	2	no	—
471	C₂³×C₄₁	—	8	2	no	—
472	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
473	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
474	Q₈×C₄₁	—	2	2	no	—
475	Q₈×C₄₁	—	2	2	no	—
476	Q₈×C₄₁	—	2	2	no	—
477	Q₈×C₄₁	—	2	2	no	—
478	Q₈×C₄₁	—	2	2	no	—
479	Q₈×C₄₁	—	4	2	no	—
480	Q₈×C₄₁	—	8	2	no	—
481	Q₈×C₄₁	—	8	1	no	—
482	D₄×C₄₁	—	2	2	no	—
483	D₄×C₄₁	—	2	2	no	—
484	D₄×C₄₁	—	2	1	no	—
485	D₄×C₄₁	—	2	1	no	—
486	D₄×C₄₁	—	2	1	no	—
487	D₄×C₄₁	—	2	1	no	—
488	D₄×C₄₁	—	2	1	no	—
489	D₄×C₄₁	—	2	1	no	—
490	D₄×C₄₁	—	2	1	no	—
491	D₄×C₄₁	—	2	2	no	—
492	D₄×C₄₁	—	4	2	no	—
493	D₄×C₄₁	—	4	2	no	—
494	D₄×C₄₁	—	4	4	no	—
495	D₄×C₄₁	—	4	2	no	—
496	D₄×C₄₁	—	8	1	no	—
497	D₄×C₄₁	—	8	1	no	—
498	D₄×C₄₁	—	8	2	no	—
499	D₄×C₄₁	—	8	2	no	—
500	D₄×C₄₁	—	8	1	no	—
501	D₄×C₄₁	—	8	2	no	—
502	D₄×C₄₁	—	8	2	no	—
503	D₄×C₄₁	—	8	2	no	—
504	D₄×C₄₁	—	8	2	no	—
505	D₄×C₄₁	—	8	1	no	—
506	D₄×C₄₁	—	8	1	no	—
507	D₄×C₄₁	—	8	2	no	—
508	D₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
509	C₂×C₄×C₄₁	—	2	2	no	—
510	C₂×C₄×C₄₁	—	2	2	no	—
511	C₂×C₄×C₄₁	—	2	1	no	—
512	C₂×C₄×C₄₁	—	2	2	no	—
513	C₂×C₄×C₄₁	—	2	1	no	—
514	C₂×C₄×C₄₁	—	2	2	no	—
515	C₂×C₄×C₄₁	—	2	1	no	—
516	C₂×C₄×C₄₁	—	2	1	no	—
517	C₂×C₄×C₄₁	—	2	2	no	—
518	C₂×C₄×C₄₁	—	2	2	no	—
519	C₂×C₄×C₄₁	—	2	1	no	—
520	C₂×C₄×C₄₁	—	2	1	no	—
521	C₂×C₄×C₄₁	—	4	1	no	—
522	C₂×C₄×C₄₁	—	4	4	no	—
523	C₂×C₄×C₄₁	—	4	2	no	—
524	C₂×C₄×C₄₁	—	4	2	no	—
525	C₂×C₄×C₄₁	—	4	2	no	—
526	C₂×C₄×C₄₁	—	4	2	no	—
527	C₂×C₄×C₄₁	—	8	1	no	—
528	C₂×C₄×C₄₁	—	8	1	no	—
529	C₂×C₄×C₄₁	—	8	2	no	—
530	C₂×C₄×C₄₁	—	8	2	no	—
531	C₂×C₄×C₄₁	—	8	2	no	—
532	C₂×C₄×C₄₁	—	8	2	no	—
533	C₂×C₄×C₄₁	—	8	1	no	—
534	C₂×C₄×C₄₁	—	8	2	no	—
535	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
537	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
540	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
541	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
542	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
544	C₈×C₄₁	—	2	1	no	—
545	C₈×C₄₁	—	2	2	no	—
546	C₈×C₄₁	—	2	1	no	—
547	C₈×C₄₁	—	2	2	no	—
548	C₈×C₄₁	—	2	1	no	—
549	C₈×C₄₁	—	2	1	no	—
550	#62041	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
551	C₂²×C₄₁	—	2	1	no	—
552	C₂²×C₄₁	—	2	2	no	—
553	C₂²×C₄₁	—	2	2	no	—
554	C₂²×C₄₁	—	2	1	no	—
555	C₂²×C₄₁	—	2	2	no	—
556	C₂²×C₄₁	—	2	1	no	—
557	C₂²×C₄₁	—	2	2	no	—
558	C₂²×C₄₁	—	4	1	no	—
559	C₂²×C₄₁	—	4	1	no	—
560	C₂²×C₄₁	—	4	1	no	—
561	C₂²×C₄₁	—	4	2	no	—
562	C₂²×C₄₁	—	4	1	no	—
563	C₂²×C₄₁	—	4	1	no	—
564	C₂²×C₄₁	—	4	1	no	—
565	C₂²×C₄₁	—	4	2	no	—
566	C₂²×C₄₁	—	4	1	no	—
567	C₂²×C₄₁	—	4	1	no	—
568	C₂²×C₄₁	—	4	1	no	—
569	C₂²×C₄₁	—	4	1	no	—
570	C₂²×C₄₁	—	4	1	no	—
571	C₂²×C₄₁	—	4	2	no	—
572	C₂²×C₄₁	—	8	4	no	—
573	C₂²×C₄₁	—	16	4	no	—
574	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
575	C₄×C₄₁	—	2	1	no	—
576	C₄×C₄₁	—	2	1	no	—
577	C₄×C₄₁	—	2	2	no	—
578	C₄×C₄₁	—	2	2	no	—
579	C₄×C₄₁	—	2	1	no	—
580	C₄×C₄₁	—	2	1	no	—
581	C₄×C₄₁	—	2	2	no	—
582	C₄×C₄₁	—	4	2	no	—
583	C₄×C₄₁	—	4	2	no	—
584	C₄×C₄₁	—	4	1	no	—
585	C₄×C₄₁	—	4	1	no	—
586	C₄×C₄₁	—	4	1	no	—
587	C₄×C₄₁	—	4	1	no	—
588	C₄×C₄₁	—	4	2	no	—
589	C₄×C₄₁	#576	1	2	yes	—
590	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
591	C₄×C₄₁	#585	1	1	yes	characteristic
592	#3546	C₂×C₄₁	1	1	yes	characteristic, complemented
593	#3520	C₂×C₄₁	1	1	yes	characteristic, complemented
594	#3397	C₂×C₄₁	1	1	yes	characteristic, complemented
595	#3393	C₂×C₄₁	1	1	yes	characteristic, complemented
596	#3367	C₂×C₄₁	1	1	yes	characteristic, complemented
597	#3358	C₂×C₄₁	1	1	yes	characteristic, complemented
598	#3333	C₂×C₄₁	1	2	yes	complemented
599	#3330	C₂×C₄₁	1	1	yes	characteristic, complemented
600	#3314	C₂×C₄₁	1	2	yes	complemented
601	#3294	C₂×C₄₁	1	1	yes	characteristic, complemented
602	#3283	C₂×C₄₁	1	1	yes	characteristic, complemented
603	#3273	C₂×C₄₁	1	2	yes	complemented
604	#3272	C₂×C₄₁	1	1	yes	characteristic, complemented
605	#3268	C₂×C₄₁	1	2	yes	complemented
606	#3262	C₂×C₄₁	1	2	yes	complemented
607	#3254	C₂×C₄₁	1	1	yes	characteristic, complemented
608	#3224	C₂×C₄₁	1	2	yes	complemented
609	#3210	C₂×C₄₁	1	1	yes	characteristic, complemented
610	#3124	C₂×C₄₁	1	2	yes	complemented
611	#3100	C₂×C₄₁	1	1	yes	characteristic, complemented
612	#3045	C₂×C₄₁	1	2	yes	complemented
613	#3036	C₂×C₄₁	1	1	yes	characteristic, complemented
614	#2993	C₂×C₄₁	1	1	yes	characteristic, complemented
615	C₂×C₄₁	—	4	1	no	—
616	C₂×C₄₁	—	4	2	no	—
617	C₂×C₄₁	—	4	2	no	—
618	C₂×C₄₁	—	8	1	no	—
619	C₂×C₄₁	—	8	1	no	—
620	C₂×C₄₁	—	8	2	no	—
621	C₂×C₄₁	—	8	1	no	—
622	C₂×C₄₁	#3488	1	1	yes	characteristic
623	C₂×C₄₁	C₂×#576	1	1	yes	characteristic
624	C₂×C₄₁	#3586	1	1	yes	characteristic
625	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	2	yes	—
626	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	2	yes	complemented
627	C₂×#135	C₂²×C₄₁	1	2	yes	complemented
628	#560	—	2	2	no	—
629	#556	C₂²×C₄₁	1	1	yes	characteristic, complemented
630	#556	C₂²×C₄₁	1	1	yes	characteristic, complemented
631	#554	C₂²×C₄₁	1	2	yes	complemented
632	#553	—	2	1	no	—
633	#552	—	2	1	no	—
634	#551	—	2	2	no	—
635	#550	C₂²×C₄₁	1	2	yes	—
636	#550	C₂²×C₄₁	1	1	yes	characteristic, complemented
637	D₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
638	#548	—	2	1	no	—
639	#547	C₂²×C₄₁	1	1	yes	characteristic
640	#547	C₂²×C₄₁	1	1	yes	characteristic
641	#547	C₂²×C₄₁	1	1	yes	characteristic, complemented
642	#546	—	2	1	no	—
643	#546	C₂²×C₄₁	1	2	yes	—
644	#546	C₂²×C₄₁	1	2	yes	complemented
645	D₄²	C₂²×C₄₁	1	1	yes	characteristic, complemented
646	#542	C₂²×C₄₁	1	2	yes	complemented
647	#542	C₂²×C₄₁	1	2	yes	complemented
648	#539	—	2	2	no	—
649	#538	—	2	2	no	—
650	#537	—	2	1	no	—
651	#535	—	2	1	no	—
652	#535	C₂²×C₄₁	1	2	yes	complemented
653	#533	C₂²×C₄₁	1	1	yes	characteristic, complemented
654	#532	C₂²×C₄₁	1	1	yes	characteristic
655	#532	C₂²×C₄₁	1	1	yes	characteristic
656	#529	C₂²×C₄₁	1	1	yes	characteristic
657	#525	—	2	1	no	—
658	C₂×C₂²⋊Q₈	—	2	1	no	—
659	#520	C₂²×C₄₁	1	2	yes	complemented
660	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
661	#496	C₂²×C₄₁	1	2	yes	complemented
662	#495	C₂²×C₄₁	1	2	yes	—
663	#494	C₂²×C₄₁	1	1	yes	characteristic, complemented
664	#492	C₂²×C₄₁	1	1	yes	characteristic, complemented
665	#489	C₂²×C₄₁	1	2	yes	complemented
666	#487	C₂²×C₄₁	1	1	yes	characteristic, complemented
667	#486	C₂²×C₄₁	1	2	yes	complemented
668	#486	C₂²×C₄₁	1	1	yes	characteristic, complemented
669	#484	C₂²×C₄₁	1	2	yes	complemented
670	#480	C₂²×C₄₁	1	1	yes	characteristic
671	#480	C₂²×C₄₁	1	1	yes	characteristic, complemented
672	#480	C₂²×C₄₁	1	2	yes	complemented
673	#477	C₂²×C₄₁	1	2	yes	complemented
674	#477	C₂²×C₄₁	1	2	yes	complemented
675	#474	C₂²×C₄₁	1	1	yes	characteristic, complemented
676	#474	C₂²×C₄₁	1	1	yes	characteristic, complemented
677	#474	C₂²×C₄₁	1	1	yes	characteristic, complemented
678	#474	C₂²×C₄₁	1	2	yes	complemented
679	#474	C₂²×C₄₁	1	1	yes	characteristic, complemented
680	#468	C₂²×C₄₁	1	2	yes	—
681	#468	C₂²×C₄₁	1	2	yes	complemented
682	#468	C₂²×C₄₁	1	2	yes	complemented
683	#468	C₂²×C₄₁	1	2	yes	complemented
684	#467	C₂²×C₄₁	1	2	yes	complemented
685	#466	C₂²×C₄₁	1	2	yes	—
686	#464	C₂²×C₄₁	1	2	yes	complemented
687	#464	C₂²×C₄₁	1	2	yes	complemented
688	#464	C₂²×C₄₁	1	2	yes	complemented
689	#464	C₂²×C₄₁	1	2	yes	complemented
690	#463	C₂²×C₄₁	1	2	yes	—
691	#463	C₂²×C₄₁	1	2	yes	complemented
692	#463	C₂²×C₄₁	1	2	yes	complemented
693	#463	C₂²×C₄₁	1	2	yes	complemented
694	#461	C₂²×C₄₁	1	1	yes	characteristic, complemented
695	#461	C₂²×C₄₁	1	1	yes	characteristic, complemented
696	#461	C₂²×C₄₁	1	1	yes	characteristic, complemented
697	#461	C₂²×C₄₁	1	1	yes	characteristic, complemented
698	#460	C₂²×C₄₁	1	2	yes	complemented
699	#460	C₂²×C₄₁	1	2	yes	complemented
700	#459	C₂²×C₄₁	1	1	yes	characteristic
701	#459	C₂²×C₄₁	1	1	yes	characteristic
702	#459	C₂²×C₄₁	1	1	yes	characteristic
703	#459	C₂²×C₄₁	1	1	yes	characteristic
704	#459	C₂²×C₄₁	1	2	yes	complemented
705	#452	C₂²×C₄₁	1	2	yes	complemented
706	#452	C₂²×C₄₁	1	2	yes	complemented
707	#452	C₂²×C₄₁	1	2	yes	complemented
708	#452	C₂²×C₄₁	1	2	yes	complemented
709	#450	C₂²×C₄₁	1	2	yes	complemented
710	#449	C₂²×C₄₁	1	2	yes	—
711	#449	C₂²×C₄₁	1	2	yes	complemented
712	#447	C₂²×C₄₁	1	1	yes	characteristic
713	#447	C₂²×C₄₁	1	2	yes	—
714	#447	C₂²×C₄₁	1	1	yes	characteristic, complemented
715	#446	C₂²×C₄₁	1	1	yes	characteristic, complemented
716	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
717	#440	C₂²×C₄₁	1	2	yes	complemented
718	#440	C₂²×C₄₁	1	2	yes	complemented
719	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	complemented
720	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
721	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
722	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
723	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
724	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
725	#436	C₂²×C₄₁	1	1	yes	characteristic, complemented
726	#436	C₂²×C₄₁	1	2	yes	complemented
727	#435	C₂²×C₄₁	1	2	yes	complemented
728	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
729	#433	C₂²×C₄₁	1	2	yes	complemented
730	#431	C₂²×C₄₁	1	1	yes	characteristic, complemented
731	#424	C₂²×C₄₁	1	2	yes	complemented
732	#423	C₂²×C₄₁	1	1	yes	characteristic, complemented
733	#417	C₂²×C₄₁	1	2	yes	complemented
734	#417	C₂²×C₄₁	1	2	yes	complemented
735	C₂×#102	C₂²×C₄₁	1	2	yes	complemented
736	C₄₁	#62041	1	1	yes	characteristic, direct product factor, Sylow
737	C₂×#41	—	2	1	no	—
738	C₂×#41	—	2	1	no	—
739	C₂×#41	—	2	1	no	—
740	C₂×#41	C₂³×C₄₁	1	2	yes	—
741	C₂×#41	C₂³×C₄₁	1	2	yes	—
742	C₂×#41	C₂³×C₄₁	1	2	yes	—
743	C₂²×Q₈	—	2	1	no	—
744	C₂²×D₄	—	2	1	no	—
745	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
746	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
747	C₂³×C₄	—	2	1	no	—
748	AGL(1,ℤ/8)	—	4	4	no	—
749	AGL(1,ℤ/8)	—	4	4	no	—
750	#135	—	4	4	no	—
751	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
752	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
753	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
754	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
755	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
756	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
757	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
758	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
759	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
760	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
761	C₂×D₈	C₂³×C₄₁	1	2	yes	—
762	C₂×D₈	C₂³×C₄₁	1	2	yes	—
763	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
764	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
765	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
766	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
767	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
768	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
769	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
770	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
771	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
772	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
773	#127	—	2	2	no	—
774	#127	C₂³×C₄₁	1	1	yes	characteristic
775	#127	C₂³×C₄₁	1	1	yes	characteristic
776	#127	C₂³×C₄₁	1	2	yes	—
777	#126	—	2	2	no	—
778	#126	—	2	2	no	—
779	#126	—	2	2	no	—
780	#126	—	2	2	no	—
781	#126	D₄×C₄₁	1	2	yes	—
782	#125	—	2	2	no	—
783	#125	—	2	1	no	—
784	#125	D₄×C₄₁	1	1	yes	characteristic
785	#124	—	2	2	no	—
786	#124	—	2	2	no	—
787	#124	—	2	1	no	—
788	#124	D₄×C₄₁	1	1	yes	characteristic
789	#124	C₂³×C₄₁	1	2	yes	—
790	#124	C₂³×C₄₁	1	2	yes	—
791	#124	C₂³×C₄₁	1	2	yes	—
792	#123	—	2	2	no	—
793	#123	—	2	2	no	—
794	#123	—	2	2	no	—
795	#123	—	2	2	no	—
796	#123	—	2	2	no	—
797	#123	—	2	2	no	—
798	#123	—	2	2	no	—
799	#123	D₄×C₄₁	1	2	yes	—
800	C₂²⋊Q₈	—	2	1	no	—
801	C₂²⋊Q₈	—	2	1	no	—
802	C₂²⋊Q₈	—	2	1	no	—
803	C₂²⋊Q₈	—	2	2	no	—
804	C₂²⋊Q₈	—	2	1	no	—
805	C₂²⋊Q₈	—	2	1	no	—
806	C₂²⋊Q₈	—	2	2	no	—
807	C₂²⋊Q₈	—	2	2	no	—
808	C₂²⋊Q₈	—	2	2	no	—
809	C₂²⋊Q₈	—	2	2	no	—
810	C₂²⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
811	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
812	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
813	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
814	#121	—	2	1	no	—
815	#121	—	2	1	no	—
816	#121	—	2	1	no	—
817	#121	—	2	1	no	—
818	#121	—	2	1	no	—
819	#121	—	2	1	no	—
820	#121	—	2	2	no	—
821	#121	—	2	2	no	—
822	#121	—	2	1	no	—
823	#121	—	2	2	no	—
824	#121	—	2	2	no	—
825	#121	—	2	2	no	—
826	#121	—	2	2	no	—
827	#121	—	2	2	no	—
828	#121	D₄×C₄₁	1	1	yes	characteristic
829	#121	C₂³×C₄₁	1	1	yes	characteristic
830	#121	C₂³×C₄₁	1	1	yes	characteristic
831	#121	C₂³×C₄₁	1	2	yes	—
832	#121	C₂³×C₄₁	1	2	yes	—
833	#120	—	2	2	no	—
834	#120	—	2	2	no	—
835	#120	—	2	2	no	—
836	#120	—	2	2	no	—
837	#120	—	2	2	no	—
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	1	yes	characteristic
843	C₄×D₄	—	2	2	no	—
844	C₄×D₄	—	2	2	no	—
845	C₄×D₄	—	2	2	no	—
846	C₄×D₄	—	2	2	no	—
847	C₄×D₄	—	2	1	no	—
848	C₄×D₄	—	2	1	no	—
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	1	no	—
851	C₄×D₄	—	2	1	no	—
852	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
853	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
854	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
855	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
856	C₄×D₄	C₂³×C₄₁	1	2	yes	—
857	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
858	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
859	C₄×D₄	C₂³×C₄₁	1	2	yes	—
860	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
861	C₄×D₄	C₂³×C₄₁	1	2	yes	—
862	#117	—	2	1	no	—
863	#117	—	2	2	no	—
864	#117	—	2	1	no	—
865	#117	—	2	1	no	—
866	#117	C₂³×C₄₁	1	2	yes	—
867	C₂×C₄⋊C₄	—	2	2	no	—
868	C₂×C₄⋊C₄	—	2	1	no	—
869	C₂×C₄⋊C₄	—	2	1	no	—
870	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
871	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
872	C₂×C₂²⋊C₄	—	2	1	no	—
873	C₂×C₂²⋊C₄	—	2	2	no	—
874	C₂×C₂²⋊C₄	—	2	2	no	—
875	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
876	#107	C₂³×C₄₁	1	1	yes	characteristic
877	#107	C₂³×C₄₁	1	1	yes	characteristic
878	#107	C₂³×C₄₁	1	1	yes	characteristic
879	#107	C₂³×C₄₁	1	1	yes	characteristic
880	#107	C₂³×C₄₁	1	2	yes	—
881	#107	C₂³×C₄₁	1	2	yes	—
882	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
883	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
884	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
885	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
886	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
887	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
888	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
889	#103	C₂³×C₄₁	1	2	yes	—
890	#103	C₂³×C₄₁	1	2	yes	—
891	#103	C₂³×C₄₁	1	2	yes	—
892	#103	C₂³×C₄₁	1	2	yes	—
893	#103	C₂³×C₄₁	1	2	yes	—
894	#103	C₂³×C₄₁	1	2	yes	—
895	#102	C₂³×C₄₁	1	1	yes	characteristic
896	#102	C₂³×C₄₁	1	2	yes	—
897	#102	C₂³×C₄₁	1	2	yes	—
898	#102	C₂³×C₄₁	1	2	yes	—
899	#102	C₂³×C₄₁	1	1	yes	characteristic
900	#102	C₂³×C₄₁	1	2	yes	—
901	#102	C₂³×C₄₁	1	2	yes	—
902	#102	C₂³×C₄₁	1	1	yes	characteristic
903	#102	C₂³×C₄₁	1	1	yes	characteristic
904	#102	C₂³×C₄₁	1	1	yes	characteristic
905	#102	C₂³×C₄₁	1	1	yes	characteristic
906	#102	C₂³×C₄₁	1	2	yes	—
907	#102	C₂³×C₄₁	1	1	yes	characteristic
908	#102	C₂³×C₄₁	1	1	yes	characteristic
909	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
910	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
911	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
912	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
913	#97	C₂³×C₄₁	1	2	yes	—
914	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
915	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
916	C₄×C₈	C₂³×C₄₁	1	2	yes	—
917	C₂⁴	—	2	1	no	—
918	C₂⁴	—	2	2	no	—
919	#41	—	2	4	no	—
920	#41	—	4	2	no	—
921	#41	—	4	2	no	—
922	#41	—	4	2	no	—
923	#41	—	4	2	no	—
924	#41	—	4	2	no	—
925	#41	—	8	2	no	—
926	#41	—	8	2	no	—
927	#41	—	8	2	no	—
928	C₂×Q₈	—	2	1	no	—
929	C₂×Q₈	—	2	2	no	—
930	C₂×Q₈	—	2	1	no	—
931	C₂×Q₈	—	8	2	no	—
932	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
933	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
934	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	—	2	1	no	—
943	C₂×D₄	—	2	1	no	—
944	C₂×D₄	—	2	1	no	—
945	C₂×D₄	—	2	1	no	—
946	C₂×D₄	—	2	1	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	4	1	no	—
952	C₂×D₄	—	4	2	no	—
953	C₂×D₄	—	4	2	no	—
954	C₂×D₄	—	8	2	no	—
955	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
956	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
957	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
958	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
959	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
960	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
961	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	2	no	—
964	C₂²×C₄	—	2	2	no	—
965	C₂²×C₄	—	2	1	no	—
966	C₂²×C₄	—	2	1	no	—
967	C₂²×C₄	—	2	1	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	2	no	—
971	C₂²×C₄	—	2	2	no	—
972	C₂²×C₄	—	2	1	no	—
973	C₂²×C₄	—	2	2	no	—
974	C₂²×C₄	—	2	1	no	—
975	C₂²×C₄	—	8	2	no	—
976	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
977	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
978	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
979	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
980	Q₁₆	—	4	2	no	—
981	Q₁₆	—	4	2	no	—
982	SD₁₆	—	2	4	no	—
983	SD₁₆	—	4	2	no	—
984	SD₁₆	—	4	2	no	—
985	SD₁₆	—	4	2	no	—
986	SD₁₆	—	4	2	no	—
987	SD₁₆	—	4	2	no	—
988	D₈	—	2	2	no	—
989	D₈	—	2	4	no	—
990	D₈	—	2	2	no	—
991	D₈	—	4	1	no	—
992	D₈	—	4	1	no	—
993	D₈	—	4	2	no	—
994	M₁₆	—	4	2	no	—
995	M₁₆	—	4	2	no	—
996	C₂×C₈	—	4	2	no	—
997	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
998	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
999	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1000	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1001	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1002	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	1	no	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	2	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	1	no	—
1014	C₄⋊C₄	—	2	1	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	2	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1019	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1020	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1021	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1022	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1023	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1024	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1025	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1026	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
1027	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1028	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	1	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	2	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	1	no	—
1048	C₂²⋊C₄	—	2	2	no	—
1049	C₂²⋊C₄	—	2	1	no	—
1050	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1051	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1052	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1053	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1054	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1055	C₄²	—	2	2	no	—
1056	C₄²	—	2	2	no	—
1057	C₄²	—	2	2	no	—
1058	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1059	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1060	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1061	C₄²	C₂⁴×C₄₁	1	2	yes	—
1062	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1063	C₂³	—	2	1	no	—
1064	C₂³	—	2	1	no	—
1065	C₂³	—	2	1	no	—
1066	C₂³	—	2	2	no	—
1067	C₂³	—	2	1	no	—
1068	C₂³	—	4	2	no	—
1069	C₂³	—	4	2	no	—
1070	C₂³	—	8	1	no	—
1071	C₂³	—	8	2	no	—
1072	C₂³	—	8	2	no	—
1073	C₂³	—	8	2	no	—
1074	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
1075	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1076	Q₈	—	2	2	no	—
1077	Q₈	—	2	2	no	—
1078	Q₈	—	2	2	no	—
1079	Q₈	—	2	2	no	—
1080	Q₈	—	2	2	no	—
1081	Q₈	—	4	2	no	—
1082	Q₈	—	8	2	no	—
1083	Q₈	—	8	1	no	—
1084	D₄	—	2	2	no	—
1085	D₄	—	2	2	no	—
1086	D₄	—	2	1	no	—
1087	D₄	—	2	1	no	—
1088	D₄	—	2	1	no	—
1089	D₄	—	2	1	no	—
1090	D₄	—	2	1	no	—
1091	D₄	—	2	1	no	—
1092	D₄	—	2	1	no	—
1093	D₄	—	2	2	no	—
1094	D₄	—	4	2	no	—
1095	D₄	—	4	2	no	—
1096	D₄	—	4	4	no	—
1097	D₄	—	4	2	no	—
1098	D₄	—	8	2	no	—
1099	D₄	—	8	1	no	—
1100	D₄	—	8	2	no	—
1101	D₄	—	8	1	no	—
1102	D₄	—	8	1	no	—
1103	D₄	—	8	2	no	—
1104	D₄	—	8	2	no	—
1105	D₄	—	8	2	no	—
1106	D₄	—	8	2	no	—
1107	D₄	—	8	1	no	—
1108	D₄	—	8	1	no	—
1109	D₄	—	8	2	no	—
1110	D₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	2	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	4	1	no	—
1124	C₂×C₄	—	4	4	no	—
1125	C₂×C₄	—	4	2	no	—
1126	C₂×C₄	—	4	2	no	—
1127	C₂×C₄	—	4	2	no	—
1128	C₂×C₄	—	4	2	no	—
1129	C₂×C₄	—	8	1	no	—
1130	C₂×C₄	—	8	1	no	—
1131	C₂×C₄	—	8	2	no	—
1132	C₂×C₄	—	8	2	no	—
1133	C₂×C₄	—	8	2	no	—
1134	C₂×C₄	—	8	2	no	—
1135	C₂×C₄	—	8	1	no	—
1136	C₂×C₄	—	8	2	no	—
1137	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1138	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1139	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1140	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1141	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1142	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1143	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1144	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1145	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
1146	C₈	—	2	1	no	—
1147	C₈	—	2	2	no	—
1148	C₈	—	2	1	no	—
1149	C₈	—	2	2	no	—
1150	C₈	—	2	1	no	—
1151	C₈	—	2	1	no	—
1152	C₂²	—	2	1	no	—
1153	C₂²	—	2	2	no	—
1154	C₂²	—	2	1	no	—
1155	C₂²	—	2	2	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	2	1	no	—
1158	C₂²	—	2	2	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	1	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	4	1	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	4	2	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	8	4	no	—
1174	C₂²	—	16	4	no	—
1175	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
1176	C₄	—	2	1	no	—
1177	C₄	—	2	2	no	—
1178	C₄	—	2	1	no	—
1179	C₄	—	2	1	no	—
1180	C₄	—	2	2	no	—
1181	C₄	—	2	2	no	—
1182	C₄	—	2	1	no	—
1183	C₄	—	4	1	no	—
1184	C₄	—	4	1	no	—
1185	C₄	—	4	1	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	2	no	—
1188	C₄	—	4	2	no	—
1189	C₄	—	4	2	no	—
1190	C₄	C₄₁×#576	1	2	yes	—
1191	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1192	C₄	C₄₁×#585	1	1	yes	characteristic
1193	C₂	—	4	1	no	—
1194	C₂	—	4	2	no	—
1195	C₂	—	4	2	no	—
1196	C₂	—	8	1	no	—
1197	C₂	—	8	1	no	—
1198	C₂	—	8	2	no	—
1199	C₂	—	8	1	no	—
1200	C₂	C₄₁×#3488	1	1	yes	characteristic
1201	C₂	C₂×C₄₁×#576	1	1	yes	characteristic
1202	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 ◁ 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×#3520	C₂	semidirect
3. C₄₁×#3397	C₂	semidirect
4. C₄₁×#3393	C₂	semidirect
5. C₄₁×#3367	C₂	semidirect
6. C₄₁×#3358	C₂	semidirect
7. C₄₁×#3333	C₂	semidirect
8. C₄₁×#3330	C₂	semidirect
9. C₄₁×#3314	C₂	semidirect
10. C₄₁×#3294	C₂	semidirect
11. C₄₁×#3283	C₂	semidirect
12. C₄₁×#3273	C₂	semidirect
13. C₄₁×#3272	C₂	semidirect
14. C₄₁×#3268	C₂	semidirect
15. C₄₁×#3262	C₂	semidirect
16. C₄₁×#3254	C₂	semidirect
17. C₄₁×#3224	C₂	semidirect
18. C₄₁×#3210	C₂	semidirect
19. C₄₁×#3124	C₂	semidirect
20. C₄₁×#3100	C₂	semidirect
21. C₄₁×#3045	C₂	semidirect
22. C₄₁×#3036	C₂	semidirect
23. C₄₁×#2993	C₂	semidirect
25. C₂×AGL(1,ℤ/8)×C₄₁	C₂²	semidirect
26. C₂×#135×C₄₁	C₂²	semidirect
28. C₄₁×#556	C₂²	semidirect
29. C₄₁×#556	C₂²	semidirect
30. C₄₁×#554	C₂²	semidirect
35. C₄₁×#550	C₂²	semidirect
36. D₄×Q₈×C₄₁	C₂²	semidirect
40. C₄₁×#547	C₂²	semidirect
43. C₄₁×#546	C₂²	semidirect
44. D₄²×C₄₁	C₂²	semidirect
45. C₄₁×#542	C₂²	semidirect
46. C₄₁×#542	C₂²	semidirect
51. C₄₁×#535	C₂²	semidirect
52. C₄₁×#533	C₂²	semidirect
58. C₄₁×#520	C₂²	semidirect
59. C₂×C₄×D₄×C₄₁	C₂²	semidirect
60. C₄₁×#496	C₂²	semidirect
62. C₄₁×#494	C₂²	semidirect
63. C₄₁×#492	C₂²	semidirect
64. C₄₁×#489	C₂²	semidirect
65. C₄₁×#487	C₂²	semidirect
66. C₄₁×#486	C₂²	semidirect
67. C₄₁×#486	C₂²	semidirect
68. C₄₁×#484	C₂²	semidirect
70. C₄₁×#480	C₂²	semidirect
71. C₄₁×#480	C₂²	semidirect
72. C₄₁×#477	C₂²	semidirect
73. C₄₁×#477	C₂²	semidirect
74. C₄₁×#474	C₂²	semidirect
75. C₄₁×#474	C₂²	semidirect
76. C₄₁×#474	C₂²	semidirect
77. C₄₁×#474	C₂²	semidirect
78. C₄₁×#474	C₂²	semidirect
80. C₄₁×#468	C₂²	semidirect
81. C₄₁×#468	C₂²	semidirect
82. C₄₁×#468	C₂²	semidirect
83. C₄₁×#467	C₂²	semidirect
85. C₄₁×#464	C₂²	semidirect
86. C₄₁×#464	C₂²	semidirect
87. C₄₁×#464	C₂²	semidirect
88. C₄₁×#464	C₂²	semidirect
90. C₄₁×#463	C₂²	semidirect
91. C₄₁×#463	C₂²	semidirect
92. C₄₁×#463	C₂²	semidirect
93. C₄₁×#461	C₂²	semidirect
94. C₄₁×#461	C₂²	semidirect
95. C₄₁×#461	C₂²	semidirect
96. C₄₁×#461	C₂²	semidirect
97. C₄₁×#460	C₂²	semidirect
98. 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×#450	C₂²	semidirect
110. C₄₁×#449	C₂²	semidirect
113. C₄₁×#447	C₂²	semidirect
114. C₄₁×#446	C₂²	semidirect
115. C₈×Q₈×C₄₁	C₂²	semidirect
116. C₄₁×#440	C₂²	semidirect
117. C₄₁×#440	C₂²	semidirect
118. C₄×Q₁₆×C₄₁	C₂²	semidirect
121. C₄×D₈×C₄₁	C₂²	semidirect
122. C₄×D₈×C₄₁	C₂²	semidirect
123. C₄×D₈×C₄₁	C₂²	semidirect
124. C₄₁×#436	C₂²	semidirect
125. C₄₁×#436	C₂²	semidirect
126. 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. C₄₁×#423	C₂²	semidirect
132. C₄₁×#417	C₂²	semidirect
133. C₄₁×#417	C₂²	semidirect
134. C₂×#102×C₄₁	C₂²	semidirect
550. #62041	C₄₁	direct (N × H)
592. #3546	C₂×C₄₁	semidirect
593. #3520	C₂×C₄₁	semidirect
594. #3397	C₂×C₄₁	semidirect
595. #3393	C₂×C₄₁	semidirect
596. #3367	C₂×C₄₁	semidirect
597. #3358	C₂×C₄₁	semidirect
598. #3333	C₂×C₄₁	semidirect
599. #3330	C₂×C₄₁	semidirect
600. #3314	C₂×C₄₁	semidirect
601. #3294	C₂×C₄₁	semidirect
602. #3283	C₂×C₄₁	semidirect
603. #3273	C₂×C₄₁	semidirect
604. #3272	C₂×C₄₁	semidirect
605. #3268	C₂×C₄₁	semidirect
606. #3262	C₂×C₄₁	semidirect
607. #3254	C₂×C₄₁	semidirect
608. #3224	C₂×C₄₁	semidirect
609. #3210	C₂×C₄₁	semidirect
610. #3124	C₂×C₄₁	semidirect
611. #3100	C₂×C₄₁	semidirect
612. #3045	C₂×C₄₁	semidirect
613. #3036	C₂×C₄₁	semidirect
614. #2993	C₂×C₄₁	semidirect
626. C₂×AGL(1,ℤ/8)	C₂²×C₄₁	semidirect
627. C₂×#135	C₂²×C₄₁	semidirect
629. #556	C₂²×C₄₁	semidirect
630. #556	C₂²×C₄₁	semidirect
631. #554	C₂²×C₄₁	semidirect
636. #550	C₂²×C₄₁	semidirect
637. D₄×Q₈	C₂²×C₄₁	semidirect
641. #547	C₂²×C₄₁	semidirect
644. #546	C₂²×C₄₁	semidirect
645. D₄²	C₂²×C₄₁	semidirect
646. #542	C₂²×C₄₁	semidirect
647. #542	C₂²×C₄₁	semidirect
652. #535	C₂²×C₄₁	semidirect
653. #533	C₂²×C₄₁	semidirect
659. #520	C₂²×C₄₁	semidirect
660. C₂×C₄×D₄	C₂²×C₄₁	semidirect
661. #496	C₂²×C₄₁	semidirect
663. #494	C₂²×C₄₁	semidirect
664. #492	C₂²×C₄₁	semidirect
665. #489	C₂²×C₄₁	semidirect
666. #487	C₂²×C₄₁	semidirect
667. #486	C₂²×C₄₁	semidirect
668. #486	C₂²×C₄₁	semidirect
669. #484	C₂²×C₄₁	semidirect
671. #480	C₂²×C₄₁	semidirect
672. #480	C₂²×C₄₁	semidirect
673. #477	C₂²×C₄₁	semidirect
674. #477	C₂²×C₄₁	semidirect
675. #474	C₂²×C₄₁	semidirect
676. #474	C₂²×C₄₁	semidirect
677. #474	C₂²×C₄₁	semidirect
678. #474	C₂²×C₄₁	semidirect
679. #474	C₂²×C₄₁	semidirect
681. #468	C₂²×C₄₁	semidirect
682. #468	C₂²×C₄₁	semidirect
683. #468	C₂²×C₄₁	semidirect
684. #467	C₂²×C₄₁	semidirect
686. #464	C₂²×C₄₁	semidirect
687. #464	C₂²×C₄₁	semidirect
688. #464	C₂²×C₄₁	semidirect
689. #464	C₂²×C₄₁	semidirect
691. #463	C₂²×C₄₁	semidirect
692. #463	C₂²×C₄₁	semidirect
693. #463	C₂²×C₄₁	semidirect
694. #461	C₂²×C₄₁	semidirect
695. #461	C₂²×C₄₁	semidirect
696. #461	C₂²×C₄₁	semidirect
697. #461	C₂²×C₄₁	semidirect
698. #460	C₂²×C₄₁	semidirect
699. #460	C₂²×C₄₁	semidirect
704. #459	C₂²×C₄₁	semidirect
705. #452	C₂²×C₄₁	semidirect
706. #452	C₂²×C₄₁	semidirect
707. #452	C₂²×C₄₁	semidirect
708. #452	C₂²×C₄₁	semidirect
709. #450	C₂²×C₄₁	semidirect
711. #449	C₂²×C₄₁	semidirect
714. #447	C₂²×C₄₁	semidirect
715. #446	C₂²×C₄₁	semidirect
716. C₈×Q₈	C₂²×C₄₁	semidirect
717. #440	C₂²×C₄₁	semidirect
718. #440	C₂²×C₄₁	semidirect
719. C₄×Q₁₆	C₂²×C₄₁	semidirect
722. C₄×D₈	C₂²×C₄₁	semidirect
723. C₄×D₈	C₂²×C₄₁	semidirect
724. C₄×D₈	C₂²×C₄₁	semidirect
725. #436	C₂²×C₄₁	semidirect
726. #436	C₂²×C₄₁	semidirect
727. #435	C₂²×C₄₁	semidirect
728. C₈×D₄	C₂²×C₄₁	semidirect
729. #433	C₂²×C₄₁	semidirect
730. #431	C₂²×C₄₁	semidirect
731. #424	C₂²×C₄₁	semidirect
732. #423	C₂²×C₄₁	semidirect
733. #417	C₂²×C₄₁	semidirect
734. #417	C₂²×C₄₁	semidirect
735. C₂×#102	C₂²×C₄₁	semidirect
736. C₄₁	#62041	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×#3520	2
C₄₁×#3397	2
C₄₁×#3393	2
C₄₁×#3367	2
C₄₁×#3358	2
C₄₁×#3333	2
C₄₁×#3330	2
C₄₁×#3314	2
C₄₁×#3294	2
C₄₁×#3283	2
C₄₁×#3273	2
C₄₁×#3272	2
C₄₁×#3268	2
C₄₁×#3262	2
C₄₁×#3254	2
C₄₁×#3224	2
C₄₁×#3210	2
C₄₁×#3124	2
C₄₁×#3100	2
C₄₁×#3045	2
C₄₁×#3036	2
C₄₁×#2993	2
#62041	41

Subgroups — C41×#62041 #23838242

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#62041 #23838242