Subgroups — C₄₁×#62068 #23838269

Order 10496.

1846 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3396	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#3328	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#3321	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3304	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#3303	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3282	C₂	1	2	yes	maximal, complemented
12	D₄×SD₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3267	C₂	1	2	yes	maximal, complemented
15	C₄₁×#3263	C₂	1	2	yes	maximal, complemented
16	C₄₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#3225	C₂	1	2	yes	maximal, complemented
18	C₄₁×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#3118	C₂	1	2	yes	maximal, complemented
20	C₄₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄₁×#3042	C₂	1	2	yes	maximal, complemented
22	C₄₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₁×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	2	yes	—
25	C₂×#135×C₄₁	C₂²	1	2	yes	—
26	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
27	C₄₁×#562	—	2	2	no	—
28	C₄₁×#559	—	2	1	no	—
29	C₄₁×#559	C₂²	1	1	yes	characteristic
30	C₄₁×#559	C₂²	1	1	yes	characteristic, complemented
31	C₄₁×#557	C₂²	1	1	yes	characteristic, complemented
32	C₄₁×#556	C₂²	1	1	yes	characteristic
33	C₄₁×#555	C₂²	1	2	yes	—
34	C₄₁×#554	—	2	1	no	—
35	C₄₁×#551	—	2	2	no	—
36	C₄₁×#550	C₂²	1	1	yes	characteristic
37	D₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
39	C₄₁×#548	—	2	1	no	—
40	C₄₁×#548	C₂²	1	2	yes	complemented
41	C₄₁×#547	C₂²	1	2	yes	complemented
42	C₄₁×#546	—	2	1	no	—
43	C₄₁×#546	C₂²	1	2	yes	—
44	D₄²×C₄₁	C₂²	1	1	yes	characteristic
45	C₄₁×#542	—	2	1	no	—
46	C₄₁×#542	C₂²	1	2	yes	—
47	C₄₁×#542	C₂²	1	2	yes	complemented
48	C₄₁×#540	—	2	1	no	—
49	C₄₁×#539	—	2	2	no	—
50	C₄₁×#538	—	2	2	no	—
51	C₄₁×#536	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, complemented
55	C₄₁×#529	—	2	1	no	—
56	C₄₁×#529	C₂²	1	1	yes	characteristic
57	C₂×#124×C₄₁	—	2	1	no	—
58	C₄₁×#518	C₂²	1	2	yes	—
59	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
60	C₄₁×#497	C₂²	1	2	yes	complemented
61	C₄₁×#495	C₂²	1	2	yes	complemented
62	C₄₁×#493	C₂²	1	1	yes	characteristic
63	C₄₁×#492	C₂²	1	1	yes	characteristic
64	C₄₁×#489	C₂²	1	2	yes	complemented
65	C₄₁×#487	C₂²	1	2	yes	complemented
66	C₄₁×#487	C₂²	1	1	yes	characteristic, complemented
67	C₄₁×#486	C₂²	1	1	yes	characteristic, complemented
68	C₄₁×#485	C₂²	1	1	yes	characteristic, complemented
69	C₄₁×#485	C₂²	1	2	yes	complemented
70	C₄₁×#485	C₂²	1	1	yes	characteristic, complemented
71	C₄₁×#482	C₂²	1	2	yes	complemented
72	C₄₁×#476	C₂²	1	2	yes	complemented
73	C₄₁×#476	C₂²	1	2	yes	complemented
74	C₄₁×#475	C₂²	1	1	yes	characteristic, complemented
75	C₄₁×#475	C₂²	1	2	yes	complemented
76	C₄₁×#475	C₂²	1	1	yes	characteristic, complemented
77	C₄₁×#475	C₂²	1	1	yes	characteristic, complemented
78	C₄₁×#474	C₂²	1	1	yes	characteristic
79	C₄₁×#470	C₂²	1	2	yes	complemented
80	C₄₁×#469	C₂²	1	2	yes	—
81	C₄₁×#465	C₂²	1	2	yes	—
82	C₄₁×#465	C₂²	1	2	yes	complemented
83	C₄₁×#465	C₂²	1	2	yes	complemented
84	C₄₁×#465	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	—
88	C₄₁×#463	C₂²	1	2	yes	—
89	C₄₁×#463	C₂²	1	2	yes	complemented
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×#462	C₂²	1	1	yes	characteristic, complemented
94	C₄₁×#462	C₂²	1	1	yes	characteristic, complemented
95	C₄₁×#461	C₂²	1	1	yes	characteristic
96	C₄₁×#461	C₂²	1	2	yes	—
97	C₄₁×#461	C₂²	1	1	yes	characteristic
98	C₄₁×#461	C₂²	1	2	yes	complemented
99	C₄₁×#461	C₂²	1	2	yes	complemented
100	C₄₁×#460	C₂²	1	1	yes	characteristic
101	C₄₁×#460	C₂²	1	1	yes	characteristic
102	C₄₁×#460	C₂²	1	1	yes	characteristic, complemented
103	C₄₁×#459	C₂²	1	1	yes	characteristic
104	C₄₁×#452	C₂²	1	1	yes	characteristic
105	C₄₁×#452	C₂²	1	1	yes	characteristic
106	C₄₁×#452	C₂²	1	2	yes	complemented
107	C₄₁×#451	C₂²	1	2	yes	complemented
108	C₄₁×#450	C₂²	1	2	yes	—
109	C₄₁×#449	C₂²	1	2	yes	—
110	C₄₁×#449	C₂²	1	2	yes	complemented
111	C₄₁×#449	C₂²	1	2	yes	complemented
112	C₄₁×#448	C₂²	1	2	yes	—
113	C₄₁×#447	C₂²	1	2	yes	—
114	C₄₁×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
116	C₄₁×#442	C₂²	1	2	yes	—
117	C₄₁×#440	C₂²	1	2	yes	complemented
118	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
120	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
121	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
122	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
123	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
124	C₄₁×#436	C₂²	1	1	yes	characteristic
125	C₄₁×#435	C₂²	1	2	yes	complemented
126	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
127	C₈×D₄×C₄₁	C₂²	1	2	yes	complemented
128	C₄₁×#433	C₂²	1	2	yes	complemented
129	C₄₁×#431	C₂²	1	1	yes	characteristic, complemented
130	C₄₁×#424	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
132	C₄₁×#419	C₂²	1	2	yes	complemented
133	C₄₁×#416	C₂²	1	2	yes	complemented
134	C₄₁×#416	C₂²	1	2	yes	complemented
135	C₂×#41×C₄₁	—	2	1	no	—
136	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
137	C₂×#41×C₄₁	C₂³	1	2	yes	—
138	C₂×#41×C₄₁	C₂³	1	2	yes	—
139	C₂²×Q₈×C₄₁	—	2	1	no	—
140	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
141	C₂²×D₄×C₄₁	—	2	1	no	—
142	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
143	AGL(1,ℤ/8)×C₄₁	—	4	4	no	—
144	#135×C₄₁	—	4	4	no	—
145	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₄₁	—	4	4	no	—
149	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
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	2	yes	—
158	C₂×D₈×C₄₁	C₂³	1	2	yes	—
159	C₂×D₈×C₄₁	C₂³	1	2	yes	—
160	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
161	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
162	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₄₁	—	2	1	no	—
164	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
167	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
170	#127×C₄₁	—	2	1	no	—
171	#127×C₄₁	C₂³	1	1	yes	characteristic
172	#127×C₄₁	C₂³	1	1	yes	characteristic
173	#126×C₄₁	—	2	2	no	—
174	#126×C₄₁	—	2	2	no	—
175	#126×C₄₁	—	2	2	no	—
176	#126×C₄₁	D₄	1	2	yes	—
177	#125×C₄₁	—	2	2	no	—
178	#125×C₄₁	—	2	1	no	—
179	#125×C₄₁	—	2	1	no	—
180	#125×C₄₁	D₄	1	1	yes	characteristic
181	#124×C₄₁	—	2	1	no	—
182	#124×C₄₁	—	2	1	no	—
183	#124×C₄₁	—	2	1	no	—
184	#124×C₄₁	—	2	2	no	—
185	#124×C₄₁	—	2	2	no	—
186	#124×C₄₁	—	2	2	no	—
187	#124×C₄₁	—	2	2	no	—
188	#124×C₄₁	—	2	2	no	—
189	#124×C₄₁	—	2	1	no	—
190	#124×C₄₁	D₄	1	1	yes	characteristic
191	#124×C₄₁	C₂³	1	2	yes	—
192	#124×C₄₁	C₂³	1	2	yes	—
193	#124×C₄₁	C₂³	1	2	yes	—
194	#123×C₄₁	—	2	2	no	—
195	#123×C₄₁	—	2	2	no	—
196	#123×C₄₁	—	2	2	no	—
197	#123×C₄₁	—	2	2	no	—
198	#123×C₄₁	—	2	2	no	—
199	#123×C₄₁	—	2	2	no	—
200	#123×C₄₁	—	2	2	no	—
201	#123×C₄₁	—	2	2	no	—
202	#123×C₄₁	—	2	2	no	—
203	#123×C₄₁	D₄	1	2	yes	—
204	C₂²⋊Q₈×C₄₁	—	2	1	no	—
205	C₂²⋊Q₈×C₄₁	—	2	1	no	—
206	C₂²⋊Q₈×C₄₁	—	2	2	no	—
207	C₂²⋊Q₈×C₄₁	—	2	2	no	—
208	C₂²⋊Q₈×C₄₁	—	2	2	no	—
209	C₂²⋊Q₈×C₄₁	—	2	2	no	—
210	C₂²⋊Q₈×C₄₁	—	2	2	no	—
211	C₂²⋊Q₈×C₄₁	—	2	2	no	—
212	C₂²⋊Q₈×C₄₁	—	2	2	no	—
213	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
214	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
215	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
216	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
217	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
218	#121×C₄₁	—	2	2	no	—
219	#121×C₄₁	—	2	2	no	—
220	#121×C₄₁	—	2	2	no	—
221	#121×C₄₁	—	2	1	no	—
222	#121×C₄₁	—	2	1	no	—
223	#121×C₄₁	—	2	1	no	—
224	#121×C₄₁	—	2	1	no	—
225	#121×C₄₁	—	2	2	no	—
226	#121×C₄₁	—	2	2	no	—
227	#121×C₄₁	D₄	1	1	yes	characteristic
228	#121×C₄₁	C₂³	1	2	yes	—
229	#121×C₄₁	C₂³	1	2	yes	—
230	#121×C₄₁	C₂³	1	2	yes	—
231	#120×C₄₁	—	2	2	no	—
232	#120×C₄₁	—	2	2	no	—
233	C₄×Q₈×C₄₁	—	2	1	no	—
234	C₄×Q₈×C₄₁	—	2	1	no	—
235	C₄×Q₈×C₄₁	—	2	1	no	—
236	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
241	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₄₁	—	2	1	no	—
243	C₄×D₄×C₄₁	—	2	1	no	—
244	C₄×D₄×C₄₁	—	2	1	no	—
245	C₄×D₄×C₄₁	—	2	2	no	—
246	C₄×D₄×C₄₁	—	2	2	no	—
247	C₄×D₄×C₄₁	—	2	1	no	—
248	C₄×D₄×C₄₁	—	2	1	no	—
249	C₄×D₄×C₄₁	—	2	1	no	—
250	C₄×D₄×C₄₁	—	2	2	no	—
251	C₄×D₄×C₄₁	—	2	1	no	—
252	C₄×D₄×C₄₁	—	2	1	no	—
253	C₄×D₄×C₄₁	—	2	1	no	—
254	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₄₁	C₂³	1	2	yes	—
257	C₄×D₄×C₄₁	C₂³	1	2	yes	—
258	C₄×D₄×C₄₁	C₂³	1	2	yes	—
259	C₄×D₄×C₄₁	C₂³	1	2	yes	—
260	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₄₁	C₂³	1	2	yes	—
262	#117×C₄₁	—	2	1	no	—
263	#117×C₄₁	—	2	2	no	—
264	#117×C₄₁	—	2	1	no	—
265	#117×C₄₁	C₂³	1	1	yes	characteristic
266	#117×C₄₁	C₂³	1	2	yes	—
267	#117×C₄₁	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
269	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
270	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
271	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
272	C₂×C₄²×C₄₁	—	2	1	no	—
273	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
274	#107×C₄₁	C₂³	1	1	yes	characteristic
275	#107×C₄₁	C₂³	1	1	yes	characteristic
276	#106×C₄₁	C₂³	1	1	yes	characteristic
277	#106×C₄₁	C₂³	1	2	yes	—
278	#106×C₄₁	C₂³	1	1	yes	characteristic
279	#106×C₄₁	C₂³	1	2	yes	—
280	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
281	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
285	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
286	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
287	#103×C₄₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
292	#103×C₄₁	C₂³	1	2	yes	—
293	#103×C₄₁	C₂³	1	2	yes	—
294	#103×C₄₁	C₂³	1	1	yes	characteristic
295	#103×C₄₁	C₂³	1	1	yes	characteristic
296	#103×C₄₁	C₂³	1	2	yes	—
297	#103×C₄₁	C₂³	1	1	yes	characteristic
298	#103×C₄₁	C₂³	1	1	yes	characteristic
299	#102×C₄₁	C₂³	1	2	yes	—
300	#102×C₄₁	C₂³	1	2	yes	—
301	#102×C₄₁	C₂³	1	2	yes	—
302	#102×C₄₁	C₂³	1	2	yes	—
303	#102×C₄₁	C₂³	1	1	yes	characteristic
304	#102×C₄₁	C₂³	1	1	yes	characteristic
305	#102×C₄₁	C₂³	1	2	yes	—
306	#102×C₄₁	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
311	#97×C₄₁	C₂³	1	2	yes	—
312	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₄₁	C₂³	1	2	yes	—
315	C₂⁴×C₄₁	—	2	2	no	—
316	#41×C₄₁	—	2	2	no	—
317	#41×C₄₁	—	4	1	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	—	8	2	no	—
323	C₂×Q₈×C₄₁	—	2	1	no	—
324	C₂×Q₈×C₄₁	—	2	1	no	—
325	C₂×Q₈×C₄₁	—	2	2	no	—
326	C₂×Q₈×C₄₁	—	2	2	no	—
327	C₂×Q₈×C₄₁	—	4	2	no	—
328	C₂×Q₈×C₄₁	—	4	2	no	—
329	C₂×Q₈×C₄₁	—	8	2	no	—
330	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₄₁	—	2	4	no	—
336	C₂×D₄×C₄₁	—	2	1	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	2	no	—
341	C₂×D₄×C₄₁	—	2	2	no	—
342	C₂×D₄×C₄₁	—	2	1	no	—
343	C₂×D₄×C₄₁	—	2	2	no	—
344	C₂×D₄×C₄₁	—	2	1	no	—
345	C₂×D₄×C₄₁	—	2	1	no	—
346	C₂×D₄×C₄₁	—	2	1	no	—
347	C₂×D₄×C₄₁	—	4	2	no	—
348	C₂×D₄×C₄₁	—	8	2	no	—
349	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
352	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
353	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₄₁	—	2	2	no	—
355	C₂²×C₄×C₄₁	—	2	1	no	—
356	C₂²×C₄×C₄₁	—	2	1	no	—
357	C₂²×C₄×C₄₁	—	2	1	no	—
358	C₂²×C₄×C₄₁	—	2	2	no	—
359	C₂²×C₄×C₄₁	—	2	2	no	—
360	C₂²×C₄×C₄₁	—	2	2	no	—
361	C₂²×C₄×C₄₁	—	2	2	no	—
362	C₂²×C₄×C₄₁	—	2	2	no	—
363	C₂²×C₄×C₄₁	—	2	2	no	—
364	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
368	Q₁₆×C₄₁	—	4	1	no	—
369	Q₁₆×C₄₁	—	4	1	no	—
370	Q₁₆×C₄₁	—	4	2	no	—
371	SD₁₆×C₄₁	—	2	2	no	—
372	SD₁₆×C₄₁	—	2	4	no	—
373	SD₁₆×C₄₁	—	2	2	no	—
374	SD₁₆×C₄₁	—	4	2	no	—
375	SD₁₆×C₄₁	—	4	2	no	—
376	SD₁₆×C₄₁	—	4	2	no	—
377	SD₁₆×C₄₁	—	4	2	no	—
378	SD₁₆×C₄₁	—	4	2	no	—
379	D₈×C₄₁	—	2	4	no	—
380	D₈×C₄₁	—	4	2	no	—
381	D₈×C₄₁	—	4	2	no	—
382	M₁₆×C₄₁	—	4	2	no	—
383	C₂×C₈×C₄₁	—	4	2	no	—
384	C₂×C₈×C₄₁	—	4	2	no	—
385	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
389	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
391	C₄⋊C₄×C₄₁	—	2	1	no	—
392	C₄⋊C₄×C₄₁	—	2	2	no	—
393	C₄⋊C₄×C₄₁	—	2	2	no	—
394	C₄⋊C₄×C₄₁	—	2	1	no	—
395	C₄⋊C₄×C₄₁	—	2	1	no	—
396	C₄⋊C₄×C₄₁	—	2	2	no	—
397	C₄⋊C₄×C₄₁	—	2	1	no	—
398	C₄⋊C₄×C₄₁	—	2	1	no	—
399	C₄⋊C₄×C₄₁	—	2	1	no	—
400	C₄⋊C₄×C₄₁	—	2	1	no	—
401	C₄⋊C₄×C₄₁	—	2	1	no	—
402	C₄⋊C₄×C₄₁	—	2	1	no	—
403	C₄⋊C₄×C₄₁	—	2	2	no	—
404	C₄⋊C₄×C₄₁	—	2	1	no	—
405	C₄⋊C₄×C₄₁	—	2	2	no	—
406	C₄⋊C₄×C₄₁	—	2	1	no	—
407	C₄⋊C₄×C₄₁	—	2	2	no	—
408	C₄⋊C₄×C₄₁	—	2	1	no	—
409	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
413	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
415	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
418	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
420	C₂²⋊C₄×C₄₁	—	2	2	no	—
421	C₂²⋊C₄×C₄₁	—	2	2	no	—
422	C₂²⋊C₄×C₄₁	—	2	1	no	—
423	C₂²⋊C₄×C₄₁	—	2	1	no	—
424	C₂²⋊C₄×C₄₁	—	2	1	no	—
425	C₂²⋊C₄×C₄₁	—	2	2	no	—
426	C₂²⋊C₄×C₄₁	—	2	1	no	—
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	2	no	—
431	C₂²⋊C₄×C₄₁	—	2	2	no	—
432	C₂²⋊C₄×C₄₁	—	2	1	no	—
433	C₂²⋊C₄×C₄₁	—	2	2	no	—
434	C₂²⋊C₄×C₄₁	—	2	2	no	—
435	C₂²⋊C₄×C₄₁	—	2	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	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
446	C₄²×C₄₁	—	2	1	no	—
447	C₄²×C₄₁	—	2	1	no	—
448	C₄²×C₄₁	—	2	1	no	—
449	C₄²×C₄₁	—	2	2	no	—
450	C₄²×C₄₁	—	2	1	no	—
451	C₄²×C₄₁	—	2	1	no	—
452	C₄²×C₄₁	—	2	2	no	—
453	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
456	C₄²×C₄₁	C₂⁴	1	2	yes	—
457	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
458	C₂³×C₄₁	—	2	1	no	—
459	C₂³×C₄₁	—	2	2	no	—
460	C₂³×C₄₁	—	2	2	no	—
461	C₂³×C₄₁	—	4	4	no	—
462	C₂³×C₄₁	—	8	2	no	—
463	C₂³×C₄₁	—	8	2	no	—
464	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
465	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
466	Q₈×C₄₁	—	2	2	no	—
467	Q₈×C₄₁	—	2	1	no	—
468	Q₈×C₄₁	—	2	1	no	—
469	Q₈×C₄₁	—	2	2	no	—
470	Q₈×C₄₁	—	2	1	no	—
471	Q₈×C₄₁	—	2	2	no	—
472	Q₈×C₄₁	—	2	1	no	—
473	Q₈×C₄₁	—	2	1	no	—
474	Q₈×C₄₁	—	2	1	no	—
475	Q₈×C₄₁	—	4	2	no	—
476	Q₈×C₄₁	—	8	1	no	—
477	Q₈×C₄₁	—	8	2	no	—
478	Q₈×C₄₁	—	8	2	no	—
479	D₄×C₄₁	—	2	2	no	—
480	D₄×C₄₁	—	2	2	no	—
481	D₄×C₄₁	—	2	2	no	—
482	D₄×C₄₁	—	2	1	no	—
483	D₄×C₄₁	—	2	2	no	—
484	D₄×C₄₁	—	2	2	no	—
485	D₄×C₄₁	—	4	2	no	—
486	D₄×C₄₁	—	4	4	no	—
487	D₄×C₄₁	—	4	2	no	—
488	D₄×C₄₁	—	4	2	no	—
489	D₄×C₄₁	—	4	2	no	—
490	D₄×C₄₁	—	8	1	no	—
491	D₄×C₄₁	—	8	1	no	—
492	D₄×C₄₁	—	8	2	no	—
493	D₄×C₄₁	—	8	2	no	—
494	D₄×C₄₁	—	8	2	no	—
495	D₄×C₄₁	—	8	2	no	—
496	D₄×C₄₁	—	8	2	no	—
497	D₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
498	C₂×C₄×C₄₁	—	2	2	no	—
499	C₂×C₄×C₄₁	—	2	1	no	—
500	C₂×C₄×C₄₁	—	2	2	no	—
501	C₂×C₄×C₄₁	—	2	2	no	—
502	C₂×C₄×C₄₁	—	2	1	no	—
503	C₂×C₄×C₄₁	—	2	1	no	—
504	C₂×C₄×C₄₁	—	2	1	no	—
505	C₂×C₄×C₄₁	—	2	1	no	—
506	C₂×C₄×C₄₁	—	2	1	no	—
507	C₂×C₄×C₄₁	—	2	1	no	—
508	C₂×C₄×C₄₁	—	2	1	no	—
509	C₂×C₄×C₄₁	—	2	2	no	—
510	C₂×C₄×C₄₁	—	2	2	no	—
511	C₂×C₄×C₄₁	—	2	1	no	—
512	C₂×C₄×C₄₁	—	4	1	no	—
513	C₂×C₄×C₄₁	—	4	2	no	—
514	C₂×C₄×C₄₁	—	4	2	no	—
515	C₂×C₄×C₄₁	—	8	1	no	—
516	C₂×C₄×C₄₁	—	8	2	no	—
517	C₂×C₄×C₄₁	—	8	2	no	—
518	C₂×C₄×C₄₁	—	8	2	no	—
519	C₂×C₄×C₄₁	—	8	2	no	—
520	C₂×C₄×C₄₁	—	8	2	no	—
521	C₂×C₄×C₄₁	—	8	2	no	—
522	C₂×C₄×C₄₁	—	8	2	no	—
523	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
532	C₈×C₄₁	—	2	1	no	—
533	C₈×C₄₁	—	2	2	no	—
534	C₈×C₄₁	—	2	2	no	—
535	C₈×C₄₁	—	2	1	no	—
536	C₈×C₄₁	—	2	1	no	—
537	C₈×C₄₁	—	2	1	no	—
538	#62068	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
539	C₂²×C₄₁	—	2	1	no	—
540	C₂²×C₄₁	—	2	2	no	—
541	C₂²×C₄₁	—	2	2	no	—
542	C₂²×C₄₁	—	2	1	no	—
543	C₂²×C₄₁	—	2	2	no	—
544	C₂²×C₄₁	—	2	1	no	—
545	C₂²×C₄₁	—	2	2	no	—
546	C₂²×C₄₁	—	4	1	no	—
547	C₂²×C₄₁	—	4	1	no	—
548	C₂²×C₄₁	—	4	2	no	—
549	C₂²×C₄₁	—	4	2	no	—
550	C₂²×C₄₁	—	4	2	no	—
551	C₂²×C₄₁	—	4	2	no	—
552	C₂²×C₄₁	—	4	2	no	—
553	C₂²×C₄₁	—	4	2	no	—
554	C₂²×C₄₁	—	16	4	no	—
555	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
556	C₄×C₄₁	—	2	1	no	—
557	C₄×C₄₁	—	2	1	no	—
558	C₄×C₄₁	—	2	2	no	—
559	C₄×C₄₁	—	2	1	no	—
560	C₄×C₄₁	—	2	2	no	—
561	C₄×C₄₁	—	2	1	no	—
562	C₄×C₄₁	—	2	2	no	—
563	C₄×C₄₁	—	4	1	no	—
564	C₄×C₄₁	—	4	1	no	—
565	C₄×C₄₁	—	4	1	no	—
566	C₄×C₄₁	—	4	1	no	—
567	C₄×C₄₁	—	4	1	no	—
568	C₄×C₄₁	—	4	2	no	—
569	C₄×C₄₁	—	4	1	no	—
570	C₄×C₄₁	—	4	1	no	—
571	C₄×C₄₁	—	4	2	no	—
572	C₄×C₄₁	#577	1	2	yes	—
573	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
574	C₄×C₄₁	#585	1	1	yes	characteristic
575	#3554	C₂×C₄₁	1	1	yes	characteristic, complemented
576	#3514	C₂×C₄₁	1	1	yes	characteristic, complemented
577	#3400	C₂×C₄₁	1	1	yes	characteristic, complemented
578	#3396	C₂×C₄₁	1	1	yes	characteristic, complemented
579	#3373	C₂×C₄₁	1	1	yes	characteristic, complemented
580	#3359	C₂×C₄₁	1	1	yes	characteristic, complemented
581	#3328	C₂×C₄₁	1	1	yes	characteristic, complemented
582	#3321	C₂×C₄₁	1	2	yes	complemented
583	#3304	C₂×C₄₁	1	1	yes	characteristic, complemented
584	#3303	C₂×C₄₁	1	2	yes	complemented
585	#3282	C₂×C₄₁	1	2	yes	complemented
586	D₄×SD₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
587	#3274	C₂×C₄₁	1	1	yes	characteristic, complemented
588	#3267	C₂×C₄₁	1	2	yes	complemented
589	#3263	C₂×C₄₁	1	2	yes	complemented
590	#3246	C₂×C₄₁	1	1	yes	characteristic, complemented
591	#3225	C₂×C₄₁	1	2	yes	complemented
592	#3207	C₂×C₄₁	1	1	yes	characteristic, complemented
593	#3118	C₂×C₄₁	1	2	yes	complemented
594	#3107	C₂×C₄₁	1	1	yes	characteristic, complemented
595	#3042	C₂×C₄₁	1	2	yes	complemented
596	#3035	C₂×C₄₁	1	1	yes	characteristic, complemented
597	#2994	C₂×C₄₁	1	1	yes	characteristic, complemented
598	C₂×C₄₁	—	4	1	no	—
599	C₂×C₄₁	—	4	2	no	—
600	C₂×C₄₁	—	4	2	no	—
601	C₂×C₄₁	—	8	2	no	—
602	C₂×C₄₁	—	8	2	no	—
603	C₂×C₄₁	#3488	1	1	yes	characteristic
604	C₂×C₄₁	C₂×#577	1	1	yes	characteristic
605	C₂×C₄₁	#3584	1	1	yes	characteristic
606	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	2	yes	—
607	C₂×#135	C₂²×C₄₁	1	2	yes	—
608	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
609	#562	—	2	2	no	—
610	#559	—	2	1	no	—
611	#559	C₂²×C₄₁	1	1	yes	characteristic
612	#559	C₂²×C₄₁	1	1	yes	characteristic, complemented
613	#557	C₂²×C₄₁	1	1	yes	characteristic, complemented
614	#556	C₂²×C₄₁	1	1	yes	characteristic
615	#555	C₂²×C₄₁	1	2	yes	—
616	#554	—	2	1	no	—
617	#551	—	2	2	no	—
618	#550	C₂²×C₄₁	1	1	yes	characteristic
619	D₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
620	D₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
621	#548	—	2	1	no	—
622	#548	C₂²×C₄₁	1	2	yes	complemented
623	#547	C₂²×C₄₁	1	2	yes	complemented
624	#546	—	2	1	no	—
625	#546	C₂²×C₄₁	1	2	yes	—
626	D₄²	C₂²×C₄₁	1	1	yes	characteristic
627	#542	—	2	1	no	—
628	#542	C₂²×C₄₁	1	2	yes	—
629	#542	C₂²×C₄₁	1	2	yes	complemented
630	#540	—	2	1	no	—
631	#539	—	2	2	no	—
632	#538	—	2	2	no	—
633	#536	C₂²×C₄₁	1	2	yes	complemented
634	#533	C₂²×C₄₁	1	1	yes	characteristic, complemented
635	#532	C₂²×C₄₁	1	1	yes	characteristic
636	#532	C₂²×C₄₁	1	1	yes	characteristic, complemented
637	#529	—	2	1	no	—
638	#529	C₂²×C₄₁	1	1	yes	characteristic
639	C₂×#124	—	2	1	no	—
640	#518	C₂²×C₄₁	1	2	yes	—
641	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
642	#497	C₂²×C₄₁	1	2	yes	complemented
643	#495	C₂²×C₄₁	1	2	yes	complemented
644	#493	C₂²×C₄₁	1	1	yes	characteristic
645	#492	C₂²×C₄₁	1	1	yes	characteristic
646	#489	C₂²×C₄₁	1	2	yes	complemented
647	#487	C₂²×C₄₁	1	1	yes	characteristic, complemented
648	#487	C₂²×C₄₁	1	2	yes	complemented
649	#486	C₂²×C₄₁	1	1	yes	characteristic, complemented
650	#485	C₂²×C₄₁	1	2	yes	complemented
651	#485	C₂²×C₄₁	1	1	yes	characteristic, complemented
652	#485	C₂²×C₄₁	1	1	yes	characteristic, complemented
653	#482	C₂²×C₄₁	1	2	yes	complemented
654	#476	C₂²×C₄₁	1	2	yes	complemented
655	#476	C₂²×C₄₁	1	2	yes	complemented
656	#475	C₂²×C₄₁	1	1	yes	characteristic, complemented
657	#475	C₂²×C₄₁	1	1	yes	characteristic, complemented
658	#475	C₂²×C₄₁	1	2	yes	complemented
659	#475	C₂²×C₄₁	1	1	yes	characteristic, complemented
660	#474	C₂²×C₄₁	1	1	yes	characteristic
661	#470	C₂²×C₄₁	1	2	yes	complemented
662	#469	C₂²×C₄₁	1	2	yes	—
663	#465	C₂²×C₄₁	1	2	yes	—
664	#465	C₂²×C₄₁	1	2	yes	complemented
665	#465	C₂²×C₄₁	1	2	yes	complemented
666	#465	C₂²×C₄₁	1	2	yes	complemented
667	#464	C₂²×C₄₁	1	2	yes	complemented
668	#464	C₂²×C₄₁	1	2	yes	complemented
669	#463	C₂²×C₄₁	1	2	yes	—
670	#463	C₂²×C₄₁	1	2	yes	—
671	#463	C₂²×C₄₁	1	2	yes	complemented
672	#463	C₂²×C₄₁	1	2	yes	complemented
673	#463	C₂²×C₄₁	1	2	yes	complemented
674	#463	C₂²×C₄₁	1	2	yes	complemented
675	#462	C₂²×C₄₁	1	1	yes	characteristic, complemented
676	#462	C₂²×C₄₁	1	1	yes	characteristic, complemented
677	#461	C₂²×C₄₁	1	2	yes	—
678	#461	C₂²×C₄₁	1	1	yes	characteristic
679	#461	C₂²×C₄₁	1	1	yes	characteristic
680	#461	C₂²×C₄₁	1	2	yes	complemented
681	#461	C₂²×C₄₁	1	2	yes	complemented
682	#460	C₂²×C₄₁	1	1	yes	characteristic
683	#460	C₂²×C₄₁	1	1	yes	characteristic
684	#460	C₂²×C₄₁	1	1	yes	characteristic, complemented
685	#459	C₂²×C₄₁	1	1	yes	characteristic
686	#452	C₂²×C₄₁	1	1	yes	characteristic
687	#452	C₂²×C₄₁	1	1	yes	characteristic
688	#452	C₂²×C₄₁	1	2	yes	complemented
689	#451	C₂²×C₄₁	1	2	yes	complemented
690	#450	C₂²×C₄₁	1	2	yes	—
691	#449	C₂²×C₄₁	1	2	yes	—
692	#449	C₂²×C₄₁	1	2	yes	complemented
693	#449	C₂²×C₄₁	1	2	yes	complemented
694	#448	C₂²×C₄₁	1	2	yes	—
695	#447	C₂²×C₄₁	1	2	yes	—
696	#446	C₂²×C₄₁	1	1	yes	characteristic, complemented
697	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
698	#442	C₂²×C₄₁	1	2	yes	—
699	#440	C₂²×C₄₁	1	2	yes	complemented
700	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
701	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
702	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
703	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
704	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
705	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
706	#436	C₂²×C₄₁	1	1	yes	characteristic
707	#435	C₂²×C₄₁	1	2	yes	complemented
708	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
709	C₈×D₄	C₂²×C₄₁	1	2	yes	complemented
710	#433	C₂²×C₄₁	1	2	yes	complemented
711	#431	C₂²×C₄₁	1	1	yes	characteristic, complemented
712	#424	C₂²×C₄₁	1	2	yes	complemented
713	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
714	#419	C₂²×C₄₁	1	2	yes	complemented
715	#416	C₂²×C₄₁	1	2	yes	complemented
716	#416	C₂²×C₄₁	1	2	yes	complemented
717	C₄₁	#62068	1	1	yes	characteristic, direct product factor, Sylow
718	C₂×#41	—	2	1	no	—
719	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
720	C₂×#41	C₂³×C₄₁	1	2	yes	—
721	C₂×#41	C₂³×C₄₁	1	2	yes	—
722	C₂²×Q₈	—	2	1	no	—
723	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
724	C₂²×D₄	—	2	1	no	—
725	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
726	AGL(1,ℤ/8)	—	4	4	no	—
727	#135	—	4	4	no	—
728	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
729	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
730	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
731	C₂×SD₁₆	—	4	4	no	—
732	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
733	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
735	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
737	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
738	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
739	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
740	C₂×D₈	C₂³×C₄₁	1	2	yes	—
741	C₂×D₈	C₂³×C₄₁	1	2	yes	—
742	C₂×D₈	C₂³×C₄₁	1	2	yes	—
743	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
744	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
745	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
746	C₄⋊Q₈	—	2	1	no	—
747	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
748	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
749	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
750	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
751	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
752	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
753	#127	—	2	1	no	—
754	#127	C₂³×C₄₁	1	1	yes	characteristic
755	#127	C₂³×C₄₁	1	1	yes	characteristic
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	—	2	2	no	—
759	#126	D₄×C₄₁	1	2	yes	—
760	#125	—	2	2	no	—
761	#125	—	2	1	no	—
762	#125	—	2	1	no	—
763	#125	D₄×C₄₁	1	1	yes	characteristic
764	#124	—	2	1	no	—
765	#124	—	2	1	no	—
766	#124	—	2	1	no	—
767	#124	—	2	2	no	—
768	#124	—	2	2	no	—
769	#124	—	2	2	no	—
770	#124	—	2	2	no	—
771	#124	—	2	2	no	—
772	#124	—	2	1	no	—
773	#124	D₄×C₄₁	1	1	yes	characteristic
774	#124	C₂³×C₄₁	1	2	yes	—
775	#124	C₂³×C₄₁	1	2	yes	—
776	#124	C₂³×C₄₁	1	2	yes	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	#123	—	2	2	no	—
786	#123	D₄×C₄₁	1	2	yes	—
787	C₂²⋊Q₈	—	2	1	no	—
788	C₂²⋊Q₈	—	2	1	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	—	2	2	no	—
796	C₂²⋊Q₈	D₄×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⋊Q₈	C₂³×C₄₁	1	2	yes	—
800	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	—	2	1	no	—
805	#121	—	2	1	no	—
806	#121	—	2	1	no	—
807	#121	—	2	1	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	D₄×C₄₁	1	1	yes	characteristic
811	#121	C₂³×C₄₁	1	2	yes	—
812	#121	C₂³×C₄₁	1	2	yes	—
813	#121	C₂³×C₄₁	1	2	yes	—
814	#120	—	2	2	no	—
815	#120	—	2	2	no	—
816	C₄×Q₈	—	2	1	no	—
817	C₄×Q₈	—	2	1	no	—
818	C₄×Q₈	—	2	1	no	—
819	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
820	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
821	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
822	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
823	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
824	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	2	no	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
838	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₄₁	1	2	yes	—
840	C₄×D₄	C₂³×C₄₁	1	2	yes	—
841	C₄×D₄	C₂³×C₄₁	1	2	yes	—
842	C₄×D₄	C₂³×C₄₁	1	2	yes	—
843	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
844	C₄×D₄	C₂³×C₄₁	1	2	yes	—
845	#117	—	2	1	no	—
846	#117	—	2	2	no	—
847	#117	—	2	1	no	—
848	#117	C₂³×C₄₁	1	1	yes	characteristic
849	#117	C₂³×C₄₁	1	2	yes	—
850	#117	C₂³×C₄₁	1	2	yes	—
851	C₂×C₄⋊C₄	—	2	2	no	—
852	C₂×C₂²⋊C₄	—	2	2	no	—
853	C₂×C₂²⋊C₄	—	2	2	no	—
854	C₂×C₂²⋊C₄	—	2	2	no	—
855	C₂×C₄²	—	2	1	no	—
856	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
857	#107	C₂³×C₄₁	1	1	yes	characteristic
858	#107	C₂³×C₄₁	1	1	yes	characteristic
859	#106	C₂³×C₄₁	1	1	yes	characteristic
860	#106	C₂³×C₄₁	1	2	yes	—
861	#106	C₂³×C₄₁	1	1	yes	characteristic
862	#106	C₂³×C₄₁	1	2	yes	—
863	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
864	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
865	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
866	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
867	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
868	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
869	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
870	#103	C₂³×C₄₁	1	1	yes	characteristic
871	#103	C₂³×C₄₁	1	2	yes	—
872	#103	C₂³×C₄₁	1	2	yes	—
873	#103	C₂³×C₄₁	1	2	yes	—
874	#103	C₂³×C₄₁	1	1	yes	characteristic
875	#103	C₂³×C₄₁	1	2	yes	—
876	#103	C₂³×C₄₁	1	2	yes	—
877	#103	C₂³×C₄₁	1	1	yes	characteristic
878	#103	C₂³×C₄₁	1	1	yes	characteristic
879	#103	C₂³×C₄₁	1	2	yes	—
880	#103	C₂³×C₄₁	1	1	yes	characteristic
881	#103	C₂³×C₄₁	1	1	yes	characteristic
882	#102	C₂³×C₄₁	1	2	yes	—
883	#102	C₂³×C₄₁	1	2	yes	—
884	#102	C₂³×C₄₁	1	2	yes	—
885	#102	C₂³×C₄₁	1	2	yes	—
886	#102	C₂³×C₄₁	1	1	yes	characteristic
887	#102	C₂³×C₄₁	1	1	yes	characteristic
888	#102	C₂³×C₄₁	1	2	yes	—
889	#102	C₂³×C₄₁	1	2	yes	—
890	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
891	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
892	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
893	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
894	#97	C₂³×C₄₁	1	2	yes	—
895	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
896	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
897	C₄×C₈	C₂³×C₄₁	1	2	yes	—
898	C₂⁴	—	2	2	no	—
899	#41	—	2	2	no	—
900	#41	—	4	1	no	—
901	#41	—	4	2	no	—
902	#41	—	4	2	no	—
903	#41	—	4	2	no	—
904	#41	—	4	2	no	—
905	#41	—	8	2	no	—
906	C₂×Q₈	—	2	1	no	—
907	C₂×Q₈	—	2	1	no	—
908	C₂×Q₈	—	2	2	no	—
909	C₂×Q₈	—	2	2	no	—
910	C₂×Q₈	—	4	2	no	—
911	C₂×Q₈	—	4	2	no	—
912	C₂×Q₈	—	8	2	no	—
913	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
914	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
915	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
916	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
917	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
918	C₂×D₄	—	2	4	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	4	2	no	—
931	C₂×D₄	—	8	2	no	—
932	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
933	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
934	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
935	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
936	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
948	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
949	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
950	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
951	Q₁₆	—	4	1	no	—
952	Q₁₆	—	4	1	no	—
953	Q₁₆	—	4	2	no	—
954	SD₁₆	—	2	2	no	—
955	SD₁₆	—	2	4	no	—
956	SD₁₆	—	2	2	no	—
957	SD₁₆	—	4	2	no	—
958	SD₁₆	—	4	2	no	—
959	SD₁₆	—	4	2	no	—
960	SD₁₆	—	4	2	no	—
961	SD₁₆	—	4	2	no	—
962	D₈	—	2	4	no	—
963	D₈	—	4	2	no	—
964	D₈	—	4	2	no	—
965	M₁₆	—	4	2	no	—
966	C₂×C₈	—	4	2	no	—
967	C₂×C₈	—	4	2	no	—
968	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
969	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
972	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
973	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
993	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
994	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
995	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
996	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
997	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
998	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
1001	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1002	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1027	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1028	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	—	2	1	no	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	2	no	—
1036	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1037	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1038	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1039	C₄²	C₂⁴×C₄₁	1	2	yes	—
1040	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	2	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	4	4	no	—
1045	C₂³	—	8	2	no	—
1046	C₂³	—	8	2	no	—
1047	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
1048	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	1	no	—
1052	Q₈	—	2	2	no	—
1053	Q₈	—	2	1	no	—
1054	Q₈	—	2	2	no	—
1055	Q₈	—	2	1	no	—
1056	Q₈	—	2	1	no	—
1057	Q₈	—	2	1	no	—
1058	Q₈	—	4	2	no	—
1059	Q₈	—	8	2	no	—
1060	Q₈	—	8	2	no	—
1061	Q₈	—	8	1	no	—
1062	D₄	—	2	2	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	1	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	2	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	4	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	8	1	no	—
1074	D₄	—	8	1	no	—
1075	D₄	—	8	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	2	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	D₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	—	8	2	no	—
1100	C₂×C₄	—	8	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	1	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	2	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1108	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1109	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1110	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1111	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1112	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1113	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1114	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
1115	C₈	—	2	1	no	—
1116	C₈	—	2	2	no	—
1117	C₈	—	2	2	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	1	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	2	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	2	no	—
1126	C₂²	—	2	1	no	—
1127	C₂²	—	2	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	4	2	no	—
1132	C₂²	—	4	2	no	—
1133	C₂²	—	4	2	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	—	4	2	no	—
1136	C₂²	—	16	4	no	—
1137	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
1138	C₄	—	2	1	no	—
1139	C₄	—	2	2	no	—
1140	C₄	—	2	1	no	—
1141	C₄	—	2	1	no	—
1142	C₄	—	2	2	no	—
1143	C₄	—	2	1	no	—
1144	C₄	—	2	2	no	—
1145	C₄	—	4	1	no	—
1146	C₄	—	4	2	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	1	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	4	1	no	—
1152	C₄	—	4	2	no	—
1153	C₄	—	4	1	no	—
1154	C₄	C₄₁×#577	1	2	yes	—
1155	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1156	C₄	C₄₁×#585	1	1	yes	characteristic
1157	C₂	—	4	2	no	—
1158	C₂	—	4	1	no	—
1159	C₂	—	4	2	no	—
1160	C₂	—	8	2	no	—
1161	C₂	—	8	2	no	—
1162	C₂	C₄₁×#3488	1	1	yes	characteristic
1163	C₂	C₂×C₄₁×#577	1	1	yes	characteristic
1164	C₂	C₄₁×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3554	C₂	semidirect
2. C₄₁×#3514	C₂	semidirect
3. C₄₁×#3400	C₂	semidirect
4. C₄₁×#3396	C₂	semidirect
5. C₄₁×#3373	C₂	semidirect
6. C₄₁×#3359	C₂	semidirect
7. C₄₁×#3328	C₂	semidirect
8. C₄₁×#3321	C₂	semidirect
9. C₄₁×#3304	C₂	semidirect
10. C₄₁×#3303	C₂	semidirect
11. C₄₁×#3282	C₂	semidirect
12. D₄×SD₁₆×C₄₁	C₂	semidirect
13. C₄₁×#3274	C₂	semidirect
14. C₄₁×#3267	C₂	semidirect
15. C₄₁×#3263	C₂	semidirect
16. C₄₁×#3246	C₂	semidirect
17. C₄₁×#3225	C₂	semidirect
18. C₄₁×#3207	C₂	semidirect
19. C₄₁×#3118	C₂	semidirect
20. C₄₁×#3107	C₂	semidirect
21. C₄₁×#3042	C₂	semidirect
22. C₄₁×#3035	C₂	semidirect
23. C₄₁×#2994	C₂	semidirect
30. C₄₁×#559	C₂²	semidirect
31. C₄₁×#557	C₂²	semidirect
40. C₄₁×#548	C₂²	semidirect
41. C₄₁×#547	C₂²	semidirect
47. C₄₁×#542	C₂²	semidirect
51. C₄₁×#536	C₂²	semidirect
52. C₄₁×#533	C₂²	semidirect
54. C₄₁×#532	C₂²	semidirect
60. C₄₁×#497	C₂²	semidirect
61. C₄₁×#495	C₂²	semidirect
64. C₄₁×#489	C₂²	semidirect
65. C₄₁×#487	C₂²	semidirect
66. C₄₁×#487	C₂²	semidirect
67. C₄₁×#486	C₂²	semidirect
68. C₄₁×#485	C₂²	semidirect
69. C₄₁×#485	C₂²	semidirect
70. C₄₁×#485	C₂²	semidirect
71. C₄₁×#482	C₂²	semidirect
72. C₄₁×#476	C₂²	semidirect
73. C₄₁×#476	C₂²	semidirect
74. C₄₁×#475	C₂²	semidirect
75. C₄₁×#475	C₂²	semidirect
76. C₄₁×#475	C₂²	semidirect
77. C₄₁×#475	C₂²	semidirect
79. C₄₁×#470	C₂²	semidirect
82. C₄₁×#465	C₂²	semidirect
83. C₄₁×#465	C₂²	semidirect
84. C₄₁×#465	C₂²	semidirect
85. C₄₁×#464	C₂²	semidirect
86. C₄₁×#464	C₂²	semidirect
89. C₄₁×#463	C₂²	semidirect
90. C₄₁×#463	C₂²	semidirect
91. C₄₁×#463	C₂²	semidirect
92. C₄₁×#463	C₂²	semidirect
93. C₄₁×#462	C₂²	semidirect
94. C₄₁×#462	C₂²	semidirect
98. C₄₁×#461	C₂²	semidirect
99. C₄₁×#461	C₂²	semidirect
102. C₄₁×#460	C₂²	semidirect
106. C₄₁×#452	C₂²	semidirect
107. C₄₁×#451	C₂²	semidirect
110. C₄₁×#449	C₂²	semidirect
111. C₄₁×#449	C₂²	semidirect
114. C₄₁×#446	C₂²	semidirect
115. C₈×Q₈×C₄₁	C₂²	semidirect
117. C₄₁×#440	C₂²	semidirect
118. C₄×Q₁₆×C₄₁	C₂²	semidirect
119. C₄×Q₁₆×C₄₁	C₂²	semidirect
123. C₄×D₈×C₄₁	C₂²	semidirect
125. C₄₁×#435	C₂²	semidirect
127. C₈×D₄×C₄₁	C₂²	semidirect
128. C₄₁×#433	C₂²	semidirect
129. C₄₁×#431	C₂²	semidirect
130. C₄₁×#424	C₂²	semidirect
131. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
132. C₄₁×#419	C₂²	semidirect
133. C₄₁×#416	C₂²	semidirect
134. C₄₁×#416	C₂²	semidirect
538. #62068	C₄₁	direct (N × H)
575. #3554	C₂×C₄₁	semidirect
576. #3514	C₂×C₄₁	semidirect
577. #3400	C₂×C₄₁	semidirect
578. #3396	C₂×C₄₁	semidirect
579. #3373	C₂×C₄₁	semidirect
580. #3359	C₂×C₄₁	semidirect
581. #3328	C₂×C₄₁	semidirect
582. #3321	C₂×C₄₁	semidirect
583. #3304	C₂×C₄₁	semidirect
584. #3303	C₂×C₄₁	semidirect
585. #3282	C₂×C₄₁	semidirect
586. D₄×SD₁₆	C₂×C₄₁	semidirect
587. #3274	C₂×C₄₁	semidirect
588. #3267	C₂×C₄₁	semidirect
589. #3263	C₂×C₄₁	semidirect
590. #3246	C₂×C₄₁	semidirect
591. #3225	C₂×C₄₁	semidirect
592. #3207	C₂×C₄₁	semidirect
593. #3118	C₂×C₄₁	semidirect
594. #3107	C₂×C₄₁	semidirect
595. #3042	C₂×C₄₁	semidirect
596. #3035	C₂×C₄₁	semidirect
597. #2994	C₂×C₄₁	semidirect
612. #559	C₂²×C₄₁	semidirect
613. #557	C₂²×C₄₁	semidirect
622. #548	C₂²×C₄₁	semidirect
623. #547	C₂²×C₄₁	semidirect
629. #542	C₂²×C₄₁	semidirect
633. #536	C₂²×C₄₁	semidirect
634. #533	C₂²×C₄₁	semidirect
636. #532	C₂²×C₄₁	semidirect
642. #497	C₂²×C₄₁	semidirect
643. #495	C₂²×C₄₁	semidirect
646. #489	C₂²×C₄₁	semidirect
647. #487	C₂²×C₄₁	semidirect
648. #487	C₂²×C₄₁	semidirect
649. #486	C₂²×C₄₁	semidirect
650. #485	C₂²×C₄₁	semidirect
651. #485	C₂²×C₄₁	semidirect
652. #485	C₂²×C₄₁	semidirect
653. #482	C₂²×C₄₁	semidirect
654. #476	C₂²×C₄₁	semidirect
655. #476	C₂²×C₄₁	semidirect
656. #475	C₂²×C₄₁	semidirect
657. #475	C₂²×C₄₁	semidirect
658. #475	C₂²×C₄₁	semidirect
659. #475	C₂²×C₄₁	semidirect
661. #470	C₂²×C₄₁	semidirect
664. #465	C₂²×C₄₁	semidirect
665. #465	C₂²×C₄₁	semidirect
666. #465	C₂²×C₄₁	semidirect
667. #464	C₂²×C₄₁	semidirect
668. #464	C₂²×C₄₁	semidirect
671. #463	C₂²×C₄₁	semidirect
672. #463	C₂²×C₄₁	semidirect
673. #463	C₂²×C₄₁	semidirect
674. #463	C₂²×C₄₁	semidirect
675. #462	C₂²×C₄₁	semidirect
676. #462	C₂²×C₄₁	semidirect
680. #461	C₂²×C₄₁	semidirect
681. #461	C₂²×C₄₁	semidirect
684. #460	C₂²×C₄₁	semidirect
688. #452	C₂²×C₄₁	semidirect
689. #451	C₂²×C₄₁	semidirect
692. #449	C₂²×C₄₁	semidirect
693. #449	C₂²×C₄₁	semidirect
696. #446	C₂²×C₄₁	semidirect
697. C₈×Q₈	C₂²×C₄₁	semidirect
699. #440	C₂²×C₄₁	semidirect
700. C₄×Q₁₆	C₂²×C₄₁	semidirect
701. C₄×Q₁₆	C₂²×C₄₁	semidirect
705. C₄×D₈	C₂²×C₄₁	semidirect
707. #435	C₂²×C₄₁	semidirect
709. C₈×D₄	C₂²×C₄₁	semidirect
710. #433	C₂²×C₄₁	semidirect
711. #431	C₂²×C₄₁	semidirect
712. #424	C₂²×C₄₁	semidirect
713. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
714. #419	C₂²×C₄₁	semidirect
715. #416	C₂²×C₄₁	semidirect
716. #416	C₂²×C₄₁	semidirect
717. C₄₁	#62068	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×#3554	2
C₄₁×#3514	2
C₄₁×#3400	2
C₄₁×#3396	2
C₄₁×#3373	2
C₄₁×#3359	2
C₄₁×#3328	2
C₄₁×#3321	2
C₄₁×#3304	2
C₄₁×#3303	2
C₄₁×#3282	2
D₄×SD₁₆×C₄₁	2
C₄₁×#3274	2
C₄₁×#3267	2
C₄₁×#3263	2
C₄₁×#3246	2
C₄₁×#3225	2
C₄₁×#3207	2
C₄₁×#3118	2
C₄₁×#3107	2
C₄₁×#3042	2
C₄₁×#3035	2
C₄₁×#2994	2
#62068	41

Subgroups — C41×#62068 #23838269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#62068 #23838269