Subgroups — C₄₁×#61608 #23837809

Order 10496.

2132 conjugacy classes of subgroups.

The subgroup lattice has 1230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3328	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3324	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#3321	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3319	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3304	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#3302	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#3287	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#3284	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#3278	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3274	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3269	C₂	1	2	yes	maximal, complemented
14	C₄₁×#3267	C₂	1	2	yes	maximal, complemented
15	C₄₁×#3216	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#3207	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#3197	C₂	1	2	yes	maximal, complemented
18	C₄₁×#3191	C₂	1	2	yes	maximal, complemented
19	C₄₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄₁×#3005	C₂	1	2	yes	maximal, complemented
22	C₄₁×#3002	C₂	1	2	yes	maximal, complemented
23	C₄₁×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₄₁	C₂²	1	2	yes	—
25	C₂×#137×C₄₁	C₂²	1	2	yes	complemented
26	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	2	yes	complemented
27	C₂×#135×C₄₁	C₂²	1	2	yes	complemented
28	C₂×#135×C₄₁	C₂²	1	2	yes	complemented
29	C₄₁×#559	—	2	1	no	—
30	C₄₁×#559	—	2	1	no	—
31	C₄₁×#556	C₂²	1	1	yes	characteristic
32	C₄₁×#556	C₂²	1	1	yes	characteristic, complemented
33	C₄₁×#555	C₂²	1	2	yes	complemented
34	C₄₁×#553	—	2	2	no	—
35	C₄₁×#550	C₂²	1	1	yes	characteristic
36	C₄₁×#550	C₂²	1	1	yes	characteristic
37	C₄₁×#550	C₂²	1	1	yes	characteristic, complemented
38	D₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
39	C₄₁×#548	C₂²	1	2	yes	—
40	C₄₁×#547	—	2	1	no	—
41	C₄₁×#547	C₂²	1	1	yes	characteristic
42	C₄₁×#547	C₂²	1	2	yes	complemented
43	C₄₁×#546	—	2	2	no	—
44	C₄₁×#546	C₂²	1	2	yes	—
45	D₄²×C₄₁	—	2	1	no	—
46	D₄²×C₄₁	C₂²	1	1	yes	characteristic
47	C₄₁×#538	—	2	2	no	—
48	C₄₁×#535	—	2	1	no	—
49	C₄₁×#533	C₂²	1	1	yes	characteristic, complemented
50	C₄₁×#532	—	2	1	no	—
51	C₄₁×#532	C₂²	1	1	yes	characteristic
52	C₄₁×#532	C₂²	1	1	yes	characteristic, complemented
53	C₄₁×#525	—	2	2	no	—
54	C₄₁×#525	C₂²	1	2	yes	—
55	C₄₁×#525	C₂²	1	2	yes	complemented
56	C₄₁×#525	C₂²	1	2	yes	complemented
57	C₄₁×#520	—	2	1	no	—
58	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄×C₄₁	—	2	1	no	—
60	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
61	C₄₁×#497	C₂²	1	2	yes	complemented
62	C₄₁×#493	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×#485	C₂²	1	2	yes	complemented
68	C₄₁×#485	C₂²	1	2	yes	complemented
69	C₄₁×#485	C₂²	1	1	yes	characteristic, complemented
70	C₄₁×#485	C₂²	1	1	yes	characteristic, complemented
71	C₄₁×#482	C₂²	1	2	yes	complemented
72	C₄₁×#482	C₂²	1	2	yes	complemented
73	C₄₁×#482	C₂²	1	2	yes	complemented
74	C₄₁×#475	C₂²	1	1	yes	characteristic, complemented
75	C₄₁×#475	C₂²	1	1	yes	characteristic, complemented
76	C₄₁×#474	C₂²	1	1	yes	characteristic, complemented
77	C₄₁×#474	C₂²	1	1	yes	characteristic, complemented
78	C₄₁×#470	C₂²	1	2	yes	complemented
79	C₄₁×#469	C₂²	1	2	yes	complemented
80	C₄₁×#468	C₂²	1	2	yes	complemented
81	C₄₁×#468	C₂²	1	2	yes	complemented
82	C₄₁×#467	C₂²	1	2	yes	complemented
83	C₄₁×#466	C₂²	1	2	yes	complemented
84	C₄₁×#465	C₂²	1	2	yes	complemented
85	C₄₁×#465	C₂²	1	2	yes	complemented
86	C₄₁×#463	C₂²	1	2	yes	complemented
87	C₄₁×#463	C₂²	1	2	yes	complemented
88	C₄₁×#462	C₂²	1	1	yes	characteristic, complemented
89	C₄₁×#462	C₂²	1	1	yes	characteristic, complemented
90	C₄₁×#462	C₂²	1	1	yes	characteristic, complemented
91	C₄₁×#461	C₂²	1	1	yes	characteristic, complemented
92	C₄₁×#460	C₂²	1	1	yes	characteristic, complemented
93	C₄₁×#460	C₂²	1	1	yes	characteristic, complemented
94	C₄₁×#460	C₂²	1	1	yes	characteristic, complemented
95	C₄₁×#459	C₂²	1	1	yes	characteristic, complemented
96	C₄₁×#452	C₂²	1	1	yes	characteristic
97	C₄₁×#452	C₂²	1	1	yes	characteristic
98	C₄₁×#452	C₂²	1	2	yes	complemented
99	C₄₁×#452	C₂²	1	2	yes	complemented
100	C₄₁×#452	C₂²	1	2	yes	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×#451	C₂²	1	2	yes	complemented
105	C₄₁×#450	C₂²	1	2	yes	complemented
106	C₄₁×#449	C₂²	1	2	yes	—
107	C₄₁×#449	C₂²	1	2	yes	complemented
108	C₄₁×#449	C₂²	1	2	yes	complemented
109	C₄₁×#449	C₂²	1	2	yes	complemented
110	C₄₁×#449	C₂²	1	2	yes	complemented
111	C₄₁×#449	C₂²	1	2	yes	complemented
112	C₄₁×#449	C₂²	1	2	yes	complemented
113	C₄₁×#448	C₂²	1	2	yes	complemented
114	C₄₁×#447	C₂²	1	2	yes	complemented
115	C₄₁×#442	C₂²	1	2	yes	complemented
116	C₄₁×#440	C₂²	1	2	yes	complemented
117	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
120	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
121	C₄₁×#436	C₂²	1	1	yes	characteristic
122	C₄₁×#436	C₂²	1	1	yes	characteristic
123	C₄₁×#435	C₂²	1	2	yes	complemented
124	C₄₁×#435	C₂²	1	2	yes	complemented
125	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
126	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
127	C₄₁×#432	C₂²	1	1	yes	characteristic, complemented
128	C₄₁×#431	C₂²	1	1	yes	characteristic, complemented
129	C₄₁×#419	C₂²	1	2	yes	complemented
130	C₄₁×#418	C₂²	1	2	yes	complemented
131	C₄₁×#416	C₂²	1	2	yes	complemented
132	C₄₁×#416	C₂²	1	2	yes	complemented
133	C₄₁×#407	C₂²	1	2	yes	complemented
134	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	complemented
135	C₂×#41×C₄₁	—	2	1	no	—
136	C₂×#41×C₄₁	—	2	2	no	—
137	C₂×#41×C₄₁	—	2	2	no	—
138	C₂×#41×C₄₁	—	4	4	no	—
139	C₂×#41×C₄₁	—	4	4	no	—
140	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
141	C₂×#41×C₄₁	C₂³	1	2	yes	—
142	C₂×#41×C₄₁	C₂³	1	2	yes	—
143	C₂×#41×C₄₁	C₂³	1	2	yes	—
144	C₂×#41×C₄₁	C₂³	1	2	yes	—
145	C₂×#41×C₄₁	C₂³	1	2	yes	—
146	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
147	C₂²×D₄×C₄₁	—	2	2	no	—
148	C₂²×D₄×C₄₁	—	2	1	no	—
149	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
150	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
151	C₂³×C₄×C₄₁	—	2	2	no	—
152	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
153	#137×C₄₁	—	4	4	no	—
154	AGL(1,ℤ/8)×C₄₁	—	4	4	no	—
155	#135×C₄₁	—	4	4	no	—
156	#135×C₄₁	—	4	4	no	—
157	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
158	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
159	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
160	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
162	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
164	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
167	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
168	C₂×D₈×C₄₁	C₂³	1	2	yes	—
169	C₂×D₈×C₄₁	C₂³	1	2	yes	—
170	C₂×D₈×C₄₁	C₂³	1	2	yes	—
171	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
172	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
173	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
174	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
175	C₄⋊Q₈×C₄₁	—	2	1	no	—
176	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
177	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
178	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
179	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
180	#127×C₄₁	—	2	1	no	—
181	#127×C₄₁	—	2	1	no	—
182	#127×C₄₁	—	2	1	no	—
183	#127×C₄₁	C₂³	1	1	yes	characteristic
184	#127×C₄₁	C₂³	1	1	yes	characteristic
185	#126×C₄₁	—	2	2	no	—
186	#126×C₄₁	—	2	2	no	—
187	#125×C₄₁	—	2	1	no	—
188	#124×C₄₁	—	2	1	no	—
189	#124×C₄₁	—	2	1	no	—
190	#124×C₄₁	—	2	2	no	—
191	#124×C₄₁	—	2	2	no	—
192	#124×C₄₁	—	2	2	no	—
193	#124×C₄₁	—	2	1	no	—
194	#124×C₄₁	C₂³	1	2	yes	—
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	C₂²⋊Q₈×C₄₁	—	2	1	no	—
203	C₂²⋊Q₈×C₄₁	—	2	2	no	—
204	C₂²⋊Q₈×C₄₁	—	2	2	no	—
205	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
206	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
207	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
208	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
209	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
211	#121×C₄₁	—	2	2	no	—
212	#121×C₄₁	—	2	1	no	—
213	#121×C₄₁	—	2	2	no	—
214	#121×C₄₁	—	2	2	no	—
215	#121×C₄₁	—	2	1	no	—
216	#121×C₄₁	—	2	1	no	—
217	#121×C₄₁	—	2	1	no	—
218	#121×C₄₁	—	2	1	no	—
219	#121×C₄₁	—	2	2	no	—
220	#121×C₄₁	—	2	2	no	—
221	#121×C₄₁	—	2	2	no	—
222	#121×C₄₁	—	2	2	no	—
223	#121×C₄₁	C₂³	1	2	yes	—
224	#121×C₄₁	C₂³	1	2	yes	—
225	#121×C₄₁	C₂³	1	2	yes	—
226	#121×C₄₁	C₂³	1	2	yes	—
227	#121×C₄₁	C₂³	1	2	yes	—
228	#120×C₄₁	—	2	2	no	—
229	#120×C₄₁	—	2	2	no	—
230	#120×C₄₁	—	2	2	no	—
231	#120×C₄₁	—	2	2	no	—
232	#120×C₄₁	—	2	2	no	—
233	C₄×Q₈×C₄₁	—	2	1	no	—
234	C₄×Q₈×C₄₁	—	2	1	no	—
235	C₄×Q₈×C₄₁	—	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×D₄×C₄₁	—	2	1	no	—
241	C₄×D₄×C₄₁	—	2	2	no	—
242	C₄×D₄×C₄₁	—	2	1	no	—
243	C₄×D₄×C₄₁	—	2	1	no	—
244	C₄×D₄×C₄₁	—	2	2	no	—
245	C₄×D₄×C₄₁	—	2	2	no	—
246	C₄×D₄×C₄₁	—	2	2	no	—
247	C₄×D₄×C₄₁	—	2	2	no	—
248	C₄×D₄×C₄₁	—	2	2	no	—
249	C₄×D₄×C₄₁	—	2	1	no	—
250	C₄×D₄×C₄₁	—	2	1	no	—
251	C₄×D₄×C₄₁	—	2	1	no	—
252	C₄×D₄×C₄₁	—	2	2	no	—
253	C₄×D₄×C₄₁	—	2	1	no	—
254	C₄×D₄×C₄₁	—	2	1	no	—
255	C₄×D₄×C₄₁	—	2	1	no	—
256	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
257	C₄×D₄×C₄₁	D₄	1	2	yes	—
258	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
259	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₄₁	C₂³	1	2	yes	—
262	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
263	C₄×D₄×C₄₁	C₂³	1	2	yes	—
264	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
265	#117×C₄₁	—	2	1	no	—
266	#117×C₄₁	—	2	2	no	—
267	#117×C₄₁	—	2	1	no	—
268	#117×C₄₁	C₂³	1	1	yes	characteristic
269	#117×C₄₁	C₂³	1	2	yes	—
270	#117×C₄₁	C₂³	1	2	yes	—
271	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
272	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
273	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
275	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
276	C₂×C₄²×C₄₁	—	2	1	no	—
277	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
278	#107×C₄₁	C₂³	1	1	yes	characteristic
279	#107×C₄₁	C₂³	1	1	yes	characteristic
280	#107×C₄₁	C₂³	1	2	yes	—
281	#106×C₄₁	C₂³	1	1	yes	characteristic
282	#106×C₄₁	C₂³	1	1	yes	characteristic
283	#106×C₄₁	C₂³	1	2	yes	—
284	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
285	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
286	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
288	#103×C₄₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
293	#103×C₄₁	C₂³	1	2	yes	—
294	#103×C₄₁	C₂³	1	2	yes	—
295	#103×C₄₁	C₂³	1	1	yes	characteristic
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	#102×C₄₁	C₂³	1	1	yes	characteristic
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	2	yes	—
305	#102×C₄₁	C₂³	1	2	yes	—
306	#102×C₄₁	C₂³	1	2	yes	—
307	#102×C₄₁	C₂³	1	2	yes	—
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	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
312	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
313	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
314	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
315	#97×C₄₁	C₂³	1	2	yes	—
316	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
318	C₂⁴×C₄₁	—	2	2	no	—
319	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
320	#41×C₄₁	—	2	2	no	—
321	#41×C₄₁	—	2	2	no	—
322	#41×C₄₁	—	2	4	no	—
323	#41×C₄₁	—	2	4	no	—
324	#41×C₄₁	—	4	2	no	—
325	#41×C₄₁	—	4	2	no	—
326	#41×C₄₁	—	4	2	no	—
327	#41×C₄₁	—	4	2	no	—
328	#41×C₄₁	—	4	4	no	—
329	#41×C₄₁	—	4	8	no	—
330	#41×C₄₁	—	4	2	no	—
331	#41×C₄₁	—	4	2	no	—
332	#41×C₄₁	—	4	2	no	—
333	#41×C₄₁	—	4	2	no	—
334	#41×C₄₁	—	4	8	no	—
335	C₂×Q₈×C₄₁	—	2	1	no	—
336	C₂×Q₈×C₄₁	—	2	2	no	—
337	C₂×Q₈×C₄₁	—	2	1	no	—
338	C₂×Q₈×C₄₁	—	2	4	no	—
339	C₂×Q₈×C₄₁	—	4	2	no	—
340	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
341	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
342	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
343	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
344	C₂×D₄×C₄₁	—	2	1	no	—
345	C₂×D₄×C₄₁	—	2	4	no	—
346	C₂×D₄×C₄₁	—	2	2	no	—
347	C₂×D₄×C₄₁	—	2	2	no	—
348	C₂×D₄×C₄₁	—	2	2	no	—
349	C₂×D₄×C₄₁	—	2	2	no	—
350	C₂×D₄×C₄₁	—	2	2	no	—
351	C₂×D₄×C₄₁	—	2	2	no	—
352	C₂×D₄×C₄₁	—	2	2	no	—
353	C₂×D₄×C₄₁	—	2	2	no	—
354	C₂×D₄×C₄₁	—	2	2	no	—
355	C₂×D₄×C₄₁	—	2	2	no	—
356	C₂×D₄×C₄₁	—	2	1	no	—
357	C₂×D₄×C₄₁	—	2	1	no	—
358	C₂×D₄×C₄₁	—	2	2	no	—
359	C₂×D₄×C₄₁	—	2	1	no	—
360	C₂×D₄×C₄₁	—	2	1	no	—
361	C₂×D₄×C₄₁	—	4	2	no	—
362	C₂×D₄×C₄₁	—	4	2	no	—
363	C₂×D₄×C₄₁	—	4	4	no	—
364	C₂×D₄×C₄₁	—	4	8	no	—
365	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
366	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
367	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
368	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
369	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
370	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₄₁	—	2	1	no	—
372	C₂²×C₄×C₄₁	—	2	2	no	—
373	C₂²×C₄×C₄₁	—	2	1	no	—
374	C₂²×C₄×C₄₁	—	2	2	no	—
375	C₂²×C₄×C₄₁	—	2	2	no	—
376	C₂²×C₄×C₄₁	—	2	2	no	—
377	C₂²×C₄×C₄₁	—	2	2	no	—
378	C₂²×C₄×C₄₁	—	2	1	no	—
379	C₂²×C₄×C₄₁	—	2	2	no	—
380	C₂²×C₄×C₄₁	—	2	2	no	—
381	C₂²×C₄×C₄₁	—	4	2	no	—
382	C₂²×C₄×C₄₁	—	4	2	no	—
383	C₂²×C₄×C₄₁	—	4	8	no	—
384	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
387	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
388	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
389	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
391	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
392	Q₁₆×C₄₁	—	2	2	no	—
393	Q₁₆×C₄₁	—	2	2	no	—
394	Q₁₆×C₄₁	—	4	2	no	—
395	Q₁₆×C₄₁	—	4	2	no	—
396	SD₁₆×C₄₁	—	2	4	no	—
397	SD₁₆×C₄₁	—	2	2	no	—
398	SD₁₆×C₄₁	—	2	2	no	—
399	SD₁₆×C₄₁	—	4	2	no	—
400	SD₁₆×C₄₁	—	4	2	no	—
401	SD₁₆×C₄₁	—	4	2	no	—
402	SD₁₆×C₄₁	—	4	2	no	—
403	D₈×C₄₁	—	2	4	no	—
404	D₈×C₄₁	—	4	2	no	—
405	D₈×C₄₁	—	4	2	no	—
406	M₁₆×C₄₁	—	4	2	no	—
407	M₁₆×C₄₁	—	4	2	no	—
408	C₂×C₈×C₄₁	—	4	2	no	—
409	C₂×C₈×C₄₁	—	4	2	no	—
410	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
411	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
412	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
413	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
414	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
415	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
416	C₄⋊C₄×C₄₁	—	2	1	no	—
417	C₄⋊C₄×C₄₁	—	2	1	no	—
418	C₄⋊C₄×C₄₁	—	2	2	no	—
419	C₄⋊C₄×C₄₁	—	2	2	no	—
420	C₄⋊C₄×C₄₁	—	2	2	no	—
421	C₄⋊C₄×C₄₁	—	2	1	no	—
422	C₄⋊C₄×C₄₁	—	2	1	no	—
423	C₄⋊C₄×C₄₁	—	2	1	no	—
424	C₄⋊C₄×C₄₁	—	2	1	no	—
425	C₄⋊C₄×C₄₁	—	2	1	no	—
426	C₄⋊C₄×C₄₁	—	2	1	no	—
427	C₄⋊C₄×C₄₁	—	2	2	no	—
428	C₄⋊C₄×C₄₁	—	2	1	no	—
429	C₄⋊C₄×C₄₁	—	2	1	no	—
430	C₄⋊C₄×C₄₁	—	2	1	no	—
431	C₄⋊C₄×C₄₁	—	2	1	no	—
432	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
433	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
434	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
435	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
436	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
440	C₂²⋊C₄×C₄₁	—	2	2	no	—
441	C₂²⋊C₄×C₄₁	—	2	1	no	—
442	C₂²⋊C₄×C₄₁	—	2	1	no	—
443	C₂²⋊C₄×C₄₁	—	2	1	no	—
444	C₂²⋊C₄×C₄₁	—	2	2	no	—
445	C₂²⋊C₄×C₄₁	—	2	2	no	—
446	C₂²⋊C₄×C₄₁	—	2	2	no	—
447	C₂²⋊C₄×C₄₁	—	2	2	no	—
448	C₂²⋊C₄×C₄₁	—	2	2	no	—
449	C₂²⋊C₄×C₄₁	—	2	2	no	—
450	C₂²⋊C₄×C₄₁	—	2	2	no	—
451	C₂²⋊C₄×C₄₁	—	2	2	no	—
452	C₂²⋊C₄×C₄₁	—	2	2	no	—
453	C₂²⋊C₄×C₄₁	—	2	1	no	—
454	C₂²⋊C₄×C₄₁	—	2	1	no	—
455	C₂²⋊C₄×C₄₁	—	2	2	no	—
456	C₂²⋊C₄×C₄₁	—	2	2	no	—
457	C₂²⋊C₄×C₄₁	—	2	2	no	—
458	C₂²⋊C₄×C₄₁	—	2	2	no	—
459	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
460	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
461	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
463	C₄²×C₄₁	—	2	1	no	—
464	C₄²×C₄₁	—	2	1	no	—
465	C₄²×C₄₁	—	2	1	no	—
466	C₄²×C₄₁	—	2	2	no	—
467	C₄²×C₄₁	—	2	2	no	—
468	C₄²×C₄₁	—	2	1	no	—
469	C₄²×C₄₁	—	2	1	no	—
470	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
471	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
472	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
473	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
474	C₂³×C₄₁	—	2	1	no	—
475	C₂³×C₄₁	—	2	2	no	—
476	C₂³×C₄₁	—	2	2	no	—
477	C₂³×C₄₁	—	4	2	no	—
478	C₂³×C₄₁	—	4	2	no	—
479	C₂³×C₄₁	—	4	2	no	—
480	C₂³×C₄₁	—	4	4	no	—
481	C₂³×C₄₁	—	4	4	no	—
482	C₂³×C₄₁	—	8	2	no	—
483	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
484	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
485	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
486	Q₈×C₄₁	—	2	1	no	—
487	Q₈×C₄₁	—	2	1	no	—
488	Q₈×C₄₁	—	2	1	no	—
489	Q₈×C₄₁	—	2	1	no	—
490	Q₈×C₄₁	—	2	2	no	—
491	Q₈×C₄₁	—	2	2	no	—
492	Q₈×C₄₁	—	2	1	no	—
493	Q₈×C₄₁	—	4	4	no	—
494	Q₈×C₄₁	—	4	2	no	—
495	Q₈×C₄₁	—	8	1	no	—
496	Q₈×C₄₁	H(5,𝔽₂)	1	2	yes	—
497	D₄×C₄₁	—	2	4	no	—
498	D₄×C₄₁	—	2	2	no	—
499	D₄×C₄₁	—	2	2	no	—
500	D₄×C₄₁	—	2	1	no	—
501	D₄×C₄₁	—	2	2	no	—
502	D₄×C₄₁	—	2	2	no	—
503	D₄×C₄₁	—	2	2	no	—
504	D₄×C₄₁	—	2	2	no	—
505	D₄×C₄₁	—	4	2	no	—
506	D₄×C₄₁	—	4	4	no	—
507	D₄×C₄₁	—	4	4	no	—
508	D₄×C₄₁	—	4	4	no	—
509	D₄×C₄₁	—	4	4	no	—
510	D₄×C₄₁	—	4	4	no	—
511	D₄×C₄₁	—	4	4	no	—
512	D₄×C₄₁	—	4	2	no	—
513	D₄×C₄₁	—	4	2	no	—
514	D₄×C₄₁	—	8	1	no	—
515	D₄×C₄₁	—	8	1	no	—
516	D₄×C₄₁	—	8	2	no	—
517	D₄×C₄₁	—	8	2	no	—
518	D₄×C₄₁	—	8	2	no	—
519	D₄×C₄₁	—	8	2	no	—
520	D₄×C₄₁	—	8	2	no	—
521	D₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
522	C₂×C₄×C₄₁	—	2	4	no	—
523	C₂×C₄×C₄₁	—	2	1	no	—
524	C₂×C₄×C₄₁	—	2	2	no	—
525	C₂×C₄×C₄₁	—	2	2	no	—
526	C₂×C₄×C₄₁	—	2	2	no	—
527	C₂×C₄×C₄₁	—	2	2	no	—
528	C₂×C₄×C₄₁	—	2	2	no	—
529	C₂×C₄×C₄₁	—	2	1	no	—
530	C₂×C₄×C₄₁	—	2	1	no	—
531	C₂×C₄×C₄₁	—	2	1	no	—
532	C₂×C₄×C₄₁	—	2	1	no	—
533	C₂×C₄×C₄₁	—	2	1	no	—
534	C₂×C₄×C₄₁	—	2	1	no	—
535	C₂×C₄×C₄₁	—	2	2	no	—
536	C₂×C₄×C₄₁	—	2	1	no	—
537	C₂×C₄×C₄₁	—	2	1	no	—
538	C₂×C₄×C₄₁	—	2	2	no	—
539	C₂×C₄×C₄₁	—	4	2	no	—
540	C₂×C₄×C₄₁	—	4	2	no	—
541	C₂×C₄×C₄₁	—	4	2	no	—
542	C₂×C₄×C₄₁	—	4	1	no	—
543	C₂×C₄×C₄₁	—	4	4	no	—
544	C₂×C₄×C₄₁	—	4	4	no	—
545	C₂×C₄×C₄₁	—	4	4	no	—
546	C₂×C₄×C₄₁	—	4	4	no	—
547	C₂×C₄×C₄₁	—	4	4	no	—
548	C₂×C₄×C₄₁	—	4	2	no	—
549	C₂×C₄×C₄₁	—	8	1	no	—
550	C₂×C₄×C₄₁	—	8	2	no	—
551	C₂×C₄×C₄₁	—	8	2	no	—
552	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
555	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
556	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
560	C₈×C₄₁	—	2	1	no	—
561	C₈×C₄₁	—	2	1	no	—
562	C₈×C₄₁	—	2	2	no	—
563	C₈×C₄₁	—	2	2	no	—
564	C₈×C₄₁	—	2	1	no	—
565	C₈×C₄₁	—	2	1	no	—
566	#61608	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
567	C₂²×C₄₁	—	2	1	no	—
568	C₂²×C₄₁	—	2	2	no	—
569	C₂²×C₄₁	—	2	2	no	—
570	C₂²×C₄₁	—	2	2	no	—
571	C₂²×C₄₁	—	2	1	no	—
572	C₂²×C₄₁	—	2	2	no	—
573	C₂²×C₄₁	—	2	2	no	—
574	C₂²×C₄₁	—	2	1	no	—
575	C₂²×C₄₁	—	2	2	no	—
576	C₂²×C₄₁	—	2	2	no	—
577	C₂²×C₄₁	—	4	1	no	—
578	C₂²×C₄₁	—	4	1	no	—
579	C₂²×C₄₁	—	4	2	no	—
580	C₂²×C₄₁	—	4	2	no	—
581	C₂²×C₄₁	—	4	2	no	—
582	C₂²×C₄₁	—	4	2	no	—
583	C₂²×C₄₁	—	4	2	no	—
584	C₂²×C₄₁	—	4	2	no	—
585	C₂²×C₄₁	—	8	4	no	—
586	C₂²×C₄₁	—	8	8	no	—
587	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
588	C₄×C₄₁	—	2	1	no	—
589	C₄×C₄₁	—	2	1	no	—
590	C₄×C₄₁	—	2	1	no	—
591	C₄×C₄₁	—	2	2	no	—
592	C₄×C₄₁	—	2	2	no	—
593	C₄×C₄₁	—	2	2	no	—
594	C₄×C₄₁	—	2	1	no	—
595	C₄×C₄₁	—	4	1	no	—
596	C₄×C₄₁	—	4	1	no	—
597	C₄×C₄₁	—	4	1	no	—
598	C₄×C₄₁	—	4	2	no	—
599	C₄×C₄₁	—	4	1	no	—
600	C₄×C₄₁	—	4	1	no	—
601	C₄×C₄₁	—	4	1	no	—
602	C₄×C₄₁	—	4	2	no	—
603	C₄×C₄₁	#575	1	2	yes	—
604	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
605	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
606	#3506	C₂×C₄₁	1	1	yes	characteristic, complemented
607	D₄×#41	C₂×C₄₁	1	1	yes	characteristic, complemented
608	#3328	C₂×C₄₁	1	1	yes	characteristic, complemented
609	#3324	C₂×C₄₁	1	1	yes	characteristic, complemented
610	#3321	C₂×C₄₁	1	2	yes	complemented
611	#3319	C₂×C₄₁	1	2	yes	complemented
612	#3304	C₂×C₄₁	1	1	yes	characteristic, complemented
613	#3302	C₂×C₄₁	1	1	yes	characteristic, complemented
614	#3287	C₂×C₄₁	1	1	yes	characteristic, complemented
615	#3284	C₂×C₄₁	1	1	yes	characteristic, complemented
616	#3278	C₂×C₄₁	1	1	yes	characteristic, complemented
617	#3274	C₂×C₄₁	1	1	yes	characteristic, complemented
618	#3269	C₂×C₄₁	1	2	yes	complemented
619	#3267	C₂×C₄₁	1	2	yes	complemented
620	#3216	C₂×C₄₁	1	1	yes	characteristic, complemented
621	#3207	C₂×C₄₁	1	1	yes	characteristic, complemented
622	#3197	C₂×C₄₁	1	2	yes	complemented
623	#3191	C₂×C₄₁	1	2	yes	complemented
624	#3115	C₂×C₄₁	1	1	yes	characteristic, complemented
625	#3107	C₂×C₄₁	1	1	yes	characteristic, complemented
626	#3005	C₂×C₄₁	1	2	yes	complemented
627	#3002	C₂×C₄₁	1	2	yes	complemented
628	#2974	C₂×C₄₁	1	1	yes	characteristic, complemented
629	C₂×C₄₁	—	4	2	no	—
630	C₂×C₄₁	—	4	1	no	—
631	C₂×C₄₁	—	4	2	no	—
632	C₂×C₄₁	—	4	2	no	—
633	C₂×C₄₁	—	8	2	no	—
634	C₂×C₄₁	—	8	2	no	—
635	C₂×C₄₁	#3484	1	1	yes	characteristic
636	C₂×C₄₁	C₂×#575	1	1	yes	characteristic
637	C₂×C₄₁	#3584	1	1	yes	characteristic
638	C₂²×#41	C₂²×C₄₁	1	2	yes	—
639	C₂×#137	C₂²×C₄₁	1	2	yes	complemented
640	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	2	yes	complemented
641	C₂×#135	C₂²×C₄₁	1	2	yes	complemented
642	C₂×#135	C₂²×C₄₁	1	2	yes	complemented
643	#559	—	2	1	no	—
644	#559	—	2	1	no	—
645	#556	C₂²×C₄₁	1	1	yes	characteristic
646	#556	C₂²×C₄₁	1	1	yes	characteristic, complemented
647	#555	C₂²×C₄₁	1	2	yes	complemented
648	#553	—	2	2	no	—
649	#550	C₂²×C₄₁	1	1	yes	characteristic
650	#550	C₂²×C₄₁	1	1	yes	characteristic
651	#550	C₂²×C₄₁	1	1	yes	characteristic, complemented
652	D₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
653	#548	C₂²×C₄₁	1	2	yes	—
654	#547	—	2	1	no	—
655	#547	C₂²×C₄₁	1	1	yes	characteristic
656	#547	C₂²×C₄₁	1	2	yes	complemented
657	#546	—	2	2	no	—
658	#546	C₂²×C₄₁	1	2	yes	—
659	D₄²	—	2	1	no	—
660	D₄²	C₂²×C₄₁	1	1	yes	characteristic
661	#538	—	2	2	no	—
662	#535	—	2	1	no	—
663	#533	C₂²×C₄₁	1	1	yes	characteristic, complemented
664	#532	—	2	1	no	—
665	#532	C₂²×C₄₁	1	1	yes	characteristic
666	#532	C₂²×C₄₁	1	1	yes	characteristic, complemented
667	#525	—	2	2	no	—
668	#525	C₂²×C₄₁	1	2	yes	—
669	#525	C₂²×C₄₁	1	2	yes	complemented
670	#525	C₂²×C₄₁	1	2	yes	complemented
671	#520	—	2	1	no	—
672	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
673	C₂×C₄×D₄	—	2	1	no	—
674	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
675	#497	C₂²×C₄₁	1	2	yes	complemented
676	#493	C₂²×C₄₁	1	1	yes	characteristic, complemented
677	#492	C₂²×C₄₁	1	1	yes	characteristic, complemented
678	#489	C₂²×C₄₁	1	2	yes	complemented
679	#487	C₂²×C₄₁	1	1	yes	characteristic, complemented
680	#486	C₂²×C₄₁	1	1	yes	characteristic, complemented
681	#485	C₂²×C₄₁	1	2	yes	complemented
682	#485	C₂²×C₄₁	1	1	yes	characteristic, complemented
683	#485	C₂²×C₄₁	1	1	yes	characteristic, complemented
684	#485	C₂²×C₄₁	1	2	yes	complemented
685	#482	C₂²×C₄₁	1	2	yes	complemented
686	#482	C₂²×C₄₁	1	2	yes	complemented
687	#482	C₂²×C₄₁	1	2	yes	complemented
688	#475	C₂²×C₄₁	1	1	yes	characteristic, complemented
689	#475	C₂²×C₄₁	1	1	yes	characteristic, complemented
690	#474	C₂²×C₄₁	1	1	yes	characteristic, complemented
691	#474	C₂²×C₄₁	1	1	yes	characteristic, complemented
692	#470	C₂²×C₄₁	1	2	yes	complemented
693	#469	C₂²×C₄₁	1	2	yes	complemented
694	#468	C₂²×C₄₁	1	2	yes	complemented
695	#468	C₂²×C₄₁	1	2	yes	complemented
696	#467	C₂²×C₄₁	1	2	yes	complemented
697	#466	C₂²×C₄₁	1	2	yes	complemented
698	#465	C₂²×C₄₁	1	2	yes	complemented
699	#465	C₂²×C₄₁	1	2	yes	complemented
700	#463	C₂²×C₄₁	1	2	yes	complemented
701	#463	C₂²×C₄₁	1	2	yes	complemented
702	#462	C₂²×C₄₁	1	1	yes	characteristic, complemented
703	#462	C₂²×C₄₁	1	1	yes	characteristic, complemented
704	#462	C₂²×C₄₁	1	1	yes	characteristic, complemented
705	#461	C₂²×C₄₁	1	1	yes	characteristic, complemented
706	#460	C₂²×C₄₁	1	1	yes	characteristic, complemented
707	#460	C₂²×C₄₁	1	1	yes	characteristic, complemented
708	#460	C₂²×C₄₁	1	1	yes	characteristic, complemented
709	#459	C₂²×C₄₁	1	1	yes	characteristic, complemented
710	#452	C₂²×C₄₁	1	1	yes	characteristic
711	#452	C₂²×C₄₁	1	1	yes	characteristic
712	#452	C₂²×C₄₁	1	2	yes	complemented
713	#452	C₂²×C₄₁	1	2	yes	complemented
714	#452	C₂²×C₄₁	1	2	yes	complemented
715	#452	C₂²×C₄₁	1	2	yes	complemented
716	#452	C₂²×C₄₁	1	2	yes	complemented
717	#452	C₂²×C₄₁	1	2	yes	complemented
718	#451	C₂²×C₄₁	1	2	yes	complemented
719	#450	C₂²×C₄₁	1	2	yes	complemented
720	#449	C₂²×C₄₁	1	2	yes	—
721	#449	C₂²×C₄₁	1	2	yes	complemented
722	#449	C₂²×C₄₁	1	2	yes	complemented
723	#449	C₂²×C₄₁	1	2	yes	complemented
724	#449	C₂²×C₄₁	1	2	yes	complemented
725	#449	C₂²×C₄₁	1	2	yes	complemented
726	#449	C₂²×C₄₁	1	2	yes	complemented
727	#448	C₂²×C₄₁	1	2	yes	complemented
728	#447	C₂²×C₄₁	1	2	yes	complemented
729	#442	C₂²×C₄₁	1	2	yes	complemented
730	#440	C₂²×C₄₁	1	2	yes	complemented
731	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
732	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
733	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
734	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
735	#436	C₂²×C₄₁	1	1	yes	characteristic
736	#436	C₂²×C₄₁	1	1	yes	characteristic
737	#435	C₂²×C₄₁	1	2	yes	complemented
738	#435	C₂²×C₄₁	1	2	yes	complemented
739	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
740	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
741	#432	C₂²×C₄₁	1	1	yes	characteristic, complemented
742	#431	C₂²×C₄₁	1	1	yes	characteristic, complemented
743	#419	C₂²×C₄₁	1	2	yes	complemented
744	#418	C₂²×C₄₁	1	2	yes	complemented
745	#416	C₂²×C₄₁	1	2	yes	complemented
746	#416	C₂²×C₄₁	1	2	yes	complemented
747	#407	C₂²×C₄₁	1	2	yes	complemented
748	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	complemented
749	C₄₁	#61608	1	1	yes	characteristic, direct product factor, Sylow
750	C₂×#41	—	2	1	no	—
751	C₂×#41	—	2	2	no	—
752	C₂×#41	—	2	2	no	—
753	C₂×#41	—	4	4	no	—
754	C₂×#41	—	4	4	no	—
755	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
756	C₂×#41	C₂³×C₄₁	1	2	yes	—
757	C₂×#41	C₂³×C₄₁	1	2	yes	—
758	C₂×#41	C₂³×C₄₁	1	2	yes	—
759	C₂×#41	C₂³×C₄₁	1	2	yes	—
760	C₂×#41	C₂³×C₄₁	1	2	yes	—
761	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
762	C₂²×D₄	—	2	2	no	—
763	C₂²×D₄	—	2	1	no	—
764	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
765	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
766	C₂³×C₄	—	2	2	no	—
767	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
768	#137	—	4	4	no	—
769	AGL(1,ℤ/8)	—	4	4	no	—
770	#135	—	4	4	no	—
771	#135	—	4	4	no	—
772	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
773	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
774	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
775	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
776	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
777	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
778	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
779	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
780	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
781	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
782	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
783	C₂×D₈	C₂³×C₄₁	1	2	yes	—
784	C₂×D₈	C₂³×C₄₁	1	2	yes	—
785	C₂×D₈	C₂³×C₄₁	1	2	yes	—
786	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
787	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
788	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
789	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
790	C₄⋊Q₈	—	2	1	no	—
791	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
792	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
793	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
794	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
795	#127	—	2	1	no	—
796	#127	—	2	1	no	—
797	#127	—	2	1	no	—
798	#127	C₂³×C₄₁	1	1	yes	characteristic
799	#127	C₂³×C₄₁	1	1	yes	characteristic
800	#126	—	2	2	no	—
801	#126	—	2	2	no	—
802	#125	—	2	1	no	—
803	#124	—	2	1	no	—
804	#124	—	2	1	no	—
805	#124	—	2	2	no	—
806	#124	—	2	2	no	—
807	#124	—	2	2	no	—
808	#124	—	2	1	no	—
809	#124	C₂³×C₄₁	1	2	yes	—
810	#123	—	2	2	no	—
811	#123	—	2	2	no	—
812	#123	—	2	2	no	—
813	#123	—	2	2	no	—
814	#123	—	2	2	no	—
815	#123	—	2	2	no	—
816	#123	—	2	2	no	—
817	C₂²⋊Q₈	—	2	1	no	—
818	C₂²⋊Q₈	—	2	2	no	—
819	C₂²⋊Q₈	—	2	2	no	—
820	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
821	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
822	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
823	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
824	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
825	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
826	#121	—	2	2	no	—
827	#121	—	2	1	no	—
828	#121	—	2	2	no	—
829	#121	—	2	2	no	—
830	#121	—	2	1	no	—
831	#121	—	2	1	no	—
832	#121	—	2	1	no	—
833	#121	—	2	1	no	—
834	#121	—	2	2	no	—
835	#121	—	2	2	no	—
836	#121	—	2	2	no	—
837	#121	—	2	2	no	—
838	#121	C₂³×C₄₁	1	2	yes	—
839	#121	C₂³×C₄₁	1	2	yes	—
840	#121	C₂³×C₄₁	1	2	yes	—
841	#121	C₂³×C₄₁	1	2	yes	—
842	#121	C₂³×C₄₁	1	2	yes	—
843	#120	—	2	2	no	—
844	#120	—	2	2	no	—
845	#120	—	2	2	no	—
846	#120	—	2	2	no	—
847	#120	—	2	2	no	—
848	C₄×Q₈	—	2	1	no	—
849	C₄×Q₈	—	2	1	no	—
850	C₄×Q₈	—	2	1	no	—
851	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
852	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
853	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
854	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
855	C₄×D₄	—	2	1	no	—
856	C₄×D₄	—	2	2	no	—
857	C₄×D₄	—	2	1	no	—
858	C₄×D₄	—	2	1	no	—
859	C₄×D₄	—	2	2	no	—
860	C₄×D₄	—	2	2	no	—
861	C₄×D₄	—	2	2	no	—
862	C₄×D₄	—	2	2	no	—
863	C₄×D₄	—	2	2	no	—
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	—	2	1	no	—
866	C₄×D₄	—	2	1	no	—
867	C₄×D₄	—	2	2	no	—
868	C₄×D₄	—	2	1	no	—
869	C₄×D₄	—	2	1	no	—
870	C₄×D₄	—	2	1	no	—
871	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
872	C₄×D₄	D₄×C₄₁	1	2	yes	—
873	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
874	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
875	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
876	C₄×D₄	C₂³×C₄₁	1	2	yes	—
877	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
878	C₄×D₄	C₂³×C₄₁	1	2	yes	—
879	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
880	#117	—	2	1	no	—
881	#117	—	2	2	no	—
882	#117	—	2	1	no	—
883	#117	C₂³×C₄₁	1	1	yes	characteristic
884	#117	C₂³×C₄₁	1	2	yes	—
885	#117	C₂³×C₄₁	1	2	yes	—
886	C₂×C₄⋊C₄	—	2	1	no	—
887	C₂×C₄⋊C₄	—	2	2	no	—
888	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
889	C₂×C₂²⋊C₄	—	2	2	no	—
890	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
891	C₂×C₄²	—	2	1	no	—
892	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
893	#107	C₂³×C₄₁	1	1	yes	characteristic
894	#107	C₂³×C₄₁	1	1	yes	characteristic
895	#107	C₂³×C₄₁	1	2	yes	—
896	#106	C₂³×C₄₁	1	1	yes	characteristic
897	#106	C₂³×C₄₁	1	1	yes	characteristic
898	#106	C₂³×C₄₁	1	2	yes	—
899	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
900	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
901	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
902	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
903	#103	C₂³×C₄₁	1	1	yes	characteristic
904	#103	C₂³×C₄₁	1	2	yes	—
905	#103	C₂³×C₄₁	1	2	yes	—
906	#103	C₂³×C₄₁	1	2	yes	—
907	#103	C₂³×C₄₁	1	1	yes	characteristic
908	#103	C₂³×C₄₁	1	2	yes	—
909	#103	C₂³×C₄₁	1	2	yes	—
910	#103	C₂³×C₄₁	1	1	yes	characteristic
911	#103	C₂³×C₄₁	1	1	yes	characteristic
912	#103	C₂³×C₄₁	1	1	yes	characteristic
913	#103	C₂³×C₄₁	1	1	yes	characteristic
914	#102	C₂³×C₄₁	1	1	yes	characteristic
915	#102	C₂³×C₄₁	1	2	yes	—
916	#102	C₂³×C₄₁	1	2	yes	—
917	#102	C₂³×C₄₁	1	2	yes	—
918	#102	C₂³×C₄₁	1	1	yes	characteristic
919	#102	C₂³×C₄₁	1	2	yes	—
920	#102	C₂³×C₄₁	1	2	yes	—
921	#102	C₂³×C₄₁	1	2	yes	—
922	#102	C₂³×C₄₁	1	2	yes	—
923	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
924	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
925	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
926	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
927	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
928	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
929	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
930	#97	C₂³×C₄₁	1	2	yes	—
931	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
932	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
933	C₂⁴	—	2	2	no	—
934	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
935	#41	—	2	2	no	—
936	#41	—	2	2	no	—
937	#41	—	2	4	no	—
938	#41	—	2	4	no	—
939	#41	—	4	2	no	—
940	#41	—	4	2	no	—
941	#41	—	4	2	no	—
942	#41	—	4	2	no	—
943	#41	—	4	8	no	—
944	#41	—	4	4	no	—
945	#41	—	4	2	no	—
946	#41	—	4	2	no	—
947	#41	—	4	2	no	—
948	#41	—	4	2	no	—
949	#41	—	4	8	no	—
950	C₂×Q₈	—	2	1	no	—
951	C₂×Q₈	—	2	2	no	—
952	C₂×Q₈	—	2	1	no	—
953	C₂×Q₈	—	2	4	no	—
954	C₂×Q₈	—	4	2	no	—
955	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
956	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
957	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
958	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
959	C₂×D₄	—	2	1	no	—
960	C₂×D₄	—	2	4	no	—
961	C₂×D₄	—	2	2	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	2	no	—
964	C₂×D₄	—	2	2	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	2	no	—
967	C₂×D₄	—	2	2	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	1	no	—
972	C₂×D₄	—	2	1	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	1	no	—
975	C₂×D₄	—	2	1	no	—
976	C₂×D₄	—	4	2	no	—
977	C₂×D₄	—	4	2	no	—
978	C₂×D₄	—	4	8	no	—
979	C₂×D₄	—	4	4	no	—
980	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
981	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
982	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
983	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
984	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
985	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
986	C₂²×C₄	—	2	1	no	—
987	C₂²×C₄	—	2	2	no	—
988	C₂²×C₄	—	2	1	no	—
989	C₂²×C₄	—	2	2	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	2	2	no	—
993	C₂²×C₄	—	2	1	no	—
994	C₂²×C₄	—	2	2	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	4	2	no	—
997	C₂²×C₄	—	4	2	no	—
998	C₂²×C₄	—	4	8	no	—
999	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1000	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1001	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
1002	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
1003	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
1004	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1005	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
1006	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
1007	Q₁₆	—	2	2	no	—
1008	Q₁₆	—	2	2	no	—
1009	Q₁₆	—	4	2	no	—
1010	Q₁₆	—	4	2	no	—
1011	SD₁₆	—	2	4	no	—
1012	SD₁₆	—	2	2	no	—
1013	SD₁₆	—	2	2	no	—
1014	SD₁₆	—	4	2	no	—
1015	SD₁₆	—	4	2	no	—
1016	SD₁₆	—	4	2	no	—
1017	SD₁₆	—	4	2	no	—
1018	D₈	—	2	4	no	—
1019	D₈	—	4	2	no	—
1020	D₈	—	4	2	no	—
1021	M₁₆	—	4	2	no	—
1022	M₁₆	—	4	2	no	—
1023	C₂×C₈	—	4	2	no	—
1024	C₂×C₈	—	4	2	no	—
1025	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1026	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1027	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1028	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1029	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1030	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	2	2	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	1	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1048	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1049	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1050	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
1051	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1052	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1053	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1054	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	1	no	—
1057	C₂²⋊C₄	—	2	1	no	—
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	1	no	—
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1075	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1076	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1077	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1078	C₄²	—	2	1	no	—
1079	C₄²	—	2	1	no	—
1080	C₄²	—	2	1	no	—
1081	C₄²	—	2	2	no	—
1082	C₄²	—	2	2	no	—
1083	C₄²	—	2	1	no	—
1084	C₄²	—	2	1	no	—
1085	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1086	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1087	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1088	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1089	C₂³	—	2	1	no	—
1090	C₂³	—	2	2	no	—
1091	C₂³	—	2	2	no	—
1092	C₂³	—	4	2	no	—
1093	C₂³	—	4	2	no	—
1094	C₂³	—	4	2	no	—
1095	C₂³	—	4	4	no	—
1096	C₂³	—	4	4	no	—
1097	C₂³	—	8	2	no	—
1098	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
1099	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
1100	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1101	Q₈	—	2	1	no	—
1102	Q₈	—	2	1	no	—
1103	Q₈	—	2	1	no	—
1104	Q₈	—	2	1	no	—
1105	Q₈	—	2	2	no	—
1106	Q₈	—	2	2	no	—
1107	Q₈	—	2	1	no	—
1108	Q₈	—	4	4	no	—
1109	Q₈	—	4	2	no	—
1110	Q₈	—	8	1	no	—
1111	Q₈	H(5,𝔽₂)×C₄₁	1	2	yes	—
1112	D₄	—	2	4	no	—
1113	D₄	—	2	2	no	—
1114	D₄	—	2	2	no	—
1115	D₄	—	2	1	no	—
1116	D₄	—	2	2	no	—
1117	D₄	—	2	2	no	—
1118	D₄	—	2	2	no	—
1119	D₄	—	2	2	no	—
1120	D₄	—	4	2	no	—
1121	D₄	—	4	4	no	—
1122	D₄	—	4	4	no	—
1123	D₄	—	4	4	no	—
1124	D₄	—	4	4	no	—
1125	D₄	—	4	4	no	—
1126	D₄	—	4	4	no	—
1127	D₄	—	4	2	no	—
1128	D₄	—	4	2	no	—
1129	D₄	—	8	1	no	—
1130	D₄	—	8	1	no	—
1131	D₄	—	8	2	no	—
1132	D₄	—	8	2	no	—
1133	D₄	—	8	2	no	—
1134	D₄	—	8	2	no	—
1135	D₄	—	8	2	no	—
1136	D₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
1137	C₂×C₄	—	2	4	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	2	no	—
1140	C₂×C₄	—	2	2	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	2	no	—
1154	C₂×C₄	—	4	2	no	—
1155	C₂×C₄	—	4	2	no	—
1156	C₂×C₄	—	4	2	no	—
1157	C₂×C₄	—	4	1	no	—
1158	C₂×C₄	—	4	4	no	—
1159	C₂×C₄	—	4	4	no	—
1160	C₂×C₄	—	4	4	no	—
1161	C₂×C₄	—	4	4	no	—
1162	C₂×C₄	—	4	4	no	—
1163	C₂×C₄	—	4	2	no	—
1164	C₂×C₄	—	8	2	no	—
1165	C₂×C₄	—	8	2	no	—
1166	C₂×C₄	—	8	1	no	—
1167	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1168	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1169	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1170	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1171	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1172	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1173	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1174	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
1175	C₈	—	2	1	no	—
1176	C₈	—	2	1	no	—
1177	C₈	—	2	2	no	—
1178	C₈	—	2	2	no	—
1179	C₈	—	2	1	no	—
1180	C₈	—	2	1	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	2	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	2	1	no	—
1185	C₂²	—	2	2	no	—
1186	C₂²	—	2	2	no	—
1187	C₂²	—	2	2	no	—
1188	C₂²	—	2	1	no	—
1189	C₂²	—	2	2	no	—
1190	C₂²	—	2	2	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	2	no	—
1194	C₂²	—	4	2	no	—
1195	C₂²	—	4	2	no	—
1196	C₂²	—	4	2	no	—
1197	C₂²	—	4	2	no	—
1198	C₂²	—	4	2	no	—
1199	C₂²	—	8	4	no	—
1200	C₂²	—	8	8	no	—
1201	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
1202	C₄	—	2	1	no	—
1203	C₄	—	2	1	no	—
1204	C₄	—	2	1	no	—
1205	C₄	—	2	1	no	—
1206	C₄	—	2	2	no	—
1207	C₄	—	2	2	no	—
1208	C₄	—	2	2	no	—
1209	C₄	—	4	1	no	—
1210	C₄	—	4	2	no	—
1211	C₄	—	4	1	no	—
1212	C₄	—	4	1	no	—
1213	C₄	—	4	1	no	—
1214	C₄	—	4	2	no	—
1215	C₄	—	4	1	no	—
1216	C₄	—	4	1	no	—
1217	C₄	C₄₁×#575	1	2	yes	—
1218	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1219	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1220	C₂	—	4	2	no	—
1221	C₂	—	4	1	no	—
1222	C₂	—	4	2	no	—
1223	C₂	—	4	2	no	—
1224	C₂	—	8	2	no	—
1225	C₂	—	8	2	no	—
1226	C₂	C₄₁×#3484	1	1	yes	characteristic
1227	C₂	C₂×C₄₁×#575	1	1	yes	characteristic
1228	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 ◁ C₂×C₄×D₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3506	C₂	semidirect
2. D₄×#41×C₄₁	C₂	semidirect
3. C₄₁×#3328	C₂	semidirect
4. C₄₁×#3324	C₂	semidirect
5. C₄₁×#3321	C₂	semidirect
6. C₄₁×#3319	C₂	semidirect
7. C₄₁×#3304	C₂	semidirect
8. C₄₁×#3302	C₂	semidirect
9. C₄₁×#3287	C₂	semidirect
10. C₄₁×#3284	C₂	semidirect
11. C₄₁×#3278	C₂	semidirect
12. C₄₁×#3274	C₂	semidirect
13. C₄₁×#3269	C₂	semidirect
14. C₄₁×#3267	C₂	semidirect
15. C₄₁×#3216	C₂	semidirect
16. C₄₁×#3207	C₂	semidirect
17. C₄₁×#3197	C₂	semidirect
18. C₄₁×#3191	C₂	semidirect
19. C₄₁×#3115	C₂	semidirect
20. C₄₁×#3107	C₂	semidirect
21. C₄₁×#3005	C₂	semidirect
22. C₄₁×#3002	C₂	semidirect
23. C₄₁×#2974	C₂	semidirect
25. C₂×#137×C₄₁	C₂²	semidirect
26. C₂×AGL(1,ℤ/8)×C₄₁	C₂²	semidirect
27. C₂×#135×C₄₁	C₂²	semidirect
28. C₂×#135×C₄₁	C₂²	semidirect
32. C₄₁×#556	C₂²	semidirect
33. C₄₁×#555	C₂²	semidirect
37. C₄₁×#550	C₂²	semidirect
42. C₄₁×#547	C₂²	semidirect
49. C₄₁×#533	C₂²	semidirect
52. C₄₁×#532	C₂²	semidirect
55. C₄₁×#525	C₂²	semidirect
56. C₄₁×#525	C₂²	semidirect
61. C₄₁×#497	C₂²	semidirect
62. C₄₁×#493	C₂²	semidirect
63. C₄₁×#492	C₂²	semidirect
64. C₄₁×#489	C₂²	semidirect
65. C₄₁×#487	C₂²	semidirect
66. C₄₁×#486	C₂²	semidirect
67. C₄₁×#485	C₂²	semidirect
68. C₄₁×#485	C₂²	semidirect
69. C₄₁×#485	C₂²	semidirect
70. C₄₁×#485	C₂²	semidirect
71. C₄₁×#482	C₂²	semidirect
72. C₄₁×#482	C₂²	semidirect
73. C₄₁×#482	C₂²	semidirect
74. C₄₁×#475	C₂²	semidirect
75. C₄₁×#475	C₂²	semidirect
76. C₄₁×#474	C₂²	semidirect
77. C₄₁×#474	C₂²	semidirect
78. C₄₁×#470	C₂²	semidirect
79. C₄₁×#469	C₂²	semidirect
80. C₄₁×#468	C₂²	semidirect
81. C₄₁×#468	C₂²	semidirect
82. C₄₁×#467	C₂²	semidirect
83. C₄₁×#466	C₂²	semidirect
84. C₄₁×#465	C₂²	semidirect
85. C₄₁×#465	C₂²	semidirect
86. C₄₁×#463	C₂²	semidirect
87. C₄₁×#463	C₂²	semidirect
88. C₄₁×#462	C₂²	semidirect
89. C₄₁×#462	C₂²	semidirect
90. C₄₁×#462	C₂²	semidirect
91. C₄₁×#461	C₂²	semidirect
92. C₄₁×#460	C₂²	semidirect
93. C₄₁×#460	C₂²	semidirect
94. C₄₁×#460	C₂²	semidirect
95. C₄₁×#459	C₂²	semidirect
98. C₄₁×#452	C₂²	semidirect
99. C₄₁×#452	C₂²	semidirect
100. C₄₁×#452	C₂²	semidirect
101. C₄₁×#452	C₂²	semidirect
102. C₄₁×#452	C₂²	semidirect
103. C₄₁×#452	C₂²	semidirect
104. C₄₁×#451	C₂²	semidirect
105. C₄₁×#450	C₂²	semidirect
107. C₄₁×#449	C₂²	semidirect
108. C₄₁×#449	C₂²	semidirect
109. C₄₁×#449	C₂²	semidirect
110. C₄₁×#449	C₂²	semidirect
111. C₄₁×#449	C₂²	semidirect
112. C₄₁×#449	C₂²	semidirect
113. C₄₁×#448	C₂²	semidirect
114. C₄₁×#447	C₂²	semidirect
115. C₄₁×#442	C₂²	semidirect
116. C₄₁×#440	C₂²	semidirect
117. C₄×Q₁₆×C₄₁	C₂²	semidirect
118. C₄×Q₁₆×C₄₁	C₂²	semidirect
119. C₄×SD₁₆×C₄₁	C₂²	semidirect
120. C₄×SD₁₆×C₄₁	C₂²	semidirect
123. C₄₁×#435	C₂²	semidirect
124. C₄₁×#435	C₂²	semidirect
125. C₈×D₄×C₄₁	C₂²	semidirect
126. C₈×D₄×C₄₁	C₂²	semidirect
127. C₄₁×#432	C₂²	semidirect
128. C₄₁×#431	C₂²	semidirect
129. C₄₁×#419	C₂²	semidirect
130. C₄₁×#418	C₂²	semidirect
131. C₄₁×#416	C₂²	semidirect
132. C₄₁×#416	C₂²	semidirect
133. C₄₁×#407	C₂²	semidirect
134. C₂×C₂²⋊C₈×C₄₁	C₂²	semidirect
566. #61608	C₄₁	direct (N × H)
606. #3506	C₂×C₄₁	semidirect
607. D₄×#41	C₂×C₄₁	semidirect
608. #3328	C₂×C₄₁	semidirect
609. #3324	C₂×C₄₁	semidirect
610. #3321	C₂×C₄₁	semidirect
611. #3319	C₂×C₄₁	semidirect
612. #3304	C₂×C₄₁	semidirect
613. #3302	C₂×C₄₁	semidirect
614. #3287	C₂×C₄₁	semidirect
615. #3284	C₂×C₄₁	semidirect
616. #3278	C₂×C₄₁	semidirect
617. #3274	C₂×C₄₁	semidirect
618. #3269	C₂×C₄₁	semidirect
619. #3267	C₂×C₄₁	semidirect
620. #3216	C₂×C₄₁	semidirect
621. #3207	C₂×C₄₁	semidirect
622. #3197	C₂×C₄₁	semidirect
623. #3191	C₂×C₄₁	semidirect
624. #3115	C₂×C₄₁	semidirect
625. #3107	C₂×C₄₁	semidirect
626. #3005	C₂×C₄₁	semidirect
627. #3002	C₂×C₄₁	semidirect
628. #2974	C₂×C₄₁	semidirect
639. C₂×#137	C₂²×C₄₁	semidirect
640. C₂×AGL(1,ℤ/8)	C₂²×C₄₁	semidirect
641. C₂×#135	C₂²×C₄₁	semidirect
642. C₂×#135	C₂²×C₄₁	semidirect
646. #556	C₂²×C₄₁	semidirect
647. #555	C₂²×C₄₁	semidirect
651. #550	C₂²×C₄₁	semidirect
656. #547	C₂²×C₄₁	semidirect
663. #533	C₂²×C₄₁	semidirect
666. #532	C₂²×C₄₁	semidirect
669. #525	C₂²×C₄₁	semidirect
670. #525	C₂²×C₄₁	semidirect
675. #497	C₂²×C₄₁	semidirect
676. #493	C₂²×C₄₁	semidirect
677. #492	C₂²×C₄₁	semidirect
678. #489	C₂²×C₄₁	semidirect
679. #487	C₂²×C₄₁	semidirect
680. #486	C₂²×C₄₁	semidirect
681. #485	C₂²×C₄₁	semidirect
682. #485	C₂²×C₄₁	semidirect
683. #485	C₂²×C₄₁	semidirect
684. #485	C₂²×C₄₁	semidirect
685. #482	C₂²×C₄₁	semidirect
686. #482	C₂²×C₄₁	semidirect
687. #482	C₂²×C₄₁	semidirect
688. #475	C₂²×C₄₁	semidirect
689. #475	C₂²×C₄₁	semidirect
690. #474	C₂²×C₄₁	semidirect
691. #474	C₂²×C₄₁	semidirect
692. #470	C₂²×C₄₁	semidirect
693. #469	C₂²×C₄₁	semidirect
694. #468	C₂²×C₄₁	semidirect
695. #468	C₂²×C₄₁	semidirect
696. #467	C₂²×C₄₁	semidirect
697. #466	C₂²×C₄₁	semidirect
698. #465	C₂²×C₄₁	semidirect
699. #465	C₂²×C₄₁	semidirect
700. #463	C₂²×C₄₁	semidirect
701. #463	C₂²×C₄₁	semidirect
702. #462	C₂²×C₄₁	semidirect
703. #462	C₂²×C₄₁	semidirect
704. #462	C₂²×C₄₁	semidirect
705. #461	C₂²×C₄₁	semidirect
706. #460	C₂²×C₄₁	semidirect
707. #460	C₂²×C₄₁	semidirect
708. #460	C₂²×C₄₁	semidirect
709. #459	C₂²×C₄₁	semidirect
712. #452	C₂²×C₄₁	semidirect
713. #452	C₂²×C₄₁	semidirect
714. #452	C₂²×C₄₁	semidirect
715. #452	C₂²×C₄₁	semidirect
716. #452	C₂²×C₄₁	semidirect
717. #452	C₂²×C₄₁	semidirect
718. #451	C₂²×C₄₁	semidirect
719. #450	C₂²×C₄₁	semidirect
721. #449	C₂²×C₄₁	semidirect
722. #449	C₂²×C₄₁	semidirect
723. #449	C₂²×C₄₁	semidirect
724. #449	C₂²×C₄₁	semidirect
725. #449	C₂²×C₄₁	semidirect
726. #449	C₂²×C₄₁	semidirect
727. #448	C₂²×C₄₁	semidirect
728. #447	C₂²×C₄₁	semidirect
729. #442	C₂²×C₄₁	semidirect
730. #440	C₂²×C₄₁	semidirect
731. C₄×Q₁₆	C₂²×C₄₁	semidirect
732. C₄×Q₁₆	C₂²×C₄₁	semidirect
733. C₄×SD₁₆	C₂²×C₄₁	semidirect
734. C₄×SD₁₆	C₂²×C₄₁	semidirect
737. #435	C₂²×C₄₁	semidirect
738. #435	C₂²×C₄₁	semidirect
739. C₈×D₄	C₂²×C₄₁	semidirect
740. C₈×D₄	C₂²×C₄₁	semidirect
741. #432	C₂²×C₄₁	semidirect
742. #431	C₂²×C₄₁	semidirect
743. #419	C₂²×C₄₁	semidirect
744. #418	C₂²×C₄₁	semidirect
745. #416	C₂²×C₄₁	semidirect
746. #416	C₂²×C₄₁	semidirect
747. #407	C₂²×C₄₁	semidirect
748. C₂×C₂²⋊C₈	C₂²×C₄₁	semidirect
749. C₄₁	#61608	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×#3506	2
D₄×#41×C₄₁	2
C₄₁×#3328	2
C₄₁×#3324	2
C₄₁×#3321	2
C₄₁×#3319	2
C₄₁×#3304	2
C₄₁×#3302	2
C₄₁×#3287	2
C₄₁×#3284	2
C₄₁×#3278	2
C₄₁×#3274	2
C₄₁×#3269	2
C₄₁×#3267	2
C₄₁×#3216	2
C₄₁×#3207	2
C₄₁×#3197	2
C₄₁×#3191	2
C₄₁×#3115	2
C₄₁×#3107	2
C₄₁×#3005	2
C₄₁×#3002	2
C₄₁×#2974	2
#61608	41

Subgroups — C41×#61608 #23837809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61608 #23837809