Subgroups — C₄₁×#60978 #23837179

Order 10496.

1856 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#540	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3259	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3257	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3241	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3234	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#3232	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#3220	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3217	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#3194	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3192	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3188	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3186	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3179	C₂	1	2	yes	maximal, complemented
16	C₄₁×#3176	C₂	1	2	yes	maximal, complemented
17	C₄₁×#3122	C₂	1	2	yes	maximal, complemented
18	C₄₁×#3119	C₂	1	2	yes	maximal, complemented
19	C₄₁×#3114	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₁×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	C₄₁×#555	—	2	1	no	—
25	C₄₁×#553	—	2	1	no	—
26	C₄₁×#553	—	2	1	no	—
27	C₄₁×#551	—	2	1	no	—
28	C₄₁×#551	—	2	1	no	—
29	C₄₁×#547	—	2	1	no	—
30	C₄₁×#546	—	2	1	no	—
31	C₄₁×#546	—	2	1	no	—
32	C₄₁×#544	C₂²	1	1	yes	characteristic, complemented
33	C₄₁×#542	C₂²	1	1	yes	characteristic, complemented
34	C₄₁×#542	C₂²	1	1	yes	characteristic, complemented
35	C₄₁×#540	—	2	1	no	—
36	C₄₁×#540	—	2	1	no	—
37	C₄₁×#540	—	2	1	no	—
38	C₄₁×#540	—	2	1	no	—
39	C₄₁×#540	C₂²	1	2	yes	—
40	C₄₁×#540	C₂²	1	2	yes	—
41	C₄₁×#540	C₂²	1	1	yes	characteristic, complemented
42	C₄₁×#540	C₂²	1	2	yes	complemented
43	C₄₁×#540	C₂²	1	2	yes	complemented
44	C₄₁×#540	C₂²	1	1	yes	characteristic, complemented
45	C₄₁×#535	C₂²	1	1	yes	characteristic, complemented
46	C₄₁×#532	C₂²	1	1	yes	characteristic
47	C₄₁×#532	C₂²	1	1	yes	characteristic
48	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic, complemented
49	C₄₁×#529	C₂²	1	1	yes	characteristic
50	C₄₁×#529	C₂²	1	1	yes	characteristic
51	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic, complemented
52	C₄₁×#525	C₂²	1	1	yes	characteristic
53	C₂×#123×C₄₁	—	2	1	no	—
54	C₂×#123×C₄₁	—	2	1	no	—
55	C₂×#121×C₄₁	—	2	1	no	—
56	C₂×#121×C₄₁	—	2	1	no	—
57	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
58	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
59	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
60	C₄₁×#520	C₂²	1	1	yes	characteristic, complemented
61	C₄₁×#518	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
64	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
65	C₄₁×#501	C₂²	1	2	yes	complemented
66	C₄₁×#499	C₂²	1	2	yes	complemented
67	C₄₁×#496	C₂²	1	2	yes	complemented
68	C₄₁×#493	C₂²	1	2	yes	complemented
69	C₄₁×#490	C₂²	1	2	yes	complemented
70	C₄₁×#490	C₂²	1	2	yes	complemented
71	C₄₁×#488	C₂²	1	2	yes	complemented
72	C₄₁×#486	C₂²	1	2	yes	complemented
73	C₄₁×#484	C₂²	1	1	yes	characteristic, complemented
74	C₄₁×#483	C₂²	1	1	yes	characteristic, complemented
75	C₄₁×#482	C₂²	1	2	yes	complemented
76	C₄₁×#482	C₂²	1	2	yes	complemented
77	C₄₁×#481	C₂²	1	1	yes	characteristic
78	C₄₁×#481	C₂²	1	1	yes	characteristic
79	C₄₁×#481	C₂²	1	1	yes	characteristic, complemented
80	C₄₁×#481	C₂²	1	2	yes	complemented
81	C₄₁×#480	C₂²	1	1	yes	characteristic
82	C₄₁×#480	C₂²	1	1	yes	characteristic
83	C₄₁×#480	C₂²	1	1	yes	characteristic, complemented
84	C₄₁×#480	C₂²	1	2	yes	complemented
85	C₄₁×#479	C₂²	1	2	yes	complemented
86	C₄₁×#478	C₂²	1	2	yes	complemented
87	C₄₁×#478	C₂²	1	2	yes	complemented
88	C₄₁×#478	C₂²	1	2	yes	complemented
89	C₄₁×#478	C₂²	1	2	yes	complemented
90	C₄₁×#478	C₂²	1	2	yes	complemented
91	C₄₁×#476	C₂²	1	2	yes	complemented
92	C₄₁×#474	C₂²	1	2	yes	complemented
93	C₄₁×#469	C₂²	1	2	yes	complemented
94	C₄₁×#469	C₂²	1	2	yes	complemented
95	C₄₁×#469	C₂²	1	2	yes	complemented
96	C₄₁×#468	C₂²	1	2	yes	complemented
97	C₄₁×#466	C₂²	1	2	yes	complemented
98	C₄₁×#466	C₂²	1	2	yes	complemented
99	C₄₁×#466	C₂²	1	2	yes	complemented
100	C₄₁×#465	C₂²	1	2	yes	complemented
101	C₄₁×#463	C₂²	1	2	yes	complemented
102	C₄₁×#463	C₂²	1	2	yes	complemented
103	C₄₁×#460	C₂²	1	2	yes	complemented
104	C₄₁×#459	C₂²	1	2	yes	complemented
105	C₄₁×#459	C₂²	1	2	yes	complemented
106	C₄₁×#459	C₂²	1	2	yes	complemented
107	C₄₁×#459	C₂²	1	2	yes	complemented
108	C₄₁×#459	C₂²	1	2	yes	complemented
109	C₄₁×#450	C₂²	1	1	yes	characteristic, complemented
110	C₄₁×#450	C₂²	1	1	yes	characteristic, complemented
111	C₄₁×#449	C₂²	1	2	yes	complemented
112	C₄₁×#449	C₂²	1	2	yes	complemented
113	C₄₁×#447	C₂²	1	1	yes	characteristic
114	C₄₁×#447	C₂²	1	1	yes	characteristic
115	C₄₁×#447	C₂²	1	1	yes	characteristic
116	C₄₁×#447	C₂²	1	1	yes	characteristic
117	C₄₁×#447	C₂²	1	1	yes	characteristic, complemented
118	C₄₁×#447	C₂²	1	1	yes	characteristic, complemented
119	C₄₁×#447	C₂²	1	2	yes	complemented
120	C₄₁×#447	C₂²	1	2	yes	complemented
121	C₄₁×#442	C₂²	1	2	yes	complemented
122	C₄₁×#442	C₂²	1	2	yes	complemented
123	C₄₁×#442	C₂²	1	2	yes	complemented
124	C₄₁×#440	C₂²	1	2	yes	complemented
125	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
126	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
127	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
128	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
129	C₄₁×#433	C₂²	1	2	yes	complemented
130	C₄₁×#433	C₂²	1	2	yes	complemented
131	C₄₁×#432	C₂²	1	1	yes	characteristic, complemented
132	C₄₁×#432	C₂²	1	1	yes	characteristic, complemented
133	C₄₁×#431	C₂²	1	1	yes	characteristic, complemented
134	C₄₁×#431	C₂²	1	1	yes	characteristic, complemented
135	C₄₁×#424	C₂²	1	2	yes	complemented
136	C₄₁×#407	C₂²	1	1	yes	characteristic
137	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
138	C₄₁×#405	C₂²	1	2	yes	complemented
139	C₂×#41×C₄₁	—	2	1	no	—
140	C₂×#41×C₄₁	—	2	1	no	—
141	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₄₁	—	2	1	no	—
143	C₂²×D₄×C₄₁	—	2	1	no	—
144	C₂²×D₄×C₄₁	—	2	1	no	—
145	C₂²×D₄×C₄₁	—	2	1	no	—
146	C₂²×D₄×C₄₁	—	2	1	no	—
147	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
148	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
149	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
150	C₂³×C₄×C₄₁	—	2	1	no	—
151	C₂³×C₄×C₄₁	—	2	1	no	—
152	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
153	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
155	C₂×D₈×C₄₁	C₂³	1	2	yes	—
156	C₂×D₈×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×D₈×C₄₁	C₂³	1	2	yes	—
161	C₂×M₁₆×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	#127×C₄₁	—	2	1	no	—
167	#127×C₄₁	—	2	1	no	—
168	#127×C₄₁	C₂³	1	2	yes	—
169	#127×C₄₁	C₂³	1	2	yes	—
170	#127×C₄₁	C₂³	1	1	yes	characteristic
171	#127×C₄₁	C₂³	1	1	yes	characteristic
172	#126×C₄₁	—	2	1	no	—
173	#126×C₄₁	—	2	1	no	—
174	#126×C₄₁	—	2	1	no	—
175	#126×C₄₁	—	2	1	no	—
176	#125×C₄₁	—	2	1	no	—
177	#125×C₄₁	—	2	1	no	—
178	#125×C₄₁	—	2	1	no	—
179	#125×C₄₁	C₂³	1	2	yes	—
180	#125×C₄₁	C₂³	1	2	yes	—
181	#125×C₄₁	C₂³	1	1	yes	characteristic
182	#125×C₄₁	C₂³	1	1	yes	characteristic
183	#124×C₄₁	—	2	1	no	—
184	#124×C₄₁	—	2	1	no	—
185	#124×C₄₁	—	2	1	no	—
186	#124×C₄₁	—	2	1	no	—
187	#124×C₄₁	C₂³	1	1	yes	characteristic
188	#124×C₄₁	C₂³	1	1	yes	characteristic
189	#123×C₄₁	—	2	1	no	—
190	#123×C₄₁	—	2	1	no	—
191	#123×C₄₁	—	2	1	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	—	2	2	no	—
198	#123×C₄₁	—	2	2	no	—
199	#123×C₄₁	—	2	2	no	—
200	#123×C₄₁	—	2	1	no	—
201	#123×C₄₁	—	2	1	no	—
202	#123×C₄₁	—	2	1	no	—
203	#123×C₄₁	—	2	1	no	—
204	#123×C₄₁	—	2	1	no	—
205	#123×C₄₁	—	2	1	no	—
206	C₂²⋊Q₈×C₄₁	—	2	1	no	—
207	C₂²⋊Q₈×C₄₁	—	2	1	no	—
208	C₂²⋊Q₈×C₄₁	—	2	1	no	—
209	C₂²⋊Q₈×C₄₁	—	2	1	no	—
210	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
211	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
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	1	no	—
219	#121×C₄₁	—	2	1	no	—
220	#121×C₄₁	—	2	1	no	—
221	#121×C₄₁	—	2	1	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	—	2	2	no	—
227	#121×C₄₁	—	2	2	no	—
228	#121×C₄₁	—	2	2	no	—
229	#121×C₄₁	—	2	2	no	—
230	#121×C₄₁	—	2	1	no	—
231	#121×C₄₁	—	2	1	no	—
232	#121×C₄₁	—	2	1	no	—
233	#121×C₄₁	—	2	1	no	—
234	#121×C₄₁	C₂³	1	1	yes	characteristic
235	#121×C₄₁	C₂³	1	1	yes	characteristic
236	#121×C₄₁	C₂³	1	2	yes	—
237	#121×C₄₁	C₂³	1	2	yes	—
238	#121×C₄₁	C₂³	1	2	yes	—
239	#121×C₄₁	C₂³	1	2	yes	—
240	#121×C₄₁	C₂³	1	1	yes	characteristic
241	#121×C₄₁	C₂³	1	1	yes	characteristic
242	#121×C₄₁	C₂³	1	1	yes	characteristic
243	#121×C₄₁	C₂³	1	1	yes	characteristic
244	#120×C₄₁	—	2	1	no	—
245	#120×C₄₁	—	2	1	no	—
246	#120×C₄₁	—	2	1	no	—
247	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
248	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
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	1	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	—	2	1	no	—
257	C₄×D₄×C₄₁	—	2	1	no	—
258	C₄×D₄×C₄₁	—	2	1	no	—
259	C₄×D₄×C₄₁	—	2	1	no	—
260	C₄×D₄×C₄₁	—	2	1	no	—
261	C₄×D₄×C₄₁	—	2	1	no	—
262	C₄×D₄×C₄₁	—	2	1	no	—
263	C₄×D₄×C₄₁	C₂³	1	2	yes	—
264	C₄×D₄×C₄₁	C₂³	1	2	yes	—
265	C₄×D₄×C₄₁	C₂³	1	2	yes	—
266	C₄×D₄×C₄₁	C₂³	1	2	yes	—
267	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
268	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
269	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
270	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
271	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
272	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
273	#117×C₄₁	—	2	1	no	—
274	#117×C₄₁	—	2	1	no	—
275	#117×C₄₁	—	2	1	no	—
276	#117×C₄₁	D₄	1	1	yes	characteristic
277	#117×C₄₁	D₄	1	1	yes	characteristic
278	#117×C₄₁	D₄	1	1	yes	characteristic
279	#117×C₄₁	D₄	1	1	yes	characteristic
280	#117×C₄₁	C₂³	1	1	yes	characteristic
281	#117×C₄₁	C₂³	1	1	yes	characteristic
282	#117×C₄₁	C₂³	1	1	yes	characteristic
283	#117×C₄₁	C₂³	1	1	yes	characteristic
284	#117×C₄₁	C₂³	1	1	yes	characteristic
285	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
286	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
287	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
288	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
289	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
290	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
294	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
295	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
296	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
297	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
298	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
299	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
300	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
301	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
302	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
303	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
304	#107×C₄₁	C₂³	1	2	yes	—
305	#107×C₄₁	C₂³	1	2	yes	—
306	#107×C₄₁	C₂³	1	2	yes	—
307	#107×C₄₁	C₂³	1	2	yes	—
308	#106×C₄₁	C₂³	1	2	yes	—
309	#106×C₄₁	C₂³	1	2	yes	—
310	#106×C₄₁	C₂³	1	2	yes	—
311	#106×C₄₁	C₂³	1	2	yes	—
312	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
313	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
314	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
315	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
316	#103×C₄₁	C₂³	1	2	yes	—
317	#103×C₄₁	C₂³	1	2	yes	—
318	#102×C₄₁	C₂³	1	2	yes	—
319	#102×C₄₁	C₂³	1	2	yes	—
320	#102×C₄₁	C₂³	1	2	yes	—
321	#102×C₄₁	C₂³	1	2	yes	—
322	#102×C₄₁	C₂³	1	2	yes	—
323	#102×C₄₁	C₂³	1	2	yes	—
324	#102×C₄₁	C₂³	1	2	yes	—
325	#102×C₄₁	C₂³	1	2	yes	—
326	#102×C₄₁	C₂³	1	2	yes	—
327	#102×C₄₁	C₂³	1	2	yes	—
328	#102×C₄₁	C₂³	1	2	yes	—
329	#102×C₄₁	C₂³	1	2	yes	—
330	#102×C₄₁	C₂³	1	2	yes	—
331	#102×C₄₁	C₂³	1	2	yes	—
332	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
333	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
334	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
335	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
336	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
337	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
338	#97×C₄₁	C₂³	1	2	yes	—
339	#97×C₄₁	C₂³	1	2	yes	—
340	C₄×C₈×C₄₁	C₂³	1	2	yes	—
341	C₄×C₈×C₄₁	C₂³	1	2	yes	—
342	C₂⁴×C₄₁	—	2	1	no	—
343	C₂⁴×C₄₁	—	2	1	no	—
344	C₂⁴×C₄₁	—	2	1	no	—
345	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
346	#41×C₄₁	—	4	2	no	—
347	#41×C₄₁	—	8	2	no	—
348	#41×C₄₁	—	8	2	no	—
349	C₂×Q₈×C₄₁	—	2	1	no	—
350	C₂×Q₈×C₄₁	—	2	1	no	—
351	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₄₁	—	2	1	no	—
353	C₂×D₄×C₄₁	—	2	1	no	—
354	C₂×D₄×C₄₁	—	2	1	no	—
355	C₂×D₄×C₄₁	—	2	1	no	—
356	C₂×D₄×C₄₁	—	2	1	no	—
357	C₂×D₄×C₄₁	—	2	2	no	—
358	C₂×D₄×C₄₁	—	2	2	no	—
359	C₂×D₄×C₄₁	—	2	2	no	—
360	C₂×D₄×C₄₁	—	2	2	no	—
361	C₂×D₄×C₄₁	—	2	1	no	—
362	C₂×D₄×C₄₁	—	2	1	no	—
363	C₂×D₄×C₄₁	—	2	1	no	—
364	C₂×D₄×C₄₁	—	2	1	no	—
365	C₂×D₄×C₄₁	—	2	1	no	—
366	C₂×D₄×C₄₁	—	2	1	no	—
367	C₂×D₄×C₄₁	—	2	1	no	—
368	C₂×D₄×C₄₁	—	2	1	no	—
369	C₂×D₄×C₄₁	—	2	1	no	—
370	C₂×D₄×C₄₁	—	2	2	no	—
371	C₂×D₄×C₄₁	—	2	2	no	—
372	C₂×D₄×C₄₁	—	2	2	no	—
373	C₂×D₄×C₄₁	—	2	2	no	—
374	C₂×D₄×C₄₁	—	4	2	no	—
375	C₂×D₄×C₄₁	—	4	2	no	—
376	C₂×D₄×C₄₁	—	4	2	no	—
377	C₂×D₄×C₄₁	—	8	2	no	—
378	C₂×D₄×C₄₁	—	8	2	no	—
379	C₂×D₄×C₄₁	—	8	2	no	—
380	C₂×D₄×C₄₁	—	8	2	no	—
381	C₂×D₄×C₄₁	—	8	2	no	—
382	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
383	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
384	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
385	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
386	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
387	C₂²×C₄×C₄₁	—	2	1	no	—
388	C₂²×C₄×C₄₁	—	2	1	no	—
389	C₂²×C₄×C₄₁	—	2	1	no	—
390	C₂²×C₄×C₄₁	—	2	1	no	—
391	C₂²×C₄×C₄₁	—	2	1	no	—
392	C₂²×C₄×C₄₁	—	2	1	no	—
393	C₂²×C₄×C₄₁	—	2	1	no	—
394	C₂²×C₄×C₄₁	—	2	1	no	—
395	C₂²×C₄×C₄₁	—	2	1	no	—
396	C₂²×C₄×C₄₁	—	2	1	no	—
397	C₂²×C₄×C₄₁	—	2	2	no	—
398	C₂²×C₄×C₄₁	—	2	2	no	—
399	C₂²×C₄×C₄₁	—	2	2	no	—
400	C₂²×C₄×C₄₁	—	2	2	no	—
401	C₂²×C₄×C₄₁	—	4	2	no	—
402	C₂²×C₄×C₄₁	—	8	2	no	—
403	C₂²×C₄×C₄₁	—	8	2	no	—
404	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
405	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
406	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
407	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
408	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
409	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
410	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
411	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
413	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
414	SD₁₆×C₄₁	—	4	2	no	—
415	SD₁₆×C₄₁	—	4	2	no	—
416	D₈×C₄₁	—	4	2	no	—
417	D₈×C₄₁	—	4	2	no	—
418	D₈×C₄₁	—	4	2	no	—
419	D₈×C₄₁	—	4	2	no	—
420	D₈×C₄₁	—	4	2	no	—
421	D₈×C₄₁	—	4	2	no	—
422	M₁₆×C₄₁	—	4	2	no	—
423	C₂×C₈×C₄₁	—	4	2	no	—
424	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
425	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
426	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
427	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
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	2	no	—
432	C₄⋊C₄×C₄₁	—	2	2	no	—
433	C₄⋊C₄×C₄₁	—	2	2	no	—
434	C₄⋊C₄×C₄₁	—	2	2	no	—
435	C₄⋊C₄×C₄₁	—	2	1	no	—
436	C₄⋊C₄×C₄₁	—	2	1	no	—
437	C₄⋊C₄×C₄₁	—	2	1	no	—
438	C₄⋊C₄×C₄₁	—	2	1	no	—
439	C₄⋊C₄×C₄₁	—	2	1	no	—
440	C₄⋊C₄×C₄₁	—	2	1	no	—
441	C₄⋊C₄×C₄₁	—	2	1	no	—
442	C₄⋊C₄×C₄₁	—	2	1	no	—
443	C₄⋊C₄×C₄₁	—	2	1	no	—
444	C₄⋊C₄×C₄₁	—	2	1	no	—
445	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
449	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
450	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
451	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
452	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
453	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
455	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
456	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
457	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
458	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
459	C₂²⋊C₄×C₄₁	—	2	1	no	—
460	C₂²⋊C₄×C₄₁	—	2	1	no	—
461	C₂²⋊C₄×C₄₁	—	2	1	no	—
462	C₂²⋊C₄×C₄₁	—	2	1	no	—
463	C₂²⋊C₄×C₄₁	—	2	1	no	—
464	C₂²⋊C₄×C₄₁	—	2	2	no	—
465	C₂²⋊C₄×C₄₁	—	2	2	no	—
466	C₂²⋊C₄×C₄₁	—	2	2	no	—
467	C₂²⋊C₄×C₄₁	—	2	2	no	—
468	C₂²⋊C₄×C₄₁	—	2	1	no	—
469	C₂²⋊C₄×C₄₁	—	2	1	no	—
470	C₂²⋊C₄×C₄₁	—	2	1	no	—
471	C₂²⋊C₄×C₄₁	—	2	1	no	—
472	C₂²⋊C₄×C₄₁	—	2	1	no	—
473	C₂²⋊C₄×C₄₁	—	2	1	no	—
474	C₂²⋊C₄×C₄₁	—	2	2	no	—
475	C₂²⋊C₄×C₄₁	—	2	2	no	—
476	C₂²⋊C₄×C₄₁	—	2	2	no	—
477	C₂²⋊C₄×C₄₁	—	2	2	no	—
478	C₂²⋊C₄×C₄₁	—	2	1	no	—
479	C₂²⋊C₄×C₄₁	—	2	1	no	—
480	C₂²⋊C₄×C₄₁	—	2	1	no	—
481	C₂²⋊C₄×C₄₁	—	2	1	no	—
482	C₂²⋊C₄×C₄₁	—	2	1	no	—
483	C₂²⋊C₄×C₄₁	—	2	1	no	—
484	C₂²⋊C₄×C₄₁	—	2	1	no	—
485	C₂²⋊C₄×C₄₁	—	2	1	no	—
486	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
487	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
488	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
489	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
490	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
491	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
492	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
493	C₂²⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
494	C₄²×C₄₁	—	2	1	no	—
495	C₄²×C₄₁	—	2	1	no	—
496	C₄²×C₄₁	—	2	1	no	—
497	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
498	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
499	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
500	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
501	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
502	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
503	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
504	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
505	C₂³×C₄₁	—	2	2	no	—
506	C₂³×C₄₁	—	2	1	no	—
507	C₂³×C₄₁	—	2	1	no	—
508	C₂³×C₄₁	—	2	1	no	—
509	C₂³×C₄₁	—	2	2	no	—
510	C₂³×C₄₁	—	2	2	no	—
511	C₂³×C₄₁	—	4	1	no	—
512	C₂³×C₄₁	—	4	1	no	—
513	C₂³×C₄₁	—	4	2	no	—
514	C₂³×C₄₁	—	4	2	no	—
515	C₂³×C₄₁	—	4	2	no	—
516	C₂³×C₄₁	—	4	2	no	—
517	C₂³×C₄₁	—	4	2	no	—
518	C₂³×C₄₁	—	4	2	no	—
519	C₂³×C₄₁	—	4	2	no	—
520	C₂³×C₄₁	—	8	1	no	—
521	C₂³×C₄₁	—	8	1	no	—
522	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
523	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
524	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
525	Q₈×C₄₁	—	2	2	no	—
526	Q₈×C₄₁	—	8	1	no	—
527	Q₈×C₄₁	—	8	1	no	—
528	D₄×C₄₁	—	2	2	no	—
529	D₄×C₄₁	—	2	2	no	—
530	D₄×C₄₁	—	2	2	no	—
531	D₄×C₄₁	—	2	2	no	—
532	D₄×C₄₁	—	2	2	no	—
533	D₄×C₄₁	—	2	2	no	—
534	D₄×C₄₁	—	2	2	no	—
535	D₄×C₄₁	—	4	2	no	—
536	D₄×C₄₁	—	4	2	no	—
537	D₄×C₄₁	—	4	2	no	—
538	D₄×C₄₁	—	4	2	no	—
539	D₄×C₄₁	—	4	2	no	—
540	D₄×C₄₁	—	4	2	no	—
541	D₄×C₄₁	—	4	2	no	—
542	D₄×C₄₁	—	8	1	no	—
543	D₄×C₄₁	—	8	1	no	—
544	D₄×C₄₁	—	8	2	no	—
545	D₄×C₄₁	—	8	2	no	—
546	D₄×C₄₁	—	8	2	no	—
547	D₄×C₄₁	—	8	2	no	—
548	D₄×C₄₁	—	8	1	no	—
549	D₄×C₄₁	—	8	1	no	—
550	D₄×C₄₁	—	8	1	no	—
551	D₄×C₄₁	—	8	2	no	—
552	D₄×C₄₁	—	8	2	no	—
553	D₄×C₄₁	—	8	2	no	—
554	D₄×C₄₁	—	8	2	no	—
555	D₄×C₄₁	—	8	1	no	—
556	D₄×C₄₁	—	8	1	no	—
557	C₂×C₄×C₄₁	—	2	2	no	—
558	C₂×C₄×C₄₁	—	2	2	no	—
559	C₂×C₄×C₄₁	—	2	2	no	—
560	C₂×C₄×C₄₁	—	2	2	no	—
561	C₂×C₄×C₄₁	—	2	2	no	—
562	C₂×C₄×C₄₁	—	2	1	no	—
563	C₂×C₄×C₄₁	—	2	1	no	—
564	C₂×C₄×C₄₁	—	2	1	no	—
565	C₂×C₄×C₄₁	—	2	1	no	—
566	C₂×C₄×C₄₁	—	2	1	no	—
567	C₂×C₄×C₄₁	—	2	2	no	—
568	C₂×C₄×C₄₁	—	2	2	no	—
569	C₂×C₄×C₄₁	—	4	1	no	—
570	C₂×C₄×C₄₁	—	4	1	no	—
571	C₂×C₄×C₄₁	—	4	1	no	—
572	C₂×C₄×C₄₁	—	4	1	no	—
573	C₂×C₄×C₄₁	—	4	1	no	—
574	C₂×C₄×C₄₁	—	4	2	no	—
575	C₂×C₄×C₄₁	—	4	2	no	—
576	C₂×C₄×C₄₁	—	4	2	no	—
577	C₂×C₄×C₄₁	—	8	1	no	—
578	C₂×C₄×C₄₁	—	8	1	no	—
579	C₂×C₄×C₄₁	—	8	2	no	—
580	C₂×C₄×C₄₁	—	8	2	no	—
581	C₂×C₄×C₄₁	—	8	2	no	—
582	C₂×C₄×C₄₁	—	8	2	no	—
583	C₂×C₄×C₄₁	—	8	1	no	—
584	C₂×C₄×C₄₁	—	8	1	no	—
585	C₂×C₄×C₄₁	—	8	1	no	—
586	C₂×C₄×C₄₁	—	8	1	no	—
587	C₂×C₄×C₄₁	—	8	1	no	—
588	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
589	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
590	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
591	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
592	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
593	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
594	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
595	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
596	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
597	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
598	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
599	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
600	C₈×C₄₁	—	2	2	no	—
601	C₈×C₄₁	—	2	2	no	—
602	C₈×C₄₁	—	2	2	no	—
603	C₈×C₄₁	—	2	2	no	—
604	#60978	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
605	C₂²×C₄₁	—	2	1	no	—
606	C₂²×C₄₁	—	2	1	no	—
607	C₂²×C₄₁	—	2	1	no	—
608	C₂²×C₄₁	—	2	1	no	—
609	C₂²×C₄₁	—	2	1	no	—
610	C₂²×C₄₁	—	2	1	no	—
611	C₂²×C₄₁	—	2	1	no	—
612	C₂²×C₄₁	—	2	1	no	—
613	C₂²×C₄₁	—	4	2	no	—
614	C₂²×C₄₁	—	4	1	no	—
615	C₂²×C₄₁	—	4	1	no	—
616	C₂²×C₄₁	—	4	2	no	—
617	C₂²×C₄₁	—	4	1	no	—
618	C₂²×C₄₁	—	4	1	no	—
619	C₂²×C₄₁	—	4	2	no	—
620	C₂²×C₄₁	—	4	2	no	—
621	C₂²×C₄₁	—	4	1	no	—
622	C₂²×C₄₁	—	4	1	no	—
623	C₂²×C₄₁	—	4	1	no	—
624	C₂²×C₄₁	—	4	2	no	—
625	C₂²×C₄₁	—	4	1	no	—
626	C₂²×C₄₁	—	4	1	no	—
627	C₂²×C₄₁	—	4	2	no	—
628	C₂²×C₄₁	—	8	2	no	—
629	C₂²×C₄₁	—	8	4	no	—
630	C₂²×C₄₁	—	8	4	no	—
631	C₂²×C₄₁	—	16	2	no	—
632	C₂²×C₄₁	#576	1	2	yes	—
633	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
634	C₄×C₄₁	—	2	1	no	—
635	C₄×C₄₁	—	2	1	no	—
636	C₄×C₄₁	—	2	1	no	—
637	C₄×C₄₁	—	2	1	no	—
638	C₄×C₄₁	—	2	1	no	—
639	C₄×C₄₁	—	2	1	no	—
640	C₄×C₄₁	—	2	1	no	—
641	C₄×C₄₁	—	2	1	no	—
642	C₄×C₄₁	—	2	1	no	—
643	C₄×C₄₁	—	2	1	no	—
644	C₄×C₄₁	—	2	1	no	—
645	C₄×C₄₁	—	4	2	no	—
646	C₄×C₄₁	—	4	1	no	—
647	C₄×C₄₁	—	4	1	no	—
648	C₄×C₄₁	—	4	2	no	—
649	C₄×C₄₁	—	4	1	no	—
650	C₄×C₄₁	—	4	1	no	—
651	C₄×C₄₁	—	4	1	no	—
652	C₄×C₄₁	#585	1	2	yes	—
653	#3494	C₂×C₄₁	1	1	yes	characteristic, complemented
654	C₂×#540	C₂×C₄₁	1	1	yes	characteristic, complemented
655	#3259	C₂×C₄₁	1	2	yes	complemented
656	#3257	C₂×C₄₁	1	2	yes	complemented
657	#3241	C₂×C₄₁	1	2	yes	complemented
658	#3234	C₂×C₄₁	1	1	yes	characteristic, complemented
659	#3232	C₂×C₄₁	1	1	yes	characteristic, complemented
660	#3220	C₂×C₄₁	1	2	yes	complemented
661	#3217	C₂×C₄₁	1	1	yes	characteristic, complemented
662	#3205	C₂×C₄₁	1	1	yes	characteristic, complemented
663	#3194	C₂×C₄₁	1	1	yes	characteristic, complemented
664	#3192	C₂×C₄₁	1	1	yes	characteristic, complemented
665	#3188	C₂×C₄₁	1	1	yes	characteristic, complemented
666	#3186	C₂×C₄₁	1	1	yes	characteristic, complemented
667	#3179	C₂×C₄₁	1	2	yes	complemented
668	#3176	C₂×C₄₁	1	2	yes	complemented
669	#3122	C₂×C₄₁	1	2	yes	complemented
670	#3119	C₂×C₄₁	1	2	yes	complemented
671	#3114	C₂×C₄₁	1	1	yes	characteristic, complemented
672	#3109	C₂×C₄₁	1	1	yes	characteristic, complemented
673	#3105	C₂×C₄₁	1	1	yes	characteristic, complemented
674	#3100	C₂×C₄₁	1	1	yes	characteristic, complemented
675	#2924	C₂×C₄₁	1	1	yes	characteristic, complemented
676	C₂×C₄₁	—	2	2	no	—
677	C₂×C₄₁	—	4	1	no	—
678	C₂×C₄₁	—	4	1	no	—
679	C₂×C₄₁	—	8	1	no	—
680	C₂×C₄₁	—	8	2	no	—
681	C₂×C₄₁	—	8	2	no	—
682	C₂×C₄₁	—	8	1	no	—
683	C₂×C₄₁	—	8	1	no	—
684	C₂×C₄₁	#3449	1	1	yes	characteristic
685	C₂×C₄₁	C₂×#576	1	1	yes	characteristic
686	C₂×C₄₁	#3585	1	1	yes	characteristic
687	#555	—	2	1	no	—
688	#553	—	2	1	no	—
689	#553	—	2	1	no	—
690	#551	—	2	1	no	—
691	#551	—	2	1	no	—
692	#547	—	2	1	no	—
693	#546	—	2	1	no	—
694	#546	—	2	1	no	—
695	#544	C₂²×C₄₁	1	1	yes	characteristic, complemented
696	#542	C₂²×C₄₁	1	1	yes	characteristic, complemented
697	#542	C₂²×C₄₁	1	1	yes	characteristic, complemented
698	#540	—	2	1	no	—
699	#540	—	2	1	no	—
700	#540	—	2	1	no	—
701	#540	—	2	1	no	—
702	#540	C₂²×C₄₁	1	2	yes	—
703	#540	C₂²×C₄₁	1	2	yes	—
704	#540	C₂²×C₄₁	1	1	yes	characteristic, complemented
705	#540	C₂²×C₄₁	1	2	yes	complemented
706	#540	C₂²×C₄₁	1	2	yes	complemented
707	#540	C₂²×C₄₁	1	1	yes	characteristic, complemented
708	#535	C₂²×C₄₁	1	1	yes	characteristic, complemented
709	#532	C₂²×C₄₁	1	1	yes	characteristic
710	#532	C₂²×C₄₁	1	1	yes	characteristic
711	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic, complemented
712	#529	C₂²×C₄₁	1	1	yes	characteristic
713	#529	C₂²×C₄₁	1	1	yes	characteristic
714	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic, complemented
715	#525	C₂²×C₄₁	1	1	yes	characteristic
716	C₂×#123	—	2	1	no	—
717	C₂×#123	—	2	1	no	—
718	C₂×#121	—	2	1	no	—
719	C₂×#121	—	2	1	no	—
720	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
721	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
722	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
723	#520	C₂²×C₄₁	1	1	yes	characteristic, complemented
724	#518	C₂²×C₄₁	1	1	yes	characteristic, complemented
725	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
726	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
727	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
728	#501	C₂²×C₄₁	1	2	yes	complemented
729	#499	C₂²×C₄₁	1	2	yes	complemented
730	#496	C₂²×C₄₁	1	2	yes	complemented
731	#493	C₂²×C₄₁	1	2	yes	complemented
732	#490	C₂²×C₄₁	1	2	yes	complemented
733	#490	C₂²×C₄₁	1	2	yes	complemented
734	#488	C₂²×C₄₁	1	2	yes	complemented
735	#486	C₂²×C₄₁	1	2	yes	complemented
736	#484	C₂²×C₄₁	1	1	yes	characteristic, complemented
737	#483	C₂²×C₄₁	1	1	yes	characteristic, complemented
738	#482	C₂²×C₄₁	1	2	yes	complemented
739	#482	C₂²×C₄₁	1	2	yes	complemented
740	#481	C₂²×C₄₁	1	1	yes	characteristic
741	#481	C₂²×C₄₁	1	1	yes	characteristic
742	#481	C₂²×C₄₁	1	1	yes	characteristic, complemented
743	#481	C₂²×C₄₁	1	2	yes	complemented
744	#480	C₂²×C₄₁	1	1	yes	characteristic
745	#480	C₂²×C₄₁	1	1	yes	characteristic
746	#480	C₂²×C₄₁	1	1	yes	characteristic, complemented
747	#480	C₂²×C₄₁	1	2	yes	complemented
748	#479	C₂²×C₄₁	1	2	yes	complemented
749	#478	C₂²×C₄₁	1	2	yes	complemented
750	#478	C₂²×C₄₁	1	2	yes	complemented
751	#478	C₂²×C₄₁	1	2	yes	complemented
752	#478	C₂²×C₄₁	1	2	yes	complemented
753	#478	C₂²×C₄₁	1	2	yes	complemented
754	#476	C₂²×C₄₁	1	2	yes	complemented
755	#474	C₂²×C₄₁	1	2	yes	complemented
756	#469	C₂²×C₄₁	1	2	yes	complemented
757	#469	C₂²×C₄₁	1	2	yes	complemented
758	#469	C₂²×C₄₁	1	2	yes	complemented
759	#468	C₂²×C₄₁	1	2	yes	complemented
760	#466	C₂²×C₄₁	1	2	yes	complemented
761	#466	C₂²×C₄₁	1	2	yes	complemented
762	#466	C₂²×C₄₁	1	2	yes	complemented
763	#465	C₂²×C₄₁	1	2	yes	complemented
764	#463	C₂²×C₄₁	1	2	yes	complemented
765	#463	C₂²×C₄₁	1	2	yes	complemented
766	#460	C₂²×C₄₁	1	2	yes	complemented
767	#459	C₂²×C₄₁	1	2	yes	complemented
768	#459	C₂²×C₄₁	1	2	yes	complemented
769	#459	C₂²×C₄₁	1	2	yes	complemented
770	#459	C₂²×C₄₁	1	2	yes	complemented
771	#459	C₂²×C₄₁	1	2	yes	complemented
772	#450	C₂²×C₄₁	1	1	yes	characteristic, complemented
773	#450	C₂²×C₄₁	1	1	yes	characteristic, complemented
774	#449	C₂²×C₄₁	1	2	yes	complemented
775	#449	C₂²×C₄₁	1	2	yes	complemented
776	#447	C₂²×C₄₁	1	1	yes	characteristic
777	#447	C₂²×C₄₁	1	1	yes	characteristic
778	#447	C₂²×C₄₁	1	1	yes	characteristic
779	#447	C₂²×C₄₁	1	1	yes	characteristic
780	#447	C₂²×C₄₁	1	1	yes	characteristic, complemented
781	#447	C₂²×C₄₁	1	1	yes	characteristic, complemented
782	#447	C₂²×C₄₁	1	2	yes	complemented
783	#447	C₂²×C₄₁	1	2	yes	complemented
784	#442	C₂²×C₄₁	1	2	yes	complemented
785	#442	C₂²×C₄₁	1	2	yes	complemented
786	#442	C₂²×C₄₁	1	2	yes	complemented
787	#440	C₂²×C₄₁	1	2	yes	complemented
788	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
789	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
790	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
791	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
792	#433	C₂²×C₄₁	1	2	yes	complemented
793	#433	C₂²×C₄₁	1	2	yes	complemented
794	#432	C₂²×C₄₁	1	1	yes	characteristic, complemented
795	#432	C₂²×C₄₁	1	1	yes	characteristic, complemented
796	#431	C₂²×C₄₁	1	1	yes	characteristic, complemented
797	#431	C₂²×C₄₁	1	1	yes	characteristic, complemented
798	#424	C₂²×C₄₁	1	2	yes	complemented
799	#407	C₂²×C₄₁	1	1	yes	characteristic
800	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
801	#405	C₂²×C₄₁	1	2	yes	complemented
802	C₄₁	#60978	1	1	yes	characteristic, direct product factor, Sylow
803	C₂×#41	—	2	1	no	—
804	C₂×#41	—	2	1	no	—
805	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
806	C₂²×D₄	—	2	1	no	—
807	C₂²×D₄	—	2	1	no	—
808	C₂²×D₄	—	2	1	no	—
809	C₂²×D₄	—	2	1	no	—
810	C₂²×D₄	—	2	1	no	—
811	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
812	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
813	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
814	C₂³×C₄	—	2	1	no	—
815	C₂³×C₄	—	2	1	no	—
816	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
817	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
818	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
819	C₂×D₈	C₂³×C₄₁	1	2	yes	—
820	C₂×D₈	C₂³×C₄₁	1	2	yes	—
821	C₂×D₈	C₂³×C₄₁	1	2	yes	—
822	C₂×D₈	C₂³×C₄₁	1	2	yes	—
823	C₂×D₈	C₂³×C₄₁	1	2	yes	—
824	C₂×D₈	C₂³×C₄₁	1	2	yes	—
825	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
826	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
827	C₄⋊Q₈	—	2	1	no	—
828	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
829	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
830	#127	—	2	1	no	—
831	#127	—	2	1	no	—
832	#127	C₂³×C₄₁	1	2	yes	—
833	#127	C₂³×C₄₁	1	2	yes	—
834	#127	C₂³×C₄₁	1	1	yes	characteristic
835	#127	C₂³×C₄₁	1	1	yes	characteristic
836	#126	—	2	1	no	—
837	#126	—	2	1	no	—
838	#126	—	2	1	no	—
839	#126	—	2	1	no	—
840	#125	—	2	1	no	—
841	#125	—	2	1	no	—
842	#125	—	2	1	no	—
843	#125	C₂³×C₄₁	1	2	yes	—
844	#125	C₂³×C₄₁	1	2	yes	—
845	#125	C₂³×C₄₁	1	1	yes	characteristic
846	#125	C₂³×C₄₁	1	1	yes	characteristic
847	#124	—	2	1	no	—
848	#124	—	2	1	no	—
849	#124	—	2	1	no	—
850	#124	—	2	1	no	—
851	#124	C₂³×C₄₁	1	1	yes	characteristic
852	#124	C₂³×C₄₁	1	1	yes	characteristic
853	#123	—	2	1	no	—
854	#123	—	2	1	no	—
855	#123	—	2	1	no	—
856	#123	—	2	2	no	—
857	#123	—	2	2	no	—
858	#123	—	2	2	no	—
859	#123	—	2	2	no	—
860	#123	—	2	2	no	—
861	#123	—	2	2	no	—
862	#123	—	2	2	no	—
863	#123	—	2	2	no	—
864	#123	—	2	1	no	—
865	#123	—	2	1	no	—
866	#123	—	2	1	no	—
867	#123	—	2	1	no	—
868	#123	—	2	1	no	—
869	#123	—	2	1	no	—
870	C₂²⋊Q₈	—	2	1	no	—
871	C₂²⋊Q₈	—	2	1	no	—
872	C₂²⋊Q₈	—	2	1	no	—
873	C₂²⋊Q₈	—	2	1	no	—
874	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
875	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
876	#121	—	2	1	no	—
877	#121	—	2	1	no	—
878	#121	—	2	1	no	—
879	#121	—	2	1	no	—
880	#121	—	2	1	no	—
881	#121	—	2	1	no	—
882	#121	—	2	1	no	—
883	#121	—	2	1	no	—
884	#121	—	2	1	no	—
885	#121	—	2	1	no	—
886	#121	—	2	2	no	—
887	#121	—	2	2	no	—
888	#121	—	2	2	no	—
889	#121	—	2	2	no	—
890	#121	—	2	2	no	—
891	#121	—	2	2	no	—
892	#121	—	2	2	no	—
893	#121	—	2	2	no	—
894	#121	—	2	1	no	—
895	#121	—	2	1	no	—
896	#121	—	2	1	no	—
897	#121	—	2	1	no	—
898	#121	C₂³×C₄₁	1	1	yes	characteristic
899	#121	C₂³×C₄₁	1	1	yes	characteristic
900	#121	C₂³×C₄₁	1	2	yes	—
901	#121	C₂³×C₄₁	1	2	yes	—
902	#121	C₂³×C₄₁	1	2	yes	—
903	#121	C₂³×C₄₁	1	2	yes	—
904	#121	C₂³×C₄₁	1	1	yes	characteristic
905	#121	C₂³×C₄₁	1	1	yes	characteristic
906	#121	C₂³×C₄₁	1	1	yes	characteristic
907	#121	C₂³×C₄₁	1	1	yes	characteristic
908	#120	—	2	1	no	—
909	#120	—	2	1	no	—
910	#120	—	2	1	no	—
911	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
912	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
913	C₄×D₄	—	2	1	no	—
914	C₄×D₄	—	2	1	no	—
915	C₄×D₄	—	2	1	no	—
916	C₄×D₄	—	2	1	no	—
917	C₄×D₄	—	2	1	no	—
918	C₄×D₄	—	2	1	no	—
919	C₄×D₄	—	2	1	no	—
920	C₄×D₄	—	2	1	no	—
921	C₄×D₄	—	2	1	no	—
922	C₄×D₄	—	2	1	no	—
923	C₄×D₄	—	2	1	no	—
924	C₄×D₄	—	2	1	no	—
925	C₄×D₄	—	2	1	no	—
926	C₄×D₄	—	2	1	no	—
927	C₄×D₄	C₂³×C₄₁	1	2	yes	—
928	C₄×D₄	C₂³×C₄₁	1	2	yes	—
929	C₄×D₄	C₂³×C₄₁	1	2	yes	—
930	C₄×D₄	C₂³×C₄₁	1	2	yes	—
931	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
932	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
933	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
934	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
935	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
936	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
937	#117	—	2	1	no	—
938	#117	—	2	1	no	—
939	#117	—	2	1	no	—
940	#117	D₄×C₄₁	1	1	yes	characteristic
941	#117	D₄×C₄₁	1	1	yes	characteristic
942	#117	D₄×C₄₁	1	1	yes	characteristic
943	#117	D₄×C₄₁	1	1	yes	characteristic
944	#117	C₂³×C₄₁	1	1	yes	characteristic
945	#117	C₂³×C₄₁	1	1	yes	characteristic
946	#117	C₂³×C₄₁	1	1	yes	characteristic
947	#117	C₂³×C₄₁	1	1	yes	characteristic
948	#117	C₂³×C₄₁	1	1	yes	characteristic
949	C₂×C₄⋊C₄	—	2	1	no	—
950	C₂×C₄⋊C₄	—	2	1	no	—
951	C₂×C₄⋊C₄	—	2	1	no	—
952	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
953	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
954	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
955	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
956	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
957	C₂×C₂²⋊C₄	—	2	1	no	—
958	C₂×C₂²⋊C₄	—	2	1	no	—
959	C₂×C₂²⋊C₄	—	2	1	no	—
960	C₂×C₂²⋊C₄	—	2	1	no	—
961	C₂×C₂²⋊C₄	—	2	1	no	—
962	C₂×C₂²⋊C₄	—	2	1	no	—
963	C₂×C₂²⋊C₄	—	2	1	no	—
964	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
965	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
966	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
967	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
968	#107	C₂³×C₄₁	1	2	yes	—
969	#107	C₂³×C₄₁	1	2	yes	—
970	#107	C₂³×C₄₁	1	2	yes	—
971	#107	C₂³×C₄₁	1	2	yes	—
972	#106	C₂³×C₄₁	1	2	yes	—
973	#106	C₂³×C₄₁	1	2	yes	—
974	#106	C₂³×C₄₁	1	2	yes	—
975	#106	C₂³×C₄₁	1	2	yes	—
976	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
977	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
978	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
979	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
980	#103	C₂³×C₄₁	1	2	yes	—
981	#103	C₂³×C₄₁	1	2	yes	—
982	#102	C₂³×C₄₁	1	2	yes	—
983	#102	C₂³×C₄₁	1	2	yes	—
984	#102	C₂³×C₄₁	1	2	yes	—
985	#102	C₂³×C₄₁	1	2	yes	—
986	#102	C₂³×C₄₁	1	2	yes	—
987	#102	C₂³×C₄₁	1	2	yes	—
988	#102	C₂³×C₄₁	1	2	yes	—
989	#102	C₂³×C₄₁	1	2	yes	—
990	#102	C₂³×C₄₁	1	2	yes	—
991	#102	C₂³×C₄₁	1	2	yes	—
992	#102	C₂³×C₄₁	1	2	yes	—
993	#102	C₂³×C₄₁	1	2	yes	—
994	#102	C₂³×C₄₁	1	2	yes	—
995	#102	C₂³×C₄₁	1	2	yes	—
996	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
997	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
998	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
999	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
1000	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
1001	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
1002	#97	C₂³×C₄₁	1	2	yes	—
1003	#97	C₂³×C₄₁	1	2	yes	—
1004	C₄×C₈	C₂³×C₄₁	1	2	yes	—
1005	C₄×C₈	C₂³×C₄₁	1	2	yes	—
1006	C₂⁴	—	2	1	no	—
1007	C₂⁴	—	2	1	no	—
1008	C₂⁴	—	2	1	no	—
1009	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
1010	#41	—	4	2	no	—
1011	#41	—	8	2	no	—
1012	#41	—	8	2	no	—
1013	C₂×Q₈	—	2	1	no	—
1014	C₂×Q₈	—	2	1	no	—
1015	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
1016	C₂×D₄	—	2	1	no	—
1017	C₂×D₄	—	2	1	no	—
1018	C₂×D₄	—	2	1	no	—
1019	C₂×D₄	—	2	1	no	—
1020	C₂×D₄	—	2	1	no	—
1021	C₂×D₄	—	2	2	no	—
1022	C₂×D₄	—	2	2	no	—
1023	C₂×D₄	—	2	2	no	—
1024	C₂×D₄	—	2	2	no	—
1025	C₂×D₄	—	2	1	no	—
1026	C₂×D₄	—	2	1	no	—
1027	C₂×D₄	—	2	1	no	—
1028	C₂×D₄	—	2	1	no	—
1029	C₂×D₄	—	2	1	no	—
1030	C₂×D₄	—	2	1	no	—
1031	C₂×D₄	—	2	1	no	—
1032	C₂×D₄	—	2	1	no	—
1033	C₂×D₄	—	2	1	no	—
1034	C₂×D₄	—	2	2	no	—
1035	C₂×D₄	—	2	2	no	—
1036	C₂×D₄	—	2	2	no	—
1037	C₂×D₄	—	2	2	no	—
1038	C₂×D₄	—	4	2	no	—
1039	C₂×D₄	—	4	2	no	—
1040	C₂×D₄	—	4	2	no	—
1041	C₂×D₄	—	8	2	no	—
1042	C₂×D₄	—	8	2	no	—
1043	C₂×D₄	—	8	2	no	—
1044	C₂×D₄	—	8	2	no	—
1045	C₂×D₄	—	8	2	no	—
1046	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
1047	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
1048	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
1049	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
1050	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
1051	C₂²×C₄	—	2	1	no	—
1052	C₂²×C₄	—	2	1	no	—
1053	C₂²×C₄	—	2	1	no	—
1054	C₂²×C₄	—	2	1	no	—
1055	C₂²×C₄	—	2	1	no	—
1056	C₂²×C₄	—	2	1	no	—
1057	C₂²×C₄	—	2	1	no	—
1058	C₂²×C₄	—	2	1	no	—
1059	C₂²×C₄	—	2	1	no	—
1060	C₂²×C₄	—	2	1	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	—	4	2	no	—
1066	C₂²×C₄	—	8	2	no	—
1067	C₂²×C₄	—	8	2	no	—
1068	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1069	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1070	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1071	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1072	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1073	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1074	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1075	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1076	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1077	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1078	SD₁₆	—	4	2	no	—
1079	SD₁₆	—	4	2	no	—
1080	D₈	—	4	2	no	—
1081	D₈	—	4	2	no	—
1082	D₈	—	4	2	no	—
1083	D₈	—	4	2	no	—
1084	D₈	—	4	2	no	—
1085	D₈	—	4	2	no	—
1086	M₁₆	—	4	2	no	—
1087	C₂×C₈	—	4	2	no	—
1088	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1089	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1090	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1091	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1092	C₄⋊C₄	—	2	1	no	—
1093	C₄⋊C₄	—	2	1	no	—
1094	C₄⋊C₄	—	2	1	no	—
1095	C₄⋊C₄	—	2	2	no	—
1096	C₄⋊C₄	—	2	2	no	—
1097	C₄⋊C₄	—	2	2	no	—
1098	C₄⋊C₄	—	2	2	no	—
1099	C₄⋊C₄	—	2	1	no	—
1100	C₄⋊C₄	—	2	1	no	—
1101	C₄⋊C₄	—	2	1	no	—
1102	C₄⋊C₄	—	2	1	no	—
1103	C₄⋊C₄	—	2	1	no	—
1104	C₄⋊C₄	—	2	1	no	—
1105	C₄⋊C₄	—	2	1	no	—
1106	C₄⋊C₄	—	2	1	no	—
1107	C₄⋊C₄	—	2	1	no	—
1108	C₄⋊C₄	—	2	1	no	—
1109	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1110	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1111	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1112	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1113	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1114	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1115	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1116	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1117	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1118	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1119	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1120	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1121	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
1122	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
1123	C₂²⋊C₄	—	2	1	no	—
1124	C₂²⋊C₄	—	2	1	no	—
1125	C₂²⋊C₄	—	2	1	no	—
1126	C₂²⋊C₄	—	2	1	no	—
1127	C₂²⋊C₄	—	2	1	no	—
1128	C₂²⋊C₄	—	2	2	no	—
1129	C₂²⋊C₄	—	2	2	no	—
1130	C₂²⋊C₄	—	2	2	no	—
1131	C₂²⋊C₄	—	2	2	no	—
1132	C₂²⋊C₄	—	2	1	no	—
1133	C₂²⋊C₄	—	2	1	no	—
1134	C₂²⋊C₄	—	2	1	no	—
1135	C₂²⋊C₄	—	2	1	no	—
1136	C₂²⋊C₄	—	2	1	no	—
1137	C₂²⋊C₄	—	2	1	no	—
1138	C₂²⋊C₄	—	2	2	no	—
1139	C₂²⋊C₄	—	2	2	no	—
1140	C₂²⋊C₄	—	2	2	no	—
1141	C₂²⋊C₄	—	2	2	no	—
1142	C₂²⋊C₄	—	2	1	no	—
1143	C₂²⋊C₄	—	2	1	no	—
1144	C₂²⋊C₄	—	2	1	no	—
1145	C₂²⋊C₄	—	2	1	no	—
1146	C₂²⋊C₄	—	2	1	no	—
1147	C₂²⋊C₄	—	2	1	no	—
1148	C₂²⋊C₄	—	2	1	no	—
1149	C₂²⋊C₄	—	2	1	no	—
1150	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1151	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1152	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1153	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1154	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1155	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1156	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1157	C₂²⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1158	C₄²	—	2	1	no	—
1159	C₄²	—	2	1	no	—
1160	C₄²	—	2	1	no	—
1161	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1162	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1163	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1164	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1165	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1166	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1167	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1168	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1169	C₂³	—	2	2	no	—
1170	C₂³	—	2	1	no	—
1171	C₂³	—	2	1	no	—
1172	C₂³	—	2	1	no	—
1173	C₂³	—	2	2	no	—
1174	C₂³	—	2	2	no	—
1175	C₂³	—	4	1	no	—
1176	C₂³	—	4	1	no	—
1177	C₂³	—	4	2	no	—
1178	C₂³	—	4	2	no	—
1179	C₂³	—	4	2	no	—
1180	C₂³	—	4	2	no	—
1181	C₂³	—	4	2	no	—
1182	C₂³	—	4	2	no	—
1183	C₂³	—	4	2	no	—
1184	C₂³	—	8	1	no	—
1185	C₂³	—	8	1	no	—
1186	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1187	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1188	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1189	Q₈	—	2	2	no	—
1190	Q₈	—	8	1	no	—
1191	Q₈	—	8	1	no	—
1192	D₄	—	2	2	no	—
1193	D₄	—	2	2	no	—
1194	D₄	—	2	2	no	—
1195	D₄	—	2	2	no	—
1196	D₄	—	2	2	no	—
1197	D₄	—	2	2	no	—
1198	D₄	—	2	2	no	—
1199	D₄	—	4	2	no	—
1200	D₄	—	4	2	no	—
1201	D₄	—	4	2	no	—
1202	D₄	—	4	2	no	—
1203	D₄	—	4	2	no	—
1204	D₄	—	4	2	no	—
1205	D₄	—	4	2	no	—
1206	D₄	—	8	2	no	—
1207	D₄	—	8	2	no	—
1208	D₄	—	8	2	no	—
1209	D₄	—	8	2	no	—
1210	D₄	—	8	1	no	—
1211	D₄	—	8	1	no	—
1212	D₄	—	8	1	no	—
1213	D₄	—	8	1	no	—
1214	D₄	—	8	2	no	—
1215	D₄	—	8	2	no	—
1216	D₄	—	8	1	no	—
1217	D₄	—	8	1	no	—
1218	D₄	—	8	2	no	—
1219	D₄	—	8	2	no	—
1220	D₄	—	8	1	no	—
1221	C₂×C₄	—	2	2	no	—
1222	C₂×C₄	—	2	2	no	—
1223	C₂×C₄	—	2	2	no	—
1224	C₂×C₄	—	2	2	no	—
1225	C₂×C₄	—	2	2	no	—
1226	C₂×C₄	—	2	1	no	—
1227	C₂×C₄	—	2	1	no	—
1228	C₂×C₄	—	2	1	no	—
1229	C₂×C₄	—	2	1	no	—
1230	C₂×C₄	—	2	1	no	—
1231	C₂×C₄	—	2	2	no	—
1232	C₂×C₄	—	2	2	no	—
1233	C₂×C₄	—	4	1	no	—
1234	C₂×C₄	—	4	1	no	—
1235	C₂×C₄	—	4	1	no	—
1236	C₂×C₄	—	4	1	no	—
1237	C₂×C₄	—	4	1	no	—
1238	C₂×C₄	—	4	2	no	—
1239	C₂×C₄	—	4	2	no	—
1240	C₂×C₄	—	4	2	no	—
1241	C₂×C₄	—	8	2	no	—
1242	C₂×C₄	—	8	2	no	—
1243	C₂×C₄	—	8	2	no	—
1244	C₂×C₄	—	8	2	no	—
1245	C₂×C₄	—	8	1	no	—
1246	C₂×C₄	—	8	1	no	—
1247	C₂×C₄	—	8	1	no	—
1248	C₂×C₄	—	8	1	no	—
1249	C₂×C₄	—	8	1	no	—
1250	C₂×C₄	—	8	1	no	—
1251	C₂×C₄	—	8	1	no	—
1252	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1253	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1254	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1255	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1256	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1257	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1258	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1259	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1260	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1261	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1262	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1263	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
1264	C₈	—	2	2	no	—
1265	C₈	—	2	2	no	—
1266	C₈	—	2	2	no	—
1267	C₈	—	2	2	no	—
1268	C₂²	—	2	1	no	—
1269	C₂²	—	2	1	no	—
1270	C₂²	—	2	1	no	—
1271	C₂²	—	2	1	no	—
1272	C₂²	—	2	1	no	—
1273	C₂²	—	2	1	no	—
1274	C₂²	—	2	1	no	—
1275	C₂²	—	2	1	no	—
1276	C₂²	—	4	1	no	—
1277	C₂²	—	4	2	no	—
1278	C₂²	—	4	1	no	—
1279	C₂²	—	4	1	no	—
1280	C₂²	—	4	2	no	—
1281	C₂²	—	4	2	no	—
1282	C₂²	—	4	1	no	—
1283	C₂²	—	4	1	no	—
1284	C₂²	—	4	2	no	—
1285	C₂²	—	4	1	no	—
1286	C₂²	—	4	1	no	—
1287	C₂²	—	4	2	no	—
1288	C₂²	—	4	2	no	—
1289	C₂²	—	4	1	no	—
1290	C₂²	—	4	1	no	—
1291	C₂²	—	8	2	no	—
1292	C₂²	—	8	4	no	—
1293	C₂²	—	8	4	no	—
1294	C₂²	—	16	2	no	—
1295	C₂²	C₄₁×#576	1	2	yes	—
1296	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
1297	C₄	—	2	1	no	—
1298	C₄	—	2	1	no	—
1299	C₄	—	2	1	no	—
1300	C₄	—	2	1	no	—
1301	C₄	—	2	1	no	—
1302	C₄	—	2	1	no	—
1303	C₄	—	2	1	no	—
1304	C₄	—	2	1	no	—
1305	C₄	—	2	1	no	—
1306	C₄	—	2	1	no	—
1307	C₄	—	2	1	no	—
1308	C₄	—	4	2	no	—
1309	C₄	—	4	1	no	—
1310	C₄	—	4	1	no	—
1311	C₄	—	4	1	no	—
1312	C₄	—	4	2	no	—
1313	C₄	—	4	1	no	—
1314	C₄	—	4	1	no	—
1315	C₄	C₄₁×#585	1	2	yes	—
1316	C₂	—	2	2	no	—
1317	C₂	—	4	1	no	—
1318	C₂	—	4	1	no	—
1319	C₂	—	8	2	no	—
1320	C₂	—	8	2	no	—
1321	C₂	—	8	1	no	—
1322	C₂	—	8	1	no	—
1323	C₂	—	8	1	no	—
1324	C₂	C₄₁×#3449	1	1	yes	characteristic
1325	C₂	C₂×C₄₁×#576	1	1	yes	characteristic
1326	C₂	C₄₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×#117×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3494	C₂	semidirect
2. C₂×C₄₁×#540	C₂	semidirect
3. C₄₁×#3259	C₂	semidirect
4. C₄₁×#3257	C₂	semidirect
5. C₄₁×#3241	C₂	semidirect
6. C₄₁×#3234	C₂	semidirect
7. C₄₁×#3232	C₂	semidirect
8. C₄₁×#3220	C₂	semidirect
9. C₄₁×#3217	C₂	semidirect
10. C₄₁×#3205	C₂	semidirect
11. C₄₁×#3194	C₂	semidirect
12. C₄₁×#3192	C₂	semidirect
13. C₄₁×#3188	C₂	semidirect
14. C₄₁×#3186	C₂	semidirect
15. C₄₁×#3179	C₂	semidirect
16. C₄₁×#3176	C₂	semidirect
17. C₄₁×#3122	C₂	semidirect
18. C₄₁×#3119	C₂	semidirect
19. C₄₁×#3114	C₂	semidirect
20. C₄₁×#3109	C₂	semidirect
21. C₄₁×#3105	C₂	semidirect
22. C₄₁×#3100	C₂	semidirect
23. C₄₁×#2924	C₂	semidirect
32. C₄₁×#544	C₂²	semidirect
33. C₄₁×#542	C₂²	semidirect
34. C₄₁×#542	C₂²	semidirect
41. C₄₁×#540	C₂²	semidirect
42. C₄₁×#540	C₂²	semidirect
43. C₄₁×#540	C₂²	semidirect
44. C₄₁×#540	C₂²	semidirect
45. C₄₁×#535	C₂²	semidirect
48. C₂×#127×C₄₁	C₂²	semidirect
51. C₂×#125×C₄₁	C₂²	semidirect
60. C₄₁×#520	C₂²	semidirect
61. C₄₁×#518	C₂²	semidirect
62. C₂×C₄×D₄×C₄₁	C₂²	semidirect
63. C₂×C₄×D₄×C₄₁	C₂²	semidirect
65. C₄₁×#501	C₂²	semidirect
66. C₄₁×#499	C₂²	semidirect
67. C₄₁×#496	C₂²	semidirect
68. C₄₁×#493	C₂²	semidirect
69. C₄₁×#490	C₂²	semidirect
70. C₄₁×#490	C₂²	semidirect
71. C₄₁×#488	C₂²	semidirect
72. C₄₁×#486	C₂²	semidirect
73. C₄₁×#484	C₂²	semidirect
74. C₄₁×#483	C₂²	semidirect
75. C₄₁×#482	C₂²	semidirect
76. C₄₁×#482	C₂²	semidirect
79. C₄₁×#481	C₂²	semidirect
80. C₄₁×#481	C₂²	semidirect
83. C₄₁×#480	C₂²	semidirect
84. C₄₁×#480	C₂²	semidirect
85. C₄₁×#479	C₂²	semidirect
86. C₄₁×#478	C₂²	semidirect
87. C₄₁×#478	C₂²	semidirect
88. C₄₁×#478	C₂²	semidirect
89. C₄₁×#478	C₂²	semidirect
90. C₄₁×#478	C₂²	semidirect
91. C₄₁×#476	C₂²	semidirect
92. C₄₁×#474	C₂²	semidirect
93. C₄₁×#469	C₂²	semidirect
94. C₄₁×#469	C₂²	semidirect
95. C₄₁×#469	C₂²	semidirect
96. C₄₁×#468	C₂²	semidirect
97. C₄₁×#466	C₂²	semidirect
98. C₄₁×#466	C₂²	semidirect
99. C₄₁×#466	C₂²	semidirect
100. C₄₁×#465	C₂²	semidirect
101. C₄₁×#463	C₂²	semidirect
102. C₄₁×#463	C₂²	semidirect
103. C₄₁×#460	C₂²	semidirect
104. C₄₁×#459	C₂²	semidirect
105. C₄₁×#459	C₂²	semidirect
106. C₄₁×#459	C₂²	semidirect
107. C₄₁×#459	C₂²	semidirect
108. C₄₁×#459	C₂²	semidirect
109. C₄₁×#450	C₂²	semidirect
110. C₄₁×#450	C₂²	semidirect
111. C₄₁×#449	C₂²	semidirect
112. C₄₁×#449	C₂²	semidirect
117. C₄₁×#447	C₂²	semidirect
118. C₄₁×#447	C₂²	semidirect
119. C₄₁×#447	C₂²	semidirect
120. C₄₁×#447	C₂²	semidirect
121. C₄₁×#442	C₂²	semidirect
122. C₄₁×#442	C₂²	semidirect
123. C₄₁×#442	C₂²	semidirect
124. C₄₁×#440	C₂²	semidirect
125. C₄×SD₁₆×C₄₁	C₂²	semidirect
126. C₄×D₈×C₄₁	C₂²	semidirect
127. C₄×D₈×C₄₁	C₂²	semidirect
128. C₄×D₈×C₄₁	C₂²	semidirect
129. C₄₁×#433	C₂²	semidirect
130. C₄₁×#433	C₂²	semidirect
131. C₄₁×#432	C₂²	semidirect
132. C₄₁×#432	C₂²	semidirect
133. C₄₁×#431	C₂²	semidirect
134. C₄₁×#431	C₂²	semidirect
135. C₄₁×#424	C₂²	semidirect
138. C₄₁×#405	C₂²	semidirect
604. #60978	C₄₁	direct (N × H)
653. #3494	C₂×C₄₁	semidirect
654. C₂×#540	C₂×C₄₁	semidirect
655. #3259	C₂×C₄₁	semidirect
656. #3257	C₂×C₄₁	semidirect
657. #3241	C₂×C₄₁	semidirect
658. #3234	C₂×C₄₁	semidirect
659. #3232	C₂×C₄₁	semidirect
660. #3220	C₂×C₄₁	semidirect
661. #3217	C₂×C₄₁	semidirect
662. #3205	C₂×C₄₁	semidirect
663. #3194	C₂×C₄₁	semidirect
664. #3192	C₂×C₄₁	semidirect
665. #3188	C₂×C₄₁	semidirect
666. #3186	C₂×C₄₁	semidirect
667. #3179	C₂×C₄₁	semidirect
668. #3176	C₂×C₄₁	semidirect
669. #3122	C₂×C₄₁	semidirect
670. #3119	C₂×C₄₁	semidirect
671. #3114	C₂×C₄₁	semidirect
672. #3109	C₂×C₄₁	semidirect
673. #3105	C₂×C₄₁	semidirect
674. #3100	C₂×C₄₁	semidirect
675. #2924	C₂×C₄₁	semidirect
695. #544	C₂²×C₄₁	semidirect
696. #542	C₂²×C₄₁	semidirect
697. #542	C₂²×C₄₁	semidirect
704. #540	C₂²×C₄₁	semidirect
705. #540	C₂²×C₄₁	semidirect
706. #540	C₂²×C₄₁	semidirect
707. #540	C₂²×C₄₁	semidirect
708. #535	C₂²×C₄₁	semidirect
711. C₂×#127	C₂²×C₄₁	semidirect
714. C₂×#125	C₂²×C₄₁	semidirect
723. #520	C₂²×C₄₁	semidirect
724. #518	C₂²×C₄₁	semidirect
725. C₂×C₄×D₄	C₂²×C₄₁	semidirect
726. C₂×C₄×D₄	C₂²×C₄₁	semidirect
728. #501	C₂²×C₄₁	semidirect
729. #499	C₂²×C₄₁	semidirect
730. #496	C₂²×C₄₁	semidirect
731. #493	C₂²×C₄₁	semidirect
732. #490	C₂²×C₄₁	semidirect
733. #490	C₂²×C₄₁	semidirect
734. #488	C₂²×C₄₁	semidirect
735. #486	C₂²×C₄₁	semidirect
736. #484	C₂²×C₄₁	semidirect
737. #483	C₂²×C₄₁	semidirect
738. #482	C₂²×C₄₁	semidirect
739. #482	C₂²×C₄₁	semidirect
742. #481	C₂²×C₄₁	semidirect
743. #481	C₂²×C₄₁	semidirect
746. #480	C₂²×C₄₁	semidirect
747. #480	C₂²×C₄₁	semidirect
748. #479	C₂²×C₄₁	semidirect
749. #478	C₂²×C₄₁	semidirect
750. #478	C₂²×C₄₁	semidirect
751. #478	C₂²×C₄₁	semidirect
752. #478	C₂²×C₄₁	semidirect
753. #478	C₂²×C₄₁	semidirect
754. #476	C₂²×C₄₁	semidirect
755. #474	C₂²×C₄₁	semidirect
756. #469	C₂²×C₄₁	semidirect
757. #469	C₂²×C₄₁	semidirect
758. #469	C₂²×C₄₁	semidirect
759. #468	C₂²×C₄₁	semidirect
760. #466	C₂²×C₄₁	semidirect
761. #466	C₂²×C₄₁	semidirect
762. #466	C₂²×C₄₁	semidirect
763. #465	C₂²×C₄₁	semidirect
764. #463	C₂²×C₄₁	semidirect
765. #463	C₂²×C₄₁	semidirect
766. #460	C₂²×C₄₁	semidirect
767. #459	C₂²×C₄₁	semidirect
768. #459	C₂²×C₄₁	semidirect
769. #459	C₂²×C₄₁	semidirect
770. #459	C₂²×C₄₁	semidirect
771. #459	C₂²×C₄₁	semidirect
772. #450	C₂²×C₄₁	semidirect
773. #450	C₂²×C₄₁	semidirect
774. #449	C₂²×C₄₁	semidirect
775. #449	C₂²×C₄₁	semidirect
780. #447	C₂²×C₄₁	semidirect
781. #447	C₂²×C₄₁	semidirect
782. #447	C₂²×C₄₁	semidirect
783. #447	C₂²×C₄₁	semidirect
784. #442	C₂²×C₄₁	semidirect
785. #442	C₂²×C₄₁	semidirect
786. #442	C₂²×C₄₁	semidirect
787. #440	C₂²×C₄₁	semidirect
788. C₄×SD₁₆	C₂²×C₄₁	semidirect
789. C₄×D₈	C₂²×C₄₁	semidirect
790. C₄×D₈	C₂²×C₄₁	semidirect
791. C₄×D₈	C₂²×C₄₁	semidirect
792. #433	C₂²×C₄₁	semidirect
793. #433	C₂²×C₄₁	semidirect
794. #432	C₂²×C₄₁	semidirect
795. #432	C₂²×C₄₁	semidirect
796. #431	C₂²×C₄₁	semidirect
797. #431	C₂²×C₄₁	semidirect
798. #424	C₂²×C₄₁	semidirect
801. #405	C₂²×C₄₁	semidirect
802. C₄₁	#60978	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×#3494	2
C₂×C₄₁×#540	2
C₄₁×#3259	2
C₄₁×#3257	2
C₄₁×#3241	2
C₄₁×#3234	2
C₄₁×#3232	2
C₄₁×#3220	2
C₄₁×#3217	2
C₄₁×#3205	2
C₄₁×#3194	2
C₄₁×#3192	2
C₄₁×#3188	2
C₄₁×#3186	2
C₄₁×#3179	2
C₄₁×#3176	2
C₄₁×#3122	2
C₄₁×#3119	2
C₄₁×#3114	2
C₄₁×#3109	2
C₄₁×#3105	2
C₄₁×#3100	2
C₄₁×#2924	2
#60978	41

Subgroups — C41×#60978 #23837179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#60978 #23837179