Subgroups — C₄₁×#61202 #23837403

Order 10496.

2068 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3332	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3328	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3321	C₂	1	4	yes	maximal, complemented
6	C₄₁×#3316	C₂	1	4	yes	maximal, complemented
7	C₄₁×#3304	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3298	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#3099	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₁×#475	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3060	C₂	1	2	yes	maximal, complemented
13	C₄₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3013	C₂	1	2	yes	maximal, complemented
15	C₄×#137×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#2935	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#2898	C₂	1	2	yes	maximal, complemented
18	C₂×2₋¹⁺⁴×C₄₁	C₂²	1	2	yes	—
19	C₂×#137×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#135×C₄₁	C₂²	1	2	yes	—
21	C₂×#131×C₄₁	C₂²	1	2	yes	—
22	C₄₁×#556	C₂²	1	2	yes	—
23	C₄₁×#555	C₂²	1	2	yes	—
24	C₄₁×#554	C₂²	1	2	yes	—
25	C₄₁×#553	—	2	2	no	—
26	C₄₁×#550	—	2	1	no	—
27	C₄₁×#550	C₂²	1	2	yes	—
28	D₄×Q₈×C₄₁	—	2	1	no	—
29	D₄×Q₈×C₄₁	C₂²	1	2	yes	—
30	C₄₁×#548	—	2	2	no	—
31	C₄₁×#548	—	2	2	no	—
32	C₄₁×#548	C₂²	1	4	yes	—
33	C₄₁×#547	C₂²	1	2	yes	—
34	C₄₁×#542	—	2	2	no	—
35	C₄₁×#537	—	2	2	no	—
36	C₄₁×#537	C₂²	1	2	yes	—
37	C₄₁×#537	C₂²	1	2	yes	—
38	C₄₁×#533	—	2	1	no	—
39	C₄₁×#532	—	2	1	no	—
40	C₄₁×#532	—	2	2	no	—
41	C₄₁×#532	C₂²	1	1	yes	characteristic
42	C₄₁×#532	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
44	C₄₁×#520	C₂²	1	2	yes	—
45	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
47	C₄₁×#489	C₂²	1	4	yes	—
48	C₄₁×#487	C₂²	1	2	yes	—
49	C₄₁×#486	C₂²	1	2	yes	—
50	C₄₁×#485	C₂²	1	4	yes	—
51	C₄₁×#483	C₂²	1	4	yes	—
52	C₄₁×#482	C₂²	1	4	yes	—
53	C₄₁×#481	C₂²	1	4	yes	—
54	C₄₁×#475	C₂²	1	2	yes	—
55	C₄₁×#475	C₂²	1	4	yes	—
56	C₄₁×#475	C₂²	1	2	yes	—
57	C₄₁×#470	C₂²	1	4	yes	—
58	C₄₁×#469	C₂²	1	4	yes	—
59	C₄₁×#465	C₂²	1	4	yes	—
60	C₄₁×#465	C₂²	1	4	yes	—
61	C₄₁×#464	C₂²	1	2	yes	—
62	C₄₁×#463	C₂²	1	2	yes	—
63	C₄₁×#462	C₂²	1	1	yes	characteristic
64	C₄₁×#461	C₂²	1	1	yes	characteristic
65	C₄₁×#460	C₂²	1	1	yes	characteristic
66	C₄₁×#459	C₂²	1	1	yes	characteristic
67	C₄₁×#452	C₂²	1	4	yes	—
68	C₄₁×#451	C₂²	1	4	yes	—
69	C₄₁×#449	C₂²	1	4	yes	—
70	C₄₁×#448	C₂²	1	4	yes	—
71	C₄₁×#441	C₂²	1	2	yes	—
72	C₄₁×#440	C₂²	1	2	yes	—
73	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	—
74	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
75	C₄₁×#436	C₂²	1	2	yes	—
76	C₄₁×#435	C₂²	1	4	yes	—
77	C₈×D₄×C₄₁	C₂²	1	2	yes	—
78	C₄₁×#428	C₂²	1	1	yes	characteristic
79	C₂×#106×C₄₁	C₂²	1	2	yes	—
80	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
81	C₄₁×#419	C₂²	1	4	yes	—
82	C₄₁×#419	C₂²	1	1	yes	characteristic
83	C₄₁×#417	C₂²	1	1	yes	characteristic
84	C₄₁×#417	C₂²	1	2	yes	—
85	C₄₁×#417	C₂²	1	4	yes	—
86	C₄₁×#417	C₂²	1	2	yes	—
87	C₄₁×#416	C₂²	1	4	yes	—
88	C₄₁×#416	C₂²	1	2	yes	—
89	C₂×#103×C₄₁	C₂²	1	4	yes	—
90	C₂×#103×C₄₁	C₂²	1	2	yes	—
91	C₄₁×#408	C₂²	1	2	yes	—
92	C₄×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
93	2₋¹⁺⁴×C₄₁	—	2	8	no	—
94	2₋¹⁺⁴×C₄₁	—	4	4	no	—
95	C₂×#41×C₄₁	—	2	4	no	—
96	C₂×#41×C₄₁	—	2	2	no	—
97	C₂×#41×C₄₁	—	2	2	no	—
98	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
99	C₂×#41×C₄₁	C₂³	1	2	yes	—
100	C₂×#41×C₄₁	C₂³	1	4	yes	—
101	C₂×#41×C₄₁	C₂³	1	2	yes	—
102	C₂²×Q₈×C₄₁	—	2	2	no	—
103	C₂²×Q₈×C₄₁	—	2	1	no	—
104	C₂²×Q₈×C₄₁	C₂³	1	4	yes	—
105	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
106	#137×C₄₁	—	2	4	no	—
107	#135×C₄₁	—	4	4	no	—
108	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
109	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
110	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
111	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
112	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
113	C₂×D₈×C₄₁	C₂³	1	2	yes	—
114	#131×C₄₁	—	4	4	no	—
115	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
116	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
117	C₂×M₁₆×C₄₁	C₂³	1	4	yes	—
118	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
119	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
120	C₄⋊Q₈×C₄₁	—	2	2	no	—
121	C₄⋊Q₈×C₄₁	—	2	1	no	—
122	C₄⋊Q₈×C₄₁	—	2	1	no	—
123	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
124	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
125	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
126	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
127	#127×C₄₁	—	2	2	no	—
128	#127×C₄₁	D₄	1	1	yes	characteristic
129	#127×C₄₁	C₂³	1	1	yes	characteristic
130	#126×C₄₁	—	2	4	no	—
131	#125×C₄₁	—	2	2	no	—
132	#124×C₄₁	—	2	2	no	—
133	#124×C₄₁	—	2	4	no	—
134	#124×C₄₁	—	2	4	no	—
135	#124×C₄₁	D₄	1	2	yes	—
136	#124×C₄₁	C₂³	1	2	yes	—
137	#123×C₄₁	—	2	4	no	—
138	C₂²⋊Q₈×C₄₁	—	2	2	no	—
139	C₂²⋊Q₈×C₄₁	—	2	2	no	—
140	C₂²⋊Q₈×C₄₁	—	2	2	no	—
141	C₂²⋊Q₈×C₄₁	—	2	4	no	—
142	C₂²⋊Q₈×C₄₁	—	2	4	no	—
143	C₂²⋊Q₈×C₄₁	—	2	4	no	—
144	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
145	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
146	#121×C₄₁	—	2	4	no	—
147	#121×C₄₁	—	2	2	no	—
148	#121×C₄₁	—	2	2	no	—
149	#121×C₄₁	—	2	4	no	—
150	#121×C₄₁	—	2	2	no	—
151	#121×C₄₁	—	2	4	no	—
152	#121×C₄₁	—	2	1	no	—
153	#121×C₄₁	—	2	1	no	—
154	#121×C₄₁	—	2	4	no	—
155	#121×C₄₁	D₄	1	2	yes	—
156	#121×C₄₁	D₄	1	2	yes	—
157	#121×C₄₁	C₂³	1	4	yes	—
158	#121×C₄₁	C₂³	1	4	yes	—
159	C₄×Q₈×C₄₁	—	2	2	no	—
160	C₄×Q₈×C₄₁	—	2	2	no	—
161	C₄×Q₈×C₄₁	—	2	1	no	—
162	C₄×Q₈×C₄₁	—	2	1	no	—
163	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
164	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
165	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₄₁	—	2	2	no	—
168	C₄×D₄×C₄₁	—	2	4	no	—
169	C₄×D₄×C₄₁	—	2	2	no	—
170	C₄×D₄×C₄₁	—	2	2	no	—
171	C₄×D₄×C₄₁	—	2	1	no	—
172	C₄×D₄×C₄₁	—	2	1	no	—
173	C₄×D₄×C₄₁	—	2	2	no	—
174	C₄×D₄×C₄₁	—	2	4	no	—
175	C₄×D₄×C₄₁	—	2	1	no	—
176	C₄×D₄×C₄₁	—	2	1	no	—
177	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₄₁	C₂³	1	2	yes	—
180	C₄×D₄×C₄₁	C₂³	1	2	yes	—
181	#117×C₄₁	—	2	2	no	—
182	#117×C₄₁	—	2	1	no	—
183	#117×C₄₁	C₂³	1	1	yes	characteristic
184	#117×C₄₁	C₂³	1	4	yes	—
185	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
186	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
187	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
190	C₂×C₄²×C₄₁	—	2	1	no	—
191	C₂×C₄²×C₄₁	—	2	1	no	—
192	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
193	#107×C₄₁	C₂³	1	2	yes	—
194	#106×C₄₁	C₂³	1	4	yes	—
195	#106×C₄₁	C₂³	1	4	yes	—
196	#106×C₄₁	C₂³	1	2	yes	—
197	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
198	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
199	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
200	#103×C₄₁	C₂³	1	4	yes	—
201	#103×C₄₁	C₂³	1	2	yes	—
202	#103×C₄₁	C₂³	1	2	yes	—
203	#103×C₄₁	C₂³	1	4	yes	—
204	#103×C₄₁	C₂³	1	4	yes	—
205	#103×C₄₁	C₂³	1	2	yes	—
206	#103×C₄₁	C₂³	1	2	yes	—
207	#103×C₄₁	C₂³	1	2	yes	—
208	#103×C₄₁	C₂³	1	4	yes	—
209	#102×C₄₁	C₂³	1	2	yes	—
210	#102×C₄₁	C₂³	1	2	yes	—
211	#102×C₄₁	C₂³	1	4	yes	—
212	#102×C₄₁	C₂³	1	2	yes	—
213	#102×C₄₁	C₂³	1	4	yes	—
214	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
215	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
216	#97×C₄₁	C₂³	1	2	yes	—
217	C₄×C₈×C₄₁	C₂³	1	2	yes	—
218	#41×C₄₁	—	2	4	no	—
219	#41×C₄₁	—	2	4	no	—
220	#41×C₄₁	—	2	8	no	—
221	#41×C₄₁	—	2	2	no	—
222	#41×C₄₁	—	2	4	no	—
223	#41×C₄₁	—	2	2	no	—
224	#41×C₄₁	—	2	4	no	—
225	#41×C₄₁	—	4	4	no	—
226	#41×C₄₁	—	4	16	no	—
227	#41×C₄₁	—	4	8	no	—
228	#41×C₄₁	—	8	4	no	—
229	C₂×Q₈×C₄₁	—	2	1	no	—
230	C₂×Q₈×C₄₁	—	2	2	no	—
231	C₂×Q₈×C₄₁	—	2	4	no	—
232	C₂×Q₈×C₄₁	—	2	2	no	—
233	C₂×Q₈×C₄₁	—	2	2	no	—
234	C₂×Q₈×C₄₁	—	2	8	no	—
235	C₂×Q₈×C₄₁	—	4	4	no	—
236	C₂×Q₈×C₄₁	—	4	8	no	—
237	C₂×Q₈×C₄₁	—	8	2	no	—
238	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
239	C₂×Q₈×C₄₁	#41	1	4	yes	complemented
240	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
242	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
243	C₂×D₄×C₄₁	—	2	1	no	—
244	C₂×D₄×C₄₁	—	2	2	no	—
245	C₂×D₄×C₄₁	—	2	4	no	—
246	C₂×D₄×C₄₁	—	2	4	no	—
247	C₂×D₄×C₄₁	—	2	4	no	—
248	C₂×D₄×C₄₁	—	2	1	no	—
249	C₂×D₄×C₄₁	—	2	1	no	—
250	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
251	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
252	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
253	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
254	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
255	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₄₁	—	2	1	no	—
257	C₂²×C₄×C₄₁	—	2	4	no	—
258	C₂²×C₄×C₄₁	—	2	1	no	—
259	C₂²×C₄×C₄₁	—	2	2	no	—
260	C₂²×C₄×C₄₁	—	2	4	no	—
261	C₂²×C₄×C₄₁	—	2	1	no	—
262	C₂²×C₄×C₄₁	—	2	1	no	—
263	C₂²×C₄×C₄₁	—	2	1	no	—
264	C₂²×C₄×C₄₁	—	2	4	no	—
265	C₂²×C₄×C₄₁	—	2	2	no	—
266	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
269	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
270	Q₁₆×C₄₁	—	2	4	no	—
271	Q₁₆×C₄₁	—	4	2	no	—
272	SD₁₆×C₄₁	—	2	4	no	—
273	SD₁₆×C₄₁	—	4	2	no	—
274	SD₁₆×C₄₁	—	4	2	no	—
275	D₈×C₄₁	—	4	2	no	—
276	M₁₆×C₄₁	—	2	2	no	—
277	M₁₆×C₄₁	—	2	2	no	—
278	M₁₆×C₄₁	—	4	4	no	—
279	C₂×C₈×C₄₁	—	2	4	no	—
280	C₂×C₈×C₄₁	—	4	4	no	—
281	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
282	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
283	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
284	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
285	C₄⋊C₄×C₄₁	—	2	2	no	—
286	C₄⋊C₄×C₄₁	—	2	2	no	—
287	C₄⋊C₄×C₄₁	—	2	2	no	—
288	C₄⋊C₄×C₄₁	—	2	2	no	—
289	C₄⋊C₄×C₄₁	—	2	2	no	—
290	C₄⋊C₄×C₄₁	—	2	4	no	—
291	C₄⋊C₄×C₄₁	—	2	1	no	—
292	C₄⋊C₄×C₄₁	—	2	1	no	—
293	C₄⋊C₄×C₄₁	—	2	1	no	—
294	C₄⋊C₄×C₄₁	—	2	1	no	—
295	C₄⋊C₄×C₄₁	—	2	1	no	—
296	C₄⋊C₄×C₄₁	—	2	4	no	—
297	C₄⋊C₄×C₄₁	—	2	4	no	—
298	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
301	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
302	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
304	C₂²⋊C₄×C₄₁	—	2	1	no	—
305	C₂²⋊C₄×C₄₁	—	2	4	no	—
306	C₂²⋊C₄×C₄₁	—	2	4	no	—
307	C₂²⋊C₄×C₄₁	—	2	4	no	—
308	C₂²⋊C₄×C₄₁	—	2	1	no	—
309	C₂²⋊C₄×C₄₁	—	2	1	no	—
310	C₂²⋊C₄×C₄₁	—	2	4	no	—
311	C₂²⋊C₄×C₄₁	—	2	2	no	—
312	C₂²⋊C₄×C₄₁	—	2	2	no	—
313	C₂²⋊C₄×C₄₁	—	2	4	no	—
314	C₂²⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
315	C₂²⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
316	C₄²×C₄₁	—	2	1	no	—
317	C₄²×C₄₁	—	2	1	no	—
318	C₄²×C₄₁	—	2	2	no	—
319	C₄²×C₄₁	—	2	2	no	—
320	C₄²×C₄₁	—	2	1	no	—
321	C₄²×C₄₁	—	2	4	no	—
322	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
325	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
326	C₂³×C₄₁	—	2	1	no	—
327	C₂³×C₄₁	—	2	2	no	—
328	C₂³×C₄₁	C₂²×D₄	1	4	yes	—
329	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
330	Q₈×C₄₁	—	2	4	no	—
331	Q₈×C₄₁	—	2	4	no	—
332	Q₈×C₄₁	—	2	2	no	—
333	Q₈×C₄₁	—	2	1	no	—
334	Q₈×C₄₁	—	2	2	no	—
335	Q₈×C₄₁	—	2	1	no	—
336	Q₈×C₄₁	—	2	2	no	—
337	Q₈×C₄₁	—	4	8	no	—
338	Q₈×C₄₁	—	4	4	no	—
339	Q₈×C₄₁	—	8	2	no	—
340	Q₈×C₄₁	C₂×#41	1	4	yes	—
341	D₄×C₄₁	—	2	8	no	—
342	D₄×C₄₁	—	2	4	no	—
343	D₄×C₄₁	—	2	4	no	—
344	D₄×C₄₁	—	2	1	no	—
345	D₄×C₄₁	—	2	2	no	—
346	D₄×C₄₁	—	2	1	no	—
347	D₄×C₄₁	—	2	2	no	—
348	D₄×C₄₁	—	4	2	no	—
349	D₄×C₄₁	—	4	8	no	—
350	D₄×C₄₁	—	4	2	no	—
351	D₄×C₄₁	—	4	4	no	—
352	D₄×C₄₁	—	4	2	no	—
353	D₄×C₄₁	—	8	1	no	—
354	D₄×C₄₁	—	8	4	no	—
355	D₄×C₄₁	—	8	4	no	—
356	C₂×C₄×C₄₁	—	2	4	no	—
357	C₂×C₄×C₄₁	—	2	2	no	—
358	C₂×C₄×C₄₁	—	2	2	no	—
359	C₂×C₄×C₄₁	—	2	4	no	—
360	C₂×C₄×C₄₁	—	2	4	no	—
361	C₂×C₄×C₄₁	—	2	1	no	—
362	C₂×C₄×C₄₁	—	2	1	no	—
363	C₂×C₄×C₄₁	—	2	2	no	—
364	C₂×C₄×C₄₁	—	2	1	no	—
365	C₂×C₄×C₄₁	—	2	4	no	—
366	C₂×C₄×C₄₁	—	2	2	no	—
367	C₂×C₄×C₄₁	—	4	1	no	—
368	C₂×C₄×C₄₁	—	4	8	no	—
369	C₂×C₄×C₄₁	—	4	8	no	—
370	C₂×C₄×C₄₁	—	4	2	no	—
371	C₂×C₄×C₄₁	—	4	4	no	—
372	C₂×C₄×C₄₁	—	4	2	no	—
373	C₂×C₄×C₄₁	—	4	2	no	—
374	C₂×C₄×C₄₁	—	8	1	no	—
375	C₂×C₄×C₄₁	—	8	2	no	—
376	C₂×C₄×C₄₁	—	8	4	no	—
377	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
380	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
384	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
385	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
386	C₈×C₄₁	—	2	2	no	—
387	C₈×C₄₁	—	2	2	no	—
388	C₈×C₄₁	—	2	2	no	—
389	C₈×C₄₁	—	2	2	no	—
390	#61202	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
391	C₂²×C₄₁	—	2	1	no	—
392	C₂²×C₄₁	—	2	1	no	—
393	C₂²×C₄₁	—	2	4	no	—
394	C₂²×C₄₁	—	2	4	no	—
395	C₂²×C₄₁	—	2	4	no	—
396	C₂²×C₄₁	—	4	1	no	—
397	C₂²×C₄₁	—	4	2	no	—
398	C₂²×C₄₁	—	4	2	no	—
399	C₂²×C₄₁	—	4	1	no	—
400	C₂²×C₄₁	—	4	1	no	—
401	C₂²×C₄₁	—	4	2	no	—
402	C₂²×C₄₁	#546	1	2	yes	—
403	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
404	C₄×C₄₁	—	2	1	no	—
405	C₄×C₄₁	—	2	1	no	—
406	C₄×C₄₁	—	2	4	no	—
407	C₄×C₄₁	—	2	4	no	—
408	C₄×C₄₁	—	2	1	no	—
409	C₄×C₄₁	—	4	1	no	—
410	C₄×C₄₁	—	4	2	no	—
411	C₄×C₄₁	—	4	2	no	—
412	C₄×C₄₁	—	4	1	no	—
413	C₄×C₄₁	—	4	1	no	—
414	C₄×C₄₁	—	4	4	no	—
415	C₄×C₄₁	#546	1	2	yes	—
416	C₄×C₄₁	#577	1	2	yes	—
417	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
418	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
419	#3511	C₂×C₄₁	1	1	yes	characteristic, complemented
420	#3497	C₂×C₄₁	1	1	yes	characteristic, complemented
421	#3332	C₂×C₄₁	1	2	yes	complemented
422	#3328	C₂×C₄₁	1	2	yes	complemented
423	#3321	C₂×C₄₁	1	4	yes	complemented
424	#3316	C₂×C₄₁	1	4	yes	complemented
425	#3304	C₂×C₄₁	1	2	yes	complemented
426	#3298	C₂×C₄₁	1	2	yes	complemented
427	#3141	C₂×C₄₁	1	1	yes	characteristic, complemented
428	#3099	C₂×C₄₁	1	2	yes	complemented
429	C₂×#475	C₂×C₄₁	1	1	yes	characteristic, complemented
430	#3060	C₂×C₄₁	1	2	yes	complemented
431	#3035	C₂×C₄₁	1	1	yes	characteristic, complemented
432	#3013	C₂×C₄₁	1	2	yes	complemented
433	C₄×#137	C₂×C₄₁	1	1	yes	characteristic, complemented
434	#2935	C₂×C₄₁	1	1	yes	characteristic, complemented
435	#2898	C₂×C₄₁	1	2	yes	complemented
436	C₂×C₄₁	—	2	2	no	—
437	C₂×C₄₁	—	4	4	no	—
438	C₂×C₄₁	—	8	1	no	—
439	C₂×C₄₁	—	8	2	no	—
440	C₂×C₄₁	C₂×#546	1	1	yes	characteristic
441	C₂×C₄₁	C₂×#577	1	1	yes	characteristic
442	C₂×C₄₁	#3586	1	1	yes	characteristic
443	C₂×2₋¹⁺⁴	C₂²×C₄₁	1	2	yes	—
444	C₂×#137	C₂²×C₄₁	1	1	yes	characteristic
445	C₂×#135	C₂²×C₄₁	1	2	yes	—
446	C₂×#131	C₂²×C₄₁	1	2	yes	—
447	#556	C₂²×C₄₁	1	2	yes	—
448	#555	C₂²×C₄₁	1	2	yes	—
449	#554	C₂²×C₄₁	1	2	yes	—
450	#553	—	2	2	no	—
451	#550	—	2	1	no	—
452	#550	C₂²×C₄₁	1	2	yes	—
453	D₄×Q₈	—	2	1	no	—
454	D₄×Q₈	C₂²×C₄₁	1	2	yes	—
455	#548	—	2	2	no	—
456	#548	—	2	2	no	—
457	#548	C₂²×C₄₁	1	4	yes	—
458	#547	C₂²×C₄₁	1	2	yes	—
459	#542	—	2	2	no	—
460	#537	—	2	2	no	—
461	#537	C₂²×C₄₁	1	2	yes	—
462	#537	C₂²×C₄₁	1	2	yes	—
463	#533	—	2	1	no	—
464	#532	—	2	1	no	—
465	#532	—	2	2	no	—
466	#532	C₂²×C₄₁	1	1	yes	characteristic
467	#532	C₂²×C₄₁	1	1	yes	characteristic
468	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
469	#520	C₂²×C₄₁	1	2	yes	—
470	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
471	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
472	#489	C₂²×C₄₁	1	4	yes	—
473	#487	C₂²×C₄₁	1	2	yes	—
474	#486	C₂²×C₄₁	1	2	yes	—
475	#485	C₂²×C₄₁	1	4	yes	—
476	#483	C₂²×C₄₁	1	4	yes	—
477	#482	C₂²×C₄₁	1	4	yes	—
478	#481	C₂²×C₄₁	1	4	yes	—
479	#475	C₂²×C₄₁	1	2	yes	—
480	#475	C₂²×C₄₁	1	2	yes	—
481	#475	C₂²×C₄₁	1	4	yes	—
482	#470	C₂²×C₄₁	1	4	yes	—
483	#469	C₂²×C₄₁	1	4	yes	—
484	#465	C₂²×C₄₁	1	4	yes	—
485	#465	C₂²×C₄₁	1	4	yes	—
486	#464	C₂²×C₄₁	1	2	yes	—
487	#463	C₂²×C₄₁	1	2	yes	—
488	#462	C₂²×C₄₁	1	1	yes	characteristic
489	#461	C₂²×C₄₁	1	1	yes	characteristic
490	#460	C₂²×C₄₁	1	1	yes	characteristic
491	#459	C₂²×C₄₁	1	1	yes	characteristic
492	#452	C₂²×C₄₁	1	4	yes	—
493	#451	C₂²×C₄₁	1	4	yes	—
494	#449	C₂²×C₄₁	1	4	yes	—
495	#448	C₂²×C₄₁	1	4	yes	—
496	#441	C₂²×C₄₁	1	2	yes	—
497	#440	C₂²×C₄₁	1	2	yes	—
498	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	—
499	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
500	#436	C₂²×C₄₁	1	2	yes	—
501	#435	C₂²×C₄₁	1	4	yes	—
502	C₈×D₄	C₂²×C₄₁	1	2	yes	—
503	#428	C₂²×C₄₁	1	1	yes	characteristic
504	C₂×#106	C₂²×C₄₁	1	2	yes	—
505	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
506	#419	C₂²×C₄₁	1	4	yes	—
507	#419	C₂²×C₄₁	1	1	yes	characteristic
508	#417	C₂²×C₄₁	1	4	yes	—
509	#417	C₂²×C₄₁	1	2	yes	—
510	#417	C₂²×C₄₁	1	2	yes	—
511	#417	C₂²×C₄₁	1	1	yes	characteristic
512	#416	C₂²×C₄₁	1	2	yes	—
513	#416	C₂²×C₄₁	1	4	yes	—
514	C₂×#103	C₂²×C₄₁	1	2	yes	—
515	C₂×#103	C₂²×C₄₁	1	4	yes	—
516	#408	C₂²×C₄₁	1	2	yes	—
517	C₄×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
518	C₄₁	#61202	1	1	yes	characteristic, direct product factor, Sylow
519	2₋¹⁺⁴	—	2	8	no	—
520	2₋¹⁺⁴	—	4	4	no	—
521	C₂×#41	—	2	4	no	—
522	C₂×#41	—	2	2	no	—
523	C₂×#41	—	2	2	no	—
524	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
525	C₂×#41	C₂³×C₄₁	1	2	yes	—
526	C₂×#41	C₂³×C₄₁	1	4	yes	—
527	C₂×#41	C₂³×C₄₁	1	2	yes	—
528	C₂²×Q₈	—	2	2	no	—
529	C₂²×Q₈	—	2	1	no	—
530	C₂²×Q₈	C₂³×C₄₁	1	4	yes	—
531	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
532	#137	—	2	4	no	—
533	#135	—	4	4	no	—
534	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
535	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
536	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
537	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
538	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
539	C₂×D₈	C₂³×C₄₁	1	2	yes	—
540	#131	—	4	4	no	—
541	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
542	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
543	C₂×M₁₆	C₂³×C₄₁	1	4	yes	—
544	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
545	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
546	C₄⋊Q₈	—	2	2	no	—
547	C₄⋊Q₈	—	2	1	no	—
548	C₄⋊Q₈	—	2	1	no	—
549	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
550	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
551	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
552	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
553	#127	—	2	2	no	—
554	#127	D₄×C₄₁	1	1	yes	characteristic
555	#127	C₂³×C₄₁	1	1	yes	characteristic
556	#126	—	2	4	no	—
557	#125	—	2	2	no	—
558	#124	—	2	2	no	—
559	#124	—	2	4	no	—
560	#124	—	2	4	no	—
561	#124	D₄×C₄₁	1	2	yes	—
562	#124	C₂³×C₄₁	1	2	yes	—
563	#123	—	2	4	no	—
564	C₂²⋊Q₈	—	2	2	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	4	no	—
568	C₂²⋊Q₈	—	2	4	no	—
569	C₂²⋊Q₈	—	2	4	no	—
570	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
571	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
572	#121	—	2	4	no	—
573	#121	—	2	2	no	—
574	#121	—	2	2	no	—
575	#121	—	2	4	no	—
576	#121	—	2	2	no	—
577	#121	—	2	4	no	—
578	#121	—	2	1	no	—
579	#121	—	2	1	no	—
580	#121	—	2	4	no	—
581	#121	D₄×C₄₁	1	2	yes	—
582	#121	D₄×C₄₁	1	2	yes	—
583	#121	C₂³×C₄₁	1	4	yes	—
584	#121	C₂³×C₄₁	1	4	yes	—
585	C₄×Q₈	—	2	2	no	—
586	C₄×Q₈	—	2	2	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
590	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
591	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
592	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	—	2	4	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	—	2	1	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	4	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
604	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
605	C₄×D₄	C₂³×C₄₁	1	2	yes	—
606	C₄×D₄	C₂³×C₄₁	1	2	yes	—
607	#117	—	2	2	no	—
608	#117	—	2	1	no	—
609	#117	C₂³×C₄₁	1	1	yes	characteristic
610	#117	C₂³×C₄₁	1	4	yes	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
616	C₂×C₄²	—	2	1	no	—
617	C₂×C₄²	—	2	1	no	—
618	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
619	#107	C₂³×C₄₁	1	2	yes	—
620	#106	C₂³×C₄₁	1	4	yes	—
621	#106	C₂³×C₄₁	1	4	yes	—
622	#106	C₂³×C₄₁	1	2	yes	—
623	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
624	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
625	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
626	#103	C₂³×C₄₁	1	4	yes	—
627	#103	C₂³×C₄₁	1	2	yes	—
628	#103	C₂³×C₄₁	1	2	yes	—
629	#103	C₂³×C₄₁	1	4	yes	—
630	#103	C₂³×C₄₁	1	4	yes	—
631	#103	C₂³×C₄₁	1	2	yes	—
632	#103	C₂³×C₄₁	1	2	yes	—
633	#103	C₂³×C₄₁	1	2	yes	—
634	#103	C₂³×C₄₁	1	4	yes	—
635	#102	C₂³×C₄₁	1	2	yes	—
636	#102	C₂³×C₄₁	1	2	yes	—
637	#102	C₂³×C₄₁	1	4	yes	—
638	#102	C₂³×C₄₁	1	2	yes	—
639	#102	C₂³×C₄₁	1	4	yes	—
640	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
641	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
642	#97	C₂³×C₄₁	1	2	yes	—
643	C₄×C₈	C₂³×C₄₁	1	2	yes	—
644	#41	—	2	4	no	—
645	#41	—	2	4	no	—
646	#41	—	2	8	no	—
647	#41	—	2	2	no	—
648	#41	—	2	4	no	—
649	#41	—	2	2	no	—
650	#41	—	2	4	no	—
651	#41	—	4	4	no	—
652	#41	—	4	16	no	—
653	#41	—	4	8	no	—
654	#41	—	8	4	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	2	2	no	—
657	C₂×Q₈	—	2	4	no	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	—	2	2	no	—
660	C₂×Q₈	—	2	8	no	—
661	C₂×Q₈	—	4	4	no	—
662	C₂×Q₈	—	4	8	no	—
663	C₂×Q₈	—	8	2	no	—
664	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
665	C₂×Q₈	#41×C₄₁	1	4	yes	complemented
666	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
667	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
668	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
669	C₂×D₄	—	2	1	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	4	no	—
672	C₂×D₄	—	2	4	no	—
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
677	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
678	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
679	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
680	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
681	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	4	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
693	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
695	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
696	Q₁₆	—	2	4	no	—
697	Q₁₆	—	4	2	no	—
698	SD₁₆	—	2	4	no	—
699	SD₁₆	—	4	2	no	—
700	SD₁₆	—	4	2	no	—
701	D₈	—	4	2	no	—
702	M₁₆	—	2	2	no	—
703	M₁₆	—	2	2	no	—
704	M₁₆	—	4	4	no	—
705	C₂×C₈	—	2	4	no	—
706	C₂×C₈	—	4	4	no	—
707	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
708	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
709	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
710	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
725	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
726	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
727	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
728	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
729	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
730	C₂²⋊C₄	—	2	1	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	1	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
741	C₂²⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
742	C₄²	—	2	1	no	—
743	C₄²	—	2	1	no	—
744	C₄²	—	2	2	no	—
745	C₄²	—	2	2	no	—
746	C₄²	—	2	1	no	—
747	C₄²	—	2	4	no	—
748	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
749	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
750	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
751	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
752	C₂³	—	2	1	no	—
753	C₂³	—	2	2	no	—
754	C₂³	C₂²×D₄×C₄₁	1	4	yes	—
755	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
756	Q₈	—	2	4	no	—
757	Q₈	—	2	4	no	—
758	Q₈	—	2	2	no	—
759	Q₈	—	2	1	no	—
760	Q₈	—	2	2	no	—
761	Q₈	—	2	1	no	—
762	Q₈	—	2	2	no	—
763	Q₈	—	4	8	no	—
764	Q₈	—	4	4	no	—
765	Q₈	—	8	2	no	—
766	Q₈	C₂×#41×C₄₁	1	4	yes	—
767	D₄	—	2	8	no	—
768	D₄	—	2	4	no	—
769	D₄	—	2	4	no	—
770	D₄	—	2	1	no	—
771	D₄	—	2	2	no	—
772	D₄	—	2	1	no	—
773	D₄	—	2	2	no	—
774	D₄	—	4	2	no	—
775	D₄	—	4	8	no	—
776	D₄	—	4	4	no	—
777	D₄	—	4	2	no	—
778	D₄	—	4	2	no	—
779	D₄	—	8	1	no	—
780	D₄	—	8	4	no	—
781	D₄	—	8	4	no	—
782	C₂×C₄	—	2	4	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	4	no	—
786	C₂×C₄	—	2	4	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	4	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	—	4	8	no	—
795	C₂×C₄	—	4	8	no	—
796	C₂×C₄	—	4	2	no	—
797	C₂×C₄	—	4	4	no	—
798	C₂×C₄	—	4	2	no	—
799	C₂×C₄	—	4	2	no	—
800	C₂×C₄	—	8	2	no	—
801	C₂×C₄	—	8	4	no	—
802	C₂×C₄	—	8	1	no	—
803	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
804	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
805	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
806	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
808	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
809	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
810	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
811	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
812	C₈	—	2	2	no	—
813	C₈	—	2	2	no	—
814	C₈	—	2	2	no	—
815	C₈	—	2	2	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	2	1	no	—
818	C₂²	—	2	4	no	—
819	C₂²	—	2	4	no	—
820	C₂²	—	2	4	no	—
821	C₂²	—	4	1	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	1	no	—
827	C₂²	C₄₁×#546	1	2	yes	—
828	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
829	C₄	—	2	1	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	4	no	—
833	C₄	—	2	4	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	4	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	1	no	—
840	C₄	C₄₁×#546	1	2	yes	—
841	C₄	C₄₁×#577	1	2	yes	—
842	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
843	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
844	C₂	—	2	2	no	—
845	C₂	—	4	4	no	—
846	C₂	—	8	1	no	—
847	C₂	—	8	2	no	—
848	C₂	C₂×C₄₁×#546	1	1	yes	characteristic
849	C₂	C₂×C₄₁×#577	1	1	yes	characteristic
850	C₂	C₄₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3511	C₂	semidirect
2. C₄₁×#3497	C₂	semidirect
3. C₄₁×#3332	C₂	semidirect
4. C₄₁×#3328	C₂	semidirect
5. C₄₁×#3321	C₂	semidirect
6. C₄₁×#3316	C₂	semidirect
7. C₄₁×#3304	C₂	semidirect
8. C₄₁×#3298	C₂	semidirect
9. C₄₁×#3141	C₂	semidirect
10. C₄₁×#3099	C₂	semidirect
11. C₂×C₄₁×#475	C₂	semidirect
12. C₄₁×#3060	C₂	semidirect
13. C₄₁×#3035	C₂	semidirect
14. C₄₁×#3013	C₂	semidirect
15. C₄×#137×C₄₁	C₂	semidirect
16. C₄₁×#2935	C₂	semidirect
17. C₄₁×#2898	C₂	semidirect
239. C₂×Q₈×C₄₁	#41	semidirect
390. #61202	C₄₁	direct (N × H)
419. #3511	C₂×C₄₁	semidirect
420. #3497	C₂×C₄₁	semidirect
421. #3332	C₂×C₄₁	semidirect
422. #3328	C₂×C₄₁	semidirect
423. #3321	C₂×C₄₁	semidirect
424. #3316	C₂×C₄₁	semidirect
425. #3304	C₂×C₄₁	semidirect
426. #3298	C₂×C₄₁	semidirect
427. #3141	C₂×C₄₁	semidirect
428. #3099	C₂×C₄₁	semidirect
429. C₂×#475	C₂×C₄₁	semidirect
430. #3060	C₂×C₄₁	semidirect
431. #3035	C₂×C₄₁	semidirect
432. #3013	C₂×C₄₁	semidirect
433. C₄×#137	C₂×C₄₁	semidirect
434. #2935	C₂×C₄₁	semidirect
435. #2898	C₂×C₄₁	semidirect
518. C₄₁	#61202	direct (N × H)
665. C₂×Q₈	#41×C₄₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄₁×#3511	2
C₄₁×#3497	2
C₄₁×#3332	2
C₄₁×#3328	2
C₄₁×#3321	2
C₄₁×#3316	2
C₄₁×#3304	2
C₄₁×#3298	2
C₄₁×#3141	2
C₄₁×#3099	2
C₂×C₄₁×#475	2
C₄₁×#3060	2
C₄₁×#3035	2
C₄₁×#3013	2
C₄×#137×C₄₁	2
C₄₁×#2935	2
C₄₁×#2898	2
#61202	41

Subgroups — C41×#61202 #23837403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61202 #23837403