Subgroups — C₄₁×#61205 #23837406

Order 10496.

2214 conjugacy classes of subgroups.

The subgroup lattice has 886 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	C₄₁×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3332	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3325	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3318	C₂	1	4	yes	maximal, complemented
6	C₄₁×#3309	C₂	1	4	yes	maximal, complemented
7	C₄₁×#3305	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3294	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#3096	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3058	C₂	1	2	yes	maximal, complemented
13	C₂×C₄₁×#459	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3008	C₂	1	2	yes	maximal, complemented
15	C₄×AGL(1,ℤ/8)×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#2935	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#2897	C₂	1	2	yes	maximal, complemented
18	C₂×H(5,𝔽₂)×C₄₁	C₂²	1	2	yes	—
19	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₄₁	C₂²	1	2	yes	complemented
21	C₂×#131×C₄₁	C₂²	1	2	yes	complemented
22	C₄₁×#559	—	2	2	no	—
23	C₄₁×#556	—	2	1	no	—
24	C₄₁×#555	C₂²	1	2	yes	complemented
25	C₄₁×#553	C₂²	1	4	yes	complemented
26	C₄₁×#550	—	2	1	no	—
27	C₄₁×#550	C₂²	1	2	yes	complemented
28	C₄₁×#550	C₂²	1	2	yes	complemented
29	C₄₁×#547	C₂²	1	2	yes	complemented
30	D₄²×C₄₁	—	2	2	no	—
31	D₄²×C₄₁	—	2	2	no	—
32	D₄²×C₄₁	C₂²	1	2	yes	complemented
33	D₄²×C₄₁	C₂²	1	2	yes	complemented
34	C₄₁×#538	—	2	2	no	—
35	C₄₁×#535	—	2	2	no	—
36	C₄₁×#535	C₂²	1	2	yes	—
37	C₄₁×#535	C₂²	1	2	yes	complemented
38	C₄₁×#533	C₂²	1	1	yes	characteristic, complemented
39	C₄₁×#532	—	2	1	no	—
40	C₄₁×#532	C₂²	1	1	yes	characteristic
41	C₂×#127×C₄₁	—	2	1	no	—
42	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
43	C₄₁×#525	—	2	2	no	—
44	C₄₁×#520	C₂²	1	2	yes	complemented
45	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
47	C₄₁×#490	C₂²	1	4	yes	complemented
48	C₄₁×#486	C₂²	1	2	yes	complemented
49	C₄₁×#486	C₂²	1	2	yes	complemented
50	C₄₁×#482	C₂²	1	4	yes	complemented
51	C₄₁×#482	C₂²	1	4	yes	complemented
52	C₄₁×#481	C₂²	1	4	yes	complemented
53	C₄₁×#480	C₂²	1	4	yes	complemented
54	C₄₁×#479	C₂²	1	2	yes	complemented
55	C₄₁×#478	C₂²	1	2	yes	complemented
56	C₄₁×#477	C₂²	1	1	yes	characteristic, complemented
57	C₄₁×#476	C₂²	1	1	yes	characteristic, complemented
58	C₄₁×#475	C₂²	1	1	yes	characteristic, complemented
59	C₄₁×#474	C₂²	1	1	yes	characteristic, complemented
60	C₄₁×#469	C₂²	1	4	yes	complemented
61	C₄₁×#469	C₂²	1	4	yes	complemented
62	C₄₁×#466	C₂²	1	4	yes	complemented
63	C₄₁×#466	C₂²	1	4	yes	complemented
64	C₄₁×#459	C₂²	1	2	yes	complemented
65	C₄₁×#459	C₂²	1	4	yes	complemented
66	C₄₁×#459	C₂²	1	2	yes	complemented
67	C₄₁×#449	C₂²	1	4	yes	complemented
68	C₄₁×#449	C₂²	1	4	yes	complemented
69	C₄₁×#447	C₂²	1	4	yes	complemented
70	C₄₁×#447	C₂²	1	4	yes	complemented
71	C₄₁×#442	C₂²	1	2	yes	complemented
72	C₄₁×#440	C₂²	1	2	yes	complemented
73	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
74	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
75	C₄₁×#436	C₂²	1	2	yes	complemented
76	C₄₁×#435	C₂²	1	4	yes	complemented
77	C₈×D₄×C₄₁	C₂²	1	2	yes	complemented
78	C₄₁×#428	C₂²	1	1	yes	characteristic, complemented
79	C₄₁×#427	C₂²	1	2	yes	complemented
80	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
81	C₄₁×#418	C₂²	1	1	yes	characteristic, complemented
82	C₄₁×#418	C₂²	1	2	yes	complemented
83	C₄₁×#418	C₂²	1	4	yes	complemented
84	C₄₁×#418	C₂²	1	2	yes	complemented
85	C₄₁×#417	C₂²	1	1	yes	characteristic
86	C₄₁×#417	C₂²	1	4	yes	complemented
87	C₄₁×#416	C₂²	1	2	yes	—
88	C₄₁×#416	C₂²	1	4	yes	complemented
89	C₂×#102×C₄₁	C₂²	1	4	yes	complemented
90	C₂×#102×C₄₁	C₂²	1	2	yes	complemented
91	C₄₁×#408	C₂²	1	2	yes	complemented
92	C₄×M₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
93	H(5,𝔽₂)×C₄₁	—	2	8	no	—
94	H(5,𝔽₂)×C₄₁	—	4	4	no	—
95	C₂×#41×C₄₁	—	2	2	no	—
96	C₂×#41×C₄₁	—	2	2	no	—
97	C₂×#41×C₄₁	C₂³	1	4	yes	—
98	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
99	C₂×#41×C₄₁	C₂³	1	2	yes	—
100	C₂²×D₄×C₄₁	—	2	2	no	—
101	C₂²×D₄×C₄₁	—	2	4	no	—
102	C₂²×D₄×C₄₁	—	2	2	no	—
103	C₂²×D₄×C₄₁	—	2	2	no	—
104	C₂²×D₄×C₄₁	—	2	1	no	—
105	C₂²×D₄×C₄₁	—	2	1	no	—
106	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
107	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
108	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
109	C₂³×C₄×C₄₁	—	2	1	no	—
110	AGL(1,ℤ/8)×C₄₁	—	2	4	no	—
111	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
112	C₂×D₈×C₄₁	—	4	4	no	—
113	C₂×D₈×C₄₁	C₂³	1	2	yes	—
114	C₂×D₈×C₄₁	C₂³	1	4	yes	—
115	C₂×D₈×C₄₁	C₂³	1	4	yes	—
116	#131×C₄₁	—	4	4	no	—
117	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
119	C₂×M₁₆×C₄₁	C₂³	1	4	yes	—
120	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
121	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
122	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
123	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
124	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
125	#127×C₄₁	—	2	2	no	—
126	#127×C₄₁	—	2	2	no	—
127	#127×C₄₁	—	2	2	no	—
128	#127×C₄₁	—	2	2	no	—
129	#127×C₄₁	—	2	1	no	—
130	#127×C₄₁	—	2	1	no	—
131	#127×C₄₁	D₄	1	1	yes	characteristic
132	#127×C₄₁	C₂³	1	2	yes	—
133	#127×C₄₁	C₂³	1	2	yes	—
134	#126×C₄₁	—	2	4	no	—
135	#125×C₄₁	C₂³	1	2	yes	—
136	#124×C₄₁	—	2	2	no	—
137	#124×C₄₁	—	2	2	no	—
138	#124×C₄₁	—	2	4	no	—
139	#124×C₄₁	D₄	1	2	yes	—
140	#123×C₄₁	—	2	4	no	—
141	#123×C₄₁	—	2	4	no	—
142	C₂²⋊Q₈×C₄₁	—	2	1	no	—
143	C₂²⋊Q₈×C₄₁	—	2	1	no	—
144	C₂²⋊Q₈×C₄₁	—	2	2	no	—
145	#121×C₄₁	—	2	2	no	—
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	4	no	—
151	#121×C₄₁	D₄	1	2	yes	—
152	#121×C₄₁	D₄	1	2	yes	—
153	#121×C₄₁	C₂³	1	4	yes	—
154	#121×C₄₁	C₂³	1	4	yes	—
155	#121×C₄₁	C₂³	1	4	yes	—
156	#121×C₄₁	C₂³	1	4	yes	—
157	#120×C₄₁	—	2	4	no	—
158	#120×C₄₁	—	2	4	no	—
159	#120×C₄₁	—	2	4	no	—
160	#120×C₄₁	—	2	4	no	—
161	C₄×Q₈×C₄₁	—	2	2	no	—
162	C₄×Q₈×C₄₁	—	2	1	no	—
163	C₄×Q₈×C₄₁	—	2	1	no	—
164	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
165	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
166	C₄×D₄×C₄₁	—	2	4	no	—
167	C₄×D₄×C₄₁	—	2	2	no	—
168	C₄×D₄×C₄₁	—	2	1	no	—
169	C₄×D₄×C₄₁	—	2	1	no	—
170	C₄×D₄×C₄₁	—	2	2	no	—
171	C₄×D₄×C₄₁	—	2	2	no	—
172	C₄×D₄×C₄₁	—	2	4	no	—
173	C₄×D₄×C₄₁	—	2	1	no	—
174	C₄×D₄×C₄₁	—	2	1	no	—
175	C₄×D₄×C₄₁	C₂³	1	2	yes	—
176	C₄×D₄×C₄₁	C₂³	1	2	yes	—
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	2	yes	—
185	#117×C₄₁	C₂³	1	4	yes	—
186	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
188	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
189	C₂×C₄²×C₄₁	—	2	1	no	—
190	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
191	#107×C₄₁	C₂³	1	2	yes	—
192	#107×C₄₁	C₂³	1	2	yes	—
193	#107×C₄₁	C₂³	1	2	yes	—
194	#106×C₄₁	C₂³	1	2	yes	—
195	#106×C₄₁	C₂³	1	2	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	2	yes	—
201	#103×C₄₁	C₂³	1	2	yes	—
202	#103×C₄₁	C₂³	1	2	yes	—
203	#102×C₄₁	C₂³	1	2	yes	—
204	#102×C₄₁	C₂³	1	4	yes	—
205	#102×C₄₁	C₂³	1	2	yes	—
206	#102×C₄₁	C₂³	1	4	yes	—
207	#102×C₄₁	C₂³	1	4	yes	—
208	#102×C₄₁	C₂³	1	2	yes	—
209	#102×C₄₁	C₂³	1	4	yes	—
210	#102×C₄₁	C₂³	1	2	yes	—
211	#102×C₄₁	C₂³	1	2	yes	—
212	#102×C₄₁	C₂³	1	4	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	C₂⁴×C₄₁	—	2	1	no	—
219	C₂⁴×C₄₁	—	2	4	no	—
220	C₂⁴×C₄₁	—	2	2	no	—
221	#41×C₄₁	—	2	4	no	—
222	#41×C₄₁	—	2	4	no	—
223	#41×C₄₁	—	2	2	no	—
224	#41×C₄₁	—	2	8	no	—
225	#41×C₄₁	—	4	4	no	—
226	#41×C₄₁	—	4	8	no	—
227	#41×C₄₁	—	8	4	no	—
228	#41×C₄₁	#41	1	4	yes	complemented
229	C₂×Q₈×C₄₁	—	2	1	no	—
230	C₂×Q₈×C₄₁	—	2	1	no	—
231	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
232	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
233	C₂×D₄×C₄₁	—	2	1	no	—
234	C₂×D₄×C₄₁	—	2	8	no	—
235	C₂×D₄×C₄₁	—	2	4	no	—
236	C₂×D₄×C₄₁	—	2	4	no	—
237	C₂×D₄×C₄₁	—	2	4	no	—
238	C₂×D₄×C₄₁	—	2	4	no	—
239	C₂×D₄×C₄₁	—	2	4	no	—
240	C₂×D₄×C₄₁	—	2	1	no	—
241	C₂×D₄×C₄₁	—	2	2	no	—
242	C₂×D₄×C₄₁	—	2	2	no	—
243	C₂×D₄×C₄₁	—	2	4	no	—
244	C₂×D₄×C₄₁	—	2	2	no	—
245	C₂×D₄×C₄₁	—	2	2	no	—
246	C₂×D₄×C₄₁	—	2	2	no	—
247	C₂×D₄×C₄₁	—	2	2	no	—
248	C₂×D₄×C₄₁	—	2	4	no	—
249	C₂×D₄×C₄₁	—	2	2	no	—
250	C₂×D₄×C₄₁	—	2	4	no	—
251	C₂×D₄×C₄₁	—	4	4	no	—
252	C₂×D₄×C₄₁	—	4	8	no	—
253	C₂×D₄×C₄₁	—	4	16	no	—
254	C₂×D₄×C₄₁	—	8	2	no	—
255	C₂×D₄×C₄₁	—	8	4	no	—
256	C₂×D₄×C₄₁	—	8	2	no	—
257	C₂×D₄×C₄₁	—	8	4	no	—
258	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
259	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
260	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
261	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
262	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
263	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
264	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₄₁	—	2	1	no	—
266	C₂²×C₄×C₄₁	—	2	1	no	—
267	C₂²×C₄×C₄₁	—	2	4	no	—
268	C₂²×C₄×C₄₁	—	2	1	no	—
269	C₂²×C₄×C₄₁	—	2	1	no	—
270	C₂²×C₄×C₄₁	—	2	2	no	—
271	C₂²×C₄×C₄₁	—	2	4	no	—
272	C₂²×C₄×C₄₁	—	2	2	no	—
273	C₂²×C₄×C₄₁	—	8	2	no	—
274	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
277	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
278	SD₁₆×C₄₁	—	2	4	no	—
279	D₈×C₄₁	—	2	4	no	—
280	D₈×C₄₁	—	4	4	no	—
281	D₈×C₄₁	—	4	4	no	—
282	M₁₆×C₄₁	—	2	2	no	—
283	M₁₆×C₄₁	—	2	2	no	—
284	M₁₆×C₄₁	—	4	4	no	—
285	C₂×C₈×C₄₁	—	2	4	no	—
286	C₂×C₈×C₄₁	—	4	4	no	—
287	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
288	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
289	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
290	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
291	C₄⋊C₄×C₄₁	—	2	1	no	—
292	C₄⋊C₄×C₄₁	—	2	4	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	2	no	—
297	C₄⋊C₄×C₄₁	—	2	2	no	—
298	C₄⋊C₄×C₄₁	—	2	1	no	—
299	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
304	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
305	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
306	C₂²⋊C₄×C₄₁	—	2	1	no	—
307	C₂²⋊C₄×C₄₁	—	2	2	no	—
308	C₂²⋊C₄×C₄₁	—	2	4	no	—
309	C₂²⋊C₄×C₄₁	—	2	2	no	—
310	C₂²⋊C₄×C₄₁	—	2	2	no	—
311	C₂²⋊C₄×C₄₁	—	2	1	no	—
312	C₂²⋊C₄×C₄₁	—	2	1	no	—
313	C₂²⋊C₄×C₄₁	—	2	4	no	—
314	C₂²⋊C₄×C₄₁	—	2	4	no	—
315	C₂²⋊C₄×C₄₁	—	2	4	no	—
316	C₂²⋊C₄×C₄₁	—	2	4	no	—
317	C₂²⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
318	C₂²⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
319	C₄²×C₄₁	—	2	1	no	—
320	C₄²×C₄₁	—	2	1	no	—
321	C₄²×C₄₁	—	2	1	no	—
322	C₄²×C₄₁	—	2	4	no	—
323	C₄²×C₄₁	—	2	2	no	—
324	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
327	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
328	C₂³×C₄₁	—	2	1	no	—
329	C₂³×C₄₁	—	2	2	no	—
330	C₂³×C₄₁	—	2	4	no	—
331	C₂³×C₄₁	—	4	8	no	—
332	C₂³×C₄₁	—	4	2	no	—
333	C₂³×C₄₁	—	4	4	no	—
334	C₂³×C₄₁	—	8	1	no	—
335	C₂³×C₄₁	—	8	1	no	—
336	C₂³×C₄₁	—	8	2	no	—
337	C₂³×C₄₁	—	8	2	no	—
338	C₂³×C₄₁	—	8	4	no	—
339	C₂³×C₄₁	—	8	4	no	—
340	C₂³×C₄₁	C₂²×D₄	1	4	yes	—
341	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
342	Q₈×C₄₁	—	2	4	no	—
343	Q₈×C₄₁	—	2	1	no	—
344	Q₈×C₄₁	—	4	2	no	—
345	Q₈×C₄₁	—	8	1	no	—
346	Q₈×C₄₁	C₂×#41	1	2	yes	—
347	D₄×C₄₁	—	2	4	no	—
348	D₄×C₄₁	—	2	8	no	—
349	D₄×C₄₁	—	2	4	no	—
350	D₄×C₄₁	—	2	4	no	—
351	D₄×C₄₁	—	2	2	no	—
352	D₄×C₄₁	—	2	4	no	—
353	D₄×C₄₁	—	2	1	no	—
354	D₄×C₄₁	—	2	2	no	—
355	D₄×C₄₁	—	2	4	no	—
356	D₄×C₄₁	—	4	2	no	—
357	D₄×C₄₁	—	4	8	no	—
358	D₄×C₄₁	—	4	8	no	—
359	D₄×C₄₁	—	4	4	no	—
360	D₄×C₄₁	—	4	2	no	—
361	D₄×C₄₁	—	4	4	no	—
362	D₄×C₄₁	—	4	4	no	—
363	D₄×C₄₁	—	8	2	no	—
364	D₄×C₄₁	—	8	2	no	—
365	D₄×C₄₁	—	8	4	no	—
366	D₄×C₄₁	—	8	4	no	—
367	D₄×C₄₁	—	8	4	no	—
368	D₄×C₄₁	—	8	4	no	—
369	D₄×C₄₁	C₂×#41	1	2	yes	—
370	C₂×C₄×C₄₁	—	2	1	no	—
371	C₂×C₄×C₄₁	—	2	4	no	—
372	C₂×C₄×C₄₁	—	2	2	no	—
373	C₂×C₄×C₄₁	—	2	4	no	—
374	C₂×C₄×C₄₁	—	2	4	no	—
375	C₂×C₄×C₄₁	—	2	2	no	—
376	C₂×C₄×C₄₁	—	2	1	no	—
377	C₂×C₄×C₄₁	—	2	1	no	—
378	C₂×C₄×C₄₁	—	2	2	no	—
379	C₂×C₄×C₄₁	—	2	2	no	—
380	C₂×C₄×C₄₁	—	4	1	no	—
381	C₂×C₄×C₄₁	—	4	8	no	—
382	C₂×C₄×C₄₁	—	4	2	no	—
383	C₂×C₄×C₄₁	—	4	4	no	—
384	C₂×C₄×C₄₁	—	4	2	no	—
385	C₂×C₄×C₄₁	—	8	2	no	—
386	C₂×C₄×C₄₁	—	8	1	no	—
387	C₂×C₄×C₄₁	—	8	4	no	—
388	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
390	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
395	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
396	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
397	C₈×C₄₁	—	2	2	no	—
398	C₈×C₄₁	—	2	2	no	—
399	C₈×C₄₁	—	2	2	no	—
400	C₈×C₄₁	—	2	2	no	—
401	#61205	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
402	C₂²×C₄₁	—	2	1	no	—
403	C₂²×C₄₁	—	2	1	no	—
404	C₂²×C₄₁	—	2	4	no	—
405	C₂²×C₄₁	—	2	4	no	—
406	C₂²×C₄₁	—	2	2	no	—
407	C₂²×C₄₁	—	2	4	no	—
408	C₂²×C₄₁	—	4	1	no	—
409	C₂²×C₄₁	—	4	1	no	—
410	C₂²×C₄₁	—	4	4	no	—
411	C₂²×C₄₁	—	4	2	no	—
412	C₂²×C₄₁	—	4	4	no	—
413	C₂²×C₄₁	—	4	2	no	—
414	C₂²×C₄₁	—	4	2	no	—
415	C₂²×C₄₁	—	4	4	no	—
416	C₂²×C₄₁	—	8	4	no	—
417	C₂²×C₄₁	—	16	4	no	—
418	C₂²×C₄₁	—	16	8	no	—
419	C₂²×C₄₁	#546	1	2	yes	—
420	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
421	C₄×C₄₁	—	2	1	no	—
422	C₄×C₄₁	—	2	1	no	—
423	C₄×C₄₁	—	2	2	no	—
424	C₄×C₄₁	—	2	4	no	—
425	C₄×C₄₁	—	2	1	no	—
426	C₄×C₄₁	—	4	1	no	—
427	C₄×C₄₁	—	4	2	no	—
428	C₄×C₄₁	—	4	2	no	—
429	C₄×C₄₁	—	4	1	no	—
430	C₄×C₄₁	—	4	2	no	—
431	C₄×C₄₁	#546	1	2	yes	—
432	C₄×C₄₁	#576	1	2	yes	—
433	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
434	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
435	#3506	C₂×C₄₁	1	1	yes	characteristic, complemented
436	#3498	C₂×C₄₁	1	1	yes	characteristic, complemented
437	#3332	C₂×C₄₁	1	2	yes	complemented
438	#3325	C₂×C₄₁	1	2	yes	complemented
439	#3318	C₂×C₄₁	1	4	yes	complemented
440	#3309	C₂×C₄₁	1	4	yes	complemented
441	#3305	C₂×C₄₁	1	2	yes	complemented
442	#3294	C₂×C₄₁	1	2	yes	complemented
443	#3138	C₂×C₄₁	1	1	yes	characteristic, complemented
444	#3096	C₂×C₄₁	1	2	yes	complemented
445	#3076	C₂×C₄₁	1	1	yes	characteristic, complemented
446	#3058	C₂×C₄₁	1	2	yes	complemented
447	C₂×#459	C₂×C₄₁	1	1	yes	characteristic, complemented
448	#3008	C₂×C₄₁	1	2	yes	complemented
449	C₄×AGL(1,ℤ/8)	C₂×C₄₁	1	1	yes	characteristic, complemented
450	#2935	C₂×C₄₁	1	1	yes	characteristic, complemented
451	#2897	C₂×C₄₁	1	2	yes	complemented
452	C₂×C₄₁	—	2	2	no	—
453	C₂×C₄₁	—	4	4	no	—
454	C₂×C₄₁	—	4	2	no	—
455	C₂×C₄₁	—	8	2	no	—
456	C₂×C₄₁	—	8	4	no	—
457	C₂×C₄₁	C₂×#546	1	1	yes	characteristic
458	C₂×C₄₁	C₂×#576	1	1	yes	characteristic
459	C₂×C₄₁	#3585	1	1	yes	characteristic
460	C₂×H(5,𝔽₂)	C₂²×C₄₁	1	2	yes	—
461	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	1	yes	characteristic
462	C₂²×D₈	C₂²×C₄₁	1	2	yes	complemented
463	C₂×#131	C₂²×C₄₁	1	2	yes	complemented
464	#559	—	2	2	no	—
465	#556	—	2	1	no	—
466	#555	C₂²×C₄₁	1	2	yes	complemented
467	#553	C₂²×C₄₁	1	4	yes	complemented
468	#550	—	2	1	no	—
469	#550	C₂²×C₄₁	1	2	yes	complemented
470	#550	C₂²×C₄₁	1	2	yes	complemented
471	#547	C₂²×C₄₁	1	2	yes	complemented
472	D₄²	—	2	2	no	—
473	D₄²	—	2	2	no	—
474	D₄²	C₂²×C₄₁	1	2	yes	complemented
475	D₄²	C₂²×C₄₁	1	2	yes	complemented
476	#538	—	2	2	no	—
477	#535	—	2	2	no	—
478	#535	C₂²×C₄₁	1	2	yes	—
479	#535	C₂²×C₄₁	1	2	yes	complemented
480	#533	C₂²×C₄₁	1	1	yes	characteristic, complemented
481	#532	—	2	1	no	—
482	#532	C₂²×C₄₁	1	1	yes	characteristic
483	C₂×#127	—	2	1	no	—
484	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
485	#525	—	2	2	no	—
486	#520	C₂²×C₄₁	1	2	yes	complemented
487	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
488	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
489	#490	C₂²×C₄₁	1	4	yes	complemented
490	#486	C₂²×C₄₁	1	2	yes	complemented
491	#486	C₂²×C₄₁	1	2	yes	complemented
492	#482	C₂²×C₄₁	1	4	yes	complemented
493	#482	C₂²×C₄₁	1	4	yes	complemented
494	#481	C₂²×C₄₁	1	4	yes	complemented
495	#480	C₂²×C₄₁	1	4	yes	complemented
496	#479	C₂²×C₄₁	1	2	yes	complemented
497	#478	C₂²×C₄₁	1	2	yes	complemented
498	#477	C₂²×C₄₁	1	1	yes	characteristic, complemented
499	#476	C₂²×C₄₁	1	1	yes	characteristic, complemented
500	#475	C₂²×C₄₁	1	1	yes	characteristic, complemented
501	#474	C₂²×C₄₁	1	1	yes	characteristic, complemented
502	#469	C₂²×C₄₁	1	4	yes	complemented
503	#469	C₂²×C₄₁	1	4	yes	complemented
504	#466	C₂²×C₄₁	1	4	yes	complemented
505	#466	C₂²×C₄₁	1	4	yes	complemented
506	#459	C₂²×C₄₁	1	2	yes	complemented
507	#459	C₂²×C₄₁	1	2	yes	complemented
508	#459	C₂²×C₄₁	1	4	yes	complemented
509	#449	C₂²×C₄₁	1	4	yes	complemented
510	#449	C₂²×C₄₁	1	4	yes	complemented
511	#447	C₂²×C₄₁	1	4	yes	complemented
512	#447	C₂²×C₄₁	1	4	yes	complemented
513	#442	C₂²×C₄₁	1	2	yes	complemented
514	#440	C₂²×C₄₁	1	2	yes	complemented
515	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
516	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
517	#436	C₂²×C₄₁	1	2	yes	complemented
518	#435	C₂²×C₄₁	1	4	yes	complemented
519	C₈×D₄	C₂²×C₄₁	1	2	yes	complemented
520	#428	C₂²×C₄₁	1	1	yes	characteristic, complemented
521	#427	C₂²×C₄₁	1	2	yes	complemented
522	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
523	#418	C₂²×C₄₁	1	2	yes	complemented
524	#418	C₂²×C₄₁	1	2	yes	complemented
525	#418	C₂²×C₄₁	1	4	yes	complemented
526	#418	C₂²×C₄₁	1	1	yes	characteristic, complemented
527	#417	C₂²×C₄₁	1	1	yes	characteristic
528	#417	C₂²×C₄₁	1	4	yes	complemented
529	#416	C₂²×C₄₁	1	2	yes	—
530	#416	C₂²×C₄₁	1	4	yes	complemented
531	C₂×#102	C₂²×C₄₁	1	2	yes	complemented
532	C₂×#102	C₂²×C₄₁	1	4	yes	complemented
533	#408	C₂²×C₄₁	1	2	yes	complemented
534	C₄×M₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
535	C₄₁	#61205	1	1	yes	characteristic, direct product factor, Sylow
536	H(5,𝔽₂)	—	2	8	no	—
537	H(5,𝔽₂)	—	4	4	no	—
538	C₂×#41	—	2	2	no	—
539	C₂×#41	—	2	2	no	—
540	C₂×#41	C₂³×C₄₁	1	4	yes	—
541	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
542	C₂×#41	C₂³×C₄₁	1	2	yes	—
543	C₂²×D₄	—	2	2	no	—
544	C₂²×D₄	—	2	4	no	—
545	C₂²×D₄	—	2	2	no	—
546	C₂²×D₄	—	2	2	no	—
547	C₂²×D₄	—	2	1	no	—
548	C₂²×D₄	—	2	1	no	—
549	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
550	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
551	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
552	C₂³×C₄	—	2	1	no	—
553	AGL(1,ℤ/8)	—	2	4	no	—
554	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
555	C₂×D₈	—	4	4	no	—
556	C₂×D₈	C₂³×C₄₁	1	2	yes	—
557	C₂×D₈	C₂³×C₄₁	1	4	yes	—
558	C₂×D₈	C₂³×C₄₁	1	4	yes	—
559	#131	—	4	4	no	—
560	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
561	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
562	C₂×M₁₆	C₂³×C₄₁	1	4	yes	—
563	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
564	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
565	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
566	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
567	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
568	#127	—	2	2	no	—
569	#127	—	2	2	no	—
570	#127	—	2	2	no	—
571	#127	—	2	2	no	—
572	#127	—	2	1	no	—
573	#127	—	2	1	no	—
574	#127	D₄×C₄₁	1	1	yes	characteristic
575	#127	C₂³×C₄₁	1	2	yes	—
576	#127	C₂³×C₄₁	1	2	yes	—
577	#126	—	2	4	no	—
578	#125	C₂³×C₄₁	1	2	yes	—
579	#124	—	2	2	no	—
580	#124	—	2	2	no	—
581	#124	—	2	4	no	—
582	#124	D₄×C₄₁	1	2	yes	—
583	#123	—	2	4	no	—
584	#123	—	2	4	no	—
585	C₂²⋊Q₈	—	2	1	no	—
586	C₂²⋊Q₈	—	2	1	no	—
587	C₂²⋊Q₈	—	2	2	no	—
588	#121	—	2	2	no	—
589	#121	—	2	4	no	—
590	#121	—	2	2	no	—
591	#121	—	2	2	no	—
592	#121	—	2	4	no	—
593	#121	—	2	4	no	—
594	#121	D₄×C₄₁	1	2	yes	—
595	#121	D₄×C₄₁	1	2	yes	—
596	#121	C₂³×C₄₁	1	4	yes	—
597	#121	C₂³×C₄₁	1	4	yes	—
598	#121	C₂³×C₄₁	1	4	yes	—
599	#121	C₂³×C₄₁	1	4	yes	—
600	#120	—	2	4	no	—
601	#120	—	2	4	no	—
602	#120	—	2	4	no	—
603	#120	—	2	4	no	—
604	C₄×Q₈	—	2	2	no	—
605	C₄×Q₈	—	2	1	no	—
606	C₄×Q₈	—	2	1	no	—
607	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
608	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
609	C₄×D₄	—	2	4	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	4	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	C₂³×C₄₁	1	2	yes	—
619	C₄×D₄	C₂³×C₄₁	1	2	yes	—
620	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
621	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
622	C₄×D₄	C₂³×C₄₁	1	2	yes	—
623	C₄×D₄	C₂³×C₄₁	1	2	yes	—
624	#117	—	2	2	no	—
625	#117	—	2	1	no	—
626	#117	C₂³×C₄₁	1	1	yes	characteristic
627	#117	C₂³×C₄₁	1	2	yes	—
628	#117	C₂³×C₄₁	1	4	yes	—
629	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₄²	—	2	1	no	—
633	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
634	#107	C₂³×C₄₁	1	2	yes	—
635	#107	C₂³×C₄₁	1	2	yes	—
636	#107	C₂³×C₄₁	1	2	yes	—
637	#106	C₂³×C₄₁	1	2	yes	—
638	#106	C₂³×C₄₁	1	2	yes	—
639	#106	C₂³×C₄₁	1	2	yes	—
640	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
641	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
642	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
643	#103	C₂³×C₄₁	1	2	yes	—
644	#103	C₂³×C₄₁	1	2	yes	—
645	#103	C₂³×C₄₁	1	2	yes	—
646	#102	C₂³×C₄₁	1	2	yes	—
647	#102	C₂³×C₄₁	1	4	yes	—
648	#102	C₂³×C₄₁	1	2	yes	—
649	#102	C₂³×C₄₁	1	4	yes	—
650	#102	C₂³×C₄₁	1	4	yes	—
651	#102	C₂³×C₄₁	1	2	yes	—
652	#102	C₂³×C₄₁	1	4	yes	—
653	#102	C₂³×C₄₁	1	2	yes	—
654	#102	C₂³×C₄₁	1	2	yes	—
655	#102	C₂³×C₄₁	1	4	yes	—
656	#102	C₂³×C₄₁	1	4	yes	—
657	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
658	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
659	#97	C₂³×C₄₁	1	2	yes	—
660	C₄×C₈	C₂³×C₄₁	1	2	yes	—
661	C₂⁴	—	2	1	no	—
662	C₂⁴	—	2	4	no	—
663	C₂⁴	—	2	2	no	—
664	#41	—	2	4	no	—
665	#41	—	2	4	no	—
666	#41	—	2	2	no	—
667	#41	—	2	8	no	—
668	#41	—	4	4	no	—
669	#41	—	4	8	no	—
670	#41	—	8	4	no	—
671	#41	#41×C₄₁	1	4	yes	complemented
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
675	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	8	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	4	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	4	no	—
694	C₂×D₄	—	4	4	no	—
695	C₂×D₄	—	4	8	no	—
696	C₂×D₄	—	4	16	no	—
697	C₂×D₄	—	8	2	no	—
698	C₂×D₄	—	8	4	no	—
699	C₂×D₄	—	8	2	no	—
700	C₂×D₄	—	8	4	no	—
701	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
702	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
703	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
704	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
705	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
706	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
707	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	4	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	8	2	no	—
717	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
718	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
720	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
721	SD₁₆	—	2	4	no	—
722	D₈	—	2	4	no	—
723	D₈	—	4	4	no	—
724	D₈	—	4	4	no	—
725	M₁₆	—	2	2	no	—
726	M₁₆	—	2	2	no	—
727	M₁₆	—	4	4	no	—
728	C₂×C₈	—	2	4	no	—
729	C₂×C₈	—	4	4	no	—
730	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
731	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
732	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
733	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
743	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
744	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
745	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
746	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
747	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
748	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
749	C₂²⋊C₄	—	2	1	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	1	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
761	C₂²⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
762	C₄²	—	2	1	no	—
763	C₄²	—	2	1	no	—
764	C₄²	—	2	1	no	—
765	C₄²	—	2	4	no	—
766	C₄²	—	2	2	no	—
767	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
768	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
769	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
770	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
771	C₂³	—	2	1	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	4	no	—
774	C₂³	—	4	8	no	—
775	C₂³	—	4	2	no	—
776	C₂³	—	4	4	no	—
777	C₂³	—	8	1	no	—
778	C₂³	—	8	1	no	—
779	C₂³	—	8	2	no	—
780	C₂³	—	8	2	no	—
781	C₂³	—	8	4	no	—
782	C₂³	—	8	4	no	—
783	C₂³	C₂²×D₄×C₄₁	1	4	yes	—
784	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
785	Q₈	—	2	4	no	—
786	Q₈	—	2	1	no	—
787	Q₈	—	4	2	no	—
788	Q₈	—	8	1	no	—
789	Q₈	C₂×#41×C₄₁	1	2	yes	—
790	D₄	—	2	4	no	—
791	D₄	—	2	8	no	—
792	D₄	—	2	4	no	—
793	D₄	—	2	4	no	—
794	D₄	—	2	2	no	—
795	D₄	—	2	4	no	—
796	D₄	—	2	1	no	—
797	D₄	—	2	2	no	—
798	D₄	—	2	4	no	—
799	D₄	—	4	2	no	—
800	D₄	—	4	8	no	—
801	D₄	—	4	8	no	—
802	D₄	—	4	4	no	—
803	D₄	—	4	4	no	—
804	D₄	—	4	2	no	—
805	D₄	—	4	4	no	—
806	D₄	—	8	2	no	—
807	D₄	—	8	2	no	—
808	D₄	—	8	4	no	—
809	D₄	—	8	4	no	—
810	D₄	—	8	4	no	—
811	D₄	—	8	4	no	—
812	D₄	C₂×#41×C₄₁	1	2	yes	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	4	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	4	no	—
817	C₂×C₄	—	2	4	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	8	no	—
825	C₂×C₄	—	4	2	no	—
826	C₂×C₄	—	4	4	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	8	2	no	—
829	C₂×C₄	—	8	1	no	—
830	C₂×C₄	—	8	4	no	—
831	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
832	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
833	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
834	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
835	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
836	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
837	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
838	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
839	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
840	C₈	—	2	2	no	—
841	C₈	—	2	2	no	—
842	C₈	—	2	2	no	—
843	C₈	—	2	2	no	—
844	C₂²	—	2	1	no	—
845	C₂²	—	2	1	no	—
846	C₂²	—	2	4	no	—
847	C₂²	—	2	4	no	—
848	C₂²	—	2	4	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	4	1	no	—
851	C₂²	—	4	1	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	4	4	no	—
854	C₂²	—	4	4	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	4	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	8	4	no	—
859	C₂²	—	16	4	no	—
860	C₂²	—	16	8	no	—
861	C₂²	C₄₁×#546	1	2	yes	—
862	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
863	C₄	—	2	1	no	—
864	C₄	—	2	1	no	—
865	C₄	—	2	1	no	—
866	C₄	—	2	2	no	—
867	C₄	—	2	4	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	1	no	—
870	C₄	—	4	2	no	—
871	C₄	—	4	1	no	—
872	C₄	—	4	2	no	—
873	C₄	C₄₁×#546	1	2	yes	—
874	C₄	C₄₁×#576	1	2	yes	—
875	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
876	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
877	C₂	—	2	2	no	—
878	C₂	—	4	4	no	—
879	C₂	—	4	2	no	—
880	C₂	—	8	2	no	—
881	C₂	—	8	4	no	—
882	C₂	C₂×C₄₁×#546	1	1	yes	characteristic
883	C₂	C₂×C₄₁×#576	1	1	yes	characteristic
884	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 ◁ C₄₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3506	C₂	semidirect
2. C₄₁×#3498	C₂	semidirect
3. C₄₁×#3332	C₂	semidirect
4. C₄₁×#3325	C₂	semidirect
5. C₄₁×#3318	C₂	semidirect
6. C₄₁×#3309	C₂	semidirect
7. C₄₁×#3305	C₂	semidirect
8. C₄₁×#3294	C₂	semidirect
9. C₄₁×#3138	C₂	semidirect
10. C₄₁×#3096	C₂	semidirect
11. C₄₁×#3076	C₂	semidirect
12. C₄₁×#3058	C₂	semidirect
13. C₂×C₄₁×#459	C₂	semidirect
14. C₄₁×#3008	C₂	semidirect
15. C₄×AGL(1,ℤ/8)×C₄₁	C₂	semidirect
16. C₄₁×#2935	C₂	semidirect
17. C₄₁×#2897	C₂	semidirect
20. C₂²×D₈×C₄₁	C₂²	semidirect
21. C₂×#131×C₄₁	C₂²	semidirect
24. C₄₁×#555	C₂²	semidirect
25. C₄₁×#553	C₂²	semidirect
27. C₄₁×#550	C₂²	semidirect
28. C₄₁×#550	C₂²	semidirect
29. C₄₁×#547	C₂²	semidirect
32. D₄²×C₄₁	C₂²	semidirect
33. D₄²×C₄₁	C₂²	semidirect
37. C₄₁×#535	C₂²	semidirect
38. C₄₁×#533	C₂²	semidirect
44. C₄₁×#520	C₂²	semidirect
46. C₂×C₄×D₄×C₄₁	C₂²	semidirect
47. C₄₁×#490	C₂²	semidirect
48. C₄₁×#486	C₂²	semidirect
49. C₄₁×#486	C₂²	semidirect
50. C₄₁×#482	C₂²	semidirect
51. C₄₁×#482	C₂²	semidirect
52. C₄₁×#481	C₂²	semidirect
53. C₄₁×#480	C₂²	semidirect
54. C₄₁×#479	C₂²	semidirect
55. C₄₁×#478	C₂²	semidirect
56. C₄₁×#477	C₂²	semidirect
57. C₄₁×#476	C₂²	semidirect
58. C₄₁×#475	C₂²	semidirect
59. C₄₁×#474	C₂²	semidirect
60. C₄₁×#469	C₂²	semidirect
61. C₄₁×#469	C₂²	semidirect
62. C₄₁×#466	C₂²	semidirect
63. C₄₁×#466	C₂²	semidirect
64. C₄₁×#459	C₂²	semidirect
65. C₄₁×#459	C₂²	semidirect
66. C₄₁×#459	C₂²	semidirect
67. C₄₁×#449	C₂²	semidirect
68. C₄₁×#449	C₂²	semidirect
69. C₄₁×#447	C₂²	semidirect
70. C₄₁×#447	C₂²	semidirect
71. C₄₁×#442	C₂²	semidirect
72. C₄₁×#440	C₂²	semidirect
73. C₄×SD₁₆×C₄₁	C₂²	semidirect
74. C₄×D₈×C₄₁	C₂²	semidirect
75. C₄₁×#436	C₂²	semidirect
76. C₄₁×#435	C₂²	semidirect
77. C₈×D₄×C₄₁	C₂²	semidirect
78. C₄₁×#428	C₂²	semidirect
79. C₄₁×#427	C₂²	semidirect
80. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
81. C₄₁×#418	C₂²	semidirect
82. C₄₁×#418	C₂²	semidirect
83. C₄₁×#418	C₂²	semidirect
84. C₄₁×#418	C₂²	semidirect
86. C₄₁×#417	C₂²	semidirect
88. C₄₁×#416	C₂²	semidirect
89. C₂×#102×C₄₁	C₂²	semidirect
90. C₂×#102×C₄₁	C₂²	semidirect
91. C₄₁×#408	C₂²	semidirect
92. C₄×M₁₆×C₄₁	C₂²	semidirect
228. #41×C₄₁	#41	semidirect
401. #61205	C₄₁	direct (N × H)
435. #3506	C₂×C₄₁	semidirect
436. #3498	C₂×C₄₁	semidirect
437. #3332	C₂×C₄₁	semidirect
438. #3325	C₂×C₄₁	semidirect
439. #3318	C₂×C₄₁	semidirect
440. #3309	C₂×C₄₁	semidirect
441. #3305	C₂×C₄₁	semidirect
442. #3294	C₂×C₄₁	semidirect
443. #3138	C₂×C₄₁	semidirect
444. #3096	C₂×C₄₁	semidirect
445. #3076	C₂×C₄₁	semidirect
446. #3058	C₂×C₄₁	semidirect
447. C₂×#459	C₂×C₄₁	semidirect
448. #3008	C₂×C₄₁	semidirect
449. C₄×AGL(1,ℤ/8)	C₂×C₄₁	semidirect
450. #2935	C₂×C₄₁	semidirect
451. #2897	C₂×C₄₁	semidirect
462. C₂²×D₈	C₂²×C₄₁	semidirect
463. C₂×#131	C₂²×C₄₁	semidirect
466. #555	C₂²×C₄₁	semidirect
467. #553	C₂²×C₄₁	semidirect
469. #550	C₂²×C₄₁	semidirect
470. #550	C₂²×C₄₁	semidirect
471. #547	C₂²×C₄₁	semidirect
474. D₄²	C₂²×C₄₁	semidirect
475. D₄²	C₂²×C₄₁	semidirect
479. #535	C₂²×C₄₁	semidirect
480. #533	C₂²×C₄₁	semidirect
486. #520	C₂²×C₄₁	semidirect
488. C₂×C₄×D₄	C₂²×C₄₁	semidirect
489. #490	C₂²×C₄₁	semidirect
490. #486	C₂²×C₄₁	semidirect
491. #486	C₂²×C₄₁	semidirect
492. #482	C₂²×C₄₁	semidirect
493. #482	C₂²×C₄₁	semidirect
494. #481	C₂²×C₄₁	semidirect
495. #480	C₂²×C₄₁	semidirect
496. #479	C₂²×C₄₁	semidirect
497. #478	C₂²×C₄₁	semidirect
498. #477	C₂²×C₄₁	semidirect
499. #476	C₂²×C₄₁	semidirect
500. #475	C₂²×C₄₁	semidirect
501. #474	C₂²×C₄₁	semidirect
502. #469	C₂²×C₄₁	semidirect
503. #469	C₂²×C₄₁	semidirect
504. #466	C₂²×C₄₁	semidirect
505. #466	C₂²×C₄₁	semidirect
506. #459	C₂²×C₄₁	semidirect
507. #459	C₂²×C₄₁	semidirect
508. #459	C₂²×C₄₁	semidirect
509. #449	C₂²×C₄₁	semidirect
510. #449	C₂²×C₄₁	semidirect
511. #447	C₂²×C₄₁	semidirect
512. #447	C₂²×C₄₁	semidirect
513. #442	C₂²×C₄₁	semidirect
514. #440	C₂²×C₄₁	semidirect
515. C₄×SD₁₆	C₂²×C₄₁	semidirect
516. C₄×D₈	C₂²×C₄₁	semidirect
517. #436	C₂²×C₄₁	semidirect
518. #435	C₂²×C₄₁	semidirect
519. C₈×D₄	C₂²×C₄₁	semidirect
520. #428	C₂²×C₄₁	semidirect
521. #427	C₂²×C₄₁	semidirect
522. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
523. #418	C₂²×C₄₁	semidirect
524. #418	C₂²×C₄₁	semidirect
525. #418	C₂²×C₄₁	semidirect
526. #418	C₂²×C₄₁	semidirect
528. #417	C₂²×C₄₁	semidirect
530. #416	C₂²×C₄₁	semidirect
531. C₂×#102	C₂²×C₄₁	semidirect
532. C₂×#102	C₂²×C₄₁	semidirect
533. #408	C₂²×C₄₁	semidirect
534. C₄×M₁₆	C₂²×C₄₁	semidirect
535. C₄₁	#61205	direct (N × H)
671. #41	#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×#3506	2
C₄₁×#3498	2
C₄₁×#3332	2
C₄₁×#3325	2
C₄₁×#3318	2
C₄₁×#3309	2
C₄₁×#3305	2
C₄₁×#3294	2
C₄₁×#3138	2
C₄₁×#3096	2
C₄₁×#3076	2
C₄₁×#3058	2
C₂×C₄₁×#459	2
C₄₁×#3008	2
C₄×AGL(1,ℤ/8)×C₄₁	2
C₄₁×#2935	2
C₄₁×#2897	2
#61205	41

Subgroups — C41×#61205 #23837406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61205 #23837406