Subgroups — C₄₁×#61347 #23837548

Order 10496.

1846 conjugacy classes of subgroups.

The subgroup lattice has 824 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×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3373	C₂	1	4	yes	maximal, complemented
4	C₄₁×#3371	C₂	1	4	yes	maximal, complemented
5	C₄₁×#3369	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3366	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3362	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3360	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#3136	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3084	C₂	1	2	yes	maximal, complemented
12	C₂×C₄₁×#476	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3045	C₂	1	2	yes	maximal, complemented
14	C₄₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#2952	C₂	1	2	yes	maximal, complemented
17	C₄×AGL(1,ℤ/8)×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×#135×C₄₁	C₂²	1	2	yes	—
20	C₄₁×#559	C₂²	1	4	yes	—
21	Q₈²×C₄₁	C₂²	1	2	yes	complemented
22	C₄₁×#557	C₂²	1	2	yes	complemented
23	C₄₁×#556	C₂²	1	2	yes	—
24	C₄₁×#555	—	2	1	no	—
25	C₄₁×#554	—	2	2	no	—
26	C₄₁×#554	C₂²	1	2	yes	complemented
27	C₄₁×#553	—	2	2	no	—
28	C₄₁×#550	C₂²	1	2	yes	—
29	D₄×Q₈×C₄₁	—	2	2	no	—
30	D₄×Q₈×C₄₁	C₂²	1	2	yes	complemented
31	C₄₁×#547	—	2	1	no	—
32	C₄₁×#544	—	2	2	no	—
33	C₄₁×#544	C₂²	1	2	yes	—
34	C₄₁×#538	—	2	2	no	—
35	C₄₁×#535	C₂²	1	2	yes	—
36	C₄₁×#533	—	2	1	no	—
37	C₄₁×#533	C₂²	1	1	yes	characteristic
38	C₄₁×#532	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊Q₈×C₄₁	—	2	1	no	—
40	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
41	C₄₁×#525	—	2	2	no	—
42	C₄₁×#520	C₂²	1	2	yes	—
43	C₄₁×#520	C₂²	1	2	yes	—
44	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
46	C₄₁×#490	C₂²	1	4	yes	—
47	C₄₁×#489	C₂²	1	4	yes	—
48	C₄₁×#489	C₂²	1	4	yes	complemented
49	C₄₁×#488	C₂²	1	4	yes	—
50	C₄₁×#487	C₂²	1	2	yes	complemented
51	C₄₁×#486	C₂²	1	4	yes	—
52	C₄₁×#486	C₂²	1	2	yes	complemented
53	C₄₁×#479	C₂²	1	4	yes	complemented
54	C₄₁×#478	C₂²	1	4	yes	complemented
55	C₄₁×#476	C₂²	1	2	yes	—
56	C₄₁×#476	C₂²	1	2	yes	—
57	C₄₁×#476	C₂²	1	4	yes	—
58	C₄₁×#476	C₂²	1	4	yes	complemented
59	C₄₁×#475	C₂²	1	4	yes	complemented
60	C₄₁×#464	C₂²	1	4	yes	—
61	C₄₁×#464	C₂²	1	2	yes	complemented
62	C₄₁×#463	C₂²	1	4	yes	—
63	C₄₁×#463	C₂²	1	2	yes	complemented
64	C₄₁×#462	C₂²	1	1	yes	characteristic, complemented
65	C₄₁×#461	C₂²	1	1	yes	characteristic, complemented
66	C₄₁×#460	C₂²	1	4	yes	—
67	C₄₁×#460	C₂²	1	1	yes	characteristic, complemented
68	C₄₁×#459	C₂²	1	4	yes	—
69	C₄₁×#459	C₂²	1	1	yes	characteristic, complemented
70	C₄₁×#446	C₂²	1	2	yes	complemented
71	C₄₁×#446	C₂²	1	4	yes	complemented
72	C₈×Q₈×C₄₁	C₂²	1	2	yes	complemented
73	C₄₁×#442	C₂²	1	2	yes	—
74	C₄₁×#442	C₂²	1	4	yes	complemented
75	C₄₁×#441	C₂²	1	4	yes	complemented
76	C₄₁×#440	C₂²	1	2	yes	—
77	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
78	C₄×SD₁₆×C₄₁	C₂²	1	4	yes	complemented
79	C₄×SD₁₆×C₄₁	C₂²	1	4	yes	complemented
80	C₄×D₈×C₄₁	C₂²	1	2	yes	—
81	C₄₁×#428	C₂²	1	1	yes	characteristic
82	C₂×#106×C₄₁	C₂²	1	2	yes	—
83	C₄₁×#424	C₂²	1	2	yes	—
84	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
85	C₄₁×#418	C₂²	1	1	yes	characteristic
86	C₄₁×#417	C₂²	1	2	yes	—
87	C₄₁×#417	C₂²	1	2	yes	—
88	C₄₁×#417	C₂²	1	1	yes	characteristic
89	C₄₁×#416	C₂²	1	2	yes	—
90	C₂×#102×C₄₁	C₂²	1	2	yes	—
91	C₄₁×#405	C₂²	1	2	yes	—
92	C₄×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
93	C₂×#41×C₄₁	—	2	2	no	—
94	C₂×#41×C₄₁	C₂³	1	2	yes	—
95	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₄₁	—	2	2	no	—
97	C₂²×Q₈×C₄₁	—	2	1	no	—
98	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₄₁	—	2	1	no	—
100	AGL(1,ℤ/8)×C₄₁	—	2	4	no	—
101	#135×C₄₁	—	2	8	no	—
102	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
105	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
106	C₂×D₈×C₄₁	C₂³	1	2	yes	—
107	C₂×D₈×C₄₁	C₂³	1	2	yes	—
108	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
109	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
111	C₄⋊Q₈×C₄₁	—	2	2	no	—
112	C₄⋊Q₈×C₄₁	—	2	2	no	—
113	C₄⋊Q₈×C₄₁	—	2	2	no	—
114	C₄⋊Q₈×C₄₁	—	2	4	no	—
115	C₄⋊Q₈×C₄₁	—	2	1	no	—
116	C₄⋊Q₈×C₄₁	—	2	1	no	—
117	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
118	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
119	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
120	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
121	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
122	C₄⋊Q₈×C₄₁	C₂³	1	4	yes	—
123	#127×C₄₁	C₂³	1	1	yes	characteristic
124	#127×C₄₁	C₂³	1	4	yes	—
125	#126×C₄₁	—	2	4	no	—
126	#125×C₄₁	—	2	2	no	—
127	#125×C₄₁	—	2	4	no	—
128	#125×C₄₁	D₄	1	2	yes	—
129	#125×C₄₁	C₂³	1	4	yes	—
130	#124×C₄₁	—	2	4	no	—
131	#124×C₄₁	C₂³	1	2	yes	—
132	#124×C₄₁	C₂³	1	4	yes	—
133	#123×C₄₁	—	2	4	no	—
134	#123×C₄₁	—	2	4	no	—
135	C₂²⋊Q₈×C₄₁	—	2	2	no	—
136	C₂²⋊Q₈×C₄₁	—	2	2	no	—
137	C₂²⋊Q₈×C₄₁	—	2	2	no	—
138	C₂²⋊Q₈×C₄₁	—	2	4	no	—
139	C₂²⋊Q₈×C₄₁	—	2	4	no	—
140	C₂²⋊Q₈×C₄₁	—	2	4	no	—
141	C₂²⋊Q₈×C₄₁	D₄	1	2	yes	—
142	C₂²⋊Q₈×C₄₁	D₄	1	2	yes	—
143	#121×C₄₁	—	2	1	no	—
144	#121×C₄₁	—	2	1	no	—
145	#121×C₄₁	—	2	2	no	—
146	#121×C₄₁	—	2	2	no	—
147	#121×C₄₁	—	2	2	no	—
148	#121×C₄₁	—	2	4	no	—
149	#120×C₄₁	—	2	4	no	—
150	C₄×Q₈×C₄₁	—	2	2	no	—
151	C₄×Q₈×C₄₁	—	2	2	no	—
152	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
153	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
154	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
155	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
156	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
157	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
158	C₄×D₄×C₄₁	—	2	1	no	—
159	C₄×D₄×C₄₁	—	2	1	no	—
160	C₄×D₄×C₄₁	—	2	4	no	—
161	C₄×D₄×C₄₁	—	2	4	no	—
162	C₄×D₄×C₄₁	—	2	4	no	—
163	C₄×D₄×C₄₁	—	2	1	no	—
164	C₄×D₄×C₄₁	—	2	1	no	—
165	C₄×D₄×C₄₁	—	2	1	no	—
166	C₄×D₄×C₄₁	—	2	1	no	—
167	C₄×D₄×C₄₁	C₂³	1	2	yes	—
168	C₄×D₄×C₄₁	C₂³	1	2	yes	—
169	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
170	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
171	C₄×D₄×C₄₁	C₂³	1	4	yes	—
172	C₄×D₄×C₄₁	C₂³	1	4	yes	—
173	#117×C₄₁	—	2	2	no	—
174	#117×C₄₁	—	2	2	no	—
175	#117×C₄₁	—	2	2	no	—
176	#117×C₄₁	—	2	1	no	—
177	#117×C₄₁	C₂³	1	1	yes	characteristic
178	#117×C₄₁	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
180	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
181	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
182	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
183	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
186	C₂×C₄²×C₄₁	—	2	1	no	—
187	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
188	#107×C₄₁	C₂³	1	2	yes	—
189	#106×C₄₁	C₂³	1	4	yes	—
190	#106×C₄₁	C₂³	1	4	yes	—
191	#106×C₄₁	C₂³	1	2	yes	—
192	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
193	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
194	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
195	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
196	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
197	#103×C₄₁	C₂³	1	2	yes	—
198	#103×C₄₁	C₂³	1	2	yes	—
199	#103×C₄₁	C₂³	1	2	yes	—
200	#103×C₄₁	C₂³	1	4	yes	—
201	#103×C₄₁	C₂³	1	4	yes	—
202	#102×C₄₁	C₂³	1	4	yes	—
203	#102×C₄₁	C₂³	1	4	yes	—
204	#102×C₄₁	C₂³	1	2	yes	—
205	#102×C₄₁	C₂³	1	2	yes	—
206	#102×C₄₁	C₂³	1	2	yes	—
207	#102×C₄₁	C₂³	1	4	yes	—
208	#102×C₄₁	C₂³	1	4	yes	—
209	#102×C₄₁	C₂³	1	2	yes	—
210	#102×C₄₁	C₂³	1	2	yes	—
211	#97×C₄₁	C₂³	1	2	yes	—
212	#97×C₄₁	C₂³	1	4	yes	—
213	C₄×C₈×C₄₁	C₂³	1	2	yes	—
214	C₄×C₈×C₄₁	C₂³	1	4	yes	—
215	C₂⁴×C₄₁	—	2	1	no	—
216	#41×C₄₁	—	2	2	no	—
217	#41×C₄₁	—	2	4	no	—
218	#41×C₄₁	—	2	4	no	—
219	#41×C₄₁	—	8	4	no	—
220	#41×C₄₁	#41	1	4	yes	complemented
221	C₂×Q₈×C₄₁	—	2	2	no	—
222	C₂×Q₈×C₄₁	—	2	4	no	—
223	C₂×Q₈×C₄₁	—	2	2	no	—
224	C₂×Q₈×C₄₁	—	8	2	no	—
225	C₂×Q₈×C₄₁	—	8	4	no	—
226	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
229	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
230	C₂×D₄×C₄₁	—	2	1	no	—
231	C₂×D₄×C₄₁	—	2	2	no	—
232	C₂×D₄×C₄₁	—	2	1	no	—
233	C₂×D₄×C₄₁	—	2	1	no	—
234	C₂×D₄×C₄₁	—	2	4	no	—
235	C₂×D₄×C₄₁	—	2	1	no	—
236	C₂×D₄×C₄₁	—	2	4	no	—
237	C₂×D₄×C₄₁	—	2	2	no	—
238	C₂×D₄×C₄₁	—	2	2	no	—
239	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
240	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
241	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₄₁	—	2	1	no	—
243	C₂²×C₄×C₄₁	—	2	1	no	—
244	C₂²×C₄×C₄₁	—	2	2	no	—
245	C₂²×C₄×C₄₁	—	2	1	no	—
246	C₂²×C₄×C₄₁	—	2	1	no	—
247	C₂²×C₄×C₄₁	—	2	2	no	—
248	C₂²×C₄×C₄₁	—	2	2	no	—
249	C₂²×C₄×C₄₁	—	2	4	no	—
250	C₂²×C₄×C₄₁	—	2	4	no	—
251	C₂²×C₄×C₄₁	—	2	2	no	—
252	C₂²×C₄×C₄₁	—	8	2	no	—
253	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
256	Q₁₆×C₄₁	—	2	4	no	—
257	SD₁₆×C₄₁	—	2	4	no	—
258	SD₁₆×C₄₁	—	2	4	no	—
259	SD₁₆×C₄₁	—	2	4	no	—
260	D₈×C₄₁	—	2	4	no	—
261	D₈×C₄₁	—	2	4	no	—
262	M₁₆×C₄₁	—	2	2	no	—
263	M₁₆×C₄₁	—	2	2	no	—
264	C₂×C₈×C₄₁	—	2	4	no	—
265	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
266	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
267	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
268	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
269	C₄⋊C₄×C₄₁	—	2	1	no	—
270	C₄⋊C₄×C₄₁	—	2	2	no	—
271	C₄⋊C₄×C₄₁	—	2	2	no	—
272	C₄⋊C₄×C₄₁	—	2	4	no	—
273	C₄⋊C₄×C₄₁	—	2	4	no	—
274	C₄⋊C₄×C₄₁	—	2	2	no	—
275	C₄⋊C₄×C₄₁	—	2	4	no	—
276	C₄⋊C₄×C₄₁	—	2	1	no	—
277	C₄⋊C₄×C₄₁	—	2	1	no	—
278	C₄⋊C₄×C₄₁	—	2	1	no	—
279	C₄⋊C₄×C₄₁	—	2	1	no	—
280	C₄⋊C₄×C₄₁	—	2	4	no	—
281	C₄⋊C₄×C₄₁	—	2	4	no	—
282	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
283	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
284	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
285	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
286	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
287	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
288	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
289	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
290	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
291	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
292	C₂²⋊C₄×C₄₁	—	2	1	no	—
293	C₂²⋊C₄×C₄₁	—	2	2	no	—
294	C₂²⋊C₄×C₄₁	—	2	2	no	—
295	C₂²⋊C₄×C₄₁	—	2	4	no	—
296	C₂²⋊C₄×C₄₁	—	2	1	no	—
297	C₂²⋊C₄×C₄₁	—	2	1	no	—
298	C₂²⋊C₄×C₄₁	—	2	4	no	—
299	C₂²⋊C₄×C₄₁	—	2	4	no	—
300	C₂²⋊C₄×C₄₁	—	2	2	no	—
301	C₂²⋊C₄×C₄₁	—	2	4	no	—
302	C₂²⋊C₄×C₄₁	—	2	2	no	—
303	C₂²⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
304	C₄²×C₄₁	—	2	1	no	—
305	C₄²×C₄₁	—	2	1	no	—
306	C₄²×C₄₁	—	2	1	no	—
307	C₄²×C₄₁	—	2	4	no	—
308	C₄²×C₄₁	—	2	4	no	—
309	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
312	C₄²×C₄₁	C₂⁴	1	4	yes	—
313	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
314	C₂³×C₄₁	—	2	1	no	—
315	C₂³×C₄₁	—	2	2	no	—
316	C₂³×C₄₁	—	2	2	no	—
317	C₂³×C₄₁	—	4	2	no	—
318	C₂³×C₄₁	—	8	1	no	—
319	C₂³×C₄₁	—	8	1	no	—
320	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
321	Q₈×C₄₁	—	2	4	no	—
322	Q₈×C₄₁	—	2	1	no	—
323	Q₈×C₄₁	—	2	2	no	—
324	Q₈×C₄₁	—	2	2	no	—
325	Q₈×C₄₁	—	4	2	no	—
326	Q₈×C₄₁	—	4	4	no	—
327	Q₈×C₄₁	—	8	2	no	—
328	Q₈×C₄₁	—	8	4	no	—
329	Q₈×C₄₁	C₂×#41	1	2	yes	—
330	D₄×C₄₁	—	2	4	no	—
331	D₄×C₄₁	—	2	2	no	—
332	D₄×C₄₁	—	2	2	no	—
333	D₄×C₄₁	—	2	1	no	—
334	D₄×C₄₁	—	2	2	no	—
335	D₄×C₄₁	—	2	2	no	—
336	D₄×C₄₁	—	4	4	no	—
337	D₄×C₄₁	—	4	2	no	—
338	D₄×C₄₁	—	4	2	no	—
339	D₄×C₄₁	—	8	1	no	—
340	D₄×C₄₁	—	8	4	no	—
341	D₄×C₄₁	—	8	4	no	—
342	D₄×C₄₁	C₂×#41	1	2	yes	—
343	C₂×C₄×C₄₁	—	2	1	no	—
344	C₂×C₄×C₄₁	—	2	4	no	—
345	C₂×C₄×C₄₁	—	2	2	no	—
346	C₂×C₄×C₄₁	—	2	2	no	—
347	C₂×C₄×C₄₁	—	2	2	no	—
348	C₂×C₄×C₄₁	—	2	1	no	—
349	C₂×C₄×C₄₁	—	2	1	no	—
350	C₂×C₄×C₄₁	—	2	4	no	—
351	C₂×C₄×C₄₁	—	4	1	no	—
352	C₂×C₄×C₄₁	—	4	2	no	—
353	C₂×C₄×C₄₁	—	4	4	no	—
354	C₂×C₄×C₄₁	—	4	2	no	—
355	C₂×C₄×C₄₁	—	4	4	no	—
356	C₂×C₄×C₄₁	—	8	2	no	—
357	C₂×C₄×C₄₁	—	8	4	no	—
358	C₂×C₄×C₄₁	—	8	4	no	—
359	C₂×C₄×C₄₁	—	8	1	no	—
360	C₂×C₄×C₄₁	—	8	2	no	—
361	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
363	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
364	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
369	C₂×C₄×C₄₁	2₋¹⁺⁴	1	2	yes	—
370	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
371	C₈×C₄₁	—	2	2	no	—
372	C₈×C₄₁	—	2	2	no	—
373	C₈×C₄₁	—	2	2	no	—
374	C₈×C₄₁	—	2	2	no	—
375	#61347	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
376	C₂²×C₄₁	—	2	1	no	—
377	C₂²×C₄₁	—	2	1	no	—
378	C₂²×C₄₁	—	2	2	no	—
379	C₂²×C₄₁	—	4	1	no	—
380	C₂²×C₄₁	—	4	1	no	—
381	C₂²×C₄₁	—	4	2	no	—
382	C₂²×C₄₁	—	4	2	no	—
383	C₂²×C₄₁	—	4	2	no	—
384	C₂²×C₄₁	—	4	2	no	—
385	C₂²×C₄₁	—	4	2	no	—
386	C₂²×C₄₁	—	4	2	no	—
387	C₂²×C₄₁	—	8	4	no	—
388	C₂²×C₄₁	#548	1	2	yes	—
389	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
390	C₄×C₄₁	—	2	1	no	—
391	C₄×C₄₁	—	2	1	no	—
392	C₄×C₄₁	—	2	4	no	—
393	C₄×C₄₁	—	2	2	no	—
394	C₄×C₄₁	—	2	1	no	—
395	C₄×C₄₁	—	2	4	no	—
396	C₄×C₄₁	—	4	1	no	—
397	C₄×C₄₁	—	4	4	no	—
398	C₄×C₄₁	—	4	2	no	—
399	C₄×C₄₁	—	4	1	no	—
400	C₄×C₄₁	—	4	2	no	—
401	C₄×C₄₁	#548	1	2	yes	—
402	C₄×C₄₁	#577	1	2	yes	—
403	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
404	C₄×C₄₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
405	#3506	C₂×C₄₁	1	1	yes	characteristic, complemented
406	#3503	C₂×C₄₁	1	1	yes	characteristic, complemented
407	#3373	C₂×C₄₁	1	4	yes	complemented
408	#3371	C₂×C₄₁	1	4	yes	complemented
409	#3369	C₂×C₄₁	1	2	yes	complemented
410	#3366	C₂×C₄₁	1	2	yes	complemented
411	#3362	C₂×C₄₁	1	2	yes	complemented
412	#3360	C₂×C₄₁	1	2	yes	complemented
413	#3141	C₂×C₄₁	1	1	yes	characteristic, complemented
414	#3136	C₂×C₄₁	1	2	yes	complemented
415	#3084	C₂×C₄₁	1	2	yes	complemented
416	C₂×#476	C₂×C₄₁	1	1	yes	characteristic, complemented
417	#3045	C₂×C₄₁	1	2	yes	complemented
418	#3035	C₂×C₄₁	1	1	yes	characteristic, complemented
419	#2962	C₂×C₄₁	1	1	yes	characteristic, complemented
420	#2952	C₂×C₄₁	1	2	yes	complemented
421	C₄×AGL(1,ℤ/8)	C₂×C₄₁	1	1	yes	characteristic, complemented
422	C₂×C₄₁	—	2	2	no	—
423	C₂×C₄₁	—	4	2	no	—
424	C₂×C₄₁	—	8	2	no	—
425	C₂×C₄₁	—	8	2	no	—
426	C₂×C₄₁	C₂×#548	1	1	yes	characteristic
427	C₂×C₄₁	C₂×#577	1	1	yes	characteristic
428	C₂×C₄₁	#3585	1	1	yes	characteristic
429	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	1	yes	characteristic
430	C₂×#135	C₂²×C₄₁	1	2	yes	—
431	#559	C₂²×C₄₁	1	4	yes	—
432	Q₈²	C₂²×C₄₁	1	2	yes	complemented
433	#557	C₂²×C₄₁	1	2	yes	complemented
434	#556	C₂²×C₄₁	1	2	yes	—
435	#555	—	2	1	no	—
436	#554	—	2	2	no	—
437	#554	C₂²×C₄₁	1	2	yes	complemented
438	#553	—	2	2	no	—
439	#550	C₂²×C₄₁	1	2	yes	—
440	D₄×Q₈	—	2	2	no	—
441	D₄×Q₈	C₂²×C₄₁	1	2	yes	complemented
442	#547	—	2	1	no	—
443	#544	—	2	2	no	—
444	#544	C₂²×C₄₁	1	2	yes	—
445	#538	—	2	2	no	—
446	#535	C₂²×C₄₁	1	2	yes	—
447	#533	—	2	1	no	—
448	#533	C₂²×C₄₁	1	1	yes	characteristic
449	#532	C₂²×C₄₁	1	1	yes	characteristic
450	C₂×C₄⋊Q₈	—	2	1	no	—
451	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
452	#525	—	2	2	no	—
453	#520	C₂²×C₄₁	1	2	yes	—
454	#520	C₂²×C₄₁	1	2	yes	—
455	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
456	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
457	#490	C₂²×C₄₁	1	4	yes	—
458	#489	C₂²×C₄₁	1	4	yes	—
459	#489	C₂²×C₄₁	1	4	yes	complemented
460	#488	C₂²×C₄₁	1	4	yes	—
461	#487	C₂²×C₄₁	1	2	yes	complemented
462	#486	C₂²×C₄₁	1	4	yes	—
463	#486	C₂²×C₄₁	1	2	yes	complemented
464	#479	C₂²×C₄₁	1	4	yes	complemented
465	#478	C₂²×C₄₁	1	4	yes	complemented
466	#476	C₂²×C₄₁	1	2	yes	—
467	#476	C₂²×C₄₁	1	2	yes	—
468	#476	C₂²×C₄₁	1	4	yes	—
469	#476	C₂²×C₄₁	1	4	yes	complemented
470	#475	C₂²×C₄₁	1	4	yes	complemented
471	#464	C₂²×C₄₁	1	4	yes	—
472	#464	C₂²×C₄₁	1	2	yes	complemented
473	#463	C₂²×C₄₁	1	4	yes	—
474	#463	C₂²×C₄₁	1	2	yes	complemented
475	#462	C₂²×C₄₁	1	1	yes	characteristic, complemented
476	#461	C₂²×C₄₁	1	1	yes	characteristic, complemented
477	#460	C₂²×C₄₁	1	4	yes	—
478	#460	C₂²×C₄₁	1	1	yes	characteristic, complemented
479	#459	C₂²×C₄₁	1	4	yes	—
480	#459	C₂²×C₄₁	1	1	yes	characteristic, complemented
481	#446	C₂²×C₄₁	1	2	yes	complemented
482	#446	C₂²×C₄₁	1	4	yes	complemented
483	C₈×Q₈	C₂²×C₄₁	1	2	yes	complemented
484	#442	C₂²×C₄₁	1	2	yes	—
485	#442	C₂²×C₄₁	1	4	yes	complemented
486	#441	C₂²×C₄₁	1	4	yes	complemented
487	#440	C₂²×C₄₁	1	2	yes	—
488	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
489	C₄×SD₁₆	C₂²×C₄₁	1	4	yes	complemented
490	C₄×SD₁₆	C₂²×C₄₁	1	4	yes	complemented
491	C₄×D₈	C₂²×C₄₁	1	2	yes	—
492	#428	C₂²×C₄₁	1	1	yes	characteristic
493	C₂×#106	C₂²×C₄₁	1	2	yes	—
494	#424	C₂²×C₄₁	1	2	yes	—
495	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
496	#418	C₂²×C₄₁	1	1	yes	characteristic
497	#417	C₂²×C₄₁	1	2	yes	—
498	#417	C₂²×C₄₁	1	2	yes	—
499	#417	C₂²×C₄₁	1	1	yes	characteristic
500	#416	C₂²×C₄₁	1	2	yes	—
501	C₂×#102	C₂²×C₄₁	1	2	yes	—
502	#405	C₂²×C₄₁	1	2	yes	—
503	C₄×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
504	C₄₁	#61347	1	1	yes	characteristic, direct product factor, Sylow
505	C₂×#41	—	2	2	no	—
506	C₂×#41	C₂³×C₄₁	1	2	yes	—
507	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
508	C₂²×Q₈	—	2	2	no	—
509	C₂²×Q₈	—	2	1	no	—
510	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
511	C₂³×C₄	—	2	1	no	—
512	AGL(1,ℤ/8)	—	2	4	no	—
513	#135	—	2	8	no	—
514	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
515	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
516	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
517	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
518	C₂×D₈	C₂³×C₄₁	1	2	yes	—
519	C₂×D₈	C₂³×C₄₁	1	2	yes	—
520	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
521	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
522	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
523	C₄⋊Q₈	—	2	2	no	—
524	C₄⋊Q₈	—	2	2	no	—
525	C₄⋊Q₈	—	2	2	no	—
526	C₄⋊Q₈	—	2	4	no	—
527	C₄⋊Q₈	—	2	1	no	—
528	C₄⋊Q₈	—	2	1	no	—
529	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
530	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
531	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
532	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
533	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
534	C₄⋊Q₈	C₂³×C₄₁	1	4	yes	—
535	#127	C₂³×C₄₁	1	1	yes	characteristic
536	#127	C₂³×C₄₁	1	4	yes	—
537	#126	—	2	4	no	—
538	#125	—	2	2	no	—
539	#125	—	2	4	no	—
540	#125	D₄×C₄₁	1	2	yes	—
541	#125	C₂³×C₄₁	1	4	yes	—
542	#124	—	2	4	no	—
543	#124	C₂³×C₄₁	1	2	yes	—
544	#124	C₂³×C₄₁	1	4	yes	—
545	#123	—	2	4	no	—
546	#123	—	2	4	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	—	2	2	no	—
549	C₂²⋊Q₈	—	2	2	no	—
550	C₂²⋊Q₈	—	2	4	no	—
551	C₂²⋊Q₈	—	2	4	no	—
552	C₂²⋊Q₈	—	2	4	no	—
553	C₂²⋊Q₈	D₄×C₄₁	1	2	yes	—
554	C₂²⋊Q₈	D₄×C₄₁	1	2	yes	—
555	#121	—	2	1	no	—
556	#121	—	2	1	no	—
557	#121	—	2	2	no	—
558	#121	—	2	2	no	—
559	#121	—	2	2	no	—
560	#121	—	2	4	no	—
561	#120	—	2	4	no	—
562	C₄×Q₈	—	2	2	no	—
563	C₄×Q₈	—	2	2	no	—
564	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
565	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
566	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
567	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
568	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
569	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
570	C₄×D₄	—	2	1	no	—
571	C₄×D₄	—	2	1	no	—
572	C₄×D₄	—	2	4	no	—
573	C₄×D₄	—	2	4	no	—
574	C₄×D₄	—	2	4	no	—
575	C₄×D₄	—	2	1	no	—
576	C₄×D₄	—	2	1	no	—
577	C₄×D₄	—	2	1	no	—
578	C₄×D₄	—	2	1	no	—
579	C₄×D₄	C₂³×C₄₁	1	2	yes	—
580	C₄×D₄	C₂³×C₄₁	1	2	yes	—
581	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
582	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
583	C₄×D₄	C₂³×C₄₁	1	4	yes	—
584	C₄×D₄	C₂³×C₄₁	1	4	yes	—
585	#117	—	2	2	no	—
586	#117	—	2	2	no	—
587	#117	—	2	2	no	—
588	#117	—	2	1	no	—
589	#117	C₂³×C₄₁	1	1	yes	characteristic
590	#117	C₂³×C₄₁	1	2	yes	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	—	2	2	no	—
593	C₂×C₄⋊C₄	—	2	2	no	—
594	C₂×C₄⋊C₄	—	2	2	no	—
595	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
597	C₂×C₂²⋊C₄	—	2	1	no	—
598	C₂×C₄²	—	2	1	no	—
599	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
600	#107	C₂³×C₄₁	1	2	yes	—
601	#106	C₂³×C₄₁	1	4	yes	—
602	#106	C₂³×C₄₁	1	4	yes	—
603	#106	C₂³×C₄₁	1	2	yes	—
604	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
605	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
606	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
607	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
608	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
609	#103	C₂³×C₄₁	1	2	yes	—
610	#103	C₂³×C₄₁	1	2	yes	—
611	#103	C₂³×C₄₁	1	2	yes	—
612	#103	C₂³×C₄₁	1	4	yes	—
613	#103	C₂³×C₄₁	1	4	yes	—
614	#102	C₂³×C₄₁	1	4	yes	—
615	#102	C₂³×C₄₁	1	4	yes	—
616	#102	C₂³×C₄₁	1	2	yes	—
617	#102	C₂³×C₄₁	1	2	yes	—
618	#102	C₂³×C₄₁	1	2	yes	—
619	#102	C₂³×C₄₁	1	4	yes	—
620	#102	C₂³×C₄₁	1	4	yes	—
621	#102	C₂³×C₄₁	1	2	yes	—
622	#102	C₂³×C₄₁	1	2	yes	—
623	#97	C₂³×C₄₁	1	2	yes	—
624	#97	C₂³×C₄₁	1	4	yes	—
625	C₄×C₈	C₂³×C₄₁	1	2	yes	—
626	C₄×C₈	C₂³×C₄₁	1	4	yes	—
627	C₂⁴	—	2	1	no	—
628	#41	—	2	2	no	—
629	#41	—	2	4	no	—
630	#41	—	2	4	no	—
631	#41	—	8	4	no	—
632	#41	#41×C₄₁	1	4	yes	complemented
633	C₂×Q₈	—	2	2	no	—
634	C₂×Q₈	—	2	4	no	—
635	C₂×Q₈	—	2	2	no	—
636	C₂×Q₈	—	8	2	no	—
637	C₂×Q₈	—	8	4	no	—
638	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
639	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
640	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
641	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	4	no	—
647	C₂×D₄	—	2	1	no	—
648	C₂×D₄	—	2	4	no	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	2	no	—
651	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
652	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
653	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	8	2	no	—
665	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
666	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
667	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
668	Q₁₆	—	2	4	no	—
669	SD₁₆	—	2	4	no	—
670	SD₁₆	—	2	4	no	—
671	SD₁₆	—	2	4	no	—
672	D₈	—	2	4	no	—
673	D₈	—	2	4	no	—
674	M₁₆	—	2	2	no	—
675	M₁₆	—	2	2	no	—
676	C₂×C₈	—	2	4	no	—
677	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
678	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
679	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
680	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
695	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
696	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
697	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
698	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
699	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
700	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
701	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
702	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
703	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
704	C₂²⋊C₄	—	2	1	no	—
705	C₂²⋊C₄	—	2	2	no	—
706	C₂²⋊C₄	—	2	2	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	1	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	2	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
716	C₄²	—	2	1	no	—
717	C₄²	—	2	1	no	—
718	C₄²	—	2	1	no	—
719	C₄²	—	2	4	no	—
720	C₄²	—	2	4	no	—
721	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
722	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
723	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
724	C₄²	C₂⁴×C₄₁	1	4	yes	—
725	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
726	C₂³	—	2	1	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	4	2	no	—
730	C₂³	—	8	1	no	—
731	C₂³	—	8	1	no	—
732	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
733	Q₈	—	2	4	no	—
734	Q₈	—	2	1	no	—
735	Q₈	—	2	2	no	—
736	Q₈	—	2	2	no	—
737	Q₈	—	4	2	no	—
738	Q₈	—	4	4	no	—
739	Q₈	—	8	2	no	—
740	Q₈	—	8	4	no	—
741	Q₈	C₂×#41×C₄₁	1	2	yes	—
742	D₄	—	2	4	no	—
743	D₄	—	2	2	no	—
744	D₄	—	2	2	no	—
745	D₄	—	2	1	no	—
746	D₄	—	2	2	no	—
747	D₄	—	2	2	no	—
748	D₄	—	4	4	no	—
749	D₄	—	4	2	no	—
750	D₄	—	4	2	no	—
751	D₄	—	8	4	no	—
752	D₄	—	8	1	no	—
753	D₄	—	8	4	no	—
754	D₄	C₂×#41×C₄₁	1	2	yes	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	4	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	4	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	2	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	—	4	4	no	—
767	C₂×C₄	—	4	2	no	—
768	C₂×C₄	—	8	2	no	—
769	C₂×C₄	—	8	4	no	—
770	C₂×C₄	—	8	4	no	—
771	C₂×C₄	—	8	1	no	—
772	C₂×C₄	—	8	2	no	—
773	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
774	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
775	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
776	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
777	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
778	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
779	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
780	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
781	C₂×C₄	2₋¹⁺⁴×C₄₁	1	2	yes	—
782	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
783	C₈	—	2	2	no	—
784	C₈	—	2	2	no	—
785	C₈	—	2	2	no	—
786	C₈	—	2	2	no	—
787	C₂²	—	2	1	no	—
788	C₂²	—	2	1	no	—
789	C₂²	—	2	2	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	8	4	no	—
799	C₂²	C₄₁×#548	1	2	yes	—
800	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
801	C₄	—	2	1	no	—
802	C₄	—	2	4	no	—
803	C₄	—	2	1	no	—
804	C₄	—	2	1	no	—
805	C₄	—	2	4	no	—
806	C₄	—	2	2	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	1	no	—
809	C₄	—	4	1	no	—
810	C₄	—	4	4	no	—
811	C₄	—	4	2	no	—
812	C₄	C₄₁×#548	1	2	yes	—
813	C₄	C₄₁×#577	1	2	yes	—
814	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
815	C₄	C₂×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
816	C₂	—	2	2	no	—
817	C₂	—	4	2	no	—
818	C₂	—	8	2	no	—
819	C₂	—	8	2	no	—
820	C₂	C₂×C₄₁×#548	1	1	yes	characteristic
821	C₂	C₂×C₄₁×#577	1	1	yes	characteristic
822	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3506	C₂	semidirect
2. C₄₁×#3503	C₂	semidirect
3. C₄₁×#3373	C₂	semidirect
4. C₄₁×#3371	C₂	semidirect
5. C₄₁×#3369	C₂	semidirect
6. C₄₁×#3366	C₂	semidirect
7. C₄₁×#3362	C₂	semidirect
8. C₄₁×#3360	C₂	semidirect
9. C₄₁×#3141	C₂	semidirect
10. C₄₁×#3136	C₂	semidirect
11. C₄₁×#3084	C₂	semidirect
12. C₂×C₄₁×#476	C₂	semidirect
13. C₄₁×#3045	C₂	semidirect
14. C₄₁×#3035	C₂	semidirect
15. C₄₁×#2962	C₂	semidirect
16. C₄₁×#2952	C₂	semidirect
17. C₄×AGL(1,ℤ/8)×C₄₁	C₂	semidirect
21. Q₈²×C₄₁	C₂²	semidirect
22. C₄₁×#557	C₂²	semidirect
26. C₄₁×#554	C₂²	semidirect
30. D₄×Q₈×C₄₁	C₂²	semidirect
48. C₄₁×#489	C₂²	semidirect
50. C₄₁×#487	C₂²	semidirect
52. C₄₁×#486	C₂²	semidirect
53. C₄₁×#479	C₂²	semidirect
54. C₄₁×#478	C₂²	semidirect
58. C₄₁×#476	C₂²	semidirect
59. C₄₁×#475	C₂²	semidirect
61. C₄₁×#464	C₂²	semidirect
63. C₄₁×#463	C₂²	semidirect
64. C₄₁×#462	C₂²	semidirect
65. C₄₁×#461	C₂²	semidirect
67. C₄₁×#460	C₂²	semidirect
69. C₄₁×#459	C₂²	semidirect
70. C₄₁×#446	C₂²	semidirect
71. C₄₁×#446	C₂²	semidirect
72. C₈×Q₈×C₄₁	C₂²	semidirect
74. C₄₁×#442	C₂²	semidirect
75. C₄₁×#441	C₂²	semidirect
78. C₄×SD₁₆×C₄₁	C₂²	semidirect
79. C₄×SD₁₆×C₄₁	C₂²	semidirect
220. #41×C₄₁	#41	semidirect
375. #61347	C₄₁	direct (N × H)
405. #3506	C₂×C₄₁	semidirect
406. #3503	C₂×C₄₁	semidirect
407. #3373	C₂×C₄₁	semidirect
408. #3371	C₂×C₄₁	semidirect
409. #3369	C₂×C₄₁	semidirect
410. #3366	C₂×C₄₁	semidirect
411. #3362	C₂×C₄₁	semidirect
412. #3360	C₂×C₄₁	semidirect
413. #3141	C₂×C₄₁	semidirect
414. #3136	C₂×C₄₁	semidirect
415. #3084	C₂×C₄₁	semidirect
416. C₂×#476	C₂×C₄₁	semidirect
417. #3045	C₂×C₄₁	semidirect
418. #3035	C₂×C₄₁	semidirect
419. #2962	C₂×C₄₁	semidirect
420. #2952	C₂×C₄₁	semidirect
421. C₄×AGL(1,ℤ/8)	C₂×C₄₁	semidirect
432. Q₈²	C₂²×C₄₁	semidirect
433. #557	C₂²×C₄₁	semidirect
437. #554	C₂²×C₄₁	semidirect
441. D₄×Q₈	C₂²×C₄₁	semidirect
459. #489	C₂²×C₄₁	semidirect
461. #487	C₂²×C₄₁	semidirect
463. #486	C₂²×C₄₁	semidirect
464. #479	C₂²×C₄₁	semidirect
465. #478	C₂²×C₄₁	semidirect
469. #476	C₂²×C₄₁	semidirect
470. #475	C₂²×C₄₁	semidirect
472. #464	C₂²×C₄₁	semidirect
474. #463	C₂²×C₄₁	semidirect
475. #462	C₂²×C₄₁	semidirect
476. #461	C₂²×C₄₁	semidirect
478. #460	C₂²×C₄₁	semidirect
480. #459	C₂²×C₄₁	semidirect
481. #446	C₂²×C₄₁	semidirect
482. #446	C₂²×C₄₁	semidirect
483. C₈×Q₈	C₂²×C₄₁	semidirect
485. #442	C₂²×C₄₁	semidirect
486. #441	C₂²×C₄₁	semidirect
489. C₄×SD₁₆	C₂²×C₄₁	semidirect
490. C₄×SD₁₆	C₂²×C₄₁	semidirect
504. C₄₁	#61347	direct (N × H)
632. #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×#3503	2
C₄₁×#3373	2
C₄₁×#3371	2
C₄₁×#3369	2
C₄₁×#3366	2
C₄₁×#3362	2
C₄₁×#3360	2
C₄₁×#3141	2
C₄₁×#3136	2
C₄₁×#3084	2
C₂×C₄₁×#476	2
C₄₁×#3045	2
C₄₁×#3035	2
C₄₁×#2962	2
C₄₁×#2952	2
C₄×AGL(1,ℤ/8)×C₄₁	2
#61347	41

Subgroups — C41×#61347 #23837548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61347 #23837548