Subgroups — C₄₁×#61417 #23837618

Order 10496.

1974 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3403	C₂	1	4	yes	maximal, complemented
4	C₄₁×#3401	C₂	1	4	yes	maximal, complemented
5	C₄₁×#3399	C₂	1	4	yes	maximal, complemented
6	C₄₁×#3397	C₂	1	4	yes	maximal, complemented
7	C₄₁×#3155	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#3154	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₁×#496	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#3043	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#3042	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3041	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3041	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3040	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#2961	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#2949	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄₁×#2948	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#2943	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#137×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×#135×C₄₁	C₂²	1	1	yes	characteristic
25	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
26	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
27	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
28	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
29	C₄₁×#559	C₂²	1	4	yes	complemented
30	C₄₁×#559	C₂²	1	4	yes	complemented
31	C₄₁×#556	C₂²	1	4	yes	complemented
32	C₄₁×#551	—	2	4	no	—
33	C₄₁×#550	C₂²	1	4	yes	complemented
34	C₄₁×#546	—	2	4	no	—
35	C₄₁×#542	—	2	2	no	—
36	C₄₁×#540	—	2	2	no	—
37	C₄₁×#536	C₂²	1	1	yes	characteristic
38	C₄₁×#535	C₂²	1	1	yes	characteristic
39	C₄₁×#535	C₂²	1	1	yes	characteristic
40	C₄₁×#535	C₂²	1	1	yes	characteristic
41	C₄₁×#533	C₂²	1	1	yes	characteristic
42	C₄₁×#532	—	2	2	no	—
43	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
44	C₄₁×#529	—	2	2	no	—
45	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
46	C₄₁×#519	C₂²	1	1	yes	characteristic
47	C₄₁×#518	C₂²	1	1	yes	characteristic
48	C₄₁×#518	C₂²	1	1	yes	characteristic
49	C₄₁×#518	C₂²	1	1	yes	characteristic
50	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
51	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
52	C₄₁×#497	C₂²	1	2	yes	complemented
53	C₄₁×#496	C₂²	1	4	yes	—
54	C₄₁×#496	C₂²	1	4	yes	—
55	C₄₁×#496	C₂²	1	2	yes	complemented
56	C₄₁×#496	C₂²	1	2	yes	complemented
57	C₄₁×#496	C₂²	1	2	yes	complemented
58	C₄₁×#495	C₂²	1	2	yes	complemented
59	C₄₁×#495	C₂²	1	2	yes	complemented
60	C₄₁×#493	C₂²	1	2	yes	complemented
61	C₄₁×#492	C₂²	1	2	yes	complemented
62	C₄₁×#464	C₂²	1	4	yes	complemented
63	C₄₁×#464	C₂²	1	4	yes	complemented
64	C₄₁×#463	C₂²	1	4	yes	complemented
65	C₄₁×#463	C₂²	1	4	yes	complemented
66	C₄₁×#463	C₂²	1	4	yes	complemented
67	C₄₁×#463	C₂²	1	4	yes	complemented
68	C₄₁×#461	C₂²	1	4	yes	complemented
69	C₄₁×#460	C₂²	1	4	yes	complemented
70	C₄₁×#460	C₂²	1	4	yes	complemented
71	C₄₁×#459	C₂²	1	4	yes	complemented
72	C₄₁×#459	C₂²	1	4	yes	complemented
73	C₄₁×#459	C₂²	1	4	yes	complemented
74	C₄₁×#446	C₂²	1	4	yes	complemented
75	C₄₁×#446	C₂²	1	4	yes	complemented
76	C₄₁×#442	C₂²	1	2	yes	complemented
77	C₄₁×#442	C₂²	1	4	yes	complemented
78	C₄₁×#441	C₂²	1	2	yes	complemented
79	C₄₁×#440	C₂²	1	2	yes	complemented
80	C₄₁×#440	C₂²	1	4	yes	complemented
81	C₄₁×#440	C₂²	1	2	yes	complemented
82	C₄×SD₁₆×C₄₁	C₂²	1	4	yes	complemented
83	C₄×D₈×C₄₁	C₂²	1	4	yes	complemented
84	C₄₁×#427	C₂²	1	1	yes	characteristic
85	C₄₁×#424	C₂²	1	1	yes	characteristic
86	C₄₁×#424	C₂²	1	1	yes	characteristic
87	C₄₁×#423	C₂²	1	1	yes	characteristic
88	C₄₁×#419	C₂²	1	1	yes	characteristic
89	C₄₁×#418	C₂²	1	1	yes	characteristic
90	C₄₁×#418	C₂²	1	1	yes	characteristic
91	C₄₁×#418	C₂²	1	1	yes	characteristic
92	C₄₁×#416	C₂²	1	1	yes	characteristic
93	C₄₁×#416	C₂²	1	1	yes	characteristic
94	C₄₁×#405	C₂²	1	1	yes	characteristic
95	C₄₁×#405	C₂²	1	1	yes	characteristic
96	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
97	C₂×#41×C₄₁	—	2	4	no	—
98	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
99	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
101	C₂²×D₄×C₄₁	—	2	2	no	—
102	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
105	#137×C₄₁	—	4	2	no	—
106	AGL(1,ℤ/8)×C₄₁	—	4	2	no	—
107	AGL(1,ℤ/8)×C₄₁	—	4	2	no	—
108	AGL(1,ℤ/8)×C₄₁	—	4	2	no	—
109	#135×C₄₁	—	2	4	no	—
110	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
111	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
112	C₂×SD₁₆×C₄₁	—	2	4	no	—
113	C₂×SD₁₆×C₄₁	—	4	2	no	—
114	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
115	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
116	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
117	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
118	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
119	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
120	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
121	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
122	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
123	C₂×D₈×C₄₁	—	2	4	no	—
124	C₂×D₈×C₄₁	—	4	2	no	—
125	C₂×D₈×C₄₁	C₂³	1	2	yes	—
126	C₂×D₈×C₄₁	C₂³	1	2	yes	—
127	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
128	C₂×D₈×C₄₁	C₂³	1	4	yes	—
129	C₂×D₈×C₄₁	C₂³	1	2	yes	—
130	C₂×D₈×C₄₁	C₂³	1	2	yes	—
131	C₂×D₈×C₄₁	C₂³	1	2	yes	—
132	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
133	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
135	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
136	C₄⋊Q₈×C₄₁	D₄	1	2	yes	—
137	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
138	#127×C₄₁	—	2	1	no	—
139	#127×C₄₁	—	2	1	no	—
140	#127×C₄₁	C₂³	1	4	yes	—
141	#127×C₄₁	C₂³	1	2	yes	—
142	#127×C₄₁	C₂³	1	2	yes	—
143	#127×C₄₁	C₂³	1	2	yes	—
144	#126×C₄₁	—	2	4	no	—
145	#126×C₄₁	—	2	4	no	—
146	#125×C₄₁	D₄	1	2	yes	—
147	#124×C₄₁	—	2	4	no	—
148	#124×C₄₁	—	2	4	no	—
149	#124×C₄₁	—	2	1	no	—
150	#124×C₄₁	—	2	1	no	—
151	#124×C₄₁	C₂³	1	4	yes	—
152	#124×C₄₁	C₂³	1	2	yes	—
153	#124×C₄₁	C₂³	1	2	yes	—
154	#124×C₄₁	C₂³	1	2	yes	—
155	#124×C₄₁	C₂³	1	2	yes	—
156	#123×C₄₁	—	2	4	no	—
157	#123×C₄₁	—	2	4	no	—
158	#123×C₄₁	—	2	4	no	—
159	#123×C₄₁	—	2	4	no	—
160	#123×C₄₁	—	2	2	no	—
161	C₂²⋊Q₈×C₄₁	—	2	4	no	—
162	C₂²⋊Q₈×C₄₁	—	2	2	no	—
163	C₂²⋊Q₈×C₄₁	D₄	1	4	yes	—
164	#121×C₄₁	—	2	2	no	—
165	#121×C₄₁	—	2	2	no	—
166	#121×C₄₁	—	2	2	no	—
167	#121×C₄₁	—	2	4	no	—
168	#121×C₄₁	—	2	4	no	—
169	#121×C₄₁	—	2	4	no	—
170	#120×C₄₁	—	2	2	no	—
171	#120×C₄₁	—	2	2	no	—
172	#120×C₄₁	—	2	2	no	—
173	C₄×Q₈×C₄₁	—	2	2	no	—
174	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
175	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
176	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
177	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
178	C₄×D₄×C₄₁	—	2	2	no	—
179	C₄×D₄×C₄₁	—	2	2	no	—
180	C₄×D₄×C₄₁	—	2	2	no	—
181	C₄×D₄×C₄₁	—	2	2	no	—
182	C₄×D₄×C₄₁	—	2	2	no	—
183	C₄×D₄×C₄₁	—	2	4	no	—
184	C₄×D₄×C₄₁	—	2	4	no	—
185	C₄×D₄×C₄₁	C₂³	1	2	yes	—
186	C₄×D₄×C₄₁	C₂³	1	2	yes	—
187	C₄×D₄×C₄₁	C₂³	1	4	yes	—
188	C₄×D₄×C₄₁	C₂³	1	4	yes	—
189	C₄×D₄×C₄₁	C₂³	1	4	yes	—
190	#117×C₄₁	—	2	4	no	—
191	#117×C₄₁	—	2	2	no	—
192	#117×C₄₁	—	2	1	no	—
193	#117×C₄₁	—	2	1	no	—
194	#117×C₄₁	C₂³	1	1	yes	characteristic
195	#117×C₄₁	C₂³	1	1	yes	characteristic
196	#117×C₄₁	C₂³	1	1	yes	characteristic
197	#117×C₄₁	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
200	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
201	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
202	C₂×C₄²×C₄₁	—	2	1	no	—
203	C₂×C₄²×C₄₁	—	2	1	no	—
204	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
205	#107×C₄₁	C₂³	1	2	yes	—
206	#106×C₄₁	C₂³	1	2	yes	—
207	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
208	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
209	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
210	#103×C₄₁	C₂³	1	2	yes	—
211	#103×C₄₁	C₂³	1	2	yes	—
212	#103×C₄₁	C₂³	1	4	yes	—
213	#102×C₄₁	C₂³	1	2	yes	—
214	#102×C₄₁	C₂³	1	2	yes	—
215	#102×C₄₁	C₂³	1	4	yes	—
216	#102×C₄₁	C₂³	1	4	yes	—
217	#102×C₄₁	C₂³	1	4	yes	—
218	#97×C₄₁	C₂³	1	2	yes	—
219	#97×C₄₁	C₂³	1	2	yes	—
220	#97×C₄₁	C₂³	1	2	yes	—
221	#97×C₄₁	C₂³	1	2	yes	—
222	C₄×C₈×C₄₁	C₂³	1	2	yes	—
223	C₄×C₈×C₄₁	C₂³	1	2	yes	—
224	C₂⁴×C₄₁	—	2	1	no	—
225	C₂⁴×C₄₁	—	2	1	no	—
226	C₂⁴×C₄₁	—	2	1	no	—
227	#41×C₄₁	—	2	2	no	—
228	#41×C₄₁	—	2	2	no	—
229	#41×C₄₁	—	2	2	no	—
230	#41×C₄₁	—	2	2	no	—
231	#41×C₄₁	—	8	8	no	—
232	C₂×Q₈×C₄₁	—	2	1	no	—
233	C₂×Q₈×C₄₁	—	2	2	no	—
234	C₂×Q₈×C₄₁	—	2	2	no	—
235	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
236	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
237	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
238	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
239	C₂×D₄×C₄₁	—	2	1	no	—
240	C₂×D₄×C₄₁	—	2	1	no	—
241	C₂×D₄×C₄₁	—	2	1	no	—
242	C₂×D₄×C₄₁	—	2	1	no	—
243	C₂×D₄×C₄₁	—	2	1	no	—
244	C₂×D₄×C₄₁	—	2	4	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	4	no	—
249	C₂×D₄×C₄₁	—	2	2	no	—
250	C₂×D₄×C₄₁	—	2	2	no	—
251	C₂×D₄×C₄₁	—	2	2	no	—
252	C₂×D₄×C₄₁	—	2	2	no	—
253	C₂×D₄×C₄₁	—	2	2	no	—
254	C₂×D₄×C₄₁	—	2	2	no	—
255	C₂×D₄×C₄₁	—	8	4	no	—
256	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
257	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
258	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
259	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
260	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
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	2	no	—
265	C₂²×C₄×C₄₁	—	2	2	no	—
266	C₂²×C₄×C₄₁	—	2	4	no	—
267	C₂²×C₄×C₄₁	—	2	4	no	—
268	C₂²×C₄×C₄₁	—	2	4	no	—
269	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
271	Q₁₆×C₄₁	—	2	2	no	—
272	Q₁₆×C₄₁	—	4	2	no	—
273	SD₁₆×C₄₁	—	2	4	no	—
274	SD₁₆×C₄₁	—	2	4	no	—
275	SD₁₆×C₄₁	—	2	2	no	—
276	SD₁₆×C₄₁	—	2	2	no	—
277	SD₁₆×C₄₁	—	4	4	no	—
278	SD₁₆×C₄₁	—	4	2	no	—
279	SD₁₆×C₄₁	—	4	2	no	—
280	SD₁₆×C₄₁	—	4	2	no	—
281	SD₁₆×C₄₁	—	4	2	no	—
282	D₈×C₄₁	—	2	4	no	—
283	D₈×C₄₁	—	2	4	no	—
284	D₈×C₄₁	—	2	2	no	—
285	D₈×C₄₁	—	4	4	no	—
286	D₈×C₄₁	—	4	2	no	—
287	D₈×C₄₁	—	4	2	no	—
288	D₈×C₄₁	—	4	2	no	—
289	M₁₆×C₄₁	—	2	2	no	—
290	M₁₆×C₄₁	—	2	2	no	—
291	C₂×C₈×C₄₁	—	2	2	no	—
292	C₂×C₈×C₄₁	#41	1	4	yes	complemented
293	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
294	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
295	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
296	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
297	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
298	C₄⋊C₄×C₄₁	—	2	2	no	—
299	C₄⋊C₄×C₄₁	—	2	2	no	—
300	C₄⋊C₄×C₄₁	—	2	4	no	—
301	C₄⋊C₄×C₄₁	—	2	4	no	—
302	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
303	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
304	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
305	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
306	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
307	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
308	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
309	C₂²⋊C₄×C₄₁	—	2	1	no	—
310	C₂²⋊C₄×C₄₁	—	2	1	no	—
311	C₂²⋊C₄×C₄₁	—	2	4	no	—
312	C₂²⋊C₄×C₄₁	—	2	4	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	2	no	—
317	C₂²⋊C₄×C₄₁	—	2	2	no	—
318	C₂²⋊C₄×C₄₁	—	2	4	no	—
319	C₂²⋊C₄×C₄₁	—	2	4	no	—
320	C₂²⋊C₄×C₄₁	—	2	4	no	—
321	C₂²⋊C₄×C₄₁	—	2	4	no	—
322	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
323	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
324	C₄²×C₄₁	—	2	2	no	—
325	C₄²×C₄₁	—	2	1	no	—
326	C₄²×C₄₁	—	2	1	no	—
327	C₄²×C₄₁	—	2	2	no	—
328	C₄²×C₄₁	—	2	4	no	—
329	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₄₁	C₂⁴	1	2	yes	—
332	C₄²×C₄₁	C₂⁴	1	2	yes	—
333	C₄²×C₄₁	C₂⁴	1	2	yes	—
334	C₂³×C₄₁	—	2	2	no	—
335	C₂³×C₄₁	—	2	1	no	—
336	C₂³×C₄₁	—	2	2	no	—
337	C₂³×C₄₁	—	2	2	no	—
338	C₂³×C₄₁	—	2	1	no	—
339	C₂³×C₄₁	—	4	2	no	—
340	C₂³×C₄₁	—	4	2	no	—
341	C₂³×C₄₁	—	4	2	no	—
342	C₂³×C₄₁	—	8	2	no	—
343	C₂³×C₄₁	—	8	2	no	—
344	C₂³×C₄₁	—	8	2	no	—
345	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
346	Q₈×C₄₁	—	2	2	no	—
347	Q₈×C₄₁	—	2	1	no	—
348	Q₈×C₄₁	—	2	1	no	—
349	Q₈×C₄₁	—	2	1	no	—
350	Q₈×C₄₁	—	2	2	no	—
351	Q₈×C₄₁	—	2	1	no	—
352	Q₈×C₄₁	—	4	4	no	—
353	Q₈×C₄₁	—	4	2	no	—
354	D₄×C₄₁	—	2	2	no	—
355	D₄×C₄₁	—	2	2	no	—
356	D₄×C₄₁	—	2	1	no	—
357	D₄×C₄₁	—	2	1	no	—
358	D₄×C₄₁	—	2	2	no	—
359	D₄×C₄₁	—	2	1	no	—
360	D₄×C₄₁	—	2	2	no	—
361	D₄×C₄₁	—	2	2	no	—
362	D₄×C₄₁	—	2	1	no	—
363	D₄×C₄₁	—	2	2	no	—
364	D₄×C₄₁	—	4	8	no	—
365	D₄×C₄₁	—	4	2	no	—
366	D₄×C₄₁	—	4	2	no	—
367	D₄×C₄₁	—	4	2	no	—
368	D₄×C₄₁	—	4	2	no	—
369	D₄×C₄₁	—	4	2	no	—
370	D₄×C₄₁	—	8	4	no	—
371	D₄×C₄₁	—	8	4	no	—
372	D₄×C₄₁	—	8	4	no	—
373	D₄×C₄₁	—	8	4	no	—
374	C₂×C₄×C₄₁	—	2	2	no	—
375	C₂×C₄×C₄₁	—	2	1	no	—
376	C₂×C₄×C₄₁	—	2	2	no	—
377	C₂×C₄×C₄₁	—	2	2	no	—
378	C₂×C₄×C₄₁	—	2	1	no	—
379	C₂×C₄×C₄₁	—	4	2	no	—
380	C₂×C₄×C₄₁	—	4	4	no	—
381	C₂×C₄×C₄₁	—	4	2	no	—
382	C₂×C₄×C₄₁	—	4	2	no	—
383	C₂×C₄×C₄₁	—	4	2	no	—
384	C₂×C₄×C₄₁	—	8	2	no	—
385	C₂×C₄×C₄₁	—	8	4	no	—
386	C₂×C₄×C₄₁	—	8	4	no	—
387	C₂×C₄×C₄₁	—	8	4	no	—
388	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
391	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
392	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
394	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
395	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
396	C₈×C₄₁	—	2	2	no	—
397	C₈×C₄₁	—	2	2	no	—
398	C₈×C₄₁	—	2	2	no	—
399	C₈×C₄₁	C₂×#41	1	2	yes	—
400	C₈×C₄₁	C₂×#41	1	2	yes	—
401	#61417	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
402	C₂²×C₄₁	—	2	2	no	—
403	C₂²×C₄₁	—	4	2	no	—
404	C₂²×C₄₁	—	4	4	no	—
405	C₂²×C₄₁	—	4	4	no	—
406	C₂²×C₄₁	—	4	2	no	—
407	C₂²×C₄₁	—	4	4	no	—
408	C₂²×C₄₁	—	4	1	no	—
409	C₂²×C₄₁	—	4	1	no	—
410	C₂²×C₄₁	—	4	2	no	—
411	C₂²×C₄₁	—	4	2	no	—
412	C₂²×C₄₁	—	4	2	no	—
413	C₂²×C₄₁	—	16	2	no	—
414	C₂²×C₄₁	—	16	2	no	—
415	C₂²×C₄₁	—	16	2	no	—
416	C₂²×C₄₁	#550	1	2	yes	—
417	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
418	C₄×C₄₁	—	2	2	no	—
419	C₄×C₄₁	—	2	2	no	—
420	C₄×C₄₁	—	2	4	no	—
421	C₄×C₄₁	—	2	4	no	—
422	C₄×C₄₁	—	4	2	no	—
423	C₄×C₄₁	—	4	2	no	—
424	C₄×C₄₁	—	4	1	no	—
425	C₄×C₄₁	—	4	1	no	—
426	C₄×C₄₁	—	4	2	no	—
427	C₄×C₄₁	#550	1	2	yes	—
428	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
429	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
430	#3510	C₂×C₄₁	1	1	yes	characteristic, complemented
431	#3508	C₂×C₄₁	1	1	yes	characteristic, complemented
432	#3403	C₂×C₄₁	1	4	yes	complemented
433	#3401	C₂×C₄₁	1	4	yes	complemented
434	#3399	C₂×C₄₁	1	4	yes	complemented
435	#3397	C₂×C₄₁	1	4	yes	complemented
436	#3155	C₂×C₄₁	1	1	yes	characteristic, complemented
437	#3154	C₂×C₄₁	1	1	yes	characteristic, complemented
438	C₂×#496	C₂×C₄₁	1	1	yes	characteristic, complemented
439	#3043	C₂×C₄₁	1	1	yes	characteristic, complemented
440	#3042	C₂×C₄₁	1	1	yes	characteristic, complemented
441	#3041	C₂×C₄₁	1	1	yes	characteristic, complemented
442	#3041	C₂×C₄₁	1	1	yes	characteristic, complemented
443	#3040	C₂×C₄₁	1	1	yes	characteristic, complemented
444	#3038	C₂×C₄₁	1	1	yes	characteristic, complemented
445	#2961	C₂×C₄₁	1	1	yes	characteristic, complemented
446	#2949	C₂×C₄₁	1	1	yes	characteristic, complemented
447	#2948	C₂×C₄₁	1	1	yes	characteristic, complemented
448	#2943	C₂×C₄₁	1	1	yes	characteristic, complemented
449	C₂×C₄₁	—	2	2	no	—
450	C₂×C₄₁	—	8	1	no	—
451	C₂×C₄₁	—	8	1	no	—
452	C₂×C₄₁	—	8	2	no	—
453	C₂×C₄₁	—	8	2	no	—
454	C₂×C₄₁	—	8	2	no	—
455	C₂×C₄₁	C₂×#550	1	1	yes	characteristic
456	C₂×C₄₁	#3585	1	2	yes	—
457	C₂×#137	C₂²×C₄₁	1	1	yes	characteristic
458	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	1	yes	characteristic
459	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	1	yes	characteristic
460	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	1	yes	characteristic
461	C₂×#135	C₂²×C₄₁	1	1	yes	characteristic
462	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
463	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
464	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
465	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
466	#559	C₂²×C₄₁	1	4	yes	complemented
467	#559	C₂²×C₄₁	1	4	yes	complemented
468	#556	C₂²×C₄₁	1	4	yes	complemented
469	#551	—	2	4	no	—
470	#550	C₂²×C₄₁	1	4	yes	complemented
471	#546	—	2	4	no	—
472	#542	—	2	2	no	—
473	#540	—	2	2	no	—
474	#536	C₂²×C₄₁	1	1	yes	characteristic
475	#535	C₂²×C₄₁	1	1	yes	characteristic
476	#535	C₂²×C₄₁	1	1	yes	characteristic
477	#535	C₂²×C₄₁	1	1	yes	characteristic
478	#533	C₂²×C₄₁	1	1	yes	characteristic
479	#532	—	2	2	no	—
480	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
481	#529	—	2	2	no	—
482	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
483	#519	C₂²×C₄₁	1	1	yes	characteristic
484	#518	C₂²×C₄₁	1	1	yes	characteristic
485	#518	C₂²×C₄₁	1	1	yes	characteristic
486	#518	C₂²×C₄₁	1	1	yes	characteristic
487	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
488	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
489	#497	C₂²×C₄₁	1	2	yes	complemented
490	#496	C₂²×C₄₁	1	4	yes	—
491	#496	C₂²×C₄₁	1	4	yes	—
492	#496	C₂²×C₄₁	1	2	yes	complemented
493	#496	C₂²×C₄₁	1	2	yes	complemented
494	#496	C₂²×C₄₁	1	2	yes	complemented
495	#495	C₂²×C₄₁	1	2	yes	complemented
496	#495	C₂²×C₄₁	1	2	yes	complemented
497	#493	C₂²×C₄₁	1	2	yes	complemented
498	#492	C₂²×C₄₁	1	2	yes	complemented
499	#464	C₂²×C₄₁	1	4	yes	complemented
500	#464	C₂²×C₄₁	1	4	yes	complemented
501	#463	C₂²×C₄₁	1	4	yes	complemented
502	#463	C₂²×C₄₁	1	4	yes	complemented
503	#463	C₂²×C₄₁	1	4	yes	complemented
504	#463	C₂²×C₄₁	1	4	yes	complemented
505	#461	C₂²×C₄₁	1	4	yes	complemented
506	#460	C₂²×C₄₁	1	4	yes	complemented
507	#460	C₂²×C₄₁	1	4	yes	complemented
508	#459	C₂²×C₄₁	1	4	yes	complemented
509	#459	C₂²×C₄₁	1	4	yes	complemented
510	#459	C₂²×C₄₁	1	4	yes	complemented
511	#446	C₂²×C₄₁	1	4	yes	complemented
512	#446	C₂²×C₄₁	1	4	yes	complemented
513	#442	C₂²×C₄₁	1	2	yes	complemented
514	#442	C₂²×C₄₁	1	4	yes	complemented
515	#441	C₂²×C₄₁	1	2	yes	complemented
516	#440	C₂²×C₄₁	1	2	yes	complemented
517	#440	C₂²×C₄₁	1	4	yes	complemented
518	#440	C₂²×C₄₁	1	2	yes	complemented
519	C₄×SD₁₆	C₂²×C₄₁	1	4	yes	complemented
520	C₄×D₈	C₂²×C₄₁	1	4	yes	complemented
521	#427	C₂²×C₄₁	1	1	yes	characteristic
522	#424	C₂²×C₄₁	1	1	yes	characteristic
523	#424	C₂²×C₄₁	1	1	yes	characteristic
524	#423	C₂²×C₄₁	1	1	yes	characteristic
525	#419	C₂²×C₄₁	1	1	yes	characteristic
526	#418	C₂²×C₄₁	1	1	yes	characteristic
527	#418	C₂²×C₄₁	1	1	yes	characteristic
528	#418	C₂²×C₄₁	1	1	yes	characteristic
529	#416	C₂²×C₄₁	1	1	yes	characteristic
530	#416	C₂²×C₄₁	1	1	yes	characteristic
531	#405	C₂²×C₄₁	1	1	yes	characteristic
532	#405	C₂²×C₄₁	1	1	yes	characteristic
533	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
534	C₄₁	#61417	1	1	yes	characteristic, direct product factor, Sylow
535	C₂×#41	—	2	4	no	—
536	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
537	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
538	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
539	C₂²×D₄	—	2	2	no	—
540	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
541	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
542	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
543	#137	—	4	2	no	—
544	AGL(1,ℤ/8)	—	4	2	no	—
545	AGL(1,ℤ/8)	—	4	2	no	—
546	AGL(1,ℤ/8)	—	4	2	no	—
547	#135	—	2	4	no	—
548	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
549	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
550	C₂×SD₁₆	—	2	4	no	—
551	C₂×SD₁₆	—	4	2	no	—
552	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
553	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
554	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
555	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
556	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
557	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
558	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
559	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
560	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
561	C₂×D₈	—	2	4	no	—
562	C₂×D₈	—	4	2	no	—
563	C₂×D₈	C₂³×C₄₁	1	2	yes	—
564	C₂×D₈	C₂³×C₄₁	1	2	yes	—
565	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
566	C₂×D₈	C₂³×C₄₁	1	4	yes	—
567	C₂×D₈	C₂³×C₄₁	1	2	yes	—
568	C₂×D₈	C₂³×C₄₁	1	2	yes	—
569	C₂×D₈	C₂³×C₄₁	1	2	yes	—
570	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
571	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
572	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
573	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
574	C₄⋊Q₈	D₄×C₄₁	1	2	yes	—
575	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
576	#127	—	2	1	no	—
577	#127	—	2	1	no	—
578	#127	C₂³×C₄₁	1	4	yes	—
579	#127	C₂³×C₄₁	1	2	yes	—
580	#127	C₂³×C₄₁	1	2	yes	—
581	#127	C₂³×C₄₁	1	2	yes	—
582	#126	—	2	4	no	—
583	#126	—	2	4	no	—
584	#125	D₄×C₄₁	1	2	yes	—
585	#124	—	2	4	no	—
586	#124	—	2	4	no	—
587	#124	—	2	1	no	—
588	#124	—	2	1	no	—
589	#124	C₂³×C₄₁	1	4	yes	—
590	#124	C₂³×C₄₁	1	2	yes	—
591	#124	C₂³×C₄₁	1	2	yes	—
592	#124	C₂³×C₄₁	1	2	yes	—
593	#124	C₂³×C₄₁	1	2	yes	—
594	#123	—	2	4	no	—
595	#123	—	2	4	no	—
596	#123	—	2	4	no	—
597	#123	—	2	4	no	—
598	#123	—	2	2	no	—
599	C₂²⋊Q₈	—	2	4	no	—
600	C₂²⋊Q₈	—	2	2	no	—
601	C₂²⋊Q₈	D₄×C₄₁	1	4	yes	—
602	#121	—	2	2	no	—
603	#121	—	2	2	no	—
604	#121	—	2	2	no	—
605	#121	—	2	4	no	—
606	#121	—	2	4	no	—
607	#121	—	2	4	no	—
608	#120	—	2	2	no	—
609	#120	—	2	2	no	—
610	#120	—	2	2	no	—
611	C₄×Q₈	—	2	2	no	—
612	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
613	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
614	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
615	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	4	no	—
622	C₄×D₄	—	2	4	no	—
623	C₄×D₄	C₂³×C₄₁	1	2	yes	—
624	C₄×D₄	C₂³×C₄₁	1	2	yes	—
625	C₄×D₄	C₂³×C₄₁	1	4	yes	—
626	C₄×D₄	C₂³×C₄₁	1	4	yes	—
627	C₄×D₄	C₂³×C₄₁	1	4	yes	—
628	#117	—	2	4	no	—
629	#117	—	2	2	no	—
630	#117	—	2	1	no	—
631	#117	—	2	1	no	—
632	#117	C₂³×C₄₁	1	1	yes	characteristic
633	#117	C₂³×C₄₁	1	1	yes	characteristic
634	#117	C₂³×C₄₁	1	1	yes	characteristic
635	#117	C₂³×C₄₁	1	1	yes	characteristic
636	C₂×C₂²⋊C₄	—	2	2	no	—
637	C₂×C₂²⋊C₄	—	2	2	no	—
638	C₂×C₂²⋊C₄	—	2	2	no	—
639	C₂×C₂²⋊C₄	—	2	2	no	—
640	C₂×C₄²	—	2	1	no	—
641	C₂×C₄²	—	2	1	no	—
642	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
643	#107	C₂³×C₄₁	1	2	yes	—
644	#106	C₂³×C₄₁	1	2	yes	—
645	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
646	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
647	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
648	#103	C₂³×C₄₁	1	2	yes	—
649	#103	C₂³×C₄₁	1	2	yes	—
650	#103	C₂³×C₄₁	1	4	yes	—
651	#102	C₂³×C₄₁	1	2	yes	—
652	#102	C₂³×C₄₁	1	2	yes	—
653	#102	C₂³×C₄₁	1	4	yes	—
654	#102	C₂³×C₄₁	1	4	yes	—
655	#102	C₂³×C₄₁	1	4	yes	—
656	#97	C₂³×C₄₁	1	2	yes	—
657	#97	C₂³×C₄₁	1	2	yes	—
658	#97	C₂³×C₄₁	1	2	yes	—
659	#97	C₂³×C₄₁	1	2	yes	—
660	C₄×C₈	C₂³×C₄₁	1	2	yes	—
661	C₄×C₈	C₂³×C₄₁	1	2	yes	—
662	C₂⁴	—	2	1	no	—
663	C₂⁴	—	2	1	no	—
664	C₂⁴	—	2	1	no	—
665	#41	—	2	2	no	—
666	#41	—	2	2	no	—
667	#41	—	2	2	no	—
668	#41	—	2	2	no	—
669	#41	—	8	8	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
674	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
675	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
676	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	4	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	2	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	8	4	no	—
694	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
695	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
696	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
697	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
698	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
709	Q₁₆	—	2	2	no	—
710	Q₁₆	—	4	2	no	—
711	SD₁₆	—	2	4	no	—
712	SD₁₆	—	2	4	no	—
713	SD₁₆	—	2	2	no	—
714	SD₁₆	—	2	2	no	—
715	SD₁₆	—	4	4	no	—
716	SD₁₆	—	4	2	no	—
717	SD₁₆	—	4	2	no	—
718	SD₁₆	—	4	2	no	—
719	SD₁₆	—	4	2	no	—
720	D₈	—	2	4	no	—
721	D₈	—	2	4	no	—
722	D₈	—	2	2	no	—
723	D₈	—	4	4	no	—
724	D₈	—	4	2	no	—
725	D₈	—	4	2	no	—
726	D₈	—	4	2	no	—
727	M₁₆	—	2	2	no	—
728	M₁₆	—	2	2	no	—
729	C₂×C₈	—	2	2	no	—
730	C₂×C₈	#41×C₄₁	1	4	yes	complemented
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	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
735	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
741	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
742	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
743	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
744	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
745	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
746	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	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	2	yes	—
761	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
762	C₄²	—	2	2	no	—
763	C₄²	—	2	1	no	—
764	C₄²	—	2	1	no	—
765	C₄²	—	2	2	no	—
766	C₄²	—	2	4	no	—
767	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
768	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
769	C₄²	C₂⁴×C₄₁	1	2	yes	—
770	C₄²	C₂⁴×C₄₁	1	2	yes	—
771	C₄²	C₂⁴×C₄₁	1	2	yes	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	1	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	4	2	no	—
778	C₂³	—	4	2	no	—
779	C₂³	—	4	2	no	—
780	C₂³	—	8	2	no	—
781	C₂³	—	8	2	no	—
782	C₂³	—	8	2	no	—
783	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
784	Q₈	—	2	2	no	—
785	Q₈	—	2	1	no	—
786	Q₈	—	2	1	no	—
787	Q₈	—	2	1	no	—
788	Q₈	—	2	2	no	—
789	Q₈	—	2	1	no	—
790	Q₈	—	4	4	no	—
791	Q₈	—	4	2	no	—
792	D₄	—	2	2	no	—
793	D₄	—	2	2	no	—
794	D₄	—	2	1	no	—
795	D₄	—	2	1	no	—
796	D₄	—	2	2	no	—
797	D₄	—	2	1	no	—
798	D₄	—	2	2	no	—
799	D₄	—	2	2	no	—
800	D₄	—	2	1	no	—
801	D₄	—	2	2	no	—
802	D₄	—	4	8	no	—
803	D₄	—	4	2	no	—
804	D₄	—	4	2	no	—
805	D₄	—	4	2	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	2	no	—
808	D₄	—	8	4	no	—
809	D₄	—	8	4	no	—
810	D₄	—	8	4	no	—
811	D₄	—	8	4	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	4	2	no	—
822	C₂×C₄	—	8	4	no	—
823	C₂×C₄	—	8	4	no	—
824	C₂×C₄	—	8	2	no	—
825	C₂×C₄	—	8	4	no	—
826	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
827	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
828	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
829	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
830	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
831	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
832	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
833	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
834	C₈	—	2	2	no	—
835	C₈	—	2	2	no	—
836	C₈	—	2	2	no	—
837	C₈	C₂×#41×C₄₁	1	2	yes	—
838	C₈	C₂×#41×C₄₁	1	2	yes	—
839	C₂²	—	2	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	4	no	—
842	C₂²	—	4	4	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	4	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	16	2	no	—
851	C₂²	—	16	2	no	—
852	C₂²	—	16	2	no	—
853	C₂²	C₄₁×#550	1	2	yes	—
854	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
855	C₄	—	2	2	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	4	no	—
858	C₄	—	2	4	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	1	no	—
863	C₄	—	4	2	no	—
864	C₄	C₄₁×#550	1	2	yes	—
865	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
866	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
867	C₂	—	2	2	no	—
868	C₂	—	8	2	no	—
869	C₂	—	8	2	no	—
870	C₂	—	8	2	no	—
871	C₂	—	8	1	no	—
872	C₂	—	8	1	no	—
873	C₂	C₂×C₄₁×#550	1	1	yes	characteristic
874	C₂	C₄₁×#3585	1	2	yes	—

	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×#3510	C₂	semidirect
2. C₄₁×#3508	C₂	semidirect
3. C₄₁×#3403	C₂	semidirect
4. C₄₁×#3401	C₂	semidirect
5. C₄₁×#3399	C₂	semidirect
6. C₄₁×#3397	C₂	semidirect
7. C₄₁×#3155	C₂	semidirect
8. C₄₁×#3154	C₂	semidirect
9. C₂×C₄₁×#496	C₂	semidirect
10. C₄₁×#3043	C₂	semidirect
11. C₄₁×#3042	C₂	semidirect
12. C₄₁×#3041	C₂	semidirect
13. C₄₁×#3041	C₂	semidirect
14. C₄₁×#3040	C₂	semidirect
15. C₄₁×#3038	C₂	semidirect
16. C₄₁×#2961	C₂	semidirect
17. C₄₁×#2949	C₂	semidirect
18. C₄₁×#2948	C₂	semidirect
19. C₄₁×#2943	C₂	semidirect
29. C₄₁×#559	C₂²	semidirect
30. C₄₁×#559	C₂²	semidirect
31. C₄₁×#556	C₂²	semidirect
33. C₄₁×#550	C₂²	semidirect
52. C₄₁×#497	C₂²	semidirect
55. C₄₁×#496	C₂²	semidirect
56. C₄₁×#496	C₂²	semidirect
57. C₄₁×#496	C₂²	semidirect
58. C₄₁×#495	C₂²	semidirect
59. C₄₁×#495	C₂²	semidirect
60. C₄₁×#493	C₂²	semidirect
61. C₄₁×#492	C₂²	semidirect
62. C₄₁×#464	C₂²	semidirect
63. C₄₁×#464	C₂²	semidirect
64. C₄₁×#463	C₂²	semidirect
65. C₄₁×#463	C₂²	semidirect
66. C₄₁×#463	C₂²	semidirect
67. C₄₁×#463	C₂²	semidirect
68. C₄₁×#461	C₂²	semidirect
69. C₄₁×#460	C₂²	semidirect
70. C₄₁×#460	C₂²	semidirect
71. C₄₁×#459	C₂²	semidirect
72. C₄₁×#459	C₂²	semidirect
73. C₄₁×#459	C₂²	semidirect
74. C₄₁×#446	C₂²	semidirect
75. C₄₁×#446	C₂²	semidirect
76. C₄₁×#442	C₂²	semidirect
77. C₄₁×#442	C₂²	semidirect
78. C₄₁×#441	C₂²	semidirect
79. C₄₁×#440	C₂²	semidirect
80. C₄₁×#440	C₂²	semidirect
81. C₄₁×#440	C₂²	semidirect
82. C₄×SD₁₆×C₄₁	C₂²	semidirect
83. C₄×D₈×C₄₁	C₂²	semidirect
292. C₂×C₈×C₄₁	#41	semidirect
401. #61417	C₄₁	direct (N × H)
430. #3510	C₂×C₄₁	semidirect
431. #3508	C₂×C₄₁	semidirect
432. #3403	C₂×C₄₁	semidirect
433. #3401	C₂×C₄₁	semidirect
434. #3399	C₂×C₄₁	semidirect
435. #3397	C₂×C₄₁	semidirect
436. #3155	C₂×C₄₁	semidirect
437. #3154	C₂×C₄₁	semidirect
438. C₂×#496	C₂×C₄₁	semidirect
439. #3043	C₂×C₄₁	semidirect
440. #3042	C₂×C₄₁	semidirect
441. #3041	C₂×C₄₁	semidirect
442. #3041	C₂×C₄₁	semidirect
443. #3040	C₂×C₄₁	semidirect
444. #3038	C₂×C₄₁	semidirect
445. #2961	C₂×C₄₁	semidirect
446. #2949	C₂×C₄₁	semidirect
447. #2948	C₂×C₄₁	semidirect
448. #2943	C₂×C₄₁	semidirect
466. #559	C₂²×C₄₁	semidirect
467. #559	C₂²×C₄₁	semidirect
468. #556	C₂²×C₄₁	semidirect
470. #550	C₂²×C₄₁	semidirect
489. #497	C₂²×C₄₁	semidirect
492. #496	C₂²×C₄₁	semidirect
493. #496	C₂²×C₄₁	semidirect
494. #496	C₂²×C₄₁	semidirect
495. #495	C₂²×C₄₁	semidirect
496. #495	C₂²×C₄₁	semidirect
497. #493	C₂²×C₄₁	semidirect
498. #492	C₂²×C₄₁	semidirect
499. #464	C₂²×C₄₁	semidirect
500. #464	C₂²×C₄₁	semidirect
501. #463	C₂²×C₄₁	semidirect
502. #463	C₂²×C₄₁	semidirect
503. #463	C₂²×C₄₁	semidirect
504. #463	C₂²×C₄₁	semidirect
505. #461	C₂²×C₄₁	semidirect
506. #460	C₂²×C₄₁	semidirect
507. #460	C₂²×C₄₁	semidirect
508. #459	C₂²×C₄₁	semidirect
509. #459	C₂²×C₄₁	semidirect
510. #459	C₂²×C₄₁	semidirect
511. #446	C₂²×C₄₁	semidirect
512. #446	C₂²×C₄₁	semidirect
513. #442	C₂²×C₄₁	semidirect
514. #442	C₂²×C₄₁	semidirect
515. #441	C₂²×C₄₁	semidirect
516. #440	C₂²×C₄₁	semidirect
517. #440	C₂²×C₄₁	semidirect
518. #440	C₂²×C₄₁	semidirect
519. C₄×SD₁₆	C₂²×C₄₁	semidirect
520. C₄×D₈	C₂²×C₄₁	semidirect
534. C₄₁	#61417	direct (N × H)
730. C₂×C₈	#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×#3510	2
C₄₁×#3508	2
C₄₁×#3403	2
C₄₁×#3401	2
C₄₁×#3399	2
C₄₁×#3397	2
C₄₁×#3155	2
C₄₁×#3154	2
C₂×C₄₁×#496	2
C₄₁×#3043	2
C₄₁×#3042	2
C₄₁×#3041	2
C₄₁×#3040	2
C₄₁×#3038	2
C₄₁×#2961	2
C₄₁×#2949	2
C₄₁×#2948	2
C₄₁×#2943	2
#61417	41

Subgroups — C41×#61417 #23837618

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61417 #23837618