Subgroups — C₄₁×#61407 #23837608

Order 10496.

1922 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3401	C₂	1	4	yes	maximal, complemented
4	C₄₁×#3399	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3398	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3394	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3394	C₂	1	4	yes	maximal, complemented
8	C₄₁×#3392	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3154	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3147	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#3046	C₂	1	2	yes	maximal, complemented
12	C₄₁×#3045	C₂	1	2	yes	maximal, complemented
13	C₄₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3036	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#2960	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#2952	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×SD₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#137×C₄₁	C₂²	1	2	yes	—
19	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	2	yes	—
20	C₂×#135×C₄₁	C₂²	1	2	yes	—
21	C₂×#135×C₄₁	C₂²	1	2	yes	—
22	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
23	C₄₁×#559	C₂²	1	4	yes	—
24	C₄₁×#559	C₂²	1	2	yes	complemented
25	C₄₁×#557	C₂²	1	2	yes	complemented
26	C₄₁×#556	—	2	1	no	—
27	C₄₁×#556	C₂²	1	2	yes	—
28	C₄₁×#556	C₂²	1	4	yes	complemented
29	C₄₁×#555	—	2	1	no	—
30	C₄₁×#554	—	2	1	no	—
31	C₄₁×#553	—	2	2	no	—
32	C₄₁×#552	—	2	2	no	—
33	C₄₁×#550	C₂²	1	2	yes	—
34	C₄₁×#547	—	2	1	no	—
35	C₄₁×#539	—	2	2	no	—
36	C₄₁×#538	—	2	2	no	—
37	C₄₁×#536	C₂²	1	2	yes	—
38	C₄₁×#535	C₂²	1	2	yes	—
39	C₄₁×#533	C₂²	1	1	yes	characteristic
40	C₄₁×#532	C₂²	1	1	yes	characteristic
41	C₄₁×#532	C₂²	1	1	yes	characteristic
42	C₄₁×#529	—	2	2	no	—
43	C₄₁×#525	—	2	2	no	—
44	C₄₁×#520	C₂²	1	2	yes	—
45	C₄₁×#520	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
48	C₄₁×#497	C₂²	1	4	yes	—
49	C₄₁×#496	C₂²	1	4	yes	—
50	C₄₁×#495	C₂²	1	4	yes	—
51	C₄₁×#495	C₂²	1	2	yes	complemented
52	C₄₁×#495	C₂²	1	2	yes	complemented
53	C₄₁×#494	C₂²	1	1	yes	characteristic, complemented
54	C₄₁×#493	C₂²	1	1	yes	characteristic, complemented
55	C₄₁×#492	C₂²	1	4	yes	—
56	C₄₁×#492	C₂²	1	1	yes	characteristic, complemented
57	C₄₁×#492	C₂²	1	1	yes	characteristic, complemented
58	C₄₁×#464	C₂²	1	4	yes	—
59	C₄₁×#464	C₂²	1	4	yes	complemented
60	C₄₁×#464	C₂²	1	4	yes	complemented
61	C₄₁×#463	C₂²	1	4	yes	—
62	C₄₁×#463	C₂²	1	4	yes	—
63	C₄₁×#463	C₂²	1	4	yes	complemented
64	C₄₁×#462	C₂²	1	2	yes	complemented
65	C₄₁×#462	C₂²	1	4	yes	complemented
66	C₄₁×#461	C₂²	1	2	yes	—
67	C₄₁×#461	C₂²	1	4	yes	complemented
68	C₄₁×#460	C₂²	1	4	yes	—
69	C₄₁×#460	C₂²	1	2	yes	complemented
70	C₄₁×#459	C₂²	1	2	yes	—
71	C₄₁×#459	C₂²	1	4	yes	—
72	C₄₁×#446	C₂²	1	2	yes	complemented
73	C₄₁×#446	C₂²	1	2	yes	complemented
74	C₈×Q₈×C₄₁	C₂²	1	2	yes	complemented
75	C₈×Q₈×C₄₁	C₂²	1	2	yes	complemented
76	C₄₁×#442	C₂²	1	4	yes	complemented
77	C₄₁×#441	C₂²	1	4	yes	complemented
78	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
79	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
80	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
81	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
82	C₄×SD₁₆×C₄₁	C₂²	1	4	yes	complemented
83	C₄×SD₁₆×C₄₁	C₂²	1	4	yes	complemented
84	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
85	C₄₁×#424	C₂²	1	2	yes	—
86	C₄₁×#423	C₂²	1	1	yes	characteristic
87	C₄₁×#417	C₂²	1	2	yes	—
88	C₄₁×#417	C₂²	1	2	yes	—
89	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
90	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
91	C₄₁×#405	C₂²	1	2	yes	—
92	C₂×C₄×C₈×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	2	yes	—
96	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₄₁	—	2	1	no	—
99	#137×C₄₁	—	4	4	no	—
100	AGL(1,ℤ/8)×C₄₁	—	4	4	no	—
101	#135×C₄₁	—	2	8	no	—
102	#135×C₄₁	—	4	4	no	—
103	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
104	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
105	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
106	C₂×SD₁₆×C₄₁	—	2	4	no	—
107	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
108	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
109	C₂×SD₁₆×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×SD₁₆×C₄₁	C₂³	1	4	yes	—
114	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
115	C₂×D₈×C₄₁	C₂³	1	2	yes	—
116	C₂×D₈×C₄₁	C₂³	1	2	yes	—
117	C₂×D₈×C₄₁	C₂³	1	4	yes	—
118	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
119	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
121	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
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	C₄⋊Q₈×C₄₁	C₂³	1	4	yes	—
126	#127×C₄₁	C₂³	1	1	yes	characteristic
127	#127×C₄₁	C₂³	1	1	yes	characteristic
128	#127×C₄₁	C₂³	1	4	yes	—
129	#126×C₄₁	—	2	4	no	—
130	#126×C₄₁	—	2	4	no	—
131	#126×C₄₁	—	2	4	no	—
132	#125×C₄₁	—	2	2	no	—
133	#125×C₄₁	—	2	4	no	—
134	#125×C₄₁	D₄	1	2	yes	—
135	#124×C₄₁	—	2	2	no	—
136	#124×C₄₁	—	2	4	no	—
137	#124×C₄₁	C₂³	1	2	yes	—
138	#124×C₄₁	C₂³	1	2	yes	—
139	#124×C₄₁	C₂³	1	4	yes	—
140	#124×C₄₁	C₂³	1	4	yes	—
141	#123×C₄₁	—	2	4	no	—
142	#123×C₄₁	—	2	4	no	—
143	#123×C₄₁	—	2	4	no	—
144	#123×C₄₁	—	2	4	no	—
145	C₂²⋊Q₈×C₄₁	—	2	2	no	—
146	C₂²⋊Q₈×C₄₁	—	2	4	no	—
147	C₂²⋊Q₈×C₄₁	—	2	2	no	—
148	C₂²⋊Q₈×C₄₁	—	2	2	no	—
149	C₂²⋊Q₈×C₄₁	D₄	1	2	yes	—
150	C₂²⋊Q₈×C₄₁	D₄	1	2	yes	—
151	#121×C₄₁	—	2	1	no	—
152	#121×C₄₁	—	2	1	no	—
153	#121×C₄₁	—	2	1	no	—
154	#121×C₄₁	—	2	1	no	—
155	#121×C₄₁	—	2	2	no	—
156	#121×C₄₁	—	2	2	no	—
157	#121×C₄₁	—	2	2	no	—
158	#121×C₄₁	—	2	4	no	—
159	#120×C₄₁	—	2	4	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	4	yes	—
166	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
167	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
168	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
169	C₄×D₄×C₄₁	—	2	4	no	—
170	C₄×D₄×C₄₁	—	2	2	no	—
171	C₄×D₄×C₄₁	—	2	4	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	—	2	1	no	—
176	C₄×D₄×C₄₁	—	2	1	no	—
177	C₄×D₄×C₄₁	—	2	1	no	—
178	C₄×D₄×C₄₁	—	2	1	no	—
179	C₄×D₄×C₄₁	C₂³	1	2	yes	—
180	C₄×D₄×C₄₁	C₂³	1	2	yes	—
181	C₄×D₄×C₄₁	C₂³	1	4	yes	—
182	C₄×D₄×C₄₁	C₂³	1	4	yes	—
183	#117×C₄₁	—	2	2	no	—
184	#117×C₄₁	—	2	2	no	—
185	#117×C₄₁	—	2	2	no	—
186	#117×C₄₁	—	2	4	no	—
187	#117×C₄₁	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
189	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
190	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
191	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
194	C₂×C₄²×C₄₁	—	2	1	no	—
195	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
196	#106×C₄₁	C₂³	1	2	yes	—
197	#106×C₄₁	C₂³	1	2	yes	—
198	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
199	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
200	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
201	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
202	#103×C₄₁	C₂³	1	2	yes	—
203	#103×C₄₁	C₂³	1	2	yes	—
204	#103×C₄₁	C₂³	1	4	yes	—
205	#103×C₄₁	C₂³	1	4	yes	—
206	#102×C₄₁	C₂³	1	2	yes	—
207	#102×C₄₁	C₂³	1	2	yes	—
208	#102×C₄₁	C₂³	1	4	yes	—
209	#102×C₄₁	C₂³	1	4	yes	—
210	#97×C₄₁	C₂³	1	4	yes	—
211	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
212	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
213	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
214	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
215	C₄×C₈×C₄₁	C₂³	1	4	yes	—
216	C₂⁴×C₄₁	—	2	1	no	—
217	#41×C₄₁	—	2	4	no	—
218	#41×C₄₁	—	2	4	no	—
219	#41×C₄₁	—	2	4	no	—
220	#41×C₄₁	—	2	4	no	—
221	#41×C₄₁	—	8	4	no	—
222	C₂×Q₈×C₄₁	—	2	1	no	—
223	C₂×Q₈×C₄₁	—	2	2	no	—
224	C₂×Q₈×C₄₁	—	2	2	no	—
225	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
226	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
228	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
229	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
230	C₂×D₄×C₄₁	—	2	2	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	1	no	—
235	C₂×D₄×C₄₁	—	2	4	no	—
236	C₂×D₄×C₄₁	—	2	1	no	—
237	C₂×D₄×C₄₁	—	2	1	no	—
238	C₂×D₄×C₄₁	—	2	4	no	—
239	C₂×D₄×C₄₁	—	2	2	no	—
240	C₂×D₄×C₄₁	—	2	2	no	—
241	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
242	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
243	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₄₁	—	2	1	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	2	no	—
250	C₂²×C₄×C₄₁	—	2	4	no	—
251	C₂²×C₄×C₄₁	—	2	4	no	—
252	C₂²×C₄×C₄₁	—	2	2	no	—
253	C₂²×C₄×C₄₁	—	8	2	no	—
254	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
257	Q₁₆×C₄₁	—	2	4	no	—
258	Q₁₆×C₄₁	—	4	2	no	—
259	Q₁₆×C₄₁	—	4	4	no	—
260	SD₁₆×C₄₁	—	2	4	no	—
261	SD₁₆×C₄₁	—	2	4	no	—
262	SD₁₆×C₄₁	—	2	4	no	—
263	SD₁₆×C₄₁	—	2	4	no	—
264	SD₁₆×C₄₁	—	4	2	no	—
265	SD₁₆×C₄₁	—	4	2	no	—
266	SD₁₆×C₄₁	—	4	4	no	—
267	SD₁₆×C₄₁	—	4	4	no	—
268	D₈×C₄₁	—	2	4	no	—
269	D₈×C₄₁	—	4	2	no	—
270	D₈×C₄₁	—	4	4	no	—
271	M₁₆×C₄₁	—	2	4	no	—
272	C₂×C₈×C₄₁	—	2	2	no	—
273	C₂×C₈×C₄₁	#41	1	4	yes	complemented
274	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
275	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
276	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
277	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
278	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
279	C₄⋊C₄×C₄₁	—	2	1	no	—
280	C₄⋊C₄×C₄₁	—	2	1	no	—
281	C₄⋊C₄×C₄₁	—	2	4	no	—
282	C₄⋊C₄×C₄₁	—	2	4	no	—
283	C₄⋊C₄×C₄₁	—	2	2	no	—
284	C₄⋊C₄×C₄₁	—	2	2	no	—
285	C₄⋊C₄×C₄₁	—	2	1	no	—
286	C₄⋊C₄×C₄₁	—	2	4	no	—
287	C₄⋊C₄×C₄₁	—	2	1	no	—
288	C₄⋊C₄×C₄₁	—	2	1	no	—
289	C₄⋊C₄×C₄₁	—	2	1	no	—
290	C₄⋊C₄×C₄₁	—	2	4	no	—
291	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
292	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
293	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
294	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
295	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
296	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
298	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
299	C₂²⋊C₄×C₄₁	—	2	2	no	—
300	C₂²⋊C₄×C₄₁	—	2	2	no	—
301	C₂²⋊C₄×C₄₁	—	2	2	no	—
302	C₂²⋊C₄×C₄₁	—	2	4	no	—
303	C₂²⋊C₄×C₄₁	—	2	4	no	—
304	C₂²⋊C₄×C₄₁	—	2	4	no	—
305	C₂²⋊C₄×C₄₁	—	2	4	no	—
306	C₂²⋊C₄×C₄₁	—	2	2	no	—
307	C₂²⋊C₄×C₄₁	—	2	4	no	—
308	C₂²⋊C₄×C₄₁	—	2	2	no	—
309	C₂²⋊C₄×C₄₁	—	2	2	no	—
310	C₂²⋊C₄×C₄₁	—	2	4	no	—
311	C₂²⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
312	C₄²×C₄₁	—	2	2	no	—
313	C₄²×C₄₁	—	2	2	no	—
314	C₄²×C₄₁	—	2	4	no	—
315	C₄²×C₄₁	—	2	4	no	—
316	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
319	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
320	C₄²×C₄₁	C₂⁴	1	4	yes	—
321	C₂³×C₄₁	—	2	2	no	—
322	C₂³×C₄₁	—	2	2	no	—
323	C₂³×C₄₁	—	2	2	no	—
324	C₂³×C₄₁	—	4	2	no	—
325	C₂³×C₄₁	—	8	1	no	—
326	C₂³×C₄₁	—	8	1	no	—
327	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
328	Q₈×C₄₁	—	2	4	no	—
329	Q₈×C₄₁	—	2	2	no	—
330	Q₈×C₄₁	—	2	2	no	—
331	Q₈×C₄₁	—	2	2	no	—
332	Q₈×C₄₁	—	2	2	no	—
333	Q₈×C₄₁	—	2	2	no	—
334	Q₈×C₄₁	—	2	2	no	—
335	Q₈×C₄₁	—	4	2	no	—
336	Q₈×C₄₁	—	4	2	no	—
337	D₄×C₄₁	—	2	2	no	—
338	D₄×C₄₁	—	2	2	no	—
339	D₄×C₄₁	—	2	2	no	—
340	D₄×C₄₁	—	2	2	no	—
341	D₄×C₄₁	—	2	2	no	—
342	D₄×C₄₁	—	2	2	no	—
343	D₄×C₄₁	—	4	4	no	—
344	D₄×C₄₁	—	4	4	no	—
345	D₄×C₄₁	—	4	2	no	—
346	D₄×C₄₁	—	4	2	no	—
347	D₄×C₄₁	—	4	2	no	—
348	D₄×C₄₁	—	8	1	no	—
349	D₄×C₄₁	—	8	1	no	—
350	D₄×C₄₁	—	8	4	no	—
351	D₄×C₄₁	—	8	4	no	—
352	C₂×C₄×C₄₁	—	2	2	no	—
353	C₂×C₄×C₄₁	—	2	2	no	—
354	C₂×C₄×C₄₁	—	2	2	no	—
355	C₂×C₄×C₄₁	—	2	2	no	—
356	C₂×C₄×C₄₁	—	2	2	no	—
357	C₂×C₄×C₄₁	—	2	2	no	—
358	C₂×C₄×C₄₁	—	4	1	no	—
359	C₂×C₄×C₄₁	—	4	2	no	—
360	C₂×C₄×C₄₁	—	4	4	no	—
361	C₂×C₄×C₄₁	—	4	4	no	—
362	C₂×C₄×C₄₁	—	4	4	no	—
363	C₂×C₄×C₄₁	—	8	4	no	—
364	C₂×C₄×C₄₁	—	8	2	no	—
365	C₂×C₄×C₄₁	—	8	4	no	—
366	C₂×C₄×C₄₁	—	8	1	no	—
367	C₂×C₄×C₄₁	—	8	1	no	—
368	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
370	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
371	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
376	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
377	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
378	C₈×C₄₁	—	2	1	no	—
379	C₈×C₄₁	—	2	1	no	—
380	C₈×C₄₁	—	2	4	no	—
381	C₈×C₄₁	C₂×#41	1	2	yes	—
382	C₈×C₄₁	C₂×#41	1	2	yes	—
383	#61407	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
384	C₂²×C₄₁	—	2	1	no	—
385	C₂²×C₄₁	—	2	1	no	—
386	C₂²×C₄₁	—	4	2	no	—
387	C₂²×C₄₁	—	4	2	no	—
388	C₂²×C₄₁	—	4	2	no	—
389	C₂²×C₄₁	—	4	2	no	—
390	C₂²×C₄₁	—	4	2	no	—
391	C₂²×C₄₁	—	4	2	no	—
392	C₂²×C₄₁	—	4	2	no	—
393	C₂²×C₄₁	—	4	2	no	—
394	C₂²×C₄₁	—	4	2	no	—
395	C₂²×C₄₁	—	8	4	no	—
396	C₂²×C₄₁	#550	1	2	yes	—
397	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
398	C₄×C₄₁	—	2	1	no	—
399	C₄×C₄₁	—	2	1	no	—
400	C₄×C₄₁	—	2	4	no	—
401	C₄×C₄₁	—	2	1	no	—
402	C₄×C₄₁	—	2	4	no	—
403	C₄×C₄₁	—	4	2	no	—
404	C₄×C₄₁	—	4	2	no	—
405	C₄×C₄₁	—	4	2	no	—
406	C₄×C₄₁	—	4	2	no	—
407	C₄×C₄₁	—	4	2	no	—
408	C₄×C₄₁	#550	1	2	yes	—
409	C₄×C₄₁	#577	1	2	yes	—
410	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
411	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
412	#3507	C₂×C₄₁	1	1	yes	characteristic, complemented
413	#3506	C₂×C₄₁	1	1	yes	characteristic, complemented
414	#3401	C₂×C₄₁	1	4	yes	complemented
415	#3399	C₂×C₄₁	1	2	yes	complemented
416	#3398	C₂×C₄₁	1	2	yes	complemented
417	#3394	C₂×C₄₁	1	2	yes	complemented
418	#3394	C₂×C₄₁	1	4	yes	complemented
419	#3392	C₂×C₄₁	1	2	yes	complemented
420	#3154	C₂×C₄₁	1	2	yes	complemented
421	#3147	C₂×C₄₁	1	1	yes	characteristic, complemented
422	#3046	C₂×C₄₁	1	2	yes	complemented
423	#3045	C₂×C₄₁	1	2	yes	complemented
424	#3037	C₂×C₄₁	1	1	yes	characteristic, complemented
425	#3036	C₂×C₄₁	1	1	yes	characteristic, complemented
426	#2960	C₂×C₄₁	1	1	yes	characteristic, complemented
427	#2952	C₂×C₄₁	1	2	yes	complemented
428	C₂×C₄×SD₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
429	C₂×C₄₁	—	2	2	no	—
430	C₂×C₄₁	—	8	2	no	—
431	C₂×C₄₁	—	8	2	no	—
432	C₂×C₄₁	—	8	2	no	—
433	C₂×C₄₁	C₂×#550	1	1	yes	characteristic
434	C₂×C₄₁	C₂×#577	1	1	yes	characteristic
435	C₂×C₄₁	#3584	1	1	yes	characteristic
436	C₂×#137	C₂²×C₄₁	1	2	yes	—
437	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	2	yes	—
438	C₂×#135	C₂²×C₄₁	1	2	yes	—
439	C₂×#135	C₂²×C₄₁	1	2	yes	—
440	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
441	#559	C₂²×C₄₁	1	4	yes	—
442	#559	C₂²×C₄₁	1	2	yes	complemented
443	#557	C₂²×C₄₁	1	2	yes	complemented
444	#556	—	2	1	no	—
445	#556	C₂²×C₄₁	1	2	yes	—
446	#556	C₂²×C₄₁	1	4	yes	complemented
447	#555	—	2	1	no	—
448	#554	—	2	1	no	—
449	#553	—	2	2	no	—
450	#552	—	2	2	no	—
451	#550	C₂²×C₄₁	1	2	yes	—
452	#547	—	2	1	no	—
453	#539	—	2	2	no	—
454	#538	—	2	2	no	—
455	#536	C₂²×C₄₁	1	2	yes	—
456	#535	C₂²×C₄₁	1	2	yes	—
457	#533	C₂²×C₄₁	1	1	yes	characteristic
458	#532	C₂²×C₄₁	1	1	yes	characteristic
459	#532	C₂²×C₄₁	1	1	yes	characteristic
460	#529	—	2	2	no	—
461	#525	—	2	2	no	—
462	#520	C₂²×C₄₁	1	2	yes	—
463	#520	C₂²×C₄₁	1	2	yes	—
464	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
465	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
466	#497	C₂²×C₄₁	1	4	yes	—
467	#496	C₂²×C₄₁	1	4	yes	—
468	#495	C₂²×C₄₁	1	4	yes	—
469	#495	C₂²×C₄₁	1	2	yes	complemented
470	#495	C₂²×C₄₁	1	2	yes	complemented
471	#494	C₂²×C₄₁	1	1	yes	characteristic, complemented
472	#493	C₂²×C₄₁	1	1	yes	characteristic, complemented
473	#492	C₂²×C₄₁	1	4	yes	—
474	#492	C₂²×C₄₁	1	1	yes	characteristic, complemented
475	#492	C₂²×C₄₁	1	1	yes	characteristic, complemented
476	#464	C₂²×C₄₁	1	4	yes	—
477	#464	C₂²×C₄₁	1	4	yes	complemented
478	#464	C₂²×C₄₁	1	4	yes	complemented
479	#463	C₂²×C₄₁	1	4	yes	—
480	#463	C₂²×C₄₁	1	4	yes	—
481	#463	C₂²×C₄₁	1	4	yes	complemented
482	#462	C₂²×C₄₁	1	2	yes	complemented
483	#462	C₂²×C₄₁	1	4	yes	complemented
484	#461	C₂²×C₄₁	1	2	yes	—
485	#461	C₂²×C₄₁	1	4	yes	complemented
486	#460	C₂²×C₄₁	1	4	yes	—
487	#460	C₂²×C₄₁	1	2	yes	complemented
488	#459	C₂²×C₄₁	1	2	yes	—
489	#459	C₂²×C₄₁	1	4	yes	—
490	#446	C₂²×C₄₁	1	2	yes	complemented
491	#446	C₂²×C₄₁	1	2	yes	complemented
492	C₈×Q₈	C₂²×C₄₁	1	2	yes	complemented
493	C₈×Q₈	C₂²×C₄₁	1	2	yes	complemented
494	#442	C₂²×C₄₁	1	4	yes	complemented
495	#441	C₂²×C₄₁	1	4	yes	complemented
496	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
497	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
498	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
499	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
500	C₄×SD₁₆	C₂²×C₄₁	1	4	yes	complemented
501	C₄×SD₁₆	C₂²×C₄₁	1	4	yes	complemented
502	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
503	#424	C₂²×C₄₁	1	2	yes	—
504	#423	C₂²×C₄₁	1	1	yes	characteristic
505	#417	C₂²×C₄₁	1	2	yes	—
506	#417	C₂²×C₄₁	1	2	yes	—
507	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
508	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
509	#405	C₂²×C₄₁	1	2	yes	—
510	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
511	C₄₁	#61407	1	1	yes	characteristic, direct product factor, Sylow
512	C₂×#41	—	2	2	no	—
513	C₂×#41	C₂³×C₄₁	1	2	yes	—
514	C₂×#41	C₂³×C₄₁	1	2	yes	—
515	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
516	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
517	C₂³×C₄	—	2	1	no	—
518	#137	—	4	4	no	—
519	AGL(1,ℤ/8)	—	4	4	no	—
520	#135	—	2	8	no	—
521	#135	—	4	4	no	—
522	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
523	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
524	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
525	C₂×SD₁₆	—	2	4	no	—
526	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
527	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
528	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
529	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
530	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
531	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
532	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
533	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
534	C₂×D₈	C₂³×C₄₁	1	2	yes	—
535	C₂×D₈	C₂³×C₄₁	1	2	yes	—
536	C₂×D₈	C₂³×C₄₁	1	4	yes	—
537	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
538	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
539	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
540	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
541	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
542	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
543	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
544	C₄⋊Q₈	C₂³×C₄₁	1	4	yes	—
545	#127	C₂³×C₄₁	1	1	yes	characteristic
546	#127	C₂³×C₄₁	1	1	yes	characteristic
547	#127	C₂³×C₄₁	1	4	yes	—
548	#126	—	2	4	no	—
549	#126	—	2	4	no	—
550	#126	—	2	4	no	—
551	#125	—	2	2	no	—
552	#125	—	2	4	no	—
553	#125	D₄×C₄₁	1	2	yes	—
554	#124	—	2	2	no	—
555	#124	—	2	4	no	—
556	#124	C₂³×C₄₁	1	2	yes	—
557	#124	C₂³×C₄₁	1	2	yes	—
558	#124	C₂³×C₄₁	1	4	yes	—
559	#124	C₂³×C₄₁	1	4	yes	—
560	#123	—	2	4	no	—
561	#123	—	2	4	no	—
562	#123	—	2	4	no	—
563	#123	—	2	4	no	—
564	C₂²⋊Q₈	—	2	2	no	—
565	C₂²⋊Q₈	—	2	4	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	D₄×C₄₁	1	2	yes	—
569	C₂²⋊Q₈	D₄×C₄₁	1	2	yes	—
570	#121	—	2	1	no	—
571	#121	—	2	1	no	—
572	#121	—	2	1	no	—
573	#121	—	2	1	no	—
574	#121	—	2	2	no	—
575	#121	—	2	2	no	—
576	#121	—	2	2	no	—
577	#121	—	2	4	no	—
578	#120	—	2	4	no	—
579	C₄×Q₈	—	2	2	no	—
580	C₄×Q₈	—	2	1	no	—
581	C₄×Q₈	—	2	1	no	—
582	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
583	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
584	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
585	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
586	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
587	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
588	C₄×D₄	—	2	4	no	—
589	C₄×D₄	—	2	2	no	—
590	C₄×D₄	—	2	4	no	—
591	C₄×D₄	—	2	4	no	—
592	C₄×D₄	—	2	1	no	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	C₂³×C₄₁	1	2	yes	—
599	C₄×D₄	C₂³×C₄₁	1	2	yes	—
600	C₄×D₄	C₂³×C₄₁	1	4	yes	—
601	C₄×D₄	C₂³×C₄₁	1	4	yes	—
602	#117	—	2	2	no	—
603	#117	—	2	2	no	—
604	#117	—	2	2	no	—
605	#117	—	2	4	no	—
606	#117	C₂³×C₄₁	1	2	yes	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	—	2	2	no	—
609	C₂×C₄⋊C₄	—	2	2	no	—
610	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₄²	—	2	1	no	—
614	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
615	#106	C₂³×C₄₁	1	2	yes	—
616	#106	C₂³×C₄₁	1	2	yes	—
617	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
618	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
619	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
620	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
621	#103	C₂³×C₄₁	1	2	yes	—
622	#103	C₂³×C₄₁	1	2	yes	—
623	#103	C₂³×C₄₁	1	4	yes	—
624	#103	C₂³×C₄₁	1	4	yes	—
625	#102	C₂³×C₄₁	1	2	yes	—
626	#102	C₂³×C₄₁	1	2	yes	—
627	#102	C₂³×C₄₁	1	4	yes	—
628	#102	C₂³×C₄₁	1	4	yes	—
629	#97	C₂³×C₄₁	1	4	yes	—
630	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
631	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
632	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
633	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
634	C₄×C₈	C₂³×C₄₁	1	4	yes	—
635	C₂⁴	—	2	1	no	—
636	#41	—	2	4	no	—
637	#41	—	2	4	no	—
638	#41	—	2	4	no	—
639	#41	—	2	4	no	—
640	#41	—	8	4	no	—
641	C₂×Q₈	—	2	1	no	—
642	C₂×Q₈	—	2	2	no	—
643	C₂×Q₈	—	2	2	no	—
644	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
645	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
646	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
647	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
648	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	2	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	4	no	—
655	C₂×D₄	—	2	1	no	—
656	C₂×D₄	—	2	1	no	—
657	C₂×D₄	—	2	4	no	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
661	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
662	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	4	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	8	2	no	—
673	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
674	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
676	Q₁₆	—	2	4	no	—
677	Q₁₆	—	4	2	no	—
678	Q₁₆	—	4	4	no	—
679	SD₁₆	—	2	4	no	—
680	SD₁₆	—	2	4	no	—
681	SD₁₆	—	2	4	no	—
682	SD₁₆	—	2	4	no	—
683	SD₁₆	—	4	2	no	—
684	SD₁₆	—	4	2	no	—
685	SD₁₆	—	4	4	no	—
686	SD₁₆	—	4	4	no	—
687	D₈	—	2	4	no	—
688	D₈	—	4	2	no	—
689	D₈	—	4	4	no	—
690	M₁₆	—	2	4	no	—
691	C₂×C₈	—	2	2	no	—
692	C₂×C₈	#41×C₄₁	1	4	yes	complemented
693	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
694	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
695	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
696	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
697	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
711	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
712	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
713	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
714	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
715	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
716	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
717	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
718	C₂²⋊C₄	—	2	2	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
731	C₄²	—	2	2	no	—
732	C₄²	—	2	2	no	—
733	C₄²	—	2	4	no	—
734	C₄²	—	2	4	no	—
735	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
736	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
737	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
738	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
739	C₄²	C₂⁴×C₄₁	1	4	yes	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	4	2	no	—
744	C₂³	—	8	1	no	—
745	C₂³	—	8	1	no	—
746	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
747	Q₈	—	2	4	no	—
748	Q₈	—	2	2	no	—
749	Q₈	—	2	2	no	—
750	Q₈	—	2	2	no	—
751	Q₈	—	2	2	no	—
752	Q₈	—	2	2	no	—
753	Q₈	—	2	2	no	—
754	Q₈	—	4	2	no	—
755	Q₈	—	4	2	no	—
756	D₄	—	2	2	no	—
757	D₄	—	2	2	no	—
758	D₄	—	2	2	no	—
759	D₄	—	2	2	no	—
760	D₄	—	2	2	no	—
761	D₄	—	2	2	no	—
762	D₄	—	4	4	no	—
763	D₄	—	4	4	no	—
764	D₄	—	4	2	no	—
765	D₄	—	4	2	no	—
766	D₄	—	4	2	no	—
767	D₄	—	8	4	no	—
768	D₄	—	8	1	no	—
769	D₄	—	8	1	no	—
770	D₄	—	8	4	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	2	no	—
779	C₂×C₄	—	4	4	no	—
780	C₂×C₄	—	4	4	no	—
781	C₂×C₄	—	4	4	no	—
782	C₂×C₄	—	8	2	no	—
783	C₂×C₄	—	8	4	no	—
784	C₂×C₄	—	8	4	no	—
785	C₂×C₄	—	8	1	no	—
786	C₂×C₄	—	8	1	no	—
787	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
788	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
789	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
790	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
791	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
793	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
794	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
795	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
796	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
797	C₈	—	2	1	no	—
798	C₈	—	2	1	no	—
799	C₈	—	2	4	no	—
800	C₈	C₂×#41×C₄₁	1	2	yes	—
801	C₈	C₂×#41×C₄₁	1	2	yes	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	8	4	no	—
814	C₂²	C₄₁×#550	1	2	yes	—
815	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
816	C₄	—	2	1	no	—
817	C₄	—	2	4	no	—
818	C₄	—	2	1	no	—
819	C₄	—	2	1	no	—
820	C₄	—	2	4	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	C₄₁×#550	1	2	yes	—
827	C₄	C₄₁×#577	1	2	yes	—
828	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
829	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
830	C₂	—	2	2	no	—
831	C₂	—	8	2	no	—
832	C₂	—	8	2	no	—
833	C₂	—	8	2	no	—
834	C₂	C₂×C₄₁×#550	1	1	yes	characteristic
835	C₂	C₂×C₄₁×#577	1	1	yes	characteristic
836	C₂	C₄₁×#3584	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×#3507	C₂	semidirect
2. C₄₁×#3506	C₂	semidirect
3. C₄₁×#3401	C₂	semidirect
4. C₄₁×#3399	C₂	semidirect
5. C₄₁×#3398	C₂	semidirect
6. C₄₁×#3394	C₂	semidirect
7. C₄₁×#3394	C₂	semidirect
8. C₄₁×#3392	C₂	semidirect
9. C₄₁×#3154	C₂	semidirect
10. C₄₁×#3147	C₂	semidirect
11. C₄₁×#3046	C₂	semidirect
12. C₄₁×#3045	C₂	semidirect
13. C₄₁×#3037	C₂	semidirect
14. C₄₁×#3036	C₂	semidirect
15. C₄₁×#2960	C₂	semidirect
16. C₄₁×#2952	C₂	semidirect
17. C₂×C₄×SD₁₆×C₄₁	C₂	semidirect
24. C₄₁×#559	C₂²	semidirect
25. C₄₁×#557	C₂²	semidirect
28. C₄₁×#556	C₂²	semidirect
51. C₄₁×#495	C₂²	semidirect
52. C₄₁×#495	C₂²	semidirect
53. C₄₁×#494	C₂²	semidirect
54. C₄₁×#493	C₂²	semidirect
56. C₄₁×#492	C₂²	semidirect
57. C₄₁×#492	C₂²	semidirect
59. C₄₁×#464	C₂²	semidirect
60. C₄₁×#464	C₂²	semidirect
63. C₄₁×#463	C₂²	semidirect
64. C₄₁×#462	C₂²	semidirect
65. C₄₁×#462	C₂²	semidirect
67. C₄₁×#461	C₂²	semidirect
69. C₄₁×#460	C₂²	semidirect
72. C₄₁×#446	C₂²	semidirect
73. C₄₁×#446	C₂²	semidirect
74. C₈×Q₈×C₄₁	C₂²	semidirect
75. C₈×Q₈×C₄₁	C₂²	semidirect
76. C₄₁×#442	C₂²	semidirect
77. C₄₁×#441	C₂²	semidirect
82. C₄×SD₁₆×C₄₁	C₂²	semidirect
83. C₄×SD₁₆×C₄₁	C₂²	semidirect
273. C₂×C₈×C₄₁	#41	semidirect
383. #61407	C₄₁	direct (N × H)
412. #3507	C₂×C₄₁	semidirect
413. #3506	C₂×C₄₁	semidirect
414. #3401	C₂×C₄₁	semidirect
415. #3399	C₂×C₄₁	semidirect
416. #3398	C₂×C₄₁	semidirect
417. #3394	C₂×C₄₁	semidirect
418. #3394	C₂×C₄₁	semidirect
419. #3392	C₂×C₄₁	semidirect
420. #3154	C₂×C₄₁	semidirect
421. #3147	C₂×C₄₁	semidirect
422. #3046	C₂×C₄₁	semidirect
423. #3045	C₂×C₄₁	semidirect
424. #3037	C₂×C₄₁	semidirect
425. #3036	C₂×C₄₁	semidirect
426. #2960	C₂×C₄₁	semidirect
427. #2952	C₂×C₄₁	semidirect
428. C₂×C₄×SD₁₆	C₂×C₄₁	semidirect
442. #559	C₂²×C₄₁	semidirect
443. #557	C₂²×C₄₁	semidirect
446. #556	C₂²×C₄₁	semidirect
469. #495	C₂²×C₄₁	semidirect
470. #495	C₂²×C₄₁	semidirect
471. #494	C₂²×C₄₁	semidirect
472. #493	C₂²×C₄₁	semidirect
474. #492	C₂²×C₄₁	semidirect
475. #492	C₂²×C₄₁	semidirect
477. #464	C₂²×C₄₁	semidirect
478. #464	C₂²×C₄₁	semidirect
481. #463	C₂²×C₄₁	semidirect
482. #462	C₂²×C₄₁	semidirect
483. #462	C₂²×C₄₁	semidirect
485. #461	C₂²×C₄₁	semidirect
487. #460	C₂²×C₄₁	semidirect
490. #446	C₂²×C₄₁	semidirect
491. #446	C₂²×C₄₁	semidirect
492. C₈×Q₈	C₂²×C₄₁	semidirect
493. C₈×Q₈	C₂²×C₄₁	semidirect
494. #442	C₂²×C₄₁	semidirect
495. #441	C₂²×C₄₁	semidirect
500. C₄×SD₁₆	C₂²×C₄₁	semidirect
501. C₄×SD₁₆	C₂²×C₄₁	semidirect
511. C₄₁	#61407	direct (N × H)
692. 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×#3507	2
C₄₁×#3506	2
C₄₁×#3401	2
C₄₁×#3399	2
C₄₁×#3398	2
C₄₁×#3394	2
C₄₁×#3392	2
C₄₁×#3154	2
C₄₁×#3147	2
C₄₁×#3046	2
C₄₁×#3045	2
C₄₁×#3037	2
C₄₁×#3036	2
C₄₁×#2960	2
C₄₁×#2952	2
C₂×C₄×SD₁₆×C₄₁	2
#61407	41

Subgroups — C41×#61407 #23837608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61407 #23837608