Subgroups — C₄₁×#61961 #23838162

Order 10496.

2178 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3399	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3373	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3332	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3306	C₂	1	4	yes	maximal, complemented
7	C₄₁×#3274	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3264	C₂	1	4	yes	maximal, complemented
9	C₄₁×#3253	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#3214	C₂	1	2	yes	maximal, complemented
12	C₄₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3109	C₂	1	2	yes	maximal, complemented
14	C₄₁×#3101	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3036	C₂	1	2	yes	maximal, complemented
16	C₂×C₄₁×#459	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#2989	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₄₁	—	2	1	no	—
19	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	4	yes	complemented
20	C₂²×D₈×C₄₁	C₂²	1	2	yes	—
21	C₄₁×#559	—	2	1	no	—
22	C₄₁×#559	C₂²	1	2	yes	complemented
23	C₄₁×#550	—	2	1	no	—
24	C₄₁×#550	C₂²	1	2	yes	complemented
25	C₄₁×#550	C₂²	1	1	yes	characteristic, complemented
26	D₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
27	C₄₁×#548	—	2	1	no	—
28	C₄₁×#547	C₂²	1	2	yes	—
29	C₄₁×#547	C₂²	1	1	yes	characteristic, complemented
30	C₄₁×#546	—	2	2	no	—
31	C₄₁×#546	—	2	1	no	—
32	C₄₁×#546	—	2	2	no	—
33	C₄₁×#546	C₂²	1	4	yes	complemented
34	D₄²×C₄₁	C₂²	1	2	yes	—
35	D₄²×C₄₁	C₂²	1	1	yes	characteristic, complemented
36	C₄₁×#540	—	2	2	no	—
37	C₄₁×#535	—	2	1	no	—
38	C₄₁×#533	C₂²	1	1	yes	characteristic, complemented
39	C₄₁×#532	C₂²	1	1	yes	characteristic
40	C₄₁×#532	C₂²	1	2	yes	complemented
41	C₄₁×#532	C₂²	1	2	yes	complemented
42	C₄₁×#532	C₂²	1	2	yes	complemented
43	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic, complemented
44	C₄₁×#525	—	2	1	no	—
45	C₄₁×#525	—	2	2	no	—
46	C₄₁×#518	—	2	1	no	—
47	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	complemented
50	C₄₁×#496	C₂²	1	4	yes	complemented
51	C₄₁×#493	C₂²	1	2	yes	complemented
52	C₄₁×#489	C₂²	1	4	yes	complemented
53	C₄₁×#486	C₂²	1	2	yes	complemented
54	C₄₁×#483	C₂²	1	2	yes	complemented
55	C₄₁×#481	C₂²	1	4	yes	complemented
56	C₄₁×#476	C₂²	1	4	yes	complemented
57	C₄₁×#476	C₂²	1	1	yes	characteristic, complemented
58	C₄₁×#476	C₂²	1	1	yes	characteristic, complemented
59	C₄₁×#476	C₂²	1	2	yes	complemented
60	C₄₁×#475	C₂²	1	2	yes	complemented
61	C₄₁×#469	C₂²	1	4	yes	complemented
62	C₄₁×#469	C₂²	1	4	yes	complemented
63	C₄₁×#465	C₂²	1	4	yes	complemented
64	C₄₁×#463	C₂²	1	4	yes	complemented
65	C₄₁×#463	C₂²	1	4	yes	complemented
66	C₄₁×#461	C₂²	1	1	yes	characteristic, complemented
67	C₄₁×#461	C₂²	1	2	yes	complemented
68	C₄₁×#461	C₂²	1	1	yes	characteristic, complemented
69	C₄₁×#460	C₂²	1	2	yes	complemented
70	C₄₁×#459	C₂²	1	2	yes	—
71	C₄₁×#459	C₂²	1	2	yes	—
72	C₄₁×#459	C₂²	1	2	yes	complemented
73	C₄₁×#459	C₂²	1	2	yes	complemented
74	C₄₁×#459	C₂²	1	2	yes	complemented
75	C₄₁×#459	C₂²	1	4	yes	complemented
76	C₄₁×#459	C₂²	1	2	yes	complemented
77	C₄₁×#450	C₂²	1	2	yes	—
78	C₄₁×#449	C₂²	1	4	yes	complemented
79	C₄₁×#449	C₂²	1	4	yes	complemented
80	C₄₁×#447	C₂²	1	4	yes	complemented
81	C₄₁×#447	C₂²	1	4	yes	complemented
82	C₄₁×#446	C₂²	1	2	yes	complemented
83	C₄₁×#442	C₂²	1	4	yes	complemented
84	C₄₁×#442	C₂²	1	4	yes	complemented
85	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
86	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
87	C₄₁×#436	C₂²	1	2	yes	complemented
88	C₄₁×#435	C₂²	1	4	yes	complemented
89	C₄₁×#432	C₂²	1	2	yes	complemented
90	C₄₁×#431	C₂²	1	1	yes	characteristic, complemented
91	C₄₁×#423	C₂²	1	2	yes	complemented
92	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
93	C₄₁×#417	C₂²	1	4	yes	complemented
94	C₂×#102×C₄₁	C₂²	1	2	yes	complemented
95	C₂×#41×C₄₁	—	2	1	no	—
96	C₂×#41×C₄₁	—	2	2	no	—
97	C₂×#41×C₄₁	—	2	1	no	—
98	C₂×#41×C₄₁	—	2	1	no	—
99	C₂×#41×C₄₁	—	2	2	no	—
100	C₂×#41×C₄₁	—	2	2	no	—
101	C₂×#41×C₄₁	—	4	8	no	—
102	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
103	C₂×#41×C₄₁	C₂³	1	4	yes	—
104	C₂²×Q₈×C₄₁	—	2	1	no	—
105	C₂²×D₄×C₄₁	—	2	2	no	—
106	C₂²×D₄×C₄₁	—	2	1	no	—
107	C₂²×D₄×C₄₁	—	2	1	no	—
108	C₂²×D₄×C₄₁	—	2	1	no	—
109	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
111	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
112	C₂³×C₄×C₄₁	—	2	1	no	—
113	C₂³×C₄×C₄₁	—	2	2	no	—
114	AGL(1,ℤ/8)×C₄₁	—	4	8	no	—
115	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
116	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
117	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
118	C₂×D₈×C₄₁	—	4	4	no	—
119	C₂×D₈×C₄₁	C₂³	1	4	yes	—
120	C₂×D₈×C₄₁	C₂³	1	4	yes	—
121	C₂×D₈×C₄₁	C₂³	1	4	yes	—
122	C₂×D₈×C₄₁	C₂³	1	4	yes	—
123	C₂×M₁₆×C₄₁	C₂³	1	4	yes	—
124	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
125	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
126	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
127	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
128	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
129	#127×C₄₁	—	2	2	no	—
130	#127×C₄₁	—	2	1	no	—
131	#127×C₄₁	—	2	1	no	—
132	#127×C₄₁	C₂³	1	2	yes	—
133	#127×C₄₁	C₂³	1	2	yes	—
134	#127×C₄₁	C₂³	1	1	yes	characteristic
135	#127×C₄₁	C₂³	1	2	yes	—
136	#125×C₄₁	—	2	1	no	—
137	#124×C₄₁	—	2	2	no	—
138	#124×C₄₁	—	2	1	no	—
139	#124×C₄₁	—	2	2	no	—
140	#124×C₄₁	—	2	2	no	—
141	#124×C₄₁	C₂³	1	4	yes	—
142	#123×C₄₁	—	2	4	no	—
143	#123×C₄₁	—	2	4	no	—
144	#123×C₄₁	—	2	2	no	—
145	#123×C₄₁	—	2	2	no	—
146	#123×C₄₁	—	2	2	no	—
147	C₂²⋊Q₈×C₄₁	—	2	1	no	—
148	C₂²⋊Q₈×C₄₁	—	2	1	no	—
149	C₂²⋊Q₈×C₄₁	—	2	2	no	—
150	C₂²⋊Q₈×C₄₁	—	2	2	no	—
151	C₂²⋊Q₈×C₄₁	—	2	1	no	—
152	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
153	#121×C₄₁	—	2	1	no	—
154	#121×C₄₁	—	2	2	no	—
155	#121×C₄₁	—	2	2	no	—
156	#121×C₄₁	—	2	2	no	—
157	#121×C₄₁	—	2	2	no	—
158	#121×C₄₁	—	2	2	no	—
159	#121×C₄₁	—	2	1	no	—
160	#121×C₄₁	—	2	1	no	—
161	#121×C₄₁	—	2	2	no	—
162	#121×C₄₁	—	2	4	no	—
163	#121×C₄₁	—	2	4	no	—
164	#121×C₄₁	C₂³	1	2	yes	—
165	#121×C₄₁	C₂³	1	2	yes	—
166	#121×C₄₁	C₂³	1	2	yes	—
167	#121×C₄₁	C₂³	1	4	yes	—
168	#120×C₄₁	—	2	4	no	—
169	#120×C₄₁	—	2	2	no	—
170	#120×C₄₁	—	2	2	no	—
171	#120×C₄₁	—	2	2	no	—
172	C₄×Q₈×C₄₁	—	2	1	no	—
173	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
174	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
175	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₄₁	—	2	2	no	—
177	C₄×D₄×C₄₁	—	2	2	no	—
178	C₄×D₄×C₄₁	—	2	1	no	—
179	C₄×D₄×C₄₁	—	2	1	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	2	no	—
184	C₄×D₄×C₄₁	—	2	1	no	—
185	C₄×D₄×C₄₁	—	2	2	no	—
186	C₄×D₄×C₄₁	—	2	2	no	—
187	C₄×D₄×C₄₁	D₄	1	2	yes	—
188	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
189	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
192	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
193	C₄×D₄×C₄₁	C₂³	1	2	yes	—
194	C₄×D₄×C₄₁	C₂³	1	2	yes	—
195	C₄×D₄×C₄₁	C₂³	1	2	yes	—
196	C₄×D₄×C₄₁	C₂³	1	4	yes	—
197	C₄×D₄×C₄₁	C₂³	1	2	yes	—
198	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
199	#117×C₄₁	—	2	1	no	—
200	#117×C₄₁	D₄	1	1	yes	characteristic
201	#117×C₄₁	D₄	1	2	yes	—
202	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
205	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
206	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
207	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
209	#106×C₄₁	C₂³	1	2	yes	—
210	#106×C₄₁	C₂³	1	2	yes	—
211	#106×C₄₁	C₂³	1	4	yes	—
212	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
213	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
214	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
215	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
216	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
217	#103×C₄₁	C₂³	1	2	yes	—
218	#103×C₄₁	C₂³	1	4	yes	—
219	#103×C₄₁	C₂³	1	2	yes	—
220	#102×C₄₁	C₂³	1	4	yes	—
221	#102×C₄₁	C₂³	1	4	yes	—
222	#102×C₄₁	C₂³	1	4	yes	—
223	#102×C₄₁	C₂³	1	2	yes	—
224	#102×C₄₁	C₂³	1	2	yes	—
225	#102×C₄₁	C₂³	1	4	yes	—
226	#102×C₄₁	C₂³	1	4	yes	—
227	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
228	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
229	#97×C₄₁	C₂³	1	4	yes	—
230	C₄×C₈×C₄₁	C₂³	1	2	yes	—
231	C₂⁴×C₄₁	—	2	2	no	—
232	C₂⁴×C₄₁	—	2	1	no	—
233	C₂⁴×C₄₁	—	2	2	no	—
234	#41×C₄₁	—	2	4	no	—
235	#41×C₄₁	—	4	8	no	—
236	#41×C₄₁	—	4	4	no	—
237	#41×C₄₁	—	4	4	no	—
238	#41×C₄₁	—	4	8	no	—
239	#41×C₄₁	—	4	4	no	—
240	#41×C₄₁	—	4	4	no	—
241	#41×C₄₁	—	4	4	no	—
242	#41×C₄₁	—	8	4	no	—
243	C₂×Q₈×C₄₁	—	2	1	no	—
244	C₂×Q₈×C₄₁	—	2	2	no	—
245	C₂×Q₈×C₄₁	—	2	1	no	—
246	C₂×Q₈×C₄₁	—	4	4	no	—
247	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
248	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
249	C₂×D₄×C₄₁	—	2	2	no	—
250	C₂×D₄×C₄₁	—	2	4	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	4	no	—
255	C₂×D₄×C₄₁	—	2	4	no	—
256	C₂×D₄×C₄₁	—	2	2	no	—
257	C₂×D₄×C₄₁	—	2	1	no	—
258	C₂×D₄×C₄₁	—	2	2	no	—
259	C₂×D₄×C₄₁	—	2	2	no	—
260	C₂×D₄×C₄₁	—	2	2	no	—
261	C₂×D₄×C₄₁	—	2	2	no	—
262	C₂×D₄×C₄₁	—	2	1	no	—
263	C₂×D₄×C₄₁	—	2	2	no	—
264	C₂×D₄×C₄₁	—	2	1	no	—
265	C₂×D₄×C₄₁	—	2	2	no	—
266	C₂×D₄×C₄₁	—	2	2	no	—
267	C₂×D₄×C₄₁	—	4	1	no	—
268	C₂×D₄×C₄₁	—	4	2	no	—
269	C₂×D₄×C₄₁	—	4	2	no	—
270	C₂×D₄×C₄₁	—	4	2	no	—
271	C₂×D₄×C₄₁	—	4	8	no	—
272	C₂×D₄×C₄₁	—	4	4	no	—
273	C₂×D₄×C₄₁	—	4	4	no	—
274	C₂×D₄×C₄₁	—	8	2	no	—
275	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
276	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
277	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
278	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
279	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
280	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₄₁	—	2	2	no	—
282	C₂²×C₄×C₄₁	—	2	1	no	—
283	C₂²×C₄×C₄₁	—	2	1	no	—
284	C₂²×C₄×C₄₁	—	2	1	no	—
285	C₂²×C₄×C₄₁	—	2	2	no	—
286	C₂²×C₄×C₄₁	—	2	2	no	—
287	C₂²×C₄×C₄₁	—	2	1	no	—
288	C₂²×C₄×C₄₁	—	2	2	no	—
289	C₂²×C₄×C₄₁	—	2	1	no	—
290	C₂²×C₄×C₄₁	—	2	4	no	—
291	C₂²×C₄×C₄₁	—	2	4	no	—
292	C₂²×C₄×C₄₁	—	4	8	no	—
293	C₂²×C₄×C₄₁	—	4	4	no	—
294	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
295	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
296	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
300	SD₁₆×C₄₁	—	2	4	no	—
301	SD₁₆×C₄₁	—	4	2	no	—
302	SD₁₆×C₄₁	—	4	4	no	—
303	D₈×C₄₁	—	2	8	no	—
304	D₈×C₄₁	—	4	4	no	—
305	D₈×C₄₁	—	4	4	no	—
306	D₈×C₄₁	—	4	4	no	—
307	M₁₆×C₄₁	—	4	4	no	—
308	C₂×C₈×C₄₁	—	4	2	no	—
309	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
310	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
311	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
312	C₄⋊C₄×C₄₁	—	2	2	no	—
313	C₄⋊C₄×C₄₁	—	2	1	no	—
314	C₄⋊C₄×C₄₁	—	2	1	no	—
315	C₄⋊C₄×C₄₁	—	2	1	no	—
316	C₄⋊C₄×C₄₁	—	2	1	no	—
317	C₄⋊C₄×C₄₁	—	2	2	no	—
318	C₄⋊C₄×C₄₁	—	2	1	no	—
319	C₄⋊C₄×C₄₁	—	2	2	no	—
320	C₄⋊C₄×C₄₁	—	2	2	no	—
321	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
322	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
323	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
324	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
325	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
326	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
327	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
328	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
329	C₂²⋊C₄×C₄₁	—	2	2	no	—
330	C₂²⋊C₄×C₄₁	—	2	1	no	—
331	C₂²⋊C₄×C₄₁	—	2	4	no	—
332	C₂²⋊C₄×C₄₁	—	2	4	no	—
333	C₂²⋊C₄×C₄₁	—	2	2	no	—
334	C₂²⋊C₄×C₄₁	—	2	1	no	—
335	C₂²⋊C₄×C₄₁	—	2	2	no	—
336	C₂²⋊C₄×C₄₁	—	2	1	no	—
337	C₂²⋊C₄×C₄₁	—	2	1	no	—
338	C₂²⋊C₄×C₄₁	—	2	2	no	—
339	C₂²⋊C₄×C₄₁	—	2	2	no	—
340	C₂²⋊C₄×C₄₁	—	2	2	no	—
341	C₂²⋊C₄×C₄₁	—	2	2	no	—
342	C₂²⋊C₄×C₄₁	—	2	4	no	—
343	C₂²⋊C₄×C₄₁	—	2	4	no	—
344	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
345	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
346	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
347	C₄²×C₄₁	—	2	2	no	—
348	C₄²×C₄₁	C₂×D₄	1	2	yes	—
349	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
350	C₄²×C₄₁	C₂×D₄	1	2	yes	—
351	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
352	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
353	C₄²×C₄₁	C₂⁴	1	2	yes	—
354	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
355	C₂³×C₄₁	—	2	1	no	—
356	C₂³×C₄₁	—	2	4	no	—
357	C₂³×C₄₁	—	2	1	no	—
358	C₂³×C₄₁	—	2	2	no	—
359	C₂³×C₄₁	—	4	2	no	—
360	C₂³×C₄₁	—	4	4	no	—
361	C₂³×C₄₁	—	4	4	no	—
362	C₂³×C₄₁	—	4	2	no	—
363	C₂³×C₄₁	—	4	4	no	—
364	C₂³×C₄₁	—	8	1	no	—
365	C₂³×C₄₁	—	8	2	no	—
366	C₂³×C₄₁	—	8	2	no	—
367	C₂³×C₄₁	—	8	2	no	—
368	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
369	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
370	Q₈×C₄₁	—	2	2	no	—
371	Q₈×C₄₁	—	2	2	no	—
372	Q₈×C₄₁	—	2	2	no	—
373	Q₈×C₄₁	—	4	4	no	—
374	Q₈×C₄₁	—	4	2	no	—
375	Q₈×C₄₁	—	4	2	no	—
376	D₄×C₄₁	—	2	4	no	—
377	D₄×C₄₁	—	2	2	no	—
378	D₄×C₄₁	—	2	4	no	—
379	D₄×C₄₁	—	2	1	no	—
380	D₄×C₄₁	—	2	2	no	—
381	D₄×C₄₁	—	2	1	no	—
382	D₄×C₄₁	—	2	2	no	—
383	D₄×C₄₁	—	2	4	no	—
384	D₄×C₄₁	—	2	1	no	—
385	D₄×C₄₁	—	4	4	no	—
386	D₄×C₄₁	—	4	2	no	—
387	D₄×C₄₁	—	4	4	no	—
388	D₄×C₄₁	—	4	4	no	—
389	D₄×C₄₁	—	4	4	no	—
390	D₄×C₄₁	—	4	4	no	—
391	D₄×C₄₁	—	4	4	no	—
392	D₄×C₄₁	—	4	4	no	—
393	D₄×C₄₁	—	4	4	no	—
394	D₄×C₄₁	—	4	2	no	—
395	D₄×C₄₁	—	8	2	no	—
396	D₄×C₄₁	—	8	1	no	—
397	D₄×C₄₁	—	8	2	no	—
398	D₄×C₄₁	—	8	2	no	—
399	D₄×C₄₁	—	8	4	no	—
400	D₄×C₄₁	—	8	4	no	—
401	D₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
402	C₂×C₄×C₄₁	—	2	4	no	—
403	C₂×C₄×C₄₁	—	2	1	no	—
404	C₂×C₄×C₄₁	—	2	2	no	—
405	C₂×C₄×C₄₁	—	2	1	no	—
406	C₂×C₄×C₄₁	—	2	2	no	—
407	C₂×C₄×C₄₁	—	2	2	no	—
408	C₂×C₄×C₄₁	—	2	2	no	—
409	C₂×C₄×C₄₁	—	2	1	no	—
410	C₂×C₄×C₄₁	—	2	2	no	—
411	C₂×C₄×C₄₁	—	2	1	no	—
412	C₂×C₄×C₄₁	—	4	1	no	—
413	C₂×C₄×C₄₁	—	4	2	no	—
414	C₂×C₄×C₄₁	—	4	4	no	—
415	C₂×C₄×C₄₁	—	4	4	no	—
416	C₂×C₄×C₄₁	—	4	4	no	—
417	C₂×C₄×C₄₁	—	4	2	no	—
418	C₂×C₄×C₄₁	—	4	2	no	—
419	C₂×C₄×C₄₁	—	4	2	no	—
420	C₂×C₄×C₄₁	—	4	2	no	—
421	C₂×C₄×C₄₁	—	4	4	no	—
422	C₂×C₄×C₄₁	—	4	2	no	—
423	C₂×C₄×C₄₁	—	8	4	no	—
424	C₂×C₄×C₄₁	—	8	4	no	—
425	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	4	yes	complemented
426	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
428	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
435	C₈×C₄₁	—	2	4	no	—
436	C₈×C₄₁	—	2	2	no	—
437	C₈×C₄₁	—	2	2	no	—
438	#61961	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
439	C₂²×C₄₁	—	2	1	no	—
440	C₂²×C₄₁	—	2	1	no	—
441	C₂²×C₄₁	—	2	2	no	—
442	C₂²×C₄₁	—	2	2	no	—
443	C₂²×C₄₁	—	2	2	no	—
444	C₂²×C₄₁	—	2	2	no	—
445	C₂²×C₄₁	—	4	1	no	—
446	C₂²×C₄₁	—	4	1	no	—
447	C₂²×C₄₁	—	4	4	no	—
448	C₂²×C₄₁	—	4	1	no	—
449	C₂²×C₄₁	—	4	2	no	—
450	C₂²×C₄₁	—	4	4	no	—
451	C₂²×C₄₁	—	4	1	no	—
452	C₂²×C₄₁	—	4	2	no	—
453	C₂²×C₄₁	—	4	2	no	—
454	C₂²×C₄₁	—	4	1	no	—
455	C₂²×C₄₁	—	4	4	no	—
456	C₂²×C₄₁	—	8	4	no	—
457	C₂²×C₄₁	—	8	8	no	—
458	C₂²×C₄₁	—	16	4	no	—
459	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
460	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
461	C₄×C₄₁	—	2	1	no	—
462	C₄×C₄₁	—	2	2	no	—
463	C₄×C₄₁	—	2	1	no	—
464	C₄×C₄₁	—	2	2	no	—
465	C₄×C₄₁	—	2	1	no	—
466	C₄×C₄₁	—	2	2	no	—
467	C₄×C₄₁	—	4	2	no	—
468	C₄×C₄₁	—	4	2	no	—
469	C₄×C₄₁	—	4	1	no	—
470	C₄×C₄₁	—	4	2	no	—
471	C₄×C₄₁	—	4	1	no	—
472	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
473	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
474	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
475	C₄×C₄₁	#585	1	1	yes	characteristic
476	#3508	C₂×C₄₁	1	1	yes	characteristic, complemented
477	D₄×#41	C₂×C₄₁	1	1	yes	characteristic, complemented
478	#3399	C₂×C₄₁	1	2	yes	complemented
479	#3373	C₂×C₄₁	1	2	yes	complemented
480	#3332	C₂×C₄₁	1	2	yes	complemented
481	#3306	C₂×C₄₁	1	4	yes	complemented
482	#3274	C₂×C₄₁	1	2	yes	complemented
483	#3264	C₂×C₄₁	1	4	yes	complemented
484	#3253	C₂×C₄₁	1	2	yes	complemented
485	#3246	C₂×C₄₁	1	1	yes	characteristic, complemented
486	#3214	C₂×C₄₁	1	2	yes	complemented
487	#3205	C₂×C₄₁	1	1	yes	characteristic, complemented
488	#3109	C₂×C₄₁	1	2	yes	complemented
489	#3101	C₂×C₄₁	1	1	yes	characteristic, complemented
490	#3036	C₂×C₄₁	1	2	yes	complemented
491	C₂×#459	C₂×C₄₁	1	1	yes	characteristic, complemented
492	#2989	C₂×C₄₁	1	1	yes	characteristic, complemented
493	C₂×C₄₁	—	2	2	no	—
494	C₂×C₄₁	—	4	2	no	—
495	C₂×C₄₁	—	4	2	no	—
496	C₂×C₄₁	—	8	1	no	—
497	C₂×C₄₁	—	8	2	no	—
498	C₂×C₄₁	—	8	4	no	—
499	C₂×C₄₁	#3488	1	1	yes	characteristic
500	C₂×C₄₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
501	C₂×C₄₁	#3585	1	1	yes	characteristic
502	C₂²×#41	—	2	1	no	—
503	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	4	yes	complemented
504	C₂²×D₈	C₂²×C₄₁	1	2	yes	—
505	#559	—	2	1	no	—
506	#559	C₂²×C₄₁	1	2	yes	complemented
507	#550	—	2	1	no	—
508	#550	C₂²×C₄₁	1	2	yes	complemented
509	#550	C₂²×C₄₁	1	1	yes	characteristic, complemented
510	D₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
511	#548	—	2	1	no	—
512	#547	C₂²×C₄₁	1	2	yes	—
513	#547	C₂²×C₄₁	1	1	yes	characteristic, complemented
514	#546	—	2	2	no	—
515	#546	—	2	1	no	—
516	#546	—	2	2	no	—
517	#546	C₂²×C₄₁	1	4	yes	complemented
518	D₄²	C₂²×C₄₁	1	2	yes	—
519	D₄²	C₂²×C₄₁	1	1	yes	characteristic, complemented
520	#540	—	2	2	no	—
521	#535	—	2	1	no	—
522	#533	C₂²×C₄₁	1	1	yes	characteristic, complemented
523	#532	C₂²×C₄₁	1	1	yes	characteristic
524	#532	C₂²×C₄₁	1	2	yes	complemented
525	#532	C₂²×C₄₁	1	2	yes	complemented
526	#532	C₂²×C₄₁	1	2	yes	complemented
527	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic, complemented
528	#525	—	2	1	no	—
529	#525	—	2	2	no	—
530	#518	—	2	1	no	—
531	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
532	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
533	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	complemented
534	#496	C₂²×C₄₁	1	4	yes	complemented
535	#493	C₂²×C₄₁	1	2	yes	complemented
536	#489	C₂²×C₄₁	1	4	yes	complemented
537	#486	C₂²×C₄₁	1	2	yes	complemented
538	#483	C₂²×C₄₁	1	2	yes	complemented
539	#481	C₂²×C₄₁	1	4	yes	complemented
540	#476	C₂²×C₄₁	1	1	yes	characteristic, complemented
541	#476	C₂²×C₄₁	1	1	yes	characteristic, complemented
542	#476	C₂²×C₄₁	1	2	yes	complemented
543	#476	C₂²×C₄₁	1	4	yes	complemented
544	#475	C₂²×C₄₁	1	2	yes	complemented
545	#469	C₂²×C₄₁	1	4	yes	complemented
546	#469	C₂²×C₄₁	1	4	yes	complemented
547	#465	C₂²×C₄₁	1	4	yes	complemented
548	#463	C₂²×C₄₁	1	4	yes	complemented
549	#463	C₂²×C₄₁	1	4	yes	complemented
550	#461	C₂²×C₄₁	1	1	yes	characteristic, complemented
551	#461	C₂²×C₄₁	1	1	yes	characteristic, complemented
552	#461	C₂²×C₄₁	1	2	yes	complemented
553	#460	C₂²×C₄₁	1	2	yes	complemented
554	#459	C₂²×C₄₁	1	2	yes	—
555	#459	C₂²×C₄₁	1	2	yes	—
556	#459	C₂²×C₄₁	1	2	yes	complemented
557	#459	C₂²×C₄₁	1	2	yes	complemented
558	#459	C₂²×C₄₁	1	4	yes	complemented
559	#459	C₂²×C₄₁	1	2	yes	complemented
560	#459	C₂²×C₄₁	1	2	yes	complemented
561	#450	C₂²×C₄₁	1	2	yes	—
562	#449	C₂²×C₄₁	1	4	yes	complemented
563	#449	C₂²×C₄₁	1	4	yes	complemented
564	#447	C₂²×C₄₁	1	4	yes	complemented
565	#447	C₂²×C₄₁	1	4	yes	complemented
566	#446	C₂²×C₄₁	1	2	yes	complemented
567	#442	C₂²×C₄₁	1	4	yes	complemented
568	#442	C₂²×C₄₁	1	4	yes	complemented
569	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
570	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
571	#436	C₂²×C₄₁	1	2	yes	complemented
572	#435	C₂²×C₄₁	1	4	yes	complemented
573	#432	C₂²×C₄₁	1	2	yes	complemented
574	#431	C₂²×C₄₁	1	1	yes	characteristic, complemented
575	#423	C₂²×C₄₁	1	2	yes	complemented
576	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
577	#417	C₂²×C₄₁	1	4	yes	complemented
578	C₂×#102	C₂²×C₄₁	1	2	yes	complemented
579	C₄₁	#61961	1	1	yes	characteristic, direct product factor, Sylow
580	C₂×#41	—	2	1	no	—
581	C₂×#41	—	2	2	no	—
582	C₂×#41	—	2	1	no	—
583	C₂×#41	—	2	1	no	—
584	C₂×#41	—	2	2	no	—
585	C₂×#41	—	2	2	no	—
586	C₂×#41	—	4	8	no	—
587	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
588	C₂×#41	C₂³×C₄₁	1	4	yes	—
589	C₂²×Q₈	—	2	1	no	—
590	C₂²×D₄	—	2	2	no	—
591	C₂²×D₄	—	2	1	no	—
592	C₂²×D₄	—	2	1	no	—
593	C₂²×D₄	—	2	1	no	—
594	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
595	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
596	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
597	C₂³×C₄	—	2	1	no	—
598	C₂³×C₄	—	2	2	no	—
599	AGL(1,ℤ/8)	—	4	8	no	—
600	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
601	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
602	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
603	C₂×D₈	—	4	4	no	—
604	C₂×D₈	C₂³×C₄₁	1	4	yes	—
605	C₂×D₈	C₂³×C₄₁	1	4	yes	—
606	C₂×D₈	C₂³×C₄₁	1	4	yes	—
607	C₂×D₈	C₂³×C₄₁	1	4	yes	—
608	C₂×M₁₆	C₂³×C₄₁	1	4	yes	—
609	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
610	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
611	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
612	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
613	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
614	#127	—	2	2	no	—
615	#127	—	2	1	no	—
616	#127	—	2	1	no	—
617	#127	C₂³×C₄₁	1	2	yes	—
618	#127	C₂³×C₄₁	1	2	yes	—
619	#127	C₂³×C₄₁	1	1	yes	characteristic
620	#127	C₂³×C₄₁	1	2	yes	—
621	#125	—	2	1	no	—
622	#124	—	2	2	no	—
623	#124	—	2	1	no	—
624	#124	—	2	2	no	—
625	#124	—	2	2	no	—
626	#124	C₂³×C₄₁	1	4	yes	—
627	#123	—	2	4	no	—
628	#123	—	2	4	no	—
629	#123	—	2	2	no	—
630	#123	—	2	2	no	—
631	#123	—	2	2	no	—
632	C₂²⋊Q₈	—	2	1	no	—
633	C₂²⋊Q₈	—	2	1	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	—	2	1	no	—
637	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
638	#121	—	2	1	no	—
639	#121	—	2	2	no	—
640	#121	—	2	2	no	—
641	#121	—	2	2	no	—
642	#121	—	2	2	no	—
643	#121	—	2	2	no	—
644	#121	—	2	1	no	—
645	#121	—	2	1	no	—
646	#121	—	2	2	no	—
647	#121	—	2	4	no	—
648	#121	—	2	4	no	—
649	#121	C₂³×C₄₁	1	2	yes	—
650	#121	C₂³×C₄₁	1	2	yes	—
651	#121	C₂³×C₄₁	1	2	yes	—
652	#121	C₂³×C₄₁	1	4	yes	—
653	#120	—	2	4	no	—
654	#120	—	2	2	no	—
655	#120	—	2	2	no	—
656	#120	—	2	2	no	—
657	C₄×Q₈	—	2	1	no	—
658	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
659	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
660	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
661	C₄×D₄	—	2	2	no	—
662	C₄×D₄	—	2	2	no	—
663	C₄×D₄	—	2	1	no	—
664	C₄×D₄	—	2	1	no	—
665	C₄×D₄	—	2	2	no	—
666	C₄×D₄	—	2	2	no	—
667	C₄×D₄	—	2	2	no	—
668	C₄×D₄	—	2	2	no	—
669	C₄×D₄	—	2	1	no	—
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	D₄×C₄₁	1	2	yes	—
673	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
674	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
675	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
676	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
677	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
678	C₄×D₄	C₂³×C₄₁	1	2	yes	—
679	C₄×D₄	C₂³×C₄₁	1	2	yes	—
680	C₄×D₄	C₂³×C₄₁	1	2	yes	—
681	C₄×D₄	C₂³×C₄₁	1	4	yes	—
682	C₄×D₄	C₂³×C₄₁	1	2	yes	—
683	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
684	#117	—	2	1	no	—
685	#117	D₄×C₄₁	1	1	yes	characteristic
686	#117	D₄×C₄₁	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
689	C₂×C₂²⋊C₄	—	2	1	no	—
690	C₂×C₂²⋊C₄	—	2	2	no	—
691	C₂×C₂²⋊C₄	—	2	4	no	—
692	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
693	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
694	#106	C₂³×C₄₁	1	2	yes	—
695	#106	C₂³×C₄₁	1	2	yes	—
696	#106	C₂³×C₄₁	1	4	yes	—
697	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
698	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
699	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
700	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
701	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
702	#103	C₂³×C₄₁	1	2	yes	—
703	#103	C₂³×C₄₁	1	4	yes	—
704	#103	C₂³×C₄₁	1	2	yes	—
705	#102	C₂³×C₄₁	1	4	yes	—
706	#102	C₂³×C₄₁	1	4	yes	—
707	#102	C₂³×C₄₁	1	4	yes	—
708	#102	C₂³×C₄₁	1	2	yes	—
709	#102	C₂³×C₄₁	1	2	yes	—
710	#102	C₂³×C₄₁	1	4	yes	—
711	#102	C₂³×C₄₁	1	4	yes	—
712	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
713	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
714	#97	C₂³×C₄₁	1	4	yes	—
715	C₄×C₈	C₂³×C₄₁	1	2	yes	—
716	C₂⁴	—	2	2	no	—
717	C₂⁴	—	2	1	no	—
718	C₂⁴	—	2	2	no	—
719	#41	—	2	4	no	—
720	#41	—	4	8	no	—
721	#41	—	4	4	no	—
722	#41	—	4	4	no	—
723	#41	—	4	8	no	—
724	#41	—	4	4	no	—
725	#41	—	4	4	no	—
726	#41	—	4	4	no	—
727	#41	—	8	4	no	—
728	C₂×Q₈	—	2	1	no	—
729	C₂×Q₈	—	2	2	no	—
730	C₂×Q₈	—	2	1	no	—
731	C₂×Q₈	—	4	4	no	—
732	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
733	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	4	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	2	no	—
739	C₂×D₄	—	2	4	no	—
740	C₂×D₄	—	2	4	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	2	1	no	—
743	C₂×D₄	—	2	2	no	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	1	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	1	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	4	1	no	—
753	C₂×D₄	—	4	2	no	—
754	C₂×D₄	—	4	2	no	—
755	C₂×D₄	—	4	2	no	—
756	C₂×D₄	—	4	8	no	—
757	C₂×D₄	—	4	4	no	—
758	C₂×D₄	—	4	4	no	—
759	C₂×D₄	—	8	2	no	—
760	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
761	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
762	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
763	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
764	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
765	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	1	no	—
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	2	1	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	1	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	1	no	—
775	C₂²×C₄	—	2	4	no	—
776	C₂²×C₄	—	2	4	no	—
777	C₂²×C₄	—	4	8	no	—
778	C₂²×C₄	—	4	4	no	—
779	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
780	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
781	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
782	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
785	SD₁₆	—	2	4	no	—
786	SD₁₆	—	4	2	no	—
787	SD₁₆	—	4	4	no	—
788	D₈	—	2	8	no	—
789	D₈	—	4	4	no	—
790	D₈	—	4	4	no	—
791	D₈	—	4	4	no	—
792	M₁₆	—	4	4	no	—
793	C₂×C₈	—	4	2	no	—
794	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
795	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
796	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	1	no	—
799	C₄⋊C₄	—	2	1	no	—
800	C₄⋊C₄	—	2	1	no	—
801	C₄⋊C₄	—	2	1	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	1	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
807	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
808	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
809	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
810	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
811	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
812	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
813	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	1	no	—
816	C₂²⋊C₄	—	2	4	no	—
817	C₂²⋊C₄	—	2	4	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	1	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	1	no	—
822	C₂²⋊C₄	—	2	1	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	2	4	no	—
829	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
830	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
831	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
832	C₄²	—	2	2	no	—
833	C₄²	C₂×D₄×C₄₁	1	2	yes	—
834	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
835	C₄²	C₂×D₄×C₄₁	1	2	yes	—
836	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
837	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
838	C₄²	C₂⁴×C₄₁	1	2	yes	—
839	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
840	C₂³	—	2	1	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	1	no	—
843	C₂³	—	2	4	no	—
844	C₂³	—	4	2	no	—
845	C₂³	—	4	4	no	—
846	C₂³	—	4	4	no	—
847	C₂³	—	4	2	no	—
848	C₂³	—	4	4	no	—
849	C₂³	—	8	1	no	—
850	C₂³	—	8	2	no	—
851	C₂³	—	8	2	no	—
852	C₂³	—	8	2	no	—
853	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
854	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
855	Q₈	—	2	2	no	—
856	Q₈	—	2	2	no	—
857	Q₈	—	2	2	no	—
858	Q₈	—	4	4	no	—
859	Q₈	—	4	2	no	—
860	Q₈	—	4	2	no	—
861	D₄	—	2	4	no	—
862	D₄	—	2	2	no	—
863	D₄	—	2	4	no	—
864	D₄	—	2	1	no	—
865	D₄	—	2	2	no	—
866	D₄	—	2	1	no	—
867	D₄	—	2	2	no	—
868	D₄	—	2	4	no	—
869	D₄	—	2	1	no	—
870	D₄	—	4	4	no	—
871	D₄	—	4	2	no	—
872	D₄	—	4	4	no	—
873	D₄	—	4	4	no	—
874	D₄	—	4	4	no	—
875	D₄	—	4	4	no	—
876	D₄	—	4	4	no	—
877	D₄	—	4	2	no	—
878	D₄	—	4	4	no	—
879	D₄	—	4	4	no	—
880	D₄	—	8	2	no	—
881	D₄	—	8	2	no	—
882	D₄	—	8	2	no	—
883	D₄	—	8	1	no	—
884	D₄	—	8	4	no	—
885	D₄	—	8	4	no	—
886	D₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
887	C₂×C₄	—	2	4	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	4	1	no	—
898	C₂×C₄	—	4	2	no	—
899	C₂×C₄	—	4	4	no	—
900	C₂×C₄	—	4	4	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	4	2	no	—
903	C₂×C₄	—	4	2	no	—
904	C₂×C₄	—	4	2	no	—
905	C₂×C₄	—	4	2	no	—
906	C₂×C₄	—	4	4	no	—
907	C₂×C₄	—	4	2	no	—
908	C₂×C₄	—	8	4	no	—
909	C₂×C₄	—	8	4	no	—
910	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	4	yes	complemented
911	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
912	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
913	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
914	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
915	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
916	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
917	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
918	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
919	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
920	C₈	—	2	4	no	—
921	C₈	—	2	2	no	—
922	C₈	—	2	2	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	4	1	no	—
930	C₂²	—	4	1	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	1	no	—
933	C₂²	—	4	4	no	—
934	C₂²	—	4	4	no	—
935	C₂²	—	4	1	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	4	4	no	—
938	C₂²	—	4	1	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	8	4	no	—
941	C₂²	—	8	8	no	—
942	C₂²	—	16	4	no	—
943	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
944	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
945	C₄	—	2	2	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	2	no	—
950	C₄	—	2	1	no	—
951	C₄	—	4	1	no	—
952	C₄	—	4	2	no	—
953	C₄	—	4	1	no	—
954	C₄	—	4	2	no	—
955	C₄	—	4	2	no	—
956	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
957	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
958	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
959	C₄	C₄₁×#585	1	1	yes	characteristic
960	C₂	—	2	2	no	—
961	C₂	—	4	2	no	—
962	C₂	—	4	2	no	—
963	C₂	—	8	1	no	—
964	C₂	—	8	2	no	—
965	C₂	—	8	4	no	—
966	C₂	C₄₁×#3488	1	1	yes	characteristic
967	C₂	C₂²×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
968	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 ◁ C₄×#41×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3508	C₂	semidirect
2. D₄×#41×C₄₁	C₂	semidirect
3. C₄₁×#3399	C₂	semidirect
4. C₄₁×#3373	C₂	semidirect
5. C₄₁×#3332	C₂	semidirect
6. C₄₁×#3306	C₂	semidirect
7. C₄₁×#3274	C₂	semidirect
8. C₄₁×#3264	C₂	semidirect
9. C₄₁×#3253	C₂	semidirect
10. C₄₁×#3246	C₂	semidirect
11. C₄₁×#3214	C₂	semidirect
12. C₄₁×#3205	C₂	semidirect
13. C₄₁×#3109	C₂	semidirect
14. C₄₁×#3101	C₂	semidirect
15. C₄₁×#3036	C₂	semidirect
16. C₂×C₄₁×#459	C₂	semidirect
17. C₄₁×#2989	C₂	semidirect
19. C₂×AGL(1,ℤ/8)×C₄₁	C₂²	semidirect
22. C₄₁×#559	C₂²	semidirect
24. C₄₁×#550	C₂²	semidirect
25. C₄₁×#550	C₂²	semidirect
26. D₄×Q₈×C₄₁	C₂²	semidirect
29. C₄₁×#547	C₂²	semidirect
33. C₄₁×#546	C₂²	semidirect
35. D₄²×C₄₁	C₂²	semidirect
38. C₄₁×#533	C₂²	semidirect
40. C₄₁×#532	C₂²	semidirect
41. C₄₁×#532	C₂²	semidirect
42. C₄₁×#532	C₂²	semidirect
43. C₂×#127×C₄₁	C₂²	semidirect
49. C₂×C₄×D₄×C₄₁	C₂²	semidirect
50. C₄₁×#496	C₂²	semidirect
51. C₄₁×#493	C₂²	semidirect
52. C₄₁×#489	C₂²	semidirect
53. C₄₁×#486	C₂²	semidirect
54. C₄₁×#483	C₂²	semidirect
55. C₄₁×#481	C₂²	semidirect
56. C₄₁×#476	C₂²	semidirect
57. C₄₁×#476	C₂²	semidirect
58. C₄₁×#476	C₂²	semidirect
59. C₄₁×#476	C₂²	semidirect
60. C₄₁×#475	C₂²	semidirect
61. C₄₁×#469	C₂²	semidirect
62. C₄₁×#469	C₂²	semidirect
63. C₄₁×#465	C₂²	semidirect
64. C₄₁×#463	C₂²	semidirect
65. C₄₁×#463	C₂²	semidirect
66. C₄₁×#461	C₂²	semidirect
67. C₄₁×#461	C₂²	semidirect
68. C₄₁×#461	C₂²	semidirect
69. C₄₁×#460	C₂²	semidirect
72. C₄₁×#459	C₂²	semidirect
73. C₄₁×#459	C₂²	semidirect
74. C₄₁×#459	C₂²	semidirect
75. C₄₁×#459	C₂²	semidirect
76. C₄₁×#459	C₂²	semidirect
78. C₄₁×#449	C₂²	semidirect
79. C₄₁×#449	C₂²	semidirect
80. C₄₁×#447	C₂²	semidirect
81. C₄₁×#447	C₂²	semidirect
82. C₄₁×#446	C₂²	semidirect
83. C₄₁×#442	C₂²	semidirect
84. C₄₁×#442	C₂²	semidirect
85. C₄×SD₁₆×C₄₁	C₂²	semidirect
86. C₄×SD₁₆×C₄₁	C₂²	semidirect
87. C₄₁×#436	C₂²	semidirect
88. C₄₁×#435	C₂²	semidirect
89. C₄₁×#432	C₂²	semidirect
90. C₄₁×#431	C₂²	semidirect
91. C₄₁×#423	C₂²	semidirect
92. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
93. C₄₁×#417	C₂²	semidirect
94. C₂×#102×C₄₁	C₂²	semidirect
425. C₂×C₄×C₄₁	AGL(1,ℤ/8)	semidirect
438. #61961	C₄₁	direct (N × H)
476. #3508	C₂×C₄₁	semidirect
477. D₄×#41	C₂×C₄₁	semidirect
478. #3399	C₂×C₄₁	semidirect
479. #3373	C₂×C₄₁	semidirect
480. #3332	C₂×C₄₁	semidirect
481. #3306	C₂×C₄₁	semidirect
482. #3274	C₂×C₄₁	semidirect
483. #3264	C₂×C₄₁	semidirect
484. #3253	C₂×C₄₁	semidirect
485. #3246	C₂×C₄₁	semidirect
486. #3214	C₂×C₄₁	semidirect
487. #3205	C₂×C₄₁	semidirect
488. #3109	C₂×C₄₁	semidirect
489. #3101	C₂×C₄₁	semidirect
490. #3036	C₂×C₄₁	semidirect
491. C₂×#459	C₂×C₄₁	semidirect
492. #2989	C₂×C₄₁	semidirect
503. C₂×AGL(1,ℤ/8)	C₂²×C₄₁	semidirect
506. #559	C₂²×C₄₁	semidirect
508. #550	C₂²×C₄₁	semidirect
509. #550	C₂²×C₄₁	semidirect
510. D₄×Q₈	C₂²×C₄₁	semidirect
513. #547	C₂²×C₄₁	semidirect
517. #546	C₂²×C₄₁	semidirect
519. D₄²	C₂²×C₄₁	semidirect
522. #533	C₂²×C₄₁	semidirect
524. #532	C₂²×C₄₁	semidirect
525. #532	C₂²×C₄₁	semidirect
526. #532	C₂²×C₄₁	semidirect
527. C₂×#127	C₂²×C₄₁	semidirect
533. C₂×C₄×D₄	C₂²×C₄₁	semidirect
534. #496	C₂²×C₄₁	semidirect
535. #493	C₂²×C₄₁	semidirect
536. #489	C₂²×C₄₁	semidirect
537. #486	C₂²×C₄₁	semidirect
538. #483	C₂²×C₄₁	semidirect
539. #481	C₂²×C₄₁	semidirect
540. #476	C₂²×C₄₁	semidirect
541. #476	C₂²×C₄₁	semidirect
542. #476	C₂²×C₄₁	semidirect
543. #476	C₂²×C₄₁	semidirect
544. #475	C₂²×C₄₁	semidirect
545. #469	C₂²×C₄₁	semidirect
546. #469	C₂²×C₄₁	semidirect
547. #465	C₂²×C₄₁	semidirect
548. #463	C₂²×C₄₁	semidirect
549. #463	C₂²×C₄₁	semidirect
550. #461	C₂²×C₄₁	semidirect
551. #461	C₂²×C₄₁	semidirect
552. #461	C₂²×C₄₁	semidirect
553. #460	C₂²×C₄₁	semidirect
556. #459	C₂²×C₄₁	semidirect
557. #459	C₂²×C₄₁	semidirect
558. #459	C₂²×C₄₁	semidirect
559. #459	C₂²×C₄₁	semidirect
560. #459	C₂²×C₄₁	semidirect
562. #449	C₂²×C₄₁	semidirect
563. #449	C₂²×C₄₁	semidirect
564. #447	C₂²×C₄₁	semidirect
565. #447	C₂²×C₄₁	semidirect
566. #446	C₂²×C₄₁	semidirect
567. #442	C₂²×C₄₁	semidirect
568. #442	C₂²×C₄₁	semidirect
569. C₄×SD₁₆	C₂²×C₄₁	semidirect
570. C₄×SD₁₆	C₂²×C₄₁	semidirect
571. #436	C₂²×C₄₁	semidirect
572. #435	C₂²×C₄₁	semidirect
573. #432	C₂²×C₄₁	semidirect
574. #431	C₂²×C₄₁	semidirect
575. #423	C₂²×C₄₁	semidirect
576. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
577. #417	C₂²×C₄₁	semidirect
578. C₂×#102	C₂²×C₄₁	semidirect
579. C₄₁	#61961	direct (N × H)
910. C₂×C₄	AGL(1,ℤ/8)×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3508	2
D₄×#41×C₄₁	2
C₄₁×#3399	2
C₄₁×#3373	2
C₄₁×#3332	2
C₄₁×#3306	2
C₄₁×#3274	2
C₄₁×#3264	2
C₄₁×#3253	2
C₄₁×#3246	2
C₄₁×#3214	2
C₄₁×#3205	2
C₄₁×#3109	2
C₄₁×#3101	2
C₄₁×#3036	2
C₂×C₄₁×#459	2
C₄₁×#2989	2
#61961	41

Subgroups — C41×#61961 #23838162

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61961 #23838162