Subgroups — C₄₁×#61583 #23837784

Order 10496.

2118 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3505	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#548	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3327	C₂	1	4	yes	maximal, complemented
4	C₄₁×#3326	C₂	1	4	yes	maximal, complemented
5	C₄₁×#3277	C₂	1	4	yes	maximal, complemented
6	C₄₁×#3275	C₂	1	4	yes	maximal, complemented
7	C₄₁×#3211	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3195	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#3194	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3193	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#3108	C₂	1	2	yes	maximal, complemented
12	C₄₁×#3007	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3006	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3004	C₂	1	2	yes	maximal, complemented
15	C₄₁×#2975	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
18	C₂×#137×C₄₁	C₂²	1	4	yes	complemented
19	C₂×#137×C₄₁	C₂²	1	2	yes	complemented
20	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	2	yes	complemented
21	C₄₁×#553	—	2	2	no	—
22	C₄₁×#553	C₂²	1	2	yes	complemented
23	C₄₁×#552	C₂²	1	2	yes	complemented
24	C₄₁×#551	—	2	2	no	—
25	C₄₁×#548	—	2	2	no	—
26	C₄₁×#548	—	2	2	no	—
27	C₄₁×#548	C₂²	1	4	yes	—
28	C₄₁×#548	C₂²	1	4	yes	complemented
29	C₄₁×#548	C₂²	1	2	yes	complemented
30	C₄₁×#546	C₂²	1	2	yes	complemented
31	C₄₁×#539	—	2	1	no	—
32	C₄₁×#538	—	2	1	no	—
33	C₄₁×#534	—	2	1	no	—
34	C₄₁×#529	C₂²	1	2	yes	—
35	C₂×#124×C₄₁	—	2	1	no	—
36	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic, complemented
37	C₄₁×#525	C₂²	1	2	yes	—
38	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
39	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
41	C₂×#121×C₄₁	—	2	1	no	—
42	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
43	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic, complemented
44	C₄₁×#518	—	2	1	no	—
45	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×D₄×C₄₁	—	2	1	no	—
47	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
48	C₄₁×#495	C₂²	1	4	yes	complemented
49	C₄₁×#488	C₂²	1	4	yes	complemented
50	C₄₁×#484	C₂²	1	2	yes	complemented
51	C₄₁×#483	C₂²	1	2	yes	complemented
52	C₄₁×#483	C₂²	1	2	yes	complemented
53	C₄₁×#482	C₂²	1	4	yes	complemented
54	C₄₁×#480	C₂²	1	2	yes	—
55	C₄₁×#479	C₂²	1	4	yes	complemented
56	C₄₁×#470	C₂²	1	4	yes	complemented
57	C₄₁×#469	C₂²	1	4	yes	complemented
58	C₄₁×#468	C₂²	1	4	yes	complemented
59	C₄₁×#468	C₂²	1	4	yes	complemented
60	C₄₁×#464	C₂²	1	4	yes	complemented
61	C₄₁×#464	C₂²	1	4	yes	complemented
62	C₄₁×#463	C₂²	1	4	yes	complemented
63	C₄₁×#452	C₂²	1	4	yes	complemented
64	C₄₁×#451	C₂²	1	4	yes	complemented
65	C₄₁×#451	C₂²	1	2	yes	complemented
66	C₄₁×#451	C₂²	1	2	yes	complemented
67	C₄₁×#451	C₂²	1	2	yes	complemented
68	C₄₁×#450	C₂²	1	2	yes	complemented
69	C₄₁×#450	C₂²	1	2	yes	complemented
70	C₄₁×#449	C₂²	1	4	yes	complemented
71	C₄₁×#449	C₂²	1	4	yes	complemented
72	C₄₁×#448	C₂²	1	2	yes	—
73	C₄₁×#448	C₂²	1	2	yes	—
74	C₄₁×#448	C₂²	1	4	yes	complemented
75	C₄₁×#447	C₂²	1	2	yes	—
76	C₄×Q₁₆×C₄₁	C₂²	1	4	yes	complemented
77	C₄×SD₁₆×C₄₁	C₂²	1	4	yes	complemented
78	C₄₁×#436	C₂²	1	4	yes	complemented
79	C₄₁×#436	C₂²	1	4	yes	complemented
80	C₄₁×#431	C₂²	1	2	yes	complemented
81	C₄₁×#419	C₂²	1	4	yes	complemented
82	C₄₁×#417	C₂²	1	2	yes	complemented
83	C₄₁×#417	C₂²	1	2	yes	complemented
84	C₄₁×#407	C₂²	1	1	yes	characteristic
85	C₄₁×#407	C₂²	1	1	yes	characteristic
86	C₄₁×#407	C₂²	1	2	yes	complemented
87	C₂×#41×C₄₁	—	2	1	no	—
88	C₂×#41×C₄₁	—	2	1	no	—
89	C₂×#41×C₄₁	—	4	4	no	—
90	C₂×#41×C₄₁	C₂³	1	2	yes	—
91	C₂×#41×C₄₁	C₂³	1	2	yes	—
92	C₂×#41×C₄₁	C₂³	1	2	yes	—
93	C₂²×Q₈×C₄₁	—	2	1	no	—
94	C₂²×Q₈×C₄₁	—	2	2	no	—
95	C₂²×Q₈×C₄₁	—	4	4	no	—
96	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₄₁	C₂³	1	4	yes	—
98	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
99	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₄₁	—	2	1	no	—
101	C₂²×D₄×C₄₁	—	2	1	no	—
102	C₂²×D₄×C₄₁	—	2	1	no	—
103	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
104	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
105	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₄₁	—	2	1	no	—
107	C₂³×C₄×C₄₁	—	2	1	no	—
108	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
110	#137×C₄₁	—	4	8	no	—
111	#137×C₄₁	—	4	4	no	—
112	AGL(1,ℤ/8)×C₄₁	—	4	4	no	—
113	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
114	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
115	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
116	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
117	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
118	C₂×D₈×C₄₁	C₂³	1	4	yes	—
119	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
120	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
121	C₂×M₁₆×C₄₁	C₂³	1	4	yes	—
122	#126×C₄₁	—	2	2	no	—
123	#126×C₄₁	—	2	2	no	—
124	#126×C₄₁	—	2	2	no	—
125	#125×C₄₁	—	2	2	no	—
126	#125×C₄₁	C₂³	1	2	yes	—
127	#124×C₄₁	—	2	4	no	—
128	#124×C₄₁	—	2	4	no	—
129	#124×C₄₁	—	2	2	no	—
130	#124×C₄₁	—	2	2	no	—
131	#124×C₄₁	C₂³	1	4	yes	—
132	#124×C₄₁	C₂³	1	2	yes	—
133	#123×C₄₁	—	2	2	no	—
134	#123×C₄₁	—	2	2	no	—
135	#123×C₄₁	—	2	2	no	—
136	#123×C₄₁	—	2	2	no	—
137	#123×C₄₁	—	2	2	no	—
138	C₂²⋊Q₈×C₄₁	—	2	1	no	—
139	C₂²⋊Q₈×C₄₁	—	2	1	no	—
140	C₂²⋊Q₈×C₄₁	—	2	1	no	—
141	C₂²⋊Q₈×C₄₁	—	2	1	no	—
142	C₂²⋊Q₈×C₄₁	—	2	4	no	—
143	C₂²⋊Q₈×C₄₁	—	2	4	no	—
144	C₂²⋊Q₈×C₄₁	—	2	2	no	—
145	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
146	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
147	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
148	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
149	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
150	#121×C₄₁	—	2	4	no	—
151	#121×C₄₁	—	2	4	no	—
152	#121×C₄₁	—	2	2	no	—
153	#121×C₄₁	—	2	2	no	—
154	#121×C₄₁	—	2	1	no	—
155	#121×C₄₁	—	2	1	no	—
156	#121×C₄₁	—	2	2	no	—
157	#121×C₄₁	—	2	2	no	—
158	#121×C₄₁	C₂³	1	2	yes	—
159	#121×C₄₁	C₂³	1	2	yes	—
160	#121×C₄₁	C₂³	1	4	yes	—
161	#121×C₄₁	C₂³	1	2	yes	—
162	#120×C₄₁	—	2	2	no	—
163	#120×C₄₁	—	2	2	no	—
164	C₄×Q₈×C₄₁	—	2	2	no	—
165	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
166	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
167	C₄×D₄×C₄₁	—	2	2	no	—
168	C₄×D₄×C₄₁	—	2	2	no	—
169	C₄×D₄×C₄₁	—	2	2	no	—
170	C₄×D₄×C₄₁	—	2	4	no	—
171	C₄×D₄×C₄₁	—	2	4	no	—
172	C₄×D₄×C₄₁	—	2	2	no	—
173	C₄×D₄×C₄₁	—	2	2	no	—
174	C₄×D₄×C₄₁	D₄	1	2	yes	—
175	C₄×D₄×C₄₁	D₄	1	2	yes	—
176	C₄×D₄×C₄₁	C₂³	1	2	yes	—
177	C₄×D₄×C₄₁	C₂³	1	2	yes	—
178	C₄×D₄×C₄₁	C₂³	1	2	yes	—
179	#117×C₄₁	—	2	2	no	—
180	#117×C₄₁	—	2	2	no	—
181	#117×C₄₁	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
183	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
184	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
185	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
190	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
191	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
192	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
193	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
194	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
195	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
196	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
198	C₂×C₄²×C₄₁	—	2	1	no	—
199	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
200	#107×C₄₁	C₂³	1	4	yes	—
201	#106×C₄₁	C₂³	1	4	yes	—
202	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
203	#103×C₄₁	C₂³	1	4	yes	—
204	#103×C₄₁	C₂³	1	4	yes	—
205	#103×C₄₁	C₂³	1	4	yes	—
206	#103×C₄₁	C₂³	1	4	yes	—
207	#103×C₄₁	C₂³	1	4	yes	—
208	#102×C₄₁	C₂³	1	4	yes	—
209	#102×C₄₁	C₂³	1	4	yes	—
210	#102×C₄₁	C₂³	1	4	yes	—
211	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
212	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
213	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
214	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
215	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
216	C₄×C₈×C₄₁	C₂³	1	4	yes	—
217	C₂⁴×C₄₁	—	2	1	no	—
218	C₂⁴×C₄₁	—	2	1	no	—
219	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
220	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
221	#41×C₄₁	—	2	4	no	—
222	#41×C₄₁	—	2	4	no	—
223	#41×C₄₁	—	4	2	no	—
224	#41×C₄₁	—	4	2	no	—
225	#41×C₄₁	—	4	4	no	—
226	#41×C₄₁	—	4	4	no	—
227	#41×C₄₁	—	4	4	no	—
228	C₂×Q₈×C₄₁	—	2	4	no	—
229	C₂×Q₈×C₄₁	—	2	1	no	—
230	C₂×Q₈×C₄₁	—	2	4	no	—
231	C₂×Q₈×C₄₁	—	2	1	no	—
232	C₂×Q₈×C₄₁	—	2	1	no	—
233	C₂×Q₈×C₄₁	—	2	8	no	—
234	C₂×Q₈×C₄₁	—	4	4	no	—
235	C₂×Q₈×C₄₁	—	4	2	no	—
236	C₂×Q₈×C₄₁	—	4	4	no	—
237	C₂×Q₈×C₄₁	—	4	2	no	—
238	C₂×Q₈×C₄₁	—	4	8	no	—
239	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
240	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
242	C₂×D₄×C₄₁	—	2	2	no	—
243	C₂×D₄×C₄₁	—	2	4	no	—
244	C₂×D₄×C₄₁	—	2	2	no	—
245	C₂×D₄×C₄₁	—	2	2	no	—
246	C₂×D₄×C₄₁	—	2	2	no	—
247	C₂×D₄×C₄₁	—	2	2	no	—
248	C₂×D₄×C₄₁	—	2	2	no	—
249	C₂×D₄×C₄₁	—	2	1	no	—
250	C₂×D₄×C₄₁	—	2	1	no	—
251	C₂×D₄×C₄₁	—	4	2	no	—
252	C₂×D₄×C₄₁	—	4	2	no	—
253	C₂×D₄×C₄₁	—	4	2	no	—
254	C₂×D₄×C₄₁	—	4	4	no	—
255	C₂×D₄×C₄₁	—	4	4	no	—
256	C₂×D₄×C₄₁	—	4	4	no	—
257	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
258	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
259	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
260	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
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	1	no	—
265	C₂²×C₄×C₄₁	—	2	4	no	—
266	C₂²×C₄×C₄₁	—	2	1	no	—
267	C₂²×C₄×C₄₁	—	2	1	no	—
268	C₂²×C₄×C₄₁	—	2	2	no	—
269	C₂²×C₄×C₄₁	—	2	2	no	—
270	C₂²×C₄×C₄₁	—	2	2	no	—
271	C₂²×C₄×C₄₁	—	2	2	no	—
272	C₂²×C₄×C₄₁	—	4	2	no	—
273	C₂²×C₄×C₄₁	—	4	2	no	—
274	C₂²×C₄×C₄₁	—	4	4	no	—
275	C₂²×C₄×C₄₁	—	4	4	no	—
276	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
283	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
287	Q₁₆×C₄₁	—	2	8	no	—
288	Q₁₆×C₄₁	—	4	4	no	—
289	SD₁₆×C₄₁	—	2	8	no	—
290	SD₁₆×C₄₁	—	4	4	no	—
291	SD₁₆×C₄₁	—	4	4	no	—
292	D₈×C₄₁	—	4	4	no	—
293	M₁₆×C₄₁	—	4	2	no	—
294	M₁₆×C₄₁	—	4	4	no	—
295	M₁₆×C₄₁	—	4	2	no	—
296	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
297	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
298	C₄⋊C₄×C₄₁	—	2	2	no	—
299	C₄⋊C₄×C₄₁	—	2	2	no	—
300	C₄⋊C₄×C₄₁	—	2	2	no	—
301	C₄⋊C₄×C₄₁	—	2	4	no	—
302	C₄⋊C₄×C₄₁	—	2	2	no	—
303	C₄⋊C₄×C₄₁	—	2	1	no	—
304	C₄⋊C₄×C₄₁	—	2	1	no	—
305	C₄⋊C₄×C₄₁	—	2	1	no	—
306	C₄⋊C₄×C₄₁	—	2	2	no	—
307	C₄⋊C₄×C₄₁	—	2	2	no	—
308	C₄⋊C₄×C₄₁	—	2	2	no	—
309	C₄⋊C₄×C₄₁	—	2	2	no	—
310	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
311	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
312	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
313	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
314	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
315	C₂²⋊C₄×C₄₁	—	2	2	no	—
316	C₂²⋊C₄×C₄₁	—	2	2	no	—
317	C₂²⋊C₄×C₄₁	—	2	2	no	—
318	C₂²⋊C₄×C₄₁	—	2	2	no	—
319	C₂²⋊C₄×C₄₁	—	2	2	no	—
320	C₂²⋊C₄×C₄₁	—	2	2	no	—
321	C₂²⋊C₄×C₄₁	—	2	2	no	—
322	C₂²⋊C₄×C₄₁	—	2	2	no	—
323	C₂²⋊C₄×C₄₁	—	2	2	no	—
324	C₂²⋊C₄×C₄₁	—	2	4	no	—
325	C₂²⋊C₄×C₄₁	—	2	4	no	—
326	C₂²⋊C₄×C₄₁	—	2	4	no	—
327	C₂²⋊C₄×C₄₁	—	2	2	no	—
328	C₂²⋊C₄×C₄₁	—	2	2	no	—
329	C₂²⋊C₄×C₄₁	—	2	2	no	—
330	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
331	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
332	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
333	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
334	C₄²×C₄₁	—	2	4	no	—
335	C₄²×C₄₁	—	2	2	no	—
336	C₄²×C₄₁	—	2	2	no	—
337	C₄²×C₄₁	C₂×D₄	1	2	yes	—
338	C₄²×C₄₁	C₂⁴	1	2	yes	—
339	C₂³×C₄₁	—	2	2	no	—
340	C₂³×C₄₁	—	2	2	no	—
341	C₂³×C₄₁	—	2	2	no	—
342	C₂³×C₄₁	—	2	2	no	—
343	C₂³×C₄₁	—	4	1	no	—
344	C₂³×C₄₁	—	4	1	no	—
345	C₂³×C₄₁	—	4	1	no	—
346	C₂³×C₄₁	—	4	1	no	—
347	C₂³×C₄₁	—	4	2	no	—
348	C₂³×C₄₁	—	4	2	no	—
349	C₂³×C₄₁	—	4	2	no	—
350	C₂³×C₄₁	—	4	2	no	—
351	C₂³×C₄₁	—	8	1	no	—
352	C₂³×C₄₁	—	8	1	no	—
353	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
354	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
355	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
356	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
357	Q₈×C₄₁	—	2	4	no	—
358	Q₈×C₄₁	—	2	2	no	—
359	Q₈×C₄₁	—	2	4	no	—
360	Q₈×C₄₁	—	2	4	no	—
361	Q₈×C₄₁	—	4	8	no	—
362	Q₈×C₄₁	—	4	2	no	—
363	Q₈×C₄₁	—	8	1	no	—
364	Q₈×C₄₁	H(5,𝔽₂)	1	4	yes	—
365	D₄×C₄₁	—	2	2	no	—
366	D₄×C₄₁	—	2	4	no	—
367	D₄×C₄₁	—	2	2	no	—
368	D₄×C₄₁	—	4	2	no	—
369	D₄×C₄₁	—	4	2	no	—
370	D₄×C₄₁	—	4	4	no	—
371	D₄×C₄₁	—	4	4	no	—
372	D₄×C₄₁	—	4	2	no	—
373	D₄×C₄₁	—	4	4	no	—
374	D₄×C₄₁	—	4	8	no	—
375	D₄×C₄₁	—	4	4	no	—
376	D₄×C₄₁	—	8	1	no	—
377	D₄×C₄₁	—	8	2	no	—
378	D₄×C₄₁	—	8	2	no	—
379	C₂×C₄×C₄₁	—	2	4	no	—
380	C₂×C₄×C₄₁	—	2	2	no	—
381	C₂×C₄×C₄₁	—	2	2	no	—
382	C₂×C₄×C₄₁	—	2	2	no	—
383	C₂×C₄×C₄₁	—	2	4	no	—
384	C₂×C₄×C₄₁	—	2	2	no	—
385	C₂×C₄×C₄₁	—	2	2	no	—
386	C₂×C₄×C₄₁	—	2	2	no	—
387	C₂×C₄×C₄₁	—	2	2	no	—
388	C₂×C₄×C₄₁	—	2	2	no	—
389	C₂×C₄×C₄₁	—	2	2	no	—
390	C₂×C₄×C₄₁	—	2	2	no	—
391	C₂×C₄×C₄₁	—	4	1	no	—
392	C₂×C₄×C₄₁	—	4	2	no	—
393	C₂×C₄×C₄₁	—	4	1	no	—
394	C₂×C₄×C₄₁	—	4	1	no	—
395	C₂×C₄×C₄₁	—	4	1	no	—
396	C₂×C₄×C₄₁	—	4	1	no	—
397	C₂×C₄×C₄₁	—	4	4	no	—
398	C₂×C₄×C₄₁	—	4	4	no	—
399	C₂×C₄×C₄₁	—	4	8	no	—
400	C₂×C₄×C₄₁	—	4	2	no	—
401	C₂×C₄×C₄₁	—	4	2	no	—
402	C₂×C₄×C₄₁	—	4	2	no	—
403	C₂×C₄×C₄₁	—	8	2	no	—
404	C₂×C₄×C₄₁	—	8	2	no	—
405	C₂×C₄×C₄₁	—	8	1	no	—
406	C₂×C₄×C₄₁	—	8	1	no	—
407	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
408	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
409	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
411	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
414	C₈×C₄₁	—	2	4	no	—
415	C₈×C₄₁	—	2	4	no	—
416	#61583	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
417	C₂²×C₄₁	—	2	1	no	—
418	C₂²×C₄₁	—	2	1	no	—
419	C₂²×C₄₁	—	2	1	no	—
420	C₂²×C₄₁	—	2	2	no	—
421	C₂²×C₄₁	—	2	1	no	—
422	C₂²×C₄₁	—	2	2	no	—
423	C₂²×C₄₁	—	2	1	no	—
424	C₂²×C₄₁	—	2	1	no	—
425	C₂²×C₄₁	—	2	1	no	—
426	C₂²×C₄₁	—	2	2	no	—
427	C₂²×C₄₁	—	2	1	no	—
428	C₂²×C₄₁	—	4	4	no	—
429	C₂²×C₄₁	—	4	2	no	—
430	C₂²×C₄₁	—	4	2	no	—
431	C₂²×C₄₁	—	4	2	no	—
432	C₂²×C₄₁	—	4	2	no	—
433	C₂²×C₄₁	—	4	2	no	—
434	C₂²×C₄₁	—	4	2	no	—
435	C₂²×C₄₁	—	8	2	no	—
436	C₂²×C₄₁	—	8	4	no	—
437	C₂²×C₄₁	—	16	2	no	—
438	C₂²×C₄₁	#575	1	2	yes	—
439	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
440	C₄×C₄₁	—	2	2	no	—
441	C₄×C₄₁	—	2	4	no	—
442	C₄×C₄₁	—	2	1	no	—
443	C₄×C₄₁	—	2	1	no	—
444	C₄×C₄₁	—	2	1	no	—
445	C₄×C₄₁	—	2	2	no	—
446	C₄×C₄₁	—	2	2	no	—
447	C₄×C₄₁	—	4	2	no	—
448	C₄×C₄₁	—	4	2	no	—
449	C₄×C₄₁	—	4	2	no	—
450	C₄×C₄₁	—	4	2	no	—
451	C₄×C₄₁	—	4	2	no	—
452	C₄×C₄₁	C₂×H(5,𝔽₂)	1	2	yes	—
453	#3505	C₂×C₄₁	1	1	yes	characteristic, complemented
454	C₂×#548	C₂×C₄₁	1	1	yes	characteristic, complemented
455	#3327	C₂×C₄₁	1	4	yes	complemented
456	#3326	C₂×C₄₁	1	4	yes	complemented
457	#3277	C₂×C₄₁	1	4	yes	complemented
458	#3275	C₂×C₄₁	1	4	yes	complemented
459	#3211	C₂×C₄₁	1	2	yes	complemented
460	#3195	C₂×C₄₁	1	1	yes	characteristic, complemented
461	#3194	C₂×C₄₁	1	2	yes	complemented
462	#3193	C₂×C₄₁	1	1	yes	characteristic, complemented
463	#3108	C₂×C₄₁	1	2	yes	complemented
464	#3007	C₂×C₄₁	1	1	yes	characteristic, complemented
465	#3006	C₂×C₄₁	1	1	yes	characteristic, complemented
466	#3004	C₂×C₄₁	1	2	yes	complemented
467	#2975	C₂×C₄₁	1	1	yes	characteristic, complemented
468	C₂×C₄₁	—	2	2	no	—
469	C₂×C₄₁	—	4	2	no	—
470	C₂×C₄₁	—	4	1	no	—
471	C₂×C₄₁	—	4	1	no	—
472	C₂×C₄₁	—	8	2	no	—
473	C₂×C₄₁	—	8	2	no	—
474	C₂×C₄₁	#3484	1	1	yes	characteristic
475	C₂×C₄₁	C₂×#575	1	1	yes	characteristic
476	C₂×C₄₁	#3586	1	1	yes	characteristic
477	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
478	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
479	C₂×#137	C₂²×C₄₁	1	4	yes	complemented
480	C₂×#137	C₂²×C₄₁	1	2	yes	complemented
481	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	2	yes	complemented
482	#553	—	2	2	no	—
483	#553	C₂²×C₄₁	1	2	yes	complemented
484	#552	C₂²×C₄₁	1	2	yes	complemented
485	#551	—	2	2	no	—
486	#548	—	2	2	no	—
487	#548	—	2	2	no	—
488	#548	C₂²×C₄₁	1	4	yes	—
489	#548	C₂²×C₄₁	1	4	yes	complemented
490	#548	C₂²×C₄₁	1	2	yes	complemented
491	#546	C₂²×C₄₁	1	2	yes	complemented
492	#539	—	2	1	no	—
493	#538	—	2	1	no	—
494	#534	—	2	1	no	—
495	#529	C₂²×C₄₁	1	2	yes	—
496	C₂×#124	—	2	1	no	—
497	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic, complemented
498	#525	C₂²×C₄₁	1	2	yes	—
499	C₂×C₂²⋊Q₈	—	2	1	no	—
500	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
501	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
502	C₂×#121	—	2	1	no	—
503	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
504	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic, complemented
505	#518	—	2	1	no	—
506	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
507	C₂×C₄×D₄	—	2	1	no	—
508	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
509	#495	C₂²×C₄₁	1	4	yes	complemented
510	#488	C₂²×C₄₁	1	4	yes	complemented
511	#484	C₂²×C₄₁	1	2	yes	complemented
512	#483	C₂²×C₄₁	1	2	yes	complemented
513	#483	C₂²×C₄₁	1	2	yes	complemented
514	#482	C₂²×C₄₁	1	4	yes	complemented
515	#480	C₂²×C₄₁	1	2	yes	—
516	#479	C₂²×C₄₁	1	4	yes	complemented
517	#470	C₂²×C₄₁	1	4	yes	complemented
518	#469	C₂²×C₄₁	1	4	yes	complemented
519	#468	C₂²×C₄₁	1	4	yes	complemented
520	#468	C₂²×C₄₁	1	4	yes	complemented
521	#464	C₂²×C₄₁	1	4	yes	complemented
522	#464	C₂²×C₄₁	1	4	yes	complemented
523	#463	C₂²×C₄₁	1	4	yes	complemented
524	#452	C₂²×C₄₁	1	4	yes	complemented
525	#451	C₂²×C₄₁	1	2	yes	complemented
526	#451	C₂²×C₄₁	1	2	yes	complemented
527	#451	C₂²×C₄₁	1	2	yes	complemented
528	#451	C₂²×C₄₁	1	4	yes	complemented
529	#450	C₂²×C₄₁	1	2	yes	complemented
530	#450	C₂²×C₄₁	1	2	yes	complemented
531	#449	C₂²×C₄₁	1	4	yes	complemented
532	#449	C₂²×C₄₁	1	4	yes	complemented
533	#448	C₂²×C₄₁	1	2	yes	—
534	#448	C₂²×C₄₁	1	2	yes	—
535	#448	C₂²×C₄₁	1	4	yes	complemented
536	#447	C₂²×C₄₁	1	2	yes	—
537	C₄×Q₁₆	C₂²×C₄₁	1	4	yes	complemented
538	C₄×SD₁₆	C₂²×C₄₁	1	4	yes	complemented
539	#436	C₂²×C₄₁	1	4	yes	complemented
540	#436	C₂²×C₄₁	1	4	yes	complemented
541	#431	C₂²×C₄₁	1	2	yes	complemented
542	#419	C₂²×C₄₁	1	4	yes	complemented
543	#417	C₂²×C₄₁	1	2	yes	complemented
544	#417	C₂²×C₄₁	1	2	yes	complemented
545	#407	C₂²×C₄₁	1	1	yes	characteristic
546	#407	C₂²×C₄₁	1	1	yes	characteristic
547	#407	C₂²×C₄₁	1	2	yes	complemented
548	C₄₁	#61583	1	1	yes	characteristic, direct product factor, Sylow
549	C₂×#41	—	2	1	no	—
550	C₂×#41	—	2	1	no	—
551	C₂×#41	—	4	4	no	—
552	C₂×#41	C₂³×C₄₁	1	2	yes	—
553	C₂×#41	C₂³×C₄₁	1	2	yes	—
554	C₂×#41	C₂³×C₄₁	1	2	yes	—
555	C₂²×Q₈	—	2	1	no	—
556	C₂²×Q₈	—	2	2	no	—
557	C₂²×Q₈	—	4	4	no	—
558	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
559	C₂²×Q₈	C₂³×C₄₁	1	4	yes	—
560	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
561	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
562	C₂²×D₄	—	2	1	no	—
563	C₂²×D₄	—	2	1	no	—
564	C₂²×D₄	—	2	1	no	—
565	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
566	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
567	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
568	C₂³×C₄	—	2	1	no	—
569	C₂³×C₄	—	2	1	no	—
570	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
571	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
572	#137	—	4	8	no	—
573	#137	—	4	4	no	—
574	AGL(1,ℤ/8)	—	4	4	no	—
575	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
576	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
577	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
578	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
579	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
580	C₂×D₈	C₂³×C₄₁	1	4	yes	—
581	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
582	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
583	C₂×M₁₆	C₂³×C₄₁	1	4	yes	—
584	#126	—	2	2	no	—
585	#126	—	2	2	no	—
586	#126	—	2	2	no	—
587	#125	—	2	2	no	—
588	#125	C₂³×C₄₁	1	2	yes	—
589	#124	—	2	4	no	—
590	#124	—	2	4	no	—
591	#124	—	2	2	no	—
592	#124	—	2	2	no	—
593	#124	C₂³×C₄₁	1	4	yes	—
594	#124	C₂³×C₄₁	1	2	yes	—
595	#123	—	2	2	no	—
596	#123	—	2	2	no	—
597	#123	—	2	2	no	—
598	#123	—	2	2	no	—
599	#123	—	2	2	no	—
600	C₂²⋊Q₈	—	2	1	no	—
601	C₂²⋊Q₈	—	2	1	no	—
602	C₂²⋊Q₈	—	2	1	no	—
603	C₂²⋊Q₈	—	2	1	no	—
604	C₂²⋊Q₈	—	2	4	no	—
605	C₂²⋊Q₈	—	2	4	no	—
606	C₂²⋊Q₈	—	2	2	no	—
607	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
608	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
609	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
610	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
611	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
612	#121	—	2	4	no	—
613	#121	—	2	4	no	—
614	#121	—	2	2	no	—
615	#121	—	2	2	no	—
616	#121	—	2	1	no	—
617	#121	—	2	1	no	—
618	#121	—	2	2	no	—
619	#121	—	2	2	no	—
620	#121	C₂³×C₄₁	1	2	yes	—
621	#121	C₂³×C₄₁	1	2	yes	—
622	#121	C₂³×C₄₁	1	4	yes	—
623	#121	C₂³×C₄₁	1	2	yes	—
624	#120	—	2	2	no	—
625	#120	—	2	2	no	—
626	C₄×Q₈	—	2	2	no	—
627	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
628	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	4	no	—
633	C₄×D₄	—	2	4	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	D₄×C₄₁	1	2	yes	—
637	C₄×D₄	D₄×C₄₁	1	2	yes	—
638	C₄×D₄	C₂³×C₄₁	1	2	yes	—
639	C₄×D₄	C₂³×C₄₁	1	2	yes	—
640	C₄×D₄	C₂³×C₄₁	1	2	yes	—
641	#117	—	2	2	no	—
642	#117	—	2	2	no	—
643	#117	C₂³×C₄₁	1	2	yes	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	—	2	1	no	—
646	C₂×C₄⋊C₄	—	2	1	no	—
647	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	—	2	1	no	—
652	C₂×C₂²⋊C₄	—	2	1	no	—
653	C₂×C₂²⋊C₄	—	2	1	no	—
654	C₂×C₂²⋊C₄	—	2	1	no	—
655	C₂×C₂²⋊C₄	—	2	1	no	—
656	C₂×C₂²⋊C₄	—	2	1	no	—
657	C₂×C₂²⋊C₄	—	2	2	no	—
658	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
659	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
660	C₂×C₄²	—	2	1	no	—
661	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
662	#107	C₂³×C₄₁	1	4	yes	—
663	#106	C₂³×C₄₁	1	4	yes	—
664	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
665	#103	C₂³×C₄₁	1	4	yes	—
666	#103	C₂³×C₄₁	1	4	yes	—
667	#103	C₂³×C₄₁	1	4	yes	—
668	#103	C₂³×C₄₁	1	4	yes	—
669	#103	C₂³×C₄₁	1	4	yes	—
670	#102	C₂³×C₄₁	1	4	yes	—
671	#102	C₂³×C₄₁	1	4	yes	—
672	#102	C₂³×C₄₁	1	4	yes	—
673	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
674	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
675	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
676	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
677	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
678	C₄×C₈	C₂³×C₄₁	1	4	yes	—
679	C₂⁴	—	2	1	no	—
680	C₂⁴	—	2	1	no	—
681	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
682	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
683	#41	—	2	4	no	—
684	#41	—	2	4	no	—
685	#41	—	4	2	no	—
686	#41	—	4	2	no	—
687	#41	—	4	4	no	—
688	#41	—	4	4	no	—
689	#41	—	4	4	no	—
690	C₂×Q₈	—	2	4	no	—
691	C₂×Q₈	—	2	1	no	—
692	C₂×Q₈	—	2	4	no	—
693	C₂×Q₈	—	2	1	no	—
694	C₂×Q₈	—	2	1	no	—
695	C₂×Q₈	—	2	8	no	—
696	C₂×Q₈	—	4	4	no	—
697	C₂×Q₈	—	4	2	no	—
698	C₂×Q₈	—	4	4	no	—
699	C₂×Q₈	—	4	2	no	—
700	C₂×Q₈	—	4	8	no	—
701	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
702	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
703	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	4	no	—
706	C₂×D₄	—	2	2	no	—
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	2	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	1	no	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	4	2	no	—
714	C₂×D₄	—	4	2	no	—
715	C₂×D₄	—	4	2	no	—
716	C₂×D₄	—	4	4	no	—
717	C₂×D₄	—	4	4	no	—
718	C₂×D₄	—	4	4	no	—
719	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
720	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
721	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
722	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
723	C₂²×C₄	—	2	1	no	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	2	1	no	—
726	C₂²×C₄	—	2	1	no	—
727	C₂²×C₄	—	2	4	no	—
728	C₂²×C₄	—	2	1	no	—
729	C₂²×C₄	—	2	1	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	4	2	no	—
735	C₂²×C₄	—	4	2	no	—
736	C₂²×C₄	—	4	4	no	—
737	C₂²×C₄	—	4	4	no	—
738	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
739	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
740	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
741	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
742	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
743	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
744	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
749	Q₁₆	—	2	8	no	—
750	Q₁₆	—	4	4	no	—
751	SD₁₆	—	2	8	no	—
752	SD₁₆	—	4	4	no	—
753	SD₁₆	—	4	4	no	—
754	D₈	—	4	4	no	—
755	M₁₆	—	4	2	no	—
756	M₁₆	—	4	4	no	—
757	M₁₆	—	4	2	no	—
758	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
759	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	4	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	1	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
773	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
774	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
775	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
776	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
793	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
794	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
795	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
796	C₄²	—	2	4	no	—
797	C₄²	—	2	2	no	—
798	C₄²	—	2	2	no	—
799	C₄²	C₂×D₄×C₄₁	1	2	yes	—
800	C₄²	C₂⁴×C₄₁	1	2	yes	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	4	1	no	—
806	C₂³	—	4	1	no	—
807	C₂³	—	4	1	no	—
808	C₂³	—	4	1	no	—
809	C₂³	—	4	2	no	—
810	C₂³	—	4	2	no	—
811	C₂³	—	4	2	no	—
812	C₂³	—	4	2	no	—
813	C₂³	—	8	1	no	—
814	C₂³	—	8	1	no	—
815	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
816	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
817	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
818	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
819	Q₈	—	2	4	no	—
820	Q₈	—	2	2	no	—
821	Q₈	—	2	4	no	—
822	Q₈	—	2	4	no	—
823	Q₈	—	4	8	no	—
824	Q₈	—	4	2	no	—
825	Q₈	—	8	1	no	—
826	Q₈	H(5,𝔽₂)×C₄₁	1	4	yes	—
827	D₄	—	2	2	no	—
828	D₄	—	2	4	no	—
829	D₄	—	2	2	no	—
830	D₄	—	4	2	no	—
831	D₄	—	4	2	no	—
832	D₄	—	4	4	no	—
833	D₄	—	4	4	no	—
834	D₄	—	4	2	no	—
835	D₄	—	4	4	no	—
836	D₄	—	4	8	no	—
837	D₄	—	4	4	no	—
838	D₄	—	8	1	no	—
839	D₄	—	8	2	no	—
840	D₄	—	8	2	no	—
841	C₂×C₄	—	2	4	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	4	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	4	1	no	—
854	C₂×C₄	—	4	2	no	—
855	C₂×C₄	—	4	1	no	—
856	C₂×C₄	—	4	1	no	—
857	C₂×C₄	—	4	1	no	—
858	C₂×C₄	—	4	1	no	—
859	C₂×C₄	—	4	4	no	—
860	C₂×C₄	—	4	4	no	—
861	C₂×C₄	—	4	8	no	—
862	C₂×C₄	—	4	2	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	4	2	no	—
865	C₂×C₄	—	8	2	no	—
866	C₂×C₄	—	8	2	no	—
867	C₂×C₄	—	8	1	no	—
868	C₂×C₄	—	8	1	no	—
869	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
870	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
871	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
872	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
873	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
875	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
876	C₈	—	2	4	no	—
877	C₈	—	2	4	no	—
878	C₂²	—	2	1	no	—
879	C₂²	—	2	1	no	—
880	C₂²	—	2	1	no	—
881	C₂²	—	2	2	no	—
882	C₂²	—	2	1	no	—
883	C₂²	—	2	1	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	1	no	—
888	C₂²	—	2	1	no	—
889	C₂²	—	4	4	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	8	2	no	—
897	C₂²	—	8	4	no	—
898	C₂²	—	16	2	no	—
899	C₂²	C₄₁×#575	1	2	yes	—
900	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
901	C₄	—	2	2	no	—
902	C₄	—	2	2	no	—
903	C₄	—	2	4	no	—
904	C₄	—	2	1	no	—
905	C₄	—	2	1	no	—
906	C₄	—	2	1	no	—
907	C₄	—	2	2	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	2	no	—
913	C₄	C₂×H(5,𝔽₂)×C₄₁	1	2	yes	—
914	C₂	—	2	2	no	—
915	C₂	—	4	2	no	—
916	C₂	—	4	1	no	—
917	C₂	—	4	1	no	—
918	C₂	—	8	2	no	—
919	C₂	—	8	2	no	—
920	C₂	C₄₁×#3484	1	1	yes	characteristic
921	C₂	C₂×C₄₁×#575	1	1	yes	characteristic
922	C₂	C₄₁×#3586	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 ◁ C₂×C₄×D₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3505	C₂	semidirect
2. C₂×C₄₁×#548	C₂	semidirect
3. C₄₁×#3327	C₂	semidirect
4. C₄₁×#3326	C₂	semidirect
5. C₄₁×#3277	C₂	semidirect
6. C₄₁×#3275	C₂	semidirect
7. C₄₁×#3211	C₂	semidirect
8. C₄₁×#3195	C₂	semidirect
9. C₄₁×#3194	C₂	semidirect
10. C₄₁×#3193	C₂	semidirect
11. C₄₁×#3108	C₂	semidirect
12. C₄₁×#3007	C₂	semidirect
13. C₄₁×#3006	C₂	semidirect
14. C₄₁×#3004	C₂	semidirect
15. C₄₁×#2975	C₂	semidirect
17. C₂³×Q₈×C₄₁	C₂²	semidirect
18. C₂×#137×C₄₁	C₂²	semidirect
19. C₂×#137×C₄₁	C₂²	semidirect
20. C₂×AGL(1,ℤ/8)×C₄₁	C₂²	semidirect
22. C₄₁×#553	C₂²	semidirect
23. C₄₁×#552	C₂²	semidirect
28. C₄₁×#548	C₂²	semidirect
29. C₄₁×#548	C₂²	semidirect
30. C₄₁×#546	C₂²	semidirect
36. C₂×#124×C₄₁	C₂²	semidirect
43. C₂×#121×C₄₁	C₂²	semidirect
45. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
48. C₄₁×#495	C₂²	semidirect
49. C₄₁×#488	C₂²	semidirect
50. C₄₁×#484	C₂²	semidirect
51. C₄₁×#483	C₂²	semidirect
52. C₄₁×#483	C₂²	semidirect
53. C₄₁×#482	C₂²	semidirect
55. C₄₁×#479	C₂²	semidirect
56. C₄₁×#470	C₂²	semidirect
57. C₄₁×#469	C₂²	semidirect
58. C₄₁×#468	C₂²	semidirect
59. C₄₁×#468	C₂²	semidirect
60. C₄₁×#464	C₂²	semidirect
61. C₄₁×#464	C₂²	semidirect
62. C₄₁×#463	C₂²	semidirect
63. C₄₁×#452	C₂²	semidirect
64. C₄₁×#451	C₂²	semidirect
65. C₄₁×#451	C₂²	semidirect
66. C₄₁×#451	C₂²	semidirect
67. C₄₁×#451	C₂²	semidirect
68. C₄₁×#450	C₂²	semidirect
69. C₄₁×#450	C₂²	semidirect
70. C₄₁×#449	C₂²	semidirect
71. C₄₁×#449	C₂²	semidirect
74. C₄₁×#448	C₂²	semidirect
76. C₄×Q₁₆×C₄₁	C₂²	semidirect
77. C₄×SD₁₆×C₄₁	C₂²	semidirect
78. C₄₁×#436	C₂²	semidirect
79. C₄₁×#436	C₂²	semidirect
80. C₄₁×#431	C₂²	semidirect
81. C₄₁×#419	C₂²	semidirect
82. C₄₁×#417	C₂²	semidirect
83. C₄₁×#417	C₂²	semidirect
86. C₄₁×#407	C₂²	semidirect
416. #61583	C₄₁	direct (N × H)
453. #3505	C₂×C₄₁	semidirect
454. C₂×#548	C₂×C₄₁	semidirect
455. #3327	C₂×C₄₁	semidirect
456. #3326	C₂×C₄₁	semidirect
457. #3277	C₂×C₄₁	semidirect
458. #3275	C₂×C₄₁	semidirect
459. #3211	C₂×C₄₁	semidirect
460. #3195	C₂×C₄₁	semidirect
461. #3194	C₂×C₄₁	semidirect
462. #3193	C₂×C₄₁	semidirect
463. #3108	C₂×C₄₁	semidirect
464. #3007	C₂×C₄₁	semidirect
465. #3006	C₂×C₄₁	semidirect
466. #3004	C₂×C₄₁	semidirect
467. #2975	C₂×C₄₁	semidirect
478. C₂³×Q₈	C₂²×C₄₁	semidirect
479. C₂×#137	C₂²×C₄₁	semidirect
480. C₂×#137	C₂²×C₄₁	semidirect
481. C₂×AGL(1,ℤ/8)	C₂²×C₄₁	semidirect
483. #553	C₂²×C₄₁	semidirect
484. #552	C₂²×C₄₁	semidirect
489. #548	C₂²×C₄₁	semidirect
490. #548	C₂²×C₄₁	semidirect
491. #546	C₂²×C₄₁	semidirect
497. C₂×#124	C₂²×C₄₁	semidirect
504. C₂×#121	C₂²×C₄₁	semidirect
506. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
509. #495	C₂²×C₄₁	semidirect
510. #488	C₂²×C₄₁	semidirect
511. #484	C₂²×C₄₁	semidirect
512. #483	C₂²×C₄₁	semidirect
513. #483	C₂²×C₄₁	semidirect
514. #482	C₂²×C₄₁	semidirect
516. #479	C₂²×C₄₁	semidirect
517. #470	C₂²×C₄₁	semidirect
518. #469	C₂²×C₄₁	semidirect
519. #468	C₂²×C₄₁	semidirect
520. #468	C₂²×C₄₁	semidirect
521. #464	C₂²×C₄₁	semidirect
522. #464	C₂²×C₄₁	semidirect
523. #463	C₂²×C₄₁	semidirect
524. #452	C₂²×C₄₁	semidirect
525. #451	C₂²×C₄₁	semidirect
526. #451	C₂²×C₄₁	semidirect
527. #451	C₂²×C₄₁	semidirect
528. #451	C₂²×C₄₁	semidirect
529. #450	C₂²×C₄₁	semidirect
530. #450	C₂²×C₄₁	semidirect
531. #449	C₂²×C₄₁	semidirect
532. #449	C₂²×C₄₁	semidirect
535. #448	C₂²×C₄₁	semidirect
537. C₄×Q₁₆	C₂²×C₄₁	semidirect
538. C₄×SD₁₆	C₂²×C₄₁	semidirect
539. #436	C₂²×C₄₁	semidirect
540. #436	C₂²×C₄₁	semidirect
541. #431	C₂²×C₄₁	semidirect
542. #419	C₂²×C₄₁	semidirect
543. #417	C₂²×C₄₁	semidirect
544. #417	C₂²×C₄₁	semidirect
547. #407	C₂²×C₄₁	semidirect
548. C₄₁	#61583	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#3505	2
C₂×C₄₁×#548	2
C₄₁×#3327	2
C₄₁×#3326	2
C₄₁×#3277	2
C₄₁×#3275	2
C₄₁×#3211	2
C₄₁×#3195	2
C₄₁×#3194	2
C₄₁×#3193	2
C₄₁×#3108	2
C₄₁×#3007	2
C₄₁×#3006	2
C₄₁×#3004	2
C₄₁×#2975	2
#61583	41

Subgroups — C41×#61583 #23837784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61583 #23837784