Subgroups — C₄₁×#23531 #23799732

Order 10496.

1454 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,ℤ/8)×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#430	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2896	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#418	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#100×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2879	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2051	C₂	1	8	yes	maximal, complemented
8	C₄₁×#1742	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
11	C₂×AGL(1,ℤ/8)×C₄₁	—	2	2	no	—
12	C₂×AGL(1,ℤ/8)×C₄₁	—	2	4	no	—
13	C₂×AGL(1,ℤ/8)×C₄₁	—	2	4	no	—
14	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	4	yes	—
15	C₂²×SD₁₆×C₄₁	—	2	1	no	—
16	C₂²×D₈×C₄₁	—	2	1	no	—
17	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
22	C₄₁×#430	—	2	4	no	—
23	C₂×#108×C₄₁	C₂²	1	4	yes	complemented
24	C₄₁×#419	—	2	1	no	—
25	C₄₁×#418	—	2	1	no	—
26	C₄₁×#418	—	2	2	no	—
27	C₄₁×#418	—	2	2	no	—
28	C₄₁×#417	C₂²	1	4	yes	complemented
29	C₄₁×#416	—	2	2	no	—
30	C₂×#102×C₄₁	C₂²	1	4	yes	complemented
31	C₂×#100×C₄₁	—	2	4	no	—
32	C₂×#100×C₄₁	C₂²	1	4	yes	complemented
33	C₄₁×#408	—	2	2	no	—
34	C₄₁×#408	C₂²	1	4	yes	complemented
35	C₄₁×#407	—	2	2	no	—
36	C₄₁×#343	C₂²	1	4	yes	complemented
37	C₂⁵×C₄₁	—	2	1	no	—
38	C₂×#41×C₄₁	—	2	1	no	—
39	C₂×#41×C₄₁	—	2	1	no	—
40	C₂×#41×C₄₁	—	2	2	no	—
41	C₂×#41×C₄₁	—	2	2	no	—
42	C₂×#41×C₄₁	—	2	2	no	—
43	C₂×#41×C₄₁	—	2	2	no	—
44	C₂×#41×C₄₁	D₄	1	2	yes	—
45	C₂×#41×C₄₁	C₂³	1	2	yes	—
46	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₄₁	—	2	1	no	—
48	C₂²×D₄×C₄₁	—	2	1	no	—
49	C₂²×D₄×C₄₁	—	2	2	no	—
50	C₂²×D₄×C₄₁	—	2	1	no	—
51	C₂²×D₄×C₄₁	—	2	1	no	—
52	C₂²×D₄×C₄₁	—	2	1	no	—
53	C₂²×D₄×C₄₁	—	2	2	no	—
54	C₂²×D₄×C₄₁	—	2	2	no	—
55	C₂²×D₄×C₄₁	—	2	1	no	—
56	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
57	C₂²×D₄×C₄₁	D₄	1	4	yes	—
58	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
59	C₂³×C₄×C₄₁	—	2	1	no	—
60	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
61	AGL(1,ℤ/8)×C₄₁	—	2	16	no	—
62	AGL(1,ℤ/8)×C₄₁	—	2	8	no	—
63	AGL(1,ℤ/8)×C₄₁	—	2	8	no	—
64	C₂×SD₁₆×C₄₁	—	2	8	no	—
65	C₂×SD₁₆×C₄₁	—	2	4	no	—
66	C₂×D₈×C₄₁	—	2	8	no	—
67	C₂×D₈×C₄₁	—	2	4	no	—
68	C₂×M₁₆×C₄₁	—	2	2	no	—
69	C₂×M₁₆×C₄₁	—	2	1	no	—
70	C₂×M₁₆×C₄₁	—	2	2	no	—
71	C₂×M₁₆×C₄₁	—	2	2	no	—
72	C₂×M₁₆×C₄₁	—	2	1	no	—
73	C₂×M₁₆×C₄₁	—	2	1	no	—
74	C₂×M₁₆×C₄₁	—	2	2	no	—
75	C₂×M₁₆×C₄₁	—	2	2	no	—
76	C₂×M₁₆×C₄₁	—	2	2	no	—
77	C₂×M₁₆×C₄₁	—	2	2	no	—
78	C₂×M₁₆×C₄₁	D₄	1	4	yes	—
79	C₂×M₁₆×C₄₁	D₄	1	2	yes	—
80	C₂×M₁₆×C₄₁	D₄	1	2	yes	—
81	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
82	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
83	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
84	C₂²×C₈×C₄₁	—	2	1	no	—
85	C₂²×C₈×C₄₁	—	2	1	no	—
86	C₂²×C₈×C₄₁	—	2	1	no	—
87	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
88	#117×C₄₁	—	2	1	no	—
89	#117×C₄₁	—	2	1	no	—
90	#117×C₄₁	—	2	1	no	—
91	#117×C₄₁	—	2	1	no	—
92	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
93	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
94	C₂×C₄²×C₄₁	—	2	1	no	—
95	#108×C₄₁	—	2	8	no	—
96	#103×C₄₁	—	2	4	no	—
97	#102×C₄₁	—	2	4	no	—
98	#102×C₄₁	—	2	8	no	—
99	#100×C₄₁	—	2	8	no	—
100	C₂²⋊C₈×C₄₁	—	2	8	no	—
101	C₂⁴×C₄₁	—	2	1	no	—
102	C₂⁴×C₄₁	—	2	4	no	—
103	C₂⁴×C₄₁	—	2	2	no	—
104	C₂⁴×C₄₁	—	4	1	no	—
105	C₂⁴×C₄₁	—	4	1	no	—
106	C₂⁴×C₄₁	—	4	2	no	—
107	C₂⁴×C₄₁	—	8	4	no	—
108	C₂⁴×C₄₁	#41	1	1	yes	characteristic
109	#41×C₄₁	—	2	4	no	—
110	#41×C₄₁	—	2	4	no	—
111	#41×C₄₁	—	2	2	no	—
112	#41×C₄₁	—	2	2	no	—
113	#41×C₄₁	—	2	2	no	—
114	#41×C₄₁	—	2	2	no	—
115	#41×C₄₁	—	4	2	no	—
116	#41×C₄₁	—	4	2	no	—
117	#41×C₄₁	—	4	2	no	—
118	#41×C₄₁	—	4	2	no	—
119	C₂×Q₈×C₄₁	—	2	1	no	—
120	C₂×Q₈×C₄₁	—	2	2	no	—
121	C₂×Q₈×C₄₁	—	2	2	no	—
122	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
123	C₂×D₄×C₄₁	—	2	2	no	—
124	C₂×D₄×C₄₁	—	2	2	no	—
125	C₂×D₄×C₄₁	—	2	2	no	—
126	C₂×D₄×C₄₁	—	2	4	no	—
127	C₂×D₄×C₄₁	—	2	4	no	—
128	C₂×D₄×C₄₁	—	2	4	no	—
129	C₂×D₄×C₄₁	—	2	4	no	—
130	C₂×D₄×C₄₁	—	2	1	no	—
131	C₂×D₄×C₄₁	—	2	2	no	—
132	C₂×D₄×C₄₁	—	2	4	no	—
133	C₂×D₄×C₄₁	—	2	2	no	—
134	C₂×D₄×C₄₁	—	2	2	no	—
135	C₂×D₄×C₄₁	—	2	2	no	—
136	C₂×D₄×C₄₁	—	2	2	no	—
137	C₂×D₄×C₄₁	—	2	2	no	—
138	C₂×D₄×C₄₁	—	4	2	no	—
139	C₂×D₄×C₄₁	—	4	2	no	—
140	C₂×D₄×C₄₁	—	4	2	no	—
141	C₂×D₄×C₄₁	—	4	2	no	—
142	C₂×D₄×C₄₁	—	4	1	no	—
143	C₂×D₄×C₄₁	—	4	1	no	—
144	C₂×D₄×C₄₁	—	4	2	no	—
145	C₂×D₄×C₄₁	—	4	2	no	—
146	C₂×D₄×C₄₁	—	4	2	no	—
147	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
148	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₄₁	—	2	1	no	—
150	C₂²×C₄×C₄₁	—	2	2	no	—
151	C₂²×C₄×C₄₁	—	2	2	no	—
152	C₂²×C₄×C₄₁	—	2	2	no	—
153	C₂²×C₄×C₄₁	—	4	2	no	—
154	C₂²×C₄×C₄₁	—	4	2	no	—
155	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₁	#41	1	2	yes	—
162	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
163	C₂²×C₄×C₄₁	#41	1	2	yes	—
164	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
165	SD₁₆×C₄₁	—	2	16	no	—
166	D₈×C₄₁	—	2	16	no	—
167	M₁₆×C₄₁	—	2	4	no	—
168	M₁₆×C₄₁	—	2	4	no	—
169	M₁₆×C₄₁	—	2	4	no	—
170	M₁₆×C₄₁	—	2	2	no	—
171	M₁₆×C₄₁	—	2	2	no	—
172	M₁₆×C₄₁	—	2	2	no	—
173	M₁₆×C₄₁	—	2	2	no	—
174	M₁₆×C₄₁	—	2	2	no	—
175	M₁₆×C₄₁	—	4	2	no	—
176	M₁₆×C₄₁	—	4	2	no	—
177	M₁₆×C₄₁	C₂×D₄	1	4	yes	—
178	C₂×C₈×C₄₁	—	2	4	no	—
179	C₂×C₈×C₄₁	—	2	2	no	—
180	C₂×C₈×C₄₁	—	2	2	no	—
181	C₂×C₈×C₄₁	—	2	2	no	—
182	C₂×C₈×C₄₁	—	2	2	no	—
183	C₂×C₈×C₄₁	—	2	2	no	—
184	C₂×C₈×C₄₁	—	4	2	no	—
185	C₂×C₈×C₄₁	—	4	2	no	—
186	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
187	C₄⋊C₄×C₄₁	—	2	2	no	—
188	C₄⋊C₄×C₄₁	—	2	2	no	—
189	C₂²⋊C₄×C₄₁	—	4	1	no	—
190	C₂²⋊C₄×C₄₁	—	4	1	no	—
191	C₄²×C₄₁	—	4	1	no	—
192	C₄²×C₄₁	—	4	1	no	—
193	C₂³×C₄₁	—	2	2	no	—
194	C₂³×C₄₁	—	2	4	no	—
195	C₂³×C₄₁	—	4	2	no	—
196	C₂³×C₄₁	—	4	2	no	—
197	C₂³×C₄₁	—	4	2	no	—
198	C₂³×C₄₁	—	4	2	no	—
199	C₂³×C₄₁	—	4	4	no	—
200	C₂³×C₄₁	—	4	4	no	—
201	C₂³×C₄₁	—	8	2	no	—
202	C₂³×C₄₁	—	8	4	no	—
203	C₂³×C₄₁	—	8	4	no	—
204	C₂³×C₄₁	—	8	4	no	—
205	C₂³×C₄₁	—	8	8	no	—
206	C₂³×C₄₁	—	8	8	no	—
207	C₂³×C₄₁	#121	1	1	yes	characteristic
208	C₂³×C₄₁	#121	1	1	yes	characteristic
209	C₂³×C₄₁	#123	1	2	yes	—
210	C₂³×C₄₁	#124	1	2	yes	—
211	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
212	Q₈×C₄₁	—	2	2	no	—
213	Q₈×C₄₁	—	2	2	no	—
214	Q₈×C₄₁	—	4	2	no	—
215	D₄×C₄₁	—	2	2	no	—
216	D₄×C₄₁	—	2	4	no	—
217	D₄×C₄₁	—	2	4	no	—
218	D₄×C₄₁	—	2	2	no	—
219	D₄×C₄₁	—	4	2	no	—
220	D₄×C₄₁	—	4	2	no	—
221	D₄×C₄₁	—	4	4	no	—
222	D₄×C₄₁	—	4	2	no	—
223	D₄×C₄₁	—	4	2	no	—
224	D₄×C₄₁	—	4	4	no	—
225	D₄×C₄₁	—	4	4	no	—
226	D₄×C₄₁	—	4	2	no	—
227	C₂×C₄×C₄₁	—	2	2	no	—
228	C₂×C₄×C₄₁	—	4	2	no	—
229	C₂×C₄×C₄₁	—	4	2	no	—
230	C₂×C₄×C₄₁	—	4	2	no	—
231	C₂×C₄×C₄₁	—	4	4	no	—
232	C₂×C₄×C₄₁	—	4	2	no	—
233	C₂×C₄×C₄₁	—	8	2	no	—
234	C₂×C₄×C₄₁	#120	1	2	yes	—
235	C₂×C₄×C₄₁	#120	1	2	yes	—
236	C₂×C₄×C₄₁	#121	1	2	yes	—
237	C₂×C₄×C₄₁	#121	1	2	yes	—
238	C₂×C₄×C₄₁	#121	1	2	yes	—
239	C₂×C₄×C₄₁	#121	1	2	yes	—
240	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
241	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
242	C₂×C₄×C₄₁	#123	1	2	yes	—
243	C₂×C₄×C₄₁	#123	1	2	yes	—
244	C₂×C₄×C₄₁	#123	1	2	yes	—
245	C₂×C₄×C₄₁	#124	1	2	yes	—
246	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
251	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
252	C₈×C₄₁	—	2	4	no	—
253	C₈×C₄₁	—	2	4	no	—
254	C₈×C₄₁	—	4	2	no	—
255	C₈×C₄₁	—	4	2	no	—
256	#23531	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
257	C₂²×C₄₁	—	2	2	no	—
258	C₂²×C₄₁	—	2	2	no	—
259	C₂²×C₄₁	—	2	2	no	—
260	C₂²×C₄₁	—	4	2	no	—
261	C₂²×C₄₁	—	4	2	no	—
262	C₂²×C₄₁	—	4	2	no	—
263	C₂²×C₄₁	—	4	4	no	—
264	C₂²×C₄₁	—	4	4	no	—
265	C₂²×C₄₁	—	8	4	no	—
266	C₂²×C₄₁	—	8	4	no	—
267	C₂²×C₄₁	—	8	8	no	—
268	C₂²×C₄₁	—	8	8	no	—
269	C₂²×C₄₁	—	8	4	no	—
270	C₂²×C₄₁	—	8	4	no	—
271	C₂²×C₄₁	#394	1	2	yes	—
272	C₂²×C₄₁	#394	1	2	yes	—
273	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
274	C₂²×C₄₁	C₂×#123	1	1	yes	characteristic
275	C₂²×C₄₁	C₂×#124	1	1	yes	characteristic
276	C₄×C₄₁	—	4	2	no	—
277	C₄×C₄₁	—	8	2	no	—
278	C₄×C₄₁	#394	1	2	yes	—
279	C₄×C₄₁	#394	1	2	yes	—
280	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
281	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
282	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
283	C₄×C₄₁	C₂×#123	1	1	yes	characteristic
284	C₂²×AGL(1,ℤ/8)	C₂×C₄₁	1	1	yes	characteristic
285	C₂×#430	C₂×C₄₁	1	1	yes	characteristic, complemented
286	#2896	C₂×C₄₁	1	1	yes	characteristic, complemented
287	C₂×#418	C₂×C₄₁	1	1	yes	characteristic, complemented
288	C₂²×#100	C₂×C₄₁	1	1	yes	characteristic, complemented
289	#2879	C₂×C₄₁	1	1	yes	characteristic, complemented
290	#2051	C₂×C₄₁	1	8	yes	complemented
291	#1742	C₂×C₄₁	1	1	yes	characteristic, complemented
292	C₂×C₄₁	—	2	2	no	—
293	C₂×C₄₁	—	2	1	no	—
294	C₂×C₄₁	—	2	1	no	—
295	C₂×C₄₁	—	2	2	no	—
296	C₂×C₄₁	—	8	2	no	—
297	C₂×C₄₁	—	8	4	no	—
298	C₂×C₄₁	C₂×#394	1	1	yes	characteristic
299	C₂×C₄₁	#3068	1	2	yes	—
300	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
301	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
302	C₂×AGL(1,ℤ/8)	—	2	2	no	—
303	C₂×AGL(1,ℤ/8)	—	2	4	no	—
304	C₂×AGL(1,ℤ/8)	—	2	4	no	—
305	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	4	yes	—
306	C₂²×SD₁₆	—	2	1	no	—
307	C₂²×D₈	—	2	1	no	—
308	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
309	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
310	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
311	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
312	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
313	#430	—	2	4	no	—
314	C₂×#108	C₂²×C₄₁	1	4	yes	complemented
315	#419	—	2	1	no	—
316	#418	—	2	1	no	—
317	#418	—	2	2	no	—
318	#418	—	2	2	no	—
319	#417	C₂²×C₄₁	1	4	yes	complemented
320	#416	—	2	2	no	—
321	C₂×#102	C₂²×C₄₁	1	4	yes	complemented
322	C₂×#100	—	2	4	no	—
323	C₂×#100	C₂²×C₄₁	1	4	yes	complemented
324	#408	—	2	2	no	—
325	#408	C₂²×C₄₁	1	4	yes	complemented
326	#407	—	2	2	no	—
327	#343	C₂²×C₄₁	1	4	yes	complemented
328	C₄₁	#23531	1	1	yes	characteristic, direct product factor, Sylow
329	C₂⁵	—	2	1	no	—
330	C₂×#41	—	2	1	no	—
331	C₂×#41	—	2	1	no	—
332	C₂×#41	—	2	2	no	—
333	C₂×#41	—	2	2	no	—
334	C₂×#41	—	2	2	no	—
335	C₂×#41	—	2	2	no	—
336	C₂×#41	D₄×C₄₁	1	2	yes	—
337	C₂×#41	C₂³×C₄₁	1	2	yes	—
338	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
339	C₂²×D₄	—	2	1	no	—
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	—	2	2	no	—
342	C₂²×D₄	—	2	1	no	—
343	C₂²×D₄	—	2	1	no	—
344	C₂²×D₄	—	2	1	no	—
345	C₂²×D₄	—	2	2	no	—
346	C₂²×D₄	—	2	2	no	—
347	C₂²×D₄	—	2	1	no	—
348	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
349	C₂²×D₄	D₄×C₄₁	1	4	yes	—
350	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
351	C₂³×C₄	—	2	1	no	—
352	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
353	AGL(1,ℤ/8)	—	2	16	no	—
354	AGL(1,ℤ/8)	—	2	8	no	—
355	AGL(1,ℤ/8)	—	2	8	no	—
356	C₂×SD₁₆	—	2	8	no	—
357	C₂×SD₁₆	—	2	4	no	—
358	C₂×D₈	—	2	8	no	—
359	C₂×D₈	—	2	4	no	—
360	C₂×M₁₆	—	2	2	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	2	no	—
363	C₂×M₁₆	—	2	2	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	—	2	2	no	—
367	C₂×M₁₆	—	2	2	no	—
368	C₂×M₁₆	—	2	2	no	—
369	C₂×M₁₆	—	2	2	no	—
370	C₂×M₁₆	D₄×C₄₁	1	4	yes	—
371	C₂×M₁₆	D₄×C₄₁	1	2	yes	—
372	C₂×M₁₆	D₄×C₄₁	1	2	yes	—
373	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
374	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
375	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
376	C₂²×C₈	—	2	1	no	—
377	C₂²×C₈	—	2	1	no	—
378	C₂²×C₈	—	2	1	no	—
379	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
380	#117	—	2	1	no	—
381	#117	—	2	1	no	—
382	#117	—	2	1	no	—
383	#117	—	2	1	no	—
384	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₄²	—	2	1	no	—
387	#108	—	2	8	no	—
388	#103	—	2	4	no	—
389	#102	—	2	4	no	—
390	#102	—	2	8	no	—
391	#100	—	2	8	no	—
392	C₂²⋊C₈	—	2	8	no	—
393	C₂⁴	—	2	1	no	—
394	C₂⁴	—	2	4	no	—
395	C₂⁴	—	2	2	no	—
396	C₂⁴	—	4	1	no	—
397	C₂⁴	—	4	1	no	—
398	C₂⁴	—	4	2	no	—
399	C₂⁴	—	8	4	no	—
400	C₂⁴	#41×C₄₁	1	1	yes	characteristic
401	#41	—	2	4	no	—
402	#41	—	2	4	no	—
403	#41	—	2	2	no	—
404	#41	—	2	2	no	—
405	#41	—	2	2	no	—
406	#41	—	2	2	no	—
407	#41	—	4	2	no	—
408	#41	—	4	2	no	—
409	#41	—	4	2	no	—
410	#41	—	4	2	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	4	no	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	4	2	no	—
431	C₂×D₄	—	4	2	no	—
432	C₂×D₄	—	4	2	no	—
433	C₂×D₄	—	4	2	no	—
434	C₂×D₄	—	4	1	no	—
435	C₂×D₄	—	4	1	no	—
436	C₂×D₄	—	4	2	no	—
437	C₂×D₄	—	4	2	no	—
438	C₂×D₄	—	4	2	no	—
439	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
440	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	4	2	no	—
446	C₂²×C₄	—	4	2	no	—
447	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
448	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
449	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
453	C₂²×C₄	#41×C₄₁	1	2	yes	—
454	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
455	C₂²×C₄	#41×C₄₁	1	2	yes	—
456	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
457	SD₁₆	—	2	16	no	—
458	D₈	—	2	16	no	—
459	M₁₆	—	2	4	no	—
460	M₁₆	—	2	4	no	—
461	M₁₆	—	2	4	no	—
462	M₁₆	—	2	2	no	—
463	M₁₆	—	2	2	no	—
464	M₁₆	—	2	2	no	—
465	M₁₆	—	2	2	no	—
466	M₁₆	—	2	2	no	—
467	M₁₆	—	4	2	no	—
468	M₁₆	—	4	2	no	—
469	M₁₆	C₂×D₄×C₄₁	1	4	yes	—
470	C₂×C₈	—	2	4	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	4	2	no	—
477	C₂×C₈	—	4	2	no	—
478	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	4	1	no	—
483	C₄²	—	4	1	no	—
484	C₄²	—	4	1	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	2	4	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	2	no	—
489	C₂³	—	4	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	4	no	—
492	C₂³	—	4	4	no	—
493	C₂³	—	8	2	no	—
494	C₂³	—	8	4	no	—
495	C₂³	—	8	4	no	—
496	C₂³	—	8	4	no	—
497	C₂³	—	8	8	no	—
498	C₂³	—	8	8	no	—
499	C₂³	#121×C₄₁	1	1	yes	characteristic
500	C₂³	#121×C₄₁	1	1	yes	characteristic
501	C₂³	#123×C₄₁	1	2	yes	—
502	C₂³	#124×C₄₁	1	2	yes	—
503	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
504	Q₈	—	2	2	no	—
505	Q₈	—	2	2	no	—
506	Q₈	—	4	2	no	—
507	D₄	—	2	2	no	—
508	D₄	—	2	4	no	—
509	D₄	—	2	4	no	—
510	D₄	—	2	2	no	—
511	D₄	—	4	2	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	4	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	4	no	—
517	D₄	—	4	4	no	—
518	D₄	—	4	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	4	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	8	2	no	—
526	C₂×C₄	#120×C₄₁	1	2	yes	—
527	C₂×C₄	#120×C₄₁	1	2	yes	—
528	C₂×C₄	#121×C₄₁	1	2	yes	—
529	C₂×C₄	#121×C₄₁	1	2	yes	—
530	C₂×C₄	#121×C₄₁	1	2	yes	—
531	C₂×C₄	#121×C₄₁	1	2	yes	—
532	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
533	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
534	C₂×C₄	#123×C₄₁	1	2	yes	—
535	C₂×C₄	#123×C₄₁	1	2	yes	—
536	C₂×C₄	#123×C₄₁	1	2	yes	—
537	C₂×C₄	#124×C₄₁	1	2	yes	—
538	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
539	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
540	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
541	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
542	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
543	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
544	C₈	—	2	4	no	—
545	C₈	—	2	4	no	—
546	C₈	—	4	2	no	—
547	C₈	—	4	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	4	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	4	no	—
556	C₂²	—	8	4	no	—
557	C₂²	—	8	8	no	—
558	C₂²	—	8	4	no	—
559	C₂²	—	8	8	no	—
560	C₂²	—	8	4	no	—
561	C₂²	—	8	4	no	—
562	C₂²	C₄₁×#394	1	2	yes	—
563	C₂²	C₄₁×#394	1	2	yes	—
564	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
565	C₂²	C₂×#123×C₄₁	1	1	yes	characteristic
566	C₂²	C₂×#124×C₄₁	1	1	yes	characteristic
567	C₄	—	4	2	no	—
568	C₄	—	8	2	no	—
569	C₄	C₄₁×#394	1	2	yes	—
570	C₄	C₄₁×#394	1	2	yes	—
571	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
572	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
573	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
574	C₄	C₂×#123×C₄₁	1	1	yes	characteristic
575	C₂	—	2	2	no	—
576	C₂	—	2	1	no	—
577	C₂	—	2	1	no	—
578	C₂	—	2	2	no	—
579	C₂	—	8	2	no	—
580	C₂	—	8	4	no	—
581	C₂	C₂×C₄₁×#394	1	1	yes	characteristic
582	C₂	C₄₁×#3068	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×AGL(1,ℤ/8)×C₄₁	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#430	C₂	semidirect
3. C₄₁×#2896	C₂	semidirect
4. C₂×C₄₁×#418	C₂	semidirect
5. C₂²×#100×C₄₁	C₂	semidirect
6. C₄₁×#2879	C₂	semidirect
7. C₄₁×#2051	C₂	semidirect
8. C₄₁×#1742	C₂	semidirect
23. C₂×#108×C₄₁	C₂²	semidirect
28. C₄₁×#417	C₂²	semidirect
30. C₂×#102×C₄₁	C₂²	semidirect
32. C₂×#100×C₄₁	C₂²	semidirect
34. C₄₁×#408	C₂²	semidirect
36. C₄₁×#343	C₂²	semidirect
256. #23531	C₄₁	direct (N × H)
285. C₂×#430	C₂×C₄₁	semidirect
286. #2896	C₂×C₄₁	semidirect
287. C₂×#418	C₂×C₄₁	semidirect
288. C₂²×#100	C₂×C₄₁	semidirect
289. #2879	C₂×C₄₁	semidirect
290. #2051	C₂×C₄₁	semidirect
291. #1742	C₂×C₄₁	semidirect
314. C₂×#108	C₂²×C₄₁	semidirect
319. #417	C₂²×C₄₁	semidirect
321. C₂×#102	C₂²×C₄₁	semidirect
323. C₂×#100	C₂²×C₄₁	semidirect
325. #408	C₂²×C₄₁	semidirect
327. #343	C₂²×C₄₁	semidirect
328. C₄₁	#23531	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×AGL(1,ℤ/8)×C₄₁	2
C₂×C₄₁×#430	2
C₄₁×#2896	2
C₂×C₄₁×#418	2
C₂²×#100×C₄₁	2
C₄₁×#2879	2
C₄₁×#2051	2
C₄₁×#1742	2
#23531	41

Subgroups — C41×#23531 #23799732

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23531 #23799732