Subgroups — C₄₁×#24370 #23800571

Order 10496.

1670 conjugacy classes of subgroups.

The subgroup lattice has 628 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, complemented
2	C₂×C₄₁×#460	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₁×#449	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2433	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2054	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2011	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1895	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1880	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1851	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1786	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×AGL(1,ℤ/8)×C₄₁	—	2	4	no	—
15	C₂×AGL(1,ℤ/8)×C₄₁	—	2	8	no	—
16	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
17	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₈×C₄₁	C₂²	1	2	yes	—
19	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
20	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#127×C₄₁	C₂²	1	2	yes	—
22	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×#120×C₄₁	—	2	2	no	—
24	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	complemented
25	C₄₁×#460	—	2	8	no	—
26	C₄₁×#449	—	2	4	no	—
27	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	complemented
28	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic, complemented
29	C₂×#102×C₄₁	C₂²	1	2	yes	—
30	C₂×#102×C₄₁	C₂²	1	2	yes	—
31	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic, complemented
32	C₂×#102×C₄₁	C₂²	1	2	yes	complemented
33	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
34	C₄₁×#392	—	2	1	no	—
35	C₄₁×#392	—	2	1	no	—
36	C₄₁×#390	—	2	2	no	—
37	C₄₁×#390	C₂²	1	2	yes	—
38	C₄₁×#390	C₂²	1	2	yes	complemented
39	C₄₁×#380	—	2	1	no	—
40	C₄₁×#380	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
42	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
43	C₄₁×#340	C₂²	1	2	yes	complemented
44	C₄₁×#336	C₂²	1	2	yes	complemented
45	C₂⁵×C₄₁	—	2	1	no	—
46	C₂×#41×C₄₁	—	2	2	no	—
47	C₂×#41×C₄₁	—	2	4	no	—
48	C₂×#41×C₄₁	—	4	2	no	—
49	C₂×#41×C₄₁	D₄	1	4	yes	complemented
50	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₄₁	—	2	4	no	—
52	C₂²×D₄×C₄₁	—	2	1	no	—
53	C₂²×D₄×C₄₁	—	2	1	no	—
54	C₂²×D₄×C₄₁	—	2	2	no	—
55	C₂²×D₄×C₄₁	—	2	1	no	—
56	C₂²×D₄×C₄₁	—	2	2	no	—
57	C₂²×D₄×C₄₁	—	2	2	no	—
58	C₂²×D₄×C₄₁	—	2	2	no	—
59	C₂²×D₄×C₄₁	—	4	2	no	—
60	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
62	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₄₁	—	2	1	no	—
64	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
65	AGL(1,ℤ/8)×C₄₁	—	2	32	no	—
66	C₂×SD₁₆×C₄₁	—	2	4	no	—
67	C₂×SD₁₆×C₄₁	—	2	4	no	—
68	C₂×SD₁₆×C₄₁	—	2	2	no	—
69	C₂×SD₁₆×C₄₁	—	2	4	no	—
70	C₂×SD₁₆×C₄₁	D₄	1	8	yes	complemented
71	C₂×D₈×C₄₁	—	2	4	no	—
72	C₂×D₈×C₄₁	—	2	4	no	—
73	C₂×D₈×C₄₁	—	2	2	no	—
74	C₂×D₈×C₄₁	—	2	4	no	—
75	C₂×D₈×C₄₁	—	4	2	no	—
76	C₂×M₁₆×C₄₁	—	2	2	no	—
77	C₂×M₁₆×C₄₁	—	2	4	no	—
78	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
81	#127×C₄₁	—	2	4	no	—
82	#127×C₄₁	—	4	2	no	—
83	#121×C₄₁	—	2	2	no	—
84	#121×C₄₁	—	2	2	no	—
85	#120×C₄₁	—	4	8	no	—
86	C₄×Q₈×C₄₁	—	2	4	no	—
87	C₄×Q₈×C₄₁	—	4	2	no	—
88	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
89	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
98	C₂×C₄²×C₄₁	—	2	2	no	—
99	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
100	C₄⋊C₈×C₄₁	—	2	4	no	—
101	#103×C₄₁	—	2	2	no	—
102	#102×C₄₁	—	2	4	no	—
103	#102×C₄₁	—	2	2	no	—
104	#102×C₄₁	—	2	4	no	—
105	#102×C₄₁	—	4	2	no	—
106	C₂²⋊C₈×C₄₁	—	2	2	no	—
107	#95×C₄₁	—	2	1	no	—
108	#95×C₄₁	D₄	1	1	yes	characteristic
109	#95×C₄₁	D₄	1	1	yes	characteristic
110	C₂⁴×C₄₁	—	2	1	no	—
111	C₂⁴×C₄₁	—	2	2	no	—
112	C₂⁴×C₄₁	—	2	1	no	—
113	C₂⁴×C₄₁	—	4	4	no	—
114	C₂⁴×C₄₁	—	4	4	no	—
115	C₂⁴×C₄₁	—	4	2	no	—
116	C₂⁴×C₄₁	—	8	1	no	—
117	C₂⁴×C₄₁	—	8	1	no	—
118	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
119	#41×C₄₁	—	2	8	no	—
120	#41×C₄₁	—	4	4	no	—
121	#41×C₄₁	—	4	8	no	—
122	C₂×Q₈×C₄₁	—	2	1	no	—
123	C₂×Q₈×C₄₁	—	2	2	no	—
124	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
125	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
126	C₂×D₄×C₄₁	—	2	8	no	—
127	C₂×D₄×C₄₁	—	2	4	no	—
128	C₂×D₄×C₄₁	—	2	2	no	—
129	C₂×D₄×C₄₁	—	2	2	no	—
130	C₂×D₄×C₄₁	—	2	2	no	—
131	C₂×D₄×C₄₁	—	2	2	no	—
132	C₂×D₄×C₄₁	—	2	1	no	—
133	C₂×D₄×C₄₁	—	2	2	no	—
134	C₂×D₄×C₄₁	—	2	1	no	—
135	C₂×D₄×C₄₁	—	2	1	no	—
136	C₂×D₄×C₄₁	—	2	2	no	—
137	C₂×D₄×C₄₁	—	2	2	no	—
138	C₂×D₄×C₄₁	—	2	2	no	—
139	C₂×D₄×C₄₁	—	2	2	no	—
140	C₂×D₄×C₄₁	—	4	8	no	—
141	C₂×D₄×C₄₁	—	4	4	no	—
142	C₂×D₄×C₄₁	—	4	4	no	—
143	C₂×D₄×C₄₁	—	4	4	no	—
144	C₂×D₄×C₄₁	—	4	4	no	—
145	C₂×D₄×C₄₁	—	4	4	no	—
146	C₂×D₄×C₄₁	—	4	4	no	—
147	C₂×D₄×C₄₁	—	4	4	no	—
148	C₂×D₄×C₄₁	—	4	2	no	—
149	C₂×D₄×C₄₁	—	4	2	no	—
150	C₂×D₄×C₄₁	—	4	4	no	—
151	C₂×D₄×C₄₁	—	8	2	no	—
152	C₂×D₄×C₄₁	—	8	2	no	—
153	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
154	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₄₁	—	2	1	no	—
156	C₂²×C₄×C₄₁	—	2	2	no	—
157	C₂²×C₄×C₄₁	—	2	2	no	—
158	C₂²×C₄×C₄₁	—	2	4	no	—
159	C₂²×C₄×C₄₁	—	2	2	no	—
160	C₂²×C₄×C₄₁	—	2	1	no	—
161	C₂²×C₄×C₄₁	—	4	4	no	—
162	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₄₁	#41	1	2	yes	—
167	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
168	SD₁₆×C₄₁	—	2	16	no	—
169	SD₁₆×C₄₁	—	4	4	no	—
170	D₈×C₄₁	—	2	16	no	—
171	D₈×C₄₁	—	4	4	no	—
172	M₁₆×C₄₁	—	2	8	no	—
173	C₂×C₈×C₄₁	—	2	2	no	—
174	C₂×C₈×C₄₁	—	2	2	no	—
175	C₂×C₈×C₄₁	—	2	1	no	—
176	C₂×C₈×C₄₁	—	2	1	no	—
177	C₂×C₈×C₄₁	—	2	2	no	—
178	C₂×C₈×C₄₁	—	2	2	no	—
179	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
180	C₄⋊C₄×C₄₁	—	2	2	no	—
181	C₄⋊C₄×C₄₁	—	2	1	no	—
182	C₄⋊C₄×C₄₁	—	2	1	no	—
183	C₄⋊C₄×C₄₁	—	2	2	no	—
184	C₄⋊C₄×C₄₁	—	4	4	no	—
185	C₂²⋊C₄×C₄₁	—	2	4	no	—
186	C₂²⋊C₄×C₄₁	—	4	4	no	—
187	C₂²⋊C₄×C₄₁	—	4	2	no	—
188	C₂²⋊C₄×C₄₁	—	4	4	no	—
189	C₂²⋊C₄×C₄₁	—	4	4	no	—
190	C₂²⋊C₄×C₄₁	—	8	2	no	—
191	C₂²⋊C₄×C₄₁	—	8	1	no	—
192	C₄²×C₄₁	—	2	2	no	—
193	C₄²×C₄₁	—	2	2	no	—
194	C₄²×C₄₁	—	4	4	no	—
195	C₂³×C₄₁	—	2	2	no	—
196	C₂³×C₄₁	—	2	2	no	—
197	C₂³×C₄₁	—	2	1	no	—
198	C₂³×C₄₁	—	2	1	no	—
199	C₂³×C₄₁	—	2	2	no	—
200	C₂³×C₄₁	—	2	4	no	—
201	C₂³×C₄₁	—	4	8	no	—
202	C₂³×C₄₁	—	4	2	no	—
203	C₂³×C₄₁	—	4	2	no	—
204	C₂³×C₄₁	—	4	2	no	—
205	C₂³×C₄₁	—	4	2	no	—
206	C₂³×C₄₁	—	4	2	no	—
207	C₂³×C₄₁	—	4	2	no	—
208	C₂³×C₄₁	—	4	1	no	—
209	C₂³×C₄₁	—	4	2	no	—
210	C₂³×C₄₁	—	4	2	no	—
211	C₂³×C₄₁	—	4	1	no	—
212	C₂³×C₄₁	—	4	1	no	—
213	C₂³×C₄₁	—	4	2	no	—
214	C₂³×C₄₁	—	4	2	no	—
215	C₂³×C₄₁	—	4	1	no	—
216	C₂³×C₄₁	—	4	1	no	—
217	C₂³×C₄₁	—	8	4	no	—
218	C₂³×C₄₁	—	8	4	no	—
219	C₂³×C₄₁	—	8	8	no	—
220	C₂³×C₄₁	—	8	8	no	—
221	C₂³×C₄₁	#121	1	2	yes	—
222	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
223	Q₈×C₄₁	—	2	2	no	—
224	Q₈×C₄₁	—	2	4	no	—
225	Q₈×C₄₁	#120	1	4	yes	complemented
226	D₄×C₄₁	—	2	2	no	—
227	D₄×C₄₁	—	2	4	no	—
228	D₄×C₄₁	—	2	2	no	—
229	D₄×C₄₁	—	2	4	no	—
230	D₄×C₄₁	—	4	8	no	—
231	D₄×C₄₁	—	4	8	no	—
232	D₄×C₄₁	—	4	1	no	—
233	D₄×C₄₁	—	4	2	no	—
234	D₄×C₄₁	—	4	1	no	—
235	D₄×C₄₁	—	4	2	no	—
236	D₄×C₄₁	—	4	2	no	—
237	D₄×C₄₁	—	4	2	no	—
238	D₄×C₄₁	—	8	8	no	—
239	D₄×C₄₁	—	8	8	no	—
240	D₄×C₄₁	—	8	4	no	—
241	C₂×C₄×C₄₁	—	2	2	no	—
242	C₂×C₄×C₄₁	—	2	2	no	—
243	C₂×C₄×C₄₁	—	2	4	no	—
244	C₂×C₄×C₄₁	—	2	2	no	—
245	C₂×C₄×C₄₁	—	2	2	no	—
246	C₂×C₄×C₄₁	—	2	2	no	—
247	C₂×C₄×C₄₁	—	2	2	no	—
248	C₂×C₄×C₄₁	—	2	4	no	—
249	C₂×C₄×C₄₁	—	2	2	no	—
250	C₂×C₄×C₄₁	—	2	2	no	—
251	C₂×C₄×C₄₁	—	2	2	no	—
252	C₂×C₄×C₄₁	—	4	8	no	—
253	C₂×C₄×C₄₁	—	4	1	no	—
254	C₂×C₄×C₄₁	—	4	2	no	—
255	C₂×C₄×C₄₁	—	4	2	no	—
256	C₂×C₄×C₄₁	—	4	2	no	—
257	C₂×C₄×C₄₁	—	4	2	no	—
258	C₂×C₄×C₄₁	#121	1	2	yes	—
259	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	4	yes	complemented
260	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
263	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
264	C₈×C₄₁	—	2	4	no	—
265	C₈×C₄₁	—	4	1	no	—
266	C₈×C₄₁	—	4	1	no	—
267	#24370	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
268	C₂²×C₄₁	—	2	2	no	—
269	C₂²×C₄₁	—	2	2	no	—
270	C₂²×C₄₁	—	2	2	no	—
271	C₂²×C₄₁	—	4	2	no	—
272	C₂²×C₄₁	—	4	2	no	—
273	C₂²×C₄₁	—	4	2	no	—
274	C₂²×C₄₁	—	4	4	no	—
275	C₂²×C₄₁	—	4	4	no	—
276	C₂²×C₄₁	—	4	4	no	—
277	C₂²×C₄₁	—	4	2	no	—
278	C₂²×C₄₁	—	4	2	no	—
279	C₂²×C₄₁	—	8	16	no	—
280	C₂²×C₄₁	—	8	2	no	—
281	C₂²×C₄₁	—	8	2	no	—
282	C₂²×C₄₁	—	8	2	no	—
283	C₂²×C₄₁	—	8	2	no	—
284	C₂²×C₄₁	—	8	2	no	—
285	C₂²×C₄₁	—	8	2	no	—
286	C₂²×C₄₁	—	8	1	no	—
287	C₂²×C₄₁	—	8	2	no	—
288	C₂²×C₄₁	—	8	2	no	—
289	C₂²×C₄₁	—	8	1	no	—
290	C₂²×C₄₁	—	8	1	no	—
291	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
292	C₂²×C₄₁	D₄²	1	2	yes	—
293	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
294	C₂²×C₄₁	#576	1	1	yes	characteristic
295	C₂²×C₄₁	#577	1	1	yes	characteristic
296	C₄×C₄₁	—	2	2	no	—
297	C₄×C₄₁	—	2	4	no	—
298	C₄×C₄₁	—	2	4	no	—
299	C₄×C₄₁	—	4	2	no	—
300	C₄×C₄₁	—	8	2	no	—
301	C₄×C₄₁	—	8	1	no	—
302	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
303	C₄×C₄₁	#534	1	1	yes	characteristic
304	C₄×C₄₁	#546	1	2	yes	—
305	C₂²×AGL(1,ℤ/8)	C₂×C₄₁	1	1	yes	characteristic, complemented
306	C₂×#460	C₂×C₄₁	1	2	yes	complemented
307	C₂×#449	C₂×C₄₁	1	1	yes	characteristic, complemented
308	#2433	C₂×C₄₁	1	1	yes	characteristic, complemented
309	#2341	C₂×C₄₁	1	1	yes	characteristic, complemented
310	#2054	C₂×C₄₁	1	2	yes	complemented
311	#2011	C₂×C₄₁	1	2	yes	complemented
312	#1895	C₂×C₄₁	1	1	yes	characteristic, complemented
313	#1880	C₂×C₄₁	1	2	yes	complemented
314	#1851	C₂×C₄₁	1	1	yes	characteristic, complemented
315	#1786	C₂×C₄₁	1	1	yes	characteristic, complemented
316	C₂×C₄₁	—	4	2	no	—
317	C₂×C₄₁	—	8	2	no	—
318	C₂×C₄₁	—	8	4	no	—
319	C₂×C₄₁	—	16	1	no	—
320	C₂×C₄₁	#2410	1	1	yes	characteristic
321	C₂×C₄₁	#3038	1	1	yes	characteristic
322	C₂×C₄₁	#3045	1	1	yes	characteristic
323	C₂×C₄₁	#3265	1	2	yes	—
324	C₂×C₄₁	#3274	1	2	yes	—
325	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
326	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
327	C₂×AGL(1,ℤ/8)	—	2	4	no	—
328	C₂×AGL(1,ℤ/8)	—	2	8	no	—
329	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
330	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
331	C₂²×D₈	C₂²×C₄₁	1	2	yes	—
332	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
333	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
334	C₂×#127	C₂²×C₄₁	1	2	yes	—
335	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
336	C₂×#120	—	2	2	no	—
337	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	complemented
338	#460	—	2	8	no	—
339	#449	—	2	4	no	—
340	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	complemented
341	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic, complemented
342	C₂×#102	C₂²×C₄₁	1	2	yes	—
343	C₂×#102	C₂²×C₄₁	1	2	yes	—
344	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic, complemented
345	C₂×#102	C₂²×C₄₁	1	2	yes	complemented
346	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
347	#392	—	2	1	no	—
348	#392	—	2	1	no	—
349	#390	—	2	2	no	—
350	#390	C₂²×C₄₁	1	2	yes	—
351	#390	C₂²×C₄₁	1	2	yes	complemented
352	#380	—	2	1	no	—
353	#380	C₂²×C₄₁	1	1	yes	characteristic
354	C₄×C₂²⋊C₄	—	2	1	no	—
355	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
356	#340	C₂²×C₄₁	1	2	yes	complemented
357	#336	C₂²×C₄₁	1	2	yes	complemented
358	C₄₁	#24370	1	1	yes	characteristic, direct product factor, Sylow
359	C₂⁵	—	2	1	no	—
360	C₂×#41	—	2	2	no	—
361	C₂×#41	—	2	4	no	—
362	C₂×#41	—	4	2	no	—
363	C₂×#41	D₄×C₄₁	1	4	yes	complemented
364	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
365	C₂²×D₄	—	2	4	no	—
366	C₂²×D₄	—	2	1	no	—
367	C₂²×D₄	—	2	1	no	—
368	C₂²×D₄	—	2	2	no	—
369	C₂²×D₄	—	2	1	no	—
370	C₂²×D₄	—	2	2	no	—
371	C₂²×D₄	—	2	2	no	—
372	C₂²×D₄	—	2	2	no	—
373	C₂²×D₄	—	4	2	no	—
374	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
375	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
376	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
377	C₂³×C₄	—	2	1	no	—
378	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
379	AGL(1,ℤ/8)	—	2	32	no	—
380	C₂×SD₁₆	—	2	4	no	—
381	C₂×SD₁₆	—	2	4	no	—
382	C₂×SD₁₆	—	2	2	no	—
383	C₂×SD₁₆	—	2	4	no	—
384	C₂×SD₁₆	D₄×C₄₁	1	8	yes	complemented
385	C₂×D₈	—	2	4	no	—
386	C₂×D₈	—	2	4	no	—
387	C₂×D₈	—	2	2	no	—
388	C₂×D₈	—	2	4	no	—
389	C₂×D₈	—	4	2	no	—
390	C₂×M₁₆	—	2	2	no	—
391	C₂×M₁₆	—	2	4	no	—
392	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
393	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
394	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
395	#127	—	2	4	no	—
396	#127	—	4	2	no	—
397	#121	—	2	2	no	—
398	#121	—	2	2	no	—
399	#120	—	4	8	no	—
400	C₄×Q₈	—	2	4	no	—
401	C₄×Q₈	—	4	2	no	—
402	C₂×C₄⋊C₄	—	2	2	no	—
403	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
404	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
405	C₂×C₂²⋊C₄	—	2	2	no	—
406	C₂×C₂²⋊C₄	—	2	2	no	—
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₂²⋊C₄	—	2	2	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	—	2	2	no	—
411	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
412	C₂×C₄²	—	2	2	no	—
413	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
414	C₄⋊C₈	—	2	4	no	—
415	#103	—	2	2	no	—
416	#102	—	2	4	no	—
417	#102	—	2	2	no	—
418	#102	—	2	4	no	—
419	#102	—	4	2	no	—
420	C₂²⋊C₈	—	2	2	no	—
421	#95	—	2	1	no	—
422	#95	D₄×C₄₁	1	1	yes	characteristic
423	#95	D₄×C₄₁	1	1	yes	characteristic
424	C₂⁴	—	2	1	no	—
425	C₂⁴	—	2	2	no	—
426	C₂⁴	—	2	1	no	—
427	C₂⁴	—	4	4	no	—
428	C₂⁴	—	4	4	no	—
429	C₂⁴	—	4	2	no	—
430	C₂⁴	—	8	1	no	—
431	C₂⁴	—	8	1	no	—
432	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
433	#41	—	2	8	no	—
434	#41	—	4	4	no	—
435	#41	—	4	8	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	2	no	—
438	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
439	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
440	C₂×D₄	—	2	8	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	4	8	no	—
455	C₂×D₄	—	4	4	no	—
456	C₂×D₄	—	4	4	no	—
457	C₂×D₄	—	4	4	no	—
458	C₂×D₄	—	4	4	no	—
459	C₂×D₄	—	4	4	no	—
460	C₂×D₄	—	4	4	no	—
461	C₂×D₄	—	4	4	no	—
462	C₂×D₄	—	4	2	no	—
463	C₂×D₄	—	4	2	no	—
464	C₂×D₄	—	4	4	no	—
465	C₂×D₄	—	8	2	no	—
466	C₂×D₄	—	8	2	no	—
467	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
468	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	4	4	no	—
476	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
477	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
479	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
480	C₂²×C₄	#41×C₄₁	1	2	yes	—
481	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
482	SD₁₆	—	2	16	no	—
483	SD₁₆	—	4	4	no	—
484	D₈	—	2	16	no	—
485	D₈	—	4	4	no	—
486	M₁₆	—	2	8	no	—
487	C₂×C₈	—	2	2	no	—
488	C₂×C₈	—	2	2	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	2	no	—
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	4	4	no	—
499	C₂²⋊C₄	—	2	4	no	—
500	C₂²⋊C₄	—	4	4	no	—
501	C₂²⋊C₄	—	4	2	no	—
502	C₂²⋊C₄	—	4	4	no	—
503	C₂²⋊C₄	—	4	4	no	—
504	C₂²⋊C₄	—	8	2	no	—
505	C₂²⋊C₄	—	8	1	no	—
506	C₄²	—	2	2	no	—
507	C₄²	—	2	2	no	—
508	C₄²	—	4	4	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	1	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	4	no	—
515	C₂³	—	4	8	no	—
516	C₂³	—	4	2	no	—
517	C₂³	—	4	2	no	—
518	C₂³	—	4	2	no	—
519	C₂³	—	4	2	no	—
520	C₂³	—	4	2	no	—
521	C₂³	—	4	2	no	—
522	C₂³	—	4	1	no	—
523	C₂³	—	4	2	no	—
524	C₂³	—	4	2	no	—
525	C₂³	—	4	1	no	—
526	C₂³	—	4	1	no	—
527	C₂³	—	4	2	no	—
528	C₂³	—	4	2	no	—
529	C₂³	—	4	1	no	—
530	C₂³	—	4	1	no	—
531	C₂³	—	8	4	no	—
532	C₂³	—	8	4	no	—
533	C₂³	—	8	8	no	—
534	C₂³	—	8	8	no	—
535	C₂³	#121×C₄₁	1	2	yes	—
536	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
537	Q₈	—	2	2	no	—
538	Q₈	—	2	4	no	—
539	Q₈	#120×C₄₁	1	4	yes	complemented
540	D₄	—	2	2	no	—
541	D₄	—	2	4	no	—
542	D₄	—	2	2	no	—
543	D₄	—	2	4	no	—
544	D₄	—	4	8	no	—
545	D₄	—	4	8	no	—
546	D₄	—	4	1	no	—
547	D₄	—	4	2	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	2	no	—
550	D₄	—	4	2	no	—
551	D₄	—	4	2	no	—
552	D₄	—	8	8	no	—
553	D₄	—	8	8	no	—
554	D₄	—	8	4	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	4	8	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	#121×C₄₁	1	2	yes	—
573	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	4	yes	complemented
574	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
575	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
576	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
577	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
578	C₈	—	2	4	no	—
579	C₈	—	4	1	no	—
580	C₈	—	4	1	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	2	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	4	2	no	—
589	C₂²	—	4	4	no	—
590	C₂²	—	4	4	no	—
591	C₂²	—	4	4	no	—
592	C₂²	—	8	16	no	—
593	C₂²	—	8	2	no	—
594	C₂²	—	8	2	no	—
595	C₂²	—	8	2	no	—
596	C₂²	—	8	2	no	—
597	C₂²	—	8	2	no	—
598	C₂²	—	8	2	no	—
599	C₂²	—	8	1	no	—
600	C₂²	—	8	1	no	—
601	C₂²	—	8	1	no	—
602	C₂²	—	8	2	no	—
603	C₂²	—	8	2	no	—
604	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
605	C₂²	D₄²×C₄₁	1	2	yes	—
606	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
607	C₂²	C₄₁×#576	1	1	yes	characteristic
608	C₂²	C₄₁×#577	1	1	yes	characteristic
609	C₄	—	2	2	no	—
610	C₄	—	2	4	no	—
611	C₄	—	2	4	no	—
612	C₄	—	4	2	no	—
613	C₄	—	8	1	no	—
614	C₄	—	8	2	no	—
615	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
616	C₄	C₄₁×#534	1	1	yes	characteristic
617	C₄	C₄₁×#546	1	2	yes	—
618	C₂	—	4	2	no	—
619	C₂	—	8	4	no	—
620	C₂	—	8	2	no	—
621	C₂	—	16	1	no	—
622	C₂	C₄₁×#2410	1	1	yes	characteristic
623	C₂	C₄₁×#3038	1	1	yes	characteristic
624	C₂	C₄₁×#3045	1	1	yes	characteristic
625	C₂	C₄₁×#3265	1	2	yes	—
626	C₂	C₄₁×#3274	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄×C₂²⋊C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×AGL(1,ℤ/8)×C₄₁	C₂	semidirect
2. C₂×C₄₁×#460	C₂	semidirect
3. C₂×C₄₁×#449	C₂	semidirect
4. C₄₁×#2433	C₂	semidirect
5. C₄₁×#2341	C₂	semidirect
6. C₄₁×#2054	C₂	semidirect
7. C₄₁×#2011	C₂	semidirect
8. C₄₁×#1895	C₂	semidirect
9. C₄₁×#1880	C₂	semidirect
10. C₄₁×#1851	C₂	semidirect
11. C₄₁×#1786	C₂	semidirect
17. C₂²×SD₁₆×C₄₁	C₂²	semidirect
19. C₂²×D₈×C₄₁	C₂²	semidirect
24. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
27. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
28. C₂×#103×C₄₁	C₂²	semidirect
31. C₂×#102×C₄₁	C₂²	semidirect
32. C₂×#102×C₄₁	C₂²	semidirect
38. C₄₁×#390	C₂²	semidirect
43. C₄₁×#340	C₂²	semidirect
44. C₄₁×#336	C₂²	semidirect
49. C₂×#41×C₄₁	D₄	semidirect
70. C₂×SD₁₆×C₄₁	D₄	semidirect
225. Q₈×C₄₁	#120	semidirect
259. C₂×C₄×C₄₁	AGL(1,ℤ/8)	semidirect
267. #24370	C₄₁	direct (N × H)
305. C₂²×AGL(1,ℤ/8)	C₂×C₄₁	semidirect
306. C₂×#460	C₂×C₄₁	semidirect
307. C₂×#449	C₂×C₄₁	semidirect
308. #2433	C₂×C₄₁	semidirect
309. #2341	C₂×C₄₁	semidirect
310. #2054	C₂×C₄₁	semidirect
311. #2011	C₂×C₄₁	semidirect
312. #1895	C₂×C₄₁	semidirect
313. #1880	C₂×C₄₁	semidirect
314. #1851	C₂×C₄₁	semidirect
315. #1786	C₂×C₄₁	semidirect
330. C₂²×SD₁₆	C₂²×C₄₁	semidirect
332. C₂²×D₈	C₂²×C₄₁	semidirect
337. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
340. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
341. C₂×#103	C₂²×C₄₁	semidirect
344. C₂×#102	C₂²×C₄₁	semidirect
345. C₂×#102	C₂²×C₄₁	semidirect
351. #390	C₂²×C₄₁	semidirect
356. #340	C₂²×C₄₁	semidirect
357. #336	C₂²×C₄₁	semidirect
358. C₄₁	#24370	direct (N × H)
363. C₂×#41	D₄×C₄₁	semidirect
384. C₂×SD₁₆	D₄×C₄₁	semidirect
539. Q₈	#120×C₄₁	semidirect
573. 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
C₂²×AGL(1,ℤ/8)×C₄₁	2
C₂×C₄₁×#460	2
C₂×C₄₁×#449	2
C₄₁×#2433	2
C₄₁×#2341	2
C₄₁×#2054	2
C₄₁×#2011	2
C₄₁×#1895	2
C₄₁×#1880	2
C₄₁×#1851	2
C₄₁×#1786	2
#24370	41

Subgroups — C41×#24370 #23800571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24370 #23800571