Subgroups — C₄₁×#24236 #23800437

Order 10496.

1974 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#459	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#447	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×D₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2537	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2033	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1999	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1957	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1954	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1802	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1786	C₂	1	2	yes	maximal, complemented
12	C₂³×D₄×C₄₁	—	2	1	no	—
13	C₂³×D₄×C₄₁	C₂²	1	2	yes	—
14	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂²×D₈×C₄₁	C₂²	1	2	yes	complemented
16	D₄²×C₄₁	—	2	4	no	—
17	D₄²×C₄₁	—	2	4	no	—
18	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×#121×C₄₁	—	2	1	no	—
20	C₂×#121×C₄₁	—	2	1	no	—
21	C₂×#121×C₄₁	C₂²	1	2	yes	—
22	C₂×#121×C₄₁	C₂²	1	2	yes	complemented
23	C₂×#120×C₄₁	—	2	2	no	—
24	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
27	C₄₁×#459	—	2	4	no	—
28	C₄₁×#447	—	2	8	no	—
29	C₄×D₈×C₄₁	—	2	4	no	—
30	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
32	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×#102×C₄₁	C₂²	1	2	yes	—
34	C₂×#102×C₄₁	C₂²	1	2	yes	complemented
35	C₂×#102×C₄₁	C₂²	1	2	yes	complemented
36	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic, complemented
37	C₂×#102×C₄₁	C₂²	1	2	yes	complemented
38	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	complemented
39	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	complemented
40	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
41	C₄₁×#394	—	2	2	no	—
42	C₄₁×#384	C₂²	1	1	yes	characteristic, complemented
43	C₄₁×#380	—	2	1	no	—
44	C₄₁×#380	C₂²	1	2	yes	complemented
45	C₄₁×#340	C₂²	1	2	yes	complemented
46	C₂⁵×C₄₁	—	2	2	no	—
47	C₂²×D₄×C₄₁	—	2	8	no	—
48	C₂²×D₄×C₄₁	—	2	2	no	—
49	C₂²×D₄×C₄₁	—	2	4	no	—
50	C₂²×D₄×C₄₁	—	2	4	no	—
51	C₂²×D₄×C₄₁	—	2	4	no	—
52	C₂²×D₄×C₄₁	—	2	4	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	—	2	1	no	—
57	C₂²×D₄×C₄₁	—	4	2	no	—
58	C₂²×D₄×C₄₁	—	4	2	no	—
59	C₂²×D₄×C₄₁	—	4	4	no	—
60	C₂²×D₄×C₄₁	—	4	4	no	—
61	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
62	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
63	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₄₁	—	2	1	no	—
66	C₂³×C₄×C₄₁	—	2	1	no	—
67	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
68	C₂×D₈×C₄₁	—	2	2	no	—
69	C₂×D₈×C₄₁	—	2	2	no	—
70	C₂×D₈×C₄₁	—	2	4	no	—
71	C₂×D₈×C₄₁	—	2	4	no	—
72	C₂×D₈×C₄₁	—	4	2	no	—
73	C₂×D₈×C₄₁	D₄	1	4	yes	complemented
74	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
75	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
77	#127×C₄₁	—	2	2	no	—
78	#127×C₄₁	D₄	1	4	yes	complemented
79	#121×C₄₁	—	2	8	no	—
80	#121×C₄₁	—	2	4	no	—
81	#121×C₄₁	—	2	4	no	—
82	#121×C₄₁	—	2	4	no	—
83	#121×C₄₁	—	4	2	no	—
84	#121×C₄₁	—	4	4	no	—
85	#120×C₄₁	—	2	16	no	—
86	C₄×D₄×C₄₁	—	2	2	no	—
87	C₄×D₄×C₄₁	—	2	2	no	—
88	C₄×D₄×C₄₁	—	2	2	no	—
89	C₄×D₄×C₄₁	—	2	2	no	—
90	C₄×D₄×C₄₁	—	2	2	no	—
91	C₄×D₄×C₄₁	D₄	1	4	yes	complemented
92	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
93	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
94	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
100	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
103	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
104	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
105	#107×C₄₁	—	2	2	no	—
106	C₄⋊C₈×C₄₁	—	2	2	no	—
107	#102×C₄₁	—	2	2	no	—
108	#102×C₄₁	—	2	4	no	—
109	#102×C₄₁	—	2	4	no	—
110	#102×C₄₁	—	2	4	no	—
111	#102×C₄₁	—	2	2	no	—
112	#102×C₄₁	—	4	2	no	—
113	C₂²⋊C₈×C₄₁	—	2	4	no	—
114	C₂²⋊C₈×C₄₁	—	4	2	no	—
115	C₄×C₈×C₄₁	—	2	2	no	—
116	#95×C₄₁	—	2	2	no	—
117	C₂⁴×C₄₁	—	2	1	no	—
118	C₂⁴×C₄₁	—	2	8	no	—
119	C₂⁴×C₄₁	—	2	1	no	—
120	C₂⁴×C₄₁	—	2	2	no	—
121	C₂⁴×C₄₁	—	4	4	no	—
122	C₂⁴×C₄₁	—	4	4	no	—
123	C₂⁴×C₄₁	—	4	4	no	—
124	C₂⁴×C₄₁	—	4	4	no	—
125	C₂⁴×C₄₁	—	8	2	no	—
126	C₂⁴×C₄₁	—	8	2	no	—
127	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
128	C₂×D₄×C₄₁	—	2	8	no	—
129	C₂×D₄×C₄₁	—	2	8	no	—
130	C₂×D₄×C₄₁	—	2	2	no	—
131	C₂×D₄×C₄₁	—	2	4	no	—
132	C₂×D₄×C₄₁	—	2	4	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	1	no	—
138	C₂×D₄×C₄₁	—	2	2	no	—
139	C₂×D₄×C₄₁	—	2	1	no	—
140	C₂×D₄×C₄₁	—	2	2	no	—
141	C₂×D₄×C₄₁	—	2	1	no	—
142	C₂×D₄×C₄₁	—	2	1	no	—
143	C₂×D₄×C₄₁	—	2	2	no	—
144	C₂×D₄×C₄₁	—	2	1	no	—
145	C₂×D₄×C₄₁	—	2	2	no	—
146	C₂×D₄×C₄₁	—	2	1	no	—
147	C₂×D₄×C₄₁	—	4	4	no	—
148	C₂×D₄×C₄₁	—	4	4	no	—
149	C₂×D₄×C₄₁	—	4	8	no	—
150	C₂×D₄×C₄₁	—	4	8	no	—
151	C₂×D₄×C₄₁	—	4	8	no	—
152	C₂×D₄×C₄₁	—	4	32	no	—
153	C₂×D₄×C₄₁	—	4	4	no	—
154	C₂×D₄×C₄₁	—	4	4	no	—
155	C₂×D₄×C₄₁	—	4	8	no	—
156	C₂×D₄×C₄₁	—	4	4	no	—
157	C₂×D₄×C₄₁	—	4	4	no	—
158	C₂×D₄×C₄₁	—	4	2	no	—
159	C₂×D₄×C₄₁	—	4	2	no	—
160	C₂×D₄×C₄₁	—	8	1	no	—
161	C₂×D₄×C₄₁	—	8	1	no	—
162	C₂×D₄×C₄₁	—	8	2	no	—
163	C₂×D₄×C₄₁	D₈	1	4	yes	complemented
164	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
165	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
166	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
167	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	complemented
168	C₂×D₄×C₄₁	#41	1	2	yes	—
169	C₂²×C₄×C₄₁	—	2	1	no	—
170	C₂²×C₄×C₄₁	—	2	4	no	—
171	C₂²×C₄×C₄₁	—	2	2	no	—
172	C₂²×C₄×C₄₁	—	2	2	no	—
173	C₂²×C₄×C₄₁	—	2	2	no	—
174	C₂²×C₄×C₄₁	—	2	2	no	—
175	C₂²×C₄×C₄₁	—	2	2	no	—
176	C₂²×C₄×C₄₁	—	2	2	no	—
177	C₂²×C₄×C₄₁	—	2	1	no	—
178	C₂²×C₄×C₄₁	—	2	2	no	—
179	C₂²×C₄×C₄₁	—	4	2	no	—
180	C₂²×C₄×C₄₁	—	4	2	no	—
181	C₂²×C₄×C₄₁	—	4	2	no	—
182	C₂²×C₄×C₄₁	—	4	2	no	—
183	C₂²×C₄×C₄₁	—	4	2	no	—
184	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
185	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
188	D₈×C₄₁	—	2	8	no	—
189	D₈×C₄₁	—	4	8	no	—
190	C₂×C₈×C₄₁	—	2	1	no	—
191	C₂×C₈×C₄₁	—	2	1	no	—
192	C₂×C₈×C₄₁	—	2	1	no	—
193	C₂×C₈×C₄₁	—	2	2	no	—
194	C₂×C₈×C₄₁	—	2	2	no	—
195	C₂×C₈×C₄₁	—	2	1	no	—
196	C₂×C₈×C₄₁	—	2	2	no	—
197	C₂×C₈×C₄₁	—	2	1	no	—
198	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	complemented
199	C₄⋊C₄×C₄₁	—	2	2	no	—
200	C₄⋊C₄×C₄₁	—	2	1	no	—
201	C₄⋊C₄×C₄₁	—	2	1	no	—
202	C₄⋊C₄×C₄₁	—	2	2	no	—
203	C₄⋊C₄×C₄₁	—	2	1	no	—
204	C₄⋊C₄×C₄₁	—	2	2	no	—
205	C₄⋊C₄×C₄₁	—	4	2	no	—
206	C₄⋊C₄×C₄₁	—	8	1	no	—
207	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
208	C₂²⋊C₄×C₄₁	—	2	8	no	—
209	C₂²⋊C₄×C₄₁	—	2	4	no	—
210	C₂²⋊C₄×C₄₁	—	2	4	no	—
211	C₂²⋊C₄×C₄₁	—	4	4	no	—
212	C₂²⋊C₄×C₄₁	—	4	4	no	—
213	C₂²⋊C₄×C₄₁	—	4	2	no	—
214	C₄²×C₄₁	C₂×D₄	1	2	yes	—
215	C₄²×C₄₁	C₂×D₄	1	2	yes	—
216	C₂³×C₄₁	—	2	2	no	—
217	C₂³×C₄₁	—	2	2	no	—
218	C₂³×C₄₁	—	2	2	no	—
219	C₂³×C₄₁	—	2	2	no	—
220	C₂³×C₄₁	—	2	2	no	—
221	C₂³×C₄₁	—	2	2	no	—
222	C₂³×C₄₁	—	2	2	no	—
223	C₂³×C₄₁	—	2	2	no	—
224	C₂³×C₄₁	—	2	2	no	—
225	C₂³×C₄₁	—	2	4	no	—
226	C₂³×C₄₁	—	2	2	no	—
227	C₂³×C₄₁	—	4	16	no	—
228	C₂³×C₄₁	—	4	16	no	—
229	C₂³×C₄₁	—	4	1	no	—
230	C₂³×C₄₁	—	4	1	no	—
231	C₂³×C₄₁	—	4	1	no	—
232	C₂³×C₄₁	—	4	1	no	—
233	C₂³×C₄₁	—	4	1	no	—
234	C₂³×C₄₁	—	4	2	no	—
235	C₂³×C₄₁	—	4	2	no	—
236	C₂³×C₄₁	—	4	1	no	—
237	C₂³×C₄₁	—	4	1	no	—
238	C₂³×C₄₁	—	4	2	no	—
239	C₂³×C₄₁	—	4	1	no	—
240	C₂³×C₄₁	—	4	2	no	—
241	C₂³×C₄₁	—	4	1	no	—
242	C₂³×C₄₁	—	4	2	no	—
243	C₂³×C₄₁	—	4	2	no	—
244	C₂³×C₄₁	—	4	1	no	—
245	C₂³×C₄₁	—	8	8	no	—
246	C₂³×C₄₁	—	8	8	no	—
247	C₂³×C₄₁	—	8	8	no	—
248	C₂³×C₄₁	—	8	8	no	—
249	C₂³×C₄₁	—	8	8	no	—
250	C₂³×C₄₁	C₂×D₈	1	4	yes	—
251	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
252	D₄×C₄₁	—	2	2	no	—
253	D₄×C₄₁	—	2	2	no	—
254	D₄×C₄₁	—	2	2	no	—
255	D₄×C₄₁	—	2	2	no	—
256	D₄×C₄₁	—	2	4	no	—
257	D₄×C₄₁	—	2	2	no	—
258	D₄×C₄₁	—	2	4	no	—
259	D₄×C₄₁	—	2	8	no	—
260	D₄×C₄₁	—	4	16	no	—
261	D₄×C₄₁	—	4	16	no	—
262	D₄×C₄₁	—	4	2	no	—
263	D₄×C₄₁	—	4	1	no	—
264	D₄×C₄₁	—	4	2	no	—
265	D₄×C₄₁	—	4	1	no	—
266	D₄×C₄₁	—	4	8	no	—
267	D₄×C₄₁	—	8	4	no	—
268	D₄×C₄₁	—	8	8	no	—
269	D₄×C₄₁	#121	1	4	yes	complemented
270	C₂×C₄×C₄₁	—	2	1	no	—
271	C₂×C₄×C₄₁	—	2	1	no	—
272	C₂×C₄×C₄₁	—	2	2	no	—
273	C₂×C₄×C₄₁	—	2	2	no	—
274	C₂×C₄×C₄₁	—	2	2	no	—
275	C₂×C₄×C₄₁	—	2	2	no	—
276	C₂×C₄×C₄₁	—	4	1	no	—
277	C₂×C₄×C₄₁	—	4	1	no	—
278	C₂×C₄×C₄₁	—	4	2	no	—
279	C₂×C₄×C₄₁	—	4	2	no	—
280	C₂×C₄×C₄₁	—	4	2	no	—
281	C₂×C₄×C₄₁	—	4	2	no	—
282	C₂×C₄×C₄₁	—	4	8	no	—
283	C₂×C₄×C₄₁	—	4	1	no	—
284	C₂×C₄×C₄₁	—	4	2	no	—
285	C₂×C₄×C₄₁	—	4	1	no	—
286	C₂×C₄×C₄₁	—	4	2	no	—
287	C₂×C₄×C₄₁	—	4	1	no	—
288	C₂×C₄×C₄₁	—	4	2	no	—
289	C₂×C₄×C₄₁	—	8	4	no	—
290	C₂×C₄×C₄₁	#120	1	2	yes	—
291	C₂×C₄×C₄₁	#120	1	2	yes	—
292	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
293	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
294	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
299	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
300	C₈×C₄₁	—	2	2	no	—
301	C₈×C₄₁	—	4	1	no	—
302	C₈×C₄₁	—	4	2	no	—
303	#24236	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
304	C₂²×C₄₁	—	2	4	no	—
305	C₂²×C₄₁	—	2	4	no	—
306	C₂²×C₄₁	—	2	4	no	—
307	C₂²×C₄₁	—	2	4	no	—
308	C₂²×C₄₁	—	4	2	no	—
309	C₂²×C₄₁	—	4	2	no	—
310	C₂²×C₄₁	—	4	2	no	—
311	C₂²×C₄₁	—	4	2	no	—
312	C₂²×C₄₁	—	4	2	no	—
313	C₂²×C₄₁	—	4	2	no	—
314	C₂²×C₄₁	—	4	2	no	—
315	C₂²×C₄₁	—	4	2	no	—
316	C₂²×C₄₁	—	4	2	no	—
317	C₂²×C₄₁	—	4	2	no	—
318	C₂²×C₄₁	—	4	4	no	—
319	C₂²×C₄₁	—	4	2	no	—
320	C₂²×C₄₁	—	4	4	no	—
321	C₂²×C₄₁	—	4	4	no	—
322	C₂²×C₄₁	—	4	2	no	—
323	C₂²×C₄₁	—	4	2	no	—
324	C₂²×C₄₁	—	8	32	no	—
325	C₂²×C₄₁	—	8	1	no	—
326	C₂²×C₄₁	—	8	1	no	—
327	C₂²×C₄₁	—	8	2	no	—
328	C₂²×C₄₁	—	8	2	no	—
329	C₂²×C₄₁	—	8	1	no	—
330	C₂²×C₄₁	—	8	2	no	—
331	C₂²×C₄₁	—	8	1	no	—
332	C₂²×C₄₁	—	8	2	no	—
333	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
334	C₂²×C₄₁	D₄²	1	1	yes	characteristic
335	C₂²×C₄₁	#546	1	1	yes	characteristic
336	C₂²×C₄₁	C₂²×D₈	1	1	yes	characteristic
337	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
338	C₂²×C₄₁	#576	1	1	yes	characteristic
339	C₂²×C₄₁	#577	1	1	yes	characteristic
340	C₄×C₄₁	—	2	2	no	—
341	C₄×C₄₁	—	4	2	no	—
342	C₄×C₄₁	—	4	2	no	—
343	C₄×C₄₁	—	8	1	no	—
344	C₄×C₄₁	—	8	2	no	—
345	C₄×C₄₁	#447	1	4	yes	complemented
346	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
347	C₄×C₄₁	#535	1	1	yes	characteristic
348	C₄×C₄₁	D₄²	1	1	yes	characteristic
349	C₄×C₄₁	#546	1	1	yes	characteristic
350	C₂×D₄²	C₂×C₄₁	1	1	yes	characteristic, complemented
351	C₂×#459	C₂×C₄₁	1	1	yes	characteristic, complemented
352	C₂×#447	C₂×C₄₁	1	2	yes	complemented
353	C₂×C₄×D₈	C₂×C₄₁	1	1	yes	characteristic, complemented
354	#2537	C₂×C₄₁	1	1	yes	characteristic, complemented
355	#2033	C₂×C₄₁	1	2	yes	complemented
356	#1999	C₂×C₄₁	1	2	yes	complemented
357	#1957	C₂×C₄₁	1	1	yes	characteristic, complemented
358	#1954	C₂×C₄₁	1	1	yes	characteristic, complemented
359	#1802	C₂×C₄₁	1	1	yes	characteristic, complemented
360	#1786	C₂×C₄₁	1	2	yes	complemented
361	C₂×C₄₁	—	4	4	no	—
362	C₂×C₄₁	—	4	4	no	—
363	C₂×C₄₁	—	8	2	no	—
364	C₂×C₄₁	—	8	4	no	—
365	C₂×C₄₁	#2408	1	1	yes	characteristic
366	C₂×C₄₁	C₂×#447	1	1	yes	characteristic
367	C₂×C₄₁	#3012	1	1	yes	characteristic
368	C₂×C₄₁	#3272	1	1	yes	characteristic
369	C₂×C₄₁	D₄×D₈	1	1	yes	characteristic
370	C₂×C₄₁	#3294	1	1	yes	characteristic
371	C₂×C₄₁	#3325	1	1	yes	characteristic
372	C₂³×D₄	—	2	1	no	—
373	C₂³×D₄	C₂²×C₄₁	1	2	yes	—
374	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
375	C₂²×D₈	C₂²×C₄₁	1	2	yes	complemented
376	D₄²	—	2	4	no	—
377	D₄²	—	2	4	no	—
378	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
379	C₂×#121	—	2	1	no	—
380	C₂×#121	—	2	1	no	—
381	C₂×#121	C₂²×C₄₁	1	2	yes	—
382	C₂×#121	C₂²×C₄₁	1	2	yes	complemented
383	C₂×#120	—	2	2	no	—
384	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
385	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
386	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
387	#459	—	2	4	no	—
388	#447	—	2	8	no	—
389	C₄×D₈	—	2	4	no	—
390	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic, complemented
391	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
392	C₂×#102	C₂²×C₄₁	1	2	yes	—
393	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
394	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic, complemented
395	C₂×#102	C₂²×C₄₁	1	2	yes	complemented
396	C₂×#102	C₂²×C₄₁	1	2	yes	complemented
397	C₂×#102	C₂²×C₄₁	1	2	yes	complemented
398	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	complemented
399	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	complemented
400	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
401	#394	—	2	2	no	—
402	#384	C₂²×C₄₁	1	1	yes	characteristic, complemented
403	#380	—	2	1	no	—
404	#380	C₂²×C₄₁	1	2	yes	complemented
405	#340	C₂²×C₄₁	1	2	yes	complemented
406	C₄₁	#24236	1	1	yes	characteristic, direct product factor, Sylow
407	C₂⁵	—	2	2	no	—
408	C₂²×D₄	—	2	8	no	—
409	C₂²×D₄	—	2	2	no	—
410	C₂²×D₄	—	2	4	no	—
411	C₂²×D₄	—	2	4	no	—
412	C₂²×D₄	—	2	4	no	—
413	C₂²×D₄	—	2	4	no	—
414	C₂²×D₄	—	2	2	no	—
415	C₂²×D₄	—	2	2	no	—
416	C₂²×D₄	—	2	1	no	—
417	C₂²×D₄	—	2	1	no	—
418	C₂²×D₄	—	4	2	no	—
419	C₂²×D₄	—	4	2	no	—
420	C₂²×D₄	—	4	4	no	—
421	C₂²×D₄	—	4	4	no	—
422	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
423	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
424	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
425	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
426	C₂³×C₄	—	2	1	no	—
427	C₂³×C₄	—	2	1	no	—
428	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
429	C₂×D₈	—	2	2	no	—
430	C₂×D₈	—	2	2	no	—
431	C₂×D₈	—	2	4	no	—
432	C₂×D₈	—	2	4	no	—
433	C₂×D₈	—	4	2	no	—
434	C₂×D₈	D₄×C₄₁	1	4	yes	complemented
435	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
436	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
437	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
438	#127	—	2	2	no	—
439	#127	D₄×C₄₁	1	4	yes	complemented
440	#121	—	2	8	no	—
441	#121	—	2	4	no	—
442	#121	—	2	4	no	—
443	#121	—	2	4	no	—
444	#121	—	4	2	no	—
445	#121	—	4	4	no	—
446	#120	—	2	16	no	—
447	C₄×D₄	—	2	2	no	—
448	C₄×D₄	—	2	2	no	—
449	C₄×D₄	—	2	2	no	—
450	C₄×D₄	—	2	2	no	—
451	C₄×D₄	—	2	2	no	—
452	C₄×D₄	D₄×C₄₁	1	4	yes	complemented
453	C₂×C₄⋊C₄	—	2	1	no	—
454	C₂×C₄⋊C₄	—	2	1	no	—
455	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
459	C₂×C₂²⋊C₄	—	2	1	no	—
460	C₂×C₂²⋊C₄	—	2	2	no	—
461	C₂×C₂²⋊C₄	—	2	2	no	—
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₂²⋊C₄	—	2	2	no	—
464	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
465	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
466	#107	—	2	2	no	—
467	C₄⋊C₈	—	2	2	no	—
468	#102	—	2	2	no	—
469	#102	—	2	4	no	—
470	#102	—	2	4	no	—
471	#102	—	2	4	no	—
472	#102	—	2	2	no	—
473	#102	—	4	2	no	—
474	C₂²⋊C₈	—	2	4	no	—
475	C₂²⋊C₈	—	4	2	no	—
476	C₄×C₈	—	2	2	no	—
477	#95	—	2	2	no	—
478	C₂⁴	—	2	1	no	—
479	C₂⁴	—	2	8	no	—
480	C₂⁴	—	2	1	no	—
481	C₂⁴	—	2	2	no	—
482	C₂⁴	—	4	4	no	—
483	C₂⁴	—	4	4	no	—
484	C₂⁴	—	4	4	no	—
485	C₂⁴	—	4	4	no	—
486	C₂⁴	—	8	2	no	—
487	C₂⁴	—	8	2	no	—
488	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
489	C₂×D₄	—	2	8	no	—
490	C₂×D₄	—	2	8	no	—
491	C₂×D₄	—	2	2	no	—
492	C₂×D₄	—	2	4	no	—
493	C₂×D₄	—	2	4	no	—
494	C₂×D₄	—	2	2	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	2	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	2	2	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	2	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	2	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	4	4	no	—
509	C₂×D₄	—	4	4	no	—
510	C₂×D₄	—	4	8	no	—
511	C₂×D₄	—	4	8	no	—
512	C₂×D₄	—	4	8	no	—
513	C₂×D₄	—	4	32	no	—
514	C₂×D₄	—	4	4	no	—
515	C₂×D₄	—	4	4	no	—
516	C₂×D₄	—	4	8	no	—
517	C₂×D₄	—	4	4	no	—
518	C₂×D₄	—	4	4	no	—
519	C₂×D₄	—	4	2	no	—
520	C₂×D₄	—	4	2	no	—
521	C₂×D₄	—	8	1	no	—
522	C₂×D₄	—	8	1	no	—
523	C₂×D₄	—	8	2	no	—
524	C₂×D₄	D₈×C₄₁	1	4	yes	complemented
525	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
526	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
527	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
528	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	complemented
529	C₂×D₄	#41×C₄₁	1	2	yes	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	—	2	2	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	2	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	4	2	no	—
541	C₂²×C₄	—	4	2	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	—	4	2	no	—
544	C₂²×C₄	—	4	2	no	—
545	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
546	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
547	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
548	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
549	D₈	—	2	8	no	—
550	D₈	—	4	8	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	2	no	—
555	C₂×C₈	—	2	2	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	2	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	complemented
560	C₄⋊C₄	—	2	2	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	4	2	no	—
567	C₄⋊C₄	—	8	1	no	—
568	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
569	C₂²⋊C₄	—	2	8	no	—
570	C₂²⋊C₄	—	2	4	no	—
571	C₂²⋊C₄	—	2	4	no	—
572	C₂²⋊C₄	—	4	4	no	—
573	C₂²⋊C₄	—	4	4	no	—
574	C₂²⋊C₄	—	4	2	no	—
575	C₄²	C₂×D₄×C₄₁	1	2	yes	—
576	C₄²	C₂×D₄×C₄₁	1	2	yes	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	2	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	2	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	4	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	4	16	no	—
589	C₂³	—	4	16	no	—
590	C₂³	—	4	1	no	—
591	C₂³	—	4	1	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	2	no	—
596	C₂³	—	4	2	no	—
597	C₂³	—	4	1	no	—
598	C₂³	—	4	1	no	—
599	C₂³	—	4	2	no	—
600	C₂³	—	4	1	no	—
601	C₂³	—	4	2	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	4	2	no	—
604	C₂³	—	4	2	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	8	8	no	—
607	C₂³	—	8	8	no	—
608	C₂³	—	8	8	no	—
609	C₂³	—	8	8	no	—
610	C₂³	—	8	8	no	—
611	C₂³	C₂×D₈×C₄₁	1	4	yes	—
612	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
613	D₄	—	2	2	no	—
614	D₄	—	2	2	no	—
615	D₄	—	2	2	no	—
616	D₄	—	2	2	no	—
617	D₄	—	2	4	no	—
618	D₄	—	2	2	no	—
619	D₄	—	2	4	no	—
620	D₄	—	2	8	no	—
621	D₄	—	4	16	no	—
622	D₄	—	4	16	no	—
623	D₄	—	4	2	no	—
624	D₄	—	4	2	no	—
625	D₄	—	4	1	no	—
626	D₄	—	4	1	no	—
627	D₄	—	4	8	no	—
628	D₄	—	8	4	no	—
629	D₄	—	8	8	no	—
630	D₄	#121×C₄₁	1	4	yes	complemented
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	2	no	—
640	C₂×C₄	—	4	2	no	—
641	C₂×C₄	—	4	2	no	—
642	C₂×C₄	—	4	2	no	—
643	C₂×C₄	—	4	8	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	2	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	2	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	2	no	—
650	C₂×C₄	—	8	4	no	—
651	C₂×C₄	#120×C₄₁	1	2	yes	—
652	C₂×C₄	#120×C₄₁	1	2	yes	—
653	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
654	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
655	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
656	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
657	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
658	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
659	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
660	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
661	C₈	—	2	2	no	—
662	C₈	—	4	1	no	—
663	C₈	—	4	2	no	—
664	C₂²	—	2	4	no	—
665	C₂²	—	2	4	no	—
666	C₂²	—	2	4	no	—
667	C₂²	—	2	4	no	—
668	C₂²	—	4	2	no	—
669	C₂²	—	4	2	no	—
670	C₂²	—	4	2	no	—
671	C₂²	—	4	2	no	—
672	C₂²	—	4	2	no	—
673	C₂²	—	4	2	no	—
674	C₂²	—	4	2	no	—
675	C₂²	—	4	2	no	—
676	C₂²	—	4	2	no	—
677	C₂²	—	4	2	no	—
678	C₂²	—	4	4	no	—
679	C₂²	—	4	2	no	—
680	C₂²	—	4	4	no	—
681	C₂²	—	4	4	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	4	2	no	—
684	C₂²	—	8	32	no	—
685	C₂²	—	8	2	no	—
686	C₂²	—	8	1	no	—
687	C₂²	—	8	2	no	—
688	C₂²	—	8	1	no	—
689	C₂²	—	8	1	no	—
690	C₂²	—	8	1	no	—
691	C₂²	—	8	2	no	—
692	C₂²	—	8	2	no	—
693	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
694	C₂²	D₄²×C₄₁	1	1	yes	characteristic
695	C₂²	C₄₁×#546	1	1	yes	characteristic
696	C₂²	C₂²×D₈×C₄₁	1	1	yes	characteristic
697	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
698	C₂²	C₄₁×#576	1	1	yes	characteristic
699	C₂²	C₄₁×#577	1	1	yes	characteristic
700	C₄	—	2	2	no	—
701	C₄	—	4	2	no	—
702	C₄	—	4	2	no	—
703	C₄	—	8	1	no	—
704	C₄	—	8	2	no	—
705	C₄	C₄₁×#447	1	4	yes	complemented
706	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
707	C₄	C₄₁×#535	1	1	yes	characteristic
708	C₄	D₄²×C₄₁	1	1	yes	characteristic
709	C₄	C₄₁×#546	1	1	yes	characteristic
710	C₂	—	4	4	no	—
711	C₂	—	4	4	no	—
712	C₂	—	8	4	no	—
713	C₂	—	8	2	no	—
714	C₂	C₄₁×#2408	1	1	yes	characteristic
715	C₂	C₂×C₄₁×#447	1	1	yes	characteristic
716	C₂	C₄₁×#3012	1	1	yes	characteristic
717	C₂	C₄₁×#3272	1	1	yes	characteristic
718	C₂	D₄×D₈×C₄₁	1	1	yes	characteristic
719	C₂	C₄₁×#3294	1	1	yes	characteristic
720	C₂	C₄₁×#3325	1	1	yes	characteristic

	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 ◁ C₂×C₄×D₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×D₄²×C₄₁	C₂	semidirect
2. C₂×C₄₁×#459	C₂	semidirect
3. C₂×C₄₁×#447	C₂	semidirect
4. C₂×C₄×D₈×C₄₁	C₂	semidirect
5. C₄₁×#2537	C₂	semidirect
6. C₄₁×#2033	C₂	semidirect
7. C₄₁×#1999	C₂	semidirect
8. C₄₁×#1957	C₂	semidirect
9. C₄₁×#1954	C₂	semidirect
10. C₄₁×#1802	C₂	semidirect
11. C₄₁×#1786	C₂	semidirect
15. C₂²×D₈×C₄₁	C₂²	semidirect
22. C₂×#121×C₄₁	C₂²	semidirect
26. C₂×C₄×D₄×C₄₁	C₂²	semidirect
30. C₂×#107×C₄₁	C₂²	semidirect
31. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
34. C₂×#102×C₄₁	C₂²	semidirect
35. C₂×#102×C₄₁	C₂²	semidirect
36. C₂×#102×C₄₁	C₂²	semidirect
37. C₂×#102×C₄₁	C₂²	semidirect
38. C₂×C₂²⋊C₈×C₄₁	C₂²	semidirect
39. C₂×C₂²⋊C₈×C₄₁	C₂²	semidirect
40. C₂×C₄×C₈×C₄₁	C₂²	semidirect
42. C₄₁×#384	C₂²	semidirect
44. C₄₁×#380	C₂²	semidirect
45. C₄₁×#340	C₂²	semidirect
73. C₂×D₈×C₄₁	D₄	semidirect
78. #127×C₄₁	D₄	semidirect
91. C₄×D₄×C₄₁	D₄	semidirect
163. C₂×D₄×C₄₁	D₈	semidirect
167. C₂×D₄×C₄₁	C₂×D₄	semidirect
198. C₂×C₈×C₄₁	C₂×D₄	semidirect
269. D₄×C₄₁	#121	semidirect
303. #24236	C₄₁	direct (N × H)
345. C₄×C₄₁	#447	semidirect
350. C₂×D₄²	C₂×C₄₁	semidirect
351. C₂×#459	C₂×C₄₁	semidirect
352. C₂×#447	C₂×C₄₁	semidirect
353. C₂×C₄×D₈	C₂×C₄₁	semidirect
354. #2537	C₂×C₄₁	semidirect
355. #2033	C₂×C₄₁	semidirect
356. #1999	C₂×C₄₁	semidirect
357. #1957	C₂×C₄₁	semidirect
358. #1954	C₂×C₄₁	semidirect
359. #1802	C₂×C₄₁	semidirect
360. #1786	C₂×C₄₁	semidirect
375. C₂²×D₈	C₂²×C₄₁	semidirect
382. C₂×#121	C₂²×C₄₁	semidirect
386. C₂×C₄×D₄	C₂²×C₄₁	semidirect
390. C₂×#107	C₂²×C₄₁	semidirect
391. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
394. C₂×#102	C₂²×C₄₁	semidirect
395. C₂×#102	C₂²×C₄₁	semidirect
396. C₂×#102	C₂²×C₄₁	semidirect
397. C₂×#102	C₂²×C₄₁	semidirect
398. C₂×C₂²⋊C₈	C₂²×C₄₁	semidirect
399. C₂×C₂²⋊C₈	C₂²×C₄₁	semidirect
400. C₂×C₄×C₈	C₂²×C₄₁	semidirect
402. #384	C₂²×C₄₁	semidirect
404. #380	C₂²×C₄₁	semidirect
405. #340	C₂²×C₄₁	semidirect
406. C₄₁	#24236	direct (N × H)
434. C₂×D₈	D₄×C₄₁	semidirect
439. #127	D₄×C₄₁	semidirect
452. C₄×D₄	D₄×C₄₁	semidirect
524. C₂×D₄	D₈×C₄₁	semidirect
528. C₂×D₄	C₂×D₄×C₄₁	semidirect
559. C₂×C₈	C₂×D₄×C₄₁	semidirect
630. D₄	#121×C₄₁	semidirect
705. C₄	C₄₁×#447	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄²×C₄₁	2
C₂×C₄₁×#459	2
C₂×C₄₁×#447	2
C₂×C₄×D₈×C₄₁	2
C₄₁×#2537	2
C₄₁×#2033	2
C₄₁×#1999	2
C₄₁×#1957	2
C₄₁×#1954	2
C₄₁×#1802	2
C₄₁×#1786	2
#24236	41

Subgroups — C41×#24236 #23800437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24236 #23800437