Subgroups — C₄₁×#20917 #23797118

Order 10496.

1698 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#575	C₂	1	1	yes	maximal, characteristic
2	C₂²×#131×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#421	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#421	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₁×#408	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1876	C₂	1	8	yes	maximal, complemented
7	C₄₁×#1738	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1729	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
10	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
11	C₄₁×#575	—	2	4	no	—
12	C₄₁×#575	—	2	4	no	—
13	C₂×#137×C₄₁	C₄	1	2	yes	complemented
14	C₂×#137×C₄₁	C₄	1	2	yes	complemented
15	C₂×AGL(1,ℤ/8)×C₄₁	C₄	1	2	yes	complemented
16	C₂×AGL(1,ℤ/8)×C₄₁	C₄	1	2	yes	complemented
17	C₂×#135×C₄₁	C₂²	1	4	yes	—
18	C₂×#131×C₄₁	—	2	4	no	—
19	C₂×#131×C₄₁	—	2	4	no	—
20	C₂×#131×C₄₁	—	2	2	no	—
21	C₂×#131×C₄₁	C₂²	1	4	yes	complemented
22	C₂²×M₁₆×C₄₁	—	2	1	no	—
23	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
24	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
25	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
26	C₂³×C₈×C₄₁	—	2	1	no	—
27	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
29	C₄₁×#421	—	2	4	no	—
30	C₄₁×#421	—	2	4	no	—
31	C₂×#104×C₄₁	C₂²	1	4	yes	complemented
32	C₂×#104×C₄₁	C₂²	1	4	yes	complemented
33	C₄₁×#408	—	2	1	no	—
34	C₄₁×#408	—	2	1	no	—
35	C₄₁×#408	C₂²	1	4	yes	complemented
36	C₂×C₂²⋊C₈×C₄₁	—	2	2	no	—
37	C₄₁×#341	C₂²	1	4	yes	complemented
38	C₄₁×#336	C₂²	1	4	yes	complemented
39	C₂×#41×C₄₁	—	2	2	no	—
40	C₂×#41×C₄₁	—	2	1	no	—
41	C₂×#41×C₄₁	—	2	1	no	—
42	C₂×#41×C₄₁	—	2	1	no	—
43	C₂×#41×C₄₁	—	2	2	no	—
44	C₂×#41×C₄₁	—	2	1	no	—
45	C₂×#41×C₄₁	—	2	2	no	—
46	C₂×#41×C₄₁	—	2	2	no	—
47	C₂×#41×C₄₁	—	2	2	no	—
48	C₂×#41×C₄₁	—	2	2	no	—
49	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
50	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
51	C₂×#41×C₄₁	D₄	1	4	yes	—
52	C₂×#41×C₄₁	D₄	1	4	yes	—
53	C₂×#41×C₄₁	C₂³	1	2	yes	—
54	C₂×#41×C₄₁	C₂³	1	2	yes	—
55	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
56	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
57	C₂²×D₄×C₄₁	—	2	1	no	—
58	C₂²×D₄×C₄₁	—	2	1	no	—
59	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
60	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₄₁	—	2	1	no	—
62	C₂³×C₄×C₄₁	—	2	1	no	—
63	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
64	#137×C₄₁	—	2	8	no	—
65	#137×C₄₁	—	2	8	no	—
66	AGL(1,ℤ/8)×C₄₁	—	2	8	no	—
67	AGL(1,ℤ/8)×C₄₁	—	2	8	no	—
68	#135×C₄₁	—	2	8	no	—
69	#135×C₄₁	—	2	8	no	—
70	C₂×Q₁₆×C₄₁	C₂×C₄	1	4	yes	—
71	C₂×SD₁₆×C₄₁	C₂×C₄	1	4	yes	—
72	C₂×SD₁₆×C₄₁	C₂×C₄	1	4	yes	—
73	C₂×D₈×C₄₁	C₂×C₄	1	4	yes	—
74	#131×C₄₁	—	2	16	no	—
75	#131×C₄₁	—	2	8	no	—
76	#131×C₄₁	—	2	8	no	—
77	C₂×M₁₆×C₄₁	—	2	8	no	—
78	C₂×M₁₆×C₄₁	—	2	2	no	—
79	C₂×M₁₆×C₄₁	—	2	1	no	—
80	C₂×M₁₆×C₄₁	—	2	2	no	—
81	C₂×M₁₆×C₄₁	—	2	2	no	—
82	C₂×M₁₆×C₄₁	—	2	1	no	—
83	C₂×M₁₆×C₄₁	—	2	4	no	—
84	C₂×M₁₆×C₄₁	—	2	2	no	—
85	C₂×M₁₆×C₄₁	—	2	2	no	—
86	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	—
87	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	—
88	C₂×M₁₆×C₄₁	D₄	1	4	yes	—
89	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
90	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
91	C₂²×C₈×C₄₁	—	2	8	no	—
92	C₂²×C₈×C₄₁	—	2	1	no	—
93	C₂²×C₈×C₄₁	—	2	2	no	—
94	C₂²×C₈×C₄₁	—	2	2	no	—
95	C₂²×C₈×C₄₁	—	2	4	no	—
96	C₂²×C₈×C₄₁	—	2	1	no	—
97	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
98	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
99	C₂²×C₈×C₄₁	D₄	1	2	yes	—
100	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
101	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
102	#117×C₄₁	—	2	2	no	—
103	#117×C₄₁	—	2	2	no	—
104	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
106	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
107	#104×C₄₁	—	2	8	no	—
108	#104×C₄₁	—	2	8	no	—
109	C₂²⋊C₈×C₄₁	—	2	4	no	—
110	C₂²⋊C₈×C₄₁	—	2	4	no	—
111	C₂⁴×C₄₁	—	2	1	no	—
112	C₂⁴×C₄₁	—	2	1	no	—
113	C₂⁴×C₄₁	#41	1	1	yes	characteristic
114	#41×C₄₁	—	2	4	no	—
115	#41×C₄₁	—	2	4	no	—
116	#41×C₄₁	—	2	4	no	—
117	#41×C₄₁	—	2	4	no	—
118	#41×C₄₁	—	2	4	no	—
119	#41×C₄₁	—	2	2	no	—
120	#41×C₄₁	—	2	2	no	—
121	#41×C₄₁	—	2	4	no	—
122	#41×C₄₁	—	2	4	no	—
123	#41×C₄₁	—	2	2	no	—
124	#41×C₄₁	—	2	2	no	—
125	#41×C₄₁	—	2	2	no	—
126	#41×C₄₁	—	2	2	no	—
127	#41×C₄₁	—	4	2	no	—
128	#41×C₄₁	—	4	2	no	—
129	#41×C₄₁	—	4	2	no	—
130	#41×C₄₁	—	4	2	no	—
131	#41×C₄₁	C₂²⋊C₄	1	8	yes	—
132	#41×C₄₁	C₂×D₄	1	4	yes	—
133	#41×C₄₁	C₂×D₄	1	4	yes	—
134	C₂×Q₈×C₄₁	—	2	1	no	—
135	C₂×Q₈×C₄₁	—	2	2	no	—
136	C₂×Q₈×C₄₁	—	2	1	no	—
137	C₂×Q₈×C₄₁	—	2	2	no	—
138	C₂×Q₈×C₄₁	—	2	2	no	—
139	C₂×Q₈×C₄₁	C₂²⋊C₄	1	4	yes	—
140	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
141	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
142	C₂×D₄×C₄₁	—	2	2	no	—
143	C₂×D₄×C₄₁	—	2	4	no	—
144	C₂×D₄×C₄₁	—	2	4	no	—
145	C₂×D₄×C₄₁	—	2	2	no	—
146	C₂×D₄×C₄₁	—	2	2	no	—
147	C₂×D₄×C₄₁	—	2	2	no	—
148	C₂×D₄×C₄₁	—	2	2	no	—
149	C₂×D₄×C₄₁	—	2	2	no	—
150	C₂×D₄×C₄₁	—	2	1	no	—
151	C₂×D₄×C₄₁	—	2	2	no	—
152	C₂×D₄×C₄₁	—	2	1	no	—
153	C₂×D₄×C₄₁	—	4	2	no	—
154	C₂×D₄×C₄₁	—	4	2	no	—
155	C₂×D₄×C₄₁	C₂²⋊C₄	1	4	yes	—
156	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
157	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
158	C₂²×C₄×C₄₁	—	2	1	no	—
159	C₂²×C₄×C₄₁	—	2	2	no	—
160	C₂²×C₄×C₄₁	—	2	4	no	—
161	C₂²×C₄×C₄₁	—	2	4	no	—
162	C₂²×C₄×C₄₁	—	2	2	no	—
163	C₂²×C₄×C₄₁	—	2	1	no	—
164	C₂²×C₄×C₄₁	—	2	2	no	—
165	C₂²×C₄×C₄₁	—	2	2	no	—
166	C₂²×C₄×C₄₁	—	2	2	no	—
167	C₂²×C₄×C₄₁	—	4	2	no	—
168	C₂²×C₄×C₄₁	—	4	2	no	—
169	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
177	C₂²×C₄×C₄₁	#41	1	2	yes	—
178	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
179	Q₁₆×C₄₁	—	2	8	no	—
180	SD₁₆×C₄₁	—	2	8	no	—
181	SD₁₆×C₄₁	—	2	8	no	—
182	D₈×C₄₁	—	2	8	no	—
183	M₁₆×C₄₁	—	2	16	no	—
184	M₁₆×C₄₁	—	2	4	no	—
185	M₁₆×C₄₁	—	2	4	no	—
186	M₁₆×C₄₁	—	2	4	no	—
187	M₁₆×C₄₁	—	2	2	no	—
188	M₁₆×C₄₁	—	2	2	no	—
189	M₁₆×C₄₁	—	2	2	no	—
190	M₁₆×C₄₁	—	4	2	no	—
191	M₁₆×C₄₁	C₂×D₄	1	4	yes	—
192	C₂×C₈×C₄₁	—	2	16	no	—
193	C₂×C₈×C₄₁	—	2	2	no	—
194	C₂×C₈×C₄₁	—	2	4	no	—
195	C₂×C₈×C₄₁	—	2	2	no	—
196	C₂×C₈×C₄₁	—	2	4	no	—
197	C₂×C₈×C₄₁	—	2	2	no	—
198	C₂×C₈×C₄₁	—	2	2	no	—
199	C₂×C₈×C₄₁	—	2	2	no	—
200	C₂×C₈×C₄₁	—	2	2	no	—
201	C₂×C₈×C₄₁	—	2	2	no	—
202	C₂×C₈×C₄₁	—	2	2	no	—
203	C₂×C₈×C₄₁	—	4	2	no	—
204	C₂×C₈×C₄₁	C₂²×C₄	1	4	yes	—
205	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
206	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
207	C₄⋊C₄×C₄₁	—	4	2	no	—
208	C₂²⋊C₄×C₄₁	—	4	2	no	—
209	C₄²×C₄₁	—	2	2	no	—
210	C₄²×C₄₁	—	2	2	no	—
211	C₂³×C₄₁	—	2	2	no	—
212	C₂³×C₄₁	—	2	4	no	—
213	C₂³×C₄₁	—	2	2	no	—
214	C₂³×C₄₁	—	4	2	no	—
215	C₂³×C₄₁	—	4	4	no	—
216	C₂³×C₄₁	—	4	4	no	—
217	C₂³×C₄₁	—	4	2	no	—
218	C₂³×C₄₁	C₄×D₄	1	1	yes	characteristic
219	C₂³×C₄₁	C₄×D₄	1	1	yes	characteristic
220	C₂³×C₄₁	#121	1	2	yes	—
221	C₂³×C₄₁	#123	1	2	yes	—
222	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
223	Q₈×C₄₁	—	2	2	no	—
224	Q₈×C₄₁	—	2	4	no	—
225	Q₈×C₄₁	—	2	2	no	—
226	Q₈×C₄₁	—	2	2	no	—
227	Q₈×C₄₁	—	4	2	no	—
228	Q₈×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
229	D₄×C₄₁	—	2	4	no	—
230	D₄×C₄₁	—	2	4	no	—
231	D₄×C₄₁	—	2	8	no	—
232	D₄×C₄₁	—	2	2	no	—
233	D₄×C₄₁	—	2	2	no	—
234	D₄×C₄₁	—	2	2	no	—
235	D₄×C₄₁	—	2	4	no	—
236	D₄×C₄₁	—	4	2	no	—
237	D₄×C₄₁	—	4	2	no	—
238	D₄×C₄₁	—	4	4	no	—
239	D₄×C₄₁	—	4	2	no	—
240	D₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
241	C₂×C₄×C₄₁	—	2	2	no	—
242	C₂×C₄×C₄₁	—	2	4	no	—
243	C₂×C₄×C₄₁	—	2	4	no	—
244	C₂×C₄×C₄₁	—	2	4	no	—
245	C₂×C₄×C₄₁	—	2	8	no	—
246	C₂×C₄×C₄₁	—	2	2	no	—
247	C₂×C₄×C₄₁	—	4	2	no	—
248	C₂×C₄×C₄₁	—	4	2	no	—
249	C₂×C₄×C₄₁	—	4	2	no	—
250	C₂×C₄×C₄₁	—	4	4	no	—
251	C₂×C₄×C₄₁	—	4	4	no	—
252	C₂×C₄×C₄₁	—	4	2	no	—
253	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
254	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
255	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
256	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
257	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
258	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
259	C₂×C₄×C₄₁	#120	1	2	yes	—
260	C₂×C₄×C₄₁	#120	1	2	yes	—
261	C₂×C₄×C₄₁	#121	1	2	yes	—
262	C₂×C₄×C₄₁	#121	1	2	yes	—
263	C₂×C₄×C₄₁	#121	1	2	yes	—
264	C₂×C₄×C₄₁	#123	1	2	yes	—
265	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
266	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
271	C₈×C₄₁	—	2	4	no	—
272	C₈×C₄₁	—	2	2	no	—
273	C₈×C₄₁	—	2	4	no	—
274	C₈×C₄₁	—	2	2	no	—
275	C₈×C₄₁	—	4	2	no	—
276	#20917	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
277	C₂²×C₄₁	—	2	2	no	—
278	C₂²×C₄₁	—	2	2	no	—
279	C₂²×C₄₁	—	2	2	no	—
280	C₂²×C₄₁	—	2	4	no	—
281	C₂²×C₄₁	—	4	2	no	—
282	C₂²×C₄₁	—	4	2	no	—
283	C₂²×C₄₁	—	4	8	no	—
284	C₂²×C₄₁	—	4	4	no	—
285	C₂²×C₄₁	—	4	4	no	—
286	C₂²×C₄₁	—	4	2	no	—
287	C₂²×C₄₁	—	8	4	no	—
288	C₂²×C₄₁	#386	1	2	yes	—
289	C₂²×C₄₁	#386	1	2	yes	—
290	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
291	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
292	C₂²×C₄₁	C₂×#123	1	1	yes	characteristic
293	C₄×C₄₁	—	2	4	no	—
294	C₄×C₄₁	—	4	2	no	—
295	C₄×C₄₁	—	8	2	no	—
296	C₄×C₄₁	#386	1	2	yes	—
297	C₄×C₄₁	#386	1	2	yes	—
298	C₄×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
299	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
300	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
301	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
302	C₂×#575	C₂×C₄₁	1	1	yes	characteristic
303	C₂²×#131	C₂×C₄₁	1	1	yes	characteristic, complemented
304	C₂×#421	C₂×C₄₁	1	1	yes	characteristic, complemented
305	C₂×#421	C₂×C₄₁	1	1	yes	characteristic, complemented
306	C₂×#408	C₂×C₄₁	1	1	yes	characteristic, complemented
307	#1876	C₂×C₄₁	1	8	yes	complemented
308	#1738	C₂×C₄₁	1	1	yes	characteristic, complemented
309	#1729	C₂×C₄₁	1	1	yes	characteristic, complemented
310	C₂×C₄₁	—	2	1	no	—
311	C₂×C₄₁	—	2	2	no	—
312	C₂×C₄₁	—	2	2	no	—
313	C₂×C₄₁	—	2	1	no	—
314	C₂×C₄₁	—	4	4	no	—
315	C₂×C₄₁	—	8	2	no	—
316	C₂×C₄₁	C₂×#386	1	1	yes	characteristic
317	C₂×C₄₁	#2955	1	2	yes	—
318	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
319	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
320	#575	—	2	4	no	—
321	#575	—	2	4	no	—
322	C₂×#137	C₄×C₄₁	1	2	yes	complemented
323	C₂×#137	C₄×C₄₁	1	2	yes	complemented
324	C₂×AGL(1,ℤ/8)	C₄×C₄₁	1	2	yes	complemented
325	C₂×AGL(1,ℤ/8)	C₄×C₄₁	1	2	yes	complemented
326	C₂×#135	C₂²×C₄₁	1	4	yes	—
327	C₂×#131	—	2	4	no	—
328	C₂×#131	—	2	4	no	—
329	C₂×#131	—	2	2	no	—
330	C₂×#131	C₂²×C₄₁	1	4	yes	complemented
331	C₂²×M₁₆	—	2	1	no	—
332	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
333	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
334	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
335	C₂³×C₈	—	2	1	no	—
336	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
337	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
338	#421	—	2	4	no	—
339	#421	—	2	4	no	—
340	C₂×#104	C₂²×C₄₁	1	4	yes	complemented
341	C₂×#104	C₂²×C₄₁	1	4	yes	complemented
342	#408	—	2	1	no	—
343	#408	—	2	1	no	—
344	#408	C₂²×C₄₁	1	4	yes	complemented
345	C₂×C₂²⋊C₈	—	2	2	no	—
346	#341	C₂²×C₄₁	1	4	yes	complemented
347	#336	C₂²×C₄₁	1	4	yes	complemented
348	C₄₁	#20917	1	1	yes	characteristic, direct product factor, Sylow
349	C₂×#41	—	2	2	no	—
350	C₂×#41	—	2	1	no	—
351	C₂×#41	—	2	1	no	—
352	C₂×#41	—	2	1	no	—
353	C₂×#41	—	2	2	no	—
354	C₂×#41	—	2	1	no	—
355	C₂×#41	—	2	2	no	—
356	C₂×#41	—	2	2	no	—
357	C₂×#41	—	2	2	no	—
358	C₂×#41	—	2	2	no	—
359	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
360	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
361	C₂×#41	D₄×C₄₁	1	4	yes	—
362	C₂×#41	D₄×C₄₁	1	4	yes	—
363	C₂×#41	C₂³×C₄₁	1	2	yes	—
364	C₂×#41	C₂³×C₄₁	1	2	yes	—
365	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
366	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
367	C₂²×D₄	—	2	1	no	—
368	C₂²×D₄	—	2	1	no	—
369	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
370	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
371	C₂³×C₄	—	2	1	no	—
372	C₂³×C₄	—	2	1	no	—
373	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
374	#137	—	2	8	no	—
375	#137	—	2	8	no	—
376	AGL(1,ℤ/8)	—	2	8	no	—
377	AGL(1,ℤ/8)	—	2	8	no	—
378	#135	—	2	8	no	—
379	#135	—	2	8	no	—
380	C₂×Q₁₆	C₂×C₄×C₄₁	1	4	yes	—
381	C₂×SD₁₆	C₂×C₄×C₄₁	1	4	yes	—
382	C₂×SD₁₆	C₂×C₄×C₄₁	1	4	yes	—
383	C₂×D₈	C₂×C₄×C₄₁	1	4	yes	—
384	#131	—	2	16	no	—
385	#131	—	2	8	no	—
386	#131	—	2	8	no	—
387	C₂×M₁₆	—	2	8	no	—
388	C₂×M₁₆	—	2	2	no	—
389	C₂×M₁₆	—	2	1	no	—
390	C₂×M₁₆	—	2	2	no	—
391	C₂×M₁₆	—	2	2	no	—
392	C₂×M₁₆	—	2	1	no	—
393	C₂×M₁₆	—	2	4	no	—
394	C₂×M₁₆	—	2	2	no	—
395	C₂×M₁₆	—	2	2	no	—
396	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	—
397	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	—
398	C₂×M₁₆	D₄×C₄₁	1	4	yes	—
399	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
400	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
401	C₂²×C₈	—	2	8	no	—
402	C₂²×C₈	—	2	1	no	—
403	C₂²×C₈	—	2	2	no	—
404	C₂²×C₈	—	2	2	no	—
405	C₂²×C₈	—	2	4	no	—
406	C₂²×C₈	—	2	1	no	—
407	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
408	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
409	C₂²×C₈	D₄×C₄₁	1	2	yes	—
410	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
411	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
412	#117	—	2	2	no	—
413	#117	—	2	2	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
417	#104	—	2	8	no	—
418	#104	—	2	8	no	—
419	C₂²⋊C₈	—	2	4	no	—
420	C₂²⋊C₈	—	2	4	no	—
421	C₂⁴	—	2	1	no	—
422	C₂⁴	—	2	1	no	—
423	C₂⁴	#41×C₄₁	1	1	yes	characteristic
424	#41	—	2	4	no	—
425	#41	—	2	4	no	—
426	#41	—	2	4	no	—
427	#41	—	2	4	no	—
428	#41	—	2	4	no	—
429	#41	—	2	2	no	—
430	#41	—	2	2	no	—
431	#41	—	2	4	no	—
432	#41	—	2	4	no	—
433	#41	—	2	2	no	—
434	#41	—	2	2	no	—
435	#41	—	2	2	no	—
436	#41	—	2	2	no	—
437	#41	—	4	2	no	—
438	#41	—	4	2	no	—
439	#41	—	4	2	no	—
440	#41	—	4	2	no	—
441	#41	C₂²⋊C₄×C₄₁	1	8	yes	—
442	#41	C₂×D₄×C₄₁	1	4	yes	—
443	#41	C₂×D₄×C₄₁	1	4	yes	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	2	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	2	no	—
448	C₂×Q₈	—	2	2	no	—
449	C₂×Q₈	C₂²⋊C₄×C₄₁	1	4	yes	—
450	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
451	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	4	2	no	—
464	C₂×D₄	—	4	2	no	—
465	C₂×D₄	C₂²⋊C₄×C₄₁	1	4	yes	—
466	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
467	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	4	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	4	2	no	—
479	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
480	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
482	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
483	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
484	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
486	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
487	C₂²×C₄	#41×C₄₁	1	2	yes	—
488	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
489	Q₁₆	—	2	8	no	—
490	SD₁₆	—	2	8	no	—
491	SD₁₆	—	2	8	no	—
492	D₈	—	2	8	no	—
493	M₁₆	—	2	16	no	—
494	M₁₆	—	2	4	no	—
495	M₁₆	—	2	4	no	—
496	M₁₆	—	2	4	no	—
497	M₁₆	—	2	2	no	—
498	M₁₆	—	2	2	no	—
499	M₁₆	—	2	2	no	—
500	M₁₆	—	4	2	no	—
501	M₁₆	C₂×D₄×C₄₁	1	4	yes	—
502	C₂×C₈	—	2	16	no	—
503	C₂×C₈	—	2	2	no	—
504	C₂×C₈	—	2	4	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	2	4	no	—
507	C₂×C₈	—	2	2	no	—
508	C₂×C₈	—	2	2	no	—
509	C₂×C₈	—	2	2	no	—
510	C₂×C₈	—	2	2	no	—
511	C₂×C₈	—	2	2	no	—
512	C₂×C₈	—	2	2	no	—
513	C₂×C₈	—	4	2	no	—
514	C₂×C₈	C₂²×C₄×C₄₁	1	4	yes	—
515	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
516	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
517	C₄⋊C₄	—	4	2	no	—
518	C₂²⋊C₄	—	4	2	no	—
519	C₄²	—	2	2	no	—
520	C₄²	—	2	2	no	—
521	C₂³	—	2	2	no	—
522	C₂³	—	2	4	no	—
523	C₂³	—	2	2	no	—
524	C₂³	—	4	2	no	—
525	C₂³	—	4	4	no	—
526	C₂³	—	4	4	no	—
527	C₂³	—	4	2	no	—
528	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
529	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
530	C₂³	#121×C₄₁	1	2	yes	—
531	C₂³	#123×C₄₁	1	2	yes	—
532	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
533	Q₈	—	2	2	no	—
534	Q₈	—	2	4	no	—
535	Q₈	—	2	2	no	—
536	Q₈	—	2	2	no	—
537	Q₈	—	4	2	no	—
538	Q₈	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
539	D₄	—	2	4	no	—
540	D₄	—	2	4	no	—
541	D₄	—	2	8	no	—
542	D₄	—	2	2	no	—
543	D₄	—	2	2	no	—
544	D₄	—	2	2	no	—
545	D₄	—	2	4	no	—
546	D₄	—	4	2	no	—
547	D₄	—	4	2	no	—
548	D₄	—	4	4	no	—
549	D₄	—	4	2	no	—
550	D₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	8	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	4	no	—
561	C₂×C₄	—	4	4	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
564	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
565	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
566	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
567	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
568	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
569	C₂×C₄	#120×C₄₁	1	2	yes	—
570	C₂×C₄	#120×C₄₁	1	2	yes	—
571	C₂×C₄	#121×C₄₁	1	2	yes	—
572	C₂×C₄	#121×C₄₁	1	2	yes	—
573	C₂×C₄	#121×C₄₁	1	2	yes	—
574	C₂×C₄	#123×C₄₁	1	2	yes	—
575	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
576	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
577	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
578	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
579	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
580	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
581	C₈	—	2	4	no	—
582	C₈	—	2	2	no	—
583	C₈	—	2	4	no	—
584	C₈	—	2	2	no	—
585	C₈	—	4	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	2	2	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	4	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	4	8	no	—
593	C₂²	—	4	4	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	4	no	—
596	C₂²	—	8	4	no	—
597	C₂²	C₄₁×#386	1	2	yes	—
598	C₂²	C₄₁×#386	1	2	yes	—
599	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
600	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
601	C₂²	C₂×#123×C₄₁	1	1	yes	characteristic
602	C₄	—	2	4	no	—
603	C₄	—	4	2	no	—
604	C₄	—	8	2	no	—
605	C₄	C₄₁×#386	1	2	yes	—
606	C₄	C₄₁×#386	1	2	yes	—
607	C₄	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
608	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
609	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
610	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
611	C₂	—	2	1	no	—
612	C₂	—	2	2	no	—
613	C₂	—	2	2	no	—
614	C₂	—	2	1	no	—
615	C₂	—	4	4	no	—
616	C₂	—	8	2	no	—
617	C₂	C₂×C₄₁×#386	1	1	yes	characteristic
618	C₂	C₄₁×#2955	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂²×C₄₁	C₂×C₄×D₄
prime radical	C₂×C₄₁×#575	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂³×C₈×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#131×C₄₁	C₂	semidirect
3. C₂×C₄₁×#421	C₂	semidirect
4. C₂×C₄₁×#421	C₂	semidirect
5. C₂×C₄₁×#408	C₂	semidirect
6. C₄₁×#1876	C₂	semidirect
7. C₄₁×#1738	C₂	semidirect
8. C₄₁×#1729	C₂	semidirect
13. C₂×#137×C₄₁	C₄	semidirect
14. C₂×#137×C₄₁	C₄	semidirect
15. C₂×AGL(1,ℤ/8)×C₄₁	C₄	semidirect
16. C₂×AGL(1,ℤ/8)×C₄₁	C₄	semidirect
21. C₂×#131×C₄₁	C₂²	semidirect
31. C₂×#104×C₄₁	C₂²	semidirect
32. C₂×#104×C₄₁	C₂²	semidirect
35. C₄₁×#408	C₂²	semidirect
37. C₄₁×#341	C₂²	semidirect
38. C₄₁×#336	C₂²	semidirect
276. #20917	C₄₁	direct (N × H)
303. C₂²×#131	C₂×C₄₁	semidirect
304. C₂×#421	C₂×C₄₁	semidirect
305. C₂×#421	C₂×C₄₁	semidirect
306. C₂×#408	C₂×C₄₁	semidirect
307. #1876	C₂×C₄₁	semidirect
308. #1738	C₂×C₄₁	semidirect
309. #1729	C₂×C₄₁	semidirect
322. C₂×#137	C₄×C₄₁	semidirect
323. C₂×#137	C₄×C₄₁	semidirect
324. C₂×AGL(1,ℤ/8)	C₄×C₄₁	semidirect
325. C₂×AGL(1,ℤ/8)	C₄×C₄₁	semidirect
330. C₂×#131	C₂²×C₄₁	semidirect
340. C₂×#104	C₂²×C₄₁	semidirect
341. C₂×#104	C₂²×C₄₁	semidirect
344. #408	C₂²×C₄₁	semidirect
346. #341	C₂²×C₄₁	semidirect
347. #336	C₂²×C₄₁	semidirect
348. C₄₁	#20917	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#575	2
C₂²×#131×C₄₁	2
C₂×C₄₁×#421	2
C₂×C₄₁×#408	2
C₄₁×#1876	2
C₄₁×#1738	2
C₄₁×#1729	2
#20917	41

Subgroups — C41×#20917 #23797118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#20917 #23797118