Subgroups — C₄₁×#21206 #23797407

Order 10496.

1718 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#535	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#417	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#418	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#416	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#102×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2317	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1961	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1959	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1958	C₂	1	2	yes	maximal, complemented
11	C₄₁×#1957	C₂	1	2	yes	maximal, complemented
12	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₄₁×#535	—	2	4	no	—
17	C₄₁×#535	C₄	1	8	yes	complemented
18	C₂×#127×C₄₁	C₂²	1	2	yes	—
19	C₂×#124×C₄₁	C₂²	1	2	yes	—
20	C₂×#121×C₄₁	—	2	2	no	—
21	C₂×#120×C₄₁	—	2	2	no	—
22	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
25	C₄₁×#418	—	2	4	no	—
26	C₄₁×#417	—	2	4	no	—
27	C₄₁×#416	—	2	4	no	—
28	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic, complemented
29	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic, complemented
30	C₂×#103×C₄₁	C₂²	1	2	yes	complemented
31	C₂×#102×C₄₁	—	2	4	no	—
32	C₂×#102×C₄₁	C₂²	1	2	yes	—
33	C₂×#102×C₄₁	C₂²	1	2	yes	—
34	C₂×#102×C₄₁	C₂²	1	2	yes	—
35	C₂×#102×C₄₁	C₂²	1	2	yes	—
36	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic, complemented
37	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic, complemented
38	C₂×#102×C₄₁	C₂²	1	2	yes	complemented
39	C₄₁×#405	—	2	4	no	—
40	C₂×#97×C₄₁	C₂²	1	2	yes	complemented
41	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	complemented
42	C₄₁×#389	—	2	2	no	—
43	C₄₁×#385	—	2	2	no	—
44	C₄₁×#384	C₂²	1	2	yes	complemented
45	C₄₁×#382	C₂²	1	2	yes	complemented
46	C₂⁵×C₄₁	—	2	1	no	—
47	C₂×#41×C₄₁	—	2	2	no	—
48	C₂×#41×C₄₁	—	2	2	no	—
49	C₂×#41×C₄₁	—	2	2	no	—
50	C₂×#41×C₄₁	—	2	2	no	—
51	C₂×#41×C₄₁	—	2	2	no	—
52	C₂×#41×C₄₁	C₂×C₄	1	4	yes	—
53	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₄₁	—	2	1	no	—
55	C₂²×D₄×C₄₁	—	2	2	no	—
56	C₂²×D₄×C₄₁	—	2	2	no	—
57	C₂²×D₄×C₄₁	—	2	1	no	—
58	C₂²×D₄×C₄₁	—	2	2	no	—
59	C₂²×D₄×C₄₁	—	2	4	no	—
60	C₂²×D₄×C₄₁	—	2	2	no	—
61	C₂²×D₄×C₄₁	—	2	2	no	—
62	C₂²×D₄×C₄₁	C₂×C₄	1	4	yes	—
63	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
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	1	yes	characteristic
68	C₂×M₁₆×C₄₁	—	2	2	no	—
69	C₂×M₁₆×C₄₁	—	2	2	no	—
70	C₂×M₁₆×C₄₁	D₄	1	4	yes	complemented
71	C₂²×C₈×C₄₁	—	2	2	no	—
72	C₂²×C₈×C₄₁	—	2	2	no	—
73	C₂²×C₈×C₄₁	D₄	1	4	yes	complemented
74	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
77	#127×C₄₁	—	2	4	no	—
78	#127×C₄₁	C₂×C₄	1	8	yes	complemented
79	#124×C₄₁	—	2	4	no	—
80	#124×C₄₁	C₂×C₄	1	8	yes	complemented
81	#121×C₄₁	—	2	16	no	—
82	#120×C₄₁	—	2	16	no	—
83	#117×C₄₁	—	2	2	no	—
84	#117×C₄₁	—	2	2	no	—
85	#117×C₄₁	C₂×C₄	1	4	yes	—
86	#117×C₄₁	D₄	1	4	yes	—
87	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
88	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
89	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
90	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
91	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
92	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
96	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
98	C₂×C₄²×C₄₁	—	2	1	no	—
99	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
100	#103×C₄₁	—	2	2	no	—
101	#103×C₄₁	—	2	2	no	—
102	#103×C₄₁	—	2	4	no	—
103	#102×C₄₁	—	2	4	no	—
104	#102×C₄₁	—	2	4	no	—
105	#102×C₄₁	—	2	4	no	—
106	#102×C₄₁	—	2	4	no	—
107	#102×C₄₁	—	2	2	no	—
108	#102×C₄₁	—	2	2	no	—
109	#102×C₄₁	—	2	4	no	—
110	#97×C₄₁	—	2	4	no	—
111	C₄×C₈×C₄₁	—	2	4	no	—
112	#95×C₄₁	—	2	4	no	—
113	C₂⁴×C₄₁	—	2	2	no	—
114	C₂⁴×C₄₁	—	2	1	no	—
115	C₂⁴×C₄₁	—	2	4	no	—
116	C₂⁴×C₄₁	—	4	2	no	—
117	C₂⁴×C₄₁	—	4	2	no	—
118	C₂⁴×C₄₁	—	8	2	no	—
119	C₂⁴×C₄₁	—	8	2	no	—
120	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
121	#41×C₄₁	—	2	8	no	—
122	#41×C₄₁	—	2	8	no	—
123	#41×C₄₁	—	4	4	no	—
124	#41×C₄₁	—	4	4	no	—
125	C₂×Q₈×C₄₁	—	2	1	no	—
126	C₂×Q₈×C₄₁	—	2	1	no	—
127	C₂×Q₈×C₄₁	—	2	1	no	—
128	C₂×Q₈×C₄₁	—	2	1	no	—
129	C₂×Q₈×C₄₁	—	2	1	no	—
130	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
131	C₂×D₄×C₄₁	—	2	4	no	—
132	C₂×D₄×C₄₁	—	2	4	no	—
133	C₂×D₄×C₄₁	—	2	16	no	—
134	C₂×D₄×C₄₁	—	2	8	no	—
135	C₂×D₄×C₄₁	—	2	8	no	—
136	C₂×D₄×C₄₁	—	2	2	no	—
137	C₂×D₄×C₄₁	—	2	2	no	—
138	C₂×D₄×C₄₁	—	2	1	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	2	no	—
143	C₂×D₄×C₄₁	—	2	2	no	—
144	C₂×D₄×C₄₁	—	2	1	no	—
145	C₂×D₄×C₄₁	—	2	1	no	—
146	C₂×D₄×C₄₁	—	4	2	no	—
147	C₂×D₄×C₄₁	—	4	2	no	—
148	C₂×D₄×C₄₁	—	4	4	no	—
149	C₂×D₄×C₄₁	—	4	4	no	—
150	C₂×D₄×C₄₁	—	4	2	no	—
151	C₂×D₄×C₄₁	—	4	2	no	—
152	C₂×D₄×C₄₁	—	8	4	no	—
153	C₂×D₄×C₄₁	—	8	4	no	—
154	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
155	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
156	C₂²×C₄×C₄₁	—	2	1	no	—
157	C₂²×C₄×C₄₁	—	2	4	no	—
158	C₂²×C₄×C₄₁	—	2	1	no	—
159	C₂²×C₄×C₄₁	—	2	2	no	—
160	C₂²×C₄×C₄₁	—	2	1	no	—
161	C₂²×C₄×C₄₁	—	4	2	no	—
162	C₂²×C₄×C₄₁	—	4	2	no	—
163	C₂²×C₄×C₄₁	—	4	2	no	—
164	C₂²×C₄×C₄₁	—	8	2	no	—
165	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
166	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
167	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₄₁	#41	1	2	yes	—
172	C₂²×C₄×C₄₁	#41	1	2	yes	—
173	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
174	M₁₆×C₄₁	—	2	8	no	—
175	C₂×C₈×C₄₁	—	2	8	no	—
176	C₂×C₈×C₄₁	—	2	1	no	—
177	C₂×C₈×C₄₁	—	2	2	no	—
178	C₂×C₈×C₄₁	—	2	1	no	—
179	C₂×C₈×C₄₁	—	2	1	no	—
180	C₂×C₈×C₄₁	—	2	1	no	—
181	C₂×C₈×C₄₁	—	2	2	no	—
182	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
183	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
184	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
185	C₄⋊C₄×C₄₁	—	2	2	no	—
186	C₄⋊C₄×C₄₁	—	2	1	no	—
187	C₄⋊C₄×C₄₁	—	2	1	no	—
188	C₄⋊C₄×C₄₁	—	2	2	no	—
189	C₄⋊C₄×C₄₁	—	2	1	no	—
190	C₄⋊C₄×C₄₁	—	2	1	no	—
191	C₄⋊C₄×C₄₁	—	4	2	no	—
192	C₄⋊C₄×C₄₁	—	8	4	no	—
193	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	8	yes	—
194	C₂²⋊C₄×C₄₁	—	2	16	no	—
195	C₂²⋊C₄×C₄₁	—	4	2	no	—
196	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	8	yes	—
197	C₄²×C₄₁	—	4	2	no	—
198	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
199	C₄²×C₄₁	C₂×D₄	1	4	yes	—
200	C₂³×C₄₁	—	2	2	no	—
201	C₂³×C₄₁	—	2	2	no	—
202	C₂³×C₄₁	—	2	4	no	—
203	C₂³×C₄₁	—	2	2	no	—
204	C₂³×C₄₁	—	4	1	no	—
205	C₂³×C₄₁	—	4	2	no	—
206	C₂³×C₄₁	—	4	1	no	—
207	C₂³×C₄₁	—	4	2	no	—
208	C₂³×C₄₁	—	4	2	no	—
209	C₂³×C₄₁	—	4	4	no	—
210	C₂³×C₄₁	—	4	2	no	—
211	C₂³×C₄₁	—	4	4	no	—
212	C₂³×C₄₁	—	4	8	no	—
213	C₂³×C₄₁	—	8	8	no	—
214	C₂³×C₄₁	—	8	8	no	—
215	C₂³×C₄₁	—	8	4	no	—
216	C₂³×C₄₁	—	8	4	no	—
217	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
218	C₂³×C₄₁	#124	1	2	yes	—
219	C₂³×C₄₁	#127	1	2	yes	—
220	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
221	Q₈×C₄₁	—	2	2	no	—
222	Q₈×C₄₁	—	2	2	no	—
223	Q₈×C₄₁	—	4	1	no	—
224	Q₈×C₄₁	—	4	1	no	—
225	D₄×C₄₁	—	2	4	no	—
226	D₄×C₄₁	—	2	4	no	—
227	D₄×C₄₁	—	2	2	no	—
228	D₄×C₄₁	—	2	2	no	—
229	D₄×C₄₁	—	4	8	no	—
230	D₄×C₄₁	—	4	2	no	—
231	D₄×C₄₁	—	4	2	no	—
232	D₄×C₄₁	—	4	1	no	—
233	D₄×C₄₁	—	4	1	no	—
234	D₄×C₄₁	—	4	8	no	—
235	D₄×C₄₁	—	8	16	no	—
236	C₂×C₄×C₄₁	—	2	4	no	—
237	C₂×C₄×C₄₁	—	2	4	no	—
238	C₂×C₄×C₄₁	—	2	2	no	—
239	C₂×C₄×C₄₁	—	4	1	no	—
240	C₂×C₄×C₄₁	—	4	1	no	—
241	C₂×C₄×C₄₁	—	4	8	no	—
242	C₂×C₄×C₄₁	—	4	1	no	—
243	C₂×C₄×C₄₁	—	4	1	no	—
244	C₂×C₄×C₄₁	—	4	2	no	—
245	C₂×C₄×C₄₁	—	4	2	no	—
246	C₂×C₄×C₄₁	—	4	4	no	—
247	C₂×C₄×C₄₁	—	4	2	no	—
248	C₂×C₄×C₄₁	—	8	4	no	—
249	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	8	yes	—
250	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
251	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
252	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
253	C₂×C₄×C₄₁	#121	1	4	yes	—
254	C₂×C₄×C₄₁	#121	1	4	yes	—
255	C₂×C₄×C₄₁	#124	1	2	yes	—
256	C₂×C₄×C₄₁	#127	1	2	yes	—
257	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
258	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
262	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
263	C₈×C₄₁	—	2	2	no	—
264	C₈×C₄₁	—	2	2	no	—
265	C₈×C₄₁	—	2	4	no	—
266	#21206	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂²×C₄₁	—	2	4	no	—
268	C₂²×C₄₁	—	2	4	no	—
269	C₂²×C₄₁	—	2	2	no	—
270	C₂²×C₄₁	—	2	2	no	—
271	C₂²×C₄₁	—	4	4	no	—
272	C₂²×C₄₁	—	4	8	no	—
273	C₂²×C₄₁	—	4	2	no	—
274	C₂²×C₄₁	—	4	4	no	—
275	C₂²×C₄₁	—	8	16	no	—
276	C₂²×C₄₁	—	8	2	no	—
277	C₂²×C₄₁	—	8	4	no	—
278	C₂²×C₄₁	—	8	1	no	—
279	C₂²×C₄₁	—	8	2	no	—
280	C₂²×C₄₁	—	8	1	no	—
281	C₂²×C₄₁	—	8	2	no	—
282	C₂²×C₄₁	#390	1	4	yes	—
283	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
284	C₂²×C₄₁	C₂×#124	1	1	yes	characteristic
285	C₂²×C₄₁	C₂×#127	1	1	yes	characteristic
286	C₂²×C₄₁	#576	1	2	yes	—
287	C₂²×C₄₁	#577	1	2	yes	—
288	C₄×C₄₁	—	2	8	no	—
289	C₄×C₄₁	—	4	2	no	—
290	C₄×C₄₁	—	8	1	no	—
291	C₄×C₄₁	—	8	1	no	—
292	C₄×C₄₁	—	8	2	no	—
293	C₄×C₄₁	#390	1	4	yes	—
294	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
295	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
296	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
297	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
298	C₂×#535	C₂×C₄₁	1	1	yes	characteristic
299	C₂×#417	C₂×C₄₁	1	1	yes	characteristic, complemented
300	C₂×#418	C₂×C₄₁	1	1	yes	characteristic, complemented
301	C₂×#416	C₂×C₄₁	1	1	yes	characteristic, complemented
302	C₂²×#102	C₂×C₄₁	1	1	yes	characteristic, complemented
303	C₂×#405	C₂×C₄₁	1	1	yes	characteristic, complemented
304	#2317	C₂×C₄₁	1	1	yes	characteristic, complemented
305	#1961	C₂×C₄₁	1	2	yes	complemented
306	#1959	C₂×C₄₁	1	2	yes	complemented
307	#1958	C₂×C₄₁	1	2	yes	complemented
308	#1957	C₂×C₄₁	1	2	yes	complemented
309	C₂×C₄₁	—	2	4	no	—
310	C₂×C₄₁	—	8	2	no	—
311	C₂×C₄₁	—	8	4	no	—
312	C₂×C₄₁	C₂×#390	1	1	yes	characteristic
313	C₂×C₄₁	#2897	1	2	yes	—
314	C₂×C₄₁	#3136	1	2	yes	—
315	C₂×C₄₁	#3154	1	1	yes	characteristic
316	C₂×C₄₁	#3155	1	1	yes	characteristic
317	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
318	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
319	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
320	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
321	#535	—	2	4	no	—
322	#535	C₄×C₄₁	1	8	yes	complemented
323	C₂×#127	C₂²×C₄₁	1	2	yes	—
324	C₂×#124	C₂²×C₄₁	1	2	yes	—
325	C₂×#121	—	2	2	no	—
326	C₂×#120	—	2	2	no	—
327	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
328	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
329	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
330	#418	—	2	4	no	—
331	#417	—	2	4	no	—
332	#416	—	2	4	no	—
333	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic, complemented
334	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic, complemented
335	C₂×#103	C₂²×C₄₁	1	2	yes	complemented
336	C₂×#102	—	2	4	no	—
337	C₂×#102	C₂²×C₄₁	1	2	yes	—
338	C₂×#102	C₂²×C₄₁	1	2	yes	—
339	C₂×#102	C₂²×C₄₁	1	2	yes	—
340	C₂×#102	C₂²×C₄₁	1	2	yes	—
341	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic, complemented
342	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic, complemented
343	C₂×#102	C₂²×C₄₁	1	2	yes	complemented
344	#405	—	2	4	no	—
345	C₂×#97	C₂²×C₄₁	1	2	yes	complemented
346	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	complemented
347	#389	—	2	2	no	—
348	#385	—	2	2	no	—
349	#384	C₂²×C₄₁	1	2	yes	complemented
350	#382	C₂²×C₄₁	1	2	yes	complemented
351	C₄₁	#21206	1	1	yes	characteristic, direct product factor, Sylow
352	C₂⁵	—	2	1	no	—
353	C₂×#41	—	2	2	no	—
354	C₂×#41	—	2	2	no	—
355	C₂×#41	—	2	2	no	—
356	C₂×#41	—	2	2	no	—
357	C₂×#41	—	2	2	no	—
358	C₂×#41	C₂×C₄×C₄₁	1	4	yes	—
359	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
360	C₂²×D₄	—	2	1	no	—
361	C₂²×D₄	—	2	2	no	—
362	C₂²×D₄	—	2	2	no	—
363	C₂²×D₄	—	2	1	no	—
364	C₂²×D₄	—	2	2	no	—
365	C₂²×D₄	—	2	4	no	—
366	C₂²×D₄	—	2	2	no	—
367	C₂²×D₄	—	2	2	no	—
368	C₂²×D₄	C₂×C₄×C₄₁	1	4	yes	—
369	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
370	C₂²×D₄	C₂³×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	C₂×M₁₆	—	2	2	no	—
375	C₂×M₁₆	—	2	2	no	—
376	C₂×M₁₆	D₄×C₄₁	1	4	yes	complemented
377	C₂²×C₈	—	2	2	no	—
378	C₂²×C₈	—	2	2	no	—
379	C₂²×C₈	D₄×C₄₁	1	4	yes	complemented
380	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
381	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
382	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
383	#127	—	2	4	no	—
384	#127	C₂×C₄×C₄₁	1	8	yes	complemented
385	#124	—	2	4	no	—
386	#124	C₂×C₄×C₄₁	1	8	yes	complemented
387	#121	—	2	16	no	—
388	#120	—	2	16	no	—
389	#117	—	2	2	no	—
390	#117	—	2	2	no	—
391	#117	C₂×C₄×C₄₁	1	4	yes	—
392	#117	D₄×C₄₁	1	4	yes	—
393	C₂×C₄⋊C₄	—	2	2	no	—
394	C₂×C₄⋊C₄	—	2	2	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	4	no	—
397	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
398	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
401	C₂×C₂²⋊C₄	—	2	4	no	—
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
404	C₂×C₄²	—	2	1	no	—
405	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
406	#103	—	2	2	no	—
407	#103	—	2	2	no	—
408	#103	—	2	4	no	—
409	#102	—	2	4	no	—
410	#102	—	2	4	no	—
411	#102	—	2	4	no	—
412	#102	—	2	4	no	—
413	#102	—	2	2	no	—
414	#102	—	2	2	no	—
415	#102	—	2	4	no	—
416	#97	—	2	4	no	—
417	C₄×C₈	—	2	4	no	—
418	#95	—	2	4	no	—
419	C₂⁴	—	2	2	no	—
420	C₂⁴	—	2	1	no	—
421	C₂⁴	—	2	4	no	—
422	C₂⁴	—	4	2	no	—
423	C₂⁴	—	4	2	no	—
424	C₂⁴	—	8	2	no	—
425	C₂⁴	—	8	2	no	—
426	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
427	#41	—	2	8	no	—
428	#41	—	2	8	no	—
429	#41	—	4	4	no	—
430	#41	—	4	4	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	16	no	—
440	C₂×D₄	—	2	8	no	—
441	C₂×D₄	—	2	8	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	4	2	no	—
453	C₂×D₄	—	4	2	no	—
454	C₂×D₄	—	4	4	no	—
455	C₂×D₄	—	4	4	no	—
456	C₂×D₄	—	4	2	no	—
457	C₂×D₄	—	4	2	no	—
458	C₂×D₄	—	8	4	no	—
459	C₂×D₄	—	8	4	no	—
460	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
461	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	4	2	no	—
468	C₂²×C₄	—	4	2	no	—
469	C₂²×C₄	—	4	2	no	—
470	C₂²×C₄	—	8	2	no	—
471	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
472	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
473	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
475	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
476	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
477	C₂²×C₄	#41×C₄₁	1	2	yes	—
478	C₂²×C₄	#41×C₄₁	1	2	yes	—
479	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
480	M₁₆	—	2	8	no	—
481	C₂×C₈	—	2	8	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	2	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	2	no	—
488	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
489	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
490	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	4	2	no	—
498	C₄⋊C₄	—	8	4	no	—
499	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	8	yes	—
500	C₂²⋊C₄	—	2	16	no	—
501	C₂²⋊C₄	—	4	2	no	—
502	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	8	yes	—
503	C₄²	—	4	2	no	—
504	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
505	C₄²	C₂×D₄×C₄₁	1	4	yes	—
506	C₂³	—	2	2	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	4	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	4	1	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	4	1	no	—
513	C₂³	—	4	2	no	—
514	C₂³	—	4	2	no	—
515	C₂³	—	4	4	no	—
516	C₂³	—	4	2	no	—
517	C₂³	—	4	4	no	—
518	C₂³	—	4	8	no	—
519	C₂³	—	8	8	no	—
520	C₂³	—	8	8	no	—
521	C₂³	—	8	4	no	—
522	C₂³	—	8	4	no	—
523	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
524	C₂³	#124×C₄₁	1	2	yes	—
525	C₂³	#127×C₄₁	1	2	yes	—
526	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
527	Q₈	—	2	2	no	—
528	Q₈	—	2	2	no	—
529	Q₈	—	4	1	no	—
530	Q₈	—	4	1	no	—
531	D₄	—	2	4	no	—
532	D₄	—	2	4	no	—
533	D₄	—	2	2	no	—
534	D₄	—	2	2	no	—
535	D₄	—	4	8	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	1	no	—
539	D₄	—	4	1	no	—
540	D₄	—	4	8	no	—
541	D₄	—	8	16	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	8	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	4	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	8	4	no	—
555	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	8	yes	—
556	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
557	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
558	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
559	C₂×C₄	#121×C₄₁	1	4	yes	—
560	C₂×C₄	#121×C₄₁	1	4	yes	—
561	C₂×C₄	#124×C₄₁	1	2	yes	—
562	C₂×C₄	#127×C₄₁	1	2	yes	—
563	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
564	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
565	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
566	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
567	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
568	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
569	C₈	—	2	2	no	—
570	C₈	—	2	2	no	—
571	C₈	—	2	4	no	—
572	C₂²	—	2	4	no	—
573	C₂²	—	2	4	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	4	no	—
578	C₂²	—	4	4	no	—
579	C₂²	—	4	8	no	—
580	C₂²	—	8	16	no	—
581	C₂²	—	8	4	no	—
582	C₂²	—	8	2	no	—
583	C₂²	—	8	2	no	—
584	C₂²	—	8	1	no	—
585	C₂²	—	8	2	no	—
586	C₂²	—	8	1	no	—
587	C₂²	C₄₁×#390	1	4	yes	—
588	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
589	C₂²	C₂×#124×C₄₁	1	1	yes	characteristic
590	C₂²	C₂×#127×C₄₁	1	1	yes	characteristic
591	C₂²	C₄₁×#576	1	2	yes	—
592	C₂²	C₄₁×#577	1	2	yes	—
593	C₄	—	2	8	no	—
594	C₄	—	4	2	no	—
595	C₄	—	8	1	no	—
596	C₄	—	8	2	no	—
597	C₄	—	8	1	no	—
598	C₄	C₄₁×#390	1	4	yes	—
599	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
600	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
601	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
602	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
603	C₂	—	2	4	no	—
604	C₂	—	8	4	no	—
605	C₂	—	8	2	no	—
606	C₂	C₂×C₄₁×#390	1	1	yes	characteristic
607	C₂	C₄₁×#2897	1	2	yes	—
608	C₂	C₄₁×#3136	1	2	yes	—
609	C₂	C₄₁×#3154	1	1	yes	characteristic
610	C₂	C₄₁×#3155	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#535	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×#117×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#417	C₂	semidirect
3. C₂×C₄₁×#418	C₂	semidirect
4. C₂×C₄₁×#416	C₂	semidirect
5. C₂²×#102×C₄₁	C₂	semidirect
6. C₂×C₄₁×#405	C₂	semidirect
7. C₄₁×#2317	C₂	semidirect
8. C₄₁×#1961	C₂	semidirect
9. C₄₁×#1959	C₂	semidirect
10. C₄₁×#1958	C₂	semidirect
11. C₄₁×#1957	C₂	semidirect
17. C₄₁×#535	C₄	semidirect
28. C₂×#103×C₄₁	C₂²	semidirect
29. C₂×#103×C₄₁	C₂²	semidirect
30. C₂×#103×C₄₁	C₂²	semidirect
36. C₂×#102×C₄₁	C₂²	semidirect
37. C₂×#102×C₄₁	C₂²	semidirect
38. C₂×#102×C₄₁	C₂²	semidirect
40. C₂×#97×C₄₁	C₂²	semidirect
41. C₂×C₄×C₈×C₄₁	C₂²	semidirect
44. C₄₁×#384	C₂²	semidirect
45. C₄₁×#382	C₂²	semidirect
70. C₂×M₁₆×C₄₁	D₄	semidirect
73. C₂²×C₈×C₄₁	D₄	semidirect
78. #127×C₄₁	C₂×C₄	semidirect
80. #124×C₄₁	C₂×C₄	semidirect
266. #21206	C₄₁	direct (N × H)
299. C₂×#417	C₂×C₄₁	semidirect
300. C₂×#418	C₂×C₄₁	semidirect
301. C₂×#416	C₂×C₄₁	semidirect
302. C₂²×#102	C₂×C₄₁	semidirect
303. C₂×#405	C₂×C₄₁	semidirect
304. #2317	C₂×C₄₁	semidirect
305. #1961	C₂×C₄₁	semidirect
306. #1959	C₂×C₄₁	semidirect
307. #1958	C₂×C₄₁	semidirect
308. #1957	C₂×C₄₁	semidirect
322. #535	C₄×C₄₁	semidirect
333. C₂×#103	C₂²×C₄₁	semidirect
334. C₂×#103	C₂²×C₄₁	semidirect
335. C₂×#103	C₂²×C₄₁	semidirect
341. C₂×#102	C₂²×C₄₁	semidirect
342. C₂×#102	C₂²×C₄₁	semidirect
343. C₂×#102	C₂²×C₄₁	semidirect
345. C₂×#97	C₂²×C₄₁	semidirect
346. C₂×C₄×C₈	C₂²×C₄₁	semidirect
349. #384	C₂²×C₄₁	semidirect
350. #382	C₂²×C₄₁	semidirect
351. C₄₁	#21206	direct (N × H)
376. C₂×M₁₆	D₄×C₄₁	semidirect
379. C₂²×C₈	D₄×C₄₁	semidirect
384. #127	C₂×C₄×C₄₁	semidirect
386. #124	C₂×C₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#535	2
C₂×C₄₁×#417	2
C₂×C₄₁×#418	2
C₂×C₄₁×#416	2
C₂²×#102×C₄₁	2
C₂×C₄₁×#405	2
C₄₁×#2317	2
C₄₁×#1961	2
C₄₁×#1959	2
C₄₁×#1958	2
C₄₁×#1957	2
#21206	41

Subgroups — C41×#21206 #23797407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21206 #23797407