Subgroups — C₄₁×#21421 #23797622

Order 10496.

1222 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#529	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2283	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#117×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1996	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1964	C₂	1	2	yes	maximal
6	C₄₁×#1899	C₂	1	4	yes	maximal, complemented
7	C₄×#99×C₄₁	C₂	1	4	yes	maximal, complemented
8	C₄₁×#529	—	2	1	no	—
9	C₄₁×#529	—	2	1	no	—
10	C₄₁×#529	—	2	1	no	—
11	C₄₁×#529	—	2	1	no	—
12	C₄₁×#529	—	2	1	no	—
13	C₄₁×#529	—	2	1	no	—
14	C₄₁×#529	—	2	1	no	—
15	C₄₁×#529	—	2	1	no	—
16	C₂×#126×C₄₁	C₄	1	2	yes	complemented
17	C₂×#125×C₄₁	C₄	1	1	yes	characteristic, complemented
18	C₂×#124×C₄₁	C₄	1	1	yes	characteristic, complemented
19	C₂×#123×C₄₁	C₂²	1	2	yes	—
20	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₄₁	C₄	1	1	yes	characteristic, complemented
23	C₂×C₄×D₄×C₄₁	C₄	1	1	yes	characteristic, complemented
24	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
25	C₂×#117×C₄₁	C₄	1	2	yes	complemented
26	C₂×#117×C₄₁	C₂²	1	2	yes	—
27	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×#99×C₄₁	C₂²	1	8	yes	—
29	C₄₁×#383	—	2	1	no	—
30	C₄₁×#382	—	2	1	no	—
31	C₄₁×#381	C₂²	1	2	yes	—
32	C₄₁×#380	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
34	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
35	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
36	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
37	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
38	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
39	C₄₁×#376	—	2	1	no	—
40	C₄₁×#376	—	2	1	no	—
41	C₄³×C₄₁	—	2	1	no	—
42	C₄₁×#342	C₂²	1	8	yes	—
43	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
45	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
46	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
50	#126×C₄₁	—	2	2	no	—
51	#126×C₄₁	—	2	2	no	—
52	#126×C₄₁	—	2	2	no	—
53	#126×C₄₁	—	2	2	no	—
54	#125×C₄₁	—	2	1	no	—
55	#125×C₄₁	—	2	1	no	—
56	#125×C₄₁	—	2	1	no	—
57	#125×C₄₁	—	2	1	no	—
58	#124×C₄₁	—	2	1	no	—
59	#124×C₄₁	—	2	1	no	—
60	#124×C₄₁	—	2	1	no	—
61	#124×C₄₁	—	2	1	no	—
62	#123×C₄₁	—	2	2	no	—
63	#123×C₄₁	—	2	2	no	—
64	#123×C₄₁	—	2	2	no	—
65	#123×C₄₁	—	2	2	no	—
66	C₂²⋊Q₈×C₄₁	—	2	1	no	—
67	C₂²⋊Q₈×C₄₁	—	2	1	no	—
68	C₂²⋊Q₈×C₄₁	—	2	1	no	—
69	C₂²⋊Q₈×C₄₁	—	2	1	no	—
70	#121×C₄₁	—	2	1	no	—
71	#121×C₄₁	—	2	1	no	—
72	#121×C₄₁	—	2	1	no	—
73	#121×C₄₁	—	2	1	no	—
74	C₄×Q₈×C₄₁	—	2	1	no	—
75	C₄×Q₈×C₄₁	—	2	1	no	—
76	C₄×Q₈×C₄₁	—	2	1	no	—
77	C₄×Q₈×C₄₁	—	2	1	no	—
78	C₄×D₄×C₄₁	—	2	2	no	—
79	C₄×D₄×C₄₁	—	2	2	no	—
80	C₄×D₄×C₄₁	—	2	2	no	—
81	C₄×D₄×C₄₁	—	2	2	no	—
82	C₄×D₄×C₄₁	—	2	1	no	—
83	C₄×D₄×C₄₁	—	2	1	no	—
84	C₄×D₄×C₄₁	—	2	1	no	—
85	C₄×D₄×C₄₁	—	2	1	no	—
86	#117×C₄₁	—	2	8	no	—
87	#117×C₄₁	—	2	2	no	—
88	#117×C₄₁	—	2	2	no	—
89	#117×C₄₁	—	2	2	no	—
90	#117×C₄₁	—	2	2	no	—
91	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
92	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
93	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
94	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
95	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
97	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
99	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
100	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
101	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
102	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
103	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
105	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
106	C₂×C₄²×C₄₁	—	2	2	no	—
107	C₂×C₄²×C₄₁	—	2	2	no	—
108	C₂×C₄²×C₄₁	—	2	2	no	—
109	C₂×C₄²×C₄₁	—	2	2	no	—
110	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
111	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
120	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
121	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
122	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
123	#99×C₄₁	—	2	16	no	—
124	#95×C₄₁	—	2	2	no	—
125	#95×C₄₁	—	2	2	no	—
126	#95×C₄₁	—	2	2	no	—
127	#95×C₄₁	—	2	2	no	—
128	#95×C₄₁	—	2	2	no	—
129	#95×C₄₁	—	2	2	no	—
130	C₂⁴×C₄₁	C₂²×C₄	1	2	yes	—
131	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
132	C₂×Q₈×C₄₁	—	2	1	no	—
133	C₂×Q₈×C₄₁	—	2	1	no	—
134	C₂×Q₈×C₄₁	—	4	2	no	—
135	C₂×D₄×C₄₁	—	2	2	no	—
136	C₂×D₄×C₄₁	—	2	2	no	—
137	C₂×D₄×C₄₁	—	2	8	no	—
138	C₂×D₄×C₄₁	—	2	1	no	—
139	C₂×D₄×C₄₁	—	2	1	no	—
140	C₂×D₄×C₄₁	—	4	2	no	—
141	C₂²×C₄×C₄₁	—	2	4	no	—
142	C₂²×C₄×C₄₁	—	2	4	no	—
143	C₂²×C₄×C₄₁	—	2	2	no	—
144	C₂²×C₄×C₄₁	—	2	2	no	—
145	C₂²×C₄×C₄₁	—	2	4	no	—
146	C₂²×C₄×C₄₁	—	4	2	no	—
147	C₂²×C₄×C₄₁	—	4	2	no	—
148	C₂²×C₄×C₄₁	—	4	4	no	—
149	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
150	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
155	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
156	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₁	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
170	C₄⋊C₄×C₄₁	—	2	8	no	—
171	C₄⋊C₄×C₄₁	—	2	2	no	—
172	C₄⋊C₄×C₄₁	—	2	2	no	—
173	C₄⋊C₄×C₄₁	—	2	2	no	—
174	C₄⋊C₄×C₄₁	—	2	2	no	—
175	C₄⋊C₄×C₄₁	—	2	1	no	—
176	C₄⋊C₄×C₄₁	—	2	1	no	—
177	C₄⋊C₄×C₄₁	—	2	2	no	—
178	C₄⋊C₄×C₄₁	—	2	2	no	—
179	C₄⋊C₄×C₄₁	—	2	1	no	—
180	C₄⋊C₄×C₄₁	—	2	1	no	—
181	C₄⋊C₄×C₄₁	—	2	2	no	—
182	C₄⋊C₄×C₄₁	—	2	2	no	—
183	C₄⋊C₄×C₄₁	—	4	4	no	—
184	C₂²⋊C₄×C₄₁	—	2	2	no	—
185	C₂²⋊C₄×C₄₁	—	2	2	no	—
186	C₂²⋊C₄×C₄₁	—	2	4	no	—
187	C₂²⋊C₄×C₄₁	—	2	2	no	—
188	C₂²⋊C₄×C₄₁	—	2	2	no	—
189	C₂²⋊C₄×C₄₁	—	2	2	no	—
190	C₂²⋊C₄×C₄₁	—	2	2	no	—
191	C₂²⋊C₄×C₄₁	—	2	2	no	—
192	C₂²⋊C₄×C₄₁	—	2	2	no	—
193	C₂²⋊C₄×C₄₁	—	2	2	no	—
194	C₂²⋊C₄×C₄₁	—	2	2	no	—
195	C₂²⋊C₄×C₄₁	—	2	8	no	—
196	C₂²⋊C₄×C₄₁	#41	1	8	yes	—
197	C₄²×C₄₁	—	2	8	no	—
198	C₄²×C₄₁	—	2	2	no	—
199	C₄²×C₄₁	—	2	2	no	—
200	C₄²×C₄₁	—	4	4	no	—
201	C₄²×C₄₁	—	4	4	no	—
202	C₄²×C₄₁	—	4	4	no	—
203	C₄²×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
204	C₄²×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
205	C₄²×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
206	C₄²×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
207	C₄²×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
208	C₄²×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
209	C₄²×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
210	C₄²×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
211	C₄²×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
212	C₄²×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
213	C₄²×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
214	C₄²×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
215	C₄²×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
216	C₄²×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
217	C₄²×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
218	C₄²×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
219	C₂³×C₄₁	—	2	2	no	—
220	C₂³×C₄₁	—	2	4	no	—
221	C₂³×C₄₁	—	4	1	no	—
222	C₂³×C₄₁	—	4	1	no	—
223	C₂³×C₄₁	—	4	2	no	—
224	C₂³×C₄₁	—	4	2	no	—
225	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
226	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
227	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
228	C₂³×C₄₁	C₂×#41	1	4	yes	—
229	Q₈×C₄₁	—	4	2	no	—
230	Q₈×C₄₁	—	4	2	no	—
231	D₄×C₄₁	—	4	2	no	—
232	D₄×C₄₁	—	4	4	no	—
233	D₄×C₄₁	—	4	4	no	—
234	D₄×C₄₁	—	4	2	no	—
235	C₂×C₄×C₄₁	—	2	2	no	—
236	C₂×C₄×C₄₁	—	2	2	no	—
237	C₂×C₄×C₄₁	—	2	2	no	—
238	C₂×C₄×C₄₁	—	2	2	no	—
239	C₂×C₄×C₄₁	—	2	2	no	—
240	C₂×C₄×C₄₁	—	2	2	no	—
241	C₂×C₄×C₄₁	—	2	2	no	—
242	C₂×C₄×C₄₁	—	2	2	no	—
243	C₂×C₄×C₄₁	—	2	2	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	2	no	—
249	C₂×C₄×C₄₁	—	2	2	no	—
250	C₂×C₄×C₄₁	—	2	4	no	—
251	C₂×C₄×C₄₁	—	2	8	no	—
252	C₂×C₄×C₄₁	—	4	1	no	—
253	C₂×C₄×C₄₁	—	4	1	no	—
254	C₂×C₄×C₄₁	—	4	1	no	—
255	C₂×C₄×C₄₁	—	4	1	no	—
256	C₂×C₄×C₄₁	—	4	1	no	—
257	C₂×C₄×C₄₁	—	4	1	no	—
258	C₂×C₄×C₄₁	—	4	4	no	—
259	C₂×C₄×C₄₁	—	4	4	no	—
260	C₂×C₄×C₄₁	—	4	4	no	—
261	C₂×C₄×C₄₁	—	4	4	no	—
262	C₂×C₄×C₄₁	—	4	2	no	—
263	C₂×C₄×C₄₁	—	4	2	no	—
264	C₂×C₄×C₄₁	—	4	4	no	—
265	C₂×C₄×C₄₁	—	4	4	no	—
266	C₂×C₄×C₄₁	—	4	4	no	—
267	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
277	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	#21421	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
280	C₂²×C₄₁	—	2	1	no	—
281	C₂²×C₄₁	—	2	1	no	—
282	C₂²×C₄₁	—	2	1	no	—
283	C₂²×C₄₁	—	2	1	no	—
284	C₂²×C₄₁	—	2	1	no	—
285	C₂²×C₄₁	—	2	1	no	—
286	C₂²×C₄₁	—	4	4	no	—
287	C₂²×C₄₁	—	4	2	no	—
288	C₂²×C₄₁	—	4	2	no	—
289	C₂²×C₄₁	—	4	2	no	—
290	C₂²×C₄₁	—	8	4	no	—
291	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
292	C₂²×C₄₁	C₄×#41	1	2	yes	—
293	C₂²×C₄₁	#525	1	2	yes	—
294	C₂²×C₄₁	#532	1	2	yes	—
295	C₄×C₄₁	—	2	1	no	—
296	C₄×C₄₁	—	2	1	no	—
297	C₄×C₄₁	—	2	1	no	—
298	C₄×C₄₁	—	2	1	no	—
299	C₄×C₄₁	—	2	1	no	—
300	C₄×C₄₁	—	2	1	no	—
301	C₄×C₄₁	—	2	1	no	—
302	C₄×C₄₁	—	2	1	no	—
303	C₄×C₄₁	—	2	1	no	—
304	C₄×C₄₁	—	2	1	no	—
305	C₄×C₄₁	—	4	8	no	—
306	C₄×C₄₁	—	4	2	no	—
307	C₄×C₄₁	—	4	2	no	—
308	C₄×C₄₁	—	4	2	no	—
309	C₄×C₄₁	—	8	4	no	—
310	C₄×C₄₁	#410	1	2	yes	—
311	C₄×C₄₁	#410	1	2	yes	—
312	C₂×#529	C₂×C₄₁	1	1	yes	characteristic
313	#2283	C₂×C₄₁	1	1	yes	characteristic, complemented
314	C₄×#117	C₂×C₄₁	1	1	yes	characteristic, complemented
315	#1996	C₂×C₄₁	1	2	yes	complemented
316	#1964	C₂×C₄₁	1	2	yes	—
317	#1899	C₂×C₄₁	1	4	yes	complemented
318	C₄×#99	C₂×C₄₁	1	4	yes	complemented
319	C₂×C₄₁	—	2	2	no	—
320	C₂×C₄₁	—	2	2	no	—
321	C₂×C₄₁	—	2	2	no	—
322	C₂×C₄₁	—	8	2	no	—
323	C₂×C₄₁	#2297	1	1	yes	characteristic
324	C₂×C₄₁	C₂×#410	1	1	yes	characteristic
325	C₂×C₄₁	C₂×#410	1	1	yes	characteristic
326	#529	—	2	1	no	—
327	#529	—	2	1	no	—
328	#529	—	2	1	no	—
329	#529	—	2	1	no	—
330	#529	—	2	1	no	—
331	#529	—	2	1	no	—
332	#529	—	2	1	no	—
333	#529	—	2	1	no	—
334	C₂×#126	C₄×C₄₁	1	2	yes	complemented
335	C₂×#125	C₄×C₄₁	1	1	yes	characteristic, complemented
336	C₂×#124	C₄×C₄₁	1	1	yes	characteristic, complemented
337	C₂×#123	C₂²×C₄₁	1	2	yes	—
338	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
339	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
340	C₂×C₄×Q₈	C₄×C₄₁	1	1	yes	characteristic, complemented
341	C₂×C₄×D₄	C₄×C₄₁	1	1	yes	characteristic, complemented
342	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
343	C₂×#117	C₄×C₄₁	1	2	yes	complemented
344	C₂×#117	C₂²×C₄₁	1	2	yes	—
345	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
346	C₂×#99	C₂²×C₄₁	1	8	yes	—
347	#383	—	2	1	no	—
348	#382	—	2	1	no	—
349	#381	C₂²×C₄₁	1	2	yes	—
350	#380	C₂²×C₄₁	1	2	yes	—
351	C₄×C₄⋊C₄	—	2	1	no	—
352	C₄×C₄⋊C₄	—	2	1	no	—
353	C₄×C₄⋊C₄	—	2	1	no	—
354	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
355	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
356	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
357	#376	—	2	1	no	—
358	#376	—	2	1	no	—
359	C₄³	—	2	1	no	—
360	#342	C₂²×C₄₁	1	8	yes	—
361	C₄₁	#21421	1	1	yes	characteristic, direct product factor, Sylow
362	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
363	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
364	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
365	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
366	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
367	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
368	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
369	#126	—	2	2	no	—
370	#126	—	2	2	no	—
371	#126	—	2	2	no	—
372	#126	—	2	2	no	—
373	#125	—	2	1	no	—
374	#125	—	2	1	no	—
375	#125	—	2	1	no	—
376	#125	—	2	1	no	—
377	#124	—	2	1	no	—
378	#124	—	2	1	no	—
379	#124	—	2	1	no	—
380	#124	—	2	1	no	—
381	#123	—	2	2	no	—
382	#123	—	2	2	no	—
383	#123	—	2	2	no	—
384	#123	—	2	2	no	—
385	C₂²⋊Q₈	—	2	1	no	—
386	C₂²⋊Q₈	—	2	1	no	—
387	C₂²⋊Q₈	—	2	1	no	—
388	C₂²⋊Q₈	—	2	1	no	—
389	#121	—	2	1	no	—
390	#121	—	2	1	no	—
391	#121	—	2	1	no	—
392	#121	—	2	1	no	—
393	C₄×Q₈	—	2	1	no	—
394	C₄×Q₈	—	2	1	no	—
395	C₄×Q₈	—	2	1	no	—
396	C₄×Q₈	—	2	1	no	—
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	—	2	2	no	—
400	C₄×D₄	—	2	2	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	—	2	1	no	—
404	C₄×D₄	—	2	1	no	—
405	#117	—	2	8	no	—
406	#117	—	2	2	no	—
407	#117	—	2	2	no	—
408	#117	—	2	2	no	—
409	#117	—	2	2	no	—
410	C₂×C₄⋊C₄	—	2	2	no	—
411	C₂×C₄⋊C₄	—	2	2	no	—
412	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
413	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
414	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
416	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
418	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
419	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
420	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
421	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
425	C₂×C₄²	—	2	2	no	—
426	C₂×C₄²	—	2	2	no	—
427	C₂×C₄²	—	2	2	no	—
428	C₂×C₄²	—	2	2	no	—
429	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
430	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
431	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
432	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
433	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
434	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
435	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
436	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
437	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
438	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
439	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
440	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
441	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
442	#99	—	2	16	no	—
443	#95	—	2	2	no	—
444	#95	—	2	2	no	—
445	#95	—	2	2	no	—
446	#95	—	2	2	no	—
447	#95	—	2	2	no	—
448	#95	—	2	2	no	—
449	C₂⁴	C₂²×C₄×C₄₁	1	2	yes	—
450	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	4	2	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	8	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	4	2	no	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	4	2	no	—
466	C₂²×C₄	—	4	2	no	—
467	C₂²×C₄	—	4	4	no	—
468	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
469	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
470	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
471	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
472	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
473	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
474	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
475	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
476	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
487	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
488	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
489	C₄⋊C₄	—	2	8	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	4	4	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	4	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	2	no	—
514	C₂²⋊C₄	—	2	8	no	—
515	C₂²⋊C₄	#41×C₄₁	1	8	yes	—
516	C₄²	—	2	8	no	—
517	C₄²	—	2	2	no	—
518	C₄²	—	2	2	no	—
519	C₄²	—	4	4	no	—
520	C₄²	—	4	4	no	—
521	C₄²	—	4	4	no	—
522	C₄²	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
523	C₄²	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
524	C₄²	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
525	C₄²	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
526	C₄²	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
527	C₄²	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
528	C₄²	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
529	C₄²	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
530	C₄²	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
531	C₄²	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
532	C₄²	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
533	C₄²	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
534	C₄²	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
535	C₄²	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
536	C₄²	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
537	C₄²	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
538	C₂³	—	2	2	no	—
539	C₂³	—	2	4	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	4	1	no	—
542	C₂³	—	4	2	no	—
543	C₂³	—	4	2	no	—
544	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
545	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
546	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
547	C₂³	C₂×#41×C₄₁	1	4	yes	—
548	Q₈	—	4	2	no	—
549	Q₈	—	4	2	no	—
550	D₄	—	4	2	no	—
551	D₄	—	4	4	no	—
552	D₄	—	4	4	no	—
553	D₄	—	4	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	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	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	8	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	4	no	—
578	C₂×C₄	—	4	4	no	—
579	C₂×C₄	—	4	4	no	—
580	C₂×C₄	—	4	4	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	4	no	—
584	C₂×C₄	—	4	4	no	—
585	C₂×C₄	—	4	4	no	—
586	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
587	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
588	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
589	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
590	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
591	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
592	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
593	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
594	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
595	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
596	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
597	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
598	C₂²	—	2	1	no	—
599	C₂²	—	2	1	no	—
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	4	4	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	8	4	no	—
609	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
610	C₂²	C₄×#41×C₄₁	1	2	yes	—
611	C₂²	C₄₁×#525	1	2	yes	—
612	C₂²	C₄₁×#532	1	2	yes	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	1	no	—
623	C₄	—	4	8	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	2	no	—
626	C₄	—	4	2	no	—
627	C₄	—	8	4	no	—
628	C₄	C₄₁×#410	1	2	yes	—
629	C₄	C₄₁×#410	1	2	yes	—
630	C₂	—	2	2	no	—
631	C₂	—	2	2	no	—
632	C₂	—	2	2	no	—
633	C₂	—	8	2	no	—
634	C₂	C₄₁×#2297	1	1	yes	characteristic
635	C₂	C₂×C₄₁×#410	1	1	yes	characteristic
636	C₂	C₂×C₄₁×#410	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₁	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₄₁
Frattini, cosocle	C₂⁴	C₂⁴×C₄₁
socle	C₂²×C₄₁	C₂²×C₂²⋊C₄
prime radical	C₂×#121×C₄₁	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2283	C₂	semidirect
3. C₄×#117×C₄₁	C₂	semidirect
4. C₄₁×#1996	C₂	semidirect
6. C₄₁×#1899	C₂	semidirect
7. C₄×#99×C₄₁	C₂	semidirect
16. C₂×#126×C₄₁	C₄	semidirect
17. C₂×#125×C₄₁	C₄	semidirect
18. C₂×#124×C₄₁	C₄	semidirect
22. C₂×C₄×Q₈×C₄₁	C₄	semidirect
23. C₂×C₄×D₄×C₄₁	C₄	semidirect
25. C₂×#117×C₄₁	C₄	semidirect
279. #21421	C₄₁	direct (N × H)
313. #2283	C₂×C₄₁	semidirect
314. C₄×#117	C₂×C₄₁	semidirect
315. #1996	C₂×C₄₁	semidirect
317. #1899	C₂×C₄₁	semidirect
318. C₄×#99	C₂×C₄₁	semidirect
334. C₂×#126	C₄×C₄₁	semidirect
335. C₂×#125	C₄×C₄₁	semidirect
336. C₂×#124	C₄×C₄₁	semidirect
340. C₂×C₄×Q₈	C₄×C₄₁	semidirect
341. C₂×C₄×D₄	C₄×C₄₁	semidirect
343. C₂×#117	C₄×C₄₁	semidirect
361. C₄₁	#21421	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×#529	2
C₄₁×#2283	2
C₄×#117×C₄₁	2
C₄₁×#1996	2
C₄₁×#1964	2
C₄₁×#1899	2
C₄×#99×C₄₁	2
#21421	41

Subgroups — C41×#21421 #23797622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21421 #23797622