Subgroups — C₂×C₄₁×#1880 #23797124

Order 10496.

2038 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, socle	C₂⁴×C₄₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂³×D₄×C₄₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×Q₈×C₄₁	C₂	semidirect
3. C₂²×#103×C₄₁	C₂	semidirect
6. C₄₁×#1880	C₂	direct (N × H)
7. C₂×C₄₁×#340	C₂	semidirect
8. C₂×C₄₁×#336	C₂	semidirect
13. C₂²×SD₁₆×C₄₁	C₄	semidirect
20. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
29. C₂×#103×C₄₁	C₂²	semidirect
34. C₄₁×#340	C₂²	semidirect
35. C₄₁×#336	C₂²	semidirect
62. C₂×SD₁₆×C₄₁	C₂×C₄	semidirect
114. C₂×Q₈×C₄₁	C₂²⋊C₄	semidirect
148. C₂²×C₄×C₄₁	SD₁₆	semidirect
207. Q₈×C₄₁	C₂×C₂²⋊C₄	semidirect
239. C₂×C₄×C₄₁	C₂×SD₁₆	semidirect
248. C₂×#1880	C₄₁	direct (N × H)
282. C₂²×C₄×Q₈	C₂×C₄₁	semidirect
283. C₂²×#103	C₂×C₄₁	semidirect
286. #1880	C₂×C₄₁	direct (N × H)
287. C₂×#340	C₂×C₄₁	semidirect
288. C₂×#336	C₂×C₄₁	semidirect
290. C₂×C₄₁	#1880	direct (N × H)
302. C₂²×SD₁₆	C₄×C₄₁	semidirect
309. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
318. C₂×#103	C₂²×C₄₁	semidirect
323. #340	C₂²×C₄₁	semidirect
324. #336	C₂²×C₄₁	semidirect
325. C₄₁	C₂×#1880	direct (N × H)
352. C₂×SD₁₆	C₂×C₄×C₄₁	semidirect
404. C₂×Q₈	C₂²⋊C₄×C₄₁	semidirect
438. C₂²×C₄	SD₁₆×C₄₁	semidirect
497. Q₈	C₂×C₂²⋊C₄×C₄₁	semidirect
529. C₂×C₄	C₂×SD₁₆×C₄₁	semidirect
571. C₂	C₄₁×#1880	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×SD₁₆×C₄₁	2
C₂²×C₄×Q₈×C₄₁	2
C₂²×#103×C₄₁	2
C₂²×#102×C₄₁	2
C₂×C₄₁×#390	2
C₄₁×#1880	2
C₂×C₄₁×#340	2
C₂×C₄₁×#336	2
C₂×#1880	41

Subgroups — C2×C41×#1880 #23797124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#1880 #23797124