Subgroups — C₂×C₄₁×#1882 #23797141

Order 10496.

1802 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#520	C₂	1	1	yes	maximal, characteristic
3	C₂²×#104×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₁×#419	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₁×#391	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1882	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₄₁×#343	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₁×#339	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
10	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
11	C₂×#137×C₄₁	—	2	4	no	—
12	C₂×#137×C₄₁	—	2	2	no	—
13	C₂×#137×C₄₁	C₄	1	8	yes	complemented
14	C₂×#137×C₄₁	C₂²	1	4	yes	—
15	C₂²×Q₁₆×C₄₁	—	2	1	no	—
16	C₂²×SD₁₆×C₄₁	—	2	1	no	—
17	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
19	C₄₁×#520	—	2	2	no	—
20	C₄₁×#520	—	2	2	no	—
21	C₄₁×#520	—	2	2	no	—
22	C₄₁×#520	C₂²	1	4	yes	—
23	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
24	C₂×C₄×D₄×C₄₁	—	2	1	no	—
25	C₂×C₄×D₄×C₄₁	—	2	2	no	—
26	C₂×#117×C₄₁	—	2	1	no	—
27	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₄₁	—	2	1	no	—
29	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×#104×C₄₁	—	2	4	no	—
32	C₂×#104×C₄₁	C₂²	1	4	yes	—
33	C₄₁×#419	—	2	2	no	—
34	C₄₁×#419	C₂²	1	4	yes	complemented
35	C₂×#103×C₄₁	—	2	1	no	—
36	C₂×#103×C₄₁	—	2	1	no	—
37	C₄₁×#391	—	2	2	no	—
38	C₄₁×#391	C₂²	1	4	yes	complemented
39	C₂×#95×C₄₁	—	2	2	no	—
40	C₄₁×#343	C₂²	1	4	yes	complemented
41	C₄₁×#339	C₂²	1	4	yes	complemented
42	C₂×#41×C₄₁	—	2	1	no	—
43	C₂×#41×C₄₁	—	2	1	no	—
44	C₂×#41×C₄₁	—	2	2	no	—
45	C₂×#41×C₄₁	—	2	2	no	—
46	C₂×#41×C₄₁	C₂×C₄	1	4	yes	—
47	C₂×#41×C₄₁	D₄	1	4	yes	—
48	C₂×#41×C₄₁	D₄	1	2	yes	—
49	C₂×#41×C₄₁	C₂³	1	2	yes	—
50	C₂²×Q₈×C₄₁	—	2	1	no	—
51	C₂²×Q₈×C₄₁	—	2	2	no	—
52	C₂²×Q₈×C₄₁	—	2	1	no	—
53	C₂²×Q₈×C₄₁	—	2	1	no	—
54	C₂²×Q₈×C₄₁	—	2	2	no	—
55	C₂²×Q₈×C₄₁	—	2	1	no	—
56	C₂²×Q₈×C₄₁	—	2	1	no	—
57	C₂²×Q₈×C₄₁	—	2	2	no	—
58	C₂²×Q₈×C₄₁	C₂×C₄	1	4	yes	complemented
59	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
60	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
61	C₂²×D₄×C₄₁	—	2	1	no	—
62	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₄₁	—	2	1	no	—
64	C₂³×C₄×C₄₁	—	2	1	no	—
65	C₂³×C₄×C₄₁	—	2	1	no	—
66	C₂³×C₄×C₄₁	—	2	2	no	—
67	C₂³×C₄×C₄₁	D₄	1	2	yes	—
68	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
69	#137×C₄₁	—	2	16	no	—
70	#137×C₄₁	—	2	8	no	—
71	#137×C₄₁	C₂×C₄	1	16	yes	complemented
72	C₂×Q₁₆×C₄₁	—	2	8	no	—
73	C₂×Q₁₆×C₄₁	—	2	4	no	—
74	C₂×SD₁₆×C₄₁	—	2	8	no	—
75	C₂×SD₁₆×C₄₁	—	2	4	no	—
76	C₂×M₁₆×C₄₁	—	2	2	no	—
77	C₂×M₁₆×C₄₁	—	2	1	no	—
78	C₂×M₁₆×C₄₁	—	2	1	no	—
79	C₂×M₁₆×C₄₁	—	2	2	no	—
80	C₂×M₁₆×C₄₁	—	2	2	no	—
81	C₂×M₁₆×C₄₁	C₂×C₄	1	4	yes	complemented
82	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
83	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
84	C₂²×C₈×C₄₁	—	2	1	no	—
85	C₂²×C₈×C₄₁	—	2	1	no	—
86	C₄×Q₈×C₄₁	—	2	4	no	—
87	C₄×Q₈×C₄₁	—	2	4	no	—
88	C₄×D₄×C₄₁	—	2	8	no	—
89	C₄×D₄×C₄₁	—	2	4	no	—
90	C₄×D₄×C₄₁	—	2	4	no	—
91	C₄×D₄×C₄₁	—	2	8	no	—
92	#117×C₄₁	—	2	4	no	—
93	#117×C₄₁	—	2	1	no	—
94	#117×C₄₁	—	2	1	no	—
95	#117×C₄₁	—	2	4	no	—
96	#117×C₄₁	D₄	1	2	yes	—
97	#117×C₄₁	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
99	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
100	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
101	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
102	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
103	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
104	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
105	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
106	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
109	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
110	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
111	C₂×C₄²×C₄₁	—	2	2	no	—
112	C₂×C₄²×C₄₁	—	2	1	no	—
113	C₂×C₄²×C₄₁	—	2	2	no	—
114	C₂×C₄²×C₄₁	—	2	2	no	—
115	C₂×C₄²×C₄₁	—	2	1	no	—
116	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
117	#104×C₄₁	—	2	8	no	—
118	#103×C₄₁	—	2	4	no	—
119	#103×C₄₁	—	2	4	no	—
120	#95×C₄₁	—	2	8	no	—
121	C₂⁴×C₄₁	—	2	1	no	—
122	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
123	#41×C₄₁	—	2	4	no	—
124	#41×C₄₁	—	2	4	no	—
125	#41×C₄₁	—	2	4	no	—
126	#41×C₄₁	—	2	4	no	—
127	#41×C₄₁	—	2	4	no	—
128	#41×C₄₁	—	2	2	no	—
129	#41×C₄₁	—	2	2	no	—
130	#41×C₄₁	C₂²⋊C₄	1	8	yes	—
131	#41×C₄₁	C₂²×C₄	1	4	yes	—
132	#41×C₄₁	C₂×D₄	1	4	yes	—
133	C₂×Q₈×C₄₁	—	2	4	no	—
134	C₂×Q₈×C₄₁	—	2	1	no	—
135	C₂×Q₈×C₄₁	—	2	2	no	—
136	C₂×Q₈×C₄₁	—	2	2	no	—
137	C₂×Q₈×C₄₁	—	2	4	no	—
138	C₂×Q₈×C₄₁	—	2	4	no	—
139	C₂×Q₈×C₄₁	—	2	4	no	—
140	C₂×Q₈×C₄₁	—	2	4	no	—
141	C₂×Q₈×C₄₁	—	2	2	no	—
142	C₂×Q₈×C₄₁	—	2	2	no	—
143	C₂×Q₈×C₄₁	—	2	2	no	—
144	C₂×Q₈×C₄₁	—	2	2	no	—
145	C₂×Q₈×C₄₁	—	4	1	no	—
146	C₂×Q₈×C₄₁	—	4	1	no	—
147	C₂×Q₈×C₄₁	—	4	2	no	—
148	C₂×Q₈×C₄₁	—	4	2	no	—
149	C₂×Q₈×C₄₁	—	4	2	no	—
150	C₂×Q₈×C₄₁	—	4	2	no	—
151	C₂×Q₈×C₄₁	—	4	2	no	—
152	C₂×Q₈×C₄₁	C₂²⋊C₄	1	4	yes	—
153	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	complemented
154	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
155	C₂×D₄×C₄₁	—	2	4	no	—
156	C₂×D₄×C₄₁	—	2	2	no	—
157	C₂×D₄×C₄₁	—	2	4	no	—
158	C₂×D₄×C₄₁	—	2	2	no	—
159	C₂×D₄×C₄₁	—	2	1	no	—
160	C₂×D₄×C₄₁	—	2	2	no	—
161	C₂×D₄×C₄₁	C₂²⋊C₄	1	4	yes	—
162	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₄₁	—	2	1	no	—
164	C₂²×C₄×C₄₁	—	2	4	no	—
165	C₂²×C₄×C₄₁	—	2	2	no	—
166	C₂²×C₄×C₄₁	—	2	4	no	—
167	C₂²×C₄×C₄₁	—	2	2	no	—
168	C₂²×C₄×C₄₁	—	2	4	no	—
169	C₂²×C₄×C₄₁	—	2	4	no	—
170	C₂²×C₄×C₄₁	—	2	1	no	—
171	C₂²×C₄×C₄₁	—	2	2	no	—
172	C₂²×C₄×C₄₁	—	2	1	no	—
173	C₂²×C₄×C₄₁	—	2	2	no	—
174	C₂²×C₄×C₄₁	—	2	2	no	—
175	C₂²×C₄×C₄₁	—	2	8	no	—
176	C₂²×C₄×C₄₁	—	2	2	no	—
177	C₂²×C₄×C₄₁	—	4	2	no	—
178	C₂²×C₄×C₄₁	—	4	1	no	—
179	C₂²×C₄×C₄₁	—	4	1	no	—
180	C₂²×C₄×C₄₁	—	4	2	no	—
181	C₂²×C₄×C₄₁	—	4	2	no	—
182	C₂²×C₄×C₄₁	—	4	4	no	—
183	C₂²×C₄×C₄₁	—	8	4	no	—
184	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
185	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
186	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
189	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₄₁	#41	1	2	yes	—
193	C₂²×C₄×C₄₁	#41	1	2	yes	—
194	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
195	Q₁₆×C₄₁	—	2	16	no	—
196	SD₁₆×C₄₁	—	2	16	no	—
197	M₁₆×C₄₁	—	2	4	no	—
198	M₁₆×C₄₁	—	2	2	no	—
199	M₁₆×C₄₁	—	2	2	no	—
200	M₁₆×C₄₁	—	2	2	no	—
201	M₁₆×C₄₁	—	4	2	no	—
202	M₁₆×C₄₁	C₂²×C₄	1	4	yes	complemented
203	C₂×C₈×C₄₁	—	2	4	no	—
204	C₂×C₈×C₄₁	—	2	2	no	—
205	C₂×C₈×C₄₁	—	2	2	no	—
206	C₂×C₈×C₄₁	—	4	2	no	—
207	C₄⋊C₄×C₄₁	—	2	8	no	—
208	C₄⋊C₄×C₄₁	—	2	2	no	—
209	C₄⋊C₄×C₄₁	—	2	1	no	—
210	C₄⋊C₄×C₄₁	—	2	2	no	—
211	C₄⋊C₄×C₄₁	—	2	1	no	—
212	C₄⋊C₄×C₄₁	—	2	2	no	—
213	C₄⋊C₄×C₄₁	—	2	2	no	—
214	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
215	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
216	C₂²⋊C₄×C₄₁	—	2	8	no	—
217	C₂²⋊C₄×C₄₁	—	2	2	no	—
218	C₂²⋊C₄×C₄₁	—	2	2	no	—
219	C₄²×C₄₁	—	2	8	no	—
220	C₄²×C₄₁	—	2	2	no	—
221	C₄²×C₄₁	—	2	2	no	—
222	C₄²×C₄₁	—	2	2	no	—
223	C₄²×C₄₁	—	2	2	no	—
224	C₄²×C₄₁	—	4	2	no	—
225	C₂³×C₄₁	—	2	2	no	—
226	C₂³×C₄₁	—	2	2	no	—
227	C₂³×C₄₁	—	2	2	no	—
228	C₂³×C₄₁	—	2	4	no	—
229	C₂³×C₄₁	—	4	2	no	—
230	C₂³×C₄₁	—	4	2	no	—
231	C₂³×C₄₁	C₄×D₄	1	2	yes	—
232	C₂³×C₄₁	#120	1	1	yes	characteristic
233	C₂³×C₄₁	#120	1	1	yes	characteristic
234	C₂³×C₄₁	#121	1	2	yes	—
235	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
236	Q₈×C₄₁	—	2	2	no	—
237	Q₈×C₄₁	—	2	4	no	—
238	Q₈×C₄₁	—	2	4	no	—
239	Q₈×C₄₁	—	2	4	no	—
240	Q₈×C₄₁	—	4	2	no	—
241	Q₈×C₄₁	—	4	2	no	—
242	Q₈×C₄₁	—	4	4	no	—
243	Q₈×C₄₁	—	4	4	no	—
244	Q₈×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
245	D₄×C₄₁	—	2	4	no	—
246	D₄×C₄₁	—	2	4	no	—
247	D₄×C₄₁	—	2	8	no	—
248	D₄×C₄₁	—	2	2	no	—
249	D₄×C₄₁	—	2	4	no	—
250	D₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
251	C₂×C₄×C₄₁	—	2	2	no	—
252	C₂×C₄×C₄₁	—	2	4	no	—
253	C₂×C₄×C₄₁	—	2	4	no	—
254	C₂×C₄×C₄₁	—	2	4	no	—
255	C₂×C₄×C₄₁	—	2	8	no	—
256	C₂×C₄×C₄₁	—	2	4	no	—
257	C₂×C₄×C₄₁	—	2	4	no	—
258	C₂×C₄×C₄₁	—	2	2	no	—
259	C₂×C₄×C₄₁	—	2	4	no	—
260	C₂×C₄×C₄₁	—	2	2	no	—
261	C₂×C₄×C₄₁	—	4	8	no	—
262	C₂×C₄×C₄₁	—	4	2	no	—
263	C₂×C₄×C₄₁	—	4	2	no	—
264	C₂×C₄×C₄₁	—	4	2	no	—
265	C₂×C₄×C₄₁	—	4	2	no	—
266	C₂×C₄×C₄₁	—	4	4	no	—
267	C₂×C₄×C₄₁	—	4	4	no	—
268	C₂×C₄×C₄₁	—	4	4	no	—
269	C₂×C₄×C₄₁	—	4	2	no	—
270	C₂×C₄×C₄₁	—	4	2	no	—
271	C₂×C₄×C₄₁	—	4	4	no	—
272	C₂×C₄×C₄₁	—	8	2	no	—
273	C₂×C₄×C₄₁	—	8	8	no	—
274	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
275	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
276	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
277	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
278	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
279	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
280	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
281	C₂×C₄×C₄₁	#121	1	2	yes	—
282	C₂×C₄×C₄₁	#121	1	2	yes	—
283	C₂×C₄×C₄₁	#121	1	2	yes	—
284	C₂×C₄×C₄₁	#123	1	2	yes	—
285	C₂×C₄×C₄₁	#123	1	2	yes	—
286	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
287	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
292	C₈×C₄₁	—	2	4	no	—
293	C₈×C₄₁	—	4	2	no	—
294	C₂×#1882	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
295	C₂²×C₄₁	—	2	4	no	—
296	C₂²×C₄₁	—	2	4	no	—
297	C₂²×C₄₁	—	2	1	no	—
298	C₂²×C₄₁	—	2	1	no	—
299	C₂²×C₄₁	—	2	1	no	—
300	C₂²×C₄₁	—	2	1	no	—
301	C₂²×C₄₁	—	2	4	no	—
302	C₂²×C₄₁	—	4	8	no	—
303	C₂²×C₄₁	—	4	2	no	—
304	C₂²×C₄₁	—	4	2	no	—
305	C₂²×C₄₁	#386	1	2	yes	—
306	C₂²×C₄₁	#386	1	2	yes	—
307	C₂²×C₄₁	#455	1	2	yes	—
308	C₂²×C₄₁	#456	1	2	yes	—
309	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
310	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
311	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
312	C₄×C₄₁	—	2	4	no	—
313	C₄×C₄₁	—	4	4	no	—
314	C₄×C₄₁	—	4	4	no	—
315	C₄×C₄₁	—	4	2	no	—
316	C₄×C₄₁	—	4	2	no	—
317	C₄×C₄₁	—	4	4	no	—
318	C₄×C₄₁	#386	1	2	yes	—
319	C₄×C₄₁	#386	1	2	yes	—
320	C₄×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
321	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
322	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
323	C₄×C₄₁	C₂×#123	1	1	yes	characteristic
324	C₂²×#137	C₂×C₄₁	1	1	yes	characteristic
325	C₂×#520	C₂×C₄₁	1	1	yes	characteristic
326	C₂²×#104	C₂×C₄₁	1	1	yes	characteristic
327	C₂×#419	C₂×C₄₁	1	1	yes	characteristic, complemented
328	C₂×#391	C₂×C₄₁	1	1	yes	characteristic, complemented
329	#1882	C₂×C₄₁	1	8	yes	direct product factor
330	C₂×#343	C₂×C₄₁	1	1	yes	characteristic, complemented
331	C₂×#339	C₂×C₄₁	1	1	yes	characteristic, complemented
332	C₂×C₄₁	—	2	1	no	—
333	C₂×C₄₁	—	2	1	no	—
334	C₂×C₄₁	—	2	2	no	—
335	C₂×C₄₁	—	4	4	no	—
336	C₂×C₄₁	#1882	1	4	yes	direct product factor
337	C₂×C₄₁	C₂×#386	1	1	yes	characteristic
338	C₂×C₄₁	C₂×#455	1	1	yes	characteristic
339	C₂×C₄₁	C₂×#456	1	1	yes	characteristic
340	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
341	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
342	C₂×#137	—	2	4	no	—
343	C₂×#137	—	2	2	no	—
344	C₂×#137	C₄×C₄₁	1	8	yes	complemented
345	C₂×#137	C₂²×C₄₁	1	4	yes	—
346	C₂²×Q₁₆	—	2	1	no	—
347	C₂²×SD₁₆	—	2	1	no	—
348	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
349	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
350	#520	—	2	2	no	—
351	#520	—	2	2	no	—
352	#520	—	2	2	no	—
353	#520	C₂²×C₄₁	1	4	yes	—
354	C₂×C₄×Q₈	—	2	1	no	—
355	C₂×C₄×D₄	—	2	1	no	—
356	C₂×C₄×D₄	—	2	2	no	—
357	C₂×#117	—	2	1	no	—
358	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
359	C₂²×C₄⋊C₄	—	2	1	no	—
360	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
361	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
362	C₂×#104	—	2	4	no	—
363	C₂×#104	C₂²×C₄₁	1	4	yes	—
364	#419	—	2	2	no	—
365	#419	C₂²×C₄₁	1	4	yes	complemented
366	C₂×#103	—	2	1	no	—
367	C₂×#103	—	2	1	no	—
368	#391	—	2	2	no	—
369	#391	C₂²×C₄₁	1	4	yes	complemented
370	C₂×#95	—	2	2	no	—
371	#343	C₂²×C₄₁	1	4	yes	complemented
372	#339	C₂²×C₄₁	1	4	yes	complemented
373	C₄₁	C₂×#1882	1	1	yes	characteristic, direct product factor, Sylow
374	C₂×#41	—	2	1	no	—
375	C₂×#41	—	2	1	no	—
376	C₂×#41	—	2	2	no	—
377	C₂×#41	—	2	2	no	—
378	C₂×#41	C₂×C₄×C₄₁	1	4	yes	—
379	C₂×#41	D₄×C₄₁	1	4	yes	—
380	C₂×#41	D₄×C₄₁	1	2	yes	—
381	C₂×#41	C₂³×C₄₁	1	2	yes	—
382	C₂²×Q₈	—	2	1	no	—
383	C₂²×Q₈	—	2	2	no	—
384	C₂²×Q₈	—	2	1	no	—
385	C₂²×Q₈	—	2	1	no	—
386	C₂²×Q₈	—	2	2	no	—
387	C₂²×Q₈	—	2	1	no	—
388	C₂²×Q₈	—	2	1	no	—
389	C₂²×Q₈	—	2	2	no	—
390	C₂²×Q₈	C₂×C₄×C₄₁	1	4	yes	complemented
391	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
392	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
393	C₂²×D₄	—	2	1	no	—
394	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
395	C₂³×C₄	—	2	1	no	—
396	C₂³×C₄	—	2	1	no	—
397	C₂³×C₄	—	2	1	no	—
398	C₂³×C₄	—	2	2	no	—
399	C₂³×C₄	D₄×C₄₁	1	2	yes	—
400	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
401	#137	—	2	16	no	—
402	#137	—	2	8	no	—
403	#137	C₂×C₄×C₄₁	1	16	yes	complemented
404	C₂×Q₁₆	—	2	8	no	—
405	C₂×Q₁₆	—	2	4	no	—
406	C₂×SD₁₆	—	2	8	no	—
407	C₂×SD₁₆	—	2	4	no	—
408	C₂×M₁₆	—	2	2	no	—
409	C₂×M₁₆	—	2	1	no	—
410	C₂×M₁₆	—	2	1	no	—
411	C₂×M₁₆	—	2	2	no	—
412	C₂×M₁₆	—	2	2	no	—
413	C₂×M₁₆	C₂×C₄×C₄₁	1	4	yes	complemented
414	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
415	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
416	C₂²×C₈	—	2	1	no	—
417	C₂²×C₈	—	2	1	no	—
418	C₄×Q₈	—	2	4	no	—
419	C₄×Q₈	—	2	4	no	—
420	C₄×D₄	—	2	8	no	—
421	C₄×D₄	—	2	4	no	—
422	C₄×D₄	—	2	4	no	—
423	C₄×D₄	—	2	8	no	—
424	#117	—	2	4	no	—
425	#117	—	2	1	no	—
426	#117	—	2	1	no	—
427	#117	—	2	4	no	—
428	#117	D₄×C₄₁	1	2	yes	—
429	#117	C₂³×C₄₁	1	2	yes	—
430	C₂×C₄⋊C₄	—	2	2	no	—
431	C₂×C₄⋊C₄	—	2	4	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	2	1	no	—
436	C₂×C₄⋊C₄	—	2	4	no	—
437	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
438	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
439	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
441	C₂×C₂²⋊C₄	—	2	2	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₄²	—	2	2	no	—
444	C₂×C₄²	—	2	1	no	—
445	C₂×C₄²	—	2	2	no	—
446	C₂×C₄²	—	2	2	no	—
447	C₂×C₄²	—	2	1	no	—
448	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
449	#104	—	2	8	no	—
450	#103	—	2	4	no	—
451	#103	—	2	4	no	—
452	#95	—	2	8	no	—
453	C₂⁴	—	2	1	no	—
454	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
455	#41	—	2	4	no	—
456	#41	—	2	4	no	—
457	#41	—	2	4	no	—
458	#41	—	2	4	no	—
459	#41	—	2	4	no	—
460	#41	—	2	2	no	—
461	#41	—	2	2	no	—
462	#41	C₂²⋊C₄×C₄₁	1	8	yes	—
463	#41	C₂²×C₄×C₄₁	1	4	yes	—
464	#41	C₂×D₄×C₄₁	1	4	yes	—
465	C₂×Q₈	—	2	4	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	2	no	—
468	C₂×Q₈	—	2	2	no	—
469	C₂×Q₈	—	2	4	no	—
470	C₂×Q₈	—	2	4	no	—
471	C₂×Q₈	—	2	4	no	—
472	C₂×Q₈	—	2	4	no	—
473	C₂×Q₈	—	2	2	no	—
474	C₂×Q₈	—	2	2	no	—
475	C₂×Q₈	—	2	2	no	—
476	C₂×Q₈	—	2	2	no	—
477	C₂×Q₈	—	4	1	no	—
478	C₂×Q₈	—	4	1	no	—
479	C₂×Q₈	—	4	2	no	—
480	C₂×Q₈	—	4	2	no	—
481	C₂×Q₈	—	4	2	no	—
482	C₂×Q₈	—	4	2	no	—
483	C₂×Q₈	—	4	2	no	—
484	C₂×Q₈	C₂²⋊C₄×C₄₁	1	4	yes	—
485	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	complemented
486	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
487	C₂×D₄	—	2	4	no	—
488	C₂×D₄	—	2	2	no	—
489	C₂×D₄	—	2	4	no	—
490	C₂×D₄	—	2	2	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	2	no	—
493	C₂×D₄	C₂²⋊C₄×C₄₁	1	4	yes	—
494	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	4	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	4	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	2	4	no	—
501	C₂²×C₄	—	2	4	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	2	8	no	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	4	2	no	—
510	C₂²×C₄	—	4	1	no	—
511	C₂²×C₄	—	4	1	no	—
512	C₂²×C₄	—	4	2	no	—
513	C₂²×C₄	—	4	2	no	—
514	C₂²×C₄	—	4	4	no	—
515	C₂²×C₄	—	8	4	no	—
516	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
517	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
518	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
519	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
520	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
521	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
522	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
523	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
524	C₂²×C₄	#41×C₄₁	1	2	yes	—
525	C₂²×C₄	#41×C₄₁	1	2	yes	—
526	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
527	Q₁₆	—	2	16	no	—
528	SD₁₆	—	2	16	no	—
529	M₁₆	—	2	4	no	—
530	M₁₆	—	2	2	no	—
531	M₁₆	—	2	2	no	—
532	M₁₆	—	2	2	no	—
533	M₁₆	—	4	2	no	—
534	M₁₆	C₂²×C₄×C₄₁	1	4	yes	complemented
535	C₂×C₈	—	2	4	no	—
536	C₂×C₈	—	2	2	no	—
537	C₂×C₈	—	2	2	no	—
538	C₂×C₈	—	4	2	no	—
539	C₄⋊C₄	—	2	8	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	2	no	—
545	C₄⋊C₄	—	2	2	no	—
546	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
547	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
548	C₂²⋊C₄	—	2	8	no	—
549	C₂²⋊C₄	—	2	2	no	—
550	C₂²⋊C₄	—	2	2	no	—
551	C₄²	—	2	8	no	—
552	C₄²	—	2	2	no	—
553	C₄²	—	2	2	no	—
554	C₄²	—	2	2	no	—
555	C₄²	—	2	2	no	—
556	C₄²	—	4	2	no	—
557	C₂³	—	2	2	no	—
558	C₂³	—	2	2	no	—
559	C₂³	—	2	2	no	—
560	C₂³	—	2	4	no	—
561	C₂³	—	4	2	no	—
562	C₂³	—	4	2	no	—
563	C₂³	C₄×D₄×C₄₁	1	2	yes	—
564	C₂³	#120×C₄₁	1	1	yes	characteristic
565	C₂³	#120×C₄₁	1	1	yes	characteristic
566	C₂³	#121×C₄₁	1	2	yes	—
567	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
568	Q₈	—	2	2	no	—
569	Q₈	—	2	4	no	—
570	Q₈	—	2	4	no	—
571	Q₈	—	2	4	no	—
572	Q₈	—	4	2	no	—
573	Q₈	—	4	2	no	—
574	Q₈	—	4	4	no	—
575	Q₈	—	4	4	no	—
576	Q₈	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
577	D₄	—	2	4	no	—
578	D₄	—	2	4	no	—
579	D₄	—	2	8	no	—
580	D₄	—	2	2	no	—
581	D₄	—	2	4	no	—
582	D₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	8	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	4	8	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	4	4	no	—
599	C₂×C₄	—	4	4	no	—
600	C₂×C₄	—	4	4	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	4	no	—
604	C₂×C₄	—	8	2	no	—
605	C₂×C₄	—	8	8	no	—
606	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
607	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
608	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
609	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
610	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
611	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
612	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
613	C₂×C₄	#121×C₄₁	1	2	yes	—
614	C₂×C₄	#121×C₄₁	1	2	yes	—
615	C₂×C₄	#121×C₄₁	1	2	yes	—
616	C₂×C₄	#123×C₄₁	1	2	yes	—
617	C₂×C₄	#123×C₄₁	1	2	yes	—
618	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
619	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
620	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
621	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
622	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
623	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
624	C₈	—	2	4	no	—
625	C₈	—	4	2	no	—
626	C₂²	—	2	4	no	—
627	C₂²	—	2	4	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	4	no	—
633	C₂²	—	4	8	no	—
634	C₂²	—	4	2	no	—
635	C₂²	—	4	2	no	—
636	C₂²	C₄₁×#386	1	2	yes	—
637	C₂²	C₄₁×#386	1	2	yes	—
638	C₂²	C₄₁×#455	1	2	yes	—
639	C₂²	C₄₁×#456	1	2	yes	—
640	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
641	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
642	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
643	C₄	—	2	4	no	—
644	C₄	—	4	4	no	—
645	C₄	—	4	4	no	—
646	C₄	—	4	4	no	—
647	C₄	—	4	2	no	—
648	C₄	—	4	2	no	—
649	C₄	C₄₁×#386	1	2	yes	—
650	C₄	C₄₁×#386	1	2	yes	—
651	C₄	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
652	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
653	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
654	C₄	C₂×#123×C₄₁	1	1	yes	characteristic
655	C₂	—	2	1	no	—
656	C₂	—	2	1	no	—
657	C₂	—	2	2	no	—
658	C₂	—	4	4	no	—
659	C₂	C₄₁×#1882	1	4	yes	direct product factor
660	C₂	C₂×C₄₁×#386	1	1	yes	characteristic
661	C₂	C₂×C₄₁×#455	1	1	yes	characteristic
662	C₂	C₂×C₄₁×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	#120
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×#41×C₄₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₄₁×#419	C₂	semidirect
5. C₂×C₄₁×#391	C₂	semidirect
6. C₄₁×#1882	C₂	direct (N × H)
7. C₂×C₄₁×#343	C₂	semidirect
8. C₂×C₄₁×#339	C₂	semidirect
13. C₂×#137×C₄₁	C₄	semidirect
34. C₄₁×#419	C₂²	semidirect
38. C₄₁×#391	C₂²	semidirect
40. C₄₁×#343	C₂²	semidirect
41. C₄₁×#339	C₂²	semidirect
58. C₂²×Q₈×C₄₁	C₂×C₄	semidirect
71. #137×C₄₁	C₂×C₄	semidirect
81. C₂×M₁₆×C₄₁	C₂×C₄	semidirect
153. C₂×Q₈×C₄₁	C₂²×C₄	semidirect
202. M₁₆×C₄₁	C₂²×C₄	semidirect
294. C₂×#1882	C₄₁	direct (N × H)
327. C₂×#419	C₂×C₄₁	semidirect
328. C₂×#391	C₂×C₄₁	semidirect
329. #1882	C₂×C₄₁	direct (N × H)
330. C₂×#343	C₂×C₄₁	semidirect
331. C₂×#339	C₂×C₄₁	semidirect
336. C₂×C₄₁	#1882	direct (N × H)
344. C₂×#137	C₄×C₄₁	semidirect
365. #419	C₂²×C₄₁	semidirect
369. #391	C₂²×C₄₁	semidirect
371. #343	C₂²×C₄₁	semidirect
372. #339	C₂²×C₄₁	semidirect
373. C₄₁	C₂×#1882	direct (N × H)
390. C₂²×Q₈	C₂×C₄×C₄₁	semidirect
403. #137	C₂×C₄×C₄₁	semidirect
413. C₂×M₁₆	C₂×C₄×C₄₁	semidirect
485. C₂×Q₈	C₂²×C₄×C₄₁	semidirect
534. M₁₆	C₂²×C₄×C₄₁	semidirect
659. C₂	C₄₁×#1882	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#137×C₄₁	2
C₂×C₄₁×#520	2
C₂²×#104×C₄₁	2
C₂×C₄₁×#419	2
C₂×C₄₁×#391	2
C₄₁×#1882	2
C₂×C₄₁×#343	2
C₂×C₄₁×#339	2
C₂×#1882	41

Subgroups — C2×C41×#1882 #23797141

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#1882 #23797141