Subgroups — C₄₁×#33001 #23809202

Order 10496.

1242 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3428	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#3095	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3007	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2499	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1882	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1882	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1860	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1859	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1826	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1822	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1789	C₂	1	1	yes	maximal, characteristic
12	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#137×C₄₁	C₂²	1	2	yes	—
14	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₄₁×#520	—	2	1	no	—
16	C₄₁×#520	—	2	1	no	—
17	C₄₁×#520	C₂²	1	2	yes	—
18	C₄₁×#520	C₂²	1	2	yes	—
19	C₄₁×#519	—	2	1	no	—
20	C₄₁×#518	—	2	1	no	—
21	C₄₁×#518	—	2	2	no	—
22	C₄×#41×C₄₁	—	2	2	no	—
23	C₄×#41×C₄₁	—	2	2	no	—
24	C₂×#117×C₄₁	—	2	2	no	—
25	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
27	C₄₁×#485	—	2	2	no	—
28	C₄₁×#484	—	2	1	no	—
29	C₄₁×#483	—	2	1	no	—
30	C₄₁×#452	—	2	2	no	—
31	C₄₁×#451	—	2	1	no	—
32	C₄₁×#450	—	2	1	no	—
33	C₄₁×#428	C₂²	1	2	yes	complemented
34	C₂×#104×C₄₁	C₂²	1	2	yes	—
35	C₂×#104×C₄₁	C₂²	1	2	yes	—
36	C₄₁×#419	C₂²	1	2	yes	complemented
37	C₄₁×#417	C₂²	1	2	yes	—
38	C₄₁×#407	C₂²	1	1	yes	characteristic
39	C₄₁×#407	C₂²	1	1	yes	characteristic
40	C₄₁×#397	—	2	2	no	—
41	C₄₁×#391	C₂²	1	1	yes	characteristic, complemented
42	C₄₁×#391	C₂²	1	1	yes	characteristic, complemented
43	C₄₁×#387	—	2	2	no	—
44	C₄₁×#384	C₂²	1	1	yes	characteristic, complemented
45	C₄₁×#382	C₂²	1	1	yes	characteristic, complemented
46	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
47	C₄₁×#343	C₂²	1	2	yes	complemented
48	C₄₁×#343	C₂²	1	2	yes	complemented
49	C₄₁×#339	C₂²	1	2	yes	complemented
50	C₄₁×#339	C₂²	1	2	yes	complemented
51	C₂×#41×C₄₁	—	2	4	no	—
52	C₂×#41×C₄₁	—	2	4	no	—
53	C₂×#41×C₄₁	—	2	1	no	—
54	C₂×#41×C₄₁	—	2	1	no	—
55	C₂×#41×C₄₁	D₄	1	2	yes	—
56	C₂×#41×C₄₁	C₂³	1	2	yes	—
57	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₄₁	—	2	1	no	—
60	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₄₁	—	2	1	no	—
62	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
63	#137×C₄₁	—	2	4	no	—
64	#137×C₄₁	—	2	4	no	—
65	C₂×Q₁₆×C₄₁	—	2	2	no	—
66	C₂×SD₁₆×C₄₁	—	2	2	no	—
67	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
68	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
69	C₂²⋊Q₈×C₄₁	—	2	1	no	—
70	C₂²⋊Q₈×C₄₁	—	2	1	no	—
71	C₂²⋊Q₈×C₄₁	—	2	1	no	—
72	C₂²⋊Q₈×C₄₁	—	2	1	no	—
73	C₄×Q₈×C₄₁	—	2	2	no	—
74	C₄×Q₈×C₄₁	—	2	2	no	—
75	C₄×Q₈×C₄₁	—	2	2	no	—
76	C₄×Q₈×C₄₁	—	2	2	no	—
77	C₄×D₄×C₄₁	—	2	4	no	—
78	C₄×D₄×C₄₁	—	2	4	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	2	no	—
83	C₄×D₄×C₄₁	—	2	4	no	—
84	C₄×D₄×C₄₁	—	2	4	no	—
85	#117×C₄₁	—	2	4	no	—
86	#117×C₄₁	—	2	4	no	—
87	#117×C₄₁	—	2	1	no	—
88	#117×C₄₁	—	2	1	no	—
89	#117×C₄₁	—	2	1	no	—
90	#117×C₄₁	—	2	1	no	—
91	#117×C₄₁	—	2	1	no	—
92	#117×C₄₁	—	2	1	no	—
93	#117×C₄₁	—	2	2	no	—
94	#117×C₄₁	—	2	2	no	—
95	#117×C₄₁	D₄	1	2	yes	—
96	#117×C₄₁	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
98	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
99	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
100	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
101	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
107	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
111	C₂×C₄²×C₄₁	—	2	4	no	—
112	C₂×C₄²×C₄₁	—	2	1	no	—
113	C₂×C₄²×C₄₁	D₄	1	2	yes	—
114	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
116	#107×C₄₁	—	2	2	no	—
117	#106×C₄₁	—	2	2	no	—
118	#104×C₄₁	—	2	4	no	—
119	#104×C₄₁	—	2	4	no	—
120	#103×C₄₁	—	2	2	no	—
121	#103×C₄₁	—	2	2	no	—
122	#103×C₄₁	—	2	2	no	—
123	#102×C₄₁	—	2	2	no	—
124	C₂²⋊C₈×C₄₁	—	2	1	no	—
125	C₂²⋊C₈×C₄₁	—	2	1	no	—
126	C₂²⋊C₈×C₄₁	—	2	1	no	—
127	C₂²⋊C₈×C₄₁	—	2	1	no	—
128	#95×C₄₁	—	2	1	no	—
129	#95×C₄₁	—	2	2	no	—
130	#95×C₄₁	—	2	2	no	—
131	#95×C₄₁	—	2	2	no	—
132	C₂⁴×C₄₁	—	2	1	no	—
133	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
134	#41×C₄₁	—	2	4	no	—
135	#41×C₄₁	—	2	4	no	—
136	#41×C₄₁	—	2	8	no	—
137	#41×C₄₁	—	2	4	no	—
138	#41×C₄₁	—	2	4	no	—
139	#41×C₄₁	—	2	2	no	—
140	#41×C₄₁	—	2	2	no	—
141	#41×C₄₁	#41	1	4	yes	—
142	#41×C₄₁	#41	1	4	yes	—
143	C₂×Q₈×C₄₁	—	2	4	no	—
144	C₂×Q₈×C₄₁	—	2	1	no	—
145	C₂×Q₈×C₄₁	—	2	1	no	—
146	C₂×Q₈×C₄₁	—	2	1	no	—
147	C₂×Q₈×C₄₁	—	2	2	no	—
148	C₂×Q₈×C₄₁	—	2	2	no	—
149	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
150	C₂×D₄×C₄₁	—	2	4	no	—
151	C₂×D₄×C₄₁	—	2	4	no	—
152	C₂×D₄×C₄₁	—	2	2	no	—
153	C₂×D₄×C₄₁	—	2	2	no	—
154	C₂×D₄×C₄₁	—	2	4	no	—
155	C₂×D₄×C₄₁	—	2	1	no	—
156	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₄₁	—	2	8	no	—
158	C₂²×C₄×C₄₁	—	2	1	no	—
159	C₂²×C₄×C₄₁	—	2	2	no	—
160	C₂²×C₄×C₄₁	—	2	2	no	—
161	C₂²×C₄×C₄₁	—	2	2	no	—
162	C₂²×C₄×C₄₁	—	2	2	no	—
163	C₂²×C₄×C₄₁	—	2	1	no	—
164	C₂²×C₄×C₄₁	—	2	4	no	—
165	C₂²×C₄×C₄₁	—	2	4	no	—
166	C₂²×C₄×C₄₁	—	2	1	no	—
167	C₂²×C₄×C₄₁	—	2	1	no	—
168	C₂²×C₄×C₄₁	—	2	1	no	—
169	C₂²×C₄×C₄₁	—	2	1	no	—
170	C₂²×C₄×C₄₁	—	2	1	no	—
171	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
177	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
179	Q₁₆×C₄₁	—	4	4	no	—
180	SD₁₆×C₄₁	—	4	4	no	—
181	M₁₆×C₄₁	—	2	2	no	—
182	M₁₆×C₄₁	—	2	2	no	—
183	M₁₆×C₄₁	—	2	2	no	—
184	M₁₆×C₄₁	—	2	2	no	—
185	C₂×C₈×C₄₁	—	2	2	no	—
186	C₂×C₈×C₄₁	—	2	2	no	—
187	C₄⋊C₄×C₄₁	—	2	4	no	—
188	C₄⋊C₄×C₄₁	—	2	4	no	—
189	C₄⋊C₄×C₄₁	—	2	1	no	—
190	C₄⋊C₄×C₄₁	—	2	1	no	—
191	C₄⋊C₄×C₄₁	—	2	1	no	—
192	C₄⋊C₄×C₄₁	—	2	1	no	—
193	C₄⋊C₄×C₄₁	—	2	1	no	—
194	C₄⋊C₄×C₄₁	—	2	1	no	—
195	C₄⋊C₄×C₄₁	—	2	1	no	—
196	C₄⋊C₄×C₄₁	—	2	1	no	—
197	C₄⋊C₄×C₄₁	—	4	4	no	—
198	C₄⋊C₄×C₄₁	—	4	1	no	—
199	C₄⋊C₄×C₄₁	—	4	1	no	—
200	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
201	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
202	C₂²⋊C₄×C₄₁	—	2	4	no	—
203	C₂²⋊C₄×C₄₁	—	2	4	no	—
204	C₂²⋊C₄×C₄₁	—	2	2	no	—
205	C₂²⋊C₄×C₄₁	—	2	2	no	—
206	C₂²⋊C₄×C₄₁	—	2	2	no	—
207	C₂²⋊C₄×C₄₁	—	2	2	no	—
208	C₂²⋊C₄×C₄₁	—	4	2	no	—
209	C₂²⋊C₄×C₄₁	—	4	1	no	—
210	C₂²⋊C₄×C₄₁	—	4	1	no	—
211	C₄²×C₄₁	—	2	4	no	—
212	C₄²×C₄₁	—	2	4	no	—
213	C₄²×C₄₁	—	2	2	no	—
214	C₄²×C₄₁	—	2	2	no	—
215	C₄²×C₄₁	—	2	2	no	—
216	C₄²×C₄₁	—	2	2	no	—
217	C₄²×C₄₁	—	2	2	no	—
218	C₄²×C₄₁	—	2	2	no	—
219	C₂³×C₄₁	—	2	4	no	—
220	C₂³×C₄₁	—	2	2	no	—
221	C₂³×C₄₁	—	2	1	no	—
222	C₂³×C₄₁	—	2	1	no	—
223	C₂³×C₄₁	—	4	1	no	—
224	C₂³×C₄₁	—	4	1	no	—
225	C₂³×C₄₁	—	8	1	no	—
226	C₂³×C₄₁	—	8	1	no	—
227	C₂³×C₄₁	#120	1	1	yes	characteristic
228	C₂³×C₄₁	#120	1	1	yes	characteristic
229	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
230	Q₈×C₄₁	—	2	4	no	—
231	Q₈×C₄₁	—	2	2	no	—
232	Q₈×C₄₁	—	4	2	no	—
233	Q₈×C₄₁	—	4	2	no	—
234	Q₈×C₄₁	#123	1	4	yes	—
235	D₄×C₄₁	—	2	8	no	—
236	D₄×C₄₁	—	2	4	no	—
237	D₄×C₄₁	—	2	4	no	—
238	D₄×C₄₁	—	2	4	no	—
239	D₄×C₄₁	—	2	2	no	—
240	D₄×C₄₁	#123	1	4	yes	—
241	C₂×C₄×C₄₁	—	2	4	no	—
242	C₂×C₄×C₄₁	—	2	8	no	—
243	C₂×C₄×C₄₁	—	2	2	no	—
244	C₂×C₄×C₄₁	—	2	1	no	—
245	C₂×C₄×C₄₁	—	2	1	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	4	no	—
250	C₂×C₄×C₄₁	—	2	4	no	—
251	C₂×C₄×C₄₁	—	2	2	no	—
252	C₂×C₄×C₄₁	—	2	2	no	—
253	C₂×C₄×C₄₁	—	2	2	no	—
254	C₂×C₄×C₄₁	—	2	2	no	—
255	C₂×C₄×C₄₁	—	2	2	no	—
256	C₂×C₄×C₄₁	—	2	2	no	—
257	C₂×C₄×C₄₁	—	4	1	no	—
258	C₂×C₄×C₄₁	—	4	1	no	—
259	C₂×C₄×C₄₁	—	4	2	no	—
260	C₂×C₄×C₄₁	—	4	2	no	—
261	C₂×C₄×C₄₁	—	4	1	no	—
262	C₂×C₄×C₄₁	—	4	2	no	—
263	C₂×C₄×C₄₁	—	4	1	no	—
264	C₂×C₄×C₄₁	—	4	1	no	—
265	C₂×C₄×C₄₁	—	4	1	no	—
266	C₂×C₄×C₄₁	—	4	1	no	—
267	C₂×C₄×C₄₁	—	4	1	no	—
268	C₂×C₄×C₄₁	—	4	1	no	—
269	C₂×C₄×C₄₁	—	8	1	no	—
270	C₂×C₄×C₄₁	—	8	1	no	—
271	C₂×C₄×C₄₁	—	8	4	no	—
272	C₂×C₄×C₄₁	—	8	4	no	—
273	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
274	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
275	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
278	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
279	C₈×C₄₁	—	4	2	no	—
280	C₈×C₄₁	—	4	2	no	—
281	#33001	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	2	4	no	—
287	C₂²×C₄₁	—	2	1	no	—
288	C₂²×C₄₁	—	2	1	no	—
289	C₂²×C₄₁	—	2	1	no	—
290	C₂²×C₄₁	—	2	1	no	—
291	C₂²×C₄₁	—	4	2	no	—
292	C₂²×C₄₁	—	4	2	no	—
293	C₂²×C₄₁	—	8	1	no	—
294	C₂²×C₄₁	—	8	1	no	—
295	C₂²×C₄₁	—	8	4	no	—
296	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
297	C₂²×C₄₁	#525	1	1	yes	characteristic
298	C₂²×C₄₁	#525	1	1	yes	characteristic
299	C₄×C₄₁	—	2	1	no	—
300	C₄×C₄₁	—	2	4	no	—
301	C₄×C₄₁	—	2	1	no	—
302	C₄×C₄₁	—	4	2	no	—
303	C₄×C₄₁	—	4	2	no	—
304	C₄×C₄₁	—	4	2	no	—
305	C₄×C₄₁	—	4	2	no	—
306	C₄×C₄₁	—	4	2	no	—
307	C₄×C₄₁	—	8	1	no	—
308	C₄×C₄₁	—	8	1	no	—
309	C₄×C₄₁	—	8	1	no	—
310	C₄×C₄₁	C₂×#123	1	2	yes	—
311	C₄×C₄₁	#525	1	2	yes	—
312	#3428	C₂×C₄₁	1	1	yes	characteristic
313	#3095	C₂×C₄₁	1	1	yes	characteristic, complemented
314	#3007	C₂×C₄₁	1	1	yes	characteristic
315	#2499	C₂×C₄₁	1	1	yes	characteristic, complemented
316	#1882	C₂×C₄₁	1	2	yes	complemented
317	#1882	C₂×C₄₁	1	2	yes	complemented
318	#1860	C₂×C₄₁	1	2	yes	complemented
319	#1859	C₂×C₄₁	1	2	yes	complemented
320	#1826	C₂×C₄₁	1	1	yes	characteristic, complemented
321	#1822	C₂×C₄₁	1	1	yes	characteristic, complemented
322	#1789	C₂×C₄₁	1	1	yes	characteristic
323	C₂×C₄₁	—	2	1	no	—
324	C₂×C₄₁	—	2	1	no	—
325	C₂×C₄₁	—	4	1	no	—
326	C₂×C₄₁	—	4	1	no	—
327	C₂×C₄₁	—	4	4	no	—
328	C₂×C₄₁	#2849	1	1	yes	characteristic
329	C₂×C₄₁	#3018	1	1	yes	characteristic
330	C₂×C₄₁	#3022	1	1	yes	characteristic
331	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
332	C₂×#137	C₂²×C₄₁	1	2	yes	—
333	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
334	#520	—	2	1	no	—
335	#520	—	2	1	no	—
336	#520	C₂²×C₄₁	1	2	yes	—
337	#520	C₂²×C₄₁	1	2	yes	—
338	#519	—	2	1	no	—
339	#518	—	2	1	no	—
340	#518	—	2	2	no	—
341	C₄×#41	—	2	2	no	—
342	C₄×#41	—	2	2	no	—
343	C₂×#117	—	2	2	no	—
344	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
345	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
346	#485	—	2	2	no	—
347	#484	—	2	1	no	—
348	#483	—	2	1	no	—
349	#452	—	2	2	no	—
350	#451	—	2	1	no	—
351	#450	—	2	1	no	—
352	#428	C₂²×C₄₁	1	2	yes	complemented
353	C₂×#104	C₂²×C₄₁	1	2	yes	—
354	C₂×#104	C₂²×C₄₁	1	2	yes	—
355	#419	C₂²×C₄₁	1	2	yes	complemented
356	#417	C₂²×C₄₁	1	2	yes	—
357	#407	C₂²×C₄₁	1	1	yes	characteristic
358	#407	C₂²×C₄₁	1	1	yes	characteristic
359	#397	—	2	2	no	—
360	#391	C₂²×C₄₁	1	1	yes	characteristic, complemented
361	#391	C₂²×C₄₁	1	1	yes	characteristic, complemented
362	#387	—	2	2	no	—
363	#384	C₂²×C₄₁	1	1	yes	characteristic, complemented
364	#382	C₂²×C₄₁	1	1	yes	characteristic, complemented
365	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
366	#343	C₂²×C₄₁	1	2	yes	complemented
367	#343	C₂²×C₄₁	1	2	yes	complemented
368	#339	C₂²×C₄₁	1	2	yes	complemented
369	#339	C₂²×C₄₁	1	2	yes	complemented
370	C₄₁	#33001	1	1	yes	characteristic, direct product factor, Sylow
371	C₂×#41	—	2	4	no	—
372	C₂×#41	—	2	4	no	—
373	C₂×#41	—	2	1	no	—
374	C₂×#41	—	2	1	no	—
375	C₂×#41	D₄×C₄₁	1	2	yes	—
376	C₂×#41	C₂³×C₄₁	1	2	yes	—
377	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
378	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
379	C₂²×D₄	—	2	1	no	—
380	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
381	C₂³×C₄	—	2	1	no	—
382	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
383	#137	—	2	4	no	—
384	#137	—	2	4	no	—
385	C₂×Q₁₆	—	2	2	no	—
386	C₂×SD₁₆	—	2	2	no	—
387	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
388	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
389	C₂²⋊Q₈	—	2	1	no	—
390	C₂²⋊Q₈	—	2	1	no	—
391	C₂²⋊Q₈	—	2	1	no	—
392	C₂²⋊Q₈	—	2	1	no	—
393	C₄×Q₈	—	2	2	no	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×Q₈	—	2	2	no	—
396	C₄×Q₈	—	2	2	no	—
397	C₄×D₄	—	2	4	no	—
398	C₄×D₄	—	2	4	no	—
399	C₄×D₄	—	2	2	no	—
400	C₄×D₄	—	2	2	no	—
401	C₄×D₄	—	2	2	no	—
402	C₄×D₄	—	2	2	no	—
403	C₄×D₄	—	2	4	no	—
404	C₄×D₄	—	2	4	no	—
405	#117	—	2	4	no	—
406	#117	—	2	4	no	—
407	#117	—	2	1	no	—
408	#117	—	2	1	no	—
409	#117	—	2	1	no	—
410	#117	—	2	1	no	—
411	#117	—	2	1	no	—
412	#117	—	2	1	no	—
413	#117	—	2	2	no	—
414	#117	—	2	2	no	—
415	#117	D₄×C₄₁	1	2	yes	—
416	#117	C₂³×C₄₁	1	2	yes	—
417	C₂×C₄⋊C₄	—	2	2	no	—
418	C₂×C₄⋊C₄	—	2	2	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	2	2	no	—
421	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
422	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	—	2	4	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
431	C₂×C₄²	—	2	4	no	—
432	C₂×C₄²	—	2	1	no	—
433	C₂×C₄²	D₄×C₄₁	1	2	yes	—
434	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
436	#107	—	2	2	no	—
437	#106	—	2	2	no	—
438	#104	—	2	4	no	—
439	#104	—	2	4	no	—
440	#103	—	2	2	no	—
441	#103	—	2	2	no	—
442	#103	—	2	2	no	—
443	#102	—	2	2	no	—
444	C₂²⋊C₈	—	2	1	no	—
445	C₂²⋊C₈	—	2	1	no	—
446	C₂²⋊C₈	—	2	1	no	—
447	C₂²⋊C₈	—	2	1	no	—
448	#95	—	2	1	no	—
449	#95	—	2	2	no	—
450	#95	—	2	2	no	—
451	#95	—	2	2	no	—
452	C₂⁴	—	2	1	no	—
453	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
454	#41	—	2	4	no	—
455	#41	—	2	4	no	—
456	#41	—	2	8	no	—
457	#41	—	2	4	no	—
458	#41	—	2	4	no	—
459	#41	—	2	2	no	—
460	#41	—	2	2	no	—
461	#41	#41×C₄₁	1	4	yes	—
462	#41	#41×C₄₁	1	4	yes	—
463	C₂×Q₈	—	2	4	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	2	no	—
468	C₂×Q₈	—	2	2	no	—
469	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
470	C₂×D₄	—	2	4	no	—
471	C₂×D₄	—	2	4	no	—
472	C₂×D₄	—	2	2	no	—
473	C₂×D₄	—	2	2	no	—
474	C₂×D₄	—	2	4	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
477	C₂²×C₄	—	2	8	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
492	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
493	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
495	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
496	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
497	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
498	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
499	Q₁₆	—	4	4	no	—
500	SD₁₆	—	4	4	no	—
501	M₁₆	—	2	2	no	—
502	M₁₆	—	2	2	no	—
503	M₁₆	—	2	2	no	—
504	M₁₆	—	2	2	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	2	2	no	—
507	C₄⋊C₄	—	2	4	no	—
508	C₄⋊C₄	—	2	4	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	4	4	no	—
518	C₄⋊C₄	—	4	1	no	—
519	C₄⋊C₄	—	4	1	no	—
520	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
521	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
522	C₂²⋊C₄	—	2	4	no	—
523	C₂²⋊C₄	—	2	4	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	2	2	no	—
528	C₂²⋊C₄	—	4	2	no	—
529	C₂²⋊C₄	—	4	1	no	—
530	C₂²⋊C₄	—	4	1	no	—
531	C₄²	—	2	4	no	—
532	C₄²	—	2	4	no	—
533	C₄²	—	2	2	no	—
534	C₄²	—	2	2	no	—
535	C₄²	—	2	2	no	—
536	C₄²	—	2	2	no	—
537	C₄²	—	2	2	no	—
538	C₄²	—	2	2	no	—
539	C₂³	—	2	4	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	1	no	—
542	C₂³	—	2	1	no	—
543	C₂³	—	4	1	no	—
544	C₂³	—	4	1	no	—
545	C₂³	—	8	1	no	—
546	C₂³	—	8	1	no	—
547	C₂³	#120×C₄₁	1	1	yes	characteristic
548	C₂³	#120×C₄₁	1	1	yes	characteristic
549	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
550	Q₈	—	2	4	no	—
551	Q₈	—	2	2	no	—
552	Q₈	—	4	2	no	—
553	Q₈	—	4	2	no	—
554	Q₈	#123×C₄₁	1	4	yes	—
555	D₄	—	2	8	no	—
556	D₄	—	2	4	no	—
557	D₄	—	2	4	no	—
558	D₄	—	2	4	no	—
559	D₄	—	2	2	no	—
560	D₄	#123×C₄₁	1	4	yes	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	8	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	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	4	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	8	1	no	—
590	C₂×C₄	—	8	1	no	—
591	C₂×C₄	—	8	4	no	—
592	C₂×C₄	—	8	4	no	—
593	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
594	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
595	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
596	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
597	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
598	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
599	C₈	—	4	2	no	—
600	C₈	—	4	2	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	4	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	8	1	no	—
613	C₂²	—	8	1	no	—
614	C₂²	—	8	4	no	—
615	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
616	C₂²	C₄₁×#525	1	1	yes	characteristic
617	C₂²	C₄₁×#525	1	1	yes	characteristic
618	C₄	—	2	1	no	—
619	C₄	—	2	4	no	—
620	C₄	—	2	1	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	2	no	—
623	C₄	—	4	2	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	2	no	—
626	C₄	—	8	1	no	—
627	C₄	—	8	1	no	—
628	C₄	—	8	1	no	—
629	C₄	C₂×#123×C₄₁	1	2	yes	—
630	C₄	C₄₁×#525	1	2	yes	—
631	C₂	—	2	1	no	—
632	C₂	—	2	1	no	—
633	C₂	—	4	1	no	—
634	C₂	—	4	1	no	—
635	C₂	—	4	4	no	—
636	C₂	C₄₁×#2849	1	1	yes	characteristic
637	C₂	C₄₁×#3018	1	1	yes	characteristic
638	C₂	C₄₁×#3022	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₄₁×#3095	C₂	semidirect
4. C₄₁×#2499	C₂	semidirect
5. C₄₁×#1882	C₂	semidirect
6. C₄₁×#1882	C₂	semidirect
7. C₄₁×#1860	C₂	semidirect
8. C₄₁×#1859	C₂	semidirect
9. C₄₁×#1826	C₂	semidirect
10. C₄₁×#1822	C₂	semidirect
33. C₄₁×#428	C₂²	semidirect
36. C₄₁×#419	C₂²	semidirect
41. C₄₁×#391	C₂²	semidirect
42. C₄₁×#391	C₂²	semidirect
44. C₄₁×#384	C₂²	semidirect
45. C₄₁×#382	C₂²	semidirect
47. C₄₁×#343	C₂²	semidirect
48. C₄₁×#343	C₂²	semidirect
49. C₄₁×#339	C₂²	semidirect
50. C₄₁×#339	C₂²	semidirect
281. #33001	C₄₁	direct (N × H)
313. #3095	C₂×C₄₁	semidirect
315. #2499	C₂×C₄₁	semidirect
316. #1882	C₂×C₄₁	semidirect
317. #1882	C₂×C₄₁	semidirect
318. #1860	C₂×C₄₁	semidirect
319. #1859	C₂×C₄₁	semidirect
320. #1826	C₂×C₄₁	semidirect
321. #1822	C₂×C₄₁	semidirect
352. #428	C₂²×C₄₁	semidirect
355. #419	C₂²×C₄₁	semidirect
360. #391	C₂²×C₄₁	semidirect
361. #391	C₂²×C₄₁	semidirect
363. #384	C₂²×C₄₁	semidirect
364. #382	C₂²×C₄₁	semidirect
366. #343	C₂²×C₄₁	semidirect
367. #343	C₂²×C₄₁	semidirect
368. #339	C₂²×C₄₁	semidirect
369. #339	C₂²×C₄₁	semidirect
370. C₄₁	#33001	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#3428	2
C₄₁×#3095	2
C₄₁×#3007	2
C₄₁×#2499	2
C₄₁×#1882	2
C₄₁×#1860	2
C₄₁×#1859	2
C₄₁×#1826	2
C₄₁×#1822	2
C₄₁×#1789	2
#33001	41

Subgroups — C41×#33001 #23809202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33001 #23809202