Subgroups — C₄₁×#17600 #23793801

Order 10496.

982 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3520	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2974	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2319	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1520	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1516	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1513	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1511	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1509	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1506	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1503	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1500	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#556	C₄	1	1	yes	characteristic, complemented
13	C₄₁×#554	—	2	1	no	—
14	C₄₁×#552	C₄	1	2	yes	complemented
15	C₄₁×#551	—	2	2	no	—
16	D₄×Q₈×C₄₁	C₄	1	1	yes	characteristic, complemented
17	C₄₁×#548	C₄	1	2	yes	complemented
18	C₄₁×#547	C₄	1	1	yes	characteristic, complemented
19	C₄₁×#547	C₄	1	1	yes	characteristic, complemented
20	C₄₁×#546	—	2	1	no	—
21	C₄₁×#542	—	2	1	no	—
22	C₄₁×#539	—	2	2	no	—
23	C₄₁×#533	C₂²	1	1	yes	characteristic
24	C₄₁×#529	C₂²	1	1	yes	characteristic
25	C₄₁×#525	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
27	C₄₁×#520	—	2	1	no	—
28	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
29	C₄₁×#436	—	2	1	no	—
30	C₄₁×#435	—	2	2	no	—
31	C₈×D₄×C₄₁	—	2	1	no	—
32	C₄₁×#432	C₂²	1	1	yes	characteristic
33	C₄₁×#431	C₂²	1	1	yes	characteristic
34	C₄₁×#407	C₂²	1	2	yes	—
35	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
36	C₄₁×#390	—	2	1	no	—
37	C₄₁×#389	—	2	1	no	—
38	C₄₁×#388	—	2	2	no	—
39	C₄₁×#381	C₂²	1	2	yes	—
40	C₄₁×#380	C₂²	1	2	yes	—
41	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
42	C₄₁×#376	C₂²	1	1	yes	characteristic
43	C₄₁×#328	C₂²	1	1	yes	characteristic
44	C₄₁×#328	C₂²	1	1	yes	characteristic
45	C₄₁×#328	C₂²	1	2	yes	—
46	C₄₁×#328	C₂²	1	2	yes	—
47	C₄₁×#328	C₂²	1	2	yes	—
48	C₄₁×#328	C₂²	1	2	yes	—
49	C₄₁×#328	C₂²	1	2	yes	—
50	C₄₁×#327	C₂²	1	1	yes	characteristic
51	C₄₁×#327	C₂²	1	1	yes	characteristic
52	C₄₁×#327	C₂²	1	2	yes	—
53	C₂×#41×C₄₁	—	2	1	no	—
54	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
55	C₂²×Q₈×C₄₁	C₂×C₄	1	2	yes	—
56	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
58	C₂×M₁₆×C₄₁	—	2	2	no	—
59	C₂²×C₈×C₄₁	—	2	2	no	—
60	C₄⋊Q₈×C₄₁	—	2	1	no	—
61	C₄⋊Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
62	C₄⋊Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
63	#126×C₄₁	—	2	2	no	—
64	#126×C₄₁	—	2	2	no	—
65	#126×C₄₁	—	2	1	no	—
66	#125×C₄₁	—	2	2	no	—
67	#125×C₄₁	—	2	1	no	—
68	#125×C₄₁	C₂×C₄	1	1	yes	characteristic
69	#124×C₄₁	—	2	1	no	—
70	#124×C₄₁	—	2	2	no	—
71	#124×C₄₁	C₂×C₄	1	1	yes	characteristic
72	#123×C₄₁	—	2	2	no	—
73	#123×C₄₁	—	2	2	no	—
74	#123×C₄₁	—	2	1	no	—
75	#123×C₄₁	—	2	2	no	—
76	#123×C₄₁	—	2	2	no	—
77	C₂²⋊Q₈×C₄₁	—	2	2	no	—
78	C₂²⋊Q₈×C₄₁	—	2	2	no	—
79	C₂²⋊Q₈×C₄₁	—	2	1	no	—
80	C₂²⋊Q₈×C₄₁	—	2	2	no	—
81	C₂²⋊Q₈×C₄₁	—	2	1	no	—
82	C₂²⋊Q₈×C₄₁	—	2	2	no	—
83	C₂²⋊Q₈×C₄₁	C₂×C₄	1	2	yes	—
84	C₂²⋊Q₈×C₄₁	C₂×C₄	1	2	yes	—
85	C₂²⋊Q₈×C₄₁	C₂×C₄	1	2	yes	—
86	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
87	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
88	#121×C₄₁	—	2	2	no	—
89	#121×C₄₁	—	2	1	no	—
90	#121×C₄₁	C₂×C₄	1	2	yes	—
91	#121×C₄₁	C₂³	1	1	yes	characteristic
92	#120×C₄₁	—	2	2	no	—
93	C₄×Q₈×C₄₁	—	2	1	no	—
94	C₄×Q₈×C₄₁	—	2	1	no	—
95	C₄×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
96	C₄×Q₈×C₄₁	C₂×C₄	1	2	yes	—
97	C₄×D₄×C₄₁	—	2	1	no	—
98	C₄×D₄×C₄₁	—	2	2	no	—
99	C₄×D₄×C₄₁	—	2	2	no	—
100	C₄×D₄×C₄₁	—	2	1	no	—
101	C₄×D₄×C₄₁	—	2	2	no	—
102	C₄×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
103	C₄×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
104	C₄×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
105	C₄×D₄×C₄₁	C₂×C₄	1	2	yes	—
106	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
107	C₄×D₄×C₄₁	D₄	1	2	yes	—
108	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
109	#117×C₄₁	—	2	1	no	—
110	#117×C₄₁	—	2	2	no	—
111	#117×C₄₁	—	2	1	no	—
112	#117×C₄₁	C₂×C₄	1	2	yes	—
113	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
114	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
115	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
116	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
117	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
118	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
120	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
121	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
122	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
123	C₂×C₄²×C₄₁	—	2	1	no	—
124	C₂×C₄²×C₄₁	—	2	1	no	—
125	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
126	C₄⋊C₈×C₄₁	—	2	1	no	—
127	C₄⋊C₈×C₄₁	—	2	1	no	—
128	C₂²⋊C₈×C₄₁	—	2	2	no	—
129	C₂²⋊C₈×C₄₁	—	2	2	no	—
130	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
131	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
132	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
133	#97×C₄₁	—	2	1	no	—
134	C₄×C₈×C₄₁	—	2	1	no	—
135	#95×C₄₁	—	2	1	no	—
136	#95×C₄₁	—	2	2	no	—
137	#95×C₄₁	C₂³	1	1	yes	characteristic
138	#95×C₄₁	C₂³	1	1	yes	characteristic
139	#95×C₄₁	C₂³	1	2	yes	—
140	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
141	#41×C₄₁	—	4	4	no	—
142	#41×C₄₁	—	8	2	no	—
143	C₂×Q₈×C₄₁	—	2	1	no	—
144	C₂×Q₈×C₄₁	—	2	2	no	—
145	C₂×Q₈×C₄₁	—	8	2	no	—
146	C₂×Q₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
147	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
148	C₂×D₄×C₄₁	—	2	2	no	—
149	C₂×D₄×C₄₁	—	2	1	no	—
150	C₂×D₄×C₄₁	—	2	2	no	—
151	C₂×D₄×C₄₁	—	4	2	no	—
152	C₂×D₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
153	C₂×D₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
154	C₂×D₄×C₄₁	C₂²⋊C₄	1	2	yes	—
155	C₂×D₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₁	—	2	2	no	—
157	C₂²×C₄×C₄₁	—	2	2	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	—	2	1	no	—
162	C₂²×C₄×C₄₁	—	2	2	no	—
163	C₂²×C₄×C₄₁	—	8	2	no	—
164	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
165	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
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	2	yes	—
169	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
172	M₁₆×C₄₁	—	8	2	no	—
173	C₂×C₈×C₄₁	—	2	1	no	—
174	C₂×C₈×C₄₁	—	2	1	no	—
175	C₂×C₈×C₄₁	—	2	2	no	—
176	C₂×C₈×C₄₁	—	8	2	no	—
177	C₄⋊C₄×C₄₁	—	2	2	no	—
178	C₄⋊C₄×C₄₁	—	2	1	no	—
179	C₄⋊C₄×C₄₁	—	2	2	no	—
180	C₄⋊C₄×C₄₁	—	2	2	no	—
181	C₄⋊C₄×C₄₁	—	2	1	no	—
182	C₄⋊C₄×C₄₁	—	2	1	no	—
183	C₄⋊C₄×C₄₁	—	2	1	no	—
184	C₄⋊C₄×C₄₁	—	2	2	no	—
185	C₄⋊C₄×C₄₁	—	2	1	no	—
186	C₄⋊C₄×C₄₁	—	2	2	no	—
187	C₄⋊C₄×C₄₁	—	2	1	no	—
188	C₄⋊C₄×C₄₁	—	2	1	no	—
189	C₄⋊C₄×C₄₁	—	2	2	no	—
190	C₄⋊C₄×C₄₁	—	4	2	no	—
191	C₄⋊C₄×C₄₁	—	8	2	no	—
192	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
193	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
194	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
195	C₄⋊C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
196	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
197	C₄⋊C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
198	C₂²⋊C₄×C₄₁	—	2	2	no	—
199	C₂²⋊C₄×C₄₁	—	2	2	no	—
200	C₂²⋊C₄×C₄₁	—	2	2	no	—
201	C₂²⋊C₄×C₄₁	—	2	2	no	—
202	C₂²⋊C₄×C₄₁	—	2	1	no	—
203	C₂²⋊C₄×C₄₁	—	2	2	no	—
204	C₂²⋊C₄×C₄₁	—	2	1	no	—
205	C₂²⋊C₄×C₄₁	—	2	1	no	—
206	C₂²⋊C₄×C₄₁	—	2	2	no	—
207	C₂²⋊C₄×C₄₁	—	2	1	no	—
208	C₂²⋊C₄×C₄₁	—	2	1	no	—
209	C₂²⋊C₄×C₄₁	—	8	2	no	—
210	C₂²⋊C₄×C₄₁	—	8	2	no	—
211	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
212	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
213	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
214	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
215	C₄²×C₄₁	—	2	2	no	—
216	C₄²×C₄₁	—	2	2	no	—
217	C₄²×C₄₁	—	2	1	no	—
218	C₄²×C₄₁	—	4	2	no	—
219	C₄²×C₄₁	—	8	1	no	—
220	C₄²×C₄₁	C₂²×C₄	1	1	yes	characteristic
221	C₄²×C₄₁	C₂²×C₄	1	1	yes	characteristic
222	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
223	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
224	C₂³×C₄₁	—	2	2	no	—
225	C₂³×C₄₁	—	2	2	no	—
226	C₂³×C₄₁	—	2	1	no	—
227	C₂³×C₄₁	—	4	2	no	—
228	C₂³×C₄₁	—	4	2	no	—
229	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
230	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
231	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
232	Q₈×C₄₁	—	4	1	no	—
233	Q₈×C₄₁	—	4	2	no	—
234	Q₈×C₄₁	—	4	2	no	—
235	Q₈×C₄₁	—	8	2	no	—
236	D₄×C₄₁	—	2	2	no	—
237	D₄×C₄₁	—	2	2	no	—
238	D₄×C₄₁	—	4	2	no	—
239	D₄×C₄₁	—	4	1	no	—
240	D₄×C₄₁	—	4	4	no	—
241	D₄×C₄₁	—	4	1	no	—
242	D₄×C₄₁	—	4	1	no	—
243	D₄×C₄₁	—	8	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	1	no	—
248	C₂×C₄×C₄₁	—	2	2	no	—
249	C₂×C₄×C₄₁	—	2	1	no	—
250	C₂×C₄×C₄₁	—	2	2	no	—
251	C₂×C₄×C₄₁	—	2	1	no	—
252	C₂×C₄×C₄₁	—	4	2	no	—
253	C₂×C₄×C₄₁	—	4	2	no	—
254	C₂×C₄×C₄₁	—	4	2	no	—
255	C₂×C₄×C₄₁	—	4	1	no	—
256	C₂×C₄×C₄₁	—	4	2	no	—
257	C₂×C₄×C₄₁	—	4	2	no	—
258	C₂×C₄×C₄₁	—	4	4	no	—
259	C₂×C₄×C₄₁	—	4	2	no	—
260	C₂×C₄×C₄₁	—	4	1	no	—
261	C₂×C₄×C₄₁	—	4	1	no	—
262	C₂×C₄×C₄₁	—	4	1	no	—
263	C₂×C₄×C₄₁	—	4	2	no	—
264	C₂×C₄×C₄₁	—	4	2	no	—
265	C₂×C₄×C₄₁	—	4	1	no	—
266	C₂×C₄×C₄₁	—	4	2	no	—
267	C₂×C₄×C₄₁	—	4	1	no	—
268	C₂×C₄×C₄₁	—	4	1	no	—
269	C₂×C₄×C₄₁	—	8	2	no	—
270	C₂×C₄×C₄₁	—	8	2	no	—
271	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
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	2	yes	—
276	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
277	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
278	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
279	C₈×C₄₁	—	4	1	no	—
280	C₈×C₄₁	—	4	2	no	—
281	C₈×C₄₁	—	4	1	no	—
282	#17600	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
283	C₂²×C₄₁	—	2	1	no	—
284	C₂²×C₄₁	—	2	1	no	—
285	C₂²×C₄₁	—	2	2	no	—
286	C₂²×C₄₁	—	2	2	no	—
287	C₂²×C₄₁	—	2	2	no	—
288	C₂²×C₄₁	—	2	2	no	—
289	C₂²×C₄₁	—	2	2	no	—
290	C₂²×C₄₁	—	2	2	no	—
291	C₂²×C₄₁	—	4	1	no	—
292	C₂²×C₄₁	—	4	1	no	—
293	C₂²×C₄₁	—	4	1	no	—
294	C₂²×C₄₁	—	8	2	no	—
295	C₂²×C₄₁	—	8	2	no	—
296	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
297	C₂²×C₄₁	#577	1	1	yes	characteristic
298	C₂²×C₄₁	#578	1	1	yes	characteristic
299	C₄×C₄₁	—	2	1	no	—
300	C₄×C₄₁	—	2	1	no	—
301	C₄×C₄₁	—	2	2	no	—
302	C₄×C₄₁	—	2	2	no	—
303	C₄×C₄₁	—	2	1	no	—
304	C₄×C₄₁	—	2	1	no	—
305	C₄×C₄₁	—	2	1	no	—
306	C₄×C₄₁	—	4	2	no	—
307	C₄×C₄₁	—	4	1	no	—
308	C₄×C₄₁	—	4	1	no	—
309	C₄×C₄₁	—	4	1	no	—
310	C₄×C₄₁	—	4	2	no	—
311	C₄×C₄₁	—	8	1	no	—
312	C₄×C₄₁	—	8	2	no	—
313	C₄×C₄₁	—	8	1	no	—
314	C₄×C₄₁	#421	1	2	yes	—
315	#3520	C₂×C₄₁	1	1	yes	characteristic
316	#2974	C₂×C₄₁	1	1	yes	characteristic, complemented
317	#2319	C₂×C₄₁	1	1	yes	characteristic, complemented
318	#1520	C₂×C₄₁	1	2	yes	complemented
319	#1516	C₂×C₄₁	1	2	yes	complemented
320	#1513	C₂×C₄₁	1	2	yes	complemented
321	#1511	C₂×C₄₁	1	2	yes	complemented
322	#1509	C₂×C₄₁	1	1	yes	characteristic, complemented
323	#1506	C₂×C₄₁	1	1	yes	characteristic, complemented
324	#1503	C₂×C₄₁	1	1	yes	characteristic, complemented
325	#1500	C₂×C₄₁	1	1	yes	characteristic, complemented
326	C₂×C₄₁	—	2	1	no	—
327	C₂×C₄₁	—	2	1	no	—
328	C₂×C₄₁	—	4	2	no	—
329	C₂×C₄₁	—	4	2	no	—
330	C₂×C₄₁	—	8	1	no	—
331	C₂×C₄₁	#2883	1	1	yes	characteristic
332	C₂×C₄₁	#2898	1	1	yes	characteristic
333	C₂×C₄₁	C₂×#421	1	1	yes	characteristic
334	#556	C₄×C₄₁	1	1	yes	characteristic, complemented
335	#554	—	2	1	no	—
336	#552	C₄×C₄₁	1	2	yes	complemented
337	#551	—	2	2	no	—
338	D₄×Q₈	C₄×C₄₁	1	1	yes	characteristic, complemented
339	#548	C₄×C₄₁	1	2	yes	complemented
340	#547	C₄×C₄₁	1	1	yes	characteristic, complemented
341	#547	C₄×C₄₁	1	1	yes	characteristic, complemented
342	#546	—	2	1	no	—
343	#542	—	2	1	no	—
344	#539	—	2	2	no	—
345	#533	C₂²×C₄₁	1	1	yes	characteristic
346	#529	C₂²×C₄₁	1	1	yes	characteristic
347	#525	C₂²×C₄₁	1	2	yes	—
348	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
349	#520	—	2	1	no	—
350	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
351	#436	—	2	1	no	—
352	#435	—	2	2	no	—
353	C₈×D₄	—	2	1	no	—
354	#432	C₂²×C₄₁	1	1	yes	characteristic
355	#431	C₂²×C₄₁	1	1	yes	characteristic
356	#407	C₂²×C₄₁	1	2	yes	—
357	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
358	#390	—	2	1	no	—
359	#389	—	2	1	no	—
360	#388	—	2	2	no	—
361	#381	C₂²×C₄₁	1	2	yes	—
362	#380	C₂²×C₄₁	1	2	yes	—
363	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
364	#376	C₂²×C₄₁	1	1	yes	characteristic
365	#328	C₂²×C₄₁	1	1	yes	characteristic
366	#328	C₂²×C₄₁	1	1	yes	characteristic
367	#328	C₂²×C₄₁	1	2	yes	—
368	#328	C₂²×C₄₁	1	2	yes	—
369	#328	C₂²×C₄₁	1	2	yes	—
370	#328	C₂²×C₄₁	1	2	yes	—
371	#328	C₂²×C₄₁	1	2	yes	—
372	#327	C₂²×C₄₁	1	1	yes	characteristic
373	#327	C₂²×C₄₁	1	1	yes	characteristic
374	#327	C₂²×C₄₁	1	2	yes	—
375	C₄₁	#17600	1	1	yes	characteristic, direct product factor, Sylow
376	C₂×#41	—	2	1	no	—
377	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
378	C₂²×Q₈	C₂×C₄×C₄₁	1	2	yes	—
379	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
380	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
381	C₂×M₁₆	—	2	2	no	—
382	C₂²×C₈	—	2	2	no	—
383	C₄⋊Q₈	—	2	1	no	—
384	C₄⋊Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
385	C₄⋊Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
386	#126	—	2	2	no	—
387	#126	—	2	2	no	—
388	#126	—	2	1	no	—
389	#125	—	2	2	no	—
390	#125	—	2	1	no	—
391	#125	C₂×C₄×C₄₁	1	1	yes	characteristic
392	#124	—	2	1	no	—
393	#124	—	2	2	no	—
394	#124	C₂×C₄×C₄₁	1	1	yes	characteristic
395	#123	—	2	2	no	—
396	#123	—	2	2	no	—
397	#123	—	2	1	no	—
398	#123	—	2	2	no	—
399	#123	—	2	2	no	—
400	C₂²⋊Q₈	—	2	2	no	—
401	C₂²⋊Q₈	—	2	2	no	—
402	C₂²⋊Q₈	—	2	1	no	—
403	C₂²⋊Q₈	—	2	2	no	—
404	C₂²⋊Q₈	—	2	1	no	—
405	C₂²⋊Q₈	—	2	2	no	—
406	C₂²⋊Q₈	C₂×C₄×C₄₁	1	2	yes	—
407	C₂²⋊Q₈	C₂×C₄×C₄₁	1	2	yes	—
408	C₂²⋊Q₈	C₂×C₄×C₄₁	1	2	yes	—
409	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
410	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
411	#121	—	2	2	no	—
412	#121	—	2	1	no	—
413	#121	C₂×C₄×C₄₁	1	2	yes	—
414	#121	C₂³×C₄₁	1	1	yes	characteristic
415	#120	—	2	2	no	—
416	C₄×Q₈	—	2	1	no	—
417	C₄×Q₈	—	2	1	no	—
418	C₄×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
419	C₄×Q₈	C₂×C₄×C₄₁	1	2	yes	—
420	C₄×D₄	—	2	1	no	—
421	C₄×D₄	—	2	2	no	—
422	C₄×D₄	—	2	2	no	—
423	C₄×D₄	—	2	1	no	—
424	C₄×D₄	—	2	2	no	—
425	C₄×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
426	C₄×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
427	C₄×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
428	C₄×D₄	C₂×C₄×C₄₁	1	2	yes	—
429	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
430	C₄×D₄	D₄×C₄₁	1	2	yes	—
431	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
432	#117	—	2	1	no	—
433	#117	—	2	2	no	—
434	#117	—	2	1	no	—
435	#117	C₂×C₄×C₄₁	1	2	yes	—
436	C₂×C₄⋊C₄	—	2	2	no	—
437	C₂×C₄⋊C₄	—	2	1	no	—
438	C₂×C₄⋊C₄	—	2	1	no	—
439	C₂×C₄⋊C₄	—	2	2	no	—
440	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
441	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
442	C₂×C₂²⋊C₄	—	2	2	no	—
443	C₂×C₂²⋊C₄	—	2	2	no	—
444	C₂×C₂²⋊C₄	—	2	2	no	—
445	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
446	C₂×C₄²	—	2	1	no	—
447	C₂×C₄²	—	2	1	no	—
448	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
449	C₄⋊C₈	—	2	1	no	—
450	C₄⋊C₈	—	2	1	no	—
451	C₂²⋊C₈	—	2	2	no	—
452	C₂²⋊C₈	—	2	2	no	—
453	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
454	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
455	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
456	#97	—	2	1	no	—
457	C₄×C₈	—	2	1	no	—
458	#95	—	2	1	no	—
459	#95	—	2	2	no	—
460	#95	C₂³×C₄₁	1	1	yes	characteristic
461	#95	C₂³×C₄₁	1	1	yes	characteristic
462	#95	C₂³×C₄₁	1	2	yes	—
463	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
464	#41	—	4	4	no	—
465	#41	—	8	2	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	2	no	—
468	C₂×Q₈	—	8	2	no	—
469	C₂×Q₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
470	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	2	no	—
474	C₂×D₄	—	4	2	no	—
475	C₂×D₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
476	C₂×D₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
477	C₂×D₄	C₂²⋊C₄×C₄₁	1	2	yes	—
478	C₂×D₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	8	2	no	—
487	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
488	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
489	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
490	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
491	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
492	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
493	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
494	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
495	M₁₆	—	8	2	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	8	2	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	4	2	no	—
514	C₄⋊C₄	—	8	2	no	—
515	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
516	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
517	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
519	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
520	C₄⋊C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	2	1	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	2	1	no	—
528	C₂²⋊C₄	—	2	1	no	—
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	1	no	—
531	C₂²⋊C₄	—	2	1	no	—
532	C₂²⋊C₄	—	8	2	no	—
533	C₂²⋊C₄	—	8	2	no	—
534	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
535	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
536	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
537	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
538	C₄²	—	2	2	no	—
539	C₄²	—	2	2	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	4	2	no	—
542	C₄²	—	8	1	no	—
543	C₄²	C₂²×C₄×C₄₁	1	1	yes	characteristic
544	C₄²	C₂²×C₄×C₄₁	1	1	yes	characteristic
545	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
546	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
547	C₂³	—	2	2	no	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	1	no	—
550	C₂³	—	4	2	no	—
551	C₂³	—	4	2	no	—
552	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
553	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
554	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
555	Q₈	—	4	1	no	—
556	Q₈	—	4	2	no	—
557	Q₈	—	4	2	no	—
558	Q₈	—	8	2	no	—
559	D₄	—	2	2	no	—
560	D₄	—	2	2	no	—
561	D₄	—	4	2	no	—
562	D₄	—	4	1	no	—
563	D₄	—	4	4	no	—
564	D₄	—	4	1	no	—
565	D₄	—	4	1	no	—
566	D₄	—	8	2	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	4	2	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	4	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	2	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	8	2	no	—
593	C₂×C₄	—	8	2	no	—
594	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
595	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
596	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
597	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
598	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
599	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
600	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
601	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
602	C₈	—	4	1	no	—
603	C₈	—	4	2	no	—
604	C₈	—	4	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	4	1	no	—
614	C₂²	—	4	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	—	8	2	no	—
617	C₂²	—	8	2	no	—
618	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
619	C₂²	C₄₁×#577	1	1	yes	characteristic
620	C₂²	C₄₁×#578	1	1	yes	characteristic
621	C₄	—	2	1	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	2	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	1	no	—
632	C₄	—	4	2	no	—
633	C₄	—	8	1	no	—
634	C₄	—	8	2	no	—
635	C₄	—	8	1	no	—
636	C₄	C₄₁×#421	1	2	yes	—
637	C₂	—	2	1	no	—
638	C₂	—	2	1	no	—
639	C₂	—	4	2	no	—
640	C₂	—	4	2	no	—
641	C₂	—	8	1	no	—
642	C₂	C₄₁×#2883	1	1	yes	characteristic
643	C₂	C₄₁×#2898	1	1	yes	characteristic
644	C₂	C₂×C₄₁×#421	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₄₁×#3520	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄×D₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2974	C₂	semidirect
3. C₄₁×#2319	C₂	semidirect
4. C₄₁×#1520	C₂	semidirect
5. C₄₁×#1516	C₂	semidirect
6. C₄₁×#1513	C₂	semidirect
7. C₄₁×#1511	C₂	semidirect
8. C₄₁×#1509	C₂	semidirect
9. C₄₁×#1506	C₂	semidirect
10. C₄₁×#1503	C₂	semidirect
11. C₄₁×#1500	C₂	semidirect
12. C₄₁×#556	C₄	semidirect
14. C₄₁×#552	C₄	semidirect
16. D₄×Q₈×C₄₁	C₄	semidirect
17. C₄₁×#548	C₄	semidirect
18. C₄₁×#547	C₄	semidirect
19. C₄₁×#547	C₄	semidirect
282. #17600	C₄₁	direct (N × H)
316. #2974	C₂×C₄₁	semidirect
317. #2319	C₂×C₄₁	semidirect
318. #1520	C₂×C₄₁	semidirect
319. #1516	C₂×C₄₁	semidirect
320. #1513	C₂×C₄₁	semidirect
321. #1511	C₂×C₄₁	semidirect
322. #1509	C₂×C₄₁	semidirect
323. #1506	C₂×C₄₁	semidirect
324. #1503	C₂×C₄₁	semidirect
325. #1500	C₂×C₄₁	semidirect
334. #556	C₄×C₄₁	semidirect
336. #552	C₄×C₄₁	semidirect
338. D₄×Q₈	C₄×C₄₁	semidirect
339. #548	C₄×C₄₁	semidirect
340. #547	C₄×C₄₁	semidirect
341. #547	C₄×C₄₁	semidirect
375. C₄₁	#17600	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×#3520	2
C₄₁×#2974	2
C₄₁×#2319	2
C₄₁×#1520	2
C₄₁×#1516	2
C₄₁×#1513	2
C₄₁×#1511	2
C₄₁×#1509	2
C₄₁×#1506	2
C₄₁×#1503	2
C₄₁×#1500	2
#17600	41

Subgroups — C41×#17600 #23793801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#17600 #23793801