Subgroups — C₄₁×#18687 #23794888

Order 10496.

1010 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3253	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3147	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1632	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1631	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1622	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1621	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1560	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1493	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1492	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₄₁	—	2	2	no	—
13	C₄₁×#562	—	2	2	no	—
14	C₄₁×#554	—	2	1	no	—
15	C₄₁×#554	C₂²	1	2	yes	—
16	C₄₁×#550	—	2	1	no	—
17	C₄₁×#550	C₂²	1	2	yes	—
18	C₄₁×#547	—	2	1	no	—
19	C₄₁×#547	—	2	1	no	—
20	C₄₁×#540	—	2	2	no	—
21	C₄₁×#537	—	2	2	no	—
22	C₄₁×#537	—	2	2	no	—
23	C₄₁×#533	C₂²	1	1	yes	characteristic
24	C₄₁×#532	C₂²	1	1	yes	characteristic
25	C₄₁×#532	C₂²	1	1	yes	characteristic
26	C₄₁×#532	C₂²	1	1	yes	characteristic
27	C₄₁×#495	—	2	2	no	—
28	C₄₁×#494	C₂²	1	1	yes	characteristic
29	C₄₁×#493	C₂²	1	1	yes	characteristic
30	C₄₁×#492	C₂²	1	1	yes	characteristic
31	C₄₁×#492	C₂²	1	1	yes	characteristic
32	C₄₁×#477	C₂²	1	2	yes	—
33	C₄₁×#476	—	2	1	no	—
34	C₄₁×#476	C₂²	1	2	yes	—
35	C₄₁×#474	—	2	1	no	—
36	C₄₁×#469	—	2	2	no	—
37	C₄₁×#468	—	2	2	no	—
38	C₄₁×#461	—	2	1	no	—
39	C₄₁×#460	C₂²	1	2	yes	—
40	C₄₁×#459	—	2	1	no	—
41	C₄₁×#459	C₂²	1	2	yes	—
42	C₄₁×#423	C₂²	1	1	yes	characteristic
43	C₄₁×#423	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
45	C₄₁×#333	C₂²	1	2	yes	—
46	C₄₁×#331	C₂²	1	2	yes	—
47	C₄₁×Q₈⋊C₈	C₂²	1	2	yes	—
48	C₄₁×Q₈⋊C₈	C₂²	1	2	yes	—
49	C₄₁×D₄⋊C₈	C₂²	1	2	yes	—
50	C₄₁×D₄⋊C₈	C₂²	1	2	yes	—
51	C₂×#41×C₄₁	—	2	2	no	—
52	C₂×#41×C₄₁	—	2	2	no	—
53	C₂×#41×C₄₁	—	2	1	no	—
54	C₂×#41×C₄₁	—	2	1	no	—
55	C₂×#41×C₄₁	D₄	1	2	yes	—
56	#135×C₄₁	—	4	8	no	—
57	C₂×Q₁₆×C₄₁	—	2	2	no	—
58	C₂×SD₁₆×C₄₁	—	2	2	no	—
59	C₂×SD₁₆×C₄₁	—	2	2	no	—
60	C₂×SD₁₆×C₄₁	—	2	2	no	—
61	C₂×D₈×C₄₁	—	2	2	no	—
62	C₂×D₈×C₄₁	—	2	2	no	—
63	C₂×M₁₆×C₄₁	—	2	1	no	—
64	C₂×M₁₆×C₄₁	—	2	1	no	—
65	C₂²×C₈×C₄₁	—	2	1	no	—
66	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
67	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
68	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
69	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
70	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
71	#127×C₄₁	—	2	2	no	—
72	#127×C₄₁	D₄	1	1	yes	characteristic
73	#127×C₄₁	C₂³	1	1	yes	characteristic
74	#127×C₄₁	C₂³	1	1	yes	characteristic
75	#125×C₄₁	—	2	2	no	—
76	#125×C₄₁	—	2	1	no	—
77	#124×C₄₁	—	2	1	no	—
78	#124×C₄₁	—	2	1	no	—
79	#124×C₄₁	D₄	1	2	yes	—
80	#123×C₄₁	—	2	4	no	—
81	#123×C₄₁	—	2	4	no	—
82	C₂²⋊Q₈×C₄₁	—	2	2	no	—
83	C₂²⋊Q₈×C₄₁	—	2	4	no	—
84	C₂²⋊Q₈×C₄₁	—	2	2	no	—
85	C₂²⋊Q₈×C₄₁	—	2	4	no	—
86	C₂²⋊Q₈×C₄₁	—	2	1	no	—
87	C₂²⋊Q₈×C₄₁	D₄	1	2	yes	—
88	#121×C₄₁	—	2	4	no	—
89	#121×C₄₁	—	2	4	no	—
90	#121×C₄₁	—	2	2	no	—
91	#121×C₄₁	—	2	4	no	—
92	#121×C₄₁	—	2	4	no	—
93	#121×C₄₁	—	2	1	no	—
94	#121×C₄₁	—	2	1	no	—
95	#121×C₄₁	—	2	1	no	—
96	#121×C₄₁	—	2	2	no	—
97	#121×C₄₁	—	2	1	no	—
98	#121×C₄₁	—	2	1	no	—
99	#121×C₄₁	D₄	1	2	yes	—
100	C₄×Q₈×C₄₁	—	2	1	no	—
101	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
102	C₄×D₄×C₄₁	—	2	2	no	—
103	C₄×D₄×C₄₁	—	2	2	no	—
104	C₄×D₄×C₄₁	—	2	1	no	—
105	C₄×D₄×C₄₁	—	2	1	no	—
106	C₄×D₄×C₄₁	—	2	1	no	—
107	C₄×D₄×C₄₁	—	2	1	no	—
108	C₄×D₄×C₄₁	—	2	1	no	—
109	C₄×D₄×C₄₁	C₂³	1	2	yes	—
110	#117×C₄₁	—	2	1	no	—
111	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
112	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
113	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
114	#107×C₄₁	—	2	2	no	—
115	#106×C₄₁	—	2	2	no	—
116	C₄⋊C₈×C₄₁	—	2	1	no	—
117	C₄⋊C₈×C₄₁	—	2	1	no	—
118	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
119	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
120	#103×C₄₁	—	2	2	no	—
121	#102×C₄₁	—	2	2	no	—
122	#102×C₄₁	—	2	2	no	—
123	#102×C₄₁	—	2	2	no	—
124	C₄×C₈×C₄₁	—	2	1	no	—
125	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
126	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
127	#41×C₄₁	—	4	4	no	—
128	#41×C₄₁	—	4	4	no	—
129	#41×C₄₁	—	8	1	no	—
130	#41×C₄₁	—	8	1	no	—
131	#41×C₄₁	—	8	2	no	—
132	#41×C₄₁	—	8	2	no	—
133	#41×C₄₁	—	8	4	no	—
134	C₂×Q₈×C₄₁	—	2	1	no	—
135	C₂×Q₈×C₄₁	—	2	1	no	—
136	C₂×Q₈×C₄₁	—	2	1	no	—
137	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
138	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
139	C₂×D₄×C₄₁	—	2	4	no	—
140	C₂×D₄×C₄₁	—	2	4	no	—
141	C₂×D₄×C₄₁	—	2	2	no	—
142	C₂×D₄×C₄₁	—	2	2	no	—
143	C₂×D₄×C₄₁	—	2	1	no	—
144	C₂×D₄×C₄₁	—	2	1	no	—
145	C₂×D₄×C₄₁	—	2	1	no	—
146	C₂×D₄×C₄₁	—	2	1	no	—
147	C₂×D₄×C₄₁	—	2	1	no	—
148	C₂×D₄×C₄₁	—	2	1	no	—
149	C₂×D₄×C₄₁	—	2	1	no	—
150	C₂×D₄×C₄₁	—	4	1	no	—
151	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
152	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₄₁	—	2	4	no	—
154	C₂²×C₄×C₄₁	—	2	4	no	—
155	C₂²×C₄×C₄₁	—	2	2	no	—
156	C₂²×C₄×C₄₁	—	2	2	no	—
157	C₂²×C₄×C₄₁	—	4	1	no	—
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	Q₁₆×C₄₁	—	4	4	no	—
162	SD₁₆×C₄₁	—	4	4	no	—
163	SD₁₆×C₄₁	—	4	4	no	—
164	SD₁₆×C₄₁	—	8	2	no	—
165	D₈×C₄₁	—	4	4	no	—
166	D₈×C₄₁	—	8	2	no	—
167	M₁₆×C₄₁	—	8	1	no	—
168	M₁₆×C₄₁	—	8	1	no	—
169	C₂×C₈×C₄₁	—	2	4	no	—
170	C₂×C₈×C₄₁	—	2	1	no	—
171	C₂×C₈×C₄₁	—	2	1	no	—
172	C₂×C₈×C₄₁	—	2	2	no	—
173	C₂×C₈×C₄₁	—	2	2	no	—
174	C₄⋊C₄×C₄₁	—	2	4	no	—
175	C₄⋊C₄×C₄₁	—	2	4	no	—
176	C₄⋊C₄×C₄₁	—	2	1	no	—
177	C₄⋊C₄×C₄₁	—	2	1	no	—
178	C₄⋊C₄×C₄₁	—	2	1	no	—
179	C₄⋊C₄×C₄₁	—	2	1	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	2	no	—
184	C₄⋊C₄×C₄₁	—	2	1	no	—
185	C₄⋊C₄×C₄₁	—	2	1	no	—
186	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
187	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
188	C₂²⋊C₄×C₄₁	—	2	4	no	—
189	C₂²⋊C₄×C₄₁	—	2	4	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	—	4	1	no	—
196	C₂²⋊C₄×C₄₁	—	4	1	no	—
197	C₄²×C₄₁	—	2	2	no	—
198	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
199	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
201	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
202	C₂³×C₄₁	—	2	2	no	—
203	C₂³×C₄₁	—	2	2	no	—
204	C₂³×C₄₁	—	4	1	no	—
205	C₂³×C₄₁	#120	1	1	yes	characteristic
206	Q₈×C₄₁	—	2	2	no	—
207	Q₈×C₄₁	—	2	2	no	—
208	Q₈×C₄₁	—	4	2	no	—
209	Q₈×C₄₁	—	4	2	no	—
210	Q₈×C₄₁	—	4	2	no	—
211	Q₈×C₄₁	—	8	1	no	—
212	D₄×C₄₁	—	2	2	no	—
213	D₄×C₄₁	—	2	2	no	—
214	D₄×C₄₁	—	4	2	no	—
215	D₄×C₄₁	—	4	2	no	—
216	D₄×C₄₁	—	4	1	no	—
217	D₄×C₄₁	—	4	1	no	—
218	D₄×C₄₁	—	4	1	no	—
219	D₄×C₄₁	—	4	1	no	—
220	D₄×C₄₁	—	4	1	no	—
221	D₄×C₄₁	—	4	1	no	—
222	D₄×C₄₁	—	4	1	no	—
223	D₄×C₄₁	—	4	1	no	—
224	D₄×C₄₁	—	4	2	no	—
225	D₄×C₄₁	—	8	1	no	—
226	D₄×C₄₁	—	8	2	no	—
227	D₄×C₄₁	—	8	2	no	—
228	D₄×C₄₁	—	8	4	no	—
229	D₄×C₄₁	—	8	4	no	—
230	D₄×C₄₁	—	8	2	no	—
231	C₂×C₄×C₄₁	—	2	1	no	—
232	C₂×C₄×C₄₁	—	2	1	no	—
233	C₂×C₄×C₄₁	—	2	1	no	—
234	C₂×C₄×C₄₁	—	2	1	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	—	4	2	no	—
241	C₂×C₄×C₄₁	—	4	2	no	—
242	C₂×C₄×C₄₁	—	4	4	no	—
243	C₂×C₄×C₄₁	—	4	1	no	—
244	C₂×C₄×C₄₁	—	8	4	no	—
245	C₂×C₄×C₄₁	—	8	4	no	—
246	C₂×C₄×C₄₁	—	8	2	no	—
247	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
248	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
249	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
250	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
253	C₈×C₄₁	—	2	2	no	—
254	C₈×C₄₁	—	2	2	no	—
255	C₈×C₄₁	—	4	2	no	—
256	C₈×C₄₁	—	4	2	no	—
257	#18687	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
258	C₂²×C₄₁	—	2	1	no	—
259	C₂²×C₄₁	—	2	1	no	—
260	C₂²×C₄₁	—	2	1	no	—
261	C₂²×C₄₁	—	4	2	no	—
262	C₂²×C₄₁	—	4	2	no	—
263	C₂²×C₄₁	—	4	2	no	—
264	C₂²×C₄₁	—	4	2	no	—
265	C₂²×C₄₁	—	4	2	no	—
266	C₂²×C₄₁	—	4	2	no	—
267	C₂²×C₄₁	—	8	1	no	—
268	C₂²×C₄₁	—	8	1	no	—
269	C₂²×C₄₁	—	8	1	no	—
270	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
271	C₄×C₄₁	—	2	1	no	—
272	C₄×C₄₁	—	2	1	no	—
273	C₄×C₄₁	—	2	1	no	—
274	C₄×C₄₁	—	4	2	no	—
275	C₄×C₄₁	—	4	2	no	—
276	C₄×C₄₁	—	4	2	no	—
277	C₄×C₄₁	—	4	2	no	—
278	C₄×C₄₁	—	8	1	no	—
279	C₄×C₄₁	#453	1	2	yes	—
280	C₄×C₄₁	#576	1	1	yes	characteristic
281	C₄×C₄₁	#577	1	1	yes	characteristic
282	C₄×C₄₁	#577	1	1	yes	characteristic
283	C₄×C₄₁	#578	1	1	yes	characteristic
284	#3548	C₂×C₄₁	1	1	yes	characteristic, complemented
285	#3254	C₂×C₄₁	1	1	yes	characteristic, complemented
286	#3253	C₂×C₄₁	1	1	yes	characteristic, complemented
287	#3147	C₂×C₄₁	1	1	yes	characteristic, complemented
288	#1632	C₂×C₄₁	1	2	yes	complemented
289	#1631	C₂×C₄₁	1	2	yes	complemented
290	#1622	C₂×C₄₁	1	2	yes	complemented
291	#1621	C₂×C₄₁	1	2	yes	complemented
292	#1560	C₂×C₄₁	1	1	yes	characteristic, complemented
293	#1493	C₂×C₄₁	1	1	yes	characteristic, complemented
294	#1492	C₂×C₄₁	1	1	yes	characteristic, complemented
295	C₂×C₄₁	—	4	1	no	—
296	C₂×C₄₁	—	8	2	no	—
297	C₂×C₄₁	—	8	2	no	—
298	C₂×C₄₁	—	16	1	no	—
299	C₂×C₄₁	#3012	1	1	yes	characteristic
300	C₂×C₄₁	#3013	1	1	yes	characteristic
301	C₂×C₄₁	C₂×#453	1	1	yes	characteristic
302	C₂×#135	—	2	2	no	—
303	#562	—	2	2	no	—
304	#554	—	2	1	no	—
305	#554	C₂²×C₄₁	1	2	yes	—
306	#550	—	2	1	no	—
307	#550	C₂²×C₄₁	1	2	yes	—
308	#547	—	2	1	no	—
309	#547	—	2	1	no	—
310	#540	—	2	2	no	—
311	#537	—	2	2	no	—
312	#537	—	2	2	no	—
313	#533	C₂²×C₄₁	1	1	yes	characteristic
314	#532	C₂²×C₄₁	1	1	yes	characteristic
315	#532	C₂²×C₄₁	1	1	yes	characteristic
316	#532	C₂²×C₄₁	1	1	yes	characteristic
317	#495	—	2	2	no	—
318	#494	C₂²×C₄₁	1	1	yes	characteristic
319	#493	C₂²×C₄₁	1	1	yes	characteristic
320	#492	C₂²×C₄₁	1	1	yes	characteristic
321	#492	C₂²×C₄₁	1	1	yes	characteristic
322	#477	C₂²×C₄₁	1	2	yes	—
323	#476	—	2	1	no	—
324	#476	C₂²×C₄₁	1	2	yes	—
325	#474	—	2	1	no	—
326	#469	—	2	2	no	—
327	#468	—	2	2	no	—
328	#461	—	2	1	no	—
329	#460	C₂²×C₄₁	1	2	yes	—
330	#459	—	2	1	no	—
331	#459	C₂²×C₄₁	1	2	yes	—
332	#423	C₂²×C₄₁	1	1	yes	characteristic
333	#423	C₂²×C₄₁	1	1	yes	characteristic
334	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
335	#333	C₂²×C₄₁	1	2	yes	—
336	#331	C₂²×C₄₁	1	2	yes	—
337	Q₈⋊C₈	C₂²×C₄₁	1	2	yes	—
338	Q₈⋊C₈	C₂²×C₄₁	1	2	yes	—
339	D₄⋊C₈	C₂²×C₄₁	1	2	yes	—
340	D₄⋊C₈	C₂²×C₄₁	1	2	yes	—
341	C₄₁	#18687	1	1	yes	characteristic, direct product factor, Sylow
342	C₂×#41	—	2	2	no	—
343	C₂×#41	—	2	2	no	—
344	C₂×#41	—	2	1	no	—
345	C₂×#41	—	2	1	no	—
346	C₂×#41	D₄×C₄₁	1	2	yes	—
347	#135	—	4	8	no	—
348	C₂×Q₁₆	—	2	2	no	—
349	C₂×SD₁₆	—	2	2	no	—
350	C₂×SD₁₆	—	2	2	no	—
351	C₂×SD₁₆	—	2	2	no	—
352	C₂×D₈	—	2	2	no	—
353	C₂×D₈	—	2	2	no	—
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂²×C₈	—	2	1	no	—
357	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
358	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
359	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
360	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
361	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
362	#127	—	2	2	no	—
363	#127	D₄×C₄₁	1	1	yes	characteristic
364	#127	C₂³×C₄₁	1	1	yes	characteristic
365	#127	C₂³×C₄₁	1	1	yes	characteristic
366	#125	—	2	2	no	—
367	#125	—	2	1	no	—
368	#124	—	2	1	no	—
369	#124	—	2	1	no	—
370	#124	D₄×C₄₁	1	2	yes	—
371	#123	—	2	4	no	—
372	#123	—	2	4	no	—
373	C₂²⋊Q₈	—	2	2	no	—
374	C₂²⋊Q₈	—	2	4	no	—
375	C₂²⋊Q₈	—	2	2	no	—
376	C₂²⋊Q₈	—	2	4	no	—
377	C₂²⋊Q₈	—	2	1	no	—
378	C₂²⋊Q₈	D₄×C₄₁	1	2	yes	—
379	#121	—	2	4	no	—
380	#121	—	2	4	no	—
381	#121	—	2	2	no	—
382	#121	—	2	4	no	—
383	#121	—	2	4	no	—
384	#121	—	2	1	no	—
385	#121	—	2	1	no	—
386	#121	—	2	1	no	—
387	#121	—	2	2	no	—
388	#121	—	2	1	no	—
389	#121	—	2	1	no	—
390	#121	D₄×C₄₁	1	2	yes	—
391	C₄×Q₈	—	2	1	no	—
392	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
393	C₄×D₄	—	2	2	no	—
394	C₄×D₄	—	2	2	no	—
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	C₂³×C₄₁	1	2	yes	—
401	#117	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	2	no	—
403	C₂×C₄⋊C₄	—	2	2	no	—
404	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
405	#107	—	2	2	no	—
406	#106	—	2	2	no	—
407	C₄⋊C₈	—	2	1	no	—
408	C₄⋊C₈	—	2	1	no	—
409	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
410	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
411	#103	—	2	2	no	—
412	#102	—	2	2	no	—
413	#102	—	2	2	no	—
414	#102	—	2	2	no	—
415	C₄×C₈	—	2	1	no	—
416	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
417	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
418	#41	—	4	4	no	—
419	#41	—	4	4	no	—
420	#41	—	8	1	no	—
421	#41	—	8	1	no	—
422	#41	—	8	2	no	—
423	#41	—	8	2	no	—
424	#41	—	8	4	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
429	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
430	C₂×D₄	—	2	4	no	—
431	C₂×D₄	—	2	4	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	4	1	no	—
442	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
443	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	4	1	no	—
449	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
452	Q₁₆	—	4	4	no	—
453	SD₁₆	—	4	4	no	—
454	SD₁₆	—	4	4	no	—
455	SD₁₆	—	8	2	no	—
456	D₈	—	4	4	no	—
457	D₈	—	8	2	no	—
458	M₁₆	—	8	1	no	—
459	M₁₆	—	8	1	no	—
460	C₂×C₈	—	2	4	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
478	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	2	2	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	4	1	no	—
487	C₂²⋊C₄	—	4	1	no	—
488	C₄²	—	2	2	no	—
489	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
490	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
491	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
492	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
493	C₂³	—	2	2	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	4	1	no	—
496	C₂³	#120×C₄₁	1	1	yes	characteristic
497	Q₈	—	2	2	no	—
498	Q₈	—	2	2	no	—
499	Q₈	—	4	2	no	—
500	Q₈	—	4	2	no	—
501	Q₈	—	4	2	no	—
502	Q₈	—	8	1	no	—
503	D₄	—	2	2	no	—
504	D₄	—	2	2	no	—
505	D₄	—	4	2	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	1	no	—
508	D₄	—	4	1	no	—
509	D₄	—	4	1	no	—
510	D₄	—	4	1	no	—
511	D₄	—	4	1	no	—
512	D₄	—	4	1	no	—
513	D₄	—	4	1	no	—
514	D₄	—	4	1	no	—
515	D₄	—	4	2	no	—
516	D₄	—	8	1	no	—
517	D₄	—	8	2	no	—
518	D₄	—	8	2	no	—
519	D₄	—	8	4	no	—
520	D₄	—	8	4	no	—
521	D₄	—	8	2	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	4	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	8	4	no	—
536	C₂×C₄	—	8	4	no	—
537	C₂×C₄	—	8	2	no	—
538	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
539	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
540	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
541	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
542	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
543	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
544	C₈	—	2	2	no	—
545	C₈	—	2	2	no	—
546	C₈	—	4	2	no	—
547	C₈	—	4	2	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	8	1	no	—
558	C₂²	—	8	1	no	—
559	C₂²	—	8	1	no	—
560	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	2	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	2	no	—
568	C₄	—	8	1	no	—
569	C₄	C₄₁×#453	1	2	yes	—
570	C₄	C₄₁×#576	1	1	yes	characteristic
571	C₄	C₄₁×#577	1	1	yes	characteristic
572	C₄	C₄₁×#577	1	1	yes	characteristic
573	C₄	C₄₁×#578	1	1	yes	characteristic
574	C₂	—	4	1	no	—
575	C₂	—	8	2	no	—
576	C₂	—	8	2	no	—
577	C₂	—	16	1	no	—
578	C₂	C₄₁×#3012	1	1	yes	characteristic
579	C₂	C₄₁×#3013	1	1	yes	characteristic
580	C₂	C₂×C₄₁×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3548	C₂	semidirect
2. C₄₁×#3254	C₂	semidirect
3. C₄₁×#3253	C₂	semidirect
4. C₄₁×#3147	C₂	semidirect
5. C₄₁×#1632	C₂	semidirect
6. C₄₁×#1631	C₂	semidirect
7. C₄₁×#1622	C₂	semidirect
8. C₄₁×#1621	C₂	semidirect
9. C₄₁×#1560	C₂	semidirect
10. C₄₁×#1493	C₂	semidirect
11. C₄₁×#1492	C₂	semidirect
257. #18687	C₄₁	direct (N × H)
284. #3548	C₂×C₄₁	semidirect
285. #3254	C₂×C₄₁	semidirect
286. #3253	C₂×C₄₁	semidirect
287. #3147	C₂×C₄₁	semidirect
288. #1632	C₂×C₄₁	semidirect
289. #1631	C₂×C₄₁	semidirect
290. #1622	C₂×C₄₁	semidirect
291. #1621	C₂×C₄₁	semidirect
292. #1560	C₂×C₄₁	semidirect
293. #1493	C₂×C₄₁	semidirect
294. #1492	C₂×C₄₁	semidirect
341. C₄₁	#18687	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×#3548	2
C₄₁×#3254	2
C₄₁×#3253	2
C₄₁×#3147	2
C₄₁×#1632	2
C₄₁×#1631	2
C₄₁×#1622	2
C₄₁×#1621	2
C₄₁×#1560	2
C₄₁×#1493	2
C₄₁×#1492	2
#18687	41

Subgroups — C41×#18687 #23794888

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#18687 #23794888