Subgroups — C₄₁×#18510 #23794711

Order 10496.

1062 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3483	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3147	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3106	C₂	1	2	yes	maximal, complemented
4	C₄₁×#1634	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1633	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1631	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1624	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1623	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1621	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1543	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1476	C₂	1	2	yes	maximal, complemented
12	C₂×#135×C₄₁	—	2	2	no	—
13	Q₈²×C₄₁	C₂²	1	1	yes	characteristic
14	C₄₁×#555	—	2	2	no	—
15	C₄₁×#555	—	2	2	no	—
16	C₄₁×#555	C₂²	1	1	yes	characteristic
17	C₄₁×#550	—	2	2	no	—
18	C₄₁×#550	C₂²	1	2	yes	—
19	C₄₁×#532	—	2	2	no	—
20	C₄₁×#532	—	2	2	no	—
21	C₄₁×#532	C₂²	1	1	yes	characteristic
22	C₄₁×#532	C₂²	1	1	yes	characteristic
23	C₄×#41×C₄₁	—	2	2	no	—
24	C₄×#41×C₄₁	C₂²	1	2	yes	—
25	C₄₁×#495	—	2	2	no	—
26	C₄₁×#494	C₂²	1	1	yes	characteristic
27	C₄₁×#493	C₂²	1	1	yes	characteristic
28	C₄₁×#492	C₂²	1	1	yes	characteristic
29	C₄₁×#492	C₂²	1	1	yes	characteristic
30	C₄₁×#482	—	2	2	no	—
31	C₄₁×#477	C₂²	1	2	yes	—
32	C₄₁×#476	C₂²	1	2	yes	—
33	C₄₁×#460	C₂²	1	2	yes	—
34	C₄₁×#459	C₂²	1	2	yes	—
35	C₄₁×#449	—	2	2	no	—
36	C₄×SD₁₆×C₄₁	—	2	2	no	—
37	C₄×D₈×C₄₁	—	2	2	no	—
38	C₄₁×#431	C₂²	1	2	yes	—
39	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
40	C₄₁×#333	C₂²	1	1	yes	characteristic
41	C₄₁×#333	C₂²	1	1	yes	characteristic
42	C₄₁×#331	C₂²	1	2	yes	—
43	C₄₁×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₄₁×Q₈⋊C₈	C₂²	1	2	yes	—
45	C₄₁×D₄⋊C₈	C₂²	1	2	yes	—
46	C₄₁×D₄⋊C₈	C₂²	1	2	yes	—
47	C₂×#41×C₄₁	—	2	2	no	—
48	C₂×#41×C₄₁	—	2	2	no	—
49	C₂×#41×C₄₁	—	2	1	no	—
50	C₂×#41×C₄₁	D₄	1	2	yes	—
51	C₂×#41×C₄₁	D₄	1	2	yes	—
52	#135×C₄₁	—	4	8	no	—
53	C₂×Q₁₆×C₄₁	—	2	2	no	—
54	C₂×SD₁₆×C₄₁	—	2	2	no	—
55	C₂×SD₁₆×C₄₁	—	2	2	no	—
56	C₂×SD₁₆×C₄₁	—	2	2	no	—
57	C₂×D₈×C₄₁	—	2	2	no	—
58	C₂×D₈×C₄₁	—	2	2	no	—
59	C₂²×C₈×C₄₁	—	2	1	no	—
60	C₄⋊Q₈×C₄₁	—	2	2	no	—
61	C₄⋊Q₈×C₄₁	—	2	2	no	—
62	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
63	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
64	#127×C₄₁	—	2	2	no	—
65	#127×C₄₁	—	2	2	no	—
66	#127×C₄₁	C₂³	1	1	yes	characteristic
67	#127×C₄₁	C₂³	1	1	yes	characteristic
68	#124×C₄₁	—	2	2	no	—
69	#124×C₄₁	—	2	4	no	—
70	#124×C₄₁	—	2	2	no	—
71	#124×C₄₁	—	2	1	no	—
72	#124×C₄₁	D₄	1	2	yes	—
73	#121×C₄₁	—	2	4	no	—
74	#121×C₄₁	—	2	4	no	—
75	#121×C₄₁	—	2	2	no	—
76	#121×C₄₁	—	2	4	no	—
77	#121×C₄₁	—	2	2	no	—
78	#121×C₄₁	—	2	2	no	—
79	#121×C₄₁	—	2	2	no	—
80	C₄×Q₈×C₄₁	—	2	2	no	—
81	C₄×Q₈×C₄₁	D₄	1	2	yes	—
82	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
83	C₄×D₄×C₄₁	—	2	4	no	—
84	C₄×D₄×C₄₁	—	2	4	no	—
85	C₄×D₄×C₄₁	—	2	2	no	—
86	C₄×D₄×C₄₁	—	2	2	no	—
87	C₄×D₄×C₄₁	—	2	2	no	—
88	C₄×D₄×C₄₁	—	2	2	no	—
89	C₄×D₄×C₄₁	—	2	2	no	—
90	C₄×D₄×C₄₁	D₄	1	2	yes	—
91	C₄×D₄×C₄₁	C₂³	1	2	yes	—
92	#117×C₄₁	—	2	4	no	—
93	#117×C₄₁	—	2	2	no	—
94	#117×C₄₁	—	2	2	no	—
95	#117×C₄₁	D₄	1	2	yes	—
96	C₂×C₄²×C₄₁	—	2	2	no	—
97	C₂×C₄²×C₄₁	—	2	2	no	—
98	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
99	#107×C₄₁	—	2	2	no	—
100	#106×C₄₁	—	2	2	no	—
101	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
102	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
103	#103×C₄₁	—	2	2	no	—
104	#102×C₄₁	—	2	2	no	—
105	#102×C₄₁	—	2	2	no	—
106	#102×C₄₁	—	2	2	no	—
107	C₂²⋊C₈×C₄₁	—	2	2	no	—
108	C₄×C₈×C₄₁	—	2	1	no	—
109	C₄×C₈×C₄₁	—	2	2	no	—
110	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
112	#41×C₄₁	—	2	4	no	—
113	#41×C₄₁	—	4	2	no	—
114	#41×C₄₁	—	4	4	no	—
115	#41×C₄₁	—	4	4	no	—
116	#41×C₄₁	—	4	4	no	—
117	#41×C₄₁	—	4	4	no	—
118	#41×C₄₁	—	8	4	no	—
119	C₂×Q₈×C₄₁	—	2	2	no	—
120	C₂×Q₈×C₄₁	—	2	1	no	—
121	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
122	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
123	C₂×D₄×C₄₁	—	2	4	no	—
124	C₂×D₄×C₄₁	—	2	2	no	—
125	C₂×D₄×C₄₁	—	2	2	no	—
126	C₂×D₄×C₄₁	—	2	4	no	—
127	C₂×D₄×C₄₁	—	2	2	no	—
128	C₂×D₄×C₄₁	—	2	2	no	—
129	C₂×D₄×C₄₁	—	2	2	no	—
130	C₂×D₄×C₄₁	—	2	1	no	—
131	C₂×D₄×C₄₁	—	4	1	no	—
132	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
133	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
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	2	no	—
139	C₂²×C₄×C₄₁	—	4	1	no	—
140	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
142	Q₁₆×C₄₁	—	4	4	no	—
143	SD₁₆×C₄₁	—	4	4	no	—
144	SD₁₆×C₄₁	—	4	4	no	—
145	SD₁₆×C₄₁	—	4	4	no	—
146	D₈×C₄₁	—	4	4	no	—
147	D₈×C₄₁	—	4	4	no	—
148	C₂×C₈×C₄₁	—	2	4	no	—
149	C₂×C₈×C₄₁	—	2	1	no	—
150	C₂×C₈×C₄₁	—	2	1	no	—
151	C₂×C₈×C₄₁	—	2	2	no	—
152	C₂×C₈×C₄₁	—	2	2	no	—
153	C₄⋊C₄×C₄₁	—	2	4	no	—
154	C₄⋊C₄×C₄₁	—	2	2	no	—
155	C₄⋊C₄×C₄₁	—	2	2	no	—
156	C₄⋊C₄×C₄₁	—	2	2	no	—
157	C₄⋊C₄×C₄₁	—	2	2	no	—
158	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
159	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
160	C₂²⋊C₄×C₄₁	—	2	4	no	—
161	C₂²⋊C₄×C₄₁	—	2	4	no	—
162	C₂²⋊C₄×C₄₁	—	2	2	no	—
163	C₂²⋊C₄×C₄₁	—	2	4	no	—
164	C₂²⋊C₄×C₄₁	—	2	2	no	—
165	C₂²⋊C₄×C₄₁	—	2	2	no	—
166	C₂²⋊C₄×C₄₁	—	4	2	no	—
167	C₄²×C₄₁	—	2	2	no	—
168	C₄²×C₄₁	—	2	2	no	—
169	C₄²×C₄₁	—	2	2	no	—
170	C₄²×C₄₁	—	2	2	no	—
171	C₄²×C₄₁	—	2	2	no	—
172	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₄₁	C₂×D₄	1	2	yes	—
174	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
175	C₂³×C₄₁	—	2	2	no	—
176	C₂³×C₄₁	—	2	2	no	—
177	C₂³×C₄₁	—	4	1	no	—
178	C₂³×C₄₁	#120	1	1	yes	characteristic
179	Q₈×C₄₁	—	2	2	no	—
180	Q₈×C₄₁	—	4	2	no	—
181	Q₈×C₄₁	—	4	2	no	—
182	Q₈×C₄₁	—	8	2	no	—
183	Q₈×C₄₁	#135	1	4	yes	complemented
184	D₄×C₄₁	—	2	2	no	—
185	D₄×C₄₁	—	2	2	no	—
186	D₄×C₄₁	—	4	4	no	—
187	D₄×C₄₁	—	4	2	no	—
188	D₄×C₄₁	—	4	8	no	—
189	D₄×C₄₁	—	4	2	no	—
190	D₄×C₄₁	—	4	2	no	—
191	D₄×C₄₁	—	4	2	no	—
192	D₄×C₄₁	—	4	2	no	—
193	D₄×C₄₁	—	4	2	no	—
194	D₄×C₄₁	—	8	2	no	—
195	D₄×C₄₁	—	8	2	no	—
196	D₄×C₄₁	—	8	4	no	—
197	D₄×C₄₁	—	8	2	no	—
198	C₂×C₄×C₄₁	—	2	2	no	—
199	C₂×C₄×C₄₁	—	2	2	no	—
200	C₂×C₄×C₄₁	—	2	2	no	—
201	C₂×C₄×C₄₁	—	2	2	no	—
202	C₂×C₄×C₄₁	—	2	2	no	—
203	C₂×C₄×C₄₁	—	2	2	no	—
204	C₂×C₄×C₄₁	—	2	2	no	—
205	C₂×C₄×C₄₁	—	4	4	no	—
206	C₂×C₄×C₄₁	—	4	8	no	—
207	C₂×C₄×C₄₁	—	4	2	no	—
208	C₂×C₄×C₄₁	—	4	2	no	—
209	C₂×C₄×C₄₁	—	4	4	no	—
210	C₂×C₄×C₄₁	—	4	4	no	—
211	C₂×C₄×C₄₁	—	4	1	no	—
212	C₂×C₄×C₄₁	—	8	2	no	—
213	C₂×C₄×C₄₁	#120	1	2	yes	—
214	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
215	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
217	C₈×C₄₁	—	2	2	no	—
218	C₈×C₄₁	—	2	2	no	—
219	C₈×C₄₁	—	4	2	no	—
220	C₈×C₄₁	—	4	2	no	—
221	#18510	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂²×C₄₁	—	2	2	no	—
223	C₂²×C₄₁	—	2	1	no	—
224	C₂²×C₄₁	—	4	2	no	—
225	C₂²×C₄₁	—	4	4	no	—
226	C₂²×C₄₁	—	4	2	no	—
227	C₂²×C₄₁	—	4	2	no	—
228	C₂²×C₄₁	—	4	2	no	—
229	C₂²×C₄₁	—	8	2	no	—
230	C₂²×C₄₁	—	8	1	no	—
231	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
232	C₄×C₄₁	—	2	2	no	—
233	C₄×C₄₁	—	2	4	no	—
234	C₄×C₄₁	—	2	1	no	—
235	C₄×C₄₁	—	4	2	no	—
236	C₄×C₄₁	—	4	2	no	—
237	C₄×C₄₁	—	4	2	no	—
238	C₄×C₄₁	—	8	1	no	—
239	C₄×C₄₁	#453	1	2	yes	—
240	C₄×C₄₁	C₂×#135	1	2	yes	—
241	C₄×C₄₁	#575	1	2	yes	—
242	#3483	C₂×C₄₁	1	1	yes	characteristic, complemented
243	#3147	C₂×C₄₁	1	1	yes	characteristic, complemented
244	#3106	C₂×C₄₁	1	2	yes	complemented
245	#1634	C₂×C₄₁	1	1	yes	characteristic, complemented
246	#1633	C₂×C₄₁	1	1	yes	characteristic, complemented
247	#1631	C₂×C₄₁	1	2	yes	complemented
248	#1624	C₂×C₄₁	1	1	yes	characteristic, complemented
249	#1623	C₂×C₄₁	1	1	yes	characteristic, complemented
250	#1621	C₂×C₄₁	1	2	yes	complemented
251	#1543	C₂×C₄₁	1	1	yes	characteristic, complemented
252	#1476	C₂×C₄₁	1	2	yes	complemented
253	C₂×C₄₁	—	4	1	no	—
254	C₂×C₄₁	—	8	2	no	—
255	C₂×C₄₁	—	8	2	no	—
256	C₂×C₄₁	—	16	1	no	—
257	C₂×C₄₁	#3002	1	2	yes	—
258	C₂×C₄₁	C₂×#453	1	1	yes	characteristic
259	C₂×#135	—	2	2	no	—
260	Q₈²	C₂²×C₄₁	1	1	yes	characteristic
261	#555	—	2	2	no	—
262	#555	—	2	2	no	—
263	#555	C₂²×C₄₁	1	1	yes	characteristic
264	#550	—	2	2	no	—
265	#550	C₂²×C₄₁	1	2	yes	—
266	#532	—	2	2	no	—
267	#532	—	2	2	no	—
268	#532	C₂²×C₄₁	1	1	yes	characteristic
269	#532	C₂²×C₄₁	1	1	yes	characteristic
270	C₄×#41	—	2	2	no	—
271	C₄×#41	C₂²×C₄₁	1	2	yes	—
272	#495	—	2	2	no	—
273	#494	C₂²×C₄₁	1	1	yes	characteristic
274	#493	C₂²×C₄₁	1	1	yes	characteristic
275	#492	C₂²×C₄₁	1	1	yes	characteristic
276	#492	C₂²×C₄₁	1	1	yes	characteristic
277	#482	—	2	2	no	—
278	#477	C₂²×C₄₁	1	2	yes	—
279	#476	C₂²×C₄₁	1	2	yes	—
280	#460	C₂²×C₄₁	1	2	yes	—
281	#459	C₂²×C₄₁	1	2	yes	—
282	#449	—	2	2	no	—
283	C₄×SD₁₆	—	2	2	no	—
284	C₄×D₈	—	2	2	no	—
285	#431	C₂²×C₄₁	1	2	yes	—
286	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
287	#333	C₂²×C₄₁	1	1	yes	characteristic
288	#333	C₂²×C₄₁	1	1	yes	characteristic
289	#331	C₂²×C₄₁	1	2	yes	—
290	Q₈⋊C₈	C₂²×C₄₁	1	2	yes	—
291	Q₈⋊C₈	C₂²×C₄₁	1	2	yes	—
292	D₄⋊C₈	C₂²×C₄₁	1	2	yes	—
293	D₄⋊C₈	C₂²×C₄₁	1	2	yes	—
294	C₄₁	#18510	1	1	yes	characteristic, direct product factor, Sylow
295	C₂×#41	—	2	2	no	—
296	C₂×#41	—	2	2	no	—
297	C₂×#41	—	2	1	no	—
298	C₂×#41	D₄×C₄₁	1	2	yes	—
299	C₂×#41	D₄×C₄₁	1	2	yes	—
300	#135	—	4	8	no	—
301	C₂×Q₁₆	—	2	2	no	—
302	C₂×SD₁₆	—	2	2	no	—
303	C₂×SD₁₆	—	2	2	no	—
304	C₂×SD₁₆	—	2	2	no	—
305	C₂×D₈	—	2	2	no	—
306	C₂×D₈	—	2	2	no	—
307	C₂²×C₈	—	2	1	no	—
308	C₄⋊Q₈	—	2	2	no	—
309	C₄⋊Q₈	—	2	2	no	—
310	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
311	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
312	#127	—	2	2	no	—
313	#127	—	2	2	no	—
314	#127	C₂³×C₄₁	1	1	yes	characteristic
315	#127	C₂³×C₄₁	1	1	yes	characteristic
316	#124	—	2	2	no	—
317	#124	—	2	4	no	—
318	#124	—	2	2	no	—
319	#124	—	2	1	no	—
320	#124	D₄×C₄₁	1	2	yes	—
321	#121	—	2	4	no	—
322	#121	—	2	4	no	—
323	#121	—	2	2	no	—
324	#121	—	2	4	no	—
325	#121	—	2	2	no	—
326	#121	—	2	2	no	—
327	#121	—	2	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	D₄×C₄₁	1	2	yes	—
330	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
331	C₄×D₄	—	2	4	no	—
332	C₄×D₄	—	2	4	no	—
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	—	2	2	no	—
335	C₄×D₄	—	2	2	no	—
336	C₄×D₄	—	2	2	no	—
337	C₄×D₄	—	2	2	no	—
338	C₄×D₄	D₄×C₄₁	1	2	yes	—
339	C₄×D₄	C₂³×C₄₁	1	2	yes	—
340	#117	—	2	4	no	—
341	#117	—	2	2	no	—
342	#117	—	2	2	no	—
343	#117	D₄×C₄₁	1	2	yes	—
344	C₂×C₄²	—	2	2	no	—
345	C₂×C₄²	—	2	2	no	—
346	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
347	#107	—	2	2	no	—
348	#106	—	2	2	no	—
349	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
350	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
351	#103	—	2	2	no	—
352	#102	—	2	2	no	—
353	#102	—	2	2	no	—
354	#102	—	2	2	no	—
355	C₂²⋊C₈	—	2	2	no	—
356	C₄×C₈	—	2	1	no	—
357	C₄×C₈	—	2	2	no	—
358	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
359	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
360	#41	—	2	4	no	—
361	#41	—	4	2	no	—
362	#41	—	4	4	no	—
363	#41	—	4	4	no	—
364	#41	—	4	4	no	—
365	#41	—	4	4	no	—
366	#41	—	8	4	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
370	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
371	C₂×D₄	—	2	4	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	4	1	no	—
380	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
381	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	4	1	no	—
388	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
389	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
390	Q₁₆	—	4	4	no	—
391	SD₁₆	—	4	4	no	—
392	SD₁₆	—	4	4	no	—
393	SD₁₆	—	4	4	no	—
394	D₈	—	4	4	no	—
395	D₈	—	4	4	no	—
396	C₂×C₈	—	2	4	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
407	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
408	C₂²⋊C₄	—	2	4	no	—
409	C₂²⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	2	4	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	4	2	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	2	2	no	—
420	C₄²	C₂×D₄×C₄₁	1	2	yes	—
421	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
422	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	4	1	no	—
426	C₂³	#120×C₄₁	1	1	yes	characteristic
427	Q₈	—	2	2	no	—
428	Q₈	—	4	2	no	—
429	Q₈	—	4	2	no	—
430	Q₈	—	8	2	no	—
431	Q₈	#135×C₄₁	1	4	yes	complemented
432	D₄	—	2	2	no	—
433	D₄	—	2	2	no	—
434	D₄	—	4	4	no	—
435	D₄	—	4	2	no	—
436	D₄	—	4	8	no	—
437	D₄	—	4	2	no	—
438	D₄	—	4	2	no	—
439	D₄	—	4	2	no	—
440	D₄	—	4	2	no	—
441	D₄	—	4	2	no	—
442	D₄	—	8	2	no	—
443	D₄	—	8	2	no	—
444	D₄	—	8	4	no	—
445	D₄	—	8	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	8	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	8	2	no	—
461	C₂×C₄	#120×C₄₁	1	2	yes	—
462	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
465	C₈	—	2	2	no	—
466	C₈	—	2	2	no	—
467	C₈	—	4	2	no	—
468	C₈	—	4	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	4	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	1	no	—
478	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
479	C₄	—	2	2	no	—
480	C₄	—	2	4	no	—
481	C₄	—	2	1	no	—
482	C₄	—	4	2	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	2	no	—
485	C₄	—	8	1	no	—
486	C₄	C₄₁×#453	1	2	yes	—
487	C₄	C₂×#135×C₄₁	1	2	yes	—
488	C₄	C₄₁×#575	1	2	yes	—
489	C₂	—	4	1	no	—
490	C₂	—	8	2	no	—
491	C₂	—	8	2	no	—
492	C₂	—	16	1	no	—
493	C₂	C₄₁×#3002	1	2	yes	—
494	C₂	C₂×C₄₁×#453	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₁	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
socle	C₂²×C₄₁	C₂×#120
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3483	C₂	semidirect
2. C₄₁×#3147	C₂	semidirect
3. C₄₁×#3106	C₂	semidirect
4. C₄₁×#1634	C₂	semidirect
5. C₄₁×#1633	C₂	semidirect
6. C₄₁×#1631	C₂	semidirect
7. C₄₁×#1624	C₂	semidirect
8. C₄₁×#1623	C₂	semidirect
9. C₄₁×#1621	C₂	semidirect
10. C₄₁×#1543	C₂	semidirect
11. C₄₁×#1476	C₂	semidirect
183. Q₈×C₄₁	#135	semidirect
221. #18510	C₄₁	direct (N × H)
242. #3483	C₂×C₄₁	semidirect
243. #3147	C₂×C₄₁	semidirect
244. #3106	C₂×C₄₁	semidirect
245. #1634	C₂×C₄₁	semidirect
246. #1633	C₂×C₄₁	semidirect
247. #1631	C₂×C₄₁	semidirect
248. #1624	C₂×C₄₁	semidirect
249. #1623	C₂×C₄₁	semidirect
250. #1621	C₂×C₄₁	semidirect
251. #1543	C₂×C₄₁	semidirect
252. #1476	C₂×C₄₁	semidirect
294. C₄₁	#18510	direct (N × H)
431. Q₈	#135×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3483	2
C₄₁×#3147	2
C₄₁×#3106	2
C₄₁×#1634	2
C₄₁×#1633	2
C₄₁×#1631	2
C₄₁×#1624	2
C₄₁×#1623	2
C₄₁×#1621	2
C₄₁×#1543	2
C₄₁×#1476	2
#18510	41

Subgroups — C41×#18510 #23794711

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#18510 #23794711