Subgroups — C₄₁×#19128 #23795329

Order 10496.

664 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3169	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3106	C₂	1	2	yes	maximal, complemented
3	C₈×#41×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1678	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1677	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1675	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1668	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1667	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1564	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1543	C₂	1	2	yes	maximal, complemented
12	C₄₁×#532	C₂²	1	2	yes	—
13	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
14	C₄₁×#500	C₂²	1	1	yes	characteristic
15	C₄₁×#493	C₂²	1	1	yes	characteristic
16	C₄₁×#486	C₂²	1	2	yes	—
17	C₄₁×#482	—	2	2	no	—
18	C₄₁×#477	C₂²	1	2	yes	—
19	C₄₁×#476	C₂²	1	2	yes	—
20	C₄₁×#466	—	2	1	no	—
21	C₄₁×#466	—	2	1	no	—
22	C₄₁×#460	C₂²	1	2	yes	—
23	C₄₁×#459	C₂²	1	2	yes	—
24	C₄₁×#449	—	2	2	no	—
25	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic
26	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic
27	C₄×SD₁₆×C₄₁	—	2	2	no	—
28	C₄×D₈×C₄₁	—	2	2	no	—
29	C₄×D₈×C₄₁	—	2	1	no	—
30	C₄×D₈×C₄₁	—	2	1	no	—
31	C₈×D₄×C₄₁	—	2	1	no	—
32	C₈×D₄×C₄₁	—	2	1	no	—
33	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
34	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
35	C₄₁×#431	—	2	1	no	—
36	C₄₁×#431	C₂²	1	1	yes	characteristic
37	C₄₁×#431	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₄₁	—	2	1	no	—
39	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
40	C₄₁×#335	C₂²	1	1	yes	characteristic
41	C₄₁×#335	C₂²	1	1	yes	characteristic
42	C₄₁×#334	C₂²	1	2	yes	—
43	C₄₁×#333	C₂²	1	2	yes	—
44	C₄₁×#333	C₂²	1	2	yes	—
45	C₄₁×#331	C₂²	1	2	yes	—
46	C₄₁×#331	C₂²	1	2	yes	—
47	C₂×#41×C₄₁	—	2	2	no	—
48	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
49	C₂×SD₁₆×C₄₁	—	2	2	no	—
50	C₂×D₈×C₄₁	—	2	2	no	—
51	C₂×D₈×C₄₁	—	2	1	no	—
52	C₂×D₈×C₄₁	—	2	1	no	—
53	C₂²×C₈×C₄₁	—	2	1	no	—
54	C₂²×C₈×C₄₁	—	2	1	no	—
55	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
57	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
58	#127×C₄₁	C₂³	1	2	yes	—
59	#124×C₄₁	—	2	2	no	—
60	#121×C₄₁	—	2	2	no	—
61	#121×C₄₁	—	2	2	no	—
62	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
63	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
64	C₄×D₄×C₄₁	—	2	1	no	—
65	C₄×D₄×C₄₁	—	2	1	no	—
66	C₄×D₄×C₄₁	—	2	2	no	—
67	C₄×D₄×C₄₁	—	2	2	no	—
68	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
69	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
70	#117×C₄₁	—	2	1	no	—
71	#117×C₄₁	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₄₁	—	2	1	no	—
73	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
74	#107×C₄₁	—	2	1	no	—
75	#107×C₄₁	—	2	1	no	—
76	#107×C₄₁	—	2	2	no	—
77	#106×C₄₁	—	2	2	no	—
78	C₄⋊C₈×C₄₁	—	2	1	no	—
79	C₄⋊C₈×C₄₁	—	2	1	no	—
80	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
81	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
82	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
83	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
84	#103×C₄₁	—	2	2	no	—
85	#102×C₄₁	—	2	2	no	—
86	#102×C₄₁	—	2	2	no	—
87	#102×C₄₁	—	2	2	no	—
88	#102×C₄₁	—	2	2	no	—
89	#102×C₄₁	—	2	2	no	—
90	C₂²⋊C₈×C₄₁	—	2	1	no	—
91	C₂²⋊C₈×C₄₁	—	2	2	no	—
92	C₂²⋊C₈×C₄₁	—	2	1	no	—
93	C₂²⋊C₈×C₄₁	—	2	1	no	—
94	C₄×C₈×C₄₁	—	2	1	no	—
95	C₄×C₈×C₄₁	—	2	1	no	—
96	C₄×C₈×C₄₁	—	2	1	no	—
97	C₄×C₈×C₄₁	—	2	2	no	—
98	C₄×C₈×C₄₁	D₄	1	1	yes	characteristic
99	C₄×C₈×C₄₁	D₄	1	1	yes	characteristic
100	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
102	#41×C₄₁	—	2	2	no	—
103	#41×C₄₁	—	2	2	no	—
104	#41×C₄₁	—	8	4	no	—
105	C₂×Q₈×C₄₁	—	2	2	no	—
106	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
107	C₂×D₄×C₄₁	—	2	1	no	—
108	C₂×D₄×C₄₁	—	2	2	no	—
109	C₂×D₄×C₄₁	—	2	2	no	—
110	C₂×D₄×C₄₁	—	2	2	no	—
111	C₂×D₄×C₄₁	—	4	2	no	—
112	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₁	—	2	1	no	—
114	C₂²×C₄×C₄₁	—	2	1	no	—
115	C₂²×C₄×C₄₁	—	2	1	no	—
116	C₂²×C₄×C₄₁	—	4	2	no	—
117	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
120	SD₁₆×C₄₁	—	4	4	no	—
121	D₈×C₄₁	—	4	2	no	—
122	D₈×C₄₁	—	4	4	no	—
123	D₈×C₄₁	—	4	2	no	—
124	C₂×C₈×C₄₁	—	2	2	no	—
125	C₂×C₈×C₄₁	—	2	1	no	—
126	C₂×C₈×C₄₁	—	2	1	no	—
127	C₂×C₈×C₄₁	—	2	2	no	—
128	C₂×C₈×C₄₁	—	2	2	no	—
129	C₂×C₈×C₄₁	—	4	1	no	—
130	C₂×C₈×C₄₁	—	4	2	no	—
131	C₂×C₈×C₄₁	—	4	2	no	—
132	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
136	C₄⋊C₄×C₄₁	—	2	1	no	—
137	C₄⋊C₄×C₄₁	—	2	1	no	—
138	C₄⋊C₄×C₄₁	—	2	2	no	—
139	C₄⋊C₄×C₄₁	—	2	2	no	—
140	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
141	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
142	C₂²⋊C₄×C₄₁	—	2	1	no	—
143	C₂²⋊C₄×C₄₁	—	2	1	no	—
144	C₂²⋊C₄×C₄₁	—	2	1	no	—
145	C₂²⋊C₄×C₄₁	—	4	2	no	—
146	C₂²⋊C₄×C₄₁	—	4	2	no	—
147	C₄²×C₄₁	—	2	1	no	—
148	C₄²×C₄₁	—	2	1	no	—
149	C₄²×C₄₁	—	2	1	no	—
150	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₄₁	#41	1	1	yes	characteristic
153	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
154	C₂³×C₄₁	—	2	1	no	—
155	C₂³×C₄₁	—	4	2	no	—
156	C₂³×C₄₁	#121	1	1	yes	characteristic
157	Q₈×C₄₁	—	2	1	no	—
158	Q₈×C₄₁	—	8	2	no	—
159	Q₈×C₄₁	#135	1	2	yes	—
160	D₄×C₄₁	—	2	4	no	—
161	D₄×C₄₁	—	2	1	no	—
162	D₄×C₄₁	—	4	2	no	—
163	D₄×C₄₁	—	4	2	no	—
164	D₄×C₄₁	—	4	2	no	—
165	D₄×C₄₁	—	4	2	no	—
166	D₄×C₄₁	—	8	2	no	—
167	D₄×C₄₁	—	8	4	no	—
168	D₄×C₄₁	#135	1	2	yes	—
169	C₂×C₄×C₄₁	—	2	4	no	—
170	C₂×C₄×C₄₁	—	2	1	no	—
171	C₂×C₄×C₄₁	—	2	1	no	—
172	C₂×C₄×C₄₁	—	2	1	no	—
173	C₂×C₄×C₄₁	—	2	1	no	—
174	C₂×C₄×C₄₁	—	2	1	no	—
175	C₂×C₄×C₄₁	—	2	2	no	—
176	C₂×C₄×C₄₁	—	2	1	no	—
177	C₂×C₄×C₄₁	—	2	1	no	—
178	C₂×C₄×C₄₁	—	4	1	no	—
179	C₂×C₄×C₄₁	—	4	1	no	—
180	C₂×C₄×C₄₁	—	4	2	no	—
181	C₂×C₄×C₄₁	—	4	2	no	—
182	C₂×C₄×C₄₁	—	8	4	no	—
183	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
184	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
185	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
186	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
189	C₈×C₄₁	—	2	1	no	—
190	C₈×C₄₁	—	2	1	no	—
191	C₈×C₄₁	—	2	1	no	—
192	C₈×C₄₁	—	4	1	no	—
193	C₈×C₄₁	—	4	2	no	—
194	C₈×C₄₁	—	4	2	no	—
195	C₈×C₄₁	—	4	1	no	—
196	C₈×C₄₁	#135	1	2	yes	—
197	#19128	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂²×C₄₁	—	2	1	no	—
199	C₂²×C₄₁	—	2	1	no	—
200	C₂²×C₄₁	—	2	2	no	—
201	C₂²×C₄₁	—	2	1	no	—
202	C₂²×C₄₁	—	4	1	no	—
203	C₂²×C₄₁	—	4	1	no	—
204	C₂²×C₄₁	—	8	2	no	—
205	C₂²×C₄₁	—	8	2	no	—
206	C₂²×C₄₁	—	8	2	no	—
207	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
208	C₄×C₄₁	—	2	1	no	—
209	C₄×C₄₁	—	2	1	no	—
210	C₄×C₄₁	—	2	2	no	—
211	C₄×C₄₁	—	2	1	no	—
212	C₄×C₄₁	—	4	1	no	—
213	C₄×C₄₁	—	4	1	no	—
214	C₄×C₄₁	—	8	2	no	—
215	C₄×C₄₁	#472	1	2	yes	—
216	C₄×C₄₁	C₂×#135	1	1	yes	characteristic
217	C₄×C₄₁	C₂×#135	1	1	yes	characteristic
218	C₄×C₄₁	C₂×#135	1	1	yes	characteristic
219	C₄×C₄₁	#575	1	1	yes	characteristic
220	#3169	C₂×C₄₁	1	1	yes	characteristic, complemented
221	#3106	C₂×C₄₁	1	2	yes	complemented
222	C₈×#41	C₂×C₄₁	1	1	yes	characteristic, complemented
223	#1678	C₂×C₄₁	1	2	yes	complemented
224	#1677	C₂×C₄₁	1	2	yes	complemented
225	#1676	C₂×C₄₁	1	1	yes	characteristic, complemented
226	#1675	C₂×C₄₁	1	1	yes	characteristic, complemented
227	#1668	C₂×C₄₁	1	1	yes	characteristic, complemented
228	#1667	C₂×C₄₁	1	1	yes	characteristic, complemented
229	#1564	C₂×C₄₁	1	1	yes	characteristic, complemented
230	#1543	C₂×C₄₁	1	2	yes	complemented
231	C₂×C₄₁	—	4	1	no	—
232	C₂×C₄₁	—	4	2	no	—
233	C₂×C₄₁	—	16	2	no	—
234	C₂×C₄₁	#3035	1	1	yes	characteristic
235	C₂×C₄₁	#3050	1	1	yes	characteristic
236	C₂×C₄₁	C₂×#472	1	1	yes	characteristic
237	#532	C₂²×C₄₁	1	2	yes	—
238	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
239	#500	C₂²×C₄₁	1	1	yes	characteristic
240	#493	C₂²×C₄₁	1	1	yes	characteristic
241	#486	C₂²×C₄₁	1	2	yes	—
242	#482	—	2	2	no	—
243	#477	C₂²×C₄₁	1	2	yes	—
244	#476	C₂²×C₄₁	1	2	yes	—
245	#466	—	2	1	no	—
246	#466	—	2	1	no	—
247	#460	C₂²×C₄₁	1	2	yes	—
248	#459	C₂²×C₄₁	1	2	yes	—
249	#449	—	2	2	no	—
250	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic
251	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic
252	C₄×SD₁₆	—	2	2	no	—
253	C₄×D₈	—	2	2	no	—
254	C₄×D₈	—	2	1	no	—
255	C₄×D₈	—	2	1	no	—
256	C₈×D₄	—	2	1	no	—
257	C₈×D₄	—	2	1	no	—
258	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
259	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
260	#431	—	2	1	no	—
261	#431	C₂²×C₄₁	1	1	yes	characteristic
262	#431	C₂²×C₄₁	1	2	yes	—
263	C₂×C₄×C₈	—	2	1	no	—
264	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
265	#335	C₂²×C₄₁	1	1	yes	characteristic
266	#335	C₂²×C₄₁	1	1	yes	characteristic
267	#334	C₂²×C₄₁	1	2	yes	—
268	#333	C₂²×C₄₁	1	2	yes	—
269	#333	C₂²×C₄₁	1	2	yes	—
270	#331	C₂²×C₄₁	1	2	yes	—
271	#331	C₂²×C₄₁	1	2	yes	—
272	C₄₁	#19128	1	1	yes	characteristic, direct product factor, Sylow
273	C₂×#41	—	2	2	no	—
274	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
275	C₂×SD₁₆	—	2	2	no	—
276	C₂×D₈	—	2	2	no	—
277	C₂×D₈	—	2	1	no	—
278	C₂×D₈	—	2	1	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
282	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
283	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
284	#127	C₂³×C₄₁	1	2	yes	—
285	#124	—	2	2	no	—
286	#121	—	2	2	no	—
287	#121	—	2	2	no	—
288	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
289	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	2	2	no	—
293	C₄×D₄	—	2	2	no	—
294	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
295	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
296	#117	—	2	1	no	—
297	#117	D₄×C₄₁	1	1	yes	characteristic
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
300	#107	—	2	1	no	—
301	#107	—	2	1	no	—
302	#107	—	2	2	no	—
303	#106	—	2	2	no	—
304	C₄⋊C₈	—	2	1	no	—
305	C₄⋊C₈	—	2	1	no	—
306	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
307	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
308	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
309	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
310	#103	—	2	2	no	—
311	#102	—	2	2	no	—
312	#102	—	2	2	no	—
313	#102	—	2	2	no	—
314	#102	—	2	2	no	—
315	#102	—	2	2	no	—
316	C₂²⋊C₈	—	2	1	no	—
317	C₂²⋊C₈	—	2	2	no	—
318	C₂²⋊C₈	—	2	1	no	—
319	C₂²⋊C₈	—	2	1	no	—
320	C₄×C₈	—	2	1	no	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	—	2	2	no	—
324	C₄×C₈	D₄×C₄₁	1	1	yes	characteristic
325	C₄×C₈	D₄×C₄₁	1	1	yes	characteristic
326	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
327	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
328	#41	—	2	2	no	—
329	#41	—	2	2	no	—
330	#41	—	8	4	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
345	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
346	SD₁₆	—	4	4	no	—
347	D₈	—	4	2	no	—
348	D₈	—	4	4	no	—
349	D₈	—	4	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	4	1	no	—
356	C₂×C₈	—	4	2	no	—
357	C₂×C₈	—	4	2	no	—
358	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
359	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
360	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
361	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
367	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	4	2	no	—
372	C₂²⋊C₄	—	4	2	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
377	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
378	C₄²	#41×C₄₁	1	1	yes	characteristic
379	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
380	C₂³	—	2	1	no	—
381	C₂³	—	4	2	no	—
382	C₂³	#121×C₄₁	1	1	yes	characteristic
383	Q₈	—	2	1	no	—
384	Q₈	—	8	2	no	—
385	Q₈	#135×C₄₁	1	2	yes	—
386	D₄	—	2	4	no	—
387	D₄	—	2	1	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	8	2	no	—
393	D₄	—	8	4	no	—
394	D₄	#135×C₄₁	1	2	yes	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	8	4	no	—
409	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
410	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
411	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
414	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
415	C₈	—	2	1	no	—
416	C₈	—	2	1	no	—
417	C₈	—	2	1	no	—
418	C₈	—	4	1	no	—
419	C₈	—	4	2	no	—
420	C₈	—	4	2	no	—
421	C₈	—	4	1	no	—
422	C₈	#135×C₄₁	1	2	yes	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	8	2	no	—
432	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	8	2	no	—
440	C₄	C₄₁×#472	1	2	yes	—
441	C₄	C₂×#135×C₄₁	1	1	yes	characteristic
442	C₄	C₂×#135×C₄₁	1	1	yes	characteristic
443	C₄	C₂×#135×C₄₁	1	1	yes	characteristic
444	C₄	C₄₁×#575	1	1	yes	characteristic
445	C₂	—	4	1	no	—
446	C₂	—	4	2	no	—
447	C₂	—	16	2	no	—
448	C₂	C₄₁×#3035	1	1	yes	characteristic
449	C₂	C₄₁×#3050	1	1	yes	characteristic
450	C₂	C₂×C₄₁×#472	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₁	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
socle	C₂²×C₄₁	C₂×#121
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×#3169	C₂	semidirect
2. C₄₁×#3106	C₂	semidirect
3. C₈×#41×C₄₁	C₂	semidirect
4. C₄₁×#1678	C₂	semidirect
5. C₄₁×#1677	C₂	semidirect
6. C₄₁×#1676	C₂	semidirect
7. C₄₁×#1675	C₂	semidirect
8. C₄₁×#1668	C₂	semidirect
9. C₄₁×#1667	C₂	semidirect
10. C₄₁×#1564	C₂	semidirect
11. C₄₁×#1543	C₂	semidirect
197. #19128	C₄₁	direct (N × H)
220. #3169	C₂×C₄₁	semidirect
221. #3106	C₂×C₄₁	semidirect
222. C₈×#41	C₂×C₄₁	semidirect
223. #1678	C₂×C₄₁	semidirect
224. #1677	C₂×C₄₁	semidirect
225. #1676	C₂×C₄₁	semidirect
226. #1675	C₂×C₄₁	semidirect
227. #1668	C₂×C₄₁	semidirect
228. #1667	C₂×C₄₁	semidirect
229. #1564	C₂×C₄₁	semidirect
230. #1543	C₂×C₄₁	semidirect
272. C₄₁	#19128	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×#3169	2
C₄₁×#3106	2
C₈×#41×C₄₁	2
C₄₁×#1678	2
C₄₁×#1677	2
C₄₁×#1676	2
C₄₁×#1675	2
C₄₁×#1668	2
C₄₁×#1667	2
C₄₁×#1564	2
C₄₁×#1543	2
#19128	41

Subgroups — C41×#19128 #23795329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#19128 #23795329