Subgroups — C₄₁×#12714 #23788915

Order 10496.

974 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3487	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2134	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2128	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2120	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1796	C₂	1	2	yes	maximal, complemented
6	C₂×2₋¹⁺⁴×C₄₁	C₂²	1	1	yes	characteristic
7	C₂²×#41×C₄₁	C₄	1	1	yes	characteristic, complemented
8	C₄₁×#550	—	2	2	no	—
9	C₄₁×#550	—	2	2	no	—
10	C₄₁×#548	—	2	2	no	—
11	C₄₁×#548	—	2	2	no	—
12	C₄₁×#535	—	2	2	no	—
13	C₄₁×#535	C₄	1	1	yes	characteristic, complemented
14	C₄₁×#535	C₂²	1	1	yes	characteristic
15	C₄₁×#525	—	2	2	no	—
16	C₄₁×#525	C₄	1	1	yes	characteristic, complemented
17	C₄₁×#525	C₂²	1	1	yes	characteristic
18	C₄₁×#519	C₄	1	1	yes	characteristic, complemented
19	C₄₁×#421	—	2	2	no	—
20	C₄₁×#419	—	2	2	no	—
21	C₄₁×#413	C₂²	1	2	yes	—
22	C₄₁×#410	C₂²	1	2	yes	—
23	C₄₁×#355	—	2	2	no	—
24	C₄₁×#353	—	2	2	no	—
25	C₄₁×#352	—	2	2	no	—
26	C₄₁×AΣL(1,𝔽₁₆)	—	2	2	no	—
27	2₋¹⁺⁴×C₄₁	—	4	4	no	—
28	C₂×#41×C₄₁	—	2	2	no	—
29	C₂×#41×C₄₁	—	2	2	no	—
30	C₂×#41×C₄₁	—	2	2	no	—
31	C₂×#41×C₄₁	—	2	1	no	—
32	C₂×#41×C₄₁	—	4	4	no	—
33	C₂×#41×C₄₁	C₂×C₄	1	1	yes	characteristic
34	C₂×#41×C₄₁	D₄	1	2	yes	—
35	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
36	C₂²×Q₈×C₄₁	—	2	1	no	—
37	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×Q₈×C₄₁	D₄	1	2	yes	—
39	C₂²×D₄×C₄₁	—	2	1	no	—
40	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₁	—	2	1	no	—
42	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
43	C₂×M₁₆×C₄₁	—	2	2	no	—
44	#127×C₄₁	—	2	4	no	—
45	#127×C₄₁	—	2	1	no	—
46	#127×C₄₁	D₄	1	2	yes	—
47	#124×C₄₁	—	2	4	no	—
48	#124×C₄₁	—	2	1	no	—
49	#124×C₄₁	D₄	1	2	yes	—
50	#123×C₄₁	—	2	1	no	—
51	#123×C₄₁	D₄	1	2	yes	—
52	C₂²⋊Q₈×C₄₁	—	2	4	no	—
53	C₂²⋊Q₈×C₄₁	—	2	1	no	—
54	C₂²⋊Q₈×C₄₁	—	2	1	no	—
55	#121×C₄₁	—	2	4	no	—
56	#121×C₄₁	—	2	4	no	—
57	#121×C₄₁	—	2	4	no	—
58	#121×C₄₁	—	2	1	no	—
59	#121×C₄₁	—	2	2	no	—
60	#121×C₄₁	—	2	1	no	—
61	#121×C₄₁	—	2	2	no	—
62	#120×C₄₁	—	2	1	no	—
63	#120×C₄₁	—	2	2	no	—
64	#120×C₄₁	—	2	2	no	—
65	#120×C₄₁	D₄	1	2	yes	—
66	C₄×Q₈×C₄₁	—	2	2	no	—
67	C₄×Q₈×C₄₁	—	2	2	no	—
68	C₄×D₄×C₄₁	—	2	4	no	—
69	C₄×D₄×C₄₁	—	2	4	no	—
70	C₄×D₄×C₄₁	—	2	2	no	—
71	C₄×D₄×C₄₁	—	2	2	no	—
72	#117×C₄₁	—	2	2	no	—
73	#117×C₄₁	—	2	2	no	—
74	#117×C₄₁	C₂×C₄	1	1	yes	characteristic
75	#117×C₄₁	C₂×C₄	1	1	yes	characteristic
76	#104×C₄₁	—	4	4	no	—
77	#103×C₄₁	—	4	4	no	—
78	#101×C₄₁	—	2	2	no	—
79	#100×C₄₁	—	2	2	no	—
80	#99×C₄₁	—	2	2	no	—
81	#99×C₄₁	—	2	2	no	—
82	C₂⁴×C₄₁	—	2	1	no	—
83	C₂⁴×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
84	#41×C₄₁	—	2	4	no	—
85	#41×C₄₁	—	4	2	no	—
86	#41×C₄₁	—	4	2	no	—
87	#41×C₄₁	—	4	2	no	—
88	#41×C₄₁	—	4	8	no	—
89	#41×C₄₁	—	4	8	no	—
90	#41×C₄₁	—	4	4	no	—
91	#41×C₄₁	—	4	4	no	—
92	#41×C₄₁	—	4	4	no	—
93	C₂×Q₈×C₄₁	—	2	4	no	—
94	C₂×Q₈×C₄₁	—	2	1	no	—
95	C₂×Q₈×C₄₁	—	2	2	no	—
96	C₂×Q₈×C₄₁	—	2	4	no	—
97	C₂×Q₈×C₄₁	—	4	2	no	—
98	C₂×Q₈×C₄₁	—	4	4	no	—
99	C₂×Q₈×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×Q₈×C₄₁	C₂²⋊C₄	1	2	yes	—
101	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
102	C₂×D₄×C₄₁	—	2	4	no	—
103	C₂×D₄×C₄₁	—	2	1	no	—
104	C₂×D₄×C₄₁	—	2	2	no	—
105	C₂×D₄×C₄₁	—	2	4	no	—
106	C₂×D₄×C₄₁	—	2	2	no	—
107	C₂×D₄×C₄₁	—	2	4	no	—
108	C₂×D₄×C₄₁	—	2	2	no	—
109	C₂×D₄×C₄₁	—	2	1	no	—
110	C₂×D₄×C₄₁	—	4	4	no	—
111	C₂×D₄×C₄₁	—	4	2	no	—
112	C₂×D₄×C₄₁	C₂²⋊C₄	1	2	yes	—
113	C₂×D₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
114	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
115	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₁	—	2	1	no	—
117	C₂²×C₄×C₄₁	—	2	4	no	—
118	C₂²×C₄×C₄₁	—	2	2	no	—
119	C₂²×C₄×C₄₁	—	2	1	no	—
120	C₂²×C₄×C₄₁	—	2	1	no	—
121	C₂²×C₄×C₄₁	—	2	1	no	—
122	C₂²×C₄×C₄₁	—	2	2	no	—
123	C₂²×C₄×C₄₁	—	4	4	no	—
124	C₂²×C₄×C₄₁	—	4	2	no	—
125	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
128	M₁₆×C₄₁	—	4	2	no	—
129	M₁₆×C₄₁	—	4	2	no	—
130	C₂×C₈×C₄₁	—	4	2	no	—
131	C₄⋊C₄×C₄₁	—	2	4	no	—
132	C₄⋊C₄×C₄₁	—	2	2	no	—
133	C₄⋊C₄×C₄₁	—	2	1	no	—
134	C₄⋊C₄×C₄₁	—	2	1	no	—
135	C₄⋊C₄×C₄₁	—	2	2	no	—
136	C₄⋊C₄×C₄₁	—	4	2	no	—
137	C₂²⋊C₄×C₄₁	—	2	2	no	—
138	C₂²⋊C₄×C₄₁	—	2	4	no	—
139	C₂²⋊C₄×C₄₁	—	2	2	no	—
140	C₂²⋊C₄×C₄₁	—	2	1	no	—
141	C₂²⋊C₄×C₄₁	—	2	2	no	—
142	C₂²⋊C₄×C₄₁	—	2	4	no	—
143	C₂²⋊C₄×C₄₁	—	2	2	no	—
144	C₂²⋊C₄×C₄₁	—	4	2	no	—
145	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
146	C₄²×C₄₁	—	2	4	no	—
147	C₄²×C₄₁	—	2	1	no	—
148	C₄²×C₄₁	—	4	2	no	—
149	C₄²×C₄₁	C₂²⋊C₄	1	2	yes	—
150	C₂³×C₄₁	—	2	1	no	—
151	C₂³×C₄₁	—	2	2	no	—
152	C₂³×C₄₁	—	2	1	no	—
153	C₂³×C₄₁	—	4	2	no	—
154	C₂³×C₄₁	—	4	1	no	—
155	C₂³×C₄₁	—	8	1	no	—
156	C₂³×C₄₁	—	8	2	no	—
157	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂³×C₄₁	#120	1	2	yes	—
159	Q₈×C₄₁	—	2	4	no	—
160	Q₈×C₄₁	—	2	2	no	—
161	Q₈×C₄₁	—	2	2	no	—
162	Q₈×C₄₁	—	4	1	no	—
163	Q₈×C₄₁	—	4	4	no	—
164	Q₈×C₄₁	#99	1	4	yes	—
165	D₄×C₄₁	—	2	2	no	—
166	D₄×C₄₁	—	4	2	no	—
167	D₄×C₄₁	—	4	1	no	—
168	D₄×C₄₁	—	4	4	no	—
169	D₄×C₄₁	—	4	2	no	—
170	D₄×C₄₁	—	4	8	no	—
171	D₄×C₄₁	—	4	2	no	—
172	D₄×C₄₁	—	4	2	no	—
173	D₄×C₄₁	—	8	4	no	—
174	D₄×C₄₁	—	8	2	no	—
175	D₄×C₄₁	—	8	4	no	—
176	D₄×C₄₁	—	8	2	no	—
177	C₂×C₄×C₄₁	—	2	4	no	—
178	C₂×C₄×C₄₁	—	2	2	no	—
179	C₂×C₄×C₄₁	—	2	2	no	—
180	C₂×C₄×C₄₁	—	2	2	no	—
181	C₂×C₄×C₄₁	—	2	2	no	—
182	C₂×C₄×C₄₁	—	2	2	no	—
183	C₂×C₄×C₄₁	—	2	2	no	—
184	C₂×C₄×C₄₁	—	2	1	no	—
185	C₂×C₄×C₄₁	—	2	1	no	—
186	C₂×C₄×C₄₁	—	4	4	no	—
187	C₂×C₄×C₄₁	—	4	4	no	—
188	C₂×C₄×C₄₁	—	4	8	no	—
189	C₂×C₄×C₄₁	—	4	2	no	—
190	C₂×C₄×C₄₁	—	4	2	no	—
191	C₂×C₄×C₄₁	—	4	2	no	—
192	C₂×C₄×C₄₁	—	4	1	no	—
193	C₂×C₄×C₄₁	—	8	2	no	—
194	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₄₁	#120	1	2	yes	—
197	C₈×C₄₁	—	8	2	no	—
198	#12714	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂²×C₄₁	—	2	1	no	—
200	C₂²×C₄₁	—	2	2	no	—
201	C₂²×C₄₁	—	4	2	no	—
202	C₂²×C₄₁	—	4	1	no	—
203	C₂²×C₄₁	—	4	2	no	—
204	C₂²×C₄₁	—	4	1	no	—
205	C₂²×C₄₁	—	4	1	no	—
206	C₂²×C₄₁	—	4	4	no	—
207	C₂²×C₄₁	—	4	1	no	—
208	C₂²×C₄₁	—	4	1	no	—
209	C₂²×C₄₁	—	4	2	no	—
210	C₂²×C₄₁	—	8	2	no	—
211	C₂²×C₄₁	—	8	4	no	—
212	C₂²×C₄₁	#379	1	1	yes	characteristic
213	C₄×C₄₁	—	2	2	no	—
214	C₄×C₄₁	—	2	4	no	—
215	C₄×C₄₁	—	2	1	no	—
216	C₄×C₄₁	—	4	2	no	—
217	C₄×C₄₁	—	4	2	no	—
218	C₄×C₄₁	—	4	1	no	—
219	C₄×C₄₁	—	4	1	no	—
220	C₄×C₄₁	—	16	2	no	—
221	C₄×C₄₁	C₂×#99	1	2	yes	—
222	#3487	C₂×C₄₁	1	1	yes	characteristic
223	#2134	C₂×C₄₁	1	1	yes	characteristic, complemented
224	#2128	C₂×C₄₁	1	1	yes	characteristic, complemented
225	#2120	C₂×C₄₁	1	2	yes	complemented
226	#1796	C₂×C₄₁	1	2	yes	complemented
227	C₂×C₄₁	—	2	1	no	—
228	C₂×C₄₁	—	4	2	no	—
229	C₂×C₄₁	—	4	1	no	—
230	C₂×C₄₁	—	8	1	no	—
231	C₂×C₄₁	—	8	1	no	—
232	C₂×C₄₁	—	8	2	no	—
233	C₂×C₄₁	#1781	1	1	yes	characteristic
234	C₂×2₋¹⁺⁴	C₂²×C₄₁	1	1	yes	characteristic
235	C₂²×#41	C₄×C₄₁	1	1	yes	characteristic, complemented
236	#550	—	2	2	no	—
237	#550	—	2	2	no	—
238	#548	—	2	2	no	—
239	#548	—	2	2	no	—
240	#535	—	2	2	no	—
241	#535	C₄×C₄₁	1	1	yes	characteristic, complemented
242	#535	C₂²×C₄₁	1	1	yes	characteristic
243	#525	—	2	2	no	—
244	#525	C₄×C₄₁	1	1	yes	characteristic, complemented
245	#525	C₂²×C₄₁	1	1	yes	characteristic
246	#519	C₄×C₄₁	1	1	yes	characteristic, complemented
247	#421	—	2	2	no	—
248	#419	—	2	2	no	—
249	#413	C₂²×C₄₁	1	2	yes	—
250	#410	C₂²×C₄₁	1	2	yes	—
251	#355	—	2	2	no	—
252	#353	—	2	2	no	—
253	#352	—	2	2	no	—
254	AΣL(1,𝔽₁₆)	—	2	2	no	—
255	C₄₁	#12714	1	1	yes	characteristic, direct product factor, Sylow
256	2₋¹⁺⁴	—	4	4	no	—
257	C₂×#41	—	2	2	no	—
258	C₂×#41	—	2	2	no	—
259	C₂×#41	—	2	2	no	—
260	C₂×#41	—	2	1	no	—
261	C₂×#41	—	4	4	no	—
262	C₂×#41	C₂×C₄×C₄₁	1	1	yes	characteristic
263	C₂×#41	D₄×C₄₁	1	2	yes	—
264	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
265	C₂²×Q₈	—	2	1	no	—
266	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
267	C₂²×Q₈	D₄×C₄₁	1	2	yes	—
268	C₂²×D₄	—	2	1	no	—
269	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
270	C₂³×C₄	—	2	1	no	—
271	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
272	C₂×M₁₆	—	2	2	no	—
273	#127	—	2	4	no	—
274	#127	—	2	1	no	—
275	#127	D₄×C₄₁	1	2	yes	—
276	#124	—	2	4	no	—
277	#124	—	2	1	no	—
278	#124	D₄×C₄₁	1	2	yes	—
279	#123	—	2	1	no	—
280	#123	D₄×C₄₁	1	2	yes	—
281	C₂²⋊Q₈	—	2	4	no	—
282	C₂²⋊Q₈	—	2	1	no	—
283	C₂²⋊Q₈	—	2	1	no	—
284	#121	—	2	4	no	—
285	#121	—	2	4	no	—
286	#121	—	2	4	no	—
287	#121	—	2	1	no	—
288	#121	—	2	2	no	—
289	#121	—	2	1	no	—
290	#121	—	2	2	no	—
291	#120	—	2	1	no	—
292	#120	—	2	2	no	—
293	#120	—	2	2	no	—
294	#120	D₄×C₄₁	1	2	yes	—
295	C₄×Q₈	—	2	2	no	—
296	C₄×Q₈	—	2	2	no	—
297	C₄×D₄	—	2	4	no	—
298	C₄×D₄	—	2	4	no	—
299	C₄×D₄	—	2	2	no	—
300	C₄×D₄	—	2	2	no	—
301	#117	—	2	2	no	—
302	#117	—	2	2	no	—
303	#117	C₂×C₄×C₄₁	1	1	yes	characteristic
304	#117	C₂×C₄×C₄₁	1	1	yes	characteristic
305	#104	—	4	4	no	—
306	#103	—	4	4	no	—
307	#101	—	2	2	no	—
308	#100	—	2	2	no	—
309	#99	—	2	2	no	—
310	#99	—	2	2	no	—
311	C₂⁴	—	2	1	no	—
312	C₂⁴	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
313	#41	—	2	4	no	—
314	#41	—	4	2	no	—
315	#41	—	4	2	no	—
316	#41	—	4	2	no	—
317	#41	—	4	8	no	—
318	#41	—	4	8	no	—
319	#41	—	4	4	no	—
320	#41	—	4	4	no	—
321	#41	—	4	4	no	—
322	C₂×Q₈	—	2	4	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	4	no	—
326	C₂×Q₈	—	4	2	no	—
327	C₂×Q₈	—	4	4	no	—
328	C₂×Q₈	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
329	C₂×Q₈	C₂²⋊C₄×C₄₁	1	2	yes	—
330	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	4	4	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
342	C₂×D₄	C₂²⋊C₄×C₄₁	1	2	yes	—
343	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
344	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	4	4	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
355	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
357	M₁₆	—	4	2	no	—
358	M₁₆	—	4	2	no	—
359	C₂×C₈	—	4	2	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	4	2	no	—
374	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
375	C₄²	—	2	4	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	4	2	no	—
378	C₄²	C₂²⋊C₄×C₄₁	1	2	yes	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	4	2	no	—
383	C₂³	—	4	1	no	—
384	C₂³	—	8	1	no	—
385	C₂³	—	8	2	no	—
386	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
387	C₂³	#120×C₄₁	1	2	yes	—
388	Q₈	—	2	4	no	—
389	Q₈	—	2	2	no	—
390	Q₈	—	2	2	no	—
391	Q₈	—	4	1	no	—
392	Q₈	—	4	4	no	—
393	Q₈	#99×C₄₁	1	4	yes	—
394	D₄	—	2	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	1	no	—
397	D₄	—	4	4	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	8	no	—
400	D₄	—	4	2	no	—
401	D₄	—	4	2	no	—
402	D₄	—	8	4	no	—
403	D₄	—	8	2	no	—
404	D₄	—	8	4	no	—
405	D₄	—	8	2	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	8	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	8	2	no	—
423	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
424	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
425	C₂×C₄	#120×C₄₁	1	2	yes	—
426	C₈	—	8	2	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	8	2	no	—
439	C₂²	—	8	4	no	—
440	C₂²	C₄₁×#379	1	1	yes	characteristic
441	C₄	—	2	2	no	—
442	C₄	—	2	4	no	—
443	C₄	—	2	1	no	—
444	C₄	—	4	2	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	1	no	—
447	C₄	—	4	1	no	—
448	C₄	—	16	2	no	—
449	C₄	C₂×#99×C₄₁	1	2	yes	—
450	C₂	—	2	1	no	—
451	C₂	—	4	2	no	—
452	C₂	—	4	1	no	—
453	C₂	—	8	2	no	—
454	C₂	—	8	1	no	—
455	C₂	—	8	1	no	—
456	C₂	C₄₁×#1781	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₄₁	#1781
commutator	C₂²×C₄	C₂²×C₄×C₄₁
Frattini, cosocle	C₂×#41	C₂³×C₄₁
prime radical	C₄₁×#3487	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄₁ ◁ C₂×C₄×C₄₁ ◁ C₂×2₋¹⁺⁴×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2134	C₂	semidirect
3. C₄₁×#2128	C₂	semidirect
4. C₄₁×#2120	C₂	semidirect
5. C₄₁×#1796	C₂	semidirect
7. C₂²×#41×C₄₁	C₄	semidirect
13. C₄₁×#535	C₄	semidirect
16. C₄₁×#525	C₄	semidirect
18. C₄₁×#519	C₄	semidirect
198. #12714	C₄₁	direct (N × H)
223. #2134	C₂×C₄₁	semidirect
224. #2128	C₂×C₄₁	semidirect
225. #2120	C₂×C₄₁	semidirect
226. #1796	C₂×C₄₁	semidirect
235. C₂²×#41	C₄×C₄₁	semidirect
241. #535	C₄×C₄₁	semidirect
244. #525	C₄×C₄₁	semidirect
246. #519	C₄×C₄₁	semidirect
255. C₄₁	#12714	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×#3487	2
C₄₁×#2134	2
C₄₁×#2128	2
C₄₁×#2120	2
C₄₁×#1796	2
#12714	41

Subgroups — C41×#12714 #23788915

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#12714 #23788915