Subgroups — C₄₁×#25983 #23802184

Order 10496.

884 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3084	C₂	1	2	yes	maximal, complemented
2	C₄₁×#2897	C₂	1	2	yes	maximal
3	C₄₁×#2094	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2063	C₂	1	2	yes	maximal, complemented
5	C₄₁×#2027	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1866	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1859	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1815	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1792	C₂	1	1	yes	maximal, characteristic
10	C₂×H(5,𝔽₂)×C₄₁	C₂²	1	1	yes	characteristic
11	C₂×#131×C₄₁	C₂²	1	2	yes	—
12	C₄₁×#544	C₂²	1	1	yes	characteristic, complemented
13	C₄₁×#520	C₂²	1	2	yes	—
14	C₄₁×#479	—	2	2	no	—
15	C₄₁×#478	—	2	2	no	—
16	C₄₁×#476	—	2	2	no	—
17	C₄₁×#475	—	2	2	no	—
18	C₂×#108×C₄₁	C₂²	1	2	yes	complemented
19	C₄₁×#428	C₂²	1	2	yes	complemented
20	C₂×#106×C₄₁	C₂²	1	2	yes	complemented
21	C₄₁×#424	C₂²	1	2	yes	complemented
22	C₂×#104×C₄₁	C₂²	1	2	yes	—
23	C₄₁×#418	—	2	2	no	—
24	C₄₁×#418	C₂²	1	2	yes	—
25	C₄₁×#417	—	2	2	no	—
26	C₄₁×#417	C₂²	1	2	yes	—
27	C₄₁×#417	C₂²	1	2	yes	—
28	C₄₁×#416	—	2	2	no	—
29	C₄₁×#416	C₂²	1	2	yes	—
30	C₂×#102×C₄₁	—	2	2	no	—
31	C₂×#102×C₄₁	C₂²	1	2	yes	—
32	C₂×#100×C₄₁	C₂²	1	1	yes	characteristic
33	C₄₁×#390	C₂²	1	1	yes	characteristic
34	C₄₁×#384	C₂²	1	1	yes	characteristic, complemented
35	C₄₁×#343	C₂²	1	1	yes	characteristic, complemented
36	C₄₁×#343	C₂²	1	2	yes	complemented
37	C₄₁×#339	C₂²	1	2	yes	complemented
38	C₄₁×#336	C₂²	1	1	yes	characteristic, complemented
39	H(5,𝔽₂)×C₄₁	—	2	4	no	—
40	H(5,𝔽₂)×C₄₁	—	4	1	no	—
41	H(5,𝔽₂)×C₄₁	Q₈	1	4	yes	complemented
42	C₂×#41×C₄₁	—	2	2	no	—
43	C₂×#41×C₄₁	C₂³	1	2	yes	—
44	C₂²×D₄×C₄₁	—	2	2	no	—
45	C₂²×D₄×C₄₁	—	4	1	no	—
46	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
47	#131×C₄₁	—	2	4	no	—
48	#131×C₄₁	—	4	2	no	—
49	C₂×M₁₆×C₄₁	—	2	2	no	—
50	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
51	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
52	C₂²×C₈×C₄₁	—	2	2	no	—
53	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
54	C₄⋊Q₈×C₄₁	—	2	2	no	—
55	#125×C₄₁	—	2	2	no	—
56	C₂²⋊Q₈×C₄₁	—	4	1	no	—
57	C₄×Q₈×C₄₁	—	2	2	no	—
58	C₄×D₄×C₄₁	—	2	2	no	—
59	C₄×D₄×C₄₁	—	4	2	no	—
60	#117×C₄₁	—	2	2	no	—
61	#117×C₄₁	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₁	—	4	1	no	—
64	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₄₁	—	4	1	no	—
67	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
68	#108×C₄₁	—	4	2	no	—
69	#107×C₄₁	—	2	2	no	—
70	#106×C₄₁	—	2	2	no	—
71	#106×C₄₁	—	2	2	no	—
72	#106×C₄₁	—	2	2	no	—
73	C₄⋊C₈×C₄₁	—	2	2	no	—
74	C₄⋊C₈×C₄₁	—	2	2	no	—
75	#104×C₄₁	—	2	4	no	—
76	#103×C₄₁	—	2	2	no	—
77	#103×C₄₁	—	2	2	no	—
78	#103×C₄₁	D₄	1	2	yes	—
79	#103×C₄₁	D₄	1	2	yes	—
80	#102×C₄₁	—	2	2	no	—
81	#102×C₄₁	—	2	2	no	—
82	#102×C₄₁	—	2	2	no	—
83	#102×C₄₁	—	2	2	no	—
84	#102×C₄₁	—	2	2	no	—
85	#102×C₄₁	—	2	2	no	—
86	#102×C₄₁	D₄	1	2	yes	—
87	#102×C₄₁	D₄	1	2	yes	—
88	#100×C₄₁	—	4	1	no	—
89	C₂⁴×C₄₁	—	2	1	no	—
90	C₂⁴×C₄₁	—	4	1	no	—
91	#41×C₄₁	—	2	2	no	—
92	#41×C₄₁	—	2	2	no	—
93	#41×C₄₁	—	2	8	no	—
94	#41×C₄₁	—	4	4	no	—
95	#41×C₄₁	C₂×Q₈	1	4	yes	—
96	#41×C₄₁	#41	1	4	yes	—
97	C₂×Q₈×C₄₁	—	4	1	no	—
98	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
99	C₂×D₄×C₄₁	—	2	2	no	—
100	C₂×D₄×C₄₁	—	2	8	no	—
101	C₂×D₄×C₄₁	—	2	2	no	—
102	C₂×D₄×C₄₁	—	2	2	no	—
103	C₂×D₄×C₄₁	—	2	1	no	—
104	C₂×D₄×C₄₁	—	4	4	no	—
105	C₂×D₄×C₄₁	—	4	2	no	—
106	C₂×D₄×C₄₁	—	4	4	no	—
107	C₂×D₄×C₄₁	—	4	4	no	—
108	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
109	C₂×D₄×C₄₁	C₂×Q₈	1	2	yes	—
110	C₂²×C₄×C₄₁	—	2	2	no	—
111	C₂²×C₄×C₄₁	—	2	1	no	—
112	C₂²×C₄×C₄₁	—	2	1	no	—
113	C₂²×C₄×C₄₁	—	2	2	no	—
114	C₂²×C₄×C₄₁	—	4	1	no	—
115	C₂²×C₄×C₄₁	—	4	2	no	—
116	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
117	M₁₆×C₄₁	—	2	2	no	—
118	M₁₆×C₄₁	—	2	2	no	—
119	M₁₆×C₄₁	—	2	2	no	—
120	M₁₆×C₄₁	—	2	2	no	—
121	M₁₆×C₄₁	—	4	4	no	—
122	C₂×C₈×C₄₁	—	2	2	no	—
123	C₂×C₈×C₄₁	—	2	2	no	—
124	C₂×C₈×C₄₁	—	2	2	no	—
125	C₂×C₈×C₄₁	—	2	2	no	—
126	C₂×C₈×C₄₁	—	4	4	no	—
127	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₄₁	—	2	2	no	—
130	C₄⋊C₄×C₄₁	—	2	2	no	—
131	C₄⋊C₄×C₄₁	—	2	2	no	—
132	C₄⋊C₄×C₄₁	—	4	2	no	—
133	C₄⋊C₄×C₄₁	—	4	1	no	—
134	C₄⋊C₄×C₄₁	—	4	2	no	—
135	C₄⋊C₄×C₄₁	—	8	2	no	—
136	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
137	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
138	C₂²⋊C₄×C₄₁	—	2	2	no	—
139	C₂²⋊C₄×C₄₁	—	4	2	no	—
140	C₂²⋊C₄×C₄₁	—	8	2	no	—
141	C₄²×C₄₁	—	2	2	no	—
142	C₄²×C₄₁	—	2	2	no	—
143	C₄²×C₄₁	—	4	2	no	—
144	C₂³×C₄₁	—	2	2	no	—
145	C₂³×C₄₁	—	2	2	no	—
146	C₂³×C₄₁	—	4	4	no	—
147	C₂³×C₄₁	—	4	1	no	—
148	C₂³×C₄₁	—	4	1	no	—
149	C₂³×C₄₁	—	8	1	no	—
150	C₂³×C₄₁	—	8	1	no	—
151	C₂³×C₄₁	—	16	1	no	—
152	C₂³×C₄₁	—	16	1	no	—
153	C₂³×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
154	Q₈×C₄₁	—	2	2	no	—
155	Q₈×C₄₁	—	16	1	no	—
156	Q₈×C₄₁	C₂²⋊Q₈	1	4	yes	—
157	D₄×C₄₁	—	2	4	no	—
158	D₄×C₄₁	—	2	4	no	—
159	D₄×C₄₁	—	2	4	no	—
160	D₄×C₄₁	—	2	2	no	—
161	D₄×C₄₁	—	4	8	no	—
162	D₄×C₄₁	—	4	2	no	—
163	D₄×C₄₁	C₂²⋊Q₈	1	4	yes	—
164	C₂×C₄×C₄₁	—	2	2	no	—
165	C₂×C₄×C₄₁	—	2	4	no	—
166	C₂×C₄×C₄₁	—	2	4	no	—
167	C₂×C₄×C₄₁	—	2	2	no	—
168	C₂×C₄×C₄₁	—	2	2	no	—
169	C₂×C₄×C₄₁	—	2	2	no	—
170	C₂×C₄×C₄₁	—	4	4	no	—
171	C₂×C₄×C₄₁	—	4	1	no	—
172	C₂×C₄×C₄₁	—	4	1	no	—
173	C₂×C₄×C₄₁	—	4	2	no	—
174	C₂×C₄×C₄₁	—	4	1	no	—
175	C₂×C₄×C₄₁	—	8	1	no	—
176	C₂×C₄×C₄₁	—	8	2	no	—
177	C₂×C₄×C₄₁	—	16	2	no	—
178	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
179	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
181	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
182	C₈×C₄₁	—	2	2	no	—
183	C₈×C₄₁	—	2	2	no	—
184	C₈×C₄₁	—	4	2	no	—
185	C₈×C₄₁	—	4	2	no	—
186	#25983	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂²×C₄₁	—	2	1	no	—
188	C₂²×C₄₁	—	2	1	no	—
189	C₂²×C₄₁	—	2	4	no	—
190	C₂²×C₄₁	—	4	2	no	—
191	C₂²×C₄₁	—	4	2	no	—
192	C₂²×C₄₁	—	4	2	no	—
193	C₂²×C₄₁	—	8	2	no	—
194	C₂²×C₄₁	—	8	1	no	—
195	C₂²×C₄₁	—	8	1	no	—
196	C₂²×C₄₁	—	16	1	no	—
197	C₂²×C₄₁	—	16	4	no	—
198	C₂²×C₄₁	#543	1	1	yes	characteristic
199	C₂²×C₄₁	D₄²	1	1	yes	characteristic
200	C₂²×C₄₁	#551	1	1	yes	characteristic
201	C₄×C₄₁	—	2	4	no	—
202	C₄×C₄₁	—	4	2	no	—
203	C₄×C₄₁	—	4	2	no	—
204	C₄×C₄₁	—	4	2	no	—
205	C₄×C₄₁	—	8	2	no	—
206	C₄×C₄₁	—	8	1	no	—
207	C₄×C₄₁	C₂×C₂²⋊Q₈	1	2	yes	—
208	C₄×C₄₁	#546	1	2	yes	—
209	#3084	C₂×C₄₁	1	2	yes	complemented
210	#2897	C₂×C₄₁	1	2	yes	—
211	#2094	C₂×C₄₁	1	1	yes	characteristic, complemented
212	#2063	C₂×C₄₁	1	2	yes	complemented
213	#2027	C₂×C₄₁	1	1	yes	characteristic, complemented
214	#1866	C₂×C₄₁	1	2	yes	complemented
215	#1859	C₂×C₄₁	1	2	yes	complemented
216	#1815	C₂×C₄₁	1	2	yes	complemented
217	#1792	C₂×C₄₁	1	1	yes	characteristic
218	C₂×C₄₁	—	2	1	no	—
219	C₂×C₄₁	—	2	1	no	—
220	C₂×C₄₁	—	4	4	no	—
221	C₂×C₄₁	—	8	2	no	—
222	C₂×C₄₁	#2437	1	1	yes	characteristic
223	C₂×C₄₁	#3288	1	1	yes	characteristic
224	C₂×C₄₁	#3291	1	1	yes	characteristic
225	C₂×H(5,𝔽₂)	C₂²×C₄₁	1	1	yes	characteristic
226	C₂×#131	C₂²×C₄₁	1	2	yes	—
227	#544	C₂²×C₄₁	1	1	yes	characteristic, complemented
228	#520	C₂²×C₄₁	1	2	yes	—
229	#479	—	2	2	no	—
230	#478	—	2	2	no	—
231	#476	—	2	2	no	—
232	#475	—	2	2	no	—
233	C₂×#108	C₂²×C₄₁	1	2	yes	complemented
234	#428	C₂²×C₄₁	1	2	yes	complemented
235	C₂×#106	C₂²×C₄₁	1	2	yes	complemented
236	#424	C₂²×C₄₁	1	2	yes	complemented
237	C₂×#104	C₂²×C₄₁	1	2	yes	—
238	#418	—	2	2	no	—
239	#418	C₂²×C₄₁	1	2	yes	—
240	#417	—	2	2	no	—
241	#417	C₂²×C₄₁	1	2	yes	—
242	#417	C₂²×C₄₁	1	2	yes	—
243	#416	—	2	2	no	—
244	#416	C₂²×C₄₁	1	2	yes	—
245	C₂×#102	—	2	2	no	—
246	C₂×#102	C₂²×C₄₁	1	2	yes	—
247	C₂×#100	C₂²×C₄₁	1	1	yes	characteristic
248	#390	C₂²×C₄₁	1	1	yes	characteristic
249	#384	C₂²×C₄₁	1	1	yes	characteristic, complemented
250	#343	C₂²×C₄₁	1	2	yes	complemented
251	#343	C₂²×C₄₁	1	1	yes	characteristic, complemented
252	#339	C₂²×C₄₁	1	2	yes	complemented
253	#336	C₂²×C₄₁	1	1	yes	characteristic, complemented
254	C₄₁	#25983	1	1	yes	characteristic, direct product factor, Sylow
255	H(5,𝔽₂)	—	2	4	no	—
256	H(5,𝔽₂)	—	4	1	no	—
257	H(5,𝔽₂)	Q₈×C₄₁	1	4	yes	complemented
258	C₂×#41	—	2	2	no	—
259	C₂×#41	C₂³×C₄₁	1	2	yes	—
260	C₂²×D₄	—	2	2	no	—
261	C₂²×D₄	—	4	1	no	—
262	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
263	#131	—	2	4	no	—
264	#131	—	4	2	no	—
265	C₂×M₁₆	—	2	2	no	—
266	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
267	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
268	C₂²×C₈	—	2	2	no	—
269	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
270	C₄⋊Q₈	—	2	2	no	—
271	#125	—	2	2	no	—
272	C₂²⋊Q₈	—	4	1	no	—
273	C₄×Q₈	—	2	2	no	—
274	C₄×D₄	—	2	2	no	—
275	C₄×D₄	—	4	2	no	—
276	#117	—	2	2	no	—
277	#117	C₂³×C₄₁	1	2	yes	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	4	1	no	—
280	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	—	4	1	no	—
283	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
284	#108	—	4	2	no	—
285	#107	—	2	2	no	—
286	#106	—	2	2	no	—
287	#106	—	2	2	no	—
288	#106	—	2	2	no	—
289	C₄⋊C₈	—	2	2	no	—
290	C₄⋊C₈	—	2	2	no	—
291	#104	—	2	4	no	—
292	#103	—	2	2	no	—
293	#103	—	2	2	no	—
294	#103	D₄×C₄₁	1	2	yes	—
295	#103	D₄×C₄₁	1	2	yes	—
296	#102	—	2	2	no	—
297	#102	—	2	2	no	—
298	#102	—	2	2	no	—
299	#102	—	2	2	no	—
300	#102	—	2	2	no	—
301	#102	—	2	2	no	—
302	#102	D₄×C₄₁	1	2	yes	—
303	#102	D₄×C₄₁	1	2	yes	—
304	#100	—	4	1	no	—
305	C₂⁴	—	2	1	no	—
306	C₂⁴	—	4	1	no	—
307	#41	—	2	2	no	—
308	#41	—	2	2	no	—
309	#41	—	2	8	no	—
310	#41	—	4	4	no	—
311	#41	C₂×Q₈×C₄₁	1	4	yes	—
312	#41	#41×C₄₁	1	4	yes	—
313	C₂×Q₈	—	4	1	no	—
314	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	8	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	4	4	no	—
321	C₂×D₄	—	4	2	no	—
322	C₂×D₄	—	4	4	no	—
323	C₂×D₄	—	4	4	no	—
324	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
325	C₂×D₄	C₂×Q₈×C₄₁	1	2	yes	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
333	M₁₆	—	2	2	no	—
334	M₁₆	—	2	2	no	—
335	M₁₆	—	2	2	no	—
336	M₁₆	—	2	2	no	—
337	M₁₆	—	4	4	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	4	4	no	—
343	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
344	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	—	4	1	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	8	2	no	—
352	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
353	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
354	C₂²⋊C₄	—	2	2	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₂²⋊C₄	—	8	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	4	2	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	4	4	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	8	1	no	—
366	C₂³	—	8	1	no	—
367	C₂³	—	16	1	no	—
368	C₂³	—	16	1	no	—
369	C₂³	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
370	Q₈	—	2	2	no	—
371	Q₈	—	16	1	no	—
372	Q₈	C₂²⋊Q₈×C₄₁	1	4	yes	—
373	D₄	—	2	4	no	—
374	D₄	—	2	4	no	—
375	D₄	—	2	4	no	—
376	D₄	—	2	2	no	—
377	D₄	—	4	8	no	—
378	D₄	—	4	2	no	—
379	D₄	C₂²⋊Q₈×C₄₁	1	4	yes	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	8	1	no	—
392	C₂×C₄	—	8	2	no	—
393	C₂×C₄	—	16	2	no	—
394	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
395	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
396	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
397	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	2	2	no	—
400	C₈	—	4	2	no	—
401	C₈	—	4	2	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	8	2	no	—
409	C₂²	—	8	1	no	—
410	C₂²	—	8	1	no	—
411	C₂²	—	16	1	no	—
412	C₂²	—	16	4	no	—
413	C₂²	C₄₁×#543	1	1	yes	characteristic
414	C₂²	D₄²×C₄₁	1	1	yes	characteristic
415	C₂²	C₄₁×#551	1	1	yes	characteristic
416	C₄	—	2	4	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	8	2	no	—
421	C₄	—	8	1	no	—
422	C₄	C₂×C₂²⋊Q₈×C₄₁	1	2	yes	—
423	C₄	C₄₁×#546	1	2	yes	—
424	C₂	—	2	1	no	—
425	C₂	—	2	1	no	—
426	C₂	—	4	4	no	—
427	C₂	—	8	2	no	—
428	C₂	C₄₁×#2437	1	1	yes	characteristic
429	C₂	C₄₁×#3288	1	1	yes	characteristic
430	C₂	C₄₁×#3291	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×H(5,𝔽₂)×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂²×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3084	C₂	semidirect
3. C₄₁×#2094	C₂	semidirect
4. C₄₁×#2063	C₂	semidirect
5. C₄₁×#2027	C₂	semidirect
6. C₄₁×#1866	C₂	semidirect
7. C₄₁×#1859	C₂	semidirect
8. C₄₁×#1815	C₂	semidirect
12. C₄₁×#544	C₂²	semidirect
18. C₂×#108×C₄₁	C₂²	semidirect
19. C₄₁×#428	C₂²	semidirect
20. C₂×#106×C₄₁	C₂²	semidirect
21. C₄₁×#424	C₂²	semidirect
34. C₄₁×#384	C₂²	semidirect
35. C₄₁×#343	C₂²	semidirect
36. C₄₁×#343	C₂²	semidirect
37. C₄₁×#339	C₂²	semidirect
38. C₄₁×#336	C₂²	semidirect
41. H(5,𝔽₂)×C₄₁	Q₈	semidirect
186. #25983	C₄₁	direct (N × H)
209. #3084	C₂×C₄₁	semidirect
211. #2094	C₂×C₄₁	semidirect
212. #2063	C₂×C₄₁	semidirect
213. #2027	C₂×C₄₁	semidirect
214. #1866	C₂×C₄₁	semidirect
215. #1859	C₂×C₄₁	semidirect
216. #1815	C₂×C₄₁	semidirect
227. #544	C₂²×C₄₁	semidirect
233. C₂×#108	C₂²×C₄₁	semidirect
234. #428	C₂²×C₄₁	semidirect
235. C₂×#106	C₂²×C₄₁	semidirect
236. #424	C₂²×C₄₁	semidirect
249. #384	C₂²×C₄₁	semidirect
250. #343	C₂²×C₄₁	semidirect
251. #343	C₂²×C₄₁	semidirect
252. #339	C₂²×C₄₁	semidirect
253. #336	C₂²×C₄₁	semidirect
254. C₄₁	#25983	direct (N × H)
257. H(5,𝔽₂)	Q₈×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3084	2
C₄₁×#2897	2
C₄₁×#2094	2
C₄₁×#2063	2
C₄₁×#2027	2
C₄₁×#1866	2
C₄₁×#1859	2
C₄₁×#1815	2
C₄₁×#1792	2
#25983	41

Subgroups — C41×#25983 #23802184

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25983 #23802184