Subgroups — C₄₁×#32895 #23809096

Order 10496.

3540 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×2₋¹⁺⁶	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3027	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3021	C₂	1	3	yes	maximal, complemented
4	C₄₁×#3010	C₂	1	3	yes	maximal, complemented
5	C₄₁×#1796	C₂	1	3	yes	maximal, complemented
6	C₄₁×#1794	C₂	1	3	yes	maximal, complemented
7	C₄₁×#1791	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#585	—	2	4	no	—
9	C₄₁×#585	—	2	6	no	—
10	C₄₁×#585	—	2	6	no	—
11	C₄₁×#585	C₂²	1	3	yes	—
12	C₄₁×#585	C₂²	1	1	yes	characteristic
13	C₂×2₋¹⁺⁴×C₄₁	—	2	6	no	—
14	C₂×2₋¹⁺⁴×C₄₁	—	2	6	no	—
15	C₂×2₋¹⁺⁴×C₄₁	C₂²	1	3	yes	—
16	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	3	yes	complemented
17	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
18	C₄₁×#535	C₂²	1	3	yes	complemented
19	C₄₁×B(4,𝔽₂)	—	2	4	no	—
20	C₄₁×#454	—	2	6	no	—
21	C₄₁×#453	—	2	6	no	—
22	C₄₁×#449	—	2	6	no	—
23	C₄₁×#448	—	2	6	no	—
24	C₄₁×#421	C₂²	1	6	yes	complemented
25	C₄₁×#419	C₂²	1	3	yes	complemented
26	C₄₁×#416	C₂²	1	3	yes	complemented
27	C₄₁×#413	C₂²	1	3	yes	complemented
28	C₄₁×#410	C₂²	1	3	yes	complemented
29	C₄₁×#408	C₂²	1	3	yes	complemented
30	2₋¹⁺⁴×C₄₁	—	2	12	no	—
31	2₋¹⁺⁴×C₄₁	—	2	24	no	—
32	2₋¹⁺⁴×C₄₁	—	2	24	no	—
33	2₋¹⁺⁴×C₄₁	—	2	12	no	—
34	2₋¹⁺⁴×C₄₁	—	2	12	no	—
35	2₋¹⁺⁴×C₄₁	—	2	3	no	—
36	2₋¹⁺⁴×C₄₁	—	2	6	no	—
37	2₋¹⁺⁴×C₄₁	—	2	12	no	—
38	2₋¹⁺⁴×C₄₁	D₄	1	6	yes	complemented
39	H(5,𝔽₂)×C₄₁	—	2	4	no	—
40	H(5,𝔽₂)×C₄₁	—	2	12	no	—
41	H(5,𝔽₂)×C₄₁	—	2	24	no	—
42	H(5,𝔽₂)×C₄₁	—	2	6	no	—
43	H(5,𝔽₂)×C₄₁	—	2	3	no	—
44	H(5,𝔽₂)×C₄₁	—	2	6	no	—
45	H(5,𝔽₂)×C₄₁	D₄	1	4	yes	—
46	H(5,𝔽₂)×C₄₁	D₄	1	6	yes	complemented
47	C₂×#41×C₄₁	—	2	12	no	—
48	C₂×#41×C₄₁	—	2	12	no	—
49	C₂×#41×C₄₁	—	2	24	no	—
50	C₂×#41×C₄₁	—	2	24	no	—
51	C₂×#41×C₄₁	—	2	24	no	—
52	C₂×#41×C₄₁	—	2	12	no	—
53	C₂×#41×C₄₁	—	2	3	no	—
54	C₂×#41×C₄₁	—	2	6	no	—
55	C₂×#41×C₄₁	—	2	6	no	—
56	C₂×#41×C₄₁	—	2	6	no	—
57	C₂×#41×C₄₁	D₄	1	6	yes	complemented
58	C₂×#41×C₄₁	C₂³	1	3	yes	—
59	C₂×#41×C₄₁	C₂³	1	3	yes	—
60	C₂²×Q₈×C₄₁	—	2	12	no	—
61	C₂²×Q₈×C₄₁	—	2	4	no	—
62	C₂²×Q₈×C₄₁	—	2	3	no	—
63	C₂²×Q₈×C₄₁	D₄	1	6	yes	complemented
64	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
66	AGL(1,ℤ/8)×C₄₁	—	2	12	no	—
67	C₂×SD₁₆×C₄₁	—	2	6	no	—
68	C₂×SD₁₆×C₄₁	—	2	3	no	—
69	C₂×D₈×C₄₁	—	2	3	no	—
70	C₂×M₁₆×C₄₁	C₂³	1	3	yes	—
71	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
72	#127×C₄₁	—	2	3	no	—
73	#124×C₄₁	—	2	3	no	—
74	#121×C₄₁	—	2	6	no	—
75	#120×C₄₁	—	2	6	no	—
76	#117×C₄₁	C₂³	1	3	yes	—
77	#104×C₄₁	—	2	12	no	—
78	#103×C₄₁	—	2	3	no	—
79	#103×C₄₁	—	2	6	no	—
80	#102×C₄₁	—	2	3	no	—
81	#101×C₄₁	—	2	3	no	—
82	#100×C₄₁	—	2	3	no	—
83	#99×C₄₁	—	2	6	no	—
84	C₂²⋊C₈×C₄₁	—	2	6	no	—
85	C₂⁴×C₄₁	—	2	1	no	—
86	#41×C₄₁	—	2	48	no	—
87	#41×C₄₁	—	2	24	no	—
88	#41×C₄₁	—	2	48	no	—
89	#41×C₄₁	—	2	8	no	—
90	#41×C₄₁	—	2	24	no	—
91	#41×C₄₁	—	2	48	no	—
92	#41×C₄₁	—	2	24	no	—
93	#41×C₄₁	—	2	12	no	—
94	#41×C₄₁	—	2	12	no	—
95	#41×C₄₁	—	2	12	no	—
96	#41×C₄₁	—	2	4	no	—
97	#41×C₄₁	—	2	12	no	—
98	#41×C₄₁	—	2	12	no	—
99	#41×C₄₁	—	2	12	no	—
100	#41×C₄₁	—	2	12	no	—
101	#41×C₄₁	—	2	12	no	—
102	#41×C₄₁	—	2	12	no	—
103	#41×C₄₁	—	2	6	no	—
104	#41×C₄₁	—	2	6	no	—
105	#41×C₄₁	—	2	6	no	—
106	#41×C₄₁	C₂×D₄	1	12	yes	—
107	C₂×Q₈×C₄₁	—	2	24	no	—
108	C₂×Q₈×C₄₁	—	2	24	no	—
109	C₂×Q₈×C₄₁	—	2	24	no	—
110	C₂×Q₈×C₄₁	—	2	6	no	—
111	C₂×Q₈×C₄₁	—	2	6	no	—
112	C₂×Q₈×C₄₁	—	2	12	no	—
113	C₂×Q₈×C₄₁	—	2	12	no	—
114	C₂×Q₈×C₄₁	—	2	12	no	—
115	C₂×Q₈×C₄₁	—	2	6	no	—
116	C₂×Q₈×C₄₁	—	2	3	no	—
117	C₂×Q₈×C₄₁	C₂×D₄	1	3	yes	—
118	C₂×Q₈×C₄₁	C₂×D₄	1	6	yes	—
119	C₂×Q₈×C₄₁	C₂×D₄	1	3	yes	—
120	C₂×D₄×C₄₁	—	2	24	no	—
121	C₂×D₄×C₄₁	—	2	24	no	—
122	C₂×D₄×C₄₁	—	2	24	no	—
123	C₂×D₄×C₄₁	—	2	6	no	—
124	C₂×D₄×C₄₁	—	2	6	no	—
125	C₂×D₄×C₄₁	—	2	12	no	—
126	C₂×D₄×C₄₁	—	2	12	no	—
127	C₂×D₄×C₄₁	—	2	6	no	—
128	C₂×D₄×C₄₁	—	2	3	no	—
129	C₂×D₄×C₄₁	—	2	12	no	—
130	C₂×D₄×C₄₁	—	2	3	no	—
131	C₂×D₄×C₄₁	—	2	3	no	—
132	C₂×D₄×C₄₁	—	4	6	no	—
133	C₂×D₄×C₄₁	C₂×D₄	1	6	yes	—
134	C₂×D₄×C₄₁	C₂×D₄	1	3	yes	—
135	C₂×D₄×C₄₁	C₂×D₄	1	3	yes	—
136	C₂²×C₄×C₄₁	—	2	8	no	—
137	C₂²×C₄×C₄₁	—	2	24	no	—
138	C₂²×C₄×C₄₁	—	2	12	no	—
139	C₂²×C₄×C₄₁	—	2	4	no	—
140	C₂²×C₄×C₄₁	—	2	6	no	—
141	C₂²×C₄×C₄₁	—	2	1	no	—
142	C₂²×C₄×C₄₁	—	2	6	no	—
143	C₂²×C₄×C₄₁	—	2	3	no	—
144	C₂²×C₄×C₄₁	C₂×D₄	1	6	yes	—
145	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
146	SD₁₆×C₄₁	—	4	4	no	—
147	SD₁₆×C₄₁	—	4	6	no	—
148	D₈×C₄₁	—	4	6	no	—
149	M₁₆×C₄₁	—	2	6	no	—
150	C₂×C₈×C₄₁	—	2	3	no	—
151	C₂×C₈×C₄₁	—	2	3	no	—
152	C₄⋊C₄×C₄₁	—	2	3	no	—
153	C₂²⋊C₄×C₄₁	—	2	3	no	—
154	C₂²⋊C₄×C₄₁	—	4	6	no	—
155	C₄²×C₄₁	—	2	3	no	—
156	C₂³×C₄₁	—	2	4	no	—
157	C₂³×C₄₁	—	2	12	no	—
158	C₂³×C₄₁	—	2	3	no	—
159	C₂³×C₄₁	—	4	3	no	—
160	C₂³×C₄₁	—	16	1	no	—
161	C₂³×C₄₁	#120	1	6	yes	—
162	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
163	Q₈×C₄₁	—	2	12	no	—
164	Q₈×C₄₁	—	2	24	no	—
165	Q₈×C₄₁	—	2	4	no	—
166	Q₈×C₄₁	—	2	3	no	—
167	Q₈×C₄₁	—	2	6	no	—
168	Q₈×C₄₁	—	2	6	no	—
169	Q₈×C₄₁	#120	1	6	yes	—
170	Q₈×C₄₁	#120	1	4	yes	—
171	D₄×C₄₁	—	2	24	no	—
172	D₄×C₄₁	—	2	24	no	—
173	D₄×C₄₁	—	2	12	no	—
174	D₄×C₄₁	—	2	12	no	—
175	D₄×C₄₁	—	2	12	no	—
176	D₄×C₄₁	—	2	12	no	—
177	D₄×C₄₁	—	2	3	no	—
178	D₄×C₄₁	—	2	6	no	—
179	D₄×C₄₁	—	4	3	no	—
180	D₄×C₄₁	—	4	1	no	—
181	D₄×C₄₁	—	16	6	no	—
182	D₄×C₄₁	#120	1	6	yes	—
183	C₂×C₄×C₄₁	—	2	12	no	—
184	C₂×C₄×C₄₁	—	2	24	no	—
185	C₂×C₄×C₄₁	—	2	24	no	—
186	C₂×C₄×C₄₁	—	2	24	no	—
187	C₂×C₄×C₄₁	—	2	12	no	—
188	C₂×C₄×C₄₁	—	2	3	no	—
189	C₂×C₄×C₄₁	—	2	6	no	—
190	C₂×C₄×C₄₁	—	2	12	no	—
191	C₂×C₄×C₄₁	—	2	6	no	—
192	C₂×C₄×C₄₁	—	2	6	no	—
193	C₂×C₄×C₄₁	—	4	3	no	—
194	C₂×C₄×C₄₁	#120	1	6	yes	—
195	C₂×C₄×C₄₁	C₂²×D₄	1	3	yes	—
196	C₂×C₄×C₄₁	C₂²×D₄	1	3	yes	—
197	C₈×C₄₁	—	4	1	no	—
198	C₈×C₄₁	—	4	3	no	—
199	#32895	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂²×C₄₁	—	2	6	no	—
201	C₂²×C₄₁	—	2	6	no	—
202	C₂²×C₄₁	—	4	1	no	—
203	C₂²×C₄₁	—	4	6	no	—
204	C₂²×C₄₁	—	8	3	no	—
205	C₂²×C₄₁	—	8	6	no	—
206	C₂²×C₄₁	—	8	4	no	—
207	C₂²×C₄₁	—	8	12	no	—
208	C₂²×C₄₁	—	8	1	no	—
209	C₂²×C₄₁	C₂×#120	1	3	yes	—
210	C₄×C₄₁	—	2	4	no	—
211	C₄×C₄₁	—	2	6	no	—
212	C₄×C₄₁	—	2	6	no	—
213	C₄×C₄₁	—	8	3	no	—
214	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
215	C₄×C₄₁	C₂×#120	1	3	yes	—
216	2₋¹⁺⁶	C₂×C₄₁	1	1	yes	characteristic, complemented
217	#3027	C₂×C₄₁	1	1	yes	characteristic, complemented
218	#3021	C₂×C₄₁	1	3	yes	complemented
219	#3010	C₂×C₄₁	1	3	yes	complemented
220	#1796	C₂×C₄₁	1	3	yes	complemented
221	#1794	C₂×C₄₁	1	3	yes	complemented
222	#1791	C₂×C₄₁	1	1	yes	characteristic, complemented
223	C₂×C₄₁	—	2	3	no	—
224	C₂×C₄₁	—	4	6	no	—
225	C₂×C₄₁	—	4	6	no	—
226	C₂×C₄₁	—	16	1	no	—
227	C₂×C₄₁	#2846	1	1	yes	characteristic
228	#585	—	2	4	no	—
229	#585	—	2	6	no	—
230	#585	—	2	6	no	—
231	#585	C₂²×C₄₁	1	3	yes	—
232	#585	C₂²×C₄₁	1	1	yes	characteristic
233	C₂×2₋¹⁺⁴	—	2	6	no	—
234	C₂×2₋¹⁺⁴	—	2	6	no	—
235	C₂×2₋¹⁺⁴	C₂²×C₄₁	1	3	yes	—
236	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	3	yes	complemented
237	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
238	#535	C₂²×C₄₁	1	3	yes	complemented
239	B(4,𝔽₂)	—	2	4	no	—
240	#454	—	2	6	no	—
241	#453	—	2	6	no	—
242	#449	—	2	6	no	—
243	#448	—	2	6	no	—
244	#421	C₂²×C₄₁	1	6	yes	complemented
245	#419	C₂²×C₄₁	1	3	yes	complemented
246	#416	C₂²×C₄₁	1	3	yes	complemented
247	#413	C₂²×C₄₁	1	3	yes	complemented
248	#410	C₂²×C₄₁	1	3	yes	complemented
249	#408	C₂²×C₄₁	1	3	yes	complemented
250	C₄₁	#32895	1	1	yes	characteristic, direct product factor, Sylow
251	2₋¹⁺⁴	—	2	12	no	—
252	2₋¹⁺⁴	—	2	24	no	—
253	2₋¹⁺⁴	—	2	24	no	—
254	2₋¹⁺⁴	—	2	12	no	—
255	2₋¹⁺⁴	—	2	12	no	—
256	2₋¹⁺⁴	—	2	3	no	—
257	2₋¹⁺⁴	—	2	6	no	—
258	2₋¹⁺⁴	—	2	12	no	—
259	2₋¹⁺⁴	D₄×C₄₁	1	6	yes	complemented
260	H(5,𝔽₂)	—	2	4	no	—
261	H(5,𝔽₂)	—	2	12	no	—
262	H(5,𝔽₂)	—	2	24	no	—
263	H(5,𝔽₂)	—	2	6	no	—
264	H(5,𝔽₂)	—	2	3	no	—
265	H(5,𝔽₂)	—	2	6	no	—
266	H(5,𝔽₂)	D₄×C₄₁	1	4	yes	—
267	H(5,𝔽₂)	D₄×C₄₁	1	6	yes	complemented
268	C₂×#41	—	2	12	no	—
269	C₂×#41	—	2	12	no	—
270	C₂×#41	—	2	24	no	—
271	C₂×#41	—	2	24	no	—
272	C₂×#41	—	2	24	no	—
273	C₂×#41	—	2	12	no	—
274	C₂×#41	—	2	3	no	—
275	C₂×#41	—	2	6	no	—
276	C₂×#41	—	2	6	no	—
277	C₂×#41	—	2	6	no	—
278	C₂×#41	D₄×C₄₁	1	6	yes	complemented
279	C₂×#41	C₂³×C₄₁	1	3	yes	—
280	C₂×#41	C₂³×C₄₁	1	3	yes	—
281	C₂²×Q₈	—	2	12	no	—
282	C₂²×Q₈	—	2	4	no	—
283	C₂²×Q₈	—	2	3	no	—
284	C₂²×Q₈	D₄×C₄₁	1	6	yes	complemented
285	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
286	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
287	AGL(1,ℤ/8)	—	2	12	no	—
288	C₂×SD₁₆	—	2	6	no	—
289	C₂×SD₁₆	—	2	3	no	—
290	C₂×D₈	—	2	3	no	—
291	C₂×M₁₆	C₂³×C₄₁	1	3	yes	—
292	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
293	#127	—	2	3	no	—
294	#124	—	2	3	no	—
295	#121	—	2	6	no	—
296	#120	—	2	6	no	—
297	#117	C₂³×C₄₁	1	3	yes	—
298	#104	—	2	12	no	—
299	#103	—	2	3	no	—
300	#103	—	2	6	no	—
301	#102	—	2	3	no	—
302	#101	—	2	3	no	—
303	#100	—	2	3	no	—
304	#99	—	2	6	no	—
305	C₂²⋊C₈	—	2	6	no	—
306	C₂⁴	—	2	1	no	—
307	#41	—	2	48	no	—
308	#41	—	2	24	no	—
309	#41	—	2	48	no	—
310	#41	—	2	8	no	—
311	#41	—	2	24	no	—
312	#41	—	2	48	no	—
313	#41	—	2	24	no	—
314	#41	—	2	12	no	—
315	#41	—	2	12	no	—
316	#41	—	2	12	no	—
317	#41	—	2	4	no	—
318	#41	—	2	12	no	—
319	#41	—	2	12	no	—
320	#41	—	2	12	no	—
321	#41	—	2	12	no	—
322	#41	—	2	12	no	—
323	#41	—	2	12	no	—
324	#41	—	2	6	no	—
325	#41	—	2	6	no	—
326	#41	—	2	6	no	—
327	#41	C₂×D₄×C₄₁	1	12	yes	—
328	C₂×Q₈	—	2	24	no	—
329	C₂×Q₈	—	2	24	no	—
330	C₂×Q₈	—	2	24	no	—
331	C₂×Q₈	—	2	6	no	—
332	C₂×Q₈	—	2	6	no	—
333	C₂×Q₈	—	2	12	no	—
334	C₂×Q₈	—	2	12	no	—
335	C₂×Q₈	—	2	12	no	—
336	C₂×Q₈	—	2	6	no	—
337	C₂×Q₈	—	2	3	no	—
338	C₂×Q₈	C₂×D₄×C₄₁	1	3	yes	—
339	C₂×Q₈	C₂×D₄×C₄₁	1	6	yes	—
340	C₂×Q₈	C₂×D₄×C₄₁	1	3	yes	—
341	C₂×D₄	—	2	24	no	—
342	C₂×D₄	—	2	24	no	—
343	C₂×D₄	—	2	24	no	—
344	C₂×D₄	—	2	6	no	—
345	C₂×D₄	—	2	6	no	—
346	C₂×D₄	—	2	12	no	—
347	C₂×D₄	—	2	12	no	—
348	C₂×D₄	—	2	6	no	—
349	C₂×D₄	—	2	3	no	—
350	C₂×D₄	—	2	12	no	—
351	C₂×D₄	—	2	3	no	—
352	C₂×D₄	—	2	3	no	—
353	C₂×D₄	—	4	6	no	—
354	C₂×D₄	C₂×D₄×C₄₁	1	6	yes	—
355	C₂×D₄	C₂×D₄×C₄₁	1	3	yes	—
356	C₂×D₄	C₂×D₄×C₄₁	1	3	yes	—
357	C₂²×C₄	—	2	8	no	—
358	C₂²×C₄	—	2	24	no	—
359	C₂²×C₄	—	2	12	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	6	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	6	no	—
364	C₂²×C₄	—	2	3	no	—
365	C₂²×C₄	C₂×D₄×C₄₁	1	6	yes	—
366	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
367	SD₁₆	—	4	4	no	—
368	SD₁₆	—	4	6	no	—
369	D₈	—	4	6	no	—
370	M₁₆	—	2	6	no	—
371	C₂×C₈	—	2	3	no	—
372	C₂×C₈	—	2	3	no	—
373	C₄⋊C₄	—	2	3	no	—
374	C₂²⋊C₄	—	2	3	no	—
375	C₂²⋊C₄	—	4	6	no	—
376	C₄²	—	2	3	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	2	12	no	—
379	C₂³	—	2	3	no	—
380	C₂³	—	4	3	no	—
381	C₂³	—	16	1	no	—
382	C₂³	#120×C₄₁	1	6	yes	—
383	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
384	Q₈	—	2	12	no	—
385	Q₈	—	2	24	no	—
386	Q₈	—	2	4	no	—
387	Q₈	—	2	3	no	—
388	Q₈	—	2	6	no	—
389	Q₈	—	2	6	no	—
390	Q₈	#120×C₄₁	1	6	yes	—
391	Q₈	#120×C₄₁	1	4	yes	—
392	D₄	—	2	24	no	—
393	D₄	—	2	24	no	—
394	D₄	—	2	12	no	—
395	D₄	—	2	12	no	—
396	D₄	—	2	12	no	—
397	D₄	—	2	12	no	—
398	D₄	—	2	3	no	—
399	D₄	—	2	6	no	—
400	D₄	—	4	3	no	—
401	D₄	—	4	1	no	—
402	D₄	—	16	6	no	—
403	D₄	#120×C₄₁	1	6	yes	—
404	C₂×C₄	—	2	12	no	—
405	C₂×C₄	—	2	24	no	—
406	C₂×C₄	—	2	24	no	—
407	C₂×C₄	—	2	24	no	—
408	C₂×C₄	—	2	12	no	—
409	C₂×C₄	—	2	3	no	—
410	C₂×C₄	—	2	6	no	—
411	C₂×C₄	—	2	12	no	—
412	C₂×C₄	—	2	6	no	—
413	C₂×C₄	—	2	6	no	—
414	C₂×C₄	—	4	3	no	—
415	C₂×C₄	#120×C₄₁	1	6	yes	—
416	C₂×C₄	C₂²×D₄×C₄₁	1	3	yes	—
417	C₂×C₄	C₂²×D₄×C₄₁	1	3	yes	—
418	C₈	—	4	1	no	—
419	C₈	—	4	3	no	—
420	C₂²	—	2	6	no	—
421	C₂²	—	2	6	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	6	no	—
424	C₂²	—	8	3	no	—
425	C₂²	—	8	6	no	—
426	C₂²	—	8	4	no	—
427	C₂²	—	8	12	no	—
428	C₂²	—	8	1	no	—
429	C₂²	C₂×#120×C₄₁	1	3	yes	—
430	C₄	—	2	4	no	—
431	C₄	—	2	6	no	—
432	C₄	—	2	6	no	—
433	C₄	—	8	3	no	—
434	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
435	C₄	C₂×#120×C₄₁	1	3	yes	—
436	C₂	—	2	3	no	—
437	C₂	—	4	6	no	—
438	C₂	—	4	6	no	—
439	C₂	—	16	1	no	—
440	C₂	C₄₁×#2846	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₄₁	#2846
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄₁ ◁ C₂²×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×2₋¹⁺⁶	C₂	semidirect
2. C₄₁×#3027	C₂	semidirect
3. C₄₁×#3021	C₂	semidirect
4. C₄₁×#3010	C₂	semidirect
5. C₄₁×#1796	C₂	semidirect
6. C₄₁×#1794	C₂	semidirect
7. C₄₁×#1791	C₂	semidirect
16. C₂×AGL(1,ℤ/8)×C₄₁	C₂²	semidirect
17. C₂²×SD₁₆×C₄₁	C₂²	semidirect
18. C₄₁×#535	C₂²	semidirect
24. C₄₁×#421	C₂²	semidirect
25. C₄₁×#419	C₂²	semidirect
26. C₄₁×#416	C₂²	semidirect
27. C₄₁×#413	C₂²	semidirect
28. C₄₁×#410	C₂²	semidirect
29. C₄₁×#408	C₂²	semidirect
38. 2₋¹⁺⁴×C₄₁	D₄	semidirect
46. H(5,𝔽₂)×C₄₁	D₄	semidirect
57. C₂×#41×C₄₁	D₄	semidirect
63. C₂²×Q₈×C₄₁	D₄	semidirect
199. #32895	C₄₁	direct (N × H)
216. 2₋¹⁺⁶	C₂×C₄₁	semidirect
217. #3027	C₂×C₄₁	semidirect
218. #3021	C₂×C₄₁	semidirect
219. #3010	C₂×C₄₁	semidirect
220. #1796	C₂×C₄₁	semidirect
221. #1794	C₂×C₄₁	semidirect
222. #1791	C₂×C₄₁	semidirect
236. C₂×AGL(1,ℤ/8)	C₂²×C₄₁	semidirect
237. C₂²×SD₁₆	C₂²×C₄₁	semidirect
238. #535	C₂²×C₄₁	semidirect
244. #421	C₂²×C₄₁	semidirect
245. #419	C₂²×C₄₁	semidirect
246. #416	C₂²×C₄₁	semidirect
247. #413	C₂²×C₄₁	semidirect
248. #410	C₂²×C₄₁	semidirect
249. #408	C₂²×C₄₁	semidirect
250. C₄₁	#32895	direct (N × H)
259. 2₋¹⁺⁴	D₄×C₄₁	semidirect
267. H(5,𝔽₂)	D₄×C₄₁	semidirect
278. C₂×#41	D₄×C₄₁	semidirect
284. C₂²×Q₈	D₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×2₋¹⁺⁶	2
C₄₁×#3027	2
C₄₁×#3021	2
C₄₁×#3010	2
C₄₁×#1796	2
C₄₁×#1794	2
C₄₁×#1791	2
#32895	41

Subgroups — C41×#32895 #23809096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#32895 #23809096