Subgroups — C₂×C₄₁×#2901 #23836293

Order 10496.

4946 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#585	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#568	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×#41×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2901	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₄₁×#421	C₂	1	6	yes	maximal, complemented
6	C₂²×#104×C₄₁	C₂	1	6	yes	maximal, complemented
7	C₄₁×#585	—	2	4	no	—
8	C₄₁×#585	—	2	4	no	—
9	C₄₁×#585	C₄	1	8	yes	complemented
10	C₄₁×#585	C₂²	1	8	yes	—
11	C₂×2₋¹⁺⁴×C₄₁	—	2	1	no	—
12	C₂×2₋¹⁺⁴×C₄₁	C₄	1	4	yes	complemented
13	C₂×H(5,𝔽₂)×C₄₁	—	2	3	no	—
14	C₂×H(5,𝔽₂)×C₄₁	C₄	1	4	yes	complemented
15	C₂²×#41×C₄₁	—	2	4	no	—
16	C₂²×#41×C₄₁	C₂²	1	6	yes	—
17	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
18	C₄₁×#568	—	2	4	no	—
19	C₄₁×#568	C₂²	1	8	yes	complemented
20	C₂×#131×C₄₁	—	2	4	no	—
21	C₂²×M₁₆×C₄₁	C₂²	1	6	yes	complemented
22	C₄×#41×C₄₁	—	2	4	no	—
23	C₄×#41×C₄₁	C₂²	1	8	yes	complemented
24	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
25	C₂×C₄×D₄×C₄₁	—	2	3	no	—
26	C₂×#117×C₄₁	C₂²	1	3	yes	complemented
27	C₂²×C₄²×C₄₁	C₂²	1	3	yes	complemented
28	C₄₁×#421	C₂²	1	48	yes	complemented
29	C₂×#104×C₄₁	C₂²	1	4	yes	complemented
30	C₂×#104×C₄₁	C₂²	1	12	yes	complemented
31	C₂×#104×C₄₁	C₂²	1	48	yes	complemented
32	2₋¹⁺⁴×C₄₁	—	2	16	no	—
33	2₋¹⁺⁴×C₄₁	—	2	8	no	—
34	2₋¹⁺⁴×C₄₁	—	2	8	no	—
35	2₋¹⁺⁴×C₄₁	C₂×C₄	1	32	yes	complemented
36	H(5,𝔽₂)×C₄₁	—	2	16	no	—
37	H(5,𝔽₂)×C₄₁	—	2	24	no	—
38	H(5,𝔽₂)×C₄₁	—	2	24	no	—
39	H(5,𝔽₂)×C₄₁	C₂×C₄	1	32	yes	complemented
40	C₂×#41×C₄₁	—	2	32	no	—
41	C₂×#41×C₄₁	—	2	32	no	—
42	C₂×#41×C₄₁	—	2	4	no	—
43	C₂×#41×C₄₁	—	2	12	no	—
44	C₂×#41×C₄₁	—	2	6	no	—
45	C₂×#41×C₄₁	—	2	6	no	—
46	C₂×#41×C₄₁	—	2	12	no	—
47	C₂×#41×C₄₁	—	2	12	no	—
48	C₂×#41×C₄₁	C₂×C₄	1	4	yes	—
49	C₂×#41×C₄₁	C₂×C₄	1	4	yes	—
50	C₂×#41×C₄₁	C₂×C₄	1	12	yes	complemented
51	C₂×#41×C₄₁	C₂×C₄	1	24	yes	complemented
52	C₂×#41×C₄₁	D₄	1	4	yes	—
53	C₂×#41×C₄₁	D₄	1	4	yes	—
54	C₂×#41×C₄₁	D₄	1	4	yes	—
55	C₂×#41×C₄₁	C₂³	1	4	yes	—
56	C₂×#41×C₄₁	C₂³	1	24	yes	—
57	C₂×#41×C₄₁	C₂³	1	4	yes	—
58	C₂²×Q₈×C₄₁	—	2	4	no	—
59	C₂²×Q₈×C₄₁	C₂×C₄	1	6	yes	complemented
60	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₄₁	—	2	6	no	—
62	C₂²×D₄×C₄₁	—	2	12	no	—
63	C₂²×D₄×C₄₁	C₂×C₄	1	6	yes	complemented
64	C₂²×D₄×C₄₁	D₄	1	3	yes	—
65	C₂³×C₄×C₄₁	—	2	6	no	—
66	C₂³×C₄×C₄₁	—	2	3	no	—
67	C₂³×C₄×C₄₁	C₂³	1	3	yes	—
68	#131×C₄₁	—	2	32	no	—
69	C₂×M₁₆×C₄₁	—	2	6	no	—
70	C₂×M₁₆×C₄₁	—	2	12	no	—
71	C₂×M₁₆×C₄₁	C₂³	1	4	yes	—
72	C₂×M₁₆×C₄₁	C₂³	1	24	yes	complemented
73	C₂²×C₈×C₄₁	—	2	6	no	—
74	C₄×Q₈×C₄₁	—	2	8	no	—
75	C₄×D₄×C₄₁	—	2	24	no	—
76	#117×C₄₁	—	2	6	no	—
77	#117×C₄₁	C₂³	1	12	yes	complemented
78	C₂×C₄⋊C₄×C₄₁	—	2	3	no	—
79	C₂×C₂²⋊C₄×C₄₁	—	2	3	no	—
80	C₂×C₄²×C₄₁	—	2	3	no	—
81	C₂×C₄²×C₄₁	—	2	6	no	—
82	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₄₁	C₂³	1	3	yes	—
84	C₂×C₄²×C₄₁	C₂³	1	12	yes	complemented
85	#104×C₄₁	C₂³	1	16	yes	complemented
86	#104×C₄₁	C₂³	1	48	yes	complemented
87	C₂⁴×C₄₁	—	2	6	no	—
88	C₂⁴×C₄₁	C₂×D₄	1	3	yes	—
89	#41×C₄₁	—	2	32	no	—
90	#41×C₄₁	—	2	96	no	—
91	#41×C₄₁	—	2	24	no	—
92	#41×C₄₁	—	2	24	no	—
93	#41×C₄₁	—	2	24	no	—
94	#41×C₄₁	—	2	4	no	—
95	#41×C₄₁	—	2	24	no	—
96	#41×C₄₁	—	2	4	no	—
97	#41×C₄₁	—	2	24	no	—
98	#41×C₄₁	C₂²⋊C₄	1	16	yes	—
99	#41×C₄₁	C₂²⋊C₄	1	16	yes	—
100	#41×C₄₁	C₂²×C₄	1	8	yes	—
101	#41×C₄₁	C₂²×C₄	1	16	yes	—
102	#41×C₄₁	C₂²×C₄	1	48	yes	complemented
103	#41×C₄₁	C₂×D₄	1	16	yes	—
104	#41×C₄₁	C₂⁴	1	8	yes	—
105	C₂×Q₈×C₄₁	—	2	32	no	—
106	C₂×Q₈×C₄₁	—	2	6	no	—
107	C₂×Q₈×C₄₁	—	2	12	no	—
108	C₂×Q₈×C₄₁	C₂²⋊C₄	1	4	yes	—
109	C₂×Q₈×C₄₁	C₂²⋊C₄	1	4	yes	—
110	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
111	C₂×Q₈×C₄₁	C₂²×C₄	1	24	yes	complemented
112	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
113	C₂×D₄×C₄₁	—	2	12	no	—
114	C₂×D₄×C₄₁	—	2	24	no	—
115	C₂×D₄×C₄₁	—	2	4	no	—
116	C₂×D₄×C₄₁	—	2	24	no	—
117	C₂×D₄×C₄₁	—	2	96	no	—
118	C₂×D₄×C₄₁	—	2	6	no	—
119	C₂×D₄×C₄₁	—	2	12	no	—
120	C₂×D₄×C₄₁	C₂²⋊C₄	1	12	yes	—
121	C₂×D₄×C₄₁	C₂²⋊C₄	1	12	yes	—
122	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
123	C₂×D₄×C₄₁	C₂²×C₄	1	24	yes	complemented
124	C₂×D₄×C₄₁	C₂×D₄	1	12	yes	—
125	C₂²×C₄×C₄₁	—	2	6	no	—
126	C₂²×C₄×C₄₁	—	2	1	no	—
127	C₂²×C₄×C₄₁	—	2	12	no	—
128	C₂²×C₄×C₄₁	—	2	24	no	—
129	C₂²×C₄×C₄₁	—	2	24	no	—
130	C₂²×C₄×C₄₁	—	2	4	no	—
131	C₂²×C₄×C₄₁	—	2	3	no	—
132	C₂²×C₄×C₄₁	—	2	12	no	—
133	C₂²×C₄×C₄₁	—	4	12	no	—
134	C₂²×C₄×C₄₁	C₂²×C₄	1	6	yes	—
135	C₂²×C₄×C₄₁	C₂²×C₄	1	6	yes	—
136	C₂²×C₄×C₄₁	C₂×D₄	1	3	yes	—
137	C₂²×C₄×C₄₁	C₂×D₄	1	6	yes	—
138	C₂²×C₄×C₄₁	C₂×D₄	1	6	yes	—
139	C₂²×C₄×C₄₁	C₂×D₄	1	6	yes	—
140	C₂²×C₄×C₄₁	C₂⁴	1	6	yes	—
141	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
142	M₁₆×C₄₁	—	2	4	no	—
143	M₁₆×C₄₁	—	2	24	no	—
144	M₁₆×C₄₁	C₂⁴	1	8	yes	—
145	C₂×C₈×C₄₁	—	2	24	no	—
146	C₂×C₈×C₄₁	—	2	4	no	—
147	C₄⋊C₄×C₄₁	—	2	12	no	—
148	C₂²⋊C₄×C₄₁	—	2	12	no	—
149	C₄²×C₄₁	—	2	1	no	—
150	C₄²×C₄₁	—	2	3	no	—
151	C₄²×C₄₁	—	2	12	no	—
152	C₄²×C₄₁	C₂⁴	1	2	yes	—
153	C₄²×C₄₁	C₂⁴	1	6	yes	—
154	C₂³×C₄₁	—	2	4	no	—
155	C₂³×C₄₁	—	2	24	no	—
156	C₂³×C₄₁	—	4	6	no	—
157	C₂³×C₄₁	—	8	12	no	—
158	C₂³×C₄₁	C₂×C₂²⋊C₄	1	6	yes	—
159	C₂³×C₄₁	C₂×C₂²⋊C₄	1	6	yes	—
160	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
161	C₂³×C₄₁	C₂²×D₄	1	6	yes	—
162	Q₈×C₄₁	—	2	4	no	—
163	Q₈×C₄₁	—	2	24	no	—
164	Q₈×C₄₁	C₂×C₂²⋊C₄	1	16	yes	—
165	Q₈×C₄₁	C₂³×C₄	1	8	yes	—
166	D₄×C₄₁	—	2	8	no	—
167	D₄×C₄₁	—	2	48	no	—
168	D₄×C₄₁	—	2	8	no	—
169	D₄×C₄₁	—	2	4	no	—
170	D₄×C₄₁	—	2	24	no	—
171	D₄×C₄₁	C₂×C₂²⋊C₄	1	48	yes	—
172	D₄×C₄₁	C₂³×C₄	1	8	yes	—
173	C₂×C₄×C₄₁	—	2	4	no	—
174	C₂×C₄×C₄₁	—	2	4	no	—
175	C₂×C₄×C₄₁	—	2	24	no	—
176	C₂×C₄×C₄₁	—	2	2	no	—
177	C₂×C₄×C₄₁	—	2	8	no	—
178	C₂×C₄×C₄₁	—	2	48	no	—
179	C₂×C₄×C₄₁	—	2	8	no	—
180	C₂×C₄×C₄₁	—	2	6	no	—
181	C₂×C₄×C₄₁	—	4	24	no	—
182	C₂×C₄×C₄₁	—	4	6	no	—
183	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	6	yes	—
184	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	12	yes	—
185	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	12	yes	—
186	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	6	yes	—
187	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
188	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₄₁	C₂³×C₄	1	12	yes	—
190	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₄₁	C₂²×D₄	1	6	yes	—
192	C₂×C₄×C₄₁	C₂²×D₄	1	12	yes	—
193	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
196	C₈×C₄₁	—	2	8	no	—
197	C₂×#2901	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂²×C₄₁	—	2	2	no	—
199	C₂²×C₄₁	—	2	12	no	—
200	C₂²×C₄₁	—	2	8	no	—
201	C₂²×C₄₁	—	4	6	no	—
202	C₂²×C₄₁	—	4	6	no	—
203	C₂²×C₄₁	—	4	8	no	—
204	C₂²×C₄₁	—	8	24	no	—
205	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	12	yes	—
206	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
207	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
208	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
209	C₄×C₄₁	—	2	4	no	—
210	C₄×C₄₁	—	2	8	no	—
211	C₄×C₄₁	—	4	6	no	—
212	C₄×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
213	C₄×C₄₁	C₂²×C₂²⋊C₄	1	12	yes	—
214	C₄×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
215	C₄×C₄₁	C₂⁴×C₄	1	1	yes	characteristic
216	C₄×C₄₁	C₂³×D₄	1	1	yes	characteristic
217	C₂×#585	C₂×C₄₁	1	1	yes	characteristic
218	C₂×#568	C₂×C₄₁	1	1	yes	characteristic, complemented
219	C₂×C₄×#41	C₂×C₄₁	1	1	yes	characteristic, complemented
220	#2901	C₂×C₄₁	1	16	yes	direct product factor
221	C₂×#421	C₂×C₄₁	1	6	yes	complemented
222	C₂²×#104	C₂×C₄₁	1	6	yes	complemented
223	C₂×C₄₁	—	2	1	no	—
224	C₂×C₄₁	—	2	1	no	—
225	C₂×C₄₁	—	2	12	no	—
226	C₂×C₄₁	—	4	8	no	—
227	C₂×C₄₁	#2901	1	2	yes	direct product factor
228	C₂×C₄₁	C₂³×C₂²⋊C₄	1	1	yes	characteristic
229	#585	—	2	4	no	—
230	#585	—	2	4	no	—
231	#585	C₄×C₄₁	1	8	yes	complemented
232	#585	C₂²×C₄₁	1	8	yes	—
233	C₂×2₋¹⁺⁴	—	2	1	no	—
234	C₂×2₋¹⁺⁴	C₄×C₄₁	1	4	yes	complemented
235	C₂×H(5,𝔽₂)	—	2	3	no	—
236	C₂×H(5,𝔽₂)	C₄×C₄₁	1	4	yes	complemented
237	C₂²×#41	—	2	4	no	—
238	C₂²×#41	C₂²×C₄₁	1	6	yes	—
239	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
240	#568	—	2	4	no	—
241	#568	C₂²×C₄₁	1	8	yes	complemented
242	C₂×#131	—	2	4	no	—
243	C₂²×M₁₆	C₂²×C₄₁	1	6	yes	complemented
244	C₄×#41	—	2	4	no	—
245	C₄×#41	C₂²×C₄₁	1	8	yes	complemented
246	C₂×C₄×Q₈	—	2	1	no	—
247	C₂×C₄×D₄	—	2	3	no	—
248	C₂×#117	C₂²×C₄₁	1	3	yes	complemented
249	C₂²×C₄²	C₂²×C₄₁	1	3	yes	complemented
250	#421	C₂²×C₄₁	1	48	yes	complemented
251	C₂×#104	C₂²×C₄₁	1	4	yes	complemented
252	C₂×#104	C₂²×C₄₁	1	12	yes	complemented
253	C₂×#104	C₂²×C₄₁	1	48	yes	complemented
254	C₄₁	C₂×#2901	1	1	yes	characteristic, direct product factor, Sylow
255	2₋¹⁺⁴	—	2	16	no	—
256	2₋¹⁺⁴	—	2	8	no	—
257	2₋¹⁺⁴	—	2	8	no	—
258	2₋¹⁺⁴	C₂×C₄×C₄₁	1	32	yes	complemented
259	H(5,𝔽₂)	—	2	16	no	—
260	H(5,𝔽₂)	—	2	24	no	—
261	H(5,𝔽₂)	—	2	24	no	—
262	H(5,𝔽₂)	C₂×C₄×C₄₁	1	32	yes	complemented
263	C₂×#41	—	2	32	no	—
264	C₂×#41	—	2	32	no	—
265	C₂×#41	—	2	4	no	—
266	C₂×#41	—	2	12	no	—
267	C₂×#41	—	2	6	no	—
268	C₂×#41	—	2	6	no	—
269	C₂×#41	—	2	12	no	—
270	C₂×#41	—	2	12	no	—
271	C₂×#41	C₂×C₄×C₄₁	1	4	yes	—
272	C₂×#41	C₂×C₄×C₄₁	1	4	yes	—
273	C₂×#41	C₂×C₄×C₄₁	1	12	yes	complemented
274	C₂×#41	C₂×C₄×C₄₁	1	24	yes	complemented
275	C₂×#41	D₄×C₄₁	1	4	yes	—
276	C₂×#41	D₄×C₄₁	1	4	yes	—
277	C₂×#41	D₄×C₄₁	1	4	yes	—
278	C₂×#41	C₂³×C₄₁	1	4	yes	—
279	C₂×#41	C₂³×C₄₁	1	24	yes	—
280	C₂×#41	C₂³×C₄₁	1	4	yes	—
281	C₂²×Q₈	—	2	4	no	—
282	C₂²×Q₈	C₂×C₄×C₄₁	1	6	yes	complemented
283	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
284	C₂²×D₄	—	2	6	no	—
285	C₂²×D₄	—	2	12	no	—
286	C₂²×D₄	C₂×C₄×C₄₁	1	6	yes	complemented
287	C₂²×D₄	D₄×C₄₁	1	3	yes	—
288	C₂³×C₄	—	2	6	no	—
289	C₂³×C₄	—	2	3	no	—
290	C₂³×C₄	C₂³×C₄₁	1	3	yes	—
291	#131	—	2	32	no	—
292	C₂×M₁₆	—	2	6	no	—
293	C₂×M₁₆	—	2	12	no	—
294	C₂×M₁₆	C₂³×C₄₁	1	4	yes	—
295	C₂×M₁₆	C₂³×C₄₁	1	24	yes	complemented
296	C₂²×C₈	—	2	6	no	—
297	C₄×Q₈	—	2	8	no	—
298	C₄×D₄	—	2	24	no	—
299	#117	—	2	6	no	—
300	#117	C₂³×C₄₁	1	12	yes	complemented
301	C₂×C₄⋊C₄	—	2	3	no	—
302	C₂×C₂²⋊C₄	—	2	3	no	—
303	C₂×C₄²	—	2	3	no	—
304	C₂×C₄²	—	2	6	no	—
305	C₂×C₄²	C₂³×C₄₁	1	3	yes	—
306	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₄₁	1	12	yes	complemented
308	#104	C₂³×C₄₁	1	16	yes	complemented
309	#104	C₂³×C₄₁	1	48	yes	complemented
310	C₂⁴	—	2	6	no	—
311	C₂⁴	C₂×D₄×C₄₁	1	3	yes	—
312	#41	—	2	32	no	—
313	#41	—	2	96	no	—
314	#41	—	2	24	no	—
315	#41	—	2	24	no	—
316	#41	—	2	24	no	—
317	#41	—	2	4	no	—
318	#41	—	2	24	no	—
319	#41	—	2	4	no	—
320	#41	—	2	24	no	—
321	#41	C₂²⋊C₄×C₄₁	1	16	yes	—
322	#41	C₂²⋊C₄×C₄₁	1	16	yes	—
323	#41	C₂²×C₄×C₄₁	1	8	yes	—
324	#41	C₂²×C₄×C₄₁	1	16	yes	—
325	#41	C₂²×C₄×C₄₁	1	48	yes	complemented
326	#41	C₂×D₄×C₄₁	1	16	yes	—
327	#41	C₂⁴×C₄₁	1	8	yes	—
328	C₂×Q₈	—	2	32	no	—
329	C₂×Q₈	—	2	6	no	—
330	C₂×Q₈	—	2	12	no	—
331	C₂×Q₈	C₂²⋊C₄×C₄₁	1	4	yes	—
332	C₂×Q₈	C₂²⋊C₄×C₄₁	1	4	yes	—
333	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
334	C₂×Q₈	C₂²×C₄×C₄₁	1	24	yes	complemented
335	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
336	C₂×D₄	—	2	12	no	—
337	C₂×D₄	—	2	24	no	—
338	C₂×D₄	—	2	4	no	—
339	C₂×D₄	—	2	24	no	—
340	C₂×D₄	—	2	96	no	—
341	C₂×D₄	—	2	6	no	—
342	C₂×D₄	—	2	12	no	—
343	C₂×D₄	C₂²⋊C₄×C₄₁	1	12	yes	—
344	C₂×D₄	C₂²⋊C₄×C₄₁	1	12	yes	—
345	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
346	C₂×D₄	C₂²×C₄×C₄₁	1	24	yes	complemented
347	C₂×D₄	C₂×D₄×C₄₁	1	12	yes	—
348	C₂²×C₄	—	2	6	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	12	no	—
351	C₂²×C₄	—	2	24	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	24	no	—
354	C₂²×C₄	—	2	3	no	—
355	C₂²×C₄	—	2	12	no	—
356	C₂²×C₄	—	4	12	no	—
357	C₂²×C₄	C₂²×C₄×C₄₁	1	6	yes	—
358	C₂²×C₄	C₂²×C₄×C₄₁	1	6	yes	—
359	C₂²×C₄	C₂×D₄×C₄₁	1	3	yes	—
360	C₂²×C₄	C₂×D₄×C₄₁	1	6	yes	—
361	C₂²×C₄	C₂×D₄×C₄₁	1	6	yes	—
362	C₂²×C₄	C₂×D₄×C₄₁	1	6	yes	—
363	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
364	C₂²×C₄	C₂⁴×C₄₁	1	6	yes	—
365	M₁₆	—	2	4	no	—
366	M₁₆	—	2	24	no	—
367	M₁₆	C₂⁴×C₄₁	1	8	yes	—
368	C₂×C₈	—	2	4	no	—
369	C₂×C₈	—	2	24	no	—
370	C₄⋊C₄	—	2	12	no	—
371	C₂²⋊C₄	—	2	12	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	3	no	—
374	C₄²	—	2	12	no	—
375	C₄²	C₂⁴×C₄₁	1	2	yes	—
376	C₄²	C₂⁴×C₄₁	1	6	yes	—
377	C₂³	—	2	4	no	—
378	C₂³	—	2	24	no	—
379	C₂³	—	4	6	no	—
380	C₂³	—	8	12	no	—
381	C₂³	C₂×C₂²⋊C₄×C₄₁	1	6	yes	—
382	C₂³	C₂×C₂²⋊C₄×C₄₁	1	6	yes	—
383	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
384	C₂³	C₂²×D₄×C₄₁	1	6	yes	—
385	Q₈	—	2	4	no	—
386	Q₈	—	2	24	no	—
387	Q₈	C₂×C₂²⋊C₄×C₄₁	1	16	yes	—
388	Q₈	C₂³×C₄×C₄₁	1	8	yes	—
389	D₄	—	2	8	no	—
390	D₄	—	2	48	no	—
391	D₄	—	2	8	no	—
392	D₄	—	2	4	no	—
393	D₄	—	2	24	no	—
394	D₄	C₂×C₂²⋊C₄×C₄₁	1	48	yes	—
395	D₄	C₂³×C₄×C₄₁	1	8	yes	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	24	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	48	no	—
402	C₂×C₄	—	2	8	no	—
403	C₂×C₄	—	2	6	no	—
404	C₂×C₄	—	4	24	no	—
405	C₂×C₄	—	4	6	no	—
406	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	6	yes	—
407	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	12	yes	—
408	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	12	yes	—
409	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	6	yes	—
410	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
411	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
412	C₂×C₄	C₂³×C₄×C₄₁	1	12	yes	—
413	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
414	C₂×C₄	C₂²×D₄×C₄₁	1	6	yes	—
415	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₄₁	1	12	yes	—
417	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
418	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
419	C₈	—	2	8	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	12	no	—
422	C₂²	—	2	8	no	—
423	C₂²	—	4	6	no	—
424	C₂²	—	4	6	no	—
425	C₂²	—	4	8	no	—
426	C₂²	—	8	24	no	—
427	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	12	yes	—
428	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
429	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
430	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
431	C₄	—	2	4	no	—
432	C₄	—	2	8	no	—
433	C₄	—	4	6	no	—
434	C₄	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
435	C₄	C₂²×C₂²⋊C₄×C₄₁	1	12	yes	—
436	C₄	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
437	C₄	C₂⁴×C₄×C₄₁	1	1	yes	characteristic
438	C₄	C₂³×D₄×C₄₁	1	1	yes	characteristic
439	C₂	—	2	1	no	—
440	C₂	—	2	1	no	—
441	C₂	—	2	12	no	—
442	C₂	—	4	8	no	—
443	C₂	C₄₁×#2901	1	2	yes	direct product factor
444	C₂	C₂³×C₂²⋊C₄×C₄₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₁	C₂²×D₄
commutator	C₄	C₂⁴×C₄×C₄₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
socle	C₂²×C₄₁	C₂²×C₂²⋊C₄
prime radical	C₂×C₄₁×#585	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂²×#41×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#568	C₂	semidirect
3. C₂×C₄×#41×C₄₁	C₂	semidirect
4. C₄₁×#2901	C₂	direct (N × H)
5. C₂×C₄₁×#421	C₂	semidirect
6. C₂²×#104×C₄₁	C₂	semidirect
9. C₄₁×#585	C₄	semidirect
12. C₂×2₋¹⁺⁴×C₄₁	C₄	semidirect
14. C₂×H(5,𝔽₂)×C₄₁	C₄	semidirect
19. C₄₁×#568	C₂²	semidirect
21. C₂²×M₁₆×C₄₁	C₂²	semidirect
23. C₄×#41×C₄₁	C₂²	semidirect
26. C₂×#117×C₄₁	C₂²	semidirect
27. C₂²×C₄²×C₄₁	C₂²	semidirect
28. C₄₁×#421	C₂²	semidirect
29. C₂×#104×C₄₁	C₂²	semidirect
30. C₂×#104×C₄₁	C₂²	semidirect
31. C₂×#104×C₄₁	C₂²	semidirect
35. 2₋¹⁺⁴×C₄₁	C₂×C₄	semidirect
39. H(5,𝔽₂)×C₄₁	C₂×C₄	semidirect
50. C₂×#41×C₄₁	C₂×C₄	semidirect
51. C₂×#41×C₄₁	C₂×C₄	semidirect
59. C₂²×Q₈×C₄₁	C₂×C₄	semidirect
63. C₂²×D₄×C₄₁	C₂×C₄	semidirect
72. C₂×M₁₆×C₄₁	C₂³	semidirect
77. #117×C₄₁	C₂³	semidirect
84. C₂×C₄²×C₄₁	C₂³	semidirect
85. #104×C₄₁	C₂³	semidirect
86. #104×C₄₁	C₂³	semidirect
102. #41×C₄₁	C₂²×C₄	semidirect
111. C₂×Q₈×C₄₁	C₂²×C₄	semidirect
123. C₂×D₄×C₄₁	C₂²×C₄	semidirect
197. C₂×#2901	C₄₁	direct (N × H)
218. C₂×#568	C₂×C₄₁	semidirect
219. C₂×C₄×#41	C₂×C₄₁	semidirect
220. #2901	C₂×C₄₁	direct (N × H)
221. C₂×#421	C₂×C₄₁	semidirect
222. C₂²×#104	C₂×C₄₁	semidirect
227. C₂×C₄₁	#2901	direct (N × H)
231. #585	C₄×C₄₁	semidirect
234. C₂×2₋¹⁺⁴	C₄×C₄₁	semidirect
236. C₂×H(5,𝔽₂)	C₄×C₄₁	semidirect
241. #568	C₂²×C₄₁	semidirect
243. C₂²×M₁₆	C₂²×C₄₁	semidirect
245. C₄×#41	C₂²×C₄₁	semidirect
248. C₂×#117	C₂²×C₄₁	semidirect
249. C₂²×C₄²	C₂²×C₄₁	semidirect
250. #421	C₂²×C₄₁	semidirect
251. C₂×#104	C₂²×C₄₁	semidirect
252. C₂×#104	C₂²×C₄₁	semidirect
253. C₂×#104	C₂²×C₄₁	semidirect
254. C₄₁	C₂×#2901	direct (N × H)
258. 2₋¹⁺⁴	C₂×C₄×C₄₁	semidirect
262. H(5,𝔽₂)	C₂×C₄×C₄₁	semidirect
273. C₂×#41	C₂×C₄×C₄₁	semidirect
274. C₂×#41	C₂×C₄×C₄₁	semidirect
282. C₂²×Q₈	C₂×C₄×C₄₁	semidirect
286. C₂²×D₄	C₂×C₄×C₄₁	semidirect
295. C₂×M₁₆	C₂³×C₄₁	semidirect
300. #117	C₂³×C₄₁	semidirect
307. C₂×C₄²	C₂³×C₄₁	semidirect
308. #104	C₂³×C₄₁	semidirect
309. #104	C₂³×C₄₁	semidirect
325. #41	C₂²×C₄×C₄₁	semidirect
334. C₂×Q₈	C₂²×C₄×C₄₁	semidirect
346. C₂×D₄	C₂²×C₄×C₄₁	semidirect
443. C₂	C₄₁×#2901	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#585	2
C₂×C₄₁×#568	2
C₂×C₄×#41×C₄₁	2
C₄₁×#2901	2
C₂×C₄₁×#421	2
C₂²×#104×C₄₁	2
C₂×#2901	41

Subgroups — C2×C41×#2901 #23836293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#2901 #23836293