Subgroups — C₄₁×#25412 #23801613

Order 10496.

1038 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#467	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#466	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×Q₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2426	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2042	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2000	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1970	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1942	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1880	C₂	1	2	yes	maximal, complemented
11	C₈×C₂²⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
14	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×#124×C₄₁	C₂²	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
18	C₂×#121×C₄₁	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
20	C₄₁×#495	—	2	4	no	—
21	C₄₁×#467	—	2	4	no	—
22	C₄₁×#466	—	2	4	no	—
23	C₄×Q₁₆×C₄₁	—	2	4	no	—
24	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#103×C₄₁	C₂²	1	2	yes	—
27	C₂×#103×C₄₁	C₂²	1	2	yes	—
28	C₂×#102×C₄₁	C₂²	1	2	yes	—
29	C₂×#102×C₄₁	C₂²	1	2	yes	—
30	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
33	C₄₁×#396	—	2	2	no	—
34	C₄₁×#394	—	2	2	no	—
35	C₄₁×#390	—	2	2	no	—
36	C₄₁×#390	C₂²	1	2	yes	—
37	C₄₁×#389	C₂²	1	2	yes	—
38	C₄₁×#388	—	2	2	no	—
39	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
40	C₄₁×#340	C₂²	1	2	yes	—
41	C₄₁×#336	C₂²	1	1	yes	characteristic
42	C₄₁×#336	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
44	C₂²×D₄×C₄₁	—	2	2	no	—
45	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
46	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
47	C₂×Q₁₆×C₄₁	—	2	2	no	—
48	C₂×Q₁₆×C₄₁	—	2	2	no	—
49	C₂×Q₁₆×C₄₁	D₄	1	4	yes	complemented
50	C₂×SD₁₆×C₄₁	—	2	4	no	—
51	C₂×SD₁₆×C₄₁	—	2	4	no	—
52	C₂×SD₁₆×C₄₁	—	4	2	no	—
53	C₂×D₈×C₄₁	—	2	2	no	—
54	C₂×D₈×C₄₁	—	2	2	no	—
55	C₂×D₈×C₄₁	—	2	2	no	—
56	C₂²×C₈×C₄₁	—	2	2	no	—
57	C₂²×C₈×C₄₁	—	2	2	no	—
58	C₂²×C₈×C₄₁	—	2	2	no	—
59	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
63	#124×C₄₁	—	2	4	no	—
64	#124×C₄₁	—	4	2	no	—
65	C₂²⋊Q₈×C₄₁	—	2	4	no	—
66	C₂²⋊Q₈×C₄₁	—	4	2	no	—
67	#121×C₄₁	—	2	4	no	—
68	#121×C₄₁	—	4	2	no	—
69	C₄×Q₈×C₄₁	—	2	4	no	—
70	C₄×Q₈×C₄₁	—	4	2	no	—
71	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
72	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
73	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
74	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
76	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₄₁	—	2	2	no	—
85	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
87	#107×C₄₁	—	2	2	no	—
88	#107×C₄₁	D₄	1	4	yes	—
89	#103×C₄₁	—	2	4	no	—
90	#103×C₄₁	—	2	4	no	—
91	#102×C₄₁	—	2	4	no	—
92	#102×C₄₁	—	4	2	no	—
93	C₂²⋊C₈×C₄₁	—	2	2	no	—
94	C₄×C₈×C₄₁	—	2	2	no	—
95	C₄×C₈×C₄₁	—	2	2	no	—
96	#95×C₄₁	—	2	2	no	—
97	#95×C₄₁	D₄	1	1	yes	characteristic
98	#95×C₄₁	D₄	1	1	yes	characteristic
99	C₂⁴×C₄₁	—	2	2	no	—
100	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
101	C₂×Q₈×C₄₁	—	2	2	no	—
102	C₂×Q₈×C₄₁	—	2	2	no	—
103	C₂×Q₈×C₄₁	—	2	2	no	—
104	C₂×Q₈×C₄₁	—	2	2	no	—
105	C₂×Q₈×C₄₁	—	2	2	no	—
106	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
107	C₂×D₄×C₄₁	—	2	2	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	—	2	2	no	—
112	C₂×D₄×C₄₁	—	2	2	no	—
113	C₂×D₄×C₄₁	—	4	4	no	—
114	C₂×D₄×C₄₁	—	4	4	no	—
115	C₂×D₄×C₄₁	—	8	2	no	—
116	C₂²×C₄×C₄₁	—	2	2	no	—
117	C₂²×C₄×C₄₁	—	2	2	no	—
118	C₂²×C₄×C₄₁	—	2	1	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	1	no	—
123	C₂²×C₄×C₄₁	—	2	1	no	—
124	C₂²×C₄×C₄₁	—	2	2	no	—
125	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
131	Q₁₆×C₄₁	—	2	8	no	—
132	SD₁₆×C₄₁	—	4	8	no	—
133	D₈×C₄₁	—	4	4	no	—
134	C₂×C₈×C₄₁	—	2	1	no	—
135	C₂×C₈×C₄₁	—	2	1	no	—
136	C₂×C₈×C₄₁	—	2	1	no	—
137	C₂×C₈×C₄₁	—	2	1	no	—
138	C₂×C₈×C₄₁	—	2	1	no	—
139	C₂×C₈×C₄₁	—	2	1	no	—
140	C₂×C₈×C₄₁	—	2	1	no	—
141	C₂×C₈×C₄₁	—	2	1	no	—
142	C₂×C₈×C₄₁	—	4	4	no	—
143	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₄₁	#41	1	2	yes	—
146	C₂×C₈×C₄₁	#41	1	2	yes	—
147	C₄⋊C₄×C₄₁	—	2	2	no	—
148	C₄⋊C₄×C₄₁	—	2	2	no	—
149	C₄⋊C₄×C₄₁	—	2	2	no	—
150	C₄⋊C₄×C₄₁	—	4	4	no	—
151	C₄⋊C₄×C₄₁	—	4	4	no	—
152	C₄⋊C₄×C₄₁	—	8	2	no	—
153	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
154	C₂²⋊C₄×C₄₁	—	2	2	no	—
155	C₂²⋊C₄×C₄₁	—	2	2	no	—
156	C₂²⋊C₄×C₄₁	—	4	4	no	—
157	C₂²⋊C₄×C₄₁	—	4	4	no	—
158	C₂²⋊C₄×C₄₁	—	4	4	no	—
159	C₂²⋊C₄×C₄₁	—	4	4	no	—
160	C₂²⋊C₄×C₄₁	—	4	4	no	—
161	C₂²⋊C₄×C₄₁	—	8	2	no	—
162	C₄²×C₄₁	—	2	1	no	—
163	C₄²×C₄₁	—	2	1	no	—
164	C₄²×C₄₁	—	2	1	no	—
165	C₄²×C₄₁	—	2	1	no	—
166	C₄²×C₄₁	—	4	4	no	—
167	C₂³×C₄₁	—	2	1	no	—
168	C₂³×C₄₁	—	2	1	no	—
169	C₂³×C₄₁	—	2	1	no	—
170	C₂³×C₄₁	—	2	1	no	—
171	C₂³×C₄₁	—	2	1	no	—
172	C₂³×C₄₁	—	2	1	no	—
173	C₂³×C₄₁	—	4	2	no	—
174	C₂³×C₄₁	—	4	2	no	—
175	C₂³×C₄₁	—	4	2	no	—
176	C₂³×C₄₁	—	4	2	no	—
177	C₂³×C₄₁	—	4	2	no	—
178	C₂³×C₄₁	—	4	2	no	—
179	C₂³×C₄₁	—	4	2	no	—
180	C₂³×C₄₁	#135	1	2	yes	—
181	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₄₁	—	2	4	no	—
183	Q₈×C₄₁	—	2	4	no	—
184	Q₈×C₄₁	—	4	2	no	—
185	Q₈×C₄₁	—	4	2	no	—
186	D₄×C₄₁	—	4	2	no	—
187	D₄×C₄₁	—	4	2	no	—
188	D₄×C₄₁	—	4	2	no	—
189	D₄×C₄₁	—	4	2	no	—
190	D₄×C₄₁	—	8	8	no	—
191	C₂×C₄×C₄₁	—	2	1	no	—
192	C₂×C₄×C₄₁	—	2	1	no	—
193	C₂×C₄×C₄₁	—	2	1	no	—
194	C₂×C₄×C₄₁	—	2	1	no	—
195	C₂×C₄×C₄₁	—	2	1	no	—
196	C₂×C₄×C₄₁	—	2	1	no	—
197	C₂×C₄×C₄₁	—	2	4	no	—
198	C₂×C₄×C₄₁	—	2	1	no	—
199	C₂×C₄×C₄₁	—	2	4	no	—
200	C₂×C₄×C₄₁	—	2	1	no	—
201	C₂×C₄×C₄₁	—	2	1	no	—
202	C₂×C₄×C₄₁	—	2	1	no	—
203	C₂×C₄×C₄₁	—	2	1	no	—
204	C₂×C₄×C₄₁	—	2	1	no	—
205	C₂×C₄×C₄₁	—	2	1	no	—
206	C₂×C₄×C₄₁	—	2	1	no	—
207	C₂×C₄×C₄₁	—	4	2	no	—
208	C₂×C₄×C₄₁	—	4	2	no	—
209	C₂×C₄×C₄₁	—	4	2	no	—
210	C₂×C₄×C₄₁	—	4	2	no	—
211	C₂×C₄×C₄₁	—	4	1	no	—
212	C₂×C₄×C₄₁	—	4	1	no	—
213	C₂×C₄×C₄₁	—	4	1	no	—
214	C₂×C₄×C₄₁	—	4	1	no	—
215	C₂×C₄×C₄₁	—	4	2	no	—
216	C₂×C₄×C₄₁	—	4	2	no	—
217	C₂×C₄×C₄₁	—	4	2	no	—
218	C₂×C₄×C₄₁	#135	1	2	yes	—
219	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
224	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
225	C₈×C₄₁	—	2	2	no	—
226	C₈×C₄₁	—	4	1	no	—
227	C₈×C₄₁	—	4	1	no	—
228	C₈×C₄₁	#121	1	4	yes	—
229	#25412	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂²×C₄₁	—	2	2	no	—
231	C₂²×C₄₁	—	2	2	no	—
232	C₂²×C₄₁	—	2	2	no	—
233	C₂²×C₄₁	—	4	1	no	—
234	C₂²×C₄₁	—	4	1	no	—
235	C₂²×C₄₁	—	4	1	no	—
236	C₂²×C₄₁	—	4	1	no	—
237	C₂²×C₄₁	—	8	2	no	—
238	C₂²×C₄₁	—	8	2	no	—
239	C₂²×C₄₁	—	8	2	no	—
240	C₂²×C₄₁	—	8	2	no	—
241	C₂²×C₄₁	—	8	2	no	—
242	C₂²×C₄₁	—	8	2	no	—
243	C₂²×C₄₁	—	8	2	no	—
244	C₂²×C₄₁	#532	1	1	yes	characteristic
245	C₂²×C₄₁	D₄²	1	1	yes	characteristic
246	C₂²×C₄₁	D₄²	1	1	yes	characteristic
247	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
248	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
249	C₂²×C₄₁	#576	1	1	yes	characteristic
250	C₂²×C₄₁	#578	1	1	yes	characteristic
251	C₄×C₄₁	—	2	2	no	—
252	C₄×C₄₁	—	4	1	no	—
253	C₄×C₄₁	—	4	4	no	—
254	C₄×C₄₁	—	4	1	no	—
255	C₄×C₄₁	—	4	4	no	—
256	C₄×C₄₁	—	4	1	no	—
257	C₄×C₄₁	—	4	1	no	—
258	C₄×C₄₁	—	8	2	no	—
259	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
260	C₄×C₄₁	#540	1	1	yes	characteristic
261	C₄×C₄₁	#546	1	1	yes	characteristic
262	C₄×C₄₁	#550	1	1	yes	characteristic
263	C₂×#495	C₂×C₄₁	1	1	yes	characteristic, complemented
264	C₂×#467	C₂×C₄₁	1	1	yes	characteristic, complemented
265	C₂×#466	C₂×C₄₁	1	1	yes	characteristic
266	C₂×C₄×Q₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
267	#2426	C₂×C₄₁	1	2	yes	complemented
268	#2042	C₂×C₄₁	1	2	yes	complemented
269	#2000	C₂×C₄₁	1	2	yes	complemented
270	#1970	C₂×C₄₁	1	1	yes	characteristic, complemented
271	#1942	C₂×C₄₁	1	1	yes	characteristic, complemented
272	#1880	C₂×C₄₁	1	2	yes	complemented
273	C₈×C₂²⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
274	C₂×C₄₁	—	4	2	no	—
275	C₂×C₄₁	—	16	2	no	—
276	C₂×C₄₁	#2428	1	1	yes	characteristic
277	C₂×C₄₁	#3168	1	1	yes	characteristic
278	C₂×C₄₁	#3175	1	1	yes	characteristic
279	C₂×C₄₁	#3280	1	1	yes	characteristic
280	C₂×C₄₁	#3285	1	1	yes	characteristic
281	C₂×C₄₁	#3285	1	1	yes	characteristic
282	C₂×C₄₁	#3287	1	1	yes	characteristic
283	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
284	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
285	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
286	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
287	C₂×#124	C₂²×C₄₁	1	2	yes	—
288	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
289	C₂×#121	C₂²×C₄₁	1	2	yes	—
290	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
291	#495	—	2	4	no	—
292	#467	—	2	4	no	—
293	#466	—	2	4	no	—
294	C₄×Q₁₆	—	2	4	no	—
295	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
296	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
297	C₂×#103	C₂²×C₄₁	1	2	yes	—
298	C₂×#103	C₂²×C₄₁	1	2	yes	—
299	C₂×#102	C₂²×C₄₁	1	2	yes	—
300	C₂×#102	C₂²×C₄₁	1	2	yes	—
301	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
302	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
303	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
304	#396	—	2	2	no	—
305	#394	—	2	2	no	—
306	#390	—	2	2	no	—
307	#390	C₂²×C₄₁	1	2	yes	—
308	#389	C₂²×C₄₁	1	2	yes	—
309	#388	—	2	2	no	—
310	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
311	#340	C₂²×C₄₁	1	2	yes	—
312	#336	C₂²×C₄₁	1	1	yes	characteristic
313	#336	C₂²×C₄₁	1	1	yes	characteristic
314	C₄₁	#25412	1	1	yes	characteristic, direct product factor, Sylow
315	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
316	C₂²×D₄	—	2	2	no	—
317	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
318	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
319	C₂×Q₁₆	—	2	2	no	—
320	C₂×Q₁₆	—	2	2	no	—
321	C₂×Q₁₆	D₄×C₄₁	1	4	yes	complemented
322	C₂×SD₁₆	—	2	4	no	—
323	C₂×SD₁₆	—	2	4	no	—
324	C₂×SD₁₆	—	4	2	no	—
325	C₂×D₈	—	2	2	no	—
326	C₂×D₈	—	2	2	no	—
327	C₂×D₈	—	2	2	no	—
328	C₂²×C₈	—	2	2	no	—
329	C₂²×C₈	—	2	2	no	—
330	C₂²×C₈	—	2	2	no	—
331	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
332	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
333	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
334	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
335	#124	—	2	4	no	—
336	#124	—	4	2	no	—
337	C₂²⋊Q₈	—	2	4	no	—
338	C₂²⋊Q₈	—	4	2	no	—
339	#121	—	2	4	no	—
340	#121	—	4	2	no	—
341	C₄×Q₈	—	2	4	no	—
342	C₄×Q₈	—	4	2	no	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₄⋊C₄	—	2	2	no	—
345	C₂×C₄⋊C₄	—	2	2	no	—
346	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
347	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₂²⋊C₄	—	2	2	no	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
355	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
356	C₂×C₄²	—	2	2	no	—
357	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
359	#107	—	2	2	no	—
360	#107	D₄×C₄₁	1	4	yes	—
361	#103	—	2	4	no	—
362	#103	—	2	4	no	—
363	#102	—	2	4	no	—
364	#102	—	4	2	no	—
365	C₂²⋊C₈	—	2	2	no	—
366	C₄×C₈	—	2	2	no	—
367	C₄×C₈	—	2	2	no	—
368	#95	—	2	2	no	—
369	#95	D₄×C₄₁	1	1	yes	characteristic
370	#95	D₄×C₄₁	1	1	yes	characteristic
371	C₂⁴	—	2	2	no	—
372	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	4	4	no	—
386	C₂×D₄	—	4	4	no	—
387	C₂×D₄	—	8	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
402	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
403	Q₁₆	—	2	8	no	—
404	SD₁₆	—	4	8	no	—
405	D₈	—	4	4	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	4	4	no	—
415	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
416	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
417	C₂×C₈	#41×C₄₁	1	2	yes	—
418	C₂×C₈	#41×C₄₁	1	2	yes	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	4	4	no	—
423	C₄⋊C₄	—	4	4	no	—
424	C₄⋊C₄	—	8	2	no	—
425	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	4	4	no	—
429	C₂²⋊C₄	—	4	4	no	—
430	C₂²⋊C₄	—	4	4	no	—
431	C₂²⋊C₄	—	4	4	no	—
432	C₂²⋊C₄	—	4	4	no	—
433	C₂²⋊C₄	—	8	2	no	—
434	C₄²	—	2	1	no	—
435	C₄²	—	2	1	no	—
436	C₄²	—	2	1	no	—
437	C₄²	—	2	1	no	—
438	C₄²	—	4	4	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	2	1	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	2	1	no	—
443	C₂³	—	2	1	no	—
444	C₂³	—	2	1	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	#135×C₄₁	1	2	yes	—
453	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
454	Q₈	—	2	4	no	—
455	Q₈	—	2	4	no	—
456	Q₈	—	4	2	no	—
457	Q₈	—	4	2	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	4	2	no	—
461	D₄	—	4	2	no	—
462	D₄	—	8	8	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	#135×C₄₁	1	2	yes	—
491	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
492	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
493	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
494	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
495	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
496	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
497	C₈	—	2	2	no	—
498	C₈	—	4	1	no	—
499	C₈	—	4	1	no	—
500	C₈	#121×C₄₁	1	4	yes	—
501	C₂²	—	2	2	no	—
502	C₂²	—	2	2	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	4	1	no	—
508	C₂²	—	8	2	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	2	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	8	2	no	—
513	C₂²	—	8	2	no	—
514	C₂²	—	8	2	no	—
515	C₂²	C₄₁×#532	1	1	yes	characteristic
516	C₂²	D₄²×C₄₁	1	1	yes	characteristic
517	C₂²	D₄²×C₄₁	1	1	yes	characteristic
518	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
519	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
520	C₂²	C₄₁×#576	1	1	yes	characteristic
521	C₂²	C₄₁×#578	1	1	yes	characteristic
522	C₄	—	2	2	no	—
523	C₄	—	4	1	no	—
524	C₄	—	4	4	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	4	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	8	2	no	—
530	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
531	C₄	C₄₁×#540	1	1	yes	characteristic
532	C₄	C₄₁×#546	1	1	yes	characteristic
533	C₄	C₄₁×#550	1	1	yes	characteristic
534	C₂	—	4	2	no	—
535	C₂	—	16	2	no	—
536	C₂	C₄₁×#2428	1	1	yes	characteristic
537	C₂	C₄₁×#3168	1	1	yes	characteristic
538	C₂	C₄₁×#3175	1	1	yes	characteristic
539	C₂	C₄₁×#3280	1	1	yes	characteristic
540	C₂	C₄₁×#3285	1	1	yes	characteristic
541	C₂	C₄₁×#3285	1	1	yes	characteristic
542	C₂	C₄₁×#3287	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#466	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄×C₂²⋊C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#495	C₂	semidirect
2. C₂×C₄₁×#467	C₂	semidirect
4. C₂×C₄×Q₁₆×C₄₁	C₂	semidirect
5. C₄₁×#2426	C₂	semidirect
6. C₄₁×#2042	C₂	semidirect
7. C₄₁×#2000	C₂	semidirect
8. C₄₁×#1970	C₂	semidirect
9. C₄₁×#1942	C₂	semidirect
10. C₄₁×#1880	C₂	semidirect
11. C₈×C₂²⋊C₄×C₄₁	C₂	semidirect
49. C₂×Q₁₆×C₄₁	D₄	semidirect
229. #25412	C₄₁	direct (N × H)
263. C₂×#495	C₂×C₄₁	semidirect
264. C₂×#467	C₂×C₄₁	semidirect
266. C₂×C₄×Q₁₆	C₂×C₄₁	semidirect
267. #2426	C₂×C₄₁	semidirect
268. #2042	C₂×C₄₁	semidirect
269. #2000	C₂×C₄₁	semidirect
270. #1970	C₂×C₄₁	semidirect
271. #1942	C₂×C₄₁	semidirect
272. #1880	C₂×C₄₁	semidirect
273. C₈×C₂²⋊C₄	C₂×C₄₁	semidirect
314. C₄₁	#25412	direct (N × H)
321. C₂×Q₁₆	D₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#495	2
C₂×C₄₁×#467	2
C₂×C₄₁×#466	2
C₂×C₄×Q₁₆×C₄₁	2
C₄₁×#2426	2
C₄₁×#2042	2
C₄₁×#2000	2
C₄₁×#1970	2
C₄₁×#1942	2
C₄₁×#1880	2
C₈×C₂²⋊C₄×C₄₁	2
#25412	41

Subgroups — C41×#25412 #23801613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25412 #23801613