Subgroups — C₄₁×#24271 #23800472

Order 10496.

1452 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#470	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#469	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#435	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2407	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2055	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2000	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1972	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1971	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1807	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1788	C₂	1	2	yes	maximal, complemented
12	C₂²×#41×C₄₁	C₂²	1	2	yes	—
13	C₂×#135×C₄₁	—	2	4	no	—
14	C₂×#135×C₄₁	—	2	4	no	—
15	C₂×#135×C₄₁	—	2	4	no	—
16	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
18	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
22	C₂×#121×C₄₁	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
24	C₄₁×#470	—	2	4	no	—
25	C₄₁×#469	—	2	4	no	—
26	C₄₁×#435	—	2	4	no	—
27	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×#103×C₄₁	C₂²	1	2	yes	—
31	C₂×#103×C₄₁	C₂²	1	2	yes	—
32	C₂×#102×C₄₁	C₂²	1	2	yes	—
33	C₂×#102×C₄₁	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
36	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
37	C₄₁×#394	—	2	2	no	—
38	C₄₁×#392	—	2	2	no	—
39	C₄₁×#391	C₂²	1	2	yes	—
40	C₄₁×#390	C₂²	1	2	yes	—
41	C₄₁×#386	—	2	2	no	—
42	C₄₁×#385	—	2	2	no	—
43	C₄₁×#380	C₂²	1	2	yes	—
44	C₄₁×#340	C₂²	1	2	yes	—
45	C₂×#41×C₄₁	—	2	4	no	—
46	C₂×#41×C₄₁	—	2	4	no	—
47	C₂×#41×C₄₁	—	2	4	no	—
48	C₂×#41×C₄₁	—	2	4	no	—
49	C₂×#41×C₄₁	—	4	2	no	—
50	C₂×#41×C₄₁	—	4	2	no	—
51	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
52	C₂²×D₄×C₄₁	—	2	2	no	—
53	C₂²×D₄×C₄₁	—	2	2	no	—
54	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
55	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
56	C₂³×C₄×C₄₁	—	2	2	no	—
57	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
59	#135×C₄₁	—	2	32	no	—
60	C₂×Q₁₆×C₄₁	—	2	2	no	—
61	C₂×Q₁₆×C₄₁	—	2	2	no	—
62	C₂×Q₁₆×C₄₁	D₄	1	4	yes	complemented
63	C₂×SD₁₆×C₄₁	—	2	4	no	—
64	C₂×SD₁₆×C₄₁	—	2	4	no	—
65	C₂×SD₁₆×C₄₁	—	2	4	no	—
66	C₂×D₈×C₄₁	—	2	2	no	—
67	C₂×D₈×C₄₁	—	2	2	no	—
68	C₂×D₈×C₄₁	D₄	1	4	yes	complemented
69	C₂×M₁₆×C₄₁	—	2	2	no	—
70	C₂×M₁₆×C₄₁	—	2	2	no	—
71	C₂×M₁₆×C₄₁	—	2	2	no	—
72	C₂²×C₈×C₄₁	—	2	2	no	—
73	C₂²×C₈×C₄₁	—	2	2	no	—
74	C₂²×C₈×C₄₁	D₄	1	4	yes	complemented
75	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
79	C₂²⋊Q₈×C₄₁	—	2	4	no	—
80	C₂²⋊Q₈×C₄₁	—	4	2	no	—
81	#121×C₄₁	—	2	4	no	—
82	#121×C₄₁	—	4	2	no	—
83	C₄×D₄×C₄₁	—	2	2	no	—
84	C₄×D₄×C₄₁	—	2	2	no	—
85	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
86	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
89	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
97	#106×C₄₁	—	2	2	no	—
98	#106×C₄₁	—	2	2	no	—
99	C₄⋊C₈×C₄₁	—	2	2	no	—
100	#103×C₄₁	—	2	4	no	—
101	#103×C₄₁	—	4	2	no	—
102	#102×C₄₁	—	2	4	no	—
103	#102×C₄₁	—	4	2	no	—
104	C₂²⋊C₈×C₄₁	—	2	2	no	—
105	C₂²⋊C₈×C₄₁	—	2	2	no	—
106	#97×C₄₁	—	2	2	no	—
107	#95×C₄₁	—	2	2	no	—
108	#95×C₄₁	—	2	2	no	—
109	#95×C₄₁	—	2	2	no	—
110	C₂⁴×C₄₁	—	2	2	no	—
111	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
112	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
113	#41×C₄₁	—	2	16	no	—
114	#41×C₄₁	—	4	8	no	—
115	#41×C₄₁	—	4	8	no	—
116	#41×C₄₁	—	4	8	no	—
117	C₂×Q₈×C₄₁	—	2	2	no	—
118	C₂×Q₈×C₄₁	—	2	2	no	—
119	C₂×Q₈×C₄₁	—	2	2	no	—
120	C₂×Q₈×C₄₁	—	2	2	no	—
121	C₂×Q₈×C₄₁	—	2	2	no	—
122	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
123	C₂×D₄×C₄₁	—	2	2	no	—
124	C₂×D₄×C₄₁	—	2	2	no	—
125	C₂×D₄×C₄₁	—	2	2	no	—
126	C₂×D₄×C₄₁	—	2	2	no	—
127	C₂×D₄×C₄₁	—	2	2	no	—
128	C₂×D₄×C₄₁	—	2	2	no	—
129	C₂×D₄×C₄₁	—	4	2	no	—
130	C₂×D₄×C₄₁	—	4	4	no	—
131	C₂×D₄×C₄₁	—	4	4	no	—
132	C₂×D₄×C₄₁	—	4	4	no	—
133	C₂×D₄×C₄₁	—	4	4	no	—
134	C₂×D₄×C₄₁	—	4	4	no	—
135	C₂×D₄×C₄₁	—	8	2	no	—
136	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
137	C₂²×C₄×C₄₁	—	2	1	no	—
138	C₂²×C₄×C₄₁	—	2	1	no	—
139	C₂²×C₄×C₄₁	—	2	1	no	—
140	C₂²×C₄×C₄₁	—	2	1	no	—
141	C₂²×C₄×C₄₁	—	2	2	no	—
142	C₂²×C₄×C₄₁	—	2	1	no	—
143	C₂²×C₄×C₄₁	—	2	1	no	—
144	C₂²×C₄×C₄₁	—	2	1	no	—
145	C₂²×C₄×C₄₁	—	2	1	no	—
146	C₂²×C₄×C₄₁	—	2	1	no	—
147	C₂²×C₄×C₄₁	—	2	1	no	—
148	C₂²×C₄×C₄₁	—	2	2	no	—
149	C₂²×C₄×C₄₁	—	2	2	no	—
150	C₂²×C₄×C₄₁	—	4	4	no	—
151	C₂²×C₄×C₄₁	—	4	4	no	—
152	C₂²×C₄×C₄₁	—	4	4	no	—
153	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₄₁	#41	1	2	yes	—
159	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
160	Q₁₆×C₄₁	—	2	8	no	—
161	SD₁₆×C₄₁	—	2	16	no	—
162	D₈×C₄₁	—	2	8	no	—
163	M₁₆×C₄₁	—	4	4	no	—
164	C₂×C₈×C₄₁	—	2	1	no	—
165	C₂×C₈×C₄₁	—	2	1	no	—
166	C₂×C₈×C₄₁	—	2	8	no	—
167	C₂×C₈×C₄₁	—	2	1	no	—
168	C₂×C₈×C₄₁	—	2	1	no	—
169	C₂×C₈×C₄₁	—	2	1	no	—
170	C₂×C₈×C₄₁	—	2	1	no	—
171	C₂×C₈×C₄₁	—	2	1	no	—
172	C₂×C₈×C₄₁	—	2	1	no	—
173	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
174	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
175	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
176	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
177	C₄⋊C₄×C₄₁	—	2	2	no	—
178	C₄⋊C₄×C₄₁	—	2	2	no	—
179	C₄⋊C₄×C₄₁	—	2	2	no	—
180	C₄⋊C₄×C₄₁	—	2	2	no	—
181	C₄⋊C₄×C₄₁	—	2	2	no	—
182	C₄⋊C₄×C₄₁	—	4	4	no	—
183	C₂²⋊C₄×C₄₁	—	2	2	no	—
184	C₂²⋊C₄×C₄₁	—	2	2	no	—
185	C₂²⋊C₄×C₄₁	—	4	4	no	—
186	C₂²⋊C₄×C₄₁	—	4	4	no	—
187	C₂²⋊C₄×C₄₁	—	4	4	no	—
188	C₂²⋊C₄×C₄₁	—	8	2	no	—
189	C₂²⋊C₄×C₄₁	—	8	2	no	—
190	C₄²×C₄₁	—	2	1	no	—
191	C₄²×C₄₁	—	2	1	no	—
192	C₂³×C₄₁	—	2	1	no	—
193	C₂³×C₄₁	—	2	1	no	—
194	C₂³×C₄₁	—	2	2	no	—
195	C₂³×C₄₁	—	2	2	no	—
196	C₂³×C₄₁	—	2	1	no	—
197	C₂³×C₄₁	—	2	1	no	—
198	C₂³×C₄₁	—	2	4	no	—
199	C₂³×C₄₁	—	2	1	no	—
200	C₂³×C₄₁	—	2	2	no	—
201	C₂³×C₄₁	—	2	2	no	—
202	C₂³×C₄₁	—	4	2	no	—
203	C₂³×C₄₁	—	4	2	no	—
204	C₂³×C₄₁	—	4	2	no	—
205	C₂³×C₄₁	—	4	2	no	—
206	C₂³×C₄₁	—	4	2	no	—
207	C₂³×C₄₁	—	4	2	no	—
208	C₂³×C₄₁	#121	1	2	yes	—
209	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
210	Q₈×C₄₁	—	2	4	no	—
211	Q₈×C₄₁	—	2	4	no	—
212	Q₈×C₄₁	—	4	2	no	—
213	Q₈×C₄₁	—	4	2	no	—
214	D₄×C₄₁	—	2	4	no	—
215	D₄×C₄₁	—	2	4	no	—
216	D₄×C₄₁	—	4	4	no	—
217	D₄×C₄₁	—	4	16	no	—
218	D₄×C₄₁	—	4	2	no	—
219	D₄×C₄₁	—	4	2	no	—
220	D₄×C₄₁	—	8	8	no	—
221	C₂×C₄×C₄₁	—	2	1	no	—
222	C₂×C₄×C₄₁	—	2	1	no	—
223	C₂×C₄×C₄₁	—	2	2	no	—
224	C₂×C₄×C₄₁	—	2	2	no	—
225	C₂×C₄×C₄₁	—	2	2	no	—
226	C₂×C₄×C₄₁	—	2	2	no	—
227	C₂×C₄×C₄₁	—	2	1	no	—
228	C₂×C₄×C₄₁	—	2	1	no	—
229	C₂×C₄×C₄₁	—	2	1	no	—
230	C₂×C₄×C₄₁	—	2	1	no	—
231	C₂×C₄×C₄₁	—	2	4	no	—
232	C₂×C₄×C₄₁	—	2	1	no	—
233	C₂×C₄×C₄₁	—	2	2	no	—
234	C₂×C₄×C₄₁	—	2	2	no	—
235	C₂×C₄×C₄₁	—	4	16	no	—
236	C₂×C₄×C₄₁	—	4	2	no	—
237	C₂×C₄×C₄₁	—	4	2	no	—
238	C₂×C₄×C₄₁	—	4	1	no	—
239	C₂×C₄×C₄₁	—	4	1	no	—
240	C₂×C₄×C₄₁	—	4	1	no	—
241	C₂×C₄×C₄₁	—	4	1	no	—
242	C₂×C₄×C₄₁	—	4	2	no	—
243	C₂×C₄×C₄₁	—	4	2	no	—
244	C₂×C₄×C₄₁	—	4	2	no	—
245	C₂×C₄×C₄₁	—	4	2	no	—
246	C₂×C₄×C₄₁	—	4	2	no	—
247	C₂×C₄×C₄₁	—	4	2	no	—
248	C₂×C₄×C₄₁	#121	1	2	yes	—
249	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
253	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
254	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
255	C₈×C₄₁	—	2	2	no	—
256	C₈×C₄₁	—	4	1	no	—
257	C₈×C₄₁	—	4	1	no	—
258	C₈×C₄₁	#120	1	4	yes	—
259	#24271	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
260	C₂²×C₄₁	—	2	2	no	—
261	C₂²×C₄₁	—	2	2	no	—
262	C₂²×C₄₁	—	2	2	no	—
263	C₂²×C₄₁	—	4	2	no	—
264	C₂²×C₄₁	—	4	2	no	—
265	C₂²×C₄₁	—	4	4	no	—
266	C₂²×C₄₁	—	4	1	no	—
267	C₂²×C₄₁	—	4	2	no	—
268	C₂²×C₄₁	—	4	4	no	—
269	C₂²×C₄₁	—	4	4	no	—
270	C₂²×C₄₁	—	4	2	no	—
271	C₂²×C₄₁	—	4	1	no	—
272	C₂²×C₄₁	—	4	1	no	—
273	C₂²×C₄₁	—	8	2	no	—
274	C₂²×C₄₁	—	8	2	no	—
275	C₂²×C₄₁	—	8	2	no	—
276	C₂²×C₄₁	—	8	2	no	—
277	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
278	C₂²×C₄₁	D₄²	1	1	yes	characteristic
279	C₂²×C₄₁	D₄²	1	1	yes	characteristic
280	C₂²×C₄₁	#575	1	2	yes	—
281	C₂²×C₄₁	#577	1	2	yes	—
282	C₄×C₄₁	—	2	2	no	—
283	C₄×C₄₁	—	4	1	no	—
284	C₄×C₄₁	—	4	4	no	—
285	C₄×C₄₁	—	4	1	no	—
286	C₄×C₄₁	—	4	1	no	—
287	C₄×C₄₁	—	8	2	no	—
288	C₄×C₄₁	—	8	2	no	—
289	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
290	C₄×C₄₁	#535	1	1	yes	characteristic
291	C₄×C₄₁	#546	1	1	yes	characteristic
292	C₄×C₄₁	#546	1	1	yes	characteristic
293	C₂²×#135	C₂×C₄₁	1	1	yes	characteristic, complemented
294	C₂×#470	C₂×C₄₁	1	1	yes	characteristic, complemented
295	C₂×#469	C₂×C₄₁	1	1	yes	characteristic, complemented
296	C₂×#435	C₂×C₄₁	1	1	yes	characteristic, complemented
297	#2407	C₂×C₄₁	1	2	yes	complemented
298	#2055	C₂×C₄₁	1	2	yes	complemented
299	#2000	C₂×C₄₁	1	2	yes	complemented
300	#1972	C₂×C₄₁	1	1	yes	characteristic, complemented
301	#1971	C₂×C₄₁	1	1	yes	characteristic, complemented
302	#1807	C₂×C₄₁	1	1	yes	characteristic, complemented
303	#1788	C₂×C₄₁	1	2	yes	complemented
304	C₂×C₄₁	—	4	2	no	—
305	C₂×C₄₁	—	8	1	no	—
306	C₂×C₄₁	—	8	4	no	—
307	C₂×C₄₁	#2408	1	1	yes	characteristic
308	C₂×C₄₁	#3054	1	1	yes	characteristic
309	C₂×C₄₁	#3060	1	1	yes	characteristic
310	C₂×C₄₁	#3267	1	2	yes	—
311	C₂×C₄₁	#3271	1	2	yes	—
312	C₂²×#41	C₂²×C₄₁	1	2	yes	—
313	C₂×#135	—	2	4	no	—
314	C₂×#135	—	2	4	no	—
315	C₂×#135	—	2	4	no	—
316	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
317	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
318	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
319	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
320	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
321	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
322	C₂×#121	C₂²×C₄₁	1	2	yes	—
323	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
324	#470	—	2	4	no	—
325	#469	—	2	4	no	—
326	#435	—	2	4	no	—
327	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
328	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
329	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
330	C₂×#103	C₂²×C₄₁	1	2	yes	—
331	C₂×#103	C₂²×C₄₁	1	2	yes	—
332	C₂×#102	C₂²×C₄₁	1	2	yes	—
333	C₂×#102	C₂²×C₄₁	1	2	yes	—
334	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
335	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
336	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
337	#394	—	2	2	no	—
338	#392	—	2	2	no	—
339	#391	C₂²×C₄₁	1	2	yes	—
340	#390	C₂²×C₄₁	1	2	yes	—
341	#386	—	2	2	no	—
342	#385	—	2	2	no	—
343	#380	C₂²×C₄₁	1	2	yes	—
344	#340	C₂²×C₄₁	1	2	yes	—
345	C₄₁	#24271	1	1	yes	characteristic, direct product factor, Sylow
346	C₂×#41	—	2	4	no	—
347	C₂×#41	—	2	4	no	—
348	C₂×#41	—	2	4	no	—
349	C₂×#41	—	2	4	no	—
350	C₂×#41	—	4	2	no	—
351	C₂×#41	—	4	2	no	—
352	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
353	C₂²×D₄	—	2	2	no	—
354	C₂²×D₄	—	2	2	no	—
355	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
356	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
357	C₂³×C₄	—	2	2	no	—
358	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
359	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
360	#135	—	2	32	no	—
361	C₂×Q₁₆	—	2	2	no	—
362	C₂×Q₁₆	—	2	2	no	—
363	C₂×Q₁₆	D₄×C₄₁	1	4	yes	complemented
364	C₂×SD₁₆	—	2	4	no	—
365	C₂×SD₁₆	—	2	4	no	—
366	C₂×SD₁₆	—	2	4	no	—
367	C₂×D₈	—	2	2	no	—
368	C₂×D₈	—	2	2	no	—
369	C₂×D₈	D₄×C₄₁	1	4	yes	complemented
370	C₂×M₁₆	—	2	2	no	—
371	C₂×M₁₆	—	2	2	no	—
372	C₂×M₁₆	—	2	2	no	—
373	C₂²×C₈	—	2	2	no	—
374	C₂²×C₈	—	2	2	no	—
375	C₂²×C₈	D₄×C₄₁	1	4	yes	complemented
376	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
377	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
378	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
379	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
380	C₂²⋊Q₈	—	2	4	no	—
381	C₂²⋊Q₈	—	4	2	no	—
382	#121	—	2	4	no	—
383	#121	—	4	2	no	—
384	C₄×D₄	—	2	2	no	—
385	C₄×D₄	—	2	2	no	—
386	C₂×C₄⋊C₄	—	2	2	no	—
387	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
389	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
390	C₂×C₂²⋊C₄	—	2	2	no	—
391	C₂×C₂²⋊C₄	—	2	2	no	—
392	C₂×C₂²⋊C₄	—	2	2	no	—
393	C₂×C₂²⋊C₄	—	2	2	no	—
394	C₂×C₂²⋊C₄	—	2	2	no	—
395	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
396	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
397	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
398	#106	—	2	2	no	—
399	#106	—	2	2	no	—
400	C₄⋊C₈	—	2	2	no	—
401	#103	—	2	4	no	—
402	#103	—	4	2	no	—
403	#102	—	2	4	no	—
404	#102	—	4	2	no	—
405	C₂²⋊C₈	—	2	2	no	—
406	C₂²⋊C₈	—	2	2	no	—
407	#97	—	2	2	no	—
408	#95	—	2	2	no	—
409	#95	—	2	2	no	—
410	#95	—	2	2	no	—
411	C₂⁴	—	2	2	no	—
412	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
413	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
414	#41	—	2	16	no	—
415	#41	—	4	8	no	—
416	#41	—	4	8	no	—
417	#41	—	4	8	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	2	2	no	—
422	C₂×Q₈	—	2	2	no	—
423	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	4	2	no	—
431	C₂×D₄	—	4	4	no	—
432	C₂×D₄	—	4	4	no	—
433	C₂×D₄	—	4	4	no	—
434	C₂×D₄	—	4	4	no	—
435	C₂×D₄	—	4	4	no	—
436	C₂×D₄	—	8	2	no	—
437	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	4	4	no	—
452	C₂²×C₄	—	4	4	no	—
453	C₂²×C₄	—	4	4	no	—
454	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
459	C₂²×C₄	#41×C₄₁	1	2	yes	—
460	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
461	Q₁₆	—	2	8	no	—
462	SD₁₆	—	2	16	no	—
463	D₈	—	2	8	no	—
464	M₁₆	—	4	4	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	8	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
475	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
476	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
477	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	4	4	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	4	4	no	—
487	C₂²⋊C₄	—	4	4	no	—
488	C₂²⋊C₄	—	4	4	no	—
489	C₂²⋊C₄	—	8	2	no	—
490	C₂²⋊C₄	—	8	2	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₂³	—	2	1	no	—
494	C₂³	—	2	1	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	2	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	2	2	no	—
502	C₂³	—	2	2	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	4	2	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	4	2	no	—
507	C₂³	—	4	2	no	—
508	C₂³	—	4	2	no	—
509	C₂³	#121×C₄₁	1	2	yes	—
510	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
511	Q₈	—	2	4	no	—
512	Q₈	—	2	4	no	—
513	Q₈	—	4	2	no	—
514	Q₈	—	4	2	no	—
515	D₄	—	2	4	no	—
516	D₄	—	2	4	no	—
517	D₄	—	4	4	no	—
518	D₄	—	4	16	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	2	no	—
521	D₄	—	8	8	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	4	16	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	#121×C₄₁	1	2	yes	—
550	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
551	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
553	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
554	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
555	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
556	C₈	—	2	2	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₈	#120×C₄₁	1	4	yes	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	4	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	8	2	no	—
574	C₂²	—	8	2	no	—
575	C₂²	—	8	2	no	—
576	C₂²	—	8	2	no	—
577	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
578	C₂²	D₄²×C₄₁	1	1	yes	characteristic
579	C₂²	D₄²×C₄₁	1	1	yes	characteristic
580	C₂²	C₄₁×#575	1	2	yes	—
581	C₂²	C₄₁×#577	1	2	yes	—
582	C₄	—	2	2	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	4	no	—
587	C₄	—	8	2	no	—
588	C₄	—	8	2	no	—
589	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
590	C₄	C₄₁×#535	1	1	yes	characteristic
591	C₄	C₄₁×#546	1	1	yes	characteristic
592	C₄	C₄₁×#546	1	1	yes	characteristic
593	C₂	—	4	2	no	—
594	C₂	—	8	1	no	—
595	C₂	—	8	4	no	—
596	C₂	C₄₁×#2408	1	1	yes	characteristic
597	C₂	C₄₁×#3054	1	1	yes	characteristic
598	C₂	C₄₁×#3060	1	1	yes	characteristic
599	C₂	C₄₁×#3267	1	2	yes	—
600	C₂	C₄₁×#3271	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂²×#135×C₄₁	C₂	semidirect
2. C₂×C₄₁×#470	C₂	semidirect
3. C₂×C₄₁×#469	C₂	semidirect
4. C₂×C₄₁×#435	C₂	semidirect
5. C₄₁×#2407	C₂	semidirect
6. C₄₁×#2055	C₂	semidirect
7. C₄₁×#2000	C₂	semidirect
8. C₄₁×#1972	C₂	semidirect
9. C₄₁×#1971	C₂	semidirect
10. C₄₁×#1807	C₂	semidirect
11. C₄₁×#1788	C₂	semidirect
62. C₂×Q₁₆×C₄₁	D₄	semidirect
68. C₂×D₈×C₄₁	D₄	semidirect
74. C₂²×C₈×C₄₁	D₄	semidirect
259. #24271	C₄₁	direct (N × H)
293. C₂²×#135	C₂×C₄₁	semidirect
294. C₂×#470	C₂×C₄₁	semidirect
295. C₂×#469	C₂×C₄₁	semidirect
296. C₂×#435	C₂×C₄₁	semidirect
297. #2407	C₂×C₄₁	semidirect
298. #2055	C₂×C₄₁	semidirect
299. #2000	C₂×C₄₁	semidirect
300. #1972	C₂×C₄₁	semidirect
301. #1971	C₂×C₄₁	semidirect
302. #1807	C₂×C₄₁	semidirect
303. #1788	C₂×C₄₁	semidirect
345. C₄₁	#24271	direct (N × H)
363. C₂×Q₁₆	D₄×C₄₁	semidirect
369. C₂×D₈	D₄×C₄₁	semidirect
375. C₂²×C₈	D₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#135×C₄₁	2
C₂×C₄₁×#470	2
C₂×C₄₁×#469	2
C₂×C₄₁×#435	2
C₄₁×#2407	2
C₄₁×#2055	2
C₄₁×#2000	2
C₄₁×#1972	2
C₄₁×#1971	2
C₄₁×#1807	2
C₄₁×#1788	2
#24271	41

Subgroups — C41×#24271 #23800472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24271 #23800472