Subgroups — C₄₁×#36731 #23812932

Order 10496.

2130 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2847	C₂	1	2	yes	maximal, complemented
2	C₄₁×#2743	C₂	1	4	yes	maximal, complemented
3	C₄₁×#2740	C₂	1	4	yes	maximal, complemented
4	C₄₁×#2699	C₂	1	4	yes	maximal, complemented
5	C₄₁×#2688	C₂	1	4	yes	maximal, complemented
6	C₄₁×#2656	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2646	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#2444	C₂	1	4	yes	maximal, complemented
9	C₄₁×#2424	C₂	1	4	yes	maximal, complemented
10	C₄₁×#2325	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₁×#381	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#121×C₄₁	C₂²	1	2	yes	—
14	C₂×#121×C₄₁	C₂²	1	2	yes	—
15	C₂×#121×C₄₁	C₂²	1	2	yes	—
16	C₂×#121×C₄₁	C₂²	1	4	yes	—
17	C₂×#121×C₄₁	C₂²	1	4	yes	—
18	C₂×#120×C₄₁	C₂²	1	4	yes	—
19	C₂×C₄×D₄×C₄₁	C₂²	1	4	yes	—
20	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
21	C₄₁×#400	C₂²	1	4	yes	complemented
22	C₄₁×#400	C₂²	1	4	yes	complemented
23	C₄₁×#399	C₂²	1	4	yes	complemented
24	C₄₁×#398	C₂²	1	4	yes	complemented
25	C₄₁×#397	C₂²	1	4	yes	complemented
26	C₄₁×#397	C₂²	1	4	yes	complemented
27	C₄₁×#396	C₂²	1	4	yes	—
28	C₄₁×#394	C₂²	1	4	yes	—
29	C₄₁×#394	C₂²	1	4	yes	—
30	C₄₁×#394	C₂²	1	4	yes	complemented
31	C₄₁×#392	C₂²	1	4	yes	—
32	C₄₁×#392	C₂²	1	4	yes	complemented
33	C₄₁×#390	C₂²	1	4	yes	—
34	C₄₁×#388	C₂²	1	4	yes	—
35	C₄₁×#388	C₂²	1	4	yes	complemented
36	C₄₁×#388	C₂²	1	4	yes	complemented
37	C₄₁×#387	C₂²	1	4	yes	complemented
38	C₄₁×#387	C₂²	1	4	yes	complemented
39	C₄₁×#386	C₂²	1	4	yes	—
40	C₄₁×#386	C₂²	1	4	yes	—
41	C₄₁×#386	C₂²	1	4	yes	—
42	C₄₁×#386	C₂²	1	4	yes	—
43	C₄₁×#386	C₂²	1	4	yes	—
44	C₄₁×#386	C₂²	1	4	yes	complemented
45	C₄₁×#386	C₂²	1	4	yes	complemented
46	C₄₁×#385	C₂²	1	4	yes	—
47	C₄₁×#385	C₂²	1	4	yes	complemented
48	C₄₁×#381	C₂²	1	4	yes	—
49	C₄₁×#381	C₂²	1	4	yes	—
50	C₄₁×#381	C₂²	1	4	yes	complemented
51	C₄₁×#380	C₂²	1	2	yes	—
52	C₄₁×#380	C₂²	1	2	yes	—
53	C₄₁×#380	C₂²	1	2	yes	—
54	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
55	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
56	C₂×#95×C₄₁	C₂²	1	2	yes	—
57	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
59	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
60	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
61	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
62	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
63	C₂³×C₄×C₄₁	—	2	4	no	—
64	C₂³×C₄×C₄₁	—	4	4	no	—
65	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
66	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
67	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
68	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
69	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
71	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
72	#121×C₄₁	—	2	8	no	—
73	#121×C₄₁	—	4	8	no	—
74	#121×C₄₁	—	4	4	no	—
75	#121×C₄₁	—	4	4	no	—
76	#121×C₄₁	—	4	8	no	—
77	#120×C₄₁	—	4	8	no	—
78	C₄×D₄×C₄₁	—	4	8	no	—
79	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
81	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
86	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
87	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
88	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
89	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
90	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
91	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
92	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
93	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
98	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
99	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
100	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
101	#95×C₄₁	C₂³	1	4	yes	—
102	#95×C₄₁	C₂³	1	4	yes	—
103	#95×C₄₁	C₂³	1	4	yes	—
104	#95×C₄₁	C₂³	1	4	yes	—
105	#95×C₄₁	C₂³	1	4	yes	—
106	#95×C₄₁	C₂³	1	4	yes	—
107	#95×C₄₁	C₂³	1	4	yes	—
108	#95×C₄₁	C₂³	1	4	yes	—
109	#95×C₄₁	C₂³	1	4	yes	—
110	#95×C₄₁	C₂³	1	4	yes	—
111	#95×C₄₁	C₂³	1	4	yes	—
112	C₂⁴×C₄₁	—	2	2	no	—
113	C₂⁴×C₄₁	—	2	4	no	—
114	C₂⁴×C₄₁	—	2	4	no	—
115	C₂⁴×C₄₁	—	4	1	no	—
116	C₂⁴×C₄₁	—	4	1	no	—
117	C₂⁴×C₄₁	C₂⁴	1	4	yes	—
118	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
119	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
120	C₂×D₄×C₄₁	—	2	8	no	—
121	C₂×D₄×C₄₁	—	2	8	no	—
122	C₂×D₄×C₄₁	—	2	8	no	—
123	C₂×D₄×C₄₁	—	2	8	no	—
124	C₂×D₄×C₄₁	—	2	8	no	—
125	C₂×D₄×C₄₁	—	2	4	no	—
126	C₂×D₄×C₄₁	—	4	4	no	—
127	C₂×D₄×C₄₁	—	4	4	no	—
128	C₂×D₄×C₄₁	—	4	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	C₂²×C₄×C₄₁	—	2	2	no	—
136	C₂²×C₄×C₄₁	—	2	4	no	—
137	C₂²×C₄×C₄₁	—	2	4	no	—
138	C₂²×C₄×C₄₁	—	2	4	no	—
139	C₂²×C₄×C₄₁	—	2	4	no	—
140	C₂²×C₄×C₄₁	—	2	4	no	—
141	C₂²×C₄×C₄₁	—	2	4	no	—
142	C₂²×C₄×C₄₁	—	4	2	no	—
143	C₂²×C₄×C₄₁	—	4	2	no	—
144	C₂²×C₄×C₄₁	—	4	2	no	—
145	C₂²×C₄×C₄₁	—	4	2	no	—
146	C₂²×C₄×C₄₁	—	4	2	no	—
147	C₂²×C₄×C₄₁	—	4	2	no	—
148	C₂²×C₄×C₄₁	—	4	4	no	—
149	C₂²×C₄×C₄₁	—	4	4	no	—
150	C₂²×C₄×C₄₁	—	4	2	no	—
151	C₂²×C₄×C₄₁	—	4	4	no	—
152	C₂²×C₄×C₄₁	—	4	2	no	—
153	C₂²×C₄×C₄₁	—	4	16	no	—
154	C₂²×C₄×C₄₁	#41	1	4	yes	—
155	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
157	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
163	C₄⋊C₄×C₄₁	—	2	4	no	—
164	C₄⋊C₄×C₄₁	—	4	4	no	—
165	C₄⋊C₄×C₄₁	—	4	4	no	—
166	C₄⋊C₄×C₄₁	—	4	2	no	—
167	C₄⋊C₄×C₄₁	—	4	2	no	—
168	C₄⋊C₄×C₄₁	—	4	4	no	—
169	C₄⋊C₄×C₄₁	—	4	4	no	—
170	C₂²⋊C₄×C₄₁	—	2	8	no	—
171	C₂²⋊C₄×C₄₁	—	2	8	no	—
172	C₂²⋊C₄×C₄₁	—	2	8	no	—
173	C₂²⋊C₄×C₄₁	—	4	4	no	—
174	C₂²⋊C₄×C₄₁	—	4	4	no	—
175	C₂²⋊C₄×C₄₁	—	4	4	no	—
176	C₂²⋊C₄×C₄₁	—	4	4	no	—
177	C₂²⋊C₄×C₄₁	—	4	4	no	—
178	C₂²⋊C₄×C₄₁	—	4	4	no	—
179	C₂²⋊C₄×C₄₁	—	4	4	no	—
180	C₂²⋊C₄×C₄₁	—	4	4	no	—
181	C₂²⋊C₄×C₄₁	—	4	4	no	—
182	C₂²⋊C₄×C₄₁	—	4	4	no	—
183	C₄²×C₄₁	—	4	4	no	—
184	C₂³×C₄₁	—	2	2	no	—
185	C₂³×C₄₁	—	2	1	no	—
186	C₂³×C₄₁	—	2	1	no	—
187	C₂³×C₄₁	—	2	8	no	—
188	C₂³×C₄₁	—	2	2	no	—
189	C₂³×C₄₁	—	2	2	no	—
190	C₂³×C₄₁	—	2	2	no	—
191	C₂³×C₄₁	—	2	2	no	—
192	C₂³×C₄₁	—	2	2	no	—
193	C₂³×C₄₁	—	2	2	no	—
194	C₂³×C₄₁	—	2	4	no	—
195	C₂³×C₄₁	—	2	4	no	—
196	C₂³×C₄₁	—	2	4	no	—
197	C₂³×C₄₁	—	2	4	no	—
198	C₂³×C₄₁	—	2	4	no	—
199	C₂³×C₄₁	—	2	4	no	—
200	C₂³×C₄₁	—	2	4	no	—
201	C₂³×C₄₁	—	4	8	no	—
202	C₂³×C₄₁	—	4	8	no	—
203	C₂³×C₄₁	—	4	4	no	—
204	C₂³×C₄₁	—	4	4	no	—
205	C₂³×C₄₁	C₂×#41	1	2	yes	—
206	C₂³×C₄₁	H(5,𝔽₂)	1	4	yes	—
207	C₂³×C₄₁	H(5,𝔽₂)	1	4	yes	—
208	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
209	D₄×C₄₁	—	4	16	no	—
210	D₄×C₄₁	—	8	4	no	—
211	D₄×C₄₁	—	8	8	no	—
212	D₄×C₄₁	—	8	8	no	—
213	D₄×C₄₁	—	8	8	no	—
214	C₂×C₄×C₄₁	—	2	2	no	—
215	C₂×C₄×C₄₁	—	2	2	no	—
216	C₂×C₄×C₄₁	—	2	4	no	—
217	C₂×C₄×C₄₁	—	2	1	no	—
218	C₂×C₄×C₄₁	—	2	1	no	—
219	C₂×C₄×C₄₁	—	2	4	no	—
220	C₂×C₄×C₄₁	—	2	4	no	—
221	C₂×C₄×C₄₁	—	2	4	no	—
222	C₂×C₄×C₄₁	—	2	4	no	—
223	C₂×C₄×C₄₁	—	2	4	no	—
224	C₂×C₄×C₄₁	—	2	4	no	—
225	C₂×C₄×C₄₁	—	2	4	no	—
226	C₂×C₄×C₄₁	—	2	4	no	—
227	C₂×C₄×C₄₁	—	2	4	no	—
228	C₂×C₄×C₄₁	—	2	2	no	—
229	C₂×C₄×C₄₁	—	2	2	no	—
230	C₂×C₄×C₄₁	—	2	4	no	—
231	C₂×C₄×C₄₁	—	2	4	no	—
232	C₂×C₄×C₄₁	—	2	4	no	—
233	C₂×C₄×C₄₁	—	2	4	no	—
234	C₂×C₄×C₄₁	—	2	4	no	—
235	C₂×C₄×C₄₁	—	4	4	no	—
236	C₂×C₄×C₄₁	—	4	8	no	—
237	C₂×C₄×C₄₁	—	4	8	no	—
238	C₂×C₄×C₄₁	—	4	4	no	—
239	C₂×C₄×C₄₁	—	8	4	no	—
240	C₂×C₄×C₄₁	—	8	4	no	—
241	C₂×C₄×C₄₁	—	8	8	no	—
242	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
243	#36731	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₂²×C₄₁	—	2	2	no	—
245	C₂²×C₄₁	—	2	2	no	—
246	C₂²×C₄₁	—	2	4	no	—
247	C₂²×C₄₁	—	2	4	no	—
248	C₂²×C₄₁	—	2	4	no	—
249	C₂²×C₄₁	—	2	4	no	—
250	C₂²×C₄₁	—	2	4	no	—
251	C₂²×C₄₁	—	4	16	no	—
252	C₂²×C₄₁	—	4	2	no	—
253	C₂²×C₄₁	—	4	2	no	—
254	C₂²×C₄₁	—	4	2	no	—
255	C₂²×C₄₁	—	4	2	no	—
256	C₂²×C₄₁	—	4	4	no	—
257	C₂²×C₄₁	—	4	4	no	—
258	C₂²×C₄₁	—	4	4	no	—
259	C₂²×C₄₁	—	4	4	no	—
260	C₂²×C₄₁	—	4	4	no	—
261	C₂²×C₄₁	—	4	4	no	—
262	C₂²×C₄₁	—	4	4	no	—
263	C₂²×C₄₁	#540	1	4	yes	—
264	C₂²×C₄₁	C₂²×#41	1	1	yes	characteristic
265	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	2	yes	—
266	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	2	yes	—
267	C₂²×C₄₁	#585	1	1	yes	characteristic
268	C₂²×C₄₁	#585	1	1	yes	characteristic
269	C₄×C₄₁	—	2	4	no	—
270	C₄×C₄₁	—	4	4	no	—
271	C₄×C₄₁	—	4	1	no	—
272	C₄×C₄₁	—	4	1	no	—
273	C₄×C₄₁	—	4	4	no	—
274	C₄×C₄₁	—	4	4	no	—
275	C₄×C₄₁	—	4	4	no	—
276	C₄×C₄₁	—	4	4	no	—
277	#2847	C₂×C₄₁	1	2	yes	complemented
278	#2743	C₂×C₄₁	1	4	yes	complemented
279	#2740	C₂×C₄₁	1	4	yes	complemented
280	#2699	C₂×C₄₁	1	4	yes	complemented
281	#2688	C₂×C₄₁	1	4	yes	complemented
282	#2656	C₂×C₄₁	1	1	yes	characteristic, complemented
283	#2646	C₂×C₄₁	1	1	yes	characteristic, complemented
284	#2444	C₂×C₄₁	1	4	yes	complemented
285	#2424	C₂×C₄₁	1	4	yes	complemented
286	#2325	C₂×C₄₁	1	2	yes	complemented
287	C₂×#381	C₂×C₄₁	1	1	yes	characteristic, complemented
288	C₂×C₄₁	—	2	4	no	—
289	C₂×C₄₁	—	4	4	no	—
290	C₂×C₄₁	—	8	4	no	—
291	C₂×C₄₁	C₂×#540	1	1	yes	characteristic
292	C₂×C₄₁	#3490	1	1	yes	characteristic
293	C₂×C₄₁	#3493	1	1	yes	characteristic
294	C₂×C₄₁	#3534	1	2	yes	—
295	C₂×C₄₁	#3534	1	2	yes	—
296	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
297	C₂×#121	C₂²×C₄₁	1	2	yes	—
298	C₂×#121	C₂²×C₄₁	1	2	yes	—
299	C₂×#121	C₂²×C₄₁	1	2	yes	—
300	C₂×#121	C₂²×C₄₁	1	4	yes	—
301	C₂×#121	C₂²×C₄₁	1	4	yes	—
302	C₂×#120	C₂²×C₄₁	1	4	yes	—
303	C₂×C₄×D₄	C₂²×C₄₁	1	4	yes	—
304	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
305	#400	C₂²×C₄₁	1	4	yes	complemented
306	#400	C₂²×C₄₁	1	4	yes	complemented
307	#399	C₂²×C₄₁	1	4	yes	complemented
308	#398	C₂²×C₄₁	1	4	yes	complemented
309	#397	C₂²×C₄₁	1	4	yes	complemented
310	#397	C₂²×C₄₁	1	4	yes	complemented
311	#396	C₂²×C₄₁	1	4	yes	—
312	#394	C₂²×C₄₁	1	4	yes	—
313	#394	C₂²×C₄₁	1	4	yes	—
314	#394	C₂²×C₄₁	1	4	yes	complemented
315	#392	C₂²×C₄₁	1	4	yes	—
316	#392	C₂²×C₄₁	1	4	yes	complemented
317	#390	C₂²×C₄₁	1	4	yes	—
318	#388	C₂²×C₄₁	1	4	yes	—
319	#388	C₂²×C₄₁	1	4	yes	complemented
320	#388	C₂²×C₄₁	1	4	yes	complemented
321	#387	C₂²×C₄₁	1	4	yes	complemented
322	#387	C₂²×C₄₁	1	4	yes	complemented
323	#386	C₂²×C₄₁	1	4	yes	—
324	#386	C₂²×C₄₁	1	4	yes	—
325	#386	C₂²×C₄₁	1	4	yes	—
326	#386	C₂²×C₄₁	1	4	yes	—
327	#386	C₂²×C₄₁	1	4	yes	—
328	#386	C₂²×C₄₁	1	4	yes	complemented
329	#386	C₂²×C₄₁	1	4	yes	complemented
330	#385	C₂²×C₄₁	1	4	yes	—
331	#385	C₂²×C₄₁	1	4	yes	complemented
332	#381	C₂²×C₄₁	1	4	yes	—
333	#381	C₂²×C₄₁	1	4	yes	—
334	#381	C₂²×C₄₁	1	4	yes	complemented
335	#380	C₂²×C₄₁	1	2	yes	—
336	#380	C₂²×C₄₁	1	2	yes	—
337	#380	C₂²×C₄₁	1	2	yes	—
338	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
339	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
340	C₂×#95	C₂²×C₄₁	1	2	yes	—
341	C₄₁	#36731	1	1	yes	characteristic, direct product factor, Sylow
342	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
343	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
344	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
345	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
346	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
347	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
348	C₂³×C₄	—	2	4	no	—
349	C₂³×C₄	—	4	4	no	—
350	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
351	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
352	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
353	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
354	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
355	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
356	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
357	#121	—	2	8	no	—
358	#121	—	4	8	no	—
359	#121	—	4	4	no	—
360	#121	—	4	4	no	—
361	#121	—	4	8	no	—
362	#120	—	4	8	no	—
363	C₄×D₄	—	4	8	no	—
364	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
366	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
367	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
369	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
370	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
371	C₂×C₂²⋊C₄	—	4	4	no	—
372	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
376	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
382	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
385	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
386	#95	C₂³×C₄₁	1	4	yes	—
387	#95	C₂³×C₄₁	1	4	yes	—
388	#95	C₂³×C₄₁	1	4	yes	—
389	#95	C₂³×C₄₁	1	4	yes	—
390	#95	C₂³×C₄₁	1	4	yes	—
391	#95	C₂³×C₄₁	1	4	yes	—
392	#95	C₂³×C₄₁	1	4	yes	—
393	#95	C₂³×C₄₁	1	4	yes	—
394	#95	C₂³×C₄₁	1	4	yes	—
395	#95	C₂³×C₄₁	1	4	yes	—
396	#95	C₂³×C₄₁	1	4	yes	—
397	C₂⁴	—	2	2	no	—
398	C₂⁴	—	2	4	no	—
399	C₂⁴	—	2	4	no	—
400	C₂⁴	—	4	1	no	—
401	C₂⁴	—	4	1	no	—
402	C₂⁴	C₂⁴×C₄₁	1	4	yes	—
403	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
404	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
405	C₂×D₄	—	2	8	no	—
406	C₂×D₄	—	2	8	no	—
407	C₂×D₄	—	2	8	no	—
408	C₂×D₄	—	2	8	no	—
409	C₂×D₄	—	2	8	no	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	4	4	no	—
412	C₂×D₄	—	4	4	no	—
413	C₂×D₄	—	4	2	no	—
414	C₂×D₄	—	4	2	no	—
415	C₂×D₄	—	4	4	no	—
416	C₂×D₄	—	4	4	no	—
417	C₂×D₄	—	4	4	no	—
418	C₂×D₄	—	4	4	no	—
419	C₂×D₄	—	4	4	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	4	2	no	—
428	C₂²×C₄	—	4	2	no	—
429	C₂²×C₄	—	4	2	no	—
430	C₂²×C₄	—	4	2	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	—	4	4	no	—
434	C₂²×C₄	—	4	4	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	—	4	4	no	—
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	—	4	16	no	—
439	C₂²×C₄	#41×C₄₁	1	4	yes	—
440	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
441	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
442	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
443	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
444	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
445	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
446	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
447	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	4	4	no	—
450	C₄⋊C₄	—	4	2	no	—
451	C₄⋊C₄	—	4	2	no	—
452	C₄⋊C₄	—	4	4	no	—
453	C₄⋊C₄	—	4	4	no	—
454	C₄⋊C₄	—	4	4	no	—
455	C₂²⋊C₄	—	2	8	no	—
456	C₂²⋊C₄	—	2	8	no	—
457	C₂²⋊C₄	—	2	8	no	—
458	C₂²⋊C₄	—	4	4	no	—
459	C₂²⋊C₄	—	4	4	no	—
460	C₂²⋊C₄	—	4	4	no	—
461	C₂²⋊C₄	—	4	4	no	—
462	C₂²⋊C₄	—	4	4	no	—
463	C₂²⋊C₄	—	4	4	no	—
464	C₂²⋊C₄	—	4	4	no	—
465	C₂²⋊C₄	—	4	4	no	—
466	C₂²⋊C₄	—	4	4	no	—
467	C₂²⋊C₄	—	4	4	no	—
468	C₄²	—	4	4	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	1	no	—
471	C₂³	—	2	1	no	—
472	C₂³	—	2	8	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	2	4	no	—
481	C₂³	—	2	4	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	4	no	—
485	C₂³	—	2	4	no	—
486	C₂³	—	4	8	no	—
487	C₂³	—	4	8	no	—
488	C₂³	—	4	4	no	—
489	C₂³	—	4	4	no	—
490	C₂³	C₂×#41×C₄₁	1	2	yes	—
491	C₂³	H(5,𝔽₂)×C₄₁	1	4	yes	—
492	C₂³	H(5,𝔽₂)×C₄₁	1	4	yes	—
493	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
494	D₄	—	4	16	no	—
495	D₄	—	8	4	no	—
496	D₄	—	8	8	no	—
497	D₄	—	8	8	no	—
498	D₄	—	8	8	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	4	4	no	—
521	C₂×C₄	—	4	8	no	—
522	C₂×C₄	—	4	8	no	—
523	C₂×C₄	—	4	4	no	—
524	C₂×C₄	—	8	4	no	—
525	C₂×C₄	—	8	4	no	—
526	C₂×C₄	—	8	8	no	—
527	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	4	no	—
531	C₂²	—	2	4	no	—
532	C₂²	—	2	4	no	—
533	C₂²	—	2	4	no	—
534	C₂²	—	2	4	no	—
535	C₂²	—	4	16	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	4	4	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	4	4	no	—
544	C₂²	—	4	4	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	4	4	no	—
547	C₂²	C₄₁×#540	1	4	yes	—
548	C₂²	C₂²×#41×C₄₁	1	1	yes	characteristic
549	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	2	yes	—
550	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	2	yes	—
551	C₂²	C₄₁×#585	1	1	yes	characteristic
552	C₂²	C₄₁×#585	1	1	yes	characteristic
553	C₄	—	2	4	no	—
554	C₄	—	4	4	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	1	no	—
557	C₄	—	4	4	no	—
558	C₄	—	4	4	no	—
559	C₄	—	4	4	no	—
560	C₄	—	4	4	no	—
561	C₂	—	2	4	no	—
562	C₂	—	4	4	no	—
563	C₂	—	8	4	no	—
564	C₂	C₂×C₄₁×#540	1	1	yes	characteristic
565	C₂	C₄₁×#3490	1	1	yes	characteristic
566	C₂	C₄₁×#3493	1	1	yes	characteristic
567	C₂	C₄₁×#3534	1	2	yes	—
568	C₂	C₄₁×#3534	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#2847	C₂	semidirect
2. C₄₁×#2743	C₂	semidirect
3. C₄₁×#2740	C₂	semidirect
4. C₄₁×#2699	C₂	semidirect
5. C₄₁×#2688	C₂	semidirect
6. C₄₁×#2656	C₂	semidirect
7. C₄₁×#2646	C₂	semidirect
8. C₄₁×#2444	C₂	semidirect
9. C₄₁×#2424	C₂	semidirect
10. C₄₁×#2325	C₂	semidirect
11. C₂×C₄₁×#381	C₂	semidirect
21. C₄₁×#400	C₂²	semidirect
22. C₄₁×#400	C₂²	semidirect
23. C₄₁×#399	C₂²	semidirect
24. C₄₁×#398	C₂²	semidirect
25. C₄₁×#397	C₂²	semidirect
26. C₄₁×#397	C₂²	semidirect
30. C₄₁×#394	C₂²	semidirect
32. C₄₁×#392	C₂²	semidirect
35. C₄₁×#388	C₂²	semidirect
36. C₄₁×#388	C₂²	semidirect
37. C₄₁×#387	C₂²	semidirect
38. C₄₁×#387	C₂²	semidirect
44. C₄₁×#386	C₂²	semidirect
45. C₄₁×#386	C₂²	semidirect
47. C₄₁×#385	C₂²	semidirect
50. C₄₁×#381	C₂²	semidirect
243. #36731	C₄₁	direct (N × H)
277. #2847	C₂×C₄₁	semidirect
278. #2743	C₂×C₄₁	semidirect
279. #2740	C₂×C₄₁	semidirect
280. #2699	C₂×C₄₁	semidirect
281. #2688	C₂×C₄₁	semidirect
282. #2656	C₂×C₄₁	semidirect
283. #2646	C₂×C₄₁	semidirect
284. #2444	C₂×C₄₁	semidirect
285. #2424	C₂×C₄₁	semidirect
286. #2325	C₂×C₄₁	semidirect
287. C₂×#381	C₂×C₄₁	semidirect
305. #400	C₂²×C₄₁	semidirect
306. #400	C₂²×C₄₁	semidirect
307. #399	C₂²×C₄₁	semidirect
308. #398	C₂²×C₄₁	semidirect
309. #397	C₂²×C₄₁	semidirect
310. #397	C₂²×C₄₁	semidirect
314. #394	C₂²×C₄₁	semidirect
316. #392	C₂²×C₄₁	semidirect
319. #388	C₂²×C₄₁	semidirect
320. #388	C₂²×C₄₁	semidirect
321. #387	C₂²×C₄₁	semidirect
322. #387	C₂²×C₄₁	semidirect
328. #386	C₂²×C₄₁	semidirect
329. #386	C₂²×C₄₁	semidirect
331. #385	C₂²×C₄₁	semidirect
334. #381	C₂²×C₄₁	semidirect
341. C₄₁	#36731	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#2847	2
C₄₁×#2743	2
C₄₁×#2740	2
C₄₁×#2699	2
C₄₁×#2688	2
C₄₁×#2656	2
C₄₁×#2646	2
C₄₁×#2444	2
C₄₁×#2424	2
C₄₁×#2325	2
C₂×C₄₁×#381	2
#36731	41

Subgroups — C41×#36731 #23812932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#36731 #23812932