Subgroups — C₄₁×#26231 #23802432

Order 10496.

862 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#485	C₂	1	2	yes	maximal, complemented
2	C₄₁×#2542	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2354	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2036	C₂	1	2	yes	maximal, complemented
5	C₄₁×#2035	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1981	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1956	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1954	C₂	1	1	yes	maximal, characteristic
9	C₄₁×#1948	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1873	C₂	1	2	yes	maximal, complemented
11	C₄×#107×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
14	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×#117×C₄₁	C₂²	1	2	yes	—
17	C₄₁×#485	—	2	8	no	—
18	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#106×C₄₁	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×#103×C₄₁	C₂²	1	2	yes	—
23	C₂×#103×C₄₁	C₂²	1	2	yes	—
24	C₂×#103×C₄₁	C₂²	1	2	yes	—
25	C₂×#103×C₄₁	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
29	C₄₁×#399	—	2	2	no	—
30	C₄₁×#390	—	2	1	no	—
31	C₄₁×#390	—	2	1	no	—
32	C₄₁×#388	—	2	2	no	—
33	C₄₁×#384	—	2	1	no	—
34	C₄₁×#384	C₂²	1	1	yes	characteristic
35	C₄₁×#380	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
37	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
39	C₄₁×#340	C₂²	1	1	yes	characteristic
40	C₄₁×#340	C₂²	1	1	yes	characteristic
41	C₄₁×#340	C₂²	1	2	yes	—
42	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
43	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
45	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
48	C₄⋊Q₈×C₄₁	—	2	2	no	—
49	C₄⋊Q₈×C₄₁	—	2	2	no	—
50	C₂²⋊Q₈×C₄₁	—	2	4	no	—
51	C₂²⋊Q₈×C₄₁	—	2	4	no	—
52	C₂²⋊Q₈×C₄₁	—	4	2	no	—
53	C₂²⋊Q₈×C₄₁	—	4	2	no	—
54	C₄×D₄×C₄₁	—	2	2	no	—
55	C₄×D₄×C₄₁	—	2	2	no	—
56	#117×C₄₁	—	2	4	no	—
57	#117×C₄₁	—	4	2	no	—
58	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
75	C₂×C₄²×C₄₁	—	2	2	no	—
76	C₂×C₄²×C₄₁	—	2	1	no	—
77	C₂×C₄²×C₄₁	—	2	1	no	—
78	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
79	#107×C₄₁	—	2	2	no	—
80	#107×C₄₁	D₄	1	4	yes	complemented
81	#106×C₄₁	—	2	4	no	—
82	C₄⋊C₈×C₄₁	—	2	2	no	—
83	#103×C₄₁	—	2	4	no	—
84	#103×C₄₁	—	2	4	no	—
85	#103×C₄₁	—	4	2	no	—
86	#103×C₄₁	—	4	2	no	—
87	C₂²⋊C₈×C₄₁	—	2	4	no	—
88	C₂²⋊C₈×C₄₁	—	4	2	no	—
89	C₄×C₈×C₄₁	—	2	2	no	—
90	#95×C₄₁	—	2	2	no	—
91	#95×C₄₁	—	2	1	no	—
92	#95×C₄₁	—	2	1	no	—
93	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
94	C₂×Q₈×C₄₁	—	2	2	no	—
95	C₂×Q₈×C₄₁	—	2	2	no	—
96	C₂×Q₈×C₄₁	—	2	2	no	—
97	C₂×Q₈×C₄₁	—	2	2	no	—
98	C₂×Q₈×C₄₁	—	2	2	no	—
99	C₂×Q₈×C₄₁	—	2	2	no	—
100	C₂×D₄×C₄₁	—	2	2	no	—
101	C₂×D₄×C₄₁	—	2	2	no	—
102	C₂×D₄×C₄₁	—	2	2	no	—
103	C₂²×C₄×C₄₁	—	2	1	no	—
104	C₂²×C₄×C₄₁	—	2	1	no	—
105	C₂²×C₄×C₄₁	—	2	1	no	—
106	C₂²×C₄×C₄₁	—	2	2	no	—
107	C₂²×C₄×C₄₁	—	2	2	no	—
108	C₂²×C₄×C₄₁	—	2	2	no	—
109	C₂²×C₄×C₄₁	—	2	2	no	—
110	C₂²×C₄×C₄₁	—	2	2	no	—
111	C₂²×C₄×C₄₁	—	2	2	no	—
112	C₂²×C₄×C₄₁	—	2	1	no	—
113	C₂²×C₄×C₄₁	—	2	2	no	—
114	C₂²×C₄×C₄₁	—	2	2	no	—
115	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
119	C₂×C₈×C₄₁	—	2	1	no	—
120	C₂×C₈×C₄₁	—	2	1	no	—
121	C₂×C₈×C₄₁	—	2	2	no	—
122	C₂×C₈×C₄₁	—	2	1	no	—
123	C₂×C₈×C₄₁	—	2	2	no	—
124	C₂×C₈×C₄₁	—	2	1	no	—
125	C₂×C₈×C₄₁	—	2	2	no	—
126	C₂×C₈×C₄₁	—	2	1	no	—
127	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₄₁	—	2	2	no	—
129	C₄⋊C₄×C₄₁	—	2	1	no	—
130	C₄⋊C₄×C₄₁	—	2	1	no	—
131	C₄⋊C₄×C₄₁	—	2	1	no	—
132	C₄⋊C₄×C₄₁	—	2	2	no	—
133	C₄⋊C₄×C₄₁	—	2	1	no	—
134	C₄⋊C₄×C₄₁	—	2	1	no	—
135	C₄⋊C₄×C₄₁	—	2	2	no	—
136	C₄⋊C₄×C₄₁	—	4	4	no	—
137	C₄⋊C₄×C₄₁	—	4	4	no	—
138	C₄⋊C₄×C₄₁	—	4	2	no	—
139	C₄⋊C₄×C₄₁	—	4	2	no	—
140	C₄⋊C₄×C₄₁	—	4	2	no	—
141	C₄⋊C₄×C₄₁	—	8	1	no	—
142	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
143	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
144	C₄⋊C₄×C₄₁	#41	1	2	yes	—
145	C₂²⋊C₄×C₄₁	—	2	4	no	—
146	C₂²⋊C₄×C₄₁	—	4	4	no	—
147	C₂²⋊C₄×C₄₁	—	4	4	no	—
148	C₂²⋊C₄×C₄₁	—	4	4	no	—
149	C₂²⋊C₄×C₄₁	—	8	2	no	—
150	C₄²×C₄₁	—	4	4	no	—
151	C₄²×C₄₁	—	4	2	no	—
152	C₄²×C₄₁	—	4	2	no	—
153	C₄²×C₄₁	#41	1	2	yes	—
154	C₄²×C₄₁	#41	1	2	yes	—
155	C₂³×C₄₁	—	2	2	no	—
156	C₂³×C₄₁	—	2	2	no	—
157	C₂³×C₄₁	—	2	2	no	—
158	C₂³×C₄₁	—	2	2	no	—
159	C₂³×C₄₁	—	2	2	no	—
160	C₂³×C₄₁	—	2	2	no	—
161	C₂³×C₄₁	—	2	2	no	—
162	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
163	Q₈×C₄₁	—	4	2	no	—
164	Q₈×C₄₁	—	4	2	no	—
165	Q₈×C₄₁	—	4	2	no	—
166	Q₈×C₄₁	—	4	2	no	—
167	D₄×C₄₁	—	4	4	no	—
168	C₂×C₄×C₄₁	—	2	1	no	—
169	C₂×C₄×C₄₁	—	2	1	no	—
170	C₂×C₄×C₄₁	—	2	2	no	—
171	C₂×C₄×C₄₁	—	2	2	no	—
172	C₂×C₄×C₄₁	—	2	2	no	—
173	C₂×C₄×C₄₁	—	2	2	no	—
174	C₂×C₄×C₄₁	—	2	2	no	—
175	C₂×C₄×C₄₁	—	2	2	no	—
176	C₂×C₄×C₄₁	—	4	1	no	—
177	C₂×C₄×C₄₁	—	4	1	no	—
178	C₂×C₄×C₄₁	—	4	1	no	—
179	C₂×C₄×C₄₁	—	4	1	no	—
180	C₂×C₄×C₄₁	—	4	1	no	—
181	C₂×C₄×C₄₁	—	4	1	no	—
182	C₂×C₄×C₄₁	—	4	2	no	—
183	C₂×C₄×C₄₁	—	4	2	no	—
184	C₂×C₄×C₄₁	—	4	2	no	—
185	C₂×C₄×C₄₁	—	4	2	no	—
186	C₂×C₄×C₄₁	—	4	2	no	—
187	C₂×C₄×C₄₁	—	4	2	no	—
188	C₂×C₄×C₄₁	—	4	2	no	—
189	C₂×C₄×C₄₁	—	4	2	no	—
190	C₂×C₄×C₄₁	—	4	1	no	—
191	C₂×C₄×C₄₁	—	4	1	no	—
192	C₂×C₄×C₄₁	—	4	2	no	—
193	C₂×C₄×C₄₁	—	4	1	no	—
194	C₂×C₄×C₄₁	—	4	2	no	—
195	C₂×C₄×C₄₁	#123	1	2	yes	—
196	C₂×C₄×C₄₁	#123	1	2	yes	—
197	C₂×C₄×C₄₁	#135	1	2	yes	—
198	C₂×C₄×C₄₁	#137	1	2	yes	—
199	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
205	C₈×C₄₁	—	2	2	no	—
206	C₈×C₄₁	—	4	1	no	—
207	C₈×C₄₁	—	4	2	no	—
208	#26231	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂²×C₄₁	—	4	2	no	—
210	C₂²×C₄₁	—	4	2	no	—
211	C₂²×C₄₁	—	4	2	no	—
212	C₂²×C₄₁	—	4	2	no	—
213	C₂²×C₄₁	—	4	2	no	—
214	C₂²×C₄₁	—	4	2	no	—
215	C₂²×C₄₁	—	4	2	no	—
216	C₂²×C₄₁	C₂×#123	1	1	yes	characteristic
217	C₂²×C₄₁	D₄²	1	1	yes	characteristic
218	C₂²×C₄₁	#546	1	1	yes	characteristic
219	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
220	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
221	C₂²×C₄₁	#577	1	1	yes	characteristic
222	C₂²×C₄₁	#578	1	1	yes	characteristic
223	C₄×C₄₁	—	2	2	no	—
224	C₄×C₄₁	—	4	2	no	—
225	C₄×C₄₁	—	4	2	no	—
226	C₄×C₄₁	—	4	2	no	—
227	C₄×C₄₁	—	4	2	no	—
228	C₄×C₄₁	—	8	2	no	—
229	C₄×C₄₁	—	8	2	no	—
230	C₄×C₄₁	—	8	1	no	—
231	C₄×C₄₁	#485	1	4	yes	complemented
232	C₄×C₄₁	#532	1	1	yes	characteristic
233	C₄×C₄₁	#540	1	1	yes	characteristic
234	C₄×C₄₁	#550	1	1	yes	characteristic
235	C₄×C₄₁	#559	1	1	yes	characteristic
236	C₂×#485	C₂×C₄₁	1	2	yes	complemented
237	#2542	C₂×C₄₁	1	1	yes	characteristic
238	#2354	C₂×C₄₁	1	1	yes	characteristic
239	#2036	C₂×C₄₁	1	2	yes	complemented
240	#2035	C₂×C₄₁	1	2	yes	complemented
241	#1981	C₂×C₄₁	1	1	yes	characteristic, complemented
242	#1956	C₂×C₄₁	1	1	yes	characteristic, complemented
243	#1954	C₂×C₄₁	1	1	yes	characteristic
244	#1948	C₂×C₄₁	1	1	yes	characteristic, complemented
245	#1873	C₂×C₄₁	1	2	yes	complemented
246	C₄×#107	C₂×C₄₁	1	1	yes	characteristic, complemented
247	C₂×C₄₁	—	8	2	no	—
248	C₂×C₄₁	#2445	1	1	yes	characteristic
249	C₂×C₄₁	C₂×#485	1	1	yes	characteristic
250	C₂×C₄₁	#3097	1	1	yes	characteristic
251	C₂×C₄₁	#3278	1	1	yes	characteristic
252	C₂×C₄₁	#3283	1	1	yes	characteristic
253	C₂×C₄₁	#3303	1	1	yes	characteristic
254	C₂×C₄₁	#3328	1	1	yes	characteristic
255	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
256	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
257	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
258	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
259	C₂×#117	C₂²×C₄₁	1	2	yes	—
260	#485	—	2	8	no	—
261	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
262	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
263	C₂×#106	C₂²×C₄₁	1	2	yes	—
264	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
265	C₂×#103	C₂²×C₄₁	1	2	yes	—
266	C₂×#103	C₂²×C₄₁	1	2	yes	—
267	C₂×#103	C₂²×C₄₁	1	2	yes	—
268	C₂×#103	C₂²×C₄₁	1	2	yes	—
269	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
270	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
271	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
272	#399	—	2	2	no	—
273	#390	—	2	1	no	—
274	#390	—	2	1	no	—
275	#388	—	2	2	no	—
276	#384	—	2	1	no	—
277	#384	C₂²×C₄₁	1	1	yes	characteristic
278	#380	C₂²×C₄₁	1	2	yes	—
279	C₄×C₄⋊C₄	—	2	1	no	—
280	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
281	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
282	#340	C₂²×C₄₁	1	1	yes	characteristic
283	#340	C₂²×C₄₁	1	2	yes	—
284	#340	C₂²×C₄₁	1	1	yes	characteristic
285	C₄₁	#26231	1	1	yes	characteristic, direct product factor, Sylow
286	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
287	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
288	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
289	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
291	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
292	C₄⋊Q₈	—	2	2	no	—
293	C₄⋊Q₈	—	2	2	no	—
294	C₂²⋊Q₈	—	2	4	no	—
295	C₂²⋊Q₈	—	2	4	no	—
296	C₂²⋊Q₈	—	4	2	no	—
297	C₂²⋊Q₈	—	4	2	no	—
298	C₄×D₄	—	2	2	no	—
299	C₄×D₄	—	2	2	no	—
300	#117	—	2	4	no	—
301	#117	—	4	2	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	—	2	1	no	—
321	C₂×C₄²	—	2	1	no	—
322	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
323	#107	—	2	2	no	—
324	#107	D₄×C₄₁	1	4	yes	complemented
325	#106	—	2	4	no	—
326	C₄⋊C₈	—	2	2	no	—
327	#103	—	2	4	no	—
328	#103	—	2	4	no	—
329	#103	—	4	2	no	—
330	#103	—	4	2	no	—
331	C₂²⋊C₈	—	2	4	no	—
332	C₂²⋊C₈	—	4	2	no	—
333	C₄×C₈	—	2	2	no	—
334	#95	—	2	2	no	—
335	#95	—	2	1	no	—
336	#95	—	2	1	no	—
337	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
362	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	4	4	no	—
381	C₄⋊C₄	—	4	4	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	—	8	1	no	—
386	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
387	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
388	C₄⋊C₄	#41×C₄₁	1	2	yes	—
389	C₂²⋊C₄	—	2	4	no	—
390	C₂²⋊C₄	—	4	4	no	—
391	C₂²⋊C₄	—	4	4	no	—
392	C₂²⋊C₄	—	4	4	no	—
393	C₂²⋊C₄	—	8	2	no	—
394	C₄²	—	4	4	no	—
395	C₄²	—	4	2	no	—
396	C₄²	—	4	2	no	—
397	C₄²	#41×C₄₁	1	2	yes	—
398	C₄²	#41×C₄₁	1	2	yes	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
407	Q₈	—	4	2	no	—
408	Q₈	—	4	2	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	4	2	no	—
411	D₄	—	4	4	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	#123×C₄₁	1	2	yes	—
440	C₂×C₄	#123×C₄₁	1	2	yes	—
441	C₂×C₄	#135×C₄₁	1	2	yes	—
442	C₂×C₄	#137×C₄₁	1	2	yes	—
443	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
444	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
445	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
446	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
447	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
448	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
449	C₈	—	2	2	no	—
450	C₈	—	4	1	no	—
451	C₈	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	C₂×#123×C₄₁	1	1	yes	characteristic
460	C₂²	D₄²×C₄₁	1	1	yes	characteristic
461	C₂²	C₄₁×#546	1	1	yes	characteristic
462	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
463	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
464	C₂²	C₄₁×#577	1	1	yes	characteristic
465	C₂²	C₄₁×#578	1	1	yes	characteristic
466	C₄	—	2	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	8	1	no	—
472	C₄	—	8	2	no	—
473	C₄	—	8	2	no	—
474	C₄	C₄₁×#485	1	4	yes	complemented
475	C₄	C₄₁×#532	1	1	yes	characteristic
476	C₄	C₄₁×#540	1	1	yes	characteristic
477	C₄	C₄₁×#550	1	1	yes	characteristic
478	C₄	C₄₁×#559	1	1	yes	characteristic
479	C₂	—	8	2	no	—
480	C₂	C₄₁×#2445	1	1	yes	characteristic
481	C₂	C₂×C₄₁×#485	1	1	yes	characteristic
482	C₂	C₄₁×#3097	1	1	yes	characteristic
483	C₂	C₄₁×#3278	1	1	yes	characteristic
484	C₂	C₄₁×#3283	1	1	yes	characteristic
485	C₂	C₄₁×#3303	1	1	yes	characteristic
486	C₂	C₄₁×#3328	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×D₄×C₄₁	D₄
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. C₂×C₄₁×#485	C₂	semidirect
4. C₄₁×#2036	C₂	semidirect
5. C₄₁×#2035	C₂	semidirect
6. C₄₁×#1981	C₂	semidirect
7. C₄₁×#1956	C₂	semidirect
9. C₄₁×#1948	C₂	semidirect
10. C₄₁×#1873	C₂	semidirect
11. C₄×#107×C₄₁	C₂	semidirect
80. #107×C₄₁	D₄	semidirect
208. #26231	C₄₁	direct (N × H)
231. C₄×C₄₁	#485	semidirect
236. C₂×#485	C₂×C₄₁	semidirect
239. #2036	C₂×C₄₁	semidirect
240. #2035	C₂×C₄₁	semidirect
241. #1981	C₂×C₄₁	semidirect
242. #1956	C₂×C₄₁	semidirect
244. #1948	C₂×C₄₁	semidirect
245. #1873	C₂×C₄₁	semidirect
246. C₄×#107	C₂×C₄₁	semidirect
285. C₄₁	#26231	direct (N × H)
324. #107	D₄×C₄₁	semidirect
474. C₄	C₄₁×#485	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#485	2
C₄₁×#2542	2
C₄₁×#2354	2
C₄₁×#2036	2
C₄₁×#2035	2
C₄₁×#1981	2
C₄₁×#1956	2
C₄₁×#1954	2
C₄₁×#1948	2
C₄₁×#1873	2
C₄×#107×C₄₁	2
#26231	41

Subgroups — C41×#26231 #23802432

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#26231 #23802432