Subgroups — C₄₁×#20872 #23797073

Order 10496.

1502 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#427	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#416	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₁×#416	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#2296	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1865	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1864	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1863	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1862	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1735	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₁×#336	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₄×#41×C₄₁	—	2	4	no	—
16	C₄×#41×C₄₁	—	2	4	no	—
17	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₄₁	—	2	2	no	—
19	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
20	C₂×#117×C₄₁	—	2	1	no	—
21	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₄₁	—	2	1	no	—
25	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
26	C₄₁×#427	—	2	4	no	—
27	C₂×#107×C₄₁	C₂²	1	2	yes	—
28	C₂×#106×C₄₁	C₂²	1	2	yes	—
29	C₄₁×#416	—	2	4	no	—
30	C₄₁×#416	C₄	1	8	yes	complemented
31	C₂×#103×C₄₁	C₂²	1	2	yes	—
32	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
34	C₂×#102×C₄₁	C₂²	1	2	yes	—
35	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
36	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
37	C₄₁×#389	C₂²	1	2	yes	—
38	C₄₁×#389	C₂²	1	2	yes	—
39	C₄₁×#385	—	2	2	no	—
40	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
41	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
42	C₄₁×#340	C₂²	1	2	yes	—
43	C₄₁×#340	C₂²	1	2	yes	—
44	C₄₁×#336	C₂²	1	2	yes	—
45	C₄₁×#336	C₂²	1	2	yes	—
46	C₂×#41×C₄₁	—	2	2	no	—
47	C₂×#41×C₄₁	—	2	2	no	—
48	C₂×#41×C₄₁	—	2	2	no	—
49	C₂×#41×C₄₁	C₂×C₄	1	4	yes	—
50	C₂×#41×C₄₁	D₄	1	4	yes	—
51	C₂×#41×C₄₁	Q₈	1	4	yes	—
52	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₄₁	—	2	1	no	—
54	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₄₁	—	2	1	no	—
56	C₂³×C₄×C₄₁	—	2	2	no	—
57	C₂³×C₄×C₄₁	D₄	1	2	yes	—
58	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₄₁	—	2	2	no	—
60	C₂²×C₈×C₄₁	—	2	2	no	—
61	C₂²×C₈×C₄₁	—	2	2	no	—
62	C₂²×C₈×C₄₁	—	2	2	no	—
63	C₂²×C₈×C₄₁	—	2	2	no	—
64	C₂²×C₈×C₄₁	C₂×C₄	1	4	yes	complemented
65	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
66	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
68	C₄×Q₈×C₄₁	—	2	4	no	—
69	C₄×Q₈×C₄₁	—	2	4	no	—
70	C₄×D₄×C₄₁	—	2	16	no	—
71	C₄×D₄×C₄₁	—	2	4	no	—
72	C₄×D₄×C₄₁	—	2	4	no	—
73	#117×C₄₁	—	2	8	no	—
74	#117×C₄₁	—	2	2	no	—
75	#117×C₄₁	—	2	2	no	—
76	#117×C₄₁	—	2	2	no	—
77	#117×C₄₁	—	2	2	no	—
78	#117×C₄₁	C₂×C₄	1	4	yes	complemented
79	#117×C₄₁	D₄	1	4	yes	—
80	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
81	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
82	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
83	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
87	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
91	C₂×C₄²×C₄₁	—	2	8	no	—
92	C₂×C₄²×C₄₁	—	2	2	no	—
93	C₂×C₄²×C₄₁	—	2	2	no	—
94	C₂×C₄²×C₄₁	—	2	2	no	—
95	C₂×C₄²×C₄₁	—	2	1	no	—
96	C₂×C₄²×C₄₁	—	2	1	no	—
97	C₂×C₄²×C₄₁	—	2	1	no	—
98	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
101	#107×C₄₁	—	2	4	no	—
102	#106×C₄₁	—	2	4	no	—
103	#103×C₄₁	—	2	4	no	—
104	#103×C₄₁	C₂×C₄	1	4	yes	complemented
105	#103×C₄₁	C₂×C₄	1	4	yes	complemented
106	#102×C₄₁	—	2	4	no	—
107	#102×C₄₁	C₂×C₄	1	4	yes	complemented
108	#102×C₄₁	C₂×C₄	1	4	yes	complemented
109	#95×C₄₁	—	2	2	no	—
110	#95×C₄₁	—	2	2	no	—
111	C₂⁴×C₄₁	—	2	1	no	—
112	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
113	#41×C₄₁	—	2	8	no	—
114	#41×C₄₁	—	2	8	no	—
115	#41×C₄₁	—	2	8	no	—
116	#41×C₄₁	C₄⋊C₄	1	16	yes	complemented
117	C₂×Q₈×C₄₁	—	2	1	no	—
118	C₂×Q₈×C₄₁	—	2	1	no	—
119	C₂×Q₈×C₄₁	—	2	1	no	—
120	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
121	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
122	C₂×Q₈×C₄₁	C₂×Q₈	1	2	yes	—
123	C₂×D₄×C₄₁	—	2	4	no	—
124	C₂×D₄×C₄₁	—	2	4	no	—
125	C₂×D₄×C₄₁	—	2	4	no	—
126	C₂×D₄×C₄₁	—	2	1	no	—
127	C₂×D₄×C₄₁	—	2	1	no	—
128	C₂×D₄×C₄₁	—	2	1	no	—
129	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
130	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
131	C₂×D₄×C₄₁	C₂×Q₈	1	2	yes	—
132	C₂²×C₄×C₄₁	—	2	1	no	—
133	C₂²×C₄×C₄₁	—	2	4	no	—
134	C₂²×C₄×C₄₁	—	2	4	no	—
135	C₂²×C₄×C₄₁	—	2	4	no	—
136	C₂²×C₄×C₄₁	—	2	8	no	—
137	C₂²×C₄×C₄₁	—	2	4	no	—
138	C₂²×C₄×C₄₁	—	2	1	no	—
139	C₂²×C₄×C₄₁	—	2	1	no	—
140	C₂²×C₄×C₄₁	—	2	2	no	—
141	C₂²×C₄×C₄₁	—	2	4	no	—
142	C₂²×C₄×C₄₁	—	2	2	no	—
143	C₂²×C₄×C₄₁	—	4	2	no	—
144	C₂²×C₄×C₄₁	—	4	4	no	—
145	C₂²×C₄×C₄₁	—	4	4	no	—
146	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
147	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
153	C₂²×C₄×C₄₁	#41	1	2	yes	—
154	C₂²×C₄×C₄₁	#41	1	2	yes	—
155	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
156	C₂×C₈×C₄₁	—	2	8	no	—
157	C₂×C₈×C₄₁	—	2	1	no	—
158	C₂×C₈×C₄₁	—	2	1	no	—
159	C₂×C₈×C₄₁	—	2	1	no	—
160	C₂×C₈×C₄₁	—	2	1	no	—
161	C₂×C₈×C₄₁	—	2	2	no	—
162	C₂×C₈×C₄₁	—	2	2	no	—
163	C₂×C₈×C₄₁	—	2	2	no	—
164	C₂×C₈×C₄₁	—	4	4	no	—
165	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
166	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
167	C₄⋊C₄×C₄₁	—	2	8	no	—
168	C₄⋊C₄×C₄₁	—	2	2	no	—
169	C₄⋊C₄×C₄₁	—	2	1	no	—
170	C₄⋊C₄×C₄₁	—	2	1	no	—
171	C₄⋊C₄×C₄₁	—	2	2	no	—
172	C₄⋊C₄×C₄₁	—	2	2	no	—
173	C₄⋊C₄×C₄₁	—	4	4	no	—
174	C₄⋊C₄×C₄₁	—	4	4	no	—
175	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
176	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
177	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
178	C₂²⋊C₄×C₄₁	—	2	8	no	—
179	C₂²⋊C₄×C₄₁	—	2	4	no	—
180	C₂²⋊C₄×C₄₁	—	2	4	no	—
181	C₂²⋊C₄×C₄₁	—	4	2	no	—
182	C₄²×C₄₁	—	2	8	no	—
183	C₄²×C₄₁	—	2	4	no	—
184	C₄²×C₄₁	—	2	2	no	—
185	C₄²×C₄₁	—	2	4	no	—
186	C₄²×C₄₁	—	2	2	no	—
187	C₄²×C₄₁	—	2	2	no	—
188	C₄²×C₄₁	—	2	2	no	—
189	C₄²×C₄₁	—	4	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	2	no	—
195	C₂³×C₄₁	—	4	2	no	—
196	C₂³×C₄₁	—	4	2	no	—
197	C₂³×C₄₁	C₄×D₄	1	2	yes	—
198	C₂³×C₄₁	#120	1	2	yes	—
199	C₂³×C₄₁	C₂²⋊Q₈	1	2	yes	—
200	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
201	Q₈×C₄₁	—	2	2	no	—
202	Q₈×C₄₁	—	2	2	no	—
203	Q₈×C₄₁	—	2	2	no	—
204	Q₈×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
205	D₄×C₄₁	—	2	16	no	—
206	D₄×C₄₁	—	2	2	no	—
207	D₄×C₄₁	—	2	2	no	—
208	D₄×C₄₁	—	2	2	no	—
209	D₄×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
210	C₂×C₄×C₄₁	—	2	2	no	—
211	C₂×C₄×C₄₁	—	2	2	no	—
212	C₂×C₄×C₄₁	—	2	2	no	—
213	C₂×C₄×C₄₁	—	2	2	no	—
214	C₂×C₄×C₄₁	—	2	2	no	—
215	C₂×C₄×C₄₁	—	2	16	no	—
216	C₂×C₄×C₄₁	—	2	2	no	—
217	C₂×C₄×C₄₁	—	2	2	no	—
218	C₂×C₄×C₄₁	—	2	2	no	—
219	C₂×C₄×C₄₁	—	2	4	no	—
220	C₂×C₄×C₄₁	—	2	2	no	—
221	C₂×C₄×C₄₁	—	2	2	no	—
222	C₂×C₄×C₄₁	—	4	8	no	—
223	C₂×C₄×C₄₁	—	4	16	no	—
224	C₂×C₄×C₄₁	—	4	2	no	—
225	C₂×C₄×C₄₁	—	4	2	no	—
226	C₂×C₄×C₄₁	—	4	2	no	—
227	C₂×C₄×C₄₁	—	4	2	no	—
228	C₂×C₄×C₄₁	—	4	2	no	—
229	C₂×C₄×C₄₁	—	4	2	no	—
230	C₂×C₄×C₄₁	—	4	2	no	—
231	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
232	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
233	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
234	C₂×C₄×C₄₁	#120	1	2	yes	—
235	C₂×C₄×C₄₁	C₂²⋊Q₈	1	4	yes	—
236	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
237	C₂×C₄×C₄₁	#123	1	4	yes	—
238	C₂×C₄×C₄₁	#135	1	4	yes	—
239	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
240	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
243	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
245	C₈×C₄₁	—	2	2	no	—
246	C₈×C₄₁	—	2	2	no	—
247	C₈×C₄₁	—	4	2	no	—
248	#20872	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
249	C₂²×C₄₁	—	2	4	no	—
250	C₂²×C₄₁	—	2	2	no	—
251	C₂²×C₄₁	—	2	2	no	—
252	C₂²×C₄₁	—	2	4	no	—
253	C₂²×C₄₁	—	2	4	no	—
254	C₂²×C₄₁	—	4	4	no	—
255	C₂²×C₄₁	—	4	2	no	—
256	C₂²×C₄₁	—	4	2	no	—
257	C₂²×C₄₁	—	4	4	no	—
258	C₂²×C₄₁	#385	1	4	yes	—
259	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
260	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
261	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
262	C₂²×C₄₁	C₂×#135	1	2	yes	—
263	C₂²×C₄₁	#575	1	2	yes	—
264	C₄×C₄₁	—	2	4	no	—
265	C₄×C₄₁	—	2	4	no	—
266	C₄×C₄₁	—	4	2	no	—
267	C₄×C₄₁	—	4	2	no	—
268	C₄×C₄₁	—	4	2	no	—
269	C₄×C₄₁	—	4	4	no	—
270	C₄×C₄₁	—	8	2	no	—
271	C₄×C₄₁	#385	1	4	yes	—
272	C₄×C₄₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
273	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
274	C₄×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
275	C₄×C₄₁	C₂×#123	1	1	yes	characteristic
276	C₂×C₄×#41	C₂×C₄₁	1	1	yes	characteristic
277	C₂×#427	C₂×C₄₁	1	1	yes	characteristic, complemented
278	C₂×#416	C₂×C₄₁	1	1	yes	characteristic
279	C₂×#416	C₂×C₄₁	1	1	yes	characteristic
280	#2296	C₂×C₄₁	1	1	yes	characteristic, complemented
281	#1865	C₂×C₄₁	1	2	yes	complemented
282	#1864	C₂×C₄₁	1	2	yes	complemented
283	#1863	C₂×C₄₁	1	2	yes	complemented
284	#1862	C₂×C₄₁	1	2	yes	complemented
285	#1735	C₂×C₄₁	1	1	yes	characteristic, complemented
286	C₂×#336	C₂×C₄₁	1	1	yes	characteristic, complemented
287	C₂×C₄₁	—	2	4	no	—
288	C₂×C₄₁	—	4	4	no	—
289	C₂×C₄₁	C₂×#385	1	1	yes	characteristic
290	C₂×C₄₁	C₄×#135	1	1	yes	characteristic
291	C₂×C₄₁	#2943	1	1	yes	characteristic
292	C₂×C₄₁	#3002	1	2	yes	—
293	C₂×C₄₁	#3076	1	2	yes	—
294	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
295	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
296	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
297	C₄×#41	—	2	4	no	—
298	C₄×#41	—	2	4	no	—
299	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
300	C₂×C₄×D₄	—	2	2	no	—
301	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
302	C₂×#117	—	2	1	no	—
303	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
304	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
305	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
306	C₂²×C₄²	—	2	1	no	—
307	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
308	#427	—	2	4	no	—
309	C₂×#107	C₂²×C₄₁	1	2	yes	—
310	C₂×#106	C₂²×C₄₁	1	2	yes	—
311	#416	—	2	4	no	—
312	#416	C₄×C₄₁	1	8	yes	complemented
313	C₂×#103	C₂²×C₄₁	1	2	yes	—
314	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
315	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
316	C₂×#102	C₂²×C₄₁	1	2	yes	—
317	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
318	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
319	#389	C₂²×C₄₁	1	2	yes	—
320	#389	C₂²×C₄₁	1	2	yes	—
321	#385	—	2	2	no	—
322	C₄×C₄⋊C₄	—	2	1	no	—
323	C₄×C₄⋊C₄	—	2	1	no	—
324	#340	C₂²×C₄₁	1	2	yes	—
325	#340	C₂²×C₄₁	1	2	yes	—
326	#336	C₂²×C₄₁	1	2	yes	—
327	#336	C₂²×C₄₁	1	2	yes	—
328	C₄₁	#20872	1	1	yes	characteristic, direct product factor, Sylow
329	C₂×#41	—	2	2	no	—
330	C₂×#41	—	2	2	no	—
331	C₂×#41	—	2	2	no	—
332	C₂×#41	C₂×C₄×C₄₁	1	4	yes	—
333	C₂×#41	D₄×C₄₁	1	4	yes	—
334	C₂×#41	Q₈×C₄₁	1	4	yes	—
335	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
336	C₂²×D₄	—	2	1	no	—
337	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
338	C₂³×C₄	—	2	1	no	—
339	C₂³×C₄	—	2	2	no	—
340	C₂³×C₄	D₄×C₄₁	1	2	yes	—
341	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
342	C₂²×C₈	—	2	2	no	—
343	C₂²×C₈	—	2	2	no	—
344	C₂²×C₈	—	2	2	no	—
345	C₂²×C₈	—	2	2	no	—
346	C₂²×C₈	—	2	2	no	—
347	C₂²×C₈	C₂×C₄×C₄₁	1	4	yes	complemented
348	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
349	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
350	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
351	C₄×Q₈	—	2	4	no	—
352	C₄×Q₈	—	2	4	no	—
353	C₄×D₄	—	2	16	no	—
354	C₄×D₄	—	2	4	no	—
355	C₄×D₄	—	2	4	no	—
356	#117	—	2	8	no	—
357	#117	—	2	2	no	—
358	#117	—	2	2	no	—
359	#117	—	2	2	no	—
360	#117	—	2	2	no	—
361	#117	C₂×C₄×C₄₁	1	4	yes	complemented
362	#117	D₄×C₄₁	1	4	yes	—
363	C₂×C₄⋊C₄	—	2	2	no	—
364	C₂×C₄⋊C₄	—	2	2	no	—
365	C₂×C₄⋊C₄	—	2	2	no	—
366	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
367	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₄²	—	2	8	no	—
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	—	2	1	no	—
377	C₂×C₄²	—	2	2	no	—
378	C₂×C₄²	—	2	2	no	—
379	C₂×C₄²	—	2	2	no	—
380	C₂×C₄²	—	2	1	no	—
381	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
382	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
383	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
384	#107	—	2	4	no	—
385	#106	—	2	4	no	—
386	#103	—	2	4	no	—
387	#103	C₂×C₄×C₄₁	1	4	yes	complemented
388	#103	C₂×C₄×C₄₁	1	4	yes	complemented
389	#102	—	2	4	no	—
390	#102	C₂×C₄×C₄₁	1	4	yes	complemented
391	#102	C₂×C₄×C₄₁	1	4	yes	complemented
392	#95	—	2	2	no	—
393	#95	—	2	2	no	—
394	C₂⁴	—	2	1	no	—
395	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
396	#41	—	2	8	no	—
397	#41	—	2	8	no	—
398	#41	—	2	8	no	—
399	#41	C₄⋊C₄×C₄₁	1	16	yes	complemented
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
404	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
405	C₂×Q₈	C₂×Q₈×C₄₁	1	2	yes	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	4	no	—
408	C₂×D₄	—	2	4	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
413	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
414	C₂×D₄	C₂×Q₈×C₄₁	1	2	yes	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	8	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	4	2	no	—
427	C₂²×C₄	—	4	4	no	—
428	C₂²×C₄	—	4	4	no	—
429	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
430	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
431	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
432	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
433	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
435	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
436	C₂²×C₄	#41×C₄₁	1	2	yes	—
437	C₂²×C₄	#41×C₄₁	1	2	yes	—
438	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
439	C₂×C₈	—	2	8	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	4	4	no	—
448	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
449	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
450	C₄⋊C₄	—	2	8	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	4	4	no	—
457	C₄⋊C₄	—	4	4	no	—
458	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
459	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
460	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	2	4	no	—
463	C₂²⋊C₄	—	2	4	no	—
464	C₂²⋊C₄	—	4	2	no	—
465	C₄²	—	2	8	no	—
466	C₄²	—	2	4	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	2	4	no	—
469	C₄²	—	2	2	no	—
470	C₄²	—	2	2	no	—
471	C₄²	—	2	2	no	—
472	C₄²	—	4	2	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	—	4	2	no	—
479	C₂³	—	4	2	no	—
480	C₂³	C₄×D₄×C₄₁	1	2	yes	—
481	C₂³	#120×C₄₁	1	2	yes	—
482	C₂³	C₂²⋊Q₈×C₄₁	1	2	yes	—
483	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
484	Q₈	—	2	2	no	—
485	Q₈	—	2	2	no	—
486	Q₈	—	2	2	no	—
487	Q₈	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
488	D₄	—	2	16	no	—
489	D₄	—	2	2	no	—
490	D₄	—	2	2	no	—
491	D₄	—	2	2	no	—
492	D₄	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	16	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	4	8	no	—
506	C₂×C₄	—	4	16	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
515	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
516	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
517	C₂×C₄	#120×C₄₁	1	2	yes	—
518	C₂×C₄	C₂²⋊Q₈×C₄₁	1	4	yes	—
519	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
520	C₂×C₄	#123×C₄₁	1	4	yes	—
521	C₂×C₄	#135×C₄₁	1	4	yes	—
522	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
524	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
525	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
526	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
527	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
528	C₈	—	2	2	no	—
529	C₈	—	2	2	no	—
530	C₈	—	4	2	no	—
531	C₂²	—	2	4	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	4	no	—
535	C₂²	—	2	4	no	—
536	C₂²	—	4	4	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	4	no	—
540	C₂²	C₄₁×#385	1	4	yes	—
541	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
542	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
543	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
544	C₂²	C₂×#135×C₄₁	1	2	yes	—
545	C₂²	C₄₁×#575	1	2	yes	—
546	C₄	—	2	4	no	—
547	C₄	—	2	4	no	—
548	C₄	—	4	2	no	—
549	C₄	—	4	2	no	—
550	C₄	—	4	2	no	—
551	C₄	—	4	4	no	—
552	C₄	—	8	2	no	—
553	C₄	C₄₁×#385	1	4	yes	—
554	C₄	C₂²×C₄⋊C₄×C₄₁	1	1	yes	characteristic
555	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
556	C₄	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
557	C₄	C₂×#123×C₄₁	1	1	yes	characteristic
558	C₂	—	2	4	no	—
559	C₂	—	4	4	no	—
560	C₂	C₂×C₄₁×#385	1	1	yes	characteristic
561	C₂	C₄×#135×C₄₁	1	1	yes	characteristic
562	C₂	C₄₁×#2943	1	1	yes	characteristic
563	C₂	C₄₁×#3002	1	2	yes	—
564	C₂	C₄₁×#3076	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂³×C₄₁	C₂²×D₄
prime radical	C₂²×#41×C₄₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#427	C₂	semidirect
5. C₄₁×#2296	C₂	semidirect
6. C₄₁×#1865	C₂	semidirect
7. C₄₁×#1864	C₂	semidirect
8. C₄₁×#1863	C₂	semidirect
9. C₄₁×#1862	C₂	semidirect
10. C₄₁×#1735	C₂	semidirect
11. C₂×C₄₁×#336	C₂	semidirect
30. C₄₁×#416	C₄	semidirect
64. C₂²×C₈×C₄₁	C₂×C₄	semidirect
78. #117×C₄₁	C₂×C₄	semidirect
104. #103×C₄₁	C₂×C₄	semidirect
105. #103×C₄₁	C₂×C₄	semidirect
107. #102×C₄₁	C₂×C₄	semidirect
108. #102×C₄₁	C₂×C₄	semidirect
116. #41×C₄₁	C₄⋊C₄	semidirect
248. #20872	C₄₁	direct (N × H)
277. C₂×#427	C₂×C₄₁	semidirect
280. #2296	C₂×C₄₁	semidirect
281. #1865	C₂×C₄₁	semidirect
282. #1864	C₂×C₄₁	semidirect
283. #1863	C₂×C₄₁	semidirect
284. #1862	C₂×C₄₁	semidirect
285. #1735	C₂×C₄₁	semidirect
286. C₂×#336	C₂×C₄₁	semidirect
312. #416	C₄×C₄₁	semidirect
328. C₄₁	#20872	direct (N × H)
347. C₂²×C₈	C₂×C₄×C₄₁	semidirect
361. #117	C₂×C₄×C₄₁	semidirect
387. #103	C₂×C₄×C₄₁	semidirect
388. #103	C₂×C₄×C₄₁	semidirect
390. #102	C₂×C₄×C₄₁	semidirect
391. #102	C₂×C₄×C₄₁	semidirect
399. #41	C₄⋊C₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₄₁	2
C₂×C₄₁×#427	2
C₂×C₄₁×#416	2
C₄₁×#2296	2
C₄₁×#1865	2
C₄₁×#1864	2
C₄₁×#1863	2
C₄₁×#1862	2
C₄₁×#1735	2
C₂×C₄₁×#336	2
#20872	41

Subgroups — C41×#20872 #23797073

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#20872 #23797073