Subgroups — C₄₁×#34809 #23811010

Order 10496.

2926 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×#117×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2487	C₂	1	2	yes	maximal, complemented
4	C₄₁×#2486	C₂	1	2	yes	maximal, complemented
5	C₄₁×#2485	C₂	1	4	yes	maximal, complemented
6	C₄₁×#2484	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2483	C₂	1	2	yes	maximal, complemented
8	C₄₁×#2482	C₂	1	2	yes	maximal, complemented
9	C₄₁×#2405	C₂	1	2	yes	maximal
10	C₄₁×#2395	C₂	1	4	yes	maximal, complemented
11	C₄×#123×C₄₁	C₂	1	4	yes	maximal, complemented
12	C₄₁×#2296	C₂	1	2	yes	maximal, complemented
13	C₄₁×#2280	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#2280	C₂	1	2	yes	maximal, complemented
15	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#123×C₄₁	C₂²	1	4	yes	—
19	C₂×C₄×D₄×C₄₁	—	2	8	no	—
20	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
24	C₂×#117×C₄₁	—	2	8	no	—
25	C₂×#117×C₄₁	C₂²	1	2	yes	—
26	C₂×#117×C₄₁	C₂²	1	2	yes	—
27	C₂×#117×C₄₁	C₂²	1	2	yes	—
28	C₂×#117×C₄₁	C₂²	1	2	yes	complemented
29	C₂×#117×C₄₁	C₂²	1	2	yes	complemented
30	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
34	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₄₁	C₂²	1	2	yes	complemented
38	C₄₁×#400	C₂²	1	4	yes	complemented
39	C₄₁×#399	C₂²	1	4	yes	complemented
40	C₄₁×#398	C₂²	1	4	yes	complemented
41	C₄₁×#397	C₂²	1	4	yes	complemented
42	C₄₁×#397	C₂²	1	8	yes	complemented
43	C₄₁×#394	C₂²	1	8	yes	—
44	C₄₁×#389	C₂²	1	4	yes	complemented
45	C₄₁×#389	C₂²	1	4	yes	complemented
46	C₄₁×#388	C₂²	1	8	yes	complemented
47	C₄₁×#387	C₂²	1	8	yes	complemented
48	C₄₁×#386	C₂²	1	4	yes	—
49	C₄₁×#385	C₂²	1	4	yes	—
50	C₄₁×#385	C₂²	1	4	yes	—
51	C₄₁×#385	C₂²	1	4	yes	complemented
52	C₄₁×#381	C₂²	1	2	yes	—
53	C₄₁×#381	C₂²	1	4	yes	—
54	C₄₁×#381	C₂²	1	4	yes	complemented
55	C₄₁×#380	C₂²	1	2	yes	complemented
56	C₄₁×#380	C₂²	1	4	yes	complemented
57	C₄₁×#380	C₂²	1	4	yes	complemented
58	C₄₁×#380	C₂²	1	2	yes	complemented
59	C₄₁×#379	C₂²	1	4	yes	—
60	C₄₁×#379	C₂²	1	2	yes	—
61	C₄×C₄⋊C₄×C₄₁	C₂²	1	8	yes	complemented
62	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊C₄×C₄₁	C₂²	1	8	yes	complemented
64	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	complemented
65	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
66	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₄₁	—	2	4	no	—
68	C₂²×D₄×C₄₁	—	2	8	no	—
69	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
70	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
71	C₂³×C₄×C₄₁	—	2	8	no	—
72	C₂³×C₄×C₄₁	—	2	4	no	—
73	C₂³×C₄×C₄₁	—	2	8	no	—
74	C₂³×C₄×C₄₁	D₄	1	8	yes	—
75	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
77	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
79	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
80	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
87	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
88	#123×C₄₁	—	2	16	no	—
89	C₄×D₄×C₄₁	—	2	8	no	—
90	C₄×D₄×C₄₁	—	2	8	no	—
91	C₄×D₄×C₄₁	—	2	8	no	—
92	C₄×D₄×C₄₁	—	2	8	no	—
93	#117×C₄₁	—	2	8	no	—
94	#117×C₄₁	—	2	8	no	—
95	#117×C₄₁	—	2	8	no	—
96	#117×C₄₁	—	2	8	no	—
97	#117×C₄₁	—	2	8	no	—
98	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
99	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
100	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
101	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
108	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
109	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
110	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
111	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
112	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
113	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
115	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
118	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
122	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
123	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
124	C₂×C₄²×C₄₁	—	2	4	no	—
125	C₂×C₄²×C₄₁	—	2	8	no	—
126	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
127	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
128	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
129	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
130	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
131	#95×C₄₁	C₂³	1	8	yes	—
132	#95×C₄₁	C₂³	1	8	yes	—
133	#95×C₄₁	C₂³	1	4	yes	—
134	#95×C₄₁	C₂³	1	4	yes	—
135	#95×C₄₁	C₂³	1	8	yes	—
136	#95×C₄₁	C₂³	1	8	yes	—
137	C₂⁴×C₄₁	—	2	2	no	—
138	C₂⁴×C₄₁	—	2	4	no	—
139	C₂⁴×C₄₁	—	2	4	no	—
140	C₂⁴×C₄₁	—	2	4	no	—
141	C₂⁴×C₄₁	—	2	4	no	—
142	C₂⁴×C₄₁	—	4	2	no	—
143	C₂⁴×C₄₁	—	4	2	no	—
144	C₂⁴×C₄₁	C₂×D₄	1	4	yes	—
145	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
146	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
147	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
148	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
149	C₂×D₄×C₄₁	—	2	32	no	—
150	C₂×D₄×C₄₁	—	2	4	no	—
151	C₂×D₄×C₄₁	—	2	4	no	—
152	C₂×D₄×C₄₁	—	2	4	no	—
153	C₂×D₄×C₄₁	—	2	4	no	—
154	C₂×D₄×C₄₁	—	2	4	no	—
155	C₂×D₄×C₄₁	#41	1	8	yes	—
156	C₂²×C₄×C₄₁	—	2	2	no	—
157	C₂²×C₄×C₄₁	—	2	4	no	—
158	C₂²×C₄×C₄₁	—	2	32	no	—
159	C₂²×C₄×C₄₁	—	2	4	no	—
160	C₂²×C₄×C₄₁	—	2	4	no	—
161	C₂²×C₄×C₄₁	—	2	4	no	—
162	C₂²×C₄×C₄₁	—	2	4	no	—
163	C₂²×C₄×C₄₁	—	2	4	no	—
164	C₂²×C₄×C₄₁	—	2	2	no	—
165	C₂²×C₄×C₄₁	—	2	4	no	—
166	C₂²×C₄×C₄₁	—	2	4	no	—
167	C₂²×C₄×C₄₁	—	2	2	no	—
168	C₂²×C₄×C₄₁	—	2	8	no	—
169	C₂²×C₄×C₄₁	—	2	4	no	—
170	C₂²×C₄×C₄₁	—	2	4	no	—
171	C₂²×C₄×C₄₁	—	2	4	no	—
172	C₂²×C₄×C₄₁	—	2	8	no	—
173	C₂²×C₄×C₄₁	—	2	8	no	—
174	C₂²×C₄×C₄₁	—	4	4	no	—
175	C₂²×C₄×C₄₁	—	4	2	no	—
176	C₂²×C₄×C₄₁	—	4	16	no	—
177	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
178	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
179	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
180	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
181	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
182	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
183	C₂²×C₄×C₄₁	#41	1	8	yes	—
184	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
186	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
194	C₄⋊C₄×C₄₁	—	2	4	no	—
195	C₄⋊C₄×C₄₁	—	2	4	no	—
196	C₄⋊C₄×C₄₁	—	2	4	no	—
197	C₄⋊C₄×C₄₁	—	2	4	no	—
198	C₄⋊C₄×C₄₁	—	2	4	no	—
199	C₄⋊C₄×C₄₁	—	2	4	no	—
200	C₄⋊C₄×C₄₁	—	2	8	no	—
201	C₄⋊C₄×C₄₁	—	2	16	no	—
202	C₄⋊C₄×C₄₁	—	4	8	no	—
203	C₂²⋊C₄×C₄₁	—	2	8	no	—
204	C₂²⋊C₄×C₄₁	—	2	8	no	—
205	C₂²⋊C₄×C₄₁	—	2	4	no	—
206	C₂²⋊C₄×C₄₁	—	2	4	no	—
207	C₂²⋊C₄×C₄₁	—	2	8	no	—
208	C₂²⋊C₄×C₄₁	—	2	8	no	—
209	C₂²⋊C₄×C₄₁	—	2	16	no	—
210	C₂²⋊C₄×C₄₁	—	2	4	no	—
211	C₂²⋊C₄×C₄₁	—	2	4	no	—
212	C₂²⋊C₄×C₄₁	—	4	4	no	—
213	C₂²⋊C₄×C₄₁	—	4	8	no	—
214	C₄²×C₄₁	—	2	8	no	—
215	C₄²×C₄₁	—	2	8	no	—
216	C₄²×C₄₁	—	2	4	no	—
217	C₄²×C₄₁	—	2	4	no	—
218	C₄²×C₄₁	—	2	8	no	—
219	C₂³×C₄₁	—	2	2	no	—
220	C₂³×C₄₁	—	2	2	no	—
221	C₂³×C₄₁	—	2	2	no	—
222	C₂³×C₄₁	—	2	2	no	—
223	C₂³×C₄₁	—	2	8	no	—
224	C₂³×C₄₁	—	2	8	no	—
225	C₂³×C₄₁	—	2	8	no	—
226	C₂³×C₄₁	—	2	2	no	—
227	C₂³×C₄₁	—	2	2	no	—
228	C₂³×C₄₁	—	2	4	no	—
229	C₂³×C₄₁	—	2	2	no	—
230	C₂³×C₄₁	—	2	2	no	—
231	C₂³×C₄₁	—	2	2	no	—
232	C₂³×C₄₁	—	2	4	no	—
233	C₂³×C₄₁	—	4	4	no	—
234	C₂³×C₄₁	—	4	16	no	—
235	C₂³×C₄₁	—	4	16	no	—
236	C₂³×C₄₁	—	4	4	no	—
237	C₂³×C₄₁	—	4	4	no	—
238	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
239	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
240	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
241	C₂³×C₄₁	C₂×#41	1	4	yes	—
242	C₂³×C₄₁	C₂×#41	1	4	yes	—
243	C₂³×C₄₁	C₂×#41	1	4	yes	—
244	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
245	D₄×C₄₁	—	2	16	no	—
246	D₄×C₄₁	—	2	16	no	—
247	C₂×C₄×C₄₁	—	2	8	no	—
248	C₂×C₄×C₄₁	—	2	8	no	—
249	C₂×C₄×C₄₁	—	2	2	no	—
250	C₂×C₄×C₄₁	—	2	2	no	—
251	C₂×C₄×C₄₁	—	2	2	no	—
252	C₂×C₄×C₄₁	—	2	2	no	—
253	C₂×C₄×C₄₁	—	2	8	no	—
254	C₂×C₄×C₄₁	—	2	8	no	—
255	C₂×C₄×C₄₁	—	2	8	no	—
256	C₂×C₄×C₄₁	—	2	8	no	—
257	C₂×C₄×C₄₁	—	2	2	no	—
258	C₂×C₄×C₄₁	—	2	4	no	—
259	C₂×C₄×C₄₁	—	2	4	no	—
260	C₂×C₄×C₄₁	—	2	2	no	—
261	C₂×C₄×C₄₁	—	2	8	no	—
262	C₂×C₄×C₄₁	—	2	8	no	—
263	C₂×C₄×C₄₁	—	2	8	no	—
264	C₂×C₄×C₄₁	—	2	4	no	—
265	C₂×C₄×C₄₁	—	2	8	no	—
266	C₂×C₄×C₄₁	—	2	8	no	—
267	C₂×C₄×C₄₁	—	2	4	no	—
268	C₂×C₄×C₄₁	—	4	8	no	—
269	C₂×C₄×C₄₁	—	4	4	no	—
270	C₂×C₄×C₄₁	—	4	4	no	—
271	C₂×C₄×C₄₁	—	4	8	no	—
272	C₂×C₄×C₄₁	—	4	8	no	—
273	C₂×C₄×C₄₁	—	4	8	no	—
274	C₂×C₄×C₄₁	#123	1	16	yes	complemented
275	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
276	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
277	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
278	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
279	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
280	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
281	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
282	#34809	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
283	C₂²×C₄₁	—	2	2	no	—
284	C₂²×C₄₁	—	2	2	no	—
285	C₂²×C₄₁	—	2	2	no	—
286	C₂²×C₄₁	—	2	2	no	—
287	C₂²×C₄₁	—	2	8	no	—
288	C₂²×C₄₁	—	2	8	no	—
289	C₂²×C₄₁	—	2	2	no	—
290	C₂²×C₄₁	—	2	2	no	—
291	C₂²×C₄₁	—	2	4	no	—
292	C₂²×C₄₁	—	2	2	no	—
293	C₂²×C₄₁	—	2	8	no	—
294	C₂²×C₄₁	—	4	16	no	—
295	C₂²×C₄₁	—	4	16	no	—
296	C₂²×C₄₁	—	4	2	no	—
297	C₂²×C₄₁	—	4	2	no	—
298	C₂²×C₄₁	—	4	4	no	—
299	C₂²×C₄₁	—	4	4	no	—
300	C₂²×C₄₁	C₂×#123	1	4	yes	—
301	C₂²×C₄₁	#525	1	4	yes	—
302	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
303	C₂²×C₄₁	C₂²×#41	1	2	yes	—
304	C₂²×C₄₁	C₂²×#41	1	2	yes	—
305	C₂²×C₄₁	#585	1	2	yes	—
306	C₄×C₄₁	—	2	2	no	—
307	C₄×C₄₁	—	2	2	no	—
308	C₄×C₄₁	—	2	4	no	—
309	C₄×C₄₁	—	4	2	no	—
310	C₄×C₄₁	—	4	4	no	—
311	C₄×C₄₁	—	4	2	no	—
312	C₄×C₄₁	—	4	4	no	—
313	C₄×C₄₁	—	4	8	no	—
314	C₄×C₄₁	C₂×#123	1	4	yes	—
315	C₄×C₄₁	C₂×#123	1	4	yes	—
316	C₂²×C₄×D₄	C₂×C₄₁	1	1	yes	characteristic
317	C₂²×#117	C₂×C₄₁	1	1	yes	characteristic, complemented
318	#2487	C₂×C₄₁	1	2	yes	complemented
319	#2486	C₂×C₄₁	1	2	yes	complemented
320	#2485	C₂×C₄₁	1	4	yes	complemented
321	#2484	C₂×C₄₁	1	2	yes	complemented
322	#2483	C₂×C₄₁	1	2	yes	complemented
323	#2482	C₂×C₄₁	1	2	yes	complemented
324	#2405	C₂×C₄₁	1	2	yes	—
325	#2395	C₂×C₄₁	1	4	yes	complemented
326	C₄×#123	C₂×C₄₁	1	4	yes	complemented
327	#2296	C₂×C₄₁	1	2	yes	complemented
328	#2280	C₂×C₄₁	1	2	yes	complemented
329	#2280	C₂×C₄₁	1	1	yes	characteristic, complemented
330	C₂×C₄₁	—	2	4	no	—
331	C₂×C₄₁	—	2	4	no	—
332	C₂×C₄₁	—	4	2	no	—
333	C₂×C₄₁	—	4	4	no	—
334	C₂×C₄₁	C₂²×#123	1	1	yes	characteristic
335	C₂×C₄₁	C₂×#525	1	1	yes	characteristic
336	C₂×C₄₁	#3449	1	1	yes	characteristic
337	C₂×C₄₁	#3475	1	4	yes	—
338	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
339	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
340	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
341	C₂×#123	C₂²×C₄₁	1	4	yes	—
342	C₂×C₄×D₄	—	2	8	no	—
343	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
344	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
345	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
346	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
347	C₂×#117	—	2	8	no	—
348	C₂×#117	C₂²×C₄₁	1	2	yes	—
349	C₂×#117	C₂²×C₄₁	1	2	yes	—
350	C₂×#117	C₂²×C₄₁	1	2	yes	—
351	C₂×#117	C₂²×C₄₁	1	2	yes	complemented
352	C₂×#117	C₂²×C₄₁	1	2	yes	complemented
353	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
354	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
355	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
356	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
357	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
358	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
359	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
360	C₂²×C₄²	C₂²×C₄₁	1	2	yes	complemented
361	#400	C₂²×C₄₁	1	4	yes	complemented
362	#399	C₂²×C₄₁	1	4	yes	complemented
363	#398	C₂²×C₄₁	1	4	yes	complemented
364	#397	C₂²×C₄₁	1	4	yes	complemented
365	#397	C₂²×C₄₁	1	8	yes	complemented
366	#394	C₂²×C₄₁	1	8	yes	—
367	#389	C₂²×C₄₁	1	4	yes	complemented
368	#389	C₂²×C₄₁	1	4	yes	complemented
369	#388	C₂²×C₄₁	1	8	yes	complemented
370	#387	C₂²×C₄₁	1	8	yes	complemented
371	#386	C₂²×C₄₁	1	4	yes	—
372	#385	C₂²×C₄₁	1	4	yes	—
373	#385	C₂²×C₄₁	1	4	yes	—
374	#385	C₂²×C₄₁	1	4	yes	complemented
375	#381	C₂²×C₄₁	1	2	yes	—
376	#381	C₂²×C₄₁	1	4	yes	—
377	#381	C₂²×C₄₁	1	4	yes	complemented
378	#380	C₂²×C₄₁	1	2	yes	complemented
379	#380	C₂²×C₄₁	1	4	yes	complemented
380	#380	C₂²×C₄₁	1	4	yes	complemented
381	#380	C₂²×C₄₁	1	2	yes	complemented
382	#379	C₂²×C₄₁	1	4	yes	—
383	#379	C₂²×C₄₁	1	2	yes	—
384	C₄×C₄⋊C₄	C₂²×C₄₁	1	8	yes	complemented
385	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	complemented
386	C₄×C₂²⋊C₄	C₂²×C₄₁	1	8	yes	complemented
387	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	complemented
388	C₄₁	#34809	1	1	yes	characteristic, direct product factor, Sylow
389	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
390	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
391	C₂²×D₄	—	2	4	no	—
392	C₂²×D₄	—	2	8	no	—
393	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
394	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
395	C₂³×C₄	—	2	8	no	—
396	C₂³×C₄	—	2	4	no	—
397	C₂³×C₄	—	2	8	no	—
398	C₂³×C₄	D₄×C₄₁	1	8	yes	—
399	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
400	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
401	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
402	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
403	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
404	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
405	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
406	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
407	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
408	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
409	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
410	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
411	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
412	#123	—	2	16	no	—
413	C₄×D₄	—	2	8	no	—
414	C₄×D₄	—	2	8	no	—
415	C₄×D₄	—	2	8	no	—
416	C₄×D₄	—	2	8	no	—
417	#117	—	2	8	no	—
418	#117	—	2	8	no	—
419	#117	—	2	8	no	—
420	#117	—	2	8	no	—
421	#117	—	2	8	no	—
422	C₂×C₄⋊C₄	—	2	4	no	—
423	C₂×C₄⋊C₄	—	2	4	no	—
424	C₂×C₄⋊C₄	—	2	4	no	—
425	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
426	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
427	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
428	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
429	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
430	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
431	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
432	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
433	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
434	C₂×C₂²⋊C₄	—	2	8	no	—
435	C₂×C₂²⋊C₄	—	2	4	no	—
436	C₂×C₂²⋊C₄	—	2	4	no	—
437	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
444	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
448	C₂×C₄²	—	2	8	no	—
449	C₂×C₄²	—	2	4	no	—
450	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
451	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
452	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
453	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
454	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
455	#95	C₂³×C₄₁	1	8	yes	—
456	#95	C₂³×C₄₁	1	8	yes	—
457	#95	C₂³×C₄₁	1	4	yes	—
458	#95	C₂³×C₄₁	1	4	yes	—
459	#95	C₂³×C₄₁	1	8	yes	—
460	#95	C₂³×C₄₁	1	8	yes	—
461	C₂⁴	—	2	2	no	—
462	C₂⁴	—	2	4	no	—
463	C₂⁴	—	2	4	no	—
464	C₂⁴	—	2	4	no	—
465	C₂⁴	—	2	4	no	—
466	C₂⁴	—	4	2	no	—
467	C₂⁴	—	4	2	no	—
468	C₂⁴	C₂×D₄×C₄₁	1	4	yes	—
469	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
470	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
471	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
472	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
473	C₂×D₄	—	2	32	no	—
474	C₂×D₄	—	2	4	no	—
475	C₂×D₄	—	2	4	no	—
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	2	4	no	—
478	C₂×D₄	—	2	4	no	—
479	C₂×D₄	#41×C₄₁	1	8	yes	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	32	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	4	no	—
487	C₂²×C₄	—	2	4	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	4	no	—
490	C₂²×C₄	—	2	4	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	8	no	—
493	C₂²×C₄	—	2	4	no	—
494	C₂²×C₄	—	2	4	no	—
495	C₂²×C₄	—	2	4	no	—
496	C₂²×C₄	—	2	8	no	—
497	C₂²×C₄	—	2	8	no	—
498	C₂²×C₄	—	4	4	no	—
499	C₂²×C₄	—	4	2	no	—
500	C₂²×C₄	—	4	16	no	—
501	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
502	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
503	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
504	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
505	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
506	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
507	C₂²×C₄	#41×C₄₁	1	8	yes	—
508	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
509	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
510	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
511	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
512	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
513	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
514	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
515	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
516	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
517	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
518	C₄⋊C₄	—	2	4	no	—
519	C₄⋊C₄	—	2	4	no	—
520	C₄⋊C₄	—	2	4	no	—
521	C₄⋊C₄	—	2	4	no	—
522	C₄⋊C₄	—	2	4	no	—
523	C₄⋊C₄	—	2	4	no	—
524	C₄⋊C₄	—	2	8	no	—
525	C₄⋊C₄	—	2	16	no	—
526	C₄⋊C₄	—	4	8	no	—
527	C₂²⋊C₄	—	2	8	no	—
528	C₂²⋊C₄	—	2	8	no	—
529	C₂²⋊C₄	—	2	4	no	—
530	C₂²⋊C₄	—	2	4	no	—
531	C₂²⋊C₄	—	2	8	no	—
532	C₂²⋊C₄	—	2	8	no	—
533	C₂²⋊C₄	—	2	16	no	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	4	no	—
536	C₂²⋊C₄	—	4	4	no	—
537	C₂²⋊C₄	—	4	8	no	—
538	C₄²	—	2	8	no	—
539	C₄²	—	2	8	no	—
540	C₄²	—	2	4	no	—
541	C₄²	—	2	4	no	—
542	C₄²	—	2	8	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	2	8	no	—
548	C₂³	—	2	8	no	—
549	C₂³	—	2	8	no	—
550	C₂³	—	2	2	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	2	4	no	—
553	C₂³	—	2	2	no	—
554	C₂³	—	2	2	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	2	4	no	—
557	C₂³	—	4	4	no	—
558	C₂³	—	4	16	no	—
559	C₂³	—	4	16	no	—
560	C₂³	—	4	4	no	—
561	C₂³	—	4	4	no	—
562	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
563	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
564	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
565	C₂³	C₂×#41×C₄₁	1	4	yes	—
566	C₂³	C₂×#41×C₄₁	1	4	yes	—
567	C₂³	C₂×#41×C₄₁	1	4	yes	—
568	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
569	D₄	—	2	16	no	—
570	D₄	—	2	16	no	—
571	C₂×C₄	—	2	8	no	—
572	C₂×C₄	—	2	8	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	8	no	—
578	C₂×C₄	—	2	8	no	—
579	C₂×C₄	—	2	8	no	—
580	C₂×C₄	—	2	8	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	8	no	—
586	C₂×C₄	—	2	8	no	—
587	C₂×C₄	—	2	8	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	8	no	—
590	C₂×C₄	—	2	8	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	4	8	no	—
593	C₂×C₄	—	4	4	no	—
594	C₂×C₄	—	4	4	no	—
595	C₂×C₄	—	4	8	no	—
596	C₂×C₄	—	4	8	no	—
597	C₂×C₄	—	4	8	no	—
598	C₂×C₄	#123×C₄₁	1	16	yes	complemented
599	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
600	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
601	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
602	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
603	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
604	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
605	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	8	no	—
611	C₂²	—	2	8	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	4	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	8	no	—
617	C₂²	—	4	16	no	—
618	C₂²	—	4	16	no	—
619	C₂²	—	4	2	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	4	4	no	—
622	C₂²	—	4	4	no	—
623	C₂²	C₂×#123×C₄₁	1	4	yes	—
624	C₂²	C₄₁×#525	1	4	yes	—
625	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
626	C₂²	C₂²×#41×C₄₁	1	2	yes	—
627	C₂²	C₂²×#41×C₄₁	1	2	yes	—
628	C₂²	C₄₁×#585	1	2	yes	—
629	C₄	—	2	2	no	—
630	C₄	—	2	2	no	—
631	C₄	—	2	4	no	—
632	C₄	—	4	2	no	—
633	C₄	—	4	4	no	—
634	C₄	—	4	2	no	—
635	C₄	—	4	4	no	—
636	C₄	—	4	8	no	—
637	C₄	C₂×#123×C₄₁	1	4	yes	—
638	C₄	C₂×#123×C₄₁	1	4	yes	—
639	C₂	—	2	4	no	—
640	C₂	—	2	4	no	—
641	C₂	—	4	2	no	—
642	C₂	—	4	4	no	—
643	C₂	C₂²×#123×C₄₁	1	1	yes	characteristic
644	C₂	C₂×C₄₁×#525	1	1	yes	characteristic
645	C₂	C₄₁×#3449	1	1	yes	characteristic
646	C₂	C₄₁×#3475	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₁
socle	C₂³×C₄₁	C₂⁵
prime radical	C₂³×D₄×C₄₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#117×C₄₁	C₂	semidirect
3. C₄₁×#2487	C₂	semidirect
4. C₄₁×#2486	C₂	semidirect
5. C₄₁×#2485	C₂	semidirect
6. C₄₁×#2484	C₂	semidirect
7. C₄₁×#2483	C₂	semidirect
8. C₄₁×#2482	C₂	semidirect
10. C₄₁×#2395	C₂	semidirect
11. C₄×#123×C₄₁	C₂	semidirect
12. C₄₁×#2296	C₂	semidirect
13. C₄₁×#2280	C₂	semidirect
14. C₄₁×#2280	C₂	semidirect
28. C₂×#117×C₄₁	C₂²	semidirect
29. C₂×#117×C₄₁	C₂²	semidirect
31. C₂²×C₄⋊C₄×C₄₁	C₂²	semidirect
32. C₂²×C₄⋊C₄×C₄₁	C₂²	semidirect
37. C₂²×C₄²×C₄₁	C₂²	semidirect
38. C₄₁×#400	C₂²	semidirect
39. C₄₁×#399	C₂²	semidirect
40. C₄₁×#398	C₂²	semidirect
41. C₄₁×#397	C₂²	semidirect
42. C₄₁×#397	C₂²	semidirect
44. C₄₁×#389	C₂²	semidirect
45. C₄₁×#389	C₂²	semidirect
46. C₄₁×#388	C₂²	semidirect
47. C₄₁×#387	C₂²	semidirect
51. C₄₁×#385	C₂²	semidirect
54. C₄₁×#381	C₂²	semidirect
55. C₄₁×#380	C₂²	semidirect
56. C₄₁×#380	C₂²	semidirect
57. C₄₁×#380	C₂²	semidirect
58. C₄₁×#380	C₂²	semidirect
61. C₄×C₄⋊C₄×C₄₁	C₂²	semidirect
62. C₄×C₂²⋊C₄×C₄₁	C₂²	semidirect
63. C₄×C₂²⋊C₄×C₄₁	C₂²	semidirect
64. C₄×C₂²⋊C₄×C₄₁	C₂²	semidirect
274. C₂×C₄×C₄₁	#123	semidirect
282. #34809	C₄₁	direct (N × H)
317. C₂²×#117	C₂×C₄₁	semidirect
318. #2487	C₂×C₄₁	semidirect
319. #2486	C₂×C₄₁	semidirect
320. #2485	C₂×C₄₁	semidirect
321. #2484	C₂×C₄₁	semidirect
322. #2483	C₂×C₄₁	semidirect
323. #2482	C₂×C₄₁	semidirect
325. #2395	C₂×C₄₁	semidirect
326. C₄×#123	C₂×C₄₁	semidirect
327. #2296	C₂×C₄₁	semidirect
328. #2280	C₂×C₄₁	semidirect
329. #2280	C₂×C₄₁	semidirect
351. C₂×#117	C₂²×C₄₁	semidirect
352. C₂×#117	C₂²×C₄₁	semidirect
354. C₂²×C₄⋊C₄	C₂²×C₄₁	semidirect
355. C₂²×C₄⋊C₄	C₂²×C₄₁	semidirect
360. C₂²×C₄²	C₂²×C₄₁	semidirect
361. #400	C₂²×C₄₁	semidirect
362. #399	C₂²×C₄₁	semidirect
363. #398	C₂²×C₄₁	semidirect
364. #397	C₂²×C₄₁	semidirect
365. #397	C₂²×C₄₁	semidirect
367. #389	C₂²×C₄₁	semidirect
368. #389	C₂²×C₄₁	semidirect
369. #388	C₂²×C₄₁	semidirect
370. #387	C₂²×C₄₁	semidirect
374. #385	C₂²×C₄₁	semidirect
377. #381	C₂²×C₄₁	semidirect
378. #380	C₂²×C₄₁	semidirect
379. #380	C₂²×C₄₁	semidirect
380. #380	C₂²×C₄₁	semidirect
381. #380	C₂²×C₄₁	semidirect
384. C₄×C₄⋊C₄	C₂²×C₄₁	semidirect
385. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
386. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
387. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
388. C₄₁	#34809	direct (N × H)
598. C₂×C₄	#123×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₄₁	2
C₂²×#117×C₄₁	2
C₄₁×#2487	2
C₄₁×#2486	2
C₄₁×#2485	2
C₄₁×#2484	2
C₄₁×#2483	2
C₄₁×#2482	2
C₄₁×#2405	2
C₄₁×#2395	2
C₄×#123×C₄₁	2
C₄₁×#2296	2
C₄₁×#2280	2
#34809	41

Subgroups — C41×#34809 #23811010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#34809 #23811010