Subgroups — C₂×C₄₁×#2636 #23810787

Order 10496.

3218 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#126×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2636	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₄₁×#400	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₁×#399	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₁×#396	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₁×#394	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₁×#394	C₂	1	2	yes	maximal, complemented
9	C₂×C₄₁×#392	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄₁×#386	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₁×#385	C₂	1	2	yes	maximal, complemented
12	C₂×C₄₁×#382	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₄₁	C₂²	1	2	yes	—
15	C₂⁴×C₄×C₄₁	C₂²	1	2	yes	—
16	C₂×#126×C₄₁	—	2	8	no	—
17	C₂×#126×C₄₁	C₂²	1	8	yes	complemented
18	C₂×C₄×D₄×C₄₁	—	2	8	no	—
19	C₂×C₄×D₄×C₄₁	C₂²	1	8	yes	complemented
20	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
25	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
32	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
33	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
34	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
35	C₄₁×#400	C₂²	1	8	yes	complemented
36	C₄₁×#399	C₂²	1	8	yes	complemented
37	C₄₁×#396	C₂²	1	16	yes	complemented
38	C₄₁×#394	C₂²	1	8	yes	complemented
39	C₄₁×#394	C₂²	1	16	yes	complemented
40	C₄₁×#392	C₂²	1	8	yes	—
41	C₄₁×#386	C₂²	1	16	yes	complemented
42	C₄₁×#385	C₂²	1	16	yes	complemented
43	C₄₁×#382	C₂²	1	8	yes	complemented
44	C₂×#95×C₄₁	C₂²	1	2	yes	—
45	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
46	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
47	C₂×#95×C₄₁	C₂²	1	2	yes	—
48	C₂×#95×C₄₁	C₂²	1	2	yes	—
49	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
50	C₂⁵×C₄₁	C₂³	1	2	yes	—
51	C₂²×D₄×C₄₁	—	2	8	no	—
52	C₂²×D₄×C₄₁	—	2	8	no	—
53	C₂²×D₄×C₄₁	—	2	4	no	—
54	C₂²×D₄×C₄₁	—	4	4	no	—
55	C₂²×D₄×C₄₁	—	4	4	no	—
56	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
57	C₂²×D₄×C₄₁	C₂³	1	8	yes	—
58	C₂³×C₄×C₄₁	—	2	8	no	—
59	C₂³×C₄×C₄₁	—	4	4	no	—
60	C₂³×C₄×C₄₁	—	4	4	no	—
61	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
65	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
66	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
67	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₄₁	C₂³	1	8	yes	—
71	#126×C₄₁	—	2	32	no	—
72	C₄×D₄×C₄₁	—	2	32	no	—
73	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
74	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
75	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
76	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
77	C₂×C₄⋊C₄×C₄₁	—	4	4	no	—
78	C₂×C₄⋊C₄×C₄₁	—	4	4	no	—
79	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
81	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
82	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
84	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
85	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
86	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
87	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
88	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
89	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
90	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
91	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
92	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
93	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	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	8	yes	—
98	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
99	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
100	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
101	C₂×C₄²×C₄₁	D₄	1	8	yes	complemented
102	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
103	#95×C₄₁	C₂³	1	8	yes	—
104	#95×C₄₁	C₂³	1	4	yes	—
105	#95×C₄₁	C₂³	1	4	yes	—
106	#95×C₄₁	C₂³	1	8	yes	—
107	#95×C₄₁	C₂³	1	8	yes	—
108	C₂⁴×C₄₁	—	2	4	no	—
109	C₂⁴×C₄₁	—	2	4	no	—
110	C₂⁴×C₄₁	—	2	4	no	—
111	C₂⁴×C₄₁	—	2	4	no	—
112	C₂⁴×C₄₁	—	2	4	no	—
113	C₂⁴×C₄₁	—	2	4	no	—
114	C₂⁴×C₄₁	—	2	2	no	—
115	C₂⁴×C₄₁	—	2	4	no	—
116	C₂⁴×C₄₁	—	2	4	no	—
117	C₂⁴×C₄₁	—	2	2	no	—
118	C₂⁴×C₄₁	—	2	2	no	—
119	C₂⁴×C₄₁	#41	1	8	yes	—
120	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
121	C₂⁴×C₄₁	C₂⁴	1	4	yes	—
122	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
123	C₂×D₄×C₄₁	—	2	32	no	—
124	C₂×D₄×C₄₁	—	2	16	no	—
125	C₂×D₄×C₄₁	—	2	16	no	—
126	C₂×D₄×C₄₁	—	2	8	no	—
127	C₂×D₄×C₄₁	—	4	8	no	—
128	C₂×D₄×C₄₁	—	4	8	no	—
129	C₂×D₄×C₄₁	—	4	32	no	—
130	C₂²×C₄×C₄₁	—	2	4	no	—
131	C₂²×C₄×C₄₁	—	2	2	no	—
132	C₂²×C₄×C₄₁	—	2	4	no	—
133	C₂²×C₄×C₄₁	—	2	2	no	—
134	C₂²×C₄×C₄₁	—	2	2	no	—
135	C₂²×C₄×C₄₁	—	2	2	no	—
136	C₂²×C₄×C₄₁	—	2	2	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	2	no	—
142	C₂²×C₄×C₄₁	—	2	4	no	—
143	C₂²×C₄×C₄₁	—	2	4	no	—
144	C₂²×C₄×C₄₁	—	2	4	no	—
145	C₂²×C₄×C₄₁	—	2	4	no	—
146	C₂²×C₄×C₄₁	—	2	4	no	—
147	C₂²×C₄×C₄₁	—	2	4	no	—
148	C₂²×C₄×C₄₁	—	2	4	no	—
149	C₂²×C₄×C₄₁	—	2	2	no	—
150	C₂²×C₄×C₄₁	—	2	16	no	—
151	C₂²×C₄×C₄₁	—	4	8	no	—
152	C₂²×C₄×C₄₁	—	4	8	no	—
153	C₂²×C₄×C₄₁	—	4	32	no	—
154	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
155	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
156	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
157	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₄₁	C₂⁴	1	2	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	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
166	C₄⋊C₄×C₄₁	—	2	8	no	—
167	C₄⋊C₄×C₄₁	—	2	8	no	—
168	C₄⋊C₄×C₄₁	—	2	8	no	—
169	C₄⋊C₄×C₄₁	—	2	8	no	—
170	C₄⋊C₄×C₄₁	—	4	8	no	—
171	C₄⋊C₄×C₄₁	—	4	8	no	—
172	C₂²⋊C₄×C₄₁	—	2	16	no	—
173	C₂²⋊C₄×C₄₁	—	2	16	no	—
174	C₂²⋊C₄×C₄₁	—	2	8	no	—
175	C₂²⋊C₄×C₄₁	—	2	8	no	—
176	C₂²⋊C₄×C₄₁	—	2	8	no	—
177	C₂²⋊C₄×C₄₁	—	4	8	no	—
178	C₂²⋊C₄×C₄₁	—	4	8	no	—
179	C₂²⋊C₄×C₄₁	—	4	8	no	—
180	C₄²×C₄₁	C₂×D₄	1	16	yes	complemented
181	C₂³×C₄₁	—	2	16	no	—
182	C₂³×C₄₁	—	2	16	no	—
183	C₂³×C₄₁	—	2	16	no	—
184	C₂³×C₄₁	—	2	4	no	—
185	C₂³×C₄₁	—	2	4	no	—
186	C₂³×C₄₁	—	2	4	no	—
187	C₂³×C₄₁	—	2	4	no	—
188	C₂³×C₄₁	—	2	4	no	—
189	C₂³×C₄₁	—	2	4	no	—
190	C₂³×C₄₁	—	2	2	no	—
191	C₂³×C₄₁	—	2	4	no	—
192	C₂³×C₄₁	—	2	4	no	—
193	C₂³×C₄₁	—	2	2	no	—
194	C₂³×C₄₁	—	2	2	no	—
195	C₂³×C₄₁	—	4	8	no	—
196	C₂³×C₄₁	—	4	8	no	—
197	C₂³×C₄₁	—	4	8	no	—
198	C₂³×C₄₁	—	4	8	no	—
199	C₂³×C₄₁	—	4	4	no	—
200	C₂³×C₄₁	—	4	4	no	—
201	C₂³×C₄₁	—	4	4	no	—
202	C₂³×C₄₁	—	4	8	no	—
203	C₂³×C₄₁	—	4	8	no	—
204	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
205	C₂³×C₄₁	C₂×#41	1	8	yes	—
206	C₂³×C₄₁	C₂×#41	1	4	yes	—
207	C₂³×C₄₁	H(5,𝔽₂)	1	4	yes	—
208	C₂³×C₄₁	H(5,𝔽₂)	1	2	yes	—
209	C₂³×C₄₁	2₋¹⁺⁴	1	2	yes	—
210	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
211	D₄×C₄₁	—	2	32	no	—
212	D₄×C₄₁	—	4	32	no	—
213	C₂×C₄×C₄₁	—	2	8	no	—
214	C₂×C₄×C₄₁	—	2	8	no	—
215	C₂×C₄×C₄₁	—	2	8	no	—
216	C₂×C₄×C₄₁	—	2	4	no	—
217	C₂×C₄×C₄₁	—	2	2	no	—
218	C₂×C₄×C₄₁	—	2	4	no	—
219	C₂×C₄×C₄₁	—	2	2	no	—
220	C₂×C₄×C₄₁	—	2	2	no	—
221	C₂×C₄×C₄₁	—	2	2	no	—
222	C₂×C₄×C₄₁	—	2	2	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	2	no	—
228	C₂×C₄×C₄₁	—	2	4	no	—
229	C₂×C₄×C₄₁	—	2	4	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	—	2	2	no	—
236	C₂×C₄×C₄₁	—	4	32	no	—
237	C₂×C₄×C₄₁	—	4	4	no	—
238	C₂×C₄×C₄₁	—	4	4	no	—
239	C₂×C₄×C₄₁	—	4	8	no	—
240	C₂×C₄×C₄₁	—	4	4	no	—
241	C₂×C₄×C₄₁	—	4	8	no	—
242	C₂×C₄×C₄₁	—	4	8	no	—
243	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
244	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
245	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
246	C₂×#2636	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₂²×C₄₁	—	2	8	no	—
248	C₂²×C₄₁	—	2	8	no	—
249	C₂²×C₄₁	—	2	8	no	—
250	C₂²×C₄₁	—	4	32	no	—
251	C₂²×C₄₁	—	4	4	no	—
252	C₂²×C₄₁	—	4	4	no	—
253	C₂²×C₄₁	—	4	4	no	—
254	C₂²×C₄₁	—	4	4	no	—
255	C₂²×C₄₁	—	4	2	no	—
256	C₂²×C₄₁	—	4	2	no	—
257	C₂²×C₄₁	—	4	2	no	—
258	C₂²×C₄₁	—	4	4	no	—
259	C₂²×C₄₁	—	4	4	no	—
260	C₂²×C₄₁	—	8	8	no	—
261	C₂²×C₄₁	#525	1	4	yes	—
262	C₂²×C₄₁	#535	1	4	yes	—
263	C₂²×C₄₁	#537	1	4	yes	—
264	C₂²×C₄₁	#538	1	8	yes	—
265	C₂²×C₄₁	#539	1	8	yes	—
266	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
267	C₂²×C₄₁	C₂²×#41	1	2	yes	—
268	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	2	yes	—
269	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
270	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
271	C₄×C₄₁	—	2	4	no	—
272	C₄×C₄₁	—	2	4	no	—
273	C₄×C₄₁	—	2	4	no	—
274	C₄×C₄₁	—	4	2	no	—
275	C₄×C₄₁	—	4	2	no	—
276	C₄×C₄₁	—	4	4	no	—
277	C₄×C₄₁	—	4	2	no	—
278	C₄×C₄₁	—	4	4	no	—
279	C₄×C₄₁	—	4	4	no	—
280	C₂²×#126	C₂×C₄₁	1	1	yes	characteristic, complemented
281	C₂²×C₄×D₄	C₂×C₄₁	1	1	yes	characteristic, complemented
282	#2636	C₂×C₄₁	1	16	yes	direct product factor
283	C₂×#400	C₂×C₄₁	1	1	yes	characteristic, complemented
284	C₂×#399	C₂×C₄₁	1	1	yes	characteristic, complemented
285	C₂×#396	C₂×C₄₁	1	2	yes	complemented
286	C₂×#394	C₂×C₄₁	1	2	yes	complemented
287	C₂×#394	C₂×C₄₁	1	1	yes	characteristic, complemented
288	C₂×#392	C₂×C₄₁	1	1	yes	characteristic
289	C₂×#386	C₂×C₄₁	1	2	yes	complemented
290	C₂×#385	C₂×C₄₁	1	2	yes	complemented
291	C₂×#382	C₂×C₄₁	1	1	yes	characteristic, complemented
292	C₂×C₄₁	—	4	8	no	—
293	C₂×C₄₁	—	8	2	no	—
294	C₂×C₄₁	#2636	1	8	yes	direct product factor
295	C₂×C₄₁	C₂×#525	1	1	yes	characteristic
296	C₂×C₄₁	C₂×#535	1	1	yes	characteristic
297	C₂×C₄₁	C₂×#537	1	1	yes	characteristic
298	C₂×C₄₁	C₂×#538	1	2	yes	—
299	C₂×C₄₁	C₂×#539	1	2	yes	—
300	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
301	C₂³×D₄	C₂²×C₄₁	1	2	yes	—
302	C₂⁴×C₄	C₂²×C₄₁	1	2	yes	—
303	C₂×#126	—	2	8	no	—
304	C₂×#126	C₂²×C₄₁	1	8	yes	complemented
305	C₂×C₄×D₄	—	2	8	no	—
306	C₂×C₄×D₄	C₂²×C₄₁	1	8	yes	complemented
307	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
308	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
309	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
310	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
311	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
312	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
313	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
314	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
315	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
316	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
317	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
318	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
319	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
320	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
321	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
322	#400	C₂²×C₄₁	1	8	yes	complemented
323	#399	C₂²×C₄₁	1	8	yes	complemented
324	#396	C₂²×C₄₁	1	16	yes	complemented
325	#394	C₂²×C₄₁	1	8	yes	complemented
326	#394	C₂²×C₄₁	1	16	yes	complemented
327	#392	C₂²×C₄₁	1	8	yes	—
328	#386	C₂²×C₄₁	1	16	yes	complemented
329	#385	C₂²×C₄₁	1	16	yes	complemented
330	#382	C₂²×C₄₁	1	8	yes	complemented
331	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
332	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
333	C₂×#95	C₂²×C₄₁	1	2	yes	—
334	C₂×#95	C₂²×C₄₁	1	2	yes	—
335	C₂×#95	C₂²×C₄₁	1	2	yes	—
336	C₄₁	C₂×#2636	1	1	yes	characteristic, direct product factor, Sylow
337	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
338	C₂⁵	C₂³×C₄₁	1	2	yes	—
339	C₂²×D₄	—	2	8	no	—
340	C₂²×D₄	—	2	8	no	—
341	C₂²×D₄	—	2	4	no	—
342	C₂²×D₄	—	4	4	no	—
343	C₂²×D₄	—	4	4	no	—
344	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
345	C₂²×D₄	C₂³×C₄₁	1	8	yes	—
346	C₂³×C₄	—	2	8	no	—
347	C₂³×C₄	—	4	4	no	—
348	C₂³×C₄	—	4	4	no	—
349	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
350	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
351	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
352	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
353	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
354	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
355	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
356	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
357	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₄₁	1	8	yes	—
359	#126	—	2	32	no	—
360	C₄×D₄	—	2	32	no	—
361	C₂×C₄⋊C₄	—	2	4	no	—
362	C₂×C₄⋊C₄	—	2	4	no	—
363	C₂×C₄⋊C₄	—	2	4	no	—
364	C₂×C₄⋊C₄	—	2	4	no	—
365	C₂×C₄⋊C₄	—	4	4	no	—
366	C₂×C₄⋊C₄	—	4	4	no	—
367	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	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×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
372	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
373	C₂×C₂²⋊C₄	—	2	8	no	—
374	C₂×C₂²⋊C₄	—	2	8	no	—
375	C₂×C₂²⋊C₄	—	2	4	no	—
376	C₂×C₂²⋊C₄	—	2	4	no	—
377	C₂×C₂²⋊C₄	—	2	4	no	—
378	C₂×C₂²⋊C₄	—	4	4	no	—
379	C₂×C₂²⋊C₄	—	4	4	no	—
380	C₂×C₂²⋊C₄	—	4	4	no	—
381	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	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×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
389	C₂×C₄²	D₄×C₄₁	1	8	yes	complemented
390	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
391	#95	C₂³×C₄₁	1	8	yes	—
392	#95	C₂³×C₄₁	1	4	yes	—
393	#95	C₂³×C₄₁	1	4	yes	—
394	#95	C₂³×C₄₁	1	8	yes	—
395	#95	C₂³×C₄₁	1	8	yes	—
396	C₂⁴	—	2	4	no	—
397	C₂⁴	—	2	4	no	—
398	C₂⁴	—	2	4	no	—
399	C₂⁴	—	2	4	no	—
400	C₂⁴	—	2	4	no	—
401	C₂⁴	—	2	4	no	—
402	C₂⁴	—	2	2	no	—
403	C₂⁴	—	2	4	no	—
404	C₂⁴	—	2	4	no	—
405	C₂⁴	—	2	2	no	—
406	C₂⁴	—	2	2	no	—
407	C₂⁴	#41×C₄₁	1	8	yes	—
408	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
409	C₂⁴	C₂⁴×C₄₁	1	4	yes	—
410	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
411	C₂×D₄	—	2	32	no	—
412	C₂×D₄	—	2	16	no	—
413	C₂×D₄	—	2	16	no	—
414	C₂×D₄	—	2	8	no	—
415	C₂×D₄	—	4	8	no	—
416	C₂×D₄	—	4	8	no	—
417	C₂×D₄	—	4	32	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	16	no	—
439	C₂²×C₄	—	4	8	no	—
440	C₂²×C₄	—	4	8	no	—
441	C₂²×C₄	—	4	32	no	—
442	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
443	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
444	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
445	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
446	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
447	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
448	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
449	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
450	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
451	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
452	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
453	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
454	C₄⋊C₄	—	2	8	no	—
455	C₄⋊C₄	—	2	8	no	—
456	C₄⋊C₄	—	2	8	no	—
457	C₄⋊C₄	—	2	8	no	—
458	C₄⋊C₄	—	4	8	no	—
459	C₄⋊C₄	—	4	8	no	—
460	C₂²⋊C₄	—	2	16	no	—
461	C₂²⋊C₄	—	2	16	no	—
462	C₂²⋊C₄	—	2	8	no	—
463	C₂²⋊C₄	—	2	8	no	—
464	C₂²⋊C₄	—	2	8	no	—
465	C₂²⋊C₄	—	4	8	no	—
466	C₂²⋊C₄	—	4	8	no	—
467	C₂²⋊C₄	—	4	8	no	—
468	C₄²	C₂×D₄×C₄₁	1	16	yes	complemented
469	C₂³	—	2	16	no	—
470	C₂³	—	2	16	no	—
471	C₂³	—	2	16	no	—
472	C₂³	—	2	4	no	—
473	C₂³	—	2	4	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	4	no	—
476	C₂³	—	2	4	no	—
477	C₂³	—	2	4	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	2	4	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	4	8	no	—
484	C₂³	—	4	8	no	—
485	C₂³	—	4	8	no	—
486	C₂³	—	4	8	no	—
487	C₂³	—	4	4	no	—
488	C₂³	—	4	4	no	—
489	C₂³	—	4	4	no	—
490	C₂³	—	4	8	no	—
491	C₂³	—	4	8	no	—
492	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
493	C₂³	C₂×#41×C₄₁	1	8	yes	—
494	C₂³	C₂×#41×C₄₁	1	4	yes	—
495	C₂³	H(5,𝔽₂)×C₄₁	1	4	yes	—
496	C₂³	H(5,𝔽₂)×C₄₁	1	2	yes	—
497	C₂³	2₋¹⁺⁴×C₄₁	1	2	yes	—
498	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
499	D₄	—	2	32	no	—
500	D₄	—	4	32	no	—
501	C₂×C₄	—	2	8	no	—
502	C₂×C₄	—	2	8	no	—
503	C₂×C₄	—	2	8	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	2	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	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	4	32	no	—
525	C₂×C₄	—	4	4	no	—
526	C₂×C₄	—	4	8	no	—
527	C₂×C₄	—	4	4	no	—
528	C₂×C₄	—	4	4	no	—
529	C₂×C₄	—	4	8	no	—
530	C₂×C₄	—	4	8	no	—
531	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
532	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
533	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
534	C₂²	—	2	8	no	—
535	C₂²	—	2	8	no	—
536	C₂²	—	2	8	no	—
537	C₂²	—	4	32	no	—
538	C₂²	—	4	4	no	—
539	C₂²	—	4	4	no	—
540	C₂²	—	4	4	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	4	4	no	—
547	C₂²	—	8	8	no	—
548	C₂²	C₄₁×#525	1	4	yes	—
549	C₂²	C₄₁×#535	1	4	yes	—
550	C₂²	C₄₁×#537	1	4	yes	—
551	C₂²	C₄₁×#538	1	8	yes	—
552	C₂²	C₄₁×#539	1	8	yes	—
553	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
554	C₂²	C₂²×#41×C₄₁	1	2	yes	—
555	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	2	yes	—
556	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
557	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
558	C₄	—	2	4	no	—
559	C₄	—	2	4	no	—
560	C₄	—	2	4	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	4	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	4	no	—
566	C₄	—	4	4	no	—
567	C₂	—	4	8	no	—
568	C₂	—	8	2	no	—
569	C₂	C₄₁×#2636	1	8	yes	direct product factor
570	C₂	C₂×C₄₁×#525	1	1	yes	characteristic
571	C₂	C₂×C₄₁×#535	1	1	yes	characteristic
572	C₂	C₂×C₄₁×#537	1	1	yes	characteristic
573	C₂	C₂×C₄₁×#538	1	2	yes	—
574	C₂	C₂×C₄₁×#539	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₄₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₁
prime radical	C₂×C₄₁×#392	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#126×C₄₁	C₂	semidirect
2. C₂²×C₄×D₄×C₄₁	C₂	semidirect
3. C₄₁×#2636	C₂	direct (N × H)
4. C₂×C₄₁×#400	C₂	semidirect
5. C₂×C₄₁×#399	C₂	semidirect
6. C₂×C₄₁×#396	C₂	semidirect
7. C₂×C₄₁×#394	C₂	semidirect
8. C₂×C₄₁×#394	C₂	semidirect
10. C₂×C₄₁×#386	C₂	semidirect
11. C₂×C₄₁×#385	C₂	semidirect
12. C₂×C₄₁×#382	C₂	semidirect
17. C₂×#126×C₄₁	C₂²	semidirect
19. C₂×C₄×D₄×C₄₁	C₂²	semidirect
35. C₄₁×#400	C₂²	semidirect
36. C₄₁×#399	C₂²	semidirect
37. C₄₁×#396	C₂²	semidirect
38. C₄₁×#394	C₂²	semidirect
39. C₄₁×#394	C₂²	semidirect
41. C₄₁×#386	C₂²	semidirect
42. C₄₁×#385	C₂²	semidirect
43. C₄₁×#382	C₂²	semidirect
101. C₂×C₄²×C₄₁	D₄	semidirect
180. C₄²×C₄₁	C₂×D₄	semidirect
246. C₂×#2636	C₄₁	direct (N × H)
280. C₂²×#126	C₂×C₄₁	semidirect
281. C₂²×C₄×D₄	C₂×C₄₁	semidirect
282. #2636	C₂×C₄₁	direct (N × H)
283. C₂×#400	C₂×C₄₁	semidirect
284. C₂×#399	C₂×C₄₁	semidirect
285. C₂×#396	C₂×C₄₁	semidirect
286. C₂×#394	C₂×C₄₁	semidirect
287. C₂×#394	C₂×C₄₁	semidirect
289. C₂×#386	C₂×C₄₁	semidirect
290. C₂×#385	C₂×C₄₁	semidirect
291. C₂×#382	C₂×C₄₁	semidirect
294. C₂×C₄₁	#2636	direct (N × H)
304. C₂×#126	C₂²×C₄₁	semidirect
306. C₂×C₄×D₄	C₂²×C₄₁	semidirect
322. #400	C₂²×C₄₁	semidirect
323. #399	C₂²×C₄₁	semidirect
324. #396	C₂²×C₄₁	semidirect
325. #394	C₂²×C₄₁	semidirect
326. #394	C₂²×C₄₁	semidirect
328. #386	C₂²×C₄₁	semidirect
329. #385	C₂²×C₄₁	semidirect
330. #382	C₂²×C₄₁	semidirect
336. C₄₁	C₂×#2636	direct (N × H)
389. C₂×C₄²	D₄×C₄₁	semidirect
468. C₄²	C₂×D₄×C₄₁	semidirect
569. C₂	C₄₁×#2636	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#126×C₄₁	2
C₂²×C₄×D₄×C₄₁	2
C₄₁×#2636	2
C₂×C₄₁×#400	2
C₂×C₄₁×#399	2
C₂×C₄₁×#396	2
C₂×C₄₁×#394	2
C₂×C₄₁×#392	2
C₂×C₄₁×#386	2
C₂×C₄₁×#385	2
C₂×C₄₁×#382	2
C₂×#2636	41

Subgroups — C2×C41×#2636 #23810787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#2636 #23810787