Subgroups — C₂×C₄₁×#2609 #23811069

Order 10496.

3070 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#117×C₄₁	C₂	1	2	yes	maximal, complemented
2	C₄₁×#2609	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₄₁×#398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#396	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₁×#394	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄₁×#388	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₁×#387	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₁×#386	C₂	1	2	yes	maximal
9	C₂×C₄₁×#385	C₂	1	2	yes	maximal, complemented
10	C₂×C₄₁×#382	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₄₁	C₂²	1	2	yes	—
13	C₂×#117×C₄₁	—	2	16	no	—
14	C₂×#117×C₄₁	C₂²	1	16	yes	complemented
15	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
26	C₂²×C₄²×C₄₁	C₂²	1	2	yes	—
27	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
28	C₄₁×#398	C₂²	1	8	yes	complemented
29	C₄₁×#396	C₂²	1	16	yes	complemented
30	C₄₁×#394	C₂²	1	8	yes	—
31	C₄₁×#388	C₂²	1	16	yes	complemented
32	C₄₁×#387	C₂²	1	16	yes	complemented
33	C₄₁×#386	C₂²	1	16	yes	—
34	C₄₁×#385	C₂²	1	16	yes	complemented
35	C₄₁×#382	C₂²	1	8	yes	complemented
36	C₂×#95×C₄₁	C₂²	1	2	yes	—
37	C₂×#95×C₄₁	C₂²	1	2	yes	—
38	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×#95×C₄₁	C₂²	1	2	yes	—
40	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
41	C₂×#95×C₄₁	C₂²	1	2	yes	—
42	C₂⁵×C₄₁	C₂³	1	2	yes	—
43	C₂²×D₄×C₄₁	—	2	8	no	—
44	C₂²×D₄×C₄₁	—	4	2	no	—
45	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
46	C₂³×C₄×C₄₁	—	2	8	no	—
47	C₂³×C₄×C₄₁	—	2	8	no	—
48	C₂³×C₄×C₄₁	—	2	8	no	—
49	C₂³×C₄×C₄₁	C₂³	1	8	yes	—
50	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
51	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
52	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
54	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
56	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
58	#117×C₄₁	—	2	64	no	—
59	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
60	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
62	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
63	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
64	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
65	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
66	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
67	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
68	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
71	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
72	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
73	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
74	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
75	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
76	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
77	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
78	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
79	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
80	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
81	C₂×C₄²×C₄₁	—	2	8	no	—
82	C₂×C₄²×C₄₁	D₄	1	8	yes	complemented
83	C₂×C₄²×C₄₁	C₂³	1	8	yes	—
84	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
85	#95×C₄₁	C₂³	1	8	yes	—
86	#95×C₄₁	C₂³	1	8	yes	—
87	#95×C₄₁	C₂³	1	4	yes	—
88	#95×C₄₁	C₂³	1	8	yes	—
89	#95×C₄₁	C₂³	1	4	yes	—
90	#95×C₄₁	C₂³	1	8	yes	—
91	C₂⁴×C₄₁	—	2	4	no	—
92	C₂⁴×C₄₁	—	2	4	no	—
93	C₂⁴×C₄₁	—	2	4	no	—
94	C₂⁴×C₄₁	—	2	4	no	—
95	C₂⁴×C₄₁	—	2	4	no	—
96	C₂⁴×C₄₁	—	2	4	no	—
97	C₂⁴×C₄₁	#41	1	8	yes	—
98	C₂⁴×C₄₁	C₂⁴	1	4	yes	—
99	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
100	C₂×D₄×C₄₁	—	2	16	no	—
101	C₂×D₄×C₄₁	—	4	4	no	—
102	C₂×D₄×C₄₁	—	4	16	no	—
103	C₂²×C₄×C₄₁	—	2	64	no	—
104	C₂²×C₄×C₄₁	—	2	4	no	—
105	C₂²×C₄×C₄₁	—	2	16	no	—
106	C₂²×C₄×C₄₁	—	2	4	no	—
107	C₂²×C₄×C₄₁	—	2	4	no	—
108	C₂²×C₄×C₄₁	—	2	4	no	—
109	C₂²×C₄×C₄₁	—	2	2	no	—
110	C₂²×C₄×C₄₁	—	2	2	no	—
111	C₂²×C₄×C₄₁	—	2	16	no	—
112	C₂²×C₄×C₄₁	—	2	16	no	—
113	C₂²×C₄×C₄₁	—	2	4	no	—
114	C₂²×C₄×C₄₁	—	2	4	no	—
115	C₂²×C₄×C₄₁	—	2	4	no	—
116	C₂²×C₄×C₄₁	—	2	4	no	—
117	C₂²×C₄×C₄₁	—	2	4	no	—
118	C₂²×C₄×C₄₁	—	2	4	no	—
119	C₂²×C₄×C₄₁	—	2	4	no	—
120	C₂²×C₄×C₄₁	—	2	4	no	—
121	C₂²×C₄×C₄₁	—	2	4	no	—
122	C₂²×C₄×C₄₁	—	2	4	no	—
123	C₂²×C₄×C₄₁	—	2	2	no	—
124	C₂²×C₄×C₄₁	—	2	2	no	—
125	C₂²×C₄×C₄₁	—	2	4	no	—
126	C₂²×C₄×C₄₁	C₂×D₄	1	8	yes	—
127	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
128	C₂²×C₄×C₄₁	#41	1	8	yes	—
129	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
130	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
131	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
137	C₄⋊C₄×C₄₁	—	2	16	no	—
138	C₄⋊C₄×C₄₁	—	2	16	no	—
139	C₄⋊C₄×C₄₁	—	2	16	no	—
140	C₄⋊C₄×C₄₁	—	4	4	no	—
141	C₄⋊C₄×C₄₁	—	4	4	no	—
142	C₄⋊C₄×C₄₁	—	4	4	no	—
143	C₂²⋊C₄×C₄₁	—	2	16	no	—
144	C₂²⋊C₄×C₄₁	—	2	16	no	—
145	C₂²⋊C₄×C₄₁	—	2	16	no	—
146	C₂²⋊C₄×C₄₁	—	2	16	no	—
147	C₂²⋊C₄×C₄₁	—	4	8	no	—
148	C₄²×C₄₁	—	2	16	no	—
149	C₄²×C₄₁	C₂×D₄	1	16	yes	complemented
150	C₂³×C₄₁	—	2	16	no	—
151	C₂³×C₄₁	—	2	16	no	—
152	C₂³×C₄₁	—	2	16	no	—
153	C₂³×C₄₁	—	2	4	no	—
154	C₂³×C₄₁	—	2	4	no	—
155	C₂³×C₄₁	—	2	4	no	—
156	C₂³×C₄₁	—	2	4	no	—
157	C₂³×C₄₁	—	2	4	no	—
158	C₂³×C₄₁	—	2	4	no	—
159	C₂³×C₄₁	—	4	8	no	—
160	C₂³×C₄₁	—	4	8	no	—
161	C₂³×C₄₁	—	4	8	no	—
162	C₂³×C₄₁	—	4	8	no	—
163	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
164	C₂³×C₄₁	C₂×#41	1	8	yes	—
165	C₂³×C₄₁	C₂×#41	1	4	yes	—
166	C₂³×C₄₁	C₂×#41	1	4	yes	—
167	C₂³×C₄₁	H(5,𝔽₂)	1	2	yes	—
168	C₂³×C₄₁	2₋¹⁺⁴	1	2	yes	—
169	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
170	D₄×C₄₁	—	4	16	no	—
171	C₂×C₄×C₄₁	—	2	64	no	—
172	C₂×C₄×C₄₁	—	2	16	no	—
173	C₂×C₄×C₄₁	—	2	16	no	—
174	C₂×C₄×C₄₁	—	2	8	no	—
175	C₂×C₄×C₄₁	—	2	4	no	—
176	C₂×C₄×C₄₁	—	2	4	no	—
177	C₂×C₄×C₄₁	—	2	4	no	—
178	C₂×C₄×C₄₁	—	2	4	no	—
179	C₂×C₄×C₄₁	—	2	2	no	—
180	C₂×C₄×C₄₁	—	2	2	no	—
181	C₂×C₄×C₄₁	—	2	4	no	—
182	C₂×C₄×C₄₁	—	2	4	no	—
183	C₂×C₄×C₄₁	—	2	4	no	—
184	C₂×C₄×C₄₁	—	2	4	no	—
185	C₂×C₄×C₄₁	—	2	4	no	—
186	C₂×C₄×C₄₁	—	2	4	no	—
187	C₂×C₄×C₄₁	—	2	4	no	—
188	C₂×C₄×C₄₁	—	2	4	no	—
189	C₂×C₄×C₄₁	—	2	4	no	—
190	C₂×C₄×C₄₁	—	2	4	no	—
191	C₂×C₄×C₄₁	—	2	2	no	—
192	C₂×C₄×C₄₁	—	2	2	no	—
193	C₂×C₄×C₄₁	—	2	4	no	—
194	C₂×C₄×C₄₁	—	4	8	no	—
195	C₂×C₄×C₄₁	—	4	8	no	—
196	C₂×C₄×C₄₁	—	4	4	no	—
197	C₂×C₄×C₄₁	—	4	4	no	—
198	C₂×C₄×C₄₁	—	4	8	no	—
199	C₂×C₄×C₄₁	C₂²×D₄	1	8	yes	—
200	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
201	C₂×C₄×C₄₁	C₂×#41	1	8	yes	—
202	C₂×#2609	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂²×C₄₁	—	2	8	no	—
204	C₂²×C₄₁	—	2	8	no	—
205	C₂²×C₄₁	—	2	8	no	—
206	C₂²×C₄₁	—	4	32	no	—
207	C₂²×C₄₁	—	4	4	no	—
208	C₂²×C₄₁	—	4	4	no	—
209	C₂²×C₄₁	—	4	4	no	—
210	C₂²×C₄₁	—	4	4	no	—
211	C₂²×C₄₁	#525	1	8	yes	—
212	C₂²×C₄₁	#537	1	4	yes	—
213	C₂²×C₄₁	#551	1	4	yes	—
214	C₂²×C₄₁	#552	1	8	yes	—
215	C₂²×C₄₁	#555	1	4	yes	—
216	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
217	C₂²×C₄₁	C₂²×#41	1	2	yes	—
218	C₂²×C₄₁	C₂²×#41	1	2	yes	—
219	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
220	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
221	C₄×C₄₁	—	2	8	no	—
222	C₄×C₄₁	—	2	8	no	—
223	C₄×C₄₁	—	2	4	no	—
224	C₄×C₄₁	—	4	4	no	—
225	C₄×C₄₁	—	4	4	no	—
226	C₄×C₄₁	—	4	2	no	—
227	C₄×C₄₁	—	4	2	no	—
228	C₄×C₄₁	—	4	4	no	—
229	C₂²×#117	C₂×C₄₁	1	2	yes	complemented
230	#2609	C₂×C₄₁	1	16	yes	direct product factor
231	C₂×#398	C₂×C₄₁	1	1	yes	characteristic, complemented
232	C₂×#396	C₂×C₄₁	1	2	yes	complemented
233	C₂×#394	C₂×C₄₁	1	1	yes	characteristic
234	C₂×#388	C₂×C₄₁	1	2	yes	complemented
235	C₂×#387	C₂×C₄₁	1	2	yes	complemented
236	C₂×#386	C₂×C₄₁	1	2	yes	—
237	C₂×#385	C₂×C₄₁	1	2	yes	complemented
238	C₂×#382	C₂×C₄₁	1	1	yes	characteristic, complemented
239	C₂×C₄₁	—	4	8	no	—
240	C₂×C₄₁	#2609	1	8	yes	direct product factor
241	C₂×C₄₁	C₂×#525	1	2	yes	—
242	C₂×C₄₁	C₂×#537	1	1	yes	characteristic
243	C₂×C₄₁	C₂×#551	1	1	yes	characteristic
244	C₂×C₄₁	C₂×#552	1	2	yes	—
245	C₂×C₄₁	C₂×#555	1	1	yes	characteristic
246	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
247	C₂⁴×C₄	C₂²×C₄₁	1	2	yes	—
248	C₂×#117	—	2	16	no	—
249	C₂×#117	C₂²×C₄₁	1	16	yes	complemented
250	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
251	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
252	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
253	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
254	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
255	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
256	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
257	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
258	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
259	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
260	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
261	C₂²×C₄²	C₂²×C₄₁	1	2	yes	—
262	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
263	#398	C₂²×C₄₁	1	8	yes	complemented
264	#396	C₂²×C₄₁	1	16	yes	complemented
265	#394	C₂²×C₄₁	1	8	yes	—
266	#388	C₂²×C₄₁	1	16	yes	complemented
267	#387	C₂²×C₄₁	1	16	yes	complemented
268	#386	C₂²×C₄₁	1	16	yes	—
269	#385	C₂²×C₄₁	1	16	yes	complemented
270	#382	C₂²×C₄₁	1	8	yes	complemented
271	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
272	C₂×#95	C₂²×C₄₁	1	2	yes	—
273	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
274	C₂×#95	C₂²×C₄₁	1	2	yes	—
275	C₂×#95	C₂²×C₄₁	1	2	yes	—
276	C₂×#95	C₂²×C₄₁	1	2	yes	—
277	C₄₁	C₂×#2609	1	1	yes	characteristic, direct product factor, Sylow
278	C₂⁵	C₂³×C₄₁	1	2	yes	—
279	C₂²×D₄	—	2	8	no	—
280	C₂²×D₄	—	4	2	no	—
281	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
282	C₂³×C₄	—	2	8	no	—
283	C₂³×C₄	—	2	8	no	—
284	C₂³×C₄	—	2	8	no	—
285	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
287	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
288	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
289	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
290	C₂³×C₄	C₂³×C₄₁	1	8	yes	—
291	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
292	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
293	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
294	#117	—	2	64	no	—
295	C₂×C₄⋊C₄	—	2	8	no	—
296	C₂×C₄⋊C₄	—	2	8	no	—
297	C₂×C₄⋊C₄	—	2	8	no	—
298	C₂×C₄⋊C₄	—	4	2	no	—
299	C₂×C₄⋊C₄	—	4	2	no	—
300	C₂×C₄⋊C₄	—	4	2	no	—
301	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
302	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
303	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
304	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
305	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
306	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
307	C₂×C₂²⋊C₄	—	2	8	no	—
308	C₂×C₂²⋊C₄	—	2	8	no	—
309	C₂×C₂²⋊C₄	—	2	8	no	—
310	C₂×C₂²⋊C₄	—	2	8	no	—
311	C₂×C₂²⋊C₄	—	4	4	no	—
312	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
313	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
314	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
315	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
316	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
317	C₂×C₄²	—	2	8	no	—
318	C₂×C₄²	D₄×C₄₁	1	8	yes	complemented
319	C₂×C₄²	C₂³×C₄₁	1	8	yes	—
320	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
321	#95	C₂³×C₄₁	1	8	yes	—
322	#95	C₂³×C₄₁	1	8	yes	—
323	#95	C₂³×C₄₁	1	4	yes	—
324	#95	C₂³×C₄₁	1	8	yes	—
325	#95	C₂³×C₄₁	1	4	yes	—
326	#95	C₂³×C₄₁	1	8	yes	—
327	C₂⁴	—	2	4	no	—
328	C₂⁴	—	2	4	no	—
329	C₂⁴	—	2	4	no	—
330	C₂⁴	—	2	4	no	—
331	C₂⁴	—	2	4	no	—
332	C₂⁴	—	2	4	no	—
333	C₂⁴	#41×C₄₁	1	8	yes	—
334	C₂⁴	C₂⁴×C₄₁	1	4	yes	—
335	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
336	C₂×D₄	—	2	16	no	—
337	C₂×D₄	—	4	4	no	—
338	C₂×D₄	—	4	16	no	—
339	C₂²×C₄	—	2	64	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	16	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	16	no	—
348	C₂²×C₄	—	2	16	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	C₂×D₄×C₄₁	1	8	yes	—
363	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
364	C₂²×C₄	#41×C₄₁	1	8	yes	—
365	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
366	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
367	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
368	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
369	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
370	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
371	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
372	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
373	C₄⋊C₄	—	2	16	no	—
374	C₄⋊C₄	—	2	16	no	—
375	C₄⋊C₄	—	2	16	no	—
376	C₄⋊C₄	—	4	4	no	—
377	C₄⋊C₄	—	4	4	no	—
378	C₄⋊C₄	—	4	4	no	—
379	C₂²⋊C₄	—	2	16	no	—
380	C₂²⋊C₄	—	2	16	no	—
381	C₂²⋊C₄	—	2	16	no	—
382	C₂²⋊C₄	—	2	16	no	—
383	C₂²⋊C₄	—	4	8	no	—
384	C₄²	—	2	16	no	—
385	C₄²	C₂×D₄×C₄₁	1	16	yes	complemented
386	C₂³	—	2	16	no	—
387	C₂³	—	2	16	no	—
388	C₂³	—	2	16	no	—
389	C₂³	—	2	4	no	—
390	C₂³	—	2	4	no	—
391	C₂³	—	2	4	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	2	4	no	—
394	C₂³	—	2	4	no	—
395	C₂³	—	4	8	no	—
396	C₂³	—	4	8	no	—
397	C₂³	—	4	8	no	—
398	C₂³	—	4	8	no	—
399	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
400	C₂³	C₂×#41×C₄₁	1	8	yes	—
401	C₂³	C₂×#41×C₄₁	1	4	yes	—
402	C₂³	C₂×#41×C₄₁	1	4	yes	—
403	C₂³	H(5,𝔽₂)×C₄₁	1	2	yes	—
404	C₂³	2₋¹⁺⁴×C₄₁	1	2	yes	—
405	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
406	D₄	—	4	16	no	—
407	C₂×C₄	—	2	64	no	—
408	C₂×C₄	—	2	16	no	—
409	C₂×C₄	—	2	16	no	—
410	C₂×C₄	—	2	8	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	4	8	no	—
431	C₂×C₄	—	4	8	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	—	4	8	no	—
435	C₂×C₄	C₂²×D₄×C₄₁	1	8	yes	—
436	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
437	C₂×C₄	C₂×#41×C₄₁	1	8	yes	—
438	C₂²	—	2	8	no	—
439	C₂²	—	2	8	no	—
440	C₂²	—	2	8	no	—
441	C₂²	—	4	32	no	—
442	C₂²	—	4	4	no	—
443	C₂²	—	4	4	no	—
444	C₂²	—	4	4	no	—
445	C₂²	—	4	4	no	—
446	C₂²	C₄₁×#525	1	8	yes	—
447	C₂²	C₄₁×#537	1	4	yes	—
448	C₂²	C₄₁×#551	1	4	yes	—
449	C₂²	C₄₁×#552	1	8	yes	—
450	C₂²	C₄₁×#555	1	4	yes	—
451	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
452	C₂²	C₂²×#41×C₄₁	1	2	yes	—
453	C₂²	C₂²×#41×C₄₁	1	2	yes	—
454	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
455	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
456	C₄	—	2	8	no	—
457	C₄	—	2	8	no	—
458	C₄	—	2	4	no	—
459	C₄	—	4	4	no	—
460	C₄	—	4	4	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	4	no	—
464	C₂	—	4	8	no	—
465	C₂	C₄₁×#2609	1	8	yes	direct product factor
466	C₂	C₂×C₄₁×#525	1	2	yes	—
467	C₂	C₂×C₄₁×#537	1	1	yes	characteristic
468	C₂	C₂×C₄₁×#551	1	1	yes	characteristic
469	C₂	C₂×C₄₁×#552	1	2	yes	—
470	C₂	C₂×C₄₁×#555	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₁
prime radical	C₂³×D₄×C₄₁	C₂²
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×#117×C₄₁	C₂	semidirect
2. C₄₁×#2609	C₂	direct (N × H)
3. C₂×C₄₁×#398	C₂	semidirect
4. C₂×C₄₁×#396	C₂	semidirect
6. C₂×C₄₁×#388	C₂	semidirect
7. C₂×C₄₁×#387	C₂	semidirect
9. C₂×C₄₁×#385	C₂	semidirect
10. C₂×C₄₁×#382	C₂	semidirect
14. C₂×#117×C₄₁	C₂²	semidirect
28. C₄₁×#398	C₂²	semidirect
29. C₄₁×#396	C₂²	semidirect
31. C₄₁×#388	C₂²	semidirect
32. C₄₁×#387	C₂²	semidirect
34. C₄₁×#385	C₂²	semidirect
35. C₄₁×#382	C₂²	semidirect
82. C₂×C₄²×C₄₁	D₄	semidirect
149. C₄²×C₄₁	C₂×D₄	semidirect
202. C₂×#2609	C₄₁	direct (N × H)
229. C₂²×#117	C₂×C₄₁	semidirect
230. #2609	C₂×C₄₁	direct (N × H)
231. C₂×#398	C₂×C₄₁	semidirect
232. C₂×#396	C₂×C₄₁	semidirect
234. C₂×#388	C₂×C₄₁	semidirect
235. C₂×#387	C₂×C₄₁	semidirect
237. C₂×#385	C₂×C₄₁	semidirect
238. C₂×#382	C₂×C₄₁	semidirect
240. C₂×C₄₁	#2609	direct (N × H)
249. C₂×#117	C₂²×C₄₁	semidirect
263. #398	C₂²×C₄₁	semidirect
264. #396	C₂²×C₄₁	semidirect
266. #388	C₂²×C₄₁	semidirect
267. #387	C₂²×C₄₁	semidirect
269. #385	C₂²×C₄₁	semidirect
270. #382	C₂²×C₄₁	semidirect
277. C₄₁	C₂×#2609	direct (N × H)
318. C₂×C₄²	D₄×C₄₁	semidirect
385. C₄²	C₂×D₄×C₄₁	semidirect
465. C₂	C₄₁×#2609	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×#117×C₄₁	2
C₄₁×#2609	2
C₂×C₄₁×#398	2
C₂×C₄₁×#396	2
C₂×C₄₁×#394	2
C₂×C₄₁×#388	2
C₂×C₄₁×#387	2
C₂×C₄₁×#386	2
C₂×C₄₁×#385	2
C₂×C₄₁×#382	2
C₂×#2609	41

Subgroups — C2×C41×#2609 #23811069

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#2609 #23811069