Subgroups — C₂×C₄₁×#2411 #23810930

Order 10496.

4946 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#123×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#120×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×#117×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₂²⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2411	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₄₁×#396	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₁×#394	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₁×#390	C₂	1	2	yes	maximal, complemented
9	C₂×C₄₁×#388	C₂	1	2	yes	maximal, complemented
10	C₂×C₄₁×#386	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₁×#385	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄₁×#379	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁶×C₄₁	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₄₁	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#123×C₄₁	—	2	8	no	—
19	C₂×#123×C₄₁	C₂²	1	8	yes	complemented
20	C₂×#120×C₄₁	—	2	8	no	—
21	C₂×#120×C₄₁	C₂²	1	8	yes	—
22	C₂×#117×C₄₁	—	2	8	no	—
23	C₂×#117×C₄₁	C₂²	1	8	yes	complemented
24	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	complemented
26	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	complemented
28	C₂²×C₂²⋊C₄×C₄₁	—	2	8	no	—
29	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
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×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
35	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
36	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	8	yes	complemented
38	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	complemented
41	C₂²×C₄²×C₄₁	C₂²	1	2	yes	complemented
42	C₄₁×#396	C₂²	1	16	yes	complemented
43	C₄₁×#394	C₂²	1	16	yes	complemented
44	C₄₁×#390	C₂²	1	16	yes	complemented
45	C₄₁×#388	C₂²	1	16	yes	complemented
46	C₄₁×#386	C₂²	1	8	yes	complemented
47	C₄₁×#385	C₂²	1	8	yes	complemented
48	C₄₁×#379	C₂²	1	8	yes	complemented
49	C₂×#95×C₄₁	C₂²	1	2	yes	complemented
50	C₂×#95×C₄₁	C₂²	1	2	yes	complemented
51	C₂⁵×C₄₁	—	2	4	no	—
52	C₂⁵×C₄₁	—	2	8	no	—
53	C₂⁵×C₄₁	—	2	4	no	—
54	C₂⁵×C₄₁	—	2	4	no	—
55	C₂⁵×C₄₁	—	4	4	no	—
56	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
57	C₂⁵×C₄₁	C₂³	1	2	yes	—
58	C₂⁵×C₄₁	C₂³	1	4	yes	—
59	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₄₁	—	2	4	no	—
61	C₂²×D₄×C₄₁	—	2	4	no	—
62	C₂²×D₄×C₄₁	—	2	8	no	—
63	C₂²×D₄×C₄₁	—	2	4	no	—
64	C₂²×D₄×C₄₁	—	2	8	no	—
65	C₂²×D₄×C₄₁	—	4	4	no	—
66	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
67	C₂²×D₄×C₄₁	C₂³	1	8	yes	—
68	C₂³×C₄×C₄₁	—	2	4	no	—
69	C₂³×C₄×C₄₁	—	2	4	no	—
70	C₂³×C₄×C₄₁	—	2	4	no	—
71	C₂³×C₄×C₄₁	—	4	4	no	—
72	C₂³×C₄×C₄₁	D₄	1	8	yes	complemented
73	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
74	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
79	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
80	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
82	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
83	#123×C₄₁	—	2	32	no	—
84	#120×C₄₁	—	2	32	no	—
85	#117×C₄₁	—	2	32	no	—
86	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
87	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
88	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
89	C₂×C₄⋊C₄×C₄₁	—	4	4	no	—
90	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	complemented
91	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	complemented
92	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	complemented
93	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	complemented
94	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
95	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
96	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
97	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
98	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
99	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
100	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
101	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
102	C₂×C₂²⋊C₄×C₄₁	—	2	32	no	—
103	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
104	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
105	C₂×C₂²⋊C₄×C₄₁	D₄	1	8	yes	—
106	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
107	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
108	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
110	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
111	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
112	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
113	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	complemented
115	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	complemented
116	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	complemented
117	C₂×C₄²×C₄₁	—	2	8	no	—
118	C₂×C₄²×C₄₁	C₂³	1	8	yes	complemented
119	#95×C₄₁	C₂³	1	8	yes	complemented
120	#95×C₄₁	C₂³	1	8	yes	complemented
121	C₂⁴×C₄₁	—	2	4	no	—
122	C₂⁴×C₄₁	—	2	4	no	—
123	C₂⁴×C₄₁	—	2	32	no	—
124	C₂⁴×C₄₁	—	2	8	no	—
125	C₂⁴×C₄₁	—	2	4	no	—
126	C₂⁴×C₄₁	—	2	4	no	—
127	C₂⁴×C₄₁	—	2	16	no	—
128	C₂⁴×C₄₁	—	2	4	no	—
129	C₂⁴×C₄₁	—	2	4	no	—
130	C₂⁴×C₄₁	—	2	4	no	—
131	C₂⁴×C₄₁	—	2	4	no	—
132	C₂⁴×C₄₁	—	2	2	no	—
133	C₂⁴×C₄₁	—	2	8	no	—
134	C₂⁴×C₄₁	—	2	2	no	—
135	C₂⁴×C₄₁	—	2	2	no	—
136	C₂⁴×C₄₁	—	2	4	no	—
137	C₂⁴×C₄₁	—	2	8	no	—
138	C₂⁴×C₄₁	—	2	4	no	—
139	C₂⁴×C₄₁	—	4	8	no	—
140	C₂⁴×C₄₁	—	4	32	no	—
141	C₂⁴×C₄₁	—	4	32	no	—
142	C₂⁴×C₄₁	—	4	16	no	—
143	C₂⁴×C₄₁	—	4	16	no	—
144	C₂⁴×C₄₁	C₂×D₄	1	4	yes	—
145	C₂⁴×C₄₁	C₂×D₄	1	4	yes	—
146	C₂⁴×C₄₁	#41	1	8	yes	—
147	C₂⁴×C₄₁	#41	1	4	yes	—
148	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
149	C₂⁴×C₄₁	C₂⁴	1	4	yes	—
150	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
151	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
152	C₂×D₄×C₄₁	—	2	8	no	—
153	C₂×D₄×C₄₁	—	2	8	no	—
154	C₂×D₄×C₄₁	—	2	16	no	—
155	C₂×D₄×C₄₁	—	2	8	no	—
156	C₂×D₄×C₄₁	—	2	16	no	—
157	C₂×D₄×C₄₁	—	4	8	no	—
158	C₂×D₄×C₄₁	—	4	32	no	—
159	C₂×D₄×C₄₁	—	4	16	no	—
160	C₂²×C₄×C₄₁	—	2	32	no	—
161	C₂²×C₄×C₄₁	—	2	2	no	—
162	C₂²×C₄×C₄₁	—	2	2	no	—
163	C₂²×C₄×C₄₁	—	2	8	no	—
164	C₂²×C₄×C₄₁	—	2	2	no	—
165	C₂²×C₄×C₄₁	—	2	2	no	—
166	C₂²×C₄×C₄₁	—	2	8	no	—
167	C₂²×C₄×C₄₁	—	2	4	no	—
168	C₂²×C₄×C₄₁	—	2	4	no	—
169	C₂²×C₄×C₄₁	—	2	4	no	—
170	C₂²×C₄×C₄₁	—	2	2	no	—
171	C₂²×C₄×C₄₁	—	2	2	no	—
172	C₂²×C₄×C₄₁	—	2	8	no	—
173	C₂²×C₄×C₄₁	—	2	4	no	—
174	C₂²×C₄×C₄₁	—	2	2	no	—
175	C₂²×C₄×C₄₁	—	2	2	no	—
176	C₂²×C₄×C₄₁	—	2	4	no	—
177	C₂²×C₄×C₄₁	—	2	4	no	—
178	C₂²×C₄×C₄₁	—	2	2	no	—
179	C₂²×C₄×C₄₁	—	2	4	no	—
180	C₂²×C₄×C₄₁	—	2	4	no	—
181	C₂²×C₄×C₄₁	—	2	4	no	—
182	C₂²×C₄×C₄₁	—	2	4	no	—
183	C₂²×C₄×C₄₁	—	4	8	no	—
184	C₂²×C₄×C₄₁	—	4	16	no	—
185	C₂²×C₄×C₄₁	C₂×D₄	1	8	yes	—
186	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
187	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
188	C₂²×C₄×C₄₁	C₂×D₄	1	16	yes	complemented
189	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
191	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
197	C₄⋊C₄×C₄₁	—	2	16	no	—
198	C₄⋊C₄×C₄₁	—	2	8	no	—
199	C₄⋊C₄×C₄₁	—	2	8	no	—
200	C₄⋊C₄×C₄₁	—	4	8	no	—
201	C₂²⋊C₄×C₄₁	—	2	8	no	—
202	C₂²⋊C₄×C₄₁	—	2	8	no	—
203	C₂²⋊C₄×C₄₁	—	2	16	no	—
204	C₂²⋊C₄×C₄₁	—	2	16	no	—
205	C₂²⋊C₄×C₄₁	—	2	16	no	—
206	C₂²⋊C₄×C₄₁	—	2	16	no	—
207	C₂²⋊C₄×C₄₁	—	2	8	no	—
208	C₂²⋊C₄×C₄₁	—	2	8	no	—
209	C₂²⋊C₄×C₄₁	—	4	8	no	—
210	C₂²⋊C₄×C₄₁	—	4	8	no	—
211	C₂²⋊C₄×C₄₁	C₂×D₄	1	16	yes	—
212	C₄²×C₄₁	—	2	16	no	—
213	C₂³×C₄₁	—	2	8	no	—
214	C₂³×C₄₁	—	2	8	no	—
215	C₂³×C₄₁	—	2	16	no	—
216	C₂³×C₄₁	—	2	16	no	—
217	C₂³×C₄₁	—	2	4	no	—
218	C₂³×C₄₁	—	2	4	no	—
219	C₂³×C₄₁	—	2	32	no	—
220	C₂³×C₄₁	—	2	16	no	—
221	C₂³×C₄₁	—	2	16	no	—
222	C₂³×C₄₁	—	2	16	no	—
223	C₂³×C₄₁	—	2	4	no	—
224	C₂³×C₄₁	—	2	4	no	—
225	C₂³×C₄₁	—	2	4	no	—
226	C₂³×C₄₁	—	2	4	no	—
227	C₂³×C₄₁	—	2	4	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	—	2	4	no	—
234	C₂³×C₄₁	—	4	32	no	—
235	C₂³×C₄₁	—	4	32	no	—
236	C₂³×C₄₁	—	4	128	no	—
237	C₂³×C₄₁	—	4	16	no	—
238	C₂³×C₄₁	—	4	16	no	—
239	C₂³×C₄₁	—	4	8	no	—
240	C₂³×C₄₁	—	4	8	no	—
241	C₂³×C₄₁	—	4	8	no	—
242	C₂³×C₄₁	—	4	8	no	—
243	C₂³×C₄₁	—	4	4	no	—
244	C₂³×C₄₁	—	4	4	no	—
245	C₂³×C₄₁	—	4	4	no	—
246	C₂³×C₄₁	—	4	8	no	—
247	C₂³×C₄₁	—	4	8	no	—
248	C₂³×C₄₁	#121	1	16	yes	—
249	C₂³×C₄₁	C₂²×D₄	1	4	yes	—
250	C₂³×C₄₁	C₂²×D₄	1	4	yes	—
251	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
252	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
253	C₂³×C₄₁	C₂×#41	1	8	yes	—
254	C₂³×C₄₁	C₂×#41	1	4	yes	—
255	C₂³×C₄₁	C₂×#41	1	2	yes	—
256	C₂³×C₄₁	C₂×#41	1	4	yes	—
257	C₂³×C₄₁	H(5,𝔽₂)	1	4	yes	—
258	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
259	D₄×C₄₁	—	4	32	no	—
260	D₄×C₄₁	—	4	16	no	—
261	C₂×C₄×C₄₁	—	2	8	no	—
262	C₂×C₄×C₄₁	—	2	8	no	—
263	C₂×C₄×C₄₁	—	2	32	no	—
264	C₂×C₄×C₄₁	—	2	16	no	—
265	C₂×C₄×C₄₁	—	2	2	no	—
266	C₂×C₄×C₄₁	—	2	2	no	—
267	C₂×C₄×C₄₁	—	2	2	no	—
268	C₂×C₄×C₄₁	—	2	2	no	—
269	C₂×C₄×C₄₁	—	2	4	no	—
270	C₂×C₄×C₄₁	—	2	4	no	—
271	C₂×C₄×C₄₁	—	2	4	no	—
272	C₂×C₄×C₄₁	—	2	2	no	—
273	C₂×C₄×C₄₁	—	2	2	no	—
274	C₂×C₄×C₄₁	—	2	4	no	—
275	C₂×C₄×C₄₁	—	2	2	no	—
276	C₂×C₄×C₄₁	—	2	2	no	—
277	C₂×C₄×C₄₁	—	2	4	no	—
278	C₂×C₄×C₄₁	—	2	4	no	—
279	C₂×C₄×C₄₁	—	2	2	no	—
280	C₂×C₄×C₄₁	—	2	4	no	—
281	C₂×C₄×C₄₁	—	2	4	no	—
282	C₂×C₄×C₄₁	—	2	4	no	—
283	C₂×C₄×C₄₁	—	2	4	no	—
284	C₂×C₄×C₄₁	—	4	16	no	—
285	C₂×C₄×C₄₁	—	4	4	no	—
286	C₂×C₄×C₄₁	—	4	4	no	—
287	C₂×C₄×C₄₁	—	4	4	no	—
288	C₂×C₄×C₄₁	—	4	8	no	—
289	C₂×C₄×C₄₁	—	4	8	no	—
290	C₂×C₄×C₄₁	C₂²×D₄	1	8	yes	—
291	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
292	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
293	C₂×#2411	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
294	C₂²×C₄₁	—	2	32	no	—
295	C₂²×C₄₁	—	2	4	no	—
296	C₂²×C₄₁	—	2	4	no	—
297	C₂²×C₄₁	—	2	8	no	—
298	C₂²×C₄₁	—	2	8	no	—
299	C₂²×C₄₁	—	2	8	no	—
300	C₂²×C₄₁	—	2	8	no	—
301	C₂²×C₄₁	—	2	8	no	—
302	C₂²×C₄₁	—	4	64	no	—
303	C₂²×C₄₁	—	4	4	no	—
304	C₂²×C₄₁	—	4	32	no	—
305	C₂²×C₄₁	—	4	4	no	—
306	C₂²×C₄₁	—	4	4	no	—
307	C₂²×C₄₁	—	4	4	no	—
308	C₂²×C₄₁	—	4	2	no	—
309	C₂²×C₄₁	—	4	2	no	—
310	C₂²×C₄₁	—	4	2	no	—
311	C₂²×C₄₁	—	4	4	no	—
312	C₂²×C₄₁	—	4	4	no	—
313	C₂²×C₄₁	—	8	8	no	—
314	C₂²×C₄₁	C₂×#121	1	8	yes	—
315	C₂²×C₄₁	C₂×#121	1	4	yes	—
316	C₂²×C₄₁	#525	1	4	yes	—
317	C₂²×C₄₁	#535	1	4	yes	—
318	C₂²×C₄₁	#546	1	8	yes	—
319	C₂²×C₄₁	#551	1	8	yes	—
320	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
321	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
322	C₂²×C₄₁	C₂²×#41	1	1	yes	characteristic
323	C₂²×C₄₁	C₂²×#41	1	2	yes	—
324	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	2	yes	—
325	C₄×C₄₁	—	2	4	no	—
326	C₄×C₄₁	—	2	4	no	—
327	C₄×C₄₁	—	2	8	no	—
328	C₄×C₄₁	—	4	2	no	—
329	C₄×C₄₁	—	4	2	no	—
330	C₄×C₄₁	—	4	2	no	—
331	C₄×C₄₁	—	4	4	no	—
332	C₄×C₄₁	—	4	4	no	—
333	C₂²×#123	C₂×C₄₁	1	1	yes	characteristic, complemented
334	C₂²×#120	C₂×C₄₁	1	1	yes	characteristic
335	C₂²×#117	C₂×C₄₁	1	1	yes	characteristic, complemented
336	C₂³×C₂²⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
337	#2411	C₂×C₄₁	1	16	yes	direct product factor
338	C₂×#396	C₂×C₄₁	1	2	yes	complemented
339	C₂×#394	C₂×C₄₁	1	2	yes	complemented
340	C₂×#390	C₂×C₄₁	1	2	yes	complemented
341	C₂×#388	C₂×C₄₁	1	2	yes	complemented
342	C₂×#386	C₂×C₄₁	1	1	yes	characteristic, complemented
343	C₂×#385	C₂×C₄₁	1	1	yes	characteristic, complemented
344	C₂×#379	C₂×C₄₁	1	1	yes	characteristic, complemented
345	C₂×C₄₁	—	2	8	no	—
346	C₂×C₄₁	—	4	8	no	—
347	C₂×C₄₁	—	8	2	no	—
348	C₂×C₄₁	#2411	1	8	yes	direct product factor
349	C₂×C₄₁	C₂²×#121	1	1	yes	characteristic
350	C₂×C₄₁	C₂×#525	1	1	yes	characteristic
351	C₂×C₄₁	C₂×#535	1	1	yes	characteristic
352	C₂×C₄₁	C₂×#546	1	2	yes	—
353	C₂×C₄₁	C₂×#551	1	2	yes	—
354	C₂⁶	C₂²×C₄₁	1	1	yes	characteristic
355	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
356	C₂³×D₄	C₂²×C₄₁	1	2	yes	—
357	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
358	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
359	C₂×#123	—	2	8	no	—
360	C₂×#123	C₂²×C₄₁	1	8	yes	complemented
361	C₂×#120	—	2	8	no	—
362	C₂×#120	C₂²×C₄₁	1	8	yes	—
363	C₂×#117	—	2	8	no	—
364	C₂×#117	C₂²×C₄₁	1	8	yes	complemented
365	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	complemented
366	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
367	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
368	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	complemented
369	C₂²×C₂²⋊C₄	—	2	8	no	—
370	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
371	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
372	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
373	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
374	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
375	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
376	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
377	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
378	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	8	yes	complemented
379	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
380	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
381	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	complemented
382	C₂²×C₄²	C₂²×C₄₁	1	2	yes	complemented
383	#396	C₂²×C₄₁	1	16	yes	complemented
384	#394	C₂²×C₄₁	1	16	yes	complemented
385	#390	C₂²×C₄₁	1	16	yes	complemented
386	#388	C₂²×C₄₁	1	16	yes	complemented
387	#386	C₂²×C₄₁	1	8	yes	complemented
388	#385	C₂²×C₄₁	1	8	yes	complemented
389	#379	C₂²×C₄₁	1	8	yes	complemented
390	C₂×#95	C₂²×C₄₁	1	2	yes	complemented
391	C₂×#95	C₂²×C₄₁	1	2	yes	complemented
392	C₄₁	C₂×#2411	1	1	yes	characteristic, direct product factor, Sylow
393	C₂⁵	—	2	4	no	—
394	C₂⁵	—	2	8	no	—
395	C₂⁵	—	2	4	no	—
396	C₂⁵	—	2	4	no	—
397	C₂⁵	—	4	4	no	—
398	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
399	C₂⁵	C₂³×C₄₁	1	2	yes	—
400	C₂⁵	C₂³×C₄₁	1	4	yes	—
401	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
402	C₂²×D₄	—	2	4	no	—
403	C₂²×D₄	—	2	4	no	—
404	C₂²×D₄	—	2	8	no	—
405	C₂²×D₄	—	2	4	no	—
406	C₂²×D₄	—	2	8	no	—
407	C₂²×D₄	—	4	4	no	—
408	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
409	C₂²×D₄	C₂³×C₄₁	1	8	yes	—
410	C₂³×C₄	—	2	4	no	—
411	C₂³×C₄	—	2	4	no	—
412	C₂³×C₄	—	2	4	no	—
413	C₂³×C₄	—	4	4	no	—
414	C₂³×C₄	D₄×C₄₁	1	8	yes	complemented
415	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
416	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
417	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
418	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
419	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
420	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
421	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
422	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
423	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
424	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
425	#123	—	2	32	no	—
426	#120	—	2	32	no	—
427	#117	—	2	32	no	—
428	C₂×C₄⋊C₄	—	2	8	no	—
429	C₂×C₄⋊C₄	—	2	4	no	—
430	C₂×C₄⋊C₄	—	2	4	no	—
431	C₂×C₄⋊C₄	—	4	4	no	—
432	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	complemented
433	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	complemented
434	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	complemented
435	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	complemented
436	C₂×C₂²⋊C₄	—	2	4	no	—
437	C₂×C₂²⋊C₄	—	2	4	no	—
438	C₂×C₂²⋊C₄	—	2	8	no	—
439	C₂×C₂²⋊C₄	—	2	8	no	—
440	C₂×C₂²⋊C₄	—	2	8	no	—
441	C₂×C₂²⋊C₄	—	2	8	no	—
442	C₂×C₂²⋊C₄	—	2	4	no	—
443	C₂×C₂²⋊C₄	—	2	4	no	—
444	C₂×C₂²⋊C₄	—	2	32	no	—
445	C₂×C₂²⋊C₄	—	4	4	no	—
446	C₂×C₂²⋊C₄	—	4	4	no	—
447	C₂×C₂²⋊C₄	D₄×C₄₁	1	8	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	complemented
457	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	complemented
458	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	complemented
459	C₂×C₄²	—	2	8	no	—
460	C₂×C₄²	C₂³×C₄₁	1	8	yes	complemented
461	#95	C₂³×C₄₁	1	8	yes	complemented
462	#95	C₂³×C₄₁	1	8	yes	complemented
463	C₂⁴	—	2	4	no	—
464	C₂⁴	—	2	4	no	—
465	C₂⁴	—	2	32	no	—
466	C₂⁴	—	2	8	no	—
467	C₂⁴	—	2	4	no	—
468	C₂⁴	—	2	4	no	—
469	C₂⁴	—	2	16	no	—
470	C₂⁴	—	2	4	no	—
471	C₂⁴	—	2	4	no	—
472	C₂⁴	—	2	4	no	—
473	C₂⁴	—	2	4	no	—
474	C₂⁴	—	2	2	no	—
475	C₂⁴	—	2	8	no	—
476	C₂⁴	—	2	2	no	—
477	C₂⁴	—	2	2	no	—
478	C₂⁴	—	2	4	no	—
479	C₂⁴	—	2	8	no	—
480	C₂⁴	—	2	4	no	—
481	C₂⁴	—	4	8	no	—
482	C₂⁴	—	4	32	no	—
483	C₂⁴	—	4	32	no	—
484	C₂⁴	—	4	16	no	—
485	C₂⁴	—	4	16	no	—
486	C₂⁴	C₂×D₄×C₄₁	1	4	yes	—
487	C₂⁴	C₂×D₄×C₄₁	1	4	yes	—
488	C₂⁴	#41×C₄₁	1	8	yes	—
489	C₂⁴	#41×C₄₁	1	4	yes	—
490	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
491	C₂⁴	C₂⁴×C₄₁	1	4	yes	—
492	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
493	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
494	C₂×D₄	—	2	8	no	—
495	C₂×D₄	—	2	8	no	—
496	C₂×D₄	—	2	16	no	—
497	C₂×D₄	—	2	8	no	—
498	C₂×D₄	—	2	16	no	—
499	C₂×D₄	—	4	8	no	—
500	C₂×D₄	—	4	32	no	—
501	C₂×D₄	—	4	16	no	—
502	C₂²×C₄	—	2	32	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	8	no	—
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	2	2	no	—
508	C₂²×C₄	—	2	8	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	2	4	no	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	8	no	—
515	C₂²×C₄	—	2	4	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	4	no	—
519	C₂²×C₄	—	2	4	no	—
520	C₂²×C₄	—	2	2	no	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	—	2	4	no	—
523	C₂²×C₄	—	2	4	no	—
524	C₂²×C₄	—	2	4	no	—
525	C₂²×C₄	—	4	8	no	—
526	C₂²×C₄	—	4	16	no	—
527	C₂²×C₄	C₂×D₄×C₄₁	1	8	yes	—
528	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
529	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
530	C₂²×C₄	C₂×D₄×C₄₁	1	16	yes	complemented
531	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
532	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
533	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
534	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
535	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
536	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
537	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
538	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
539	C₄⋊C₄	—	2	16	no	—
540	C₄⋊C₄	—	2	8	no	—
541	C₄⋊C₄	—	2	8	no	—
542	C₄⋊C₄	—	4	8	no	—
543	C₂²⋊C₄	—	2	8	no	—
544	C₂²⋊C₄	—	2	8	no	—
545	C₂²⋊C₄	—	2	16	no	—
546	C₂²⋊C₄	—	2	16	no	—
547	C₂²⋊C₄	—	2	16	no	—
548	C₂²⋊C₄	—	2	16	no	—
549	C₂²⋊C₄	—	2	8	no	—
550	C₂²⋊C₄	—	2	8	no	—
551	C₂²⋊C₄	—	4	8	no	—
552	C₂²⋊C₄	—	4	8	no	—
553	C₂²⋊C₄	C₂×D₄×C₄₁	1	16	yes	—
554	C₄²	—	2	16	no	—
555	C₂³	—	2	8	no	—
556	C₂³	—	2	8	no	—
557	C₂³	—	2	16	no	—
558	C₂³	—	2	16	no	—
559	C₂³	—	2	4	no	—
560	C₂³	—	2	4	no	—
561	C₂³	—	2	32	no	—
562	C₂³	—	2	16	no	—
563	C₂³	—	2	16	no	—
564	C₂³	—	2	16	no	—
565	C₂³	—	2	4	no	—
566	C₂³	—	2	4	no	—
567	C₂³	—	2	4	no	—
568	C₂³	—	2	4	no	—
569	C₂³	—	2	4	no	—
570	C₂³	—	2	4	no	—
571	C₂³	—	2	2	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	4	no	—
575	C₂³	—	2	4	no	—
576	C₂³	—	4	32	no	—
577	C₂³	—	4	32	no	—
578	C₂³	—	4	128	no	—
579	C₂³	—	4	16	no	—
580	C₂³	—	4	16	no	—
581	C₂³	—	4	8	no	—
582	C₂³	—	4	8	no	—
583	C₂³	—	4	8	no	—
584	C₂³	—	4	8	no	—
585	C₂³	—	4	4	no	—
586	C₂³	—	4	4	no	—
587	C₂³	—	4	4	no	—
588	C₂³	—	4	8	no	—
589	C₂³	—	4	8	no	—
590	C₂³	#121×C₄₁	1	16	yes	—
591	C₂³	C₂²×D₄×C₄₁	1	4	yes	—
592	C₂³	C₂²×D₄×C₄₁	1	4	yes	—
593	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
594	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
595	C₂³	C₂×#41×C₄₁	1	8	yes	—
596	C₂³	C₂×#41×C₄₁	1	4	yes	—
597	C₂³	C₂×#41×C₄₁	1	2	yes	—
598	C₂³	C₂×#41×C₄₁	1	4	yes	—
599	C₂³	H(5,𝔽₂)×C₄₁	1	4	yes	—
600	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
601	D₄	—	4	32	no	—
602	D₄	—	4	16	no	—
603	C₂×C₄	—	2	8	no	—
604	C₂×C₄	—	2	8	no	—
605	C₂×C₄	—	2	32	no	—
606	C₂×C₄	—	2	16	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	4	16	no	—
627	C₂×C₄	—	4	4	no	—
628	C₂×C₄	—	4	4	no	—
629	C₂×C₄	—	4	8	no	—
630	C₂×C₄	—	4	4	no	—
631	C₂×C₄	—	4	8	no	—
632	C₂×C₄	C₂²×D₄×C₄₁	1	8	yes	—
633	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
634	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
635	C₂²	—	2	32	no	—
636	C₂²	—	2	4	no	—
637	C₂²	—	2	4	no	—
638	C₂²	—	2	8	no	—
639	C₂²	—	2	8	no	—
640	C₂²	—	2	8	no	—
641	C₂²	—	2	8	no	—
642	C₂²	—	2	8	no	—
643	C₂²	—	4	64	no	—
644	C₂²	—	4	4	no	—
645	C₂²	—	4	32	no	—
646	C₂²	—	4	4	no	—
647	C₂²	—	4	4	no	—
648	C₂²	—	4	4	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	4	4	no	—
653	C₂²	—	4	4	no	—
654	C₂²	—	8	8	no	—
655	C₂²	C₂×#121×C₄₁	1	8	yes	—
656	C₂²	C₂×#121×C₄₁	1	4	yes	—
657	C₂²	C₄₁×#525	1	4	yes	—
658	C₂²	C₄₁×#535	1	4	yes	—
659	C₂²	C₄₁×#546	1	8	yes	—
660	C₂²	C₄₁×#551	1	8	yes	—
661	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
662	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
663	C₂²	C₂²×#41×C₄₁	1	1	yes	characteristic
664	C₂²	C₂²×#41×C₄₁	1	2	yes	—
665	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	2	yes	—
666	C₄	—	2	4	no	—
667	C₄	—	2	4	no	—
668	C₄	—	2	8	no	—
669	C₄	—	4	2	no	—
670	C₄	—	4	2	no	—
671	C₄	—	4	4	no	—
672	C₄	—	4	2	no	—
673	C₄	—	4	4	no	—
674	C₂	—	2	8	no	—
675	C₂	—	4	8	no	—
676	C₂	—	8	2	no	—
677	C₂	C₄₁×#2411	1	8	yes	direct product factor
678	C₂	C₂²×#121×C₄₁	1	1	yes	characteristic
679	C₂	C₂×C₄₁×#525	1	1	yes	characteristic
680	C₂	C₂×C₄₁×#535	1	1	yes	characteristic
681	C₂	C₂×C₄₁×#546	1	2	yes	—
682	C₂	C₂×C₄₁×#551	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₄₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₁
prime radical	C₂²×#120×C₄₁	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×#123×C₄₁	C₂	semidirect
3. C₂²×#117×C₄₁	C₂	semidirect
4. C₂³×C₂²⋊C₄×C₄₁	C₂	semidirect
5. C₄₁×#2411	C₂	direct (N × H)
6. C₂×C₄₁×#396	C₂	semidirect
7. C₂×C₄₁×#394	C₂	semidirect
8. C₂×C₄₁×#390	C₂	semidirect
9. C₂×C₄₁×#388	C₂	semidirect
10. C₂×C₄₁×#386	C₂	semidirect
11. C₂×C₄₁×#385	C₂	semidirect
12. C₂×C₄₁×#379	C₂	semidirect
19. C₂×#123×C₄₁	C₂²	semidirect
23. C₂×#117×C₄₁	C₂²	semidirect
24. C₂²×C₄⋊C₄×C₄₁	C₂²	semidirect
25. C₂²×C₄⋊C₄×C₄₁	C₂²	semidirect
26. C₂²×C₄⋊C₄×C₄₁	C₂²	semidirect
27. C₂²×C₄⋊C₄×C₄₁	C₂²	semidirect
37. C₂²×C₂²⋊C₄×C₄₁	C₂²	semidirect
38. C₂²×C₂²⋊C₄×C₄₁	C₂²	semidirect
39. C₂²×C₂²⋊C₄×C₄₁	C₂²	semidirect
40. C₂²×C₂²⋊C₄×C₄₁	C₂²	semidirect
41. C₂²×C₄²×C₄₁	C₂²	semidirect
42. C₄₁×#396	C₂²	semidirect
43. C₄₁×#394	C₂²	semidirect
44. C₄₁×#390	C₂²	semidirect
45. C₄₁×#388	C₂²	semidirect
46. C₄₁×#386	C₂²	semidirect
47. C₄₁×#385	C₂²	semidirect
48. C₄₁×#379	C₂²	semidirect
49. C₂×#95×C₄₁	C₂²	semidirect
50. C₂×#95×C₄₁	C₂²	semidirect
72. C₂³×C₄×C₄₁	D₄	semidirect
90. C₂×C₄⋊C₄×C₄₁	C₂³	semidirect
91. C₂×C₄⋊C₄×C₄₁	C₂³	semidirect
92. C₂×C₄⋊C₄×C₄₁	C₂³	semidirect
93. C₂×C₄⋊C₄×C₄₁	C₂³	semidirect
114. C₂×C₂²⋊C₄×C₄₁	C₂³	semidirect
115. C₂×C₂²⋊C₄×C₄₁	C₂³	semidirect
116. C₂×C₂²⋊C₄×C₄₁	C₂³	semidirect
118. C₂×C₄²×C₄₁	C₂³	semidirect
119. #95×C₄₁	C₂³	semidirect
120. #95×C₄₁	C₂³	semidirect
188. C₂²×C₄×C₄₁	C₂×D₄	semidirect
293. C₂×#2411	C₄₁	direct (N × H)
333. C₂²×#123	C₂×C₄₁	semidirect
335. C₂²×#117	C₂×C₄₁	semidirect
336. C₂³×C₂²⋊C₄	C₂×C₄₁	semidirect
337. #2411	C₂×C₄₁	direct (N × H)
338. C₂×#396	C₂×C₄₁	semidirect
339. C₂×#394	C₂×C₄₁	semidirect
340. C₂×#390	C₂×C₄₁	semidirect
341. C₂×#388	C₂×C₄₁	semidirect
342. C₂×#386	C₂×C₄₁	semidirect
343. C₂×#385	C₂×C₄₁	semidirect
344. C₂×#379	C₂×C₄₁	semidirect
348. C₂×C₄₁	#2411	direct (N × H)
360. C₂×#123	C₂²×C₄₁	semidirect
364. C₂×#117	C₂²×C₄₁	semidirect
365. C₂²×C₄⋊C₄	C₂²×C₄₁	semidirect
366. C₂²×C₄⋊C₄	C₂²×C₄₁	semidirect
367. C₂²×C₄⋊C₄	C₂²×C₄₁	semidirect
368. C₂²×C₄⋊C₄	C₂²×C₄₁	semidirect
378. C₂²×C₂²⋊C₄	C₂²×C₄₁	semidirect
379. C₂²×C₂²⋊C₄	C₂²×C₄₁	semidirect
380. C₂²×C₂²⋊C₄	C₂²×C₄₁	semidirect
381. C₂²×C₂²⋊C₄	C₂²×C₄₁	semidirect
382. C₂²×C₄²	C₂²×C₄₁	semidirect
383. #396	C₂²×C₄₁	semidirect
384. #394	C₂²×C₄₁	semidirect
385. #390	C₂²×C₄₁	semidirect
386. #388	C₂²×C₄₁	semidirect
387. #386	C₂²×C₄₁	semidirect
388. #385	C₂²×C₄₁	semidirect
389. #379	C₂²×C₄₁	semidirect
390. C₂×#95	C₂²×C₄₁	semidirect
391. C₂×#95	C₂²×C₄₁	semidirect
392. C₄₁	C₂×#2411	direct (N × H)
414. C₂³×C₄	D₄×C₄₁	semidirect
432. C₂×C₄⋊C₄	C₂³×C₄₁	semidirect
433. C₂×C₄⋊C₄	C₂³×C₄₁	semidirect
434. C₂×C₄⋊C₄	C₂³×C₄₁	semidirect
435. C₂×C₄⋊C₄	C₂³×C₄₁	semidirect
456. C₂×C₂²⋊C₄	C₂³×C₄₁	semidirect
457. C₂×C₂²⋊C₄	C₂³×C₄₁	semidirect
458. C₂×C₂²⋊C₄	C₂³×C₄₁	semidirect
460. C₂×C₄²	C₂³×C₄₁	semidirect
461. #95	C₂³×C₄₁	semidirect
462. #95	C₂³×C₄₁	semidirect
530. C₂²×C₄	C₂×D₄×C₄₁	semidirect
677. C₂	C₄₁×#2411	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×#123×C₄₁	2
C₂²×#120×C₄₁	2
C₂²×#117×C₄₁	2
C₂³×C₂²⋊C₄×C₄₁	2
C₄₁×#2411	2
C₂×C₄₁×#396	2
C₂×C₄₁×#394	2
C₂×C₄₁×#390	2
C₂×C₄₁×#388	2
C₂×C₄₁×#386	2
C₂×C₄₁×#385	2
C₂×C₄₁×#379	2
C₂×#2411	41

Subgroups — C2×C41×#2411 #23810930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#2411 #23810930