Subgroups — C₄₁×#23127 #23799328

Order 10496.

1078 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#466	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2361	C₂	1	2	yes	maximal, complemented
3	C₄₁×#1934	C₂	1	2	yes	maximal, complemented
4	C₄₁×#1918	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1879	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1874	C₂	1	2	yes	maximal, complemented
7	C₄×#102×C₄₁	C₂	1	2	yes	maximal, complemented
8	C₈×C₂²⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₁×#340	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
12	C₂×#121×C₄₁	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₄₁	—	2	2	no	—
14	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
16	C₄₁×#466	C₄	1	8	yes	complemented
17	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#102×C₄₁	C₂²	1	2	yes	—
19	C₂×#102×C₄₁	C₂²	1	2	yes	—
20	C₂×#102×C₄₁	C₂²	1	2	yes	—
21	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
23	C₄₁×#390	C₂²	1	2	yes	—
24	C₄₁×#389	C₂²	1	2	yes	—
25	C₄₁×#388	—	2	2	no	—
26	C₄₁×#386	—	2	2	no	—
27	C₄₁×#385	—	2	2	no	—
28	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
29	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
30	C₄₁×#340	C₂²	1	1	yes	characteristic
31	C₄₁×#340	C₂²	1	2	yes	—
32	C₄₁×#340	C₂²	1	2	yes	—
33	C₄₁×#340	C₂²	1	2	yes	—
34	C₄₁×#340	C₂²	1	1	yes	characteristic
35	C₄₁×#336	C₂²	1	2	yes	—
36	C₂²×D₄×C₄₁	—	2	2	no	—
37	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
38	C₂³×C₄×C₄₁	—	2	2	no	—
39	C₂³×C₄×C₄₁	—	2	2	no	—
40	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
41	C₂×D₈×C₄₁	—	4	2	no	—
42	C₂×D₈×C₄₁	C₂×C₄	1	4	yes	complemented
43	C₂²×C₈×C₄₁	—	4	2	no	—
44	C₂²×C₈×C₄₁	C₂×C₄	1	4	yes	complemented
45	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
46	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
48	#121×C₄₁	—	2	4	no	—
49	#121×C₄₁	C₂×C₄	1	8	yes	complemented
50	C₄×D₄×C₄₁	—	2	4	no	—
51	C₄×D₄×C₄₁	—	4	2	no	—
52	C₄×D₄×C₄₁	—	4	8	no	—
53	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
54	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
57	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₁	—	2	2	no	—
67	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
68	#107×C₄₁	C₂×C₄	1	4	yes	complemented
69	#102×C₄₁	—	2	4	no	—
70	#102×C₄₁	—	4	2	no	—
71	#102×C₄₁	C₂×C₄	1	8	yes	complemented
72	C₂²⋊C₈×C₄₁	—	2	2	no	—
73	C₄×C₈×C₄₁	—	4	2	no	—
74	#95×C₄₁	—	2	2	no	—
75	#95×C₄₁	—	2	2	no	—
76	#95×C₄₁	D₄	1	2	yes	—
77	C₂⁴×C₄₁	—	2	2	no	—
78	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
79	C₂×D₄×C₄₁	—	2	8	no	—
80	C₂×D₄×C₄₁	—	2	2	no	—
81	C₂×D₄×C₄₁	—	2	2	no	—
82	C₂×D₄×C₄₁	—	2	2	no	—
83	C₂×D₄×C₄₁	—	2	2	no	—
84	C₂×D₄×C₄₁	—	2	2	no	—
85	C₂×D₄×C₄₁	—	4	4	no	—
86	C₂×D₄×C₄₁	—	4	4	no	—
87	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₄₁	—	2	2	no	—
89	C₂²×C₄×C₄₁	—	2	2	no	—
90	C₂²×C₄×C₄₁	—	2	2	no	—
91	C₂²×C₄×C₄₁	—	2	2	no	—
92	C₂²×C₄×C₄₁	—	2	2	no	—
93	C₂²×C₄×C₄₁	—	4	4	no	—
94	C₂²×C₄×C₄₁	—	4	4	no	—
95	C₂²×C₄×C₄₁	—	4	4	no	—
96	C₂²×C₄×C₄₁	—	4	4	no	—
97	C₂²×C₄×C₄₁	—	8	2	no	—
98	C₂²×C₄×C₄₁	—	8	2	no	—
99	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₁	#41	1	2	yes	—
104	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
105	D₈×C₄₁	—	4	4	no	—
106	C₂×C₈×C₄₁	—	2	2	no	—
107	C₂×C₈×C₄₁	—	2	2	no	—
108	C₂×C₈×C₄₁	—	2	2	no	—
109	C₂×C₈×C₄₁	—	2	2	no	—
110	C₂×C₈×C₄₁	—	2	2	no	—
111	C₂×C₈×C₄₁	—	4	4	no	—
112	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
114	C₄⋊C₄×C₄₁	—	2	2	no	—
115	C₄⋊C₄×C₄₁	—	2	2	no	—
116	C₄⋊C₄×C₄₁	—	2	2	no	—
117	C₄⋊C₄×C₄₁	—	2	2	no	—
118	C₄⋊C₄×C₄₁	—	4	4	no	—
119	C₄⋊C₄×C₄₁	—	4	4	no	—
120	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
121	C₄⋊C₄×C₄₁	#41	1	4	yes	—
122	C₂²⋊C₄×C₄₁	—	2	2	no	—
123	C₂²⋊C₄×C₄₁	—	2	8	no	—
124	C₂²⋊C₄×C₄₁	—	4	4	no	—
125	C₂²⋊C₄×C₄₁	—	4	4	no	—
126	C₂²⋊C₄×C₄₁	—	8	2	no	—
127	C₂²⋊C₄×C₄₁	D₈	1	4	yes	complemented
128	C₄²×C₄₁	—	2	2	no	—
129	C₄²×C₄₁	—	2	2	no	—
130	C₄²×C₄₁	—	4	4	no	—
131	C₂³×C₄₁	—	2	2	no	—
132	C₂³×C₄₁	—	2	2	no	—
133	C₂³×C₄₁	—	2	4	no	—
134	C₂³×C₄₁	—	4	2	no	—
135	C₂³×C₄₁	—	4	2	no	—
136	C₂³×C₄₁	—	4	2	no	—
137	C₂³×C₄₁	—	4	2	no	—
138	C₂³×C₄₁	—	4	2	no	—
139	C₂³×C₄₁	—	4	2	no	—
140	C₂³×C₄₁	C₄×D₄	1	2	yes	—
141	C₂³×C₄₁	C₂×D₈	1	2	yes	—
142	C₂³×C₄₁	#135	1	2	yes	—
143	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
144	D₄×C₄₁	—	2	4	no	—
145	D₄×C₄₁	—	2	4	no	—
146	D₄×C₄₁	—	4	16	no	—
147	D₄×C₄₁	—	4	2	no	—
148	D₄×C₄₁	—	4	2	no	—
149	C₂×C₄×C₄₁	—	2	2	no	—
150	C₂×C₄×C₄₁	—	2	2	no	—
151	C₂×C₄×C₄₁	—	2	2	no	—
152	C₂×C₄×C₄₁	—	2	2	no	—
153	C₂×C₄×C₄₁	—	2	2	no	—
154	C₂×C₄×C₄₁	—	2	4	no	—
155	C₂×C₄×C₄₁	—	2	4	no	—
156	C₂×C₄×C₄₁	—	2	2	no	—
157	C₂×C₄×C₄₁	—	2	4	no	—
158	C₂×C₄×C₄₁	—	2	2	no	—
159	C₂×C₄×C₄₁	—	2	2	no	—
160	C₂×C₄×C₄₁	—	4	2	no	—
161	C₂×C₄×C₄₁	—	4	2	no	—
162	C₂×C₄×C₄₁	—	4	2	no	—
163	C₂×C₄×C₄₁	—	4	2	no	—
164	C₂×C₄×C₄₁	—	4	2	no	—
165	C₂×C₄×C₄₁	—	4	2	no	—
166	C₂×C₄×C₄₁	—	4	2	no	—
167	C₂×C₄×C₄₁	—	8	8	no	—
168	C₂×C₄×C₄₁	—	8	8	no	—
169	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₄₁	C₂×D₈	1	4	yes	—
171	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
173	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
175	C₈×C₄₁	—	2	2	no	—
176	C₈×C₄₁	—	2	2	no	—
177	C₈×C₄₁	—	4	2	no	—
178	#23127	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂²×C₄₁	—	2	2	no	—
180	C₂²×C₄₁	—	2	2	no	—
181	C₂²×C₄₁	—	2	4	no	—
182	C₂²×C₄₁	—	2	4	no	—
183	C₂²×C₄₁	—	4	4	no	—
184	C₂²×C₄₁	—	4	4	no	—
185	C₂²×C₄₁	—	4	4	no	—
186	C₂²×C₄₁	—	8	2	no	—
187	C₂²×C₄₁	—	8	2	no	—
188	C₂²×C₄₁	—	8	2	no	—
189	C₂²×C₄₁	—	8	2	no	—
190	C₂²×C₄₁	C₄×D₈	1	4	yes	—
191	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
192	C₂²×C₄₁	#546	1	2	yes	—
193	C₂²×C₄₁	C₂²×D₈	1	1	yes	characteristic
194	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
195	C₂²×C₄₁	#577	1	2	yes	—
196	C₄×C₄₁	—	2	2	no	—
197	C₄×C₄₁	—	2	4	no	—
198	C₄×C₄₁	—	4	4	no	—
199	C₄×C₄₁	—	4	4	no	—
200	C₄×C₄₁	—	4	2	no	—
201	C₄×C₄₁	—	8	2	no	—
202	C₄×C₄₁	C₄×#41	1	1	yes	characteristic
203	C₄×C₄₁	#518	1	1	yes	characteristic
204	C₄×C₄₁	#553	1	2	yes	—
205	C₂×#466	C₂×C₄₁	1	1	yes	characteristic
206	#2361	C₂×C₄₁	1	2	yes	complemented
207	#1934	C₂×C₄₁	1	2	yes	complemented
208	#1918	C₂×C₄₁	1	2	yes	complemented
209	#1879	C₂×C₄₁	1	2	yes	complemented
210	#1874	C₂×C₄₁	1	2	yes	complemented
211	C₄×#102	C₂×C₄₁	1	2	yes	complemented
212	C₈×C₂²⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
213	C₂×#340	C₂×C₄₁	1	1	yes	characteristic, complemented
214	C₂×C₄₁	—	2	4	no	—
215	C₂×C₄₁	—	8	4	no	—
216	C₂×C₄₁	#2364	1	1	yes	characteristic
217	C₂×C₄₁	C₂×C₄×D₈	1	1	yes	characteristic
218	C₂×C₄₁	#2952	1	1	yes	characteristic
219	C₂×C₄₁	#3294	1	2	yes	—
220	C₂×C₄₁	#3301	1	2	yes	—
221	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
222	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
223	C₂×#121	C₂²×C₄₁	1	2	yes	—
224	C₂×C₄×D₄	—	2	2	no	—
225	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
226	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
227	#466	C₄×C₄₁	1	8	yes	complemented
228	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
229	C₂×#102	C₂²×C₄₁	1	2	yes	—
230	C₂×#102	C₂²×C₄₁	1	2	yes	—
231	C₂×#102	C₂²×C₄₁	1	2	yes	—
232	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
233	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
234	#390	C₂²×C₄₁	1	2	yes	—
235	#389	C₂²×C₄₁	1	2	yes	—
236	#388	—	2	2	no	—
237	#386	—	2	2	no	—
238	#385	—	2	2	no	—
239	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
240	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
241	#340	C₂²×C₄₁	1	2	yes	—
242	#340	C₂²×C₄₁	1	2	yes	—
243	#340	C₂²×C₄₁	1	2	yes	—
244	#340	C₂²×C₄₁	1	1	yes	characteristic
245	#340	C₂²×C₄₁	1	1	yes	characteristic
246	#336	C₂²×C₄₁	1	2	yes	—
247	C₄₁	#23127	1	1	yes	characteristic, direct product factor, Sylow
248	C₂²×D₄	—	2	2	no	—
249	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
250	C₂³×C₄	—	2	2	no	—
251	C₂³×C₄	—	2	2	no	—
252	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
253	C₂×D₈	—	4	2	no	—
254	C₂×D₈	C₂×C₄×C₄₁	1	4	yes	complemented
255	C₂²×C₈	—	4	2	no	—
256	C₂²×C₈	C₂×C₄×C₄₁	1	4	yes	complemented
257	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
258	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
260	#121	—	2	4	no	—
261	#121	C₂×C₄×C₄₁	1	8	yes	complemented
262	C₄×D₄	—	2	4	no	—
263	C₄×D₄	—	4	2	no	—
264	C₄×D₄	—	4	8	no	—
265	C₂×C₄⋊C₄	—	2	4	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	4	2	no	—
269	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
280	#107	C₂×C₄×C₄₁	1	4	yes	complemented
281	#102	—	2	4	no	—
282	#102	—	4	2	no	—
283	#102	C₂×C₄×C₄₁	1	8	yes	complemented
284	C₂²⋊C₈	—	2	2	no	—
285	C₄×C₈	—	4	2	no	—
286	#95	—	2	2	no	—
287	#95	—	2	2	no	—
288	#95	D₄×C₄₁	1	2	yes	—
289	C₂⁴	—	2	2	no	—
290	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
291	C₂×D₄	—	2	8	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	4	4	no	—
298	C₂×D₄	—	4	4	no	—
299	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	4	4	no	—
308	C₂²×C₄	—	4	4	no	—
309	C₂²×C₄	—	8	2	no	—
310	C₂²×C₄	—	8	2	no	—
311	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
315	C₂²×C₄	#41×C₄₁	1	2	yes	—
316	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
317	D₈	—	4	4	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	4	4	no	—
324	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
325	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	4	4	no	—
331	C₄⋊C₄	—	4	4	no	—
332	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
333	C₄⋊C₄	#41×C₄₁	1	4	yes	—
334	C₂²⋊C₄	—	2	2	no	—
335	C₂²⋊C₄	—	2	8	no	—
336	C₂²⋊C₄	—	4	4	no	—
337	C₂²⋊C₄	—	4	4	no	—
338	C₂²⋊C₄	—	8	2	no	—
339	C₂²⋊C₄	D₈×C₄₁	1	4	yes	complemented
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	4	4	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	4	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	2	no	—
352	C₂³	C₄×D₄×C₄₁	1	2	yes	—
353	C₂³	C₂×D₈×C₄₁	1	2	yes	—
354	C₂³	#135×C₄₁	1	2	yes	—
355	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
356	D₄	—	2	4	no	—
357	D₄	—	2	4	no	—
358	D₄	—	4	16	no	—
359	D₄	—	4	2	no	—
360	D₄	—	4	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	8	8	no	—
380	C₂×C₄	—	8	8	no	—
381	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
382	C₂×C₄	C₂×D₈×C₄₁	1	4	yes	—
383	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
384	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
385	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
386	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
387	C₈	—	2	2	no	—
388	C₈	—	2	2	no	—
389	C₈	—	4	2	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	2	4	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	4	4	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	C₄×D₈×C₄₁	1	4	yes	—
402	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
403	C₂²	C₄₁×#546	1	2	yes	—
404	C₂²	C₂²×D₈×C₄₁	1	1	yes	characteristic
405	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
406	C₂²	C₄₁×#577	1	2	yes	—
407	C₄	—	2	4	no	—
408	C₄	—	2	2	no	—
409	C₄	—	4	4	no	—
410	C₄	—	4	2	no	—
411	C₄	—	4	4	no	—
412	C₄	—	8	2	no	—
413	C₄	C₄×#41×C₄₁	1	1	yes	characteristic
414	C₄	C₄₁×#518	1	1	yes	characteristic
415	C₄	C₄₁×#553	1	2	yes	—
416	C₂	—	2	4	no	—
417	C₂	—	8	4	no	—
418	C₂	C₄₁×#2364	1	1	yes	characteristic
419	C₂	C₂×C₄×D₈×C₄₁	1	1	yes	characteristic
420	C₂	C₄₁×#2952	1	1	yes	characteristic
421	C₂	C₄₁×#3294	1	2	yes	—
422	C₂	C₄₁×#3301	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#466	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄×C₂²⋊C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2361	C₂	semidirect
3. C₄₁×#1934	C₂	semidirect
4. C₄₁×#1918	C₂	semidirect
5. C₄₁×#1879	C₂	semidirect
6. C₄₁×#1874	C₂	semidirect
7. C₄×#102×C₄₁	C₂	semidirect
8. C₈×C₂²⋊C₄×C₄₁	C₂	semidirect
9. C₂×C₄₁×#340	C₂	semidirect
16. C₄₁×#466	C₄	semidirect
42. C₂×D₈×C₄₁	C₂×C₄	semidirect
44. C₂²×C₈×C₄₁	C₂×C₄	semidirect
49. #121×C₄₁	C₂×C₄	semidirect
68. #107×C₄₁	C₂×C₄	semidirect
71. #102×C₄₁	C₂×C₄	semidirect
127. C₂²⋊C₄×C₄₁	D₈	semidirect
178. #23127	C₄₁	direct (N × H)
206. #2361	C₂×C₄₁	semidirect
207. #1934	C₂×C₄₁	semidirect
208. #1918	C₂×C₄₁	semidirect
209. #1879	C₂×C₄₁	semidirect
210. #1874	C₂×C₄₁	semidirect
211. C₄×#102	C₂×C₄₁	semidirect
212. C₈×C₂²⋊C₄	C₂×C₄₁	semidirect
213. C₂×#340	C₂×C₄₁	semidirect
227. #466	C₄×C₄₁	semidirect
247. C₄₁	#23127	direct (N × H)
254. C₂×D₈	C₂×C₄×C₄₁	semidirect
256. C₂²×C₈	C₂×C₄×C₄₁	semidirect
261. #121	C₂×C₄×C₄₁	semidirect
280. #107	C₂×C₄×C₄₁	semidirect
283. #102	C₂×C₄×C₄₁	semidirect
339. C₂²⋊C₄	D₈×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#466	2
C₄₁×#2361	2
C₄₁×#1934	2
C₄₁×#1918	2
C₄₁×#1879	2
C₄₁×#1874	2
C₄×#102×C₄₁	2
C₈×C₂²⋊C₄×C₄₁	2
C₂×C₄₁×#340	2
#23127	41

Subgroups — C41×#23127 #23799328

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23127 #23799328