Subgroups — C₄₁×#21809 #23798010

Order 10496.

1398 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2285	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1982	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1981	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1959	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1788	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₄₁	C₂²	1	2	yes	—
9	C₄₁×#532	—	2	4	no	—
10	C₄₁×#532	C₄	1	8	yes	complemented
11	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
12	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#124×C₄₁	C₂²	1	2	yes	—
14	C₂×#121×C₄₁	—	2	1	no	—
15	C₂×#121×C₄₁	—	2	1	no	—
16	C₂×C₄×D₄×C₄₁	—	2	1	no	—
17	C₂×C₄×D₄×C₄₁	—	2	1	no	—
18	C₂×#117×C₄₁	—	2	1	no	—
19	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
20	C₄₁×#432	—	2	4	no	—
21	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
22	C₂×#103×C₄₁	C₂²	1	8	yes	—
23	C₂×#102×C₄₁	C₂²	1	8	yes	—
24	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
25	C₂×#97×C₄₁	C₂²	1	2	yes	—
26	C₄₁×#384	C₂²	1	2	yes	—
27	C₄₁×#382	—	2	1	no	—
28	C₄₁×#380	—	2	1	no	—
29	C₄₁×#380	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
31	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
32	C₂×#41×C₄₁	—	2	4	no	—
33	C₂×#41×C₄₁	—	4	8	no	—
34	C₂×#41×C₄₁	C₂×C₄	1	8	yes	—
35	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
36	C₂²×D₄×C₄₁	—	2	2	no	—
37	C₂²×D₄×C₄₁	—	2	1	no	—
38	C₂²×D₄×C₄₁	—	2	1	no	—
39	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
40	C₂³×C₄×C₄₁	—	2	2	no	—
41	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
45	C₄⋊Q₈×C₄₁	—	2	2	no	—
46	C₄⋊Q₈×C₄₁	C₂×C₄	1	4	yes	—
47	#127×C₄₁	—	2	2	no	—
48	#127×C₄₁	C₂×C₄	1	4	yes	—
49	#124×C₄₁	—	2	4	no	—
50	#124×C₄₁	C₂×C₄	1	8	yes	—
51	#121×C₄₁	—	2	8	no	—
52	#121×C₄₁	—	2	8	no	—
53	C₄×D₄×C₄₁	—	2	8	no	—
54	C₄×D₄×C₄₁	—	2	8	no	—
55	#117×C₄₁	—	4	4	no	—
56	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
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×C₄²×C₄₁	—	2	2	no	—
65	C₂×C₄²×C₄₁	C₂×C₄	1	4	yes	—
66	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₄₁	D₄	1	4	yes	—
69	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₄₁	—	2	4	no	—
72	#103×C₄₁	—	4	8	no	—
73	#102×C₄₁	—	4	8	no	—
74	C₂²⋊C₈×C₄₁	—	2	4	no	—
75	#97×C₄₁	—	2	4	no	—
76	#95×C₄₁	—	2	2	no	—
77	#95×C₄₁	—	2	2	no	—
78	C₂⁴×C₄₁	—	2	2	no	—
79	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
80	#41×C₄₁	—	4	16	no	—
81	#41×C₄₁	—	4	16	no	—
82	C₂×Q₈×C₄₁	—	2	2	no	—
83	C₂×Q₈×C₄₁	—	2	8	no	—
84	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
85	C₂×D₄×C₄₁	—	2	8	no	—
86	C₂×D₄×C₄₁	—	2	4	no	—
87	C₂×D₄×C₄₁	—	2	4	no	—
88	C₂×D₄×C₄₁	—	2	2	no	—
89	C₂×D₄×C₄₁	—	2	8	no	—
90	C₂×D₄×C₄₁	—	4	4	no	—
91	C₂×D₄×C₄₁	—	4	8	no	—
92	C₂×D₄×C₄₁	—	4	2	no	—
93	C₂×D₄×C₄₁	—	4	2	no	—
94	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
95	C₂²×C₄×C₄₁	—	2	2	no	—
96	C₂²×C₄×C₄₁	—	2	2	no	—
97	C₂²×C₄×C₄₁	—	2	4	no	—
98	C₂²×C₄×C₄₁	—	2	2	no	—
99	C₂²×C₄×C₄₁	—	2	8	no	—
100	C₂²×C₄×C₄₁	—	2	4	no	—
101	C₂²×C₄×C₄₁	—	4	2	no	—
102	C₂²×C₄×C₄₁	—	4	8	no	—
103	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
104	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
105	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
113	C₂×C₈×C₄₁	—	2	4	no	—
114	C₂×C₈×C₄₁	—	2	8	no	—
115	C₄⋊C₄×C₄₁	—	2	4	no	—
116	C₄⋊C₄×C₄₁	—	2	4	no	—
117	C₄⋊C₄×C₄₁	—	2	4	no	—
118	C₄⋊C₄×C₄₁	—	2	4	no	—
119	C₄⋊C₄×C₄₁	—	4	4	no	—
120	C₄⋊C₄×C₄₁	—	4	4	no	—
121	C₂²⋊C₄×C₄₁	—	2	8	no	—
122	C₂²⋊C₄×C₄₁	—	2	8	no	—
123	C₂²⋊C₄×C₄₁	—	4	4	no	—
124	C₄²×C₄₁	—	4	4	no	—
125	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
126	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
127	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
128	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
129	C₄²×C₄₁	C₂×D₄	1	2	yes	—
130	C₄²×C₄₁	C₂×D₄	1	2	yes	—
131	C₂³×C₄₁	—	2	2	no	—
132	C₂³×C₄₁	—	2	1	no	—
133	C₂³×C₄₁	—	2	1	no	—
134	C₂³×C₄₁	—	2	2	no	—
135	C₂³×C₄₁	—	2	4	no	—
136	C₂³×C₄₁	—	4	4	no	—
137	C₂³×C₄₁	—	4	2	no	—
138	C₂³×C₄₁	—	4	2	no	—
139	C₂³×C₄₁	—	4	4	no	—
140	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
141	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
142	Q₈×C₄₁	—	2	8	no	—
143	Q₈×C₄₁	—	4	4	no	—
144	D₄×C₄₁	—	2	8	no	—
145	D₄×C₄₁	—	4	8	no	—
146	D₄×C₄₁	—	4	16	no	—
147	D₄×C₄₁	—	4	4	no	—
148	D₄×C₄₁	—	4	8	no	—
149	C₂×C₄×C₄₁	—	2	2	no	—
150	C₂×C₄×C₄₁	—	2	1	no	—
151	C₂×C₄×C₄₁	—	2	1	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	8	no	—
157	C₂×C₄×C₄₁	—	2	4	no	—
158	C₂×C₄×C₄₁	—	4	4	no	—
159	C₂×C₄×C₄₁	—	4	16	no	—
160	C₂×C₄×C₄₁	—	4	4	no	—
161	C₂×C₄×C₄₁	—	4	4	no	—
162	C₂×C₄×C₄₁	—	4	4	no	—
163	C₂×C₄×C₄₁	—	4	4	no	—
164	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
170	C₂×C₄×C₄₁	#137	1	2	yes	—
171	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₁	H(5,𝔽₂)	1	4	yes	—
174	C₈×C₄₁	—	4	4	no	—
175	#21809	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂²×C₄₁	—	2	2	no	—
177	C₂²×C₄₁	—	2	2	no	—
178	C₂²×C₄₁	—	2	2	no	—
179	C₂²×C₄₁	—	4	2	no	—
180	C₂²×C₄₁	—	4	2	no	—
181	C₂²×C₄₁	—	4	4	no	—
182	C₂²×C₄₁	—	4	4	no	—
183	C₂²×C₄₁	—	4	4	no	—
184	C₂²×C₄₁	—	8	4	no	—
185	C₂²×C₄₁	—	8	4	no	—
186	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
187	C₂²×C₄₁	#535	1	2	yes	—
188	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
190	C₂²×C₄₁	#575	1	2	yes	—
191	C₄×C₄₁	—	2	2	no	—
192	C₄×C₄₁	—	2	2	no	—
193	C₄×C₄₁	—	2	2	no	—
194	C₄×C₄₁	—	2	2	no	—
195	C₄×C₄₁	—	4	4	no	—
196	C₄×C₄₁	—	8	4	no	—
197	C₄×C₄₁	#417	1	4	yes	—
198	C₄×C₄₁	#518	1	2	yes	—
199	C₄×C₄₁	#535	1	2	yes	—
200	C₂×#532	C₂×C₄₁	1	1	yes	characteristic
201	C₂×#432	C₂×C₄₁	1	1	yes	characteristic, complemented
202	#2285	C₂×C₄₁	1	1	yes	characteristic, complemented
203	#1982	C₂×C₄₁	1	2	yes	complemented
204	#1981	C₂×C₄₁	1	2	yes	complemented
205	#1959	C₂×C₄₁	1	4	yes	complemented
206	#1788	C₂×C₄₁	1	4	yes	complemented
207	C₂×C₄₁	—	4	2	no	—
208	C₂×C₄₁	—	8	4	no	—
209	C₂×C₄₁	#2309	1	1	yes	characteristic
210	C₂×C₄₁	C₂×#417	1	1	yes	characteristic
211	C₂×C₄₁	#2896	1	1	yes	characteristic
212	C₂×C₄₁	#3214	1	2	yes	—
213	C₂×C₄₁	#3216	1	2	yes	—
214	C₂²×#41	C₂²×C₄₁	1	2	yes	—
215	#532	—	2	4	no	—
216	#532	C₄×C₄₁	1	8	yes	complemented
217	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
218	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
219	C₂×#124	C₂²×C₄₁	1	2	yes	—
220	C₂×#121	—	2	1	no	—
221	C₂×#121	—	2	1	no	—
222	C₂×C₄×D₄	—	2	1	no	—
223	C₂×C₄×D₄	—	2	1	no	—
224	C₂×#117	—	2	1	no	—
225	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
226	#432	—	2	4	no	—
227	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
228	C₂×#103	C₂²×C₄₁	1	8	yes	—
229	C₂×#102	C₂²×C₄₁	1	8	yes	—
230	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
231	C₂×#97	C₂²×C₄₁	1	2	yes	—
232	#384	C₂²×C₄₁	1	2	yes	—
233	#382	—	2	1	no	—
234	#380	—	2	1	no	—
235	#380	C₂²×C₄₁	1	2	yes	—
236	C₄×C₄⋊C₄	—	2	1	no	—
237	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
238	C₄₁	#21809	1	1	yes	characteristic, direct product factor, Sylow
239	C₂×#41	—	2	4	no	—
240	C₂×#41	—	4	8	no	—
241	C₂×#41	C₂×C₄×C₄₁	1	8	yes	—
242	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
243	C₂²×D₄	—	2	2	no	—
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	—	2	1	no	—
246	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
247	C₂³×C₄	—	2	2	no	—
248	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
249	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
250	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
252	C₄⋊Q₈	—	2	2	no	—
253	C₄⋊Q₈	C₂×C₄×C₄₁	1	4	yes	—
254	#127	—	2	2	no	—
255	#127	C₂×C₄×C₄₁	1	4	yes	—
256	#124	—	2	4	no	—
257	#124	C₂×C₄×C₄₁	1	8	yes	—
258	#121	—	2	8	no	—
259	#121	—	2	8	no	—
260	C₄×D₄	—	2	8	no	—
261	C₄×D₄	—	2	8	no	—
262	#117	—	4	4	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₄²	—	2	2	no	—
272	C₂×C₄²	C₂×C₄×C₄₁	1	4	yes	—
273	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
274	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
275	C₂×C₄²	D₄×C₄₁	1	4	yes	—
276	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
278	C₄⋊C₈	—	2	4	no	—
279	#103	—	4	8	no	—
280	#102	—	4	8	no	—
281	C₂²⋊C₈	—	2	4	no	—
282	#97	—	2	4	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	C₂⁴	—	2	2	no	—
286	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
287	#41	—	4	16	no	—
288	#41	—	4	16	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	8	no	—
291	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
292	C₂×D₄	—	2	8	no	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	2	4	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	8	no	—
297	C₂×D₄	—	4	4	no	—
298	C₂×D₄	—	4	8	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	8	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	—	4	8	no	—
310	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
311	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
312	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
319	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	—	2	8	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	4	4	no	—
327	C₄⋊C₄	—	4	4	no	—
328	C₂²⋊C₄	—	2	8	no	—
329	C₂²⋊C₄	—	2	8	no	—
330	C₂²⋊C₄	—	4	4	no	—
331	C₄²	—	4	4	no	—
332	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
333	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
334	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
335	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
336	C₄²	C₂×D₄×C₄₁	1	2	yes	—
337	C₄²	C₂×D₄×C₄₁	1	2	yes	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	4	no	—
343	C₂³	—	4	4	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	4	no	—
347	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
348	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
349	Q₈	—	2	8	no	—
350	Q₈	—	4	4	no	—
351	D₄	—	2	8	no	—
352	D₄	—	4	8	no	—
353	D₄	—	4	16	no	—
354	D₄	—	4	4	no	—
355	D₄	—	4	8	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	8	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	16	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
372	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
373	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
374	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
375	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
376	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
377	C₂×C₄	#137×C₄₁	1	2	yes	—
378	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
379	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
380	C₂×C₄	H(5,𝔽₂)×C₄₁	1	4	yes	—
381	C₈	—	4	4	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	4	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	8	4	no	—
391	C₂²	—	8	4	no	—
392	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
393	C₂²	C₄₁×#535	1	2	yes	—
394	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
395	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
396	C₂²	C₄₁×#575	1	2	yes	—
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	4	4	no	—
402	C₄	—	8	4	no	—
403	C₄	C₄₁×#417	1	4	yes	—
404	C₄	C₄₁×#518	1	2	yes	—
405	C₄	C₄₁×#535	1	2	yes	—
406	C₂	—	4	2	no	—
407	C₂	—	8	4	no	—
408	C₂	C₄₁×#2309	1	1	yes	characteristic
409	C₂	C₂×C₄₁×#417	1	1	yes	characteristic
410	C₂	C₄₁×#2896	1	1	yes	characteristic
411	C₂	C₄₁×#3214	1	2	yes	—
412	C₂	C₄₁×#3216	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×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#432	C₂	semidirect
3. C₄₁×#2285	C₂	semidirect
4. C₄₁×#1982	C₂	semidirect
5. C₄₁×#1981	C₂	semidirect
6. C₄₁×#1959	C₂	semidirect
7. C₄₁×#1788	C₂	semidirect
10. C₄₁×#532	C₄	semidirect
175. #21809	C₄₁	direct (N × H)
201. C₂×#432	C₂×C₄₁	semidirect
202. #2285	C₂×C₄₁	semidirect
203. #1982	C₂×C₄₁	semidirect
204. #1981	C₂×C₄₁	semidirect
205. #1959	C₂×C₄₁	semidirect
206. #1788	C₂×C₄₁	semidirect
216. #532	C₄×C₄₁	semidirect
238. C₄₁	#21809	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#532	2
C₂×C₄₁×#432	2
C₄₁×#2285	2
C₄₁×#1982	2
C₄₁×#1981	2
C₄₁×#1959	2
C₄₁×#1788	2
#21809	41

Subgroups — C41×#21809 #23798010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21809 #23798010