Subgroups — C₂×C₄₁×#1959 #23797397

Order 10496.

1814 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#124×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×#103×C₄₁	C₂	1	2	yes	maximal, complemented
3	C₂²×#102×C₄₁	C₂	1	2	yes	maximal
4	C₂²×#97×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₁×#384	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1959	C₂	1	8	yes	maximal, direct product factor
7	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
8	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₄₁	C₂²	1	2	yes	—
10	C₂×#124×C₄₁	—	2	2	no	—
11	C₂×#124×C₄₁	—	2	4	no	—
12	C₂×#124×C₄₁	C₄	1	8	yes	complemented
13	C₂×#124×C₄₁	C₂²	1	4	yes	—
14	C₂²×C₄⋊C₄×C₄₁	—	2	2	no	—
15	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₄₁	—	2	2	no	—
17	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#103×C₄₁	—	2	8	no	—
19	C₂×#103×C₄₁	C₂²	1	8	yes	complemented
20	C₂×#102×C₄₁	—	2	8	no	—
21	C₂×#102×C₄₁	C₂²	1	8	yes	—
22	C₂×#97×C₄₁	—	2	4	no	—
23	C₂×#97×C₄₁	C₂²	1	4	yes	complemented
24	C₄₁×#384	—	2	2	no	—
25	C₄₁×#384	C₂²	1	4	yes	complemented
26	C₂⁵×C₄₁	—	2	1	no	—
27	C₂²×Q₈×C₄₁	—	2	2	no	—
28	C₂²×Q₈×C₄₁	—	2	1	no	—
29	C₂²×Q₈×C₄₁	—	2	4	no	—
30	C₂²×Q₈×C₄₁	—	2	4	no	—
31	C₂²×Q₈×C₄₁	C₂×C₄	1	4	yes	—
32	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
33	C₂²×D₄×C₄₁	—	2	4	no	—
34	C₂²×D₄×C₄₁	—	2	1	no	—
35	C₂²×D₄×C₄₁	—	2	2	no	—
36	C₂²×D₄×C₄₁	—	2	4	no	—
37	C₂²×D₄×C₄₁	C₂×C₄	1	4	yes	—
38	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
39	C₂³×C₄×C₄₁	—	2	1	no	—
40	C₂³×C₄×C₄₁	—	2	2	no	—
41	C₂³×C₄×C₄₁	D₄	1	2	yes	—
42	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₄₁	—	2	4	no	—
44	C₂²×C₈×C₄₁	—	2	4	no	—
45	C₂²×C₈×C₄₁	D₄	1	8	yes	—
46	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
47	#124×C₄₁	—	2	16	no	—
48	#124×C₄₁	—	2	8	no	—
49	#124×C₄₁	C₂×C₄	1	16	yes	complemented
50	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
51	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
52	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
53	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₁	—	4	8	no	—
55	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
56	C₂×C₂²⋊C₄×C₄₁	—	2	16	no	—
57	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
58	C₂×C₄²×C₄₁	C₂×C₄	1	4	yes	—
59	C₂×C₄²×C₄₁	D₄	1	2	yes	—
60	C₂×C₄²×C₄₁	D₄	1	4	yes	—
61	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
62	#103×C₄₁	—	2	16	no	—
63	#102×C₄₁	—	2	16	no	—
64	#97×C₄₁	—	2	8	no	—
65	C₂⁴×C₄₁	—	2	4	no	—
66	C₂⁴×C₄₁	—	2	2	no	—
67	C₂⁴×C₄₁	—	4	2	no	—
68	C₂⁴×C₄₁	—	4	2	no	—
69	C₂⁴×C₄₁	—	4	4	no	—
70	C₂⁴×C₄₁	—	4	4	no	—
71	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
72	C₂×Q₈×C₄₁	—	2	4	no	—
73	C₂×Q₈×C₄₁	—	2	2	no	—
74	C₂×Q₈×C₄₁	—	2	16	no	—
75	C₂×Q₈×C₄₁	—	2	4	no	—
76	C₂×Q₈×C₄₁	—	2	4	no	—
77	C₂×Q₈×C₄₁	—	4	8	no	—
78	C₂×Q₈×C₄₁	—	4	2	no	—
79	C₂×Q₈×C₄₁	—	4	2	no	—
80	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
81	C₂×D₄×C₄₁	—	2	4	no	—
82	C₂×D₄×C₄₁	—	2	16	no	—
83	C₂×D₄×C₄₁	—	2	4	no	—
84	C₂×D₄×C₄₁	—	2	2	no	—
85	C₂×D₄×C₄₁	—	2	4	no	—
86	C₂×D₄×C₄₁	—	4	8	no	—
87	C₂×D₄×C₄₁	—	4	2	no	—
88	C₂×D₄×C₄₁	—	4	2	no	—
89	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₄₁	—	2	4	no	—
91	C₂²×C₄×C₄₁	—	2	4	no	—
92	C₂²×C₄×C₄₁	—	2	4	no	—
93	C₂²×C₄×C₄₁	—	2	2	no	—
94	C₂²×C₄×C₄₁	—	2	4	no	—
95	C₂²×C₄×C₄₁	—	4	2	no	—
96	C₂²×C₄×C₄₁	—	4	2	no	—
97	C₂²×C₄×C₄₁	—	4	4	no	—
98	C₂²×C₄×C₄₁	—	4	8	no	—
99	C₂²×C₄×C₄₁	C₂²⋊C₄	1	8	yes	—
100	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₄₁	#41	1	4	yes	—
106	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
107	C₂×C₈×C₄₁	—	2	16	no	—
108	C₂×C₈×C₄₁	—	2	4	no	—
109	C₂×C₈×C₄₁	—	2	4	no	—
110	C₂×C₈×C₄₁	C₂×D₄	1	8	yes	—
111	C₄⋊C₄×C₄₁	—	2	4	no	—
112	C₄⋊C₄×C₄₁	—	2	4	no	—
113	C₄⋊C₄×C₄₁	—	4	16	no	—
114	C₄⋊C₄×C₄₁	—	4	4	no	—
115	C₂²⋊C₄×C₄₁	—	2	32	no	—
116	C₄²×C₄₁	C₂²⋊C₄	1	8	yes	—
117	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
118	C₄²×C₄₁	C₂×D₄	1	4	yes	—
119	C₂³×C₄₁	—	2	4	no	—
120	C₂³×C₄₁	—	4	2	no	—
121	C₂³×C₄₁	—	4	2	no	—
122	C₂³×C₄₁	—	4	4	no	—
123	C₂³×C₄₁	—	4	4	no	—
124	C₂³×C₄₁	—	4	8	no	—
125	C₂³×C₄₁	—	4	16	no	—
126	C₂³×C₄₁	—	8	8	no	—
127	C₂³×C₄₁	—	8	4	no	—
128	C₂³×C₄₁	—	8	4	no	—
129	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
130	C₂³×C₄₁	#124	1	2	yes	—
131	C₂³×C₄₁	#127	1	2	yes	—
132	C₂³×C₄₁	AGL(1,ℤ/8)	1	4	yes	—
133	C₂³×C₄₁	#137	1	4	yes	—
134	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
135	Q₈×C₄₁	—	2	8	no	—
136	Q₈×C₄₁	—	4	4	no	—
137	Q₈×C₄₁	—	4	8	no	—
138	D₄×C₄₁	—	2	8	no	—
139	D₄×C₄₁	—	4	4	no	—
140	D₄×C₄₁	—	4	8	no	—
141	C₂×C₄×C₄₁	—	2	4	no	—
142	C₂×C₄×C₄₁	—	2	4	no	—
143	C₂×C₄×C₄₁	—	2	16	no	—
144	C₂×C₄×C₄₁	—	2	4	no	—
145	C₂×C₄×C₄₁	—	4	2	no	—
146	C₂×C₄×C₄₁	—	4	2	no	—
147	C₂×C₄×C₄₁	—	4	8	no	—
148	C₂×C₄×C₄₁	—	4	4	no	—
149	C₂×C₄×C₄₁	—	4	8	no	—
150	C₂×C₄×C₄₁	—	8	8	no	—
151	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	8	yes	—
152	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂×C₄×C₄₁	C₄×D₄	1	8	yes	—
154	C₂×C₄×C₄₁	#121	1	8	yes	—
155	C₂×C₄×C₄₁	#124	1	2	yes	—
156	C₂×C₄×C₄₁	#127	1	2	yes	—
157	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
159	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
161	C₈×C₄₁	—	2	8	no	—
162	C₂×#1959	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂²×C₄₁	—	4	8	no	—
164	C₂²×C₄₁	—	4	4	no	—
165	C₂²×C₄₁	—	8	4	no	—
166	C₂²×C₄₁	—	8	2	no	—
167	C₂²×C₄₁	—	8	2	no	—
168	C₂²×C₄₁	—	8	16	no	—
169	C₂²×C₄₁	#390	1	4	yes	—
170	C₂²×C₄₁	#417	1	8	yes	—
171	C₂²×C₄₁	#489	1	8	yes	—
172	C₂²×C₄₁	#496	1	4	yes	—
173	C₂²×C₄₁	#497	1	4	yes	—
174	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
175	C₂²×C₄₁	C₂×#124	1	1	yes	characteristic
176	C₂²×C₄₁	C₂×#127	1	1	yes	characteristic
177	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
178	C₂²×C₄₁	C₂×#137	1	2	yes	—
179	C₄×C₄₁	—	2	8	no	—
180	C₄×C₄₁	—	4	4	no	—
181	C₄×C₄₁	—	8	4	no	—
182	C₄×C₄₁	#390	1	4	yes	—
183	C₄×C₄₁	C₂×C₄×D₄	1	2	yes	—
184	C₄×C₄₁	C₂×#121	1	2	yes	—
185	C₂²×#124	C₂×C₄₁	1	1	yes	characteristic
186	C₂²×#103	C₂×C₄₁	1	2	yes	complemented
187	C₂²×#102	C₂×C₄₁	1	2	yes	—
188	C₂²×#97	C₂×C₄₁	1	1	yes	characteristic, complemented
189	C₂×#384	C₂×C₄₁	1	1	yes	characteristic, complemented
190	#1959	C₂×C₄₁	1	8	yes	direct product factor
191	C₂×C₄₁	—	8	4	no	—
192	C₂×C₄₁	#1959	1	8	yes	direct product factor
193	C₂×C₄₁	C₂×#390	1	1	yes	characteristic
194	C₂×C₄₁	C₂×#417	1	2	yes	—
195	C₂×C₄₁	C₂×#489	1	2	yes	—
196	C₂×C₄₁	C₂×#496	1	1	yes	characteristic
197	C₂×C₄₁	C₂×#497	1	1	yes	characteristic
198	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
199	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
200	C₂³×C₈	C₂²×C₄₁	1	2	yes	—
201	C₂×#124	—	2	2	no	—
202	C₂×#124	—	2	4	no	—
203	C₂×#124	C₄×C₄₁	1	8	yes	complemented
204	C₂×#124	C₂²×C₄₁	1	4	yes	—
205	C₂²×C₄⋊C₄	—	2	2	no	—
206	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
207	C₂²×C₂²⋊C₄	—	2	2	no	—
208	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
209	C₂×#103	—	2	8	no	—
210	C₂×#103	C₂²×C₄₁	1	8	yes	complemented
211	C₂×#102	—	2	8	no	—
212	C₂×#102	C₂²×C₄₁	1	8	yes	—
213	C₂×#97	—	2	4	no	—
214	C₂×#97	C₂²×C₄₁	1	4	yes	complemented
215	#384	—	2	2	no	—
216	#384	C₂²×C₄₁	1	4	yes	complemented
217	C₄₁	C₂×#1959	1	1	yes	characteristic, direct product factor, Sylow
218	C₂⁵	—	2	1	no	—
219	C₂²×Q₈	—	2	2	no	—
220	C₂²×Q₈	—	2	1	no	—
221	C₂²×Q₈	—	2	4	no	—
222	C₂²×Q₈	—	2	4	no	—
223	C₂²×Q₈	C₂×C₄×C₄₁	1	4	yes	—
224	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
225	C₂²×D₄	—	2	4	no	—
226	C₂²×D₄	—	2	1	no	—
227	C₂²×D₄	—	2	2	no	—
228	C₂²×D₄	—	2	4	no	—
229	C₂²×D₄	C₂×C₄×C₄₁	1	4	yes	—
230	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
231	C₂³×C₄	—	2	1	no	—
232	C₂³×C₄	—	2	2	no	—
233	C₂³×C₄	D₄×C₄₁	1	2	yes	—
234	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
235	C₂²×C₈	—	2	4	no	—
236	C₂²×C₈	—	2	4	no	—
237	C₂²×C₈	D₄×C₄₁	1	8	yes	—
238	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
239	#124	—	2	16	no	—
240	#124	—	2	8	no	—
241	#124	C₂×C₄×C₄₁	1	16	yes	complemented
242	C₂×C₄⋊C₄	—	2	4	no	—
243	C₂×C₄⋊C₄	—	2	4	no	—
244	C₂×C₄⋊C₄	—	2	8	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	4	8	no	—
247	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
248	C₂×C₂²⋊C₄	—	2	16	no	—
249	C₂×C₂²⋊C₄	—	2	8	no	—
250	C₂×C₄²	C₂×C₄×C₄₁	1	4	yes	—
251	C₂×C₄²	D₄×C₄₁	1	2	yes	—
252	C₂×C₄²	D₄×C₄₁	1	4	yes	—
253	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
254	#103	—	2	16	no	—
255	#102	—	2	16	no	—
256	#97	—	2	8	no	—
257	C₂⁴	—	2	4	no	—
258	C₂⁴	—	2	2	no	—
259	C₂⁴	—	4	2	no	—
260	C₂⁴	—	4	2	no	—
261	C₂⁴	—	4	4	no	—
262	C₂⁴	—	4	4	no	—
263	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
264	C₂×Q₈	—	2	4	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	2	16	no	—
267	C₂×Q₈	—	2	4	no	—
268	C₂×Q₈	—	2	4	no	—
269	C₂×Q₈	—	4	8	no	—
270	C₂×Q₈	—	4	2	no	—
271	C₂×Q₈	—	4	2	no	—
272	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
273	C₂×D₄	—	2	4	no	—
274	C₂×D₄	—	2	16	no	—
275	C₂×D₄	—	2	4	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	4	8	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂×D₄	—	4	2	no	—
281	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	4	no	—
290	C₂²×C₄	—	4	8	no	—
291	C₂²×C₄	C₂²⋊C₄×C₄₁	1	8	yes	—
292	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
293	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
294	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
297	C₂²×C₄	#41×C₄₁	1	4	yes	—
298	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
299	C₂×C₈	—	2	16	no	—
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	—	2	4	no	—
302	C₂×C₈	C₂×D₄×C₄₁	1	8	yes	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	4	16	no	—
306	C₄⋊C₄	—	4	4	no	—
307	C₂²⋊C₄	—	2	32	no	—
308	C₄²	C₂²⋊C₄×C₄₁	1	8	yes	—
309	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
310	C₄²	C₂×D₄×C₄₁	1	4	yes	—
311	C₂³	—	2	4	no	—
312	C₂³	—	4	2	no	—
313	C₂³	—	4	2	no	—
314	C₂³	—	4	4	no	—
315	C₂³	—	4	4	no	—
316	C₂³	—	4	8	no	—
317	C₂³	—	4	16	no	—
318	C₂³	—	8	8	no	—
319	C₂³	—	8	4	no	—
320	C₂³	—	8	4	no	—
321	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
322	C₂³	#124×C₄₁	1	2	yes	—
323	C₂³	#127×C₄₁	1	2	yes	—
324	C₂³	AGL(1,ℤ/8)×C₄₁	1	4	yes	—
325	C₂³	#137×C₄₁	1	4	yes	—
326	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
327	Q₈	—	2	8	no	—
328	Q₈	—	4	4	no	—
329	Q₈	—	4	8	no	—
330	D₄	—	2	8	no	—
331	D₄	—	4	4	no	—
332	D₄	—	4	8	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	16	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	8	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	8	no	—
342	C₂×C₄	—	8	8	no	—
343	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	8	yes	—
344	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
345	C₂×C₄	C₄×D₄×C₄₁	1	8	yes	—
346	C₂×C₄	#121×C₄₁	1	8	yes	—
347	C₂×C₄	#124×C₄₁	1	2	yes	—
348	C₂×C₄	#127×C₄₁	1	2	yes	—
349	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
350	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
351	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
352	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
353	C₈	—	2	8	no	—
354	C₂²	—	4	4	no	—
355	C₂²	—	4	8	no	—
356	C₂²	—	8	4	no	—
357	C₂²	—	8	2	no	—
358	C₂²	—	8	2	no	—
359	C₂²	—	8	16	no	—
360	C₂²	C₄₁×#390	1	4	yes	—
361	C₂²	C₄₁×#417	1	8	yes	—
362	C₂²	C₄₁×#489	1	8	yes	—
363	C₂²	C₄₁×#496	1	4	yes	—
364	C₂²	C₄₁×#497	1	4	yes	—
365	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
366	C₂²	C₂×#124×C₄₁	1	1	yes	characteristic
367	C₂²	C₂×#127×C₄₁	1	1	yes	characteristic
368	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
369	C₂²	C₂×#137×C₄₁	1	2	yes	—
370	C₄	—	2	8	no	—
371	C₄	—	4	4	no	—
372	C₄	—	8	4	no	—
373	C₄	C₄₁×#390	1	4	yes	—
374	C₄	C₂×C₄×D₄×C₄₁	1	2	yes	—
375	C₄	C₂×#121×C₄₁	1	2	yes	—
376	C₂	—	8	4	no	—
377	C₂	C₄₁×#1959	1	8	yes	direct product factor
378	C₂	C₂×C₄₁×#390	1	1	yes	characteristic
379	C₂	C₂×C₄₁×#417	1	2	yes	—
380	C₂	C₂×C₄₁×#489	1	2	yes	—
381	C₂	C₂×C₄₁×#496	1	1	yes	characteristic
382	C₂	C₂×C₄₁×#497	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂³×D₄×C₄₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#103×C₄₁	C₂	semidirect
4. C₂²×#97×C₄₁	C₂	semidirect
5. C₂×C₄₁×#384	C₂	semidirect
6. C₄₁×#1959	C₂	direct (N × H)
12. C₂×#124×C₄₁	C₄	semidirect
19. C₂×#103×C₄₁	C₂²	semidirect
23. C₂×#97×C₄₁	C₂²	semidirect
25. C₄₁×#384	C₂²	semidirect
49. #124×C₄₁	C₂×C₄	semidirect
162. C₂×#1959	C₄₁	direct (N × H)
186. C₂²×#103	C₂×C₄₁	semidirect
188. C₂²×#97	C₂×C₄₁	semidirect
189. C₂×#384	C₂×C₄₁	semidirect
190. #1959	C₂×C₄₁	direct (N × H)
192. C₂×C₄₁	#1959	direct (N × H)
203. C₂×#124	C₄×C₄₁	semidirect
210. C₂×#103	C₂²×C₄₁	semidirect
214. C₂×#97	C₂²×C₄₁	semidirect
216. #384	C₂²×C₄₁	semidirect
217. C₄₁	C₂×#1959	direct (N × H)
241. #124	C₂×C₄×C₄₁	semidirect
377. C₂	C₄₁×#1959	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×#124×C₄₁	2
C₂²×#103×C₄₁	2
C₂²×#102×C₄₁	2
C₂²×#97×C₄₁	2
C₂×C₄₁×#384	2
C₄₁×#1959	2
C₂×#1959	41

Subgroups — C2×C41×#1959 #23797397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#1959 #23797397