Subgroups — C₂×C₄₁×#1805 #23796845

Order 10496.

1510 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×#103×C₄₁	C₂	1	2	yes	maximal
4	C₂×C₄₁×#382	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1805	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₁×#340	C₂	1	2	yes	maximal
7	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₄₁	C₂²	1	2	yes	—
9	C₂×C₄×Q₈×C₄₁	—	2	4	no	—
10	C₂×C₄×Q₈×C₄₁	—	2	2	no	—
11	C₂×C₄×Q₈×C₄₁	C₄	1	8	yes	complemented
12	C₂×C₄×Q₈×C₄₁	C₂²	1	4	yes	—
13	C₂²×C₄⋊C₄×C₄₁	—	2	1	no	—
14	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₄₁	—	2	1	no	—
17	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₄₁	—	2	4	no	—
19	C₂×C₄⋊C₈×C₄₁	C₂²	1	4	yes	—
20	C₂×#103×C₄₁	—	2	8	no	—
21	C₂×#103×C₄₁	C₂²	1	8	yes	—
22	C₄₁×#382	—	2	2	no	—
23	C₄₁×#382	C₂²	1	4	yes	—
24	C₂×#95×C₄₁	—	2	1	no	—
25	C₂×#95×C₄₁	—	2	1	no	—
26	C₄₁×#340	C₂²	1	8	yes	—
27	C₂²×Q₈×C₄₁	—	2	2	no	—
28	C₂²×Q₈×C₄₁	—	2	1	no	—
29	C₂²×Q₈×C₄₁	—	2	2	no	—
30	C₂²×Q₈×C₄₁	—	2	2	no	—
31	C₂²×Q₈×C₄₁	C₂×C₄	1	4	yes	—
32	C₂²×Q₈×C₄₁	D₄	1	4	yes	—
33	C₂²×Q₈×C₄₁	Q₈	1	4	yes	—
34	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
35	C₂³×C₄×C₄₁	—	2	1	no	—
36	C₂³×C₄×C₄₁	—	2	1	no	—
37	C₂³×C₄×C₄₁	—	2	2	no	—
38	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₄₁	—	2	4	no	—
42	C₂²×C₈×C₄₁	—	2	4	no	—
43	C₂²×C₈×C₄₁	—	2	4	no	—
44	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
45	C₄×Q₈×C₄₁	—	2	16	no	—
46	C₄×Q₈×C₄₁	—	2	8	no	—
47	C₄×Q₈×C₄₁	C₂×C₄	1	16	yes	complemented
48	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
49	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
50	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
51	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
53	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
54	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
56	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
57	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
58	C₂×C₄²×C₄₁	—	2	8	no	—
59	C₂×C₄²×C₄₁	—	2	4	no	—
60	C₂×C₄²×C₄₁	C₂×C₄	1	4	yes	—
61	C₂×C₄²×C₄₁	D₄	1	2	yes	—
62	C₂×C₄²×C₄₁	D₄	1	4	yes	—
63	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
64	C₄⋊C₈×C₄₁	—	2	8	no	—
65	#103×C₄₁	—	2	16	no	—
66	#95×C₄₁	—	2	4	no	—
67	#95×C₄₁	—	2	4	no	—
68	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
69	C₂×Q₈×C₄₁	—	2	4	no	—
70	C₂×Q₈×C₄₁	—	2	8	no	—
71	C₂×Q₈×C₄₁	—	2	4	no	—
72	C₂×Q₈×C₄₁	—	2	8	no	—
73	C₂×Q₈×C₄₁	—	2	4	no	—
74	C₂×Q₈×C₄₁	—	2	8	no	—
75	C₂×Q₈×C₄₁	—	2	2	no	—
76	C₂×Q₈×C₄₁	—	2	2	no	—
77	C₂×Q₈×C₄₁	—	2	2	no	—
78	C₂×Q₈×C₄₁	C₄⋊C₄	1	16	yes	—
79	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
80	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
81	C₂×Q₈×C₄₁	C₂×Q₈	1	4	yes	—
82	C₂²×C₄×C₄₁	—	2	4	no	—
83	C₂²×C₄×C₄₁	—	2	4	no	—
84	C₂²×C₄×C₄₁	—	2	4	no	—
85	C₂²×C₄×C₄₁	—	2	4	no	—
86	C₂²×C₄×C₄₁	—	2	4	no	—
87	C₂²×C₄×C₄₁	—	2	2	no	—
88	C₂²×C₄×C₄₁	—	2	4	no	—
89	C₂²×C₄×C₄₁	—	2	2	no	—
90	C₂²×C₄×C₄₁	—	2	4	no	—
91	C₂²×C₄×C₄₁	—	4	4	no	—
92	C₂²×C₄×C₄₁	—	4	4	no	—
93	C₂²×C₄×C₄₁	—	4	4	no	—
94	C₂²×C₄×C₄₁	—	4	4	no	—
95	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
96	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
97	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
104	C₂²×C₄×C₄₁	#41	1	2	yes	—
105	C₂²×C₄×C₄₁	#41	1	2	yes	—
106	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
107	C₂×C₈×C₄₁	—	2	4	no	—
108	C₂×C₈×C₄₁	—	2	4	no	—
109	C₂×C₈×C₄₁	—	2	4	no	—
110	C₂×C₈×C₄₁	—	4	8	no	—
111	C₄⋊C₄×C₄₁	—	2	16	no	—
112	C₄⋊C₄×C₄₁	—	2	4	no	—
113	C₄⋊C₄×C₄₁	—	2	2	no	—
114	C₄⋊C₄×C₄₁	—	2	4	no	—
115	C₄⋊C₄×C₄₁	—	2	4	no	—
116	C₄⋊C₄×C₄₁	—	4	4	no	—
117	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
118	C₄²×C₄₁	—	2	16	no	—
119	C₄²×C₄₁	C₂²⋊C₄	1	8	yes	—
120	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
121	C₄²×C₄₁	C₂×D₄	1	4	yes	—
122	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
123	C₂³×C₄₁	#121	1	2	yes	—
124	C₂³×C₄₁	C₂²⋊Q₈	1	2	yes	—
125	C₂³×C₄₁	#135	1	4	yes	—
126	C₂³×C₄₁	#137	1	4	yes	—
127	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
128	Q₈×C₄₁	—	2	4	no	—
129	Q₈×C₄₁	—	2	4	no	—
130	Q₈×C₄₁	—	2	4	no	—
131	Q₈×C₄₁	—	2	16	no	—
132	Q₈×C₄₁	C₂×C₄⋊C₄	1	8	yes	—
133	C₂×C₄×C₄₁	—	2	4	no	—
134	C₂×C₄×C₄₁	—	2	4	no	—
135	C₂×C₄×C₄₁	—	2	4	no	—
136	C₂×C₄×C₄₁	—	2	4	no	—
137	C₂×C₄×C₄₁	—	2	4	no	—
138	C₂×C₄×C₄₁	—	2	16	no	—
139	C₂×C₄×C₄₁	—	2	8	no	—
140	C₂×C₄×C₄₁	—	2	8	no	—
141	C₂×C₄×C₄₁	—	2	4	no	—
142	C₂×C₄×C₄₁	—	4	4	no	—
143	C₂×C₄×C₄₁	—	4	8	no	—
144	C₂×C₄×C₄₁	—	4	4	no	—
145	C₂×C₄×C₄₁	—	4	4	no	—
146	C₂×C₄×C₄₁	—	4	4	no	—
147	C₂×C₄×C₄₁	—	8	8	no	—
148	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
149	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
150	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
152	C₂×C₄×C₄₁	#117	1	4	yes	—
153	C₂×C₄×C₄₁	#121	1	4	yes	—
154	C₂×C₄×C₄₁	#121	1	2	yes	—
155	C₂×C₄×C₄₁	C₂²⋊Q₈	1	4	yes	—
156	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
157	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
161	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
163	C₈×C₄₁	—	4	4	no	—
164	C₂×#1805	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂²×C₄₁	#380	1	4	yes	—
166	C₂²×C₄₁	#416	1	4	yes	—
167	C₂²×C₄₁	#419	1	4	yes	—
168	C₂²×C₄₁	#464	1	8	yes	—
169	C₂²×C₄₁	#479	1	8	yes	—
170	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
171	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
172	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
173	C₂²×C₄₁	C₂×#135	1	2	yes	—
174	C₂²×C₄₁	C₂×#137	1	2	yes	—
175	C₄×C₄₁	—	2	4	no	—
176	C₄×C₄₁	—	2	4	no	—
177	C₄×C₄₁	—	2	8	no	—
178	C₄×C₄₁	—	4	4	no	—
179	C₄×C₄₁	—	8	4	no	—
180	C₄×C₄₁	#380	1	4	yes	—
181	C₄×C₄₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
182	C₄×C₄₁	C₂×#117	1	1	yes	characteristic
183	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
184	C₄×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
185	C₂²×C₄×Q₈	C₂×C₄₁	1	1	yes	characteristic
186	C₂²×C₄⋊C₈	C₂×C₄₁	1	1	yes	characteristic
187	C₂²×#103	C₂×C₄₁	1	2	yes	—
188	C₂×#382	C₂×C₄₁	1	1	yes	characteristic
189	#1805	C₂×C₄₁	1	8	yes	direct product factor
190	C₂×#340	C₂×C₄₁	1	2	yes	—
191	C₂×C₄₁	#1805	1	8	yes	direct product factor
192	C₂×C₄₁	C₂×#380	1	1	yes	characteristic
193	C₂×C₄₁	C₂×#416	1	1	yes	characteristic
194	C₂×C₄₁	C₂×#419	1	1	yes	characteristic
195	C₂×C₄₁	C₂×#464	1	2	yes	—
196	C₂×C₄₁	C₂×#479	1	2	yes	—
197	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
198	C₂³×C₈	C₂²×C₄₁	1	2	yes	—
199	C₂×C₄×Q₈	—	2	4	no	—
200	C₂×C₄×Q₈	—	2	2	no	—
201	C₂×C₄×Q₈	C₄×C₄₁	1	8	yes	complemented
202	C₂×C₄×Q₈	C₂²×C₄₁	1	4	yes	—
203	C₂²×C₄⋊C₄	—	2	1	no	—
204	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
205	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
206	C₂²×C₄²	—	2	1	no	—
207	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
208	C₂×C₄⋊C₈	—	2	4	no	—
209	C₂×C₄⋊C₈	C₂²×C₄₁	1	4	yes	—
210	C₂×#103	—	2	8	no	—
211	C₂×#103	C₂²×C₄₁	1	8	yes	—
212	#382	—	2	2	no	—
213	#382	C₂²×C₄₁	1	4	yes	—
214	C₂×#95	—	2	1	no	—
215	C₂×#95	—	2	1	no	—
216	#340	C₂²×C₄₁	1	8	yes	—
217	C₄₁	C₂×#1805	1	1	yes	characteristic, direct product factor, Sylow
218	C₂²×Q₈	—	2	2	no	—
219	C₂²×Q₈	—	2	1	no	—
220	C₂²×Q₈	—	2	2	no	—
221	C₂²×Q₈	—	2	2	no	—
222	C₂²×Q₈	C₂×C₄×C₄₁	1	4	yes	—
223	C₂²×Q₈	D₄×C₄₁	1	4	yes	—
224	C₂²×Q₈	Q₈×C₄₁	1	4	yes	—
225	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
226	C₂³×C₄	—	2	1	no	—
227	C₂³×C₄	—	2	1	no	—
228	C₂³×C₄	—	2	2	no	—
229	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
230	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
231	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
232	C₂²×C₈	—	2	4	no	—
233	C₂²×C₈	—	2	4	no	—
234	C₂²×C₈	—	2	4	no	—
235	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
236	C₄×Q₈	—	2	16	no	—
237	C₄×Q₈	—	2	8	no	—
238	C₄×Q₈	C₂×C₄×C₄₁	1	16	yes	complemented
239	C₂×C₄⋊C₄	—	2	8	no	—
240	C₂×C₄⋊C₄	—	2	4	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	4	no	—
244	C₂×C₄⋊C₄	—	2	4	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
247	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
248	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
249	C₂×C₄²	—	2	8	no	—
250	C₂×C₄²	—	2	4	no	—
251	C₂×C₄²	C₂×C₄×C₄₁	1	4	yes	—
252	C₂×C₄²	D₄×C₄₁	1	2	yes	—
253	C₂×C₄²	D₄×C₄₁	1	4	yes	—
254	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
255	C₄⋊C₈	—	2	8	no	—
256	#103	—	2	16	no	—
257	#95	—	2	4	no	—
258	#95	—	2	4	no	—
259	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
260	C₂×Q₈	—	2	4	no	—
261	C₂×Q₈	—	2	8	no	—
262	C₂×Q₈	—	2	4	no	—
263	C₂×Q₈	—	2	8	no	—
264	C₂×Q₈	—	2	4	no	—
265	C₂×Q₈	—	2	8	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×Q₈	—	2	2	no	—
269	C₂×Q₈	C₄⋊C₄×C₄₁	1	16	yes	—
270	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
271	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
272	C₂×Q₈	C₂×Q₈×C₄₁	1	4	yes	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	4	4	no	—
283	C₂²×C₄	—	4	4	no	—
284	C₂²×C₄	—	4	4	no	—
285	C₂²×C₄	—	4	4	no	—
286	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
287	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
288	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
289	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
290	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
293	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
294	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
295	C₂²×C₄	#41×C₄₁	1	2	yes	—
296	C₂²×C₄	#41×C₄₁	1	2	yes	—
297	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	—	4	8	no	—
302	C₄⋊C₄	—	2	16	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	4	4	no	—
308	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
309	C₄²	—	2	16	no	—
310	C₄²	C₂²⋊C₄×C₄₁	1	8	yes	—
311	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
312	C₄²	C₂×D₄×C₄₁	1	4	yes	—
313	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
314	C₂³	#121×C₄₁	1	2	yes	—
315	C₂³	C₂²⋊Q₈×C₄₁	1	2	yes	—
316	C₂³	#135×C₄₁	1	4	yes	—
317	C₂³	#137×C₄₁	1	4	yes	—
318	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
319	Q₈	—	2	4	no	—
320	Q₈	—	2	4	no	—
321	Q₈	—	2	4	no	—
322	Q₈	—	2	16	no	—
323	Q₈	C₂×C₄⋊C₄×C₄₁	1	8	yes	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	16	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	8	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	—	4	4	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	8	8	no	—
339	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
340	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
341	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
342	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
343	C₂×C₄	#117×C₄₁	1	4	yes	—
344	C₂×C₄	#121×C₄₁	1	4	yes	—
345	C₂×C₄	#121×C₄₁	1	2	yes	—
346	C₂×C₄	C₂²⋊Q₈×C₄₁	1	4	yes	—
347	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
348	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
349	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
350	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
351	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
352	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
353	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
354	C₈	—	4	4	no	—
355	C₂²	C₄₁×#380	1	4	yes	—
356	C₂²	C₄₁×#416	1	4	yes	—
357	C₂²	C₄₁×#419	1	4	yes	—
358	C₂²	C₄₁×#464	1	8	yes	—
359	C₂²	C₄₁×#479	1	8	yes	—
360	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
361	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
362	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
363	C₂²	C₂×#135×C₄₁	1	2	yes	—
364	C₂²	C₂×#137×C₄₁	1	2	yes	—
365	C₄	—	2	8	no	—
366	C₄	—	2	4	no	—
367	C₄	—	2	4	no	—
368	C₄	—	4	4	no	—
369	C₄	—	8	4	no	—
370	C₄	C₄₁×#380	1	4	yes	—
371	C₄	C₂²×C₄⋊C₄×C₄₁	1	1	yes	characteristic
372	C₄	C₂×#117×C₄₁	1	1	yes	characteristic
373	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
374	C₄	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
375	C₂	C₄₁×#1805	1	8	yes	direct product factor
376	C₂	C₂×C₄₁×#380	1	1	yes	characteristic
377	C₂	C₂×C₄₁×#416	1	1	yes	characteristic
378	C₂	C₂×C₄₁×#419	1	1	yes	characteristic
379	C₂	C₂×C₄₁×#464	1	2	yes	—
380	C₂	C₂×C₄₁×#479	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
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
5. C₄₁×#1805	C₂	direct (N × H)
11. C₂×C₄×Q₈×C₄₁	C₄	semidirect
47. C₄×Q₈×C₄₁	C₂×C₄	semidirect
164. C₂×#1805	C₄₁	direct (N × H)
189. #1805	C₂×C₄₁	direct (N × H)
191. C₂×C₄₁	#1805	direct (N × H)
201. C₂×C₄×Q₈	C₄×C₄₁	semidirect
217. C₄₁	C₂×#1805	direct (N × H)
238. C₄×Q₈	C₂×C₄×C₄₁	semidirect
375. C₂	C₄₁×#1805	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×C₄×Q₈×C₄₁	2
C₂²×C₄⋊C₈×C₄₁	2
C₂²×#103×C₄₁	2
C₂×C₄₁×#382	2
C₄₁×#1805	2
C₂×C₄₁×#340	2
C₂×#1805	41

Subgroups — C2×C41×#1805 #23796845

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#1805 #23796845