Subgroups — C₂×C₄₁×#1701 #23795341

Order 10496.

810 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×#486	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#459	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₁×#436	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1701	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₁×#334	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₁×#332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₁×#331	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×SD₁₆×C₄₁	—	2	1	no	—
10	C₂²×D₈×C₄₁	—	2	1	no	—
11	C₂²×M₁₆×C₄₁	—	2	1	no	—
12	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
15	C₄₁×#486	—	2	2	no	—
16	C₄₁×#486	C₂²	1	4	yes	complemented
17	C₄₁×#461	—	2	2	no	—
18	C₄₁×#461	C₂²	1	4	yes	complemented
19	C₄₁×#459	—	2	2	no	—
20	C₄₁×#459	C₂²	1	4	yes	—
21	C₄₁×#436	—	2	2	no	—
22	C₄₁×#436	C₂²	1	4	yes	complemented
23	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#103×C₄₁	—	2	1	no	—
27	C₂×#102×C₄₁	—	2	1	no	—
28	C₂×#102×C₄₁	—	2	1	no	—
29	C₂×#102×C₄₁	—	2	1	no	—
30	C₂×C₂²⋊C₈×C₄₁	—	2	1	no	—
31	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
32	C₄₁×#334	C₂²	1	4	yes	complemented
33	C₄₁×#332	C₂²	1	4	yes	complemented
34	C₄₁×#331	C₂²	1	4	yes	complemented
35	C₂²×Q₈×C₄₁	—	2	1	no	—
36	C₂²×D₄×C₄₁	—	2	1	no	—
37	C₂²×D₄×C₄₁	—	2	1	no	—
38	C₂²×D₄×C₄₁	—	2	1	no	—
39	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₁	—	2	1	no	—
41	C₂×SD₁₆×C₄₁	—	2	4	no	—
42	C₂×SD₁₆×C₄₁	—	4	4	no	—
43	C₂×D₈×C₄₁	—	2	4	no	—
44	C₂×D₈×C₄₁	—	4	4	no	—
45	C₂×M₁₆×C₄₁	—	2	4	no	—
46	C₂×M₁₆×C₄₁	—	4	4	no	—
47	C₂²×C₈×C₄₁	—	2	1	no	—
48	C₂²×C₈×C₄₁	—	2	1	no	—
49	C₂²×C₈×C₄₁	—	2	1	no	—
50	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
52	C₄⋊Q₈×C₄₁	—	2	1	no	—
53	C₄⋊Q₈×C₄₁	—	2	1	no	—
54	C₄⋊Q₈×C₄₁	—	2	1	no	—
55	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
56	#127×C₄₁	—	2	1	no	—
57	#127×C₄₁	—	2	1	no	—
58	#127×C₄₁	—	2	1	no	—
59	#127×C₄₁	C₂³	1	2	yes	—
60	C₄×D₄×C₄₁	—	2	1	no	—
61	C₄×D₄×C₄₁	—	2	1	no	—
62	C₄×D₄×C₄₁	D₄	1	2	yes	—
63	C₄×D₄×C₄₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
68	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
69	C₄⋊C₈×C₄₁	—	2	1	no	—
70	C₄⋊C₈×C₄₁	—	2	1	no	—
71	C₄⋊C₈×C₄₁	—	2	1	no	—
72	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
73	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
74	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
75	#103×C₄₁	—	2	4	no	—
76	#102×C₄₁	—	2	4	no	—
77	#102×C₄₁	—	2	4	no	—
78	#102×C₄₁	—	2	4	no	—
79	C₂²⋊C₈×C₄₁	—	2	4	no	—
80	C₄×C₈×C₄₁	D₄	1	2	yes	—
81	C₄×C₈×C₄₁	C₂³	1	2	yes	—
82	C₂⁴×C₄₁	—	2	1	no	—
83	C₂⁴×C₄₁	—	4	1	no	—
84	C₂×Q₈×C₄₁	—	2	2	no	—
85	C₂×Q₈×C₄₁	—	4	1	no	—
86	C₂×Q₈×C₄₁	—	4	2	no	—
87	C₂×Q₈×C₄₁	—	4	2	no	—
88	C₂×D₄×C₄₁	—	2	1	no	—
89	C₂×D₄×C₄₁	—	2	2	no	—
90	C₂×D₄×C₄₁	—	2	2	no	—
91	C₂×D₄×C₄₁	—	2	2	no	—
92	C₂×D₄×C₄₁	—	2	2	no	—
93	C₂×D₄×C₄₁	—	2	2	no	—
94	C₂×D₄×C₄₁	—	4	1	no	—
95	C₂×D₄×C₄₁	—	4	1	no	—
96	C₂×D₄×C₄₁	—	4	1	no	—
97	C₂×D₄×C₄₁	—	4	2	no	—
98	C₂×D₄×C₄₁	—	4	2	no	—
99	C₂×D₄×C₄₁	—	4	2	no	—
100	C₂×D₄×C₄₁	—	4	2	no	—
101	C₂×D₄×C₄₁	—	8	2	no	—
102	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₁	—	2	1	no	—
104	C₂²×C₄×C₄₁	—	2	2	no	—
105	C₂²×C₄×C₄₁	—	2	2	no	—
106	C₂²×C₄×C₄₁	—	4	2	no	—
107	C₂²×C₄×C₄₁	—	4	2	no	—
108	C₂²×C₄×C₄₁	—	4	1	no	—
109	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
112	SD₁₆×C₄₁	—	4	8	no	—
113	D₈×C₄₁	—	4	8	no	—
114	M₁₆×C₄₁	—	4	8	no	—
115	C₂×C₈×C₄₁	—	2	2	no	—
116	C₂×C₈×C₄₁	—	2	2	no	—
117	C₂×C₈×C₄₁	—	2	2	no	—
118	C₂×C₈×C₄₁	—	2	2	no	—
119	C₂×C₈×C₄₁	—	2	2	no	—
120	C₂×C₈×C₄₁	—	4	2	no	—
121	C₂×C₈×C₄₁	—	4	2	no	—
122	C₂×C₈×C₄₁	—	4	2	no	—
123	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
125	C₄⋊C₄×C₄₁	—	2	1	no	—
126	C₄⋊C₄×C₄₁	—	2	2	no	—
127	C₄⋊C₄×C₄₁	—	2	2	no	—
128	C₄⋊C₄×C₄₁	—	4	1	no	—
129	C₄⋊C₄×C₄₁	—	4	1	no	—
130	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
131	C₂²⋊C₄×C₄₁	—	2	2	no	—
132	C₂²⋊C₄×C₄₁	—	2	2	no	—
133	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₁	#41	1	1	yes	characteristic
136	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
137	C₂³×C₄₁	—	2	2	no	—
138	C₂³×C₄₁	—	4	2	no	—
139	C₂³×C₄₁	—	4	2	no	—
140	C₂³×C₄₁	—	4	2	no	—
141	C₂³×C₄₁	—	4	2	no	—
142	C₂³×C₄₁	—	8	2	no	—
143	C₂³×C₄₁	—	8	2	no	—
144	C₂³×C₄₁	—	8	2	no	—
145	C₂³×C₄₁	#121	1	1	yes	characteristic
146	Q₈×C₄₁	—	4	2	no	—
147	Q₈×C₄₁	—	4	2	no	—
148	Q₈×C₄₁	—	8	2	no	—
149	D₄×C₄₁	—	2	2	no	—
150	D₄×C₄₁	—	2	2	no	—
151	D₄×C₄₁	—	4	2	no	—
152	D₄×C₄₁	—	4	2	no	—
153	D₄×C₄₁	—	4	2	no	—
154	D₄×C₄₁	—	4	2	no	—
155	D₄×C₄₁	—	4	2	no	—
156	D₄×C₄₁	—	8	2	no	—
157	D₄×C₄₁	—	8	2	no	—
158	D₄×C₄₁	—	8	2	no	—
159	D₄×C₄₁	—	8	2	no	—
160	C₂×C₄×C₄₁	—	2	2	no	—
161	C₂×C₄×C₄₁	—	2	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	4	no	—
166	C₂×C₄×C₄₁	—	4	2	no	—
167	C₂×C₄×C₄₁	—	8	2	no	—
168	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
169	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
170	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
171	C₂×C₄×C₄₁	#135	1	2	yes	—
172	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
173	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
174	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
175	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
178	C₈×C₄₁	—	2	2	no	—
179	C₈×C₄₁	—	2	2	no	—
180	C₈×C₄₁	—	4	2	no	—
181	C₈×C₄₁	—	4	2	no	—
182	C₈×C₄₁	—	4	2	no	—
183	C₂×#1701	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂²×C₄₁	—	4	2	no	—
185	C₂²×C₄₁	—	4	2	no	—
186	C₂²×C₄₁	—	4	2	no	—
187	C₂²×C₄₁	—	8	4	no	—
188	C₂²×C₄₁	—	8	2	no	—
189	C₂²×C₄₁	—	8	2	no	—
190	C₂²×C₄₁	—	8	2	no	—
191	C₂²×C₄₁	—	16	4	no	—
192	C₂²×C₄₁	#463	1	2	yes	—
193	C₂²×C₄₁	#469	1	2	yes	—
194	C₂²×C₄₁	#471	1	2	yes	—
195	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
196	C₄×C₄₁	—	2	1	no	—
197	C₄×C₄₁	—	2	1	no	—
198	C₄×C₄₁	—	4	2	no	—
199	C₄×C₄₁	—	8	2	no	—
200	C₄×C₄₁	#463	1	2	yes	—
201	C₄×C₄₁	#469	1	2	yes	—
202	C₄×C₄₁	C₂×#135	1	1	yes	characteristic
203	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
204	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
205	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
206	C₂×#486	C₂×C₄₁	1	1	yes	characteristic, complemented
207	C₂×#461	C₂×C₄₁	1	1	yes	characteristic, complemented
208	C₂×#459	C₂×C₄₁	1	1	yes	characteristic
209	C₂×#436	C₂×C₄₁	1	1	yes	characteristic, complemented
210	#1701	C₂×C₄₁	1	8	yes	direct product factor
211	C₂×#334	C₂×C₄₁	1	1	yes	characteristic, complemented
212	C₂×#332	C₂×C₄₁	1	1	yes	characteristic, complemented
213	C₂×#331	C₂×C₄₁	1	1	yes	characteristic, complemented
214	C₂×C₄₁	—	8	2	no	—
215	C₂×C₄₁	—	16	2	no	—
216	C₂×C₄₁	#1701	1	4	yes	direct product factor
217	C₂×C₄₁	C₂×#463	1	1	yes	characteristic
218	C₂×C₄₁	C₂×#469	1	1	yes	characteristic
219	C₂×C₄₁	C₂×#471	1	1	yes	characteristic
220	C₂²×SD₁₆	—	2	1	no	—
221	C₂²×D₈	—	2	1	no	—
222	C₂²×M₁₆	—	2	1	no	—
223	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
224	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
225	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
226	#486	—	2	2	no	—
227	#486	C₂²×C₄₁	1	4	yes	complemented
228	#461	—	2	2	no	—
229	#461	C₂²×C₄₁	1	4	yes	complemented
230	#459	—	2	2	no	—
231	#459	C₂²×C₄₁	1	4	yes	—
232	#436	—	2	2	no	—
233	#436	C₂²×C₄₁	1	4	yes	complemented
234	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
235	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
236	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
237	C₂×#103	—	2	1	no	—
238	C₂×#102	—	2	1	no	—
239	C₂×#102	—	2	1	no	—
240	C₂×#102	—	2	1	no	—
241	C₂×C₂²⋊C₈	—	2	1	no	—
242	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
243	#334	C₂²×C₄₁	1	4	yes	complemented
244	#332	C₂²×C₄₁	1	4	yes	complemented
245	#331	C₂²×C₄₁	1	4	yes	complemented
246	C₄₁	C₂×#1701	1	1	yes	characteristic, direct product factor, Sylow
247	C₂²×Q₈	—	2	1	no	—
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	—	2	1	no	—
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
252	C₂³×C₄	—	2	1	no	—
253	C₂×SD₁₆	—	2	4	no	—
254	C₂×SD₁₆	—	4	4	no	—
255	C₂×D₈	—	2	4	no	—
256	C₂×D₈	—	4	4	no	—
257	C₂×M₁₆	—	2	4	no	—
258	C₂×M₁₆	—	4	4	no	—
259	C₂²×C₈	—	2	1	no	—
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
263	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
264	C₄⋊Q₈	—	2	1	no	—
265	C₄⋊Q₈	—	2	1	no	—
266	C₄⋊Q₈	—	2	1	no	—
267	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
268	#127	—	2	1	no	—
269	#127	—	2	1	no	—
270	#127	—	2	1	no	—
271	#127	C₂³×C₄₁	1	2	yes	—
272	C₄×D₄	—	2	1	no	—
273	C₄×D₄	—	2	1	no	—
274	C₄×D₄	D₄×C₄₁	1	2	yes	—
275	C₄×D₄	C₂³×C₄₁	1	2	yes	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	—	2	1	no	—
280	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	—	2	1	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
285	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
286	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
287	#103	—	2	4	no	—
288	#102	—	2	4	no	—
289	#102	—	2	4	no	—
290	#102	—	2	4	no	—
291	C₂²⋊C₈	—	2	4	no	—
292	C₄×C₈	D₄×C₄₁	1	2	yes	—
293	C₄×C₈	C₂³×C₄₁	1	2	yes	—
294	C₂⁴	—	2	1	no	—
295	C₂⁴	—	4	1	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	4	2	no	—
299	C₂×Q₈	—	4	2	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	—	4	2	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	8	2	no	—
314	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	—	4	2	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
323	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
324	SD₁₆	—	4	8	no	—
325	D₈	—	4	8	no	—
326	M₁₆	—	4	8	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	4	2	no	—
333	C₂×C₈	—	4	2	no	—
334	C₂×C₈	—	4	2	no	—
335	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
336	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	—	4	1	no	—
342	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
343	C₂²⋊C₄	—	2	2	no	—
344	C₂²⋊C₄	—	2	2	no	—
345	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
346	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
347	C₄²	#41×C₄₁	1	1	yes	characteristic
348	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
349	C₂³	—	2	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	8	2	no	—
355	C₂³	—	8	2	no	—
356	C₂³	—	8	2	no	—
357	C₂³	#121×C₄₁	1	1	yes	characteristic
358	Q₈	—	4	2	no	—
359	Q₈	—	4	2	no	—
360	Q₈	—	8	2	no	—
361	D₄	—	2	2	no	—
362	D₄	—	2	2	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	4	2	no	—
368	D₄	—	8	2	no	—
369	D₄	—	8	2	no	—
370	D₄	—	8	2	no	—
371	D₄	—	8	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	8	2	no	—
380	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
381	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
382	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
383	C₂×C₄	#135×C₄₁	1	2	yes	—
384	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
385	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
386	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
387	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
388	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
389	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
390	C₈	—	2	2	no	—
391	C₈	—	2	2	no	—
392	C₈	—	4	2	no	—
393	C₈	—	4	2	no	—
394	C₈	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	8	4	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	16	4	no	—
403	C₂²	C₄₁×#463	1	2	yes	—
404	C₂²	C₄₁×#469	1	2	yes	—
405	C₂²	C₄₁×#471	1	2	yes	—
406	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	4	2	no	—
410	C₄	—	8	2	no	—
411	C₄	C₄₁×#463	1	2	yes	—
412	C₄	C₄₁×#469	1	2	yes	—
413	C₄	C₂×#135×C₄₁	1	1	yes	characteristic
414	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
415	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
416	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
417	C₂	—	8	2	no	—
418	C₂	—	16	2	no	—
419	C₂	C₄₁×#1701	1	4	yes	direct product factor
420	C₂	C₂×C₄₁×#463	1	1	yes	characteristic
421	C₂	C₂×C₄₁×#469	1	1	yes	characteristic
422	C₂	C₂×C₄₁×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#459	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#486	C₂	semidirect
2. C₂×C₄₁×#461	C₂	semidirect
4. C₂×C₄₁×#436	C₂	semidirect
5. C₄₁×#1701	C₂	direct (N × H)
6. C₂×C₄₁×#334	C₂	semidirect
7. C₂×C₄₁×#332	C₂	semidirect
8. C₂×C₄₁×#331	C₂	semidirect
16. C₄₁×#486	C₂²	semidirect
18. C₄₁×#461	C₂²	semidirect
22. C₄₁×#436	C₂²	semidirect
32. C₄₁×#334	C₂²	semidirect
33. C₄₁×#332	C₂²	semidirect
34. C₄₁×#331	C₂²	semidirect
183. C₂×#1701	C₄₁	direct (N × H)
206. C₂×#486	C₂×C₄₁	semidirect
207. C₂×#461	C₂×C₄₁	semidirect
209. C₂×#436	C₂×C₄₁	semidirect
210. #1701	C₂×C₄₁	direct (N × H)
211. C₂×#334	C₂×C₄₁	semidirect
212. C₂×#332	C₂×C₄₁	semidirect
213. C₂×#331	C₂×C₄₁	semidirect
216. C₂×C₄₁	#1701	direct (N × H)
227. #486	C₂²×C₄₁	semidirect
229. #461	C₂²×C₄₁	semidirect
233. #436	C₂²×C₄₁	semidirect
243. #334	C₂²×C₄₁	semidirect
244. #332	C₂²×C₄₁	semidirect
245. #331	C₂²×C₄₁	semidirect
246. C₄₁	C₂×#1701	direct (N × H)
419. C₂	C₄₁×#1701	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×#486	2
C₂×C₄₁×#461	2
C₂×C₄₁×#459	2
C₂×C₄₁×#436	2
C₄₁×#1701	2
C₂×C₄₁×#334	2
C₂×C₄₁×#332	2
C₂×C₄₁×#331	2
C₂×#1701	41

Subgroups — C2×C41×#1701 #23795341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#1701 #23795341