Subgroups — C₄₁×#33525 #23809726

Order 10496.

1086 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#578	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×Q₃₂×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3059	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2189	C₂	1	4	yes	maximal, complemented
6	C₄₁×#2188	C₂	1	4	yes	maximal, complemented
7	C₄₁×#2141	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#2138	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#2113	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×2₋¹⁺⁴×C₄₁	—	2	1	no	—
11	C₄₁×#578	—	2	4	no	—
12	C₄₁×#578	—	2	4	no	—
13	C₂×#137×C₄₁	—	2	1	no	—
14	C₂×#137×C₄₁	—	2	2	no	—
15	C₂×#135×C₄₁	C₂²	1	2	yes	—
16	C₂×#135×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₄₁	C₂²	1	2	yes	—
19	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#131×C₄₁	C₂²	1	1	yes	characteristic
21	C₄₁×#536	—	2	1	no	—
22	C₄₁×#510	—	2	4	no	—
23	C₂×Q₃₂×C₄₁	—	2	4	no	—
24	C₂×Q₃₂×C₄₁	C₂²	1	4	yes	—
25	C₂×Q₃₂×C₄₁	C₂²	1	2	yes	—
26	C₂×SD₃₂×C₄₁	C₂²	1	2	yes	—
27	C₂×M₃₂×C₄₁	C₂²	1	1	yes	characteristic
28	C₂²×C₁₆×C₄₁	C₂²	1	1	yes	characteristic
29	C₄₁×#470	—	2	2	no	—
30	C₄₁×#467	C₂²	1	4	yes	—
31	C₄₁×#427	C₂²	1	1	yes	characteristic
32	C₄₁×#419	—	2	1	no	—
33	C₄₁×#358	C₂²	1	2	yes	—
34	C₄₁×#358	C₂²	1	4	yes	—
35	C₄₁×#357	C₂²	1	2	yes	—
36	C₄₁×C₂²⋊C₁₆	C₂²	1	4	yes	—
37	2₋¹⁺⁴×C₄₁	—	2	8	no	—
38	2₋¹⁺⁴×C₄₁	—	4	4	no	—
39	C₂×#41×C₄₁	—	2	2	no	—
40	C₂×#41×C₄₁	—	2	1	no	—
41	C₂×#41×C₄₁	—	4	2	no	—
42	C₂×#41×C₄₁	—	4	1	no	—
43	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
44	C₂²×Q₈×C₄₁	—	2	2	no	—
45	C₂²×Q₈×C₄₁	—	2	1	no	—
46	C₂²×Q₈×C₄₁	—	2	1	no	—
47	C₂²×Q₈×C₄₁	—	4	1	no	—
48	#137×C₄₁	—	2	8	no	—
49	#137×C₄₁	—	2	16	no	—
50	#135×C₄₁	—	2	4	no	—
51	#135×C₄₁	—	2	4	no	—
52	#135×C₄₁	—	2	2	no	—
53	#135×C₄₁	D₄	1	4	yes	—
54	C₂×Q₁₆×C₄₁	—	2	4	no	—
55	C₂×Q₁₆×C₄₁	—	2	4	no	—
56	C₂×Q₁₆×C₄₁	—	2	2	no	—
57	C₂×Q₁₆×C₄₁	—	2	1	no	—
58	C₂×Q₁₆×C₄₁	—	2	2	no	—
59	C₂×Q₁₆×C₄₁	—	2	2	no	—
60	C₂×Q₁₆×C₄₁	—	2	2	no	—
61	C₂×Q₁₆×C₄₁	—	2	1	no	—
62	C₂×Q₁₆×C₄₁	D₄	1	4	yes	—
63	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
64	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
65	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
66	C₂×SD₁₆×C₄₁	—	2	2	no	—
67	C₂×SD₁₆×C₄₁	—	2	1	no	—
68	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
69	#131×C₄₁	—	2	2	no	—
70	#131×C₄₁	—	2	2	no	—
71	C₂×M₁₆×C₄₁	D₄	1	1	yes	characteristic
72	C₂×M₁₆×C₄₁	D₄	1	2	yes	—
73	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
74	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
75	C₄⋊Q₈×C₄₁	—	4	1	no	—
76	#124×C₄₁	—	4	1	no	—
77	#123×C₄₁	—	4	2	no	—
78	C₂²⋊Q₈×C₄₁	—	2	4	no	—
79	#117×C₄₁	—	2	1	no	—
80	Q₃₂×C₄₁	—	2	8	no	—
81	Q₃₂×C₄₁	—	2	4	no	—
82	SD₃₂×C₄₁	—	2	4	no	—
83	M₃₂×C₄₁	—	2	2	no	—
84	C₂×C₁₆×C₄₁	—	2	2	no	—
85	C₂×C₁₆×C₄₁	C₂³	1	2	yes	—
86	C₂×C₁₆×C₄₁	C₂³	1	2	yes	—
87	#107×C₄₁	C₂³	1	2	yes	—
88	#106×C₄₁	—	2	1	no	—
89	#103×C₄₁	—	2	4	no	—
90	#41×C₄₁	—	2	2	no	—
91	#41×C₄₁	—	2	2	no	—
92	#41×C₄₁	—	2	8	no	—
93	#41×C₄₁	—	2	4	no	—
94	#41×C₄₁	—	4	4	no	—
95	#41×C₄₁	—	4	16	no	—
96	#41×C₄₁	—	4	8	no	—
97	#41×C₄₁	—	4	2	no	—
98	C₂×Q₈×C₄₁	—	2	8	no	—
99	C₂×Q₈×C₄₁	—	2	4	no	—
100	C₂×Q₈×C₄₁	—	2	2	no	—
101	C₂×Q₈×C₄₁	—	2	1	no	—
102	C₂×Q₈×C₄₁	—	2	2	no	—
103	C₂×Q₈×C₄₁	—	4	4	no	—
104	C₂×Q₈×C₄₁	—	4	8	no	—
105	C₂×Q₈×C₄₁	—	4	2	no	—
106	C₂×Q₈×C₄₁	—	4	1	no	—
107	C₂×Q₈×C₄₁	—	4	1	no	—
108	C₂×Q₈×C₄₁	—	4	2	no	—
109	C₂×Q₈×C₄₁	—	4	2	no	—
110	C₂×Q₈×C₄₁	—	4	2	no	—
111	C₂×Q₈×C₄₁	D₈	1	1	yes	characteristic
112	C₂×D₄×C₄₁	—	2	1	no	—
113	C₂×D₄×C₄₁	—	4	2	no	—
114	C₂×D₄×C₄₁	—	4	1	no	—
115	C₂×D₄×C₄₁	D₈	1	2	yes	—
116	C₂×D₄×C₄₁	D₈	1	1	yes	characteristic
117	C₂²×C₄×C₄₁	—	4	2	no	—
118	C₂²×C₄×C₄₁	—	4	1	no	—
119	C₂²×C₄×C₄₁	—	4	2	no	—
120	C₂²×C₄×C₄₁	—	4	1	no	—
121	C₂²×C₄×C₄₁	—	4	1	no	—
122	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
124	Q₁₆×C₄₁	—	2	8	no	—
125	Q₁₆×C₄₁	—	2	4	no	—
126	Q₁₆×C₄₁	—	2	1	no	—
127	Q₁₆×C₄₁	—	2	2	no	—
128	Q₁₆×C₄₁	—	2	2	no	—
129	Q₁₆×C₄₁	—	2	2	no	—
130	Q₁₆×C₄₁	—	4	2	no	—
131	Q₁₆×C₄₁	C₂×D₄	1	2	yes	—
132	Q₁₆×C₄₁	C₂×D₄	1	4	yes	—
133	SD₁₆×C₄₁	—	2	8	no	—
134	SD₁₆×C₄₁	—	2	4	no	—
135	D₈×C₄₁	—	2	1	no	—
136	D₈×C₄₁	C₂×D₄	1	2	yes	—
137	M₁₆×C₄₁	—	2	2	no	—
138	M₁₆×C₄₁	—	2	4	no	—
139	C₂×C₈×C₄₁	—	2	2	no	—
140	C₂×C₈×C₄₁	—	2	2	no	—
141	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
146	C₄⋊C₄×C₄₁	—	2	2	no	—
147	C₄⋊C₄×C₄₁	—	4	4	no	—
148	C₂²⋊C₄×C₄₁	—	4	1	no	—
149	C₂²⋊C₄×C₄₁	—	4	4	no	—
150	C₄²×C₄₁	—	4	1	no	—
151	C₁₆×C₄₁	—	2	2	no	—
152	C₁₆×C₄₁	—	2	2	no	—
153	C₂³×C₄₁	—	4	1	no	—
154	C₂³×C₄₁	C₂×D₈	1	2	yes	—
155	C₂³×C₄₁	C₂×D₈	1	1	yes	characteristic
156	Q₈×C₄₁	—	2	2	no	—
157	Q₈×C₄₁	—	2	4	no	—
158	Q₈×C₄₁	—	2	2	no	—
159	Q₈×C₄₁	—	4	8	no	—
160	Q₈×C₄₁	—	4	1	no	—
161	Q₈×C₄₁	—	4	2	no	—
162	Q₈×C₄₁	—	4	4	no	—
163	Q₈×C₄₁	—	4	2	no	—
164	Q₈×C₄₁	—	4	2	no	—
165	Q₈×C₄₁	—	8	2	no	—
166	D₄×C₄₁	—	2	4	no	—
167	D₄×C₄₁	—	2	2	no	—
168	D₄×C₄₁	—	2	2	no	—
169	D₄×C₄₁	—	4	8	no	—
170	D₄×C₄₁	—	4	4	no	—
171	D₄×C₄₁	—	4	1	no	—
172	C₂×C₄×C₄₁	—	2	2	no	—
173	C₂×C₄×C₄₁	—	2	2	no	—
174	C₂×C₄×C₄₁	—	4	8	no	—
175	C₂×C₄×C₄₁	—	4	8	no	—
176	C₂×C₄×C₄₁	—	4	2	no	—
177	C₂×C₄×C₄₁	—	4	1	no	—
178	C₂×C₄×C₄₁	—	4	4	no	—
179	C₂×C₄×C₄₁	—	4	4	no	—
180	C₂×C₄×C₄₁	—	4	2	no	—
181	C₂×C₄×C₄₁	—	4	2	no	—
182	C₂×C₄×C₄₁	—	8	2	no	—
183	C₂×C₄×C₄₁	#120	1	2	yes	—
184	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
185	C₂×C₄×C₄₁	C₂×D₈	1	1	yes	characteristic
186	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
187	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
188	C₈×C₄₁	—	2	2	no	—
189	C₈×C₄₁	#120	1	2	yes	—
190	C₈×C₄₁	C₂²×D₄	1	1	yes	characteristic
191	C₈×C₄₁	C₂²×D₄	1	1	yes	characteristic
192	#33525	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₂²×C₄₁	—	2	2	no	—
194	C₂²×C₄₁	—	2	4	no	—
195	C₂²×C₄₁	—	2	2	no	—
196	C₂²×C₄₁	—	4	2	no	—
197	C₂²×C₄₁	—	8	2	no	—
198	C₂²×C₄₁	#447	1	2	yes	—
199	C₂²×C₄₁	C₂²×D₈	1	1	yes	characteristic
200	C₄×C₄₁	—	2	2	no	—
201	C₄×C₄₁	—	4	4	no	—
202	C₄×C₄₁	—	4	2	no	—
203	C₄×C₄₁	—	8	2	no	—
204	C₄×C₄₁	—	8	2	no	—
205	C₄×C₄₁	#447	1	2	yes	—
206	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
207	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
208	C₂×#578	C₂×C₄₁	1	1	yes	characteristic
209	C₂×#510	C₂×C₄₁	1	1	yes	characteristic, complemented
210	C₂²×Q₃₂	C₂×C₄₁	1	1	yes	characteristic, complemented
211	#3059	C₂×C₄₁	1	1	yes	characteristic, complemented
212	#2189	C₂×C₄₁	1	4	yes	complemented
213	#2188	C₂×C₄₁	1	4	yes	complemented
214	#2141	C₂×C₄₁	1	1	yes	characteristic, complemented
215	#2138	C₂×C₄₁	1	1	yes	characteristic, complemented
216	#2113	C₂×C₄₁	1	1	yes	characteristic, complemented
217	C₂×C₄₁	—	2	2	no	—
218	C₂×C₄₁	—	4	2	no	—
219	C₂×C₄₁	—	8	2	no	—
220	C₂×C₄₁	C₂×#447	1	1	yes	characteristic
221	C₂×C₄₁	#3417	1	2	yes	—
222	C₂×2₋¹⁺⁴	—	2	1	no	—
223	#578	—	2	4	no	—
224	#578	—	2	4	no	—
225	C₂×#137	—	2	1	no	—
226	C₂×#137	—	2	2	no	—
227	C₂×#135	C₂²×C₄₁	1	2	yes	—
228	C₂×#135	C₂²×C₄₁	1	1	yes	characteristic
229	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
230	C₂²×Q₁₆	C₂²×C₄₁	1	2	yes	—
231	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
232	C₂×#131	C₂²×C₄₁	1	1	yes	characteristic
233	#536	—	2	1	no	—
234	#510	—	2	4	no	—
235	C₂×Q₃₂	—	2	4	no	—
236	C₂×Q₃₂	C₂²×C₄₁	1	4	yes	—
237	C₂×Q₃₂	C₂²×C₄₁	1	2	yes	—
238	C₂×SD₃₂	C₂²×C₄₁	1	2	yes	—
239	C₂×M₃₂	C₂²×C₄₁	1	1	yes	characteristic
240	C₂²×C₁₆	C₂²×C₄₁	1	1	yes	characteristic
241	#470	—	2	2	no	—
242	#467	C₂²×C₄₁	1	4	yes	—
243	#427	C₂²×C₄₁	1	1	yes	characteristic
244	#419	—	2	1	no	—
245	#358	C₂²×C₄₁	1	2	yes	—
246	#358	C₂²×C₄₁	1	4	yes	—
247	#357	C₂²×C₄₁	1	2	yes	—
248	C₂²⋊C₁₆	C₂²×C₄₁	1	4	yes	—
249	C₄₁	#33525	1	1	yes	characteristic, direct product factor, Sylow
250	2₋¹⁺⁴	—	2	8	no	—
251	2₋¹⁺⁴	—	4	4	no	—
252	C₂×#41	—	2	2	no	—
253	C₂×#41	—	2	1	no	—
254	C₂×#41	—	4	2	no	—
255	C₂×#41	—	4	1	no	—
256	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
257	C₂²×Q₈	—	2	2	no	—
258	C₂²×Q₈	—	2	1	no	—
259	C₂²×Q₈	—	2	1	no	—
260	C₂²×Q₈	—	4	1	no	—
261	#137	—	2	8	no	—
262	#137	—	2	16	no	—
263	#135	—	2	4	no	—
264	#135	—	2	4	no	—
265	#135	—	2	2	no	—
266	#135	D₄×C₄₁	1	4	yes	—
267	C₂×Q₁₆	—	2	4	no	—
268	C₂×Q₁₆	—	2	4	no	—
269	C₂×Q₁₆	—	2	2	no	—
270	C₂×Q₁₆	—	2	1	no	—
271	C₂×Q₁₆	—	2	2	no	—
272	C₂×Q₁₆	—	2	2	no	—
273	C₂×Q₁₆	—	2	2	no	—
274	C₂×Q₁₆	—	2	1	no	—
275	C₂×Q₁₆	D₄×C₄₁	1	4	yes	—
276	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
277	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
278	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
279	C₂×SD₁₆	—	2	2	no	—
280	C₂×SD₁₆	—	2	1	no	—
281	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
282	#131	—	2	2	no	—
283	#131	—	2	2	no	—
284	C₂×M₁₆	D₄×C₄₁	1	1	yes	characteristic
285	C₂×M₁₆	D₄×C₄₁	1	2	yes	—
286	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
287	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
288	C₄⋊Q₈	—	4	1	no	—
289	#124	—	4	1	no	—
290	#123	—	4	2	no	—
291	C₂²⋊Q₈	—	2	4	no	—
292	#117	—	2	1	no	—
293	Q₃₂	—	2	8	no	—
294	Q₃₂	—	2	4	no	—
295	SD₃₂	—	2	4	no	—
296	M₃₂	—	2	2	no	—
297	C₂×C₁₆	—	2	2	no	—
298	C₂×C₁₆	C₂³×C₄₁	1	2	yes	—
299	C₂×C₁₆	C₂³×C₄₁	1	2	yes	—
300	#107	C₂³×C₄₁	1	2	yes	—
301	#106	—	2	1	no	—
302	#103	—	2	4	no	—
303	#41	—	2	2	no	—
304	#41	—	2	2	no	—
305	#41	—	2	8	no	—
306	#41	—	2	4	no	—
307	#41	—	4	4	no	—
308	#41	—	4	16	no	—
309	#41	—	4	8	no	—
310	#41	—	4	2	no	—
311	C₂×Q₈	—	2	8	no	—
312	C₂×Q₈	—	2	4	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	4	4	no	—
317	C₂×Q₈	—	4	8	no	—
318	C₂×Q₈	—	4	2	no	—
319	C₂×Q₈	—	4	1	no	—
320	C₂×Q₈	—	4	1	no	—
321	C₂×Q₈	—	4	2	no	—
322	C₂×Q₈	—	4	2	no	—
323	C₂×Q₈	—	4	2	no	—
324	C₂×Q₈	D₈×C₄₁	1	1	yes	characteristic
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	4	2	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂×D₄	D₈×C₄₁	1	2	yes	—
329	C₂×D₄	D₈×C₄₁	1	1	yes	characteristic
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	1	no	—
334	C₂²×C₄	—	4	1	no	—
335	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
337	Q₁₆	—	2	8	no	—
338	Q₁₆	—	2	4	no	—
339	Q₁₆	—	2	1	no	—
340	Q₁₆	—	2	2	no	—
341	Q₁₆	—	2	2	no	—
342	Q₁₆	—	2	2	no	—
343	Q₁₆	—	4	2	no	—
344	Q₁₆	C₂×D₄×C₄₁	1	2	yes	—
345	Q₁₆	C₂×D₄×C₄₁	1	4	yes	—
346	SD₁₆	—	2	8	no	—
347	SD₁₆	—	2	4	no	—
348	D₈	—	2	1	no	—
349	D₈	C₂×D₄×C₄₁	1	2	yes	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	2	4	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
355	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
356	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
357	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
358	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	4	4	no	—
361	C₂²⋊C₄	—	4	1	no	—
362	C₂²⋊C₄	—	4	4	no	—
363	C₄²	—	4	1	no	—
364	C₁₆	—	2	2	no	—
365	C₁₆	—	2	2	no	—
366	C₂³	—	4	1	no	—
367	C₂³	C₂×D₈×C₄₁	1	2	yes	—
368	C₂³	C₂×D₈×C₄₁	1	1	yes	characteristic
369	Q₈	—	2	2	no	—
370	Q₈	—	2	4	no	—
371	Q₈	—	2	2	no	—
372	Q₈	—	4	8	no	—
373	Q₈	—	4	1	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	4	4	no	—
376	Q₈	—	4	2	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	8	2	no	—
379	D₄	—	2	4	no	—
380	D₄	—	2	2	no	—
381	D₄	—	2	2	no	—
382	D₄	—	4	8	no	—
383	D₄	—	4	4	no	—
384	D₄	—	4	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	4	8	no	—
388	C₂×C₄	—	4	8	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	4	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	8	2	no	—
396	C₂×C₄	#120×C₄₁	1	2	yes	—
397	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
398	C₂×C₄	C₂×D₈×C₄₁	1	1	yes	characteristic
399	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
400	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
401	C₈	—	2	2	no	—
402	C₈	#120×C₄₁	1	2	yes	—
403	C₈	C₂²×D₄×C₄₁	1	1	yes	characteristic
404	C₈	C₂²×D₄×C₄₁	1	1	yes	characteristic
405	C₂²	—	2	2	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	8	2	no	—
410	C₂²	C₄₁×#447	1	2	yes	—
411	C₂²	C₂²×D₈×C₄₁	1	1	yes	characteristic
412	C₄	—	2	2	no	—
413	C₄	—	4	4	no	—
414	C₄	—	4	2	no	—
415	C₄	—	8	2	no	—
416	C₄	—	8	2	no	—
417	C₄	C₄₁×#447	1	2	yes	—
418	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
419	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
420	C₂	—	2	2	no	—
421	C₂	—	4	2	no	—
422	C₂	—	8	2	no	—
423	C₂	C₂×C₄₁×#447	1	1	yes	characteristic
424	C₂	C₄₁×#3417	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#578	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×#41×C₄₁ ◁ C₂×#131×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#510	C₂	semidirect
3. C₂²×Q₃₂×C₄₁	C₂	semidirect
4. C₄₁×#3059	C₂	semidirect
5. C₄₁×#2189	C₂	semidirect
6. C₄₁×#2188	C₂	semidirect
7. C₄₁×#2141	C₂	semidirect
8. C₄₁×#2138	C₂	semidirect
9. C₄₁×#2113	C₂	semidirect
192. #33525	C₄₁	direct (N × H)
209. C₂×#510	C₂×C₄₁	semidirect
210. C₂²×Q₃₂	C₂×C₄₁	semidirect
211. #3059	C₂×C₄₁	semidirect
212. #2189	C₂×C₄₁	semidirect
213. #2188	C₂×C₄₁	semidirect
214. #2141	C₂×C₄₁	semidirect
215. #2138	C₂×C₄₁	semidirect
216. #2113	C₂×C₄₁	semidirect
249. C₄₁	#33525	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×#578	2
C₂×C₄₁×#510	2
C₂²×Q₃₂×C₄₁	2
C₄₁×#3059	2
C₄₁×#2189	2
C₄₁×#2188	2
C₄₁×#2141	2
C₄₁×#2138	2
C₄₁×#2113	2
#33525	41

Subgroups — C41×#33525 #23809726

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33525 #23809726