Subgroups — C₄₁×#11039 #23787240

Order 10496.

1294 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#575	C₂	1	1	yes	maximal, characteristic
2	C₂²×#104×C₄₁	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₁×#413	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₁×#338	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1728	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#41×C₄₁	C₂²	1	2	yes	—
7	C₄₁×#575	—	2	4	no	—
8	C₄₁×#575	—	2	2	no	—
9	C₄₁×#575	C₄	1	4	yes	complemented
10	C₂×#137×C₄₁	—	2	2	no	—
11	C₂×AGL(1,ℤ/8)×C₄₁	—	2	2	no	—
12	C₂×#135×C₄₁	—	2	2	no	—
13	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
15	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×#104×C₄₁	—	2	4	no	—
18	C₂×#104×C₄₁	—	2	4	no	—
19	C₂×#104×C₄₁	—	2	4	no	—
20	C₄₁×#413	—	2	4	no	—
21	C₄₁×#413	—	2	4	no	—
22	C₂×#101×C₄₁	—	2	2	no	—
23	C₂×#100×C₄₁	—	2	2	no	—
24	C₄₁×#338	—	2	2	no	—
25	C₄₁×#336	—	2	2	no	—
26	C₂×#41×C₄₁	—	2	2	no	—
27	C₂×#41×C₄₁	—	2	2	no	—
28	C₂×#41×C₄₁	—	2	2	no	—
29	C₂×#41×C₄₁	—	2	2	no	—
30	C₂×#41×C₄₁	—	2	2	no	—
31	C₂×#41×C₄₁	—	2	2	no	—
32	C₂×#41×C₄₁	—	2	2	no	—
33	C₂×#41×C₄₁	—	2	2	no	—
34	C₂×#41×C₄₁	—	2	2	no	—
35	C₂×#41×C₄₁	—	2	2	no	—
36	C₂×#41×C₄₁	C₂×C₄	1	4	yes	—
37	C₂×#41×C₄₁	D₄	1	4	yes	—
38	C₂²×Q₈×C₄₁	D₄	1	2	yes	—
39	C₂²×D₄×C₄₁	—	2	2	no	—
40	C₂²×D₄×C₄₁	D₄	1	2	yes	—
41	C₂³×C₄×C₄₁	—	2	2	no	—
42	C₂³×C₄×C₄₁	—	2	1	no	—
43	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
44	#137×C₄₁	—	2	8	no	—
45	#137×C₄₁	—	2	8	no	—
46	AGL(1,ℤ/8)×C₄₁	—	2	8	no	—
47	AGL(1,ℤ/8)×C₄₁	—	2	8	no	—
48	#135×C₄₁	—	2	8	no	—
49	#135×C₄₁	—	2	8	no	—
50	C₂×Q₁₆×C₄₁	—	2	2	no	—
51	C₂×SD₁₆×C₄₁	—	2	4	no	—
52	C₂×D₈×C₄₁	—	2	2	no	—
53	C₂×M₁₆×C₄₁	—	2	2	no	—
54	C₂×M₁₆×C₄₁	—	2	2	no	—
55	C₂×M₁₆×C₄₁	—	2	2	no	—
56	C₂×M₁₆×C₄₁	—	2	1	no	—
57	C₂×M₁₆×C₄₁	—	2	2	no	—
58	C₂×M₁₆×C₄₁	—	2	2	no	—
59	C₂×M₁₆×C₄₁	—	2	2	no	—
60	C₂×M₁₆×C₄₁	—	2	2	no	—
61	C₂×M₁₆×C₄₁	—	2	2	no	—
62	C₂×M₁₆×C₄₁	—	2	2	no	—
63	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	—
64	C₂×M₁₆×C₄₁	D₄	1	2	yes	—
65	C₂×M₁₆×C₄₁	D₄	1	4	yes	—
66	C₂×M₁₆×C₄₁	D₄	1	2	yes	—
67	C₂²×C₈×C₄₁	—	2	1	no	—
68	C₂²×C₈×C₄₁	—	2	2	no	—
69	C₂²×C₈×C₄₁	D₄	1	2	yes	—
70	C₂×C₄²×C₄₁	—	2	2	no	—
71	C₂×C₄²×C₄₁	—	2	2	no	—
72	C₂×C₄²×C₄₁	—	2	1	no	—
73	C₂×C₄²×C₄₁	D₄	1	2	yes	—
74	#104×C₄₁	—	2	16	no	—
75	#101×C₄₁	—	2	8	no	—
76	#100×C₄₁	—	2	8	no	—
77	C₂⁴×C₄₁	—	2	2	no	—
78	C₂⁴×C₄₁	#41	1	1	yes	characteristic
79	#41×C₄₁	—	2	4	no	—
80	#41×C₄₁	—	2	4	no	—
81	#41×C₄₁	—	2	4	no	—
82	#41×C₄₁	—	2	4	no	—
83	#41×C₄₁	—	2	4	no	—
84	#41×C₄₁	—	2	4	no	—
85	#41×C₄₁	—	2	4	no	—
86	#41×C₄₁	—	2	4	no	—
87	#41×C₄₁	—	4	2	no	—
88	#41×C₄₁	—	4	2	no	—
89	#41×C₄₁	—	4	2	no	—
90	#41×C₄₁	—	4	2	no	—
91	#41×C₄₁	—	4	2	no	—
92	#41×C₄₁	—	4	2	no	—
93	#41×C₄₁	—	4	2	no	—
94	#41×C₄₁	—	4	2	no	—
95	C₂×Q₈×C₄₁	—	2	2	no	—
96	C₂×Q₈×C₄₁	—	2	2	no	—
97	C₂×Q₈×C₄₁	—	2	2	no	—
98	C₂×Q₈×C₄₁	—	2	2	no	—
99	C₂×Q₈×C₄₁	—	2	2	no	—
100	C₂×Q₈×C₄₁	C₂²⋊C₄	1	4	yes	—
101	C₂×D₄×C₄₁	—	2	4	no	—
102	C₂×D₄×C₄₁	—	2	4	no	—
103	C₂×D₄×C₄₁	—	2	2	no	—
104	C₂×D₄×C₄₁	—	2	2	no	—
105	C₂×D₄×C₄₁	—	2	2	no	—
106	C₂×D₄×C₄₁	—	2	2	no	—
107	C₂×D₄×C₄₁	—	2	2	no	—
108	C₂×D₄×C₄₁	—	4	2	no	—
109	C₂×D₄×C₄₁	—	4	2	no	—
110	C₂×D₄×C₄₁	—	4	2	no	—
111	C₂×D₄×C₄₁	—	4	2	no	—
112	C₂×D₄×C₄₁	C₂²⋊C₄	1	4	yes	—
113	C₂²×C₄×C₄₁	—	2	2	no	—
114	C₂²×C₄×C₄₁	—	2	2	no	—
115	C₂²×C₄×C₄₁	—	2	4	no	—
116	C₂²×C₄×C₄₁	—	2	4	no	—
117	C₂²×C₄×C₄₁	—	4	4	no	—
118	C₂²×C₄×C₄₁	—	4	2	no	—
119	C₂²×C₄×C₄₁	—	4	2	no	—
120	C₂²×C₄×C₄₁	—	4	2	no	—
121	C₂²×C₄×C₄₁	—	4	2	no	—
122	C₂²×C₄×C₄₁	—	4	2	no	—
123	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
132	C₂²×C₄×C₄₁	#41	1	2	yes	—
133	Q₁₆×C₄₁	—	2	8	no	—
134	SD₁₆×C₄₁	—	2	16	no	—
135	D₈×C₄₁	—	2	8	no	—
136	M₁₆×C₄₁	—	2	4	no	—
137	M₁₆×C₄₁	—	2	4	no	—
138	M₁₆×C₄₁	—	2	4	no	—
139	M₁₆×C₄₁	—	2	4	no	—
140	M₁₆×C₄₁	—	2	4	no	—
141	M₁₆×C₄₁	—	4	2	no	—
142	M₁₆×C₄₁	—	4	2	no	—
143	M₁₆×C₄₁	—	4	2	no	—
144	C₂×C₈×C₄₁	—	2	2	no	—
145	C₂×C₈×C₄₁	—	2	2	no	—
146	C₂×C₈×C₄₁	—	2	4	no	—
147	C₂×C₈×C₄₁	—	2	2	no	—
148	C₂×C₈×C₄₁	—	4	1	no	—
149	C₂×C₈×C₄₁	—	4	2	no	—
150	C₂×C₈×C₄₁	—	4	2	no	—
151	C₂×C₈×C₄₁	—	4	1	no	—
152	C₂×C₈×C₄₁	C₂²⋊C₄	1	4	yes	—
153	C₄²×C₄₁	—	2	4	no	—
154	C₄²×C₄₁	—	4	1	no	—
155	C₄²×C₄₁	—	4	1	no	—
156	C₂³×C₄₁	—	2	4	no	—
157	C₂³×C₄₁	—	4	2	no	—
158	C₂³×C₄₁	—	4	2	no	—
159	C₂³×C₄₁	—	4	2	no	—
160	C₂³×C₄₁	—	8	4	no	—
161	C₂³×C₄₁	C₄×D₄	1	1	yes	characteristic
162	C₂³×C₄₁	#121	1	1	yes	characteristic
163	C₂³×C₄₁	#121	1	2	yes	—
164	C₂³×C₄₁	#123	1	2	yes	—
165	C₂³×C₄₁	#124	1	1	yes	characteristic
166	Q₈×C₄₁	—	2	4	no	—
167	Q₈×C₄₁	—	2	4	no	—
168	Q₈×C₄₁	—	4	2	no	—
169	Q₈×C₄₁	—	4	2	no	—
170	D₄×C₄₁	—	2	4	no	—
171	D₄×C₄₁	—	2	4	no	—
172	D₄×C₄₁	—	4	4	no	—
173	D₄×C₄₁	—	4	4	no	—
174	D₄×C₄₁	—	4	4	no	—
175	D₄×C₄₁	—	4	4	no	—
176	D₄×C₄₁	—	4	2	no	—
177	D₄×C₄₁	—	4	2	no	—
178	C₂×C₄×C₄₁	—	2	4	no	—
179	C₂×C₄×C₄₁	—	2	4	no	—
180	C₂×C₄×C₄₁	—	4	2	no	—
181	C₂×C₄×C₄₁	—	4	8	no	—
182	C₂×C₄×C₄₁	—	4	2	no	—
183	C₂×C₄×C₄₁	—	4	2	no	—
184	C₂×C₄×C₄₁	—	4	2	no	—
185	C₂×C₄×C₄₁	—	4	4	no	—
186	C₂×C₄×C₄₁	—	4	4	no	—
187	C₂×C₄×C₄₁	—	4	4	no	—
188	C₂×C₄×C₄₁	—	4	4	no	—
189	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
190	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
193	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
194	C₂×C₄×C₄₁	#120	1	2	yes	—
195	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
196	C₂×C₄×C₄₁	#120	1	2	yes	—
197	C₂×C₄×C₄₁	#120	1	2	yes	—
198	C₂×C₄×C₄₁	#121	1	2	yes	—
199	C₂×C₄×C₄₁	#121	1	2	yes	—
200	C₂×C₄×C₄₁	#121	1	2	yes	—
201	C₂×C₄×C₄₁	#121	1	2	yes	—
202	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
203	C₂×C₄×C₄₁	#123	1	2	yes	—
204	C₂×C₄×C₄₁	#124	1	1	yes	characteristic
205	C₂×C₄×C₄₁	#127	1	1	yes	characteristic
206	C₂×C₄×C₄₁	#127	1	1	yes	characteristic
207	C₈×C₄₁	—	2	4	no	—
208	C₈×C₄₁	—	4	4	no	—
209	C₈×C₄₁	—	4	2	no	—
210	#11039	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂²×C₄₁	—	2	2	no	—
212	C₂²×C₄₁	—	2	4	no	—
213	C₂²×C₄₁	—	4	2	no	—
214	C₂²×C₄₁	—	4	1	no	—
215	C₂²×C₄₁	—	4	1	no	—
216	C₂²×C₄₁	—	4	4	no	—
217	C₂²×C₄₁	—	8	4	no	—
218	C₂²×C₄₁	—	8	4	no	—
219	C₂²×C₄₁	—	8	4	no	—
220	C₂²×C₄₁	#386	1	2	yes	—
221	C₂²×C₄₁	#390	1	1	yes	characteristic
222	C₂²×C₄₁	#392	1	1	yes	characteristic
223	C₂²×C₄₁	#394	1	2	yes	—
224	C₂²×C₄₁	#394	1	1	yes	characteristic
225	C₄×C₄₁	—	4	4	no	—
226	C₄×C₄₁	—	4	4	no	—
227	C₄×C₄₁	#379	1	1	yes	characteristic
228	C₄×C₄₁	#386	1	2	yes	—
229	C₄×C₄₁	#390	1	1	yes	characteristic
230	C₄×C₄₁	#392	1	2	yes	—
231	C₄×C₄₁	#392	1	1	yes	characteristic
232	C₄×C₄₁	#394	1	1	yes	characteristic
233	C₂×#575	C₂×C₄₁	1	1	yes	characteristic
234	C₂²×#104	C₂×C₄₁	1	2	yes	complemented
235	C₂×#413	C₂×C₄₁	1	2	yes	complemented
236	C₂×#338	C₂×C₄₁	1	1	yes	characteristic, complemented
237	#1728	C₂×C₄₁	1	1	yes	characteristic, complemented
238	C₂×C₄₁	—	2	1	no	—
239	C₂×C₄₁	—	2	2	no	—
240	C₂×C₄₁	—	2	2	no	—
241	C₂×C₄₁	—	2	1	no	—
242	C₂×C₄₁	—	8	4	no	—
243	C₂×C₄₁	#1438	1	1	yes	characteristic
244	C₂×C₄₁	#2050	1	2	yes	—
245	C₂²×#41	C₂²×C₄₁	1	2	yes	—
246	#575	—	2	4	no	—
247	#575	—	2	2	no	—
248	#575	C₄×C₄₁	1	4	yes	complemented
249	C₂×#137	—	2	2	no	—
250	C₂×AGL(1,ℤ/8)	—	2	2	no	—
251	C₂×#135	—	2	2	no	—
252	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
253	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
254	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
255	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
256	C₂×#104	—	2	4	no	—
257	C₂×#104	—	2	4	no	—
258	C₂×#104	—	2	4	no	—
259	#413	—	2	4	no	—
260	#413	—	2	4	no	—
261	C₂×#101	—	2	2	no	—
262	C₂×#100	—	2	2	no	—
263	#338	—	2	2	no	—
264	#336	—	2	2	no	—
265	C₄₁	#11039	1	1	yes	characteristic, direct product factor, Sylow
266	C₂×#41	—	2	2	no	—
267	C₂×#41	—	2	2	no	—
268	C₂×#41	—	2	2	no	—
269	C₂×#41	—	2	2	no	—
270	C₂×#41	—	2	2	no	—
271	C₂×#41	—	2	2	no	—
272	C₂×#41	—	2	2	no	—
273	C₂×#41	—	2	2	no	—
274	C₂×#41	—	2	2	no	—
275	C₂×#41	—	2	2	no	—
276	C₂×#41	C₂×C₄×C₄₁	1	4	yes	—
277	C₂×#41	D₄×C₄₁	1	4	yes	—
278	C₂²×Q₈	D₄×C₄₁	1	2	yes	—
279	C₂²×D₄	—	2	2	no	—
280	C₂²×D₄	D₄×C₄₁	1	2	yes	—
281	C₂³×C₄	—	2	2	no	—
282	C₂³×C₄	—	2	1	no	—
283	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
284	#137	—	2	8	no	—
285	#137	—	2	8	no	—
286	AGL(1,ℤ/8)	—	2	8	no	—
287	AGL(1,ℤ/8)	—	2	8	no	—
288	#135	—	2	8	no	—
289	#135	—	2	8	no	—
290	C₂×Q₁₆	—	2	2	no	—
291	C₂×SD₁₆	—	2	4	no	—
292	C₂×D₈	—	2	2	no	—
293	C₂×M₁₆	—	2	2	no	—
294	C₂×M₁₆	—	2	2	no	—
295	C₂×M₁₆	—	2	2	no	—
296	C₂×M₁₆	—	2	1	no	—
297	C₂×M₁₆	—	2	2	no	—
298	C₂×M₁₆	—	2	2	no	—
299	C₂×M₁₆	—	2	2	no	—
300	C₂×M₁₆	—	2	2	no	—
301	C₂×M₁₆	—	2	2	no	—
302	C₂×M₁₆	—	2	2	no	—
303	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	—
304	C₂×M₁₆	D₄×C₄₁	1	2	yes	—
305	C₂×M₁₆	D₄×C₄₁	1	4	yes	—
306	C₂×M₁₆	D₄×C₄₁	1	2	yes	—
307	C₂²×C₈	—	2	1	no	—
308	C₂²×C₈	—	2	2	no	—
309	C₂²×C₈	D₄×C₄₁	1	2	yes	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	D₄×C₄₁	1	2	yes	—
314	#104	—	2	16	no	—
315	#101	—	2	8	no	—
316	#100	—	2	8	no	—
317	C₂⁴	—	2	2	no	—
318	C₂⁴	#41×C₄₁	1	1	yes	characteristic
319	#41	—	2	4	no	—
320	#41	—	2	4	no	—
321	#41	—	2	4	no	—
322	#41	—	2	4	no	—
323	#41	—	2	4	no	—
324	#41	—	2	4	no	—
325	#41	—	2	4	no	—
326	#41	—	2	4	no	—
327	#41	—	4	2	no	—
328	#41	—	4	2	no	—
329	#41	—	4	2	no	—
330	#41	—	4	2	no	—
331	#41	—	4	2	no	—
332	#41	—	4	2	no	—
333	#41	—	4	2	no	—
334	#41	—	4	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	C₂²⋊C₄×C₄₁	1	4	yes	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	4	2	no	—
349	C₂×D₄	—	4	2	no	—
350	C₂×D₄	—	4	2	no	—
351	C₂×D₄	—	4	2	no	—
352	C₂×D₄	C₂²⋊C₄×C₄₁	1	4	yes	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	4	4	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	2	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
365	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
366	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
371	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
372	C₂²×C₄	#41×C₄₁	1	2	yes	—
373	Q₁₆	—	2	8	no	—
374	SD₁₆	—	2	16	no	—
375	D₈	—	2	8	no	—
376	M₁₆	—	2	4	no	—
377	M₁₆	—	2	4	no	—
378	M₁₆	—	2	4	no	—
379	M₁₆	—	2	4	no	—
380	M₁₆	—	2	4	no	—
381	M₁₆	—	4	2	no	—
382	M₁₆	—	4	2	no	—
383	M₁₆	—	4	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	4	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	4	1	no	—
389	C₂×C₈	—	4	2	no	—
390	C₂×C₈	—	4	2	no	—
391	C₂×C₈	—	4	1	no	—
392	C₂×C₈	C₂²⋊C₄×C₄₁	1	4	yes	—
393	C₄²	—	2	4	no	—
394	C₄²	—	4	1	no	—
395	C₄²	—	4	1	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	8	4	no	—
401	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
402	C₂³	#121×C₄₁	1	1	yes	characteristic
403	C₂³	#121×C₄₁	1	2	yes	—
404	C₂³	#123×C₄₁	1	2	yes	—
405	C₂³	#124×C₄₁	1	1	yes	characteristic
406	Q₈	—	2	4	no	—
407	Q₈	—	2	4	no	—
408	Q₈	—	4	2	no	—
409	Q₈	—	4	2	no	—
410	D₄	—	2	4	no	—
411	D₄	—	2	4	no	—
412	D₄	—	4	4	no	—
413	D₄	—	4	4	no	—
414	D₄	—	4	4	no	—
415	D₄	—	4	4	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	2	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	8	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
430	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
431	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
432	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
433	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
434	C₂×C₄	#120×C₄₁	1	2	yes	—
435	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
436	C₂×C₄	#120×C₄₁	1	2	yes	—
437	C₂×C₄	#120×C₄₁	1	2	yes	—
438	C₂×C₄	#121×C₄₁	1	2	yes	—
439	C₂×C₄	#121×C₄₁	1	2	yes	—
440	C₂×C₄	#121×C₄₁	1	2	yes	—
441	C₂×C₄	#121×C₄₁	1	2	yes	—
442	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
443	C₂×C₄	#123×C₄₁	1	2	yes	—
444	C₂×C₄	#124×C₄₁	1	1	yes	characteristic
445	C₂×C₄	#127×C₄₁	1	1	yes	characteristic
446	C₂×C₄	#127×C₄₁	1	1	yes	characteristic
447	C₈	—	2	4	no	—
448	C₈	—	4	4	no	—
449	C₈	—	4	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	4	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	1	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	8	4	no	—
457	C₂²	—	8	4	no	—
458	C₂²	—	8	4	no	—
459	C₂²	C₄₁×#386	1	2	yes	—
460	C₂²	C₄₁×#390	1	1	yes	characteristic
461	C₂²	C₄₁×#392	1	1	yes	characteristic
462	C₂²	C₄₁×#394	1	2	yes	—
463	C₂²	C₄₁×#394	1	1	yes	characteristic
464	C₄	—	4	4	no	—
465	C₄	—	4	4	no	—
466	C₄	C₄₁×#379	1	1	yes	characteristic
467	C₄	C₄₁×#386	1	2	yes	—
468	C₄	C₄₁×#390	1	1	yes	characteristic
469	C₄	C₄₁×#392	1	2	yes	—
470	C₄	C₄₁×#392	1	1	yes	characteristic
471	C₄	C₄₁×#394	1	1	yes	characteristic
472	C₂	—	2	1	no	—
473	C₂	—	2	2	no	—
474	C₂	—	2	2	no	—
475	C₂	—	2	1	no	—
476	C₂	—	8	4	no	—
477	C₂	C₄₁×#1438	1	1	yes	characteristic
478	C₂	C₄₁×#2050	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₁	#124
commutator	C₂²×C₄	C₂²×C₄×C₄₁
Frattini, cosocle	C₂³×C₄	C₂³×C₄₁
socle	C₂²×C₄₁	#394
prime radical	C₂×C₄₁×#575	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#104×C₄₁	C₂	semidirect
3. C₂×C₄₁×#413	C₂	semidirect
4. C₂×C₄₁×#338	C₂	semidirect
5. C₄₁×#1728	C₂	semidirect
9. C₄₁×#575	C₄	semidirect
210. #11039	C₄₁	direct (N × H)
234. C₂²×#104	C₂×C₄₁	semidirect
235. C₂×#413	C₂×C₄₁	semidirect
236. C₂×#338	C₂×C₄₁	semidirect
237. #1728	C₂×C₄₁	semidirect
248. #575	C₄×C₄₁	semidirect
265. C₄₁	#11039	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×#575	2
C₂²×#104×C₄₁	2
C₂×C₄₁×#413	2
C₂×C₄₁×#338	2
C₄₁×#1728	2
#11039	41

Subgroups — C41×#11039 #23787240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#11039 #23787240