Subgroups — C₄₁×#23181 #23799382

Order 10496.

914 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3150	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#444	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#443	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2935	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1980	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1975	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1974	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1876	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1876	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1778	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1771	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#135×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#135×C₄₁	C₂²	1	2	yes	—
15	C₂×#131×C₄₁	C₂²	1	2	yes	—
16	C₂×#131×C₄₁	C₂²	1	2	yes	—
17	C₄₁×#532	C₂²	1	2	yes	—
18	C₄₁×#497	C₄	1	2	yes	complemented
19	C₄₁×#497	C₄	1	2	yes	complemented
20	C₄₁×#496	C₄	1	2	yes	complemented
21	C₄₁×#496	C₄	1	2	yes	complemented
22	C₄₁×#444	—	2	4	no	—
23	C₄₁×#443	—	2	4	no	—
24	C₄₁×#436	—	2	2	no	—
25	C₄₁×#435	—	2	2	no	—
26	C₄₁×#435	—	2	2	no	—
27	C₈×D₄×C₄₁	—	2	2	no	—
28	C₂×#108×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×#108×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×#104×C₄₁	C₂²	1	2	yes	—
32	C₂×#104×C₄₁	C₂²	1	2	yes	—
33	C₂×#104×C₄₁	C₂²	1	2	yes	—
34	C₂×#104×C₄₁	C₂²	1	2	yes	—
35	C₄₁×#408	C₂²	1	2	yes	—
36	C₄₁×#408	C₂²	1	2	yes	—
37	C₄×M₁₆×C₄₁	C₂²	1	2	yes	—
38	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
42	C₄₁×#341	C₂²	1	2	yes	—
43	C₄₁×#336	C₂²	1	1	yes	characteristic
44	C₄₁×#336	C₂²	1	1	yes	characteristic
45	C₂×#41×C₄₁	C₂³	1	2	yes	—
46	C₂×#41×C₄₁	C₂³	1	2	yes	—
47	#135×C₄₁	—	2	2	no	—
48	#135×C₄₁	—	2	2	no	—
49	#135×C₄₁	—	2	2	no	—
50	#135×C₄₁	—	2	2	no	—
51	#135×C₄₁	—	4	2	no	—
52	#135×C₄₁	—	4	2	no	—
53	C₂×Q₁₆×C₄₁	C₂×C₄	1	1	yes	characteristic
54	C₂×Q₁₆×C₄₁	C₂×C₄	1	1	yes	characteristic
55	C₂×Q₁₆×C₄₁	C₂×C₄	1	2	yes	—
56	C₂×SD₁₆×C₄₁	C₂×C₄	1	2	yes	—
57	C₂×SD₁₆×C₄₁	C₂×C₄	1	2	yes	—
58	C₂×SD₁₆×C₄₁	C₂×C₄	1	2	yes	—
59	C₂×SD₁₆×C₄₁	C₂×C₄	1	2	yes	—
60	C₂×D₈×C₄₁	C₂×C₄	1	1	yes	characteristic
61	C₂×D₈×C₄₁	C₂×C₄	1	1	yes	characteristic
62	C₂×D₈×C₄₁	C₂×C₄	1	2	yes	—
63	#131×C₄₁	—	2	4	no	—
64	#131×C₄₁	—	2	4	no	—
65	#131×C₄₁	—	4	2	no	—
66	#131×C₄₁	—	4	2	no	—
67	C₂×M₁₆×C₄₁	—	2	2	no	—
68	C₂×M₁₆×C₄₁	—	2	2	no	—
69	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
70	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
71	C₂²×C₈×C₄₁	—	2	2	no	—
72	C₂²×C₈×C₄₁	—	2	2	no	—
73	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
77	C₄⋊Q₈×C₄₁	C₂×C₄	1	2	yes	—
78	#127×C₄₁	C₂×C₄	1	2	yes	—
79	#124×C₄₁	C₂×C₄	1	2	yes	—
80	#124×C₄₁	C₂×C₄	1	2	yes	—
81	#121×C₄₁	—	2	2	no	—
82	#121×C₄₁	—	2	2	no	—
83	C₄×D₄×C₄₁	—	2	2	no	—
84	C₄×D₄×C₄₁	—	2	2	no	—
85	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
86	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
89	#108×C₄₁	—	2	2	no	—
90	#108×C₄₁	D₄	1	4	yes	complemented
91	C₄⋊C₈×C₄₁	D₄	1	2	yes	—
92	C₄⋊C₈×C₄₁	D₄	1	2	yes	—
93	#104×C₄₁	—	2	4	no	—
94	#104×C₄₁	—	2	4	no	—
95	#104×C₄₁	—	4	2	no	—
96	#104×C₄₁	—	4	2	no	—
97	C₂²⋊C₈×C₄₁	—	2	2	no	—
98	C₂²⋊C₈×C₄₁	—	2	2	no	—
99	C₂²⋊C₈×C₄₁	—	2	2	no	—
100	C₂²⋊C₈×C₄₁	—	2	2	no	—
101	#97×C₄₁	—	2	2	no	—
102	#97×C₄₁	—	2	2	no	—
103	#97×C₄₁	C₂×C₄	1	2	yes	—
104	#97×C₄₁	C₂×C₄	1	2	yes	—
105	C₄×C₈×C₄₁	—	2	2	no	—
106	C₄×C₈×C₄₁	—	2	2	no	—
107	#95×C₄₁	—	2	1	no	—
108	#41×C₄₁	—	2	2	no	—
109	#41×C₄₁	—	2	2	no	—
110	#41×C₄₁	—	2	2	no	—
111	#41×C₄₁	—	2	2	no	—
112	#41×C₄₁	—	2	2	no	—
113	#41×C₄₁	—	2	2	no	—
114	#41×C₄₁	—	2	2	no	—
115	#41×C₄₁	—	2	2	no	—
116	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
117	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
118	C₂×D₄×C₄₁	—	2	2	no	—
119	C₂×D₄×C₄₁	—	2	2	no	—
120	C₂×D₄×C₄₁	—	2	2	no	—
121	C₂×D₄×C₄₁	—	2	2	no	—
122	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
123	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₄₁	—	2	1	no	—
125	C₂²×C₄×C₄₁	—	2	2	no	—
126	C₂²×C₄×C₄₁	—	2	2	no	—
127	C₂²×C₄×C₄₁	—	2	1	no	—
128	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
129	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
130	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
131	Q₁₆×C₄₁	—	2	2	no	—
132	Q₁₆×C₄₁	—	2	2	no	—
133	Q₁₆×C₄₁	—	4	2	no	—
134	SD₁₆×C₄₁	—	2	4	no	—
135	SD₁₆×C₄₁	—	2	4	no	—
136	SD₁₆×C₄₁	—	4	2	no	—
137	SD₁₆×C₄₁	—	4	2	no	—
138	D₈×C₄₁	—	2	2	no	—
139	D₈×C₄₁	—	2	2	no	—
140	D₈×C₄₁	—	4	2	no	—
141	M₁₆×C₄₁	—	2	2	no	—
142	M₁₆×C₄₁	—	2	2	no	—
143	M₁₆×C₄₁	—	2	2	no	—
144	M₁₆×C₄₁	—	4	4	no	—
145	M₁₆×C₄₁	—	4	4	no	—
146	M₁₆×C₄₁	C₂×D₄	1	4	yes	—
147	C₂×C₈×C₄₁	—	2	1	no	—
148	C₂×C₈×C₄₁	—	2	1	no	—
149	C₂×C₈×C₄₁	—	2	2	no	—
150	C₂×C₈×C₄₁	—	2	1	no	—
151	C₂×C₈×C₄₁	—	2	1	no	—
152	C₂×C₈×C₄₁	—	2	1	no	—
153	C₂×C₈×C₄₁	—	2	1	no	—
154	C₂×C₈×C₄₁	—	2	2	no	—
155	C₂×C₈×C₄₁	—	4	4	no	—
156	C₂×C₈×C₄₁	—	4	4	no	—
157	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
158	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
161	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
162	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
164	C₂×C₈×C₄₁	#41	1	2	yes	—
165	C₄⋊C₄×C₄₁	—	2	2	no	—
166	C₄⋊C₄×C₄₁	—	2	2	no	—
167	C₄⋊C₄×C₄₁	—	4	2	no	—
168	C₂²⋊C₄×C₄₁	—	2	2	no	—
169	C₂²⋊C₄×C₄₁	—	2	2	no	—
170	C₂²⋊C₄×C₄₁	—	2	2	no	—
171	C₂²⋊C₄×C₄₁	—	2	2	no	—
172	C₄²×C₄₁	—	2	1	no	—
173	C₄²×C₄₁	—	2	1	no	—
174	C₄²×C₄₁	—	2	1	no	—
175	C₄²×C₄₁	—	2	1	no	—
176	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
177	C₄²×C₄₁	C₂×D₄	1	2	yes	—
178	C₂³×C₄₁	—	2	2	no	—
179	C₂³×C₄₁	—	2	2	no	—
180	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
181	Q₈×C₄₁	—	2	2	no	—
182	Q₈×C₄₁	—	2	2	no	—
183	Q₈×C₄₁	—	2	2	no	—
184	Q₈×C₄₁	—	2	2	no	—
185	D₄×C₄₁	—	2	2	no	—
186	D₄×C₄₁	—	2	2	no	—
187	D₄×C₄₁	—	2	2	no	—
188	D₄×C₄₁	—	2	2	no	—
189	D₄×C₄₁	—	4	4	no	—
190	D₄×C₄₁	—	4	2	no	—
191	D₄×C₄₁	—	4	2	no	—
192	D₄×C₄₁	—	4	2	no	—
193	D₄×C₄₁	—	4	2	no	—
194	D₄×C₄₁	—	8	2	no	—
195	C₂×C₄×C₄₁	—	2	2	no	—
196	C₂×C₄×C₄₁	—	2	2	no	—
197	C₂×C₄×C₄₁	—	2	2	no	—
198	C₂×C₄×C₄₁	—	4	1	no	—
199	C₂×C₄×C₄₁	—	4	1	no	—
200	C₂×C₄×C₄₁	—	4	1	no	—
201	C₂×C₄×C₄₁	—	4	1	no	—
202	C₂×C₄×C₄₁	—	4	2	no	—
203	C₂×C₄×C₄₁	—	4	2	no	—
204	C₂×C₄×C₄₁	—	4	2	no	—
205	C₂×C₄×C₄₁	—	4	2	no	—
206	C₂×C₄×C₄₁	—	4	1	no	—
207	C₂×C₄×C₄₁	—	4	1	no	—
208	C₂×C₄×C₄₁	—	4	1	no	—
209	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
210	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
211	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
217	C₈×C₄₁	—	2	2	no	—
218	C₈×C₄₁	—	2	1	no	—
219	C₈×C₄₁	—	2	2	no	—
220	C₈×C₄₁	—	2	1	no	—
221	C₈×C₄₁	—	2	4	no	—
222	C₈×C₄₁	—	4	2	no	—
223	C₈×C₄₁	C₄×D₄	1	2	yes	—
224	C₈×C₄₁	C₄×D₄	1	2	yes	—
225	#23181	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
226	C₂²×C₄₁	—	2	1	no	—
227	C₂²×C₄₁	—	2	1	no	—
228	C₂²×C₄₁	—	4	2	no	—
229	C₂²×C₄₁	—	4	2	no	—
230	C₂²×C₄₁	—	4	2	no	—
231	C₂²×C₄₁	—	4	2	no	—
232	C₂²×C₄₁	—	4	2	no	—
233	C₂²×C₄₁	—	4	2	no	—
234	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
235	C₂²×C₄₁	#550	1	1	yes	characteristic
236	C₂²×C₄₁	#559	1	1	yes	characteristic
237	C₄×C₄₁	—	2	2	no	—
238	C₄×C₄₁	—	2	2	no	—
239	C₄×C₄₁	—	4	2	no	—
240	C₄×C₄₁	—	4	2	no	—
241	C₄×C₄₁	—	4	2	no	—
242	C₄×C₄₁	—	8	1	no	—
243	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
244	C₄×C₄₁	#518	1	1	yes	characteristic
245	C₄×C₄₁	D₄²	1	1	yes	characteristic
246	C₄×C₄₁	#550	1	1	yes	characteristic
247	#3150	C₂×C₄₁	1	1	yes	characteristic
248	C₂×#444	C₂×C₄₁	1	1	yes	characteristic, complemented
249	C₂×#443	C₂×C₄₁	1	1	yes	characteristic, complemented
250	#2935	C₂×C₄₁	1	2	yes	complemented
251	#1980	C₂×C₄₁	1	2	yes	complemented
252	#1975	C₂×C₄₁	1	1	yes	characteristic, complemented
253	#1974	C₂×C₄₁	1	1	yes	characteristic, complemented
254	#1876	C₂×C₄₁	1	2	yes	complemented
255	#1876	C₂×C₄₁	1	2	yes	complemented
256	#1778	C₂×C₄₁	1	1	yes	characteristic, complemented
257	#1771	C₂×C₄₁	1	1	yes	characteristic, complemented
258	C₂×C₄₁	—	2	1	no	—
259	C₂×C₄₁	—	2	1	no	—
260	C₂×C₄₁	—	8	2	no	—
261	C₂×C₄₁	—	8	2	no	—
262	C₂×C₄₁	#2366	1	1	yes	characteristic
263	C₂×C₄₁	#2955	1	1	yes	characteristic
264	C₂×C₄₁	#2956	1	1	yes	characteristic
265	C₂×#135	C₂²×C₄₁	1	1	yes	characteristic
266	C₂×#135	C₂²×C₄₁	1	1	yes	characteristic
267	C₂×#135	C₂²×C₄₁	1	2	yes	—
268	C₂×#131	C₂²×C₄₁	1	2	yes	—
269	C₂×#131	C₂²×C₄₁	1	2	yes	—
270	#532	C₂²×C₄₁	1	2	yes	—
271	#497	C₄×C₄₁	1	2	yes	complemented
272	#497	C₄×C₄₁	1	2	yes	complemented
273	#496	C₄×C₄₁	1	2	yes	complemented
274	#496	C₄×C₄₁	1	2	yes	complemented
275	#444	—	2	4	no	—
276	#443	—	2	4	no	—
277	#436	—	2	2	no	—
278	#435	—	2	2	no	—
279	#435	—	2	2	no	—
280	C₈×D₄	—	2	2	no	—
281	C₂×#108	C₂²×C₄₁	1	1	yes	characteristic
282	C₂×#108	C₂²×C₄₁	1	1	yes	characteristic
283	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
284	C₂×#104	C₂²×C₄₁	1	2	yes	—
285	C₂×#104	C₂²×C₄₁	1	2	yes	—
286	C₂×#104	C₂²×C₄₁	1	2	yes	—
287	C₂×#104	C₂²×C₄₁	1	2	yes	—
288	#408	C₂²×C₄₁	1	2	yes	—
289	#408	C₂²×C₄₁	1	2	yes	—
290	C₄×M₁₆	C₂²×C₄₁	1	2	yes	—
291	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
292	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
293	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
294	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
295	#341	C₂²×C₄₁	1	2	yes	—
296	#336	C₂²×C₄₁	1	1	yes	characteristic
297	#336	C₂²×C₄₁	1	1	yes	characteristic
298	C₄₁	#23181	1	1	yes	characteristic, direct product factor, Sylow
299	C₂×#41	C₂³×C₄₁	1	2	yes	—
300	C₂×#41	C₂³×C₄₁	1	2	yes	—
301	#135	—	2	2	no	—
302	#135	—	2	2	no	—
303	#135	—	2	2	no	—
304	#135	—	2	2	no	—
305	#135	—	4	2	no	—
306	#135	—	4	2	no	—
307	C₂×Q₁₆	C₂×C₄×C₄₁	1	1	yes	characteristic
308	C₂×Q₁₆	C₂×C₄×C₄₁	1	1	yes	characteristic
309	C₂×Q₁₆	C₂×C₄×C₄₁	1	2	yes	—
310	C₂×SD₁₆	C₂×C₄×C₄₁	1	2	yes	—
311	C₂×SD₁₆	C₂×C₄×C₄₁	1	2	yes	—
312	C₂×SD₁₆	C₂×C₄×C₄₁	1	2	yes	—
313	C₂×SD₁₆	C₂×C₄×C₄₁	1	2	yes	—
314	C₂×D₈	C₂×C₄×C₄₁	1	1	yes	characteristic
315	C₂×D₈	C₂×C₄×C₄₁	1	1	yes	characteristic
316	C₂×D₈	C₂×C₄×C₄₁	1	2	yes	—
317	#131	—	2	4	no	—
318	#131	—	2	4	no	—
319	#131	—	4	2	no	—
320	#131	—	4	2	no	—
321	C₂×M₁₆	—	2	2	no	—
322	C₂×M₁₆	—	2	2	no	—
323	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
324	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
325	C₂²×C₈	—	2	2	no	—
326	C₂²×C₈	—	2	2	no	—
327	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
328	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
329	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
330	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
331	C₄⋊Q₈	C₂×C₄×C₄₁	1	2	yes	—
332	#127	C₂×C₄×C₄₁	1	2	yes	—
333	#124	C₂×C₄×C₄₁	1	2	yes	—
334	#124	C₂×C₄×C₄₁	1	2	yes	—
335	#121	—	2	2	no	—
336	#121	—	2	2	no	—
337	C₄×D₄	—	2	2	no	—
338	C₄×D₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
341	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
342	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
343	#108	—	2	2	no	—
344	#108	D₄×C₄₁	1	4	yes	complemented
345	C₄⋊C₈	D₄×C₄₁	1	2	yes	—
346	C₄⋊C₈	D₄×C₄₁	1	2	yes	—
347	#104	—	2	4	no	—
348	#104	—	2	4	no	—
349	#104	—	4	2	no	—
350	#104	—	4	2	no	—
351	C₂²⋊C₈	—	2	2	no	—
352	C₂²⋊C₈	—	2	2	no	—
353	C₂²⋊C₈	—	2	2	no	—
354	C₂²⋊C₈	—	2	2	no	—
355	#97	—	2	2	no	—
356	#97	—	2	2	no	—
357	#97	C₂×C₄×C₄₁	1	2	yes	—
358	#97	C₂×C₄×C₄₁	1	2	yes	—
359	C₄×C₈	—	2	2	no	—
360	C₄×C₈	—	2	2	no	—
361	#95	—	2	1	no	—
362	#41	—	2	2	no	—
363	#41	—	2	2	no	—
364	#41	—	2	2	no	—
365	#41	—	2	2	no	—
366	#41	—	2	2	no	—
367	#41	—	2	2	no	—
368	#41	—	2	2	no	—
369	#41	—	2	2	no	—
370	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
371	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
377	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
383	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
384	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
385	Q₁₆	—	2	2	no	—
386	Q₁₆	—	2	2	no	—
387	Q₁₆	—	4	2	no	—
388	SD₁₆	—	2	4	no	—
389	SD₁₆	—	2	4	no	—
390	SD₁₆	—	4	2	no	—
391	SD₁₆	—	4	2	no	—
392	D₈	—	2	2	no	—
393	D₈	—	2	2	no	—
394	D₈	—	4	2	no	—
395	M₁₆	—	2	2	no	—
396	M₁₆	—	2	2	no	—
397	M₁₆	—	2	2	no	—
398	M₁₆	—	4	4	no	—
399	M₁₆	—	4	4	no	—
400	M₁₆	C₂×D₄×C₄₁	1	4	yes	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	4	4	no	—
410	C₂×C₈	—	4	4	no	—
411	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
412	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
413	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
414	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
415	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
416	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
417	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
418	C₂×C₈	#41×C₄₁	1	2	yes	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	4	2	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	2	1	no	—
430	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
431	C₄²	C₂×D₄×C₄₁	1	2	yes	—
432	C₂³	—	2	2	no	—
433	C₂³	—	2	2	no	—
434	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
435	Q₈	—	2	2	no	—
436	Q₈	—	2	2	no	—
437	Q₈	—	2	2	no	—
438	Q₈	—	2	2	no	—
439	D₄	—	2	2	no	—
440	D₄	—	2	2	no	—
441	D₄	—	2	2	no	—
442	D₄	—	2	2	no	—
443	D₄	—	4	4	no	—
444	D₄	—	4	2	no	—
445	D₄	—	4	2	no	—
446	D₄	—	4	2	no	—
447	D₄	—	4	2	no	—
448	D₄	—	8	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
464	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
465	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
466	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
467	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
468	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
469	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
470	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
471	C₈	—	2	2	no	—
472	C₈	—	2	1	no	—
473	C₈	—	2	2	no	—
474	C₈	—	2	1	no	—
475	C₈	—	2	4	no	—
476	C₈	—	4	2	no	—
477	C₈	C₄×D₄×C₄₁	1	2	yes	—
478	C₈	C₄×D₄×C₄₁	1	2	yes	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
488	C₂²	C₄₁×#550	1	1	yes	characteristic
489	C₂²	C₄₁×#559	1	1	yes	characteristic
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	2	no	—
494	C₄	—	4	2	no	—
495	C₄	—	8	1	no	—
496	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
497	C₄	C₄₁×#518	1	1	yes	characteristic
498	C₄	D₄²×C₄₁	1	1	yes	characteristic
499	C₄	C₄₁×#550	1	1	yes	characteristic
500	C₂	—	2	1	no	—
501	C₂	—	2	1	no	—
502	C₂	—	8	2	no	—
503	C₂	—	8	2	no	—
504	C₂	C₄₁×#2366	1	1	yes	characteristic
505	C₂	C₄₁×#2955	1	1	yes	characteristic
506	C₂	C₄₁×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂²×C₄₁	C₂×C₄×D₄
prime radical	C₄₁×#3150	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂×C₄⋊C₈×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#444	C₂	semidirect
3. C₂×C₄₁×#443	C₂	semidirect
4. C₄₁×#2935	C₂	semidirect
5. C₄₁×#1980	C₂	semidirect
6. C₄₁×#1975	C₂	semidirect
7. C₄₁×#1974	C₂	semidirect
8. C₄₁×#1876	C₂	semidirect
9. C₄₁×#1876	C₂	semidirect
10. C₄₁×#1778	C₂	semidirect
11. C₄₁×#1771	C₂	semidirect
18. C₄₁×#497	C₄	semidirect
19. C₄₁×#497	C₄	semidirect
20. C₄₁×#496	C₄	semidirect
21. C₄₁×#496	C₄	semidirect
90. #108×C₄₁	D₄	semidirect
225. #23181	C₄₁	direct (N × H)
248. C₂×#444	C₂×C₄₁	semidirect
249. C₂×#443	C₂×C₄₁	semidirect
250. #2935	C₂×C₄₁	semidirect
251. #1980	C₂×C₄₁	semidirect
252. #1975	C₂×C₄₁	semidirect
253. #1974	C₂×C₄₁	semidirect
254. #1876	C₂×C₄₁	semidirect
255. #1876	C₂×C₄₁	semidirect
256. #1778	C₂×C₄₁	semidirect
257. #1771	C₂×C₄₁	semidirect
271. #497	C₄×C₄₁	semidirect
272. #497	C₄×C₄₁	semidirect
273. #496	C₄×C₄₁	semidirect
274. #496	C₄×C₄₁	semidirect
298. C₄₁	#23181	direct (N × H)
344. #108	D₄×C₄₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄₁×#3150	2
C₂×C₄₁×#444	2
C₂×C₄₁×#443	2
C₄₁×#2935	2
C₄₁×#1980	2
C₄₁×#1975	2
C₄₁×#1974	2
C₄₁×#1876	2
C₄₁×#1778	2
C₄₁×#1771	2
#23181	41

Subgroups — C41×#23181 #23799382

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23181 #23799382