Subgroups — C₄₁×#23020 #23799221

Order 10496.

874 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3054	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#443	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2933	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₁×#430	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1975	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1945	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1929	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1871	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1866	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1773	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1753	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#131×C₄₁	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
15	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
16	C₄₁×#525	C₂²	1	2	yes	—
17	C₄₁×#470	C₄	1	2	yes	complemented
18	C₄₁×#469	C₄	1	2	yes	complemented
19	C₄₁×#468	C₄	1	2	yes	complemented
20	C₄₁×#468	C₄	1	2	yes	complemented
21	C₄₁×#443	—	2	4	no	—
22	C₄₁×#436	—	2	2	no	—
23	C₄₁×#435	—	2	2	no	—
24	C₄₁×#435	—	2	2	no	—
25	C₈×D₄×C₄₁	—	2	2	no	—
26	C₄₁×#430	—	2	4	no	—
27	C₂×#108×C₄₁	C₂²	1	2	yes	—
28	C₂×#108×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×#108×C₄₁	C₂²	1	1	yes	characteristic
30	C₄₁×#427	C₂²	1	1	yes	characteristic
31	C₄₁×#424	C₂²	1	2	yes	—
32	C₂×#104×C₄₁	C₂²	1	2	yes	—
33	C₂×#104×C₄₁	C₂²	1	2	yes	—
34	C₄₁×#416	C₂²	1	2	yes	—
35	C₄₁×#408	C₂²	1	2	yes	—
36	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
37	C₄₁×#405	C₂²	1	2	yes	—
38	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
41	C₄₁×#339	C₂²	1	2	yes	—
42	C₄₁×#339	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	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
47	#135×C₄₁	—	2	2	no	—
48	#135×C₄₁	—	2	2	no	—
49	C₂×Q₁₆×C₄₁	C₂×C₄	1	1	yes	characteristic
50	C₂×SD₁₆×C₄₁	C₂×C₄	1	2	yes	—
51	C₂×D₈×C₄₁	C₂×C₄	1	1	yes	characteristic
52	#131×C₄₁	—	2	4	no	—
53	#131×C₄₁	—	4	2	no	—
54	C₂×M₁₆×C₄₁	—	2	2	no	—
55	C₂×M₁₆×C₄₁	—	2	2	no	—
56	C₂×M₁₆×C₄₁	—	2	2	no	—
57	C₂×M₁₆×C₄₁	—	2	2	no	—
58	C₂×M₁₆×C₄₁	—	2	4	no	—
59	C₂×M₁₆×C₄₁	—	4	2	no	—
60	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	—
61	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	—
62	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
63	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
64	C₂²×C₈×C₄₁	—	2	2	no	—
65	C₂²×C₈×C₄₁	—	2	2	no	—
66	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
70	#123×C₄₁	—	2	2	no	—
71	C₂²⋊Q₈×C₄₁	C₂×C₄	1	2	yes	—
72	C₂²⋊Q₈×C₄₁	C₂×C₄	1	2	yes	—
73	#121×C₄₁	C₂×C₄	1	2	yes	—
74	#121×C₄₁	C₂×C₄	1	2	yes	—
75	#120×C₄₁	—	2	2	no	—
76	C₄×D₄×C₄₁	—	2	2	no	—
77	C₄×D₄×C₄₁	—	2	2	no	—
78	#117×C₄₁	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
80	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
82	#108×C₄₁	—	2	4	no	—
83	#108×C₄₁	—	2	2	no	—
84	#108×C₄₁	D₄	1	4	yes	complemented
85	#107×C₄₁	C₂×C₄	1	1	yes	characteristic
86	#107×C₄₁	C₂×C₄	1	1	yes	characteristic
87	#106×C₄₁	C₂×C₄	1	2	yes	—
88	C₄⋊C₈×C₄₁	—	2	2	no	—
89	C₄⋊C₈×C₄₁	—	2	2	no	—
90	#104×C₄₁	—	2	4	no	—
91	#104×C₄₁	—	4	2	no	—
92	#103×C₄₁	C₂×C₄	1	2	yes	—
93	#103×C₄₁	C₂×C₄	1	2	yes	—
94	#102×C₄₁	C₂×C₄	1	2	yes	—
95	#102×C₄₁	C₂×C₄	1	2	yes	—
96	C₂²⋊C₈×C₄₁	—	2	2	no	—
97	C₂²⋊C₈×C₄₁	—	2	2	no	—
98	C₂²⋊C₈×C₄₁	D₄	1	2	yes	—
99	C₂²⋊C₈×C₄₁	D₄	1	2	yes	—
100	#97×C₄₁	—	2	2	no	—
101	#97×C₄₁	—	2	2	no	—
102	C₄×C₈×C₄₁	—	2	2	no	—
103	C₄×C₈×C₄₁	—	2	2	no	—
104	#95×C₄₁	—	2	1	no	—
105	C₂⁴×C₄₁	#41	1	1	yes	characteristic
106	#41×C₄₁	—	2	2	no	—
107	#41×C₄₁	—	2	2	no	—
108	#41×C₄₁	—	2	2	no	—
109	#41×C₄₁	—	2	2	no	—
110	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
111	C₂×D₄×C₄₁	—	2	2	no	—
112	C₂×D₄×C₄₁	—	2	2	no	—
113	C₂×D₄×C₄₁	—	2	2	no	—
114	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₄₁	—	2	1	no	—
116	C₂²×C₄×C₄₁	—	2	1	no	—
117	C₂²×C₄×C₄₁	—	2	1	no	—
118	C₂²×C₄×C₄₁	—	2	1	no	—
119	C₂²×C₄×C₄₁	—	2	1	no	—
120	C₂²×C₄×C₄₁	—	2	2	no	—
121	C₂²×C₄×C₄₁	—	2	1	no	—
122	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
125	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
126	Q₁₆×C₄₁	—	2	2	no	—
127	SD₁₆×C₄₁	—	2	4	no	—
128	D₈×C₄₁	—	2	2	no	—
129	M₁₆×C₄₁	—	2	2	no	—
130	M₁₆×C₄₁	—	2	4	no	—
131	M₁₆×C₄₁	—	2	4	no	—
132	M₁₆×C₄₁	—	2	2	no	—
133	M₁₆×C₄₁	—	2	2	no	—
134	M₁₆×C₄₁	—	4	4	no	—
135	M₁₆×C₄₁	—	4	4	no	—
136	M₁₆×C₄₁	C₂×D₄	1	4	yes	—
137	C₂×C₈×C₄₁	—	2	1	no	—
138	C₂×C₈×C₄₁	—	2	1	no	—
139	C₂×C₈×C₄₁	—	2	2	no	—
140	C₂×C₈×C₄₁	—	2	1	no	—
141	C₂×C₈×C₄₁	—	2	1	no	—
142	C₂×C₈×C₄₁	—	2	1	no	—
143	C₂×C₈×C₄₁	—	2	1	no	—
144	C₂×C₈×C₄₁	—	2	2	no	—
145	C₂×C₈×C₄₁	—	4	4	no	—
146	C₂×C₈×C₄₁	—	4	4	no	—
147	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
148	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
154	C₂×C₈×C₄₁	#41	1	2	yes	—
155	C₄⋊C₄×C₄₁	—	2	2	no	—
156	C₄⋊C₄×C₄₁	—	2	2	no	—
157	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
158	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
159	C₂²⋊C₄×C₄₁	—	2	2	no	—
160	C₂²⋊C₄×C₄₁	—	2	2	no	—
161	C₂²⋊C₄×C₄₁	—	2	2	no	—
162	C₂²⋊C₄×C₄₁	—	2	2	no	—
163	C₂²⋊C₄×C₄₁	—	2	2	no	—
164	C₂²⋊C₄×C₄₁	—	4	2	no	—
165	C₄²×C₄₁	—	2	2	no	—
166	C₄²×C₄₁	—	2	1	no	—
167	C₄²×C₄₁	—	2	1	no	—
168	C₄²×C₄₁	—	2	1	no	—
169	C₄²×C₄₁	—	2	1	no	—
170	C₂³×C₄₁	—	2	1	no	—
171	C₂³×C₄₁	—	2	1	no	—
172	C₂³×C₄₁	—	2	2	no	—
173	C₂³×C₄₁	—	4	1	no	—
174	C₂³×C₄₁	—	4	1	no	—
175	C₂³×C₄₁	C₄×D₄	1	2	yes	—
176	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
177	Q₈×C₄₁	—	2	2	no	—
178	Q₈×C₄₁	—	2	2	no	—
179	D₄×C₄₁	—	2	2	no	—
180	D₄×C₄₁	—	2	2	no	—
181	D₄×C₄₁	—	4	4	no	—
182	D₄×C₄₁	—	4	2	no	—
183	D₄×C₄₁	—	4	2	no	—
184	D₄×C₄₁	—	8	2	no	—
185	C₂×C₄×C₄₁	—	2	1	no	—
186	C₂×C₄×C₄₁	—	2	1	no	—
187	C₂×C₄×C₄₁	—	2	2	no	—
188	C₂×C₄×C₄₁	—	2	2	no	—
189	C₂×C₄×C₄₁	—	2	2	no	—
190	C₂×C₄×C₄₁	—	2	2	no	—
191	C₂×C₄×C₄₁	—	2	2	no	—
192	C₂×C₄×C₄₁	—	2	2	no	—
193	C₂×C₄×C₄₁	—	2	2	no	—
194	C₂×C₄×C₄₁	—	2	2	no	—
195	C₂×C₄×C₄₁	—	4	1	no	—
196	C₂×C₄×C₄₁	—	4	1	no	—
197	C₂×C₄×C₄₁	—	4	2	no	—
198	C₂×C₄×C₄₁	—	4	2	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	C₄×D₄	1	2	yes	—
203	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
208	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
209	C₈×C₄₁	—	2	2	no	—
210	C₈×C₄₁	—	2	1	no	—
211	C₈×C₄₁	—	2	1	no	—
212	C₈×C₄₁	—	2	4	no	—
213	C₈×C₄₁	—	2	2	no	—
214	C₈×C₄₁	—	4	2	no	—
215	C₈×C₄₁	C₄×D₄	1	2	yes	—
216	C₈×C₄₁	C₄×D₄	1	2	yes	—
217	#23020	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂²×C₄₁	—	2	1	no	—
219	C₂²×C₄₁	—	2	1	no	—
220	C₂²×C₄₁	—	2	2	no	—
221	C₂²×C₄₁	—	2	2	no	—
222	C₂²×C₄₁	—	2	2	no	—
223	C₂²×C₄₁	—	4	2	no	—
224	C₂²×C₄₁	—	4	2	no	—
225	C₂²×C₄₁	—	4	2	no	—
226	C₂²×C₄₁	—	8	1	no	—
227	C₂²×C₄₁	—	8	1	no	—
228	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
229	C₂²×C₄₁	#548	1	1	yes	characteristic
230	C₂²×C₄₁	#553	1	1	yes	characteristic
231	C₄×C₄₁	—	2	2	no	—
232	C₄×C₄₁	—	4	2	no	—
233	C₄×C₄₁	—	4	2	no	—
234	C₄×C₄₁	—	4	2	no	—
235	C₄×C₄₁	—	4	2	no	—
236	C₄×C₄₁	—	8	1	no	—
237	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
238	C₄×C₄₁	#520	1	1	yes	characteristic
239	C₄×C₄₁	D₄²	1	1	yes	characteristic
240	C₄×C₄₁	#547	1	1	yes	characteristic
241	#3054	C₂×C₄₁	1	1	yes	characteristic
242	C₂×#443	C₂×C₄₁	1	1	yes	characteristic, complemented
243	#2933	C₂×C₄₁	1	2	yes	complemented
244	C₂×#430	C₂×C₄₁	1	1	yes	characteristic, complemented
245	#1975	C₂×C₄₁	1	1	yes	characteristic, complemented
246	#1945	C₂×C₄₁	1	1	yes	characteristic, complemented
247	#1929	C₂×C₄₁	1	2	yes	complemented
248	#1871	C₂×C₄₁	1	2	yes	complemented
249	#1866	C₂×C₄₁	1	2	yes	complemented
250	#1773	C₂×C₄₁	1	1	yes	characteristic, complemented
251	#1753	C₂×C₄₁	1	1	yes	characteristic, complemented
252	C₂×C₄₁	—	2	1	no	—
253	C₂×C₄₁	—	2	1	no	—
254	C₂×C₄₁	—	4	2	no	—
255	C₂×C₄₁	—	8	2	no	—
256	C₂×C₄₁	#2361	1	1	yes	characteristic
257	C₂×C₄₁	#2955	1	1	yes	characteristic
258	C₂×C₄₁	#2956	1	1	yes	characteristic
259	C₂×#135	C₂²×C₄₁	1	1	yes	characteristic
260	C₂×#131	C₂²×C₄₁	1	2	yes	—
261	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
262	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
263	#525	C₂²×C₄₁	1	2	yes	—
264	#470	C₄×C₄₁	1	2	yes	complemented
265	#469	C₄×C₄₁	1	2	yes	complemented
266	#468	C₄×C₄₁	1	2	yes	complemented
267	#468	C₄×C₄₁	1	2	yes	complemented
268	#443	—	2	4	no	—
269	#436	—	2	2	no	—
270	#435	—	2	2	no	—
271	#435	—	2	2	no	—
272	C₈×D₄	—	2	2	no	—
273	#430	—	2	4	no	—
274	C₂×#108	C₂²×C₄₁	1	2	yes	—
275	C₂×#108	C₂²×C₄₁	1	1	yes	characteristic
276	C₂×#108	C₂²×C₄₁	1	1	yes	characteristic
277	#427	C₂²×C₄₁	1	1	yes	characteristic
278	#424	C₂²×C₄₁	1	2	yes	—
279	C₂×#104	C₂²×C₄₁	1	2	yes	—
280	C₂×#104	C₂²×C₄₁	1	2	yes	—
281	#416	C₂²×C₄₁	1	2	yes	—
282	#408	C₂²×C₄₁	1	2	yes	—
283	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
284	#405	C₂²×C₄₁	1	2	yes	—
285	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
286	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
287	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
288	#339	C₂²×C₄₁	1	2	yes	—
289	#339	C₂²×C₄₁	1	2	yes	—
290	#336	C₂²×C₄₁	1	1	yes	characteristic
291	#336	C₂²×C₄₁	1	1	yes	characteristic
292	C₄₁	#23020	1	1	yes	characteristic, direct product factor, Sylow
293	C₂×#41	C₂³×C₄₁	1	2	yes	—
294	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
295	#135	—	2	2	no	—
296	#135	—	2	2	no	—
297	C₂×Q₁₆	C₂×C₄×C₄₁	1	1	yes	characteristic
298	C₂×SD₁₆	C₂×C₄×C₄₁	1	2	yes	—
299	C₂×D₈	C₂×C₄×C₄₁	1	1	yes	characteristic
300	#131	—	2	4	no	—
301	#131	—	4	2	no	—
302	C₂×M₁₆	—	2	2	no	—
303	C₂×M₁₆	—	2	2	no	—
304	C₂×M₁₆	—	2	2	no	—
305	C₂×M₁₆	—	2	2	no	—
306	C₂×M₁₆	—	2	4	no	—
307	C₂×M₁₆	—	4	2	no	—
308	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	—
309	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	—
310	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
311	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
312	C₂²×C₈	—	2	2	no	—
313	C₂²×C₈	—	2	2	no	—
314	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
315	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
316	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
318	#123	—	2	2	no	—
319	C₂²⋊Q₈	C₂×C₄×C₄₁	1	2	yes	—
320	C₂²⋊Q₈	C₂×C₄×C₄₁	1	2	yes	—
321	#121	C₂×C₄×C₄₁	1	2	yes	—
322	#121	C₂×C₄×C₄₁	1	2	yes	—
323	#120	—	2	2	no	—
324	C₄×D₄	—	2	2	no	—
325	C₄×D₄	—	2	2	no	—
326	#117	C₂³×C₄₁	1	2	yes	—
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
330	#108	—	2	4	no	—
331	#108	—	2	2	no	—
332	#108	D₄×C₄₁	1	4	yes	complemented
333	#107	C₂×C₄×C₄₁	1	1	yes	characteristic
334	#107	C₂×C₄×C₄₁	1	1	yes	characteristic
335	#106	C₂×C₄×C₄₁	1	2	yes	—
336	C₄⋊C₈	—	2	2	no	—
337	C₄⋊C₈	—	2	2	no	—
338	#104	—	2	4	no	—
339	#104	—	4	2	no	—
340	#103	C₂×C₄×C₄₁	1	2	yes	—
341	#103	C₂×C₄×C₄₁	1	2	yes	—
342	#102	C₂×C₄×C₄₁	1	2	yes	—
343	#102	C₂×C₄×C₄₁	1	2	yes	—
344	C₂²⋊C₈	—	2	2	no	—
345	C₂²⋊C₈	—	2	2	no	—
346	C₂²⋊C₈	D₄×C₄₁	1	2	yes	—
347	C₂²⋊C₈	D₄×C₄₁	1	2	yes	—
348	#97	—	2	2	no	—
349	#97	—	2	2	no	—
350	C₄×C₈	—	2	2	no	—
351	C₄×C₈	—	2	2	no	—
352	#95	—	2	1	no	—
353	C₂⁴	#41×C₄₁	1	1	yes	characteristic
354	#41	—	2	2	no	—
355	#41	—	2	2	no	—
356	#41	—	2	2	no	—
357	#41	—	2	2	no	—
358	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
371	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
372	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
373	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
374	Q₁₆	—	2	2	no	—
375	SD₁₆	—	2	4	no	—
376	D₈	—	2	2	no	—
377	M₁₆	—	2	2	no	—
378	M₁₆	—	2	4	no	—
379	M₁₆	—	2	4	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	—	2	2	no	—
382	M₁₆	—	4	4	no	—
383	M₁₆	—	4	4	no	—
384	M₁₆	C₂×D₄×C₄₁	1	4	yes	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	4	4	no	—
394	C₂×C₈	—	4	4	no	—
395	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
396	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
397	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
398	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
399	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
400	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
401	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
402	C₂×C₈	#41×C₄₁	1	2	yes	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
406	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	4	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	1	no	—
423	C₂³	C₄×D₄×C₄₁	1	2	yes	—
424	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
425	Q₈	—	2	2	no	—
426	Q₈	—	2	2	no	—
427	D₄	—	2	2	no	—
428	D₄	—	2	2	no	—
429	D₄	—	4	4	no	—
430	D₄	—	4	2	no	—
431	D₄	—	4	2	no	—
432	D₄	—	8	2	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
451	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
452	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
454	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
455	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
456	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
457	C₈	—	2	2	no	—
458	C₈	—	2	1	no	—
459	C₈	—	2	1	no	—
460	C₈	—	2	4	no	—
461	C₈	—	2	2	no	—
462	C₈	—	4	2	no	—
463	C₈	C₄×D₄×C₄₁	1	2	yes	—
464	C₈	C₄×D₄×C₄₁	1	2	yes	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	8	1	no	—
474	C₂²	—	8	1	no	—
475	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
476	C₂²	C₄₁×#548	1	1	yes	characteristic
477	C₂²	C₄₁×#553	1	1	yes	characteristic
478	C₄	—	2	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	2	no	—
482	C₄	—	4	2	no	—
483	C₄	—	8	1	no	—
484	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
485	C₄	C₄₁×#520	1	1	yes	characteristic
486	C₄	D₄²×C₄₁	1	1	yes	characteristic
487	C₄	C₄₁×#547	1	1	yes	characteristic
488	C₂	—	2	1	no	—
489	C₂	—	2	1	no	—
490	C₂	—	4	2	no	—
491	C₂	—	8	2	no	—
492	C₂	C₄₁×#2361	1	1	yes	characteristic
493	C₂	C₄₁×#2955	1	1	yes	characteristic
494	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×#3054	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂×C₂²⋊C₈×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#443	C₂	semidirect
3. C₄₁×#2933	C₂	semidirect
4. C₂×C₄₁×#430	C₂	semidirect
5. C₄₁×#1975	C₂	semidirect
6. C₄₁×#1945	C₂	semidirect
7. C₄₁×#1929	C₂	semidirect
8. C₄₁×#1871	C₂	semidirect
9. C₄₁×#1866	C₂	semidirect
10. C₄₁×#1773	C₂	semidirect
11. C₄₁×#1753	C₂	semidirect
17. C₄₁×#470	C₄	semidirect
18. C₄₁×#469	C₄	semidirect
19. C₄₁×#468	C₄	semidirect
20. C₄₁×#468	C₄	semidirect
84. #108×C₄₁	D₄	semidirect
217. #23020	C₄₁	direct (N × H)
242. C₂×#443	C₂×C₄₁	semidirect
243. #2933	C₂×C₄₁	semidirect
244. C₂×#430	C₂×C₄₁	semidirect
245. #1975	C₂×C₄₁	semidirect
246. #1945	C₂×C₄₁	semidirect
247. #1929	C₂×C₄₁	semidirect
248. #1871	C₂×C₄₁	semidirect
249. #1866	C₂×C₄₁	semidirect
250. #1773	C₂×C₄₁	semidirect
251. #1753	C₂×C₄₁	semidirect
264. #470	C₄×C₄₁	semidirect
265. #469	C₄×C₄₁	semidirect
266. #468	C₄×C₄₁	semidirect
267. #468	C₄×C₄₁	semidirect
292. C₄₁	#23020	direct (N × H)
332. #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×#3054	2
C₂×C₄₁×#443	2
C₄₁×#2933	2
C₂×C₄₁×#430	2
C₄₁×#1975	2
C₄₁×#1945	2
C₄₁×#1929	2
C₄₁×#1871	2
C₄₁×#1866	2
C₄₁×#1773	2
C₄₁×#1753	2
#23020	41

Subgroups — C41×#23020 #23799221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23020 #23799221