Subgroups — C₄₁×#24290 #23800491

Order 10496.

1294 conjugacy classes of subgroups.

The subgroup lattice has 620 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, complemented
2	C₂×C₄₁×#473	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3061	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3013	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₁×#443	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2052	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2007	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1974	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1969	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1816	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1793	C₂	1	2	yes	maximal, complemented
12	C₂×2₋¹⁺⁴×C₄₁	C₂²	1	2	yes	—
13	C₄₁×#578	—	2	4	no	—
14	C₄₁×#578	—	2	4	no	—
15	C₂×#137×C₄₁	—	2	2	no	—
16	C₂×#137×C₄₁	C₂²	1	2	yes	—
17	C₂×#137×C₄₁	C₂²	1	2	yes	—
18	C₂×#135×C₄₁	—	2	1	no	—
19	C₂×#135×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#135×C₄₁	C₂²	1	1	yes	characteristic
21	C₂²×Q₁₆×C₄₁	—	2	1	no	—
22	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×#131×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×#131×C₄₁	C₂²	1	1	yes	characteristic
25	C₄₁×#537	C₂²	1	2	yes	—
26	C₄₁×#473	—	2	4	no	—
27	C₄₁×#468	—	2	2	no	—
28	C₄₁×#467	—	2	1	no	—
29	C₄₁×#466	—	2	1	no	—
30	C₄₁×#452	—	2	2	no	—
31	C₄₁×#451	—	2	2	no	—
32	C₄₁×#449	—	2	2	no	—
33	C₄₁×#448	—	2	2	no	—
34	C₄₁×#443	—	2	4	no	—
35	C₂×#108×C₄₁	C₂²	1	1	yes	characteristic
36	C₂×#108×C₄₁	C₂²	1	1	yes	characteristic
37	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
38	C₂×#104×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×#104×C₄₁	C₂²	1	1	yes	characteristic
40	C₂×#104×C₄₁	C₂²	1	2	yes	—
41	C₄₁×#417	C₂²	1	2	yes	—
42	C₄₁×#417	C₂²	1	2	yes	—
43	C₂×#103×C₄₁	C₂²	1	2	yes	—
44	C₂×#101×C₄₁	C₂²	1	2	yes	—
45	C₄₁×#408	C₂²	1	2	yes	—
46	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
47	C₄₁×#391	C₂²	1	2	yes	—
48	C₄₁×#343	C₂²	1	2	yes	—
49	2₋¹⁺⁴×C₄₁	—	2	4	no	—
50	2₋¹⁺⁴×C₄₁	—	2	4	no	—
51	2₋¹⁺⁴×C₄₁	—	2	4	no	—
52	2₋¹⁺⁴×C₄₁	—	4	2	no	—
53	C₂×#41×C₄₁	—	2	2	no	—
54	C₂×#41×C₄₁	—	2	2	no	—
55	C₂×#41×C₄₁	—	4	2	no	—
56	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
57	C₂×#41×C₄₁	C₂³	1	2	yes	—
58	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₄₁	—	2	2	no	—
60	C₂²×Q₈×C₄₁	—	2	2	no	—
61	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
62	#137×C₄₁	—	2	16	no	—
63	#137×C₄₁	—	2	4	no	—
64	#137×C₄₁	—	2	4	no	—
65	#137×C₄₁	—	2	4	no	—
66	#137×C₄₁	—	4	2	no	—
67	#135×C₄₁	—	2	8	no	—
68	#135×C₄₁	—	2	2	no	—
69	#135×C₄₁	—	2	2	no	—
70	#135×C₄₁	—	2	2	no	—
71	#135×C₄₁	—	2	2	no	—
72	C₂×Q₁₆×C₄₁	—	2	8	no	—
73	C₂×Q₁₆×C₄₁	—	2	2	no	—
74	C₂×Q₁₆×C₄₁	—	2	2	no	—
75	C₂×Q₁₆×C₄₁	—	2	1	no	—
76	C₂×Q₁₆×C₄₁	—	2	1	no	—
77	C₂×Q₁₆×C₄₁	—	2	2	no	—
78	C₂×Q₁₆×C₄₁	D₄	1	1	yes	characteristic
79	C₂×Q₁₆×C₄₁	D₄	1	1	yes	characteristic
80	C₂×Q₁₆×C₄₁	D₄	1	4	yes	complemented
81	C₂×SD₁₆×C₄₁	—	2	2	no	—
82	C₂×SD₁₆×C₄₁	—	2	2	no	—
83	C₂×SD₁₆×C₄₁	D₄	1	2	yes	—
84	C₂×SD₁₆×C₄₁	D₄	1	1	yes	characteristic
85	C₂×SD₁₆×C₄₁	D₄	1	1	yes	characteristic
86	C₂×D₈×C₄₁	D₄	1	1	yes	characteristic
87	C₂×D₈×C₄₁	D₄	1	1	yes	characteristic
88	#131×C₄₁	—	2	2	no	—
89	#131×C₄₁	—	2	2	no	—
90	#131×C₄₁	—	2	2	no	—
91	#131×C₄₁	D₄	1	4	yes	complemented
92	C₂×M₁₆×C₄₁	—	2	1	no	—
93	C₂×M₁₆×C₄₁	—	2	1	no	—
94	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
95	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
96	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₄₁	—	2	1	no	—
98	C₂²×C₈×C₄₁	—	2	1	no	—
99	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
101	C₂²⋊Q₈×C₄₁	—	2	2	no	—
102	C₂²⋊Q₈×C₄₁	—	2	2	no	—
103	#121×C₄₁	—	2	2	no	—
104	#121×C₄₁	—	2	2	no	—
105	#121×C₄₁	—	4	2	no	—
106	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
107	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
108	#108×C₄₁	—	2	2	no	—
109	#108×C₄₁	—	2	2	no	—
110	#107×C₄₁	—	2	1	no	—
111	#107×C₄₁	—	2	1	no	—
112	#104×C₄₁	—	2	2	no	—
113	#104×C₄₁	—	2	2	no	—
114	#104×C₄₁	—	4	2	no	—
115	#103×C₄₁	—	2	2	no	—
116	#103×C₄₁	—	2	2	no	—
117	#103×C₄₁	—	2	2	no	—
118	#103×C₄₁	—	2	2	no	—
119	#102×C₄₁	—	2	2	no	—
120	#102×C₄₁	—	2	2	no	—
121	#101×C₄₁	—	2	4	no	—
122	C₂²⋊C₈×C₄₁	—	2	2	no	—
123	C₂²⋊C₈×C₄₁	—	2	2	no	—
124	C₄×C₈×C₄₁	—	2	2	no	—
125	#95×C₄₁	—	4	2	no	—
126	#41×C₄₁	—	2	1	no	—
127	#41×C₄₁	—	2	1	no	—
128	#41×C₄₁	—	2	8	no	—
129	#41×C₄₁	—	2	1	no	—
130	#41×C₄₁	—	2	1	no	—
131	#41×C₄₁	—	2	2	no	—
132	#41×C₄₁	—	2	2	no	—
133	#41×C₄₁	—	2	1	no	—
134	#41×C₄₁	—	2	2	no	—
135	#41×C₄₁	—	2	2	no	—
136	#41×C₄₁	—	2	1	no	—
137	#41×C₄₁	—	4	4	no	—
138	#41×C₄₁	—	4	8	no	—
139	#41×C₄₁	—	4	4	no	—
140	#41×C₄₁	—	4	8	no	—
141	#41×C₄₁	—	4	4	no	—
142	#41×C₄₁	C₂×D₄	1	2	yes	—
143	#41×C₄₁	#41	1	2	yes	—
144	C₂×Q₈×C₄₁	—	2	2	no	—
145	C₂×Q₈×C₄₁	—	2	8	no	—
146	C₂×Q₈×C₄₁	—	2	2	no	—
147	C₂×Q₈×C₄₁	—	2	2	no	—
148	C₂×Q₈×C₄₁	—	2	2	no	—
149	C₂×Q₈×C₄₁	—	2	2	no	—
150	C₂×Q₈×C₄₁	—	4	2	no	—
151	C₂×Q₈×C₄₁	—	4	4	no	—
152	C₂×Q₈×C₄₁	—	4	4	no	—
153	C₂×Q₈×C₄₁	—	4	4	no	—
154	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
155	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
156	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
157	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
158	C₂×D₄×C₄₁	—	2	1	no	—
159	C₂×D₄×C₄₁	—	2	1	no	—
160	C₂×D₄×C₄₁	—	2	2	no	—
161	C₂×D₄×C₄₁	—	4	2	no	—
162	C₂×D₄×C₄₁	—	4	2	no	—
163	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
164	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
165	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₄₁	—	2	1	no	—
167	C₂²×C₄×C₄₁	—	2	1	no	—
168	C₂²×C₄×C₄₁	—	2	2	no	—
169	C₂²×C₄×C₄₁	—	2	2	no	—
170	C₂²×C₄×C₄₁	—	2	1	no	—
171	C₂²×C₄×C₄₁	—	2	2	no	—
172	C₂²×C₄×C₄₁	—	4	2	no	—
173	C₂²×C₄×C₄₁	—	4	2	no	—
174	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
175	Q₁₆×C₄₁	—	2	8	no	—
176	Q₁₆×C₄₁	—	2	2	no	—
177	Q₁₆×C₄₁	—	2	2	no	—
178	Q₁₆×C₄₁	—	2	4	no	—
179	Q₁₆×C₄₁	—	2	4	no	—
180	Q₁₆×C₄₁	—	4	4	no	—
181	SD₁₆×C₄₁	—	2	8	no	—
182	SD₁₆×C₄₁	—	2	2	no	—
183	SD₁₆×C₄₁	—	2	2	no	—
184	SD₁₆×C₄₁	—	2	4	no	—
185	SD₁₆×C₄₁	—	4	4	no	—
186	D₈×C₄₁	—	2	2	no	—
187	D₈×C₄₁	—	2	2	no	—
188	M₁₆×C₄₁	—	2	1	no	—
189	M₁₆×C₄₁	—	2	4	no	—
190	M₁₆×C₄₁	—	2	1	no	—
191	M₁₆×C₄₁	—	2	2	no	—
192	M₁₆×C₄₁	—	2	1	no	—
193	M₁₆×C₄₁	—	2	2	no	—
194	M₁₆×C₄₁	—	4	2	no	—
195	M₁₆×C₄₁	C₂×D₄	1	2	yes	—
196	C₂×C₈×C₄₁	—	2	1	no	—
197	C₂×C₈×C₄₁	—	2	1	no	—
198	C₂×C₈×C₄₁	—	2	1	no	—
199	C₂×C₈×C₄₁	—	2	4	no	—
200	C₂×C₈×C₄₁	—	2	2	no	—
201	C₂×C₈×C₄₁	—	2	1	no	—
202	C₂×C₈×C₄₁	—	4	2	no	—
203	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
204	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
205	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
206	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
207	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
208	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
209	C₄⋊C₄×C₄₁	—	2	2	no	—
210	C₄⋊C₄×C₄₁	—	2	2	no	—
211	C₄⋊C₄×C₄₁	—	4	2	no	—
212	C₂²⋊C₄×C₄₁	—	4	2	no	—
213	C₂²⋊C₄×C₄₁	—	4	2	no	—
214	C₄²×C₄₁	—	2	1	no	—
215	C₄²×C₄₁	—	2	1	no	—
216	C₂³×C₄₁	—	2	1	no	—
217	C₂³×C₄₁	—	2	1	no	—
218	C₂³×C₄₁	—	2	2	no	—
219	C₂³×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
220	Q₈×C₄₁	—	2	1	no	—
221	Q₈×C₄₁	—	2	4	no	—
222	Q₈×C₄₁	—	2	2	no	—
223	Q₈×C₄₁	—	2	1	no	—
224	Q₈×C₄₁	—	2	4	no	—
225	Q₈×C₄₁	—	2	1	no	—
226	Q₈×C₄₁	—	2	2	no	—
227	Q₈×C₄₁	—	4	8	no	—
228	Q₈×C₄₁	—	4	2	no	—
229	Q₈×C₄₁	—	4	2	no	—
230	Q₈×C₄₁	#121	1	2	yes	—
231	D₄×C₄₁	—	2	2	no	—
232	D₄×C₄₁	—	2	2	no	—
233	D₄×C₄₁	—	2	2	no	—
234	D₄×C₄₁	—	2	1	no	—
235	D₄×C₄₁	—	2	1	no	—
236	D₄×C₄₁	—	2	1	no	—
237	D₄×C₄₁	—	2	2	no	—
238	D₄×C₄₁	—	4	8	no	—
239	D₄×C₄₁	—	4	1	no	—
240	D₄×C₄₁	—	4	2	no	—
241	D₄×C₄₁	—	4	1	no	—
242	D₄×C₄₁	—	4	2	no	—
243	D₄×C₄₁	—	16	2	no	—
244	D₄×C₄₁	#121	1	2	yes	—
245	C₂×C₄×C₄₁	—	2	1	no	—
246	C₂×C₄×C₄₁	—	2	2	no	—
247	C₂×C₄×C₄₁	—	2	2	no	—
248	C₂×C₄×C₄₁	—	2	2	no	—
249	C₂×C₄×C₄₁	—	2	1	no	—
250	C₂×C₄×C₄₁	—	2	2	no	—
251	C₂×C₄×C₄₁	—	2	4	no	—
252	C₂×C₄×C₄₁	—	4	8	no	—
253	C₂×C₄×C₄₁	—	4	1	no	—
254	C₂×C₄×C₄₁	—	4	8	no	—
255	C₂×C₄×C₄₁	—	4	1	no	—
256	C₂×C₄×C₄₁	—	4	2	no	—
257	C₂×C₄×C₄₁	—	4	2	no	—
258	C₂×C₄×C₄₁	—	4	1	no	—
259	C₂×C₄×C₄₁	—	4	2	no	—
260	C₂×C₄×C₄₁	—	4	2	no	—
261	C₂×C₄×C₄₁	—	4	1	no	—
262	C₂×C₄×C₄₁	—	4	2	no	—
263	C₂×C₄×C₄₁	—	8	2	no	—
264	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
269	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
270	C₈×C₄₁	—	2	2	no	—
271	C₈×C₄₁	—	2	1	no	—
272	C₈×C₄₁	—	2	1	no	—
273	C₈×C₄₁	—	4	1	no	—
274	C₈×C₄₁	—	4	2	no	—
275	C₈×C₄₁	#120	1	2	yes	—
276	C₈×C₄₁	#120	1	2	yes	—
277	#24290	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
278	C₂²×C₄₁	—	2	1	no	—
279	C₂²×C₄₁	—	2	1	no	—
280	C₂²×C₄₁	—	2	2	no	—
281	C₂²×C₄₁	—	4	1	no	—
282	C₂²×C₄₁	—	4	1	no	—
283	C₂²×C₄₁	—	4	2	no	—
284	C₂²×C₄₁	—	4	1	no	—
285	C₂²×C₄₁	—	4	1	no	—
286	C₂²×C₄₁	—	4	2	no	—
287	C₂²×C₄₁	—	4	1	no	—
288	C₂²×C₄₁	—	4	2	no	—
289	C₂²×C₄₁	#535	1	1	yes	characteristic
290	C₂²×C₄₁	D₄²	1	1	yes	characteristic
291	C₂²×C₄₁	#546	1	1	yes	characteristic
292	C₄×C₄₁	—	2	2	no	—
293	C₄×C₄₁	—	4	2	no	—
294	C₄×C₄₁	—	4	2	no	—
295	C₄×C₄₁	—	4	4	no	—
296	C₄×C₄₁	—	4	1	no	—
297	C₄×C₄₁	—	8	2	no	—
298	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
299	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
300	C₄×C₄₁	D₄²	1	1	yes	characteristic
301	C₄×C₄₁	#546	1	1	yes	characteristic
302	C₂×#578	C₂×C₄₁	1	1	yes	characteristic, complemented
303	C₂×#473	C₂×C₄₁	1	1	yes	characteristic, complemented
304	#3061	C₂×C₄₁	1	1	yes	characteristic, complemented
305	#3013	C₂×C₄₁	1	2	yes	complemented
306	C₂×#443	C₂×C₄₁	1	1	yes	characteristic, complemented
307	#2052	C₂×C₄₁	1	2	yes	complemented
308	#2007	C₂×C₄₁	1	2	yes	complemented
309	#1974	C₂×C₄₁	1	1	yes	characteristic, complemented
310	#1969	C₂×C₄₁	1	1	yes	characteristic, complemented
311	#1816	C₂×C₄₁	1	1	yes	characteristic, complemented
312	#1793	C₂×C₄₁	1	2	yes	complemented
313	C₂×C₄₁	—	2	1	no	—
314	C₂×C₄₁	—	2	1	no	—
315	C₂×C₄₁	—	4	2	no	—
316	C₂×C₄₁	—	8	2	no	—
317	C₂×C₄₁	—	8	1	no	—
318	C₂×C₄₁	#2408	1	1	yes	characteristic
319	C₂×C₄₁	#3290	1	1	yes	characteristic
320	C₂×C₄₁	#3293	1	1	yes	characteristic
321	C₂×2₋¹⁺⁴	C₂²×C₄₁	1	2	yes	—
322	#578	—	2	4	no	—
323	#578	—	2	4	no	—
324	C₂×#137	—	2	2	no	—
325	C₂×#137	C₂²×C₄₁	1	2	yes	—
326	C₂×#137	C₂²×C₄₁	1	2	yes	—
327	C₂×#135	—	2	1	no	—
328	C₂×#135	C₂²×C₄₁	1	1	yes	characteristic
329	C₂×#135	C₂²×C₄₁	1	1	yes	characteristic
330	C₂²×Q₁₆	—	2	1	no	—
331	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
332	C₂×#131	C₂²×C₄₁	1	1	yes	characteristic
333	C₂×#131	C₂²×C₄₁	1	1	yes	characteristic
334	#537	C₂²×C₄₁	1	2	yes	—
335	#473	—	2	4	no	—
336	#468	—	2	2	no	—
337	#467	—	2	1	no	—
338	#466	—	2	1	no	—
339	#452	—	2	2	no	—
340	#451	—	2	2	no	—
341	#449	—	2	2	no	—
342	#448	—	2	2	no	—
343	#443	—	2	4	no	—
344	C₂×#108	C₂²×C₄₁	1	1	yes	characteristic
345	C₂×#108	C₂²×C₄₁	1	1	yes	characteristic
346	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
347	C₂×#104	C₂²×C₄₁	1	1	yes	characteristic
348	C₂×#104	C₂²×C₄₁	1	1	yes	characteristic
349	C₂×#104	C₂²×C₄₁	1	2	yes	—
350	#417	C₂²×C₄₁	1	2	yes	—
351	#417	C₂²×C₄₁	1	2	yes	—
352	C₂×#103	C₂²×C₄₁	1	2	yes	—
353	C₂×#101	C₂²×C₄₁	1	2	yes	—
354	#408	C₂²×C₄₁	1	2	yes	—
355	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
356	#391	C₂²×C₄₁	1	2	yes	—
357	#343	C₂²×C₄₁	1	2	yes	—
358	C₄₁	#24290	1	1	yes	characteristic, direct product factor, Sylow
359	2₋¹⁺⁴	—	2	4	no	—
360	2₋¹⁺⁴	—	2	4	no	—
361	2₋¹⁺⁴	—	2	4	no	—
362	2₋¹⁺⁴	—	4	2	no	—
363	C₂×#41	—	2	2	no	—
364	C₂×#41	—	2	2	no	—
365	C₂×#41	—	4	2	no	—
366	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
367	C₂×#41	C₂³×C₄₁	1	2	yes	—
368	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
369	C₂²×Q₈	—	2	2	no	—
370	C₂²×Q₈	—	2	2	no	—
371	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
372	#137	—	2	16	no	—
373	#137	—	2	4	no	—
374	#137	—	2	4	no	—
375	#137	—	2	4	no	—
376	#137	—	4	2	no	—
377	#135	—	2	8	no	—
378	#135	—	2	2	no	—
379	#135	—	2	2	no	—
380	#135	—	2	2	no	—
381	#135	—	2	2	no	—
382	C₂×Q₁₆	—	2	8	no	—
383	C₂×Q₁₆	—	2	2	no	—
384	C₂×Q₁₆	—	2	2	no	—
385	C₂×Q₁₆	—	2	1	no	—
386	C₂×Q₁₆	—	2	1	no	—
387	C₂×Q₁₆	—	2	2	no	—
388	C₂×Q₁₆	D₄×C₄₁	1	1	yes	characteristic
389	C₂×Q₁₆	D₄×C₄₁	1	1	yes	characteristic
390	C₂×Q₁₆	D₄×C₄₁	1	4	yes	complemented
391	C₂×SD₁₆	—	2	2	no	—
392	C₂×SD₁₆	—	2	2	no	—
393	C₂×SD₁₆	D₄×C₄₁	1	2	yes	—
394	C₂×SD₁₆	D₄×C₄₁	1	1	yes	characteristic
395	C₂×SD₁₆	D₄×C₄₁	1	1	yes	characteristic
396	C₂×D₈	D₄×C₄₁	1	1	yes	characteristic
397	C₂×D₈	D₄×C₄₁	1	1	yes	characteristic
398	#131	—	2	2	no	—
399	#131	—	2	2	no	—
400	#131	—	2	2	no	—
401	#131	D₄×C₄₁	1	4	yes	complemented
402	C₂×M₁₆	—	2	1	no	—
403	C₂×M₁₆	—	2	1	no	—
404	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
405	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
406	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
407	C₂²×C₈	—	2	1	no	—
408	C₂²×C₈	—	2	1	no	—
409	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
411	C₂²⋊Q₈	—	2	2	no	—
412	C₂²⋊Q₈	—	2	2	no	—
413	#121	—	2	2	no	—
414	#121	—	2	2	no	—
415	#121	—	4	2	no	—
416	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
417	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
418	#108	—	2	2	no	—
419	#108	—	2	2	no	—
420	#107	—	2	1	no	—
421	#107	—	2	1	no	—
422	#104	—	2	2	no	—
423	#104	—	2	2	no	—
424	#104	—	4	2	no	—
425	#103	—	2	2	no	—
426	#103	—	2	2	no	—
427	#103	—	2	2	no	—
428	#103	—	2	2	no	—
429	#102	—	2	2	no	—
430	#102	—	2	2	no	—
431	#101	—	2	4	no	—
432	C₂²⋊C₈	—	2	2	no	—
433	C₂²⋊C₈	—	2	2	no	—
434	C₄×C₈	—	2	2	no	—
435	#95	—	4	2	no	—
436	#41	—	2	1	no	—
437	#41	—	2	1	no	—
438	#41	—	2	8	no	—
439	#41	—	2	1	no	—
440	#41	—	2	1	no	—
441	#41	—	2	2	no	—
442	#41	—	2	2	no	—
443	#41	—	2	1	no	—
444	#41	—	2	2	no	—
445	#41	—	2	2	no	—
446	#41	—	2	1	no	—
447	#41	—	4	4	no	—
448	#41	—	4	8	no	—
449	#41	—	4	4	no	—
450	#41	—	4	8	no	—
451	#41	—	4	4	no	—
452	#41	C₂×D₄×C₄₁	1	2	yes	—
453	#41	#41×C₄₁	1	2	yes	—
454	C₂×Q₈	—	2	2	no	—
455	C₂×Q₈	—	2	8	no	—
456	C₂×Q₈	—	2	2	no	—
457	C₂×Q₈	—	2	2	no	—
458	C₂×Q₈	—	2	2	no	—
459	C₂×Q₈	—	2	2	no	—
460	C₂×Q₈	—	4	2	no	—
461	C₂×Q₈	—	4	4	no	—
462	C₂×Q₈	—	4	4	no	—
463	C₂×Q₈	—	4	4	no	—
464	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
465	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
466	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
467	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	4	2	no	—
472	C₂×D₄	—	4	2	no	—
473	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
474	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
475	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	4	2	no	—
483	C₂²×C₄	—	4	2	no	—
484	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
485	Q₁₆	—	2	8	no	—
486	Q₁₆	—	2	2	no	—
487	Q₁₆	—	2	2	no	—
488	Q₁₆	—	2	4	no	—
489	Q₁₆	—	2	4	no	—
490	Q₁₆	—	4	4	no	—
491	SD₁₆	—	2	8	no	—
492	SD₁₆	—	2	2	no	—
493	SD₁₆	—	2	2	no	—
494	SD₁₆	—	2	4	no	—
495	SD₁₆	—	4	4	no	—
496	D₈	—	2	2	no	—
497	D₈	—	2	2	no	—
498	M₁₆	—	2	1	no	—
499	M₁₆	—	2	4	no	—
500	M₁₆	—	2	1	no	—
501	M₁₆	—	2	2	no	—
502	M₁₆	—	2	1	no	—
503	M₁₆	—	2	2	no	—
504	M₁₆	—	4	2	no	—
505	M₁₆	C₂×D₄×C₄₁	1	2	yes	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	4	no	—
510	C₂×C₈	—	2	2	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	4	2	no	—
513	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
514	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
515	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
516	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
517	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
518	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	4	2	no	—
522	C₂²⋊C₄	—	4	2	no	—
523	C₂²⋊C₄	—	4	2	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	2	1	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	2	no	—
529	C₂³	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
530	Q₈	—	2	1	no	—
531	Q₈	—	2	4	no	—
532	Q₈	—	2	2	no	—
533	Q₈	—	2	1	no	—
534	Q₈	—	2	4	no	—
535	Q₈	—	2	1	no	—
536	Q₈	—	2	2	no	—
537	Q₈	—	4	8	no	—
538	Q₈	—	4	2	no	—
539	Q₈	—	4	2	no	—
540	Q₈	#121×C₄₁	1	2	yes	—
541	D₄	—	2	2	no	—
542	D₄	—	2	2	no	—
543	D₄	—	2	2	no	—
544	D₄	—	2	1	no	—
545	D₄	—	2	1	no	—
546	D₄	—	2	1	no	—
547	D₄	—	2	2	no	—
548	D₄	—	4	8	no	—
549	D₄	—	4	2	no	—
550	D₄	—	4	1	no	—
551	D₄	—	4	2	no	—
552	D₄	—	4	1	no	—
553	D₄	—	16	2	no	—
554	D₄	#121×C₄₁	1	2	yes	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	4	8	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	8	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	8	2	no	—
574	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
575	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
576	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
577	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
578	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
579	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
580	C₈	—	2	2	no	—
581	C₈	—	2	1	no	—
582	C₈	—	2	1	no	—
583	C₈	—	4	1	no	—
584	C₈	—	4	2	no	—
585	C₈	#120×C₄₁	1	2	yes	—
586	C₈	#120×C₄₁	1	2	yes	—
587	C₂²	—	2	1	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	2	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	2	no	—
598	C₂²	C₄₁×#535	1	1	yes	characteristic
599	C₂²	D₄²×C₄₁	1	1	yes	characteristic
600	C₂²	C₄₁×#546	1	1	yes	characteristic
601	C₄	—	2	2	no	—
602	C₄	—	4	2	no	—
603	C₄	—	4	2	no	—
604	C₄	—	4	4	no	—
605	C₄	—	4	1	no	—
606	C₄	—	8	2	no	—
607	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
608	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
609	C₄	D₄²×C₄₁	1	1	yes	characteristic
610	C₄	C₄₁×#546	1	1	yes	characteristic
611	C₂	—	2	1	no	—
612	C₂	—	2	1	no	—
613	C₂	—	4	2	no	—
614	C₂	—	8	2	no	—
615	C₂	—	8	1	no	—
616	C₂	C₄₁×#2408	1	1	yes	characteristic
617	C₂	C₄₁×#3290	1	1	yes	characteristic
618	C₂	C₄₁×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂²×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#578	C₂	semidirect
2. C₂×C₄₁×#473	C₂	semidirect
3. C₄₁×#3061	C₂	semidirect
4. C₄₁×#3013	C₂	semidirect
5. C₂×C₄₁×#443	C₂	semidirect
6. C₄₁×#2052	C₂	semidirect
7. C₄₁×#2007	C₂	semidirect
8. C₄₁×#1974	C₂	semidirect
9. C₄₁×#1969	C₂	semidirect
10. C₄₁×#1816	C₂	semidirect
11. C₄₁×#1793	C₂	semidirect
80. C₂×Q₁₆×C₄₁	D₄	semidirect
91. #131×C₄₁	D₄	semidirect
277. #24290	C₄₁	direct (N × H)
302. C₂×#578	C₂×C₄₁	semidirect
303. C₂×#473	C₂×C₄₁	semidirect
304. #3061	C₂×C₄₁	semidirect
305. #3013	C₂×C₄₁	semidirect
306. C₂×#443	C₂×C₄₁	semidirect
307. #2052	C₂×C₄₁	semidirect
308. #2007	C₂×C₄₁	semidirect
309. #1974	C₂×C₄₁	semidirect
310. #1969	C₂×C₄₁	semidirect
311. #1816	C₂×C₄₁	semidirect
312. #1793	C₂×C₄₁	semidirect
358. C₄₁	#24290	direct (N × H)
390. C₂×Q₁₆	D₄×C₄₁	semidirect
401. #131	D₄×C₄₁	semidirect

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×#473	2
C₄₁×#3061	2
C₄₁×#3013	2
C₂×C₄₁×#443	2
C₄₁×#2052	2
C₄₁×#2007	2
C₄₁×#1974	2
C₄₁×#1969	2
C₄₁×#1816	2
C₄₁×#1793	2
#24290	41

Subgroups — C41×#24290 #23800491

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24290 #23800491